%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SEU799^1 : TPTP v9.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.VJcdblHalM true
% Computer : n012.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 04:56:26 PM UTC 2025
% Result : Theorem 121.32s 16.00s
% Output : Refutation 122.84s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.13 % Problem : SEU799^1 : TPTP v9.2.0. Released v3.7.0.
% 0.12/0.14 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.VJcdblHalM true
% 0.19/0.36 % Computer : n012.cluster.edu
% 0.19/0.36 % Model : x86_64 x86_64
% 0.19/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.36 % Memory : 8042.1875MB
% 0.19/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.19/0.36 % CPULimit : 300
% 0.19/0.36 % WCLimit : 300
% 0.19/0.36 % DateTime : Wed Oct 1 16:14:08 EDT 2025
% 0.19/0.36 % CPUTime :
% 0.19/0.36 % Running portfolio for 300 s
% 0.19/0.36 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.36 % Number of cores: 8
% 0.19/0.36 % Python version: Python 3.6.8
% 0.19/0.36 % Running in HO mode
% 0.45/0.61 % Total configuration time : 828
% 0.45/0.61 % Estimated wc time : 1656
% 0.45/0.61 % Estimated cpu time (8 cpus) : 207.0
% 0.49/0.70 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
% 0.49/0.71 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.50/0.74 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
% 0.50/0.74 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s
% 0.50/0.74 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s
% 0.50/0.75 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
% 0.50/0.75 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.50/0.75 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s
% 121.32/16.00 % Solved by lams/40_b.comb.sh.
% 121.32/16.00 % done 0 iterations in 14.914s
% 121.32/16.00 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 121.32/16.00 % SZS output start Refutation
% 121.32/16.00 thf(setadjoinAx_type, type, setadjoinAx: $o).
% 121.32/16.00 thf(cartprodfstpairEq_type, type, cartprodfstpairEq: $o).
% 121.32/16.00 thf('#sk48_type', type, '#sk48': $i).
% 121.32/16.00 thf(notdexE_type, type, notdexE: $o).
% 121.32/16.00 thf(setunionAx_type, type, setunionAx: $o).
% 121.32/16.00 thf(setminusELneg_type, type, setminusELneg: $o).
% 121.32/16.00 thf(breln1unionEcases_type, type, breln1unionEcases: $o).
% 121.32/16.00 thf(powersetE_type, type, powersetE: $o).
% 121.32/16.00 thf(woz1_1_type, type, woz1_1: $o).
% 121.32/16.00 thf(omegaSAx_type, type, omegaSAx: $o).
% 121.32/16.00 thf(breln1unionI_type, type, breln1unionI: $o).
% 121.32/16.00 thf(complementSubsetComplementIntersect_type, type, complementSubsetComplementIntersect:
% 121.32/16.00 $o).
% 121.32/16.00 thf('#sk12_type', type, '#sk12': $i > $i > $i).
% 121.32/16.00 thf(exuI1_type, type, exuI1: $o).
% 121.32/16.00 thf(exuI2_type, type, exuI2: $o).
% 121.32/16.00 thf(notequalI2_type, type, notequalI2: $o).
% 121.32/16.00 thf(kfstsingleton_type, type, kfstsingleton: $o).
% 121.32/16.00 thf(kpairiskpair_type, type, kpairiskpair: $o).
% 121.32/16.00 thf(upairsubunion_type, type, upairsubunion: $o).
% 121.32/16.00 thf(binunionTE_type, type, binunionTE: $o).
% 121.32/16.00 thf(binunionTEcontra_type, type, binunionTEcontra: $o).
% 121.32/16.00 thf(powerset__Cong_type, type, powerset__Cong: $o).
% 121.32/16.00 thf(setukpairinjR2_type, type, setukpairinjR2: $o).
% 121.32/16.00 thf(singletonsuniq_type, type, singletonsuniq: $o).
% 121.32/16.00 thf(setminusILneg_type, type, setminusILneg: $o).
% 121.32/16.00 thf(wellorderingAx_type, type, wellorderingAx: $o).
% 121.32/16.00 thf(kpairsurjEq_type, type, kpairsurjEq: $o).
% 121.32/16.00 thf(funcextLem_type, type, funcextLem: $o).
% 121.32/16.00 thf(setadjoinSub2_type, type, setadjoinSub2: $o).
% 121.32/16.00 thf(binintersectSubset5_type, type, binintersectSubset5: $o).
% 121.32/16.00 thf(upairinpowunion_type, type, upairinpowunion: $o).
% 121.32/16.00 thf(eta1_type, type, eta1: $o).
% 121.32/16.00 thf(complementTnotintersectT_type, type, complementTnotintersectT: $o).
% 121.32/16.00 thf(setoftrueEq_type, type, setoftrueEq: $o).
% 121.32/16.00 thf(apProp_type, type, apProp: $o).
% 121.32/16.00 thf(setextT_type, type, setextT: $o).
% 121.32/16.00 thf(inIntersectImpInIntersectUnions_type, type, inIntersectImpInIntersectUnions:
% 121.32/16.00 $o).
% 121.32/16.00 thf(emptyset__Cong_type, type, emptyset__Cong: $o).
% 121.32/16.00 thf(cartprodmempaircEq_type, type, cartprodmempaircEq: $o).
% 121.32/16.00 thf(breln1invprop_type, type, breln1invprop: $o).
% 121.32/16.00 thf(lamProp_type, type, lamProp: $o).
% 121.32/16.00 thf(dpsetconstrSub_type, type, dpsetconstrSub: $o).
% 121.32/16.00 thf(ex1E1_type, type, ex1E1: $o).
% 121.32/16.00 thf(sepInPowerset_type, type, sepInPowerset: $o).
% 121.32/16.00 thf(setukpairIR_type, type, setukpairIR: $o).
% 121.32/16.00 thf(brelnall1_type, type, brelnall1: $o).
% 121.32/16.00 thf(binunionE_type, type, binunionE: $o).
% 121.32/16.00 thf(setext_type, type, setext: $o).
% 121.32/16.00 thf(complementTcontraSubset_type, type, complementTcontraSubset: $o).
% 121.32/16.00 thf(emptyinPowerset_type, type, emptyinPowerset: $o).
% 121.32/16.00 thf(binintersectTELcontra_type, type, binintersectTELcontra: $o).
% 121.32/16.00 thf(ubforcartprodlem1_type, type, ubforcartprodlem1: $o).
% 121.32/16.00 thf(iftrue_type, type, iftrue: $o).
% 121.32/16.00 thf(woz13rule4_type, type, woz13rule4: $o).
% 121.32/16.00 thf(descr__Cong_type, type, descr__Cong: $o).
% 121.32/16.00 thf(funcGraphProp2_type, type, funcGraphProp2: $o).
% 121.32/16.00 thf(theprop_type, type, theprop: $o).
% 121.32/16.00 thf(image1I_type, type, image1I: $o).
% 121.32/16.00 thf(binintersectSubset1_type, type, binintersectSubset1: $o).
% 121.32/16.00 thf(in_type, type, in: $i > $i > $o).
% 121.32/16.00 thf(cartprodsndpairEq_type, type, cartprodsndpairEq: $o).
% 121.32/16.00 thf(quantDeMorgan1_type, type, quantDeMorgan1: $o).
% 121.32/16.00 thf(setukpairinjL2_type, type, setukpairinjL2: $o).
% 121.32/16.00 thf(demorgan1_type, type, demorgan1: $o).
% 121.32/16.00 thf(setadjoinIR_type, type, setadjoinIR: $o).
% 121.32/16.00 thf(complementInPowersetComplementIntersect_type, type, complementInPowersetComplementIntersect:
% 121.32/16.00 $o).
% 121.32/16.00 thf(inIntersectImpInUnion_type, type, inIntersectImpInUnion: $o).
% 121.32/16.00 thf(breln1SetBreln1_type, type, breln1SetBreln1: $o).
% 121.32/16.00 thf(setadjoin__Cong_type, type, setadjoin__Cong: $o).
% 121.32/16.00 thf(ksndpairEq_type, type, ksndpairEq: $o).
% 121.32/16.00 thf(ex1I2_type, type, ex1I2: $o).
% 121.32/16.00 thf(symdiffI2_type, type, symdiffI2: $o).
% 121.32/16.00 thf(ap2apEq2_type, type, ap2apEq2: $o).
% 121.32/16.00 thf(ifSingleton_type, type, ifSingleton: $o).
% 121.32/16.00 thf(upairset2IR_type, type, upairset2IR: $o).
% 121.32/16.00 thf(iftrueProp1_type, type, iftrueProp1: $o).
% 121.32/16.00 thf(complementTI1_type, type, complementTI1: $o).
% 121.32/16.00 thf(subsetE_type, type, subsetE: $o).
% 121.32/16.00 thf(prop2set2propI_type, type, prop2set2propI: $o).
% 121.32/16.00 thf(doubleComplementSub2_type, type, doubleComplementSub2: $o).
% 121.32/16.00 thf(complementUnionInPowersetComplement_type, type, complementUnionInPowersetComplement:
% 121.32/16.00 $o).
% 121.32/16.00 thf(iffalse_type, type, iffalse: $o).
% 121.32/16.00 thf(dsetconstrEL_type, type, dsetconstrEL: $o).
% 121.32/16.00 thf(setbeta_type, type, setbeta: $o).
% 121.32/16.00 thf(eqinunit_type, type, eqinunit: $o).
% 121.32/16.00 thf(upairsetIL_type, type, upairsetIL: $o).
% 121.32/16.00 thf(powersetI1_type, type, powersetI1: $o).
% 121.32/16.00 thf(cartprodfstin_type, type, cartprodfstin: $o).
% 121.32/16.00 thf(lamp_type, type, lamp: $o).
% 121.32/16.00 thf(iffalseProp1_type, type, iffalseProp1: $o).
% 121.32/16.00 thf(breln1invI_type, type, breln1invI: $o).
% 121.32/16.00 thf(binintersectSubset3_type, type, binintersectSubset3: $o).
% 121.32/16.00 thf(breln1unionE_type, type, breln1unionE: $o).
% 121.32/16.00 thf(ksndsingleton_type, type, ksndsingleton: $o).
% 121.32/16.00 thf(setminusIRneg_type, type, setminusIRneg: $o).
% 121.32/16.00 thf(lam2lamEq_type, type, lam2lamEq: $o).
% 121.32/16.00 thf(powersetAx_type, type, powersetAx: $o).
% 121.32/16.00 thf(woz2Ex_type, type, woz2Ex: $o).
% 121.32/16.00 thf(eta2_type, type, eta2: $o).
% 121.32/16.00 thf(binintersectSubset4_type, type, binintersectSubset4: $o).
% 121.32/16.00 thf(singletoninpowunion_type, type, singletoninpowunion: $o).
% 121.32/16.00 thf(image1Ex_type, type, image1Ex: $o).
% 121.32/16.00 thf(powersetI_type, type, powersetI: $o).
% 121.32/16.00 thf(cartprodmempair_type, type, cartprodmempair: $o).
% 121.32/16.00 thf(powersetTE1_type, type, powersetTE1: $o).
% 121.32/16.00 thf(upairsetIR_type, type, upairsetIR: $o).
% 121.32/16.00 thf(cartprodpairsurjEq_type, type, cartprodpairsurjEq: $o).
% 121.32/16.00 thf(lam2p_type, type, lam2p: $o).
% 121.32/16.00 thf(contraSubsetComplement_type, type, contraSubsetComplement: $o).
% 121.32/16.00 thf(doubleComplementSub1_type, type, doubleComplementSub1: $o).
% 121.32/16.00 thf(cartprodpairmemEL_type, type, cartprodpairmemEL: $o).
% 121.32/16.00 thf(setOfPairsIsBReln1_type, type, setOfPairsIsBReln1: $o).
% 121.32/16.00 thf(inCongP_type, type, inCongP: $o).
% 121.32/16.00 thf(setukpairinjR11_type, type, setukpairinjR11: $o).
% 121.32/16.00 thf(setadjoinSub_type, type, setadjoinSub: $o).
% 121.32/16.00 thf(exuE3e_type, type, exuE3e: $o).
% 121.32/16.00 thf(emptysetE_type, type, emptysetE: $o).
% 121.32/16.00 thf(woz13rule2_type, type, woz13rule2: $o).
% 121.32/16.00 thf(binintersectSubset2_type, type, binintersectSubset2: $o).
% 121.32/16.00 thf(image1E_type, type, image1E: $o).
% 121.32/16.00 thf(setunionI_type, type, setunionI: $o).
% 121.32/16.00 thf(breln1unionIR_type, type, breln1unionIR: $o).
% 121.32/16.00 thf(binintersectTERcontra_type, type, binintersectTERcontra: $o).
% 121.32/16.00 thf(setunion__Cong_type, type, setunion__Cong: $o).
% 121.32/16.00 thf(prop2setI_type, type, prop2setI: $o).
% 121.32/16.00 thf(nonemptyImpWitness_type, type, nonemptyImpWitness: $o).
% 121.32/16.00 thf(setminusER_type, type, setminusER: $o).
% 121.32/16.00 thf(exuE2_type, type, exuE2: $o).
% 121.32/16.00 thf(woz1_2_type, type, woz1_2: $o).
% 121.32/16.00 thf(emptyset_type, type, emptyset: $i).
% 121.32/16.00 thf(setukpairinjR12_type, type, setukpairinjR12: $o).
% 121.32/16.00 thf(funcGraphProp1_type, type, funcGraphProp1: $o).
% 121.32/16.00 thf(powersetsubset_type, type, powersetsubset: $o).
% 121.32/16.00 thf(upairequniteq_type, type, upairequniteq: $o).
% 121.32/16.00 thf(dpsetconstrEL1_type, type, dpsetconstrEL1: $o).
% 121.32/16.00 thf(subPowSU_type, type, subPowSU: $o).
% 121.32/16.00 thf(breln1compprop_type, type, breln1compprop: $o).
% 121.32/16.00 thf(woz2B_type, type, woz2B: $o).
% 121.32/16.00 thf(notequalI1_type, type, notequalI1: $o).
% 121.32/16.00 thf(demorgan2b_type, type, demorgan2b: $o).
% 121.32/16.00 thf(notinemptyset_type, type, notinemptyset: $o).
% 121.32/16.00 thf(nonemptyI1_type, type, nonemptyI1: $o).
% 121.32/16.00 thf(breln1unionIL_type, type, breln1unionIL: $o).
% 121.32/16.00 thf(subsetTrans_type, type, subsetTrans: $o).
% 121.32/16.00 thf(setukpairinjR_type, type, setukpairinjR: $o).
% 121.32/16.00 thf(infuncsetfunc_type, type, infuncsetfunc: $o).
% 121.32/16.00 thf(kpairp_type, type, kpairp: $o).
% 121.32/16.00 thf(setukpairinjR1_type, type, setukpairinjR1: $o).
% 121.32/16.00 thf(setminusI_type, type, setminusI: $o).
% 121.32/16.00 thf(binunionIL_type, type, binunionIL: $o).
% 121.32/16.00 thf(setOfPairsIsBReln_type, type, setOfPairsIsBReln: $o).
% 121.32/16.00 thf(setukpairinjL1_type, type, setukpairinjL1: $o).
% 121.32/16.00 thf(setunionsingleton_type, type, setunionsingleton: $o).
% 121.32/16.00 thf(powersetTI1_type, type, powersetTI1: $o).
% 121.32/16.00 thf(subsetE2_type, type, subsetE2: $o).
% 121.32/16.00 thf(image1Ex1_type, type, image1Ex1: $o).
% 121.32/16.00 thf(singletonsswitch_type, type, singletonsswitch: $o).
% 121.32/16.00 thf(ubforcartprodlem3_type, type, ubforcartprodlem3: $o).
% 121.32/16.00 thf(setextsub_type, type, setextsub: $o).
% 121.32/16.00 thf(binunionLsub_type, type, binunionLsub: $o).
% 121.32/16.00 thf(contrasubsetT1_type, type, contrasubsetT1: $o).
% 121.32/16.00 thf(setunionsingleton1_type, type, setunionsingleton1: $o).
% 121.32/16.00 thf(breln1compE_type, type, breln1compE: $o).
% 121.32/16.00 thf(emptysetsubset_type, type, emptysetsubset: $o).
% 121.32/16.00 thf(quantDeMorgan3_type, type, quantDeMorgan3: $o).
% 121.32/16.00 thf(dpsetconstrERa_type, type, dpsetconstrERa: $o).
% 121.32/16.00 thf(setunionE_type, type, setunionE: $o).
% 121.32/16.00 thf(setminusSubset1_type, type, setminusSubset1: $o).
% 121.32/16.00 thf(complementT_lem_type, type, complementT_lem: $o).
% 121.32/16.00 thf(binintersectT_lem_type, type, binintersectT_lem: $o).
% 121.32/16.00 thf(emptyinunitempty_type, type, emptyinunitempty: $o).
% 121.32/16.00 thf(binunionIR_type, type, binunionIR: $o).
% 121.32/16.00 thf(setadjoinE_type, type, setadjoinE: $o).
% 121.32/16.00 thf(doubleComplementEq_type, type, doubleComplementEq: $o).
% 121.32/16.00 thf(eqbreln1_type, type, eqbreln1: $o).
% 121.32/16.00 thf(cartprodpairmemER_type, type, cartprodpairmemER: $o).
% 121.32/16.00 thf(dpsetconstrER_type, type, dpsetconstrER: $o).
% 121.32/16.00 thf(doubleComplementE1_type, type, doubleComplementE1: $o).
% 121.32/16.00 thf(setadjoinIL_type, type, setadjoinIL: $o).
% 121.32/16.00 thf(exuE1_type, type, exuE1: $o).
% 121.32/16.00 thf(ubforcartprodlem2_type, type, ubforcartprodlem2: $o).
% 121.32/16.00 thf(binintersectRsub_type, type, binintersectRsub: $o).
% 121.32/16.00 thf(setminusLsub_type, type, setminusLsub: $o).
% 121.32/16.00 thf(notinsingleton_type, type, notinsingleton: $o).
% 121.32/16.00 thf(intersectInPowersetIntersectUnions_type, type, intersectInPowersetIntersectUnions:
% 121.32/16.00 $o).
% 121.32/16.00 thf(dpsetconstrEL2_type, type, dpsetconstrEL2: $o).
% 121.32/16.00 thf(eqimpsubset2_type, type, eqimpsubset2: $o).
% 121.32/16.00 thf(exuEu_type, type, exuEu: $o).
% 121.32/16.00 thf(emptysetimpfalse_type, type, emptysetimpfalse: $o).
% 121.32/16.00 thf(upairsetE_type, type, upairsetE: $o).
% 121.32/16.00 thf(omega0Ax_type, type, omega0Ax: $o).
% 121.32/16.00 thf(breln1invE_type, type, breln1invE: $o).
% 121.32/16.00 thf(breln1unionCommutes_type, type, breln1unionCommutes: $o).
% 121.32/16.00 thf(funcGraphProp3_type, type, funcGraphProp3: $o).
% 121.32/16.00 thf(app_type, type, app: $o).
% 121.32/16.00 thf(funcImageSingleton_type, type, funcImageSingleton: $o).
% 121.32/16.00 thf(dpsetconstrI_type, type, dpsetconstrI: $o).
% 121.32/16.00 thf(notsubsetI_type, type, notsubsetI: $o).
% 121.32/16.00 thf(powersetT_lem_type, type, powersetT_lem: $o).
% 121.32/16.00 thf(woz2W_type, type, woz2W: $o).
% 121.32/16.00 thf(iffalseProp2_type, type, iffalseProp2: $o).
% 121.32/16.00 thf(quantDeMorgan4_type, type, quantDeMorgan4: $o).
% 121.32/16.00 thf(setextAx_type, type, setextAx: $o).
% 121.32/16.00 thf(breln1all1_type, type, breln1all1: $o).
% 121.32/16.00 thf(choice2fnsingleton_type, type, choice2fnsingleton: $o).
% 121.32/16.00 thf(breln1compI_type, type, breln1compI: $o).
% 121.32/16.00 thf(demorgan2a1_type, type, demorgan2a1: $o).
% 121.32/16.00 thf(powersetE1_type, type, powersetE1: $o).
% 121.32/16.00 thf(bs114d_type, type, bs114d: $o).
% 121.32/16.00 thf(complementTE1_type, type, complementTE1: $o).
% 121.32/16.00 thf(noeltsimpempty_type, type, noeltsimpempty: $o).
% 121.32/16.00 thf(breln1all2_type, type, breln1all2: $o).
% 121.32/16.00 thf(contrasubsetT2_type, type, contrasubsetT2: $o).
% 121.32/16.00 thf(inIntersectImpInUnion2_type, type, inIntersectImpInUnion2: $o).
% 121.32/16.00 thf(demorgan2b2_type, type, demorgan2b2: $o).
% 121.32/16.00 thf(binintersectLsub_type, type, binintersectLsub: $o).
% 121.32/16.00 thf(subsetI1_type, type, subsetI1: $o).
% 121.32/16.00 thf(symdiffE_type, type, symdiffE: $o).
% 121.32/16.00 thf(woz13rule1_type, type, woz13rule1: $o).
% 121.32/16.00 thf(breln1unionprop_type, type, breln1unionprop: $o).
% 121.32/16.00 thf(descrp_type, type, descrp: $o).
% 121.32/16.00 thf(dsetconstr__Cong_type, type, dsetconstr__Cong: $o).
% 121.32/16.00 thf(foundationAx_type, type, foundationAx: $o).
% 121.32/16.00 thf(brelnall2_type, type, brelnall2: $o).
% 121.32/16.00 thf(emptysetAx_type, type, emptysetAx: $o).
% 121.32/16.00 thf(emptyI_type, type, emptyI: $o).
% 121.32/16.00 thf(setadjoinOr_type, type, setadjoinOr: $o).
% 121.32/16.00 thf(binintersectEL_type, type, binintersectEL: $o).
% 121.32/16.00 thf(emptyE1_type, type, emptyE1: $o).
% 121.32/16.00 thf(demorgan2a_type, type, demorgan2a: $o).
% 121.32/16.00 thf(woz1_3_type, type, woz1_3: $o).
% 121.32/16.00 thf(emptyInPowerset_type, type, emptyInPowerset: $o).
% 121.32/16.00 thf(vacuousDall_type, type, vacuousDall: $o).
% 121.32/16.00 thf(dsetconstr_type, type, dsetconstr: $i > ($i > $o) > $i).
% 121.32/16.00 thf(dsetconstrER_type, type, dsetconstrER: $o).
% 121.32/16.00 thf(demorgan1a_type, type, demorgan1a: $o).
% 121.32/16.00 thf(ifp_type, type, ifp: $o).
% 121.32/16.00 thf(funcSet_type, type, funcSet: $i > $i > $i).
% 121.32/16.00 thf(binintersectI_type, type, binintersectI: $o).
% 121.32/16.00 thf(beta1_type, type, beta1: $o).
% 121.32/16.00 thf(funcext2_type, type, funcext2: $o).
% 121.32/16.00 thf(subbreln_type, type, subbreln: $o).
% 121.32/16.00 thf(cartprodpairin_type, type, cartprodpairin: $o).
% 121.32/16.00 thf(cartprodmempair1_type, type, cartprodmempair1: $o).
% 121.32/16.00 thf(subbreln1_type, type, subbreln1: $o).
% 121.32/16.00 thf(demorgan2a2_type, type, demorgan2a2: $o).
% 121.32/16.00 thf(image1Equiv_type, type, image1Equiv: $o).
% 121.32/16.00 thf(subsetTI_type, type, subsetTI: $o).
% 121.32/16.00 thf(setminusT_lem_type, type, setminusT_lem: $o).
% 121.32/16.00 thf(ap2p_type, type, ap2p: $o).
% 121.32/16.00 thf(doubleComplementI1_type, type, doubleComplementI1: $o).
% 121.32/16.00 thf(binunionT_lem_type, type, binunionT_lem: $o).
% 121.32/16.00 thf(symdiffI1_type, type, symdiffI1: $o).
% 121.32/16.00 thf(woz1_4_type, type, woz1_4: $o).
% 121.32/16.00 thf('#sk47_type', type, '#sk47': $i).
% 121.32/16.00 thf(kfstpairEq_type, type, kfstpairEq: $o).
% 121.32/16.00 thf(subsetI2_type, type, subsetI2: $o).
% 121.32/16.00 thf(symdiffIneg1_type, type, symdiffIneg1: $o).
% 121.32/16.00 thf(theeq_type, type, theeq: $o).
% 121.32/16.00 thf(setminusERneg_type, type, setminusERneg: $o).
% 121.32/16.00 thf(symdiffIneg2_type, type, symdiffIneg2: $o).
% 121.32/16.00 thf(binunionTIRcontra_type, type, binunionTIRcontra: $o).
% 121.32/16.00 thf(omega__Cong_type, type, omega__Cong: $o).
% 121.32/16.00 thf(demorgan1b_type, type, demorgan1b: $o).
% 121.32/16.00 thf(subsetRefl_type, type, subsetRefl: $o).
% 121.32/16.00 thf(uniqinunit_type, type, uniqinunit: $o).
% 121.32/16.00 thf(eqbreln_type, type, eqbreln: $o).
% 121.32/16.00 thf(inComplementUnionImpNotIn1_type, type, inComplementUnionImpNotIn1: $o).
% 121.32/16.00 thf(funcinfuncset_type, type, funcinfuncset: $o).
% 121.32/16.00 thf(breln1compEex_type, type, breln1compEex: $o).
% 121.32/16.00 thf(contrasubsetT_type, type, contrasubsetT: $o).
% 121.32/16.00 thf(setminusSubset2_type, type, setminusSubset2: $o).
% 121.32/16.00 thf(prop2setE_type, type, prop2setE: $o).
% 121.32/16.00 thf(binunionEcases_type, type, binunionEcases: $o).
% 121.32/16.00 thf(omega_type, type, omega: $i).
% 121.32/16.00 thf(nonemptyI_type, type, nonemptyI: $o).
% 121.32/16.00 thf(disjointsetsI1_type, type, disjointsetsI1: $o).
% 121.32/16.00 thf(woz2A_type, type, woz2A: $o).
% 121.32/16.00 thf(injective_type, type, injective: $i > $i > $i > $o).
% 121.32/16.00 thf(exuE3u_type, type, exuE3u: $o).
% 121.32/16.00 thf(setminusEL_type, type, setminusEL: $o).
% 121.32/16.00 thf(funcGraphProp4_type, type, funcGraphProp4: $o).
% 121.32/16.00 thf(woz1_5_type, type, woz1_5: $o).
% 121.32/16.00 thf(demorgan2_type, type, demorgan2: $o).
% 121.32/16.00 thf(setunionsingleton2_type, type, setunionsingleton2: $o).
% 121.32/16.00 thf(sepSubset_type, type, sepSubset: $o).
% 121.32/16.00 thf(inComplementUnionImpInComplement1_type, type, inComplementUnionImpInComplement1:
% 121.32/16.00 $o).
% 121.32/16.00 thf(funcext_type, type, funcext: $o).
% 121.32/16.00 thf(upairset2E_type, type, upairset2E: $o).
% 121.32/16.00 thf(eqimpsubset1_type, type, eqimpsubset1: $o).
% 121.32/16.00 thf(exuI3_type, type, exuI3: $o).
% 121.32/16.00 thf(notdallE_type, type, notdallE: $o).
% 121.32/16.00 thf(iftrueProp2_type, type, iftrueProp2: $o).
% 121.32/16.00 thf(binintersectER_type, type, binintersectER: $o).
% 121.32/16.00 thf(woz13rule0_type, type, woz13rule0: $o).
% 121.32/16.00 thf(dsetconstrI_type, type, dsetconstrI: $o).
% 121.32/16.00 thf(beta2_type, type, beta2: $o).
% 121.32/16.00 thf(setadjoin_type, type, setadjoin: $i > $i > $i).
% 121.32/16.00 thf(exu__Cong_type, type, exu__Cong: $o).
% 121.32/16.00 thf(cartprodsndin_type, type, cartprodsndin: $o).
% 121.32/16.00 thf(iftrueorfalse_type, type, iftrueorfalse: $o).
% 121.32/16.00 thf(quantDeMorgan2_type, type, quantDeMorgan2: $o).
% 121.32/16.00 thf(ex1I_type, type, ex1I: $o).
% 121.32/16.00 thf(secondinupair_type, type, secondinupair: $o).
% 121.32/16.00 thf(singletonprop_type, type, singletonprop: $o).
% 121.32/16.00 thf(singletonsubset_type, type, singletonsubset: $o).
% 121.32/16.00 thf(singletoninpowerset_type, type, singletoninpowerset: $o).
% 121.32/16.00 thf(subsetemptysetimpeq_type, type, subsetemptysetimpeq: $o).
% 121.32/16.00 thf(injFuncInInjFuncSet_type, type, injFuncInInjFuncSet: $o).
% 121.32/16.00 thf(ex1E2_type, type, ex1E2: $o).
% 121.32/16.00 thf(replAx_type, type, replAx: $o).
% 121.32/16.00 thf(nonemptyE1_type, type, nonemptyE1: $o).
% 121.32/16.00 thf(omegaIndAx_type, type, omegaIndAx: $o).
% 121.32/16.00 thf(setukpairIL_type, type, setukpairIL: $o).
% 121.32/16.00 thf(setunionE2_type, type, setunionE2: $o).
% 121.32/16.00 thf(inPowerset_type, type, inPowerset: $o).
% 121.32/16.00 thf(injFuncSet_type, type, injFuncSet: $i > $i > $i).
% 121.32/16.00 thf(binunionTILcontra_type, type, binunionTILcontra: $o).
% 121.32/16.00 thf(ap2apEq1_type, type, ap2apEq1: $o).
% 121.32/16.00 thf(contrasubsetT3_type, type, contrasubsetT3: $o).
% 121.32/16.00 thf(woz13rule3_type, type, woz13rule3: $o).
% 121.32/16.00 thf(complementImpComplementIntersect_type, type, complementImpComplementIntersect:
% 121.32/16.00 $o).
% 121.32/16.00 thf(in__Cong_type, type, in__Cong: $o).
% 121.32/16.00 thf(setukpairinjL_type, type, setukpairinjL: $o).
% 121.32/16.00 thf(binunionRsub_type, type, binunionRsub: $o).
% 121.32/16.00 thf(subset2powerset_type, type, subset2powerset: $o).
% 121.32/16.00 thf(s_comb_type, type, '#S': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > (A > B) > A > C)).
% 121.32/16.00 thf(c_comb_type, type, '#C': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > B > A > C)).
% 121.32/16.00 thf(b_comb_type, type, '#B': !>[A:$tType, B:$tType, C:$tType]: ((A > B) > (C > A) > C > B)).
% 121.32/16.00 thf(k_comb_type, type, '#K': !>[A:$tType, B:$tType]: (B > A > B)).
% 121.32/16.00 thf(i_comb_type, type, '#I': !>[A:$tType]: (A > A)).
% 121.32/16.00 thf(injFuncSetFuncIn, conjecture,
% 121.32/16.00 (( setextAx ) =>
% 121.32/16.00 ( ( emptysetAx ) =>
% 121.32/16.00 ( ( setadjoinAx ) =>
% 121.32/16.00 ( ( powersetAx ) =>
% 121.32/16.00 ( ( setunionAx ) =>
% 121.32/16.00 ( ( omega0Ax ) =>
% 121.32/16.00 ( ( omegaSAx ) =>
% 121.32/16.00 ( ( omegaIndAx ) =>
% 121.32/16.00 ( ( replAx ) =>
% 121.32/16.00 ( ( foundationAx ) =>
% 121.32/16.00 ( ( wellorderingAx ) =>
% 121.32/16.00 ( ( descrp ) =>
% 121.32/16.00 ( ( dsetconstrI ) =>
% 121.32/16.00 ( ( dsetconstrEL ) =>
% 121.32/16.00 ( ( dsetconstrER ) =>
% 121.32/16.00 ( ( exuE1 ) =>
% 121.32/16.00 ( ( prop2setE ) =>
% 121.32/16.00 ( ( emptysetE ) =>
% 121.32/16.00 ( ( emptysetimpfalse ) =>
% 121.32/16.00 ( ( notinemptyset ) =>
% 121.32/16.00 ( ( exuE3e ) =>
% 121.32/16.00 ( ( setext ) =>
% 121.32/16.00 ( ( emptyI ) =>
% 121.32/16.00 ( ( noeltsimpempty ) =>
% 121.32/16.00 ( ( setbeta ) =>
% 121.32/16.00 ( ( nonemptyE1 ) =>
% 121.32/16.00 ( ( nonemptyI ) =>
% 121.32/16.00 ( ( nonemptyI1 ) =>
% 121.32/16.00 ( ( setadjoinIL ) =>
% 121.32/16.00 ( ( emptyinunitempty ) =>
% 121.32/16.00 ( ( setadjoinIR ) =>
% 121.32/16.00 ( ( setadjoinE ) =>
% 121.32/16.00 ( (
% 121.32/16.00 setadjoinOr ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 setoftrueEq ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 powersetI ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 emptyinPowerset ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 emptyInPowerset ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 powersetE ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 setunionI ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 setunionE ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 subPowSU ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 exuE2 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 nonemptyImpWitness ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 uniqinunit ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 notinsingleton ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 eqinunit ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 singletonsswitch ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 upairsetE ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 upairsetIL ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 upairsetIR ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 emptyE1 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 vacuousDall ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 quantDeMorgan1 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 quantDeMorgan2 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 quantDeMorgan3 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 quantDeMorgan4 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 prop2setI ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 prop2set2propI ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 notdexE ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 notdallE ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 exuI1 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 exuI3 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 exuI2 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 inCongP ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 in__Cong ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 exuE3u ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 exu__Cong ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 emptyset__Cong ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 setadjoin__Cong ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 powerset__Cong ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 setunion__Cong ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 omega__Cong ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 exuEu ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 descr__Cong ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 dsetconstr__Cong ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 subsetI1 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 eqimpsubset2 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 eqimpsubset1 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 subsetI2 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 emptysetsubset ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 subsetE ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 subsetE2 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 notsubsetI ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 notequalI1 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 notequalI2 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 subsetRefl ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 subsetTrans ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 setadjoinSub ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 setadjoinSub2 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 subset2powerset ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 setextsub ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 subsetemptysetimpeq ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 powersetI1 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 powersetE1 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 inPowerset ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 powersetsubset ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 sepInPowerset ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 sepSubset ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 binunionIL ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 upairset2IR ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 binunionIR ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 binunionEcases ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 binunionE ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 binunionLsub ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 binunionRsub ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 binintersectI ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 binintersectSubset5 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 binintersectEL ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 binintersectLsub ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 binintersectSubset2 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 binintersectSubset3 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 binintersectER ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 disjointsetsI1 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 binintersectRsub ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 binintersectSubset4 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 binintersectSubset1 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 bs114d ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 setminusI ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 setminusEL ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 setminusER ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 setminusSubset2 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 setminusERneg ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 setminusELneg ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 setminusILneg ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 setminusIRneg ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 setminusLsub ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 setminusSubset1 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 symdiffE ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 symdiffI1 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 symdiffI2 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 symdiffIneg1 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 symdiffIneg2 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 secondinupair ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 setukpairIL ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 setukpairIR ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 kpairiskpair ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 kpairp ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 singletonsubset ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 singletoninpowerset ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 singletoninpowunion ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 upairset2E ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 upairsubunion ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 upairinpowunion ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 ubforcartprodlem1 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 ubforcartprodlem2 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 ubforcartprodlem3 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 cartprodpairin ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 cartprodmempair1 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 cartprodmempair ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 setunionE2 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 setunionsingleton1 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 setunionsingleton2 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 setunionsingleton ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 singletonprop ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 ex1E1 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 ex1I ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 ex1I2 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 singletonsuniq ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 setukpairinjL1 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 kfstsingleton ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 theprop ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 kfstpairEq ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 cartprodfstin ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 setukpairinjL2 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 setukpairinjL ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 setukpairinjR11 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 setukpairinjR12 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 setukpairinjR1 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 upairequniteq ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 setukpairinjR2 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 setukpairinjR ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 ksndsingleton ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 ksndpairEq ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 kpairsurjEq ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 cartprodsndin ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 cartprodpairmemEL ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 cartprodpairmemER ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 cartprodmempaircEq ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 cartprodfstpairEq ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 cartprodsndpairEq ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 cartprodpairsurjEq ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 dpsetconstrI ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 dpsetconstrSub ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 setOfPairsIsBReln ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 dpsetconstrERa ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 dpsetconstrEL1 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 dpsetconstrEL2 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 dpsetconstrER ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 funcImageSingleton ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 apProp ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 app ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 infuncsetfunc ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 ap2p ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 funcinfuncset ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 lamProp ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 lamp ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 lam2p ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 brelnall1 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 brelnall2 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 ex1E2 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 funcGraphProp1 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 funcGraphProp3 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 funcGraphProp2 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 funcextLem ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 funcGraphProp4 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 subbreln ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 eqbreln ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 funcext ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 funcext2 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 ap2apEq1 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 ap2apEq2 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 beta1 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 eta1 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 lam2lamEq ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 beta2 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 eta2 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 iffalseProp1 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 iffalseProp2 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 iftrueProp1 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 iftrueProp2 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 ifSingleton ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 ifp ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 theeq ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 iftrue ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 iffalse ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 iftrueorfalse ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 binintersectT_lem ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 binunionT_lem ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 powersetT_lem ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 setminusT_lem ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 complementT_lem ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 setextT ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 subsetTI ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 powersetTI1 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 powersetTE1 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 complementTI1 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 complementTE1 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 binintersectTELcontra ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 binintersectTERcontra ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 contrasubsetT ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 contrasubsetT1 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 contrasubsetT2 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 contrasubsetT3 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 doubleComplementI1 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 doubleComplementE1 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 doubleComplementSub1 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 doubleComplementSub2 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 doubleComplementEq ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 complementTnotintersectT ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 complementImpComplementIntersect ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 complementSubsetComplementIntersect ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 complementInPowersetComplementIntersect ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 contraSubsetComplement ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 complementTcontraSubset ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 binunionTILcontra ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 binunionTIRcontra ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 inIntersectImpInUnion ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 inIntersectImpInUnion2 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 inIntersectImpInIntersectUnions ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 intersectInPowersetIntersectUnions ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 inComplementUnionImpNotIn1 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 inComplementUnionImpInComplement1 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 binunionTE ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 binunionTEcontra ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 demorgan2a1 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 complementUnionInPowersetComplement ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 demorgan2a2 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 demorgan1a ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 demorgan1b ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 demorgan1 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 demorgan2a ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 demorgan2b2 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 demorgan2b ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 demorgan2 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 woz13rule0 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 woz13rule1 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 woz13rule2 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 woz13rule3 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 woz13rule4 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 woz1_1 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 woz1_2 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 woz1_3 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 woz1_4 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 woz1_5 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 breln1all2 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 breln1SetBreln1 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 choice2fnsingleton ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 setOfPairsIsBReln1 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 breln1all1 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 subbreln1 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 eqbreln1 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 breln1invprop ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 breln1invI ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 breln1invE ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 breln1compprop ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 breln1compI ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 breln1compE ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 breln1compEex ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 breln1unionprop ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 breln1unionIL ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 breln1unionIR ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 breln1unionI ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 breln1unionE ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 breln1unionEcases ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 breln1unionCommutes ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 woz2Ex ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 woz2W ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 woz2A ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 woz2B ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 image1Ex ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 image1Ex1 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 image1Equiv ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 image1E ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 image1I ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 injFuncInInjFuncSet ) =>
% 121.32/16.00 (
% 121.32/16.00 ![
% 121.32/16.00 A:$i,B:$i,
% 121.32/16.00 Xf:$i]:
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 in @
% 121.32/16.00 Xf @
% 121.32/16.00 (
% 121.32/16.00 injFuncSet
% 121.32/16.00 @
% 121.32/16.00 A @ B ) ) =>
% 121.32/16.00 (
% 121.32/16.00 in @
% 121.32/16.00 Xf @
% 121.32/16.00 (
% 121.32/16.00 funcSet @
% 121.32/16.00 A @ B ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 121.32/16.00 thf(zf_stmt_0, negated_conjecture,
% 121.32/16.00 (~( ( setextAx ) =>
% 121.32/16.00 ( ( emptysetAx ) =>
% 121.32/16.00 ( ( setadjoinAx ) =>
% 121.32/16.00 ( ( powersetAx ) =>
% 121.32/16.00 ( ( setunionAx ) =>
% 121.32/16.00 ( ( omega0Ax ) =>
% 121.32/16.00 ( ( omegaSAx ) =>
% 121.32/16.00 ( ( omegaIndAx ) =>
% 121.32/16.00 ( ( replAx ) =>
% 121.32/16.00 ( ( foundationAx ) =>
% 121.32/16.00 ( ( wellorderingAx ) =>
% 121.32/16.00 ( ( descrp ) =>
% 121.32/16.00 ( ( dsetconstrI ) =>
% 121.32/16.00 ( ( dsetconstrEL ) =>
% 121.32/16.00 ( ( dsetconstrER ) =>
% 121.32/16.00 ( ( exuE1 ) =>
% 121.32/16.00 ( ( prop2setE ) =>
% 121.32/16.00 ( ( emptysetE ) =>
% 121.32/16.00 ( ( emptysetimpfalse ) =>
% 121.32/16.00 ( ( notinemptyset ) =>
% 121.32/16.00 ( ( exuE3e ) =>
% 121.32/16.00 ( ( setext ) =>
% 121.32/16.00 ( ( emptyI ) =>
% 121.32/16.00 ( ( noeltsimpempty ) =>
% 121.32/16.00 ( ( setbeta ) =>
% 121.32/16.00 ( ( nonemptyE1 ) =>
% 121.32/16.00 ( ( nonemptyI ) =>
% 121.32/16.00 ( ( nonemptyI1 ) =>
% 121.32/16.00 ( ( setadjoinIL ) =>
% 121.32/16.00 ( ( emptyinunitempty ) =>
% 121.32/16.00 ( ( setadjoinIR ) =>
% 121.32/16.00 ( (
% 121.32/16.00 setadjoinE ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 setadjoinOr ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 setoftrueEq ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 powersetI ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 emptyinPowerset ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 emptyInPowerset ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 powersetE ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 setunionI ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 setunionE ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 subPowSU ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 exuE2 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 nonemptyImpWitness ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 uniqinunit ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 notinsingleton ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 eqinunit ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 singletonsswitch ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 upairsetE ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 upairsetIL ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 upairsetIR ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 emptyE1 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 vacuousDall ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 quantDeMorgan1 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 quantDeMorgan2 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 quantDeMorgan3 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 quantDeMorgan4 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 prop2setI ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 prop2set2propI ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 notdexE ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 notdallE ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 exuI1 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 exuI3 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 exuI2 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 inCongP ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 in__Cong ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 exuE3u ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 exu__Cong ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 emptyset__Cong ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 setadjoin__Cong ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 powerset__Cong ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 setunion__Cong ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 omega__Cong ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 exuEu ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 descr__Cong ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 dsetconstr__Cong ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 subsetI1 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 eqimpsubset2 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 eqimpsubset1 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 subsetI2 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 emptysetsubset ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 subsetE ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 subsetE2 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 notsubsetI ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 notequalI1 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 notequalI2 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 subsetRefl ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 subsetTrans ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 setadjoinSub ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 setadjoinSub2 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 subset2powerset ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 setextsub ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 subsetemptysetimpeq ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 powersetI1 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 powersetE1 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 inPowerset ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 powersetsubset ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 sepInPowerset ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 sepSubset ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 binunionIL ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 upairset2IR ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 binunionIR ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 binunionEcases ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 binunionE ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 binunionLsub ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 binunionRsub ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 binintersectI ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 binintersectSubset5 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 binintersectEL ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 binintersectLsub ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 binintersectSubset2 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 binintersectSubset3 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 binintersectER ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 disjointsetsI1 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 binintersectRsub ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 binintersectSubset4 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 binintersectSubset1 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 bs114d ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 setminusI ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 setminusEL ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 setminusER ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 setminusSubset2 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 setminusERneg ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 setminusELneg ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 setminusILneg ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 setminusIRneg ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 setminusLsub ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 setminusSubset1 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 symdiffE ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 symdiffI1 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 symdiffI2 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 symdiffIneg1 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 symdiffIneg2 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 secondinupair ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 setukpairIL ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 setukpairIR ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 kpairiskpair ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 kpairp ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 singletonsubset ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 singletoninpowerset ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 singletoninpowunion ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 upairset2E ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 upairsubunion ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 upairinpowunion ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 ubforcartprodlem1 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 ubforcartprodlem2 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 ubforcartprodlem3 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 cartprodpairin ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 cartprodmempair1 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 cartprodmempair ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 setunionE2 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 setunionsingleton1 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 setunionsingleton2 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 setunionsingleton ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 singletonprop ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 ex1E1 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 ex1I ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 ex1I2 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 singletonsuniq ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 setukpairinjL1 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 kfstsingleton ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 theprop ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 kfstpairEq ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 cartprodfstin ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 setukpairinjL2 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 setukpairinjL ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 setukpairinjR11 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 setukpairinjR12 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 setukpairinjR1 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 upairequniteq ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 setukpairinjR2 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 setukpairinjR ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 ksndsingleton ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 ksndpairEq ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 kpairsurjEq ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 cartprodsndin ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 cartprodpairmemEL ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 cartprodpairmemER ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 cartprodmempaircEq ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 cartprodfstpairEq ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 cartprodsndpairEq ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 cartprodpairsurjEq ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 dpsetconstrI ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 dpsetconstrSub ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 setOfPairsIsBReln ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 dpsetconstrERa ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 dpsetconstrEL1 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 dpsetconstrEL2 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 dpsetconstrER ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 funcImageSingleton ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 apProp ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 app ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 infuncsetfunc ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 ap2p ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 funcinfuncset ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 lamProp ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 lamp ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 lam2p ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 brelnall1 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 brelnall2 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 ex1E2 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 funcGraphProp1 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 funcGraphProp3 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 funcGraphProp2 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 funcextLem ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 funcGraphProp4 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 subbreln ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 eqbreln ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 funcext ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 funcext2 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 ap2apEq1 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 ap2apEq2 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 beta1 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 eta1 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 lam2lamEq ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 beta2 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 eta2 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 iffalseProp1 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 iffalseProp2 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 iftrueProp1 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 iftrueProp2 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 ifSingleton ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 ifp ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 theeq ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 iftrue ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 iffalse ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 iftrueorfalse ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 binintersectT_lem ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 binunionT_lem ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 powersetT_lem ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 setminusT_lem ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 complementT_lem ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 setextT ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 subsetTI ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 powersetTI1 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 powersetTE1 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 complementTI1 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 complementTE1 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 binintersectTELcontra ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 binintersectTERcontra ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 contrasubsetT ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 contrasubsetT1 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 contrasubsetT2 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 contrasubsetT3 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 doubleComplementI1 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 doubleComplementE1 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 doubleComplementSub1 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 doubleComplementSub2 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 doubleComplementEq ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 complementTnotintersectT ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 complementImpComplementIntersect ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 complementSubsetComplementIntersect ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 complementInPowersetComplementIntersect ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 contraSubsetComplement ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 complementTcontraSubset ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 binunionTILcontra ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 binunionTIRcontra ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 inIntersectImpInUnion ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 inIntersectImpInUnion2 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 inIntersectImpInIntersectUnions ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 intersectInPowersetIntersectUnions ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 inComplementUnionImpNotIn1 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 inComplementUnionImpInComplement1 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 binunionTE ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 binunionTEcontra ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 demorgan2a1 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 complementUnionInPowersetComplement ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 demorgan2a2 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 demorgan1a ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 demorgan1b ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 demorgan1 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 demorgan2a ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 demorgan2b2 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 demorgan2b ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 demorgan2 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 woz13rule0 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 woz13rule1 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 woz13rule2 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 woz13rule3 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 woz13rule4 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 woz1_1 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 woz1_2 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 woz1_3 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 woz1_4 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 woz1_5 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 breln1all2 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 breln1SetBreln1 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 choice2fnsingleton ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 setOfPairsIsBReln1 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 breln1all1 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 subbreln1 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 eqbreln1 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 breln1invprop ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 breln1invI ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 breln1invE ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 breln1compprop ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 breln1compI ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 breln1compE ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 breln1compEex ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 breln1unionprop ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 breln1unionIL ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 breln1unionIR ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 breln1unionI ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 breln1unionE ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 breln1unionEcases ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 breln1unionCommutes ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 woz2Ex ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 woz2W ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 woz2A ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 woz2B ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 image1Ex ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 image1Ex1 ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 image1Equiv ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 image1E ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 image1I ) =>
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 injFuncInInjFuncSet ) =>
% 121.32/16.00 (
% 121.32/16.00 ![
% 121.32/16.00 A:$i,
% 121.32/16.00 B:$i,
% 121.32/16.00 Xf:$i]:
% 121.32/16.00 (
% 121.32/16.00 (
% 121.32/16.00 in @
% 121.32/16.00 Xf @
% 121.32/16.00 (
% 121.32/16.00 injFuncSet
% 121.32/16.00 @
% 121.32/16.00 A @ B ) ) =>
% 121.32/16.00 (
% 121.32/16.00 in @
% 121.32/16.00 Xf @
% 121.32/16.00 (
% 121.32/16.00 funcSet @
% 121.32/16.00 A @ B ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )),
% 121.32/16.00 inference('cnf.neg', [status(esa)], [injFuncSetFuncIn])).
% 121.32/16.00 thf(zip_derived_cl0, plain,
% 121.32/16.00 (~ (((setextAx) =>
% 121.32/16.00 (((emptysetAx) =>
% 121.32/16.00 (((setadjoinAx) =>
% 121.32/16.00 (((powersetAx) =>
% 121.32/16.00 (((setunionAx) =>
% 121.32/16.00 (((omega0Ax) =>
% 121.32/16.00 (((omegaSAx) =>
% 121.32/16.00 (((omegaIndAx) =>
% 121.32/16.00 (((replAx) =>
% 121.32/16.00 (((foundationAx) =>
% 121.32/16.00 (((wellorderingAx) =>
% 121.32/16.00 (((descrp) =>
% 121.32/16.00 (((dsetconstrI) =>
% 121.32/16.00 (((dsetconstrEL) =>
% 121.32/16.00 (((dsetconstrER) =>
% 121.32/16.00 (((exuE1) =>
% 121.32/16.00 (((prop2setE) =>
% 121.32/16.00 (((emptysetE) =>
% 121.32/16.00 (((emptysetimpfalse) =>
% 121.32/16.00 (((notinemptyset) =>
% 121.32/16.00 (((exuE3e) =>
% 121.32/16.00 (((setext) =>
% 121.32/16.00 (((emptyI) =>
% 121.32/16.00 (((noeltsimpempty) =>
% 121.32/16.00 (((setbeta) =>
% 121.32/16.00 (((nonemptyE1) =>
% 121.32/16.00 (((nonemptyI) =>
% 121.32/16.00 (((nonemptyI1) =>
% 121.32/16.00 (((setadjoinIL) =>
% 121.32/16.00 (((emptyinunitempty) =>
% 121.32/16.00 ((
% 121.32/16.00 (setadjoinIR) =>
% 121.32/16.00 ((
% 121.32/16.00 (setadjoinE) =>
% 121.32/16.00 ((
% 121.32/16.00 (setadjoinOr) =>
% 121.32/16.00 ((
% 121.32/16.00 (setoftrueEq) =>
% 121.32/16.00 ((
% 121.32/16.00 (powersetI) =>
% 121.32/16.00 ((
% 121.32/16.00 (emptyinPowerset) =>
% 121.32/16.00 ((
% 121.32/16.00 (emptyInPowerset) =>
% 121.32/16.00 ((
% 121.32/16.00 (powersetE) =>
% 121.32/16.00 ((
% 121.32/16.00 (setunionI) =>
% 121.32/16.00 ((
% 121.32/16.00 (setunionE) =>
% 121.32/16.00 ((
% 121.32/16.00 (subPowSU) =>
% 121.32/16.00 ((
% 121.32/16.00 (exuE2) =>
% 121.32/16.00 ((
% 121.32/16.00 (nonemptyImpWitness) =>
% 121.32/16.00 ((
% 121.32/16.00 (uniqinunit) =>
% 121.32/16.00 ((
% 121.32/16.00 (notinsingleton) =>
% 121.32/16.00 ((
% 121.32/16.00 (eqinunit) =>
% 121.32/16.00 ((
% 121.32/16.00 (singletonsswitch) =>
% 121.32/16.00 ((
% 121.32/16.00 (upairsetE) =>
% 121.32/16.00 ((
% 121.32/16.00 (upairsetIL) =>
% 121.32/16.00 ((
% 121.32/16.00 (upairsetIR) =>
% 121.32/16.00 ((
% 121.32/16.00 (emptyE1) =>
% 121.32/16.00 ((
% 121.32/16.00 (vacuousDall) =>
% 121.32/16.00 ((
% 121.32/16.00 (quantDeMorgan1) =>
% 121.32/16.00 ((
% 121.32/16.00 (quantDeMorgan2) =>
% 121.32/16.00 ((
% 121.32/16.00 (quantDeMorgan3) =>
% 121.32/16.00 ((
% 121.32/16.00 (quantDeMorgan4) =>
% 121.32/16.00 ((
% 121.32/16.00 (prop2setI) =>
% 121.32/16.00 ((
% 121.32/16.00 (prop2set2propI) =>
% 121.32/16.00 ((
% 121.32/16.00 (notdexE) =>
% 121.32/16.00 ((
% 121.32/16.00 (notdallE) =>
% 121.32/16.00 ((
% 121.32/16.00 (exuI1) =>
% 121.32/16.00 ((
% 121.32/16.00 (exuI3) =>
% 121.32/16.00 ((
% 121.32/16.00 (exuI2) =>
% 121.32/16.00 ((
% 121.32/16.00 (inCongP) =>
% 121.32/16.00 ((
% 121.32/16.00 (in__Cong) =>
% 121.32/16.00 ((
% 121.32/16.00 (exuE3u) =>
% 121.32/16.00 ((
% 121.32/16.00 (exu__Cong) =>
% 121.32/16.00 ((
% 121.32/16.00 (emptyset__Cong) =>
% 121.32/16.00 ((
% 121.32/16.00 (setadjoin__Cong) =>
% 121.32/16.00 ((
% 121.32/16.00 (powerset__Cong) =>
% 121.32/16.00 ((
% 121.32/16.00 (setunion__Cong) =>
% 121.32/16.00 ((
% 121.32/16.00 (omega__Cong) =>
% 121.32/16.00 ((
% 121.32/16.00 (exuEu) =>
% 121.32/16.00 ((
% 121.32/16.00 (descr__Cong) =>
% 121.32/16.00 ((
% 121.32/16.00 (dsetconstr__Cong) =>
% 121.32/16.00 ((
% 121.32/16.00 (subsetI1) =>
% 121.32/16.00 ((
% 121.32/16.00 (eqimpsubset2) =>
% 121.32/16.00 ((
% 121.32/16.00 (eqimpsubset1) =>
% 121.32/16.00 ((
% 121.32/16.00 (subsetI2) =>
% 121.32/16.00 ((
% 121.32/16.00 (emptysetsubset) =>
% 121.32/16.00 ((
% 121.32/16.00 (subsetE) =>
% 121.32/16.00 ((
% 121.32/16.00 (subsetE2) =>
% 121.32/16.00 ((
% 121.32/16.00 (notsubsetI) =>
% 121.32/16.00 ((
% 121.32/16.00 (notequalI1) =>
% 121.32/16.00 ((
% 121.32/16.00 (notequalI2) =>
% 121.32/16.00 ((
% 121.32/16.00 (subsetRefl) =>
% 121.32/16.00 ((
% 121.32/16.00 (subsetTrans) =>
% 121.32/16.00 ((
% 121.32/16.00 (setadjoinSub) =>
% 121.32/16.00 ((
% 121.32/16.00 (setadjoinSub2) =>
% 121.32/16.00 ((
% 121.32/16.00 (subset2powerset) =>
% 121.32/16.00 ((
% 121.32/16.00 (setextsub) =>
% 121.32/16.00 ((
% 121.32/16.00 (subsetemptysetimpeq) =>
% 121.32/16.00 ((
% 121.32/16.00 (powersetI1) =>
% 121.32/16.00 ((
% 121.32/16.00 (powersetE1) =>
% 121.32/16.00 ((
% 121.32/16.00 (inPowerset) =>
% 121.32/16.00 ((
% 121.32/16.00 (powersetsubset) =>
% 121.32/16.00 ((
% 121.32/16.00 (sepInPowerset) =>
% 121.32/16.00 ((
% 121.32/16.00 (sepSubset) =>
% 121.32/16.00 ((
% 121.32/16.00 (binunionIL) =>
% 121.32/16.00 ((
% 121.32/16.00 (upairset2IR) =>
% 121.32/16.00 ((
% 121.32/16.00 (binunionIR) =>
% 121.32/16.00 ((
% 121.32/16.00 (binunionEcases) =>
% 121.32/16.00 ((
% 121.32/16.00 (binunionE) =>
% 121.32/16.00 ((
% 121.32/16.00 (binunionLsub) =>
% 121.32/16.00 ((
% 121.32/16.00 (binunionRsub) =>
% 121.32/16.00 ((
% 121.32/16.00 (binintersectI) =>
% 121.32/16.00 ((
% 121.32/16.00 (binintersectSubset5) =>
% 121.32/16.00 ((
% 121.32/16.00 (binintersectEL) =>
% 121.32/16.00 ((
% 121.32/16.00 (binintersectLsub) =>
% 121.32/16.00 ((
% 121.32/16.00 (binintersectSubset2) =>
% 121.32/16.00 ((
% 121.32/16.00 (binintersectSubset3) =>
% 121.32/16.00 ((
% 121.32/16.00 (binintersectER) =>
% 121.32/16.00 ((
% 121.32/16.00 (disjointsetsI1) =>
% 121.32/16.00 ((
% 121.32/16.00 (binintersectRsub) =>
% 121.32/16.00 ((
% 121.32/16.00 (binintersectSubset4) =>
% 121.32/16.00 ((
% 121.32/16.00 (binintersectSubset1) =>
% 121.32/16.00 ((
% 121.32/16.00 (bs114d) =>
% 121.32/16.00 ((
% 121.32/16.00 (setminusI) =>
% 121.32/16.00 ((
% 121.32/16.00 (setminusEL) =>
% 121.32/16.00 ((
% 121.32/16.00 (setminusER) =>
% 121.32/16.00 ((
% 121.32/16.00 (setminusSubset2) =>
% 121.32/16.00 ((
% 121.32/16.00 (setminusERneg) =>
% 121.32/16.00 ((
% 121.32/16.00 (setminusELneg) =>
% 121.32/16.00 ((
% 121.32/16.00 (setminusILneg) =>
% 121.32/16.00 ((
% 121.32/16.00 (setminusIRneg) =>
% 121.32/16.00 ((
% 121.32/16.00 (setminusLsub) =>
% 121.32/16.00 ((
% 121.32/16.00 (setminusSubset1) =>
% 121.32/16.00 ((
% 121.32/16.00 (symdiffE) =>
% 121.32/16.00 ((
% 121.32/16.00 (symdiffI1) =>
% 121.32/16.00 ((
% 121.32/16.00 (symdiffI2) =>
% 121.32/16.00 ((
% 121.32/16.00 (symdiffIneg1) =>
% 121.32/16.00 ((
% 121.32/16.00 (symdiffIneg2) =>
% 121.32/16.00 ((
% 121.32/16.00 (secondinupair) =>
% 121.32/16.00 ((
% 121.32/16.00 (setukpairIL) =>
% 121.32/16.00 ((
% 121.32/16.00 (setukpairIR) =>
% 121.32/16.00 ((
% 121.32/16.00 (kpairiskpair) =>
% 121.32/16.00 ((
% 121.32/16.00 (kpairp) =>
% 121.32/16.00 ((
% 121.32/16.00 (singletonsubset) =>
% 121.32/16.00 ((
% 121.32/16.00 (singletoninpowerset) =>
% 121.32/16.00 ((
% 121.32/16.00 (singletoninpowunion) =>
% 121.32/16.00 ((
% 121.32/16.00 (upairset2E) =>
% 121.32/16.00 ((
% 121.32/16.00 (upairsubunion) =>
% 121.32/16.00 ((
% 121.32/16.00 (upairinpowunion) =>
% 121.32/16.00 ((
% 121.32/16.00 (ubforcartprodlem1) =>
% 121.32/16.00 ((
% 121.32/16.00 (ubforcartprodlem2) =>
% 121.32/16.00 ((
% 121.32/16.00 (ubforcartprodlem3) =>
% 121.32/16.00 ((
% 121.32/16.00 (cartprodpairin) =>
% 121.32/16.00 ((
% 121.32/16.00 (cartprodmempair1) =>
% 121.32/16.00 ((
% 121.32/16.00 (cartprodmempair) =>
% 121.32/16.00 ((
% 121.32/16.00 (setunionE2) =>
% 121.32/16.00 ((
% 121.32/16.00 (setunionsingleton1) =>
% 121.32/16.00 ((
% 121.32/16.00 (setunionsingleton2) =>
% 121.32/16.00 ((
% 121.32/16.00 (setunionsingleton) =>
% 121.32/16.00 ((
% 121.32/16.00 (singletonprop) =>
% 121.32/16.00 ((
% 121.32/16.00 (ex1E1) =>
% 121.32/16.00 ((
% 121.32/16.00 (ex1I) =>
% 121.32/16.00 ((
% 121.32/16.00 (ex1I2) =>
% 121.32/16.00 ((
% 121.32/16.00 (singletonsuniq) =>
% 121.32/16.00 ((
% 121.32/16.00 (setukpairinjL1) =>
% 121.32/16.00 ((
% 121.32/16.00 (kfstsingleton) =>
% 121.32/16.00 ((
% 121.32/16.00 (theprop) =>
% 121.32/16.00 ((
% 121.32/16.00 (kfstpairEq) =>
% 121.32/16.00 ((
% 121.32/16.00 (cartprodfstin) =>
% 121.32/16.00 ((
% 121.32/16.00 (setukpairinjL2) =>
% 121.32/16.00 ((
% 121.32/16.00 (setukpairinjL) =>
% 121.32/16.00 ((
% 121.32/16.00 (setukpairinjR11) =>
% 121.32/16.00 ((
% 121.32/16.00 (setukpairinjR12) =>
% 121.32/16.00 ((
% 121.32/16.00 (setukpairinjR1) =>
% 121.32/16.00 ((
% 121.32/16.00 (upairequniteq) =>
% 121.32/16.00 ((
% 121.32/16.00 (setukpairinjR2) =>
% 121.32/16.00 ((
% 121.32/16.00 (setukpairinjR) =>
% 121.32/16.00 ((
% 121.32/16.00 (ksndsingleton) =>
% 121.32/16.00 ((
% 121.32/16.00 (ksndpairEq) =>
% 121.32/16.00 ((
% 121.32/16.00 (kpairsurjEq) =>
% 121.32/16.00 ((
% 121.32/16.00 (cartprodsndin) =>
% 121.32/16.00 ((
% 121.32/16.00 (cartprodpairmemEL) =>
% 121.32/16.00 ((
% 121.32/16.00 (cartprodpairmemER) =>
% 121.32/16.00 ((
% 121.32/16.00 (cartprodmempaircEq) =>
% 121.32/16.00 ((
% 121.32/16.00 (cartprodfstpairEq) =>
% 121.32/16.00 ((
% 121.32/16.00 (cartprodsndpairEq) =>
% 121.32/16.00 ((
% 121.32/16.00 (cartprodpairsurjEq) =>
% 121.32/16.00 ((
% 121.32/16.00 (dpsetconstrI) =>
% 121.32/16.00 ((
% 121.32/16.00 (dpsetconstrSub) =>
% 121.32/16.00 ((
% 121.32/16.00 (setOfPairsIsBReln) =>
% 121.32/16.00 ((
% 121.32/16.00 (dpsetconstrERa) =>
% 121.32/16.00 ((
% 121.32/16.00 (dpsetconstrEL1) =>
% 121.32/16.00 ((
% 121.32/16.00 (dpsetconstrEL2) =>
% 121.32/16.00 ((
% 121.32/16.00 (dpsetconstrER) =>
% 121.32/16.00 ((
% 121.32/16.00 (funcImageSingleton) =>
% 121.32/16.00 ((
% 121.32/16.00 (apProp) =>
% 121.32/16.00 ((
% 121.32/16.00 (app) =>
% 121.32/16.00 ((
% 121.32/16.00 (infuncsetfunc) =>
% 121.32/16.00 ((
% 121.32/16.00 (ap2p) =>
% 121.32/16.00 ((
% 121.32/16.00 (funcinfuncset) =>
% 121.32/16.00 ((
% 121.32/16.00 (lamProp) =>
% 121.32/16.00 ((
% 121.32/16.00 (lamp) =>
% 121.32/16.00 ((
% 121.32/16.00 (lam2p) =>
% 121.32/16.00 ((
% 121.32/16.00 (brelnall1) =>
% 121.32/16.00 ((
% 121.32/16.00 (brelnall2) =>
% 121.32/16.00 ((
% 121.32/16.00 (ex1E2) =>
% 121.32/16.00 ((
% 121.32/16.00 (funcGraphProp1) =>
% 121.32/16.00 ((
% 121.32/16.00 (funcGraphProp3) =>
% 121.32/16.00 ((
% 121.32/16.00 (funcGraphProp2) =>
% 121.32/16.00 ((
% 121.32/16.00 (funcextLem) =>
% 121.32/16.00 ((
% 121.32/16.00 (funcGraphProp4) =>
% 121.32/16.00 ((
% 121.32/16.00 (subbreln) =>
% 121.32/16.00 ((
% 121.32/16.00 (eqbreln) =>
% 121.32/16.00 ((
% 121.32/16.00 (funcext) =>
% 121.32/16.00 ((
% 121.32/16.00 (funcext2) =>
% 121.32/16.00 ((
% 121.32/16.00 (ap2apEq1) =>
% 121.32/16.00 ((
% 121.32/16.00 (ap2apEq2) =>
% 121.32/16.00 ((
% 121.32/16.00 (beta1) =>
% 121.32/16.00 ((
% 121.32/16.00 (eta1) =>
% 121.32/16.00 ((
% 121.32/16.00 (lam2lamEq) =>
% 121.32/16.00 ((
% 121.32/16.00 (beta2) =>
% 121.32/16.00 ((
% 121.32/16.00 (eta2) =>
% 121.32/16.00 ((
% 121.32/16.00 (iffalseProp1) =>
% 121.32/16.00 ((
% 121.32/16.00 (iffalseProp2) =>
% 121.32/16.00 ((
% 121.32/16.00 (iftrueProp1) =>
% 121.32/16.00 ((
% 121.32/16.00 (iftrueProp2) =>
% 121.32/16.00 ((
% 121.32/16.00 (ifSingleton) =>
% 121.32/16.00 ((
% 121.32/16.00 (ifp) =>
% 121.32/16.00 ((
% 121.32/16.00 (theeq) =>
% 121.32/16.00 ((
% 121.32/16.00 (iftrue) =>
% 121.32/16.00 ((
% 121.32/16.00 (iffalse) =>
% 121.32/16.00 ((
% 121.32/16.00 (iftrueorfalse) =>
% 121.32/16.00 ((
% 121.32/16.00 (binintersectT_lem) =>
% 121.32/16.00 ((
% 121.32/16.00 (binunionT_lem) =>
% 121.32/16.00 ((
% 121.32/16.00 (powersetT_lem) =>
% 121.32/16.00 ((
% 121.32/16.00 (setminusT_lem) =>
% 121.32/16.00 ((
% 121.32/16.00 (complementT_lem) =>
% 121.32/16.00 ((
% 121.32/16.00 (setextT) =>
% 121.32/16.00 ((
% 121.32/16.00 (subsetTI) =>
% 121.32/16.00 ((
% 121.32/16.00 (powersetTI1) =>
% 121.32/16.00 ((
% 121.32/16.00 (powersetTE1) =>
% 121.32/16.00 ((
% 121.32/16.00 (complementTI1) =>
% 121.32/16.00 ((
% 121.32/16.00 (complementTE1) =>
% 121.32/16.00 ((
% 121.32/16.00 (binintersectTELcontra) =>
% 121.32/16.00 ((
% 121.32/16.00 (binintersectTERcontra) =>
% 121.32/16.00 ((
% 121.32/16.00 (contrasubsetT) =>
% 121.32/16.00 ((
% 121.32/16.00 (contrasubsetT1) =>
% 121.32/16.00 ((
% 121.32/16.00 (contrasubsetT2) =>
% 121.32/16.00 ((
% 121.32/16.00 (contrasubsetT3) =>
% 121.32/16.00 ((
% 121.32/16.00 (doubleComplementI1) =>
% 121.32/16.00 ((
% 121.32/16.00 (doubleComplementE1) =>
% 121.32/16.00 ((
% 121.32/16.00 (doubleComplementSub1) =>
% 121.32/16.00 ((
% 121.32/16.00 (doubleComplementSub2) =>
% 121.32/16.00 ((
% 121.32/16.00 (doubleComplementEq) =>
% 121.32/16.00 ((
% 121.32/16.00 (complementTnotintersectT) =>
% 121.32/16.00 ((
% 121.32/16.00 (complementImpComplementIntersect) =>
% 121.32/16.00 ((
% 121.32/16.00 (complementSubsetComplementIntersect) =>
% 121.32/16.00 ((
% 121.32/16.00 (complementInPowersetComplementIntersect) =>
% 121.32/16.00 ((
% 121.32/16.00 (contraSubsetComplement) =>
% 121.32/16.00 ((
% 121.32/16.00 (complementTcontraSubset) =>
% 121.32/16.00 ((
% 121.32/16.00 (binunionTILcontra) =>
% 121.32/16.00 ((
% 121.32/16.00 (binunionTIRcontra) =>
% 121.32/16.00 ((
% 121.32/16.00 (inIntersectImpInUnion) =>
% 121.32/16.00 ((
% 121.32/16.00 (inIntersectImpInUnion2) =>
% 121.32/16.00 ((
% 121.32/16.00 (inIntersectImpInIntersectUnions) =>
% 121.32/16.00 ((
% 121.32/16.00 (intersectInPowersetIntersectUnions) =>
% 121.32/16.00 ((
% 121.32/16.00 (inComplementUnionImpNotIn1) =>
% 121.32/16.00 ((
% 121.32/16.00 (inComplementUnionImpInComplement1) =>
% 121.32/16.00 ((
% 121.32/16.00 (binunionTE) =>
% 121.32/16.00 ((
% 121.32/16.00 (binunionTEcontra) =>
% 121.32/16.00 ((
% 121.32/16.00 (demorgan2a1) =>
% 121.32/16.00 ((
% 121.32/16.00 (complementUnionInPowersetComplement) =>
% 121.32/16.00 ((
% 121.32/16.00 (demorgan2a2) =>
% 121.32/16.00 ((
% 121.32/16.00 (demorgan1a) =>
% 121.32/16.00 ((
% 121.32/16.00 (demorgan1b) =>
% 121.32/16.00 ((
% 121.32/16.00 (demorgan1) =>
% 121.32/16.00 ((
% 121.32/16.00 (demorgan2a) =>
% 121.32/16.00 ((
% 121.32/16.00 (demorgan2b2) =>
% 121.32/16.00 ((
% 121.32/16.00 (demorgan2b) =>
% 121.32/16.00 ((
% 121.32/16.00 (demorgan2) =>
% 121.32/16.00 ((
% 121.32/16.00 (woz13rule0) =>
% 121.32/16.00 ((
% 121.32/16.00 (woz13rule1) =>
% 121.32/16.00 ((
% 121.32/16.00 (woz13rule2) =>
% 121.32/16.00 ((
% 121.32/16.00 (woz13rule3) =>
% 121.32/16.00 ((
% 121.32/16.00 (woz13rule4) =>
% 121.32/16.00 ((
% 121.32/16.00 (woz1_1) =>
% 121.32/16.00 ((
% 121.32/16.00 (woz1_2) =>
% 121.32/16.00 ((
% 121.32/16.00 (woz1_3) =>
% 121.32/16.00 ((
% 121.32/16.00 (woz1_4) =>
% 121.32/16.00 ((
% 121.32/16.00 (woz1_5) =>
% 121.32/16.00 ((
% 121.32/16.00 (breln1all2) =>
% 121.32/16.00 ((
% 121.32/16.00 (breln1SetBreln1) =>
% 121.32/16.00 ((
% 121.32/16.00 (choice2fnsingleton) =>
% 121.32/16.00 ((
% 121.32/16.00 (setOfPairsIsBReln1) =>
% 121.32/16.00 ((
% 121.32/16.00 (breln1all1) =>
% 121.32/16.00 ((
% 121.32/16.00 (subbreln1) =>
% 121.32/16.00 ((
% 121.32/16.00 (eqbreln1) =>
% 121.32/16.00 ((
% 121.32/16.00 (breln1invprop) =>
% 121.32/16.00 ((
% 121.32/16.00 (breln1invI) =>
% 121.32/16.00 ((
% 121.32/16.00 (breln1invE) =>
% 121.32/16.00 ((
% 121.32/16.00 (breln1compprop) =>
% 121.32/16.00 ((
% 121.32/16.00 (breln1compI) =>
% 121.32/16.00 ((
% 121.32/16.00 (breln1compE) =>
% 121.32/16.00 ((
% 121.32/16.00 (breln1compEex) =>
% 121.32/16.00 ((
% 121.32/16.00 (breln1unionprop) =>
% 121.32/16.00 ((
% 121.32/16.00 (breln1unionIL) =>
% 121.32/16.00 ((
% 121.32/16.00 (breln1unionIR) =>
% 121.32/16.00 ((
% 121.32/16.00 (breln1unionI) =>
% 121.32/16.00 ((
% 121.32/16.00 (breln1unionE) =>
% 121.32/16.00 ((
% 121.32/16.00 (breln1unionEcases) =>
% 121.32/16.00 ((
% 121.32/16.00 (breln1unionCommutes) =>
% 121.32/16.00 ((
% 121.32/16.00 (woz2Ex) =>
% 121.32/16.00 ((
% 121.32/16.00 (woz2W) =>
% 121.32/16.00 ((
% 121.32/16.00 (woz2A) =>
% 121.32/16.00 ((
% 121.32/16.00 (woz2B) =>
% 121.32/16.00 ((
% 121.32/16.00 (image1Ex) =>
% 121.32/16.00 ((
% 121.32/16.00 (image1Ex1) =>
% 121.32/16.00 ((
% 121.32/16.00 (image1Equiv) =>
% 121.32/16.00 ((
% 121.32/16.00 (image1E) =>
% 121.32/16.00 ((
% 121.32/16.00 (image1I) =>
% 121.32/16.00 ((
% 121.32/16.00 (injFuncInInjFuncSet) =>
% 121.32/16.00 ((
% 121.32/16.00 (!!) @ (
% 121.32/16.00 ^[Y0 : $i]:
% 121.32/16.00 ((
% 121.32/16.00 (!!) @ (
% 121.32/16.00 ^[Y1 : $i]:
% 121.32/16.00 ((
% 121.32/16.00 (!!) @ (
% 121.32/16.00 ^[Y2 : $i]:
% 121.32/16.00 ((
% 121.32/16.00 (in @
% 121.32/16.00 Y2 @
% 121.32/16.00 (
% 121.32/16.00 injFuncSet @
% 121.32/16.00 Y0 @ Y1)) =>
% 121.32/16.00 (in @
% 121.32/16.00 Y2 @
% 121.32/16.00 (
% 121.32/16.00 funcSet @
% 121.32/16.00 Y0 @ Y1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 121.32/16.00 inference('cnf', [status(esa)], [zf_stmt_0])).
% 121.32/16.00 thf(zip_derived_cl1, plain,
% 121.32/16.00 (~ (((setextAx) =>
% 121.32/16.00 (((emptysetAx) =>
% 121.32/16.00 (((setadjoinAx) =>
% 121.32/16.00 (((powersetAx) =>
% 121.32/16.00 (((setunionAx) =>
% 121.32/16.00 (((omega0Ax) =>
% 121.32/16.00 (((omegaSAx) =>
% 121.32/16.00 (((omegaIndAx) =>
% 121.32/16.00 (((replAx) =>
% 121.32/16.00 (((foundationAx) =>
% 121.32/16.00 (((wellorderingAx) =>
% 121.32/16.00 (((descrp) =>
% 121.32/16.00 (((dsetconstrI) =>
% 121.32/16.00 (((dsetconstrEL) =>
% 121.32/16.00 (((dsetconstrER) =>
% 121.32/16.00 (((exuE1) =>
% 121.32/16.00 (((prop2setE) =>
% 121.32/16.00 (((emptysetE) =>
% 121.32/16.00 (((emptysetimpfalse) =>
% 121.32/16.00 (((notinemptyset) =>
% 121.32/16.00 (((exuE3e) =>
% 121.32/16.00 (((setext) =>
% 121.32/16.00 (((emptyI) =>
% 121.32/16.00 (((noeltsimpempty) =>
% 121.32/16.00 (((setbeta) =>
% 121.32/16.00 (((nonemptyE1) =>
% 121.32/16.00 (((nonemptyI) =>
% 121.32/16.00 (((nonemptyI1) =>
% 121.32/16.00 (((setadjoinIL) =>
% 121.32/16.00 (((emptyinunitempty) =>
% 121.32/16.00 ((
% 121.32/16.00 (setadjoinIR) =>
% 121.32/16.00 ((
% 121.32/16.00 (setadjoinE) =>
% 121.32/16.00 ((
% 121.32/16.00 (setadjoinOr) =>
% 121.32/16.00 ((
% 121.32/16.00 (setoftrueEq) =>
% 121.32/16.00 ((
% 121.32/16.00 (powersetI) =>
% 121.32/16.00 ((
% 121.32/16.00 (emptyinPowerset) =>
% 121.32/16.00 ((
% 121.32/16.00 (emptyInPowerset) =>
% 121.32/16.00 ((
% 121.32/16.00 (powersetE) =>
% 121.32/16.00 ((
% 121.32/16.00 (setunionI) =>
% 121.32/16.00 ((
% 121.32/16.00 (setunionE) =>
% 121.32/16.00 ((
% 121.32/16.00 (subPowSU) =>
% 121.32/16.00 ((
% 121.32/16.00 (exuE2) =>
% 121.32/16.00 ((
% 121.32/16.00 (nonemptyImpWitness) =>
% 121.32/16.00 ((
% 121.32/16.00 (uniqinunit) =>
% 121.32/16.00 ((
% 121.32/16.00 (notinsingleton) =>
% 121.32/16.00 ((
% 121.32/16.00 (eqinunit) =>
% 121.32/16.00 ((
% 121.32/16.00 (singletonsswitch) =>
% 121.32/16.00 ((
% 121.32/16.00 (upairsetE) =>
% 121.32/16.00 ((
% 121.32/16.00 (upairsetIL) =>
% 121.32/16.00 ((
% 121.32/16.00 (upairsetIR) =>
% 121.32/16.00 ((
% 121.32/16.00 (emptyE1) =>
% 121.32/16.00 ((
% 121.32/16.00 (vacuousDall) =>
% 121.32/16.00 ((
% 121.32/16.00 (quantDeMorgan1) =>
% 121.32/16.00 ((
% 121.32/16.00 (quantDeMorgan2) =>
% 121.32/16.00 ((
% 121.32/16.00 (quantDeMorgan3) =>
% 121.32/16.00 ((
% 121.32/16.00 (quantDeMorgan4) =>
% 121.32/16.00 ((
% 121.32/16.00 (prop2setI) =>
% 121.32/16.00 ((
% 121.32/16.00 (prop2set2propI) =>
% 121.32/16.00 ((
% 121.32/16.00 (notdexE) =>
% 121.32/16.00 ((
% 121.32/16.00 (notdallE) =>
% 121.32/16.00 ((
% 121.32/16.00 (exuI1) =>
% 121.32/16.00 ((
% 121.32/16.00 (exuI3) =>
% 121.32/16.00 ((
% 121.32/16.00 (exuI2) =>
% 121.32/16.00 ((
% 121.32/16.00 (inCongP) =>
% 121.32/16.00 ((
% 121.32/16.00 (in__Cong) =>
% 121.32/16.00 ((
% 121.32/16.00 (exuE3u) =>
% 121.32/16.00 ((
% 121.32/16.00 (exu__Cong) =>
% 121.32/16.00 ((
% 121.32/16.00 (emptyset__Cong) =>
% 121.32/16.00 ((
% 121.32/16.00 (setadjoin__Cong) =>
% 121.32/16.00 ((
% 121.32/16.00 (powerset__Cong) =>
% 121.32/16.00 ((
% 121.32/16.00 (setunion__Cong) =>
% 121.32/16.00 ((
% 121.32/16.00 (omega__Cong) =>
% 121.32/16.00 ((
% 121.32/16.00 (exuEu) =>
% 121.32/16.00 ((
% 121.32/16.00 (descr__Cong) =>
% 121.32/16.00 ((
% 121.32/16.00 (dsetconstr__Cong) =>
% 121.32/16.00 ((
% 121.32/16.00 (subsetI1) =>
% 121.32/16.00 ((
% 121.32/16.00 (eqimpsubset2) =>
% 121.32/16.00 ((
% 121.32/16.00 (eqimpsubset1) =>
% 121.32/16.00 ((
% 121.32/16.00 (subsetI2) =>
% 121.32/16.00 ((
% 121.32/16.00 (emptysetsubset) =>
% 121.32/16.00 ((
% 121.32/16.00 (subsetE) =>
% 121.32/16.00 ((
% 121.32/16.00 (subsetE2) =>
% 121.32/16.00 ((
% 121.32/16.00 (notsubsetI) =>
% 121.32/16.00 ((
% 121.32/16.00 (notequalI1) =>
% 121.32/16.00 ((
% 121.32/16.00 (notequalI2) =>
% 121.32/16.00 ((
% 121.32/16.00 (subsetRefl) =>
% 121.32/16.00 ((
% 121.32/16.00 (subsetTrans) =>
% 121.32/16.00 ((
% 121.32/16.00 (setadjoinSub) =>
% 121.32/16.01 ((
% 121.32/16.01 (setadjoinSub2) =>
% 121.32/16.01 ((
% 121.32/16.01 (subset2powerset) =>
% 121.32/16.01 ((
% 121.32/16.01 (setextsub) =>
% 121.32/16.01 ((
% 121.32/16.01 (subsetemptysetimpeq) =>
% 121.32/16.01 ((
% 121.32/16.01 (powersetI1) =>
% 121.32/16.01 ((
% 121.32/16.01 (powersetE1) =>
% 121.32/16.01 ((
% 121.32/16.01 (inPowerset) =>
% 121.32/16.01 ((
% 121.32/16.01 (powersetsubset) =>
% 121.32/16.01 ((
% 121.32/16.01 (sepInPowerset) =>
% 121.32/16.01 ((
% 121.32/16.01 (sepSubset) =>
% 121.32/16.01 ((
% 121.32/16.01 (binunionIL) =>
% 121.32/16.01 ((
% 121.32/16.01 (upairset2IR) =>
% 121.32/16.01 ((
% 121.32/16.01 (binunionIR) =>
% 121.32/16.01 ((
% 121.32/16.01 (binunionEcases) =>
% 121.32/16.01 ((
% 121.32/16.01 (binunionE) =>
% 121.32/16.01 ((
% 121.32/16.01 (binunionLsub) =>
% 121.32/16.01 ((
% 121.32/16.01 (binunionRsub) =>
% 121.32/16.01 ((
% 121.32/16.01 (binintersectI) =>
% 121.32/16.01 ((
% 121.32/16.01 (binintersectSubset5) =>
% 121.32/16.01 ((
% 121.32/16.01 (binintersectEL) =>
% 121.32/16.01 ((
% 121.32/16.01 (binintersectLsub) =>
% 121.32/16.01 ((
% 121.32/16.01 (binintersectSubset2) =>
% 121.32/16.01 ((
% 121.32/16.01 (binintersectSubset3) =>
% 121.32/16.01 ((
% 121.32/16.01 (binintersectER) =>
% 121.32/16.01 ((
% 121.32/16.01 (disjointsetsI1) =>
% 121.32/16.01 ((
% 121.32/16.01 (binintersectRsub) =>
% 121.32/16.01 ((
% 121.32/16.01 (binintersectSubset4) =>
% 121.32/16.01 ((
% 121.32/16.01 (binintersectSubset1) =>
% 121.32/16.01 ((
% 121.32/16.01 (bs114d) =>
% 121.32/16.01 ((
% 121.32/16.01 (setminusI) =>
% 121.32/16.01 ((
% 121.32/16.01 (setminusEL) =>
% 121.32/16.01 ((
% 121.32/16.01 (setminusER) =>
% 121.32/16.01 ((
% 121.32/16.01 (setminusSubset2) =>
% 121.32/16.01 ((
% 121.32/16.01 (setminusERneg) =>
% 121.32/16.01 ((
% 121.32/16.01 (setminusELneg) =>
% 121.32/16.01 ((
% 121.32/16.01 (setminusILneg) =>
% 121.32/16.01 ((
% 121.32/16.01 (setminusIRneg) =>
% 121.32/16.01 ((
% 121.32/16.01 (setminusLsub) =>
% 121.32/16.01 ((
% 121.32/16.01 (setminusSubset1) =>
% 121.32/16.01 ((
% 121.32/16.01 (symdiffE) =>
% 121.32/16.01 ((
% 121.32/16.01 (symdiffI1) =>
% 121.32/16.01 ((
% 121.32/16.01 (symdiffI2) =>
% 121.32/16.01 ((
% 121.32/16.01 (symdiffIneg1) =>
% 121.32/16.01 ((
% 121.32/16.01 (symdiffIneg2) =>
% 121.32/16.01 ((
% 121.32/16.01 (secondinupair) =>
% 121.32/16.01 ((
% 121.32/16.01 (setukpairIL) =>
% 121.32/16.01 ((
% 121.32/16.01 (setukpairIR) =>
% 121.32/16.01 ((
% 121.32/16.01 (kpairiskpair) =>
% 121.32/16.01 ((
% 121.32/16.01 (kpairp) =>
% 121.32/16.01 ((
% 121.32/16.01 (singletonsubset) =>
% 121.32/16.01 ((
% 121.32/16.01 (singletoninpowerset) =>
% 121.32/16.01 ((
% 121.32/16.01 (singletoninpowunion) =>
% 121.32/16.01 ((
% 121.32/16.01 (upairset2E) =>
% 121.32/16.01 ((
% 121.32/16.01 (upairsubunion) =>
% 121.32/16.01 ((
% 121.32/16.01 (upairinpowunion) =>
% 121.32/16.01 ((
% 121.32/16.01 (ubforcartprodlem1) =>
% 121.32/16.01 ((
% 121.32/16.01 (ubforcartprodlem2) =>
% 121.32/16.01 ((
% 121.32/16.01 (ubforcartprodlem3) =>
% 121.32/16.01 ((
% 121.32/16.01 (cartprodpairin) =>
% 121.32/16.01 ((
% 121.32/16.01 (cartprodmempair1) =>
% 121.32/16.01 ((
% 121.32/16.01 (cartprodmempair) =>
% 121.32/16.01 ((
% 121.32/16.01 (setunionE2) =>
% 121.32/16.01 ((
% 121.32/16.01 (setunionsingleton1) =>
% 121.32/16.01 ((
% 121.32/16.01 (setunionsingleton2) =>
% 121.32/16.01 ((
% 121.32/16.01 (setunionsingleton) =>
% 121.32/16.01 ((
% 121.32/16.01 (singletonprop) =>
% 121.32/16.01 ((
% 121.32/16.01 (ex1E1) =>
% 121.32/16.01 ((
% 121.32/16.01 (ex1I) =>
% 121.32/16.01 ((
% 121.32/16.01 (ex1I2) =>
% 121.32/16.01 ((
% 121.32/16.01 (singletonsuniq) =>
% 121.32/16.01 ((
% 121.32/16.01 (setukpairinjL1) =>
% 121.32/16.01 ((
% 121.32/16.01 (kfstsingleton) =>
% 121.32/16.01 ((
% 121.32/16.01 (theprop) =>
% 121.32/16.01 ((
% 121.32/16.01 (kfstpairEq) =>
% 121.32/16.01 ((
% 121.32/16.01 (cartprodfstin) =>
% 121.32/16.01 ((
% 121.32/16.01 (setukpairinjL2) =>
% 121.32/16.01 ((
% 121.32/16.01 (setukpairinjL) =>
% 121.32/16.01 ((
% 121.32/16.01 (setukpairinjR11) =>
% 121.32/16.01 ((
% 121.32/16.01 (setukpairinjR12) =>
% 121.32/16.01 ((
% 121.32/16.01 (setukpairinjR1) =>
% 121.32/16.01 ((
% 121.32/16.01 (upairequniteq) =>
% 121.32/16.01 ((
% 121.32/16.01 (setukpairinjR2) =>
% 121.32/16.01 ((
% 121.32/16.01 (setukpairinjR) =>
% 121.32/16.01 ((
% 121.32/16.01 (ksndsingleton) =>
% 121.32/16.01 ((
% 121.32/16.01 (ksndpairEq) =>
% 121.32/16.01 ((
% 121.32/16.01 (kpairsurjEq) =>
% 121.32/16.01 ((
% 121.32/16.01 (cartprodsndin) =>
% 121.32/16.01 ((
% 121.32/16.01 (cartprodpairmemEL) =>
% 121.32/16.01 ((
% 121.32/16.01 (cartprodpairmemER) =>
% 121.32/16.01 ((
% 121.32/16.01 (cartprodmempaircEq) =>
% 121.32/16.01 ((
% 121.32/16.01 (cartprodfstpairEq) =>
% 121.32/16.01 ((
% 121.32/16.01 (cartprodsndpairEq) =>
% 121.32/16.01 ((
% 121.32/16.01 (cartprodpairsurjEq) =>
% 121.32/16.01 ((
% 121.32/16.01 (dpsetconstrI) =>
% 121.32/16.01 ((
% 121.32/16.01 (dpsetconstrSub) =>
% 121.32/16.01 ((
% 121.32/16.01 (setOfPairsIsBReln) =>
% 121.32/16.01 ((
% 121.32/16.01 (dpsetconstrERa) =>
% 121.32/16.01 ((
% 121.32/16.01 (dpsetconstrEL1) =>
% 121.32/16.01 ((
% 121.32/16.01 (dpsetconstrEL2) =>
% 121.32/16.01 ((
% 121.32/16.01 (dpsetconstrER) =>
% 121.32/16.01 ((
% 121.32/16.01 (funcImageSingleton) =>
% 121.32/16.01 ((
% 121.32/16.01 (apProp) =>
% 121.32/16.01 ((
% 121.32/16.01 (app) =>
% 121.32/16.01 ((
% 121.32/16.01 (infuncsetfunc) =>
% 121.32/16.01 ((
% 121.32/16.01 (ap2p) =>
% 121.32/16.01 ((
% 121.32/16.01 (funcinfuncset) =>
% 121.32/16.01 ((
% 121.32/16.01 (lamProp) =>
% 121.32/16.01 ((
% 121.32/16.01 (lamp) =>
% 121.32/16.01 ((
% 121.32/16.01 (lam2p) =>
% 121.32/16.01 ((
% 121.32/16.01 (brelnall1) =>
% 121.32/16.01 ((
% 121.32/16.01 (brelnall2) =>
% 121.32/16.01 ((
% 121.32/16.01 (ex1E2) =>
% 121.32/16.01 ((
% 121.32/16.01 (funcGraphProp1) =>
% 121.32/16.01 ((
% 121.32/16.01 (funcGraphProp3) =>
% 121.32/16.01 ((
% 121.32/16.01 (funcGraphProp2) =>
% 121.32/16.01 ((
% 121.32/16.01 (funcextLem) =>
% 121.32/16.01 ((
% 121.32/16.01 (funcGraphProp4) =>
% 121.32/16.01 ((
% 121.32/16.01 (subbreln) =>
% 121.32/16.01 ((
% 121.32/16.01 (eqbreln) =>
% 121.32/16.01 ((
% 121.32/16.01 (funcext) =>
% 121.32/16.01 ((
% 121.32/16.01 (funcext2) =>
% 121.32/16.01 ((
% 121.32/16.01 (ap2apEq1) =>
% 121.32/16.01 ((
% 121.32/16.01 (ap2apEq2) =>
% 121.32/16.01 ((
% 121.32/16.01 (beta1) =>
% 121.32/16.01 ((
% 121.32/16.01 (eta1) =>
% 121.32/16.01 ((
% 121.32/16.01 (lam2lamEq) =>
% 121.32/16.01 ((
% 121.32/16.01 (beta2) =>
% 121.32/16.01 ((
% 121.32/16.01 (eta2) =>
% 121.32/16.01 ((
% 121.32/16.01 (iffalseProp1) =>
% 121.32/16.01 ((
% 121.32/16.01 (iffalseProp2) =>
% 121.32/16.01 ((
% 121.32/16.01 (iftrueProp1) =>
% 121.32/16.01 ((
% 121.32/16.01 (iftrueProp2) =>
% 121.32/16.01 ((
% 121.32/16.01 (ifSingleton) =>
% 121.32/16.01 ((
% 121.32/16.01 (ifp) =>
% 121.32/16.01 ((
% 121.32/16.01 (theeq) =>
% 121.32/16.01 ((
% 121.32/16.01 (iftrue) =>
% 121.32/16.01 ((
% 121.32/16.01 (iffalse) =>
% 121.32/16.01 ((
% 121.32/16.01 (iftrueorfalse) =>
% 121.32/16.01 ((
% 121.32/16.01 (binintersectT_lem) =>
% 121.32/16.01 ((
% 121.32/16.01 (binunionT_lem) =>
% 121.32/16.01 ((
% 121.32/16.01 (powersetT_lem) =>
% 121.32/16.01 ((
% 121.32/16.01 (setminusT_lem) =>
% 121.32/16.01 ((
% 121.32/16.01 (complementT_lem) =>
% 121.32/16.01 ((
% 121.32/16.01 (setextT) =>
% 121.32/16.01 ((
% 121.32/16.01 (subsetTI) =>
% 121.32/16.01 ((
% 121.32/16.01 (powersetTI1) =>
% 121.32/16.01 ((
% 121.32/16.01 (powersetTE1) =>
% 121.32/16.01 ((
% 121.32/16.01 (complementTI1) =>
% 121.32/16.01 ((
% 121.32/16.01 (complementTE1) =>
% 121.32/16.01 ((
% 121.32/16.01 (binintersectTELcontra) =>
% 121.32/16.01 ((
% 121.32/16.01 (binintersectTERcontra) =>
% 121.32/16.01 ((
% 121.32/16.01 (contrasubsetT) =>
% 121.32/16.01 ((
% 121.32/16.01 (contrasubsetT1) =>
% 121.32/16.01 ((
% 121.32/16.01 (contrasubsetT2) =>
% 121.32/16.01 ((
% 121.32/16.01 (contrasubsetT3) =>
% 121.32/16.01 ((
% 121.32/16.01 (doubleComplementI1) =>
% 121.32/16.01 ((
% 121.32/16.01 (doubleComplementE1) =>
% 121.32/16.01 ((
% 121.32/16.01 (doubleComplementSub1) =>
% 121.32/16.01 ((
% 121.32/16.01 (doubleComplementSub2) =>
% 121.32/16.01 ((
% 121.32/16.01 (doubleComplementEq) =>
% 121.32/16.01 ((
% 121.32/16.01 (complementTnotintersectT) =>
% 121.32/16.01 ((
% 121.32/16.01 (complementImpComplementIntersect) =>
% 121.32/16.01 ((
% 121.32/16.01 (complementSubsetComplementIntersect) =>
% 121.32/16.01 ((
% 121.32/16.01 (complementInPowersetComplementIntersect) =>
% 121.32/16.01 ((
% 121.32/16.01 (contraSubsetComplement) =>
% 121.32/16.01 ((
% 121.32/16.01 (complementTcontraSubset) =>
% 121.32/16.01 ((
% 121.32/16.01 (binunionTILcontra) =>
% 121.32/16.01 ((
% 121.32/16.01 (binunionTIRcontra) =>
% 121.32/16.01 ((
% 121.32/16.01 (inIntersectImpInUnion) =>
% 121.32/16.01 ((
% 121.32/16.01 (inIntersectImpInUnion2) =>
% 121.32/16.01 ((
% 121.32/16.01 (inIntersectImpInIntersectUnions) =>
% 121.32/16.01 ((
% 121.32/16.01 (intersectInPowersetIntersectUnions) =>
% 121.32/16.01 ((
% 121.32/16.01 (inComplementUnionImpNotIn1) =>
% 121.32/16.01 ((
% 121.32/16.01 (inComplementUnionImpInComplement1) =>
% 121.32/16.01 ((
% 121.32/16.01 (binunionTE) =>
% 121.32/16.01 ((
% 121.32/16.01 (binunionTEcontra) =>
% 121.32/16.01 ((
% 121.32/16.01 (demorgan2a1) =>
% 121.32/16.01 ((
% 121.32/16.01 (complementUnionInPowersetComplement) =>
% 121.32/16.01 ((
% 121.32/16.01 (demorgan2a2) =>
% 121.32/16.01 ((
% 121.32/16.01 (demorgan1a) =>
% 121.32/16.01 ((
% 121.32/16.01 (demorgan1b) =>
% 121.32/16.01 ((
% 121.32/16.01 (demorgan1) =>
% 121.32/16.01 ((
% 121.32/16.01 (demorgan2a) =>
% 121.32/16.01 ((
% 121.32/16.01 (demorgan2b2) =>
% 121.32/16.01 ((
% 121.32/16.01 (demorgan2b) =>
% 121.32/16.01 ((
% 121.32/16.01 (demorgan2) =>
% 121.32/16.01 ((
% 121.32/16.01 (woz13rule0) =>
% 121.32/16.01 ((
% 121.32/16.01 (woz13rule1) =>
% 121.32/16.01 ((
% 121.32/16.01 (woz13rule2) =>
% 121.32/16.01 ((
% 121.32/16.01 (woz13rule3) =>
% 121.32/16.01 ((
% 121.32/16.01 (woz13rule4) =>
% 121.32/16.01 ((
% 121.32/16.01 (woz1_1) =>
% 121.32/16.01 ((
% 121.32/16.01 (woz1_2) =>
% 121.32/16.01 ((
% 121.32/16.01 (woz1_3) =>
% 121.32/16.01 ((
% 121.32/16.01 (woz1_4) =>
% 121.32/16.01 ((
% 121.32/16.01 (woz1_5) =>
% 121.32/16.01 ((
% 121.32/16.01 (breln1all2) =>
% 121.32/16.01 ((
% 121.32/16.01 (breln1SetBreln1) =>
% 121.32/16.01 ((
% 121.32/16.01 (choice2fnsingleton) =>
% 121.32/16.01 ((
% 121.32/16.01 (setOfPairsIsBReln1) =>
% 121.32/16.01 ((
% 121.32/16.01 (breln1all1) =>
% 121.32/16.01 ((
% 121.32/16.01 (subbreln1) =>
% 121.32/16.01 ((
% 121.32/16.01 (eqbreln1) =>
% 121.32/16.01 ((
% 121.32/16.01 (breln1invprop) =>
% 121.32/16.01 ((
% 121.32/16.01 (breln1invI) =>
% 121.32/16.01 ((
% 121.32/16.01 (breln1invE) =>
% 121.32/16.01 ((
% 121.32/16.01 (breln1compprop) =>
% 121.32/16.01 ((
% 121.32/16.01 (breln1compI) =>
% 121.32/16.01 ((
% 121.32/16.01 (breln1compE) =>
% 121.32/16.01 ((
% 121.32/16.01 (breln1compEex) =>
% 121.32/16.01 ((
% 121.32/16.01 (breln1unionprop) =>
% 121.32/16.01 ((
% 121.32/16.01 (breln1unionIL) =>
% 121.32/16.01 ((
% 121.32/16.01 (breln1unionIR) =>
% 121.32/16.01 ((
% 121.32/16.01 (breln1unionI) =>
% 121.32/16.01 ((
% 121.32/16.01 (breln1unionE) =>
% 121.32/16.01 ((
% 121.32/16.01 (breln1unionEcases) =>
% 121.32/16.01 ((
% 121.32/16.01 (breln1unionCommutes) =>
% 121.32/16.01 ((
% 121.32/16.01 (woz2Ex) =>
% 121.32/16.01 ((
% 121.32/16.01 (woz2W) =>
% 121.32/16.01 ((
% 121.32/16.01 (woz2A) =>
% 121.32/16.01 ((
% 121.32/16.01 (woz2B) =>
% 121.32/16.01 ((
% 121.32/16.01 (image1Ex) =>
% 121.32/16.01 ((
% 121.32/16.01 (image1Ex1) =>
% 121.32/16.01 ((
% 121.32/16.01 (image1Equiv) =>
% 121.32/16.01 ((
% 121.32/16.01 (image1E) =>
% 121.32/16.01 ((
% 121.32/16.01 (image1I) =>
% 121.32/16.01 ((
% 121.32/16.01 (injFuncInInjFuncSet) =>
% 121.32/16.01 ((
% 121.32/16.01 (!!) @ (
% 121.32/16.01 (('#B') @ (
% 121.32/16.01 !!) @
% 121.32/16.01 (
% 121.32/16.01 (
% 121.32/16.01 ('#B') @ (
% 121.32/16.01 (
% 121.32/16.01 ('#B') @ (
% 121.32/16.01 !!))) @
% 121.32/16.01 (
% 121.32/16.01 (
% 121.32/16.01 ('#S') @ (
% 121.32/16.01 (
% 121.32/16.01 ('#B') @ (
% 121.32/16.01 '#S') @
% 121.32/16.01 (
% 121.32/16.01 (
% 121.32/16.01 ('#B') @ (
% 121.32/16.01 (
% 121.32/16.01 ('#B') @ (
% 121.32/16.01 '#S'))) @
% 121.32/16.01 (
% 121.32/16.01 (
% 121.32/16.01 ('#B') @ (
% 121.32/16.01 (
% 121.32/16.01 ('#B') @ (
% 121.32/16.01 (
% 121.32/16.01 ('#B') @ (
% 121.32/16.01 =>))))) @
% 121.32/16.01 (
% 121.32/16.01 (
% 121.32/16.01 ('#B') @ (
% 121.32/16.01 (
% 121.32/16.01 ('#B') @ (
% 121.32/16.01 (
% 121.32/16.01 ('#C') @ in)))) @
% 121.32/16.01 injFuncSet)))))))) @
% 121.32/16.01 (
% 121.32/16.01 (
% 121.32/16.01 ('#B') @ (
% 121.32/16.01 (
% 121.32/16.01 ('#B') @ (
% 121.32/16.01 (
% 121.32/16.01 ('#C') @ in)))) @
% 121.32/16.01 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 121.32/16.01 inference('lams2combs', [status(thm)], [zip_derived_cl0])).
% 121.32/16.01 thf(omega0Ax, axiom,(( omega0Ax ) = ((in @ emptyset @ omega)))).
% 121.32/16.01 thf('0', plain, (( omega0Ax ) = ( in @ emptyset @ omega )),
% 121.32/16.01 define([status(thm)])).
% 121.32/16.01 thf(emptyinunitempty, axiom,(( emptyinunitempty ) =
% 121.32/16.01 ((in @ emptyset @ (setadjoin @ emptyset @ emptyset))))).
% 121.32/16.01 thf('1', plain,
% 121.32/16.01 (( emptyinunitempty ) =
% 121.32/16.01 ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )),
% 121.32/16.01 define([status(thm)])).
% 121.32/16.01 thf(emptyset__Cong, axiom,(( emptyset__Cong ) =
% 121.32/16.01 ((((emptyset) = (emptyset)))))).
% 121.32/16.01 thf('2', plain, (( emptyset__Cong ) = ( ( emptyset ) = ( emptyset ) )),
% 121.32/16.01 define([status(thm)])).
% 121.32/16.01 thf(omega__Cong, axiom,(( omega__Cong ) = ((((omega) = (omega)))))).
% 121.32/16.01 thf('3', plain, (( omega__Cong ) = ( ( omega ) = ( omega ) )),
% 121.32/16.01 define([status(thm)])).
% 121.32/16.01 thf(zip_derived_cl2, plain,
% 121.32/16.01 (~ (((setextAx) =>
% 121.32/16.01 (((emptysetAx) =>
% 121.32/16.01 (((setadjoinAx) =>
% 121.32/16.01 (((powersetAx) =>
% 121.32/16.01 (((setunionAx) =>
% 121.32/16.01 (((in @ emptyset @ omega) =>
% 121.32/16.01 (((omegaSAx) =>
% 121.32/16.01 (((omegaIndAx) =>
% 121.32/16.01 (((replAx) =>
% 121.32/16.01 (((foundationAx) =>
% 121.32/16.01 (((wellorderingAx) =>
% 121.32/16.01 (((descrp) =>
% 121.32/16.01 (((dsetconstrI) =>
% 121.32/16.01 (((dsetconstrEL) =>
% 121.32/16.01 (((dsetconstrER) =>
% 121.32/16.01 (((exuE1) =>
% 121.32/16.01 (((prop2setE) =>
% 121.32/16.01 (((emptysetE) =>
% 121.32/16.01 (((emptysetimpfalse) =>
% 121.32/16.01 (((notinemptyset) =>
% 121.32/16.01 (((exuE3e) =>
% 121.32/16.01 (((setext) =>
% 121.32/16.01 (((emptyI) =>
% 121.32/16.01 (((noeltsimpempty) =>
% 121.32/16.01 (((setbeta) =>
% 121.32/16.01 (((nonemptyE1) =>
% 121.32/16.01 (((nonemptyI) =>
% 121.32/16.01 (((nonemptyI1) =>
% 121.32/16.01 (((setadjoinIL) =>
% 121.32/16.01 (((in @
% 121.32/16.01 emptyset @
% 121.32/16.01 (setadjoin @
% 121.32/16.01 emptyset @
% 121.32/16.01 emptyset)) =>
% 121.32/16.01 ((
% 121.32/16.01 (setadjoinIR) =>
% 121.32/16.01 ((
% 121.32/16.01 (setadjoinE) =>
% 121.32/16.01 ((
% 121.32/16.01 (setadjoinOr) =>
% 121.32/16.01 ((
% 121.32/16.01 (setoftrueEq) =>
% 121.32/16.01 ((
% 121.32/16.01 (powersetI) =>
% 121.32/16.01 ((
% 121.32/16.01 (emptyinPowerset) =>
% 121.32/16.01 ((
% 121.32/16.01 (emptyInPowerset) =>
% 121.32/16.01 ((
% 121.32/16.01 (powersetE) =>
% 121.32/16.01 ((
% 121.32/16.01 (setunionI) =>
% 121.32/16.01 ((
% 121.32/16.01 (setunionE) =>
% 121.32/16.01 ((
% 121.32/16.01 (subPowSU) =>
% 121.32/16.01 ((
% 121.32/16.01 (exuE2) =>
% 121.32/16.01 ((
% 121.32/16.01 (nonemptyImpWitness) =>
% 121.32/16.01 ((
% 121.32/16.01 (uniqinunit) =>
% 121.32/16.01 ((
% 121.32/16.01 (notinsingleton) =>
% 121.32/16.01 ((
% 121.32/16.01 (eqinunit) =>
% 121.32/16.01 ((
% 121.32/16.01 (singletonsswitch) =>
% 121.32/16.01 ((
% 121.32/16.01 (upairsetE) =>
% 121.32/16.01 ((
% 121.32/16.01 (upairsetIL) =>
% 121.32/16.01 ((
% 121.32/16.01 (upairsetIR) =>
% 121.32/16.01 ((
% 121.32/16.01 (emptyE1) =>
% 121.32/16.01 ((
% 121.32/16.01 (vacuousDall) =>
% 121.32/16.01 ((
% 121.32/16.01 (quantDeMorgan1) =>
% 121.32/16.01 ((
% 121.32/16.01 (quantDeMorgan2) =>
% 121.32/16.01 ((
% 121.32/16.01 (quantDeMorgan3) =>
% 121.32/16.01 ((
% 121.32/16.01 (quantDeMorgan4) =>
% 121.32/16.01 ((
% 121.32/16.01 (prop2setI) =>
% 121.32/16.01 ((
% 121.32/16.01 (prop2set2propI) =>
% 121.32/16.01 ((
% 121.32/16.01 (notdexE) =>
% 121.32/16.01 ((
% 121.32/16.01 (notdallE) =>
% 121.32/16.01 ((
% 121.32/16.01 (exuI1) =>
% 121.32/16.01 ((
% 121.32/16.01 (exuI3) =>
% 121.32/16.01 ((
% 121.32/16.01 (exuI2) =>
% 121.32/16.01 ((
% 121.32/16.01 (inCongP) =>
% 121.32/16.01 ((
% 121.32/16.01 (in__Cong) =>
% 121.32/16.01 ((
% 121.32/16.01 (exuE3u) =>
% 121.32/16.01 ((
% 121.32/16.01 (exu__Cong) =>
% 121.32/16.01 ((
% 121.32/16.01 ((
% 121.32/16.01 (emptyset) =
% 121.32/16.01 (emptyset))) =>
% 121.32/16.01 ((
% 121.32/16.01 (setadjoin__Cong) =>
% 121.32/16.01 ((
% 121.32/16.01 (powerset__Cong) =>
% 121.32/16.01 ((
% 121.32/16.01 (setunion__Cong) =>
% 121.32/16.01 ((
% 121.32/16.01 ((
% 121.32/16.01 (omega) =
% 121.32/16.01 (omega))) =>
% 121.32/16.01 ((
% 121.32/16.01 (exuEu) =>
% 121.32/16.01 ((
% 121.32/16.01 (descr__Cong) =>
% 121.32/16.01 ((
% 121.32/16.01 (dsetconstr__Cong) =>
% 121.32/16.01 ((
% 121.32/16.01 (subsetI1) =>
% 121.32/16.01 ((
% 121.32/16.01 (eqimpsubset2) =>
% 121.32/16.01 ((
% 121.32/16.01 (eqimpsubset1) =>
% 121.32/16.01 ((
% 121.32/16.01 (subsetI2) =>
% 121.32/16.01 ((
% 121.32/16.01 (emptysetsubset) =>
% 121.32/16.01 ((
% 121.32/16.01 (subsetE) =>
% 121.32/16.01 ((
% 121.32/16.01 (subsetE2) =>
% 121.32/16.01 ((
% 121.32/16.01 (notsubsetI) =>
% 121.32/16.01 ((
% 121.32/16.01 (notequalI1) =>
% 121.32/16.01 ((
% 121.32/16.01 (notequalI2) =>
% 121.32/16.01 ((
% 121.32/16.01 (subsetRefl) =>
% 121.32/16.01 ((
% 121.32/16.01 (subsetTrans) =>
% 121.32/16.01 ((
% 121.32/16.01 (setadjoinSub) =>
% 121.32/16.01 ((
% 121.32/16.01 (setadjoinSub2) =>
% 121.32/16.01 ((
% 121.32/16.01 (subset2powerset) =>
% 121.32/16.01 ((
% 121.32/16.01 (setextsub) =>
% 121.32/16.01 ((
% 121.32/16.01 (subsetemptysetimpeq) =>
% 121.32/16.01 ((
% 121.32/16.01 (powersetI1) =>
% 121.32/16.01 ((
% 121.32/16.01 (powersetE1) =>
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% 121.32/16.01 ((
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% 121.32/16.01 ((
% 121.32/16.01 (eqinunit) =>
% 121.32/16.01 ((
% 121.32/16.01 (singletonsswitch) =>
% 121.32/16.01 ((
% 121.32/16.01 (upairsetE) =>
% 121.32/16.01 ((
% 121.32/16.01 (upairsetIL) =>
% 121.32/16.01 ((
% 121.32/16.01 (upairsetIR) =>
% 121.32/16.01 ((
% 121.32/16.01 (emptyE1) =>
% 121.32/16.01 ((
% 121.32/16.01 (vacuousDall) =>
% 121.32/16.01 ((
% 121.32/16.01 (quantDeMorgan1) =>
% 121.32/16.01 ((
% 121.32/16.01 (quantDeMorgan2) =>
% 121.32/16.01 ((
% 121.32/16.01 (quantDeMorgan3) =>
% 121.32/16.01 ((
% 121.32/16.01 (quantDeMorgan4) =>
% 121.32/16.01 ((
% 121.32/16.01 (prop2setI) =>
% 121.32/16.01 ((
% 121.32/16.01 (prop2set2propI) =>
% 121.32/16.01 ((
% 121.32/16.01 (notdexE) =>
% 121.32/16.01 ((
% 121.32/16.01 (notdallE) =>
% 121.32/16.01 ((
% 121.32/16.01 (exuI1) =>
% 121.32/16.01 ((
% 121.32/16.01 (exuI3) =>
% 121.32/16.01 ((
% 121.32/16.01 (exuI2) =>
% 121.32/16.01 ((
% 121.32/16.01 (inCongP) =>
% 121.32/16.01 ((
% 121.32/16.01 (in__Cong) =>
% 121.32/16.01 ((
% 121.32/16.01 (exuE3u) =>
% 121.32/16.01 ((
% 121.32/16.01 (exu__Cong) =>
% 121.32/16.01 ((
% 121.32/16.01 (setadjoin__Cong) =>
% 121.32/16.01 ((
% 121.32/16.01 (powerset__Cong) =>
% 121.32/16.01 ((
% 121.32/16.01 (setunion__Cong) =>
% 121.32/16.01 ((
% 121.32/16.01 (exuEu) =>
% 121.32/16.01 ((
% 121.32/16.01 (descr__Cong) =>
% 121.32/16.01 ((
% 121.32/16.01 (dsetconstr__Cong) =>
% 121.32/16.01 ((
% 121.32/16.01 (subsetI1) =>
% 121.32/16.01 ((
% 121.32/16.01 (eqimpsubset2) =>
% 121.32/16.01 ((
% 121.32/16.01 (eqimpsubset1) =>
% 121.32/16.01 ((
% 121.32/16.01 (subsetI2) =>
% 121.32/16.01 ((
% 121.32/16.01 (emptysetsubset) =>
% 121.32/16.01 ((
% 121.32/16.01 (subsetE) =>
% 121.32/16.01 ((
% 121.32/16.01 (subsetE2) =>
% 121.32/16.01 ((
% 121.32/16.01 (notsubsetI) =>
% 121.32/16.01 ((
% 121.32/16.01 (notequalI1) =>
% 121.32/16.01 ((
% 121.32/16.01 (notequalI2) =>
% 121.32/16.01 ((
% 121.32/16.01 (subsetRefl) =>
% 121.32/16.01 ((
% 121.32/16.01 (subsetTrans) =>
% 121.32/16.01 ((
% 121.32/16.01 (setadjoinSub) =>
% 121.32/16.01 ((
% 121.32/16.01 (setadjoinSub2) =>
% 121.32/16.01 ((
% 121.32/16.01 (subset2powerset) =>
% 121.32/16.01 ((
% 121.32/16.01 (setextsub) =>
% 121.32/16.01 ((
% 121.32/16.01 (subsetemptysetimpeq) =>
% 121.32/16.01 ((
% 121.32/16.01 (powersetI1) =>
% 121.32/16.01 ((
% 121.32/16.01 (powersetE1) =>
% 121.32/16.01 ((
% 121.32/16.01 (inPowerset) =>
% 121.32/16.01 ((
% 121.32/16.01 (powersetsubset) =>
% 121.32/16.01 ((
% 121.32/16.01 (sepInPowerset) =>
% 121.32/16.01 ((
% 121.32/16.01 (sepSubset) =>
% 121.32/16.01 ((
% 121.32/16.01 (binunionIL) =>
% 121.32/16.01 ((
% 121.32/16.01 (upairset2IR) =>
% 121.32/16.01 ((
% 121.32/16.01 (binunionIR) =>
% 121.32/16.01 ((
% 121.32/16.01 (binunionEcases) =>
% 121.32/16.01 ((
% 121.32/16.01 (binunionE) =>
% 121.32/16.01 ((
% 121.32/16.01 (binunionLsub) =>
% 121.32/16.01 ((
% 121.32/16.01 (binunionRsub) =>
% 121.32/16.01 ((
% 121.32/16.01 (binintersectI) =>
% 121.32/16.01 ((
% 121.32/16.01 (binintersectSubset5) =>
% 121.32/16.01 ((
% 121.32/16.01 (binintersectEL) =>
% 121.32/16.01 ((
% 121.32/16.01 (binintersectLsub) =>
% 121.32/16.01 ((
% 121.32/16.01 (binintersectSubset2) =>
% 121.32/16.01 ((
% 121.32/16.01 (binintersectSubset3) =>
% 121.32/16.01 ((
% 121.32/16.01 (binintersectER) =>
% 121.32/16.01 ((
% 121.32/16.01 (disjointsetsI1) =>
% 121.32/16.01 ((
% 121.32/16.01 (binintersectRsub) =>
% 121.32/16.01 ((
% 121.32/16.01 (binintersectSubset4) =>
% 121.32/16.01 ((
% 121.32/16.01 (binintersectSubset1) =>
% 121.32/16.01 ((
% 121.32/16.01 (bs114d) =>
% 121.32/16.01 ((
% 121.32/16.01 (setminusI) =>
% 121.32/16.01 ((
% 121.32/16.01 (setminusEL) =>
% 121.32/16.01 ((
% 121.32/16.01 (setminusER) =>
% 121.32/16.01 ((
% 121.32/16.01 (setminusSubset2) =>
% 121.32/16.01 ((
% 121.32/16.01 (setminusERneg) =>
% 121.32/16.01 ((
% 121.32/16.01 (setminusELneg) =>
% 121.32/16.01 ((
% 121.32/16.01 (setminusILneg) =>
% 121.32/16.01 ((
% 121.32/16.01 (setminusIRneg) =>
% 121.32/16.01 ((
% 121.32/16.01 (setminusLsub) =>
% 121.32/16.01 ((
% 121.32/16.01 (setminusSubset1) =>
% 121.32/16.01 ((
% 121.32/16.01 (symdiffE) =>
% 121.32/16.01 ((
% 121.32/16.01 (symdiffI1) =>
% 121.32/16.01 ((
% 121.32/16.01 (symdiffI2) =>
% 121.32/16.01 ((
% 121.32/16.01 (symdiffIneg1) =>
% 121.32/16.01 ((
% 121.32/16.01 (symdiffIneg2) =>
% 121.32/16.01 ((
% 121.32/16.01 (secondinupair) =>
% 121.32/16.01 ((
% 121.32/16.01 (setukpairIL) =>
% 121.32/16.01 ((
% 121.32/16.01 (setukpairIR) =>
% 121.32/16.01 ((
% 121.32/16.01 (kpairiskpair) =>
% 121.32/16.01 ((
% 121.32/16.01 (kpairp) =>
% 121.32/16.01 ((
% 121.32/16.01 (singletonsubset) =>
% 121.32/16.01 ((
% 121.32/16.01 (singletoninpowerset) =>
% 121.32/16.01 ((
% 121.32/16.01 (singletoninpowunion) =>
% 121.32/16.01 ((
% 121.32/16.01 (upairset2E) =>
% 121.32/16.01 ((
% 121.32/16.01 (upairsubunion) =>
% 121.32/16.01 ((
% 121.32/16.01 (upairinpowunion) =>
% 121.32/16.01 ((
% 121.32/16.01 (ubforcartprodlem1) =>
% 121.32/16.01 ((
% 121.32/16.01 (ubforcartprodlem2) =>
% 121.32/16.01 ((
% 121.32/16.01 (ubforcartprodlem3) =>
% 121.32/16.01 ((
% 121.32/16.01 (cartprodpairin) =>
% 121.32/16.01 ((
% 121.32/16.01 (cartprodmempair1) =>
% 121.32/16.01 ((
% 121.32/16.01 (cartprodmempair) =>
% 121.32/16.01 ((
% 121.32/16.01 (setunionE2) =>
% 121.32/16.01 ((
% 121.32/16.01 (setunionsingleton1) =>
% 121.32/16.01 ((
% 121.32/16.01 (setunionsingleton2) =>
% 121.32/16.01 ((
% 121.32/16.01 (setunionsingleton) =>
% 121.32/16.01 ((
% 121.32/16.01 (singletonprop) =>
% 121.32/16.01 ((
% 121.32/16.01 (ex1E1) =>
% 121.32/16.01 ((
% 121.32/16.01 (ex1I) =>
% 121.32/16.01 ((
% 121.32/16.01 (ex1I2) =>
% 121.32/16.01 ((
% 121.32/16.01 (singletonsuniq) =>
% 121.32/16.01 ((
% 121.32/16.01 (setukpairinjL1) =>
% 121.32/16.01 ((
% 121.32/16.01 (kfstsingleton) =>
% 121.32/16.01 ((
% 121.32/16.01 (theprop) =>
% 121.32/16.01 ((
% 121.32/16.01 (kfstpairEq) =>
% 121.32/16.01 ((
% 121.32/16.01 (cartprodfstin) =>
% 121.32/16.01 ((
% 121.32/16.01 (setukpairinjL2) =>
% 121.32/16.01 ((
% 121.32/16.01 (setukpairinjL) =>
% 121.32/16.01 ((
% 121.32/16.01 (setukpairinjR11) =>
% 121.32/16.01 ((
% 121.32/16.01 (setukpairinjR12) =>
% 121.32/16.01 ((
% 121.32/16.01 (setukpairinjR1) =>
% 121.32/16.01 ((
% 121.32/16.01 (upairequniteq) =>
% 121.32/16.01 ((
% 121.32/16.01 (setukpairinjR2) =>
% 121.32/16.01 ((
% 121.32/16.01 (setukpairinjR) =>
% 121.32/16.01 ((
% 121.32/16.01 (ksndsingleton) =>
% 121.32/16.01 ((
% 121.32/16.01 (ksndpairEq) =>
% 121.32/16.01 ((
% 121.32/16.01 (kpairsurjEq) =>
% 121.32/16.01 ((
% 121.32/16.01 (cartprodsndin) =>
% 121.32/16.01 ((
% 121.32/16.01 (cartprodpairmemEL) =>
% 121.32/16.01 ((
% 121.32/16.01 (cartprodpairmemER) =>
% 121.32/16.01 ((
% 121.32/16.01 (cartprodmempaircEq) =>
% 121.32/16.01 ((
% 121.32/16.01 (cartprodfstpairEq) =>
% 121.32/16.01 ((
% 121.32/16.01 (cartprodsndpairEq) =>
% 121.32/16.01 ((
% 121.32/16.01 (cartprodpairsurjEq) =>
% 121.32/16.01 ((
% 121.32/16.01 (dpsetconstrI) =>
% 121.32/16.01 ((
% 121.32/16.01 (dpsetconstrSub) =>
% 121.32/16.01 ((
% 121.32/16.01 (setOfPairsIsBReln) =>
% 121.32/16.01 ((
% 121.32/16.01 (dpsetconstrERa) =>
% 121.32/16.01 ((
% 121.32/16.01 (dpsetconstrEL1) =>
% 121.32/16.01 ((
% 121.32/16.01 (dpsetconstrEL2) =>
% 121.32/16.01 ((
% 121.32/16.01 (dpsetconstrER) =>
% 121.32/16.01 ((
% 121.32/16.01 (funcImageSingleton) =>
% 121.32/16.01 ((
% 121.32/16.01 (apProp) =>
% 121.32/16.01 ((
% 121.32/16.01 (app) =>
% 121.32/16.01 ((
% 121.32/16.01 (infuncsetfunc) =>
% 121.32/16.01 ((
% 121.32/16.01 (ap2p) =>
% 121.32/16.01 ((
% 121.32/16.01 (funcinfuncset) =>
% 121.32/16.01 ((
% 121.32/16.01 (lamProp) =>
% 121.32/16.01 ((
% 121.32/16.01 (lamp) =>
% 121.32/16.01 ((
% 121.32/16.01 (lam2p) =>
% 121.32/16.01 ((
% 121.32/16.01 (brelnall1) =>
% 121.32/16.01 ((
% 121.32/16.01 (brelnall2) =>
% 121.32/16.01 ((
% 121.32/16.01 (ex1E2) =>
% 121.32/16.01 ((
% 121.32/16.01 (funcGraphProp1) =>
% 121.32/16.01 ((
% 121.32/16.01 (funcGraphProp3) =>
% 121.32/16.01 ((
% 121.32/16.01 (funcGraphProp2) =>
% 121.32/16.01 ((
% 121.32/16.01 (funcextLem) =>
% 121.32/16.01 ((
% 121.32/16.01 (funcGraphProp4) =>
% 121.32/16.01 ((
% 121.32/16.01 (subbreln) =>
% 121.32/16.01 ((
% 121.32/16.01 (eqbreln) =>
% 121.32/16.01 ((
% 121.32/16.01 (funcext) =>
% 121.32/16.01 ((
% 121.32/16.01 (funcext2) =>
% 121.32/16.01 ((
% 121.32/16.01 (ap2apEq1) =>
% 121.32/16.01 ((
% 121.32/16.01 (ap2apEq2) =>
% 121.32/16.01 ((
% 121.32/16.01 (beta1) =>
% 121.32/16.01 ((
% 121.32/16.01 (eta1) =>
% 121.32/16.01 ((
% 121.32/16.01 (lam2lamEq) =>
% 121.32/16.01 ((
% 121.32/16.01 (beta2) =>
% 121.32/16.01 ((
% 121.32/16.01 (eta2) =>
% 121.32/16.01 ((
% 121.32/16.01 (iffalseProp1) =>
% 121.32/16.01 ((
% 121.32/16.01 (iffalseProp2) =>
% 121.32/16.01 ((
% 121.32/16.01 (iftrueProp1) =>
% 121.32/16.01 ((
% 121.32/16.01 (iftrueProp2) =>
% 121.32/16.01 ((
% 121.32/16.01 (ifSingleton) =>
% 121.32/16.01 ((
% 121.32/16.01 (ifp) =>
% 121.32/16.01 ((
% 121.32/16.01 (theeq) =>
% 121.32/16.01 ((
% 121.32/16.01 (iftrue) =>
% 121.32/16.01 ((
% 121.32/16.01 (iffalse) =>
% 121.32/16.01 ((
% 121.32/16.01 (iftrueorfalse) =>
% 121.32/16.01 ((
% 121.32/16.01 (binintersectT_lem) =>
% 121.32/16.01 ((
% 121.32/16.01 (binunionT_lem) =>
% 121.32/16.01 ((
% 121.32/16.01 (powersetT_lem) =>
% 121.32/16.01 ((
% 121.32/16.01 (setminusT_lem) =>
% 121.32/16.01 ((
% 121.32/16.01 (complementT_lem) =>
% 121.32/16.01 ((
% 121.32/16.01 (setextT) =>
% 121.32/16.01 ((
% 121.32/16.01 (subsetTI) =>
% 121.32/16.01 ((
% 121.32/16.01 (powersetTI1) =>
% 121.32/16.01 ((
% 121.32/16.01 (powersetTE1) =>
% 121.32/16.01 ((
% 121.32/16.01 (complementTI1) =>
% 121.32/16.01 ((
% 121.32/16.01 (complementTE1) =>
% 121.32/16.01 ((
% 121.32/16.01 (binintersectTELcontra) =>
% 121.32/16.01 ((
% 121.32/16.01 (binintersectTERcontra) =>
% 121.32/16.01 ((
% 121.32/16.01 (contrasubsetT) =>
% 121.32/16.01 ((
% 121.32/16.01 (contrasubsetT1) =>
% 121.32/16.01 ((
% 121.32/16.01 (contrasubsetT2) =>
% 121.32/16.01 ((
% 121.32/16.01 (contrasubsetT3) =>
% 121.32/16.01 ((
% 121.32/16.01 (doubleComplementI1) =>
% 121.32/16.01 ((
% 121.32/16.01 (doubleComplementE1) =>
% 121.32/16.01 ((
% 121.32/16.01 (doubleComplementSub1) =>
% 121.32/16.01 ((
% 121.32/16.01 (doubleComplementSub2) =>
% 121.32/16.01 ((
% 121.32/16.01 (doubleComplementEq) =>
% 121.32/16.01 ((
% 121.32/16.01 (complementTnotintersectT) =>
% 121.32/16.01 ((
% 121.32/16.01 (complementImpComplementIntersect) =>
% 121.32/16.01 ((
% 121.32/16.01 (complementSubsetComplementIntersect) =>
% 121.32/16.01 ((
% 121.32/16.01 (complementInPowersetComplementIntersect) =>
% 121.32/16.01 ((
% 121.32/16.01 (contraSubsetComplement) =>
% 121.32/16.01 ((
% 121.32/16.01 (complementTcontraSubset) =>
% 121.32/16.01 ((
% 121.32/16.01 (binunionTILcontra) =>
% 121.32/16.01 ((
% 121.32/16.01 (binunionTIRcontra) =>
% 121.32/16.01 ((
% 121.32/16.01 (inIntersectImpInUnion) =>
% 121.32/16.01 ((
% 121.32/16.01 (inIntersectImpInUnion2) =>
% 121.32/16.01 ((
% 121.32/16.01 (inIntersectImpInIntersectUnions) =>
% 121.32/16.01 ((
% 121.32/16.01 (intersectInPowersetIntersectUnions) =>
% 121.32/16.01 ((
% 121.32/16.01 (inComplementUnionImpNotIn1) =>
% 121.32/16.01 ((
% 121.32/16.01 (inComplementUnionImpInComplement1) =>
% 121.32/16.01 ((
% 121.32/16.01 (binunionTE) =>
% 121.32/16.01 ((
% 121.32/16.01 (binunionTEcontra) =>
% 121.32/16.01 ((
% 121.32/16.01 (demorgan2a1) =>
% 121.32/16.01 ((
% 121.32/16.01 (complementUnionInPowersetComplement) =>
% 121.32/16.01 ((
% 121.32/16.01 (demorgan2a2) =>
% 121.32/16.01 ((
% 121.32/16.01 (demorgan1a) =>
% 121.32/16.01 ((
% 121.32/16.01 (demorgan1b) =>
% 121.32/16.01 ((
% 121.32/16.01 (demorgan1) =>
% 121.32/16.01 ((
% 121.32/16.01 (demorgan2a) =>
% 121.32/16.01 ((
% 121.32/16.01 (demorgan2b2) =>
% 121.32/16.01 ((
% 121.32/16.01 (demorgan2b) =>
% 121.32/16.01 ((
% 121.32/16.01 (demorgan2) =>
% 121.32/16.01 ((
% 121.32/16.01 (woz13rule0) =>
% 121.32/16.01 ((
% 121.32/16.01 (woz13rule1) =>
% 121.32/16.01 ((
% 121.32/16.01 (woz13rule2) =>
% 121.32/16.01 ((
% 121.32/16.01 (woz13rule3) =>
% 121.32/16.01 ((
% 121.32/16.01 (woz13rule4) =>
% 121.32/16.01 ((
% 121.32/16.01 (woz1_1) =>
% 121.32/16.01 ((
% 121.32/16.01 (woz1_2) =>
% 121.32/16.01 ((
% 121.32/16.01 (woz1_3) =>
% 121.32/16.01 ((
% 121.32/16.01 (woz1_4) =>
% 121.32/16.01 ((
% 121.32/16.01 (woz1_5) =>
% 121.32/16.01 ((
% 121.32/16.01 (breln1all2) =>
% 121.32/16.01 ((
% 121.32/16.01 (breln1SetBreln1) =>
% 121.32/16.01 ((
% 121.32/16.01 (choice2fnsingleton) =>
% 121.32/16.01 ((
% 121.32/16.01 (setOfPairsIsBReln1) =>
% 121.32/16.01 ((
% 121.32/16.01 (breln1all1) =>
% 121.32/16.01 ((
% 121.32/16.01 (subbreln1) =>
% 121.32/16.01 ((
% 121.32/16.01 (eqbreln1) =>
% 121.32/16.01 ((
% 121.32/16.01 (breln1invprop) =>
% 121.32/16.01 ((
% 121.32/16.01 (breln1invI) =>
% 121.32/16.01 ((
% 121.32/16.01 (breln1invE) =>
% 121.32/16.01 ((
% 121.32/16.01 (breln1compprop) =>
% 121.32/16.01 ((
% 121.32/16.01 (breln1compI) =>
% 121.32/16.01 ((
% 121.32/16.01 (breln1compE) =>
% 121.32/16.01 ((
% 121.32/16.01 (breln1compEex) =>
% 121.32/16.01 ((
% 121.32/16.01 (breln1unionprop) =>
% 121.32/16.01 ((
% 121.32/16.01 (breln1unionIL) =>
% 121.32/16.01 ((
% 121.32/16.01 (breln1unionIR) =>
% 121.32/16.01 ((
% 121.32/16.01 (breln1unionI) =>
% 121.32/16.01 ((
% 121.32/16.01 (breln1unionE) =>
% 121.65/16.01 ((
% 121.65/16.01 (breln1unionEcases) =>
% 121.65/16.01 ((
% 121.65/16.01 (breln1unionCommutes) =>
% 121.65/16.01 ((
% 121.65/16.01 (woz2Ex) =>
% 121.65/16.01 ((
% 121.65/16.01 (woz2W) =>
% 121.65/16.01 ((
% 121.65/16.01 (woz2A) =>
% 121.65/16.01 ((
% 121.65/16.01 (woz2B) =>
% 121.65/16.01 ((
% 121.65/16.01 (image1Ex) =>
% 121.65/16.01 ((
% 121.65/16.01 (image1Ex1) =>
% 121.65/16.01 ((
% 121.65/16.01 (image1Equiv) =>
% 121.65/16.01 ((
% 121.65/16.01 (image1E) =>
% 121.65/16.01 ((
% 121.65/16.01 (image1I) =>
% 121.65/16.01 ((
% 121.65/16.01 (injFuncInInjFuncSet) =>
% 121.65/16.01 ((
% 121.65/16.01 (!!) @ (
% 121.65/16.01 (('#B') @ (
% 121.65/16.01 !!) @
% 121.65/16.01 (
% 121.65/16.01 (
% 121.65/16.01 ('#B') @ (
% 121.65/16.01 (
% 121.65/16.01 ('#B') @ (
% 121.65/16.01 !!))) @
% 121.65/16.01 (
% 121.65/16.01 (
% 121.65/16.01 ('#S') @ (
% 121.65/16.01 (
% 121.65/16.01 ('#B') @ (
% 121.65/16.01 '#S') @
% 121.65/16.01 (
% 121.65/16.01 (
% 121.65/16.01 ('#B') @ (
% 121.65/16.01 (
% 121.65/16.01 ('#B') @ (
% 121.65/16.01 '#S'))) @
% 121.65/16.01 (
% 121.65/16.01 (
% 121.65/16.01 ('#B') @ (
% 121.65/16.01 (
% 121.65/16.01 ('#B') @ (
% 121.65/16.01 (
% 121.65/16.01 ('#B') @ (
% 121.65/16.01 =>))))) @
% 121.65/16.01 (
% 121.65/16.01 (
% 121.65/16.01 ('#B') @ (
% 121.65/16.01 (
% 121.65/16.01 ('#B') @ (
% 121.65/16.01 (
% 121.65/16.01 ('#C') @ in)))) @
% 121.65/16.01 injFuncSet)))))))) @
% 121.65/16.01 (
% 121.65/16.01 (
% 121.65/16.01 ('#B') @ (
% 121.65/16.01 (
% 121.65/16.01 ('#B') @ (
% 121.65/16.01 (
% 121.65/16.01 ('#C') @ in)))) @
% 121.65/16.01 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 121.65/16.01 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl2])).
% 121.65/16.01 thf(zip_derived_cl5, plain,
% 121.65/16.01 (~ (((emptysetAx) =>
% 121.65/16.01 (((setadjoinAx) =>
% 121.65/16.01 (((powersetAx) =>
% 121.65/16.01 (((setunionAx) =>
% 121.65/16.01 (((in @ emptyset @ omega) =>
% 121.65/16.01 (((omegaSAx) =>
% 121.65/16.01 (((omegaIndAx) =>
% 121.65/16.01 (((replAx) =>
% 121.65/16.01 (((foundationAx) =>
% 121.65/16.01 (((wellorderingAx) =>
% 121.65/16.01 (((descrp) =>
% 121.65/16.01 (((dsetconstrI) =>
% 121.65/16.01 (((dsetconstrEL) =>
% 121.65/16.01 (((dsetconstrER) =>
% 121.65/16.01 (((exuE1) =>
% 121.65/16.01 (((prop2setE) =>
% 121.65/16.01 (((emptysetE) =>
% 121.65/16.01 (((emptysetimpfalse) =>
% 121.65/16.01 (((notinemptyset) =>
% 121.65/16.01 (((exuE3e) =>
% 121.65/16.01 (((setext) =>
% 121.65/16.01 (((emptyI) =>
% 121.65/16.01 (((noeltsimpempty) =>
% 121.65/16.01 (((setbeta) =>
% 121.65/16.01 (((nonemptyE1) =>
% 121.65/16.01 (((nonemptyI) =>
% 121.65/16.01 (((nonemptyI1) =>
% 121.65/16.01 (((setadjoinIL) =>
% 121.65/16.01 (((in @
% 121.65/16.01 emptyset @
% 121.65/16.01 (setadjoin @
% 121.65/16.01 emptyset @
% 121.65/16.01 emptyset)) =>
% 121.65/16.01 (((setadjoinIR) =>
% 121.65/16.01 ((
% 121.65/16.01 (setadjoinE) =>
% 121.65/16.01 ((
% 121.65/16.01 (setadjoinOr) =>
% 121.65/16.01 ((
% 121.65/16.01 (setoftrueEq) =>
% 121.65/16.01 ((
% 121.65/16.01 (powersetI) =>
% 121.65/16.01 ((
% 121.65/16.01 (emptyinPowerset) =>
% 121.65/16.01 ((
% 121.65/16.01 (emptyInPowerset) =>
% 121.65/16.01 ((
% 121.65/16.01 (powersetE) =>
% 121.65/16.01 ((
% 121.65/16.01 (setunionI) =>
% 121.65/16.01 ((
% 121.65/16.01 (setunionE) =>
% 121.65/16.01 ((
% 121.65/16.01 (subPowSU) =>
% 121.65/16.01 ((
% 121.65/16.01 (exuE2) =>
% 121.65/16.01 ((
% 121.65/16.01 (nonemptyImpWitness) =>
% 121.65/16.01 ((
% 121.65/16.01 (uniqinunit) =>
% 121.65/16.01 ((
% 121.65/16.01 (notinsingleton) =>
% 121.65/16.01 ((
% 121.65/16.01 (eqinunit) =>
% 121.65/16.01 ((
% 121.65/16.01 (singletonsswitch) =>
% 121.65/16.01 ((
% 121.65/16.01 (upairsetE) =>
% 121.65/16.01 ((
% 121.65/16.01 (upairsetIL) =>
% 121.65/16.01 ((
% 121.65/16.01 (upairsetIR) =>
% 121.65/16.01 ((
% 121.65/16.01 (emptyE1) =>
% 121.65/16.01 ((
% 121.65/16.01 (vacuousDall) =>
% 121.65/16.01 ((
% 121.65/16.01 (quantDeMorgan1) =>
% 121.65/16.01 ((
% 121.65/16.01 (quantDeMorgan2) =>
% 121.65/16.01 ((
% 121.65/16.01 (quantDeMorgan3) =>
% 121.65/16.01 ((
% 121.65/16.01 (quantDeMorgan4) =>
% 121.65/16.01 ((
% 121.65/16.01 (prop2setI) =>
% 121.65/16.01 ((
% 121.65/16.01 (prop2set2propI) =>
% 121.65/16.01 ((
% 121.65/16.01 (notdexE) =>
% 121.65/16.01 ((
% 121.65/16.01 (notdallE) =>
% 121.65/16.01 ((
% 121.65/16.01 (exuI1) =>
% 121.65/16.01 ((
% 121.65/16.01 (exuI3) =>
% 121.65/16.01 ((
% 121.65/16.01 (exuI2) =>
% 121.65/16.01 ((
% 121.65/16.01 (inCongP) =>
% 121.65/16.01 ((
% 121.65/16.01 (in__Cong) =>
% 121.65/16.01 ((
% 121.65/16.01 (exuE3u) =>
% 121.65/16.01 ((
% 121.65/16.01 (exu__Cong) =>
% 121.65/16.01 ((
% 121.65/16.01 (setadjoin__Cong) =>
% 121.65/16.01 ((
% 121.65/16.01 (powerset__Cong) =>
% 121.65/16.01 ((
% 121.65/16.01 (setunion__Cong) =>
% 121.65/16.01 ((
% 121.65/16.01 (exuEu) =>
% 121.65/16.01 ((
% 121.65/16.01 (descr__Cong) =>
% 121.65/16.01 ((
% 121.65/16.01 (dsetconstr__Cong) =>
% 121.65/16.01 ((
% 121.65/16.01 (subsetI1) =>
% 121.65/16.01 ((
% 121.65/16.01 (eqimpsubset2) =>
% 121.65/16.01 ((
% 121.65/16.01 (eqimpsubset1) =>
% 121.65/16.01 ((
% 121.65/16.01 (subsetI2) =>
% 121.65/16.01 ((
% 121.65/16.01 (emptysetsubset) =>
% 121.65/16.01 ((
% 121.65/16.01 (subsetE) =>
% 121.65/16.01 ((
% 121.65/16.01 (subsetE2) =>
% 121.65/16.01 ((
% 121.65/16.01 (notsubsetI) =>
% 121.65/16.01 ((
% 121.65/16.01 (notequalI1) =>
% 121.65/16.01 ((
% 121.65/16.01 (notequalI2) =>
% 121.65/16.01 ((
% 121.65/16.01 (subsetRefl) =>
% 121.65/16.01 ((
% 121.65/16.01 (subsetTrans) =>
% 121.65/16.01 ((
% 121.65/16.01 (setadjoinSub) =>
% 121.65/16.01 ((
% 121.65/16.01 (setadjoinSub2) =>
% 121.65/16.01 ((
% 121.65/16.01 (subset2powerset) =>
% 121.65/16.01 ((
% 121.65/16.01 (setextsub) =>
% 121.65/16.01 ((
% 121.65/16.01 (subsetemptysetimpeq) =>
% 121.65/16.01 ((
% 121.65/16.01 (powersetI1) =>
% 121.65/16.01 ((
% 121.65/16.01 (powersetE1) =>
% 121.65/16.01 ((
% 121.65/16.01 (inPowerset) =>
% 121.65/16.01 ((
% 121.65/16.01 (powersetsubset) =>
% 121.65/16.01 ((
% 121.65/16.01 (sepInPowerset) =>
% 121.65/16.01 ((
% 121.65/16.01 (sepSubset) =>
% 121.65/16.01 ((
% 121.65/16.01 (binunionIL) =>
% 121.65/16.01 ((
% 121.65/16.01 (upairset2IR) =>
% 121.65/16.01 ((
% 121.65/16.01 (binunionIR) =>
% 121.65/16.01 ((
% 121.65/16.01 (binunionEcases) =>
% 121.65/16.01 ((
% 121.65/16.01 (binunionE) =>
% 121.65/16.01 ((
% 121.65/16.01 (binunionLsub) =>
% 121.65/16.01 ((
% 121.65/16.01 (binunionRsub) =>
% 121.65/16.01 ((
% 121.65/16.01 (binintersectI) =>
% 121.65/16.01 ((
% 121.65/16.01 (binintersectSubset5) =>
% 121.65/16.01 ((
% 121.65/16.01 (binintersectEL) =>
% 121.65/16.01 ((
% 121.65/16.01 (binintersectLsub) =>
% 121.65/16.01 ((
% 121.65/16.01 (binintersectSubset2) =>
% 121.65/16.01 ((
% 121.65/16.01 (binintersectSubset3) =>
% 121.65/16.01 ((
% 121.65/16.01 (binintersectER) =>
% 121.65/16.01 ((
% 121.65/16.01 (disjointsetsI1) =>
% 121.65/16.01 ((
% 121.65/16.01 (binintersectRsub) =>
% 121.65/16.01 ((
% 121.65/16.01 (binintersectSubset4) =>
% 121.65/16.01 ((
% 121.65/16.01 (binintersectSubset1) =>
% 121.65/16.01 ((
% 121.65/16.01 (bs114d) =>
% 121.65/16.01 ((
% 121.65/16.01 (setminusI) =>
% 121.65/16.01 ((
% 121.65/16.01 (setminusEL) =>
% 121.65/16.01 ((
% 121.65/16.01 (setminusER) =>
% 121.65/16.01 ((
% 121.65/16.01 (setminusSubset2) =>
% 121.65/16.01 ((
% 121.65/16.01 (setminusERneg) =>
% 121.65/16.01 ((
% 121.65/16.01 (setminusELneg) =>
% 121.65/16.01 ((
% 121.65/16.01 (setminusILneg) =>
% 121.65/16.01 ((
% 121.65/16.01 (setminusIRneg) =>
% 121.65/16.01 ((
% 121.65/16.01 (setminusLsub) =>
% 121.65/16.01 ((
% 121.65/16.01 (setminusSubset1) =>
% 121.65/16.01 ((
% 121.65/16.01 (symdiffE) =>
% 121.65/16.01 ((
% 121.65/16.01 (symdiffI1) =>
% 121.65/16.01 ((
% 121.65/16.01 (symdiffI2) =>
% 121.65/16.01 ((
% 121.65/16.01 (symdiffIneg1) =>
% 121.65/16.01 ((
% 121.65/16.01 (symdiffIneg2) =>
% 121.65/16.01 ((
% 121.65/16.01 (secondinupair) =>
% 121.65/16.01 ((
% 121.65/16.01 (setukpairIL) =>
% 121.65/16.01 ((
% 121.65/16.01 (setukpairIR) =>
% 121.65/16.01 ((
% 121.65/16.01 (kpairiskpair) =>
% 121.65/16.01 ((
% 121.65/16.01 (kpairp) =>
% 121.65/16.01 ((
% 121.65/16.01 (singletonsubset) =>
% 121.65/16.01 ((
% 121.65/16.01 (singletoninpowerset) =>
% 121.65/16.01 ((
% 121.65/16.01 (singletoninpowunion) =>
% 121.65/16.01 ((
% 121.65/16.01 (upairset2E) =>
% 121.65/16.01 ((
% 121.65/16.01 (upairsubunion) =>
% 121.65/16.01 ((
% 121.65/16.01 (upairinpowunion) =>
% 121.65/16.01 ((
% 121.65/16.01 (ubforcartprodlem1) =>
% 121.65/16.01 ((
% 121.65/16.01 (ubforcartprodlem2) =>
% 121.65/16.01 ((
% 121.65/16.01 (ubforcartprodlem3) =>
% 121.65/16.01 ((
% 121.65/16.01 (cartprodpairin) =>
% 121.65/16.01 ((
% 121.65/16.01 (cartprodmempair1) =>
% 121.65/16.01 ((
% 121.65/16.01 (cartprodmempair) =>
% 121.65/16.01 ((
% 121.65/16.01 (setunionE2) =>
% 121.65/16.01 ((
% 121.65/16.01 (setunionsingleton1) =>
% 121.65/16.01 ((
% 121.65/16.01 (setunionsingleton2) =>
% 121.65/16.01 ((
% 121.65/16.01 (setunionsingleton) =>
% 121.65/16.01 ((
% 121.65/16.01 (singletonprop) =>
% 121.65/16.01 ((
% 121.65/16.01 (ex1E1) =>
% 121.65/16.01 ((
% 121.65/16.01 (ex1I) =>
% 121.65/16.01 ((
% 121.65/16.01 (ex1I2) =>
% 121.65/16.01 ((
% 121.65/16.01 (singletonsuniq) =>
% 121.65/16.01 ((
% 121.65/16.01 (setukpairinjL1) =>
% 121.65/16.01 ((
% 121.65/16.01 (kfstsingleton) =>
% 121.65/16.01 ((
% 121.65/16.01 (theprop) =>
% 121.65/16.01 ((
% 121.65/16.01 (kfstpairEq) =>
% 121.65/16.01 ((
% 121.65/16.01 (cartprodfstin) =>
% 121.65/16.01 ((
% 121.65/16.01 (setukpairinjL2) =>
% 121.65/16.01 ((
% 121.65/16.01 (setukpairinjL) =>
% 121.65/16.01 ((
% 121.65/16.01 (setukpairinjR11) =>
% 121.65/16.01 ((
% 121.65/16.01 (setukpairinjR12) =>
% 121.65/16.01 ((
% 121.65/16.01 (setukpairinjR1) =>
% 121.65/16.01 ((
% 121.65/16.01 (upairequniteq) =>
% 121.65/16.01 ((
% 121.65/16.01 (setukpairinjR2) =>
% 121.65/16.01 ((
% 121.65/16.01 (setukpairinjR) =>
% 121.65/16.01 ((
% 121.65/16.01 (ksndsingleton) =>
% 121.65/16.01 ((
% 121.65/16.01 (ksndpairEq) =>
% 121.65/16.01 ((
% 121.65/16.01 (kpairsurjEq) =>
% 121.65/16.01 ((
% 121.65/16.01 (cartprodsndin) =>
% 121.65/16.01 ((
% 121.65/16.01 (cartprodpairmemEL) =>
% 121.65/16.01 ((
% 121.65/16.01 (cartprodpairmemER) =>
% 121.65/16.01 ((
% 121.65/16.01 (cartprodmempaircEq) =>
% 121.65/16.01 ((
% 121.65/16.01 (cartprodfstpairEq) =>
% 121.65/16.01 ((
% 121.65/16.01 (cartprodsndpairEq) =>
% 121.65/16.01 ((
% 121.65/16.01 (cartprodpairsurjEq) =>
% 121.65/16.01 ((
% 121.65/16.01 (dpsetconstrI) =>
% 121.65/16.01 ((
% 121.65/16.01 (dpsetconstrSub) =>
% 121.65/16.01 ((
% 121.65/16.01 (setOfPairsIsBReln) =>
% 121.65/16.01 ((
% 121.65/16.01 (dpsetconstrERa) =>
% 121.65/16.01 ((
% 121.65/16.01 (dpsetconstrEL1) =>
% 121.65/16.01 ((
% 121.65/16.01 (dpsetconstrEL2) =>
% 121.65/16.01 ((
% 121.65/16.01 (dpsetconstrER) =>
% 121.65/16.01 ((
% 121.65/16.01 (funcImageSingleton) =>
% 121.65/16.01 ((
% 121.65/16.01 (apProp) =>
% 121.65/16.01 ((
% 121.65/16.01 (app) =>
% 121.65/16.01 ((
% 121.65/16.01 (infuncsetfunc) =>
% 121.65/16.01 ((
% 121.65/16.01 (ap2p) =>
% 121.65/16.01 ((
% 121.65/16.01 (funcinfuncset) =>
% 121.65/16.01 ((
% 121.65/16.01 (lamProp) =>
% 121.65/16.01 ((
% 121.65/16.01 (lamp) =>
% 121.65/16.01 ((
% 121.65/16.01 (lam2p) =>
% 121.65/16.01 ((
% 121.65/16.01 (brelnall1) =>
% 121.65/16.01 ((
% 121.65/16.01 (brelnall2) =>
% 121.65/16.01 ((
% 121.65/16.01 (ex1E2) =>
% 121.65/16.01 ((
% 121.65/16.01 (funcGraphProp1) =>
% 121.65/16.01 ((
% 121.65/16.01 (funcGraphProp3) =>
% 121.65/16.01 ((
% 121.65/16.01 (funcGraphProp2) =>
% 121.65/16.01 ((
% 121.65/16.01 (funcextLem) =>
% 121.65/16.01 ((
% 121.65/16.01 (funcGraphProp4) =>
% 121.65/16.01 ((
% 121.65/16.01 (subbreln) =>
% 121.65/16.01 ((
% 121.65/16.01 (eqbreln) =>
% 121.65/16.01 ((
% 121.65/16.01 (funcext) =>
% 121.65/16.01 ((
% 121.65/16.01 (funcext2) =>
% 121.65/16.01 ((
% 121.65/16.01 (ap2apEq1) =>
% 121.65/16.01 ((
% 121.65/16.01 (ap2apEq2) =>
% 121.65/16.01 ((
% 121.65/16.01 (beta1) =>
% 121.65/16.01 ((
% 121.65/16.01 (eta1) =>
% 121.65/16.01 ((
% 121.65/16.01 (lam2lamEq) =>
% 121.65/16.01 ((
% 121.65/16.01 (beta2) =>
% 121.65/16.01 ((
% 121.65/16.01 (eta2) =>
% 121.65/16.01 ((
% 121.65/16.01 (iffalseProp1) =>
% 121.65/16.01 ((
% 121.65/16.01 (iffalseProp2) =>
% 121.65/16.01 ((
% 121.65/16.01 (iftrueProp1) =>
% 121.65/16.01 ((
% 121.65/16.01 (iftrueProp2) =>
% 121.65/16.01 ((
% 121.65/16.01 (ifSingleton) =>
% 121.65/16.01 ((
% 121.65/16.01 (ifp) =>
% 121.65/16.01 ((
% 121.65/16.01 (theeq) =>
% 121.65/16.01 ((
% 121.65/16.01 (iftrue) =>
% 121.65/16.01 ((
% 121.65/16.01 (iffalse) =>
% 121.65/16.01 ((
% 121.65/16.01 (iftrueorfalse) =>
% 121.65/16.01 ((
% 121.65/16.01 (binintersectT_lem) =>
% 121.65/16.01 ((
% 121.65/16.01 (binunionT_lem) =>
% 121.65/16.01 ((
% 121.65/16.01 (powersetT_lem) =>
% 121.65/16.01 ((
% 121.65/16.01 (setminusT_lem) =>
% 121.65/16.01 ((
% 121.65/16.01 (complementT_lem) =>
% 121.65/16.01 ((
% 121.65/16.01 (setextT) =>
% 121.65/16.01 ((
% 121.65/16.01 (subsetTI) =>
% 121.65/16.01 ((
% 121.65/16.01 (powersetTI1) =>
% 121.65/16.01 ((
% 121.65/16.01 (powersetTE1) =>
% 121.65/16.01 ((
% 121.65/16.01 (complementTI1) =>
% 121.65/16.01 ((
% 121.65/16.01 (complementTE1) =>
% 121.65/16.01 ((
% 121.65/16.01 (binintersectTELcontra) =>
% 121.65/16.01 ((
% 121.65/16.01 (binintersectTERcontra) =>
% 121.65/16.01 ((
% 121.65/16.01 (contrasubsetT) =>
% 121.65/16.01 ((
% 121.65/16.01 (contrasubsetT1) =>
% 121.65/16.01 ((
% 121.65/16.01 (contrasubsetT2) =>
% 121.65/16.01 ((
% 121.65/16.01 (contrasubsetT3) =>
% 121.65/16.01 ((
% 121.65/16.01 (doubleComplementI1) =>
% 121.65/16.01 ((
% 121.65/16.01 (doubleComplementE1) =>
% 121.65/16.01 ((
% 121.65/16.01 (doubleComplementSub1) =>
% 121.65/16.01 ((
% 121.65/16.01 (doubleComplementSub2) =>
% 121.65/16.01 ((
% 121.65/16.01 (doubleComplementEq) =>
% 121.65/16.01 ((
% 121.65/16.01 (complementTnotintersectT) =>
% 121.65/16.01 ((
% 121.65/16.01 (complementImpComplementIntersect) =>
% 121.65/16.01 ((
% 121.65/16.01 (complementSubsetComplementIntersect) =>
% 121.65/16.01 ((
% 121.65/16.01 (complementInPowersetComplementIntersect) =>
% 121.65/16.01 ((
% 121.65/16.01 (contraSubsetComplement) =>
% 121.65/16.01 ((
% 121.65/16.01 (complementTcontraSubset) =>
% 121.65/16.01 ((
% 121.65/16.01 (binunionTILcontra) =>
% 121.65/16.01 ((
% 121.65/16.01 (binunionTIRcontra) =>
% 121.65/16.01 ((
% 121.65/16.01 (inIntersectImpInUnion) =>
% 121.65/16.01 ((
% 121.65/16.01 (inIntersectImpInUnion2) =>
% 121.65/16.01 ((
% 121.65/16.01 (inIntersectImpInIntersectUnions) =>
% 121.65/16.01 ((
% 121.65/16.01 (intersectInPowersetIntersectUnions) =>
% 121.65/16.01 ((
% 121.65/16.01 (inComplementUnionImpNotIn1) =>
% 121.65/16.01 ((
% 121.65/16.01 (inComplementUnionImpInComplement1) =>
% 121.65/16.01 ((
% 121.65/16.01 (binunionTE) =>
% 121.65/16.01 ((
% 121.65/16.01 (binunionTEcontra) =>
% 121.65/16.01 ((
% 121.65/16.01 (demorgan2a1) =>
% 121.65/16.01 ((
% 121.65/16.01 (complementUnionInPowersetComplement) =>
% 121.65/16.01 ((
% 121.65/16.01 (demorgan2a2) =>
% 121.65/16.01 ((
% 121.65/16.01 (demorgan1a) =>
% 121.65/16.01 ((
% 121.65/16.01 (demorgan1b) =>
% 121.65/16.01 ((
% 121.65/16.01 (demorgan1) =>
% 121.65/16.01 ((
% 121.65/16.01 (demorgan2a) =>
% 121.65/16.01 ((
% 121.65/16.01 (demorgan2b2) =>
% 121.65/16.01 ((
% 121.65/16.01 (demorgan2b) =>
% 121.65/16.01 ((
% 121.65/16.01 (demorgan2) =>
% 121.65/16.01 ((
% 121.65/16.01 (woz13rule0) =>
% 121.65/16.01 ((
% 121.65/16.01 (woz13rule1) =>
% 121.65/16.01 ((
% 121.65/16.01 (woz13rule2) =>
% 121.65/16.01 ((
% 121.65/16.01 (woz13rule3) =>
% 121.65/16.01 ((
% 121.65/16.01 (woz13rule4) =>
% 121.65/16.01 ((
% 121.65/16.01 (woz1_1) =>
% 121.65/16.01 ((
% 121.65/16.01 (woz1_2) =>
% 121.65/16.01 ((
% 121.65/16.01 (woz1_3) =>
% 121.65/16.01 ((
% 121.65/16.01 (woz1_4) =>
% 121.65/16.01 ((
% 121.65/16.01 (woz1_5) =>
% 121.65/16.01 ((
% 121.65/16.01 (breln1all2) =>
% 121.65/16.01 ((
% 121.65/16.01 (breln1SetBreln1) =>
% 121.65/16.01 ((
% 121.65/16.01 (choice2fnsingleton) =>
% 121.65/16.01 ((
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% 121.65/16.01 ((
% 121.65/16.01 (breln1all1) =>
% 121.65/16.01 ((
% 121.65/16.01 (subbreln1) =>
% 121.65/16.01 ((
% 121.65/16.01 (eqbreln1) =>
% 121.65/16.01 ((
% 121.65/16.01 (breln1invprop) =>
% 121.65/16.01 ((
% 121.65/16.01 (breln1invI) =>
% 121.65/16.01 ((
% 121.65/16.01 (breln1invE) =>
% 121.65/16.01 ((
% 121.65/16.01 (breln1compprop) =>
% 121.65/16.01 ((
% 121.65/16.01 (breln1compI) =>
% 121.65/16.01 ((
% 121.65/16.01 (breln1compE) =>
% 121.65/16.01 ((
% 121.65/16.01 (breln1compEex) =>
% 121.65/16.01 ((
% 121.65/16.01 (breln1unionprop) =>
% 121.65/16.01 ((
% 121.65/16.01 (breln1unionIL) =>
% 121.65/16.01 ((
% 121.65/16.01 (breln1unionIR) =>
% 121.65/16.01 ((
% 121.65/16.01 (breln1unionI) =>
% 121.65/16.01 ((
% 121.65/16.01 (breln1unionE) =>
% 121.65/16.01 ((
% 121.65/16.01 (breln1unionEcases) =>
% 121.65/16.01 ((
% 121.65/16.01 (breln1unionCommutes) =>
% 121.65/16.01 ((
% 121.65/16.01 (woz2Ex) =>
% 121.65/16.01 ((
% 121.65/16.01 (woz2W) =>
% 121.65/16.01 ((
% 121.65/16.01 (woz2A) =>
% 121.65/16.01 ((
% 121.65/16.01 (woz2B) =>
% 121.65/16.01 ((
% 121.65/16.01 (image1Ex) =>
% 121.65/16.01 ((
% 121.65/16.01 (image1Ex1) =>
% 121.65/16.01 ((
% 121.65/16.01 (image1Equiv) =>
% 121.65/16.01 ((
% 121.65/16.01 (image1E) =>
% 121.65/16.01 ((
% 121.65/16.01 (image1I) =>
% 121.65/16.01 ((
% 121.65/16.01 (injFuncInInjFuncSet) =>
% 121.65/16.01 ((
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% 121.65/16.01 (('#B') @ (
% 121.65/16.01 !!) @
% 121.65/16.01 (
% 121.65/16.01 (
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% 121.65/16.01 (
% 121.65/16.01 ('#B') @ (
% 121.65/16.01 !!))) @
% 121.65/16.01 (
% 121.65/16.01 (
% 121.65/16.01 ('#S') @ (
% 121.65/16.01 (
% 121.65/16.01 ('#B') @ (
% 121.65/16.01 '#S') @
% 121.65/16.01 (
% 121.65/16.01 (
% 121.65/16.01 ('#B') @ (
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% 121.65/16.01 ('#B') @ (
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% 121.65/16.01 (
% 121.65/16.01 (
% 121.65/16.01 ('#B') @ (
% 121.65/16.01 (
% 121.65/16.01 ('#B') @ (
% 121.65/16.01 (
% 121.65/16.01 ('#B') @ (
% 121.65/16.01 =>))))) @
% 121.65/16.01 (
% 121.65/16.01 (
% 121.65/16.01 ('#B') @ (
% 121.65/16.01 (
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% 121.65/16.01 (
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% 121.65/16.01 injFuncSet)))))))) @
% 121.65/16.01 (
% 121.65/16.01 (
% 121.65/16.01 ('#B') @ (
% 121.65/16.01 (
% 121.65/16.01 ('#B') @ (
% 121.65/16.01 (
% 121.65/16.01 ('#C') @ in)))) @
% 121.65/16.01 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 121.65/16.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3])).
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% 121.65/16.01 (((prop2setE) =>
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% 121.65/16.01 ((
% 121.65/16.01 (setoftrueEq) =>
% 121.65/16.01 ((
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% 121.65/16.01 ((
% 121.65/16.01 (emptyinPowerset) =>
% 121.65/16.01 ((
% 121.65/16.01 (emptyInPowerset) =>
% 121.65/16.01 ((
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% 121.65/16.01 ((
% 121.65/16.01 (setunionE) =>
% 121.65/16.01 ((
% 121.65/16.01 (subPowSU) =>
% 121.65/16.01 ((
% 121.65/16.01 (exuE2) =>
% 121.65/16.01 ((
% 121.65/16.01 (nonemptyImpWitness) =>
% 121.65/16.01 ((
% 121.65/16.01 (uniqinunit) =>
% 121.65/16.01 ((
% 121.65/16.01 (notinsingleton) =>
% 121.65/16.01 ((
% 121.65/16.01 (eqinunit) =>
% 121.65/16.01 ((
% 121.65/16.01 (singletonsswitch) =>
% 121.65/16.01 ((
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% 121.65/16.01 ((
% 121.65/16.01 (upairsetIL) =>
% 121.65/16.01 ((
% 121.65/16.01 (upairsetIR) =>
% 121.65/16.01 ((
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% 121.65/16.01 ((
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% 121.65/16.01 ((
% 121.65/16.01 (quantDeMorgan1) =>
% 121.65/16.01 ((
% 121.65/16.01 (quantDeMorgan2) =>
% 121.65/16.01 ((
% 121.65/16.01 (quantDeMorgan3) =>
% 121.65/16.01 ((
% 121.65/16.01 (quantDeMorgan4) =>
% 121.65/16.01 ((
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% 121.65/16.01 ((
% 121.65/16.01 (prop2set2propI) =>
% 121.65/16.01 ((
% 121.65/16.01 (notdexE) =>
% 121.65/16.01 ((
% 121.65/16.01 (notdallE) =>
% 121.65/16.01 ((
% 121.65/16.01 (exuI1) =>
% 121.65/16.01 ((
% 121.65/16.01 (exuI3) =>
% 121.65/16.01 ((
% 121.65/16.01 (exuI2) =>
% 121.65/16.01 ((
% 121.65/16.01 (inCongP) =>
% 121.65/16.01 ((
% 121.65/16.01 (in__Cong) =>
% 121.65/16.01 ((
% 121.65/16.01 (exuE3u) =>
% 121.65/16.01 ((
% 121.65/16.01 (exu__Cong) =>
% 121.65/16.01 ((
% 121.65/16.01 (setadjoin__Cong) =>
% 121.65/16.01 ((
% 121.65/16.01 (powerset__Cong) =>
% 121.65/16.01 ((
% 121.65/16.01 (setunion__Cong) =>
% 121.65/16.01 ((
% 121.65/16.01 (exuEu) =>
% 121.65/16.01 ((
% 121.65/16.01 (descr__Cong) =>
% 121.65/16.01 ((
% 121.65/16.01 (dsetconstr__Cong) =>
% 121.65/16.01 ((
% 121.65/16.01 (subsetI1) =>
% 121.65/16.01 ((
% 121.65/16.01 (eqimpsubset2) =>
% 121.65/16.01 ((
% 121.65/16.01 (eqimpsubset1) =>
% 121.65/16.01 ((
% 121.65/16.01 (subsetI2) =>
% 121.65/16.01 ((
% 121.65/16.01 (emptysetsubset) =>
% 121.65/16.01 ((
% 121.65/16.01 (subsetE) =>
% 121.65/16.01 ((
% 121.65/16.01 (subsetE2) =>
% 121.65/16.01 ((
% 121.65/16.01 (notsubsetI) =>
% 121.65/16.01 ((
% 121.65/16.01 (notequalI1) =>
% 121.65/16.01 ((
% 121.65/16.01 (notequalI2) =>
% 121.65/16.01 ((
% 121.65/16.01 (subsetRefl) =>
% 121.65/16.01 ((
% 121.65/16.01 (subsetTrans) =>
% 121.65/16.01 ((
% 121.65/16.01 (setadjoinSub) =>
% 121.65/16.01 ((
% 121.65/16.01 (setadjoinSub2) =>
% 121.65/16.01 ((
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% 121.65/16.01 ((
% 121.65/16.01 (setextsub) =>
% 121.65/16.01 ((
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% 121.65/16.01 ((
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% 121.65/16.01 ((
% 121.65/16.01 (powersetE1) =>
% 121.65/16.01 ((
% 121.65/16.01 (inPowerset) =>
% 121.65/16.01 ((
% 121.65/16.01 (powersetsubset) =>
% 121.65/16.01 ((
% 121.65/16.01 (sepInPowerset) =>
% 121.65/16.01 ((
% 121.65/16.01 (sepSubset) =>
% 121.65/16.01 ((
% 121.65/16.01 (binunionIL) =>
% 121.65/16.01 ((
% 121.65/16.01 (upairset2IR) =>
% 121.65/16.01 ((
% 121.65/16.01 (binunionIR) =>
% 121.65/16.01 ((
% 121.65/16.01 (binunionEcases) =>
% 121.65/16.01 ((
% 121.65/16.01 (binunionE) =>
% 121.65/16.01 ((
% 121.65/16.01 (binunionLsub) =>
% 121.65/16.01 ((
% 121.65/16.01 (binunionRsub) =>
% 121.65/16.01 ((
% 121.65/16.01 (binintersectI) =>
% 121.65/16.01 ((
% 121.65/16.01 (binintersectSubset5) =>
% 121.65/16.01 ((
% 121.65/16.01 (binintersectEL) =>
% 121.65/16.01 ((
% 121.65/16.01 (binintersectLsub) =>
% 121.65/16.01 ((
% 121.65/16.01 (binintersectSubset2) =>
% 121.65/16.01 ((
% 121.65/16.01 (binintersectSubset3) =>
% 121.65/16.01 ((
% 121.65/16.01 (binintersectER) =>
% 121.65/16.01 ((
% 121.65/16.01 (disjointsetsI1) =>
% 121.65/16.01 ((
% 121.65/16.01 (binintersectRsub) =>
% 121.65/16.01 ((
% 121.65/16.01 (binintersectSubset4) =>
% 121.65/16.01 ((
% 121.65/16.01 (binintersectSubset1) =>
% 121.65/16.01 ((
% 121.65/16.01 (bs114d) =>
% 121.65/16.01 ((
% 121.65/16.01 (setminusI) =>
% 121.65/16.01 ((
% 121.65/16.01 (setminusEL) =>
% 121.65/16.01 ((
% 121.65/16.01 (setminusER) =>
% 121.65/16.01 ((
% 121.65/16.01 (setminusSubset2) =>
% 121.65/16.01 ((
% 121.65/16.01 (setminusERneg) =>
% 121.65/16.01 ((
% 121.65/16.01 (setminusELneg) =>
% 121.65/16.01 ((
% 121.65/16.01 (setminusILneg) =>
% 121.65/16.01 ((
% 121.65/16.01 (setminusIRneg) =>
% 121.65/16.01 ((
% 121.65/16.01 (setminusLsub) =>
% 121.65/16.01 ((
% 121.65/16.01 (setminusSubset1) =>
% 121.65/16.01 ((
% 121.65/16.01 (symdiffE) =>
% 121.65/16.01 ((
% 121.65/16.01 (symdiffI1) =>
% 121.65/16.01 ((
% 121.65/16.01 (symdiffI2) =>
% 121.65/16.01 ((
% 121.65/16.01 (symdiffIneg1) =>
% 121.65/16.01 ((
% 121.65/16.01 (symdiffIneg2) =>
% 121.65/16.01 ((
% 121.65/16.01 (secondinupair) =>
% 121.65/16.01 ((
% 121.65/16.01 (setukpairIL) =>
% 121.65/16.01 ((
% 121.65/16.01 (setukpairIR) =>
% 121.65/16.01 ((
% 121.65/16.01 (kpairiskpair) =>
% 121.65/16.01 ((
% 121.65/16.01 (kpairp) =>
% 121.65/16.01 ((
% 121.65/16.01 (singletonsubset) =>
% 121.65/16.01 ((
% 121.65/16.01 (singletoninpowerset) =>
% 121.65/16.01 ((
% 121.65/16.01 (singletoninpowunion) =>
% 121.65/16.01 ((
% 121.65/16.01 (upairset2E) =>
% 121.65/16.01 ((
% 121.65/16.01 (upairsubunion) =>
% 121.65/16.01 ((
% 121.65/16.01 (upairinpowunion) =>
% 121.65/16.01 ((
% 121.65/16.01 (ubforcartprodlem1) =>
% 121.65/16.01 ((
% 121.65/16.01 (ubforcartprodlem2) =>
% 121.65/16.01 ((
% 121.65/16.01 (ubforcartprodlem3) =>
% 121.65/16.01 ((
% 121.65/16.01 (cartprodpairin) =>
% 121.65/16.01 ((
% 121.65/16.01 (cartprodmempair1) =>
% 121.65/16.01 ((
% 121.65/16.01 (cartprodmempair) =>
% 121.65/16.01 ((
% 121.65/16.01 (setunionE2) =>
% 121.65/16.01 ((
% 121.65/16.01 (setunionsingleton1) =>
% 121.65/16.01 ((
% 121.65/16.01 (setunionsingleton2) =>
% 121.65/16.01 ((
% 121.65/16.01 (setunionsingleton) =>
% 121.65/16.01 ((
% 121.65/16.01 (singletonprop) =>
% 121.65/16.01 ((
% 121.65/16.01 (ex1E1) =>
% 121.65/16.01 ((
% 121.65/16.01 (ex1I) =>
% 121.65/16.01 ((
% 121.65/16.01 (ex1I2) =>
% 121.65/16.01 ((
% 121.65/16.01 (singletonsuniq) =>
% 121.65/16.01 ((
% 121.65/16.01 (setukpairinjL1) =>
% 121.65/16.01 ((
% 121.65/16.01 (kfstsingleton) =>
% 121.65/16.01 ((
% 121.65/16.01 (theprop) =>
% 121.65/16.01 ((
% 121.65/16.01 (kfstpairEq) =>
% 121.65/16.01 ((
% 121.65/16.01 (cartprodfstin) =>
% 121.65/16.01 ((
% 121.65/16.01 (setukpairinjL2) =>
% 121.65/16.01 ((
% 121.65/16.01 (setukpairinjL) =>
% 121.65/16.01 ((
% 121.65/16.01 (setukpairinjR11) =>
% 121.65/16.01 ((
% 121.65/16.01 (setukpairinjR12) =>
% 121.65/16.01 ((
% 121.65/16.01 (setukpairinjR1) =>
% 121.65/16.01 ((
% 121.65/16.01 (upairequniteq) =>
% 121.65/16.01 ((
% 121.65/16.01 (setukpairinjR2) =>
% 121.65/16.01 ((
% 121.65/16.01 (setukpairinjR) =>
% 121.65/16.01 ((
% 121.65/16.01 (ksndsingleton) =>
% 121.65/16.01 ((
% 121.65/16.01 (ksndpairEq) =>
% 121.65/16.01 ((
% 121.65/16.01 (kpairsurjEq) =>
% 121.65/16.01 ((
% 121.65/16.01 (cartprodsndin) =>
% 121.65/16.01 ((
% 121.65/16.01 (cartprodpairmemEL) =>
% 121.65/16.01 ((
% 121.65/16.01 (cartprodpairmemER) =>
% 121.65/16.01 ((
% 121.65/16.01 (cartprodmempaircEq) =>
% 121.65/16.01 ((
% 121.65/16.01 (cartprodfstpairEq) =>
% 121.65/16.01 ((
% 121.65/16.01 (cartprodsndpairEq) =>
% 121.65/16.01 ((
% 121.65/16.01 (cartprodpairsurjEq) =>
% 121.65/16.01 ((
% 121.65/16.01 (dpsetconstrI) =>
% 121.65/16.01 ((
% 121.65/16.01 (dpsetconstrSub) =>
% 121.65/16.01 ((
% 121.65/16.01 (setOfPairsIsBReln) =>
% 121.65/16.01 ((
% 121.65/16.01 (dpsetconstrERa) =>
% 121.65/16.01 ((
% 121.65/16.01 (dpsetconstrEL1) =>
% 121.65/16.01 ((
% 121.65/16.01 (dpsetconstrEL2) =>
% 121.65/16.01 ((
% 121.65/16.01 (dpsetconstrER) =>
% 121.65/16.01 ((
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% 121.65/16.01 ((
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% 121.65/16.01 ((
% 121.65/16.01 (lamp) =>
% 121.65/16.01 ((
% 121.65/16.01 (lam2p) =>
% 121.65/16.01 ((
% 121.65/16.01 (brelnall1) =>
% 121.65/16.01 ((
% 121.65/16.01 (brelnall2) =>
% 121.65/16.01 ((
% 121.65/16.01 (ex1E2) =>
% 121.65/16.01 ((
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% 121.65/16.01 ((
% 121.65/16.01 (funcGraphProp3) =>
% 121.65/16.01 ((
% 121.65/16.01 (funcGraphProp2) =>
% 121.65/16.01 ((
% 121.65/16.01 (funcextLem) =>
% 121.65/16.01 ((
% 121.65/16.01 (funcGraphProp4) =>
% 121.65/16.01 ((
% 121.65/16.01 (subbreln) =>
% 121.65/16.01 ((
% 121.65/16.01 (eqbreln) =>
% 121.65/16.01 ((
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% 121.65/16.01 ((
% 121.65/16.01 (funcext2) =>
% 121.65/16.01 ((
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% 121.65/16.01 ((
% 121.65/16.01 (ap2apEq2) =>
% 121.65/16.01 ((
% 121.65/16.01 (beta1) =>
% 121.65/16.01 ((
% 121.65/16.01 (eta1) =>
% 121.65/16.01 ((
% 121.65/16.01 (lam2lamEq) =>
% 121.65/16.01 ((
% 121.65/16.01 (beta2) =>
% 121.65/16.01 ((
% 121.65/16.01 (eta2) =>
% 121.65/16.01 ((
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% 121.65/16.01 ((
% 121.65/16.01 (iffalseProp2) =>
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% 121.65/16.01 ((
% 121.65/16.01 (iftrueProp2) =>
% 121.65/16.01 ((
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% 121.65/16.01 ((
% 121.65/16.01 (ifp) =>
% 121.65/16.01 ((
% 121.65/16.01 (theeq) =>
% 121.65/16.01 ((
% 121.65/16.01 (iftrue) =>
% 121.65/16.01 ((
% 121.65/16.01 (iffalse) =>
% 121.65/16.01 ((
% 121.65/16.01 (iftrueorfalse) =>
% 121.65/16.01 ((
% 121.65/16.01 (binintersectT_lem) =>
% 121.65/16.01 ((
% 121.65/16.01 (binunionT_lem) =>
% 121.65/16.01 ((
% 121.65/16.01 (powersetT_lem) =>
% 121.65/16.01 ((
% 121.65/16.01 (setminusT_lem) =>
% 121.65/16.01 ((
% 121.65/16.01 (complementT_lem) =>
% 121.65/16.01 ((
% 121.65/16.01 (setextT) =>
% 121.65/16.01 ((
% 121.65/16.01 (subsetTI) =>
% 121.65/16.01 ((
% 121.65/16.01 (powersetTI1) =>
% 121.65/16.01 ((
% 121.65/16.01 (powersetTE1) =>
% 121.65/16.01 ((
% 121.65/16.01 (complementTI1) =>
% 121.65/16.01 ((
% 121.65/16.01 (complementTE1) =>
% 121.65/16.01 ((
% 121.65/16.01 (binintersectTELcontra) =>
% 121.65/16.01 ((
% 121.65/16.01 (binintersectTERcontra) =>
% 121.65/16.01 ((
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% 121.65/16.01 ((
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% 121.65/16.01 ((
% 121.65/16.01 (contrasubsetT2) =>
% 121.65/16.01 ((
% 121.65/16.01 (contrasubsetT3) =>
% 121.65/16.01 ((
% 121.65/16.01 (doubleComplementI1) =>
% 121.65/16.01 ((
% 121.65/16.01 (doubleComplementE1) =>
% 121.65/16.01 ((
% 121.65/16.01 (doubleComplementSub1) =>
% 121.65/16.01 ((
% 121.65/16.01 (doubleComplementSub2) =>
% 121.65/16.01 ((
% 121.65/16.01 (doubleComplementEq) =>
% 121.65/16.01 ((
% 121.65/16.01 (complementTnotintersectT) =>
% 121.65/16.01 ((
% 121.65/16.01 (complementImpComplementIntersect) =>
% 121.65/16.01 ((
% 121.65/16.01 (complementSubsetComplementIntersect) =>
% 121.65/16.01 ((
% 121.65/16.01 (complementInPowersetComplementIntersect) =>
% 121.65/16.01 ((
% 121.65/16.01 (contraSubsetComplement) =>
% 121.65/16.01 ((
% 121.65/16.01 (complementTcontraSubset) =>
% 121.65/16.01 ((
% 121.65/16.01 (binunionTILcontra) =>
% 121.65/16.01 ((
% 121.65/16.01 (binunionTIRcontra) =>
% 121.65/16.01 ((
% 121.65/16.01 (inIntersectImpInUnion) =>
% 121.65/16.01 ((
% 121.65/16.01 (inIntersectImpInUnion2) =>
% 121.65/16.01 ((
% 121.65/16.01 (inIntersectImpInIntersectUnions) =>
% 121.65/16.01 ((
% 121.65/16.01 (intersectInPowersetIntersectUnions) =>
% 121.65/16.01 ((
% 121.65/16.01 (inComplementUnionImpNotIn1) =>
% 121.65/16.01 ((
% 121.65/16.01 (inComplementUnionImpInComplement1) =>
% 121.65/16.01 ((
% 121.65/16.01 (binunionTE) =>
% 121.65/16.01 ((
% 121.65/16.01 (binunionTEcontra) =>
% 121.65/16.01 ((
% 121.65/16.01 (demorgan2a1) =>
% 121.65/16.01 ((
% 121.65/16.01 (complementUnionInPowersetComplement) =>
% 121.65/16.01 ((
% 121.65/16.01 (demorgan2a2) =>
% 121.65/16.01 ((
% 121.65/16.01 (demorgan1a) =>
% 121.65/16.01 ((
% 121.65/16.01 (demorgan1b) =>
% 121.65/16.01 ((
% 121.65/16.01 (demorgan1) =>
% 121.65/16.01 ((
% 121.65/16.01 (demorgan2a) =>
% 121.65/16.01 ((
% 121.65/16.01 (demorgan2b2) =>
% 121.65/16.01 ((
% 121.65/16.01 (demorgan2b) =>
% 121.65/16.01 ((
% 121.65/16.01 (demorgan2) =>
% 121.65/16.01 ((
% 121.65/16.01 (woz13rule0) =>
% 121.65/16.01 ((
% 121.65/16.01 (woz13rule1) =>
% 121.65/16.01 ((
% 121.65/16.01 (woz13rule2) =>
% 121.65/16.01 ((
% 121.65/16.01 (woz13rule3) =>
% 121.65/16.01 ((
% 121.65/16.01 (woz13rule4) =>
% 121.65/16.01 ((
% 121.65/16.01 (woz1_1) =>
% 121.65/16.01 ((
% 121.65/16.01 (woz1_2) =>
% 121.65/16.01 ((
% 121.65/16.01 (woz1_3) =>
% 121.65/16.01 ((
% 121.65/16.01 (woz1_4) =>
% 121.65/16.01 ((
% 121.65/16.01 (woz1_5) =>
% 121.65/16.01 ((
% 121.65/16.01 (breln1all2) =>
% 121.65/16.01 ((
% 121.65/16.01 (breln1SetBreln1) =>
% 121.65/16.01 ((
% 121.65/16.01 (choice2fnsingleton) =>
% 121.65/16.01 ((
% 121.65/16.01 (setOfPairsIsBReln1) =>
% 121.65/16.01 ((
% 121.65/16.01 (breln1all1) =>
% 121.65/16.01 ((
% 121.65/16.01 (subbreln1) =>
% 121.65/16.01 ((
% 121.65/16.01 (eqbreln1) =>
% 121.65/16.01 ((
% 121.65/16.01 (breln1invprop) =>
% 121.65/16.01 ((
% 121.65/16.01 (breln1invI) =>
% 121.65/16.01 ((
% 121.65/16.01 (breln1invE) =>
% 121.65/16.01 ((
% 121.65/16.01 (breln1compprop) =>
% 121.65/16.01 ((
% 121.65/16.01 (breln1compI) =>
% 121.65/16.01 ((
% 121.65/16.01 (breln1compE) =>
% 121.65/16.01 ((
% 121.65/16.01 (breln1compEex) =>
% 121.65/16.01 ((
% 121.65/16.01 (breln1unionprop) =>
% 121.65/16.01 ((
% 121.65/16.01 (breln1unionIL) =>
% 121.65/16.01 ((
% 121.65/16.01 (breln1unionIR) =>
% 121.65/16.01 ((
% 121.65/16.01 (breln1unionI) =>
% 121.65/16.01 ((
% 121.65/16.01 (breln1unionE) =>
% 121.65/16.01 ((
% 121.65/16.01 (breln1unionEcases) =>
% 121.65/16.01 ((
% 121.65/16.01 (breln1unionCommutes) =>
% 121.65/16.01 ((
% 121.65/16.01 (woz2Ex) =>
% 121.65/16.01 ((
% 121.65/16.01 (woz2W) =>
% 121.65/16.01 ((
% 121.65/16.01 (woz2A) =>
% 121.65/16.01 ((
% 121.65/16.01 (woz2B) =>
% 121.65/16.01 ((
% 121.65/16.01 (image1Ex) =>
% 121.65/16.01 ((
% 121.65/16.01 (image1Ex1) =>
% 121.65/16.01 ((
% 121.65/16.01 (image1Equiv) =>
% 121.65/16.01 ((
% 121.65/16.01 (image1E) =>
% 121.65/16.01 ((
% 121.65/16.01 (image1I) =>
% 121.65/16.01 ((
% 121.65/16.01 (injFuncInInjFuncSet) =>
% 121.65/16.01 ((
% 121.65/16.01 (!!) @ (
% 121.65/16.01 (('#B') @ (
% 121.65/16.01 !!) @
% 121.65/16.01 (
% 121.65/16.01 (
% 121.65/16.01 ('#B') @ (
% 121.65/16.01 (
% 121.65/16.01 ('#B') @ (
% 121.65/16.01 !!))) @
% 121.65/16.01 (
% 121.65/16.01 (
% 121.65/16.01 ('#S') @ (
% 121.65/16.01 (
% 121.65/16.01 ('#B') @ (
% 121.65/16.01 '#S') @
% 121.65/16.01 (
% 121.65/16.01 (
% 121.65/16.01 ('#B') @ (
% 121.65/16.01 (
% 121.65/16.01 ('#B') @ (
% 121.65/16.01 '#S'))) @
% 121.65/16.01 (
% 121.65/16.01 (
% 121.65/16.01 ('#B') @ (
% 121.65/16.01 (
% 121.65/16.01 ('#B') @ (
% 121.65/16.01 (
% 121.65/16.01 ('#B') @ (
% 121.65/16.01 =>))))) @
% 121.65/16.01 (
% 121.65/16.01 (
% 121.65/16.01 ('#B') @ (
% 121.65/16.01 (
% 121.65/16.01 ('#B') @ (
% 121.65/16.01 (
% 121.65/16.01 ('#C') @ in)))) @
% 121.65/16.01 injFuncSet)))))))) @
% 121.65/16.01 (
% 121.65/16.01 (
% 121.65/16.01 ('#B') @ (
% 121.65/16.01 (
% 121.65/16.01 ('#B') @ (
% 121.65/16.01 (
% 121.65/16.01 ('#C') @ in)))) @
% 121.65/16.01 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 121.65/16.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl5])).
% 121.65/16.01 thf(zip_derived_cl13, plain,
% 121.65/16.01 (~ (((powersetAx) =>
% 121.65/16.01 (((setunionAx) =>
% 121.65/16.01 (((in @ emptyset @ omega) =>
% 121.65/16.01 (((omegaSAx) =>
% 121.65/16.01 (((omegaIndAx) =>
% 121.65/16.01 (((replAx) =>
% 121.65/16.01 (((foundationAx) =>
% 121.65/16.01 (((wellorderingAx) =>
% 121.65/16.01 (((descrp) =>
% 121.65/16.01 (((dsetconstrI) =>
% 121.65/16.01 (((dsetconstrEL) =>
% 121.65/16.01 (((dsetconstrER) =>
% 121.65/16.01 (((exuE1) =>
% 121.65/16.01 (((prop2setE) =>
% 121.65/16.01 (((emptysetE) =>
% 121.65/16.01 (((emptysetimpfalse) =>
% 121.65/16.01 (((notinemptyset) =>
% 121.65/16.01 (((exuE3e) =>
% 121.65/16.01 (((setext) =>
% 121.65/16.01 (((emptyI) =>
% 121.65/16.01 (((noeltsimpempty) =>
% 121.65/16.01 (((setbeta) =>
% 121.65/16.01 (((nonemptyE1) =>
% 121.65/16.01 (((nonemptyI) =>
% 121.65/16.01 (((nonemptyI1) =>
% 121.65/16.01 (((setadjoinIL) =>
% 121.65/16.01 (((in @
% 121.65/16.01 emptyset @
% 121.65/16.01 (setadjoin @
% 121.65/16.01 emptyset @
% 121.65/16.01 emptyset)) =>
% 121.65/16.01 (((setadjoinIR) =>
% 121.65/16.01 (((setadjoinE) =>
% 121.65/16.01 (((setadjoinOr) =>
% 121.65/16.01 ((
% 121.65/16.01 (setoftrueEq) =>
% 121.65/16.01 ((
% 121.65/16.01 (powersetI) =>
% 121.65/16.01 ((
% 121.65/16.01 (emptyinPowerset) =>
% 121.65/16.01 ((
% 121.65/16.01 (emptyInPowerset) =>
% 121.65/16.01 ((
% 121.65/16.01 (powersetE) =>
% 121.65/16.01 ((
% 121.65/16.01 (setunionI) =>
% 121.65/16.01 ((
% 121.65/16.01 (setunionE) =>
% 121.65/16.01 ((
% 121.65/16.01 (subPowSU) =>
% 121.65/16.01 ((
% 121.65/16.01 (exuE2) =>
% 121.65/16.01 ((
% 121.65/16.01 (nonemptyImpWitness) =>
% 121.65/16.01 ((
% 121.65/16.01 (uniqinunit) =>
% 121.65/16.01 ((
% 121.65/16.01 (notinsingleton) =>
% 121.65/16.01 ((
% 121.65/16.01 (eqinunit) =>
% 121.65/16.01 ((
% 121.65/16.01 (singletonsswitch) =>
% 121.65/16.01 ((
% 121.65/16.01 (upairsetE) =>
% 121.65/16.01 ((
% 121.65/16.01 (upairsetIL) =>
% 121.65/16.01 ((
% 121.65/16.01 (upairsetIR) =>
% 121.65/16.01 ((
% 121.65/16.01 (emptyE1) =>
% 121.65/16.01 ((
% 121.65/16.01 (vacuousDall) =>
% 121.65/16.01 ((
% 121.65/16.01 (quantDeMorgan1) =>
% 121.65/16.01 ((
% 121.65/16.01 (quantDeMorgan2) =>
% 121.65/16.01 ((
% 121.65/16.01 (quantDeMorgan3) =>
% 121.65/16.01 ((
% 121.65/16.01 (quantDeMorgan4) =>
% 121.65/16.01 ((
% 121.65/16.01 (prop2setI) =>
% 121.65/16.01 ((
% 121.65/16.01 (prop2set2propI) =>
% 121.65/16.01 ((
% 121.65/16.01 (notdexE) =>
% 121.65/16.01 ((
% 121.65/16.01 (notdallE) =>
% 121.65/16.01 ((
% 121.65/16.01 (exuI1) =>
% 121.65/16.01 ((
% 121.65/16.01 (exuI3) =>
% 121.65/16.01 ((
% 121.65/16.01 (exuI2) =>
% 121.65/16.01 ((
% 121.65/16.01 (inCongP) =>
% 121.65/16.01 ((
% 121.65/16.01 (in__Cong) =>
% 121.65/16.01 ((
% 121.65/16.01 (exuE3u) =>
% 121.65/16.01 ((
% 121.65/16.01 (exu__Cong) =>
% 121.65/16.01 ((
% 121.65/16.01 (setadjoin__Cong) =>
% 121.65/16.01 ((
% 121.65/16.01 (powerset__Cong) =>
% 121.65/16.01 ((
% 121.65/16.01 (setunion__Cong) =>
% 121.65/16.01 ((
% 121.65/16.01 (exuEu) =>
% 121.65/16.01 ((
% 121.65/16.01 (descr__Cong) =>
% 121.65/16.01 ((
% 121.65/16.01 (dsetconstr__Cong) =>
% 121.65/16.01 ((
% 121.65/16.01 (subsetI1) =>
% 121.65/16.01 ((
% 121.65/16.01 (eqimpsubset2) =>
% 121.65/16.01 ((
% 121.65/16.01 (eqimpsubset1) =>
% 121.65/16.01 ((
% 121.65/16.01 (subsetI2) =>
% 121.65/16.01 ((
% 121.65/16.01 (emptysetsubset) =>
% 121.65/16.01 ((
% 121.65/16.01 (subsetE) =>
% 121.65/16.01 ((
% 121.65/16.01 (subsetE2) =>
% 121.65/16.01 ((
% 121.65/16.01 (notsubsetI) =>
% 121.65/16.01 ((
% 121.65/16.01 (notequalI1) =>
% 121.65/16.01 ((
% 121.65/16.01 (notequalI2) =>
% 121.65/16.01 ((
% 121.65/16.01 (subsetRefl) =>
% 121.65/16.01 ((
% 121.65/16.01 (subsetTrans) =>
% 121.65/16.01 ((
% 121.65/16.01 (setadjoinSub) =>
% 121.65/16.01 ((
% 121.65/16.01 (setadjoinSub2) =>
% 121.65/16.01 ((
% 121.65/16.01 (subset2powerset) =>
% 121.65/16.01 ((
% 121.65/16.01 (setextsub) =>
% 121.65/16.01 ((
% 121.65/16.01 (subsetemptysetimpeq) =>
% 121.65/16.01 ((
% 121.65/16.01 (powersetI1) =>
% 121.65/16.01 ((
% 121.65/16.01 (powersetE1) =>
% 121.65/16.01 ((
% 121.65/16.01 (inPowerset) =>
% 121.65/16.01 ((
% 121.65/16.01 (powersetsubset) =>
% 121.65/16.01 ((
% 121.65/16.01 (sepInPowerset) =>
% 121.65/16.01 ((
% 121.65/16.01 (sepSubset) =>
% 121.65/16.01 ((
% 121.65/16.01 (binunionIL) =>
% 121.65/16.01 ((
% 121.65/16.01 (upairset2IR) =>
% 121.65/16.01 ((
% 121.65/16.01 (binunionIR) =>
% 121.65/16.01 ((
% 121.65/16.01 (binunionEcases) =>
% 121.65/16.01 ((
% 121.65/16.01 (binunionE) =>
% 121.65/16.01 ((
% 121.65/16.01 (binunionLsub) =>
% 121.65/16.01 ((
% 121.65/16.01 (binunionRsub) =>
% 121.65/16.01 ((
% 121.65/16.01 (binintersectI) =>
% 121.65/16.01 ((
% 121.65/16.01 (binintersectSubset5) =>
% 121.65/16.01 ((
% 121.65/16.01 (binintersectEL) =>
% 121.65/16.01 ((
% 121.65/16.01 (binintersectLsub) =>
% 121.65/16.01 ((
% 121.65/16.01 (binintersectSubset2) =>
% 121.65/16.01 ((
% 121.65/16.01 (binintersectSubset3) =>
% 121.65/16.01 ((
% 121.65/16.01 (binintersectER) =>
% 121.65/16.01 ((
% 121.65/16.01 (disjointsetsI1) =>
% 121.65/16.01 ((
% 121.65/16.01 (binintersectRsub) =>
% 121.65/16.01 ((
% 121.65/16.01 (binintersectSubset4) =>
% 121.65/16.01 ((
% 121.65/16.01 (binintersectSubset1) =>
% 121.65/16.01 ((
% 121.65/16.01 (bs114d) =>
% 121.65/16.01 ((
% 121.65/16.01 (setminusI) =>
% 121.65/16.01 ((
% 121.65/16.01 (setminusEL) =>
% 121.65/16.01 ((
% 121.65/16.01 (setminusER) =>
% 121.65/16.01 ((
% 121.65/16.01 (setminusSubset2) =>
% 121.65/16.01 ((
% 121.65/16.01 (setminusERneg) =>
% 121.65/16.01 ((
% 121.65/16.01 (setminusELneg) =>
% 121.65/16.01 ((
% 121.65/16.01 (setminusILneg) =>
% 121.65/16.01 ((
% 121.65/16.01 (setminusIRneg) =>
% 121.65/16.01 ((
% 121.65/16.01 (setminusLsub) =>
% 121.65/16.01 ((
% 121.65/16.01 (setminusSubset1) =>
% 121.65/16.01 ((
% 121.65/16.01 (symdiffE) =>
% 121.65/16.01 ((
% 121.65/16.01 (symdiffI1) =>
% 121.65/16.01 ((
% 121.65/16.01 (symdiffI2) =>
% 121.65/16.01 ((
% 121.65/16.01 (symdiffIneg1) =>
% 121.65/16.01 ((
% 121.65/16.01 (symdiffIneg2) =>
% 121.65/16.01 ((
% 121.65/16.01 (secondinupair) =>
% 121.65/16.01 ((
% 121.65/16.01 (setukpairIL) =>
% 121.65/16.01 ((
% 121.65/16.01 (setukpairIR) =>
% 121.65/16.01 ((
% 121.65/16.01 (kpairiskpair) =>
% 121.65/16.01 ((
% 121.65/16.01 (kpairp) =>
% 121.65/16.01 ((
% 121.65/16.01 (singletonsubset) =>
% 121.65/16.01 ((
% 121.65/16.01 (singletoninpowerset) =>
% 121.65/16.01 ((
% 121.65/16.01 (singletoninpowunion) =>
% 121.65/16.01 ((
% 121.65/16.01 (upairset2E) =>
% 121.65/16.01 ((
% 121.65/16.01 (upairsubunion) =>
% 121.65/16.01 ((
% 121.65/16.01 (upairinpowunion) =>
% 121.65/16.01 ((
% 121.65/16.01 (ubforcartprodlem1) =>
% 121.65/16.01 ((
% 121.65/16.01 (ubforcartprodlem2) =>
% 121.65/16.01 ((
% 121.65/16.01 (ubforcartprodlem3) =>
% 121.65/16.01 ((
% 121.65/16.01 (cartprodpairin) =>
% 121.65/16.01 ((
% 121.65/16.01 (cartprodmempair1) =>
% 121.65/16.01 ((
% 121.65/16.01 (cartprodmempair) =>
% 121.65/16.01 ((
% 121.65/16.01 (setunionE2) =>
% 121.65/16.01 ((
% 121.65/16.01 (setunionsingleton1) =>
% 121.65/16.01 ((
% 121.65/16.01 (setunionsingleton2) =>
% 121.65/16.01 ((
% 121.65/16.01 (setunionsingleton) =>
% 121.65/16.01 ((
% 121.65/16.01 (singletonprop) =>
% 121.65/16.01 ((
% 121.65/16.01 (ex1E1) =>
% 121.65/16.01 ((
% 121.65/16.01 (ex1I) =>
% 121.65/16.01 ((
% 121.65/16.01 (ex1I2) =>
% 121.65/16.01 ((
% 121.65/16.01 (singletonsuniq) =>
% 121.65/16.01 ((
% 121.65/16.01 (setukpairinjL1) =>
% 121.65/16.01 ((
% 121.65/16.01 (kfstsingleton) =>
% 121.65/16.01 ((
% 121.65/16.01 (theprop) =>
% 121.65/16.01 ((
% 121.65/16.01 (kfstpairEq) =>
% 121.65/16.01 ((
% 121.65/16.01 (cartprodfstin) =>
% 121.65/16.01 ((
% 121.65/16.01 (setukpairinjL2) =>
% 121.65/16.01 ((
% 121.65/16.01 (setukpairinjL) =>
% 121.65/16.01 ((
% 121.65/16.01 (setukpairinjR11) =>
% 121.65/16.01 ((
% 121.65/16.01 (setukpairinjR12) =>
% 121.65/16.01 ((
% 121.65/16.01 (setukpairinjR1) =>
% 121.65/16.01 ((
% 121.65/16.01 (upairequniteq) =>
% 121.65/16.01 ((
% 121.65/16.01 (setukpairinjR2) =>
% 121.65/16.01 ((
% 121.65/16.01 (setukpairinjR) =>
% 121.65/16.01 ((
% 121.65/16.01 (ksndsingleton) =>
% 121.65/16.01 ((
% 121.65/16.01 (ksndpairEq) =>
% 121.65/16.01 ((
% 121.65/16.01 (kpairsurjEq) =>
% 121.65/16.01 ((
% 121.65/16.01 (cartprodsndin) =>
% 121.65/16.01 ((
% 121.65/16.01 (cartprodpairmemEL) =>
% 121.65/16.01 ((
% 121.65/16.01 (cartprodpairmemER) =>
% 121.65/16.01 ((
% 121.65/16.01 (cartprodmempaircEq) =>
% 121.65/16.01 ((
% 121.65/16.01 (cartprodfstpairEq) =>
% 121.65/16.01 ((
% 121.65/16.01 (cartprodsndpairEq) =>
% 121.65/16.01 ((
% 121.65/16.01 (cartprodpairsurjEq) =>
% 121.65/16.01 ((
% 121.65/16.01 (dpsetconstrI) =>
% 121.65/16.01 ((
% 121.65/16.01 (dpsetconstrSub) =>
% 121.65/16.01 ((
% 121.65/16.01 (setOfPairsIsBReln) =>
% 121.65/16.01 ((
% 121.65/16.01 (dpsetconstrERa) =>
% 121.65/16.01 ((
% 121.65/16.01 (dpsetconstrEL1) =>
% 121.65/16.01 ((
% 121.65/16.01 (dpsetconstrEL2) =>
% 121.65/16.01 ((
% 121.65/16.01 (dpsetconstrER) =>
% 121.65/16.01 ((
% 121.65/16.01 (funcImageSingleton) =>
% 121.65/16.01 ((
% 121.65/16.01 (apProp) =>
% 121.65/16.01 ((
% 121.65/16.01 (app) =>
% 121.65/16.01 ((
% 121.65/16.01 (infuncsetfunc) =>
% 121.65/16.01 ((
% 121.65/16.01 (ap2p) =>
% 121.65/16.01 ((
% 121.65/16.01 (funcinfuncset) =>
% 121.65/16.01 ((
% 121.65/16.01 (lamProp) =>
% 121.65/16.01 ((
% 121.65/16.01 (lamp) =>
% 121.65/16.01 ((
% 121.65/16.01 (lam2p) =>
% 121.65/16.01 ((
% 121.65/16.01 (brelnall1) =>
% 121.65/16.01 ((
% 121.65/16.01 (brelnall2) =>
% 121.65/16.01 ((
% 121.65/16.01 (ex1E2) =>
% 121.65/16.01 ((
% 121.65/16.01 (funcGraphProp1) =>
% 121.65/16.01 ((
% 121.65/16.01 (funcGraphProp3) =>
% 121.65/16.01 ((
% 121.65/16.01 (funcGraphProp2) =>
% 121.65/16.01 ((
% 121.65/16.01 (funcextLem) =>
% 121.65/16.01 ((
% 121.65/16.01 (funcGraphProp4) =>
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% 121.65/16.01 ((
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% 121.65/16.01 (funcext2) =>
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% 121.65/16.01 ((
% 121.65/16.01 (ap2apEq2) =>
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% 121.65/16.01 (beta1) =>
% 121.65/16.01 ((
% 121.65/16.01 (eta1) =>
% 121.65/16.01 ((
% 121.65/16.01 (lam2lamEq) =>
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% 121.65/16.01 (beta2) =>
% 121.65/16.01 ((
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% 121.65/16.01 ((
% 121.65/16.01 (iftrueProp2) =>
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% 121.65/16.01 ((
% 121.65/16.01 (binintersectTERcontra) =>
% 121.65/16.01 ((
% 121.65/16.01 (contrasubsetT) =>
% 121.65/16.01 ((
% 121.65/16.01 (contrasubsetT1) =>
% 121.65/16.01 ((
% 121.65/16.01 (contrasubsetT2) =>
% 121.65/16.01 ((
% 121.65/16.01 (contrasubsetT3) =>
% 121.65/16.01 ((
% 121.65/16.01 (doubleComplementI1) =>
% 121.65/16.01 ((
% 121.65/16.01 (doubleComplementE1) =>
% 121.65/16.01 ((
% 121.65/16.01 (doubleComplementSub1) =>
% 121.65/16.01 ((
% 121.65/16.01 (doubleComplementSub2) =>
% 121.65/16.01 ((
% 121.65/16.01 (doubleComplementEq) =>
% 121.65/16.01 ((
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% 121.65/16.01 (contraSubsetComplement) =>
% 121.65/16.01 ((
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% 121.65/16.01 ((
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% 121.65/16.01 ((
% 121.65/16.01 (binunionTIRcontra) =>
% 121.65/16.01 ((
% 121.65/16.01 (inIntersectImpInUnion) =>
% 121.65/16.01 ((
% 121.65/16.01 (inIntersectImpInUnion2) =>
% 121.65/16.01 ((
% 121.65/16.01 (inIntersectImpInIntersectUnions) =>
% 121.65/16.01 ((
% 121.65/16.01 (intersectInPowersetIntersectUnions) =>
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% 121.65/16.01 ((
% 121.65/16.01 (binunionTEcontra) =>
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% 121.65/16.01 ((
% 121.65/16.01 (complementUnionInPowersetComplement) =>
% 121.65/16.01 ((
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% 121.65/16.01 ((
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% 121.65/16.01 ((
% 121.65/16.01 (demorgan1) =>
% 121.65/16.01 ((
% 121.65/16.01 (demorgan2a) =>
% 121.65/16.01 ((
% 121.65/16.01 (demorgan2b2) =>
% 121.65/16.01 ((
% 121.65/16.01 (demorgan2b) =>
% 121.65/16.01 ((
% 121.65/16.01 (demorgan2) =>
% 121.65/16.01 ((
% 121.65/16.01 (woz13rule0) =>
% 121.65/16.01 ((
% 121.65/16.01 (woz13rule1) =>
% 121.65/16.01 ((
% 121.65/16.01 (woz13rule2) =>
% 121.65/16.01 ((
% 121.65/16.01 (woz13rule3) =>
% 121.65/16.01 ((
% 121.65/16.01 (woz13rule4) =>
% 121.65/16.01 ((
% 121.65/16.01 (woz1_1) =>
% 121.65/16.01 ((
% 121.65/16.01 (woz1_2) =>
% 121.65/16.01 ((
% 121.65/16.01 (woz1_3) =>
% 121.65/16.01 ((
% 121.65/16.01 (woz1_4) =>
% 121.65/16.01 ((
% 121.65/16.01 (woz1_5) =>
% 121.65/16.01 ((
% 121.65/16.01 (breln1all2) =>
% 121.65/16.01 ((
% 121.65/16.01 (breln1SetBreln1) =>
% 121.65/16.01 ((
% 121.65/16.01 (choice2fnsingleton) =>
% 121.65/16.01 ((
% 121.65/16.01 (setOfPairsIsBReln1) =>
% 121.65/16.01 ((
% 121.65/16.01 (breln1all1) =>
% 121.65/16.01 ((
% 121.65/16.01 (subbreln1) =>
% 121.65/16.01 ((
% 121.65/16.01 (eqbreln1) =>
% 121.65/16.01 ((
% 121.65/16.01 (breln1invprop) =>
% 121.65/16.01 ((
% 121.65/16.01 (breln1invI) =>
% 121.65/16.01 ((
% 121.65/16.01 (breln1invE) =>
% 121.65/16.01 ((
% 121.65/16.01 (breln1compprop) =>
% 121.65/16.01 ((
% 121.65/16.01 (breln1compI) =>
% 121.65/16.01 ((
% 121.65/16.01 (breln1compE) =>
% 121.65/16.01 ((
% 121.65/16.01 (breln1compEex) =>
% 121.65/16.01 ((
% 121.65/16.01 (breln1unionprop) =>
% 121.65/16.01 ((
% 121.65/16.01 (breln1unionIL) =>
% 121.65/16.01 ((
% 121.65/16.01 (breln1unionIR) =>
% 121.65/16.01 ((
% 121.65/16.01 (breln1unionI) =>
% 121.65/16.01 ((
% 121.65/16.01 (breln1unionE) =>
% 121.65/16.01 ((
% 121.65/16.01 (breln1unionEcases) =>
% 121.65/16.01 ((
% 121.65/16.01 (breln1unionCommutes) =>
% 121.65/16.01 ((
% 121.65/16.01 (woz2Ex) =>
% 121.65/16.01 ((
% 121.65/16.01 (woz2W) =>
% 121.65/16.01 ((
% 121.65/16.01 (woz2A) =>
% 121.65/16.01 ((
% 121.65/16.01 (woz2B) =>
% 121.65/16.01 ((
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% 121.65/16.01 ((
% 121.65/16.01 (image1Ex1) =>
% 121.65/16.01 ((
% 121.65/16.01 (image1Equiv) =>
% 121.65/16.01 ((
% 121.65/16.01 (image1E) =>
% 121.65/16.01 ((
% 121.65/16.01 (image1I) =>
% 121.65/16.01 ((
% 121.65/16.01 (injFuncInInjFuncSet) =>
% 121.65/16.01 ((
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% 121.65/16.01 (('#B') @ (
% 121.65/16.01 !!) @
% 121.65/16.01 (
% 121.65/16.01 (
% 121.65/16.01 ('#B') @ (
% 121.65/16.01 (
% 121.65/16.01 ('#B') @ (
% 121.65/16.01 !!))) @
% 121.65/16.01 (
% 121.65/16.01 (
% 121.65/16.01 ('#S') @ (
% 121.65/16.01 (
% 121.65/16.01 ('#B') @ (
% 121.65/16.01 '#S') @
% 121.65/16.01 (
% 121.65/16.01 (
% 121.65/16.01 ('#B') @ (
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% 121.65/16.01 ('#B') @ (
% 121.65/16.01 (
% 121.65/16.01 ('#B') @ (
% 121.65/16.01 (
% 121.65/16.01 ('#B') @ (
% 121.65/16.01 =>))))) @
% 121.65/16.01 (
% 121.65/16.01 (
% 121.65/16.01 ('#B') @ (
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% 121.65/16.01 (
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% 121.65/16.01 injFuncSet)))))))) @
% 121.65/16.01 (
% 121.65/16.01 (
% 121.65/16.01 ('#B') @ (
% 121.65/16.01 (
% 121.65/16.01 ('#B') @ (
% 121.65/16.01 (
% 121.65/16.01 ('#C') @ in)))) @
% 121.65/16.01 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 121.65/16.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl8])).
% 121.65/16.01 thf(zip_derived_cl19, plain,
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% 121.65/16.01 (((exuE3e) =>
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% 121.65/16.01 ((
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% 121.65/16.01 ((
% 121.65/16.01 (powersetE) =>
% 121.65/16.01 ((
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% 121.65/16.01 ((
% 121.65/16.01 (setunionE) =>
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% 121.65/16.01 ((
% 121.65/16.01 (exuE2) =>
% 121.65/16.01 ((
% 121.65/16.01 (nonemptyImpWitness) =>
% 121.65/16.01 ((
% 121.65/16.01 (uniqinunit) =>
% 121.65/16.01 ((
% 121.65/16.01 (notinsingleton) =>
% 121.65/16.01 ((
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% 121.65/16.01 ((
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% 121.65/16.01 ((
% 121.65/16.01 (upairsetE) =>
% 121.65/16.01 ((
% 121.65/16.01 (upairsetIL) =>
% 121.65/16.01 ((
% 121.65/16.01 (upairsetIR) =>
% 121.65/16.01 ((
% 121.65/16.01 (emptyE1) =>
% 121.65/16.01 ((
% 121.65/16.01 (vacuousDall) =>
% 121.65/16.01 ((
% 121.65/16.01 (quantDeMorgan1) =>
% 121.65/16.01 ((
% 121.65/16.01 (quantDeMorgan2) =>
% 121.65/16.01 ((
% 121.65/16.01 (quantDeMorgan3) =>
% 121.65/16.01 ((
% 121.65/16.01 (quantDeMorgan4) =>
% 121.65/16.01 ((
% 121.65/16.01 (prop2setI) =>
% 121.65/16.01 ((
% 121.65/16.01 (prop2set2propI) =>
% 121.65/16.01 ((
% 121.65/16.01 (notdexE) =>
% 121.65/16.01 ((
% 121.65/16.01 (notdallE) =>
% 121.65/16.01 ((
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% 121.65/16.01 ((
% 121.65/16.01 (exuI3) =>
% 121.65/16.01 ((
% 121.65/16.01 (exuI2) =>
% 121.65/16.01 ((
% 121.65/16.01 (inCongP) =>
% 121.65/16.01 ((
% 121.65/16.01 (in__Cong) =>
% 121.65/16.01 ((
% 121.65/16.01 (exuE3u) =>
% 121.65/16.01 ((
% 121.65/16.01 (exu__Cong) =>
% 121.65/16.01 ((
% 121.65/16.01 (setadjoin__Cong) =>
% 121.65/16.01 ((
% 121.65/16.01 (powerset__Cong) =>
% 121.65/16.01 ((
% 121.65/16.01 (setunion__Cong) =>
% 121.65/16.01 ((
% 121.65/16.01 (exuEu) =>
% 121.65/16.01 ((
% 121.65/16.01 (descr__Cong) =>
% 121.65/16.01 ((
% 121.65/16.01 (dsetconstr__Cong) =>
% 121.65/16.01 ((
% 121.65/16.01 (subsetI1) =>
% 121.65/16.01 ((
% 121.65/16.01 (eqimpsubset2) =>
% 121.65/16.01 ((
% 121.65/16.01 (eqimpsubset1) =>
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% 121.65/16.01 (subsetI2) =>
% 121.65/16.01 ((
% 121.65/16.01 (emptysetsubset) =>
% 121.65/16.01 ((
% 121.65/16.01 (subsetE) =>
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% 121.65/16.01 (subsetE2) =>
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% 121.65/16.01 ((
% 121.65/16.01 (notequalI1) =>
% 121.65/16.01 ((
% 121.65/16.01 (notequalI2) =>
% 121.65/16.01 ((
% 121.65/16.01 (subsetRefl) =>
% 121.65/16.01 ((
% 121.65/16.01 (subsetTrans) =>
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% 121.65/16.01 ((
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% 121.65/16.01 ((
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% 121.65/16.01 ((
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% 121.65/16.01 ((
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% 121.65/16.01 ((
% 121.65/16.01 (powersetE1) =>
% 121.65/16.01 ((
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% 121.65/16.01 ((
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% 121.65/16.01 ((
% 121.65/16.01 (sepSubset) =>
% 121.65/16.01 ((
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% 121.65/16.01 ((
% 121.65/16.01 (upairset2IR) =>
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% 121.65/16.01 ((
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% 121.65/16.01 ((
% 121.65/16.01 (binunionE) =>
% 121.65/16.01 ((
% 121.65/16.01 (binunionLsub) =>
% 121.65/16.01 ((
% 121.65/16.01 (binunionRsub) =>
% 121.65/16.01 ((
% 121.65/16.01 (binintersectI) =>
% 121.65/16.01 ((
% 121.65/16.01 (binintersectSubset5) =>
% 121.65/16.01 ((
% 121.65/16.01 (binintersectEL) =>
% 121.65/16.01 ((
% 121.65/16.01 (binintersectLsub) =>
% 121.65/16.01 ((
% 121.65/16.01 (binintersectSubset2) =>
% 121.65/16.01 ((
% 121.65/16.01 (binintersectSubset3) =>
% 121.65/16.01 ((
% 121.65/16.01 (binintersectER) =>
% 121.65/16.01 ((
% 121.65/16.01 (disjointsetsI1) =>
% 121.65/16.01 ((
% 121.65/16.01 (binintersectRsub) =>
% 121.65/16.01 ((
% 121.65/16.01 (binintersectSubset4) =>
% 121.65/16.01 ((
% 121.65/16.01 (binintersectSubset1) =>
% 121.65/16.01 ((
% 121.65/16.01 (bs114d) =>
% 121.65/16.01 ((
% 121.65/16.01 (setminusI) =>
% 121.65/16.01 ((
% 121.65/16.01 (setminusEL) =>
% 121.65/16.01 ((
% 121.65/16.01 (setminusER) =>
% 121.65/16.01 ((
% 121.65/16.01 (setminusSubset2) =>
% 121.65/16.01 ((
% 121.65/16.01 (setminusERneg) =>
% 121.65/16.01 ((
% 121.65/16.01 (setminusELneg) =>
% 121.65/16.01 ((
% 121.65/16.01 (setminusILneg) =>
% 121.65/16.01 ((
% 121.65/16.01 (setminusIRneg) =>
% 121.65/16.01 ((
% 121.65/16.01 (setminusLsub) =>
% 121.65/16.01 ((
% 121.65/16.01 (setminusSubset1) =>
% 121.65/16.01 ((
% 121.65/16.01 (symdiffE) =>
% 121.65/16.01 ((
% 121.65/16.01 (symdiffI1) =>
% 121.65/16.01 ((
% 121.65/16.01 (symdiffI2) =>
% 121.65/16.01 ((
% 121.65/16.01 (symdiffIneg1) =>
% 121.65/16.01 ((
% 121.65/16.01 (symdiffIneg2) =>
% 121.65/16.01 ((
% 121.65/16.01 (secondinupair) =>
% 121.65/16.01 ((
% 121.65/16.01 (setukpairIL) =>
% 121.65/16.01 ((
% 121.65/16.01 (setukpairIR) =>
% 121.65/16.01 ((
% 121.65/16.01 (kpairiskpair) =>
% 121.65/16.01 ((
% 121.65/16.01 (kpairp) =>
% 121.65/16.01 ((
% 121.65/16.01 (singletonsubset) =>
% 121.65/16.01 ((
% 121.65/16.01 (singletoninpowerset) =>
% 121.65/16.01 ((
% 121.65/16.01 (singletoninpowunion) =>
% 121.65/16.01 ((
% 121.65/16.01 (upairset2E) =>
% 121.65/16.01 ((
% 121.65/16.01 (upairsubunion) =>
% 121.65/16.01 ((
% 121.65/16.01 (upairinpowunion) =>
% 121.65/16.01 ((
% 121.65/16.01 (ubforcartprodlem1) =>
% 121.65/16.01 ((
% 121.65/16.01 (ubforcartprodlem2) =>
% 121.65/16.01 ((
% 121.65/16.01 (ubforcartprodlem3) =>
% 121.65/16.01 ((
% 121.65/16.01 (cartprodpairin) =>
% 121.65/16.01 ((
% 121.65/16.01 (cartprodmempair1) =>
% 121.65/16.01 ((
% 121.65/16.01 (cartprodmempair) =>
% 121.65/16.01 ((
% 121.65/16.01 (setunionE2) =>
% 121.65/16.01 ((
% 121.65/16.01 (setunionsingleton1) =>
% 121.65/16.01 ((
% 121.65/16.01 (setunionsingleton2) =>
% 121.65/16.01 ((
% 121.65/16.01 (setunionsingleton) =>
% 121.65/16.01 ((
% 121.65/16.01 (singletonprop) =>
% 121.65/16.01 ((
% 121.65/16.01 (ex1E1) =>
% 121.65/16.01 ((
% 121.65/16.01 (ex1I) =>
% 121.65/16.01 ((
% 121.65/16.01 (ex1I2) =>
% 121.65/16.01 ((
% 121.65/16.01 (singletonsuniq) =>
% 121.65/16.01 ((
% 121.65/16.01 (setukpairinjL1) =>
% 121.65/16.01 ((
% 121.65/16.01 (kfstsingleton) =>
% 121.65/16.01 ((
% 121.65/16.01 (theprop) =>
% 121.65/16.01 ((
% 121.65/16.01 (kfstpairEq) =>
% 121.65/16.01 ((
% 121.65/16.01 (cartprodfstin) =>
% 121.65/16.01 ((
% 121.65/16.01 (setukpairinjL2) =>
% 121.65/16.01 ((
% 121.65/16.01 (setukpairinjL) =>
% 121.65/16.01 ((
% 121.65/16.01 (setukpairinjR11) =>
% 121.65/16.01 ((
% 121.65/16.01 (setukpairinjR12) =>
% 121.65/16.01 ((
% 121.65/16.01 (setukpairinjR1) =>
% 121.65/16.01 ((
% 121.65/16.01 (upairequniteq) =>
% 121.65/16.01 ((
% 121.65/16.01 (setukpairinjR2) =>
% 121.65/16.01 ((
% 121.65/16.01 (setukpairinjR) =>
% 121.65/16.01 ((
% 121.65/16.01 (ksndsingleton) =>
% 121.65/16.01 ((
% 121.65/16.01 (ksndpairEq) =>
% 121.65/16.01 ((
% 121.65/16.01 (kpairsurjEq) =>
% 121.65/16.01 ((
% 121.65/16.01 (cartprodsndin) =>
% 121.65/16.01 ((
% 121.65/16.01 (cartprodpairmemEL) =>
% 121.65/16.01 ((
% 121.65/16.01 (cartprodpairmemER) =>
% 121.65/16.01 ((
% 121.65/16.01 (cartprodmempaircEq) =>
% 121.65/16.01 ((
% 121.65/16.01 (cartprodfstpairEq) =>
% 121.65/16.01 ((
% 121.65/16.01 (cartprodsndpairEq) =>
% 121.65/16.01 ((
% 121.65/16.01 (cartprodpairsurjEq) =>
% 121.65/16.01 ((
% 121.65/16.01 (dpsetconstrI) =>
% 121.65/16.01 ((
% 121.65/16.01 (dpsetconstrSub) =>
% 121.65/16.01 ((
% 121.65/16.01 (setOfPairsIsBReln) =>
% 121.65/16.01 ((
% 121.65/16.01 (dpsetconstrERa) =>
% 121.65/16.01 ((
% 121.65/16.01 (dpsetconstrEL1) =>
% 121.65/16.01 ((
% 121.65/16.01 (dpsetconstrEL2) =>
% 121.65/16.01 ((
% 121.65/16.01 (dpsetconstrER) =>
% 121.65/16.01 ((
% 121.65/16.01 (funcImageSingleton) =>
% 121.65/16.01 ((
% 121.65/16.01 (apProp) =>
% 121.65/16.01 ((
% 121.65/16.01 (app) =>
% 121.65/16.01 ((
% 121.65/16.01 (infuncsetfunc) =>
% 121.65/16.01 ((
% 121.65/16.01 (ap2p) =>
% 121.65/16.01 ((
% 121.65/16.01 (funcinfuncset) =>
% 121.65/16.01 ((
% 121.65/16.01 (lamProp) =>
% 121.65/16.01 ((
% 121.65/16.01 (lamp) =>
% 121.65/16.01 ((
% 121.65/16.01 (lam2p) =>
% 121.65/16.01 ((
% 121.65/16.01 (brelnall1) =>
% 121.65/16.01 ((
% 121.65/16.01 (brelnall2) =>
% 121.65/16.01 ((
% 121.65/16.01 (ex1E2) =>
% 121.65/16.01 ((
% 121.65/16.01 (funcGraphProp1) =>
% 121.65/16.01 ((
% 121.65/16.01 (funcGraphProp3) =>
% 121.65/16.01 ((
% 121.65/16.01 (funcGraphProp2) =>
% 121.65/16.01 ((
% 121.65/16.01 (funcextLem) =>
% 121.65/16.01 ((
% 121.65/16.01 (funcGraphProp4) =>
% 121.65/16.01 ((
% 121.65/16.01 (subbreln) =>
% 121.65/16.01 ((
% 121.65/16.01 (eqbreln) =>
% 121.65/16.01 ((
% 121.65/16.01 (funcext) =>
% 121.65/16.01 ((
% 121.65/16.01 (funcext2) =>
% 121.65/16.01 ((
% 121.65/16.01 (ap2apEq1) =>
% 121.65/16.01 ((
% 121.65/16.01 (ap2apEq2) =>
% 121.65/16.01 ((
% 121.65/16.01 (beta1) =>
% 121.65/16.01 ((
% 121.65/16.01 (eta1) =>
% 121.65/16.01 ((
% 121.65/16.01 (lam2lamEq) =>
% 121.65/16.01 ((
% 121.65/16.01 (beta2) =>
% 121.65/16.01 ((
% 121.65/16.01 (eta2) =>
% 121.65/16.01 ((
% 121.65/16.01 (iffalseProp1) =>
% 121.65/16.01 ((
% 121.65/16.01 (iffalseProp2) =>
% 121.65/16.01 ((
% 121.65/16.01 (iftrueProp1) =>
% 121.65/16.01 ((
% 121.65/16.01 (iftrueProp2) =>
% 121.65/16.01 ((
% 121.65/16.01 (ifSingleton) =>
% 121.65/16.01 ((
% 121.65/16.01 (ifp) =>
% 121.65/16.01 ((
% 121.65/16.01 (theeq) =>
% 121.65/16.01 ((
% 121.65/16.01 (iftrue) =>
% 121.65/16.01 ((
% 121.65/16.01 (iffalse) =>
% 121.65/16.01 ((
% 121.65/16.01 (iftrueorfalse) =>
% 121.65/16.01 ((
% 121.65/16.01 (binintersectT_lem) =>
% 121.65/16.01 ((
% 121.65/16.01 (binunionT_lem) =>
% 121.65/16.01 ((
% 121.65/16.01 (powersetT_lem) =>
% 121.65/16.01 ((
% 121.65/16.01 (setminusT_lem) =>
% 121.65/16.01 ((
% 121.65/16.01 (complementT_lem) =>
% 121.65/16.01 ((
% 121.65/16.01 (setextT) =>
% 121.65/16.01 ((
% 121.65/16.01 (subsetTI) =>
% 121.65/16.01 ((
% 121.65/16.01 (powersetTI1) =>
% 121.65/16.01 ((
% 121.65/16.01 (powersetTE1) =>
% 121.65/16.01 ((
% 121.65/16.01 (complementTI1) =>
% 121.65/16.01 ((
% 121.65/16.01 (complementTE1) =>
% 121.65/16.01 ((
% 121.65/16.01 (binintersectTELcontra) =>
% 121.65/16.01 ((
% 121.65/16.01 (binintersectTERcontra) =>
% 121.65/16.01 ((
% 121.65/16.01 (contrasubsetT) =>
% 121.65/16.01 ((
% 121.65/16.01 (contrasubsetT1) =>
% 121.65/16.01 ((
% 121.65/16.01 (contrasubsetT2) =>
% 121.65/16.01 ((
% 121.65/16.01 (contrasubsetT3) =>
% 121.65/16.01 ((
% 121.65/16.01 (doubleComplementI1) =>
% 121.65/16.01 ((
% 121.65/16.01 (doubleComplementE1) =>
% 121.65/16.01 ((
% 121.65/16.01 (doubleComplementSub1) =>
% 121.65/16.01 ((
% 121.65/16.01 (doubleComplementSub2) =>
% 121.65/16.01 ((
% 121.65/16.01 (doubleComplementEq) =>
% 121.65/16.01 ((
% 121.65/16.01 (complementTnotintersectT) =>
% 121.65/16.01 ((
% 121.65/16.01 (complementImpComplementIntersect) =>
% 121.65/16.01 ((
% 121.65/16.01 (complementSubsetComplementIntersect) =>
% 121.65/16.01 ((
% 121.65/16.01 (complementInPowersetComplementIntersect) =>
% 121.65/16.01 ((
% 121.65/16.01 (contraSubsetComplement) =>
% 121.65/16.01 ((
% 121.65/16.01 (complementTcontraSubset) =>
% 121.65/16.01 ((
% 121.65/16.01 (binunionTILcontra) =>
% 121.65/16.01 ((
% 121.65/16.01 (binunionTIRcontra) =>
% 121.65/16.01 ((
% 121.65/16.01 (inIntersectImpInUnion) =>
% 121.65/16.01 ((
% 121.65/16.01 (inIntersectImpInUnion2) =>
% 121.65/16.01 ((
% 121.65/16.01 (inIntersectImpInIntersectUnions) =>
% 121.65/16.01 ((
% 121.65/16.01 (intersectInPowersetIntersectUnions) =>
% 121.65/16.01 ((
% 121.65/16.01 (inComplementUnionImpNotIn1) =>
% 121.65/16.01 ((
% 121.65/16.01 (inComplementUnionImpInComplement1) =>
% 121.65/16.01 ((
% 121.65/16.01 (binunionTE) =>
% 121.65/16.01 ((
% 121.65/16.01 (binunionTEcontra) =>
% 121.65/16.01 ((
% 121.65/16.01 (demorgan2a1) =>
% 121.65/16.01 ((
% 121.65/16.01 (complementUnionInPowersetComplement) =>
% 121.65/16.01 ((
% 121.65/16.01 (demorgan2a2) =>
% 121.65/16.01 ((
% 121.65/16.01 (demorgan1a) =>
% 121.65/16.01 ((
% 121.65/16.01 (demorgan1b) =>
% 121.65/16.01 ((
% 121.65/16.01 (demorgan1) =>
% 121.65/16.01 ((
% 121.65/16.01 (demorgan2a) =>
% 121.65/16.01 ((
% 121.65/16.01 (demorgan2b2) =>
% 121.65/16.01 ((
% 121.65/16.01 (demorgan2b) =>
% 121.65/16.01 ((
% 121.65/16.01 (demorgan2) =>
% 121.65/16.01 ((
% 121.65/16.01 (woz13rule0) =>
% 121.65/16.01 ((
% 121.65/16.01 (woz13rule1) =>
% 121.65/16.01 ((
% 121.65/16.01 (woz13rule2) =>
% 121.65/16.01 ((
% 121.65/16.01 (woz13rule3) =>
% 121.65/16.01 ((
% 121.65/16.01 (woz13rule4) =>
% 121.65/16.01 ((
% 121.65/16.01 (woz1_1) =>
% 121.65/16.01 ((
% 121.65/16.01 (woz1_2) =>
% 121.65/16.01 ((
% 121.65/16.01 (woz1_3) =>
% 121.65/16.01 ((
% 121.65/16.01 (woz1_4) =>
% 121.65/16.01 ((
% 121.65/16.01 (woz1_5) =>
% 121.65/16.01 ((
% 121.65/16.01 (breln1all2) =>
% 121.65/16.01 ((
% 121.65/16.01 (breln1SetBreln1) =>
% 121.65/16.01 ((
% 121.65/16.01 (choice2fnsingleton) =>
% 121.65/16.01 ((
% 121.65/16.01 (setOfPairsIsBReln1) =>
% 121.65/16.01 ((
% 121.65/16.01 (breln1all1) =>
% 121.65/16.01 ((
% 121.65/16.01 (subbreln1) =>
% 121.65/16.01 ((
% 121.65/16.01 (eqbreln1) =>
% 121.65/16.01 ((
% 121.65/16.01 (breln1invprop) =>
% 121.65/16.01 ((
% 121.65/16.01 (breln1invI) =>
% 121.65/16.01 ((
% 121.65/16.01 (breln1invE) =>
% 121.65/16.01 ((
% 121.65/16.01 (breln1compprop) =>
% 121.65/16.01 ((
% 121.65/16.01 (breln1compI) =>
% 121.65/16.01 ((
% 121.65/16.01 (breln1compE) =>
% 121.65/16.01 ((
% 121.65/16.01 (breln1compEex) =>
% 121.65/16.01 ((
% 121.65/16.01 (breln1unionprop) =>
% 121.65/16.01 ((
% 121.65/16.01 (breln1unionIL) =>
% 121.65/16.01 ((
% 121.65/16.01 (breln1unionIR) =>
% 121.65/16.01 ((
% 121.65/16.01 (breln1unionI) =>
% 121.65/16.01 ((
% 121.65/16.01 (breln1unionE) =>
% 121.65/16.01 ((
% 121.65/16.01 (breln1unionEcases) =>
% 121.65/16.01 ((
% 121.65/16.01 (breln1unionCommutes) =>
% 121.65/16.01 ((
% 121.65/16.01 (woz2Ex) =>
% 121.65/16.01 ((
% 121.65/16.01 (woz2W) =>
% 121.65/16.01 ((
% 121.65/16.01 (woz2A) =>
% 121.65/16.01 ((
% 121.65/16.01 (woz2B) =>
% 121.65/16.01 ((
% 121.65/16.01 (image1Ex) =>
% 121.65/16.01 ((
% 121.65/16.01 (image1Ex1) =>
% 121.65/16.01 ((
% 121.65/16.01 (image1Equiv) =>
% 121.65/16.01 ((
% 121.65/16.01 (image1E) =>
% 121.65/16.01 ((
% 121.65/16.01 (image1I) =>
% 121.65/16.01 ((
% 121.65/16.01 (injFuncInInjFuncSet) =>
% 121.65/16.01 ((
% 121.65/16.01 (!!) @ (
% 121.65/16.01 (('#B') @ (
% 121.65/16.01 !!) @
% 121.65/16.01 (
% 121.65/16.01 (
% 121.65/16.01 ('#B') @ (
% 121.65/16.01 (
% 121.65/16.01 ('#B') @ (
% 121.65/16.01 !!))) @
% 121.65/16.01 (
% 121.65/16.01 (
% 121.65/16.01 ('#S') @ (
% 121.65/16.01 (
% 121.65/16.01 ('#B') @ (
% 121.65/16.01 '#S') @
% 121.65/16.01 (
% 121.65/16.01 (
% 121.65/16.01 ('#B') @ (
% 121.65/16.01 (
% 121.65/16.01 ('#B') @ (
% 121.65/16.01 '#S'))) @
% 121.65/16.01 (
% 121.65/16.01 (
% 121.65/16.01 ('#B') @ (
% 121.65/16.01 (
% 121.65/16.01 ('#B') @ (
% 121.65/16.01 (
% 121.65/16.01 ('#B') @ (
% 121.65/16.01 =>))))) @
% 121.65/16.01 (
% 121.65/16.01 (
% 121.65/16.01 ('#B') @ (
% 121.65/16.01 (
% 121.65/16.01 ('#B') @ (
% 121.65/16.01 (
% 121.65/16.01 ('#C') @ in)))) @
% 121.65/16.01 injFuncSet)))))))) @
% 121.65/16.01 (
% 121.65/16.01 (
% 121.65/16.01 ('#B') @ (
% 121.65/16.01 (
% 121.65/16.01 ('#B') @ (
% 121.65/16.01 (
% 121.65/16.01 ('#C') @ in)))) @
% 121.65/16.01 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 121.65/16.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl13])).
% 121.65/16.01 thf(zip_derived_cl25, plain,
% 121.65/16.01 (~ (((in @ emptyset @ omega) =>
% 121.65/16.01 (((omegaSAx) =>
% 121.65/16.01 (((omegaIndAx) =>
% 121.65/16.01 (((replAx) =>
% 121.65/16.01 (((foundationAx) =>
% 121.65/16.01 (((wellorderingAx) =>
% 121.65/16.01 (((descrp) =>
% 121.65/16.01 (((dsetconstrI) =>
% 121.65/16.01 (((dsetconstrEL) =>
% 121.65/16.01 (((dsetconstrER) =>
% 121.65/16.01 (((exuE1) =>
% 121.65/16.01 (((prop2setE) =>
% 121.65/16.01 (((emptysetE) =>
% 121.65/16.01 (((emptysetimpfalse) =>
% 121.65/16.01 (((notinemptyset) =>
% 121.65/16.01 (((exuE3e) =>
% 121.65/16.01 (((setext) =>
% 121.65/16.01 (((emptyI) =>
% 121.65/16.01 (((noeltsimpempty) =>
% 121.65/16.01 (((setbeta) =>
% 121.65/16.01 (((nonemptyE1) =>
% 121.65/16.01 (((nonemptyI) =>
% 121.65/16.01 (((nonemptyI1) =>
% 121.65/16.01 (((setadjoinIL) =>
% 121.65/16.01 (((in @ emptyset @
% 121.65/16.01 (setadjoin @
% 121.65/16.01 emptyset @ emptyset)) =>
% 121.65/16.01 (((setadjoinIR) =>
% 121.65/16.01 (((setadjoinE) =>
% 121.65/16.01 (((setadjoinOr) =>
% 121.65/16.01 (((setoftrueEq) =>
% 121.65/16.01 (((powersetI) =>
% 121.65/16.01 ((
% 121.65/16.01 (emptyinPowerset) =>
% 121.65/16.01 ((
% 121.65/16.01 (emptyInPowerset) =>
% 121.65/16.01 ((
% 121.65/16.01 (powersetE) =>
% 121.65/16.01 ((
% 121.65/16.01 (setunionI) =>
% 121.65/16.01 ((
% 121.65/16.01 (setunionE) =>
% 121.65/16.01 ((
% 121.65/16.01 (subPowSU) =>
% 121.65/16.01 ((
% 121.65/16.01 (exuE2) =>
% 121.65/16.01 ((
% 121.65/16.01 (nonemptyImpWitness) =>
% 121.65/16.01 ((
% 121.65/16.01 (uniqinunit) =>
% 121.65/16.01 ((
% 121.65/16.01 (notinsingleton) =>
% 121.65/16.01 ((
% 121.65/16.01 (eqinunit) =>
% 121.65/16.01 ((
% 121.65/16.01 (singletonsswitch) =>
% 121.65/16.01 ((
% 121.65/16.01 (upairsetE) =>
% 121.65/16.01 ((
% 121.65/16.01 (upairsetIL) =>
% 121.65/16.01 ((
% 121.65/16.01 (upairsetIR) =>
% 121.65/16.01 ((
% 121.65/16.01 (emptyE1) =>
% 121.65/16.01 ((
% 121.65/16.01 (vacuousDall) =>
% 121.65/16.01 ((
% 121.65/16.01 (quantDeMorgan1) =>
% 121.65/16.01 ((
% 121.65/16.01 (quantDeMorgan2) =>
% 121.65/16.01 ((
% 121.65/16.01 (quantDeMorgan3) =>
% 121.65/16.01 ((
% 121.65/16.01 (quantDeMorgan4) =>
% 121.65/16.01 ((
% 121.65/16.01 (prop2setI) =>
% 121.65/16.01 ((
% 121.65/16.01 (prop2set2propI) =>
% 121.65/16.01 ((
% 121.65/16.01 (notdexE) =>
% 121.65/16.01 ((
% 121.65/16.01 (notdallE) =>
% 121.65/16.01 ((
% 121.65/16.01 (exuI1) =>
% 121.65/16.01 ((
% 121.65/16.01 (exuI3) =>
% 121.65/16.01 ((
% 121.65/16.01 (exuI2) =>
% 121.65/16.01 ((
% 121.65/16.01 (inCongP) =>
% 121.65/16.01 ((
% 121.65/16.01 (in__Cong) =>
% 121.65/16.01 ((
% 121.65/16.01 (exuE3u) =>
% 121.65/16.01 ((
% 121.65/16.01 (exu__Cong) =>
% 121.65/16.01 ((
% 121.65/16.01 (setadjoin__Cong) =>
% 121.65/16.01 ((
% 121.65/16.01 (powerset__Cong) =>
% 121.65/16.01 ((
% 121.65/16.01 (setunion__Cong) =>
% 121.65/16.01 ((
% 121.65/16.01 (exuEu) =>
% 121.65/16.01 ((
% 121.65/16.01 (descr__Cong) =>
% 121.65/16.01 ((
% 121.65/16.01 (dsetconstr__Cong) =>
% 121.65/16.01 ((
% 121.65/16.01 (subsetI1) =>
% 121.65/16.01 ((
% 121.65/16.01 (eqimpsubset2) =>
% 121.65/16.01 ((
% 121.65/16.01 (eqimpsubset1) =>
% 121.65/16.01 ((
% 121.65/16.01 (subsetI2) =>
% 121.65/16.01 ((
% 121.65/16.01 (emptysetsubset) =>
% 121.65/16.01 ((
% 121.65/16.01 (subsetE) =>
% 121.65/16.01 ((
% 121.65/16.01 (subsetE2) =>
% 121.65/16.01 ((
% 121.65/16.01 (notsubsetI) =>
% 121.65/16.01 ((
% 121.65/16.01 (notequalI1) =>
% 121.65/16.01 ((
% 121.65/16.01 (notequalI2) =>
% 121.65/16.01 ((
% 121.65/16.01 (subsetRefl) =>
% 121.65/16.01 ((
% 121.65/16.01 (subsetTrans) =>
% 121.65/16.01 ((
% 121.65/16.01 (setadjoinSub) =>
% 121.65/16.01 ((
% 121.65/16.01 (setadjoinSub2) =>
% 121.65/16.01 ((
% 121.65/16.01 (subset2powerset) =>
% 121.65/16.01 ((
% 121.65/16.01 (setextsub) =>
% 121.65/16.01 ((
% 121.65/16.01 (subsetemptysetimpeq) =>
% 121.65/16.01 ((
% 121.65/16.01 (powersetI1) =>
% 121.65/16.01 ((
% 121.65/16.01 (powersetE1) =>
% 121.65/16.01 ((
% 121.65/16.01 (inPowerset) =>
% 121.65/16.01 ((
% 121.65/16.01 (powersetsubset) =>
% 121.65/16.01 ((
% 121.65/16.01 (sepInPowerset) =>
% 121.65/16.01 ((
% 121.65/16.01 (sepSubset) =>
% 121.65/16.01 ((
% 121.65/16.01 (binunionIL) =>
% 121.65/16.01 ((
% 121.65/16.01 (upairset2IR) =>
% 121.65/16.01 ((
% 121.65/16.01 (binunionIR) =>
% 121.65/16.01 ((
% 121.65/16.01 (binunionEcases) =>
% 121.65/16.01 ((
% 121.65/16.01 (binunionE) =>
% 121.65/16.01 ((
% 121.65/16.01 (binunionLsub) =>
% 121.65/16.01 ((
% 121.65/16.01 (binunionRsub) =>
% 121.65/16.01 ((
% 121.65/16.01 (binintersectI) =>
% 121.65/16.01 ((
% 121.65/16.01 (binintersectSubset5) =>
% 121.65/16.01 ((
% 121.65/16.01 (binintersectEL) =>
% 121.65/16.01 ((
% 121.65/16.01 (binintersectLsub) =>
% 121.65/16.01 ((
% 121.65/16.01 (binintersectSubset2) =>
% 121.65/16.01 ((
% 121.65/16.01 (binintersectSubset3) =>
% 121.65/16.01 ((
% 121.65/16.01 (binintersectER) =>
% 121.65/16.01 ((
% 121.65/16.01 (disjointsetsI1) =>
% 121.65/16.01 ((
% 121.65/16.01 (binintersectRsub) =>
% 121.65/16.01 ((
% 121.65/16.01 (binintersectSubset4) =>
% 121.65/16.01 ((
% 121.65/16.01 (binintersectSubset1) =>
% 121.65/16.01 ((
% 121.65/16.01 (bs114d) =>
% 121.65/16.01 ((
% 121.65/16.01 (setminusI) =>
% 121.65/16.01 ((
% 121.65/16.01 (setminusEL) =>
% 121.65/16.01 ((
% 121.65/16.01 (setminusER) =>
% 121.65/16.01 ((
% 121.65/16.01 (setminusSubset2) =>
% 121.65/16.01 ((
% 121.65/16.01 (setminusERneg) =>
% 121.65/16.01 ((
% 121.65/16.01 (setminusELneg) =>
% 121.65/16.01 ((
% 121.65/16.01 (setminusILneg) =>
% 121.65/16.01 ((
% 121.65/16.01 (setminusIRneg) =>
% 121.65/16.01 ((
% 121.65/16.01 (setminusLsub) =>
% 121.65/16.01 ((
% 121.65/16.01 (setminusSubset1) =>
% 121.65/16.01 ((
% 121.65/16.01 (symdiffE) =>
% 121.65/16.01 ((
% 121.65/16.01 (symdiffI1) =>
% 121.65/16.01 ((
% 121.65/16.01 (symdiffI2) =>
% 121.65/16.01 ((
% 121.65/16.01 (symdiffIneg1) =>
% 121.65/16.01 ((
% 121.65/16.01 (symdiffIneg2) =>
% 121.65/16.01 ((
% 121.65/16.01 (secondinupair) =>
% 121.65/16.01 ((
% 121.65/16.01 (setukpairIL) =>
% 121.65/16.01 ((
% 121.65/16.01 (setukpairIR) =>
% 121.65/16.01 ((
% 121.65/16.01 (kpairiskpair) =>
% 121.65/16.01 ((
% 121.65/16.01 (kpairp) =>
% 121.65/16.01 ((
% 121.65/16.01 (singletonsubset) =>
% 121.65/16.01 ((
% 121.65/16.01 (singletoninpowerset) =>
% 121.65/16.01 ((
% 121.65/16.01 (singletoninpowunion) =>
% 121.65/16.01 ((
% 121.65/16.01 (upairset2E) =>
% 121.65/16.01 ((
% 121.65/16.01 (upairsubunion) =>
% 121.65/16.01 ((
% 121.65/16.01 (upairinpowunion) =>
% 121.65/16.01 ((
% 121.65/16.01 (ubforcartprodlem1) =>
% 121.65/16.01 ((
% 121.65/16.01 (ubforcartprodlem2) =>
% 121.65/16.01 ((
% 121.65/16.01 (ubforcartprodlem3) =>
% 121.65/16.01 ((
% 121.65/16.01 (cartprodpairin) =>
% 121.65/16.01 ((
% 121.65/16.01 (cartprodmempair1) =>
% 121.65/16.01 ((
% 121.65/16.01 (cartprodmempair) =>
% 121.65/16.01 ((
% 121.65/16.01 (setunionE2) =>
% 121.65/16.01 ((
% 121.65/16.01 (setunionsingleton1) =>
% 121.65/16.01 ((
% 121.65/16.01 (setunionsingleton2) =>
% 121.65/16.01 ((
% 121.65/16.01 (setunionsingleton) =>
% 121.65/16.01 ((
% 121.65/16.01 (singletonprop) =>
% 121.65/16.01 ((
% 121.65/16.01 (ex1E1) =>
% 121.65/16.01 ((
% 121.65/16.01 (ex1I) =>
% 121.65/16.01 ((
% 121.65/16.01 (ex1I2) =>
% 121.65/16.01 ((
% 121.65/16.01 (singletonsuniq) =>
% 121.65/16.01 ((
% 121.65/16.01 (setukpairinjL1) =>
% 121.65/16.01 ((
% 121.65/16.01 (kfstsingleton) =>
% 121.65/16.01 ((
% 121.65/16.01 (theprop) =>
% 121.65/16.01 ((
% 121.65/16.01 (kfstpairEq) =>
% 121.65/16.01 ((
% 121.65/16.01 (cartprodfstin) =>
% 121.65/16.01 ((
% 121.65/16.01 (setukpairinjL2) =>
% 121.65/16.01 ((
% 121.65/16.01 (setukpairinjL) =>
% 121.65/16.01 ((
% 121.65/16.01 (setukpairinjR11) =>
% 121.65/16.01 ((
% 121.65/16.01 (setukpairinjR12) =>
% 121.65/16.01 ((
% 121.65/16.01 (setukpairinjR1) =>
% 121.65/16.01 ((
% 121.65/16.01 (upairequniteq) =>
% 121.65/16.01 ((
% 121.65/16.01 (setukpairinjR2) =>
% 121.65/16.01 ((
% 121.65/16.01 (setukpairinjR) =>
% 121.65/16.01 ((
% 121.65/16.01 (ksndsingleton) =>
% 121.65/16.01 ((
% 121.65/16.01 (ksndpairEq) =>
% 121.65/16.01 ((
% 121.65/16.01 (kpairsurjEq) =>
% 121.65/16.01 ((
% 121.65/16.01 (cartprodsndin) =>
% 121.65/16.01 ((
% 121.65/16.01 (cartprodpairmemEL) =>
% 121.65/16.01 ((
% 121.65/16.01 (cartprodpairmemER) =>
% 121.65/16.01 ((
% 121.65/16.01 (cartprodmempaircEq) =>
% 121.65/16.01 ((
% 121.65/16.01 (cartprodfstpairEq) =>
% 121.65/16.01 ((
% 121.65/16.01 (cartprodsndpairEq) =>
% 121.65/16.01 ((
% 121.65/16.01 (cartprodpairsurjEq) =>
% 121.65/16.01 ((
% 121.65/16.01 (dpsetconstrI) =>
% 121.65/16.01 ((
% 121.65/16.01 (dpsetconstrSub) =>
% 121.65/16.01 ((
% 121.65/16.01 (setOfPairsIsBReln) =>
% 121.65/16.01 ((
% 121.65/16.01 (dpsetconstrERa) =>
% 121.65/16.01 ((
% 121.65/16.01 (dpsetconstrEL1) =>
% 121.65/16.01 ((
% 121.65/16.01 (dpsetconstrEL2) =>
% 121.65/16.01 ((
% 121.65/16.01 (dpsetconstrER) =>
% 121.65/16.01 ((
% 121.65/16.01 (funcImageSingleton) =>
% 121.65/16.01 ((
% 121.65/16.01 (apProp) =>
% 121.65/16.01 ((
% 121.65/16.01 (app) =>
% 121.65/16.01 ((
% 121.65/16.01 (infuncsetfunc) =>
% 121.65/16.01 ((
% 121.65/16.01 (ap2p) =>
% 121.65/16.01 ((
% 121.65/16.01 (funcinfuncset) =>
% 121.65/16.01 ((
% 121.65/16.01 (lamProp) =>
% 121.65/16.01 ((
% 121.65/16.01 (lamp) =>
% 121.65/16.01 ((
% 121.65/16.01 (lam2p) =>
% 121.65/16.01 ((
% 121.65/16.01 (brelnall1) =>
% 121.65/16.01 ((
% 121.65/16.01 (brelnall2) =>
% 121.65/16.01 ((
% 121.65/16.01 (ex1E2) =>
% 121.65/16.01 ((
% 121.65/16.01 (funcGraphProp1) =>
% 121.65/16.01 ((
% 121.65/16.01 (funcGraphProp3) =>
% 121.65/16.01 ((
% 121.65/16.01 (funcGraphProp2) =>
% 121.65/16.01 ((
% 121.65/16.01 (funcextLem) =>
% 121.65/16.01 ((
% 121.65/16.01 (funcGraphProp4) =>
% 121.65/16.01 ((
% 121.65/16.01 (subbreln) =>
% 121.65/16.01 ((
% 121.65/16.01 (eqbreln) =>
% 121.65/16.01 ((
% 121.65/16.01 (funcext) =>
% 121.65/16.01 ((
% 121.65/16.01 (funcext2) =>
% 121.65/16.01 ((
% 121.65/16.01 (ap2apEq1) =>
% 121.65/16.01 ((
% 121.65/16.01 (ap2apEq2) =>
% 121.65/16.01 ((
% 121.65/16.01 (beta1) =>
% 121.65/16.01 ((
% 121.65/16.01 (eta1) =>
% 121.65/16.01 ((
% 121.65/16.01 (lam2lamEq) =>
% 121.65/16.01 ((
% 121.65/16.01 (beta2) =>
% 121.65/16.01 ((
% 121.65/16.01 (eta2) =>
% 121.65/16.01 ((
% 121.65/16.01 (iffalseProp1) =>
% 121.65/16.01 ((
% 121.65/16.01 (iffalseProp2) =>
% 121.65/16.01 ((
% 121.65/16.01 (iftrueProp1) =>
% 121.65/16.01 ((
% 121.65/16.01 (iftrueProp2) =>
% 121.65/16.01 ((
% 121.65/16.01 (ifSingleton) =>
% 121.65/16.01 ((
% 121.65/16.01 (ifp) =>
% 121.65/16.01 ((
% 121.65/16.01 (theeq) =>
% 121.65/16.01 ((
% 121.65/16.01 (iftrue) =>
% 121.65/16.01 ((
% 121.65/16.01 (iffalse) =>
% 121.65/16.01 ((
% 121.65/16.01 (iftrueorfalse) =>
% 121.65/16.01 ((
% 121.65/16.01 (binintersectT_lem) =>
% 121.65/16.01 ((
% 121.65/16.01 (binunionT_lem) =>
% 121.65/16.01 ((
% 121.65/16.01 (powersetT_lem) =>
% 121.65/16.01 ((
% 121.65/16.01 (setminusT_lem) =>
% 121.65/16.01 ((
% 121.65/16.01 (complementT_lem) =>
% 121.65/16.01 ((
% 121.65/16.01 (setextT) =>
% 121.65/16.01 ((
% 121.65/16.01 (subsetTI) =>
% 121.65/16.01 ((
% 121.65/16.01 (powersetTI1) =>
% 121.65/16.01 ((
% 121.65/16.01 (powersetTE1) =>
% 121.65/16.01 ((
% 121.65/16.01 (complementTI1) =>
% 121.65/16.01 ((
% 121.65/16.01 (complementTE1) =>
% 121.65/16.01 ((
% 121.65/16.01 (binintersectTELcontra) =>
% 121.65/16.01 ((
% 121.65/16.01 (binintersectTERcontra) =>
% 121.65/16.01 ((
% 121.65/16.01 (contrasubsetT) =>
% 121.65/16.01 ((
% 121.65/16.01 (contrasubsetT1) =>
% 121.65/16.01 ((
% 121.65/16.01 (contrasubsetT2) =>
% 121.65/16.01 ((
% 121.65/16.01 (contrasubsetT3) =>
% 121.65/16.01 ((
% 121.65/16.01 (doubleComplementI1) =>
% 121.65/16.01 ((
% 121.65/16.01 (doubleComplementE1) =>
% 121.65/16.01 ((
% 121.65/16.01 (doubleComplementSub1) =>
% 121.65/16.01 ((
% 121.65/16.01 (doubleComplementSub2) =>
% 121.65/16.01 ((
% 121.65/16.01 (doubleComplementEq) =>
% 121.65/16.01 ((
% 121.65/16.01 (complementTnotintersectT) =>
% 121.65/16.01 ((
% 121.65/16.01 (complementImpComplementIntersect) =>
% 121.65/16.01 ((
% 121.65/16.01 (complementSubsetComplementIntersect) =>
% 121.65/16.01 ((
% 121.65/16.01 (complementInPowersetComplementIntersect) =>
% 121.65/16.01 ((
% 121.65/16.01 (contraSubsetComplement) =>
% 121.65/16.01 ((
% 121.65/16.01 (complementTcontraSubset) =>
% 121.65/16.01 ((
% 121.65/16.01 (binunionTILcontra) =>
% 121.65/16.01 ((
% 121.65/16.01 (binunionTIRcontra) =>
% 121.65/16.01 ((
% 121.65/16.01 (inIntersectImpInUnion) =>
% 121.65/16.01 ((
% 121.65/16.01 (inIntersectImpInUnion2) =>
% 121.65/16.01 ((
% 121.65/16.01 (inIntersectImpInIntersectUnions) =>
% 121.65/16.01 ((
% 121.65/16.01 (intersectInPowersetIntersectUnions) =>
% 121.65/16.01 ((
% 121.65/16.01 (inComplementUnionImpNotIn1) =>
% 121.65/16.01 ((
% 121.65/16.01 (inComplementUnionImpInComplement1) =>
% 121.65/16.01 ((
% 121.65/16.01 (binunionTE) =>
% 121.65/16.01 ((
% 121.65/16.01 (binunionTEcontra) =>
% 121.65/16.01 ((
% 121.65/16.01 (demorgan2a1) =>
% 121.65/16.01 ((
% 121.65/16.01 (complementUnionInPowersetComplement) =>
% 121.65/16.01 ((
% 121.65/16.01 (demorgan2a2) =>
% 121.65/16.01 ((
% 121.65/16.01 (demorgan1a) =>
% 121.65/16.01 ((
% 121.65/16.01 (demorgan1b) =>
% 121.65/16.01 ((
% 121.65/16.01 (demorgan1) =>
% 121.65/16.01 ((
% 121.65/16.01 (demorgan2a) =>
% 121.65/16.01 ((
% 121.65/16.01 (demorgan2b2) =>
% 121.65/16.01 ((
% 121.65/16.01 (demorgan2b) =>
% 121.65/16.01 ((
% 121.65/16.01 (demorgan2) =>
% 121.65/16.01 ((
% 121.65/16.01 (woz13rule0) =>
% 121.65/16.01 ((
% 121.65/16.01 (woz13rule1) =>
% 121.65/16.01 ((
% 121.65/16.01 (woz13rule2) =>
% 121.65/16.01 ((
% 121.65/16.01 (woz13rule3) =>
% 121.65/16.01 ((
% 121.65/16.01 (woz13rule4) =>
% 121.65/16.01 ((
% 121.65/16.01 (woz1_1) =>
% 121.65/16.01 ((
% 121.65/16.01 (woz1_2) =>
% 121.65/16.01 ((
% 121.65/16.01 (woz1_3) =>
% 121.65/16.01 ((
% 121.65/16.01 (woz1_4) =>
% 121.65/16.01 ((
% 121.65/16.01 (woz1_5) =>
% 121.65/16.01 ((
% 121.65/16.01 (breln1all2) =>
% 121.65/16.01 ((
% 121.65/16.01 (breln1SetBreln1) =>
% 121.65/16.01 ((
% 121.65/16.01 (choice2fnsingleton) =>
% 121.65/16.01 ((
% 121.65/16.01 (setOfPairsIsBReln1) =>
% 121.65/16.01 ((
% 121.65/16.01 (breln1all1) =>
% 121.65/16.01 ((
% 121.65/16.01 (subbreln1) =>
% 121.65/16.01 ((
% 121.65/16.01 (eqbreln1) =>
% 121.65/16.01 ((
% 121.65/16.01 (breln1invprop) =>
% 121.65/16.01 ((
% 121.65/16.01 (breln1invI) =>
% 121.65/16.01 ((
% 121.65/16.01 (breln1invE) =>
% 121.65/16.01 ((
% 121.65/16.01 (breln1compprop) =>
% 121.65/16.01 ((
% 121.65/16.01 (breln1compI) =>
% 121.65/16.01 ((
% 121.65/16.01 (breln1compE) =>
% 121.65/16.01 ((
% 121.65/16.01 (breln1compEex) =>
% 121.65/16.01 ((
% 121.65/16.01 (breln1unionprop) =>
% 121.65/16.01 ((
% 121.65/16.01 (breln1unionIL) =>
% 121.65/16.01 ((
% 121.65/16.01 (breln1unionIR) =>
% 121.65/16.01 ((
% 121.65/16.01 (breln1unionI) =>
% 121.65/16.01 ((
% 121.65/16.01 (breln1unionE) =>
% 121.65/16.01 ((
% 121.65/16.01 (breln1unionEcases) =>
% 121.65/16.01 ((
% 121.65/16.01 (breln1unionCommutes) =>
% 121.65/16.01 ((
% 121.65/16.01 (woz2Ex) =>
% 121.65/16.01 ((
% 121.65/16.01 (woz2W) =>
% 121.65/16.01 ((
% 121.65/16.01 (woz2A) =>
% 121.65/16.01 ((
% 121.65/16.01 (woz2B) =>
% 121.65/16.01 ((
% 121.65/16.01 (image1Ex) =>
% 121.65/16.01 ((
% 121.65/16.01 (image1Ex1) =>
% 121.65/16.01 ((
% 121.65/16.01 (image1Equiv) =>
% 121.65/16.01 ((
% 121.65/16.01 (image1E) =>
% 121.65/16.01 ((
% 121.65/16.01 (image1I) =>
% 121.65/16.01 ((
% 121.65/16.01 (injFuncInInjFuncSet) =>
% 121.65/16.01 ((
% 121.65/16.01 (!!) @ (
% 121.65/16.01 (('#B') @ (
% 121.65/16.01 !!) @
% 121.65/16.01 (
% 121.65/16.01 (
% 121.65/16.01 ('#B') @ (
% 121.65/16.01 (
% 121.65/16.01 ('#B') @ (
% 121.65/16.01 !!))) @
% 121.65/16.01 (
% 121.65/16.01 (
% 121.65/16.01 ('#S') @ (
% 121.65/16.01 (
% 121.65/16.01 ('#B') @ (
% 121.65/16.01 '#S') @
% 121.65/16.01 (
% 121.65/16.01 (
% 121.65/16.01 ('#B') @ (
% 121.65/16.01 (
% 121.65/16.01 ('#B') @ (
% 121.65/16.01 '#S'))) @
% 121.65/16.01 (
% 121.65/16.01 (
% 121.65/16.01 ('#B') @ (
% 121.65/16.01 (
% 121.65/16.01 ('#B') @ (
% 121.65/16.01 (
% 121.65/16.01 ('#B') @ (
% 121.65/16.01 =>))))) @
% 121.65/16.01 (
% 121.65/16.01 (
% 121.65/16.01 ('#B') @ (
% 121.65/16.01 (
% 121.65/16.01 ('#B') @ (
% 121.65/16.01 (
% 121.65/16.01 ('#C') @ in)))) @
% 121.65/16.01 injFuncSet)))))))) @
% 121.65/16.01 (
% 121.65/16.01 (
% 121.65/16.01 ('#B') @ (
% 121.65/16.01 (
% 121.65/16.01 ('#B') @ (
% 121.65/16.01 (
% 121.65/16.01 ('#C') @ in)))) @
% 121.65/16.01 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 121.65/16.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl19])).
% 121.65/16.01 thf(zip_derived_cl33, plain,
% 121.65/16.01 (~ (((omegaSAx) =>
% 121.65/16.01 (((omegaIndAx) =>
% 121.65/16.01 (((replAx) =>
% 121.65/16.01 (((foundationAx) =>
% 121.65/16.01 (((wellorderingAx) =>
% 121.65/16.01 (((descrp) =>
% 121.65/16.01 (((dsetconstrI) =>
% 121.65/16.01 (((dsetconstrEL) =>
% 121.65/16.01 (((dsetconstrER) =>
% 121.65/16.01 (((exuE1) =>
% 121.65/16.01 (((prop2setE) =>
% 121.65/16.01 (((emptysetE) =>
% 121.65/16.01 (((emptysetimpfalse) =>
% 121.65/16.01 (((notinemptyset) =>
% 121.65/16.01 (((exuE3e) =>
% 121.65/16.01 (((setext) =>
% 121.65/16.01 (((emptyI) =>
% 121.65/16.01 (((noeltsimpempty) =>
% 121.65/16.01 (((setbeta) =>
% 121.65/16.01 (((nonemptyE1) =>
% 121.65/16.01 (((nonemptyI) =>
% 121.65/16.01 (((nonemptyI1) =>
% 121.65/16.01 (((setadjoinIL) =>
% 121.65/16.01 (((in @ emptyset @
% 121.65/16.01 (setadjoin @
% 121.65/16.01 emptyset @ emptyset)) =>
% 121.65/16.01 (((setadjoinIR) =>
% 121.65/16.01 (((setadjoinE) =>
% 121.65/16.01 (((setadjoinOr) =>
% 121.65/16.01 (((setoftrueEq) =>
% 121.65/16.01 (((powersetI) =>
% 121.65/16.01 (((emptyinPowerset) =>
% 121.65/16.01 ((
% 121.65/16.01 (emptyInPowerset) =>
% 121.65/16.01 ((
% 121.65/16.01 (powersetE) =>
% 121.65/16.01 ((
% 121.65/16.01 (setunionI) =>
% 121.65/16.01 ((
% 121.65/16.01 (setunionE) =>
% 121.65/16.01 ((
% 121.65/16.01 (subPowSU) =>
% 121.65/16.01 ((
% 121.65/16.01 (exuE2) =>
% 121.65/16.01 ((
% 121.65/16.01 (nonemptyImpWitness) =>
% 121.65/16.01 ((
% 121.65/16.01 (uniqinunit) =>
% 121.65/16.01 ((
% 121.65/16.01 (notinsingleton) =>
% 121.65/16.01 ((
% 121.65/16.01 (eqinunit) =>
% 121.65/16.01 ((
% 121.65/16.01 (singletonsswitch) =>
% 121.65/16.01 ((
% 121.65/16.01 (upairsetE) =>
% 121.65/16.01 ((
% 121.65/16.01 (upairsetIL) =>
% 121.65/16.01 ((
% 121.65/16.01 (upairsetIR) =>
% 121.65/16.01 ((
% 121.65/16.01 (emptyE1) =>
% 121.65/16.01 ((
% 121.65/16.01 (vacuousDall) =>
% 121.65/16.01 ((
% 121.65/16.01 (quantDeMorgan1) =>
% 121.65/16.01 ((
% 121.65/16.01 (quantDeMorgan2) =>
% 121.65/16.01 ((
% 121.65/16.01 (quantDeMorgan3) =>
% 121.65/16.01 ((
% 121.65/16.01 (quantDeMorgan4) =>
% 121.65/16.01 ((
% 121.65/16.01 (prop2setI) =>
% 121.65/16.01 ((
% 121.65/16.01 (prop2set2propI) =>
% 121.65/16.01 ((
% 121.65/16.01 (notdexE) =>
% 121.65/16.01 ((
% 121.65/16.01 (notdallE) =>
% 121.65/16.01 ((
% 121.65/16.01 (exuI1) =>
% 121.65/16.01 ((
% 121.65/16.01 (exuI3) =>
% 121.65/16.01 ((
% 121.65/16.01 (exuI2) =>
% 121.65/16.01 ((
% 121.65/16.01 (inCongP) =>
% 121.65/16.01 ((
% 121.65/16.01 (in__Cong) =>
% 121.65/16.01 ((
% 121.65/16.01 (exuE3u) =>
% 121.65/16.01 ((
% 121.65/16.01 (exu__Cong) =>
% 121.65/16.01 ((
% 121.65/16.01 (setadjoin__Cong) =>
% 121.65/16.01 ((
% 121.65/16.01 (powerset__Cong) =>
% 121.65/16.01 ((
% 121.65/16.01 (setunion__Cong) =>
% 121.65/16.01 ((
% 121.65/16.01 (exuEu) =>
% 121.65/16.01 ((
% 121.65/16.01 (descr__Cong) =>
% 121.65/16.01 ((
% 121.65/16.01 (dsetconstr__Cong) =>
% 121.65/16.01 ((
% 121.65/16.01 (subsetI1) =>
% 121.65/16.01 ((
% 121.65/16.01 (eqimpsubset2) =>
% 121.65/16.01 ((
% 121.65/16.01 (eqimpsubset1) =>
% 121.65/16.01 ((
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% 121.65/16.01 ((
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% 121.65/16.01 (cartprodmempaircEq) =>
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% 121.65/16.01 (cartprodsndpairEq) =>
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% 121.65/16.01 (cartprodpairsurjEq) =>
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% 121.65/16.02 '#S'))) @
% 121.65/16.02 (
% 121.65/16.02 (
% 121.65/16.02 ('#B') @ (
% 121.65/16.02 (
% 121.65/16.02 ('#B') @ (
% 121.65/16.02 (
% 121.65/16.02 ('#B') @ (
% 121.65/16.02 =>))))) @
% 121.65/16.02 (
% 121.65/16.02 (
% 121.65/16.02 ('#B') @ (
% 121.65/16.02 (
% 121.65/16.02 ('#B') @ (
% 121.65/16.02 (
% 121.65/16.02 ('#C') @ in)))) @
% 121.65/16.02 injFuncSet)))))))) @
% 121.65/16.02 (
% 121.65/16.02 (
% 121.65/16.02 ('#B') @ (
% 121.65/16.02 (
% 121.65/16.02 ('#B') @ (
% 121.65/16.02 (
% 121.65/16.02 ('#C') @ in)))) @
% 121.65/16.02 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 121.65/16.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl33])).
% 121.65/16.02 thf(zip_derived_cl46, plain,
% 121.65/16.02 (~ (((replAx) =>
% 121.65/16.02 (((foundationAx) =>
% 121.65/16.02 (((wellorderingAx) =>
% 121.65/16.02 (((descrp) =>
% 121.65/16.02 (((dsetconstrI) =>
% 121.65/16.02 (((dsetconstrEL) =>
% 121.65/16.02 (((dsetconstrER) =>
% 121.65/16.02 (((exuE1) =>
% 121.65/16.02 (((prop2setE) =>
% 121.65/16.02 (((emptysetE) =>
% 121.65/16.02 (((emptysetimpfalse) =>
% 121.65/16.02 (((notinemptyset) =>
% 121.65/16.02 (((exuE3e) =>
% 121.65/16.02 (((setext) =>
% 121.65/16.02 (((emptyI) =>
% 121.65/16.02 (((noeltsimpempty) =>
% 121.65/16.02 (((setbeta) =>
% 121.65/16.02 (((nonemptyE1) =>
% 121.65/16.02 (((nonemptyI) =>
% 121.65/16.02 (((nonemptyI1) =>
% 121.65/16.02 (((setadjoinIL) =>
% 121.65/16.02 (((in @ emptyset @
% 121.65/16.02 (setadjoin @ emptyset @
% 121.65/16.02 emptyset)) =>
% 121.65/16.02 (((setadjoinIR) =>
% 121.65/16.02 (((setadjoinE) =>
% 121.65/16.02 (((setadjoinOr) =>
% 121.65/16.02 (((setoftrueEq) =>
% 121.65/16.02 (((powersetI) =>
% 121.65/16.02 (((emptyinPowerset) =>
% 121.65/16.02 (((emptyInPowerset) =>
% 121.65/16.02 (((powersetE) =>
% 121.65/16.02 ((
% 121.65/16.02 (setunionI) =>
% 121.65/16.02 ((
% 121.65/16.02 (setunionE) =>
% 121.65/16.02 ((
% 121.65/16.02 (subPowSU) =>
% 121.65/16.02 ((
% 121.65/16.02 (exuE2) =>
% 121.65/16.02 ((
% 121.65/16.02 (nonemptyImpWitness) =>
% 121.65/16.02 ((
% 121.65/16.02 (uniqinunit) =>
% 121.65/16.02 ((
% 121.65/16.02 (notinsingleton) =>
% 121.65/16.02 ((
% 121.65/16.02 (eqinunit) =>
% 121.65/16.02 ((
% 121.65/16.02 (singletonsswitch) =>
% 121.65/16.02 ((
% 121.65/16.02 (upairsetE) =>
% 121.65/16.02 ((
% 121.65/16.02 (upairsetIL) =>
% 121.65/16.02 ((
% 121.65/16.02 (upairsetIR) =>
% 121.65/16.02 ((
% 121.65/16.02 (emptyE1) =>
% 121.65/16.02 ((
% 121.65/16.02 (vacuousDall) =>
% 121.65/16.02 ((
% 121.65/16.02 (quantDeMorgan1) =>
% 121.65/16.02 ((
% 121.65/16.02 (quantDeMorgan2) =>
% 121.65/16.02 ((
% 121.65/16.02 (quantDeMorgan3) =>
% 121.65/16.02 ((
% 121.65/16.02 (quantDeMorgan4) =>
% 121.65/16.02 ((
% 121.65/16.02 (prop2setI) =>
% 121.65/16.02 ((
% 121.65/16.02 (prop2set2propI) =>
% 121.65/16.02 ((
% 121.65/16.02 (notdexE) =>
% 121.65/16.02 ((
% 121.65/16.02 (notdallE) =>
% 121.65/16.02 ((
% 121.65/16.02 (exuI1) =>
% 121.65/16.02 ((
% 121.65/16.02 (exuI3) =>
% 121.65/16.02 ((
% 121.65/16.02 (exuI2) =>
% 121.65/16.02 ((
% 121.65/16.02 (inCongP) =>
% 121.65/16.02 ((
% 121.65/16.02 (in__Cong) =>
% 121.65/16.02 ((
% 121.65/16.02 (exuE3u) =>
% 121.65/16.02 ((
% 121.65/16.02 (exu__Cong) =>
% 121.65/16.02 ((
% 121.65/16.02 (setadjoin__Cong) =>
% 121.65/16.02 ((
% 121.65/16.02 (powerset__Cong) =>
% 121.65/16.02 ((
% 121.65/16.02 (setunion__Cong) =>
% 121.65/16.02 ((
% 121.65/16.02 (exuEu) =>
% 121.65/16.02 ((
% 121.65/16.02 (descr__Cong) =>
% 121.65/16.02 ((
% 121.65/16.02 (dsetconstr__Cong) =>
% 121.65/16.02 ((
% 121.65/16.02 (subsetI1) =>
% 121.65/16.02 ((
% 121.65/16.02 (eqimpsubset2) =>
% 121.65/16.02 ((
% 121.65/16.02 (eqimpsubset1) =>
% 121.65/16.02 ((
% 121.65/16.02 (subsetI2) =>
% 121.65/16.02 ((
% 121.65/16.02 (emptysetsubset) =>
% 121.65/16.02 ((
% 121.65/16.02 (subsetE) =>
% 121.65/16.02 ((
% 121.65/16.02 (subsetE2) =>
% 121.65/16.02 ((
% 121.65/16.02 (notsubsetI) =>
% 121.65/16.02 ((
% 121.65/16.02 (notequalI1) =>
% 121.65/16.02 ((
% 121.65/16.02 (notequalI2) =>
% 121.65/16.02 ((
% 121.65/16.02 (subsetRefl) =>
% 121.65/16.02 ((
% 121.65/16.02 (subsetTrans) =>
% 121.65/16.02 ((
% 121.65/16.02 (setadjoinSub) =>
% 121.65/16.02 ((
% 121.65/16.02 (setadjoinSub2) =>
% 121.65/16.02 ((
% 121.65/16.02 (subset2powerset) =>
% 121.65/16.02 ((
% 121.65/16.02 (setextsub) =>
% 121.65/16.02 ((
% 121.65/16.02 (subsetemptysetimpeq) =>
% 121.65/16.02 ((
% 121.65/16.02 (powersetI1) =>
% 121.65/16.02 ((
% 121.65/16.02 (powersetE1) =>
% 121.65/16.02 ((
% 121.65/16.02 (inPowerset) =>
% 121.65/16.02 ((
% 121.65/16.02 (powersetsubset) =>
% 121.65/16.02 ((
% 121.65/16.02 (sepInPowerset) =>
% 121.65/16.02 ((
% 121.65/16.02 (sepSubset) =>
% 121.65/16.02 ((
% 121.65/16.02 (binunionIL) =>
% 121.65/16.02 ((
% 121.65/16.02 (upairset2IR) =>
% 121.65/16.02 ((
% 121.65/16.02 (binunionIR) =>
% 121.65/16.02 ((
% 121.65/16.02 (binunionEcases) =>
% 121.65/16.02 ((
% 121.65/16.02 (binunionE) =>
% 121.65/16.02 ((
% 121.65/16.02 (binunionLsub) =>
% 121.65/16.02 ((
% 121.65/16.02 (binunionRsub) =>
% 121.65/16.02 ((
% 121.65/16.02 (binintersectI) =>
% 121.65/16.02 ((
% 121.65/16.02 (binintersectSubset5) =>
% 121.65/16.02 ((
% 121.65/16.02 (binintersectEL) =>
% 121.65/16.02 ((
% 121.65/16.02 (binintersectLsub) =>
% 121.65/16.02 ((
% 121.65/16.02 (binintersectSubset2) =>
% 121.65/16.02 ((
% 121.65/16.02 (binintersectSubset3) =>
% 121.65/16.02 ((
% 121.65/16.02 (binintersectER) =>
% 121.65/16.02 ((
% 121.65/16.02 (disjointsetsI1) =>
% 121.65/16.02 ((
% 121.65/16.02 (binintersectRsub) =>
% 121.65/16.02 ((
% 121.65/16.02 (binintersectSubset4) =>
% 121.65/16.02 ((
% 121.65/16.02 (binintersectSubset1) =>
% 121.65/16.02 ((
% 121.65/16.02 (bs114d) =>
% 121.65/16.02 ((
% 121.65/16.02 (setminusI) =>
% 121.65/16.02 ((
% 121.65/16.02 (setminusEL) =>
% 121.65/16.02 ((
% 121.65/16.02 (setminusER) =>
% 121.65/16.02 ((
% 121.65/16.02 (setminusSubset2) =>
% 121.65/16.02 ((
% 121.65/16.02 (setminusERneg) =>
% 121.65/16.02 ((
% 121.65/16.02 (setminusELneg) =>
% 121.65/16.02 ((
% 121.65/16.02 (setminusILneg) =>
% 121.65/16.02 ((
% 121.65/16.02 (setminusIRneg) =>
% 121.65/16.02 ((
% 121.65/16.02 (setminusLsub) =>
% 121.65/16.02 ((
% 121.65/16.02 (setminusSubset1) =>
% 121.65/16.02 ((
% 121.65/16.02 (symdiffE) =>
% 121.65/16.02 ((
% 121.65/16.02 (symdiffI1) =>
% 121.65/16.02 ((
% 121.65/16.02 (symdiffI2) =>
% 121.65/16.02 ((
% 121.65/16.02 (symdiffIneg1) =>
% 121.65/16.02 ((
% 121.65/16.02 (symdiffIneg2) =>
% 121.65/16.02 ((
% 121.65/16.02 (secondinupair) =>
% 121.65/16.02 ((
% 121.65/16.02 (setukpairIL) =>
% 121.65/16.02 ((
% 121.65/16.02 (setukpairIR) =>
% 121.65/16.02 ((
% 121.65/16.02 (kpairiskpair) =>
% 121.65/16.02 ((
% 121.65/16.02 (kpairp) =>
% 121.65/16.02 ((
% 121.65/16.02 (singletonsubset) =>
% 121.65/16.02 ((
% 121.65/16.02 (singletoninpowerset) =>
% 121.65/16.02 ((
% 121.65/16.02 (singletoninpowunion) =>
% 121.65/16.02 ((
% 121.65/16.02 (upairset2E) =>
% 121.65/16.02 ((
% 121.65/16.02 (upairsubunion) =>
% 121.65/16.02 ((
% 121.65/16.02 (upairinpowunion) =>
% 121.65/16.02 ((
% 121.65/16.02 (ubforcartprodlem1) =>
% 121.65/16.02 ((
% 121.65/16.02 (ubforcartprodlem2) =>
% 121.65/16.02 ((
% 121.65/16.02 (ubforcartprodlem3) =>
% 121.65/16.02 ((
% 121.65/16.02 (cartprodpairin) =>
% 121.65/16.02 ((
% 121.65/16.02 (cartprodmempair1) =>
% 121.65/16.02 ((
% 121.65/16.02 (cartprodmempair) =>
% 121.65/16.02 ((
% 121.65/16.02 (setunionE2) =>
% 121.65/16.02 ((
% 121.65/16.02 (setunionsingleton1) =>
% 121.65/16.02 ((
% 121.65/16.02 (setunionsingleton2) =>
% 121.65/16.02 ((
% 121.65/16.02 (setunionsingleton) =>
% 121.65/16.02 ((
% 121.65/16.02 (singletonprop) =>
% 121.65/16.02 ((
% 121.65/16.02 (ex1E1) =>
% 121.65/16.02 ((
% 121.65/16.02 (ex1I) =>
% 121.65/16.02 ((
% 121.65/16.02 (ex1I2) =>
% 121.65/16.02 ((
% 121.65/16.02 (singletonsuniq) =>
% 121.65/16.02 ((
% 121.65/16.02 (setukpairinjL1) =>
% 121.65/16.02 ((
% 121.65/16.02 (kfstsingleton) =>
% 121.65/16.02 ((
% 121.65/16.02 (theprop) =>
% 121.65/16.02 ((
% 121.65/16.02 (kfstpairEq) =>
% 121.65/16.02 ((
% 121.65/16.02 (cartprodfstin) =>
% 121.65/16.02 ((
% 121.65/16.02 (setukpairinjL2) =>
% 121.65/16.02 ((
% 121.65/16.02 (setukpairinjL) =>
% 121.65/16.02 ((
% 121.65/16.02 (setukpairinjR11) =>
% 121.65/16.02 ((
% 121.65/16.02 (setukpairinjR12) =>
% 121.65/16.02 ((
% 121.65/16.02 (setukpairinjR1) =>
% 121.65/16.02 ((
% 121.65/16.02 (upairequniteq) =>
% 121.65/16.02 ((
% 121.65/16.02 (setukpairinjR2) =>
% 121.65/16.02 ((
% 121.65/16.02 (setukpairinjR) =>
% 121.65/16.02 ((
% 121.65/16.02 (ksndsingleton) =>
% 121.65/16.02 ((
% 121.65/16.02 (ksndpairEq) =>
% 121.65/16.02 ((
% 121.65/16.02 (kpairsurjEq) =>
% 121.65/16.02 ((
% 121.65/16.02 (cartprodsndin) =>
% 121.65/16.02 ((
% 121.65/16.02 (cartprodpairmemEL) =>
% 121.65/16.02 ((
% 121.65/16.02 (cartprodpairmemER) =>
% 121.65/16.02 ((
% 121.65/16.02 (cartprodmempaircEq) =>
% 121.65/16.02 ((
% 121.65/16.02 (cartprodfstpairEq) =>
% 121.65/16.02 ((
% 121.65/16.02 (cartprodsndpairEq) =>
% 121.65/16.02 ((
% 121.65/16.02 (cartprodpairsurjEq) =>
% 121.65/16.02 ((
% 121.65/16.02 (dpsetconstrI) =>
% 121.65/16.02 ((
% 121.65/16.02 (dpsetconstrSub) =>
% 121.65/16.02 ((
% 121.65/16.02 (setOfPairsIsBReln) =>
% 121.65/16.02 ((
% 121.65/16.02 (dpsetconstrERa) =>
% 121.65/16.02 ((
% 121.65/16.02 (dpsetconstrEL1) =>
% 121.65/16.02 ((
% 121.65/16.02 (dpsetconstrEL2) =>
% 121.65/16.02 ((
% 121.65/16.02 (dpsetconstrER) =>
% 121.65/16.02 ((
% 121.65/16.02 (funcImageSingleton) =>
% 121.65/16.02 ((
% 121.65/16.02 (apProp) =>
% 121.65/16.02 ((
% 121.65/16.02 (app) =>
% 121.65/16.02 ((
% 121.65/16.02 (infuncsetfunc) =>
% 121.65/16.02 ((
% 121.65/16.02 (ap2p) =>
% 121.65/16.02 ((
% 121.65/16.02 (funcinfuncset) =>
% 121.65/16.02 ((
% 121.65/16.02 (lamProp) =>
% 121.65/16.02 ((
% 121.65/16.02 (lamp) =>
% 121.65/16.02 ((
% 121.65/16.02 (lam2p) =>
% 121.65/16.02 ((
% 121.65/16.02 (brelnall1) =>
% 121.65/16.02 ((
% 121.65/16.02 (brelnall2) =>
% 121.65/16.02 ((
% 121.65/16.02 (ex1E2) =>
% 121.65/16.02 ((
% 121.65/16.02 (funcGraphProp1) =>
% 121.65/16.02 ((
% 121.65/16.02 (funcGraphProp3) =>
% 121.65/16.02 ((
% 121.65/16.02 (funcGraphProp2) =>
% 121.65/16.02 ((
% 121.65/16.02 (funcextLem) =>
% 121.65/16.02 ((
% 121.65/16.02 (funcGraphProp4) =>
% 121.65/16.02 ((
% 121.65/16.02 (subbreln) =>
% 121.65/16.02 ((
% 121.65/16.02 (eqbreln) =>
% 121.65/16.02 ((
% 121.65/16.02 (funcext) =>
% 121.65/16.02 ((
% 121.65/16.02 (funcext2) =>
% 121.65/16.02 ((
% 121.65/16.02 (ap2apEq1) =>
% 121.65/16.02 ((
% 121.65/16.02 (ap2apEq2) =>
% 121.65/16.02 ((
% 121.65/16.02 (beta1) =>
% 121.65/16.02 ((
% 121.65/16.02 (eta1) =>
% 121.65/16.02 ((
% 121.65/16.02 (lam2lamEq) =>
% 121.65/16.02 ((
% 121.65/16.02 (beta2) =>
% 121.65/16.02 ((
% 121.65/16.02 (eta2) =>
% 121.65/16.02 ((
% 121.65/16.02 (iffalseProp1) =>
% 121.65/16.02 ((
% 121.65/16.02 (iffalseProp2) =>
% 121.65/16.02 ((
% 121.65/16.02 (iftrueProp1) =>
% 121.65/16.02 ((
% 121.65/16.02 (iftrueProp2) =>
% 121.65/16.02 ((
% 121.65/16.02 (ifSingleton) =>
% 121.65/16.02 ((
% 121.65/16.02 (ifp) =>
% 121.65/16.02 ((
% 121.65/16.02 (theeq) =>
% 121.65/16.02 ((
% 121.65/16.02 (iftrue) =>
% 121.65/16.02 ((
% 121.65/16.02 (iffalse) =>
% 121.65/16.02 ((
% 121.65/16.02 (iftrueorfalse) =>
% 121.65/16.02 ((
% 121.65/16.02 (binintersectT_lem) =>
% 121.65/16.02 ((
% 121.65/16.02 (binunionT_lem) =>
% 121.65/16.02 ((
% 121.65/16.02 (powersetT_lem) =>
% 121.65/16.02 ((
% 121.65/16.02 (setminusT_lem) =>
% 121.65/16.02 ((
% 121.65/16.02 (complementT_lem) =>
% 121.65/16.02 ((
% 121.65/16.02 (setextT) =>
% 121.65/16.02 ((
% 121.65/16.02 (subsetTI) =>
% 121.65/16.02 ((
% 121.65/16.02 (powersetTI1) =>
% 121.65/16.02 ((
% 121.65/16.02 (powersetTE1) =>
% 121.65/16.02 ((
% 121.65/16.02 (complementTI1) =>
% 121.65/16.02 ((
% 121.65/16.02 (complementTE1) =>
% 121.65/16.02 ((
% 121.65/16.02 (binintersectTELcontra) =>
% 121.65/16.02 ((
% 121.65/16.02 (binintersectTERcontra) =>
% 121.65/16.02 ((
% 121.65/16.02 (contrasubsetT) =>
% 121.65/16.02 ((
% 121.65/16.02 (contrasubsetT1) =>
% 121.65/16.02 ((
% 121.65/16.02 (contrasubsetT2) =>
% 121.65/16.02 ((
% 121.65/16.02 (contrasubsetT3) =>
% 121.65/16.02 ((
% 121.65/16.02 (doubleComplementI1) =>
% 121.65/16.02 ((
% 121.65/16.02 (doubleComplementE1) =>
% 121.65/16.02 ((
% 121.65/16.02 (doubleComplementSub1) =>
% 121.65/16.02 ((
% 121.65/16.02 (doubleComplementSub2) =>
% 121.65/16.02 ((
% 121.65/16.02 (doubleComplementEq) =>
% 121.65/16.02 ((
% 121.65/16.02 (complementTnotintersectT) =>
% 121.65/16.02 ((
% 121.65/16.02 (complementImpComplementIntersect) =>
% 121.65/16.02 ((
% 121.65/16.02 (complementSubsetComplementIntersect) =>
% 121.65/16.02 ((
% 121.65/16.02 (complementInPowersetComplementIntersect) =>
% 121.65/16.02 ((
% 121.65/16.02 (contraSubsetComplement) =>
% 121.65/16.02 ((
% 121.65/16.02 (complementTcontraSubset) =>
% 121.65/16.02 ((
% 121.65/16.02 (binunionTILcontra) =>
% 121.65/16.02 ((
% 121.65/16.02 (binunionTIRcontra) =>
% 121.65/16.02 ((
% 121.65/16.02 (inIntersectImpInUnion) =>
% 121.65/16.02 ((
% 121.65/16.02 (inIntersectImpInUnion2) =>
% 121.65/16.02 ((
% 121.65/16.02 (inIntersectImpInIntersectUnions) =>
% 121.65/16.02 ((
% 121.65/16.02 (intersectInPowersetIntersectUnions) =>
% 121.65/16.02 ((
% 121.65/16.02 (inComplementUnionImpNotIn1) =>
% 121.65/16.02 ((
% 121.65/16.02 (inComplementUnionImpInComplement1) =>
% 121.65/16.02 ((
% 121.65/16.02 (binunionTE) =>
% 121.65/16.02 ((
% 121.65/16.02 (binunionTEcontra) =>
% 121.65/16.02 ((
% 121.65/16.02 (demorgan2a1) =>
% 121.65/16.02 ((
% 121.65/16.02 (complementUnionInPowersetComplement) =>
% 121.65/16.02 ((
% 121.65/16.02 (demorgan2a2) =>
% 121.65/16.02 ((
% 121.65/16.02 (demorgan1a) =>
% 121.65/16.02 ((
% 121.65/16.02 (demorgan1b) =>
% 121.65/16.02 ((
% 121.65/16.02 (demorgan1) =>
% 121.65/16.02 ((
% 121.65/16.02 (demorgan2a) =>
% 121.65/16.02 ((
% 121.65/16.02 (demorgan2b2) =>
% 121.65/16.02 ((
% 121.65/16.02 (demorgan2b) =>
% 121.65/16.02 ((
% 121.65/16.02 (demorgan2) =>
% 121.65/16.02 ((
% 121.65/16.02 (woz13rule0) =>
% 121.65/16.02 ((
% 121.65/16.02 (woz13rule1) =>
% 121.65/16.02 ((
% 121.65/16.02 (woz13rule2) =>
% 121.65/16.02 ((
% 121.65/16.02 (woz13rule3) =>
% 121.65/16.02 ((
% 121.65/16.02 (woz13rule4) =>
% 121.65/16.02 ((
% 121.65/16.02 (woz1_1) =>
% 121.65/16.02 ((
% 121.65/16.02 (woz1_2) =>
% 121.65/16.02 ((
% 121.65/16.02 (woz1_3) =>
% 121.65/16.02 ((
% 121.65/16.02 (woz1_4) =>
% 121.65/16.02 ((
% 121.65/16.02 (woz1_5) =>
% 121.65/16.02 ((
% 121.65/16.02 (breln1all2) =>
% 121.65/16.02 ((
% 121.65/16.02 (breln1SetBreln1) =>
% 121.65/16.02 ((
% 121.65/16.02 (choice2fnsingleton) =>
% 121.65/16.02 ((
% 121.65/16.02 (setOfPairsIsBReln1) =>
% 121.65/16.02 ((
% 121.65/16.02 (breln1all1) =>
% 121.65/16.02 ((
% 121.65/16.02 (subbreln1) =>
% 121.65/16.02 ((
% 121.65/16.02 (eqbreln1) =>
% 121.65/16.02 ((
% 121.65/16.02 (breln1invprop) =>
% 121.65/16.02 ((
% 121.65/16.02 (breln1invI) =>
% 121.65/16.02 ((
% 121.65/16.02 (breln1invE) =>
% 121.65/16.02 ((
% 121.65/16.02 (breln1compprop) =>
% 121.65/16.02 ((
% 121.65/16.02 (breln1compI) =>
% 121.65/16.02 ((
% 121.65/16.02 (breln1compE) =>
% 121.65/16.02 ((
% 121.65/16.02 (breln1compEex) =>
% 121.65/16.02 ((
% 121.65/16.02 (breln1unionprop) =>
% 121.65/16.02 ((
% 121.65/16.02 (breln1unionIL) =>
% 121.65/16.02 ((
% 121.65/16.02 (breln1unionIR) =>
% 121.65/16.02 ((
% 121.65/16.02 (breln1unionI) =>
% 121.65/16.02 ((
% 121.65/16.02 (breln1unionE) =>
% 121.65/16.02 ((
% 121.65/16.02 (breln1unionEcases) =>
% 121.65/16.02 ((
% 121.65/16.02 (breln1unionCommutes) =>
% 121.65/16.02 ((
% 121.65/16.02 (woz2Ex) =>
% 121.65/16.02 ((
% 121.65/16.02 (woz2W) =>
% 121.65/16.02 ((
% 121.65/16.02 (woz2A) =>
% 121.65/16.02 ((
% 121.65/16.02 (woz2B) =>
% 121.65/16.02 ((
% 121.65/16.02 (image1Ex) =>
% 121.65/16.02 ((
% 121.65/16.02 (image1Ex1) =>
% 121.65/16.02 ((
% 121.65/16.02 (image1Equiv) =>
% 121.65/16.02 ((
% 121.65/16.02 (image1E) =>
% 121.65/16.02 ((
% 121.65/16.02 (image1I) =>
% 121.65/16.02 ((
% 121.65/16.02 (injFuncInInjFuncSet) =>
% 121.65/16.02 ((
% 121.65/16.02 (!!) @ (
% 121.65/16.02 (('#B') @ (
% 121.65/16.02 !!) @
% 121.65/16.02 (
% 121.65/16.02 (
% 121.65/16.02 ('#B') @ (
% 121.65/16.02 (
% 121.65/16.02 ('#B') @ (
% 121.65/16.02 !!))) @
% 121.65/16.02 (
% 121.65/16.02 (
% 121.65/16.02 ('#S') @ (
% 121.65/16.02 (
% 121.65/16.02 ('#B') @ (
% 121.65/16.02 '#S') @
% 121.65/16.02 (
% 121.65/16.02 (
% 121.65/16.02 ('#B') @ (
% 121.65/16.02 (
% 121.65/16.02 ('#B') @ (
% 121.65/16.02 '#S'))) @
% 121.65/16.02 (
% 121.65/16.02 (
% 121.65/16.02 ('#B') @ (
% 121.65/16.02 (
% 121.65/16.02 ('#B') @ (
% 121.65/16.02 (
% 121.65/16.02 ('#B') @ (
% 121.65/16.02 =>))))) @
% 121.65/16.02 (
% 121.65/16.02 (
% 121.65/16.02 ('#B') @ (
% 121.65/16.02 (
% 121.65/16.02 ('#B') @ (
% 121.65/16.02 (
% 121.65/16.02 ('#C') @ in)))) @
% 121.65/16.02 injFuncSet)))))))) @
% 121.65/16.02 (
% 121.65/16.02 (
% 121.65/16.02 ('#B') @ (
% 121.65/16.02 (
% 121.65/16.02 ('#B') @ (
% 121.65/16.02 (
% 121.65/16.02 ('#C') @ in)))) @
% 121.65/16.02 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 121.65/16.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl40])).
% 121.65/16.02 thf(zip_derived_cl52, plain,
% 121.65/16.02 (~ (((foundationAx) =>
% 121.65/16.02 (((wellorderingAx) =>
% 121.65/16.02 (((descrp) =>
% 121.65/16.02 (((dsetconstrI) =>
% 121.65/16.02 (((dsetconstrEL) =>
% 121.65/16.02 (((dsetconstrER) =>
% 121.65/16.02 (((exuE1) =>
% 121.65/16.02 (((prop2setE) =>
% 121.65/16.02 (((emptysetE) =>
% 121.65/16.02 (((emptysetimpfalse) =>
% 121.65/16.02 (((notinemptyset) =>
% 121.65/16.02 (((exuE3e) =>
% 121.65/16.02 (((setext) =>
% 121.65/16.02 (((emptyI) =>
% 121.65/16.02 (((noeltsimpempty) =>
% 121.65/16.02 (((setbeta) =>
% 121.65/16.02 (((nonemptyE1) =>
% 121.65/16.02 (((nonemptyI) =>
% 121.65/16.02 (((nonemptyI1) =>
% 121.65/16.02 (((setadjoinIL) =>
% 121.65/16.02 (((in @ emptyset @
% 121.65/16.02 (setadjoin @ emptyset @
% 121.65/16.02 emptyset)) =>
% 121.65/16.02 (((setadjoinIR) =>
% 121.65/16.02 (((setadjoinE) =>
% 121.65/16.02 (((setadjoinOr) =>
% 121.65/16.02 (((setoftrueEq) =>
% 121.65/16.02 (((powersetI) =>
% 121.65/16.02 (((emptyinPowerset) =>
% 121.65/16.02 (((emptyInPowerset) =>
% 121.65/16.02 (((powersetE) =>
% 121.65/16.02 (((setunionI) =>
% 121.65/16.02 ((
% 121.65/16.02 (setunionE) =>
% 121.65/16.02 ((
% 121.65/16.02 (subPowSU) =>
% 121.65/16.02 ((
% 121.65/16.02 (exuE2) =>
% 121.65/16.02 ((
% 121.65/16.02 (nonemptyImpWitness) =>
% 121.65/16.02 ((
% 121.65/16.02 (uniqinunit) =>
% 121.65/16.02 ((
% 121.65/16.02 (notinsingleton) =>
% 121.65/16.02 ((
% 121.65/16.02 (eqinunit) =>
% 121.65/16.02 ((
% 121.65/16.02 (singletonsswitch) =>
% 121.65/16.02 ((
% 121.65/16.02 (upairsetE) =>
% 121.65/16.02 ((
% 121.65/16.02 (upairsetIL) =>
% 121.65/16.02 ((
% 121.65/16.02 (upairsetIR) =>
% 121.65/16.02 ((
% 121.65/16.02 (emptyE1) =>
% 121.65/16.02 ((
% 121.65/16.02 (vacuousDall) =>
% 121.65/16.02 ((
% 121.65/16.02 (quantDeMorgan1) =>
% 121.65/16.02 ((
% 121.65/16.02 (quantDeMorgan2) =>
% 121.65/16.02 ((
% 121.65/16.02 (quantDeMorgan3) =>
% 121.65/16.02 ((
% 121.65/16.02 (quantDeMorgan4) =>
% 121.65/16.02 ((
% 121.65/16.02 (prop2setI) =>
% 121.65/16.02 ((
% 121.65/16.02 (prop2set2propI) =>
% 121.65/16.02 ((
% 121.65/16.02 (notdexE) =>
% 121.65/16.02 ((
% 121.65/16.02 (notdallE) =>
% 121.65/16.02 ((
% 121.65/16.02 (exuI1) =>
% 121.65/16.02 ((
% 121.65/16.02 (exuI3) =>
% 121.65/16.02 ((
% 121.65/16.02 (exuI2) =>
% 121.65/16.02 ((
% 121.65/16.02 (inCongP) =>
% 121.65/16.02 ((
% 121.65/16.02 (in__Cong) =>
% 121.65/16.02 ((
% 121.65/16.02 (exuE3u) =>
% 121.65/16.02 ((
% 121.65/16.02 (exu__Cong) =>
% 121.65/16.02 ((
% 121.65/16.02 (setadjoin__Cong) =>
% 121.65/16.02 ((
% 121.65/16.02 (powerset__Cong) =>
% 121.65/16.02 ((
% 121.65/16.02 (setunion__Cong) =>
% 121.65/16.02 ((
% 121.65/16.02 (exuEu) =>
% 121.65/16.02 ((
% 121.65/16.02 (descr__Cong) =>
% 121.65/16.02 ((
% 121.65/16.02 (dsetconstr__Cong) =>
% 121.65/16.02 ((
% 121.65/16.02 (subsetI1) =>
% 121.65/16.02 ((
% 121.65/16.02 (eqimpsubset2) =>
% 121.65/16.02 ((
% 121.65/16.02 (eqimpsubset1) =>
% 121.65/16.02 ((
% 121.65/16.02 (subsetI2) =>
% 121.65/16.02 ((
% 121.65/16.02 (emptysetsubset) =>
% 121.65/16.02 ((
% 121.65/16.02 (subsetE) =>
% 121.65/16.02 ((
% 121.65/16.02 (subsetE2) =>
% 121.65/16.02 ((
% 121.65/16.02 (notsubsetI) =>
% 121.65/16.02 ((
% 121.65/16.02 (notequalI1) =>
% 121.65/16.02 ((
% 121.65/16.02 (notequalI2) =>
% 121.65/16.02 ((
% 121.65/16.02 (subsetRefl) =>
% 121.65/16.02 ((
% 121.65/16.02 (subsetTrans) =>
% 121.65/16.02 ((
% 121.65/16.02 (setadjoinSub) =>
% 121.65/16.02 ((
% 121.65/16.02 (setadjoinSub2) =>
% 121.65/16.02 ((
% 121.65/16.02 (subset2powerset) =>
% 121.65/16.02 ((
% 121.65/16.02 (setextsub) =>
% 121.65/16.02 ((
% 121.65/16.02 (subsetemptysetimpeq) =>
% 121.65/16.02 ((
% 121.65/16.02 (powersetI1) =>
% 121.65/16.02 ((
% 121.65/16.02 (powersetE1) =>
% 121.65/16.02 ((
% 121.65/16.02 (inPowerset) =>
% 121.65/16.02 ((
% 121.65/16.02 (powersetsubset) =>
% 121.65/16.02 ((
% 121.65/16.02 (sepInPowerset) =>
% 121.65/16.02 ((
% 121.65/16.02 (sepSubset) =>
% 121.65/16.02 ((
% 121.65/16.02 (binunionIL) =>
% 121.65/16.02 ((
% 121.65/16.02 (upairset2IR) =>
% 121.65/16.02 ((
% 121.65/16.02 (binunionIR) =>
% 121.65/16.02 ((
% 121.65/16.02 (binunionEcases) =>
% 121.65/16.02 ((
% 121.65/16.02 (binunionE) =>
% 121.65/16.02 ((
% 121.65/16.02 (binunionLsub) =>
% 121.65/16.02 ((
% 121.65/16.02 (binunionRsub) =>
% 121.65/16.02 ((
% 121.65/16.02 (binintersectI) =>
% 121.65/16.02 ((
% 121.65/16.02 (binintersectSubset5) =>
% 121.65/16.02 ((
% 121.65/16.02 (binintersectEL) =>
% 121.65/16.02 ((
% 121.65/16.02 (binintersectLsub) =>
% 121.65/16.02 ((
% 121.65/16.02 (binintersectSubset2) =>
% 121.65/16.02 ((
% 121.65/16.02 (binintersectSubset3) =>
% 121.65/16.02 ((
% 121.65/16.02 (binintersectER) =>
% 121.65/16.02 ((
% 121.65/16.02 (disjointsetsI1) =>
% 121.65/16.02 ((
% 121.65/16.02 (binintersectRsub) =>
% 121.65/16.02 ((
% 121.65/16.02 (binintersectSubset4) =>
% 121.65/16.02 ((
% 121.65/16.02 (binintersectSubset1) =>
% 121.65/16.02 ((
% 121.65/16.02 (bs114d) =>
% 121.65/16.02 ((
% 121.65/16.02 (setminusI) =>
% 121.65/16.02 ((
% 121.65/16.02 (setminusEL) =>
% 121.65/16.02 ((
% 121.65/16.02 (setminusER) =>
% 121.65/16.02 ((
% 121.65/16.02 (setminusSubset2) =>
% 121.65/16.02 ((
% 121.65/16.02 (setminusERneg) =>
% 121.65/16.02 ((
% 121.65/16.02 (setminusELneg) =>
% 121.65/16.02 ((
% 121.65/16.02 (setminusILneg) =>
% 121.65/16.02 ((
% 121.65/16.02 (setminusIRneg) =>
% 121.65/16.02 ((
% 121.65/16.02 (setminusLsub) =>
% 121.65/16.02 ((
% 121.65/16.02 (setminusSubset1) =>
% 121.65/16.02 ((
% 121.65/16.02 (symdiffE) =>
% 121.65/16.02 ((
% 121.65/16.02 (symdiffI1) =>
% 121.65/16.02 ((
% 121.65/16.02 (symdiffI2) =>
% 121.65/16.02 ((
% 121.65/16.02 (symdiffIneg1) =>
% 121.65/16.02 ((
% 121.65/16.02 (symdiffIneg2) =>
% 121.65/16.02 ((
% 121.65/16.02 (secondinupair) =>
% 121.65/16.02 ((
% 121.65/16.02 (setukpairIL) =>
% 121.65/16.02 ((
% 121.65/16.02 (setukpairIR) =>
% 121.65/16.02 ((
% 121.65/16.02 (kpairiskpair) =>
% 121.65/16.02 ((
% 121.65/16.02 (kpairp) =>
% 121.65/16.02 ((
% 121.65/16.02 (singletonsubset) =>
% 121.65/16.02 ((
% 121.65/16.02 (singletoninpowerset) =>
% 121.65/16.02 ((
% 121.65/16.02 (singletoninpowunion) =>
% 121.65/16.02 ((
% 121.65/16.02 (upairset2E) =>
% 121.65/16.02 ((
% 121.65/16.02 (upairsubunion) =>
% 121.65/16.02 ((
% 121.65/16.02 (upairinpowunion) =>
% 121.65/16.02 ((
% 121.65/16.02 (ubforcartprodlem1) =>
% 121.65/16.02 ((
% 121.65/16.02 (ubforcartprodlem2) =>
% 121.65/16.02 ((
% 121.65/16.02 (ubforcartprodlem3) =>
% 121.65/16.02 ((
% 121.65/16.02 (cartprodpairin) =>
% 121.65/16.02 ((
% 121.65/16.02 (cartprodmempair1) =>
% 121.65/16.02 ((
% 121.65/16.02 (cartprodmempair) =>
% 121.65/16.02 ((
% 121.65/16.02 (setunionE2) =>
% 121.65/16.02 ((
% 121.65/16.02 (setunionsingleton1) =>
% 121.65/16.02 ((
% 121.65/16.02 (setunionsingleton2) =>
% 121.65/16.02 ((
% 121.65/16.02 (setunionsingleton) =>
% 121.65/16.02 ((
% 121.65/16.02 (singletonprop) =>
% 121.65/16.02 ((
% 121.65/16.02 (ex1E1) =>
% 121.65/16.02 ((
% 121.65/16.02 (ex1I) =>
% 121.65/16.02 ((
% 121.65/16.02 (ex1I2) =>
% 121.65/16.02 ((
% 121.65/16.02 (singletonsuniq) =>
% 121.65/16.02 ((
% 121.65/16.02 (setukpairinjL1) =>
% 121.65/16.02 ((
% 121.65/16.02 (kfstsingleton) =>
% 121.65/16.02 ((
% 121.65/16.02 (theprop) =>
% 121.65/16.02 ((
% 121.65/16.02 (kfstpairEq) =>
% 121.65/16.02 ((
% 121.65/16.02 (cartprodfstin) =>
% 121.65/16.02 ((
% 121.65/16.02 (setukpairinjL2) =>
% 121.65/16.02 ((
% 121.65/16.02 (setukpairinjL) =>
% 121.65/16.02 ((
% 121.65/16.02 (setukpairinjR11) =>
% 121.65/16.02 ((
% 121.65/16.02 (setukpairinjR12) =>
% 121.65/16.02 ((
% 121.65/16.02 (setukpairinjR1) =>
% 121.65/16.02 ((
% 121.65/16.02 (upairequniteq) =>
% 121.65/16.02 ((
% 121.65/16.02 (setukpairinjR2) =>
% 121.65/16.02 ((
% 121.65/16.02 (setukpairinjR) =>
% 121.65/16.02 ((
% 121.65/16.02 (ksndsingleton) =>
% 121.65/16.02 ((
% 121.65/16.02 (ksndpairEq) =>
% 121.65/16.02 ((
% 121.65/16.02 (kpairsurjEq) =>
% 121.65/16.02 ((
% 121.65/16.02 (cartprodsndin) =>
% 121.65/16.02 ((
% 121.65/16.02 (cartprodpairmemEL) =>
% 121.65/16.02 ((
% 121.65/16.02 (cartprodpairmemER) =>
% 121.65/16.02 ((
% 121.65/16.02 (cartprodmempaircEq) =>
% 121.65/16.02 ((
% 121.65/16.02 (cartprodfstpairEq) =>
% 121.65/16.02 ((
% 121.65/16.02 (cartprodsndpairEq) =>
% 121.65/16.02 ((
% 121.65/16.02 (cartprodpairsurjEq) =>
% 121.65/16.02 ((
% 121.65/16.02 (dpsetconstrI) =>
% 121.65/16.02 ((
% 121.65/16.02 (dpsetconstrSub) =>
% 121.65/16.02 ((
% 121.65/16.02 (setOfPairsIsBReln) =>
% 121.65/16.02 ((
% 121.65/16.02 (dpsetconstrERa) =>
% 121.65/16.02 ((
% 121.65/16.02 (dpsetconstrEL1) =>
% 121.65/16.02 ((
% 121.65/16.02 (dpsetconstrEL2) =>
% 121.65/16.02 ((
% 121.65/16.02 (dpsetconstrER) =>
% 121.65/16.02 ((
% 121.65/16.02 (funcImageSingleton) =>
% 121.65/16.02 ((
% 121.65/16.02 (apProp) =>
% 121.65/16.02 ((
% 121.65/16.02 (app) =>
% 121.65/16.02 ((
% 121.65/16.02 (infuncsetfunc) =>
% 121.65/16.02 ((
% 121.65/16.02 (ap2p) =>
% 121.65/16.02 ((
% 121.65/16.02 (funcinfuncset) =>
% 121.65/16.02 ((
% 121.65/16.02 (lamProp) =>
% 121.65/16.02 ((
% 121.65/16.02 (lamp) =>
% 121.65/16.02 ((
% 121.65/16.02 (lam2p) =>
% 121.65/16.02 ((
% 121.65/16.02 (brelnall1) =>
% 121.65/16.02 ((
% 121.65/16.02 (brelnall2) =>
% 121.65/16.02 ((
% 121.65/16.02 (ex1E2) =>
% 121.65/16.02 ((
% 121.65/16.02 (funcGraphProp1) =>
% 121.65/16.02 ((
% 121.65/16.02 (funcGraphProp3) =>
% 121.65/16.02 ((
% 121.65/16.02 (funcGraphProp2) =>
% 121.65/16.02 ((
% 121.65/16.02 (funcextLem) =>
% 121.65/16.02 ((
% 121.65/16.02 (funcGraphProp4) =>
% 121.65/16.02 ((
% 121.65/16.02 (subbreln) =>
% 121.65/16.02 ((
% 121.65/16.02 (eqbreln) =>
% 121.65/16.02 ((
% 121.65/16.02 (funcext) =>
% 121.65/16.02 ((
% 121.65/16.02 (funcext2) =>
% 121.65/16.02 ((
% 121.65/16.02 (ap2apEq1) =>
% 121.65/16.02 ((
% 121.65/16.02 (ap2apEq2) =>
% 121.65/16.02 ((
% 121.65/16.02 (beta1) =>
% 121.65/16.02 ((
% 121.65/16.02 (eta1) =>
% 121.65/16.02 ((
% 121.65/16.02 (lam2lamEq) =>
% 121.65/16.02 ((
% 121.65/16.02 (beta2) =>
% 121.65/16.02 ((
% 121.65/16.02 (eta2) =>
% 121.65/16.02 ((
% 121.65/16.02 (iffalseProp1) =>
% 121.65/16.02 ((
% 121.65/16.02 (iffalseProp2) =>
% 121.65/16.02 ((
% 121.65/16.02 (iftrueProp1) =>
% 121.65/16.02 ((
% 121.65/16.02 (iftrueProp2) =>
% 121.65/16.02 ((
% 121.65/16.02 (ifSingleton) =>
% 121.65/16.02 ((
% 121.65/16.02 (ifp) =>
% 121.65/16.02 ((
% 121.65/16.02 (theeq) =>
% 121.65/16.02 ((
% 121.65/16.02 (iftrue) =>
% 121.65/16.02 ((
% 121.65/16.02 (iffalse) =>
% 121.65/16.02 ((
% 121.65/16.02 (iftrueorfalse) =>
% 121.65/16.02 ((
% 121.65/16.02 (binintersectT_lem) =>
% 121.65/16.02 ((
% 121.65/16.02 (binunionT_lem) =>
% 121.65/16.02 ((
% 121.65/16.02 (powersetT_lem) =>
% 121.65/16.02 ((
% 121.65/16.02 (setminusT_lem) =>
% 121.65/16.02 ((
% 121.65/16.02 (complementT_lem) =>
% 121.65/16.02 ((
% 121.65/16.02 (setextT) =>
% 121.65/16.02 ((
% 121.65/16.02 (subsetTI) =>
% 121.65/16.02 ((
% 121.65/16.02 (powersetTI1) =>
% 121.65/16.02 ((
% 121.65/16.02 (powersetTE1) =>
% 121.65/16.02 ((
% 121.65/16.02 (complementTI1) =>
% 121.65/16.02 ((
% 121.65/16.02 (complementTE1) =>
% 121.65/16.02 ((
% 121.65/16.02 (binintersectTELcontra) =>
% 121.65/16.02 ((
% 121.65/16.02 (binintersectTERcontra) =>
% 121.65/16.02 ((
% 121.65/16.02 (contrasubsetT) =>
% 121.65/16.02 ((
% 121.65/16.02 (contrasubsetT1) =>
% 121.65/16.02 ((
% 121.65/16.02 (contrasubsetT2) =>
% 121.65/16.02 ((
% 121.65/16.02 (contrasubsetT3) =>
% 121.65/16.02 ((
% 121.65/16.02 (doubleComplementI1) =>
% 121.65/16.02 ((
% 121.65/16.02 (doubleComplementE1) =>
% 121.65/16.02 ((
% 121.65/16.02 (doubleComplementSub1) =>
% 121.65/16.02 ((
% 121.65/16.02 (doubleComplementSub2) =>
% 121.65/16.02 ((
% 121.65/16.02 (doubleComplementEq) =>
% 121.65/16.02 ((
% 121.65/16.02 (complementTnotintersectT) =>
% 121.65/16.02 ((
% 121.65/16.02 (complementImpComplementIntersect) =>
% 121.65/16.02 ((
% 121.65/16.02 (complementSubsetComplementIntersect) =>
% 121.65/16.02 ((
% 121.65/16.02 (complementInPowersetComplementIntersect) =>
% 121.65/16.02 ((
% 121.65/16.02 (contraSubsetComplement) =>
% 121.65/16.02 ((
% 121.65/16.02 (complementTcontraSubset) =>
% 121.65/16.02 ((
% 121.65/16.02 (binunionTILcontra) =>
% 121.65/16.02 ((
% 121.65/16.02 (binunionTIRcontra) =>
% 121.65/16.02 ((
% 121.65/16.02 (inIntersectImpInUnion) =>
% 121.65/16.02 ((
% 121.65/16.02 (inIntersectImpInUnion2) =>
% 121.65/16.02 ((
% 121.65/16.02 (inIntersectImpInIntersectUnions) =>
% 121.65/16.02 ((
% 121.65/16.02 (intersectInPowersetIntersectUnions) =>
% 121.65/16.02 ((
% 121.65/16.02 (inComplementUnionImpNotIn1) =>
% 121.65/16.02 ((
% 121.65/16.02 (inComplementUnionImpInComplement1) =>
% 121.65/16.02 ((
% 121.65/16.02 (binunionTE) =>
% 121.65/16.02 ((
% 121.65/16.02 (binunionTEcontra) =>
% 121.65/16.02 ((
% 121.65/16.02 (demorgan2a1) =>
% 121.65/16.02 ((
% 121.65/16.02 (complementUnionInPowersetComplement) =>
% 121.65/16.02 ((
% 121.65/16.02 (demorgan2a2) =>
% 121.65/16.02 ((
% 121.65/16.02 (demorgan1a) =>
% 121.65/16.02 ((
% 121.65/16.02 (demorgan1b) =>
% 121.65/16.02 ((
% 121.65/16.02 (demorgan1) =>
% 121.65/16.02 ((
% 121.65/16.02 (demorgan2a) =>
% 121.65/16.02 ((
% 121.65/16.02 (demorgan2b2) =>
% 121.65/16.02 ((
% 121.65/16.02 (demorgan2b) =>
% 121.65/16.02 ((
% 121.65/16.02 (demorgan2) =>
% 121.65/16.02 ((
% 121.65/16.02 (woz13rule0) =>
% 121.65/16.02 ((
% 121.65/16.02 (woz13rule1) =>
% 121.65/16.02 ((
% 121.65/16.02 (woz13rule2) =>
% 121.65/16.02 ((
% 121.65/16.02 (woz13rule3) =>
% 121.65/16.02 ((
% 121.65/16.02 (woz13rule4) =>
% 121.65/16.02 ((
% 121.65/16.02 (woz1_1) =>
% 121.65/16.02 ((
% 121.65/16.02 (woz1_2) =>
% 121.65/16.02 ((
% 121.65/16.02 (woz1_3) =>
% 121.65/16.02 ((
% 121.65/16.02 (woz1_4) =>
% 121.65/16.02 ((
% 121.65/16.02 (woz1_5) =>
% 121.65/16.02 ((
% 121.65/16.02 (breln1all2) =>
% 121.65/16.02 ((
% 121.65/16.02 (breln1SetBreln1) =>
% 121.65/16.02 ((
% 121.65/16.02 (choice2fnsingleton) =>
% 121.65/16.02 ((
% 121.65/16.02 (setOfPairsIsBReln1) =>
% 121.65/16.02 ((
% 121.65/16.02 (breln1all1) =>
% 121.65/16.02 ((
% 121.65/16.02 (subbreln1) =>
% 121.65/16.02 ((
% 121.65/16.02 (eqbreln1) =>
% 121.65/16.02 ((
% 121.65/16.02 (breln1invprop) =>
% 121.65/16.02 ((
% 121.65/16.02 (breln1invI) =>
% 121.65/16.02 ((
% 121.65/16.02 (breln1invE) =>
% 121.65/16.02 ((
% 121.65/16.02 (breln1compprop) =>
% 121.65/16.02 ((
% 121.65/16.02 (breln1compI) =>
% 121.65/16.02 ((
% 121.65/16.02 (breln1compE) =>
% 121.65/16.02 ((
% 121.65/16.02 (breln1compEex) =>
% 121.65/16.02 ((
% 121.65/16.02 (breln1unionprop) =>
% 121.65/16.02 ((
% 121.65/16.02 (breln1unionIL) =>
% 121.65/16.02 ((
% 121.65/16.02 (breln1unionIR) =>
% 121.65/16.02 ((
% 121.65/16.02 (breln1unionI) =>
% 121.65/16.02 ((
% 121.65/16.02 (breln1unionE) =>
% 121.65/16.02 ((
% 121.65/16.02 (breln1unionEcases) =>
% 121.65/16.02 ((
% 121.65/16.02 (breln1unionCommutes) =>
% 121.65/16.02 ((
% 121.65/16.02 (woz2Ex) =>
% 121.65/16.02 ((
% 121.65/16.02 (woz2W) =>
% 121.65/16.02 ((
% 121.65/16.02 (woz2A) =>
% 121.65/16.02 ((
% 121.65/16.02 (woz2B) =>
% 121.65/16.02 ((
% 121.65/16.02 (image1Ex) =>
% 121.65/16.02 ((
% 121.65/16.02 (image1Ex1) =>
% 121.65/16.02 ((
% 121.65/16.02 (image1Equiv) =>
% 121.65/16.02 ((
% 121.65/16.02 (image1E) =>
% 121.65/16.02 ((
% 121.65/16.02 (image1I) =>
% 121.65/16.02 ((
% 121.65/16.02 (injFuncInInjFuncSet) =>
% 121.65/16.02 ((
% 121.65/16.02 (!!) @ (
% 121.65/16.02 (('#B') @ (
% 121.65/16.02 !!) @
% 121.65/16.02 (
% 121.65/16.02 (
% 121.65/16.02 ('#B') @ (
% 121.65/16.02 (
% 121.65/16.02 ('#B') @ (
% 121.65/16.02 !!))) @
% 121.65/16.02 (
% 121.65/16.02 (
% 121.65/16.02 ('#S') @ (
% 121.65/16.02 (
% 121.65/16.02 ('#B') @ (
% 121.65/16.02 '#S') @
% 121.65/16.02 (
% 121.65/16.02 (
% 121.65/16.02 ('#B') @ (
% 121.65/16.02 (
% 121.65/16.02 ('#B') @ (
% 121.65/16.02 '#S'))) @
% 121.65/16.02 (
% 121.65/16.02 (
% 121.65/16.02 ('#B') @ (
% 121.65/16.02 (
% 121.65/16.02 ('#B') @ (
% 121.65/16.02 (
% 121.65/16.02 ('#B') @ (
% 121.65/16.02 =>))))) @
% 121.65/16.02 (
% 121.65/16.02 (
% 121.65/16.02 ('#B') @ (
% 121.65/16.02 (
% 121.65/16.02 ('#B') @ (
% 121.65/16.02 (
% 121.65/16.02 ('#C') @ in)))) @
% 121.65/16.02 injFuncSet)))))))) @
% 121.65/16.02 (
% 121.65/16.02 (
% 121.65/16.02 ('#B') @ (
% 121.65/16.02 (
% 121.65/16.02 ('#B') @ (
% 121.65/16.02 (
% 121.65/16.02 ('#C') @ in)))) @
% 121.65/16.02 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 121.65/16.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl46])).
% 121.65/16.02 thf(zip_derived_cl58, plain,
% 121.65/16.02 (~ (((wellorderingAx) =>
% 121.65/16.02 (((descrp) =>
% 121.65/16.02 (((dsetconstrI) =>
% 121.65/16.02 (((dsetconstrEL) =>
% 121.65/16.02 (((dsetconstrER) =>
% 121.65/16.02 (((exuE1) =>
% 121.65/16.02 (((prop2setE) =>
% 121.65/16.02 (((emptysetE) =>
% 121.65/16.02 (((emptysetimpfalse) =>
% 121.65/16.02 (((notinemptyset) =>
% 121.65/16.02 (((exuE3e) =>
% 121.65/16.02 (((setext) =>
% 121.65/16.02 (((emptyI) =>
% 121.65/16.02 (((noeltsimpempty) =>
% 121.65/16.02 (((setbeta) =>
% 121.65/16.02 (((nonemptyE1) =>
% 121.65/16.02 (((nonemptyI) =>
% 121.65/16.02 (((nonemptyI1) =>
% 121.65/16.02 (((setadjoinIL) =>
% 121.65/16.02 (((in @ emptyset @
% 121.65/16.02 (setadjoin @ emptyset @
% 121.65/16.02 emptyset)) =>
% 121.65/16.02 (((setadjoinIR) =>
% 121.65/16.02 (((setadjoinE) =>
% 121.65/16.02 (((setadjoinOr) =>
% 121.65/16.02 (((setoftrueEq) =>
% 121.65/16.02 (((powersetI) =>
% 121.65/16.02 (((emptyinPowerset) =>
% 121.65/16.02 (((emptyInPowerset) =>
% 121.65/16.02 (((powersetE) =>
% 121.65/16.02 (((setunionI) =>
% 121.65/16.02 (((setunionE) =>
% 121.65/16.02 ((
% 121.65/16.02 (subPowSU) =>
% 121.65/16.02 ((
% 121.65/16.02 (exuE2) =>
% 121.65/16.02 ((
% 121.65/16.02 (nonemptyImpWitness) =>
% 121.65/16.02 ((
% 121.65/16.02 (uniqinunit) =>
% 121.65/16.02 ((
% 121.65/16.02 (notinsingleton) =>
% 121.65/16.02 ((
% 121.65/16.02 (eqinunit) =>
% 121.65/16.02 ((
% 121.65/16.02 (singletonsswitch) =>
% 121.65/16.02 ((
% 121.65/16.02 (upairsetE) =>
% 121.65/16.02 ((
% 121.65/16.02 (upairsetIL) =>
% 121.65/16.02 ((
% 121.65/16.02 (upairsetIR) =>
% 121.65/16.02 ((
% 121.65/16.02 (emptyE1) =>
% 121.65/16.02 ((
% 121.65/16.02 (vacuousDall) =>
% 121.65/16.02 ((
% 121.65/16.02 (quantDeMorgan1) =>
% 121.65/16.02 ((
% 121.65/16.02 (quantDeMorgan2) =>
% 121.65/16.02 ((
% 121.65/16.02 (quantDeMorgan3) =>
% 121.65/16.02 ((
% 121.65/16.02 (quantDeMorgan4) =>
% 121.65/16.02 ((
% 121.65/16.02 (prop2setI) =>
% 121.65/16.02 ((
% 121.65/16.02 (prop2set2propI) =>
% 121.65/16.02 ((
% 121.65/16.02 (notdexE) =>
% 121.65/16.02 ((
% 121.65/16.02 (notdallE) =>
% 121.65/16.02 ((
% 121.65/16.02 (exuI1) =>
% 121.65/16.02 ((
% 121.65/16.02 (exuI3) =>
% 121.65/16.02 ((
% 121.65/16.02 (exuI2) =>
% 121.65/16.02 ((
% 121.65/16.02 (inCongP) =>
% 121.65/16.02 ((
% 121.65/16.02 (in__Cong) =>
% 121.65/16.02 ((
% 121.65/16.02 (exuE3u) =>
% 121.65/16.02 ((
% 121.65/16.02 (exu__Cong) =>
% 121.65/16.02 ((
% 121.65/16.02 (setadjoin__Cong) =>
% 121.65/16.02 ((
% 121.65/16.02 (powerset__Cong) =>
% 121.65/16.02 ((
% 121.65/16.02 (setunion__Cong) =>
% 121.65/16.02 ((
% 121.65/16.02 (exuEu) =>
% 121.65/16.02 ((
% 121.65/16.02 (descr__Cong) =>
% 121.65/16.02 ((
% 121.65/16.02 (dsetconstr__Cong) =>
% 121.65/16.02 ((
% 121.65/16.02 (subsetI1) =>
% 121.65/16.02 ((
% 121.65/16.02 (eqimpsubset2) =>
% 121.65/16.02 ((
% 121.65/16.02 (eqimpsubset1) =>
% 121.65/16.02 ((
% 121.65/16.02 (subsetI2) =>
% 121.65/16.02 ((
% 121.65/16.02 (emptysetsubset) =>
% 121.65/16.02 ((
% 121.65/16.02 (subsetE) =>
% 121.65/16.02 ((
% 121.65/16.02 (subsetE2) =>
% 121.65/16.02 ((
% 121.65/16.02 (notsubsetI) =>
% 121.65/16.02 ((
% 121.65/16.02 (notequalI1) =>
% 121.65/16.02 ((
% 121.65/16.02 (notequalI2) =>
% 121.65/16.02 ((
% 121.65/16.02 (subsetRefl) =>
% 121.65/16.02 ((
% 121.65/16.02 (subsetTrans) =>
% 121.65/16.02 ((
% 121.65/16.02 (setadjoinSub) =>
% 121.65/16.02 ((
% 121.65/16.02 (setadjoinSub2) =>
% 121.65/16.02 ((
% 121.65/16.02 (subset2powerset) =>
% 121.65/16.02 ((
% 121.65/16.02 (setextsub) =>
% 121.65/16.02 ((
% 121.65/16.02 (subsetemptysetimpeq) =>
% 121.65/16.02 ((
% 121.65/16.02 (powersetI1) =>
% 121.65/16.02 ((
% 121.65/16.02 (powersetE1) =>
% 121.65/16.02 ((
% 121.65/16.02 (inPowerset) =>
% 121.65/16.02 ((
% 121.65/16.02 (powersetsubset) =>
% 121.65/16.02 ((
% 121.65/16.02 (sepInPowerset) =>
% 121.65/16.02 ((
% 121.65/16.02 (sepSubset) =>
% 121.65/16.02 ((
% 121.65/16.02 (binunionIL) =>
% 121.65/16.02 ((
% 121.65/16.02 (upairset2IR) =>
% 121.65/16.02 ((
% 121.65/16.02 (binunionIR) =>
% 121.65/16.02 ((
% 121.65/16.02 (binunionEcases) =>
% 121.65/16.02 ((
% 121.65/16.02 (binunionE) =>
% 121.65/16.02 ((
% 121.65/16.02 (binunionLsub) =>
% 121.65/16.02 ((
% 121.65/16.02 (binunionRsub) =>
% 121.65/16.02 ((
% 121.65/16.02 (binintersectI) =>
% 121.65/16.02 ((
% 121.65/16.02 (binintersectSubset5) =>
% 121.65/16.02 ((
% 121.65/16.02 (binintersectEL) =>
% 121.65/16.02 ((
% 121.65/16.02 (binintersectLsub) =>
% 121.65/16.02 ((
% 121.65/16.02 (binintersectSubset2) =>
% 121.65/16.02 ((
% 121.65/16.02 (binintersectSubset3) =>
% 121.65/16.02 ((
% 121.65/16.02 (binintersectER) =>
% 121.65/16.02 ((
% 121.65/16.02 (disjointsetsI1) =>
% 121.65/16.02 ((
% 121.65/16.02 (binintersectRsub) =>
% 121.65/16.02 ((
% 121.65/16.02 (binintersectSubset4) =>
% 121.65/16.02 ((
% 121.65/16.02 (binintersectSubset1) =>
% 121.65/16.02 ((
% 121.65/16.02 (bs114d) =>
% 121.65/16.02 ((
% 121.65/16.02 (setminusI) =>
% 121.65/16.02 ((
% 121.65/16.02 (setminusEL) =>
% 121.65/16.02 ((
% 121.65/16.02 (setminusER) =>
% 121.65/16.02 ((
% 121.65/16.02 (setminusSubset2) =>
% 121.65/16.02 ((
% 121.65/16.02 (setminusERneg) =>
% 121.65/16.02 ((
% 121.65/16.02 (setminusELneg) =>
% 121.65/16.02 ((
% 121.65/16.02 (setminusILneg) =>
% 121.65/16.02 ((
% 121.65/16.02 (setminusIRneg) =>
% 121.65/16.02 ((
% 121.65/16.02 (setminusLsub) =>
% 121.65/16.02 ((
% 121.65/16.02 (setminusSubset1) =>
% 121.65/16.02 ((
% 121.65/16.02 (symdiffE) =>
% 121.65/16.02 ((
% 121.65/16.02 (symdiffI1) =>
% 121.65/16.02 ((
% 121.65/16.02 (symdiffI2) =>
% 121.65/16.02 ((
% 121.65/16.02 (symdiffIneg1) =>
% 121.65/16.02 ((
% 121.65/16.02 (symdiffIneg2) =>
% 121.65/16.02 ((
% 121.65/16.02 (secondinupair) =>
% 121.65/16.02 ((
% 121.65/16.02 (setukpairIL) =>
% 121.65/16.02 ((
% 121.65/16.02 (setukpairIR) =>
% 121.65/16.02 ((
% 121.65/16.02 (kpairiskpair) =>
% 121.65/16.02 ((
% 121.65/16.02 (kpairp) =>
% 121.65/16.02 ((
% 121.65/16.02 (singletonsubset) =>
% 121.65/16.02 ((
% 121.65/16.02 (singletoninpowerset) =>
% 121.65/16.02 ((
% 121.65/16.02 (singletoninpowunion) =>
% 121.65/16.02 ((
% 121.65/16.02 (upairset2E) =>
% 121.65/16.02 ((
% 121.65/16.02 (upairsubunion) =>
% 121.65/16.02 ((
% 121.65/16.02 (upairinpowunion) =>
% 121.65/16.02 ((
% 121.65/16.02 (ubforcartprodlem1) =>
% 121.65/16.02 ((
% 121.65/16.02 (ubforcartprodlem2) =>
% 121.65/16.02 ((
% 121.65/16.02 (ubforcartprodlem3) =>
% 121.65/16.02 ((
% 121.65/16.02 (cartprodpairin) =>
% 121.65/16.02 ((
% 121.65/16.02 (cartprodmempair1) =>
% 121.65/16.02 ((
% 121.65/16.02 (cartprodmempair) =>
% 121.65/16.02 ((
% 121.65/16.02 (setunionE2) =>
% 121.65/16.02 ((
% 121.65/16.02 (setunionsingleton1) =>
% 121.65/16.02 ((
% 121.65/16.02 (setunionsingleton2) =>
% 121.65/16.02 ((
% 121.65/16.02 (setunionsingleton) =>
% 121.65/16.02 ((
% 121.65/16.02 (singletonprop) =>
% 121.65/16.02 ((
% 121.65/16.02 (ex1E1) =>
% 121.65/16.02 ((
% 121.65/16.02 (ex1I) =>
% 121.65/16.02 ((
% 121.65/16.02 (ex1I2) =>
% 121.65/16.02 ((
% 121.65/16.02 (singletonsuniq) =>
% 121.65/16.02 ((
% 121.65/16.02 (setukpairinjL1) =>
% 121.65/16.02 ((
% 121.65/16.02 (kfstsingleton) =>
% 121.65/16.02 ((
% 121.65/16.02 (theprop) =>
% 121.65/16.02 ((
% 121.65/16.02 (kfstpairEq) =>
% 121.65/16.02 ((
% 121.65/16.02 (cartprodfstin) =>
% 121.65/16.02 ((
% 121.65/16.02 (setukpairinjL2) =>
% 121.65/16.02 ((
% 121.65/16.02 (setukpairinjL) =>
% 121.65/16.02 ((
% 121.65/16.02 (setukpairinjR11) =>
% 121.65/16.02 ((
% 121.65/16.02 (setukpairinjR12) =>
% 121.65/16.02 ((
% 121.65/16.02 (setukpairinjR1) =>
% 121.65/16.02 ((
% 121.65/16.02 (upairequniteq) =>
% 121.65/16.02 ((
% 121.65/16.02 (setukpairinjR2) =>
% 121.65/16.02 ((
% 121.65/16.02 (setukpairinjR) =>
% 121.65/16.02 ((
% 121.65/16.02 (ksndsingleton) =>
% 121.65/16.02 ((
% 121.65/16.02 (ksndpairEq) =>
% 121.65/16.02 ((
% 121.65/16.02 (kpairsurjEq) =>
% 121.65/16.02 ((
% 121.65/16.02 (cartprodsndin) =>
% 121.65/16.02 ((
% 121.65/16.02 (cartprodpairmemEL) =>
% 121.65/16.02 ((
% 121.65/16.02 (cartprodpairmemER) =>
% 121.65/16.02 ((
% 121.65/16.02 (cartprodmempaircEq) =>
% 121.65/16.02 ((
% 121.65/16.02 (cartprodfstpairEq) =>
% 121.65/16.02 ((
% 121.65/16.02 (cartprodsndpairEq) =>
% 121.65/16.02 ((
% 121.65/16.02 (cartprodpairsurjEq) =>
% 121.65/16.02 ((
% 121.65/16.02 (dpsetconstrI) =>
% 121.65/16.02 ((
% 121.65/16.02 (dpsetconstrSub) =>
% 121.65/16.02 ((
% 121.65/16.02 (setOfPairsIsBReln) =>
% 121.65/16.02 ((
% 121.65/16.02 (dpsetconstrERa) =>
% 121.65/16.02 ((
% 121.65/16.02 (dpsetconstrEL1) =>
% 121.65/16.02 ((
% 121.65/16.02 (dpsetconstrEL2) =>
% 121.65/16.02 ((
% 121.65/16.02 (dpsetconstrER) =>
% 121.65/16.02 ((
% 121.65/16.02 (funcImageSingleton) =>
% 121.65/16.02 ((
% 121.65/16.02 (apProp) =>
% 121.65/16.02 ((
% 121.65/16.02 (app) =>
% 121.65/16.02 ((
% 121.65/16.02 (infuncsetfunc) =>
% 121.65/16.02 ((
% 121.65/16.02 (ap2p) =>
% 121.65/16.02 ((
% 121.65/16.02 (funcinfuncset) =>
% 121.65/16.02 ((
% 121.65/16.02 (lamProp) =>
% 121.65/16.02 ((
% 121.65/16.02 (lamp) =>
% 121.65/16.02 ((
% 121.65/16.02 (lam2p) =>
% 121.65/16.02 ((
% 121.65/16.02 (brelnall1) =>
% 121.65/16.02 ((
% 121.65/16.02 (brelnall2) =>
% 121.65/16.02 ((
% 121.65/16.02 (ex1E2) =>
% 121.65/16.02 ((
% 121.65/16.02 (funcGraphProp1) =>
% 121.65/16.02 ((
% 121.65/16.02 (funcGraphProp3) =>
% 121.65/16.02 ((
% 121.65/16.02 (funcGraphProp2) =>
% 121.65/16.02 ((
% 121.65/16.02 (funcextLem) =>
% 121.65/16.02 ((
% 121.65/16.02 (funcGraphProp4) =>
% 121.65/16.02 ((
% 121.65/16.02 (subbreln) =>
% 121.65/16.02 ((
% 121.65/16.02 (eqbreln) =>
% 121.65/16.02 ((
% 121.65/16.02 (funcext) =>
% 121.65/16.02 ((
% 121.65/16.02 (funcext2) =>
% 121.65/16.02 ((
% 121.65/16.02 (ap2apEq1) =>
% 121.65/16.02 ((
% 121.65/16.02 (ap2apEq2) =>
% 121.65/16.02 ((
% 121.65/16.02 (beta1) =>
% 121.65/16.02 ((
% 121.65/16.02 (eta1) =>
% 121.65/16.02 ((
% 121.65/16.02 (lam2lamEq) =>
% 121.65/16.02 ((
% 121.65/16.02 (beta2) =>
% 121.65/16.02 ((
% 121.65/16.02 (eta2) =>
% 121.65/16.02 ((
% 121.65/16.02 (iffalseProp1) =>
% 121.65/16.02 ((
% 121.65/16.02 (iffalseProp2) =>
% 121.65/16.02 ((
% 121.65/16.02 (iftrueProp1) =>
% 121.65/16.02 ((
% 121.65/16.02 (iftrueProp2) =>
% 121.65/16.02 ((
% 121.65/16.02 (ifSingleton) =>
% 121.65/16.02 ((
% 121.65/16.02 (ifp) =>
% 121.65/16.02 ((
% 121.65/16.02 (theeq) =>
% 121.65/16.02 ((
% 121.65/16.02 (iftrue) =>
% 121.65/16.02 ((
% 121.65/16.02 (iffalse) =>
% 121.65/16.02 ((
% 121.65/16.02 (iftrueorfalse) =>
% 121.65/16.02 ((
% 121.65/16.02 (binintersectT_lem) =>
% 121.65/16.02 ((
% 121.65/16.02 (binunionT_lem) =>
% 121.65/16.02 ((
% 121.65/16.02 (powersetT_lem) =>
% 121.65/16.02 ((
% 121.65/16.02 (setminusT_lem) =>
% 121.65/16.02 ((
% 121.65/16.02 (complementT_lem) =>
% 121.65/16.02 ((
% 121.65/16.02 (setextT) =>
% 121.65/16.02 ((
% 121.65/16.02 (subsetTI) =>
% 121.65/16.02 ((
% 121.65/16.02 (powersetTI1) =>
% 121.65/16.02 ((
% 121.65/16.02 (powersetTE1) =>
% 121.65/16.02 ((
% 121.65/16.02 (complementTI1) =>
% 121.65/16.02 ((
% 121.65/16.02 (complementTE1) =>
% 121.65/16.02 ((
% 121.65/16.02 (binintersectTELcontra) =>
% 121.65/16.02 ((
% 121.65/16.02 (binintersectTERcontra) =>
% 121.65/16.02 ((
% 121.65/16.02 (contrasubsetT) =>
% 121.65/16.02 ((
% 121.65/16.02 (contrasubsetT1) =>
% 121.65/16.02 ((
% 121.65/16.02 (contrasubsetT2) =>
% 121.65/16.02 ((
% 121.65/16.02 (contrasubsetT3) =>
% 121.65/16.02 ((
% 121.65/16.02 (doubleComplementI1) =>
% 121.65/16.02 ((
% 121.65/16.02 (doubleComplementE1) =>
% 121.65/16.02 ((
% 121.65/16.02 (doubleComplementSub1) =>
% 121.65/16.02 ((
% 121.65/16.02 (doubleComplementSub2) =>
% 121.65/16.02 ((
% 121.65/16.02 (doubleComplementEq) =>
% 121.65/16.02 ((
% 121.65/16.02 (complementTnotintersectT) =>
% 121.65/16.02 ((
% 121.65/16.02 (complementImpComplementIntersect) =>
% 121.65/16.02 ((
% 121.65/16.02 (complementSubsetComplementIntersect) =>
% 121.65/16.02 ((
% 121.65/16.02 (complementInPowersetComplementIntersect) =>
% 121.65/16.02 ((
% 121.65/16.02 (contraSubsetComplement) =>
% 121.65/16.02 ((
% 121.65/16.02 (complementTcontraSubset) =>
% 121.65/16.02 ((
% 121.65/16.02 (binunionTILcontra) =>
% 121.65/16.02 ((
% 121.65/16.02 (binunionTIRcontra) =>
% 121.65/16.02 ((
% 121.65/16.02 (inIntersectImpInUnion) =>
% 121.65/16.02 ((
% 121.65/16.02 (inIntersectImpInUnion2) =>
% 121.65/16.02 ((
% 121.65/16.02 (inIntersectImpInIntersectUnions) =>
% 121.65/16.02 ((
% 121.65/16.02 (intersectInPowersetIntersectUnions) =>
% 121.65/16.02 ((
% 121.65/16.02 (inComplementUnionImpNotIn1) =>
% 121.65/16.02 ((
% 121.65/16.02 (inComplementUnionImpInComplement1) =>
% 121.65/16.02 ((
% 121.65/16.02 (binunionTE) =>
% 121.65/16.02 ((
% 121.65/16.02 (binunionTEcontra) =>
% 121.65/16.02 ((
% 121.65/16.02 (demorgan2a1) =>
% 121.65/16.02 ((
% 121.65/16.02 (complementUnionInPowersetComplement) =>
% 121.65/16.02 ((
% 121.65/16.02 (demorgan2a2) =>
% 121.65/16.02 ((
% 121.65/16.02 (demorgan1a) =>
% 121.65/16.02 ((
% 121.65/16.02 (demorgan1b) =>
% 121.65/16.02 ((
% 121.65/16.02 (demorgan1) =>
% 121.65/16.02 ((
% 121.65/16.02 (demorgan2a) =>
% 121.65/16.02 ((
% 121.65/16.02 (demorgan2b2) =>
% 121.65/16.02 ((
% 121.65/16.02 (demorgan2b) =>
% 121.65/16.02 ((
% 121.65/16.02 (demorgan2) =>
% 121.65/16.02 ((
% 121.65/16.02 (woz13rule0) =>
% 121.65/16.02 ((
% 121.65/16.02 (woz13rule1) =>
% 121.65/16.02 ((
% 121.65/16.02 (woz13rule2) =>
% 121.65/16.02 ((
% 121.65/16.02 (woz13rule3) =>
% 121.65/16.02 ((
% 121.65/16.02 (woz13rule4) =>
% 121.65/16.02 ((
% 121.65/16.02 (woz1_1) =>
% 121.65/16.02 ((
% 121.65/16.02 (woz1_2) =>
% 121.65/16.02 ((
% 121.65/16.02 (woz1_3) =>
% 121.65/16.02 ((
% 121.65/16.02 (woz1_4) =>
% 121.65/16.02 ((
% 121.65/16.02 (woz1_5) =>
% 121.65/16.02 ((
% 121.65/16.02 (breln1all2) =>
% 121.65/16.02 ((
% 121.65/16.02 (breln1SetBreln1) =>
% 121.65/16.02 ((
% 121.65/16.02 (choice2fnsingleton) =>
% 121.65/16.02 ((
% 121.65/16.02 (setOfPairsIsBReln1) =>
% 121.65/16.02 ((
% 121.65/16.02 (breln1all1) =>
% 121.65/16.02 ((
% 121.65/16.02 (subbreln1) =>
% 121.65/16.02 ((
% 121.65/16.02 (eqbreln1) =>
% 121.65/16.02 ((
% 121.65/16.02 (breln1invprop) =>
% 121.65/16.02 ((
% 121.65/16.02 (breln1invI) =>
% 121.65/16.02 ((
% 121.65/16.02 (breln1invE) =>
% 121.65/16.02 ((
% 121.65/16.02 (breln1compprop) =>
% 121.65/16.02 ((
% 121.65/16.02 (breln1compI) =>
% 121.65/16.02 ((
% 121.65/16.02 (breln1compE) =>
% 121.65/16.02 ((
% 121.65/16.02 (breln1compEex) =>
% 121.65/16.02 ((
% 121.65/16.02 (breln1unionprop) =>
% 121.65/16.02 ((
% 121.65/16.02 (breln1unionIL) =>
% 121.65/16.02 ((
% 121.65/16.02 (breln1unionIR) =>
% 121.65/16.02 ((
% 121.65/16.02 (breln1unionI) =>
% 121.65/16.02 ((
% 121.65/16.02 (breln1unionE) =>
% 121.65/16.02 ((
% 121.65/16.02 (breln1unionEcases) =>
% 121.65/16.02 ((
% 121.65/16.02 (breln1unionCommutes) =>
% 121.65/16.02 ((
% 121.65/16.02 (woz2Ex) =>
% 121.65/16.02 ((
% 121.65/16.02 (woz2W) =>
% 121.65/16.02 ((
% 121.65/16.02 (woz2A) =>
% 121.65/16.02 ((
% 121.65/16.02 (woz2B) =>
% 121.65/16.02 ((
% 121.65/16.02 (image1Ex) =>
% 121.65/16.02 ((
% 121.65/16.02 (image1Ex1) =>
% 121.65/16.02 ((
% 121.65/16.02 (image1Equiv) =>
% 121.65/16.02 ((
% 121.65/16.02 (image1E) =>
% 121.65/16.02 ((
% 121.65/16.02 (image1I) =>
% 121.65/16.02 ((
% 121.65/16.02 (injFuncInInjFuncSet) =>
% 121.65/16.02 ((
% 121.65/16.02 (!!) @ (
% 121.65/16.02 (('#B') @ (
% 121.65/16.02 !!) @
% 121.65/16.02 (
% 121.65/16.02 (
% 121.65/16.02 ('#B') @ (
% 121.65/16.02 (
% 121.65/16.02 ('#B') @ (
% 121.65/16.02 !!))) @
% 121.65/16.02 (
% 121.65/16.02 (
% 121.65/16.02 ('#S') @ (
% 121.65/16.02 (
% 121.65/16.02 ('#B') @ (
% 121.65/16.02 '#S') @
% 121.65/16.02 (
% 121.65/16.02 (
% 121.65/16.02 ('#B') @ (
% 121.65/16.02 (
% 121.65/16.02 ('#B') @ (
% 121.65/16.02 '#S'))) @
% 121.65/16.02 (
% 121.65/16.02 (
% 121.65/16.02 ('#B') @ (
% 121.65/16.02 (
% 121.65/16.02 ('#B') @ (
% 121.65/16.02 (
% 121.65/16.02 ('#B') @ (
% 121.65/16.02 =>))))) @
% 121.65/16.02 (
% 121.65/16.02 (
% 121.65/16.02 ('#B') @ (
% 121.65/16.02 (
% 121.65/16.02 ('#B') @ (
% 121.65/16.02 (
% 121.65/16.02 ('#C') @ in)))) @
% 121.65/16.02 injFuncSet)))))))) @
% 121.65/16.02 (
% 121.65/16.02 (
% 121.65/16.02 ('#B') @ (
% 121.65/16.02 (
% 121.65/16.02 ('#B') @ (
% 121.65/16.02 (
% 121.65/16.02 ('#C') @ in)))) @
% 121.65/16.02 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 121.65/16.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl52])).
% 121.65/16.02 thf(zip_derived_cl64, plain,
% 121.65/16.02 (~ (((descrp) =>
% 121.65/16.02 (((dsetconstrI) =>
% 121.65/16.02 (((dsetconstrEL) =>
% 121.65/16.02 (((dsetconstrER) =>
% 121.65/16.02 (((exuE1) =>
% 121.65/16.02 (((prop2setE) =>
% 121.65/16.02 (((emptysetE) =>
% 121.65/16.02 (((emptysetimpfalse) =>
% 121.65/16.02 (((notinemptyset) =>
% 121.65/16.02 (((exuE3e) =>
% 121.65/16.02 (((setext) =>
% 121.65/16.02 (((emptyI) =>
% 121.65/16.02 (((noeltsimpempty) =>
% 121.65/16.02 (((setbeta) =>
% 121.65/16.02 (((nonemptyE1) =>
% 121.65/16.02 (((nonemptyI) =>
% 121.65/16.02 (((nonemptyI1) =>
% 121.65/16.02 (((setadjoinIL) =>
% 121.65/16.02 (((in @ emptyset @
% 121.65/16.02 (setadjoin @ emptyset @ emptyset)) =>
% 121.65/16.02 (((setadjoinIR) =>
% 121.65/16.02 (((setadjoinE) =>
% 121.65/16.02 (((setadjoinOr) =>
% 121.65/16.02 (((setoftrueEq) =>
% 121.65/16.02 (((powersetI) =>
% 121.65/16.02 (((emptyinPowerset) =>
% 121.65/16.02 (((emptyInPowerset) =>
% 121.65/16.02 (((powersetE) =>
% 121.65/16.02 (((setunionI) =>
% 121.65/16.02 (((setunionE) =>
% 121.65/16.02 (((subPowSU) =>
% 121.65/16.02 ((
% 121.65/16.02 (exuE2) =>
% 121.65/16.02 ((
% 121.65/16.02 (nonemptyImpWitness) =>
% 121.65/16.02 ((
% 121.65/16.02 (uniqinunit) =>
% 121.65/16.02 ((
% 121.65/16.02 (notinsingleton) =>
% 121.65/16.02 ((
% 121.65/16.02 (eqinunit) =>
% 121.65/16.02 ((
% 121.65/16.02 (singletonsswitch) =>
% 121.65/16.02 ((
% 121.65/16.02 (upairsetE) =>
% 121.65/16.02 ((
% 121.65/16.02 (upairsetIL) =>
% 121.65/16.02 ((
% 121.65/16.02 (upairsetIR) =>
% 121.65/16.02 ((
% 121.65/16.02 (emptyE1) =>
% 121.65/16.02 ((
% 121.65/16.02 (vacuousDall) =>
% 121.65/16.02 ((
% 121.65/16.02 (quantDeMorgan1) =>
% 121.65/16.02 ((
% 121.65/16.02 (quantDeMorgan2) =>
% 121.65/16.02 ((
% 121.65/16.02 (quantDeMorgan3) =>
% 121.65/16.02 ((
% 121.65/16.02 (quantDeMorgan4) =>
% 121.65/16.02 ((
% 121.65/16.02 (prop2setI) =>
% 121.65/16.02 ((
% 121.65/16.02 (prop2set2propI) =>
% 121.65/16.02 ((
% 121.65/16.02 (notdexE) =>
% 121.65/16.02 ((
% 121.65/16.02 (notdallE) =>
% 121.65/16.02 ((
% 121.65/16.02 (exuI1) =>
% 121.65/16.02 ((
% 121.65/16.02 (exuI3) =>
% 121.65/16.02 ((
% 121.65/16.02 (exuI2) =>
% 121.65/16.02 ((
% 121.65/16.02 (inCongP) =>
% 121.65/16.02 ((
% 121.65/16.02 (in__Cong) =>
% 121.65/16.02 ((
% 121.65/16.02 (exuE3u) =>
% 121.65/16.02 ((
% 121.65/16.02 (exu__Cong) =>
% 121.65/16.02 ((
% 121.65/16.02 (setadjoin__Cong) =>
% 121.65/16.02 ((
% 121.65/16.02 (powerset__Cong) =>
% 121.65/16.02 ((
% 121.65/16.02 (setunion__Cong) =>
% 121.65/16.02 ((
% 121.65/16.02 (exuEu) =>
% 121.65/16.02 ((
% 121.65/16.02 (descr__Cong) =>
% 121.65/16.02 ((
% 121.65/16.02 (dsetconstr__Cong) =>
% 121.65/16.02 ((
% 121.65/16.02 (subsetI1) =>
% 121.65/16.02 ((
% 121.65/16.02 (eqimpsubset2) =>
% 121.65/16.02 ((
% 121.65/16.02 (eqimpsubset1) =>
% 121.65/16.02 ((
% 121.65/16.02 (subsetI2) =>
% 121.65/16.02 ((
% 121.65/16.02 (emptysetsubset) =>
% 121.65/16.02 ((
% 121.65/16.02 (subsetE) =>
% 121.65/16.02 ((
% 121.65/16.02 (subsetE2) =>
% 121.65/16.02 ((
% 121.65/16.02 (notsubsetI) =>
% 121.65/16.02 ((
% 121.65/16.02 (notequalI1) =>
% 121.65/16.02 ((
% 121.65/16.02 (notequalI2) =>
% 121.65/16.02 ((
% 121.65/16.02 (subsetRefl) =>
% 121.65/16.02 ((
% 121.65/16.02 (subsetTrans) =>
% 121.65/16.02 ((
% 121.65/16.02 (setadjoinSub) =>
% 121.65/16.02 ((
% 121.65/16.02 (setadjoinSub2) =>
% 121.65/16.02 ((
% 121.65/16.02 (subset2powerset) =>
% 121.65/16.02 ((
% 121.65/16.02 (setextsub) =>
% 121.65/16.02 ((
% 121.65/16.02 (subsetemptysetimpeq) =>
% 121.65/16.02 ((
% 121.65/16.02 (powersetI1) =>
% 121.65/16.02 ((
% 121.65/16.02 (powersetE1) =>
% 121.65/16.02 ((
% 121.65/16.02 (inPowerset) =>
% 121.65/16.02 ((
% 121.65/16.02 (powersetsubset) =>
% 121.65/16.02 ((
% 121.65/16.02 (sepInPowerset) =>
% 121.65/16.02 ((
% 121.65/16.02 (sepSubset) =>
% 121.65/16.02 ((
% 121.65/16.02 (binunionIL) =>
% 121.65/16.02 ((
% 121.65/16.02 (upairset2IR) =>
% 121.65/16.02 ((
% 121.65/16.02 (binunionIR) =>
% 121.65/16.02 ((
% 121.65/16.02 (binunionEcases) =>
% 121.65/16.02 ((
% 121.65/16.02 (binunionE) =>
% 121.65/16.02 ((
% 121.65/16.02 (binunionLsub) =>
% 121.65/16.02 ((
% 121.65/16.02 (binunionRsub) =>
% 121.65/16.02 ((
% 121.65/16.02 (binintersectI) =>
% 121.65/16.02 ((
% 121.65/16.02 (binintersectSubset5) =>
% 121.65/16.02 ((
% 121.65/16.02 (binintersectEL) =>
% 121.65/16.02 ((
% 121.65/16.02 (binintersectLsub) =>
% 121.65/16.02 ((
% 121.65/16.02 (binintersectSubset2) =>
% 121.65/16.02 ((
% 121.65/16.02 (binintersectSubset3) =>
% 121.65/16.02 ((
% 121.65/16.02 (binintersectER) =>
% 121.65/16.02 ((
% 121.65/16.02 (disjointsetsI1) =>
% 121.65/16.02 ((
% 121.65/16.02 (binintersectRsub) =>
% 121.65/16.02 ((
% 121.65/16.02 (binintersectSubset4) =>
% 121.65/16.02 ((
% 121.65/16.02 (binintersectSubset1) =>
% 121.65/16.02 ((
% 121.65/16.02 (bs114d) =>
% 121.65/16.02 ((
% 121.65/16.02 (setminusI) =>
% 121.65/16.02 ((
% 121.65/16.02 (setminusEL) =>
% 121.65/16.02 ((
% 121.65/16.02 (setminusER) =>
% 121.65/16.02 ((
% 121.65/16.02 (setminusSubset2) =>
% 121.65/16.02 ((
% 121.65/16.02 (setminusERneg) =>
% 121.65/16.02 ((
% 121.65/16.02 (setminusELneg) =>
% 121.65/16.02 ((
% 121.65/16.02 (setminusILneg) =>
% 121.65/16.02 ((
% 121.65/16.02 (setminusIRneg) =>
% 121.65/16.02 ((
% 121.65/16.02 (setminusLsub) =>
% 121.65/16.02 ((
% 121.65/16.02 (setminusSubset1) =>
% 121.65/16.02 ((
% 121.65/16.02 (symdiffE) =>
% 121.65/16.02 ((
% 121.65/16.02 (symdiffI1) =>
% 121.65/16.02 ((
% 121.65/16.02 (symdiffI2) =>
% 121.65/16.02 ((
% 121.65/16.02 (symdiffIneg1) =>
% 121.65/16.02 ((
% 121.65/16.02 (symdiffIneg2) =>
% 121.65/16.02 ((
% 121.65/16.02 (secondinupair) =>
% 121.65/16.02 ((
% 121.65/16.02 (setukpairIL) =>
% 121.65/16.02 ((
% 121.65/16.02 (setukpairIR) =>
% 121.65/16.02 ((
% 121.65/16.02 (kpairiskpair) =>
% 121.65/16.02 ((
% 121.65/16.02 (kpairp) =>
% 121.65/16.02 ((
% 121.65/16.02 (singletonsubset) =>
% 121.65/16.02 ((
% 121.65/16.02 (singletoninpowerset) =>
% 121.65/16.02 ((
% 121.65/16.02 (singletoninpowunion) =>
% 121.65/16.02 ((
% 121.65/16.02 (upairset2E) =>
% 121.65/16.02 ((
% 121.65/16.02 (upairsubunion) =>
% 121.65/16.02 ((
% 121.65/16.02 (upairinpowunion) =>
% 121.65/16.02 ((
% 121.65/16.02 (ubforcartprodlem1) =>
% 121.65/16.02 ((
% 121.65/16.02 (ubforcartprodlem2) =>
% 121.65/16.02 ((
% 121.65/16.02 (ubforcartprodlem3) =>
% 121.65/16.02 ((
% 121.65/16.02 (cartprodpairin) =>
% 121.65/16.02 ((
% 121.65/16.02 (cartprodmempair1) =>
% 121.65/16.02 ((
% 121.65/16.02 (cartprodmempair) =>
% 121.65/16.02 ((
% 121.65/16.02 (setunionE2) =>
% 121.65/16.02 ((
% 121.65/16.02 (setunionsingleton1) =>
% 121.65/16.02 ((
% 121.65/16.02 (setunionsingleton2) =>
% 121.65/16.02 ((
% 121.65/16.02 (setunionsingleton) =>
% 121.65/16.02 ((
% 121.65/16.02 (singletonprop) =>
% 121.65/16.02 ((
% 121.65/16.02 (ex1E1) =>
% 121.65/16.02 ((
% 121.65/16.02 (ex1I) =>
% 121.65/16.02 ((
% 121.65/16.02 (ex1I2) =>
% 121.65/16.02 ((
% 121.65/16.02 (singletonsuniq) =>
% 121.65/16.02 ((
% 121.65/16.02 (setukpairinjL1) =>
% 121.65/16.02 ((
% 121.65/16.02 (kfstsingleton) =>
% 121.65/16.02 ((
% 121.65/16.02 (theprop) =>
% 121.65/16.02 ((
% 121.65/16.02 (kfstpairEq) =>
% 121.65/16.02 ((
% 121.65/16.02 (cartprodfstin) =>
% 121.65/16.02 ((
% 121.65/16.02 (setukpairinjL2) =>
% 121.65/16.02 ((
% 121.65/16.02 (setukpairinjL) =>
% 121.65/16.02 ((
% 121.65/16.02 (setukpairinjR11) =>
% 121.65/16.02 ((
% 121.65/16.02 (setukpairinjR12) =>
% 121.65/16.02 ((
% 121.65/16.02 (setukpairinjR1) =>
% 121.65/16.02 ((
% 121.65/16.02 (upairequniteq) =>
% 121.65/16.02 ((
% 121.65/16.02 (setukpairinjR2) =>
% 121.65/16.02 ((
% 121.65/16.02 (setukpairinjR) =>
% 121.65/16.02 ((
% 121.65/16.02 (ksndsingleton) =>
% 121.65/16.02 ((
% 121.65/16.02 (ksndpairEq) =>
% 121.65/16.02 ((
% 121.65/16.02 (kpairsurjEq) =>
% 121.65/16.02 ((
% 121.65/16.02 (cartprodsndin) =>
% 121.65/16.02 ((
% 121.65/16.02 (cartprodpairmemEL) =>
% 121.65/16.02 ((
% 121.65/16.02 (cartprodpairmemER) =>
% 121.65/16.02 ((
% 121.65/16.02 (cartprodmempaircEq) =>
% 121.65/16.02 ((
% 121.65/16.02 (cartprodfstpairEq) =>
% 121.65/16.02 ((
% 121.65/16.02 (cartprodsndpairEq) =>
% 121.65/16.02 ((
% 121.65/16.02 (cartprodpairsurjEq) =>
% 121.65/16.02 ((
% 121.65/16.02 (dpsetconstrI) =>
% 121.65/16.02 ((
% 121.65/16.02 (dpsetconstrSub) =>
% 121.65/16.02 ((
% 121.65/16.02 (setOfPairsIsBReln) =>
% 121.65/16.02 ((
% 121.65/16.02 (dpsetconstrERa) =>
% 121.65/16.02 ((
% 121.65/16.02 (dpsetconstrEL1) =>
% 121.65/16.02 ((
% 121.65/16.02 (dpsetconstrEL2) =>
% 121.65/16.02 ((
% 121.65/16.02 (dpsetconstrER) =>
% 121.65/16.02 ((
% 121.65/16.02 (funcImageSingleton) =>
% 121.65/16.02 ((
% 121.65/16.02 (apProp) =>
% 121.65/16.02 ((
% 121.65/16.02 (app) =>
% 121.65/16.02 ((
% 121.65/16.02 (infuncsetfunc) =>
% 121.65/16.02 ((
% 121.65/16.02 (ap2p) =>
% 121.65/16.02 ((
% 121.65/16.02 (funcinfuncset) =>
% 121.65/16.02 ((
% 121.65/16.02 (lamProp) =>
% 121.65/16.02 ((
% 121.65/16.02 (lamp) =>
% 121.65/16.02 ((
% 121.65/16.02 (lam2p) =>
% 121.65/16.02 ((
% 121.65/16.02 (brelnall1) =>
% 121.65/16.02 ((
% 121.65/16.02 (brelnall2) =>
% 121.65/16.02 ((
% 121.65/16.02 (ex1E2) =>
% 121.65/16.02 ((
% 121.65/16.02 (funcGraphProp1) =>
% 121.65/16.02 ((
% 121.65/16.02 (funcGraphProp3) =>
% 121.65/16.02 ((
% 121.65/16.02 (funcGraphProp2) =>
% 121.65/16.02 ((
% 121.65/16.02 (funcextLem) =>
% 121.65/16.02 ((
% 121.65/16.02 (funcGraphProp4) =>
% 121.65/16.02 ((
% 121.65/16.02 (subbreln) =>
% 121.65/16.02 ((
% 121.65/16.02 (eqbreln) =>
% 121.65/16.02 ((
% 121.65/16.02 (funcext) =>
% 121.65/16.02 ((
% 121.65/16.02 (funcext2) =>
% 121.65/16.02 ((
% 121.65/16.02 (ap2apEq1) =>
% 121.65/16.02 ((
% 121.65/16.02 (ap2apEq2) =>
% 121.65/16.02 ((
% 121.65/16.02 (beta1) =>
% 121.65/16.02 ((
% 121.65/16.02 (eta1) =>
% 121.65/16.02 ((
% 121.65/16.02 (lam2lamEq) =>
% 121.65/16.02 ((
% 121.65/16.02 (beta2) =>
% 121.65/16.02 ((
% 121.65/16.02 (eta2) =>
% 121.65/16.02 ((
% 121.65/16.02 (iffalseProp1) =>
% 121.65/16.02 ((
% 121.65/16.02 (iffalseProp2) =>
% 121.65/16.02 ((
% 121.65/16.02 (iftrueProp1) =>
% 121.65/16.02 ((
% 121.65/16.02 (iftrueProp2) =>
% 121.65/16.02 ((
% 121.65/16.02 (ifSingleton) =>
% 121.65/16.02 ((
% 121.65/16.02 (ifp) =>
% 121.65/16.02 ((
% 121.65/16.02 (theeq) =>
% 121.65/16.02 ((
% 121.65/16.02 (iftrue) =>
% 121.65/16.02 ((
% 121.65/16.02 (iffalse) =>
% 121.65/16.02 ((
% 121.65/16.02 (iftrueorfalse) =>
% 121.65/16.02 ((
% 121.65/16.02 (binintersectT_lem) =>
% 121.65/16.02 ((
% 121.65/16.02 (binunionT_lem) =>
% 121.65/16.02 ((
% 121.65/16.02 (powersetT_lem) =>
% 121.65/16.02 ((
% 121.65/16.02 (setminusT_lem) =>
% 121.65/16.02 ((
% 121.65/16.02 (complementT_lem) =>
% 121.65/16.02 ((
% 121.65/16.02 (setextT) =>
% 121.65/16.02 ((
% 121.65/16.02 (subsetTI) =>
% 121.65/16.02 ((
% 121.65/16.02 (powersetTI1) =>
% 121.65/16.02 ((
% 121.65/16.02 (powersetTE1) =>
% 121.65/16.02 ((
% 121.65/16.02 (complementTI1) =>
% 121.65/16.02 ((
% 121.65/16.02 (complementTE1) =>
% 121.65/16.02 ((
% 121.65/16.02 (binintersectTELcontra) =>
% 121.65/16.02 ((
% 121.65/16.02 (binintersectTERcontra) =>
% 121.65/16.02 ((
% 121.65/16.02 (contrasubsetT) =>
% 121.65/16.02 ((
% 121.65/16.02 (contrasubsetT1) =>
% 121.65/16.02 ((
% 121.65/16.02 (contrasubsetT2) =>
% 121.65/16.02 ((
% 121.65/16.02 (contrasubsetT3) =>
% 121.65/16.02 ((
% 121.65/16.02 (doubleComplementI1) =>
% 121.65/16.02 ((
% 121.65/16.02 (doubleComplementE1) =>
% 121.65/16.02 ((
% 121.65/16.02 (doubleComplementSub1) =>
% 121.65/16.02 ((
% 121.65/16.02 (doubleComplementSub2) =>
% 121.65/16.02 ((
% 121.65/16.02 (doubleComplementEq) =>
% 121.65/16.02 ((
% 121.65/16.02 (complementTnotintersectT) =>
% 121.65/16.02 ((
% 121.65/16.02 (complementImpComplementIntersect) =>
% 121.65/16.02 ((
% 121.65/16.02 (complementSubsetComplementIntersect) =>
% 121.65/16.02 ((
% 121.65/16.02 (complementInPowersetComplementIntersect) =>
% 121.65/16.02 ((
% 121.65/16.02 (contraSubsetComplement) =>
% 121.65/16.02 ((
% 121.65/16.02 (complementTcontraSubset) =>
% 121.65/16.02 ((
% 121.65/16.02 (binunionTILcontra) =>
% 121.65/16.02 ((
% 121.65/16.02 (binunionTIRcontra) =>
% 121.65/16.02 ((
% 121.65/16.02 (inIntersectImpInUnion) =>
% 121.65/16.02 ((
% 121.65/16.02 (inIntersectImpInUnion2) =>
% 121.65/16.02 ((
% 121.65/16.02 (inIntersectImpInIntersectUnions) =>
% 121.65/16.02 ((
% 121.65/16.02 (intersectInPowersetIntersectUnions) =>
% 121.65/16.02 ((
% 121.65/16.02 (inComplementUnionImpNotIn1) =>
% 121.65/16.02 ((
% 121.65/16.02 (inComplementUnionImpInComplement1) =>
% 121.65/16.02 ((
% 121.65/16.02 (binunionTE) =>
% 121.65/16.02 ((
% 121.65/16.02 (binunionTEcontra) =>
% 121.65/16.02 ((
% 121.65/16.02 (demorgan2a1) =>
% 121.65/16.02 ((
% 121.65/16.02 (complementUnionInPowersetComplement) =>
% 121.65/16.02 ((
% 121.65/16.02 (demorgan2a2) =>
% 121.65/16.02 ((
% 121.65/16.02 (demorgan1a) =>
% 121.65/16.02 ((
% 121.65/16.02 (demorgan1b) =>
% 121.65/16.02 ((
% 121.65/16.02 (demorgan1) =>
% 121.65/16.02 ((
% 121.65/16.02 (demorgan2a) =>
% 121.65/16.02 ((
% 121.65/16.02 (demorgan2b2) =>
% 121.65/16.02 ((
% 121.65/16.02 (demorgan2b) =>
% 121.65/16.02 ((
% 121.65/16.02 (demorgan2) =>
% 121.65/16.02 ((
% 121.65/16.02 (woz13rule0) =>
% 121.65/16.02 ((
% 121.65/16.02 (woz13rule1) =>
% 121.65/16.02 ((
% 121.65/16.02 (woz13rule2) =>
% 121.65/16.02 ((
% 121.65/16.02 (woz13rule3) =>
% 121.65/16.02 ((
% 121.65/16.02 (woz13rule4) =>
% 121.65/16.02 ((
% 121.65/16.02 (woz1_1) =>
% 121.65/16.02 ((
% 121.65/16.02 (woz1_2) =>
% 121.65/16.02 ((
% 121.65/16.02 (woz1_3) =>
% 121.65/16.02 ((
% 121.65/16.02 (woz1_4) =>
% 121.65/16.02 ((
% 121.65/16.02 (woz1_5) =>
% 121.65/16.02 ((
% 121.65/16.02 (breln1all2) =>
% 121.65/16.02 ((
% 121.65/16.02 (breln1SetBreln1) =>
% 121.65/16.02 ((
% 121.65/16.02 (choice2fnsingleton) =>
% 121.65/16.02 ((
% 121.65/16.02 (setOfPairsIsBReln1) =>
% 121.65/16.02 ((
% 121.65/16.02 (breln1all1) =>
% 121.65/16.02 ((
% 121.65/16.02 (subbreln1) =>
% 121.65/16.02 ((
% 121.65/16.02 (eqbreln1) =>
% 121.65/16.02 ((
% 121.65/16.02 (breln1invprop) =>
% 121.65/16.02 ((
% 121.65/16.02 (breln1invI) =>
% 121.65/16.02 ((
% 121.65/16.02 (breln1invE) =>
% 121.65/16.02 ((
% 121.65/16.02 (breln1compprop) =>
% 121.65/16.02 ((
% 121.65/16.02 (breln1compI) =>
% 121.65/16.02 ((
% 121.65/16.02 (breln1compE) =>
% 121.65/16.02 ((
% 121.65/16.02 (breln1compEex) =>
% 121.65/16.02 ((
% 121.65/16.02 (breln1unionprop) =>
% 121.65/16.02 ((
% 121.65/16.02 (breln1unionIL) =>
% 121.65/16.02 ((
% 121.65/16.02 (breln1unionIR) =>
% 121.65/16.02 ((
% 121.65/16.02 (breln1unionI) =>
% 121.65/16.02 ((
% 121.65/16.02 (breln1unionE) =>
% 121.65/16.02 ((
% 121.65/16.02 (breln1unionEcases) =>
% 121.65/16.02 ((
% 121.65/16.02 (breln1unionCommutes) =>
% 121.65/16.02 ((
% 121.65/16.02 (woz2Ex) =>
% 121.65/16.02 ((
% 121.65/16.02 (woz2W) =>
% 121.65/16.02 ((
% 121.65/16.02 (woz2A) =>
% 121.65/16.02 ((
% 121.65/16.02 (woz2B) =>
% 121.65/16.02 ((
% 121.65/16.02 (image1Ex) =>
% 121.65/16.02 ((
% 121.65/16.02 (image1Ex1) =>
% 121.65/16.02 ((
% 121.65/16.02 (image1Equiv) =>
% 121.65/16.02 ((
% 121.65/16.02 (image1E) =>
% 121.65/16.02 ((
% 121.65/16.02 (image1I) =>
% 121.65/16.02 ((
% 121.65/16.02 (injFuncInInjFuncSet) =>
% 121.65/16.02 ((
% 121.65/16.02 (!!) @ (
% 121.65/16.02 (('#B') @ (
% 121.65/16.02 !!) @
% 121.65/16.02 (
% 121.65/16.02 (
% 121.65/16.02 ('#B') @ (
% 121.65/16.02 (
% 121.65/16.02 ('#B') @ (
% 121.65/16.02 !!))) @
% 121.65/16.02 (
% 121.65/16.02 (
% 121.65/16.02 ('#S') @ (
% 121.65/16.02 (
% 121.65/16.02 ('#B') @ (
% 121.65/16.02 '#S') @
% 121.65/16.02 (
% 121.65/16.02 (
% 121.65/16.02 ('#B') @ (
% 121.65/16.02 (
% 121.65/16.02 ('#B') @ (
% 121.65/16.02 '#S'))) @
% 121.65/16.02 (
% 121.65/16.02 (
% 121.65/16.02 ('#B') @ (
% 121.65/16.02 (
% 121.65/16.02 ('#B') @ (
% 121.65/16.02 (
% 121.65/16.02 ('#B') @ (
% 121.65/16.02 =>))))) @
% 121.65/16.02 (
% 121.65/16.02 (
% 121.65/16.02 ('#B') @ (
% 121.65/16.02 (
% 121.65/16.02 ('#B') @ (
% 121.65/16.02 (
% 121.65/16.02 ('#C') @ in)))) @
% 121.65/16.02 injFuncSet)))))))) @
% 121.65/16.02 (
% 121.65/16.02 (
% 121.65/16.02 ('#B') @ (
% 121.65/16.02 (
% 121.65/16.02 ('#B') @ (
% 121.65/16.02 (
% 121.65/16.02 ('#C') @ in)))) @
% 121.65/16.02 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 121.65/16.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl58])).
% 121.65/16.02 thf(zip_derived_cl71, plain,
% 121.65/16.02 (~ (((dsetconstrI) =>
% 121.65/16.02 (((dsetconstrEL) =>
% 121.65/16.02 (((dsetconstrER) =>
% 121.65/16.02 (((exuE1) =>
% 121.65/16.02 (((prop2setE) =>
% 121.65/16.02 (((emptysetE) =>
% 121.65/16.02 (((emptysetimpfalse) =>
% 121.65/16.02 (((notinemptyset) =>
% 121.65/16.02 (((exuE3e) =>
% 121.65/16.02 (((setext) =>
% 121.65/16.02 (((emptyI) =>
% 121.65/16.02 (((noeltsimpempty) =>
% 121.65/16.02 (((setbeta) =>
% 121.65/16.02 (((nonemptyE1) =>
% 121.65/16.02 (((nonemptyI) =>
% 121.65/16.02 (((nonemptyI1) =>
% 121.65/16.02 (((setadjoinIL) =>
% 121.65/16.02 (((in @ emptyset @
% 121.65/16.02 (setadjoin @ emptyset @ emptyset)) =>
% 121.65/16.02 (((setadjoinIR) =>
% 121.65/16.02 (((setadjoinE) =>
% 121.65/16.02 (((setadjoinOr) =>
% 121.65/16.02 (((setoftrueEq) =>
% 121.65/16.02 (((powersetI) =>
% 121.65/16.02 (((emptyinPowerset) =>
% 121.65/16.02 (((emptyInPowerset) =>
% 121.65/16.02 (((powersetE) =>
% 121.65/16.02 (((setunionI) =>
% 121.65/16.02 (((setunionE) =>
% 121.65/16.02 (((subPowSU) =>
% 121.65/16.02 (((exuE2) =>
% 121.65/16.02 ((
% 121.65/16.02 (nonemptyImpWitness) =>
% 121.65/16.02 ((
% 121.65/16.02 (uniqinunit) =>
% 121.65/16.02 ((
% 121.65/16.02 (notinsingleton) =>
% 121.65/16.02 ((
% 121.65/16.02 (eqinunit) =>
% 121.65/16.02 ((
% 121.65/16.02 (singletonsswitch) =>
% 121.65/16.02 ((
% 121.65/16.02 (upairsetE) =>
% 121.65/16.02 ((
% 121.65/16.02 (upairsetIL) =>
% 121.65/16.02 ((
% 121.65/16.02 (upairsetIR) =>
% 121.65/16.02 ((
% 121.65/16.02 (emptyE1) =>
% 121.65/16.02 ((
% 121.65/16.02 (vacuousDall) =>
% 121.65/16.02 ((
% 121.65/16.02 (quantDeMorgan1) =>
% 121.65/16.02 ((
% 121.65/16.02 (quantDeMorgan2) =>
% 121.65/16.02 ((
% 121.65/16.02 (quantDeMorgan3) =>
% 121.65/16.02 ((
% 121.65/16.02 (quantDeMorgan4) =>
% 121.65/16.02 ((
% 121.65/16.02 (prop2setI) =>
% 121.65/16.02 ((
% 121.65/16.02 (prop2set2propI) =>
% 121.65/16.02 ((
% 121.65/16.02 (notdexE) =>
% 121.65/16.02 ((
% 121.65/16.02 (notdallE) =>
% 121.65/16.02 ((
% 121.65/16.02 (exuI1) =>
% 121.65/16.02 ((
% 121.65/16.02 (exuI3) =>
% 121.65/16.02 ((
% 121.65/16.02 (exuI2) =>
% 121.65/16.02 ((
% 121.65/16.02 (inCongP) =>
% 121.65/16.02 ((
% 121.65/16.02 (in__Cong) =>
% 121.65/16.02 ((
% 121.65/16.02 (exuE3u) =>
% 121.65/16.02 ((
% 121.65/16.02 (exu__Cong) =>
% 121.65/16.02 ((
% 121.65/16.02 (setadjoin__Cong) =>
% 121.65/16.02 ((
% 121.65/16.02 (powerset__Cong) =>
% 121.65/16.02 ((
% 121.65/16.02 (setunion__Cong) =>
% 121.65/16.02 ((
% 121.65/16.02 (exuEu) =>
% 121.65/16.02 ((
% 121.65/16.02 (descr__Cong) =>
% 121.65/16.02 ((
% 121.65/16.02 (dsetconstr__Cong) =>
% 121.65/16.02 ((
% 121.65/16.02 (subsetI1) =>
% 121.65/16.02 ((
% 121.65/16.02 (eqimpsubset2) =>
% 121.65/16.02 ((
% 121.65/16.02 (eqimpsubset1) =>
% 121.65/16.02 ((
% 121.65/16.02 (subsetI2) =>
% 121.65/16.02 ((
% 121.65/16.02 (emptysetsubset) =>
% 121.65/16.02 ((
% 121.65/16.02 (subsetE) =>
% 121.65/16.02 ((
% 121.65/16.02 (subsetE2) =>
% 121.65/16.02 ((
% 121.65/16.02 (notsubsetI) =>
% 121.65/16.02 ((
% 121.65/16.02 (notequalI1) =>
% 121.65/16.02 ((
% 121.65/16.02 (notequalI2) =>
% 121.65/16.02 ((
% 121.65/16.02 (subsetRefl) =>
% 121.65/16.02 ((
% 121.65/16.02 (subsetTrans) =>
% 121.65/16.02 ((
% 121.65/16.02 (setadjoinSub) =>
% 121.65/16.02 ((
% 121.65/16.02 (setadjoinSub2) =>
% 121.65/16.02 ((
% 121.65/16.02 (subset2powerset) =>
% 121.65/16.02 ((
% 121.65/16.02 (setextsub) =>
% 121.65/16.02 ((
% 121.65/16.02 (subsetemptysetimpeq) =>
% 121.65/16.02 ((
% 121.65/16.02 (powersetI1) =>
% 121.65/16.02 ((
% 121.65/16.02 (powersetE1) =>
% 121.65/16.02 ((
% 121.65/16.02 (inPowerset) =>
% 121.65/16.02 ((
% 121.65/16.02 (powersetsubset) =>
% 121.65/16.02 ((
% 121.65/16.02 (sepInPowerset) =>
% 121.65/16.02 ((
% 121.65/16.02 (sepSubset) =>
% 121.65/16.02 ((
% 121.65/16.02 (binunionIL) =>
% 121.65/16.02 ((
% 121.65/16.02 (upairset2IR) =>
% 121.65/16.02 ((
% 121.65/16.02 (binunionIR) =>
% 121.65/16.02 ((
% 121.65/16.02 (binunionEcases) =>
% 121.65/16.02 ((
% 121.65/16.02 (binunionE) =>
% 121.65/16.02 ((
% 121.65/16.02 (binunionLsub) =>
% 121.65/16.02 ((
% 121.65/16.02 (binunionRsub) =>
% 121.65/16.02 ((
% 121.65/16.02 (binintersectI) =>
% 121.65/16.02 ((
% 121.65/16.02 (binintersectSubset5) =>
% 121.65/16.02 ((
% 121.65/16.02 (binintersectEL) =>
% 121.65/16.02 ((
% 121.65/16.02 (binintersectLsub) =>
% 121.65/16.02 ((
% 121.65/16.02 (binintersectSubset2) =>
% 121.65/16.02 ((
% 121.65/16.02 (binintersectSubset3) =>
% 121.65/16.02 ((
% 121.65/16.02 (binintersectER) =>
% 121.65/16.02 ((
% 121.65/16.02 (disjointsetsI1) =>
% 121.65/16.02 ((
% 121.65/16.02 (binintersectRsub) =>
% 121.65/16.02 ((
% 121.65/16.02 (binintersectSubset4) =>
% 121.65/16.02 ((
% 121.65/16.02 (binintersectSubset1) =>
% 121.65/16.02 ((
% 121.65/16.02 (bs114d) =>
% 121.65/16.02 ((
% 121.65/16.02 (setminusI) =>
% 121.65/16.02 ((
% 121.65/16.02 (setminusEL) =>
% 121.65/16.02 ((
% 121.65/16.02 (setminusER) =>
% 121.65/16.02 ((
% 121.65/16.02 (setminusSubset2) =>
% 121.65/16.02 ((
% 121.65/16.02 (setminusERneg) =>
% 121.65/16.02 ((
% 121.65/16.02 (setminusELneg) =>
% 121.65/16.02 ((
% 121.65/16.02 (setminusILneg) =>
% 121.65/16.02 ((
% 121.65/16.02 (setminusIRneg) =>
% 121.65/16.02 ((
% 121.65/16.02 (setminusLsub) =>
% 121.65/16.02 ((
% 121.65/16.02 (setminusSubset1) =>
% 121.65/16.02 ((
% 121.65/16.02 (symdiffE) =>
% 121.65/16.02 ((
% 121.65/16.02 (symdiffI1) =>
% 121.65/16.02 ((
% 121.65/16.02 (symdiffI2) =>
% 121.65/16.02 ((
% 121.65/16.02 (symdiffIneg1) =>
% 121.65/16.02 ((
% 121.65/16.02 (symdiffIneg2) =>
% 121.65/16.02 ((
% 121.65/16.02 (secondinupair) =>
% 121.65/16.02 ((
% 121.65/16.02 (setukpairIL) =>
% 121.65/16.02 ((
% 121.65/16.02 (setukpairIR) =>
% 121.65/16.02 ((
% 121.65/16.02 (kpairiskpair) =>
% 121.65/16.02 ((
% 121.65/16.02 (kpairp) =>
% 121.65/16.02 ((
% 121.65/16.02 (singletonsubset) =>
% 121.65/16.02 ((
% 121.65/16.02 (singletoninpowerset) =>
% 121.65/16.02 ((
% 121.65/16.02 (singletoninpowunion) =>
% 121.65/16.02 ((
% 121.65/16.02 (upairset2E) =>
% 121.65/16.02 ((
% 121.65/16.02 (upairsubunion) =>
% 121.65/16.02 ((
% 121.65/16.02 (upairinpowunion) =>
% 121.65/16.02 ((
% 121.65/16.02 (ubforcartprodlem1) =>
% 121.65/16.02 ((
% 121.65/16.02 (ubforcartprodlem2) =>
% 121.65/16.02 ((
% 121.65/16.02 (ubforcartprodlem3) =>
% 121.65/16.02 ((
% 121.65/16.02 (cartprodpairin) =>
% 121.65/16.02 ((
% 121.65/16.02 (cartprodmempair1) =>
% 121.65/16.02 ((
% 121.65/16.02 (cartprodmempair) =>
% 121.65/16.02 ((
% 121.65/16.02 (setunionE2) =>
% 121.65/16.02 ((
% 121.65/16.02 (setunionsingleton1) =>
% 121.65/16.02 ((
% 121.65/16.02 (setunionsingleton2) =>
% 121.65/16.02 ((
% 121.65/16.02 (setunionsingleton) =>
% 121.65/16.02 ((
% 121.65/16.02 (singletonprop) =>
% 121.65/16.02 ((
% 121.65/16.02 (ex1E1) =>
% 121.65/16.02 ((
% 121.65/16.02 (ex1I) =>
% 121.65/16.02 ((
% 121.65/16.02 (ex1I2) =>
% 121.65/16.02 ((
% 121.65/16.02 (singletonsuniq) =>
% 121.65/16.02 ((
% 121.65/16.02 (setukpairinjL1) =>
% 121.65/16.02 ((
% 121.65/16.02 (kfstsingleton) =>
% 121.65/16.02 ((
% 121.65/16.02 (theprop) =>
% 121.65/16.02 ((
% 121.65/16.02 (kfstpairEq) =>
% 121.65/16.02 ((
% 121.65/16.02 (cartprodfstin) =>
% 121.65/16.02 ((
% 121.65/16.02 (setukpairinjL2) =>
% 121.65/16.02 ((
% 121.65/16.02 (setukpairinjL) =>
% 121.65/16.02 ((
% 121.65/16.02 (setukpairinjR11) =>
% 121.65/16.02 ((
% 121.65/16.02 (setukpairinjR12) =>
% 121.65/16.02 ((
% 121.65/16.02 (setukpairinjR1) =>
% 121.65/16.02 ((
% 121.65/16.02 (upairequniteq) =>
% 121.65/16.02 ((
% 121.65/16.02 (setukpairinjR2) =>
% 121.65/16.02 ((
% 121.65/16.02 (setukpairinjR) =>
% 121.65/16.02 ((
% 121.65/16.02 (ksndsingleton) =>
% 121.65/16.02 ((
% 121.65/16.02 (ksndpairEq) =>
% 121.65/16.02 ((
% 121.65/16.02 (kpairsurjEq) =>
% 121.65/16.02 ((
% 121.65/16.02 (cartprodsndin) =>
% 121.65/16.02 ((
% 121.65/16.02 (cartprodpairmemEL) =>
% 121.65/16.02 ((
% 121.65/16.02 (cartprodpairmemER) =>
% 121.65/16.02 ((
% 121.65/16.02 (cartprodmempaircEq) =>
% 121.65/16.02 ((
% 121.65/16.02 (cartprodfstpairEq) =>
% 121.65/16.02 ((
% 121.65/16.02 (cartprodsndpairEq) =>
% 121.65/16.02 ((
% 121.65/16.02 (cartprodpairsurjEq) =>
% 121.65/16.02 ((
% 121.65/16.02 (dpsetconstrI) =>
% 121.65/16.02 ((
% 121.65/16.02 (dpsetconstrSub) =>
% 121.65/16.02 ((
% 121.65/16.02 (setOfPairsIsBReln) =>
% 121.65/16.02 ((
% 121.65/16.02 (dpsetconstrERa) =>
% 121.65/16.02 ((
% 121.65/16.02 (dpsetconstrEL1) =>
% 121.65/16.02 ((
% 121.65/16.02 (dpsetconstrEL2) =>
% 121.65/16.02 ((
% 121.65/16.02 (dpsetconstrER) =>
% 121.65/16.02 ((
% 121.65/16.02 (funcImageSingleton) =>
% 121.65/16.02 ((
% 121.65/16.02 (apProp) =>
% 121.65/16.02 ((
% 121.65/16.02 (app) =>
% 121.65/16.02 ((
% 121.65/16.02 (infuncsetfunc) =>
% 121.65/16.02 ((
% 121.65/16.02 (ap2p) =>
% 121.65/16.02 ((
% 121.65/16.02 (funcinfuncset) =>
% 121.65/16.02 ((
% 121.65/16.02 (lamProp) =>
% 121.65/16.02 ((
% 121.65/16.02 (lamp) =>
% 121.65/16.02 ((
% 121.65/16.02 (lam2p) =>
% 121.65/16.02 ((
% 121.65/16.02 (brelnall1) =>
% 121.65/16.02 ((
% 121.65/16.02 (brelnall2) =>
% 121.65/16.02 ((
% 121.65/16.02 (ex1E2) =>
% 121.65/16.02 ((
% 121.65/16.02 (funcGraphProp1) =>
% 121.65/16.02 ((
% 121.65/16.02 (funcGraphProp3) =>
% 121.65/16.02 ((
% 121.65/16.02 (funcGraphProp2) =>
% 121.65/16.02 ((
% 121.65/16.02 (funcextLem) =>
% 121.65/16.02 ((
% 121.65/16.02 (funcGraphProp4) =>
% 121.65/16.02 ((
% 121.65/16.02 (subbreln) =>
% 121.65/16.02 ((
% 121.65/16.02 (eqbreln) =>
% 121.65/16.02 ((
% 121.65/16.02 (funcext) =>
% 121.65/16.02 ((
% 121.65/16.02 (funcext2) =>
% 121.65/16.02 ((
% 121.65/16.02 (ap2apEq1) =>
% 121.65/16.02 ((
% 121.65/16.02 (ap2apEq2) =>
% 121.65/16.02 ((
% 121.65/16.02 (beta1) =>
% 121.65/16.02 ((
% 121.65/16.02 (eta1) =>
% 121.65/16.02 ((
% 121.65/16.02 (lam2lamEq) =>
% 121.65/16.02 ((
% 121.65/16.02 (beta2) =>
% 121.65/16.02 ((
% 121.65/16.02 (eta2) =>
% 121.65/16.02 ((
% 121.65/16.02 (iffalseProp1) =>
% 121.65/16.02 ((
% 121.65/16.02 (iffalseProp2) =>
% 121.65/16.02 ((
% 121.65/16.02 (iftrueProp1) =>
% 121.65/16.02 ((
% 121.65/16.02 (iftrueProp2) =>
% 121.65/16.02 ((
% 121.65/16.02 (ifSingleton) =>
% 121.65/16.02 ((
% 121.65/16.02 (ifp) =>
% 121.65/16.02 ((
% 121.65/16.02 (theeq) =>
% 121.65/16.02 ((
% 121.65/16.02 (iftrue) =>
% 121.65/16.02 ((
% 121.65/16.02 (iffalse) =>
% 121.65/16.02 ((
% 121.65/16.02 (iftrueorfalse) =>
% 121.65/16.02 ((
% 121.65/16.02 (binintersectT_lem) =>
% 121.65/16.02 ((
% 121.65/16.02 (binunionT_lem) =>
% 121.65/16.02 ((
% 121.65/16.02 (powersetT_lem) =>
% 121.65/16.02 ((
% 121.65/16.02 (setminusT_lem) =>
% 121.65/16.02 ((
% 121.65/16.02 (complementT_lem) =>
% 121.65/16.02 ((
% 121.65/16.02 (setextT) =>
% 121.65/16.02 ((
% 121.65/16.02 (subsetTI) =>
% 121.65/16.02 ((
% 121.65/16.02 (powersetTI1) =>
% 121.65/16.02 ((
% 121.65/16.02 (powersetTE1) =>
% 121.65/16.02 ((
% 121.65/16.02 (complementTI1) =>
% 121.65/16.02 ((
% 121.65/16.02 (complementTE1) =>
% 121.65/16.02 ((
% 121.65/16.02 (binintersectTELcontra) =>
% 121.65/16.02 ((
% 121.65/16.02 (binintersectTERcontra) =>
% 121.65/16.02 ((
% 121.65/16.02 (contrasubsetT) =>
% 121.65/16.02 ((
% 121.65/16.02 (contrasubsetT1) =>
% 121.65/16.02 ((
% 121.65/16.02 (contrasubsetT2) =>
% 121.65/16.02 ((
% 121.65/16.02 (contrasubsetT3) =>
% 121.65/16.02 ((
% 121.65/16.02 (doubleComplementI1) =>
% 121.65/16.02 ((
% 121.65/16.02 (doubleComplementE1) =>
% 121.65/16.02 ((
% 121.65/16.02 (doubleComplementSub1) =>
% 121.65/16.02 ((
% 121.65/16.02 (doubleComplementSub2) =>
% 121.65/16.02 ((
% 121.65/16.02 (doubleComplementEq) =>
% 121.65/16.02 ((
% 121.65/16.02 (complementTnotintersectT) =>
% 121.65/16.02 ((
% 121.65/16.02 (complementImpComplementIntersect) =>
% 121.65/16.02 ((
% 121.65/16.02 (complementSubsetComplementIntersect) =>
% 121.65/16.02 ((
% 121.65/16.02 (complementInPowersetComplementIntersect) =>
% 121.65/16.02 ((
% 121.65/16.02 (contraSubsetComplement) =>
% 121.65/16.02 ((
% 121.65/16.02 (complementTcontraSubset) =>
% 121.65/16.02 ((
% 121.65/16.02 (binunionTILcontra) =>
% 121.65/16.02 ((
% 121.65/16.02 (binunionTIRcontra) =>
% 121.65/16.02 ((
% 121.65/16.02 (inIntersectImpInUnion) =>
% 121.65/16.02 ((
% 121.65/16.02 (inIntersectImpInUnion2) =>
% 121.65/16.02 ((
% 121.65/16.02 (inIntersectImpInIntersectUnions) =>
% 121.65/16.02 ((
% 121.65/16.02 (intersectInPowersetIntersectUnions) =>
% 121.65/16.02 ((
% 121.65/16.02 (inComplementUnionImpNotIn1) =>
% 121.65/16.02 ((
% 121.65/16.02 (inComplementUnionImpInComplement1) =>
% 121.65/16.02 ((
% 121.65/16.02 (binunionTE) =>
% 121.65/16.02 ((
% 121.65/16.02 (binunionTEcontra) =>
% 121.65/16.02 ((
% 121.65/16.02 (demorgan2a1) =>
% 121.65/16.02 ((
% 121.65/16.02 (complementUnionInPowersetComplement) =>
% 121.65/16.02 ((
% 121.65/16.02 (demorgan2a2) =>
% 121.65/16.02 ((
% 121.65/16.02 (demorgan1a) =>
% 121.65/16.02 ((
% 121.65/16.02 (demorgan1b) =>
% 121.65/16.02 ((
% 121.65/16.02 (demorgan1) =>
% 121.65/16.02 ((
% 121.65/16.02 (demorgan2a) =>
% 121.65/16.02 ((
% 121.65/16.02 (demorgan2b2) =>
% 121.65/16.02 ((
% 121.65/16.02 (demorgan2b) =>
% 121.65/16.02 ((
% 121.65/16.02 (demorgan2) =>
% 121.65/16.02 ((
% 121.65/16.02 (woz13rule0) =>
% 121.65/16.02 ((
% 121.65/16.02 (woz13rule1) =>
% 121.65/16.02 ((
% 121.65/16.02 (woz13rule2) =>
% 121.65/16.02 ((
% 121.65/16.02 (woz13rule3) =>
% 121.65/16.02 ((
% 121.65/16.02 (woz13rule4) =>
% 121.65/16.02 ((
% 121.65/16.02 (woz1_1) =>
% 121.65/16.02 ((
% 121.65/16.02 (woz1_2) =>
% 121.65/16.02 ((
% 121.65/16.02 (woz1_3) =>
% 121.65/16.02 ((
% 121.65/16.02 (woz1_4) =>
% 121.65/16.02 ((
% 121.65/16.02 (woz1_5) =>
% 121.65/16.02 ((
% 121.65/16.02 (breln1all2) =>
% 121.65/16.02 ((
% 121.65/16.02 (breln1SetBreln1) =>
% 121.65/16.02 ((
% 121.65/16.02 (choice2fnsingleton) =>
% 121.65/16.02 ((
% 121.65/16.02 (setOfPairsIsBReln1) =>
% 121.65/16.02 ((
% 121.65/16.02 (breln1all1) =>
% 121.65/16.02 ((
% 121.65/16.02 (subbreln1) =>
% 121.65/16.02 ((
% 121.65/16.02 (eqbreln1) =>
% 121.65/16.02 ((
% 121.65/16.02 (breln1invprop) =>
% 121.65/16.02 ((
% 121.65/16.02 (breln1invI) =>
% 121.65/16.02 ((
% 121.65/16.02 (breln1invE) =>
% 121.65/16.02 ((
% 121.65/16.02 (breln1compprop) =>
% 121.65/16.02 ((
% 121.65/16.02 (breln1compI) =>
% 121.65/16.02 ((
% 121.65/16.02 (breln1compE) =>
% 121.65/16.02 ((
% 121.65/16.02 (breln1compEex) =>
% 121.65/16.02 ((
% 121.65/16.02 (breln1unionprop) =>
% 121.65/16.02 ((
% 121.65/16.02 (breln1unionIL) =>
% 121.65/16.02 ((
% 121.65/16.02 (breln1unionIR) =>
% 121.65/16.02 ((
% 121.65/16.02 (breln1unionI) =>
% 121.65/16.02 ((
% 121.65/16.02 (breln1unionE) =>
% 121.65/16.02 ((
% 121.65/16.02 (breln1unionEcases) =>
% 121.65/16.02 ((
% 121.65/16.02 (breln1unionCommutes) =>
% 121.65/16.02 ((
% 121.65/16.02 (woz2Ex) =>
% 121.65/16.02 ((
% 121.65/16.02 (woz2W) =>
% 121.65/16.02 ((
% 121.65/16.02 (woz2A) =>
% 121.65/16.02 ((
% 121.65/16.02 (woz2B) =>
% 121.65/16.02 ((
% 121.65/16.02 (image1Ex) =>
% 121.65/16.02 ((
% 121.65/16.02 (image1Ex1) =>
% 121.65/16.02 ((
% 121.65/16.02 (image1Equiv) =>
% 121.65/16.02 ((
% 121.65/16.02 (image1E) =>
% 121.65/16.02 ((
% 121.65/16.02 (image1I) =>
% 121.65/16.02 ((
% 121.65/16.02 (injFuncInInjFuncSet) =>
% 121.65/16.02 ((
% 121.65/16.02 (!!) @ (
% 121.65/16.02 (('#B') @ (
% 121.65/16.02 !!) @
% 121.65/16.02 (
% 121.65/16.02 (
% 121.65/16.02 ('#B') @ (
% 121.65/16.02 (
% 121.65/16.02 ('#B') @ (
% 121.65/16.02 !!))) @
% 121.65/16.02 (
% 121.65/16.02 (
% 121.65/16.02 ('#S') @ (
% 121.65/16.02 (
% 121.65/16.02 ('#B') @ (
% 121.65/16.02 '#S') @
% 121.65/16.02 (
% 121.65/16.02 (
% 121.65/16.02 ('#B') @ (
% 121.65/16.02 (
% 121.65/16.02 ('#B') @ (
% 121.65/16.02 '#S'))) @
% 121.65/16.02 (
% 121.65/16.02 (
% 121.65/16.02 ('#B') @ (
% 121.65/16.02 (
% 121.65/16.02 ('#B') @ (
% 121.65/16.02 (
% 121.65/16.02 ('#B') @ (
% 121.65/16.02 =>))))) @
% 121.65/16.02 (
% 121.65/16.02 (
% 121.65/16.02 ('#B') @ (
% 121.65/16.02 (
% 121.65/16.02 ('#B') @ (
% 121.65/16.02 (
% 121.65/16.02 ('#C') @ in)))) @
% 121.65/16.02 injFuncSet)))))))) @
% 121.65/16.02 (
% 121.65/16.02 (
% 121.65/16.02 ('#B') @ (
% 121.65/16.02 (
% 121.65/16.02 ('#B') @ (
% 121.65/16.02 (
% 121.65/16.02 ('#C') @ in)))) @
% 121.65/16.02 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 121.65/16.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl64])).
% 121.65/16.02 thf(zip_derived_cl79, plain,
% 121.65/16.02 (~ (((dsetconstrEL) =>
% 121.65/16.02 (((dsetconstrER) =>
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% 121.65/16.02 (((emptysetimpfalse) =>
% 121.65/16.02 (((notinemptyset) =>
% 121.65/16.02 (((exuE3e) =>
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% 121.65/16.02 (((emptyI) =>
% 121.65/16.02 (((noeltsimpempty) =>
% 121.65/16.02 (((setbeta) =>
% 121.65/16.02 (((nonemptyE1) =>
% 121.65/16.02 (((nonemptyI) =>
% 121.65/16.02 (((nonemptyI1) =>
% 121.65/16.02 (((setadjoinIL) =>
% 121.65/16.02 (((in @ emptyset @
% 121.65/16.02 (setadjoin @ emptyset @ emptyset)) =>
% 121.65/16.02 (((setadjoinIR) =>
% 121.65/16.02 (((setadjoinE) =>
% 121.65/16.02 (((setadjoinOr) =>
% 121.65/16.02 (((setoftrueEq) =>
% 121.65/16.02 (((powersetI) =>
% 121.65/16.02 (((emptyinPowerset) =>
% 121.65/16.02 (((emptyInPowerset) =>
% 121.65/16.02 (((powersetE) =>
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% 121.65/16.02 (((setunionE) =>
% 121.65/16.02 (((subPowSU) =>
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% 121.65/16.02 (((nonemptyImpWitness) =>
% 121.65/16.02 ((
% 121.65/16.02 (uniqinunit) =>
% 121.65/16.02 ((
% 121.65/16.02 (notinsingleton) =>
% 121.65/16.02 ((
% 121.65/16.02 (eqinunit) =>
% 121.65/16.02 ((
% 121.65/16.02 (singletonsswitch) =>
% 121.65/16.02 ((
% 121.65/16.02 (upairsetE) =>
% 121.65/16.02 ((
% 121.65/16.02 (upairsetIL) =>
% 121.65/16.02 ((
% 121.65/16.02 (upairsetIR) =>
% 121.65/16.02 ((
% 121.65/16.02 (emptyE1) =>
% 121.65/16.02 ((
% 121.65/16.02 (vacuousDall) =>
% 121.65/16.02 ((
% 121.65/16.02 (quantDeMorgan1) =>
% 121.65/16.02 ((
% 121.65/16.02 (quantDeMorgan2) =>
% 121.65/16.02 ((
% 121.65/16.02 (quantDeMorgan3) =>
% 121.65/16.02 ((
% 121.65/16.02 (quantDeMorgan4) =>
% 121.65/16.02 ((
% 121.65/16.02 (prop2setI) =>
% 121.65/16.02 ((
% 121.65/16.02 (prop2set2propI) =>
% 121.65/16.02 ((
% 121.65/16.02 (notdexE) =>
% 121.65/16.02 ((
% 121.65/16.02 (notdallE) =>
% 121.65/16.02 ((
% 121.65/16.02 (exuI1) =>
% 121.65/16.02 ((
% 121.65/16.02 (exuI3) =>
% 121.65/16.02 ((
% 121.65/16.02 (exuI2) =>
% 121.65/16.02 ((
% 121.65/16.02 (inCongP) =>
% 121.65/16.02 ((
% 121.65/16.02 (in__Cong) =>
% 121.65/16.02 ((
% 121.65/16.02 (exuE3u) =>
% 121.65/16.02 ((
% 121.65/16.02 (exu__Cong) =>
% 121.65/16.02 ((
% 121.65/16.02 (setadjoin__Cong) =>
% 121.65/16.02 ((
% 121.65/16.02 (powerset__Cong) =>
% 121.65/16.02 ((
% 121.65/16.02 (setunion__Cong) =>
% 121.65/16.02 ((
% 121.65/16.02 (exuEu) =>
% 121.65/16.02 ((
% 121.65/16.02 (descr__Cong) =>
% 121.65/16.02 ((
% 121.65/16.02 (dsetconstr__Cong) =>
% 121.65/16.02 ((
% 121.65/16.02 (subsetI1) =>
% 121.65/16.02 ((
% 121.65/16.02 (eqimpsubset2) =>
% 121.65/16.02 ((
% 121.65/16.02 (eqimpsubset1) =>
% 121.65/16.02 ((
% 121.65/16.02 (subsetI2) =>
% 121.65/16.02 ((
% 121.65/16.02 (emptysetsubset) =>
% 121.65/16.02 ((
% 121.65/16.02 (subsetE) =>
% 121.65/16.02 ((
% 121.65/16.02 (subsetE2) =>
% 121.65/16.02 ((
% 121.65/16.02 (notsubsetI) =>
% 121.65/16.02 ((
% 121.65/16.02 (notequalI1) =>
% 121.65/16.02 ((
% 121.65/16.02 (notequalI2) =>
% 121.65/16.02 ((
% 121.65/16.02 (subsetRefl) =>
% 121.65/16.02 ((
% 121.65/16.02 (subsetTrans) =>
% 121.65/16.02 ((
% 121.65/16.02 (setadjoinSub) =>
% 121.65/16.02 ((
% 121.65/16.02 (setadjoinSub2) =>
% 121.65/16.02 ((
% 121.65/16.02 (subset2powerset) =>
% 121.65/16.02 ((
% 121.65/16.02 (setextsub) =>
% 121.65/16.02 ((
% 121.65/16.02 (subsetemptysetimpeq) =>
% 121.65/16.02 ((
% 121.65/16.02 (powersetI1) =>
% 121.65/16.02 ((
% 121.65/16.02 (powersetE1) =>
% 121.65/16.02 ((
% 121.65/16.02 (inPowerset) =>
% 121.65/16.02 ((
% 121.65/16.02 (powersetsubset) =>
% 121.65/16.02 ((
% 121.65/16.02 (sepInPowerset) =>
% 121.65/16.02 ((
% 121.65/16.02 (sepSubset) =>
% 121.65/16.02 ((
% 121.65/16.02 (binunionIL) =>
% 121.65/16.02 ((
% 121.65/16.02 (upairset2IR) =>
% 121.65/16.02 ((
% 121.65/16.02 (binunionIR) =>
% 121.65/16.02 ((
% 121.65/16.02 (binunionEcases) =>
% 121.65/16.02 ((
% 121.65/16.02 (binunionE) =>
% 121.65/16.02 ((
% 121.65/16.02 (binunionLsub) =>
% 121.65/16.02 ((
% 121.65/16.02 (binunionRsub) =>
% 121.65/16.02 ((
% 121.65/16.02 (binintersectI) =>
% 121.65/16.02 ((
% 121.65/16.02 (binintersectSubset5) =>
% 121.65/16.02 ((
% 121.65/16.02 (binintersectEL) =>
% 121.65/16.02 ((
% 121.65/16.02 (binintersectLsub) =>
% 121.65/16.02 ((
% 121.65/16.02 (binintersectSubset2) =>
% 121.65/16.02 ((
% 121.65/16.02 (binintersectSubset3) =>
% 121.65/16.02 ((
% 121.65/16.02 (binintersectER) =>
% 121.65/16.02 ((
% 121.65/16.02 (disjointsetsI1) =>
% 121.65/16.02 ((
% 121.65/16.02 (binintersectRsub) =>
% 121.65/16.02 ((
% 121.65/16.02 (binintersectSubset4) =>
% 121.65/16.02 ((
% 121.65/16.02 (binintersectSubset1) =>
% 121.65/16.02 ((
% 121.65/16.02 (bs114d) =>
% 121.65/16.02 ((
% 121.65/16.02 (setminusI) =>
% 121.65/16.02 ((
% 121.65/16.02 (setminusEL) =>
% 121.65/16.02 ((
% 121.65/16.02 (setminusER) =>
% 121.65/16.02 ((
% 121.65/16.02 (setminusSubset2) =>
% 121.65/16.02 ((
% 121.65/16.02 (setminusERneg) =>
% 121.65/16.02 ((
% 121.65/16.02 (setminusELneg) =>
% 121.65/16.02 ((
% 121.65/16.02 (setminusILneg) =>
% 121.65/16.02 ((
% 121.65/16.02 (setminusIRneg) =>
% 121.65/16.02 ((
% 121.65/16.02 (setminusLsub) =>
% 121.65/16.02 ((
% 121.65/16.02 (setminusSubset1) =>
% 121.65/16.02 ((
% 121.65/16.02 (symdiffE) =>
% 121.65/16.02 ((
% 121.65/16.02 (symdiffI1) =>
% 121.65/16.02 ((
% 121.65/16.02 (symdiffI2) =>
% 121.65/16.02 ((
% 121.65/16.02 (symdiffIneg1) =>
% 121.65/16.02 ((
% 121.65/16.02 (symdiffIneg2) =>
% 121.65/16.02 ((
% 121.65/16.02 (secondinupair) =>
% 121.65/16.02 ((
% 121.65/16.02 (setukpairIL) =>
% 121.65/16.02 ((
% 121.65/16.02 (setukpairIR) =>
% 121.65/16.02 ((
% 121.65/16.02 (kpairiskpair) =>
% 121.65/16.02 ((
% 121.65/16.02 (kpairp) =>
% 121.65/16.02 ((
% 121.65/16.02 (singletonsubset) =>
% 121.65/16.02 ((
% 121.65/16.02 (singletoninpowerset) =>
% 121.65/16.02 ((
% 121.65/16.02 (singletoninpowunion) =>
% 121.65/16.02 ((
% 121.65/16.02 (upairset2E) =>
% 121.65/16.02 ((
% 121.65/16.02 (upairsubunion) =>
% 121.65/16.02 ((
% 121.65/16.02 (upairinpowunion) =>
% 121.65/16.02 ((
% 121.65/16.02 (ubforcartprodlem1) =>
% 121.65/16.02 ((
% 121.65/16.02 (ubforcartprodlem2) =>
% 121.65/16.02 ((
% 121.65/16.02 (ubforcartprodlem3) =>
% 121.65/16.02 ((
% 121.65/16.02 (cartprodpairin) =>
% 121.65/16.02 ((
% 121.65/16.02 (cartprodmempair1) =>
% 121.65/16.02 ((
% 121.65/16.02 (cartprodmempair) =>
% 121.65/16.02 ((
% 121.65/16.02 (setunionE2) =>
% 121.65/16.02 ((
% 121.65/16.02 (setunionsingleton1) =>
% 121.65/16.02 ((
% 121.65/16.02 (setunionsingleton2) =>
% 121.65/16.02 ((
% 121.65/16.02 (setunionsingleton) =>
% 121.65/16.02 ((
% 121.65/16.02 (singletonprop) =>
% 121.65/16.02 ((
% 121.65/16.02 (ex1E1) =>
% 121.65/16.02 ((
% 121.65/16.02 (ex1I) =>
% 121.65/16.02 ((
% 121.65/16.02 (ex1I2) =>
% 121.65/16.02 ((
% 121.65/16.02 (singletonsuniq) =>
% 121.65/16.02 ((
% 121.65/16.02 (setukpairinjL1) =>
% 121.65/16.02 ((
% 121.65/16.02 (kfstsingleton) =>
% 121.65/16.02 ((
% 121.65/16.02 (theprop) =>
% 121.65/16.02 ((
% 121.65/16.02 (kfstpairEq) =>
% 121.65/16.02 ((
% 121.65/16.02 (cartprodfstin) =>
% 121.65/16.02 ((
% 121.65/16.02 (setukpairinjL2) =>
% 121.65/16.02 ((
% 121.65/16.02 (setukpairinjL) =>
% 121.65/16.02 ((
% 121.65/16.02 (setukpairinjR11) =>
% 121.65/16.02 ((
% 121.65/16.02 (setukpairinjR12) =>
% 121.65/16.02 ((
% 121.65/16.02 (setukpairinjR1) =>
% 121.65/16.02 ((
% 121.65/16.02 (upairequniteq) =>
% 121.65/16.02 ((
% 121.65/16.02 (setukpairinjR2) =>
% 121.65/16.02 ((
% 121.65/16.02 (setukpairinjR) =>
% 121.65/16.02 ((
% 121.65/16.02 (ksndsingleton) =>
% 121.65/16.02 ((
% 121.65/16.02 (ksndpairEq) =>
% 121.65/16.02 ((
% 121.65/16.02 (kpairsurjEq) =>
% 121.65/16.02 ((
% 121.65/16.02 (cartprodsndin) =>
% 121.65/16.02 ((
% 121.65/16.02 (cartprodpairmemEL) =>
% 121.65/16.02 ((
% 121.65/16.02 (cartprodpairmemER) =>
% 121.65/16.02 ((
% 121.65/16.02 (cartprodmempaircEq) =>
% 121.65/16.02 ((
% 121.65/16.02 (cartprodfstpairEq) =>
% 121.65/16.02 ((
% 121.65/16.02 (cartprodsndpairEq) =>
% 121.65/16.02 ((
% 121.65/16.02 (cartprodpairsurjEq) =>
% 121.65/16.02 ((
% 121.65/16.02 (dpsetconstrI) =>
% 121.65/16.02 ((
% 121.65/16.02 (dpsetconstrSub) =>
% 121.65/16.02 ((
% 121.65/16.02 (setOfPairsIsBReln) =>
% 121.65/16.02 ((
% 121.65/16.02 (dpsetconstrERa) =>
% 121.65/16.02 ((
% 121.65/16.02 (dpsetconstrEL1) =>
% 121.65/16.02 ((
% 121.65/16.02 (dpsetconstrEL2) =>
% 121.65/16.02 ((
% 121.65/16.02 (dpsetconstrER) =>
% 121.65/16.02 ((
% 121.65/16.02 (funcImageSingleton) =>
% 121.65/16.02 ((
% 121.65/16.02 (apProp) =>
% 121.65/16.02 ((
% 121.65/16.02 (app) =>
% 121.65/16.02 ((
% 121.65/16.02 (infuncsetfunc) =>
% 121.65/16.02 ((
% 121.65/16.02 (ap2p) =>
% 121.65/16.02 ((
% 121.65/16.02 (funcinfuncset) =>
% 121.65/16.02 ((
% 121.65/16.02 (lamProp) =>
% 121.65/16.02 ((
% 121.65/16.02 (lamp) =>
% 121.65/16.02 ((
% 121.65/16.02 (lam2p) =>
% 121.65/16.02 ((
% 121.65/16.02 (brelnall1) =>
% 121.65/16.02 ((
% 121.65/16.02 (brelnall2) =>
% 121.65/16.02 ((
% 121.65/16.02 (ex1E2) =>
% 121.65/16.02 ((
% 121.65/16.02 (funcGraphProp1) =>
% 121.65/16.02 ((
% 121.65/16.02 (funcGraphProp3) =>
% 121.65/16.02 ((
% 121.65/16.02 (funcGraphProp2) =>
% 121.65/16.02 ((
% 121.65/16.02 (funcextLem) =>
% 121.65/16.02 ((
% 121.65/16.02 (funcGraphProp4) =>
% 121.65/16.02 ((
% 121.65/16.02 (subbreln) =>
% 121.65/16.02 ((
% 121.65/16.02 (eqbreln) =>
% 121.65/16.02 ((
% 121.65/16.02 (funcext) =>
% 121.65/16.02 ((
% 121.65/16.02 (funcext2) =>
% 121.65/16.02 ((
% 121.65/16.02 (ap2apEq1) =>
% 121.65/16.02 ((
% 121.65/16.02 (ap2apEq2) =>
% 121.65/16.02 ((
% 121.65/16.02 (beta1) =>
% 121.65/16.02 ((
% 121.65/16.02 (eta1) =>
% 121.65/16.02 ((
% 121.65/16.02 (lam2lamEq) =>
% 121.65/16.02 ((
% 121.65/16.02 (beta2) =>
% 121.65/16.02 ((
% 121.65/16.02 (eta2) =>
% 121.65/16.02 ((
% 121.65/16.02 (iffalseProp1) =>
% 121.65/16.02 ((
% 121.65/16.02 (iffalseProp2) =>
% 121.65/16.02 ((
% 121.65/16.02 (iftrueProp1) =>
% 121.65/16.02 ((
% 121.65/16.02 (iftrueProp2) =>
% 121.65/16.02 ((
% 121.65/16.02 (ifSingleton) =>
% 121.65/16.02 ((
% 121.65/16.02 (ifp) =>
% 121.65/16.02 ((
% 121.65/16.02 (theeq) =>
% 121.65/16.02 ((
% 121.65/16.02 (iftrue) =>
% 121.65/16.02 ((
% 121.65/16.02 (iffalse) =>
% 121.65/16.02 ((
% 121.65/16.02 (iftrueorfalse) =>
% 121.65/16.02 ((
% 121.65/16.02 (binintersectT_lem) =>
% 121.65/16.02 ((
% 121.65/16.02 (binunionT_lem) =>
% 121.65/16.02 ((
% 121.65/16.02 (powersetT_lem) =>
% 121.65/16.02 ((
% 121.65/16.02 (setminusT_lem) =>
% 121.65/16.02 ((
% 121.65/16.02 (complementT_lem) =>
% 121.65/16.02 ((
% 121.65/16.02 (setextT) =>
% 121.65/16.02 ((
% 121.65/16.02 (subsetTI) =>
% 121.65/16.02 ((
% 121.65/16.02 (powersetTI1) =>
% 121.65/16.02 ((
% 121.65/16.02 (powersetTE1) =>
% 121.65/16.02 ((
% 121.65/16.02 (complementTI1) =>
% 121.65/16.02 ((
% 121.65/16.02 (complementTE1) =>
% 121.65/16.02 ((
% 121.65/16.02 (binintersectTELcontra) =>
% 121.65/16.02 ((
% 121.65/16.02 (binintersectTERcontra) =>
% 121.65/16.02 ((
% 121.65/16.02 (contrasubsetT) =>
% 121.65/16.02 ((
% 121.65/16.02 (contrasubsetT1) =>
% 121.65/16.02 ((
% 121.65/16.02 (contrasubsetT2) =>
% 121.65/16.02 ((
% 121.65/16.02 (contrasubsetT3) =>
% 121.65/16.02 ((
% 121.65/16.02 (doubleComplementI1) =>
% 121.65/16.02 ((
% 121.65/16.02 (doubleComplementE1) =>
% 121.65/16.02 ((
% 121.65/16.02 (doubleComplementSub1) =>
% 121.65/16.02 ((
% 121.65/16.02 (doubleComplementSub2) =>
% 121.65/16.02 ((
% 121.65/16.02 (doubleComplementEq) =>
% 121.65/16.02 ((
% 121.65/16.02 (complementTnotintersectT) =>
% 121.65/16.02 ((
% 121.65/16.02 (complementImpComplementIntersect) =>
% 121.65/16.02 ((
% 121.65/16.02 (complementSubsetComplementIntersect) =>
% 121.65/16.02 ((
% 121.65/16.02 (complementInPowersetComplementIntersect) =>
% 121.65/16.02 ((
% 121.65/16.02 (contraSubsetComplement) =>
% 121.65/16.02 ((
% 121.65/16.02 (complementTcontraSubset) =>
% 121.65/16.02 ((
% 121.65/16.02 (binunionTILcontra) =>
% 121.65/16.02 ((
% 121.65/16.02 (binunionTIRcontra) =>
% 121.65/16.02 ((
% 121.65/16.02 (inIntersectImpInUnion) =>
% 121.65/16.02 ((
% 121.65/16.02 (inIntersectImpInUnion2) =>
% 121.65/16.02 ((
% 121.65/16.02 (inIntersectImpInIntersectUnions) =>
% 121.65/16.02 ((
% 121.65/16.02 (intersectInPowersetIntersectUnions) =>
% 121.65/16.02 ((
% 121.65/16.02 (inComplementUnionImpNotIn1) =>
% 121.65/16.02 ((
% 121.65/16.02 (inComplementUnionImpInComplement1) =>
% 121.65/16.02 ((
% 121.65/16.02 (binunionTE) =>
% 121.65/16.02 ((
% 121.65/16.02 (binunionTEcontra) =>
% 121.65/16.02 ((
% 121.65/16.02 (demorgan2a1) =>
% 121.65/16.02 ((
% 121.65/16.02 (complementUnionInPowersetComplement) =>
% 121.65/16.02 ((
% 121.65/16.02 (demorgan2a2) =>
% 121.65/16.02 ((
% 121.65/16.02 (demorgan1a) =>
% 121.65/16.02 ((
% 121.65/16.02 (demorgan1b) =>
% 121.65/16.02 ((
% 121.65/16.02 (demorgan1) =>
% 121.65/16.02 ((
% 121.65/16.02 (demorgan2a) =>
% 121.65/16.02 ((
% 121.65/16.02 (demorgan2b2) =>
% 121.65/16.02 ((
% 121.65/16.02 (demorgan2b) =>
% 121.65/16.02 ((
% 121.65/16.02 (demorgan2) =>
% 121.65/16.02 ((
% 121.65/16.02 (woz13rule0) =>
% 121.65/16.02 ((
% 121.65/16.02 (woz13rule1) =>
% 121.65/16.02 ((
% 121.65/16.02 (woz13rule2) =>
% 121.65/16.02 ((
% 121.65/16.02 (woz13rule3) =>
% 121.65/16.02 ((
% 121.65/16.02 (woz13rule4) =>
% 121.65/16.02 ((
% 121.65/16.02 (woz1_1) =>
% 121.65/16.02 ((
% 121.65/16.02 (woz1_2) =>
% 121.65/16.02 ((
% 121.65/16.02 (woz1_3) =>
% 121.65/16.02 ((
% 121.65/16.02 (woz1_4) =>
% 121.65/16.02 ((
% 121.65/16.02 (woz1_5) =>
% 121.65/16.02 ((
% 121.65/16.02 (breln1all2) =>
% 121.65/16.02 ((
% 121.65/16.02 (breln1SetBreln1) =>
% 121.65/16.02 ((
% 121.65/16.02 (choice2fnsingleton) =>
% 121.65/16.02 ((
% 121.65/16.02 (setOfPairsIsBReln1) =>
% 121.65/16.02 ((
% 121.65/16.02 (breln1all1) =>
% 121.65/16.02 ((
% 121.65/16.02 (subbreln1) =>
% 121.65/16.02 ((
% 121.65/16.02 (eqbreln1) =>
% 121.65/16.02 ((
% 121.65/16.02 (breln1invprop) =>
% 121.65/16.02 ((
% 121.65/16.02 (breln1invI) =>
% 121.65/16.02 ((
% 121.65/16.02 (breln1invE) =>
% 121.65/16.02 ((
% 121.65/16.02 (breln1compprop) =>
% 121.65/16.02 ((
% 121.65/16.02 (breln1compI) =>
% 121.65/16.02 ((
% 121.65/16.02 (breln1compE) =>
% 121.65/16.02 ((
% 121.65/16.02 (breln1compEex) =>
% 121.65/16.02 ((
% 121.65/16.02 (breln1unionprop) =>
% 121.65/16.02 ((
% 121.65/16.02 (breln1unionIL) =>
% 121.65/16.02 ((
% 121.65/16.02 (breln1unionIR) =>
% 121.65/16.02 ((
% 121.65/16.02 (breln1unionI) =>
% 121.65/16.02 ((
% 121.65/16.02 (breln1unionE) =>
% 121.65/16.02 ((
% 121.65/16.02 (breln1unionEcases) =>
% 121.65/16.02 ((
% 121.65/16.02 (breln1unionCommutes) =>
% 121.65/16.02 ((
% 121.65/16.02 (woz2Ex) =>
% 121.65/16.02 ((
% 121.65/16.02 (woz2W) =>
% 121.65/16.02 ((
% 121.65/16.02 (woz2A) =>
% 121.65/16.02 ((
% 121.65/16.02 (woz2B) =>
% 121.65/16.02 ((
% 121.65/16.02 (image1Ex) =>
% 121.65/16.02 ((
% 121.65/16.02 (image1Ex1) =>
% 121.65/16.02 ((
% 121.65/16.02 (image1Equiv) =>
% 121.65/16.02 ((
% 121.65/16.02 (image1E) =>
% 121.65/16.02 ((
% 121.65/16.02 (image1I) =>
% 121.65/16.02 ((
% 121.65/16.02 (injFuncInInjFuncSet) =>
% 121.65/16.02 ((
% 121.65/16.02 (!!) @ (
% 121.65/16.02 (('#B') @ (
% 121.65/16.02 !!) @
% 121.65/16.02 (
% 121.65/16.02 (
% 121.65/16.02 ('#B') @ (
% 121.65/16.02 (
% 121.65/16.02 ('#B') @ (
% 121.65/16.02 !!))) @
% 121.65/16.02 (
% 121.65/16.02 (
% 121.65/16.02 ('#S') @ (
% 121.65/16.02 (
% 121.65/16.02 ('#B') @ (
% 121.65/16.02 '#S') @
% 121.65/16.02 (
% 121.65/16.02 (
% 121.65/16.02 ('#B') @ (
% 121.65/16.02 (
% 121.65/16.02 ('#B') @ (
% 121.65/16.02 '#S'))) @
% 121.65/16.02 (
% 121.65/16.02 (
% 121.65/16.02 ('#B') @ (
% 121.65/16.02 (
% 121.65/16.02 ('#B') @ (
% 121.65/16.02 (
% 121.65/16.02 ('#B') @ (
% 121.65/16.02 =>))))) @
% 121.65/16.02 (
% 121.65/16.02 (
% 121.65/16.02 ('#B') @ (
% 121.65/16.02 (
% 121.65/16.02 ('#B') @ (
% 121.65/16.02 (
% 121.65/16.02 ('#C') @ in)))) @
% 121.65/16.02 injFuncSet)))))))) @
% 121.65/16.02 (
% 121.65/16.02 (
% 121.65/16.02 ('#B') @ (
% 121.65/16.02 (
% 121.65/16.02 ('#B') @ (
% 121.65/16.02 (
% 121.65/16.02 ('#C') @ in)))) @
% 121.65/16.02 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 121.65/16.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl71])).
% 121.65/16.02 thf(zip_derived_cl89, plain,
% 121.65/16.02 (~ (((dsetconstrER) =>
% 121.65/16.02 (((exuE1) =>
% 121.65/16.02 (((prop2setE) =>
% 121.65/16.02 (((emptysetE) =>
% 121.65/16.02 (((emptysetimpfalse) =>
% 121.65/16.02 (((notinemptyset) =>
% 121.65/16.02 (((exuE3e) =>
% 121.65/16.02 (((setext) =>
% 121.65/16.02 (((emptyI) =>
% 121.65/16.02 (((noeltsimpempty) =>
% 121.65/16.02 (((setbeta) =>
% 121.65/16.02 (((nonemptyE1) =>
% 121.65/16.02 (((nonemptyI) =>
% 121.65/16.02 (((nonemptyI1) =>
% 121.65/16.02 (((setadjoinIL) =>
% 121.65/16.02 (((in @ emptyset @
% 121.65/16.02 (setadjoin @ emptyset @ emptyset)) =>
% 121.65/16.02 (((setadjoinIR) =>
% 121.65/16.02 (((setadjoinE) =>
% 121.65/16.02 (((setadjoinOr) =>
% 121.65/16.02 (((setoftrueEq) =>
% 121.65/16.02 (((powersetI) =>
% 121.65/16.02 (((emptyinPowerset) =>
% 121.65/16.02 (((emptyInPowerset) =>
% 121.65/16.02 (((powersetE) =>
% 121.65/16.02 (((setunionI) =>
% 121.65/16.02 (((setunionE) =>
% 121.65/16.02 (((subPowSU) =>
% 121.65/16.02 (((exuE2) =>
% 121.65/16.02 (((nonemptyImpWitness) =>
% 121.65/16.02 (((uniqinunit) =>
% 121.65/16.02 ((
% 121.65/16.02 (notinsingleton) =>
% 121.65/16.02 ((
% 121.65/16.02 (eqinunit) =>
% 121.65/16.02 ((
% 121.65/16.02 (singletonsswitch) =>
% 121.65/16.02 ((
% 121.65/16.02 (upairsetE) =>
% 121.65/16.02 ((
% 121.65/16.02 (upairsetIL) =>
% 121.65/16.02 ((
% 121.65/16.02 (upairsetIR) =>
% 121.65/16.02 ((
% 121.65/16.02 (emptyE1) =>
% 121.65/16.02 ((
% 121.65/16.02 (vacuousDall) =>
% 121.65/16.02 ((
% 121.65/16.02 (quantDeMorgan1) =>
% 121.65/16.02 ((
% 121.65/16.02 (quantDeMorgan2) =>
% 121.65/16.02 ((
% 121.65/16.02 (quantDeMorgan3) =>
% 121.65/16.02 ((
% 121.65/16.02 (quantDeMorgan4) =>
% 121.65/16.02 ((
% 121.65/16.02 (prop2setI) =>
% 121.65/16.02 ((
% 121.65/16.02 (prop2set2propI) =>
% 121.65/16.02 ((
% 121.65/16.02 (notdexE) =>
% 121.65/16.02 ((
% 121.65/16.02 (notdallE) =>
% 121.65/16.02 ((
% 121.65/16.02 (exuI1) =>
% 121.65/16.02 ((
% 121.65/16.02 (exuI3) =>
% 121.65/16.02 ((
% 121.65/16.02 (exuI2) =>
% 121.65/16.02 ((
% 121.65/16.02 (inCongP) =>
% 121.65/16.02 ((
% 121.65/16.02 (in__Cong) =>
% 121.65/16.02 ((
% 121.65/16.02 (exuE3u) =>
% 121.65/16.02 ((
% 121.65/16.02 (exu__Cong) =>
% 121.65/16.02 ((
% 121.65/16.02 (setadjoin__Cong) =>
% 121.65/16.02 ((
% 121.65/16.02 (powerset__Cong) =>
% 121.65/16.02 ((
% 121.65/16.02 (setunion__Cong) =>
% 121.65/16.02 ((
% 121.65/16.02 (exuEu) =>
% 121.65/16.02 ((
% 121.65/16.02 (descr__Cong) =>
% 121.65/16.02 ((
% 121.65/16.02 (dsetconstr__Cong) =>
% 121.65/16.02 ((
% 121.65/16.02 (subsetI1) =>
% 121.65/16.02 ((
% 121.65/16.02 (eqimpsubset2) =>
% 121.65/16.02 ((
% 121.65/16.02 (eqimpsubset1) =>
% 121.65/16.02 ((
% 121.65/16.02 (subsetI2) =>
% 121.65/16.02 ((
% 121.65/16.02 (emptysetsubset) =>
% 121.65/16.02 ((
% 121.65/16.02 (subsetE) =>
% 121.65/16.02 ((
% 121.65/16.02 (subsetE2) =>
% 121.65/16.02 ((
% 121.65/16.02 (notsubsetI) =>
% 121.65/16.02 ((
% 121.65/16.02 (notequalI1) =>
% 121.65/16.02 ((
% 121.65/16.02 (notequalI2) =>
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% 121.65/16.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl79])).
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% 121.65/16.02 (quantDeMorgan1) =>
% 121.65/16.02 ((
% 121.65/16.02 (quantDeMorgan2) =>
% 121.65/16.02 ((
% 121.65/16.02 (quantDeMorgan3) =>
% 121.65/16.02 ((
% 121.65/16.02 (quantDeMorgan4) =>
% 121.65/16.02 ((
% 121.65/16.02 (prop2setI) =>
% 121.65/16.02 ((
% 121.65/16.02 (prop2set2propI) =>
% 121.65/16.02 ((
% 121.65/16.02 (notdexE) =>
% 121.65/16.02 ((
% 121.65/16.02 (notdallE) =>
% 121.65/16.02 ((
% 121.65/16.02 (exuI1) =>
% 121.65/16.02 ((
% 121.65/16.02 (exuI3) =>
% 121.65/16.02 ((
% 121.65/16.02 (exuI2) =>
% 121.65/16.02 ((
% 121.65/16.02 (inCongP) =>
% 121.65/16.02 ((
% 121.65/16.02 (in__Cong) =>
% 121.65/16.02 ((
% 121.65/16.02 (exuE3u) =>
% 121.65/16.02 ((
% 121.65/16.02 (exu__Cong) =>
% 121.65/16.02 ((
% 121.65/16.02 (setadjoin__Cong) =>
% 121.65/16.02 ((
% 121.65/16.02 (powerset__Cong) =>
% 121.65/16.02 ((
% 121.65/16.02 (setunion__Cong) =>
% 121.65/16.02 ((
% 121.65/16.02 (exuEu) =>
% 121.65/16.02 ((
% 121.65/16.02 (descr__Cong) =>
% 121.65/16.02 ((
% 121.65/16.02 (dsetconstr__Cong) =>
% 121.65/16.02 ((
% 121.65/16.02 (subsetI1) =>
% 121.65/16.02 ((
% 121.65/16.02 (eqimpsubset2) =>
% 121.65/16.02 ((
% 121.65/16.02 (eqimpsubset1) =>
% 121.65/16.02 ((
% 121.65/16.02 (subsetI2) =>
% 121.65/16.02 ((
% 121.65/16.02 (emptysetsubset) =>
% 121.65/16.02 ((
% 121.65/16.02 (subsetE) =>
% 121.65/16.02 ((
% 121.65/16.02 (subsetE2) =>
% 121.65/16.02 ((
% 121.65/16.02 (notsubsetI) =>
% 121.65/16.02 ((
% 121.65/16.02 (notequalI1) =>
% 121.65/16.02 ((
% 121.65/16.02 (notequalI2) =>
% 121.65/16.02 ((
% 121.65/16.02 (subsetRefl) =>
% 121.65/16.02 ((
% 121.65/16.02 (subsetTrans) =>
% 121.65/16.02 ((
% 121.65/16.02 (setadjoinSub) =>
% 121.65/16.02 ((
% 121.65/16.02 (setadjoinSub2) =>
% 121.65/16.02 ((
% 121.65/16.02 (subset2powerset) =>
% 121.65/16.02 ((
% 121.65/16.02 (setextsub) =>
% 121.65/16.02 ((
% 121.65/16.02 (subsetemptysetimpeq) =>
% 121.65/16.02 ((
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% 121.65/16.02 ((
% 121.65/16.02 (powersetE1) =>
% 121.65/16.02 ((
% 121.65/16.02 (inPowerset) =>
% 121.65/16.02 ((
% 121.65/16.02 (powersetsubset) =>
% 121.65/16.02 ((
% 121.65/16.02 (sepInPowerset) =>
% 121.65/16.02 ((
% 121.65/16.02 (sepSubset) =>
% 121.65/16.02 ((
% 121.65/16.02 (binunionIL) =>
% 121.65/16.02 ((
% 121.65/16.02 (upairset2IR) =>
% 121.65/16.02 ((
% 121.65/16.02 (binunionIR) =>
% 121.65/16.02 ((
% 121.65/16.02 (binunionEcases) =>
% 121.65/16.02 ((
% 121.65/16.02 (binunionE) =>
% 121.65/16.02 ((
% 121.65/16.02 (binunionLsub) =>
% 121.65/16.02 ((
% 121.65/16.02 (binunionRsub) =>
% 121.65/16.02 ((
% 121.65/16.02 (binintersectI) =>
% 121.65/16.02 ((
% 121.65/16.02 (binintersectSubset5) =>
% 121.65/16.02 ((
% 121.65/16.02 (binintersectEL) =>
% 121.65/16.02 ((
% 121.65/16.02 (binintersectLsub) =>
% 121.65/16.02 ((
% 121.65/16.02 (binintersectSubset2) =>
% 121.65/16.02 ((
% 121.65/16.02 (binintersectSubset3) =>
% 121.65/16.02 ((
% 121.65/16.02 (binintersectER) =>
% 121.65/16.02 ((
% 121.65/16.02 (disjointsetsI1) =>
% 121.65/16.02 ((
% 121.65/16.02 (binintersectRsub) =>
% 121.65/16.02 ((
% 121.65/16.02 (binintersectSubset4) =>
% 121.65/16.02 ((
% 121.65/16.02 (binintersectSubset1) =>
% 121.65/16.02 ((
% 121.65/16.02 (bs114d) =>
% 121.65/16.02 ((
% 121.65/16.02 (setminusI) =>
% 121.65/16.02 ((
% 121.65/16.02 (setminusEL) =>
% 121.65/16.02 ((
% 121.65/16.02 (setminusER) =>
% 121.65/16.02 ((
% 121.65/16.02 (setminusSubset2) =>
% 121.65/16.02 ((
% 121.65/16.02 (setminusERneg) =>
% 121.65/16.02 ((
% 121.65/16.02 (setminusELneg) =>
% 121.65/16.02 ((
% 121.65/16.02 (setminusILneg) =>
% 121.65/16.02 ((
% 121.65/16.02 (setminusIRneg) =>
% 121.65/16.02 ((
% 121.65/16.02 (setminusLsub) =>
% 121.65/16.02 ((
% 121.65/16.02 (setminusSubset1) =>
% 121.65/16.02 ((
% 121.65/16.02 (symdiffE) =>
% 121.65/16.02 ((
% 121.65/16.02 (symdiffI1) =>
% 121.65/16.02 ((
% 121.65/16.02 (symdiffI2) =>
% 121.65/16.02 ((
% 121.65/16.02 (symdiffIneg1) =>
% 121.65/16.02 ((
% 121.65/16.02 (symdiffIneg2) =>
% 121.65/16.02 ((
% 121.65/16.02 (secondinupair) =>
% 121.65/16.02 ((
% 121.65/16.02 (setukpairIL) =>
% 121.65/16.02 ((
% 121.65/16.02 (setukpairIR) =>
% 121.65/16.02 ((
% 121.65/16.02 (kpairiskpair) =>
% 121.65/16.03 ((
% 121.65/16.03 (kpairp) =>
% 121.65/16.03 ((
% 121.65/16.03 (singletonsubset) =>
% 121.65/16.03 ((
% 121.65/16.03 (singletoninpowerset) =>
% 121.65/16.03 ((
% 121.65/16.03 (singletoninpowunion) =>
% 121.65/16.03 ((
% 121.65/16.03 (upairset2E) =>
% 121.65/16.03 ((
% 121.65/16.03 (upairsubunion) =>
% 121.65/16.03 ((
% 121.65/16.03 (upairinpowunion) =>
% 121.65/16.03 ((
% 121.65/16.03 (ubforcartprodlem1) =>
% 121.65/16.03 ((
% 121.65/16.03 (ubforcartprodlem2) =>
% 121.65/16.03 ((
% 121.65/16.03 (ubforcartprodlem3) =>
% 121.65/16.03 ((
% 121.65/16.03 (cartprodpairin) =>
% 121.65/16.03 ((
% 121.65/16.03 (cartprodmempair1) =>
% 121.65/16.03 ((
% 121.65/16.03 (cartprodmempair) =>
% 121.65/16.03 ((
% 121.65/16.03 (setunionE2) =>
% 121.65/16.03 ((
% 121.65/16.03 (setunionsingleton1) =>
% 121.65/16.03 ((
% 121.65/16.03 (setunionsingleton2) =>
% 121.65/16.03 ((
% 121.65/16.03 (setunionsingleton) =>
% 121.65/16.03 ((
% 121.65/16.03 (singletonprop) =>
% 121.65/16.03 ((
% 121.65/16.03 (ex1E1) =>
% 121.65/16.03 ((
% 121.65/16.03 (ex1I) =>
% 121.65/16.03 ((
% 121.65/16.03 (ex1I2) =>
% 121.65/16.03 ((
% 121.65/16.03 (singletonsuniq) =>
% 121.65/16.03 ((
% 121.65/16.03 (setukpairinjL1) =>
% 121.65/16.03 ((
% 121.65/16.03 (kfstsingleton) =>
% 121.65/16.03 ((
% 121.65/16.03 (theprop) =>
% 121.65/16.03 ((
% 121.65/16.03 (kfstpairEq) =>
% 121.65/16.03 ((
% 121.65/16.03 (cartprodfstin) =>
% 121.65/16.03 ((
% 121.65/16.03 (setukpairinjL2) =>
% 121.65/16.03 ((
% 121.65/16.03 (setukpairinjL) =>
% 121.65/16.03 ((
% 121.65/16.03 (setukpairinjR11) =>
% 121.65/16.03 ((
% 121.65/16.03 (setukpairinjR12) =>
% 121.65/16.03 ((
% 121.65/16.03 (setukpairinjR1) =>
% 121.65/16.03 ((
% 121.65/16.03 (upairequniteq) =>
% 121.65/16.03 ((
% 121.65/16.03 (setukpairinjR2) =>
% 121.65/16.03 ((
% 121.65/16.03 (setukpairinjR) =>
% 121.65/16.03 ((
% 121.65/16.03 (ksndsingleton) =>
% 121.65/16.03 ((
% 121.65/16.03 (ksndpairEq) =>
% 121.65/16.03 ((
% 121.65/16.03 (kpairsurjEq) =>
% 121.65/16.03 ((
% 121.65/16.03 (cartprodsndin) =>
% 121.65/16.03 ((
% 121.65/16.03 (cartprodpairmemEL) =>
% 121.65/16.03 ((
% 121.65/16.03 (cartprodpairmemER) =>
% 121.65/16.03 ((
% 121.65/16.03 (cartprodmempaircEq) =>
% 121.65/16.03 ((
% 121.65/16.03 (cartprodfstpairEq) =>
% 121.65/16.03 ((
% 121.65/16.03 (cartprodsndpairEq) =>
% 121.65/16.03 ((
% 121.65/16.03 (cartprodpairsurjEq) =>
% 121.65/16.03 ((
% 121.65/16.03 (dpsetconstrI) =>
% 121.65/16.03 ((
% 121.65/16.03 (dpsetconstrSub) =>
% 121.65/16.03 ((
% 121.65/16.03 (setOfPairsIsBReln) =>
% 121.65/16.03 ((
% 121.65/16.03 (dpsetconstrERa) =>
% 121.65/16.03 ((
% 121.65/16.03 (dpsetconstrEL1) =>
% 121.65/16.03 ((
% 121.65/16.03 (dpsetconstrEL2) =>
% 121.65/16.03 ((
% 121.65/16.03 (dpsetconstrER) =>
% 121.65/16.03 ((
% 121.65/16.03 (funcImageSingleton) =>
% 121.65/16.03 ((
% 121.65/16.03 (apProp) =>
% 121.65/16.03 ((
% 121.65/16.03 (app) =>
% 121.65/16.03 ((
% 121.65/16.03 (infuncsetfunc) =>
% 121.65/16.03 ((
% 121.65/16.03 (ap2p) =>
% 121.65/16.03 ((
% 121.65/16.03 (funcinfuncset) =>
% 121.65/16.03 ((
% 121.65/16.03 (lamProp) =>
% 121.65/16.03 ((
% 121.65/16.03 (lamp) =>
% 121.65/16.03 ((
% 121.65/16.03 (lam2p) =>
% 121.65/16.03 ((
% 121.65/16.03 (brelnall1) =>
% 121.65/16.03 ((
% 121.65/16.03 (brelnall2) =>
% 121.65/16.03 ((
% 121.65/16.03 (ex1E2) =>
% 121.65/16.03 ((
% 121.65/16.03 (funcGraphProp1) =>
% 121.65/16.03 ((
% 121.65/16.03 (funcGraphProp3) =>
% 121.65/16.03 ((
% 121.65/16.03 (funcGraphProp2) =>
% 121.65/16.03 ((
% 121.65/16.03 (funcextLem) =>
% 121.65/16.03 ((
% 121.65/16.03 (funcGraphProp4) =>
% 121.65/16.03 ((
% 121.65/16.03 (subbreln) =>
% 121.65/16.03 ((
% 121.65/16.03 (eqbreln) =>
% 121.65/16.03 ((
% 121.65/16.03 (funcext) =>
% 121.65/16.03 ((
% 121.65/16.03 (funcext2) =>
% 121.65/16.03 ((
% 121.65/16.03 (ap2apEq1) =>
% 121.65/16.03 ((
% 121.65/16.03 (ap2apEq2) =>
% 121.65/16.03 ((
% 121.65/16.03 (beta1) =>
% 121.65/16.03 ((
% 121.65/16.03 (eta1) =>
% 121.65/16.03 ((
% 121.65/16.03 (lam2lamEq) =>
% 121.65/16.03 ((
% 121.65/16.03 (beta2) =>
% 121.65/16.03 ((
% 121.65/16.03 (eta2) =>
% 121.65/16.03 ((
% 121.65/16.03 (iffalseProp1) =>
% 121.65/16.03 ((
% 121.65/16.03 (iffalseProp2) =>
% 121.65/16.03 ((
% 121.65/16.03 (iftrueProp1) =>
% 121.65/16.03 ((
% 121.65/16.03 (iftrueProp2) =>
% 121.65/16.03 ((
% 121.65/16.03 (ifSingleton) =>
% 121.65/16.03 ((
% 121.65/16.03 (ifp) =>
% 121.65/16.03 ((
% 121.65/16.03 (theeq) =>
% 121.65/16.03 ((
% 121.65/16.03 (iftrue) =>
% 121.65/16.03 ((
% 121.65/16.03 (iffalse) =>
% 121.65/16.03 ((
% 121.65/16.03 (iftrueorfalse) =>
% 121.65/16.03 ((
% 121.65/16.03 (binintersectT_lem) =>
% 121.65/16.03 ((
% 121.65/16.03 (binunionT_lem) =>
% 121.65/16.03 ((
% 121.65/16.03 (powersetT_lem) =>
% 121.65/16.03 ((
% 121.65/16.03 (setminusT_lem) =>
% 121.65/16.03 ((
% 121.65/16.03 (complementT_lem) =>
% 121.65/16.03 ((
% 121.65/16.03 (setextT) =>
% 121.65/16.03 ((
% 121.65/16.03 (subsetTI) =>
% 121.65/16.03 ((
% 121.65/16.03 (powersetTI1) =>
% 121.65/16.03 ((
% 121.65/16.03 (powersetTE1) =>
% 121.65/16.03 ((
% 121.65/16.03 (complementTI1) =>
% 121.65/16.03 ((
% 121.65/16.03 (complementTE1) =>
% 121.65/16.03 ((
% 121.65/16.03 (binintersectTELcontra) =>
% 121.65/16.03 ((
% 121.65/16.03 (binintersectTERcontra) =>
% 121.65/16.03 ((
% 121.65/16.03 (contrasubsetT) =>
% 121.65/16.03 ((
% 121.65/16.03 (contrasubsetT1) =>
% 121.65/16.03 ((
% 121.65/16.03 (contrasubsetT2) =>
% 121.65/16.03 ((
% 121.65/16.03 (contrasubsetT3) =>
% 121.65/16.03 ((
% 121.65/16.03 (doubleComplementI1) =>
% 121.65/16.03 ((
% 121.65/16.03 (doubleComplementE1) =>
% 121.65/16.03 ((
% 121.65/16.03 (doubleComplementSub1) =>
% 121.65/16.03 ((
% 121.65/16.03 (doubleComplementSub2) =>
% 121.65/16.03 ((
% 121.65/16.03 (doubleComplementEq) =>
% 121.65/16.03 ((
% 121.65/16.03 (complementTnotintersectT) =>
% 121.65/16.03 ((
% 121.65/16.03 (complementImpComplementIntersect) =>
% 121.65/16.03 ((
% 121.65/16.03 (complementSubsetComplementIntersect) =>
% 121.65/16.03 ((
% 121.65/16.03 (complementInPowersetComplementIntersect) =>
% 121.65/16.03 ((
% 121.65/16.03 (contraSubsetComplement) =>
% 121.65/16.03 ((
% 121.65/16.03 (complementTcontraSubset) =>
% 121.65/16.03 ((
% 121.65/16.03 (binunionTILcontra) =>
% 121.65/16.03 ((
% 121.65/16.03 (binunionTIRcontra) =>
% 121.65/16.03 ((
% 121.65/16.03 (inIntersectImpInUnion) =>
% 121.65/16.03 ((
% 121.65/16.03 (inIntersectImpInUnion2) =>
% 121.65/16.03 ((
% 121.65/16.03 (inIntersectImpInIntersectUnions) =>
% 121.65/16.03 ((
% 121.65/16.03 (intersectInPowersetIntersectUnions) =>
% 121.65/16.03 ((
% 121.65/16.03 (inComplementUnionImpNotIn1) =>
% 121.65/16.03 ((
% 121.65/16.03 (inComplementUnionImpInComplement1) =>
% 121.65/16.03 ((
% 121.65/16.03 (binunionTE) =>
% 121.65/16.03 ((
% 121.65/16.03 (binunionTEcontra) =>
% 121.65/16.03 ((
% 121.65/16.03 (demorgan2a1) =>
% 121.65/16.03 ((
% 121.65/16.03 (complementUnionInPowersetComplement) =>
% 121.65/16.03 ((
% 121.65/16.03 (demorgan2a2) =>
% 121.65/16.03 ((
% 121.65/16.03 (demorgan1a) =>
% 121.65/16.03 ((
% 121.65/16.03 (demorgan1b) =>
% 121.65/16.03 ((
% 121.65/16.03 (demorgan1) =>
% 121.65/16.03 ((
% 121.65/16.03 (demorgan2a) =>
% 121.65/16.03 ((
% 121.65/16.03 (demorgan2b2) =>
% 121.65/16.03 ((
% 121.65/16.03 (demorgan2b) =>
% 121.65/16.03 ((
% 121.65/16.03 (demorgan2) =>
% 121.65/16.03 ((
% 121.65/16.03 (woz13rule0) =>
% 121.65/16.03 ((
% 121.65/16.03 (woz13rule1) =>
% 121.65/16.03 ((
% 121.65/16.03 (woz13rule2) =>
% 121.65/16.03 ((
% 121.65/16.03 (woz13rule3) =>
% 121.65/16.03 ((
% 121.65/16.03 (woz13rule4) =>
% 121.65/16.03 ((
% 121.65/16.03 (woz1_1) =>
% 121.65/16.03 ((
% 121.65/16.03 (woz1_2) =>
% 121.65/16.03 ((
% 121.65/16.03 (woz1_3) =>
% 121.65/16.03 ((
% 121.65/16.03 (woz1_4) =>
% 121.65/16.03 ((
% 121.65/16.03 (woz1_5) =>
% 121.65/16.03 ((
% 121.65/16.03 (breln1all2) =>
% 121.65/16.03 ((
% 121.65/16.03 (breln1SetBreln1) =>
% 121.65/16.03 ((
% 121.65/16.03 (choice2fnsingleton) =>
% 121.65/16.03 ((
% 121.65/16.03 (setOfPairsIsBReln1) =>
% 121.65/16.03 ((
% 121.65/16.03 (breln1all1) =>
% 121.65/16.03 ((
% 121.65/16.03 (subbreln1) =>
% 121.65/16.03 ((
% 121.65/16.03 (eqbreln1) =>
% 121.65/16.03 ((
% 121.65/16.03 (breln1invprop) =>
% 121.65/16.03 ((
% 121.65/16.03 (breln1invI) =>
% 121.65/16.03 ((
% 121.65/16.03 (breln1invE) =>
% 121.65/16.03 ((
% 121.65/16.03 (breln1compprop) =>
% 121.65/16.03 ((
% 121.65/16.03 (breln1compI) =>
% 121.65/16.03 ((
% 121.65/16.03 (breln1compE) =>
% 121.65/16.03 ((
% 121.65/16.03 (breln1compEex) =>
% 121.65/16.03 ((
% 121.65/16.03 (breln1unionprop) =>
% 121.65/16.03 ((
% 121.65/16.03 (breln1unionIL) =>
% 121.65/16.03 ((
% 121.65/16.03 (breln1unionIR) =>
% 121.65/16.03 ((
% 121.65/16.03 (breln1unionI) =>
% 121.65/16.03 ((
% 121.65/16.03 (breln1unionE) =>
% 121.65/16.03 ((
% 121.65/16.03 (breln1unionEcases) =>
% 121.65/16.03 ((
% 121.65/16.03 (breln1unionCommutes) =>
% 121.65/16.03 ((
% 121.65/16.03 (woz2Ex) =>
% 121.65/16.03 ((
% 121.65/16.03 (woz2W) =>
% 121.65/16.03 ((
% 121.65/16.03 (woz2A) =>
% 121.65/16.03 ((
% 121.65/16.03 (woz2B) =>
% 121.65/16.03 ((
% 121.65/16.03 (image1Ex) =>
% 121.65/16.03 ((
% 121.65/16.03 (image1Ex1) =>
% 121.65/16.03 ((
% 121.65/16.03 (image1Equiv) =>
% 121.65/16.03 ((
% 121.65/16.03 (image1E) =>
% 121.65/16.03 ((
% 121.65/16.03 (image1I) =>
% 121.65/16.03 ((
% 121.65/16.03 (injFuncInInjFuncSet) =>
% 121.65/16.03 ((
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% 121.65/16.03 (
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% 121.65/16.03 ('#B') @ (
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% 121.65/16.03 (
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% 121.65/16.03 (
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% 121.65/16.03 injFuncSet)))))))) @
% 121.65/16.03 (
% 121.65/16.03 (
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% 121.65/16.03 (
% 121.65/16.03 ('#B') @ (
% 121.65/16.03 (
% 121.65/16.03 ('#C') @ in)))) @
% 121.65/16.03 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 121.65/16.03 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl89])).
% 121.65/16.03 thf(zip_derived_cl123, plain,
% 121.65/16.03 (~ (((prop2setE) =>
% 121.65/16.03 (((emptysetE) =>
% 121.65/16.03 (((emptysetimpfalse) =>
% 121.65/16.03 (((notinemptyset) =>
% 121.65/16.03 (((exuE3e) =>
% 121.65/16.03 (((setext) =>
% 121.65/16.03 (((emptyI) =>
% 121.65/16.03 (((noeltsimpempty) =>
% 121.65/16.03 (((setbeta) =>
% 121.65/16.03 (((nonemptyE1) =>
% 121.65/16.03 (((nonemptyI) =>
% 121.65/16.03 (((nonemptyI1) =>
% 121.65/16.03 (((setadjoinIL) =>
% 121.65/16.03 (((in @ emptyset @
% 121.65/16.03 (setadjoin @ emptyset @ emptyset)) =>
% 121.65/16.03 (((setadjoinIR) =>
% 121.65/16.03 (((setadjoinE) =>
% 121.65/16.03 (((setadjoinOr) =>
% 121.65/16.03 (((setoftrueEq) =>
% 121.65/16.03 (((powersetI) =>
% 121.65/16.03 (((emptyinPowerset) =>
% 121.65/16.03 (((emptyInPowerset) =>
% 121.65/16.03 (((powersetE) =>
% 121.65/16.03 (((setunionI) =>
% 121.65/16.03 (((setunionE) =>
% 121.65/16.03 (((subPowSU) =>
% 121.65/16.03 (((exuE2) =>
% 121.65/16.03 (((nonemptyImpWitness) =>
% 121.65/16.03 (((uniqinunit) =>
% 121.65/16.03 (((notinsingleton) =>
% 121.65/16.03 (((eqinunit) =>
% 121.65/16.03 ((
% 121.65/16.03 (singletonsswitch) =>
% 121.65/16.03 ((
% 121.65/16.03 (upairsetE) =>
% 121.65/16.03 ((
% 121.65/16.03 (upairsetIL) =>
% 121.65/16.03 ((
% 121.65/16.03 (upairsetIR) =>
% 121.65/16.03 ((
% 121.65/16.03 (emptyE1) =>
% 121.65/16.03 ((
% 121.65/16.03 (vacuousDall) =>
% 121.65/16.03 ((
% 121.65/16.03 (quantDeMorgan1) =>
% 121.65/16.03 ((
% 121.65/16.03 (quantDeMorgan2) =>
% 121.65/16.03 ((
% 121.65/16.03 (quantDeMorgan3) =>
% 121.65/16.03 ((
% 121.65/16.03 (quantDeMorgan4) =>
% 121.65/16.03 ((
% 121.65/16.03 (prop2setI) =>
% 121.65/16.03 ((
% 121.65/16.03 (prop2set2propI) =>
% 121.65/16.03 ((
% 121.65/16.03 (notdexE) =>
% 121.65/16.03 ((
% 121.65/16.03 (notdallE) =>
% 121.65/16.03 ((
% 121.65/16.03 (exuI1) =>
% 121.65/16.03 ((
% 121.65/16.03 (exuI3) =>
% 121.65/16.03 ((
% 121.65/16.03 (exuI2) =>
% 121.65/16.03 ((
% 121.65/16.03 (inCongP) =>
% 121.65/16.03 ((
% 121.65/16.03 (in__Cong) =>
% 121.65/16.03 ((
% 121.65/16.03 (exuE3u) =>
% 121.65/16.03 ((
% 121.65/16.03 (exu__Cong) =>
% 121.65/16.03 ((
% 121.65/16.03 (setadjoin__Cong) =>
% 121.65/16.03 ((
% 121.65/16.03 (powerset__Cong) =>
% 121.65/16.03 ((
% 121.65/16.03 (setunion__Cong) =>
% 121.65/16.03 ((
% 121.65/16.03 (exuEu) =>
% 121.65/16.03 ((
% 121.65/16.03 (descr__Cong) =>
% 121.65/16.03 ((
% 121.65/16.03 (dsetconstr__Cong) =>
% 121.65/16.03 ((
% 121.65/16.03 (subsetI1) =>
% 121.65/16.03 ((
% 121.65/16.03 (eqimpsubset2) =>
% 121.65/16.03 ((
% 121.65/16.03 (eqimpsubset1) =>
% 121.65/16.03 ((
% 121.65/16.03 (subsetI2) =>
% 121.65/16.03 ((
% 121.65/16.03 (emptysetsubset) =>
% 121.65/16.03 ((
% 121.65/16.03 (subsetE) =>
% 121.65/16.03 ((
% 121.65/16.03 (subsetE2) =>
% 121.65/16.03 ((
% 121.65/16.03 (notsubsetI) =>
% 121.65/16.03 ((
% 121.65/16.03 (notequalI1) =>
% 121.65/16.03 ((
% 121.65/16.03 (notequalI2) =>
% 121.65/16.03 ((
% 121.65/16.03 (subsetRefl) =>
% 121.65/16.03 ((
% 121.65/16.03 (subsetTrans) =>
% 121.65/16.03 ((
% 121.65/16.03 (setadjoinSub) =>
% 121.65/16.03 ((
% 121.65/16.03 (setadjoinSub2) =>
% 121.65/16.03 ((
% 121.65/16.03 (subset2powerset) =>
% 121.65/16.03 ((
% 121.65/16.03 (setextsub) =>
% 121.65/16.03 ((
% 121.65/16.03 (subsetemptysetimpeq) =>
% 121.65/16.03 ((
% 121.65/16.03 (powersetI1) =>
% 121.65/16.03 ((
% 121.65/16.03 (powersetE1) =>
% 121.65/16.03 ((
% 121.65/16.03 (inPowerset) =>
% 121.65/16.03 ((
% 121.65/16.03 (powersetsubset) =>
% 121.65/16.03 ((
% 121.65/16.03 (sepInPowerset) =>
% 121.65/16.03 ((
% 121.65/16.03 (sepSubset) =>
% 121.65/16.03 ((
% 121.65/16.03 (binunionIL) =>
% 121.65/16.03 ((
% 121.65/16.03 (upairset2IR) =>
% 121.65/16.03 ((
% 121.65/16.03 (binunionIR) =>
% 121.65/16.03 ((
% 121.65/16.03 (binunionEcases) =>
% 121.65/16.03 ((
% 121.65/16.03 (binunionE) =>
% 121.65/16.03 ((
% 121.65/16.03 (binunionLsub) =>
% 121.65/16.03 ((
% 121.65/16.03 (binunionRsub) =>
% 121.65/16.03 ((
% 121.65/16.03 (binintersectI) =>
% 121.65/16.03 ((
% 121.65/16.03 (binintersectSubset5) =>
% 121.65/16.03 ((
% 121.65/16.03 (binintersectEL) =>
% 121.65/16.03 ((
% 121.65/16.03 (binintersectLsub) =>
% 121.65/16.03 ((
% 121.65/16.03 (binintersectSubset2) =>
% 121.65/16.03 ((
% 121.65/16.03 (binintersectSubset3) =>
% 121.65/16.03 ((
% 121.65/16.03 (binintersectER) =>
% 121.65/16.03 ((
% 121.65/16.03 (disjointsetsI1) =>
% 121.65/16.03 ((
% 121.65/16.03 (binintersectRsub) =>
% 121.65/16.03 ((
% 121.65/16.03 (binintersectSubset4) =>
% 121.65/16.03 ((
% 121.65/16.03 (binintersectSubset1) =>
% 121.65/16.03 ((
% 121.65/16.03 (bs114d) =>
% 121.65/16.03 ((
% 121.65/16.03 (setminusI) =>
% 121.65/16.03 ((
% 121.65/16.03 (setminusEL) =>
% 121.65/16.03 ((
% 121.65/16.03 (setminusER) =>
% 121.65/16.03 ((
% 121.65/16.03 (setminusSubset2) =>
% 121.65/16.03 ((
% 121.65/16.03 (setminusERneg) =>
% 121.65/16.03 ((
% 121.65/16.03 (setminusELneg) =>
% 121.65/16.03 ((
% 121.65/16.03 (setminusILneg) =>
% 121.65/16.03 ((
% 121.65/16.03 (setminusIRneg) =>
% 121.65/16.03 ((
% 121.65/16.03 (setminusLsub) =>
% 121.65/16.03 ((
% 121.65/16.03 (setminusSubset1) =>
% 121.65/16.03 ((
% 121.65/16.03 (symdiffE) =>
% 121.65/16.03 ((
% 121.65/16.03 (symdiffI1) =>
% 121.65/16.03 ((
% 121.65/16.03 (symdiffI2) =>
% 121.65/16.03 ((
% 121.65/16.03 (symdiffIneg1) =>
% 121.65/16.03 ((
% 121.65/16.03 (symdiffIneg2) =>
% 121.65/16.03 ((
% 121.65/16.03 (secondinupair) =>
% 121.65/16.03 ((
% 121.65/16.03 (setukpairIL) =>
% 121.65/16.03 ((
% 121.65/16.03 (setukpairIR) =>
% 121.65/16.03 ((
% 121.65/16.03 (kpairiskpair) =>
% 121.65/16.03 ((
% 121.65/16.03 (kpairp) =>
% 121.65/16.03 ((
% 121.65/16.03 (singletonsubset) =>
% 121.65/16.03 ((
% 121.65/16.03 (singletoninpowerset) =>
% 121.65/16.03 ((
% 121.65/16.03 (singletoninpowunion) =>
% 121.65/16.03 ((
% 121.65/16.03 (upairset2E) =>
% 121.65/16.03 ((
% 121.65/16.03 (upairsubunion) =>
% 121.65/16.03 ((
% 121.65/16.03 (upairinpowunion) =>
% 121.65/16.03 ((
% 121.65/16.03 (ubforcartprodlem1) =>
% 121.65/16.03 ((
% 121.65/16.03 (ubforcartprodlem2) =>
% 121.65/16.03 ((
% 121.65/16.03 (ubforcartprodlem3) =>
% 121.65/16.03 ((
% 121.65/16.03 (cartprodpairin) =>
% 121.65/16.03 ((
% 121.65/16.03 (cartprodmempair1) =>
% 121.65/16.03 ((
% 121.65/16.03 (cartprodmempair) =>
% 121.65/16.03 ((
% 121.65/16.03 (setunionE2) =>
% 121.65/16.03 ((
% 121.65/16.03 (setunionsingleton1) =>
% 121.65/16.03 ((
% 121.65/16.03 (setunionsingleton2) =>
% 121.65/16.03 ((
% 121.65/16.03 (setunionsingleton) =>
% 121.65/16.03 ((
% 121.65/16.03 (singletonprop) =>
% 121.65/16.03 ((
% 121.65/16.03 (ex1E1) =>
% 121.65/16.03 ((
% 121.65/16.03 (ex1I) =>
% 121.65/16.03 ((
% 121.65/16.03 (ex1I2) =>
% 121.65/16.03 ((
% 121.65/16.03 (singletonsuniq) =>
% 121.65/16.03 ((
% 121.65/16.03 (setukpairinjL1) =>
% 121.65/16.03 ((
% 121.65/16.03 (kfstsingleton) =>
% 121.65/16.03 ((
% 121.65/16.03 (theprop) =>
% 121.65/16.03 ((
% 121.65/16.03 (kfstpairEq) =>
% 121.65/16.03 ((
% 121.65/16.03 (cartprodfstin) =>
% 121.65/16.03 ((
% 121.65/16.03 (setukpairinjL2) =>
% 121.65/16.03 ((
% 121.65/16.03 (setukpairinjL) =>
% 121.65/16.03 ((
% 121.65/16.03 (setukpairinjR11) =>
% 121.65/16.03 ((
% 121.65/16.03 (setukpairinjR12) =>
% 121.65/16.03 ((
% 121.65/16.03 (setukpairinjR1) =>
% 121.65/16.03 ((
% 121.65/16.03 (upairequniteq) =>
% 121.65/16.03 ((
% 121.65/16.03 (setukpairinjR2) =>
% 121.65/16.03 ((
% 121.65/16.03 (setukpairinjR) =>
% 121.65/16.03 ((
% 121.65/16.03 (ksndsingleton) =>
% 121.65/16.03 ((
% 121.65/16.03 (ksndpairEq) =>
% 121.65/16.03 ((
% 121.65/16.03 (kpairsurjEq) =>
% 121.65/16.03 ((
% 121.65/16.03 (cartprodsndin) =>
% 121.65/16.03 ((
% 121.65/16.03 (cartprodpairmemEL) =>
% 121.65/16.03 ((
% 121.65/16.03 (cartprodpairmemER) =>
% 121.65/16.03 ((
% 121.65/16.03 (cartprodmempaircEq) =>
% 121.65/16.03 ((
% 121.65/16.03 (cartprodfstpairEq) =>
% 121.65/16.03 ((
% 121.65/16.03 (cartprodsndpairEq) =>
% 121.65/16.03 ((
% 121.65/16.03 (cartprodpairsurjEq) =>
% 121.65/16.03 ((
% 121.65/16.03 (dpsetconstrI) =>
% 121.65/16.03 ((
% 121.65/16.03 (dpsetconstrSub) =>
% 121.65/16.03 ((
% 121.65/16.03 (setOfPairsIsBReln) =>
% 121.65/16.03 ((
% 121.65/16.03 (dpsetconstrERa) =>
% 121.65/16.03 ((
% 121.65/16.03 (dpsetconstrEL1) =>
% 121.65/16.03 ((
% 121.65/16.03 (dpsetconstrEL2) =>
% 121.65/16.03 ((
% 121.65/16.03 (dpsetconstrER) =>
% 121.65/16.03 ((
% 121.65/16.03 (funcImageSingleton) =>
% 121.65/16.03 ((
% 121.65/16.03 (apProp) =>
% 121.65/16.03 ((
% 121.65/16.03 (app) =>
% 121.65/16.03 ((
% 121.65/16.03 (infuncsetfunc) =>
% 121.65/16.03 ((
% 121.65/16.03 (ap2p) =>
% 121.65/16.03 ((
% 121.65/16.03 (funcinfuncset) =>
% 121.65/16.03 ((
% 121.65/16.03 (lamProp) =>
% 121.65/16.03 ((
% 121.65/16.03 (lamp) =>
% 121.65/16.03 ((
% 121.65/16.03 (lam2p) =>
% 121.65/16.03 ((
% 121.65/16.03 (brelnall1) =>
% 121.65/16.03 ((
% 121.65/16.03 (brelnall2) =>
% 121.65/16.03 ((
% 121.65/16.03 (ex1E2) =>
% 121.65/16.03 ((
% 121.65/16.03 (funcGraphProp1) =>
% 121.65/16.03 ((
% 121.65/16.03 (funcGraphProp3) =>
% 121.65/16.03 ((
% 121.65/16.03 (funcGraphProp2) =>
% 121.65/16.03 ((
% 121.65/16.03 (funcextLem) =>
% 121.65/16.03 ((
% 121.65/16.03 (funcGraphProp4) =>
% 121.65/16.03 ((
% 121.65/16.03 (subbreln) =>
% 121.65/16.03 ((
% 121.65/16.03 (eqbreln) =>
% 121.65/16.03 ((
% 121.65/16.03 (funcext) =>
% 121.65/16.03 ((
% 121.65/16.03 (funcext2) =>
% 121.65/16.03 ((
% 121.65/16.03 (ap2apEq1) =>
% 121.65/16.03 ((
% 121.65/16.03 (ap2apEq2) =>
% 121.65/16.03 ((
% 121.65/16.03 (beta1) =>
% 121.65/16.03 ((
% 121.65/16.03 (eta1) =>
% 121.65/16.03 ((
% 121.65/16.03 (lam2lamEq) =>
% 121.65/16.03 ((
% 121.65/16.03 (beta2) =>
% 121.65/16.03 ((
% 121.65/16.03 (eta2) =>
% 121.65/16.03 ((
% 121.65/16.03 (iffalseProp1) =>
% 121.65/16.03 ((
% 121.65/16.03 (iffalseProp2) =>
% 121.65/16.03 ((
% 121.65/16.03 (iftrueProp1) =>
% 121.65/16.03 ((
% 121.65/16.03 (iftrueProp2) =>
% 121.65/16.03 ((
% 121.65/16.03 (ifSingleton) =>
% 121.65/16.03 ((
% 121.65/16.03 (ifp) =>
% 121.65/16.03 ((
% 121.65/16.03 (theeq) =>
% 121.65/16.03 ((
% 121.65/16.03 (iftrue) =>
% 121.65/16.03 ((
% 121.65/16.03 (iffalse) =>
% 121.65/16.03 ((
% 121.65/16.03 (iftrueorfalse) =>
% 121.65/16.03 ((
% 121.65/16.03 (binintersectT_lem) =>
% 121.65/16.03 ((
% 121.65/16.03 (binunionT_lem) =>
% 121.65/16.03 ((
% 121.65/16.03 (powersetT_lem) =>
% 121.65/16.03 ((
% 121.65/16.03 (setminusT_lem) =>
% 121.65/16.03 ((
% 121.65/16.03 (complementT_lem) =>
% 121.65/16.03 ((
% 121.65/16.03 (setextT) =>
% 121.65/16.03 ((
% 121.65/16.03 (subsetTI) =>
% 121.65/16.03 ((
% 121.65/16.03 (powersetTI1) =>
% 121.65/16.03 ((
% 121.65/16.03 (powersetTE1) =>
% 121.65/16.03 ((
% 121.65/16.03 (complementTI1) =>
% 121.65/16.03 ((
% 121.65/16.03 (complementTE1) =>
% 121.65/16.03 ((
% 121.65/16.03 (binintersectTELcontra) =>
% 121.65/16.03 ((
% 121.65/16.03 (binintersectTERcontra) =>
% 121.65/16.03 ((
% 121.65/16.03 (contrasubsetT) =>
% 121.65/16.03 ((
% 121.65/16.03 (contrasubsetT1) =>
% 121.65/16.03 ((
% 121.65/16.03 (contrasubsetT2) =>
% 121.65/16.03 ((
% 121.65/16.03 (contrasubsetT3) =>
% 121.65/16.03 ((
% 121.65/16.03 (doubleComplementI1) =>
% 121.65/16.03 ((
% 121.65/16.03 (doubleComplementE1) =>
% 121.65/16.03 ((
% 121.65/16.03 (doubleComplementSub1) =>
% 121.65/16.03 ((
% 121.65/16.03 (doubleComplementSub2) =>
% 121.65/16.03 ((
% 121.65/16.03 (doubleComplementEq) =>
% 121.65/16.03 ((
% 121.65/16.03 (complementTnotintersectT) =>
% 121.65/16.03 ((
% 121.65/16.03 (complementImpComplementIntersect) =>
% 121.65/16.03 ((
% 121.65/16.03 (complementSubsetComplementIntersect) =>
% 121.65/16.03 ((
% 121.65/16.03 (complementInPowersetComplementIntersect) =>
% 121.65/16.03 ((
% 121.65/16.03 (contraSubsetComplement) =>
% 121.65/16.03 ((
% 121.65/16.03 (complementTcontraSubset) =>
% 121.65/16.03 ((
% 121.65/16.03 (binunionTILcontra) =>
% 121.65/16.03 ((
% 121.65/16.03 (binunionTIRcontra) =>
% 121.65/16.03 ((
% 121.65/16.03 (inIntersectImpInUnion) =>
% 121.65/16.03 ((
% 121.65/16.03 (inIntersectImpInUnion2) =>
% 121.65/16.03 ((
% 121.65/16.03 (inIntersectImpInIntersectUnions) =>
% 121.65/16.03 ((
% 121.65/16.03 (intersectInPowersetIntersectUnions) =>
% 121.65/16.03 ((
% 121.65/16.03 (inComplementUnionImpNotIn1) =>
% 121.65/16.03 ((
% 121.65/16.03 (inComplementUnionImpInComplement1) =>
% 121.65/16.03 ((
% 121.65/16.03 (binunionTE) =>
% 121.65/16.03 ((
% 121.65/16.03 (binunionTEcontra) =>
% 121.65/16.03 ((
% 121.65/16.03 (demorgan2a1) =>
% 121.65/16.03 ((
% 121.65/16.03 (complementUnionInPowersetComplement) =>
% 121.65/16.03 ((
% 121.65/16.03 (demorgan2a2) =>
% 121.65/16.03 ((
% 121.65/16.03 (demorgan1a) =>
% 121.65/16.03 ((
% 121.65/16.03 (demorgan1b) =>
% 121.65/16.03 ((
% 121.65/16.03 (demorgan1) =>
% 121.65/16.03 ((
% 121.65/16.03 (demorgan2a) =>
% 121.65/16.03 ((
% 121.65/16.03 (demorgan2b2) =>
% 121.65/16.03 ((
% 121.65/16.03 (demorgan2b) =>
% 121.65/16.03 ((
% 121.65/16.03 (demorgan2) =>
% 121.65/16.03 ((
% 121.65/16.03 (woz13rule0) =>
% 121.65/16.03 ((
% 121.65/16.03 (woz13rule1) =>
% 121.65/16.03 ((
% 121.65/16.03 (woz13rule2) =>
% 121.65/16.03 ((
% 121.65/16.03 (woz13rule3) =>
% 121.65/16.03 ((
% 121.65/16.03 (woz13rule4) =>
% 121.65/16.03 ((
% 121.65/16.03 (woz1_1) =>
% 121.65/16.03 ((
% 121.65/16.03 (woz1_2) =>
% 121.65/16.03 ((
% 121.65/16.03 (woz1_3) =>
% 121.65/16.03 ((
% 121.65/16.03 (woz1_4) =>
% 121.65/16.03 ((
% 121.65/16.03 (woz1_5) =>
% 121.65/16.03 ((
% 121.65/16.03 (breln1all2) =>
% 121.65/16.03 ((
% 121.65/16.03 (breln1SetBreln1) =>
% 121.65/16.03 ((
% 121.65/16.03 (choice2fnsingleton) =>
% 121.65/16.03 ((
% 121.65/16.03 (setOfPairsIsBReln1) =>
% 121.65/16.03 ((
% 121.65/16.03 (breln1all1) =>
% 121.65/16.03 ((
% 121.65/16.03 (subbreln1) =>
% 121.65/16.03 ((
% 121.65/16.03 (eqbreln1) =>
% 121.65/16.03 ((
% 121.65/16.03 (breln1invprop) =>
% 121.65/16.03 ((
% 121.65/16.03 (breln1invI) =>
% 121.65/16.03 ((
% 121.65/16.03 (breln1invE) =>
% 121.65/16.03 ((
% 121.65/16.03 (breln1compprop) =>
% 121.65/16.03 ((
% 121.65/16.03 (breln1compI) =>
% 121.65/16.03 ((
% 121.65/16.03 (breln1compE) =>
% 121.65/16.03 ((
% 121.65/16.03 (breln1compEex) =>
% 121.65/16.03 ((
% 121.65/16.03 (breln1unionprop) =>
% 121.65/16.03 ((
% 121.65/16.03 (breln1unionIL) =>
% 121.65/16.03 ((
% 121.65/16.03 (breln1unionIR) =>
% 121.65/16.03 ((
% 121.65/16.03 (breln1unionI) =>
% 121.65/16.03 ((
% 121.65/16.03 (breln1unionE) =>
% 121.65/16.03 ((
% 121.65/16.03 (breln1unionEcases) =>
% 121.65/16.03 ((
% 121.65/16.03 (breln1unionCommutes) =>
% 121.65/16.03 ((
% 121.65/16.03 (woz2Ex) =>
% 121.65/16.03 ((
% 121.65/16.03 (woz2W) =>
% 121.65/16.03 ((
% 121.65/16.03 (woz2A) =>
% 121.65/16.03 ((
% 121.65/16.03 (woz2B) =>
% 121.65/16.03 ((
% 121.65/16.03 (image1Ex) =>
% 121.65/16.03 ((
% 121.65/16.03 (image1Ex1) =>
% 121.65/16.03 ((
% 121.65/16.03 (image1Equiv) =>
% 121.65/16.03 ((
% 121.65/16.03 (image1E) =>
% 121.65/16.03 ((
% 121.65/16.03 (image1I) =>
% 121.65/16.03 ((
% 121.65/16.03 (injFuncInInjFuncSet) =>
% 121.65/16.03 ((
% 121.65/16.03 (!!) @ (
% 121.65/16.03 (('#B') @ (
% 121.65/16.03 !!) @
% 121.65/16.03 (
% 121.65/16.03 (
% 121.65/16.03 ('#B') @ (
% 121.65/16.03 (
% 121.65/16.03 ('#B') @ (
% 121.65/16.03 !!))) @
% 121.65/16.03 (
% 121.65/16.03 (
% 121.65/16.03 ('#S') @ (
% 121.65/16.03 (
% 121.65/16.03 ('#B') @ (
% 121.65/16.03 '#S') @
% 121.65/16.03 (
% 121.65/16.03 (
% 121.65/16.03 ('#B') @ (
% 121.65/16.03 (
% 121.65/16.03 ('#B') @ (
% 121.65/16.03 '#S'))) @
% 121.65/16.03 (
% 121.65/16.03 (
% 121.65/16.03 ('#B') @ (
% 121.65/16.03 (
% 121.65/16.03 ('#B') @ (
% 121.65/16.03 (
% 121.65/16.03 ('#B') @ (
% 121.65/16.03 =>))))) @
% 121.65/16.03 (
% 121.65/16.03 (
% 121.65/16.03 ('#B') @ (
% 121.65/16.03 (
% 121.65/16.03 ('#B') @ (
% 121.65/16.03 (
% 121.65/16.03 ('#C') @ in)))) @
% 121.65/16.03 injFuncSet)))))))) @
% 121.65/16.03 (
% 121.65/16.03 (
% 121.65/16.03 ('#B') @ (
% 121.65/16.03 (
% 121.65/16.03 ('#B') @ (
% 121.65/16.03 (
% 121.65/16.03 ('#C') @ in)))) @
% 121.65/16.03 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 121.65/16.03 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl105])).
% 121.65/16.03 thf(zip_derived_cl142, plain,
% 121.65/16.03 (~ (((emptysetE) =>
% 121.65/16.03 (((emptysetimpfalse) =>
% 121.65/16.03 (((notinemptyset) =>
% 121.65/16.03 (((exuE3e) =>
% 121.65/16.03 (((setext) =>
% 121.65/16.03 (((emptyI) =>
% 121.65/16.03 (((noeltsimpempty) =>
% 121.65/16.03 (((setbeta) =>
% 121.65/16.03 (((nonemptyE1) =>
% 121.65/16.03 (((nonemptyI) =>
% 121.65/16.03 (((nonemptyI1) =>
% 121.65/16.03 (((setadjoinIL) =>
% 121.65/16.03 (((in @ emptyset @
% 121.65/16.03 (setadjoin @ emptyset @ emptyset)) =>
% 121.65/16.03 (((setadjoinIR) =>
% 121.65/16.03 (((setadjoinE) =>
% 121.65/16.03 (((setadjoinOr) =>
% 121.65/16.03 (((setoftrueEq) =>
% 121.65/16.03 (((powersetI) =>
% 121.65/16.03 (((emptyinPowerset) =>
% 121.65/16.03 (((emptyInPowerset) =>
% 121.65/16.03 (((powersetE) =>
% 121.65/16.03 (((setunionI) =>
% 121.65/16.03 (((setunionE) =>
% 121.65/16.03 (((subPowSU) =>
% 121.65/16.03 (((exuE2) =>
% 121.65/16.03 (((nonemptyImpWitness) =>
% 121.65/16.03 (((uniqinunit) =>
% 121.65/16.03 (((notinsingleton) =>
% 121.65/16.03 (((eqinunit) =>
% 121.65/16.03 (((singletonsswitch) =>
% 121.65/16.03 ((
% 121.65/16.03 (upairsetE) =>
% 121.65/16.03 ((
% 121.65/16.03 (upairsetIL) =>
% 121.65/16.03 ((
% 121.65/16.03 (upairsetIR) =>
% 121.65/16.03 ((
% 121.65/16.03 (emptyE1) =>
% 121.65/16.03 ((
% 121.65/16.03 (vacuousDall) =>
% 121.65/16.03 ((
% 121.65/16.03 (quantDeMorgan1) =>
% 121.65/16.03 ((
% 121.65/16.03 (quantDeMorgan2) =>
% 121.65/16.03 ((
% 121.65/16.03 (quantDeMorgan3) =>
% 121.65/16.03 ((
% 121.65/16.03 (quantDeMorgan4) =>
% 121.65/16.03 ((
% 121.65/16.03 (prop2setI) =>
% 121.65/16.03 ((
% 121.65/16.03 (prop2set2propI) =>
% 121.65/16.03 ((
% 121.65/16.03 (notdexE) =>
% 121.65/16.03 ((
% 121.65/16.03 (notdallE) =>
% 121.65/16.03 ((
% 121.65/16.03 (exuI1) =>
% 121.65/16.03 ((
% 121.65/16.03 (exuI3) =>
% 121.65/16.03 ((
% 121.65/16.03 (exuI2) =>
% 121.65/16.03 ((
% 121.65/16.03 (inCongP) =>
% 121.65/16.03 ((
% 121.65/16.03 (in__Cong) =>
% 121.65/16.03 ((
% 121.65/16.03 (exuE3u) =>
% 121.65/16.03 ((
% 121.65/16.03 (exu__Cong) =>
% 121.65/16.03 ((
% 121.65/16.03 (setadjoin__Cong) =>
% 121.65/16.03 ((
% 121.65/16.03 (powerset__Cong) =>
% 121.65/16.03 ((
% 121.65/16.03 (setunion__Cong) =>
% 121.65/16.03 ((
% 121.65/16.03 (exuEu) =>
% 121.65/16.03 ((
% 121.65/16.03 (descr__Cong) =>
% 121.65/16.03 ((
% 121.65/16.03 (dsetconstr__Cong) =>
% 121.65/16.03 ((
% 121.65/16.03 (subsetI1) =>
% 121.65/16.03 ((
% 121.65/16.03 (eqimpsubset2) =>
% 121.65/16.03 ((
% 121.65/16.03 (eqimpsubset1) =>
% 121.65/16.03 ((
% 121.65/16.03 (subsetI2) =>
% 121.65/16.03 ((
% 121.65/16.03 (emptysetsubset) =>
% 121.65/16.03 ((
% 121.65/16.03 (subsetE) =>
% 121.65/16.03 ((
% 121.65/16.03 (subsetE2) =>
% 121.65/16.03 ((
% 121.65/16.03 (notsubsetI) =>
% 121.65/16.03 ((
% 121.65/16.03 (notequalI1) =>
% 121.65/16.03 ((
% 121.65/16.03 (notequalI2) =>
% 121.65/16.03 ((
% 121.65/16.03 (subsetRefl) =>
% 121.65/16.03 ((
% 121.65/16.03 (subsetTrans) =>
% 121.65/16.03 ((
% 121.65/16.03 (setadjoinSub) =>
% 121.65/16.03 ((
% 121.65/16.03 (setadjoinSub2) =>
% 121.65/16.03 ((
% 121.65/16.03 (subset2powerset) =>
% 121.65/16.03 ((
% 121.65/16.03 (setextsub) =>
% 121.65/16.03 ((
% 121.65/16.03 (subsetemptysetimpeq) =>
% 121.65/16.03 ((
% 121.65/16.03 (powersetI1) =>
% 121.65/16.03 ((
% 121.65/16.03 (powersetE1) =>
% 121.65/16.03 ((
% 121.65/16.03 (inPowerset) =>
% 121.65/16.03 ((
% 121.65/16.03 (powersetsubset) =>
% 121.65/16.03 ((
% 121.65/16.03 (sepInPowerset) =>
% 121.65/16.03 ((
% 121.65/16.03 (sepSubset) =>
% 121.65/16.03 ((
% 121.65/16.03 (binunionIL) =>
% 121.65/16.03 ((
% 121.65/16.03 (upairset2IR) =>
% 121.65/16.03 ((
% 121.65/16.03 (binunionIR) =>
% 121.65/16.03 ((
% 121.65/16.03 (binunionEcases) =>
% 121.65/16.03 ((
% 121.65/16.03 (binunionE) =>
% 121.65/16.03 ((
% 121.65/16.03 (binunionLsub) =>
% 121.65/16.03 ((
% 121.65/16.03 (binunionRsub) =>
% 121.65/16.03 ((
% 121.65/16.03 (binintersectI) =>
% 121.65/16.03 ((
% 121.65/16.03 (binintersectSubset5) =>
% 121.65/16.03 ((
% 121.65/16.03 (binintersectEL) =>
% 121.65/16.03 ((
% 121.65/16.03 (binintersectLsub) =>
% 121.65/16.03 ((
% 121.65/16.03 (binintersectSubset2) =>
% 121.65/16.03 ((
% 121.65/16.03 (binintersectSubset3) =>
% 121.65/16.03 ((
% 121.65/16.03 (binintersectER) =>
% 121.65/16.03 ((
% 121.65/16.03 (disjointsetsI1) =>
% 121.65/16.03 ((
% 121.65/16.03 (binintersectRsub) =>
% 121.65/16.03 ((
% 121.65/16.03 (binintersectSubset4) =>
% 121.65/16.03 ((
% 121.65/16.03 (binintersectSubset1) =>
% 121.65/16.03 ((
% 121.65/16.03 (bs114d) =>
% 121.65/16.03 ((
% 121.65/16.03 (setminusI) =>
% 121.65/16.03 ((
% 121.65/16.03 (setminusEL) =>
% 121.65/16.03 ((
% 121.65/16.03 (setminusER) =>
% 121.65/16.03 ((
% 121.65/16.03 (setminusSubset2) =>
% 121.65/16.03 ((
% 121.65/16.03 (setminusERneg) =>
% 121.65/16.03 ((
% 121.65/16.03 (setminusELneg) =>
% 121.65/16.03 ((
% 121.65/16.03 (setminusILneg) =>
% 121.65/16.03 ((
% 121.65/16.03 (setminusIRneg) =>
% 121.65/16.03 ((
% 121.65/16.03 (setminusLsub) =>
% 121.65/16.03 ((
% 121.65/16.03 (setminusSubset1) =>
% 121.65/16.03 ((
% 121.65/16.03 (symdiffE) =>
% 121.65/16.03 ((
% 121.65/16.03 (symdiffI1) =>
% 121.65/16.03 ((
% 121.65/16.03 (symdiffI2) =>
% 121.65/16.03 ((
% 121.65/16.03 (symdiffIneg1) =>
% 121.65/16.03 ((
% 121.65/16.03 (symdiffIneg2) =>
% 121.65/16.03 ((
% 121.65/16.03 (secondinupair) =>
% 121.65/16.03 ((
% 121.65/16.03 (setukpairIL) =>
% 121.65/16.03 ((
% 121.65/16.03 (setukpairIR) =>
% 121.65/16.03 ((
% 121.65/16.03 (kpairiskpair) =>
% 121.65/16.03 ((
% 121.65/16.03 (kpairp) =>
% 121.65/16.03 ((
% 121.65/16.03 (singletonsubset) =>
% 121.65/16.03 ((
% 121.65/16.03 (singletoninpowerset) =>
% 121.65/16.03 ((
% 121.65/16.03 (singletoninpowunion) =>
% 121.65/16.03 ((
% 121.65/16.03 (upairset2E) =>
% 121.65/16.03 ((
% 121.65/16.03 (upairsubunion) =>
% 121.65/16.03 ((
% 121.65/16.03 (upairinpowunion) =>
% 121.65/16.03 ((
% 121.65/16.03 (ubforcartprodlem1) =>
% 121.65/16.03 ((
% 121.65/16.03 (ubforcartprodlem2) =>
% 121.65/16.03 ((
% 121.65/16.03 (ubforcartprodlem3) =>
% 121.65/16.03 ((
% 121.65/16.03 (cartprodpairin) =>
% 121.65/16.03 ((
% 121.65/16.03 (cartprodmempair1) =>
% 121.65/16.03 ((
% 121.65/16.03 (cartprodmempair) =>
% 121.65/16.03 ((
% 121.65/16.03 (setunionE2) =>
% 121.65/16.03 ((
% 121.65/16.03 (setunionsingleton1) =>
% 121.65/16.03 ((
% 121.65/16.03 (setunionsingleton2) =>
% 121.65/16.03 ((
% 121.65/16.03 (setunionsingleton) =>
% 121.65/16.03 ((
% 121.65/16.03 (singletonprop) =>
% 121.65/16.03 ((
% 121.65/16.03 (ex1E1) =>
% 121.65/16.03 ((
% 121.65/16.03 (ex1I) =>
% 121.65/16.03 ((
% 121.65/16.03 (ex1I2) =>
% 121.65/16.03 ((
% 121.65/16.03 (singletonsuniq) =>
% 121.65/16.03 ((
% 121.65/16.03 (setukpairinjL1) =>
% 121.65/16.03 ((
% 121.65/16.03 (kfstsingleton) =>
% 121.65/16.03 ((
% 121.65/16.03 (theprop) =>
% 121.65/16.03 ((
% 121.65/16.03 (kfstpairEq) =>
% 121.65/16.03 ((
% 121.65/16.03 (cartprodfstin) =>
% 121.65/16.03 ((
% 121.65/16.03 (setukpairinjL2) =>
% 121.65/16.03 ((
% 121.65/16.03 (setukpairinjL) =>
% 121.65/16.03 ((
% 121.65/16.03 (setukpairinjR11) =>
% 121.65/16.03 ((
% 121.65/16.03 (setukpairinjR12) =>
% 121.65/16.03 ((
% 121.65/16.03 (setukpairinjR1) =>
% 121.65/16.03 ((
% 121.65/16.03 (upairequniteq) =>
% 121.65/16.03 ((
% 121.65/16.03 (setukpairinjR2) =>
% 121.65/16.03 ((
% 121.65/16.03 (setukpairinjR) =>
% 121.65/16.03 ((
% 121.65/16.03 (ksndsingleton) =>
% 121.65/16.03 ((
% 121.65/16.03 (ksndpairEq) =>
% 121.65/16.03 ((
% 121.65/16.03 (kpairsurjEq) =>
% 121.65/16.03 ((
% 121.65/16.03 (cartprodsndin) =>
% 121.65/16.03 ((
% 121.65/16.03 (cartprodpairmemEL) =>
% 121.65/16.03 ((
% 121.65/16.03 (cartprodpairmemER) =>
% 121.65/16.03 ((
% 121.65/16.03 (cartprodmempaircEq) =>
% 121.65/16.03 ((
% 121.65/16.03 (cartprodfstpairEq) =>
% 121.65/16.03 ((
% 121.65/16.03 (cartprodsndpairEq) =>
% 121.65/16.03 ((
% 121.65/16.03 (cartprodpairsurjEq) =>
% 121.65/16.03 ((
% 121.65/16.03 (dpsetconstrI) =>
% 121.65/16.03 ((
% 121.65/16.03 (dpsetconstrSub) =>
% 121.65/16.03 ((
% 121.65/16.03 (setOfPairsIsBReln) =>
% 121.65/16.03 ((
% 121.65/16.03 (dpsetconstrERa) =>
% 121.65/16.03 ((
% 121.65/16.03 (dpsetconstrEL1) =>
% 121.65/16.03 ((
% 121.65/16.03 (dpsetconstrEL2) =>
% 121.65/16.03 ((
% 121.65/16.03 (dpsetconstrER) =>
% 121.65/16.03 ((
% 121.65/16.03 (funcImageSingleton) =>
% 121.65/16.03 ((
% 121.65/16.03 (apProp) =>
% 121.65/16.03 ((
% 121.65/16.03 (app) =>
% 121.65/16.03 ((
% 121.65/16.03 (infuncsetfunc) =>
% 121.65/16.03 ((
% 121.65/16.03 (ap2p) =>
% 121.65/16.03 ((
% 121.65/16.03 (funcinfuncset) =>
% 121.65/16.03 ((
% 121.65/16.03 (lamProp) =>
% 121.65/16.03 ((
% 121.65/16.03 (lamp) =>
% 121.65/16.03 ((
% 121.65/16.03 (lam2p) =>
% 121.65/16.03 ((
% 121.65/16.03 (brelnall1) =>
% 121.65/16.03 ((
% 121.65/16.03 (brelnall2) =>
% 121.65/16.03 ((
% 121.65/16.03 (ex1E2) =>
% 121.65/16.03 ((
% 121.65/16.03 (funcGraphProp1) =>
% 121.65/16.03 ((
% 121.65/16.03 (funcGraphProp3) =>
% 121.65/16.03 ((
% 121.65/16.03 (funcGraphProp2) =>
% 121.65/16.03 ((
% 121.65/16.03 (funcextLem) =>
% 121.65/16.03 ((
% 121.65/16.03 (funcGraphProp4) =>
% 121.65/16.03 ((
% 121.65/16.03 (subbreln) =>
% 121.65/16.03 ((
% 121.65/16.03 (eqbreln) =>
% 121.65/16.03 ((
% 121.65/16.03 (funcext) =>
% 121.65/16.03 ((
% 121.65/16.03 (funcext2) =>
% 121.65/16.03 ((
% 121.65/16.03 (ap2apEq1) =>
% 121.65/16.03 ((
% 121.65/16.03 (ap2apEq2) =>
% 121.65/16.03 ((
% 121.65/16.03 (beta1) =>
% 121.65/16.03 ((
% 121.65/16.03 (eta1) =>
% 121.65/16.03 ((
% 121.65/16.03 (lam2lamEq) =>
% 121.65/16.03 ((
% 121.65/16.03 (beta2) =>
% 121.65/16.03 ((
% 121.65/16.03 (eta2) =>
% 121.65/16.03 ((
% 121.65/16.03 (iffalseProp1) =>
% 121.65/16.03 ((
% 121.65/16.03 (iffalseProp2) =>
% 121.65/16.03 ((
% 121.65/16.03 (iftrueProp1) =>
% 121.65/16.03 ((
% 121.65/16.03 (iftrueProp2) =>
% 121.65/16.03 ((
% 121.65/16.03 (ifSingleton) =>
% 121.65/16.03 ((
% 121.65/16.03 (ifp) =>
% 121.65/16.03 ((
% 121.65/16.03 (theeq) =>
% 121.65/16.03 ((
% 121.65/16.03 (iftrue) =>
% 121.65/16.03 ((
% 121.65/16.03 (iffalse) =>
% 121.65/16.03 ((
% 121.65/16.03 (iftrueorfalse) =>
% 121.65/16.03 ((
% 121.65/16.03 (binintersectT_lem) =>
% 121.65/16.03 ((
% 121.65/16.03 (binunionT_lem) =>
% 121.65/16.03 ((
% 121.65/16.03 (powersetT_lem) =>
% 121.65/16.03 ((
% 121.65/16.03 (setminusT_lem) =>
% 121.65/16.03 ((
% 121.65/16.03 (complementT_lem) =>
% 121.65/16.03 ((
% 121.65/16.03 (setextT) =>
% 121.65/16.03 ((
% 121.65/16.03 (subsetTI) =>
% 121.65/16.03 ((
% 121.65/16.03 (powersetTI1) =>
% 121.65/16.03 ((
% 121.65/16.03 (powersetTE1) =>
% 121.65/16.03 ((
% 121.65/16.03 (complementTI1) =>
% 121.65/16.03 ((
% 121.65/16.03 (complementTE1) =>
% 121.65/16.03 ((
% 121.65/16.03 (binintersectTELcontra) =>
% 121.65/16.03 ((
% 121.65/16.03 (binintersectTERcontra) =>
% 121.65/16.03 ((
% 121.65/16.03 (contrasubsetT) =>
% 121.65/16.03 ((
% 121.65/16.03 (contrasubsetT1) =>
% 121.65/16.03 ((
% 121.65/16.03 (contrasubsetT2) =>
% 121.65/16.03 ((
% 121.65/16.03 (contrasubsetT3) =>
% 121.65/16.03 ((
% 121.65/16.03 (doubleComplementI1) =>
% 121.65/16.03 ((
% 121.65/16.03 (doubleComplementE1) =>
% 121.65/16.03 ((
% 121.65/16.03 (doubleComplementSub1) =>
% 121.65/16.03 ((
% 121.65/16.03 (doubleComplementSub2) =>
% 121.65/16.03 ((
% 121.65/16.03 (doubleComplementEq) =>
% 121.65/16.03 ((
% 121.65/16.03 (complementTnotintersectT) =>
% 121.65/16.03 ((
% 121.65/16.03 (complementImpComplementIntersect) =>
% 121.65/16.03 ((
% 121.65/16.03 (complementSubsetComplementIntersect) =>
% 121.65/16.03 ((
% 121.65/16.03 (complementInPowersetComplementIntersect) =>
% 121.65/16.03 ((
% 121.65/16.03 (contraSubsetComplement) =>
% 121.65/16.03 ((
% 121.65/16.03 (complementTcontraSubset) =>
% 121.65/16.03 ((
% 121.65/16.03 (binunionTILcontra) =>
% 121.65/16.03 ((
% 121.65/16.03 (binunionTIRcontra) =>
% 121.65/16.03 ((
% 121.65/16.03 (inIntersectImpInUnion) =>
% 121.65/16.03 ((
% 121.65/16.03 (inIntersectImpInUnion2) =>
% 121.65/16.03 ((
% 121.65/16.03 (inIntersectImpInIntersectUnions) =>
% 121.65/16.03 ((
% 121.65/16.03 (intersectInPowersetIntersectUnions) =>
% 121.65/16.03 ((
% 121.65/16.03 (inComplementUnionImpNotIn1) =>
% 121.65/16.03 ((
% 121.65/16.03 (inComplementUnionImpInComplement1) =>
% 121.65/16.03 ((
% 121.65/16.03 (binunionTE) =>
% 121.65/16.03 ((
% 121.65/16.03 (binunionTEcontra) =>
% 121.65/16.03 ((
% 121.65/16.03 (demorgan2a1) =>
% 121.65/16.03 ((
% 121.65/16.03 (complementUnionInPowersetComplement) =>
% 121.65/16.03 ((
% 121.65/16.03 (demorgan2a2) =>
% 121.65/16.03 ((
% 121.65/16.03 (demorgan1a) =>
% 121.65/16.03 ((
% 121.65/16.03 (demorgan1b) =>
% 121.65/16.03 ((
% 121.65/16.03 (demorgan1) =>
% 121.65/16.03 ((
% 121.65/16.03 (demorgan2a) =>
% 121.65/16.03 ((
% 121.65/16.03 (demorgan2b2) =>
% 121.65/16.03 ((
% 121.65/16.03 (demorgan2b) =>
% 121.65/16.03 ((
% 121.65/16.03 (demorgan2) =>
% 121.65/16.03 ((
% 121.65/16.03 (woz13rule0) =>
% 121.65/16.03 ((
% 121.65/16.03 (woz13rule1) =>
% 121.65/16.03 ((
% 121.65/16.03 (woz13rule2) =>
% 121.65/16.03 ((
% 121.65/16.03 (woz13rule3) =>
% 121.65/16.03 ((
% 121.65/16.03 (woz13rule4) =>
% 121.65/16.03 ((
% 121.65/16.03 (woz1_1) =>
% 121.65/16.03 ((
% 121.65/16.03 (woz1_2) =>
% 121.65/16.03 ((
% 121.65/16.03 (woz1_3) =>
% 121.65/16.03 ((
% 121.65/16.03 (woz1_4) =>
% 121.65/16.03 ((
% 121.65/16.03 (woz1_5) =>
% 121.65/16.03 ((
% 121.65/16.03 (breln1all2) =>
% 121.65/16.03 ((
% 121.65/16.03 (breln1SetBreln1) =>
% 121.65/16.03 ((
% 121.65/16.03 (choice2fnsingleton) =>
% 121.65/16.03 ((
% 121.65/16.03 (setOfPairsIsBReln1) =>
% 121.65/16.03 ((
% 121.65/16.03 (breln1all1) =>
% 121.65/16.03 ((
% 121.65/16.03 (subbreln1) =>
% 121.65/16.03 ((
% 121.65/16.03 (eqbreln1) =>
% 121.65/16.03 ((
% 121.65/16.03 (breln1invprop) =>
% 121.65/16.03 ((
% 121.65/16.03 (breln1invI) =>
% 121.65/16.03 ((
% 121.65/16.03 (breln1invE) =>
% 121.65/16.03 ((
% 121.65/16.03 (breln1compprop) =>
% 121.65/16.03 ((
% 121.65/16.03 (breln1compI) =>
% 121.65/16.03 ((
% 121.65/16.03 (breln1compE) =>
% 121.65/16.03 ((
% 121.65/16.03 (breln1compEex) =>
% 121.65/16.03 ((
% 121.65/16.03 (breln1unionprop) =>
% 121.65/16.03 ((
% 121.65/16.03 (breln1unionIL) =>
% 121.65/16.03 ((
% 121.65/16.03 (breln1unionIR) =>
% 121.65/16.03 ((
% 121.65/16.03 (breln1unionI) =>
% 121.65/16.03 ((
% 121.65/16.03 (breln1unionE) =>
% 121.65/16.03 ((
% 121.65/16.03 (breln1unionEcases) =>
% 121.65/16.03 ((
% 121.65/16.03 (breln1unionCommutes) =>
% 121.65/16.03 ((
% 121.65/16.03 (woz2Ex) =>
% 121.65/16.03 ((
% 121.65/16.03 (woz2W) =>
% 121.65/16.03 ((
% 121.65/16.03 (woz2A) =>
% 121.65/16.03 ((
% 121.65/16.03 (woz2B) =>
% 121.65/16.03 ((
% 121.65/16.03 (image1Ex) =>
% 121.65/16.03 ((
% 121.65/16.03 (image1Ex1) =>
% 121.65/16.03 ((
% 121.65/16.03 (image1Equiv) =>
% 121.65/16.03 ((
% 121.65/16.03 (image1E) =>
% 121.65/16.03 ((
% 121.65/16.03 (image1I) =>
% 121.65/16.03 ((
% 121.65/16.03 (injFuncInInjFuncSet) =>
% 121.65/16.03 ((
% 121.65/16.03 (!!) @ (
% 121.65/16.03 (('#B') @ (
% 121.65/16.03 !!) @
% 121.65/16.03 (
% 121.65/16.03 (
% 121.65/16.03 ('#B') @ (
% 121.65/16.03 (
% 121.65/16.03 ('#B') @ (
% 121.65/16.03 !!))) @
% 121.65/16.03 (
% 121.65/16.03 (
% 121.65/16.03 ('#S') @ (
% 121.65/16.03 (
% 121.65/16.03 ('#B') @ (
% 121.65/16.03 '#S') @
% 121.65/16.03 (
% 121.65/16.03 (
% 121.65/16.03 ('#B') @ (
% 121.65/16.03 (
% 121.65/16.03 ('#B') @ (
% 121.65/16.03 '#S'))) @
% 121.65/16.03 (
% 121.65/16.03 (
% 121.65/16.03 ('#B') @ (
% 121.65/16.03 (
% 121.65/16.03 ('#B') @ (
% 121.65/16.03 (
% 121.65/16.03 ('#B') @ (
% 121.65/16.03 =>))))) @
% 121.65/16.03 (
% 121.65/16.03 (
% 121.65/16.03 ('#B') @ (
% 121.65/16.03 (
% 121.65/16.03 ('#B') @ (
% 121.65/16.03 (
% 121.65/16.03 ('#C') @ in)))) @
% 121.65/16.03 injFuncSet)))))))) @
% 121.65/16.03 (
% 121.65/16.03 (
% 121.65/16.03 ('#B') @ (
% 121.65/16.03 (
% 121.65/16.03 ('#B') @ (
% 121.65/16.03 (
% 121.65/16.03 ('#C') @ in)))) @
% 121.65/16.03 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 121.65/16.03 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl123])).
% 121.65/16.03 thf(zip_derived_cl158, plain,
% 121.65/16.03 (~ (((emptysetimpfalse) =>
% 121.65/16.03 (((notinemptyset) =>
% 121.65/16.03 (((exuE3e) =>
% 121.65/16.03 (((setext) =>
% 121.65/16.03 (((emptyI) =>
% 121.65/16.03 (((noeltsimpempty) =>
% 121.65/16.03 (((setbeta) =>
% 121.65/16.03 (((nonemptyE1) =>
% 121.65/16.03 (((nonemptyI) =>
% 121.65/16.03 (((nonemptyI1) =>
% 121.65/16.03 (((setadjoinIL) =>
% 121.65/16.03 (((in @ emptyset @
% 121.65/16.03 (setadjoin @ emptyset @ emptyset)) =>
% 121.65/16.03 (((setadjoinIR) =>
% 121.65/16.03 (((setadjoinE) =>
% 121.65/16.03 (((setadjoinOr) =>
% 121.65/16.03 (((setoftrueEq) =>
% 121.65/16.03 (((powersetI) =>
% 121.65/16.03 (((emptyinPowerset) =>
% 121.65/16.03 (((emptyInPowerset) =>
% 121.65/16.03 (((powersetE) =>
% 121.65/16.03 (((setunionI) =>
% 121.65/16.03 (((setunionE) =>
% 121.65/16.03 (((subPowSU) =>
% 121.65/16.03 (((exuE2) =>
% 121.65/16.03 (((nonemptyImpWitness) =>
% 121.65/16.03 (((uniqinunit) =>
% 121.65/16.03 (((notinsingleton) =>
% 121.65/16.03 (((eqinunit) =>
% 121.65/16.03 (((singletonsswitch) =>
% 121.65/16.03 (((upairsetE) =>
% 121.65/16.03 ((
% 121.65/16.03 (upairsetIL) =>
% 121.65/16.03 ((
% 121.65/16.03 (upairsetIR) =>
% 121.65/16.03 ((
% 121.65/16.03 (emptyE1) =>
% 121.65/16.03 ((
% 121.65/16.03 (vacuousDall) =>
% 121.65/16.03 ((
% 121.65/16.03 (quantDeMorgan1) =>
% 121.65/16.03 ((
% 121.65/16.03 (quantDeMorgan2) =>
% 121.65/16.03 ((
% 121.65/16.03 (quantDeMorgan3) =>
% 121.65/16.03 ((
% 121.65/16.03 (quantDeMorgan4) =>
% 121.65/16.03 ((
% 121.65/16.03 (prop2setI) =>
% 121.65/16.03 ((
% 121.65/16.03 (prop2set2propI) =>
% 121.65/16.03 ((
% 121.65/16.03 (notdexE) =>
% 121.65/16.03 ((
% 121.65/16.03 (notdallE) =>
% 121.65/16.03 ((
% 121.65/16.03 (exuI1) =>
% 121.65/16.03 ((
% 121.65/16.03 (exuI3) =>
% 121.65/16.03 ((
% 121.65/16.03 (exuI2) =>
% 121.65/16.03 ((
% 121.65/16.03 (inCongP) =>
% 121.65/16.03 ((
% 121.65/16.03 (in__Cong) =>
% 121.65/16.03 ((
% 121.65/16.03 (exuE3u) =>
% 121.65/16.03 ((
% 121.65/16.03 (exu__Cong) =>
% 121.65/16.03 ((
% 121.65/16.03 (setadjoin__Cong) =>
% 121.65/16.03 ((
% 121.65/16.03 (powerset__Cong) =>
% 121.65/16.03 ((
% 121.65/16.03 (setunion__Cong) =>
% 121.65/16.03 ((
% 121.65/16.03 (exuEu) =>
% 121.65/16.03 ((
% 121.65/16.03 (descr__Cong) =>
% 121.65/16.03 ((
% 121.65/16.03 (dsetconstr__Cong) =>
% 121.65/16.03 ((
% 121.65/16.03 (subsetI1) =>
% 121.65/16.03 ((
% 121.65/16.03 (eqimpsubset2) =>
% 121.65/16.03 ((
% 121.65/16.03 (eqimpsubset1) =>
% 121.65/16.03 ((
% 121.65/16.03 (subsetI2) =>
% 121.65/16.03 ((
% 121.65/16.03 (emptysetsubset) =>
% 121.65/16.03 ((
% 121.65/16.03 (subsetE) =>
% 121.65/16.03 ((
% 121.65/16.03 (subsetE2) =>
% 121.65/16.03 ((
% 121.65/16.03 (notsubsetI) =>
% 121.65/16.03 ((
% 121.65/16.03 (notequalI1) =>
% 121.65/16.03 ((
% 121.65/16.03 (notequalI2) =>
% 121.65/16.03 ((
% 121.65/16.03 (subsetRefl) =>
% 121.65/16.03 ((
% 121.65/16.03 (subsetTrans) =>
% 121.65/16.03 ((
% 121.65/16.03 (setadjoinSub) =>
% 121.65/16.03 ((
% 121.65/16.03 (setadjoinSub2) =>
% 121.65/16.03 ((
% 121.65/16.03 (subset2powerset) =>
% 121.65/16.03 ((
% 121.65/16.03 (setextsub) =>
% 121.65/16.03 ((
% 121.65/16.03 (subsetemptysetimpeq) =>
% 121.65/16.03 ((
% 121.65/16.03 (powersetI1) =>
% 121.65/16.03 ((
% 121.65/16.03 (powersetE1) =>
% 121.65/16.03 ((
% 121.65/16.03 (inPowerset) =>
% 121.65/16.03 ((
% 121.65/16.03 (powersetsubset) =>
% 121.65/16.03 ((
% 121.65/16.03 (sepInPowerset) =>
% 121.65/16.03 ((
% 121.65/16.03 (sepSubset) =>
% 121.65/16.03 ((
% 121.65/16.03 (binunionIL) =>
% 121.65/16.03 ((
% 121.65/16.03 (upairset2IR) =>
% 121.65/16.03 ((
% 121.65/16.03 (binunionIR) =>
% 121.65/16.03 ((
% 121.65/16.03 (binunionEcases) =>
% 121.65/16.03 ((
% 121.65/16.03 (binunionE) =>
% 121.65/16.03 ((
% 121.65/16.03 (binunionLsub) =>
% 121.65/16.03 ((
% 121.65/16.03 (binunionRsub) =>
% 121.65/16.03 ((
% 121.65/16.03 (binintersectI) =>
% 121.65/16.03 ((
% 121.65/16.03 (binintersectSubset5) =>
% 121.65/16.03 ((
% 121.65/16.03 (binintersectEL) =>
% 121.65/16.03 ((
% 121.65/16.03 (binintersectLsub) =>
% 121.65/16.03 ((
% 121.65/16.03 (binintersectSubset2) =>
% 121.65/16.03 ((
% 121.65/16.03 (binintersectSubset3) =>
% 121.65/16.03 ((
% 121.65/16.03 (binintersectER) =>
% 121.65/16.03 ((
% 121.65/16.03 (disjointsetsI1) =>
% 121.65/16.03 ((
% 121.65/16.03 (binintersectRsub) =>
% 121.65/16.03 ((
% 121.65/16.03 (binintersectSubset4) =>
% 121.65/16.03 ((
% 121.65/16.03 (binintersectSubset1) =>
% 121.65/16.03 ((
% 121.65/16.03 (bs114d) =>
% 121.65/16.03 ((
% 121.65/16.03 (setminusI) =>
% 121.65/16.03 ((
% 121.65/16.03 (setminusEL) =>
% 121.65/16.03 ((
% 121.65/16.03 (setminusER) =>
% 121.65/16.03 ((
% 121.65/16.03 (setminusSubset2) =>
% 121.65/16.03 ((
% 121.65/16.03 (setminusERneg) =>
% 121.65/16.03 ((
% 121.65/16.03 (setminusELneg) =>
% 121.65/16.03 ((
% 121.65/16.03 (setminusILneg) =>
% 121.65/16.03 ((
% 121.65/16.03 (setminusIRneg) =>
% 121.65/16.03 ((
% 121.65/16.03 (setminusLsub) =>
% 121.65/16.03 ((
% 121.65/16.03 (setminusSubset1) =>
% 121.65/16.03 ((
% 121.65/16.03 (symdiffE) =>
% 121.65/16.03 ((
% 121.65/16.03 (symdiffI1) =>
% 121.65/16.03 ((
% 121.65/16.03 (symdiffI2) =>
% 121.65/16.03 ((
% 121.65/16.03 (symdiffIneg1) =>
% 121.65/16.03 ((
% 121.65/16.03 (symdiffIneg2) =>
% 121.65/16.03 ((
% 121.65/16.03 (secondinupair) =>
% 121.65/16.03 ((
% 121.65/16.03 (setukpairIL) =>
% 121.65/16.03 ((
% 121.65/16.03 (setukpairIR) =>
% 121.65/16.03 ((
% 121.65/16.03 (kpairiskpair) =>
% 121.65/16.03 ((
% 121.65/16.03 (kpairp) =>
% 121.65/16.03 ((
% 121.65/16.03 (singletonsubset) =>
% 121.65/16.03 ((
% 121.65/16.03 (singletoninpowerset) =>
% 121.65/16.03 ((
% 121.65/16.03 (singletoninpowunion) =>
% 121.65/16.03 ((
% 121.65/16.03 (upairset2E) =>
% 121.65/16.03 ((
% 121.65/16.03 (upairsubunion) =>
% 121.65/16.03 ((
% 121.65/16.03 (upairinpowunion) =>
% 121.65/16.03 ((
% 121.65/16.03 (ubforcartprodlem1) =>
% 121.65/16.03 ((
% 121.65/16.03 (ubforcartprodlem2) =>
% 121.65/16.03 ((
% 121.65/16.03 (ubforcartprodlem3) =>
% 121.65/16.03 ((
% 121.65/16.03 (cartprodpairin) =>
% 121.65/16.03 ((
% 121.65/16.03 (cartprodmempair1) =>
% 121.65/16.03 ((
% 121.65/16.03 (cartprodmempair) =>
% 121.65/16.03 ((
% 121.65/16.03 (setunionE2) =>
% 121.65/16.03 ((
% 121.65/16.03 (setunionsingleton1) =>
% 121.65/16.03 ((
% 121.65/16.03 (setunionsingleton2) =>
% 121.65/16.03 ((
% 121.65/16.03 (setunionsingleton) =>
% 121.65/16.03 ((
% 121.65/16.03 (singletonprop) =>
% 121.65/16.03 ((
% 121.65/16.03 (ex1E1) =>
% 121.65/16.03 ((
% 121.65/16.03 (ex1I) =>
% 121.65/16.03 ((
% 121.65/16.03 (ex1I2) =>
% 121.65/16.03 ((
% 121.65/16.03 (singletonsuniq) =>
% 121.65/16.03 ((
% 121.65/16.03 (setukpairinjL1) =>
% 121.65/16.03 ((
% 121.65/16.03 (kfstsingleton) =>
% 121.65/16.03 ((
% 121.65/16.03 (theprop) =>
% 121.65/16.03 ((
% 121.65/16.03 (kfstpairEq) =>
% 121.65/16.03 ((
% 121.65/16.03 (cartprodfstin) =>
% 121.65/16.03 ((
% 121.65/16.03 (setukpairinjL2) =>
% 121.65/16.03 ((
% 121.65/16.03 (setukpairinjL) =>
% 121.65/16.03 ((
% 121.65/16.03 (setukpairinjR11) =>
% 121.65/16.03 ((
% 121.65/16.03 (setukpairinjR12) =>
% 121.65/16.03 ((
% 121.65/16.03 (setukpairinjR1) =>
% 121.65/16.03 ((
% 121.65/16.03 (upairequniteq) =>
% 121.65/16.03 ((
% 121.65/16.03 (setukpairinjR2) =>
% 121.65/16.03 ((
% 121.65/16.03 (setukpairinjR) =>
% 121.65/16.03 ((
% 121.65/16.03 (ksndsingleton) =>
% 121.65/16.03 ((
% 121.65/16.03 (ksndpairEq) =>
% 121.65/16.03 ((
% 121.65/16.03 (kpairsurjEq) =>
% 121.65/16.03 ((
% 121.65/16.03 (cartprodsndin) =>
% 121.65/16.03 ((
% 121.65/16.03 (cartprodpairmemEL) =>
% 121.65/16.03 ((
% 121.65/16.03 (cartprodpairmemER) =>
% 121.65/16.03 ((
% 121.65/16.03 (cartprodmempaircEq) =>
% 121.65/16.03 ((
% 121.65/16.03 (cartprodfstpairEq) =>
% 121.65/16.03 ((
% 121.65/16.03 (cartprodsndpairEq) =>
% 121.65/16.03 ((
% 121.65/16.03 (cartprodpairsurjEq) =>
% 121.65/16.03 ((
% 121.65/16.03 (dpsetconstrI) =>
% 121.65/16.03 ((
% 121.65/16.03 (dpsetconstrSub) =>
% 121.65/16.03 ((
% 121.65/16.03 (setOfPairsIsBReln) =>
% 121.65/16.03 ((
% 121.65/16.03 (dpsetconstrERa) =>
% 121.65/16.03 ((
% 121.65/16.03 (dpsetconstrEL1) =>
% 121.65/16.03 ((
% 121.65/16.03 (dpsetconstrEL2) =>
% 121.65/16.03 ((
% 121.65/16.03 (dpsetconstrER) =>
% 121.65/16.03 ((
% 121.65/16.03 (funcImageSingleton) =>
% 121.65/16.03 ((
% 121.65/16.03 (apProp) =>
% 121.65/16.03 ((
% 121.65/16.03 (app) =>
% 121.65/16.03 ((
% 121.65/16.03 (infuncsetfunc) =>
% 121.65/16.03 ((
% 121.65/16.03 (ap2p) =>
% 121.65/16.03 ((
% 121.65/16.03 (funcinfuncset) =>
% 121.65/16.03 ((
% 121.65/16.03 (lamProp) =>
% 121.65/16.03 ((
% 121.65/16.03 (lamp) =>
% 121.65/16.03 ((
% 121.65/16.03 (lam2p) =>
% 121.65/16.03 ((
% 121.65/16.03 (brelnall1) =>
% 121.65/16.03 ((
% 121.65/16.03 (brelnall2) =>
% 121.65/16.03 ((
% 121.65/16.03 (ex1E2) =>
% 121.65/16.03 ((
% 121.65/16.03 (funcGraphProp1) =>
% 121.65/16.03 ((
% 121.65/16.03 (funcGraphProp3) =>
% 121.65/16.03 ((
% 121.65/16.03 (funcGraphProp2) =>
% 121.65/16.03 ((
% 121.65/16.03 (funcextLem) =>
% 121.65/16.03 ((
% 121.65/16.03 (funcGraphProp4) =>
% 121.65/16.03 ((
% 121.65/16.03 (subbreln) =>
% 121.65/16.03 ((
% 121.65/16.03 (eqbreln) =>
% 121.65/16.03 ((
% 121.65/16.03 (funcext) =>
% 121.65/16.03 ((
% 121.65/16.03 (funcext2) =>
% 121.65/16.03 ((
% 121.65/16.03 (ap2apEq1) =>
% 121.65/16.03 ((
% 121.65/16.03 (ap2apEq2) =>
% 121.65/16.03 ((
% 121.65/16.03 (beta1) =>
% 121.65/16.03 ((
% 121.65/16.03 (eta1) =>
% 121.65/16.03 ((
% 121.65/16.03 (lam2lamEq) =>
% 121.65/16.03 ((
% 121.65/16.03 (beta2) =>
% 121.65/16.03 ((
% 121.65/16.03 (eta2) =>
% 121.65/16.03 ((
% 121.65/16.03 (iffalseProp1) =>
% 121.65/16.03 ((
% 121.65/16.03 (iffalseProp2) =>
% 121.65/16.03 ((
% 121.65/16.03 (iftrueProp1) =>
% 121.65/16.03 ((
% 121.65/16.03 (iftrueProp2) =>
% 121.65/16.03 ((
% 121.65/16.03 (ifSingleton) =>
% 121.65/16.03 ((
% 121.65/16.03 (ifp) =>
% 121.65/16.03 ((
% 121.65/16.03 (theeq) =>
% 121.65/16.03 ((
% 121.65/16.03 (iftrue) =>
% 121.65/16.03 ((
% 121.65/16.03 (iffalse) =>
% 121.65/16.03 ((
% 121.65/16.03 (iftrueorfalse) =>
% 121.65/16.03 ((
% 121.65/16.03 (binintersectT_lem) =>
% 121.65/16.03 ((
% 121.65/16.03 (binunionT_lem) =>
% 121.65/16.03 ((
% 121.65/16.03 (powersetT_lem) =>
% 121.65/16.03 ((
% 121.65/16.03 (setminusT_lem) =>
% 121.65/16.03 ((
% 121.65/16.03 (complementT_lem) =>
% 121.65/16.03 ((
% 121.65/16.03 (setextT) =>
% 121.65/16.03 ((
% 121.65/16.03 (subsetTI) =>
% 121.65/16.03 ((
% 121.65/16.03 (powersetTI1) =>
% 121.65/16.03 ((
% 121.65/16.03 (powersetTE1) =>
% 121.65/16.03 ((
% 121.65/16.03 (complementTI1) =>
% 121.65/16.03 ((
% 121.65/16.03 (complementTE1) =>
% 121.65/16.03 ((
% 121.65/16.03 (binintersectTELcontra) =>
% 121.65/16.03 ((
% 121.65/16.03 (binintersectTERcontra) =>
% 121.65/16.03 ((
% 121.65/16.03 (contrasubsetT) =>
% 121.65/16.03 ((
% 121.65/16.03 (contrasubsetT1) =>
% 121.65/16.03 ((
% 121.65/16.03 (contrasubsetT2) =>
% 121.65/16.03 ((
% 121.65/16.03 (contrasubsetT3) =>
% 121.65/16.03 ((
% 121.65/16.03 (doubleComplementI1) =>
% 121.65/16.03 ((
% 121.65/16.03 (doubleComplementE1) =>
% 121.65/16.03 ((
% 121.65/16.03 (doubleComplementSub1) =>
% 121.65/16.03 ((
% 121.65/16.03 (doubleComplementSub2) =>
% 121.65/16.03 ((
% 121.65/16.03 (doubleComplementEq) =>
% 121.65/16.03 ((
% 121.65/16.03 (complementTnotintersectT) =>
% 121.65/16.03 ((
% 121.65/16.03 (complementImpComplementIntersect) =>
% 121.65/16.03 ((
% 121.65/16.03 (complementSubsetComplementIntersect) =>
% 121.65/16.03 ((
% 121.65/16.03 (complementInPowersetComplementIntersect) =>
% 121.65/16.03 ((
% 121.65/16.03 (contraSubsetComplement) =>
% 121.65/16.03 ((
% 121.65/16.03 (complementTcontraSubset) =>
% 121.65/16.03 ((
% 121.65/16.03 (binunionTILcontra) =>
% 121.65/16.03 ((
% 121.65/16.03 (binunionTIRcontra) =>
% 121.65/16.03 ((
% 121.65/16.03 (inIntersectImpInUnion) =>
% 121.65/16.03 ((
% 121.65/16.03 (inIntersectImpInUnion2) =>
% 121.65/16.03 ((
% 121.65/16.03 (inIntersectImpInIntersectUnions) =>
% 121.65/16.03 ((
% 121.65/16.03 (intersectInPowersetIntersectUnions) =>
% 121.65/16.03 ((
% 121.65/16.03 (inComplementUnionImpNotIn1) =>
% 121.65/16.03 ((
% 121.65/16.03 (inComplementUnionImpInComplement1) =>
% 121.65/16.03 ((
% 121.65/16.03 (binunionTE) =>
% 121.65/16.03 ((
% 121.65/16.03 (binunionTEcontra) =>
% 121.65/16.03 ((
% 121.65/16.03 (demorgan2a1) =>
% 121.65/16.03 ((
% 121.65/16.03 (complementUnionInPowersetComplement) =>
% 121.65/16.03 ((
% 121.65/16.03 (demorgan2a2) =>
% 121.65/16.03 ((
% 121.65/16.03 (demorgan1a) =>
% 121.65/16.03 ((
% 121.65/16.03 (demorgan1b) =>
% 121.65/16.03 ((
% 121.65/16.03 (demorgan1) =>
% 121.65/16.03 ((
% 121.65/16.03 (demorgan2a) =>
% 121.65/16.03 ((
% 121.65/16.03 (demorgan2b2) =>
% 121.65/16.03 ((
% 121.65/16.03 (demorgan2b) =>
% 121.65/16.03 ((
% 121.65/16.03 (demorgan2) =>
% 121.65/16.03 ((
% 121.65/16.03 (woz13rule0) =>
% 121.65/16.03 ((
% 121.65/16.03 (woz13rule1) =>
% 121.65/16.03 ((
% 121.65/16.03 (woz13rule2) =>
% 121.65/16.03 ((
% 121.65/16.03 (woz13rule3) =>
% 121.65/16.03 ((
% 121.65/16.03 (woz13rule4) =>
% 121.65/16.03 ((
% 121.65/16.03 (woz1_1) =>
% 121.65/16.03 ((
% 121.65/16.03 (woz1_2) =>
% 121.65/16.03 ((
% 121.65/16.03 (woz1_3) =>
% 121.65/16.03 ((
% 121.65/16.03 (woz1_4) =>
% 121.65/16.03 ((
% 121.65/16.03 (woz1_5) =>
% 121.65/16.03 ((
% 121.65/16.03 (breln1all2) =>
% 121.65/16.03 ((
% 121.65/16.03 (breln1SetBreln1) =>
% 121.65/16.03 ((
% 121.65/16.03 (choice2fnsingleton) =>
% 121.65/16.03 ((
% 121.65/16.03 (setOfPairsIsBReln1) =>
% 121.65/16.03 ((
% 121.65/16.03 (breln1all1) =>
% 121.65/16.03 ((
% 121.65/16.03 (subbreln1) =>
% 121.65/16.03 ((
% 121.65/16.03 (eqbreln1) =>
% 121.65/16.03 ((
% 121.65/16.03 (breln1invprop) =>
% 121.65/16.03 ((
% 121.65/16.03 (breln1invI) =>
% 121.65/16.03 ((
% 121.65/16.03 (breln1invE) =>
% 121.65/16.03 ((
% 121.65/16.03 (breln1compprop) =>
% 121.65/16.03 ((
% 121.65/16.03 (breln1compI) =>
% 121.65/16.03 ((
% 121.65/16.03 (breln1compE) =>
% 121.65/16.03 ((
% 121.65/16.03 (breln1compEex) =>
% 121.65/16.03 ((
% 121.65/16.03 (breln1unionprop) =>
% 121.65/16.03 ((
% 121.65/16.03 (breln1unionIL) =>
% 121.65/16.03 ((
% 121.65/16.03 (breln1unionIR) =>
% 121.65/16.03 ((
% 121.65/16.03 (breln1unionI) =>
% 121.65/16.03 ((
% 121.65/16.03 (breln1unionE) =>
% 121.65/16.03 ((
% 121.65/16.03 (breln1unionEcases) =>
% 121.65/16.03 ((
% 121.65/16.03 (breln1unionCommutes) =>
% 121.65/16.03 ((
% 121.65/16.03 (woz2Ex) =>
% 121.65/16.03 ((
% 121.65/16.03 (woz2W) =>
% 121.65/16.03 ((
% 121.65/16.03 (woz2A) =>
% 121.65/16.03 ((
% 121.65/16.03 (woz2B) =>
% 121.65/16.03 ((
% 121.65/16.03 (image1Ex) =>
% 121.65/16.03 ((
% 121.65/16.03 (image1Ex1) =>
% 121.65/16.03 ((
% 121.65/16.03 (image1Equiv) =>
% 121.65/16.03 ((
% 121.65/16.03 (image1E) =>
% 121.65/16.03 ((
% 121.65/16.03 (image1I) =>
% 121.65/16.03 ((
% 121.65/16.03 (injFuncInInjFuncSet) =>
% 121.65/16.03 ((
% 121.65/16.03 (!!) @ (
% 121.65/16.03 (('#B') @ (
% 121.65/16.03 !!) @
% 121.65/16.03 (
% 121.65/16.03 (
% 121.65/16.03 ('#B') @ (
% 121.65/16.03 (
% 121.65/16.03 ('#B') @ (
% 121.65/16.03 !!))) @
% 121.65/16.03 (
% 121.65/16.03 (
% 121.65/16.03 ('#S') @ (
% 121.65/16.03 (
% 121.65/16.03 ('#B') @ (
% 121.65/16.03 '#S') @
% 121.65/16.03 (
% 121.65/16.03 (
% 121.65/16.03 ('#B') @ (
% 121.65/16.03 (
% 121.65/16.03 ('#B') @ (
% 121.65/16.03 '#S'))) @
% 121.65/16.03 (
% 121.65/16.03 (
% 121.65/16.03 ('#B') @ (
% 121.65/16.03 (
% 121.65/16.03 ('#B') @ (
% 121.65/16.03 (
% 121.65/16.03 ('#B') @ (
% 121.65/16.03 =>))))) @
% 121.65/16.03 (
% 121.65/16.03 (
% 121.65/16.03 ('#B') @ (
% 121.65/16.03 (
% 121.65/16.03 ('#B') @ (
% 121.65/16.03 (
% 121.65/16.03 ('#C') @ in)))) @
% 121.65/16.03 injFuncSet)))))))) @
% 121.65/16.03 (
% 121.65/16.03 (
% 121.65/16.03 ('#B') @ (
% 121.65/16.03 (
% 121.65/16.03 ('#B') @ (
% 121.65/16.03 (
% 121.65/16.03 ('#C') @ in)))) @
% 121.65/16.03 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 121.65/16.03 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl142])).
% 121.65/16.03 thf(zip_derived_cl174, plain,
% 121.65/16.03 (~ (((notinemptyset) =>
% 121.65/16.03 (((exuE3e) =>
% 121.65/16.03 (((setext) =>
% 121.65/16.03 (((emptyI) =>
% 121.65/16.03 (((noeltsimpempty) =>
% 121.65/16.03 (((setbeta) =>
% 121.65/16.03 (((nonemptyE1) =>
% 121.65/16.03 (((nonemptyI) =>
% 121.65/16.03 (((nonemptyI1) =>
% 121.65/16.03 (((setadjoinIL) =>
% 121.65/16.03 (((in @ emptyset @
% 121.65/16.03 (setadjoin @ emptyset @ emptyset)) =>
% 121.65/16.03 (((setadjoinIR) =>
% 121.65/16.03 (((setadjoinE) =>
% 121.65/16.03 (((setadjoinOr) =>
% 121.65/16.03 (((setoftrueEq) =>
% 121.65/16.03 (((powersetI) =>
% 121.65/16.03 (((emptyinPowerset) =>
% 121.65/16.03 (((emptyInPowerset) =>
% 121.65/16.03 (((powersetE) =>
% 121.65/16.03 (((setunionI) =>
% 121.65/16.03 (((setunionE) =>
% 121.65/16.03 (((subPowSU) =>
% 121.65/16.03 (((exuE2) =>
% 121.65/16.03 (((nonemptyImpWitness) =>
% 121.65/16.03 (((uniqinunit) =>
% 121.65/16.03 (((notinsingleton) =>
% 121.65/16.03 (((eqinunit) =>
% 121.65/16.03 (((singletonsswitch) =>
% 121.65/16.03 (((upairsetE) =>
% 121.65/16.03 (((upairsetIL) =>
% 121.65/16.03 ((
% 121.65/16.03 (upairsetIR) =>
% 121.65/16.03 ((
% 121.65/16.03 (emptyE1) =>
% 121.65/16.03 ((
% 121.65/16.03 (vacuousDall) =>
% 121.65/16.03 ((
% 121.65/16.03 (quantDeMorgan1) =>
% 121.65/16.03 ((
% 121.65/16.03 (quantDeMorgan2) =>
% 121.65/16.03 ((
% 121.65/16.03 (quantDeMorgan3) =>
% 121.65/16.03 ((
% 121.65/16.03 (quantDeMorgan4) =>
% 121.65/16.03 ((
% 121.65/16.03 (prop2setI) =>
% 121.65/16.03 ((
% 121.65/16.03 (prop2set2propI) =>
% 121.65/16.03 ((
% 121.65/16.03 (notdexE) =>
% 121.65/16.03 ((
% 121.65/16.03 (notdallE) =>
% 121.65/16.03 ((
% 121.65/16.03 (exuI1) =>
% 121.65/16.03 ((
% 121.65/16.03 (exuI3) =>
% 121.65/16.03 ((
% 121.65/16.03 (exuI2) =>
% 121.65/16.03 ((
% 121.65/16.03 (inCongP) =>
% 121.65/16.03 ((
% 121.65/16.03 (in__Cong) =>
% 121.65/16.03 ((
% 121.65/16.03 (exuE3u) =>
% 121.65/16.03 ((
% 121.65/16.03 (exu__Cong) =>
% 121.65/16.03 ((
% 121.65/16.03 (setadjoin__Cong) =>
% 121.65/16.03 ((
% 121.65/16.03 (powerset__Cong) =>
% 121.65/16.03 ((
% 121.65/16.03 (setunion__Cong) =>
% 121.65/16.03 ((
% 121.65/16.03 (exuEu) =>
% 121.65/16.03 ((
% 121.65/16.03 (descr__Cong) =>
% 121.65/16.03 ((
% 121.65/16.03 (dsetconstr__Cong) =>
% 121.65/16.03 ((
% 121.65/16.03 (subsetI1) =>
% 121.65/16.03 ((
% 121.65/16.03 (eqimpsubset2) =>
% 121.65/16.03 ((
% 121.65/16.03 (eqimpsubset1) =>
% 121.65/16.03 ((
% 121.65/16.03 (subsetI2) =>
% 121.65/16.03 ((
% 121.65/16.03 (emptysetsubset) =>
% 121.65/16.03 ((
% 121.65/16.03 (subsetE) =>
% 121.65/16.03 ((
% 121.65/16.03 (subsetE2) =>
% 121.65/16.03 ((
% 121.65/16.03 (notsubsetI) =>
% 121.65/16.03 ((
% 121.65/16.03 (notequalI1) =>
% 121.65/16.03 ((
% 121.65/16.03 (notequalI2) =>
% 121.65/16.03 ((
% 121.65/16.03 (subsetRefl) =>
% 121.65/16.03 ((
% 121.65/16.03 (subsetTrans) =>
% 121.65/16.03 ((
% 121.65/16.03 (setadjoinSub) =>
% 121.65/16.03 ((
% 121.65/16.03 (setadjoinSub2) =>
% 121.65/16.03 ((
% 121.65/16.03 (subset2powerset) =>
% 121.65/16.03 ((
% 121.65/16.03 (setextsub) =>
% 121.65/16.03 ((
% 121.65/16.03 (subsetemptysetimpeq) =>
% 121.65/16.03 ((
% 121.65/16.03 (powersetI1) =>
% 121.65/16.03 ((
% 121.65/16.03 (powersetE1) =>
% 121.65/16.03 ((
% 121.65/16.03 (inPowerset) =>
% 121.65/16.03 ((
% 121.65/16.03 (powersetsubset) =>
% 121.65/16.03 ((
% 121.65/16.03 (sepInPowerset) =>
% 121.65/16.03 ((
% 121.65/16.03 (sepSubset) =>
% 121.65/16.03 ((
% 121.65/16.03 (binunionIL) =>
% 121.65/16.03 ((
% 121.65/16.03 (upairset2IR) =>
% 121.65/16.03 ((
% 121.65/16.03 (binunionIR) =>
% 121.65/16.03 ((
% 121.65/16.03 (binunionEcases) =>
% 121.65/16.03 ((
% 121.65/16.03 (binunionE) =>
% 121.65/16.03 ((
% 121.65/16.03 (binunionLsub) =>
% 121.65/16.03 ((
% 121.65/16.03 (binunionRsub) =>
% 121.65/16.03 ((
% 121.65/16.03 (binintersectI) =>
% 121.65/16.03 ((
% 121.65/16.03 (binintersectSubset5) =>
% 121.65/16.03 ((
% 121.65/16.03 (binintersectEL) =>
% 121.65/16.03 ((
% 121.65/16.03 (binintersectLsub) =>
% 121.65/16.03 ((
% 121.65/16.03 (binintersectSubset2) =>
% 121.65/16.03 ((
% 121.65/16.03 (binintersectSubset3) =>
% 121.65/16.03 ((
% 121.65/16.03 (binintersectER) =>
% 121.65/16.03 ((
% 121.65/16.03 (disjointsetsI1) =>
% 121.65/16.03 ((
% 121.65/16.03 (binintersectRsub) =>
% 121.65/16.03 ((
% 121.65/16.03 (binintersectSubset4) =>
% 121.65/16.03 ((
% 121.65/16.03 (binintersectSubset1) =>
% 121.65/16.03 ((
% 121.65/16.03 (bs114d) =>
% 121.65/16.03 ((
% 121.65/16.03 (setminusI) =>
% 121.65/16.03 ((
% 121.65/16.03 (setminusEL) =>
% 121.65/16.03 ((
% 121.65/16.03 (setminusER) =>
% 121.65/16.03 ((
% 121.65/16.03 (setminusSubset2) =>
% 121.65/16.03 ((
% 121.65/16.03 (setminusERneg) =>
% 121.65/16.03 ((
% 121.65/16.03 (setminusELneg) =>
% 121.65/16.03 ((
% 121.65/16.03 (setminusILneg) =>
% 121.65/16.03 ((
% 121.65/16.03 (setminusIRneg) =>
% 121.65/16.03 ((
% 121.65/16.03 (setminusLsub) =>
% 121.65/16.03 ((
% 121.65/16.03 (setminusSubset1) =>
% 121.65/16.03 ((
% 121.65/16.03 (symdiffE) =>
% 121.65/16.03 ((
% 121.65/16.03 (symdiffI1) =>
% 121.65/16.03 ((
% 121.65/16.03 (symdiffI2) =>
% 121.65/16.03 ((
% 121.65/16.03 (symdiffIneg1) =>
% 121.65/16.03 ((
% 121.65/16.03 (symdiffIneg2) =>
% 121.65/16.03 ((
% 121.65/16.03 (secondinupair) =>
% 121.65/16.03 ((
% 121.65/16.03 (setukpairIL) =>
% 121.65/16.03 ((
% 121.65/16.03 (setukpairIR) =>
% 121.65/16.03 ((
% 121.65/16.03 (kpairiskpair) =>
% 121.65/16.03 ((
% 121.65/16.03 (kpairp) =>
% 121.65/16.03 ((
% 121.65/16.03 (singletonsubset) =>
% 121.65/16.03 ((
% 121.65/16.03 (singletoninpowerset) =>
% 121.65/16.03 ((
% 121.65/16.03 (singletoninpowunion) =>
% 121.65/16.03 ((
% 121.65/16.03 (upairset2E) =>
% 121.65/16.03 ((
% 121.65/16.03 (upairsubunion) =>
% 121.65/16.03 ((
% 121.65/16.03 (upairinpowunion) =>
% 121.65/16.03 ((
% 121.65/16.03 (ubforcartprodlem1) =>
% 121.65/16.03 ((
% 121.65/16.03 (ubforcartprodlem2) =>
% 121.65/16.03 ((
% 121.65/16.03 (ubforcartprodlem3) =>
% 121.65/16.03 ((
% 121.65/16.03 (cartprodpairin) =>
% 121.65/16.03 ((
% 121.65/16.03 (cartprodmempair1) =>
% 121.65/16.03 ((
% 121.65/16.03 (cartprodmempair) =>
% 121.65/16.03 ((
% 121.65/16.03 (setunionE2) =>
% 121.65/16.03 ((
% 121.65/16.03 (setunionsingleton1) =>
% 121.65/16.03 ((
% 121.65/16.03 (setunionsingleton2) =>
% 121.65/16.03 ((
% 121.65/16.03 (setunionsingleton) =>
% 121.65/16.03 ((
% 121.65/16.03 (singletonprop) =>
% 121.65/16.03 ((
% 121.65/16.03 (ex1E1) =>
% 121.65/16.03 ((
% 121.65/16.03 (ex1I) =>
% 121.65/16.03 ((
% 121.65/16.03 (ex1I2) =>
% 121.65/16.03 ((
% 121.65/16.03 (singletonsuniq) =>
% 121.65/16.03 ((
% 121.65/16.03 (setukpairinjL1) =>
% 121.65/16.03 ((
% 121.65/16.03 (kfstsingleton) =>
% 121.65/16.03 ((
% 121.65/16.03 (theprop) =>
% 121.65/16.03 ((
% 121.65/16.03 (kfstpairEq) =>
% 121.65/16.03 ((
% 121.65/16.03 (cartprodfstin) =>
% 121.65/16.03 ((
% 121.65/16.03 (setukpairinjL2) =>
% 121.65/16.03 ((
% 121.65/16.03 (setukpairinjL) =>
% 121.65/16.03 ((
% 121.65/16.03 (setukpairinjR11) =>
% 121.65/16.03 ((
% 121.65/16.03 (setukpairinjR12) =>
% 121.65/16.03 ((
% 121.65/16.03 (setukpairinjR1) =>
% 121.65/16.03 ((
% 121.65/16.03 (upairequniteq) =>
% 121.65/16.03 ((
% 121.65/16.03 (setukpairinjR2) =>
% 121.65/16.03 ((
% 121.65/16.03 (setukpairinjR) =>
% 121.65/16.03 ((
% 121.65/16.03 (ksndsingleton) =>
% 121.65/16.03 ((
% 121.65/16.03 (ksndpairEq) =>
% 121.65/16.03 ((
% 121.65/16.03 (kpairsurjEq) =>
% 121.65/16.03 ((
% 121.65/16.03 (cartprodsndin) =>
% 121.65/16.03 ((
% 121.65/16.03 (cartprodpairmemEL) =>
% 121.65/16.03 ((
% 121.65/16.03 (cartprodpairmemER) =>
% 121.65/16.03 ((
% 121.65/16.03 (cartprodmempaircEq) =>
% 121.65/16.03 ((
% 121.65/16.03 (cartprodfstpairEq) =>
% 121.65/16.03 ((
% 121.65/16.03 (cartprodsndpairEq) =>
% 121.65/16.03 ((
% 121.65/16.03 (cartprodpairsurjEq) =>
% 121.65/16.03 ((
% 121.65/16.03 (dpsetconstrI) =>
% 121.65/16.03 ((
% 121.65/16.03 (dpsetconstrSub) =>
% 121.65/16.03 ((
% 121.65/16.03 (setOfPairsIsBReln) =>
% 121.65/16.03 ((
% 121.65/16.03 (dpsetconstrERa) =>
% 121.65/16.03 ((
% 121.65/16.03 (dpsetconstrEL1) =>
% 121.65/16.03 ((
% 121.65/16.03 (dpsetconstrEL2) =>
% 121.65/16.03 ((
% 121.65/16.03 (dpsetconstrER) =>
% 121.65/16.03 ((
% 121.65/16.03 (funcImageSingleton) =>
% 121.65/16.03 ((
% 121.65/16.03 (apProp) =>
% 121.65/16.03 ((
% 121.65/16.03 (app) =>
% 121.65/16.03 ((
% 121.65/16.03 (infuncsetfunc) =>
% 121.65/16.03 ((
% 121.65/16.03 (ap2p) =>
% 121.65/16.03 ((
% 121.65/16.03 (funcinfuncset) =>
% 121.65/16.03 ((
% 121.65/16.03 (lamProp) =>
% 121.65/16.03 ((
% 121.65/16.03 (lamp) =>
% 121.65/16.03 ((
% 121.65/16.03 (lam2p) =>
% 121.65/16.03 ((
% 121.65/16.03 (brelnall1) =>
% 121.65/16.03 ((
% 121.65/16.03 (brelnall2) =>
% 121.65/16.03 ((
% 121.65/16.03 (ex1E2) =>
% 121.65/16.03 ((
% 121.65/16.03 (funcGraphProp1) =>
% 121.65/16.03 ((
% 121.65/16.03 (funcGraphProp3) =>
% 121.65/16.03 ((
% 121.65/16.03 (funcGraphProp2) =>
% 121.65/16.03 ((
% 121.65/16.03 (funcextLem) =>
% 121.65/16.03 ((
% 121.65/16.03 (funcGraphProp4) =>
% 121.65/16.03 ((
% 121.65/16.03 (subbreln) =>
% 121.65/16.03 ((
% 121.65/16.03 (eqbreln) =>
% 121.65/16.03 ((
% 121.65/16.03 (funcext) =>
% 121.65/16.03 ((
% 121.65/16.03 (funcext2) =>
% 121.65/16.03 ((
% 121.65/16.03 (ap2apEq1) =>
% 121.65/16.03 ((
% 121.65/16.03 (ap2apEq2) =>
% 121.65/16.03 ((
% 121.65/16.03 (beta1) =>
% 121.65/16.03 ((
% 121.65/16.03 (eta1) =>
% 121.65/16.03 ((
% 121.65/16.03 (lam2lamEq) =>
% 121.65/16.03 ((
% 121.65/16.03 (beta2) =>
% 121.65/16.03 ((
% 121.65/16.03 (eta2) =>
% 121.65/16.03 ((
% 121.65/16.03 (iffalseProp1) =>
% 121.65/16.03 ((
% 121.65/16.03 (iffalseProp2) =>
% 121.65/16.03 ((
% 121.65/16.03 (iftrueProp1) =>
% 121.65/16.03 ((
% 121.65/16.03 (iftrueProp2) =>
% 121.65/16.03 ((
% 121.65/16.03 (ifSingleton) =>
% 121.65/16.03 ((
% 121.65/16.03 (ifp) =>
% 121.65/16.03 ((
% 121.65/16.03 (theeq) =>
% 121.65/16.03 ((
% 121.65/16.03 (iftrue) =>
% 121.65/16.03 ((
% 121.65/16.03 (iffalse) =>
% 121.65/16.03 ((
% 121.65/16.03 (iftrueorfalse) =>
% 121.65/16.03 ((
% 121.65/16.03 (binintersectT_lem) =>
% 121.65/16.03 ((
% 121.65/16.03 (binunionT_lem) =>
% 121.65/16.03 ((
% 121.65/16.03 (powersetT_lem) =>
% 121.65/16.03 ((
% 121.65/16.03 (setminusT_lem) =>
% 121.65/16.03 ((
% 121.65/16.03 (complementT_lem) =>
% 121.65/16.03 ((
% 121.65/16.03 (setextT) =>
% 121.65/16.03 ((
% 121.65/16.03 (subsetTI) =>
% 121.65/16.03 ((
% 121.65/16.03 (powersetTI1) =>
% 121.65/16.03 ((
% 121.65/16.03 (powersetTE1) =>
% 121.65/16.03 ((
% 121.65/16.03 (complementTI1) =>
% 121.65/16.03 ((
% 121.65/16.03 (complementTE1) =>
% 121.65/16.03 ((
% 121.65/16.03 (binintersectTELcontra) =>
% 121.65/16.03 ((
% 121.65/16.03 (binintersectTERcontra) =>
% 121.65/16.03 ((
% 121.65/16.03 (contrasubsetT) =>
% 121.65/16.03 ((
% 121.65/16.03 (contrasubsetT1) =>
% 121.65/16.03 ((
% 121.65/16.03 (contrasubsetT2) =>
% 121.65/16.03 ((
% 121.65/16.03 (contrasubsetT3) =>
% 121.65/16.03 ((
% 121.65/16.03 (doubleComplementI1) =>
% 121.65/16.03 ((
% 121.65/16.03 (doubleComplementE1) =>
% 121.65/16.03 ((
% 121.65/16.03 (doubleComplementSub1) =>
% 121.65/16.03 ((
% 121.65/16.03 (doubleComplementSub2) =>
% 121.65/16.03 ((
% 121.65/16.03 (doubleComplementEq) =>
% 121.65/16.03 ((
% 121.65/16.03 (complementTnotintersectT) =>
% 121.65/16.03 ((
% 121.65/16.03 (complementImpComplementIntersect) =>
% 121.65/16.03 ((
% 121.65/16.03 (complementSubsetComplementIntersect) =>
% 121.65/16.03 ((
% 121.65/16.03 (complementInPowersetComplementIntersect) =>
% 121.65/16.03 ((
% 121.65/16.03 (contraSubsetComplement) =>
% 121.65/16.03 ((
% 121.65/16.03 (complementTcontraSubset) =>
% 121.65/16.03 ((
% 121.65/16.03 (binunionTILcontra) =>
% 121.65/16.03 ((
% 121.65/16.03 (binunionTIRcontra) =>
% 121.65/16.03 ((
% 121.65/16.03 (inIntersectImpInUnion) =>
% 121.65/16.03 ((
% 121.65/16.03 (inIntersectImpInUnion2) =>
% 121.65/16.03 ((
% 121.65/16.03 (inIntersectImpInIntersectUnions) =>
% 121.65/16.03 ((
% 121.65/16.03 (intersectInPowersetIntersectUnions) =>
% 121.65/16.03 ((
% 121.65/16.03 (inComplementUnionImpNotIn1) =>
% 121.65/16.03 ((
% 121.65/16.03 (inComplementUnionImpInComplement1) =>
% 121.65/16.03 ((
% 121.65/16.03 (binunionTE) =>
% 121.65/16.03 ((
% 121.65/16.03 (binunionTEcontra) =>
% 121.65/16.03 ((
% 121.65/16.03 (demorgan2a1) =>
% 121.65/16.03 ((
% 121.65/16.03 (complementUnionInPowersetComplement) =>
% 121.65/16.03 ((
% 121.65/16.03 (demorgan2a2) =>
% 121.65/16.03 ((
% 121.65/16.03 (demorgan1a) =>
% 121.65/16.03 ((
% 121.65/16.03 (demorgan1b) =>
% 121.65/16.03 ((
% 121.65/16.03 (demorgan1) =>
% 121.65/16.03 ((
% 121.65/16.03 (demorgan2a) =>
% 121.65/16.03 ((
% 121.65/16.03 (demorgan2b2) =>
% 121.65/16.03 ((
% 121.65/16.03 (demorgan2b) =>
% 121.65/16.03 ((
% 121.65/16.03 (demorgan2) =>
% 121.65/16.03 ((
% 121.65/16.03 (woz13rule0) =>
% 121.65/16.03 ((
% 121.65/16.03 (woz13rule1) =>
% 121.65/16.03 ((
% 121.65/16.03 (woz13rule2) =>
% 121.65/16.03 ((
% 121.65/16.03 (woz13rule3) =>
% 121.65/16.03 ((
% 121.65/16.03 (woz13rule4) =>
% 121.65/16.03 ((
% 121.65/16.03 (woz1_1) =>
% 121.65/16.03 ((
% 121.65/16.03 (woz1_2) =>
% 121.65/16.03 ((
% 121.65/16.03 (woz1_3) =>
% 121.65/16.03 ((
% 121.65/16.03 (woz1_4) =>
% 121.65/16.03 ((
% 121.65/16.03 (woz1_5) =>
% 121.65/16.03 ((
% 121.65/16.03 (breln1all2) =>
% 121.65/16.03 ((
% 121.65/16.03 (breln1SetBreln1) =>
% 121.65/16.03 ((
% 121.65/16.03 (choice2fnsingleton) =>
% 121.65/16.03 ((
% 121.65/16.03 (setOfPairsIsBReln1) =>
% 121.65/16.03 ((
% 121.65/16.03 (breln1all1) =>
% 121.65/16.03 ((
% 121.65/16.03 (subbreln1) =>
% 121.65/16.03 ((
% 121.65/16.03 (eqbreln1) =>
% 121.65/16.03 ((
% 121.65/16.03 (breln1invprop) =>
% 121.65/16.03 ((
% 121.65/16.03 (breln1invI) =>
% 121.65/16.03 ((
% 121.65/16.03 (breln1invE) =>
% 121.65/16.03 ((
% 121.65/16.03 (breln1compprop) =>
% 121.65/16.03 ((
% 121.65/16.03 (breln1compI) =>
% 121.65/16.03 ((
% 121.65/16.03 (breln1compE) =>
% 121.65/16.03 ((
% 121.65/16.03 (breln1compEex) =>
% 121.65/16.03 ((
% 121.65/16.03 (breln1unionprop) =>
% 121.65/16.03 ((
% 121.65/16.03 (breln1unionIL) =>
% 121.65/16.03 ((
% 121.65/16.03 (breln1unionIR) =>
% 121.65/16.03 ((
% 121.65/16.03 (breln1unionI) =>
% 121.65/16.03 ((
% 121.65/16.03 (breln1unionE) =>
% 121.65/16.03 ((
% 121.65/16.03 (breln1unionEcases) =>
% 121.65/16.03 ((
% 121.65/16.03 (breln1unionCommutes) =>
% 121.65/16.03 ((
% 121.65/16.03 (woz2Ex) =>
% 121.65/16.03 ((
% 121.65/16.03 (woz2W) =>
% 121.65/16.03 ((
% 121.65/16.03 (woz2A) =>
% 121.65/16.03 ((
% 121.65/16.03 (woz2B) =>
% 121.65/16.03 ((
% 121.65/16.03 (image1Ex) =>
% 121.65/16.03 ((
% 121.65/16.03 (image1Ex1) =>
% 121.65/16.03 ((
% 121.65/16.03 (image1Equiv) =>
% 121.65/16.03 ((
% 121.65/16.03 (image1E) =>
% 121.65/16.03 ((
% 121.65/16.03 (image1I) =>
% 121.65/16.03 ((
% 121.65/16.03 (injFuncInInjFuncSet) =>
% 121.65/16.03 ((
% 121.65/16.03 (!!) @ (
% 121.65/16.03 (('#B') @ (
% 121.65/16.03 !!) @
% 121.65/16.03 (
% 121.65/16.03 (
% 121.65/16.03 ('#B') @ (
% 121.65/16.03 (
% 121.65/16.03 ('#B') @ (
% 121.65/16.03 !!))) @
% 121.65/16.03 (
% 121.65/16.03 (
% 121.65/16.03 ('#S') @ (
% 121.65/16.03 (
% 121.65/16.03 ('#B') @ (
% 121.65/16.03 '#S') @
% 121.65/16.03 (
% 121.65/16.03 (
% 121.65/16.03 ('#B') @ (
% 121.65/16.03 (
% 121.65/16.03 ('#B') @ (
% 121.65/16.03 '#S'))) @
% 121.65/16.03 (
% 121.65/16.03 (
% 121.65/16.03 ('#B') @ (
% 121.65/16.03 (
% 121.65/16.03 ('#B') @ (
% 121.65/16.03 (
% 121.65/16.03 ('#B') @ (
% 121.65/16.03 =>))))) @
% 121.65/16.03 (
% 121.65/16.03 (
% 121.65/16.03 ('#B') @ (
% 121.65/16.03 (
% 121.65/16.03 ('#B') @ (
% 121.65/16.03 (
% 121.65/16.03 ('#C') @ in)))) @
% 121.65/16.03 injFuncSet)))))))) @
% 121.65/16.03 (
% 121.65/16.03 (
% 121.65/16.03 ('#B') @ (
% 121.65/16.03 (
% 121.65/16.03 ('#B') @ (
% 121.65/16.03 (
% 121.65/16.03 ('#C') @ in)))) @
% 121.65/16.03 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 121.65/16.03 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl158])).
% 121.65/16.03 thf(zip_derived_cl189, plain,
% 121.65/16.03 (~ (((exuE3e) =>
% 121.65/16.03 (((setext) =>
% 121.65/16.03 (((emptyI) =>
% 121.65/16.03 (((noeltsimpempty) =>
% 121.65/16.03 (((setbeta) =>
% 121.65/16.03 (((nonemptyE1) =>
% 121.65/16.03 (((nonemptyI) =>
% 121.65/16.03 (((nonemptyI1) =>
% 121.65/16.03 (((setadjoinIL) =>
% 121.65/16.03 (((in @ emptyset @
% 121.65/16.03 (setadjoin @ emptyset @ emptyset)) =>
% 121.65/16.03 (((setadjoinIR) =>
% 121.65/16.03 (((setadjoinE) =>
% 121.65/16.03 (((setadjoinOr) =>
% 121.65/16.03 (((setoftrueEq) =>
% 121.65/16.03 (((powersetI) =>
% 121.65/16.03 (((emptyinPowerset) =>
% 121.65/16.03 (((emptyInPowerset) =>
% 121.65/16.03 (((powersetE) =>
% 121.65/16.03 (((setunionI) =>
% 121.65/16.03 (((setunionE) =>
% 121.65/16.03 (((subPowSU) =>
% 121.65/16.03 (((exuE2) =>
% 121.65/16.03 (((nonemptyImpWitness) =>
% 121.65/16.03 (((uniqinunit) =>
% 121.65/16.03 (((notinsingleton) =>
% 121.65/16.03 (((eqinunit) =>
% 121.65/16.03 (((singletonsswitch) =>
% 121.65/16.03 (((upairsetE) =>
% 121.65/16.03 (((upairsetIL) =>
% 121.65/16.03 (((upairsetIR) =>
% 121.65/16.03 ((
% 121.65/16.03 (emptyE1) =>
% 121.65/16.03 ((
% 121.65/16.03 (vacuousDall) =>
% 121.65/16.03 ((
% 121.65/16.03 (quantDeMorgan1) =>
% 121.65/16.03 ((
% 121.65/16.03 (quantDeMorgan2) =>
% 121.65/16.03 ((
% 121.65/16.03 (quantDeMorgan3) =>
% 121.65/16.03 ((
% 121.65/16.03 (quantDeMorgan4) =>
% 121.65/16.03 ((
% 121.65/16.03 (prop2setI) =>
% 121.65/16.03 ((
% 121.65/16.03 (prop2set2propI) =>
% 121.65/16.03 ((
% 121.65/16.03 (notdexE) =>
% 121.65/16.03 ((
% 121.65/16.03 (notdallE) =>
% 121.65/16.03 ((
% 121.65/16.03 (exuI1) =>
% 121.65/16.03 ((
% 121.65/16.03 (exuI3) =>
% 121.65/16.03 ((
% 121.65/16.03 (exuI2) =>
% 121.65/16.03 ((
% 121.65/16.03 (inCongP) =>
% 121.65/16.03 ((
% 121.65/16.03 (in__Cong) =>
% 121.65/16.03 ((
% 121.65/16.03 (exuE3u) =>
% 121.65/16.03 ((
% 121.65/16.03 (exu__Cong) =>
% 121.65/16.03 ((
% 121.65/16.03 (setadjoin__Cong) =>
% 121.65/16.03 ((
% 121.65/16.03 (powerset__Cong) =>
% 121.65/16.03 ((
% 121.65/16.03 (setunion__Cong) =>
% 121.65/16.03 ((
% 121.65/16.03 (exuEu) =>
% 121.65/16.03 ((
% 121.65/16.03 (descr__Cong) =>
% 121.65/16.03 ((
% 121.65/16.03 (dsetconstr__Cong) =>
% 121.65/16.03 ((
% 121.65/16.03 (subsetI1) =>
% 121.65/16.03 ((
% 121.65/16.03 (eqimpsubset2) =>
% 121.65/16.03 ((
% 121.65/16.03 (eqimpsubset1) =>
% 121.65/16.03 ((
% 121.65/16.03 (subsetI2) =>
% 121.65/16.03 ((
% 121.65/16.03 (emptysetsubset) =>
% 121.65/16.03 ((
% 121.65/16.03 (subsetE) =>
% 121.65/16.03 ((
% 121.65/16.03 (subsetE2) =>
% 121.65/16.03 ((
% 121.65/16.03 (notsubsetI) =>
% 121.65/16.03 ((
% 121.65/16.03 (notequalI1) =>
% 121.65/16.03 ((
% 121.65/16.03 (notequalI2) =>
% 121.65/16.03 ((
% 121.65/16.03 (subsetRefl) =>
% 121.65/16.03 ((
% 121.65/16.03 (subsetTrans) =>
% 121.65/16.03 ((
% 121.65/16.03 (setadjoinSub) =>
% 121.65/16.03 ((
% 121.65/16.03 (setadjoinSub2) =>
% 121.65/16.03 ((
% 121.65/16.03 (subset2powerset) =>
% 121.65/16.03 ((
% 121.65/16.03 (setextsub) =>
% 121.65/16.03 ((
% 121.65/16.03 (subsetemptysetimpeq) =>
% 121.65/16.03 ((
% 121.65/16.03 (powersetI1) =>
% 121.65/16.03 ((
% 121.65/16.03 (powersetE1) =>
% 121.65/16.03 ((
% 121.65/16.03 (inPowerset) =>
% 121.65/16.03 ((
% 121.65/16.03 (powersetsubset) =>
% 121.65/16.03 ((
% 121.65/16.03 (sepInPowerset) =>
% 121.65/16.03 ((
% 121.65/16.03 (sepSubset) =>
% 121.65/16.03 ((
% 121.65/16.03 (binunionIL) =>
% 121.65/16.03 ((
% 121.65/16.03 (upairset2IR) =>
% 121.65/16.03 ((
% 121.65/16.03 (binunionIR) =>
% 121.65/16.03 ((
% 121.65/16.03 (binunionEcases) =>
% 121.65/16.03 ((
% 121.65/16.03 (binunionE) =>
% 121.65/16.03 ((
% 121.65/16.03 (binunionLsub) =>
% 121.65/16.03 ((
% 121.65/16.03 (binunionRsub) =>
% 121.65/16.03 ((
% 121.65/16.03 (binintersectI) =>
% 121.65/16.03 ((
% 121.65/16.03 (binintersectSubset5) =>
% 121.65/16.03 ((
% 121.65/16.03 (binintersectEL) =>
% 121.65/16.03 ((
% 121.65/16.03 (binintersectLsub) =>
% 121.65/16.03 ((
% 121.65/16.03 (binintersectSubset2) =>
% 121.65/16.03 ((
% 121.65/16.03 (binintersectSubset3) =>
% 121.65/16.03 ((
% 121.65/16.03 (binintersectER) =>
% 121.65/16.03 ((
% 121.65/16.03 (disjointsetsI1) =>
% 121.65/16.03 ((
% 121.65/16.03 (binintersectRsub) =>
% 121.65/16.03 ((
% 121.65/16.03 (binintersectSubset4) =>
% 121.65/16.03 ((
% 121.65/16.03 (binintersectSubset1) =>
% 121.65/16.03 ((
% 121.65/16.03 (bs114d) =>
% 121.65/16.03 ((
% 121.65/16.03 (setminusI) =>
% 121.65/16.03 ((
% 121.65/16.03 (setminusEL) =>
% 121.65/16.03 ((
% 121.65/16.03 (setminusER) =>
% 121.65/16.03 ((
% 121.65/16.03 (setminusSubset2) =>
% 121.65/16.03 ((
% 121.65/16.03 (setminusERneg) =>
% 121.65/16.03 ((
% 121.65/16.03 (setminusELneg) =>
% 121.65/16.03 ((
% 121.65/16.03 (setminusILneg) =>
% 121.65/16.03 ((
% 121.65/16.03 (setminusIRneg) =>
% 121.65/16.03 ((
% 121.65/16.03 (setminusLsub) =>
% 121.65/16.03 ((
% 121.65/16.03 (setminusSubset1) =>
% 121.65/16.03 ((
% 121.65/16.03 (symdiffE) =>
% 121.65/16.03 ((
% 121.65/16.03 (symdiffI1) =>
% 121.65/16.03 ((
% 121.65/16.03 (symdiffI2) =>
% 121.65/16.03 ((
% 121.65/16.03 (symdiffIneg1) =>
% 121.65/16.03 ((
% 121.65/16.03 (symdiffIneg2) =>
% 121.65/16.03 ((
% 121.65/16.03 (secondinupair) =>
% 121.65/16.03 ((
% 121.65/16.03 (setukpairIL) =>
% 121.65/16.03 ((
% 121.65/16.03 (setukpairIR) =>
% 121.65/16.03 ((
% 121.65/16.03 (kpairiskpair) =>
% 121.65/16.03 ((
% 121.65/16.03 (kpairp) =>
% 121.65/16.03 ((
% 121.65/16.03 (singletonsubset) =>
% 121.65/16.03 ((
% 121.65/16.03 (singletoninpowerset) =>
% 121.65/16.03 ((
% 121.65/16.03 (singletoninpowunion) =>
% 121.65/16.03 ((
% 121.65/16.03 (upairset2E) =>
% 121.65/16.03 ((
% 121.65/16.03 (upairsubunion) =>
% 121.65/16.03 ((
% 121.65/16.03 (upairinpowunion) =>
% 121.65/16.03 ((
% 121.65/16.03 (ubforcartprodlem1) =>
% 121.65/16.03 ((
% 121.65/16.03 (ubforcartprodlem2) =>
% 121.65/16.03 ((
% 121.65/16.03 (ubforcartprodlem3) =>
% 121.65/16.03 ((
% 121.65/16.03 (cartprodpairin) =>
% 121.65/16.03 ((
% 121.65/16.03 (cartprodmempair1) =>
% 121.65/16.03 ((
% 121.65/16.03 (cartprodmempair) =>
% 121.65/16.03 ((
% 121.65/16.03 (setunionE2) =>
% 121.65/16.03 ((
% 121.65/16.03 (setunionsingleton1) =>
% 121.65/16.03 ((
% 121.65/16.03 (setunionsingleton2) =>
% 121.65/16.03 ((
% 121.65/16.03 (setunionsingleton) =>
% 121.65/16.03 ((
% 121.65/16.03 (singletonprop) =>
% 121.65/16.03 ((
% 121.65/16.03 (ex1E1) =>
% 121.65/16.03 ((
% 121.65/16.03 (ex1I) =>
% 121.65/16.03 ((
% 121.65/16.03 (ex1I2) =>
% 121.65/16.03 ((
% 121.65/16.03 (singletonsuniq) =>
% 121.65/16.03 ((
% 121.65/16.03 (setukpairinjL1) =>
% 121.65/16.03 ((
% 121.65/16.03 (kfstsingleton) =>
% 121.65/16.03 ((
% 121.65/16.03 (theprop) =>
% 121.65/16.03 ((
% 121.65/16.03 (kfstpairEq) =>
% 121.65/16.03 ((
% 121.65/16.03 (cartprodfstin) =>
% 121.65/16.03 ((
% 121.65/16.03 (setukpairinjL2) =>
% 121.65/16.03 ((
% 121.65/16.03 (setukpairinjL) =>
% 121.65/16.03 ((
% 121.65/16.03 (setukpairinjR11) =>
% 121.65/16.03 ((
% 121.65/16.03 (setukpairinjR12) =>
% 121.65/16.03 ((
% 121.65/16.03 (setukpairinjR1) =>
% 121.65/16.03 ((
% 121.65/16.03 (upairequniteq) =>
% 121.65/16.03 ((
% 121.65/16.03 (setukpairinjR2) =>
% 121.65/16.03 ((
% 121.65/16.03 (setukpairinjR) =>
% 121.65/16.03 ((
% 121.65/16.03 (ksndsingleton) =>
% 121.65/16.03 ((
% 121.65/16.03 (ksndpairEq) =>
% 121.65/16.03 ((
% 121.65/16.03 (kpairsurjEq) =>
% 121.65/16.03 ((
% 121.65/16.03 (cartprodsndin) =>
% 121.65/16.03 ((
% 121.65/16.03 (cartprodpairmemEL) =>
% 121.65/16.03 ((
% 121.65/16.03 (cartprodpairmemER) =>
% 121.65/16.03 ((
% 121.65/16.03 (cartprodmempaircEq) =>
% 121.65/16.03 ((
% 121.65/16.03 (cartprodfstpairEq) =>
% 121.65/16.03 ((
% 121.65/16.03 (cartprodsndpairEq) =>
% 121.65/16.03 ((
% 121.65/16.03 (cartprodpairsurjEq) =>
% 121.65/16.03 ((
% 121.65/16.03 (dpsetconstrI) =>
% 121.65/16.03 ((
% 121.65/16.03 (dpsetconstrSub) =>
% 121.65/16.03 ((
% 121.65/16.03 (setOfPairsIsBReln) =>
% 121.65/16.03 ((
% 121.65/16.03 (dpsetconstrERa) =>
% 121.65/16.03 ((
% 121.65/16.03 (dpsetconstrEL1) =>
% 121.65/16.03 ((
% 121.65/16.03 (dpsetconstrEL2) =>
% 121.65/16.03 ((
% 121.65/16.03 (dpsetconstrER) =>
% 121.65/16.03 ((
% 121.65/16.03 (funcImageSingleton) =>
% 121.65/16.03 ((
% 121.65/16.03 (apProp) =>
% 121.65/16.03 ((
% 121.65/16.03 (app) =>
% 121.65/16.03 ((
% 121.65/16.03 (infuncsetfunc) =>
% 121.65/16.03 ((
% 121.65/16.03 (ap2p) =>
% 121.65/16.03 ((
% 121.65/16.03 (funcinfuncset) =>
% 121.65/16.03 ((
% 121.65/16.03 (lamProp) =>
% 121.65/16.03 ((
% 121.65/16.03 (lamp) =>
% 121.65/16.03 ((
% 121.65/16.03 (lam2p) =>
% 121.65/16.03 ((
% 121.65/16.03 (brelnall1) =>
% 121.65/16.03 ((
% 121.65/16.03 (brelnall2) =>
% 121.65/16.03 ((
% 121.65/16.03 (ex1E2) =>
% 121.65/16.03 ((
% 121.65/16.03 (funcGraphProp1) =>
% 121.65/16.03 ((
% 121.65/16.03 (funcGraphProp3) =>
% 121.65/16.03 ((
% 121.65/16.03 (funcGraphProp2) =>
% 121.65/16.03 ((
% 121.65/16.03 (funcextLem) =>
% 121.65/16.03 ((
% 121.65/16.03 (funcGraphProp4) =>
% 121.65/16.03 ((
% 121.65/16.03 (subbreln) =>
% 121.65/16.03 ((
% 121.65/16.03 (eqbreln) =>
% 121.65/16.03 ((
% 121.65/16.03 (funcext) =>
% 121.65/16.03 ((
% 121.65/16.03 (funcext2) =>
% 121.65/16.03 ((
% 121.65/16.03 (ap2apEq1) =>
% 121.65/16.03 ((
% 121.65/16.03 (ap2apEq2) =>
% 121.65/16.03 ((
% 121.65/16.03 (beta1) =>
% 121.65/16.03 ((
% 121.65/16.03 (eta1) =>
% 121.65/16.03 ((
% 121.65/16.03 (lam2lamEq) =>
% 121.65/16.03 ((
% 121.65/16.03 (beta2) =>
% 121.65/16.03 ((
% 121.65/16.03 (eta2) =>
% 121.65/16.03 ((
% 121.65/16.03 (iffalseProp1) =>
% 121.65/16.03 ((
% 121.65/16.03 (iffalseProp2) =>
% 121.65/16.03 ((
% 121.65/16.03 (iftrueProp1) =>
% 121.65/16.03 ((
% 121.65/16.03 (iftrueProp2) =>
% 121.65/16.03 ((
% 121.65/16.03 (ifSingleton) =>
% 121.65/16.03 ((
% 121.65/16.03 (ifp) =>
% 121.65/16.03 ((
% 121.65/16.03 (theeq) =>
% 121.65/16.03 ((
% 121.65/16.03 (iftrue) =>
% 121.65/16.03 ((
% 121.65/16.03 (iffalse) =>
% 121.65/16.03 ((
% 121.65/16.03 (iftrueorfalse) =>
% 121.65/16.03 ((
% 121.65/16.03 (binintersectT_lem) =>
% 121.65/16.03 ((
% 121.65/16.03 (binunionT_lem) =>
% 121.65/16.03 ((
% 121.65/16.03 (powersetT_lem) =>
% 121.65/16.03 ((
% 121.65/16.03 (setminusT_lem) =>
% 121.65/16.03 ((
% 121.65/16.03 (complementT_lem) =>
% 121.65/16.03 ((
% 121.65/16.03 (setextT) =>
% 121.65/16.03 ((
% 121.65/16.03 (subsetTI) =>
% 121.65/16.03 ((
% 121.65/16.03 (powersetTI1) =>
% 121.65/16.03 ((
% 121.65/16.03 (powersetTE1) =>
% 121.65/16.03 ((
% 121.65/16.03 (complementTI1) =>
% 121.65/16.03 ((
% 121.65/16.03 (complementTE1) =>
% 121.65/16.03 ((
% 121.65/16.03 (binintersectTELcontra) =>
% 121.65/16.03 ((
% 121.65/16.03 (binintersectTERcontra) =>
% 121.65/16.03 ((
% 121.65/16.03 (contrasubsetT) =>
% 121.65/16.03 ((
% 121.65/16.03 (contrasubsetT1) =>
% 121.65/16.03 ((
% 121.65/16.03 (contrasubsetT2) =>
% 121.65/16.03 ((
% 121.65/16.03 (contrasubsetT3) =>
% 121.65/16.03 ((
% 121.65/16.03 (doubleComplementI1) =>
% 121.65/16.03 ((
% 121.65/16.03 (doubleComplementE1) =>
% 121.65/16.03 ((
% 121.65/16.03 (doubleComplementSub1) =>
% 121.65/16.03 ((
% 121.65/16.03 (doubleComplementSub2) =>
% 121.65/16.03 ((
% 121.65/16.03 (doubleComplementEq) =>
% 121.65/16.03 ((
% 121.65/16.03 (complementTnotintersectT) =>
% 121.65/16.03 ((
% 121.65/16.03 (complementImpComplementIntersect) =>
% 121.65/16.03 ((
% 121.65/16.03 (complementSubsetComplementIntersect) =>
% 121.65/16.03 ((
% 121.65/16.03 (complementInPowersetComplementIntersect) =>
% 121.65/16.03 ((
% 121.65/16.03 (contraSubsetComplement) =>
% 121.65/16.03 ((
% 121.65/16.03 (complementTcontraSubset) =>
% 121.65/16.03 ((
% 121.65/16.03 (binunionTILcontra) =>
% 121.65/16.03 ((
% 121.65/16.03 (binunionTIRcontra) =>
% 121.65/16.03 ((
% 121.65/16.03 (inIntersectImpInUnion) =>
% 121.65/16.03 ((
% 121.65/16.03 (inIntersectImpInUnion2) =>
% 121.65/16.03 ((
% 121.65/16.03 (inIntersectImpInIntersectUnions) =>
% 121.65/16.03 ((
% 121.65/16.03 (intersectInPowersetIntersectUnions) =>
% 121.65/16.03 ((
% 121.65/16.03 (inComplementUnionImpNotIn1) =>
% 121.65/16.03 ((
% 121.65/16.03 (inComplementUnionImpInComplement1) =>
% 121.65/16.03 ((
% 121.65/16.03 (binunionTE) =>
% 121.65/16.03 ((
% 121.65/16.03 (binunionTEcontra) =>
% 121.65/16.03 ((
% 121.65/16.03 (demorgan2a1) =>
% 121.65/16.03 ((
% 121.65/16.03 (complementUnionInPowersetComplement) =>
% 121.65/16.03 ((
% 121.65/16.03 (demorgan2a2) =>
% 121.65/16.03 ((
% 121.65/16.03 (demorgan1a) =>
% 121.65/16.03 ((
% 121.65/16.03 (demorgan1b) =>
% 121.65/16.03 ((
% 121.65/16.03 (demorgan1) =>
% 121.65/16.03 ((
% 121.65/16.03 (demorgan2a) =>
% 121.65/16.03 ((
% 121.65/16.03 (demorgan2b2) =>
% 121.65/16.03 ((
% 121.65/16.03 (demorgan2b) =>
% 121.65/16.03 ((
% 121.65/16.03 (demorgan2) =>
% 121.65/16.03 ((
% 121.65/16.03 (woz13rule0) =>
% 121.65/16.03 ((
% 121.65/16.03 (woz13rule1) =>
% 121.65/16.03 ((
% 121.65/16.03 (woz13rule2) =>
% 121.65/16.03 ((
% 121.65/16.03 (woz13rule3) =>
% 121.65/16.03 ((
% 121.65/16.03 (woz13rule4) =>
% 121.65/16.03 ((
% 121.65/16.03 (woz1_1) =>
% 121.65/16.03 ((
% 121.65/16.03 (woz1_2) =>
% 121.65/16.03 ((
% 121.65/16.03 (woz1_3) =>
% 121.65/16.03 ((
% 121.65/16.03 (woz1_4) =>
% 121.65/16.03 ((
% 121.65/16.03 (woz1_5) =>
% 121.65/16.03 ((
% 121.65/16.03 (breln1all2) =>
% 121.65/16.03 ((
% 121.65/16.03 (breln1SetBreln1) =>
% 121.65/16.03 ((
% 121.65/16.03 (choice2fnsingleton) =>
% 121.65/16.03 ((
% 121.65/16.03 (setOfPairsIsBReln1) =>
% 121.65/16.03 ((
% 121.65/16.03 (breln1all1) =>
% 121.65/16.03 ((
% 121.65/16.03 (subbreln1) =>
% 121.65/16.03 ((
% 121.65/16.03 (eqbreln1) =>
% 121.65/16.03 ((
% 121.65/16.03 (breln1invprop) =>
% 121.65/16.03 ((
% 121.65/16.03 (breln1invI) =>
% 121.65/16.03 ((
% 121.65/16.03 (breln1invE) =>
% 121.65/16.03 ((
% 121.65/16.03 (breln1compprop) =>
% 121.65/16.03 ((
% 121.65/16.03 (breln1compI) =>
% 121.65/16.03 ((
% 121.65/16.03 (breln1compE) =>
% 121.65/16.03 ((
% 121.65/16.03 (breln1compEex) =>
% 121.65/16.03 ((
% 121.65/16.03 (breln1unionprop) =>
% 121.65/16.03 ((
% 121.65/16.03 (breln1unionIL) =>
% 121.65/16.03 ((
% 121.65/16.03 (breln1unionIR) =>
% 121.65/16.03 ((
% 121.65/16.03 (breln1unionI) =>
% 121.65/16.03 ((
% 121.65/16.03 (breln1unionE) =>
% 121.65/16.03 ((
% 121.65/16.03 (breln1unionEcases) =>
% 121.65/16.03 ((
% 121.65/16.03 (breln1unionCommutes) =>
% 121.65/16.03 ((
% 121.65/16.03 (woz2Ex) =>
% 121.65/16.03 ((
% 121.65/16.03 (woz2W) =>
% 121.65/16.03 ((
% 121.65/16.03 (woz2A) =>
% 121.65/16.03 ((
% 121.65/16.03 (woz2B) =>
% 121.65/16.03 ((
% 121.65/16.03 (image1Ex) =>
% 121.65/16.03 ((
% 121.65/16.03 (image1Ex1) =>
% 121.65/16.03 ((
% 121.65/16.03 (image1Equiv) =>
% 121.65/16.03 ((
% 121.65/16.03 (image1E) =>
% 121.65/16.03 ((
% 121.65/16.03 (image1I) =>
% 121.65/16.03 ((
% 121.65/16.03 (injFuncInInjFuncSet) =>
% 121.65/16.03 ((
% 121.65/16.03 (!!) @ (
% 121.65/16.03 (('#B') @ (
% 121.65/16.03 !!) @
% 121.65/16.03 (
% 121.65/16.03 (
% 121.65/16.03 ('#B') @ (
% 121.65/16.03 (
% 121.65/16.03 ('#B') @ (
% 121.65/16.03 !!))) @
% 121.65/16.03 (
% 121.65/16.03 (
% 121.65/16.03 ('#S') @ (
% 121.65/16.03 (
% 121.65/16.03 ('#B') @ (
% 121.65/16.03 '#S') @
% 121.65/16.03 (
% 121.65/16.03 (
% 121.65/16.03 ('#B') @ (
% 121.65/16.03 (
% 121.65/16.03 ('#B') @ (
% 121.65/16.03 '#S'))) @
% 121.65/16.03 (
% 121.65/16.03 (
% 121.65/16.03 ('#B') @ (
% 121.65/16.03 (
% 121.65/16.03 ('#B') @ (
% 121.65/16.03 (
% 121.65/16.03 ('#B') @ (
% 121.65/16.03 =>))))) @
% 121.65/16.03 (
% 121.65/16.03 (
% 121.65/16.03 ('#B') @ (
% 121.65/16.03 (
% 121.65/16.03 ('#B') @ (
% 121.65/16.03 (
% 121.65/16.03 ('#C') @ in)))) @
% 121.65/16.03 injFuncSet)))))))) @
% 121.65/16.03 (
% 121.65/16.03 (
% 121.65/16.03 ('#B') @ (
% 121.65/16.03 (
% 121.65/16.03 ('#B') @ (
% 121.65/16.03 (
% 121.65/16.03 ('#C') @ in)))) @
% 121.65/16.03 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 121.65/16.03 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl174])).
% 121.65/16.03 thf(zip_derived_cl206, plain,
% 121.65/16.03 (~ (((setext) =>
% 121.65/16.03 (((emptyI) =>
% 121.65/16.03 (((noeltsimpempty) =>
% 121.65/16.03 (((setbeta) =>
% 121.65/16.03 (((nonemptyE1) =>
% 121.65/16.03 (((nonemptyI) =>
% 121.65/16.03 (((nonemptyI1) =>
% 121.65/16.03 (((setadjoinIL) =>
% 121.65/16.03 (((in @ emptyset @
% 121.65/16.03 (setadjoin @ emptyset @ emptyset)) =>
% 121.65/16.03 (((setadjoinIR) =>
% 121.65/16.03 (((setadjoinE) =>
% 121.65/16.03 (((setadjoinOr) =>
% 121.65/16.03 (((setoftrueEq) =>
% 121.65/16.03 (((powersetI) =>
% 121.65/16.03 (((emptyinPowerset) =>
% 121.65/16.03 (((emptyInPowerset) =>
% 121.65/16.03 (((powersetE) =>
% 121.65/16.03 (((setunionI) =>
% 121.65/16.03 (((setunionE) =>
% 121.65/16.03 (((subPowSU) =>
% 121.65/16.03 (((exuE2) =>
% 121.65/16.03 (((nonemptyImpWitness) =>
% 121.65/16.03 (((uniqinunit) =>
% 121.65/16.03 (((notinsingleton) =>
% 121.65/16.03 (((eqinunit) =>
% 121.65/16.03 (((singletonsswitch) =>
% 121.65/16.03 (((upairsetE) =>
% 121.65/16.03 (((upairsetIL) =>
% 121.65/16.03 (((upairsetIR) =>
% 121.65/16.03 (((emptyE1) =>
% 121.65/16.03 ((
% 121.65/16.03 (vacuousDall) =>
% 121.65/16.03 ((
% 121.65/16.03 (quantDeMorgan1) =>
% 121.65/16.03 ((
% 121.65/16.03 (quantDeMorgan2) =>
% 121.65/16.03 ((
% 121.65/16.03 (quantDeMorgan3) =>
% 121.65/16.03 ((
% 121.65/16.03 (quantDeMorgan4) =>
% 121.65/16.03 ((
% 121.65/16.03 (prop2setI) =>
% 121.65/16.03 ((
% 121.65/16.03 (prop2set2propI) =>
% 121.65/16.03 ((
% 121.65/16.03 (notdexE) =>
% 121.65/16.03 ((
% 121.65/16.03 (notdallE) =>
% 121.65/16.03 ((
% 121.65/16.03 (exuI1) =>
% 121.65/16.03 ((
% 121.65/16.03 (exuI3) =>
% 121.65/16.03 ((
% 121.65/16.03 (exuI2) =>
% 121.65/16.03 ((
% 121.65/16.03 (inCongP) =>
% 121.65/16.03 ((
% 121.65/16.03 (in__Cong) =>
% 121.65/16.03 ((
% 121.65/16.03 (exuE3u) =>
% 121.65/16.03 ((
% 121.65/16.03 (exu__Cong) =>
% 121.65/16.03 ((
% 121.65/16.03 (setadjoin__Cong) =>
% 121.65/16.03 ((
% 121.65/16.03 (powerset__Cong) =>
% 121.65/16.03 ((
% 121.65/16.03 (setunion__Cong) =>
% 121.65/16.03 ((
% 121.65/16.03 (exuEu) =>
% 121.65/16.03 ((
% 121.65/16.03 (descr__Cong) =>
% 121.65/16.03 ((
% 121.65/16.03 (dsetconstr__Cong) =>
% 121.65/16.03 ((
% 121.65/16.03 (subsetI1) =>
% 121.65/16.03 ((
% 121.65/16.03 (eqimpsubset2) =>
% 121.65/16.03 ((
% 121.65/16.03 (eqimpsubset1) =>
% 121.65/16.03 ((
% 121.65/16.03 (subsetI2) =>
% 121.65/16.03 ((
% 121.65/16.03 (emptysetsubset) =>
% 121.65/16.03 ((
% 121.65/16.03 (subsetE) =>
% 121.65/16.03 ((
% 121.65/16.03 (subsetE2) =>
% 121.65/16.03 ((
% 121.65/16.03 (notsubsetI) =>
% 121.65/16.03 ((
% 121.65/16.03 (notequalI1) =>
% 121.65/16.03 ((
% 121.65/16.03 (notequalI2) =>
% 121.65/16.03 ((
% 121.65/16.03 (subsetRefl) =>
% 121.65/16.03 ((
% 121.65/16.03 (subsetTrans) =>
% 121.65/16.03 ((
% 121.65/16.03 (setadjoinSub) =>
% 121.65/16.03 ((
% 121.65/16.03 (setadjoinSub2) =>
% 121.65/16.03 ((
% 121.65/16.03 (subset2powerset) =>
% 121.65/16.03 ((
% 121.65/16.03 (setextsub) =>
% 121.65/16.03 ((
% 121.65/16.03 (subsetemptysetimpeq) =>
% 121.65/16.03 ((
% 121.65/16.03 (powersetI1) =>
% 121.65/16.03 ((
% 121.65/16.03 (powersetE1) =>
% 121.65/16.03 ((
% 121.65/16.03 (inPowerset) =>
% 121.65/16.03 ((
% 121.65/16.03 (powersetsubset) =>
% 121.65/16.03 ((
% 121.65/16.03 (sepInPowerset) =>
% 121.65/16.03 ((
% 121.65/16.03 (sepSubset) =>
% 121.65/16.03 ((
% 121.65/16.03 (binunionIL) =>
% 121.65/16.03 ((
% 121.65/16.03 (upairset2IR) =>
% 121.65/16.03 ((
% 121.65/16.03 (binunionIR) =>
% 121.65/16.03 ((
% 121.65/16.03 (binunionEcases) =>
% 121.65/16.03 ((
% 121.65/16.03 (binunionE) =>
% 121.65/16.03 ((
% 121.65/16.03 (binunionLsub) =>
% 121.65/16.03 ((
% 121.65/16.03 (binunionRsub) =>
% 121.65/16.03 ((
% 121.65/16.03 (binintersectI) =>
% 121.65/16.03 ((
% 121.65/16.03 (binintersectSubset5) =>
% 121.65/16.03 ((
% 121.65/16.03 (binintersectEL) =>
% 121.65/16.03 ((
% 121.65/16.03 (binintersectLsub) =>
% 121.65/16.03 ((
% 121.65/16.03 (binintersectSubset2) =>
% 121.65/16.03 ((
% 121.65/16.03 (binintersectSubset3) =>
% 121.65/16.03 ((
% 121.65/16.03 (binintersectER) =>
% 121.65/16.03 ((
% 121.65/16.03 (disjointsetsI1) =>
% 121.65/16.03 ((
% 121.65/16.03 (binintersectRsub) =>
% 121.65/16.03 ((
% 121.65/16.03 (binintersectSubset4) =>
% 121.65/16.03 ((
% 121.65/16.03 (binintersectSubset1) =>
% 121.65/16.03 ((
% 121.65/16.03 (bs114d) =>
% 121.65/16.03 ((
% 121.65/16.03 (setminusI) =>
% 121.65/16.03 ((
% 121.65/16.03 (setminusEL) =>
% 121.65/16.03 ((
% 121.65/16.03 (setminusER) =>
% 121.65/16.03 ((
% 121.65/16.03 (setminusSubset2) =>
% 121.65/16.03 ((
% 121.65/16.03 (setminusERneg) =>
% 121.65/16.03 ((
% 121.65/16.03 (setminusELneg) =>
% 121.65/16.03 ((
% 121.65/16.03 (setminusILneg) =>
% 121.65/16.03 ((
% 121.65/16.03 (setminusIRneg) =>
% 121.65/16.03 ((
% 121.65/16.03 (setminusLsub) =>
% 121.65/16.03 ((
% 121.65/16.03 (setminusSubset1) =>
% 121.65/16.03 ((
% 121.65/16.03 (symdiffE) =>
% 121.65/16.03 ((
% 121.65/16.03 (symdiffI1) =>
% 121.65/16.03 ((
% 121.65/16.03 (symdiffI2) =>
% 121.65/16.03 ((
% 121.65/16.03 (symdiffIneg1) =>
% 121.65/16.03 ((
% 121.65/16.03 (symdiffIneg2) =>
% 121.65/16.03 ((
% 121.65/16.03 (secondinupair) =>
% 121.65/16.03 ((
% 121.65/16.03 (setukpairIL) =>
% 121.65/16.03 ((
% 121.65/16.03 (setukpairIR) =>
% 121.65/16.03 ((
% 121.65/16.03 (kpairiskpair) =>
% 121.65/16.03 ((
% 121.65/16.03 (kpairp) =>
% 121.65/16.03 ((
% 121.65/16.03 (singletonsubset) =>
% 121.65/16.03 ((
% 121.65/16.03 (singletoninpowerset) =>
% 121.65/16.03 ((
% 121.65/16.03 (singletoninpowunion) =>
% 121.65/16.03 ((
% 121.65/16.03 (upairset2E) =>
% 121.65/16.03 ((
% 121.65/16.03 (upairsubunion) =>
% 121.65/16.03 ((
% 121.65/16.03 (upairinpowunion) =>
% 121.65/16.03 ((
% 121.65/16.03 (ubforcartprodlem1) =>
% 121.65/16.03 ((
% 121.65/16.03 (ubforcartprodlem2) =>
% 121.65/16.03 ((
% 121.65/16.03 (ubforcartprodlem3) =>
% 121.65/16.03 ((
% 121.65/16.03 (cartprodpairin) =>
% 121.65/16.03 ((
% 121.65/16.03 (cartprodmempair1) =>
% 121.65/16.03 ((
% 121.65/16.03 (cartprodmempair) =>
% 121.65/16.03 ((
% 121.65/16.03 (setunionE2) =>
% 121.65/16.03 ((
% 121.65/16.03 (setunionsingleton1) =>
% 121.65/16.03 ((
% 121.65/16.03 (setunionsingleton2) =>
% 121.65/16.03 ((
% 121.65/16.03 (setunionsingleton) =>
% 121.65/16.03 ((
% 121.65/16.03 (singletonprop) =>
% 121.65/16.03 ((
% 121.65/16.03 (ex1E1) =>
% 121.65/16.03 ((
% 121.65/16.03 (ex1I) =>
% 121.65/16.03 ((
% 121.65/16.03 (ex1I2) =>
% 121.65/16.03 ((
% 121.65/16.03 (singletonsuniq) =>
% 121.65/16.03 ((
% 121.65/16.03 (setukpairinjL1) =>
% 121.65/16.03 ((
% 121.65/16.03 (kfstsingleton) =>
% 121.65/16.03 ((
% 121.65/16.03 (theprop) =>
% 121.65/16.03 ((
% 121.65/16.03 (kfstpairEq) =>
% 121.65/16.03 ((
% 121.65/16.03 (cartprodfstin) =>
% 121.65/16.03 ((
% 121.65/16.03 (setukpairinjL2) =>
% 121.65/16.03 ((
% 121.65/16.03 (setukpairinjL) =>
% 121.65/16.03 ((
% 121.65/16.03 (setukpairinjR11) =>
% 121.65/16.03 ((
% 121.65/16.03 (setukpairinjR12) =>
% 121.65/16.03 ((
% 121.65/16.03 (setukpairinjR1) =>
% 121.65/16.03 ((
% 121.65/16.03 (upairequniteq) =>
% 121.65/16.03 ((
% 121.65/16.03 (setukpairinjR2) =>
% 121.65/16.03 ((
% 121.65/16.03 (setukpairinjR) =>
% 121.65/16.03 ((
% 121.65/16.03 (ksndsingleton) =>
% 121.65/16.03 ((
% 121.65/16.03 (ksndpairEq) =>
% 121.65/16.03 ((
% 121.65/16.03 (kpairsurjEq) =>
% 121.65/16.03 ((
% 121.65/16.03 (cartprodsndin) =>
% 121.65/16.03 ((
% 121.65/16.03 (cartprodpairmemEL) =>
% 121.65/16.03 ((
% 121.65/16.03 (cartprodpairmemER) =>
% 121.65/16.03 ((
% 121.65/16.03 (cartprodmempaircEq) =>
% 121.65/16.03 ((
% 121.65/16.03 (cartprodfstpairEq) =>
% 121.65/16.03 ((
% 121.65/16.03 (cartprodsndpairEq) =>
% 121.65/16.03 ((
% 121.65/16.03 (cartprodpairsurjEq) =>
% 121.65/16.03 ((
% 121.65/16.03 (dpsetconstrI) =>
% 121.65/16.03 ((
% 121.65/16.03 (dpsetconstrSub) =>
% 121.65/16.03 ((
% 121.65/16.03 (setOfPairsIsBReln) =>
% 121.65/16.03 ((
% 121.65/16.03 (dpsetconstrERa) =>
% 121.65/16.03 ((
% 121.65/16.03 (dpsetconstrEL1) =>
% 121.65/16.03 ((
% 121.65/16.03 (dpsetconstrEL2) =>
% 121.65/16.03 ((
% 121.65/16.03 (dpsetconstrER) =>
% 121.65/16.03 ((
% 121.65/16.03 (funcImageSingleton) =>
% 121.65/16.03 ((
% 121.65/16.03 (apProp) =>
% 121.65/16.03 ((
% 121.65/16.03 (app) =>
% 121.65/16.03 ((
% 121.65/16.03 (infuncsetfunc) =>
% 121.65/16.03 ((
% 121.65/16.03 (ap2p) =>
% 121.65/16.03 ((
% 121.65/16.03 (funcinfuncset) =>
% 121.65/16.03 ((
% 121.65/16.03 (lamProp) =>
% 121.65/16.03 ((
% 121.65/16.03 (lamp) =>
% 121.65/16.03 ((
% 121.65/16.03 (lam2p) =>
% 121.65/16.03 ((
% 121.65/16.03 (brelnall1) =>
% 121.65/16.03 ((
% 121.65/16.03 (brelnall2) =>
% 121.65/16.03 ((
% 121.65/16.03 (ex1E2) =>
% 121.65/16.03 ((
% 121.65/16.03 (funcGraphProp1) =>
% 121.65/16.03 ((
% 121.65/16.03 (funcGraphProp3) =>
% 121.65/16.03 ((
% 121.65/16.03 (funcGraphProp2) =>
% 121.65/16.03 ((
% 121.65/16.03 (funcextLem) =>
% 121.65/16.03 ((
% 121.65/16.03 (funcGraphProp4) =>
% 121.65/16.03 ((
% 121.65/16.03 (subbreln) =>
% 121.65/16.03 ((
% 121.65/16.03 (eqbreln) =>
% 121.65/16.03 ((
% 121.65/16.03 (funcext) =>
% 121.65/16.03 ((
% 121.65/16.03 (funcext2) =>
% 121.65/16.03 ((
% 121.65/16.03 (ap2apEq1) =>
% 121.65/16.03 ((
% 121.65/16.03 (ap2apEq2) =>
% 121.65/16.03 ((
% 121.65/16.03 (beta1) =>
% 121.65/16.03 ((
% 121.65/16.03 (eta1) =>
% 121.65/16.03 ((
% 121.65/16.03 (lam2lamEq) =>
% 121.65/16.03 ((
% 121.65/16.03 (beta2) =>
% 121.65/16.03 ((
% 121.65/16.03 (eta2) =>
% 121.65/16.03 ((
% 121.65/16.03 (iffalseProp1) =>
% 121.65/16.03 ((
% 121.65/16.03 (iffalseProp2) =>
% 121.65/16.03 ((
% 121.65/16.03 (iftrueProp1) =>
% 121.65/16.03 ((
% 121.65/16.03 (iftrueProp2) =>
% 121.65/16.03 ((
% 121.65/16.03 (ifSingleton) =>
% 121.65/16.03 ((
% 121.65/16.03 (ifp) =>
% 121.65/16.03 ((
% 121.65/16.03 (theeq) =>
% 121.65/16.03 ((
% 121.65/16.03 (iftrue) =>
% 121.65/16.03 ((
% 121.65/16.03 (iffalse) =>
% 121.65/16.03 ((
% 121.65/16.03 (iftrueorfalse) =>
% 121.65/16.03 ((
% 121.65/16.03 (binintersectT_lem) =>
% 121.65/16.03 ((
% 121.65/16.03 (binunionT_lem) =>
% 121.65/16.03 ((
% 121.65/16.03 (powersetT_lem) =>
% 121.65/16.03 ((
% 121.65/16.03 (setminusT_lem) =>
% 121.65/16.03 ((
% 121.65/16.03 (complementT_lem) =>
% 121.65/16.03 ((
% 121.65/16.03 (setextT) =>
% 121.65/16.03 ((
% 121.65/16.03 (subsetTI) =>
% 121.65/16.03 ((
% 121.65/16.03 (powersetTI1) =>
% 121.65/16.03 ((
% 121.65/16.03 (powersetTE1) =>
% 121.65/16.03 ((
% 121.65/16.03 (complementTI1) =>
% 121.65/16.03 ((
% 121.65/16.03 (complementTE1) =>
% 121.65/16.03 ((
% 121.65/16.03 (binintersectTELcontra) =>
% 121.65/16.03 ((
% 121.65/16.03 (binintersectTERcontra) =>
% 121.65/16.03 ((
% 121.65/16.03 (contrasubsetT) =>
% 121.65/16.03 ((
% 121.65/16.03 (contrasubsetT1) =>
% 121.65/16.03 ((
% 121.65/16.03 (contrasubsetT2) =>
% 121.65/16.03 ((
% 121.65/16.03 (contrasubsetT3) =>
% 121.65/16.03 ((
% 121.65/16.03 (doubleComplementI1) =>
% 121.65/16.03 ((
% 121.65/16.03 (doubleComplementE1) =>
% 121.65/16.03 ((
% 121.65/16.03 (doubleComplementSub1) =>
% 121.65/16.03 ((
% 121.65/16.03 (doubleComplementSub2) =>
% 121.65/16.03 ((
% 121.65/16.03 (doubleComplementEq) =>
% 121.65/16.03 ((
% 121.65/16.03 (complementTnotintersectT) =>
% 121.65/16.03 ((
% 121.65/16.03 (complementImpComplementIntersect) =>
% 121.65/16.03 ((
% 121.65/16.03 (complementSubsetComplementIntersect) =>
% 121.65/16.03 ((
% 121.65/16.03 (complementInPowersetComplementIntersect) =>
% 121.65/16.03 ((
% 121.65/16.03 (contraSubsetComplement) =>
% 121.65/16.03 ((
% 121.65/16.03 (complementTcontraSubset) =>
% 121.65/16.03 ((
% 121.65/16.03 (binunionTILcontra) =>
% 121.65/16.03 ((
% 121.65/16.03 (binunionTIRcontra) =>
% 121.65/16.03 ((
% 121.65/16.03 (inIntersectImpInUnion) =>
% 121.65/16.03 ((
% 121.65/16.03 (inIntersectImpInUnion2) =>
% 121.65/16.03 ((
% 121.65/16.03 (inIntersectImpInIntersectUnions) =>
% 121.65/16.03 ((
% 121.65/16.03 (intersectInPowersetIntersectUnions) =>
% 121.65/16.03 ((
% 121.65/16.03 (inComplementUnionImpNotIn1) =>
% 121.65/16.03 ((
% 121.65/16.03 (inComplementUnionImpInComplement1) =>
% 121.65/16.03 ((
% 121.65/16.03 (binunionTE) =>
% 121.65/16.03 ((
% 121.65/16.03 (binunionTEcontra) =>
% 121.65/16.03 ((
% 121.65/16.03 (demorgan2a1) =>
% 121.65/16.03 ((
% 121.65/16.03 (complementUnionInPowersetComplement) =>
% 121.65/16.03 ((
% 121.65/16.03 (demorgan2a2) =>
% 121.65/16.03 ((
% 121.65/16.03 (demorgan1a) =>
% 121.65/16.03 ((
% 121.65/16.03 (demorgan1b) =>
% 121.65/16.03 ((
% 121.65/16.03 (demorgan1) =>
% 121.65/16.03 ((
% 121.65/16.03 (demorgan2a) =>
% 121.65/16.03 ((
% 121.65/16.03 (demorgan2b2) =>
% 121.65/16.03 ((
% 121.65/16.03 (demorgan2b) =>
% 121.65/16.03 ((
% 121.65/16.03 (demorgan2) =>
% 121.65/16.03 ((
% 121.65/16.03 (woz13rule0) =>
% 121.65/16.03 ((
% 121.65/16.03 (woz13rule1) =>
% 121.65/16.03 ((
% 121.65/16.03 (woz13rule2) =>
% 121.65/16.03 ((
% 121.65/16.03 (woz13rule3) =>
% 121.65/16.03 ((
% 121.65/16.03 (woz13rule4) =>
% 121.65/16.03 ((
% 121.65/16.03 (woz1_1) =>
% 121.65/16.03 ((
% 121.65/16.03 (woz1_2) =>
% 121.65/16.03 ((
% 121.65/16.03 (woz1_3) =>
% 121.65/16.03 ((
% 121.65/16.03 (woz1_4) =>
% 121.65/16.03 ((
% 121.65/16.03 (woz1_5) =>
% 121.65/16.03 ((
% 121.65/16.03 (breln1all2) =>
% 121.65/16.03 ((
% 121.65/16.03 (breln1SetBreln1) =>
% 121.65/16.03 ((
% 121.65/16.03 (choice2fnsingleton) =>
% 121.65/16.03 ((
% 121.65/16.03 (setOfPairsIsBReln1) =>
% 121.65/16.03 ((
% 121.65/16.03 (breln1all1) =>
% 121.65/16.03 ((
% 121.65/16.03 (subbreln1) =>
% 121.65/16.03 ((
% 121.65/16.03 (eqbreln1) =>
% 121.65/16.03 ((
% 121.65/16.03 (breln1invprop) =>
% 121.65/16.03 ((
% 121.65/16.03 (breln1invI) =>
% 121.65/16.03 ((
% 121.65/16.03 (breln1invE) =>
% 121.65/16.03 ((
% 121.65/16.03 (breln1compprop) =>
% 121.65/16.03 ((
% 121.65/16.03 (breln1compI) =>
% 121.65/16.03 ((
% 121.65/16.03 (breln1compE) =>
% 121.65/16.03 ((
% 121.65/16.03 (breln1compEex) =>
% 121.65/16.03 ((
% 121.65/16.03 (breln1unionprop) =>
% 121.65/16.03 ((
% 121.65/16.03 (breln1unionIL) =>
% 121.65/16.03 ((
% 121.65/16.03 (breln1unionIR) =>
% 121.65/16.03 ((
% 121.65/16.03 (breln1unionI) =>
% 121.65/16.03 ((
% 121.65/16.03 (breln1unionE) =>
% 121.65/16.03 ((
% 121.65/16.03 (breln1unionEcases) =>
% 121.65/16.03 ((
% 121.65/16.03 (breln1unionCommutes) =>
% 121.65/16.03 ((
% 121.65/16.03 (woz2Ex) =>
% 121.65/16.03 ((
% 121.65/16.03 (woz2W) =>
% 121.65/16.03 ((
% 121.65/16.03 (woz2A) =>
% 121.65/16.03 ((
% 121.65/16.03 (woz2B) =>
% 121.65/16.03 ((
% 121.65/16.03 (image1Ex) =>
% 121.65/16.03 ((
% 121.65/16.03 (image1Ex1) =>
% 121.65/16.03 ((
% 121.65/16.03 (image1Equiv) =>
% 121.65/16.03 ((
% 121.65/16.03 (image1E) =>
% 121.65/16.03 ((
% 121.65/16.03 (image1I) =>
% 121.65/16.03 ((
% 121.65/16.03 (injFuncInInjFuncSet) =>
% 121.65/16.03 ((
% 121.65/16.03 (!!) @ (
% 121.65/16.03 (('#B') @ (
% 121.65/16.03 !!) @
% 121.65/16.03 (
% 121.65/16.03 (
% 121.65/16.03 ('#B') @ (
% 121.65/16.03 (
% 121.65/16.03 ('#B') @ (
% 121.65/16.03 !!))) @
% 121.65/16.03 (
% 121.65/16.03 (
% 121.65/16.03 ('#S') @ (
% 121.65/16.03 (
% 121.65/16.03 ('#B') @ (
% 121.65/16.03 '#S') @
% 121.65/16.03 (
% 121.65/16.03 (
% 121.65/16.03 ('#B') @ (
% 121.65/16.03 (
% 121.65/16.03 ('#B') @ (
% 121.65/16.03 '#S'))) @
% 121.65/16.03 (
% 121.65/16.03 (
% 121.65/16.03 ('#B') @ (
% 121.65/16.03 (
% 121.65/16.03 ('#B') @ (
% 121.65/16.03 (
% 121.65/16.03 ('#B') @ (
% 121.65/16.03 =>))))) @
% 121.65/16.03 (
% 121.65/16.03 (
% 121.65/16.03 ('#B') @ (
% 121.65/16.03 (
% 121.65/16.03 ('#B') @ (
% 121.65/16.03 (
% 121.65/16.03 ('#C') @ in)))) @
% 121.65/16.03 injFuncSet)))))))) @
% 121.65/16.03 (
% 121.65/16.03 (
% 121.65/16.03 ('#B') @ (
% 121.65/16.03 (
% 121.65/16.03 ('#B') @ (
% 121.65/16.03 (
% 121.65/16.03 ('#C') @ in)))) @
% 121.65/16.03 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 121.65/16.03 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl189])).
% 121.65/16.03 thf(zip_derived_cl222, plain,
% 121.65/16.03 (~ (((emptyI) =>
% 121.65/16.03 (((noeltsimpempty) =>
% 121.65/16.03 (((setbeta) =>
% 121.65/16.03 (((nonemptyE1) =>
% 121.65/16.03 (((nonemptyI) =>
% 121.65/16.03 (((nonemptyI1) =>
% 121.65/16.03 (((setadjoinIL) =>
% 121.65/16.03 (((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) =>
% 121.65/16.03 (((setadjoinIR) =>
% 121.65/16.03 (((setadjoinE) =>
% 121.65/16.03 (((setadjoinOr) =>
% 121.65/16.03 (((setoftrueEq) =>
% 121.65/16.03 (((powersetI) =>
% 121.65/16.03 (((emptyinPowerset) =>
% 121.65/16.03 (((emptyInPowerset) =>
% 121.65/16.03 (((powersetE) =>
% 121.65/16.03 (((setunionI) =>
% 121.65/16.03 (((setunionE) =>
% 121.65/16.03 (((subPowSU) =>
% 121.65/16.03 (((exuE2) =>
% 121.65/16.03 (((nonemptyImpWitness) =>
% 121.65/16.03 (((uniqinunit) =>
% 121.65/16.03 (((notinsingleton) =>
% 121.65/16.03 (((eqinunit) =>
% 121.65/16.03 (((singletonsswitch) =>
% 121.65/16.03 (((upairsetE) =>
% 121.65/16.03 (((upairsetIL) =>
% 121.65/16.03 (((upairsetIR) =>
% 121.65/16.03 (((emptyE1) =>
% 121.65/16.03 (((vacuousDall) =>
% 121.65/16.03 ((
% 121.65/16.03 (quantDeMorgan1) =>
% 121.65/16.03 ((
% 121.65/16.03 (quantDeMorgan2) =>
% 121.65/16.03 ((
% 121.65/16.03 (quantDeMorgan3) =>
% 121.65/16.03 ((
% 121.65/16.03 (quantDeMorgan4) =>
% 121.65/16.03 ((
% 121.65/16.03 (prop2setI) =>
% 121.65/16.03 ((
% 121.65/16.03 (prop2set2propI) =>
% 121.65/16.03 ((
% 121.65/16.03 (notdexE) =>
% 121.65/16.03 ((
% 121.65/16.03 (notdallE) =>
% 121.65/16.03 ((
% 121.65/16.03 (exuI1) =>
% 121.65/16.03 ((
% 121.65/16.03 (exuI3) =>
% 121.65/16.03 ((
% 121.65/16.03 (exuI2) =>
% 121.65/16.03 ((
% 121.65/16.03 (inCongP) =>
% 121.65/16.03 ((
% 121.65/16.03 (in__Cong) =>
% 121.65/16.03 ((
% 121.65/16.03 (exuE3u) =>
% 121.65/16.03 ((
% 121.65/16.03 (exu__Cong) =>
% 121.65/16.03 ((
% 121.65/16.03 (setadjoin__Cong) =>
% 121.65/16.03 ((
% 121.65/16.03 (powerset__Cong) =>
% 121.65/16.03 ((
% 121.65/16.03 (setunion__Cong) =>
% 121.65/16.03 ((
% 121.65/16.03 (exuEu) =>
% 121.65/16.03 ((
% 121.65/16.03 (descr__Cong) =>
% 121.65/16.03 ((
% 121.65/16.03 (dsetconstr__Cong) =>
% 121.65/16.03 ((
% 121.65/16.03 (subsetI1) =>
% 121.65/16.03 ((
% 121.65/16.03 (eqimpsubset2) =>
% 121.65/16.03 ((
% 121.65/16.03 (eqimpsubset1) =>
% 121.65/16.03 ((
% 121.65/16.03 (subsetI2) =>
% 121.65/16.03 ((
% 121.65/16.03 (emptysetsubset) =>
% 121.65/16.03 ((
% 121.65/16.03 (subsetE) =>
% 121.65/16.03 ((
% 121.65/16.03 (subsetE2) =>
% 121.65/16.03 ((
% 121.65/16.03 (notsubsetI) =>
% 121.65/16.03 ((
% 121.65/16.03 (notequalI1) =>
% 121.65/16.03 ((
% 121.65/16.03 (notequalI2) =>
% 121.65/16.03 ((
% 121.65/16.03 (subsetRefl) =>
% 121.65/16.03 ((
% 121.65/16.03 (subsetTrans) =>
% 121.65/16.03 ((
% 121.65/16.03 (setadjoinSub) =>
% 121.65/16.03 ((
% 121.65/16.03 (setadjoinSub2) =>
% 121.65/16.03 ((
% 121.65/16.03 (subset2powerset) =>
% 121.65/16.03 ((
% 121.65/16.03 (setextsub) =>
% 121.65/16.03 ((
% 121.65/16.03 (subsetemptysetimpeq) =>
% 121.65/16.03 ((
% 121.65/16.03 (powersetI1) =>
% 121.65/16.03 ((
% 121.65/16.03 (powersetE1) =>
% 121.65/16.03 ((
% 121.65/16.03 (inPowerset) =>
% 121.65/16.03 ((
% 121.65/16.03 (powersetsubset) =>
% 121.65/16.03 ((
% 121.65/16.03 (sepInPowerset) =>
% 121.65/16.03 ((
% 121.65/16.03 (sepSubset) =>
% 121.65/16.03 ((
% 121.65/16.03 (binunionIL) =>
% 121.65/16.03 ((
% 121.65/16.03 (upairset2IR) =>
% 121.65/16.03 ((
% 121.65/16.03 (binunionIR) =>
% 121.65/16.03 ((
% 121.65/16.03 (binunionEcases) =>
% 121.65/16.03 ((
% 121.65/16.03 (binunionE) =>
% 121.65/16.03 ((
% 121.65/16.03 (binunionLsub) =>
% 121.65/16.03 ((
% 121.65/16.03 (binunionRsub) =>
% 121.65/16.03 ((
% 121.65/16.03 (binintersectI) =>
% 121.65/16.03 ((
% 121.65/16.03 (binintersectSubset5) =>
% 121.65/16.03 ((
% 121.65/16.03 (binintersectEL) =>
% 121.65/16.03 ((
% 121.65/16.03 (binintersectLsub) =>
% 121.65/16.03 ((
% 121.65/16.03 (binintersectSubset2) =>
% 121.65/16.03 ((
% 121.65/16.03 (binintersectSubset3) =>
% 121.65/16.03 ((
% 121.65/16.03 (binintersectER) =>
% 121.65/16.03 ((
% 121.65/16.03 (disjointsetsI1) =>
% 121.65/16.03 ((
% 121.65/16.03 (binintersectRsub) =>
% 121.65/16.03 ((
% 121.65/16.03 (binintersectSubset4) =>
% 121.65/16.03 ((
% 121.65/16.03 (binintersectSubset1) =>
% 121.65/16.03 ((
% 121.65/16.03 (bs114d) =>
% 121.65/16.03 ((
% 121.65/16.03 (setminusI) =>
% 121.65/16.03 ((
% 121.65/16.03 (setminusEL) =>
% 121.65/16.03 ((
% 121.65/16.03 (setminusER) =>
% 121.65/16.03 ((
% 121.65/16.03 (setminusSubset2) =>
% 121.65/16.03 ((
% 121.65/16.03 (setminusERneg) =>
% 121.65/16.03 ((
% 121.65/16.03 (setminusELneg) =>
% 121.65/16.03 ((
% 121.65/16.03 (setminusILneg) =>
% 121.65/16.03 ((
% 121.65/16.03 (setminusIRneg) =>
% 121.65/16.03 ((
% 121.65/16.03 (setminusLsub) =>
% 121.65/16.03 ((
% 121.65/16.03 (setminusSubset1) =>
% 121.65/16.03 ((
% 121.65/16.03 (symdiffE) =>
% 121.65/16.03 ((
% 121.65/16.03 (symdiffI1) =>
% 121.65/16.03 ((
% 121.65/16.03 (symdiffI2) =>
% 121.65/16.03 ((
% 121.65/16.03 (symdiffIneg1) =>
% 121.65/16.03 ((
% 121.65/16.03 (symdiffIneg2) =>
% 121.65/16.03 ((
% 121.65/16.03 (secondinupair) =>
% 121.65/16.03 ((
% 121.65/16.03 (setukpairIL) =>
% 121.65/16.03 ((
% 121.65/16.03 (setukpairIR) =>
% 121.65/16.03 ((
% 121.65/16.03 (kpairiskpair) =>
% 121.65/16.03 ((
% 121.65/16.03 (kpairp) =>
% 121.65/16.03 ((
% 121.65/16.03 (singletonsubset) =>
% 121.65/16.03 ((
% 121.65/16.03 (singletoninpowerset) =>
% 121.65/16.03 ((
% 121.65/16.03 (singletoninpowunion) =>
% 121.65/16.03 ((
% 121.65/16.03 (upairset2E) =>
% 121.65/16.03 ((
% 121.65/16.03 (upairsubunion) =>
% 121.65/16.03 ((
% 121.65/16.03 (upairinpowunion) =>
% 121.65/16.03 ((
% 121.65/16.03 (ubforcartprodlem1) =>
% 121.65/16.03 ((
% 121.65/16.03 (ubforcartprodlem2) =>
% 121.65/16.03 ((
% 121.65/16.03 (ubforcartprodlem3) =>
% 121.65/16.03 ((
% 121.65/16.03 (cartprodpairin) =>
% 121.65/16.03 ((
% 121.65/16.03 (cartprodmempair1) =>
% 121.65/16.03 ((
% 121.65/16.03 (cartprodmempair) =>
% 121.65/16.03 ((
% 121.65/16.03 (setunionE2) =>
% 121.65/16.03 ((
% 121.65/16.03 (setunionsingleton1) =>
% 121.65/16.03 ((
% 121.65/16.03 (setunionsingleton2) =>
% 121.65/16.03 ((
% 121.65/16.03 (setunionsingleton) =>
% 121.65/16.03 ((
% 121.65/16.03 (singletonprop) =>
% 121.65/16.03 ((
% 121.65/16.03 (ex1E1) =>
% 121.65/16.03 ((
% 121.65/16.03 (ex1I) =>
% 121.65/16.03 ((
% 121.65/16.03 (ex1I2) =>
% 121.65/16.03 ((
% 121.65/16.03 (singletonsuniq) =>
% 121.65/16.03 ((
% 121.65/16.03 (setukpairinjL1) =>
% 121.65/16.03 ((
% 121.65/16.03 (kfstsingleton) =>
% 121.65/16.03 ((
% 121.65/16.03 (theprop) =>
% 121.65/16.03 ((
% 121.65/16.03 (kfstpairEq) =>
% 121.65/16.03 ((
% 121.65/16.03 (cartprodfstin) =>
% 121.65/16.03 ((
% 121.65/16.03 (setukpairinjL2) =>
% 121.65/16.03 ((
% 121.65/16.03 (setukpairinjL) =>
% 121.65/16.03 ((
% 121.65/16.03 (setukpairinjR11) =>
% 121.65/16.03 ((
% 121.65/16.03 (setukpairinjR12) =>
% 121.65/16.03 ((
% 121.65/16.03 (setukpairinjR1) =>
% 121.65/16.03 ((
% 121.65/16.03 (upairequniteq) =>
% 121.65/16.03 ((
% 121.65/16.03 (setukpairinjR2) =>
% 121.65/16.03 ((
% 121.65/16.03 (setukpairinjR) =>
% 121.65/16.03 ((
% 121.65/16.03 (ksndsingleton) =>
% 121.65/16.03 ((
% 121.65/16.03 (ksndpairEq) =>
% 121.65/16.03 ((
% 121.65/16.03 (kpairsurjEq) =>
% 121.65/16.03 ((
% 121.65/16.03 (cartprodsndin) =>
% 121.65/16.03 ((
% 121.65/16.03 (cartprodpairmemEL) =>
% 121.65/16.03 ((
% 121.65/16.03 (cartprodpairmemER) =>
% 121.65/16.03 ((
% 121.65/16.03 (cartprodmempaircEq) =>
% 121.65/16.03 ((
% 121.65/16.03 (cartprodfstpairEq) =>
% 121.65/16.03 ((
% 121.65/16.03 (cartprodsndpairEq) =>
% 121.65/16.03 ((
% 121.65/16.03 (cartprodpairsurjEq) =>
% 121.65/16.03 ((
% 121.65/16.03 (dpsetconstrI) =>
% 121.65/16.03 ((
% 121.65/16.03 (dpsetconstrSub) =>
% 121.65/16.03 ((
% 121.65/16.03 (setOfPairsIsBReln) =>
% 121.65/16.03 ((
% 121.65/16.03 (dpsetconstrERa) =>
% 121.65/16.03 ((
% 121.65/16.03 (dpsetconstrEL1) =>
% 121.65/16.03 ((
% 121.65/16.03 (dpsetconstrEL2) =>
% 121.65/16.03 ((
% 121.65/16.03 (dpsetconstrER) =>
% 121.65/16.03 ((
% 121.65/16.03 (funcImageSingleton) =>
% 121.65/16.03 ((
% 121.65/16.03 (apProp) =>
% 121.65/16.03 ((
% 121.65/16.03 (app) =>
% 121.65/16.03 ((
% 121.65/16.03 (infuncsetfunc) =>
% 121.65/16.03 ((
% 121.65/16.03 (ap2p) =>
% 121.65/16.03 ((
% 121.65/16.03 (funcinfuncset) =>
% 121.65/16.03 ((
% 121.65/16.03 (lamProp) =>
% 121.65/16.03 ((
% 121.65/16.03 (lamp) =>
% 121.65/16.03 ((
% 121.65/16.03 (lam2p) =>
% 121.65/16.03 ((
% 121.65/16.03 (brelnall1) =>
% 121.65/16.03 ((
% 121.65/16.03 (brelnall2) =>
% 121.65/16.03 ((
% 121.65/16.03 (ex1E2) =>
% 121.65/16.03 ((
% 121.65/16.03 (funcGraphProp1) =>
% 121.65/16.03 ((
% 121.65/16.03 (funcGraphProp3) =>
% 121.65/16.03 ((
% 121.65/16.03 (funcGraphProp2) =>
% 121.65/16.03 ((
% 121.65/16.03 (funcextLem) =>
% 121.65/16.03 ((
% 121.65/16.03 (funcGraphProp4) =>
% 121.65/16.03 ((
% 121.65/16.03 (subbreln) =>
% 121.65/16.03 ((
% 121.65/16.03 (eqbreln) =>
% 121.65/16.03 ((
% 121.65/16.03 (funcext) =>
% 121.65/16.03 ((
% 121.65/16.03 (funcext2) =>
% 121.65/16.03 ((
% 121.65/16.03 (ap2apEq1) =>
% 121.65/16.03 ((
% 121.65/16.03 (ap2apEq2) =>
% 121.65/16.03 ((
% 121.65/16.03 (beta1) =>
% 121.65/16.03 ((
% 121.65/16.03 (eta1) =>
% 121.65/16.03 ((
% 121.65/16.03 (lam2lamEq) =>
% 121.65/16.03 ((
% 121.65/16.03 (beta2) =>
% 121.65/16.03 ((
% 121.65/16.03 (eta2) =>
% 121.65/16.03 ((
% 121.65/16.03 (iffalseProp1) =>
% 121.65/16.03 ((
% 121.65/16.03 (iffalseProp2) =>
% 121.65/16.03 ((
% 121.65/16.03 (iftrueProp1) =>
% 121.65/16.03 ((
% 121.65/16.03 (iftrueProp2) =>
% 121.65/16.03 ((
% 121.65/16.03 (ifSingleton) =>
% 121.65/16.03 ((
% 121.65/16.03 (ifp) =>
% 121.65/16.03 ((
% 121.65/16.03 (theeq) =>
% 121.65/16.03 ((
% 121.65/16.03 (iftrue) =>
% 121.65/16.03 ((
% 121.65/16.03 (iffalse) =>
% 121.65/16.03 ((
% 121.65/16.03 (iftrueorfalse) =>
% 121.65/16.03 ((
% 121.65/16.03 (binintersectT_lem) =>
% 121.65/16.03 ((
% 121.65/16.03 (binunionT_lem) =>
% 121.65/16.03 ((
% 121.65/16.03 (powersetT_lem) =>
% 121.65/16.03 ((
% 121.65/16.03 (setminusT_lem) =>
% 121.65/16.03 ((
% 121.65/16.03 (complementT_lem) =>
% 121.65/16.03 ((
% 121.65/16.03 (setextT) =>
% 121.65/16.03 ((
% 121.65/16.03 (subsetTI) =>
% 121.65/16.03 ((
% 121.65/16.03 (powersetTI1) =>
% 121.65/16.03 ((
% 121.65/16.03 (powersetTE1) =>
% 121.65/16.03 ((
% 121.65/16.03 (complementTI1) =>
% 121.65/16.03 ((
% 121.65/16.03 (complementTE1) =>
% 121.65/16.03 ((
% 121.65/16.03 (binintersectTELcontra) =>
% 121.65/16.03 ((
% 121.65/16.03 (binintersectTERcontra) =>
% 121.65/16.03 ((
% 121.65/16.03 (contrasubsetT) =>
% 121.65/16.03 ((
% 121.65/16.03 (contrasubsetT1) =>
% 121.65/16.03 ((
% 121.65/16.03 (contrasubsetT2) =>
% 121.65/16.03 ((
% 121.65/16.03 (contrasubsetT3) =>
% 121.65/16.03 ((
% 121.65/16.03 (doubleComplementI1) =>
% 121.65/16.03 ((
% 121.65/16.03 (doubleComplementE1) =>
% 121.65/16.03 ((
% 121.65/16.03 (doubleComplementSub1) =>
% 121.65/16.03 ((
% 121.65/16.03 (doubleComplementSub2) =>
% 121.65/16.03 ((
% 121.65/16.03 (doubleComplementEq) =>
% 121.65/16.03 ((
% 121.65/16.03 (complementTnotintersectT) =>
% 121.65/16.03 ((
% 121.65/16.03 (complementImpComplementIntersect) =>
% 121.65/16.03 ((
% 121.65/16.03 (complementSubsetComplementIntersect) =>
% 121.65/16.03 ((
% 121.65/16.03 (complementInPowersetComplementIntersect) =>
% 121.65/16.03 ((
% 121.65/16.03 (contraSubsetComplement) =>
% 121.65/16.03 ((
% 121.65/16.03 (complementTcontraSubset) =>
% 121.65/16.03 ((
% 121.65/16.03 (binunionTILcontra) =>
% 121.65/16.03 ((
% 121.65/16.03 (binunionTIRcontra) =>
% 121.65/16.03 ((
% 121.65/16.03 (inIntersectImpInUnion) =>
% 121.65/16.03 ((
% 121.65/16.03 (inIntersectImpInUnion2) =>
% 121.65/16.03 ((
% 121.65/16.03 (inIntersectImpInIntersectUnions) =>
% 121.65/16.03 ((
% 121.65/16.03 (intersectInPowersetIntersectUnions) =>
% 121.65/16.03 ((
% 121.65/16.03 (inComplementUnionImpNotIn1) =>
% 121.65/16.03 ((
% 121.65/16.03 (inComplementUnionImpInComplement1) =>
% 121.65/16.03 ((
% 121.65/16.03 (binunionTE) =>
% 121.65/16.03 ((
% 121.65/16.03 (binunionTEcontra) =>
% 121.65/16.03 ((
% 121.65/16.03 (demorgan2a1) =>
% 121.65/16.03 ((
% 121.65/16.03 (complementUnionInPowersetComplement) =>
% 121.65/16.03 ((
% 121.65/16.03 (demorgan2a2) =>
% 121.65/16.03 ((
% 121.65/16.03 (demorgan1a) =>
% 121.65/16.03 ((
% 121.65/16.03 (demorgan1b) =>
% 121.65/16.03 ((
% 121.65/16.03 (demorgan1) =>
% 121.65/16.03 ((
% 121.65/16.03 (demorgan2a) =>
% 121.65/16.03 ((
% 121.65/16.03 (demorgan2b2) =>
% 121.65/16.03 ((
% 121.65/16.03 (demorgan2b) =>
% 121.65/16.03 ((
% 121.65/16.03 (demorgan2) =>
% 121.65/16.03 ((
% 121.65/16.03 (woz13rule0) =>
% 121.65/16.03 ((
% 121.65/16.03 (woz13rule1) =>
% 121.65/16.03 ((
% 121.65/16.03 (woz13rule2) =>
% 121.65/16.03 ((
% 121.65/16.03 (woz13rule3) =>
% 121.65/16.03 ((
% 121.65/16.03 (woz13rule4) =>
% 121.65/16.03 ((
% 121.65/16.03 (woz1_1) =>
% 121.65/16.03 ((
% 121.65/16.03 (woz1_2) =>
% 121.65/16.03 ((
% 121.65/16.03 (woz1_3) =>
% 121.65/16.03 ((
% 121.65/16.03 (woz1_4) =>
% 121.65/16.03 ((
% 121.65/16.03 (woz1_5) =>
% 121.65/16.03 ((
% 121.65/16.03 (breln1all2) =>
% 121.65/16.03 ((
% 121.65/16.03 (breln1SetBreln1) =>
% 121.65/16.03 ((
% 121.65/16.03 (choice2fnsingleton) =>
% 121.65/16.03 ((
% 121.65/16.03 (setOfPairsIsBReln1) =>
% 121.65/16.03 ((
% 121.65/16.03 (breln1all1) =>
% 121.65/16.03 ((
% 121.65/16.03 (subbreln1) =>
% 121.65/16.03 ((
% 121.65/16.03 (eqbreln1) =>
% 121.65/16.03 ((
% 121.65/16.03 (breln1invprop) =>
% 121.65/16.03 ((
% 121.65/16.03 (breln1invI) =>
% 121.65/16.03 ((
% 121.65/16.03 (breln1invE) =>
% 121.65/16.03 ((
% 121.65/16.03 (breln1compprop) =>
% 121.65/16.03 ((
% 121.65/16.03 (breln1compI) =>
% 121.65/16.03 ((
% 121.65/16.03 (breln1compE) =>
% 121.65/16.03 ((
% 121.65/16.03 (breln1compEex) =>
% 121.65/16.03 ((
% 121.65/16.03 (breln1unionprop) =>
% 121.65/16.03 ((
% 121.65/16.03 (breln1unionIL) =>
% 121.65/16.03 ((
% 121.65/16.03 (breln1unionIR) =>
% 121.65/16.03 ((
% 121.65/16.03 (breln1unionI) =>
% 121.65/16.03 ((
% 121.65/16.03 (breln1unionE) =>
% 121.65/16.03 ((
% 121.65/16.03 (breln1unionEcases) =>
% 121.65/16.03 ((
% 121.65/16.03 (breln1unionCommutes) =>
% 121.65/16.03 ((
% 121.65/16.03 (woz2Ex) =>
% 121.65/16.03 ((
% 121.65/16.03 (woz2W) =>
% 121.65/16.03 ((
% 121.65/16.03 (woz2A) =>
% 121.65/16.03 ((
% 121.65/16.03 (woz2B) =>
% 121.65/16.03 ((
% 121.65/16.03 (image1Ex) =>
% 121.65/16.03 ((
% 121.65/16.03 (image1Ex1) =>
% 121.65/16.03 ((
% 121.65/16.03 (image1Equiv) =>
% 121.65/16.03 ((
% 121.65/16.03 (image1E) =>
% 121.65/16.03 ((
% 121.65/16.03 (image1I) =>
% 121.65/16.03 ((
% 121.65/16.03 (injFuncInInjFuncSet) =>
% 121.65/16.03 ((
% 121.65/16.03 (!!) @ (
% 121.65/16.03 (('#B') @ (
% 121.65/16.03 !!) @
% 121.65/16.03 (
% 121.65/16.03 (
% 121.65/16.03 ('#B') @ (
% 121.65/16.03 (
% 121.65/16.03 ('#B') @ (
% 121.65/16.03 !!))) @
% 121.65/16.03 (
% 121.65/16.03 (
% 121.65/16.03 ('#S') @ (
% 121.65/16.03 (
% 121.65/16.03 ('#B') @ (
% 121.65/16.03 '#S') @
% 121.65/16.03 (
% 121.65/16.03 (
% 121.65/16.03 ('#B') @ (
% 121.65/16.03 (
% 121.65/16.03 ('#B') @ (
% 121.65/16.03 '#S'))) @
% 121.65/16.03 (
% 121.65/16.03 (
% 121.65/16.03 ('#B') @ (
% 121.65/16.03 (
% 121.65/16.03 ('#B') @ (
% 121.65/16.03 (
% 121.65/16.03 ('#B') @ (
% 121.65/16.03 =>))))) @
% 121.65/16.03 (
% 121.65/16.03 (
% 121.65/16.03 ('#B') @ (
% 121.65/16.03 (
% 121.65/16.03 ('#B') @ (
% 121.65/16.03 (
% 121.65/16.03 ('#C') @ in)))) @
% 121.65/16.03 injFuncSet)))))))) @
% 121.65/16.03 (
% 121.65/16.03 (
% 121.65/16.03 ('#B') @ (
% 121.65/16.03 (
% 121.65/16.03 ('#B') @ (
% 121.65/16.03 (
% 121.65/16.03 ('#C') @ in)))) @
% 121.65/16.03 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 121.65/16.03 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl206])).
% 121.65/16.03 thf(zip_derived_cl236, plain,
% 121.65/16.03 (~ (((noeltsimpempty) =>
% 121.65/16.03 (((setbeta) =>
% 121.65/16.03 (((nonemptyE1) =>
% 121.65/16.03 (((nonemptyI) =>
% 121.65/16.03 (((nonemptyI1) =>
% 121.65/16.03 (((setadjoinIL) =>
% 121.65/16.03 (((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) =>
% 121.65/16.03 (((setadjoinIR) =>
% 121.65/16.03 (((setadjoinE) =>
% 121.65/16.03 (((setadjoinOr) =>
% 121.65/16.03 (((setoftrueEq) =>
% 121.65/16.03 (((powersetI) =>
% 121.65/16.03 (((emptyinPowerset) =>
% 121.65/16.03 (((emptyInPowerset) =>
% 121.65/16.03 (((powersetE) =>
% 121.65/16.03 (((setunionI) =>
% 121.65/16.03 (((setunionE) =>
% 121.65/16.03 (((subPowSU) =>
% 121.65/16.03 (((exuE2) =>
% 121.65/16.03 (((nonemptyImpWitness) =>
% 121.65/16.03 (((uniqinunit) =>
% 121.65/16.03 (((notinsingleton) =>
% 121.65/16.03 (((eqinunit) =>
% 121.65/16.03 (((singletonsswitch) =>
% 121.65/16.03 (((upairsetE) =>
% 121.65/16.03 (((upairsetIL) =>
% 121.65/16.03 (((upairsetIR) =>
% 121.65/16.03 (((emptyE1) =>
% 121.65/16.03 (((vacuousDall) =>
% 121.65/16.03 (((quantDeMorgan1) =>
% 121.65/16.03 ((
% 121.65/16.03 (quantDeMorgan2) =>
% 121.65/16.03 ((
% 121.65/16.03 (quantDeMorgan3) =>
% 121.65/16.03 ((
% 121.65/16.03 (quantDeMorgan4) =>
% 121.65/16.03 ((
% 121.65/16.03 (prop2setI) =>
% 121.65/16.03 ((
% 121.65/16.03 (prop2set2propI) =>
% 121.65/16.03 ((
% 121.65/16.03 (notdexE) =>
% 121.65/16.03 ((
% 121.65/16.03 (notdallE) =>
% 121.65/16.03 ((
% 121.65/16.03 (exuI1) =>
% 121.65/16.03 ((
% 121.65/16.03 (exuI3) =>
% 121.65/16.03 ((
% 121.65/16.03 (exuI2) =>
% 121.65/16.03 ((
% 121.65/16.03 (inCongP) =>
% 121.65/16.03 ((
% 121.65/16.03 (in__Cong) =>
% 121.65/16.03 ((
% 121.65/16.03 (exuE3u) =>
% 121.65/16.03 ((
% 121.65/16.03 (exu__Cong) =>
% 121.65/16.03 ((
% 121.65/16.03 (setadjoin__Cong) =>
% 121.65/16.03 ((
% 121.65/16.03 (powerset__Cong) =>
% 121.65/16.03 ((
% 121.65/16.03 (setunion__Cong) =>
% 121.65/16.03 ((
% 121.65/16.03 (exuEu) =>
% 121.65/16.03 ((
% 121.65/16.03 (descr__Cong) =>
% 121.65/16.03 ((
% 121.65/16.03 (dsetconstr__Cong) =>
% 121.65/16.03 ((
% 121.65/16.03 (subsetI1) =>
% 121.65/16.03 ((
% 121.65/16.03 (eqimpsubset2) =>
% 121.65/16.03 ((
% 121.65/16.03 (eqimpsubset1) =>
% 121.65/16.03 ((
% 121.65/16.03 (subsetI2) =>
% 121.65/16.03 ((
% 121.65/16.03 (emptysetsubset) =>
% 121.65/16.03 ((
% 121.65/16.03 (subsetE) =>
% 121.65/16.03 ((
% 121.65/16.03 (subsetE2) =>
% 121.65/16.03 ((
% 121.65/16.03 (notsubsetI) =>
% 121.65/16.03 ((
% 121.65/16.03 (notequalI1) =>
% 121.65/16.03 ((
% 121.65/16.03 (notequalI2) =>
% 121.65/16.03 ((
% 121.65/16.03 (subsetRefl) =>
% 121.65/16.03 ((
% 121.65/16.03 (subsetTrans) =>
% 121.65/16.03 ((
% 121.65/16.03 (setadjoinSub) =>
% 121.65/16.03 ((
% 121.65/16.03 (setadjoinSub2) =>
% 121.65/16.03 ((
% 121.65/16.03 (subset2powerset) =>
% 121.65/16.03 ((
% 121.65/16.03 (setextsub) =>
% 121.65/16.03 ((
% 121.65/16.03 (subsetemptysetimpeq) =>
% 121.65/16.03 ((
% 121.65/16.03 (powersetI1) =>
% 121.65/16.03 ((
% 121.65/16.03 (powersetE1) =>
% 121.65/16.03 ((
% 121.65/16.03 (inPowerset) =>
% 121.65/16.03 ((
% 121.65/16.03 (powersetsubset) =>
% 121.65/16.03 ((
% 121.65/16.03 (sepInPowerset) =>
% 121.65/16.03 ((
% 121.65/16.03 (sepSubset) =>
% 121.65/16.03 ((
% 121.65/16.03 (binunionIL) =>
% 121.65/16.03 ((
% 121.65/16.03 (upairset2IR) =>
% 121.65/16.03 ((
% 121.65/16.03 (binunionIR) =>
% 121.65/16.03 ((
% 121.65/16.03 (binunionEcases) =>
% 121.65/16.03 ((
% 121.65/16.03 (binunionE) =>
% 121.65/16.03 ((
% 121.65/16.03 (binunionLsub) =>
% 121.65/16.03 ((
% 121.65/16.03 (binunionRsub) =>
% 121.65/16.03 ((
% 121.65/16.03 (binintersectI) =>
% 121.65/16.03 ((
% 121.65/16.03 (binintersectSubset5) =>
% 121.65/16.03 ((
% 121.65/16.03 (binintersectEL) =>
% 121.65/16.03 ((
% 121.65/16.03 (binintersectLsub) =>
% 121.65/16.03 ((
% 121.65/16.03 (binintersectSubset2) =>
% 121.65/16.03 ((
% 121.65/16.03 (binintersectSubset3) =>
% 121.65/16.03 ((
% 121.65/16.03 (binintersectER) =>
% 121.65/16.03 ((
% 121.65/16.03 (disjointsetsI1) =>
% 121.65/16.03 ((
% 121.65/16.03 (binintersectRsub) =>
% 121.65/16.03 ((
% 121.65/16.03 (binintersectSubset4) =>
% 121.65/16.03 ((
% 121.65/16.03 (binintersectSubset1) =>
% 121.65/16.03 ((
% 121.65/16.03 (bs114d) =>
% 121.65/16.03 ((
% 121.65/16.03 (setminusI) =>
% 121.65/16.03 ((
% 121.65/16.03 (setminusEL) =>
% 121.65/16.03 ((
% 121.65/16.03 (setminusER) =>
% 121.65/16.03 ((
% 121.65/16.03 (setminusSubset2) =>
% 121.65/16.03 ((
% 121.65/16.03 (setminusERneg) =>
% 121.65/16.03 ((
% 121.65/16.03 (setminusELneg) =>
% 121.65/16.03 ((
% 121.65/16.03 (setminusILneg) =>
% 121.65/16.03 ((
% 121.65/16.03 (setminusIRneg) =>
% 121.65/16.03 ((
% 121.65/16.03 (setminusLsub) =>
% 121.65/16.03 ((
% 121.65/16.03 (setminusSubset1) =>
% 121.65/16.03 ((
% 121.65/16.03 (symdiffE) =>
% 121.65/16.03 ((
% 121.65/16.03 (symdiffI1) =>
% 121.65/16.03 ((
% 121.65/16.03 (symdiffI2) =>
% 121.65/16.03 ((
% 121.65/16.03 (symdiffIneg1) =>
% 121.65/16.03 ((
% 121.65/16.03 (symdiffIneg2) =>
% 121.65/16.03 ((
% 121.65/16.03 (secondinupair) =>
% 121.65/16.03 ((
% 121.65/16.03 (setukpairIL) =>
% 121.65/16.03 ((
% 121.65/16.03 (setukpairIR) =>
% 121.65/16.03 ((
% 121.65/16.03 (kpairiskpair) =>
% 121.65/16.03 ((
% 121.65/16.03 (kpairp) =>
% 121.65/16.03 ((
% 121.65/16.03 (singletonsubset) =>
% 121.65/16.03 ((
% 121.65/16.03 (singletoninpowerset) =>
% 121.65/16.03 ((
% 121.65/16.03 (singletoninpowunion) =>
% 121.65/16.03 ((
% 121.65/16.03 (upairset2E) =>
% 121.65/16.03 ((
% 121.65/16.03 (upairsubunion) =>
% 121.65/16.03 ((
% 121.65/16.03 (upairinpowunion) =>
% 121.65/16.03 ((
% 121.65/16.03 (ubforcartprodlem1) =>
% 121.65/16.03 ((
% 121.65/16.03 (ubforcartprodlem2) =>
% 121.65/16.03 ((
% 121.65/16.03 (ubforcartprodlem3) =>
% 121.65/16.03 ((
% 121.65/16.03 (cartprodpairin) =>
% 121.65/16.03 ((
% 121.65/16.03 (cartprodmempair1) =>
% 121.65/16.03 ((
% 121.65/16.03 (cartprodmempair) =>
% 121.65/16.03 ((
% 121.65/16.03 (setunionE2) =>
% 121.65/16.03 ((
% 121.65/16.03 (setunionsingleton1) =>
% 121.65/16.03 ((
% 121.65/16.03 (setunionsingleton2) =>
% 121.65/16.03 ((
% 121.65/16.03 (setunionsingleton) =>
% 121.65/16.03 ((
% 121.65/16.03 (singletonprop) =>
% 121.65/16.03 ((
% 121.65/16.03 (ex1E1) =>
% 121.65/16.03 ((
% 121.65/16.03 (ex1I) =>
% 121.65/16.03 ((
% 121.65/16.03 (ex1I2) =>
% 121.65/16.03 ((
% 121.65/16.03 (singletonsuniq) =>
% 121.65/16.03 ((
% 121.65/16.03 (setukpairinjL1) =>
% 121.65/16.03 ((
% 121.65/16.03 (kfstsingleton) =>
% 121.65/16.03 ((
% 121.65/16.03 (theprop) =>
% 121.65/16.03 ((
% 121.65/16.03 (kfstpairEq) =>
% 121.65/16.03 ((
% 121.65/16.03 (cartprodfstin) =>
% 121.65/16.03 ((
% 121.65/16.03 (setukpairinjL2) =>
% 121.65/16.03 ((
% 121.65/16.03 (setukpairinjL) =>
% 121.65/16.03 ((
% 121.65/16.03 (setukpairinjR11) =>
% 121.65/16.03 ((
% 121.65/16.03 (setukpairinjR12) =>
% 121.65/16.03 ((
% 121.65/16.03 (setukpairinjR1) =>
% 121.65/16.03 ((
% 121.65/16.03 (upairequniteq) =>
% 121.65/16.03 ((
% 121.65/16.03 (setukpairinjR2) =>
% 121.65/16.03 ((
% 121.65/16.03 (setukpairinjR) =>
% 121.65/16.03 ((
% 121.65/16.03 (ksndsingleton) =>
% 121.65/16.03 ((
% 121.65/16.03 (ksndpairEq) =>
% 121.65/16.03 ((
% 121.65/16.03 (kpairsurjEq) =>
% 121.65/16.03 ((
% 121.65/16.03 (cartprodsndin) =>
% 121.65/16.03 ((
% 121.65/16.03 (cartprodpairmemEL) =>
% 121.65/16.03 ((
% 121.65/16.03 (cartprodpairmemER) =>
% 121.65/16.03 ((
% 121.65/16.03 (cartprodmempaircEq) =>
% 121.65/16.03 ((
% 121.65/16.03 (cartprodfstpairEq) =>
% 121.65/16.03 ((
% 121.65/16.03 (cartprodsndpairEq) =>
% 121.65/16.03 ((
% 121.65/16.03 (cartprodpairsurjEq) =>
% 121.65/16.03 ((
% 121.65/16.03 (dpsetconstrI) =>
% 121.65/16.03 ((
% 121.65/16.03 (dpsetconstrSub) =>
% 121.65/16.03 ((
% 121.65/16.03 (setOfPairsIsBReln) =>
% 121.65/16.03 ((
% 121.65/16.03 (dpsetconstrERa) =>
% 121.65/16.03 ((
% 121.65/16.03 (dpsetconstrEL1) =>
% 121.65/16.03 ((
% 121.65/16.03 (dpsetconstrEL2) =>
% 121.65/16.03 ((
% 121.65/16.03 (dpsetconstrER) =>
% 121.65/16.03 ((
% 121.65/16.03 (funcImageSingleton) =>
% 121.65/16.03 ((
% 121.65/16.03 (apProp) =>
% 121.65/16.03 ((
% 121.65/16.03 (app) =>
% 121.65/16.03 ((
% 121.65/16.03 (infuncsetfunc) =>
% 121.65/16.03 ((
% 121.65/16.03 (ap2p) =>
% 121.65/16.03 ((
% 121.65/16.03 (funcinfuncset) =>
% 121.65/16.03 ((
% 121.65/16.03 (lamProp) =>
% 121.65/16.03 ((
% 121.65/16.03 (lamp) =>
% 121.65/16.03 ((
% 121.65/16.03 (lam2p) =>
% 121.65/16.03 ((
% 121.65/16.03 (brelnall1) =>
% 121.65/16.03 ((
% 121.65/16.03 (brelnall2) =>
% 121.65/16.03 ((
% 121.65/16.03 (ex1E2) =>
% 121.65/16.03 ((
% 121.65/16.03 (funcGraphProp1) =>
% 121.65/16.03 ((
% 121.65/16.03 (funcGraphProp3) =>
% 121.65/16.03 ((
% 121.65/16.03 (funcGraphProp2) =>
% 121.65/16.03 ((
% 121.65/16.03 (funcextLem) =>
% 121.65/16.03 ((
% 121.65/16.03 (funcGraphProp4) =>
% 121.65/16.03 ((
% 121.65/16.03 (subbreln) =>
% 121.65/16.03 ((
% 121.65/16.03 (eqbreln) =>
% 121.65/16.03 ((
% 121.65/16.03 (funcext) =>
% 121.65/16.03 ((
% 121.65/16.03 (funcext2) =>
% 121.65/16.03 ((
% 121.65/16.03 (ap2apEq1) =>
% 121.65/16.03 ((
% 121.65/16.03 (ap2apEq2) =>
% 121.65/16.03 ((
% 121.65/16.03 (beta1) =>
% 121.65/16.03 ((
% 121.65/16.03 (eta1) =>
% 121.65/16.03 ((
% 121.65/16.03 (lam2lamEq) =>
% 121.65/16.03 ((
% 121.65/16.03 (beta2) =>
% 121.65/16.03 ((
% 121.65/16.03 (eta2) =>
% 121.65/16.03 ((
% 121.65/16.03 (iffalseProp1) =>
% 121.65/16.03 ((
% 121.65/16.03 (iffalseProp2) =>
% 121.65/16.03 ((
% 121.65/16.03 (iftrueProp1) =>
% 121.65/16.03 ((
% 121.65/16.03 (iftrueProp2) =>
% 121.65/16.03 ((
% 121.65/16.03 (ifSingleton) =>
% 121.65/16.03 ((
% 121.65/16.03 (ifp) =>
% 121.65/16.03 ((
% 121.65/16.03 (theeq) =>
% 121.65/16.03 ((
% 121.65/16.03 (iftrue) =>
% 121.65/16.03 ((
% 121.65/16.03 (iffalse) =>
% 121.65/16.03 ((
% 121.65/16.03 (iftrueorfalse) =>
% 121.65/16.03 ((
% 121.65/16.03 (binintersectT_lem) =>
% 121.65/16.03 ((
% 121.65/16.03 (binunionT_lem) =>
% 121.65/16.03 ((
% 121.65/16.03 (powersetT_lem) =>
% 121.65/16.03 ((
% 121.65/16.03 (setminusT_lem) =>
% 121.65/16.03 ((
% 121.65/16.03 (complementT_lem) =>
% 121.65/16.03 ((
% 121.65/16.03 (setextT) =>
% 121.65/16.03 ((
% 121.65/16.03 (subsetTI) =>
% 121.65/16.03 ((
% 121.65/16.03 (powersetTI1) =>
% 121.65/16.03 ((
% 121.65/16.03 (powersetTE1) =>
% 121.65/16.03 ((
% 121.65/16.03 (complementTI1) =>
% 121.65/16.03 ((
% 121.65/16.03 (complementTE1) =>
% 121.65/16.03 ((
% 121.65/16.03 (binintersectTELcontra) =>
% 121.65/16.03 ((
% 121.65/16.03 (binintersectTERcontra) =>
% 121.65/16.03 ((
% 121.65/16.03 (contrasubsetT) =>
% 121.65/16.03 ((
% 121.65/16.03 (contrasubsetT1) =>
% 121.65/16.03 ((
% 121.65/16.03 (contrasubsetT2) =>
% 121.65/16.03 ((
% 121.65/16.03 (contrasubsetT3) =>
% 121.65/16.03 ((
% 121.65/16.03 (doubleComplementI1) =>
% 121.65/16.03 ((
% 121.65/16.03 (doubleComplementE1) =>
% 121.65/16.03 ((
% 121.65/16.03 (doubleComplementSub1) =>
% 121.65/16.03 ((
% 121.65/16.03 (doubleComplementSub2) =>
% 121.65/16.03 ((
% 121.65/16.03 (doubleComplementEq) =>
% 121.65/16.03 ((
% 121.65/16.03 (complementTnotintersectT) =>
% 121.65/16.03 ((
% 121.65/16.03 (complementImpComplementIntersect) =>
% 121.65/16.03 ((
% 121.65/16.03 (complementSubsetComplementIntersect) =>
% 121.65/16.03 ((
% 121.65/16.03 (complementInPowersetComplementIntersect) =>
% 121.65/16.03 ((
% 121.65/16.03 (contraSubsetComplement) =>
% 121.65/16.03 ((
% 121.65/16.03 (complementTcontraSubset) =>
% 121.65/16.03 ((
% 121.65/16.03 (binunionTILcontra) =>
% 121.65/16.03 ((
% 121.65/16.03 (binunionTIRcontra) =>
% 121.65/16.03 ((
% 121.65/16.03 (inIntersectImpInUnion) =>
% 121.65/16.03 ((
% 121.65/16.03 (inIntersectImpInUnion2) =>
% 121.65/16.03 ((
% 121.65/16.03 (inIntersectImpInIntersectUnions) =>
% 121.65/16.03 ((
% 121.65/16.03 (intersectInPowersetIntersectUnions) =>
% 121.65/16.03 ((
% 121.65/16.03 (inComplementUnionImpNotIn1) =>
% 121.65/16.03 ((
% 121.65/16.03 (inComplementUnionImpInComplement1) =>
% 121.65/16.03 ((
% 121.65/16.03 (binunionTE) =>
% 121.65/16.03 ((
% 121.65/16.03 (binunionTEcontra) =>
% 121.65/16.03 ((
% 121.65/16.03 (demorgan2a1) =>
% 121.65/16.03 ((
% 121.65/16.03 (complementUnionInPowersetComplement) =>
% 121.65/16.03 ((
% 121.65/16.03 (demorgan2a2) =>
% 121.65/16.03 ((
% 121.65/16.03 (demorgan1a) =>
% 121.65/16.03 ((
% 121.65/16.03 (demorgan1b) =>
% 121.65/16.03 ((
% 121.65/16.03 (demorgan1) =>
% 121.65/16.03 ((
% 121.65/16.03 (demorgan2a) =>
% 121.65/16.03 ((
% 121.65/16.03 (demorgan2b2) =>
% 121.65/16.03 ((
% 121.65/16.03 (demorgan2b) =>
% 121.65/16.03 ((
% 121.65/16.03 (demorgan2) =>
% 121.65/16.03 ((
% 121.65/16.03 (woz13rule0) =>
% 121.65/16.03 ((
% 121.65/16.03 (woz13rule1) =>
% 121.65/16.03 ((
% 121.65/16.03 (woz13rule2) =>
% 121.65/16.03 ((
% 121.65/16.03 (woz13rule3) =>
% 121.65/16.03 ((
% 121.65/16.03 (woz13rule4) =>
% 121.65/16.03 ((
% 121.65/16.03 (woz1_1) =>
% 121.65/16.03 ((
% 121.65/16.03 (woz1_2) =>
% 121.65/16.03 ((
% 121.65/16.03 (woz1_3) =>
% 121.65/16.03 ((
% 121.65/16.03 (woz1_4) =>
% 121.65/16.03 ((
% 121.65/16.03 (woz1_5) =>
% 121.65/16.03 ((
% 121.65/16.03 (breln1all2) =>
% 121.65/16.03 ((
% 121.65/16.03 (breln1SetBreln1) =>
% 121.65/16.03 ((
% 121.65/16.03 (choice2fnsingleton) =>
% 121.65/16.03 ((
% 121.65/16.03 (setOfPairsIsBReln1) =>
% 121.65/16.03 ((
% 121.65/16.03 (breln1all1) =>
% 121.65/16.03 ((
% 121.65/16.03 (subbreln1) =>
% 121.65/16.03 ((
% 121.65/16.03 (eqbreln1) =>
% 121.65/16.03 ((
% 121.65/16.03 (breln1invprop) =>
% 121.65/16.03 ((
% 121.65/16.03 (breln1invI) =>
% 121.65/16.03 ((
% 121.65/16.03 (breln1invE) =>
% 121.65/16.03 ((
% 121.65/16.03 (breln1compprop) =>
% 121.65/16.03 ((
% 121.65/16.03 (breln1compI) =>
% 121.65/16.03 ((
% 121.65/16.03 (breln1compE) =>
% 121.65/16.03 ((
% 121.65/16.03 (breln1compEex) =>
% 121.65/16.03 ((
% 121.65/16.03 (breln1unionprop) =>
% 121.65/16.03 ((
% 121.65/16.03 (breln1unionIL) =>
% 121.65/16.03 ((
% 121.65/16.03 (breln1unionIR) =>
% 121.65/16.03 ((
% 121.65/16.03 (breln1unionI) =>
% 121.65/16.03 ((
% 121.65/16.03 (breln1unionE) =>
% 121.65/16.03 ((
% 121.65/16.03 (breln1unionEcases) =>
% 121.65/16.03 ((
% 121.65/16.03 (breln1unionCommutes) =>
% 121.65/16.03 ((
% 121.65/16.03 (woz2Ex) =>
% 121.65/16.03 ((
% 121.65/16.03 (woz2W) =>
% 121.65/16.03 ((
% 121.65/16.03 (woz2A) =>
% 121.65/16.03 ((
% 121.65/16.03 (woz2B) =>
% 121.65/16.03 ((
% 121.65/16.03 (image1Ex) =>
% 121.65/16.03 ((
% 121.65/16.03 (image1Ex1) =>
% 121.65/16.03 ((
% 121.65/16.03 (image1Equiv) =>
% 121.65/16.03 ((
% 121.65/16.03 (image1E) =>
% 121.65/16.03 ((
% 121.65/16.03 (image1I) =>
% 121.65/16.03 ((
% 121.65/16.03 (injFuncInInjFuncSet) =>
% 121.65/16.03 ((
% 121.65/16.03 (!!) @ (
% 121.65/16.03 (('#B') @ (
% 121.65/16.03 !!) @
% 121.65/16.03 (
% 121.65/16.03 (
% 121.65/16.03 ('#B') @ (
% 121.65/16.03 (
% 121.65/16.03 ('#B') @ (
% 121.65/16.03 !!))) @
% 121.65/16.03 (
% 121.65/16.03 (
% 121.65/16.03 ('#S') @ (
% 121.65/16.03 (
% 121.65/16.03 ('#B') @ (
% 121.65/16.03 '#S') @
% 121.65/16.03 (
% 121.65/16.03 (
% 121.65/16.03 ('#B') @ (
% 121.65/16.03 (
% 121.65/16.03 ('#B') @ (
% 121.65/16.03 '#S'))) @
% 121.65/16.03 (
% 121.65/16.03 (
% 121.65/16.03 ('#B') @ (
% 121.65/16.03 (
% 121.65/16.03 ('#B') @ (
% 121.65/16.03 (
% 121.65/16.03 ('#B') @ (
% 121.65/16.03 =>))))) @
% 121.65/16.03 (
% 121.65/16.03 (
% 121.65/16.03 ('#B') @ (
% 121.65/16.03 (
% 121.65/16.03 ('#B') @ (
% 121.65/16.03 (
% 121.65/16.03 ('#C') @ in)))) @
% 121.65/16.03 injFuncSet)))))))) @
% 121.65/16.03 (
% 121.65/16.03 (
% 121.65/16.03 ('#B') @ (
% 121.65/16.03 (
% 121.65/16.03 ('#B') @ (
% 121.65/16.03 (
% 121.65/16.03 ('#C') @ in)))) @
% 121.65/16.03 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 121.65/16.03 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl222])).
% 121.65/16.03 thf(zip_derived_cl251, plain,
% 121.65/16.03 (~ (((setbeta) =>
% 121.65/16.03 (((nonemptyE1) =>
% 121.65/16.03 (((nonemptyI) =>
% 121.65/16.03 (((nonemptyI1) =>
% 121.65/16.03 (((setadjoinIL) =>
% 121.65/16.03 (((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) =>
% 121.65/16.03 (((setadjoinIR) =>
% 121.65/16.03 (((setadjoinE) =>
% 121.65/16.03 (((setadjoinOr) =>
% 121.65/16.03 (((setoftrueEq) =>
% 121.65/16.03 (((powersetI) =>
% 121.65/16.03 (((emptyinPowerset) =>
% 121.65/16.03 (((emptyInPowerset) =>
% 121.65/16.03 (((powersetE) =>
% 121.65/16.03 (((setunionI) =>
% 121.65/16.03 (((setunionE) =>
% 121.65/16.03 (((subPowSU) =>
% 121.65/16.03 (((exuE2) =>
% 121.65/16.03 (((nonemptyImpWitness) =>
% 121.65/16.03 (((uniqinunit) =>
% 121.65/16.03 (((notinsingleton) =>
% 121.65/16.03 (((eqinunit) =>
% 121.65/16.03 (((singletonsswitch) =>
% 121.65/16.03 (((upairsetE) =>
% 121.65/16.03 (((upairsetIL) =>
% 121.65/16.03 (((upairsetIR) =>
% 121.65/16.03 (((emptyE1) =>
% 121.65/16.03 (((vacuousDall) =>
% 121.65/16.03 (((quantDeMorgan1) =>
% 121.65/16.03 (((quantDeMorgan2) =>
% 121.65/16.03 ((
% 121.65/16.03 (quantDeMorgan3) =>
% 121.65/16.03 ((
% 121.65/16.03 (quantDeMorgan4) =>
% 121.65/16.03 ((
% 121.65/16.03 (prop2setI) =>
% 121.65/16.03 ((
% 121.65/16.03 (prop2set2propI) =>
% 121.65/16.03 ((
% 121.65/16.03 (notdexE) =>
% 121.65/16.03 ((
% 121.65/16.03 (notdallE) =>
% 121.65/16.03 ((
% 121.65/16.03 (exuI1) =>
% 121.65/16.03 ((
% 121.65/16.03 (exuI3) =>
% 121.65/16.03 ((
% 121.65/16.03 (exuI2) =>
% 121.65/16.03 ((
% 121.65/16.03 (inCongP) =>
% 121.65/16.03 ((
% 121.65/16.03 (in__Cong) =>
% 121.65/16.03 ((
% 121.65/16.03 (exuE3u) =>
% 121.65/16.03 ((
% 121.65/16.03 (exu__Cong) =>
% 121.65/16.03 ((
% 121.65/16.03 (setadjoin__Cong) =>
% 121.65/16.03 ((
% 121.65/16.03 (powerset__Cong) =>
% 121.65/16.03 ((
% 121.65/16.03 (setunion__Cong) =>
% 121.65/16.03 ((
% 121.65/16.03 (exuEu) =>
% 121.65/16.03 ((
% 121.65/16.03 (descr__Cong) =>
% 121.65/16.03 ((
% 121.65/16.03 (dsetconstr__Cong) =>
% 121.65/16.03 ((
% 121.65/16.03 (subsetI1) =>
% 121.65/16.03 ((
% 121.65/16.03 (eqimpsubset2) =>
% 121.65/16.03 ((
% 121.65/16.03 (eqimpsubset1) =>
% 121.65/16.03 ((
% 121.65/16.03 (subsetI2) =>
% 121.65/16.03 ((
% 121.65/16.03 (emptysetsubset) =>
% 121.65/16.03 ((
% 121.65/16.03 (subsetE) =>
% 121.65/16.03 ((
% 121.65/16.03 (subsetE2) =>
% 121.65/16.03 ((
% 121.65/16.03 (notsubsetI) =>
% 121.65/16.03 ((
% 121.65/16.03 (notequalI1) =>
% 121.65/16.03 ((
% 121.65/16.03 (notequalI2) =>
% 121.65/16.03 ((
% 121.65/16.03 (subsetRefl) =>
% 121.65/16.03 ((
% 121.65/16.03 (subsetTrans) =>
% 121.65/16.03 ((
% 121.65/16.03 (setadjoinSub) =>
% 121.65/16.03 ((
% 121.65/16.03 (setadjoinSub2) =>
% 121.65/16.03 ((
% 121.65/16.03 (subset2powerset) =>
% 121.65/16.03 ((
% 121.65/16.03 (setextsub) =>
% 121.65/16.03 ((
% 121.65/16.03 (subsetemptysetimpeq) =>
% 121.65/16.03 ((
% 121.65/16.03 (powersetI1) =>
% 121.65/16.03 ((
% 121.65/16.03 (powersetE1) =>
% 121.65/16.03 ((
% 121.65/16.03 (inPowerset) =>
% 121.65/16.03 ((
% 121.65/16.03 (powersetsubset) =>
% 121.65/16.03 ((
% 121.65/16.03 (sepInPowerset) =>
% 121.65/16.03 ((
% 121.65/16.03 (sepSubset) =>
% 121.65/16.03 ((
% 121.65/16.03 (binunionIL) =>
% 121.65/16.03 ((
% 121.65/16.03 (upairset2IR) =>
% 121.65/16.03 ((
% 121.65/16.03 (binunionIR) =>
% 121.65/16.03 ((
% 121.65/16.03 (binunionEcases) =>
% 121.65/16.03 ((
% 121.65/16.03 (binunionE) =>
% 121.65/16.03 ((
% 121.65/16.03 (binunionLsub) =>
% 121.65/16.03 ((
% 121.65/16.03 (binunionRsub) =>
% 121.65/16.03 ((
% 121.65/16.03 (binintersectI) =>
% 121.65/16.03 ((
% 121.65/16.03 (binintersectSubset5) =>
% 121.65/16.03 ((
% 121.65/16.03 (binintersectEL) =>
% 121.65/16.03 ((
% 121.65/16.03 (binintersectLsub) =>
% 121.65/16.03 ((
% 121.65/16.03 (binintersectSubset2) =>
% 121.65/16.03 ((
% 121.65/16.03 (binintersectSubset3) =>
% 121.65/16.03 ((
% 121.65/16.03 (binintersectER) =>
% 121.65/16.03 ((
% 121.65/16.03 (disjointsetsI1) =>
% 121.65/16.03 ((
% 121.65/16.03 (binintersectRsub) =>
% 121.65/16.03 ((
% 121.65/16.03 (binintersectSubset4) =>
% 121.65/16.03 ((
% 121.65/16.03 (binintersectSubset1) =>
% 121.65/16.03 ((
% 121.65/16.03 (bs114d) =>
% 121.65/16.03 ((
% 121.65/16.03 (setminusI) =>
% 121.65/16.03 ((
% 121.65/16.03 (setminusEL) =>
% 121.65/16.03 ((
% 121.65/16.03 (setminusER) =>
% 121.65/16.03 ((
% 121.65/16.03 (setminusSubset2) =>
% 121.65/16.03 ((
% 121.65/16.03 (setminusERneg) =>
% 121.65/16.03 ((
% 121.65/16.03 (setminusELneg) =>
% 121.65/16.03 ((
% 121.65/16.03 (setminusILneg) =>
% 121.65/16.03 ((
% 121.65/16.03 (setminusIRneg) =>
% 121.65/16.03 ((
% 121.65/16.03 (setminusLsub) =>
% 121.65/16.03 ((
% 121.65/16.03 (setminusSubset1) =>
% 121.65/16.03 ((
% 121.65/16.03 (symdiffE) =>
% 121.65/16.03 ((
% 121.65/16.03 (symdiffI1) =>
% 121.65/16.03 ((
% 121.65/16.03 (symdiffI2) =>
% 121.65/16.03 ((
% 121.65/16.03 (symdiffIneg1) =>
% 121.65/16.03 ((
% 121.65/16.03 (symdiffIneg2) =>
% 121.65/16.03 ((
% 121.65/16.03 (secondinupair) =>
% 121.65/16.03 ((
% 121.65/16.03 (setukpairIL) =>
% 121.65/16.03 ((
% 121.65/16.03 (setukpairIR) =>
% 121.65/16.03 ((
% 121.65/16.03 (kpairiskpair) =>
% 121.65/16.03 ((
% 121.65/16.03 (kpairp) =>
% 121.65/16.03 ((
% 121.65/16.03 (singletonsubset) =>
% 121.65/16.03 ((
% 121.65/16.03 (singletoninpowerset) =>
% 121.65/16.03 ((
% 121.65/16.03 (singletoninpowunion) =>
% 121.65/16.03 ((
% 121.65/16.03 (upairset2E) =>
% 121.65/16.03 ((
% 121.65/16.03 (upairsubunion) =>
% 121.65/16.03 ((
% 121.65/16.03 (upairinpowunion) =>
% 121.65/16.03 ((
% 121.65/16.03 (ubforcartprodlem1) =>
% 121.65/16.03 ((
% 121.65/16.03 (ubforcartprodlem2) =>
% 121.65/16.03 ((
% 121.65/16.03 (ubforcartprodlem3) =>
% 121.65/16.03 ((
% 121.65/16.03 (cartprodpairin) =>
% 121.65/16.03 ((
% 121.65/16.03 (cartprodmempair1) =>
% 121.65/16.03 ((
% 121.65/16.03 (cartprodmempair) =>
% 121.65/16.03 ((
% 121.65/16.03 (setunionE2) =>
% 121.65/16.04 ((
% 121.65/16.04 (setunionsingleton1) =>
% 121.65/16.04 ((
% 121.65/16.04 (setunionsingleton2) =>
% 121.65/16.04 ((
% 121.65/16.04 (setunionsingleton) =>
% 121.65/16.04 ((
% 121.65/16.04 (singletonprop) =>
% 121.65/16.04 ((
% 121.65/16.04 (ex1E1) =>
% 121.65/16.04 ((
% 121.65/16.04 (ex1I) =>
% 121.65/16.04 ((
% 121.65/16.04 (ex1I2) =>
% 121.65/16.04 ((
% 121.65/16.04 (singletonsuniq) =>
% 121.65/16.04 ((
% 121.65/16.04 (setukpairinjL1) =>
% 121.65/16.04 ((
% 121.65/16.04 (kfstsingleton) =>
% 121.65/16.04 ((
% 121.65/16.04 (theprop) =>
% 121.65/16.04 ((
% 121.65/16.04 (kfstpairEq) =>
% 121.65/16.04 ((
% 121.65/16.04 (cartprodfstin) =>
% 121.65/16.04 ((
% 121.65/16.04 (setukpairinjL2) =>
% 121.65/16.04 ((
% 121.65/16.04 (setukpairinjL) =>
% 121.65/16.04 ((
% 121.65/16.04 (setukpairinjR11) =>
% 121.65/16.04 ((
% 121.65/16.04 (setukpairinjR12) =>
% 121.65/16.04 ((
% 121.65/16.04 (setukpairinjR1) =>
% 121.65/16.04 ((
% 121.65/16.04 (upairequniteq) =>
% 121.65/16.04 ((
% 121.65/16.04 (setukpairinjR2) =>
% 121.65/16.04 ((
% 121.65/16.04 (setukpairinjR) =>
% 121.65/16.04 ((
% 121.65/16.04 (ksndsingleton) =>
% 121.65/16.04 ((
% 121.65/16.04 (ksndpairEq) =>
% 121.65/16.04 ((
% 121.65/16.04 (kpairsurjEq) =>
% 121.65/16.04 ((
% 121.65/16.04 (cartprodsndin) =>
% 121.65/16.04 ((
% 121.65/16.04 (cartprodpairmemEL) =>
% 121.65/16.04 ((
% 121.65/16.04 (cartprodpairmemER) =>
% 121.65/16.04 ((
% 121.65/16.04 (cartprodmempaircEq) =>
% 121.65/16.04 ((
% 121.65/16.04 (cartprodfstpairEq) =>
% 121.65/16.04 ((
% 121.65/16.04 (cartprodsndpairEq) =>
% 121.65/16.04 ((
% 121.65/16.04 (cartprodpairsurjEq) =>
% 121.65/16.04 ((
% 121.65/16.04 (dpsetconstrI) =>
% 121.65/16.04 ((
% 121.65/16.04 (dpsetconstrSub) =>
% 121.65/16.04 ((
% 121.65/16.04 (setOfPairsIsBReln) =>
% 121.65/16.04 ((
% 121.65/16.04 (dpsetconstrERa) =>
% 121.65/16.04 ((
% 121.65/16.04 (dpsetconstrEL1) =>
% 121.65/16.04 ((
% 121.65/16.04 (dpsetconstrEL2) =>
% 121.65/16.04 ((
% 121.65/16.04 (dpsetconstrER) =>
% 121.65/16.04 ((
% 121.65/16.04 (funcImageSingleton) =>
% 121.65/16.04 ((
% 121.65/16.04 (apProp) =>
% 121.65/16.04 ((
% 121.65/16.04 (app) =>
% 121.65/16.04 ((
% 121.65/16.04 (infuncsetfunc) =>
% 121.65/16.04 ((
% 121.65/16.04 (ap2p) =>
% 121.65/16.04 ((
% 121.65/16.04 (funcinfuncset) =>
% 121.65/16.04 ((
% 121.65/16.04 (lamProp) =>
% 121.65/16.04 ((
% 121.65/16.04 (lamp) =>
% 121.65/16.04 ((
% 121.65/16.04 (lam2p) =>
% 121.65/16.04 ((
% 121.65/16.04 (brelnall1) =>
% 121.65/16.04 ((
% 121.65/16.04 (brelnall2) =>
% 121.65/16.04 ((
% 121.65/16.04 (ex1E2) =>
% 121.65/16.04 ((
% 121.65/16.04 (funcGraphProp1) =>
% 121.65/16.04 ((
% 121.65/16.04 (funcGraphProp3) =>
% 121.65/16.04 ((
% 121.65/16.04 (funcGraphProp2) =>
% 121.65/16.04 ((
% 121.65/16.04 (funcextLem) =>
% 121.65/16.04 ((
% 121.65/16.04 (funcGraphProp4) =>
% 121.65/16.04 ((
% 121.65/16.04 (subbreln) =>
% 121.65/16.04 ((
% 121.65/16.04 (eqbreln) =>
% 121.65/16.04 ((
% 121.65/16.04 (funcext) =>
% 121.65/16.04 ((
% 121.65/16.04 (funcext2) =>
% 121.65/16.04 ((
% 121.65/16.04 (ap2apEq1) =>
% 121.65/16.04 ((
% 121.65/16.04 (ap2apEq2) =>
% 121.65/16.04 ((
% 121.65/16.04 (beta1) =>
% 121.65/16.04 ((
% 121.65/16.04 (eta1) =>
% 121.65/16.04 ((
% 121.65/16.04 (lam2lamEq) =>
% 121.65/16.04 ((
% 121.65/16.04 (beta2) =>
% 121.65/16.04 ((
% 121.65/16.04 (eta2) =>
% 121.65/16.04 ((
% 121.65/16.04 (iffalseProp1) =>
% 121.65/16.04 ((
% 121.65/16.04 (iffalseProp2) =>
% 121.65/16.04 ((
% 121.65/16.04 (iftrueProp1) =>
% 121.65/16.04 ((
% 121.65/16.04 (iftrueProp2) =>
% 121.65/16.04 ((
% 121.65/16.04 (ifSingleton) =>
% 121.65/16.04 ((
% 121.65/16.04 (ifp) =>
% 121.65/16.04 ((
% 121.65/16.04 (theeq) =>
% 121.65/16.04 ((
% 121.65/16.04 (iftrue) =>
% 121.65/16.04 ((
% 121.65/16.04 (iffalse) =>
% 121.65/16.04 ((
% 121.65/16.04 (iftrueorfalse) =>
% 121.65/16.04 ((
% 121.65/16.04 (binintersectT_lem) =>
% 121.65/16.04 ((
% 121.65/16.04 (binunionT_lem) =>
% 121.65/16.04 ((
% 121.65/16.04 (powersetT_lem) =>
% 121.65/16.04 ((
% 121.65/16.04 (setminusT_lem) =>
% 121.65/16.04 ((
% 121.65/16.04 (complementT_lem) =>
% 121.65/16.04 ((
% 121.65/16.04 (setextT) =>
% 121.65/16.04 ((
% 121.65/16.04 (subsetTI) =>
% 121.65/16.04 ((
% 121.65/16.04 (powersetTI1) =>
% 121.65/16.04 ((
% 121.65/16.04 (powersetTE1) =>
% 121.65/16.04 ((
% 121.65/16.04 (complementTI1) =>
% 121.65/16.04 ((
% 121.65/16.04 (complementTE1) =>
% 121.65/16.04 ((
% 121.65/16.04 (binintersectTELcontra) =>
% 121.65/16.04 ((
% 121.65/16.04 (binintersectTERcontra) =>
% 121.65/16.04 ((
% 121.65/16.04 (contrasubsetT) =>
% 121.65/16.04 ((
% 121.65/16.04 (contrasubsetT1) =>
% 121.65/16.04 ((
% 121.65/16.04 (contrasubsetT2) =>
% 121.65/16.04 ((
% 121.65/16.04 (contrasubsetT3) =>
% 121.65/16.04 ((
% 121.65/16.04 (doubleComplementI1) =>
% 121.65/16.04 ((
% 121.65/16.04 (doubleComplementE1) =>
% 121.65/16.04 ((
% 121.65/16.04 (doubleComplementSub1) =>
% 121.65/16.04 ((
% 121.65/16.04 (doubleComplementSub2) =>
% 121.65/16.04 ((
% 121.65/16.04 (doubleComplementEq) =>
% 121.65/16.04 ((
% 121.65/16.04 (complementTnotintersectT) =>
% 121.65/16.04 ((
% 121.65/16.04 (complementImpComplementIntersect) =>
% 121.65/16.04 ((
% 121.65/16.04 (complementSubsetComplementIntersect) =>
% 121.65/16.04 ((
% 121.65/16.04 (complementInPowersetComplementIntersect) =>
% 121.65/16.04 ((
% 121.65/16.04 (contraSubsetComplement) =>
% 121.65/16.04 ((
% 121.65/16.04 (complementTcontraSubset) =>
% 121.65/16.04 ((
% 121.65/16.04 (binunionTILcontra) =>
% 121.65/16.04 ((
% 121.65/16.04 (binunionTIRcontra) =>
% 121.65/16.04 ((
% 121.65/16.04 (inIntersectImpInUnion) =>
% 121.65/16.04 ((
% 121.65/16.04 (inIntersectImpInUnion2) =>
% 121.65/16.04 ((
% 121.65/16.04 (inIntersectImpInIntersectUnions) =>
% 121.65/16.04 ((
% 121.65/16.04 (intersectInPowersetIntersectUnions) =>
% 121.65/16.04 ((
% 121.65/16.04 (inComplementUnionImpNotIn1) =>
% 121.65/16.04 ((
% 121.65/16.04 (inComplementUnionImpInComplement1) =>
% 121.65/16.04 ((
% 121.65/16.04 (binunionTE) =>
% 121.65/16.04 ((
% 121.65/16.04 (binunionTEcontra) =>
% 121.65/16.04 ((
% 121.65/16.04 (demorgan2a1) =>
% 121.65/16.04 ((
% 121.65/16.04 (complementUnionInPowersetComplement) =>
% 121.65/16.04 ((
% 121.65/16.04 (demorgan2a2) =>
% 121.65/16.04 ((
% 121.65/16.04 (demorgan1a) =>
% 121.65/16.04 ((
% 121.65/16.04 (demorgan1b) =>
% 121.65/16.04 ((
% 121.65/16.04 (demorgan1) =>
% 121.65/16.04 ((
% 121.65/16.04 (demorgan2a) =>
% 121.65/16.04 ((
% 121.65/16.04 (demorgan2b2) =>
% 121.65/16.04 ((
% 121.65/16.04 (demorgan2b) =>
% 121.65/16.04 ((
% 121.65/16.04 (demorgan2) =>
% 121.65/16.04 ((
% 121.65/16.04 (woz13rule0) =>
% 121.65/16.04 ((
% 121.65/16.04 (woz13rule1) =>
% 121.65/16.04 ((
% 121.65/16.04 (woz13rule2) =>
% 121.65/16.04 ((
% 121.65/16.04 (woz13rule3) =>
% 121.65/16.04 ((
% 121.65/16.04 (woz13rule4) =>
% 121.65/16.04 ((
% 121.65/16.04 (woz1_1) =>
% 121.65/16.04 ((
% 121.65/16.04 (woz1_2) =>
% 121.65/16.04 ((
% 121.65/16.04 (woz1_3) =>
% 121.65/16.04 ((
% 121.65/16.04 (woz1_4) =>
% 121.65/16.04 ((
% 121.65/16.04 (woz1_5) =>
% 121.65/16.04 ((
% 121.65/16.04 (breln1all2) =>
% 121.65/16.04 ((
% 121.65/16.04 (breln1SetBreln1) =>
% 121.65/16.04 ((
% 121.65/16.04 (choice2fnsingleton) =>
% 121.65/16.04 ((
% 121.65/16.04 (setOfPairsIsBReln1) =>
% 121.65/16.04 ((
% 121.65/16.04 (breln1all1) =>
% 121.65/16.04 ((
% 121.65/16.04 (subbreln1) =>
% 121.65/16.04 ((
% 121.65/16.04 (eqbreln1) =>
% 121.65/16.04 ((
% 121.65/16.04 (breln1invprop) =>
% 121.65/16.04 ((
% 121.65/16.04 (breln1invI) =>
% 121.65/16.04 ((
% 121.65/16.04 (breln1invE) =>
% 121.65/16.04 ((
% 121.65/16.04 (breln1compprop) =>
% 121.65/16.04 ((
% 121.65/16.04 (breln1compI) =>
% 121.65/16.04 ((
% 121.65/16.04 (breln1compE) =>
% 121.65/16.04 ((
% 121.65/16.04 (breln1compEex) =>
% 121.65/16.04 ((
% 121.65/16.04 (breln1unionprop) =>
% 121.65/16.04 ((
% 121.65/16.04 (breln1unionIL) =>
% 121.65/16.04 ((
% 121.65/16.04 (breln1unionIR) =>
% 121.65/16.04 ((
% 121.65/16.04 (breln1unionI) =>
% 121.65/16.04 ((
% 121.65/16.04 (breln1unionE) =>
% 121.65/16.04 ((
% 121.65/16.04 (breln1unionEcases) =>
% 121.65/16.04 ((
% 121.65/16.04 (breln1unionCommutes) =>
% 121.65/16.04 ((
% 121.65/16.04 (woz2Ex) =>
% 121.65/16.04 ((
% 121.65/16.04 (woz2W) =>
% 121.65/16.04 ((
% 121.65/16.04 (woz2A) =>
% 121.65/16.04 ((
% 121.65/16.04 (woz2B) =>
% 121.65/16.04 ((
% 121.65/16.04 (image1Ex) =>
% 121.65/16.04 ((
% 121.65/16.04 (image1Ex1) =>
% 121.65/16.04 ((
% 121.65/16.04 (image1Equiv) =>
% 121.65/16.04 ((
% 121.65/16.04 (image1E) =>
% 121.65/16.04 ((
% 121.65/16.04 (image1I) =>
% 121.65/16.04 ((
% 121.65/16.04 (injFuncInInjFuncSet) =>
% 121.65/16.04 ((
% 121.65/16.04 (!!) @ (
% 121.65/16.04 (('#B') @ (
% 121.65/16.04 !!) @
% 121.65/16.04 (
% 121.65/16.04 (
% 121.65/16.04 ('#B') @ (
% 121.65/16.04 (
% 121.65/16.04 ('#B') @ (
% 121.65/16.04 !!))) @
% 121.65/16.04 (
% 121.65/16.04 (
% 121.65/16.04 ('#S') @ (
% 121.65/16.04 (
% 121.65/16.04 ('#B') @ (
% 121.65/16.04 '#S') @
% 121.65/16.04 (
% 121.65/16.04 (
% 121.65/16.04 ('#B') @ (
% 121.65/16.04 (
% 121.65/16.04 ('#B') @ (
% 121.65/16.04 '#S'))) @
% 121.65/16.04 (
% 121.65/16.04 (
% 121.65/16.04 ('#B') @ (
% 121.65/16.04 (
% 121.65/16.04 ('#B') @ (
% 121.65/16.04 (
% 121.65/16.04 ('#B') @ (
% 121.65/16.04 =>))))) @
% 121.65/16.04 (
% 121.65/16.04 (
% 121.65/16.04 ('#B') @ (
% 121.65/16.04 (
% 121.65/16.04 ('#B') @ (
% 121.65/16.04 (
% 121.65/16.04 ('#C') @ in)))) @
% 121.65/16.04 injFuncSet)))))))) @
% 121.65/16.04 (
% 121.65/16.04 (
% 121.65/16.04 ('#B') @ (
% 121.65/16.04 (
% 121.65/16.04 ('#B') @ (
% 121.65/16.04 (
% 121.65/16.04 ('#C') @ in)))) @
% 121.65/16.04 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 121.65/16.04 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl236])).
% 121.65/16.04 thf(zip_derived_cl264, plain,
% 121.65/16.04 (~ (((nonemptyE1) =>
% 121.65/16.04 (((nonemptyI) =>
% 121.65/16.04 (((nonemptyI1) =>
% 121.65/16.04 (((setadjoinIL) =>
% 121.65/16.04 (((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) =>
% 121.65/16.04 (((setadjoinIR) =>
% 121.65/16.04 (((setadjoinE) =>
% 121.65/16.04 (((setadjoinOr) =>
% 121.65/16.04 (((setoftrueEq) =>
% 121.65/16.04 (((powersetI) =>
% 121.65/16.04 (((emptyinPowerset) =>
% 121.65/16.04 (((emptyInPowerset) =>
% 121.65/16.04 (((powersetE) =>
% 121.65/16.04 (((setunionI) =>
% 121.65/16.04 (((setunionE) =>
% 121.65/16.04 (((subPowSU) =>
% 121.65/16.04 (((exuE2) =>
% 121.65/16.04 (((nonemptyImpWitness) =>
% 121.65/16.04 (((uniqinunit) =>
% 121.65/16.04 (((notinsingleton) =>
% 121.65/16.04 (((eqinunit) =>
% 121.65/16.04 (((singletonsswitch) =>
% 121.65/16.04 (((upairsetE) =>
% 121.65/16.04 (((upairsetIL) =>
% 121.65/16.04 (((upairsetIR) =>
% 121.65/16.04 (((emptyE1) =>
% 121.65/16.04 (((vacuousDall) =>
% 121.65/16.04 (((quantDeMorgan1) =>
% 121.65/16.04 (((quantDeMorgan2) =>
% 121.65/16.04 (((quantDeMorgan3) =>
% 121.65/16.04 ((
% 121.65/16.04 (quantDeMorgan4) =>
% 121.65/16.04 ((
% 121.65/16.04 (prop2setI) =>
% 121.65/16.04 ((
% 121.65/16.04 (prop2set2propI) =>
% 121.65/16.04 ((
% 121.65/16.04 (notdexE) =>
% 121.65/16.04 ((
% 121.65/16.04 (notdallE) =>
% 121.65/16.04 ((
% 121.65/16.04 (exuI1) =>
% 121.65/16.04 ((
% 121.65/16.04 (exuI3) =>
% 121.65/16.04 ((
% 121.65/16.04 (exuI2) =>
% 121.65/16.04 ((
% 121.65/16.04 (inCongP) =>
% 121.65/16.04 ((
% 121.65/16.04 (in__Cong) =>
% 121.65/16.04 ((
% 121.65/16.04 (exuE3u) =>
% 121.65/16.04 ((
% 121.65/16.04 (exu__Cong) =>
% 121.65/16.04 ((
% 121.65/16.04 (setadjoin__Cong) =>
% 121.65/16.04 ((
% 121.65/16.04 (powerset__Cong) =>
% 121.65/16.04 ((
% 121.65/16.04 (setunion__Cong) =>
% 121.65/16.04 ((
% 121.65/16.04 (exuEu) =>
% 121.65/16.04 ((
% 121.65/16.04 (descr__Cong) =>
% 121.65/16.04 ((
% 121.65/16.04 (dsetconstr__Cong) =>
% 121.65/16.04 ((
% 121.65/16.04 (subsetI1) =>
% 121.65/16.04 ((
% 121.65/16.04 (eqimpsubset2) =>
% 121.65/16.04 ((
% 121.65/16.04 (eqimpsubset1) =>
% 121.65/16.04 ((
% 121.65/16.04 (subsetI2) =>
% 121.65/16.04 ((
% 121.65/16.04 (emptysetsubset) =>
% 121.65/16.04 ((
% 121.65/16.04 (subsetE) =>
% 121.65/16.04 ((
% 121.65/16.04 (subsetE2) =>
% 121.65/16.04 ((
% 121.65/16.04 (notsubsetI) =>
% 121.65/16.04 ((
% 121.65/16.04 (notequalI1) =>
% 121.65/16.04 ((
% 121.65/16.04 (notequalI2) =>
% 121.65/16.04 ((
% 121.65/16.04 (subsetRefl) =>
% 121.65/16.04 ((
% 121.65/16.04 (subsetTrans) =>
% 121.65/16.04 ((
% 121.65/16.04 (setadjoinSub) =>
% 121.65/16.04 ((
% 121.65/16.04 (setadjoinSub2) =>
% 121.65/16.04 ((
% 121.65/16.04 (subset2powerset) =>
% 121.65/16.04 ((
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% 121.65/16.04 ((
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% 121.65/16.04 ((
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% 121.65/16.04 ((
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% 121.65/16.04 (inPowerset) =>
% 121.65/16.04 ((
% 121.65/16.04 (powersetsubset) =>
% 121.65/16.04 ((
% 121.65/16.04 (sepInPowerset) =>
% 121.65/16.04 ((
% 121.65/16.04 (sepSubset) =>
% 121.65/16.04 ((
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% 121.65/16.04 ((
% 121.65/16.04 (upairset2IR) =>
% 121.65/16.04 ((
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% 121.65/16.04 ((
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% 121.65/16.04 ((
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% 121.65/16.04 ((
% 121.65/16.04 (binunionRsub) =>
% 121.65/16.04 ((
% 121.65/16.04 (binintersectI) =>
% 121.65/16.04 ((
% 121.65/16.04 (binintersectSubset5) =>
% 121.65/16.04 ((
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% 121.65/16.04 ((
% 121.65/16.04 (binintersectLsub) =>
% 121.65/16.04 ((
% 121.65/16.04 (binintersectSubset2) =>
% 121.65/16.04 ((
% 121.65/16.04 (binintersectSubset3) =>
% 121.65/16.04 ((
% 121.65/16.04 (binintersectER) =>
% 121.65/16.04 ((
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% 121.65/16.04 ((
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% 121.65/16.04 ((
% 121.65/16.04 (binintersectSubset4) =>
% 121.65/16.04 ((
% 121.65/16.04 (binintersectSubset1) =>
% 121.65/16.04 ((
% 121.65/16.04 (bs114d) =>
% 121.65/16.04 ((
% 121.65/16.04 (setminusI) =>
% 121.65/16.04 ((
% 121.65/16.04 (setminusEL) =>
% 121.65/16.04 ((
% 121.65/16.04 (setminusER) =>
% 121.65/16.04 ((
% 121.65/16.04 (setminusSubset2) =>
% 121.65/16.04 ((
% 121.65/16.04 (setminusERneg) =>
% 121.65/16.04 ((
% 121.65/16.04 (setminusELneg) =>
% 121.65/16.04 ((
% 121.65/16.04 (setminusILneg) =>
% 121.65/16.04 ((
% 121.65/16.04 (setminusIRneg) =>
% 121.65/16.04 ((
% 121.65/16.04 (setminusLsub) =>
% 121.65/16.04 ((
% 121.65/16.04 (setminusSubset1) =>
% 121.65/16.04 ((
% 121.65/16.04 (symdiffE) =>
% 121.65/16.04 ((
% 121.65/16.04 (symdiffI1) =>
% 121.65/16.04 ((
% 121.65/16.04 (symdiffI2) =>
% 121.65/16.04 ((
% 121.65/16.04 (symdiffIneg1) =>
% 121.65/16.04 ((
% 121.65/16.04 (symdiffIneg2) =>
% 121.65/16.04 ((
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% 121.65/16.04 ((
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% 121.65/16.04 ((
% 121.65/16.04 (setukpairIR) =>
% 121.65/16.04 ((
% 121.65/16.04 (kpairiskpair) =>
% 121.65/16.04 ((
% 121.65/16.04 (kpairp) =>
% 121.65/16.04 ((
% 121.65/16.04 (singletonsubset) =>
% 121.65/16.04 ((
% 121.65/16.04 (singletoninpowerset) =>
% 121.65/16.04 ((
% 121.65/16.04 (singletoninpowunion) =>
% 121.65/16.04 ((
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% 121.65/16.04 ((
% 121.65/16.04 (upairsubunion) =>
% 121.65/16.04 ((
% 121.65/16.04 (upairinpowunion) =>
% 121.65/16.04 ((
% 121.65/16.04 (ubforcartprodlem1) =>
% 121.65/16.04 ((
% 121.65/16.04 (ubforcartprodlem2) =>
% 121.65/16.04 ((
% 121.65/16.04 (ubforcartprodlem3) =>
% 121.65/16.04 ((
% 121.65/16.04 (cartprodpairin) =>
% 121.65/16.04 ((
% 121.65/16.04 (cartprodmempair1) =>
% 121.65/16.04 ((
% 121.65/16.04 (cartprodmempair) =>
% 121.65/16.04 ((
% 121.65/16.04 (setunionE2) =>
% 121.65/16.04 ((
% 121.65/16.04 (setunionsingleton1) =>
% 121.65/16.04 ((
% 121.65/16.04 (setunionsingleton2) =>
% 121.65/16.04 ((
% 121.65/16.04 (setunionsingleton) =>
% 121.65/16.04 ((
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% 121.65/16.04 ((
% 121.65/16.04 (ex1E1) =>
% 121.65/16.04 ((
% 121.65/16.04 (ex1I) =>
% 121.65/16.04 ((
% 121.65/16.04 (ex1I2) =>
% 121.65/16.04 ((
% 121.65/16.04 (singletonsuniq) =>
% 121.65/16.04 ((
% 121.65/16.04 (setukpairinjL1) =>
% 121.65/16.04 ((
% 121.65/16.04 (kfstsingleton) =>
% 121.65/16.04 ((
% 121.65/16.04 (theprop) =>
% 121.65/16.04 ((
% 121.65/16.04 (kfstpairEq) =>
% 121.65/16.04 ((
% 121.65/16.04 (cartprodfstin) =>
% 121.65/16.04 ((
% 121.65/16.04 (setukpairinjL2) =>
% 121.65/16.04 ((
% 121.65/16.04 (setukpairinjL) =>
% 121.65/16.04 ((
% 121.65/16.04 (setukpairinjR11) =>
% 121.65/16.04 ((
% 121.65/16.04 (setukpairinjR12) =>
% 121.65/16.04 ((
% 121.65/16.04 (setukpairinjR1) =>
% 121.65/16.04 ((
% 121.65/16.04 (upairequniteq) =>
% 121.65/16.04 ((
% 121.65/16.04 (setukpairinjR2) =>
% 121.65/16.04 ((
% 121.65/16.04 (setukpairinjR) =>
% 121.65/16.04 ((
% 121.65/16.04 (ksndsingleton) =>
% 121.65/16.04 ((
% 121.65/16.04 (ksndpairEq) =>
% 121.65/16.04 ((
% 121.65/16.04 (kpairsurjEq) =>
% 121.65/16.04 ((
% 121.65/16.04 (cartprodsndin) =>
% 121.65/16.04 ((
% 121.65/16.04 (cartprodpairmemEL) =>
% 121.65/16.04 ((
% 121.65/16.04 (cartprodpairmemER) =>
% 121.65/16.04 ((
% 121.65/16.04 (cartprodmempaircEq) =>
% 121.65/16.04 ((
% 121.65/16.04 (cartprodfstpairEq) =>
% 121.65/16.04 ((
% 121.65/16.04 (cartprodsndpairEq) =>
% 121.65/16.04 ((
% 121.65/16.04 (cartprodpairsurjEq) =>
% 121.65/16.04 ((
% 121.65/16.04 (dpsetconstrI) =>
% 121.65/16.04 ((
% 121.65/16.04 (dpsetconstrSub) =>
% 121.65/16.04 ((
% 121.65/16.04 (setOfPairsIsBReln) =>
% 121.65/16.04 ((
% 121.65/16.04 (dpsetconstrERa) =>
% 121.65/16.04 ((
% 121.65/16.04 (dpsetconstrEL1) =>
% 121.65/16.04 ((
% 121.65/16.04 (dpsetconstrEL2) =>
% 121.65/16.04 ((
% 121.65/16.04 (dpsetconstrER) =>
% 121.65/16.04 ((
% 121.65/16.04 (funcImageSingleton) =>
% 121.65/16.04 ((
% 121.65/16.04 (apProp) =>
% 121.65/16.04 ((
% 121.65/16.04 (app) =>
% 121.65/16.04 ((
% 121.65/16.04 (infuncsetfunc) =>
% 121.65/16.04 ((
% 121.65/16.04 (ap2p) =>
% 121.65/16.04 ((
% 121.65/16.04 (funcinfuncset) =>
% 121.65/16.04 ((
% 121.65/16.04 (lamProp) =>
% 121.65/16.04 ((
% 121.65/16.04 (lamp) =>
% 121.65/16.04 ((
% 121.65/16.04 (lam2p) =>
% 121.65/16.04 ((
% 121.65/16.04 (brelnall1) =>
% 121.65/16.04 ((
% 121.65/16.04 (brelnall2) =>
% 121.65/16.04 ((
% 121.65/16.04 (ex1E2) =>
% 121.65/16.04 ((
% 121.65/16.04 (funcGraphProp1) =>
% 121.65/16.04 ((
% 121.65/16.04 (funcGraphProp3) =>
% 121.65/16.04 ((
% 121.65/16.04 (funcGraphProp2) =>
% 121.65/16.04 ((
% 121.65/16.04 (funcextLem) =>
% 121.65/16.04 ((
% 121.65/16.04 (funcGraphProp4) =>
% 121.65/16.04 ((
% 121.65/16.04 (subbreln) =>
% 121.65/16.04 ((
% 121.65/16.04 (eqbreln) =>
% 121.65/16.04 ((
% 121.65/16.04 (funcext) =>
% 121.65/16.04 ((
% 121.65/16.04 (funcext2) =>
% 121.65/16.04 ((
% 121.65/16.04 (ap2apEq1) =>
% 121.65/16.04 ((
% 121.65/16.04 (ap2apEq2) =>
% 121.65/16.04 ((
% 121.65/16.04 (beta1) =>
% 121.65/16.04 ((
% 121.65/16.04 (eta1) =>
% 121.65/16.04 ((
% 121.65/16.04 (lam2lamEq) =>
% 121.65/16.04 ((
% 121.65/16.04 (beta2) =>
% 121.65/16.04 ((
% 121.65/16.04 (eta2) =>
% 121.65/16.04 ((
% 121.65/16.04 (iffalseProp1) =>
% 121.65/16.04 ((
% 121.65/16.04 (iffalseProp2) =>
% 121.65/16.04 ((
% 121.65/16.04 (iftrueProp1) =>
% 121.65/16.04 ((
% 121.65/16.04 (iftrueProp2) =>
% 121.65/16.04 ((
% 121.65/16.04 (ifSingleton) =>
% 121.65/16.04 ((
% 121.65/16.04 (ifp) =>
% 121.65/16.04 ((
% 121.65/16.04 (theeq) =>
% 121.65/16.04 ((
% 121.65/16.04 (iftrue) =>
% 121.65/16.04 ((
% 121.65/16.04 (iffalse) =>
% 121.65/16.04 ((
% 121.65/16.04 (iftrueorfalse) =>
% 121.65/16.04 ((
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% 121.65/16.04 ((
% 121.65/16.04 (binunionT_lem) =>
% 121.65/16.04 ((
% 121.65/16.04 (powersetT_lem) =>
% 121.65/16.04 ((
% 121.65/16.04 (setminusT_lem) =>
% 121.65/16.04 ((
% 121.65/16.04 (complementT_lem) =>
% 121.65/16.04 ((
% 121.65/16.04 (setextT) =>
% 121.65/16.04 ((
% 121.65/16.04 (subsetTI) =>
% 121.65/16.04 ((
% 121.65/16.04 (powersetTI1) =>
% 121.65/16.04 ((
% 121.65/16.04 (powersetTE1) =>
% 121.65/16.04 ((
% 121.65/16.04 (complementTI1) =>
% 121.65/16.04 ((
% 121.65/16.04 (complementTE1) =>
% 121.65/16.04 ((
% 121.65/16.04 (binintersectTELcontra) =>
% 121.65/16.04 ((
% 121.65/16.04 (binintersectTERcontra) =>
% 121.65/16.04 ((
% 121.65/16.04 (contrasubsetT) =>
% 121.65/16.04 ((
% 121.65/16.04 (contrasubsetT1) =>
% 121.65/16.04 ((
% 121.65/16.04 (contrasubsetT2) =>
% 121.65/16.04 ((
% 121.65/16.04 (contrasubsetT3) =>
% 121.65/16.04 ((
% 121.65/16.04 (doubleComplementI1) =>
% 121.65/16.04 ((
% 121.65/16.04 (doubleComplementE1) =>
% 121.65/16.04 ((
% 121.65/16.04 (doubleComplementSub1) =>
% 121.65/16.04 ((
% 121.65/16.04 (doubleComplementSub2) =>
% 121.65/16.04 ((
% 121.65/16.04 (doubleComplementEq) =>
% 121.65/16.04 ((
% 121.65/16.04 (complementTnotintersectT) =>
% 121.65/16.04 ((
% 121.65/16.04 (complementImpComplementIntersect) =>
% 121.65/16.04 ((
% 121.65/16.04 (complementSubsetComplementIntersect) =>
% 121.65/16.04 ((
% 121.65/16.04 (complementInPowersetComplementIntersect) =>
% 121.65/16.04 ((
% 121.65/16.04 (contraSubsetComplement) =>
% 121.65/16.04 ((
% 121.65/16.04 (complementTcontraSubset) =>
% 121.65/16.04 ((
% 121.65/16.04 (binunionTILcontra) =>
% 121.65/16.04 ((
% 121.65/16.04 (binunionTIRcontra) =>
% 121.65/16.04 ((
% 121.65/16.04 (inIntersectImpInUnion) =>
% 121.65/16.04 ((
% 121.65/16.04 (inIntersectImpInUnion2) =>
% 121.65/16.04 ((
% 121.65/16.04 (inIntersectImpInIntersectUnions) =>
% 121.65/16.04 ((
% 121.65/16.04 (intersectInPowersetIntersectUnions) =>
% 121.65/16.04 ((
% 121.65/16.04 (inComplementUnionImpNotIn1) =>
% 121.65/16.04 ((
% 121.65/16.04 (inComplementUnionImpInComplement1) =>
% 121.65/16.04 ((
% 121.65/16.04 (binunionTE) =>
% 121.65/16.04 ((
% 121.65/16.04 (binunionTEcontra) =>
% 121.65/16.04 ((
% 121.65/16.04 (demorgan2a1) =>
% 121.65/16.04 ((
% 121.65/16.04 (complementUnionInPowersetComplement) =>
% 121.65/16.04 ((
% 121.65/16.04 (demorgan2a2) =>
% 121.65/16.04 ((
% 121.65/16.04 (demorgan1a) =>
% 121.65/16.04 ((
% 121.65/16.04 (demorgan1b) =>
% 121.65/16.04 ((
% 121.65/16.04 (demorgan1) =>
% 121.65/16.04 ((
% 121.65/16.04 (demorgan2a) =>
% 121.65/16.04 ((
% 121.65/16.04 (demorgan2b2) =>
% 121.65/16.04 ((
% 121.65/16.04 (demorgan2b) =>
% 121.65/16.04 ((
% 121.65/16.04 (demorgan2) =>
% 121.65/16.04 ((
% 121.65/16.04 (woz13rule0) =>
% 121.65/16.04 ((
% 121.65/16.04 (woz13rule1) =>
% 121.65/16.04 ((
% 121.65/16.04 (woz13rule2) =>
% 121.65/16.04 ((
% 121.65/16.04 (woz13rule3) =>
% 121.65/16.04 ((
% 121.65/16.04 (woz13rule4) =>
% 121.65/16.04 ((
% 121.65/16.04 (woz1_1) =>
% 121.65/16.04 ((
% 121.65/16.04 (woz1_2) =>
% 121.65/16.04 ((
% 121.65/16.04 (woz1_3) =>
% 121.65/16.04 ((
% 121.65/16.04 (woz1_4) =>
% 121.65/16.04 ((
% 121.65/16.04 (woz1_5) =>
% 121.65/16.04 ((
% 121.65/16.04 (breln1all2) =>
% 121.65/16.04 ((
% 121.65/16.04 (breln1SetBreln1) =>
% 121.65/16.04 ((
% 121.65/16.04 (choice2fnsingleton) =>
% 121.65/16.04 ((
% 121.65/16.04 (setOfPairsIsBReln1) =>
% 121.65/16.04 ((
% 121.65/16.04 (breln1all1) =>
% 121.65/16.04 ((
% 121.65/16.04 (subbreln1) =>
% 121.65/16.04 ((
% 121.65/16.04 (eqbreln1) =>
% 121.65/16.04 ((
% 121.65/16.04 (breln1invprop) =>
% 121.65/16.04 ((
% 121.65/16.04 (breln1invI) =>
% 121.65/16.04 ((
% 121.65/16.04 (breln1invE) =>
% 121.65/16.04 ((
% 121.65/16.04 (breln1compprop) =>
% 121.65/16.04 ((
% 121.65/16.04 (breln1compI) =>
% 121.65/16.04 ((
% 121.65/16.04 (breln1compE) =>
% 121.65/16.04 ((
% 121.65/16.04 (breln1compEex) =>
% 121.65/16.04 ((
% 121.65/16.04 (breln1unionprop) =>
% 121.65/16.04 ((
% 121.65/16.04 (breln1unionIL) =>
% 121.65/16.04 ((
% 121.65/16.04 (breln1unionIR) =>
% 121.65/16.04 ((
% 121.65/16.04 (breln1unionI) =>
% 121.65/16.04 ((
% 121.65/16.04 (breln1unionE) =>
% 121.65/16.04 ((
% 121.65/16.04 (breln1unionEcases) =>
% 121.65/16.04 ((
% 121.65/16.04 (breln1unionCommutes) =>
% 121.65/16.04 ((
% 121.65/16.04 (woz2Ex) =>
% 121.65/16.04 ((
% 121.65/16.04 (woz2W) =>
% 121.65/16.04 ((
% 121.65/16.04 (woz2A) =>
% 121.65/16.04 ((
% 121.65/16.04 (woz2B) =>
% 121.65/16.04 ((
% 121.65/16.04 (image1Ex) =>
% 121.65/16.04 ((
% 121.65/16.04 (image1Ex1) =>
% 121.65/16.04 ((
% 121.65/16.04 (image1Equiv) =>
% 121.65/16.04 ((
% 121.65/16.04 (image1E) =>
% 121.65/16.04 ((
% 121.65/16.04 (image1I) =>
% 121.65/16.04 ((
% 121.65/16.04 (injFuncInInjFuncSet) =>
% 121.65/16.04 ((
% 121.65/16.04 (!!) @ (
% 121.65/16.04 (('#B') @ (
% 121.65/16.04 !!) @
% 121.65/16.04 (
% 121.65/16.04 (
% 121.65/16.04 ('#B') @ (
% 121.65/16.04 (
% 121.65/16.04 ('#B') @ (
% 121.65/16.04 !!))) @
% 121.65/16.04 (
% 121.65/16.04 (
% 121.65/16.04 ('#S') @ (
% 121.65/16.04 (
% 121.65/16.04 ('#B') @ (
% 121.65/16.04 '#S') @
% 121.65/16.04 (
% 121.65/16.04 (
% 121.65/16.04 ('#B') @ (
% 121.65/16.04 (
% 121.65/16.04 ('#B') @ (
% 121.65/16.04 '#S'))) @
% 121.65/16.04 (
% 121.65/16.04 (
% 121.65/16.04 ('#B') @ (
% 121.65/16.04 (
% 121.65/16.04 ('#B') @ (
% 121.65/16.04 (
% 121.65/16.04 ('#B') @ (
% 121.65/16.04 =>))))) @
% 121.65/16.04 (
% 121.65/16.04 (
% 121.65/16.04 ('#B') @ (
% 121.65/16.04 (
% 121.65/16.04 ('#B') @ (
% 121.65/16.04 (
% 121.65/16.04 ('#C') @ in)))) @
% 121.65/16.04 injFuncSet)))))))) @
% 121.65/16.04 (
% 121.65/16.04 (
% 121.65/16.04 ('#B') @ (
% 121.65/16.04 (
% 121.65/16.04 ('#B') @ (
% 121.65/16.04 (
% 121.65/16.04 ('#C') @ in)))) @
% 121.65/16.04 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 121.65/16.04 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl251])).
% 121.65/16.04 thf(zip_derived_cl280, plain,
% 121.65/16.04 (~ (((nonemptyI) =>
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% 121.65/16.04 (((setadjoinIR) =>
% 121.65/16.04 (((setadjoinE) =>
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% 121.65/16.04 (((setoftrueEq) =>
% 121.65/16.04 (((powersetI) =>
% 121.65/16.04 (((emptyinPowerset) =>
% 121.65/16.04 (((emptyInPowerset) =>
% 121.65/16.04 (((powersetE) =>
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% 121.65/16.04 (((setunionE) =>
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% 121.65/16.04 (((exuE2) =>
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% 121.65/16.04 (((upairsetIR) =>
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% 121.65/16.04 (((quantDeMorgan2) =>
% 121.65/16.04 (((quantDeMorgan3) =>
% 121.65/16.04 (((quantDeMorgan4) =>
% 121.65/16.04 ((
% 121.65/16.04 (prop2setI) =>
% 121.65/16.04 ((
% 121.65/16.04 (prop2set2propI) =>
% 121.65/16.04 ((
% 121.65/16.04 (notdexE) =>
% 121.65/16.04 ((
% 121.65/16.04 (notdallE) =>
% 121.65/16.04 ((
% 121.65/16.04 (exuI1) =>
% 121.65/16.04 ((
% 121.65/16.04 (exuI3) =>
% 121.65/16.04 ((
% 121.65/16.04 (exuI2) =>
% 121.65/16.04 ((
% 121.65/16.04 (inCongP) =>
% 121.65/16.04 ((
% 121.65/16.04 (in__Cong) =>
% 121.65/16.04 ((
% 121.65/16.04 (exuE3u) =>
% 121.65/16.04 ((
% 121.65/16.04 (exu__Cong) =>
% 121.65/16.04 ((
% 121.65/16.04 (setadjoin__Cong) =>
% 121.65/16.04 ((
% 121.65/16.04 (powerset__Cong) =>
% 121.65/16.04 ((
% 121.65/16.04 (setunion__Cong) =>
% 121.65/16.04 ((
% 121.65/16.04 (exuEu) =>
% 121.65/16.04 ((
% 121.65/16.04 (descr__Cong) =>
% 121.65/16.04 ((
% 121.65/16.04 (dsetconstr__Cong) =>
% 121.65/16.04 ((
% 121.65/16.04 (subsetI1) =>
% 121.65/16.04 ((
% 121.65/16.04 (eqimpsubset2) =>
% 121.65/16.04 ((
% 121.65/16.04 (eqimpsubset1) =>
% 121.65/16.04 ((
% 121.65/16.04 (subsetI2) =>
% 121.65/16.04 ((
% 121.65/16.04 (emptysetsubset) =>
% 121.65/16.04 ((
% 121.65/16.04 (subsetE) =>
% 121.65/16.04 ((
% 121.65/16.04 (subsetE2) =>
% 121.65/16.04 ((
% 121.65/16.04 (notsubsetI) =>
% 121.65/16.04 ((
% 121.65/16.04 (notequalI1) =>
% 121.65/16.04 ((
% 121.65/16.04 (notequalI2) =>
% 121.65/16.04 ((
% 121.65/16.04 (subsetRefl) =>
% 121.65/16.04 ((
% 121.65/16.04 (subsetTrans) =>
% 121.65/16.04 ((
% 121.65/16.04 (setadjoinSub) =>
% 121.65/16.04 ((
% 121.65/16.04 (setadjoinSub2) =>
% 121.65/16.04 ((
% 121.65/16.04 (subset2powerset) =>
% 121.65/16.04 ((
% 121.65/16.04 (setextsub) =>
% 121.65/16.04 ((
% 121.65/16.04 (subsetemptysetimpeq) =>
% 121.65/16.04 ((
% 121.65/16.04 (powersetI1) =>
% 121.65/16.04 ((
% 121.65/16.04 (powersetE1) =>
% 121.65/16.04 ((
% 121.65/16.04 (inPowerset) =>
% 121.65/16.04 ((
% 121.65/16.04 (powersetsubset) =>
% 121.65/16.04 ((
% 121.65/16.04 (sepInPowerset) =>
% 121.65/16.04 ((
% 121.65/16.04 (sepSubset) =>
% 121.65/16.04 ((
% 121.65/16.04 (binunionIL) =>
% 121.65/16.04 ((
% 121.65/16.04 (upairset2IR) =>
% 121.65/16.04 ((
% 121.65/16.04 (binunionIR) =>
% 121.65/16.04 ((
% 121.65/16.04 (binunionEcases) =>
% 121.65/16.04 ((
% 121.65/16.04 (binunionE) =>
% 121.65/16.04 ((
% 121.65/16.04 (binunionLsub) =>
% 121.65/16.04 ((
% 121.65/16.04 (binunionRsub) =>
% 121.65/16.04 ((
% 121.65/16.04 (binintersectI) =>
% 121.65/16.04 ((
% 121.65/16.04 (binintersectSubset5) =>
% 121.65/16.04 ((
% 121.65/16.04 (binintersectEL) =>
% 121.65/16.04 ((
% 121.65/16.04 (binintersectLsub) =>
% 121.65/16.04 ((
% 121.65/16.04 (binintersectSubset2) =>
% 121.65/16.04 ((
% 121.65/16.04 (binintersectSubset3) =>
% 121.65/16.04 ((
% 121.65/16.04 (binintersectER) =>
% 121.65/16.04 ((
% 121.65/16.04 (disjointsetsI1) =>
% 121.65/16.04 ((
% 121.65/16.04 (binintersectRsub) =>
% 121.65/16.04 ((
% 121.65/16.04 (binintersectSubset4) =>
% 121.65/16.04 ((
% 121.65/16.04 (binintersectSubset1) =>
% 121.65/16.04 ((
% 121.65/16.04 (bs114d) =>
% 121.65/16.04 ((
% 121.65/16.04 (setminusI) =>
% 121.65/16.04 ((
% 121.65/16.04 (setminusEL) =>
% 121.65/16.04 ((
% 121.65/16.04 (setminusER) =>
% 121.65/16.04 ((
% 121.65/16.04 (setminusSubset2) =>
% 121.65/16.04 ((
% 121.65/16.04 (setminusERneg) =>
% 121.65/16.04 ((
% 121.65/16.04 (setminusELneg) =>
% 121.65/16.04 ((
% 121.65/16.04 (setminusILneg) =>
% 121.65/16.04 ((
% 121.65/16.04 (setminusIRneg) =>
% 121.65/16.04 ((
% 121.65/16.04 (setminusLsub) =>
% 121.65/16.04 ((
% 121.65/16.04 (setminusSubset1) =>
% 121.65/16.04 ((
% 121.65/16.04 (symdiffE) =>
% 121.65/16.04 ((
% 121.65/16.04 (symdiffI1) =>
% 121.65/16.04 ((
% 121.65/16.04 (symdiffI2) =>
% 121.65/16.04 ((
% 121.65/16.04 (symdiffIneg1) =>
% 121.65/16.04 ((
% 121.65/16.04 (symdiffIneg2) =>
% 121.65/16.04 ((
% 121.65/16.04 (secondinupair) =>
% 121.65/16.04 ((
% 121.65/16.04 (setukpairIL) =>
% 121.65/16.04 ((
% 121.65/16.04 (setukpairIR) =>
% 121.65/16.04 ((
% 121.65/16.04 (kpairiskpair) =>
% 121.65/16.04 ((
% 121.65/16.04 (kpairp) =>
% 121.65/16.04 ((
% 121.65/16.04 (singletonsubset) =>
% 121.65/16.04 ((
% 121.65/16.04 (singletoninpowerset) =>
% 121.65/16.04 ((
% 121.65/16.04 (singletoninpowunion) =>
% 121.65/16.04 ((
% 121.65/16.04 (upairset2E) =>
% 121.65/16.04 ((
% 121.65/16.04 (upairsubunion) =>
% 121.65/16.04 ((
% 121.65/16.04 (upairinpowunion) =>
% 121.65/16.04 ((
% 121.65/16.04 (ubforcartprodlem1) =>
% 121.65/16.04 ((
% 121.65/16.04 (ubforcartprodlem2) =>
% 121.65/16.04 ((
% 121.65/16.04 (ubforcartprodlem3) =>
% 121.65/16.04 ((
% 121.65/16.04 (cartprodpairin) =>
% 121.65/16.04 ((
% 121.65/16.04 (cartprodmempair1) =>
% 121.65/16.04 ((
% 121.65/16.04 (cartprodmempair) =>
% 121.65/16.04 ((
% 121.65/16.04 (setunionE2) =>
% 121.65/16.04 ((
% 121.65/16.04 (setunionsingleton1) =>
% 121.65/16.04 ((
% 121.65/16.04 (setunionsingleton2) =>
% 121.65/16.04 ((
% 121.65/16.04 (setunionsingleton) =>
% 121.65/16.04 ((
% 121.65/16.04 (singletonprop) =>
% 121.65/16.04 ((
% 121.65/16.04 (ex1E1) =>
% 121.65/16.04 ((
% 121.65/16.04 (ex1I) =>
% 121.65/16.04 ((
% 121.65/16.04 (ex1I2) =>
% 121.65/16.04 ((
% 121.65/16.04 (singletonsuniq) =>
% 121.65/16.04 ((
% 121.65/16.04 (setukpairinjL1) =>
% 121.65/16.04 ((
% 121.65/16.04 (kfstsingleton) =>
% 121.65/16.04 ((
% 121.65/16.04 (theprop) =>
% 121.65/16.04 ((
% 121.65/16.04 (kfstpairEq) =>
% 121.65/16.04 ((
% 121.65/16.04 (cartprodfstin) =>
% 121.65/16.04 ((
% 121.65/16.04 (setukpairinjL2) =>
% 121.65/16.04 ((
% 121.65/16.04 (setukpairinjL) =>
% 121.65/16.04 ((
% 121.65/16.04 (setukpairinjR11) =>
% 121.65/16.04 ((
% 121.65/16.04 (setukpairinjR12) =>
% 121.65/16.04 ((
% 121.65/16.04 (setukpairinjR1) =>
% 121.65/16.04 ((
% 121.65/16.04 (upairequniteq) =>
% 121.65/16.04 ((
% 121.65/16.04 (setukpairinjR2) =>
% 121.65/16.04 ((
% 121.65/16.04 (setukpairinjR) =>
% 121.65/16.04 ((
% 121.65/16.04 (ksndsingleton) =>
% 121.65/16.04 ((
% 121.65/16.04 (ksndpairEq) =>
% 121.65/16.04 ((
% 121.65/16.04 (kpairsurjEq) =>
% 121.65/16.04 ((
% 121.65/16.04 (cartprodsndin) =>
% 121.65/16.04 ((
% 121.65/16.04 (cartprodpairmemEL) =>
% 121.65/16.04 ((
% 121.65/16.04 (cartprodpairmemER) =>
% 121.65/16.04 ((
% 121.65/16.04 (cartprodmempaircEq) =>
% 121.65/16.04 ((
% 121.65/16.04 (cartprodfstpairEq) =>
% 121.65/16.04 ((
% 121.65/16.04 (cartprodsndpairEq) =>
% 121.65/16.04 ((
% 121.65/16.04 (cartprodpairsurjEq) =>
% 121.65/16.04 ((
% 121.65/16.04 (dpsetconstrI) =>
% 121.65/16.04 ((
% 121.65/16.04 (dpsetconstrSub) =>
% 121.65/16.04 ((
% 121.65/16.04 (setOfPairsIsBReln) =>
% 121.65/16.04 ((
% 121.65/16.04 (dpsetconstrERa) =>
% 121.65/16.04 ((
% 121.65/16.04 (dpsetconstrEL1) =>
% 121.65/16.04 ((
% 121.65/16.04 (dpsetconstrEL2) =>
% 121.65/16.04 ((
% 121.65/16.04 (dpsetconstrER) =>
% 121.65/16.04 ((
% 121.65/16.04 (funcImageSingleton) =>
% 121.65/16.04 ((
% 121.65/16.04 (apProp) =>
% 121.65/16.04 ((
% 121.65/16.04 (app) =>
% 121.65/16.04 ((
% 121.65/16.04 (infuncsetfunc) =>
% 121.65/16.04 ((
% 121.65/16.04 (ap2p) =>
% 121.65/16.04 ((
% 121.65/16.04 (funcinfuncset) =>
% 121.65/16.04 ((
% 121.65/16.04 (lamProp) =>
% 121.65/16.04 ((
% 121.65/16.04 (lamp) =>
% 121.65/16.04 ((
% 121.65/16.04 (lam2p) =>
% 121.65/16.04 ((
% 121.65/16.04 (brelnall1) =>
% 121.65/16.04 ((
% 121.65/16.04 (brelnall2) =>
% 121.65/16.04 ((
% 121.65/16.04 (ex1E2) =>
% 121.65/16.04 ((
% 121.65/16.04 (funcGraphProp1) =>
% 121.65/16.04 ((
% 121.65/16.04 (funcGraphProp3) =>
% 121.65/16.04 ((
% 121.65/16.04 (funcGraphProp2) =>
% 121.65/16.04 ((
% 121.65/16.04 (funcextLem) =>
% 121.65/16.04 ((
% 121.65/16.04 (funcGraphProp4) =>
% 121.65/16.04 ((
% 121.65/16.04 (subbreln) =>
% 121.65/16.04 ((
% 121.65/16.04 (eqbreln) =>
% 121.65/16.04 ((
% 121.65/16.04 (funcext) =>
% 121.65/16.04 ((
% 121.65/16.04 (funcext2) =>
% 121.65/16.04 ((
% 121.65/16.04 (ap2apEq1) =>
% 121.65/16.04 ((
% 121.65/16.04 (ap2apEq2) =>
% 121.65/16.04 ((
% 121.65/16.04 (beta1) =>
% 121.65/16.04 ((
% 121.65/16.04 (eta1) =>
% 121.65/16.04 ((
% 121.65/16.04 (lam2lamEq) =>
% 121.65/16.04 ((
% 121.65/16.04 (beta2) =>
% 121.65/16.04 ((
% 121.65/16.04 (eta2) =>
% 121.65/16.04 ((
% 121.65/16.04 (iffalseProp1) =>
% 121.65/16.04 ((
% 121.65/16.04 (iffalseProp2) =>
% 121.65/16.04 ((
% 121.65/16.04 (iftrueProp1) =>
% 121.65/16.04 ((
% 121.65/16.04 (iftrueProp2) =>
% 121.65/16.04 ((
% 121.65/16.04 (ifSingleton) =>
% 121.65/16.04 ((
% 121.65/16.04 (ifp) =>
% 121.65/16.04 ((
% 121.65/16.04 (theeq) =>
% 121.65/16.04 ((
% 121.65/16.04 (iftrue) =>
% 121.65/16.04 ((
% 121.65/16.04 (iffalse) =>
% 121.65/16.04 ((
% 121.65/16.04 (iftrueorfalse) =>
% 121.65/16.04 ((
% 121.65/16.04 (binintersectT_lem) =>
% 121.65/16.04 ((
% 121.65/16.04 (binunionT_lem) =>
% 121.65/16.04 ((
% 121.65/16.04 (powersetT_lem) =>
% 121.65/16.04 ((
% 121.65/16.04 (setminusT_lem) =>
% 121.65/16.04 ((
% 121.65/16.04 (complementT_lem) =>
% 121.65/16.04 ((
% 121.65/16.04 (setextT) =>
% 121.65/16.04 ((
% 121.65/16.04 (subsetTI) =>
% 121.65/16.04 ((
% 121.65/16.04 (powersetTI1) =>
% 121.65/16.04 ((
% 121.65/16.04 (powersetTE1) =>
% 121.65/16.04 ((
% 121.65/16.04 (complementTI1) =>
% 121.65/16.04 ((
% 121.65/16.04 (complementTE1) =>
% 121.65/16.04 ((
% 121.65/16.04 (binintersectTELcontra) =>
% 121.65/16.04 ((
% 121.65/16.04 (binintersectTERcontra) =>
% 121.65/16.04 ((
% 121.65/16.04 (contrasubsetT) =>
% 121.65/16.04 ((
% 121.65/16.04 (contrasubsetT1) =>
% 121.65/16.04 ((
% 121.65/16.04 (contrasubsetT2) =>
% 121.65/16.04 ((
% 121.65/16.04 (contrasubsetT3) =>
% 121.65/16.04 ((
% 121.65/16.04 (doubleComplementI1) =>
% 121.65/16.04 ((
% 121.65/16.04 (doubleComplementE1) =>
% 121.65/16.04 ((
% 121.65/16.04 (doubleComplementSub1) =>
% 121.65/16.04 ((
% 121.65/16.04 (doubleComplementSub2) =>
% 121.65/16.04 ((
% 121.65/16.04 (doubleComplementEq) =>
% 121.65/16.04 ((
% 121.65/16.04 (complementTnotintersectT) =>
% 121.65/16.04 ((
% 121.65/16.04 (complementImpComplementIntersect) =>
% 121.65/16.04 ((
% 121.65/16.04 (complementSubsetComplementIntersect) =>
% 121.65/16.04 ((
% 121.65/16.04 (complementInPowersetComplementIntersect) =>
% 121.65/16.04 ((
% 121.65/16.04 (contraSubsetComplement) =>
% 121.65/16.04 ((
% 121.65/16.04 (complementTcontraSubset) =>
% 121.65/16.04 ((
% 121.65/16.04 (binunionTILcontra) =>
% 121.65/16.04 ((
% 121.65/16.04 (binunionTIRcontra) =>
% 121.65/16.04 ((
% 121.65/16.04 (inIntersectImpInUnion) =>
% 121.65/16.04 ((
% 121.65/16.04 (inIntersectImpInUnion2) =>
% 121.65/16.04 ((
% 121.65/16.04 (inIntersectImpInIntersectUnions) =>
% 121.65/16.04 ((
% 121.65/16.04 (intersectInPowersetIntersectUnions) =>
% 121.65/16.04 ((
% 121.65/16.04 (inComplementUnionImpNotIn1) =>
% 121.65/16.04 ((
% 121.65/16.04 (inComplementUnionImpInComplement1) =>
% 121.65/16.04 ((
% 121.65/16.04 (binunionTE) =>
% 121.65/16.04 ((
% 121.65/16.04 (binunionTEcontra) =>
% 121.65/16.04 ((
% 121.65/16.04 (demorgan2a1) =>
% 121.65/16.04 ((
% 121.65/16.04 (complementUnionInPowersetComplement) =>
% 121.65/16.04 ((
% 121.65/16.04 (demorgan2a2) =>
% 121.65/16.04 ((
% 121.65/16.04 (demorgan1a) =>
% 121.65/16.04 ((
% 121.65/16.04 (demorgan1b) =>
% 121.65/16.04 ((
% 121.65/16.04 (demorgan1) =>
% 121.65/16.04 ((
% 121.65/16.04 (demorgan2a) =>
% 121.65/16.04 ((
% 121.65/16.04 (demorgan2b2) =>
% 121.65/16.04 ((
% 121.65/16.04 (demorgan2b) =>
% 121.65/16.04 ((
% 121.65/16.04 (demorgan2) =>
% 121.65/16.04 ((
% 121.65/16.04 (woz13rule0) =>
% 121.65/16.04 ((
% 121.65/16.04 (woz13rule1) =>
% 121.65/16.04 ((
% 121.65/16.04 (woz13rule2) =>
% 121.65/16.04 ((
% 121.65/16.04 (woz13rule3) =>
% 121.65/16.04 ((
% 121.65/16.04 (woz13rule4) =>
% 121.65/16.04 ((
% 121.65/16.04 (woz1_1) =>
% 121.65/16.04 ((
% 121.65/16.04 (woz1_2) =>
% 121.65/16.04 ((
% 121.65/16.04 (woz1_3) =>
% 121.65/16.04 ((
% 121.65/16.04 (woz1_4) =>
% 121.65/16.04 ((
% 121.65/16.04 (woz1_5) =>
% 121.65/16.04 ((
% 121.65/16.04 (breln1all2) =>
% 121.65/16.04 ((
% 121.65/16.04 (breln1SetBreln1) =>
% 121.65/16.04 ((
% 121.65/16.04 (choice2fnsingleton) =>
% 121.65/16.04 ((
% 121.65/16.04 (setOfPairsIsBReln1) =>
% 121.65/16.04 ((
% 121.65/16.04 (breln1all1) =>
% 121.65/16.04 ((
% 121.65/16.04 (subbreln1) =>
% 121.65/16.04 ((
% 121.65/16.04 (eqbreln1) =>
% 121.65/16.04 ((
% 121.65/16.04 (breln1invprop) =>
% 121.65/16.04 ((
% 121.65/16.04 (breln1invI) =>
% 121.65/16.04 ((
% 121.65/16.04 (breln1invE) =>
% 121.65/16.04 ((
% 121.65/16.04 (breln1compprop) =>
% 121.65/16.04 ((
% 121.65/16.04 (breln1compI) =>
% 121.65/16.04 ((
% 121.65/16.04 (breln1compE) =>
% 121.65/16.04 ((
% 121.65/16.04 (breln1compEex) =>
% 121.65/16.04 ((
% 121.65/16.04 (breln1unionprop) =>
% 121.65/16.04 ((
% 121.65/16.04 (breln1unionIL) =>
% 121.65/16.04 ((
% 121.65/16.04 (breln1unionIR) =>
% 121.65/16.04 ((
% 121.65/16.04 (breln1unionI) =>
% 121.65/16.04 ((
% 121.65/16.04 (breln1unionE) =>
% 121.65/16.04 ((
% 121.65/16.04 (breln1unionEcases) =>
% 121.65/16.04 ((
% 121.65/16.04 (breln1unionCommutes) =>
% 121.65/16.04 ((
% 121.65/16.04 (woz2Ex) =>
% 121.65/16.04 ((
% 121.65/16.04 (woz2W) =>
% 121.65/16.04 ((
% 121.65/16.04 (woz2A) =>
% 121.65/16.04 ((
% 121.65/16.04 (woz2B) =>
% 121.65/16.04 ((
% 121.65/16.04 (image1Ex) =>
% 121.65/16.04 ((
% 121.65/16.04 (image1Ex1) =>
% 121.65/16.04 ((
% 121.65/16.04 (image1Equiv) =>
% 121.65/16.04 ((
% 121.65/16.04 (image1E) =>
% 121.65/16.04 ((
% 121.65/16.04 (image1I) =>
% 121.65/16.04 ((
% 121.65/16.04 (injFuncInInjFuncSet) =>
% 121.65/16.04 ((
% 121.65/16.04 (!!) @ (
% 121.65/16.04 (('#B') @ (
% 121.65/16.04 !!) @
% 121.65/16.04 (
% 121.65/16.04 (
% 121.65/16.04 ('#B') @ (
% 121.65/16.04 (
% 121.65/16.04 ('#B') @ (
% 121.65/16.04 !!))) @
% 121.65/16.04 (
% 121.65/16.04 (
% 121.65/16.04 ('#S') @ (
% 121.65/16.04 (
% 121.65/16.04 ('#B') @ (
% 121.65/16.04 '#S') @
% 121.65/16.04 (
% 121.65/16.04 (
% 121.65/16.04 ('#B') @ (
% 121.65/16.04 (
% 121.65/16.04 ('#B') @ (
% 121.65/16.04 '#S'))) @
% 121.65/16.04 (
% 121.65/16.04 (
% 121.65/16.04 ('#B') @ (
% 121.65/16.04 (
% 121.65/16.04 ('#B') @ (
% 121.65/16.04 (
% 121.65/16.04 ('#B') @ (
% 121.65/16.04 =>))))) @
% 121.65/16.04 (
% 121.65/16.04 (
% 121.65/16.04 ('#B') @ (
% 121.65/16.04 (
% 121.65/16.04 ('#B') @ (
% 121.65/16.04 (
% 121.65/16.04 ('#C') @ in)))) @
% 121.65/16.04 injFuncSet)))))))) @
% 121.65/16.04 (
% 121.65/16.04 (
% 121.65/16.04 ('#B') @ (
% 121.65/16.04 (
% 121.65/16.04 ('#B') @ (
% 121.65/16.04 (
% 121.65/16.04 ('#C') @ in)))) @
% 121.65/16.04 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 121.65/16.04 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl264])).
% 121.65/16.04 thf(zip_derived_cl293, plain,
% 121.65/16.04 (~ (((nonemptyI1) =>
% 121.65/16.04 (((setadjoinIL) =>
% 121.65/16.04 (((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) =>
% 121.65/16.04 (((setadjoinIR) =>
% 121.65/16.04 (((setadjoinE) =>
% 121.65/16.04 (((setadjoinOr) =>
% 121.65/16.04 (((setoftrueEq) =>
% 121.65/16.04 (((powersetI) =>
% 121.65/16.04 (((emptyinPowerset) =>
% 121.65/16.04 (((emptyInPowerset) =>
% 121.65/16.04 (((powersetE) =>
% 121.65/16.04 (((setunionI) =>
% 121.65/16.04 (((setunionE) =>
% 121.65/16.04 (((subPowSU) =>
% 121.65/16.04 (((exuE2) =>
% 121.65/16.04 (((nonemptyImpWitness) =>
% 121.65/16.04 (((uniqinunit) =>
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% 121.65/16.04 (
% 121.65/16.04 ('#C') @ in)))) @
% 121.65/16.04 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 121.65/16.04 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl280])).
% 121.65/16.04 thf(zip_derived_cl307, plain,
% 121.65/16.04 (~ (((setadjoinIL) =>
% 121.65/16.04 (((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) =>
% 121.65/16.04 (((setadjoinIR) =>
% 121.65/16.04 (((setadjoinE) =>
% 121.65/16.04 (((setadjoinOr) =>
% 121.65/16.04 (((setoftrueEq) =>
% 121.65/16.04 (((powersetI) =>
% 121.65/16.04 (((emptyinPowerset) =>
% 121.65/16.04 (((emptyInPowerset) =>
% 121.65/16.04 (((powersetE) =>
% 121.65/16.04 (((setunionI) =>
% 121.65/16.04 (((setunionE) =>
% 121.65/16.04 (((subPowSU) =>
% 121.65/16.04 (((exuE2) =>
% 121.65/16.04 (((nonemptyImpWitness) =>
% 121.65/16.04 (((uniqinunit) =>
% 121.65/16.04 (((notinsingleton) =>
% 121.65/16.04 (((eqinunit) =>
% 121.65/16.04 (((singletonsswitch) =>
% 121.65/16.04 (((upairsetE) =>
% 121.65/16.04 (((upairsetIL) =>
% 121.65/16.04 (((upairsetIR) =>
% 121.65/16.04 (((emptyE1) =>
% 121.65/16.04 (((vacuousDall) =>
% 121.65/16.04 (((quantDeMorgan1) =>
% 121.65/16.04 (((quantDeMorgan2) =>
% 121.65/16.04 (((quantDeMorgan3) =>
% 121.65/16.04 (((quantDeMorgan4) =>
% 121.65/16.04 (((prop2setI) =>
% 121.65/16.04 (((prop2set2propI) =>
% 121.65/16.04 ((
% 121.65/16.04 (notdexE) =>
% 121.65/16.04 ((
% 121.65/16.04 (notdallE) =>
% 121.65/16.04 ((
% 121.65/16.04 (exuI1) =>
% 121.65/16.04 ((
% 121.65/16.04 (exuI3) =>
% 121.65/16.04 ((
% 121.65/16.04 (exuI2) =>
% 121.65/16.04 ((
% 121.65/16.04 (inCongP) =>
% 121.65/16.04 ((
% 121.65/16.04 (in__Cong) =>
% 121.65/16.04 ((
% 121.65/16.04 (exuE3u) =>
% 121.65/16.04 ((
% 121.65/16.04 (exu__Cong) =>
% 121.65/16.04 ((
% 121.65/16.04 (setadjoin__Cong) =>
% 121.65/16.04 ((
% 121.65/16.04 (powerset__Cong) =>
% 121.65/16.04 ((
% 121.65/16.04 (setunion__Cong) =>
% 121.65/16.04 ((
% 121.65/16.04 (exuEu) =>
% 121.65/16.04 ((
% 121.65/16.04 (descr__Cong) =>
% 121.65/16.04 ((
% 121.65/16.04 (dsetconstr__Cong) =>
% 121.65/16.04 ((
% 121.65/16.04 (subsetI1) =>
% 121.65/16.04 ((
% 121.65/16.04 (eqimpsubset2) =>
% 121.65/16.04 ((
% 121.65/16.04 (eqimpsubset1) =>
% 121.65/16.04 ((
% 121.65/16.04 (subsetI2) =>
% 121.65/16.04 ((
% 121.65/16.04 (emptysetsubset) =>
% 121.65/16.04 ((
% 121.65/16.04 (subsetE) =>
% 121.65/16.04 ((
% 121.65/16.04 (subsetE2) =>
% 121.65/16.04 ((
% 121.65/16.04 (notsubsetI) =>
% 121.65/16.04 ((
% 121.65/16.04 (notequalI1) =>
% 121.65/16.04 ((
% 121.65/16.04 (notequalI2) =>
% 121.65/16.04 ((
% 121.65/16.04 (subsetRefl) =>
% 121.65/16.04 ((
% 121.65/16.04 (subsetTrans) =>
% 121.65/16.04 ((
% 121.65/16.04 (setadjoinSub) =>
% 121.65/16.04 ((
% 121.65/16.04 (setadjoinSub2) =>
% 121.65/16.04 ((
% 121.65/16.04 (subset2powerset) =>
% 121.65/16.04 ((
% 121.65/16.04 (setextsub) =>
% 121.65/16.04 ((
% 121.65/16.04 (subsetemptysetimpeq) =>
% 121.65/16.04 ((
% 121.65/16.04 (powersetI1) =>
% 121.65/16.04 ((
% 121.65/16.04 (powersetE1) =>
% 121.65/16.04 ((
% 121.65/16.04 (inPowerset) =>
% 121.65/16.04 ((
% 121.65/16.04 (powersetsubset) =>
% 121.65/16.04 ((
% 121.65/16.04 (sepInPowerset) =>
% 121.65/16.04 ((
% 121.65/16.04 (sepSubset) =>
% 121.65/16.04 ((
% 121.65/16.04 (binunionIL) =>
% 121.65/16.04 ((
% 121.65/16.04 (upairset2IR) =>
% 121.65/16.04 ((
% 121.65/16.04 (binunionIR) =>
% 121.65/16.04 ((
% 121.65/16.04 (binunionEcases) =>
% 121.65/16.04 ((
% 121.65/16.04 (binunionE) =>
% 121.65/16.04 ((
% 121.65/16.04 (binunionLsub) =>
% 121.65/16.04 ((
% 121.65/16.04 (binunionRsub) =>
% 121.65/16.04 ((
% 121.65/16.04 (binintersectI) =>
% 121.65/16.04 ((
% 121.65/16.04 (binintersectSubset5) =>
% 121.65/16.04 ((
% 121.65/16.04 (binintersectEL) =>
% 121.65/16.04 ((
% 121.65/16.04 (binintersectLsub) =>
% 121.65/16.04 ((
% 121.65/16.04 (binintersectSubset2) =>
% 121.65/16.04 ((
% 121.65/16.04 (binintersectSubset3) =>
% 121.65/16.04 ((
% 121.65/16.04 (binintersectER) =>
% 121.65/16.04 ((
% 121.65/16.04 (disjointsetsI1) =>
% 121.65/16.04 ((
% 121.65/16.04 (binintersectRsub) =>
% 121.65/16.04 ((
% 121.65/16.04 (binintersectSubset4) =>
% 121.65/16.04 ((
% 121.65/16.04 (binintersectSubset1) =>
% 121.65/16.04 ((
% 121.65/16.04 (bs114d) =>
% 121.65/16.04 ((
% 121.65/16.04 (setminusI) =>
% 121.65/16.04 ((
% 121.65/16.04 (setminusEL) =>
% 121.65/16.04 ((
% 121.65/16.04 (setminusER) =>
% 121.65/16.04 ((
% 121.65/16.04 (setminusSubset2) =>
% 121.65/16.04 ((
% 121.65/16.04 (setminusERneg) =>
% 121.65/16.04 ((
% 121.65/16.04 (setminusELneg) =>
% 121.65/16.04 ((
% 121.65/16.04 (setminusILneg) =>
% 121.65/16.04 ((
% 121.65/16.04 (setminusIRneg) =>
% 121.65/16.04 ((
% 121.65/16.04 (setminusLsub) =>
% 121.65/16.04 ((
% 121.65/16.04 (setminusSubset1) =>
% 121.65/16.04 ((
% 121.65/16.04 (symdiffE) =>
% 121.65/16.04 ((
% 121.65/16.04 (symdiffI1) =>
% 121.65/16.04 ((
% 121.65/16.04 (symdiffI2) =>
% 121.65/16.04 ((
% 121.65/16.04 (symdiffIneg1) =>
% 121.65/16.04 ((
% 121.65/16.04 (symdiffIneg2) =>
% 121.65/16.04 ((
% 121.65/16.04 (secondinupair) =>
% 121.65/16.04 ((
% 121.65/16.04 (setukpairIL) =>
% 121.65/16.04 ((
% 121.65/16.04 (setukpairIR) =>
% 121.65/16.04 ((
% 121.65/16.04 (kpairiskpair) =>
% 121.65/16.04 ((
% 121.65/16.04 (kpairp) =>
% 121.65/16.04 ((
% 121.65/16.04 (singletonsubset) =>
% 121.65/16.04 ((
% 121.65/16.04 (singletoninpowerset) =>
% 121.65/16.04 ((
% 121.65/16.04 (singletoninpowunion) =>
% 121.65/16.04 ((
% 121.65/16.04 (upairset2E) =>
% 121.65/16.04 ((
% 121.65/16.04 (upairsubunion) =>
% 121.65/16.04 ((
% 121.65/16.04 (upairinpowunion) =>
% 121.65/16.04 ((
% 121.65/16.04 (ubforcartprodlem1) =>
% 121.65/16.04 ((
% 121.65/16.04 (ubforcartprodlem2) =>
% 121.65/16.04 ((
% 121.65/16.04 (ubforcartprodlem3) =>
% 121.65/16.04 ((
% 121.65/16.04 (cartprodpairin) =>
% 121.65/16.04 ((
% 121.65/16.04 (cartprodmempair1) =>
% 121.65/16.04 ((
% 121.65/16.04 (cartprodmempair) =>
% 121.65/16.04 ((
% 121.65/16.04 (setunionE2) =>
% 121.65/16.04 ((
% 121.65/16.04 (setunionsingleton1) =>
% 121.65/16.04 ((
% 121.65/16.04 (setunionsingleton2) =>
% 121.65/16.04 ((
% 121.65/16.04 (setunionsingleton) =>
% 121.65/16.04 ((
% 121.65/16.04 (singletonprop) =>
% 121.65/16.04 ((
% 121.65/16.04 (ex1E1) =>
% 121.65/16.04 ((
% 121.65/16.04 (ex1I) =>
% 121.65/16.04 ((
% 121.65/16.04 (ex1I2) =>
% 121.65/16.04 ((
% 121.65/16.04 (singletonsuniq) =>
% 121.65/16.04 ((
% 121.65/16.04 (setukpairinjL1) =>
% 121.65/16.04 ((
% 121.65/16.04 (kfstsingleton) =>
% 121.65/16.04 ((
% 121.65/16.04 (theprop) =>
% 121.65/16.04 ((
% 121.65/16.04 (kfstpairEq) =>
% 121.65/16.04 ((
% 121.65/16.04 (cartprodfstin) =>
% 121.65/16.04 ((
% 121.65/16.04 (setukpairinjL2) =>
% 121.65/16.04 ((
% 121.65/16.04 (setukpairinjL) =>
% 121.65/16.04 ((
% 121.65/16.04 (setukpairinjR11) =>
% 121.65/16.04 ((
% 121.65/16.04 (setukpairinjR12) =>
% 121.65/16.04 ((
% 121.65/16.04 (setukpairinjR1) =>
% 121.65/16.04 ((
% 121.65/16.04 (upairequniteq) =>
% 121.65/16.04 ((
% 121.65/16.04 (setukpairinjR2) =>
% 121.65/16.04 ((
% 121.65/16.04 (setukpairinjR) =>
% 121.65/16.04 ((
% 121.65/16.04 (ksndsingleton) =>
% 121.65/16.04 ((
% 121.65/16.04 (ksndpairEq) =>
% 121.65/16.04 ((
% 121.65/16.04 (kpairsurjEq) =>
% 121.65/16.04 ((
% 121.65/16.04 (cartprodsndin) =>
% 121.65/16.04 ((
% 121.65/16.04 (cartprodpairmemEL) =>
% 121.65/16.04 ((
% 121.65/16.04 (cartprodpairmemER) =>
% 121.65/16.04 ((
% 121.65/16.04 (cartprodmempaircEq) =>
% 121.65/16.04 ((
% 121.65/16.04 (cartprodfstpairEq) =>
% 121.65/16.04 ((
% 121.65/16.04 (cartprodsndpairEq) =>
% 121.65/16.04 ((
% 121.65/16.04 (cartprodpairsurjEq) =>
% 121.65/16.04 ((
% 121.65/16.04 (dpsetconstrI) =>
% 121.65/16.04 ((
% 121.65/16.04 (dpsetconstrSub) =>
% 121.65/16.04 ((
% 121.65/16.04 (setOfPairsIsBReln) =>
% 121.65/16.04 ((
% 121.65/16.04 (dpsetconstrERa) =>
% 121.65/16.04 ((
% 121.65/16.04 (dpsetconstrEL1) =>
% 121.65/16.04 ((
% 121.65/16.04 (dpsetconstrEL2) =>
% 121.65/16.04 ((
% 121.65/16.04 (dpsetconstrER) =>
% 121.65/16.04 ((
% 121.65/16.04 (funcImageSingleton) =>
% 121.65/16.04 ((
% 121.65/16.04 (apProp) =>
% 121.65/16.04 ((
% 121.65/16.04 (app) =>
% 121.65/16.04 ((
% 121.65/16.04 (infuncsetfunc) =>
% 121.65/16.04 ((
% 121.65/16.04 (ap2p) =>
% 121.65/16.04 ((
% 121.65/16.04 (funcinfuncset) =>
% 121.65/16.04 ((
% 121.65/16.04 (lamProp) =>
% 121.65/16.04 ((
% 121.65/16.04 (lamp) =>
% 121.65/16.04 ((
% 121.65/16.04 (lam2p) =>
% 121.65/16.04 ((
% 121.65/16.04 (brelnall1) =>
% 121.65/16.04 ((
% 121.65/16.04 (brelnall2) =>
% 121.65/16.04 ((
% 121.65/16.04 (ex1E2) =>
% 121.65/16.04 ((
% 121.65/16.04 (funcGraphProp1) =>
% 121.65/16.04 ((
% 121.65/16.04 (funcGraphProp3) =>
% 121.65/16.04 ((
% 121.65/16.04 (funcGraphProp2) =>
% 121.65/16.04 ((
% 121.65/16.04 (funcextLem) =>
% 121.65/16.04 ((
% 121.65/16.04 (funcGraphProp4) =>
% 121.65/16.04 ((
% 121.65/16.04 (subbreln) =>
% 121.65/16.04 ((
% 121.65/16.04 (eqbreln) =>
% 121.65/16.04 ((
% 121.65/16.04 (funcext) =>
% 121.65/16.04 ((
% 121.65/16.04 (funcext2) =>
% 121.65/16.04 ((
% 121.65/16.04 (ap2apEq1) =>
% 121.65/16.04 ((
% 121.65/16.04 (ap2apEq2) =>
% 121.65/16.04 ((
% 121.65/16.04 (beta1) =>
% 121.65/16.04 ((
% 121.65/16.04 (eta1) =>
% 121.65/16.04 ((
% 121.65/16.04 (lam2lamEq) =>
% 121.65/16.04 ((
% 121.65/16.04 (beta2) =>
% 121.65/16.04 ((
% 121.65/16.04 (eta2) =>
% 121.65/16.04 ((
% 121.65/16.04 (iffalseProp1) =>
% 121.65/16.04 ((
% 121.65/16.04 (iffalseProp2) =>
% 121.65/16.04 ((
% 121.65/16.04 (iftrueProp1) =>
% 121.65/16.04 ((
% 121.65/16.04 (iftrueProp2) =>
% 121.65/16.04 ((
% 121.65/16.04 (ifSingleton) =>
% 121.65/16.04 ((
% 121.65/16.04 (ifp) =>
% 121.65/16.04 ((
% 121.65/16.04 (theeq) =>
% 121.65/16.04 ((
% 121.65/16.04 (iftrue) =>
% 121.65/16.04 ((
% 121.65/16.04 (iffalse) =>
% 121.65/16.04 ((
% 121.65/16.04 (iftrueorfalse) =>
% 121.65/16.04 ((
% 121.65/16.04 (binintersectT_lem) =>
% 121.65/16.04 ((
% 121.65/16.04 (binunionT_lem) =>
% 121.65/16.04 ((
% 121.65/16.04 (powersetT_lem) =>
% 121.65/16.04 ((
% 121.65/16.04 (setminusT_lem) =>
% 121.65/16.04 ((
% 121.65/16.04 (complementT_lem) =>
% 121.65/16.04 ((
% 121.65/16.04 (setextT) =>
% 121.65/16.04 ((
% 121.65/16.04 (subsetTI) =>
% 121.65/16.04 ((
% 121.65/16.04 (powersetTI1) =>
% 121.65/16.04 ((
% 121.65/16.04 (powersetTE1) =>
% 121.65/16.04 ((
% 121.65/16.04 (complementTI1) =>
% 121.65/16.04 ((
% 121.65/16.04 (complementTE1) =>
% 121.65/16.04 ((
% 121.65/16.04 (binintersectTELcontra) =>
% 121.65/16.04 ((
% 121.65/16.04 (binintersectTERcontra) =>
% 121.65/16.04 ((
% 121.65/16.04 (contrasubsetT) =>
% 121.65/16.04 ((
% 121.65/16.04 (contrasubsetT1) =>
% 121.65/16.04 ((
% 121.65/16.04 (contrasubsetT2) =>
% 121.65/16.04 ((
% 121.65/16.04 (contrasubsetT3) =>
% 121.65/16.04 ((
% 121.65/16.04 (doubleComplementI1) =>
% 121.65/16.04 ((
% 121.65/16.04 (doubleComplementE1) =>
% 121.65/16.04 ((
% 121.65/16.04 (doubleComplementSub1) =>
% 121.65/16.04 ((
% 121.65/16.04 (doubleComplementSub2) =>
% 121.65/16.04 ((
% 121.65/16.04 (doubleComplementEq) =>
% 121.65/16.04 ((
% 121.65/16.04 (complementTnotintersectT) =>
% 121.65/16.04 ((
% 121.65/16.04 (complementImpComplementIntersect) =>
% 121.65/16.04 ((
% 121.65/16.04 (complementSubsetComplementIntersect) =>
% 121.65/16.04 ((
% 121.65/16.04 (complementInPowersetComplementIntersect) =>
% 121.65/16.04 ((
% 121.65/16.04 (contraSubsetComplement) =>
% 121.65/16.04 ((
% 121.65/16.04 (complementTcontraSubset) =>
% 121.65/16.04 ((
% 121.65/16.04 (binunionTILcontra) =>
% 121.65/16.04 ((
% 121.65/16.04 (binunionTIRcontra) =>
% 121.65/16.04 ((
% 121.65/16.04 (inIntersectImpInUnion) =>
% 121.65/16.04 ((
% 121.65/16.04 (inIntersectImpInUnion2) =>
% 121.65/16.04 ((
% 121.65/16.04 (inIntersectImpInIntersectUnions) =>
% 121.65/16.04 ((
% 121.65/16.04 (intersectInPowersetIntersectUnions) =>
% 121.65/16.04 ((
% 121.65/16.04 (inComplementUnionImpNotIn1) =>
% 121.65/16.04 ((
% 121.65/16.04 (inComplementUnionImpInComplement1) =>
% 121.65/16.04 ((
% 121.65/16.04 (binunionTE) =>
% 121.65/16.04 ((
% 121.65/16.04 (binunionTEcontra) =>
% 121.65/16.04 ((
% 121.65/16.04 (demorgan2a1) =>
% 121.65/16.04 ((
% 121.65/16.04 (complementUnionInPowersetComplement) =>
% 121.65/16.04 ((
% 121.65/16.04 (demorgan2a2) =>
% 121.65/16.04 ((
% 121.65/16.04 (demorgan1a) =>
% 121.65/16.04 ((
% 121.65/16.04 (demorgan1b) =>
% 121.65/16.04 ((
% 121.65/16.04 (demorgan1) =>
% 121.65/16.04 ((
% 121.65/16.04 (demorgan2a) =>
% 121.65/16.04 ((
% 121.65/16.04 (demorgan2b2) =>
% 121.65/16.04 ((
% 121.65/16.04 (demorgan2b) =>
% 121.65/16.04 ((
% 121.65/16.04 (demorgan2) =>
% 121.65/16.04 ((
% 121.65/16.04 (woz13rule0) =>
% 121.65/16.04 ((
% 121.65/16.04 (woz13rule1) =>
% 121.65/16.04 ((
% 121.65/16.04 (woz13rule2) =>
% 121.65/16.04 ((
% 121.65/16.04 (woz13rule3) =>
% 121.65/16.04 ((
% 121.65/16.04 (woz13rule4) =>
% 121.65/16.04 ((
% 121.65/16.04 (woz1_1) =>
% 121.65/16.04 ((
% 121.65/16.04 (woz1_2) =>
% 121.65/16.04 ((
% 121.65/16.04 (woz1_3) =>
% 121.65/16.04 ((
% 121.65/16.04 (woz1_4) =>
% 121.65/16.04 ((
% 121.65/16.04 (woz1_5) =>
% 121.65/16.04 ((
% 121.65/16.04 (breln1all2) =>
% 121.65/16.04 ((
% 121.65/16.04 (breln1SetBreln1) =>
% 121.65/16.04 ((
% 121.65/16.04 (choice2fnsingleton) =>
% 121.65/16.04 ((
% 121.65/16.04 (setOfPairsIsBReln1) =>
% 121.65/16.04 ((
% 121.65/16.04 (breln1all1) =>
% 121.65/16.04 ((
% 121.65/16.04 (subbreln1) =>
% 121.65/16.04 ((
% 121.65/16.04 (eqbreln1) =>
% 121.65/16.04 ((
% 121.65/16.04 (breln1invprop) =>
% 121.65/16.04 ((
% 121.65/16.04 (breln1invI) =>
% 121.65/16.04 ((
% 121.65/16.04 (breln1invE) =>
% 121.65/16.04 ((
% 121.65/16.04 (breln1compprop) =>
% 121.65/16.04 ((
% 121.65/16.04 (breln1compI) =>
% 121.65/16.04 ((
% 121.65/16.04 (breln1compE) =>
% 121.65/16.04 ((
% 121.65/16.04 (breln1compEex) =>
% 121.65/16.04 ((
% 121.65/16.04 (breln1unionprop) =>
% 121.65/16.04 ((
% 121.65/16.04 (breln1unionIL) =>
% 121.65/16.04 ((
% 121.65/16.04 (breln1unionIR) =>
% 121.65/16.04 ((
% 121.65/16.04 (breln1unionI) =>
% 121.65/16.04 ((
% 121.65/16.04 (breln1unionE) =>
% 121.65/16.04 ((
% 121.65/16.04 (breln1unionEcases) =>
% 121.65/16.04 ((
% 121.65/16.04 (breln1unionCommutes) =>
% 121.65/16.04 ((
% 121.65/16.04 (woz2Ex) =>
% 121.65/16.04 ((
% 121.65/16.04 (woz2W) =>
% 121.65/16.04 ((
% 121.65/16.04 (woz2A) =>
% 121.65/16.04 ((
% 121.65/16.04 (woz2B) =>
% 121.65/16.04 ((
% 121.65/16.04 (image1Ex) =>
% 121.65/16.04 ((
% 121.65/16.04 (image1Ex1) =>
% 121.65/16.04 ((
% 121.65/16.04 (image1Equiv) =>
% 121.65/16.04 ((
% 121.65/16.04 (image1E) =>
% 121.65/16.04 ((
% 121.65/16.04 (image1I) =>
% 121.65/16.04 ((
% 121.65/16.04 (injFuncInInjFuncSet) =>
% 121.65/16.04 ((
% 121.65/16.04 (!!) @ (
% 121.65/16.04 (('#B') @ (
% 121.65/16.04 !!) @
% 121.65/16.04 (
% 121.65/16.04 (
% 121.65/16.04 ('#B') @ (
% 121.65/16.04 (
% 121.65/16.04 ('#B') @ (
% 121.65/16.04 !!))) @
% 121.65/16.04 (
% 121.65/16.04 (
% 121.65/16.04 ('#S') @ (
% 121.65/16.04 (
% 121.65/16.04 ('#B') @ (
% 121.65/16.04 '#S') @
% 121.65/16.04 (
% 121.65/16.04 (
% 121.65/16.04 ('#B') @ (
% 121.65/16.04 (
% 121.65/16.04 ('#B') @ (
% 121.65/16.04 '#S'))) @
% 121.65/16.04 (
% 121.65/16.04 (
% 121.65/16.04 ('#B') @ (
% 121.65/16.04 (
% 121.65/16.04 ('#B') @ (
% 121.65/16.04 (
% 121.65/16.04 ('#B') @ (
% 121.65/16.04 =>))))) @
% 121.65/16.04 (
% 121.65/16.04 (
% 121.65/16.04 ('#B') @ (
% 121.65/16.04 (
% 121.65/16.04 ('#B') @ (
% 121.65/16.04 (
% 121.65/16.04 ('#C') @ in)))) @
% 121.65/16.04 injFuncSet)))))))) @
% 121.65/16.04 (
% 121.65/16.04 (
% 121.65/16.04 ('#B') @ (
% 121.65/16.04 (
% 121.65/16.04 ('#B') @ (
% 121.65/16.04 (
% 121.65/16.04 ('#C') @ in)))) @
% 121.65/16.04 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 121.65/16.04 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl293])).
% 121.65/16.04 thf(zip_derived_cl322, plain,
% 121.65/16.04 (~ (((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) =>
% 121.65/16.04 (((setadjoinIR) =>
% 121.65/16.04 (((setadjoinE) =>
% 121.65/16.04 (((setadjoinOr) =>
% 121.65/16.04 (((setoftrueEq) =>
% 121.65/16.04 (((powersetI) =>
% 121.65/16.04 (((emptyinPowerset) =>
% 121.65/16.04 (((emptyInPowerset) =>
% 121.65/16.04 (((powersetE) =>
% 121.65/16.04 (((setunionI) =>
% 121.65/16.04 (((setunionE) =>
% 121.65/16.04 (((subPowSU) =>
% 121.65/16.04 (((exuE2) =>
% 121.65/16.04 (((nonemptyImpWitness) =>
% 121.65/16.04 (((uniqinunit) =>
% 121.65/16.04 (((notinsingleton) =>
% 121.65/16.04 (((eqinunit) =>
% 121.65/16.04 (((singletonsswitch) =>
% 121.65/16.04 (((upairsetE) =>
% 121.65/16.04 (((upairsetIL) =>
% 121.65/16.04 (((upairsetIR) =>
% 121.65/16.04 (((emptyE1) =>
% 121.65/16.04 (((vacuousDall) =>
% 121.65/16.04 (((quantDeMorgan1) =>
% 121.65/16.04 (((quantDeMorgan2) =>
% 121.65/16.04 (((quantDeMorgan3) =>
% 121.65/16.04 (((quantDeMorgan4) =>
% 121.65/16.04 (((prop2setI) =>
% 121.65/16.04 (((prop2set2propI) =>
% 121.65/16.04 (((notdexE) =>
% 121.65/16.04 ((
% 121.65/16.04 (notdallE) =>
% 121.65/16.04 ((
% 121.65/16.04 (exuI1) =>
% 121.65/16.04 ((
% 121.65/16.04 (exuI3) =>
% 121.65/16.04 ((
% 121.65/16.04 (exuI2) =>
% 121.65/16.04 ((
% 121.65/16.04 (inCongP) =>
% 121.65/16.04 ((
% 121.65/16.04 (in__Cong) =>
% 121.65/16.04 ((
% 121.65/16.04 (exuE3u) =>
% 121.65/16.04 ((
% 121.65/16.04 (exu__Cong) =>
% 121.65/16.04 ((
% 121.65/16.04 (setadjoin__Cong) =>
% 121.65/16.04 ((
% 121.65/16.04 (powerset__Cong) =>
% 121.65/16.04 ((
% 121.65/16.04 (setunion__Cong) =>
% 121.65/16.04 ((
% 121.65/16.04 (exuEu) =>
% 121.65/16.04 ((
% 121.65/16.04 (descr__Cong) =>
% 121.65/16.04 ((
% 121.65/16.04 (dsetconstr__Cong) =>
% 121.65/16.04 ((
% 121.65/16.04 (subsetI1) =>
% 121.65/16.04 ((
% 121.65/16.04 (eqimpsubset2) =>
% 121.65/16.04 ((
% 121.65/16.04 (eqimpsubset1) =>
% 121.65/16.04 ((
% 121.65/16.04 (subsetI2) =>
% 121.65/16.04 ((
% 121.65/16.04 (emptysetsubset) =>
% 121.65/16.04 ((
% 121.65/16.04 (subsetE) =>
% 121.65/16.04 ((
% 121.65/16.04 (subsetE2) =>
% 121.65/16.04 ((
% 121.65/16.04 (notsubsetI) =>
% 121.65/16.04 ((
% 121.65/16.04 (notequalI1) =>
% 121.65/16.04 ((
% 121.65/16.04 (notequalI2) =>
% 121.65/16.04 ((
% 121.65/16.04 (subsetRefl) =>
% 121.65/16.04 ((
% 121.65/16.04 (subsetTrans) =>
% 121.65/16.04 ((
% 121.65/16.04 (setadjoinSub) =>
% 121.65/16.04 ((
% 121.65/16.04 (setadjoinSub2) =>
% 121.65/16.04 ((
% 121.65/16.04 (subset2powerset) =>
% 121.65/16.04 ((
% 121.65/16.04 (setextsub) =>
% 121.65/16.04 ((
% 121.65/16.04 (subsetemptysetimpeq) =>
% 121.65/16.04 ((
% 121.65/16.04 (powersetI1) =>
% 121.65/16.04 ((
% 121.65/16.04 (powersetE1) =>
% 121.65/16.04 ((
% 121.65/16.04 (inPowerset) =>
% 121.65/16.04 ((
% 121.65/16.04 (powersetsubset) =>
% 121.65/16.04 ((
% 121.65/16.04 (sepInPowerset) =>
% 121.65/16.04 ((
% 121.65/16.04 (sepSubset) =>
% 121.65/16.04 ((
% 121.65/16.04 (binunionIL) =>
% 121.65/16.04 ((
% 121.65/16.04 (upairset2IR) =>
% 121.65/16.04 ((
% 121.65/16.04 (binunionIR) =>
% 121.65/16.04 ((
% 121.65/16.04 (binunionEcases) =>
% 121.65/16.04 ((
% 121.65/16.04 (binunionE) =>
% 121.65/16.04 ((
% 121.65/16.04 (binunionLsub) =>
% 121.65/16.04 ((
% 121.65/16.04 (binunionRsub) =>
% 121.65/16.04 ((
% 121.65/16.04 (binintersectI) =>
% 121.65/16.04 ((
% 121.65/16.04 (binintersectSubset5) =>
% 121.65/16.04 ((
% 121.65/16.04 (binintersectEL) =>
% 121.65/16.04 ((
% 121.65/16.04 (binintersectLsub) =>
% 121.65/16.04 ((
% 121.65/16.04 (binintersectSubset2) =>
% 121.65/16.04 ((
% 121.65/16.04 (binintersectSubset3) =>
% 121.65/16.04 ((
% 121.65/16.04 (binintersectER) =>
% 121.65/16.04 ((
% 121.65/16.04 (disjointsetsI1) =>
% 121.65/16.04 ((
% 121.65/16.04 (binintersectRsub) =>
% 121.65/16.04 ((
% 121.65/16.04 (binintersectSubset4) =>
% 121.65/16.04 ((
% 121.65/16.04 (binintersectSubset1) =>
% 121.65/16.04 ((
% 121.65/16.04 (bs114d) =>
% 121.65/16.04 ((
% 121.65/16.04 (setminusI) =>
% 121.65/16.04 ((
% 121.65/16.04 (setminusEL) =>
% 121.65/16.04 ((
% 121.65/16.04 (setminusER) =>
% 121.65/16.04 ((
% 121.65/16.04 (setminusSubset2) =>
% 121.65/16.04 ((
% 121.65/16.04 (setminusERneg) =>
% 121.65/16.04 ((
% 121.65/16.04 (setminusELneg) =>
% 121.65/16.04 ((
% 121.65/16.04 (setminusILneg) =>
% 121.65/16.04 ((
% 121.65/16.04 (setminusIRneg) =>
% 121.65/16.04 ((
% 121.65/16.04 (setminusLsub) =>
% 121.65/16.04 ((
% 121.65/16.04 (setminusSubset1) =>
% 121.65/16.04 ((
% 121.65/16.04 (symdiffE) =>
% 121.65/16.04 ((
% 121.65/16.04 (symdiffI1) =>
% 121.65/16.04 ((
% 121.65/16.04 (symdiffI2) =>
% 121.65/16.04 ((
% 121.65/16.04 (symdiffIneg1) =>
% 121.65/16.04 ((
% 121.65/16.04 (symdiffIneg2) =>
% 121.65/16.04 ((
% 121.65/16.04 (secondinupair) =>
% 121.65/16.04 ((
% 121.65/16.04 (setukpairIL) =>
% 121.65/16.04 ((
% 121.65/16.04 (setukpairIR) =>
% 121.65/16.04 ((
% 121.65/16.04 (kpairiskpair) =>
% 121.65/16.04 ((
% 121.65/16.04 (kpairp) =>
% 121.65/16.04 ((
% 121.65/16.04 (singletonsubset) =>
% 121.65/16.04 ((
% 121.65/16.04 (singletoninpowerset) =>
% 121.65/16.04 ((
% 121.65/16.04 (singletoninpowunion) =>
% 121.65/16.04 ((
% 121.65/16.04 (upairset2E) =>
% 121.65/16.04 ((
% 121.65/16.04 (upairsubunion) =>
% 121.65/16.04 ((
% 121.65/16.04 (upairinpowunion) =>
% 121.65/16.04 ((
% 121.65/16.04 (ubforcartprodlem1) =>
% 121.65/16.04 ((
% 121.65/16.04 (ubforcartprodlem2) =>
% 121.65/16.04 ((
% 121.65/16.04 (ubforcartprodlem3) =>
% 121.65/16.04 ((
% 121.65/16.04 (cartprodpairin) =>
% 121.65/16.04 ((
% 121.65/16.04 (cartprodmempair1) =>
% 121.65/16.04 ((
% 121.65/16.04 (cartprodmempair) =>
% 121.65/16.04 ((
% 121.65/16.04 (setunionE2) =>
% 121.65/16.04 ((
% 121.65/16.04 (setunionsingleton1) =>
% 121.65/16.04 ((
% 121.65/16.04 (setunionsingleton2) =>
% 121.65/16.04 ((
% 121.65/16.04 (setunionsingleton) =>
% 121.65/16.04 ((
% 121.65/16.04 (singletonprop) =>
% 121.65/16.04 ((
% 121.65/16.04 (ex1E1) =>
% 121.65/16.04 ((
% 121.65/16.04 (ex1I) =>
% 121.65/16.04 ((
% 121.65/16.04 (ex1I2) =>
% 121.65/16.04 ((
% 121.65/16.04 (singletonsuniq) =>
% 121.65/16.04 ((
% 121.65/16.04 (setukpairinjL1) =>
% 121.65/16.04 ((
% 121.65/16.04 (kfstsingleton) =>
% 121.65/16.04 ((
% 121.65/16.04 (theprop) =>
% 121.65/16.04 ((
% 121.65/16.04 (kfstpairEq) =>
% 121.65/16.04 ((
% 121.65/16.04 (cartprodfstin) =>
% 121.65/16.04 ((
% 121.65/16.04 (setukpairinjL2) =>
% 121.65/16.04 ((
% 121.65/16.04 (setukpairinjL) =>
% 121.65/16.04 ((
% 121.65/16.04 (setukpairinjR11) =>
% 121.65/16.04 ((
% 121.65/16.04 (setukpairinjR12) =>
% 121.65/16.04 ((
% 121.65/16.04 (setukpairinjR1) =>
% 121.65/16.04 ((
% 121.65/16.04 (upairequniteq) =>
% 121.65/16.04 ((
% 121.65/16.04 (setukpairinjR2) =>
% 121.65/16.04 ((
% 121.65/16.04 (setukpairinjR) =>
% 121.65/16.04 ((
% 121.65/16.04 (ksndsingleton) =>
% 121.65/16.04 ((
% 121.65/16.04 (ksndpairEq) =>
% 121.65/16.04 ((
% 121.65/16.04 (kpairsurjEq) =>
% 121.65/16.04 ((
% 121.65/16.04 (cartprodsndin) =>
% 121.65/16.04 ((
% 121.65/16.04 (cartprodpairmemEL) =>
% 121.65/16.04 ((
% 121.65/16.04 (cartprodpairmemER) =>
% 121.65/16.04 ((
% 121.65/16.04 (cartprodmempaircEq) =>
% 121.65/16.04 ((
% 121.65/16.04 (cartprodfstpairEq) =>
% 121.65/16.04 ((
% 121.65/16.04 (cartprodsndpairEq) =>
% 121.65/16.04 ((
% 121.65/16.04 (cartprodpairsurjEq) =>
% 121.65/16.04 ((
% 121.65/16.04 (dpsetconstrI) =>
% 121.65/16.04 ((
% 121.65/16.04 (dpsetconstrSub) =>
% 121.65/16.04 ((
% 121.65/16.04 (setOfPairsIsBReln) =>
% 121.65/16.04 ((
% 121.65/16.04 (dpsetconstrERa) =>
% 121.65/16.04 ((
% 121.65/16.04 (dpsetconstrEL1) =>
% 121.65/16.04 ((
% 121.65/16.04 (dpsetconstrEL2) =>
% 121.65/16.04 ((
% 121.65/16.04 (dpsetconstrER) =>
% 121.65/16.04 ((
% 121.65/16.04 (funcImageSingleton) =>
% 121.65/16.04 ((
% 121.65/16.04 (apProp) =>
% 121.65/16.04 ((
% 121.65/16.04 (app) =>
% 121.65/16.04 ((
% 121.65/16.04 (infuncsetfunc) =>
% 121.65/16.04 ((
% 121.65/16.04 (ap2p) =>
% 121.65/16.04 ((
% 121.65/16.04 (funcinfuncset) =>
% 121.65/16.04 ((
% 121.65/16.04 (lamProp) =>
% 121.65/16.04 ((
% 121.65/16.04 (lamp) =>
% 121.65/16.04 ((
% 121.65/16.04 (lam2p) =>
% 121.65/16.04 ((
% 121.65/16.04 (brelnall1) =>
% 121.65/16.04 ((
% 121.65/16.04 (brelnall2) =>
% 121.65/16.04 ((
% 121.65/16.04 (ex1E2) =>
% 121.65/16.04 ((
% 121.65/16.04 (funcGraphProp1) =>
% 121.65/16.04 ((
% 121.65/16.04 (funcGraphProp3) =>
% 121.65/16.04 ((
% 121.65/16.04 (funcGraphProp2) =>
% 121.65/16.04 ((
% 121.65/16.04 (funcextLem) =>
% 121.65/16.04 ((
% 121.65/16.04 (funcGraphProp4) =>
% 121.65/16.04 ((
% 121.65/16.04 (subbreln) =>
% 121.65/16.04 ((
% 121.65/16.04 (eqbreln) =>
% 121.65/16.04 ((
% 121.65/16.04 (funcext) =>
% 121.65/16.04 ((
% 121.65/16.04 (funcext2) =>
% 121.65/16.04 ((
% 121.65/16.04 (ap2apEq1) =>
% 121.65/16.04 ((
% 121.65/16.04 (ap2apEq2) =>
% 121.65/16.04 ((
% 121.65/16.04 (beta1) =>
% 121.65/16.04 ((
% 121.65/16.04 (eta1) =>
% 121.65/16.04 ((
% 121.65/16.04 (lam2lamEq) =>
% 121.65/16.04 ((
% 121.65/16.04 (beta2) =>
% 121.65/16.04 ((
% 121.65/16.04 (eta2) =>
% 121.65/16.04 ((
% 121.65/16.04 (iffalseProp1) =>
% 121.65/16.04 ((
% 121.65/16.04 (iffalseProp2) =>
% 121.65/16.04 ((
% 121.65/16.04 (iftrueProp1) =>
% 121.65/16.04 ((
% 121.65/16.04 (iftrueProp2) =>
% 121.65/16.04 ((
% 121.65/16.04 (ifSingleton) =>
% 121.65/16.04 ((
% 121.65/16.04 (ifp) =>
% 121.65/16.04 ((
% 121.65/16.04 (theeq) =>
% 121.65/16.04 ((
% 121.65/16.04 (iftrue) =>
% 121.65/16.04 ((
% 121.65/16.04 (iffalse) =>
% 121.65/16.04 ((
% 121.65/16.04 (iftrueorfalse) =>
% 121.65/16.04 ((
% 121.65/16.04 (binintersectT_lem) =>
% 121.65/16.04 ((
% 121.65/16.04 (binunionT_lem) =>
% 121.65/16.04 ((
% 121.65/16.04 (powersetT_lem) =>
% 121.65/16.04 ((
% 121.65/16.04 (setminusT_lem) =>
% 121.65/16.04 ((
% 121.65/16.04 (complementT_lem) =>
% 121.65/16.04 ((
% 121.65/16.04 (setextT) =>
% 121.65/16.04 ((
% 121.65/16.04 (subsetTI) =>
% 121.65/16.04 ((
% 121.65/16.04 (powersetTI1) =>
% 121.65/16.04 ((
% 121.65/16.04 (powersetTE1) =>
% 121.65/16.04 ((
% 121.65/16.04 (complementTI1) =>
% 121.65/16.04 ((
% 121.65/16.04 (complementTE1) =>
% 121.65/16.04 ((
% 121.65/16.04 (binintersectTELcontra) =>
% 121.65/16.04 ((
% 121.65/16.04 (binintersectTERcontra) =>
% 121.65/16.04 ((
% 121.65/16.04 (contrasubsetT) =>
% 121.65/16.04 ((
% 121.65/16.04 (contrasubsetT1) =>
% 121.65/16.04 ((
% 121.65/16.04 (contrasubsetT2) =>
% 121.65/16.04 ((
% 121.65/16.04 (contrasubsetT3) =>
% 121.65/16.04 ((
% 121.65/16.04 (doubleComplementI1) =>
% 121.65/16.04 ((
% 121.65/16.04 (doubleComplementE1) =>
% 121.65/16.04 ((
% 121.65/16.04 (doubleComplementSub1) =>
% 121.65/16.04 ((
% 121.65/16.04 (doubleComplementSub2) =>
% 121.65/16.04 ((
% 121.65/16.04 (doubleComplementEq) =>
% 121.65/16.04 ((
% 121.65/16.04 (complementTnotintersectT) =>
% 121.65/16.04 ((
% 121.65/16.04 (complementImpComplementIntersect) =>
% 121.65/16.04 ((
% 121.65/16.04 (complementSubsetComplementIntersect) =>
% 121.65/16.04 ((
% 121.65/16.04 (complementInPowersetComplementIntersect) =>
% 121.65/16.04 ((
% 121.65/16.04 (contraSubsetComplement) =>
% 121.65/16.04 ((
% 121.65/16.04 (complementTcontraSubset) =>
% 121.65/16.04 ((
% 121.65/16.04 (binunionTILcontra) =>
% 121.65/16.04 ((
% 121.65/16.04 (binunionTIRcontra) =>
% 121.65/16.04 ((
% 121.65/16.04 (inIntersectImpInUnion) =>
% 121.65/16.04 ((
% 121.65/16.04 (inIntersectImpInUnion2) =>
% 121.65/16.04 ((
% 121.65/16.04 (inIntersectImpInIntersectUnions) =>
% 121.65/16.04 ((
% 121.65/16.04 (intersectInPowersetIntersectUnions) =>
% 121.65/16.04 ((
% 121.65/16.04 (inComplementUnionImpNotIn1) =>
% 121.65/16.04 ((
% 121.65/16.04 (inComplementUnionImpInComplement1) =>
% 121.65/16.04 ((
% 121.65/16.04 (binunionTE) =>
% 121.65/16.04 ((
% 121.65/16.04 (binunionTEcontra) =>
% 121.65/16.04 ((
% 121.65/16.04 (demorgan2a1) =>
% 121.65/16.04 ((
% 121.65/16.04 (complementUnionInPowersetComplement) =>
% 121.65/16.04 ((
% 121.65/16.04 (demorgan2a2) =>
% 121.65/16.04 ((
% 121.65/16.04 (demorgan1a) =>
% 121.65/16.04 ((
% 121.65/16.04 (demorgan1b) =>
% 121.65/16.04 ((
% 121.65/16.04 (demorgan1) =>
% 121.65/16.04 ((
% 121.65/16.04 (demorgan2a) =>
% 121.65/16.04 ((
% 121.65/16.04 (demorgan2b2) =>
% 121.65/16.04 ((
% 121.65/16.04 (demorgan2b) =>
% 121.65/16.04 ((
% 121.65/16.04 (demorgan2) =>
% 121.65/16.04 ((
% 121.65/16.04 (woz13rule0) =>
% 121.65/16.04 ((
% 121.65/16.04 (woz13rule1) =>
% 121.65/16.04 ((
% 121.65/16.04 (woz13rule2) =>
% 121.65/16.04 ((
% 121.65/16.04 (woz13rule3) =>
% 121.65/16.04 ((
% 121.65/16.04 (woz13rule4) =>
% 121.65/16.04 ((
% 121.65/16.04 (woz1_1) =>
% 121.65/16.04 ((
% 121.65/16.04 (woz1_2) =>
% 121.65/16.04 ((
% 121.65/16.04 (woz1_3) =>
% 121.65/16.04 ((
% 121.65/16.04 (woz1_4) =>
% 121.65/16.04 ((
% 121.65/16.04 (woz1_5) =>
% 121.65/16.04 ((
% 121.65/16.04 (breln1all2) =>
% 121.65/16.04 ((
% 121.65/16.04 (breln1SetBreln1) =>
% 121.65/16.04 ((
% 121.65/16.04 (choice2fnsingleton) =>
% 121.65/16.04 ((
% 121.65/16.04 (setOfPairsIsBReln1) =>
% 121.65/16.04 ((
% 121.65/16.04 (breln1all1) =>
% 121.65/16.04 ((
% 121.65/16.04 (subbreln1) =>
% 121.65/16.04 ((
% 121.65/16.04 (eqbreln1) =>
% 121.65/16.04 ((
% 121.65/16.04 (breln1invprop) =>
% 121.65/16.04 ((
% 121.65/16.04 (breln1invI) =>
% 121.65/16.04 ((
% 121.65/16.04 (breln1invE) =>
% 121.65/16.04 ((
% 121.65/16.04 (breln1compprop) =>
% 121.65/16.04 ((
% 121.65/16.04 (breln1compI) =>
% 121.65/16.04 ((
% 121.65/16.04 (breln1compE) =>
% 121.65/16.04 ((
% 121.65/16.04 (breln1compEex) =>
% 121.65/16.04 ((
% 121.65/16.04 (breln1unionprop) =>
% 121.65/16.04 ((
% 121.65/16.04 (breln1unionIL) =>
% 121.65/16.04 ((
% 121.65/16.04 (breln1unionIR) =>
% 121.65/16.04 ((
% 121.65/16.04 (breln1unionI) =>
% 121.65/16.04 ((
% 121.65/16.04 (breln1unionE) =>
% 121.65/16.04 ((
% 121.65/16.04 (breln1unionEcases) =>
% 121.65/16.04 ((
% 121.65/16.04 (breln1unionCommutes) =>
% 121.65/16.04 ((
% 121.65/16.04 (woz2Ex) =>
% 121.65/16.04 ((
% 121.65/16.04 (woz2W) =>
% 121.65/16.04 ((
% 121.65/16.04 (woz2A) =>
% 121.65/16.04 ((
% 121.65/16.04 (woz2B) =>
% 121.65/16.04 ((
% 121.65/16.04 (image1Ex) =>
% 121.65/16.04 ((
% 121.65/16.04 (image1Ex1) =>
% 121.65/16.04 ((
% 121.65/16.04 (image1Equiv) =>
% 121.65/16.04 ((
% 121.65/16.04 (image1E) =>
% 121.65/16.04 ((
% 121.65/16.04 (image1I) =>
% 121.65/16.04 ((
% 121.65/16.04 (injFuncInInjFuncSet) =>
% 121.65/16.04 ((
% 121.65/16.04 (!!) @ (
% 121.65/16.04 (('#B') @ (
% 121.65/16.04 !!) @
% 121.65/16.04 (
% 121.65/16.04 (
% 121.65/16.04 ('#B') @ (
% 121.65/16.04 (
% 121.65/16.04 ('#B') @ (
% 121.65/16.04 !!))) @
% 121.65/16.04 (
% 121.65/16.04 (
% 121.65/16.04 ('#S') @ (
% 121.65/16.04 (
% 121.65/16.04 ('#B') @ (
% 121.65/16.04 '#S') @
% 121.65/16.04 (
% 121.65/16.04 (
% 121.65/16.04 ('#B') @ (
% 121.65/16.04 (
% 121.65/16.04 ('#B') @ (
% 121.65/16.04 '#S'))) @
% 121.65/16.04 (
% 121.65/16.04 (
% 121.65/16.04 ('#B') @ (
% 121.65/16.04 (
% 121.65/16.04 ('#B') @ (
% 121.65/16.04 (
% 121.65/16.04 ('#B') @ (
% 121.65/16.04 =>))))) @
% 121.65/16.04 (
% 121.65/16.04 (
% 121.65/16.04 ('#B') @ (
% 121.65/16.04 (
% 121.65/16.04 ('#B') @ (
% 121.65/16.04 (
% 121.65/16.04 ('#C') @ in)))) @
% 121.65/16.04 injFuncSet)))))))) @
% 121.65/16.04 (
% 121.65/16.04 (
% 121.65/16.04 ('#B') @ (
% 121.65/16.04 (
% 121.65/16.04 ('#B') @ (
% 121.65/16.04 (
% 121.65/16.04 ('#C') @ in)))) @
% 121.65/16.04 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 121.65/16.04 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl307])).
% 121.65/16.04 thf(zip_derived_cl337, plain,
% 121.65/16.04 (~ (((setadjoinIR) =>
% 121.65/16.04 (((setadjoinE) =>
% 121.65/16.04 (((setadjoinOr) =>
% 121.65/16.04 (((setoftrueEq) =>
% 121.65/16.04 (((powersetI) =>
% 121.65/16.04 (((emptyinPowerset) =>
% 121.65/16.04 (((emptyInPowerset) =>
% 121.65/16.04 (((powersetE) =>
% 121.65/16.04 (((setunionI) =>
% 121.65/16.04 (((setunionE) =>
% 121.65/16.04 (((subPowSU) =>
% 121.65/16.04 (((exuE2) =>
% 121.65/16.04 (((nonemptyImpWitness) =>
% 121.65/16.04 (((uniqinunit) =>
% 121.65/16.04 (((notinsingleton) =>
% 121.65/16.04 (((eqinunit) =>
% 121.65/16.04 (((singletonsswitch) =>
% 121.65/16.04 (((upairsetE) =>
% 121.65/16.04 (((upairsetIL) =>
% 121.65/16.04 (((upairsetIR) =>
% 121.65/16.04 (((emptyE1) =>
% 121.65/16.04 (((vacuousDall) =>
% 121.65/16.04 (((quantDeMorgan1) =>
% 121.65/16.04 (((quantDeMorgan2) =>
% 121.65/16.04 (((quantDeMorgan3) =>
% 121.65/16.04 (((quantDeMorgan4) =>
% 121.65/16.04 (((prop2setI) =>
% 121.65/16.04 (((prop2set2propI) =>
% 121.65/16.04 (((notdexE) =>
% 121.65/16.04 (((notdallE) =>
% 121.65/16.04 ((
% 121.65/16.04 (exuI1) =>
% 121.65/16.04 ((
% 121.65/16.04 (exuI3) =>
% 121.65/16.04 ((
% 121.65/16.04 (exuI2) =>
% 121.65/16.04 ((
% 121.65/16.04 (inCongP) =>
% 121.65/16.04 ((
% 121.65/16.04 (in__Cong) =>
% 121.65/16.04 ((
% 121.65/16.04 (exuE3u) =>
% 121.65/16.04 ((
% 121.65/16.04 (exu__Cong) =>
% 121.65/16.04 ((
% 121.65/16.04 (setadjoin__Cong) =>
% 121.65/16.04 ((
% 121.65/16.04 (powerset__Cong) =>
% 121.65/16.04 ((
% 121.65/16.04 (setunion__Cong) =>
% 121.65/16.04 ((
% 121.65/16.04 (exuEu) =>
% 121.65/16.04 ((
% 121.65/16.04 (descr__Cong) =>
% 121.65/16.04 ((
% 121.65/16.04 (dsetconstr__Cong) =>
% 121.65/16.04 ((
% 121.65/16.04 (subsetI1) =>
% 121.65/16.04 ((
% 121.65/16.04 (eqimpsubset2) =>
% 121.65/16.04 ((
% 121.65/16.04 (eqimpsubset1) =>
% 121.65/16.04 ((
% 121.65/16.04 (subsetI2) =>
% 121.65/16.04 ((
% 121.65/16.04 (emptysetsubset) =>
% 121.65/16.04 ((
% 121.65/16.04 (subsetE) =>
% 121.65/16.04 ((
% 121.65/16.04 (subsetE2) =>
% 121.65/16.04 ((
% 121.65/16.04 (notsubsetI) =>
% 121.65/16.04 ((
% 121.65/16.04 (notequalI1) =>
% 121.65/16.04 ((
% 121.65/16.04 (notequalI2) =>
% 121.65/16.04 ((
% 121.65/16.04 (subsetRefl) =>
% 121.65/16.04 ((
% 121.65/16.04 (subsetTrans) =>
% 121.65/16.04 ((
% 121.65/16.04 (setadjoinSub) =>
% 121.65/16.04 ((
% 121.65/16.04 (setadjoinSub2) =>
% 121.65/16.04 ((
% 121.65/16.04 (subset2powerset) =>
% 121.65/16.04 ((
% 121.65/16.04 (setextsub) =>
% 121.65/16.04 ((
% 121.65/16.04 (subsetemptysetimpeq) =>
% 121.65/16.04 ((
% 121.65/16.04 (powersetI1) =>
% 121.65/16.04 ((
% 121.65/16.04 (powersetE1) =>
% 121.65/16.04 ((
% 121.65/16.04 (inPowerset) =>
% 121.65/16.04 ((
% 121.65/16.04 (powersetsubset) =>
% 121.65/16.04 ((
% 121.65/16.04 (sepInPowerset) =>
% 121.65/16.04 ((
% 121.65/16.04 (sepSubset) =>
% 121.65/16.04 ((
% 121.65/16.04 (binunionIL) =>
% 121.65/16.04 ((
% 121.65/16.04 (upairset2IR) =>
% 121.65/16.04 ((
% 121.65/16.04 (binunionIR) =>
% 121.65/16.04 ((
% 121.65/16.04 (binunionEcases) =>
% 121.65/16.04 ((
% 121.65/16.04 (binunionE) =>
% 121.65/16.04 ((
% 121.65/16.04 (binunionLsub) =>
% 121.65/16.04 ((
% 121.65/16.04 (binunionRsub) =>
% 121.65/16.04 ((
% 121.65/16.04 (binintersectI) =>
% 121.65/16.04 ((
% 121.65/16.04 (binintersectSubset5) =>
% 121.65/16.04 ((
% 121.65/16.04 (binintersectEL) =>
% 121.65/16.04 ((
% 121.65/16.04 (binintersectLsub) =>
% 121.65/16.04 ((
% 121.65/16.04 (binintersectSubset2) =>
% 121.65/16.04 ((
% 121.65/16.04 (binintersectSubset3) =>
% 121.65/16.04 ((
% 121.65/16.04 (binintersectER) =>
% 121.65/16.04 ((
% 121.65/16.04 (disjointsetsI1) =>
% 121.65/16.04 ((
% 121.65/16.04 (binintersectRsub) =>
% 121.65/16.04 ((
% 121.65/16.04 (binintersectSubset4) =>
% 121.65/16.04 ((
% 121.65/16.04 (binintersectSubset1) =>
% 121.65/16.04 ((
% 121.65/16.04 (bs114d) =>
% 121.84/16.04 ((
% 121.84/16.04 (setminusI) =>
% 121.84/16.04 ((
% 121.84/16.04 (setminusEL) =>
% 121.84/16.04 ((
% 121.84/16.04 (setminusER) =>
% 121.84/16.04 ((
% 121.84/16.04 (setminusSubset2) =>
% 121.84/16.04 ((
% 121.84/16.04 (setminusERneg) =>
% 121.84/16.04 ((
% 121.84/16.04 (setminusELneg) =>
% 121.84/16.04 ((
% 121.84/16.04 (setminusILneg) =>
% 121.84/16.04 ((
% 121.84/16.04 (setminusIRneg) =>
% 121.84/16.04 ((
% 121.84/16.04 (setminusLsub) =>
% 121.84/16.04 ((
% 121.84/16.04 (setminusSubset1) =>
% 121.84/16.04 ((
% 121.84/16.04 (symdiffE) =>
% 121.84/16.04 ((
% 121.84/16.04 (symdiffI1) =>
% 121.84/16.04 ((
% 121.84/16.04 (symdiffI2) =>
% 121.84/16.04 ((
% 121.84/16.04 (symdiffIneg1) =>
% 121.84/16.04 ((
% 121.84/16.04 (symdiffIneg2) =>
% 121.84/16.04 ((
% 121.84/16.04 (secondinupair) =>
% 121.84/16.04 ((
% 121.84/16.04 (setukpairIL) =>
% 121.84/16.04 ((
% 121.84/16.04 (setukpairIR) =>
% 121.84/16.04 ((
% 121.84/16.04 (kpairiskpair) =>
% 121.84/16.04 ((
% 121.84/16.04 (kpairp) =>
% 121.84/16.04 ((
% 121.84/16.04 (singletonsubset) =>
% 121.84/16.04 ((
% 121.84/16.04 (singletoninpowerset) =>
% 121.84/16.04 ((
% 121.84/16.04 (singletoninpowunion) =>
% 121.84/16.04 ((
% 121.84/16.04 (upairset2E) =>
% 121.84/16.04 ((
% 121.84/16.04 (upairsubunion) =>
% 121.84/16.04 ((
% 121.84/16.04 (upairinpowunion) =>
% 121.84/16.04 ((
% 121.84/16.04 (ubforcartprodlem1) =>
% 121.84/16.04 ((
% 121.84/16.04 (ubforcartprodlem2) =>
% 121.84/16.04 ((
% 121.84/16.04 (ubforcartprodlem3) =>
% 121.84/16.04 ((
% 121.84/16.04 (cartprodpairin) =>
% 121.84/16.04 ((
% 121.84/16.04 (cartprodmempair1) =>
% 121.84/16.04 ((
% 121.84/16.04 (cartprodmempair) =>
% 121.84/16.04 ((
% 121.84/16.04 (setunionE2) =>
% 121.84/16.04 ((
% 121.84/16.04 (setunionsingleton1) =>
% 121.84/16.04 ((
% 121.84/16.04 (setunionsingleton2) =>
% 121.84/16.04 ((
% 121.84/16.04 (setunionsingleton) =>
% 121.84/16.04 ((
% 121.84/16.04 (singletonprop) =>
% 121.84/16.04 ((
% 121.84/16.04 (ex1E1) =>
% 121.84/16.04 ((
% 121.84/16.04 (ex1I) =>
% 121.84/16.04 ((
% 121.84/16.04 (ex1I2) =>
% 121.84/16.04 ((
% 121.84/16.04 (singletonsuniq) =>
% 121.84/16.04 ((
% 121.84/16.04 (setukpairinjL1) =>
% 121.84/16.04 ((
% 121.84/16.04 (kfstsingleton) =>
% 121.84/16.04 ((
% 121.84/16.04 (theprop) =>
% 121.84/16.04 ((
% 121.84/16.04 (kfstpairEq) =>
% 121.84/16.04 ((
% 121.84/16.04 (cartprodfstin) =>
% 121.84/16.04 ((
% 121.84/16.04 (setukpairinjL2) =>
% 121.84/16.04 ((
% 121.84/16.04 (setukpairinjL) =>
% 121.84/16.04 ((
% 121.84/16.04 (setukpairinjR11) =>
% 121.84/16.04 ((
% 121.84/16.04 (setukpairinjR12) =>
% 121.84/16.04 ((
% 121.84/16.04 (setukpairinjR1) =>
% 121.84/16.04 ((
% 121.84/16.04 (upairequniteq) =>
% 121.84/16.04 ((
% 121.84/16.04 (setukpairinjR2) =>
% 121.84/16.04 ((
% 121.84/16.04 (setukpairinjR) =>
% 121.84/16.04 ((
% 121.84/16.04 (ksndsingleton) =>
% 121.84/16.04 ((
% 121.84/16.04 (ksndpairEq) =>
% 121.84/16.04 ((
% 121.84/16.04 (kpairsurjEq) =>
% 121.84/16.04 ((
% 121.84/16.04 (cartprodsndin) =>
% 121.84/16.04 ((
% 121.84/16.04 (cartprodpairmemEL) =>
% 121.84/16.04 ((
% 121.84/16.04 (cartprodpairmemER) =>
% 121.84/16.04 ((
% 121.84/16.04 (cartprodmempaircEq) =>
% 121.84/16.04 ((
% 121.84/16.04 (cartprodfstpairEq) =>
% 121.84/16.04 ((
% 121.84/16.04 (cartprodsndpairEq) =>
% 121.84/16.04 ((
% 121.84/16.04 (cartprodpairsurjEq) =>
% 121.84/16.04 ((
% 121.84/16.04 (dpsetconstrI) =>
% 121.84/16.04 ((
% 121.84/16.04 (dpsetconstrSub) =>
% 121.84/16.04 ((
% 121.84/16.04 (setOfPairsIsBReln) =>
% 121.84/16.04 ((
% 121.84/16.04 (dpsetconstrERa) =>
% 121.84/16.04 ((
% 121.84/16.04 (dpsetconstrEL1) =>
% 121.84/16.04 ((
% 121.84/16.04 (dpsetconstrEL2) =>
% 121.84/16.04 ((
% 121.84/16.04 (dpsetconstrER) =>
% 121.84/16.04 ((
% 121.84/16.04 (funcImageSingleton) =>
% 121.84/16.04 ((
% 121.84/16.04 (apProp) =>
% 121.84/16.04 ((
% 121.84/16.04 (app) =>
% 121.84/16.04 ((
% 121.84/16.04 (infuncsetfunc) =>
% 121.84/16.04 ((
% 121.84/16.04 (ap2p) =>
% 121.84/16.04 ((
% 121.84/16.04 (funcinfuncset) =>
% 121.84/16.04 ((
% 121.84/16.04 (lamProp) =>
% 121.84/16.04 ((
% 121.84/16.04 (lamp) =>
% 121.84/16.04 ((
% 121.84/16.04 (lam2p) =>
% 121.84/16.04 ((
% 121.84/16.04 (brelnall1) =>
% 121.84/16.04 ((
% 121.84/16.04 (brelnall2) =>
% 121.84/16.04 ((
% 121.84/16.04 (ex1E2) =>
% 121.84/16.04 ((
% 121.84/16.04 (funcGraphProp1) =>
% 121.84/16.04 ((
% 121.84/16.04 (funcGraphProp3) =>
% 121.84/16.04 ((
% 121.84/16.04 (funcGraphProp2) =>
% 121.84/16.04 ((
% 121.84/16.04 (funcextLem) =>
% 121.84/16.04 ((
% 121.84/16.04 (funcGraphProp4) =>
% 121.84/16.04 ((
% 121.84/16.04 (subbreln) =>
% 121.84/16.04 ((
% 121.84/16.04 (eqbreln) =>
% 121.84/16.04 ((
% 121.84/16.04 (funcext) =>
% 121.84/16.04 ((
% 121.84/16.04 (funcext2) =>
% 121.84/16.04 ((
% 121.84/16.04 (ap2apEq1) =>
% 121.84/16.04 ((
% 121.84/16.04 (ap2apEq2) =>
% 121.84/16.04 ((
% 121.84/16.04 (beta1) =>
% 121.84/16.04 ((
% 121.84/16.04 (eta1) =>
% 121.84/16.04 ((
% 121.84/16.04 (lam2lamEq) =>
% 121.84/16.04 ((
% 121.84/16.04 (beta2) =>
% 121.84/16.04 ((
% 121.84/16.04 (eta2) =>
% 121.84/16.04 ((
% 121.84/16.04 (iffalseProp1) =>
% 121.84/16.04 ((
% 121.84/16.04 (iffalseProp2) =>
% 121.84/16.04 ((
% 121.84/16.04 (iftrueProp1) =>
% 121.84/16.04 ((
% 121.84/16.04 (iftrueProp2) =>
% 121.84/16.04 ((
% 121.84/16.04 (ifSingleton) =>
% 121.84/16.04 ((
% 121.84/16.04 (ifp) =>
% 121.84/16.04 ((
% 121.84/16.04 (theeq) =>
% 121.84/16.04 ((
% 121.84/16.04 (iftrue) =>
% 121.84/16.04 ((
% 121.84/16.04 (iffalse) =>
% 121.84/16.04 ((
% 121.84/16.04 (iftrueorfalse) =>
% 121.84/16.04 ((
% 121.84/16.04 (binintersectT_lem) =>
% 121.84/16.04 ((
% 121.84/16.04 (binunionT_lem) =>
% 121.84/16.04 ((
% 121.84/16.04 (powersetT_lem) =>
% 121.84/16.04 ((
% 121.84/16.04 (setminusT_lem) =>
% 121.84/16.04 ((
% 121.84/16.04 (complementT_lem) =>
% 121.84/16.04 ((
% 121.84/16.04 (setextT) =>
% 121.84/16.04 ((
% 121.84/16.04 (subsetTI) =>
% 121.84/16.04 ((
% 121.84/16.04 (powersetTI1) =>
% 121.84/16.04 ((
% 121.84/16.04 (powersetTE1) =>
% 121.84/16.04 ((
% 121.84/16.04 (complementTI1) =>
% 121.84/16.04 ((
% 121.84/16.04 (complementTE1) =>
% 121.84/16.04 ((
% 121.84/16.04 (binintersectTELcontra) =>
% 121.84/16.04 ((
% 121.84/16.04 (binintersectTERcontra) =>
% 121.84/16.04 ((
% 121.84/16.04 (contrasubsetT) =>
% 121.84/16.04 ((
% 121.84/16.04 (contrasubsetT1) =>
% 121.84/16.04 ((
% 121.84/16.04 (contrasubsetT2) =>
% 121.84/16.04 ((
% 121.84/16.04 (contrasubsetT3) =>
% 121.84/16.04 ((
% 121.84/16.04 (doubleComplementI1) =>
% 121.84/16.04 ((
% 121.84/16.04 (doubleComplementE1) =>
% 121.84/16.04 ((
% 121.84/16.04 (doubleComplementSub1) =>
% 121.84/16.04 ((
% 121.84/16.04 (doubleComplementSub2) =>
% 121.84/16.04 ((
% 121.84/16.04 (doubleComplementEq) =>
% 121.84/16.04 ((
% 121.84/16.04 (complementTnotintersectT) =>
% 121.84/16.04 ((
% 121.84/16.04 (complementImpComplementIntersect) =>
% 121.84/16.04 ((
% 121.84/16.04 (complementSubsetComplementIntersect) =>
% 121.84/16.04 ((
% 121.84/16.04 (complementInPowersetComplementIntersect) =>
% 121.84/16.04 ((
% 121.84/16.04 (contraSubsetComplement) =>
% 121.84/16.04 ((
% 121.84/16.04 (complementTcontraSubset) =>
% 121.84/16.04 ((
% 121.84/16.04 (binunionTILcontra) =>
% 121.84/16.04 ((
% 121.84/16.04 (binunionTIRcontra) =>
% 121.84/16.04 ((
% 121.84/16.04 (inIntersectImpInUnion) =>
% 121.84/16.04 ((
% 121.84/16.04 (inIntersectImpInUnion2) =>
% 121.84/16.04 ((
% 121.84/16.04 (inIntersectImpInIntersectUnions) =>
% 121.84/16.04 ((
% 121.84/16.04 (intersectInPowersetIntersectUnions) =>
% 121.84/16.04 ((
% 121.84/16.04 (inComplementUnionImpNotIn1) =>
% 121.84/16.04 ((
% 121.84/16.04 (inComplementUnionImpInComplement1) =>
% 121.84/16.04 ((
% 121.84/16.04 (binunionTE) =>
% 121.84/16.04 ((
% 121.84/16.04 (binunionTEcontra) =>
% 121.84/16.04 ((
% 121.84/16.04 (demorgan2a1) =>
% 121.84/16.04 ((
% 121.84/16.04 (complementUnionInPowersetComplement) =>
% 121.84/16.04 ((
% 121.84/16.04 (demorgan2a2) =>
% 121.84/16.04 ((
% 121.84/16.04 (demorgan1a) =>
% 121.84/16.04 ((
% 121.84/16.04 (demorgan1b) =>
% 121.84/16.04 ((
% 121.84/16.04 (demorgan1) =>
% 121.84/16.04 ((
% 121.84/16.04 (demorgan2a) =>
% 121.84/16.04 ((
% 121.84/16.04 (demorgan2b2) =>
% 121.84/16.04 ((
% 121.84/16.04 (demorgan2b) =>
% 121.84/16.04 ((
% 121.84/16.04 (demorgan2) =>
% 121.84/16.04 ((
% 121.84/16.04 (woz13rule0) =>
% 121.84/16.04 ((
% 121.84/16.04 (woz13rule1) =>
% 121.84/16.04 ((
% 121.84/16.04 (woz13rule2) =>
% 121.84/16.04 ((
% 121.84/16.04 (woz13rule3) =>
% 121.84/16.04 ((
% 121.84/16.04 (woz13rule4) =>
% 121.84/16.04 ((
% 121.84/16.04 (woz1_1) =>
% 121.84/16.04 ((
% 121.84/16.04 (woz1_2) =>
% 121.84/16.04 ((
% 121.84/16.04 (woz1_3) =>
% 121.84/16.04 ((
% 121.84/16.04 (woz1_4) =>
% 121.84/16.04 ((
% 121.84/16.04 (woz1_5) =>
% 121.84/16.04 ((
% 121.84/16.04 (breln1all2) =>
% 121.84/16.04 ((
% 121.84/16.04 (breln1SetBreln1) =>
% 121.84/16.04 ((
% 121.84/16.04 (choice2fnsingleton) =>
% 121.84/16.04 ((
% 121.84/16.04 (setOfPairsIsBReln1) =>
% 121.84/16.04 ((
% 121.84/16.04 (breln1all1) =>
% 121.84/16.04 ((
% 121.84/16.04 (subbreln1) =>
% 121.84/16.04 ((
% 121.84/16.04 (eqbreln1) =>
% 121.84/16.04 ((
% 121.84/16.04 (breln1invprop) =>
% 121.84/16.04 ((
% 121.84/16.04 (breln1invI) =>
% 121.84/16.04 ((
% 121.84/16.04 (breln1invE) =>
% 121.84/16.04 ((
% 121.84/16.04 (breln1compprop) =>
% 121.84/16.04 ((
% 121.84/16.04 (breln1compI) =>
% 121.84/16.04 ((
% 121.84/16.04 (breln1compE) =>
% 121.84/16.04 ((
% 121.84/16.04 (breln1compEex) =>
% 121.84/16.04 ((
% 121.84/16.04 (breln1unionprop) =>
% 121.84/16.04 ((
% 121.84/16.04 (breln1unionIL) =>
% 121.84/16.04 ((
% 121.84/16.04 (breln1unionIR) =>
% 121.84/16.04 ((
% 121.84/16.04 (breln1unionI) =>
% 121.84/16.04 ((
% 121.84/16.04 (breln1unionE) =>
% 121.84/16.04 ((
% 121.84/16.04 (breln1unionEcases) =>
% 121.84/16.04 ((
% 121.84/16.04 (breln1unionCommutes) =>
% 121.84/16.04 ((
% 121.84/16.04 (woz2Ex) =>
% 121.84/16.04 ((
% 121.84/16.04 (woz2W) =>
% 121.84/16.04 ((
% 121.84/16.04 (woz2A) =>
% 121.84/16.04 ((
% 121.84/16.04 (woz2B) =>
% 121.84/16.04 ((
% 121.84/16.04 (image1Ex) =>
% 121.84/16.04 ((
% 121.84/16.04 (image1Ex1) =>
% 121.84/16.04 ((
% 121.84/16.04 (image1Equiv) =>
% 121.84/16.04 ((
% 121.84/16.04 (image1E) =>
% 121.84/16.04 ((
% 121.84/16.04 (image1I) =>
% 121.84/16.04 ((
% 121.84/16.04 (injFuncInInjFuncSet) =>
% 121.84/16.04 ((
% 121.84/16.04 (!!) @ (
% 121.84/16.04 (('#B') @ (
% 121.84/16.04 !!) @
% 121.84/16.04 (
% 121.84/16.04 (
% 121.84/16.04 ('#B') @ (
% 121.84/16.04 (
% 121.84/16.04 ('#B') @ (
% 121.84/16.04 !!))) @
% 121.84/16.04 (
% 121.84/16.04 (
% 121.84/16.04 ('#S') @ (
% 121.84/16.04 (
% 121.84/16.04 ('#B') @ (
% 121.84/16.04 '#S') @
% 121.84/16.04 (
% 121.84/16.04 (
% 121.84/16.04 ('#B') @ (
% 121.84/16.04 (
% 121.84/16.04 ('#B') @ (
% 121.84/16.04 '#S'))) @
% 121.84/16.04 (
% 121.84/16.04 (
% 121.84/16.04 ('#B') @ (
% 121.84/16.04 (
% 121.84/16.04 ('#B') @ (
% 121.84/16.04 (
% 121.84/16.04 ('#B') @ (
% 121.84/16.04 =>))))) @
% 121.84/16.04 (
% 121.84/16.04 (
% 121.84/16.04 ('#B') @ (
% 121.84/16.04 (
% 121.84/16.04 ('#B') @ (
% 121.84/16.04 (
% 121.84/16.04 ('#C') @ in)))) @
% 121.84/16.04 injFuncSet)))))))) @
% 121.84/16.04 (
% 121.84/16.04 (
% 121.84/16.04 ('#B') @ (
% 121.84/16.04 (
% 121.84/16.04 ('#B') @ (
% 121.84/16.04 (
% 121.84/16.04 ('#C') @ in)))) @
% 121.84/16.04 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 121.84/16.04 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl322])).
% 121.84/16.04 thf(zip_derived_cl349, plain,
% 121.84/16.04 (~ (((setadjoinE) =>
% 121.84/16.04 (((setadjoinOr) =>
% 121.84/16.04 (((setoftrueEq) =>
% 121.84/16.04 (((powersetI) =>
% 121.84/16.04 (((emptyinPowerset) =>
% 121.84/16.04 (((emptyInPowerset) =>
% 121.84/16.04 (((powersetE) =>
% 121.84/16.04 (((setunionI) =>
% 121.84/16.04 (((setunionE) =>
% 121.84/16.04 (((subPowSU) =>
% 121.84/16.04 (((exuE2) =>
% 121.84/16.04 (((nonemptyImpWitness) =>
% 121.84/16.04 (((uniqinunit) =>
% 121.84/16.04 (((notinsingleton) =>
% 121.84/16.04 (((eqinunit) =>
% 121.84/16.04 (((singletonsswitch) =>
% 121.84/16.04 (((upairsetE) =>
% 121.84/16.04 (((upairsetIL) =>
% 121.84/16.04 (((upairsetIR) =>
% 121.84/16.04 (((emptyE1) =>
% 121.84/16.04 (((vacuousDall) =>
% 121.84/16.04 (((quantDeMorgan1) =>
% 121.84/16.04 (((quantDeMorgan2) =>
% 121.84/16.04 (((quantDeMorgan3) =>
% 121.84/16.04 (((quantDeMorgan4) =>
% 121.84/16.04 (((prop2setI) =>
% 121.84/16.04 (((prop2set2propI) =>
% 121.84/16.04 (((notdexE) =>
% 121.84/16.04 (((notdallE) =>
% 121.84/16.04 (((exuI1) =>
% 121.84/16.04 ((
% 121.84/16.04 (exuI3) =>
% 121.84/16.04 ((
% 121.84/16.04 (exuI2) =>
% 121.84/16.04 ((
% 121.84/16.04 (inCongP) =>
% 121.84/16.04 ((
% 121.84/16.04 (in__Cong) =>
% 121.84/16.04 ((
% 121.84/16.04 (exuE3u) =>
% 121.84/16.04 ((
% 121.84/16.04 (exu__Cong) =>
% 121.84/16.04 ((
% 121.84/16.04 (setadjoin__Cong) =>
% 121.84/16.04 ((
% 121.84/16.04 (powerset__Cong) =>
% 121.84/16.04 ((
% 121.84/16.04 (setunion__Cong) =>
% 121.84/16.04 ((
% 121.84/16.04 (exuEu) =>
% 121.84/16.04 ((
% 121.84/16.04 (descr__Cong) =>
% 121.84/16.04 ((
% 121.84/16.04 (dsetconstr__Cong) =>
% 121.84/16.04 ((
% 121.84/16.04 (subsetI1) =>
% 121.84/16.04 ((
% 121.84/16.04 (eqimpsubset2) =>
% 121.84/16.04 ((
% 121.84/16.04 (eqimpsubset1) =>
% 121.84/16.04 ((
% 121.84/16.04 (subsetI2) =>
% 121.84/16.04 ((
% 121.84/16.04 (emptysetsubset) =>
% 121.84/16.04 ((
% 121.84/16.04 (subsetE) =>
% 121.84/16.04 ((
% 121.84/16.04 (subsetE2) =>
% 121.84/16.04 ((
% 121.84/16.04 (notsubsetI) =>
% 121.84/16.04 ((
% 121.84/16.04 (notequalI1) =>
% 121.84/16.04 ((
% 121.84/16.04 (notequalI2) =>
% 121.84/16.04 ((
% 121.84/16.04 (subsetRefl) =>
% 121.84/16.04 ((
% 121.84/16.04 (subsetTrans) =>
% 121.84/16.04 ((
% 121.84/16.04 (setadjoinSub) =>
% 121.84/16.04 ((
% 121.84/16.04 (setadjoinSub2) =>
% 121.84/16.04 ((
% 121.84/16.04 (subset2powerset) =>
% 121.84/16.04 ((
% 121.84/16.04 (setextsub) =>
% 121.84/16.04 ((
% 121.84/16.04 (subsetemptysetimpeq) =>
% 121.84/16.04 ((
% 121.84/16.04 (powersetI1) =>
% 121.84/16.04 ((
% 121.84/16.04 (powersetE1) =>
% 121.84/16.04 ((
% 121.84/16.04 (inPowerset) =>
% 121.84/16.04 ((
% 121.84/16.04 (powersetsubset) =>
% 121.84/16.04 ((
% 121.84/16.04 (sepInPowerset) =>
% 121.84/16.04 ((
% 121.84/16.04 (sepSubset) =>
% 121.84/16.04 ((
% 121.84/16.04 (binunionIL) =>
% 121.84/16.04 ((
% 121.84/16.04 (upairset2IR) =>
% 121.84/16.04 ((
% 121.84/16.04 (binunionIR) =>
% 121.84/16.04 ((
% 121.84/16.04 (binunionEcases) =>
% 121.84/16.04 ((
% 121.84/16.04 (binunionE) =>
% 121.84/16.04 ((
% 121.84/16.04 (binunionLsub) =>
% 121.84/16.04 ((
% 121.84/16.04 (binunionRsub) =>
% 121.84/16.04 ((
% 121.84/16.04 (binintersectI) =>
% 121.84/16.04 ((
% 121.84/16.04 (binintersectSubset5) =>
% 121.84/16.04 ((
% 121.84/16.04 (binintersectEL) =>
% 121.84/16.04 ((
% 121.84/16.04 (binintersectLsub) =>
% 121.84/16.04 ((
% 121.84/16.04 (binintersectSubset2) =>
% 121.84/16.04 ((
% 121.84/16.04 (binintersectSubset3) =>
% 121.84/16.04 ((
% 121.84/16.04 (binintersectER) =>
% 121.84/16.04 ((
% 121.84/16.04 (disjointsetsI1) =>
% 121.84/16.04 ((
% 121.84/16.04 (binintersectRsub) =>
% 121.84/16.04 ((
% 121.84/16.04 (binintersectSubset4) =>
% 121.84/16.04 ((
% 121.84/16.04 (binintersectSubset1) =>
% 121.84/16.04 ((
% 121.84/16.04 (bs114d) =>
% 121.84/16.04 ((
% 121.84/16.04 (setminusI) =>
% 121.84/16.04 ((
% 121.84/16.04 (setminusEL) =>
% 121.84/16.04 ((
% 121.84/16.04 (setminusER) =>
% 121.84/16.04 ((
% 121.84/16.04 (setminusSubset2) =>
% 121.84/16.04 ((
% 121.84/16.04 (setminusERneg) =>
% 121.84/16.04 ((
% 121.84/16.04 (setminusELneg) =>
% 121.84/16.04 ((
% 121.84/16.04 (setminusILneg) =>
% 121.84/16.04 ((
% 121.84/16.04 (setminusIRneg) =>
% 121.84/16.04 ((
% 121.84/16.04 (setminusLsub) =>
% 121.84/16.04 ((
% 121.84/16.04 (setminusSubset1) =>
% 121.84/16.04 ((
% 121.84/16.04 (symdiffE) =>
% 121.84/16.04 ((
% 121.84/16.04 (symdiffI1) =>
% 121.84/16.04 ((
% 121.84/16.04 (symdiffI2) =>
% 121.84/16.04 ((
% 121.84/16.04 (symdiffIneg1) =>
% 121.84/16.04 ((
% 121.84/16.04 (symdiffIneg2) =>
% 121.84/16.04 ((
% 121.84/16.04 (secondinupair) =>
% 121.84/16.04 ((
% 121.84/16.04 (setukpairIL) =>
% 121.84/16.04 ((
% 121.84/16.04 (setukpairIR) =>
% 121.84/16.04 ((
% 121.84/16.04 (kpairiskpair) =>
% 121.84/16.04 ((
% 121.84/16.04 (kpairp) =>
% 121.84/16.04 ((
% 121.84/16.04 (singletonsubset) =>
% 121.84/16.04 ((
% 121.84/16.04 (singletoninpowerset) =>
% 121.84/16.04 ((
% 121.84/16.04 (singletoninpowunion) =>
% 121.84/16.04 ((
% 121.84/16.04 (upairset2E) =>
% 121.84/16.04 ((
% 121.84/16.04 (upairsubunion) =>
% 121.84/16.04 ((
% 121.84/16.04 (upairinpowunion) =>
% 121.84/16.04 ((
% 121.84/16.04 (ubforcartprodlem1) =>
% 121.84/16.04 ((
% 121.84/16.04 (ubforcartprodlem2) =>
% 121.84/16.04 ((
% 121.84/16.04 (ubforcartprodlem3) =>
% 121.84/16.04 ((
% 121.84/16.04 (cartprodpairin) =>
% 121.84/16.04 ((
% 121.84/16.04 (cartprodmempair1) =>
% 121.84/16.04 ((
% 121.84/16.04 (cartprodmempair) =>
% 121.84/16.04 ((
% 121.84/16.04 (setunionE2) =>
% 121.84/16.04 ((
% 121.84/16.04 (setunionsingleton1) =>
% 121.84/16.04 ((
% 121.84/16.04 (setunionsingleton2) =>
% 121.84/16.04 ((
% 121.84/16.04 (setunionsingleton) =>
% 121.84/16.04 ((
% 121.84/16.04 (singletonprop) =>
% 121.84/16.04 ((
% 121.84/16.04 (ex1E1) =>
% 121.84/16.04 ((
% 121.84/16.04 (ex1I) =>
% 121.84/16.04 ((
% 121.84/16.04 (ex1I2) =>
% 121.84/16.04 ((
% 121.84/16.04 (singletonsuniq) =>
% 121.84/16.04 ((
% 121.84/16.04 (setukpairinjL1) =>
% 121.84/16.04 ((
% 121.84/16.04 (kfstsingleton) =>
% 121.84/16.04 ((
% 121.84/16.04 (theprop) =>
% 121.84/16.04 ((
% 121.84/16.04 (kfstpairEq) =>
% 121.84/16.04 ((
% 121.84/16.04 (cartprodfstin) =>
% 121.84/16.04 ((
% 121.84/16.04 (setukpairinjL2) =>
% 121.84/16.04 ((
% 121.84/16.04 (setukpairinjL) =>
% 121.84/16.04 ((
% 121.84/16.04 (setukpairinjR11) =>
% 121.84/16.04 ((
% 121.84/16.04 (setukpairinjR12) =>
% 121.84/16.04 ((
% 121.84/16.04 (setukpairinjR1) =>
% 121.84/16.04 ((
% 121.84/16.04 (upairequniteq) =>
% 121.84/16.04 ((
% 121.84/16.04 (setukpairinjR2) =>
% 121.84/16.04 ((
% 121.84/16.04 (setukpairinjR) =>
% 121.84/16.04 ((
% 121.84/16.04 (ksndsingleton) =>
% 121.84/16.04 ((
% 121.84/16.04 (ksndpairEq) =>
% 121.84/16.04 ((
% 121.84/16.04 (kpairsurjEq) =>
% 121.84/16.04 ((
% 121.84/16.04 (cartprodsndin) =>
% 121.84/16.04 ((
% 121.84/16.04 (cartprodpairmemEL) =>
% 121.84/16.04 ((
% 121.84/16.04 (cartprodpairmemER) =>
% 121.84/16.04 ((
% 121.84/16.04 (cartprodmempaircEq) =>
% 121.84/16.04 ((
% 121.84/16.04 (cartprodfstpairEq) =>
% 121.84/16.04 ((
% 121.84/16.04 (cartprodsndpairEq) =>
% 121.84/16.04 ((
% 121.84/16.04 (cartprodpairsurjEq) =>
% 121.84/16.04 ((
% 121.84/16.04 (dpsetconstrI) =>
% 121.84/16.04 ((
% 121.84/16.04 (dpsetconstrSub) =>
% 121.84/16.04 ((
% 121.84/16.04 (setOfPairsIsBReln) =>
% 121.84/16.04 ((
% 121.84/16.04 (dpsetconstrERa) =>
% 121.84/16.04 ((
% 121.84/16.04 (dpsetconstrEL1) =>
% 121.84/16.04 ((
% 121.84/16.04 (dpsetconstrEL2) =>
% 121.84/16.04 ((
% 121.84/16.04 (dpsetconstrER) =>
% 121.84/16.04 ((
% 121.84/16.04 (funcImageSingleton) =>
% 121.84/16.04 ((
% 121.84/16.04 (apProp) =>
% 121.84/16.04 ((
% 121.84/16.04 (app) =>
% 121.84/16.04 ((
% 121.84/16.04 (infuncsetfunc) =>
% 121.84/16.04 ((
% 121.84/16.04 (ap2p) =>
% 121.84/16.04 ((
% 121.84/16.04 (funcinfuncset) =>
% 121.84/16.04 ((
% 121.84/16.04 (lamProp) =>
% 121.84/16.04 ((
% 121.84/16.04 (lamp) =>
% 121.84/16.04 ((
% 121.84/16.04 (lam2p) =>
% 121.84/16.04 ((
% 121.84/16.04 (brelnall1) =>
% 121.84/16.04 ((
% 121.84/16.04 (brelnall2) =>
% 121.84/16.04 ((
% 121.84/16.04 (ex1E2) =>
% 121.84/16.04 ((
% 121.84/16.04 (funcGraphProp1) =>
% 121.84/16.04 ((
% 121.84/16.04 (funcGraphProp3) =>
% 121.84/16.04 ((
% 121.84/16.04 (funcGraphProp2) =>
% 121.84/16.04 ((
% 121.84/16.04 (funcextLem) =>
% 121.84/16.04 ((
% 121.84/16.04 (funcGraphProp4) =>
% 121.84/16.04 ((
% 121.84/16.04 (subbreln) =>
% 121.84/16.04 ((
% 121.84/16.04 (eqbreln) =>
% 121.84/16.04 ((
% 121.84/16.04 (funcext) =>
% 121.84/16.04 ((
% 121.84/16.04 (funcext2) =>
% 121.84/16.04 ((
% 121.84/16.04 (ap2apEq1) =>
% 121.84/16.04 ((
% 121.84/16.04 (ap2apEq2) =>
% 121.84/16.04 ((
% 121.84/16.04 (beta1) =>
% 121.84/16.04 ((
% 121.84/16.04 (eta1) =>
% 121.84/16.04 ((
% 121.84/16.04 (lam2lamEq) =>
% 121.84/16.04 ((
% 121.84/16.04 (beta2) =>
% 121.84/16.04 ((
% 121.84/16.04 (eta2) =>
% 121.84/16.04 ((
% 121.84/16.04 (iffalseProp1) =>
% 121.84/16.04 ((
% 121.84/16.04 (iffalseProp2) =>
% 121.84/16.04 ((
% 121.84/16.04 (iftrueProp1) =>
% 121.84/16.04 ((
% 121.84/16.04 (iftrueProp2) =>
% 121.84/16.04 ((
% 121.84/16.04 (ifSingleton) =>
% 121.84/16.04 ((
% 121.84/16.04 (ifp) =>
% 121.84/16.04 ((
% 121.84/16.04 (theeq) =>
% 121.84/16.04 ((
% 121.84/16.04 (iftrue) =>
% 121.84/16.04 ((
% 121.84/16.04 (iffalse) =>
% 121.84/16.04 ((
% 121.84/16.04 (iftrueorfalse) =>
% 121.84/16.04 ((
% 121.84/16.04 (binintersectT_lem) =>
% 121.84/16.04 ((
% 121.84/16.04 (binunionT_lem) =>
% 121.84/16.04 ((
% 121.84/16.04 (powersetT_lem) =>
% 121.84/16.04 ((
% 121.84/16.04 (setminusT_lem) =>
% 121.84/16.04 ((
% 121.84/16.04 (complementT_lem) =>
% 121.84/16.04 ((
% 121.84/16.04 (setextT) =>
% 121.84/16.04 ((
% 121.84/16.04 (subsetTI) =>
% 121.84/16.04 ((
% 121.84/16.04 (powersetTI1) =>
% 121.84/16.04 ((
% 121.84/16.04 (powersetTE1) =>
% 121.84/16.04 ((
% 121.84/16.04 (complementTI1) =>
% 121.84/16.04 ((
% 121.84/16.04 (complementTE1) =>
% 121.84/16.04 ((
% 121.84/16.04 (binintersectTELcontra) =>
% 121.84/16.04 ((
% 121.84/16.04 (binintersectTERcontra) =>
% 121.84/16.04 ((
% 121.84/16.04 (contrasubsetT) =>
% 121.84/16.04 ((
% 121.84/16.04 (contrasubsetT1) =>
% 121.84/16.04 ((
% 121.84/16.04 (contrasubsetT2) =>
% 121.84/16.04 ((
% 121.84/16.04 (contrasubsetT3) =>
% 121.84/16.04 ((
% 121.84/16.04 (doubleComplementI1) =>
% 121.84/16.04 ((
% 121.84/16.04 (doubleComplementE1) =>
% 121.84/16.04 ((
% 121.84/16.04 (doubleComplementSub1) =>
% 121.84/16.04 ((
% 121.84/16.04 (doubleComplementSub2) =>
% 121.84/16.04 ((
% 121.84/16.04 (doubleComplementEq) =>
% 121.84/16.04 ((
% 121.84/16.04 (complementTnotintersectT) =>
% 121.84/16.04 ((
% 121.84/16.04 (complementImpComplementIntersect) =>
% 121.84/16.04 ((
% 121.84/16.04 (complementSubsetComplementIntersect) =>
% 121.84/16.04 ((
% 121.84/16.04 (complementInPowersetComplementIntersect) =>
% 121.84/16.04 ((
% 121.84/16.04 (contraSubsetComplement) =>
% 121.84/16.04 ((
% 121.84/16.04 (complementTcontraSubset) =>
% 121.84/16.04 ((
% 121.84/16.04 (binunionTILcontra) =>
% 121.84/16.04 ((
% 121.84/16.04 (binunionTIRcontra) =>
% 121.84/16.04 ((
% 121.84/16.04 (inIntersectImpInUnion) =>
% 121.84/16.04 ((
% 121.84/16.04 (inIntersectImpInUnion2) =>
% 121.84/16.04 ((
% 121.84/16.04 (inIntersectImpInIntersectUnions) =>
% 121.84/16.04 ((
% 121.84/16.04 (intersectInPowersetIntersectUnions) =>
% 121.84/16.04 ((
% 121.84/16.04 (inComplementUnionImpNotIn1) =>
% 121.84/16.04 ((
% 121.84/16.04 (inComplementUnionImpInComplement1) =>
% 121.84/16.04 ((
% 121.84/16.04 (binunionTE) =>
% 121.84/16.04 ((
% 121.84/16.04 (binunionTEcontra) =>
% 121.84/16.04 ((
% 121.84/16.04 (demorgan2a1) =>
% 121.84/16.04 ((
% 121.84/16.04 (complementUnionInPowersetComplement) =>
% 121.84/16.04 ((
% 121.84/16.04 (demorgan2a2) =>
% 121.84/16.04 ((
% 121.84/16.04 (demorgan1a) =>
% 121.84/16.04 ((
% 121.84/16.04 (demorgan1b) =>
% 121.84/16.04 ((
% 121.84/16.04 (demorgan1) =>
% 121.84/16.04 ((
% 121.84/16.04 (demorgan2a) =>
% 121.84/16.04 ((
% 121.84/16.04 (demorgan2b2) =>
% 121.84/16.04 ((
% 121.84/16.04 (demorgan2b) =>
% 121.84/16.04 ((
% 121.84/16.04 (demorgan2) =>
% 121.84/16.04 ((
% 121.84/16.04 (woz13rule0) =>
% 121.84/16.04 ((
% 121.84/16.04 (woz13rule1) =>
% 121.84/16.04 ((
% 121.84/16.04 (woz13rule2) =>
% 121.84/16.04 ((
% 121.84/16.04 (woz13rule3) =>
% 121.84/16.04 ((
% 121.84/16.04 (woz13rule4) =>
% 121.84/16.04 ((
% 121.84/16.04 (woz1_1) =>
% 121.84/16.04 ((
% 121.84/16.04 (woz1_2) =>
% 121.84/16.04 ((
% 121.84/16.04 (woz1_3) =>
% 121.84/16.04 ((
% 121.84/16.04 (woz1_4) =>
% 121.84/16.04 ((
% 121.84/16.04 (woz1_5) =>
% 121.84/16.04 ((
% 121.84/16.04 (breln1all2) =>
% 121.84/16.04 ((
% 121.84/16.04 (breln1SetBreln1) =>
% 121.84/16.04 ((
% 121.84/16.04 (choice2fnsingleton) =>
% 121.84/16.04 ((
% 121.84/16.04 (setOfPairsIsBReln1) =>
% 121.84/16.04 ((
% 121.84/16.04 (breln1all1) =>
% 121.84/16.04 ((
% 121.84/16.04 (subbreln1) =>
% 121.84/16.04 ((
% 121.84/16.04 (eqbreln1) =>
% 121.84/16.04 ((
% 121.84/16.04 (breln1invprop) =>
% 121.84/16.04 ((
% 121.84/16.04 (breln1invI) =>
% 121.84/16.04 ((
% 121.84/16.04 (breln1invE) =>
% 121.84/16.04 ((
% 121.84/16.04 (breln1compprop) =>
% 121.84/16.04 ((
% 121.84/16.04 (breln1compI) =>
% 121.84/16.04 ((
% 121.84/16.04 (breln1compE) =>
% 121.84/16.04 ((
% 121.84/16.04 (breln1compEex) =>
% 121.84/16.04 ((
% 121.84/16.04 (breln1unionprop) =>
% 121.84/16.04 ((
% 121.84/16.04 (breln1unionIL) =>
% 121.84/16.04 ((
% 121.84/16.04 (breln1unionIR) =>
% 121.84/16.04 ((
% 121.84/16.04 (breln1unionI) =>
% 121.84/16.04 ((
% 121.84/16.04 (breln1unionE) =>
% 121.84/16.04 ((
% 121.84/16.04 (breln1unionEcases) =>
% 121.84/16.04 ((
% 121.84/16.04 (breln1unionCommutes) =>
% 121.84/16.04 ((
% 121.84/16.04 (woz2Ex) =>
% 121.84/16.04 ((
% 121.84/16.04 (woz2W) =>
% 121.84/16.04 ((
% 121.84/16.04 (woz2A) =>
% 121.84/16.04 ((
% 121.84/16.04 (woz2B) =>
% 121.84/16.04 ((
% 121.84/16.04 (image1Ex) =>
% 121.84/16.04 ((
% 121.84/16.04 (image1Ex1) =>
% 121.84/16.04 ((
% 121.84/16.04 (image1Equiv) =>
% 121.84/16.04 ((
% 121.84/16.04 (image1E) =>
% 121.84/16.04 ((
% 121.84/16.04 (image1I) =>
% 121.84/16.04 ((
% 121.84/16.04 (injFuncInInjFuncSet) =>
% 121.84/16.04 ((
% 121.84/16.04 (!!) @ (
% 121.84/16.04 (('#B') @ (
% 121.84/16.04 !!) @
% 121.84/16.04 (
% 121.84/16.04 (
% 121.84/16.04 ('#B') @ (
% 121.84/16.04 (
% 121.84/16.04 ('#B') @ (
% 121.84/16.04 !!))) @
% 121.84/16.04 (
% 121.84/16.04 (
% 121.84/16.04 ('#S') @ (
% 121.84/16.04 (
% 121.84/16.04 ('#B') @ (
% 121.84/16.04 '#S') @
% 121.84/16.04 (
% 121.84/16.04 (
% 121.84/16.04 ('#B') @ (
% 121.84/16.04 (
% 121.84/16.04 ('#B') @ (
% 121.84/16.04 '#S'))) @
% 121.84/16.04 (
% 121.84/16.04 (
% 121.84/16.04 ('#B') @ (
% 121.84/16.04 (
% 121.84/16.04 ('#B') @ (
% 121.84/16.04 (
% 121.84/16.04 ('#B') @ (
% 121.84/16.04 =>))))) @
% 121.84/16.04 (
% 121.84/16.04 (
% 121.84/16.04 ('#B') @ (
% 121.84/16.04 (
% 121.84/16.04 ('#B') @ (
% 121.84/16.04 (
% 121.84/16.04 ('#C') @ in)))) @
% 121.84/16.04 injFuncSet)))))))) @
% 121.84/16.04 (
% 121.84/16.04 (
% 121.84/16.04 ('#B') @ (
% 121.84/16.04 (
% 121.84/16.04 ('#B') @ (
% 121.84/16.04 (
% 121.84/16.04 ('#C') @ in)))) @
% 121.84/16.04 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 121.84/16.04 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl337])).
% 121.84/16.04 thf(zip_derived_cl355, plain,
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% 121.84/16.04 (((emptyInPowerset) =>
% 121.84/16.04 (((powersetE) =>
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% 121.84/16.04 (((setunionE) =>
% 121.84/16.04 (((subPowSU) =>
% 121.84/16.04 (((exuE2) =>
% 121.84/16.04 (((nonemptyImpWitness) =>
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% 121.84/16.04 (((notinsingleton) =>
% 121.84/16.04 (((eqinunit) =>
% 121.84/16.04 (((singletonsswitch) =>
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% 121.84/16.04 (((upairsetIL) =>
% 121.84/16.04 (((upairsetIR) =>
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% 121.84/16.04 (((quantDeMorgan1) =>
% 121.84/16.04 (((quantDeMorgan2) =>
% 121.84/16.04 (((quantDeMorgan3) =>
% 121.84/16.04 (((quantDeMorgan4) =>
% 121.84/16.04 (((prop2setI) =>
% 121.84/16.04 (((prop2set2propI) =>
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% 121.84/16.04 (((notdallE) =>
% 121.84/16.04 (((exuI1) =>
% 121.84/16.04 (((exuI3) =>
% 121.84/16.04 ((
% 121.84/16.04 (exuI2) =>
% 121.84/16.04 ((
% 121.84/16.04 (inCongP) =>
% 121.84/16.04 ((
% 121.84/16.04 (in__Cong) =>
% 121.84/16.04 ((
% 121.84/16.04 (exuE3u) =>
% 121.84/16.04 ((
% 121.84/16.04 (exu__Cong) =>
% 121.84/16.04 ((
% 121.84/16.04 (setadjoin__Cong) =>
% 121.84/16.04 ((
% 121.84/16.04 (powerset__Cong) =>
% 121.84/16.04 ((
% 121.84/16.04 (setunion__Cong) =>
% 121.84/16.04 ((
% 121.84/16.04 (exuEu) =>
% 121.84/16.04 ((
% 121.84/16.04 (descr__Cong) =>
% 121.84/16.04 ((
% 121.84/16.04 (dsetconstr__Cong) =>
% 121.84/16.04 ((
% 121.84/16.04 (subsetI1) =>
% 121.84/16.04 ((
% 121.84/16.04 (eqimpsubset2) =>
% 121.84/16.04 ((
% 121.84/16.04 (eqimpsubset1) =>
% 121.84/16.04 ((
% 121.84/16.04 (subsetI2) =>
% 121.84/16.04 ((
% 121.84/16.04 (emptysetsubset) =>
% 121.84/16.04 ((
% 121.84/16.04 (subsetE) =>
% 121.84/16.04 ((
% 121.84/16.04 (subsetE2) =>
% 121.84/16.04 ((
% 121.84/16.04 (notsubsetI) =>
% 121.84/16.04 ((
% 121.84/16.04 (notequalI1) =>
% 121.84/16.04 ((
% 121.84/16.04 (notequalI2) =>
% 121.84/16.04 ((
% 121.84/16.04 (subsetRefl) =>
% 121.84/16.04 ((
% 121.84/16.04 (subsetTrans) =>
% 121.84/16.04 ((
% 121.84/16.04 (setadjoinSub) =>
% 121.84/16.04 ((
% 121.84/16.04 (setadjoinSub2) =>
% 121.84/16.04 ((
% 121.84/16.04 (subset2powerset) =>
% 121.84/16.04 ((
% 121.84/16.04 (setextsub) =>
% 121.84/16.04 ((
% 121.84/16.04 (subsetemptysetimpeq) =>
% 121.84/16.04 ((
% 121.84/16.04 (powersetI1) =>
% 121.84/16.04 ((
% 121.84/16.04 (powersetE1) =>
% 121.84/16.04 ((
% 121.84/16.04 (inPowerset) =>
% 121.84/16.04 ((
% 121.84/16.04 (powersetsubset) =>
% 121.84/16.04 ((
% 121.84/16.04 (sepInPowerset) =>
% 121.84/16.04 ((
% 121.84/16.04 (sepSubset) =>
% 121.84/16.04 ((
% 121.84/16.04 (binunionIL) =>
% 121.84/16.04 ((
% 121.84/16.04 (upairset2IR) =>
% 121.84/16.04 ((
% 121.84/16.04 (binunionIR) =>
% 121.84/16.04 ((
% 121.84/16.04 (binunionEcases) =>
% 121.84/16.04 ((
% 121.84/16.04 (binunionE) =>
% 121.84/16.04 ((
% 121.84/16.04 (binunionLsub) =>
% 121.84/16.04 ((
% 121.84/16.04 (binunionRsub) =>
% 121.84/16.04 ((
% 121.84/16.04 (binintersectI) =>
% 121.84/16.04 ((
% 121.84/16.04 (binintersectSubset5) =>
% 121.84/16.04 ((
% 121.84/16.04 (binintersectEL) =>
% 121.84/16.04 ((
% 121.84/16.04 (binintersectLsub) =>
% 121.84/16.04 ((
% 121.84/16.04 (binintersectSubset2) =>
% 121.84/16.04 ((
% 121.84/16.04 (binintersectSubset3) =>
% 121.84/16.04 ((
% 121.84/16.04 (binintersectER) =>
% 121.84/16.04 ((
% 121.84/16.04 (disjointsetsI1) =>
% 121.84/16.04 ((
% 121.84/16.04 (binintersectRsub) =>
% 121.84/16.04 ((
% 121.84/16.04 (binintersectSubset4) =>
% 121.84/16.04 ((
% 121.84/16.04 (binintersectSubset1) =>
% 121.84/16.04 ((
% 121.84/16.04 (bs114d) =>
% 121.84/16.04 ((
% 121.84/16.04 (setminusI) =>
% 121.84/16.04 ((
% 121.84/16.04 (setminusEL) =>
% 121.84/16.04 ((
% 121.84/16.04 (setminusER) =>
% 121.84/16.04 ((
% 121.84/16.04 (setminusSubset2) =>
% 121.84/16.04 ((
% 121.84/16.04 (setminusERneg) =>
% 121.84/16.04 ((
% 121.84/16.04 (setminusELneg) =>
% 121.84/16.04 ((
% 121.84/16.04 (setminusILneg) =>
% 121.84/16.04 ((
% 121.84/16.04 (setminusIRneg) =>
% 121.84/16.04 ((
% 121.84/16.04 (setminusLsub) =>
% 121.84/16.04 ((
% 121.84/16.04 (setminusSubset1) =>
% 121.84/16.04 ((
% 121.84/16.04 (symdiffE) =>
% 121.84/16.04 ((
% 121.84/16.04 (symdiffI1) =>
% 121.84/16.04 ((
% 121.84/16.04 (symdiffI2) =>
% 121.84/16.04 ((
% 121.84/16.04 (symdiffIneg1) =>
% 121.84/16.04 ((
% 121.84/16.04 (symdiffIneg2) =>
% 121.84/16.04 ((
% 121.84/16.04 (secondinupair) =>
% 121.84/16.04 ((
% 121.84/16.04 (setukpairIL) =>
% 121.84/16.04 ((
% 121.84/16.04 (setukpairIR) =>
% 121.84/16.04 ((
% 121.84/16.04 (kpairiskpair) =>
% 121.84/16.04 ((
% 121.84/16.04 (kpairp) =>
% 121.84/16.04 ((
% 121.84/16.04 (singletonsubset) =>
% 121.84/16.04 ((
% 121.84/16.04 (singletoninpowerset) =>
% 121.84/16.04 ((
% 121.84/16.04 (singletoninpowunion) =>
% 121.84/16.04 ((
% 121.84/16.04 (upairset2E) =>
% 121.84/16.04 ((
% 121.84/16.04 (upairsubunion) =>
% 121.84/16.04 ((
% 121.84/16.04 (upairinpowunion) =>
% 121.84/16.04 ((
% 121.84/16.04 (ubforcartprodlem1) =>
% 121.84/16.04 ((
% 121.84/16.04 (ubforcartprodlem2) =>
% 121.84/16.04 ((
% 121.84/16.04 (ubforcartprodlem3) =>
% 121.84/16.04 ((
% 121.84/16.04 (cartprodpairin) =>
% 121.84/16.04 ((
% 121.84/16.04 (cartprodmempair1) =>
% 121.84/16.04 ((
% 121.84/16.04 (cartprodmempair) =>
% 121.84/16.04 ((
% 121.84/16.04 (setunionE2) =>
% 121.84/16.04 ((
% 121.84/16.04 (setunionsingleton1) =>
% 121.84/16.04 ((
% 121.84/16.04 (setunionsingleton2) =>
% 121.84/16.04 ((
% 121.84/16.04 (setunionsingleton) =>
% 121.84/16.04 ((
% 121.84/16.04 (singletonprop) =>
% 121.84/16.04 ((
% 121.84/16.04 (ex1E1) =>
% 121.84/16.04 ((
% 121.84/16.04 (ex1I) =>
% 121.84/16.04 ((
% 121.84/16.04 (ex1I2) =>
% 121.84/16.04 ((
% 121.84/16.04 (singletonsuniq) =>
% 121.84/16.04 ((
% 121.84/16.04 (setukpairinjL1) =>
% 121.84/16.04 ((
% 121.84/16.04 (kfstsingleton) =>
% 121.84/16.04 ((
% 121.84/16.04 (theprop) =>
% 121.84/16.04 ((
% 121.84/16.04 (kfstpairEq) =>
% 121.84/16.04 ((
% 121.84/16.04 (cartprodfstin) =>
% 121.84/16.04 ((
% 121.84/16.04 (setukpairinjL2) =>
% 121.84/16.04 ((
% 121.84/16.04 (setukpairinjL) =>
% 121.84/16.04 ((
% 121.84/16.04 (setukpairinjR11) =>
% 121.84/16.04 ((
% 121.84/16.04 (setukpairinjR12) =>
% 121.84/16.04 ((
% 121.84/16.04 (setukpairinjR1) =>
% 121.84/16.04 ((
% 121.84/16.04 (upairequniteq) =>
% 121.84/16.04 ((
% 121.84/16.04 (setukpairinjR2) =>
% 121.84/16.04 ((
% 121.84/16.04 (setukpairinjR) =>
% 121.84/16.04 ((
% 121.84/16.04 (ksndsingleton) =>
% 121.84/16.04 ((
% 121.84/16.04 (ksndpairEq) =>
% 121.84/16.04 ((
% 121.84/16.04 (kpairsurjEq) =>
% 121.84/16.04 ((
% 121.84/16.04 (cartprodsndin) =>
% 121.84/16.04 ((
% 121.84/16.04 (cartprodpairmemEL) =>
% 121.84/16.04 ((
% 121.84/16.04 (cartprodpairmemER) =>
% 121.84/16.04 ((
% 121.84/16.04 (cartprodmempaircEq) =>
% 121.84/16.04 ((
% 121.84/16.04 (cartprodfstpairEq) =>
% 121.84/16.04 ((
% 121.84/16.04 (cartprodsndpairEq) =>
% 121.84/16.04 ((
% 121.84/16.04 (cartprodpairsurjEq) =>
% 121.84/16.04 ((
% 121.84/16.04 (dpsetconstrI) =>
% 121.84/16.04 ((
% 121.84/16.04 (dpsetconstrSub) =>
% 121.84/16.04 ((
% 121.84/16.04 (setOfPairsIsBReln) =>
% 121.84/16.04 ((
% 121.84/16.04 (dpsetconstrERa) =>
% 121.84/16.04 ((
% 121.84/16.04 (dpsetconstrEL1) =>
% 121.84/16.04 ((
% 121.84/16.04 (dpsetconstrEL2) =>
% 121.84/16.04 ((
% 121.84/16.04 (dpsetconstrER) =>
% 121.84/16.04 ((
% 121.84/16.04 (funcImageSingleton) =>
% 121.84/16.04 ((
% 121.84/16.04 (apProp) =>
% 121.84/16.04 ((
% 121.84/16.04 (app) =>
% 121.84/16.04 ((
% 121.84/16.04 (infuncsetfunc) =>
% 121.84/16.04 ((
% 121.84/16.04 (ap2p) =>
% 121.84/16.04 ((
% 121.84/16.04 (funcinfuncset) =>
% 121.84/16.04 ((
% 121.84/16.04 (lamProp) =>
% 121.84/16.04 ((
% 121.84/16.04 (lamp) =>
% 121.84/16.04 ((
% 121.84/16.04 (lam2p) =>
% 121.84/16.04 ((
% 121.84/16.04 (brelnall1) =>
% 121.84/16.04 ((
% 121.84/16.04 (brelnall2) =>
% 121.84/16.04 ((
% 121.84/16.04 (ex1E2) =>
% 121.84/16.04 ((
% 121.84/16.04 (funcGraphProp1) =>
% 121.84/16.04 ((
% 121.84/16.04 (funcGraphProp3) =>
% 121.84/16.04 ((
% 121.84/16.04 (funcGraphProp2) =>
% 121.84/16.04 ((
% 121.84/16.04 (funcextLem) =>
% 121.84/16.04 ((
% 121.84/16.04 (funcGraphProp4) =>
% 121.84/16.04 ((
% 121.84/16.04 (subbreln) =>
% 121.84/16.04 ((
% 121.84/16.04 (eqbreln) =>
% 121.84/16.04 ((
% 121.84/16.04 (funcext) =>
% 121.84/16.04 ((
% 121.84/16.04 (funcext2) =>
% 121.84/16.04 ((
% 121.84/16.04 (ap2apEq1) =>
% 121.84/16.04 ((
% 121.84/16.04 (ap2apEq2) =>
% 121.84/16.04 ((
% 121.84/16.04 (beta1) =>
% 121.84/16.04 ((
% 121.84/16.04 (eta1) =>
% 121.84/16.04 ((
% 121.84/16.04 (lam2lamEq) =>
% 121.84/16.04 ((
% 121.84/16.04 (beta2) =>
% 121.84/16.04 ((
% 121.84/16.04 (eta2) =>
% 121.84/16.04 ((
% 121.84/16.04 (iffalseProp1) =>
% 121.84/16.04 ((
% 121.84/16.04 (iffalseProp2) =>
% 121.84/16.04 ((
% 121.84/16.04 (iftrueProp1) =>
% 121.84/16.04 ((
% 121.84/16.04 (iftrueProp2) =>
% 121.84/16.04 ((
% 121.84/16.04 (ifSingleton) =>
% 121.84/16.04 ((
% 121.84/16.04 (ifp) =>
% 121.84/16.04 ((
% 121.84/16.04 (theeq) =>
% 121.84/16.04 ((
% 121.84/16.04 (iftrue) =>
% 121.84/16.04 ((
% 121.84/16.04 (iffalse) =>
% 121.84/16.04 ((
% 121.84/16.04 (iftrueorfalse) =>
% 121.84/16.04 ((
% 121.84/16.04 (binintersectT_lem) =>
% 121.84/16.04 ((
% 121.84/16.04 (binunionT_lem) =>
% 121.84/16.04 ((
% 121.84/16.04 (powersetT_lem) =>
% 121.84/16.04 ((
% 121.84/16.04 (setminusT_lem) =>
% 121.84/16.04 ((
% 121.84/16.04 (complementT_lem) =>
% 121.84/16.04 ((
% 121.84/16.04 (setextT) =>
% 121.84/16.04 ((
% 121.84/16.04 (subsetTI) =>
% 121.84/16.04 ((
% 121.84/16.04 (powersetTI1) =>
% 121.84/16.04 ((
% 121.84/16.04 (powersetTE1) =>
% 121.84/16.04 ((
% 121.84/16.04 (complementTI1) =>
% 121.84/16.04 ((
% 121.84/16.04 (complementTE1) =>
% 121.84/16.04 ((
% 121.84/16.04 (binintersectTELcontra) =>
% 121.84/16.04 ((
% 121.84/16.04 (binintersectTERcontra) =>
% 121.84/16.04 ((
% 121.84/16.04 (contrasubsetT) =>
% 121.84/16.04 ((
% 121.84/16.04 (contrasubsetT1) =>
% 121.84/16.04 ((
% 121.84/16.04 (contrasubsetT2) =>
% 121.84/16.04 ((
% 121.84/16.04 (contrasubsetT3) =>
% 121.84/16.04 ((
% 121.84/16.04 (doubleComplementI1) =>
% 121.84/16.04 ((
% 121.84/16.04 (doubleComplementE1) =>
% 121.84/16.04 ((
% 121.84/16.04 (doubleComplementSub1) =>
% 121.84/16.04 ((
% 121.84/16.04 (doubleComplementSub2) =>
% 121.84/16.04 ((
% 121.84/16.04 (doubleComplementEq) =>
% 121.84/16.04 ((
% 121.84/16.04 (complementTnotintersectT) =>
% 121.84/16.04 ((
% 121.84/16.04 (complementImpComplementIntersect) =>
% 121.84/16.04 ((
% 121.84/16.04 (complementSubsetComplementIntersect) =>
% 121.84/16.04 ((
% 121.84/16.04 (complementInPowersetComplementIntersect) =>
% 121.84/16.04 ((
% 121.84/16.04 (contraSubsetComplement) =>
% 121.84/16.04 ((
% 121.84/16.04 (complementTcontraSubset) =>
% 121.84/16.04 ((
% 121.84/16.04 (binunionTILcontra) =>
% 121.84/16.04 ((
% 121.84/16.04 (binunionTIRcontra) =>
% 121.84/16.04 ((
% 121.84/16.04 (inIntersectImpInUnion) =>
% 121.84/16.04 ((
% 121.84/16.04 (inIntersectImpInUnion2) =>
% 121.84/16.04 ((
% 121.84/16.04 (inIntersectImpInIntersectUnions) =>
% 121.84/16.04 ((
% 121.84/16.04 (intersectInPowersetIntersectUnions) =>
% 121.84/16.04 ((
% 121.84/16.04 (inComplementUnionImpNotIn1) =>
% 121.84/16.04 ((
% 121.84/16.04 (inComplementUnionImpInComplement1) =>
% 121.84/16.04 ((
% 121.84/16.04 (binunionTE) =>
% 121.84/16.04 ((
% 121.84/16.04 (binunionTEcontra) =>
% 121.84/16.04 ((
% 121.84/16.04 (demorgan2a1) =>
% 121.84/16.04 ((
% 121.84/16.04 (complementUnionInPowersetComplement) =>
% 121.84/16.04 ((
% 121.84/16.04 (demorgan2a2) =>
% 121.84/16.04 ((
% 121.84/16.04 (demorgan1a) =>
% 121.84/16.04 ((
% 121.84/16.04 (demorgan1b) =>
% 121.84/16.04 ((
% 121.84/16.04 (demorgan1) =>
% 121.84/16.04 ((
% 121.84/16.04 (demorgan2a) =>
% 121.84/16.04 ((
% 121.84/16.04 (demorgan2b2) =>
% 121.84/16.04 ((
% 121.84/16.04 (demorgan2b) =>
% 121.84/16.04 ((
% 121.84/16.04 (demorgan2) =>
% 121.84/16.04 ((
% 121.84/16.04 (woz13rule0) =>
% 121.84/16.04 ((
% 121.84/16.04 (woz13rule1) =>
% 121.84/16.04 ((
% 121.84/16.04 (woz13rule2) =>
% 121.84/16.04 ((
% 121.84/16.04 (woz13rule3) =>
% 121.84/16.04 ((
% 121.84/16.04 (woz13rule4) =>
% 121.84/16.04 ((
% 121.84/16.04 (woz1_1) =>
% 121.84/16.04 ((
% 121.84/16.04 (woz1_2) =>
% 121.84/16.04 ((
% 121.84/16.04 (woz1_3) =>
% 121.84/16.04 ((
% 121.84/16.04 (woz1_4) =>
% 121.84/16.04 ((
% 121.84/16.04 (woz1_5) =>
% 121.84/16.04 ((
% 121.84/16.04 (breln1all2) =>
% 121.84/16.04 ((
% 121.84/16.04 (breln1SetBreln1) =>
% 121.84/16.04 ((
% 121.84/16.04 (choice2fnsingleton) =>
% 121.84/16.04 ((
% 121.84/16.04 (setOfPairsIsBReln1) =>
% 121.84/16.04 ((
% 121.84/16.04 (breln1all1) =>
% 121.84/16.04 ((
% 121.84/16.04 (subbreln1) =>
% 121.84/16.04 ((
% 121.84/16.04 (eqbreln1) =>
% 121.84/16.04 ((
% 121.84/16.04 (breln1invprop) =>
% 121.84/16.04 ((
% 121.84/16.04 (breln1invI) =>
% 121.84/16.04 ((
% 121.84/16.04 (breln1invE) =>
% 121.84/16.04 ((
% 121.84/16.04 (breln1compprop) =>
% 121.84/16.04 ((
% 121.84/16.04 (breln1compI) =>
% 121.84/16.04 ((
% 121.84/16.04 (breln1compE) =>
% 121.84/16.04 ((
% 121.84/16.04 (breln1compEex) =>
% 121.84/16.04 ((
% 121.84/16.04 (breln1unionprop) =>
% 121.84/16.04 ((
% 121.84/16.04 (breln1unionIL) =>
% 121.84/16.04 ((
% 121.84/16.04 (breln1unionIR) =>
% 121.84/16.04 ((
% 121.84/16.04 (breln1unionI) =>
% 121.84/16.04 ((
% 121.84/16.04 (breln1unionE) =>
% 121.84/16.04 ((
% 121.84/16.04 (breln1unionEcases) =>
% 121.84/16.04 ((
% 121.84/16.04 (breln1unionCommutes) =>
% 121.84/16.04 ((
% 121.84/16.04 (woz2Ex) =>
% 121.84/16.04 ((
% 121.84/16.04 (woz2W) =>
% 121.84/16.04 ((
% 121.84/16.04 (woz2A) =>
% 121.84/16.04 ((
% 121.84/16.04 (woz2B) =>
% 121.84/16.04 ((
% 121.84/16.04 (image1Ex) =>
% 121.84/16.04 ((
% 121.84/16.04 (image1Ex1) =>
% 121.84/16.04 ((
% 121.84/16.04 (image1Equiv) =>
% 121.84/16.04 ((
% 121.84/16.04 (image1E) =>
% 121.84/16.04 ((
% 121.84/16.04 (image1I) =>
% 121.84/16.04 ((
% 121.84/16.04 (injFuncInInjFuncSet) =>
% 121.84/16.04 ((
% 121.84/16.04 (!!) @ (
% 121.84/16.04 (('#B') @ (
% 121.84/16.04 !!) @
% 121.84/16.04 (
% 121.84/16.04 (
% 121.84/16.04 ('#B') @ (
% 121.84/16.04 (
% 121.84/16.04 ('#B') @ (
% 121.84/16.04 !!))) @
% 121.84/16.04 (
% 121.84/16.04 (
% 121.84/16.04 ('#S') @ (
% 121.84/16.04 (
% 121.84/16.04 ('#B') @ (
% 121.84/16.04 '#S') @
% 121.84/16.04 (
% 121.84/16.04 (
% 121.84/16.04 ('#B') @ (
% 121.84/16.04 (
% 121.84/16.04 ('#B') @ (
% 121.84/16.04 '#S'))) @
% 121.84/16.04 (
% 121.84/16.04 (
% 121.84/16.04 ('#B') @ (
% 121.84/16.04 (
% 121.84/16.04 ('#B') @ (
% 121.84/16.04 (
% 121.84/16.04 ('#B') @ (
% 121.84/16.04 =>))))) @
% 121.84/16.04 (
% 121.84/16.04 (
% 121.84/16.04 ('#B') @ (
% 121.84/16.04 (
% 121.84/16.04 ('#B') @ (
% 121.84/16.04 (
% 121.84/16.04 ('#C') @ in)))) @
% 121.84/16.04 injFuncSet)))))))) @
% 121.84/16.04 (
% 121.84/16.04 (
% 121.84/16.04 ('#B') @ (
% 121.84/16.04 (
% 121.84/16.04 ('#B') @ (
% 121.84/16.04 (
% 121.84/16.04 ('#C') @ in)))) @
% 121.84/16.04 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 121.84/16.04 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl349])).
% 121.84/16.04 thf(zip_derived_cl362, plain,
% 121.84/16.04 (~ (((setoftrueEq) =>
% 121.84/16.04 (((powersetI) =>
% 121.84/16.04 (((emptyinPowerset) =>
% 121.84/16.04 (((emptyInPowerset) =>
% 121.84/16.04 (((powersetE) =>
% 121.84/16.04 (((setunionI) =>
% 121.84/16.04 (((setunionE) =>
% 121.84/16.04 (((subPowSU) =>
% 121.84/16.04 (((exuE2) =>
% 121.84/16.04 (((nonemptyImpWitness) =>
% 121.84/16.04 (((uniqinunit) =>
% 121.84/16.04 (((notinsingleton) =>
% 121.84/16.04 (((eqinunit) =>
% 121.84/16.04 (((singletonsswitch) =>
% 121.84/16.04 (((upairsetE) =>
% 121.84/16.04 (((upairsetIL) =>
% 121.84/16.04 (((upairsetIR) =>
% 121.84/16.04 (((emptyE1) =>
% 121.84/16.04 (((vacuousDall) =>
% 121.84/16.04 (((quantDeMorgan1) =>
% 121.84/16.04 (((quantDeMorgan2) =>
% 121.84/16.04 (((quantDeMorgan3) =>
% 121.84/16.04 (((quantDeMorgan4) =>
% 121.84/16.04 (((prop2setI) =>
% 121.84/16.04 (((prop2set2propI) =>
% 121.84/16.04 (((notdexE) =>
% 121.84/16.04 (((notdallE) =>
% 121.84/16.04 (((exuI1) =>
% 121.84/16.04 (((exuI3) =>
% 121.84/16.04 (((exuI2) =>
% 121.84/16.04 ((
% 121.84/16.04 (inCongP) =>
% 121.84/16.04 ((
% 121.84/16.04 (in__Cong) =>
% 121.84/16.04 ((
% 121.84/16.04 (exuE3u) =>
% 121.84/16.04 ((
% 121.84/16.04 (exu__Cong) =>
% 121.84/16.04 ((
% 121.84/16.04 (setadjoin__Cong) =>
% 121.84/16.04 ((
% 121.84/16.04 (powerset__Cong) =>
% 121.84/16.04 ((
% 121.84/16.04 (setunion__Cong) =>
% 121.84/16.04 ((
% 121.84/16.04 (exuEu) =>
% 121.84/16.04 ((
% 121.84/16.04 (descr__Cong) =>
% 121.84/16.04 ((
% 121.84/16.04 (dsetconstr__Cong) =>
% 121.84/16.04 ((
% 121.84/16.04 (subsetI1) =>
% 121.84/16.04 ((
% 121.84/16.04 (eqimpsubset2) =>
% 121.84/16.04 ((
% 121.84/16.04 (eqimpsubset1) =>
% 121.84/16.04 ((
% 121.84/16.04 (subsetI2) =>
% 121.84/16.04 ((
% 121.84/16.04 (emptysetsubset) =>
% 121.84/16.04 ((
% 121.84/16.04 (subsetE) =>
% 121.84/16.04 ((
% 121.84/16.04 (subsetE2) =>
% 121.84/16.04 ((
% 121.84/16.04 (notsubsetI) =>
% 121.84/16.04 ((
% 121.84/16.04 (notequalI1) =>
% 121.84/16.04 ((
% 121.84/16.04 (notequalI2) =>
% 121.84/16.04 ((
% 121.84/16.04 (subsetRefl) =>
% 121.84/16.04 ((
% 121.84/16.04 (subsetTrans) =>
% 121.84/16.04 ((
% 121.84/16.04 (setadjoinSub) =>
% 121.84/16.04 ((
% 121.84/16.04 (setadjoinSub2) =>
% 121.84/16.04 ((
% 121.84/16.04 (subset2powerset) =>
% 121.84/16.04 ((
% 121.84/16.04 (setextsub) =>
% 121.84/16.04 ((
% 121.84/16.04 (subsetemptysetimpeq) =>
% 121.84/16.04 ((
% 121.84/16.04 (powersetI1) =>
% 121.84/16.04 ((
% 121.84/16.04 (powersetE1) =>
% 121.84/16.04 ((
% 121.84/16.04 (inPowerset) =>
% 121.84/16.04 ((
% 121.84/16.04 (powersetsubset) =>
% 121.84/16.04 ((
% 121.84/16.04 (sepInPowerset) =>
% 121.84/16.04 ((
% 121.84/16.04 (sepSubset) =>
% 121.84/16.04 ((
% 121.84/16.04 (binunionIL) =>
% 121.84/16.04 ((
% 121.84/16.04 (upairset2IR) =>
% 121.84/16.04 ((
% 121.84/16.04 (binunionIR) =>
% 121.84/16.04 ((
% 121.84/16.04 (binunionEcases) =>
% 121.84/16.04 ((
% 121.84/16.04 (binunionE) =>
% 121.84/16.04 ((
% 121.84/16.04 (binunionLsub) =>
% 121.84/16.04 ((
% 121.84/16.04 (binunionRsub) =>
% 121.84/16.04 ((
% 121.84/16.04 (binintersectI) =>
% 121.84/16.04 ((
% 121.84/16.04 (binintersectSubset5) =>
% 121.84/16.04 ((
% 121.84/16.04 (binintersectEL) =>
% 121.84/16.04 ((
% 121.84/16.04 (binintersectLsub) =>
% 121.84/16.04 ((
% 121.84/16.04 (binintersectSubset2) =>
% 121.84/16.04 ((
% 121.84/16.04 (binintersectSubset3) =>
% 121.84/16.04 ((
% 121.84/16.04 (binintersectER) =>
% 121.84/16.04 ((
% 121.84/16.04 (disjointsetsI1) =>
% 121.84/16.04 ((
% 121.84/16.04 (binintersectRsub) =>
% 121.84/16.04 ((
% 121.84/16.04 (binintersectSubset4) =>
% 121.84/16.04 ((
% 121.84/16.04 (binintersectSubset1) =>
% 121.84/16.04 ((
% 121.84/16.04 (bs114d) =>
% 121.84/16.04 ((
% 121.84/16.04 (setminusI) =>
% 121.84/16.04 ((
% 121.84/16.04 (setminusEL) =>
% 121.84/16.04 ((
% 121.84/16.04 (setminusER) =>
% 121.84/16.04 ((
% 121.84/16.04 (setminusSubset2) =>
% 121.84/16.04 ((
% 121.84/16.04 (setminusERneg) =>
% 121.84/16.04 ((
% 121.84/16.04 (setminusELneg) =>
% 121.84/16.04 ((
% 121.84/16.04 (setminusILneg) =>
% 121.84/16.04 ((
% 121.84/16.04 (setminusIRneg) =>
% 121.84/16.04 ((
% 121.84/16.04 (setminusLsub) =>
% 121.84/16.04 ((
% 121.84/16.04 (setminusSubset1) =>
% 121.84/16.04 ((
% 121.84/16.04 (symdiffE) =>
% 121.84/16.04 ((
% 121.84/16.04 (symdiffI1) =>
% 121.84/16.04 ((
% 121.84/16.04 (symdiffI2) =>
% 121.84/16.04 ((
% 121.84/16.04 (symdiffIneg1) =>
% 121.84/16.04 ((
% 121.84/16.04 (symdiffIneg2) =>
% 121.84/16.04 ((
% 121.84/16.04 (secondinupair) =>
% 121.84/16.04 ((
% 121.84/16.04 (setukpairIL) =>
% 121.84/16.04 ((
% 121.84/16.04 (setukpairIR) =>
% 121.84/16.04 ((
% 121.84/16.04 (kpairiskpair) =>
% 121.84/16.04 ((
% 121.84/16.04 (kpairp) =>
% 121.84/16.04 ((
% 121.84/16.04 (singletonsubset) =>
% 121.84/16.04 ((
% 121.84/16.04 (singletoninpowerset) =>
% 121.84/16.04 ((
% 121.84/16.04 (singletoninpowunion) =>
% 121.84/16.04 ((
% 121.84/16.04 (upairset2E) =>
% 121.84/16.04 ((
% 121.84/16.04 (upairsubunion) =>
% 121.84/16.04 ((
% 121.84/16.04 (upairinpowunion) =>
% 121.84/16.04 ((
% 121.84/16.04 (ubforcartprodlem1) =>
% 121.84/16.04 ((
% 121.84/16.04 (ubforcartprodlem2) =>
% 121.84/16.04 ((
% 121.84/16.04 (ubforcartprodlem3) =>
% 121.84/16.04 ((
% 121.84/16.04 (cartprodpairin) =>
% 121.84/16.04 ((
% 121.84/16.04 (cartprodmempair1) =>
% 121.84/16.04 ((
% 121.84/16.04 (cartprodmempair) =>
% 121.84/16.04 ((
% 121.84/16.04 (setunionE2) =>
% 121.84/16.04 ((
% 121.84/16.04 (setunionsingleton1) =>
% 121.84/16.04 ((
% 121.84/16.04 (setunionsingleton2) =>
% 121.84/16.04 ((
% 121.84/16.04 (setunionsingleton) =>
% 121.84/16.04 ((
% 121.84/16.04 (singletonprop) =>
% 121.84/16.04 ((
% 121.84/16.04 (ex1E1) =>
% 121.84/16.04 ((
% 121.84/16.04 (ex1I) =>
% 121.84/16.04 ((
% 121.84/16.04 (ex1I2) =>
% 121.84/16.04 ((
% 121.84/16.04 (singletonsuniq) =>
% 121.84/16.04 ((
% 121.84/16.04 (setukpairinjL1) =>
% 121.84/16.04 ((
% 121.84/16.04 (kfstsingleton) =>
% 121.84/16.04 ((
% 121.84/16.04 (theprop) =>
% 121.84/16.04 ((
% 121.84/16.04 (kfstpairEq) =>
% 121.84/16.04 ((
% 121.84/16.04 (cartprodfstin) =>
% 121.84/16.04 ((
% 121.84/16.04 (setukpairinjL2) =>
% 121.84/16.04 ((
% 121.84/16.04 (setukpairinjL) =>
% 121.84/16.04 ((
% 121.84/16.04 (setukpairinjR11) =>
% 121.84/16.04 ((
% 121.84/16.04 (setukpairinjR12) =>
% 121.84/16.04 ((
% 121.84/16.04 (setukpairinjR1) =>
% 121.84/16.04 ((
% 121.84/16.04 (upairequniteq) =>
% 121.84/16.04 ((
% 121.84/16.04 (setukpairinjR2) =>
% 121.84/16.04 ((
% 121.84/16.04 (setukpairinjR) =>
% 121.84/16.04 ((
% 121.84/16.04 (ksndsingleton) =>
% 121.84/16.04 ((
% 121.84/16.04 (ksndpairEq) =>
% 121.84/16.04 ((
% 121.84/16.04 (kpairsurjEq) =>
% 121.84/16.04 ((
% 121.84/16.04 (cartprodsndin) =>
% 121.84/16.04 ((
% 121.84/16.04 (cartprodpairmemEL) =>
% 121.84/16.04 ((
% 121.84/16.04 (cartprodpairmemER) =>
% 121.84/16.04 ((
% 121.84/16.04 (cartprodmempaircEq) =>
% 121.84/16.04 ((
% 121.84/16.04 (cartprodfstpairEq) =>
% 121.84/16.04 ((
% 121.84/16.04 (cartprodsndpairEq) =>
% 121.84/16.04 ((
% 121.84/16.04 (cartprodpairsurjEq) =>
% 121.84/16.04 ((
% 121.84/16.04 (dpsetconstrI) =>
% 121.84/16.04 ((
% 121.84/16.04 (dpsetconstrSub) =>
% 121.84/16.04 ((
% 121.84/16.04 (setOfPairsIsBReln) =>
% 121.84/16.04 ((
% 121.84/16.04 (dpsetconstrERa) =>
% 121.84/16.04 ((
% 121.84/16.04 (dpsetconstrEL1) =>
% 121.84/16.04 ((
% 121.84/16.04 (dpsetconstrEL2) =>
% 121.84/16.04 ((
% 121.84/16.04 (dpsetconstrER) =>
% 121.84/16.04 ((
% 121.84/16.04 (funcImageSingleton) =>
% 121.84/16.04 ((
% 121.84/16.04 (apProp) =>
% 121.84/16.04 ((
% 121.84/16.04 (app) =>
% 121.84/16.04 ((
% 121.84/16.04 (infuncsetfunc) =>
% 121.84/16.04 ((
% 121.84/16.04 (ap2p) =>
% 121.84/16.04 ((
% 121.84/16.04 (funcinfuncset) =>
% 121.84/16.04 ((
% 121.84/16.04 (lamProp) =>
% 121.84/16.04 ((
% 121.84/16.04 (lamp) =>
% 121.84/16.04 ((
% 121.84/16.04 (lam2p) =>
% 121.84/16.04 ((
% 121.84/16.04 (brelnall1) =>
% 121.84/16.04 ((
% 121.84/16.04 (brelnall2) =>
% 121.84/16.04 ((
% 121.84/16.04 (ex1E2) =>
% 121.84/16.04 ((
% 121.84/16.04 (funcGraphProp1) =>
% 121.84/16.04 ((
% 121.84/16.04 (funcGraphProp3) =>
% 121.84/16.04 ((
% 121.84/16.04 (funcGraphProp2) =>
% 121.84/16.04 ((
% 121.84/16.04 (funcextLem) =>
% 121.84/16.04 ((
% 121.84/16.04 (funcGraphProp4) =>
% 121.84/16.04 ((
% 121.84/16.04 (subbreln) =>
% 121.84/16.04 ((
% 121.84/16.04 (eqbreln) =>
% 121.84/16.04 ((
% 121.84/16.04 (funcext) =>
% 121.84/16.04 ((
% 121.84/16.04 (funcext2) =>
% 121.84/16.04 ((
% 121.84/16.04 (ap2apEq1) =>
% 121.84/16.04 ((
% 121.84/16.04 (ap2apEq2) =>
% 121.84/16.04 ((
% 121.84/16.04 (beta1) =>
% 121.84/16.04 ((
% 121.84/16.04 (eta1) =>
% 121.84/16.04 ((
% 121.84/16.04 (lam2lamEq) =>
% 121.84/16.05 ((
% 121.84/16.05 (beta2) =>
% 121.84/16.05 ((
% 121.84/16.05 (eta2) =>
% 121.84/16.05 ((
% 121.84/16.05 (iffalseProp1) =>
% 121.84/16.05 ((
% 121.84/16.05 (iffalseProp2) =>
% 121.84/16.05 ((
% 121.84/16.05 (iftrueProp1) =>
% 121.84/16.05 ((
% 121.84/16.05 (iftrueProp2) =>
% 121.84/16.05 ((
% 121.84/16.05 (ifSingleton) =>
% 121.84/16.05 ((
% 121.84/16.05 (ifp) =>
% 121.84/16.05 ((
% 121.84/16.05 (theeq) =>
% 121.84/16.05 ((
% 121.84/16.05 (iftrue) =>
% 121.84/16.05 ((
% 121.84/16.05 (iffalse) =>
% 121.84/16.05 ((
% 121.84/16.05 (iftrueorfalse) =>
% 121.84/16.05 ((
% 121.84/16.05 (binintersectT_lem) =>
% 121.84/16.05 ((
% 121.84/16.05 (binunionT_lem) =>
% 121.84/16.05 ((
% 121.84/16.05 (powersetT_lem) =>
% 121.84/16.05 ((
% 121.84/16.05 (setminusT_lem) =>
% 121.84/16.05 ((
% 121.84/16.05 (complementT_lem) =>
% 121.84/16.05 ((
% 121.84/16.05 (setextT) =>
% 121.84/16.05 ((
% 121.84/16.05 (subsetTI) =>
% 121.84/16.05 ((
% 121.84/16.05 (powersetTI1) =>
% 121.84/16.05 ((
% 121.84/16.05 (powersetTE1) =>
% 121.84/16.05 ((
% 121.84/16.05 (complementTI1) =>
% 121.84/16.05 ((
% 121.84/16.05 (complementTE1) =>
% 121.84/16.05 ((
% 121.84/16.05 (binintersectTELcontra) =>
% 121.84/16.05 ((
% 121.84/16.05 (binintersectTERcontra) =>
% 121.84/16.05 ((
% 121.84/16.05 (contrasubsetT) =>
% 121.84/16.05 ((
% 121.84/16.05 (contrasubsetT1) =>
% 121.84/16.05 ((
% 121.84/16.05 (contrasubsetT2) =>
% 121.84/16.05 ((
% 121.84/16.05 (contrasubsetT3) =>
% 121.84/16.05 ((
% 121.84/16.05 (doubleComplementI1) =>
% 121.84/16.05 ((
% 121.84/16.05 (doubleComplementE1) =>
% 121.84/16.05 ((
% 121.84/16.05 (doubleComplementSub1) =>
% 121.84/16.05 ((
% 121.84/16.05 (doubleComplementSub2) =>
% 121.84/16.05 ((
% 121.84/16.05 (doubleComplementEq) =>
% 121.84/16.05 ((
% 121.84/16.05 (complementTnotintersectT) =>
% 121.84/16.05 ((
% 121.84/16.05 (complementImpComplementIntersect) =>
% 121.84/16.05 ((
% 121.84/16.05 (complementSubsetComplementIntersect) =>
% 121.84/16.05 ((
% 121.84/16.05 (complementInPowersetComplementIntersect) =>
% 121.84/16.05 ((
% 121.84/16.05 (contraSubsetComplement) =>
% 121.84/16.05 ((
% 121.84/16.05 (complementTcontraSubset) =>
% 121.84/16.05 ((
% 121.84/16.05 (binunionTILcontra) =>
% 121.84/16.05 ((
% 121.84/16.05 (binunionTIRcontra) =>
% 121.84/16.05 ((
% 121.84/16.05 (inIntersectImpInUnion) =>
% 121.84/16.05 ((
% 121.84/16.05 (inIntersectImpInUnion2) =>
% 121.84/16.05 ((
% 121.84/16.05 (inIntersectImpInIntersectUnions) =>
% 121.84/16.05 ((
% 121.84/16.05 (intersectInPowersetIntersectUnions) =>
% 121.84/16.05 ((
% 121.84/16.05 (inComplementUnionImpNotIn1) =>
% 121.84/16.05 ((
% 121.84/16.05 (inComplementUnionImpInComplement1) =>
% 121.84/16.05 ((
% 121.84/16.05 (binunionTE) =>
% 121.84/16.05 ((
% 121.84/16.05 (binunionTEcontra) =>
% 121.84/16.05 ((
% 121.84/16.05 (demorgan2a1) =>
% 121.84/16.05 ((
% 121.84/16.05 (complementUnionInPowersetComplement) =>
% 121.84/16.05 ((
% 121.84/16.05 (demorgan2a2) =>
% 121.84/16.05 ((
% 121.84/16.05 (demorgan1a) =>
% 121.84/16.05 ((
% 121.84/16.05 (demorgan1b) =>
% 121.84/16.05 ((
% 121.84/16.05 (demorgan1) =>
% 121.84/16.05 ((
% 121.84/16.05 (demorgan2a) =>
% 121.84/16.05 ((
% 121.84/16.05 (demorgan2b2) =>
% 121.84/16.05 ((
% 121.84/16.05 (demorgan2b) =>
% 121.84/16.05 ((
% 121.84/16.05 (demorgan2) =>
% 121.84/16.05 ((
% 121.84/16.05 (woz13rule0) =>
% 121.84/16.05 ((
% 121.84/16.05 (woz13rule1) =>
% 121.84/16.05 ((
% 121.84/16.05 (woz13rule2) =>
% 121.84/16.05 ((
% 121.84/16.05 (woz13rule3) =>
% 121.84/16.05 ((
% 121.84/16.05 (woz13rule4) =>
% 121.84/16.05 ((
% 121.84/16.05 (woz1_1) =>
% 121.84/16.05 ((
% 121.84/16.05 (woz1_2) =>
% 121.84/16.05 ((
% 121.84/16.05 (woz1_3) =>
% 121.84/16.05 ((
% 121.84/16.05 (woz1_4) =>
% 121.84/16.05 ((
% 121.84/16.05 (woz1_5) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1all2) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1SetBreln1) =>
% 121.84/16.05 ((
% 121.84/16.05 (choice2fnsingleton) =>
% 121.84/16.05 ((
% 121.84/16.05 (setOfPairsIsBReln1) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1all1) =>
% 121.84/16.05 ((
% 121.84/16.05 (subbreln1) =>
% 121.84/16.05 ((
% 121.84/16.05 (eqbreln1) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1invprop) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1invI) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1invE) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1compprop) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1compI) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1compE) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1compEex) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1unionprop) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1unionIL) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1unionIR) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1unionI) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1unionE) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1unionEcases) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1unionCommutes) =>
% 121.84/16.05 ((
% 121.84/16.05 (woz2Ex) =>
% 121.84/16.05 ((
% 121.84/16.05 (woz2W) =>
% 121.84/16.05 ((
% 121.84/16.05 (woz2A) =>
% 121.84/16.05 ((
% 121.84/16.05 (woz2B) =>
% 121.84/16.05 ((
% 121.84/16.05 (image1Ex) =>
% 121.84/16.05 ((
% 121.84/16.05 (image1Ex1) =>
% 121.84/16.05 ((
% 121.84/16.05 (image1Equiv) =>
% 121.84/16.05 ((
% 121.84/16.05 (image1E) =>
% 121.84/16.05 ((
% 121.84/16.05 (image1I) =>
% 121.84/16.05 ((
% 121.84/16.05 (injFuncInInjFuncSet) =>
% 121.84/16.05 ((
% 121.84/16.05 (!!) @ (
% 121.84/16.05 (('#B') @ (
% 121.84/16.05 !!) @
% 121.84/16.05 (
% 121.84/16.05 (
% 121.84/16.05 ('#B') @ (
% 121.84/16.05 (
% 121.84/16.05 ('#B') @ (
% 121.84/16.05 !!))) @
% 121.84/16.05 (
% 121.84/16.05 (
% 121.84/16.05 ('#S') @ (
% 121.84/16.05 (
% 121.84/16.05 ('#B') @ (
% 121.84/16.05 '#S') @
% 121.84/16.05 (
% 121.84/16.05 (
% 121.84/16.05 ('#B') @ (
% 121.84/16.05 (
% 121.84/16.05 ('#B') @ (
% 121.84/16.05 '#S'))) @
% 121.84/16.05 (
% 121.84/16.05 (
% 121.84/16.05 ('#B') @ (
% 121.84/16.05 (
% 121.84/16.05 ('#B') @ (
% 121.84/16.05 (
% 121.84/16.05 ('#B') @ (
% 121.84/16.05 =>))))) @
% 121.84/16.05 (
% 121.84/16.05 (
% 121.84/16.05 ('#B') @ (
% 121.84/16.05 (
% 121.84/16.05 ('#B') @ (
% 121.84/16.05 (
% 121.84/16.05 ('#C') @ in)))) @
% 121.84/16.05 injFuncSet)))))))) @
% 121.84/16.05 (
% 121.84/16.05 (
% 121.84/16.05 ('#B') @ (
% 121.84/16.05 (
% 121.84/16.05 ('#B') @ (
% 121.84/16.05 (
% 121.84/16.05 ('#C') @ in)))) @
% 121.84/16.05 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 121.84/16.05 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl355])).
% 121.84/16.05 thf(zip_derived_cl369, plain,
% 121.84/16.05 (~ (((powersetI) =>
% 121.84/16.05 (((emptyinPowerset) =>
% 121.84/16.05 (((emptyInPowerset) =>
% 121.84/16.05 (((powersetE) =>
% 121.84/16.05 (((setunionI) =>
% 121.84/16.05 (((setunionE) =>
% 121.84/16.05 (((subPowSU) =>
% 121.84/16.05 (((exuE2) =>
% 121.84/16.05 (((nonemptyImpWitness) =>
% 121.84/16.05 (((uniqinunit) =>
% 121.84/16.05 (((notinsingleton) =>
% 121.84/16.05 (((eqinunit) =>
% 121.84/16.05 (((singletonsswitch) =>
% 121.84/16.05 (((upairsetE) =>
% 121.84/16.05 (((upairsetIL) =>
% 121.84/16.05 (((upairsetIR) =>
% 121.84/16.05 (((emptyE1) =>
% 121.84/16.05 (((vacuousDall) =>
% 121.84/16.05 (((quantDeMorgan1) =>
% 121.84/16.05 (((quantDeMorgan2) =>
% 121.84/16.05 (((quantDeMorgan3) =>
% 121.84/16.05 (((quantDeMorgan4) =>
% 121.84/16.05 (((prop2setI) =>
% 121.84/16.05 (((prop2set2propI) =>
% 121.84/16.05 (((notdexE) =>
% 121.84/16.05 (((notdallE) =>
% 121.84/16.05 (((exuI1) =>
% 121.84/16.05 (((exuI3) =>
% 121.84/16.05 (((exuI2) =>
% 121.84/16.05 (((inCongP) =>
% 121.84/16.05 ((
% 121.84/16.05 (in__Cong) =>
% 121.84/16.05 ((
% 121.84/16.05 (exuE3u) =>
% 121.84/16.05 ((
% 121.84/16.05 (exu__Cong) =>
% 121.84/16.05 ((
% 121.84/16.05 (setadjoin__Cong) =>
% 121.84/16.05 ((
% 121.84/16.05 (powerset__Cong) =>
% 121.84/16.05 ((
% 121.84/16.05 (setunion__Cong) =>
% 121.84/16.05 ((
% 121.84/16.05 (exuEu) =>
% 121.84/16.05 ((
% 121.84/16.05 (descr__Cong) =>
% 121.84/16.05 ((
% 121.84/16.05 (dsetconstr__Cong) =>
% 121.84/16.05 ((
% 121.84/16.05 (subsetI1) =>
% 121.84/16.05 ((
% 121.84/16.05 (eqimpsubset2) =>
% 121.84/16.05 ((
% 121.84/16.05 (eqimpsubset1) =>
% 121.84/16.05 ((
% 121.84/16.05 (subsetI2) =>
% 121.84/16.05 ((
% 121.84/16.05 (emptysetsubset) =>
% 121.84/16.05 ((
% 121.84/16.05 (subsetE) =>
% 121.84/16.05 ((
% 121.84/16.05 (subsetE2) =>
% 121.84/16.05 ((
% 121.84/16.05 (notsubsetI) =>
% 121.84/16.05 ((
% 121.84/16.05 (notequalI1) =>
% 121.84/16.05 ((
% 121.84/16.05 (notequalI2) =>
% 121.84/16.05 ((
% 121.84/16.05 (subsetRefl) =>
% 121.84/16.05 ((
% 121.84/16.05 (subsetTrans) =>
% 121.84/16.05 ((
% 121.84/16.05 (setadjoinSub) =>
% 121.84/16.05 ((
% 121.84/16.05 (setadjoinSub2) =>
% 121.84/16.05 ((
% 121.84/16.05 (subset2powerset) =>
% 121.84/16.05 ((
% 121.84/16.05 (setextsub) =>
% 121.84/16.05 ((
% 121.84/16.05 (subsetemptysetimpeq) =>
% 121.84/16.05 ((
% 121.84/16.05 (powersetI1) =>
% 121.84/16.05 ((
% 121.84/16.05 (powersetE1) =>
% 121.84/16.05 ((
% 121.84/16.05 (inPowerset) =>
% 121.84/16.05 ((
% 121.84/16.05 (powersetsubset) =>
% 121.84/16.05 ((
% 121.84/16.05 (sepInPowerset) =>
% 121.84/16.05 ((
% 121.84/16.05 (sepSubset) =>
% 121.84/16.05 ((
% 121.84/16.05 (binunionIL) =>
% 121.84/16.05 ((
% 121.84/16.05 (upairset2IR) =>
% 121.84/16.05 ((
% 121.84/16.05 (binunionIR) =>
% 121.84/16.05 ((
% 121.84/16.05 (binunionEcases) =>
% 121.84/16.05 ((
% 121.84/16.05 (binunionE) =>
% 121.84/16.05 ((
% 121.84/16.05 (binunionLsub) =>
% 121.84/16.05 ((
% 121.84/16.05 (binunionRsub) =>
% 121.84/16.05 ((
% 121.84/16.05 (binintersectI) =>
% 121.84/16.05 ((
% 121.84/16.05 (binintersectSubset5) =>
% 121.84/16.05 ((
% 121.84/16.05 (binintersectEL) =>
% 121.84/16.05 ((
% 121.84/16.05 (binintersectLsub) =>
% 121.84/16.05 ((
% 121.84/16.05 (binintersectSubset2) =>
% 121.84/16.05 ((
% 121.84/16.05 (binintersectSubset3) =>
% 121.84/16.05 ((
% 121.84/16.05 (binintersectER) =>
% 121.84/16.05 ((
% 121.84/16.05 (disjointsetsI1) =>
% 121.84/16.05 ((
% 121.84/16.05 (binintersectRsub) =>
% 121.84/16.05 ((
% 121.84/16.05 (binintersectSubset4) =>
% 121.84/16.05 ((
% 121.84/16.05 (binintersectSubset1) =>
% 121.84/16.05 ((
% 121.84/16.05 (bs114d) =>
% 121.84/16.05 ((
% 121.84/16.05 (setminusI) =>
% 121.84/16.05 ((
% 121.84/16.05 (setminusEL) =>
% 121.84/16.05 ((
% 121.84/16.05 (setminusER) =>
% 121.84/16.05 ((
% 121.84/16.05 (setminusSubset2) =>
% 121.84/16.05 ((
% 121.84/16.05 (setminusERneg) =>
% 121.84/16.05 ((
% 121.84/16.05 (setminusELneg) =>
% 121.84/16.05 ((
% 121.84/16.05 (setminusILneg) =>
% 121.84/16.05 ((
% 121.84/16.05 (setminusIRneg) =>
% 121.84/16.05 ((
% 121.84/16.05 (setminusLsub) =>
% 121.84/16.05 ((
% 121.84/16.05 (setminusSubset1) =>
% 121.84/16.05 ((
% 121.84/16.05 (symdiffE) =>
% 121.84/16.05 ((
% 121.84/16.05 (symdiffI1) =>
% 121.84/16.05 ((
% 121.84/16.05 (symdiffI2) =>
% 121.84/16.05 ((
% 121.84/16.05 (symdiffIneg1) =>
% 121.84/16.05 ((
% 121.84/16.05 (symdiffIneg2) =>
% 121.84/16.05 ((
% 121.84/16.05 (secondinupair) =>
% 121.84/16.05 ((
% 121.84/16.05 (setukpairIL) =>
% 121.84/16.05 ((
% 121.84/16.05 (setukpairIR) =>
% 121.84/16.05 ((
% 121.84/16.05 (kpairiskpair) =>
% 121.84/16.05 ((
% 121.84/16.05 (kpairp) =>
% 121.84/16.05 ((
% 121.84/16.05 (singletonsubset) =>
% 121.84/16.05 ((
% 121.84/16.05 (singletoninpowerset) =>
% 121.84/16.05 ((
% 121.84/16.05 (singletoninpowunion) =>
% 121.84/16.05 ((
% 121.84/16.05 (upairset2E) =>
% 121.84/16.05 ((
% 121.84/16.05 (upairsubunion) =>
% 121.84/16.05 ((
% 121.84/16.05 (upairinpowunion) =>
% 121.84/16.05 ((
% 121.84/16.05 (ubforcartprodlem1) =>
% 121.84/16.05 ((
% 121.84/16.05 (ubforcartprodlem2) =>
% 121.84/16.05 ((
% 121.84/16.05 (ubforcartprodlem3) =>
% 121.84/16.05 ((
% 121.84/16.05 (cartprodpairin) =>
% 121.84/16.05 ((
% 121.84/16.05 (cartprodmempair1) =>
% 121.84/16.05 ((
% 121.84/16.05 (cartprodmempair) =>
% 121.84/16.05 ((
% 121.84/16.05 (setunionE2) =>
% 121.84/16.05 ((
% 121.84/16.05 (setunionsingleton1) =>
% 121.84/16.05 ((
% 121.84/16.05 (setunionsingleton2) =>
% 121.84/16.05 ((
% 121.84/16.05 (setunionsingleton) =>
% 121.84/16.05 ((
% 121.84/16.05 (singletonprop) =>
% 121.84/16.05 ((
% 121.84/16.05 (ex1E1) =>
% 121.84/16.05 ((
% 121.84/16.05 (ex1I) =>
% 121.84/16.05 ((
% 121.84/16.05 (ex1I2) =>
% 121.84/16.05 ((
% 121.84/16.05 (singletonsuniq) =>
% 121.84/16.05 ((
% 121.84/16.05 (setukpairinjL1) =>
% 121.84/16.05 ((
% 121.84/16.05 (kfstsingleton) =>
% 121.84/16.05 ((
% 121.84/16.05 (theprop) =>
% 121.84/16.05 ((
% 121.84/16.05 (kfstpairEq) =>
% 121.84/16.05 ((
% 121.84/16.05 (cartprodfstin) =>
% 121.84/16.05 ((
% 121.84/16.05 (setukpairinjL2) =>
% 121.84/16.05 ((
% 121.84/16.05 (setukpairinjL) =>
% 121.84/16.05 ((
% 121.84/16.05 (setukpairinjR11) =>
% 121.84/16.05 ((
% 121.84/16.05 (setukpairinjR12) =>
% 121.84/16.05 ((
% 121.84/16.05 (setukpairinjR1) =>
% 121.84/16.05 ((
% 121.84/16.05 (upairequniteq) =>
% 121.84/16.05 ((
% 121.84/16.05 (setukpairinjR2) =>
% 121.84/16.05 ((
% 121.84/16.05 (setukpairinjR) =>
% 121.84/16.05 ((
% 121.84/16.05 (ksndsingleton) =>
% 121.84/16.05 ((
% 121.84/16.05 (ksndpairEq) =>
% 121.84/16.05 ((
% 121.84/16.05 (kpairsurjEq) =>
% 121.84/16.05 ((
% 121.84/16.05 (cartprodsndin) =>
% 121.84/16.05 ((
% 121.84/16.05 (cartprodpairmemEL) =>
% 121.84/16.05 ((
% 121.84/16.05 (cartprodpairmemER) =>
% 121.84/16.05 ((
% 121.84/16.05 (cartprodmempaircEq) =>
% 121.84/16.05 ((
% 121.84/16.05 (cartprodfstpairEq) =>
% 121.84/16.05 ((
% 121.84/16.05 (cartprodsndpairEq) =>
% 121.84/16.05 ((
% 121.84/16.05 (cartprodpairsurjEq) =>
% 121.84/16.05 ((
% 121.84/16.05 (dpsetconstrI) =>
% 121.84/16.05 ((
% 121.84/16.05 (dpsetconstrSub) =>
% 121.84/16.05 ((
% 121.84/16.05 (setOfPairsIsBReln) =>
% 121.84/16.05 ((
% 121.84/16.05 (dpsetconstrERa) =>
% 121.84/16.05 ((
% 121.84/16.05 (dpsetconstrEL1) =>
% 121.84/16.05 ((
% 121.84/16.05 (dpsetconstrEL2) =>
% 121.84/16.05 ((
% 121.84/16.05 (dpsetconstrER) =>
% 121.84/16.05 ((
% 121.84/16.05 (funcImageSingleton) =>
% 121.84/16.05 ((
% 121.84/16.05 (apProp) =>
% 121.84/16.05 ((
% 121.84/16.05 (app) =>
% 121.84/16.05 ((
% 121.84/16.05 (infuncsetfunc) =>
% 121.84/16.05 ((
% 121.84/16.05 (ap2p) =>
% 121.84/16.05 ((
% 121.84/16.05 (funcinfuncset) =>
% 121.84/16.05 ((
% 121.84/16.05 (lamProp) =>
% 121.84/16.05 ((
% 121.84/16.05 (lamp) =>
% 121.84/16.05 ((
% 121.84/16.05 (lam2p) =>
% 121.84/16.05 ((
% 121.84/16.05 (brelnall1) =>
% 121.84/16.05 ((
% 121.84/16.05 (brelnall2) =>
% 121.84/16.05 ((
% 121.84/16.05 (ex1E2) =>
% 121.84/16.05 ((
% 121.84/16.05 (funcGraphProp1) =>
% 121.84/16.05 ((
% 121.84/16.05 (funcGraphProp3) =>
% 121.84/16.05 ((
% 121.84/16.05 (funcGraphProp2) =>
% 121.84/16.05 ((
% 121.84/16.05 (funcextLem) =>
% 121.84/16.05 ((
% 121.84/16.05 (funcGraphProp4) =>
% 121.84/16.05 ((
% 121.84/16.05 (subbreln) =>
% 121.84/16.05 ((
% 121.84/16.05 (eqbreln) =>
% 121.84/16.05 ((
% 121.84/16.05 (funcext) =>
% 121.84/16.05 ((
% 121.84/16.05 (funcext2) =>
% 121.84/16.05 ((
% 121.84/16.05 (ap2apEq1) =>
% 121.84/16.05 ((
% 121.84/16.05 (ap2apEq2) =>
% 121.84/16.05 ((
% 121.84/16.05 (beta1) =>
% 121.84/16.05 ((
% 121.84/16.05 (eta1) =>
% 121.84/16.05 ((
% 121.84/16.05 (lam2lamEq) =>
% 121.84/16.05 ((
% 121.84/16.05 (beta2) =>
% 121.84/16.05 ((
% 121.84/16.05 (eta2) =>
% 121.84/16.05 ((
% 121.84/16.05 (iffalseProp1) =>
% 121.84/16.05 ((
% 121.84/16.05 (iffalseProp2) =>
% 121.84/16.05 ((
% 121.84/16.05 (iftrueProp1) =>
% 121.84/16.05 ((
% 121.84/16.05 (iftrueProp2) =>
% 121.84/16.05 ((
% 121.84/16.05 (ifSingleton) =>
% 121.84/16.05 ((
% 121.84/16.05 (ifp) =>
% 121.84/16.05 ((
% 121.84/16.05 (theeq) =>
% 121.84/16.05 ((
% 121.84/16.05 (iftrue) =>
% 121.84/16.05 ((
% 121.84/16.05 (iffalse) =>
% 121.84/16.05 ((
% 121.84/16.05 (iftrueorfalse) =>
% 121.84/16.05 ((
% 121.84/16.05 (binintersectT_lem) =>
% 121.84/16.05 ((
% 121.84/16.05 (binunionT_lem) =>
% 121.84/16.05 ((
% 121.84/16.05 (powersetT_lem) =>
% 121.84/16.05 ((
% 121.84/16.05 (setminusT_lem) =>
% 121.84/16.05 ((
% 121.84/16.05 (complementT_lem) =>
% 121.84/16.05 ((
% 121.84/16.05 (setextT) =>
% 121.84/16.05 ((
% 121.84/16.05 (subsetTI) =>
% 121.84/16.05 ((
% 121.84/16.05 (powersetTI1) =>
% 121.84/16.05 ((
% 121.84/16.05 (powersetTE1) =>
% 121.84/16.05 ((
% 121.84/16.05 (complementTI1) =>
% 121.84/16.05 ((
% 121.84/16.05 (complementTE1) =>
% 121.84/16.05 ((
% 121.84/16.05 (binintersectTELcontra) =>
% 121.84/16.05 ((
% 121.84/16.05 (binintersectTERcontra) =>
% 121.84/16.05 ((
% 121.84/16.05 (contrasubsetT) =>
% 121.84/16.05 ((
% 121.84/16.05 (contrasubsetT1) =>
% 121.84/16.05 ((
% 121.84/16.05 (contrasubsetT2) =>
% 121.84/16.05 ((
% 121.84/16.05 (contrasubsetT3) =>
% 121.84/16.05 ((
% 121.84/16.05 (doubleComplementI1) =>
% 121.84/16.05 ((
% 121.84/16.05 (doubleComplementE1) =>
% 121.84/16.05 ((
% 121.84/16.05 (doubleComplementSub1) =>
% 121.84/16.05 ((
% 121.84/16.05 (doubleComplementSub2) =>
% 121.84/16.05 ((
% 121.84/16.05 (doubleComplementEq) =>
% 121.84/16.05 ((
% 121.84/16.05 (complementTnotintersectT) =>
% 121.84/16.05 ((
% 121.84/16.05 (complementImpComplementIntersect) =>
% 121.84/16.05 ((
% 121.84/16.05 (complementSubsetComplementIntersect) =>
% 121.84/16.05 ((
% 121.84/16.05 (complementInPowersetComplementIntersect) =>
% 121.84/16.05 ((
% 121.84/16.05 (contraSubsetComplement) =>
% 121.84/16.05 ((
% 121.84/16.05 (complementTcontraSubset) =>
% 121.84/16.05 ((
% 121.84/16.05 (binunionTILcontra) =>
% 121.84/16.05 ((
% 121.84/16.05 (binunionTIRcontra) =>
% 121.84/16.05 ((
% 121.84/16.05 (inIntersectImpInUnion) =>
% 121.84/16.05 ((
% 121.84/16.05 (inIntersectImpInUnion2) =>
% 121.84/16.05 ((
% 121.84/16.05 (inIntersectImpInIntersectUnions) =>
% 121.84/16.05 ((
% 121.84/16.05 (intersectInPowersetIntersectUnions) =>
% 121.84/16.05 ((
% 121.84/16.05 (inComplementUnionImpNotIn1) =>
% 121.84/16.05 ((
% 121.84/16.05 (inComplementUnionImpInComplement1) =>
% 121.84/16.05 ((
% 121.84/16.05 (binunionTE) =>
% 121.84/16.05 ((
% 121.84/16.05 (binunionTEcontra) =>
% 121.84/16.05 ((
% 121.84/16.05 (demorgan2a1) =>
% 121.84/16.05 ((
% 121.84/16.05 (complementUnionInPowersetComplement) =>
% 121.84/16.05 ((
% 121.84/16.05 (demorgan2a2) =>
% 121.84/16.05 ((
% 121.84/16.05 (demorgan1a) =>
% 121.84/16.05 ((
% 121.84/16.05 (demorgan1b) =>
% 121.84/16.05 ((
% 121.84/16.05 (demorgan1) =>
% 121.84/16.05 ((
% 121.84/16.05 (demorgan2a) =>
% 121.84/16.05 ((
% 121.84/16.05 (demorgan2b2) =>
% 121.84/16.05 ((
% 121.84/16.05 (demorgan2b) =>
% 121.84/16.05 ((
% 121.84/16.05 (demorgan2) =>
% 121.84/16.05 ((
% 121.84/16.05 (woz13rule0) =>
% 121.84/16.05 ((
% 121.84/16.05 (woz13rule1) =>
% 121.84/16.05 ((
% 121.84/16.05 (woz13rule2) =>
% 121.84/16.05 ((
% 121.84/16.05 (woz13rule3) =>
% 121.84/16.05 ((
% 121.84/16.05 (woz13rule4) =>
% 121.84/16.05 ((
% 121.84/16.05 (woz1_1) =>
% 121.84/16.05 ((
% 121.84/16.05 (woz1_2) =>
% 121.84/16.05 ((
% 121.84/16.05 (woz1_3) =>
% 121.84/16.05 ((
% 121.84/16.05 (woz1_4) =>
% 121.84/16.05 ((
% 121.84/16.05 (woz1_5) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1all2) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1SetBreln1) =>
% 121.84/16.05 ((
% 121.84/16.05 (choice2fnsingleton) =>
% 121.84/16.05 ((
% 121.84/16.05 (setOfPairsIsBReln1) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1all1) =>
% 121.84/16.05 ((
% 121.84/16.05 (subbreln1) =>
% 121.84/16.05 ((
% 121.84/16.05 (eqbreln1) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1invprop) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1invI) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1invE) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1compprop) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1compI) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1compE) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1compEex) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1unionprop) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1unionIL) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1unionIR) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1unionI) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1unionE) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1unionEcases) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1unionCommutes) =>
% 121.84/16.05 ((
% 121.84/16.05 (woz2Ex) =>
% 121.84/16.05 ((
% 121.84/16.05 (woz2W) =>
% 121.84/16.05 ((
% 121.84/16.05 (woz2A) =>
% 121.84/16.05 ((
% 121.84/16.05 (woz2B) =>
% 121.84/16.05 ((
% 121.84/16.05 (image1Ex) =>
% 121.84/16.05 ((
% 121.84/16.05 (image1Ex1) =>
% 121.84/16.05 ((
% 121.84/16.05 (image1Equiv) =>
% 121.84/16.05 ((
% 121.84/16.05 (image1E) =>
% 121.84/16.05 ((
% 121.84/16.05 (image1I) =>
% 121.84/16.05 ((
% 121.84/16.05 (injFuncInInjFuncSet) =>
% 121.84/16.05 ((
% 121.84/16.05 (!!) @ (
% 121.84/16.05 (('#B') @ (
% 121.84/16.05 !!) @
% 121.84/16.05 (
% 121.84/16.05 (
% 121.84/16.05 ('#B') @ (
% 121.84/16.05 (
% 121.84/16.05 ('#B') @ (
% 121.84/16.05 !!))) @
% 121.84/16.05 (
% 121.84/16.05 (
% 121.84/16.05 ('#S') @ (
% 121.84/16.05 (
% 121.84/16.05 ('#B') @ (
% 121.84/16.05 '#S') @
% 121.84/16.05 (
% 121.84/16.05 (
% 121.84/16.05 ('#B') @ (
% 121.84/16.05 (
% 121.84/16.05 ('#B') @ (
% 121.84/16.05 '#S'))) @
% 121.84/16.05 (
% 121.84/16.05 (
% 121.84/16.05 ('#B') @ (
% 121.84/16.05 (
% 121.84/16.05 ('#B') @ (
% 121.84/16.05 (
% 121.84/16.05 ('#B') @ (
% 121.84/16.05 =>))))) @
% 121.84/16.05 (
% 121.84/16.05 (
% 121.84/16.05 ('#B') @ (
% 121.84/16.05 (
% 121.84/16.05 ('#B') @ (
% 121.84/16.05 (
% 121.84/16.05 ('#C') @ in)))) @
% 121.84/16.05 injFuncSet)))))))) @
% 121.84/16.05 (
% 121.84/16.05 (
% 121.84/16.05 ('#B') @ (
% 121.84/16.05 (
% 121.84/16.05 ('#B') @ (
% 121.84/16.05 (
% 121.84/16.05 ('#C') @ in)))) @
% 121.84/16.05 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 121.84/16.05 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl362])).
% 121.84/16.05 thf(zip_derived_cl376, plain,
% 121.84/16.05 (~ (((emptyinPowerset) =>
% 121.84/16.05 (((emptyInPowerset) =>
% 121.84/16.05 (((powersetE) =>
% 121.84/16.05 (((setunionI) =>
% 121.84/16.05 (((setunionE) =>
% 121.84/16.05 (((subPowSU) =>
% 121.84/16.05 (((exuE2) =>
% 121.84/16.05 (((nonemptyImpWitness) =>
% 121.84/16.05 (((uniqinunit) =>
% 121.84/16.05 (((notinsingleton) =>
% 121.84/16.05 (((eqinunit) =>
% 121.84/16.05 (((singletonsswitch) =>
% 121.84/16.05 (((upairsetE) =>
% 121.84/16.05 (((upairsetIL) =>
% 121.84/16.05 (((upairsetIR) =>
% 121.84/16.05 (((emptyE1) =>
% 121.84/16.05 (((vacuousDall) =>
% 121.84/16.05 (((quantDeMorgan1) =>
% 121.84/16.05 (((quantDeMorgan2) =>
% 121.84/16.05 (((quantDeMorgan3) =>
% 121.84/16.05 (((quantDeMorgan4) =>
% 121.84/16.05 (((prop2setI) =>
% 121.84/16.05 (((prop2set2propI) =>
% 121.84/16.05 (((notdexE) =>
% 121.84/16.05 (((notdallE) =>
% 121.84/16.05 (((exuI1) =>
% 121.84/16.05 (((exuI3) =>
% 121.84/16.05 (((exuI2) =>
% 121.84/16.05 (((inCongP) =>
% 121.84/16.05 (((in__Cong) =>
% 121.84/16.05 ((
% 121.84/16.05 (exuE3u) =>
% 121.84/16.05 ((
% 121.84/16.05 (exu__Cong) =>
% 121.84/16.05 ((
% 121.84/16.05 (setadjoin__Cong) =>
% 121.84/16.05 ((
% 121.84/16.05 (powerset__Cong) =>
% 121.84/16.05 ((
% 121.84/16.05 (setunion__Cong) =>
% 121.84/16.05 ((
% 121.84/16.05 (exuEu) =>
% 121.84/16.05 ((
% 121.84/16.05 (descr__Cong) =>
% 121.84/16.05 ((
% 121.84/16.05 (dsetconstr__Cong) =>
% 121.84/16.05 ((
% 121.84/16.05 (subsetI1) =>
% 121.84/16.05 ((
% 121.84/16.05 (eqimpsubset2) =>
% 121.84/16.05 ((
% 121.84/16.05 (eqimpsubset1) =>
% 121.84/16.05 ((
% 121.84/16.05 (subsetI2) =>
% 121.84/16.05 ((
% 121.84/16.05 (emptysetsubset) =>
% 121.84/16.05 ((
% 121.84/16.05 (subsetE) =>
% 121.84/16.05 ((
% 121.84/16.05 (subsetE2) =>
% 121.84/16.05 ((
% 121.84/16.05 (notsubsetI) =>
% 121.84/16.05 ((
% 121.84/16.05 (notequalI1) =>
% 121.84/16.05 ((
% 121.84/16.05 (notequalI2) =>
% 121.84/16.05 ((
% 121.84/16.05 (subsetRefl) =>
% 121.84/16.05 ((
% 121.84/16.05 (subsetTrans) =>
% 121.84/16.05 ((
% 121.84/16.05 (setadjoinSub) =>
% 121.84/16.05 ((
% 121.84/16.05 (setadjoinSub2) =>
% 121.84/16.05 ((
% 121.84/16.05 (subset2powerset) =>
% 121.84/16.05 ((
% 121.84/16.05 (setextsub) =>
% 121.84/16.05 ((
% 121.84/16.05 (subsetemptysetimpeq) =>
% 121.84/16.05 ((
% 121.84/16.05 (powersetI1) =>
% 121.84/16.05 ((
% 121.84/16.05 (powersetE1) =>
% 121.84/16.05 ((
% 121.84/16.05 (inPowerset) =>
% 121.84/16.05 ((
% 121.84/16.05 (powersetsubset) =>
% 121.84/16.05 ((
% 121.84/16.05 (sepInPowerset) =>
% 121.84/16.05 ((
% 121.84/16.05 (sepSubset) =>
% 121.84/16.05 ((
% 121.84/16.05 (binunionIL) =>
% 121.84/16.05 ((
% 121.84/16.05 (upairset2IR) =>
% 121.84/16.05 ((
% 121.84/16.05 (binunionIR) =>
% 121.84/16.05 ((
% 121.84/16.05 (binunionEcases) =>
% 121.84/16.05 ((
% 121.84/16.05 (binunionE) =>
% 121.84/16.05 ((
% 121.84/16.05 (binunionLsub) =>
% 121.84/16.05 ((
% 121.84/16.05 (binunionRsub) =>
% 121.84/16.05 ((
% 121.84/16.05 (binintersectI) =>
% 121.84/16.05 ((
% 121.84/16.05 (binintersectSubset5) =>
% 121.84/16.05 ((
% 121.84/16.05 (binintersectEL) =>
% 121.84/16.05 ((
% 121.84/16.05 (binintersectLsub) =>
% 121.84/16.05 ((
% 121.84/16.05 (binintersectSubset2) =>
% 121.84/16.05 ((
% 121.84/16.05 (binintersectSubset3) =>
% 121.84/16.05 ((
% 121.84/16.05 (binintersectER) =>
% 121.84/16.05 ((
% 121.84/16.05 (disjointsetsI1) =>
% 121.84/16.05 ((
% 121.84/16.05 (binintersectRsub) =>
% 121.84/16.05 ((
% 121.84/16.05 (binintersectSubset4) =>
% 121.84/16.05 ((
% 121.84/16.05 (binintersectSubset1) =>
% 121.84/16.05 ((
% 121.84/16.05 (bs114d) =>
% 121.84/16.05 ((
% 121.84/16.05 (setminusI) =>
% 121.84/16.05 ((
% 121.84/16.05 (setminusEL) =>
% 121.84/16.05 ((
% 121.84/16.05 (setminusER) =>
% 121.84/16.05 ((
% 121.84/16.05 (setminusSubset2) =>
% 121.84/16.05 ((
% 121.84/16.05 (setminusERneg) =>
% 121.84/16.05 ((
% 121.84/16.05 (setminusELneg) =>
% 121.84/16.05 ((
% 121.84/16.05 (setminusILneg) =>
% 121.84/16.05 ((
% 121.84/16.05 (setminusIRneg) =>
% 121.84/16.05 ((
% 121.84/16.05 (setminusLsub) =>
% 121.84/16.05 ((
% 121.84/16.05 (setminusSubset1) =>
% 121.84/16.05 ((
% 121.84/16.05 (symdiffE) =>
% 121.84/16.05 ((
% 121.84/16.05 (symdiffI1) =>
% 121.84/16.05 ((
% 121.84/16.05 (symdiffI2) =>
% 121.84/16.05 ((
% 121.84/16.05 (symdiffIneg1) =>
% 121.84/16.05 ((
% 121.84/16.05 (symdiffIneg2) =>
% 121.84/16.05 ((
% 121.84/16.05 (secondinupair) =>
% 121.84/16.05 ((
% 121.84/16.05 (setukpairIL) =>
% 121.84/16.05 ((
% 121.84/16.05 (setukpairIR) =>
% 121.84/16.05 ((
% 121.84/16.05 (kpairiskpair) =>
% 121.84/16.05 ((
% 121.84/16.05 (kpairp) =>
% 121.84/16.05 ((
% 121.84/16.05 (singletonsubset) =>
% 121.84/16.05 ((
% 121.84/16.05 (singletoninpowerset) =>
% 121.84/16.05 ((
% 121.84/16.05 (singletoninpowunion) =>
% 121.84/16.05 ((
% 121.84/16.05 (upairset2E) =>
% 121.84/16.05 ((
% 121.84/16.05 (upairsubunion) =>
% 121.84/16.05 ((
% 121.84/16.05 (upairinpowunion) =>
% 121.84/16.05 ((
% 121.84/16.05 (ubforcartprodlem1) =>
% 121.84/16.05 ((
% 121.84/16.05 (ubforcartprodlem2) =>
% 121.84/16.05 ((
% 121.84/16.05 (ubforcartprodlem3) =>
% 121.84/16.05 ((
% 121.84/16.05 (cartprodpairin) =>
% 121.84/16.05 ((
% 121.84/16.05 (cartprodmempair1) =>
% 121.84/16.05 ((
% 121.84/16.05 (cartprodmempair) =>
% 121.84/16.05 ((
% 121.84/16.05 (setunionE2) =>
% 121.84/16.05 ((
% 121.84/16.05 (setunionsingleton1) =>
% 121.84/16.05 ((
% 121.84/16.05 (setunionsingleton2) =>
% 121.84/16.05 ((
% 121.84/16.05 (setunionsingleton) =>
% 121.84/16.05 ((
% 121.84/16.05 (singletonprop) =>
% 121.84/16.05 ((
% 121.84/16.05 (ex1E1) =>
% 121.84/16.05 ((
% 121.84/16.05 (ex1I) =>
% 121.84/16.05 ((
% 121.84/16.05 (ex1I2) =>
% 121.84/16.05 ((
% 121.84/16.05 (singletonsuniq) =>
% 121.84/16.05 ((
% 121.84/16.05 (setukpairinjL1) =>
% 121.84/16.05 ((
% 121.84/16.05 (kfstsingleton) =>
% 121.84/16.05 ((
% 121.84/16.05 (theprop) =>
% 121.84/16.05 ((
% 121.84/16.05 (kfstpairEq) =>
% 121.84/16.05 ((
% 121.84/16.05 (cartprodfstin) =>
% 121.84/16.05 ((
% 121.84/16.05 (setukpairinjL2) =>
% 121.84/16.05 ((
% 121.84/16.05 (setukpairinjL) =>
% 121.84/16.05 ((
% 121.84/16.05 (setukpairinjR11) =>
% 121.84/16.05 ((
% 121.84/16.05 (setukpairinjR12) =>
% 121.84/16.05 ((
% 121.84/16.05 (setukpairinjR1) =>
% 121.84/16.05 ((
% 121.84/16.05 (upairequniteq) =>
% 121.84/16.05 ((
% 121.84/16.05 (setukpairinjR2) =>
% 121.84/16.05 ((
% 121.84/16.05 (setukpairinjR) =>
% 121.84/16.05 ((
% 121.84/16.05 (ksndsingleton) =>
% 121.84/16.05 ((
% 121.84/16.05 (ksndpairEq) =>
% 121.84/16.05 ((
% 121.84/16.05 (kpairsurjEq) =>
% 121.84/16.05 ((
% 121.84/16.05 (cartprodsndin) =>
% 121.84/16.05 ((
% 121.84/16.05 (cartprodpairmemEL) =>
% 121.84/16.05 ((
% 121.84/16.05 (cartprodpairmemER) =>
% 121.84/16.05 ((
% 121.84/16.05 (cartprodmempaircEq) =>
% 121.84/16.05 ((
% 121.84/16.05 (cartprodfstpairEq) =>
% 121.84/16.05 ((
% 121.84/16.05 (cartprodsndpairEq) =>
% 121.84/16.05 ((
% 121.84/16.05 (cartprodpairsurjEq) =>
% 121.84/16.05 ((
% 121.84/16.05 (dpsetconstrI) =>
% 121.84/16.05 ((
% 121.84/16.05 (dpsetconstrSub) =>
% 121.84/16.05 ((
% 121.84/16.05 (setOfPairsIsBReln) =>
% 121.84/16.05 ((
% 121.84/16.05 (dpsetconstrERa) =>
% 121.84/16.05 ((
% 121.84/16.05 (dpsetconstrEL1) =>
% 121.84/16.05 ((
% 121.84/16.05 (dpsetconstrEL2) =>
% 121.84/16.05 ((
% 121.84/16.05 (dpsetconstrER) =>
% 121.84/16.05 ((
% 121.84/16.05 (funcImageSingleton) =>
% 121.84/16.05 ((
% 121.84/16.05 (apProp) =>
% 121.84/16.05 ((
% 121.84/16.05 (app) =>
% 121.84/16.05 ((
% 121.84/16.05 (infuncsetfunc) =>
% 121.84/16.05 ((
% 121.84/16.05 (ap2p) =>
% 121.84/16.05 ((
% 121.84/16.05 (funcinfuncset) =>
% 121.84/16.05 ((
% 121.84/16.05 (lamProp) =>
% 121.84/16.05 ((
% 121.84/16.05 (lamp) =>
% 121.84/16.05 ((
% 121.84/16.05 (lam2p) =>
% 121.84/16.05 ((
% 121.84/16.05 (brelnall1) =>
% 121.84/16.05 ((
% 121.84/16.05 (brelnall2) =>
% 121.84/16.05 ((
% 121.84/16.05 (ex1E2) =>
% 121.84/16.05 ((
% 121.84/16.05 (funcGraphProp1) =>
% 121.84/16.05 ((
% 121.84/16.05 (funcGraphProp3) =>
% 121.84/16.05 ((
% 121.84/16.05 (funcGraphProp2) =>
% 121.84/16.05 ((
% 121.84/16.05 (funcextLem) =>
% 121.84/16.05 ((
% 121.84/16.05 (funcGraphProp4) =>
% 121.84/16.05 ((
% 121.84/16.05 (subbreln) =>
% 121.84/16.05 ((
% 121.84/16.05 (eqbreln) =>
% 121.84/16.05 ((
% 121.84/16.05 (funcext) =>
% 121.84/16.05 ((
% 121.84/16.05 (funcext2) =>
% 121.84/16.05 ((
% 121.84/16.05 (ap2apEq1) =>
% 121.84/16.05 ((
% 121.84/16.05 (ap2apEq2) =>
% 121.84/16.05 ((
% 121.84/16.05 (beta1) =>
% 121.84/16.05 ((
% 121.84/16.05 (eta1) =>
% 121.84/16.05 ((
% 121.84/16.05 (lam2lamEq) =>
% 121.84/16.05 ((
% 121.84/16.05 (beta2) =>
% 121.84/16.05 ((
% 121.84/16.05 (eta2) =>
% 121.84/16.05 ((
% 121.84/16.05 (iffalseProp1) =>
% 121.84/16.05 ((
% 121.84/16.05 (iffalseProp2) =>
% 121.84/16.05 ((
% 121.84/16.05 (iftrueProp1) =>
% 121.84/16.05 ((
% 121.84/16.05 (iftrueProp2) =>
% 121.84/16.05 ((
% 121.84/16.05 (ifSingleton) =>
% 121.84/16.05 ((
% 121.84/16.05 (ifp) =>
% 121.84/16.05 ((
% 121.84/16.05 (theeq) =>
% 121.84/16.05 ((
% 121.84/16.05 (iftrue) =>
% 121.84/16.05 ((
% 121.84/16.05 (iffalse) =>
% 121.84/16.05 ((
% 121.84/16.05 (iftrueorfalse) =>
% 121.84/16.05 ((
% 121.84/16.05 (binintersectT_lem) =>
% 121.84/16.05 ((
% 121.84/16.05 (binunionT_lem) =>
% 121.84/16.05 ((
% 121.84/16.05 (powersetT_lem) =>
% 121.84/16.05 ((
% 121.84/16.05 (setminusT_lem) =>
% 121.84/16.05 ((
% 121.84/16.05 (complementT_lem) =>
% 121.84/16.05 ((
% 121.84/16.05 (setextT) =>
% 121.84/16.05 ((
% 121.84/16.05 (subsetTI) =>
% 121.84/16.05 ((
% 121.84/16.05 (powersetTI1) =>
% 121.84/16.05 ((
% 121.84/16.05 (powersetTE1) =>
% 121.84/16.05 ((
% 121.84/16.05 (complementTI1) =>
% 121.84/16.05 ((
% 121.84/16.05 (complementTE1) =>
% 121.84/16.05 ((
% 121.84/16.05 (binintersectTELcontra) =>
% 121.84/16.05 ((
% 121.84/16.05 (binintersectTERcontra) =>
% 121.84/16.05 ((
% 121.84/16.05 (contrasubsetT) =>
% 121.84/16.05 ((
% 121.84/16.05 (contrasubsetT1) =>
% 121.84/16.05 ((
% 121.84/16.05 (contrasubsetT2) =>
% 121.84/16.05 ((
% 121.84/16.05 (contrasubsetT3) =>
% 121.84/16.05 ((
% 121.84/16.05 (doubleComplementI1) =>
% 121.84/16.05 ((
% 121.84/16.05 (doubleComplementE1) =>
% 121.84/16.05 ((
% 121.84/16.05 (doubleComplementSub1) =>
% 121.84/16.05 ((
% 121.84/16.05 (doubleComplementSub2) =>
% 121.84/16.05 ((
% 121.84/16.05 (doubleComplementEq) =>
% 121.84/16.05 ((
% 121.84/16.05 (complementTnotintersectT) =>
% 121.84/16.05 ((
% 121.84/16.05 (complementImpComplementIntersect) =>
% 121.84/16.05 ((
% 121.84/16.05 (complementSubsetComplementIntersect) =>
% 121.84/16.05 ((
% 121.84/16.05 (complementInPowersetComplementIntersect) =>
% 121.84/16.05 ((
% 121.84/16.05 (contraSubsetComplement) =>
% 121.84/16.05 ((
% 121.84/16.05 (complementTcontraSubset) =>
% 121.84/16.05 ((
% 121.84/16.05 (binunionTILcontra) =>
% 121.84/16.05 ((
% 121.84/16.05 (binunionTIRcontra) =>
% 121.84/16.05 ((
% 121.84/16.05 (inIntersectImpInUnion) =>
% 121.84/16.05 ((
% 121.84/16.05 (inIntersectImpInUnion2) =>
% 121.84/16.05 ((
% 121.84/16.05 (inIntersectImpInIntersectUnions) =>
% 121.84/16.05 ((
% 121.84/16.05 (intersectInPowersetIntersectUnions) =>
% 121.84/16.05 ((
% 121.84/16.05 (inComplementUnionImpNotIn1) =>
% 121.84/16.05 ((
% 121.84/16.05 (inComplementUnionImpInComplement1) =>
% 121.84/16.05 ((
% 121.84/16.05 (binunionTE) =>
% 121.84/16.05 ((
% 121.84/16.05 (binunionTEcontra) =>
% 121.84/16.05 ((
% 121.84/16.05 (demorgan2a1) =>
% 121.84/16.05 ((
% 121.84/16.05 (complementUnionInPowersetComplement) =>
% 121.84/16.05 ((
% 121.84/16.05 (demorgan2a2) =>
% 121.84/16.05 ((
% 121.84/16.05 (demorgan1a) =>
% 121.84/16.05 ((
% 121.84/16.05 (demorgan1b) =>
% 121.84/16.05 ((
% 121.84/16.05 (demorgan1) =>
% 121.84/16.05 ((
% 121.84/16.05 (demorgan2a) =>
% 121.84/16.05 ((
% 121.84/16.05 (demorgan2b2) =>
% 121.84/16.05 ((
% 121.84/16.05 (demorgan2b) =>
% 121.84/16.05 ((
% 121.84/16.05 (demorgan2) =>
% 121.84/16.05 ((
% 121.84/16.05 (woz13rule0) =>
% 121.84/16.05 ((
% 121.84/16.05 (woz13rule1) =>
% 121.84/16.05 ((
% 121.84/16.05 (woz13rule2) =>
% 121.84/16.05 ((
% 121.84/16.05 (woz13rule3) =>
% 121.84/16.05 ((
% 121.84/16.05 (woz13rule4) =>
% 121.84/16.05 ((
% 121.84/16.05 (woz1_1) =>
% 121.84/16.05 ((
% 121.84/16.05 (woz1_2) =>
% 121.84/16.05 ((
% 121.84/16.05 (woz1_3) =>
% 121.84/16.05 ((
% 121.84/16.05 (woz1_4) =>
% 121.84/16.05 ((
% 121.84/16.05 (woz1_5) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1all2) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1SetBreln1) =>
% 121.84/16.05 ((
% 121.84/16.05 (choice2fnsingleton) =>
% 121.84/16.05 ((
% 121.84/16.05 (setOfPairsIsBReln1) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1all1) =>
% 121.84/16.05 ((
% 121.84/16.05 (subbreln1) =>
% 121.84/16.05 ((
% 121.84/16.05 (eqbreln1) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1invprop) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1invI) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1invE) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1compprop) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1compI) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1compE) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1compEex) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1unionprop) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1unionIL) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1unionIR) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1unionI) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1unionE) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1unionEcases) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1unionCommutes) =>
% 121.84/16.05 ((
% 121.84/16.05 (woz2Ex) =>
% 121.84/16.05 ((
% 121.84/16.05 (woz2W) =>
% 121.84/16.05 ((
% 121.84/16.05 (woz2A) =>
% 121.84/16.05 ((
% 121.84/16.05 (woz2B) =>
% 121.84/16.05 ((
% 121.84/16.05 (image1Ex) =>
% 121.84/16.05 ((
% 121.84/16.05 (image1Ex1) =>
% 121.84/16.05 ((
% 121.84/16.05 (image1Equiv) =>
% 121.84/16.05 ((
% 121.84/16.05 (image1E) =>
% 121.84/16.05 ((
% 121.84/16.05 (image1I) =>
% 121.84/16.05 ((
% 121.84/16.05 (injFuncInInjFuncSet) =>
% 121.84/16.05 ((
% 121.84/16.05 (!!) @ (
% 121.84/16.05 (('#B') @ (
% 121.84/16.05 !!) @
% 121.84/16.05 (
% 121.84/16.05 (
% 121.84/16.05 ('#B') @ (
% 121.84/16.05 (
% 121.84/16.05 ('#B') @ (
% 121.84/16.05 !!))) @
% 121.84/16.05 (
% 121.84/16.05 (
% 121.84/16.05 ('#S') @ (
% 121.84/16.05 (
% 121.84/16.05 ('#B') @ (
% 121.84/16.05 '#S') @
% 121.84/16.05 (
% 121.84/16.05 (
% 121.84/16.05 ('#B') @ (
% 121.84/16.05 (
% 121.84/16.05 ('#B') @ (
% 121.84/16.05 '#S'))) @
% 121.84/16.05 (
% 121.84/16.05 (
% 121.84/16.05 ('#B') @ (
% 121.84/16.05 (
% 121.84/16.05 ('#B') @ (
% 121.84/16.05 (
% 121.84/16.05 ('#B') @ (
% 121.84/16.05 =>))))) @
% 121.84/16.05 (
% 121.84/16.05 (
% 121.84/16.05 ('#B') @ (
% 121.84/16.05 (
% 121.84/16.05 ('#B') @ (
% 121.84/16.05 (
% 121.84/16.05 ('#C') @ in)))) @
% 121.84/16.05 injFuncSet)))))))) @
% 121.84/16.05 (
% 121.84/16.05 (
% 121.84/16.05 ('#B') @ (
% 121.84/16.05 (
% 121.84/16.05 ('#B') @ (
% 121.84/16.05 (
% 121.84/16.05 ('#C') @ in)))) @
% 121.84/16.05 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 121.84/16.05 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl369])).
% 121.84/16.05 thf(zip_derived_cl384, plain,
% 121.84/16.05 (~ (((emptyInPowerset) =>
% 121.84/16.05 (((powersetE) =>
% 121.84/16.05 (((setunionI) =>
% 121.84/16.05 (((setunionE) =>
% 121.84/16.05 (((subPowSU) =>
% 121.84/16.05 (((exuE2) =>
% 121.84/16.05 (((nonemptyImpWitness) =>
% 121.84/16.05 (((uniqinunit) =>
% 121.84/16.05 (((notinsingleton) =>
% 121.84/16.05 (((eqinunit) =>
% 121.84/16.05 (((singletonsswitch) =>
% 121.84/16.05 (((upairsetE) =>
% 121.84/16.05 (((upairsetIL) =>
% 121.84/16.05 (((upairsetIR) =>
% 121.84/16.05 (((emptyE1) =>
% 121.84/16.05 (((vacuousDall) =>
% 121.84/16.05 (((quantDeMorgan1) =>
% 121.84/16.05 (((quantDeMorgan2) =>
% 121.84/16.05 (((quantDeMorgan3) =>
% 121.84/16.05 (((quantDeMorgan4) =>
% 121.84/16.05 (((prop2setI) =>
% 121.84/16.05 (((prop2set2propI) =>
% 121.84/16.05 (((notdexE) =>
% 121.84/16.05 (((notdallE) =>
% 121.84/16.05 (((exuI1) =>
% 121.84/16.05 (((exuI3) =>
% 121.84/16.05 (((exuI2) =>
% 121.84/16.05 (((inCongP) =>
% 121.84/16.05 (((in__Cong) =>
% 121.84/16.05 (((exuE3u) =>
% 121.84/16.05 ((
% 121.84/16.05 (exu__Cong) =>
% 121.84/16.05 ((
% 121.84/16.05 (setadjoin__Cong) =>
% 121.84/16.05 ((
% 121.84/16.05 (powerset__Cong) =>
% 121.84/16.05 ((
% 121.84/16.05 (setunion__Cong) =>
% 121.84/16.05 ((
% 121.84/16.05 (exuEu) =>
% 121.84/16.05 ((
% 121.84/16.05 (descr__Cong) =>
% 121.84/16.05 ((
% 121.84/16.05 (dsetconstr__Cong) =>
% 121.84/16.05 ((
% 121.84/16.05 (subsetI1) =>
% 121.84/16.05 ((
% 121.84/16.05 (eqimpsubset2) =>
% 121.84/16.05 ((
% 121.84/16.05 (eqimpsubset1) =>
% 121.84/16.05 ((
% 121.84/16.05 (subsetI2) =>
% 121.84/16.05 ((
% 121.84/16.05 (emptysetsubset) =>
% 121.84/16.05 ((
% 121.84/16.05 (subsetE) =>
% 121.84/16.05 ((
% 121.84/16.05 (subsetE2) =>
% 121.84/16.05 ((
% 121.84/16.05 (notsubsetI) =>
% 121.84/16.05 ((
% 121.84/16.05 (notequalI1) =>
% 121.84/16.05 ((
% 121.84/16.05 (notequalI2) =>
% 121.84/16.05 ((
% 121.84/16.05 (subsetRefl) =>
% 121.84/16.05 ((
% 121.84/16.05 (subsetTrans) =>
% 121.84/16.05 ((
% 121.84/16.05 (setadjoinSub) =>
% 121.84/16.05 ((
% 121.84/16.05 (setadjoinSub2) =>
% 121.84/16.05 ((
% 121.84/16.05 (subset2powerset) =>
% 121.84/16.05 ((
% 121.84/16.05 (setextsub) =>
% 121.84/16.05 ((
% 121.84/16.05 (subsetemptysetimpeq) =>
% 121.84/16.05 ((
% 121.84/16.05 (powersetI1) =>
% 121.84/16.05 ((
% 121.84/16.05 (powersetE1) =>
% 121.84/16.05 ((
% 121.84/16.05 (inPowerset) =>
% 121.84/16.05 ((
% 121.84/16.05 (powersetsubset) =>
% 121.84/16.05 ((
% 121.84/16.05 (sepInPowerset) =>
% 121.84/16.05 ((
% 121.84/16.05 (sepSubset) =>
% 121.84/16.05 ((
% 121.84/16.05 (binunionIL) =>
% 121.84/16.05 ((
% 121.84/16.05 (upairset2IR) =>
% 121.84/16.05 ((
% 121.84/16.05 (binunionIR) =>
% 121.84/16.05 ((
% 121.84/16.05 (binunionEcases) =>
% 121.84/16.05 ((
% 121.84/16.05 (binunionE) =>
% 121.84/16.05 ((
% 121.84/16.05 (binunionLsub) =>
% 121.84/16.05 ((
% 121.84/16.05 (binunionRsub) =>
% 121.84/16.05 ((
% 121.84/16.05 (binintersectI) =>
% 121.84/16.05 ((
% 121.84/16.05 (binintersectSubset5) =>
% 121.84/16.05 ((
% 121.84/16.05 (binintersectEL) =>
% 121.84/16.05 ((
% 121.84/16.05 (binintersectLsub) =>
% 121.84/16.05 ((
% 121.84/16.05 (binintersectSubset2) =>
% 121.84/16.05 ((
% 121.84/16.05 (binintersectSubset3) =>
% 121.84/16.05 ((
% 121.84/16.05 (binintersectER) =>
% 121.84/16.05 ((
% 121.84/16.05 (disjointsetsI1) =>
% 121.84/16.05 ((
% 121.84/16.05 (binintersectRsub) =>
% 121.84/16.05 ((
% 121.84/16.05 (binintersectSubset4) =>
% 121.84/16.05 ((
% 121.84/16.05 (binintersectSubset1) =>
% 121.84/16.05 ((
% 121.84/16.05 (bs114d) =>
% 121.84/16.05 ((
% 121.84/16.05 (setminusI) =>
% 121.84/16.05 ((
% 121.84/16.05 (setminusEL) =>
% 121.84/16.05 ((
% 121.84/16.05 (setminusER) =>
% 121.84/16.05 ((
% 121.84/16.05 (setminusSubset2) =>
% 121.84/16.05 ((
% 121.84/16.05 (setminusERneg) =>
% 121.84/16.05 ((
% 121.84/16.05 (setminusELneg) =>
% 121.84/16.05 ((
% 121.84/16.05 (setminusILneg) =>
% 121.84/16.05 ((
% 121.84/16.05 (setminusIRneg) =>
% 121.84/16.05 ((
% 121.84/16.05 (setminusLsub) =>
% 121.84/16.05 ((
% 121.84/16.05 (setminusSubset1) =>
% 121.84/16.05 ((
% 121.84/16.05 (symdiffE) =>
% 121.84/16.05 ((
% 121.84/16.05 (symdiffI1) =>
% 121.84/16.05 ((
% 121.84/16.05 (symdiffI2) =>
% 121.84/16.05 ((
% 121.84/16.05 (symdiffIneg1) =>
% 121.84/16.05 ((
% 121.84/16.05 (symdiffIneg2) =>
% 121.84/16.05 ((
% 121.84/16.05 (secondinupair) =>
% 121.84/16.05 ((
% 121.84/16.05 (setukpairIL) =>
% 121.84/16.05 ((
% 121.84/16.05 (setukpairIR) =>
% 121.84/16.05 ((
% 121.84/16.05 (kpairiskpair) =>
% 121.84/16.05 ((
% 121.84/16.05 (kpairp) =>
% 121.84/16.05 ((
% 121.84/16.05 (singletonsubset) =>
% 121.84/16.05 ((
% 121.84/16.05 (singletoninpowerset) =>
% 121.84/16.05 ((
% 121.84/16.05 (singletoninpowunion) =>
% 121.84/16.05 ((
% 121.84/16.05 (upairset2E) =>
% 121.84/16.05 ((
% 121.84/16.05 (upairsubunion) =>
% 121.84/16.05 ((
% 121.84/16.05 (upairinpowunion) =>
% 121.84/16.05 ((
% 121.84/16.05 (ubforcartprodlem1) =>
% 121.84/16.05 ((
% 121.84/16.05 (ubforcartprodlem2) =>
% 121.84/16.05 ((
% 121.84/16.05 (ubforcartprodlem3) =>
% 121.84/16.05 ((
% 121.84/16.05 (cartprodpairin) =>
% 121.84/16.05 ((
% 121.84/16.05 (cartprodmempair1) =>
% 121.84/16.05 ((
% 121.84/16.05 (cartprodmempair) =>
% 121.84/16.05 ((
% 121.84/16.05 (setunionE2) =>
% 121.84/16.05 ((
% 121.84/16.05 (setunionsingleton1) =>
% 121.84/16.05 ((
% 121.84/16.05 (setunionsingleton2) =>
% 121.84/16.05 ((
% 121.84/16.05 (setunionsingleton) =>
% 121.84/16.05 ((
% 121.84/16.05 (singletonprop) =>
% 121.84/16.05 ((
% 121.84/16.05 (ex1E1) =>
% 121.84/16.05 ((
% 121.84/16.05 (ex1I) =>
% 121.84/16.05 ((
% 121.84/16.05 (ex1I2) =>
% 121.84/16.05 ((
% 121.84/16.05 (singletonsuniq) =>
% 121.84/16.05 ((
% 121.84/16.05 (setukpairinjL1) =>
% 121.84/16.05 ((
% 121.84/16.05 (kfstsingleton) =>
% 121.84/16.05 ((
% 121.84/16.05 (theprop) =>
% 121.84/16.05 ((
% 121.84/16.05 (kfstpairEq) =>
% 121.84/16.05 ((
% 121.84/16.05 (cartprodfstin) =>
% 121.84/16.05 ((
% 121.84/16.05 (setukpairinjL2) =>
% 121.84/16.05 ((
% 121.84/16.05 (setukpairinjL) =>
% 121.84/16.05 ((
% 121.84/16.05 (setukpairinjR11) =>
% 121.84/16.05 ((
% 121.84/16.05 (setukpairinjR12) =>
% 121.84/16.05 ((
% 121.84/16.05 (setukpairinjR1) =>
% 121.84/16.05 ((
% 121.84/16.05 (upairequniteq) =>
% 121.84/16.05 ((
% 121.84/16.05 (setukpairinjR2) =>
% 121.84/16.05 ((
% 121.84/16.05 (setukpairinjR) =>
% 121.84/16.05 ((
% 121.84/16.05 (ksndsingleton) =>
% 121.84/16.05 ((
% 121.84/16.05 (ksndpairEq) =>
% 121.84/16.05 ((
% 121.84/16.05 (kpairsurjEq) =>
% 121.84/16.05 ((
% 121.84/16.05 (cartprodsndin) =>
% 121.84/16.05 ((
% 121.84/16.05 (cartprodpairmemEL) =>
% 121.84/16.05 ((
% 121.84/16.05 (cartprodpairmemER) =>
% 121.84/16.05 ((
% 121.84/16.05 (cartprodmempaircEq) =>
% 121.84/16.05 ((
% 121.84/16.05 (cartprodfstpairEq) =>
% 121.84/16.05 ((
% 121.84/16.05 (cartprodsndpairEq) =>
% 121.84/16.05 ((
% 121.84/16.05 (cartprodpairsurjEq) =>
% 121.84/16.05 ((
% 121.84/16.05 (dpsetconstrI) =>
% 121.84/16.05 ((
% 121.84/16.05 (dpsetconstrSub) =>
% 121.84/16.05 ((
% 121.84/16.05 (setOfPairsIsBReln) =>
% 121.84/16.05 ((
% 121.84/16.05 (dpsetconstrERa) =>
% 121.84/16.05 ((
% 121.84/16.05 (dpsetconstrEL1) =>
% 121.84/16.05 ((
% 121.84/16.05 (dpsetconstrEL2) =>
% 121.84/16.05 ((
% 121.84/16.05 (dpsetconstrER) =>
% 121.84/16.05 ((
% 121.84/16.05 (funcImageSingleton) =>
% 121.84/16.05 ((
% 121.84/16.05 (apProp) =>
% 121.84/16.05 ((
% 121.84/16.05 (app) =>
% 121.84/16.05 ((
% 121.84/16.05 (infuncsetfunc) =>
% 121.84/16.05 ((
% 121.84/16.05 (ap2p) =>
% 121.84/16.05 ((
% 121.84/16.05 (funcinfuncset) =>
% 121.84/16.05 ((
% 121.84/16.05 (lamProp) =>
% 121.84/16.05 ((
% 121.84/16.05 (lamp) =>
% 121.84/16.05 ((
% 121.84/16.05 (lam2p) =>
% 121.84/16.05 ((
% 121.84/16.05 (brelnall1) =>
% 121.84/16.05 ((
% 121.84/16.05 (brelnall2) =>
% 121.84/16.05 ((
% 121.84/16.05 (ex1E2) =>
% 121.84/16.05 ((
% 121.84/16.05 (funcGraphProp1) =>
% 121.84/16.05 ((
% 121.84/16.05 (funcGraphProp3) =>
% 121.84/16.05 ((
% 121.84/16.05 (funcGraphProp2) =>
% 121.84/16.05 ((
% 121.84/16.05 (funcextLem) =>
% 121.84/16.05 ((
% 121.84/16.05 (funcGraphProp4) =>
% 121.84/16.05 ((
% 121.84/16.05 (subbreln) =>
% 121.84/16.05 ((
% 121.84/16.05 (eqbreln) =>
% 121.84/16.05 ((
% 121.84/16.05 (funcext) =>
% 121.84/16.05 ((
% 121.84/16.05 (funcext2) =>
% 121.84/16.05 ((
% 121.84/16.05 (ap2apEq1) =>
% 121.84/16.05 ((
% 121.84/16.05 (ap2apEq2) =>
% 121.84/16.05 ((
% 121.84/16.05 (beta1) =>
% 121.84/16.05 ((
% 121.84/16.05 (eta1) =>
% 121.84/16.05 ((
% 121.84/16.05 (lam2lamEq) =>
% 121.84/16.05 ((
% 121.84/16.05 (beta2) =>
% 121.84/16.05 ((
% 121.84/16.05 (eta2) =>
% 121.84/16.05 ((
% 121.84/16.05 (iffalseProp1) =>
% 121.84/16.05 ((
% 121.84/16.05 (iffalseProp2) =>
% 121.84/16.05 ((
% 121.84/16.05 (iftrueProp1) =>
% 121.84/16.05 ((
% 121.84/16.05 (iftrueProp2) =>
% 121.84/16.05 ((
% 121.84/16.05 (ifSingleton) =>
% 121.84/16.05 ((
% 121.84/16.05 (ifp) =>
% 121.84/16.05 ((
% 121.84/16.05 (theeq) =>
% 121.84/16.05 ((
% 121.84/16.05 (iftrue) =>
% 121.84/16.05 ((
% 121.84/16.05 (iffalse) =>
% 121.84/16.05 ((
% 121.84/16.05 (iftrueorfalse) =>
% 121.84/16.05 ((
% 121.84/16.05 (binintersectT_lem) =>
% 121.84/16.05 ((
% 121.84/16.05 (binunionT_lem) =>
% 121.84/16.05 ((
% 121.84/16.05 (powersetT_lem) =>
% 121.84/16.05 ((
% 121.84/16.05 (setminusT_lem) =>
% 121.84/16.05 ((
% 121.84/16.05 (complementT_lem) =>
% 121.84/16.05 ((
% 121.84/16.05 (setextT) =>
% 121.84/16.05 ((
% 121.84/16.05 (subsetTI) =>
% 121.84/16.05 ((
% 121.84/16.05 (powersetTI1) =>
% 121.84/16.05 ((
% 121.84/16.05 (powersetTE1) =>
% 121.84/16.05 ((
% 121.84/16.05 (complementTI1) =>
% 121.84/16.05 ((
% 121.84/16.05 (complementTE1) =>
% 121.84/16.05 ((
% 121.84/16.05 (binintersectTELcontra) =>
% 121.84/16.05 ((
% 121.84/16.05 (binintersectTERcontra) =>
% 121.84/16.05 ((
% 121.84/16.05 (contrasubsetT) =>
% 121.84/16.05 ((
% 121.84/16.05 (contrasubsetT1) =>
% 121.84/16.05 ((
% 121.84/16.05 (contrasubsetT2) =>
% 121.84/16.05 ((
% 121.84/16.05 (contrasubsetT3) =>
% 121.84/16.05 ((
% 121.84/16.05 (doubleComplementI1) =>
% 121.84/16.05 ((
% 121.84/16.05 (doubleComplementE1) =>
% 121.84/16.05 ((
% 121.84/16.05 (doubleComplementSub1) =>
% 121.84/16.05 ((
% 121.84/16.05 (doubleComplementSub2) =>
% 121.84/16.05 ((
% 121.84/16.05 (doubleComplementEq) =>
% 121.84/16.05 ((
% 121.84/16.05 (complementTnotintersectT) =>
% 121.84/16.05 ((
% 121.84/16.05 (complementImpComplementIntersect) =>
% 121.84/16.05 ((
% 121.84/16.05 (complementSubsetComplementIntersect) =>
% 121.84/16.05 ((
% 121.84/16.05 (complementInPowersetComplementIntersect) =>
% 121.84/16.05 ((
% 121.84/16.05 (contraSubsetComplement) =>
% 121.84/16.05 ((
% 121.84/16.05 (complementTcontraSubset) =>
% 121.84/16.05 ((
% 121.84/16.05 (binunionTILcontra) =>
% 121.84/16.05 ((
% 121.84/16.05 (binunionTIRcontra) =>
% 121.84/16.05 ((
% 121.84/16.05 (inIntersectImpInUnion) =>
% 121.84/16.05 ((
% 121.84/16.05 (inIntersectImpInUnion2) =>
% 121.84/16.05 ((
% 121.84/16.05 (inIntersectImpInIntersectUnions) =>
% 121.84/16.05 ((
% 121.84/16.05 (intersectInPowersetIntersectUnions) =>
% 121.84/16.05 ((
% 121.84/16.05 (inComplementUnionImpNotIn1) =>
% 121.84/16.05 ((
% 121.84/16.05 (inComplementUnionImpInComplement1) =>
% 121.84/16.05 ((
% 121.84/16.05 (binunionTE) =>
% 121.84/16.05 ((
% 121.84/16.05 (binunionTEcontra) =>
% 121.84/16.05 ((
% 121.84/16.05 (demorgan2a1) =>
% 121.84/16.05 ((
% 121.84/16.05 (complementUnionInPowersetComplement) =>
% 121.84/16.05 ((
% 121.84/16.05 (demorgan2a2) =>
% 121.84/16.05 ((
% 121.84/16.05 (demorgan1a) =>
% 121.84/16.05 ((
% 121.84/16.05 (demorgan1b) =>
% 121.84/16.05 ((
% 121.84/16.05 (demorgan1) =>
% 121.84/16.05 ((
% 121.84/16.05 (demorgan2a) =>
% 121.84/16.05 ((
% 121.84/16.05 (demorgan2b2) =>
% 121.84/16.05 ((
% 121.84/16.05 (demorgan2b) =>
% 121.84/16.05 ((
% 121.84/16.05 (demorgan2) =>
% 121.84/16.05 ((
% 121.84/16.05 (woz13rule0) =>
% 121.84/16.05 ((
% 121.84/16.05 (woz13rule1) =>
% 121.84/16.05 ((
% 121.84/16.05 (woz13rule2) =>
% 121.84/16.05 ((
% 121.84/16.05 (woz13rule3) =>
% 121.84/16.05 ((
% 121.84/16.05 (woz13rule4) =>
% 121.84/16.05 ((
% 121.84/16.05 (woz1_1) =>
% 121.84/16.05 ((
% 121.84/16.05 (woz1_2) =>
% 121.84/16.05 ((
% 121.84/16.05 (woz1_3) =>
% 121.84/16.05 ((
% 121.84/16.05 (woz1_4) =>
% 121.84/16.05 ((
% 121.84/16.05 (woz1_5) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1all2) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1SetBreln1) =>
% 121.84/16.05 ((
% 121.84/16.05 (choice2fnsingleton) =>
% 121.84/16.05 ((
% 121.84/16.05 (setOfPairsIsBReln1) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1all1) =>
% 121.84/16.05 ((
% 121.84/16.05 (subbreln1) =>
% 121.84/16.05 ((
% 121.84/16.05 (eqbreln1) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1invprop) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1invI) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1invE) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1compprop) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1compI) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1compE) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1compEex) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1unionprop) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1unionIL) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1unionIR) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1unionI) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1unionE) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1unionEcases) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1unionCommutes) =>
% 121.84/16.05 ((
% 121.84/16.05 (woz2Ex) =>
% 121.84/16.05 ((
% 121.84/16.05 (woz2W) =>
% 121.84/16.05 ((
% 121.84/16.05 (woz2A) =>
% 121.84/16.05 ((
% 121.84/16.05 (woz2B) =>
% 121.84/16.05 ((
% 121.84/16.05 (image1Ex) =>
% 121.84/16.05 ((
% 121.84/16.05 (image1Ex1) =>
% 121.84/16.05 ((
% 121.84/16.05 (image1Equiv) =>
% 121.84/16.05 ((
% 121.84/16.05 (image1E) =>
% 121.84/16.05 ((
% 121.84/16.05 (image1I) =>
% 121.84/16.05 ((
% 121.84/16.05 (injFuncInInjFuncSet) =>
% 121.84/16.05 ((
% 121.84/16.05 (!!) @ (
% 121.84/16.05 (('#B') @ (
% 121.84/16.05 !!) @
% 121.84/16.05 (
% 121.84/16.05 (
% 121.84/16.05 ('#B') @ (
% 121.84/16.05 (
% 121.84/16.05 ('#B') @ (
% 121.84/16.05 !!))) @
% 121.84/16.05 (
% 121.84/16.05 (
% 121.84/16.05 ('#S') @ (
% 121.84/16.05 (
% 121.84/16.05 ('#B') @ (
% 121.84/16.05 '#S') @
% 121.84/16.05 (
% 121.84/16.05 (
% 121.84/16.05 ('#B') @ (
% 121.84/16.05 (
% 121.84/16.05 ('#B') @ (
% 121.84/16.05 '#S'))) @
% 121.84/16.05 (
% 121.84/16.05 (
% 121.84/16.05 ('#B') @ (
% 121.84/16.05 (
% 121.84/16.05 ('#B') @ (
% 121.84/16.05 (
% 121.84/16.05 ('#B') @ (
% 121.84/16.05 =>))))) @
% 121.84/16.05 (
% 121.84/16.05 (
% 121.84/16.05 ('#B') @ (
% 121.84/16.05 (
% 121.84/16.05 ('#B') @ (
% 121.84/16.05 (
% 121.84/16.05 ('#C') @ in)))) @
% 121.84/16.05 injFuncSet)))))))) @
% 121.84/16.05 (
% 121.84/16.05 (
% 121.84/16.05 ('#B') @ (
% 121.84/16.05 (
% 121.84/16.05 ('#B') @ (
% 121.84/16.05 (
% 121.84/16.05 ('#C') @ in)))) @
% 121.84/16.05 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 121.84/16.05 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl376])).
% 121.84/16.05 thf(zip_derived_cl392, plain,
% 121.84/16.05 (~ (((powersetE) =>
% 121.84/16.05 (((setunionI) =>
% 121.84/16.05 (((setunionE) =>
% 121.84/16.05 (((subPowSU) =>
% 121.84/16.05 (((exuE2) =>
% 121.84/16.05 (((nonemptyImpWitness) =>
% 121.84/16.05 (((uniqinunit) =>
% 121.84/16.05 (((notinsingleton) =>
% 121.84/16.05 (((eqinunit) =>
% 121.84/16.05 (((singletonsswitch) =>
% 121.84/16.05 (((upairsetE) =>
% 121.84/16.05 (((upairsetIL) =>
% 121.84/16.05 (((upairsetIR) =>
% 121.84/16.05 (((emptyE1) =>
% 121.84/16.05 (((vacuousDall) =>
% 121.84/16.05 (((quantDeMorgan1) =>
% 121.84/16.05 (((quantDeMorgan2) =>
% 121.84/16.05 (((quantDeMorgan3) =>
% 121.84/16.05 (((quantDeMorgan4) =>
% 121.84/16.05 (((prop2setI) =>
% 121.84/16.05 (((prop2set2propI) =>
% 121.84/16.05 (((notdexE) =>
% 121.84/16.05 (((notdallE) =>
% 121.84/16.05 (((exuI1) =>
% 121.84/16.05 (((exuI3) =>
% 121.84/16.05 (((exuI2) =>
% 121.84/16.05 (((inCongP) =>
% 121.84/16.05 (((in__Cong) =>
% 121.84/16.05 (((exuE3u) =>
% 121.84/16.05 (((exu__Cong) =>
% 121.84/16.05 ((
% 121.84/16.05 (setadjoin__Cong) =>
% 121.84/16.05 ((
% 121.84/16.05 (powerset__Cong) =>
% 121.84/16.05 ((
% 121.84/16.05 (setunion__Cong) =>
% 121.84/16.05 ((
% 121.84/16.05 (exuEu) =>
% 121.84/16.05 ((
% 121.84/16.05 (descr__Cong) =>
% 121.84/16.05 ((
% 121.84/16.05 (dsetconstr__Cong) =>
% 121.84/16.05 ((
% 121.84/16.05 (subsetI1) =>
% 121.84/16.05 ((
% 121.84/16.05 (eqimpsubset2) =>
% 121.84/16.05 ((
% 121.84/16.05 (eqimpsubset1) =>
% 121.84/16.05 ((
% 121.84/16.05 (subsetI2) =>
% 121.84/16.05 ((
% 121.84/16.05 (emptysetsubset) =>
% 121.84/16.05 ((
% 121.84/16.05 (subsetE) =>
% 121.84/16.05 ((
% 121.84/16.05 (subsetE2) =>
% 121.84/16.05 ((
% 121.84/16.05 (notsubsetI) =>
% 121.84/16.05 ((
% 121.84/16.05 (notequalI1) =>
% 121.84/16.05 ((
% 121.84/16.05 (notequalI2) =>
% 121.84/16.05 ((
% 121.84/16.05 (subsetRefl) =>
% 121.84/16.05 ((
% 121.84/16.05 (subsetTrans) =>
% 121.84/16.05 ((
% 121.84/16.05 (setadjoinSub) =>
% 121.84/16.05 ((
% 121.84/16.05 (setadjoinSub2) =>
% 121.84/16.05 ((
% 121.84/16.05 (subset2powerset) =>
% 121.84/16.05 ((
% 121.84/16.05 (setextsub) =>
% 121.84/16.05 ((
% 121.84/16.05 (subsetemptysetimpeq) =>
% 121.84/16.05 ((
% 121.84/16.05 (powersetI1) =>
% 121.84/16.05 ((
% 121.84/16.05 (powersetE1) =>
% 121.84/16.05 ((
% 121.84/16.05 (inPowerset) =>
% 121.84/16.05 ((
% 121.84/16.05 (powersetsubset) =>
% 121.84/16.05 ((
% 121.84/16.05 (sepInPowerset) =>
% 121.84/16.05 ((
% 121.84/16.05 (sepSubset) =>
% 121.84/16.05 ((
% 121.84/16.05 (binunionIL) =>
% 121.84/16.05 ((
% 121.84/16.05 (upairset2IR) =>
% 121.84/16.05 ((
% 121.84/16.05 (binunionIR) =>
% 121.84/16.05 ((
% 121.84/16.05 (binunionEcases) =>
% 121.84/16.05 ((
% 121.84/16.05 (binunionE) =>
% 121.84/16.05 ((
% 121.84/16.05 (binunionLsub) =>
% 121.84/16.05 ((
% 121.84/16.05 (binunionRsub) =>
% 121.84/16.05 ((
% 121.84/16.05 (binintersectI) =>
% 121.84/16.05 ((
% 121.84/16.05 (binintersectSubset5) =>
% 121.84/16.05 ((
% 121.84/16.05 (binintersectEL) =>
% 121.84/16.05 ((
% 121.84/16.05 (binintersectLsub) =>
% 121.84/16.05 ((
% 121.84/16.05 (binintersectSubset2) =>
% 121.84/16.05 ((
% 121.84/16.05 (binintersectSubset3) =>
% 121.84/16.05 ((
% 121.84/16.05 (binintersectER) =>
% 121.84/16.05 ((
% 121.84/16.05 (disjointsetsI1) =>
% 121.84/16.05 ((
% 121.84/16.05 (binintersectRsub) =>
% 121.84/16.05 ((
% 121.84/16.05 (binintersectSubset4) =>
% 121.84/16.05 ((
% 121.84/16.05 (binintersectSubset1) =>
% 121.84/16.05 ((
% 121.84/16.05 (bs114d) =>
% 121.84/16.05 ((
% 121.84/16.05 (setminusI) =>
% 121.84/16.05 ((
% 121.84/16.05 (setminusEL) =>
% 121.84/16.05 ((
% 121.84/16.05 (setminusER) =>
% 121.84/16.05 ((
% 121.84/16.05 (setminusSubset2) =>
% 121.84/16.05 ((
% 121.84/16.05 (setminusERneg) =>
% 121.84/16.05 ((
% 121.84/16.05 (setminusELneg) =>
% 121.84/16.05 ((
% 121.84/16.05 (setminusILneg) =>
% 121.84/16.05 ((
% 121.84/16.05 (setminusIRneg) =>
% 121.84/16.05 ((
% 121.84/16.05 (setminusLsub) =>
% 121.84/16.05 ((
% 121.84/16.05 (setminusSubset1) =>
% 121.84/16.05 ((
% 121.84/16.05 (symdiffE) =>
% 121.84/16.05 ((
% 121.84/16.05 (symdiffI1) =>
% 121.84/16.05 ((
% 121.84/16.05 (symdiffI2) =>
% 121.84/16.05 ((
% 121.84/16.05 (symdiffIneg1) =>
% 121.84/16.05 ((
% 121.84/16.05 (symdiffIneg2) =>
% 121.84/16.05 ((
% 121.84/16.05 (secondinupair) =>
% 121.84/16.05 ((
% 121.84/16.05 (setukpairIL) =>
% 121.84/16.05 ((
% 121.84/16.05 (setukpairIR) =>
% 121.84/16.05 ((
% 121.84/16.05 (kpairiskpair) =>
% 121.84/16.05 ((
% 121.84/16.05 (kpairp) =>
% 121.84/16.05 ((
% 121.84/16.05 (singletonsubset) =>
% 121.84/16.05 ((
% 121.84/16.05 (singletoninpowerset) =>
% 121.84/16.05 ((
% 121.84/16.05 (singletoninpowunion) =>
% 121.84/16.05 ((
% 121.84/16.05 (upairset2E) =>
% 121.84/16.05 ((
% 121.84/16.05 (upairsubunion) =>
% 121.84/16.05 ((
% 121.84/16.05 (upairinpowunion) =>
% 121.84/16.05 ((
% 121.84/16.05 (ubforcartprodlem1) =>
% 121.84/16.05 ((
% 121.84/16.05 (ubforcartprodlem2) =>
% 121.84/16.05 ((
% 121.84/16.05 (ubforcartprodlem3) =>
% 121.84/16.05 ((
% 121.84/16.05 (cartprodpairin) =>
% 121.84/16.05 ((
% 121.84/16.05 (cartprodmempair1) =>
% 121.84/16.05 ((
% 121.84/16.05 (cartprodmempair) =>
% 121.84/16.05 ((
% 121.84/16.05 (setunionE2) =>
% 121.84/16.05 ((
% 121.84/16.05 (setunionsingleton1) =>
% 121.84/16.05 ((
% 121.84/16.05 (setunionsingleton2) =>
% 121.84/16.05 ((
% 121.84/16.05 (setunionsingleton) =>
% 121.84/16.05 ((
% 121.84/16.05 (singletonprop) =>
% 121.84/16.05 ((
% 121.84/16.05 (ex1E1) =>
% 121.84/16.05 ((
% 121.84/16.05 (ex1I) =>
% 121.84/16.05 ((
% 121.84/16.05 (ex1I2) =>
% 121.84/16.05 ((
% 121.84/16.05 (singletonsuniq) =>
% 121.84/16.05 ((
% 121.84/16.05 (setukpairinjL1) =>
% 121.84/16.05 ((
% 121.84/16.05 (kfstsingleton) =>
% 121.84/16.05 ((
% 121.84/16.05 (theprop) =>
% 121.84/16.05 ((
% 121.84/16.05 (kfstpairEq) =>
% 121.84/16.05 ((
% 121.84/16.05 (cartprodfstin) =>
% 121.84/16.05 ((
% 121.84/16.05 (setukpairinjL2) =>
% 121.84/16.05 ((
% 121.84/16.05 (setukpairinjL) =>
% 121.84/16.05 ((
% 121.84/16.05 (setukpairinjR11) =>
% 121.84/16.05 ((
% 121.84/16.05 (setukpairinjR12) =>
% 121.84/16.05 ((
% 121.84/16.05 (setukpairinjR1) =>
% 121.84/16.05 ((
% 121.84/16.05 (upairequniteq) =>
% 121.84/16.05 ((
% 121.84/16.05 (setukpairinjR2) =>
% 121.84/16.05 ((
% 121.84/16.05 (setukpairinjR) =>
% 121.84/16.05 ((
% 121.84/16.05 (ksndsingleton) =>
% 121.84/16.05 ((
% 121.84/16.05 (ksndpairEq) =>
% 121.84/16.05 ((
% 121.84/16.05 (kpairsurjEq) =>
% 121.84/16.05 ((
% 121.84/16.05 (cartprodsndin) =>
% 121.84/16.05 ((
% 121.84/16.05 (cartprodpairmemEL) =>
% 121.84/16.05 ((
% 121.84/16.05 (cartprodpairmemER) =>
% 121.84/16.05 ((
% 121.84/16.05 (cartprodmempaircEq) =>
% 121.84/16.05 ((
% 121.84/16.05 (cartprodfstpairEq) =>
% 121.84/16.05 ((
% 121.84/16.05 (cartprodsndpairEq) =>
% 121.84/16.05 ((
% 121.84/16.05 (cartprodpairsurjEq) =>
% 121.84/16.05 ((
% 121.84/16.05 (dpsetconstrI) =>
% 121.84/16.05 ((
% 121.84/16.05 (dpsetconstrSub) =>
% 121.84/16.05 ((
% 121.84/16.05 (setOfPairsIsBReln) =>
% 121.84/16.05 ((
% 121.84/16.05 (dpsetconstrERa) =>
% 121.84/16.05 ((
% 121.84/16.05 (dpsetconstrEL1) =>
% 121.84/16.05 ((
% 121.84/16.05 (dpsetconstrEL2) =>
% 121.84/16.05 ((
% 121.84/16.05 (dpsetconstrER) =>
% 121.84/16.05 ((
% 121.84/16.05 (funcImageSingleton) =>
% 121.84/16.05 ((
% 121.84/16.05 (apProp) =>
% 121.84/16.05 ((
% 121.84/16.05 (app) =>
% 121.84/16.05 ((
% 121.84/16.05 (infuncsetfunc) =>
% 121.84/16.05 ((
% 121.84/16.05 (ap2p) =>
% 121.84/16.05 ((
% 121.84/16.05 (funcinfuncset) =>
% 121.84/16.05 ((
% 121.84/16.05 (lamProp) =>
% 121.84/16.05 ((
% 121.84/16.05 (lamp) =>
% 121.84/16.05 ((
% 121.84/16.05 (lam2p) =>
% 121.84/16.05 ((
% 121.84/16.05 (brelnall1) =>
% 121.84/16.05 ((
% 121.84/16.05 (brelnall2) =>
% 121.84/16.05 ((
% 121.84/16.05 (ex1E2) =>
% 121.84/16.05 ((
% 121.84/16.05 (funcGraphProp1) =>
% 121.84/16.05 ((
% 121.84/16.05 (funcGraphProp3) =>
% 121.84/16.05 ((
% 121.84/16.05 (funcGraphProp2) =>
% 121.84/16.05 ((
% 121.84/16.05 (funcextLem) =>
% 121.84/16.05 ((
% 121.84/16.05 (funcGraphProp4) =>
% 121.84/16.05 ((
% 121.84/16.05 (subbreln) =>
% 121.84/16.05 ((
% 121.84/16.05 (eqbreln) =>
% 121.84/16.05 ((
% 121.84/16.05 (funcext) =>
% 121.84/16.05 ((
% 121.84/16.05 (funcext2) =>
% 121.84/16.05 ((
% 121.84/16.05 (ap2apEq1) =>
% 121.84/16.05 ((
% 121.84/16.05 (ap2apEq2) =>
% 121.84/16.05 ((
% 121.84/16.05 (beta1) =>
% 121.84/16.05 ((
% 121.84/16.05 (eta1) =>
% 121.84/16.05 ((
% 121.84/16.05 (lam2lamEq) =>
% 121.84/16.05 ((
% 121.84/16.05 (beta2) =>
% 121.84/16.05 ((
% 121.84/16.05 (eta2) =>
% 121.84/16.05 ((
% 121.84/16.05 (iffalseProp1) =>
% 121.84/16.05 ((
% 121.84/16.05 (iffalseProp2) =>
% 121.84/16.05 ((
% 121.84/16.05 (iftrueProp1) =>
% 121.84/16.05 ((
% 121.84/16.05 (iftrueProp2) =>
% 121.84/16.05 ((
% 121.84/16.05 (ifSingleton) =>
% 121.84/16.05 ((
% 121.84/16.05 (ifp) =>
% 121.84/16.05 ((
% 121.84/16.05 (theeq) =>
% 121.84/16.05 ((
% 121.84/16.05 (iftrue) =>
% 121.84/16.05 ((
% 121.84/16.05 (iffalse) =>
% 121.84/16.05 ((
% 121.84/16.05 (iftrueorfalse) =>
% 121.84/16.05 ((
% 121.84/16.05 (binintersectT_lem) =>
% 121.84/16.05 ((
% 121.84/16.05 (binunionT_lem) =>
% 121.84/16.05 ((
% 121.84/16.05 (powersetT_lem) =>
% 121.84/16.05 ((
% 121.84/16.05 (setminusT_lem) =>
% 121.84/16.05 ((
% 121.84/16.05 (complementT_lem) =>
% 121.84/16.05 ((
% 121.84/16.05 (setextT) =>
% 121.84/16.05 ((
% 121.84/16.05 (subsetTI) =>
% 121.84/16.05 ((
% 121.84/16.05 (powersetTI1) =>
% 121.84/16.05 ((
% 121.84/16.05 (powersetTE1) =>
% 121.84/16.05 ((
% 121.84/16.05 (complementTI1) =>
% 121.84/16.05 ((
% 121.84/16.05 (complementTE1) =>
% 121.84/16.05 ((
% 121.84/16.05 (binintersectTELcontra) =>
% 121.84/16.05 ((
% 121.84/16.05 (binintersectTERcontra) =>
% 121.84/16.05 ((
% 121.84/16.05 (contrasubsetT) =>
% 121.84/16.05 ((
% 121.84/16.05 (contrasubsetT1) =>
% 121.84/16.05 ((
% 121.84/16.05 (contrasubsetT2) =>
% 121.84/16.05 ((
% 121.84/16.05 (contrasubsetT3) =>
% 121.84/16.05 ((
% 121.84/16.05 (doubleComplementI1) =>
% 121.84/16.05 ((
% 121.84/16.05 (doubleComplementE1) =>
% 121.84/16.05 ((
% 121.84/16.05 (doubleComplementSub1) =>
% 121.84/16.05 ((
% 121.84/16.05 (doubleComplementSub2) =>
% 121.84/16.05 ((
% 121.84/16.05 (doubleComplementEq) =>
% 121.84/16.05 ((
% 121.84/16.05 (complementTnotintersectT) =>
% 121.84/16.05 ((
% 121.84/16.05 (complementImpComplementIntersect) =>
% 121.84/16.05 ((
% 121.84/16.05 (complementSubsetComplementIntersect) =>
% 121.84/16.05 ((
% 121.84/16.05 (complementInPowersetComplementIntersect) =>
% 121.84/16.05 ((
% 121.84/16.05 (contraSubsetComplement) =>
% 121.84/16.05 ((
% 121.84/16.05 (complementTcontraSubset) =>
% 121.84/16.05 ((
% 121.84/16.05 (binunionTILcontra) =>
% 121.84/16.05 ((
% 121.84/16.05 (binunionTIRcontra) =>
% 121.84/16.05 ((
% 121.84/16.05 (inIntersectImpInUnion) =>
% 121.84/16.05 ((
% 121.84/16.05 (inIntersectImpInUnion2) =>
% 121.84/16.05 ((
% 121.84/16.05 (inIntersectImpInIntersectUnions) =>
% 121.84/16.05 ((
% 121.84/16.05 (intersectInPowersetIntersectUnions) =>
% 121.84/16.05 ((
% 121.84/16.05 (inComplementUnionImpNotIn1) =>
% 121.84/16.05 ((
% 121.84/16.05 (inComplementUnionImpInComplement1) =>
% 121.84/16.05 ((
% 121.84/16.05 (binunionTE) =>
% 121.84/16.05 ((
% 121.84/16.05 (binunionTEcontra) =>
% 121.84/16.05 ((
% 121.84/16.05 (demorgan2a1) =>
% 121.84/16.05 ((
% 121.84/16.05 (complementUnionInPowersetComplement) =>
% 121.84/16.05 ((
% 121.84/16.05 (demorgan2a2) =>
% 121.84/16.05 ((
% 121.84/16.05 (demorgan1a) =>
% 121.84/16.05 ((
% 121.84/16.05 (demorgan1b) =>
% 121.84/16.05 ((
% 121.84/16.05 (demorgan1) =>
% 121.84/16.05 ((
% 121.84/16.05 (demorgan2a) =>
% 121.84/16.05 ((
% 121.84/16.05 (demorgan2b2) =>
% 121.84/16.05 ((
% 121.84/16.05 (demorgan2b) =>
% 121.84/16.05 ((
% 121.84/16.05 (demorgan2) =>
% 121.84/16.05 ((
% 121.84/16.05 (woz13rule0) =>
% 121.84/16.05 ((
% 121.84/16.05 (woz13rule1) =>
% 121.84/16.05 ((
% 121.84/16.05 (woz13rule2) =>
% 121.84/16.05 ((
% 121.84/16.05 (woz13rule3) =>
% 121.84/16.05 ((
% 121.84/16.05 (woz13rule4) =>
% 121.84/16.05 ((
% 121.84/16.05 (woz1_1) =>
% 121.84/16.05 ((
% 121.84/16.05 (woz1_2) =>
% 121.84/16.05 ((
% 121.84/16.05 (woz1_3) =>
% 121.84/16.05 ((
% 121.84/16.05 (woz1_4) =>
% 121.84/16.05 ((
% 121.84/16.05 (woz1_5) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1all2) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1SetBreln1) =>
% 121.84/16.05 ((
% 121.84/16.05 (choice2fnsingleton) =>
% 121.84/16.05 ((
% 121.84/16.05 (setOfPairsIsBReln1) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1all1) =>
% 121.84/16.05 ((
% 121.84/16.05 (subbreln1) =>
% 121.84/16.05 ((
% 121.84/16.05 (eqbreln1) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1invprop) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1invI) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1invE) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1compprop) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1compI) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1compE) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1compEex) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1unionprop) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1unionIL) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1unionIR) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1unionI) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1unionE) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1unionEcases) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1unionCommutes) =>
% 121.84/16.05 ((
% 121.84/16.05 (woz2Ex) =>
% 121.84/16.05 ((
% 121.84/16.05 (woz2W) =>
% 121.84/16.05 ((
% 121.84/16.05 (woz2A) =>
% 121.84/16.05 ((
% 121.84/16.05 (woz2B) =>
% 121.84/16.05 ((
% 121.84/16.05 (image1Ex) =>
% 121.84/16.05 ((
% 121.84/16.05 (image1Ex1) =>
% 121.84/16.05 ((
% 121.84/16.05 (image1Equiv) =>
% 121.84/16.05 ((
% 121.84/16.05 (image1E) =>
% 121.84/16.05 ((
% 121.84/16.05 (image1I) =>
% 121.84/16.05 ((
% 121.84/16.05 (injFuncInInjFuncSet) =>
% 121.84/16.05 ((
% 121.84/16.05 (!!) @ (
% 121.84/16.05 (('#B') @ (
% 121.84/16.05 !!) @
% 121.84/16.05 (
% 121.84/16.05 (
% 121.84/16.05 ('#B') @ (
% 121.84/16.05 (
% 121.84/16.05 ('#B') @ (
% 121.84/16.05 !!))) @
% 121.84/16.05 (
% 121.84/16.05 (
% 121.84/16.05 ('#S') @ (
% 121.84/16.05 (
% 121.84/16.05 ('#B') @ (
% 121.84/16.05 '#S') @
% 121.84/16.05 (
% 121.84/16.05 (
% 121.84/16.05 ('#B') @ (
% 121.84/16.05 (
% 121.84/16.05 ('#B') @ (
% 121.84/16.05 '#S'))) @
% 121.84/16.05 (
% 121.84/16.05 (
% 121.84/16.05 ('#B') @ (
% 121.84/16.05 (
% 121.84/16.05 ('#B') @ (
% 121.84/16.05 (
% 121.84/16.05 ('#B') @ (
% 121.84/16.05 =>))))) @
% 121.84/16.05 (
% 121.84/16.05 (
% 121.84/16.05 ('#B') @ (
% 121.84/16.05 (
% 121.84/16.05 ('#B') @ (
% 121.84/16.05 (
% 121.84/16.05 ('#C') @ in)))) @
% 121.84/16.05 injFuncSet)))))))) @
% 121.84/16.05 (
% 121.84/16.05 (
% 121.84/16.05 ('#B') @ (
% 121.84/16.05 (
% 121.84/16.05 ('#B') @ (
% 121.84/16.05 (
% 121.84/16.05 ('#C') @ in)))) @
% 121.84/16.05 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 121.84/16.05 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl384])).
% 121.84/16.05 thf(zip_derived_cl400, plain,
% 121.84/16.05 (~ (((setunionI) =>
% 121.84/16.05 (((setunionE) =>
% 121.84/16.05 (((subPowSU) =>
% 121.84/16.05 (((exuE2) =>
% 121.84/16.05 (((nonemptyImpWitness) =>
% 121.84/16.05 (((uniqinunit) =>
% 121.84/16.05 (((notinsingleton) =>
% 121.84/16.05 (((eqinunit) =>
% 121.84/16.05 (((singletonsswitch) =>
% 121.84/16.05 (((upairsetE) =>
% 121.84/16.05 (((upairsetIL) =>
% 121.84/16.05 (((upairsetIR) =>
% 121.84/16.05 (((emptyE1) =>
% 121.84/16.05 (((vacuousDall) =>
% 121.84/16.05 (((quantDeMorgan1) =>
% 121.84/16.05 (((quantDeMorgan2) =>
% 121.84/16.05 (((quantDeMorgan3) =>
% 121.84/16.05 (((quantDeMorgan4) =>
% 121.84/16.05 (((prop2setI) =>
% 121.84/16.05 (((prop2set2propI) =>
% 121.84/16.05 (((notdexE) =>
% 121.84/16.05 (((notdallE) =>
% 121.84/16.05 (((exuI1) =>
% 121.84/16.05 (((exuI3) =>
% 121.84/16.05 (((exuI2) =>
% 121.84/16.05 (((inCongP) =>
% 121.84/16.05 (((in__Cong) =>
% 121.84/16.05 (((exuE3u) =>
% 121.84/16.05 (((exu__Cong) =>
% 121.84/16.05 (((setadjoin__Cong) =>
% 121.84/16.05 ((
% 121.84/16.05 (powerset__Cong) =>
% 121.84/16.05 ((
% 121.84/16.05 (setunion__Cong) =>
% 121.84/16.05 ((
% 121.84/16.05 (exuEu) =>
% 121.84/16.05 ((
% 121.84/16.05 (descr__Cong) =>
% 121.84/16.05 ((
% 121.84/16.05 (dsetconstr__Cong) =>
% 121.84/16.05 ((
% 121.84/16.05 (subsetI1) =>
% 121.84/16.05 ((
% 121.84/16.05 (eqimpsubset2) =>
% 121.84/16.05 ((
% 121.84/16.05 (eqimpsubset1) =>
% 121.84/16.05 ((
% 121.84/16.05 (subsetI2) =>
% 121.84/16.05 ((
% 121.84/16.05 (emptysetsubset) =>
% 121.84/16.05 ((
% 121.84/16.05 (subsetE) =>
% 121.84/16.05 ((
% 121.84/16.05 (subsetE2) =>
% 121.84/16.05 ((
% 121.84/16.05 (notsubsetI) =>
% 121.84/16.05 ((
% 121.84/16.05 (notequalI1) =>
% 121.84/16.05 ((
% 121.84/16.05 (notequalI2) =>
% 121.84/16.05 ((
% 121.84/16.05 (subsetRefl) =>
% 121.84/16.05 ((
% 121.84/16.05 (subsetTrans) =>
% 121.84/16.05 ((
% 121.84/16.05 (setadjoinSub) =>
% 121.84/16.05 ((
% 121.84/16.05 (setadjoinSub2) =>
% 121.84/16.05 ((
% 121.84/16.05 (subset2powerset) =>
% 121.84/16.05 ((
% 121.84/16.05 (setextsub) =>
% 121.84/16.05 ((
% 121.84/16.05 (subsetemptysetimpeq) =>
% 121.84/16.05 ((
% 121.84/16.05 (powersetI1) =>
% 121.84/16.05 ((
% 121.84/16.05 (powersetE1) =>
% 121.84/16.05 ((
% 121.84/16.05 (inPowerset) =>
% 121.84/16.05 ((
% 121.84/16.05 (powersetsubset) =>
% 121.84/16.05 ((
% 121.84/16.05 (sepInPowerset) =>
% 121.84/16.05 ((
% 121.84/16.05 (sepSubset) =>
% 121.84/16.05 ((
% 121.84/16.05 (binunionIL) =>
% 121.84/16.05 ((
% 121.84/16.05 (upairset2IR) =>
% 121.84/16.05 ((
% 121.84/16.05 (binunionIR) =>
% 121.84/16.05 ((
% 121.84/16.05 (binunionEcases) =>
% 121.84/16.05 ((
% 121.84/16.05 (binunionE) =>
% 121.84/16.05 ((
% 121.84/16.05 (binunionLsub) =>
% 121.84/16.05 ((
% 121.84/16.05 (binunionRsub) =>
% 121.84/16.05 ((
% 121.84/16.05 (binintersectI) =>
% 121.84/16.05 ((
% 121.84/16.05 (binintersectSubset5) =>
% 121.84/16.05 ((
% 121.84/16.05 (binintersectEL) =>
% 121.84/16.05 ((
% 121.84/16.05 (binintersectLsub) =>
% 121.84/16.05 ((
% 121.84/16.05 (binintersectSubset2) =>
% 121.84/16.05 ((
% 121.84/16.05 (binintersectSubset3) =>
% 121.84/16.05 ((
% 121.84/16.05 (binintersectER) =>
% 121.84/16.05 ((
% 121.84/16.05 (disjointsetsI1) =>
% 121.84/16.05 ((
% 121.84/16.05 (binintersectRsub) =>
% 121.84/16.05 ((
% 121.84/16.05 (binintersectSubset4) =>
% 121.84/16.05 ((
% 121.84/16.05 (binintersectSubset1) =>
% 121.84/16.05 ((
% 121.84/16.05 (bs114d) =>
% 121.84/16.05 ((
% 121.84/16.05 (setminusI) =>
% 121.84/16.05 ((
% 121.84/16.05 (setminusEL) =>
% 121.84/16.05 ((
% 121.84/16.05 (setminusER) =>
% 121.84/16.05 ((
% 121.84/16.05 (setminusSubset2) =>
% 121.84/16.05 ((
% 121.84/16.05 (setminusERneg) =>
% 121.84/16.05 ((
% 121.84/16.05 (setminusELneg) =>
% 121.84/16.05 ((
% 121.84/16.05 (setminusILneg) =>
% 121.84/16.05 ((
% 121.84/16.05 (setminusIRneg) =>
% 121.84/16.05 ((
% 121.84/16.05 (setminusLsub) =>
% 121.84/16.05 ((
% 121.84/16.05 (setminusSubset1) =>
% 121.84/16.05 ((
% 121.84/16.05 (symdiffE) =>
% 121.84/16.05 ((
% 121.84/16.05 (symdiffI1) =>
% 121.84/16.05 ((
% 121.84/16.05 (symdiffI2) =>
% 121.84/16.05 ((
% 121.84/16.05 (symdiffIneg1) =>
% 121.84/16.05 ((
% 121.84/16.05 (symdiffIneg2) =>
% 121.84/16.05 ((
% 121.84/16.05 (secondinupair) =>
% 121.84/16.05 ((
% 121.84/16.05 (setukpairIL) =>
% 121.84/16.05 ((
% 121.84/16.05 (setukpairIR) =>
% 121.84/16.05 ((
% 121.84/16.05 (kpairiskpair) =>
% 121.84/16.05 ((
% 121.84/16.05 (kpairp) =>
% 121.84/16.05 ((
% 121.84/16.05 (singletonsubset) =>
% 121.84/16.05 ((
% 121.84/16.05 (singletoninpowerset) =>
% 121.84/16.05 ((
% 121.84/16.05 (singletoninpowunion) =>
% 121.84/16.05 ((
% 121.84/16.05 (upairset2E) =>
% 121.84/16.05 ((
% 121.84/16.05 (upairsubunion) =>
% 121.84/16.05 ((
% 121.84/16.05 (upairinpowunion) =>
% 121.84/16.05 ((
% 121.84/16.05 (ubforcartprodlem1) =>
% 121.84/16.05 ((
% 121.84/16.05 (ubforcartprodlem2) =>
% 121.84/16.05 ((
% 121.84/16.05 (ubforcartprodlem3) =>
% 121.84/16.05 ((
% 121.84/16.05 (cartprodpairin) =>
% 121.84/16.05 ((
% 121.84/16.05 (cartprodmempair1) =>
% 121.84/16.05 ((
% 121.84/16.05 (cartprodmempair) =>
% 121.84/16.05 ((
% 121.84/16.05 (setunionE2) =>
% 121.84/16.05 ((
% 121.84/16.05 (setunionsingleton1) =>
% 121.84/16.05 ((
% 121.84/16.05 (setunionsingleton2) =>
% 121.84/16.05 ((
% 121.84/16.05 (setunionsingleton) =>
% 121.84/16.05 ((
% 121.84/16.05 (singletonprop) =>
% 121.84/16.05 ((
% 121.84/16.05 (ex1E1) =>
% 121.84/16.05 ((
% 121.84/16.05 (ex1I) =>
% 121.84/16.05 ((
% 121.84/16.05 (ex1I2) =>
% 121.84/16.05 ((
% 121.84/16.05 (singletonsuniq) =>
% 121.84/16.05 ((
% 121.84/16.05 (setukpairinjL1) =>
% 121.84/16.05 ((
% 121.84/16.05 (kfstsingleton) =>
% 121.84/16.05 ((
% 121.84/16.05 (theprop) =>
% 121.84/16.05 ((
% 121.84/16.05 (kfstpairEq) =>
% 121.84/16.05 ((
% 121.84/16.05 (cartprodfstin) =>
% 121.84/16.05 ((
% 121.84/16.05 (setukpairinjL2) =>
% 121.84/16.05 ((
% 121.84/16.05 (setukpairinjL) =>
% 121.84/16.05 ((
% 121.84/16.05 (setukpairinjR11) =>
% 121.84/16.05 ((
% 121.84/16.05 (setukpairinjR12) =>
% 121.84/16.05 ((
% 121.84/16.05 (setukpairinjR1) =>
% 121.84/16.05 ((
% 121.84/16.05 (upairequniteq) =>
% 121.84/16.05 ((
% 121.84/16.05 (setukpairinjR2) =>
% 121.84/16.05 ((
% 121.84/16.05 (setukpairinjR) =>
% 121.84/16.05 ((
% 121.84/16.05 (ksndsingleton) =>
% 121.84/16.05 ((
% 121.84/16.05 (ksndpairEq) =>
% 121.84/16.05 ((
% 121.84/16.05 (kpairsurjEq) =>
% 121.84/16.05 ((
% 121.84/16.05 (cartprodsndin) =>
% 121.84/16.05 ((
% 121.84/16.05 (cartprodpairmemEL) =>
% 121.84/16.05 ((
% 121.84/16.05 (cartprodpairmemER) =>
% 121.84/16.05 ((
% 121.84/16.05 (cartprodmempaircEq) =>
% 121.84/16.05 ((
% 121.84/16.05 (cartprodfstpairEq) =>
% 121.84/16.05 ((
% 121.84/16.05 (cartprodsndpairEq) =>
% 121.84/16.05 ((
% 121.84/16.05 (cartprodpairsurjEq) =>
% 121.84/16.05 ((
% 121.84/16.05 (dpsetconstrI) =>
% 121.84/16.05 ((
% 121.84/16.05 (dpsetconstrSub) =>
% 121.84/16.05 ((
% 121.84/16.05 (setOfPairsIsBReln) =>
% 121.84/16.05 ((
% 121.84/16.05 (dpsetconstrERa) =>
% 121.84/16.05 ((
% 121.84/16.05 (dpsetconstrEL1) =>
% 121.84/16.05 ((
% 121.84/16.05 (dpsetconstrEL2) =>
% 121.84/16.05 ((
% 121.84/16.05 (dpsetconstrER) =>
% 121.84/16.05 ((
% 121.84/16.05 (funcImageSingleton) =>
% 121.84/16.05 ((
% 121.84/16.05 (apProp) =>
% 121.84/16.05 ((
% 121.84/16.05 (app) =>
% 121.84/16.05 ((
% 121.84/16.05 (infuncsetfunc) =>
% 121.84/16.05 ((
% 121.84/16.05 (ap2p) =>
% 121.84/16.05 ((
% 121.84/16.05 (funcinfuncset) =>
% 121.84/16.05 ((
% 121.84/16.05 (lamProp) =>
% 121.84/16.05 ((
% 121.84/16.05 (lamp) =>
% 121.84/16.05 ((
% 121.84/16.05 (lam2p) =>
% 121.84/16.05 ((
% 121.84/16.05 (brelnall1) =>
% 121.84/16.05 ((
% 121.84/16.05 (brelnall2) =>
% 121.84/16.05 ((
% 121.84/16.05 (ex1E2) =>
% 121.84/16.05 ((
% 121.84/16.05 (funcGraphProp1) =>
% 121.84/16.05 ((
% 121.84/16.05 (funcGraphProp3) =>
% 121.84/16.05 ((
% 121.84/16.05 (funcGraphProp2) =>
% 121.84/16.05 ((
% 121.84/16.05 (funcextLem) =>
% 121.84/16.05 ((
% 121.84/16.05 (funcGraphProp4) =>
% 121.84/16.05 ((
% 121.84/16.05 (subbreln) =>
% 121.84/16.05 ((
% 121.84/16.05 (eqbreln) =>
% 121.84/16.05 ((
% 121.84/16.05 (funcext) =>
% 121.84/16.05 ((
% 121.84/16.05 (funcext2) =>
% 121.84/16.05 ((
% 121.84/16.05 (ap2apEq1) =>
% 121.84/16.05 ((
% 121.84/16.05 (ap2apEq2) =>
% 121.84/16.05 ((
% 121.84/16.05 (beta1) =>
% 121.84/16.05 ((
% 121.84/16.05 (eta1) =>
% 121.84/16.05 ((
% 121.84/16.05 (lam2lamEq) =>
% 121.84/16.05 ((
% 121.84/16.05 (beta2) =>
% 121.84/16.05 ((
% 121.84/16.05 (eta2) =>
% 121.84/16.05 ((
% 121.84/16.05 (iffalseProp1) =>
% 121.84/16.05 ((
% 121.84/16.05 (iffalseProp2) =>
% 121.84/16.05 ((
% 121.84/16.05 (iftrueProp1) =>
% 121.84/16.05 ((
% 121.84/16.05 (iftrueProp2) =>
% 121.84/16.05 ((
% 121.84/16.05 (ifSingleton) =>
% 121.84/16.05 ((
% 121.84/16.05 (ifp) =>
% 121.84/16.05 ((
% 121.84/16.05 (theeq) =>
% 121.84/16.05 ((
% 121.84/16.05 (iftrue) =>
% 121.84/16.05 ((
% 121.84/16.05 (iffalse) =>
% 121.84/16.05 ((
% 121.84/16.05 (iftrueorfalse) =>
% 121.84/16.05 ((
% 121.84/16.05 (binintersectT_lem) =>
% 121.84/16.05 ((
% 121.84/16.05 (binunionT_lem) =>
% 121.84/16.05 ((
% 121.84/16.05 (powersetT_lem) =>
% 121.84/16.05 ((
% 121.84/16.05 (setminusT_lem) =>
% 121.84/16.05 ((
% 121.84/16.05 (complementT_lem) =>
% 121.84/16.05 ((
% 121.84/16.05 (setextT) =>
% 121.84/16.05 ((
% 121.84/16.05 (subsetTI) =>
% 121.84/16.05 ((
% 121.84/16.05 (powersetTI1) =>
% 121.84/16.05 ((
% 121.84/16.05 (powersetTE1) =>
% 121.84/16.05 ((
% 121.84/16.05 (complementTI1) =>
% 121.84/16.05 ((
% 121.84/16.05 (complementTE1) =>
% 121.84/16.05 ((
% 121.84/16.05 (binintersectTELcontra) =>
% 121.84/16.05 ((
% 121.84/16.05 (binintersectTERcontra) =>
% 121.84/16.05 ((
% 121.84/16.05 (contrasubsetT) =>
% 121.84/16.05 ((
% 121.84/16.05 (contrasubsetT1) =>
% 121.84/16.05 ((
% 121.84/16.05 (contrasubsetT2) =>
% 121.84/16.05 ((
% 121.84/16.05 (contrasubsetT3) =>
% 121.84/16.05 ((
% 121.84/16.05 (doubleComplementI1) =>
% 121.84/16.05 ((
% 121.84/16.05 (doubleComplementE1) =>
% 121.84/16.05 ((
% 121.84/16.05 (doubleComplementSub1) =>
% 121.84/16.05 ((
% 121.84/16.05 (doubleComplementSub2) =>
% 121.84/16.05 ((
% 121.84/16.05 (doubleComplementEq) =>
% 121.84/16.05 ((
% 121.84/16.05 (complementTnotintersectT) =>
% 121.84/16.05 ((
% 121.84/16.05 (complementImpComplementIntersect) =>
% 121.84/16.05 ((
% 121.84/16.05 (complementSubsetComplementIntersect) =>
% 121.84/16.05 ((
% 121.84/16.05 (complementInPowersetComplementIntersect) =>
% 121.84/16.05 ((
% 121.84/16.05 (contraSubsetComplement) =>
% 121.84/16.05 ((
% 121.84/16.05 (complementTcontraSubset) =>
% 121.84/16.05 ((
% 121.84/16.05 (binunionTILcontra) =>
% 121.84/16.05 ((
% 121.84/16.05 (binunionTIRcontra) =>
% 121.84/16.05 ((
% 121.84/16.05 (inIntersectImpInUnion) =>
% 121.84/16.05 ((
% 121.84/16.05 (inIntersectImpInUnion2) =>
% 121.84/16.05 ((
% 121.84/16.05 (inIntersectImpInIntersectUnions) =>
% 121.84/16.05 ((
% 121.84/16.05 (intersectInPowersetIntersectUnions) =>
% 121.84/16.05 ((
% 121.84/16.05 (inComplementUnionImpNotIn1) =>
% 121.84/16.05 ((
% 121.84/16.05 (inComplementUnionImpInComplement1) =>
% 121.84/16.05 ((
% 121.84/16.05 (binunionTE) =>
% 121.84/16.05 ((
% 121.84/16.05 (binunionTEcontra) =>
% 121.84/16.05 ((
% 121.84/16.05 (demorgan2a1) =>
% 121.84/16.05 ((
% 121.84/16.05 (complementUnionInPowersetComplement) =>
% 121.84/16.05 ((
% 121.84/16.05 (demorgan2a2) =>
% 121.84/16.05 ((
% 121.84/16.05 (demorgan1a) =>
% 121.84/16.05 ((
% 121.84/16.05 (demorgan1b) =>
% 121.84/16.05 ((
% 121.84/16.05 (demorgan1) =>
% 121.84/16.05 ((
% 121.84/16.05 (demorgan2a) =>
% 121.84/16.05 ((
% 121.84/16.05 (demorgan2b2) =>
% 121.84/16.05 ((
% 121.84/16.05 (demorgan2b) =>
% 121.84/16.05 ((
% 121.84/16.05 (demorgan2) =>
% 121.84/16.05 ((
% 121.84/16.05 (woz13rule0) =>
% 121.84/16.05 ((
% 121.84/16.05 (woz13rule1) =>
% 121.84/16.05 ((
% 121.84/16.05 (woz13rule2) =>
% 121.84/16.05 ((
% 121.84/16.05 (woz13rule3) =>
% 121.84/16.05 ((
% 121.84/16.05 (woz13rule4) =>
% 121.84/16.05 ((
% 121.84/16.05 (woz1_1) =>
% 121.84/16.05 ((
% 121.84/16.05 (woz1_2) =>
% 121.84/16.05 ((
% 121.84/16.05 (woz1_3) =>
% 121.84/16.05 ((
% 121.84/16.05 (woz1_4) =>
% 121.84/16.05 ((
% 121.84/16.05 (woz1_5) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1all2) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1SetBreln1) =>
% 121.84/16.05 ((
% 121.84/16.05 (choice2fnsingleton) =>
% 121.84/16.05 ((
% 121.84/16.05 (setOfPairsIsBReln1) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1all1) =>
% 121.84/16.05 ((
% 121.84/16.05 (subbreln1) =>
% 121.84/16.05 ((
% 121.84/16.05 (eqbreln1) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1invprop) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1invI) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1invE) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1compprop) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1compI) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1compE) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1compEex) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1unionprop) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1unionIL) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1unionIR) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1unionI) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1unionE) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1unionEcases) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1unionCommutes) =>
% 121.84/16.05 ((
% 121.84/16.05 (woz2Ex) =>
% 121.84/16.05 ((
% 121.84/16.05 (woz2W) =>
% 121.84/16.05 ((
% 121.84/16.05 (woz2A) =>
% 121.84/16.05 ((
% 121.84/16.05 (woz2B) =>
% 121.84/16.05 ((
% 121.84/16.05 (image1Ex) =>
% 121.84/16.05 ((
% 121.84/16.05 (image1Ex1) =>
% 121.84/16.05 ((
% 121.84/16.05 (image1Equiv) =>
% 121.84/16.05 ((
% 121.84/16.05 (image1E) =>
% 121.84/16.05 ((
% 121.84/16.05 (image1I) =>
% 121.84/16.05 ((
% 121.84/16.05 (injFuncInInjFuncSet) =>
% 121.84/16.05 ((
% 121.84/16.05 (!!) @ (
% 121.84/16.05 (('#B') @ (
% 121.84/16.05 !!) @
% 121.84/16.05 (
% 121.84/16.05 (
% 121.84/16.05 ('#B') @ (
% 121.84/16.05 (
% 121.84/16.05 ('#B') @ (
% 121.84/16.05 !!))) @
% 121.84/16.05 (
% 121.84/16.05 (
% 121.84/16.05 ('#S') @ (
% 121.84/16.05 (
% 121.84/16.05 ('#B') @ (
% 121.84/16.05 '#S') @
% 121.84/16.05 (
% 121.84/16.05 (
% 121.84/16.05 ('#B') @ (
% 121.84/16.05 (
% 121.84/16.05 ('#B') @ (
% 121.84/16.05 '#S'))) @
% 121.84/16.05 (
% 121.84/16.05 (
% 121.84/16.05 ('#B') @ (
% 121.84/16.05 (
% 121.84/16.05 ('#B') @ (
% 121.84/16.05 (
% 121.84/16.05 ('#B') @ (
% 121.84/16.05 =>))))) @
% 121.84/16.05 (
% 121.84/16.05 (
% 121.84/16.05 ('#B') @ (
% 121.84/16.05 (
% 121.84/16.05 ('#B') @ (
% 121.84/16.05 (
% 121.84/16.05 ('#C') @ in)))) @
% 121.84/16.05 injFuncSet)))))))) @
% 121.84/16.05 (
% 121.84/16.05 (
% 121.84/16.05 ('#B') @ (
% 121.84/16.05 (
% 121.84/16.05 ('#B') @ (
% 121.84/16.05 (
% 121.84/16.05 ('#C') @ in)))) @
% 121.84/16.05 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 121.84/16.05 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl392])).
% 121.84/16.05 thf(zip_derived_cl408, plain,
% 121.84/16.05 (~ (((setunionE) =>
% 121.84/16.05 (((subPowSU) =>
% 121.84/16.05 (((exuE2) =>
% 121.84/16.05 (((nonemptyImpWitness) =>
% 121.84/16.05 (((uniqinunit) =>
% 121.84/16.05 (((notinsingleton) =>
% 121.84/16.05 (((eqinunit) =>
% 121.84/16.05 (((singletonsswitch) =>
% 121.84/16.05 (((upairsetE) =>
% 121.84/16.05 (((upairsetIL) =>
% 121.84/16.05 (((upairsetIR) =>
% 121.84/16.05 (((emptyE1) =>
% 121.84/16.05 (((vacuousDall) =>
% 121.84/16.05 (((quantDeMorgan1) =>
% 121.84/16.05 (((quantDeMorgan2) =>
% 121.84/16.05 (((quantDeMorgan3) =>
% 121.84/16.05 (((quantDeMorgan4) =>
% 121.84/16.05 (((prop2setI) =>
% 121.84/16.05 (((prop2set2propI) =>
% 121.84/16.05 (((notdexE) =>
% 121.84/16.05 (((notdallE) =>
% 121.84/16.05 (((exuI1) =>
% 121.84/16.05 (((exuI3) =>
% 121.84/16.05 (((exuI2) =>
% 121.84/16.05 (((inCongP) =>
% 121.84/16.05 (((in__Cong) =>
% 121.84/16.05 (((exuE3u) =>
% 121.84/16.05 (((exu__Cong) =>
% 121.84/16.05 (((setadjoin__Cong) =>
% 121.84/16.05 (((powerset__Cong) =>
% 121.84/16.05 ((
% 121.84/16.05 (setunion__Cong) =>
% 121.84/16.05 ((
% 121.84/16.05 (exuEu) =>
% 121.84/16.05 ((
% 121.84/16.05 (descr__Cong) =>
% 121.84/16.05 ((
% 121.84/16.05 (dsetconstr__Cong) =>
% 121.84/16.05 ((
% 121.84/16.05 (subsetI1) =>
% 121.84/16.05 ((
% 121.84/16.05 (eqimpsubset2) =>
% 121.84/16.05 ((
% 121.84/16.05 (eqimpsubset1) =>
% 121.84/16.05 ((
% 121.84/16.05 (subsetI2) =>
% 121.84/16.05 ((
% 121.84/16.05 (emptysetsubset) =>
% 121.84/16.05 ((
% 121.84/16.05 (subsetE) =>
% 121.84/16.05 ((
% 121.84/16.05 (subsetE2) =>
% 121.84/16.05 ((
% 121.84/16.05 (notsubsetI) =>
% 121.84/16.05 ((
% 121.84/16.05 (notequalI1) =>
% 121.84/16.05 ((
% 121.84/16.05 (notequalI2) =>
% 121.84/16.05 ((
% 121.84/16.05 (subsetRefl) =>
% 121.84/16.05 ((
% 121.84/16.05 (subsetTrans) =>
% 121.84/16.05 ((
% 121.84/16.05 (setadjoinSub) =>
% 121.84/16.05 ((
% 121.84/16.05 (setadjoinSub2) =>
% 121.84/16.05 ((
% 121.84/16.05 (subset2powerset) =>
% 121.84/16.05 ((
% 121.84/16.05 (setextsub) =>
% 121.84/16.05 ((
% 121.84/16.05 (subsetemptysetimpeq) =>
% 121.84/16.05 ((
% 121.84/16.05 (powersetI1) =>
% 121.84/16.05 ((
% 121.84/16.05 (powersetE1) =>
% 121.84/16.05 ((
% 121.84/16.05 (inPowerset) =>
% 121.84/16.05 ((
% 121.84/16.05 (powersetsubset) =>
% 121.84/16.05 ((
% 121.84/16.05 (sepInPowerset) =>
% 121.84/16.05 ((
% 121.84/16.05 (sepSubset) =>
% 121.84/16.05 ((
% 121.84/16.05 (binunionIL) =>
% 121.84/16.05 ((
% 121.84/16.05 (upairset2IR) =>
% 121.84/16.05 ((
% 121.84/16.05 (binunionIR) =>
% 121.84/16.05 ((
% 121.84/16.05 (binunionEcases) =>
% 121.84/16.05 ((
% 121.84/16.05 (binunionE) =>
% 121.84/16.05 ((
% 121.84/16.05 (binunionLsub) =>
% 121.84/16.05 ((
% 121.84/16.05 (binunionRsub) =>
% 121.84/16.05 ((
% 121.84/16.05 (binintersectI) =>
% 121.84/16.05 ((
% 121.84/16.05 (binintersectSubset5) =>
% 121.84/16.05 ((
% 121.84/16.05 (binintersectEL) =>
% 121.84/16.05 ((
% 121.84/16.05 (binintersectLsub) =>
% 121.84/16.05 ((
% 121.84/16.05 (binintersectSubset2) =>
% 121.84/16.05 ((
% 121.84/16.05 (binintersectSubset3) =>
% 121.84/16.05 ((
% 121.84/16.05 (binintersectER) =>
% 121.84/16.05 ((
% 121.84/16.05 (disjointsetsI1) =>
% 121.84/16.05 ((
% 121.84/16.05 (binintersectRsub) =>
% 121.84/16.05 ((
% 121.84/16.05 (binintersectSubset4) =>
% 121.84/16.05 ((
% 121.84/16.05 (binintersectSubset1) =>
% 121.84/16.05 ((
% 121.84/16.05 (bs114d) =>
% 121.84/16.05 ((
% 121.84/16.05 (setminusI) =>
% 121.84/16.05 ((
% 121.84/16.05 (setminusEL) =>
% 121.84/16.05 ((
% 121.84/16.05 (setminusER) =>
% 121.84/16.05 ((
% 121.84/16.05 (setminusSubset2) =>
% 121.84/16.05 ((
% 121.84/16.05 (setminusERneg) =>
% 121.84/16.05 ((
% 121.84/16.05 (setminusELneg) =>
% 121.84/16.05 ((
% 121.84/16.05 (setminusILneg) =>
% 121.84/16.05 ((
% 121.84/16.05 (setminusIRneg) =>
% 121.84/16.05 ((
% 121.84/16.05 (setminusLsub) =>
% 121.84/16.05 ((
% 121.84/16.05 (setminusSubset1) =>
% 121.84/16.05 ((
% 121.84/16.05 (symdiffE) =>
% 121.84/16.05 ((
% 121.84/16.05 (symdiffI1) =>
% 121.84/16.05 ((
% 121.84/16.05 (symdiffI2) =>
% 121.84/16.05 ((
% 121.84/16.05 (symdiffIneg1) =>
% 121.84/16.05 ((
% 121.84/16.05 (symdiffIneg2) =>
% 121.84/16.05 ((
% 121.84/16.05 (secondinupair) =>
% 121.84/16.05 ((
% 121.84/16.05 (setukpairIL) =>
% 121.84/16.05 ((
% 121.84/16.05 (setukpairIR) =>
% 121.84/16.05 ((
% 121.84/16.05 (kpairiskpair) =>
% 121.84/16.05 ((
% 121.84/16.05 (kpairp) =>
% 121.84/16.05 ((
% 121.84/16.05 (singletonsubset) =>
% 121.84/16.05 ((
% 121.84/16.05 (singletoninpowerset) =>
% 121.84/16.05 ((
% 121.84/16.05 (singletoninpowunion) =>
% 121.84/16.05 ((
% 121.84/16.05 (upairset2E) =>
% 121.84/16.05 ((
% 121.84/16.05 (upairsubunion) =>
% 121.84/16.05 ((
% 121.84/16.05 (upairinpowunion) =>
% 121.84/16.05 ((
% 121.84/16.05 (ubforcartprodlem1) =>
% 121.84/16.05 ((
% 121.84/16.05 (ubforcartprodlem2) =>
% 121.84/16.05 ((
% 121.84/16.05 (ubforcartprodlem3) =>
% 121.84/16.05 ((
% 121.84/16.05 (cartprodpairin) =>
% 121.84/16.05 ((
% 121.84/16.05 (cartprodmempair1) =>
% 121.84/16.05 ((
% 121.84/16.05 (cartprodmempair) =>
% 121.84/16.05 ((
% 121.84/16.05 (setunionE2) =>
% 121.84/16.05 ((
% 121.84/16.05 (setunionsingleton1) =>
% 121.84/16.05 ((
% 121.84/16.05 (setunionsingleton2) =>
% 121.84/16.05 ((
% 121.84/16.05 (setunionsingleton) =>
% 121.84/16.05 ((
% 121.84/16.05 (singletonprop) =>
% 121.84/16.05 ((
% 121.84/16.05 (ex1E1) =>
% 121.84/16.05 ((
% 121.84/16.05 (ex1I) =>
% 121.84/16.05 ((
% 121.84/16.05 (ex1I2) =>
% 121.84/16.05 ((
% 121.84/16.05 (singletonsuniq) =>
% 121.84/16.05 ((
% 121.84/16.05 (setukpairinjL1) =>
% 121.84/16.05 ((
% 121.84/16.05 (kfstsingleton) =>
% 121.84/16.05 ((
% 121.84/16.05 (theprop) =>
% 121.84/16.05 ((
% 121.84/16.05 (kfstpairEq) =>
% 121.84/16.05 ((
% 121.84/16.05 (cartprodfstin) =>
% 121.84/16.05 ((
% 121.84/16.05 (setukpairinjL2) =>
% 121.84/16.05 ((
% 121.84/16.05 (setukpairinjL) =>
% 121.84/16.05 ((
% 121.84/16.05 (setukpairinjR11) =>
% 121.84/16.05 ((
% 121.84/16.05 (setukpairinjR12) =>
% 121.84/16.05 ((
% 121.84/16.05 (setukpairinjR1) =>
% 121.84/16.05 ((
% 121.84/16.05 (upairequniteq) =>
% 121.84/16.05 ((
% 121.84/16.05 (setukpairinjR2) =>
% 121.84/16.05 ((
% 121.84/16.05 (setukpairinjR) =>
% 121.84/16.05 ((
% 121.84/16.05 (ksndsingleton) =>
% 121.84/16.05 ((
% 121.84/16.05 (ksndpairEq) =>
% 121.84/16.05 ((
% 121.84/16.05 (kpairsurjEq) =>
% 121.84/16.05 ((
% 121.84/16.05 (cartprodsndin) =>
% 121.84/16.05 ((
% 121.84/16.05 (cartprodpairmemEL) =>
% 121.84/16.05 ((
% 121.84/16.05 (cartprodpairmemER) =>
% 121.84/16.05 ((
% 121.84/16.05 (cartprodmempaircEq) =>
% 121.84/16.05 ((
% 121.84/16.05 (cartprodfstpairEq) =>
% 121.84/16.05 ((
% 121.84/16.05 (cartprodsndpairEq) =>
% 121.84/16.05 ((
% 121.84/16.05 (cartprodpairsurjEq) =>
% 121.84/16.05 ((
% 121.84/16.05 (dpsetconstrI) =>
% 121.84/16.05 ((
% 121.84/16.05 (dpsetconstrSub) =>
% 121.84/16.05 ((
% 121.84/16.05 (setOfPairsIsBReln) =>
% 121.84/16.05 ((
% 121.84/16.05 (dpsetconstrERa) =>
% 121.84/16.05 ((
% 121.84/16.05 (dpsetconstrEL1) =>
% 121.84/16.05 ((
% 121.84/16.05 (dpsetconstrEL2) =>
% 121.84/16.05 ((
% 121.84/16.05 (dpsetconstrER) =>
% 121.84/16.05 ((
% 121.84/16.05 (funcImageSingleton) =>
% 121.84/16.05 ((
% 121.84/16.05 (apProp) =>
% 121.84/16.05 ((
% 121.84/16.05 (app) =>
% 121.84/16.05 ((
% 121.84/16.05 (infuncsetfunc) =>
% 121.84/16.05 ((
% 121.84/16.05 (ap2p) =>
% 121.84/16.05 ((
% 121.84/16.05 (funcinfuncset) =>
% 121.84/16.05 ((
% 121.84/16.05 (lamProp) =>
% 121.84/16.05 ((
% 121.84/16.05 (lamp) =>
% 121.84/16.05 ((
% 121.84/16.05 (lam2p) =>
% 121.84/16.05 ((
% 121.84/16.05 (brelnall1) =>
% 121.84/16.05 ((
% 121.84/16.05 (brelnall2) =>
% 121.84/16.05 ((
% 121.84/16.05 (ex1E2) =>
% 121.84/16.05 ((
% 121.84/16.05 (funcGraphProp1) =>
% 121.84/16.05 ((
% 121.84/16.05 (funcGraphProp3) =>
% 121.84/16.05 ((
% 121.84/16.05 (funcGraphProp2) =>
% 121.84/16.05 ((
% 121.84/16.05 (funcextLem) =>
% 121.84/16.05 ((
% 121.84/16.05 (funcGraphProp4) =>
% 121.84/16.05 ((
% 121.84/16.05 (subbreln) =>
% 121.84/16.05 ((
% 121.84/16.05 (eqbreln) =>
% 121.84/16.05 ((
% 121.84/16.05 (funcext) =>
% 121.84/16.05 ((
% 121.84/16.05 (funcext2) =>
% 121.84/16.05 ((
% 121.84/16.05 (ap2apEq1) =>
% 121.84/16.05 ((
% 121.84/16.05 (ap2apEq2) =>
% 121.84/16.05 ((
% 121.84/16.05 (beta1) =>
% 121.84/16.05 ((
% 121.84/16.05 (eta1) =>
% 121.84/16.05 ((
% 121.84/16.05 (lam2lamEq) =>
% 121.84/16.05 ((
% 121.84/16.05 (beta2) =>
% 121.84/16.05 ((
% 121.84/16.05 (eta2) =>
% 121.84/16.05 ((
% 121.84/16.05 (iffalseProp1) =>
% 121.84/16.05 ((
% 121.84/16.05 (iffalseProp2) =>
% 121.84/16.05 ((
% 121.84/16.05 (iftrueProp1) =>
% 121.84/16.05 ((
% 121.84/16.05 (iftrueProp2) =>
% 121.84/16.05 ((
% 121.84/16.05 (ifSingleton) =>
% 121.84/16.05 ((
% 121.84/16.05 (ifp) =>
% 121.84/16.05 ((
% 121.84/16.05 (theeq) =>
% 121.84/16.05 ((
% 121.84/16.05 (iftrue) =>
% 121.84/16.05 ((
% 121.84/16.05 (iffalse) =>
% 121.84/16.05 ((
% 121.84/16.05 (iftrueorfalse) =>
% 121.84/16.05 ((
% 121.84/16.05 (binintersectT_lem) =>
% 121.84/16.05 ((
% 121.84/16.05 (binunionT_lem) =>
% 121.84/16.05 ((
% 121.84/16.05 (powersetT_lem) =>
% 121.84/16.05 ((
% 121.84/16.05 (setminusT_lem) =>
% 121.84/16.05 ((
% 121.84/16.05 (complementT_lem) =>
% 121.84/16.05 ((
% 121.84/16.05 (setextT) =>
% 121.84/16.05 ((
% 121.84/16.05 (subsetTI) =>
% 121.84/16.05 ((
% 121.84/16.05 (powersetTI1) =>
% 121.84/16.05 ((
% 121.84/16.05 (powersetTE1) =>
% 121.84/16.05 ((
% 121.84/16.05 (complementTI1) =>
% 121.84/16.05 ((
% 121.84/16.05 (complementTE1) =>
% 121.84/16.05 ((
% 121.84/16.05 (binintersectTELcontra) =>
% 121.84/16.05 ((
% 121.84/16.05 (binintersectTERcontra) =>
% 121.84/16.05 ((
% 121.84/16.05 (contrasubsetT) =>
% 121.84/16.05 ((
% 121.84/16.05 (contrasubsetT1) =>
% 121.84/16.05 ((
% 121.84/16.05 (contrasubsetT2) =>
% 121.84/16.05 ((
% 121.84/16.05 (contrasubsetT3) =>
% 121.84/16.05 ((
% 121.84/16.05 (doubleComplementI1) =>
% 121.84/16.05 ((
% 121.84/16.05 (doubleComplementE1) =>
% 121.84/16.05 ((
% 121.84/16.05 (doubleComplementSub1) =>
% 121.84/16.05 ((
% 121.84/16.05 (doubleComplementSub2) =>
% 121.84/16.05 ((
% 121.84/16.05 (doubleComplementEq) =>
% 121.84/16.05 ((
% 121.84/16.05 (complementTnotintersectT) =>
% 121.84/16.05 ((
% 121.84/16.05 (complementImpComplementIntersect) =>
% 121.84/16.05 ((
% 121.84/16.05 (complementSubsetComplementIntersect) =>
% 121.84/16.05 ((
% 121.84/16.05 (complementInPowersetComplementIntersect) =>
% 121.84/16.05 ((
% 121.84/16.05 (contraSubsetComplement) =>
% 121.84/16.05 ((
% 121.84/16.05 (complementTcontraSubset) =>
% 121.84/16.05 ((
% 121.84/16.05 (binunionTILcontra) =>
% 121.84/16.05 ((
% 121.84/16.05 (binunionTIRcontra) =>
% 121.84/16.05 ((
% 121.84/16.05 (inIntersectImpInUnion) =>
% 121.84/16.05 ((
% 121.84/16.05 (inIntersectImpInUnion2) =>
% 121.84/16.05 ((
% 121.84/16.05 (inIntersectImpInIntersectUnions) =>
% 121.84/16.05 ((
% 121.84/16.05 (intersectInPowersetIntersectUnions) =>
% 121.84/16.05 ((
% 121.84/16.05 (inComplementUnionImpNotIn1) =>
% 121.84/16.05 ((
% 121.84/16.05 (inComplementUnionImpInComplement1) =>
% 121.84/16.05 ((
% 121.84/16.05 (binunionTE) =>
% 121.84/16.05 ((
% 121.84/16.05 (binunionTEcontra) =>
% 121.84/16.05 ((
% 121.84/16.05 (demorgan2a1) =>
% 121.84/16.05 ((
% 121.84/16.05 (complementUnionInPowersetComplement) =>
% 121.84/16.05 ((
% 121.84/16.05 (demorgan2a2) =>
% 121.84/16.05 ((
% 121.84/16.05 (demorgan1a) =>
% 121.84/16.05 ((
% 121.84/16.05 (demorgan1b) =>
% 121.84/16.05 ((
% 121.84/16.05 (demorgan1) =>
% 121.84/16.05 ((
% 121.84/16.05 (demorgan2a) =>
% 121.84/16.05 ((
% 121.84/16.05 (demorgan2b2) =>
% 121.84/16.05 ((
% 121.84/16.05 (demorgan2b) =>
% 121.84/16.05 ((
% 121.84/16.05 (demorgan2) =>
% 121.84/16.05 ((
% 121.84/16.05 (woz13rule0) =>
% 121.84/16.05 ((
% 121.84/16.05 (woz13rule1) =>
% 121.84/16.05 ((
% 121.84/16.05 (woz13rule2) =>
% 121.84/16.05 ((
% 121.84/16.05 (woz13rule3) =>
% 121.84/16.05 ((
% 121.84/16.05 (woz13rule4) =>
% 121.84/16.05 ((
% 121.84/16.05 (woz1_1) =>
% 121.84/16.05 ((
% 121.84/16.05 (woz1_2) =>
% 121.84/16.05 ((
% 121.84/16.05 (woz1_3) =>
% 121.84/16.05 ((
% 121.84/16.05 (woz1_4) =>
% 121.84/16.05 ((
% 121.84/16.05 (woz1_5) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1all2) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1SetBreln1) =>
% 121.84/16.05 ((
% 121.84/16.05 (choice2fnsingleton) =>
% 121.84/16.05 ((
% 121.84/16.05 (setOfPairsIsBReln1) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1all1) =>
% 121.84/16.05 ((
% 121.84/16.05 (subbreln1) =>
% 121.84/16.05 ((
% 121.84/16.05 (eqbreln1) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1invprop) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1invI) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1invE) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1compprop) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1compI) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1compE) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1compEex) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1unionprop) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1unionIL) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1unionIR) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1unionI) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1unionE) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1unionEcases) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1unionCommutes) =>
% 121.84/16.05 ((
% 121.84/16.05 (woz2Ex) =>
% 121.84/16.05 ((
% 121.84/16.05 (woz2W) =>
% 121.84/16.05 ((
% 121.84/16.05 (woz2A) =>
% 121.84/16.05 ((
% 121.84/16.05 (woz2B) =>
% 121.84/16.05 ((
% 121.84/16.05 (image1Ex) =>
% 121.84/16.05 ((
% 121.84/16.05 (image1Ex1) =>
% 121.84/16.05 ((
% 121.84/16.05 (image1Equiv) =>
% 121.84/16.05 ((
% 121.84/16.05 (image1E) =>
% 121.84/16.05 ((
% 121.84/16.05 (image1I) =>
% 121.84/16.05 ((
% 121.84/16.05 (injFuncInInjFuncSet) =>
% 121.84/16.05 ((
% 121.84/16.05 (!!) @ (
% 121.84/16.05 (('#B') @ (
% 121.84/16.05 !!) @
% 121.84/16.05 (
% 121.84/16.05 (
% 121.84/16.05 ('#B') @ (
% 121.84/16.05 (
% 121.84/16.05 ('#B') @ (
% 121.84/16.05 !!))) @
% 121.84/16.05 (
% 121.84/16.05 (
% 121.84/16.05 ('#S') @ (
% 121.84/16.05 (
% 121.84/16.05 ('#B') @ (
% 121.84/16.05 '#S') @
% 121.84/16.05 (
% 121.84/16.05 (
% 121.84/16.05 ('#B') @ (
% 121.84/16.05 (
% 121.84/16.05 ('#B') @ (
% 121.84/16.05 '#S'))) @
% 121.84/16.05 (
% 121.84/16.05 (
% 121.84/16.05 ('#B') @ (
% 121.84/16.05 (
% 121.84/16.05 ('#B') @ (
% 121.84/16.05 (
% 121.84/16.05 ('#B') @ (
% 121.84/16.05 =>))))) @
% 121.84/16.05 (
% 121.84/16.05 (
% 121.84/16.05 ('#B') @ (
% 121.84/16.05 (
% 121.84/16.05 ('#B') @ (
% 121.84/16.05 (
% 121.84/16.05 ('#C') @ in)))) @
% 121.84/16.05 injFuncSet)))))))) @
% 121.84/16.05 (
% 121.84/16.05 (
% 121.84/16.05 ('#B') @ (
% 121.84/16.05 (
% 121.84/16.05 ('#B') @ (
% 121.84/16.05 (
% 121.84/16.05 ('#C') @ in)))) @
% 121.84/16.05 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 121.84/16.05 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl400])).
% 121.84/16.05 thf(zip_derived_cl417, plain,
% 121.84/16.05 (~ (((subPowSU) =>
% 121.84/16.05 (((exuE2) =>
% 121.84/16.05 (((nonemptyImpWitness) =>
% 121.84/16.05 (((uniqinunit) =>
% 121.84/16.05 (((notinsingleton) =>
% 121.84/16.05 (((eqinunit) =>
% 121.84/16.05 (((singletonsswitch) =>
% 121.84/16.05 (((upairsetE) =>
% 121.84/16.05 (((upairsetIL) =>
% 121.84/16.05 (((upairsetIR) =>
% 121.84/16.05 (((emptyE1) =>
% 121.84/16.05 (((vacuousDall) =>
% 121.84/16.05 (((quantDeMorgan1) =>
% 121.84/16.05 (((quantDeMorgan2) =>
% 121.84/16.05 (((quantDeMorgan3) =>
% 121.84/16.05 (((quantDeMorgan4) =>
% 121.84/16.05 (((prop2setI) =>
% 121.84/16.05 (((prop2set2propI) =>
% 121.84/16.05 (((notdexE) =>
% 121.84/16.05 (((notdallE) =>
% 121.84/16.05 (((exuI1) =>
% 121.84/16.05 (((exuI3) =>
% 121.84/16.05 (((exuI2) =>
% 121.84/16.05 (((inCongP) =>
% 121.84/16.05 (((in__Cong) =>
% 121.84/16.05 (((exuE3u) =>
% 121.84/16.05 (((exu__Cong) =>
% 121.84/16.05 (((setadjoin__Cong) =>
% 121.84/16.05 (((powerset__Cong) =>
% 121.84/16.05 (((setunion__Cong) =>
% 121.84/16.05 ((
% 121.84/16.05 (exuEu) =>
% 121.84/16.05 ((
% 121.84/16.05 (descr__Cong) =>
% 121.84/16.05 ((
% 121.84/16.05 (dsetconstr__Cong) =>
% 121.84/16.05 ((
% 121.84/16.05 (subsetI1) =>
% 121.84/16.05 ((
% 121.84/16.05 (eqimpsubset2) =>
% 121.84/16.05 ((
% 121.84/16.05 (eqimpsubset1) =>
% 121.84/16.05 ((
% 121.84/16.05 (subsetI2) =>
% 121.84/16.05 ((
% 121.84/16.05 (emptysetsubset) =>
% 121.84/16.05 ((
% 121.84/16.05 (subsetE) =>
% 121.84/16.05 ((
% 121.84/16.05 (subsetE2) =>
% 121.84/16.05 ((
% 121.84/16.05 (notsubsetI) =>
% 121.84/16.05 ((
% 121.84/16.05 (notequalI1) =>
% 121.84/16.05 ((
% 121.84/16.05 (notequalI2) =>
% 121.84/16.05 ((
% 121.84/16.05 (subsetRefl) =>
% 121.84/16.05 ((
% 121.84/16.05 (subsetTrans) =>
% 121.84/16.05 ((
% 121.84/16.05 (setadjoinSub) =>
% 121.84/16.05 ((
% 121.84/16.05 (setadjoinSub2) =>
% 121.84/16.05 ((
% 121.84/16.05 (subset2powerset) =>
% 121.84/16.05 ((
% 121.84/16.05 (setextsub) =>
% 121.84/16.05 ((
% 121.84/16.05 (subsetemptysetimpeq) =>
% 121.84/16.05 ((
% 121.84/16.05 (powersetI1) =>
% 121.84/16.05 ((
% 121.84/16.05 (powersetE1) =>
% 121.84/16.05 ((
% 121.84/16.05 (inPowerset) =>
% 121.84/16.05 ((
% 121.84/16.05 (powersetsubset) =>
% 121.84/16.05 ((
% 121.84/16.05 (sepInPowerset) =>
% 121.84/16.05 ((
% 121.84/16.05 (sepSubset) =>
% 121.84/16.05 ((
% 121.84/16.05 (binunionIL) =>
% 121.84/16.05 ((
% 121.84/16.05 (upairset2IR) =>
% 121.84/16.05 ((
% 121.84/16.05 (binunionIR) =>
% 121.84/16.05 ((
% 121.84/16.05 (binunionEcases) =>
% 121.84/16.05 ((
% 121.84/16.05 (binunionE) =>
% 121.84/16.05 ((
% 121.84/16.05 (binunionLsub) =>
% 121.84/16.05 ((
% 121.84/16.05 (binunionRsub) =>
% 121.84/16.05 ((
% 121.84/16.05 (binintersectI) =>
% 121.84/16.05 ((
% 121.84/16.05 (binintersectSubset5) =>
% 121.84/16.05 ((
% 121.84/16.05 (binintersectEL) =>
% 121.84/16.05 ((
% 121.84/16.05 (binintersectLsub) =>
% 121.84/16.05 ((
% 121.84/16.05 (binintersectSubset2) =>
% 121.84/16.05 ((
% 121.84/16.05 (binintersectSubset3) =>
% 121.84/16.05 ((
% 121.84/16.05 (binintersectER) =>
% 121.84/16.05 ((
% 121.84/16.05 (disjointsetsI1) =>
% 121.84/16.05 ((
% 121.84/16.05 (binintersectRsub) =>
% 121.84/16.05 ((
% 121.84/16.05 (binintersectSubset4) =>
% 121.84/16.05 ((
% 121.84/16.05 (binintersectSubset1) =>
% 121.84/16.05 ((
% 121.84/16.05 (bs114d) =>
% 121.84/16.05 ((
% 121.84/16.05 (setminusI) =>
% 121.84/16.05 ((
% 121.84/16.05 (setminusEL) =>
% 121.84/16.05 ((
% 121.84/16.05 (setminusER) =>
% 121.84/16.05 ((
% 121.84/16.05 (setminusSubset2) =>
% 121.84/16.05 ((
% 121.84/16.05 (setminusERneg) =>
% 121.84/16.05 ((
% 121.84/16.05 (setminusELneg) =>
% 121.84/16.05 ((
% 121.84/16.05 (setminusILneg) =>
% 121.84/16.05 ((
% 121.84/16.05 (setminusIRneg) =>
% 121.84/16.05 ((
% 121.84/16.05 (setminusLsub) =>
% 121.84/16.05 ((
% 121.84/16.05 (setminusSubset1) =>
% 121.84/16.05 ((
% 121.84/16.05 (symdiffE) =>
% 121.84/16.05 ((
% 121.84/16.05 (symdiffI1) =>
% 121.84/16.05 ((
% 121.84/16.05 (symdiffI2) =>
% 121.84/16.05 ((
% 121.84/16.05 (symdiffIneg1) =>
% 121.84/16.05 ((
% 121.84/16.05 (symdiffIneg2) =>
% 121.84/16.05 ((
% 121.84/16.05 (secondinupair) =>
% 121.84/16.05 ((
% 121.84/16.05 (setukpairIL) =>
% 121.84/16.05 ((
% 121.84/16.05 (setukpairIR) =>
% 121.84/16.05 ((
% 121.84/16.05 (kpairiskpair) =>
% 121.84/16.05 ((
% 121.84/16.05 (kpairp) =>
% 121.84/16.05 ((
% 121.84/16.05 (singletonsubset) =>
% 121.84/16.05 ((
% 121.84/16.05 (singletoninpowerset) =>
% 121.84/16.05 ((
% 121.84/16.05 (singletoninpowunion) =>
% 121.84/16.05 ((
% 121.84/16.05 (upairset2E) =>
% 121.84/16.05 ((
% 121.84/16.05 (upairsubunion) =>
% 121.84/16.05 ((
% 121.84/16.05 (upairinpowunion) =>
% 121.84/16.05 ((
% 121.84/16.05 (ubforcartprodlem1) =>
% 121.84/16.05 ((
% 121.84/16.05 (ubforcartprodlem2) =>
% 121.84/16.05 ((
% 121.84/16.05 (ubforcartprodlem3) =>
% 121.84/16.05 ((
% 121.84/16.05 (cartprodpairin) =>
% 121.84/16.05 ((
% 121.84/16.05 (cartprodmempair1) =>
% 121.84/16.05 ((
% 121.84/16.05 (cartprodmempair) =>
% 121.84/16.05 ((
% 121.84/16.05 (setunionE2) =>
% 121.84/16.05 ((
% 121.84/16.05 (setunionsingleton1) =>
% 121.84/16.05 ((
% 121.84/16.05 (setunionsingleton2) =>
% 121.84/16.05 ((
% 121.84/16.05 (setunionsingleton) =>
% 121.84/16.05 ((
% 121.84/16.05 (singletonprop) =>
% 121.84/16.05 ((
% 121.84/16.05 (ex1E1) =>
% 121.84/16.05 ((
% 121.84/16.05 (ex1I) =>
% 121.84/16.05 ((
% 121.84/16.05 (ex1I2) =>
% 121.84/16.05 ((
% 121.84/16.05 (singletonsuniq) =>
% 121.84/16.05 ((
% 121.84/16.05 (setukpairinjL1) =>
% 121.84/16.05 ((
% 121.84/16.05 (kfstsingleton) =>
% 121.84/16.05 ((
% 121.84/16.05 (theprop) =>
% 121.84/16.05 ((
% 121.84/16.05 (kfstpairEq) =>
% 121.84/16.05 ((
% 121.84/16.05 (cartprodfstin) =>
% 121.84/16.05 ((
% 121.84/16.05 (setukpairinjL2) =>
% 121.84/16.05 ((
% 121.84/16.05 (setukpairinjL) =>
% 121.84/16.05 ((
% 121.84/16.05 (setukpairinjR11) =>
% 121.84/16.05 ((
% 121.84/16.05 (setukpairinjR12) =>
% 121.84/16.05 ((
% 121.84/16.05 (setukpairinjR1) =>
% 121.84/16.05 ((
% 121.84/16.05 (upairequniteq) =>
% 121.84/16.05 ((
% 121.84/16.05 (setukpairinjR2) =>
% 121.84/16.05 ((
% 121.84/16.05 (setukpairinjR) =>
% 121.84/16.05 ((
% 121.84/16.05 (ksndsingleton) =>
% 121.84/16.05 ((
% 121.84/16.05 (ksndpairEq) =>
% 121.84/16.05 ((
% 121.84/16.05 (kpairsurjEq) =>
% 121.84/16.05 ((
% 121.84/16.05 (cartprodsndin) =>
% 121.84/16.05 ((
% 121.84/16.05 (cartprodpairmemEL) =>
% 121.84/16.05 ((
% 121.84/16.05 (cartprodpairmemER) =>
% 121.84/16.05 ((
% 121.84/16.05 (cartprodmempaircEq) =>
% 121.84/16.05 ((
% 121.84/16.05 (cartprodfstpairEq) =>
% 121.84/16.05 ((
% 121.84/16.05 (cartprodsndpairEq) =>
% 121.84/16.05 ((
% 121.84/16.05 (cartprodpairsurjEq) =>
% 121.84/16.05 ((
% 121.84/16.05 (dpsetconstrI) =>
% 121.84/16.05 ((
% 121.84/16.05 (dpsetconstrSub) =>
% 121.84/16.05 ((
% 121.84/16.05 (setOfPairsIsBReln) =>
% 121.84/16.05 ((
% 121.84/16.05 (dpsetconstrERa) =>
% 121.84/16.05 ((
% 121.84/16.05 (dpsetconstrEL1) =>
% 121.84/16.05 ((
% 121.84/16.05 (dpsetconstrEL2) =>
% 121.84/16.05 ((
% 121.84/16.05 (dpsetconstrER) =>
% 121.84/16.05 ((
% 121.84/16.05 (funcImageSingleton) =>
% 121.84/16.05 ((
% 121.84/16.05 (apProp) =>
% 121.84/16.05 ((
% 121.84/16.05 (app) =>
% 121.84/16.05 ((
% 121.84/16.05 (infuncsetfunc) =>
% 121.84/16.05 ((
% 121.84/16.05 (ap2p) =>
% 121.84/16.05 ((
% 121.84/16.05 (funcinfuncset) =>
% 121.84/16.05 ((
% 121.84/16.05 (lamProp) =>
% 121.84/16.05 ((
% 121.84/16.05 (lamp) =>
% 121.84/16.05 ((
% 121.84/16.05 (lam2p) =>
% 121.84/16.05 ((
% 121.84/16.05 (brelnall1) =>
% 121.84/16.05 ((
% 121.84/16.05 (brelnall2) =>
% 121.84/16.05 ((
% 121.84/16.05 (ex1E2) =>
% 121.84/16.05 ((
% 121.84/16.05 (funcGraphProp1) =>
% 121.84/16.05 ((
% 121.84/16.05 (funcGraphProp3) =>
% 121.84/16.05 ((
% 121.84/16.05 (funcGraphProp2) =>
% 121.84/16.05 ((
% 121.84/16.05 (funcextLem) =>
% 121.84/16.05 ((
% 121.84/16.05 (funcGraphProp4) =>
% 121.84/16.05 ((
% 121.84/16.05 (subbreln) =>
% 121.84/16.05 ((
% 121.84/16.05 (eqbreln) =>
% 121.84/16.05 ((
% 121.84/16.05 (funcext) =>
% 121.84/16.05 ((
% 121.84/16.05 (funcext2) =>
% 121.84/16.05 ((
% 121.84/16.05 (ap2apEq1) =>
% 121.84/16.05 ((
% 121.84/16.05 (ap2apEq2) =>
% 121.84/16.05 ((
% 121.84/16.05 (beta1) =>
% 121.84/16.05 ((
% 121.84/16.05 (eta1) =>
% 121.84/16.05 ((
% 121.84/16.05 (lam2lamEq) =>
% 121.84/16.05 ((
% 121.84/16.05 (beta2) =>
% 121.84/16.05 ((
% 121.84/16.05 (eta2) =>
% 121.84/16.05 ((
% 121.84/16.05 (iffalseProp1) =>
% 121.84/16.05 ((
% 121.84/16.05 (iffalseProp2) =>
% 121.84/16.05 ((
% 121.84/16.05 (iftrueProp1) =>
% 121.84/16.05 ((
% 121.84/16.05 (iftrueProp2) =>
% 121.84/16.05 ((
% 121.84/16.05 (ifSingleton) =>
% 121.84/16.05 ((
% 121.84/16.05 (ifp) =>
% 121.84/16.05 ((
% 121.84/16.05 (theeq) =>
% 121.84/16.05 ((
% 121.84/16.05 (iftrue) =>
% 121.84/16.05 ((
% 121.84/16.05 (iffalse) =>
% 121.84/16.05 ((
% 121.84/16.05 (iftrueorfalse) =>
% 121.84/16.05 ((
% 121.84/16.05 (binintersectT_lem) =>
% 121.84/16.05 ((
% 121.84/16.05 (binunionT_lem) =>
% 121.84/16.05 ((
% 121.84/16.05 (powersetT_lem) =>
% 121.84/16.05 ((
% 121.84/16.05 (setminusT_lem) =>
% 121.84/16.05 ((
% 121.84/16.05 (complementT_lem) =>
% 121.84/16.05 ((
% 121.84/16.05 (setextT) =>
% 121.84/16.05 ((
% 121.84/16.05 (subsetTI) =>
% 121.84/16.05 ((
% 121.84/16.05 (powersetTI1) =>
% 121.84/16.05 ((
% 121.84/16.05 (powersetTE1) =>
% 121.84/16.05 ((
% 121.84/16.05 (complementTI1) =>
% 121.84/16.05 ((
% 121.84/16.05 (complementTE1) =>
% 121.84/16.05 ((
% 121.84/16.05 (binintersectTELcontra) =>
% 121.84/16.05 ((
% 121.84/16.05 (binintersectTERcontra) =>
% 121.84/16.05 ((
% 121.84/16.05 (contrasubsetT) =>
% 121.84/16.05 ((
% 121.84/16.05 (contrasubsetT1) =>
% 121.84/16.05 ((
% 121.84/16.05 (contrasubsetT2) =>
% 121.84/16.05 ((
% 121.84/16.05 (contrasubsetT3) =>
% 121.84/16.05 ((
% 121.84/16.05 (doubleComplementI1) =>
% 121.84/16.05 ((
% 121.84/16.05 (doubleComplementE1) =>
% 121.84/16.05 ((
% 121.84/16.05 (doubleComplementSub1) =>
% 121.84/16.05 ((
% 121.84/16.05 (doubleComplementSub2) =>
% 121.84/16.05 ((
% 121.84/16.05 (doubleComplementEq) =>
% 121.84/16.05 ((
% 121.84/16.05 (complementTnotintersectT) =>
% 121.84/16.05 ((
% 121.84/16.05 (complementImpComplementIntersect) =>
% 121.84/16.05 ((
% 121.84/16.05 (complementSubsetComplementIntersect) =>
% 121.84/16.05 ((
% 121.84/16.05 (complementInPowersetComplementIntersect) =>
% 121.84/16.05 ((
% 121.84/16.05 (contraSubsetComplement) =>
% 121.84/16.05 ((
% 121.84/16.05 (complementTcontraSubset) =>
% 121.84/16.05 ((
% 121.84/16.05 (binunionTILcontra) =>
% 121.84/16.05 ((
% 121.84/16.05 (binunionTIRcontra) =>
% 121.84/16.05 ((
% 121.84/16.05 (inIntersectImpInUnion) =>
% 121.84/16.05 ((
% 121.84/16.05 (inIntersectImpInUnion2) =>
% 121.84/16.05 ((
% 121.84/16.05 (inIntersectImpInIntersectUnions) =>
% 121.84/16.05 ((
% 121.84/16.05 (intersectInPowersetIntersectUnions) =>
% 121.84/16.05 ((
% 121.84/16.05 (inComplementUnionImpNotIn1) =>
% 121.84/16.05 ((
% 121.84/16.05 (inComplementUnionImpInComplement1) =>
% 121.84/16.05 ((
% 121.84/16.05 (binunionTE) =>
% 121.84/16.05 ((
% 121.84/16.05 (binunionTEcontra) =>
% 121.84/16.05 ((
% 121.84/16.05 (demorgan2a1) =>
% 121.84/16.05 ((
% 121.84/16.05 (complementUnionInPowersetComplement) =>
% 121.84/16.05 ((
% 121.84/16.05 (demorgan2a2) =>
% 121.84/16.05 ((
% 121.84/16.05 (demorgan1a) =>
% 121.84/16.05 ((
% 121.84/16.05 (demorgan1b) =>
% 121.84/16.05 ((
% 121.84/16.05 (demorgan1) =>
% 121.84/16.05 ((
% 121.84/16.05 (demorgan2a) =>
% 121.84/16.05 ((
% 121.84/16.05 (demorgan2b2) =>
% 121.84/16.05 ((
% 121.84/16.05 (demorgan2b) =>
% 121.84/16.05 ((
% 121.84/16.05 (demorgan2) =>
% 121.84/16.05 ((
% 121.84/16.05 (woz13rule0) =>
% 121.84/16.05 ((
% 121.84/16.05 (woz13rule1) =>
% 121.84/16.05 ((
% 121.84/16.05 (woz13rule2) =>
% 121.84/16.05 ((
% 121.84/16.05 (woz13rule3) =>
% 121.84/16.05 ((
% 121.84/16.05 (woz13rule4) =>
% 121.84/16.05 ((
% 121.84/16.05 (woz1_1) =>
% 121.84/16.05 ((
% 121.84/16.05 (woz1_2) =>
% 121.84/16.05 ((
% 121.84/16.05 (woz1_3) =>
% 121.84/16.05 ((
% 121.84/16.05 (woz1_4) =>
% 121.84/16.05 ((
% 121.84/16.05 (woz1_5) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1all2) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1SetBreln1) =>
% 121.84/16.05 ((
% 121.84/16.05 (choice2fnsingleton) =>
% 121.84/16.05 ((
% 121.84/16.05 (setOfPairsIsBReln1) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1all1) =>
% 121.84/16.05 ((
% 121.84/16.05 (subbreln1) =>
% 121.84/16.05 ((
% 121.84/16.05 (eqbreln1) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1invprop) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1invI) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1invE) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1compprop) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1compI) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1compE) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1compEex) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1unionprop) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1unionIL) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1unionIR) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1unionI) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1unionE) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1unionEcases) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1unionCommutes) =>
% 121.84/16.05 ((
% 121.84/16.05 (woz2Ex) =>
% 121.84/16.05 ((
% 121.84/16.05 (woz2W) =>
% 121.84/16.05 ((
% 121.84/16.05 (woz2A) =>
% 121.84/16.05 ((
% 121.84/16.05 (woz2B) =>
% 121.84/16.05 ((
% 121.84/16.05 (image1Ex) =>
% 121.84/16.05 ((
% 121.84/16.05 (image1Ex1) =>
% 121.84/16.05 ((
% 121.84/16.05 (image1Equiv) =>
% 121.84/16.05 ((
% 121.84/16.05 (image1E) =>
% 121.84/16.05 ((
% 121.84/16.05 (image1I) =>
% 121.84/16.05 ((
% 121.84/16.05 (injFuncInInjFuncSet) =>
% 121.84/16.05 ((
% 121.84/16.05 (!!) @ (
% 121.84/16.05 (('#B') @ (
% 121.84/16.05 !!) @
% 121.84/16.05 (
% 121.84/16.05 (
% 121.84/16.05 ('#B') @ (
% 121.84/16.05 (
% 121.84/16.05 ('#B') @ (
% 121.84/16.05 !!))) @
% 121.84/16.05 (
% 121.84/16.05 (
% 121.84/16.05 ('#S') @ (
% 121.84/16.05 (
% 121.84/16.05 ('#B') @ (
% 121.84/16.05 '#S') @
% 121.84/16.05 (
% 121.84/16.05 (
% 121.84/16.05 ('#B') @ (
% 121.84/16.05 (
% 121.84/16.05 ('#B') @ (
% 121.84/16.05 '#S'))) @
% 121.84/16.05 (
% 121.84/16.05 (
% 121.84/16.05 ('#B') @ (
% 121.84/16.05 (
% 121.84/16.05 ('#B') @ (
% 121.84/16.05 (
% 121.84/16.05 ('#B') @ (
% 121.84/16.05 =>))))) @
% 121.84/16.05 (
% 121.84/16.05 (
% 121.84/16.05 ('#B') @ (
% 121.84/16.05 (
% 121.84/16.05 ('#B') @ (
% 121.84/16.05 (
% 121.84/16.05 ('#C') @ in)))) @
% 121.84/16.05 injFuncSet)))))))) @
% 121.84/16.05 (
% 121.84/16.05 (
% 121.84/16.05 ('#B') @ (
% 121.84/16.05 (
% 121.84/16.05 ('#B') @ (
% 121.84/16.05 (
% 121.84/16.05 ('#C') @ in)))) @
% 121.84/16.05 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 121.84/16.05 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl408])).
% 121.84/16.05 thf(zip_derived_cl428, plain,
% 121.84/16.05 (~ (((exuE2) =>
% 121.84/16.05 (((nonemptyImpWitness) =>
% 121.84/16.05 (((uniqinunit) =>
% 121.84/16.05 (((notinsingleton) =>
% 121.84/16.05 (((eqinunit) =>
% 121.84/16.05 (((singletonsswitch) =>
% 121.84/16.05 (((upairsetE) =>
% 121.84/16.05 (((upairsetIL) =>
% 121.84/16.05 (((upairsetIR) =>
% 121.84/16.05 (((emptyE1) =>
% 121.84/16.05 (((vacuousDall) =>
% 121.84/16.05 (((quantDeMorgan1) =>
% 121.84/16.05 (((quantDeMorgan2) =>
% 121.84/16.05 (((quantDeMorgan3) =>
% 121.84/16.05 (((quantDeMorgan4) =>
% 121.84/16.05 (((prop2setI) =>
% 121.84/16.05 (((prop2set2propI) =>
% 121.84/16.05 (((notdexE) =>
% 121.84/16.05 (((notdallE) =>
% 121.84/16.05 (((exuI1) =>
% 121.84/16.05 (((exuI3) =>
% 121.84/16.05 (((exuI2) =>
% 121.84/16.05 (((inCongP) =>
% 121.84/16.05 (((in__Cong) =>
% 121.84/16.05 (((exuE3u) =>
% 121.84/16.05 (((exu__Cong) =>
% 121.84/16.05 (((setadjoin__Cong) =>
% 121.84/16.05 (((powerset__Cong) =>
% 121.84/16.05 (((setunion__Cong) =>
% 121.84/16.05 (((exuEu) =>
% 121.84/16.05 ((
% 121.84/16.05 (descr__Cong) =>
% 121.84/16.05 ((
% 121.84/16.05 (dsetconstr__Cong) =>
% 121.84/16.05 ((
% 121.84/16.05 (subsetI1) =>
% 121.84/16.05 ((
% 121.84/16.05 (eqimpsubset2) =>
% 121.84/16.05 ((
% 121.84/16.05 (eqimpsubset1) =>
% 121.84/16.05 ((
% 121.84/16.05 (subsetI2) =>
% 121.84/16.05 ((
% 121.84/16.05 (emptysetsubset) =>
% 121.84/16.05 ((
% 121.84/16.05 (subsetE) =>
% 121.84/16.05 ((
% 121.84/16.05 (subsetE2) =>
% 121.84/16.05 ((
% 121.84/16.05 (notsubsetI) =>
% 121.84/16.05 ((
% 121.84/16.05 (notequalI1) =>
% 121.84/16.05 ((
% 121.84/16.05 (notequalI2) =>
% 121.84/16.05 ((
% 121.84/16.05 (subsetRefl) =>
% 121.84/16.05 ((
% 121.84/16.05 (subsetTrans) =>
% 121.84/16.05 ((
% 121.84/16.05 (setadjoinSub) =>
% 121.84/16.05 ((
% 121.84/16.05 (setadjoinSub2) =>
% 121.84/16.05 ((
% 121.84/16.05 (subset2powerset) =>
% 121.84/16.05 ((
% 121.84/16.05 (setextsub) =>
% 121.84/16.05 ((
% 121.84/16.05 (subsetemptysetimpeq) =>
% 121.84/16.05 ((
% 121.84/16.05 (powersetI1) =>
% 121.84/16.05 ((
% 121.84/16.05 (powersetE1) =>
% 121.84/16.05 ((
% 121.84/16.05 (inPowerset) =>
% 121.84/16.05 ((
% 121.84/16.05 (powersetsubset) =>
% 121.84/16.05 ((
% 121.84/16.05 (sepInPowerset) =>
% 121.84/16.05 ((
% 121.84/16.05 (sepSubset) =>
% 121.84/16.05 ((
% 121.84/16.05 (binunionIL) =>
% 121.84/16.05 ((
% 121.84/16.05 (upairset2IR) =>
% 121.84/16.05 ((
% 121.84/16.05 (binunionIR) =>
% 121.84/16.05 ((
% 121.84/16.05 (binunionEcases) =>
% 121.84/16.05 ((
% 121.84/16.05 (binunionE) =>
% 121.84/16.05 ((
% 121.84/16.05 (binunionLsub) =>
% 121.84/16.05 ((
% 121.84/16.05 (binunionRsub) =>
% 121.84/16.05 ((
% 121.84/16.05 (binintersectI) =>
% 121.84/16.05 ((
% 121.84/16.05 (binintersectSubset5) =>
% 121.84/16.05 ((
% 121.84/16.05 (binintersectEL) =>
% 121.84/16.05 ((
% 121.84/16.05 (binintersectLsub) =>
% 121.84/16.05 ((
% 121.84/16.05 (binintersectSubset2) =>
% 121.84/16.05 ((
% 121.84/16.05 (binintersectSubset3) =>
% 121.84/16.05 ((
% 121.84/16.05 (binintersectER) =>
% 121.84/16.05 ((
% 121.84/16.05 (disjointsetsI1) =>
% 121.84/16.05 ((
% 121.84/16.05 (binintersectRsub) =>
% 121.84/16.05 ((
% 121.84/16.05 (binintersectSubset4) =>
% 121.84/16.05 ((
% 121.84/16.05 (binintersectSubset1) =>
% 121.84/16.05 ((
% 121.84/16.05 (bs114d) =>
% 121.84/16.05 ((
% 121.84/16.05 (setminusI) =>
% 121.84/16.05 ((
% 121.84/16.05 (setminusEL) =>
% 121.84/16.05 ((
% 121.84/16.05 (setminusER) =>
% 121.84/16.05 ((
% 121.84/16.05 (setminusSubset2) =>
% 121.84/16.05 ((
% 121.84/16.05 (setminusERneg) =>
% 121.84/16.05 ((
% 121.84/16.05 (setminusELneg) =>
% 121.84/16.05 ((
% 121.84/16.05 (setminusILneg) =>
% 121.84/16.05 ((
% 121.84/16.05 (setminusIRneg) =>
% 121.84/16.05 ((
% 121.84/16.05 (setminusLsub) =>
% 121.84/16.05 ((
% 121.84/16.05 (setminusSubset1) =>
% 121.84/16.05 ((
% 121.84/16.05 (symdiffE) =>
% 121.84/16.05 ((
% 121.84/16.05 (symdiffI1) =>
% 121.84/16.05 ((
% 121.84/16.05 (symdiffI2) =>
% 121.84/16.05 ((
% 121.84/16.05 (symdiffIneg1) =>
% 121.84/16.05 ((
% 121.84/16.05 (symdiffIneg2) =>
% 121.84/16.05 ((
% 121.84/16.05 (secondinupair) =>
% 121.84/16.05 ((
% 121.84/16.05 (setukpairIL) =>
% 121.84/16.05 ((
% 121.84/16.05 (setukpairIR) =>
% 121.84/16.05 ((
% 121.84/16.05 (kpairiskpair) =>
% 121.84/16.05 ((
% 121.84/16.05 (kpairp) =>
% 121.84/16.05 ((
% 121.84/16.05 (singletonsubset) =>
% 121.84/16.05 ((
% 121.84/16.05 (singletoninpowerset) =>
% 121.84/16.05 ((
% 121.84/16.05 (singletoninpowunion) =>
% 121.84/16.05 ((
% 121.84/16.05 (upairset2E) =>
% 121.84/16.05 ((
% 121.84/16.05 (upairsubunion) =>
% 121.84/16.05 ((
% 121.84/16.05 (upairinpowunion) =>
% 121.84/16.05 ((
% 121.84/16.05 (ubforcartprodlem1) =>
% 121.84/16.05 ((
% 121.84/16.05 (ubforcartprodlem2) =>
% 121.84/16.05 ((
% 121.84/16.05 (ubforcartprodlem3) =>
% 121.84/16.05 ((
% 121.84/16.05 (cartprodpairin) =>
% 121.84/16.05 ((
% 121.84/16.05 (cartprodmempair1) =>
% 121.84/16.05 ((
% 121.84/16.05 (cartprodmempair) =>
% 121.84/16.05 ((
% 121.84/16.05 (setunionE2) =>
% 121.84/16.05 ((
% 121.84/16.05 (setunionsingleton1) =>
% 121.84/16.05 ((
% 121.84/16.05 (setunionsingleton2) =>
% 121.84/16.05 ((
% 121.84/16.05 (setunionsingleton) =>
% 121.84/16.05 ((
% 121.84/16.05 (singletonprop) =>
% 121.84/16.05 ((
% 121.84/16.05 (ex1E1) =>
% 121.84/16.05 ((
% 121.84/16.05 (ex1I) =>
% 121.84/16.05 ((
% 121.84/16.05 (ex1I2) =>
% 121.84/16.05 ((
% 121.84/16.05 (singletonsuniq) =>
% 121.84/16.05 ((
% 121.84/16.05 (setukpairinjL1) =>
% 121.84/16.05 ((
% 121.84/16.05 (kfstsingleton) =>
% 121.84/16.05 ((
% 121.84/16.05 (theprop) =>
% 121.84/16.05 ((
% 121.84/16.05 (kfstpairEq) =>
% 121.84/16.05 ((
% 121.84/16.05 (cartprodfstin) =>
% 121.84/16.05 ((
% 121.84/16.05 (setukpairinjL2) =>
% 121.84/16.05 ((
% 121.84/16.05 (setukpairinjL) =>
% 121.84/16.05 ((
% 121.84/16.05 (setukpairinjR11) =>
% 121.84/16.05 ((
% 121.84/16.05 (setukpairinjR12) =>
% 121.84/16.05 ((
% 121.84/16.05 (setukpairinjR1) =>
% 121.84/16.05 ((
% 121.84/16.05 (upairequniteq) =>
% 121.84/16.05 ((
% 121.84/16.05 (setukpairinjR2) =>
% 121.84/16.05 ((
% 121.84/16.05 (setukpairinjR) =>
% 121.84/16.05 ((
% 121.84/16.05 (ksndsingleton) =>
% 121.84/16.05 ((
% 121.84/16.05 (ksndpairEq) =>
% 121.84/16.05 ((
% 121.84/16.05 (kpairsurjEq) =>
% 121.84/16.05 ((
% 121.84/16.05 (cartprodsndin) =>
% 121.84/16.05 ((
% 121.84/16.05 (cartprodpairmemEL) =>
% 121.84/16.05 ((
% 121.84/16.05 (cartprodpairmemER) =>
% 121.84/16.05 ((
% 121.84/16.05 (cartprodmempaircEq) =>
% 121.84/16.05 ((
% 121.84/16.05 (cartprodfstpairEq) =>
% 121.84/16.05 ((
% 121.84/16.05 (cartprodsndpairEq) =>
% 121.84/16.05 ((
% 121.84/16.05 (cartprodpairsurjEq) =>
% 121.84/16.05 ((
% 121.84/16.05 (dpsetconstrI) =>
% 121.84/16.05 ((
% 121.84/16.05 (dpsetconstrSub) =>
% 121.84/16.05 ((
% 121.84/16.05 (setOfPairsIsBReln) =>
% 121.84/16.05 ((
% 121.84/16.05 (dpsetconstrERa) =>
% 121.84/16.05 ((
% 121.84/16.05 (dpsetconstrEL1) =>
% 121.84/16.05 ((
% 121.84/16.05 (dpsetconstrEL2) =>
% 121.84/16.05 ((
% 121.84/16.05 (dpsetconstrER) =>
% 121.84/16.05 ((
% 121.84/16.05 (funcImageSingleton) =>
% 121.84/16.05 ((
% 121.84/16.05 (apProp) =>
% 121.84/16.05 ((
% 121.84/16.05 (app) =>
% 121.84/16.05 ((
% 121.84/16.05 (infuncsetfunc) =>
% 121.84/16.05 ((
% 121.84/16.05 (ap2p) =>
% 121.84/16.05 ((
% 121.84/16.05 (funcinfuncset) =>
% 121.84/16.05 ((
% 121.84/16.05 (lamProp) =>
% 121.84/16.05 ((
% 121.84/16.05 (lamp) =>
% 121.84/16.05 ((
% 121.84/16.05 (lam2p) =>
% 121.84/16.05 ((
% 121.84/16.05 (brelnall1) =>
% 121.84/16.05 ((
% 121.84/16.05 (brelnall2) =>
% 121.84/16.05 ((
% 121.84/16.05 (ex1E2) =>
% 121.84/16.05 ((
% 121.84/16.05 (funcGraphProp1) =>
% 121.84/16.05 ((
% 121.84/16.05 (funcGraphProp3) =>
% 121.84/16.05 ((
% 121.84/16.05 (funcGraphProp2) =>
% 121.84/16.05 ((
% 121.84/16.05 (funcextLem) =>
% 121.84/16.05 ((
% 121.84/16.05 (funcGraphProp4) =>
% 121.84/16.05 ((
% 121.84/16.05 (subbreln) =>
% 121.84/16.05 ((
% 121.84/16.05 (eqbreln) =>
% 121.84/16.05 ((
% 121.84/16.05 (funcext) =>
% 121.84/16.05 ((
% 121.84/16.05 (funcext2) =>
% 121.84/16.05 ((
% 121.84/16.05 (ap2apEq1) =>
% 121.84/16.05 ((
% 121.84/16.05 (ap2apEq2) =>
% 121.84/16.05 ((
% 121.84/16.05 (beta1) =>
% 121.84/16.05 ((
% 121.84/16.05 (eta1) =>
% 121.84/16.05 ((
% 121.84/16.05 (lam2lamEq) =>
% 121.84/16.05 ((
% 121.84/16.05 (beta2) =>
% 121.84/16.05 ((
% 121.84/16.05 (eta2) =>
% 121.84/16.05 ((
% 121.84/16.05 (iffalseProp1) =>
% 121.84/16.05 ((
% 121.84/16.05 (iffalseProp2) =>
% 121.84/16.05 ((
% 121.84/16.05 (iftrueProp1) =>
% 121.84/16.05 ((
% 121.84/16.05 (iftrueProp2) =>
% 121.84/16.05 ((
% 121.84/16.05 (ifSingleton) =>
% 121.84/16.05 ((
% 121.84/16.05 (ifp) =>
% 121.84/16.05 ((
% 121.84/16.05 (theeq) =>
% 121.84/16.05 ((
% 121.84/16.05 (iftrue) =>
% 121.84/16.05 ((
% 121.84/16.05 (iffalse) =>
% 121.84/16.05 ((
% 121.84/16.05 (iftrueorfalse) =>
% 121.84/16.05 ((
% 121.84/16.05 (binintersectT_lem) =>
% 121.84/16.05 ((
% 121.84/16.05 (binunionT_lem) =>
% 121.84/16.05 ((
% 121.84/16.05 (powersetT_lem) =>
% 121.84/16.05 ((
% 121.84/16.05 (setminusT_lem) =>
% 121.84/16.05 ((
% 121.84/16.05 (complementT_lem) =>
% 121.84/16.05 ((
% 121.84/16.05 (setextT) =>
% 121.84/16.05 ((
% 121.84/16.05 (subsetTI) =>
% 121.84/16.05 ((
% 121.84/16.05 (powersetTI1) =>
% 121.84/16.05 ((
% 121.84/16.05 (powersetTE1) =>
% 121.84/16.05 ((
% 121.84/16.05 (complementTI1) =>
% 121.84/16.05 ((
% 121.84/16.05 (complementTE1) =>
% 121.84/16.05 ((
% 121.84/16.05 (binintersectTELcontra) =>
% 121.84/16.05 ((
% 121.84/16.05 (binintersectTERcontra) =>
% 121.84/16.05 ((
% 121.84/16.05 (contrasubsetT) =>
% 121.84/16.05 ((
% 121.84/16.05 (contrasubsetT1) =>
% 121.84/16.05 ((
% 121.84/16.05 (contrasubsetT2) =>
% 121.84/16.05 ((
% 121.84/16.05 (contrasubsetT3) =>
% 121.84/16.05 ((
% 121.84/16.05 (doubleComplementI1) =>
% 121.84/16.05 ((
% 121.84/16.05 (doubleComplementE1) =>
% 121.84/16.05 ((
% 121.84/16.05 (doubleComplementSub1) =>
% 121.84/16.05 ((
% 121.84/16.05 (doubleComplementSub2) =>
% 121.84/16.05 ((
% 121.84/16.05 (doubleComplementEq) =>
% 121.84/16.05 ((
% 121.84/16.05 (complementTnotintersectT) =>
% 121.84/16.05 ((
% 121.84/16.05 (complementImpComplementIntersect) =>
% 121.84/16.05 ((
% 121.84/16.05 (complementSubsetComplementIntersect) =>
% 121.84/16.05 ((
% 121.84/16.05 (complementInPowersetComplementIntersect) =>
% 121.84/16.05 ((
% 121.84/16.05 (contraSubsetComplement) =>
% 121.84/16.05 ((
% 121.84/16.05 (complementTcontraSubset) =>
% 121.84/16.05 ((
% 121.84/16.05 (binunionTILcontra) =>
% 121.84/16.05 ((
% 121.84/16.05 (binunionTIRcontra) =>
% 121.84/16.05 ((
% 121.84/16.05 (inIntersectImpInUnion) =>
% 121.84/16.05 ((
% 121.84/16.05 (inIntersectImpInUnion2) =>
% 121.84/16.05 ((
% 121.84/16.05 (inIntersectImpInIntersectUnions) =>
% 121.84/16.05 ((
% 121.84/16.05 (intersectInPowersetIntersectUnions) =>
% 121.84/16.05 ((
% 121.84/16.05 (inComplementUnionImpNotIn1) =>
% 121.84/16.05 ((
% 121.84/16.05 (inComplementUnionImpInComplement1) =>
% 121.84/16.05 ((
% 121.84/16.05 (binunionTE) =>
% 121.84/16.05 ((
% 121.84/16.05 (binunionTEcontra) =>
% 121.84/16.05 ((
% 121.84/16.05 (demorgan2a1) =>
% 121.84/16.05 ((
% 121.84/16.05 (complementUnionInPowersetComplement) =>
% 121.84/16.05 ((
% 121.84/16.05 (demorgan2a2) =>
% 121.84/16.05 ((
% 121.84/16.05 (demorgan1a) =>
% 121.84/16.05 ((
% 121.84/16.05 (demorgan1b) =>
% 121.84/16.05 ((
% 121.84/16.05 (demorgan1) =>
% 121.84/16.05 ((
% 121.84/16.05 (demorgan2a) =>
% 121.84/16.05 ((
% 121.84/16.05 (demorgan2b2) =>
% 121.84/16.05 ((
% 121.84/16.05 (demorgan2b) =>
% 121.84/16.05 ((
% 121.84/16.05 (demorgan2) =>
% 121.84/16.05 ((
% 121.84/16.05 (woz13rule0) =>
% 121.84/16.05 ((
% 121.84/16.05 (woz13rule1) =>
% 121.84/16.05 ((
% 121.84/16.05 (woz13rule2) =>
% 121.84/16.05 ((
% 121.84/16.05 (woz13rule3) =>
% 121.84/16.05 ((
% 121.84/16.05 (woz13rule4) =>
% 121.84/16.05 ((
% 121.84/16.05 (woz1_1) =>
% 121.84/16.05 ((
% 121.84/16.05 (woz1_2) =>
% 121.84/16.05 ((
% 121.84/16.05 (woz1_3) =>
% 121.84/16.05 ((
% 121.84/16.05 (woz1_4) =>
% 121.84/16.05 ((
% 121.84/16.05 (woz1_5) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1all2) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1SetBreln1) =>
% 121.84/16.05 ((
% 121.84/16.05 (choice2fnsingleton) =>
% 121.84/16.05 ((
% 121.84/16.05 (setOfPairsIsBReln1) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1all1) =>
% 121.84/16.05 ((
% 121.84/16.05 (subbreln1) =>
% 121.84/16.05 ((
% 121.84/16.05 (eqbreln1) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1invprop) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1invI) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1invE) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1compprop) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1compI) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1compE) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1compEex) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1unionprop) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1unionIL) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1unionIR) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1unionI) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1unionE) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1unionEcases) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1unionCommutes) =>
% 121.84/16.05 ((
% 121.84/16.05 (woz2Ex) =>
% 121.84/16.05 ((
% 121.84/16.05 (woz2W) =>
% 121.84/16.05 ((
% 121.84/16.05 (woz2A) =>
% 121.84/16.05 ((
% 121.84/16.05 (woz2B) =>
% 121.84/16.05 ((
% 121.84/16.05 (image1Ex) =>
% 121.84/16.05 ((
% 121.84/16.05 (image1Ex1) =>
% 121.84/16.05 ((
% 121.84/16.05 (image1Equiv) =>
% 121.84/16.05 ((
% 121.84/16.05 (image1E) =>
% 121.84/16.05 ((
% 121.84/16.05 (image1I) =>
% 121.84/16.05 ((
% 121.84/16.05 (injFuncInInjFuncSet) =>
% 121.84/16.05 ((
% 121.84/16.05 (!!) @ (
% 121.84/16.05 (('#B') @ (
% 121.84/16.05 !!) @
% 121.84/16.05 (
% 121.84/16.05 (
% 121.84/16.05 ('#B') @ (
% 121.84/16.05 (
% 121.84/16.05 ('#B') @ (
% 121.84/16.05 !!))) @
% 121.84/16.05 (
% 121.84/16.05 (
% 121.84/16.05 ('#S') @ (
% 121.84/16.05 (
% 121.84/16.05 ('#B') @ (
% 121.84/16.05 '#S') @
% 121.84/16.05 (
% 121.84/16.05 (
% 121.84/16.05 ('#B') @ (
% 121.84/16.05 (
% 121.84/16.05 ('#B') @ (
% 121.84/16.05 '#S'))) @
% 121.84/16.05 (
% 121.84/16.05 (
% 121.84/16.05 ('#B') @ (
% 121.84/16.05 (
% 121.84/16.05 ('#B') @ (
% 121.84/16.05 (
% 121.84/16.05 ('#B') @ (
% 121.84/16.05 =>))))) @
% 121.84/16.05 (
% 121.84/16.05 (
% 121.84/16.05 ('#B') @ (
% 121.84/16.05 (
% 121.84/16.05 ('#B') @ (
% 121.84/16.05 (
% 121.84/16.05 ('#C') @ in)))) @
% 121.84/16.05 injFuncSet)))))))) @
% 121.84/16.05 (
% 121.84/16.05 (
% 121.84/16.05 ('#B') @ (
% 121.84/16.05 (
% 121.84/16.05 ('#B') @ (
% 121.84/16.05 (
% 121.84/16.05 ('#C') @ in)))) @
% 121.84/16.05 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 121.84/16.05 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl417])).
% 121.84/16.05 thf(zip_derived_cl439, plain,
% 121.84/16.05 (~ (((nonemptyImpWitness) =>
% 121.84/16.05 (((uniqinunit) =>
% 121.84/16.05 (((notinsingleton) =>
% 121.84/16.05 (((eqinunit) =>
% 121.84/16.05 (((singletonsswitch) =>
% 121.84/16.05 (((upairsetE) =>
% 121.84/16.05 (((upairsetIL) =>
% 121.84/16.05 (((upairsetIR) =>
% 121.84/16.05 (((emptyE1) =>
% 121.84/16.05 (((vacuousDall) =>
% 121.84/16.05 (((quantDeMorgan1) =>
% 121.84/16.05 (((quantDeMorgan2) =>
% 121.84/16.05 (((quantDeMorgan3) =>
% 121.84/16.05 (((quantDeMorgan4) =>
% 121.84/16.05 (((prop2setI) =>
% 121.84/16.05 (((prop2set2propI) =>
% 121.84/16.05 (((notdexE) =>
% 121.84/16.05 (((notdallE) =>
% 121.84/16.05 (((exuI1) =>
% 121.84/16.05 (((exuI3) =>
% 121.84/16.05 (((exuI2) =>
% 121.84/16.05 (((inCongP) =>
% 121.84/16.05 (((in__Cong) =>
% 121.84/16.05 (((exuE3u) =>
% 121.84/16.05 (((exu__Cong) =>
% 121.84/16.05 (((setadjoin__Cong) =>
% 121.84/16.05 (((powerset__Cong) =>
% 121.84/16.05 (((setunion__Cong) =>
% 121.84/16.05 (((exuEu) =>
% 121.84/16.05 (((descr__Cong) =>
% 121.84/16.05 ((
% 121.84/16.05 (dsetconstr__Cong) =>
% 121.84/16.05 ((
% 121.84/16.05 (subsetI1) =>
% 121.84/16.05 ((
% 121.84/16.05 (eqimpsubset2) =>
% 121.84/16.05 ((
% 121.84/16.05 (eqimpsubset1) =>
% 121.84/16.05 ((
% 121.84/16.05 (subsetI2) =>
% 121.84/16.05 ((
% 121.84/16.05 (emptysetsubset) =>
% 121.84/16.05 ((
% 121.84/16.05 (subsetE) =>
% 121.84/16.05 ((
% 121.84/16.05 (subsetE2) =>
% 121.84/16.05 ((
% 121.84/16.05 (notsubsetI) =>
% 121.84/16.05 ((
% 121.84/16.05 (notequalI1) =>
% 121.84/16.05 ((
% 121.84/16.05 (notequalI2) =>
% 121.84/16.05 ((
% 121.84/16.05 (subsetRefl) =>
% 121.84/16.05 ((
% 121.84/16.05 (subsetTrans) =>
% 121.84/16.05 ((
% 121.84/16.05 (setadjoinSub) =>
% 121.84/16.05 ((
% 121.84/16.05 (setadjoinSub2) =>
% 121.84/16.05 ((
% 121.84/16.05 (subset2powerset) =>
% 121.84/16.05 ((
% 121.84/16.05 (setextsub) =>
% 121.84/16.05 ((
% 121.84/16.05 (subsetemptysetimpeq) =>
% 121.84/16.05 ((
% 121.84/16.05 (powersetI1) =>
% 121.84/16.05 ((
% 121.84/16.05 (powersetE1) =>
% 121.84/16.05 ((
% 121.84/16.05 (inPowerset) =>
% 121.84/16.05 ((
% 121.84/16.05 (powersetsubset) =>
% 121.84/16.05 ((
% 121.84/16.05 (sepInPowerset) =>
% 121.84/16.05 ((
% 121.84/16.05 (sepSubset) =>
% 121.84/16.05 ((
% 121.84/16.05 (binunionIL) =>
% 121.84/16.05 ((
% 121.84/16.05 (upairset2IR) =>
% 121.84/16.05 ((
% 121.84/16.05 (binunionIR) =>
% 121.84/16.05 ((
% 121.84/16.05 (binunionEcases) =>
% 121.84/16.05 ((
% 121.84/16.05 (binunionE) =>
% 121.84/16.05 ((
% 121.84/16.05 (binunionLsub) =>
% 121.84/16.05 ((
% 121.84/16.05 (binunionRsub) =>
% 121.84/16.05 ((
% 121.84/16.05 (binintersectI) =>
% 121.84/16.05 ((
% 121.84/16.05 (binintersectSubset5) =>
% 121.84/16.05 ((
% 121.84/16.05 (binintersectEL) =>
% 121.84/16.05 ((
% 121.84/16.05 (binintersectLsub) =>
% 121.84/16.05 ((
% 121.84/16.05 (binintersectSubset2) =>
% 121.84/16.05 ((
% 121.84/16.05 (binintersectSubset3) =>
% 121.84/16.05 ((
% 121.84/16.05 (binintersectER) =>
% 121.84/16.05 ((
% 121.84/16.05 (disjointsetsI1) =>
% 121.84/16.05 ((
% 121.84/16.05 (binintersectRsub) =>
% 121.84/16.05 ((
% 121.84/16.05 (binintersectSubset4) =>
% 121.84/16.05 ((
% 121.84/16.05 (binintersectSubset1) =>
% 121.84/16.05 ((
% 121.84/16.05 (bs114d) =>
% 121.84/16.05 ((
% 121.84/16.05 (setminusI) =>
% 121.84/16.05 ((
% 121.84/16.05 (setminusEL) =>
% 121.84/16.05 ((
% 121.84/16.05 (setminusER) =>
% 121.84/16.05 ((
% 121.84/16.05 (setminusSubset2) =>
% 121.84/16.05 ((
% 121.84/16.05 (setminusERneg) =>
% 121.84/16.05 ((
% 121.84/16.05 (setminusELneg) =>
% 121.84/16.05 ((
% 121.84/16.05 (setminusILneg) =>
% 121.84/16.05 ((
% 121.84/16.05 (setminusIRneg) =>
% 121.84/16.05 ((
% 121.84/16.05 (setminusLsub) =>
% 121.84/16.05 ((
% 121.84/16.05 (setminusSubset1) =>
% 121.84/16.05 ((
% 121.84/16.05 (symdiffE) =>
% 121.84/16.05 ((
% 121.84/16.05 (symdiffI1) =>
% 121.84/16.05 ((
% 121.84/16.05 (symdiffI2) =>
% 121.84/16.05 ((
% 121.84/16.05 (symdiffIneg1) =>
% 121.84/16.05 ((
% 121.84/16.05 (symdiffIneg2) =>
% 121.84/16.05 ((
% 121.84/16.05 (secondinupair) =>
% 121.84/16.05 ((
% 121.84/16.05 (setukpairIL) =>
% 121.84/16.05 ((
% 121.84/16.05 (setukpairIR) =>
% 121.84/16.05 ((
% 121.84/16.05 (kpairiskpair) =>
% 121.84/16.05 ((
% 121.84/16.05 (kpairp) =>
% 121.84/16.05 ((
% 121.84/16.05 (singletonsubset) =>
% 121.84/16.05 ((
% 121.84/16.05 (singletoninpowerset) =>
% 121.84/16.05 ((
% 121.84/16.05 (singletoninpowunion) =>
% 121.84/16.05 ((
% 121.84/16.05 (upairset2E) =>
% 121.84/16.05 ((
% 121.84/16.05 (upairsubunion) =>
% 121.84/16.05 ((
% 121.84/16.05 (upairinpowunion) =>
% 121.84/16.05 ((
% 121.84/16.05 (ubforcartprodlem1) =>
% 121.84/16.05 ((
% 121.84/16.05 (ubforcartprodlem2) =>
% 121.84/16.05 ((
% 121.84/16.05 (ubforcartprodlem3) =>
% 121.84/16.05 ((
% 121.84/16.05 (cartprodpairin) =>
% 121.84/16.05 ((
% 121.84/16.05 (cartprodmempair1) =>
% 121.84/16.05 ((
% 121.84/16.05 (cartprodmempair) =>
% 121.84/16.05 ((
% 121.84/16.05 (setunionE2) =>
% 121.84/16.05 ((
% 121.84/16.05 (setunionsingleton1) =>
% 121.84/16.05 ((
% 121.84/16.05 (setunionsingleton2) =>
% 121.84/16.05 ((
% 121.84/16.05 (setunionsingleton) =>
% 121.84/16.05 ((
% 121.84/16.05 (singletonprop) =>
% 121.84/16.05 ((
% 121.84/16.05 (ex1E1) =>
% 121.84/16.05 ((
% 121.84/16.05 (ex1I) =>
% 121.84/16.05 ((
% 121.84/16.05 (ex1I2) =>
% 121.84/16.05 ((
% 121.84/16.05 (singletonsuniq) =>
% 121.84/16.05 ((
% 121.84/16.05 (setukpairinjL1) =>
% 121.84/16.05 ((
% 121.84/16.05 (kfstsingleton) =>
% 121.84/16.05 ((
% 121.84/16.05 (theprop) =>
% 121.84/16.05 ((
% 121.84/16.05 (kfstpairEq) =>
% 121.84/16.05 ((
% 121.84/16.05 (cartprodfstin) =>
% 121.84/16.05 ((
% 121.84/16.05 (setukpairinjL2) =>
% 121.84/16.05 ((
% 121.84/16.05 (setukpairinjL) =>
% 121.84/16.05 ((
% 121.84/16.05 (setukpairinjR11) =>
% 121.84/16.05 ((
% 121.84/16.05 (setukpairinjR12) =>
% 121.84/16.05 ((
% 121.84/16.05 (setukpairinjR1) =>
% 121.84/16.05 ((
% 121.84/16.05 (upairequniteq) =>
% 121.84/16.05 ((
% 121.84/16.05 (setukpairinjR2) =>
% 121.84/16.05 ((
% 121.84/16.05 (setukpairinjR) =>
% 121.84/16.05 ((
% 121.84/16.05 (ksndsingleton) =>
% 121.84/16.05 ((
% 121.84/16.05 (ksndpairEq) =>
% 121.84/16.05 ((
% 121.84/16.05 (kpairsurjEq) =>
% 121.84/16.05 ((
% 121.84/16.05 (cartprodsndin) =>
% 121.84/16.05 ((
% 121.84/16.05 (cartprodpairmemEL) =>
% 121.84/16.05 ((
% 121.84/16.05 (cartprodpairmemER) =>
% 121.84/16.05 ((
% 121.84/16.05 (cartprodmempaircEq) =>
% 121.84/16.05 ((
% 121.84/16.05 (cartprodfstpairEq) =>
% 121.84/16.05 ((
% 121.84/16.05 (cartprodsndpairEq) =>
% 121.84/16.05 ((
% 121.84/16.05 (cartprodpairsurjEq) =>
% 121.84/16.05 ((
% 121.84/16.05 (dpsetconstrI) =>
% 121.84/16.05 ((
% 121.84/16.05 (dpsetconstrSub) =>
% 121.84/16.05 ((
% 121.84/16.05 (setOfPairsIsBReln) =>
% 121.84/16.05 ((
% 121.84/16.05 (dpsetconstrERa) =>
% 121.84/16.05 ((
% 121.84/16.05 (dpsetconstrEL1) =>
% 121.84/16.05 ((
% 121.84/16.05 (dpsetconstrEL2) =>
% 121.84/16.05 ((
% 121.84/16.05 (dpsetconstrER) =>
% 121.84/16.05 ((
% 121.84/16.05 (funcImageSingleton) =>
% 121.84/16.05 ((
% 121.84/16.05 (apProp) =>
% 121.84/16.05 ((
% 121.84/16.05 (app) =>
% 121.84/16.05 ((
% 121.84/16.05 (infuncsetfunc) =>
% 121.84/16.05 ((
% 121.84/16.05 (ap2p) =>
% 121.84/16.05 ((
% 121.84/16.05 (funcinfuncset) =>
% 121.84/16.05 ((
% 121.84/16.05 (lamProp) =>
% 121.84/16.05 ((
% 121.84/16.05 (lamp) =>
% 121.84/16.05 ((
% 121.84/16.05 (lam2p) =>
% 121.84/16.05 ((
% 121.84/16.05 (brelnall1) =>
% 121.84/16.05 ((
% 121.84/16.05 (brelnall2) =>
% 121.84/16.05 ((
% 121.84/16.05 (ex1E2) =>
% 121.84/16.05 ((
% 121.84/16.05 (funcGraphProp1) =>
% 121.84/16.05 ((
% 121.84/16.05 (funcGraphProp3) =>
% 121.84/16.05 ((
% 121.84/16.05 (funcGraphProp2) =>
% 121.84/16.05 ((
% 121.84/16.05 (funcextLem) =>
% 121.84/16.05 ((
% 121.84/16.05 (funcGraphProp4) =>
% 121.84/16.05 ((
% 121.84/16.05 (subbreln) =>
% 121.84/16.05 ((
% 121.84/16.05 (eqbreln) =>
% 121.84/16.05 ((
% 121.84/16.05 (funcext) =>
% 121.84/16.05 ((
% 121.84/16.05 (funcext2) =>
% 121.84/16.05 ((
% 121.84/16.05 (ap2apEq1) =>
% 121.84/16.05 ((
% 121.84/16.05 (ap2apEq2) =>
% 121.84/16.05 ((
% 121.84/16.05 (beta1) =>
% 121.84/16.05 ((
% 121.84/16.05 (eta1) =>
% 121.84/16.05 ((
% 121.84/16.05 (lam2lamEq) =>
% 121.84/16.05 ((
% 121.84/16.05 (beta2) =>
% 121.84/16.05 ((
% 121.84/16.05 (eta2) =>
% 121.84/16.05 ((
% 121.84/16.05 (iffalseProp1) =>
% 121.84/16.05 ((
% 121.84/16.05 (iffalseProp2) =>
% 121.84/16.05 ((
% 121.84/16.05 (iftrueProp1) =>
% 121.84/16.05 ((
% 121.84/16.05 (iftrueProp2) =>
% 121.84/16.05 ((
% 121.84/16.05 (ifSingleton) =>
% 121.84/16.05 ((
% 121.84/16.05 (ifp) =>
% 121.84/16.05 ((
% 121.84/16.05 (theeq) =>
% 121.84/16.05 ((
% 121.84/16.05 (iftrue) =>
% 121.84/16.05 ((
% 121.84/16.05 (iffalse) =>
% 121.84/16.05 ((
% 121.84/16.05 (iftrueorfalse) =>
% 121.84/16.05 ((
% 121.84/16.05 (binintersectT_lem) =>
% 121.84/16.05 ((
% 121.84/16.05 (binunionT_lem) =>
% 121.84/16.05 ((
% 121.84/16.05 (powersetT_lem) =>
% 121.84/16.05 ((
% 121.84/16.05 (setminusT_lem) =>
% 121.84/16.05 ((
% 121.84/16.05 (complementT_lem) =>
% 121.84/16.05 ((
% 121.84/16.05 (setextT) =>
% 121.84/16.05 ((
% 121.84/16.05 (subsetTI) =>
% 121.84/16.05 ((
% 121.84/16.05 (powersetTI1) =>
% 121.84/16.05 ((
% 121.84/16.05 (powersetTE1) =>
% 121.84/16.05 ((
% 121.84/16.05 (complementTI1) =>
% 121.84/16.05 ((
% 121.84/16.05 (complementTE1) =>
% 121.84/16.05 ((
% 121.84/16.05 (binintersectTELcontra) =>
% 121.84/16.05 ((
% 121.84/16.05 (binintersectTERcontra) =>
% 121.84/16.05 ((
% 121.84/16.05 (contrasubsetT) =>
% 121.84/16.05 ((
% 121.84/16.05 (contrasubsetT1) =>
% 121.84/16.05 ((
% 121.84/16.05 (contrasubsetT2) =>
% 121.84/16.05 ((
% 121.84/16.05 (contrasubsetT3) =>
% 121.84/16.05 ((
% 121.84/16.05 (doubleComplementI1) =>
% 121.84/16.05 ((
% 121.84/16.05 (doubleComplementE1) =>
% 121.84/16.05 ((
% 121.84/16.05 (doubleComplementSub1) =>
% 121.84/16.05 ((
% 121.84/16.05 (doubleComplementSub2) =>
% 121.84/16.05 ((
% 121.84/16.05 (doubleComplementEq) =>
% 121.84/16.05 ((
% 121.84/16.05 (complementTnotintersectT) =>
% 121.84/16.05 ((
% 121.84/16.05 (complementImpComplementIntersect) =>
% 121.84/16.05 ((
% 121.84/16.05 (complementSubsetComplementIntersect) =>
% 121.84/16.05 ((
% 121.84/16.05 (complementInPowersetComplementIntersect) =>
% 121.84/16.05 ((
% 121.84/16.05 (contraSubsetComplement) =>
% 121.84/16.05 ((
% 121.84/16.05 (complementTcontraSubset) =>
% 121.84/16.05 ((
% 121.84/16.05 (binunionTILcontra) =>
% 121.84/16.05 ((
% 121.84/16.05 (binunionTIRcontra) =>
% 121.84/16.05 ((
% 121.84/16.05 (inIntersectImpInUnion) =>
% 121.84/16.05 ((
% 121.84/16.05 (inIntersectImpInUnion2) =>
% 121.84/16.05 ((
% 121.84/16.05 (inIntersectImpInIntersectUnions) =>
% 121.84/16.05 ((
% 121.84/16.05 (intersectInPowersetIntersectUnions) =>
% 121.84/16.05 ((
% 121.84/16.05 (inComplementUnionImpNotIn1) =>
% 121.84/16.05 ((
% 121.84/16.05 (inComplementUnionImpInComplement1) =>
% 121.84/16.05 ((
% 121.84/16.05 (binunionTE) =>
% 121.84/16.05 ((
% 121.84/16.05 (binunionTEcontra) =>
% 121.84/16.05 ((
% 121.84/16.05 (demorgan2a1) =>
% 121.84/16.05 ((
% 121.84/16.05 (complementUnionInPowersetComplement) =>
% 121.84/16.05 ((
% 121.84/16.05 (demorgan2a2) =>
% 121.84/16.05 ((
% 121.84/16.05 (demorgan1a) =>
% 121.84/16.05 ((
% 121.84/16.05 (demorgan1b) =>
% 121.84/16.05 ((
% 121.84/16.05 (demorgan1) =>
% 121.84/16.05 ((
% 121.84/16.05 (demorgan2a) =>
% 121.84/16.05 ((
% 121.84/16.05 (demorgan2b2) =>
% 121.84/16.05 ((
% 121.84/16.05 (demorgan2b) =>
% 121.84/16.05 ((
% 121.84/16.05 (demorgan2) =>
% 121.84/16.05 ((
% 121.84/16.05 (woz13rule0) =>
% 121.84/16.05 ((
% 121.84/16.05 (woz13rule1) =>
% 121.84/16.05 ((
% 121.84/16.05 (woz13rule2) =>
% 121.84/16.05 ((
% 121.84/16.05 (woz13rule3) =>
% 121.84/16.05 ((
% 121.84/16.05 (woz13rule4) =>
% 121.84/16.05 ((
% 121.84/16.05 (woz1_1) =>
% 121.84/16.05 ((
% 121.84/16.05 (woz1_2) =>
% 121.84/16.05 ((
% 121.84/16.05 (woz1_3) =>
% 121.84/16.05 ((
% 121.84/16.05 (woz1_4) =>
% 121.84/16.05 ((
% 121.84/16.05 (woz1_5) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1all2) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1SetBreln1) =>
% 121.84/16.05 ((
% 121.84/16.05 (choice2fnsingleton) =>
% 121.84/16.05 ((
% 121.84/16.05 (setOfPairsIsBReln1) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1all1) =>
% 121.84/16.05 ((
% 121.84/16.05 (subbreln1) =>
% 121.84/16.05 ((
% 121.84/16.05 (eqbreln1) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1invprop) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1invI) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1invE) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1compprop) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1compI) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1compE) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1compEex) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1unionprop) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1unionIL) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1unionIR) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1unionI) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1unionE) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1unionEcases) =>
% 121.84/16.05 ((
% 121.84/16.05 (breln1unionCommutes) =>
% 121.84/16.05 ((
% 121.84/16.05 (woz2Ex) =>
% 121.84/16.05 ((
% 121.84/16.05 (woz2W) =>
% 121.84/16.05 ((
% 121.84/16.05 (woz2A) =>
% 121.84/16.05 ((
% 121.84/16.05 (woz2B) =>
% 121.84/16.05 ((
% 121.84/16.05 (image1Ex) =>
% 121.84/16.05 ((
% 121.84/16.05 (image1Ex1) =>
% 121.84/16.05 ((
% 121.84/16.05 (image1Equiv) =>
% 121.84/16.05 ((
% 121.84/16.05 (image1E) =>
% 121.84/16.05 ((
% 121.84/16.05 (image1I) =>
% 121.84/16.05 ((
% 121.84/16.05 (injFuncInInjFuncSet) =>
% 121.84/16.05 ((
% 121.84/16.05 (!!) @ (
% 121.84/16.05 (('#B') @ (
% 121.84/16.05 !!) @
% 121.84/16.05 (
% 121.84/16.05 (
% 121.84/16.05 ('#B') @ (
% 121.84/16.05 (
% 121.84/16.05 ('#B') @ (
% 121.84/16.05 !!))) @
% 121.84/16.05 (
% 121.84/16.05 (
% 121.84/16.05 ('#S') @ (
% 121.84/16.05 (
% 121.84/16.05 ('#B') @ (
% 121.84/16.05 '#S') @
% 121.84/16.05 (
% 121.84/16.05 (
% 121.84/16.05 ('#B') @ (
% 121.84/16.05 (
% 121.84/16.05 ('#B') @ (
% 121.84/16.05 '#S'))) @
% 121.84/16.05 (
% 121.84/16.05 (
% 121.84/16.05 ('#B') @ (
% 121.84/16.05 (
% 121.84/16.05 ('#B') @ (
% 121.84/16.05 (
% 121.84/16.05 ('#B') @ (
% 121.84/16.05 =>))))) @
% 121.84/16.05 (
% 121.84/16.05 (
% 121.84/16.05 ('#B') @ (
% 121.84/16.05 (
% 121.84/16.05 ('#B') @ (
% 121.84/16.05 (
% 121.84/16.05 ('#C') @ in)))) @
% 121.84/16.05 injFuncSet)))))))) @
% 121.84/16.05 (
% 121.84/16.05 (
% 121.84/16.05 ('#B') @ (
% 121.84/16.05 (
% 121.84/16.05 ('#B') @ (
% 121.84/16.05 (
% 121.84/16.05 ('#C') @ in)))) @
% 121.84/16.05 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 121.84/16.05 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl428])).
% 121.84/16.05 thf(zip_derived_cl449, plain,
% 121.84/16.05 (~ (((uniqinunit) =>
% 121.84/16.05 (((notinsingleton) =>
% 121.84/16.05 (((eqinunit) =>
% 121.84/16.05 (((singletonsswitch) =>
% 121.84/16.05 (((upairsetE) =>
% 121.84/16.05 (((upairsetIL) =>
% 121.84/16.05 (((upairsetIR) =>
% 121.84/16.05 (((emptyE1) =>
% 121.84/16.05 (((vacuousDall) =>
% 121.84/16.05 (((quantDeMorgan1) =>
% 121.84/16.05 (((quantDeMorgan2) =>
% 121.84/16.05 (((quantDeMorgan3) =>
% 121.84/16.05 (((quantDeMorgan4) =>
% 121.84/16.05 (((prop2setI) =>
% 121.84/16.05 (((prop2set2propI) =>
% 121.84/16.05 (((notdexE) =>
% 121.84/16.05 (((notdallE) =>
% 121.84/16.05 (((exuI1) =>
% 121.84/16.05 (((exuI3) =>
% 121.84/16.05 (((exuI2) =>
% 121.84/16.05 (((inCongP) =>
% 121.84/16.05 (((in__Cong) =>
% 121.84/16.05 (((exuE3u) =>
% 121.84/16.05 (((exu__Cong) =>
% 121.84/16.05 (((setadjoin__Cong) =>
% 121.84/16.05 (((powerset__Cong) =>
% 121.84/16.05 (((setunion__Cong) =>
% 121.84/16.05 (((exuEu) =>
% 121.84/16.05 (((descr__Cong) =>
% 121.84/16.05 (((dsetconstr__Cong) =>
% 121.84/16.05 ((
% 121.84/16.05 (subsetI1) =>
% 121.84/16.06 ((
% 121.84/16.06 (eqimpsubset2) =>
% 121.84/16.06 ((
% 121.84/16.06 (eqimpsubset1) =>
% 121.84/16.06 ((
% 121.84/16.06 (subsetI2) =>
% 121.84/16.06 ((
% 121.84/16.06 (emptysetsubset) =>
% 121.84/16.06 ((
% 121.84/16.06 (subsetE) =>
% 121.84/16.06 ((
% 121.84/16.06 (subsetE2) =>
% 121.84/16.06 ((
% 121.84/16.06 (notsubsetI) =>
% 121.84/16.06 ((
% 121.84/16.06 (notequalI1) =>
% 121.84/16.06 ((
% 121.84/16.06 (notequalI2) =>
% 121.84/16.06 ((
% 121.84/16.06 (subsetRefl) =>
% 121.84/16.06 ((
% 121.84/16.06 (subsetTrans) =>
% 121.84/16.06 ((
% 121.84/16.06 (setadjoinSub) =>
% 121.84/16.06 ((
% 121.84/16.06 (setadjoinSub2) =>
% 121.84/16.06 ((
% 121.84/16.06 (subset2powerset) =>
% 121.84/16.06 ((
% 121.84/16.06 (setextsub) =>
% 121.84/16.06 ((
% 121.84/16.06 (subsetemptysetimpeq) =>
% 121.84/16.06 ((
% 121.84/16.06 (powersetI1) =>
% 121.84/16.06 ((
% 121.84/16.06 (powersetE1) =>
% 121.84/16.06 ((
% 121.84/16.06 (inPowerset) =>
% 121.84/16.06 ((
% 121.84/16.06 (powersetsubset) =>
% 121.84/16.06 ((
% 121.84/16.06 (sepInPowerset) =>
% 121.84/16.06 ((
% 121.84/16.06 (sepSubset) =>
% 121.84/16.06 ((
% 121.84/16.06 (binunionIL) =>
% 121.84/16.06 ((
% 121.84/16.06 (upairset2IR) =>
% 121.84/16.06 ((
% 121.84/16.06 (binunionIR) =>
% 121.84/16.06 ((
% 121.84/16.06 (binunionEcases) =>
% 121.84/16.06 ((
% 121.84/16.06 (binunionE) =>
% 121.84/16.06 ((
% 121.84/16.06 (binunionLsub) =>
% 121.84/16.06 ((
% 121.84/16.06 (binunionRsub) =>
% 121.84/16.06 ((
% 121.84/16.06 (binintersectI) =>
% 121.84/16.06 ((
% 121.84/16.06 (binintersectSubset5) =>
% 121.84/16.06 ((
% 121.84/16.06 (binintersectEL) =>
% 121.84/16.06 ((
% 121.84/16.06 (binintersectLsub) =>
% 121.84/16.06 ((
% 121.84/16.06 (binintersectSubset2) =>
% 121.84/16.06 ((
% 121.84/16.06 (binintersectSubset3) =>
% 121.84/16.06 ((
% 121.84/16.06 (binintersectER) =>
% 121.84/16.06 ((
% 121.84/16.06 (disjointsetsI1) =>
% 121.84/16.06 ((
% 121.84/16.06 (binintersectRsub) =>
% 121.84/16.06 ((
% 121.84/16.06 (binintersectSubset4) =>
% 121.84/16.06 ((
% 121.84/16.06 (binintersectSubset1) =>
% 121.84/16.06 ((
% 121.84/16.06 (bs114d) =>
% 121.84/16.06 ((
% 121.84/16.06 (setminusI) =>
% 121.84/16.06 ((
% 121.84/16.06 (setminusEL) =>
% 121.84/16.06 ((
% 121.84/16.06 (setminusER) =>
% 121.84/16.06 ((
% 121.84/16.06 (setminusSubset2) =>
% 121.84/16.06 ((
% 121.84/16.06 (setminusERneg) =>
% 121.84/16.06 ((
% 121.84/16.06 (setminusELneg) =>
% 121.84/16.06 ((
% 121.84/16.06 (setminusILneg) =>
% 121.84/16.06 ((
% 121.84/16.06 (setminusIRneg) =>
% 121.84/16.06 ((
% 121.84/16.06 (setminusLsub) =>
% 121.84/16.06 ((
% 121.84/16.06 (setminusSubset1) =>
% 121.84/16.06 ((
% 121.84/16.06 (symdiffE) =>
% 121.84/16.06 ((
% 121.84/16.06 (symdiffI1) =>
% 121.84/16.06 ((
% 121.84/16.06 (symdiffI2) =>
% 121.84/16.06 ((
% 121.84/16.06 (symdiffIneg1) =>
% 121.84/16.06 ((
% 121.84/16.06 (symdiffIneg2) =>
% 121.84/16.06 ((
% 121.84/16.06 (secondinupair) =>
% 121.84/16.06 ((
% 121.84/16.06 (setukpairIL) =>
% 121.84/16.06 ((
% 121.84/16.06 (setukpairIR) =>
% 121.84/16.06 ((
% 121.84/16.06 (kpairiskpair) =>
% 121.84/16.06 ((
% 121.84/16.06 (kpairp) =>
% 121.84/16.06 ((
% 121.84/16.06 (singletonsubset) =>
% 121.84/16.06 ((
% 121.84/16.06 (singletoninpowerset) =>
% 121.84/16.06 ((
% 121.84/16.06 (singletoninpowunion) =>
% 121.84/16.06 ((
% 121.84/16.06 (upairset2E) =>
% 121.84/16.06 ((
% 121.84/16.06 (upairsubunion) =>
% 121.84/16.06 ((
% 121.84/16.06 (upairinpowunion) =>
% 121.84/16.06 ((
% 121.84/16.06 (ubforcartprodlem1) =>
% 121.84/16.06 ((
% 121.84/16.06 (ubforcartprodlem2) =>
% 121.84/16.06 ((
% 121.84/16.06 (ubforcartprodlem3) =>
% 121.84/16.06 ((
% 121.84/16.06 (cartprodpairin) =>
% 121.84/16.06 ((
% 121.84/16.06 (cartprodmempair1) =>
% 121.84/16.06 ((
% 121.84/16.06 (cartprodmempair) =>
% 121.84/16.06 ((
% 121.84/16.06 (setunionE2) =>
% 121.84/16.06 ((
% 121.84/16.06 (setunionsingleton1) =>
% 121.84/16.06 ((
% 121.84/16.06 (setunionsingleton2) =>
% 121.84/16.06 ((
% 121.84/16.06 (setunionsingleton) =>
% 121.84/16.06 ((
% 121.84/16.06 (singletonprop) =>
% 121.84/16.06 ((
% 121.84/16.06 (ex1E1) =>
% 121.84/16.06 ((
% 121.84/16.06 (ex1I) =>
% 121.84/16.06 ((
% 121.84/16.06 (ex1I2) =>
% 121.84/16.06 ((
% 121.84/16.06 (singletonsuniq) =>
% 121.84/16.06 ((
% 121.84/16.06 (setukpairinjL1) =>
% 121.84/16.06 ((
% 121.84/16.06 (kfstsingleton) =>
% 121.84/16.06 ((
% 121.84/16.06 (theprop) =>
% 121.84/16.06 ((
% 121.84/16.06 (kfstpairEq) =>
% 121.84/16.06 ((
% 121.84/16.06 (cartprodfstin) =>
% 121.84/16.06 ((
% 121.84/16.06 (setukpairinjL2) =>
% 121.84/16.06 ((
% 121.84/16.06 (setukpairinjL) =>
% 121.84/16.06 ((
% 121.84/16.06 (setukpairinjR11) =>
% 121.84/16.06 ((
% 121.84/16.06 (setukpairinjR12) =>
% 121.84/16.06 ((
% 121.84/16.06 (setukpairinjR1) =>
% 121.84/16.06 ((
% 121.84/16.06 (upairequniteq) =>
% 121.84/16.06 ((
% 121.84/16.06 (setukpairinjR2) =>
% 121.84/16.06 ((
% 121.84/16.06 (setukpairinjR) =>
% 121.84/16.06 ((
% 121.84/16.06 (ksndsingleton) =>
% 121.84/16.06 ((
% 121.84/16.06 (ksndpairEq) =>
% 121.84/16.06 ((
% 121.84/16.06 (kpairsurjEq) =>
% 121.84/16.06 ((
% 121.84/16.06 (cartprodsndin) =>
% 121.84/16.06 ((
% 121.84/16.06 (cartprodpairmemEL) =>
% 121.84/16.06 ((
% 121.84/16.06 (cartprodpairmemER) =>
% 121.84/16.06 ((
% 121.84/16.06 (cartprodmempaircEq) =>
% 121.84/16.06 ((
% 121.84/16.06 (cartprodfstpairEq) =>
% 121.84/16.06 ((
% 121.84/16.06 (cartprodsndpairEq) =>
% 121.84/16.06 ((
% 121.84/16.06 (cartprodpairsurjEq) =>
% 121.84/16.06 ((
% 121.84/16.06 (dpsetconstrI) =>
% 121.84/16.06 ((
% 121.84/16.06 (dpsetconstrSub) =>
% 121.84/16.06 ((
% 121.84/16.06 (setOfPairsIsBReln) =>
% 121.84/16.06 ((
% 121.84/16.06 (dpsetconstrERa) =>
% 121.84/16.06 ((
% 121.84/16.06 (dpsetconstrEL1) =>
% 121.84/16.06 ((
% 121.84/16.06 (dpsetconstrEL2) =>
% 121.84/16.06 ((
% 121.84/16.06 (dpsetconstrER) =>
% 121.84/16.06 ((
% 121.84/16.06 (funcImageSingleton) =>
% 121.84/16.06 ((
% 121.84/16.06 (apProp) =>
% 121.84/16.06 ((
% 121.84/16.06 (app) =>
% 121.84/16.06 ((
% 121.84/16.06 (infuncsetfunc) =>
% 121.84/16.06 ((
% 121.84/16.06 (ap2p) =>
% 121.84/16.06 ((
% 121.84/16.06 (funcinfuncset) =>
% 121.84/16.06 ((
% 121.84/16.06 (lamProp) =>
% 121.84/16.06 ((
% 121.84/16.06 (lamp) =>
% 121.84/16.06 ((
% 121.84/16.06 (lam2p) =>
% 121.84/16.06 ((
% 121.84/16.06 (brelnall1) =>
% 121.84/16.06 ((
% 121.84/16.06 (brelnall2) =>
% 121.84/16.06 ((
% 121.84/16.06 (ex1E2) =>
% 121.84/16.06 ((
% 121.84/16.06 (funcGraphProp1) =>
% 121.84/16.06 ((
% 121.84/16.06 (funcGraphProp3) =>
% 121.84/16.06 ((
% 121.84/16.06 (funcGraphProp2) =>
% 121.84/16.06 ((
% 121.84/16.06 (funcextLem) =>
% 121.84/16.06 ((
% 121.84/16.06 (funcGraphProp4) =>
% 121.84/16.06 ((
% 121.84/16.06 (subbreln) =>
% 121.84/16.06 ((
% 121.84/16.06 (eqbreln) =>
% 121.84/16.06 ((
% 121.84/16.06 (funcext) =>
% 121.84/16.06 ((
% 121.84/16.06 (funcext2) =>
% 121.84/16.06 ((
% 121.84/16.06 (ap2apEq1) =>
% 121.84/16.06 ((
% 121.84/16.06 (ap2apEq2) =>
% 121.84/16.06 ((
% 121.84/16.06 (beta1) =>
% 121.84/16.06 ((
% 121.84/16.06 (eta1) =>
% 121.84/16.06 ((
% 121.84/16.06 (lam2lamEq) =>
% 121.84/16.06 ((
% 121.84/16.06 (beta2) =>
% 121.84/16.06 ((
% 121.84/16.06 (eta2) =>
% 121.84/16.06 ((
% 121.84/16.06 (iffalseProp1) =>
% 121.84/16.06 ((
% 121.84/16.06 (iffalseProp2) =>
% 121.84/16.06 ((
% 121.84/16.06 (iftrueProp1) =>
% 121.84/16.06 ((
% 121.84/16.06 (iftrueProp2) =>
% 121.84/16.06 ((
% 121.84/16.06 (ifSingleton) =>
% 121.84/16.06 ((
% 121.84/16.06 (ifp) =>
% 121.84/16.06 ((
% 121.84/16.06 (theeq) =>
% 121.84/16.06 ((
% 121.84/16.06 (iftrue) =>
% 121.84/16.06 ((
% 121.84/16.06 (iffalse) =>
% 121.84/16.06 ((
% 121.84/16.06 (iftrueorfalse) =>
% 121.84/16.06 ((
% 121.84/16.06 (binintersectT_lem) =>
% 121.84/16.06 ((
% 121.84/16.06 (binunionT_lem) =>
% 121.84/16.06 ((
% 121.84/16.06 (powersetT_lem) =>
% 121.84/16.06 ((
% 121.84/16.06 (setminusT_lem) =>
% 121.84/16.06 ((
% 121.84/16.06 (complementT_lem) =>
% 121.84/16.06 ((
% 121.84/16.06 (setextT) =>
% 121.84/16.06 ((
% 121.84/16.06 (subsetTI) =>
% 121.84/16.06 ((
% 121.84/16.06 (powersetTI1) =>
% 121.84/16.06 ((
% 121.84/16.06 (powersetTE1) =>
% 121.84/16.06 ((
% 121.84/16.06 (complementTI1) =>
% 121.84/16.06 ((
% 121.84/16.06 (complementTE1) =>
% 121.84/16.06 ((
% 121.84/16.06 (binintersectTELcontra) =>
% 121.84/16.06 ((
% 121.84/16.06 (binintersectTERcontra) =>
% 121.84/16.06 ((
% 121.84/16.06 (contrasubsetT) =>
% 121.84/16.06 ((
% 121.84/16.06 (contrasubsetT1) =>
% 121.84/16.06 ((
% 121.84/16.06 (contrasubsetT2) =>
% 121.84/16.06 ((
% 121.84/16.06 (contrasubsetT3) =>
% 121.84/16.06 ((
% 121.84/16.06 (doubleComplementI1) =>
% 121.84/16.06 ((
% 121.84/16.06 (doubleComplementE1) =>
% 121.84/16.06 ((
% 121.84/16.06 (doubleComplementSub1) =>
% 121.84/16.06 ((
% 121.84/16.06 (doubleComplementSub2) =>
% 121.84/16.06 ((
% 121.84/16.06 (doubleComplementEq) =>
% 121.84/16.06 ((
% 121.84/16.06 (complementTnotintersectT) =>
% 121.84/16.06 ((
% 121.84/16.06 (complementImpComplementIntersect) =>
% 121.84/16.06 ((
% 121.84/16.06 (complementSubsetComplementIntersect) =>
% 121.84/16.06 ((
% 121.84/16.06 (complementInPowersetComplementIntersect) =>
% 121.84/16.06 ((
% 121.84/16.06 (contraSubsetComplement) =>
% 121.84/16.06 ((
% 121.84/16.06 (complementTcontraSubset) =>
% 121.84/16.06 ((
% 121.84/16.06 (binunionTILcontra) =>
% 121.84/16.06 ((
% 121.84/16.06 (binunionTIRcontra) =>
% 121.84/16.06 ((
% 121.84/16.06 (inIntersectImpInUnion) =>
% 121.84/16.06 ((
% 121.84/16.06 (inIntersectImpInUnion2) =>
% 121.84/16.06 ((
% 121.84/16.06 (inIntersectImpInIntersectUnions) =>
% 121.84/16.06 ((
% 121.84/16.06 (intersectInPowersetIntersectUnions) =>
% 121.84/16.06 ((
% 121.84/16.06 (inComplementUnionImpNotIn1) =>
% 121.84/16.06 ((
% 121.84/16.06 (inComplementUnionImpInComplement1) =>
% 121.84/16.06 ((
% 121.84/16.06 (binunionTE) =>
% 121.84/16.06 ((
% 121.84/16.06 (binunionTEcontra) =>
% 121.84/16.06 ((
% 121.84/16.06 (demorgan2a1) =>
% 121.84/16.06 ((
% 121.84/16.06 (complementUnionInPowersetComplement) =>
% 121.84/16.06 ((
% 121.84/16.06 (demorgan2a2) =>
% 121.84/16.06 ((
% 121.84/16.06 (demorgan1a) =>
% 121.84/16.06 ((
% 121.84/16.06 (demorgan1b) =>
% 121.84/16.06 ((
% 121.84/16.06 (demorgan1) =>
% 121.84/16.06 ((
% 121.84/16.06 (demorgan2a) =>
% 121.84/16.06 ((
% 121.84/16.06 (demorgan2b2) =>
% 121.84/16.06 ((
% 121.84/16.06 (demorgan2b) =>
% 121.84/16.06 ((
% 121.84/16.06 (demorgan2) =>
% 121.84/16.06 ((
% 121.84/16.06 (woz13rule0) =>
% 121.84/16.06 ((
% 121.84/16.06 (woz13rule1) =>
% 121.84/16.06 ((
% 121.84/16.06 (woz13rule2) =>
% 121.84/16.06 ((
% 121.84/16.06 (woz13rule3) =>
% 121.84/16.06 ((
% 121.84/16.06 (woz13rule4) =>
% 121.84/16.06 ((
% 121.84/16.06 (woz1_1) =>
% 121.84/16.06 ((
% 121.84/16.06 (woz1_2) =>
% 121.84/16.06 ((
% 121.84/16.06 (woz1_3) =>
% 121.84/16.06 ((
% 121.84/16.06 (woz1_4) =>
% 121.84/16.06 ((
% 121.84/16.06 (woz1_5) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1all2) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1SetBreln1) =>
% 121.84/16.06 ((
% 121.84/16.06 (choice2fnsingleton) =>
% 121.84/16.06 ((
% 121.84/16.06 (setOfPairsIsBReln1) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1all1) =>
% 121.84/16.06 ((
% 121.84/16.06 (subbreln1) =>
% 121.84/16.06 ((
% 121.84/16.06 (eqbreln1) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1invprop) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1invI) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1invE) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1compprop) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1compI) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1compE) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1compEex) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1unionprop) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1unionIL) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1unionIR) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1unionI) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1unionE) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1unionEcases) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1unionCommutes) =>
% 121.84/16.06 ((
% 121.84/16.06 (woz2Ex) =>
% 121.84/16.06 ((
% 121.84/16.06 (woz2W) =>
% 121.84/16.06 ((
% 121.84/16.06 (woz2A) =>
% 121.84/16.06 ((
% 121.84/16.06 (woz2B) =>
% 121.84/16.06 ((
% 121.84/16.06 (image1Ex) =>
% 121.84/16.06 ((
% 121.84/16.06 (image1Ex1) =>
% 121.84/16.06 ((
% 121.84/16.06 (image1Equiv) =>
% 121.84/16.06 ((
% 121.84/16.06 (image1E) =>
% 121.84/16.06 ((
% 121.84/16.06 (image1I) =>
% 121.84/16.06 ((
% 121.84/16.06 (injFuncInInjFuncSet) =>
% 121.84/16.06 ((
% 121.84/16.06 (!!) @ (
% 121.84/16.06 (('#B') @ (
% 121.84/16.06 !!) @
% 121.84/16.06 (
% 121.84/16.06 (
% 121.84/16.06 ('#B') @ (
% 121.84/16.06 (
% 121.84/16.06 ('#B') @ (
% 121.84/16.06 !!))) @
% 121.84/16.06 (
% 121.84/16.06 (
% 121.84/16.06 ('#S') @ (
% 121.84/16.06 (
% 121.84/16.06 ('#B') @ (
% 121.84/16.06 '#S') @
% 121.84/16.06 (
% 121.84/16.06 (
% 121.84/16.06 ('#B') @ (
% 121.84/16.06 (
% 121.84/16.06 ('#B') @ (
% 121.84/16.06 '#S'))) @
% 121.84/16.06 (
% 121.84/16.06 (
% 121.84/16.06 ('#B') @ (
% 121.84/16.06 (
% 121.84/16.06 ('#B') @ (
% 121.84/16.06 (
% 121.84/16.06 ('#B') @ (
% 121.84/16.06 =>))))) @
% 121.84/16.06 (
% 121.84/16.06 (
% 121.84/16.06 ('#B') @ (
% 121.84/16.06 (
% 121.84/16.06 ('#B') @ (
% 121.84/16.06 (
% 121.84/16.06 ('#C') @ in)))) @
% 121.84/16.06 injFuncSet)))))))) @
% 121.84/16.06 (
% 121.84/16.06 (
% 121.84/16.06 ('#B') @ (
% 121.84/16.06 (
% 121.84/16.06 ('#B') @ (
% 121.84/16.06 (
% 121.84/16.06 ('#C') @ in)))) @
% 121.84/16.06 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 121.84/16.06 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl439])).
% 121.84/16.06 thf(zip_derived_cl458, plain,
% 121.84/16.06 (~ (((notinsingleton) =>
% 121.84/16.06 (((eqinunit) =>
% 121.84/16.06 (((singletonsswitch) =>
% 121.84/16.06 (((upairsetE) =>
% 121.84/16.06 (((upairsetIL) =>
% 121.84/16.06 (((upairsetIR) =>
% 121.84/16.06 (((emptyE1) =>
% 121.84/16.06 (((vacuousDall) =>
% 121.84/16.06 (((quantDeMorgan1) =>
% 121.84/16.06 (((quantDeMorgan2) =>
% 121.84/16.06 (((quantDeMorgan3) =>
% 121.84/16.06 (((quantDeMorgan4) =>
% 121.84/16.06 (((prop2setI) =>
% 121.84/16.06 (((prop2set2propI) =>
% 121.84/16.06 (((notdexE) =>
% 121.84/16.06 (((notdallE) =>
% 121.84/16.06 (((exuI1) =>
% 121.84/16.06 (((exuI3) =>
% 121.84/16.06 (((exuI2) =>
% 121.84/16.06 (((inCongP) =>
% 121.84/16.06 (((in__Cong) =>
% 121.84/16.06 (((exuE3u) =>
% 121.84/16.06 (((exu__Cong) =>
% 121.84/16.06 (((setadjoin__Cong) =>
% 121.84/16.06 (((powerset__Cong) =>
% 121.84/16.06 (((setunion__Cong) =>
% 121.84/16.06 (((exuEu) =>
% 121.84/16.06 (((descr__Cong) =>
% 121.84/16.06 (((dsetconstr__Cong) =>
% 121.84/16.06 (((subsetI1) =>
% 121.84/16.06 ((
% 121.84/16.06 (eqimpsubset2) =>
% 121.84/16.06 ((
% 121.84/16.06 (eqimpsubset1) =>
% 121.84/16.06 ((
% 121.84/16.06 (subsetI2) =>
% 121.84/16.06 ((
% 121.84/16.06 (emptysetsubset) =>
% 121.84/16.06 ((
% 121.84/16.06 (subsetE) =>
% 121.84/16.06 ((
% 121.84/16.06 (subsetE2) =>
% 121.84/16.06 ((
% 121.84/16.06 (notsubsetI) =>
% 121.84/16.06 ((
% 121.84/16.06 (notequalI1) =>
% 121.84/16.06 ((
% 121.84/16.06 (notequalI2) =>
% 121.84/16.06 ((
% 121.84/16.06 (subsetRefl) =>
% 121.84/16.06 ((
% 121.84/16.06 (subsetTrans) =>
% 121.84/16.06 ((
% 121.84/16.06 (setadjoinSub) =>
% 121.84/16.06 ((
% 121.84/16.06 (setadjoinSub2) =>
% 121.84/16.06 ((
% 121.84/16.06 (subset2powerset) =>
% 121.84/16.06 ((
% 121.84/16.06 (setextsub) =>
% 121.84/16.06 ((
% 121.84/16.06 (subsetemptysetimpeq) =>
% 121.84/16.06 ((
% 121.84/16.06 (powersetI1) =>
% 121.84/16.06 ((
% 121.84/16.06 (powersetE1) =>
% 121.84/16.06 ((
% 121.84/16.06 (inPowerset) =>
% 121.84/16.06 ((
% 121.84/16.06 (powersetsubset) =>
% 121.84/16.06 ((
% 121.84/16.06 (sepInPowerset) =>
% 121.84/16.06 ((
% 121.84/16.06 (sepSubset) =>
% 121.84/16.06 ((
% 121.84/16.06 (binunionIL) =>
% 121.84/16.06 ((
% 121.84/16.06 (upairset2IR) =>
% 121.84/16.06 ((
% 121.84/16.06 (binunionIR) =>
% 121.84/16.06 ((
% 121.84/16.06 (binunionEcases) =>
% 121.84/16.06 ((
% 121.84/16.06 (binunionE) =>
% 121.84/16.06 ((
% 121.84/16.06 (binunionLsub) =>
% 121.84/16.06 ((
% 121.84/16.06 (binunionRsub) =>
% 121.84/16.06 ((
% 121.84/16.06 (binintersectI) =>
% 121.84/16.06 ((
% 121.84/16.06 (binintersectSubset5) =>
% 121.84/16.06 ((
% 121.84/16.06 (binintersectEL) =>
% 121.84/16.06 ((
% 121.84/16.06 (binintersectLsub) =>
% 121.84/16.06 ((
% 121.84/16.06 (binintersectSubset2) =>
% 121.84/16.06 ((
% 121.84/16.06 (binintersectSubset3) =>
% 121.84/16.06 ((
% 121.84/16.06 (binintersectER) =>
% 121.84/16.06 ((
% 121.84/16.06 (disjointsetsI1) =>
% 121.84/16.06 ((
% 121.84/16.06 (binintersectRsub) =>
% 121.84/16.06 ((
% 121.84/16.06 (binintersectSubset4) =>
% 121.84/16.06 ((
% 121.84/16.06 (binintersectSubset1) =>
% 121.84/16.06 ((
% 121.84/16.06 (bs114d) =>
% 121.84/16.06 ((
% 121.84/16.06 (setminusI) =>
% 121.84/16.06 ((
% 121.84/16.06 (setminusEL) =>
% 121.84/16.06 ((
% 121.84/16.06 (setminusER) =>
% 121.84/16.06 ((
% 121.84/16.06 (setminusSubset2) =>
% 121.84/16.06 ((
% 121.84/16.06 (setminusERneg) =>
% 121.84/16.06 ((
% 121.84/16.06 (setminusELneg) =>
% 121.84/16.06 ((
% 121.84/16.06 (setminusILneg) =>
% 121.84/16.06 ((
% 121.84/16.06 (setminusIRneg) =>
% 121.84/16.06 ((
% 121.84/16.06 (setminusLsub) =>
% 121.84/16.06 ((
% 121.84/16.06 (setminusSubset1) =>
% 121.84/16.06 ((
% 121.84/16.06 (symdiffE) =>
% 121.84/16.06 ((
% 121.84/16.06 (symdiffI1) =>
% 121.84/16.06 ((
% 121.84/16.06 (symdiffI2) =>
% 121.84/16.06 ((
% 121.84/16.06 (symdiffIneg1) =>
% 121.84/16.06 ((
% 121.84/16.06 (symdiffIneg2) =>
% 121.84/16.06 ((
% 121.84/16.06 (secondinupair) =>
% 121.84/16.06 ((
% 121.84/16.06 (setukpairIL) =>
% 121.84/16.06 ((
% 121.84/16.06 (setukpairIR) =>
% 121.84/16.06 ((
% 121.84/16.06 (kpairiskpair) =>
% 121.84/16.06 ((
% 121.84/16.06 (kpairp) =>
% 121.84/16.06 ((
% 121.84/16.06 (singletonsubset) =>
% 121.84/16.06 ((
% 121.84/16.06 (singletoninpowerset) =>
% 121.84/16.06 ((
% 121.84/16.06 (singletoninpowunion) =>
% 121.84/16.06 ((
% 121.84/16.06 (upairset2E) =>
% 121.84/16.06 ((
% 121.84/16.06 (upairsubunion) =>
% 121.84/16.06 ((
% 121.84/16.06 (upairinpowunion) =>
% 121.84/16.06 ((
% 121.84/16.06 (ubforcartprodlem1) =>
% 121.84/16.06 ((
% 121.84/16.06 (ubforcartprodlem2) =>
% 121.84/16.06 ((
% 121.84/16.06 (ubforcartprodlem3) =>
% 121.84/16.06 ((
% 121.84/16.06 (cartprodpairin) =>
% 121.84/16.06 ((
% 121.84/16.06 (cartprodmempair1) =>
% 121.84/16.06 ((
% 121.84/16.06 (cartprodmempair) =>
% 121.84/16.06 ((
% 121.84/16.06 (setunionE2) =>
% 121.84/16.06 ((
% 121.84/16.06 (setunionsingleton1) =>
% 121.84/16.06 ((
% 121.84/16.06 (setunionsingleton2) =>
% 121.84/16.06 ((
% 121.84/16.06 (setunionsingleton) =>
% 121.84/16.06 ((
% 121.84/16.06 (singletonprop) =>
% 121.84/16.06 ((
% 121.84/16.06 (ex1E1) =>
% 121.84/16.06 ((
% 121.84/16.06 (ex1I) =>
% 121.84/16.06 ((
% 121.84/16.06 (ex1I2) =>
% 121.84/16.06 ((
% 121.84/16.06 (singletonsuniq) =>
% 121.84/16.06 ((
% 121.84/16.06 (setukpairinjL1) =>
% 121.84/16.06 ((
% 121.84/16.06 (kfstsingleton) =>
% 121.84/16.06 ((
% 121.84/16.06 (theprop) =>
% 121.84/16.06 ((
% 121.84/16.06 (kfstpairEq) =>
% 121.84/16.06 ((
% 121.84/16.06 (cartprodfstin) =>
% 121.84/16.06 ((
% 121.84/16.06 (setukpairinjL2) =>
% 121.84/16.06 ((
% 121.84/16.06 (setukpairinjL) =>
% 121.84/16.06 ((
% 121.84/16.06 (setukpairinjR11) =>
% 121.84/16.06 ((
% 121.84/16.06 (setukpairinjR12) =>
% 121.84/16.06 ((
% 121.84/16.06 (setukpairinjR1) =>
% 121.84/16.06 ((
% 121.84/16.06 (upairequniteq) =>
% 121.84/16.06 ((
% 121.84/16.06 (setukpairinjR2) =>
% 121.84/16.06 ((
% 121.84/16.06 (setukpairinjR) =>
% 121.84/16.06 ((
% 121.84/16.06 (ksndsingleton) =>
% 121.84/16.06 ((
% 121.84/16.06 (ksndpairEq) =>
% 121.84/16.06 ((
% 121.84/16.06 (kpairsurjEq) =>
% 121.84/16.06 ((
% 121.84/16.06 (cartprodsndin) =>
% 121.84/16.06 ((
% 121.84/16.06 (cartprodpairmemEL) =>
% 121.84/16.06 ((
% 121.84/16.06 (cartprodpairmemER) =>
% 121.84/16.06 ((
% 121.84/16.06 (cartprodmempaircEq) =>
% 121.84/16.06 ((
% 121.84/16.06 (cartprodfstpairEq) =>
% 121.84/16.06 ((
% 121.84/16.06 (cartprodsndpairEq) =>
% 121.84/16.06 ((
% 121.84/16.06 (cartprodpairsurjEq) =>
% 121.84/16.06 ((
% 121.84/16.06 (dpsetconstrI) =>
% 121.84/16.06 ((
% 121.84/16.06 (dpsetconstrSub) =>
% 121.84/16.06 ((
% 121.84/16.06 (setOfPairsIsBReln) =>
% 121.84/16.06 ((
% 121.84/16.06 (dpsetconstrERa) =>
% 121.84/16.06 ((
% 121.84/16.06 (dpsetconstrEL1) =>
% 121.84/16.06 ((
% 121.84/16.06 (dpsetconstrEL2) =>
% 121.84/16.06 ((
% 121.84/16.06 (dpsetconstrER) =>
% 121.84/16.06 ((
% 121.84/16.06 (funcImageSingleton) =>
% 121.84/16.06 ((
% 121.84/16.06 (apProp) =>
% 121.84/16.06 ((
% 121.84/16.06 (app) =>
% 121.84/16.06 ((
% 121.84/16.06 (infuncsetfunc) =>
% 121.84/16.06 ((
% 121.84/16.06 (ap2p) =>
% 121.84/16.06 ((
% 121.84/16.06 (funcinfuncset) =>
% 121.84/16.06 ((
% 121.84/16.06 (lamProp) =>
% 121.84/16.06 ((
% 121.84/16.06 (lamp) =>
% 121.84/16.06 ((
% 121.84/16.06 (lam2p) =>
% 121.84/16.06 ((
% 121.84/16.06 (brelnall1) =>
% 121.84/16.06 ((
% 121.84/16.06 (brelnall2) =>
% 121.84/16.06 ((
% 121.84/16.06 (ex1E2) =>
% 121.84/16.06 ((
% 121.84/16.06 (funcGraphProp1) =>
% 121.84/16.06 ((
% 121.84/16.06 (funcGraphProp3) =>
% 121.84/16.06 ((
% 121.84/16.06 (funcGraphProp2) =>
% 121.84/16.06 ((
% 121.84/16.06 (funcextLem) =>
% 121.84/16.06 ((
% 121.84/16.06 (funcGraphProp4) =>
% 121.84/16.06 ((
% 121.84/16.06 (subbreln) =>
% 121.84/16.06 ((
% 121.84/16.06 (eqbreln) =>
% 121.84/16.06 ((
% 121.84/16.06 (funcext) =>
% 121.84/16.06 ((
% 121.84/16.06 (funcext2) =>
% 121.84/16.06 ((
% 121.84/16.06 (ap2apEq1) =>
% 121.84/16.06 ((
% 121.84/16.06 (ap2apEq2) =>
% 121.84/16.06 ((
% 121.84/16.06 (beta1) =>
% 121.84/16.06 ((
% 121.84/16.06 (eta1) =>
% 121.84/16.06 ((
% 121.84/16.06 (lam2lamEq) =>
% 121.84/16.06 ((
% 121.84/16.06 (beta2) =>
% 121.84/16.06 ((
% 121.84/16.06 (eta2) =>
% 121.84/16.06 ((
% 121.84/16.06 (iffalseProp1) =>
% 121.84/16.06 ((
% 121.84/16.06 (iffalseProp2) =>
% 121.84/16.06 ((
% 121.84/16.06 (iftrueProp1) =>
% 121.84/16.06 ((
% 121.84/16.06 (iftrueProp2) =>
% 121.84/16.06 ((
% 121.84/16.06 (ifSingleton) =>
% 121.84/16.06 ((
% 121.84/16.06 (ifp) =>
% 121.84/16.06 ((
% 121.84/16.06 (theeq) =>
% 121.84/16.06 ((
% 121.84/16.06 (iftrue) =>
% 121.84/16.06 ((
% 121.84/16.06 (iffalse) =>
% 121.84/16.06 ((
% 121.84/16.06 (iftrueorfalse) =>
% 121.84/16.06 ((
% 121.84/16.06 (binintersectT_lem) =>
% 121.84/16.06 ((
% 121.84/16.06 (binunionT_lem) =>
% 121.84/16.06 ((
% 121.84/16.06 (powersetT_lem) =>
% 121.84/16.06 ((
% 121.84/16.06 (setminusT_lem) =>
% 121.84/16.06 ((
% 121.84/16.06 (complementT_lem) =>
% 121.84/16.06 ((
% 121.84/16.06 (setextT) =>
% 121.84/16.06 ((
% 121.84/16.06 (subsetTI) =>
% 121.84/16.06 ((
% 121.84/16.06 (powersetTI1) =>
% 121.84/16.06 ((
% 121.84/16.06 (powersetTE1) =>
% 121.84/16.06 ((
% 121.84/16.06 (complementTI1) =>
% 121.84/16.06 ((
% 121.84/16.06 (complementTE1) =>
% 121.84/16.06 ((
% 121.84/16.06 (binintersectTELcontra) =>
% 121.84/16.06 ((
% 121.84/16.06 (binintersectTERcontra) =>
% 121.84/16.06 ((
% 121.84/16.06 (contrasubsetT) =>
% 121.84/16.06 ((
% 121.84/16.06 (contrasubsetT1) =>
% 121.84/16.06 ((
% 121.84/16.06 (contrasubsetT2) =>
% 121.84/16.06 ((
% 121.84/16.06 (contrasubsetT3) =>
% 121.84/16.06 ((
% 121.84/16.06 (doubleComplementI1) =>
% 121.84/16.06 ((
% 121.84/16.06 (doubleComplementE1) =>
% 121.84/16.06 ((
% 121.84/16.06 (doubleComplementSub1) =>
% 121.84/16.06 ((
% 121.84/16.06 (doubleComplementSub2) =>
% 121.84/16.06 ((
% 121.84/16.06 (doubleComplementEq) =>
% 121.84/16.06 ((
% 121.84/16.06 (complementTnotintersectT) =>
% 121.84/16.06 ((
% 121.84/16.06 (complementImpComplementIntersect) =>
% 121.84/16.06 ((
% 121.84/16.06 (complementSubsetComplementIntersect) =>
% 121.84/16.06 ((
% 121.84/16.06 (complementInPowersetComplementIntersect) =>
% 121.84/16.06 ((
% 121.84/16.06 (contraSubsetComplement) =>
% 121.84/16.06 ((
% 121.84/16.06 (complementTcontraSubset) =>
% 121.84/16.06 ((
% 121.84/16.06 (binunionTILcontra) =>
% 121.84/16.06 ((
% 121.84/16.06 (binunionTIRcontra) =>
% 121.84/16.06 ((
% 121.84/16.06 (inIntersectImpInUnion) =>
% 121.84/16.06 ((
% 121.84/16.06 (inIntersectImpInUnion2) =>
% 121.84/16.06 ((
% 121.84/16.06 (inIntersectImpInIntersectUnions) =>
% 121.84/16.06 ((
% 121.84/16.06 (intersectInPowersetIntersectUnions) =>
% 121.84/16.06 ((
% 121.84/16.06 (inComplementUnionImpNotIn1) =>
% 121.84/16.06 ((
% 121.84/16.06 (inComplementUnionImpInComplement1) =>
% 121.84/16.06 ((
% 121.84/16.06 (binunionTE) =>
% 121.84/16.06 ((
% 121.84/16.06 (binunionTEcontra) =>
% 121.84/16.06 ((
% 121.84/16.06 (demorgan2a1) =>
% 121.84/16.06 ((
% 121.84/16.06 (complementUnionInPowersetComplement) =>
% 121.84/16.06 ((
% 121.84/16.06 (demorgan2a2) =>
% 121.84/16.06 ((
% 121.84/16.06 (demorgan1a) =>
% 121.84/16.06 ((
% 121.84/16.06 (demorgan1b) =>
% 121.84/16.06 ((
% 121.84/16.06 (demorgan1) =>
% 121.84/16.06 ((
% 121.84/16.06 (demorgan2a) =>
% 121.84/16.06 ((
% 121.84/16.06 (demorgan2b2) =>
% 121.84/16.06 ((
% 121.84/16.06 (demorgan2b) =>
% 121.84/16.06 ((
% 121.84/16.06 (demorgan2) =>
% 121.84/16.06 ((
% 121.84/16.06 (woz13rule0) =>
% 121.84/16.06 ((
% 121.84/16.06 (woz13rule1) =>
% 121.84/16.06 ((
% 121.84/16.06 (woz13rule2) =>
% 121.84/16.06 ((
% 121.84/16.06 (woz13rule3) =>
% 121.84/16.06 ((
% 121.84/16.06 (woz13rule4) =>
% 121.84/16.06 ((
% 121.84/16.06 (woz1_1) =>
% 121.84/16.06 ((
% 121.84/16.06 (woz1_2) =>
% 121.84/16.06 ((
% 121.84/16.06 (woz1_3) =>
% 121.84/16.06 ((
% 121.84/16.06 (woz1_4) =>
% 121.84/16.06 ((
% 121.84/16.06 (woz1_5) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1all2) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1SetBreln1) =>
% 121.84/16.06 ((
% 121.84/16.06 (choice2fnsingleton) =>
% 121.84/16.06 ((
% 121.84/16.06 (setOfPairsIsBReln1) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1all1) =>
% 121.84/16.06 ((
% 121.84/16.06 (subbreln1) =>
% 121.84/16.06 ((
% 121.84/16.06 (eqbreln1) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1invprop) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1invI) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1invE) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1compprop) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1compI) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1compE) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1compEex) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1unionprop) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1unionIL) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1unionIR) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1unionI) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1unionE) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1unionEcases) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1unionCommutes) =>
% 121.84/16.06 ((
% 121.84/16.06 (woz2Ex) =>
% 121.84/16.06 ((
% 121.84/16.06 (woz2W) =>
% 121.84/16.06 ((
% 121.84/16.06 (woz2A) =>
% 121.84/16.06 ((
% 121.84/16.06 (woz2B) =>
% 121.84/16.06 ((
% 121.84/16.06 (image1Ex) =>
% 121.84/16.06 ((
% 121.84/16.06 (image1Ex1) =>
% 121.84/16.06 ((
% 121.84/16.06 (image1Equiv) =>
% 121.84/16.06 ((
% 121.84/16.06 (image1E) =>
% 121.84/16.06 ((
% 121.84/16.06 (image1I) =>
% 121.84/16.06 ((
% 121.84/16.06 (injFuncInInjFuncSet) =>
% 121.84/16.06 ((
% 121.84/16.06 (!!) @ (
% 121.84/16.06 (('#B') @ (
% 121.84/16.06 !!) @
% 121.84/16.06 (
% 121.84/16.06 (
% 121.84/16.06 ('#B') @ (
% 121.84/16.06 (
% 121.84/16.06 ('#B') @ (
% 121.84/16.06 !!))) @
% 121.84/16.06 (
% 121.84/16.06 (
% 121.84/16.06 ('#S') @ (
% 121.84/16.06 (
% 121.84/16.06 ('#B') @ (
% 121.84/16.06 '#S') @
% 121.84/16.06 (
% 121.84/16.06 (
% 121.84/16.06 ('#B') @ (
% 121.84/16.06 (
% 121.84/16.06 ('#B') @ (
% 121.84/16.06 '#S'))) @
% 121.84/16.06 (
% 121.84/16.06 (
% 121.84/16.06 ('#B') @ (
% 121.84/16.06 (
% 121.84/16.06 ('#B') @ (
% 121.84/16.06 (
% 121.84/16.06 ('#B') @ (
% 121.84/16.06 =>))))) @
% 121.84/16.06 (
% 121.84/16.06 (
% 121.84/16.06 ('#B') @ (
% 121.84/16.06 (
% 121.84/16.06 ('#B') @ (
% 121.84/16.06 (
% 121.84/16.06 ('#C') @ in)))) @
% 121.84/16.06 injFuncSet)))))))) @
% 121.84/16.06 (
% 121.84/16.06 (
% 121.84/16.06 ('#B') @ (
% 121.84/16.06 (
% 121.84/16.06 ('#B') @ (
% 121.84/16.06 (
% 121.84/16.06 ('#C') @ in)))) @
% 121.84/16.06 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 121.84/16.06 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl449])).
% 121.84/16.06 thf(zip_derived_cl467, plain,
% 121.84/16.06 (~ (((eqinunit) =>
% 121.84/16.06 (((singletonsswitch) =>
% 121.84/16.06 (((upairsetE) =>
% 121.84/16.06 (((upairsetIL) =>
% 121.84/16.06 (((upairsetIR) =>
% 121.84/16.06 (((emptyE1) =>
% 121.84/16.06 (((vacuousDall) =>
% 121.84/16.06 (((quantDeMorgan1) =>
% 121.84/16.06 (((quantDeMorgan2) =>
% 121.84/16.06 (((quantDeMorgan3) =>
% 121.84/16.06 (((quantDeMorgan4) =>
% 121.84/16.06 (((prop2setI) =>
% 121.84/16.06 (((prop2set2propI) =>
% 121.84/16.06 (((notdexE) =>
% 121.84/16.06 (((notdallE) =>
% 121.84/16.06 (((exuI1) =>
% 121.84/16.06 (((exuI3) =>
% 121.84/16.06 (((exuI2) =>
% 121.84/16.06 (((inCongP) =>
% 121.84/16.06 (((in__Cong) =>
% 121.84/16.06 (((exuE3u) =>
% 121.84/16.06 (((exu__Cong) =>
% 121.84/16.06 (((setadjoin__Cong) =>
% 121.84/16.06 (((powerset__Cong) =>
% 121.84/16.06 (((setunion__Cong) =>
% 121.84/16.06 (((exuEu) =>
% 121.84/16.06 (((descr__Cong) =>
% 121.84/16.06 (((dsetconstr__Cong) =>
% 121.84/16.06 (((subsetI1) =>
% 121.84/16.06 (((eqimpsubset2) =>
% 121.84/16.06 ((
% 121.84/16.06 (eqimpsubset1) =>
% 121.84/16.06 ((
% 121.84/16.06 (subsetI2) =>
% 121.84/16.06 ((
% 121.84/16.06 (emptysetsubset) =>
% 121.84/16.06 ((
% 121.84/16.06 (subsetE) =>
% 121.84/16.06 ((
% 121.84/16.06 (subsetE2) =>
% 121.84/16.06 ((
% 121.84/16.06 (notsubsetI) =>
% 121.84/16.06 ((
% 121.84/16.06 (notequalI1) =>
% 121.84/16.06 ((
% 121.84/16.06 (notequalI2) =>
% 121.84/16.06 ((
% 121.84/16.06 (subsetRefl) =>
% 121.84/16.06 ((
% 121.84/16.06 (subsetTrans) =>
% 121.84/16.06 ((
% 121.84/16.06 (setadjoinSub) =>
% 121.84/16.06 ((
% 121.84/16.06 (setadjoinSub2) =>
% 121.84/16.06 ((
% 121.84/16.06 (subset2powerset) =>
% 121.84/16.06 ((
% 121.84/16.06 (setextsub) =>
% 121.84/16.06 ((
% 121.84/16.06 (subsetemptysetimpeq) =>
% 121.84/16.06 ((
% 121.84/16.06 (powersetI1) =>
% 121.84/16.06 ((
% 121.84/16.06 (powersetE1) =>
% 121.84/16.06 ((
% 121.84/16.06 (inPowerset) =>
% 121.84/16.06 ((
% 121.84/16.06 (powersetsubset) =>
% 121.84/16.06 ((
% 121.84/16.06 (sepInPowerset) =>
% 121.84/16.06 ((
% 121.84/16.06 (sepSubset) =>
% 121.84/16.06 ((
% 121.84/16.06 (binunionIL) =>
% 121.84/16.06 ((
% 121.84/16.06 (upairset2IR) =>
% 121.84/16.06 ((
% 121.84/16.06 (binunionIR) =>
% 121.84/16.06 ((
% 121.84/16.06 (binunionEcases) =>
% 121.84/16.06 ((
% 121.84/16.06 (binunionE) =>
% 121.84/16.06 ((
% 121.84/16.06 (binunionLsub) =>
% 121.84/16.06 ((
% 121.84/16.06 (binunionRsub) =>
% 121.84/16.06 ((
% 121.84/16.06 (binintersectI) =>
% 121.84/16.06 ((
% 121.84/16.06 (binintersectSubset5) =>
% 121.84/16.06 ((
% 121.84/16.06 (binintersectEL) =>
% 121.84/16.06 ((
% 121.84/16.06 (binintersectLsub) =>
% 121.84/16.06 ((
% 121.84/16.06 (binintersectSubset2) =>
% 121.84/16.06 ((
% 121.84/16.06 (binintersectSubset3) =>
% 121.84/16.06 ((
% 121.84/16.06 (binintersectER) =>
% 121.84/16.06 ((
% 121.84/16.06 (disjointsetsI1) =>
% 121.84/16.06 ((
% 121.84/16.06 (binintersectRsub) =>
% 121.84/16.06 ((
% 121.84/16.06 (binintersectSubset4) =>
% 121.84/16.06 ((
% 121.84/16.06 (binintersectSubset1) =>
% 121.84/16.06 ((
% 121.84/16.06 (bs114d) =>
% 121.84/16.06 ((
% 121.84/16.06 (setminusI) =>
% 121.84/16.06 ((
% 121.84/16.06 (setminusEL) =>
% 121.84/16.06 ((
% 121.84/16.06 (setminusER) =>
% 121.84/16.06 ((
% 121.84/16.06 (setminusSubset2) =>
% 121.84/16.06 ((
% 121.84/16.06 (setminusERneg) =>
% 121.84/16.06 ((
% 121.84/16.06 (setminusELneg) =>
% 121.84/16.06 ((
% 121.84/16.06 (setminusILneg) =>
% 121.84/16.06 ((
% 121.84/16.06 (setminusIRneg) =>
% 121.84/16.06 ((
% 121.84/16.06 (setminusLsub) =>
% 121.84/16.06 ((
% 121.84/16.06 (setminusSubset1) =>
% 121.84/16.06 ((
% 121.84/16.06 (symdiffE) =>
% 121.84/16.06 ((
% 121.84/16.06 (symdiffI1) =>
% 121.84/16.06 ((
% 121.84/16.06 (symdiffI2) =>
% 121.84/16.06 ((
% 121.84/16.06 (symdiffIneg1) =>
% 121.84/16.06 ((
% 121.84/16.06 (symdiffIneg2) =>
% 121.84/16.06 ((
% 121.84/16.06 (secondinupair) =>
% 121.84/16.06 ((
% 121.84/16.06 (setukpairIL) =>
% 121.84/16.06 ((
% 121.84/16.06 (setukpairIR) =>
% 121.84/16.06 ((
% 121.84/16.06 (kpairiskpair) =>
% 121.84/16.06 ((
% 121.84/16.06 (kpairp) =>
% 121.84/16.06 ((
% 121.84/16.06 (singletonsubset) =>
% 121.84/16.06 ((
% 121.84/16.06 (singletoninpowerset) =>
% 121.84/16.06 ((
% 121.84/16.06 (singletoninpowunion) =>
% 121.84/16.06 ((
% 121.84/16.06 (upairset2E) =>
% 121.84/16.06 ((
% 121.84/16.06 (upairsubunion) =>
% 121.84/16.06 ((
% 121.84/16.06 (upairinpowunion) =>
% 121.84/16.06 ((
% 121.84/16.06 (ubforcartprodlem1) =>
% 121.84/16.06 ((
% 121.84/16.06 (ubforcartprodlem2) =>
% 121.84/16.06 ((
% 121.84/16.06 (ubforcartprodlem3) =>
% 121.84/16.06 ((
% 121.84/16.06 (cartprodpairin) =>
% 121.84/16.06 ((
% 121.84/16.06 (cartprodmempair1) =>
% 121.84/16.06 ((
% 121.84/16.06 (cartprodmempair) =>
% 121.84/16.06 ((
% 121.84/16.06 (setunionE2) =>
% 121.84/16.06 ((
% 121.84/16.06 (setunionsingleton1) =>
% 121.84/16.06 ((
% 121.84/16.06 (setunionsingleton2) =>
% 121.84/16.06 ((
% 121.84/16.06 (setunionsingleton) =>
% 121.84/16.06 ((
% 121.84/16.06 (singletonprop) =>
% 121.84/16.06 ((
% 121.84/16.06 (ex1E1) =>
% 121.84/16.06 ((
% 121.84/16.06 (ex1I) =>
% 121.84/16.06 ((
% 121.84/16.06 (ex1I2) =>
% 121.84/16.06 ((
% 121.84/16.06 (singletonsuniq) =>
% 121.84/16.06 ((
% 121.84/16.06 (setukpairinjL1) =>
% 121.84/16.06 ((
% 121.84/16.06 (kfstsingleton) =>
% 121.84/16.06 ((
% 121.84/16.06 (theprop) =>
% 121.84/16.06 ((
% 121.84/16.06 (kfstpairEq) =>
% 121.84/16.06 ((
% 121.84/16.06 (cartprodfstin) =>
% 121.84/16.06 ((
% 121.84/16.06 (setukpairinjL2) =>
% 121.84/16.06 ((
% 121.84/16.06 (setukpairinjL) =>
% 121.84/16.06 ((
% 121.84/16.06 (setukpairinjR11) =>
% 121.84/16.06 ((
% 121.84/16.06 (setukpairinjR12) =>
% 121.84/16.06 ((
% 121.84/16.06 (setukpairinjR1) =>
% 121.84/16.06 ((
% 121.84/16.06 (upairequniteq) =>
% 121.84/16.06 ((
% 121.84/16.06 (setukpairinjR2) =>
% 121.84/16.06 ((
% 121.84/16.06 (setukpairinjR) =>
% 121.84/16.06 ((
% 121.84/16.06 (ksndsingleton) =>
% 121.84/16.06 ((
% 121.84/16.06 (ksndpairEq) =>
% 121.84/16.06 ((
% 121.84/16.06 (kpairsurjEq) =>
% 121.84/16.06 ((
% 121.84/16.06 (cartprodsndin) =>
% 121.84/16.06 ((
% 121.84/16.06 (cartprodpairmemEL) =>
% 121.84/16.06 ((
% 121.84/16.06 (cartprodpairmemER) =>
% 121.84/16.06 ((
% 121.84/16.06 (cartprodmempaircEq) =>
% 121.84/16.06 ((
% 121.84/16.06 (cartprodfstpairEq) =>
% 121.84/16.06 ((
% 121.84/16.06 (cartprodsndpairEq) =>
% 121.84/16.06 ((
% 121.84/16.06 (cartprodpairsurjEq) =>
% 121.84/16.06 ((
% 121.84/16.06 (dpsetconstrI) =>
% 121.84/16.06 ((
% 121.84/16.06 (dpsetconstrSub) =>
% 121.84/16.06 ((
% 121.84/16.06 (setOfPairsIsBReln) =>
% 121.84/16.06 ((
% 121.84/16.06 (dpsetconstrERa) =>
% 121.84/16.06 ((
% 121.84/16.06 (dpsetconstrEL1) =>
% 121.84/16.06 ((
% 121.84/16.06 (dpsetconstrEL2) =>
% 121.84/16.06 ((
% 121.84/16.06 (dpsetconstrER) =>
% 121.84/16.06 ((
% 121.84/16.06 (funcImageSingleton) =>
% 121.84/16.06 ((
% 121.84/16.06 (apProp) =>
% 121.84/16.06 ((
% 121.84/16.06 (app) =>
% 121.84/16.06 ((
% 121.84/16.06 (infuncsetfunc) =>
% 121.84/16.06 ((
% 121.84/16.06 (ap2p) =>
% 121.84/16.06 ((
% 121.84/16.06 (funcinfuncset) =>
% 121.84/16.06 ((
% 121.84/16.06 (lamProp) =>
% 121.84/16.06 ((
% 121.84/16.06 (lamp) =>
% 121.84/16.06 ((
% 121.84/16.06 (lam2p) =>
% 121.84/16.06 ((
% 121.84/16.06 (brelnall1) =>
% 121.84/16.06 ((
% 121.84/16.06 (brelnall2) =>
% 121.84/16.06 ((
% 121.84/16.06 (ex1E2) =>
% 121.84/16.06 ((
% 121.84/16.06 (funcGraphProp1) =>
% 121.84/16.06 ((
% 121.84/16.06 (funcGraphProp3) =>
% 121.84/16.06 ((
% 121.84/16.06 (funcGraphProp2) =>
% 121.84/16.06 ((
% 121.84/16.06 (funcextLem) =>
% 121.84/16.06 ((
% 121.84/16.06 (funcGraphProp4) =>
% 121.84/16.06 ((
% 121.84/16.06 (subbreln) =>
% 121.84/16.06 ((
% 121.84/16.06 (eqbreln) =>
% 121.84/16.06 ((
% 121.84/16.06 (funcext) =>
% 121.84/16.06 ((
% 121.84/16.06 (funcext2) =>
% 121.84/16.06 ((
% 121.84/16.06 (ap2apEq1) =>
% 121.84/16.06 ((
% 121.84/16.06 (ap2apEq2) =>
% 121.84/16.06 ((
% 121.84/16.06 (beta1) =>
% 121.84/16.06 ((
% 121.84/16.06 (eta1) =>
% 121.84/16.06 ((
% 121.84/16.06 (lam2lamEq) =>
% 121.84/16.06 ((
% 121.84/16.06 (beta2) =>
% 121.84/16.06 ((
% 121.84/16.06 (eta2) =>
% 121.84/16.06 ((
% 121.84/16.06 (iffalseProp1) =>
% 121.84/16.06 ((
% 121.84/16.06 (iffalseProp2) =>
% 121.84/16.06 ((
% 121.84/16.06 (iftrueProp1) =>
% 121.84/16.06 ((
% 121.84/16.06 (iftrueProp2) =>
% 121.84/16.06 ((
% 121.84/16.06 (ifSingleton) =>
% 121.84/16.06 ((
% 121.84/16.06 (ifp) =>
% 121.84/16.06 ((
% 121.84/16.06 (theeq) =>
% 121.84/16.06 ((
% 121.84/16.06 (iftrue) =>
% 121.84/16.06 ((
% 121.84/16.06 (iffalse) =>
% 121.84/16.06 ((
% 121.84/16.06 (iftrueorfalse) =>
% 121.84/16.06 ((
% 121.84/16.06 (binintersectT_lem) =>
% 121.84/16.06 ((
% 121.84/16.06 (binunionT_lem) =>
% 121.84/16.06 ((
% 121.84/16.06 (powersetT_lem) =>
% 121.84/16.06 ((
% 121.84/16.06 (setminusT_lem) =>
% 121.84/16.06 ((
% 121.84/16.06 (complementT_lem) =>
% 121.84/16.06 ((
% 121.84/16.06 (setextT) =>
% 121.84/16.06 ((
% 121.84/16.06 (subsetTI) =>
% 121.84/16.06 ((
% 121.84/16.06 (powersetTI1) =>
% 121.84/16.06 ((
% 121.84/16.06 (powersetTE1) =>
% 121.84/16.06 ((
% 121.84/16.06 (complementTI1) =>
% 121.84/16.06 ((
% 121.84/16.06 (complementTE1) =>
% 121.84/16.06 ((
% 121.84/16.06 (binintersectTELcontra) =>
% 121.84/16.06 ((
% 121.84/16.06 (binintersectTERcontra) =>
% 121.84/16.06 ((
% 121.84/16.06 (contrasubsetT) =>
% 121.84/16.06 ((
% 121.84/16.06 (contrasubsetT1) =>
% 121.84/16.06 ((
% 121.84/16.06 (contrasubsetT2) =>
% 121.84/16.06 ((
% 121.84/16.06 (contrasubsetT3) =>
% 121.84/16.06 ((
% 121.84/16.06 (doubleComplementI1) =>
% 121.84/16.06 ((
% 121.84/16.06 (doubleComplementE1) =>
% 121.84/16.06 ((
% 121.84/16.06 (doubleComplementSub1) =>
% 121.84/16.06 ((
% 121.84/16.06 (doubleComplementSub2) =>
% 121.84/16.06 ((
% 121.84/16.06 (doubleComplementEq) =>
% 121.84/16.06 ((
% 121.84/16.06 (complementTnotintersectT) =>
% 121.84/16.06 ((
% 121.84/16.06 (complementImpComplementIntersect) =>
% 121.84/16.06 ((
% 121.84/16.06 (complementSubsetComplementIntersect) =>
% 121.84/16.06 ((
% 121.84/16.06 (complementInPowersetComplementIntersect) =>
% 121.84/16.06 ((
% 121.84/16.06 (contraSubsetComplement) =>
% 121.84/16.06 ((
% 121.84/16.06 (complementTcontraSubset) =>
% 121.84/16.06 ((
% 121.84/16.06 (binunionTILcontra) =>
% 121.84/16.06 ((
% 121.84/16.06 (binunionTIRcontra) =>
% 121.84/16.06 ((
% 121.84/16.06 (inIntersectImpInUnion) =>
% 121.84/16.06 ((
% 121.84/16.06 (inIntersectImpInUnion2) =>
% 121.84/16.06 ((
% 121.84/16.06 (inIntersectImpInIntersectUnions) =>
% 121.84/16.06 ((
% 121.84/16.06 (intersectInPowersetIntersectUnions) =>
% 121.84/16.06 ((
% 121.84/16.06 (inComplementUnionImpNotIn1) =>
% 121.84/16.06 ((
% 121.84/16.06 (inComplementUnionImpInComplement1) =>
% 121.84/16.06 ((
% 121.84/16.06 (binunionTE) =>
% 121.84/16.06 ((
% 121.84/16.06 (binunionTEcontra) =>
% 121.84/16.06 ((
% 121.84/16.06 (demorgan2a1) =>
% 121.84/16.06 ((
% 121.84/16.06 (complementUnionInPowersetComplement) =>
% 121.84/16.06 ((
% 121.84/16.06 (demorgan2a2) =>
% 121.84/16.06 ((
% 121.84/16.06 (demorgan1a) =>
% 121.84/16.06 ((
% 121.84/16.06 (demorgan1b) =>
% 121.84/16.06 ((
% 121.84/16.06 (demorgan1) =>
% 121.84/16.06 ((
% 121.84/16.06 (demorgan2a) =>
% 121.84/16.06 ((
% 121.84/16.06 (demorgan2b2) =>
% 121.84/16.06 ((
% 121.84/16.06 (demorgan2b) =>
% 121.84/16.06 ((
% 121.84/16.06 (demorgan2) =>
% 121.84/16.06 ((
% 121.84/16.06 (woz13rule0) =>
% 121.84/16.06 ((
% 121.84/16.06 (woz13rule1) =>
% 121.84/16.06 ((
% 121.84/16.06 (woz13rule2) =>
% 121.84/16.06 ((
% 121.84/16.06 (woz13rule3) =>
% 121.84/16.06 ((
% 121.84/16.06 (woz13rule4) =>
% 121.84/16.06 ((
% 121.84/16.06 (woz1_1) =>
% 121.84/16.06 ((
% 121.84/16.06 (woz1_2) =>
% 121.84/16.06 ((
% 121.84/16.06 (woz1_3) =>
% 121.84/16.06 ((
% 121.84/16.06 (woz1_4) =>
% 121.84/16.06 ((
% 121.84/16.06 (woz1_5) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1all2) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1SetBreln1) =>
% 121.84/16.06 ((
% 121.84/16.06 (choice2fnsingleton) =>
% 121.84/16.06 ((
% 121.84/16.06 (setOfPairsIsBReln1) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1all1) =>
% 121.84/16.06 ((
% 121.84/16.06 (subbreln1) =>
% 121.84/16.06 ((
% 121.84/16.06 (eqbreln1) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1invprop) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1invI) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1invE) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1compprop) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1compI) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1compE) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1compEex) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1unionprop) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1unionIL) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1unionIR) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1unionI) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1unionE) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1unionEcases) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1unionCommutes) =>
% 121.84/16.06 ((
% 121.84/16.06 (woz2Ex) =>
% 121.84/16.06 ((
% 121.84/16.06 (woz2W) =>
% 121.84/16.06 ((
% 121.84/16.06 (woz2A) =>
% 121.84/16.06 ((
% 121.84/16.06 (woz2B) =>
% 121.84/16.06 ((
% 121.84/16.06 (image1Ex) =>
% 121.84/16.06 ((
% 121.84/16.06 (image1Ex1) =>
% 121.84/16.06 ((
% 121.84/16.06 (image1Equiv) =>
% 121.84/16.06 ((
% 121.84/16.06 (image1E) =>
% 121.84/16.06 ((
% 121.84/16.06 (image1I) =>
% 121.84/16.06 ((
% 121.84/16.06 (injFuncInInjFuncSet) =>
% 121.84/16.06 ((
% 121.84/16.06 (!!) @ (
% 121.84/16.06 (('#B') @ (
% 121.84/16.06 !!) @
% 121.84/16.06 (
% 121.84/16.06 (
% 121.84/16.06 ('#B') @ (
% 121.84/16.06 (
% 121.84/16.06 ('#B') @ (
% 121.84/16.06 !!))) @
% 121.84/16.06 (
% 121.84/16.06 (
% 121.84/16.06 ('#S') @ (
% 121.84/16.06 (
% 121.84/16.06 ('#B') @ (
% 121.84/16.06 '#S') @
% 121.84/16.06 (
% 121.84/16.06 (
% 121.84/16.06 ('#B') @ (
% 121.84/16.06 (
% 121.84/16.06 ('#B') @ (
% 121.84/16.06 '#S'))) @
% 121.84/16.06 (
% 121.84/16.06 (
% 121.84/16.06 ('#B') @ (
% 121.84/16.06 (
% 121.84/16.06 ('#B') @ (
% 121.84/16.06 (
% 121.84/16.06 ('#B') @ (
% 121.84/16.06 =>))))) @
% 121.84/16.06 (
% 121.84/16.06 (
% 121.84/16.06 ('#B') @ (
% 121.84/16.06 (
% 121.84/16.06 ('#B') @ (
% 121.84/16.06 (
% 121.84/16.06 ('#C') @ in)))) @
% 121.84/16.06 injFuncSet)))))))) @
% 121.84/16.06 (
% 121.84/16.06 (
% 121.84/16.06 ('#B') @ (
% 121.84/16.06 (
% 121.84/16.06 ('#B') @ (
% 121.84/16.06 (
% 121.84/16.06 ('#C') @ in)))) @
% 121.84/16.06 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 121.84/16.06 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl458])).
% 121.84/16.06 thf(zip_derived_cl475, plain,
% 121.84/16.06 (~ (((singletonsswitch) =>
% 121.84/16.06 (((upairsetE) =>
% 121.84/16.06 (((upairsetIL) =>
% 121.84/16.06 (((upairsetIR) =>
% 121.84/16.06 (((emptyE1) =>
% 121.84/16.06 (((vacuousDall) =>
% 121.84/16.06 (((quantDeMorgan1) =>
% 121.84/16.06 (((quantDeMorgan2) =>
% 121.84/16.06 (((quantDeMorgan3) =>
% 121.84/16.06 (((quantDeMorgan4) =>
% 121.84/16.06 (((prop2setI) =>
% 121.84/16.06 (((prop2set2propI) =>
% 121.84/16.06 (((notdexE) =>
% 121.84/16.06 (((notdallE) =>
% 121.84/16.06 (((exuI1) =>
% 121.84/16.06 (((exuI3) =>
% 121.84/16.06 (((exuI2) =>
% 121.84/16.06 (((inCongP) =>
% 121.84/16.06 (((in__Cong) =>
% 121.84/16.06 (((exuE3u) =>
% 121.84/16.06 (((exu__Cong) =>
% 121.84/16.06 (((setadjoin__Cong) =>
% 121.84/16.06 (((powerset__Cong) =>
% 121.84/16.06 (((setunion__Cong) =>
% 121.84/16.06 (((exuEu) =>
% 121.84/16.06 (((descr__Cong) =>
% 121.84/16.06 (((dsetconstr__Cong) =>
% 121.84/16.06 (((subsetI1) =>
% 121.84/16.06 (((eqimpsubset2) =>
% 121.84/16.06 (((eqimpsubset1) =>
% 121.84/16.06 ((
% 121.84/16.06 (subsetI2) =>
% 121.84/16.06 ((
% 121.84/16.06 (emptysetsubset) =>
% 121.84/16.06 ((
% 121.84/16.06 (subsetE) =>
% 121.84/16.06 ((
% 121.84/16.06 (subsetE2) =>
% 121.84/16.06 ((
% 121.84/16.06 (notsubsetI) =>
% 121.84/16.06 ((
% 121.84/16.06 (notequalI1) =>
% 121.84/16.06 ((
% 121.84/16.06 (notequalI2) =>
% 121.84/16.06 ((
% 121.84/16.06 (subsetRefl) =>
% 121.84/16.06 ((
% 121.84/16.06 (subsetTrans) =>
% 121.84/16.06 ((
% 121.84/16.06 (setadjoinSub) =>
% 121.84/16.06 ((
% 121.84/16.06 (setadjoinSub2) =>
% 121.84/16.06 ((
% 121.84/16.06 (subset2powerset) =>
% 121.84/16.06 ((
% 121.84/16.06 (setextsub) =>
% 121.84/16.06 ((
% 121.84/16.06 (subsetemptysetimpeq) =>
% 121.84/16.06 ((
% 121.84/16.06 (powersetI1) =>
% 121.84/16.06 ((
% 121.84/16.06 (powersetE1) =>
% 121.84/16.06 ((
% 121.84/16.06 (inPowerset) =>
% 121.84/16.06 ((
% 121.84/16.06 (powersetsubset) =>
% 121.84/16.06 ((
% 121.84/16.06 (sepInPowerset) =>
% 121.84/16.06 ((
% 121.84/16.06 (sepSubset) =>
% 121.84/16.06 ((
% 121.84/16.06 (binunionIL) =>
% 121.84/16.06 ((
% 121.84/16.06 (upairset2IR) =>
% 121.84/16.06 ((
% 121.84/16.06 (binunionIR) =>
% 121.84/16.06 ((
% 121.84/16.06 (binunionEcases) =>
% 121.84/16.06 ((
% 121.84/16.06 (binunionE) =>
% 121.84/16.06 ((
% 121.84/16.06 (binunionLsub) =>
% 121.84/16.06 ((
% 121.84/16.06 (binunionRsub) =>
% 121.84/16.06 ((
% 121.84/16.06 (binintersectI) =>
% 121.84/16.06 ((
% 121.84/16.06 (binintersectSubset5) =>
% 121.84/16.06 ((
% 121.84/16.06 (binintersectEL) =>
% 121.84/16.06 ((
% 121.84/16.06 (binintersectLsub) =>
% 121.84/16.06 ((
% 121.84/16.06 (binintersectSubset2) =>
% 121.84/16.06 ((
% 121.84/16.06 (binintersectSubset3) =>
% 121.84/16.06 ((
% 121.84/16.06 (binintersectER) =>
% 121.84/16.06 ((
% 121.84/16.06 (disjointsetsI1) =>
% 121.84/16.06 ((
% 121.84/16.06 (binintersectRsub) =>
% 121.84/16.06 ((
% 121.84/16.06 (binintersectSubset4) =>
% 121.84/16.06 ((
% 121.84/16.06 (binintersectSubset1) =>
% 121.84/16.06 ((
% 121.84/16.06 (bs114d) =>
% 121.84/16.06 ((
% 121.84/16.06 (setminusI) =>
% 121.84/16.06 ((
% 121.84/16.06 (setminusEL) =>
% 121.84/16.06 ((
% 121.84/16.06 (setminusER) =>
% 121.84/16.06 ((
% 121.84/16.06 (setminusSubset2) =>
% 121.84/16.06 ((
% 121.84/16.06 (setminusERneg) =>
% 121.84/16.06 ((
% 121.84/16.06 (setminusELneg) =>
% 121.84/16.06 ((
% 121.84/16.06 (setminusILneg) =>
% 121.84/16.06 ((
% 121.84/16.06 (setminusIRneg) =>
% 121.84/16.06 ((
% 121.84/16.06 (setminusLsub) =>
% 121.84/16.06 ((
% 121.84/16.06 (setminusSubset1) =>
% 121.84/16.06 ((
% 121.84/16.06 (symdiffE) =>
% 121.84/16.06 ((
% 121.84/16.06 (symdiffI1) =>
% 121.84/16.06 ((
% 121.84/16.06 (symdiffI2) =>
% 121.84/16.06 ((
% 121.84/16.06 (symdiffIneg1) =>
% 121.84/16.06 ((
% 121.84/16.06 (symdiffIneg2) =>
% 121.84/16.06 ((
% 121.84/16.06 (secondinupair) =>
% 121.84/16.06 ((
% 121.84/16.06 (setukpairIL) =>
% 121.84/16.06 ((
% 121.84/16.06 (setukpairIR) =>
% 121.84/16.06 ((
% 121.84/16.06 (kpairiskpair) =>
% 121.84/16.06 ((
% 121.84/16.06 (kpairp) =>
% 121.84/16.06 ((
% 121.84/16.06 (singletonsubset) =>
% 121.84/16.06 ((
% 121.84/16.06 (singletoninpowerset) =>
% 121.84/16.06 ((
% 121.84/16.06 (singletoninpowunion) =>
% 121.84/16.06 ((
% 121.84/16.06 (upairset2E) =>
% 121.84/16.06 ((
% 121.84/16.06 (upairsubunion) =>
% 121.84/16.06 ((
% 121.84/16.06 (upairinpowunion) =>
% 121.84/16.06 ((
% 121.84/16.06 (ubforcartprodlem1) =>
% 121.84/16.06 ((
% 121.84/16.06 (ubforcartprodlem2) =>
% 121.84/16.06 ((
% 121.84/16.06 (ubforcartprodlem3) =>
% 121.84/16.06 ((
% 121.84/16.06 (cartprodpairin) =>
% 121.84/16.06 ((
% 121.84/16.06 (cartprodmempair1) =>
% 121.84/16.06 ((
% 121.84/16.06 (cartprodmempair) =>
% 121.84/16.06 ((
% 121.84/16.06 (setunionE2) =>
% 121.84/16.06 ((
% 121.84/16.06 (setunionsingleton1) =>
% 121.84/16.06 ((
% 121.84/16.06 (setunionsingleton2) =>
% 121.84/16.06 ((
% 121.84/16.06 (setunionsingleton) =>
% 121.84/16.06 ((
% 121.84/16.06 (singletonprop) =>
% 121.84/16.06 ((
% 121.84/16.06 (ex1E1) =>
% 121.84/16.06 ((
% 121.84/16.06 (ex1I) =>
% 121.84/16.06 ((
% 121.84/16.06 (ex1I2) =>
% 121.84/16.06 ((
% 121.84/16.06 (singletonsuniq) =>
% 121.84/16.06 ((
% 121.84/16.06 (setukpairinjL1) =>
% 121.84/16.06 ((
% 121.84/16.06 (kfstsingleton) =>
% 121.84/16.06 ((
% 121.84/16.06 (theprop) =>
% 121.84/16.06 ((
% 121.84/16.06 (kfstpairEq) =>
% 121.84/16.06 ((
% 121.84/16.06 (cartprodfstin) =>
% 121.84/16.06 ((
% 121.84/16.06 (setukpairinjL2) =>
% 121.84/16.06 ((
% 121.84/16.06 (setukpairinjL) =>
% 121.84/16.06 ((
% 121.84/16.06 (setukpairinjR11) =>
% 121.84/16.06 ((
% 121.84/16.06 (setukpairinjR12) =>
% 121.84/16.06 ((
% 121.84/16.06 (setukpairinjR1) =>
% 121.84/16.06 ((
% 121.84/16.06 (upairequniteq) =>
% 121.84/16.06 ((
% 121.84/16.06 (setukpairinjR2) =>
% 121.84/16.06 ((
% 121.84/16.06 (setukpairinjR) =>
% 121.84/16.06 ((
% 121.84/16.06 (ksndsingleton) =>
% 121.84/16.06 ((
% 121.84/16.06 (ksndpairEq) =>
% 121.84/16.06 ((
% 121.84/16.06 (kpairsurjEq) =>
% 121.84/16.06 ((
% 121.84/16.06 (cartprodsndin) =>
% 121.84/16.06 ((
% 121.84/16.06 (cartprodpairmemEL) =>
% 121.84/16.06 ((
% 121.84/16.06 (cartprodpairmemER) =>
% 121.84/16.06 ((
% 121.84/16.06 (cartprodmempaircEq) =>
% 121.84/16.06 ((
% 121.84/16.06 (cartprodfstpairEq) =>
% 121.84/16.06 ((
% 121.84/16.06 (cartprodsndpairEq) =>
% 121.84/16.06 ((
% 121.84/16.06 (cartprodpairsurjEq) =>
% 121.84/16.06 ((
% 121.84/16.06 (dpsetconstrI) =>
% 121.84/16.06 ((
% 121.84/16.06 (dpsetconstrSub) =>
% 121.84/16.06 ((
% 121.84/16.06 (setOfPairsIsBReln) =>
% 121.84/16.06 ((
% 121.84/16.06 (dpsetconstrERa) =>
% 121.84/16.06 ((
% 121.84/16.06 (dpsetconstrEL1) =>
% 121.84/16.06 ((
% 121.84/16.06 (dpsetconstrEL2) =>
% 121.84/16.06 ((
% 121.84/16.06 (dpsetconstrER) =>
% 121.84/16.06 ((
% 121.84/16.06 (funcImageSingleton) =>
% 121.84/16.06 ((
% 121.84/16.06 (apProp) =>
% 121.84/16.06 ((
% 121.84/16.06 (app) =>
% 121.84/16.06 ((
% 121.84/16.06 (infuncsetfunc) =>
% 121.84/16.06 ((
% 121.84/16.06 (ap2p) =>
% 121.84/16.06 ((
% 121.84/16.06 (funcinfuncset) =>
% 121.84/16.06 ((
% 121.84/16.06 (lamProp) =>
% 121.84/16.06 ((
% 121.84/16.06 (lamp) =>
% 121.84/16.06 ((
% 121.84/16.06 (lam2p) =>
% 121.84/16.06 ((
% 121.84/16.06 (brelnall1) =>
% 121.84/16.06 ((
% 121.84/16.06 (brelnall2) =>
% 121.84/16.06 ((
% 121.84/16.06 (ex1E2) =>
% 121.84/16.06 ((
% 121.84/16.06 (funcGraphProp1) =>
% 121.84/16.06 ((
% 121.84/16.06 (funcGraphProp3) =>
% 121.84/16.06 ((
% 121.84/16.06 (funcGraphProp2) =>
% 121.84/16.06 ((
% 121.84/16.06 (funcextLem) =>
% 121.84/16.06 ((
% 121.84/16.06 (funcGraphProp4) =>
% 121.84/16.06 ((
% 121.84/16.06 (subbreln) =>
% 121.84/16.06 ((
% 121.84/16.06 (eqbreln) =>
% 121.84/16.06 ((
% 121.84/16.06 (funcext) =>
% 121.84/16.06 ((
% 121.84/16.06 (funcext2) =>
% 121.84/16.06 ((
% 121.84/16.06 (ap2apEq1) =>
% 121.84/16.06 ((
% 121.84/16.06 (ap2apEq2) =>
% 121.84/16.06 ((
% 121.84/16.06 (beta1) =>
% 121.84/16.06 ((
% 121.84/16.06 (eta1) =>
% 121.84/16.06 ((
% 121.84/16.06 (lam2lamEq) =>
% 121.84/16.06 ((
% 121.84/16.06 (beta2) =>
% 121.84/16.06 ((
% 121.84/16.06 (eta2) =>
% 121.84/16.06 ((
% 121.84/16.06 (iffalseProp1) =>
% 121.84/16.06 ((
% 121.84/16.06 (iffalseProp2) =>
% 121.84/16.06 ((
% 121.84/16.06 (iftrueProp1) =>
% 121.84/16.06 ((
% 121.84/16.06 (iftrueProp2) =>
% 121.84/16.06 ((
% 121.84/16.06 (ifSingleton) =>
% 121.84/16.06 ((
% 121.84/16.06 (ifp) =>
% 121.84/16.06 ((
% 121.84/16.06 (theeq) =>
% 121.84/16.06 ((
% 121.84/16.06 (iftrue) =>
% 121.84/16.06 ((
% 121.84/16.06 (iffalse) =>
% 121.84/16.06 ((
% 121.84/16.06 (iftrueorfalse) =>
% 121.84/16.06 ((
% 121.84/16.06 (binintersectT_lem) =>
% 121.84/16.06 ((
% 121.84/16.06 (binunionT_lem) =>
% 121.84/16.06 ((
% 121.84/16.06 (powersetT_lem) =>
% 121.84/16.06 ((
% 121.84/16.06 (setminusT_lem) =>
% 121.84/16.06 ((
% 121.84/16.06 (complementT_lem) =>
% 121.84/16.06 ((
% 121.84/16.06 (setextT) =>
% 121.84/16.06 ((
% 121.84/16.06 (subsetTI) =>
% 121.84/16.06 ((
% 121.84/16.06 (powersetTI1) =>
% 121.84/16.06 ((
% 121.84/16.06 (powersetTE1) =>
% 121.84/16.06 ((
% 121.84/16.06 (complementTI1) =>
% 121.84/16.06 ((
% 121.84/16.06 (complementTE1) =>
% 121.84/16.06 ((
% 121.84/16.06 (binintersectTELcontra) =>
% 121.84/16.06 ((
% 121.84/16.06 (binintersectTERcontra) =>
% 121.84/16.06 ((
% 121.84/16.06 (contrasubsetT) =>
% 121.84/16.06 ((
% 121.84/16.06 (contrasubsetT1) =>
% 121.84/16.06 ((
% 121.84/16.06 (contrasubsetT2) =>
% 121.84/16.06 ((
% 121.84/16.06 (contrasubsetT3) =>
% 121.84/16.06 ((
% 121.84/16.06 (doubleComplementI1) =>
% 121.84/16.06 ((
% 121.84/16.06 (doubleComplementE1) =>
% 121.84/16.06 ((
% 121.84/16.06 (doubleComplementSub1) =>
% 121.84/16.06 ((
% 121.84/16.06 (doubleComplementSub2) =>
% 121.84/16.06 ((
% 121.84/16.06 (doubleComplementEq) =>
% 121.84/16.06 ((
% 121.84/16.06 (complementTnotintersectT) =>
% 121.84/16.06 ((
% 121.84/16.06 (complementImpComplementIntersect) =>
% 121.84/16.06 ((
% 121.84/16.06 (complementSubsetComplementIntersect) =>
% 121.84/16.06 ((
% 121.84/16.06 (complementInPowersetComplementIntersect) =>
% 121.84/16.06 ((
% 121.84/16.06 (contraSubsetComplement) =>
% 121.84/16.06 ((
% 121.84/16.06 (complementTcontraSubset) =>
% 121.84/16.06 ((
% 121.84/16.06 (binunionTILcontra) =>
% 121.84/16.06 ((
% 121.84/16.06 (binunionTIRcontra) =>
% 121.84/16.06 ((
% 121.84/16.06 (inIntersectImpInUnion) =>
% 121.84/16.06 ((
% 121.84/16.06 (inIntersectImpInUnion2) =>
% 121.84/16.06 ((
% 121.84/16.06 (inIntersectImpInIntersectUnions) =>
% 121.84/16.06 ((
% 121.84/16.06 (intersectInPowersetIntersectUnions) =>
% 121.84/16.06 ((
% 121.84/16.06 (inComplementUnionImpNotIn1) =>
% 121.84/16.06 ((
% 121.84/16.06 (inComplementUnionImpInComplement1) =>
% 121.84/16.06 ((
% 121.84/16.06 (binunionTE) =>
% 121.84/16.06 ((
% 121.84/16.06 (binunionTEcontra) =>
% 121.84/16.06 ((
% 121.84/16.06 (demorgan2a1) =>
% 121.84/16.06 ((
% 121.84/16.06 (complementUnionInPowersetComplement) =>
% 121.84/16.06 ((
% 121.84/16.06 (demorgan2a2) =>
% 121.84/16.06 ((
% 121.84/16.06 (demorgan1a) =>
% 121.84/16.06 ((
% 121.84/16.06 (demorgan1b) =>
% 121.84/16.06 ((
% 121.84/16.06 (demorgan1) =>
% 121.84/16.06 ((
% 121.84/16.06 (demorgan2a) =>
% 121.84/16.06 ((
% 121.84/16.06 (demorgan2b2) =>
% 121.84/16.06 ((
% 121.84/16.06 (demorgan2b) =>
% 121.84/16.06 ((
% 121.84/16.06 (demorgan2) =>
% 121.84/16.06 ((
% 121.84/16.06 (woz13rule0) =>
% 121.84/16.06 ((
% 121.84/16.06 (woz13rule1) =>
% 121.84/16.06 ((
% 121.84/16.06 (woz13rule2) =>
% 121.84/16.06 ((
% 121.84/16.06 (woz13rule3) =>
% 121.84/16.06 ((
% 121.84/16.06 (woz13rule4) =>
% 121.84/16.06 ((
% 121.84/16.06 (woz1_1) =>
% 121.84/16.06 ((
% 121.84/16.06 (woz1_2) =>
% 121.84/16.06 ((
% 121.84/16.06 (woz1_3) =>
% 121.84/16.06 ((
% 121.84/16.06 (woz1_4) =>
% 121.84/16.06 ((
% 121.84/16.06 (woz1_5) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1all2) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1SetBreln1) =>
% 121.84/16.06 ((
% 121.84/16.06 (choice2fnsingleton) =>
% 121.84/16.06 ((
% 121.84/16.06 (setOfPairsIsBReln1) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1all1) =>
% 121.84/16.06 ((
% 121.84/16.06 (subbreln1) =>
% 121.84/16.06 ((
% 121.84/16.06 (eqbreln1) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1invprop) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1invI) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1invE) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1compprop) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1compI) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1compE) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1compEex) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1unionprop) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1unionIL) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1unionIR) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1unionI) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1unionE) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1unionEcases) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1unionCommutes) =>
% 121.84/16.06 ((
% 121.84/16.06 (woz2Ex) =>
% 121.84/16.06 ((
% 121.84/16.06 (woz2W) =>
% 121.84/16.06 ((
% 121.84/16.06 (woz2A) =>
% 121.84/16.06 ((
% 121.84/16.06 (woz2B) =>
% 121.84/16.06 ((
% 121.84/16.06 (image1Ex) =>
% 121.84/16.06 ((
% 121.84/16.06 (image1Ex1) =>
% 121.84/16.06 ((
% 121.84/16.06 (image1Equiv) =>
% 121.84/16.06 ((
% 121.84/16.06 (image1E) =>
% 121.84/16.06 ((
% 121.84/16.06 (image1I) =>
% 121.84/16.06 ((
% 121.84/16.06 (injFuncInInjFuncSet) =>
% 121.84/16.06 ((
% 121.84/16.06 (!!) @ (
% 121.84/16.06 (('#B') @ (
% 121.84/16.06 !!) @
% 121.84/16.06 (
% 121.84/16.06 (
% 121.84/16.06 ('#B') @ (
% 121.84/16.06 (
% 121.84/16.06 ('#B') @ (
% 121.84/16.06 !!))) @
% 121.84/16.06 (
% 121.84/16.06 (
% 121.84/16.06 ('#S') @ (
% 121.84/16.06 (
% 121.84/16.06 ('#B') @ (
% 121.84/16.06 '#S') @
% 121.84/16.06 (
% 121.84/16.06 (
% 121.84/16.06 ('#B') @ (
% 121.84/16.06 (
% 121.84/16.06 ('#B') @ (
% 121.84/16.06 '#S'))) @
% 121.84/16.06 (
% 121.84/16.06 (
% 121.84/16.06 ('#B') @ (
% 121.84/16.06 (
% 121.84/16.06 ('#B') @ (
% 121.84/16.06 (
% 121.84/16.06 ('#B') @ (
% 121.84/16.06 =>))))) @
% 121.84/16.06 (
% 121.84/16.06 (
% 121.84/16.06 ('#B') @ (
% 121.84/16.06 (
% 121.84/16.06 ('#B') @ (
% 121.84/16.06 (
% 121.84/16.06 ('#C') @ in)))) @
% 121.84/16.06 injFuncSet)))))))) @
% 121.84/16.06 (
% 121.84/16.06 (
% 121.84/16.06 ('#B') @ (
% 121.84/16.06 (
% 121.84/16.06 ('#B') @ (
% 121.84/16.06 (
% 121.84/16.06 ('#C') @ in)))) @
% 121.84/16.06 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 121.84/16.06 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl467])).
% 121.84/16.06 thf(zip_derived_cl485, plain,
% 121.84/16.06 (~ (((upairsetE) =>
% 121.84/16.06 (((upairsetIL) =>
% 121.84/16.06 (((upairsetIR) =>
% 121.84/16.06 (((emptyE1) =>
% 121.84/16.06 (((vacuousDall) =>
% 121.84/16.06 (((quantDeMorgan1) =>
% 121.84/16.06 (((quantDeMorgan2) =>
% 121.84/16.06 (((quantDeMorgan3) =>
% 121.84/16.06 (((quantDeMorgan4) =>
% 121.84/16.06 (((prop2setI) =>
% 121.84/16.06 (((prop2set2propI) =>
% 121.84/16.06 (((notdexE) =>
% 121.84/16.06 (((notdallE) =>
% 121.84/16.06 (((exuI1) =>
% 121.84/16.06 (((exuI3) =>
% 121.84/16.06 (((exuI2) =>
% 121.84/16.06 (((inCongP) =>
% 121.84/16.06 (((in__Cong) =>
% 121.84/16.06 (((exuE3u) =>
% 121.84/16.06 (((exu__Cong) =>
% 121.84/16.06 (((setadjoin__Cong) =>
% 121.84/16.06 (((powerset__Cong) =>
% 121.84/16.06 (((setunion__Cong) =>
% 121.84/16.06 (((exuEu) =>
% 121.84/16.06 (((descr__Cong) =>
% 121.84/16.06 (((dsetconstr__Cong) =>
% 121.84/16.06 (((subsetI1) =>
% 121.84/16.06 (((eqimpsubset2) =>
% 121.84/16.06 (((eqimpsubset1) =>
% 121.84/16.06 (((subsetI2) =>
% 121.84/16.06 ((
% 121.84/16.06 (emptysetsubset) =>
% 121.84/16.06 ((
% 121.84/16.06 (subsetE) =>
% 121.84/16.06 ((
% 121.84/16.06 (subsetE2) =>
% 121.84/16.06 ((
% 121.84/16.06 (notsubsetI) =>
% 121.84/16.06 ((
% 121.84/16.06 (notequalI1) =>
% 121.84/16.06 ((
% 121.84/16.06 (notequalI2) =>
% 121.84/16.06 ((
% 121.84/16.06 (subsetRefl) =>
% 121.84/16.06 ((
% 121.84/16.06 (subsetTrans) =>
% 121.84/16.06 ((
% 121.84/16.06 (setadjoinSub) =>
% 121.84/16.06 ((
% 121.84/16.06 (setadjoinSub2) =>
% 121.84/16.06 ((
% 121.84/16.06 (subset2powerset) =>
% 121.84/16.06 ((
% 121.84/16.06 (setextsub) =>
% 121.84/16.06 ((
% 121.84/16.06 (subsetemptysetimpeq) =>
% 121.84/16.06 ((
% 121.84/16.06 (powersetI1) =>
% 121.84/16.06 ((
% 121.84/16.06 (powersetE1) =>
% 121.84/16.06 ((
% 121.84/16.06 (inPowerset) =>
% 121.84/16.06 ((
% 121.84/16.06 (powersetsubset) =>
% 121.84/16.06 ((
% 121.84/16.06 (sepInPowerset) =>
% 121.84/16.06 ((
% 121.84/16.06 (sepSubset) =>
% 121.84/16.06 ((
% 121.84/16.06 (binunionIL) =>
% 121.84/16.06 ((
% 121.84/16.06 (upairset2IR) =>
% 121.84/16.06 ((
% 121.84/16.06 (binunionIR) =>
% 121.84/16.06 ((
% 121.84/16.06 (binunionEcases) =>
% 121.84/16.06 ((
% 121.84/16.06 (binunionE) =>
% 121.84/16.06 ((
% 121.84/16.06 (binunionLsub) =>
% 121.84/16.06 ((
% 121.84/16.06 (binunionRsub) =>
% 121.84/16.06 ((
% 121.84/16.06 (binintersectI) =>
% 121.84/16.06 ((
% 121.84/16.06 (binintersectSubset5) =>
% 121.84/16.06 ((
% 121.84/16.06 (binintersectEL) =>
% 121.84/16.06 ((
% 121.84/16.06 (binintersectLsub) =>
% 121.84/16.06 ((
% 121.84/16.06 (binintersectSubset2) =>
% 121.84/16.06 ((
% 121.84/16.06 (binintersectSubset3) =>
% 121.84/16.06 ((
% 121.84/16.06 (binintersectER) =>
% 121.84/16.06 ((
% 121.84/16.06 (disjointsetsI1) =>
% 121.84/16.06 ((
% 121.84/16.06 (binintersectRsub) =>
% 121.84/16.06 ((
% 121.84/16.06 (binintersectSubset4) =>
% 121.84/16.06 ((
% 121.84/16.06 (binintersectSubset1) =>
% 121.84/16.06 ((
% 121.84/16.06 (bs114d) =>
% 121.84/16.06 ((
% 121.84/16.06 (setminusI) =>
% 121.84/16.06 ((
% 121.84/16.06 (setminusEL) =>
% 121.84/16.06 ((
% 121.84/16.06 (setminusER) =>
% 121.84/16.06 ((
% 121.84/16.06 (setminusSubset2) =>
% 121.84/16.06 ((
% 121.84/16.06 (setminusERneg) =>
% 121.84/16.06 ((
% 121.84/16.06 (setminusELneg) =>
% 121.84/16.06 ((
% 121.84/16.06 (setminusILneg) =>
% 121.84/16.06 ((
% 121.84/16.06 (setminusIRneg) =>
% 121.84/16.06 ((
% 121.84/16.06 (setminusLsub) =>
% 121.84/16.06 ((
% 121.84/16.06 (setminusSubset1) =>
% 121.84/16.06 ((
% 121.84/16.06 (symdiffE) =>
% 121.84/16.06 ((
% 121.84/16.06 (symdiffI1) =>
% 121.84/16.06 ((
% 121.84/16.06 (symdiffI2) =>
% 121.84/16.06 ((
% 121.84/16.06 (symdiffIneg1) =>
% 121.84/16.06 ((
% 121.84/16.06 (symdiffIneg2) =>
% 121.84/16.06 ((
% 121.84/16.06 (secondinupair) =>
% 121.84/16.06 ((
% 121.84/16.06 (setukpairIL) =>
% 121.84/16.06 ((
% 121.84/16.06 (setukpairIR) =>
% 121.84/16.06 ((
% 121.84/16.06 (kpairiskpair) =>
% 121.84/16.06 ((
% 121.84/16.06 (kpairp) =>
% 121.84/16.06 ((
% 121.84/16.06 (singletonsubset) =>
% 121.84/16.06 ((
% 121.84/16.06 (singletoninpowerset) =>
% 121.84/16.06 ((
% 121.84/16.06 (singletoninpowunion) =>
% 121.84/16.06 ((
% 121.84/16.06 (upairset2E) =>
% 121.84/16.06 ((
% 121.84/16.06 (upairsubunion) =>
% 121.84/16.06 ((
% 121.84/16.06 (upairinpowunion) =>
% 121.84/16.06 ((
% 121.84/16.06 (ubforcartprodlem1) =>
% 121.84/16.06 ((
% 121.84/16.06 (ubforcartprodlem2) =>
% 121.84/16.06 ((
% 121.84/16.06 (ubforcartprodlem3) =>
% 121.84/16.06 ((
% 121.84/16.06 (cartprodpairin) =>
% 121.84/16.06 ((
% 121.84/16.06 (cartprodmempair1) =>
% 121.84/16.06 ((
% 121.84/16.06 (cartprodmempair) =>
% 121.84/16.06 ((
% 121.84/16.06 (setunionE2) =>
% 121.84/16.06 ((
% 121.84/16.06 (setunionsingleton1) =>
% 121.84/16.06 ((
% 121.84/16.06 (setunionsingleton2) =>
% 121.84/16.06 ((
% 121.84/16.06 (setunionsingleton) =>
% 121.84/16.06 ((
% 121.84/16.06 (singletonprop) =>
% 121.84/16.06 ((
% 121.84/16.06 (ex1E1) =>
% 121.84/16.06 ((
% 121.84/16.06 (ex1I) =>
% 121.84/16.06 ((
% 121.84/16.06 (ex1I2) =>
% 121.84/16.06 ((
% 121.84/16.06 (singletonsuniq) =>
% 121.84/16.06 ((
% 121.84/16.06 (setukpairinjL1) =>
% 121.84/16.06 ((
% 121.84/16.06 (kfstsingleton) =>
% 121.84/16.06 ((
% 121.84/16.06 (theprop) =>
% 121.84/16.06 ((
% 121.84/16.06 (kfstpairEq) =>
% 121.84/16.06 ((
% 121.84/16.06 (cartprodfstin) =>
% 121.84/16.06 ((
% 121.84/16.06 (setukpairinjL2) =>
% 121.84/16.06 ((
% 121.84/16.06 (setukpairinjL) =>
% 121.84/16.06 ((
% 121.84/16.06 (setukpairinjR11) =>
% 121.84/16.06 ((
% 121.84/16.06 (setukpairinjR12) =>
% 121.84/16.06 ((
% 121.84/16.06 (setukpairinjR1) =>
% 121.84/16.06 ((
% 121.84/16.06 (upairequniteq) =>
% 121.84/16.06 ((
% 121.84/16.06 (setukpairinjR2) =>
% 121.84/16.06 ((
% 121.84/16.06 (setukpairinjR) =>
% 121.84/16.06 ((
% 121.84/16.06 (ksndsingleton) =>
% 121.84/16.06 ((
% 121.84/16.06 (ksndpairEq) =>
% 121.84/16.06 ((
% 121.84/16.06 (kpairsurjEq) =>
% 121.84/16.06 ((
% 121.84/16.06 (cartprodsndin) =>
% 121.84/16.06 ((
% 121.84/16.06 (cartprodpairmemEL) =>
% 121.84/16.06 ((
% 121.84/16.06 (cartprodpairmemER) =>
% 121.84/16.06 ((
% 121.84/16.06 (cartprodmempaircEq) =>
% 121.84/16.06 ((
% 121.84/16.06 (cartprodfstpairEq) =>
% 121.84/16.06 ((
% 121.84/16.06 (cartprodsndpairEq) =>
% 121.84/16.06 ((
% 121.84/16.06 (cartprodpairsurjEq) =>
% 121.84/16.06 ((
% 121.84/16.06 (dpsetconstrI) =>
% 121.84/16.06 ((
% 121.84/16.06 (dpsetconstrSub) =>
% 121.84/16.06 ((
% 121.84/16.06 (setOfPairsIsBReln) =>
% 121.84/16.06 ((
% 121.84/16.06 (dpsetconstrERa) =>
% 121.84/16.06 ((
% 121.84/16.06 (dpsetconstrEL1) =>
% 121.84/16.06 ((
% 121.84/16.06 (dpsetconstrEL2) =>
% 121.84/16.06 ((
% 121.84/16.06 (dpsetconstrER) =>
% 121.84/16.06 ((
% 121.84/16.06 (funcImageSingleton) =>
% 121.84/16.06 ((
% 121.84/16.06 (apProp) =>
% 121.84/16.06 ((
% 121.84/16.06 (app) =>
% 121.84/16.06 ((
% 121.84/16.06 (infuncsetfunc) =>
% 121.84/16.06 ((
% 121.84/16.06 (ap2p) =>
% 121.84/16.06 ((
% 121.84/16.06 (funcinfuncset) =>
% 121.84/16.06 ((
% 121.84/16.06 (lamProp) =>
% 121.84/16.06 ((
% 121.84/16.06 (lamp) =>
% 121.84/16.06 ((
% 121.84/16.06 (lam2p) =>
% 121.84/16.06 ((
% 121.84/16.06 (brelnall1) =>
% 121.84/16.06 ((
% 121.84/16.06 (brelnall2) =>
% 121.84/16.06 ((
% 121.84/16.06 (ex1E2) =>
% 121.84/16.06 ((
% 121.84/16.06 (funcGraphProp1) =>
% 121.84/16.06 ((
% 121.84/16.06 (funcGraphProp3) =>
% 121.84/16.06 ((
% 121.84/16.06 (funcGraphProp2) =>
% 121.84/16.06 ((
% 121.84/16.06 (funcextLem) =>
% 121.84/16.06 ((
% 121.84/16.06 (funcGraphProp4) =>
% 121.84/16.06 ((
% 121.84/16.06 (subbreln) =>
% 121.84/16.06 ((
% 121.84/16.06 (eqbreln) =>
% 121.84/16.06 ((
% 121.84/16.06 (funcext) =>
% 121.84/16.06 ((
% 121.84/16.06 (funcext2) =>
% 121.84/16.06 ((
% 121.84/16.06 (ap2apEq1) =>
% 121.84/16.06 ((
% 121.84/16.06 (ap2apEq2) =>
% 121.84/16.06 ((
% 121.84/16.06 (beta1) =>
% 121.84/16.06 ((
% 121.84/16.06 (eta1) =>
% 121.84/16.06 ((
% 121.84/16.06 (lam2lamEq) =>
% 121.84/16.06 ((
% 121.84/16.06 (beta2) =>
% 121.84/16.06 ((
% 121.84/16.06 (eta2) =>
% 121.84/16.06 ((
% 121.84/16.06 (iffalseProp1) =>
% 121.84/16.06 ((
% 121.84/16.06 (iffalseProp2) =>
% 121.84/16.06 ((
% 121.84/16.06 (iftrueProp1) =>
% 121.84/16.06 ((
% 121.84/16.06 (iftrueProp2) =>
% 121.84/16.06 ((
% 121.84/16.06 (ifSingleton) =>
% 121.84/16.06 ((
% 121.84/16.06 (ifp) =>
% 121.84/16.06 ((
% 121.84/16.06 (theeq) =>
% 121.84/16.06 ((
% 121.84/16.06 (iftrue) =>
% 121.84/16.06 ((
% 121.84/16.06 (iffalse) =>
% 121.84/16.06 ((
% 121.84/16.06 (iftrueorfalse) =>
% 121.84/16.06 ((
% 121.84/16.06 (binintersectT_lem) =>
% 121.84/16.06 ((
% 121.84/16.06 (binunionT_lem) =>
% 121.84/16.06 ((
% 121.84/16.06 (powersetT_lem) =>
% 121.84/16.06 ((
% 121.84/16.06 (setminusT_lem) =>
% 121.84/16.06 ((
% 121.84/16.06 (complementT_lem) =>
% 121.84/16.06 ((
% 121.84/16.06 (setextT) =>
% 121.84/16.06 ((
% 121.84/16.06 (subsetTI) =>
% 121.84/16.06 ((
% 121.84/16.06 (powersetTI1) =>
% 121.84/16.06 ((
% 121.84/16.06 (powersetTE1) =>
% 121.84/16.06 ((
% 121.84/16.06 (complementTI1) =>
% 121.84/16.06 ((
% 121.84/16.06 (complementTE1) =>
% 121.84/16.06 ((
% 121.84/16.06 (binintersectTELcontra) =>
% 121.84/16.06 ((
% 121.84/16.06 (binintersectTERcontra) =>
% 121.84/16.06 ((
% 121.84/16.06 (contrasubsetT) =>
% 121.84/16.06 ((
% 121.84/16.06 (contrasubsetT1) =>
% 121.84/16.06 ((
% 121.84/16.06 (contrasubsetT2) =>
% 121.84/16.06 ((
% 121.84/16.06 (contrasubsetT3) =>
% 121.84/16.06 ((
% 121.84/16.06 (doubleComplementI1) =>
% 121.84/16.06 ((
% 121.84/16.06 (doubleComplementE1) =>
% 121.84/16.06 ((
% 121.84/16.06 (doubleComplementSub1) =>
% 121.84/16.06 ((
% 121.84/16.06 (doubleComplementSub2) =>
% 121.84/16.06 ((
% 121.84/16.06 (doubleComplementEq) =>
% 121.84/16.06 ((
% 121.84/16.06 (complementTnotintersectT) =>
% 121.84/16.06 ((
% 121.84/16.06 (complementImpComplementIntersect) =>
% 121.84/16.06 ((
% 121.84/16.06 (complementSubsetComplementIntersect) =>
% 121.84/16.06 ((
% 121.84/16.06 (complementInPowersetComplementIntersect) =>
% 121.84/16.06 ((
% 121.84/16.06 (contraSubsetComplement) =>
% 121.84/16.06 ((
% 121.84/16.06 (complementTcontraSubset) =>
% 121.84/16.06 ((
% 121.84/16.06 (binunionTILcontra) =>
% 121.84/16.06 ((
% 121.84/16.06 (binunionTIRcontra) =>
% 121.84/16.06 ((
% 121.84/16.06 (inIntersectImpInUnion) =>
% 121.84/16.06 ((
% 121.84/16.06 (inIntersectImpInUnion2) =>
% 121.84/16.06 ((
% 121.84/16.06 (inIntersectImpInIntersectUnions) =>
% 121.84/16.06 ((
% 121.84/16.06 (intersectInPowersetIntersectUnions) =>
% 121.84/16.06 ((
% 121.84/16.06 (inComplementUnionImpNotIn1) =>
% 121.84/16.06 ((
% 121.84/16.06 (inComplementUnionImpInComplement1) =>
% 121.84/16.06 ((
% 121.84/16.06 (binunionTE) =>
% 121.84/16.06 ((
% 121.84/16.06 (binunionTEcontra) =>
% 121.84/16.06 ((
% 121.84/16.06 (demorgan2a1) =>
% 121.84/16.06 ((
% 121.84/16.06 (complementUnionInPowersetComplement) =>
% 121.84/16.06 ((
% 121.84/16.06 (demorgan2a2) =>
% 121.84/16.06 ((
% 121.84/16.06 (demorgan1a) =>
% 121.84/16.06 ((
% 121.84/16.06 (demorgan1b) =>
% 121.84/16.06 ((
% 121.84/16.06 (demorgan1) =>
% 121.84/16.06 ((
% 121.84/16.06 (demorgan2a) =>
% 121.84/16.06 ((
% 121.84/16.06 (demorgan2b2) =>
% 121.84/16.06 ((
% 121.84/16.06 (demorgan2b) =>
% 121.84/16.06 ((
% 121.84/16.06 (demorgan2) =>
% 121.84/16.06 ((
% 121.84/16.06 (woz13rule0) =>
% 121.84/16.06 ((
% 121.84/16.06 (woz13rule1) =>
% 121.84/16.06 ((
% 121.84/16.06 (woz13rule2) =>
% 121.84/16.06 ((
% 121.84/16.06 (woz13rule3) =>
% 121.84/16.06 ((
% 121.84/16.06 (woz13rule4) =>
% 121.84/16.06 ((
% 121.84/16.06 (woz1_1) =>
% 121.84/16.06 ((
% 121.84/16.06 (woz1_2) =>
% 121.84/16.06 ((
% 121.84/16.06 (woz1_3) =>
% 121.84/16.06 ((
% 121.84/16.06 (woz1_4) =>
% 121.84/16.06 ((
% 121.84/16.06 (woz1_5) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1all2) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1SetBreln1) =>
% 121.84/16.06 ((
% 121.84/16.06 (choice2fnsingleton) =>
% 121.84/16.06 ((
% 121.84/16.06 (setOfPairsIsBReln1) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1all1) =>
% 121.84/16.06 ((
% 121.84/16.06 (subbreln1) =>
% 121.84/16.06 ((
% 121.84/16.06 (eqbreln1) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1invprop) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1invI) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1invE) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1compprop) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1compI) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1compE) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1compEex) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1unionprop) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1unionIL) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1unionIR) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1unionI) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1unionE) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1unionEcases) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1unionCommutes) =>
% 121.84/16.06 ((
% 121.84/16.06 (woz2Ex) =>
% 121.84/16.06 ((
% 121.84/16.06 (woz2W) =>
% 121.84/16.06 ((
% 121.84/16.06 (woz2A) =>
% 121.84/16.06 ((
% 121.84/16.06 (woz2B) =>
% 121.84/16.06 ((
% 121.84/16.06 (image1Ex) =>
% 121.84/16.06 ((
% 121.84/16.06 (image1Ex1) =>
% 121.84/16.06 ((
% 121.84/16.06 (image1Equiv) =>
% 121.84/16.06 ((
% 121.84/16.06 (image1E) =>
% 121.84/16.06 ((
% 121.84/16.06 (image1I) =>
% 121.84/16.06 ((
% 121.84/16.06 (injFuncInInjFuncSet) =>
% 121.84/16.06 ((
% 121.84/16.06 (!!) @ (
% 121.84/16.06 (('#B') @ (
% 121.84/16.06 !!) @
% 121.84/16.06 (
% 121.84/16.06 (
% 121.84/16.06 ('#B') @ (
% 121.84/16.06 (
% 121.84/16.06 ('#B') @ (
% 121.84/16.06 !!))) @
% 121.84/16.06 (
% 121.84/16.06 (
% 121.84/16.06 ('#S') @ (
% 121.84/16.06 (
% 121.84/16.06 ('#B') @ (
% 121.84/16.06 '#S') @
% 121.84/16.06 (
% 121.84/16.06 (
% 121.84/16.06 ('#B') @ (
% 121.84/16.06 (
% 121.84/16.06 ('#B') @ (
% 121.84/16.06 '#S'))) @
% 121.84/16.06 (
% 121.84/16.06 (
% 121.84/16.06 ('#B') @ (
% 121.84/16.06 (
% 121.84/16.06 ('#B') @ (
% 121.84/16.06 (
% 121.84/16.06 ('#B') @ (
% 121.84/16.06 =>))))) @
% 121.84/16.06 (
% 121.84/16.06 (
% 121.84/16.06 ('#B') @ (
% 121.84/16.06 (
% 121.84/16.06 ('#B') @ (
% 121.84/16.06 (
% 121.84/16.06 ('#C') @ in)))) @
% 121.84/16.06 injFuncSet)))))))) @
% 121.84/16.06 (
% 121.84/16.06 (
% 121.84/16.06 ('#B') @ (
% 121.84/16.06 (
% 121.84/16.06 ('#B') @ (
% 121.84/16.06 (
% 121.84/16.06 ('#C') @ in)))) @
% 121.84/16.06 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 121.84/16.06 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl475])).
% 121.84/16.06 thf(zip_derived_cl496, plain,
% 121.84/16.06 (~ (((upairsetIL) =>
% 121.84/16.06 (((upairsetIR) =>
% 121.84/16.06 (((emptyE1) =>
% 121.84/16.06 (((vacuousDall) =>
% 121.84/16.06 (((quantDeMorgan1) =>
% 121.84/16.06 (((quantDeMorgan2) =>
% 121.84/16.06 (((quantDeMorgan3) =>
% 121.84/16.06 (((quantDeMorgan4) =>
% 121.84/16.06 (((prop2setI) =>
% 121.84/16.06 (((prop2set2propI) =>
% 121.84/16.06 (((notdexE) =>
% 121.84/16.06 (((notdallE) =>
% 121.84/16.06 (((exuI1) =>
% 121.84/16.06 (((exuI3) =>
% 121.84/16.06 (((exuI2) =>
% 121.84/16.06 (((inCongP) =>
% 121.84/16.06 (((in__Cong) =>
% 121.84/16.06 (((exuE3u) =>
% 121.84/16.06 (((exu__Cong) =>
% 121.84/16.06 (((setadjoin__Cong) =>
% 121.84/16.06 (((powerset__Cong) =>
% 121.84/16.06 (((setunion__Cong) =>
% 121.84/16.06 (((exuEu) =>
% 121.84/16.06 (((descr__Cong) =>
% 121.84/16.06 (((dsetconstr__Cong) =>
% 121.84/16.06 (((subsetI1) =>
% 121.84/16.06 (((eqimpsubset2) =>
% 121.84/16.06 (((eqimpsubset1) =>
% 121.84/16.06 (((subsetI2) =>
% 121.84/16.06 (((emptysetsubset) =>
% 121.84/16.06 ((
% 121.84/16.06 (subsetE) =>
% 121.84/16.06 ((
% 121.84/16.06 (subsetE2) =>
% 121.84/16.06 ((
% 121.84/16.06 (notsubsetI) =>
% 121.84/16.06 ((
% 121.84/16.06 (notequalI1) =>
% 121.84/16.06 ((
% 121.84/16.06 (notequalI2) =>
% 121.84/16.06 ((
% 121.84/16.06 (subsetRefl) =>
% 121.84/16.06 ((
% 121.84/16.06 (subsetTrans) =>
% 121.84/16.06 ((
% 121.84/16.06 (setadjoinSub) =>
% 121.84/16.06 ((
% 121.84/16.06 (setadjoinSub2) =>
% 121.84/16.06 ((
% 121.84/16.06 (subset2powerset) =>
% 121.84/16.06 ((
% 121.84/16.06 (setextsub) =>
% 121.84/16.06 ((
% 121.84/16.06 (subsetemptysetimpeq) =>
% 121.84/16.06 ((
% 121.84/16.06 (powersetI1) =>
% 121.84/16.06 ((
% 121.84/16.06 (powersetE1) =>
% 121.84/16.06 ((
% 121.84/16.06 (inPowerset) =>
% 121.84/16.06 ((
% 121.84/16.06 (powersetsubset) =>
% 121.84/16.06 ((
% 121.84/16.06 (sepInPowerset) =>
% 121.84/16.06 ((
% 121.84/16.06 (sepSubset) =>
% 121.84/16.06 ((
% 121.84/16.06 (binunionIL) =>
% 121.84/16.06 ((
% 121.84/16.06 (upairset2IR) =>
% 121.84/16.06 ((
% 121.84/16.06 (binunionIR) =>
% 121.84/16.06 ((
% 121.84/16.06 (binunionEcases) =>
% 121.84/16.06 ((
% 121.84/16.06 (binunionE) =>
% 121.84/16.06 ((
% 121.84/16.06 (binunionLsub) =>
% 121.84/16.06 ((
% 121.84/16.06 (binunionRsub) =>
% 121.84/16.06 ((
% 121.84/16.06 (binintersectI) =>
% 121.84/16.06 ((
% 121.84/16.06 (binintersectSubset5) =>
% 121.84/16.06 ((
% 121.84/16.06 (binintersectEL) =>
% 121.84/16.06 ((
% 121.84/16.06 (binintersectLsub) =>
% 121.84/16.06 ((
% 121.84/16.06 (binintersectSubset2) =>
% 121.84/16.06 ((
% 121.84/16.06 (binintersectSubset3) =>
% 121.84/16.06 ((
% 121.84/16.06 (binintersectER) =>
% 121.84/16.06 ((
% 121.84/16.06 (disjointsetsI1) =>
% 121.84/16.06 ((
% 121.84/16.06 (binintersectRsub) =>
% 121.84/16.06 ((
% 121.84/16.06 (binintersectSubset4) =>
% 121.84/16.06 ((
% 121.84/16.06 (binintersectSubset1) =>
% 121.84/16.06 ((
% 121.84/16.06 (bs114d) =>
% 121.84/16.06 ((
% 121.84/16.06 (setminusI) =>
% 121.84/16.06 ((
% 121.84/16.06 (setminusEL) =>
% 121.84/16.06 ((
% 121.84/16.06 (setminusER) =>
% 121.84/16.06 ((
% 121.84/16.06 (setminusSubset2) =>
% 121.84/16.06 ((
% 121.84/16.06 (setminusERneg) =>
% 121.84/16.06 ((
% 121.84/16.06 (setminusELneg) =>
% 121.84/16.06 ((
% 121.84/16.06 (setminusILneg) =>
% 121.84/16.06 ((
% 121.84/16.06 (setminusIRneg) =>
% 121.84/16.06 ((
% 121.84/16.06 (setminusLsub) =>
% 121.84/16.06 ((
% 121.84/16.06 (setminusSubset1) =>
% 121.84/16.06 ((
% 121.84/16.06 (symdiffE) =>
% 121.84/16.06 ((
% 121.84/16.06 (symdiffI1) =>
% 121.84/16.06 ((
% 121.84/16.06 (symdiffI2) =>
% 121.84/16.06 ((
% 121.84/16.06 (symdiffIneg1) =>
% 121.84/16.06 ((
% 121.84/16.06 (symdiffIneg2) =>
% 121.84/16.06 ((
% 121.84/16.06 (secondinupair) =>
% 121.84/16.06 ((
% 121.84/16.06 (setukpairIL) =>
% 121.84/16.06 ((
% 121.84/16.06 (setukpairIR) =>
% 121.84/16.06 ((
% 121.84/16.06 (kpairiskpair) =>
% 121.84/16.06 ((
% 121.84/16.06 (kpairp) =>
% 121.84/16.06 ((
% 121.84/16.06 (singletonsubset) =>
% 121.84/16.06 ((
% 121.84/16.06 (singletoninpowerset) =>
% 121.84/16.06 ((
% 121.84/16.06 (singletoninpowunion) =>
% 121.84/16.06 ((
% 121.84/16.06 (upairset2E) =>
% 121.84/16.06 ((
% 121.84/16.06 (upairsubunion) =>
% 121.84/16.06 ((
% 121.84/16.06 (upairinpowunion) =>
% 121.84/16.06 ((
% 121.84/16.06 (ubforcartprodlem1) =>
% 121.84/16.06 ((
% 121.84/16.06 (ubforcartprodlem2) =>
% 121.84/16.06 ((
% 121.84/16.06 (ubforcartprodlem3) =>
% 121.84/16.06 ((
% 121.84/16.06 (cartprodpairin) =>
% 121.84/16.06 ((
% 121.84/16.06 (cartprodmempair1) =>
% 121.84/16.06 ((
% 121.84/16.06 (cartprodmempair) =>
% 121.84/16.06 ((
% 121.84/16.06 (setunionE2) =>
% 121.84/16.06 ((
% 121.84/16.06 (setunionsingleton1) =>
% 121.84/16.06 ((
% 121.84/16.06 (setunionsingleton2) =>
% 121.84/16.06 ((
% 121.84/16.06 (setunionsingleton) =>
% 121.84/16.06 ((
% 121.84/16.06 (singletonprop) =>
% 121.84/16.06 ((
% 121.84/16.06 (ex1E1) =>
% 121.84/16.06 ((
% 121.84/16.06 (ex1I) =>
% 121.84/16.06 ((
% 121.84/16.06 (ex1I2) =>
% 121.84/16.06 ((
% 121.84/16.06 (singletonsuniq) =>
% 121.84/16.06 ((
% 121.84/16.06 (setukpairinjL1) =>
% 121.84/16.06 ((
% 121.84/16.06 (kfstsingleton) =>
% 121.84/16.06 ((
% 121.84/16.06 (theprop) =>
% 121.84/16.06 ((
% 121.84/16.06 (kfstpairEq) =>
% 121.84/16.06 ((
% 121.84/16.06 (cartprodfstin) =>
% 121.84/16.06 ((
% 121.84/16.06 (setukpairinjL2) =>
% 121.84/16.06 ((
% 121.84/16.06 (setukpairinjL) =>
% 121.84/16.06 ((
% 121.84/16.06 (setukpairinjR11) =>
% 121.84/16.06 ((
% 121.84/16.06 (setukpairinjR12) =>
% 121.84/16.06 ((
% 121.84/16.06 (setukpairinjR1) =>
% 121.84/16.06 ((
% 121.84/16.06 (upairequniteq) =>
% 121.84/16.06 ((
% 121.84/16.06 (setukpairinjR2) =>
% 121.84/16.06 ((
% 121.84/16.06 (setukpairinjR) =>
% 121.84/16.06 ((
% 121.84/16.06 (ksndsingleton) =>
% 121.84/16.06 ((
% 121.84/16.06 (ksndpairEq) =>
% 121.84/16.06 ((
% 121.84/16.06 (kpairsurjEq) =>
% 121.84/16.06 ((
% 121.84/16.06 (cartprodsndin) =>
% 121.84/16.06 ((
% 121.84/16.06 (cartprodpairmemEL) =>
% 121.84/16.06 ((
% 121.84/16.06 (cartprodpairmemER) =>
% 121.84/16.06 ((
% 121.84/16.06 (cartprodmempaircEq) =>
% 121.84/16.06 ((
% 121.84/16.06 (cartprodfstpairEq) =>
% 121.84/16.06 ((
% 121.84/16.06 (cartprodsndpairEq) =>
% 121.84/16.06 ((
% 121.84/16.06 (cartprodpairsurjEq) =>
% 121.84/16.06 ((
% 121.84/16.06 (dpsetconstrI) =>
% 121.84/16.06 ((
% 121.84/16.06 (dpsetconstrSub) =>
% 121.84/16.06 ((
% 121.84/16.06 (setOfPairsIsBReln) =>
% 121.84/16.06 ((
% 121.84/16.06 (dpsetconstrERa) =>
% 121.84/16.06 ((
% 121.84/16.06 (dpsetconstrEL1) =>
% 121.84/16.06 ((
% 121.84/16.06 (dpsetconstrEL2) =>
% 121.84/16.06 ((
% 121.84/16.06 (dpsetconstrER) =>
% 121.84/16.06 ((
% 121.84/16.06 (funcImageSingleton) =>
% 121.84/16.06 ((
% 121.84/16.06 (apProp) =>
% 121.84/16.06 ((
% 121.84/16.06 (app) =>
% 121.84/16.06 ((
% 121.84/16.06 (infuncsetfunc) =>
% 121.84/16.06 ((
% 121.84/16.06 (ap2p) =>
% 121.84/16.06 ((
% 121.84/16.06 (funcinfuncset) =>
% 121.84/16.06 ((
% 121.84/16.06 (lamProp) =>
% 121.84/16.06 ((
% 121.84/16.06 (lamp) =>
% 121.84/16.06 ((
% 121.84/16.06 (lam2p) =>
% 121.84/16.06 ((
% 121.84/16.06 (brelnall1) =>
% 121.84/16.06 ((
% 121.84/16.06 (brelnall2) =>
% 121.84/16.06 ((
% 121.84/16.06 (ex1E2) =>
% 121.84/16.06 ((
% 121.84/16.06 (funcGraphProp1) =>
% 121.84/16.06 ((
% 121.84/16.06 (funcGraphProp3) =>
% 121.84/16.06 ((
% 121.84/16.06 (funcGraphProp2) =>
% 121.84/16.06 ((
% 121.84/16.06 (funcextLem) =>
% 121.84/16.06 ((
% 121.84/16.06 (funcGraphProp4) =>
% 121.84/16.06 ((
% 121.84/16.06 (subbreln) =>
% 121.84/16.06 ((
% 121.84/16.06 (eqbreln) =>
% 121.84/16.06 ((
% 121.84/16.06 (funcext) =>
% 121.84/16.06 ((
% 121.84/16.06 (funcext2) =>
% 121.84/16.06 ((
% 121.84/16.06 (ap2apEq1) =>
% 121.84/16.06 ((
% 121.84/16.06 (ap2apEq2) =>
% 121.84/16.06 ((
% 121.84/16.06 (beta1) =>
% 121.84/16.06 ((
% 121.84/16.06 (eta1) =>
% 121.84/16.06 ((
% 121.84/16.06 (lam2lamEq) =>
% 121.84/16.06 ((
% 121.84/16.06 (beta2) =>
% 121.84/16.06 ((
% 121.84/16.06 (eta2) =>
% 121.84/16.06 ((
% 121.84/16.06 (iffalseProp1) =>
% 121.84/16.06 ((
% 121.84/16.06 (iffalseProp2) =>
% 121.84/16.06 ((
% 121.84/16.06 (iftrueProp1) =>
% 121.84/16.06 ((
% 121.84/16.06 (iftrueProp2) =>
% 121.84/16.06 ((
% 121.84/16.06 (ifSingleton) =>
% 121.84/16.06 ((
% 121.84/16.06 (ifp) =>
% 121.84/16.06 ((
% 121.84/16.06 (theeq) =>
% 121.84/16.06 ((
% 121.84/16.06 (iftrue) =>
% 121.84/16.06 ((
% 121.84/16.06 (iffalse) =>
% 121.84/16.06 ((
% 121.84/16.06 (iftrueorfalse) =>
% 121.84/16.06 ((
% 121.84/16.06 (binintersectT_lem) =>
% 121.84/16.06 ((
% 121.84/16.06 (binunionT_lem) =>
% 121.84/16.06 ((
% 121.84/16.06 (powersetT_lem) =>
% 121.84/16.06 ((
% 121.84/16.06 (setminusT_lem) =>
% 121.84/16.06 ((
% 121.84/16.06 (complementT_lem) =>
% 121.84/16.06 ((
% 121.84/16.06 (setextT) =>
% 121.84/16.06 ((
% 121.84/16.06 (subsetTI) =>
% 121.84/16.06 ((
% 121.84/16.06 (powersetTI1) =>
% 121.84/16.06 ((
% 121.84/16.06 (powersetTE1) =>
% 121.84/16.06 ((
% 121.84/16.06 (complementTI1) =>
% 121.84/16.06 ((
% 121.84/16.06 (complementTE1) =>
% 121.84/16.06 ((
% 121.84/16.06 (binintersectTELcontra) =>
% 121.84/16.06 ((
% 121.84/16.06 (binintersectTERcontra) =>
% 121.84/16.06 ((
% 121.84/16.06 (contrasubsetT) =>
% 121.84/16.06 ((
% 121.84/16.06 (contrasubsetT1) =>
% 121.84/16.06 ((
% 121.84/16.06 (contrasubsetT2) =>
% 121.84/16.06 ((
% 121.84/16.06 (contrasubsetT3) =>
% 121.84/16.06 ((
% 121.84/16.06 (doubleComplementI1) =>
% 121.84/16.06 ((
% 121.84/16.06 (doubleComplementE1) =>
% 121.84/16.06 ((
% 121.84/16.06 (doubleComplementSub1) =>
% 121.84/16.06 ((
% 121.84/16.06 (doubleComplementSub2) =>
% 121.84/16.06 ((
% 121.84/16.06 (doubleComplementEq) =>
% 121.84/16.06 ((
% 121.84/16.06 (complementTnotintersectT) =>
% 121.84/16.06 ((
% 121.84/16.06 (complementImpComplementIntersect) =>
% 121.84/16.06 ((
% 121.84/16.06 (complementSubsetComplementIntersect) =>
% 121.84/16.06 ((
% 121.84/16.06 (complementInPowersetComplementIntersect) =>
% 121.84/16.06 ((
% 121.84/16.06 (contraSubsetComplement) =>
% 121.84/16.06 ((
% 121.84/16.06 (complementTcontraSubset) =>
% 121.84/16.06 ((
% 121.84/16.06 (binunionTILcontra) =>
% 121.84/16.06 ((
% 121.84/16.06 (binunionTIRcontra) =>
% 121.84/16.06 ((
% 121.84/16.06 (inIntersectImpInUnion) =>
% 121.84/16.06 ((
% 121.84/16.06 (inIntersectImpInUnion2) =>
% 121.84/16.06 ((
% 121.84/16.06 (inIntersectImpInIntersectUnions) =>
% 121.84/16.06 ((
% 121.84/16.06 (intersectInPowersetIntersectUnions) =>
% 121.84/16.06 ((
% 121.84/16.06 (inComplementUnionImpNotIn1) =>
% 121.84/16.06 ((
% 121.84/16.06 (inComplementUnionImpInComplement1) =>
% 121.84/16.06 ((
% 121.84/16.06 (binunionTE) =>
% 121.84/16.06 ((
% 121.84/16.06 (binunionTEcontra) =>
% 121.84/16.06 ((
% 121.84/16.06 (demorgan2a1) =>
% 121.84/16.06 ((
% 121.84/16.06 (complementUnionInPowersetComplement) =>
% 121.84/16.06 ((
% 121.84/16.06 (demorgan2a2) =>
% 121.84/16.06 ((
% 121.84/16.06 (demorgan1a) =>
% 121.84/16.06 ((
% 121.84/16.06 (demorgan1b) =>
% 121.84/16.06 ((
% 121.84/16.06 (demorgan1) =>
% 121.84/16.06 ((
% 121.84/16.06 (demorgan2a) =>
% 121.84/16.06 ((
% 121.84/16.06 (demorgan2b2) =>
% 121.84/16.06 ((
% 121.84/16.06 (demorgan2b) =>
% 121.84/16.06 ((
% 121.84/16.06 (demorgan2) =>
% 121.84/16.06 ((
% 121.84/16.06 (woz13rule0) =>
% 121.84/16.06 ((
% 121.84/16.06 (woz13rule1) =>
% 121.84/16.06 ((
% 121.84/16.06 (woz13rule2) =>
% 121.84/16.06 ((
% 121.84/16.06 (woz13rule3) =>
% 121.84/16.06 ((
% 121.84/16.06 (woz13rule4) =>
% 121.84/16.06 ((
% 121.84/16.06 (woz1_1) =>
% 121.84/16.06 ((
% 121.84/16.06 (woz1_2) =>
% 121.84/16.06 ((
% 121.84/16.06 (woz1_3) =>
% 121.84/16.06 ((
% 121.84/16.06 (woz1_4) =>
% 121.84/16.06 ((
% 121.84/16.06 (woz1_5) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1all2) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1SetBreln1) =>
% 121.84/16.06 ((
% 121.84/16.06 (choice2fnsingleton) =>
% 121.84/16.06 ((
% 121.84/16.06 (setOfPairsIsBReln1) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1all1) =>
% 121.84/16.06 ((
% 121.84/16.06 (subbreln1) =>
% 121.84/16.06 ((
% 121.84/16.06 (eqbreln1) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1invprop) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1invI) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1invE) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1compprop) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1compI) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1compE) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1compEex) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1unionprop) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1unionIL) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1unionIR) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1unionI) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1unionE) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1unionEcases) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1unionCommutes) =>
% 121.84/16.06 ((
% 121.84/16.06 (woz2Ex) =>
% 121.84/16.06 ((
% 121.84/16.06 (woz2W) =>
% 121.84/16.06 ((
% 121.84/16.06 (woz2A) =>
% 121.84/16.06 ((
% 121.84/16.06 (woz2B) =>
% 121.84/16.06 ((
% 121.84/16.06 (image1Ex) =>
% 121.84/16.06 ((
% 121.84/16.06 (image1Ex1) =>
% 121.84/16.06 ((
% 121.84/16.06 (image1Equiv) =>
% 121.84/16.06 ((
% 121.84/16.06 (image1E) =>
% 121.84/16.06 ((
% 121.84/16.06 (image1I) =>
% 121.84/16.06 ((
% 121.84/16.06 (injFuncInInjFuncSet) =>
% 121.84/16.06 ((
% 121.84/16.06 (!!) @ (
% 121.84/16.06 (('#B') @ (
% 121.84/16.06 !!) @
% 121.84/16.06 (
% 121.84/16.06 (
% 121.84/16.06 ('#B') @ (
% 121.84/16.06 (
% 121.84/16.06 ('#B') @ (
% 121.84/16.06 !!))) @
% 121.84/16.06 (
% 121.84/16.06 (
% 121.84/16.06 ('#S') @ (
% 121.84/16.06 (
% 121.84/16.06 ('#B') @ (
% 121.84/16.06 '#S') @
% 121.84/16.06 (
% 121.84/16.06 (
% 121.84/16.06 ('#B') @ (
% 121.84/16.06 (
% 121.84/16.06 ('#B') @ (
% 121.84/16.06 '#S'))) @
% 121.84/16.06 (
% 121.84/16.06 (
% 121.84/16.06 ('#B') @ (
% 121.84/16.06 (
% 121.84/16.06 ('#B') @ (
% 121.84/16.06 (
% 121.84/16.06 ('#B') @ (
% 121.84/16.06 =>))))) @
% 121.84/16.06 (
% 121.84/16.06 (
% 121.84/16.06 ('#B') @ (
% 121.84/16.06 (
% 121.84/16.06 ('#B') @ (
% 121.84/16.06 (
% 121.84/16.06 ('#C') @ in)))) @
% 121.84/16.06 injFuncSet)))))))) @
% 121.84/16.06 (
% 121.84/16.06 (
% 121.84/16.06 ('#B') @ (
% 121.84/16.06 (
% 121.84/16.06 ('#B') @ (
% 121.84/16.06 (
% 121.84/16.06 ('#C') @ in)))) @
% 121.84/16.06 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 121.84/16.06 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl485])).
% 121.84/16.06 thf(zip_derived_cl507, plain,
% 121.84/16.06 (~ (((upairsetIR) =>
% 121.84/16.06 (((emptyE1) =>
% 121.84/16.06 (((vacuousDall) =>
% 121.84/16.06 (((quantDeMorgan1) =>
% 121.84/16.06 (((quantDeMorgan2) =>
% 121.84/16.06 (((quantDeMorgan3) =>
% 121.84/16.06 (((quantDeMorgan4) =>
% 121.84/16.06 (((prop2setI) =>
% 121.84/16.06 (((prop2set2propI) =>
% 121.84/16.06 (((notdexE) =>
% 121.84/16.06 (((notdallE) =>
% 121.84/16.06 (((exuI1) =>
% 121.84/16.06 (((exuI3) =>
% 121.84/16.06 (((exuI2) =>
% 121.84/16.06 (((inCongP) =>
% 121.84/16.06 (((in__Cong) =>
% 121.84/16.06 (((exuE3u) =>
% 121.84/16.06 (((exu__Cong) =>
% 121.84/16.06 (((setadjoin__Cong) =>
% 121.84/16.06 (((powerset__Cong) =>
% 121.84/16.06 (((setunion__Cong) =>
% 121.84/16.06 (((exuEu) =>
% 121.84/16.06 (((descr__Cong) =>
% 121.84/16.06 (((dsetconstr__Cong) =>
% 121.84/16.06 (((subsetI1) =>
% 121.84/16.06 (((eqimpsubset2) =>
% 121.84/16.06 (((eqimpsubset1) =>
% 121.84/16.06 (((subsetI2) =>
% 121.84/16.06 (((emptysetsubset) =>
% 121.84/16.06 (((subsetE) =>
% 121.84/16.06 ((
% 121.84/16.06 (subsetE2) =>
% 121.84/16.06 ((
% 121.84/16.06 (notsubsetI) =>
% 121.84/16.06 ((
% 121.84/16.06 (notequalI1) =>
% 121.84/16.06 ((
% 121.84/16.06 (notequalI2) =>
% 121.84/16.06 ((
% 121.84/16.06 (subsetRefl) =>
% 121.84/16.06 ((
% 121.84/16.06 (subsetTrans) =>
% 121.84/16.06 ((
% 121.84/16.06 (setadjoinSub) =>
% 121.84/16.06 ((
% 121.84/16.06 (setadjoinSub2) =>
% 121.84/16.06 ((
% 121.84/16.06 (subset2powerset) =>
% 121.84/16.06 ((
% 121.84/16.06 (setextsub) =>
% 121.84/16.06 ((
% 121.84/16.06 (subsetemptysetimpeq) =>
% 121.84/16.06 ((
% 121.84/16.06 (powersetI1) =>
% 121.84/16.06 ((
% 121.84/16.06 (powersetE1) =>
% 121.84/16.06 ((
% 121.84/16.06 (inPowerset) =>
% 121.84/16.06 ((
% 121.84/16.06 (powersetsubset) =>
% 121.84/16.06 ((
% 121.84/16.06 (sepInPowerset) =>
% 121.84/16.06 ((
% 121.84/16.06 (sepSubset) =>
% 121.84/16.06 ((
% 121.84/16.06 (binunionIL) =>
% 121.84/16.06 ((
% 121.84/16.06 (upairset2IR) =>
% 121.84/16.06 ((
% 121.84/16.06 (binunionIR) =>
% 121.84/16.06 ((
% 121.84/16.06 (binunionEcases) =>
% 121.84/16.06 ((
% 121.84/16.06 (binunionE) =>
% 121.84/16.06 ((
% 121.84/16.06 (binunionLsub) =>
% 121.84/16.06 ((
% 121.84/16.06 (binunionRsub) =>
% 121.84/16.06 ((
% 121.84/16.06 (binintersectI) =>
% 121.84/16.06 ((
% 121.84/16.06 (binintersectSubset5) =>
% 121.84/16.06 ((
% 121.84/16.06 (binintersectEL) =>
% 121.84/16.06 ((
% 121.84/16.06 (binintersectLsub) =>
% 121.84/16.06 ((
% 121.84/16.06 (binintersectSubset2) =>
% 121.84/16.06 ((
% 121.84/16.06 (binintersectSubset3) =>
% 121.84/16.06 ((
% 121.84/16.06 (binintersectER) =>
% 121.84/16.06 ((
% 121.84/16.06 (disjointsetsI1) =>
% 121.84/16.06 ((
% 121.84/16.06 (binintersectRsub) =>
% 121.84/16.06 ((
% 121.84/16.06 (binintersectSubset4) =>
% 121.84/16.06 ((
% 121.84/16.06 (binintersectSubset1) =>
% 121.84/16.06 ((
% 121.84/16.06 (bs114d) =>
% 121.84/16.06 ((
% 121.84/16.06 (setminusI) =>
% 121.84/16.06 ((
% 121.84/16.06 (setminusEL) =>
% 121.84/16.06 ((
% 121.84/16.06 (setminusER) =>
% 121.84/16.06 ((
% 121.84/16.06 (setminusSubset2) =>
% 121.84/16.06 ((
% 121.84/16.06 (setminusERneg) =>
% 121.84/16.06 ((
% 121.84/16.06 (setminusELneg) =>
% 121.84/16.06 ((
% 121.84/16.06 (setminusILneg) =>
% 121.84/16.06 ((
% 121.84/16.06 (setminusIRneg) =>
% 121.84/16.06 ((
% 121.84/16.06 (setminusLsub) =>
% 121.84/16.06 ((
% 121.84/16.06 (setminusSubset1) =>
% 121.84/16.06 ((
% 121.84/16.06 (symdiffE) =>
% 121.84/16.06 ((
% 121.84/16.06 (symdiffI1) =>
% 121.84/16.06 ((
% 121.84/16.06 (symdiffI2) =>
% 121.84/16.06 ((
% 121.84/16.06 (symdiffIneg1) =>
% 121.84/16.06 ((
% 121.84/16.06 (symdiffIneg2) =>
% 121.84/16.06 ((
% 121.84/16.06 (secondinupair) =>
% 121.84/16.06 ((
% 121.84/16.06 (setukpairIL) =>
% 121.84/16.06 ((
% 121.84/16.06 (setukpairIR) =>
% 121.84/16.06 ((
% 121.84/16.06 (kpairiskpair) =>
% 121.84/16.06 ((
% 121.84/16.06 (kpairp) =>
% 121.84/16.06 ((
% 121.84/16.06 (singletonsubset) =>
% 121.84/16.06 ((
% 121.84/16.06 (singletoninpowerset) =>
% 121.84/16.06 ((
% 121.84/16.06 (singletoninpowunion) =>
% 121.84/16.06 ((
% 121.84/16.06 (upairset2E) =>
% 121.84/16.06 ((
% 121.84/16.06 (upairsubunion) =>
% 121.84/16.06 ((
% 121.84/16.06 (upairinpowunion) =>
% 121.84/16.06 ((
% 121.84/16.06 (ubforcartprodlem1) =>
% 121.84/16.06 ((
% 121.84/16.06 (ubforcartprodlem2) =>
% 121.84/16.06 ((
% 121.84/16.06 (ubforcartprodlem3) =>
% 121.84/16.06 ((
% 121.84/16.06 (cartprodpairin) =>
% 121.84/16.06 ((
% 121.84/16.06 (cartprodmempair1) =>
% 121.84/16.06 ((
% 121.84/16.06 (cartprodmempair) =>
% 121.84/16.06 ((
% 121.84/16.06 (setunionE2) =>
% 121.84/16.06 ((
% 121.84/16.06 (setunionsingleton1) =>
% 121.84/16.06 ((
% 121.84/16.06 (setunionsingleton2) =>
% 121.84/16.06 ((
% 121.84/16.06 (setunionsingleton) =>
% 121.84/16.06 ((
% 121.84/16.06 (singletonprop) =>
% 121.84/16.06 ((
% 121.84/16.06 (ex1E1) =>
% 121.84/16.06 ((
% 121.84/16.06 (ex1I) =>
% 121.84/16.06 ((
% 121.84/16.06 (ex1I2) =>
% 121.84/16.06 ((
% 121.84/16.06 (singletonsuniq) =>
% 121.84/16.06 ((
% 121.84/16.06 (setukpairinjL1) =>
% 121.84/16.06 ((
% 121.84/16.06 (kfstsingleton) =>
% 121.84/16.06 ((
% 121.84/16.06 (theprop) =>
% 121.84/16.06 ((
% 121.84/16.06 (kfstpairEq) =>
% 121.84/16.06 ((
% 121.84/16.06 (cartprodfstin) =>
% 121.84/16.06 ((
% 121.84/16.06 (setukpairinjL2) =>
% 121.84/16.06 ((
% 121.84/16.06 (setukpairinjL) =>
% 121.84/16.06 ((
% 121.84/16.06 (setukpairinjR11) =>
% 121.84/16.06 ((
% 121.84/16.06 (setukpairinjR12) =>
% 121.84/16.06 ((
% 121.84/16.06 (setukpairinjR1) =>
% 121.84/16.06 ((
% 121.84/16.06 (upairequniteq) =>
% 121.84/16.06 ((
% 121.84/16.06 (setukpairinjR2) =>
% 121.84/16.06 ((
% 121.84/16.06 (setukpairinjR) =>
% 121.84/16.06 ((
% 121.84/16.06 (ksndsingleton) =>
% 121.84/16.06 ((
% 121.84/16.06 (ksndpairEq) =>
% 121.84/16.06 ((
% 121.84/16.06 (kpairsurjEq) =>
% 121.84/16.06 ((
% 121.84/16.06 (cartprodsndin) =>
% 121.84/16.06 ((
% 121.84/16.06 (cartprodpairmemEL) =>
% 121.84/16.06 ((
% 121.84/16.06 (cartprodpairmemER) =>
% 121.84/16.06 ((
% 121.84/16.06 (cartprodmempaircEq) =>
% 121.84/16.06 ((
% 121.84/16.06 (cartprodfstpairEq) =>
% 121.84/16.06 ((
% 121.84/16.06 (cartprodsndpairEq) =>
% 121.84/16.06 ((
% 121.84/16.06 (cartprodpairsurjEq) =>
% 121.84/16.06 ((
% 121.84/16.06 (dpsetconstrI) =>
% 121.84/16.06 ((
% 121.84/16.06 (dpsetconstrSub) =>
% 121.84/16.06 ((
% 121.84/16.06 (setOfPairsIsBReln) =>
% 121.84/16.06 ((
% 121.84/16.06 (dpsetconstrERa) =>
% 121.84/16.06 ((
% 121.84/16.06 (dpsetconstrEL1) =>
% 121.84/16.06 ((
% 121.84/16.06 (dpsetconstrEL2) =>
% 121.84/16.06 ((
% 121.84/16.06 (dpsetconstrER) =>
% 121.84/16.06 ((
% 121.84/16.06 (funcImageSingleton) =>
% 121.84/16.06 ((
% 121.84/16.06 (apProp) =>
% 121.84/16.06 ((
% 121.84/16.06 (app) =>
% 121.84/16.06 ((
% 121.84/16.06 (infuncsetfunc) =>
% 121.84/16.06 ((
% 121.84/16.06 (ap2p) =>
% 121.84/16.06 ((
% 121.84/16.06 (funcinfuncset) =>
% 121.84/16.06 ((
% 121.84/16.06 (lamProp) =>
% 121.84/16.06 ((
% 121.84/16.06 (lamp) =>
% 121.84/16.06 ((
% 121.84/16.06 (lam2p) =>
% 121.84/16.06 ((
% 121.84/16.06 (brelnall1) =>
% 121.84/16.06 ((
% 121.84/16.06 (brelnall2) =>
% 121.84/16.06 ((
% 121.84/16.06 (ex1E2) =>
% 121.84/16.06 ((
% 121.84/16.06 (funcGraphProp1) =>
% 121.84/16.06 ((
% 121.84/16.06 (funcGraphProp3) =>
% 121.84/16.06 ((
% 121.84/16.06 (funcGraphProp2) =>
% 121.84/16.06 ((
% 121.84/16.06 (funcextLem) =>
% 121.84/16.06 ((
% 121.84/16.06 (funcGraphProp4) =>
% 121.84/16.06 ((
% 121.84/16.06 (subbreln) =>
% 121.84/16.06 ((
% 121.84/16.06 (eqbreln) =>
% 121.84/16.06 ((
% 121.84/16.06 (funcext) =>
% 121.84/16.06 ((
% 121.84/16.06 (funcext2) =>
% 121.84/16.06 ((
% 121.84/16.06 (ap2apEq1) =>
% 121.84/16.06 ((
% 121.84/16.06 (ap2apEq2) =>
% 121.84/16.06 ((
% 121.84/16.06 (beta1) =>
% 121.84/16.06 ((
% 121.84/16.06 (eta1) =>
% 121.84/16.06 ((
% 121.84/16.06 (lam2lamEq) =>
% 121.84/16.06 ((
% 121.84/16.06 (beta2) =>
% 121.84/16.06 ((
% 121.84/16.06 (eta2) =>
% 121.84/16.06 ((
% 121.84/16.06 (iffalseProp1) =>
% 121.84/16.06 ((
% 121.84/16.06 (iffalseProp2) =>
% 121.84/16.06 ((
% 121.84/16.06 (iftrueProp1) =>
% 121.84/16.06 ((
% 121.84/16.06 (iftrueProp2) =>
% 121.84/16.06 ((
% 121.84/16.06 (ifSingleton) =>
% 121.84/16.06 ((
% 121.84/16.06 (ifp) =>
% 121.84/16.06 ((
% 121.84/16.06 (theeq) =>
% 121.84/16.06 ((
% 121.84/16.06 (iftrue) =>
% 121.84/16.06 ((
% 121.84/16.06 (iffalse) =>
% 121.84/16.06 ((
% 121.84/16.06 (iftrueorfalse) =>
% 121.84/16.06 ((
% 121.84/16.06 (binintersectT_lem) =>
% 121.84/16.06 ((
% 121.84/16.06 (binunionT_lem) =>
% 121.84/16.06 ((
% 121.84/16.06 (powersetT_lem) =>
% 121.84/16.06 ((
% 121.84/16.06 (setminusT_lem) =>
% 121.84/16.06 ((
% 121.84/16.06 (complementT_lem) =>
% 121.84/16.06 ((
% 121.84/16.06 (setextT) =>
% 121.84/16.06 ((
% 121.84/16.06 (subsetTI) =>
% 121.84/16.06 ((
% 121.84/16.06 (powersetTI1) =>
% 121.84/16.06 ((
% 121.84/16.06 (powersetTE1) =>
% 121.84/16.06 ((
% 121.84/16.06 (complementTI1) =>
% 121.84/16.06 ((
% 121.84/16.06 (complementTE1) =>
% 121.84/16.06 ((
% 121.84/16.06 (binintersectTELcontra) =>
% 121.84/16.06 ((
% 121.84/16.06 (binintersectTERcontra) =>
% 121.84/16.06 ((
% 121.84/16.06 (contrasubsetT) =>
% 121.84/16.06 ((
% 121.84/16.06 (contrasubsetT1) =>
% 121.84/16.06 ((
% 121.84/16.06 (contrasubsetT2) =>
% 121.84/16.06 ((
% 121.84/16.06 (contrasubsetT3) =>
% 121.84/16.06 ((
% 121.84/16.06 (doubleComplementI1) =>
% 121.84/16.06 ((
% 121.84/16.06 (doubleComplementE1) =>
% 121.84/16.06 ((
% 121.84/16.06 (doubleComplementSub1) =>
% 121.84/16.06 ((
% 121.84/16.06 (doubleComplementSub2) =>
% 121.84/16.06 ((
% 121.84/16.06 (doubleComplementEq) =>
% 121.84/16.06 ((
% 121.84/16.06 (complementTnotintersectT) =>
% 121.84/16.06 ((
% 121.84/16.06 (complementImpComplementIntersect) =>
% 121.84/16.06 ((
% 121.84/16.06 (complementSubsetComplementIntersect) =>
% 121.84/16.06 ((
% 121.84/16.06 (complementInPowersetComplementIntersect) =>
% 121.84/16.06 ((
% 121.84/16.06 (contraSubsetComplement) =>
% 121.84/16.06 ((
% 121.84/16.06 (complementTcontraSubset) =>
% 121.84/16.06 ((
% 121.84/16.06 (binunionTILcontra) =>
% 121.84/16.06 ((
% 121.84/16.06 (binunionTIRcontra) =>
% 121.84/16.06 ((
% 121.84/16.06 (inIntersectImpInUnion) =>
% 121.84/16.06 ((
% 121.84/16.06 (inIntersectImpInUnion2) =>
% 121.84/16.06 ((
% 121.84/16.06 (inIntersectImpInIntersectUnions) =>
% 121.84/16.06 ((
% 121.84/16.06 (intersectInPowersetIntersectUnions) =>
% 121.84/16.06 ((
% 121.84/16.06 (inComplementUnionImpNotIn1) =>
% 121.84/16.06 ((
% 121.84/16.06 (inComplementUnionImpInComplement1) =>
% 121.84/16.06 ((
% 121.84/16.06 (binunionTE) =>
% 121.84/16.06 ((
% 121.84/16.06 (binunionTEcontra) =>
% 121.84/16.06 ((
% 121.84/16.06 (demorgan2a1) =>
% 121.84/16.06 ((
% 121.84/16.06 (complementUnionInPowersetComplement) =>
% 121.84/16.06 ((
% 121.84/16.06 (demorgan2a2) =>
% 121.84/16.06 ((
% 121.84/16.06 (demorgan1a) =>
% 121.84/16.06 ((
% 121.84/16.06 (demorgan1b) =>
% 121.84/16.06 ((
% 121.84/16.06 (demorgan1) =>
% 121.84/16.06 ((
% 121.84/16.06 (demorgan2a) =>
% 121.84/16.06 ((
% 121.84/16.06 (demorgan2b2) =>
% 121.84/16.06 ((
% 121.84/16.06 (demorgan2b) =>
% 121.84/16.06 ((
% 121.84/16.06 (demorgan2) =>
% 121.84/16.06 ((
% 121.84/16.06 (woz13rule0) =>
% 121.84/16.06 ((
% 121.84/16.06 (woz13rule1) =>
% 121.84/16.06 ((
% 121.84/16.06 (woz13rule2) =>
% 121.84/16.06 ((
% 121.84/16.06 (woz13rule3) =>
% 121.84/16.06 ((
% 121.84/16.06 (woz13rule4) =>
% 121.84/16.06 ((
% 121.84/16.06 (woz1_1) =>
% 121.84/16.06 ((
% 121.84/16.06 (woz1_2) =>
% 121.84/16.06 ((
% 121.84/16.06 (woz1_3) =>
% 121.84/16.06 ((
% 121.84/16.06 (woz1_4) =>
% 121.84/16.06 ((
% 121.84/16.06 (woz1_5) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1all2) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1SetBreln1) =>
% 121.84/16.06 ((
% 121.84/16.06 (choice2fnsingleton) =>
% 121.84/16.06 ((
% 121.84/16.06 (setOfPairsIsBReln1) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1all1) =>
% 121.84/16.06 ((
% 121.84/16.06 (subbreln1) =>
% 121.84/16.06 ((
% 121.84/16.06 (eqbreln1) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1invprop) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1invI) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1invE) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1compprop) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1compI) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1compE) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1compEex) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1unionprop) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1unionIL) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1unionIR) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1unionI) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1unionE) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1unionEcases) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1unionCommutes) =>
% 121.84/16.06 ((
% 121.84/16.06 (woz2Ex) =>
% 121.84/16.06 ((
% 121.84/16.06 (woz2W) =>
% 121.84/16.06 ((
% 121.84/16.06 (woz2A) =>
% 121.84/16.06 ((
% 121.84/16.06 (woz2B) =>
% 121.84/16.06 ((
% 121.84/16.06 (image1Ex) =>
% 121.84/16.06 ((
% 121.84/16.06 (image1Ex1) =>
% 121.84/16.06 ((
% 121.84/16.06 (image1Equiv) =>
% 121.84/16.06 ((
% 121.84/16.06 (image1E) =>
% 121.84/16.06 ((
% 121.84/16.06 (image1I) =>
% 121.84/16.06 ((
% 121.84/16.06 (injFuncInInjFuncSet) =>
% 121.84/16.06 ((
% 121.84/16.06 (!!) @ (
% 121.84/16.06 (('#B') @ (
% 121.84/16.06 !!) @
% 121.84/16.06 (
% 121.84/16.06 (
% 121.84/16.06 ('#B') @ (
% 121.84/16.06 (
% 121.84/16.06 ('#B') @ (
% 121.84/16.06 !!))) @
% 121.84/16.06 (
% 121.84/16.06 (
% 121.84/16.06 ('#S') @ (
% 121.84/16.06 (
% 121.84/16.06 ('#B') @ (
% 121.84/16.06 '#S') @
% 121.84/16.06 (
% 121.84/16.06 (
% 121.84/16.06 ('#B') @ (
% 121.84/16.06 (
% 121.84/16.06 ('#B') @ (
% 121.84/16.06 '#S'))) @
% 121.84/16.06 (
% 121.84/16.06 (
% 121.84/16.06 ('#B') @ (
% 121.84/16.06 (
% 121.84/16.06 ('#B') @ (
% 121.84/16.06 (
% 121.84/16.06 ('#B') @ (
% 121.84/16.06 =>))))) @
% 121.84/16.06 (
% 121.84/16.06 (
% 121.84/16.06 ('#B') @ (
% 121.84/16.06 (
% 121.84/16.06 ('#B') @ (
% 121.84/16.06 (
% 121.84/16.06 ('#C') @ in)))) @
% 121.84/16.06 injFuncSet)))))))) @
% 121.84/16.06 (
% 121.84/16.06 (
% 121.84/16.06 ('#B') @ (
% 121.84/16.06 (
% 121.84/16.06 ('#B') @ (
% 121.84/16.06 (
% 121.84/16.06 ('#C') @ in)))) @
% 121.84/16.06 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 121.84/16.06 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl496])).
% 121.84/16.06 thf(zip_derived_cl517, plain,
% 121.84/16.06 (~ (((emptyE1) =>
% 121.84/16.06 (((vacuousDall) =>
% 121.84/16.06 (((quantDeMorgan1) =>
% 121.84/16.06 (((quantDeMorgan2) =>
% 121.84/16.06 (((quantDeMorgan3) =>
% 121.84/16.06 (((quantDeMorgan4) =>
% 121.84/16.06 (((prop2setI) =>
% 121.84/16.06 (((prop2set2propI) =>
% 121.84/16.06 (((notdexE) =>
% 121.84/16.06 (((notdallE) =>
% 121.84/16.06 (((exuI1) =>
% 121.84/16.06 (((exuI3) =>
% 121.84/16.06 (((exuI2) =>
% 121.84/16.06 (((inCongP) =>
% 121.84/16.06 (((in__Cong) =>
% 121.84/16.06 (((exuE3u) =>
% 121.84/16.06 (((exu__Cong) =>
% 121.84/16.06 (((setadjoin__Cong) =>
% 121.84/16.06 (((powerset__Cong) =>
% 121.84/16.06 (((setunion__Cong) =>
% 121.84/16.06 (((exuEu) =>
% 121.84/16.06 (((descr__Cong) =>
% 121.84/16.06 (((dsetconstr__Cong) =>
% 121.84/16.06 (((subsetI1) =>
% 121.84/16.06 (((eqimpsubset2) =>
% 121.84/16.06 (((eqimpsubset1) =>
% 121.84/16.06 (((subsetI2) =>
% 121.84/16.06 (((emptysetsubset) =>
% 121.84/16.06 (((subsetE) =>
% 121.84/16.06 (((subsetE2) =>
% 121.84/16.06 ((
% 121.84/16.06 (notsubsetI) =>
% 121.84/16.06 ((
% 121.84/16.06 (notequalI1) =>
% 121.84/16.06 ((
% 121.84/16.06 (notequalI2) =>
% 121.84/16.06 ((
% 121.84/16.06 (subsetRefl) =>
% 121.84/16.06 ((
% 121.84/16.06 (subsetTrans) =>
% 121.84/16.06 ((
% 121.84/16.06 (setadjoinSub) =>
% 121.84/16.06 ((
% 121.84/16.06 (setadjoinSub2) =>
% 121.84/16.06 ((
% 121.84/16.06 (subset2powerset) =>
% 121.84/16.06 ((
% 121.84/16.06 (setextsub) =>
% 121.84/16.06 ((
% 121.84/16.06 (subsetemptysetimpeq) =>
% 121.84/16.06 ((
% 121.84/16.06 (powersetI1) =>
% 121.84/16.06 ((
% 121.84/16.06 (powersetE1) =>
% 121.84/16.06 ((
% 121.84/16.06 (inPowerset) =>
% 121.84/16.06 ((
% 121.84/16.06 (powersetsubset) =>
% 121.84/16.06 ((
% 121.84/16.06 (sepInPowerset) =>
% 121.84/16.06 ((
% 121.84/16.06 (sepSubset) =>
% 121.84/16.06 ((
% 121.84/16.06 (binunionIL) =>
% 121.84/16.06 ((
% 121.84/16.06 (upairset2IR) =>
% 121.84/16.06 ((
% 121.84/16.06 (binunionIR) =>
% 121.84/16.06 ((
% 121.84/16.06 (binunionEcases) =>
% 121.84/16.06 ((
% 121.84/16.06 (binunionE) =>
% 121.84/16.06 ((
% 121.84/16.06 (binunionLsub) =>
% 121.84/16.06 ((
% 121.84/16.06 (binunionRsub) =>
% 121.84/16.06 ((
% 121.84/16.06 (binintersectI) =>
% 121.84/16.06 ((
% 121.84/16.06 (binintersectSubset5) =>
% 121.84/16.06 ((
% 121.84/16.06 (binintersectEL) =>
% 121.84/16.06 ((
% 121.84/16.06 (binintersectLsub) =>
% 121.84/16.06 ((
% 121.84/16.06 (binintersectSubset2) =>
% 121.84/16.06 ((
% 121.84/16.06 (binintersectSubset3) =>
% 121.84/16.06 ((
% 121.84/16.06 (binintersectER) =>
% 121.84/16.06 ((
% 121.84/16.06 (disjointsetsI1) =>
% 121.84/16.06 ((
% 121.84/16.06 (binintersectRsub) =>
% 121.84/16.06 ((
% 121.84/16.06 (binintersectSubset4) =>
% 121.84/16.06 ((
% 121.84/16.06 (binintersectSubset1) =>
% 121.84/16.06 ((
% 121.84/16.06 (bs114d) =>
% 121.84/16.06 ((
% 121.84/16.06 (setminusI) =>
% 121.84/16.06 ((
% 121.84/16.06 (setminusEL) =>
% 121.84/16.06 ((
% 121.84/16.06 (setminusER) =>
% 121.84/16.06 ((
% 121.84/16.06 (setminusSubset2) =>
% 121.84/16.06 ((
% 121.84/16.06 (setminusERneg) =>
% 121.84/16.06 ((
% 121.84/16.06 (setminusELneg) =>
% 121.84/16.06 ((
% 121.84/16.06 (setminusILneg) =>
% 121.84/16.06 ((
% 121.84/16.06 (setminusIRneg) =>
% 121.84/16.06 ((
% 121.84/16.06 (setminusLsub) =>
% 121.84/16.06 ((
% 121.84/16.06 (setminusSubset1) =>
% 121.84/16.06 ((
% 121.84/16.06 (symdiffE) =>
% 121.84/16.06 ((
% 121.84/16.06 (symdiffI1) =>
% 121.84/16.06 ((
% 121.84/16.06 (symdiffI2) =>
% 121.84/16.06 ((
% 121.84/16.06 (symdiffIneg1) =>
% 121.84/16.06 ((
% 121.84/16.06 (symdiffIneg2) =>
% 121.84/16.06 ((
% 121.84/16.06 (secondinupair) =>
% 121.84/16.06 ((
% 121.84/16.06 (setukpairIL) =>
% 121.84/16.06 ((
% 121.84/16.06 (setukpairIR) =>
% 121.84/16.06 ((
% 121.84/16.06 (kpairiskpair) =>
% 121.84/16.06 ((
% 121.84/16.06 (kpairp) =>
% 121.84/16.06 ((
% 121.84/16.06 (singletonsubset) =>
% 121.84/16.06 ((
% 121.84/16.06 (singletoninpowerset) =>
% 121.84/16.06 ((
% 121.84/16.06 (singletoninpowunion) =>
% 121.84/16.06 ((
% 121.84/16.06 (upairset2E) =>
% 121.84/16.06 ((
% 121.84/16.06 (upairsubunion) =>
% 121.84/16.06 ((
% 121.84/16.06 (upairinpowunion) =>
% 121.84/16.06 ((
% 121.84/16.06 (ubforcartprodlem1) =>
% 121.84/16.06 ((
% 121.84/16.06 (ubforcartprodlem2) =>
% 121.84/16.06 ((
% 121.84/16.06 (ubforcartprodlem3) =>
% 121.84/16.06 ((
% 121.84/16.06 (cartprodpairin) =>
% 121.84/16.06 ((
% 121.84/16.06 (cartprodmempair1) =>
% 121.84/16.06 ((
% 121.84/16.06 (cartprodmempair) =>
% 121.84/16.06 ((
% 121.84/16.06 (setunionE2) =>
% 121.84/16.06 ((
% 121.84/16.06 (setunionsingleton1) =>
% 121.84/16.06 ((
% 121.84/16.06 (setunionsingleton2) =>
% 121.84/16.06 ((
% 121.84/16.06 (setunionsingleton) =>
% 121.84/16.06 ((
% 121.84/16.06 (singletonprop) =>
% 121.84/16.06 ((
% 121.84/16.06 (ex1E1) =>
% 121.84/16.06 ((
% 121.84/16.06 (ex1I) =>
% 121.84/16.06 ((
% 121.84/16.06 (ex1I2) =>
% 121.84/16.06 ((
% 121.84/16.06 (singletonsuniq) =>
% 121.84/16.06 ((
% 121.84/16.06 (setukpairinjL1) =>
% 121.84/16.06 ((
% 121.84/16.06 (kfstsingleton) =>
% 121.84/16.06 ((
% 121.84/16.06 (theprop) =>
% 121.84/16.06 ((
% 121.84/16.06 (kfstpairEq) =>
% 121.84/16.06 ((
% 121.84/16.06 (cartprodfstin) =>
% 121.84/16.06 ((
% 121.84/16.06 (setukpairinjL2) =>
% 121.84/16.06 ((
% 121.84/16.06 (setukpairinjL) =>
% 121.84/16.06 ((
% 121.84/16.06 (setukpairinjR11) =>
% 121.84/16.06 ((
% 121.84/16.06 (setukpairinjR12) =>
% 121.84/16.06 ((
% 121.84/16.06 (setukpairinjR1) =>
% 121.84/16.06 ((
% 121.84/16.06 (upairequniteq) =>
% 121.84/16.06 ((
% 121.84/16.06 (setukpairinjR2) =>
% 121.84/16.06 ((
% 121.84/16.06 (setukpairinjR) =>
% 121.84/16.06 ((
% 121.84/16.06 (ksndsingleton) =>
% 121.84/16.06 ((
% 121.84/16.06 (ksndpairEq) =>
% 121.84/16.06 ((
% 121.84/16.06 (kpairsurjEq) =>
% 121.84/16.06 ((
% 121.84/16.06 (cartprodsndin) =>
% 121.84/16.06 ((
% 121.84/16.06 (cartprodpairmemEL) =>
% 121.84/16.06 ((
% 121.84/16.06 (cartprodpairmemER) =>
% 121.84/16.06 ((
% 121.84/16.06 (cartprodmempaircEq) =>
% 121.84/16.06 ((
% 121.84/16.06 (cartprodfstpairEq) =>
% 121.84/16.06 ((
% 121.84/16.06 (cartprodsndpairEq) =>
% 121.84/16.06 ((
% 121.84/16.06 (cartprodpairsurjEq) =>
% 121.84/16.06 ((
% 121.84/16.06 (dpsetconstrI) =>
% 121.84/16.06 ((
% 121.84/16.06 (dpsetconstrSub) =>
% 121.84/16.06 ((
% 121.84/16.06 (setOfPairsIsBReln) =>
% 121.84/16.06 ((
% 121.84/16.06 (dpsetconstrERa) =>
% 121.84/16.06 ((
% 121.84/16.06 (dpsetconstrEL1) =>
% 121.84/16.06 ((
% 121.84/16.06 (dpsetconstrEL2) =>
% 121.84/16.06 ((
% 121.84/16.06 (dpsetconstrER) =>
% 121.84/16.06 ((
% 121.84/16.06 (funcImageSingleton) =>
% 121.84/16.06 ((
% 121.84/16.06 (apProp) =>
% 121.84/16.06 ((
% 121.84/16.06 (app) =>
% 121.84/16.06 ((
% 121.84/16.06 (infuncsetfunc) =>
% 121.84/16.06 ((
% 121.84/16.06 (ap2p) =>
% 121.84/16.06 ((
% 121.84/16.06 (funcinfuncset) =>
% 121.84/16.06 ((
% 121.84/16.06 (lamProp) =>
% 121.84/16.06 ((
% 121.84/16.06 (lamp) =>
% 121.84/16.06 ((
% 121.84/16.06 (lam2p) =>
% 121.84/16.06 ((
% 121.84/16.06 (brelnall1) =>
% 121.84/16.06 ((
% 121.84/16.06 (brelnall2) =>
% 121.84/16.06 ((
% 121.84/16.06 (ex1E2) =>
% 121.84/16.06 ((
% 121.84/16.06 (funcGraphProp1) =>
% 121.84/16.06 ((
% 121.84/16.06 (funcGraphProp3) =>
% 121.84/16.06 ((
% 121.84/16.06 (funcGraphProp2) =>
% 121.84/16.06 ((
% 121.84/16.06 (funcextLem) =>
% 121.84/16.06 ((
% 121.84/16.06 (funcGraphProp4) =>
% 121.84/16.06 ((
% 121.84/16.06 (subbreln) =>
% 121.84/16.06 ((
% 121.84/16.06 (eqbreln) =>
% 121.84/16.06 ((
% 121.84/16.06 (funcext) =>
% 121.84/16.06 ((
% 121.84/16.06 (funcext2) =>
% 121.84/16.06 ((
% 121.84/16.06 (ap2apEq1) =>
% 121.84/16.06 ((
% 121.84/16.06 (ap2apEq2) =>
% 121.84/16.06 ((
% 121.84/16.06 (beta1) =>
% 121.84/16.06 ((
% 121.84/16.06 (eta1) =>
% 121.84/16.06 ((
% 121.84/16.06 (lam2lamEq) =>
% 121.84/16.06 ((
% 121.84/16.06 (beta2) =>
% 121.84/16.06 ((
% 121.84/16.06 (eta2) =>
% 121.84/16.06 ((
% 121.84/16.06 (iffalseProp1) =>
% 121.84/16.06 ((
% 121.84/16.06 (iffalseProp2) =>
% 121.84/16.06 ((
% 121.84/16.06 (iftrueProp1) =>
% 121.84/16.06 ((
% 121.84/16.06 (iftrueProp2) =>
% 121.84/16.06 ((
% 121.84/16.06 (ifSingleton) =>
% 121.84/16.06 ((
% 121.84/16.06 (ifp) =>
% 121.84/16.06 ((
% 121.84/16.06 (theeq) =>
% 121.84/16.06 ((
% 121.84/16.06 (iftrue) =>
% 121.84/16.06 ((
% 121.84/16.06 (iffalse) =>
% 121.84/16.06 ((
% 121.84/16.06 (iftrueorfalse) =>
% 121.84/16.06 ((
% 121.84/16.06 (binintersectT_lem) =>
% 121.84/16.06 ((
% 121.84/16.06 (binunionT_lem) =>
% 121.84/16.06 ((
% 121.84/16.06 (powersetT_lem) =>
% 121.84/16.06 ((
% 121.84/16.06 (setminusT_lem) =>
% 121.84/16.06 ((
% 121.84/16.06 (complementT_lem) =>
% 121.84/16.06 ((
% 121.84/16.06 (setextT) =>
% 121.84/16.06 ((
% 121.84/16.06 (subsetTI) =>
% 121.84/16.06 ((
% 121.84/16.06 (powersetTI1) =>
% 121.84/16.06 ((
% 121.84/16.06 (powersetTE1) =>
% 121.84/16.06 ((
% 121.84/16.06 (complementTI1) =>
% 121.84/16.06 ((
% 121.84/16.06 (complementTE1) =>
% 121.84/16.06 ((
% 121.84/16.06 (binintersectTELcontra) =>
% 121.84/16.06 ((
% 121.84/16.06 (binintersectTERcontra) =>
% 121.84/16.06 ((
% 121.84/16.06 (contrasubsetT) =>
% 121.84/16.06 ((
% 121.84/16.06 (contrasubsetT1) =>
% 121.84/16.06 ((
% 121.84/16.06 (contrasubsetT2) =>
% 121.84/16.06 ((
% 121.84/16.06 (contrasubsetT3) =>
% 121.84/16.06 ((
% 121.84/16.06 (doubleComplementI1) =>
% 121.84/16.06 ((
% 121.84/16.06 (doubleComplementE1) =>
% 121.84/16.06 ((
% 121.84/16.06 (doubleComplementSub1) =>
% 121.84/16.06 ((
% 121.84/16.06 (doubleComplementSub2) =>
% 121.84/16.06 ((
% 121.84/16.06 (doubleComplementEq) =>
% 121.84/16.06 ((
% 121.84/16.06 (complementTnotintersectT) =>
% 121.84/16.06 ((
% 121.84/16.06 (complementImpComplementIntersect) =>
% 121.84/16.06 ((
% 121.84/16.06 (complementSubsetComplementIntersect) =>
% 121.84/16.06 ((
% 121.84/16.06 (complementInPowersetComplementIntersect) =>
% 121.84/16.06 ((
% 121.84/16.06 (contraSubsetComplement) =>
% 121.84/16.06 ((
% 121.84/16.06 (complementTcontraSubset) =>
% 121.84/16.06 ((
% 121.84/16.06 (binunionTILcontra) =>
% 121.84/16.06 ((
% 121.84/16.06 (binunionTIRcontra) =>
% 121.84/16.06 ((
% 121.84/16.06 (inIntersectImpInUnion) =>
% 121.84/16.06 ((
% 121.84/16.06 (inIntersectImpInUnion2) =>
% 121.84/16.06 ((
% 121.84/16.06 (inIntersectImpInIntersectUnions) =>
% 121.84/16.06 ((
% 121.84/16.06 (intersectInPowersetIntersectUnions) =>
% 121.84/16.06 ((
% 121.84/16.06 (inComplementUnionImpNotIn1) =>
% 121.84/16.06 ((
% 121.84/16.06 (inComplementUnionImpInComplement1) =>
% 121.84/16.06 ((
% 121.84/16.06 (binunionTE) =>
% 121.84/16.06 ((
% 121.84/16.06 (binunionTEcontra) =>
% 121.84/16.06 ((
% 121.84/16.06 (demorgan2a1) =>
% 121.84/16.06 ((
% 121.84/16.06 (complementUnionInPowersetComplement) =>
% 121.84/16.06 ((
% 121.84/16.06 (demorgan2a2) =>
% 121.84/16.06 ((
% 121.84/16.06 (demorgan1a) =>
% 121.84/16.06 ((
% 121.84/16.06 (demorgan1b) =>
% 121.84/16.06 ((
% 121.84/16.06 (demorgan1) =>
% 121.84/16.06 ((
% 121.84/16.06 (demorgan2a) =>
% 121.84/16.06 ((
% 121.84/16.06 (demorgan2b2) =>
% 121.84/16.06 ((
% 121.84/16.06 (demorgan2b) =>
% 121.84/16.06 ((
% 121.84/16.06 (demorgan2) =>
% 121.84/16.06 ((
% 121.84/16.06 (woz13rule0) =>
% 121.84/16.06 ((
% 121.84/16.06 (woz13rule1) =>
% 121.84/16.06 ((
% 121.84/16.06 (woz13rule2) =>
% 121.84/16.06 ((
% 121.84/16.06 (woz13rule3) =>
% 121.84/16.06 ((
% 121.84/16.06 (woz13rule4) =>
% 121.84/16.06 ((
% 121.84/16.06 (woz1_1) =>
% 121.84/16.06 ((
% 121.84/16.06 (woz1_2) =>
% 121.84/16.06 ((
% 121.84/16.06 (woz1_3) =>
% 121.84/16.06 ((
% 121.84/16.06 (woz1_4) =>
% 121.84/16.06 ((
% 121.84/16.06 (woz1_5) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1all2) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1SetBreln1) =>
% 121.84/16.06 ((
% 121.84/16.06 (choice2fnsingleton) =>
% 121.84/16.06 ((
% 121.84/16.06 (setOfPairsIsBReln1) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1all1) =>
% 121.84/16.06 ((
% 121.84/16.06 (subbreln1) =>
% 121.84/16.06 ((
% 121.84/16.06 (eqbreln1) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1invprop) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1invI) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1invE) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1compprop) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1compI) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1compE) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1compEex) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1unionprop) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1unionIL) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1unionIR) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1unionI) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1unionE) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1unionEcases) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1unionCommutes) =>
% 121.84/16.06 ((
% 121.84/16.06 (woz2Ex) =>
% 121.84/16.06 ((
% 121.84/16.06 (woz2W) =>
% 121.84/16.06 ((
% 121.84/16.06 (woz2A) =>
% 121.84/16.06 ((
% 121.84/16.06 (woz2B) =>
% 121.84/16.06 ((
% 121.84/16.06 (image1Ex) =>
% 121.84/16.06 ((
% 121.84/16.06 (image1Ex1) =>
% 121.84/16.06 ((
% 121.84/16.06 (image1Equiv) =>
% 121.84/16.06 ((
% 121.84/16.06 (image1E) =>
% 121.84/16.06 ((
% 121.84/16.06 (image1I) =>
% 121.84/16.06 ((
% 121.84/16.06 (injFuncInInjFuncSet) =>
% 121.84/16.06 ((
% 121.84/16.06 (!!) @ (
% 121.84/16.06 (('#B') @ (
% 121.84/16.06 !!) @
% 121.84/16.06 (
% 121.84/16.06 (
% 121.84/16.06 ('#B') @ (
% 121.84/16.06 (
% 121.84/16.06 ('#B') @ (
% 121.84/16.06 !!))) @
% 121.84/16.06 (
% 121.84/16.06 (
% 121.84/16.06 ('#S') @ (
% 121.84/16.06 (
% 121.84/16.06 ('#B') @ (
% 121.84/16.06 '#S') @
% 121.84/16.06 (
% 121.84/16.06 (
% 121.84/16.06 ('#B') @ (
% 121.84/16.06 (
% 121.84/16.06 ('#B') @ (
% 121.84/16.06 '#S'))) @
% 121.84/16.06 (
% 121.84/16.06 (
% 121.84/16.06 ('#B') @ (
% 121.84/16.06 (
% 121.84/16.06 ('#B') @ (
% 121.84/16.06 (
% 121.84/16.06 ('#B') @ (
% 121.84/16.06 =>))))) @
% 121.84/16.06 (
% 121.84/16.06 (
% 121.84/16.06 ('#B') @ (
% 121.84/16.06 (
% 121.84/16.06 ('#B') @ (
% 121.84/16.06 (
% 121.84/16.06 ('#C') @ in)))) @
% 121.84/16.06 injFuncSet)))))))) @
% 121.84/16.06 (
% 121.84/16.06 (
% 121.84/16.06 ('#B') @ (
% 121.84/16.06 (
% 121.84/16.06 ('#B') @ (
% 121.84/16.06 (
% 121.84/16.06 ('#C') @ in)))) @
% 121.84/16.06 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 121.84/16.06 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl507])).
% 121.84/16.06 thf(zip_derived_cl528, plain,
% 121.84/16.06 (~ (((vacuousDall) =>
% 121.84/16.06 (((quantDeMorgan1) =>
% 121.84/16.06 (((quantDeMorgan2) =>
% 121.84/16.06 (((quantDeMorgan3) =>
% 121.84/16.06 (((quantDeMorgan4) =>
% 121.84/16.06 (((prop2setI) =>
% 121.84/16.06 (((prop2set2propI) =>
% 121.84/16.06 (((notdexE) =>
% 121.84/16.06 (((notdallE) =>
% 121.84/16.06 (((exuI1) =>
% 121.84/16.06 (((exuI3) =>
% 121.84/16.06 (((exuI2) =>
% 121.84/16.06 (((inCongP) =>
% 121.84/16.06 (((in__Cong) =>
% 121.84/16.06 (((exuE3u) =>
% 121.84/16.06 (((exu__Cong) =>
% 121.84/16.06 (((setadjoin__Cong) =>
% 121.84/16.06 (((powerset__Cong) =>
% 121.84/16.06 (((setunion__Cong) =>
% 121.84/16.06 (((exuEu) =>
% 121.84/16.06 (((descr__Cong) =>
% 121.84/16.06 (((dsetconstr__Cong) =>
% 121.84/16.06 (((subsetI1) =>
% 121.84/16.06 (((eqimpsubset2) =>
% 121.84/16.06 (((eqimpsubset1) =>
% 121.84/16.06 (((subsetI2) =>
% 121.84/16.06 (((emptysetsubset) =>
% 121.84/16.06 (((subsetE) =>
% 121.84/16.06 (((subsetE2) =>
% 121.84/16.06 (((notsubsetI) =>
% 121.84/16.06 ((
% 121.84/16.06 (notequalI1) =>
% 121.84/16.06 ((
% 121.84/16.06 (notequalI2) =>
% 121.84/16.06 ((
% 121.84/16.06 (subsetRefl) =>
% 121.84/16.06 ((
% 121.84/16.06 (subsetTrans) =>
% 121.84/16.06 ((
% 121.84/16.06 (setadjoinSub) =>
% 121.84/16.06 ((
% 121.84/16.06 (setadjoinSub2) =>
% 121.84/16.06 ((
% 121.84/16.06 (subset2powerset) =>
% 121.84/16.06 ((
% 121.84/16.06 (setextsub) =>
% 121.84/16.06 ((
% 121.84/16.06 (subsetemptysetimpeq) =>
% 121.84/16.06 ((
% 121.84/16.06 (powersetI1) =>
% 121.84/16.06 ((
% 121.84/16.06 (powersetE1) =>
% 121.84/16.06 ((
% 121.84/16.06 (inPowerset) =>
% 121.84/16.06 ((
% 121.84/16.06 (powersetsubset) =>
% 121.84/16.06 ((
% 121.84/16.06 (sepInPowerset) =>
% 121.84/16.06 ((
% 121.84/16.06 (sepSubset) =>
% 121.84/16.06 ((
% 121.84/16.06 (binunionIL) =>
% 121.84/16.06 ((
% 121.84/16.06 (upairset2IR) =>
% 121.84/16.06 ((
% 121.84/16.06 (binunionIR) =>
% 121.84/16.06 ((
% 121.84/16.06 (binunionEcases) =>
% 121.84/16.06 ((
% 121.84/16.06 (binunionE) =>
% 121.84/16.06 ((
% 121.84/16.06 (binunionLsub) =>
% 121.84/16.06 ((
% 121.84/16.06 (binunionRsub) =>
% 121.84/16.06 ((
% 121.84/16.06 (binintersectI) =>
% 121.84/16.06 ((
% 121.84/16.06 (binintersectSubset5) =>
% 121.84/16.06 ((
% 121.84/16.06 (binintersectEL) =>
% 121.84/16.06 ((
% 121.84/16.06 (binintersectLsub) =>
% 121.84/16.06 ((
% 121.84/16.06 (binintersectSubset2) =>
% 121.84/16.06 ((
% 121.84/16.06 (binintersectSubset3) =>
% 121.84/16.06 ((
% 121.84/16.06 (binintersectER) =>
% 121.84/16.06 ((
% 121.84/16.06 (disjointsetsI1) =>
% 121.84/16.06 ((
% 121.84/16.06 (binintersectRsub) =>
% 121.84/16.06 ((
% 121.84/16.06 (binintersectSubset4) =>
% 121.84/16.06 ((
% 121.84/16.06 (binintersectSubset1) =>
% 121.84/16.06 ((
% 121.84/16.06 (bs114d) =>
% 121.84/16.06 ((
% 121.84/16.06 (setminusI) =>
% 121.84/16.06 ((
% 121.84/16.06 (setminusEL) =>
% 121.84/16.06 ((
% 121.84/16.06 (setminusER) =>
% 121.84/16.06 ((
% 121.84/16.06 (setminusSubset2) =>
% 121.84/16.06 ((
% 121.84/16.06 (setminusERneg) =>
% 121.84/16.06 ((
% 121.84/16.06 (setminusELneg) =>
% 121.84/16.06 ((
% 121.84/16.06 (setminusILneg) =>
% 121.84/16.06 ((
% 121.84/16.06 (setminusIRneg) =>
% 121.84/16.06 ((
% 121.84/16.06 (setminusLsub) =>
% 121.84/16.06 ((
% 121.84/16.06 (setminusSubset1) =>
% 121.84/16.06 ((
% 121.84/16.06 (symdiffE) =>
% 121.84/16.06 ((
% 121.84/16.06 (symdiffI1) =>
% 121.84/16.06 ((
% 121.84/16.06 (symdiffI2) =>
% 121.84/16.06 ((
% 121.84/16.06 (symdiffIneg1) =>
% 121.84/16.06 ((
% 121.84/16.06 (symdiffIneg2) =>
% 121.84/16.06 ((
% 121.84/16.06 (secondinupair) =>
% 121.84/16.06 ((
% 121.84/16.06 (setukpairIL) =>
% 121.84/16.06 ((
% 121.84/16.06 (setukpairIR) =>
% 121.84/16.06 ((
% 121.84/16.06 (kpairiskpair) =>
% 121.84/16.06 ((
% 121.84/16.06 (kpairp) =>
% 121.84/16.06 ((
% 121.84/16.06 (singletonsubset) =>
% 121.84/16.06 ((
% 121.84/16.06 (singletoninpowerset) =>
% 121.84/16.06 ((
% 121.84/16.06 (singletoninpowunion) =>
% 121.84/16.06 ((
% 121.84/16.06 (upairset2E) =>
% 121.84/16.06 ((
% 121.84/16.06 (upairsubunion) =>
% 121.84/16.06 ((
% 121.84/16.06 (upairinpowunion) =>
% 121.84/16.06 ((
% 121.84/16.06 (ubforcartprodlem1) =>
% 121.84/16.06 ((
% 121.84/16.06 (ubforcartprodlem2) =>
% 121.84/16.06 ((
% 121.84/16.06 (ubforcartprodlem3) =>
% 121.84/16.06 ((
% 121.84/16.06 (cartprodpairin) =>
% 121.84/16.06 ((
% 121.84/16.06 (cartprodmempair1) =>
% 121.84/16.06 ((
% 121.84/16.06 (cartprodmempair) =>
% 121.84/16.06 ((
% 121.84/16.06 (setunionE2) =>
% 121.84/16.06 ((
% 121.84/16.06 (setunionsingleton1) =>
% 121.84/16.06 ((
% 121.84/16.06 (setunionsingleton2) =>
% 121.84/16.06 ((
% 121.84/16.06 (setunionsingleton) =>
% 121.84/16.06 ((
% 121.84/16.06 (singletonprop) =>
% 121.84/16.06 ((
% 121.84/16.06 (ex1E1) =>
% 121.84/16.06 ((
% 121.84/16.06 (ex1I) =>
% 121.84/16.06 ((
% 121.84/16.06 (ex1I2) =>
% 121.84/16.06 ((
% 121.84/16.06 (singletonsuniq) =>
% 121.84/16.06 ((
% 121.84/16.06 (setukpairinjL1) =>
% 121.84/16.06 ((
% 121.84/16.06 (kfstsingleton) =>
% 121.84/16.06 ((
% 121.84/16.06 (theprop) =>
% 121.84/16.06 ((
% 121.84/16.06 (kfstpairEq) =>
% 121.84/16.06 ((
% 121.84/16.06 (cartprodfstin) =>
% 121.84/16.06 ((
% 121.84/16.06 (setukpairinjL2) =>
% 121.84/16.06 ((
% 121.84/16.06 (setukpairinjL) =>
% 121.84/16.06 ((
% 121.84/16.06 (setukpairinjR11) =>
% 121.84/16.06 ((
% 121.84/16.06 (setukpairinjR12) =>
% 121.84/16.06 ((
% 121.84/16.06 (setukpairinjR1) =>
% 121.84/16.06 ((
% 121.84/16.06 (upairequniteq) =>
% 121.84/16.06 ((
% 121.84/16.06 (setukpairinjR2) =>
% 121.84/16.06 ((
% 121.84/16.06 (setukpairinjR) =>
% 121.84/16.06 ((
% 121.84/16.06 (ksndsingleton) =>
% 121.84/16.06 ((
% 121.84/16.06 (ksndpairEq) =>
% 121.84/16.06 ((
% 121.84/16.06 (kpairsurjEq) =>
% 121.84/16.06 ((
% 121.84/16.06 (cartprodsndin) =>
% 121.84/16.06 ((
% 121.84/16.06 (cartprodpairmemEL) =>
% 121.84/16.06 ((
% 121.84/16.06 (cartprodpairmemER) =>
% 121.84/16.06 ((
% 121.84/16.06 (cartprodmempaircEq) =>
% 121.84/16.06 ((
% 121.84/16.06 (cartprodfstpairEq) =>
% 121.84/16.06 ((
% 121.84/16.06 (cartprodsndpairEq) =>
% 121.84/16.06 ((
% 121.84/16.06 (cartprodpairsurjEq) =>
% 121.84/16.06 ((
% 121.84/16.06 (dpsetconstrI) =>
% 121.84/16.06 ((
% 121.84/16.06 (dpsetconstrSub) =>
% 121.84/16.06 ((
% 121.84/16.06 (setOfPairsIsBReln) =>
% 121.84/16.06 ((
% 121.84/16.06 (dpsetconstrERa) =>
% 121.84/16.06 ((
% 121.84/16.06 (dpsetconstrEL1) =>
% 121.84/16.06 ((
% 121.84/16.06 (dpsetconstrEL2) =>
% 121.84/16.06 ((
% 121.84/16.06 (dpsetconstrER) =>
% 121.84/16.06 ((
% 121.84/16.06 (funcImageSingleton) =>
% 121.84/16.06 ((
% 121.84/16.06 (apProp) =>
% 121.84/16.06 ((
% 121.84/16.06 (app) =>
% 121.84/16.06 ((
% 121.84/16.06 (infuncsetfunc) =>
% 121.84/16.06 ((
% 121.84/16.06 (ap2p) =>
% 121.84/16.06 ((
% 121.84/16.06 (funcinfuncset) =>
% 121.84/16.06 ((
% 121.84/16.06 (lamProp) =>
% 121.84/16.06 ((
% 121.84/16.06 (lamp) =>
% 121.84/16.06 ((
% 121.84/16.06 (lam2p) =>
% 121.84/16.06 ((
% 121.84/16.06 (brelnall1) =>
% 121.84/16.06 ((
% 121.84/16.06 (brelnall2) =>
% 121.84/16.06 ((
% 121.84/16.06 (ex1E2) =>
% 121.84/16.06 ((
% 121.84/16.06 (funcGraphProp1) =>
% 121.84/16.06 ((
% 121.84/16.06 (funcGraphProp3) =>
% 121.84/16.06 ((
% 121.84/16.06 (funcGraphProp2) =>
% 121.84/16.06 ((
% 121.84/16.06 (funcextLem) =>
% 121.84/16.06 ((
% 121.84/16.06 (funcGraphProp4) =>
% 121.84/16.06 ((
% 121.84/16.06 (subbreln) =>
% 121.84/16.06 ((
% 121.84/16.06 (eqbreln) =>
% 121.84/16.06 ((
% 121.84/16.06 (funcext) =>
% 121.84/16.06 ((
% 121.84/16.06 (funcext2) =>
% 121.84/16.06 ((
% 121.84/16.06 (ap2apEq1) =>
% 121.84/16.06 ((
% 121.84/16.06 (ap2apEq2) =>
% 121.84/16.06 ((
% 121.84/16.06 (beta1) =>
% 121.84/16.06 ((
% 121.84/16.06 (eta1) =>
% 121.84/16.06 ((
% 121.84/16.06 (lam2lamEq) =>
% 121.84/16.06 ((
% 121.84/16.06 (beta2) =>
% 121.84/16.06 ((
% 121.84/16.06 (eta2) =>
% 121.84/16.06 ((
% 121.84/16.06 (iffalseProp1) =>
% 121.84/16.06 ((
% 121.84/16.06 (iffalseProp2) =>
% 121.84/16.06 ((
% 121.84/16.06 (iftrueProp1) =>
% 121.84/16.06 ((
% 121.84/16.06 (iftrueProp2) =>
% 121.84/16.06 ((
% 121.84/16.06 (ifSingleton) =>
% 121.84/16.06 ((
% 121.84/16.06 (ifp) =>
% 121.84/16.06 ((
% 121.84/16.06 (theeq) =>
% 121.84/16.06 ((
% 121.84/16.06 (iftrue) =>
% 121.84/16.06 ((
% 121.84/16.06 (iffalse) =>
% 121.84/16.06 ((
% 121.84/16.06 (iftrueorfalse) =>
% 121.84/16.06 ((
% 121.84/16.06 (binintersectT_lem) =>
% 121.84/16.06 ((
% 121.84/16.06 (binunionT_lem) =>
% 121.84/16.06 ((
% 121.84/16.06 (powersetT_lem) =>
% 121.84/16.06 ((
% 121.84/16.06 (setminusT_lem) =>
% 121.84/16.06 ((
% 121.84/16.06 (complementT_lem) =>
% 121.84/16.06 ((
% 121.84/16.06 (setextT) =>
% 121.84/16.06 ((
% 121.84/16.06 (subsetTI) =>
% 121.84/16.06 ((
% 121.84/16.06 (powersetTI1) =>
% 121.84/16.06 ((
% 121.84/16.06 (powersetTE1) =>
% 121.84/16.06 ((
% 121.84/16.06 (complementTI1) =>
% 121.84/16.06 ((
% 121.84/16.06 (complementTE1) =>
% 121.84/16.06 ((
% 121.84/16.06 (binintersectTELcontra) =>
% 121.84/16.06 ((
% 121.84/16.06 (binintersectTERcontra) =>
% 121.84/16.06 ((
% 121.84/16.06 (contrasubsetT) =>
% 121.84/16.06 ((
% 121.84/16.06 (contrasubsetT1) =>
% 121.84/16.06 ((
% 121.84/16.06 (contrasubsetT2) =>
% 121.84/16.06 ((
% 121.84/16.06 (contrasubsetT3) =>
% 121.84/16.06 ((
% 121.84/16.06 (doubleComplementI1) =>
% 121.84/16.06 ((
% 121.84/16.06 (doubleComplementE1) =>
% 121.84/16.06 ((
% 121.84/16.06 (doubleComplementSub1) =>
% 121.84/16.06 ((
% 121.84/16.06 (doubleComplementSub2) =>
% 121.84/16.06 ((
% 121.84/16.06 (doubleComplementEq) =>
% 121.84/16.06 ((
% 121.84/16.06 (complementTnotintersectT) =>
% 121.84/16.06 ((
% 121.84/16.06 (complementImpComplementIntersect) =>
% 121.84/16.06 ((
% 121.84/16.06 (complementSubsetComplementIntersect) =>
% 121.84/16.06 ((
% 121.84/16.06 (complementInPowersetComplementIntersect) =>
% 121.84/16.06 ((
% 121.84/16.06 (contraSubsetComplement) =>
% 121.84/16.06 ((
% 121.84/16.06 (complementTcontraSubset) =>
% 121.84/16.06 ((
% 121.84/16.06 (binunionTILcontra) =>
% 121.84/16.06 ((
% 121.84/16.06 (binunionTIRcontra) =>
% 121.84/16.06 ((
% 121.84/16.06 (inIntersectImpInUnion) =>
% 121.84/16.06 ((
% 121.84/16.06 (inIntersectImpInUnion2) =>
% 121.84/16.06 ((
% 121.84/16.06 (inIntersectImpInIntersectUnions) =>
% 121.84/16.06 ((
% 121.84/16.06 (intersectInPowersetIntersectUnions) =>
% 121.84/16.06 ((
% 121.84/16.06 (inComplementUnionImpNotIn1) =>
% 121.84/16.06 ((
% 121.84/16.06 (inComplementUnionImpInComplement1) =>
% 121.84/16.06 ((
% 121.84/16.06 (binunionTE) =>
% 121.84/16.06 ((
% 121.84/16.06 (binunionTEcontra) =>
% 121.84/16.06 ((
% 121.84/16.06 (demorgan2a1) =>
% 121.84/16.06 ((
% 121.84/16.06 (complementUnionInPowersetComplement) =>
% 121.84/16.06 ((
% 121.84/16.06 (demorgan2a2) =>
% 121.84/16.06 ((
% 121.84/16.06 (demorgan1a) =>
% 121.84/16.06 ((
% 121.84/16.06 (demorgan1b) =>
% 121.84/16.06 ((
% 121.84/16.06 (demorgan1) =>
% 121.84/16.06 ((
% 121.84/16.06 (demorgan2a) =>
% 121.84/16.06 ((
% 121.84/16.06 (demorgan2b2) =>
% 121.84/16.06 ((
% 121.84/16.06 (demorgan2b) =>
% 121.84/16.06 ((
% 121.84/16.06 (demorgan2) =>
% 121.84/16.06 ((
% 121.84/16.06 (woz13rule0) =>
% 121.84/16.06 ((
% 121.84/16.06 (woz13rule1) =>
% 121.84/16.06 ((
% 121.84/16.06 (woz13rule2) =>
% 121.84/16.06 ((
% 121.84/16.06 (woz13rule3) =>
% 121.84/16.06 ((
% 121.84/16.06 (woz13rule4) =>
% 121.84/16.06 ((
% 121.84/16.06 (woz1_1) =>
% 121.84/16.06 ((
% 121.84/16.06 (woz1_2) =>
% 121.84/16.06 ((
% 121.84/16.06 (woz1_3) =>
% 121.84/16.06 ((
% 121.84/16.06 (woz1_4) =>
% 121.84/16.06 ((
% 121.84/16.06 (woz1_5) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1all2) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1SetBreln1) =>
% 121.84/16.06 ((
% 121.84/16.06 (choice2fnsingleton) =>
% 121.84/16.06 ((
% 121.84/16.06 (setOfPairsIsBReln1) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1all1) =>
% 121.84/16.06 ((
% 121.84/16.06 (subbreln1) =>
% 121.84/16.06 ((
% 121.84/16.06 (eqbreln1) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1invprop) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1invI) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1invE) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1compprop) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1compI) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1compE) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1compEex) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1unionprop) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1unionIL) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1unionIR) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1unionI) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1unionE) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1unionEcases) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1unionCommutes) =>
% 121.84/16.06 ((
% 121.84/16.06 (woz2Ex) =>
% 121.84/16.06 ((
% 121.84/16.06 (woz2W) =>
% 121.84/16.06 ((
% 121.84/16.06 (woz2A) =>
% 121.84/16.06 ((
% 121.84/16.06 (woz2B) =>
% 121.84/16.06 ((
% 121.84/16.06 (image1Ex) =>
% 121.84/16.06 ((
% 121.84/16.06 (image1Ex1) =>
% 121.84/16.06 ((
% 121.84/16.06 (image1Equiv) =>
% 121.84/16.06 ((
% 121.84/16.06 (image1E) =>
% 121.84/16.06 ((
% 121.84/16.06 (image1I) =>
% 121.84/16.06 ((
% 121.84/16.06 (injFuncInInjFuncSet) =>
% 121.84/16.06 ((
% 121.84/16.06 (!!) @ (
% 121.84/16.06 (('#B') @ (
% 121.84/16.06 !!) @
% 121.84/16.06 (
% 121.84/16.06 (
% 121.84/16.06 ('#B') @ (
% 121.84/16.06 (
% 121.84/16.06 ('#B') @ (
% 121.84/16.06 !!))) @
% 121.84/16.06 (
% 121.84/16.06 (
% 121.84/16.06 ('#S') @ (
% 121.84/16.06 (
% 121.84/16.06 ('#B') @ (
% 121.84/16.06 '#S') @
% 121.84/16.06 (
% 121.84/16.06 (
% 121.84/16.06 ('#B') @ (
% 121.84/16.06 (
% 121.84/16.06 ('#B') @ (
% 121.84/16.06 '#S'))) @
% 121.84/16.06 (
% 121.84/16.06 (
% 121.84/16.06 ('#B') @ (
% 121.84/16.06 (
% 121.84/16.06 ('#B') @ (
% 121.84/16.06 (
% 121.84/16.06 ('#B') @ (
% 121.84/16.06 =>))))) @
% 121.84/16.06 (
% 121.84/16.06 (
% 121.84/16.06 ('#B') @ (
% 121.84/16.06 (
% 121.84/16.06 ('#B') @ (
% 121.84/16.06 (
% 121.84/16.06 ('#C') @ in)))) @
% 121.84/16.06 injFuncSet)))))))) @
% 121.84/16.06 (
% 121.84/16.06 (
% 121.84/16.06 ('#B') @ (
% 121.84/16.06 (
% 121.84/16.06 ('#B') @ (
% 121.84/16.06 (
% 121.84/16.06 ('#C') @ in)))) @
% 121.84/16.06 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 121.84/16.06 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl517])).
% 121.84/16.06 thf(zip_derived_cl537, plain,
% 121.84/16.06 (~ (((quantDeMorgan1) =>
% 121.84/16.06 (((quantDeMorgan2) =>
% 121.84/16.06 (((quantDeMorgan3) =>
% 121.84/16.06 (((quantDeMorgan4) =>
% 121.84/16.06 (((prop2setI) =>
% 121.84/16.06 (((prop2set2propI) =>
% 121.84/16.06 (((notdexE) =>
% 121.84/16.06 (((notdallE) =>
% 121.84/16.06 (((exuI1) =>
% 121.84/16.06 (((exuI3) =>
% 121.84/16.06 (((exuI2) =>
% 121.84/16.06 (((inCongP) =>
% 121.84/16.06 (((in__Cong) =>
% 121.84/16.06 (((exuE3u) =>
% 121.84/16.06 (((exu__Cong) =>
% 121.84/16.06 (((setadjoin__Cong) =>
% 121.84/16.06 (((powerset__Cong) =>
% 121.84/16.06 (((setunion__Cong) =>
% 121.84/16.06 (((exuEu) =>
% 121.84/16.06 (((descr__Cong) =>
% 121.84/16.06 (((dsetconstr__Cong) =>
% 121.84/16.06 (((subsetI1) =>
% 121.84/16.06 (((eqimpsubset2) =>
% 121.84/16.06 (((eqimpsubset1) =>
% 121.84/16.06 (((subsetI2) =>
% 121.84/16.06 (((emptysetsubset) =>
% 121.84/16.06 (((subsetE) =>
% 121.84/16.06 (((subsetE2) =>
% 121.84/16.06 (((notsubsetI) =>
% 121.84/16.06 (((notequalI1) =>
% 121.84/16.06 ((
% 121.84/16.06 (notequalI2) =>
% 121.84/16.06 ((
% 121.84/16.06 (subsetRefl) =>
% 121.84/16.06 ((
% 121.84/16.06 (subsetTrans) =>
% 121.84/16.06 ((
% 121.84/16.06 (setadjoinSub) =>
% 121.84/16.06 ((
% 121.84/16.06 (setadjoinSub2) =>
% 121.84/16.06 ((
% 121.84/16.06 (subset2powerset) =>
% 121.84/16.06 ((
% 121.84/16.06 (setextsub) =>
% 121.84/16.06 ((
% 121.84/16.06 (subsetemptysetimpeq) =>
% 121.84/16.06 ((
% 121.84/16.06 (powersetI1) =>
% 121.84/16.06 ((
% 121.84/16.06 (powersetE1) =>
% 121.84/16.06 ((
% 121.84/16.06 (inPowerset) =>
% 121.84/16.06 ((
% 121.84/16.06 (powersetsubset) =>
% 121.84/16.06 ((
% 121.84/16.06 (sepInPowerset) =>
% 121.84/16.06 ((
% 121.84/16.06 (sepSubset) =>
% 121.84/16.06 ((
% 121.84/16.06 (binunionIL) =>
% 121.84/16.06 ((
% 121.84/16.06 (upairset2IR) =>
% 121.84/16.06 ((
% 121.84/16.06 (binunionIR) =>
% 121.84/16.06 ((
% 121.84/16.06 (binunionEcases) =>
% 121.84/16.06 ((
% 121.84/16.06 (binunionE) =>
% 121.84/16.06 ((
% 121.84/16.06 (binunionLsub) =>
% 121.84/16.06 ((
% 121.84/16.06 (binunionRsub) =>
% 121.84/16.06 ((
% 121.84/16.06 (binintersectI) =>
% 121.84/16.06 ((
% 121.84/16.06 (binintersectSubset5) =>
% 121.84/16.06 ((
% 121.84/16.06 (binintersectEL) =>
% 121.84/16.06 ((
% 121.84/16.06 (binintersectLsub) =>
% 121.84/16.06 ((
% 121.84/16.06 (binintersectSubset2) =>
% 121.84/16.06 ((
% 121.84/16.06 (binintersectSubset3) =>
% 121.84/16.06 ((
% 121.84/16.06 (binintersectER) =>
% 121.84/16.06 ((
% 121.84/16.06 (disjointsetsI1) =>
% 121.84/16.06 ((
% 121.84/16.06 (binintersectRsub) =>
% 121.84/16.06 ((
% 121.84/16.06 (binintersectSubset4) =>
% 121.84/16.06 ((
% 121.84/16.06 (binintersectSubset1) =>
% 121.84/16.06 ((
% 121.84/16.06 (bs114d) =>
% 121.84/16.06 ((
% 121.84/16.06 (setminusI) =>
% 121.84/16.06 ((
% 121.84/16.06 (setminusEL) =>
% 121.84/16.06 ((
% 121.84/16.06 (setminusER) =>
% 121.84/16.06 ((
% 121.84/16.06 (setminusSubset2) =>
% 121.84/16.06 ((
% 121.84/16.06 (setminusERneg) =>
% 121.84/16.06 ((
% 121.84/16.06 (setminusELneg) =>
% 121.84/16.06 ((
% 121.84/16.06 (setminusILneg) =>
% 121.84/16.06 ((
% 121.84/16.06 (setminusIRneg) =>
% 121.84/16.06 ((
% 121.84/16.06 (setminusLsub) =>
% 121.84/16.06 ((
% 121.84/16.06 (setminusSubset1) =>
% 121.84/16.06 ((
% 121.84/16.06 (symdiffE) =>
% 121.84/16.06 ((
% 121.84/16.06 (symdiffI1) =>
% 121.84/16.06 ((
% 121.84/16.06 (symdiffI2) =>
% 121.84/16.06 ((
% 121.84/16.06 (symdiffIneg1) =>
% 121.84/16.06 ((
% 121.84/16.06 (symdiffIneg2) =>
% 121.84/16.06 ((
% 121.84/16.06 (secondinupair) =>
% 121.84/16.06 ((
% 121.84/16.06 (setukpairIL) =>
% 121.84/16.06 ((
% 121.84/16.06 (setukpairIR) =>
% 121.84/16.06 ((
% 121.84/16.06 (kpairiskpair) =>
% 121.84/16.06 ((
% 121.84/16.06 (kpairp) =>
% 121.84/16.06 ((
% 121.84/16.06 (singletonsubset) =>
% 121.84/16.06 ((
% 121.84/16.06 (singletoninpowerset) =>
% 121.84/16.06 ((
% 121.84/16.06 (singletoninpowunion) =>
% 121.84/16.06 ((
% 121.84/16.06 (upairset2E) =>
% 121.84/16.06 ((
% 121.84/16.06 (upairsubunion) =>
% 121.84/16.06 ((
% 121.84/16.06 (upairinpowunion) =>
% 121.84/16.06 ((
% 121.84/16.06 (ubforcartprodlem1) =>
% 121.84/16.06 ((
% 121.84/16.06 (ubforcartprodlem2) =>
% 121.84/16.06 ((
% 121.84/16.06 (ubforcartprodlem3) =>
% 121.84/16.06 ((
% 121.84/16.06 (cartprodpairin) =>
% 121.84/16.06 ((
% 121.84/16.06 (cartprodmempair1) =>
% 121.84/16.06 ((
% 121.84/16.06 (cartprodmempair) =>
% 121.84/16.06 ((
% 121.84/16.06 (setunionE2) =>
% 121.84/16.06 ((
% 121.84/16.06 (setunionsingleton1) =>
% 121.84/16.06 ((
% 121.84/16.06 (setunionsingleton2) =>
% 121.84/16.06 ((
% 121.84/16.06 (setunionsingleton) =>
% 121.84/16.06 ((
% 121.84/16.06 (singletonprop) =>
% 121.84/16.06 ((
% 121.84/16.06 (ex1E1) =>
% 121.84/16.06 ((
% 121.84/16.06 (ex1I) =>
% 121.84/16.06 ((
% 121.84/16.06 (ex1I2) =>
% 121.84/16.06 ((
% 121.84/16.06 (singletonsuniq) =>
% 121.84/16.06 ((
% 121.84/16.06 (setukpairinjL1) =>
% 121.84/16.06 ((
% 121.84/16.06 (kfstsingleton) =>
% 121.84/16.06 ((
% 121.84/16.06 (theprop) =>
% 121.84/16.06 ((
% 121.84/16.06 (kfstpairEq) =>
% 121.84/16.06 ((
% 121.84/16.06 (cartprodfstin) =>
% 121.84/16.06 ((
% 121.84/16.06 (setukpairinjL2) =>
% 121.84/16.06 ((
% 121.84/16.06 (setukpairinjL) =>
% 121.84/16.06 ((
% 121.84/16.06 (setukpairinjR11) =>
% 121.84/16.06 ((
% 121.84/16.06 (setukpairinjR12) =>
% 121.84/16.06 ((
% 121.84/16.06 (setukpairinjR1) =>
% 121.84/16.06 ((
% 121.84/16.06 (upairequniteq) =>
% 121.84/16.06 ((
% 121.84/16.06 (setukpairinjR2) =>
% 121.84/16.06 ((
% 121.84/16.06 (setukpairinjR) =>
% 121.84/16.06 ((
% 121.84/16.06 (ksndsingleton) =>
% 121.84/16.06 ((
% 121.84/16.06 (ksndpairEq) =>
% 121.84/16.06 ((
% 121.84/16.06 (kpairsurjEq) =>
% 121.84/16.06 ((
% 121.84/16.06 (cartprodsndin) =>
% 121.84/16.06 ((
% 121.84/16.06 (cartprodpairmemEL) =>
% 121.84/16.06 ((
% 121.84/16.06 (cartprodpairmemER) =>
% 121.84/16.06 ((
% 121.84/16.06 (cartprodmempaircEq) =>
% 121.84/16.06 ((
% 121.84/16.06 (cartprodfstpairEq) =>
% 121.84/16.06 ((
% 121.84/16.06 (cartprodsndpairEq) =>
% 121.84/16.06 ((
% 121.84/16.06 (cartprodpairsurjEq) =>
% 121.84/16.06 ((
% 121.84/16.06 (dpsetconstrI) =>
% 121.84/16.06 ((
% 121.84/16.06 (dpsetconstrSub) =>
% 121.84/16.06 ((
% 121.84/16.06 (setOfPairsIsBReln) =>
% 121.84/16.06 ((
% 121.84/16.06 (dpsetconstrERa) =>
% 121.84/16.06 ((
% 121.84/16.06 (dpsetconstrEL1) =>
% 121.84/16.06 ((
% 121.84/16.06 (dpsetconstrEL2) =>
% 121.84/16.06 ((
% 121.84/16.06 (dpsetconstrER) =>
% 121.84/16.06 ((
% 121.84/16.06 (funcImageSingleton) =>
% 121.84/16.06 ((
% 121.84/16.06 (apProp) =>
% 121.84/16.06 ((
% 121.84/16.06 (app) =>
% 121.84/16.06 ((
% 121.84/16.06 (infuncsetfunc) =>
% 121.84/16.06 ((
% 121.84/16.06 (ap2p) =>
% 121.84/16.06 ((
% 121.84/16.06 (funcinfuncset) =>
% 121.84/16.06 ((
% 121.84/16.06 (lamProp) =>
% 121.84/16.06 ((
% 121.84/16.06 (lamp) =>
% 121.84/16.06 ((
% 121.84/16.06 (lam2p) =>
% 121.84/16.06 ((
% 121.84/16.06 (brelnall1) =>
% 121.84/16.06 ((
% 121.84/16.06 (brelnall2) =>
% 121.84/16.06 ((
% 121.84/16.06 (ex1E2) =>
% 121.84/16.06 ((
% 121.84/16.06 (funcGraphProp1) =>
% 121.84/16.06 ((
% 121.84/16.06 (funcGraphProp3) =>
% 121.84/16.06 ((
% 121.84/16.06 (funcGraphProp2) =>
% 121.84/16.06 ((
% 121.84/16.06 (funcextLem) =>
% 121.84/16.06 ((
% 121.84/16.06 (funcGraphProp4) =>
% 121.84/16.06 ((
% 121.84/16.06 (subbreln) =>
% 121.84/16.06 ((
% 121.84/16.06 (eqbreln) =>
% 121.84/16.06 ((
% 121.84/16.06 (funcext) =>
% 121.84/16.06 ((
% 121.84/16.06 (funcext2) =>
% 121.84/16.06 ((
% 121.84/16.06 (ap2apEq1) =>
% 121.84/16.06 ((
% 121.84/16.06 (ap2apEq2) =>
% 121.84/16.06 ((
% 121.84/16.06 (beta1) =>
% 121.84/16.06 ((
% 121.84/16.06 (eta1) =>
% 121.84/16.06 ((
% 121.84/16.06 (lam2lamEq) =>
% 121.84/16.06 ((
% 121.84/16.06 (beta2) =>
% 121.84/16.06 ((
% 121.84/16.06 (eta2) =>
% 121.84/16.06 ((
% 121.84/16.06 (iffalseProp1) =>
% 121.84/16.06 ((
% 121.84/16.06 (iffalseProp2) =>
% 121.84/16.06 ((
% 121.84/16.06 (iftrueProp1) =>
% 121.84/16.06 ((
% 121.84/16.06 (iftrueProp2) =>
% 121.84/16.06 ((
% 121.84/16.06 (ifSingleton) =>
% 121.84/16.06 ((
% 121.84/16.06 (ifp) =>
% 121.84/16.06 ((
% 121.84/16.06 (theeq) =>
% 121.84/16.06 ((
% 121.84/16.06 (iftrue) =>
% 121.84/16.06 ((
% 121.84/16.06 (iffalse) =>
% 121.84/16.06 ((
% 121.84/16.06 (iftrueorfalse) =>
% 121.84/16.06 ((
% 121.84/16.06 (binintersectT_lem) =>
% 121.84/16.06 ((
% 121.84/16.06 (binunionT_lem) =>
% 121.84/16.06 ((
% 121.84/16.06 (powersetT_lem) =>
% 121.84/16.06 ((
% 121.84/16.06 (setminusT_lem) =>
% 121.84/16.06 ((
% 121.84/16.06 (complementT_lem) =>
% 121.84/16.06 ((
% 121.84/16.06 (setextT) =>
% 121.84/16.06 ((
% 121.84/16.06 (subsetTI) =>
% 121.84/16.06 ((
% 121.84/16.06 (powersetTI1) =>
% 121.84/16.06 ((
% 121.84/16.06 (powersetTE1) =>
% 121.84/16.06 ((
% 121.84/16.06 (complementTI1) =>
% 121.84/16.06 ((
% 121.84/16.06 (complementTE1) =>
% 121.84/16.06 ((
% 121.84/16.06 (binintersectTELcontra) =>
% 121.84/16.06 ((
% 121.84/16.06 (binintersectTERcontra) =>
% 121.84/16.06 ((
% 121.84/16.06 (contrasubsetT) =>
% 121.84/16.06 ((
% 121.84/16.06 (contrasubsetT1) =>
% 121.84/16.06 ((
% 121.84/16.06 (contrasubsetT2) =>
% 121.84/16.06 ((
% 121.84/16.06 (contrasubsetT3) =>
% 121.84/16.06 ((
% 121.84/16.06 (doubleComplementI1) =>
% 121.84/16.06 ((
% 121.84/16.06 (doubleComplementE1) =>
% 121.84/16.06 ((
% 121.84/16.06 (doubleComplementSub1) =>
% 121.84/16.06 ((
% 121.84/16.06 (doubleComplementSub2) =>
% 121.84/16.06 ((
% 121.84/16.06 (doubleComplementEq) =>
% 121.84/16.06 ((
% 121.84/16.06 (complementTnotintersectT) =>
% 121.84/16.06 ((
% 121.84/16.06 (complementImpComplementIntersect) =>
% 121.84/16.06 ((
% 121.84/16.06 (complementSubsetComplementIntersect) =>
% 121.84/16.06 ((
% 121.84/16.06 (complementInPowersetComplementIntersect) =>
% 121.84/16.06 ((
% 121.84/16.06 (contraSubsetComplement) =>
% 121.84/16.06 ((
% 121.84/16.06 (complementTcontraSubset) =>
% 121.84/16.06 ((
% 121.84/16.06 (binunionTILcontra) =>
% 121.84/16.06 ((
% 121.84/16.06 (binunionTIRcontra) =>
% 121.84/16.06 ((
% 121.84/16.06 (inIntersectImpInUnion) =>
% 121.84/16.06 ((
% 121.84/16.06 (inIntersectImpInUnion2) =>
% 121.84/16.06 ((
% 121.84/16.06 (inIntersectImpInIntersectUnions) =>
% 121.84/16.06 ((
% 121.84/16.06 (intersectInPowersetIntersectUnions) =>
% 121.84/16.06 ((
% 121.84/16.06 (inComplementUnionImpNotIn1) =>
% 121.84/16.06 ((
% 121.84/16.06 (inComplementUnionImpInComplement1) =>
% 121.84/16.06 ((
% 121.84/16.06 (binunionTE) =>
% 121.84/16.06 ((
% 121.84/16.06 (binunionTEcontra) =>
% 121.84/16.06 ((
% 121.84/16.06 (demorgan2a1) =>
% 121.84/16.06 ((
% 121.84/16.06 (complementUnionInPowersetComplement) =>
% 121.84/16.06 ((
% 121.84/16.06 (demorgan2a2) =>
% 121.84/16.06 ((
% 121.84/16.06 (demorgan1a) =>
% 121.84/16.06 ((
% 121.84/16.06 (demorgan1b) =>
% 121.84/16.06 ((
% 121.84/16.06 (demorgan1) =>
% 121.84/16.06 ((
% 121.84/16.06 (demorgan2a) =>
% 121.84/16.06 ((
% 121.84/16.06 (demorgan2b2) =>
% 121.84/16.06 ((
% 121.84/16.06 (demorgan2b) =>
% 121.84/16.06 ((
% 121.84/16.06 (demorgan2) =>
% 121.84/16.06 ((
% 121.84/16.06 (woz13rule0) =>
% 121.84/16.06 ((
% 121.84/16.06 (woz13rule1) =>
% 121.84/16.06 ((
% 121.84/16.06 (woz13rule2) =>
% 121.84/16.06 ((
% 121.84/16.06 (woz13rule3) =>
% 121.84/16.06 ((
% 121.84/16.06 (woz13rule4) =>
% 121.84/16.06 ((
% 121.84/16.06 (woz1_1) =>
% 121.84/16.06 ((
% 121.84/16.06 (woz1_2) =>
% 121.84/16.06 ((
% 121.84/16.06 (woz1_3) =>
% 121.84/16.06 ((
% 121.84/16.06 (woz1_4) =>
% 121.84/16.06 ((
% 121.84/16.06 (woz1_5) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1all2) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1SetBreln1) =>
% 121.84/16.06 ((
% 121.84/16.06 (choice2fnsingleton) =>
% 121.84/16.06 ((
% 121.84/16.06 (setOfPairsIsBReln1) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1all1) =>
% 121.84/16.06 ((
% 121.84/16.06 (subbreln1) =>
% 121.84/16.06 ((
% 121.84/16.06 (eqbreln1) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1invprop) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1invI) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1invE) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1compprop) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1compI) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1compE) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1compEex) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1unionprop) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1unionIL) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1unionIR) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1unionI) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1unionE) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1unionEcases) =>
% 121.84/16.06 ((
% 121.84/16.06 (breln1unionCommutes) =>
% 121.84/16.06 ((
% 121.84/16.06 (woz2Ex) =>
% 121.84/16.06 ((
% 121.84/16.06 (woz2W) =>
% 121.84/16.06 ((
% 121.84/16.06 (woz2A) =>
% 121.84/16.06 ((
% 121.84/16.06 (woz2B) =>
% 121.84/16.06 ((
% 121.84/16.06 (image1Ex) =>
% 121.84/16.06 ((
% 121.84/16.06 (image1Ex1) =>
% 121.84/16.06 ((
% 121.84/16.06 (image1Equiv) =>
% 121.84/16.06 ((
% 121.84/16.06 (image1E) =>
% 121.84/16.06 ((
% 121.84/16.06 (image1I) =>
% 121.84/16.06 ((
% 121.84/16.06 (injFuncInInjFuncSet) =>
% 121.84/16.06 ((
% 121.84/16.06 (!!) @ (
% 121.84/16.06 (('#B') @ (
% 121.84/16.06 !!) @
% 121.84/16.06 (
% 121.84/16.06 (
% 121.84/16.06 ('#B') @ (
% 121.84/16.06 (
% 121.84/16.06 ('#B') @ (
% 121.84/16.06 !!))) @
% 121.84/16.06 (
% 121.84/16.06 (
% 121.84/16.06 ('#S') @ (
% 121.84/16.06 (
% 121.84/16.06 ('#B') @ (
% 121.84/16.06 '#S') @
% 121.84/16.06 (
% 121.84/16.06 (
% 121.84/16.06 ('#B') @ (
% 121.84/16.06 (
% 121.84/16.06 ('#B') @ (
% 121.84/16.06 '#S'))) @
% 121.84/16.06 (
% 121.84/16.06 (
% 121.84/16.06 ('#B') @ (
% 121.84/16.06 (
% 121.84/16.06 ('#B') @ (
% 121.84/16.06 (
% 121.84/16.06 ('#B') @ (
% 121.84/16.06 =>))))) @
% 121.84/16.06 (
% 121.84/16.06 (
% 121.84/16.06 ('#B') @ (
% 121.84/16.06 (
% 121.84/16.06 ('#B') @ (
% 121.84/16.06 (
% 121.84/16.06 ('#C') @ in)))) @
% 121.84/16.06 injFuncSet)))))))) @
% 121.84/16.06 (
% 121.84/16.06 (
% 121.84/16.06 ('#B') @ (
% 121.84/16.06 (
% 121.84/16.06 ('#B') @ (
% 121.84/16.06 (
% 121.84/16.06 ('#C') @ in)))) @
% 121.84/16.06 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 121.84/16.07 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl528])).
% 121.84/16.07 thf(zip_derived_cl546, plain,
% 121.84/16.07 (~ (((quantDeMorgan2) =>
% 121.84/16.07 (((quantDeMorgan3) =>
% 121.84/16.07 (((quantDeMorgan4) =>
% 121.84/16.07 (((prop2setI) =>
% 121.84/16.07 (((prop2set2propI) =>
% 121.84/16.07 (((notdexE) =>
% 121.84/16.07 (((notdallE) =>
% 121.84/16.07 (((exuI1) =>
% 121.84/16.07 (((exuI3) =>
% 121.84/16.07 (((exuI2) =>
% 121.84/16.07 (((inCongP) =>
% 121.84/16.07 (((in__Cong) =>
% 121.84/16.07 (((exuE3u) =>
% 121.84/16.07 (((exu__Cong) =>
% 121.84/16.07 (((setadjoin__Cong) =>
% 121.84/16.07 (((powerset__Cong) =>
% 121.84/16.07 (((setunion__Cong) =>
% 121.84/16.07 (((exuEu) =>
% 121.84/16.07 (((descr__Cong) =>
% 121.84/16.07 (((dsetconstr__Cong) =>
% 121.84/16.07 (((subsetI1) =>
% 121.84/16.07 (((eqimpsubset2) =>
% 121.84/16.07 (((eqimpsubset1) =>
% 121.84/16.07 (((subsetI2) =>
% 121.84/16.07 (((emptysetsubset) =>
% 121.84/16.07 (((subsetE) =>
% 121.84/16.07 (((subsetE2) =>
% 121.84/16.07 (((notsubsetI) =>
% 121.84/16.07 (((notequalI1) =>
% 121.84/16.07 (((notequalI2) =>
% 121.84/16.07 ((
% 121.84/16.07 (subsetRefl) =>
% 121.84/16.07 ((
% 121.84/16.07 (subsetTrans) =>
% 121.84/16.07 ((
% 121.84/16.07 (setadjoinSub) =>
% 121.84/16.07 ((
% 121.84/16.07 (setadjoinSub2) =>
% 121.84/16.07 ((
% 121.84/16.07 (subset2powerset) =>
% 121.84/16.07 ((
% 121.84/16.07 (setextsub) =>
% 121.84/16.07 ((
% 121.84/16.07 (subsetemptysetimpeq) =>
% 121.84/16.07 ((
% 121.84/16.07 (powersetI1) =>
% 121.84/16.07 ((
% 121.84/16.07 (powersetE1) =>
% 121.84/16.07 ((
% 121.84/16.07 (inPowerset) =>
% 121.84/16.07 ((
% 121.84/16.07 (powersetsubset) =>
% 121.84/16.07 ((
% 121.84/16.07 (sepInPowerset) =>
% 121.84/16.07 ((
% 121.84/16.07 (sepSubset) =>
% 121.84/16.07 ((
% 121.84/16.07 (binunionIL) =>
% 121.84/16.07 ((
% 121.84/16.07 (upairset2IR) =>
% 121.84/16.07 ((
% 121.84/16.07 (binunionIR) =>
% 121.84/16.07 ((
% 121.84/16.07 (binunionEcases) =>
% 121.84/16.07 ((
% 121.84/16.07 (binunionE) =>
% 121.84/16.07 ((
% 121.84/16.07 (binunionLsub) =>
% 121.84/16.07 ((
% 121.84/16.07 (binunionRsub) =>
% 121.84/16.07 ((
% 121.84/16.07 (binintersectI) =>
% 121.84/16.07 ((
% 121.84/16.07 (binintersectSubset5) =>
% 121.84/16.07 ((
% 121.84/16.07 (binintersectEL) =>
% 121.84/16.07 ((
% 121.84/16.07 (binintersectLsub) =>
% 121.84/16.07 ((
% 121.84/16.07 (binintersectSubset2) =>
% 121.84/16.07 ((
% 121.84/16.07 (binintersectSubset3) =>
% 121.84/16.07 ((
% 121.84/16.07 (binintersectER) =>
% 121.84/16.07 ((
% 121.84/16.07 (disjointsetsI1) =>
% 121.84/16.07 ((
% 121.84/16.07 (binintersectRsub) =>
% 121.84/16.07 ((
% 121.84/16.07 (binintersectSubset4) =>
% 121.84/16.07 ((
% 121.84/16.07 (binintersectSubset1) =>
% 121.84/16.07 ((
% 121.84/16.07 (bs114d) =>
% 121.84/16.07 ((
% 121.84/16.07 (setminusI) =>
% 121.84/16.07 ((
% 121.84/16.07 (setminusEL) =>
% 121.84/16.07 ((
% 121.84/16.07 (setminusER) =>
% 121.84/16.07 ((
% 121.84/16.07 (setminusSubset2) =>
% 121.84/16.07 ((
% 121.84/16.07 (setminusERneg) =>
% 121.84/16.07 ((
% 121.84/16.07 (setminusELneg) =>
% 121.84/16.07 ((
% 121.84/16.07 (setminusILneg) =>
% 121.84/16.07 ((
% 121.84/16.07 (setminusIRneg) =>
% 121.84/16.07 ((
% 121.84/16.07 (setminusLsub) =>
% 121.84/16.07 ((
% 121.84/16.07 (setminusSubset1) =>
% 121.84/16.07 ((
% 121.84/16.07 (symdiffE) =>
% 121.84/16.07 ((
% 121.84/16.07 (symdiffI1) =>
% 121.84/16.07 ((
% 121.84/16.07 (symdiffI2) =>
% 121.84/16.07 ((
% 121.84/16.07 (symdiffIneg1) =>
% 121.84/16.07 ((
% 121.84/16.07 (symdiffIneg2) =>
% 121.84/16.07 ((
% 121.84/16.07 (secondinupair) =>
% 121.84/16.07 ((
% 121.84/16.07 (setukpairIL) =>
% 121.84/16.07 ((
% 121.84/16.07 (setukpairIR) =>
% 121.84/16.07 ((
% 121.84/16.07 (kpairiskpair) =>
% 121.84/16.07 ((
% 121.84/16.07 (kpairp) =>
% 121.84/16.07 ((
% 121.84/16.07 (singletonsubset) =>
% 121.84/16.07 ((
% 121.84/16.07 (singletoninpowerset) =>
% 121.84/16.07 ((
% 121.84/16.07 (singletoninpowunion) =>
% 121.84/16.07 ((
% 121.84/16.07 (upairset2E) =>
% 121.84/16.07 ((
% 121.84/16.07 (upairsubunion) =>
% 121.84/16.07 ((
% 121.84/16.07 (upairinpowunion) =>
% 121.84/16.07 ((
% 121.84/16.07 (ubforcartprodlem1) =>
% 121.84/16.07 ((
% 121.84/16.07 (ubforcartprodlem2) =>
% 121.84/16.07 ((
% 121.84/16.07 (ubforcartprodlem3) =>
% 121.84/16.07 ((
% 121.84/16.07 (cartprodpairin) =>
% 121.84/16.07 ((
% 121.84/16.07 (cartprodmempair1) =>
% 121.84/16.07 ((
% 121.84/16.07 (cartprodmempair) =>
% 121.84/16.07 ((
% 121.84/16.07 (setunionE2) =>
% 121.84/16.07 ((
% 121.84/16.07 (setunionsingleton1) =>
% 121.84/16.07 ((
% 121.84/16.07 (setunionsingleton2) =>
% 121.84/16.07 ((
% 121.84/16.07 (setunionsingleton) =>
% 121.84/16.07 ((
% 121.84/16.07 (singletonprop) =>
% 121.84/16.07 ((
% 121.84/16.07 (ex1E1) =>
% 121.84/16.07 ((
% 121.84/16.07 (ex1I) =>
% 121.84/16.07 ((
% 121.84/16.07 (ex1I2) =>
% 121.84/16.07 ((
% 121.84/16.07 (singletonsuniq) =>
% 121.84/16.07 ((
% 121.84/16.07 (setukpairinjL1) =>
% 121.84/16.07 ((
% 121.84/16.07 (kfstsingleton) =>
% 121.84/16.07 ((
% 121.84/16.07 (theprop) =>
% 121.84/16.07 ((
% 121.84/16.07 (kfstpairEq) =>
% 121.84/16.07 ((
% 121.84/16.07 (cartprodfstin) =>
% 121.84/16.07 ((
% 121.84/16.07 (setukpairinjL2) =>
% 121.84/16.07 ((
% 121.84/16.07 (setukpairinjL) =>
% 121.84/16.07 ((
% 121.84/16.07 (setukpairinjR11) =>
% 121.84/16.07 ((
% 121.84/16.07 (setukpairinjR12) =>
% 121.84/16.07 ((
% 121.84/16.07 (setukpairinjR1) =>
% 121.84/16.07 ((
% 121.84/16.07 (upairequniteq) =>
% 121.84/16.07 ((
% 121.84/16.07 (setukpairinjR2) =>
% 121.84/16.07 ((
% 121.84/16.07 (setukpairinjR) =>
% 121.84/16.07 ((
% 121.84/16.07 (ksndsingleton) =>
% 121.84/16.07 ((
% 121.84/16.07 (ksndpairEq) =>
% 121.84/16.07 ((
% 121.84/16.07 (kpairsurjEq) =>
% 121.84/16.07 ((
% 121.84/16.07 (cartprodsndin) =>
% 121.84/16.07 ((
% 121.84/16.07 (cartprodpairmemEL) =>
% 121.84/16.07 ((
% 121.84/16.07 (cartprodpairmemER) =>
% 121.84/16.07 ((
% 121.84/16.07 (cartprodmempaircEq) =>
% 121.84/16.07 ((
% 121.84/16.07 (cartprodfstpairEq) =>
% 121.84/16.07 ((
% 121.84/16.07 (cartprodsndpairEq) =>
% 121.84/16.07 ((
% 121.84/16.07 (cartprodpairsurjEq) =>
% 121.84/16.07 ((
% 121.84/16.07 (dpsetconstrI) =>
% 121.84/16.07 ((
% 121.84/16.07 (dpsetconstrSub) =>
% 121.84/16.07 ((
% 121.84/16.07 (setOfPairsIsBReln) =>
% 121.84/16.07 ((
% 121.84/16.07 (dpsetconstrERa) =>
% 121.84/16.07 ((
% 121.84/16.07 (dpsetconstrEL1) =>
% 121.84/16.07 ((
% 121.84/16.07 (dpsetconstrEL2) =>
% 121.84/16.07 ((
% 121.84/16.07 (dpsetconstrER) =>
% 121.84/16.07 ((
% 121.84/16.07 (funcImageSingleton) =>
% 121.84/16.07 ((
% 121.84/16.07 (apProp) =>
% 121.84/16.07 ((
% 121.84/16.07 (app) =>
% 121.84/16.07 ((
% 121.84/16.07 (infuncsetfunc) =>
% 121.84/16.07 ((
% 121.84/16.07 (ap2p) =>
% 121.84/16.07 ((
% 121.84/16.07 (funcinfuncset) =>
% 121.84/16.07 ((
% 121.84/16.07 (lamProp) =>
% 121.84/16.07 ((
% 121.84/16.07 (lamp) =>
% 121.84/16.07 ((
% 121.84/16.07 (lam2p) =>
% 121.84/16.07 ((
% 121.84/16.07 (brelnall1) =>
% 121.84/16.07 ((
% 121.84/16.07 (brelnall2) =>
% 121.84/16.07 ((
% 121.84/16.07 (ex1E2) =>
% 121.84/16.07 ((
% 121.84/16.07 (funcGraphProp1) =>
% 121.84/16.07 ((
% 121.84/16.07 (funcGraphProp3) =>
% 121.84/16.07 ((
% 121.84/16.07 (funcGraphProp2) =>
% 121.84/16.07 ((
% 121.84/16.07 (funcextLem) =>
% 121.84/16.07 ((
% 121.84/16.07 (funcGraphProp4) =>
% 121.84/16.07 ((
% 121.84/16.07 (subbreln) =>
% 121.84/16.07 ((
% 121.84/16.07 (eqbreln) =>
% 121.84/16.07 ((
% 121.84/16.07 (funcext) =>
% 121.84/16.07 ((
% 121.84/16.07 (funcext2) =>
% 121.84/16.07 ((
% 121.84/16.07 (ap2apEq1) =>
% 121.84/16.07 ((
% 121.84/16.07 (ap2apEq2) =>
% 121.84/16.07 ((
% 121.84/16.07 (beta1) =>
% 121.84/16.07 ((
% 121.84/16.07 (eta1) =>
% 121.84/16.07 ((
% 121.84/16.07 (lam2lamEq) =>
% 121.84/16.07 ((
% 121.84/16.07 (beta2) =>
% 121.84/16.07 ((
% 121.84/16.07 (eta2) =>
% 121.84/16.07 ((
% 121.84/16.07 (iffalseProp1) =>
% 121.84/16.07 ((
% 121.84/16.07 (iffalseProp2) =>
% 121.84/16.07 ((
% 121.84/16.07 (iftrueProp1) =>
% 121.84/16.07 ((
% 121.84/16.07 (iftrueProp2) =>
% 121.84/16.07 ((
% 121.84/16.07 (ifSingleton) =>
% 121.84/16.07 ((
% 121.84/16.07 (ifp) =>
% 121.84/16.07 ((
% 121.84/16.07 (theeq) =>
% 121.84/16.07 ((
% 121.84/16.07 (iftrue) =>
% 121.84/16.07 ((
% 121.84/16.07 (iffalse) =>
% 121.84/16.07 ((
% 121.84/16.07 (iftrueorfalse) =>
% 121.84/16.07 ((
% 121.84/16.07 (binintersectT_lem) =>
% 121.84/16.07 ((
% 121.84/16.07 (binunionT_lem) =>
% 121.84/16.07 ((
% 121.84/16.07 (powersetT_lem) =>
% 121.84/16.07 ((
% 121.84/16.07 (setminusT_lem) =>
% 121.84/16.07 ((
% 121.84/16.07 (complementT_lem) =>
% 121.84/16.07 ((
% 121.84/16.07 (setextT) =>
% 121.84/16.07 ((
% 121.84/16.07 (subsetTI) =>
% 121.84/16.07 ((
% 121.84/16.07 (powersetTI1) =>
% 121.84/16.07 ((
% 121.84/16.07 (powersetTE1) =>
% 121.84/16.07 ((
% 121.84/16.07 (complementTI1) =>
% 121.84/16.07 ((
% 121.84/16.07 (complementTE1) =>
% 121.84/16.07 ((
% 121.84/16.07 (binintersectTELcontra) =>
% 121.84/16.07 ((
% 121.84/16.07 (binintersectTERcontra) =>
% 121.84/16.07 ((
% 121.84/16.07 (contrasubsetT) =>
% 121.84/16.07 ((
% 121.84/16.07 (contrasubsetT1) =>
% 121.84/16.07 ((
% 121.84/16.07 (contrasubsetT2) =>
% 121.84/16.07 ((
% 121.84/16.07 (contrasubsetT3) =>
% 121.84/16.07 ((
% 121.84/16.07 (doubleComplementI1) =>
% 121.84/16.07 ((
% 121.84/16.07 (doubleComplementE1) =>
% 121.84/16.07 ((
% 121.84/16.07 (doubleComplementSub1) =>
% 121.84/16.07 ((
% 121.84/16.07 (doubleComplementSub2) =>
% 121.84/16.07 ((
% 121.84/16.07 (doubleComplementEq) =>
% 121.84/16.07 ((
% 121.84/16.07 (complementTnotintersectT) =>
% 121.84/16.07 ((
% 121.84/16.07 (complementImpComplementIntersect) =>
% 121.84/16.07 ((
% 121.84/16.07 (complementSubsetComplementIntersect) =>
% 121.84/16.07 ((
% 121.84/16.07 (complementInPowersetComplementIntersect) =>
% 121.84/16.07 ((
% 121.84/16.07 (contraSubsetComplement) =>
% 121.84/16.07 ((
% 121.84/16.07 (complementTcontraSubset) =>
% 121.84/16.07 ((
% 121.84/16.07 (binunionTILcontra) =>
% 121.84/16.07 ((
% 121.84/16.07 (binunionTIRcontra) =>
% 121.84/16.07 ((
% 121.84/16.07 (inIntersectImpInUnion) =>
% 121.84/16.07 ((
% 121.84/16.07 (inIntersectImpInUnion2) =>
% 121.84/16.07 ((
% 121.84/16.07 (inIntersectImpInIntersectUnions) =>
% 121.84/16.07 ((
% 121.84/16.07 (intersectInPowersetIntersectUnions) =>
% 121.84/16.07 ((
% 121.84/16.07 (inComplementUnionImpNotIn1) =>
% 121.84/16.07 ((
% 121.84/16.07 (inComplementUnionImpInComplement1) =>
% 121.84/16.07 ((
% 121.84/16.07 (binunionTE) =>
% 121.84/16.07 ((
% 121.84/16.07 (binunionTEcontra) =>
% 121.84/16.07 ((
% 121.84/16.07 (demorgan2a1) =>
% 121.84/16.07 ((
% 121.84/16.07 (complementUnionInPowersetComplement) =>
% 121.84/16.07 ((
% 121.84/16.07 (demorgan2a2) =>
% 121.84/16.07 ((
% 121.84/16.07 (demorgan1a) =>
% 121.84/16.07 ((
% 121.84/16.07 (demorgan1b) =>
% 121.84/16.07 ((
% 121.84/16.07 (demorgan1) =>
% 121.84/16.07 ((
% 121.84/16.07 (demorgan2a) =>
% 121.84/16.07 ((
% 121.84/16.07 (demorgan2b2) =>
% 121.84/16.07 ((
% 121.84/16.07 (demorgan2b) =>
% 121.84/16.07 ((
% 121.84/16.07 (demorgan2) =>
% 121.84/16.07 ((
% 121.84/16.07 (woz13rule0) =>
% 121.84/16.07 ((
% 121.84/16.07 (woz13rule1) =>
% 121.84/16.07 ((
% 121.84/16.07 (woz13rule2) =>
% 121.84/16.07 ((
% 121.84/16.07 (woz13rule3) =>
% 121.84/16.07 ((
% 121.84/16.07 (woz13rule4) =>
% 121.84/16.07 ((
% 121.84/16.07 (woz1_1) =>
% 121.84/16.07 ((
% 121.84/16.07 (woz1_2) =>
% 121.84/16.07 ((
% 121.84/16.07 (woz1_3) =>
% 121.84/16.07 ((
% 121.84/16.07 (woz1_4) =>
% 121.84/16.07 ((
% 121.84/16.07 (woz1_5) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1all2) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1SetBreln1) =>
% 121.84/16.07 ((
% 121.84/16.07 (choice2fnsingleton) =>
% 121.84/16.07 ((
% 121.84/16.07 (setOfPairsIsBReln1) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1all1) =>
% 121.84/16.07 ((
% 121.84/16.07 (subbreln1) =>
% 121.84/16.07 ((
% 121.84/16.07 (eqbreln1) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1invprop) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1invI) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1invE) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1compprop) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1compI) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1compE) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1compEex) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1unionprop) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1unionIL) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1unionIR) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1unionI) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1unionE) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1unionEcases) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1unionCommutes) =>
% 121.84/16.07 ((
% 121.84/16.07 (woz2Ex) =>
% 121.84/16.07 ((
% 121.84/16.07 (woz2W) =>
% 121.84/16.07 ((
% 121.84/16.07 (woz2A) =>
% 121.84/16.07 ((
% 121.84/16.07 (woz2B) =>
% 121.84/16.07 ((
% 121.84/16.07 (image1Ex) =>
% 121.84/16.07 ((
% 121.84/16.07 (image1Ex1) =>
% 121.84/16.07 ((
% 121.84/16.07 (image1Equiv) =>
% 121.84/16.07 ((
% 121.84/16.07 (image1E) =>
% 121.84/16.07 ((
% 121.84/16.07 (image1I) =>
% 121.84/16.07 ((
% 121.84/16.07 (injFuncInInjFuncSet) =>
% 121.84/16.07 ((
% 121.84/16.07 (!!) @ (
% 121.84/16.07 (('#B') @ (
% 121.84/16.07 !!) @
% 121.84/16.07 (
% 121.84/16.07 (
% 121.84/16.07 ('#B') @ (
% 121.84/16.07 (
% 121.84/16.07 ('#B') @ (
% 121.84/16.07 !!))) @
% 121.84/16.07 (
% 121.84/16.07 (
% 121.84/16.07 ('#S') @ (
% 121.84/16.07 (
% 121.84/16.07 ('#B') @ (
% 121.84/16.07 '#S') @
% 121.84/16.07 (
% 121.84/16.07 (
% 121.84/16.07 ('#B') @ (
% 121.84/16.07 (
% 121.84/16.07 ('#B') @ (
% 121.84/16.07 '#S'))) @
% 121.84/16.07 (
% 121.84/16.07 (
% 121.84/16.07 ('#B') @ (
% 121.84/16.07 (
% 121.84/16.07 ('#B') @ (
% 121.84/16.07 (
% 121.84/16.07 ('#B') @ (
% 121.84/16.07 =>))))) @
% 121.84/16.07 (
% 121.84/16.07 (
% 121.84/16.07 ('#B') @ (
% 121.84/16.07 (
% 121.84/16.07 ('#B') @ (
% 121.84/16.07 (
% 121.84/16.07 ('#C') @ in)))) @
% 121.84/16.07 injFuncSet)))))))) @
% 121.84/16.07 (
% 121.84/16.07 (
% 121.84/16.07 ('#B') @ (
% 121.84/16.07 (
% 121.84/16.07 ('#B') @ (
% 121.84/16.07 (
% 121.84/16.07 ('#C') @ in)))) @
% 121.84/16.07 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 121.84/16.07 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl537])).
% 121.84/16.07 thf(zip_derived_cl553, plain,
% 121.84/16.07 (~ (((quantDeMorgan3) =>
% 121.84/16.07 (((quantDeMorgan4) =>
% 121.84/16.07 (((prop2setI) =>
% 121.84/16.07 (((prop2set2propI) =>
% 121.84/16.07 (((notdexE) =>
% 121.84/16.07 (((notdallE) =>
% 121.84/16.07 (((exuI1) =>
% 121.84/16.07 (((exuI3) =>
% 121.84/16.07 (((exuI2) =>
% 121.84/16.07 (((inCongP) =>
% 121.84/16.07 (((in__Cong) =>
% 121.84/16.07 (((exuE3u) =>
% 121.84/16.07 (((exu__Cong) =>
% 121.84/16.07 (((setadjoin__Cong) =>
% 121.84/16.07 (((powerset__Cong) =>
% 121.84/16.07 (((setunion__Cong) =>
% 121.84/16.07 (((exuEu) =>
% 121.84/16.07 (((descr__Cong) =>
% 121.84/16.07 (((dsetconstr__Cong) =>
% 121.84/16.07 (((subsetI1) =>
% 121.84/16.07 (((eqimpsubset2) =>
% 121.84/16.07 (((eqimpsubset1) =>
% 121.84/16.07 (((subsetI2) =>
% 121.84/16.07 (((emptysetsubset) =>
% 121.84/16.07 (((subsetE) =>
% 121.84/16.07 (((subsetE2) =>
% 121.84/16.07 (((notsubsetI) =>
% 121.84/16.07 (((notequalI1) =>
% 121.84/16.07 (((notequalI2) =>
% 121.84/16.07 (((subsetRefl) =>
% 121.84/16.07 ((
% 121.84/16.07 (subsetTrans) =>
% 121.84/16.07 ((
% 121.84/16.07 (setadjoinSub) =>
% 121.84/16.07 ((
% 121.84/16.07 (setadjoinSub2) =>
% 121.84/16.07 ((
% 121.84/16.07 (subset2powerset) =>
% 121.84/16.07 ((
% 121.84/16.07 (setextsub) =>
% 121.84/16.07 ((
% 121.84/16.07 (subsetemptysetimpeq) =>
% 121.84/16.07 ((
% 121.84/16.07 (powersetI1) =>
% 121.84/16.07 ((
% 121.84/16.07 (powersetE1) =>
% 121.84/16.07 ((
% 121.84/16.07 (inPowerset) =>
% 121.84/16.07 ((
% 121.84/16.07 (powersetsubset) =>
% 121.84/16.07 ((
% 121.84/16.07 (sepInPowerset) =>
% 121.84/16.07 ((
% 121.84/16.07 (sepSubset) =>
% 121.84/16.07 ((
% 121.84/16.07 (binunionIL) =>
% 121.84/16.07 ((
% 121.84/16.07 (upairset2IR) =>
% 121.84/16.07 ((
% 121.84/16.07 (binunionIR) =>
% 121.84/16.07 ((
% 121.84/16.07 (binunionEcases) =>
% 121.84/16.07 ((
% 121.84/16.07 (binunionE) =>
% 121.84/16.07 ((
% 121.84/16.07 (binunionLsub) =>
% 121.84/16.07 ((
% 121.84/16.07 (binunionRsub) =>
% 121.84/16.07 ((
% 121.84/16.07 (binintersectI) =>
% 121.84/16.07 ((
% 121.84/16.07 (binintersectSubset5) =>
% 121.84/16.07 ((
% 121.84/16.07 (binintersectEL) =>
% 121.84/16.07 ((
% 121.84/16.07 (binintersectLsub) =>
% 121.84/16.07 ((
% 121.84/16.07 (binintersectSubset2) =>
% 121.84/16.07 ((
% 121.84/16.07 (binintersectSubset3) =>
% 121.84/16.07 ((
% 121.84/16.07 (binintersectER) =>
% 121.84/16.07 ((
% 121.84/16.07 (disjointsetsI1) =>
% 121.84/16.07 ((
% 121.84/16.07 (binintersectRsub) =>
% 121.84/16.07 ((
% 121.84/16.07 (binintersectSubset4) =>
% 121.84/16.07 ((
% 121.84/16.07 (binintersectSubset1) =>
% 121.84/16.07 ((
% 121.84/16.07 (bs114d) =>
% 121.84/16.07 ((
% 121.84/16.07 (setminusI) =>
% 121.84/16.07 ((
% 121.84/16.07 (setminusEL) =>
% 121.84/16.07 ((
% 121.84/16.07 (setminusER) =>
% 121.84/16.07 ((
% 121.84/16.07 (setminusSubset2) =>
% 121.84/16.07 ((
% 121.84/16.07 (setminusERneg) =>
% 121.84/16.07 ((
% 121.84/16.07 (setminusELneg) =>
% 121.84/16.07 ((
% 121.84/16.07 (setminusILneg) =>
% 121.84/16.07 ((
% 121.84/16.07 (setminusIRneg) =>
% 121.84/16.07 ((
% 121.84/16.07 (setminusLsub) =>
% 121.84/16.07 ((
% 121.84/16.07 (setminusSubset1) =>
% 121.84/16.07 ((
% 121.84/16.07 (symdiffE) =>
% 121.84/16.07 ((
% 121.84/16.07 (symdiffI1) =>
% 121.84/16.07 ((
% 121.84/16.07 (symdiffI2) =>
% 121.84/16.07 ((
% 121.84/16.07 (symdiffIneg1) =>
% 121.84/16.07 ((
% 121.84/16.07 (symdiffIneg2) =>
% 121.84/16.07 ((
% 121.84/16.07 (secondinupair) =>
% 121.84/16.07 ((
% 121.84/16.07 (setukpairIL) =>
% 121.84/16.07 ((
% 121.84/16.07 (setukpairIR) =>
% 121.84/16.07 ((
% 121.84/16.07 (kpairiskpair) =>
% 121.84/16.07 ((
% 121.84/16.07 (kpairp) =>
% 121.84/16.07 ((
% 121.84/16.07 (singletonsubset) =>
% 121.84/16.07 ((
% 121.84/16.07 (singletoninpowerset) =>
% 121.84/16.07 ((
% 121.84/16.07 (singletoninpowunion) =>
% 121.84/16.07 ((
% 121.84/16.07 (upairset2E) =>
% 121.84/16.07 ((
% 121.84/16.07 (upairsubunion) =>
% 121.84/16.07 ((
% 121.84/16.07 (upairinpowunion) =>
% 121.84/16.07 ((
% 121.84/16.07 (ubforcartprodlem1) =>
% 121.84/16.07 ((
% 121.84/16.07 (ubforcartprodlem2) =>
% 121.84/16.07 ((
% 121.84/16.07 (ubforcartprodlem3) =>
% 121.84/16.07 ((
% 121.84/16.07 (cartprodpairin) =>
% 121.84/16.07 ((
% 121.84/16.07 (cartprodmempair1) =>
% 121.84/16.07 ((
% 121.84/16.07 (cartprodmempair) =>
% 121.84/16.07 ((
% 121.84/16.07 (setunionE2) =>
% 121.84/16.07 ((
% 121.84/16.07 (setunionsingleton1) =>
% 121.84/16.07 ((
% 121.84/16.07 (setunionsingleton2) =>
% 121.84/16.07 ((
% 121.84/16.07 (setunionsingleton) =>
% 121.84/16.07 ((
% 121.84/16.07 (singletonprop) =>
% 121.84/16.07 ((
% 121.84/16.07 (ex1E1) =>
% 121.84/16.07 ((
% 121.84/16.07 (ex1I) =>
% 121.84/16.07 ((
% 121.84/16.07 (ex1I2) =>
% 121.84/16.07 ((
% 121.84/16.07 (singletonsuniq) =>
% 121.84/16.07 ((
% 121.84/16.07 (setukpairinjL1) =>
% 121.84/16.07 ((
% 121.84/16.07 (kfstsingleton) =>
% 121.84/16.07 ((
% 121.84/16.07 (theprop) =>
% 121.84/16.07 ((
% 121.84/16.07 (kfstpairEq) =>
% 121.84/16.07 ((
% 121.84/16.07 (cartprodfstin) =>
% 121.84/16.07 ((
% 121.84/16.07 (setukpairinjL2) =>
% 121.84/16.07 ((
% 121.84/16.07 (setukpairinjL) =>
% 121.84/16.07 ((
% 121.84/16.07 (setukpairinjR11) =>
% 121.84/16.07 ((
% 121.84/16.07 (setukpairinjR12) =>
% 121.84/16.07 ((
% 121.84/16.07 (setukpairinjR1) =>
% 121.84/16.07 ((
% 121.84/16.07 (upairequniteq) =>
% 121.84/16.07 ((
% 121.84/16.07 (setukpairinjR2) =>
% 121.84/16.07 ((
% 121.84/16.07 (setukpairinjR) =>
% 121.84/16.07 ((
% 121.84/16.07 (ksndsingleton) =>
% 121.84/16.07 ((
% 121.84/16.07 (ksndpairEq) =>
% 121.84/16.07 ((
% 121.84/16.07 (kpairsurjEq) =>
% 121.84/16.07 ((
% 121.84/16.07 (cartprodsndin) =>
% 121.84/16.07 ((
% 121.84/16.07 (cartprodpairmemEL) =>
% 121.84/16.07 ((
% 121.84/16.07 (cartprodpairmemER) =>
% 121.84/16.07 ((
% 121.84/16.07 (cartprodmempaircEq) =>
% 121.84/16.07 ((
% 121.84/16.07 (cartprodfstpairEq) =>
% 121.84/16.07 ((
% 121.84/16.07 (cartprodsndpairEq) =>
% 121.84/16.07 ((
% 121.84/16.07 (cartprodpairsurjEq) =>
% 121.84/16.07 ((
% 121.84/16.07 (dpsetconstrI) =>
% 121.84/16.07 ((
% 121.84/16.07 (dpsetconstrSub) =>
% 121.84/16.07 ((
% 121.84/16.07 (setOfPairsIsBReln) =>
% 121.84/16.07 ((
% 121.84/16.07 (dpsetconstrERa) =>
% 121.84/16.07 ((
% 121.84/16.07 (dpsetconstrEL1) =>
% 121.84/16.07 ((
% 121.84/16.07 (dpsetconstrEL2) =>
% 121.84/16.07 ((
% 121.84/16.07 (dpsetconstrER) =>
% 121.84/16.07 ((
% 121.84/16.07 (funcImageSingleton) =>
% 121.84/16.07 ((
% 121.84/16.07 (apProp) =>
% 121.84/16.07 ((
% 121.84/16.07 (app) =>
% 121.84/16.07 ((
% 121.84/16.07 (infuncsetfunc) =>
% 121.84/16.07 ((
% 121.84/16.07 (ap2p) =>
% 121.84/16.07 ((
% 121.84/16.07 (funcinfuncset) =>
% 121.84/16.07 ((
% 121.84/16.07 (lamProp) =>
% 121.84/16.07 ((
% 121.84/16.07 (lamp) =>
% 121.84/16.07 ((
% 121.84/16.07 (lam2p) =>
% 121.84/16.07 ((
% 121.84/16.07 (brelnall1) =>
% 121.84/16.07 ((
% 121.84/16.07 (brelnall2) =>
% 121.84/16.07 ((
% 121.84/16.07 (ex1E2) =>
% 121.84/16.07 ((
% 121.84/16.07 (funcGraphProp1) =>
% 121.84/16.07 ((
% 121.84/16.07 (funcGraphProp3) =>
% 121.84/16.07 ((
% 121.84/16.07 (funcGraphProp2) =>
% 121.84/16.07 ((
% 121.84/16.07 (funcextLem) =>
% 121.84/16.07 ((
% 121.84/16.07 (funcGraphProp4) =>
% 121.84/16.07 ((
% 121.84/16.07 (subbreln) =>
% 121.84/16.07 ((
% 121.84/16.07 (eqbreln) =>
% 121.84/16.07 ((
% 121.84/16.07 (funcext) =>
% 121.84/16.07 ((
% 121.84/16.07 (funcext2) =>
% 121.84/16.07 ((
% 121.84/16.07 (ap2apEq1) =>
% 121.84/16.07 ((
% 121.84/16.07 (ap2apEq2) =>
% 121.84/16.07 ((
% 121.84/16.07 (beta1) =>
% 121.84/16.07 ((
% 121.84/16.07 (eta1) =>
% 121.84/16.07 ((
% 121.84/16.07 (lam2lamEq) =>
% 121.84/16.07 ((
% 121.84/16.07 (beta2) =>
% 121.84/16.07 ((
% 121.84/16.07 (eta2) =>
% 121.84/16.07 ((
% 121.84/16.07 (iffalseProp1) =>
% 121.84/16.07 ((
% 121.84/16.07 (iffalseProp2) =>
% 121.84/16.07 ((
% 121.84/16.07 (iftrueProp1) =>
% 121.84/16.07 ((
% 121.84/16.07 (iftrueProp2) =>
% 121.84/16.07 ((
% 121.84/16.07 (ifSingleton) =>
% 121.84/16.07 ((
% 121.84/16.07 (ifp) =>
% 121.84/16.07 ((
% 121.84/16.07 (theeq) =>
% 121.84/16.07 ((
% 121.84/16.07 (iftrue) =>
% 121.84/16.07 ((
% 121.84/16.07 (iffalse) =>
% 121.84/16.07 ((
% 121.84/16.07 (iftrueorfalse) =>
% 121.84/16.07 ((
% 121.84/16.07 (binintersectT_lem) =>
% 121.84/16.07 ((
% 121.84/16.07 (binunionT_lem) =>
% 121.84/16.07 ((
% 121.84/16.07 (powersetT_lem) =>
% 121.84/16.07 ((
% 121.84/16.07 (setminusT_lem) =>
% 121.84/16.07 ((
% 121.84/16.07 (complementT_lem) =>
% 121.84/16.07 ((
% 121.84/16.07 (setextT) =>
% 121.84/16.07 ((
% 121.84/16.07 (subsetTI) =>
% 121.84/16.07 ((
% 121.84/16.07 (powersetTI1) =>
% 121.84/16.07 ((
% 121.84/16.07 (powersetTE1) =>
% 121.84/16.07 ((
% 121.84/16.07 (complementTI1) =>
% 121.84/16.07 ((
% 121.84/16.07 (complementTE1) =>
% 121.84/16.07 ((
% 121.84/16.07 (binintersectTELcontra) =>
% 121.84/16.07 ((
% 121.84/16.07 (binintersectTERcontra) =>
% 121.84/16.07 ((
% 121.84/16.07 (contrasubsetT) =>
% 121.84/16.07 ((
% 121.84/16.07 (contrasubsetT1) =>
% 121.84/16.07 ((
% 121.84/16.07 (contrasubsetT2) =>
% 121.84/16.07 ((
% 121.84/16.07 (contrasubsetT3) =>
% 121.84/16.07 ((
% 121.84/16.07 (doubleComplementI1) =>
% 121.84/16.07 ((
% 121.84/16.07 (doubleComplementE1) =>
% 121.84/16.07 ((
% 121.84/16.07 (doubleComplementSub1) =>
% 121.84/16.07 ((
% 121.84/16.07 (doubleComplementSub2) =>
% 121.84/16.07 ((
% 121.84/16.07 (doubleComplementEq) =>
% 121.84/16.07 ((
% 121.84/16.07 (complementTnotintersectT) =>
% 121.84/16.07 ((
% 121.84/16.07 (complementImpComplementIntersect) =>
% 121.84/16.07 ((
% 121.84/16.07 (complementSubsetComplementIntersect) =>
% 121.84/16.07 ((
% 121.84/16.07 (complementInPowersetComplementIntersect) =>
% 121.84/16.07 ((
% 121.84/16.07 (contraSubsetComplement) =>
% 121.84/16.07 ((
% 121.84/16.07 (complementTcontraSubset) =>
% 121.84/16.07 ((
% 121.84/16.07 (binunionTILcontra) =>
% 121.84/16.07 ((
% 121.84/16.07 (binunionTIRcontra) =>
% 121.84/16.07 ((
% 121.84/16.07 (inIntersectImpInUnion) =>
% 121.84/16.07 ((
% 121.84/16.07 (inIntersectImpInUnion2) =>
% 121.84/16.07 ((
% 121.84/16.07 (inIntersectImpInIntersectUnions) =>
% 121.84/16.07 ((
% 121.84/16.07 (intersectInPowersetIntersectUnions) =>
% 121.84/16.07 ((
% 121.84/16.07 (inComplementUnionImpNotIn1) =>
% 121.84/16.07 ((
% 121.84/16.07 (inComplementUnionImpInComplement1) =>
% 121.84/16.07 ((
% 121.84/16.07 (binunionTE) =>
% 121.84/16.07 ((
% 121.84/16.07 (binunionTEcontra) =>
% 121.84/16.07 ((
% 121.84/16.07 (demorgan2a1) =>
% 121.84/16.07 ((
% 121.84/16.07 (complementUnionInPowersetComplement) =>
% 121.84/16.07 ((
% 121.84/16.07 (demorgan2a2) =>
% 121.84/16.07 ((
% 121.84/16.07 (demorgan1a) =>
% 121.84/16.07 ((
% 121.84/16.07 (demorgan1b) =>
% 121.84/16.07 ((
% 121.84/16.07 (demorgan1) =>
% 121.84/16.07 ((
% 121.84/16.07 (demorgan2a) =>
% 121.84/16.07 ((
% 121.84/16.07 (demorgan2b2) =>
% 121.84/16.07 ((
% 121.84/16.07 (demorgan2b) =>
% 121.84/16.07 ((
% 121.84/16.07 (demorgan2) =>
% 121.84/16.07 ((
% 121.84/16.07 (woz13rule0) =>
% 121.84/16.07 ((
% 121.84/16.07 (woz13rule1) =>
% 121.84/16.07 ((
% 121.84/16.07 (woz13rule2) =>
% 121.84/16.07 ((
% 121.84/16.07 (woz13rule3) =>
% 121.84/16.07 ((
% 121.84/16.07 (woz13rule4) =>
% 121.84/16.07 ((
% 121.84/16.07 (woz1_1) =>
% 121.84/16.07 ((
% 121.84/16.07 (woz1_2) =>
% 121.84/16.07 ((
% 121.84/16.07 (woz1_3) =>
% 121.84/16.07 ((
% 121.84/16.07 (woz1_4) =>
% 121.84/16.07 ((
% 121.84/16.07 (woz1_5) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1all2) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1SetBreln1) =>
% 121.84/16.07 ((
% 121.84/16.07 (choice2fnsingleton) =>
% 121.84/16.07 ((
% 121.84/16.07 (setOfPairsIsBReln1) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1all1) =>
% 121.84/16.07 ((
% 121.84/16.07 (subbreln1) =>
% 121.84/16.07 ((
% 121.84/16.07 (eqbreln1) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1invprop) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1invI) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1invE) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1compprop) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1compI) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1compE) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1compEex) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1unionprop) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1unionIL) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1unionIR) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1unionI) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1unionE) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1unionEcases) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1unionCommutes) =>
% 121.84/16.07 ((
% 121.84/16.07 (woz2Ex) =>
% 121.84/16.07 ((
% 121.84/16.07 (woz2W) =>
% 121.84/16.07 ((
% 121.84/16.07 (woz2A) =>
% 121.84/16.07 ((
% 121.84/16.07 (woz2B) =>
% 121.84/16.07 ((
% 121.84/16.07 (image1Ex) =>
% 121.84/16.07 ((
% 121.84/16.07 (image1Ex1) =>
% 121.84/16.07 ((
% 121.84/16.07 (image1Equiv) =>
% 121.84/16.07 ((
% 121.84/16.07 (image1E) =>
% 121.84/16.07 ((
% 121.84/16.07 (image1I) =>
% 121.84/16.07 ((
% 121.84/16.07 (injFuncInInjFuncSet) =>
% 121.84/16.07 ((
% 121.84/16.07 (!!) @ (
% 121.84/16.07 (('#B') @ (
% 121.84/16.07 !!) @
% 121.84/16.07 (
% 121.84/16.07 (
% 121.84/16.07 ('#B') @ (
% 121.84/16.07 (
% 121.84/16.07 ('#B') @ (
% 121.84/16.07 !!))) @
% 121.84/16.07 (
% 121.84/16.07 (
% 121.84/16.07 ('#S') @ (
% 121.84/16.07 (
% 121.84/16.07 ('#B') @ (
% 121.84/16.07 '#S') @
% 121.84/16.07 (
% 121.84/16.07 (
% 121.84/16.07 ('#B') @ (
% 121.84/16.07 (
% 121.84/16.07 ('#B') @ (
% 121.84/16.07 '#S'))) @
% 121.84/16.07 (
% 121.84/16.07 (
% 121.84/16.07 ('#B') @ (
% 121.84/16.07 (
% 121.84/16.07 ('#B') @ (
% 121.84/16.07 (
% 121.84/16.07 ('#B') @ (
% 121.84/16.07 =>))))) @
% 121.84/16.07 (
% 121.84/16.07 (
% 121.84/16.07 ('#B') @ (
% 121.84/16.07 (
% 121.84/16.07 ('#B') @ (
% 121.84/16.07 (
% 121.84/16.07 ('#C') @ in)))) @
% 121.84/16.07 injFuncSet)))))))) @
% 121.84/16.07 (
% 121.84/16.07 (
% 121.84/16.07 ('#B') @ (
% 121.84/16.07 (
% 121.84/16.07 ('#B') @ (
% 121.84/16.07 (
% 121.84/16.07 ('#C') @ in)))) @
% 121.84/16.07 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 121.84/16.07 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl546])).
% 121.84/16.07 thf(zip_derived_cl561, plain,
% 121.84/16.07 (~ (((quantDeMorgan4) =>
% 121.84/16.07 (((prop2setI) =>
% 121.84/16.07 (((prop2set2propI) =>
% 121.84/16.07 (((notdexE) =>
% 121.84/16.07 (((notdallE) =>
% 121.84/16.07 (((exuI1) =>
% 121.84/16.07 (((exuI3) =>
% 121.84/16.07 (((exuI2) =>
% 121.84/16.07 (((inCongP) =>
% 121.84/16.07 (((in__Cong) =>
% 121.84/16.07 (((exuE3u) =>
% 121.84/16.07 (((exu__Cong) =>
% 121.84/16.07 (((setadjoin__Cong) =>
% 121.84/16.07 (((powerset__Cong) =>
% 121.84/16.07 (((setunion__Cong) =>
% 121.84/16.07 (((exuEu) =>
% 121.84/16.07 (((descr__Cong) =>
% 121.84/16.07 (((dsetconstr__Cong) =>
% 121.84/16.07 (((subsetI1) =>
% 121.84/16.07 (((eqimpsubset2) =>
% 121.84/16.07 (((eqimpsubset1) =>
% 121.84/16.07 (((subsetI2) =>
% 121.84/16.07 (((emptysetsubset) =>
% 121.84/16.07 (((subsetE) =>
% 121.84/16.07 (((subsetE2) =>
% 121.84/16.07 (((notsubsetI) =>
% 121.84/16.07 (((notequalI1) =>
% 121.84/16.07 (((notequalI2) =>
% 121.84/16.07 (((subsetRefl) =>
% 121.84/16.07 (((subsetTrans) =>
% 121.84/16.07 ((
% 121.84/16.07 (setadjoinSub) =>
% 121.84/16.07 ((
% 121.84/16.07 (setadjoinSub2) =>
% 121.84/16.07 ((
% 121.84/16.07 (subset2powerset) =>
% 121.84/16.07 ((
% 121.84/16.07 (setextsub) =>
% 121.84/16.07 ((
% 121.84/16.07 (subsetemptysetimpeq) =>
% 121.84/16.07 ((
% 121.84/16.07 (powersetI1) =>
% 121.84/16.07 ((
% 121.84/16.07 (powersetE1) =>
% 121.84/16.07 ((
% 121.84/16.07 (inPowerset) =>
% 121.84/16.07 ((
% 121.84/16.07 (powersetsubset) =>
% 121.84/16.07 ((
% 121.84/16.07 (sepInPowerset) =>
% 121.84/16.07 ((
% 121.84/16.07 (sepSubset) =>
% 121.84/16.07 ((
% 121.84/16.07 (binunionIL) =>
% 121.84/16.07 ((
% 121.84/16.07 (upairset2IR) =>
% 121.84/16.07 ((
% 121.84/16.07 (binunionIR) =>
% 121.84/16.07 ((
% 121.84/16.07 (binunionEcases) =>
% 121.84/16.07 ((
% 121.84/16.07 (binunionE) =>
% 121.84/16.07 ((
% 121.84/16.07 (binunionLsub) =>
% 121.84/16.07 ((
% 121.84/16.07 (binunionRsub) =>
% 121.84/16.07 ((
% 121.84/16.07 (binintersectI) =>
% 121.84/16.07 ((
% 121.84/16.07 (binintersectSubset5) =>
% 121.84/16.07 ((
% 121.84/16.07 (binintersectEL) =>
% 121.84/16.07 ((
% 121.84/16.07 (binintersectLsub) =>
% 121.84/16.07 ((
% 121.84/16.07 (binintersectSubset2) =>
% 121.84/16.07 ((
% 121.84/16.07 (binintersectSubset3) =>
% 121.84/16.07 ((
% 121.84/16.07 (binintersectER) =>
% 121.84/16.07 ((
% 121.84/16.07 (disjointsetsI1) =>
% 121.84/16.07 ((
% 121.84/16.07 (binintersectRsub) =>
% 121.84/16.07 ((
% 121.84/16.07 (binintersectSubset4) =>
% 121.84/16.07 ((
% 121.84/16.07 (binintersectSubset1) =>
% 121.84/16.07 ((
% 121.84/16.07 (bs114d) =>
% 121.84/16.07 ((
% 121.84/16.07 (setminusI) =>
% 121.84/16.07 ((
% 121.84/16.07 (setminusEL) =>
% 121.84/16.07 ((
% 121.84/16.07 (setminusER) =>
% 121.84/16.07 ((
% 121.84/16.07 (setminusSubset2) =>
% 121.84/16.07 ((
% 121.84/16.07 (setminusERneg) =>
% 121.84/16.07 ((
% 121.84/16.07 (setminusELneg) =>
% 121.84/16.07 ((
% 121.84/16.07 (setminusILneg) =>
% 121.84/16.07 ((
% 121.84/16.07 (setminusIRneg) =>
% 121.84/16.07 ((
% 121.84/16.07 (setminusLsub) =>
% 121.84/16.07 ((
% 121.84/16.07 (setminusSubset1) =>
% 121.84/16.07 ((
% 121.84/16.07 (symdiffE) =>
% 121.84/16.07 ((
% 121.84/16.07 (symdiffI1) =>
% 121.84/16.07 ((
% 121.84/16.07 (symdiffI2) =>
% 121.84/16.07 ((
% 121.84/16.07 (symdiffIneg1) =>
% 121.84/16.07 ((
% 121.84/16.07 (symdiffIneg2) =>
% 121.84/16.07 ((
% 121.84/16.07 (secondinupair) =>
% 121.84/16.07 ((
% 121.84/16.07 (setukpairIL) =>
% 121.84/16.07 ((
% 121.84/16.07 (setukpairIR) =>
% 121.84/16.07 ((
% 121.84/16.07 (kpairiskpair) =>
% 121.84/16.07 ((
% 121.84/16.07 (kpairp) =>
% 121.84/16.07 ((
% 121.84/16.07 (singletonsubset) =>
% 121.84/16.07 ((
% 121.84/16.07 (singletoninpowerset) =>
% 121.84/16.07 ((
% 121.84/16.07 (singletoninpowunion) =>
% 121.84/16.07 ((
% 121.84/16.07 (upairset2E) =>
% 121.84/16.07 ((
% 121.84/16.07 (upairsubunion) =>
% 121.84/16.07 ((
% 121.84/16.07 (upairinpowunion) =>
% 121.84/16.07 ((
% 121.84/16.07 (ubforcartprodlem1) =>
% 121.84/16.07 ((
% 121.84/16.07 (ubforcartprodlem2) =>
% 121.84/16.07 ((
% 121.84/16.07 (ubforcartprodlem3) =>
% 121.84/16.07 ((
% 121.84/16.07 (cartprodpairin) =>
% 121.84/16.07 ((
% 121.84/16.07 (cartprodmempair1) =>
% 121.84/16.07 ((
% 121.84/16.07 (cartprodmempair) =>
% 121.84/16.07 ((
% 121.84/16.07 (setunionE2) =>
% 121.84/16.07 ((
% 121.84/16.07 (setunionsingleton1) =>
% 121.84/16.07 ((
% 121.84/16.07 (setunionsingleton2) =>
% 121.84/16.07 ((
% 121.84/16.07 (setunionsingleton) =>
% 121.84/16.07 ((
% 121.84/16.07 (singletonprop) =>
% 121.84/16.07 ((
% 121.84/16.07 (ex1E1) =>
% 121.84/16.07 ((
% 121.84/16.07 (ex1I) =>
% 121.84/16.07 ((
% 121.84/16.07 (ex1I2) =>
% 121.84/16.07 ((
% 121.84/16.07 (singletonsuniq) =>
% 121.84/16.07 ((
% 121.84/16.07 (setukpairinjL1) =>
% 121.84/16.07 ((
% 121.84/16.07 (kfstsingleton) =>
% 121.84/16.07 ((
% 121.84/16.07 (theprop) =>
% 121.84/16.07 ((
% 121.84/16.07 (kfstpairEq) =>
% 121.84/16.07 ((
% 121.84/16.07 (cartprodfstin) =>
% 121.84/16.07 ((
% 121.84/16.07 (setukpairinjL2) =>
% 121.84/16.07 ((
% 121.84/16.07 (setukpairinjL) =>
% 121.84/16.07 ((
% 121.84/16.07 (setukpairinjR11) =>
% 121.84/16.07 ((
% 121.84/16.07 (setukpairinjR12) =>
% 121.84/16.07 ((
% 121.84/16.07 (setukpairinjR1) =>
% 121.84/16.07 ((
% 121.84/16.07 (upairequniteq) =>
% 121.84/16.07 ((
% 121.84/16.07 (setukpairinjR2) =>
% 121.84/16.07 ((
% 121.84/16.07 (setukpairinjR) =>
% 121.84/16.07 ((
% 121.84/16.07 (ksndsingleton) =>
% 121.84/16.07 ((
% 121.84/16.07 (ksndpairEq) =>
% 121.84/16.07 ((
% 121.84/16.07 (kpairsurjEq) =>
% 121.84/16.07 ((
% 121.84/16.07 (cartprodsndin) =>
% 121.84/16.07 ((
% 121.84/16.07 (cartprodpairmemEL) =>
% 121.84/16.07 ((
% 121.84/16.07 (cartprodpairmemER) =>
% 121.84/16.07 ((
% 121.84/16.07 (cartprodmempaircEq) =>
% 121.84/16.07 ((
% 121.84/16.07 (cartprodfstpairEq) =>
% 121.84/16.07 ((
% 121.84/16.07 (cartprodsndpairEq) =>
% 121.84/16.07 ((
% 121.84/16.07 (cartprodpairsurjEq) =>
% 121.84/16.07 ((
% 121.84/16.07 (dpsetconstrI) =>
% 121.84/16.07 ((
% 121.84/16.07 (dpsetconstrSub) =>
% 121.84/16.07 ((
% 121.84/16.07 (setOfPairsIsBReln) =>
% 121.84/16.07 ((
% 121.84/16.07 (dpsetconstrERa) =>
% 121.84/16.07 ((
% 121.84/16.07 (dpsetconstrEL1) =>
% 121.84/16.07 ((
% 121.84/16.07 (dpsetconstrEL2) =>
% 121.84/16.07 ((
% 121.84/16.07 (dpsetconstrER) =>
% 121.84/16.07 ((
% 121.84/16.07 (funcImageSingleton) =>
% 121.84/16.07 ((
% 121.84/16.07 (apProp) =>
% 121.84/16.07 ((
% 121.84/16.07 (app) =>
% 121.84/16.07 ((
% 121.84/16.07 (infuncsetfunc) =>
% 121.84/16.07 ((
% 121.84/16.07 (ap2p) =>
% 121.84/16.07 ((
% 121.84/16.07 (funcinfuncset) =>
% 121.84/16.07 ((
% 121.84/16.07 (lamProp) =>
% 121.84/16.07 ((
% 121.84/16.07 (lamp) =>
% 121.84/16.07 ((
% 121.84/16.07 (lam2p) =>
% 121.84/16.07 ((
% 121.84/16.07 (brelnall1) =>
% 121.84/16.07 ((
% 121.84/16.07 (brelnall2) =>
% 121.84/16.07 ((
% 121.84/16.07 (ex1E2) =>
% 121.84/16.07 ((
% 121.84/16.07 (funcGraphProp1) =>
% 121.84/16.07 ((
% 121.84/16.07 (funcGraphProp3) =>
% 121.84/16.07 ((
% 121.84/16.07 (funcGraphProp2) =>
% 121.84/16.07 ((
% 121.84/16.07 (funcextLem) =>
% 121.84/16.07 ((
% 121.84/16.07 (funcGraphProp4) =>
% 121.84/16.07 ((
% 121.84/16.07 (subbreln) =>
% 121.84/16.07 ((
% 121.84/16.07 (eqbreln) =>
% 121.84/16.07 ((
% 121.84/16.07 (funcext) =>
% 121.84/16.07 ((
% 121.84/16.07 (funcext2) =>
% 121.84/16.07 ((
% 121.84/16.07 (ap2apEq1) =>
% 121.84/16.07 ((
% 121.84/16.07 (ap2apEq2) =>
% 121.84/16.07 ((
% 121.84/16.07 (beta1) =>
% 121.84/16.07 ((
% 121.84/16.07 (eta1) =>
% 121.84/16.07 ((
% 121.84/16.07 (lam2lamEq) =>
% 121.84/16.07 ((
% 121.84/16.07 (beta2) =>
% 121.84/16.07 ((
% 121.84/16.07 (eta2) =>
% 121.84/16.07 ((
% 121.84/16.07 (iffalseProp1) =>
% 121.84/16.07 ((
% 121.84/16.07 (iffalseProp2) =>
% 121.84/16.07 ((
% 121.84/16.07 (iftrueProp1) =>
% 121.84/16.07 ((
% 121.84/16.07 (iftrueProp2) =>
% 121.84/16.07 ((
% 121.84/16.07 (ifSingleton) =>
% 121.84/16.07 ((
% 121.84/16.07 (ifp) =>
% 121.84/16.07 ((
% 121.84/16.07 (theeq) =>
% 121.84/16.07 ((
% 121.84/16.07 (iftrue) =>
% 121.84/16.07 ((
% 121.84/16.07 (iffalse) =>
% 121.84/16.07 ((
% 121.84/16.07 (iftrueorfalse) =>
% 121.84/16.07 ((
% 121.84/16.07 (binintersectT_lem) =>
% 121.84/16.07 ((
% 121.84/16.07 (binunionT_lem) =>
% 121.84/16.07 ((
% 121.84/16.07 (powersetT_lem) =>
% 121.84/16.07 ((
% 121.84/16.07 (setminusT_lem) =>
% 121.84/16.07 ((
% 121.84/16.07 (complementT_lem) =>
% 121.84/16.07 ((
% 121.84/16.07 (setextT) =>
% 121.84/16.07 ((
% 121.84/16.07 (subsetTI) =>
% 121.84/16.07 ((
% 121.84/16.07 (powersetTI1) =>
% 121.84/16.07 ((
% 121.84/16.07 (powersetTE1) =>
% 121.84/16.07 ((
% 121.84/16.07 (complementTI1) =>
% 121.84/16.07 ((
% 121.84/16.07 (complementTE1) =>
% 121.84/16.07 ((
% 121.84/16.07 (binintersectTELcontra) =>
% 121.84/16.07 ((
% 121.84/16.07 (binintersectTERcontra) =>
% 121.84/16.07 ((
% 121.84/16.07 (contrasubsetT) =>
% 121.84/16.07 ((
% 121.84/16.07 (contrasubsetT1) =>
% 121.84/16.07 ((
% 121.84/16.07 (contrasubsetT2) =>
% 121.84/16.07 ((
% 121.84/16.07 (contrasubsetT3) =>
% 121.84/16.07 ((
% 121.84/16.07 (doubleComplementI1) =>
% 121.84/16.07 ((
% 121.84/16.07 (doubleComplementE1) =>
% 121.84/16.07 ((
% 121.84/16.07 (doubleComplementSub1) =>
% 121.84/16.07 ((
% 121.84/16.07 (doubleComplementSub2) =>
% 121.84/16.07 ((
% 121.84/16.07 (doubleComplementEq) =>
% 121.84/16.07 ((
% 121.84/16.07 (complementTnotintersectT) =>
% 121.84/16.07 ((
% 121.84/16.07 (complementImpComplementIntersect) =>
% 121.84/16.07 ((
% 121.84/16.07 (complementSubsetComplementIntersect) =>
% 121.84/16.07 ((
% 121.84/16.07 (complementInPowersetComplementIntersect) =>
% 121.84/16.07 ((
% 121.84/16.07 (contraSubsetComplement) =>
% 121.84/16.07 ((
% 121.84/16.07 (complementTcontraSubset) =>
% 121.84/16.07 ((
% 121.84/16.07 (binunionTILcontra) =>
% 121.84/16.07 ((
% 121.84/16.07 (binunionTIRcontra) =>
% 121.84/16.07 ((
% 121.84/16.07 (inIntersectImpInUnion) =>
% 121.84/16.07 ((
% 121.84/16.07 (inIntersectImpInUnion2) =>
% 121.84/16.07 ((
% 121.84/16.07 (inIntersectImpInIntersectUnions) =>
% 121.84/16.07 ((
% 121.84/16.07 (intersectInPowersetIntersectUnions) =>
% 121.84/16.07 ((
% 121.84/16.07 (inComplementUnionImpNotIn1) =>
% 121.84/16.07 ((
% 121.84/16.07 (inComplementUnionImpInComplement1) =>
% 121.84/16.07 ((
% 121.84/16.07 (binunionTE) =>
% 121.84/16.07 ((
% 121.84/16.07 (binunionTEcontra) =>
% 121.84/16.07 ((
% 121.84/16.07 (demorgan2a1) =>
% 121.84/16.07 ((
% 121.84/16.07 (complementUnionInPowersetComplement) =>
% 121.84/16.07 ((
% 121.84/16.07 (demorgan2a2) =>
% 121.84/16.07 ((
% 121.84/16.07 (demorgan1a) =>
% 121.84/16.07 ((
% 121.84/16.07 (demorgan1b) =>
% 121.84/16.07 ((
% 121.84/16.07 (demorgan1) =>
% 121.84/16.07 ((
% 121.84/16.07 (demorgan2a) =>
% 121.84/16.07 ((
% 121.84/16.07 (demorgan2b2) =>
% 121.84/16.07 ((
% 121.84/16.07 (demorgan2b) =>
% 121.84/16.07 ((
% 121.84/16.07 (demorgan2) =>
% 121.84/16.07 ((
% 121.84/16.07 (woz13rule0) =>
% 121.84/16.07 ((
% 121.84/16.07 (woz13rule1) =>
% 121.84/16.07 ((
% 121.84/16.07 (woz13rule2) =>
% 121.84/16.07 ((
% 121.84/16.07 (woz13rule3) =>
% 121.84/16.07 ((
% 121.84/16.07 (woz13rule4) =>
% 121.84/16.07 ((
% 121.84/16.07 (woz1_1) =>
% 121.84/16.07 ((
% 121.84/16.07 (woz1_2) =>
% 121.84/16.07 ((
% 121.84/16.07 (woz1_3) =>
% 121.84/16.07 ((
% 121.84/16.07 (woz1_4) =>
% 121.84/16.07 ((
% 121.84/16.07 (woz1_5) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1all2) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1SetBreln1) =>
% 121.84/16.07 ((
% 121.84/16.07 (choice2fnsingleton) =>
% 121.84/16.07 ((
% 121.84/16.07 (setOfPairsIsBReln1) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1all1) =>
% 121.84/16.07 ((
% 121.84/16.07 (subbreln1) =>
% 121.84/16.07 ((
% 121.84/16.07 (eqbreln1) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1invprop) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1invI) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1invE) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1compprop) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1compI) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1compE) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1compEex) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1unionprop) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1unionIL) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1unionIR) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1unionI) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1unionE) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1unionEcases) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1unionCommutes) =>
% 121.84/16.07 ((
% 121.84/16.07 (woz2Ex) =>
% 121.84/16.07 ((
% 121.84/16.07 (woz2W) =>
% 121.84/16.07 ((
% 121.84/16.07 (woz2A) =>
% 121.84/16.07 ((
% 121.84/16.07 (woz2B) =>
% 121.84/16.07 ((
% 121.84/16.07 (image1Ex) =>
% 121.84/16.07 ((
% 121.84/16.07 (image1Ex1) =>
% 121.84/16.07 ((
% 121.84/16.07 (image1Equiv) =>
% 121.84/16.07 ((
% 121.84/16.07 (image1E) =>
% 121.84/16.07 ((
% 121.84/16.07 (image1I) =>
% 121.84/16.07 ((
% 121.84/16.07 (injFuncInInjFuncSet) =>
% 121.84/16.07 ((
% 121.84/16.07 (!!) @ (
% 121.84/16.07 (('#B') @ (
% 121.84/16.07 !!) @
% 121.84/16.07 (
% 121.84/16.07 (
% 121.84/16.07 ('#B') @ (
% 121.84/16.07 (
% 121.84/16.07 ('#B') @ (
% 121.84/16.07 !!))) @
% 121.84/16.07 (
% 121.84/16.07 (
% 121.84/16.07 ('#S') @ (
% 121.84/16.07 (
% 121.84/16.07 ('#B') @ (
% 121.84/16.07 '#S') @
% 121.84/16.07 (
% 121.84/16.07 (
% 121.84/16.07 ('#B') @ (
% 121.84/16.07 (
% 121.84/16.07 ('#B') @ (
% 121.84/16.07 '#S'))) @
% 121.84/16.07 (
% 121.84/16.07 (
% 121.84/16.07 ('#B') @ (
% 121.84/16.07 (
% 121.84/16.07 ('#B') @ (
% 121.84/16.07 (
% 121.84/16.07 ('#B') @ (
% 121.84/16.07 =>))))) @
% 121.84/16.07 (
% 121.84/16.07 (
% 121.84/16.07 ('#B') @ (
% 121.84/16.07 (
% 121.84/16.07 ('#B') @ (
% 121.84/16.07 (
% 121.84/16.07 ('#C') @ in)))) @
% 121.84/16.07 injFuncSet)))))))) @
% 121.84/16.07 (
% 121.84/16.07 (
% 121.84/16.07 ('#B') @ (
% 121.84/16.07 (
% 121.84/16.07 ('#B') @ (
% 121.84/16.07 (
% 121.84/16.07 ('#C') @ in)))) @
% 121.84/16.07 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 121.84/16.07 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl553])).
% 121.84/16.07 thf(zip_derived_cl570, plain,
% 121.84/16.07 (~ (((prop2setI) =>
% 121.84/16.07 (((prop2set2propI) =>
% 121.84/16.07 (((notdexE) =>
% 121.84/16.07 (((notdallE) =>
% 121.84/16.07 (((exuI1) =>
% 121.84/16.07 (((exuI3) =>
% 121.84/16.07 (((exuI2) =>
% 121.84/16.07 (((inCongP) =>
% 121.84/16.07 (((in__Cong) =>
% 121.84/16.07 (((exuE3u) =>
% 121.84/16.07 (((exu__Cong) =>
% 121.84/16.07 (((setadjoin__Cong) =>
% 121.84/16.07 (((powerset__Cong) =>
% 121.84/16.07 (((setunion__Cong) =>
% 121.84/16.07 (((exuEu) =>
% 121.84/16.07 (((descr__Cong) =>
% 121.84/16.07 (((dsetconstr__Cong) =>
% 121.84/16.07 (((subsetI1) =>
% 121.84/16.07 (((eqimpsubset2) =>
% 121.84/16.07 (((eqimpsubset1) =>
% 121.84/16.07 (((subsetI2) =>
% 121.84/16.07 (((emptysetsubset) =>
% 121.84/16.07 (((subsetE) =>
% 121.84/16.07 (((subsetE2) =>
% 121.84/16.07 (((notsubsetI) =>
% 121.84/16.07 (((notequalI1) =>
% 121.84/16.07 (((notequalI2) =>
% 121.84/16.07 (((subsetRefl) =>
% 121.84/16.07 (((subsetTrans) =>
% 121.84/16.07 (((setadjoinSub) =>
% 121.84/16.07 ((
% 121.84/16.07 (setadjoinSub2) =>
% 121.84/16.07 ((
% 121.84/16.07 (subset2powerset) =>
% 121.84/16.07 ((
% 121.84/16.07 (setextsub) =>
% 121.84/16.07 ((
% 121.84/16.07 (subsetemptysetimpeq) =>
% 121.84/16.07 ((
% 121.84/16.07 (powersetI1) =>
% 121.84/16.07 ((
% 121.84/16.07 (powersetE1) =>
% 121.84/16.07 ((
% 121.84/16.07 (inPowerset) =>
% 121.84/16.07 ((
% 121.84/16.07 (powersetsubset) =>
% 121.84/16.07 ((
% 121.84/16.07 (sepInPowerset) =>
% 121.84/16.07 ((
% 121.84/16.07 (sepSubset) =>
% 121.84/16.07 ((
% 121.84/16.07 (binunionIL) =>
% 121.84/16.07 ((
% 121.84/16.07 (upairset2IR) =>
% 121.84/16.07 ((
% 121.84/16.07 (binunionIR) =>
% 121.84/16.07 ((
% 121.84/16.07 (binunionEcases) =>
% 121.84/16.07 ((
% 121.84/16.07 (binunionE) =>
% 121.84/16.07 ((
% 121.84/16.07 (binunionLsub) =>
% 121.84/16.07 ((
% 121.84/16.07 (binunionRsub) =>
% 121.84/16.07 ((
% 121.84/16.07 (binintersectI) =>
% 121.84/16.07 ((
% 121.84/16.07 (binintersectSubset5) =>
% 121.84/16.07 ((
% 121.84/16.07 (binintersectEL) =>
% 121.84/16.07 ((
% 121.84/16.07 (binintersectLsub) =>
% 121.84/16.07 ((
% 121.84/16.07 (binintersectSubset2) =>
% 121.84/16.07 ((
% 121.84/16.07 (binintersectSubset3) =>
% 121.84/16.07 ((
% 121.84/16.07 (binintersectER) =>
% 121.84/16.07 ((
% 121.84/16.07 (disjointsetsI1) =>
% 121.84/16.07 ((
% 121.84/16.07 (binintersectRsub) =>
% 121.84/16.07 ((
% 121.84/16.07 (binintersectSubset4) =>
% 121.84/16.07 ((
% 121.84/16.07 (binintersectSubset1) =>
% 121.84/16.07 ((
% 121.84/16.07 (bs114d) =>
% 121.84/16.07 ((
% 121.84/16.07 (setminusI) =>
% 121.84/16.07 ((
% 121.84/16.07 (setminusEL) =>
% 121.84/16.07 ((
% 121.84/16.07 (setminusER) =>
% 121.84/16.07 ((
% 121.84/16.07 (setminusSubset2) =>
% 121.84/16.07 ((
% 121.84/16.07 (setminusERneg) =>
% 121.84/16.07 ((
% 121.84/16.07 (setminusELneg) =>
% 121.84/16.07 ((
% 121.84/16.07 (setminusILneg) =>
% 121.84/16.07 ((
% 121.84/16.07 (setminusIRneg) =>
% 121.84/16.07 ((
% 121.84/16.07 (setminusLsub) =>
% 121.84/16.07 ((
% 121.84/16.07 (setminusSubset1) =>
% 121.84/16.07 ((
% 121.84/16.07 (symdiffE) =>
% 121.84/16.07 ((
% 121.84/16.07 (symdiffI1) =>
% 121.84/16.07 ((
% 121.84/16.07 (symdiffI2) =>
% 121.84/16.07 ((
% 121.84/16.07 (symdiffIneg1) =>
% 121.84/16.07 ((
% 121.84/16.07 (symdiffIneg2) =>
% 121.84/16.07 ((
% 121.84/16.07 (secondinupair) =>
% 121.84/16.07 ((
% 121.84/16.07 (setukpairIL) =>
% 121.84/16.07 ((
% 121.84/16.07 (setukpairIR) =>
% 121.84/16.07 ((
% 121.84/16.07 (kpairiskpair) =>
% 121.84/16.07 ((
% 121.84/16.07 (kpairp) =>
% 121.84/16.07 ((
% 121.84/16.07 (singletonsubset) =>
% 121.84/16.07 ((
% 121.84/16.07 (singletoninpowerset) =>
% 121.84/16.07 ((
% 121.84/16.07 (singletoninpowunion) =>
% 121.84/16.07 ((
% 121.84/16.07 (upairset2E) =>
% 121.84/16.07 ((
% 121.84/16.07 (upairsubunion) =>
% 121.84/16.07 ((
% 121.84/16.07 (upairinpowunion) =>
% 121.84/16.07 ((
% 121.84/16.07 (ubforcartprodlem1) =>
% 121.84/16.07 ((
% 121.84/16.07 (ubforcartprodlem2) =>
% 121.84/16.07 ((
% 121.84/16.07 (ubforcartprodlem3) =>
% 121.84/16.07 ((
% 121.84/16.07 (cartprodpairin) =>
% 121.84/16.07 ((
% 121.84/16.07 (cartprodmempair1) =>
% 121.84/16.07 ((
% 121.84/16.07 (cartprodmempair) =>
% 121.84/16.07 ((
% 121.84/16.07 (setunionE2) =>
% 121.84/16.07 ((
% 121.84/16.07 (setunionsingleton1) =>
% 121.84/16.07 ((
% 121.84/16.07 (setunionsingleton2) =>
% 121.84/16.07 ((
% 121.84/16.07 (setunionsingleton) =>
% 121.84/16.07 ((
% 121.84/16.07 (singletonprop) =>
% 121.84/16.07 ((
% 121.84/16.07 (ex1E1) =>
% 121.84/16.07 ((
% 121.84/16.07 (ex1I) =>
% 121.84/16.07 ((
% 121.84/16.07 (ex1I2) =>
% 121.84/16.07 ((
% 121.84/16.07 (singletonsuniq) =>
% 121.84/16.07 ((
% 121.84/16.07 (setukpairinjL1) =>
% 121.84/16.07 ((
% 121.84/16.07 (kfstsingleton) =>
% 121.84/16.07 ((
% 121.84/16.07 (theprop) =>
% 121.84/16.07 ((
% 121.84/16.07 (kfstpairEq) =>
% 121.84/16.07 ((
% 121.84/16.07 (cartprodfstin) =>
% 121.84/16.07 ((
% 121.84/16.07 (setukpairinjL2) =>
% 121.84/16.07 ((
% 121.84/16.07 (setukpairinjL) =>
% 121.84/16.07 ((
% 121.84/16.07 (setukpairinjR11) =>
% 121.84/16.07 ((
% 121.84/16.07 (setukpairinjR12) =>
% 121.84/16.07 ((
% 121.84/16.07 (setukpairinjR1) =>
% 121.84/16.07 ((
% 121.84/16.07 (upairequniteq) =>
% 121.84/16.07 ((
% 121.84/16.07 (setukpairinjR2) =>
% 121.84/16.07 ((
% 121.84/16.07 (setukpairinjR) =>
% 121.84/16.07 ((
% 121.84/16.07 (ksndsingleton) =>
% 121.84/16.07 ((
% 121.84/16.07 (ksndpairEq) =>
% 121.84/16.07 ((
% 121.84/16.07 (kpairsurjEq) =>
% 121.84/16.07 ((
% 121.84/16.07 (cartprodsndin) =>
% 121.84/16.07 ((
% 121.84/16.07 (cartprodpairmemEL) =>
% 121.84/16.07 ((
% 121.84/16.07 (cartprodpairmemER) =>
% 121.84/16.07 ((
% 121.84/16.07 (cartprodmempaircEq) =>
% 121.84/16.07 ((
% 121.84/16.07 (cartprodfstpairEq) =>
% 121.84/16.07 ((
% 121.84/16.07 (cartprodsndpairEq) =>
% 121.84/16.07 ((
% 121.84/16.07 (cartprodpairsurjEq) =>
% 121.84/16.07 ((
% 121.84/16.07 (dpsetconstrI) =>
% 121.84/16.07 ((
% 121.84/16.07 (dpsetconstrSub) =>
% 121.84/16.07 ((
% 121.84/16.07 (setOfPairsIsBReln) =>
% 121.84/16.07 ((
% 121.84/16.07 (dpsetconstrERa) =>
% 121.84/16.07 ((
% 121.84/16.07 (dpsetconstrEL1) =>
% 121.84/16.07 ((
% 121.84/16.07 (dpsetconstrEL2) =>
% 121.84/16.07 ((
% 121.84/16.07 (dpsetconstrER) =>
% 121.84/16.07 ((
% 121.84/16.07 (funcImageSingleton) =>
% 121.84/16.07 ((
% 121.84/16.07 (apProp) =>
% 121.84/16.07 ((
% 121.84/16.07 (app) =>
% 121.84/16.07 ((
% 121.84/16.07 (infuncsetfunc) =>
% 121.84/16.07 ((
% 121.84/16.07 (ap2p) =>
% 121.84/16.07 ((
% 121.84/16.07 (funcinfuncset) =>
% 121.84/16.07 ((
% 121.84/16.07 (lamProp) =>
% 121.84/16.07 ((
% 121.84/16.07 (lamp) =>
% 121.84/16.07 ((
% 121.84/16.07 (lam2p) =>
% 121.84/16.07 ((
% 121.84/16.07 (brelnall1) =>
% 121.84/16.07 ((
% 121.84/16.07 (brelnall2) =>
% 121.84/16.07 ((
% 121.84/16.07 (ex1E2) =>
% 121.84/16.07 ((
% 121.84/16.07 (funcGraphProp1) =>
% 121.84/16.07 ((
% 121.84/16.07 (funcGraphProp3) =>
% 121.84/16.07 ((
% 121.84/16.07 (funcGraphProp2) =>
% 121.84/16.07 ((
% 121.84/16.07 (funcextLem) =>
% 121.84/16.07 ((
% 121.84/16.07 (funcGraphProp4) =>
% 121.84/16.07 ((
% 121.84/16.07 (subbreln) =>
% 121.84/16.07 ((
% 121.84/16.07 (eqbreln) =>
% 121.84/16.07 ((
% 121.84/16.07 (funcext) =>
% 121.84/16.07 ((
% 121.84/16.07 (funcext2) =>
% 121.84/16.07 ((
% 121.84/16.07 (ap2apEq1) =>
% 121.84/16.07 ((
% 121.84/16.07 (ap2apEq2) =>
% 121.84/16.07 ((
% 121.84/16.07 (beta1) =>
% 121.84/16.07 ((
% 121.84/16.07 (eta1) =>
% 121.84/16.07 ((
% 121.84/16.07 (lam2lamEq) =>
% 121.84/16.07 ((
% 121.84/16.07 (beta2) =>
% 121.84/16.07 ((
% 121.84/16.07 (eta2) =>
% 121.84/16.07 ((
% 121.84/16.07 (iffalseProp1) =>
% 121.84/16.07 ((
% 121.84/16.07 (iffalseProp2) =>
% 121.84/16.07 ((
% 121.84/16.07 (iftrueProp1) =>
% 121.84/16.07 ((
% 121.84/16.07 (iftrueProp2) =>
% 121.84/16.07 ((
% 121.84/16.07 (ifSingleton) =>
% 121.84/16.07 ((
% 121.84/16.07 (ifp) =>
% 121.84/16.07 ((
% 121.84/16.07 (theeq) =>
% 121.84/16.07 ((
% 121.84/16.07 (iftrue) =>
% 121.84/16.07 ((
% 121.84/16.07 (iffalse) =>
% 121.84/16.07 ((
% 121.84/16.07 (iftrueorfalse) =>
% 121.84/16.07 ((
% 121.84/16.07 (binintersectT_lem) =>
% 121.84/16.07 ((
% 121.84/16.07 (binunionT_lem) =>
% 121.84/16.07 ((
% 121.84/16.07 (powersetT_lem) =>
% 121.84/16.07 ((
% 121.84/16.07 (setminusT_lem) =>
% 121.84/16.07 ((
% 121.84/16.07 (complementT_lem) =>
% 121.84/16.07 ((
% 121.84/16.07 (setextT) =>
% 121.84/16.07 ((
% 121.84/16.07 (subsetTI) =>
% 121.84/16.07 ((
% 121.84/16.07 (powersetTI1) =>
% 121.84/16.07 ((
% 121.84/16.07 (powersetTE1) =>
% 121.84/16.07 ((
% 121.84/16.07 (complementTI1) =>
% 121.84/16.07 ((
% 121.84/16.07 (complementTE1) =>
% 121.84/16.07 ((
% 121.84/16.07 (binintersectTELcontra) =>
% 121.84/16.07 ((
% 121.84/16.07 (binintersectTERcontra) =>
% 121.84/16.07 ((
% 121.84/16.07 (contrasubsetT) =>
% 121.84/16.07 ((
% 121.84/16.07 (contrasubsetT1) =>
% 121.84/16.07 ((
% 121.84/16.07 (contrasubsetT2) =>
% 121.84/16.07 ((
% 121.84/16.07 (contrasubsetT3) =>
% 121.84/16.07 ((
% 121.84/16.07 (doubleComplementI1) =>
% 121.84/16.07 ((
% 121.84/16.07 (doubleComplementE1) =>
% 121.84/16.07 ((
% 121.84/16.07 (doubleComplementSub1) =>
% 121.84/16.07 ((
% 121.84/16.07 (doubleComplementSub2) =>
% 121.84/16.07 ((
% 121.84/16.07 (doubleComplementEq) =>
% 121.84/16.07 ((
% 121.84/16.07 (complementTnotintersectT) =>
% 121.84/16.07 ((
% 121.84/16.07 (complementImpComplementIntersect) =>
% 121.84/16.07 ((
% 121.84/16.07 (complementSubsetComplementIntersect) =>
% 121.84/16.07 ((
% 121.84/16.07 (complementInPowersetComplementIntersect) =>
% 121.84/16.07 ((
% 121.84/16.07 (contraSubsetComplement) =>
% 121.84/16.07 ((
% 121.84/16.07 (complementTcontraSubset) =>
% 121.84/16.07 ((
% 121.84/16.07 (binunionTILcontra) =>
% 121.84/16.07 ((
% 121.84/16.07 (binunionTIRcontra) =>
% 121.84/16.07 ((
% 121.84/16.07 (inIntersectImpInUnion) =>
% 121.84/16.07 ((
% 121.84/16.07 (inIntersectImpInUnion2) =>
% 121.84/16.07 ((
% 121.84/16.07 (inIntersectImpInIntersectUnions) =>
% 121.84/16.07 ((
% 121.84/16.07 (intersectInPowersetIntersectUnions) =>
% 121.84/16.07 ((
% 121.84/16.07 (inComplementUnionImpNotIn1) =>
% 121.84/16.07 ((
% 121.84/16.07 (inComplementUnionImpInComplement1) =>
% 121.84/16.07 ((
% 121.84/16.07 (binunionTE) =>
% 121.84/16.07 ((
% 121.84/16.07 (binunionTEcontra) =>
% 121.84/16.07 ((
% 121.84/16.07 (demorgan2a1) =>
% 121.84/16.07 ((
% 121.84/16.07 (complementUnionInPowersetComplement) =>
% 121.84/16.07 ((
% 121.84/16.07 (demorgan2a2) =>
% 121.84/16.07 ((
% 121.84/16.07 (demorgan1a) =>
% 121.84/16.07 ((
% 121.84/16.07 (demorgan1b) =>
% 121.84/16.07 ((
% 121.84/16.07 (demorgan1) =>
% 121.84/16.07 ((
% 121.84/16.07 (demorgan2a) =>
% 121.84/16.07 ((
% 121.84/16.07 (demorgan2b2) =>
% 121.84/16.07 ((
% 121.84/16.07 (demorgan2b) =>
% 121.84/16.07 ((
% 121.84/16.07 (demorgan2) =>
% 121.84/16.07 ((
% 121.84/16.07 (woz13rule0) =>
% 121.84/16.07 ((
% 121.84/16.07 (woz13rule1) =>
% 121.84/16.07 ((
% 121.84/16.07 (woz13rule2) =>
% 121.84/16.07 ((
% 121.84/16.07 (woz13rule3) =>
% 121.84/16.07 ((
% 121.84/16.07 (woz13rule4) =>
% 121.84/16.07 ((
% 121.84/16.07 (woz1_1) =>
% 121.84/16.07 ((
% 121.84/16.07 (woz1_2) =>
% 121.84/16.07 ((
% 121.84/16.07 (woz1_3) =>
% 121.84/16.07 ((
% 121.84/16.07 (woz1_4) =>
% 121.84/16.07 ((
% 121.84/16.07 (woz1_5) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1all2) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1SetBreln1) =>
% 121.84/16.07 ((
% 121.84/16.07 (choice2fnsingleton) =>
% 121.84/16.07 ((
% 121.84/16.07 (setOfPairsIsBReln1) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1all1) =>
% 121.84/16.07 ((
% 121.84/16.07 (subbreln1) =>
% 121.84/16.07 ((
% 121.84/16.07 (eqbreln1) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1invprop) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1invI) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1invE) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1compprop) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1compI) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1compE) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1compEex) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1unionprop) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1unionIL) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1unionIR) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1unionI) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1unionE) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1unionEcases) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1unionCommutes) =>
% 121.84/16.07 ((
% 121.84/16.07 (woz2Ex) =>
% 121.84/16.07 ((
% 121.84/16.07 (woz2W) =>
% 121.84/16.07 ((
% 121.84/16.07 (woz2A) =>
% 121.84/16.07 ((
% 121.84/16.07 (woz2B) =>
% 121.84/16.07 ((
% 121.84/16.07 (image1Ex) =>
% 121.84/16.07 ((
% 121.84/16.07 (image1Ex1) =>
% 121.84/16.07 ((
% 121.84/16.07 (image1Equiv) =>
% 121.84/16.07 ((
% 121.84/16.07 (image1E) =>
% 121.84/16.07 ((
% 121.84/16.07 (image1I) =>
% 121.84/16.07 ((
% 121.84/16.07 (injFuncInInjFuncSet) =>
% 121.84/16.07 ((
% 121.84/16.07 (!!) @ (
% 121.84/16.07 (('#B') @ (
% 121.84/16.07 !!) @
% 121.84/16.07 (
% 121.84/16.07 (
% 121.84/16.07 ('#B') @ (
% 121.84/16.07 (
% 121.84/16.07 ('#B') @ (
% 121.84/16.07 !!))) @
% 121.84/16.07 (
% 121.84/16.07 (
% 121.84/16.07 ('#S') @ (
% 121.84/16.07 (
% 121.84/16.07 ('#B') @ (
% 121.84/16.07 '#S') @
% 121.84/16.07 (
% 121.84/16.07 (
% 121.84/16.07 ('#B') @ (
% 121.84/16.07 (
% 121.84/16.07 ('#B') @ (
% 121.84/16.07 '#S'))) @
% 121.84/16.07 (
% 121.84/16.07 (
% 121.84/16.07 ('#B') @ (
% 121.84/16.07 (
% 121.84/16.07 ('#B') @ (
% 121.84/16.07 (
% 121.84/16.07 ('#B') @ (
% 121.84/16.07 =>))))) @
% 121.84/16.07 (
% 121.84/16.07 (
% 121.84/16.07 ('#B') @ (
% 121.84/16.07 (
% 121.84/16.07 ('#B') @ (
% 121.84/16.07 (
% 121.84/16.07 ('#C') @ in)))) @
% 121.84/16.07 injFuncSet)))))))) @
% 121.84/16.07 (
% 121.84/16.07 (
% 121.84/16.07 ('#B') @ (
% 121.84/16.07 (
% 121.84/16.07 ('#B') @ (
% 121.84/16.07 (
% 121.84/16.07 ('#C') @ in)))) @
% 121.84/16.07 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 121.84/16.07 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl561])).
% 121.84/16.07 thf(zip_derived_cl578, plain,
% 121.84/16.07 (~ (((prop2set2propI) =>
% 121.84/16.07 (((notdexE) =>
% 121.84/16.07 (((notdallE) =>
% 121.84/16.07 (((exuI1) =>
% 121.84/16.07 (((exuI3) =>
% 121.84/16.07 (((exuI2) =>
% 121.84/16.07 (((inCongP) =>
% 121.84/16.07 (((in__Cong) =>
% 121.84/16.07 (((exuE3u) =>
% 121.84/16.07 (((exu__Cong) =>
% 121.84/16.07 (((setadjoin__Cong) =>
% 121.84/16.07 (((powerset__Cong) =>
% 121.84/16.07 (((setunion__Cong) =>
% 121.84/16.07 (((exuEu) =>
% 121.84/16.07 (((descr__Cong) =>
% 121.84/16.07 (((dsetconstr__Cong) =>
% 121.84/16.07 (((subsetI1) =>
% 121.84/16.07 (((eqimpsubset2) =>
% 121.84/16.07 (((eqimpsubset1) =>
% 121.84/16.07 (((subsetI2) =>
% 121.84/16.07 (((emptysetsubset) =>
% 121.84/16.07 (((subsetE) =>
% 121.84/16.07 (((subsetE2) =>
% 121.84/16.07 (((notsubsetI) =>
% 121.84/16.07 (((notequalI1) =>
% 121.84/16.07 (((notequalI2) =>
% 121.84/16.07 (((subsetRefl) =>
% 121.84/16.07 (((subsetTrans) =>
% 121.84/16.07 (((setadjoinSub) =>
% 121.84/16.07 (((setadjoinSub2) =>
% 121.84/16.07 ((
% 121.84/16.07 (subset2powerset) =>
% 121.84/16.07 ((
% 121.84/16.07 (setextsub) =>
% 121.84/16.07 ((
% 121.84/16.07 (subsetemptysetimpeq) =>
% 121.84/16.07 ((
% 121.84/16.07 (powersetI1) =>
% 121.84/16.07 ((
% 121.84/16.07 (powersetE1) =>
% 121.84/16.07 ((
% 121.84/16.07 (inPowerset) =>
% 121.84/16.07 ((
% 121.84/16.07 (powersetsubset) =>
% 121.84/16.07 ((
% 121.84/16.07 (sepInPowerset) =>
% 121.84/16.07 ((
% 121.84/16.07 (sepSubset) =>
% 121.84/16.07 ((
% 121.84/16.07 (binunionIL) =>
% 121.84/16.07 ((
% 121.84/16.07 (upairset2IR) =>
% 121.84/16.07 ((
% 121.84/16.07 (binunionIR) =>
% 121.84/16.07 ((
% 121.84/16.07 (binunionEcases) =>
% 121.84/16.07 ((
% 121.84/16.07 (binunionE) =>
% 121.84/16.07 ((
% 121.84/16.07 (binunionLsub) =>
% 121.84/16.07 ((
% 121.84/16.07 (binunionRsub) =>
% 121.84/16.07 ((
% 121.84/16.07 (binintersectI) =>
% 121.84/16.07 ((
% 121.84/16.07 (binintersectSubset5) =>
% 121.84/16.07 ((
% 121.84/16.07 (binintersectEL) =>
% 121.84/16.07 ((
% 121.84/16.07 (binintersectLsub) =>
% 121.84/16.07 ((
% 121.84/16.07 (binintersectSubset2) =>
% 121.84/16.07 ((
% 121.84/16.07 (binintersectSubset3) =>
% 121.84/16.07 ((
% 121.84/16.07 (binintersectER) =>
% 121.84/16.07 ((
% 121.84/16.07 (disjointsetsI1) =>
% 121.84/16.07 ((
% 121.84/16.07 (binintersectRsub) =>
% 121.84/16.07 ((
% 121.84/16.07 (binintersectSubset4) =>
% 121.84/16.07 ((
% 121.84/16.07 (binintersectSubset1) =>
% 121.84/16.07 ((
% 121.84/16.07 (bs114d) =>
% 121.84/16.07 ((
% 121.84/16.07 (setminusI) =>
% 121.84/16.07 ((
% 121.84/16.07 (setminusEL) =>
% 121.84/16.07 ((
% 121.84/16.07 (setminusER) =>
% 121.84/16.07 ((
% 121.84/16.07 (setminusSubset2) =>
% 121.84/16.07 ((
% 121.84/16.07 (setminusERneg) =>
% 121.84/16.07 ((
% 121.84/16.07 (setminusELneg) =>
% 121.84/16.07 ((
% 121.84/16.07 (setminusILneg) =>
% 121.84/16.07 ((
% 121.84/16.07 (setminusIRneg) =>
% 121.84/16.07 ((
% 121.84/16.07 (setminusLsub) =>
% 121.84/16.07 ((
% 121.84/16.07 (setminusSubset1) =>
% 121.84/16.07 ((
% 121.84/16.07 (symdiffE) =>
% 121.84/16.07 ((
% 121.84/16.07 (symdiffI1) =>
% 121.84/16.07 ((
% 121.84/16.07 (symdiffI2) =>
% 121.84/16.07 ((
% 121.84/16.07 (symdiffIneg1) =>
% 121.84/16.07 ((
% 121.84/16.07 (symdiffIneg2) =>
% 121.84/16.07 ((
% 121.84/16.07 (secondinupair) =>
% 121.84/16.07 ((
% 121.84/16.07 (setukpairIL) =>
% 121.84/16.07 ((
% 121.84/16.07 (setukpairIR) =>
% 121.84/16.07 ((
% 121.84/16.07 (kpairiskpair) =>
% 121.84/16.07 ((
% 121.84/16.07 (kpairp) =>
% 121.84/16.07 ((
% 121.84/16.07 (singletonsubset) =>
% 121.84/16.07 ((
% 121.84/16.07 (singletoninpowerset) =>
% 121.84/16.07 ((
% 121.84/16.07 (singletoninpowunion) =>
% 121.84/16.07 ((
% 121.84/16.07 (upairset2E) =>
% 121.84/16.07 ((
% 121.84/16.07 (upairsubunion) =>
% 121.84/16.07 ((
% 121.84/16.07 (upairinpowunion) =>
% 121.84/16.07 ((
% 121.84/16.07 (ubforcartprodlem1) =>
% 121.84/16.07 ((
% 121.84/16.07 (ubforcartprodlem2) =>
% 121.84/16.07 ((
% 121.84/16.07 (ubforcartprodlem3) =>
% 121.84/16.07 ((
% 121.84/16.07 (cartprodpairin) =>
% 121.84/16.07 ((
% 121.84/16.07 (cartprodmempair1) =>
% 121.84/16.07 ((
% 121.84/16.07 (cartprodmempair) =>
% 121.84/16.07 ((
% 121.84/16.07 (setunionE2) =>
% 121.84/16.07 ((
% 121.84/16.07 (setunionsingleton1) =>
% 121.84/16.07 ((
% 121.84/16.07 (setunionsingleton2) =>
% 121.84/16.07 ((
% 121.84/16.07 (setunionsingleton) =>
% 121.84/16.07 ((
% 121.84/16.07 (singletonprop) =>
% 121.84/16.07 ((
% 121.84/16.07 (ex1E1) =>
% 121.84/16.07 ((
% 121.84/16.07 (ex1I) =>
% 121.84/16.07 ((
% 121.84/16.07 (ex1I2) =>
% 121.84/16.07 ((
% 121.84/16.07 (singletonsuniq) =>
% 121.84/16.07 ((
% 121.84/16.07 (setukpairinjL1) =>
% 121.84/16.07 ((
% 121.84/16.07 (kfstsingleton) =>
% 121.84/16.07 ((
% 121.84/16.07 (theprop) =>
% 121.84/16.07 ((
% 121.84/16.07 (kfstpairEq) =>
% 121.84/16.07 ((
% 121.84/16.07 (cartprodfstin) =>
% 121.84/16.07 ((
% 121.84/16.07 (setukpairinjL2) =>
% 121.84/16.07 ((
% 121.84/16.07 (setukpairinjL) =>
% 121.84/16.07 ((
% 121.84/16.07 (setukpairinjR11) =>
% 121.84/16.07 ((
% 121.84/16.07 (setukpairinjR12) =>
% 121.84/16.07 ((
% 121.84/16.07 (setukpairinjR1) =>
% 121.84/16.07 ((
% 121.84/16.07 (upairequniteq) =>
% 121.84/16.07 ((
% 121.84/16.07 (setukpairinjR2) =>
% 121.84/16.07 ((
% 121.84/16.07 (setukpairinjR) =>
% 121.84/16.07 ((
% 121.84/16.07 (ksndsingleton) =>
% 121.84/16.07 ((
% 121.84/16.07 (ksndpairEq) =>
% 121.84/16.07 ((
% 121.84/16.07 (kpairsurjEq) =>
% 121.84/16.07 ((
% 121.84/16.07 (cartprodsndin) =>
% 121.84/16.07 ((
% 121.84/16.07 (cartprodpairmemEL) =>
% 121.84/16.07 ((
% 121.84/16.07 (cartprodpairmemER) =>
% 121.84/16.07 ((
% 121.84/16.07 (cartprodmempaircEq) =>
% 121.84/16.07 ((
% 121.84/16.07 (cartprodfstpairEq) =>
% 121.84/16.07 ((
% 121.84/16.07 (cartprodsndpairEq) =>
% 121.84/16.07 ((
% 121.84/16.07 (cartprodpairsurjEq) =>
% 121.84/16.07 ((
% 121.84/16.07 (dpsetconstrI) =>
% 121.84/16.07 ((
% 121.84/16.07 (dpsetconstrSub) =>
% 121.84/16.07 ((
% 121.84/16.07 (setOfPairsIsBReln) =>
% 121.84/16.07 ((
% 121.84/16.07 (dpsetconstrERa) =>
% 121.84/16.07 ((
% 121.84/16.07 (dpsetconstrEL1) =>
% 121.84/16.07 ((
% 121.84/16.07 (dpsetconstrEL2) =>
% 121.84/16.07 ((
% 121.84/16.07 (dpsetconstrER) =>
% 121.84/16.07 ((
% 121.84/16.07 (funcImageSingleton) =>
% 121.84/16.07 ((
% 121.84/16.07 (apProp) =>
% 121.84/16.07 ((
% 121.84/16.07 (app) =>
% 121.84/16.07 ((
% 121.84/16.07 (infuncsetfunc) =>
% 121.84/16.07 ((
% 121.84/16.07 (ap2p) =>
% 121.84/16.07 ((
% 121.84/16.07 (funcinfuncset) =>
% 121.84/16.07 ((
% 121.84/16.07 (lamProp) =>
% 121.84/16.07 ((
% 121.84/16.07 (lamp) =>
% 121.84/16.07 ((
% 121.84/16.07 (lam2p) =>
% 121.84/16.07 ((
% 121.84/16.07 (brelnall1) =>
% 121.84/16.07 ((
% 121.84/16.07 (brelnall2) =>
% 121.84/16.07 ((
% 121.84/16.07 (ex1E2) =>
% 121.84/16.07 ((
% 121.84/16.07 (funcGraphProp1) =>
% 121.84/16.07 ((
% 121.84/16.07 (funcGraphProp3) =>
% 121.84/16.07 ((
% 121.84/16.07 (funcGraphProp2) =>
% 121.84/16.07 ((
% 121.84/16.07 (funcextLem) =>
% 121.84/16.07 ((
% 121.84/16.07 (funcGraphProp4) =>
% 121.84/16.07 ((
% 121.84/16.07 (subbreln) =>
% 121.84/16.07 ((
% 121.84/16.07 (eqbreln) =>
% 121.84/16.07 ((
% 121.84/16.07 (funcext) =>
% 121.84/16.07 ((
% 121.84/16.07 (funcext2) =>
% 121.84/16.07 ((
% 121.84/16.07 (ap2apEq1) =>
% 121.84/16.07 ((
% 121.84/16.07 (ap2apEq2) =>
% 121.84/16.07 ((
% 121.84/16.07 (beta1) =>
% 121.84/16.07 ((
% 121.84/16.07 (eta1) =>
% 121.84/16.07 ((
% 121.84/16.07 (lam2lamEq) =>
% 121.84/16.07 ((
% 121.84/16.07 (beta2) =>
% 121.84/16.07 ((
% 121.84/16.07 (eta2) =>
% 121.84/16.07 ((
% 121.84/16.07 (iffalseProp1) =>
% 121.84/16.07 ((
% 121.84/16.07 (iffalseProp2) =>
% 121.84/16.07 ((
% 121.84/16.07 (iftrueProp1) =>
% 121.84/16.07 ((
% 121.84/16.07 (iftrueProp2) =>
% 121.84/16.07 ((
% 121.84/16.07 (ifSingleton) =>
% 121.84/16.07 ((
% 121.84/16.07 (ifp) =>
% 121.84/16.07 ((
% 121.84/16.07 (theeq) =>
% 121.84/16.07 ((
% 121.84/16.07 (iftrue) =>
% 121.84/16.07 ((
% 121.84/16.07 (iffalse) =>
% 121.84/16.07 ((
% 121.84/16.07 (iftrueorfalse) =>
% 121.84/16.07 ((
% 121.84/16.07 (binintersectT_lem) =>
% 121.84/16.07 ((
% 121.84/16.07 (binunionT_lem) =>
% 121.84/16.07 ((
% 121.84/16.07 (powersetT_lem) =>
% 121.84/16.07 ((
% 121.84/16.07 (setminusT_lem) =>
% 121.84/16.07 ((
% 121.84/16.07 (complementT_lem) =>
% 121.84/16.07 ((
% 121.84/16.07 (setextT) =>
% 121.84/16.07 ((
% 121.84/16.07 (subsetTI) =>
% 121.84/16.07 ((
% 121.84/16.07 (powersetTI1) =>
% 121.84/16.07 ((
% 121.84/16.07 (powersetTE1) =>
% 121.84/16.07 ((
% 121.84/16.07 (complementTI1) =>
% 121.84/16.07 ((
% 121.84/16.07 (complementTE1) =>
% 121.84/16.07 ((
% 121.84/16.07 (binintersectTELcontra) =>
% 121.84/16.07 ((
% 121.84/16.07 (binintersectTERcontra) =>
% 121.84/16.07 ((
% 121.84/16.07 (contrasubsetT) =>
% 121.84/16.07 ((
% 121.84/16.07 (contrasubsetT1) =>
% 121.84/16.07 ((
% 121.84/16.07 (contrasubsetT2) =>
% 121.84/16.07 ((
% 121.84/16.07 (contrasubsetT3) =>
% 121.84/16.07 ((
% 121.84/16.07 (doubleComplementI1) =>
% 121.84/16.07 ((
% 121.84/16.07 (doubleComplementE1) =>
% 121.84/16.07 ((
% 121.84/16.07 (doubleComplementSub1) =>
% 121.84/16.07 ((
% 121.84/16.07 (doubleComplementSub2) =>
% 121.84/16.07 ((
% 121.84/16.07 (doubleComplementEq) =>
% 121.84/16.07 ((
% 121.84/16.07 (complementTnotintersectT) =>
% 121.84/16.07 ((
% 121.84/16.07 (complementImpComplementIntersect) =>
% 121.84/16.07 ((
% 121.84/16.07 (complementSubsetComplementIntersect) =>
% 121.84/16.07 ((
% 121.84/16.07 (complementInPowersetComplementIntersect) =>
% 121.84/16.07 ((
% 121.84/16.07 (contraSubsetComplement) =>
% 121.84/16.07 ((
% 121.84/16.07 (complementTcontraSubset) =>
% 121.84/16.07 ((
% 121.84/16.07 (binunionTILcontra) =>
% 121.84/16.07 ((
% 121.84/16.07 (binunionTIRcontra) =>
% 121.84/16.07 ((
% 121.84/16.07 (inIntersectImpInUnion) =>
% 121.84/16.07 ((
% 121.84/16.07 (inIntersectImpInUnion2) =>
% 121.84/16.07 ((
% 121.84/16.07 (inIntersectImpInIntersectUnions) =>
% 121.84/16.07 ((
% 121.84/16.07 (intersectInPowersetIntersectUnions) =>
% 121.84/16.07 ((
% 121.84/16.07 (inComplementUnionImpNotIn1) =>
% 121.84/16.07 ((
% 121.84/16.07 (inComplementUnionImpInComplement1) =>
% 121.84/16.07 ((
% 121.84/16.07 (binunionTE) =>
% 121.84/16.07 ((
% 121.84/16.07 (binunionTEcontra) =>
% 121.84/16.07 ((
% 121.84/16.07 (demorgan2a1) =>
% 121.84/16.07 ((
% 121.84/16.07 (complementUnionInPowersetComplement) =>
% 121.84/16.07 ((
% 121.84/16.07 (demorgan2a2) =>
% 121.84/16.07 ((
% 121.84/16.07 (demorgan1a) =>
% 121.84/16.07 ((
% 121.84/16.07 (demorgan1b) =>
% 121.84/16.07 ((
% 121.84/16.07 (demorgan1) =>
% 121.84/16.07 ((
% 121.84/16.07 (demorgan2a) =>
% 121.84/16.07 ((
% 121.84/16.07 (demorgan2b2) =>
% 121.84/16.07 ((
% 121.84/16.07 (demorgan2b) =>
% 121.84/16.07 ((
% 121.84/16.07 (demorgan2) =>
% 121.84/16.07 ((
% 121.84/16.07 (woz13rule0) =>
% 121.84/16.07 ((
% 121.84/16.07 (woz13rule1) =>
% 121.84/16.07 ((
% 121.84/16.07 (woz13rule2) =>
% 121.84/16.07 ((
% 121.84/16.07 (woz13rule3) =>
% 121.84/16.07 ((
% 121.84/16.07 (woz13rule4) =>
% 121.84/16.07 ((
% 121.84/16.07 (woz1_1) =>
% 121.84/16.07 ((
% 121.84/16.07 (woz1_2) =>
% 121.84/16.07 ((
% 121.84/16.07 (woz1_3) =>
% 121.84/16.07 ((
% 121.84/16.07 (woz1_4) =>
% 121.84/16.07 ((
% 121.84/16.07 (woz1_5) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1all2) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1SetBreln1) =>
% 121.84/16.07 ((
% 121.84/16.07 (choice2fnsingleton) =>
% 121.84/16.07 ((
% 121.84/16.07 (setOfPairsIsBReln1) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1all1) =>
% 121.84/16.07 ((
% 121.84/16.07 (subbreln1) =>
% 121.84/16.07 ((
% 121.84/16.07 (eqbreln1) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1invprop) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1invI) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1invE) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1compprop) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1compI) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1compE) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1compEex) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1unionprop) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1unionIL) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1unionIR) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1unionI) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1unionE) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1unionEcases) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1unionCommutes) =>
% 121.84/16.07 ((
% 121.84/16.07 (woz2Ex) =>
% 121.84/16.07 ((
% 121.84/16.07 (woz2W) =>
% 121.84/16.07 ((
% 121.84/16.07 (woz2A) =>
% 121.84/16.07 ((
% 121.84/16.07 (woz2B) =>
% 121.84/16.07 ((
% 121.84/16.07 (image1Ex) =>
% 121.84/16.07 ((
% 121.84/16.07 (image1Ex1) =>
% 121.84/16.07 ((
% 121.84/16.07 (image1Equiv) =>
% 121.84/16.07 ((
% 121.84/16.07 (image1E) =>
% 121.84/16.07 ((
% 121.84/16.07 (image1I) =>
% 121.84/16.07 ((
% 121.84/16.07 (injFuncInInjFuncSet) =>
% 121.84/16.07 ((
% 121.84/16.07 (!!) @ (
% 121.84/16.07 (('#B') @ (
% 121.84/16.07 !!) @
% 121.84/16.07 (
% 121.84/16.07 (
% 121.84/16.07 ('#B') @ (
% 121.84/16.07 (
% 121.84/16.07 ('#B') @ (
% 121.84/16.07 !!))) @
% 121.84/16.07 (
% 121.84/16.07 (
% 121.84/16.07 ('#S') @ (
% 121.84/16.07 (
% 121.84/16.07 ('#B') @ (
% 121.84/16.07 '#S') @
% 121.84/16.07 (
% 121.84/16.07 (
% 121.84/16.07 ('#B') @ (
% 121.84/16.07 (
% 121.84/16.07 ('#B') @ (
% 121.84/16.07 '#S'))) @
% 121.84/16.07 (
% 121.84/16.07 (
% 121.84/16.07 ('#B') @ (
% 121.84/16.07 (
% 121.84/16.07 ('#B') @ (
% 121.84/16.07 (
% 121.84/16.07 ('#B') @ (
% 121.84/16.07 =>))))) @
% 121.84/16.07 (
% 121.84/16.07 (
% 121.84/16.07 ('#B') @ (
% 121.84/16.07 (
% 121.84/16.07 ('#B') @ (
% 121.84/16.07 (
% 121.84/16.07 ('#C') @ in)))) @
% 121.84/16.07 injFuncSet)))))))) @
% 121.84/16.07 (
% 121.84/16.07 (
% 121.84/16.07 ('#B') @ (
% 121.84/16.07 (
% 121.84/16.07 ('#B') @ (
% 121.84/16.07 (
% 121.84/16.07 ('#C') @ in)))) @
% 121.84/16.07 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 121.84/16.07 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl570])).
% 121.84/16.07 thf(zip_derived_cl586, plain,
% 121.84/16.07 (~ (((notdexE) =>
% 121.84/16.07 (((notdallE) =>
% 121.84/16.07 (((exuI1) =>
% 121.84/16.07 (((exuI3) =>
% 121.84/16.07 (((exuI2) =>
% 121.84/16.07 (((inCongP) =>
% 121.84/16.07 (((in__Cong) =>
% 121.84/16.07 (((exuE3u) =>
% 121.84/16.07 (((exu__Cong) =>
% 121.84/16.07 (((setadjoin__Cong) =>
% 121.84/16.07 (((powerset__Cong) =>
% 121.84/16.07 (((setunion__Cong) =>
% 121.84/16.07 (((exuEu) =>
% 121.84/16.07 (((descr__Cong) =>
% 121.84/16.07 (((dsetconstr__Cong) =>
% 121.84/16.07 (((subsetI1) =>
% 121.84/16.07 (((eqimpsubset2) =>
% 121.84/16.07 (((eqimpsubset1) =>
% 121.84/16.07 (((subsetI2) =>
% 121.84/16.07 (((emptysetsubset) =>
% 121.84/16.07 (((subsetE) =>
% 121.84/16.07 (((subsetE2) =>
% 121.84/16.07 (((notsubsetI) =>
% 121.84/16.07 (((notequalI1) =>
% 121.84/16.07 (((notequalI2) =>
% 121.84/16.07 (((subsetRefl) =>
% 121.84/16.07 (((subsetTrans) =>
% 121.84/16.07 (((setadjoinSub) =>
% 121.84/16.07 (((setadjoinSub2) =>
% 121.84/16.07 (((subset2powerset) =>
% 121.84/16.07 ((
% 121.84/16.07 (setextsub) =>
% 121.84/16.07 ((
% 121.84/16.07 (subsetemptysetimpeq) =>
% 121.84/16.07 ((
% 121.84/16.07 (powersetI1) =>
% 121.84/16.07 ((
% 121.84/16.07 (powersetE1) =>
% 121.84/16.07 ((
% 121.84/16.07 (inPowerset) =>
% 121.84/16.07 ((
% 121.84/16.07 (powersetsubset) =>
% 121.84/16.07 ((
% 121.84/16.07 (sepInPowerset) =>
% 121.84/16.07 ((
% 121.84/16.07 (sepSubset) =>
% 121.84/16.07 ((
% 121.84/16.07 (binunionIL) =>
% 121.84/16.07 ((
% 121.84/16.07 (upairset2IR) =>
% 121.84/16.07 ((
% 121.84/16.07 (binunionIR) =>
% 121.84/16.07 ((
% 121.84/16.07 (binunionEcases) =>
% 121.84/16.07 ((
% 121.84/16.07 (binunionE) =>
% 121.84/16.07 ((
% 121.84/16.07 (binunionLsub) =>
% 121.84/16.07 ((
% 121.84/16.07 (binunionRsub) =>
% 121.84/16.07 ((
% 121.84/16.07 (binintersectI) =>
% 121.84/16.07 ((
% 121.84/16.07 (binintersectSubset5) =>
% 121.84/16.07 ((
% 121.84/16.07 (binintersectEL) =>
% 121.84/16.07 ((
% 121.84/16.07 (binintersectLsub) =>
% 121.84/16.07 ((
% 121.84/16.07 (binintersectSubset2) =>
% 121.84/16.07 ((
% 121.84/16.07 (binintersectSubset3) =>
% 121.84/16.07 ((
% 121.84/16.07 (binintersectER) =>
% 121.84/16.07 ((
% 121.84/16.07 (disjointsetsI1) =>
% 121.84/16.07 ((
% 121.84/16.07 (binintersectRsub) =>
% 121.84/16.07 ((
% 121.84/16.07 (binintersectSubset4) =>
% 121.84/16.07 ((
% 121.84/16.07 (binintersectSubset1) =>
% 121.84/16.07 ((
% 121.84/16.07 (bs114d) =>
% 121.84/16.07 ((
% 121.84/16.07 (setminusI) =>
% 121.84/16.07 ((
% 121.84/16.07 (setminusEL) =>
% 121.84/16.07 ((
% 121.84/16.07 (setminusER) =>
% 121.84/16.07 ((
% 121.84/16.07 (setminusSubset2) =>
% 121.84/16.07 ((
% 121.84/16.07 (setminusERneg) =>
% 121.84/16.07 ((
% 121.84/16.07 (setminusELneg) =>
% 121.84/16.07 ((
% 121.84/16.07 (setminusILneg) =>
% 121.84/16.07 ((
% 121.84/16.07 (setminusIRneg) =>
% 121.84/16.07 ((
% 121.84/16.07 (setminusLsub) =>
% 121.84/16.07 ((
% 121.84/16.07 (setminusSubset1) =>
% 121.84/16.07 ((
% 121.84/16.07 (symdiffE) =>
% 121.84/16.07 ((
% 121.84/16.07 (symdiffI1) =>
% 121.84/16.07 ((
% 121.84/16.07 (symdiffI2) =>
% 121.84/16.07 ((
% 121.84/16.07 (symdiffIneg1) =>
% 121.84/16.07 ((
% 121.84/16.07 (symdiffIneg2) =>
% 121.84/16.07 ((
% 121.84/16.07 (secondinupair) =>
% 121.84/16.07 ((
% 121.84/16.07 (setukpairIL) =>
% 121.84/16.07 ((
% 121.84/16.07 (setukpairIR) =>
% 121.84/16.07 ((
% 121.84/16.07 (kpairiskpair) =>
% 121.84/16.07 ((
% 121.84/16.07 (kpairp) =>
% 121.84/16.07 ((
% 121.84/16.07 (singletonsubset) =>
% 121.84/16.07 ((
% 121.84/16.07 (singletoninpowerset) =>
% 121.84/16.07 ((
% 121.84/16.07 (singletoninpowunion) =>
% 121.84/16.07 ((
% 121.84/16.07 (upairset2E) =>
% 121.84/16.07 ((
% 121.84/16.07 (upairsubunion) =>
% 121.84/16.07 ((
% 121.84/16.07 (upairinpowunion) =>
% 121.84/16.07 ((
% 121.84/16.07 (ubforcartprodlem1) =>
% 121.84/16.07 ((
% 121.84/16.07 (ubforcartprodlem2) =>
% 121.84/16.07 ((
% 121.84/16.07 (ubforcartprodlem3) =>
% 121.84/16.07 ((
% 121.84/16.07 (cartprodpairin) =>
% 121.84/16.07 ((
% 121.84/16.07 (cartprodmempair1) =>
% 121.84/16.07 ((
% 121.84/16.07 (cartprodmempair) =>
% 121.84/16.07 ((
% 121.84/16.07 (setunionE2) =>
% 121.84/16.07 ((
% 121.84/16.07 (setunionsingleton1) =>
% 121.84/16.07 ((
% 121.84/16.07 (setunionsingleton2) =>
% 121.84/16.07 ((
% 121.84/16.07 (setunionsingleton) =>
% 121.84/16.07 ((
% 121.84/16.07 (singletonprop) =>
% 121.84/16.07 ((
% 121.84/16.07 (ex1E1) =>
% 121.84/16.07 ((
% 121.84/16.07 (ex1I) =>
% 121.84/16.07 ((
% 121.84/16.07 (ex1I2) =>
% 121.84/16.07 ((
% 121.84/16.07 (singletonsuniq) =>
% 121.84/16.07 ((
% 121.84/16.07 (setukpairinjL1) =>
% 121.84/16.07 ((
% 121.84/16.07 (kfstsingleton) =>
% 121.84/16.07 ((
% 121.84/16.07 (theprop) =>
% 121.84/16.07 ((
% 121.84/16.07 (kfstpairEq) =>
% 121.84/16.07 ((
% 121.84/16.07 (cartprodfstin) =>
% 121.84/16.07 ((
% 121.84/16.07 (setukpairinjL2) =>
% 121.84/16.07 ((
% 121.84/16.07 (setukpairinjL) =>
% 121.84/16.07 ((
% 121.84/16.07 (setukpairinjR11) =>
% 121.84/16.07 ((
% 121.84/16.07 (setukpairinjR12) =>
% 121.84/16.07 ((
% 121.84/16.07 (setukpairinjR1) =>
% 121.84/16.07 ((
% 121.84/16.07 (upairequniteq) =>
% 121.84/16.07 ((
% 121.84/16.07 (setukpairinjR2) =>
% 121.84/16.07 ((
% 121.84/16.07 (setukpairinjR) =>
% 121.84/16.07 ((
% 121.84/16.07 (ksndsingleton) =>
% 121.84/16.07 ((
% 121.84/16.07 (ksndpairEq) =>
% 121.84/16.07 ((
% 121.84/16.07 (kpairsurjEq) =>
% 121.84/16.07 ((
% 121.84/16.07 (cartprodsndin) =>
% 121.84/16.07 ((
% 121.84/16.07 (cartprodpairmemEL) =>
% 121.84/16.07 ((
% 121.84/16.07 (cartprodpairmemER) =>
% 121.84/16.07 ((
% 121.84/16.07 (cartprodmempaircEq) =>
% 121.84/16.07 ((
% 121.84/16.07 (cartprodfstpairEq) =>
% 121.84/16.07 ((
% 121.84/16.07 (cartprodsndpairEq) =>
% 121.84/16.07 ((
% 121.84/16.07 (cartprodpairsurjEq) =>
% 121.84/16.07 ((
% 121.84/16.07 (dpsetconstrI) =>
% 121.84/16.07 ((
% 121.84/16.07 (dpsetconstrSub) =>
% 121.84/16.07 ((
% 121.84/16.07 (setOfPairsIsBReln) =>
% 121.84/16.07 ((
% 121.84/16.07 (dpsetconstrERa) =>
% 121.84/16.07 ((
% 121.84/16.07 (dpsetconstrEL1) =>
% 121.84/16.07 ((
% 121.84/16.07 (dpsetconstrEL2) =>
% 121.84/16.07 ((
% 121.84/16.07 (dpsetconstrER) =>
% 121.84/16.07 ((
% 121.84/16.07 (funcImageSingleton) =>
% 121.84/16.07 ((
% 121.84/16.07 (apProp) =>
% 121.84/16.07 ((
% 121.84/16.07 (app) =>
% 121.84/16.07 ((
% 121.84/16.07 (infuncsetfunc) =>
% 121.84/16.07 ((
% 121.84/16.07 (ap2p) =>
% 121.84/16.07 ((
% 121.84/16.07 (funcinfuncset) =>
% 121.84/16.07 ((
% 121.84/16.07 (lamProp) =>
% 121.84/16.07 ((
% 121.84/16.07 (lamp) =>
% 121.84/16.07 ((
% 121.84/16.07 (lam2p) =>
% 121.84/16.07 ((
% 121.84/16.07 (brelnall1) =>
% 121.84/16.07 ((
% 121.84/16.07 (brelnall2) =>
% 121.84/16.07 ((
% 121.84/16.07 (ex1E2) =>
% 121.84/16.07 ((
% 121.84/16.07 (funcGraphProp1) =>
% 121.84/16.07 ((
% 121.84/16.07 (funcGraphProp3) =>
% 121.84/16.07 ((
% 121.84/16.07 (funcGraphProp2) =>
% 121.84/16.07 ((
% 121.84/16.07 (funcextLem) =>
% 121.84/16.07 ((
% 121.84/16.07 (funcGraphProp4) =>
% 121.84/16.07 ((
% 121.84/16.07 (subbreln) =>
% 121.84/16.07 ((
% 121.84/16.07 (eqbreln) =>
% 121.84/16.07 ((
% 121.84/16.07 (funcext) =>
% 121.84/16.07 ((
% 121.84/16.07 (funcext2) =>
% 121.84/16.07 ((
% 121.84/16.07 (ap2apEq1) =>
% 121.84/16.07 ((
% 121.84/16.07 (ap2apEq2) =>
% 121.84/16.07 ((
% 121.84/16.07 (beta1) =>
% 121.84/16.07 ((
% 121.84/16.07 (eta1) =>
% 121.84/16.07 ((
% 121.84/16.07 (lam2lamEq) =>
% 121.84/16.07 ((
% 121.84/16.07 (beta2) =>
% 121.84/16.07 ((
% 121.84/16.07 (eta2) =>
% 121.84/16.07 ((
% 121.84/16.07 (iffalseProp1) =>
% 121.84/16.07 ((
% 121.84/16.07 (iffalseProp2) =>
% 121.84/16.07 ((
% 121.84/16.07 (iftrueProp1) =>
% 121.84/16.07 ((
% 121.84/16.07 (iftrueProp2) =>
% 121.84/16.07 ((
% 121.84/16.07 (ifSingleton) =>
% 121.84/16.07 ((
% 121.84/16.07 (ifp) =>
% 121.84/16.07 ((
% 121.84/16.07 (theeq) =>
% 121.84/16.07 ((
% 121.84/16.07 (iftrue) =>
% 121.84/16.07 ((
% 121.84/16.07 (iffalse) =>
% 121.84/16.07 ((
% 121.84/16.07 (iftrueorfalse) =>
% 121.84/16.07 ((
% 121.84/16.07 (binintersectT_lem) =>
% 121.84/16.07 ((
% 121.84/16.07 (binunionT_lem) =>
% 121.84/16.07 ((
% 121.84/16.07 (powersetT_lem) =>
% 121.84/16.07 ((
% 121.84/16.07 (setminusT_lem) =>
% 121.84/16.07 ((
% 121.84/16.07 (complementT_lem) =>
% 121.84/16.07 ((
% 121.84/16.07 (setextT) =>
% 121.84/16.07 ((
% 121.84/16.07 (subsetTI) =>
% 121.84/16.07 ((
% 121.84/16.07 (powersetTI1) =>
% 121.84/16.07 ((
% 121.84/16.07 (powersetTE1) =>
% 121.84/16.07 ((
% 121.84/16.07 (complementTI1) =>
% 121.84/16.07 ((
% 121.84/16.07 (complementTE1) =>
% 121.84/16.07 ((
% 121.84/16.07 (binintersectTELcontra) =>
% 121.84/16.07 ((
% 121.84/16.07 (binintersectTERcontra) =>
% 121.84/16.07 ((
% 121.84/16.07 (contrasubsetT) =>
% 121.84/16.07 ((
% 121.84/16.07 (contrasubsetT1) =>
% 121.84/16.07 ((
% 121.84/16.07 (contrasubsetT2) =>
% 121.84/16.07 ((
% 121.84/16.07 (contrasubsetT3) =>
% 121.84/16.07 ((
% 121.84/16.07 (doubleComplementI1) =>
% 121.84/16.07 ((
% 121.84/16.07 (doubleComplementE1) =>
% 121.84/16.07 ((
% 121.84/16.07 (doubleComplementSub1) =>
% 121.84/16.07 ((
% 121.84/16.07 (doubleComplementSub2) =>
% 121.84/16.07 ((
% 121.84/16.07 (doubleComplementEq) =>
% 121.84/16.07 ((
% 121.84/16.07 (complementTnotintersectT) =>
% 121.84/16.07 ((
% 121.84/16.07 (complementImpComplementIntersect) =>
% 121.84/16.07 ((
% 121.84/16.07 (complementSubsetComplementIntersect) =>
% 121.84/16.07 ((
% 121.84/16.07 (complementInPowersetComplementIntersect) =>
% 121.84/16.07 ((
% 121.84/16.07 (contraSubsetComplement) =>
% 121.84/16.07 ((
% 121.84/16.07 (complementTcontraSubset) =>
% 121.84/16.07 ((
% 121.84/16.07 (binunionTILcontra) =>
% 121.84/16.07 ((
% 121.84/16.07 (binunionTIRcontra) =>
% 121.84/16.07 ((
% 121.84/16.07 (inIntersectImpInUnion) =>
% 121.84/16.07 ((
% 121.84/16.07 (inIntersectImpInUnion2) =>
% 121.84/16.07 ((
% 121.84/16.07 (inIntersectImpInIntersectUnions) =>
% 121.84/16.07 ((
% 121.84/16.07 (intersectInPowersetIntersectUnions) =>
% 121.84/16.07 ((
% 121.84/16.07 (inComplementUnionImpNotIn1) =>
% 121.84/16.07 ((
% 121.84/16.07 (inComplementUnionImpInComplement1) =>
% 121.84/16.07 ((
% 121.84/16.07 (binunionTE) =>
% 121.84/16.07 ((
% 121.84/16.07 (binunionTEcontra) =>
% 121.84/16.07 ((
% 121.84/16.07 (demorgan2a1) =>
% 121.84/16.07 ((
% 121.84/16.07 (complementUnionInPowersetComplement) =>
% 121.84/16.07 ((
% 121.84/16.07 (demorgan2a2) =>
% 121.84/16.07 ((
% 121.84/16.07 (demorgan1a) =>
% 121.84/16.07 ((
% 121.84/16.07 (demorgan1b) =>
% 121.84/16.07 ((
% 121.84/16.07 (demorgan1) =>
% 121.84/16.07 ((
% 121.84/16.07 (demorgan2a) =>
% 121.84/16.07 ((
% 121.84/16.07 (demorgan2b2) =>
% 121.84/16.07 ((
% 121.84/16.07 (demorgan2b) =>
% 121.84/16.07 ((
% 121.84/16.07 (demorgan2) =>
% 121.84/16.07 ((
% 121.84/16.07 (woz13rule0) =>
% 121.84/16.07 ((
% 121.84/16.07 (woz13rule1) =>
% 121.84/16.07 ((
% 121.84/16.07 (woz13rule2) =>
% 121.84/16.07 ((
% 121.84/16.07 (woz13rule3) =>
% 121.84/16.07 ((
% 121.84/16.07 (woz13rule4) =>
% 121.84/16.07 ((
% 121.84/16.07 (woz1_1) =>
% 121.84/16.07 ((
% 121.84/16.07 (woz1_2) =>
% 121.84/16.07 ((
% 121.84/16.07 (woz1_3) =>
% 121.84/16.07 ((
% 121.84/16.07 (woz1_4) =>
% 121.84/16.07 ((
% 121.84/16.07 (woz1_5) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1all2) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1SetBreln1) =>
% 121.84/16.07 ((
% 121.84/16.07 (choice2fnsingleton) =>
% 121.84/16.07 ((
% 121.84/16.07 (setOfPairsIsBReln1) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1all1) =>
% 121.84/16.07 ((
% 121.84/16.07 (subbreln1) =>
% 121.84/16.07 ((
% 121.84/16.07 (eqbreln1) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1invprop) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1invI) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1invE) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1compprop) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1compI) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1compE) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1compEex) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1unionprop) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1unionIL) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1unionIR) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1unionI) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1unionE) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1unionEcases) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1unionCommutes) =>
% 121.84/16.07 ((
% 121.84/16.07 (woz2Ex) =>
% 121.84/16.07 ((
% 121.84/16.07 (woz2W) =>
% 121.84/16.07 ((
% 121.84/16.07 (woz2A) =>
% 121.84/16.07 ((
% 121.84/16.07 (woz2B) =>
% 121.84/16.07 ((
% 121.84/16.07 (image1Ex) =>
% 121.84/16.07 ((
% 121.84/16.07 (image1Ex1) =>
% 121.84/16.07 ((
% 121.84/16.07 (image1Equiv) =>
% 121.84/16.07 ((
% 121.84/16.07 (image1E) =>
% 121.84/16.07 ((
% 121.84/16.07 (image1I) =>
% 121.84/16.07 ((
% 121.84/16.07 (injFuncInInjFuncSet) =>
% 121.84/16.07 ((
% 121.84/16.07 (!!) @ (
% 121.84/16.07 (('#B') @ (
% 121.84/16.07 !!) @
% 121.84/16.07 (
% 121.84/16.07 (
% 121.84/16.07 ('#B') @ (
% 121.84/16.07 (
% 121.84/16.07 ('#B') @ (
% 121.84/16.07 !!))) @
% 121.84/16.07 (
% 121.84/16.07 (
% 121.84/16.07 ('#S') @ (
% 121.84/16.07 (
% 121.84/16.07 ('#B') @ (
% 121.84/16.07 '#S') @
% 121.84/16.07 (
% 121.84/16.07 (
% 121.84/16.07 ('#B') @ (
% 121.84/16.07 (
% 121.84/16.07 ('#B') @ (
% 121.84/16.07 '#S'))) @
% 121.84/16.07 (
% 121.84/16.07 (
% 121.84/16.07 ('#B') @ (
% 121.84/16.07 (
% 121.84/16.07 ('#B') @ (
% 121.84/16.07 (
% 121.84/16.07 ('#B') @ (
% 121.84/16.07 =>))))) @
% 121.84/16.07 (
% 121.84/16.07 (
% 121.84/16.07 ('#B') @ (
% 121.84/16.07 (
% 121.84/16.07 ('#B') @ (
% 121.84/16.07 (
% 121.84/16.07 ('#C') @ in)))) @
% 121.84/16.07 injFuncSet)))))))) @
% 121.84/16.07 (
% 121.84/16.07 (
% 121.84/16.07 ('#B') @ (
% 121.84/16.07 (
% 121.84/16.07 ('#B') @ (
% 121.84/16.07 (
% 121.84/16.07 ('#C') @ in)))) @
% 121.84/16.07 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 121.84/16.07 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl578])).
% 121.84/16.07 thf(zip_derived_cl595, plain,
% 121.84/16.07 (~ (((notdallE) =>
% 121.84/16.07 (((exuI1) =>
% 121.84/16.07 (((exuI3) =>
% 121.84/16.07 (((exuI2) =>
% 121.84/16.07 (((inCongP) =>
% 121.84/16.07 (((in__Cong) =>
% 121.84/16.07 (((exuE3u) =>
% 121.84/16.07 (((exu__Cong) =>
% 121.84/16.07 (((setadjoin__Cong) =>
% 121.84/16.07 (((powerset__Cong) =>
% 121.84/16.07 (((setunion__Cong) =>
% 121.84/16.07 (((exuEu) =>
% 121.84/16.07 (((descr__Cong) =>
% 121.84/16.07 (((dsetconstr__Cong) =>
% 121.84/16.07 (((subsetI1) =>
% 121.84/16.07 (((eqimpsubset2) =>
% 121.84/16.07 (((eqimpsubset1) =>
% 121.84/16.07 (((subsetI2) =>
% 121.84/16.07 (((emptysetsubset) =>
% 121.84/16.07 (((subsetE) =>
% 121.84/16.07 (((subsetE2) =>
% 121.84/16.07 (((notsubsetI) =>
% 121.84/16.07 (((notequalI1) =>
% 121.84/16.07 (((notequalI2) =>
% 121.84/16.07 (((subsetRefl) =>
% 121.84/16.07 (((subsetTrans) =>
% 121.84/16.07 (((setadjoinSub) =>
% 121.84/16.07 (((setadjoinSub2) =>
% 121.84/16.07 (((subset2powerset) =>
% 121.84/16.07 (((setextsub) =>
% 121.84/16.07 ((
% 121.84/16.07 (subsetemptysetimpeq) =>
% 121.84/16.07 ((
% 121.84/16.07 (powersetI1) =>
% 121.84/16.07 ((
% 121.84/16.07 (powersetE1) =>
% 121.84/16.07 ((
% 121.84/16.07 (inPowerset) =>
% 121.84/16.07 ((
% 121.84/16.07 (powersetsubset) =>
% 121.84/16.07 ((
% 121.84/16.07 (sepInPowerset) =>
% 121.84/16.07 ((
% 121.84/16.07 (sepSubset) =>
% 121.84/16.07 ((
% 121.84/16.07 (binunionIL) =>
% 121.84/16.07 ((
% 121.84/16.07 (upairset2IR) =>
% 121.84/16.07 ((
% 121.84/16.07 (binunionIR) =>
% 121.84/16.07 ((
% 121.84/16.07 (binunionEcases) =>
% 121.84/16.07 ((
% 121.84/16.07 (binunionE) =>
% 121.84/16.07 ((
% 121.84/16.07 (binunionLsub) =>
% 121.84/16.07 ((
% 121.84/16.07 (binunionRsub) =>
% 121.84/16.07 ((
% 121.84/16.07 (binintersectI) =>
% 121.84/16.07 ((
% 121.84/16.07 (binintersectSubset5) =>
% 121.84/16.07 ((
% 121.84/16.07 (binintersectEL) =>
% 121.84/16.07 ((
% 121.84/16.07 (binintersectLsub) =>
% 121.84/16.07 ((
% 121.84/16.07 (binintersectSubset2) =>
% 121.84/16.07 ((
% 121.84/16.07 (binintersectSubset3) =>
% 121.84/16.07 ((
% 121.84/16.07 (binintersectER) =>
% 121.84/16.07 ((
% 121.84/16.07 (disjointsetsI1) =>
% 121.84/16.07 ((
% 121.84/16.07 (binintersectRsub) =>
% 121.84/16.07 ((
% 121.84/16.07 (binintersectSubset4) =>
% 121.84/16.07 ((
% 121.84/16.07 (binintersectSubset1) =>
% 121.84/16.07 ((
% 121.84/16.07 (bs114d) =>
% 121.84/16.07 ((
% 121.84/16.07 (setminusI) =>
% 121.84/16.07 ((
% 121.84/16.07 (setminusEL) =>
% 121.84/16.07 ((
% 121.84/16.07 (setminusER) =>
% 121.84/16.07 ((
% 121.84/16.07 (setminusSubset2) =>
% 121.84/16.07 ((
% 121.84/16.07 (setminusERneg) =>
% 121.84/16.07 ((
% 121.84/16.07 (setminusELneg) =>
% 121.84/16.07 ((
% 121.84/16.07 (setminusILneg) =>
% 121.84/16.07 ((
% 121.84/16.07 (setminusIRneg) =>
% 121.84/16.07 ((
% 121.84/16.07 (setminusLsub) =>
% 121.84/16.07 ((
% 121.84/16.07 (setminusSubset1) =>
% 121.84/16.07 ((
% 121.84/16.07 (symdiffE) =>
% 121.84/16.07 ((
% 121.84/16.07 (symdiffI1) =>
% 121.84/16.07 ((
% 121.84/16.07 (symdiffI2) =>
% 121.84/16.07 ((
% 121.84/16.07 (symdiffIneg1) =>
% 121.84/16.07 ((
% 121.84/16.07 (symdiffIneg2) =>
% 121.84/16.07 ((
% 121.84/16.07 (secondinupair) =>
% 121.84/16.07 ((
% 121.84/16.07 (setukpairIL) =>
% 121.84/16.07 ((
% 121.84/16.07 (setukpairIR) =>
% 121.84/16.07 ((
% 121.84/16.07 (kpairiskpair) =>
% 121.84/16.07 ((
% 121.84/16.07 (kpairp) =>
% 121.84/16.07 ((
% 121.84/16.07 (singletonsubset) =>
% 121.84/16.07 ((
% 121.84/16.07 (singletoninpowerset) =>
% 121.84/16.07 ((
% 121.84/16.07 (singletoninpowunion) =>
% 121.84/16.07 ((
% 121.84/16.07 (upairset2E) =>
% 121.84/16.07 ((
% 121.84/16.07 (upairsubunion) =>
% 121.84/16.07 ((
% 121.84/16.07 (upairinpowunion) =>
% 121.84/16.07 ((
% 121.84/16.07 (ubforcartprodlem1) =>
% 121.84/16.07 ((
% 121.84/16.07 (ubforcartprodlem2) =>
% 121.84/16.07 ((
% 121.84/16.07 (ubforcartprodlem3) =>
% 121.84/16.07 ((
% 121.84/16.07 (cartprodpairin) =>
% 121.84/16.07 ((
% 121.84/16.07 (cartprodmempair1) =>
% 121.84/16.07 ((
% 121.84/16.07 (cartprodmempair) =>
% 121.84/16.07 ((
% 121.84/16.07 (setunionE2) =>
% 121.84/16.07 ((
% 121.84/16.07 (setunionsingleton1) =>
% 121.84/16.07 ((
% 121.84/16.07 (setunionsingleton2) =>
% 121.84/16.07 ((
% 121.84/16.07 (setunionsingleton) =>
% 121.84/16.07 ((
% 121.84/16.07 (singletonprop) =>
% 121.84/16.07 ((
% 121.84/16.07 (ex1E1) =>
% 121.84/16.07 ((
% 121.84/16.07 (ex1I) =>
% 121.84/16.07 ((
% 121.84/16.07 (ex1I2) =>
% 121.84/16.07 ((
% 121.84/16.07 (singletonsuniq) =>
% 121.84/16.07 ((
% 121.84/16.07 (setukpairinjL1) =>
% 121.84/16.07 ((
% 121.84/16.07 (kfstsingleton) =>
% 121.84/16.07 ((
% 121.84/16.07 (theprop) =>
% 121.84/16.07 ((
% 121.84/16.07 (kfstpairEq) =>
% 121.84/16.07 ((
% 121.84/16.07 (cartprodfstin) =>
% 121.84/16.07 ((
% 121.84/16.07 (setukpairinjL2) =>
% 121.84/16.07 ((
% 121.84/16.07 (setukpairinjL) =>
% 121.84/16.07 ((
% 121.84/16.07 (setukpairinjR11) =>
% 121.84/16.07 ((
% 121.84/16.07 (setukpairinjR12) =>
% 121.84/16.07 ((
% 121.84/16.07 (setukpairinjR1) =>
% 121.84/16.07 ((
% 121.84/16.07 (upairequniteq) =>
% 121.84/16.07 ((
% 121.84/16.07 (setukpairinjR2) =>
% 121.84/16.07 ((
% 121.84/16.07 (setukpairinjR) =>
% 121.84/16.07 ((
% 121.84/16.07 (ksndsingleton) =>
% 121.84/16.07 ((
% 121.84/16.07 (ksndpairEq) =>
% 121.84/16.07 ((
% 121.84/16.07 (kpairsurjEq) =>
% 121.84/16.07 ((
% 121.84/16.07 (cartprodsndin) =>
% 121.84/16.07 ((
% 121.84/16.07 (cartprodpairmemEL) =>
% 121.84/16.07 ((
% 121.84/16.07 (cartprodpairmemER) =>
% 121.84/16.07 ((
% 121.84/16.07 (cartprodmempaircEq) =>
% 121.84/16.07 ((
% 121.84/16.07 (cartprodfstpairEq) =>
% 121.84/16.07 ((
% 121.84/16.07 (cartprodsndpairEq) =>
% 121.84/16.07 ((
% 121.84/16.07 (cartprodpairsurjEq) =>
% 121.84/16.07 ((
% 121.84/16.07 (dpsetconstrI) =>
% 121.84/16.07 ((
% 121.84/16.07 (dpsetconstrSub) =>
% 121.84/16.07 ((
% 121.84/16.07 (setOfPairsIsBReln) =>
% 121.84/16.07 ((
% 121.84/16.07 (dpsetconstrERa) =>
% 121.84/16.07 ((
% 121.84/16.07 (dpsetconstrEL1) =>
% 121.84/16.07 ((
% 121.84/16.07 (dpsetconstrEL2) =>
% 121.84/16.07 ((
% 121.84/16.07 (dpsetconstrER) =>
% 121.84/16.07 ((
% 121.84/16.07 (funcImageSingleton) =>
% 121.84/16.07 ((
% 121.84/16.07 (apProp) =>
% 121.84/16.07 ((
% 121.84/16.07 (app) =>
% 121.84/16.07 ((
% 121.84/16.07 (infuncsetfunc) =>
% 121.84/16.07 ((
% 121.84/16.07 (ap2p) =>
% 121.84/16.07 ((
% 121.84/16.07 (funcinfuncset) =>
% 121.84/16.07 ((
% 121.84/16.07 (lamProp) =>
% 121.84/16.07 ((
% 121.84/16.07 (lamp) =>
% 121.84/16.07 ((
% 121.84/16.07 (lam2p) =>
% 121.84/16.07 ((
% 121.84/16.07 (brelnall1) =>
% 121.84/16.07 ((
% 121.84/16.07 (brelnall2) =>
% 121.84/16.07 ((
% 121.84/16.07 (ex1E2) =>
% 121.84/16.07 ((
% 121.84/16.07 (funcGraphProp1) =>
% 121.84/16.07 ((
% 121.84/16.07 (funcGraphProp3) =>
% 121.84/16.07 ((
% 121.84/16.07 (funcGraphProp2) =>
% 121.84/16.07 ((
% 121.84/16.07 (funcextLem) =>
% 121.84/16.07 ((
% 121.84/16.07 (funcGraphProp4) =>
% 121.84/16.07 ((
% 121.84/16.07 (subbreln) =>
% 121.84/16.07 ((
% 121.84/16.07 (eqbreln) =>
% 121.84/16.07 ((
% 121.84/16.07 (funcext) =>
% 121.84/16.07 ((
% 121.84/16.07 (funcext2) =>
% 121.84/16.07 ((
% 121.84/16.07 (ap2apEq1) =>
% 121.84/16.07 ((
% 121.84/16.07 (ap2apEq2) =>
% 121.84/16.07 ((
% 121.84/16.07 (beta1) =>
% 121.84/16.07 ((
% 121.84/16.07 (eta1) =>
% 121.84/16.07 ((
% 121.84/16.07 (lam2lamEq) =>
% 121.84/16.07 ((
% 121.84/16.07 (beta2) =>
% 121.84/16.07 ((
% 121.84/16.07 (eta2) =>
% 121.84/16.07 ((
% 121.84/16.07 (iffalseProp1) =>
% 121.84/16.07 ((
% 121.84/16.07 (iffalseProp2) =>
% 121.84/16.07 ((
% 121.84/16.07 (iftrueProp1) =>
% 121.84/16.07 ((
% 121.84/16.07 (iftrueProp2) =>
% 121.84/16.07 ((
% 121.84/16.07 (ifSingleton) =>
% 121.84/16.07 ((
% 121.84/16.07 (ifp) =>
% 121.84/16.07 ((
% 121.84/16.07 (theeq) =>
% 121.84/16.07 ((
% 121.84/16.07 (iftrue) =>
% 121.84/16.07 ((
% 121.84/16.07 (iffalse) =>
% 121.84/16.07 ((
% 121.84/16.07 (iftrueorfalse) =>
% 121.84/16.07 ((
% 121.84/16.07 (binintersectT_lem) =>
% 121.84/16.07 ((
% 121.84/16.07 (binunionT_lem) =>
% 121.84/16.07 ((
% 121.84/16.07 (powersetT_lem) =>
% 121.84/16.07 ((
% 121.84/16.07 (setminusT_lem) =>
% 121.84/16.07 ((
% 121.84/16.07 (complementT_lem) =>
% 121.84/16.07 ((
% 121.84/16.07 (setextT) =>
% 121.84/16.07 ((
% 121.84/16.07 (subsetTI) =>
% 121.84/16.07 ((
% 121.84/16.07 (powersetTI1) =>
% 121.84/16.07 ((
% 121.84/16.07 (powersetTE1) =>
% 121.84/16.07 ((
% 121.84/16.07 (complementTI1) =>
% 121.84/16.07 ((
% 121.84/16.07 (complementTE1) =>
% 121.84/16.07 ((
% 121.84/16.07 (binintersectTELcontra) =>
% 121.84/16.07 ((
% 121.84/16.07 (binintersectTERcontra) =>
% 121.84/16.07 ((
% 121.84/16.07 (contrasubsetT) =>
% 121.84/16.07 ((
% 121.84/16.07 (contrasubsetT1) =>
% 121.84/16.07 ((
% 121.84/16.07 (contrasubsetT2) =>
% 121.84/16.07 ((
% 121.84/16.07 (contrasubsetT3) =>
% 121.84/16.07 ((
% 121.84/16.07 (doubleComplementI1) =>
% 121.84/16.07 ((
% 121.84/16.07 (doubleComplementE1) =>
% 121.84/16.07 ((
% 121.84/16.07 (doubleComplementSub1) =>
% 121.84/16.07 ((
% 121.84/16.07 (doubleComplementSub2) =>
% 121.84/16.07 ((
% 121.84/16.07 (doubleComplementEq) =>
% 121.84/16.07 ((
% 121.84/16.07 (complementTnotintersectT) =>
% 121.84/16.07 ((
% 121.84/16.07 (complementImpComplementIntersect) =>
% 121.84/16.07 ((
% 121.84/16.07 (complementSubsetComplementIntersect) =>
% 121.84/16.07 ((
% 121.84/16.07 (complementInPowersetComplementIntersect) =>
% 121.84/16.07 ((
% 121.84/16.07 (contraSubsetComplement) =>
% 121.84/16.07 ((
% 121.84/16.07 (complementTcontraSubset) =>
% 121.84/16.07 ((
% 121.84/16.07 (binunionTILcontra) =>
% 121.84/16.07 ((
% 121.84/16.07 (binunionTIRcontra) =>
% 121.84/16.07 ((
% 121.84/16.07 (inIntersectImpInUnion) =>
% 121.84/16.07 ((
% 121.84/16.07 (inIntersectImpInUnion2) =>
% 121.84/16.07 ((
% 121.84/16.07 (inIntersectImpInIntersectUnions) =>
% 121.84/16.07 ((
% 121.84/16.07 (intersectInPowersetIntersectUnions) =>
% 121.84/16.07 ((
% 121.84/16.07 (inComplementUnionImpNotIn1) =>
% 121.84/16.07 ((
% 121.84/16.07 (inComplementUnionImpInComplement1) =>
% 121.84/16.07 ((
% 121.84/16.07 (binunionTE) =>
% 121.84/16.07 ((
% 121.84/16.07 (binunionTEcontra) =>
% 121.84/16.07 ((
% 121.84/16.07 (demorgan2a1) =>
% 121.84/16.07 ((
% 121.84/16.07 (complementUnionInPowersetComplement) =>
% 121.84/16.07 ((
% 121.84/16.07 (demorgan2a2) =>
% 121.84/16.07 ((
% 121.84/16.07 (demorgan1a) =>
% 121.84/16.07 ((
% 121.84/16.07 (demorgan1b) =>
% 121.84/16.07 ((
% 121.84/16.07 (demorgan1) =>
% 121.84/16.07 ((
% 121.84/16.07 (demorgan2a) =>
% 121.84/16.07 ((
% 121.84/16.07 (demorgan2b2) =>
% 121.84/16.07 ((
% 121.84/16.07 (demorgan2b) =>
% 121.84/16.07 ((
% 121.84/16.07 (demorgan2) =>
% 121.84/16.07 ((
% 121.84/16.07 (woz13rule0) =>
% 121.84/16.07 ((
% 121.84/16.07 (woz13rule1) =>
% 121.84/16.07 ((
% 121.84/16.07 (woz13rule2) =>
% 121.84/16.07 ((
% 121.84/16.07 (woz13rule3) =>
% 121.84/16.07 ((
% 121.84/16.07 (woz13rule4) =>
% 121.84/16.07 ((
% 121.84/16.07 (woz1_1) =>
% 121.84/16.07 ((
% 121.84/16.07 (woz1_2) =>
% 121.84/16.07 ((
% 121.84/16.07 (woz1_3) =>
% 121.84/16.07 ((
% 121.84/16.07 (woz1_4) =>
% 121.84/16.07 ((
% 121.84/16.07 (woz1_5) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1all2) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1SetBreln1) =>
% 121.84/16.07 ((
% 121.84/16.07 (choice2fnsingleton) =>
% 121.84/16.07 ((
% 121.84/16.07 (setOfPairsIsBReln1) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1all1) =>
% 121.84/16.07 ((
% 121.84/16.07 (subbreln1) =>
% 121.84/16.07 ((
% 121.84/16.07 (eqbreln1) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1invprop) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1invI) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1invE) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1compprop) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1compI) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1compE) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1compEex) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1unionprop) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1unionIL) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1unionIR) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1unionI) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1unionE) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1unionEcases) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1unionCommutes) =>
% 121.84/16.07 ((
% 121.84/16.07 (woz2Ex) =>
% 121.84/16.07 ((
% 121.84/16.07 (woz2W) =>
% 121.84/16.07 ((
% 121.84/16.07 (woz2A) =>
% 121.84/16.07 ((
% 121.84/16.07 (woz2B) =>
% 121.84/16.07 ((
% 121.84/16.07 (image1Ex) =>
% 121.84/16.07 ((
% 121.84/16.07 (image1Ex1) =>
% 121.84/16.07 ((
% 121.84/16.07 (image1Equiv) =>
% 121.84/16.07 ((
% 121.84/16.07 (image1E) =>
% 121.84/16.07 ((
% 121.84/16.07 (image1I) =>
% 121.84/16.07 ((
% 121.84/16.07 (injFuncInInjFuncSet) =>
% 121.84/16.07 ((
% 121.84/16.07 (!!) @ (
% 121.84/16.07 (('#B') @ (
% 121.84/16.07 !!) @
% 121.84/16.07 (
% 121.84/16.07 (
% 121.84/16.07 ('#B') @ (
% 121.84/16.07 (
% 121.84/16.07 ('#B') @ (
% 121.84/16.07 !!))) @
% 121.84/16.07 (
% 121.84/16.07 (
% 121.84/16.07 ('#S') @ (
% 121.84/16.07 (
% 121.84/16.07 ('#B') @ (
% 121.84/16.07 '#S') @
% 121.84/16.07 (
% 121.84/16.07 (
% 121.84/16.07 ('#B') @ (
% 121.84/16.07 (
% 121.84/16.07 ('#B') @ (
% 121.84/16.07 '#S'))) @
% 121.84/16.07 (
% 121.84/16.07 (
% 121.84/16.07 ('#B') @ (
% 121.84/16.07 (
% 121.84/16.07 ('#B') @ (
% 121.84/16.07 (
% 121.84/16.07 ('#B') @ (
% 121.84/16.07 =>))))) @
% 121.84/16.07 (
% 121.84/16.07 (
% 121.84/16.07 ('#B') @ (
% 121.84/16.07 (
% 121.84/16.07 ('#B') @ (
% 121.84/16.07 (
% 121.84/16.07 ('#C') @ in)))) @
% 121.84/16.07 injFuncSet)))))))) @
% 121.84/16.07 (
% 121.84/16.07 (
% 121.84/16.07 ('#B') @ (
% 121.84/16.07 (
% 121.84/16.07 ('#B') @ (
% 121.84/16.07 (
% 121.84/16.07 ('#C') @ in)))) @
% 121.84/16.07 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 121.84/16.07 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl586])).
% 121.84/16.07 thf(zip_derived_cl606, plain,
% 121.84/16.07 (~ (((exuI1) =>
% 121.84/16.07 (((exuI3) =>
% 121.84/16.07 (((exuI2) =>
% 121.84/16.07 (((inCongP) =>
% 121.84/16.07 (((in__Cong) =>
% 121.84/16.07 (((exuE3u) =>
% 121.84/16.07 (((exu__Cong) =>
% 121.84/16.07 (((setadjoin__Cong) =>
% 121.84/16.07 (((powerset__Cong) =>
% 121.84/16.07 (((setunion__Cong) =>
% 121.84/16.07 (((exuEu) =>
% 121.84/16.07 (((descr__Cong) =>
% 121.84/16.07 (((dsetconstr__Cong) =>
% 121.84/16.07 (((subsetI1) =>
% 121.84/16.07 (((eqimpsubset2) =>
% 121.84/16.07 (((eqimpsubset1) =>
% 121.84/16.07 (((subsetI2) =>
% 121.84/16.07 (((emptysetsubset) =>
% 121.84/16.07 (((subsetE) =>
% 121.84/16.07 (((subsetE2) =>
% 121.84/16.07 (((notsubsetI) =>
% 121.84/16.07 (((notequalI1) =>
% 121.84/16.07 (((notequalI2) =>
% 121.84/16.07 (((subsetRefl) =>
% 121.84/16.07 (((subsetTrans) =>
% 121.84/16.07 (((setadjoinSub) =>
% 121.84/16.07 (((setadjoinSub2) =>
% 121.84/16.07 (((subset2powerset) =>
% 121.84/16.07 (((setextsub) =>
% 121.84/16.07 (((subsetemptysetimpeq) =>
% 121.84/16.07 ((
% 121.84/16.07 (powersetI1) =>
% 121.84/16.07 ((
% 121.84/16.07 (powersetE1) =>
% 121.84/16.07 ((
% 121.84/16.07 (inPowerset) =>
% 121.84/16.07 ((
% 121.84/16.07 (powersetsubset) =>
% 121.84/16.07 ((
% 121.84/16.07 (sepInPowerset) =>
% 121.84/16.07 ((
% 121.84/16.07 (sepSubset) =>
% 121.84/16.07 ((
% 121.84/16.07 (binunionIL) =>
% 121.84/16.07 ((
% 121.84/16.07 (upairset2IR) =>
% 121.84/16.07 ((
% 121.84/16.07 (binunionIR) =>
% 121.84/16.07 ((
% 121.84/16.07 (binunionEcases) =>
% 121.84/16.07 ((
% 121.84/16.07 (binunionE) =>
% 121.84/16.07 ((
% 121.84/16.07 (binunionLsub) =>
% 121.84/16.07 ((
% 121.84/16.07 (binunionRsub) =>
% 121.84/16.07 ((
% 121.84/16.07 (binintersectI) =>
% 121.84/16.07 ((
% 121.84/16.07 (binintersectSubset5) =>
% 121.84/16.07 ((
% 121.84/16.07 (binintersectEL) =>
% 121.84/16.07 ((
% 121.84/16.07 (binintersectLsub) =>
% 121.84/16.07 ((
% 121.84/16.07 (binintersectSubset2) =>
% 121.84/16.07 ((
% 121.84/16.07 (binintersectSubset3) =>
% 121.84/16.07 ((
% 121.84/16.07 (binintersectER) =>
% 121.84/16.07 ((
% 121.84/16.07 (disjointsetsI1) =>
% 121.84/16.07 ((
% 121.84/16.07 (binintersectRsub) =>
% 121.84/16.07 ((
% 121.84/16.07 (binintersectSubset4) =>
% 121.84/16.07 ((
% 121.84/16.07 (binintersectSubset1) =>
% 121.84/16.07 ((
% 121.84/16.07 (bs114d) =>
% 121.84/16.07 ((
% 121.84/16.07 (setminusI) =>
% 121.84/16.07 ((
% 121.84/16.07 (setminusEL) =>
% 121.84/16.07 ((
% 121.84/16.07 (setminusER) =>
% 121.84/16.07 ((
% 121.84/16.07 (setminusSubset2) =>
% 121.84/16.07 ((
% 121.84/16.07 (setminusERneg) =>
% 121.84/16.07 ((
% 121.84/16.07 (setminusELneg) =>
% 121.84/16.07 ((
% 121.84/16.07 (setminusILneg) =>
% 121.84/16.07 ((
% 121.84/16.07 (setminusIRneg) =>
% 121.84/16.07 ((
% 121.84/16.07 (setminusLsub) =>
% 121.84/16.07 ((
% 121.84/16.07 (setminusSubset1) =>
% 121.84/16.07 ((
% 121.84/16.07 (symdiffE) =>
% 121.84/16.07 ((
% 121.84/16.07 (symdiffI1) =>
% 121.84/16.07 ((
% 121.84/16.07 (symdiffI2) =>
% 121.84/16.07 ((
% 121.84/16.07 (symdiffIneg1) =>
% 121.84/16.07 ((
% 121.84/16.07 (symdiffIneg2) =>
% 121.84/16.07 ((
% 121.84/16.07 (secondinupair) =>
% 121.84/16.07 ((
% 121.84/16.07 (setukpairIL) =>
% 121.84/16.07 ((
% 121.84/16.07 (setukpairIR) =>
% 121.84/16.07 ((
% 121.84/16.07 (kpairiskpair) =>
% 121.84/16.07 ((
% 121.84/16.07 (kpairp) =>
% 121.84/16.07 ((
% 121.84/16.07 (singletonsubset) =>
% 121.84/16.07 ((
% 121.84/16.07 (singletoninpowerset) =>
% 121.84/16.07 ((
% 121.84/16.07 (singletoninpowunion) =>
% 121.84/16.07 ((
% 121.84/16.07 (upairset2E) =>
% 121.84/16.07 ((
% 121.84/16.07 (upairsubunion) =>
% 121.84/16.07 ((
% 121.84/16.07 (upairinpowunion) =>
% 121.84/16.07 ((
% 121.84/16.07 (ubforcartprodlem1) =>
% 121.84/16.07 ((
% 121.84/16.07 (ubforcartprodlem2) =>
% 121.84/16.07 ((
% 121.84/16.07 (ubforcartprodlem3) =>
% 121.84/16.07 ((
% 121.84/16.07 (cartprodpairin) =>
% 121.84/16.07 ((
% 121.84/16.07 (cartprodmempair1) =>
% 121.84/16.07 ((
% 121.84/16.07 (cartprodmempair) =>
% 121.84/16.07 ((
% 121.84/16.07 (setunionE2) =>
% 121.84/16.07 ((
% 121.84/16.07 (setunionsingleton1) =>
% 121.84/16.07 ((
% 121.84/16.07 (setunionsingleton2) =>
% 121.84/16.07 ((
% 121.84/16.07 (setunionsingleton) =>
% 121.84/16.07 ((
% 121.84/16.07 (singletonprop) =>
% 121.84/16.07 ((
% 121.84/16.07 (ex1E1) =>
% 121.84/16.07 ((
% 121.84/16.07 (ex1I) =>
% 121.84/16.07 ((
% 121.84/16.07 (ex1I2) =>
% 121.84/16.07 ((
% 121.84/16.07 (singletonsuniq) =>
% 121.84/16.07 ((
% 121.84/16.07 (setukpairinjL1) =>
% 121.84/16.07 ((
% 121.84/16.07 (kfstsingleton) =>
% 121.84/16.07 ((
% 121.84/16.07 (theprop) =>
% 121.84/16.07 ((
% 121.84/16.07 (kfstpairEq) =>
% 121.84/16.07 ((
% 121.84/16.07 (cartprodfstin) =>
% 121.84/16.07 ((
% 121.84/16.07 (setukpairinjL2) =>
% 121.84/16.07 ((
% 121.84/16.07 (setukpairinjL) =>
% 121.84/16.07 ((
% 121.84/16.07 (setukpairinjR11) =>
% 121.84/16.07 ((
% 121.84/16.07 (setukpairinjR12) =>
% 121.84/16.07 ((
% 121.84/16.07 (setukpairinjR1) =>
% 121.84/16.07 ((
% 121.84/16.07 (upairequniteq) =>
% 121.84/16.07 ((
% 121.84/16.07 (setukpairinjR2) =>
% 121.84/16.07 ((
% 121.84/16.07 (setukpairinjR) =>
% 121.84/16.07 ((
% 121.84/16.07 (ksndsingleton) =>
% 121.84/16.07 ((
% 121.84/16.07 (ksndpairEq) =>
% 121.84/16.07 ((
% 121.84/16.07 (kpairsurjEq) =>
% 121.84/16.07 ((
% 121.84/16.07 (cartprodsndin) =>
% 121.84/16.07 ((
% 121.84/16.07 (cartprodpairmemEL) =>
% 121.84/16.07 ((
% 121.84/16.07 (cartprodpairmemER) =>
% 121.84/16.07 ((
% 121.84/16.07 (cartprodmempaircEq) =>
% 121.84/16.07 ((
% 121.84/16.07 (cartprodfstpairEq) =>
% 121.84/16.07 ((
% 121.84/16.07 (cartprodsndpairEq) =>
% 121.84/16.07 ((
% 121.84/16.07 (cartprodpairsurjEq) =>
% 121.84/16.07 ((
% 121.84/16.07 (dpsetconstrI) =>
% 121.84/16.07 ((
% 121.84/16.07 (dpsetconstrSub) =>
% 121.84/16.07 ((
% 121.84/16.07 (setOfPairsIsBReln) =>
% 121.84/16.07 ((
% 121.84/16.07 (dpsetconstrERa) =>
% 121.84/16.07 ((
% 121.84/16.07 (dpsetconstrEL1) =>
% 121.84/16.07 ((
% 121.84/16.07 (dpsetconstrEL2) =>
% 121.84/16.07 ((
% 121.84/16.07 (dpsetconstrER) =>
% 121.84/16.07 ((
% 121.84/16.07 (funcImageSingleton) =>
% 121.84/16.07 ((
% 121.84/16.07 (apProp) =>
% 121.84/16.07 ((
% 121.84/16.07 (app) =>
% 121.84/16.07 ((
% 121.84/16.07 (infuncsetfunc) =>
% 121.84/16.07 ((
% 121.84/16.07 (ap2p) =>
% 121.84/16.07 ((
% 121.84/16.07 (funcinfuncset) =>
% 121.84/16.07 ((
% 121.84/16.07 (lamProp) =>
% 121.84/16.07 ((
% 121.84/16.07 (lamp) =>
% 121.84/16.07 ((
% 121.84/16.07 (lam2p) =>
% 121.84/16.07 ((
% 121.84/16.07 (brelnall1) =>
% 121.84/16.07 ((
% 121.84/16.07 (brelnall2) =>
% 121.84/16.07 ((
% 121.84/16.07 (ex1E2) =>
% 121.84/16.07 ((
% 121.84/16.07 (funcGraphProp1) =>
% 121.84/16.07 ((
% 121.84/16.07 (funcGraphProp3) =>
% 121.84/16.07 ((
% 121.84/16.07 (funcGraphProp2) =>
% 121.84/16.07 ((
% 121.84/16.07 (funcextLem) =>
% 121.84/16.07 ((
% 121.84/16.07 (funcGraphProp4) =>
% 121.84/16.07 ((
% 121.84/16.07 (subbreln) =>
% 121.84/16.07 ((
% 121.84/16.07 (eqbreln) =>
% 121.84/16.07 ((
% 121.84/16.07 (funcext) =>
% 121.84/16.07 ((
% 121.84/16.07 (funcext2) =>
% 121.84/16.07 ((
% 121.84/16.07 (ap2apEq1) =>
% 121.84/16.07 ((
% 121.84/16.07 (ap2apEq2) =>
% 121.84/16.07 ((
% 121.84/16.07 (beta1) =>
% 121.84/16.07 ((
% 121.84/16.07 (eta1) =>
% 121.84/16.07 ((
% 121.84/16.07 (lam2lamEq) =>
% 121.84/16.07 ((
% 121.84/16.07 (beta2) =>
% 121.84/16.07 ((
% 121.84/16.07 (eta2) =>
% 121.84/16.07 ((
% 121.84/16.07 (iffalseProp1) =>
% 121.84/16.07 ((
% 121.84/16.07 (iffalseProp2) =>
% 121.84/16.07 ((
% 121.84/16.07 (iftrueProp1) =>
% 121.84/16.07 ((
% 121.84/16.07 (iftrueProp2) =>
% 121.84/16.07 ((
% 121.84/16.07 (ifSingleton) =>
% 121.84/16.07 ((
% 121.84/16.07 (ifp) =>
% 121.84/16.07 ((
% 121.84/16.07 (theeq) =>
% 121.84/16.07 ((
% 121.84/16.07 (iftrue) =>
% 121.84/16.07 ((
% 121.84/16.07 (iffalse) =>
% 121.84/16.07 ((
% 121.84/16.07 (iftrueorfalse) =>
% 121.84/16.07 ((
% 121.84/16.07 (binintersectT_lem) =>
% 121.84/16.07 ((
% 121.84/16.07 (binunionT_lem) =>
% 121.84/16.07 ((
% 121.84/16.07 (powersetT_lem) =>
% 121.84/16.07 ((
% 121.84/16.07 (setminusT_lem) =>
% 121.84/16.07 ((
% 121.84/16.07 (complementT_lem) =>
% 121.84/16.07 ((
% 121.84/16.07 (setextT) =>
% 121.84/16.07 ((
% 121.84/16.07 (subsetTI) =>
% 121.84/16.07 ((
% 121.84/16.07 (powersetTI1) =>
% 121.84/16.07 ((
% 121.84/16.07 (powersetTE1) =>
% 121.84/16.07 ((
% 121.84/16.07 (complementTI1) =>
% 121.84/16.07 ((
% 121.84/16.07 (complementTE1) =>
% 121.84/16.07 ((
% 121.84/16.07 (binintersectTELcontra) =>
% 121.84/16.07 ((
% 121.84/16.07 (binintersectTERcontra) =>
% 121.84/16.07 ((
% 121.84/16.07 (contrasubsetT) =>
% 121.84/16.07 ((
% 121.84/16.07 (contrasubsetT1) =>
% 121.84/16.07 ((
% 121.84/16.07 (contrasubsetT2) =>
% 121.84/16.07 ((
% 121.84/16.07 (contrasubsetT3) =>
% 121.84/16.07 ((
% 121.84/16.07 (doubleComplementI1) =>
% 121.84/16.07 ((
% 121.84/16.07 (doubleComplementE1) =>
% 121.84/16.07 ((
% 121.84/16.07 (doubleComplementSub1) =>
% 121.84/16.07 ((
% 121.84/16.07 (doubleComplementSub2) =>
% 121.84/16.07 ((
% 121.84/16.07 (doubleComplementEq) =>
% 121.84/16.07 ((
% 121.84/16.07 (complementTnotintersectT) =>
% 121.84/16.07 ((
% 121.84/16.07 (complementImpComplementIntersect) =>
% 121.84/16.07 ((
% 121.84/16.07 (complementSubsetComplementIntersect) =>
% 121.84/16.07 ((
% 121.84/16.07 (complementInPowersetComplementIntersect) =>
% 121.84/16.07 ((
% 121.84/16.07 (contraSubsetComplement) =>
% 121.84/16.07 ((
% 121.84/16.07 (complementTcontraSubset) =>
% 121.84/16.07 ((
% 121.84/16.07 (binunionTILcontra) =>
% 121.84/16.07 ((
% 121.84/16.07 (binunionTIRcontra) =>
% 121.84/16.07 ((
% 121.84/16.07 (inIntersectImpInUnion) =>
% 121.84/16.07 ((
% 121.84/16.07 (inIntersectImpInUnion2) =>
% 121.84/16.07 ((
% 121.84/16.07 (inIntersectImpInIntersectUnions) =>
% 121.84/16.07 ((
% 121.84/16.07 (intersectInPowersetIntersectUnions) =>
% 121.84/16.07 ((
% 121.84/16.07 (inComplementUnionImpNotIn1) =>
% 121.84/16.07 ((
% 121.84/16.07 (inComplementUnionImpInComplement1) =>
% 121.84/16.07 ((
% 121.84/16.07 (binunionTE) =>
% 121.84/16.07 ((
% 121.84/16.07 (binunionTEcontra) =>
% 121.84/16.07 ((
% 121.84/16.07 (demorgan2a1) =>
% 121.84/16.07 ((
% 121.84/16.07 (complementUnionInPowersetComplement) =>
% 121.84/16.07 ((
% 121.84/16.07 (demorgan2a2) =>
% 121.84/16.07 ((
% 121.84/16.07 (demorgan1a) =>
% 121.84/16.07 ((
% 121.84/16.07 (demorgan1b) =>
% 121.84/16.07 ((
% 121.84/16.07 (demorgan1) =>
% 121.84/16.07 ((
% 121.84/16.07 (demorgan2a) =>
% 121.84/16.07 ((
% 121.84/16.07 (demorgan2b2) =>
% 121.84/16.07 ((
% 121.84/16.07 (demorgan2b) =>
% 121.84/16.07 ((
% 121.84/16.07 (demorgan2) =>
% 121.84/16.07 ((
% 121.84/16.07 (woz13rule0) =>
% 121.84/16.07 ((
% 121.84/16.07 (woz13rule1) =>
% 121.84/16.07 ((
% 121.84/16.07 (woz13rule2) =>
% 121.84/16.07 ((
% 121.84/16.07 (woz13rule3) =>
% 121.84/16.07 ((
% 121.84/16.07 (woz13rule4) =>
% 121.84/16.07 ((
% 121.84/16.07 (woz1_1) =>
% 121.84/16.07 ((
% 121.84/16.07 (woz1_2) =>
% 121.84/16.07 ((
% 121.84/16.07 (woz1_3) =>
% 121.84/16.07 ((
% 121.84/16.07 (woz1_4) =>
% 121.84/16.07 ((
% 121.84/16.07 (woz1_5) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1all2) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1SetBreln1) =>
% 121.84/16.07 ((
% 121.84/16.07 (choice2fnsingleton) =>
% 121.84/16.07 ((
% 121.84/16.07 (setOfPairsIsBReln1) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1all1) =>
% 121.84/16.07 ((
% 121.84/16.07 (subbreln1) =>
% 121.84/16.07 ((
% 121.84/16.07 (eqbreln1) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1invprop) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1invI) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1invE) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1compprop) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1compI) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1compE) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1compEex) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1unionprop) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1unionIL) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1unionIR) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1unionI) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1unionE) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1unionEcases) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1unionCommutes) =>
% 121.84/16.07 ((
% 121.84/16.07 (woz2Ex) =>
% 121.84/16.07 ((
% 121.84/16.07 (woz2W) =>
% 121.84/16.07 ((
% 121.84/16.07 (woz2A) =>
% 121.84/16.07 ((
% 121.84/16.07 (woz2B) =>
% 121.84/16.07 ((
% 121.84/16.07 (image1Ex) =>
% 121.84/16.07 ((
% 121.84/16.07 (image1Ex1) =>
% 121.84/16.07 ((
% 121.84/16.07 (image1Equiv) =>
% 121.84/16.07 ((
% 121.84/16.07 (image1E) =>
% 121.84/16.07 ((
% 121.84/16.07 (image1I) =>
% 121.84/16.07 ((
% 121.84/16.07 (injFuncInInjFuncSet) =>
% 121.84/16.07 ((
% 121.84/16.07 (!!) @ (
% 121.84/16.07 (('#B') @ (
% 121.84/16.07 !!) @
% 121.84/16.07 (
% 121.84/16.07 (
% 121.84/16.07 ('#B') @ (
% 121.84/16.07 (
% 121.84/16.07 ('#B') @ (
% 121.84/16.07 !!))) @
% 121.84/16.07 (
% 121.84/16.07 (
% 121.84/16.07 ('#S') @ (
% 121.84/16.07 (
% 121.84/16.07 ('#B') @ (
% 121.84/16.07 '#S') @
% 121.84/16.07 (
% 121.84/16.07 (
% 121.84/16.07 ('#B') @ (
% 121.84/16.07 (
% 121.84/16.07 ('#B') @ (
% 121.84/16.07 '#S'))) @
% 121.84/16.07 (
% 121.84/16.07 (
% 121.84/16.07 ('#B') @ (
% 121.84/16.07 (
% 121.84/16.07 ('#B') @ (
% 121.84/16.07 (
% 121.84/16.07 ('#B') @ (
% 121.84/16.07 =>))))) @
% 121.84/16.07 (
% 121.84/16.07 (
% 121.84/16.07 ('#B') @ (
% 121.84/16.07 (
% 121.84/16.07 ('#B') @ (
% 121.84/16.07 (
% 121.84/16.07 ('#C') @ in)))) @
% 121.84/16.07 injFuncSet)))))))) @
% 121.84/16.07 (
% 121.84/16.07 (
% 121.84/16.07 ('#B') @ (
% 121.84/16.07 (
% 121.84/16.07 ('#B') @ (
% 121.84/16.07 (
% 121.84/16.07 ('#C') @ in)))) @
% 121.84/16.07 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 121.84/16.07 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl595])).
% 121.84/16.07 thf(zip_derived_cl619, plain,
% 121.84/16.07 (~ (((exuI3) =>
% 121.84/16.07 (((exuI2) =>
% 121.84/16.07 (((inCongP) =>
% 121.84/16.07 (((in__Cong) =>
% 121.84/16.07 (((exuE3u) =>
% 121.84/16.07 (((exu__Cong) =>
% 121.84/16.07 (((setadjoin__Cong) =>
% 121.84/16.07 (((powerset__Cong) =>
% 121.84/16.07 (((setunion__Cong) =>
% 121.84/16.07 (((exuEu) =>
% 121.84/16.07 (((descr__Cong) =>
% 121.84/16.07 (((dsetconstr__Cong) =>
% 121.84/16.07 (((subsetI1) =>
% 121.84/16.07 (((eqimpsubset2) =>
% 121.84/16.07 (((eqimpsubset1) =>
% 121.84/16.07 (((subsetI2) =>
% 121.84/16.07 (((emptysetsubset) =>
% 121.84/16.07 (((subsetE) =>
% 121.84/16.07 (((subsetE2) =>
% 121.84/16.07 (((notsubsetI) =>
% 121.84/16.07 (((notequalI1) =>
% 121.84/16.07 (((notequalI2) =>
% 121.84/16.07 (((subsetRefl) =>
% 121.84/16.07 (((subsetTrans) =>
% 121.84/16.07 (((setadjoinSub) =>
% 121.84/16.07 (((setadjoinSub2) =>
% 121.84/16.07 (((subset2powerset) =>
% 121.84/16.07 (((setextsub) =>
% 121.84/16.07 (((subsetemptysetimpeq) =>
% 121.84/16.07 (((powersetI1) =>
% 121.84/16.07 ((
% 121.84/16.07 (powersetE1) =>
% 121.84/16.07 ((
% 121.84/16.07 (inPowerset) =>
% 121.84/16.07 ((
% 121.84/16.07 (powersetsubset) =>
% 121.84/16.07 ((
% 121.84/16.07 (sepInPowerset) =>
% 121.84/16.07 ((
% 121.84/16.07 (sepSubset) =>
% 121.84/16.07 ((
% 121.84/16.07 (binunionIL) =>
% 121.84/16.07 ((
% 121.84/16.07 (upairset2IR) =>
% 121.84/16.07 ((
% 121.84/16.07 (binunionIR) =>
% 121.84/16.07 ((
% 121.84/16.07 (binunionEcases) =>
% 121.84/16.07 ((
% 121.84/16.07 (binunionE) =>
% 121.84/16.07 ((
% 121.84/16.07 (binunionLsub) =>
% 121.84/16.07 ((
% 121.84/16.07 (binunionRsub) =>
% 121.84/16.07 ((
% 121.84/16.07 (binintersectI) =>
% 121.84/16.07 ((
% 121.84/16.07 (binintersectSubset5) =>
% 121.84/16.07 ((
% 121.84/16.07 (binintersectEL) =>
% 121.84/16.07 ((
% 121.84/16.07 (binintersectLsub) =>
% 121.84/16.07 ((
% 121.84/16.07 (binintersectSubset2) =>
% 121.84/16.07 ((
% 121.84/16.07 (binintersectSubset3) =>
% 121.84/16.07 ((
% 121.84/16.07 (binintersectER) =>
% 121.84/16.07 ((
% 121.84/16.07 (disjointsetsI1) =>
% 121.84/16.07 ((
% 121.84/16.07 (binintersectRsub) =>
% 121.84/16.07 ((
% 121.84/16.07 (binintersectSubset4) =>
% 121.84/16.07 ((
% 121.84/16.07 (binintersectSubset1) =>
% 121.84/16.07 ((
% 121.84/16.07 (bs114d) =>
% 121.84/16.07 ((
% 121.84/16.07 (setminusI) =>
% 121.84/16.07 ((
% 121.84/16.07 (setminusEL) =>
% 121.84/16.07 ((
% 121.84/16.07 (setminusER) =>
% 121.84/16.07 ((
% 121.84/16.07 (setminusSubset2) =>
% 121.84/16.07 ((
% 121.84/16.07 (setminusERneg) =>
% 121.84/16.07 ((
% 121.84/16.07 (setminusELneg) =>
% 121.84/16.07 ((
% 121.84/16.07 (setminusILneg) =>
% 121.84/16.07 ((
% 121.84/16.07 (setminusIRneg) =>
% 121.84/16.07 ((
% 121.84/16.07 (setminusLsub) =>
% 121.84/16.07 ((
% 121.84/16.07 (setminusSubset1) =>
% 121.84/16.07 ((
% 121.84/16.07 (symdiffE) =>
% 121.84/16.07 ((
% 121.84/16.07 (symdiffI1) =>
% 121.84/16.07 ((
% 121.84/16.07 (symdiffI2) =>
% 121.84/16.07 ((
% 121.84/16.07 (symdiffIneg1) =>
% 121.84/16.07 ((
% 121.84/16.07 (symdiffIneg2) =>
% 121.84/16.07 ((
% 121.84/16.07 (secondinupair) =>
% 121.84/16.07 ((
% 121.84/16.07 (setukpairIL) =>
% 121.84/16.07 ((
% 121.84/16.07 (setukpairIR) =>
% 121.84/16.07 ((
% 121.84/16.07 (kpairiskpair) =>
% 121.84/16.07 ((
% 121.84/16.07 (kpairp) =>
% 121.84/16.07 ((
% 121.84/16.07 (singletonsubset) =>
% 121.84/16.07 ((
% 121.84/16.07 (singletoninpowerset) =>
% 121.84/16.07 ((
% 121.84/16.07 (singletoninpowunion) =>
% 121.84/16.07 ((
% 121.84/16.07 (upairset2E) =>
% 121.84/16.07 ((
% 121.84/16.07 (upairsubunion) =>
% 121.84/16.07 ((
% 121.84/16.07 (upairinpowunion) =>
% 121.84/16.07 ((
% 121.84/16.07 (ubforcartprodlem1) =>
% 121.84/16.07 ((
% 121.84/16.07 (ubforcartprodlem2) =>
% 121.84/16.07 ((
% 121.84/16.07 (ubforcartprodlem3) =>
% 121.84/16.07 ((
% 121.84/16.07 (cartprodpairin) =>
% 121.84/16.07 ((
% 121.84/16.07 (cartprodmempair1) =>
% 121.84/16.07 ((
% 121.84/16.07 (cartprodmempair) =>
% 121.84/16.07 ((
% 121.84/16.07 (setunionE2) =>
% 121.84/16.07 ((
% 121.84/16.07 (setunionsingleton1) =>
% 121.84/16.07 ((
% 121.84/16.07 (setunionsingleton2) =>
% 121.84/16.07 ((
% 121.84/16.07 (setunionsingleton) =>
% 121.84/16.07 ((
% 121.84/16.07 (singletonprop) =>
% 121.84/16.07 ((
% 121.84/16.07 (ex1E1) =>
% 121.84/16.07 ((
% 121.84/16.07 (ex1I) =>
% 121.84/16.07 ((
% 121.84/16.07 (ex1I2) =>
% 121.84/16.07 ((
% 121.84/16.07 (singletonsuniq) =>
% 121.84/16.07 ((
% 121.84/16.07 (setukpairinjL1) =>
% 121.84/16.07 ((
% 121.84/16.07 (kfstsingleton) =>
% 121.84/16.07 ((
% 121.84/16.07 (theprop) =>
% 121.84/16.07 ((
% 121.84/16.07 (kfstpairEq) =>
% 121.84/16.07 ((
% 121.84/16.07 (cartprodfstin) =>
% 121.84/16.07 ((
% 121.84/16.07 (setukpairinjL2) =>
% 121.84/16.07 ((
% 121.84/16.07 (setukpairinjL) =>
% 121.84/16.07 ((
% 121.84/16.07 (setukpairinjR11) =>
% 121.84/16.07 ((
% 121.84/16.07 (setukpairinjR12) =>
% 121.84/16.07 ((
% 121.84/16.07 (setukpairinjR1) =>
% 121.84/16.07 ((
% 121.84/16.07 (upairequniteq) =>
% 121.84/16.07 ((
% 121.84/16.07 (setukpairinjR2) =>
% 121.84/16.07 ((
% 121.84/16.07 (setukpairinjR) =>
% 121.84/16.07 ((
% 121.84/16.07 (ksndsingleton) =>
% 121.84/16.07 ((
% 121.84/16.07 (ksndpairEq) =>
% 121.84/16.07 ((
% 121.84/16.07 (kpairsurjEq) =>
% 121.84/16.07 ((
% 121.84/16.07 (cartprodsndin) =>
% 121.84/16.07 ((
% 121.84/16.07 (cartprodpairmemEL) =>
% 121.84/16.07 ((
% 121.84/16.07 (cartprodpairmemER) =>
% 121.84/16.07 ((
% 121.84/16.07 (cartprodmempaircEq) =>
% 121.84/16.07 ((
% 121.84/16.07 (cartprodfstpairEq) =>
% 121.84/16.07 ((
% 121.84/16.07 (cartprodsndpairEq) =>
% 121.84/16.07 ((
% 121.84/16.07 (cartprodpairsurjEq) =>
% 121.84/16.07 ((
% 121.84/16.07 (dpsetconstrI) =>
% 121.84/16.07 ((
% 121.84/16.07 (dpsetconstrSub) =>
% 121.84/16.07 ((
% 121.84/16.07 (setOfPairsIsBReln) =>
% 121.84/16.07 ((
% 121.84/16.07 (dpsetconstrERa) =>
% 121.84/16.07 ((
% 121.84/16.07 (dpsetconstrEL1) =>
% 121.84/16.07 ((
% 121.84/16.07 (dpsetconstrEL2) =>
% 121.84/16.07 ((
% 121.84/16.07 (dpsetconstrER) =>
% 121.84/16.07 ((
% 121.84/16.07 (funcImageSingleton) =>
% 121.84/16.07 ((
% 121.84/16.07 (apProp) =>
% 121.84/16.07 ((
% 121.84/16.07 (app) =>
% 121.84/16.07 ((
% 121.84/16.07 (infuncsetfunc) =>
% 121.84/16.07 ((
% 121.84/16.07 (ap2p) =>
% 121.84/16.07 ((
% 121.84/16.07 (funcinfuncset) =>
% 121.84/16.07 ((
% 121.84/16.07 (lamProp) =>
% 121.84/16.07 ((
% 121.84/16.07 (lamp) =>
% 121.84/16.07 ((
% 121.84/16.07 (lam2p) =>
% 121.84/16.07 ((
% 121.84/16.07 (brelnall1) =>
% 121.84/16.07 ((
% 121.84/16.07 (brelnall2) =>
% 121.84/16.07 ((
% 121.84/16.07 (ex1E2) =>
% 121.84/16.07 ((
% 121.84/16.07 (funcGraphProp1) =>
% 121.84/16.07 ((
% 121.84/16.07 (funcGraphProp3) =>
% 121.84/16.07 ((
% 121.84/16.07 (funcGraphProp2) =>
% 121.84/16.07 ((
% 121.84/16.07 (funcextLem) =>
% 121.84/16.07 ((
% 121.84/16.07 (funcGraphProp4) =>
% 121.84/16.07 ((
% 121.84/16.07 (subbreln) =>
% 121.84/16.07 ((
% 121.84/16.07 (eqbreln) =>
% 121.84/16.07 ((
% 121.84/16.07 (funcext) =>
% 121.84/16.07 ((
% 121.84/16.07 (funcext2) =>
% 121.84/16.07 ((
% 121.84/16.07 (ap2apEq1) =>
% 121.84/16.07 ((
% 121.84/16.07 (ap2apEq2) =>
% 121.84/16.07 ((
% 121.84/16.07 (beta1) =>
% 121.84/16.07 ((
% 121.84/16.07 (eta1) =>
% 121.84/16.07 ((
% 121.84/16.07 (lam2lamEq) =>
% 121.84/16.07 ((
% 121.84/16.07 (beta2) =>
% 121.84/16.07 ((
% 121.84/16.07 (eta2) =>
% 121.84/16.07 ((
% 121.84/16.07 (iffalseProp1) =>
% 121.84/16.07 ((
% 121.84/16.07 (iffalseProp2) =>
% 121.84/16.07 ((
% 121.84/16.07 (iftrueProp1) =>
% 121.84/16.07 ((
% 121.84/16.07 (iftrueProp2) =>
% 121.84/16.07 ((
% 121.84/16.07 (ifSingleton) =>
% 121.84/16.07 ((
% 121.84/16.07 (ifp) =>
% 121.84/16.07 ((
% 121.84/16.07 (theeq) =>
% 121.84/16.07 ((
% 121.84/16.07 (iftrue) =>
% 121.84/16.07 ((
% 121.84/16.07 (iffalse) =>
% 121.84/16.07 ((
% 121.84/16.07 (iftrueorfalse) =>
% 121.84/16.07 ((
% 121.84/16.07 (binintersectT_lem) =>
% 121.84/16.07 ((
% 121.84/16.07 (binunionT_lem) =>
% 121.84/16.07 ((
% 121.84/16.07 (powersetT_lem) =>
% 121.84/16.07 ((
% 121.84/16.07 (setminusT_lem) =>
% 121.84/16.07 ((
% 121.84/16.07 (complementT_lem) =>
% 121.84/16.07 ((
% 121.84/16.07 (setextT) =>
% 121.84/16.07 ((
% 121.84/16.07 (subsetTI) =>
% 121.84/16.07 ((
% 121.84/16.07 (powersetTI1) =>
% 121.84/16.07 ((
% 121.84/16.07 (powersetTE1) =>
% 121.84/16.07 ((
% 121.84/16.07 (complementTI1) =>
% 121.84/16.07 ((
% 121.84/16.07 (complementTE1) =>
% 121.84/16.07 ((
% 121.84/16.07 (binintersectTELcontra) =>
% 121.84/16.07 ((
% 121.84/16.07 (binintersectTERcontra) =>
% 121.84/16.07 ((
% 121.84/16.07 (contrasubsetT) =>
% 121.84/16.07 ((
% 121.84/16.07 (contrasubsetT1) =>
% 121.84/16.07 ((
% 121.84/16.07 (contrasubsetT2) =>
% 121.84/16.07 ((
% 121.84/16.07 (contrasubsetT3) =>
% 121.84/16.07 ((
% 121.84/16.07 (doubleComplementI1) =>
% 121.84/16.07 ((
% 121.84/16.07 (doubleComplementE1) =>
% 121.84/16.07 ((
% 121.84/16.07 (doubleComplementSub1) =>
% 121.84/16.07 ((
% 121.84/16.07 (doubleComplementSub2) =>
% 121.84/16.07 ((
% 121.84/16.07 (doubleComplementEq) =>
% 121.84/16.07 ((
% 121.84/16.07 (complementTnotintersectT) =>
% 121.84/16.07 ((
% 121.84/16.07 (complementImpComplementIntersect) =>
% 121.84/16.07 ((
% 121.84/16.07 (complementSubsetComplementIntersect) =>
% 121.84/16.07 ((
% 121.84/16.07 (complementInPowersetComplementIntersect) =>
% 121.84/16.07 ((
% 121.84/16.07 (contraSubsetComplement) =>
% 121.84/16.07 ((
% 121.84/16.07 (complementTcontraSubset) =>
% 121.84/16.07 ((
% 121.84/16.07 (binunionTILcontra) =>
% 121.84/16.07 ((
% 121.84/16.07 (binunionTIRcontra) =>
% 121.84/16.07 ((
% 121.84/16.07 (inIntersectImpInUnion) =>
% 121.84/16.07 ((
% 121.84/16.07 (inIntersectImpInUnion2) =>
% 121.84/16.07 ((
% 121.84/16.07 (inIntersectImpInIntersectUnions) =>
% 121.84/16.07 ((
% 121.84/16.07 (intersectInPowersetIntersectUnions) =>
% 121.84/16.07 ((
% 121.84/16.07 (inComplementUnionImpNotIn1) =>
% 121.84/16.07 ((
% 121.84/16.07 (inComplementUnionImpInComplement1) =>
% 121.84/16.07 ((
% 121.84/16.07 (binunionTE) =>
% 121.84/16.07 ((
% 121.84/16.07 (binunionTEcontra) =>
% 121.84/16.07 ((
% 121.84/16.07 (demorgan2a1) =>
% 121.84/16.07 ((
% 121.84/16.07 (complementUnionInPowersetComplement) =>
% 121.84/16.07 ((
% 121.84/16.07 (demorgan2a2) =>
% 121.84/16.07 ((
% 121.84/16.07 (demorgan1a) =>
% 121.84/16.07 ((
% 121.84/16.07 (demorgan1b) =>
% 121.84/16.07 ((
% 121.84/16.07 (demorgan1) =>
% 121.84/16.07 ((
% 121.84/16.07 (demorgan2a) =>
% 121.84/16.07 ((
% 121.84/16.07 (demorgan2b2) =>
% 121.84/16.07 ((
% 121.84/16.07 (demorgan2b) =>
% 121.84/16.07 ((
% 121.84/16.07 (demorgan2) =>
% 121.84/16.07 ((
% 121.84/16.07 (woz13rule0) =>
% 121.84/16.07 ((
% 121.84/16.07 (woz13rule1) =>
% 121.84/16.07 ((
% 121.84/16.07 (woz13rule2) =>
% 121.84/16.07 ((
% 121.84/16.07 (woz13rule3) =>
% 121.84/16.07 ((
% 121.84/16.07 (woz13rule4) =>
% 121.84/16.07 ((
% 121.84/16.07 (woz1_1) =>
% 121.84/16.07 ((
% 121.84/16.07 (woz1_2) =>
% 121.84/16.07 ((
% 121.84/16.07 (woz1_3) =>
% 121.84/16.07 ((
% 121.84/16.07 (woz1_4) =>
% 121.84/16.07 ((
% 121.84/16.07 (woz1_5) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1all2) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1SetBreln1) =>
% 121.84/16.07 ((
% 121.84/16.07 (choice2fnsingleton) =>
% 121.84/16.07 ((
% 121.84/16.07 (setOfPairsIsBReln1) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1all1) =>
% 121.84/16.07 ((
% 121.84/16.07 (subbreln1) =>
% 121.84/16.07 ((
% 121.84/16.07 (eqbreln1) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1invprop) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1invI) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1invE) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1compprop) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1compI) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1compE) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1compEex) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1unionprop) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1unionIL) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1unionIR) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1unionI) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1unionE) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1unionEcases) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1unionCommutes) =>
% 121.84/16.07 ((
% 121.84/16.07 (woz2Ex) =>
% 121.84/16.07 ((
% 121.84/16.07 (woz2W) =>
% 121.84/16.07 ((
% 121.84/16.07 (woz2A) =>
% 121.84/16.07 ((
% 121.84/16.07 (woz2B) =>
% 121.84/16.07 ((
% 121.84/16.07 (image1Ex) =>
% 121.84/16.07 ((
% 121.84/16.07 (image1Ex1) =>
% 121.84/16.07 ((
% 121.84/16.07 (image1Equiv) =>
% 121.84/16.07 ((
% 121.84/16.07 (image1E) =>
% 121.84/16.07 ((
% 121.84/16.07 (image1I) =>
% 121.84/16.07 ((
% 121.84/16.07 (injFuncInInjFuncSet) =>
% 121.84/16.07 ((
% 121.84/16.07 (!!) @ (
% 121.84/16.07 (('#B') @ (
% 121.84/16.07 !!) @
% 121.84/16.07 (
% 121.84/16.07 (
% 121.84/16.07 ('#B') @ (
% 121.84/16.07 (
% 121.84/16.07 ('#B') @ (
% 121.84/16.07 !!))) @
% 121.84/16.07 (
% 121.84/16.07 (
% 121.84/16.07 ('#S') @ (
% 121.84/16.07 (
% 121.84/16.07 ('#B') @ (
% 121.84/16.07 '#S') @
% 121.84/16.07 (
% 121.84/16.07 (
% 121.84/16.07 ('#B') @ (
% 121.84/16.07 (
% 121.84/16.07 ('#B') @ (
% 121.84/16.07 '#S'))) @
% 121.84/16.07 (
% 121.84/16.07 (
% 121.84/16.07 ('#B') @ (
% 121.84/16.07 (
% 121.84/16.07 ('#B') @ (
% 121.84/16.07 (
% 121.84/16.07 ('#B') @ (
% 121.84/16.07 =>))))) @
% 121.84/16.07 (
% 121.84/16.07 (
% 121.84/16.07 ('#B') @ (
% 121.84/16.07 (
% 121.84/16.07 ('#B') @ (
% 121.84/16.07 (
% 121.84/16.07 ('#C') @ in)))) @
% 121.84/16.07 injFuncSet)))))))) @
% 121.84/16.07 (
% 121.84/16.07 (
% 121.84/16.07 ('#B') @ (
% 121.84/16.07 (
% 121.84/16.07 ('#B') @ (
% 121.84/16.07 (
% 121.84/16.07 ('#C') @ in)))) @
% 121.84/16.07 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 121.84/16.07 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl606])).
% 121.84/16.07 thf(zip_derived_cl630, plain,
% 121.84/16.07 (~ (((exuI2) =>
% 121.84/16.07 (((inCongP) =>
% 121.84/16.07 (((in__Cong) =>
% 121.84/16.07 (((exuE3u) =>
% 121.84/16.07 (((exu__Cong) =>
% 121.84/16.07 (((setadjoin__Cong) =>
% 121.84/16.07 (((powerset__Cong) =>
% 121.84/16.07 (((setunion__Cong) =>
% 121.84/16.07 (((exuEu) =>
% 121.84/16.07 (((descr__Cong) =>
% 121.84/16.07 (((dsetconstr__Cong) =>
% 121.84/16.07 (((subsetI1) =>
% 121.84/16.07 (((eqimpsubset2) =>
% 121.84/16.07 (((eqimpsubset1) =>
% 121.84/16.07 (((subsetI2) =>
% 121.84/16.07 (((emptysetsubset) =>
% 121.84/16.07 (((subsetE) =>
% 121.84/16.07 (((subsetE2) =>
% 121.84/16.07 (((notsubsetI) =>
% 121.84/16.07 (((notequalI1) =>
% 121.84/16.07 (((notequalI2) =>
% 121.84/16.07 (((subsetRefl) =>
% 121.84/16.07 (((subsetTrans) =>
% 121.84/16.07 (((setadjoinSub) =>
% 121.84/16.07 (((setadjoinSub2) =>
% 121.84/16.07 (((subset2powerset) =>
% 121.84/16.07 (((setextsub) =>
% 121.84/16.07 (((subsetemptysetimpeq) =>
% 121.84/16.07 (((powersetI1) =>
% 121.84/16.07 (((powersetE1) =>
% 121.84/16.07 ((
% 121.84/16.07 (inPowerset) =>
% 121.84/16.07 ((
% 121.84/16.07 (powersetsubset) =>
% 121.84/16.07 ((
% 121.84/16.07 (sepInPowerset) =>
% 121.84/16.07 ((
% 121.84/16.07 (sepSubset) =>
% 121.84/16.07 ((
% 121.84/16.07 (binunionIL) =>
% 121.84/16.07 ((
% 121.84/16.07 (upairset2IR) =>
% 121.84/16.07 ((
% 121.84/16.07 (binunionIR) =>
% 121.84/16.07 ((
% 121.84/16.07 (binunionEcases) =>
% 121.84/16.07 ((
% 121.84/16.07 (binunionE) =>
% 121.84/16.07 ((
% 121.84/16.07 (binunionLsub) =>
% 121.84/16.07 ((
% 121.84/16.07 (binunionRsub) =>
% 121.84/16.07 ((
% 121.84/16.07 (binintersectI) =>
% 121.84/16.07 ((
% 121.84/16.07 (binintersectSubset5) =>
% 121.84/16.07 ((
% 121.84/16.07 (binintersectEL) =>
% 121.84/16.07 ((
% 121.84/16.07 (binintersectLsub) =>
% 121.84/16.07 ((
% 121.84/16.07 (binintersectSubset2) =>
% 121.84/16.07 ((
% 121.84/16.07 (binintersectSubset3) =>
% 121.84/16.07 ((
% 121.84/16.07 (binintersectER) =>
% 121.84/16.07 ((
% 121.84/16.07 (disjointsetsI1) =>
% 121.84/16.07 ((
% 121.84/16.07 (binintersectRsub) =>
% 121.84/16.07 ((
% 121.84/16.07 (binintersectSubset4) =>
% 121.84/16.07 ((
% 121.84/16.07 (binintersectSubset1) =>
% 121.84/16.07 ((
% 121.84/16.07 (bs114d) =>
% 121.84/16.07 ((
% 121.84/16.07 (setminusI) =>
% 121.84/16.07 ((
% 121.84/16.07 (setminusEL) =>
% 121.84/16.07 ((
% 121.84/16.07 (setminusER) =>
% 121.84/16.07 ((
% 121.84/16.07 (setminusSubset2) =>
% 121.84/16.07 ((
% 121.84/16.07 (setminusERneg) =>
% 121.84/16.07 ((
% 121.84/16.07 (setminusELneg) =>
% 121.84/16.07 ((
% 121.84/16.07 (setminusILneg) =>
% 121.84/16.07 ((
% 121.84/16.07 (setminusIRneg) =>
% 121.84/16.07 ((
% 121.84/16.07 (setminusLsub) =>
% 121.84/16.07 ((
% 121.84/16.07 (setminusSubset1) =>
% 121.84/16.07 ((
% 121.84/16.07 (symdiffE) =>
% 121.84/16.07 ((
% 121.84/16.07 (symdiffI1) =>
% 121.84/16.07 ((
% 121.84/16.07 (symdiffI2) =>
% 121.84/16.07 ((
% 121.84/16.07 (symdiffIneg1) =>
% 121.84/16.07 ((
% 121.84/16.07 (symdiffIneg2) =>
% 121.84/16.07 ((
% 121.84/16.07 (secondinupair) =>
% 121.84/16.07 ((
% 121.84/16.07 (setukpairIL) =>
% 121.84/16.07 ((
% 121.84/16.07 (setukpairIR) =>
% 121.84/16.07 ((
% 121.84/16.07 (kpairiskpair) =>
% 121.84/16.07 ((
% 121.84/16.07 (kpairp) =>
% 121.84/16.07 ((
% 121.84/16.07 (singletonsubset) =>
% 121.84/16.07 ((
% 121.84/16.07 (singletoninpowerset) =>
% 121.84/16.07 ((
% 121.84/16.07 (singletoninpowunion) =>
% 121.84/16.07 ((
% 121.84/16.07 (upairset2E) =>
% 121.84/16.07 ((
% 121.84/16.07 (upairsubunion) =>
% 121.84/16.07 ((
% 121.84/16.07 (upairinpowunion) =>
% 121.84/16.07 ((
% 121.84/16.07 (ubforcartprodlem1) =>
% 121.84/16.07 ((
% 121.84/16.07 (ubforcartprodlem2) =>
% 121.84/16.07 ((
% 121.84/16.07 (ubforcartprodlem3) =>
% 121.84/16.07 ((
% 121.84/16.07 (cartprodpairin) =>
% 121.84/16.07 ((
% 121.84/16.07 (cartprodmempair1) =>
% 121.84/16.07 ((
% 121.84/16.07 (cartprodmempair) =>
% 121.84/16.07 ((
% 121.84/16.07 (setunionE2) =>
% 121.84/16.07 ((
% 121.84/16.07 (setunionsingleton1) =>
% 121.84/16.07 ((
% 121.84/16.07 (setunionsingleton2) =>
% 121.84/16.07 ((
% 121.84/16.07 (setunionsingleton) =>
% 121.84/16.07 ((
% 121.84/16.07 (singletonprop) =>
% 121.84/16.07 ((
% 121.84/16.07 (ex1E1) =>
% 121.84/16.07 ((
% 121.84/16.07 (ex1I) =>
% 121.84/16.07 ((
% 121.84/16.07 (ex1I2) =>
% 121.84/16.07 ((
% 121.84/16.07 (singletonsuniq) =>
% 121.84/16.07 ((
% 121.84/16.07 (setukpairinjL1) =>
% 121.84/16.07 ((
% 121.84/16.07 (kfstsingleton) =>
% 121.84/16.07 ((
% 121.84/16.07 (theprop) =>
% 121.84/16.07 ((
% 121.84/16.07 (kfstpairEq) =>
% 121.84/16.07 ((
% 121.84/16.07 (cartprodfstin) =>
% 121.84/16.07 ((
% 121.84/16.07 (setukpairinjL2) =>
% 121.84/16.07 ((
% 121.84/16.07 (setukpairinjL) =>
% 121.84/16.07 ((
% 121.84/16.07 (setukpairinjR11) =>
% 121.84/16.07 ((
% 121.84/16.07 (setukpairinjR12) =>
% 121.84/16.07 ((
% 121.84/16.07 (setukpairinjR1) =>
% 121.84/16.07 ((
% 121.84/16.07 (upairequniteq) =>
% 121.84/16.07 ((
% 121.84/16.07 (setukpairinjR2) =>
% 121.84/16.07 ((
% 121.84/16.07 (setukpairinjR) =>
% 121.84/16.07 ((
% 121.84/16.07 (ksndsingleton) =>
% 121.84/16.07 ((
% 121.84/16.07 (ksndpairEq) =>
% 121.84/16.07 ((
% 121.84/16.07 (kpairsurjEq) =>
% 121.84/16.07 ((
% 121.84/16.07 (cartprodsndin) =>
% 121.84/16.07 ((
% 121.84/16.07 (cartprodpairmemEL) =>
% 121.84/16.07 ((
% 121.84/16.07 (cartprodpairmemER) =>
% 121.84/16.07 ((
% 121.84/16.07 (cartprodmempaircEq) =>
% 121.84/16.07 ((
% 121.84/16.07 (cartprodfstpairEq) =>
% 121.84/16.07 ((
% 121.84/16.07 (cartprodsndpairEq) =>
% 121.84/16.07 ((
% 121.84/16.07 (cartprodpairsurjEq) =>
% 121.84/16.07 ((
% 121.84/16.07 (dpsetconstrI) =>
% 121.84/16.07 ((
% 121.84/16.07 (dpsetconstrSub) =>
% 121.84/16.07 ((
% 121.84/16.07 (setOfPairsIsBReln) =>
% 121.84/16.07 ((
% 121.84/16.07 (dpsetconstrERa) =>
% 121.84/16.07 ((
% 121.84/16.07 (dpsetconstrEL1) =>
% 121.84/16.07 ((
% 121.84/16.07 (dpsetconstrEL2) =>
% 121.84/16.07 ((
% 121.84/16.07 (dpsetconstrER) =>
% 121.84/16.07 ((
% 121.84/16.07 (funcImageSingleton) =>
% 121.84/16.07 ((
% 121.84/16.07 (apProp) =>
% 121.84/16.07 ((
% 121.84/16.07 (app) =>
% 121.84/16.07 ((
% 121.84/16.07 (infuncsetfunc) =>
% 121.84/16.07 ((
% 121.84/16.07 (ap2p) =>
% 121.84/16.07 ((
% 121.84/16.07 (funcinfuncset) =>
% 121.84/16.07 ((
% 121.84/16.07 (lamProp) =>
% 121.84/16.07 ((
% 121.84/16.07 (lamp) =>
% 121.84/16.07 ((
% 121.84/16.07 (lam2p) =>
% 121.84/16.07 ((
% 121.84/16.07 (brelnall1) =>
% 121.84/16.07 ((
% 121.84/16.07 (brelnall2) =>
% 121.84/16.07 ((
% 121.84/16.07 (ex1E2) =>
% 121.84/16.07 ((
% 121.84/16.07 (funcGraphProp1) =>
% 121.84/16.07 ((
% 121.84/16.07 (funcGraphProp3) =>
% 121.84/16.07 ((
% 121.84/16.07 (funcGraphProp2) =>
% 121.84/16.07 ((
% 121.84/16.07 (funcextLem) =>
% 121.84/16.07 ((
% 121.84/16.07 (funcGraphProp4) =>
% 121.84/16.07 ((
% 121.84/16.07 (subbreln) =>
% 121.84/16.07 ((
% 121.84/16.07 (eqbreln) =>
% 121.84/16.07 ((
% 121.84/16.07 (funcext) =>
% 121.84/16.07 ((
% 121.84/16.07 (funcext2) =>
% 121.84/16.07 ((
% 121.84/16.07 (ap2apEq1) =>
% 121.84/16.07 ((
% 121.84/16.07 (ap2apEq2) =>
% 121.84/16.07 ((
% 121.84/16.07 (beta1) =>
% 121.84/16.07 ((
% 121.84/16.07 (eta1) =>
% 121.84/16.07 ((
% 121.84/16.07 (lam2lamEq) =>
% 121.84/16.07 ((
% 121.84/16.07 (beta2) =>
% 121.84/16.07 ((
% 121.84/16.07 (eta2) =>
% 121.84/16.07 ((
% 121.84/16.07 (iffalseProp1) =>
% 121.84/16.07 ((
% 121.84/16.07 (iffalseProp2) =>
% 121.84/16.07 ((
% 121.84/16.07 (iftrueProp1) =>
% 121.84/16.07 ((
% 121.84/16.07 (iftrueProp2) =>
% 121.84/16.07 ((
% 121.84/16.07 (ifSingleton) =>
% 121.84/16.07 ((
% 121.84/16.07 (ifp) =>
% 121.84/16.07 ((
% 121.84/16.07 (theeq) =>
% 121.84/16.07 ((
% 121.84/16.07 (iftrue) =>
% 121.84/16.07 ((
% 121.84/16.07 (iffalse) =>
% 121.84/16.07 ((
% 121.84/16.07 (iftrueorfalse) =>
% 121.84/16.07 ((
% 121.84/16.07 (binintersectT_lem) =>
% 121.84/16.07 ((
% 121.84/16.07 (binunionT_lem) =>
% 121.84/16.07 ((
% 121.84/16.07 (powersetT_lem) =>
% 121.84/16.07 ((
% 121.84/16.07 (setminusT_lem) =>
% 121.84/16.07 ((
% 121.84/16.07 (complementT_lem) =>
% 121.84/16.07 ((
% 121.84/16.07 (setextT) =>
% 121.84/16.07 ((
% 121.84/16.07 (subsetTI) =>
% 121.84/16.07 ((
% 121.84/16.07 (powersetTI1) =>
% 121.84/16.07 ((
% 121.84/16.07 (powersetTE1) =>
% 121.84/16.07 ((
% 121.84/16.07 (complementTI1) =>
% 121.84/16.07 ((
% 121.84/16.07 (complementTE1) =>
% 121.84/16.07 ((
% 121.84/16.07 (binintersectTELcontra) =>
% 121.84/16.07 ((
% 121.84/16.07 (binintersectTERcontra) =>
% 121.84/16.07 ((
% 121.84/16.07 (contrasubsetT) =>
% 121.84/16.07 ((
% 121.84/16.07 (contrasubsetT1) =>
% 121.84/16.07 ((
% 121.84/16.07 (contrasubsetT2) =>
% 121.84/16.07 ((
% 121.84/16.07 (contrasubsetT3) =>
% 121.84/16.07 ((
% 121.84/16.07 (doubleComplementI1) =>
% 121.84/16.07 ((
% 121.84/16.07 (doubleComplementE1) =>
% 121.84/16.07 ((
% 121.84/16.07 (doubleComplementSub1) =>
% 121.84/16.07 ((
% 121.84/16.07 (doubleComplementSub2) =>
% 121.84/16.07 ((
% 121.84/16.07 (doubleComplementEq) =>
% 121.84/16.07 ((
% 121.84/16.07 (complementTnotintersectT) =>
% 121.84/16.07 ((
% 121.84/16.07 (complementImpComplementIntersect) =>
% 121.84/16.07 ((
% 121.84/16.07 (complementSubsetComplementIntersect) =>
% 121.84/16.07 ((
% 121.84/16.07 (complementInPowersetComplementIntersect) =>
% 121.84/16.07 ((
% 121.84/16.07 (contraSubsetComplement) =>
% 121.84/16.07 ((
% 121.84/16.07 (complementTcontraSubset) =>
% 121.84/16.07 ((
% 121.84/16.07 (binunionTILcontra) =>
% 121.84/16.07 ((
% 121.84/16.07 (binunionTIRcontra) =>
% 121.84/16.07 ((
% 121.84/16.07 (inIntersectImpInUnion) =>
% 121.84/16.07 ((
% 121.84/16.07 (inIntersectImpInUnion2) =>
% 121.84/16.07 ((
% 121.84/16.07 (inIntersectImpInIntersectUnions) =>
% 121.84/16.07 ((
% 121.84/16.07 (intersectInPowersetIntersectUnions) =>
% 121.84/16.07 ((
% 121.84/16.07 (inComplementUnionImpNotIn1) =>
% 121.84/16.07 ((
% 121.84/16.07 (inComplementUnionImpInComplement1) =>
% 121.84/16.07 ((
% 121.84/16.07 (binunionTE) =>
% 121.84/16.07 ((
% 121.84/16.07 (binunionTEcontra) =>
% 121.84/16.07 ((
% 121.84/16.07 (demorgan2a1) =>
% 121.84/16.07 ((
% 121.84/16.07 (complementUnionInPowersetComplement) =>
% 121.84/16.07 ((
% 121.84/16.07 (demorgan2a2) =>
% 121.84/16.07 ((
% 121.84/16.07 (demorgan1a) =>
% 121.84/16.07 ((
% 121.84/16.07 (demorgan1b) =>
% 121.84/16.07 ((
% 121.84/16.07 (demorgan1) =>
% 121.84/16.07 ((
% 121.84/16.07 (demorgan2a) =>
% 121.84/16.07 ((
% 121.84/16.07 (demorgan2b2) =>
% 121.84/16.07 ((
% 121.84/16.07 (demorgan2b) =>
% 121.84/16.07 ((
% 121.84/16.07 (demorgan2) =>
% 121.84/16.07 ((
% 121.84/16.07 (woz13rule0) =>
% 121.84/16.07 ((
% 121.84/16.07 (woz13rule1) =>
% 121.84/16.07 ((
% 121.84/16.07 (woz13rule2) =>
% 121.84/16.07 ((
% 121.84/16.07 (woz13rule3) =>
% 121.84/16.07 ((
% 121.84/16.07 (woz13rule4) =>
% 121.84/16.07 ((
% 121.84/16.07 (woz1_1) =>
% 121.84/16.07 ((
% 121.84/16.07 (woz1_2) =>
% 121.84/16.07 ((
% 121.84/16.07 (woz1_3) =>
% 121.84/16.07 ((
% 121.84/16.07 (woz1_4) =>
% 121.84/16.07 ((
% 121.84/16.07 (woz1_5) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1all2) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1SetBreln1) =>
% 121.84/16.07 ((
% 121.84/16.07 (choice2fnsingleton) =>
% 121.84/16.07 ((
% 121.84/16.07 (setOfPairsIsBReln1) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1all1) =>
% 121.84/16.07 ((
% 121.84/16.07 (subbreln1) =>
% 121.84/16.07 ((
% 121.84/16.07 (eqbreln1) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1invprop) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1invI) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1invE) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1compprop) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1compI) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1compE) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1compEex) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1unionprop) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1unionIL) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1unionIR) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1unionI) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1unionE) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1unionEcases) =>
% 121.84/16.07 ((
% 121.84/16.07 (breln1unionCommutes) =>
% 121.84/16.07 ((
% 121.84/16.07 (woz2Ex) =>
% 121.84/16.07 ((
% 121.84/16.07 (woz2W) =>
% 121.84/16.07 ((
% 121.84/16.07 (woz2A) =>
% 121.84/16.07 ((
% 121.84/16.07 (woz2B) =>
% 121.84/16.07 ((
% 121.84/16.07 (image1Ex) =>
% 121.84/16.07 ((
% 121.84/16.07 (image1Ex1) =>
% 121.84/16.07 ((
% 121.84/16.07 (image1Equiv) =>
% 121.84/16.07 ((
% 121.84/16.07 (image1E) =>
% 121.84/16.07 ((
% 121.84/16.07 (image1I) =>
% 121.84/16.07 ((
% 121.84/16.07 (injFuncInInjFuncSet) =>
% 121.84/16.07 ((
% 121.84/16.07 (!!) @ (
% 121.84/16.07 (('#B') @ (
% 121.84/16.07 !!) @
% 121.84/16.07 (
% 121.84/16.07 (
% 121.84/16.07 ('#B') @ (
% 121.84/16.07 (
% 121.84/16.07 ('#B') @ (
% 121.84/16.07 !!))) @
% 121.84/16.07 (
% 121.84/16.07 (
% 121.84/16.07 ('#S') @ (
% 121.84/16.07 (
% 121.84/16.07 ('#B') @ (
% 121.84/16.07 '#S') @
% 121.84/16.07 (
% 121.84/16.07 (
% 121.84/16.07 ('#B') @ (
% 121.84/16.07 (
% 121.84/16.07 ('#B') @ (
% 121.84/16.07 '#S'))) @
% 121.84/16.07 (
% 121.84/16.07 (
% 121.84/16.07 ('#B') @ (
% 121.84/16.07 (
% 121.84/16.07 ('#B') @ (
% 121.84/16.07 (
% 121.84/16.07 ('#B') @ (
% 121.84/16.07 =>))))) @
% 121.84/16.07 (
% 121.84/16.07 (
% 121.84/16.07 ('#B') @ (
% 121.84/16.07 (
% 121.84/16.07 ('#B') @ (
% 121.84/16.07 (
% 121.84/16.07 ('#C') @ in)))) @
% 121.84/16.07 injFuncSet)))))))) @
% 121.84/16.07 (
% 121.84/16.07 (
% 121.84/16.07 ('#B') @ (
% 121.84/16.07 (
% 121.84/16.07 ('#B') @ (
% 121.84/16.07 (
% 121.84/16.07 ('#C') @ in)))) @
% 121.84/16.07 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 121.84/16.07 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl619])).
% 121.84/16.07 thf(zip_derived_cl640, plain,
% 121.84/16.07 (~ (((inCongP) =>
% 121.84/16.07 (((in__Cong) =>
% 121.84/16.07 (((exuE3u) =>
% 121.84/16.07 (((exu__Cong) =>
% 121.84/16.07 (((setadjoin__Cong) =>
% 121.84/16.07 (((powerset__Cong) =>
% 121.84/16.07 (((setunion__Cong) =>
% 121.84/16.07 (((exuEu) =>
% 121.84/16.07 (((descr__Cong) =>
% 121.84/16.07 (((dsetconstr__Cong) =>
% 121.84/16.07 (((subsetI1) =>
% 121.84/16.07 (((eqimpsubset2) =>
% 121.84/16.07 (((eqimpsubset1) =>
% 121.84/16.07 (((subsetI2) =>
% 121.84/16.07 (((emptysetsubset) =>
% 121.84/16.07 (((subsetE) =>
% 121.84/16.07 (((subsetE2) =>
% 121.84/16.07 (((notsubsetI) =>
% 121.84/16.07 (((notequalI1) =>
% 121.84/16.07 (((notequalI2) =>
% 121.84/16.07 (((subsetRefl) =>
% 121.84/16.07 (((subsetTrans) =>
% 121.84/16.07 (((setadjoinSub) =>
% 121.84/16.07 (((setadjoinSub2) =>
% 121.84/16.07 (((subset2powerset) =>
% 121.84/16.07 (((setextsub) =>
% 121.84/16.07 (((subsetemptysetimpeq) =>
% 121.84/16.07 (((powersetI1) =>
% 121.84/16.07 (((powersetE1) =>
% 121.84/16.07 (((inPowerset) =>
% 121.84/16.07 ((
% 121.84/16.07 (powersetsubset) =>
% 121.84/16.07 ((
% 121.84/16.07 (sepInPowerset) =>
% 121.84/16.07 ((
% 121.84/16.07 (sepSubset) =>
% 121.84/16.07 ((
% 121.84/16.07 (binunionIL) =>
% 121.84/16.07 ((
% 121.84/16.07 (upairset2IR) =>
% 121.84/16.07 ((
% 121.84/16.07 (binunionIR) =>
% 121.84/16.07 ((
% 121.84/16.07 (binunionEcases) =>
% 121.84/16.07 ((
% 121.84/16.07 (binunionE) =>
% 121.84/16.07 ((
% 121.84/16.07 (binunionLsub) =>
% 121.84/16.07 ((
% 121.84/16.07 (binunionRsub) =>
% 121.84/16.07 ((
% 121.84/16.07 (binintersectI) =>
% 121.84/16.07 ((
% 121.84/16.07 (binintersectSubset5) =>
% 121.84/16.07 ((
% 121.84/16.07 (binintersectEL) =>
% 121.84/16.07 ((
% 121.84/16.07 (binintersectLsub) =>
% 121.84/16.07 ((
% 121.84/16.07 (binintersectSubset2) =>
% 121.84/16.07 ((
% 121.84/16.07 (binintersectSubset3) =>
% 121.84/16.07 ((
% 121.84/16.07 (binintersectER) =>
% 121.84/16.07 ((
% 121.84/16.07 (disjointsetsI1) =>
% 121.84/16.07 ((
% 121.84/16.07 (binintersectRsub) =>
% 121.84/16.07 ((
% 121.84/16.07 (binintersectSubset4) =>
% 121.84/16.07 ((
% 121.84/16.07 (binintersectSubset1) =>
% 121.84/16.07 ((
% 121.84/16.07 (bs114d) =>
% 121.84/16.07 ((
% 121.84/16.07 (setminusI) =>
% 121.84/16.07 ((
% 121.84/16.07 (setminusEL) =>
% 121.84/16.07 ((
% 121.84/16.07 (setminusER) =>
% 121.84/16.07 ((
% 121.84/16.07 (setminusSubset2) =>
% 121.84/16.07 ((
% 121.84/16.07 (setminusERneg) =>
% 121.84/16.07 ((
% 121.84/16.07 (setminusELneg) =>
% 121.84/16.07 ((
% 121.84/16.07 (setminusILneg) =>
% 121.84/16.07 ((
% 121.84/16.07 (setminusIRneg) =>
% 121.84/16.07 ((
% 121.84/16.07 (setminusLsub) =>
% 121.84/16.07 ((
% 121.84/16.07 (setminusSubset1) =>
% 121.84/16.07 ((
% 121.84/16.07 (symdiffE) =>
% 121.84/16.07 ((
% 121.84/16.07 (symdiffI1) =>
% 121.84/16.07 ((
% 121.84/16.07 (symdiffI2) =>
% 121.84/16.07 ((
% 121.84/16.07 (symdiffIneg1) =>
% 121.84/16.07 ((
% 121.84/16.07 (symdiffIneg2) =>
% 121.84/16.07 ((
% 121.84/16.07 (secondinupair) =>
% 121.84/16.07 ((
% 121.84/16.07 (setukpairIL) =>
% 121.84/16.07 ((
% 121.84/16.07 (setukpairIR) =>
% 121.84/16.07 ((
% 121.84/16.07 (kpairiskpair) =>
% 121.84/16.07 ((
% 121.84/16.07 (kpairp) =>
% 121.84/16.07 ((
% 121.84/16.07 (singletonsubset) =>
% 121.84/16.07 ((
% 121.84/16.07 (singletoninpowerset) =>
% 121.84/16.07 ((
% 121.84/16.07 (singletoninpowunion) =>
% 121.84/16.07 ((
% 121.84/16.07 (upairset2E) =>
% 121.84/16.08 ((
% 121.84/16.08 (upairsubunion) =>
% 121.84/16.08 ((
% 121.84/16.08 (upairinpowunion) =>
% 121.84/16.08 ((
% 121.84/16.08 (ubforcartprodlem1) =>
% 121.84/16.08 ((
% 121.84/16.08 (ubforcartprodlem2) =>
% 121.84/16.08 ((
% 121.84/16.08 (ubforcartprodlem3) =>
% 121.84/16.08 ((
% 121.84/16.08 (cartprodpairin) =>
% 121.84/16.08 ((
% 121.84/16.08 (cartprodmempair1) =>
% 121.84/16.08 ((
% 121.84/16.08 (cartprodmempair) =>
% 121.84/16.08 ((
% 121.84/16.08 (setunionE2) =>
% 121.84/16.08 ((
% 121.84/16.08 (setunionsingleton1) =>
% 121.84/16.08 ((
% 121.84/16.08 (setunionsingleton2) =>
% 121.84/16.08 ((
% 121.84/16.08 (setunionsingleton) =>
% 121.84/16.08 ((
% 121.84/16.08 (singletonprop) =>
% 121.84/16.08 ((
% 121.84/16.08 (ex1E1) =>
% 121.84/16.08 ((
% 121.84/16.08 (ex1I) =>
% 121.84/16.08 ((
% 121.84/16.08 (ex1I2) =>
% 121.84/16.08 ((
% 121.84/16.08 (singletonsuniq) =>
% 121.84/16.08 ((
% 121.84/16.08 (setukpairinjL1) =>
% 121.84/16.08 ((
% 121.84/16.08 (kfstsingleton) =>
% 121.84/16.08 ((
% 121.84/16.08 (theprop) =>
% 121.84/16.08 ((
% 121.84/16.08 (kfstpairEq) =>
% 121.84/16.08 ((
% 121.84/16.08 (cartprodfstin) =>
% 121.84/16.08 ((
% 121.84/16.08 (setukpairinjL2) =>
% 121.84/16.08 ((
% 121.84/16.08 (setukpairinjL) =>
% 121.84/16.08 ((
% 121.84/16.08 (setukpairinjR11) =>
% 121.84/16.08 ((
% 121.84/16.08 (setukpairinjR12) =>
% 121.84/16.08 ((
% 121.84/16.08 (setukpairinjR1) =>
% 121.84/16.08 ((
% 121.84/16.08 (upairequniteq) =>
% 121.84/16.08 ((
% 121.84/16.08 (setukpairinjR2) =>
% 121.84/16.08 ((
% 121.84/16.08 (setukpairinjR) =>
% 121.84/16.08 ((
% 121.84/16.08 (ksndsingleton) =>
% 121.84/16.08 ((
% 121.84/16.08 (ksndpairEq) =>
% 121.84/16.08 ((
% 121.84/16.08 (kpairsurjEq) =>
% 121.84/16.08 ((
% 121.84/16.08 (cartprodsndin) =>
% 121.84/16.08 ((
% 121.84/16.08 (cartprodpairmemEL) =>
% 121.84/16.08 ((
% 121.84/16.08 (cartprodpairmemER) =>
% 121.84/16.08 ((
% 121.84/16.08 (cartprodmempaircEq) =>
% 121.84/16.08 ((
% 121.84/16.08 (cartprodfstpairEq) =>
% 121.84/16.08 ((
% 121.84/16.08 (cartprodsndpairEq) =>
% 121.84/16.08 ((
% 121.84/16.08 (cartprodpairsurjEq) =>
% 121.84/16.08 ((
% 121.84/16.08 (dpsetconstrI) =>
% 121.84/16.08 ((
% 121.84/16.08 (dpsetconstrSub) =>
% 121.84/16.08 ((
% 121.84/16.08 (setOfPairsIsBReln) =>
% 121.84/16.08 ((
% 121.84/16.08 (dpsetconstrERa) =>
% 121.84/16.08 ((
% 121.84/16.08 (dpsetconstrEL1) =>
% 121.84/16.08 ((
% 121.84/16.08 (dpsetconstrEL2) =>
% 121.84/16.08 ((
% 121.84/16.08 (dpsetconstrER) =>
% 121.84/16.08 ((
% 121.84/16.08 (funcImageSingleton) =>
% 121.84/16.08 ((
% 121.84/16.08 (apProp) =>
% 121.84/16.08 ((
% 121.84/16.08 (app) =>
% 121.84/16.08 ((
% 121.84/16.08 (infuncsetfunc) =>
% 121.84/16.08 ((
% 121.84/16.08 (ap2p) =>
% 121.84/16.08 ((
% 121.84/16.08 (funcinfuncset) =>
% 121.84/16.08 ((
% 121.84/16.08 (lamProp) =>
% 121.84/16.08 ((
% 121.84/16.08 (lamp) =>
% 121.84/16.08 ((
% 121.84/16.08 (lam2p) =>
% 121.84/16.08 ((
% 121.84/16.08 (brelnall1) =>
% 121.84/16.08 ((
% 121.84/16.08 (brelnall2) =>
% 121.84/16.08 ((
% 121.84/16.08 (ex1E2) =>
% 121.84/16.08 ((
% 121.84/16.08 (funcGraphProp1) =>
% 121.84/16.08 ((
% 121.84/16.08 (funcGraphProp3) =>
% 121.84/16.08 ((
% 121.84/16.08 (funcGraphProp2) =>
% 121.84/16.08 ((
% 121.84/16.08 (funcextLem) =>
% 121.84/16.08 ((
% 121.84/16.08 (funcGraphProp4) =>
% 121.84/16.08 ((
% 121.84/16.08 (subbreln) =>
% 121.84/16.08 ((
% 121.84/16.08 (eqbreln) =>
% 121.84/16.08 ((
% 121.84/16.08 (funcext) =>
% 121.84/16.08 ((
% 121.84/16.08 (funcext2) =>
% 121.84/16.08 ((
% 121.84/16.08 (ap2apEq1) =>
% 121.84/16.08 ((
% 121.84/16.08 (ap2apEq2) =>
% 121.84/16.08 ((
% 121.84/16.08 (beta1) =>
% 121.84/16.08 ((
% 121.84/16.08 (eta1) =>
% 121.84/16.08 ((
% 121.84/16.08 (lam2lamEq) =>
% 121.84/16.08 ((
% 121.84/16.08 (beta2) =>
% 121.84/16.08 ((
% 121.84/16.08 (eta2) =>
% 121.84/16.08 ((
% 121.84/16.08 (iffalseProp1) =>
% 121.84/16.08 ((
% 121.84/16.08 (iffalseProp2) =>
% 121.84/16.08 ((
% 121.84/16.08 (iftrueProp1) =>
% 121.84/16.08 ((
% 121.84/16.08 (iftrueProp2) =>
% 121.84/16.08 ((
% 121.84/16.08 (ifSingleton) =>
% 121.84/16.08 ((
% 121.84/16.08 (ifp) =>
% 121.84/16.08 ((
% 121.84/16.08 (theeq) =>
% 121.84/16.08 ((
% 121.84/16.08 (iftrue) =>
% 121.84/16.08 ((
% 121.84/16.08 (iffalse) =>
% 121.84/16.08 ((
% 121.84/16.08 (iftrueorfalse) =>
% 121.84/16.08 ((
% 121.84/16.08 (binintersectT_lem) =>
% 121.84/16.08 ((
% 121.84/16.08 (binunionT_lem) =>
% 121.84/16.08 ((
% 121.84/16.08 (powersetT_lem) =>
% 121.84/16.08 ((
% 121.84/16.08 (setminusT_lem) =>
% 121.84/16.08 ((
% 121.84/16.08 (complementT_lem) =>
% 121.84/16.08 ((
% 121.84/16.08 (setextT) =>
% 121.84/16.08 ((
% 121.84/16.08 (subsetTI) =>
% 121.84/16.08 ((
% 121.84/16.08 (powersetTI1) =>
% 121.84/16.08 ((
% 121.84/16.08 (powersetTE1) =>
% 121.84/16.08 ((
% 121.84/16.08 (complementTI1) =>
% 121.84/16.08 ((
% 121.84/16.08 (complementTE1) =>
% 121.84/16.08 ((
% 121.84/16.08 (binintersectTELcontra) =>
% 121.84/16.08 ((
% 121.84/16.08 (binintersectTERcontra) =>
% 121.84/16.08 ((
% 121.84/16.08 (contrasubsetT) =>
% 121.84/16.08 ((
% 121.84/16.08 (contrasubsetT1) =>
% 121.84/16.08 ((
% 121.84/16.08 (contrasubsetT2) =>
% 121.84/16.08 ((
% 121.84/16.08 (contrasubsetT3) =>
% 121.84/16.08 ((
% 121.84/16.08 (doubleComplementI1) =>
% 121.84/16.08 ((
% 121.84/16.08 (doubleComplementE1) =>
% 121.84/16.08 ((
% 121.84/16.08 (doubleComplementSub1) =>
% 121.84/16.08 ((
% 121.84/16.08 (doubleComplementSub2) =>
% 121.84/16.08 ((
% 121.84/16.08 (doubleComplementEq) =>
% 121.84/16.08 ((
% 121.84/16.08 (complementTnotintersectT) =>
% 121.84/16.08 ((
% 121.84/16.08 (complementImpComplementIntersect) =>
% 121.84/16.08 ((
% 121.84/16.08 (complementSubsetComplementIntersect) =>
% 121.84/16.08 ((
% 121.84/16.08 (complementInPowersetComplementIntersect) =>
% 121.84/16.08 ((
% 121.84/16.08 (contraSubsetComplement) =>
% 121.84/16.08 ((
% 121.84/16.08 (complementTcontraSubset) =>
% 121.84/16.08 ((
% 121.84/16.08 (binunionTILcontra) =>
% 121.84/16.08 ((
% 121.84/16.08 (binunionTIRcontra) =>
% 121.84/16.08 ((
% 121.84/16.08 (inIntersectImpInUnion) =>
% 121.84/16.08 ((
% 121.84/16.08 (inIntersectImpInUnion2) =>
% 121.84/16.08 ((
% 121.84/16.08 (inIntersectImpInIntersectUnions) =>
% 121.84/16.08 ((
% 121.84/16.08 (intersectInPowersetIntersectUnions) =>
% 121.84/16.08 ((
% 121.84/16.08 (inComplementUnionImpNotIn1) =>
% 121.84/16.08 ((
% 121.84/16.08 (inComplementUnionImpInComplement1) =>
% 121.84/16.08 ((
% 121.84/16.08 (binunionTE) =>
% 121.84/16.08 ((
% 121.84/16.08 (binunionTEcontra) =>
% 121.84/16.08 ((
% 121.84/16.08 (demorgan2a1) =>
% 121.84/16.08 ((
% 121.84/16.08 (complementUnionInPowersetComplement) =>
% 121.84/16.08 ((
% 121.84/16.08 (demorgan2a2) =>
% 121.84/16.08 ((
% 121.84/16.08 (demorgan1a) =>
% 121.84/16.08 ((
% 121.84/16.08 (demorgan1b) =>
% 121.84/16.08 ((
% 121.84/16.08 (demorgan1) =>
% 121.84/16.08 ((
% 121.84/16.08 (demorgan2a) =>
% 121.84/16.08 ((
% 121.84/16.08 (demorgan2b2) =>
% 121.84/16.08 ((
% 121.84/16.08 (demorgan2b) =>
% 121.84/16.08 ((
% 121.84/16.08 (demorgan2) =>
% 121.84/16.08 ((
% 121.84/16.08 (woz13rule0) =>
% 121.84/16.08 ((
% 121.84/16.08 (woz13rule1) =>
% 121.84/16.08 ((
% 121.84/16.08 (woz13rule2) =>
% 121.84/16.08 ((
% 121.84/16.08 (woz13rule3) =>
% 121.84/16.08 ((
% 121.84/16.08 (woz13rule4) =>
% 121.84/16.08 ((
% 121.84/16.08 (woz1_1) =>
% 121.84/16.08 ((
% 121.84/16.08 (woz1_2) =>
% 121.84/16.08 ((
% 121.84/16.08 (woz1_3) =>
% 121.84/16.08 ((
% 121.84/16.08 (woz1_4) =>
% 121.84/16.08 ((
% 121.84/16.08 (woz1_5) =>
% 121.84/16.08 ((
% 121.84/16.08 (breln1all2) =>
% 121.84/16.08 ((
% 121.84/16.08 (breln1SetBreln1) =>
% 121.84/16.08 ((
% 121.84/16.08 (choice2fnsingleton) =>
% 121.84/16.08 ((
% 121.84/16.08 (setOfPairsIsBReln1) =>
% 121.84/16.08 ((
% 121.84/16.08 (breln1all1) =>
% 121.84/16.08 ((
% 121.84/16.08 (subbreln1) =>
% 121.84/16.08 ((
% 121.84/16.08 (eqbreln1) =>
% 121.84/16.08 ((
% 121.84/16.08 (breln1invprop) =>
% 121.84/16.08 ((
% 121.84/16.08 (breln1invI) =>
% 121.84/16.08 ((
% 121.84/16.08 (breln1invE) =>
% 121.84/16.08 ((
% 121.84/16.08 (breln1compprop) =>
% 121.84/16.08 ((
% 121.84/16.08 (breln1compI) =>
% 121.84/16.08 ((
% 121.84/16.08 (breln1compE) =>
% 121.84/16.08 ((
% 121.84/16.08 (breln1compEex) =>
% 121.84/16.08 ((
% 121.84/16.08 (breln1unionprop) =>
% 121.84/16.08 ((
% 121.84/16.08 (breln1unionIL) =>
% 121.84/16.08 ((
% 121.84/16.08 (breln1unionIR) =>
% 121.84/16.08 ((
% 121.84/16.08 (breln1unionI) =>
% 121.84/16.08 ((
% 121.84/16.08 (breln1unionE) =>
% 121.84/16.08 ((
% 121.84/16.08 (breln1unionEcases) =>
% 121.84/16.08 ((
% 121.84/16.08 (breln1unionCommutes) =>
% 121.84/16.08 ((
% 121.84/16.08 (woz2Ex) =>
% 121.84/16.08 ((
% 121.84/16.08 (woz2W) =>
% 121.84/16.08 ((
% 121.84/16.08 (woz2A) =>
% 121.84/16.08 ((
% 121.84/16.08 (woz2B) =>
% 121.84/16.08 ((
% 121.84/16.08 (image1Ex) =>
% 121.84/16.08 ((
% 121.84/16.08 (image1Ex1) =>
% 121.84/16.08 ((
% 121.84/16.08 (image1Equiv) =>
% 121.84/16.08 ((
% 121.84/16.08 (image1E) =>
% 121.84/16.08 ((
% 121.84/16.08 (image1I) =>
% 121.84/16.08 ((
% 121.84/16.08 (injFuncInInjFuncSet) =>
% 121.84/16.08 ((
% 121.84/16.08 (!!) @ (
% 121.84/16.08 (('#B') @ (
% 121.84/16.08 !!) @
% 121.84/16.08 (
% 121.84/16.08 (
% 121.84/16.08 ('#B') @ (
% 121.84/16.08 (
% 121.84/16.08 ('#B') @ (
% 121.84/16.08 !!))) @
% 121.84/16.08 (
% 121.84/16.08 (
% 121.84/16.08 ('#S') @ (
% 121.84/16.08 (
% 121.84/16.08 ('#B') @ (
% 121.84/16.08 '#S') @
% 121.84/16.08 (
% 121.84/16.08 (
% 121.84/16.08 ('#B') @ (
% 121.84/16.08 (
% 121.84/16.08 ('#B') @ (
% 121.84/16.08 '#S'))) @
% 121.84/16.08 (
% 121.84/16.08 (
% 121.84/16.08 ('#B') @ (
% 121.84/16.08 (
% 121.84/16.08 ('#B') @ (
% 121.84/16.08 (
% 121.84/16.08 ('#B') @ (
% 121.84/16.08 =>))))) @
% 121.84/16.08 (
% 121.84/16.08 (
% 121.84/16.08 ('#B') @ (
% 121.84/16.08 (
% 121.84/16.08 ('#B') @ (
% 121.84/16.08 (
% 121.84/16.08 ('#C') @ in)))) @
% 121.84/16.08 injFuncSet)))))))) @
% 121.84/16.08 (
% 121.84/16.08 (
% 121.84/16.08 ('#B') @ (
% 121.84/16.08 (
% 121.84/16.08 ('#B') @ (
% 121.84/16.08 (
% 121.84/16.08 ('#C') @ in)))) @
% 121.84/16.08 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 121.84/16.08 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl630])).
% 121.84/16.08 thf(zip_derived_cl650, plain,
% 121.84/16.08 (~ (((in__Cong) =>
% 121.84/16.08 (((exuE3u) =>
% 121.84/16.08 (((exu__Cong) =>
% 121.84/16.08 (((setadjoin__Cong) =>
% 121.84/16.08 (((powerset__Cong) =>
% 121.84/16.08 (((setunion__Cong) =>
% 121.84/16.08 (((exuEu) =>
% 121.84/16.08 (((descr__Cong) =>
% 121.84/16.08 (((dsetconstr__Cong) =>
% 121.84/16.08 (((subsetI1) =>
% 121.84/16.08 (((eqimpsubset2) =>
% 121.84/16.08 (((eqimpsubset1) =>
% 121.84/16.08 (((subsetI2) =>
% 121.84/16.08 (((emptysetsubset) =>
% 121.84/16.08 (((subsetE) =>
% 121.84/16.08 (((subsetE2) =>
% 121.84/16.08 (((notsubsetI) =>
% 121.84/16.08 (((notequalI1) =>
% 121.84/16.08 (((notequalI2) =>
% 121.84/16.08 (((subsetRefl) =>
% 121.84/16.08 (((subsetTrans) =>
% 121.84/16.08 (((setadjoinSub) =>
% 121.84/16.08 (((setadjoinSub2) =>
% 121.84/16.08 (((subset2powerset) =>
% 121.84/16.08 (((setextsub) =>
% 121.84/16.08 (((subsetemptysetimpeq) =>
% 121.84/16.08 (((powersetI1) =>
% 121.84/16.08 (((powersetE1) =>
% 121.84/16.08 (((inPowerset) =>
% 121.84/16.08 (((powersetsubset) =>
% 121.84/16.08 ((
% 121.84/16.08 (sepInPowerset) =>
% 121.84/16.08 ((
% 121.84/16.08 (sepSubset) =>
% 121.84/16.08 ((
% 121.84/16.08 (binunionIL) =>
% 121.84/16.08 ((
% 121.84/16.08 (upairset2IR) =>
% 121.84/16.08 ((
% 121.84/16.08 (binunionIR) =>
% 121.84/16.08 ((
% 121.84/16.08 (binunionEcases) =>
% 121.84/16.08 ((
% 121.84/16.08 (binunionE) =>
% 121.84/16.08 ((
% 121.84/16.08 (binunionLsub) =>
% 121.84/16.08 ((
% 121.84/16.08 (binunionRsub) =>
% 121.84/16.08 ((
% 121.84/16.08 (binintersectI) =>
% 121.84/16.08 ((
% 121.84/16.08 (binintersectSubset5) =>
% 121.84/16.08 ((
% 121.84/16.08 (binintersectEL) =>
% 121.84/16.08 ((
% 121.84/16.08 (binintersectLsub) =>
% 121.84/16.08 ((
% 121.84/16.08 (binintersectSubset2) =>
% 121.84/16.08 ((
% 121.84/16.08 (binintersectSubset3) =>
% 121.84/16.08 ((
% 121.84/16.08 (binintersectER) =>
% 121.84/16.08 ((
% 121.84/16.08 (disjointsetsI1) =>
% 121.84/16.08 ((
% 121.84/16.08 (binintersectRsub) =>
% 121.84/16.08 ((
% 121.84/16.08 (binintersectSubset4) =>
% 121.84/16.08 ((
% 121.84/16.08 (binintersectSubset1) =>
% 121.84/16.08 ((
% 121.84/16.08 (bs114d) =>
% 121.84/16.08 ((
% 121.84/16.08 (setminusI) =>
% 121.84/16.08 ((
% 121.84/16.08 (setminusEL) =>
% 121.84/16.08 ((
% 121.84/16.08 (setminusER) =>
% 121.84/16.08 ((
% 121.84/16.08 (setminusSubset2) =>
% 121.84/16.08 ((
% 121.84/16.08 (setminusERneg) =>
% 121.84/16.08 ((
% 121.84/16.08 (setminusELneg) =>
% 121.84/16.08 ((
% 121.84/16.08 (setminusILneg) =>
% 121.84/16.08 ((
% 121.84/16.08 (setminusIRneg) =>
% 121.84/16.08 ((
% 121.84/16.08 (setminusLsub) =>
% 121.84/16.08 ((
% 121.84/16.08 (setminusSubset1) =>
% 121.84/16.08 ((
% 121.84/16.08 (symdiffE) =>
% 121.84/16.08 ((
% 121.84/16.08 (symdiffI1) =>
% 121.84/16.08 ((
% 121.84/16.08 (symdiffI2) =>
% 121.84/16.08 ((
% 121.84/16.08 (symdiffIneg1) =>
% 121.84/16.08 ((
% 121.84/16.08 (symdiffIneg2) =>
% 121.84/16.08 ((
% 121.84/16.08 (secondinupair) =>
% 121.84/16.08 ((
% 121.84/16.08 (setukpairIL) =>
% 121.84/16.08 ((
% 121.84/16.08 (setukpairIR) =>
% 121.84/16.08 ((
% 121.84/16.08 (kpairiskpair) =>
% 121.84/16.08 ((
% 121.84/16.08 (kpairp) =>
% 121.84/16.08 ((
% 121.84/16.08 (singletonsubset) =>
% 121.84/16.08 ((
% 121.84/16.08 (singletoninpowerset) =>
% 121.84/16.08 ((
% 121.84/16.08 (singletoninpowunion) =>
% 121.84/16.08 ((
% 121.84/16.08 (upairset2E) =>
% 121.84/16.08 ((
% 121.84/16.08 (upairsubunion) =>
% 121.84/16.08 ((
% 121.84/16.08 (upairinpowunion) =>
% 121.84/16.08 ((
% 121.84/16.08 (ubforcartprodlem1) =>
% 121.84/16.08 ((
% 121.84/16.08 (ubforcartprodlem2) =>
% 121.84/16.08 ((
% 121.84/16.08 (ubforcartprodlem3) =>
% 121.84/16.08 ((
% 121.84/16.08 (cartprodpairin) =>
% 121.84/16.08 ((
% 121.84/16.08 (cartprodmempair1) =>
% 121.84/16.08 ((
% 121.84/16.08 (cartprodmempair) =>
% 121.84/16.08 ((
% 121.84/16.08 (setunionE2) =>
% 121.84/16.08 ((
% 121.84/16.08 (setunionsingleton1) =>
% 121.84/16.08 ((
% 121.84/16.08 (setunionsingleton2) =>
% 121.84/16.08 ((
% 121.84/16.08 (setunionsingleton) =>
% 121.84/16.08 ((
% 121.84/16.08 (singletonprop) =>
% 121.84/16.08 ((
% 121.84/16.08 (ex1E1) =>
% 121.84/16.08 ((
% 121.84/16.08 (ex1I) =>
% 121.84/16.08 ((
% 121.84/16.08 (ex1I2) =>
% 121.84/16.08 ((
% 121.84/16.08 (singletonsuniq) =>
% 121.84/16.08 ((
% 121.84/16.08 (setukpairinjL1) =>
% 121.84/16.08 ((
% 121.84/16.08 (kfstsingleton) =>
% 121.84/16.08 ((
% 121.84/16.08 (theprop) =>
% 121.84/16.08 ((
% 121.84/16.08 (kfstpairEq) =>
% 121.84/16.08 ((
% 121.84/16.08 (cartprodfstin) =>
% 121.84/16.08 ((
% 121.84/16.08 (setukpairinjL2) =>
% 121.84/16.08 ((
% 121.84/16.08 (setukpairinjL) =>
% 121.84/16.08 ((
% 121.84/16.08 (setukpairinjR11) =>
% 121.84/16.08 ((
% 121.84/16.08 (setukpairinjR12) =>
% 121.84/16.08 ((
% 121.84/16.08 (setukpairinjR1) =>
% 121.84/16.08 ((
% 121.84/16.08 (upairequniteq) =>
% 121.84/16.08 ((
% 121.84/16.08 (setukpairinjR2) =>
% 121.84/16.08 ((
% 121.84/16.08 (setukpairinjR) =>
% 121.84/16.08 ((
% 121.84/16.08 (ksndsingleton) =>
% 121.84/16.08 ((
% 121.84/16.08 (ksndpairEq) =>
% 121.84/16.08 ((
% 121.84/16.08 (kpairsurjEq) =>
% 121.84/16.08 ((
% 121.84/16.08 (cartprodsndin) =>
% 121.84/16.08 ((
% 121.84/16.08 (cartprodpairmemEL) =>
% 121.84/16.08 ((
% 121.84/16.08 (cartprodpairmemER) =>
% 121.84/16.08 ((
% 121.84/16.08 (cartprodmempaircEq) =>
% 121.84/16.08 ((
% 121.84/16.08 (cartprodfstpairEq) =>
% 121.84/16.08 ((
% 121.84/16.08 (cartprodsndpairEq) =>
% 121.84/16.08 ((
% 121.84/16.08 (cartprodpairsurjEq) =>
% 121.84/16.08 ((
% 121.84/16.08 (dpsetconstrI) =>
% 121.84/16.08 ((
% 121.84/16.08 (dpsetconstrSub) =>
% 121.84/16.08 ((
% 121.84/16.08 (setOfPairsIsBReln) =>
% 121.84/16.08 ((
% 121.84/16.08 (dpsetconstrERa) =>
% 121.84/16.08 ((
% 121.84/16.08 (dpsetconstrEL1) =>
% 121.84/16.08 ((
% 121.84/16.08 (dpsetconstrEL2) =>
% 121.84/16.08 ((
% 121.84/16.08 (dpsetconstrER) =>
% 121.84/16.08 ((
% 121.84/16.08 (funcImageSingleton) =>
% 121.84/16.08 ((
% 121.84/16.08 (apProp) =>
% 121.84/16.08 ((
% 121.84/16.08 (app) =>
% 121.84/16.08 ((
% 121.84/16.08 (infuncsetfunc) =>
% 121.84/16.08 ((
% 121.84/16.08 (ap2p) =>
% 121.84/16.08 ((
% 121.84/16.08 (funcinfuncset) =>
% 121.84/16.08 ((
% 121.84/16.08 (lamProp) =>
% 121.84/16.08 ((
% 121.84/16.08 (lamp) =>
% 121.84/16.08 ((
% 121.84/16.08 (lam2p) =>
% 121.84/16.08 ((
% 121.84/16.08 (brelnall1) =>
% 121.84/16.08 ((
% 121.84/16.08 (brelnall2) =>
% 121.84/16.08 ((
% 121.84/16.08 (ex1E2) =>
% 121.84/16.08 ((
% 121.84/16.08 (funcGraphProp1) =>
% 121.84/16.08 ((
% 121.84/16.08 (funcGraphProp3) =>
% 121.84/16.08 ((
% 121.84/16.08 (funcGraphProp2) =>
% 121.84/16.08 ((
% 121.84/16.08 (funcextLem) =>
% 121.84/16.08 ((
% 121.84/16.08 (funcGraphProp4) =>
% 121.84/16.08 ((
% 121.84/16.08 (subbreln) =>
% 121.84/16.08 ((
% 121.84/16.08 (eqbreln) =>
% 121.84/16.08 ((
% 121.84/16.08 (funcext) =>
% 121.84/16.08 ((
% 121.84/16.08 (funcext2) =>
% 121.84/16.08 ((
% 121.84/16.08 (ap2apEq1) =>
% 121.84/16.08 ((
% 121.84/16.08 (ap2apEq2) =>
% 121.84/16.08 ((
% 121.84/16.08 (beta1) =>
% 121.84/16.08 ((
% 121.84/16.08 (eta1) =>
% 121.84/16.08 ((
% 121.84/16.08 (lam2lamEq) =>
% 121.84/16.08 ((
% 121.84/16.08 (beta2) =>
% 121.84/16.08 ((
% 121.84/16.08 (eta2) =>
% 121.84/16.08 ((
% 121.84/16.08 (iffalseProp1) =>
% 121.84/16.08 ((
% 121.84/16.08 (iffalseProp2) =>
% 121.84/16.08 ((
% 121.84/16.08 (iftrueProp1) =>
% 121.84/16.08 ((
% 121.84/16.08 (iftrueProp2) =>
% 121.84/16.08 ((
% 121.84/16.08 (ifSingleton) =>
% 121.84/16.08 ((
% 121.84/16.08 (ifp) =>
% 121.84/16.08 ((
% 121.84/16.08 (theeq) =>
% 121.84/16.08 ((
% 121.84/16.08 (iftrue) =>
% 121.84/16.08 ((
% 121.84/16.08 (iffalse) =>
% 121.84/16.08 ((
% 121.84/16.08 (iftrueorfalse) =>
% 121.84/16.08 ((
% 121.84/16.08 (binintersectT_lem) =>
% 121.84/16.08 ((
% 121.84/16.08 (binunionT_lem) =>
% 121.84/16.08 ((
% 121.84/16.08 (powersetT_lem) =>
% 121.84/16.08 ((
% 121.84/16.08 (setminusT_lem) =>
% 121.84/16.08 ((
% 121.84/16.08 (complementT_lem) =>
% 121.84/16.08 ((
% 121.84/16.08 (setextT) =>
% 121.84/16.08 ((
% 121.84/16.08 (subsetTI) =>
% 121.84/16.08 ((
% 121.84/16.08 (powersetTI1) =>
% 121.84/16.08 ((
% 121.84/16.08 (powersetTE1) =>
% 121.84/16.08 ((
% 121.84/16.08 (complementTI1) =>
% 121.84/16.08 ((
% 121.84/16.08 (complementTE1) =>
% 121.84/16.08 ((
% 121.84/16.08 (binintersectTELcontra) =>
% 121.84/16.08 ((
% 121.84/16.08 (binintersectTERcontra) =>
% 121.84/16.08 ((
% 121.84/16.08 (contrasubsetT) =>
% 121.84/16.08 ((
% 121.84/16.08 (contrasubsetT1) =>
% 121.84/16.08 ((
% 121.84/16.08 (contrasubsetT2) =>
% 121.84/16.08 ((
% 121.84/16.08 (contrasubsetT3) =>
% 121.84/16.08 ((
% 121.84/16.08 (doubleComplementI1) =>
% 121.84/16.08 ((
% 121.84/16.08 (doubleComplementE1) =>
% 121.84/16.08 ((
% 121.84/16.08 (doubleComplementSub1) =>
% 121.84/16.08 ((
% 121.84/16.08 (doubleComplementSub2) =>
% 121.84/16.08 ((
% 121.84/16.08 (doubleComplementEq) =>
% 121.84/16.08 ((
% 121.84/16.08 (complementTnotintersectT) =>
% 121.84/16.08 ((
% 121.84/16.08 (complementImpComplementIntersect) =>
% 121.84/16.08 ((
% 121.84/16.08 (complementSubsetComplementIntersect) =>
% 121.84/16.08 ((
% 121.84/16.08 (complementInPowersetComplementIntersect) =>
% 121.84/16.08 ((
% 121.84/16.08 (contraSubsetComplement) =>
% 121.84/16.08 ((
% 121.84/16.08 (complementTcontraSubset) =>
% 121.84/16.08 ((
% 121.84/16.08 (binunionTILcontra) =>
% 121.84/16.08 ((
% 121.84/16.08 (binunionTIRcontra) =>
% 121.84/16.08 ((
% 121.84/16.08 (inIntersectImpInUnion) =>
% 121.84/16.08 ((
% 121.84/16.08 (inIntersectImpInUnion2) =>
% 121.84/16.08 ((
% 121.84/16.08 (inIntersectImpInIntersectUnions) =>
% 121.84/16.08 ((
% 121.84/16.08 (intersectInPowersetIntersectUnions) =>
% 121.84/16.08 ((
% 121.84/16.08 (inComplementUnionImpNotIn1) =>
% 121.84/16.08 ((
% 121.84/16.08 (inComplementUnionImpInComplement1) =>
% 121.84/16.08 ((
% 121.84/16.08 (binunionTE) =>
% 121.84/16.08 ((
% 121.84/16.08 (binunionTEcontra) =>
% 121.84/16.08 ((
% 121.84/16.08 (demorgan2a1) =>
% 121.84/16.08 ((
% 121.84/16.08 (complementUnionInPowersetComplement) =>
% 121.84/16.08 ((
% 121.84/16.08 (demorgan2a2) =>
% 121.84/16.08 ((
% 121.84/16.08 (demorgan1a) =>
% 121.84/16.08 ((
% 121.84/16.08 (demorgan1b) =>
% 121.84/16.08 ((
% 121.84/16.08 (demorgan1) =>
% 121.84/16.08 ((
% 121.84/16.08 (demorgan2a) =>
% 121.84/16.08 ((
% 121.84/16.08 (demorgan2b2) =>
% 121.84/16.08 ((
% 121.84/16.08 (demorgan2b) =>
% 121.84/16.08 ((
% 121.84/16.08 (demorgan2) =>
% 121.84/16.08 ((
% 121.84/16.08 (woz13rule0) =>
% 121.84/16.08 ((
% 121.84/16.08 (woz13rule1) =>
% 121.84/16.08 ((
% 121.84/16.08 (woz13rule2) =>
% 121.84/16.08 ((
% 121.84/16.08 (woz13rule3) =>
% 121.84/16.08 ((
% 121.84/16.08 (woz13rule4) =>
% 121.84/16.08 ((
% 121.84/16.08 (woz1_1) =>
% 121.84/16.08 ((
% 121.84/16.08 (woz1_2) =>
% 121.84/16.08 ((
% 121.84/16.08 (woz1_3) =>
% 121.84/16.08 ((
% 121.84/16.08 (woz1_4) =>
% 121.84/16.08 ((
% 121.84/16.08 (woz1_5) =>
% 121.84/16.08 ((
% 121.84/16.08 (breln1all2) =>
% 121.84/16.08 ((
% 121.84/16.08 (breln1SetBreln1) =>
% 121.84/16.08 ((
% 121.84/16.08 (choice2fnsingleton) =>
% 121.84/16.08 ((
% 121.84/16.08 (setOfPairsIsBReln1) =>
% 121.84/16.08 ((
% 121.84/16.08 (breln1all1) =>
% 121.84/16.08 ((
% 121.84/16.08 (subbreln1) =>
% 121.84/16.08 ((
% 121.84/16.08 (eqbreln1) =>
% 121.84/16.08 ((
% 121.84/16.08 (breln1invprop) =>
% 121.84/16.08 ((
% 121.84/16.08 (breln1invI) =>
% 121.84/16.08 ((
% 121.84/16.08 (breln1invE) =>
% 121.84/16.08 ((
% 121.84/16.08 (breln1compprop) =>
% 121.84/16.08 ((
% 121.84/16.08 (breln1compI) =>
% 121.84/16.08 ((
% 121.84/16.08 (breln1compE) =>
% 121.84/16.08 ((
% 121.84/16.08 (breln1compEex) =>
% 121.84/16.08 ((
% 121.84/16.08 (breln1unionprop) =>
% 121.84/16.08 ((
% 121.84/16.08 (breln1unionIL) =>
% 121.84/16.08 ((
% 121.84/16.08 (breln1unionIR) =>
% 121.84/16.08 ((
% 121.84/16.08 (breln1unionI) =>
% 121.84/16.08 ((
% 121.84/16.08 (breln1unionE) =>
% 121.84/16.08 ((
% 121.84/16.08 (breln1unionEcases) =>
% 121.84/16.08 ((
% 121.84/16.08 (breln1unionCommutes) =>
% 121.84/16.08 ((
% 121.84/16.08 (woz2Ex) =>
% 121.84/16.08 ((
% 121.84/16.08 (woz2W) =>
% 121.84/16.08 ((
% 121.84/16.08 (woz2A) =>
% 121.84/16.08 ((
% 121.84/16.08 (woz2B) =>
% 121.84/16.08 ((
% 121.84/16.08 (image1Ex) =>
% 121.84/16.08 ((
% 121.84/16.08 (image1Ex1) =>
% 121.84/16.08 ((
% 121.84/16.08 (image1Equiv) =>
% 121.84/16.08 ((
% 121.84/16.08 (image1E) =>
% 121.84/16.08 ((
% 121.84/16.08 (image1I) =>
% 121.84/16.08 ((
% 121.84/16.08 (injFuncInInjFuncSet) =>
% 121.84/16.08 ((
% 121.84/16.08 (!!) @ (
% 121.84/16.08 (('#B') @ (
% 121.84/16.08 !!) @
% 121.84/16.08 (
% 121.84/16.08 (
% 121.84/16.08 ('#B') @ (
% 121.84/16.08 (
% 121.84/16.08 ('#B') @ (
% 121.84/16.08 !!))) @
% 121.84/16.08 (
% 121.84/16.08 (
% 121.84/16.08 ('#S') @ (
% 121.84/16.08 (
% 121.84/16.08 ('#B') @ (
% 121.84/16.08 '#S') @
% 121.84/16.08 (
% 121.84/16.08 (
% 121.84/16.08 ('#B') @ (
% 121.84/16.08 (
% 121.84/16.08 ('#B') @ (
% 121.84/16.08 '#S'))) @
% 121.84/16.08 (
% 121.84/16.08 (
% 121.84/16.08 ('#B') @ (
% 121.84/16.08 (
% 121.84/16.08 ('#B') @ (
% 121.84/16.08 (
% 121.84/16.08 ('#B') @ (
% 121.84/16.08 =>))))) @
% 121.84/16.08 (
% 121.84/16.08 (
% 121.84/16.08 ('#B') @ (
% 121.84/16.08 (
% 121.84/16.08 ('#B') @ (
% 121.84/16.08 (
% 121.84/16.08 ('#C') @ in)))) @
% 121.84/16.08 injFuncSet)))))))) @
% 121.84/16.08 (
% 121.84/16.08 (
% 121.84/16.08 ('#B') @ (
% 121.84/16.08 (
% 121.84/16.08 ('#B') @ (
% 121.84/16.08 (
% 121.84/16.08 ('#C') @ in)))) @
% 121.84/16.08 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 121.84/16.08 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl640])).
% 121.84/16.08 thf(zip_derived_cl660, plain,
% 121.84/16.08 (~ (((exuE3u) =>
% 121.84/16.08 (((exu__Cong) =>
% 121.84/16.08 (((setadjoin__Cong) =>
% 121.84/16.08 (((powerset__Cong) =>
% 121.84/16.08 (((setunion__Cong) =>
% 121.84/16.08 (((exuEu) =>
% 121.84/16.08 (((descr__Cong) =>
% 121.84/16.08 (((dsetconstr__Cong) =>
% 121.84/16.08 (((subsetI1) =>
% 121.84/16.08 (((eqimpsubset2) =>
% 121.84/16.08 (((eqimpsubset1) =>
% 121.84/16.08 (((subsetI2) =>
% 121.84/16.08 (((emptysetsubset) =>
% 121.84/16.08 (((subsetE) =>
% 121.84/16.08 (((subsetE2) =>
% 121.84/16.08 (((notsubsetI) =>
% 121.84/16.08 (((notequalI1) =>
% 121.84/16.08 (((notequalI2) =>
% 121.84/16.08 (((subsetRefl) =>
% 121.84/16.08 (((subsetTrans) =>
% 121.84/16.08 (((setadjoinSub) =>
% 121.84/16.08 (((setadjoinSub2) =>
% 121.84/16.08 (((subset2powerset) =>
% 121.84/16.08 (((setextsub) =>
% 121.84/16.08 (((subsetemptysetimpeq) =>
% 121.84/16.08 (((powersetI1) =>
% 121.84/16.08 (((powersetE1) =>
% 121.84/16.08 (((inPowerset) =>
% 121.84/16.08 (((powersetsubset) =>
% 121.84/16.08 (((sepInPowerset) =>
% 121.84/16.08 ((
% 121.84/16.08 (sepSubset) =>
% 121.84/16.08 ((
% 121.84/16.08 (binunionIL) =>
% 121.84/16.08 ((
% 121.84/16.08 (upairset2IR) =>
% 121.84/16.08 ((
% 121.84/16.08 (binunionIR) =>
% 121.84/16.08 ((
% 121.84/16.08 (binunionEcases) =>
% 121.84/16.08 ((
% 121.84/16.08 (binunionE) =>
% 121.84/16.08 ((
% 121.84/16.08 (binunionLsub) =>
% 121.84/16.08 ((
% 121.84/16.08 (binunionRsub) =>
% 121.84/16.08 ((
% 121.84/16.08 (binintersectI) =>
% 121.84/16.08 ((
% 121.84/16.08 (binintersectSubset5) =>
% 121.84/16.08 ((
% 121.84/16.08 (binintersectEL) =>
% 121.84/16.08 ((
% 121.84/16.08 (binintersectLsub) =>
% 121.84/16.08 ((
% 121.84/16.08 (binintersectSubset2) =>
% 121.84/16.08 ((
% 121.84/16.08 (binintersectSubset3) =>
% 121.84/16.08 ((
% 121.84/16.08 (binintersectER) =>
% 121.84/16.08 ((
% 121.84/16.08 (disjointsetsI1) =>
% 121.84/16.08 ((
% 121.84/16.08 (binintersectRsub) =>
% 121.84/16.08 ((
% 121.84/16.08 (binintersectSubset4) =>
% 121.84/16.08 ((
% 121.84/16.08 (binintersectSubset1) =>
% 121.84/16.08 ((
% 121.84/16.08 (bs114d) =>
% 121.84/16.08 ((
% 121.84/16.08 (setminusI) =>
% 121.84/16.08 ((
% 121.84/16.08 (setminusEL) =>
% 121.84/16.08 ((
% 121.84/16.08 (setminusER) =>
% 121.84/16.08 ((
% 121.84/16.08 (setminusSubset2) =>
% 121.84/16.08 ((
% 121.84/16.08 (setminusERneg) =>
% 121.84/16.08 ((
% 121.84/16.08 (setminusELneg) =>
% 121.84/16.08 ((
% 121.84/16.08 (setminusILneg) =>
% 121.84/16.08 ((
% 121.84/16.08 (setminusIRneg) =>
% 121.84/16.08 ((
% 121.84/16.08 (setminusLsub) =>
% 121.84/16.08 ((
% 121.84/16.08 (setminusSubset1) =>
% 121.84/16.08 ((
% 121.84/16.08 (symdiffE) =>
% 121.84/16.08 ((
% 121.84/16.08 (symdiffI1) =>
% 121.84/16.08 ((
% 121.84/16.08 (symdiffI2) =>
% 121.84/16.08 ((
% 121.84/16.08 (symdiffIneg1) =>
% 121.84/16.08 ((
% 121.84/16.08 (symdiffIneg2) =>
% 121.84/16.08 ((
% 121.84/16.08 (secondinupair) =>
% 121.84/16.08 ((
% 121.84/16.08 (setukpairIL) =>
% 121.84/16.08 ((
% 121.84/16.08 (setukpairIR) =>
% 121.84/16.08 ((
% 121.84/16.08 (kpairiskpair) =>
% 121.84/16.08 ((
% 121.84/16.08 (kpairp) =>
% 121.84/16.08 ((
% 121.84/16.08 (singletonsubset) =>
% 121.84/16.08 ((
% 121.84/16.08 (singletoninpowerset) =>
% 121.84/16.08 ((
% 121.84/16.08 (singletoninpowunion) =>
% 121.84/16.08 ((
% 121.84/16.08 (upairset2E) =>
% 121.84/16.08 ((
% 121.84/16.08 (upairsubunion) =>
% 121.84/16.08 ((
% 121.84/16.08 (upairinpowunion) =>
% 121.84/16.08 ((
% 121.84/16.08 (ubforcartprodlem1) =>
% 121.84/16.08 ((
% 121.84/16.08 (ubforcartprodlem2) =>
% 121.84/16.08 ((
% 121.84/16.08 (ubforcartprodlem3) =>
% 121.84/16.08 ((
% 121.84/16.08 (cartprodpairin) =>
% 121.84/16.08 ((
% 121.84/16.08 (cartprodmempair1) =>
% 121.84/16.08 ((
% 121.84/16.08 (cartprodmempair) =>
% 121.84/16.08 ((
% 121.84/16.08 (setunionE2) =>
% 121.84/16.08 ((
% 121.84/16.08 (setunionsingleton1) =>
% 121.84/16.08 ((
% 121.84/16.08 (setunionsingleton2) =>
% 121.84/16.08 ((
% 121.84/16.08 (setunionsingleton) =>
% 121.84/16.08 ((
% 121.84/16.08 (singletonprop) =>
% 121.84/16.08 ((
% 121.84/16.08 (ex1E1) =>
% 121.84/16.08 ((
% 121.84/16.08 (ex1I) =>
% 121.84/16.08 ((
% 121.84/16.08 (ex1I2) =>
% 121.84/16.08 ((
% 121.84/16.08 (singletonsuniq) =>
% 121.84/16.08 ((
% 121.84/16.08 (setukpairinjL1) =>
% 121.84/16.08 ((
% 121.84/16.08 (kfstsingleton) =>
% 121.84/16.08 ((
% 121.84/16.08 (theprop) =>
% 121.84/16.08 ((
% 121.84/16.08 (kfstpairEq) =>
% 121.84/16.08 ((
% 121.84/16.08 (cartprodfstin) =>
% 121.84/16.08 ((
% 121.84/16.08 (setukpairinjL2) =>
% 121.84/16.08 ((
% 121.84/16.08 (setukpairinjL) =>
% 121.84/16.08 ((
% 121.84/16.08 (setukpairinjR11) =>
% 121.84/16.08 ((
% 121.84/16.08 (setukpairinjR12) =>
% 121.84/16.08 ((
% 121.84/16.08 (setukpairinjR1) =>
% 121.84/16.08 ((
% 121.84/16.08 (upairequniteq) =>
% 121.84/16.08 ((
% 121.84/16.08 (setukpairinjR2) =>
% 121.84/16.08 ((
% 121.84/16.08 (setukpairinjR) =>
% 121.84/16.08 ((
% 121.84/16.08 (ksndsingleton) =>
% 121.84/16.08 ((
% 121.84/16.08 (ksndpairEq) =>
% 121.84/16.08 ((
% 121.84/16.08 (kpairsurjEq) =>
% 121.84/16.08 ((
% 121.84/16.08 (cartprodsndin) =>
% 121.84/16.08 ((
% 121.84/16.08 (cartprodpairmemEL) =>
% 121.84/16.08 ((
% 121.84/16.08 (cartprodpairmemER) =>
% 121.84/16.08 ((
% 121.84/16.08 (cartprodmempaircEq) =>
% 121.84/16.08 ((
% 121.84/16.08 (cartprodfstpairEq) =>
% 121.84/16.08 ((
% 121.84/16.08 (cartprodsndpairEq) =>
% 121.84/16.08 ((
% 121.84/16.08 (cartprodpairsurjEq) =>
% 121.84/16.08 ((
% 121.84/16.08 (dpsetconstrI) =>
% 121.84/16.08 ((
% 121.84/16.08 (dpsetconstrSub) =>
% 121.84/16.08 ((
% 121.84/16.08 (setOfPairsIsBReln) =>
% 121.84/16.08 ((
% 121.84/16.08 (dpsetconstrERa) =>
% 121.84/16.08 ((
% 121.84/16.08 (dpsetconstrEL1) =>
% 121.84/16.08 ((
% 121.84/16.08 (dpsetconstrEL2) =>
% 121.84/16.08 ((
% 121.84/16.08 (dpsetconstrER) =>
% 121.84/16.08 ((
% 121.84/16.08 (funcImageSingleton) =>
% 121.84/16.08 ((
% 121.84/16.08 (apProp) =>
% 121.84/16.08 ((
% 121.84/16.08 (app) =>
% 121.84/16.08 ((
% 121.84/16.08 (infuncsetfunc) =>
% 121.84/16.08 ((
% 121.84/16.08 (ap2p) =>
% 121.84/16.08 ((
% 121.84/16.08 (funcinfuncset) =>
% 121.84/16.08 ((
% 121.84/16.08 (lamProp) =>
% 121.84/16.08 ((
% 121.84/16.08 (lamp) =>
% 121.84/16.08 ((
% 121.84/16.08 (lam2p) =>
% 121.84/16.08 ((
% 121.84/16.08 (brelnall1) =>
% 121.84/16.08 ((
% 121.84/16.08 (brelnall2) =>
% 121.84/16.08 ((
% 121.84/16.08 (ex1E2) =>
% 121.84/16.08 ((
% 121.84/16.08 (funcGraphProp1) =>
% 121.84/16.08 ((
% 121.84/16.08 (funcGraphProp3) =>
% 121.84/16.08 ((
% 121.84/16.08 (funcGraphProp2) =>
% 121.84/16.08 ((
% 121.84/16.08 (funcextLem) =>
% 121.84/16.08 ((
% 121.84/16.08 (funcGraphProp4) =>
% 121.84/16.08 ((
% 121.84/16.08 (subbreln) =>
% 121.84/16.08 ((
% 121.84/16.08 (eqbreln) =>
% 121.84/16.08 ((
% 121.84/16.08 (funcext) =>
% 121.84/16.08 ((
% 121.84/16.08 (funcext2) =>
% 121.84/16.08 ((
% 121.84/16.08 (ap2apEq1) =>
% 121.84/16.08 ((
% 121.84/16.08 (ap2apEq2) =>
% 121.84/16.08 ((
% 121.84/16.08 (beta1) =>
% 121.84/16.08 ((
% 121.84/16.08 (eta1) =>
% 121.84/16.08 ((
% 121.84/16.08 (lam2lamEq) =>
% 121.84/16.08 ((
% 121.84/16.08 (beta2) =>
% 121.84/16.08 ((
% 121.84/16.08 (eta2) =>
% 121.84/16.08 ((
% 121.84/16.08 (iffalseProp1) =>
% 121.84/16.08 ((
% 121.84/16.08 (iffalseProp2) =>
% 121.84/16.08 ((
% 121.84/16.08 (iftrueProp1) =>
% 121.84/16.08 ((
% 121.84/16.08 (iftrueProp2) =>
% 121.84/16.08 ((
% 121.84/16.08 (ifSingleton) =>
% 121.84/16.08 ((
% 121.84/16.08 (ifp) =>
% 121.84/16.08 ((
% 121.84/16.08 (theeq) =>
% 121.84/16.08 ((
% 121.84/16.08 (iftrue) =>
% 121.84/16.08 ((
% 121.84/16.08 (iffalse) =>
% 121.84/16.08 ((
% 121.84/16.08 (iftrueorfalse) =>
% 121.84/16.08 ((
% 121.84/16.08 (binintersectT_lem) =>
% 121.84/16.08 ((
% 121.84/16.08 (binunionT_lem) =>
% 121.84/16.08 ((
% 121.84/16.08 (powersetT_lem) =>
% 121.84/16.08 ((
% 121.84/16.08 (setminusT_lem) =>
% 121.84/16.08 ((
% 121.84/16.08 (complementT_lem) =>
% 121.84/16.08 ((
% 121.84/16.08 (setextT) =>
% 121.84/16.08 ((
% 121.84/16.08 (subsetTI) =>
% 121.84/16.08 ((
% 121.84/16.08 (powersetTI1) =>
% 121.84/16.08 ((
% 121.84/16.08 (powersetTE1) =>
% 121.84/16.08 ((
% 121.84/16.08 (complementTI1) =>
% 121.84/16.08 ((
% 121.84/16.08 (complementTE1) =>
% 121.84/16.08 ((
% 121.84/16.08 (binintersectTELcontra) =>
% 121.84/16.08 ((
% 121.84/16.08 (binintersectTERcontra) =>
% 121.84/16.08 ((
% 121.84/16.08 (contrasubsetT) =>
% 121.84/16.08 ((
% 121.84/16.08 (contrasubsetT1) =>
% 121.84/16.08 ((
% 121.84/16.08 (contrasubsetT2) =>
% 121.84/16.08 ((
% 121.84/16.08 (contrasubsetT3) =>
% 121.84/16.08 ((
% 121.84/16.08 (doubleComplementI1) =>
% 121.84/16.08 ((
% 121.84/16.08 (doubleComplementE1) =>
% 121.84/16.08 ((
% 121.84/16.08 (doubleComplementSub1) =>
% 121.84/16.08 ((
% 121.84/16.08 (doubleComplementSub2) =>
% 121.84/16.08 ((
% 121.84/16.08 (doubleComplementEq) =>
% 121.84/16.08 ((
% 121.84/16.08 (complementTnotintersectT) =>
% 121.84/16.08 ((
% 121.84/16.08 (complementImpComplementIntersect) =>
% 121.84/16.08 ((
% 121.84/16.08 (complementSubsetComplementIntersect) =>
% 121.84/16.08 ((
% 121.84/16.08 (complementInPowersetComplementIntersect) =>
% 121.84/16.08 ((
% 121.84/16.08 (contraSubsetComplement) =>
% 121.84/16.08 ((
% 121.84/16.08 (complementTcontraSubset) =>
% 121.84/16.08 ((
% 121.84/16.08 (binunionTILcontra) =>
% 121.84/16.08 ((
% 121.84/16.08 (binunionTIRcontra) =>
% 121.84/16.08 ((
% 121.84/16.08 (inIntersectImpInUnion) =>
% 121.84/16.08 ((
% 121.84/16.08 (inIntersectImpInUnion2) =>
% 121.84/16.08 ((
% 121.84/16.08 (inIntersectImpInIntersectUnions) =>
% 121.84/16.08 ((
% 121.84/16.08 (intersectInPowersetIntersectUnions) =>
% 121.84/16.08 ((
% 121.84/16.08 (inComplementUnionImpNotIn1) =>
% 121.84/16.08 ((
% 121.84/16.08 (inComplementUnionImpInComplement1) =>
% 121.84/16.08 ((
% 121.84/16.08 (binunionTE) =>
% 121.84/16.08 ((
% 121.84/16.08 (binunionTEcontra) =>
% 121.84/16.08 ((
% 121.84/16.08 (demorgan2a1) =>
% 121.84/16.08 ((
% 121.84/16.08 (complementUnionInPowersetComplement) =>
% 121.84/16.08 ((
% 121.84/16.08 (demorgan2a2) =>
% 121.84/16.08 ((
% 121.84/16.08 (demorgan1a) =>
% 121.84/16.08 ((
% 121.84/16.08 (demorgan1b) =>
% 121.84/16.08 ((
% 121.84/16.08 (demorgan1) =>
% 121.84/16.08 ((
% 121.84/16.08 (demorgan2a) =>
% 121.84/16.08 ((
% 121.84/16.08 (demorgan2b2) =>
% 121.84/16.08 ((
% 121.84/16.08 (demorgan2b) =>
% 121.84/16.08 ((
% 121.84/16.08 (demorgan2) =>
% 121.84/16.08 ((
% 121.84/16.08 (woz13rule0) =>
% 121.84/16.08 ((
% 121.84/16.08 (woz13rule1) =>
% 121.84/16.08 ((
% 121.84/16.08 (woz13rule2) =>
% 121.84/16.08 ((
% 121.84/16.08 (woz13rule3) =>
% 121.84/16.08 ((
% 121.84/16.08 (woz13rule4) =>
% 121.84/16.08 ((
% 121.84/16.08 (woz1_1) =>
% 121.84/16.08 ((
% 121.84/16.08 (woz1_2) =>
% 121.84/16.08 ((
% 121.84/16.08 (woz1_3) =>
% 121.84/16.08 ((
% 121.84/16.08 (woz1_4) =>
% 121.84/16.08 ((
% 121.84/16.08 (woz1_5) =>
% 121.84/16.08 ((
% 121.84/16.08 (breln1all2) =>
% 121.84/16.08 ((
% 121.84/16.08 (breln1SetBreln1) =>
% 121.84/16.08 ((
% 121.84/16.08 (choice2fnsingleton) =>
% 121.84/16.08 ((
% 121.84/16.08 (setOfPairsIsBReln1) =>
% 121.84/16.08 ((
% 121.84/16.08 (breln1all1) =>
% 121.84/16.08 ((
% 121.84/16.08 (subbreln1) =>
% 121.84/16.08 ((
% 121.84/16.08 (eqbreln1) =>
% 121.84/16.08 ((
% 121.84/16.08 (breln1invprop) =>
% 121.84/16.08 ((
% 121.84/16.08 (breln1invI) =>
% 121.84/16.08 ((
% 121.84/16.08 (breln1invE) =>
% 121.84/16.08 ((
% 121.84/16.08 (breln1compprop) =>
% 121.84/16.08 ((
% 121.84/16.08 (breln1compI) =>
% 121.84/16.08 ((
% 121.84/16.08 (breln1compE) =>
% 121.84/16.08 ((
% 121.84/16.08 (breln1compEex) =>
% 121.84/16.08 ((
% 121.84/16.08 (breln1unionprop) =>
% 121.84/16.08 ((
% 121.84/16.08 (breln1unionIL) =>
% 121.84/16.08 ((
% 121.84/16.08 (breln1unionIR) =>
% 121.84/16.08 ((
% 121.84/16.08 (breln1unionI) =>
% 121.84/16.08 ((
% 121.84/16.08 (breln1unionE) =>
% 121.84/16.08 ((
% 121.84/16.08 (breln1unionEcases) =>
% 121.84/16.08 ((
% 121.84/16.08 (breln1unionCommutes) =>
% 121.84/16.08 ((
% 121.84/16.08 (woz2Ex) =>
% 121.84/16.08 ((
% 121.84/16.08 (woz2W) =>
% 121.84/16.08 ((
% 121.84/16.08 (woz2A) =>
% 121.84/16.08 ((
% 121.84/16.08 (woz2B) =>
% 121.84/16.08 ((
% 121.84/16.08 (image1Ex) =>
% 121.84/16.08 ((
% 121.84/16.08 (image1Ex1) =>
% 121.84/16.08 ((
% 121.84/16.08 (image1Equiv) =>
% 121.84/16.08 ((
% 121.84/16.08 (image1E) =>
% 121.84/16.08 ((
% 121.84/16.08 (image1I) =>
% 121.84/16.08 ((
% 121.84/16.08 (injFuncInInjFuncSet) =>
% 121.84/16.08 ((
% 121.84/16.08 (!!) @ (
% 121.84/16.08 (('#B') @ (
% 121.84/16.08 !!) @
% 121.84/16.08 (
% 121.84/16.08 (
% 121.84/16.08 ('#B') @ (
% 121.84/16.08 (
% 121.84/16.08 ('#B') @ (
% 121.84/16.08 !!))) @
% 121.84/16.08 (
% 121.84/16.08 (
% 121.84/16.08 ('#S') @ (
% 121.84/16.08 (
% 121.84/16.08 ('#B') @ (
% 121.84/16.08 '#S') @
% 121.84/16.08 (
% 121.84/16.08 (
% 121.84/16.08 ('#B') @ (
% 121.84/16.08 (
% 121.84/16.08 ('#B') @ (
% 121.84/16.08 '#S'))) @
% 121.84/16.08 (
% 121.84/16.08 (
% 121.84/16.08 ('#B') @ (
% 121.84/16.08 (
% 121.84/16.08 ('#B') @ (
% 121.84/16.08 (
% 121.84/16.08 ('#B') @ (
% 121.84/16.08 =>))))) @
% 121.84/16.08 (
% 121.84/16.08 (
% 121.84/16.08 ('#B') @ (
% 121.84/16.08 (
% 121.84/16.08 ('#B') @ (
% 121.84/16.08 (
% 121.84/16.08 ('#C') @ in)))) @
% 121.84/16.08 injFuncSet)))))))) @
% 121.84/16.08 (
% 121.84/16.08 (
% 121.84/16.08 ('#B') @ (
% 121.84/16.08 (
% 121.84/16.08 ('#B') @ (
% 121.84/16.08 (
% 121.84/16.08 ('#C') @ in)))) @
% 121.84/16.08 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 121.84/16.08 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl650])).
% 121.84/16.08 thf(zip_derived_cl672, plain,
% 121.84/16.08 (~ (((exu__Cong) =>
% 121.84/16.08 (((setadjoin__Cong) =>
% 121.84/16.08 (((powerset__Cong) =>
% 121.84/16.08 (((setunion__Cong) =>
% 121.84/16.08 (((exuEu) =>
% 121.84/16.08 (((descr__Cong) =>
% 121.84/16.08 (((dsetconstr__Cong) =>
% 121.84/16.08 (((subsetI1) =>
% 121.84/16.08 (((eqimpsubset2) =>
% 121.84/16.08 (((eqimpsubset1) =>
% 121.84/16.08 (((subsetI2) =>
% 121.84/16.08 (((emptysetsubset) =>
% 121.84/16.08 (((subsetE) =>
% 121.84/16.08 (((subsetE2) =>
% 121.84/16.08 (((notsubsetI) =>
% 121.84/16.08 (((notequalI1) =>
% 121.84/16.08 (((notequalI2) =>
% 121.84/16.08 (((subsetRefl) =>
% 121.84/16.08 (((subsetTrans) =>
% 121.84/16.08 (((setadjoinSub) =>
% 121.84/16.08 (((setadjoinSub2) =>
% 121.84/16.08 (((subset2powerset) =>
% 121.84/16.08 (((setextsub) =>
% 121.84/16.08 (((subsetemptysetimpeq) =>
% 121.84/16.08 (((powersetI1) =>
% 121.84/16.08 (((powersetE1) =>
% 121.84/16.08 (((inPowerset) =>
% 121.84/16.08 (((powersetsubset) =>
% 121.84/16.08 (((sepInPowerset) =>
% 121.84/16.08 (((sepSubset) =>
% 121.84/16.08 ((
% 121.84/16.08 (binunionIL) =>
% 121.84/16.08 ((
% 121.84/16.08 (upairset2IR) =>
% 121.84/16.08 ((
% 121.84/16.08 (binunionIR) =>
% 121.84/16.08 ((
% 121.84/16.08 (binunionEcases) =>
% 121.84/16.08 ((
% 121.84/16.08 (binunionE) =>
% 121.84/16.08 ((
% 121.84/16.08 (binunionLsub) =>
% 121.84/16.08 ((
% 121.84/16.08 (binunionRsub) =>
% 121.84/16.08 ((
% 121.84/16.08 (binintersectI) =>
% 121.84/16.08 ((
% 121.84/16.08 (binintersectSubset5) =>
% 121.84/16.08 ((
% 121.84/16.08 (binintersectEL) =>
% 121.84/16.08 ((
% 121.84/16.08 (binintersectLsub) =>
% 121.84/16.08 ((
% 121.84/16.08 (binintersectSubset2) =>
% 121.84/16.08 ((
% 121.84/16.08 (binintersectSubset3) =>
% 121.84/16.08 ((
% 121.84/16.08 (binintersectER) =>
% 121.84/16.08 ((
% 121.84/16.08 (disjointsetsI1) =>
% 121.84/16.08 ((
% 121.84/16.08 (binintersectRsub) =>
% 121.84/16.08 ((
% 121.84/16.08 (binintersectSubset4) =>
% 121.84/16.08 ((
% 121.84/16.08 (binintersectSubset1) =>
% 121.84/16.08 ((
% 121.84/16.08 (bs114d) =>
% 121.84/16.08 ((
% 121.84/16.08 (setminusI) =>
% 121.84/16.08 ((
% 121.84/16.08 (setminusEL) =>
% 121.84/16.08 ((
% 121.84/16.08 (setminusER) =>
% 121.84/16.08 ((
% 121.84/16.08 (setminusSubset2) =>
% 121.84/16.08 ((
% 121.84/16.08 (setminusERneg) =>
% 121.84/16.08 ((
% 121.84/16.08 (setminusELneg) =>
% 121.84/16.08 ((
% 121.84/16.08 (setminusILneg) =>
% 121.84/16.08 ((
% 121.84/16.08 (setminusIRneg) =>
% 121.84/16.08 ((
% 121.84/16.08 (setminusLsub) =>
% 121.84/16.08 ((
% 121.84/16.08 (setminusSubset1) =>
% 121.84/16.08 ((
% 121.84/16.08 (symdiffE) =>
% 121.84/16.08 ((
% 121.84/16.08 (symdiffI1) =>
% 121.84/16.08 ((
% 121.84/16.08 (symdiffI2) =>
% 121.84/16.08 ((
% 121.84/16.08 (symdiffIneg1) =>
% 121.84/16.08 ((
% 121.84/16.08 (symdiffIneg2) =>
% 121.84/16.08 ((
% 121.84/16.08 (secondinupair) =>
% 121.84/16.08 ((
% 121.84/16.08 (setukpairIL) =>
% 121.84/16.08 ((
% 121.84/16.08 (setukpairIR) =>
% 121.84/16.08 ((
% 121.84/16.08 (kpairiskpair) =>
% 121.84/16.08 ((
% 121.84/16.08 (kpairp) =>
% 121.84/16.08 ((
% 121.84/16.08 (singletonsubset) =>
% 121.84/16.08 ((
% 121.84/16.08 (singletoninpowerset) =>
% 121.84/16.08 ((
% 121.84/16.08 (singletoninpowunion) =>
% 121.84/16.08 ((
% 121.84/16.08 (upairset2E) =>
% 121.84/16.08 ((
% 121.84/16.08 (upairsubunion) =>
% 121.84/16.08 ((
% 121.84/16.08 (upairinpowunion) =>
% 121.84/16.08 ((
% 121.84/16.08 (ubforcartprodlem1) =>
% 121.84/16.08 ((
% 121.84/16.08 (ubforcartprodlem2) =>
% 121.84/16.08 ((
% 121.84/16.08 (ubforcartprodlem3) =>
% 121.84/16.08 ((
% 121.84/16.08 (cartprodpairin) =>
% 121.84/16.08 ((
% 121.84/16.08 (cartprodmempair1) =>
% 121.84/16.08 ((
% 121.84/16.08 (cartprodmempair) =>
% 121.84/16.08 ((
% 121.84/16.08 (setunionE2) =>
% 121.84/16.08 ((
% 121.84/16.08 (setunionsingleton1) =>
% 121.84/16.08 ((
% 121.84/16.08 (setunionsingleton2) =>
% 121.84/16.08 ((
% 121.84/16.08 (setunionsingleton) =>
% 121.84/16.08 ((
% 121.84/16.08 (singletonprop) =>
% 121.84/16.08 ((
% 121.84/16.08 (ex1E1) =>
% 121.84/16.08 ((
% 121.84/16.08 (ex1I) =>
% 121.84/16.08 ((
% 121.84/16.08 (ex1I2) =>
% 121.84/16.08 ((
% 121.84/16.08 (singletonsuniq) =>
% 121.84/16.08 ((
% 121.84/16.08 (setukpairinjL1) =>
% 121.84/16.08 ((
% 121.84/16.08 (kfstsingleton) =>
% 121.84/16.08 ((
% 121.84/16.08 (theprop) =>
% 121.84/16.08 ((
% 121.84/16.08 (kfstpairEq) =>
% 121.84/16.08 ((
% 121.84/16.08 (cartprodfstin) =>
% 121.84/16.08 ((
% 121.84/16.08 (setukpairinjL2) =>
% 121.84/16.08 ((
% 121.84/16.08 (setukpairinjL) =>
% 121.84/16.08 ((
% 121.84/16.08 (setukpairinjR11) =>
% 121.84/16.08 ((
% 121.84/16.08 (setukpairinjR12) =>
% 121.84/16.08 ((
% 121.84/16.08 (setukpairinjR1) =>
% 121.84/16.08 ((
% 121.84/16.08 (upairequniteq) =>
% 121.84/16.08 ((
% 121.84/16.08 (setukpairinjR2) =>
% 121.84/16.08 ((
% 121.84/16.08 (setukpairinjR) =>
% 121.84/16.08 ((
% 121.84/16.08 (ksndsingleton) =>
% 121.84/16.08 ((
% 121.84/16.08 (ksndpairEq) =>
% 121.84/16.08 ((
% 121.84/16.08 (kpairsurjEq) =>
% 121.84/16.08 ((
% 121.84/16.08 (cartprodsndin) =>
% 121.84/16.08 ((
% 121.84/16.08 (cartprodpairmemEL) =>
% 121.84/16.08 ((
% 121.84/16.08 (cartprodpairmemER) =>
% 121.84/16.08 ((
% 121.84/16.08 (cartprodmempaircEq) =>
% 121.84/16.08 ((
% 121.84/16.08 (cartprodfstpairEq) =>
% 121.84/16.08 ((
% 121.84/16.08 (cartprodsndpairEq) =>
% 121.84/16.08 ((
% 121.84/16.08 (cartprodpairsurjEq) =>
% 121.84/16.08 ((
% 121.84/16.08 (dpsetconstrI) =>
% 121.84/16.08 ((
% 121.84/16.08 (dpsetconstrSub) =>
% 121.84/16.08 ((
% 121.84/16.08 (setOfPairsIsBReln) =>
% 121.84/16.08 ((
% 121.84/16.08 (dpsetconstrERa) =>
% 121.84/16.08 ((
% 121.84/16.08 (dpsetconstrEL1) =>
% 121.84/16.08 ((
% 121.84/16.08 (dpsetconstrEL2) =>
% 121.84/16.08 ((
% 121.84/16.08 (dpsetconstrER) =>
% 121.84/16.08 ((
% 121.84/16.08 (funcImageSingleton) =>
% 121.84/16.08 ((
% 121.84/16.08 (apProp) =>
% 121.84/16.08 ((
% 121.84/16.08 (app) =>
% 121.84/16.08 ((
% 121.84/16.08 (infuncsetfunc) =>
% 121.84/16.08 ((
% 121.84/16.08 (ap2p) =>
% 121.84/16.08 ((
% 121.84/16.08 (funcinfuncset) =>
% 121.84/16.08 ((
% 121.84/16.08 (lamProp) =>
% 121.84/16.08 ((
% 121.84/16.08 (lamp) =>
% 121.84/16.08 ((
% 121.84/16.08 (lam2p) =>
% 121.84/16.08 ((
% 121.84/16.08 (brelnall1) =>
% 121.84/16.08 ((
% 121.84/16.08 (brelnall2) =>
% 121.84/16.08 ((
% 121.84/16.08 (ex1E2) =>
% 121.84/16.08 ((
% 121.84/16.08 (funcGraphProp1) =>
% 121.84/16.08 ((
% 121.84/16.08 (funcGraphProp3) =>
% 121.84/16.08 ((
% 121.84/16.08 (funcGraphProp2) =>
% 121.84/16.08 ((
% 121.84/16.08 (funcextLem) =>
% 121.84/16.08 ((
% 121.84/16.08 (funcGraphProp4) =>
% 121.84/16.08 ((
% 121.84/16.08 (subbreln) =>
% 121.84/16.08 ((
% 121.84/16.08 (eqbreln) =>
% 121.84/16.08 ((
% 121.84/16.08 (funcext) =>
% 121.84/16.08 ((
% 121.84/16.08 (funcext2) =>
% 121.84/16.08 ((
% 121.84/16.08 (ap2apEq1) =>
% 121.84/16.08 ((
% 121.84/16.08 (ap2apEq2) =>
% 121.84/16.08 ((
% 121.84/16.08 (beta1) =>
% 121.84/16.08 ((
% 121.84/16.08 (eta1) =>
% 121.84/16.08 ((
% 121.84/16.08 (lam2lamEq) =>
% 121.84/16.08 ((
% 121.84/16.08 (beta2) =>
% 121.84/16.08 ((
% 121.84/16.08 (eta2) =>
% 121.84/16.08 ((
% 121.84/16.08 (iffalseProp1) =>
% 121.84/16.08 ((
% 121.84/16.08 (iffalseProp2) =>
% 121.84/16.08 ((
% 121.84/16.08 (iftrueProp1) =>
% 121.84/16.08 ((
% 121.84/16.08 (iftrueProp2) =>
% 121.84/16.08 ((
% 121.84/16.08 (ifSingleton) =>
% 121.84/16.08 ((
% 121.84/16.08 (ifp) =>
% 121.84/16.08 ((
% 121.84/16.08 (theeq) =>
% 121.84/16.08 ((
% 121.84/16.08 (iftrue) =>
% 121.84/16.08 ((
% 121.84/16.08 (iffalse) =>
% 121.84/16.08 ((
% 121.84/16.08 (iftrueorfalse) =>
% 121.84/16.08 ((
% 121.84/16.08 (binintersectT_lem) =>
% 121.84/16.08 ((
% 121.84/16.08 (binunionT_lem) =>
% 121.84/16.08 ((
% 121.84/16.08 (powersetT_lem) =>
% 121.84/16.08 ((
% 121.84/16.08 (setminusT_lem) =>
% 121.84/16.08 ((
% 121.84/16.08 (complementT_lem) =>
% 121.84/16.08 ((
% 121.84/16.08 (setextT) =>
% 121.84/16.08 ((
% 121.84/16.08 (subsetTI) =>
% 121.84/16.08 ((
% 121.84/16.08 (powersetTI1) =>
% 121.84/16.08 ((
% 121.84/16.08 (powersetTE1) =>
% 121.84/16.08 ((
% 121.84/16.08 (complementTI1) =>
% 121.84/16.08 ((
% 121.84/16.08 (complementTE1) =>
% 121.84/16.08 ((
% 121.84/16.08 (binintersectTELcontra) =>
% 121.84/16.08 ((
% 121.84/16.08 (binintersectTERcontra) =>
% 121.84/16.08 ((
% 121.84/16.08 (contrasubsetT) =>
% 121.84/16.08 ((
% 121.84/16.08 (contrasubsetT1) =>
% 121.84/16.08 ((
% 121.84/16.08 (contrasubsetT2) =>
% 121.84/16.08 ((
% 121.84/16.08 (contrasubsetT3) =>
% 121.84/16.08 ((
% 121.84/16.08 (doubleComplementI1) =>
% 121.84/16.08 ((
% 121.84/16.08 (doubleComplementE1) =>
% 121.84/16.08 ((
% 121.84/16.08 (doubleComplementSub1) =>
% 121.84/16.08 ((
% 121.84/16.08 (doubleComplementSub2) =>
% 121.84/16.08 ((
% 121.84/16.08 (doubleComplementEq) =>
% 121.84/16.08 ((
% 121.84/16.08 (complementTnotintersectT) =>
% 121.84/16.08 ((
% 121.84/16.08 (complementImpComplementIntersect) =>
% 121.84/16.08 ((
% 121.84/16.08 (complementSubsetComplementIntersect) =>
% 121.84/16.08 ((
% 121.84/16.08 (complementInPowersetComplementIntersect) =>
% 121.84/16.08 ((
% 121.84/16.08 (contraSubsetComplement) =>
% 121.84/16.08 ((
% 121.84/16.08 (complementTcontraSubset) =>
% 121.84/16.08 ((
% 121.84/16.08 (binunionTILcontra) =>
% 121.84/16.08 ((
% 121.84/16.08 (binunionTIRcontra) =>
% 121.84/16.08 ((
% 121.84/16.08 (inIntersectImpInUnion) =>
% 121.84/16.08 ((
% 121.84/16.08 (inIntersectImpInUnion2) =>
% 121.84/16.08 ((
% 121.84/16.08 (inIntersectImpInIntersectUnions) =>
% 121.84/16.08 ((
% 121.84/16.08 (intersectInPowersetIntersectUnions) =>
% 121.84/16.08 ((
% 121.84/16.08 (inComplementUnionImpNotIn1) =>
% 121.84/16.08 ((
% 121.84/16.08 (inComplementUnionImpInComplement1) =>
% 121.84/16.08 ((
% 121.84/16.08 (binunionTE) =>
% 121.84/16.08 ((
% 121.84/16.08 (binunionTEcontra) =>
% 121.84/16.08 ((
% 121.84/16.08 (demorgan2a1) =>
% 121.84/16.08 ((
% 121.84/16.08 (complementUnionInPowersetComplement) =>
% 121.84/16.08 ((
% 121.84/16.08 (demorgan2a2) =>
% 121.84/16.08 ((
% 121.84/16.08 (demorgan1a) =>
% 121.84/16.08 ((
% 121.84/16.08 (demorgan1b) =>
% 121.84/16.08 ((
% 121.84/16.08 (demorgan1) =>
% 121.84/16.08 ((
% 121.84/16.08 (demorgan2a) =>
% 121.84/16.08 ((
% 121.84/16.08 (demorgan2b2) =>
% 121.84/16.08 ((
% 121.84/16.08 (demorgan2b) =>
% 121.84/16.08 ((
% 121.84/16.08 (demorgan2) =>
% 121.84/16.08 ((
% 121.84/16.08 (woz13rule0) =>
% 121.84/16.08 ((
% 121.84/16.08 (woz13rule1) =>
% 121.84/16.08 ((
% 121.84/16.08 (woz13rule2) =>
% 121.84/16.08 ((
% 121.84/16.08 (woz13rule3) =>
% 121.84/16.08 ((
% 121.84/16.08 (woz13rule4) =>
% 121.84/16.08 ((
% 121.84/16.08 (woz1_1) =>
% 121.84/16.08 ((
% 121.84/16.08 (woz1_2) =>
% 121.84/16.08 ((
% 121.84/16.08 (woz1_3) =>
% 121.84/16.08 ((
% 121.84/16.08 (woz1_4) =>
% 121.84/16.08 ((
% 121.84/16.08 (woz1_5) =>
% 121.84/16.08 ((
% 121.84/16.08 (breln1all2) =>
% 121.84/16.08 ((
% 121.84/16.08 (breln1SetBreln1) =>
% 121.84/16.08 ((
% 121.84/16.08 (choice2fnsingleton) =>
% 121.84/16.08 ((
% 121.84/16.08 (setOfPairsIsBReln1) =>
% 121.84/16.08 ((
% 121.84/16.08 (breln1all1) =>
% 121.84/16.08 ((
% 121.84/16.08 (subbreln1) =>
% 121.84/16.08 ((
% 121.84/16.08 (eqbreln1) =>
% 121.84/16.08 ((
% 121.84/16.08 (breln1invprop) =>
% 121.84/16.08 ((
% 121.84/16.08 (breln1invI) =>
% 121.84/16.08 ((
% 121.84/16.08 (breln1invE) =>
% 121.84/16.08 ((
% 121.84/16.08 (breln1compprop) =>
% 121.84/16.08 ((
% 121.84/16.08 (breln1compI) =>
% 121.84/16.08 ((
% 121.84/16.08 (breln1compE) =>
% 121.84/16.08 ((
% 121.84/16.08 (breln1compEex) =>
% 121.84/16.08 ((
% 121.84/16.08 (breln1unionprop) =>
% 121.84/16.08 ((
% 121.84/16.08 (breln1unionIL) =>
% 121.84/16.08 ((
% 121.84/16.08 (breln1unionIR) =>
% 121.84/16.08 ((
% 121.84/16.08 (breln1unionI) =>
% 121.84/16.08 ((
% 121.84/16.08 (breln1unionE) =>
% 121.84/16.08 ((
% 121.84/16.08 (breln1unionEcases) =>
% 121.84/16.08 ((
% 121.84/16.08 (breln1unionCommutes) =>
% 121.84/16.08 ((
% 121.84/16.08 (woz2Ex) =>
% 121.84/16.08 ((
% 121.84/16.08 (woz2W) =>
% 121.84/16.08 ((
% 121.84/16.08 (woz2A) =>
% 121.84/16.08 ((
% 121.84/16.08 (woz2B) =>
% 121.84/16.08 ((
% 121.84/16.08 (image1Ex) =>
% 121.84/16.08 ((
% 121.84/16.08 (image1Ex1) =>
% 121.84/16.08 ((
% 121.84/16.08 (image1Equiv) =>
% 121.84/16.08 ((
% 121.84/16.08 (image1E) =>
% 121.84/16.08 ((
% 121.84/16.08 (image1I) =>
% 121.84/16.08 ((
% 121.84/16.08 (injFuncInInjFuncSet) =>
% 121.84/16.08 ((
% 121.84/16.08 (!!) @ (
% 121.84/16.08 (('#B') @ (
% 121.84/16.08 !!) @
% 121.84/16.08 (
% 121.84/16.08 (
% 121.84/16.08 ('#B') @ (
% 121.84/16.08 (
% 121.84/16.08 ('#B') @ (
% 121.84/16.08 !!))) @
% 121.84/16.08 (
% 121.84/16.08 (
% 121.84/16.08 ('#S') @ (
% 121.84/16.08 (
% 121.84/16.08 ('#B') @ (
% 121.84/16.08 '#S') @
% 121.84/16.08 (
% 121.84/16.08 (
% 121.84/16.08 ('#B') @ (
% 121.84/16.08 (
% 121.84/16.08 ('#B') @ (
% 121.84/16.08 '#S'))) @
% 121.84/16.08 (
% 121.84/16.08 (
% 121.84/16.08 ('#B') @ (
% 121.84/16.08 (
% 121.84/16.08 ('#B') @ (
% 121.84/16.08 (
% 121.84/16.08 ('#B') @ (
% 121.84/16.08 =>))))) @
% 121.84/16.08 (
% 121.84/16.08 (
% 121.84/16.08 ('#B') @ (
% 121.84/16.08 (
% 121.84/16.08 ('#B') @ (
% 121.84/16.08 (
% 121.84/16.08 ('#C') @ in)))) @
% 121.84/16.08 injFuncSet)))))))) @
% 121.84/16.08 (
% 121.84/16.08 (
% 121.84/16.08 ('#B') @ (
% 121.84/16.08 (
% 121.84/16.08 ('#B') @ (
% 121.84/16.08 (
% 121.84/16.08 ('#C') @ in)))) @
% 121.84/16.08 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 121.84/16.08 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl660])).
% 121.84/16.08 thf(zip_derived_cl685, plain,
% 121.84/16.08 (~ (((setadjoin__Cong) =>
% 121.84/16.08 (((powerset__Cong) =>
% 121.84/16.08 (((setunion__Cong) =>
% 121.84/16.08 (((exuEu) =>
% 121.84/16.08 (((descr__Cong) =>
% 121.84/16.08 (((dsetconstr__Cong) =>
% 121.84/16.08 (((subsetI1) =>
% 121.84/16.08 (((eqimpsubset2) =>
% 121.84/16.08 (((eqimpsubset1) =>
% 121.84/16.08 (((subsetI2) =>
% 121.84/16.08 (((emptysetsubset) =>
% 121.84/16.08 (((subsetE) =>
% 121.84/16.08 (((subsetE2) =>
% 121.84/16.08 (((notsubsetI) =>
% 121.84/16.08 (((notequalI1) =>
% 121.84/16.08 (((notequalI2) =>
% 121.84/16.08 (((subsetRefl) =>
% 121.84/16.08 (((subsetTrans) =>
% 121.84/16.08 (((setadjoinSub) =>
% 121.84/16.08 (((setadjoinSub2) =>
% 121.84/16.08 (((subset2powerset) =>
% 121.84/16.08 (((setextsub) =>
% 121.84/16.08 (((subsetemptysetimpeq) =>
% 121.84/16.08 (((powersetI1) =>
% 121.84/16.08 (((powersetE1) =>
% 121.84/16.08 (((inPowerset) =>
% 121.84/16.08 (((powersetsubset) =>
% 121.84/16.08 (((sepInPowerset) =>
% 121.84/16.08 (((sepSubset) =>
% 121.84/16.08 (((binunionIL) =>
% 121.84/16.08 ((
% 121.84/16.08 (upairset2IR) =>
% 121.84/16.08 ((
% 121.84/16.08 (binunionIR) =>
% 121.84/16.08 ((
% 121.84/16.08 (binunionEcases) =>
% 121.84/16.08 ((
% 121.84/16.08 (binunionE) =>
% 121.84/16.08 ((
% 121.84/16.08 (binunionLsub) =>
% 121.84/16.08 ((
% 121.84/16.08 (binunionRsub) =>
% 121.84/16.08 ((
% 121.84/16.08 (binintersectI) =>
% 121.84/16.08 ((
% 121.84/16.08 (binintersectSubset5) =>
% 121.84/16.08 ((
% 121.84/16.08 (binintersectEL) =>
% 121.84/16.08 ((
% 121.84/16.08 (binintersectLsub) =>
% 121.84/16.08 ((
% 121.84/16.08 (binintersectSubset2) =>
% 121.84/16.08 ((
% 121.84/16.08 (binintersectSubset3) =>
% 121.84/16.08 ((
% 121.84/16.08 (binintersectER) =>
% 121.84/16.08 ((
% 121.84/16.08 (disjointsetsI1) =>
% 121.84/16.08 ((
% 121.84/16.08 (binintersectRsub) =>
% 121.84/16.08 ((
% 121.84/16.08 (binintersectSubset4) =>
% 121.84/16.08 ((
% 121.84/16.08 (binintersectSubset1) =>
% 121.84/16.08 ((
% 121.84/16.08 (bs114d) =>
% 121.84/16.08 ((
% 121.84/16.08 (setminusI) =>
% 121.84/16.08 ((
% 121.84/16.08 (setminusEL) =>
% 121.84/16.08 ((
% 121.84/16.08 (setminusER) =>
% 121.84/16.08 ((
% 121.84/16.08 (setminusSubset2) =>
% 121.84/16.08 ((
% 121.84/16.08 (setminusERneg) =>
% 121.84/16.08 ((
% 121.84/16.08 (setminusELneg) =>
% 121.84/16.08 ((
% 121.84/16.08 (setminusILneg) =>
% 121.84/16.08 ((
% 121.84/16.08 (setminusIRneg) =>
% 121.84/16.08 ((
% 121.84/16.08 (setminusLsub) =>
% 121.84/16.08 ((
% 121.84/16.08 (setminusSubset1) =>
% 121.84/16.08 ((
% 121.84/16.08 (symdiffE) =>
% 121.84/16.08 ((
% 121.84/16.08 (symdiffI1) =>
% 121.84/16.08 ((
% 121.84/16.08 (symdiffI2) =>
% 121.84/16.08 ((
% 121.84/16.08 (symdiffIneg1) =>
% 121.84/16.08 ((
% 121.84/16.08 (symdiffIneg2) =>
% 121.84/16.08 ((
% 121.84/16.08 (secondinupair) =>
% 121.84/16.08 ((
% 121.84/16.08 (setukpairIL) =>
% 121.84/16.08 ((
% 121.84/16.08 (setukpairIR) =>
% 121.84/16.08 ((
% 121.84/16.08 (kpairiskpair) =>
% 121.84/16.08 ((
% 121.84/16.08 (kpairp) =>
% 121.84/16.08 ((
% 121.84/16.08 (singletonsubset) =>
% 121.84/16.08 ((
% 121.84/16.08 (singletoninpowerset) =>
% 121.84/16.08 ((
% 121.84/16.08 (singletoninpowunion) =>
% 121.84/16.08 ((
% 121.84/16.08 (upairset2E) =>
% 121.84/16.08 ((
% 121.84/16.08 (upairsubunion) =>
% 121.84/16.08 ((
% 121.84/16.08 (upairinpowunion) =>
% 121.84/16.08 ((
% 121.84/16.08 (ubforcartprodlem1) =>
% 121.84/16.08 ((
% 121.84/16.08 (ubforcartprodlem2) =>
% 121.84/16.08 ((
% 121.84/16.08 (ubforcartprodlem3) =>
% 121.84/16.08 ((
% 121.84/16.08 (cartprodpairin) =>
% 121.84/16.08 ((
% 121.84/16.08 (cartprodmempair1) =>
% 121.84/16.08 ((
% 121.84/16.08 (cartprodmempair) =>
% 121.84/16.08 ((
% 121.84/16.08 (setunionE2) =>
% 121.84/16.08 ((
% 121.84/16.08 (setunionsingleton1) =>
% 121.84/16.08 ((
% 121.84/16.08 (setunionsingleton2) =>
% 121.84/16.08 ((
% 121.84/16.08 (setunionsingleton) =>
% 121.84/16.08 ((
% 121.84/16.08 (singletonprop) =>
% 121.84/16.08 ((
% 121.84/16.08 (ex1E1) =>
% 121.84/16.08 ((
% 121.84/16.08 (ex1I) =>
% 121.84/16.08 ((
% 121.84/16.08 (ex1I2) =>
% 121.84/16.08 ((
% 121.84/16.08 (singletonsuniq) =>
% 121.84/16.08 ((
% 121.84/16.08 (setukpairinjL1) =>
% 121.84/16.08 ((
% 121.84/16.08 (kfstsingleton) =>
% 121.84/16.08 ((
% 121.84/16.08 (theprop) =>
% 121.84/16.08 ((
% 121.84/16.08 (kfstpairEq) =>
% 121.84/16.08 ((
% 121.84/16.08 (cartprodfstin) =>
% 121.84/16.08 ((
% 121.84/16.08 (setukpairinjL2) =>
% 121.84/16.08 ((
% 121.84/16.08 (setukpairinjL) =>
% 121.84/16.08 ((
% 121.84/16.08 (setukpairinjR11) =>
% 121.84/16.08 ((
% 121.84/16.08 (setukpairinjR12) =>
% 121.84/16.08 ((
% 121.84/16.08 (setukpairinjR1) =>
% 121.84/16.08 ((
% 121.84/16.08 (upairequniteq) =>
% 121.84/16.08 ((
% 121.84/16.08 (setukpairinjR2) =>
% 121.84/16.08 ((
% 121.84/16.08 (setukpairinjR) =>
% 121.84/16.08 ((
% 121.84/16.08 (ksndsingleton) =>
% 121.84/16.08 ((
% 121.84/16.08 (ksndpairEq) =>
% 121.84/16.08 ((
% 121.84/16.08 (kpairsurjEq) =>
% 121.84/16.08 ((
% 121.84/16.08 (cartprodsndin) =>
% 121.84/16.08 ((
% 121.84/16.08 (cartprodpairmemEL) =>
% 121.84/16.08 ((
% 121.84/16.08 (cartprodpairmemER) =>
% 121.84/16.08 ((
% 121.84/16.08 (cartprodmempaircEq) =>
% 121.84/16.08 ((
% 121.84/16.08 (cartprodfstpairEq) =>
% 121.84/16.08 ((
% 121.84/16.08 (cartprodsndpairEq) =>
% 121.84/16.08 ((
% 121.84/16.08 (cartprodpairsurjEq) =>
% 121.84/16.08 ((
% 121.84/16.08 (dpsetconstrI) =>
% 121.84/16.08 ((
% 121.84/16.08 (dpsetconstrSub) =>
% 121.84/16.08 ((
% 121.84/16.08 (setOfPairsIsBReln) =>
% 121.84/16.08 ((
% 121.84/16.08 (dpsetconstrERa) =>
% 121.84/16.08 ((
% 121.84/16.08 (dpsetconstrEL1) =>
% 121.84/16.08 ((
% 121.84/16.08 (dpsetconstrEL2) =>
% 121.84/16.08 ((
% 121.84/16.08 (dpsetconstrER) =>
% 121.84/16.08 ((
% 121.84/16.08 (funcImageSingleton) =>
% 121.84/16.08 ((
% 121.84/16.08 (apProp) =>
% 121.84/16.08 ((
% 121.84/16.08 (app) =>
% 121.84/16.08 ((
% 121.84/16.08 (infuncsetfunc) =>
% 121.84/16.08 ((
% 121.84/16.08 (ap2p) =>
% 121.84/16.08 ((
% 121.84/16.08 (funcinfuncset) =>
% 121.84/16.08 ((
% 121.84/16.08 (lamProp) =>
% 121.84/16.08 ((
% 121.84/16.08 (lamp) =>
% 121.84/16.08 ((
% 121.84/16.08 (lam2p) =>
% 121.84/16.08 ((
% 121.84/16.08 (brelnall1) =>
% 121.84/16.08 ((
% 121.84/16.08 (brelnall2) =>
% 121.84/16.08 ((
% 121.84/16.08 (ex1E2) =>
% 121.84/16.08 ((
% 121.84/16.08 (funcGraphProp1) =>
% 121.84/16.08 ((
% 121.84/16.08 (funcGraphProp3) =>
% 121.84/16.08 ((
% 121.84/16.08 (funcGraphProp2) =>
% 121.84/16.08 ((
% 121.84/16.08 (funcextLem) =>
% 121.84/16.08 ((
% 121.84/16.08 (funcGraphProp4) =>
% 121.84/16.08 ((
% 121.84/16.08 (subbreln) =>
% 121.84/16.08 ((
% 121.84/16.08 (eqbreln) =>
% 121.84/16.08 ((
% 121.84/16.08 (funcext) =>
% 121.84/16.08 ((
% 121.84/16.08 (funcext2) =>
% 121.84/16.08 ((
% 121.84/16.08 (ap2apEq1) =>
% 121.84/16.08 ((
% 121.84/16.08 (ap2apEq2) =>
% 121.84/16.08 ((
% 121.84/16.08 (beta1) =>
% 121.84/16.08 ((
% 121.84/16.08 (eta1) =>
% 121.84/16.08 ((
% 121.84/16.08 (lam2lamEq) =>
% 121.84/16.08 ((
% 121.84/16.08 (beta2) =>
% 121.84/16.08 ((
% 121.84/16.08 (eta2) =>
% 121.84/16.08 ((
% 121.84/16.08 (iffalseProp1) =>
% 121.84/16.08 ((
% 121.84/16.08 (iffalseProp2) =>
% 121.84/16.08 ((
% 121.84/16.08 (iftrueProp1) =>
% 121.84/16.08 ((
% 121.84/16.08 (iftrueProp2) =>
% 121.84/16.08 ((
% 121.84/16.08 (ifSingleton) =>
% 121.84/16.08 ((
% 121.84/16.08 (ifp) =>
% 121.84/16.08 ((
% 121.84/16.08 (theeq) =>
% 121.84/16.08 ((
% 121.84/16.08 (iftrue) =>
% 121.84/16.08 ((
% 121.84/16.08 (iffalse) =>
% 121.84/16.08 ((
% 121.84/16.08 (iftrueorfalse) =>
% 121.84/16.08 ((
% 121.84/16.08 (binintersectT_lem) =>
% 121.84/16.08 ((
% 121.84/16.08 (binunionT_lem) =>
% 121.84/16.08 ((
% 121.84/16.08 (powersetT_lem) =>
% 121.84/16.08 ((
% 121.84/16.08 (setminusT_lem) =>
% 121.84/16.08 ((
% 121.84/16.08 (complementT_lem) =>
% 121.84/16.08 ((
% 121.84/16.08 (setextT) =>
% 121.84/16.08 ((
% 121.84/16.08 (subsetTI) =>
% 121.84/16.08 ((
% 121.84/16.08 (powersetTI1) =>
% 121.84/16.08 ((
% 121.84/16.08 (powersetTE1) =>
% 121.84/16.08 ((
% 121.84/16.08 (complementTI1) =>
% 121.84/16.08 ((
% 121.84/16.08 (complementTE1) =>
% 121.84/16.08 ((
% 121.84/16.08 (binintersectTELcontra) =>
% 121.84/16.08 ((
% 121.84/16.08 (binintersectTERcontra) =>
% 121.84/16.08 ((
% 121.84/16.08 (contrasubsetT) =>
% 121.84/16.08 ((
% 121.84/16.08 (contrasubsetT1) =>
% 121.84/16.08 ((
% 121.84/16.08 (contrasubsetT2) =>
% 121.84/16.08 ((
% 121.84/16.08 (contrasubsetT3) =>
% 121.84/16.08 ((
% 121.84/16.08 (doubleComplementI1) =>
% 121.84/16.08 ((
% 121.84/16.08 (doubleComplementE1) =>
% 121.84/16.08 ((
% 121.84/16.08 (doubleComplementSub1) =>
% 121.84/16.08 ((
% 121.84/16.08 (doubleComplementSub2) =>
% 121.84/16.08 ((
% 121.84/16.08 (doubleComplementEq) =>
% 121.84/16.08 ((
% 121.84/16.08 (complementTnotintersectT) =>
% 121.84/16.08 ((
% 121.84/16.08 (complementImpComplementIntersect) =>
% 121.84/16.08 ((
% 121.84/16.08 (complementSubsetComplementIntersect) =>
% 121.84/16.08 ((
% 121.84/16.08 (complementInPowersetComplementIntersect) =>
% 121.84/16.08 ((
% 121.84/16.08 (contraSubsetComplement) =>
% 121.84/16.08 ((
% 121.84/16.08 (complementTcontraSubset) =>
% 121.84/16.08 ((
% 121.84/16.08 (binunionTILcontra) =>
% 121.84/16.08 ((
% 121.84/16.08 (binunionTIRcontra) =>
% 121.84/16.08 ((
% 121.84/16.08 (inIntersectImpInUnion) =>
% 121.84/16.08 ((
% 121.84/16.08 (inIntersectImpInUnion2) =>
% 121.84/16.08 ((
% 121.84/16.08 (inIntersectImpInIntersectUnions) =>
% 121.84/16.08 ((
% 121.84/16.08 (intersectInPowersetIntersectUnions) =>
% 121.84/16.08 ((
% 121.84/16.08 (inComplementUnionImpNotIn1) =>
% 121.84/16.08 ((
% 121.84/16.08 (inComplementUnionImpInComplement1) =>
% 121.84/16.08 ((
% 121.84/16.08 (binunionTE) =>
% 121.84/16.08 ((
% 121.84/16.08 (binunionTEcontra) =>
% 121.84/16.08 ((
% 121.84/16.08 (demorgan2a1) =>
% 121.84/16.08 ((
% 121.84/16.08 (complementUnionInPowersetComplement) =>
% 121.84/16.08 ((
% 121.84/16.08 (demorgan2a2) =>
% 121.84/16.08 ((
% 121.84/16.08 (demorgan1a) =>
% 121.84/16.08 ((
% 121.84/16.08 (demorgan1b) =>
% 121.84/16.08 ((
% 121.84/16.08 (demorgan1) =>
% 121.84/16.08 ((
% 121.84/16.08 (demorgan2a) =>
% 121.84/16.08 ((
% 121.84/16.08 (demorgan2b2) =>
% 121.84/16.08 ((
% 121.84/16.08 (demorgan2b) =>
% 121.84/16.08 ((
% 121.84/16.08 (demorgan2) =>
% 121.84/16.08 ((
% 121.84/16.08 (woz13rule0) =>
% 121.84/16.08 ((
% 121.84/16.08 (woz13rule1) =>
% 121.84/16.08 ((
% 121.84/16.08 (woz13rule2) =>
% 121.84/16.08 ((
% 121.84/16.08 (woz13rule3) =>
% 121.84/16.08 ((
% 121.84/16.08 (woz13rule4) =>
% 121.84/16.08 ((
% 121.84/16.08 (woz1_1) =>
% 121.84/16.08 ((
% 121.84/16.08 (woz1_2) =>
% 121.84/16.08 ((
% 121.84/16.08 (woz1_3) =>
% 121.84/16.08 ((
% 121.84/16.08 (woz1_4) =>
% 121.84/16.08 ((
% 121.84/16.08 (woz1_5) =>
% 121.84/16.08 ((
% 121.84/16.08 (breln1all2) =>
% 121.84/16.08 ((
% 121.84/16.08 (breln1SetBreln1) =>
% 121.84/16.08 ((
% 121.84/16.08 (choice2fnsingleton) =>
% 121.84/16.08 ((
% 121.84/16.08 (setOfPairsIsBReln1) =>
% 121.84/16.08 ((
% 121.84/16.08 (breln1all1) =>
% 121.84/16.08 ((
% 121.84/16.08 (subbreln1) =>
% 121.84/16.08 ((
% 121.84/16.08 (eqbreln1) =>
% 121.84/16.08 ((
% 121.84/16.08 (breln1invprop) =>
% 121.84/16.08 ((
% 121.84/16.08 (breln1invI) =>
% 121.84/16.08 ((
% 121.84/16.08 (breln1invE) =>
% 121.84/16.08 ((
% 121.84/16.08 (breln1compprop) =>
% 121.84/16.08 ((
% 121.84/16.08 (breln1compI) =>
% 121.84/16.08 ((
% 121.84/16.08 (breln1compE) =>
% 121.84/16.08 ((
% 121.84/16.08 (breln1compEex) =>
% 121.84/16.08 ((
% 121.84/16.08 (breln1unionprop) =>
% 121.84/16.08 ((
% 121.84/16.08 (breln1unionIL) =>
% 121.84/16.08 ((
% 121.84/16.08 (breln1unionIR) =>
% 121.84/16.08 ((
% 121.84/16.08 (breln1unionI) =>
% 121.84/16.08 ((
% 121.84/16.08 (breln1unionE) =>
% 121.84/16.08 ((
% 121.84/16.08 (breln1unionEcases) =>
% 121.84/16.08 ((
% 121.84/16.08 (breln1unionCommutes) =>
% 121.84/16.08 ((
% 121.84/16.08 (woz2Ex) =>
% 121.84/16.08 ((
% 121.84/16.08 (woz2W) =>
% 121.84/16.08 ((
% 121.84/16.08 (woz2A) =>
% 121.84/16.08 ((
% 121.84/16.08 (woz2B) =>
% 121.84/16.08 ((
% 121.84/16.08 (image1Ex) =>
% 121.84/16.08 ((
% 121.84/16.08 (image1Ex1) =>
% 121.84/16.08 ((
% 121.84/16.08 (image1Equiv) =>
% 121.84/16.08 ((
% 121.84/16.08 (image1E) =>
% 121.84/16.08 ((
% 121.84/16.08 (image1I) =>
% 121.84/16.08 ((
% 121.84/16.08 (injFuncInInjFuncSet) =>
% 121.84/16.08 ((
% 121.84/16.08 (!!) @ (
% 121.84/16.08 (('#B') @ (
% 121.84/16.08 !!) @
% 121.84/16.08 (
% 121.84/16.08 (
% 121.84/16.08 ('#B') @ (
% 121.84/16.08 (
% 121.84/16.08 ('#B') @ (
% 121.84/16.08 !!))) @
% 121.84/16.08 (
% 121.84/16.08 (
% 121.84/16.08 ('#S') @ (
% 121.84/16.08 (
% 121.84/16.08 ('#B') @ (
% 121.84/16.08 '#S') @
% 121.84/16.08 (
% 121.84/16.08 (
% 121.84/16.08 ('#B') @ (
% 121.84/16.08 (
% 121.84/16.08 ('#B') @ (
% 121.84/16.08 '#S'))) @
% 121.84/16.08 (
% 121.84/16.08 (
% 121.84/16.08 ('#B') @ (
% 121.84/16.08 (
% 121.84/16.08 ('#B') @ (
% 121.84/16.08 (
% 121.84/16.08 ('#B') @ (
% 121.84/16.08 =>))))) @
% 121.84/16.08 (
% 121.84/16.08 (
% 121.84/16.08 ('#B') @ (
% 121.84/16.08 (
% 121.84/16.08 ('#B') @ (
% 121.84/16.08 (
% 121.84/16.08 ('#C') @ in)))) @
% 121.84/16.08 injFuncSet)))))))) @
% 121.84/16.08 (
% 121.84/16.08 (
% 121.84/16.08 ('#B') @ (
% 121.84/16.08 (
% 121.84/16.08 ('#B') @ (
% 121.84/16.08 (
% 121.84/16.08 ('#C') @ in)))) @
% 121.84/16.08 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 121.84/16.08 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl672])).
% 121.84/16.08 thf(zip_derived_cl699, plain,
% 121.84/16.08 (~ (((powerset__Cong) =>
% 121.84/16.08 (((setunion__Cong) =>
% 121.84/16.08 (((exuEu) =>
% 121.84/16.08 (((descr__Cong) =>
% 121.84/16.08 (((dsetconstr__Cong) =>
% 121.84/16.08 (((subsetI1) =>
% 121.84/16.08 (((eqimpsubset2) =>
% 121.84/16.08 (((eqimpsubset1) =>
% 121.84/16.08 (((subsetI2) =>
% 121.84/16.08 (((emptysetsubset) =>
% 121.84/16.08 (((subsetE) =>
% 121.84/16.08 (((subsetE2) =>
% 121.84/16.08 (((notsubsetI) =>
% 121.84/16.08 (((notequalI1) =>
% 121.84/16.08 (((notequalI2) =>
% 121.84/16.08 (((subsetRefl) =>
% 121.84/16.08 (((subsetTrans) =>
% 121.84/16.08 (((setadjoinSub) =>
% 121.84/16.08 (((setadjoinSub2) =>
% 121.84/16.08 (((subset2powerset) =>
% 121.84/16.08 (((setextsub) =>
% 121.84/16.08 (((subsetemptysetimpeq) =>
% 121.84/16.08 (((powersetI1) =>
% 121.84/16.08 (((powersetE1) =>
% 121.84/16.08 (((inPowerset) =>
% 121.84/16.08 (((powersetsubset) =>
% 121.84/16.08 (((sepInPowerset) =>
% 121.84/16.08 (((sepSubset) =>
% 121.84/16.08 (((binunionIL) =>
% 121.84/16.08 (((upairset2IR) =>
% 121.84/16.08 ((
% 121.84/16.08 (binunionIR) =>
% 121.84/16.08 ((
% 121.84/16.08 (binunionEcases) =>
% 121.84/16.08 ((
% 121.84/16.08 (binunionE) =>
% 121.84/16.08 ((
% 121.84/16.08 (binunionLsub) =>
% 121.84/16.08 ((
% 121.84/16.08 (binunionRsub) =>
% 121.84/16.08 ((
% 121.84/16.08 (binintersectI) =>
% 121.84/16.08 ((
% 121.84/16.08 (binintersectSubset5) =>
% 121.84/16.08 ((
% 121.84/16.08 (binintersectEL) =>
% 121.84/16.08 ((
% 121.84/16.08 (binintersectLsub) =>
% 121.84/16.08 ((
% 121.84/16.08 (binintersectSubset2) =>
% 121.84/16.08 ((
% 121.84/16.08 (binintersectSubset3) =>
% 121.84/16.08 ((
% 121.84/16.08 (binintersectER) =>
% 121.84/16.08 ((
% 121.84/16.08 (disjointsetsI1) =>
% 121.84/16.08 ((
% 121.84/16.08 (binintersectRsub) =>
% 121.84/16.08 ((
% 121.84/16.08 (binintersectSubset4) =>
% 121.84/16.08 ((
% 121.84/16.08 (binintersectSubset1) =>
% 121.84/16.08 ((
% 121.84/16.08 (bs114d) =>
% 121.84/16.08 ((
% 121.84/16.08 (setminusI) =>
% 121.84/16.08 ((
% 121.84/16.08 (setminusEL) =>
% 121.84/16.08 ((
% 121.84/16.08 (setminusER) =>
% 121.84/16.08 ((
% 121.84/16.08 (setminusSubset2) =>
% 121.84/16.08 ((
% 121.84/16.08 (setminusERneg) =>
% 121.84/16.08 ((
% 121.84/16.08 (setminusELneg) =>
% 121.84/16.08 ((
% 121.84/16.08 (setminusILneg) =>
% 121.84/16.08 ((
% 121.84/16.08 (setminusIRneg) =>
% 121.84/16.08 ((
% 121.84/16.08 (setminusLsub) =>
% 121.84/16.08 ((
% 121.84/16.08 (setminusSubset1) =>
% 121.84/16.08 ((
% 121.84/16.08 (symdiffE) =>
% 121.84/16.08 ((
% 121.84/16.08 (symdiffI1) =>
% 121.84/16.08 ((
% 121.84/16.08 (symdiffI2) =>
% 121.84/16.08 ((
% 121.84/16.08 (symdiffIneg1) =>
% 121.84/16.08 ((
% 121.84/16.08 (symdiffIneg2) =>
% 121.84/16.08 ((
% 121.84/16.08 (secondinupair) =>
% 121.84/16.08 ((
% 121.84/16.08 (setukpairIL) =>
% 121.84/16.08 ((
% 121.84/16.08 (setukpairIR) =>
% 121.84/16.08 ((
% 121.84/16.08 (kpairiskpair) =>
% 121.84/16.08 ((
% 121.84/16.08 (kpairp) =>
% 121.84/16.08 ((
% 121.84/16.08 (singletonsubset) =>
% 121.84/16.08 ((
% 121.84/16.08 (singletoninpowerset) =>
% 121.84/16.08 ((
% 121.84/16.08 (singletoninpowunion) =>
% 121.84/16.08 ((
% 121.84/16.08 (upairset2E) =>
% 121.84/16.08 ((
% 121.84/16.08 (upairsubunion) =>
% 121.84/16.08 ((
% 121.84/16.08 (upairinpowunion) =>
% 121.84/16.08 ((
% 121.84/16.08 (ubforcartprodlem1) =>
% 121.84/16.08 ((
% 121.84/16.08 (ubforcartprodlem2) =>
% 121.84/16.08 ((
% 121.84/16.08 (ubforcartprodlem3) =>
% 121.84/16.08 ((
% 121.84/16.08 (cartprodpairin) =>
% 121.84/16.08 ((
% 121.84/16.08 (cartprodmempair1) =>
% 121.84/16.08 ((
% 121.84/16.08 (cartprodmempair) =>
% 121.84/16.08 ((
% 121.84/16.08 (setunionE2) =>
% 121.84/16.08 ((
% 121.84/16.08 (setunionsingleton1) =>
% 121.84/16.08 ((
% 121.84/16.08 (setunionsingleton2) =>
% 121.84/16.08 ((
% 121.84/16.08 (setunionsingleton) =>
% 121.84/16.08 ((
% 121.84/16.08 (singletonprop) =>
% 121.84/16.08 ((
% 121.84/16.08 (ex1E1) =>
% 121.84/16.08 ((
% 121.84/16.08 (ex1I) =>
% 121.84/16.08 ((
% 121.84/16.08 (ex1I2) =>
% 121.84/16.08 ((
% 121.84/16.08 (singletonsuniq) =>
% 121.84/16.08 ((
% 121.84/16.08 (setukpairinjL1) =>
% 121.84/16.08 ((
% 121.84/16.08 (kfstsingleton) =>
% 121.84/16.08 ((
% 121.84/16.08 (theprop) =>
% 121.84/16.08 ((
% 121.84/16.08 (kfstpairEq) =>
% 121.84/16.08 ((
% 121.84/16.08 (cartprodfstin) =>
% 121.84/16.08 ((
% 121.84/16.08 (setukpairinjL2) =>
% 121.84/16.08 ((
% 121.84/16.08 (setukpairinjL) =>
% 121.84/16.08 ((
% 121.84/16.08 (setukpairinjR11) =>
% 121.84/16.08 ((
% 121.84/16.08 (setukpairinjR12) =>
% 121.84/16.08 ((
% 121.84/16.08 (setukpairinjR1) =>
% 121.84/16.08 ((
% 121.84/16.08 (upairequniteq) =>
% 121.84/16.08 ((
% 121.84/16.08 (setukpairinjR2) =>
% 121.84/16.08 ((
% 121.84/16.08 (setukpairinjR) =>
% 121.84/16.08 ((
% 121.84/16.08 (ksndsingleton) =>
% 121.84/16.08 ((
% 121.84/16.08 (ksndpairEq) =>
% 121.84/16.08 ((
% 121.84/16.08 (kpairsurjEq) =>
% 121.84/16.08 ((
% 121.84/16.08 (cartprodsndin) =>
% 121.84/16.08 ((
% 121.84/16.08 (cartprodpairmemEL) =>
% 121.84/16.08 ((
% 121.84/16.08 (cartprodpairmemER) =>
% 121.84/16.08 ((
% 121.84/16.08 (cartprodmempaircEq) =>
% 121.84/16.08 ((
% 121.84/16.08 (cartprodfstpairEq) =>
% 121.84/16.08 ((
% 121.84/16.08 (cartprodsndpairEq) =>
% 121.84/16.08 ((
% 121.84/16.08 (cartprodpairsurjEq) =>
% 121.84/16.08 ((
% 121.84/16.08 (dpsetconstrI) =>
% 121.84/16.08 ((
% 121.84/16.08 (dpsetconstrSub) =>
% 121.84/16.08 ((
% 121.84/16.08 (setOfPairsIsBReln) =>
% 121.84/16.08 ((
% 121.84/16.08 (dpsetconstrERa) =>
% 121.84/16.08 ((
% 121.84/16.08 (dpsetconstrEL1) =>
% 121.84/16.08 ((
% 121.84/16.08 (dpsetconstrEL2) =>
% 121.84/16.08 ((
% 121.84/16.08 (dpsetconstrER) =>
% 121.84/16.08 ((
% 121.84/16.08 (funcImageSingleton) =>
% 121.84/16.08 ((
% 121.84/16.08 (apProp) =>
% 121.84/16.08 ((
% 121.84/16.08 (app) =>
% 121.84/16.08 ((
% 121.84/16.08 (infuncsetfunc) =>
% 121.84/16.08 ((
% 121.84/16.08 (ap2p) =>
% 121.84/16.08 ((
% 121.84/16.08 (funcinfuncset) =>
% 121.84/16.08 ((
% 121.84/16.08 (lamProp) =>
% 121.84/16.08 ((
% 121.84/16.08 (lamp) =>
% 121.84/16.08 ((
% 121.84/16.08 (lam2p) =>
% 121.84/16.08 ((
% 121.84/16.08 (brelnall1) =>
% 121.84/16.08 ((
% 121.84/16.08 (brelnall2) =>
% 121.84/16.08 ((
% 121.84/16.08 (ex1E2) =>
% 121.84/16.08 ((
% 121.84/16.08 (funcGraphProp1) =>
% 121.84/16.08 ((
% 121.84/16.08 (funcGraphProp3) =>
% 121.84/16.08 ((
% 121.84/16.08 (funcGraphProp2) =>
% 121.84/16.08 ((
% 121.84/16.08 (funcextLem) =>
% 121.84/16.08 ((
% 121.84/16.08 (funcGraphProp4) =>
% 121.84/16.08 ((
% 121.84/16.08 (subbreln) =>
% 121.84/16.08 ((
% 121.84/16.08 (eqbreln) =>
% 121.84/16.08 ((
% 121.84/16.08 (funcext) =>
% 121.84/16.08 ((
% 121.84/16.08 (funcext2) =>
% 121.84/16.08 ((
% 121.84/16.08 (ap2apEq1) =>
% 121.84/16.08 ((
% 121.84/16.08 (ap2apEq2) =>
% 121.84/16.08 ((
% 121.84/16.08 (beta1) =>
% 121.84/16.08 ((
% 121.84/16.08 (eta1) =>
% 121.84/16.08 ((
% 121.84/16.08 (lam2lamEq) =>
% 121.84/16.08 ((
% 121.84/16.08 (beta2) =>
% 121.84/16.08 ((
% 121.84/16.08 (eta2) =>
% 121.84/16.08 ((
% 121.84/16.08 (iffalseProp1) =>
% 121.84/16.08 ((
% 121.84/16.08 (iffalseProp2) =>
% 121.84/16.08 ((
% 121.84/16.08 (iftrueProp1) =>
% 121.84/16.08 ((
% 121.84/16.08 (iftrueProp2) =>
% 121.84/16.08 ((
% 121.84/16.08 (ifSingleton) =>
% 121.84/16.08 ((
% 121.84/16.08 (ifp) =>
% 121.84/16.08 ((
% 121.84/16.08 (theeq) =>
% 121.84/16.08 ((
% 121.84/16.08 (iftrue) =>
% 121.84/16.08 ((
% 121.84/16.08 (iffalse) =>
% 121.84/16.08 ((
% 121.84/16.08 (iftrueorfalse) =>
% 121.84/16.08 ((
% 121.84/16.08 (binintersectT_lem) =>
% 121.84/16.08 ((
% 121.84/16.08 (binunionT_lem) =>
% 121.84/16.08 ((
% 121.84/16.08 (powersetT_lem) =>
% 121.84/16.08 ((
% 121.84/16.08 (setminusT_lem) =>
% 121.84/16.08 ((
% 121.84/16.08 (complementT_lem) =>
% 121.84/16.08 ((
% 121.84/16.08 (setextT) =>
% 121.84/16.08 ((
% 121.84/16.08 (subsetTI) =>
% 121.84/16.08 ((
% 121.84/16.08 (powersetTI1) =>
% 121.84/16.08 ((
% 121.84/16.08 (powersetTE1) =>
% 121.84/16.08 ((
% 121.84/16.08 (complementTI1) =>
% 121.84/16.08 ((
% 121.84/16.08 (complementTE1) =>
% 121.84/16.08 ((
% 121.84/16.08 (binintersectTELcontra) =>
% 121.84/16.08 ((
% 121.84/16.08 (binintersectTERcontra) =>
% 121.84/16.08 ((
% 121.84/16.08 (contrasubsetT) =>
% 121.84/16.08 ((
% 121.84/16.08 (contrasubsetT1) =>
% 121.84/16.08 ((
% 121.84/16.08 (contrasubsetT2) =>
% 121.84/16.08 ((
% 121.84/16.08 (contrasubsetT3) =>
% 121.84/16.08 ((
% 121.84/16.08 (doubleComplementI1) =>
% 121.84/16.08 ((
% 121.84/16.08 (doubleComplementE1) =>
% 121.84/16.08 ((
% 121.84/16.08 (doubleComplementSub1) =>
% 121.84/16.08 ((
% 121.84/16.08 (doubleComplementSub2) =>
% 121.84/16.08 ((
% 121.84/16.08 (doubleComplementEq) =>
% 121.84/16.08 ((
% 121.84/16.08 (complementTnotintersectT) =>
% 121.84/16.08 ((
% 121.84/16.08 (complementImpComplementIntersect) =>
% 121.84/16.08 ((
% 121.84/16.08 (complementSubsetComplementIntersect) =>
% 121.84/16.08 ((
% 121.84/16.08 (complementInPowersetComplementIntersect) =>
% 121.84/16.08 ((
% 121.84/16.08 (contraSubsetComplement) =>
% 121.84/16.08 ((
% 121.84/16.08 (complementTcontraSubset) =>
% 121.84/16.08 ((
% 121.84/16.08 (binunionTILcontra) =>
% 121.84/16.08 ((
% 121.84/16.08 (binunionTIRcontra) =>
% 121.84/16.08 ((
% 121.84/16.08 (inIntersectImpInUnion) =>
% 121.84/16.08 ((
% 121.84/16.08 (inIntersectImpInUnion2) =>
% 121.84/16.08 ((
% 121.84/16.08 (inIntersectImpInIntersectUnions) =>
% 121.84/16.08 ((
% 121.84/16.08 (intersectInPowersetIntersectUnions) =>
% 121.84/16.08 ((
% 121.84/16.08 (inComplementUnionImpNotIn1) =>
% 121.84/16.08 ((
% 121.84/16.08 (inComplementUnionImpInComplement1) =>
% 121.84/16.08 ((
% 121.84/16.08 (binunionTE) =>
% 121.84/16.08 ((
% 121.84/16.08 (binunionTEcontra) =>
% 121.84/16.08 ((
% 121.84/16.08 (demorgan2a1) =>
% 121.84/16.08 ((
% 121.84/16.08 (complementUnionInPowersetComplement) =>
% 121.84/16.08 ((
% 121.84/16.08 (demorgan2a2) =>
% 121.84/16.08 ((
% 121.84/16.08 (demorgan1a) =>
% 121.84/16.08 ((
% 121.84/16.08 (demorgan1b) =>
% 121.84/16.08 ((
% 121.84/16.08 (demorgan1) =>
% 121.84/16.08 ((
% 121.84/16.08 (demorgan2a) =>
% 121.84/16.08 ((
% 121.84/16.08 (demorgan2b2) =>
% 121.84/16.08 ((
% 121.84/16.08 (demorgan2b) =>
% 121.84/16.08 ((
% 121.84/16.08 (demorgan2) =>
% 121.84/16.08 ((
% 121.84/16.08 (woz13rule0) =>
% 121.84/16.08 ((
% 121.84/16.08 (woz13rule1) =>
% 121.84/16.08 ((
% 121.84/16.08 (woz13rule2) =>
% 121.84/16.08 ((
% 121.84/16.08 (woz13rule3) =>
% 121.84/16.08 ((
% 121.84/16.08 (woz13rule4) =>
% 121.84/16.08 ((
% 121.84/16.08 (woz1_1) =>
% 121.84/16.08 ((
% 121.84/16.08 (woz1_2) =>
% 121.84/16.08 ((
% 121.84/16.08 (woz1_3) =>
% 121.84/16.08 ((
% 121.84/16.08 (woz1_4) =>
% 121.84/16.08 ((
% 121.84/16.08 (woz1_5) =>
% 121.84/16.08 ((
% 121.84/16.08 (breln1all2) =>
% 121.84/16.08 ((
% 121.84/16.08 (breln1SetBreln1) =>
% 121.84/16.08 ((
% 121.84/16.08 (choice2fnsingleton) =>
% 121.84/16.08 ((
% 121.84/16.08 (setOfPairsIsBReln1) =>
% 121.84/16.08 ((
% 121.84/16.08 (breln1all1) =>
% 121.84/16.08 ((
% 121.84/16.08 (subbreln1) =>
% 121.84/16.08 ((
% 121.84/16.08 (eqbreln1) =>
% 121.84/16.08 ((
% 121.84/16.08 (breln1invprop) =>
% 121.84/16.08 ((
% 121.84/16.08 (breln1invI) =>
% 121.84/16.08 ((
% 121.84/16.08 (breln1invE) =>
% 121.84/16.08 ((
% 121.84/16.08 (breln1compprop) =>
% 121.84/16.08 ((
% 121.84/16.08 (breln1compI) =>
% 121.84/16.08 ((
% 121.84/16.08 (breln1compE) =>
% 121.84/16.08 ((
% 121.84/16.08 (breln1compEex) =>
% 121.84/16.08 ((
% 121.84/16.08 (breln1unionprop) =>
% 121.84/16.08 ((
% 121.84/16.08 (breln1unionIL) =>
% 121.84/16.08 ((
% 121.84/16.08 (breln1unionIR) =>
% 121.84/16.08 ((
% 121.84/16.08 (breln1unionI) =>
% 121.84/16.08 ((
% 121.84/16.08 (breln1unionE) =>
% 121.84/16.08 ((
% 121.84/16.08 (breln1unionEcases) =>
% 121.84/16.08 ((
% 121.84/16.08 (breln1unionCommutes) =>
% 121.84/16.08 ((
% 121.84/16.08 (woz2Ex) =>
% 121.84/16.08 ((
% 121.84/16.08 (woz2W) =>
% 121.84/16.08 ((
% 121.84/16.08 (woz2A) =>
% 121.84/16.08 ((
% 121.84/16.08 (woz2B) =>
% 121.84/16.08 ((
% 121.84/16.08 (image1Ex) =>
% 121.84/16.08 ((
% 121.84/16.08 (image1Ex1) =>
% 121.84/16.08 ((
% 121.84/16.08 (image1Equiv) =>
% 121.84/16.08 ((
% 121.84/16.08 (image1E) =>
% 121.84/16.08 ((
% 121.84/16.08 (image1I) =>
% 121.84/16.08 ((
% 121.84/16.08 (injFuncInInjFuncSet) =>
% 121.84/16.08 ((
% 121.84/16.08 (!!) @ (
% 121.84/16.08 (('#B') @ (
% 121.84/16.08 !!) @
% 121.84/16.08 (
% 121.84/16.08 (
% 121.84/16.08 ('#B') @ (
% 121.84/16.08 (
% 121.84/16.08 ('#B') @ (
% 121.84/16.08 !!))) @
% 121.84/16.08 (
% 121.84/16.08 (
% 121.84/16.08 ('#S') @ (
% 121.84/16.08 (
% 121.84/16.08 ('#B') @ (
% 121.84/16.08 '#S') @
% 121.84/16.08 (
% 121.84/16.08 (
% 121.84/16.08 ('#B') @ (
% 121.84/16.08 (
% 121.84/16.08 ('#B') @ (
% 121.84/16.08 '#S'))) @
% 121.84/16.08 (
% 121.84/16.08 (
% 121.84/16.08 ('#B') @ (
% 121.84/16.08 (
% 121.84/16.08 ('#B') @ (
% 121.84/16.08 (
% 121.84/16.08 ('#B') @ (
% 121.84/16.08 =>))))) @
% 121.84/16.08 (
% 121.84/16.08 (
% 121.84/16.08 ('#B') @ (
% 121.84/16.08 (
% 121.84/16.08 ('#B') @ (
% 121.84/16.08 (
% 121.84/16.08 ('#C') @ in)))) @
% 121.84/16.08 injFuncSet)))))))) @
% 121.84/16.08 (
% 121.84/16.08 (
% 121.84/16.08 ('#B') @ (
% 121.84/16.08 (
% 121.84/16.08 ('#B') @ (
% 121.84/16.08 (
% 121.84/16.08 ('#C') @ in)))) @
% 121.84/16.08 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 121.84/16.08 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl685])).
% 121.84/16.08 thf(zip_derived_cl714, plain,
% 121.84/16.08 (~ (((setunion__Cong) =>
% 121.84/16.08 (((exuEu) =>
% 121.84/16.08 (((descr__Cong) =>
% 121.84/16.08 (((dsetconstr__Cong) =>
% 121.84/16.08 (((subsetI1) =>
% 121.84/16.08 (((eqimpsubset2) =>
% 121.84/16.08 (((eqimpsubset1) =>
% 121.84/16.08 (((subsetI2) =>
% 121.84/16.08 (((emptysetsubset) =>
% 121.84/16.08 (((subsetE) =>
% 121.84/16.08 (((subsetE2) =>
% 121.84/16.08 (((notsubsetI) =>
% 121.84/16.08 (((notequalI1) =>
% 121.84/16.08 (((notequalI2) =>
% 121.84/16.08 (((subsetRefl) =>
% 121.84/16.08 (((subsetTrans) =>
% 121.84/16.08 (((setadjoinSub) =>
% 121.84/16.08 (((setadjoinSub2) =>
% 121.84/16.08 (((subset2powerset) =>
% 121.84/16.08 (((setextsub) =>
% 121.84/16.08 (((subsetemptysetimpeq) =>
% 121.84/16.08 (((powersetI1) =>
% 121.84/16.08 (((powersetE1) =>
% 121.84/16.08 (((inPowerset) =>
% 121.84/16.08 (((powersetsubset) =>
% 121.84/16.08 (((sepInPowerset) =>
% 121.84/16.08 (((sepSubset) =>
% 121.84/16.08 (((binunionIL) =>
% 121.84/16.08 (((upairset2IR) =>
% 121.84/16.08 (((binunionIR) =>
% 121.84/16.08 ((
% 121.84/16.08 (binunionEcases) =>
% 121.84/16.08 ((
% 121.84/16.08 (binunionE) =>
% 121.84/16.08 ((
% 121.84/16.08 (binunionLsub) =>
% 121.84/16.08 ((
% 121.84/16.08 (binunionRsub) =>
% 121.84/16.08 ((
% 121.84/16.08 (binintersectI) =>
% 121.84/16.08 ((
% 121.84/16.08 (binintersectSubset5) =>
% 121.84/16.08 ((
% 121.84/16.08 (binintersectEL) =>
% 121.84/16.08 ((
% 121.84/16.08 (binintersectLsub) =>
% 121.84/16.08 ((
% 121.84/16.08 (binintersectSubset2) =>
% 121.84/16.08 ((
% 121.84/16.08 (binintersectSubset3) =>
% 121.84/16.08 ((
% 121.84/16.08 (binintersectER) =>
% 121.84/16.08 ((
% 121.84/16.08 (disjointsetsI1) =>
% 121.84/16.08 ((
% 121.84/16.08 (binintersectRsub) =>
% 121.84/16.08 ((
% 121.84/16.08 (binintersectSubset4) =>
% 121.84/16.08 ((
% 121.84/16.08 (binintersectSubset1) =>
% 121.84/16.08 ((
% 121.84/16.08 (bs114d) =>
% 121.84/16.08 ((
% 121.84/16.08 (setminusI) =>
% 121.84/16.08 ((
% 121.84/16.08 (setminusEL) =>
% 121.84/16.08 ((
% 121.84/16.08 (setminusER) =>
% 121.84/16.08 ((
% 121.84/16.08 (setminusSubset2) =>
% 121.84/16.08 ((
% 121.84/16.08 (setminusERneg) =>
% 121.84/16.08 ((
% 121.84/16.08 (setminusELneg) =>
% 121.84/16.08 ((
% 121.84/16.08 (setminusILneg) =>
% 121.84/16.08 ((
% 121.84/16.08 (setminusIRneg) =>
% 121.84/16.08 ((
% 121.84/16.08 (setminusLsub) =>
% 121.84/16.08 ((
% 121.84/16.08 (setminusSubset1) =>
% 121.84/16.08 ((
% 121.84/16.08 (symdiffE) =>
% 121.84/16.08 ((
% 121.84/16.08 (symdiffI1) =>
% 121.84/16.08 ((
% 121.84/16.08 (symdiffI2) =>
% 121.84/16.08 ((
% 121.84/16.08 (symdiffIneg1) =>
% 121.84/16.08 ((
% 121.84/16.08 (symdiffIneg2) =>
% 121.84/16.08 ((
% 121.84/16.08 (secondinupair) =>
% 121.84/16.08 ((
% 121.84/16.08 (setukpairIL) =>
% 121.84/16.08 ((
% 121.84/16.08 (setukpairIR) =>
% 121.84/16.08 ((
% 121.84/16.08 (kpairiskpair) =>
% 121.84/16.08 ((
% 121.84/16.08 (kpairp) =>
% 121.84/16.08 ((
% 121.84/16.08 (singletonsubset) =>
% 121.84/16.08 ((
% 121.84/16.08 (singletoninpowerset) =>
% 121.84/16.08 ((
% 121.84/16.08 (singletoninpowunion) =>
% 121.84/16.08 ((
% 121.84/16.08 (upairset2E) =>
% 121.84/16.08 ((
% 121.84/16.08 (upairsubunion) =>
% 121.84/16.08 ((
% 121.84/16.08 (upairinpowunion) =>
% 121.84/16.08 ((
% 121.84/16.08 (ubforcartprodlem1) =>
% 121.84/16.08 ((
% 121.84/16.08 (ubforcartprodlem2) =>
% 121.84/16.08 ((
% 121.84/16.08 (ubforcartprodlem3) =>
% 121.84/16.08 ((
% 121.84/16.08 (cartprodpairin) =>
% 121.84/16.08 ((
% 121.84/16.08 (cartprodmempair1) =>
% 121.84/16.08 ((
% 121.84/16.08 (cartprodmempair) =>
% 121.84/16.08 ((
% 121.84/16.08 (setunionE2) =>
% 121.84/16.08 ((
% 121.84/16.08 (setunionsingleton1) =>
% 121.84/16.08 ((
% 121.84/16.08 (setunionsingleton2) =>
% 121.84/16.08 ((
% 121.84/16.08 (setunionsingleton) =>
% 121.84/16.08 ((
% 121.84/16.08 (singletonprop) =>
% 121.84/16.08 ((
% 121.84/16.08 (ex1E1) =>
% 121.84/16.08 ((
% 121.84/16.08 (ex1I) =>
% 121.84/16.08 ((
% 121.84/16.08 (ex1I2) =>
% 121.84/16.08 ((
% 121.84/16.08 (singletonsuniq) =>
% 121.84/16.08 ((
% 121.84/16.08 (setukpairinjL1) =>
% 121.84/16.08 ((
% 121.84/16.08 (kfstsingleton) =>
% 121.84/16.08 ((
% 121.84/16.08 (theprop) =>
% 121.84/16.08 ((
% 121.84/16.08 (kfstpairEq) =>
% 121.84/16.08 ((
% 121.84/16.08 (cartprodfstin) =>
% 121.84/16.08 ((
% 121.84/16.08 (setukpairinjL2) =>
% 121.84/16.08 ((
% 121.84/16.08 (setukpairinjL) =>
% 121.84/16.08 ((
% 121.84/16.08 (setukpairinjR11) =>
% 121.84/16.08 ((
% 121.84/16.08 (setukpairinjR12) =>
% 121.84/16.08 ((
% 121.84/16.08 (setukpairinjR1) =>
% 121.84/16.08 ((
% 121.84/16.08 (upairequniteq) =>
% 121.84/16.08 ((
% 121.84/16.08 (setukpairinjR2) =>
% 121.84/16.08 ((
% 121.84/16.08 (setukpairinjR) =>
% 121.84/16.08 ((
% 121.84/16.08 (ksndsingleton) =>
% 121.84/16.08 ((
% 121.84/16.08 (ksndpairEq) =>
% 121.84/16.08 ((
% 121.84/16.08 (kpairsurjEq) =>
% 121.84/16.08 ((
% 121.84/16.08 (cartprodsndin) =>
% 121.84/16.08 ((
% 121.84/16.08 (cartprodpairmemEL) =>
% 121.84/16.08 ((
% 121.84/16.08 (cartprodpairmemER) =>
% 121.84/16.08 ((
% 121.84/16.08 (cartprodmempaircEq) =>
% 121.84/16.08 ((
% 121.84/16.08 (cartprodfstpairEq) =>
% 121.84/16.08 ((
% 121.84/16.08 (cartprodsndpairEq) =>
% 121.84/16.08 ((
% 121.84/16.08 (cartprodpairsurjEq) =>
% 121.84/16.08 ((
% 121.84/16.08 (dpsetconstrI) =>
% 121.84/16.08 ((
% 121.84/16.08 (dpsetconstrSub) =>
% 121.84/16.08 ((
% 121.84/16.08 (setOfPairsIsBReln) =>
% 121.84/16.08 ((
% 121.84/16.08 (dpsetconstrERa) =>
% 121.84/16.08 ((
% 121.84/16.08 (dpsetconstrEL1) =>
% 121.84/16.08 ((
% 121.84/16.08 (dpsetconstrEL2) =>
% 121.84/16.08 ((
% 121.84/16.08 (dpsetconstrER) =>
% 121.84/16.08 ((
% 121.84/16.08 (funcImageSingleton) =>
% 121.84/16.08 ((
% 121.84/16.08 (apProp) =>
% 121.84/16.08 ((
% 121.84/16.08 (app) =>
% 121.84/16.08 ((
% 121.84/16.08 (infuncsetfunc) =>
% 121.84/16.08 ((
% 121.84/16.08 (ap2p) =>
% 121.84/16.08 ((
% 121.84/16.08 (funcinfuncset) =>
% 121.84/16.08 ((
% 121.84/16.08 (lamProp) =>
% 121.84/16.08 ((
% 121.84/16.08 (lamp) =>
% 121.84/16.08 ((
% 121.84/16.08 (lam2p) =>
% 121.84/16.08 ((
% 121.84/16.08 (brelnall1) =>
% 121.84/16.08 ((
% 121.84/16.08 (brelnall2) =>
% 121.84/16.08 ((
% 121.84/16.08 (ex1E2) =>
% 121.84/16.08 ((
% 121.84/16.08 (funcGraphProp1) =>
% 121.84/16.08 ((
% 121.84/16.08 (funcGraphProp3) =>
% 121.84/16.08 ((
% 121.84/16.08 (funcGraphProp2) =>
% 121.84/16.08 ((
% 121.84/16.08 (funcextLem) =>
% 121.84/16.08 ((
% 121.84/16.08 (funcGraphProp4) =>
% 121.84/16.08 ((
% 121.84/16.08 (subbreln) =>
% 121.84/16.08 ((
% 121.84/16.08 (eqbreln) =>
% 121.84/16.08 ((
% 121.84/16.08 (funcext) =>
% 121.84/16.08 ((
% 121.84/16.08 (funcext2) =>
% 121.84/16.08 ((
% 121.84/16.08 (ap2apEq1) =>
% 121.84/16.08 ((
% 121.84/16.08 (ap2apEq2) =>
% 121.84/16.08 ((
% 121.84/16.08 (beta1) =>
% 121.84/16.08 ((
% 121.84/16.08 (eta1) =>
% 121.84/16.08 ((
% 121.84/16.08 (lam2lamEq) =>
% 121.84/16.08 ((
% 121.84/16.08 (beta2) =>
% 121.84/16.08 ((
% 121.84/16.08 (eta2) =>
% 121.84/16.08 ((
% 121.84/16.08 (iffalseProp1) =>
% 121.84/16.08 ((
% 121.84/16.08 (iffalseProp2) =>
% 121.84/16.08 ((
% 121.84/16.08 (iftrueProp1) =>
% 121.84/16.08 ((
% 121.84/16.08 (iftrueProp2) =>
% 121.84/16.08 ((
% 121.84/16.08 (ifSingleton) =>
% 121.84/16.08 ((
% 121.84/16.08 (ifp) =>
% 121.84/16.08 ((
% 121.84/16.08 (theeq) =>
% 121.84/16.08 ((
% 121.84/16.08 (iftrue) =>
% 121.84/16.08 ((
% 121.84/16.08 (iffalse) =>
% 121.84/16.08 ((
% 121.84/16.08 (iftrueorfalse) =>
% 121.84/16.08 ((
% 121.84/16.08 (binintersectT_lem) =>
% 121.84/16.08 ((
% 121.84/16.08 (binunionT_lem) =>
% 121.84/16.08 ((
% 121.84/16.08 (powersetT_lem) =>
% 121.84/16.08 ((
% 121.84/16.08 (setminusT_lem) =>
% 121.84/16.08 ((
% 121.84/16.08 (complementT_lem) =>
% 121.84/16.08 ((
% 121.84/16.08 (setextT) =>
% 121.84/16.08 ((
% 121.84/16.08 (subsetTI) =>
% 121.84/16.08 ((
% 121.84/16.08 (powersetTI1) =>
% 121.84/16.08 ((
% 121.84/16.08 (powersetTE1) =>
% 121.84/16.08 ((
% 121.84/16.08 (complementTI1) =>
% 121.84/16.08 ((
% 121.84/16.08 (complementTE1) =>
% 121.84/16.08 ((
% 121.84/16.08 (binintersectTELcontra) =>
% 121.84/16.08 ((
% 121.84/16.08 (binintersectTERcontra) =>
% 121.84/16.08 ((
% 121.84/16.08 (contrasubsetT) =>
% 121.84/16.08 ((
% 121.84/16.08 (contrasubsetT1) =>
% 121.84/16.08 ((
% 121.84/16.08 (contrasubsetT2) =>
% 121.84/16.08 ((
% 121.84/16.08 (contrasubsetT3) =>
% 121.84/16.08 ((
% 121.84/16.08 (doubleComplementI1) =>
% 121.84/16.08 ((
% 121.84/16.08 (doubleComplementE1) =>
% 121.84/16.08 ((
% 121.84/16.08 (doubleComplementSub1) =>
% 121.84/16.08 ((
% 121.84/16.08 (doubleComplementSub2) =>
% 121.84/16.08 ((
% 121.84/16.08 (doubleComplementEq) =>
% 121.84/16.08 ((
% 121.84/16.08 (complementTnotintersectT) =>
% 121.84/16.08 ((
% 121.84/16.08 (complementImpComplementIntersect) =>
% 121.84/16.08 ((
% 121.84/16.08 (complementSubsetComplementIntersect) =>
% 121.84/16.08 ((
% 121.84/16.08 (complementInPowersetComplementIntersect) =>
% 121.84/16.08 ((
% 121.84/16.08 (contraSubsetComplement) =>
% 121.84/16.08 ((
% 121.84/16.08 (complementTcontraSubset) =>
% 121.84/16.08 ((
% 121.84/16.08 (binunionTILcontra) =>
% 121.84/16.08 ((
% 121.84/16.08 (binunionTIRcontra) =>
% 121.84/16.08 ((
% 121.84/16.08 (inIntersectImpInUnion) =>
% 121.84/16.08 ((
% 121.84/16.08 (inIntersectImpInUnion2) =>
% 121.84/16.08 ((
% 121.84/16.08 (inIntersectImpInIntersectUnions) =>
% 121.84/16.08 ((
% 121.84/16.08 (intersectInPowersetIntersectUnions) =>
% 121.84/16.08 ((
% 121.84/16.08 (inComplementUnionImpNotIn1) =>
% 121.84/16.08 ((
% 121.84/16.08 (inComplementUnionImpInComplement1) =>
% 121.84/16.08 ((
% 121.84/16.08 (binunionTE) =>
% 121.84/16.08 ((
% 121.84/16.08 (binunionTEcontra) =>
% 121.84/16.08 ((
% 121.84/16.08 (demorgan2a1) =>
% 121.84/16.08 ((
% 121.84/16.08 (complementUnionInPowersetComplement) =>
% 121.84/16.08 ((
% 121.84/16.08 (demorgan2a2) =>
% 121.84/16.08 ((
% 121.84/16.08 (demorgan1a) =>
% 121.84/16.08 ((
% 121.84/16.08 (demorgan1b) =>
% 121.84/16.08 ((
% 121.84/16.08 (demorgan1) =>
% 121.84/16.08 ((
% 121.84/16.08 (demorgan2a) =>
% 121.84/16.08 ((
% 121.84/16.08 (demorgan2b2) =>
% 121.84/16.08 ((
% 121.84/16.08 (demorgan2b) =>
% 121.84/16.08 ((
% 121.84/16.08 (demorgan2) =>
% 121.84/16.08 ((
% 121.84/16.08 (woz13rule0) =>
% 121.84/16.08 ((
% 121.84/16.08 (woz13rule1) =>
% 121.84/16.08 ((
% 121.84/16.08 (woz13rule2) =>
% 121.84/16.08 ((
% 121.84/16.08 (woz13rule3) =>
% 121.84/16.08 ((
% 121.84/16.08 (woz13rule4) =>
% 121.84/16.08 ((
% 121.84/16.08 (woz1_1) =>
% 121.84/16.08 ((
% 121.84/16.08 (woz1_2) =>
% 121.84/16.08 ((
% 121.84/16.08 (woz1_3) =>
% 121.84/16.08 ((
% 121.84/16.08 (woz1_4) =>
% 121.84/16.08 ((
% 121.84/16.08 (woz1_5) =>
% 121.84/16.08 ((
% 121.84/16.08 (breln1all2) =>
% 121.84/16.08 ((
% 121.84/16.08 (breln1SetBreln1) =>
% 121.84/16.08 ((
% 121.84/16.08 (choice2fnsingleton) =>
% 121.84/16.08 ((
% 121.84/16.08 (setOfPairsIsBReln1) =>
% 121.84/16.08 ((
% 121.84/16.08 (breln1all1) =>
% 121.84/16.08 ((
% 121.84/16.08 (subbreln1) =>
% 121.84/16.08 ((
% 121.84/16.08 (eqbreln1) =>
% 121.84/16.08 ((
% 121.84/16.08 (breln1invprop) =>
% 121.84/16.08 ((
% 121.84/16.08 (breln1invI) =>
% 121.84/16.08 ((
% 121.84/16.08 (breln1invE) =>
% 121.84/16.08 ((
% 121.84/16.08 (breln1compprop) =>
% 121.84/16.08 ((
% 121.84/16.08 (breln1compI) =>
% 121.84/16.08 ((
% 121.84/16.08 (breln1compE) =>
% 121.84/16.08 ((
% 121.84/16.08 (breln1compEex) =>
% 121.84/16.08 ((
% 121.84/16.08 (breln1unionprop) =>
% 121.84/16.08 ((
% 121.84/16.08 (breln1unionIL) =>
% 121.84/16.08 ((
% 121.84/16.08 (breln1unionIR) =>
% 121.84/16.08 ((
% 121.84/16.08 (breln1unionI) =>
% 121.84/16.08 ((
% 121.84/16.08 (breln1unionE) =>
% 121.84/16.08 ((
% 121.84/16.08 (breln1unionEcases) =>
% 121.84/16.08 ((
% 121.84/16.08 (breln1unionCommutes) =>
% 121.84/16.08 ((
% 121.84/16.08 (woz2Ex) =>
% 121.84/16.08 ((
% 121.84/16.08 (woz2W) =>
% 121.84/16.08 ((
% 121.84/16.08 (woz2A) =>
% 121.84/16.08 ((
% 121.84/16.08 (woz2B) =>
% 121.84/16.08 ((
% 121.84/16.08 (image1Ex) =>
% 121.84/16.08 ((
% 121.84/16.08 (image1Ex1) =>
% 121.84/16.08 ((
% 121.84/16.08 (image1Equiv) =>
% 121.84/16.08 ((
% 121.84/16.08 (image1E) =>
% 121.84/16.08 ((
% 121.84/16.08 (image1I) =>
% 121.84/16.08 ((
% 121.84/16.08 (injFuncInInjFuncSet) =>
% 121.84/16.08 ((
% 121.84/16.08 (!!) @ (
% 121.84/16.08 (('#B') @ (
% 121.84/16.08 !!) @
% 121.84/16.08 (
% 121.84/16.08 (
% 121.84/16.08 ('#B') @ (
% 121.84/16.08 (
% 121.84/16.08 ('#B') @ (
% 121.84/16.08 !!))) @
% 121.84/16.08 (
% 121.84/16.08 (
% 121.84/16.08 ('#S') @ (
% 121.84/16.08 (
% 121.84/16.08 ('#B') @ (
% 121.84/16.08 '#S') @
% 121.84/16.08 (
% 121.84/16.08 (
% 121.84/16.08 ('#B') @ (
% 121.84/16.08 (
% 121.84/16.08 ('#B') @ (
% 121.84/16.08 '#S'))) @
% 121.84/16.08 (
% 121.84/16.08 (
% 121.84/16.08 ('#B') @ (
% 121.84/16.08 (
% 121.84/16.08 ('#B') @ (
% 121.84/16.08 (
% 121.84/16.08 ('#B') @ (
% 121.84/16.08 =>))))) @
% 121.84/16.08 (
% 121.84/16.08 (
% 121.84/16.08 ('#B') @ (
% 121.84/16.08 (
% 121.84/16.08 ('#B') @ (
% 121.84/16.08 (
% 121.84/16.08 ('#C') @ in)))) @
% 121.84/16.08 injFuncSet)))))))) @
% 121.84/16.08 (
% 121.84/16.08 (
% 121.84/16.08 ('#B') @ (
% 121.84/16.08 (
% 121.84/16.08 ('#B') @ (
% 121.84/16.08 (
% 121.84/16.08 ('#C') @ in)))) @
% 121.84/16.08 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 121.84/16.08 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl699])).
% 121.84/16.08 thf(zip_derived_cl731, plain,
% 121.84/16.08 (~ (((exuEu) =>
% 121.84/16.08 (((descr__Cong) =>
% 121.84/16.08 (((dsetconstr__Cong) =>
% 121.84/16.08 (((subsetI1) =>
% 121.84/16.08 (((eqimpsubset2) =>
% 121.84/16.08 (((eqimpsubset1) =>
% 121.84/16.08 (((subsetI2) =>
% 121.84/16.08 (((emptysetsubset) =>
% 121.84/16.08 (((subsetE) =>
% 121.84/16.08 (((subsetE2) =>
% 121.84/16.08 (((notsubsetI) =>
% 121.84/16.08 (((notequalI1) =>
% 121.84/16.08 (((notequalI2) =>
% 121.84/16.08 (((subsetRefl) =>
% 121.84/16.08 (((subsetTrans) =>
% 121.84/16.08 (((setadjoinSub) =>
% 121.84/16.08 (((setadjoinSub2) =>
% 121.84/16.08 (((subset2powerset) =>
% 121.84/16.08 (((setextsub) =>
% 121.84/16.08 (((subsetemptysetimpeq) =>
% 121.84/16.08 (((powersetI1) =>
% 121.84/16.08 (((powersetE1) =>
% 121.84/16.08 (((inPowerset) =>
% 121.84/16.08 (((powersetsubset) =>
% 121.84/16.08 (((sepInPowerset) =>
% 121.84/16.08 (((sepSubset) =>
% 121.84/16.08 (((binunionIL) =>
% 121.84/16.08 (((upairset2IR) =>
% 121.84/16.08 (((binunionIR) =>
% 121.84/16.08 (((binunionEcases) =>
% 121.84/16.08 ((
% 121.84/16.08 (binunionE) =>
% 121.84/16.08 ((
% 121.84/16.08 (binunionLsub) =>
% 121.84/16.08 ((
% 121.84/16.08 (binunionRsub) =>
% 121.84/16.08 ((
% 121.84/16.08 (binintersectI) =>
% 121.84/16.08 ((
% 121.84/16.08 (binintersectSubset5) =>
% 121.84/16.08 ((
% 121.84/16.08 (binintersectEL) =>
% 121.84/16.08 ((
% 121.84/16.08 (binintersectLsub) =>
% 121.84/16.08 ((
% 121.84/16.08 (binintersectSubset2) =>
% 121.84/16.08 ((
% 121.84/16.08 (binintersectSubset3) =>
% 121.84/16.08 ((
% 121.84/16.08 (binintersectER) =>
% 121.84/16.08 ((
% 121.84/16.08 (disjointsetsI1) =>
% 121.84/16.08 ((
% 121.84/16.08 (binintersectRsub) =>
% 121.84/16.08 ((
% 121.84/16.08 (binintersectSubset4) =>
% 121.84/16.08 ((
% 121.84/16.08 (binintersectSubset1) =>
% 121.84/16.08 ((
% 121.84/16.08 (bs114d) =>
% 121.84/16.08 ((
% 121.84/16.08 (setminusI) =>
% 121.84/16.08 ((
% 121.84/16.08 (setminusEL) =>
% 121.84/16.08 ((
% 121.84/16.08 (setminusER) =>
% 121.84/16.08 ((
% 121.84/16.08 (setminusSubset2) =>
% 121.84/16.08 ((
% 121.84/16.08 (setminusERneg) =>
% 121.84/16.08 ((
% 121.84/16.08 (setminusELneg) =>
% 121.84/16.08 ((
% 121.84/16.08 (setminusILneg) =>
% 121.84/16.08 ((
% 121.84/16.08 (setminusIRneg) =>
% 121.84/16.08 ((
% 121.84/16.08 (setminusLsub) =>
% 121.84/16.08 ((
% 121.84/16.08 (setminusSubset1) =>
% 121.84/16.08 ((
% 121.84/16.08 (symdiffE) =>
% 121.84/16.08 ((
% 121.84/16.08 (symdiffI1) =>
% 121.84/16.08 ((
% 121.84/16.08 (symdiffI2) =>
% 121.84/16.08 ((
% 121.84/16.08 (symdiffIneg1) =>
% 121.84/16.08 ((
% 121.84/16.08 (symdiffIneg2) =>
% 121.84/16.08 ((
% 121.84/16.08 (secondinupair) =>
% 121.84/16.08 ((
% 121.84/16.08 (setukpairIL) =>
% 121.84/16.08 ((
% 121.84/16.08 (setukpairIR) =>
% 121.84/16.08 ((
% 121.84/16.08 (kpairiskpair) =>
% 121.84/16.08 ((
% 121.84/16.08 (kpairp) =>
% 121.84/16.08 ((
% 121.84/16.08 (singletonsubset) =>
% 121.84/16.08 ((
% 121.84/16.08 (singletoninpowerset) =>
% 121.84/16.08 ((
% 121.84/16.08 (singletoninpowunion) =>
% 121.84/16.08 ((
% 121.84/16.08 (upairset2E) =>
% 121.84/16.08 ((
% 121.84/16.08 (upairsubunion) =>
% 121.84/16.08 ((
% 121.84/16.08 (upairinpowunion) =>
% 121.84/16.08 ((
% 121.84/16.08 (ubforcartprodlem1) =>
% 121.84/16.08 ((
% 121.84/16.08 (ubforcartprodlem2) =>
% 121.84/16.08 ((
% 121.84/16.08 (ubforcartprodlem3) =>
% 121.84/16.08 ((
% 121.84/16.08 (cartprodpairin) =>
% 121.84/16.08 ((
% 121.84/16.08 (cartprodmempair1) =>
% 121.84/16.08 ((
% 121.84/16.08 (cartprodmempair) =>
% 121.84/16.08 ((
% 121.84/16.08 (setunionE2) =>
% 121.84/16.08 ((
% 121.84/16.08 (setunionsingleton1) =>
% 121.84/16.08 ((
% 121.84/16.08 (setunionsingleton2) =>
% 121.84/16.08 ((
% 121.84/16.08 (setunionsingleton) =>
% 121.84/16.08 ((
% 121.84/16.08 (singletonprop) =>
% 121.84/16.08 ((
% 121.84/16.08 (ex1E1) =>
% 121.84/16.08 ((
% 121.84/16.08 (ex1I) =>
% 121.84/16.08 ((
% 121.84/16.08 (ex1I2) =>
% 121.84/16.08 ((
% 121.84/16.08 (singletonsuniq) =>
% 121.84/16.08 ((
% 121.84/16.08 (setukpairinjL1) =>
% 121.84/16.08 ((
% 121.84/16.08 (kfstsingleton) =>
% 121.84/16.08 ((
% 121.84/16.08 (theprop) =>
% 121.84/16.08 ((
% 121.84/16.08 (kfstpairEq) =>
% 121.84/16.08 ((
% 121.84/16.08 (cartprodfstin) =>
% 121.84/16.08 ((
% 121.84/16.08 (setukpairinjL2) =>
% 121.84/16.08 ((
% 121.84/16.08 (setukpairinjL) =>
% 121.84/16.08 ((
% 121.84/16.08 (setukpairinjR11) =>
% 121.84/16.08 ((
% 121.84/16.08 (setukpairinjR12) =>
% 121.84/16.08 ((
% 121.84/16.08 (setukpairinjR1) =>
% 121.84/16.08 ((
% 121.84/16.08 (upairequniteq) =>
% 121.84/16.08 ((
% 121.84/16.08 (setukpairinjR2) =>
% 121.84/16.08 ((
% 121.84/16.08 (setukpairinjR) =>
% 121.84/16.08 ((
% 121.84/16.08 (ksndsingleton) =>
% 121.84/16.08 ((
% 121.84/16.08 (ksndpairEq) =>
% 121.84/16.08 ((
% 121.84/16.08 (kpairsurjEq) =>
% 121.84/16.08 ((
% 121.84/16.08 (cartprodsndin) =>
% 121.84/16.08 ((
% 121.84/16.08 (cartprodpairmemEL) =>
% 121.84/16.08 ((
% 121.84/16.08 (cartprodpairmemER) =>
% 121.84/16.08 ((
% 121.84/16.08 (cartprodmempaircEq) =>
% 121.84/16.08 ((
% 121.84/16.08 (cartprodfstpairEq) =>
% 121.84/16.08 ((
% 121.84/16.08 (cartprodsndpairEq) =>
% 121.84/16.08 ((
% 121.84/16.08 (cartprodpairsurjEq) =>
% 121.84/16.08 ((
% 121.84/16.08 (dpsetconstrI) =>
% 121.84/16.08 ((
% 121.84/16.08 (dpsetconstrSub) =>
% 121.84/16.08 ((
% 121.84/16.08 (setOfPairsIsBReln) =>
% 121.84/16.08 ((
% 121.84/16.08 (dpsetconstrERa) =>
% 121.84/16.08 ((
% 121.84/16.08 (dpsetconstrEL1) =>
% 121.84/16.08 ((
% 121.84/16.08 (dpsetconstrEL2) =>
% 121.84/16.08 ((
% 121.84/16.08 (dpsetconstrER) =>
% 121.84/16.08 ((
% 121.84/16.08 (funcImageSingleton) =>
% 121.84/16.08 ((
% 121.84/16.08 (apProp) =>
% 121.84/16.08 ((
% 121.84/16.08 (app) =>
% 121.84/16.08 ((
% 121.84/16.08 (infuncsetfunc) =>
% 121.84/16.08 ((
% 121.84/16.08 (ap2p) =>
% 121.84/16.08 ((
% 121.84/16.08 (funcinfuncset) =>
% 121.84/16.08 ((
% 121.84/16.08 (lamProp) =>
% 121.84/16.08 ((
% 121.84/16.08 (lamp) =>
% 121.84/16.08 ((
% 121.84/16.08 (lam2p) =>
% 121.84/16.08 ((
% 121.84/16.08 (brelnall1) =>
% 121.84/16.08 ((
% 121.84/16.08 (brelnall2) =>
% 121.84/16.08 ((
% 121.84/16.08 (ex1E2) =>
% 121.84/16.08 ((
% 121.84/16.08 (funcGraphProp1) =>
% 121.84/16.08 ((
% 121.84/16.08 (funcGraphProp3) =>
% 121.84/16.08 ((
% 121.84/16.08 (funcGraphProp2) =>
% 121.84/16.08 ((
% 121.84/16.08 (funcextLem) =>
% 121.84/16.08 ((
% 121.84/16.08 (funcGraphProp4) =>
% 121.84/16.08 ((
% 121.84/16.08 (subbreln) =>
% 121.84/16.08 ((
% 121.84/16.08 (eqbreln) =>
% 121.84/16.08 ((
% 121.84/16.08 (funcext) =>
% 121.84/16.08 ((
% 121.84/16.08 (funcext2) =>
% 121.84/16.08 ((
% 121.84/16.08 (ap2apEq1) =>
% 121.84/16.08 ((
% 121.84/16.08 (ap2apEq2) =>
% 121.84/16.08 ((
% 121.84/16.08 (beta1) =>
% 121.84/16.08 ((
% 121.84/16.08 (eta1) =>
% 121.84/16.08 ((
% 121.84/16.08 (lam2lamEq) =>
% 121.84/16.08 ((
% 121.84/16.08 (beta2) =>
% 121.84/16.08 ((
% 121.84/16.08 (eta2) =>
% 121.84/16.08 ((
% 121.84/16.08 (iffalseProp1) =>
% 121.84/16.08 ((
% 121.84/16.08 (iffalseProp2) =>
% 121.84/16.08 ((
% 121.84/16.08 (iftrueProp1) =>
% 121.84/16.08 ((
% 121.84/16.08 (iftrueProp2) =>
% 121.84/16.08 ((
% 121.84/16.08 (ifSingleton) =>
% 121.84/16.08 ((
% 121.84/16.08 (ifp) =>
% 121.84/16.08 ((
% 121.84/16.08 (theeq) =>
% 121.84/16.08 ((
% 121.84/16.08 (iftrue) =>
% 121.84/16.08 ((
% 121.84/16.08 (iffalse) =>
% 121.84/16.08 ((
% 121.84/16.08 (iftrueorfalse) =>
% 121.84/16.08 ((
% 121.84/16.08 (binintersectT_lem) =>
% 121.84/16.08 ((
% 121.84/16.08 (binunionT_lem) =>
% 121.84/16.08 ((
% 121.84/16.08 (powersetT_lem) =>
% 121.84/16.08 ((
% 121.84/16.08 (setminusT_lem) =>
% 121.84/16.08 ((
% 121.84/16.08 (complementT_lem) =>
% 121.84/16.08 ((
% 121.84/16.08 (setextT) =>
% 121.84/16.08 ((
% 121.84/16.08 (subsetTI) =>
% 121.84/16.08 ((
% 121.84/16.08 (powersetTI1) =>
% 121.84/16.08 ((
% 121.84/16.08 (powersetTE1) =>
% 121.84/16.08 ((
% 121.84/16.08 (complementTI1) =>
% 121.84/16.08 ((
% 121.84/16.08 (complementTE1) =>
% 121.84/16.08 ((
% 121.84/16.08 (binintersectTELcontra) =>
% 121.84/16.08 ((
% 121.84/16.08 (binintersectTERcontra) =>
% 121.84/16.08 ((
% 121.84/16.08 (contrasubsetT) =>
% 121.84/16.08 ((
% 121.84/16.08 (contrasubsetT1) =>
% 121.84/16.08 ((
% 121.84/16.08 (contrasubsetT2) =>
% 121.84/16.08 ((
% 121.84/16.08 (contrasubsetT3) =>
% 121.84/16.08 ((
% 121.84/16.08 (doubleComplementI1) =>
% 121.84/16.08 ((
% 121.84/16.08 (doubleComplementE1) =>
% 121.84/16.08 ((
% 121.84/16.08 (doubleComplementSub1) =>
% 121.84/16.08 ((
% 121.84/16.08 (doubleComplementSub2) =>
% 121.84/16.08 ((
% 121.84/16.08 (doubleComplementEq) =>
% 121.84/16.08 ((
% 121.84/16.08 (complementTnotintersectT) =>
% 121.84/16.08 ((
% 121.84/16.08 (complementImpComplementIntersect) =>
% 121.84/16.08 ((
% 121.84/16.08 (complementSubsetComplementIntersect) =>
% 121.84/16.08 ((
% 121.84/16.08 (complementInPowersetComplementIntersect) =>
% 121.84/16.08 ((
% 121.84/16.08 (contraSubsetComplement) =>
% 121.84/16.08 ((
% 121.84/16.08 (complementTcontraSubset) =>
% 121.84/16.08 ((
% 121.84/16.08 (binunionTILcontra) =>
% 121.84/16.08 ((
% 121.84/16.08 (binunionTIRcontra) =>
% 121.84/16.08 ((
% 121.84/16.08 (inIntersectImpInUnion) =>
% 121.84/16.08 ((
% 121.84/16.08 (inIntersectImpInUnion2) =>
% 121.84/16.08 ((
% 121.84/16.08 (inIntersectImpInIntersectUnions) =>
% 121.84/16.08 ((
% 121.84/16.08 (intersectInPowersetIntersectUnions) =>
% 121.84/16.08 ((
% 121.84/16.08 (inComplementUnionImpNotIn1) =>
% 121.84/16.08 ((
% 121.84/16.08 (inComplementUnionImpInComplement1) =>
% 121.84/16.08 ((
% 121.84/16.08 (binunionTE) =>
% 121.84/16.08 ((
% 121.84/16.08 (binunionTEcontra) =>
% 121.84/16.08 ((
% 121.84/16.08 (demorgan2a1) =>
% 121.84/16.08 ((
% 121.84/16.08 (complementUnionInPowersetComplement) =>
% 121.84/16.08 ((
% 121.84/16.08 (demorgan2a2) =>
% 121.84/16.08 ((
% 121.84/16.08 (demorgan1a) =>
% 121.84/16.08 ((
% 121.84/16.08 (demorgan1b) =>
% 121.84/16.08 ((
% 121.84/16.08 (demorgan1) =>
% 121.84/16.08 ((
% 121.84/16.08 (demorgan2a) =>
% 121.84/16.08 ((
% 121.84/16.08 (demorgan2b2) =>
% 121.84/16.08 ((
% 121.84/16.08 (demorgan2b) =>
% 121.84/16.08 ((
% 121.84/16.08 (demorgan2) =>
% 121.84/16.08 ((
% 121.84/16.08 (woz13rule0) =>
% 121.84/16.08 ((
% 121.84/16.08 (woz13rule1) =>
% 121.84/16.08 ((
% 121.84/16.08 (woz13rule2) =>
% 121.84/16.08 ((
% 121.84/16.08 (woz13rule3) =>
% 121.84/16.08 ((
% 121.84/16.08 (woz13rule4) =>
% 121.84/16.08 ((
% 121.84/16.08 (woz1_1) =>
% 121.84/16.08 ((
% 121.84/16.08 (woz1_2) =>
% 121.84/16.08 ((
% 121.84/16.08 (woz1_3) =>
% 121.84/16.08 ((
% 121.84/16.08 (woz1_4) =>
% 121.84/16.08 ((
% 121.84/16.08 (woz1_5) =>
% 121.84/16.08 ((
% 121.84/16.08 (breln1all2) =>
% 121.84/16.08 ((
% 121.84/16.08 (breln1SetBreln1) =>
% 121.84/16.08 ((
% 121.84/16.08 (choice2fnsingleton) =>
% 121.84/16.08 ((
% 121.84/16.08 (setOfPairsIsBReln1) =>
% 121.84/16.08 ((
% 121.84/16.08 (breln1all1) =>
% 121.84/16.08 ((
% 121.84/16.08 (subbreln1) =>
% 121.84/16.08 ((
% 121.84/16.08 (eqbreln1) =>
% 121.84/16.08 ((
% 121.84/16.08 (breln1invprop) =>
% 121.84/16.08 ((
% 121.84/16.08 (breln1invI) =>
% 121.84/16.08 ((
% 121.84/16.08 (breln1invE) =>
% 121.84/16.08 ((
% 121.84/16.08 (breln1compprop) =>
% 121.84/16.08 ((
% 121.84/16.08 (breln1compI) =>
% 121.84/16.08 ((
% 121.84/16.08 (breln1compE) =>
% 121.84/16.08 ((
% 121.84/16.08 (breln1compEex) =>
% 121.84/16.08 ((
% 121.84/16.08 (breln1unionprop) =>
% 121.84/16.08 ((
% 121.84/16.08 (breln1unionIL) =>
% 121.84/16.08 ((
% 121.84/16.08 (breln1unionIR) =>
% 121.84/16.08 ((
% 121.84/16.08 (breln1unionI) =>
% 121.84/16.08 ((
% 121.84/16.08 (breln1unionE) =>
% 121.84/16.08 ((
% 121.84/16.08 (breln1unionEcases) =>
% 121.84/16.08 ((
% 121.84/16.08 (breln1unionCommutes) =>
% 121.84/16.08 ((
% 121.84/16.08 (woz2Ex) =>
% 121.84/16.08 ((
% 121.84/16.08 (woz2W) =>
% 121.84/16.08 ((
% 121.84/16.08 (woz2A) =>
% 121.84/16.08 ((
% 121.84/16.08 (woz2B) =>
% 121.84/16.08 ((
% 121.84/16.08 (image1Ex) =>
% 121.84/16.08 ((
% 121.84/16.08 (image1Ex1) =>
% 121.84/16.08 ((
% 121.84/16.08 (image1Equiv) =>
% 121.84/16.08 ((
% 121.84/16.08 (image1E) =>
% 121.84/16.08 ((
% 121.84/16.08 (image1I) =>
% 121.84/16.08 ((
% 121.84/16.08 (injFuncInInjFuncSet) =>
% 121.84/16.08 ((
% 121.84/16.08 (!!) @ (
% 121.84/16.08 (('#B') @ (
% 121.84/16.08 !!) @
% 121.84/16.08 (
% 121.84/16.08 (
% 121.84/16.08 ('#B') @ (
% 121.84/16.08 (
% 121.84/16.08 ('#B') @ (
% 121.84/16.08 !!))) @
% 121.84/16.08 (
% 121.84/16.08 (
% 121.84/16.08 ('#S') @ (
% 121.84/16.08 (
% 121.84/16.08 ('#B') @ (
% 121.84/16.08 '#S') @
% 121.84/16.08 (
% 121.84/16.08 (
% 121.84/16.08 ('#B') @ (
% 121.84/16.08 (
% 121.84/16.08 ('#B') @ (
% 121.84/16.08 '#S'))) @
% 121.84/16.08 (
% 121.84/16.08 (
% 121.84/16.08 ('#B') @ (
% 121.84/16.08 (
% 121.84/16.08 ('#B') @ (
% 121.84/16.08 (
% 121.84/16.08 ('#B') @ (
% 121.84/16.08 =>))))) @
% 121.84/16.08 (
% 121.84/16.08 (
% 121.84/16.08 ('#B') @ (
% 121.84/16.08 (
% 121.84/16.08 ('#B') @ (
% 121.84/16.08 (
% 121.84/16.08 ('#C') @ in)))) @
% 121.84/16.08 injFuncSet)))))))) @
% 121.84/16.08 (
% 121.84/16.08 (
% 121.84/16.08 ('#B') @ (
% 121.84/16.08 (
% 121.84/16.08 ('#B') @ (
% 121.84/16.08 (
% 121.84/16.08 ('#C') @ in)))) @
% 121.84/16.08 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 121.84/16.08 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl714])).
% 121.84/16.08 thf(zip_derived_cl749, plain,
% 121.84/16.08 (~ (((descr__Cong) =>
% 121.84/16.08 (((dsetconstr__Cong) =>
% 121.84/16.08 (((subsetI1) =>
% 121.84/16.08 (((eqimpsubset2) =>
% 121.84/16.08 (((eqimpsubset1) =>
% 121.84/16.08 (((subsetI2) =>
% 121.84/16.08 (((emptysetsubset) =>
% 121.84/16.08 (((subsetE) =>
% 121.84/16.08 (((subsetE2) =>
% 121.84/16.08 (((notsubsetI) =>
% 121.84/16.08 (((notequalI1) =>
% 121.84/16.08 (((notequalI2) =>
% 121.84/16.08 (((subsetRefl) =>
% 121.84/16.08 (((subsetTrans) =>
% 121.84/16.08 (((setadjoinSub) =>
% 121.84/16.08 (((setadjoinSub2) =>
% 121.84/16.08 (((subset2powerset) =>
% 121.84/16.08 (((setextsub) =>
% 121.84/16.08 (((subsetemptysetimpeq) =>
% 121.84/16.08 (((powersetI1) =>
% 121.84/16.08 (((powersetE1) =>
% 121.84/16.08 (((inPowerset) =>
% 121.84/16.08 (((powersetsubset) =>
% 121.84/16.08 (((sepInPowerset) =>
% 121.84/16.08 (((sepSubset) =>
% 121.84/16.08 (((binunionIL) =>
% 121.84/16.08 (((upairset2IR) =>
% 121.84/16.08 (((binunionIR) =>
% 121.84/16.08 (((binunionEcases) =>
% 121.84/16.08 (((binunionE) =>
% 121.84/16.08 ((
% 121.84/16.08 (binunionLsub) =>
% 121.84/16.08 ((
% 121.84/16.08 (binunionRsub) =>
% 121.84/16.08 ((
% 121.84/16.08 (binintersectI) =>
% 121.84/16.08 ((
% 121.84/16.08 (binintersectSubset5) =>
% 121.84/16.08 ((
% 121.84/16.08 (binintersectEL) =>
% 121.84/16.08 ((
% 121.84/16.08 (binintersectLsub) =>
% 121.84/16.08 ((
% 121.84/16.08 (binintersectSubset2) =>
% 121.84/16.08 ((
% 121.84/16.08 (binintersectSubset3) =>
% 121.84/16.08 ((
% 121.84/16.08 (binintersectER) =>
% 121.84/16.08 ((
% 121.84/16.08 (disjointsetsI1) =>
% 121.84/16.08 ((
% 121.84/16.10 (binintersectRsub) =>
% 121.84/16.10 ((
% 121.84/16.10 (binintersectSubset4) =>
% 121.84/16.10 ((
% 121.84/16.10 (binintersectSubset1) =>
% 121.84/16.10 ((
% 121.84/16.10 (bs114d) =>
% 121.84/16.10 ((
% 121.84/16.10 (setminusI) =>
% 121.84/16.10 ((
% 121.84/16.10 (setminusEL) =>
% 121.84/16.10 ((
% 121.84/16.10 (setminusER) =>
% 121.84/16.10 ((
% 121.84/16.10 (setminusSubset2) =>
% 121.84/16.10 ((
% 121.84/16.10 (setminusERneg) =>
% 121.84/16.10 ((
% 121.84/16.10 (setminusELneg) =>
% 121.84/16.10 ((
% 121.84/16.10 (setminusILneg) =>
% 121.84/16.10 ((
% 121.84/16.10 (setminusIRneg) =>
% 121.84/16.10 ((
% 121.84/16.10 (setminusLsub) =>
% 121.84/16.10 ((
% 121.84/16.10 (setminusSubset1) =>
% 121.84/16.10 ((
% 121.84/16.10 (symdiffE) =>
% 121.84/16.10 ((
% 121.84/16.10 (symdiffI1) =>
% 121.84/16.10 ((
% 121.84/16.10 (symdiffI2) =>
% 121.84/16.10 ((
% 121.84/16.10 (symdiffIneg1) =>
% 121.84/16.10 ((
% 121.84/16.10 (symdiffIneg2) =>
% 121.84/16.10 ((
% 121.84/16.10 (secondinupair) =>
% 121.84/16.10 ((
% 121.84/16.10 (setukpairIL) =>
% 121.84/16.10 ((
% 121.84/16.10 (setukpairIR) =>
% 121.84/16.10 ((
% 121.84/16.10 (kpairiskpair) =>
% 121.84/16.10 ((
% 121.84/16.10 (kpairp) =>
% 121.84/16.10 ((
% 121.84/16.10 (singletonsubset) =>
% 121.84/16.10 ((
% 121.84/16.10 (singletoninpowerset) =>
% 121.84/16.10 ((
% 121.84/16.10 (singletoninpowunion) =>
% 121.84/16.10 ((
% 121.84/16.10 (upairset2E) =>
% 121.84/16.10 ((
% 121.84/16.10 (upairsubunion) =>
% 121.84/16.10 ((
% 121.84/16.10 (upairinpowunion) =>
% 121.84/16.10 ((
% 121.84/16.10 (ubforcartprodlem1) =>
% 121.84/16.10 ((
% 121.84/16.10 (ubforcartprodlem2) =>
% 121.84/16.10 ((
% 121.84/16.10 (ubforcartprodlem3) =>
% 121.84/16.10 ((
% 121.84/16.10 (cartprodpairin) =>
% 121.84/16.10 ((
% 121.84/16.10 (cartprodmempair1) =>
% 121.84/16.10 ((
% 121.84/16.10 (cartprodmempair) =>
% 121.84/16.10 ((
% 121.84/16.10 (setunionE2) =>
% 121.84/16.10 ((
% 121.84/16.10 (setunionsingleton1) =>
% 121.84/16.10 ((
% 121.84/16.10 (setunionsingleton2) =>
% 121.84/16.10 ((
% 121.84/16.10 (setunionsingleton) =>
% 121.84/16.10 ((
% 121.84/16.10 (singletonprop) =>
% 121.84/16.10 ((
% 121.84/16.10 (ex1E1) =>
% 121.84/16.10 ((
% 121.84/16.10 (ex1I) =>
% 121.84/16.10 ((
% 121.84/16.10 (ex1I2) =>
% 121.84/16.10 ((
% 121.84/16.10 (singletonsuniq) =>
% 121.84/16.10 ((
% 121.84/16.10 (setukpairinjL1) =>
% 121.84/16.10 ((
% 121.84/16.10 (kfstsingleton) =>
% 121.84/16.10 ((
% 121.84/16.10 (theprop) =>
% 121.84/16.10 ((
% 121.84/16.10 (kfstpairEq) =>
% 121.84/16.10 ((
% 121.84/16.10 (cartprodfstin) =>
% 121.84/16.10 ((
% 121.84/16.10 (setukpairinjL2) =>
% 121.84/16.10 ((
% 121.84/16.10 (setukpairinjL) =>
% 121.84/16.10 ((
% 121.84/16.10 (setukpairinjR11) =>
% 121.84/16.10 ((
% 121.84/16.10 (setukpairinjR12) =>
% 121.84/16.10 ((
% 121.84/16.10 (setukpairinjR1) =>
% 121.84/16.10 ((
% 121.84/16.10 (upairequniteq) =>
% 121.84/16.10 ((
% 121.84/16.10 (setukpairinjR2) =>
% 121.84/16.10 ((
% 121.84/16.10 (setukpairinjR) =>
% 121.84/16.10 ((
% 121.84/16.10 (ksndsingleton) =>
% 121.84/16.10 ((
% 121.84/16.10 (ksndpairEq) =>
% 121.84/16.10 ((
% 121.84/16.10 (kpairsurjEq) =>
% 121.84/16.10 ((
% 121.84/16.10 (cartprodsndin) =>
% 121.84/16.10 ((
% 121.84/16.10 (cartprodpairmemEL) =>
% 121.84/16.10 ((
% 121.84/16.10 (cartprodpairmemER) =>
% 121.84/16.10 ((
% 121.84/16.10 (cartprodmempaircEq) =>
% 121.84/16.10 ((
% 121.84/16.10 (cartprodfstpairEq) =>
% 121.84/16.10 ((
% 121.84/16.10 (cartprodsndpairEq) =>
% 121.84/16.10 ((
% 121.84/16.10 (cartprodpairsurjEq) =>
% 121.84/16.10 ((
% 121.84/16.10 (dpsetconstrI) =>
% 121.84/16.10 ((
% 121.84/16.10 (dpsetconstrSub) =>
% 121.84/16.10 ((
% 121.84/16.10 (setOfPairsIsBReln) =>
% 121.84/16.10 ((
% 121.84/16.10 (dpsetconstrERa) =>
% 121.84/16.10 ((
% 121.84/16.10 (dpsetconstrEL1) =>
% 121.84/16.10 ((
% 121.84/16.10 (dpsetconstrEL2) =>
% 121.84/16.10 ((
% 121.84/16.10 (dpsetconstrER) =>
% 121.84/16.10 ((
% 121.84/16.10 (funcImageSingleton) =>
% 121.84/16.10 ((
% 121.84/16.10 (apProp) =>
% 121.84/16.10 ((
% 121.84/16.10 (app) =>
% 121.84/16.10 ((
% 121.84/16.10 (infuncsetfunc) =>
% 121.84/16.10 ((
% 121.84/16.10 (ap2p) =>
% 121.84/16.10 ((
% 121.84/16.10 (funcinfuncset) =>
% 121.84/16.10 ((
% 121.84/16.10 (lamProp) =>
% 121.84/16.10 ((
% 121.84/16.10 (lamp) =>
% 121.84/16.10 ((
% 121.84/16.10 (lam2p) =>
% 121.84/16.10 ((
% 121.84/16.10 (brelnall1) =>
% 121.84/16.10 ((
% 121.84/16.10 (brelnall2) =>
% 121.84/16.10 ((
% 121.84/16.10 (ex1E2) =>
% 121.84/16.10 ((
% 121.84/16.10 (funcGraphProp1) =>
% 121.84/16.10 ((
% 121.84/16.10 (funcGraphProp3) =>
% 121.84/16.10 ((
% 121.84/16.10 (funcGraphProp2) =>
% 121.84/16.10 ((
% 121.84/16.10 (funcextLem) =>
% 121.84/16.10 ((
% 121.84/16.10 (funcGraphProp4) =>
% 121.84/16.10 ((
% 121.84/16.10 (subbreln) =>
% 121.84/16.10 ((
% 121.84/16.10 (eqbreln) =>
% 121.84/16.10 ((
% 121.84/16.10 (funcext) =>
% 121.84/16.10 ((
% 121.84/16.10 (funcext2) =>
% 121.84/16.10 ((
% 121.84/16.10 (ap2apEq1) =>
% 121.84/16.10 ((
% 121.84/16.10 (ap2apEq2) =>
% 121.84/16.10 ((
% 121.84/16.10 (beta1) =>
% 121.84/16.10 ((
% 121.84/16.10 (eta1) =>
% 121.84/16.10 ((
% 121.84/16.10 (lam2lamEq) =>
% 121.84/16.10 ((
% 121.84/16.10 (beta2) =>
% 121.84/16.10 ((
% 121.84/16.10 (eta2) =>
% 121.84/16.10 ((
% 121.84/16.10 (iffalseProp1) =>
% 121.84/16.10 ((
% 121.84/16.10 (iffalseProp2) =>
% 121.84/16.10 ((
% 121.84/16.10 (iftrueProp1) =>
% 121.84/16.10 ((
% 121.84/16.10 (iftrueProp2) =>
% 121.84/16.10 ((
% 121.84/16.10 (ifSingleton) =>
% 121.84/16.10 ((
% 121.84/16.10 (ifp) =>
% 121.84/16.10 ((
% 121.84/16.10 (theeq) =>
% 121.84/16.10 ((
% 121.84/16.10 (iftrue) =>
% 121.84/16.10 ((
% 121.84/16.10 (iffalse) =>
% 121.84/16.10 ((
% 121.84/16.10 (iftrueorfalse) =>
% 121.84/16.10 ((
% 121.84/16.10 (binintersectT_lem) =>
% 121.84/16.10 ((
% 121.84/16.10 (binunionT_lem) =>
% 121.84/16.10 ((
% 121.84/16.10 (powersetT_lem) =>
% 121.84/16.10 ((
% 121.84/16.10 (setminusT_lem) =>
% 121.84/16.10 ((
% 121.84/16.10 (complementT_lem) =>
% 121.84/16.10 ((
% 121.84/16.10 (setextT) =>
% 121.84/16.10 ((
% 121.84/16.10 (subsetTI) =>
% 121.84/16.10 ((
% 121.84/16.10 (powersetTI1) =>
% 121.84/16.10 ((
% 121.84/16.10 (powersetTE1) =>
% 121.84/16.10 ((
% 121.84/16.10 (complementTI1) =>
% 121.84/16.10 ((
% 121.84/16.10 (complementTE1) =>
% 121.84/16.10 ((
% 121.84/16.10 (binintersectTELcontra) =>
% 121.84/16.10 ((
% 121.84/16.10 (binintersectTERcontra) =>
% 121.84/16.10 ((
% 121.84/16.10 (contrasubsetT) =>
% 121.84/16.10 ((
% 121.84/16.10 (contrasubsetT1) =>
% 121.84/16.10 ((
% 121.84/16.10 (contrasubsetT2) =>
% 121.84/16.10 ((
% 121.84/16.10 (contrasubsetT3) =>
% 121.84/16.10 ((
% 121.84/16.10 (doubleComplementI1) =>
% 121.84/16.10 ((
% 121.84/16.10 (doubleComplementE1) =>
% 121.84/16.10 ((
% 121.84/16.10 (doubleComplementSub1) =>
% 121.84/16.10 ((
% 121.84/16.10 (doubleComplementSub2) =>
% 121.84/16.10 ((
% 121.84/16.10 (doubleComplementEq) =>
% 121.84/16.10 ((
% 121.84/16.10 (complementTnotintersectT) =>
% 121.84/16.10 ((
% 121.84/16.10 (complementImpComplementIntersect) =>
% 121.84/16.10 ((
% 121.84/16.10 (complementSubsetComplementIntersect) =>
% 121.84/16.10 ((
% 121.84/16.10 (complementInPowersetComplementIntersect) =>
% 121.84/16.10 ((
% 121.84/16.10 (contraSubsetComplement) =>
% 121.84/16.10 ((
% 121.84/16.10 (complementTcontraSubset) =>
% 121.84/16.10 ((
% 121.84/16.10 (binunionTILcontra) =>
% 121.84/16.10 ((
% 121.84/16.10 (binunionTIRcontra) =>
% 121.84/16.10 ((
% 121.84/16.10 (inIntersectImpInUnion) =>
% 121.84/16.10 ((
% 121.84/16.10 (inIntersectImpInUnion2) =>
% 121.84/16.10 ((
% 121.84/16.10 (inIntersectImpInIntersectUnions) =>
% 121.84/16.10 ((
% 121.84/16.10 (intersectInPowersetIntersectUnions) =>
% 121.84/16.10 ((
% 121.84/16.10 (inComplementUnionImpNotIn1) =>
% 121.84/16.10 ((
% 121.84/16.10 (inComplementUnionImpInComplement1) =>
% 121.84/16.10 ((
% 121.84/16.10 (binunionTE) =>
% 121.84/16.10 ((
% 121.84/16.10 (binunionTEcontra) =>
% 121.84/16.10 ((
% 121.84/16.10 (demorgan2a1) =>
% 121.84/16.10 ((
% 121.84/16.10 (complementUnionInPowersetComplement) =>
% 121.84/16.10 ((
% 121.84/16.10 (demorgan2a2) =>
% 121.84/16.10 ((
% 121.84/16.10 (demorgan1a) =>
% 121.84/16.10 ((
% 121.84/16.10 (demorgan1b) =>
% 121.84/16.10 ((
% 121.84/16.10 (demorgan1) =>
% 121.84/16.10 ((
% 121.84/16.10 (demorgan2a) =>
% 121.84/16.10 ((
% 121.84/16.10 (demorgan2b2) =>
% 121.84/16.10 ((
% 121.84/16.10 (demorgan2b) =>
% 121.84/16.10 ((
% 121.84/16.10 (demorgan2) =>
% 121.84/16.10 ((
% 121.84/16.10 (woz13rule0) =>
% 121.84/16.10 ((
% 121.84/16.10 (woz13rule1) =>
% 121.84/16.10 ((
% 121.84/16.10 (woz13rule2) =>
% 121.84/16.10 ((
% 121.84/16.10 (woz13rule3) =>
% 121.84/16.10 ((
% 121.84/16.10 (woz13rule4) =>
% 121.84/16.10 ((
% 121.84/16.10 (woz1_1) =>
% 121.84/16.10 ((
% 121.84/16.10 (woz1_2) =>
% 121.84/16.10 ((
% 121.84/16.10 (woz1_3) =>
% 121.84/16.10 ((
% 121.84/16.10 (woz1_4) =>
% 121.84/16.10 ((
% 121.84/16.10 (woz1_5) =>
% 121.84/16.10 ((
% 121.84/16.10 (breln1all2) =>
% 121.84/16.10 ((
% 121.84/16.10 (breln1SetBreln1) =>
% 121.84/16.10 ((
% 121.84/16.10 (choice2fnsingleton) =>
% 121.84/16.10 ((
% 121.84/16.10 (setOfPairsIsBReln1) =>
% 121.84/16.10 ((
% 121.84/16.10 (breln1all1) =>
% 121.84/16.10 ((
% 121.84/16.10 (subbreln1) =>
% 121.84/16.10 ((
% 121.84/16.10 (eqbreln1) =>
% 121.84/16.10 ((
% 121.84/16.10 (breln1invprop) =>
% 121.84/16.10 ((
% 121.84/16.10 (breln1invI) =>
% 121.84/16.10 ((
% 121.84/16.10 (breln1invE) =>
% 121.84/16.10 ((
% 121.84/16.10 (breln1compprop) =>
% 121.84/16.10 ((
% 121.84/16.10 (breln1compI) =>
% 121.84/16.10 ((
% 121.84/16.10 (breln1compE) =>
% 121.84/16.10 ((
% 121.84/16.10 (breln1compEex) =>
% 121.84/16.10 ((
% 121.84/16.10 (breln1unionprop) =>
% 121.84/16.10 ((
% 121.84/16.10 (breln1unionIL) =>
% 121.84/16.10 ((
% 121.84/16.10 (breln1unionIR) =>
% 121.84/16.10 ((
% 121.84/16.10 (breln1unionI) =>
% 121.84/16.10 ((
% 121.84/16.10 (breln1unionE) =>
% 121.84/16.10 ((
% 121.84/16.10 (breln1unionEcases) =>
% 121.84/16.10 ((
% 121.84/16.10 (breln1unionCommutes) =>
% 121.84/16.10 ((
% 121.84/16.10 (woz2Ex) =>
% 121.84/16.10 ((
% 121.84/16.10 (woz2W) =>
% 121.84/16.10 ((
% 121.84/16.10 (woz2A) =>
% 121.84/16.10 ((
% 121.84/16.10 (woz2B) =>
% 121.84/16.10 ((
% 121.84/16.10 (image1Ex) =>
% 121.84/16.10 ((
% 121.84/16.10 (image1Ex1) =>
% 121.84/16.10 ((
% 121.84/16.10 (image1Equiv) =>
% 121.84/16.10 ((
% 121.84/16.10 (image1E) =>
% 121.84/16.10 ((
% 121.84/16.10 (image1I) =>
% 121.84/16.10 ((
% 121.84/16.10 (injFuncInInjFuncSet) =>
% 121.84/16.10 ((
% 121.84/16.10 (!!) @ (
% 121.84/16.10 (('#B') @ (
% 121.84/16.10 !!) @
% 121.84/16.10 (
% 121.84/16.10 (
% 121.84/16.10 ('#B') @ (
% 121.84/16.10 (
% 121.84/16.10 ('#B') @ (
% 121.84/16.10 !!))) @
% 121.84/16.10 (
% 121.84/16.10 (
% 121.84/16.10 ('#S') @ (
% 121.84/16.10 (
% 121.84/16.10 ('#B') @ (
% 121.84/16.10 '#S') @
% 121.84/16.10 (
% 121.84/16.10 (
% 121.84/16.10 ('#B') @ (
% 121.84/16.10 (
% 121.84/16.10 ('#B') @ (
% 121.84/16.10 '#S'))) @
% 121.84/16.10 (
% 121.84/16.10 (
% 121.84/16.10 ('#B') @ (
% 121.84/16.10 (
% 121.84/16.10 ('#B') @ (
% 121.84/16.10 (
% 121.84/16.10 ('#B') @ (
% 121.84/16.10 =>))))) @
% 121.84/16.10 (
% 121.84/16.10 (
% 121.84/16.10 ('#B') @ (
% 121.84/16.10 (
% 121.84/16.10 ('#B') @ (
% 121.84/16.10 (
% 121.84/16.10 ('#C') @ in)))) @
% 121.84/16.10 injFuncSet)))))))) @
% 121.84/16.10 (
% 121.84/16.10 (
% 121.84/16.10 ('#B') @ (
% 121.84/16.10 (
% 121.84/16.10 ('#B') @ (
% 121.84/16.10 (
% 121.84/16.10 ('#C') @ in)))) @
% 121.84/16.10 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 121.84/16.10 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl731])).
% 121.84/16.10 thf(zip_derived_cl769, plain,
% 121.84/16.10 (~ (((dsetconstr__Cong) =>
% 121.84/16.10 (((subsetI1) =>
% 121.84/16.10 (((eqimpsubset2) =>
% 121.84/16.10 (((eqimpsubset1) =>
% 121.84/16.10 (((subsetI2) =>
% 121.84/16.10 (((emptysetsubset) =>
% 121.84/16.10 (((subsetE) =>
% 121.84/16.10 (((subsetE2) =>
% 121.84/16.10 (((notsubsetI) =>
% 121.84/16.10 (((notequalI1) =>
% 121.84/16.10 (((notequalI2) =>
% 121.84/16.10 (((subsetRefl) =>
% 121.84/16.10 (((subsetTrans) =>
% 121.84/16.10 (((setadjoinSub) =>
% 121.84/16.10 (((setadjoinSub2) =>
% 121.84/16.10 (((subset2powerset) =>
% 121.84/16.10 (((setextsub) =>
% 121.84/16.10 (((subsetemptysetimpeq) =>
% 121.84/16.10 (((powersetI1) =>
% 121.84/16.10 (((powersetE1) =>
% 121.84/16.10 (((inPowerset) =>
% 121.84/16.10 (((powersetsubset) =>
% 121.84/16.10 (((sepInPowerset) =>
% 121.84/16.10 (((sepSubset) =>
% 121.84/16.10 (((binunionIL) =>
% 121.84/16.10 (((upairset2IR) =>
% 121.84/16.10 (((binunionIR) =>
% 121.84/16.10 (((binunionEcases) =>
% 121.84/16.10 (((binunionE) =>
% 121.84/16.10 (((binunionLsub) =>
% 121.84/16.10 ((
% 121.84/16.10 (binunionRsub) =>
% 121.84/16.10 ((
% 121.84/16.10 (binintersectI) =>
% 121.84/16.10 ((
% 121.84/16.10 (binintersectSubset5) =>
% 121.84/16.10 ((
% 121.84/16.10 (binintersectEL) =>
% 121.84/16.10 ((
% 121.84/16.10 (binintersectLsub) =>
% 121.84/16.10 ((
% 121.84/16.10 (binintersectSubset2) =>
% 121.84/16.10 ((
% 121.84/16.10 (binintersectSubset3) =>
% 121.84/16.10 ((
% 121.84/16.10 (binintersectER) =>
% 121.84/16.10 ((
% 121.84/16.10 (disjointsetsI1) =>
% 121.84/16.10 ((
% 121.84/16.10 (binintersectRsub) =>
% 121.84/16.10 ((
% 121.84/16.10 (binintersectSubset4) =>
% 121.84/16.10 ((
% 121.84/16.10 (binintersectSubset1) =>
% 121.84/16.10 ((
% 121.84/16.10 (bs114d) =>
% 121.84/16.10 ((
% 121.84/16.10 (setminusI) =>
% 121.84/16.10 ((
% 121.84/16.10 (setminusEL) =>
% 121.84/16.10 ((
% 121.84/16.10 (setminusER) =>
% 121.84/16.10 ((
% 121.84/16.10 (setminusSubset2) =>
% 121.84/16.10 ((
% 121.84/16.10 (setminusERneg) =>
% 121.84/16.10 ((
% 121.84/16.10 (setminusELneg) =>
% 121.84/16.10 ((
% 121.84/16.10 (setminusILneg) =>
% 121.84/16.10 ((
% 121.84/16.10 (setminusIRneg) =>
% 121.84/16.10 ((
% 121.84/16.10 (setminusLsub) =>
% 121.84/16.10 ((
% 121.84/16.10 (setminusSubset1) =>
% 121.84/16.10 ((
% 121.84/16.10 (symdiffE) =>
% 121.84/16.10 ((
% 121.84/16.10 (symdiffI1) =>
% 121.84/16.10 ((
% 121.84/16.10 (symdiffI2) =>
% 121.84/16.10 ((
% 121.84/16.10 (symdiffIneg1) =>
% 121.84/16.10 ((
% 121.84/16.10 (symdiffIneg2) =>
% 121.84/16.10 ((
% 121.84/16.10 (secondinupair) =>
% 121.84/16.10 ((
% 121.84/16.10 (setukpairIL) =>
% 121.84/16.10 ((
% 121.84/16.10 (setukpairIR) =>
% 121.84/16.10 ((
% 121.84/16.10 (kpairiskpair) =>
% 121.84/16.10 ((
% 121.84/16.10 (kpairp) =>
% 121.84/16.10 ((
% 121.84/16.10 (singletonsubset) =>
% 121.84/16.10 ((
% 121.84/16.10 (singletoninpowerset) =>
% 121.84/16.10 ((
% 121.84/16.10 (singletoninpowunion) =>
% 121.84/16.10 ((
% 121.84/16.10 (upairset2E) =>
% 121.84/16.10 ((
% 121.84/16.10 (upairsubunion) =>
% 121.84/16.10 ((
% 121.84/16.10 (upairinpowunion) =>
% 121.84/16.10 ((
% 121.84/16.10 (ubforcartprodlem1) =>
% 121.84/16.10 ((
% 121.84/16.10 (ubforcartprodlem2) =>
% 121.84/16.10 ((
% 121.84/16.10 (ubforcartprodlem3) =>
% 121.84/16.10 ((
% 121.84/16.10 (cartprodpairin) =>
% 121.84/16.10 ((
% 121.84/16.10 (cartprodmempair1) =>
% 121.84/16.10 ((
% 121.84/16.10 (cartprodmempair) =>
% 121.84/16.10 ((
% 121.84/16.10 (setunionE2) =>
% 121.84/16.10 ((
% 121.84/16.10 (setunionsingleton1) =>
% 121.84/16.10 ((
% 121.84/16.10 (setunionsingleton2) =>
% 121.84/16.10 ((
% 121.84/16.10 (setunionsingleton) =>
% 121.84/16.10 ((
% 121.84/16.10 (singletonprop) =>
% 121.84/16.10 ((
% 121.84/16.10 (ex1E1) =>
% 121.84/16.10 ((
% 121.84/16.10 (ex1I) =>
% 121.84/16.10 ((
% 121.84/16.10 (ex1I2) =>
% 121.84/16.10 ((
% 121.84/16.10 (singletonsuniq) =>
% 121.84/16.10 ((
% 121.84/16.10 (setukpairinjL1) =>
% 121.84/16.10 ((
% 121.84/16.10 (kfstsingleton) =>
% 121.84/16.10 ((
% 121.84/16.10 (theprop) =>
% 121.84/16.10 ((
% 121.84/16.10 (kfstpairEq) =>
% 121.84/16.10 ((
% 121.84/16.10 (cartprodfstin) =>
% 121.84/16.10 ((
% 121.84/16.10 (setukpairinjL2) =>
% 121.84/16.10 ((
% 121.84/16.10 (setukpairinjL) =>
% 121.84/16.10 ((
% 121.84/16.10 (setukpairinjR11) =>
% 121.84/16.10 ((
% 121.84/16.10 (setukpairinjR12) =>
% 121.84/16.10 ((
% 121.84/16.10 (setukpairinjR1) =>
% 121.84/16.10 ((
% 121.84/16.10 (upairequniteq) =>
% 121.84/16.10 ((
% 121.84/16.10 (setukpairinjR2) =>
% 121.84/16.10 ((
% 121.84/16.10 (setukpairinjR) =>
% 121.84/16.10 ((
% 121.84/16.10 (ksndsingleton) =>
% 121.84/16.10 ((
% 121.84/16.10 (ksndpairEq) =>
% 121.84/16.10 ((
% 121.84/16.10 (kpairsurjEq) =>
% 121.84/16.10 ((
% 121.84/16.10 (cartprodsndin) =>
% 121.84/16.10 ((
% 121.84/16.10 (cartprodpairmemEL) =>
% 121.84/16.10 ((
% 121.84/16.10 (cartprodpairmemER) =>
% 121.84/16.10 ((
% 121.84/16.10 (cartprodmempaircEq) =>
% 121.84/16.10 ((
% 121.84/16.10 (cartprodfstpairEq) =>
% 121.84/16.10 ((
% 121.84/16.10 (cartprodsndpairEq) =>
% 121.84/16.10 ((
% 121.84/16.10 (cartprodpairsurjEq) =>
% 121.84/16.10 ((
% 121.84/16.10 (dpsetconstrI) =>
% 121.84/16.10 ((
% 121.84/16.10 (dpsetconstrSub) =>
% 121.84/16.10 ((
% 121.84/16.10 (setOfPairsIsBReln) =>
% 121.84/16.10 ((
% 121.84/16.10 (dpsetconstrERa) =>
% 121.84/16.10 ((
% 121.84/16.10 (dpsetconstrEL1) =>
% 121.84/16.10 ((
% 121.84/16.10 (dpsetconstrEL2) =>
% 121.84/16.10 ((
% 121.84/16.10 (dpsetconstrER) =>
% 121.84/16.10 ((
% 121.84/16.10 (funcImageSingleton) =>
% 121.84/16.10 ((
% 121.84/16.10 (apProp) =>
% 121.84/16.10 ((
% 121.84/16.10 (app) =>
% 121.84/16.10 ((
% 121.84/16.10 (infuncsetfunc) =>
% 121.84/16.10 ((
% 121.84/16.10 (ap2p) =>
% 121.84/16.10 ((
% 121.84/16.10 (funcinfuncset) =>
% 121.84/16.10 ((
% 121.84/16.10 (lamProp) =>
% 121.84/16.10 ((
% 121.84/16.10 (lamp) =>
% 121.84/16.10 ((
% 121.84/16.10 (lam2p) =>
% 121.84/16.10 ((
% 121.84/16.10 (brelnall1) =>
% 121.84/16.10 ((
% 121.84/16.10 (brelnall2) =>
% 121.84/16.10 ((
% 121.84/16.10 (ex1E2) =>
% 121.84/16.10 ((
% 121.84/16.10 (funcGraphProp1) =>
% 121.84/16.10 ((
% 121.84/16.10 (funcGraphProp3) =>
% 121.84/16.10 ((
% 121.84/16.10 (funcGraphProp2) =>
% 121.84/16.10 ((
% 121.84/16.10 (funcextLem) =>
% 121.84/16.10 ((
% 121.84/16.10 (funcGraphProp4) =>
% 121.84/16.10 ((
% 121.84/16.10 (subbreln) =>
% 121.84/16.10 ((
% 121.84/16.10 (eqbreln) =>
% 121.84/16.10 ((
% 121.84/16.10 (funcext) =>
% 121.84/16.10 ((
% 121.84/16.10 (funcext2) =>
% 121.84/16.10 ((
% 121.84/16.10 (ap2apEq1) =>
% 121.84/16.10 ((
% 121.84/16.10 (ap2apEq2) =>
% 121.84/16.10 ((
% 121.84/16.10 (beta1) =>
% 121.84/16.10 ((
% 121.84/16.10 (eta1) =>
% 121.84/16.10 ((
% 121.84/16.10 (lam2lamEq) =>
% 121.84/16.10 ((
% 121.84/16.10 (beta2) =>
% 121.84/16.10 ((
% 121.84/16.10 (eta2) =>
% 121.84/16.10 ((
% 121.84/16.10 (iffalseProp1) =>
% 121.84/16.10 ((
% 121.84/16.10 (iffalseProp2) =>
% 121.84/16.10 ((
% 121.84/16.10 (iftrueProp1) =>
% 121.84/16.10 ((
% 121.84/16.10 (iftrueProp2) =>
% 121.84/16.10 ((
% 121.84/16.10 (ifSingleton) =>
% 121.84/16.10 ((
% 121.84/16.10 (ifp) =>
% 121.84/16.10 ((
% 121.84/16.10 (theeq) =>
% 121.84/16.10 ((
% 121.84/16.10 (iftrue) =>
% 121.84/16.10 ((
% 121.84/16.10 (iffalse) =>
% 121.84/16.10 ((
% 121.84/16.10 (iftrueorfalse) =>
% 121.84/16.10 ((
% 121.84/16.10 (binintersectT_lem) =>
% 121.84/16.10 ((
% 121.84/16.10 (binunionT_lem) =>
% 121.84/16.10 ((
% 121.84/16.10 (powersetT_lem) =>
% 121.84/16.10 ((
% 121.84/16.10 (setminusT_lem) =>
% 121.84/16.10 ((
% 121.84/16.10 (complementT_lem) =>
% 121.84/16.10 ((
% 121.84/16.10 (setextT) =>
% 121.84/16.10 ((
% 121.84/16.10 (subsetTI) =>
% 121.84/16.10 ((
% 121.84/16.10 (powersetTI1) =>
% 121.84/16.10 ((
% 121.84/16.10 (powersetTE1) =>
% 121.84/16.10 ((
% 121.84/16.10 (complementTI1) =>
% 121.84/16.10 ((
% 121.84/16.10 (complementTE1) =>
% 121.84/16.10 ((
% 121.84/16.10 (binintersectTELcontra) =>
% 121.84/16.10 ((
% 121.84/16.10 (binintersectTERcontra) =>
% 121.84/16.10 ((
% 121.84/16.10 (contrasubsetT) =>
% 121.84/16.10 ((
% 121.84/16.10 (contrasubsetT1) =>
% 121.84/16.10 ((
% 121.84/16.10 (contrasubsetT2) =>
% 121.84/16.10 ((
% 121.84/16.10 (contrasubsetT3) =>
% 121.84/16.10 ((
% 121.84/16.10 (doubleComplementI1) =>
% 121.84/16.10 ((
% 121.84/16.10 (doubleComplementE1) =>
% 121.84/16.10 ((
% 121.84/16.10 (doubleComplementSub1) =>
% 121.84/16.10 ((
% 121.84/16.10 (doubleComplementSub2) =>
% 121.84/16.10 ((
% 121.84/16.10 (doubleComplementEq) =>
% 121.84/16.10 ((
% 121.84/16.10 (complementTnotintersectT) =>
% 121.84/16.10 ((
% 121.84/16.10 (complementImpComplementIntersect) =>
% 121.84/16.10 ((
% 121.84/16.10 (complementSubsetComplementIntersect) =>
% 121.84/16.10 ((
% 121.84/16.10 (complementInPowersetComplementIntersect) =>
% 121.84/16.10 ((
% 121.84/16.10 (contraSubsetComplement) =>
% 121.84/16.10 ((
% 121.84/16.10 (complementTcontraSubset) =>
% 121.84/16.10 ((
% 121.84/16.10 (binunionTILcontra) =>
% 121.84/16.10 ((
% 121.84/16.10 (binunionTIRcontra) =>
% 121.84/16.10 ((
% 121.84/16.10 (inIntersectImpInUnion) =>
% 121.84/16.10 ((
% 121.84/16.10 (inIntersectImpInUnion2) =>
% 121.84/16.10 ((
% 121.84/16.10 (inIntersectImpInIntersectUnions) =>
% 121.84/16.10 ((
% 121.84/16.10 (intersectInPowersetIntersectUnions) =>
% 121.84/16.10 ((
% 121.84/16.10 (inComplementUnionImpNotIn1) =>
% 121.84/16.10 ((
% 121.84/16.10 (inComplementUnionImpInComplement1) =>
% 121.84/16.10 ((
% 121.84/16.10 (binunionTE) =>
% 121.84/16.10 ((
% 121.84/16.10 (binunionTEcontra) =>
% 121.84/16.10 ((
% 121.84/16.10 (demorgan2a1) =>
% 121.84/16.10 ((
% 121.84/16.10 (complementUnionInPowersetComplement) =>
% 121.84/16.10 ((
% 121.84/16.10 (demorgan2a2) =>
% 121.84/16.10 ((
% 121.84/16.10 (demorgan1a) =>
% 121.84/16.10 ((
% 121.84/16.10 (demorgan1b) =>
% 121.84/16.10 ((
% 121.84/16.10 (demorgan1) =>
% 121.84/16.10 ((
% 121.84/16.10 (demorgan2a) =>
% 121.84/16.10 ((
% 121.84/16.10 (demorgan2b2) =>
% 121.84/16.10 ((
% 121.84/16.10 (demorgan2b) =>
% 121.84/16.10 ((
% 121.84/16.10 (demorgan2) =>
% 121.84/16.10 ((
% 121.84/16.10 (woz13rule0) =>
% 121.84/16.10 ((
% 121.84/16.10 (woz13rule1) =>
% 121.84/16.10 ((
% 121.84/16.10 (woz13rule2) =>
% 121.84/16.10 ((
% 121.84/16.10 (woz13rule3) =>
% 121.84/16.10 ((
% 121.84/16.10 (woz13rule4) =>
% 121.84/16.10 ((
% 121.84/16.10 (woz1_1) =>
% 121.84/16.10 ((
% 121.84/16.10 (woz1_2) =>
% 121.84/16.10 ((
% 121.84/16.10 (woz1_3) =>
% 121.84/16.10 ((
% 121.84/16.10 (woz1_4) =>
% 121.84/16.10 ((
% 121.84/16.10 (woz1_5) =>
% 121.84/16.10 ((
% 121.84/16.10 (breln1all2) =>
% 121.84/16.10 ((
% 121.84/16.10 (breln1SetBreln1) =>
% 121.84/16.10 ((
% 121.84/16.10 (choice2fnsingleton) =>
% 121.84/16.10 ((
% 121.84/16.10 (setOfPairsIsBReln1) =>
% 121.84/16.10 ((
% 121.84/16.10 (breln1all1) =>
% 121.84/16.10 ((
% 121.84/16.10 (subbreln1) =>
% 121.84/16.10 ((
% 121.84/16.10 (eqbreln1) =>
% 121.84/16.10 ((
% 121.84/16.10 (breln1invprop) =>
% 121.84/16.10 ((
% 121.84/16.10 (breln1invI) =>
% 121.84/16.10 ((
% 121.84/16.10 (breln1invE) =>
% 121.84/16.10 ((
% 121.84/16.10 (breln1compprop) =>
% 121.84/16.10 ((
% 121.84/16.10 (breln1compI) =>
% 121.84/16.10 ((
% 121.84/16.10 (breln1compE) =>
% 121.84/16.10 ((
% 121.84/16.10 (breln1compEex) =>
% 121.84/16.10 ((
% 121.84/16.10 (breln1unionprop) =>
% 121.84/16.10 ((
% 121.84/16.10 (breln1unionIL) =>
% 121.84/16.10 ((
% 121.84/16.10 (breln1unionIR) =>
% 121.84/16.10 ((
% 121.84/16.10 (breln1unionI) =>
% 121.84/16.10 ((
% 121.84/16.10 (breln1unionE) =>
% 121.84/16.10 ((
% 121.84/16.10 (breln1unionEcases) =>
% 121.84/16.10 ((
% 121.84/16.10 (breln1unionCommutes) =>
% 121.84/16.10 ((
% 121.84/16.10 (woz2Ex) =>
% 121.84/16.10 ((
% 121.84/16.10 (woz2W) =>
% 121.84/16.10 ((
% 121.84/16.10 (woz2A) =>
% 121.84/16.10 ((
% 121.84/16.10 (woz2B) =>
% 121.84/16.10 ((
% 121.84/16.10 (image1Ex) =>
% 121.84/16.10 ((
% 121.84/16.10 (image1Ex1) =>
% 121.84/16.10 ((
% 121.84/16.10 (image1Equiv) =>
% 121.84/16.10 ((
% 121.84/16.10 (image1E) =>
% 121.84/16.10 ((
% 121.84/16.10 (image1I) =>
% 121.84/16.10 ((
% 121.84/16.10 (injFuncInInjFuncSet) =>
% 121.84/16.10 ((
% 121.84/16.10 (!!) @ (
% 121.84/16.10 (('#B') @ (
% 121.84/16.10 !!) @
% 121.84/16.10 (
% 121.84/16.10 (
% 121.84/16.10 ('#B') @ (
% 121.84/16.10 (
% 121.84/16.10 ('#B') @ (
% 121.84/16.10 !!))) @
% 121.84/16.10 (
% 121.84/16.10 (
% 121.84/16.10 ('#S') @ (
% 121.84/16.10 (
% 121.84/16.10 ('#B') @ (
% 121.84/16.10 '#S') @
% 121.84/16.10 (
% 121.84/16.10 (
% 121.84/16.10 ('#B') @ (
% 121.84/16.10 (
% 121.84/16.10 ('#B') @ (
% 121.84/16.10 '#S'))) @
% 121.84/16.10 (
% 121.84/16.10 (
% 121.84/16.10 ('#B') @ (
% 121.84/16.10 (
% 121.84/16.10 ('#B') @ (
% 121.84/16.10 (
% 121.84/16.10 ('#B') @ (
% 121.84/16.10 =>))))) @
% 121.84/16.10 (
% 121.84/16.10 (
% 121.84/16.10 ('#B') @ (
% 121.84/16.10 (
% 121.84/16.10 ('#B') @ (
% 121.84/16.10 (
% 121.84/16.10 ('#C') @ in)))) @
% 121.84/16.10 injFuncSet)))))))) @
% 121.84/16.10 (
% 121.84/16.10 (
% 121.84/16.10 ('#B') @ (
% 121.84/16.10 (
% 121.84/16.10 ('#B') @ (
% 121.84/16.10 (
% 121.84/16.10 ('#C') @ in)))) @
% 121.84/16.10 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 121.84/16.10 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl749])).
% 121.84/16.10 thf(zip_derived_cl789, plain,
% 121.84/16.10 (~ (((subsetI1) =>
% 121.84/16.10 (((eqimpsubset2) =>
% 121.84/16.10 (((eqimpsubset1) =>
% 121.84/16.10 (((subsetI2) =>
% 121.84/16.10 (((emptysetsubset) =>
% 121.84/16.10 (((subsetE) =>
% 121.84/16.10 (((subsetE2) =>
% 121.84/16.10 (((notsubsetI) =>
% 121.84/16.10 (((notequalI1) =>
% 121.84/16.10 (((notequalI2) =>
% 121.84/16.10 (((subsetRefl) =>
% 121.84/16.10 (((subsetTrans) =>
% 121.84/16.10 (((setadjoinSub) =>
% 121.84/16.10 (((setadjoinSub2) =>
% 121.84/16.10 (((subset2powerset) =>
% 121.84/16.10 (((setextsub) =>
% 121.84/16.10 (((subsetemptysetimpeq) =>
% 121.84/16.10 (((powersetI1) =>
% 121.84/16.10 (((powersetE1) =>
% 121.84/16.10 (((inPowerset) =>
% 121.84/16.10 (((powersetsubset) =>
% 121.84/16.10 (((sepInPowerset) =>
% 121.84/16.10 (((sepSubset) =>
% 121.84/16.10 (((binunionIL) =>
% 121.84/16.10 (((upairset2IR) =>
% 121.84/16.10 (((binunionIR) =>
% 121.84/16.10 (((binunionEcases) =>
% 121.84/16.10 (((binunionE) =>
% 121.84/16.10 (((binunionLsub) =>
% 121.84/16.10 (((binunionRsub) =>
% 121.84/16.10 ((
% 121.84/16.10 (binintersectI) =>
% 121.84/16.10 ((
% 121.84/16.10 (binintersectSubset5) =>
% 121.84/16.10 ((
% 121.84/16.10 (binintersectEL) =>
% 121.84/16.10 ((
% 121.84/16.10 (binintersectLsub) =>
% 121.84/16.10 ((
% 121.84/16.10 (binintersectSubset2) =>
% 121.84/16.10 ((
% 121.84/16.10 (binintersectSubset3) =>
% 121.84/16.10 ((
% 121.84/16.10 (binintersectER) =>
% 121.84/16.10 ((
% 121.84/16.10 (disjointsetsI1) =>
% 121.84/16.10 ((
% 121.84/16.10 (binintersectRsub) =>
% 121.84/16.10 ((
% 121.84/16.10 (binintersectSubset4) =>
% 121.84/16.10 ((
% 121.84/16.10 (binintersectSubset1) =>
% 121.84/16.10 ((
% 121.84/16.10 (bs114d) =>
% 121.84/16.10 ((
% 121.84/16.10 (setminusI) =>
% 121.84/16.10 ((
% 121.84/16.10 (setminusEL) =>
% 121.84/16.10 ((
% 121.84/16.10 (setminusER) =>
% 121.84/16.10 ((
% 121.84/16.10 (setminusSubset2) =>
% 121.84/16.10 ((
% 121.84/16.10 (setminusERneg) =>
% 121.84/16.10 ((
% 121.84/16.10 (setminusELneg) =>
% 121.84/16.10 ((
% 121.84/16.10 (setminusILneg) =>
% 121.84/16.10 ((
% 121.84/16.10 (setminusIRneg) =>
% 121.84/16.10 ((
% 121.84/16.10 (setminusLsub) =>
% 121.84/16.10 ((
% 121.84/16.10 (setminusSubset1) =>
% 121.84/16.10 ((
% 121.84/16.10 (symdiffE) =>
% 121.84/16.10 ((
% 121.84/16.10 (symdiffI1) =>
% 121.84/16.10 ((
% 121.84/16.10 (symdiffI2) =>
% 121.84/16.10 ((
% 121.84/16.10 (symdiffIneg1) =>
% 121.84/16.10 ((
% 121.84/16.10 (symdiffIneg2) =>
% 121.84/16.10 ((
% 121.84/16.10 (secondinupair) =>
% 121.84/16.10 ((
% 121.84/16.10 (setukpairIL) =>
% 121.84/16.10 ((
% 121.84/16.10 (setukpairIR) =>
% 121.84/16.10 ((
% 121.84/16.10 (kpairiskpair) =>
% 121.84/16.10 ((
% 121.84/16.10 (kpairp) =>
% 121.84/16.10 ((
% 121.84/16.10 (singletonsubset) =>
% 121.84/16.10 ((
% 121.84/16.10 (singletoninpowerset) =>
% 121.84/16.10 ((
% 121.84/16.10 (singletoninpowunion) =>
% 121.84/16.10 ((
% 121.84/16.10 (upairset2E) =>
% 121.84/16.10 ((
% 121.84/16.10 (upairsubunion) =>
% 121.84/16.10 ((
% 121.84/16.10 (upairinpowunion) =>
% 121.84/16.10 ((
% 121.84/16.10 (ubforcartprodlem1) =>
% 121.84/16.10 ((
% 121.84/16.10 (ubforcartprodlem2) =>
% 121.84/16.10 ((
% 121.84/16.10 (ubforcartprodlem3) =>
% 121.84/16.10 ((
% 121.84/16.10 (cartprodpairin) =>
% 121.84/16.10 ((
% 121.84/16.10 (cartprodmempair1) =>
% 121.84/16.10 ((
% 121.84/16.10 (cartprodmempair) =>
% 121.84/16.10 ((
% 121.84/16.10 (setunionE2) =>
% 121.84/16.10 ((
% 121.84/16.10 (setunionsingleton1) =>
% 121.84/16.10 ((
% 121.84/16.10 (setunionsingleton2) =>
% 121.84/16.10 ((
% 121.84/16.10 (setunionsingleton) =>
% 121.84/16.10 ((
% 121.84/16.10 (singletonprop) =>
% 121.84/16.10 ((
% 121.84/16.10 (ex1E1) =>
% 121.84/16.10 ((
% 121.84/16.10 (ex1I) =>
% 121.84/16.10 ((
% 121.84/16.10 (ex1I2) =>
% 121.84/16.10 ((
% 121.84/16.10 (singletonsuniq) =>
% 121.84/16.10 ((
% 121.84/16.10 (setukpairinjL1) =>
% 121.84/16.10 ((
% 121.84/16.10 (kfstsingleton) =>
% 121.84/16.10 ((
% 121.84/16.10 (theprop) =>
% 121.84/16.10 ((
% 121.84/16.10 (kfstpairEq) =>
% 121.84/16.10 ((
% 121.84/16.10 (cartprodfstin) =>
% 121.84/16.10 ((
% 121.84/16.10 (setukpairinjL2) =>
% 121.84/16.10 ((
% 121.84/16.10 (setukpairinjL) =>
% 121.84/16.10 ((
% 121.84/16.10 (setukpairinjR11) =>
% 121.84/16.10 ((
% 121.84/16.10 (setukpairinjR12) =>
% 121.84/16.10 ((
% 121.84/16.10 (setukpairinjR1) =>
% 121.84/16.10 ((
% 121.84/16.10 (upairequniteq) =>
% 121.84/16.10 ((
% 121.84/16.10 (setukpairinjR2) =>
% 121.84/16.10 ((
% 121.84/16.10 (setukpairinjR) =>
% 121.84/16.10 ((
% 121.84/16.10 (ksndsingleton) =>
% 121.84/16.10 ((
% 121.84/16.10 (ksndpairEq) =>
% 121.84/16.10 ((
% 121.84/16.10 (kpairsurjEq) =>
% 121.84/16.10 ((
% 121.84/16.10 (cartprodsndin) =>
% 121.84/16.10 ((
% 121.84/16.10 (cartprodpairmemEL) =>
% 121.84/16.10 ((
% 121.84/16.10 (cartprodpairmemER) =>
% 121.84/16.10 ((
% 121.84/16.10 (cartprodmempaircEq) =>
% 121.84/16.10 ((
% 121.84/16.10 (cartprodfstpairEq) =>
% 121.84/16.10 ((
% 121.84/16.10 (cartprodsndpairEq) =>
% 121.84/16.10 ((
% 121.84/16.10 (cartprodpairsurjEq) =>
% 121.84/16.10 ((
% 121.84/16.10 (dpsetconstrI) =>
% 121.84/16.10 ((
% 121.84/16.10 (dpsetconstrSub) =>
% 121.84/16.10 ((
% 121.84/16.10 (setOfPairsIsBReln) =>
% 121.84/16.10 ((
% 121.84/16.10 (dpsetconstrERa) =>
% 121.84/16.10 ((
% 121.84/16.10 (dpsetconstrEL1) =>
% 121.84/16.10 ((
% 121.84/16.10 (dpsetconstrEL2) =>
% 121.84/16.10 ((
% 121.84/16.10 (dpsetconstrER) =>
% 121.84/16.10 ((
% 121.84/16.10 (funcImageSingleton) =>
% 121.84/16.10 ((
% 121.84/16.10 (apProp) =>
% 121.84/16.10 ((
% 121.84/16.10 (app) =>
% 121.84/16.10 ((
% 121.84/16.10 (infuncsetfunc) =>
% 121.84/16.10 ((
% 121.84/16.10 (ap2p) =>
% 121.84/16.10 ((
% 121.84/16.10 (funcinfuncset) =>
% 121.84/16.10 ((
% 121.84/16.10 (lamProp) =>
% 121.84/16.10 ((
% 121.84/16.10 (lamp) =>
% 121.84/16.10 ((
% 121.84/16.10 (lam2p) =>
% 121.84/16.10 ((
% 121.84/16.10 (brelnall1) =>
% 121.84/16.10 ((
% 121.84/16.10 (brelnall2) =>
% 121.84/16.10 ((
% 121.84/16.10 (ex1E2) =>
% 121.84/16.10 ((
% 121.84/16.10 (funcGraphProp1) =>
% 121.84/16.10 ((
% 121.84/16.10 (funcGraphProp3) =>
% 121.84/16.10 ((
% 121.84/16.10 (funcGraphProp2) =>
% 121.84/16.10 ((
% 121.84/16.10 (funcextLem) =>
% 121.84/16.10 ((
% 121.84/16.10 (funcGraphProp4) =>
% 121.84/16.10 ((
% 121.84/16.10 (subbreln) =>
% 121.84/16.10 ((
% 121.84/16.10 (eqbreln) =>
% 121.84/16.10 ((
% 121.84/16.10 (funcext) =>
% 121.84/16.10 ((
% 121.84/16.10 (funcext2) =>
% 121.84/16.10 ((
% 121.84/16.10 (ap2apEq1) =>
% 121.84/16.10 ((
% 121.84/16.10 (ap2apEq2) =>
% 121.84/16.10 ((
% 121.84/16.10 (beta1) =>
% 121.84/16.10 ((
% 121.84/16.10 (eta1) =>
% 121.84/16.10 ((
% 121.84/16.10 (lam2lamEq) =>
% 121.84/16.10 ((
% 121.84/16.10 (beta2) =>
% 121.84/16.10 ((
% 121.84/16.10 (eta2) =>
% 121.84/16.10 ((
% 121.84/16.10 (iffalseProp1) =>
% 121.84/16.10 ((
% 121.84/16.10 (iffalseProp2) =>
% 121.84/16.10 ((
% 121.84/16.10 (iftrueProp1) =>
% 121.84/16.10 ((
% 121.84/16.10 (iftrueProp2) =>
% 121.84/16.10 ((
% 121.84/16.10 (ifSingleton) =>
% 121.84/16.10 ((
% 121.84/16.10 (ifp) =>
% 121.84/16.10 ((
% 121.84/16.10 (theeq) =>
% 121.84/16.10 ((
% 121.84/16.10 (iftrue) =>
% 121.84/16.10 ((
% 121.84/16.10 (iffalse) =>
% 121.84/16.10 ((
% 121.84/16.10 (iftrueorfalse) =>
% 121.84/16.10 ((
% 121.84/16.10 (binintersectT_lem) =>
% 121.84/16.10 ((
% 121.84/16.10 (binunionT_lem) =>
% 121.84/16.10 ((
% 121.84/16.10 (powersetT_lem) =>
% 121.84/16.10 ((
% 121.84/16.10 (setminusT_lem) =>
% 121.84/16.10 ((
% 121.84/16.10 (complementT_lem) =>
% 121.84/16.10 ((
% 121.84/16.10 (setextT) =>
% 121.84/16.10 ((
% 121.84/16.10 (subsetTI) =>
% 121.84/16.10 ((
% 121.84/16.10 (powersetTI1) =>
% 121.84/16.10 ((
% 121.84/16.10 (powersetTE1) =>
% 121.84/16.10 ((
% 121.84/16.10 (complementTI1) =>
% 121.84/16.10 ((
% 121.84/16.10 (complementTE1) =>
% 121.84/16.10 ((
% 121.84/16.10 (binintersectTELcontra) =>
% 121.84/16.10 ((
% 121.84/16.10 (binintersectTERcontra) =>
% 121.84/16.10 ((
% 121.84/16.10 (contrasubsetT) =>
% 121.84/16.10 ((
% 121.84/16.10 (contrasubsetT1) =>
% 121.84/16.10 ((
% 121.84/16.10 (contrasubsetT2) =>
% 121.84/16.10 ((
% 121.84/16.10 (contrasubsetT3) =>
% 121.84/16.10 ((
% 121.84/16.10 (doubleComplementI1) =>
% 121.84/16.10 ((
% 121.84/16.10 (doubleComplementE1) =>
% 121.84/16.10 ((
% 121.84/16.10 (doubleComplementSub1) =>
% 121.84/16.10 ((
% 121.84/16.10 (doubleComplementSub2) =>
% 121.84/16.10 ((
% 121.84/16.10 (doubleComplementEq) =>
% 121.84/16.10 ((
% 121.84/16.10 (complementTnotintersectT) =>
% 121.84/16.10 ((
% 121.84/16.10 (complementImpComplementIntersect) =>
% 121.84/16.10 ((
% 121.84/16.10 (complementSubsetComplementIntersect) =>
% 121.84/16.10 ((
% 121.84/16.10 (complementInPowersetComplementIntersect) =>
% 121.84/16.10 ((
% 121.84/16.10 (contraSubsetComplement) =>
% 121.84/16.10 ((
% 121.84/16.10 (complementTcontraSubset) =>
% 121.84/16.10 ((
% 121.84/16.10 (binunionTILcontra) =>
% 121.84/16.10 ((
% 121.84/16.10 (binunionTIRcontra) =>
% 121.84/16.10 ((
% 121.84/16.10 (inIntersectImpInUnion) =>
% 121.84/16.10 ((
% 121.84/16.10 (inIntersectImpInUnion2) =>
% 121.84/16.10 ((
% 121.84/16.10 (inIntersectImpInIntersectUnions) =>
% 121.84/16.10 ((
% 121.84/16.10 (intersectInPowersetIntersectUnions) =>
% 121.84/16.10 ((
% 121.84/16.10 (inComplementUnionImpNotIn1) =>
% 121.84/16.10 ((
% 121.84/16.10 (inComplementUnionImpInComplement1) =>
% 121.84/16.10 ((
% 121.84/16.10 (binunionTE) =>
% 121.84/16.10 ((
% 121.84/16.10 (binunionTEcontra) =>
% 121.84/16.10 ((
% 121.84/16.10 (demorgan2a1) =>
% 121.84/16.10 ((
% 121.84/16.10 (complementUnionInPowersetComplement) =>
% 121.84/16.10 ((
% 121.84/16.10 (demorgan2a2) =>
% 121.84/16.10 ((
% 121.84/16.10 (demorgan1a) =>
% 121.84/16.10 ((
% 121.84/16.10 (demorgan1b) =>
% 121.84/16.10 ((
% 121.84/16.10 (demorgan1) =>
% 121.84/16.10 ((
% 121.84/16.10 (demorgan2a) =>
% 121.84/16.10 ((
% 121.84/16.10 (demorgan2b2) =>
% 121.84/16.10 ((
% 121.84/16.10 (demorgan2b) =>
% 121.84/16.10 ((
% 121.84/16.10 (demorgan2) =>
% 121.84/16.10 ((
% 121.84/16.10 (woz13rule0) =>
% 121.84/16.10 ((
% 121.84/16.10 (woz13rule1) =>
% 121.84/16.10 ((
% 121.84/16.10 (woz13rule2) =>
% 121.84/16.10 ((
% 121.84/16.10 (woz13rule3) =>
% 121.84/16.10 ((
% 121.84/16.10 (woz13rule4) =>
% 121.84/16.10 ((
% 121.84/16.10 (woz1_1) =>
% 121.84/16.10 ((
% 121.84/16.10 (woz1_2) =>
% 121.84/16.10 ((
% 121.84/16.10 (woz1_3) =>
% 121.84/16.10 ((
% 121.84/16.10 (woz1_4) =>
% 121.84/16.10 ((
% 121.84/16.10 (woz1_5) =>
% 121.84/16.10 ((
% 121.84/16.10 (breln1all2) =>
% 121.84/16.10 ((
% 121.84/16.10 (breln1SetBreln1) =>
% 121.84/16.10 ((
% 121.84/16.10 (choice2fnsingleton) =>
% 121.84/16.10 ((
% 121.84/16.10 (setOfPairsIsBReln1) =>
% 121.84/16.10 ((
% 121.84/16.10 (breln1all1) =>
% 121.84/16.10 ((
% 121.84/16.10 (subbreln1) =>
% 121.84/16.10 ((
% 121.84/16.10 (eqbreln1) =>
% 121.84/16.10 ((
% 121.84/16.10 (breln1invprop) =>
% 121.84/16.10 ((
% 121.84/16.10 (breln1invI) =>
% 121.84/16.10 ((
% 121.84/16.10 (breln1invE) =>
% 121.84/16.10 ((
% 121.84/16.10 (breln1compprop) =>
% 121.84/16.10 ((
% 121.84/16.10 (breln1compI) =>
% 121.84/16.10 ((
% 121.84/16.10 (breln1compE) =>
% 121.84/16.10 ((
% 121.84/16.10 (breln1compEex) =>
% 121.84/16.10 ((
% 121.84/16.10 (breln1unionprop) =>
% 121.84/16.10 ((
% 121.84/16.10 (breln1unionIL) =>
% 121.84/16.10 ((
% 121.84/16.10 (breln1unionIR) =>
% 121.84/16.10 ((
% 121.84/16.10 (breln1unionI) =>
% 121.84/16.10 ((
% 121.84/16.10 (breln1unionE) =>
% 121.84/16.10 ((
% 121.84/16.10 (breln1unionEcases) =>
% 121.84/16.10 ((
% 121.84/16.10 (breln1unionCommutes) =>
% 121.84/16.10 ((
% 121.84/16.10 (woz2Ex) =>
% 121.84/16.10 ((
% 121.84/16.10 (woz2W) =>
% 121.84/16.10 ((
% 121.84/16.10 (woz2A) =>
% 121.84/16.10 ((
% 121.84/16.10 (woz2B) =>
% 121.84/16.10 ((
% 121.84/16.10 (image1Ex) =>
% 121.84/16.10 ((
% 121.84/16.10 (image1Ex1) =>
% 121.84/16.10 ((
% 121.84/16.10 (image1Equiv) =>
% 121.84/16.10 ((
% 121.84/16.10 (image1E) =>
% 121.84/16.10 ((
% 121.84/16.10 (image1I) =>
% 121.84/16.10 ((
% 121.84/16.10 (injFuncInInjFuncSet) =>
% 121.84/16.10 ((
% 121.84/16.10 (!!) @ (
% 121.84/16.10 (('#B') @ (
% 121.84/16.10 !!) @
% 121.84/16.10 (
% 121.84/16.10 (
% 121.84/16.10 ('#B') @ (
% 121.84/16.10 (
% 121.84/16.10 ('#B') @ (
% 121.84/16.10 !!))) @
% 121.84/16.10 (
% 121.84/16.10 (
% 121.84/16.10 ('#S') @ (
% 121.84/16.10 (
% 121.84/16.10 ('#B') @ (
% 121.84/16.10 '#S') @
% 121.84/16.10 (
% 121.84/16.10 (
% 121.84/16.10 ('#B') @ (
% 121.84/16.10 (
% 121.84/16.10 ('#B') @ (
% 121.84/16.10 '#S'))) @
% 121.84/16.10 (
% 121.84/16.10 (
% 121.84/16.10 ('#B') @ (
% 121.84/16.10 (
% 121.84/16.10 ('#B') @ (
% 121.84/16.10 (
% 121.84/16.10 ('#B') @ (
% 121.84/16.10 =>))))) @
% 121.84/16.10 (
% 121.84/16.10 (
% 121.84/16.10 ('#B') @ (
% 121.84/16.10 (
% 121.84/16.10 ('#B') @ (
% 121.84/16.10 (
% 121.84/16.10 ('#C') @ in)))) @
% 121.84/16.10 injFuncSet)))))))) @
% 121.84/16.10 (
% 121.84/16.10 (
% 121.84/16.10 ('#B') @ (
% 121.84/16.10 (
% 121.84/16.10 ('#B') @ (
% 121.84/16.10 (
% 121.84/16.10 ('#C') @ in)))) @
% 121.84/16.10 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 121.84/16.10 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl769])).
% 121.84/16.10 thf(zip_derived_cl807, plain,
% 121.84/16.10 (~ (((eqimpsubset2) =>
% 121.84/16.10 (((eqimpsubset1) =>
% 121.84/16.10 (((subsetI2) =>
% 121.84/16.10 (((emptysetsubset) =>
% 121.84/16.10 (((subsetE) =>
% 121.84/16.10 (((subsetE2) =>
% 121.84/16.10 (((notsubsetI) =>
% 121.84/16.10 (((notequalI1) =>
% 121.84/16.10 (((notequalI2) =>
% 121.84/16.10 (((subsetRefl) =>
% 121.84/16.10 (((subsetTrans) =>
% 121.84/16.10 (((setadjoinSub) =>
% 121.84/16.10 (((setadjoinSub2) =>
% 121.84/16.10 (((subset2powerset) =>
% 121.84/16.10 (((setextsub) =>
% 121.84/16.10 (((subsetemptysetimpeq) =>
% 121.84/16.10 (((powersetI1) =>
% 121.84/16.10 (((powersetE1) =>
% 121.84/16.10 (((inPowerset) =>
% 121.84/16.10 (((powersetsubset) =>
% 121.84/16.10 (((sepInPowerset) =>
% 121.84/16.10 (((sepSubset) =>
% 121.84/16.10 (((binunionIL) =>
% 121.84/16.10 (((upairset2IR) =>
% 121.84/16.10 (((binunionIR) =>
% 121.84/16.10 (((binunionEcases) =>
% 121.84/16.10 (((binunionE) =>
% 121.84/16.10 (((binunionLsub) =>
% 121.84/16.10 (((binunionRsub) =>
% 121.84/16.10 (((binintersectI) =>
% 121.84/16.10 ((
% 121.84/16.10 (binintersectSubset5) =>
% 121.84/16.10 ((
% 121.84/16.10 (binintersectEL) =>
% 121.84/16.10 ((
% 121.84/16.10 (binintersectLsub) =>
% 121.84/16.10 ((
% 121.84/16.10 (binintersectSubset2) =>
% 121.84/16.10 ((
% 121.84/16.10 (binintersectSubset3) =>
% 121.84/16.10 ((
% 121.84/16.10 (binintersectER) =>
% 121.84/16.10 ((
% 121.84/16.10 (disjointsetsI1) =>
% 121.84/16.10 ((
% 121.84/16.10 (binintersectRsub) =>
% 121.84/16.10 ((
% 121.84/16.10 (binintersectSubset4) =>
% 121.84/16.10 ((
% 121.84/16.10 (binintersectSubset1) =>
% 121.84/16.10 ((
% 121.84/16.10 (bs114d) =>
% 121.84/16.10 ((
% 121.84/16.10 (setminusI) =>
% 121.84/16.10 ((
% 121.84/16.10 (setminusEL) =>
% 121.84/16.10 ((
% 121.84/16.10 (setminusER) =>
% 121.84/16.10 ((
% 121.84/16.10 (setminusSubset2) =>
% 121.84/16.10 ((
% 121.84/16.10 (setminusERneg) =>
% 121.84/16.10 ((
% 121.84/16.10 (setminusELneg) =>
% 121.84/16.10 ((
% 121.84/16.10 (setminusILneg) =>
% 121.84/16.10 ((
% 121.84/16.10 (setminusIRneg) =>
% 121.84/16.10 ((
% 121.84/16.10 (setminusLsub) =>
% 121.84/16.10 ((
% 121.84/16.10 (setminusSubset1) =>
% 121.84/16.10 ((
% 121.84/16.10 (symdiffE) =>
% 121.84/16.10 ((
% 121.84/16.10 (symdiffI1) =>
% 121.84/16.10 ((
% 121.84/16.10 (symdiffI2) =>
% 121.84/16.10 ((
% 121.84/16.10 (symdiffIneg1) =>
% 121.84/16.10 ((
% 121.84/16.10 (symdiffIneg2) =>
% 121.84/16.10 ((
% 121.84/16.10 (secondinupair) =>
% 121.84/16.10 ((
% 121.84/16.10 (setukpairIL) =>
% 121.84/16.10 ((
% 121.84/16.10 (setukpairIR) =>
% 121.84/16.10 ((
% 121.84/16.10 (kpairiskpair) =>
% 121.84/16.10 ((
% 121.84/16.10 (kpairp) =>
% 121.84/16.10 ((
% 121.84/16.10 (singletonsubset) =>
% 121.84/16.10 ((
% 121.84/16.10 (singletoninpowerset) =>
% 121.84/16.10 ((
% 121.84/16.10 (singletoninpowunion) =>
% 121.84/16.10 ((
% 121.84/16.10 (upairset2E) =>
% 121.84/16.10 ((
% 121.84/16.10 (upairsubunion) =>
% 121.84/16.10 ((
% 121.84/16.10 (upairinpowunion) =>
% 121.84/16.10 ((
% 121.84/16.10 (ubforcartprodlem1) =>
% 121.84/16.10 ((
% 121.84/16.10 (ubforcartprodlem2) =>
% 121.84/16.10 ((
% 121.84/16.10 (ubforcartprodlem3) =>
% 121.84/16.10 ((
% 121.84/16.10 (cartprodpairin) =>
% 121.84/16.10 ((
% 121.84/16.10 (cartprodmempair1) =>
% 121.84/16.10 ((
% 121.84/16.10 (cartprodmempair) =>
% 121.84/16.10 ((
% 121.84/16.10 (setunionE2) =>
% 121.84/16.10 ((
% 121.84/16.10 (setunionsingleton1) =>
% 121.84/16.10 ((
% 121.84/16.10 (setunionsingleton2) =>
% 121.84/16.10 ((
% 121.84/16.10 (setunionsingleton) =>
% 121.84/16.10 ((
% 121.84/16.10 (singletonprop) =>
% 121.84/16.10 ((
% 121.84/16.10 (ex1E1) =>
% 121.84/16.10 ((
% 121.84/16.10 (ex1I) =>
% 121.84/16.10 ((
% 121.84/16.10 (ex1I2) =>
% 121.84/16.10 ((
% 121.84/16.10 (singletonsuniq) =>
% 121.84/16.10 ((
% 121.84/16.10 (setukpairinjL1) =>
% 121.84/16.10 ((
% 121.84/16.10 (kfstsingleton) =>
% 121.84/16.10 ((
% 121.84/16.10 (theprop) =>
% 121.84/16.10 ((
% 121.84/16.10 (kfstpairEq) =>
% 121.84/16.10 ((
% 121.84/16.10 (cartprodfstin) =>
% 121.84/16.10 ((
% 121.84/16.10 (setukpairinjL2) =>
% 121.84/16.10 ((
% 121.84/16.10 (setukpairinjL) =>
% 121.84/16.10 ((
% 121.84/16.10 (setukpairinjR11) =>
% 121.84/16.10 ((
% 121.84/16.10 (setukpairinjR12) =>
% 121.84/16.10 ((
% 121.84/16.10 (setukpairinjR1) =>
% 121.84/16.10 ((
% 121.84/16.10 (upairequniteq) =>
% 121.84/16.10 ((
% 121.84/16.10 (setukpairinjR2) =>
% 121.84/16.10 ((
% 121.84/16.10 (setukpairinjR) =>
% 121.84/16.10 ((
% 121.84/16.10 (ksndsingleton) =>
% 121.84/16.10 ((
% 121.84/16.10 (ksndpairEq) =>
% 121.84/16.10 ((
% 121.84/16.10 (kpairsurjEq) =>
% 121.84/16.10 ((
% 121.84/16.10 (cartprodsndin) =>
% 121.84/16.10 ((
% 121.84/16.10 (cartprodpairmemEL) =>
% 121.84/16.10 ((
% 121.84/16.10 (cartprodpairmemER) =>
% 121.84/16.10 ((
% 121.84/16.10 (cartprodmempaircEq) =>
% 121.84/16.10 ((
% 121.84/16.10 (cartprodfstpairEq) =>
% 121.84/16.10 ((
% 121.84/16.10 (cartprodsndpairEq) =>
% 121.84/16.10 ((
% 121.84/16.10 (cartprodpairsurjEq) =>
% 121.84/16.10 ((
% 121.84/16.10 (dpsetconstrI) =>
% 121.84/16.10 ((
% 121.84/16.10 (dpsetconstrSub) =>
% 121.84/16.10 ((
% 121.84/16.10 (setOfPairsIsBReln) =>
% 121.84/16.10 ((
% 121.84/16.10 (dpsetconstrERa) =>
% 121.84/16.10 ((
% 121.84/16.10 (dpsetconstrEL1) =>
% 121.84/16.10 ((
% 121.84/16.10 (dpsetconstrEL2) =>
% 121.84/16.10 ((
% 121.84/16.10 (dpsetconstrER) =>
% 121.84/16.10 ((
% 121.84/16.10 (funcImageSingleton) =>
% 121.84/16.10 ((
% 121.84/16.10 (apProp) =>
% 121.84/16.10 ((
% 121.84/16.10 (app) =>
% 121.84/16.10 ((
% 121.84/16.10 (infuncsetfunc) =>
% 121.84/16.10 ((
% 121.84/16.10 (ap2p) =>
% 121.84/16.10 ((
% 121.84/16.10 (funcinfuncset) =>
% 121.84/16.10 ((
% 121.84/16.10 (lamProp) =>
% 121.84/16.10 ((
% 121.84/16.10 (lamp) =>
% 121.84/16.10 ((
% 121.84/16.10 (lam2p) =>
% 121.84/16.10 ((
% 121.84/16.10 (brelnall1) =>
% 121.84/16.10 ((
% 121.84/16.10 (brelnall2) =>
% 121.84/16.10 ((
% 121.84/16.10 (ex1E2) =>
% 121.84/16.10 ((
% 121.84/16.10 (funcGraphProp1) =>
% 121.84/16.10 ((
% 121.84/16.10 (funcGraphProp3) =>
% 121.84/16.10 ((
% 121.84/16.10 (funcGraphProp2) =>
% 121.84/16.10 ((
% 121.84/16.10 (funcextLem) =>
% 121.84/16.10 ((
% 121.84/16.10 (funcGraphProp4) =>
% 121.84/16.10 ((
% 121.84/16.10 (subbreln) =>
% 121.84/16.10 ((
% 121.84/16.10 (eqbreln) =>
% 121.84/16.10 ((
% 121.84/16.10 (funcext) =>
% 121.84/16.10 ((
% 121.84/16.10 (funcext2) =>
% 121.84/16.10 ((
% 121.84/16.10 (ap2apEq1) =>
% 121.84/16.10 ((
% 121.84/16.10 (ap2apEq2) =>
% 121.84/16.10 ((
% 121.84/16.10 (beta1) =>
% 121.84/16.10 ((
% 121.84/16.10 (eta1) =>
% 121.84/16.10 ((
% 121.84/16.10 (lam2lamEq) =>
% 121.84/16.10 ((
% 121.84/16.10 (beta2) =>
% 121.84/16.10 ((
% 121.84/16.10 (eta2) =>
% 121.84/16.10 ((
% 121.84/16.10 (iffalseProp1) =>
% 121.84/16.10 ((
% 121.84/16.10 (iffalseProp2) =>
% 121.84/16.10 ((
% 121.84/16.10 (iftrueProp1) =>
% 121.84/16.10 ((
% 121.84/16.10 (iftrueProp2) =>
% 121.84/16.10 ((
% 121.84/16.10 (ifSingleton) =>
% 121.84/16.10 ((
% 121.84/16.10 (ifp) =>
% 121.84/16.10 ((
% 121.84/16.10 (theeq) =>
% 121.84/16.10 ((
% 121.84/16.10 (iftrue) =>
% 121.84/16.10 ((
% 121.84/16.10 (iffalse) =>
% 121.84/16.10 ((
% 121.84/16.10 (iftrueorfalse) =>
% 121.84/16.10 ((
% 121.84/16.10 (binintersectT_lem) =>
% 121.84/16.10 ((
% 121.84/16.10 (binunionT_lem) =>
% 121.84/16.10 ((
% 121.84/16.10 (powersetT_lem) =>
% 121.84/16.10 ((
% 121.84/16.10 (setminusT_lem) =>
% 121.84/16.10 ((
% 121.84/16.10 (complementT_lem) =>
% 121.84/16.10 ((
% 121.84/16.10 (setextT) =>
% 121.84/16.10 ((
% 121.84/16.10 (subsetTI) =>
% 121.84/16.10 ((
% 121.84/16.10 (powersetTI1) =>
% 121.84/16.10 ((
% 121.84/16.10 (powersetTE1) =>
% 121.84/16.10 ((
% 121.84/16.10 (complementTI1) =>
% 121.84/16.10 ((
% 121.84/16.10 (complementTE1) =>
% 121.84/16.10 ((
% 121.84/16.10 (binintersectTELcontra) =>
% 121.84/16.10 ((
% 121.84/16.10 (binintersectTERcontra) =>
% 121.84/16.10 ((
% 121.84/16.10 (contrasubsetT) =>
% 121.84/16.10 ((
% 121.84/16.10 (contrasubsetT1) =>
% 121.84/16.10 ((
% 121.84/16.10 (contrasubsetT2) =>
% 121.84/16.10 ((
% 121.84/16.10 (contrasubsetT3) =>
% 121.84/16.10 ((
% 121.84/16.10 (doubleComplementI1) =>
% 121.84/16.10 ((
% 121.84/16.10 (doubleComplementE1) =>
% 121.84/16.10 ((
% 121.84/16.10 (doubleComplementSub1) =>
% 121.84/16.10 ((
% 121.84/16.10 (doubleComplementSub2) =>
% 121.84/16.10 ((
% 121.84/16.10 (doubleComplementEq) =>
% 121.84/16.10 ((
% 121.84/16.10 (complementTnotintersectT) =>
% 121.84/16.10 ((
% 121.84/16.10 (complementImpComplementIntersect) =>
% 121.84/16.10 ((
% 121.84/16.10 (complementSubsetComplementIntersect) =>
% 121.84/16.10 ((
% 121.84/16.10 (complementInPowersetComplementIntersect) =>
% 121.84/16.10 ((
% 121.84/16.10 (contraSubsetComplement) =>
% 121.84/16.10 ((
% 121.84/16.10 (complementTcontraSubset) =>
% 121.84/16.10 ((
% 121.84/16.10 (binunionTILcontra) =>
% 121.84/16.10 ((
% 121.84/16.10 (binunionTIRcontra) =>
% 121.84/16.10 ((
% 121.84/16.10 (inIntersectImpInUnion) =>
% 121.84/16.10 ((
% 121.84/16.10 (inIntersectImpInUnion2) =>
% 121.84/16.10 ((
% 121.84/16.10 (inIntersectImpInIntersectUnions) =>
% 121.84/16.10 ((
% 121.84/16.10 (intersectInPowersetIntersectUnions) =>
% 121.84/16.10 ((
% 121.84/16.10 (inComplementUnionImpNotIn1) =>
% 121.84/16.10 ((
% 121.84/16.10 (inComplementUnionImpInComplement1) =>
% 121.84/16.10 ((
% 121.84/16.10 (binunionTE) =>
% 121.84/16.10 ((
% 121.84/16.10 (binunionTEcontra) =>
% 121.84/16.10 ((
% 121.84/16.10 (demorgan2a1) =>
% 121.84/16.10 ((
% 121.84/16.10 (complementUnionInPowersetComplement) =>
% 121.84/16.10 ((
% 121.84/16.10 (demorgan2a2) =>
% 121.84/16.10 ((
% 121.84/16.10 (demorgan1a) =>
% 121.84/16.10 ((
% 121.84/16.10 (demorgan1b) =>
% 121.84/16.10 ((
% 121.84/16.10 (demorgan1) =>
% 121.84/16.10 ((
% 121.84/16.10 (demorgan2a) =>
% 121.84/16.10 ((
% 121.84/16.10 (demorgan2b2) =>
% 121.84/16.10 ((
% 121.84/16.10 (demorgan2b) =>
% 121.84/16.10 ((
% 121.84/16.10 (demorgan2) =>
% 121.84/16.10 ((
% 121.84/16.10 (woz13rule0) =>
% 121.84/16.10 ((
% 121.84/16.10 (woz13rule1) =>
% 121.84/16.10 ((
% 121.84/16.10 (woz13rule2) =>
% 121.84/16.10 ((
% 121.84/16.10 (woz13rule3) =>
% 121.84/16.10 ((
% 121.84/16.10 (woz13rule4) =>
% 121.84/16.10 ((
% 121.84/16.10 (woz1_1) =>
% 121.84/16.10 ((
% 121.84/16.10 (woz1_2) =>
% 121.84/16.10 ((
% 121.84/16.10 (woz1_3) =>
% 121.84/16.10 ((
% 121.84/16.10 (woz1_4) =>
% 121.84/16.10 ((
% 121.84/16.10 (woz1_5) =>
% 121.84/16.10 ((
% 121.84/16.10 (breln1all2) =>
% 121.84/16.10 ((
% 121.84/16.10 (breln1SetBreln1) =>
% 121.84/16.10 ((
% 121.84/16.10 (choice2fnsingleton) =>
% 121.84/16.10 ((
% 121.84/16.10 (setOfPairsIsBReln1) =>
% 121.84/16.10 ((
% 121.84/16.10 (breln1all1) =>
% 121.84/16.10 ((
% 121.84/16.10 (subbreln1) =>
% 121.84/16.10 ((
% 121.84/16.10 (eqbreln1) =>
% 121.84/16.10 ((
% 121.84/16.10 (breln1invprop) =>
% 121.84/16.10 ((
% 121.84/16.10 (breln1invI) =>
% 121.84/16.10 ((
% 121.84/16.10 (breln1invE) =>
% 121.84/16.10 ((
% 121.84/16.10 (breln1compprop) =>
% 121.84/16.10 ((
% 121.84/16.10 (breln1compI) =>
% 121.84/16.10 ((
% 121.84/16.10 (breln1compE) =>
% 121.84/16.10 ((
% 121.84/16.10 (breln1compEex) =>
% 121.84/16.10 ((
% 121.84/16.10 (breln1unionprop) =>
% 121.84/16.10 ((
% 121.84/16.10 (breln1unionIL) =>
% 121.84/16.10 ((
% 121.84/16.10 (breln1unionIR) =>
% 121.84/16.10 ((
% 121.84/16.10 (breln1unionI) =>
% 121.84/16.10 ((
% 121.84/16.10 (breln1unionE) =>
% 121.84/16.10 ((
% 121.84/16.10 (breln1unionEcases) =>
% 121.84/16.10 ((
% 121.84/16.10 (breln1unionCommutes) =>
% 121.84/16.10 ((
% 121.84/16.10 (woz2Ex) =>
% 121.84/16.10 ((
% 121.84/16.10 (woz2W) =>
% 121.84/16.10 ((
% 121.84/16.10 (woz2A) =>
% 121.84/16.10 ((
% 121.84/16.10 (woz2B) =>
% 121.84/16.10 ((
% 121.84/16.10 (image1Ex) =>
% 121.84/16.10 ((
% 121.84/16.10 (image1Ex1) =>
% 121.84/16.10 ((
% 121.84/16.10 (image1Equiv) =>
% 121.84/16.10 ((
% 121.84/16.10 (image1E) =>
% 121.84/16.10 ((
% 121.84/16.10 (image1I) =>
% 121.84/16.10 ((
% 121.84/16.10 (injFuncInInjFuncSet) =>
% 121.84/16.10 ((
% 121.84/16.10 (!!) @ (
% 121.84/16.10 (('#B') @ (
% 121.84/16.10 !!) @
% 121.84/16.10 (
% 121.84/16.10 (
% 121.84/16.10 ('#B') @ (
% 121.84/16.10 (
% 121.84/16.10 ('#B') @ (
% 121.84/16.10 !!))) @
% 121.84/16.10 (
% 121.84/16.10 (
% 121.84/16.10 ('#S') @ (
% 121.84/16.10 (
% 121.84/16.10 ('#B') @ (
% 121.84/16.10 '#S') @
% 121.84/16.10 (
% 121.84/16.10 (
% 121.84/16.10 ('#B') @ (
% 121.84/16.10 (
% 121.84/16.10 ('#B') @ (
% 121.84/16.10 '#S'))) @
% 121.84/16.10 (
% 121.84/16.10 (
% 121.84/16.10 ('#B') @ (
% 121.84/16.10 (
% 121.84/16.10 ('#B') @ (
% 121.84/16.10 (
% 121.84/16.10 ('#B') @ (
% 121.84/16.10 =>))))) @
% 121.84/16.10 (
% 121.84/16.10 (
% 121.84/16.10 ('#B') @ (
% 121.84/16.10 (
% 121.84/16.10 ('#B') @ (
% 121.84/16.10 (
% 121.84/16.10 ('#C') @ in)))) @
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% 121.84/16.10 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl789])).
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% 121.84/16.10 ((
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% 121.84/16.10 ((
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% 121.84/16.10 ((
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% 121.84/16.10 ((
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% 121.84/16.10 ((
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% 121.84/16.10 ((
% 121.84/16.10 (singletoninpowunion) =>
% 121.84/16.10 ((
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% 121.84/16.10 ((
% 121.84/16.10 (upairsubunion) =>
% 121.84/16.10 ((
% 121.84/16.10 (upairinpowunion) =>
% 121.84/16.10 ((
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% 121.84/16.10 ((
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% 121.84/16.10 ((
% 121.84/16.10 (ubforcartprodlem3) =>
% 121.84/16.10 ((
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% 121.84/16.10 ((
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% 121.84/16.10 ((
% 121.84/16.10 (cartprodmempair) =>
% 121.84/16.10 ((
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% 121.84/16.10 ((
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% 121.84/16.10 ((
% 121.84/16.10 (setunionsingleton2) =>
% 121.84/16.10 ((
% 121.84/16.10 (setunionsingleton) =>
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% 121.84/16.10 ((
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% 121.84/16.10 ((
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% 121.84/16.10 ((
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% 121.84/16.10 ((
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% 121.84/16.10 ((
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% 121.84/16.10 ((
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% 121.84/16.10 ((
% 121.84/16.10 (theprop) =>
% 121.84/16.10 ((
% 121.84/16.10 (kfstpairEq) =>
% 121.84/16.10 ((
% 121.84/16.10 (cartprodfstin) =>
% 121.84/16.10 ((
% 121.84/16.10 (setukpairinjL2) =>
% 121.84/16.10 ((
% 121.84/16.10 (setukpairinjL) =>
% 121.84/16.10 ((
% 121.84/16.10 (setukpairinjR11) =>
% 121.84/16.10 ((
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% 121.84/16.10 ((
% 121.84/16.10 (setukpairinjR1) =>
% 121.84/16.10 ((
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% 121.84/16.10 ((
% 121.84/16.10 (setukpairinjR2) =>
% 121.84/16.10 ((
% 121.84/16.10 (setukpairinjR) =>
% 121.84/16.10 ((
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% 121.84/16.10 ((
% 121.84/16.10 (ksndpairEq) =>
% 121.84/16.10 ((
% 121.84/16.10 (kpairsurjEq) =>
% 121.84/16.10 ((
% 121.84/16.10 (cartprodsndin) =>
% 121.84/16.10 ((
% 121.84/16.10 (cartprodpairmemEL) =>
% 121.84/16.10 ((
% 121.84/16.10 (cartprodpairmemER) =>
% 121.84/16.10 ((
% 121.84/16.10 (cartprodmempaircEq) =>
% 121.84/16.10 ((
% 121.84/16.10 (cartprodfstpairEq) =>
% 121.84/16.10 ((
% 121.84/16.10 (cartprodsndpairEq) =>
% 121.84/16.10 ((
% 121.84/16.10 (cartprodpairsurjEq) =>
% 121.84/16.10 ((
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% 121.84/16.10 ((
% 121.84/16.10 (dpsetconstrSub) =>
% 121.84/16.10 ((
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% 121.84/16.10 ((
% 121.84/16.10 (dpsetconstrERa) =>
% 121.84/16.10 ((
% 121.84/16.10 (dpsetconstrEL1) =>
% 121.84/16.10 ((
% 121.84/16.10 (dpsetconstrEL2) =>
% 121.84/16.10 ((
% 121.84/16.10 (dpsetconstrER) =>
% 121.84/16.10 ((
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% 121.84/16.10 ((
% 121.84/16.10 (apProp) =>
% 121.84/16.10 ((
% 121.84/16.10 (app) =>
% 121.84/16.10 ((
% 121.84/16.10 (infuncsetfunc) =>
% 121.84/16.10 ((
% 121.84/16.10 (ap2p) =>
% 121.84/16.10 ((
% 121.84/16.10 (funcinfuncset) =>
% 121.84/16.10 ((
% 121.84/16.10 (lamProp) =>
% 121.84/16.10 ((
% 121.84/16.10 (lamp) =>
% 121.84/16.10 ((
% 121.84/16.10 (lam2p) =>
% 121.84/16.10 ((
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% 121.84/16.10 ((
% 121.84/16.10 (brelnall2) =>
% 121.84/16.10 ((
% 121.84/16.10 (ex1E2) =>
% 121.84/16.10 ((
% 121.84/16.10 (funcGraphProp1) =>
% 121.84/16.10 ((
% 121.84/16.10 (funcGraphProp3) =>
% 121.84/16.10 ((
% 121.84/16.10 (funcGraphProp2) =>
% 121.84/16.10 ((
% 121.84/16.10 (funcextLem) =>
% 121.84/16.10 ((
% 121.84/16.10 (funcGraphProp4) =>
% 121.84/16.10 ((
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% 121.84/16.10 ((
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% 121.84/16.10 ((
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% 121.84/16.10 ((
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% 121.84/16.10 ((
% 121.84/16.10 (eta1) =>
% 121.84/16.10 ((
% 121.84/16.10 (lam2lamEq) =>
% 121.84/16.10 ((
% 121.84/16.10 (beta2) =>
% 121.84/16.10 ((
% 121.84/16.10 (eta2) =>
% 121.84/16.10 ((
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% 121.84/16.10 ((
% 121.84/16.10 (iffalseProp2) =>
% 121.84/16.10 ((
% 121.84/16.10 (iftrueProp1) =>
% 121.84/16.10 ((
% 121.84/16.10 (iftrueProp2) =>
% 121.84/16.10 ((
% 121.84/16.10 (ifSingleton) =>
% 121.84/16.10 ((
% 121.84/16.10 (ifp) =>
% 121.84/16.10 ((
% 121.84/16.10 (theeq) =>
% 121.84/16.10 ((
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% 121.84/16.10 ((
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% 121.84/16.10 ((
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% 121.84/16.10 ((
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% 121.84/16.10 ((
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% 121.84/16.10 ((
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% 121.84/16.10 ((
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% 121.84/16.10 ((
% 121.84/16.10 (doubleComplementSub1) =>
% 121.84/16.10 ((
% 121.84/16.10 (doubleComplementSub2) =>
% 121.84/16.10 ((
% 121.84/16.10 (doubleComplementEq) =>
% 121.84/16.10 ((
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% 121.84/16.10 ((
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% 121.84/16.10 ((
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% 121.84/16.10 ((
% 121.84/16.10 (complementInPowersetComplementIntersect) =>
% 121.84/16.10 ((
% 121.84/16.10 (contraSubsetComplement) =>
% 121.84/16.10 ((
% 121.84/16.10 (complementTcontraSubset) =>
% 121.84/16.10 ((
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% 121.84/16.10 ((
% 121.84/16.10 (binunionTIRcontra) =>
% 121.84/16.10 ((
% 121.84/16.10 (inIntersectImpInUnion) =>
% 121.84/16.10 ((
% 121.84/16.10 (inIntersectImpInUnion2) =>
% 121.84/16.10 ((
% 121.84/16.10 (inIntersectImpInIntersectUnions) =>
% 121.84/16.10 ((
% 121.84/16.10 (intersectInPowersetIntersectUnions) =>
% 121.84/16.10 ((
% 121.84/16.10 (inComplementUnionImpNotIn1) =>
% 121.84/16.10 ((
% 121.84/16.10 (inComplementUnionImpInComplement1) =>
% 121.84/16.10 ((
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% 121.84/16.10 ((
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% 121.84/16.10 ((
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% 121.84/16.10 ((
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% 121.84/16.10 ((
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% 121.84/16.10 ((
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% 121.84/16.10 ((
% 121.84/16.10 (demorgan1b) =>
% 121.84/16.10 ((
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% 121.84/16.10 ((
% 121.84/16.10 (demorgan2a) =>
% 121.84/16.10 ((
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% 121.84/16.10 ((
% 121.84/16.10 (demorgan2b) =>
% 121.84/16.10 ((
% 121.84/16.10 (demorgan2) =>
% 121.84/16.10 ((
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% 121.84/16.10 ((
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% 121.84/16.10 ((
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% 121.84/16.10 ((
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% 121.84/16.10 ((
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% 121.84/16.10 ((
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% 121.84/16.10 ((
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% 121.84/16.10 ((
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% 121.84/16.10 ((
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% 121.84/16.10 ((
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% 121.84/16.10 ((
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% 121.84/16.10 ((
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% 121.84/16.10 ((
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% 121.84/16.10 ((
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% 121.84/16.10 ((
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% 121.84/16.10 ((
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% 121.84/16.10 ((
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% 121.84/16.10 ((
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% 121.84/16.10 ((
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% 121.84/16.10 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl807])).
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% 121.84/16.10 (binintersectLsub) =>
% 121.84/16.10 ((
% 121.84/16.10 (binintersectSubset2) =>
% 121.84/16.10 ((
% 121.84/16.10 (binintersectSubset3) =>
% 121.84/16.10 ((
% 121.84/16.10 (binintersectER) =>
% 121.84/16.10 ((
% 121.84/16.10 (disjointsetsI1) =>
% 121.84/16.10 ((
% 121.84/16.10 (binintersectRsub) =>
% 121.84/16.10 ((
% 121.84/16.10 (binintersectSubset4) =>
% 121.84/16.10 ((
% 121.84/16.10 (binintersectSubset1) =>
% 121.84/16.10 ((
% 121.84/16.10 (bs114d) =>
% 121.84/16.10 ((
% 121.84/16.10 (setminusI) =>
% 121.84/16.10 ((
% 121.84/16.10 (setminusEL) =>
% 121.84/16.10 ((
% 121.84/16.10 (setminusER) =>
% 121.84/16.10 ((
% 121.84/16.10 (setminusSubset2) =>
% 121.84/16.10 ((
% 121.84/16.10 (setminusERneg) =>
% 121.84/16.10 ((
% 121.84/16.10 (setminusELneg) =>
% 121.84/16.10 ((
% 121.84/16.10 (setminusILneg) =>
% 121.84/16.10 ((
% 121.84/16.10 (setminusIRneg) =>
% 121.84/16.10 ((
% 121.84/16.10 (setminusLsub) =>
% 121.84/16.10 ((
% 121.84/16.10 (setminusSubset1) =>
% 121.84/16.10 ((
% 121.84/16.10 (symdiffE) =>
% 121.84/16.10 ((
% 121.84/16.10 (symdiffI1) =>
% 121.84/16.10 ((
% 121.84/16.10 (symdiffI2) =>
% 121.84/16.10 ((
% 121.84/16.10 (symdiffIneg1) =>
% 121.84/16.10 ((
% 121.84/16.10 (symdiffIneg2) =>
% 121.84/16.10 ((
% 121.84/16.10 (secondinupair) =>
% 121.84/16.10 ((
% 121.84/16.10 (setukpairIL) =>
% 121.84/16.10 ((
% 121.84/16.10 (setukpairIR) =>
% 121.84/16.10 ((
% 121.84/16.10 (kpairiskpair) =>
% 121.84/16.10 ((
% 121.84/16.10 (kpairp) =>
% 121.84/16.10 ((
% 121.84/16.10 (singletonsubset) =>
% 121.84/16.10 ((
% 121.84/16.10 (singletoninpowerset) =>
% 121.84/16.10 ((
% 121.84/16.10 (singletoninpowunion) =>
% 121.84/16.10 ((
% 121.84/16.10 (upairset2E) =>
% 121.84/16.10 ((
% 121.84/16.10 (upairsubunion) =>
% 121.84/16.10 ((
% 121.84/16.10 (upairinpowunion) =>
% 121.84/16.10 ((
% 121.84/16.10 (ubforcartprodlem1) =>
% 121.84/16.10 ((
% 121.84/16.10 (ubforcartprodlem2) =>
% 121.84/16.10 ((
% 121.84/16.10 (ubforcartprodlem3) =>
% 121.84/16.10 ((
% 121.84/16.10 (cartprodpairin) =>
% 121.84/16.10 ((
% 121.84/16.10 (cartprodmempair1) =>
% 121.84/16.10 ((
% 121.84/16.10 (cartprodmempair) =>
% 121.84/16.10 ((
% 121.84/16.10 (setunionE2) =>
% 121.84/16.10 ((
% 121.84/16.10 (setunionsingleton1) =>
% 121.84/16.10 ((
% 121.84/16.10 (setunionsingleton2) =>
% 121.84/16.10 ((
% 121.84/16.10 (setunionsingleton) =>
% 121.84/16.10 ((
% 121.84/16.10 (singletonprop) =>
% 121.84/16.10 ((
% 121.84/16.10 (ex1E1) =>
% 121.84/16.10 ((
% 121.84/16.10 (ex1I) =>
% 121.84/16.10 ((
% 121.84/16.10 (ex1I2) =>
% 121.84/16.10 ((
% 121.84/16.10 (singletonsuniq) =>
% 121.84/16.10 ((
% 121.84/16.10 (setukpairinjL1) =>
% 121.84/16.10 ((
% 121.84/16.10 (kfstsingleton) =>
% 121.84/16.10 ((
% 121.84/16.10 (theprop) =>
% 121.84/16.10 ((
% 121.84/16.10 (kfstpairEq) =>
% 121.84/16.10 ((
% 121.84/16.10 (cartprodfstin) =>
% 121.84/16.10 ((
% 121.84/16.10 (setukpairinjL2) =>
% 121.84/16.10 ((
% 121.84/16.10 (setukpairinjL) =>
% 121.84/16.10 ((
% 121.84/16.10 (setukpairinjR11) =>
% 121.84/16.10 ((
% 121.84/16.10 (setukpairinjR12) =>
% 121.84/16.10 ((
% 121.84/16.10 (setukpairinjR1) =>
% 121.84/16.10 ((
% 121.84/16.10 (upairequniteq) =>
% 121.84/16.10 ((
% 121.84/16.10 (setukpairinjR2) =>
% 121.84/16.10 ((
% 121.84/16.10 (setukpairinjR) =>
% 121.84/16.10 ((
% 121.84/16.10 (ksndsingleton) =>
% 121.84/16.10 ((
% 121.84/16.10 (ksndpairEq) =>
% 121.84/16.10 ((
% 121.84/16.10 (kpairsurjEq) =>
% 121.84/16.10 ((
% 121.84/16.10 (cartprodsndin) =>
% 121.84/16.10 ((
% 121.84/16.10 (cartprodpairmemEL) =>
% 121.84/16.10 ((
% 121.84/16.10 (cartprodpairmemER) =>
% 121.84/16.10 ((
% 121.84/16.10 (cartprodmempaircEq) =>
% 121.84/16.10 ((
% 121.84/16.10 (cartprodfstpairEq) =>
% 121.84/16.10 ((
% 121.84/16.10 (cartprodsndpairEq) =>
% 121.84/16.10 ((
% 121.84/16.10 (cartprodpairsurjEq) =>
% 121.84/16.10 ((
% 121.84/16.10 (dpsetconstrI) =>
% 121.84/16.10 ((
% 121.84/16.10 (dpsetconstrSub) =>
% 121.84/16.10 ((
% 121.84/16.10 (setOfPairsIsBReln) =>
% 121.84/16.10 ((
% 121.84/16.10 (dpsetconstrERa) =>
% 121.84/16.10 ((
% 121.84/16.10 (dpsetconstrEL1) =>
% 121.84/16.10 ((
% 121.84/16.10 (dpsetconstrEL2) =>
% 121.84/16.10 ((
% 121.84/16.10 (dpsetconstrER) =>
% 121.84/16.10 ((
% 121.84/16.10 (funcImageSingleton) =>
% 121.84/16.10 ((
% 121.84/16.10 (apProp) =>
% 121.84/16.10 ((
% 121.84/16.10 (app) =>
% 121.84/16.10 ((
% 121.84/16.10 (infuncsetfunc) =>
% 121.84/16.10 ((
% 121.84/16.10 (ap2p) =>
% 121.84/16.10 ((
% 121.84/16.10 (funcinfuncset) =>
% 121.84/16.10 ((
% 121.84/16.10 (lamProp) =>
% 121.84/16.10 ((
% 121.84/16.10 (lamp) =>
% 121.84/16.10 ((
% 121.84/16.10 (lam2p) =>
% 121.84/16.10 ((
% 121.84/16.10 (brelnall1) =>
% 121.84/16.10 ((
% 121.84/16.10 (brelnall2) =>
% 121.84/16.10 ((
% 121.84/16.10 (ex1E2) =>
% 121.84/16.10 ((
% 121.84/16.10 (funcGraphProp1) =>
% 121.84/16.10 ((
% 121.84/16.10 (funcGraphProp3) =>
% 121.84/16.10 ((
% 121.84/16.10 (funcGraphProp2) =>
% 121.84/16.10 ((
% 121.84/16.10 (funcextLem) =>
% 121.84/16.10 ((
% 121.84/16.10 (funcGraphProp4) =>
% 121.84/16.10 ((
% 121.84/16.10 (subbreln) =>
% 121.84/16.10 ((
% 121.84/16.10 (eqbreln) =>
% 121.84/16.10 ((
% 121.84/16.10 (funcext) =>
% 121.84/16.10 ((
% 121.84/16.10 (funcext2) =>
% 121.84/16.10 ((
% 121.84/16.10 (ap2apEq1) =>
% 121.84/16.10 ((
% 121.84/16.10 (ap2apEq2) =>
% 121.84/16.10 ((
% 121.84/16.10 (beta1) =>
% 121.84/16.10 ((
% 121.84/16.10 (eta1) =>
% 121.84/16.10 ((
% 121.84/16.10 (lam2lamEq) =>
% 121.84/16.10 ((
% 121.84/16.10 (beta2) =>
% 121.84/16.10 ((
% 121.84/16.10 (eta2) =>
% 121.84/16.10 ((
% 121.84/16.10 (iffalseProp1) =>
% 121.84/16.10 ((
% 121.84/16.10 (iffalseProp2) =>
% 121.84/16.10 ((
% 121.84/16.10 (iftrueProp1) =>
% 121.84/16.10 ((
% 121.84/16.10 (iftrueProp2) =>
% 121.84/16.10 ((
% 121.84/16.10 (ifSingleton) =>
% 121.84/16.10 ((
% 121.84/16.10 (ifp) =>
% 121.84/16.10 ((
% 121.84/16.10 (theeq) =>
% 121.84/16.10 ((
% 121.84/16.10 (iftrue) =>
% 121.84/16.10 ((
% 121.84/16.10 (iffalse) =>
% 121.84/16.10 ((
% 121.84/16.10 (iftrueorfalse) =>
% 121.84/16.10 ((
% 121.84/16.10 (binintersectT_lem) =>
% 121.84/16.10 ((
% 121.84/16.10 (binunionT_lem) =>
% 121.84/16.10 ((
% 121.84/16.10 (powersetT_lem) =>
% 121.84/16.10 ((
% 121.84/16.10 (setminusT_lem) =>
% 121.84/16.10 ((
% 121.84/16.10 (complementT_lem) =>
% 121.84/16.10 ((
% 121.84/16.10 (setextT) =>
% 121.84/16.10 ((
% 121.84/16.10 (subsetTI) =>
% 121.84/16.10 ((
% 121.84/16.10 (powersetTI1) =>
% 121.84/16.10 ((
% 121.84/16.10 (powersetTE1) =>
% 121.84/16.10 ((
% 121.84/16.10 (complementTI1) =>
% 121.84/16.10 ((
% 121.84/16.10 (complementTE1) =>
% 121.84/16.10 ((
% 121.84/16.10 (binintersectTELcontra) =>
% 121.84/16.10 ((
% 121.84/16.10 (binintersectTERcontra) =>
% 121.84/16.10 ((
% 121.84/16.10 (contrasubsetT) =>
% 121.84/16.10 ((
% 121.84/16.10 (contrasubsetT1) =>
% 121.84/16.10 ((
% 121.84/16.10 (contrasubsetT2) =>
% 121.84/16.10 ((
% 121.84/16.10 (contrasubsetT3) =>
% 121.84/16.10 ((
% 121.84/16.10 (doubleComplementI1) =>
% 121.84/16.10 ((
% 121.84/16.10 (doubleComplementE1) =>
% 121.84/16.10 ((
% 121.84/16.10 (doubleComplementSub1) =>
% 121.84/16.10 ((
% 121.84/16.10 (doubleComplementSub2) =>
% 121.84/16.10 ((
% 121.84/16.10 (doubleComplementEq) =>
% 121.84/16.10 ((
% 121.84/16.10 (complementTnotintersectT) =>
% 121.84/16.10 ((
% 121.84/16.10 (complementImpComplementIntersect) =>
% 121.84/16.10 ((
% 121.84/16.10 (complementSubsetComplementIntersect) =>
% 121.84/16.10 ((
% 121.84/16.10 (complementInPowersetComplementIntersect) =>
% 121.84/16.10 ((
% 121.84/16.10 (contraSubsetComplement) =>
% 121.84/16.10 ((
% 121.84/16.10 (complementTcontraSubset) =>
% 121.84/16.10 ((
% 121.84/16.10 (binunionTILcontra) =>
% 121.84/16.10 ((
% 121.84/16.10 (binunionTIRcontra) =>
% 121.84/16.10 ((
% 121.84/16.10 (inIntersectImpInUnion) =>
% 121.84/16.10 ((
% 121.84/16.10 (inIntersectImpInUnion2) =>
% 121.84/16.10 ((
% 121.84/16.10 (inIntersectImpInIntersectUnions) =>
% 121.84/16.10 ((
% 121.84/16.10 (intersectInPowersetIntersectUnions) =>
% 121.84/16.10 ((
% 121.84/16.10 (inComplementUnionImpNotIn1) =>
% 121.84/16.10 ((
% 121.84/16.10 (inComplementUnionImpInComplement1) =>
% 121.84/16.10 ((
% 121.84/16.10 (binunionTE) =>
% 121.84/16.10 ((
% 121.84/16.10 (binunionTEcontra) =>
% 121.84/16.10 ((
% 121.84/16.10 (demorgan2a1) =>
% 121.84/16.10 ((
% 121.84/16.10 (complementUnionInPowersetComplement) =>
% 121.84/16.10 ((
% 121.84/16.10 (demorgan2a2) =>
% 121.84/16.10 ((
% 121.84/16.10 (demorgan1a) =>
% 121.84/16.10 ((
% 121.84/16.10 (demorgan1b) =>
% 121.84/16.10 ((
% 121.84/16.10 (demorgan1) =>
% 121.84/16.10 ((
% 121.84/16.10 (demorgan2a) =>
% 121.84/16.10 ((
% 121.84/16.10 (demorgan2b2) =>
% 121.84/16.10 ((
% 121.84/16.10 (demorgan2b) =>
% 121.84/16.10 ((
% 121.84/16.10 (demorgan2) =>
% 121.84/16.10 ((
% 121.84/16.10 (woz13rule0) =>
% 121.84/16.10 ((
% 121.84/16.10 (woz13rule1) =>
% 121.84/16.10 ((
% 121.84/16.10 (woz13rule2) =>
% 121.84/16.10 ((
% 121.84/16.10 (woz13rule3) =>
% 121.84/16.10 ((
% 121.84/16.10 (woz13rule4) =>
% 121.84/16.10 ((
% 121.84/16.10 (woz1_1) =>
% 121.84/16.10 ((
% 121.84/16.10 (woz1_2) =>
% 121.84/16.10 ((
% 121.84/16.10 (woz1_3) =>
% 121.84/16.10 ((
% 121.84/16.10 (woz1_4) =>
% 121.84/16.10 ((
% 121.84/16.10 (woz1_5) =>
% 121.84/16.10 ((
% 121.84/16.10 (breln1all2) =>
% 121.84/16.10 ((
% 121.84/16.10 (breln1SetBreln1) =>
% 121.84/16.10 ((
% 121.84/16.10 (choice2fnsingleton) =>
% 121.84/16.10 ((
% 121.84/16.10 (setOfPairsIsBReln1) =>
% 121.84/16.10 ((
% 121.84/16.10 (breln1all1) =>
% 121.84/16.10 ((
% 121.84/16.10 (subbreln1) =>
% 121.84/16.10 ((
% 121.84/16.10 (eqbreln1) =>
% 121.84/16.10 ((
% 121.84/16.10 (breln1invprop) =>
% 121.84/16.10 ((
% 121.84/16.10 (breln1invI) =>
% 121.84/16.10 ((
% 121.84/16.10 (breln1invE) =>
% 121.84/16.10 ((
% 121.84/16.10 (breln1compprop) =>
% 121.84/16.10 ((
% 121.84/16.10 (breln1compI) =>
% 121.84/16.10 ((
% 121.84/16.10 (breln1compE) =>
% 121.84/16.10 ((
% 121.84/16.10 (breln1compEex) =>
% 121.84/16.10 ((
% 121.84/16.10 (breln1unionprop) =>
% 121.84/16.10 ((
% 121.84/16.10 (breln1unionIL) =>
% 121.84/16.10 ((
% 121.84/16.10 (breln1unionIR) =>
% 121.84/16.10 ((
% 121.84/16.10 (breln1unionI) =>
% 121.84/16.10 ((
% 121.84/16.10 (breln1unionE) =>
% 121.84/16.10 ((
% 121.84/16.10 (breln1unionEcases) =>
% 121.84/16.10 ((
% 121.84/16.10 (breln1unionCommutes) =>
% 121.84/16.10 ((
% 121.84/16.10 (woz2Ex) =>
% 121.84/16.10 ((
% 121.84/16.10 (woz2W) =>
% 121.84/16.10 ((
% 121.84/16.10 (woz2A) =>
% 121.84/16.10 ((
% 121.84/16.10 (woz2B) =>
% 121.84/16.10 ((
% 121.84/16.10 (image1Ex) =>
% 121.84/16.10 ((
% 121.84/16.10 (image1Ex1) =>
% 121.84/16.10 ((
% 121.84/16.10 (image1Equiv) =>
% 121.84/16.10 ((
% 121.84/16.10 (image1E) =>
% 121.84/16.10 ((
% 121.84/16.10 (image1I) =>
% 121.84/16.10 ((
% 121.84/16.10 (injFuncInInjFuncSet) =>
% 121.84/16.10 ((
% 121.84/16.10 (!!) @ (
% 121.84/16.10 (('#B') @ (
% 121.84/16.10 !!) @
% 121.84/16.10 (
% 121.84/16.10 (
% 121.84/16.10 ('#B') @ (
% 121.84/16.10 (
% 121.84/16.10 ('#B') @ (
% 121.84/16.10 !!))) @
% 121.84/16.10 (
% 121.84/16.10 (
% 121.84/16.10 ('#S') @ (
% 121.84/16.10 (
% 121.84/16.10 ('#B') @ (
% 121.84/16.10 '#S') @
% 121.84/16.10 (
% 121.84/16.10 (
% 121.84/16.10 ('#B') @ (
% 121.84/16.10 (
% 121.84/16.10 ('#B') @ (
% 121.84/16.10 '#S'))) @
% 121.84/16.10 (
% 121.84/16.10 (
% 121.84/16.10 ('#B') @ (
% 121.84/16.10 (
% 121.84/16.10 ('#B') @ (
% 121.84/16.10 (
% 121.84/16.10 ('#B') @ (
% 121.84/16.10 =>))))) @
% 121.84/16.10 (
% 121.84/16.10 (
% 121.84/16.10 ('#B') @ (
% 121.84/16.10 (
% 121.84/16.10 ('#B') @ (
% 121.84/16.10 (
% 121.84/16.10 ('#C') @ in)))) @
% 121.84/16.10 injFuncSet)))))))) @
% 121.84/16.10 (
% 121.84/16.10 (
% 121.84/16.10 ('#B') @ (
% 121.84/16.10 (
% 121.84/16.10 ('#B') @ (
% 121.84/16.10 (
% 121.84/16.10 ('#C') @ in)))) @
% 121.84/16.10 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 121.84/16.10 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl824])).
% 121.84/16.10 thf(zip_derived_cl850, plain,
% 121.84/16.10 (~ (((emptysetsubset) =>
% 121.84/16.10 (((subsetE) =>
% 121.84/16.10 (((subsetE2) =>
% 121.84/16.10 (((notsubsetI) =>
% 121.84/16.10 (((notequalI1) =>
% 121.84/16.10 (((notequalI2) =>
% 121.84/16.10 (((subsetRefl) =>
% 121.84/16.10 (((subsetTrans) =>
% 121.84/16.10 (((setadjoinSub) =>
% 121.84/16.10 (((setadjoinSub2) =>
% 121.84/16.10 (((subset2powerset) =>
% 121.84/16.10 (((setextsub) =>
% 121.84/16.10 (((subsetemptysetimpeq) =>
% 121.84/16.10 (((powersetI1) =>
% 121.84/16.10 (((powersetE1) =>
% 121.84/16.10 (((inPowerset) =>
% 121.84/16.10 (((powersetsubset) =>
% 121.84/16.10 (((sepInPowerset) =>
% 121.84/16.10 (((sepSubset) =>
% 121.84/16.10 (((binunionIL) =>
% 121.84/16.10 (((upairset2IR) =>
% 121.84/16.10 (((binunionIR) =>
% 121.84/16.10 (((binunionEcases) =>
% 121.84/16.10 (((binunionE) =>
% 121.84/16.10 (((binunionLsub) =>
% 121.84/16.10 (((binunionRsub) =>
% 121.84/16.10 (((binintersectI) =>
% 121.84/16.10 (((binintersectSubset5) =>
% 121.84/16.10 (((binintersectEL) =>
% 121.84/16.10 (((binintersectLsub) =>
% 121.84/16.10 ((
% 121.84/16.10 (binintersectSubset2) =>
% 121.84/16.10 ((
% 121.84/16.10 (binintersectSubset3) =>
% 121.84/16.10 ((
% 121.84/16.10 (binintersectER) =>
% 121.84/16.10 ((
% 121.84/16.10 (disjointsetsI1) =>
% 121.84/16.10 ((
% 121.84/16.10 (binintersectRsub) =>
% 121.84/16.10 ((
% 121.84/16.10 (binintersectSubset4) =>
% 121.84/16.10 ((
% 121.84/16.10 (binintersectSubset1) =>
% 121.84/16.10 ((
% 121.84/16.10 (bs114d) =>
% 121.84/16.10 ((
% 121.84/16.10 (setminusI) =>
% 121.84/16.10 ((
% 121.84/16.10 (setminusEL) =>
% 121.84/16.10 ((
% 121.84/16.10 (setminusER) =>
% 121.84/16.10 ((
% 121.84/16.10 (setminusSubset2) =>
% 121.84/16.10 ((
% 121.84/16.10 (setminusERneg) =>
% 121.84/16.10 ((
% 121.84/16.10 (setminusELneg) =>
% 121.84/16.10 ((
% 121.84/16.10 (setminusILneg) =>
% 121.84/16.10 ((
% 121.84/16.10 (setminusIRneg) =>
% 121.84/16.10 ((
% 121.84/16.10 (setminusLsub) =>
% 121.84/16.10 ((
% 121.84/16.10 (setminusSubset1) =>
% 121.84/16.10 ((
% 121.84/16.10 (symdiffE) =>
% 121.84/16.10 ((
% 121.84/16.10 (symdiffI1) =>
% 121.84/16.10 ((
% 121.84/16.10 (symdiffI2) =>
% 121.84/16.10 ((
% 121.84/16.10 (symdiffIneg1) =>
% 121.84/16.10 ((
% 121.84/16.10 (symdiffIneg2) =>
% 121.84/16.10 ((
% 121.84/16.10 (secondinupair) =>
% 121.84/16.10 ((
% 121.84/16.10 (setukpairIL) =>
% 121.84/16.10 ((
% 121.84/16.10 (setukpairIR) =>
% 121.84/16.10 ((
% 121.84/16.10 (kpairiskpair) =>
% 121.84/16.10 ((
% 121.84/16.10 (kpairp) =>
% 121.84/16.10 ((
% 121.84/16.10 (singletonsubset) =>
% 121.84/16.10 ((
% 121.84/16.10 (singletoninpowerset) =>
% 121.84/16.10 ((
% 121.84/16.10 (singletoninpowunion) =>
% 121.84/16.10 ((
% 121.84/16.10 (upairset2E) =>
% 121.84/16.10 ((
% 121.84/16.10 (upairsubunion) =>
% 121.84/16.10 ((
% 121.84/16.10 (upairinpowunion) =>
% 121.84/16.10 ((
% 121.84/16.10 (ubforcartprodlem1) =>
% 121.84/16.10 ((
% 121.84/16.10 (ubforcartprodlem2) =>
% 121.84/16.10 ((
% 121.84/16.10 (ubforcartprodlem3) =>
% 121.84/16.10 ((
% 121.84/16.10 (cartprodpairin) =>
% 121.84/16.10 ((
% 121.84/16.10 (cartprodmempair1) =>
% 121.84/16.10 ((
% 121.84/16.10 (cartprodmempair) =>
% 121.84/16.10 ((
% 121.84/16.10 (setunionE2) =>
% 121.84/16.10 ((
% 121.84/16.10 (setunionsingleton1) =>
% 121.84/16.10 ((
% 121.84/16.10 (setunionsingleton2) =>
% 121.84/16.10 ((
% 121.84/16.10 (setunionsingleton) =>
% 121.84/16.10 ((
% 121.84/16.10 (singletonprop) =>
% 121.84/16.10 ((
% 121.84/16.10 (ex1E1) =>
% 121.84/16.10 ((
% 121.84/16.10 (ex1I) =>
% 121.84/16.10 ((
% 121.84/16.10 (ex1I2) =>
% 121.84/16.10 ((
% 121.84/16.10 (singletonsuniq) =>
% 121.84/16.10 ((
% 121.84/16.10 (setukpairinjL1) =>
% 121.84/16.10 ((
% 121.84/16.10 (kfstsingleton) =>
% 121.84/16.10 ((
% 121.84/16.10 (theprop) =>
% 121.84/16.10 ((
% 121.84/16.10 (kfstpairEq) =>
% 121.84/16.10 ((
% 121.84/16.10 (cartprodfstin) =>
% 121.84/16.10 ((
% 121.84/16.10 (setukpairinjL2) =>
% 121.84/16.10 ((
% 121.84/16.10 (setukpairinjL) =>
% 121.84/16.10 ((
% 121.84/16.10 (setukpairinjR11) =>
% 121.84/16.10 ((
% 121.84/16.10 (setukpairinjR12) =>
% 121.84/16.10 ((
% 121.84/16.10 (setukpairinjR1) =>
% 121.84/16.10 ((
% 121.84/16.10 (upairequniteq) =>
% 121.84/16.10 ((
% 121.84/16.10 (setukpairinjR2) =>
% 121.84/16.10 ((
% 121.84/16.10 (setukpairinjR) =>
% 121.84/16.10 ((
% 121.84/16.10 (ksndsingleton) =>
% 121.84/16.10 ((
% 121.84/16.10 (ksndpairEq) =>
% 121.84/16.10 ((
% 121.84/16.10 (kpairsurjEq) =>
% 121.84/16.10 ((
% 121.84/16.10 (cartprodsndin) =>
% 121.84/16.10 ((
% 121.84/16.10 (cartprodpairmemEL) =>
% 121.84/16.10 ((
% 121.84/16.10 (cartprodpairmemER) =>
% 121.84/16.10 ((
% 121.84/16.10 (cartprodmempaircEq) =>
% 121.84/16.10 ((
% 121.84/16.10 (cartprodfstpairEq) =>
% 121.84/16.10 ((
% 121.84/16.10 (cartprodsndpairEq) =>
% 121.84/16.10 ((
% 121.84/16.10 (cartprodpairsurjEq) =>
% 121.84/16.10 ((
% 121.84/16.10 (dpsetconstrI) =>
% 121.84/16.10 ((
% 121.84/16.10 (dpsetconstrSub) =>
% 121.84/16.10 ((
% 121.84/16.10 (setOfPairsIsBReln) =>
% 121.84/16.10 ((
% 121.84/16.10 (dpsetconstrERa) =>
% 121.84/16.10 ((
% 121.84/16.10 (dpsetconstrEL1) =>
% 121.84/16.10 ((
% 121.84/16.10 (dpsetconstrEL2) =>
% 121.84/16.10 ((
% 121.84/16.10 (dpsetconstrER) =>
% 121.84/16.10 ((
% 121.84/16.10 (funcImageSingleton) =>
% 121.84/16.10 ((
% 121.84/16.10 (apProp) =>
% 121.84/16.10 ((
% 121.84/16.10 (app) =>
% 121.84/16.10 ((
% 121.84/16.10 (infuncsetfunc) =>
% 121.84/16.10 ((
% 121.84/16.10 (ap2p) =>
% 121.84/16.10 ((
% 121.84/16.10 (funcinfuncset) =>
% 121.84/16.10 ((
% 121.84/16.10 (lamProp) =>
% 121.84/16.10 ((
% 121.84/16.10 (lamp) =>
% 121.84/16.10 ((
% 121.84/16.10 (lam2p) =>
% 121.84/16.10 ((
% 121.84/16.10 (brelnall1) =>
% 121.84/16.10 ((
% 121.84/16.10 (brelnall2) =>
% 121.84/16.10 ((
% 121.84/16.10 (ex1E2) =>
% 121.84/16.10 ((
% 121.84/16.10 (funcGraphProp1) =>
% 121.84/16.10 ((
% 121.84/16.10 (funcGraphProp3) =>
% 121.84/16.10 ((
% 121.84/16.10 (funcGraphProp2) =>
% 121.84/16.10 ((
% 121.84/16.10 (funcextLem) =>
% 121.84/16.10 ((
% 121.84/16.10 (funcGraphProp4) =>
% 121.84/16.10 ((
% 121.84/16.10 (subbreln) =>
% 121.84/16.10 ((
% 121.84/16.10 (eqbreln) =>
% 121.84/16.10 ((
% 121.84/16.10 (funcext) =>
% 121.84/16.10 ((
% 121.84/16.10 (funcext2) =>
% 121.84/16.10 ((
% 121.84/16.10 (ap2apEq1) =>
% 121.84/16.10 ((
% 121.84/16.10 (ap2apEq2) =>
% 121.84/16.10 ((
% 121.84/16.10 (beta1) =>
% 121.84/16.10 ((
% 121.84/16.10 (eta1) =>
% 121.84/16.10 ((
% 121.84/16.10 (lam2lamEq) =>
% 121.84/16.10 ((
% 121.84/16.10 (beta2) =>
% 121.84/16.10 ((
% 121.84/16.10 (eta2) =>
% 121.84/16.10 ((
% 121.84/16.10 (iffalseProp1) =>
% 121.84/16.10 ((
% 121.84/16.10 (iffalseProp2) =>
% 121.84/16.10 ((
% 121.84/16.10 (iftrueProp1) =>
% 121.84/16.10 ((
% 121.84/16.10 (iftrueProp2) =>
% 121.84/16.10 ((
% 121.84/16.10 (ifSingleton) =>
% 121.84/16.10 ((
% 121.84/16.10 (ifp) =>
% 121.84/16.10 ((
% 121.84/16.10 (theeq) =>
% 121.84/16.10 ((
% 121.84/16.10 (iftrue) =>
% 121.84/16.10 ((
% 121.84/16.10 (iffalse) =>
% 121.84/16.10 ((
% 121.84/16.10 (iftrueorfalse) =>
% 121.84/16.10 ((
% 121.84/16.10 (binintersectT_lem) =>
% 121.84/16.10 ((
% 121.84/16.10 (binunionT_lem) =>
% 121.84/16.10 ((
% 121.84/16.10 (powersetT_lem) =>
% 121.84/16.10 ((
% 121.84/16.10 (setminusT_lem) =>
% 121.84/16.10 ((
% 121.84/16.10 (complementT_lem) =>
% 121.84/16.10 ((
% 121.84/16.10 (setextT) =>
% 121.84/16.10 ((
% 121.84/16.10 (subsetTI) =>
% 121.84/16.10 ((
% 121.84/16.10 (powersetTI1) =>
% 121.84/16.10 ((
% 121.84/16.10 (powersetTE1) =>
% 121.84/16.10 ((
% 121.84/16.10 (complementTI1) =>
% 121.84/16.10 ((
% 121.84/16.10 (complementTE1) =>
% 121.84/16.10 ((
% 121.84/16.10 (binintersectTELcontra) =>
% 121.84/16.10 ((
% 121.84/16.10 (binintersectTERcontra) =>
% 121.84/16.10 ((
% 121.84/16.10 (contrasubsetT) =>
% 121.84/16.10 ((
% 121.84/16.10 (contrasubsetT1) =>
% 121.84/16.10 ((
% 121.84/16.10 (contrasubsetT2) =>
% 121.84/16.10 ((
% 121.84/16.10 (contrasubsetT3) =>
% 121.84/16.10 ((
% 121.84/16.10 (doubleComplementI1) =>
% 121.84/16.10 ((
% 121.84/16.10 (doubleComplementE1) =>
% 121.84/16.10 ((
% 121.84/16.10 (doubleComplementSub1) =>
% 121.84/16.10 ((
% 121.84/16.10 (doubleComplementSub2) =>
% 121.84/16.10 ((
% 121.84/16.10 (doubleComplementEq) =>
% 121.84/16.10 ((
% 121.84/16.10 (complementTnotintersectT) =>
% 121.84/16.10 ((
% 121.84/16.10 (complementImpComplementIntersect) =>
% 121.84/16.10 ((
% 121.84/16.10 (complementSubsetComplementIntersect) =>
% 121.84/16.10 ((
% 121.84/16.10 (complementInPowersetComplementIntersect) =>
% 121.84/16.10 ((
% 121.84/16.10 (contraSubsetComplement) =>
% 121.84/16.10 ((
% 121.84/16.10 (complementTcontraSubset) =>
% 121.84/16.10 ((
% 121.84/16.10 (binunionTILcontra) =>
% 121.84/16.10 ((
% 121.84/16.10 (binunionTIRcontra) =>
% 121.84/16.10 ((
% 121.84/16.10 (inIntersectImpInUnion) =>
% 121.84/16.10 ((
% 121.84/16.10 (inIntersectImpInUnion2) =>
% 121.84/16.10 ((
% 121.84/16.10 (inIntersectImpInIntersectUnions) =>
% 121.84/16.10 ((
% 121.84/16.10 (intersectInPowersetIntersectUnions) =>
% 121.84/16.10 ((
% 121.84/16.10 (inComplementUnionImpNotIn1) =>
% 121.84/16.10 ((
% 121.84/16.10 (inComplementUnionImpInComplement1) =>
% 121.84/16.10 ((
% 121.84/16.10 (binunionTE) =>
% 121.84/16.10 ((
% 121.84/16.10 (binunionTEcontra) =>
% 121.84/16.10 ((
% 121.84/16.10 (demorgan2a1) =>
% 121.84/16.10 ((
% 121.84/16.10 (complementUnionInPowersetComplement) =>
% 121.84/16.10 ((
% 121.84/16.10 (demorgan2a2) =>
% 121.84/16.10 ((
% 121.84/16.10 (demorgan1a) =>
% 121.84/16.10 ((
% 121.84/16.10 (demorgan1b) =>
% 121.84/16.10 ((
% 121.84/16.10 (demorgan1) =>
% 121.84/16.10 ((
% 121.84/16.10 (demorgan2a) =>
% 121.84/16.10 ((
% 121.84/16.10 (demorgan2b2) =>
% 121.84/16.10 ((
% 121.84/16.10 (demorgan2b) =>
% 121.84/16.10 ((
% 121.84/16.10 (demorgan2) =>
% 121.84/16.10 ((
% 121.84/16.10 (woz13rule0) =>
% 121.84/16.10 ((
% 121.84/16.10 (woz13rule1) =>
% 121.84/16.10 ((
% 121.84/16.10 (woz13rule2) =>
% 121.84/16.10 ((
% 121.84/16.10 (woz13rule3) =>
% 121.84/16.10 ((
% 121.84/16.10 (woz13rule4) =>
% 121.84/16.10 ((
% 121.84/16.10 (woz1_1) =>
% 121.84/16.10 ((
% 121.84/16.10 (woz1_2) =>
% 121.84/16.10 ((
% 121.84/16.10 (woz1_3) =>
% 121.84/16.10 ((
% 121.84/16.10 (woz1_4) =>
% 121.84/16.10 ((
% 121.84/16.10 (woz1_5) =>
% 121.84/16.10 ((
% 121.84/16.10 (breln1all2) =>
% 121.84/16.10 ((
% 121.84/16.10 (breln1SetBreln1) =>
% 121.84/16.10 ((
% 121.84/16.10 (choice2fnsingleton) =>
% 121.84/16.10 ((
% 121.84/16.10 (setOfPairsIsBReln1) =>
% 121.84/16.10 ((
% 121.84/16.10 (breln1all1) =>
% 121.84/16.10 ((
% 121.84/16.10 (subbreln1) =>
% 121.84/16.10 ((
% 121.84/16.10 (eqbreln1) =>
% 121.84/16.10 ((
% 121.84/16.10 (breln1invprop) =>
% 121.84/16.10 ((
% 121.84/16.10 (breln1invI) =>
% 121.84/16.10 ((
% 121.84/16.10 (breln1invE) =>
% 121.84/16.10 ((
% 121.84/16.10 (breln1compprop) =>
% 121.84/16.10 ((
% 121.84/16.10 (breln1compI) =>
% 121.84/16.10 ((
% 121.84/16.10 (breln1compE) =>
% 121.84/16.10 ((
% 121.84/16.10 (breln1compEex) =>
% 121.84/16.10 ((
% 121.84/16.10 (breln1unionprop) =>
% 121.84/16.10 ((
% 121.84/16.10 (breln1unionIL) =>
% 121.84/16.10 ((
% 121.84/16.10 (breln1unionIR) =>
% 121.84/16.10 ((
% 121.84/16.10 (breln1unionI) =>
% 121.84/16.10 ((
% 121.84/16.10 (breln1unionE) =>
% 121.84/16.10 ((
% 121.84/16.10 (breln1unionEcases) =>
% 121.84/16.10 ((
% 121.84/16.10 (breln1unionCommutes) =>
% 121.84/16.10 ((
% 121.84/16.10 (woz2Ex) =>
% 121.84/16.10 ((
% 121.84/16.10 (woz2W) =>
% 121.84/16.10 ((
% 121.84/16.10 (woz2A) =>
% 121.84/16.10 ((
% 121.84/16.10 (woz2B) =>
% 121.84/16.10 ((
% 121.84/16.10 (image1Ex) =>
% 121.84/16.10 ((
% 121.84/16.10 (image1Ex1) =>
% 121.84/16.10 ((
% 121.84/16.10 (image1Equiv) =>
% 121.84/16.10 ((
% 121.84/16.10 (image1E) =>
% 121.84/16.10 ((
% 121.84/16.10 (image1I) =>
% 121.84/16.10 ((
% 121.84/16.10 (injFuncInInjFuncSet) =>
% 121.84/16.10 ((
% 121.84/16.10 (!!) @ (
% 121.84/16.10 (('#B') @ (
% 121.84/16.10 !!) @
% 121.84/16.10 (
% 121.84/16.10 (
% 121.84/16.10 ('#B') @ (
% 121.84/16.10 (
% 121.84/16.10 ('#B') @ (
% 121.84/16.10 !!))) @
% 121.84/16.10 (
% 121.84/16.10 (
% 121.84/16.10 ('#S') @ (
% 121.84/16.10 (
% 121.84/16.10 ('#B') @ (
% 121.84/16.10 '#S') @
% 121.84/16.10 (
% 121.84/16.10 (
% 121.84/16.10 ('#B') @ (
% 121.84/16.10 (
% 121.84/16.10 ('#B') @ (
% 121.84/16.10 '#S'))) @
% 121.84/16.10 (
% 121.84/16.10 (
% 121.84/16.10 ('#B') @ (
% 121.84/16.10 (
% 121.84/16.10 ('#B') @ (
% 121.84/16.10 (
% 121.84/16.10 ('#B') @ (
% 121.84/16.10 =>))))) @
% 121.84/16.10 (
% 121.84/16.10 (
% 121.84/16.10 ('#B') @ (
% 121.84/16.10 (
% 121.84/16.10 ('#B') @ (
% 121.84/16.10 (
% 121.84/16.10 ('#C') @ in)))) @
% 121.84/16.10 injFuncSet)))))))) @
% 121.84/16.10 (
% 121.84/16.10 (
% 121.84/16.10 ('#B') @ (
% 121.84/16.10 (
% 121.84/16.10 ('#B') @ (
% 121.84/16.10 (
% 121.84/16.10 ('#C') @ in)))) @
% 121.84/16.10 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 121.84/16.10 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl838])).
% 121.84/16.10 thf(zip_derived_cl863, plain,
% 121.84/16.10 (~ (((subsetE) =>
% 121.84/16.10 (((subsetE2) =>
% 121.84/16.10 (((notsubsetI) =>
% 121.84/16.10 (((notequalI1) =>
% 121.84/16.10 (((notequalI2) =>
% 121.84/16.10 (((subsetRefl) =>
% 121.84/16.10 (((subsetTrans) =>
% 121.84/16.10 (((setadjoinSub) =>
% 121.84/16.10 (((setadjoinSub2) =>
% 121.84/16.10 (((subset2powerset) =>
% 121.84/16.10 (((setextsub) =>
% 121.84/16.10 (((subsetemptysetimpeq) =>
% 121.84/16.10 (((powersetI1) =>
% 121.84/16.10 (((powersetE1) =>
% 121.84/16.10 (((inPowerset) =>
% 121.84/16.10 (((powersetsubset) =>
% 121.84/16.10 (((sepInPowerset) =>
% 121.84/16.10 (((sepSubset) =>
% 121.84/16.10 (((binunionIL) =>
% 121.84/16.10 (((upairset2IR) =>
% 121.84/16.10 (((binunionIR) =>
% 121.84/16.10 (((binunionEcases) =>
% 121.84/16.10 (((binunionE) =>
% 121.84/16.10 (((binunionLsub) =>
% 121.84/16.10 (((binunionRsub) =>
% 121.84/16.10 (((binintersectI) =>
% 121.84/16.10 (((binintersectSubset5) =>
% 121.84/16.10 (((binintersectEL) =>
% 121.84/16.10 (((binintersectLsub) =>
% 121.84/16.10 (((binintersectSubset2) =>
% 121.84/16.10 ((
% 121.84/16.10 (binintersectSubset3) =>
% 121.84/16.10 ((
% 121.84/16.10 (binintersectER) =>
% 121.84/16.10 ((
% 121.84/16.10 (disjointsetsI1) =>
% 121.84/16.10 ((
% 121.84/16.10 (binintersectRsub) =>
% 121.84/16.10 ((
% 121.84/16.10 (binintersectSubset4) =>
% 121.84/16.10 ((
% 121.84/16.10 (binintersectSubset1) =>
% 121.84/16.10 ((
% 121.84/16.10 (bs114d) =>
% 121.84/16.10 ((
% 121.84/16.10 (setminusI) =>
% 121.84/16.10 ((
% 121.84/16.10 (setminusEL) =>
% 121.84/16.10 ((
% 121.84/16.10 (setminusER) =>
% 121.84/16.10 ((
% 121.84/16.10 (setminusSubset2) =>
% 121.84/16.10 ((
% 121.84/16.10 (setminusERneg) =>
% 121.84/16.10 ((
% 121.84/16.10 (setminusELneg) =>
% 121.84/16.10 ((
% 121.84/16.10 (setminusILneg) =>
% 121.84/16.10 ((
% 121.84/16.10 (setminusIRneg) =>
% 121.84/16.10 ((
% 121.84/16.10 (setminusLsub) =>
% 121.84/16.10 ((
% 121.84/16.10 (setminusSubset1) =>
% 121.84/16.10 ((
% 121.84/16.10 (symdiffE) =>
% 121.84/16.10 ((
% 121.84/16.10 (symdiffI1) =>
% 121.84/16.10 ((
% 121.84/16.10 (symdiffI2) =>
% 121.84/16.10 ((
% 121.84/16.10 (symdiffIneg1) =>
% 121.84/16.10 ((
% 121.84/16.10 (symdiffIneg2) =>
% 121.84/16.10 ((
% 121.84/16.10 (secondinupair) =>
% 121.84/16.10 ((
% 121.84/16.10 (setukpairIL) =>
% 121.84/16.10 ((
% 121.84/16.10 (setukpairIR) =>
% 121.84/16.10 ((
% 121.84/16.10 (kpairiskpair) =>
% 121.84/16.10 ((
% 121.84/16.10 (kpairp) =>
% 121.84/16.10 ((
% 121.84/16.10 (singletonsubset) =>
% 121.84/16.10 ((
% 121.84/16.10 (singletoninpowerset) =>
% 121.84/16.10 ((
% 121.84/16.10 (singletoninpowunion) =>
% 121.84/16.10 ((
% 121.84/16.10 (upairset2E) =>
% 121.84/16.10 ((
% 121.84/16.10 (upairsubunion) =>
% 121.84/16.10 ((
% 121.84/16.10 (upairinpowunion) =>
% 121.84/16.10 ((
% 121.84/16.10 (ubforcartprodlem1) =>
% 121.84/16.10 ((
% 121.84/16.10 (ubforcartprodlem2) =>
% 121.84/16.10 ((
% 121.84/16.10 (ubforcartprodlem3) =>
% 121.84/16.10 ((
% 121.84/16.10 (cartprodpairin) =>
% 121.84/16.10 ((
% 121.84/16.10 (cartprodmempair1) =>
% 121.84/16.10 ((
% 121.84/16.10 (cartprodmempair) =>
% 121.84/16.10 ((
% 121.84/16.10 (setunionE2) =>
% 121.84/16.10 ((
% 121.84/16.10 (setunionsingleton1) =>
% 121.84/16.10 ((
% 121.84/16.10 (setunionsingleton2) =>
% 121.84/16.10 ((
% 121.84/16.10 (setunionsingleton) =>
% 121.84/16.10 ((
% 121.84/16.10 (singletonprop) =>
% 121.84/16.10 ((
% 121.84/16.10 (ex1E1) =>
% 121.84/16.10 ((
% 121.84/16.10 (ex1I) =>
% 121.84/16.10 ((
% 121.84/16.10 (ex1I2) =>
% 121.84/16.10 ((
% 121.84/16.10 (singletonsuniq) =>
% 121.84/16.10 ((
% 121.84/16.10 (setukpairinjL1) =>
% 121.84/16.10 ((
% 121.84/16.10 (kfstsingleton) =>
% 121.84/16.10 ((
% 121.84/16.10 (theprop) =>
% 121.84/16.10 ((
% 121.84/16.10 (kfstpairEq) =>
% 121.84/16.10 ((
% 121.84/16.10 (cartprodfstin) =>
% 121.84/16.10 ((
% 121.84/16.10 (setukpairinjL2) =>
% 121.84/16.10 ((
% 121.84/16.10 (setukpairinjL) =>
% 121.84/16.10 ((
% 121.84/16.10 (setukpairinjR11) =>
% 121.84/16.10 ((
% 121.84/16.10 (setukpairinjR12) =>
% 121.84/16.10 ((
% 121.84/16.10 (setukpairinjR1) =>
% 121.84/16.10 ((
% 121.84/16.10 (upairequniteq) =>
% 121.84/16.10 ((
% 121.84/16.10 (setukpairinjR2) =>
% 121.84/16.10 ((
% 121.84/16.10 (setukpairinjR) =>
% 121.84/16.10 ((
% 121.84/16.10 (ksndsingleton) =>
% 121.84/16.10 ((
% 121.84/16.10 (ksndpairEq) =>
% 121.84/16.10 ((
% 121.84/16.10 (kpairsurjEq) =>
% 121.84/16.10 ((
% 121.84/16.10 (cartprodsndin) =>
% 121.84/16.10 ((
% 121.84/16.10 (cartprodpairmemEL) =>
% 121.84/16.10 ((
% 121.84/16.10 (cartprodpairmemER) =>
% 121.84/16.10 ((
% 121.84/16.10 (cartprodmempaircEq) =>
% 121.84/16.10 ((
% 121.84/16.10 (cartprodfstpairEq) =>
% 121.84/16.10 ((
% 121.84/16.10 (cartprodsndpairEq) =>
% 121.84/16.10 ((
% 121.84/16.10 (cartprodpairsurjEq) =>
% 121.84/16.10 ((
% 121.84/16.10 (dpsetconstrI) =>
% 121.84/16.10 ((
% 121.84/16.10 (dpsetconstrSub) =>
% 121.84/16.10 ((
% 121.84/16.10 (setOfPairsIsBReln) =>
% 121.84/16.10 ((
% 121.84/16.10 (dpsetconstrERa) =>
% 121.84/16.10 ((
% 121.84/16.10 (dpsetconstrEL1) =>
% 121.84/16.10 ((
% 121.84/16.10 (dpsetconstrEL2) =>
% 121.84/16.10 ((
% 121.84/16.10 (dpsetconstrER) =>
% 121.84/16.10 ((
% 121.84/16.10 (funcImageSingleton) =>
% 121.84/16.10 ((
% 121.84/16.10 (apProp) =>
% 121.84/16.10 ((
% 121.84/16.10 (app) =>
% 121.84/16.10 ((
% 121.84/16.10 (infuncsetfunc) =>
% 121.84/16.10 ((
% 121.84/16.10 (ap2p) =>
% 121.84/16.10 ((
% 121.84/16.10 (funcinfuncset) =>
% 121.84/16.10 ((
% 121.84/16.10 (lamProp) =>
% 121.84/16.10 ((
% 121.84/16.10 (lamp) =>
% 121.84/16.10 ((
% 121.84/16.10 (lam2p) =>
% 121.84/16.10 ((
% 121.84/16.10 (brelnall1) =>
% 121.84/16.10 ((
% 121.84/16.10 (brelnall2) =>
% 121.84/16.10 ((
% 121.84/16.10 (ex1E2) =>
% 121.84/16.10 ((
% 121.84/16.10 (funcGraphProp1) =>
% 121.84/16.10 ((
% 121.84/16.10 (funcGraphProp3) =>
% 121.84/16.10 ((
% 121.84/16.10 (funcGraphProp2) =>
% 121.84/16.10 ((
% 121.84/16.10 (funcextLem) =>
% 121.84/16.10 ((
% 121.84/16.10 (funcGraphProp4) =>
% 121.84/16.10 ((
% 121.84/16.10 (subbreln) =>
% 121.84/16.10 ((
% 121.84/16.10 (eqbreln) =>
% 121.84/16.10 ((
% 121.84/16.10 (funcext) =>
% 121.84/16.10 ((
% 121.84/16.10 (funcext2) =>
% 121.84/16.10 ((
% 121.84/16.10 (ap2apEq1) =>
% 121.84/16.10 ((
% 121.84/16.10 (ap2apEq2) =>
% 121.84/16.10 ((
% 121.84/16.10 (beta1) =>
% 121.84/16.10 ((
% 121.84/16.10 (eta1) =>
% 121.84/16.10 ((
% 121.84/16.10 (lam2lamEq) =>
% 121.84/16.10 ((
% 121.84/16.10 (beta2) =>
% 121.84/16.10 ((
% 121.84/16.10 (eta2) =>
% 121.84/16.10 ((
% 121.84/16.10 (iffalseProp1) =>
% 121.84/16.10 ((
% 121.84/16.10 (iffalseProp2) =>
% 121.84/16.10 ((
% 121.84/16.10 (iftrueProp1) =>
% 121.84/16.10 ((
% 121.84/16.10 (iftrueProp2) =>
% 121.84/16.10 ((
% 121.84/16.10 (ifSingleton) =>
% 121.84/16.10 ((
% 121.84/16.10 (ifp) =>
% 121.84/16.10 ((
% 121.84/16.10 (theeq) =>
% 121.84/16.10 ((
% 121.84/16.10 (iftrue) =>
% 121.84/16.10 ((
% 121.84/16.10 (iffalse) =>
% 121.84/16.10 ((
% 121.84/16.10 (iftrueorfalse) =>
% 121.84/16.10 ((
% 121.84/16.10 (binintersectT_lem) =>
% 121.84/16.10 ((
% 121.84/16.10 (binunionT_lem) =>
% 121.84/16.10 ((
% 121.84/16.10 (powersetT_lem) =>
% 121.84/16.10 ((
% 121.84/16.10 (setminusT_lem) =>
% 121.84/16.10 ((
% 121.84/16.10 (complementT_lem) =>
% 121.84/16.10 ((
% 121.84/16.10 (setextT) =>
% 121.84/16.10 ((
% 121.84/16.10 (subsetTI) =>
% 121.84/16.10 ((
% 121.84/16.10 (powersetTI1) =>
% 121.84/16.10 ((
% 121.84/16.10 (powersetTE1) =>
% 121.84/16.10 ((
% 121.84/16.10 (complementTI1) =>
% 121.84/16.10 ((
% 121.84/16.10 (complementTE1) =>
% 121.84/16.10 ((
% 121.84/16.10 (binintersectTELcontra) =>
% 121.84/16.10 ((
% 121.84/16.10 (binintersectTERcontra) =>
% 121.84/16.10 ((
% 121.84/16.10 (contrasubsetT) =>
% 121.84/16.10 ((
% 121.84/16.10 (contrasubsetT1) =>
% 121.84/16.10 ((
% 121.84/16.10 (contrasubsetT2) =>
% 121.84/16.10 ((
% 121.84/16.10 (contrasubsetT3) =>
% 121.84/16.10 ((
% 121.84/16.10 (doubleComplementI1) =>
% 121.84/16.10 ((
% 121.84/16.10 (doubleComplementE1) =>
% 121.84/16.10 ((
% 121.84/16.10 (doubleComplementSub1) =>
% 121.84/16.10 ((
% 121.84/16.10 (doubleComplementSub2) =>
% 121.84/16.10 ((
% 121.84/16.10 (doubleComplementEq) =>
% 121.84/16.10 ((
% 121.84/16.10 (complementTnotintersectT) =>
% 121.84/16.10 ((
% 121.84/16.10 (complementImpComplementIntersect) =>
% 121.84/16.10 ((
% 121.84/16.10 (complementSubsetComplementIntersect) =>
% 121.84/16.10 ((
% 121.84/16.10 (complementInPowersetComplementIntersect) =>
% 121.84/16.10 ((
% 121.84/16.10 (contraSubsetComplement) =>
% 121.84/16.10 ((
% 121.84/16.10 (complementTcontraSubset) =>
% 121.84/16.10 ((
% 121.84/16.10 (binunionTILcontra) =>
% 121.84/16.10 ((
% 121.84/16.10 (binunionTIRcontra) =>
% 121.84/16.10 ((
% 121.84/16.10 (inIntersectImpInUnion) =>
% 121.84/16.10 ((
% 121.84/16.10 (inIntersectImpInUnion2) =>
% 121.84/16.10 ((
% 121.84/16.10 (inIntersectImpInIntersectUnions) =>
% 121.84/16.10 ((
% 121.84/16.10 (intersectInPowersetIntersectUnions) =>
% 121.84/16.10 ((
% 121.84/16.10 (inComplementUnionImpNotIn1) =>
% 121.84/16.10 ((
% 121.84/16.10 (inComplementUnionImpInComplement1) =>
% 121.84/16.10 ((
% 121.84/16.10 (binunionTE) =>
% 121.84/16.10 ((
% 121.84/16.10 (binunionTEcontra) =>
% 121.84/16.10 ((
% 121.84/16.10 (demorgan2a1) =>
% 121.84/16.10 ((
% 121.84/16.10 (complementUnionInPowersetComplement) =>
% 121.84/16.10 ((
% 121.84/16.10 (demorgan2a2) =>
% 121.84/16.10 ((
% 121.84/16.10 (demorgan1a) =>
% 121.84/16.10 ((
% 121.84/16.10 (demorgan1b) =>
% 121.84/16.10 ((
% 121.84/16.10 (demorgan1) =>
% 121.84/16.10 ((
% 121.84/16.10 (demorgan2a) =>
% 121.84/16.10 ((
% 121.84/16.10 (demorgan2b2) =>
% 121.84/16.10 ((
% 121.84/16.10 (demorgan2b) =>
% 121.84/16.10 ((
% 121.84/16.10 (demorgan2) =>
% 121.84/16.10 ((
% 121.84/16.10 (woz13rule0) =>
% 121.84/16.10 ((
% 121.84/16.10 (woz13rule1) =>
% 121.84/16.10 ((
% 121.84/16.10 (woz13rule2) =>
% 121.84/16.10 ((
% 121.84/16.10 (woz13rule3) =>
% 121.84/16.10 ((
% 121.84/16.10 (woz13rule4) =>
% 121.84/16.10 ((
% 121.84/16.10 (woz1_1) =>
% 121.84/16.10 ((
% 121.84/16.10 (woz1_2) =>
% 121.84/16.10 ((
% 121.84/16.10 (woz1_3) =>
% 121.84/16.10 ((
% 121.84/16.10 (woz1_4) =>
% 121.84/16.10 ((
% 121.84/16.10 (woz1_5) =>
% 121.84/16.10 ((
% 121.84/16.10 (breln1all2) =>
% 121.84/16.10 ((
% 121.84/16.10 (breln1SetBreln1) =>
% 121.84/16.10 ((
% 121.84/16.10 (choice2fnsingleton) =>
% 121.84/16.10 ((
% 121.84/16.10 (setOfPairsIsBReln1) =>
% 121.84/16.10 ((
% 121.84/16.10 (breln1all1) =>
% 121.84/16.10 ((
% 121.84/16.10 (subbreln1) =>
% 121.84/16.10 ((
% 121.84/16.10 (eqbreln1) =>
% 121.84/16.10 ((
% 121.84/16.10 (breln1invprop) =>
% 121.84/16.10 ((
% 121.84/16.10 (breln1invI) =>
% 121.84/16.10 ((
% 121.84/16.10 (breln1invE) =>
% 121.84/16.10 ((
% 121.84/16.10 (breln1compprop) =>
% 121.84/16.10 ((
% 121.84/16.10 (breln1compI) =>
% 121.84/16.10 ((
% 121.84/16.10 (breln1compE) =>
% 121.84/16.10 ((
% 121.84/16.10 (breln1compEex) =>
% 121.84/16.10 ((
% 121.84/16.10 (breln1unionprop) =>
% 121.84/16.10 ((
% 121.84/16.10 (breln1unionIL) =>
% 121.84/16.10 ((
% 121.84/16.10 (breln1unionIR) =>
% 121.84/16.10 ((
% 121.84/16.10 (breln1unionI) =>
% 121.84/16.10 ((
% 121.84/16.10 (breln1unionE) =>
% 121.84/16.10 ((
% 121.84/16.10 (breln1unionEcases) =>
% 121.84/16.10 ((
% 121.84/16.10 (breln1unionCommutes) =>
% 121.84/16.10 ((
% 121.84/16.10 (woz2Ex) =>
% 121.84/16.10 ((
% 121.84/16.10 (woz2W) =>
% 121.84/16.10 ((
% 121.84/16.10 (woz2A) =>
% 121.84/16.10 ((
% 121.84/16.10 (woz2B) =>
% 121.84/16.10 ((
% 121.84/16.10 (image1Ex) =>
% 121.84/16.10 ((
% 121.84/16.10 (image1Ex1) =>
% 121.84/16.10 ((
% 121.84/16.10 (image1Equiv) =>
% 121.84/16.10 ((
% 121.84/16.10 (image1E) =>
% 121.84/16.10 ((
% 121.84/16.10 (image1I) =>
% 121.84/16.10 ((
% 121.84/16.10 (injFuncInInjFuncSet) =>
% 121.84/16.10 ((
% 121.84/16.10 (!!) @ (
% 121.84/16.10 (('#B') @ (
% 121.84/16.10 !!) @
% 121.84/16.10 (
% 121.84/16.10 (
% 121.84/16.10 ('#B') @ (
% 121.84/16.10 (
% 121.84/16.10 ('#B') @ (
% 121.84/16.10 !!))) @
% 121.84/16.10 (
% 121.84/16.10 (
% 121.84/16.10 ('#S') @ (
% 121.84/16.10 (
% 121.84/16.10 ('#B') @ (
% 121.84/16.10 '#S') @
% 121.84/16.10 (
% 121.84/16.10 (
% 121.84/16.10 ('#B') @ (
% 121.84/16.10 (
% 121.84/16.10 ('#B') @ (
% 121.84/16.10 '#S'))) @
% 121.84/16.10 (
% 121.84/16.10 (
% 121.84/16.10 ('#B') @ (
% 121.84/16.10 (
% 121.84/16.10 ('#B') @ (
% 121.84/16.10 (
% 121.84/16.10 ('#B') @ (
% 121.84/16.10 =>))))) @
% 121.84/16.10 (
% 121.84/16.10 (
% 121.84/16.10 ('#B') @ (
% 121.84/16.10 (
% 121.84/16.10 ('#B') @ (
% 121.84/16.10 (
% 121.84/16.10 ('#C') @ in)))) @
% 121.84/16.10 injFuncSet)))))))) @
% 121.84/16.10 (
% 121.84/16.10 (
% 121.84/16.10 ('#B') @ (
% 121.84/16.10 (
% 121.84/16.10 ('#B') @ (
% 121.84/16.10 (
% 121.84/16.10 ('#C') @ in)))) @
% 121.84/16.10 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 121.84/16.10 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl850])).
% 121.84/16.10 thf(zip_derived_cl878, plain,
% 121.84/16.10 (~ (((subsetE2) =>
% 121.84/16.10 (((notsubsetI) =>
% 121.84/16.10 (((notequalI1) =>
% 121.84/16.10 (((notequalI2) =>
% 121.84/16.10 (((subsetRefl) =>
% 121.84/16.10 (((subsetTrans) =>
% 121.84/16.10 (((setadjoinSub) =>
% 121.84/16.10 (((setadjoinSub2) =>
% 121.84/16.10 (((subset2powerset) =>
% 121.84/16.10 (((setextsub) =>
% 121.84/16.10 (((subsetemptysetimpeq) =>
% 121.84/16.10 (((powersetI1) =>
% 121.84/16.10 (((powersetE1) =>
% 121.84/16.10 (((inPowerset) =>
% 121.84/16.10 (((powersetsubset) =>
% 121.84/16.10 (((sepInPowerset) =>
% 121.84/16.10 (((sepSubset) =>
% 121.84/16.10 (((binunionIL) =>
% 121.84/16.10 (((upairset2IR) =>
% 121.84/16.10 (((binunionIR) =>
% 121.84/16.10 (((binunionEcases) =>
% 121.84/16.10 (((binunionE) =>
% 121.84/16.10 (((binunionLsub) =>
% 121.84/16.10 (((binunionRsub) =>
% 121.84/16.10 (((binintersectI) =>
% 121.84/16.10 (((binintersectSubset5) =>
% 121.84/16.10 (((binintersectEL) =>
% 121.84/16.10 (((binintersectLsub) =>
% 121.84/16.10 (((binintersectSubset2) =>
% 121.84/16.10 (((binintersectSubset3) =>
% 121.84/16.10 ((
% 121.84/16.10 (binintersectER) =>
% 121.84/16.10 ((
% 121.84/16.10 (disjointsetsI1) =>
% 121.84/16.10 ((
% 121.84/16.10 (binintersectRsub) =>
% 121.84/16.10 ((
% 121.84/16.10 (binintersectSubset4) =>
% 121.84/16.10 ((
% 121.84/16.10 (binintersectSubset1) =>
% 121.84/16.10 ((
% 121.84/16.10 (bs114d) =>
% 121.84/16.10 ((
% 121.84/16.10 (setminusI) =>
% 121.84/16.10 ((
% 121.84/16.10 (setminusEL) =>
% 121.84/16.10 ((
% 121.84/16.10 (setminusER) =>
% 121.84/16.10 ((
% 121.84/16.10 (setminusSubset2) =>
% 121.84/16.10 ((
% 121.84/16.10 (setminusERneg) =>
% 121.84/16.10 ((
% 121.84/16.10 (setminusELneg) =>
% 121.84/16.10 ((
% 121.84/16.10 (setminusILneg) =>
% 121.84/16.10 ((
% 121.84/16.10 (setminusIRneg) =>
% 121.84/16.10 ((
% 121.84/16.10 (setminusLsub) =>
% 121.84/16.10 ((
% 121.84/16.10 (setminusSubset1) =>
% 121.84/16.10 ((
% 121.84/16.10 (symdiffE) =>
% 121.84/16.10 ((
% 121.84/16.10 (symdiffI1) =>
% 121.84/16.10 ((
% 121.84/16.10 (symdiffI2) =>
% 121.84/16.10 ((
% 121.84/16.10 (symdiffIneg1) =>
% 121.84/16.10 ((
% 121.84/16.10 (symdiffIneg2) =>
% 121.84/16.10 ((
% 121.84/16.10 (secondinupair) =>
% 121.84/16.10 ((
% 121.84/16.10 (setukpairIL) =>
% 121.84/16.10 ((
% 121.84/16.10 (setukpairIR) =>
% 121.84/16.10 ((
% 121.84/16.10 (kpairiskpair) =>
% 121.84/16.10 ((
% 121.84/16.10 (kpairp) =>
% 121.84/16.10 ((
% 121.84/16.10 (singletonsubset) =>
% 121.84/16.10 ((
% 121.84/16.10 (singletoninpowerset) =>
% 121.84/16.10 ((
% 121.84/16.10 (singletoninpowunion) =>
% 121.84/16.10 ((
% 121.84/16.10 (upairset2E) =>
% 121.84/16.10 ((
% 121.84/16.10 (upairsubunion) =>
% 121.84/16.10 ((
% 121.84/16.10 (upairinpowunion) =>
% 121.84/16.10 ((
% 121.84/16.10 (ubforcartprodlem1) =>
% 121.84/16.10 ((
% 121.84/16.10 (ubforcartprodlem2) =>
% 121.84/16.10 ((
% 121.84/16.10 (ubforcartprodlem3) =>
% 121.84/16.10 ((
% 121.84/16.10 (cartprodpairin) =>
% 121.84/16.10 ((
% 121.84/16.10 (cartprodmempair1) =>
% 121.84/16.10 ((
% 121.84/16.10 (cartprodmempair) =>
% 121.84/16.10 ((
% 121.84/16.10 (setunionE2) =>
% 121.84/16.10 ((
% 121.84/16.10 (setunionsingleton1) =>
% 121.84/16.10 ((
% 121.84/16.10 (setunionsingleton2) =>
% 121.84/16.10 ((
% 121.84/16.10 (setunionsingleton) =>
% 121.84/16.10 ((
% 121.84/16.10 (singletonprop) =>
% 121.84/16.10 ((
% 121.84/16.10 (ex1E1) =>
% 121.84/16.10 ((
% 121.84/16.10 (ex1I) =>
% 121.84/16.10 ((
% 121.84/16.10 (ex1I2) =>
% 121.84/16.10 ((
% 121.84/16.10 (singletonsuniq) =>
% 121.84/16.10 ((
% 121.84/16.10 (setukpairinjL1) =>
% 121.84/16.10 ((
% 121.84/16.10 (kfstsingleton) =>
% 121.84/16.10 ((
% 121.84/16.10 (theprop) =>
% 121.84/16.10 ((
% 121.84/16.10 (kfstpairEq) =>
% 121.84/16.10 ((
% 121.84/16.10 (cartprodfstin) =>
% 121.84/16.10 ((
% 121.84/16.10 (setukpairinjL2) =>
% 121.84/16.10 ((
% 121.84/16.10 (setukpairinjL) =>
% 121.84/16.10 ((
% 121.84/16.10 (setukpairinjR11) =>
% 121.84/16.10 ((
% 121.84/16.10 (setukpairinjR12) =>
% 121.84/16.10 ((
% 121.84/16.10 (setukpairinjR1) =>
% 121.84/16.10 ((
% 121.84/16.10 (upairequniteq) =>
% 121.84/16.10 ((
% 121.84/16.10 (setukpairinjR2) =>
% 121.84/16.10 ((
% 121.84/16.10 (setukpairinjR) =>
% 121.84/16.10 ((
% 121.84/16.10 (ksndsingleton) =>
% 121.84/16.10 ((
% 121.84/16.10 (ksndpairEq) =>
% 121.84/16.10 ((
% 121.84/16.10 (kpairsurjEq) =>
% 121.84/16.10 ((
% 121.84/16.10 (cartprodsndin) =>
% 121.84/16.10 ((
% 121.84/16.10 (cartprodpairmemEL) =>
% 121.84/16.10 ((
% 121.84/16.10 (cartprodpairmemER) =>
% 121.84/16.10 ((
% 121.84/16.10 (cartprodmempaircEq) =>
% 121.84/16.10 ((
% 121.84/16.10 (cartprodfstpairEq) =>
% 121.84/16.10 ((
% 121.84/16.10 (cartprodsndpairEq) =>
% 121.84/16.10 ((
% 121.84/16.10 (cartprodpairsurjEq) =>
% 121.84/16.10 ((
% 121.84/16.10 (dpsetconstrI) =>
% 121.84/16.10 ((
% 121.84/16.10 (dpsetconstrSub) =>
% 121.84/16.10 ((
% 121.84/16.10 (setOfPairsIsBReln) =>
% 121.84/16.10 ((
% 121.84/16.10 (dpsetconstrERa) =>
% 121.84/16.10 ((
% 121.84/16.10 (dpsetconstrEL1) =>
% 121.84/16.10 ((
% 121.84/16.10 (dpsetconstrEL2) =>
% 121.84/16.10 ((
% 121.84/16.10 (dpsetconstrER) =>
% 121.84/16.10 ((
% 121.84/16.10 (funcImageSingleton) =>
% 121.84/16.10 ((
% 121.84/16.10 (apProp) =>
% 121.84/16.10 ((
% 121.84/16.10 (app) =>
% 121.84/16.10 ((
% 121.84/16.10 (infuncsetfunc) =>
% 121.84/16.10 ((
% 121.84/16.10 (ap2p) =>
% 121.84/16.10 ((
% 121.84/16.10 (funcinfuncset) =>
% 121.84/16.10 ((
% 121.84/16.10 (lamProp) =>
% 121.84/16.10 ((
% 121.84/16.10 (lamp) =>
% 121.84/16.10 ((
% 121.84/16.10 (lam2p) =>
% 121.84/16.10 ((
% 121.84/16.10 (brelnall1) =>
% 121.84/16.10 ((
% 121.84/16.10 (brelnall2) =>
% 121.84/16.10 ((
% 121.84/16.10 (ex1E2) =>
% 121.84/16.10 ((
% 121.84/16.10 (funcGraphProp1) =>
% 121.84/16.10 ((
% 121.84/16.10 (funcGraphProp3) =>
% 121.84/16.10 ((
% 121.84/16.10 (funcGraphProp2) =>
% 121.84/16.10 ((
% 121.84/16.10 (funcextLem) =>
% 121.84/16.10 ((
% 121.84/16.10 (funcGraphProp4) =>
% 121.84/16.10 ((
% 121.84/16.10 (subbreln) =>
% 121.84/16.10 ((
% 121.84/16.10 (eqbreln) =>
% 121.84/16.10 ((
% 121.84/16.10 (funcext) =>
% 121.84/16.10 ((
% 121.84/16.10 (funcext2) =>
% 121.84/16.10 ((
% 121.84/16.10 (ap2apEq1) =>
% 121.84/16.10 ((
% 121.84/16.10 (ap2apEq2) =>
% 121.84/16.10 ((
% 121.84/16.10 (beta1) =>
% 121.84/16.10 ((
% 121.84/16.10 (eta1) =>
% 121.84/16.10 ((
% 121.84/16.10 (lam2lamEq) =>
% 121.84/16.10 ((
% 121.84/16.10 (beta2) =>
% 121.84/16.10 ((
% 121.84/16.10 (eta2) =>
% 121.84/16.10 ((
% 121.84/16.10 (iffalseProp1) =>
% 121.84/16.10 ((
% 121.84/16.10 (iffalseProp2) =>
% 121.84/16.10 ((
% 121.84/16.10 (iftrueProp1) =>
% 121.84/16.10 ((
% 121.84/16.10 (iftrueProp2) =>
% 121.84/16.10 ((
% 121.84/16.10 (ifSingleton) =>
% 121.84/16.10 ((
% 121.84/16.10 (ifp) =>
% 121.84/16.10 ((
% 121.84/16.10 (theeq) =>
% 121.84/16.10 ((
% 121.84/16.10 (iftrue) =>
% 121.84/16.10 ((
% 121.84/16.10 (iffalse) =>
% 121.84/16.10 ((
% 121.84/16.10 (iftrueorfalse) =>
% 121.84/16.10 ((
% 121.84/16.10 (binintersectT_lem) =>
% 121.84/16.10 ((
% 121.84/16.10 (binunionT_lem) =>
% 121.84/16.10 ((
% 121.84/16.10 (powersetT_lem) =>
% 121.84/16.10 ((
% 121.84/16.10 (setminusT_lem) =>
% 121.84/16.10 ((
% 121.84/16.10 (complementT_lem) =>
% 121.84/16.10 ((
% 121.84/16.10 (setextT) =>
% 121.84/16.10 ((
% 121.84/16.10 (subsetTI) =>
% 121.84/16.10 ((
% 121.84/16.10 (powersetTI1) =>
% 121.84/16.10 ((
% 121.84/16.10 (powersetTE1) =>
% 121.84/16.10 ((
% 121.84/16.10 (complementTI1) =>
% 121.84/16.10 ((
% 121.84/16.10 (complementTE1) =>
% 121.84/16.10 ((
% 121.84/16.10 (binintersectTELcontra) =>
% 121.84/16.10 ((
% 121.84/16.10 (binintersectTERcontra) =>
% 121.84/16.10 ((
% 121.84/16.10 (contrasubsetT) =>
% 121.84/16.10 ((
% 121.84/16.10 (contrasubsetT1) =>
% 121.84/16.10 ((
% 121.84/16.10 (contrasubsetT2) =>
% 121.84/16.10 ((
% 121.84/16.10 (contrasubsetT3) =>
% 121.84/16.10 ((
% 121.84/16.10 (doubleComplementI1) =>
% 121.84/16.10 ((
% 121.84/16.10 (doubleComplementE1) =>
% 121.84/16.10 ((
% 121.84/16.10 (doubleComplementSub1) =>
% 121.84/16.10 ((
% 121.84/16.10 (doubleComplementSub2) =>
% 121.84/16.10 ((
% 121.84/16.10 (doubleComplementEq) =>
% 121.84/16.10 ((
% 121.84/16.10 (complementTnotintersectT) =>
% 121.84/16.10 ((
% 121.84/16.10 (complementImpComplementIntersect) =>
% 121.84/16.10 ((
% 121.84/16.10 (complementSubsetComplementIntersect) =>
% 121.84/16.10 ((
% 121.84/16.10 (complementInPowersetComplementIntersect) =>
% 121.84/16.10 ((
% 121.84/16.10 (contraSubsetComplement) =>
% 121.84/16.10 ((
% 121.84/16.10 (complementTcontraSubset) =>
% 121.84/16.10 ((
% 121.84/16.10 (binunionTILcontra) =>
% 121.84/16.10 ((
% 121.84/16.10 (binunionTIRcontra) =>
% 121.84/16.10 ((
% 121.84/16.10 (inIntersectImpInUnion) =>
% 121.84/16.10 ((
% 121.84/16.10 (inIntersectImpInUnion2) =>
% 121.84/16.10 ((
% 121.84/16.10 (inIntersectImpInIntersectUnions) =>
% 121.84/16.10 ((
% 121.84/16.10 (intersectInPowersetIntersectUnions) =>
% 121.84/16.10 ((
% 121.84/16.10 (inComplementUnionImpNotIn1) =>
% 121.84/16.10 ((
% 121.84/16.10 (inComplementUnionImpInComplement1) =>
% 121.84/16.10 ((
% 121.84/16.10 (binunionTE) =>
% 121.84/16.10 ((
% 121.84/16.10 (binunionTEcontra) =>
% 121.84/16.10 ((
% 121.84/16.10 (demorgan2a1) =>
% 121.84/16.10 ((
% 121.84/16.10 (complementUnionInPowersetComplement) =>
% 121.84/16.10 ((
% 121.84/16.10 (demorgan2a2) =>
% 121.84/16.10 ((
% 121.84/16.10 (demorgan1a) =>
% 121.84/16.10 ((
% 121.84/16.10 (demorgan1b) =>
% 121.84/16.10 ((
% 121.84/16.10 (demorgan1) =>
% 121.84/16.10 ((
% 121.84/16.10 (demorgan2a) =>
% 121.84/16.10 ((
% 121.84/16.10 (demorgan2b2) =>
% 121.84/16.10 ((
% 121.84/16.10 (demorgan2b) =>
% 121.84/16.10 ((
% 121.84/16.10 (demorgan2) =>
% 121.84/16.10 ((
% 121.84/16.10 (woz13rule0) =>
% 121.84/16.10 ((
% 121.84/16.10 (woz13rule1) =>
% 121.84/16.10 ((
% 121.84/16.10 (woz13rule2) =>
% 121.84/16.10 ((
% 121.84/16.10 (woz13rule3) =>
% 121.84/16.10 ((
% 121.84/16.10 (woz13rule4) =>
% 121.84/16.10 ((
% 121.84/16.10 (woz1_1) =>
% 121.84/16.10 ((
% 121.84/16.10 (woz1_2) =>
% 121.84/16.10 ((
% 121.84/16.10 (woz1_3) =>
% 121.84/16.10 ((
% 121.84/16.10 (woz1_4) =>
% 121.84/16.10 ((
% 121.84/16.10 (woz1_5) =>
% 121.84/16.10 ((
% 121.84/16.10 (breln1all2) =>
% 121.84/16.10 ((
% 121.84/16.10 (breln1SetBreln1) =>
% 121.84/16.10 ((
% 121.84/16.10 (choice2fnsingleton) =>
% 121.84/16.10 ((
% 121.84/16.10 (setOfPairsIsBReln1) =>
% 121.84/16.10 ((
% 121.84/16.10 (breln1all1) =>
% 121.84/16.10 ((
% 121.84/16.10 (subbreln1) =>
% 121.84/16.10 ((
% 121.84/16.10 (eqbreln1) =>
% 121.84/16.10 ((
% 121.84/16.10 (breln1invprop) =>
% 121.84/16.10 ((
% 121.84/16.10 (breln1invI) =>
% 121.84/16.10 ((
% 121.84/16.10 (breln1invE) =>
% 121.84/16.10 ((
% 121.84/16.10 (breln1compprop) =>
% 121.84/16.10 ((
% 121.84/16.10 (breln1compI) =>
% 121.84/16.10 ((
% 121.84/16.10 (breln1compE) =>
% 121.84/16.10 ((
% 121.84/16.10 (breln1compEex) =>
% 121.84/16.10 ((
% 121.84/16.10 (breln1unionprop) =>
% 121.84/16.10 ((
% 121.84/16.10 (breln1unionIL) =>
% 121.84/16.10 ((
% 121.84/16.10 (breln1unionIR) =>
% 121.84/16.10 ((
% 121.84/16.10 (breln1unionI) =>
% 121.84/16.10 ((
% 121.84/16.10 (breln1unionE) =>
% 121.84/16.10 ((
% 121.84/16.10 (breln1unionEcases) =>
% 121.84/16.10 ((
% 121.84/16.10 (breln1unionCommutes) =>
% 121.84/16.10 ((
% 121.84/16.10 (woz2Ex) =>
% 121.84/16.10 ((
% 121.84/16.10 (woz2W) =>
% 121.84/16.10 ((
% 121.84/16.10 (woz2A) =>
% 121.84/16.10 ((
% 121.84/16.10 (woz2B) =>
% 121.84/16.10 ((
% 121.84/16.10 (image1Ex) =>
% 121.84/16.10 ((
% 121.84/16.10 (image1Ex1) =>
% 121.84/16.10 ((
% 121.84/16.10 (image1Equiv) =>
% 121.84/16.10 ((
% 121.84/16.10 (image1E) =>
% 121.84/16.10 ((
% 121.84/16.10 (image1I) =>
% 121.84/16.10 ((
% 121.84/16.10 (injFuncInInjFuncSet) =>
% 121.84/16.10 ((
% 121.84/16.10 (!!) @ (
% 121.84/16.10 (('#B') @ (
% 121.84/16.10 !!) @
% 121.84/16.10 (
% 121.84/16.10 (
% 121.84/16.10 ('#B') @ (
% 121.84/16.10 (
% 121.84/16.10 ('#B') @ (
% 121.84/16.10 !!))) @
% 121.84/16.10 (
% 121.84/16.10 (
% 121.84/16.10 ('#S') @ (
% 121.84/16.10 (
% 121.84/16.10 ('#B') @ (
% 121.84/16.10 '#S') @
% 121.84/16.10 (
% 121.84/16.10 (
% 121.84/16.10 ('#B') @ (
% 121.84/16.10 (
% 121.84/16.10 ('#B') @ (
% 121.84/16.10 '#S'))) @
% 121.84/16.10 (
% 121.84/16.10 (
% 121.84/16.10 ('#B') @ (
% 121.84/16.10 (
% 121.84/16.10 ('#B') @ (
% 121.84/16.10 (
% 121.84/16.10 ('#B') @ (
% 121.84/16.10 =>))))) @
% 121.84/16.10 (
% 121.84/16.10 (
% 121.84/16.10 ('#B') @ (
% 121.84/16.10 (
% 121.84/16.10 ('#B') @ (
% 121.84/16.10 (
% 121.84/16.10 ('#C') @ in)))) @
% 121.84/16.10 injFuncSet)))))))) @
% 121.84/16.10 (
% 121.84/16.10 (
% 121.84/16.10 ('#B') @ (
% 121.84/16.10 (
% 121.84/16.10 ('#B') @ (
% 121.84/16.10 (
% 121.84/16.10 ('#C') @ in)))) @
% 121.84/16.10 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 121.84/16.10 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl863])).
% 121.84/16.10 thf(zip_derived_cl896, plain,
% 121.84/16.10 (~ (((notsubsetI) =>
% 121.84/16.10 (((notequalI1) =>
% 121.84/16.10 (((notequalI2) =>
% 121.84/16.10 (((subsetRefl) =>
% 121.84/16.10 (((subsetTrans) =>
% 121.84/16.10 (((setadjoinSub) =>
% 121.84/16.10 (((setadjoinSub2) =>
% 121.84/16.10 (((subset2powerset) =>
% 121.84/16.10 (((setextsub) =>
% 121.84/16.10 (((subsetemptysetimpeq) =>
% 121.84/16.10 (((powersetI1) =>
% 121.84/16.10 (((powersetE1) =>
% 121.84/16.10 (((inPowerset) =>
% 121.84/16.10 (((powersetsubset) =>
% 121.84/16.10 (((sepInPowerset) =>
% 121.84/16.10 (((sepSubset) =>
% 121.84/16.10 (((binunionIL) =>
% 121.84/16.10 (((upairset2IR) =>
% 121.84/16.10 (((binunionIR) =>
% 121.84/16.10 (((binunionEcases) =>
% 121.84/16.10 (((binunionE) =>
% 121.84/16.10 (((binunionLsub) =>
% 121.84/16.10 (((binunionRsub) =>
% 121.84/16.10 (((binintersectI) =>
% 121.84/16.10 (((binintersectSubset5) =>
% 121.84/16.10 (((binintersectEL) =>
% 121.84/16.10 (((binintersectLsub) =>
% 121.84/16.10 (((binintersectSubset2) =>
% 121.84/16.10 (((binintersectSubset3) =>
% 121.84/16.10 (((binintersectER) =>
% 121.84/16.10 ((
% 121.84/16.10 (disjointsetsI1) =>
% 121.84/16.10 ((
% 121.84/16.10 (binintersectRsub) =>
% 121.84/16.10 ((
% 121.84/16.10 (binintersectSubset4) =>
% 121.84/16.10 ((
% 121.84/16.10 (binintersectSubset1) =>
% 121.84/16.10 ((
% 121.84/16.10 (bs114d) =>
% 121.84/16.10 ((
% 121.84/16.10 (setminusI) =>
% 121.84/16.10 ((
% 121.84/16.10 (setminusEL) =>
% 121.84/16.10 ((
% 121.84/16.10 (setminusER) =>
% 121.84/16.10 ((
% 121.84/16.10 (setminusSubset2) =>
% 121.84/16.10 ((
% 121.84/16.10 (setminusERneg) =>
% 121.84/16.10 ((
% 121.84/16.10 (setminusELneg) =>
% 121.84/16.10 ((
% 121.84/16.10 (setminusILneg) =>
% 121.84/16.10 ((
% 121.84/16.10 (setminusIRneg) =>
% 121.84/16.10 ((
% 121.84/16.10 (setminusLsub) =>
% 121.84/16.10 ((
% 121.84/16.10 (setminusSubset1) =>
% 121.84/16.10 ((
% 121.84/16.10 (symdiffE) =>
% 121.84/16.10 ((
% 121.84/16.10 (symdiffI1) =>
% 121.84/16.10 ((
% 121.84/16.10 (symdiffI2) =>
% 121.84/16.10 ((
% 121.84/16.10 (symdiffIneg1) =>
% 121.84/16.10 ((
% 121.84/16.10 (symdiffIneg2) =>
% 121.84/16.10 ((
% 121.84/16.10 (secondinupair) =>
% 121.84/16.10 ((
% 121.84/16.10 (setukpairIL) =>
% 121.84/16.10 ((
% 121.84/16.10 (setukpairIR) =>
% 121.84/16.10 ((
% 121.84/16.10 (kpairiskpair) =>
% 121.84/16.10 ((
% 121.84/16.10 (kpairp) =>
% 121.84/16.10 ((
% 121.84/16.10 (singletonsubset) =>
% 121.84/16.10 ((
% 121.84/16.10 (singletoninpowerset) =>
% 121.84/16.10 ((
% 121.84/16.10 (singletoninpowunion) =>
% 121.84/16.10 ((
% 121.84/16.10 (upairset2E) =>
% 121.84/16.10 ((
% 121.84/16.10 (upairsubunion) =>
% 121.84/16.10 ((
% 121.84/16.10 (upairinpowunion) =>
% 121.84/16.10 ((
% 121.84/16.10 (ubforcartprodlem1) =>
% 121.84/16.10 ((
% 121.84/16.10 (ubforcartprodlem2) =>
% 121.84/16.10 ((
% 121.84/16.10 (ubforcartprodlem3) =>
% 121.84/16.10 ((
% 121.84/16.10 (cartprodpairin) =>
% 121.84/16.10 ((
% 121.84/16.10 (cartprodmempair1) =>
% 121.84/16.10 ((
% 121.84/16.10 (cartprodmempair) =>
% 121.84/16.10 ((
% 121.84/16.10 (setunionE2) =>
% 121.84/16.10 ((
% 121.84/16.10 (setunionsingleton1) =>
% 121.84/16.10 ((
% 121.84/16.10 (setunionsingleton2) =>
% 121.84/16.10 ((
% 121.84/16.10 (setunionsingleton) =>
% 121.84/16.10 ((
% 121.84/16.10 (singletonprop) =>
% 121.84/16.10 ((
% 121.84/16.10 (ex1E1) =>
% 121.84/16.10 ((
% 121.84/16.10 (ex1I) =>
% 121.84/16.10 ((
% 121.84/16.10 (ex1I2) =>
% 121.84/16.10 ((
% 121.84/16.10 (singletonsuniq) =>
% 121.84/16.10 ((
% 121.84/16.10 (setukpairinjL1) =>
% 121.84/16.10 ((
% 121.84/16.10 (kfstsingleton) =>
% 121.84/16.10 ((
% 121.84/16.10 (theprop) =>
% 121.84/16.10 ((
% 121.84/16.10 (kfstpairEq) =>
% 121.84/16.10 ((
% 121.84/16.10 (cartprodfstin) =>
% 121.84/16.10 ((
% 121.84/16.10 (setukpairinjL2) =>
% 121.84/16.10 ((
% 121.84/16.10 (setukpairinjL) =>
% 121.84/16.10 ((
% 121.84/16.10 (setukpairinjR11) =>
% 121.84/16.10 ((
% 121.84/16.10 (setukpairinjR12) =>
% 121.84/16.10 ((
% 121.84/16.10 (setukpairinjR1) =>
% 121.84/16.10 ((
% 121.84/16.10 (upairequniteq) =>
% 121.84/16.10 ((
% 121.84/16.10 (setukpairinjR2) =>
% 121.84/16.10 ((
% 121.84/16.10 (setukpairinjR) =>
% 121.84/16.10 ((
% 121.84/16.10 (ksndsingleton) =>
% 121.84/16.10 ((
% 121.84/16.10 (ksndpairEq) =>
% 121.84/16.10 ((
% 121.84/16.10 (kpairsurjEq) =>
% 121.84/16.10 ((
% 121.84/16.10 (cartprodsndin) =>
% 121.84/16.10 ((
% 121.84/16.10 (cartprodpairmemEL) =>
% 121.84/16.10 ((
% 121.84/16.10 (cartprodpairmemER) =>
% 121.84/16.10 ((
% 121.84/16.10 (cartprodmempaircEq) =>
% 121.84/16.10 ((
% 121.84/16.10 (cartprodfstpairEq) =>
% 121.84/16.10 ((
% 121.84/16.10 (cartprodsndpairEq) =>
% 121.84/16.10 ((
% 121.84/16.10 (cartprodpairsurjEq) =>
% 121.84/16.10 ((
% 121.84/16.10 (dpsetconstrI) =>
% 121.84/16.10 ((
% 121.84/16.10 (dpsetconstrSub) =>
% 121.84/16.10 ((
% 121.84/16.10 (setOfPairsIsBReln) =>
% 121.84/16.10 ((
% 121.84/16.10 (dpsetconstrERa) =>
% 121.84/16.10 ((
% 121.84/16.10 (dpsetconstrEL1) =>
% 121.84/16.10 ((
% 121.84/16.10 (dpsetconstrEL2) =>
% 121.84/16.10 ((
% 121.84/16.10 (dpsetconstrER) =>
% 121.84/16.10 ((
% 121.84/16.10 (funcImageSingleton) =>
% 121.84/16.10 ((
% 121.84/16.10 (apProp) =>
% 121.84/16.10 ((
% 121.84/16.10 (app) =>
% 121.84/16.10 ((
% 121.84/16.10 (infuncsetfunc) =>
% 121.84/16.10 ((
% 121.84/16.10 (ap2p) =>
% 121.84/16.10 ((
% 121.84/16.10 (funcinfuncset) =>
% 121.84/16.10 ((
% 121.84/16.10 (lamProp) =>
% 121.84/16.10 ((
% 121.84/16.10 (lamp) =>
% 121.84/16.10 ((
% 121.84/16.10 (lam2p) =>
% 121.84/16.10 ((
% 121.84/16.10 (brelnall1) =>
% 121.84/16.10 ((
% 121.84/16.10 (brelnall2) =>
% 121.84/16.10 ((
% 121.84/16.10 (ex1E2) =>
% 121.84/16.10 ((
% 121.84/16.10 (funcGraphProp1) =>
% 121.84/16.10 ((
% 121.84/16.10 (funcGraphProp3) =>
% 121.84/16.10 ((
% 121.84/16.10 (funcGraphProp2) =>
% 121.84/16.10 ((
% 121.84/16.10 (funcextLem) =>
% 121.84/16.10 ((
% 121.84/16.10 (funcGraphProp4) =>
% 121.84/16.10 ((
% 121.84/16.10 (subbreln) =>
% 121.84/16.10 ((
% 121.84/16.10 (eqbreln) =>
% 121.84/16.10 ((
% 121.84/16.10 (funcext) =>
% 121.84/16.10 ((
% 121.84/16.10 (funcext2) =>
% 121.84/16.10 ((
% 121.84/16.10 (ap2apEq1) =>
% 121.84/16.10 ((
% 121.84/16.10 (ap2apEq2) =>
% 121.84/16.10 ((
% 121.84/16.10 (beta1) =>
% 121.84/16.10 ((
% 121.84/16.10 (eta1) =>
% 121.84/16.10 ((
% 121.84/16.10 (lam2lamEq) =>
% 121.84/16.10 ((
% 121.84/16.10 (beta2) =>
% 121.84/16.10 ((
% 121.84/16.10 (eta2) =>
% 121.84/16.10 ((
% 121.84/16.10 (iffalseProp1) =>
% 121.84/16.10 ((
% 121.84/16.10 (iffalseProp2) =>
% 121.84/16.10 ((
% 121.84/16.10 (iftrueProp1) =>
% 121.84/16.10 ((
% 121.84/16.10 (iftrueProp2) =>
% 121.84/16.10 ((
% 121.84/16.10 (ifSingleton) =>
% 121.84/16.10 ((
% 121.84/16.10 (ifp) =>
% 121.84/16.10 ((
% 121.84/16.10 (theeq) =>
% 121.84/16.10 ((
% 121.84/16.10 (iftrue) =>
% 121.84/16.10 ((
% 121.84/16.10 (iffalse) =>
% 121.84/16.10 ((
% 121.84/16.10 (iftrueorfalse) =>
% 121.84/16.10 ((
% 121.84/16.10 (binintersectT_lem) =>
% 121.84/16.10 ((
% 121.84/16.10 (binunionT_lem) =>
% 121.84/16.10 ((
% 121.84/16.10 (powersetT_lem) =>
% 121.84/16.10 ((
% 121.84/16.10 (setminusT_lem) =>
% 121.84/16.10 ((
% 121.84/16.10 (complementT_lem) =>
% 121.84/16.10 ((
% 121.84/16.10 (setextT) =>
% 121.84/16.10 ((
% 121.84/16.10 (subsetTI) =>
% 121.84/16.10 ((
% 121.84/16.10 (powersetTI1) =>
% 121.84/16.10 ((
% 121.84/16.10 (powersetTE1) =>
% 121.84/16.10 ((
% 121.84/16.10 (complementTI1) =>
% 121.84/16.10 ((
% 121.84/16.10 (complementTE1) =>
% 121.84/16.10 ((
% 121.84/16.10 (binintersectTELcontra) =>
% 121.84/16.10 ((
% 121.84/16.10 (binintersectTERcontra) =>
% 121.84/16.10 ((
% 121.84/16.10 (contrasubsetT) =>
% 121.84/16.10 ((
% 121.84/16.10 (contrasubsetT1) =>
% 121.84/16.10 ((
% 121.84/16.10 (contrasubsetT2) =>
% 121.84/16.10 ((
% 121.84/16.10 (contrasubsetT3) =>
% 121.84/16.10 ((
% 121.84/16.10 (doubleComplementI1) =>
% 121.84/16.10 ((
% 121.84/16.10 (doubleComplementE1) =>
% 121.84/16.10 ((
% 121.84/16.10 (doubleComplementSub1) =>
% 121.84/16.10 ((
% 121.84/16.10 (doubleComplementSub2) =>
% 121.84/16.10 ((
% 121.84/16.10 (doubleComplementEq) =>
% 121.84/16.10 ((
% 121.84/16.10 (complementTnotintersectT) =>
% 121.84/16.10 ((
% 121.84/16.10 (complementImpComplementIntersect) =>
% 121.84/16.10 ((
% 121.84/16.10 (complementSubsetComplementIntersect) =>
% 121.84/16.10 ((
% 121.84/16.10 (complementInPowersetComplementIntersect) =>
% 121.84/16.10 ((
% 121.84/16.10 (contraSubsetComplement) =>
% 121.84/16.10 ((
% 121.84/16.10 (complementTcontraSubset) =>
% 121.84/16.10 ((
% 121.84/16.10 (binunionTILcontra) =>
% 121.84/16.10 ((
% 121.84/16.10 (binunionTIRcontra) =>
% 121.84/16.10 ((
% 121.84/16.10 (inIntersectImpInUnion) =>
% 121.84/16.10 ((
% 121.84/16.10 (inIntersectImpInUnion2) =>
% 121.84/16.10 ((
% 121.84/16.10 (inIntersectImpInIntersectUnions) =>
% 121.84/16.10 ((
% 121.84/16.10 (intersectInPowersetIntersectUnions) =>
% 121.84/16.10 ((
% 121.84/16.10 (inComplementUnionImpNotIn1) =>
% 121.84/16.10 ((
% 121.84/16.10 (inComplementUnionImpInComplement1) =>
% 121.84/16.10 ((
% 121.84/16.10 (binunionTE) =>
% 121.84/16.10 ((
% 121.84/16.10 (binunionTEcontra) =>
% 121.84/16.10 ((
% 121.84/16.10 (demorgan2a1) =>
% 121.84/16.10 ((
% 121.84/16.10 (complementUnionInPowersetComplement) =>
% 121.84/16.10 ((
% 121.84/16.10 (demorgan2a2) =>
% 121.84/16.10 ((
% 121.84/16.10 (demorgan1a) =>
% 121.84/16.10 ((
% 121.84/16.10 (demorgan1b) =>
% 121.84/16.10 ((
% 121.84/16.10 (demorgan1) =>
% 121.84/16.10 ((
% 121.84/16.10 (demorgan2a) =>
% 121.84/16.10 ((
% 121.84/16.10 (demorgan2b2) =>
% 121.84/16.10 ((
% 121.84/16.10 (demorgan2b) =>
% 121.84/16.10 ((
% 121.84/16.10 (demorgan2) =>
% 121.84/16.10 ((
% 121.84/16.10 (woz13rule0) =>
% 121.84/16.10 ((
% 121.84/16.10 (woz13rule1) =>
% 121.84/16.10 ((
% 121.84/16.10 (woz13rule2) =>
% 121.84/16.10 ((
% 121.84/16.10 (woz13rule3) =>
% 121.84/16.10 ((
% 121.84/16.10 (woz13rule4) =>
% 121.84/16.10 ((
% 121.84/16.10 (woz1_1) =>
% 121.84/16.10 ((
% 121.84/16.10 (woz1_2) =>
% 121.84/16.10 ((
% 121.84/16.10 (woz1_3) =>
% 121.84/16.10 ((
% 121.84/16.10 (woz1_4) =>
% 121.84/16.10 ((
% 121.84/16.10 (woz1_5) =>
% 121.84/16.10 ((
% 121.84/16.10 (breln1all2) =>
% 121.84/16.10 ((
% 121.84/16.10 (breln1SetBreln1) =>
% 121.84/16.10 ((
% 121.84/16.10 (choice2fnsingleton) =>
% 121.84/16.10 ((
% 121.84/16.10 (setOfPairsIsBReln1) =>
% 121.84/16.10 ((
% 121.84/16.10 (breln1all1) =>
% 121.84/16.10 ((
% 121.84/16.10 (subbreln1) =>
% 121.84/16.10 ((
% 121.84/16.10 (eqbreln1) =>
% 121.84/16.10 ((
% 121.84/16.10 (breln1invprop) =>
% 121.84/16.10 ((
% 121.84/16.10 (breln1invI) =>
% 121.84/16.10 ((
% 121.84/16.10 (breln1invE) =>
% 121.84/16.10 ((
% 121.84/16.10 (breln1compprop) =>
% 121.84/16.10 ((
% 121.84/16.10 (breln1compI) =>
% 121.84/16.10 ((
% 121.84/16.10 (breln1compE) =>
% 121.84/16.10 ((
% 121.84/16.10 (breln1compEex) =>
% 121.84/16.10 ((
% 121.84/16.10 (breln1unionprop) =>
% 121.84/16.10 ((
% 121.84/16.10 (breln1unionIL) =>
% 121.84/16.10 ((
% 121.84/16.10 (breln1unionIR) =>
% 121.84/16.10 ((
% 121.84/16.10 (breln1unionI) =>
% 121.84/16.10 ((
% 121.84/16.10 (breln1unionE) =>
% 121.84/16.10 ((
% 121.84/16.10 (breln1unionEcases) =>
% 121.84/16.10 ((
% 121.84/16.10 (breln1unionCommutes) =>
% 121.84/16.10 ((
% 121.84/16.10 (woz2Ex) =>
% 121.84/16.10 ((
% 121.84/16.10 (woz2W) =>
% 121.84/16.10 ((
% 121.84/16.10 (woz2A) =>
% 121.84/16.10 ((
% 121.84/16.10 (woz2B) =>
% 121.84/16.10 ((
% 121.84/16.10 (image1Ex) =>
% 121.84/16.10 ((
% 121.84/16.10 (image1Ex1) =>
% 121.84/16.10 ((
% 121.84/16.10 (image1Equiv) =>
% 121.84/16.10 ((
% 121.84/16.10 (image1E) =>
% 121.84/16.10 ((
% 121.84/16.10 (image1I) =>
% 121.84/16.10 ((
% 121.84/16.10 (injFuncInInjFuncSet) =>
% 121.84/16.10 ((
% 121.84/16.10 (!!) @ (
% 121.84/16.10 (('#B') @ (
% 121.84/16.10 !!) @
% 121.84/16.10 (
% 121.84/16.10 (
% 121.84/16.10 ('#B') @ (
% 121.84/16.10 (
% 121.84/16.10 ('#B') @ (
% 121.84/16.10 !!))) @
% 121.84/16.10 (
% 121.84/16.10 (
% 121.84/16.10 ('#S') @ (
% 121.84/16.10 (
% 121.84/16.10 ('#B') @ (
% 121.84/16.10 '#S') @
% 121.84/16.10 (
% 121.84/16.10 (
% 121.84/16.10 ('#B') @ (
% 121.84/16.10 (
% 121.84/16.10 ('#B') @ (
% 121.84/16.10 '#S'))) @
% 121.84/16.10 (
% 121.84/16.10 (
% 121.84/16.10 ('#B') @ (
% 121.84/16.10 (
% 121.84/16.10 ('#B') @ (
% 121.84/16.10 (
% 121.84/16.10 ('#B') @ (
% 121.84/16.10 =>))))) @
% 121.84/16.10 (
% 121.84/16.10 (
% 121.84/16.10 ('#B') @ (
% 121.84/16.10 (
% 121.84/16.10 ('#B') @ (
% 121.84/16.10 (
% 121.84/16.10 ('#C') @ in)))) @
% 121.84/16.10 injFuncSet)))))))) @
% 121.84/16.10 (
% 121.84/16.10 (
% 121.84/16.10 ('#B') @ (
% 121.84/16.10 (
% 121.84/16.10 ('#B') @ (
% 121.84/16.10 (
% 121.84/16.10 ('#C') @ in)))) @
% 121.84/16.10 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 121.84/16.10 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl878])).
% 121.84/16.10 thf(zip_derived_cl909, plain,
% 121.84/16.10 (~ (((notequalI1) =>
% 121.84/16.10 (((notequalI2) =>
% 121.84/16.10 (((subsetRefl) =>
% 121.84/16.10 (((subsetTrans) =>
% 121.84/16.10 (((setadjoinSub) =>
% 121.84/16.10 (((setadjoinSub2) =>
% 121.84/16.10 (((subset2powerset) =>
% 121.84/16.10 (((setextsub) =>
% 121.84/16.10 (((subsetemptysetimpeq) =>
% 121.84/16.10 (((powersetI1) =>
% 121.84/16.10 (((powersetE1) =>
% 121.84/16.10 (((inPowerset) =>
% 121.84/16.10 (((powersetsubset) =>
% 121.84/16.10 (((sepInPowerset) =>
% 121.84/16.10 (((sepSubset) =>
% 121.84/16.10 (((binunionIL) =>
% 121.84/16.10 (((upairset2IR) =>
% 121.84/16.10 (((binunionIR) =>
% 121.84/16.10 (((binunionEcases) =>
% 121.84/16.10 (((binunionE) =>
% 121.84/16.10 (((binunionLsub) =>
% 121.84/16.10 (((binunionRsub) =>
% 121.84/16.10 (((binintersectI) =>
% 121.84/16.10 (((binintersectSubset5) =>
% 121.84/16.10 (((binintersectEL) =>
% 121.84/16.10 (((binintersectLsub) =>
% 121.84/16.10 (((binintersectSubset2) =>
% 121.84/16.10 (((binintersectSubset3) =>
% 121.84/16.10 (((binintersectER) =>
% 121.84/16.10 (((disjointsetsI1) =>
% 121.84/16.10 ((
% 121.84/16.10 (binintersectRsub) =>
% 121.84/16.10 ((
% 121.84/16.10 (binintersectSubset4) =>
% 121.84/16.10 ((
% 121.84/16.10 (binintersectSubset1) =>
% 121.84/16.10 ((
% 121.84/16.10 (bs114d) =>
% 121.84/16.10 ((
% 121.84/16.10 (setminusI) =>
% 121.84/16.10 ((
% 121.84/16.10 (setminusEL) =>
% 121.84/16.10 ((
% 121.84/16.10 (setminusER) =>
% 121.84/16.10 ((
% 121.84/16.10 (setminusSubset2) =>
% 121.84/16.10 ((
% 121.84/16.10 (setminusERneg) =>
% 121.84/16.10 ((
% 121.84/16.10 (setminusELneg) =>
% 121.84/16.10 ((
% 121.84/16.10 (setminusILneg) =>
% 121.84/16.10 ((
% 121.84/16.10 (setminusIRneg) =>
% 121.84/16.10 ((
% 121.84/16.10 (setminusLsub) =>
% 121.84/16.10 ((
% 121.84/16.10 (setminusSubset1) =>
% 121.84/16.10 ((
% 121.84/16.10 (symdiffE) =>
% 121.84/16.10 ((
% 121.84/16.10 (symdiffI1) =>
% 121.84/16.10 ((
% 121.84/16.10 (symdiffI2) =>
% 121.84/16.10 ((
% 121.84/16.10 (symdiffIneg1) =>
% 121.84/16.10 ((
% 121.84/16.10 (symdiffIneg2) =>
% 121.84/16.10 ((
% 121.84/16.10 (secondinupair) =>
% 121.84/16.10 ((
% 121.84/16.10 (setukpairIL) =>
% 121.84/16.10 ((
% 121.84/16.10 (setukpairIR) =>
% 121.84/16.10 ((
% 121.84/16.10 (kpairiskpair) =>
% 121.84/16.10 ((
% 121.84/16.10 (kpairp) =>
% 121.84/16.10 ((
% 121.84/16.10 (singletonsubset) =>
% 121.84/16.10 ((
% 121.84/16.10 (singletoninpowerset) =>
% 121.84/16.10 ((
% 121.84/16.10 (singletoninpowunion) =>
% 121.84/16.10 ((
% 121.84/16.10 (upairset2E) =>
% 121.84/16.10 ((
% 121.84/16.10 (upairsubunion) =>
% 121.84/16.10 ((
% 121.84/16.10 (upairinpowunion) =>
% 121.84/16.10 ((
% 121.84/16.10 (ubforcartprodlem1) =>
% 121.84/16.10 ((
% 121.84/16.10 (ubforcartprodlem2) =>
% 121.84/16.10 ((
% 121.84/16.10 (ubforcartprodlem3) =>
% 121.84/16.10 ((
% 121.84/16.10 (cartprodpairin) =>
% 121.84/16.10 ((
% 121.84/16.10 (cartprodmempair1) =>
% 121.84/16.10 ((
% 121.84/16.10 (cartprodmempair) =>
% 121.84/16.10 ((
% 121.84/16.10 (setunionE2) =>
% 121.84/16.10 ((
% 121.84/16.10 (setunionsingleton1) =>
% 121.84/16.10 ((
% 121.84/16.10 (setunionsingleton2) =>
% 121.84/16.10 ((
% 121.84/16.10 (setunionsingleton) =>
% 121.84/16.10 ((
% 121.84/16.10 (singletonprop) =>
% 121.84/16.10 ((
% 121.84/16.10 (ex1E1) =>
% 121.84/16.10 ((
% 121.84/16.10 (ex1I) =>
% 121.84/16.10 ((
% 121.84/16.10 (ex1I2) =>
% 121.84/16.10 ((
% 121.84/16.10 (singletonsuniq) =>
% 121.84/16.10 ((
% 121.84/16.10 (setukpairinjL1) =>
% 121.84/16.10 ((
% 121.84/16.10 (kfstsingleton) =>
% 121.84/16.10 ((
% 121.84/16.10 (theprop) =>
% 121.84/16.10 ((
% 121.84/16.10 (kfstpairEq) =>
% 121.84/16.10 ((
% 121.84/16.10 (cartprodfstin) =>
% 121.84/16.10 ((
% 121.84/16.10 (setukpairinjL2) =>
% 121.84/16.10 ((
% 121.84/16.10 (setukpairinjL) =>
% 121.84/16.10 ((
% 121.84/16.10 (setukpairinjR11) =>
% 121.84/16.10 ((
% 121.84/16.10 (setukpairinjR12) =>
% 121.84/16.10 ((
% 121.84/16.10 (setukpairinjR1) =>
% 121.84/16.10 ((
% 121.84/16.10 (upairequniteq) =>
% 121.84/16.10 ((
% 121.84/16.10 (setukpairinjR2) =>
% 121.84/16.10 ((
% 121.84/16.10 (setukpairinjR) =>
% 121.84/16.10 ((
% 121.84/16.10 (ksndsingleton) =>
% 121.84/16.10 ((
% 121.84/16.10 (ksndpairEq) =>
% 121.84/16.10 ((
% 121.84/16.10 (kpairsurjEq) =>
% 121.84/16.10 ((
% 121.84/16.10 (cartprodsndin) =>
% 121.84/16.10 ((
% 121.84/16.10 (cartprodpairmemEL) =>
% 121.84/16.10 ((
% 121.84/16.10 (cartprodpairmemER) =>
% 121.84/16.10 ((
% 121.84/16.10 (cartprodmempaircEq) =>
% 121.84/16.10 ((
% 121.84/16.10 (cartprodfstpairEq) =>
% 121.84/16.10 ((
% 121.84/16.10 (cartprodsndpairEq) =>
% 121.84/16.10 ((
% 121.84/16.10 (cartprodpairsurjEq) =>
% 121.84/16.10 ((
% 121.84/16.10 (dpsetconstrI) =>
% 121.84/16.10 ((
% 121.84/16.10 (dpsetconstrSub) =>
% 121.84/16.10 ((
% 121.84/16.10 (setOfPairsIsBReln) =>
% 121.84/16.10 ((
% 121.84/16.10 (dpsetconstrERa) =>
% 121.84/16.10 ((
% 121.84/16.10 (dpsetconstrEL1) =>
% 121.84/16.10 ((
% 121.84/16.10 (dpsetconstrEL2) =>
% 121.84/16.10 ((
% 121.84/16.10 (dpsetconstrER) =>
% 121.84/16.10 ((
% 121.84/16.10 (funcImageSingleton) =>
% 121.84/16.10 ((
% 121.84/16.10 (apProp) =>
% 121.84/16.10 ((
% 121.84/16.10 (app) =>
% 121.84/16.10 ((
% 121.84/16.10 (infuncsetfunc) =>
% 121.84/16.10 ((
% 121.84/16.10 (ap2p) =>
% 121.84/16.10 ((
% 121.84/16.10 (funcinfuncset) =>
% 121.84/16.10 ((
% 121.84/16.10 (lamProp) =>
% 121.84/16.10 ((
% 121.84/16.10 (lamp) =>
% 121.84/16.10 ((
% 121.84/16.10 (lam2p) =>
% 121.84/16.10 ((
% 121.84/16.10 (brelnall1) =>
% 121.84/16.10 ((
% 121.84/16.10 (brelnall2) =>
% 121.84/16.10 ((
% 121.84/16.10 (ex1E2) =>
% 121.84/16.10 ((
% 121.84/16.10 (funcGraphProp1) =>
% 121.84/16.10 ((
% 121.84/16.10 (funcGraphProp3) =>
% 121.84/16.10 ((
% 121.84/16.10 (funcGraphProp2) =>
% 121.84/16.10 ((
% 121.84/16.10 (funcextLem) =>
% 121.84/16.10 ((
% 121.84/16.10 (funcGraphProp4) =>
% 121.84/16.10 ((
% 121.84/16.10 (subbreln) =>
% 121.84/16.10 ((
% 121.84/16.10 (eqbreln) =>
% 121.84/16.10 ((
% 121.84/16.10 (funcext) =>
% 121.84/16.10 ((
% 121.84/16.10 (funcext2) =>
% 121.84/16.10 ((
% 121.84/16.10 (ap2apEq1) =>
% 121.84/16.10 ((
% 121.84/16.10 (ap2apEq2) =>
% 121.84/16.10 ((
% 121.84/16.10 (beta1) =>
% 121.84/16.10 ((
% 121.84/16.10 (eta1) =>
% 121.84/16.10 ((
% 121.84/16.10 (lam2lamEq) =>
% 121.84/16.10 ((
% 121.84/16.10 (beta2) =>
% 121.84/16.10 ((
% 121.84/16.10 (eta2) =>
% 121.84/16.10 ((
% 121.84/16.10 (iffalseProp1) =>
% 121.84/16.10 ((
% 121.84/16.10 (iffalseProp2) =>
% 121.84/16.10 ((
% 121.84/16.10 (iftrueProp1) =>
% 121.84/16.10 ((
% 121.84/16.10 (iftrueProp2) =>
% 121.84/16.10 ((
% 121.84/16.10 (ifSingleton) =>
% 121.84/16.10 ((
% 121.84/16.10 (ifp) =>
% 121.84/16.10 ((
% 121.84/16.10 (theeq) =>
% 121.84/16.10 ((
% 121.84/16.10 (iftrue) =>
% 121.84/16.10 ((
% 121.84/16.10 (iffalse) =>
% 121.84/16.10 ((
% 121.84/16.10 (iftrueorfalse) =>
% 121.84/16.10 ((
% 121.84/16.10 (binintersectT_lem) =>
% 121.84/16.10 ((
% 121.84/16.10 (binunionT_lem) =>
% 121.84/16.10 ((
% 121.84/16.10 (powersetT_lem) =>
% 121.84/16.10 ((
% 121.84/16.10 (setminusT_lem) =>
% 121.84/16.10 ((
% 121.84/16.10 (complementT_lem) =>
% 121.84/16.10 ((
% 121.84/16.10 (setextT) =>
% 121.84/16.10 ((
% 121.84/16.10 (subsetTI) =>
% 121.84/16.10 ((
% 121.84/16.10 (powersetTI1) =>
% 121.84/16.10 ((
% 121.84/16.10 (powersetTE1) =>
% 121.84/16.10 ((
% 121.84/16.10 (complementTI1) =>
% 121.84/16.10 ((
% 121.84/16.10 (complementTE1) =>
% 121.84/16.10 ((
% 121.84/16.10 (binintersectTELcontra) =>
% 121.84/16.10 ((
% 121.84/16.10 (binintersectTERcontra) =>
% 121.84/16.10 ((
% 121.84/16.10 (contrasubsetT) =>
% 121.84/16.10 ((
% 121.84/16.10 (contrasubsetT1) =>
% 121.84/16.10 ((
% 121.84/16.10 (contrasubsetT2) =>
% 121.84/16.10 ((
% 121.84/16.10 (contrasubsetT3) =>
% 121.84/16.10 ((
% 121.84/16.10 (doubleComplementI1) =>
% 121.84/16.10 ((
% 121.84/16.10 (doubleComplementE1) =>
% 121.84/16.10 ((
% 121.84/16.10 (doubleComplementSub1) =>
% 121.84/16.10 ((
% 121.84/16.10 (doubleComplementSub2) =>
% 121.84/16.10 ((
% 121.84/16.10 (doubleComplementEq) =>
% 121.84/16.10 ((
% 121.84/16.10 (complementTnotintersectT) =>
% 121.84/16.10 ((
% 121.84/16.10 (complementImpComplementIntersect) =>
% 121.84/16.10 ((
% 121.84/16.10 (complementSubsetComplementIntersect) =>
% 121.84/16.10 ((
% 121.84/16.10 (complementInPowersetComplementIntersect) =>
% 121.84/16.10 ((
% 121.84/16.10 (contraSubsetComplement) =>
% 121.84/16.10 ((
% 121.84/16.10 (complementTcontraSubset) =>
% 121.84/16.10 ((
% 121.84/16.10 (binunionTILcontra) =>
% 121.84/16.10 ((
% 121.84/16.10 (binunionTIRcontra) =>
% 121.84/16.10 ((
% 121.84/16.10 (inIntersectImpInUnion) =>
% 121.84/16.10 ((
% 121.84/16.10 (inIntersectImpInUnion2) =>
% 121.84/16.10 ((
% 121.84/16.10 (inIntersectImpInIntersectUnions) =>
% 121.84/16.10 ((
% 121.84/16.10 (intersectInPowersetIntersectUnions) =>
% 121.84/16.10 ((
% 121.84/16.10 (inComplementUnionImpNotIn1) =>
% 121.84/16.10 ((
% 121.84/16.10 (inComplementUnionImpInComplement1) =>
% 121.84/16.10 ((
% 121.84/16.10 (binunionTE) =>
% 121.84/16.10 ((
% 121.84/16.10 (binunionTEcontra) =>
% 121.84/16.10 ((
% 121.84/16.10 (demorgan2a1) =>
% 121.84/16.10 ((
% 121.84/16.10 (complementUnionInPowersetComplement) =>
% 121.84/16.10 ((
% 121.84/16.10 (demorgan2a2) =>
% 121.84/16.10 ((
% 121.84/16.10 (demorgan1a) =>
% 121.84/16.10 ((
% 121.84/16.11 (demorgan1b) =>
% 121.84/16.11 ((
% 121.84/16.11 (demorgan1) =>
% 121.84/16.11 ((
% 121.84/16.11 (demorgan2a) =>
% 121.84/16.11 ((
% 121.84/16.11 (demorgan2b2) =>
% 121.84/16.11 ((
% 121.84/16.11 (demorgan2b) =>
% 121.84/16.11 ((
% 121.84/16.11 (demorgan2) =>
% 121.84/16.11 ((
% 121.84/16.11 (woz13rule0) =>
% 121.84/16.11 ((
% 121.84/16.11 (woz13rule1) =>
% 121.84/16.11 ((
% 121.84/16.11 (woz13rule2) =>
% 121.84/16.11 ((
% 121.84/16.11 (woz13rule3) =>
% 121.84/16.11 ((
% 121.84/16.11 (woz13rule4) =>
% 121.84/16.11 ((
% 121.84/16.11 (woz1_1) =>
% 121.84/16.11 ((
% 121.84/16.11 (woz1_2) =>
% 121.84/16.11 ((
% 121.84/16.11 (woz1_3) =>
% 121.84/16.11 ((
% 121.84/16.11 (woz1_4) =>
% 121.84/16.11 ((
% 121.84/16.11 (woz1_5) =>
% 121.84/16.11 ((
% 121.84/16.11 (breln1all2) =>
% 121.84/16.11 ((
% 121.84/16.11 (breln1SetBreln1) =>
% 121.84/16.11 ((
% 121.84/16.11 (choice2fnsingleton) =>
% 121.84/16.11 ((
% 121.84/16.11 (setOfPairsIsBReln1) =>
% 121.84/16.11 ((
% 121.84/16.11 (breln1all1) =>
% 121.84/16.11 ((
% 121.84/16.11 (subbreln1) =>
% 121.84/16.11 ((
% 121.84/16.11 (eqbreln1) =>
% 121.84/16.11 ((
% 121.84/16.11 (breln1invprop) =>
% 121.84/16.11 ((
% 121.84/16.11 (breln1invI) =>
% 121.84/16.11 ((
% 121.84/16.11 (breln1invE) =>
% 121.84/16.11 ((
% 121.84/16.11 (breln1compprop) =>
% 121.84/16.11 ((
% 121.84/16.11 (breln1compI) =>
% 121.84/16.11 ((
% 121.84/16.11 (breln1compE) =>
% 121.84/16.11 ((
% 121.84/16.11 (breln1compEex) =>
% 121.84/16.11 ((
% 121.84/16.11 (breln1unionprop) =>
% 121.84/16.11 ((
% 121.84/16.11 (breln1unionIL) =>
% 121.84/16.11 ((
% 121.84/16.11 (breln1unionIR) =>
% 121.84/16.11 ((
% 121.84/16.11 (breln1unionI) =>
% 121.84/16.11 ((
% 121.84/16.11 (breln1unionE) =>
% 121.84/16.11 ((
% 121.84/16.11 (breln1unionEcases) =>
% 121.84/16.11 ((
% 121.84/16.11 (breln1unionCommutes) =>
% 121.84/16.11 ((
% 121.84/16.11 (woz2Ex) =>
% 121.84/16.11 ((
% 121.84/16.11 (woz2W) =>
% 121.84/16.11 ((
% 121.84/16.11 (woz2A) =>
% 121.84/16.11 ((
% 121.84/16.11 (woz2B) =>
% 121.84/16.11 ((
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% 121.84/16.11 ((
% 121.84/16.11 (image1Ex1) =>
% 121.84/16.11 ((
% 121.84/16.11 (image1Equiv) =>
% 121.84/16.11 ((
% 121.84/16.11 (image1E) =>
% 121.84/16.11 ((
% 121.84/16.11 (image1I) =>
% 121.84/16.11 ((
% 121.84/16.11 (injFuncInInjFuncSet) =>
% 121.84/16.11 ((
% 121.84/16.11 (!!) @ (
% 121.84/16.11 (('#B') @ (
% 121.84/16.11 !!) @
% 121.84/16.11 (
% 121.84/16.11 (
% 121.84/16.11 ('#B') @ (
% 121.84/16.11 (
% 121.84/16.11 ('#B') @ (
% 121.84/16.11 !!))) @
% 121.84/16.11 (
% 121.84/16.11 (
% 121.84/16.11 ('#S') @ (
% 121.84/16.11 (
% 121.84/16.11 ('#B') @ (
% 121.84/16.11 '#S') @
% 121.84/16.11 (
% 121.84/16.11 (
% 121.84/16.11 ('#B') @ (
% 121.84/16.11 (
% 121.84/16.11 ('#B') @ (
% 121.84/16.11 '#S'))) @
% 121.84/16.11 (
% 121.84/16.11 (
% 121.84/16.11 ('#B') @ (
% 121.84/16.11 (
% 121.84/16.11 ('#B') @ (
% 121.84/16.11 (
% 121.84/16.11 ('#B') @ (
% 121.84/16.11 =>))))) @
% 121.84/16.11 (
% 121.84/16.11 (
% 121.84/16.11 ('#B') @ (
% 121.84/16.11 (
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% 121.84/16.11 (
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% 121.84/16.11 injFuncSet)))))))) @
% 121.84/16.11 (
% 121.84/16.11 (
% 121.84/16.11 ('#B') @ (
% 121.84/16.11 (
% 121.84/16.11 ('#B') @ (
% 121.84/16.11 (
% 121.84/16.11 ('#C') @ in)))) @
% 121.84/16.11 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 121.84/16.11 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl896])).
% 121.84/16.11 thf(zip_derived_cl924, plain,
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% 121.84/16.11 (((powersetE1) =>
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% 121.84/16.11 (((sepSubset) =>
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% 121.84/16.11 (((upairset2IR) =>
% 121.84/16.11 (((binunionIR) =>
% 121.84/16.11 (((binunionEcases) =>
% 121.84/16.11 (((binunionE) =>
% 121.84/16.11 (((binunionLsub) =>
% 121.84/16.11 (((binunionRsub) =>
% 121.84/16.11 (((binintersectI) =>
% 121.84/16.11 (((binintersectSubset5) =>
% 121.84/16.11 (((binintersectEL) =>
% 121.84/16.11 (((binintersectLsub) =>
% 121.84/16.11 (((binintersectSubset2) =>
% 121.84/16.11 (((binintersectSubset3) =>
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% 121.84/16.11 (((disjointsetsI1) =>
% 121.84/16.11 (((binintersectRsub) =>
% 121.84/16.11 ((
% 121.84/16.11 (binintersectSubset4) =>
% 121.84/16.11 ((
% 121.84/16.11 (binintersectSubset1) =>
% 121.84/16.11 ((
% 121.84/16.11 (bs114d) =>
% 121.84/16.11 ((
% 121.84/16.11 (setminusI) =>
% 121.84/16.11 ((
% 121.84/16.11 (setminusEL) =>
% 121.84/16.11 ((
% 121.84/16.11 (setminusER) =>
% 121.84/16.11 ((
% 121.84/16.11 (setminusSubset2) =>
% 121.84/16.11 ((
% 121.84/16.11 (setminusERneg) =>
% 121.84/16.11 ((
% 121.84/16.11 (setminusELneg) =>
% 121.84/16.11 ((
% 121.84/16.11 (setminusILneg) =>
% 121.84/16.11 ((
% 121.84/16.11 (setminusIRneg) =>
% 121.84/16.11 ((
% 121.84/16.11 (setminusLsub) =>
% 121.84/16.11 ((
% 121.84/16.11 (setminusSubset1) =>
% 121.84/16.11 ((
% 121.84/16.11 (symdiffE) =>
% 121.84/16.11 ((
% 121.84/16.11 (symdiffI1) =>
% 121.84/16.11 ((
% 121.84/16.11 (symdiffI2) =>
% 121.84/16.11 ((
% 121.84/16.11 (symdiffIneg1) =>
% 121.84/16.11 ((
% 121.84/16.11 (symdiffIneg2) =>
% 121.84/16.11 ((
% 121.84/16.11 (secondinupair) =>
% 121.84/16.11 ((
% 121.84/16.11 (setukpairIL) =>
% 121.84/16.11 ((
% 121.84/16.11 (setukpairIR) =>
% 121.84/16.11 ((
% 121.84/16.11 (kpairiskpair) =>
% 121.84/16.11 ((
% 121.84/16.11 (kpairp) =>
% 121.84/16.11 ((
% 121.84/16.11 (singletonsubset) =>
% 121.84/16.11 ((
% 121.84/16.11 (singletoninpowerset) =>
% 121.84/16.11 ((
% 121.84/16.11 (singletoninpowunion) =>
% 121.84/16.11 ((
% 121.84/16.11 (upairset2E) =>
% 121.84/16.11 ((
% 121.84/16.11 (upairsubunion) =>
% 121.84/16.11 ((
% 121.84/16.11 (upairinpowunion) =>
% 121.84/16.11 ((
% 121.84/16.11 (ubforcartprodlem1) =>
% 121.84/16.11 ((
% 121.84/16.11 (ubforcartprodlem2) =>
% 121.84/16.11 ((
% 121.84/16.11 (ubforcartprodlem3) =>
% 121.84/16.11 ((
% 121.84/16.11 (cartprodpairin) =>
% 121.84/16.11 ((
% 121.84/16.11 (cartprodmempair1) =>
% 121.84/16.11 ((
% 121.84/16.11 (cartprodmempair) =>
% 121.84/16.11 ((
% 121.84/16.11 (setunionE2) =>
% 121.84/16.11 ((
% 121.84/16.11 (setunionsingleton1) =>
% 121.84/16.11 ((
% 121.84/16.11 (setunionsingleton2) =>
% 121.84/16.11 ((
% 121.84/16.11 (setunionsingleton) =>
% 121.84/16.11 ((
% 121.84/16.11 (singletonprop) =>
% 121.84/16.11 ((
% 121.84/16.11 (ex1E1) =>
% 121.84/16.11 ((
% 121.84/16.11 (ex1I) =>
% 121.84/16.11 ((
% 121.84/16.11 (ex1I2) =>
% 121.84/16.11 ((
% 121.84/16.11 (singletonsuniq) =>
% 121.84/16.11 ((
% 121.84/16.11 (setukpairinjL1) =>
% 121.84/16.11 ((
% 121.84/16.11 (kfstsingleton) =>
% 121.84/16.11 ((
% 121.84/16.11 (theprop) =>
% 121.84/16.11 ((
% 121.84/16.11 (kfstpairEq) =>
% 121.84/16.11 ((
% 121.84/16.11 (cartprodfstin) =>
% 121.84/16.11 ((
% 121.84/16.11 (setukpairinjL2) =>
% 121.84/16.11 ((
% 121.84/16.11 (setukpairinjL) =>
% 121.84/16.11 ((
% 121.84/16.11 (setukpairinjR11) =>
% 121.84/16.11 ((
% 121.84/16.11 (setukpairinjR12) =>
% 121.84/16.11 ((
% 121.84/16.11 (setukpairinjR1) =>
% 121.84/16.11 ((
% 121.84/16.11 (upairequniteq) =>
% 121.84/16.11 ((
% 121.84/16.11 (setukpairinjR2) =>
% 121.84/16.11 ((
% 121.84/16.11 (setukpairinjR) =>
% 121.84/16.11 ((
% 121.84/16.11 (ksndsingleton) =>
% 121.84/16.11 ((
% 121.84/16.11 (ksndpairEq) =>
% 121.84/16.11 ((
% 121.84/16.11 (kpairsurjEq) =>
% 121.84/16.11 ((
% 121.84/16.11 (cartprodsndin) =>
% 121.84/16.11 ((
% 121.84/16.11 (cartprodpairmemEL) =>
% 121.84/16.11 ((
% 121.84/16.11 (cartprodpairmemER) =>
% 121.84/16.11 ((
% 121.84/16.11 (cartprodmempaircEq) =>
% 121.84/16.11 ((
% 121.84/16.11 (cartprodfstpairEq) =>
% 121.84/16.11 ((
% 121.84/16.11 (cartprodsndpairEq) =>
% 121.84/16.11 ((
% 121.84/16.11 (cartprodpairsurjEq) =>
% 121.84/16.11 ((
% 121.84/16.11 (dpsetconstrI) =>
% 121.84/16.11 ((
% 121.84/16.11 (dpsetconstrSub) =>
% 121.84/16.11 ((
% 121.84/16.11 (setOfPairsIsBReln) =>
% 121.84/16.11 ((
% 121.84/16.11 (dpsetconstrERa) =>
% 121.84/16.11 ((
% 121.84/16.11 (dpsetconstrEL1) =>
% 121.84/16.11 ((
% 121.84/16.11 (dpsetconstrEL2) =>
% 121.84/16.11 ((
% 121.84/16.11 (dpsetconstrER) =>
% 121.84/16.11 ((
% 121.84/16.11 (funcImageSingleton) =>
% 121.84/16.11 ((
% 121.84/16.11 (apProp) =>
% 121.84/16.11 ((
% 121.84/16.11 (app) =>
% 121.84/16.11 ((
% 121.84/16.11 (infuncsetfunc) =>
% 121.84/16.11 ((
% 121.84/16.11 (ap2p) =>
% 121.84/16.11 ((
% 121.84/16.11 (funcinfuncset) =>
% 121.84/16.11 ((
% 121.84/16.11 (lamProp) =>
% 121.84/16.11 ((
% 121.84/16.11 (lamp) =>
% 121.84/16.11 ((
% 121.84/16.11 (lam2p) =>
% 121.84/16.11 ((
% 121.84/16.11 (brelnall1) =>
% 121.84/16.11 ((
% 121.84/16.11 (brelnall2) =>
% 121.84/16.11 ((
% 121.84/16.11 (ex1E2) =>
% 121.84/16.11 ((
% 121.84/16.11 (funcGraphProp1) =>
% 121.84/16.11 ((
% 121.84/16.11 (funcGraphProp3) =>
% 121.84/16.11 ((
% 121.84/16.11 (funcGraphProp2) =>
% 121.84/16.11 ((
% 121.84/16.11 (funcextLem) =>
% 121.84/16.11 ((
% 121.84/16.11 (funcGraphProp4) =>
% 121.84/16.11 ((
% 121.84/16.11 (subbreln) =>
% 121.84/16.11 ((
% 121.84/16.11 (eqbreln) =>
% 121.84/16.11 ((
% 121.84/16.11 (funcext) =>
% 121.84/16.11 ((
% 121.84/16.11 (funcext2) =>
% 121.84/16.11 ((
% 121.84/16.11 (ap2apEq1) =>
% 121.84/16.11 ((
% 121.84/16.11 (ap2apEq2) =>
% 121.84/16.11 ((
% 121.84/16.11 (beta1) =>
% 121.84/16.11 ((
% 121.84/16.11 (eta1) =>
% 121.84/16.11 ((
% 121.84/16.11 (lam2lamEq) =>
% 121.84/16.11 ((
% 121.84/16.11 (beta2) =>
% 121.84/16.11 ((
% 121.84/16.11 (eta2) =>
% 121.84/16.11 ((
% 121.84/16.11 (iffalseProp1) =>
% 121.84/16.11 ((
% 121.84/16.11 (iffalseProp2) =>
% 121.84/16.11 ((
% 121.84/16.11 (iftrueProp1) =>
% 121.84/16.11 ((
% 121.84/16.11 (iftrueProp2) =>
% 121.84/16.11 ((
% 121.84/16.11 (ifSingleton) =>
% 121.84/16.11 ((
% 121.84/16.11 (ifp) =>
% 121.84/16.11 ((
% 121.84/16.11 (theeq) =>
% 121.84/16.11 ((
% 121.84/16.11 (iftrue) =>
% 121.84/16.11 ((
% 121.84/16.11 (iffalse) =>
% 121.84/16.11 ((
% 121.84/16.11 (iftrueorfalse) =>
% 121.84/16.11 ((
% 121.84/16.11 (binintersectT_lem) =>
% 121.84/16.11 ((
% 121.84/16.11 (binunionT_lem) =>
% 121.84/16.11 ((
% 121.84/16.11 (powersetT_lem) =>
% 121.84/16.11 ((
% 121.84/16.11 (setminusT_lem) =>
% 121.84/16.11 ((
% 121.84/16.11 (complementT_lem) =>
% 121.84/16.11 ((
% 121.84/16.11 (setextT) =>
% 121.84/16.11 ((
% 121.84/16.11 (subsetTI) =>
% 121.84/16.11 ((
% 121.84/16.11 (powersetTI1) =>
% 121.84/16.11 ((
% 121.84/16.11 (powersetTE1) =>
% 121.84/16.11 ((
% 121.84/16.11 (complementTI1) =>
% 121.84/16.11 ((
% 121.84/16.11 (complementTE1) =>
% 121.84/16.11 ((
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% 121.84/16.11 ((
% 121.84/16.11 (binintersectTERcontra) =>
% 121.84/16.11 ((
% 121.84/16.11 (contrasubsetT) =>
% 121.84/16.11 ((
% 121.84/16.11 (contrasubsetT1) =>
% 121.84/16.11 ((
% 121.84/16.11 (contrasubsetT2) =>
% 121.84/16.11 ((
% 121.84/16.11 (contrasubsetT3) =>
% 121.84/16.11 ((
% 121.84/16.11 (doubleComplementI1) =>
% 121.84/16.11 ((
% 121.84/16.11 (doubleComplementE1) =>
% 121.84/16.11 ((
% 121.84/16.11 (doubleComplementSub1) =>
% 121.84/16.11 ((
% 121.84/16.11 (doubleComplementSub2) =>
% 121.84/16.11 ((
% 121.84/16.11 (doubleComplementEq) =>
% 121.84/16.11 ((
% 121.84/16.11 (complementTnotintersectT) =>
% 121.84/16.11 ((
% 121.84/16.11 (complementImpComplementIntersect) =>
% 121.84/16.11 ((
% 121.84/16.11 (complementSubsetComplementIntersect) =>
% 121.84/16.11 ((
% 121.84/16.11 (complementInPowersetComplementIntersect) =>
% 121.84/16.11 ((
% 121.84/16.11 (contraSubsetComplement) =>
% 121.84/16.11 ((
% 121.84/16.11 (complementTcontraSubset) =>
% 121.84/16.11 ((
% 121.84/16.11 (binunionTILcontra) =>
% 121.84/16.11 ((
% 121.84/16.11 (binunionTIRcontra) =>
% 121.84/16.11 ((
% 121.84/16.11 (inIntersectImpInUnion) =>
% 121.84/16.11 ((
% 121.84/16.11 (inIntersectImpInUnion2) =>
% 121.84/16.11 ((
% 121.84/16.11 (inIntersectImpInIntersectUnions) =>
% 121.84/16.11 ((
% 121.84/16.11 (intersectInPowersetIntersectUnions) =>
% 121.84/16.11 ((
% 121.84/16.11 (inComplementUnionImpNotIn1) =>
% 121.84/16.11 ((
% 121.84/16.11 (inComplementUnionImpInComplement1) =>
% 121.84/16.11 ((
% 121.84/16.11 (binunionTE) =>
% 121.84/16.11 ((
% 121.84/16.11 (binunionTEcontra) =>
% 121.84/16.11 ((
% 121.84/16.11 (demorgan2a1) =>
% 121.84/16.11 ((
% 121.84/16.11 (complementUnionInPowersetComplement) =>
% 121.84/16.11 ((
% 121.84/16.11 (demorgan2a2) =>
% 121.84/16.11 ((
% 121.84/16.11 (demorgan1a) =>
% 121.84/16.11 ((
% 121.84/16.11 (demorgan1b) =>
% 121.84/16.11 ((
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% 121.84/16.11 ((
% 121.84/16.11 (demorgan2a) =>
% 121.84/16.11 ((
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% 121.84/16.11 ((
% 121.84/16.11 (demorgan2b) =>
% 121.84/16.11 ((
% 121.84/16.11 (demorgan2) =>
% 121.84/16.11 ((
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% 121.84/16.11 ((
% 121.84/16.11 (woz13rule1) =>
% 121.84/16.11 ((
% 121.84/16.11 (woz13rule2) =>
% 121.84/16.11 ((
% 121.84/16.11 (woz13rule3) =>
% 121.84/16.11 ((
% 121.84/16.11 (woz13rule4) =>
% 121.84/16.11 ((
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% 121.84/16.11 ((
% 121.84/16.11 (woz1_2) =>
% 121.84/16.11 ((
% 121.84/16.11 (woz1_3) =>
% 121.84/16.11 ((
% 121.84/16.11 (woz1_4) =>
% 121.84/16.11 ((
% 121.84/16.11 (woz1_5) =>
% 121.84/16.11 ((
% 121.84/16.11 (breln1all2) =>
% 121.84/16.11 ((
% 121.84/16.11 (breln1SetBreln1) =>
% 121.84/16.11 ((
% 121.84/16.11 (choice2fnsingleton) =>
% 121.84/16.11 ((
% 121.84/16.11 (setOfPairsIsBReln1) =>
% 121.84/16.11 ((
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% 121.84/16.11 ((
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% 121.84/16.11 ((
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% 121.84/16.11 ((
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% 121.84/16.11 ((
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% 121.84/16.11 ((
% 121.84/16.11 (breln1invE) =>
% 121.84/16.11 ((
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% 121.84/16.11 ((
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% 121.84/16.11 ((
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% 121.84/16.11 ((
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% 121.84/16.11 ((
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% 121.84/16.11 ((
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% 121.84/16.11 ((
% 121.84/16.11 (breln1unionIR) =>
% 121.84/16.11 ((
% 121.84/16.11 (breln1unionI) =>
% 121.84/16.11 ((
% 121.84/16.11 (breln1unionE) =>
% 121.84/16.11 ((
% 121.84/16.11 (breln1unionEcases) =>
% 121.84/16.11 ((
% 121.84/16.11 (breln1unionCommutes) =>
% 121.84/16.11 ((
% 121.84/16.11 (woz2Ex) =>
% 121.84/16.11 ((
% 121.84/16.11 (woz2W) =>
% 121.84/16.11 ((
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% 121.84/16.11 ((
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% 121.84/16.11 ((
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% 121.84/16.11 ((
% 121.84/16.11 (image1Ex1) =>
% 121.84/16.11 ((
% 121.84/16.11 (image1Equiv) =>
% 121.84/16.11 ((
% 121.84/16.11 (image1E) =>
% 121.84/16.11 ((
% 121.84/16.11 (image1I) =>
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% 121.84/16.11 (((binunionEcases) =>
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% 121.84/16.11 (((binunionLsub) =>
% 121.84/16.11 (((binunionRsub) =>
% 121.84/16.11 (((binintersectI) =>
% 121.84/16.11 (((binintersectSubset5) =>
% 121.84/16.11 (((binintersectEL) =>
% 121.84/16.11 (((binintersectLsub) =>
% 121.84/16.11 (((binintersectSubset2) =>
% 121.84/16.11 (((binintersectSubset3) =>
% 121.84/16.11 (((binintersectER) =>
% 121.84/16.11 (((disjointsetsI1) =>
% 121.84/16.11 (((binintersectRsub) =>
% 121.84/16.11 (((binintersectSubset4) =>
% 121.84/16.11 (((binintersectSubset1) =>
% 121.84/16.11 ((
% 121.84/16.11 (bs114d) =>
% 121.84/16.11 ((
% 121.84/16.11 (setminusI) =>
% 121.84/16.11 ((
% 121.84/16.11 (setminusEL) =>
% 121.84/16.11 ((
% 121.84/16.11 (setminusER) =>
% 121.84/16.11 ((
% 121.84/16.11 (setminusSubset2) =>
% 121.84/16.11 ((
% 121.84/16.11 (setminusERneg) =>
% 121.84/16.11 ((
% 121.84/16.11 (setminusELneg) =>
% 121.84/16.11 ((
% 121.84/16.11 (setminusILneg) =>
% 121.84/16.11 ((
% 121.84/16.11 (setminusIRneg) =>
% 121.84/16.11 ((
% 121.84/16.11 (setminusLsub) =>
% 121.84/16.11 ((
% 121.84/16.11 (setminusSubset1) =>
% 121.84/16.11 ((
% 121.84/16.11 (symdiffE) =>
% 121.84/16.11 ((
% 121.84/16.11 (symdiffI1) =>
% 121.84/16.11 ((
% 121.84/16.11 (symdiffI2) =>
% 121.84/16.11 ((
% 121.84/16.11 (symdiffIneg1) =>
% 121.84/16.11 ((
% 121.84/16.11 (symdiffIneg2) =>
% 121.84/16.11 ((
% 121.84/16.11 (secondinupair) =>
% 121.84/16.11 ((
% 121.84/16.11 (setukpairIL) =>
% 121.84/16.11 ((
% 121.84/16.11 (setukpairIR) =>
% 121.84/16.11 ((
% 121.84/16.11 (kpairiskpair) =>
% 121.84/16.11 ((
% 121.84/16.11 (kpairp) =>
% 121.84/16.11 ((
% 121.84/16.11 (singletonsubset) =>
% 121.84/16.11 ((
% 121.84/16.11 (singletoninpowerset) =>
% 121.84/16.11 ((
% 121.84/16.11 (singletoninpowunion) =>
% 121.84/16.11 ((
% 121.84/16.11 (upairset2E) =>
% 121.84/16.11 ((
% 121.84/16.11 (upairsubunion) =>
% 121.84/16.11 ((
% 121.84/16.11 (upairinpowunion) =>
% 121.84/16.11 ((
% 121.84/16.11 (ubforcartprodlem1) =>
% 121.84/16.11 ((
% 121.84/16.11 (ubforcartprodlem2) =>
% 121.84/16.11 ((
% 121.84/16.11 (ubforcartprodlem3) =>
% 121.84/16.11 ((
% 121.84/16.11 (cartprodpairin) =>
% 121.84/16.11 ((
% 121.84/16.11 (cartprodmempair1) =>
% 121.84/16.11 ((
% 121.84/16.11 (cartprodmempair) =>
% 121.84/16.11 ((
% 121.84/16.11 (setunionE2) =>
% 121.84/16.11 ((
% 121.84/16.11 (setunionsingleton1) =>
% 121.84/16.11 ((
% 121.84/16.11 (setunionsingleton2) =>
% 121.84/16.11 ((
% 121.84/16.11 (setunionsingleton) =>
% 121.84/16.11 ((
% 121.84/16.11 (singletonprop) =>
% 121.84/16.11 ((
% 121.84/16.11 (ex1E1) =>
% 121.84/16.11 ((
% 121.84/16.11 (ex1I) =>
% 121.84/16.11 ((
% 121.84/16.11 (ex1I2) =>
% 121.84/16.11 ((
% 121.84/16.11 (singletonsuniq) =>
% 121.84/16.11 ((
% 121.84/16.11 (setukpairinjL1) =>
% 121.84/16.11 ((
% 121.84/16.11 (kfstsingleton) =>
% 121.84/16.11 ((
% 121.84/16.11 (theprop) =>
% 121.84/16.11 ((
% 121.84/16.11 (kfstpairEq) =>
% 121.84/16.11 ((
% 121.84/16.11 (cartprodfstin) =>
% 121.84/16.11 ((
% 121.84/16.11 (setukpairinjL2) =>
% 121.84/16.11 ((
% 121.84/16.11 (setukpairinjL) =>
% 121.84/16.11 ((
% 121.84/16.11 (setukpairinjR11) =>
% 121.84/16.11 ((
% 121.84/16.11 (setukpairinjR12) =>
% 121.84/16.11 ((
% 121.84/16.11 (setukpairinjR1) =>
% 121.84/16.11 ((
% 121.84/16.11 (upairequniteq) =>
% 121.84/16.11 ((
% 121.84/16.11 (setukpairinjR2) =>
% 121.84/16.11 ((
% 121.84/16.11 (setukpairinjR) =>
% 121.84/16.11 ((
% 121.84/16.11 (ksndsingleton) =>
% 121.84/16.11 ((
% 121.84/16.11 (ksndpairEq) =>
% 121.84/16.11 ((
% 121.84/16.11 (kpairsurjEq) =>
% 121.84/16.11 ((
% 121.84/16.11 (cartprodsndin) =>
% 121.84/16.11 ((
% 121.84/16.11 (cartprodpairmemEL) =>
% 121.84/16.11 ((
% 121.84/16.11 (cartprodpairmemER) =>
% 121.84/16.11 ((
% 121.84/16.11 (cartprodmempaircEq) =>
% 121.84/16.11 ((
% 121.84/16.11 (cartprodfstpairEq) =>
% 121.84/16.11 ((
% 121.84/16.11 (cartprodsndpairEq) =>
% 121.84/16.11 ((
% 121.84/16.11 (cartprodpairsurjEq) =>
% 121.84/16.11 ((
% 121.84/16.11 (dpsetconstrI) =>
% 121.84/16.11 ((
% 121.84/16.11 (dpsetconstrSub) =>
% 121.84/16.11 ((
% 121.84/16.11 (setOfPairsIsBReln) =>
% 121.84/16.11 ((
% 121.84/16.11 (dpsetconstrERa) =>
% 121.84/16.11 ((
% 121.84/16.11 (dpsetconstrEL1) =>
% 121.84/16.11 ((
% 121.84/16.11 (dpsetconstrEL2) =>
% 121.84/16.11 ((
% 121.84/16.11 (dpsetconstrER) =>
% 121.84/16.11 ((
% 121.84/16.11 (funcImageSingleton) =>
% 121.84/16.11 ((
% 121.84/16.11 (apProp) =>
% 121.84/16.11 ((
% 121.84/16.11 (app) =>
% 121.84/16.11 ((
% 121.84/16.11 (infuncsetfunc) =>
% 121.84/16.11 ((
% 121.84/16.11 (ap2p) =>
% 121.84/16.11 ((
% 121.84/16.11 (funcinfuncset) =>
% 121.84/16.11 ((
% 121.84/16.11 (lamProp) =>
% 121.84/16.11 ((
% 121.84/16.11 (lamp) =>
% 121.84/16.11 ((
% 121.84/16.11 (lam2p) =>
% 121.84/16.11 ((
% 121.84/16.11 (brelnall1) =>
% 121.84/16.11 ((
% 121.84/16.11 (brelnall2) =>
% 121.84/16.11 ((
% 121.84/16.11 (ex1E2) =>
% 121.84/16.11 ((
% 121.84/16.11 (funcGraphProp1) =>
% 121.84/16.11 ((
% 121.84/16.11 (funcGraphProp3) =>
% 121.84/16.11 ((
% 121.84/16.11 (funcGraphProp2) =>
% 121.84/16.11 ((
% 121.84/16.11 (funcextLem) =>
% 121.84/16.11 ((
% 121.84/16.11 (funcGraphProp4) =>
% 121.84/16.11 ((
% 121.84/16.11 (subbreln) =>
% 121.84/16.11 ((
% 121.84/16.11 (eqbreln) =>
% 121.84/16.11 ((
% 121.84/16.11 (funcext) =>
% 121.84/16.11 ((
% 121.84/16.11 (funcext2) =>
% 121.84/16.11 ((
% 121.84/16.11 (ap2apEq1) =>
% 121.84/16.11 ((
% 121.84/16.11 (ap2apEq2) =>
% 121.84/16.11 ((
% 121.84/16.11 (beta1) =>
% 121.84/16.11 ((
% 121.84/16.11 (eta1) =>
% 121.84/16.11 ((
% 121.84/16.11 (lam2lamEq) =>
% 121.84/16.11 ((
% 121.84/16.11 (beta2) =>
% 121.84/16.11 ((
% 121.84/16.11 (eta2) =>
% 121.84/16.11 ((
% 121.84/16.11 (iffalseProp1) =>
% 121.84/16.11 ((
% 121.84/16.11 (iffalseProp2) =>
% 121.84/16.11 ((
% 121.84/16.11 (iftrueProp1) =>
% 121.84/16.11 ((
% 121.84/16.11 (iftrueProp2) =>
% 121.84/16.11 ((
% 121.84/16.11 (ifSingleton) =>
% 121.84/16.11 ((
% 121.84/16.11 (ifp) =>
% 121.84/16.11 ((
% 121.84/16.11 (theeq) =>
% 121.84/16.11 ((
% 121.84/16.11 (iftrue) =>
% 121.84/16.11 ((
% 121.84/16.11 (iffalse) =>
% 121.84/16.11 ((
% 121.84/16.11 (iftrueorfalse) =>
% 121.84/16.11 ((
% 121.84/16.11 (binintersectT_lem) =>
% 121.84/16.11 ((
% 121.84/16.11 (binunionT_lem) =>
% 121.84/16.11 ((
% 121.84/16.11 (powersetT_lem) =>
% 121.84/16.11 ((
% 121.84/16.11 (setminusT_lem) =>
% 121.84/16.11 ((
% 121.84/16.11 (complementT_lem) =>
% 121.84/16.11 ((
% 121.84/16.11 (setextT) =>
% 121.84/16.11 ((
% 121.84/16.11 (subsetTI) =>
% 121.84/16.11 ((
% 121.84/16.11 (powersetTI1) =>
% 121.84/16.11 ((
% 121.84/16.11 (powersetTE1) =>
% 121.84/16.11 ((
% 121.84/16.11 (complementTI1) =>
% 121.84/16.11 ((
% 121.84/16.11 (complementTE1) =>
% 121.84/16.11 ((
% 121.84/16.11 (binintersectTELcontra) =>
% 121.84/16.11 ((
% 121.84/16.11 (binintersectTERcontra) =>
% 121.84/16.11 ((
% 121.84/16.11 (contrasubsetT) =>
% 121.84/16.11 ((
% 121.84/16.11 (contrasubsetT1) =>
% 121.84/16.11 ((
% 121.84/16.11 (contrasubsetT2) =>
% 121.84/16.11 ((
% 121.84/16.11 (contrasubsetT3) =>
% 121.84/16.11 ((
% 121.84/16.11 (doubleComplementI1) =>
% 121.84/16.11 ((
% 121.84/16.11 (doubleComplementE1) =>
% 121.84/16.11 ((
% 121.84/16.11 (doubleComplementSub1) =>
% 121.84/16.11 ((
% 121.84/16.11 (doubleComplementSub2) =>
% 121.84/16.11 ((
% 121.84/16.11 (doubleComplementEq) =>
% 121.84/16.11 ((
% 121.84/16.11 (complementTnotintersectT) =>
% 121.84/16.11 ((
% 121.84/16.11 (complementImpComplementIntersect) =>
% 121.84/16.11 ((
% 121.84/16.11 (complementSubsetComplementIntersect) =>
% 121.84/16.11 ((
% 121.84/16.11 (complementInPowersetComplementIntersect) =>
% 121.84/16.11 ((
% 121.84/16.11 (contraSubsetComplement) =>
% 121.84/16.11 ((
% 121.84/16.11 (complementTcontraSubset) =>
% 121.84/16.11 ((
% 121.84/16.11 (binunionTILcontra) =>
% 121.84/16.11 ((
% 121.84/16.11 (binunionTIRcontra) =>
% 121.84/16.11 ((
% 121.84/16.11 (inIntersectImpInUnion) =>
% 121.84/16.11 ((
% 121.84/16.11 (inIntersectImpInUnion2) =>
% 121.84/16.11 ((
% 121.84/16.11 (inIntersectImpInIntersectUnions) =>
% 121.84/16.11 ((
% 121.84/16.11 (intersectInPowersetIntersectUnions) =>
% 121.84/16.11 ((
% 121.84/16.11 (inComplementUnionImpNotIn1) =>
% 121.84/16.11 ((
% 121.84/16.11 (inComplementUnionImpInComplement1) =>
% 121.84/16.11 ((
% 121.84/16.11 (binunionTE) =>
% 121.84/16.11 ((
% 121.84/16.11 (binunionTEcontra) =>
% 121.84/16.11 ((
% 121.84/16.11 (demorgan2a1) =>
% 121.84/16.11 ((
% 121.84/16.11 (complementUnionInPowersetComplement) =>
% 121.84/16.11 ((
% 121.84/16.11 (demorgan2a2) =>
% 121.84/16.11 ((
% 121.84/16.11 (demorgan1a) =>
% 121.84/16.11 ((
% 121.84/16.11 (demorgan1b) =>
% 121.84/16.11 ((
% 121.84/16.11 (demorgan1) =>
% 121.84/16.11 ((
% 121.84/16.11 (demorgan2a) =>
% 121.84/16.11 ((
% 121.84/16.11 (demorgan2b2) =>
% 121.84/16.11 ((
% 121.84/16.11 (demorgan2b) =>
% 121.84/16.11 ((
% 121.84/16.11 (demorgan2) =>
% 121.84/16.11 ((
% 121.84/16.11 (woz13rule0) =>
% 121.84/16.11 ((
% 121.84/16.11 (woz13rule1) =>
% 121.84/16.11 ((
% 121.84/16.11 (woz13rule2) =>
% 121.84/16.11 ((
% 121.84/16.11 (woz13rule3) =>
% 121.84/16.11 ((
% 121.84/16.11 (woz13rule4) =>
% 121.84/16.11 ((
% 121.84/16.11 (woz1_1) =>
% 121.84/16.11 ((
% 121.84/16.11 (woz1_2) =>
% 121.84/16.11 ((
% 121.84/16.11 (woz1_3) =>
% 121.84/16.11 ((
% 121.84/16.11 (woz1_4) =>
% 121.84/16.11 ((
% 121.84/16.11 (woz1_5) =>
% 121.84/16.11 ((
% 121.84/16.11 (breln1all2) =>
% 121.84/16.11 ((
% 121.84/16.11 (breln1SetBreln1) =>
% 121.84/16.11 ((
% 121.84/16.11 (choice2fnsingleton) =>
% 121.84/16.11 ((
% 121.84/16.11 (setOfPairsIsBReln1) =>
% 121.84/16.11 ((
% 121.84/16.11 (breln1all1) =>
% 121.84/16.11 ((
% 121.84/16.11 (subbreln1) =>
% 121.84/16.11 ((
% 121.84/16.11 (eqbreln1) =>
% 121.84/16.11 ((
% 121.84/16.11 (breln1invprop) =>
% 121.84/16.11 ((
% 121.84/16.11 (breln1invI) =>
% 121.84/16.11 ((
% 121.84/16.11 (breln1invE) =>
% 121.84/16.11 ((
% 121.84/16.11 (breln1compprop) =>
% 121.84/16.11 ((
% 121.84/16.11 (breln1compI) =>
% 121.84/16.11 ((
% 121.84/16.11 (breln1compE) =>
% 121.84/16.11 ((
% 121.84/16.11 (breln1compEex) =>
% 121.84/16.11 ((
% 121.84/16.11 (breln1unionprop) =>
% 121.84/16.11 ((
% 121.84/16.11 (breln1unionIL) =>
% 121.84/16.11 ((
% 121.84/16.11 (breln1unionIR) =>
% 121.84/16.11 ((
% 121.84/16.11 (breln1unionI) =>
% 121.84/16.11 ((
% 121.84/16.11 (breln1unionE) =>
% 121.84/16.11 ((
% 121.84/16.11 (breln1unionEcases) =>
% 121.84/16.11 ((
% 121.84/16.11 (breln1unionCommutes) =>
% 121.84/16.11 ((
% 121.84/16.11 (woz2Ex) =>
% 121.84/16.11 ((
% 121.84/16.11 (woz2W) =>
% 121.84/16.11 ((
% 121.84/16.11 (woz2A) =>
% 121.84/16.11 ((
% 121.84/16.11 (woz2B) =>
% 121.84/16.11 ((
% 121.84/16.11 (image1Ex) =>
% 121.84/16.11 ((
% 121.84/16.11 (image1Ex1) =>
% 121.84/16.11 ((
% 121.84/16.11 (image1Equiv) =>
% 121.84/16.11 ((
% 121.84/16.11 (image1E) =>
% 121.84/16.11 ((
% 121.84/16.11 (image1I) =>
% 121.84/16.11 ((
% 121.84/16.11 (injFuncInInjFuncSet) =>
% 121.84/16.11 ((
% 121.84/16.11 (!!) @ (
% 121.84/16.11 (('#B') @ (
% 121.84/16.11 !!) @
% 121.84/16.11 (
% 121.84/16.11 (
% 121.84/16.11 ('#B') @ (
% 121.84/16.11 (
% 121.84/16.11 ('#B') @ (
% 121.84/16.11 !!))) @
% 121.84/16.11 (
% 121.84/16.11 (
% 121.84/16.11 ('#S') @ (
% 121.84/16.11 (
% 121.84/16.11 ('#B') @ (
% 121.84/16.11 '#S') @
% 121.84/16.11 (
% 121.84/16.11 (
% 121.84/16.11 ('#B') @ (
% 121.84/16.11 (
% 121.84/16.11 ('#B') @ (
% 121.84/16.11 '#S'))) @
% 121.84/16.11 (
% 121.84/16.11 (
% 121.84/16.11 ('#B') @ (
% 121.84/16.11 (
% 121.84/16.11 ('#B') @ (
% 121.84/16.11 (
% 121.84/16.11 ('#B') @ (
% 121.84/16.11 =>))))) @
% 121.84/16.11 (
% 121.84/16.11 (
% 121.84/16.11 ('#B') @ (
% 121.84/16.11 (
% 121.84/16.11 ('#B') @ (
% 121.84/16.11 (
% 121.84/16.11 ('#C') @ in)))) @
% 121.84/16.11 injFuncSet)))))))) @
% 121.84/16.11 (
% 121.84/16.11 (
% 121.84/16.11 ('#B') @ (
% 121.84/16.11 (
% 121.84/16.11 ('#B') @ (
% 121.84/16.11 (
% 121.84/16.11 ('#C') @ in)))) @
% 121.84/16.11 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 121.84/16.11 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl938])).
% 121.84/16.11 thf(zip_derived_cl967, plain,
% 121.84/16.11 (~ (((setadjoinSub) =>
% 121.84/16.11 (((setadjoinSub2) =>
% 121.84/16.11 (((subset2powerset) =>
% 121.84/16.11 (((setextsub) =>
% 121.84/16.11 (((subsetemptysetimpeq) =>
% 121.84/16.11 (((powersetI1) =>
% 121.84/16.11 (((powersetE1) =>
% 121.84/16.11 (((inPowerset) =>
% 121.84/16.11 (((powersetsubset) =>
% 121.84/16.11 (((sepInPowerset) =>
% 121.84/16.11 (((sepSubset) =>
% 121.84/16.11 (((binunionIL) =>
% 121.84/16.11 (((upairset2IR) =>
% 121.84/16.11 (((binunionIR) =>
% 121.84/16.11 (((binunionEcases) =>
% 121.84/16.11 (((binunionE) =>
% 121.84/16.11 (((binunionLsub) =>
% 121.84/16.11 (((binunionRsub) =>
% 121.84/16.11 (((binintersectI) =>
% 121.84/16.11 (((binintersectSubset5) =>
% 121.84/16.11 (((binintersectEL) =>
% 121.84/16.11 (((binintersectLsub) =>
% 121.84/16.11 (((binintersectSubset2) =>
% 121.84/16.11 (((binintersectSubset3) =>
% 121.84/16.11 (((binintersectER) =>
% 121.84/16.11 (((disjointsetsI1) =>
% 121.84/16.11 (((binintersectRsub) =>
% 121.84/16.11 (((binintersectSubset4) =>
% 121.84/16.11 (((binintersectSubset1) =>
% 121.84/16.11 (((bs114d) =>
% 121.84/16.11 ((
% 121.84/16.11 (setminusI) =>
% 121.84/16.11 ((
% 121.84/16.11 (setminusEL) =>
% 121.84/16.11 ((
% 121.84/16.11 (setminusER) =>
% 121.84/16.11 ((
% 121.84/16.11 (setminusSubset2) =>
% 121.84/16.11 ((
% 121.84/16.11 (setminusERneg) =>
% 121.84/16.11 ((
% 121.84/16.11 (setminusELneg) =>
% 121.84/16.11 ((
% 121.84/16.11 (setminusILneg) =>
% 121.84/16.11 ((
% 121.84/16.11 (setminusIRneg) =>
% 121.84/16.11 ((
% 121.84/16.11 (setminusLsub) =>
% 121.84/16.11 ((
% 121.84/16.11 (setminusSubset1) =>
% 121.84/16.11 ((
% 121.84/16.11 (symdiffE) =>
% 121.84/16.11 ((
% 121.84/16.11 (symdiffI1) =>
% 121.84/16.11 ((
% 121.84/16.11 (symdiffI2) =>
% 121.84/16.11 ((
% 121.84/16.11 (symdiffIneg1) =>
% 121.84/16.11 ((
% 121.84/16.11 (symdiffIneg2) =>
% 121.84/16.11 ((
% 121.84/16.11 (secondinupair) =>
% 121.84/16.11 ((
% 121.84/16.11 (setukpairIL) =>
% 121.84/16.11 ((
% 121.84/16.11 (setukpairIR) =>
% 121.84/16.11 ((
% 121.84/16.11 (kpairiskpair) =>
% 121.84/16.11 ((
% 121.84/16.11 (kpairp) =>
% 121.84/16.11 ((
% 121.84/16.11 (singletonsubset) =>
% 121.84/16.11 ((
% 121.84/16.11 (singletoninpowerset) =>
% 121.84/16.11 ((
% 121.84/16.11 (singletoninpowunion) =>
% 121.84/16.11 ((
% 121.84/16.11 (upairset2E) =>
% 121.84/16.11 ((
% 121.84/16.11 (upairsubunion) =>
% 121.84/16.11 ((
% 121.84/16.11 (upairinpowunion) =>
% 121.84/16.11 ((
% 121.84/16.11 (ubforcartprodlem1) =>
% 121.84/16.11 ((
% 121.84/16.11 (ubforcartprodlem2) =>
% 121.84/16.11 ((
% 121.84/16.11 (ubforcartprodlem3) =>
% 121.84/16.11 ((
% 121.84/16.11 (cartprodpairin) =>
% 121.84/16.11 ((
% 121.84/16.11 (cartprodmempair1) =>
% 121.84/16.11 ((
% 121.84/16.11 (cartprodmempair) =>
% 121.84/16.11 ((
% 121.84/16.11 (setunionE2) =>
% 121.84/16.11 ((
% 121.84/16.11 (setunionsingleton1) =>
% 121.84/16.11 ((
% 121.84/16.11 (setunionsingleton2) =>
% 121.84/16.11 ((
% 121.84/16.11 (setunionsingleton) =>
% 121.84/16.11 ((
% 121.84/16.11 (singletonprop) =>
% 121.84/16.11 ((
% 121.84/16.11 (ex1E1) =>
% 121.84/16.11 ((
% 121.84/16.11 (ex1I) =>
% 121.84/16.11 ((
% 121.84/16.11 (ex1I2) =>
% 121.84/16.11 ((
% 121.84/16.11 (singletonsuniq) =>
% 121.84/16.11 ((
% 121.84/16.11 (setukpairinjL1) =>
% 121.84/16.11 ((
% 121.84/16.11 (kfstsingleton) =>
% 121.84/16.11 ((
% 121.84/16.11 (theprop) =>
% 121.84/16.11 ((
% 121.84/16.11 (kfstpairEq) =>
% 121.84/16.11 ((
% 121.84/16.11 (cartprodfstin) =>
% 121.84/16.11 ((
% 121.84/16.11 (setukpairinjL2) =>
% 121.84/16.11 ((
% 121.84/16.11 (setukpairinjL) =>
% 121.84/16.11 ((
% 121.84/16.11 (setukpairinjR11) =>
% 121.84/16.11 ((
% 121.84/16.11 (setukpairinjR12) =>
% 121.84/16.11 ((
% 121.84/16.11 (setukpairinjR1) =>
% 121.84/16.11 ((
% 121.84/16.11 (upairequniteq) =>
% 121.84/16.11 ((
% 121.84/16.11 (setukpairinjR2) =>
% 121.84/16.11 ((
% 121.84/16.11 (setukpairinjR) =>
% 121.84/16.11 ((
% 121.84/16.11 (ksndsingleton) =>
% 121.84/16.11 ((
% 121.84/16.11 (ksndpairEq) =>
% 121.84/16.11 ((
% 121.84/16.11 (kpairsurjEq) =>
% 121.84/16.11 ((
% 121.84/16.11 (cartprodsndin) =>
% 121.84/16.11 ((
% 121.84/16.11 (cartprodpairmemEL) =>
% 121.84/16.11 ((
% 121.84/16.11 (cartprodpairmemER) =>
% 121.84/16.11 ((
% 121.84/16.11 (cartprodmempaircEq) =>
% 121.84/16.11 ((
% 121.84/16.11 (cartprodfstpairEq) =>
% 121.84/16.11 ((
% 121.84/16.11 (cartprodsndpairEq) =>
% 121.84/16.11 ((
% 121.84/16.11 (cartprodpairsurjEq) =>
% 121.84/16.11 ((
% 121.84/16.11 (dpsetconstrI) =>
% 121.84/16.11 ((
% 121.84/16.11 (dpsetconstrSub) =>
% 121.84/16.11 ((
% 121.84/16.11 (setOfPairsIsBReln) =>
% 121.84/16.11 ((
% 121.84/16.11 (dpsetconstrERa) =>
% 121.84/16.11 ((
% 121.84/16.11 (dpsetconstrEL1) =>
% 121.84/16.11 ((
% 121.84/16.11 (dpsetconstrEL2) =>
% 121.84/16.11 ((
% 121.84/16.11 (dpsetconstrER) =>
% 121.84/16.11 ((
% 121.84/16.11 (funcImageSingleton) =>
% 121.84/16.11 ((
% 121.84/16.11 (apProp) =>
% 121.84/16.11 ((
% 121.84/16.11 (app) =>
% 121.84/16.11 ((
% 121.84/16.11 (infuncsetfunc) =>
% 121.84/16.11 ((
% 121.84/16.11 (ap2p) =>
% 121.84/16.11 ((
% 121.84/16.11 (funcinfuncset) =>
% 121.84/16.11 ((
% 121.84/16.11 (lamProp) =>
% 121.84/16.11 ((
% 121.84/16.11 (lamp) =>
% 121.84/16.11 ((
% 121.84/16.11 (lam2p) =>
% 121.84/16.11 ((
% 121.84/16.11 (brelnall1) =>
% 121.84/16.11 ((
% 121.84/16.11 (brelnall2) =>
% 121.84/16.11 ((
% 121.84/16.11 (ex1E2) =>
% 121.84/16.11 ((
% 121.84/16.11 (funcGraphProp1) =>
% 121.84/16.11 ((
% 121.84/16.11 (funcGraphProp3) =>
% 121.84/16.11 ((
% 121.84/16.11 (funcGraphProp2) =>
% 121.84/16.11 ((
% 121.84/16.11 (funcextLem) =>
% 121.84/16.11 ((
% 121.84/16.11 (funcGraphProp4) =>
% 121.84/16.11 ((
% 121.84/16.11 (subbreln) =>
% 121.84/16.11 ((
% 121.84/16.11 (eqbreln) =>
% 121.84/16.11 ((
% 121.84/16.11 (funcext) =>
% 121.84/16.11 ((
% 121.84/16.11 (funcext2) =>
% 121.84/16.11 ((
% 121.84/16.11 (ap2apEq1) =>
% 121.84/16.11 ((
% 121.84/16.11 (ap2apEq2) =>
% 121.84/16.11 ((
% 121.84/16.11 (beta1) =>
% 121.84/16.11 ((
% 121.84/16.11 (eta1) =>
% 121.84/16.11 ((
% 121.84/16.11 (lam2lamEq) =>
% 121.84/16.11 ((
% 121.84/16.11 (beta2) =>
% 121.84/16.11 ((
% 121.84/16.11 (eta2) =>
% 121.84/16.11 ((
% 121.84/16.11 (iffalseProp1) =>
% 121.84/16.11 ((
% 121.84/16.11 (iffalseProp2) =>
% 121.84/16.11 ((
% 121.84/16.11 (iftrueProp1) =>
% 121.84/16.11 ((
% 121.84/16.11 (iftrueProp2) =>
% 121.84/16.11 ((
% 121.84/16.11 (ifSingleton) =>
% 121.84/16.11 ((
% 121.84/16.11 (ifp) =>
% 121.84/16.11 ((
% 121.84/16.11 (theeq) =>
% 121.84/16.11 ((
% 121.84/16.11 (iftrue) =>
% 121.84/16.11 ((
% 121.84/16.11 (iffalse) =>
% 121.84/16.11 ((
% 121.84/16.11 (iftrueorfalse) =>
% 121.84/16.11 ((
% 121.84/16.11 (binintersectT_lem) =>
% 121.84/16.11 ((
% 121.84/16.11 (binunionT_lem) =>
% 121.84/16.11 ((
% 121.84/16.11 (powersetT_lem) =>
% 121.84/16.11 ((
% 121.84/16.11 (setminusT_lem) =>
% 121.84/16.11 ((
% 121.84/16.11 (complementT_lem) =>
% 121.84/16.11 ((
% 121.84/16.11 (setextT) =>
% 121.84/16.11 ((
% 121.84/16.11 (subsetTI) =>
% 121.84/16.11 ((
% 121.84/16.11 (powersetTI1) =>
% 121.84/16.11 ((
% 121.84/16.11 (powersetTE1) =>
% 121.84/16.11 ((
% 121.84/16.11 (complementTI1) =>
% 121.84/16.11 ((
% 121.84/16.11 (complementTE1) =>
% 121.84/16.11 ((
% 121.84/16.11 (binintersectTELcontra) =>
% 121.84/16.12 ((
% 121.84/16.12 (binintersectTERcontra) =>
% 121.84/16.12 ((
% 121.84/16.12 (contrasubsetT) =>
% 121.84/16.12 ((
% 121.84/16.12 (contrasubsetT1) =>
% 121.84/16.12 ((
% 121.84/16.12 (contrasubsetT2) =>
% 121.84/16.12 ((
% 121.84/16.12 (contrasubsetT3) =>
% 121.84/16.12 ((
% 121.84/16.12 (doubleComplementI1) =>
% 121.84/16.12 ((
% 121.84/16.12 (doubleComplementE1) =>
% 121.84/16.12 ((
% 121.84/16.12 (doubleComplementSub1) =>
% 121.84/16.12 ((
% 121.84/16.12 (doubleComplementSub2) =>
% 121.84/16.12 ((
% 121.84/16.12 (doubleComplementEq) =>
% 121.84/16.12 ((
% 121.84/16.12 (complementTnotintersectT) =>
% 121.84/16.12 ((
% 121.84/16.12 (complementImpComplementIntersect) =>
% 121.84/16.12 ((
% 121.84/16.12 (complementSubsetComplementIntersect) =>
% 121.84/16.12 ((
% 121.84/16.12 (complementInPowersetComplementIntersect) =>
% 121.84/16.12 ((
% 121.84/16.12 (contraSubsetComplement) =>
% 121.84/16.12 ((
% 121.84/16.12 (complementTcontraSubset) =>
% 121.84/16.12 ((
% 121.84/16.12 (binunionTILcontra) =>
% 121.84/16.12 ((
% 121.84/16.12 (binunionTIRcontra) =>
% 121.84/16.12 ((
% 121.84/16.12 (inIntersectImpInUnion) =>
% 121.84/16.12 ((
% 121.84/16.12 (inIntersectImpInUnion2) =>
% 121.84/16.12 ((
% 121.84/16.12 (inIntersectImpInIntersectUnions) =>
% 121.84/16.12 ((
% 121.84/16.12 (intersectInPowersetIntersectUnions) =>
% 121.84/16.12 ((
% 121.84/16.12 (inComplementUnionImpNotIn1) =>
% 121.84/16.12 ((
% 121.84/16.12 (inComplementUnionImpInComplement1) =>
% 121.84/16.12 ((
% 121.84/16.12 (binunionTE) =>
% 121.84/16.12 ((
% 121.84/16.12 (binunionTEcontra) =>
% 121.84/16.12 ((
% 121.84/16.12 (demorgan2a1) =>
% 121.84/16.12 ((
% 121.84/16.12 (complementUnionInPowersetComplement) =>
% 121.84/16.12 ((
% 121.84/16.12 (demorgan2a2) =>
% 121.84/16.12 ((
% 121.84/16.12 (demorgan1a) =>
% 121.84/16.12 ((
% 121.84/16.12 (demorgan1b) =>
% 121.84/16.12 ((
% 121.84/16.12 (demorgan1) =>
% 121.84/16.12 ((
% 121.84/16.12 (demorgan2a) =>
% 121.84/16.12 ((
% 121.84/16.12 (demorgan2b2) =>
% 121.84/16.12 ((
% 121.84/16.12 (demorgan2b) =>
% 121.84/16.12 ((
% 121.84/16.12 (demorgan2) =>
% 121.84/16.12 ((
% 121.84/16.12 (woz13rule0) =>
% 121.84/16.12 ((
% 121.84/16.12 (woz13rule1) =>
% 121.84/16.12 ((
% 121.84/16.12 (woz13rule2) =>
% 121.84/16.12 ((
% 121.84/16.12 (woz13rule3) =>
% 121.84/16.12 ((
% 121.84/16.12 (woz13rule4) =>
% 121.84/16.12 ((
% 121.84/16.12 (woz1_1) =>
% 121.84/16.12 ((
% 121.84/16.12 (woz1_2) =>
% 121.84/16.12 ((
% 121.84/16.12 (woz1_3) =>
% 121.84/16.12 ((
% 121.84/16.12 (woz1_4) =>
% 121.84/16.12 ((
% 121.84/16.12 (woz1_5) =>
% 121.84/16.12 ((
% 121.84/16.12 (breln1all2) =>
% 121.84/16.12 ((
% 121.84/16.12 (breln1SetBreln1) =>
% 121.84/16.12 ((
% 121.84/16.12 (choice2fnsingleton) =>
% 121.84/16.12 ((
% 121.84/16.12 (setOfPairsIsBReln1) =>
% 121.84/16.12 ((
% 121.84/16.12 (breln1all1) =>
% 121.84/16.12 ((
% 121.84/16.12 (subbreln1) =>
% 121.84/16.12 ((
% 121.84/16.12 (eqbreln1) =>
% 121.84/16.12 ((
% 121.84/16.12 (breln1invprop) =>
% 121.84/16.12 ((
% 121.84/16.12 (breln1invI) =>
% 121.84/16.12 ((
% 121.84/16.12 (breln1invE) =>
% 121.84/16.12 ((
% 121.84/16.12 (breln1compprop) =>
% 121.84/16.12 ((
% 121.84/16.12 (breln1compI) =>
% 121.84/16.12 ((
% 121.84/16.12 (breln1compE) =>
% 121.84/16.12 ((
% 121.84/16.12 (breln1compEex) =>
% 121.84/16.12 ((
% 121.84/16.12 (breln1unionprop) =>
% 121.84/16.12 ((
% 121.84/16.12 (breln1unionIL) =>
% 121.84/16.12 ((
% 121.84/16.12 (breln1unionIR) =>
% 121.84/16.12 ((
% 121.84/16.12 (breln1unionI) =>
% 121.84/16.12 ((
% 121.84/16.12 (breln1unionE) =>
% 121.84/16.12 ((
% 121.84/16.12 (breln1unionEcases) =>
% 121.84/16.12 ((
% 121.84/16.12 (breln1unionCommutes) =>
% 121.84/16.12 ((
% 121.84/16.12 (woz2Ex) =>
% 121.84/16.12 ((
% 121.84/16.12 (woz2W) =>
% 121.84/16.12 ((
% 121.84/16.12 (woz2A) =>
% 121.84/16.12 ((
% 121.84/16.12 (woz2B) =>
% 121.84/16.12 ((
% 121.84/16.12 (image1Ex) =>
% 121.84/16.12 ((
% 121.84/16.12 (image1Ex1) =>
% 121.84/16.12 ((
% 121.84/16.12 (image1Equiv) =>
% 121.84/16.12 ((
% 121.84/16.12 (image1E) =>
% 121.84/16.12 ((
% 121.84/16.12 (image1I) =>
% 121.84/16.12 ((
% 121.84/16.12 (injFuncInInjFuncSet) =>
% 121.84/16.12 ((
% 121.84/16.12 (!!) @ (
% 121.84/16.12 (('#B') @ (
% 121.84/16.12 !!) @
% 121.84/16.12 (
% 121.84/16.12 (
% 121.84/16.12 ('#B') @ (
% 121.84/16.12 (
% 121.84/16.12 ('#B') @ (
% 121.84/16.12 !!))) @
% 121.84/16.12 (
% 121.84/16.12 (
% 121.84/16.12 ('#S') @ (
% 121.84/16.12 (
% 121.84/16.12 ('#B') @ (
% 121.84/16.12 '#S') @
% 121.84/16.12 (
% 121.84/16.12 (
% 121.84/16.12 ('#B') @ (
% 121.84/16.12 (
% 121.84/16.12 ('#B') @ (
% 121.84/16.12 '#S'))) @
% 121.84/16.12 (
% 121.84/16.12 (
% 121.84/16.12 ('#B') @ (
% 121.84/16.12 (
% 121.84/16.12 ('#B') @ (
% 121.84/16.12 (
% 121.84/16.12 ('#B') @ (
% 121.84/16.12 =>))))) @
% 121.84/16.12 (
% 121.84/16.12 (
% 121.84/16.12 ('#B') @ (
% 121.84/16.12 (
% 121.84/16.12 ('#B') @ (
% 121.84/16.12 (
% 121.84/16.12 ('#C') @ in)))) @
% 121.84/16.12 injFuncSet)))))))) @
% 121.84/16.12 (
% 121.84/16.12 (
% 121.84/16.12 ('#B') @ (
% 121.84/16.12 (
% 121.84/16.12 ('#B') @ (
% 121.84/16.12 (
% 121.84/16.12 ('#C') @ in)))) @
% 121.84/16.12 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 121.84/16.12 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl952])).
% 121.84/16.12 thf(zip_derived_cl984, plain,
% 121.84/16.12 (~ (((setadjoinSub2) =>
% 121.84/16.12 (((subset2powerset) =>
% 121.84/16.12 (((setextsub) =>
% 121.84/16.12 (((subsetemptysetimpeq) =>
% 121.84/16.12 (((powersetI1) =>
% 121.84/16.12 (((powersetE1) =>
% 121.84/16.12 (((inPowerset) =>
% 121.84/16.12 (((powersetsubset) =>
% 121.84/16.12 (((sepInPowerset) =>
% 121.84/16.12 (((sepSubset) =>
% 121.84/16.12 (((binunionIL) =>
% 121.84/16.12 (((upairset2IR) =>
% 121.84/16.12 (((binunionIR) =>
% 121.84/16.12 (((binunionEcases) =>
% 121.84/16.12 (((binunionE) =>
% 121.84/16.12 (((binunionLsub) =>
% 121.84/16.12 (((binunionRsub) =>
% 121.84/16.12 (((binintersectI) =>
% 121.84/16.12 (((binintersectSubset5) =>
% 121.84/16.12 (((binintersectEL) =>
% 121.84/16.12 (((binintersectLsub) =>
% 121.84/16.12 (((binintersectSubset2) =>
% 121.84/16.12 (((binintersectSubset3) =>
% 121.84/16.12 (((binintersectER) =>
% 121.84/16.12 (((disjointsetsI1) =>
% 121.84/16.12 (((binintersectRsub) =>
% 121.84/16.12 (((binintersectSubset4) =>
% 121.84/16.12 (((binintersectSubset1) =>
% 121.84/16.12 (((bs114d) =>
% 121.84/16.12 (((setminusI) =>
% 121.84/16.12 ((
% 121.84/16.12 (setminusEL) =>
% 121.84/16.12 ((
% 121.84/16.12 (setminusER) =>
% 121.84/16.12 ((
% 121.84/16.12 (setminusSubset2) =>
% 121.84/16.12 ((
% 121.84/16.12 (setminusERneg) =>
% 121.84/16.12 ((
% 121.84/16.12 (setminusELneg) =>
% 121.84/16.12 ((
% 121.84/16.12 (setminusILneg) =>
% 121.84/16.12 ((
% 121.84/16.12 (setminusIRneg) =>
% 121.84/16.12 ((
% 121.84/16.12 (setminusLsub) =>
% 121.84/16.12 ((
% 121.84/16.12 (setminusSubset1) =>
% 121.84/16.12 ((
% 121.84/16.12 (symdiffE) =>
% 121.84/16.12 ((
% 121.84/16.12 (symdiffI1) =>
% 121.84/16.12 ((
% 121.84/16.12 (symdiffI2) =>
% 121.84/16.12 ((
% 121.84/16.12 (symdiffIneg1) =>
% 121.84/16.12 ((
% 121.84/16.12 (symdiffIneg2) =>
% 121.84/16.12 ((
% 121.84/16.12 (secondinupair) =>
% 121.84/16.12 ((
% 121.84/16.12 (setukpairIL) =>
% 121.84/16.12 ((
% 121.84/16.12 (setukpairIR) =>
% 121.84/16.12 ((
% 121.84/16.12 (kpairiskpair) =>
% 121.84/16.12 ((
% 121.84/16.12 (kpairp) =>
% 121.84/16.12 ((
% 121.84/16.12 (singletonsubset) =>
% 121.84/16.12 ((
% 121.84/16.12 (singletoninpowerset) =>
% 121.84/16.12 ((
% 121.84/16.12 (singletoninpowunion) =>
% 121.84/16.12 ((
% 121.84/16.12 (upairset2E) =>
% 121.84/16.12 ((
% 121.84/16.12 (upairsubunion) =>
% 121.84/16.12 ((
% 121.84/16.12 (upairinpowunion) =>
% 121.84/16.12 ((
% 121.84/16.12 (ubforcartprodlem1) =>
% 121.84/16.12 ((
% 121.84/16.12 (ubforcartprodlem2) =>
% 121.84/16.12 ((
% 121.84/16.12 (ubforcartprodlem3) =>
% 121.84/16.12 ((
% 121.84/16.12 (cartprodpairin) =>
% 121.84/16.12 ((
% 121.84/16.12 (cartprodmempair1) =>
% 121.84/16.12 ((
% 121.84/16.12 (cartprodmempair) =>
% 121.84/16.12 ((
% 121.84/16.12 (setunionE2) =>
% 121.84/16.12 ((
% 121.84/16.12 (setunionsingleton1) =>
% 121.84/16.12 ((
% 121.84/16.12 (setunionsingleton2) =>
% 121.84/16.12 ((
% 121.84/16.12 (setunionsingleton) =>
% 121.84/16.12 ((
% 121.84/16.12 (singletonprop) =>
% 121.84/16.12 ((
% 121.84/16.12 (ex1E1) =>
% 121.84/16.12 ((
% 121.84/16.12 (ex1I) =>
% 121.84/16.12 ((
% 121.84/16.12 (ex1I2) =>
% 121.84/16.12 ((
% 121.84/16.12 (singletonsuniq) =>
% 121.84/16.12 ((
% 121.84/16.12 (setukpairinjL1) =>
% 121.84/16.12 ((
% 121.84/16.12 (kfstsingleton) =>
% 121.84/16.12 ((
% 121.84/16.12 (theprop) =>
% 121.84/16.12 ((
% 121.84/16.12 (kfstpairEq) =>
% 121.84/16.12 ((
% 121.84/16.12 (cartprodfstin) =>
% 121.84/16.12 ((
% 121.84/16.12 (setukpairinjL2) =>
% 121.84/16.12 ((
% 121.84/16.12 (setukpairinjL) =>
% 121.84/16.12 ((
% 121.84/16.12 (setukpairinjR11) =>
% 121.84/16.12 ((
% 121.84/16.12 (setukpairinjR12) =>
% 121.84/16.12 ((
% 121.84/16.12 (setukpairinjR1) =>
% 121.84/16.12 ((
% 121.84/16.12 (upairequniteq) =>
% 121.84/16.12 ((
% 121.84/16.12 (setukpairinjR2) =>
% 121.84/16.12 ((
% 121.84/16.12 (setukpairinjR) =>
% 121.84/16.12 ((
% 121.84/16.12 (ksndsingleton) =>
% 121.84/16.12 ((
% 121.84/16.12 (ksndpairEq) =>
% 121.84/16.12 ((
% 121.84/16.12 (kpairsurjEq) =>
% 121.84/16.12 ((
% 121.84/16.12 (cartprodsndin) =>
% 121.84/16.12 ((
% 121.84/16.12 (cartprodpairmemEL) =>
% 121.84/16.12 ((
% 121.84/16.12 (cartprodpairmemER) =>
% 121.84/16.12 ((
% 121.84/16.12 (cartprodmempaircEq) =>
% 121.84/16.12 ((
% 121.84/16.12 (cartprodfstpairEq) =>
% 121.84/16.12 ((
% 121.84/16.12 (cartprodsndpairEq) =>
% 121.84/16.12 ((
% 121.84/16.12 (cartprodpairsurjEq) =>
% 121.84/16.12 ((
% 121.84/16.12 (dpsetconstrI) =>
% 121.84/16.12 ((
% 121.84/16.12 (dpsetconstrSub) =>
% 121.84/16.12 ((
% 121.84/16.12 (setOfPairsIsBReln) =>
% 121.84/16.12 ((
% 121.84/16.12 (dpsetconstrERa) =>
% 121.84/16.12 ((
% 121.84/16.12 (dpsetconstrEL1) =>
% 121.84/16.12 ((
% 121.84/16.12 (dpsetconstrEL2) =>
% 121.84/16.12 ((
% 121.84/16.12 (dpsetconstrER) =>
% 121.84/16.12 ((
% 121.84/16.12 (funcImageSingleton) =>
% 121.84/16.12 ((
% 121.84/16.12 (apProp) =>
% 121.84/16.12 ((
% 121.84/16.12 (app) =>
% 121.84/16.12 ((
% 121.84/16.12 (infuncsetfunc) =>
% 121.84/16.12 ((
% 121.84/16.12 (ap2p) =>
% 121.84/16.12 ((
% 121.84/16.12 (funcinfuncset) =>
% 121.84/16.12 ((
% 121.84/16.12 (lamProp) =>
% 121.84/16.12 ((
% 121.84/16.12 (lamp) =>
% 121.84/16.12 ((
% 121.84/16.12 (lam2p) =>
% 121.84/16.12 ((
% 121.84/16.12 (brelnall1) =>
% 121.84/16.12 ((
% 121.84/16.12 (brelnall2) =>
% 121.84/16.12 ((
% 121.84/16.12 (ex1E2) =>
% 121.84/16.12 ((
% 121.84/16.12 (funcGraphProp1) =>
% 121.84/16.12 ((
% 121.84/16.12 (funcGraphProp3) =>
% 121.84/16.12 ((
% 121.84/16.12 (funcGraphProp2) =>
% 121.84/16.12 ((
% 121.84/16.12 (funcextLem) =>
% 121.84/16.12 ((
% 121.84/16.12 (funcGraphProp4) =>
% 121.84/16.12 ((
% 121.84/16.12 (subbreln) =>
% 121.84/16.12 ((
% 121.84/16.12 (eqbreln) =>
% 121.84/16.12 ((
% 121.84/16.12 (funcext) =>
% 121.84/16.12 ((
% 121.84/16.12 (funcext2) =>
% 121.84/16.12 ((
% 121.84/16.12 (ap2apEq1) =>
% 121.84/16.12 ((
% 121.84/16.12 (ap2apEq2) =>
% 121.84/16.12 ((
% 121.84/16.12 (beta1) =>
% 121.84/16.12 ((
% 121.84/16.12 (eta1) =>
% 121.84/16.12 ((
% 121.84/16.12 (lam2lamEq) =>
% 121.84/16.12 ((
% 121.84/16.12 (beta2) =>
% 121.84/16.12 ((
% 121.84/16.12 (eta2) =>
% 121.84/16.12 ((
% 121.84/16.12 (iffalseProp1) =>
% 121.84/16.12 ((
% 121.84/16.12 (iffalseProp2) =>
% 121.84/16.12 ((
% 121.84/16.12 (iftrueProp1) =>
% 121.84/16.12 ((
% 121.84/16.12 (iftrueProp2) =>
% 121.84/16.12 ((
% 121.84/16.12 (ifSingleton) =>
% 121.84/16.12 ((
% 121.84/16.12 (ifp) =>
% 121.84/16.12 ((
% 121.84/16.12 (theeq) =>
% 121.84/16.12 ((
% 121.84/16.12 (iftrue) =>
% 121.84/16.12 ((
% 121.84/16.12 (iffalse) =>
% 121.84/16.12 ((
% 121.84/16.12 (iftrueorfalse) =>
% 121.84/16.12 ((
% 121.84/16.12 (binintersectT_lem) =>
% 121.84/16.12 ((
% 121.84/16.12 (binunionT_lem) =>
% 121.84/16.12 ((
% 121.84/16.12 (powersetT_lem) =>
% 121.84/16.12 ((
% 121.84/16.12 (setminusT_lem) =>
% 121.84/16.12 ((
% 121.84/16.12 (complementT_lem) =>
% 121.84/16.12 ((
% 121.84/16.12 (setextT) =>
% 121.84/16.12 ((
% 121.84/16.12 (subsetTI) =>
% 121.84/16.12 ((
% 121.84/16.12 (powersetTI1) =>
% 121.84/16.12 ((
% 121.84/16.12 (powersetTE1) =>
% 121.84/16.12 ((
% 121.84/16.12 (complementTI1) =>
% 121.84/16.12 ((
% 121.84/16.12 (complementTE1) =>
% 121.84/16.12 ((
% 121.84/16.12 (binintersectTELcontra) =>
% 121.84/16.12 ((
% 121.84/16.12 (binintersectTERcontra) =>
% 121.84/16.12 ((
% 121.84/16.12 (contrasubsetT) =>
% 121.84/16.12 ((
% 121.84/16.12 (contrasubsetT1) =>
% 121.84/16.12 ((
% 121.84/16.12 (contrasubsetT2) =>
% 121.84/16.12 ((
% 121.84/16.12 (contrasubsetT3) =>
% 121.84/16.12 ((
% 121.84/16.12 (doubleComplementI1) =>
% 121.84/16.12 ((
% 121.84/16.12 (doubleComplementE1) =>
% 121.84/16.12 ((
% 121.84/16.12 (doubleComplementSub1) =>
% 121.84/16.12 ((
% 121.84/16.12 (doubleComplementSub2) =>
% 121.84/16.12 ((
% 121.84/16.12 (doubleComplementEq) =>
% 121.84/16.12 ((
% 121.84/16.12 (complementTnotintersectT) =>
% 121.84/16.12 ((
% 121.84/16.12 (complementImpComplementIntersect) =>
% 121.84/16.12 ((
% 121.84/16.12 (complementSubsetComplementIntersect) =>
% 121.84/16.12 ((
% 121.84/16.12 (complementInPowersetComplementIntersect) =>
% 121.84/16.12 ((
% 121.84/16.12 (contraSubsetComplement) =>
% 121.84/16.12 ((
% 121.84/16.12 (complementTcontraSubset) =>
% 121.84/16.12 ((
% 121.84/16.12 (binunionTILcontra) =>
% 121.84/16.12 ((
% 121.84/16.12 (binunionTIRcontra) =>
% 121.84/16.12 ((
% 121.84/16.12 (inIntersectImpInUnion) =>
% 121.84/16.12 ((
% 121.84/16.12 (inIntersectImpInUnion2) =>
% 121.84/16.12 ((
% 121.84/16.12 (inIntersectImpInIntersectUnions) =>
% 121.84/16.12 ((
% 121.84/16.12 (intersectInPowersetIntersectUnions) =>
% 121.84/16.12 ((
% 121.84/16.12 (inComplementUnionImpNotIn1) =>
% 121.84/16.12 ((
% 121.84/16.12 (inComplementUnionImpInComplement1) =>
% 121.84/16.12 ((
% 121.84/16.12 (binunionTE) =>
% 121.84/16.12 ((
% 121.84/16.12 (binunionTEcontra) =>
% 121.84/16.12 ((
% 121.84/16.12 (demorgan2a1) =>
% 121.84/16.12 ((
% 121.84/16.12 (complementUnionInPowersetComplement) =>
% 121.84/16.12 ((
% 121.84/16.12 (demorgan2a2) =>
% 121.84/16.12 ((
% 121.84/16.12 (demorgan1a) =>
% 121.84/16.12 ((
% 121.84/16.12 (demorgan1b) =>
% 121.84/16.12 ((
% 121.84/16.12 (demorgan1) =>
% 121.84/16.12 ((
% 121.84/16.12 (demorgan2a) =>
% 121.84/16.12 ((
% 121.84/16.12 (demorgan2b2) =>
% 121.84/16.12 ((
% 121.84/16.12 (demorgan2b) =>
% 121.84/16.12 ((
% 121.84/16.12 (demorgan2) =>
% 121.84/16.12 ((
% 121.84/16.12 (woz13rule0) =>
% 121.84/16.12 ((
% 121.84/16.12 (woz13rule1) =>
% 121.84/16.12 ((
% 121.84/16.12 (woz13rule2) =>
% 121.84/16.12 ((
% 121.84/16.12 (woz13rule3) =>
% 121.84/16.12 ((
% 121.84/16.12 (woz13rule4) =>
% 121.84/16.12 ((
% 121.84/16.12 (woz1_1) =>
% 121.84/16.12 ((
% 121.84/16.12 (woz1_2) =>
% 121.84/16.12 ((
% 121.84/16.12 (woz1_3) =>
% 121.84/16.12 ((
% 121.84/16.12 (woz1_4) =>
% 121.84/16.12 ((
% 121.84/16.12 (woz1_5) =>
% 121.84/16.12 ((
% 121.84/16.12 (breln1all2) =>
% 121.84/16.12 ((
% 121.84/16.12 (breln1SetBreln1) =>
% 121.84/16.12 ((
% 121.84/16.12 (choice2fnsingleton) =>
% 121.84/16.12 ((
% 121.84/16.12 (setOfPairsIsBReln1) =>
% 121.84/16.12 ((
% 121.84/16.12 (breln1all1) =>
% 121.84/16.12 ((
% 121.84/16.12 (subbreln1) =>
% 121.84/16.12 ((
% 121.84/16.12 (eqbreln1) =>
% 121.84/16.12 ((
% 121.84/16.12 (breln1invprop) =>
% 121.84/16.12 ((
% 121.84/16.12 (breln1invI) =>
% 121.84/16.12 ((
% 121.84/16.12 (breln1invE) =>
% 121.84/16.12 ((
% 121.84/16.12 (breln1compprop) =>
% 121.84/16.12 ((
% 121.84/16.12 (breln1compI) =>
% 121.84/16.12 ((
% 121.84/16.12 (breln1compE) =>
% 121.84/16.12 ((
% 121.84/16.12 (breln1compEex) =>
% 121.84/16.12 ((
% 121.84/16.12 (breln1unionprop) =>
% 121.84/16.12 ((
% 121.84/16.12 (breln1unionIL) =>
% 121.84/16.12 ((
% 121.84/16.12 (breln1unionIR) =>
% 121.84/16.12 ((
% 121.84/16.12 (breln1unionI) =>
% 121.84/16.12 ((
% 121.84/16.12 (breln1unionE) =>
% 121.84/16.12 ((
% 121.84/16.12 (breln1unionEcases) =>
% 121.84/16.12 ((
% 121.84/16.12 (breln1unionCommutes) =>
% 121.84/16.12 ((
% 121.84/16.12 (woz2Ex) =>
% 121.84/16.12 ((
% 121.84/16.12 (woz2W) =>
% 121.84/16.12 ((
% 121.84/16.12 (woz2A) =>
% 121.84/16.12 ((
% 121.84/16.12 (woz2B) =>
% 121.84/16.12 ((
% 121.84/16.12 (image1Ex) =>
% 121.84/16.12 ((
% 121.84/16.12 (image1Ex1) =>
% 121.84/16.12 ((
% 121.84/16.12 (image1Equiv) =>
% 121.84/16.12 ((
% 121.84/16.12 (image1E) =>
% 121.84/16.12 ((
% 121.84/16.12 (image1I) =>
% 121.84/16.12 ((
% 121.84/16.12 (injFuncInInjFuncSet) =>
% 121.84/16.12 ((
% 121.84/16.12 (!!) @ (
% 121.84/16.12 (('#B') @ (
% 121.84/16.12 !!) @
% 121.84/16.12 (
% 121.84/16.12 (
% 121.84/16.12 ('#B') @ (
% 121.84/16.12 (
% 121.84/16.12 ('#B') @ (
% 121.84/16.12 !!))) @
% 121.84/16.12 (
% 121.84/16.12 (
% 121.84/16.12 ('#S') @ (
% 121.84/16.12 (
% 121.84/16.12 ('#B') @ (
% 121.84/16.12 '#S') @
% 121.84/16.12 (
% 121.84/16.12 (
% 121.84/16.12 ('#B') @ (
% 121.84/16.12 (
% 121.84/16.12 ('#B') @ (
% 121.84/16.12 '#S'))) @
% 121.84/16.12 (
% 121.84/16.12 (
% 121.84/16.12 ('#B') @ (
% 121.84/16.12 (
% 121.84/16.12 ('#B') @ (
% 121.84/16.12 (
% 121.84/16.12 ('#B') @ (
% 121.84/16.12 =>))))) @
% 121.84/16.12 (
% 121.84/16.12 (
% 121.84/16.12 ('#B') @ (
% 121.84/16.12 (
% 121.84/16.12 ('#B') @ (
% 121.84/16.12 (
% 121.84/16.12 ('#C') @ in)))) @
% 121.84/16.12 injFuncSet)))))))) @
% 121.84/16.12 (
% 121.84/16.12 (
% 121.84/16.12 ('#B') @ (
% 121.84/16.12 (
% 121.84/16.12 ('#B') @ (
% 121.84/16.12 (
% 121.84/16.12 ('#C') @ in)))) @
% 121.84/16.12 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 121.84/16.12 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl967])).
% 121.84/16.12 thf(zip_derived_cl1000, plain,
% 121.84/16.12 (~ (((subset2powerset) =>
% 121.84/16.12 (((setextsub) =>
% 121.84/16.12 (((subsetemptysetimpeq) =>
% 121.84/16.12 (((powersetI1) =>
% 121.84/16.12 (((powersetE1) =>
% 121.84/16.12 (((inPowerset) =>
% 121.84/16.12 (((powersetsubset) =>
% 121.84/16.12 (((sepInPowerset) =>
% 121.84/16.12 (((sepSubset) =>
% 121.84/16.12 (((binunionIL) =>
% 121.84/16.12 (((upairset2IR) =>
% 121.84/16.12 (((binunionIR) =>
% 121.84/16.12 (((binunionEcases) =>
% 121.84/16.12 (((binunionE) =>
% 121.84/16.12 (((binunionLsub) =>
% 121.84/16.12 (((binunionRsub) =>
% 121.84/16.12 (((binintersectI) =>
% 121.84/16.12 (((binintersectSubset5) =>
% 121.84/16.12 (((binintersectEL) =>
% 121.84/16.12 (((binintersectLsub) =>
% 121.84/16.12 (((binintersectSubset2) =>
% 121.84/16.12 (((binintersectSubset3) =>
% 121.84/16.12 (((binintersectER) =>
% 121.84/16.12 (((disjointsetsI1) =>
% 121.84/16.12 (((binintersectRsub) =>
% 121.84/16.12 (((binintersectSubset4) =>
% 121.84/16.12 (((binintersectSubset1) =>
% 121.84/16.12 (((bs114d) =>
% 121.84/16.12 (((setminusI) =>
% 121.84/16.12 (((setminusEL) =>
% 121.84/16.12 ((
% 121.84/16.12 (setminusER) =>
% 121.84/16.12 ((
% 121.84/16.12 (setminusSubset2) =>
% 121.84/16.12 ((
% 121.84/16.12 (setminusERneg) =>
% 121.84/16.12 ((
% 121.84/16.12 (setminusELneg) =>
% 121.84/16.12 ((
% 121.84/16.12 (setminusILneg) =>
% 121.84/16.12 ((
% 121.84/16.12 (setminusIRneg) =>
% 121.84/16.12 ((
% 121.84/16.12 (setminusLsub) =>
% 121.84/16.12 ((
% 121.84/16.12 (setminusSubset1) =>
% 121.84/16.12 ((
% 121.84/16.12 (symdiffE) =>
% 121.84/16.12 ((
% 121.84/16.12 (symdiffI1) =>
% 121.84/16.12 ((
% 121.84/16.12 (symdiffI2) =>
% 121.84/16.12 ((
% 121.84/16.12 (symdiffIneg1) =>
% 121.84/16.12 ((
% 121.84/16.12 (symdiffIneg2) =>
% 121.84/16.12 ((
% 121.84/16.12 (secondinupair) =>
% 121.84/16.12 ((
% 121.84/16.12 (setukpairIL) =>
% 121.84/16.12 ((
% 121.84/16.12 (setukpairIR) =>
% 121.84/16.12 ((
% 121.84/16.12 (kpairiskpair) =>
% 121.84/16.12 ((
% 121.84/16.12 (kpairp) =>
% 121.84/16.12 ((
% 121.84/16.12 (singletonsubset) =>
% 121.84/16.12 ((
% 121.84/16.12 (singletoninpowerset) =>
% 121.84/16.12 ((
% 121.84/16.12 (singletoninpowunion) =>
% 121.84/16.12 ((
% 121.84/16.12 (upairset2E) =>
% 121.84/16.12 ((
% 121.84/16.12 (upairsubunion) =>
% 121.84/16.12 ((
% 121.84/16.12 (upairinpowunion) =>
% 121.84/16.12 ((
% 121.84/16.12 (ubforcartprodlem1) =>
% 121.84/16.12 ((
% 121.84/16.12 (ubforcartprodlem2) =>
% 121.84/16.12 ((
% 121.84/16.12 (ubforcartprodlem3) =>
% 121.84/16.12 ((
% 121.84/16.12 (cartprodpairin) =>
% 121.84/16.12 ((
% 121.84/16.12 (cartprodmempair1) =>
% 121.84/16.12 ((
% 121.84/16.12 (cartprodmempair) =>
% 121.84/16.12 ((
% 121.84/16.12 (setunionE2) =>
% 121.84/16.12 ((
% 121.84/16.12 (setunionsingleton1) =>
% 121.84/16.12 ((
% 121.84/16.12 (setunionsingleton2) =>
% 121.84/16.12 ((
% 121.84/16.12 (setunionsingleton) =>
% 121.84/16.12 ((
% 121.84/16.12 (singletonprop) =>
% 121.84/16.12 ((
% 121.84/16.12 (ex1E1) =>
% 121.84/16.12 ((
% 121.84/16.12 (ex1I) =>
% 121.84/16.12 ((
% 121.84/16.12 (ex1I2) =>
% 121.84/16.12 ((
% 121.84/16.12 (singletonsuniq) =>
% 121.84/16.12 ((
% 121.84/16.12 (setukpairinjL1) =>
% 121.84/16.12 ((
% 121.84/16.12 (kfstsingleton) =>
% 121.84/16.12 ((
% 121.84/16.12 (theprop) =>
% 121.84/16.12 ((
% 121.84/16.12 (kfstpairEq) =>
% 121.84/16.12 ((
% 121.84/16.12 (cartprodfstin) =>
% 121.84/16.12 ((
% 121.84/16.12 (setukpairinjL2) =>
% 121.84/16.12 ((
% 121.84/16.12 (setukpairinjL) =>
% 121.84/16.12 ((
% 121.84/16.12 (setukpairinjR11) =>
% 121.84/16.12 ((
% 121.84/16.12 (setukpairinjR12) =>
% 121.84/16.12 ((
% 121.84/16.12 (setukpairinjR1) =>
% 121.84/16.12 ((
% 121.84/16.12 (upairequniteq) =>
% 121.84/16.12 ((
% 121.84/16.12 (setukpairinjR2) =>
% 121.84/16.12 ((
% 121.84/16.12 (setukpairinjR) =>
% 121.84/16.12 ((
% 121.84/16.12 (ksndsingleton) =>
% 121.84/16.12 ((
% 121.84/16.12 (ksndpairEq) =>
% 121.84/16.12 ((
% 121.84/16.12 (kpairsurjEq) =>
% 121.84/16.12 ((
% 121.84/16.12 (cartprodsndin) =>
% 121.84/16.12 ((
% 121.84/16.12 (cartprodpairmemEL) =>
% 121.84/16.12 ((
% 121.84/16.12 (cartprodpairmemER) =>
% 121.84/16.12 ((
% 121.84/16.12 (cartprodmempaircEq) =>
% 121.84/16.12 ((
% 121.84/16.12 (cartprodfstpairEq) =>
% 121.84/16.12 ((
% 121.84/16.12 (cartprodsndpairEq) =>
% 121.84/16.12 ((
% 121.84/16.12 (cartprodpairsurjEq) =>
% 121.84/16.12 ((
% 121.84/16.12 (dpsetconstrI) =>
% 121.84/16.12 ((
% 121.84/16.12 (dpsetconstrSub) =>
% 121.84/16.12 ((
% 121.84/16.12 (setOfPairsIsBReln) =>
% 121.84/16.12 ((
% 121.84/16.12 (dpsetconstrERa) =>
% 121.84/16.12 ((
% 121.84/16.12 (dpsetconstrEL1) =>
% 121.84/16.12 ((
% 121.84/16.12 (dpsetconstrEL2) =>
% 121.84/16.12 ((
% 121.84/16.12 (dpsetconstrER) =>
% 121.84/16.12 ((
% 121.84/16.12 (funcImageSingleton) =>
% 121.84/16.12 ((
% 121.84/16.12 (apProp) =>
% 121.84/16.12 ((
% 121.84/16.12 (app) =>
% 121.84/16.12 ((
% 121.84/16.12 (infuncsetfunc) =>
% 121.84/16.12 ((
% 121.84/16.12 (ap2p) =>
% 121.84/16.12 ((
% 121.84/16.12 (funcinfuncset) =>
% 121.84/16.12 ((
% 121.84/16.12 (lamProp) =>
% 121.84/16.12 ((
% 121.84/16.12 (lamp) =>
% 121.84/16.12 ((
% 121.84/16.12 (lam2p) =>
% 121.84/16.12 ((
% 121.84/16.12 (brelnall1) =>
% 121.84/16.12 ((
% 121.84/16.12 (brelnall2) =>
% 121.84/16.12 ((
% 121.84/16.12 (ex1E2) =>
% 121.84/16.12 ((
% 121.84/16.12 (funcGraphProp1) =>
% 121.84/16.12 ((
% 121.84/16.12 (funcGraphProp3) =>
% 121.84/16.12 ((
% 121.84/16.12 (funcGraphProp2) =>
% 121.84/16.12 ((
% 121.84/16.12 (funcextLem) =>
% 121.84/16.12 ((
% 121.84/16.12 (funcGraphProp4) =>
% 121.84/16.12 ((
% 121.84/16.12 (subbreln) =>
% 121.84/16.12 ((
% 121.84/16.12 (eqbreln) =>
% 121.84/16.12 ((
% 121.84/16.12 (funcext) =>
% 121.84/16.12 ((
% 121.84/16.12 (funcext2) =>
% 121.84/16.12 ((
% 121.84/16.12 (ap2apEq1) =>
% 121.84/16.12 ((
% 121.84/16.12 (ap2apEq2) =>
% 121.84/16.12 ((
% 121.84/16.12 (beta1) =>
% 121.84/16.12 ((
% 121.84/16.12 (eta1) =>
% 121.84/16.12 ((
% 121.84/16.12 (lam2lamEq) =>
% 121.84/16.12 ((
% 121.84/16.12 (beta2) =>
% 121.84/16.12 ((
% 121.84/16.12 (eta2) =>
% 121.84/16.12 ((
% 121.84/16.12 (iffalseProp1) =>
% 121.84/16.12 ((
% 121.84/16.12 (iffalseProp2) =>
% 121.84/16.12 ((
% 121.84/16.12 (iftrueProp1) =>
% 121.84/16.12 ((
% 121.84/16.12 (iftrueProp2) =>
% 121.84/16.12 ((
% 121.84/16.12 (ifSingleton) =>
% 121.84/16.12 ((
% 121.84/16.12 (ifp) =>
% 121.84/16.12 ((
% 121.84/16.12 (theeq) =>
% 121.84/16.12 ((
% 121.84/16.12 (iftrue) =>
% 121.84/16.12 ((
% 121.84/16.12 (iffalse) =>
% 121.84/16.12 ((
% 121.84/16.12 (iftrueorfalse) =>
% 121.84/16.12 ((
% 121.84/16.12 (binintersectT_lem) =>
% 121.84/16.12 ((
% 121.84/16.12 (binunionT_lem) =>
% 121.84/16.12 ((
% 121.84/16.12 (powersetT_lem) =>
% 121.84/16.12 ((
% 121.84/16.12 (setminusT_lem) =>
% 121.84/16.12 ((
% 121.84/16.12 (complementT_lem) =>
% 121.84/16.12 ((
% 121.84/16.12 (setextT) =>
% 121.84/16.12 ((
% 121.84/16.12 (subsetTI) =>
% 121.84/16.12 ((
% 121.84/16.12 (powersetTI1) =>
% 121.84/16.12 ((
% 121.84/16.12 (powersetTE1) =>
% 121.84/16.12 ((
% 121.84/16.12 (complementTI1) =>
% 121.84/16.12 ((
% 121.84/16.12 (complementTE1) =>
% 121.84/16.12 ((
% 121.84/16.12 (binintersectTELcontra) =>
% 121.84/16.12 ((
% 121.84/16.12 (binintersectTERcontra) =>
% 121.84/16.12 ((
% 121.84/16.12 (contrasubsetT) =>
% 121.84/16.12 ((
% 121.84/16.12 (contrasubsetT1) =>
% 121.84/16.12 ((
% 121.84/16.12 (contrasubsetT2) =>
% 121.84/16.12 ((
% 121.84/16.12 (contrasubsetT3) =>
% 121.84/16.12 ((
% 121.84/16.12 (doubleComplementI1) =>
% 121.84/16.12 ((
% 121.84/16.12 (doubleComplementE1) =>
% 121.84/16.12 ((
% 121.84/16.12 (doubleComplementSub1) =>
% 121.84/16.12 ((
% 121.84/16.12 (doubleComplementSub2) =>
% 121.84/16.12 ((
% 121.84/16.12 (doubleComplementEq) =>
% 121.84/16.12 ((
% 121.84/16.12 (complementTnotintersectT) =>
% 121.84/16.12 ((
% 121.84/16.12 (complementImpComplementIntersect) =>
% 121.84/16.12 ((
% 121.84/16.12 (complementSubsetComplementIntersect) =>
% 121.84/16.12 ((
% 121.84/16.12 (complementInPowersetComplementIntersect) =>
% 121.84/16.12 ((
% 121.84/16.12 (contraSubsetComplement) =>
% 121.84/16.12 ((
% 121.84/16.12 (complementTcontraSubset) =>
% 121.84/16.12 ((
% 121.84/16.12 (binunionTILcontra) =>
% 121.84/16.12 ((
% 121.84/16.12 (binunionTIRcontra) =>
% 121.84/16.12 ((
% 121.84/16.12 (inIntersectImpInUnion) =>
% 121.84/16.12 ((
% 121.84/16.12 (inIntersectImpInUnion2) =>
% 121.84/16.12 ((
% 121.84/16.12 (inIntersectImpInIntersectUnions) =>
% 121.84/16.12 ((
% 121.84/16.12 (intersectInPowersetIntersectUnions) =>
% 121.84/16.12 ((
% 121.84/16.12 (inComplementUnionImpNotIn1) =>
% 121.84/16.12 ((
% 121.84/16.12 (inComplementUnionImpInComplement1) =>
% 121.84/16.12 ((
% 121.84/16.12 (binunionTE) =>
% 121.84/16.12 ((
% 121.84/16.12 (binunionTEcontra) =>
% 121.84/16.12 ((
% 121.84/16.12 (demorgan2a1) =>
% 121.84/16.12 ((
% 121.84/16.12 (complementUnionInPowersetComplement) =>
% 121.84/16.12 ((
% 121.84/16.12 (demorgan2a2) =>
% 121.84/16.12 ((
% 121.84/16.12 (demorgan1a) =>
% 121.84/16.12 ((
% 121.84/16.12 (demorgan1b) =>
% 121.84/16.12 ((
% 121.84/16.12 (demorgan1) =>
% 121.84/16.12 ((
% 121.84/16.12 (demorgan2a) =>
% 121.84/16.12 ((
% 121.84/16.12 (demorgan2b2) =>
% 121.84/16.12 ((
% 121.84/16.12 (demorgan2b) =>
% 121.84/16.12 ((
% 121.84/16.12 (demorgan2) =>
% 121.84/16.12 ((
% 121.84/16.12 (woz13rule0) =>
% 121.84/16.12 ((
% 121.84/16.12 (woz13rule1) =>
% 121.84/16.12 ((
% 121.84/16.12 (woz13rule2) =>
% 121.84/16.12 ((
% 121.84/16.12 (woz13rule3) =>
% 121.84/16.12 ((
% 121.84/16.12 (woz13rule4) =>
% 121.84/16.12 ((
% 121.84/16.12 (woz1_1) =>
% 121.84/16.12 ((
% 121.84/16.12 (woz1_2) =>
% 121.84/16.12 ((
% 121.84/16.12 (woz1_3) =>
% 121.84/16.12 ((
% 121.84/16.12 (woz1_4) =>
% 121.84/16.12 ((
% 121.84/16.12 (woz1_5) =>
% 121.84/16.12 ((
% 121.84/16.12 (breln1all2) =>
% 121.84/16.12 ((
% 121.84/16.12 (breln1SetBreln1) =>
% 121.84/16.12 ((
% 121.84/16.12 (choice2fnsingleton) =>
% 121.84/16.12 ((
% 121.84/16.12 (setOfPairsIsBReln1) =>
% 121.84/16.12 ((
% 121.84/16.12 (breln1all1) =>
% 121.84/16.12 ((
% 121.84/16.12 (subbreln1) =>
% 121.84/16.12 ((
% 121.84/16.12 (eqbreln1) =>
% 121.84/16.12 ((
% 121.84/16.12 (breln1invprop) =>
% 121.84/16.12 ((
% 121.84/16.12 (breln1invI) =>
% 121.84/16.12 ((
% 121.84/16.12 (breln1invE) =>
% 121.84/16.12 ((
% 121.84/16.12 (breln1compprop) =>
% 121.84/16.12 ((
% 121.84/16.12 (breln1compI) =>
% 121.84/16.12 ((
% 121.84/16.12 (breln1compE) =>
% 121.84/16.12 ((
% 121.84/16.12 (breln1compEex) =>
% 121.84/16.12 ((
% 121.84/16.12 (breln1unionprop) =>
% 121.84/16.12 ((
% 121.84/16.12 (breln1unionIL) =>
% 121.84/16.12 ((
% 121.84/16.12 (breln1unionIR) =>
% 121.84/16.12 ((
% 121.84/16.12 (breln1unionI) =>
% 121.84/16.12 ((
% 121.84/16.12 (breln1unionE) =>
% 121.84/16.12 ((
% 121.84/16.12 (breln1unionEcases) =>
% 121.84/16.12 ((
% 121.84/16.12 (breln1unionCommutes) =>
% 121.84/16.12 ((
% 121.84/16.12 (woz2Ex) =>
% 121.84/16.12 ((
% 121.84/16.12 (woz2W) =>
% 121.84/16.12 ((
% 121.84/16.12 (woz2A) =>
% 121.84/16.12 ((
% 121.84/16.12 (woz2B) =>
% 121.84/16.12 ((
% 121.84/16.12 (image1Ex) =>
% 121.84/16.12 ((
% 121.84/16.12 (image1Ex1) =>
% 121.84/16.12 ((
% 121.84/16.12 (image1Equiv) =>
% 121.84/16.12 ((
% 121.84/16.12 (image1E) =>
% 121.84/16.12 ((
% 121.84/16.12 (image1I) =>
% 121.84/16.12 ((
% 121.84/16.12 (injFuncInInjFuncSet) =>
% 121.84/16.12 ((
% 121.84/16.12 (!!) @ (
% 121.84/16.12 (('#B') @ (
% 121.84/16.12 !!) @
% 121.84/16.12 (
% 121.84/16.12 (
% 121.84/16.12 ('#B') @ (
% 121.84/16.12 (
% 121.84/16.12 ('#B') @ (
% 121.84/16.12 !!))) @
% 121.84/16.12 (
% 121.84/16.12 (
% 121.84/16.12 ('#S') @ (
% 121.84/16.12 (
% 121.84/16.12 ('#B') @ (
% 121.84/16.12 '#S') @
% 121.84/16.12 (
% 121.84/16.12 (
% 121.84/16.12 ('#B') @ (
% 121.84/16.12 (
% 121.84/16.12 ('#B') @ (
% 121.84/16.12 '#S'))) @
% 121.84/16.12 (
% 121.84/16.12 (
% 121.84/16.12 ('#B') @ (
% 121.84/16.12 (
% 121.84/16.12 ('#B') @ (
% 121.84/16.12 (
% 121.84/16.12 ('#B') @ (
% 121.84/16.12 =>))))) @
% 121.84/16.12 (
% 121.84/16.12 (
% 121.84/16.12 ('#B') @ (
% 121.84/16.12 (
% 121.84/16.12 ('#B') @ (
% 121.84/16.12 (
% 121.84/16.12 ('#C') @ in)))) @
% 121.84/16.12 injFuncSet)))))))) @
% 121.84/16.12 (
% 121.84/16.12 (
% 121.84/16.12 ('#B') @ (
% 121.84/16.12 (
% 121.84/16.12 ('#B') @ (
% 121.84/16.12 (
% 121.84/16.12 ('#C') @ in)))) @
% 121.84/16.12 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 121.84/16.12 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl984])).
% 121.84/16.12 thf(zip_derived_cl1015, plain,
% 121.84/16.12 (~ (((setextsub) =>
% 121.84/16.12 (((subsetemptysetimpeq) =>
% 121.84/16.12 (((powersetI1) =>
% 121.84/16.12 (((powersetE1) =>
% 121.84/16.12 (((inPowerset) =>
% 121.84/16.12 (((powersetsubset) =>
% 121.84/16.12 (((sepInPowerset) =>
% 121.84/16.12 (((sepSubset) =>
% 121.84/16.12 (((binunionIL) =>
% 121.84/16.12 (((upairset2IR) =>
% 121.84/16.12 (((binunionIR) =>
% 121.84/16.12 (((binunionEcases) =>
% 121.84/16.12 (((binunionE) =>
% 121.84/16.12 (((binunionLsub) =>
% 121.84/16.12 (((binunionRsub) =>
% 121.84/16.12 (((binintersectI) =>
% 121.84/16.12 (((binintersectSubset5) =>
% 121.84/16.12 (((binintersectEL) =>
% 121.84/16.12 (((binintersectLsub) =>
% 121.84/16.12 (((binintersectSubset2) =>
% 121.84/16.12 (((binintersectSubset3) =>
% 121.84/16.12 (((binintersectER) =>
% 121.84/16.12 (((disjointsetsI1) =>
% 121.84/16.12 (((binintersectRsub) =>
% 121.84/16.12 (((binintersectSubset4) =>
% 121.84/16.12 (((binintersectSubset1) =>
% 121.84/16.12 (((bs114d) =>
% 121.84/16.12 (((setminusI) =>
% 121.84/16.12 (((setminusEL) =>
% 121.84/16.12 (((setminusER) =>
% 121.84/16.12 ((
% 121.84/16.12 (setminusSubset2) =>
% 121.84/16.12 ((
% 121.84/16.12 (setminusERneg) =>
% 121.84/16.12 ((
% 121.84/16.12 (setminusELneg) =>
% 121.84/16.12 ((
% 121.84/16.12 (setminusILneg) =>
% 121.84/16.12 ((
% 121.84/16.12 (setminusIRneg) =>
% 121.84/16.12 ((
% 121.84/16.12 (setminusLsub) =>
% 121.84/16.12 ((
% 121.84/16.12 (setminusSubset1) =>
% 121.84/16.12 ((
% 121.84/16.12 (symdiffE) =>
% 121.84/16.12 ((
% 121.84/16.12 (symdiffI1) =>
% 121.84/16.12 ((
% 121.84/16.12 (symdiffI2) =>
% 121.84/16.12 ((
% 121.84/16.12 (symdiffIneg1) =>
% 121.84/16.12 ((
% 121.84/16.12 (symdiffIneg2) =>
% 121.84/16.12 ((
% 121.84/16.12 (secondinupair) =>
% 121.84/16.12 ((
% 121.84/16.12 (setukpairIL) =>
% 121.84/16.12 ((
% 121.84/16.12 (setukpairIR) =>
% 121.84/16.12 ((
% 121.84/16.12 (kpairiskpair) =>
% 121.84/16.12 ((
% 121.84/16.12 (kpairp) =>
% 121.84/16.12 ((
% 121.84/16.12 (singletonsubset) =>
% 121.84/16.12 ((
% 121.84/16.12 (singletoninpowerset) =>
% 121.84/16.12 ((
% 121.84/16.12 (singletoninpowunion) =>
% 121.84/16.12 ((
% 121.84/16.12 (upairset2E) =>
% 121.84/16.12 ((
% 121.84/16.12 (upairsubunion) =>
% 121.84/16.12 ((
% 121.84/16.12 (upairinpowunion) =>
% 121.84/16.12 ((
% 121.84/16.12 (ubforcartprodlem1) =>
% 121.84/16.12 ((
% 121.84/16.12 (ubforcartprodlem2) =>
% 121.84/16.12 ((
% 121.84/16.12 (ubforcartprodlem3) =>
% 121.84/16.12 ((
% 121.84/16.12 (cartprodpairin) =>
% 121.84/16.12 ((
% 121.84/16.12 (cartprodmempair1) =>
% 121.84/16.12 ((
% 121.84/16.12 (cartprodmempair) =>
% 121.84/16.12 ((
% 121.84/16.12 (setunionE2) =>
% 121.84/16.12 ((
% 121.84/16.12 (setunionsingleton1) =>
% 121.84/16.12 ((
% 121.84/16.12 (setunionsingleton2) =>
% 121.84/16.12 ((
% 121.84/16.12 (setunionsingleton) =>
% 121.84/16.12 ((
% 121.84/16.12 (singletonprop) =>
% 121.84/16.12 ((
% 121.84/16.12 (ex1E1) =>
% 121.84/16.12 ((
% 121.84/16.12 (ex1I) =>
% 121.84/16.12 ((
% 121.84/16.12 (ex1I2) =>
% 121.84/16.12 ((
% 121.84/16.12 (singletonsuniq) =>
% 121.84/16.12 ((
% 121.84/16.12 (setukpairinjL1) =>
% 121.84/16.12 ((
% 121.84/16.12 (kfstsingleton) =>
% 121.84/16.12 ((
% 121.84/16.12 (theprop) =>
% 121.84/16.12 ((
% 121.84/16.12 (kfstpairEq) =>
% 121.84/16.12 ((
% 121.84/16.12 (cartprodfstin) =>
% 121.84/16.12 ((
% 121.84/16.12 (setukpairinjL2) =>
% 121.84/16.12 ((
% 121.84/16.12 (setukpairinjL) =>
% 121.84/16.12 ((
% 121.84/16.12 (setukpairinjR11) =>
% 121.84/16.12 ((
% 121.84/16.12 (setukpairinjR12) =>
% 121.84/16.12 ((
% 121.84/16.12 (setukpairinjR1) =>
% 121.84/16.12 ((
% 121.84/16.12 (upairequniteq) =>
% 121.84/16.12 ((
% 121.84/16.12 (setukpairinjR2) =>
% 121.84/16.12 ((
% 121.84/16.12 (setukpairinjR) =>
% 121.84/16.12 ((
% 121.84/16.12 (ksndsingleton) =>
% 121.84/16.12 ((
% 121.84/16.12 (ksndpairEq) =>
% 121.84/16.12 ((
% 121.84/16.12 (kpairsurjEq) =>
% 121.84/16.12 ((
% 121.84/16.12 (cartprodsndin) =>
% 121.84/16.12 ((
% 121.84/16.12 (cartprodpairmemEL) =>
% 121.84/16.12 ((
% 121.84/16.12 (cartprodpairmemER) =>
% 121.84/16.12 ((
% 121.84/16.12 (cartprodmempaircEq) =>
% 121.84/16.12 ((
% 121.84/16.12 (cartprodfstpairEq) =>
% 121.84/16.12 ((
% 121.84/16.12 (cartprodsndpairEq) =>
% 121.84/16.12 ((
% 121.84/16.12 (cartprodpairsurjEq) =>
% 121.84/16.12 ((
% 121.84/16.12 (dpsetconstrI) =>
% 121.84/16.12 ((
% 121.84/16.12 (dpsetconstrSub) =>
% 121.84/16.12 ((
% 121.84/16.12 (setOfPairsIsBReln) =>
% 121.84/16.12 ((
% 121.84/16.12 (dpsetconstrERa) =>
% 121.84/16.12 ((
% 121.84/16.12 (dpsetconstrEL1) =>
% 121.84/16.12 ((
% 121.84/16.12 (dpsetconstrEL2) =>
% 121.84/16.12 ((
% 121.84/16.12 (dpsetconstrER) =>
% 121.84/16.12 ((
% 121.84/16.12 (funcImageSingleton) =>
% 121.84/16.12 ((
% 121.84/16.12 (apProp) =>
% 121.84/16.12 ((
% 121.84/16.12 (app) =>
% 121.84/16.12 ((
% 121.84/16.12 (infuncsetfunc) =>
% 121.84/16.12 ((
% 121.84/16.12 (ap2p) =>
% 121.84/16.12 ((
% 121.84/16.12 (funcinfuncset) =>
% 121.84/16.12 ((
% 121.84/16.12 (lamProp) =>
% 121.84/16.12 ((
% 121.84/16.12 (lamp) =>
% 121.84/16.12 ((
% 121.84/16.12 (lam2p) =>
% 121.84/16.12 ((
% 121.84/16.12 (brelnall1) =>
% 121.84/16.12 ((
% 121.84/16.12 (brelnall2) =>
% 121.84/16.12 ((
% 121.84/16.12 (ex1E2) =>
% 121.84/16.12 ((
% 121.84/16.12 (funcGraphProp1) =>
% 121.84/16.12 ((
% 121.84/16.12 (funcGraphProp3) =>
% 121.84/16.12 ((
% 121.84/16.12 (funcGraphProp2) =>
% 121.84/16.12 ((
% 121.84/16.12 (funcextLem) =>
% 121.84/16.12 ((
% 121.84/16.12 (funcGraphProp4) =>
% 121.84/16.12 ((
% 121.84/16.12 (subbreln) =>
% 121.84/16.12 ((
% 121.84/16.12 (eqbreln) =>
% 121.84/16.12 ((
% 121.84/16.12 (funcext) =>
% 121.84/16.12 ((
% 121.84/16.12 (funcext2) =>
% 121.84/16.12 ((
% 121.84/16.12 (ap2apEq1) =>
% 121.84/16.12 ((
% 121.84/16.12 (ap2apEq2) =>
% 121.84/16.12 ((
% 121.84/16.12 (beta1) =>
% 121.84/16.12 ((
% 121.84/16.12 (eta1) =>
% 121.84/16.12 ((
% 121.84/16.12 (lam2lamEq) =>
% 121.84/16.12 ((
% 121.84/16.12 (beta2) =>
% 121.84/16.12 ((
% 121.84/16.12 (eta2) =>
% 121.84/16.12 ((
% 121.84/16.12 (iffalseProp1) =>
% 121.84/16.12 ((
% 121.84/16.12 (iffalseProp2) =>
% 121.84/16.12 ((
% 121.84/16.12 (iftrueProp1) =>
% 121.84/16.12 ((
% 121.84/16.12 (iftrueProp2) =>
% 121.84/16.12 ((
% 121.84/16.12 (ifSingleton) =>
% 121.84/16.12 ((
% 121.84/16.12 (ifp) =>
% 121.84/16.12 ((
% 121.84/16.12 (theeq) =>
% 121.84/16.12 ((
% 121.84/16.12 (iftrue) =>
% 121.84/16.12 ((
% 121.84/16.12 (iffalse) =>
% 121.84/16.12 ((
% 121.84/16.12 (iftrueorfalse) =>
% 121.84/16.12 ((
% 121.84/16.12 (binintersectT_lem) =>
% 121.84/16.12 ((
% 121.84/16.12 (binunionT_lem) =>
% 121.84/16.12 ((
% 121.84/16.12 (powersetT_lem) =>
% 121.84/16.12 ((
% 121.84/16.12 (setminusT_lem) =>
% 121.84/16.12 ((
% 121.84/16.12 (complementT_lem) =>
% 121.84/16.12 ((
% 121.84/16.12 (setextT) =>
% 121.84/16.12 ((
% 121.84/16.12 (subsetTI) =>
% 121.84/16.12 ((
% 121.84/16.12 (powersetTI1) =>
% 121.84/16.12 ((
% 121.84/16.12 (powersetTE1) =>
% 121.84/16.12 ((
% 121.84/16.12 (complementTI1) =>
% 121.84/16.12 ((
% 121.84/16.12 (complementTE1) =>
% 121.84/16.12 ((
% 121.84/16.12 (binintersectTELcontra) =>
% 121.84/16.12 ((
% 121.84/16.12 (binintersectTERcontra) =>
% 121.84/16.12 ((
% 121.84/16.12 (contrasubsetT) =>
% 121.84/16.12 ((
% 121.84/16.12 (contrasubsetT1) =>
% 121.84/16.12 ((
% 121.84/16.12 (contrasubsetT2) =>
% 121.84/16.12 ((
% 121.84/16.12 (contrasubsetT3) =>
% 121.84/16.12 ((
% 121.84/16.12 (doubleComplementI1) =>
% 121.84/16.12 ((
% 121.84/16.12 (doubleComplementE1) =>
% 121.84/16.12 ((
% 121.84/16.12 (doubleComplementSub1) =>
% 121.84/16.12 ((
% 121.84/16.12 (doubleComplementSub2) =>
% 121.84/16.12 ((
% 121.84/16.12 (doubleComplementEq) =>
% 121.84/16.12 ((
% 121.84/16.12 (complementTnotintersectT) =>
% 121.84/16.12 ((
% 121.84/16.12 (complementImpComplementIntersect) =>
% 121.84/16.12 ((
% 121.84/16.12 (complementSubsetComplementIntersect) =>
% 121.84/16.12 ((
% 121.84/16.12 (complementInPowersetComplementIntersect) =>
% 121.84/16.12 ((
% 121.84/16.12 (contraSubsetComplement) =>
% 121.84/16.12 ((
% 121.84/16.12 (complementTcontraSubset) =>
% 121.84/16.12 ((
% 121.84/16.12 (binunionTILcontra) =>
% 121.84/16.12 ((
% 121.84/16.12 (binunionTIRcontra) =>
% 121.84/16.12 ((
% 121.84/16.12 (inIntersectImpInUnion) =>
% 121.84/16.12 ((
% 121.84/16.12 (inIntersectImpInUnion2) =>
% 121.84/16.12 ((
% 121.84/16.12 (inIntersectImpInIntersectUnions) =>
% 121.84/16.12 ((
% 121.84/16.12 (intersectInPowersetIntersectUnions) =>
% 121.84/16.12 ((
% 121.84/16.12 (inComplementUnionImpNotIn1) =>
% 121.84/16.12 ((
% 121.84/16.12 (inComplementUnionImpInComplement1) =>
% 121.84/16.12 ((
% 121.84/16.12 (binunionTE) =>
% 121.84/16.12 ((
% 121.84/16.12 (binunionTEcontra) =>
% 121.84/16.12 ((
% 121.84/16.12 (demorgan2a1) =>
% 121.84/16.12 ((
% 121.84/16.12 (complementUnionInPowersetComplement) =>
% 121.84/16.12 ((
% 121.84/16.12 (demorgan2a2) =>
% 121.84/16.12 ((
% 121.84/16.12 (demorgan1a) =>
% 121.84/16.12 ((
% 121.84/16.12 (demorgan1b) =>
% 121.84/16.12 ((
% 121.84/16.12 (demorgan1) =>
% 121.84/16.12 ((
% 121.84/16.12 (demorgan2a) =>
% 121.84/16.12 ((
% 121.84/16.12 (demorgan2b2) =>
% 121.84/16.12 ((
% 121.84/16.12 (demorgan2b) =>
% 121.84/16.12 ((
% 121.84/16.12 (demorgan2) =>
% 121.84/16.12 ((
% 121.84/16.12 (woz13rule0) =>
% 121.84/16.12 ((
% 121.84/16.12 (woz13rule1) =>
% 121.84/16.12 ((
% 121.84/16.12 (woz13rule2) =>
% 121.84/16.12 ((
% 121.84/16.12 (woz13rule3) =>
% 121.84/16.12 ((
% 121.84/16.12 (woz13rule4) =>
% 121.84/16.12 ((
% 121.84/16.12 (woz1_1) =>
% 121.84/16.12 ((
% 121.84/16.12 (woz1_2) =>
% 121.84/16.12 ((
% 121.84/16.12 (woz1_3) =>
% 121.84/16.12 ((
% 121.84/16.12 (woz1_4) =>
% 121.84/16.12 ((
% 121.84/16.12 (woz1_5) =>
% 121.84/16.12 ((
% 121.84/16.12 (breln1all2) =>
% 121.84/16.12 ((
% 121.84/16.12 (breln1SetBreln1) =>
% 121.84/16.12 ((
% 121.84/16.12 (choice2fnsingleton) =>
% 121.84/16.12 ((
% 121.84/16.12 (setOfPairsIsBReln1) =>
% 121.84/16.12 ((
% 121.84/16.12 (breln1all1) =>
% 121.84/16.12 ((
% 121.84/16.12 (subbreln1) =>
% 121.84/16.12 ((
% 121.84/16.12 (eqbreln1) =>
% 121.84/16.12 ((
% 121.84/16.12 (breln1invprop) =>
% 121.84/16.12 ((
% 121.84/16.12 (breln1invI) =>
% 121.84/16.12 ((
% 121.84/16.12 (breln1invE) =>
% 121.84/16.12 ((
% 121.84/16.12 (breln1compprop) =>
% 121.84/16.12 ((
% 121.84/16.12 (breln1compI) =>
% 121.84/16.12 ((
% 121.84/16.12 (breln1compE) =>
% 121.84/16.12 ((
% 121.84/16.12 (breln1compEex) =>
% 121.84/16.12 ((
% 121.84/16.12 (breln1unionprop) =>
% 121.84/16.12 ((
% 121.84/16.12 (breln1unionIL) =>
% 121.84/16.12 ((
% 121.84/16.12 (breln1unionIR) =>
% 121.84/16.12 ((
% 121.84/16.12 (breln1unionI) =>
% 121.84/16.12 ((
% 121.84/16.12 (breln1unionE) =>
% 121.84/16.12 ((
% 121.84/16.12 (breln1unionEcases) =>
% 121.84/16.12 ((
% 121.84/16.12 (breln1unionCommutes) =>
% 121.84/16.12 ((
% 121.84/16.12 (woz2Ex) =>
% 121.84/16.12 ((
% 121.84/16.12 (woz2W) =>
% 121.84/16.12 ((
% 121.84/16.12 (woz2A) =>
% 121.84/16.12 ((
% 121.84/16.12 (woz2B) =>
% 121.84/16.12 ((
% 121.84/16.12 (image1Ex) =>
% 121.84/16.12 ((
% 121.84/16.12 (image1Ex1) =>
% 121.84/16.12 ((
% 121.84/16.12 (image1Equiv) =>
% 121.84/16.12 ((
% 121.84/16.12 (image1E) =>
% 121.84/16.12 ((
% 121.84/16.12 (image1I) =>
% 121.84/16.12 ((
% 121.84/16.12 (injFuncInInjFuncSet) =>
% 121.84/16.12 ((
% 121.84/16.12 (!!) @ (
% 121.84/16.12 (('#B') @ (
% 121.84/16.12 !!) @
% 121.84/16.12 (
% 121.84/16.12 (
% 121.84/16.12 ('#B') @ (
% 121.84/16.12 (
% 121.84/16.12 ('#B') @ (
% 121.84/16.12 !!))) @
% 121.84/16.12 (
% 121.84/16.12 (
% 121.84/16.12 ('#S') @ (
% 121.84/16.12 (
% 121.84/16.12 ('#B') @ (
% 121.84/16.12 '#S') @
% 121.84/16.12 (
% 121.84/16.12 (
% 121.84/16.12 ('#B') @ (
% 121.84/16.12 (
% 121.84/16.12 ('#B') @ (
% 121.84/16.12 '#S'))) @
% 121.84/16.12 (
% 121.84/16.12 (
% 121.84/16.12 ('#B') @ (
% 121.84/16.12 (
% 121.84/16.12 ('#B') @ (
% 121.84/16.12 (
% 121.84/16.12 ('#B') @ (
% 121.84/16.12 =>))))) @
% 121.84/16.12 (
% 121.84/16.12 (
% 121.84/16.12 ('#B') @ (
% 121.84/16.12 (
% 121.84/16.12 ('#B') @ (
% 121.84/16.12 (
% 121.84/16.12 ('#C') @ in)))) @
% 121.84/16.12 injFuncSet)))))))) @
% 121.84/16.12 (
% 121.84/16.12 (
% 121.84/16.12 ('#B') @ (
% 121.84/16.12 (
% 121.84/16.12 ('#B') @ (
% 121.84/16.12 (
% 121.84/16.12 ('#C') @ in)))) @
% 121.84/16.12 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 121.84/16.12 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1000])).
% 121.84/16.12 thf(zip_derived_cl1027, plain,
% 121.84/16.12 (~ (((subsetemptysetimpeq) =>
% 121.84/16.12 (((powersetI1) =>
% 121.84/16.12 (((powersetE1) =>
% 121.84/16.12 (((inPowerset) =>
% 121.84/16.12 (((powersetsubset) =>
% 121.84/16.12 (((sepInPowerset) =>
% 121.84/16.12 (((sepSubset) =>
% 121.84/16.12 (((binunionIL) =>
% 121.84/16.12 (((upairset2IR) =>
% 121.84/16.12 (((binunionIR) =>
% 121.84/16.12 (((binunionEcases) =>
% 121.84/16.12 (((binunionE) =>
% 121.84/16.12 (((binunionLsub) =>
% 121.84/16.12 (((binunionRsub) =>
% 121.84/16.12 (((binintersectI) =>
% 121.84/16.12 (((binintersectSubset5) =>
% 121.84/16.12 (((binintersectEL) =>
% 121.84/16.12 (((binintersectLsub) =>
% 121.84/16.12 (((binintersectSubset2) =>
% 121.84/16.12 (((binintersectSubset3) =>
% 121.84/16.12 (((binintersectER) =>
% 121.84/16.12 (((disjointsetsI1) =>
% 121.84/16.12 (((binintersectRsub) =>
% 121.84/16.12 (((binintersectSubset4) =>
% 121.84/16.12 (((binintersectSubset1) =>
% 121.84/16.12 (((bs114d) =>
% 121.84/16.12 (((setminusI) =>
% 121.84/16.12 (((setminusEL) =>
% 121.84/16.12 (((setminusER) =>
% 121.84/16.12 (((setminusSubset2) =>
% 121.84/16.12 ((
% 121.84/16.12 (setminusERneg) =>
% 121.84/16.12 ((
% 121.84/16.12 (setminusELneg) =>
% 121.84/16.12 ((
% 121.84/16.12 (setminusILneg) =>
% 121.84/16.12 ((
% 121.84/16.12 (setminusIRneg) =>
% 121.84/16.12 ((
% 121.84/16.12 (setminusLsub) =>
% 121.84/16.12 ((
% 121.84/16.12 (setminusSubset1) =>
% 121.84/16.12 ((
% 121.84/16.12 (symdiffE) =>
% 121.84/16.12 ((
% 121.84/16.12 (symdiffI1) =>
% 121.84/16.12 ((
% 121.84/16.12 (symdiffI2) =>
% 121.84/16.12 ((
% 121.84/16.12 (symdiffIneg1) =>
% 121.84/16.12 ((
% 121.84/16.12 (symdiffIneg2) =>
% 121.84/16.12 ((
% 121.84/16.12 (secondinupair) =>
% 121.84/16.12 ((
% 121.84/16.12 (setukpairIL) =>
% 121.84/16.12 ((
% 121.84/16.12 (setukpairIR) =>
% 121.84/16.12 ((
% 121.84/16.12 (kpairiskpair) =>
% 121.84/16.12 ((
% 121.84/16.12 (kpairp) =>
% 121.84/16.12 ((
% 121.84/16.12 (singletonsubset) =>
% 121.84/16.12 ((
% 121.84/16.12 (singletoninpowerset) =>
% 121.84/16.12 ((
% 121.84/16.12 (singletoninpowunion) =>
% 121.84/16.12 ((
% 121.84/16.12 (upairset2E) =>
% 121.84/16.12 ((
% 121.84/16.12 (upairsubunion) =>
% 121.84/16.12 ((
% 121.84/16.12 (upairinpowunion) =>
% 121.84/16.12 ((
% 121.84/16.12 (ubforcartprodlem1) =>
% 121.84/16.12 ((
% 121.84/16.12 (ubforcartprodlem2) =>
% 121.84/16.12 ((
% 121.84/16.12 (ubforcartprodlem3) =>
% 121.84/16.12 ((
% 121.84/16.12 (cartprodpairin) =>
% 121.84/16.12 ((
% 121.84/16.12 (cartprodmempair1) =>
% 121.84/16.12 ((
% 121.84/16.12 (cartprodmempair) =>
% 121.84/16.12 ((
% 121.84/16.12 (setunionE2) =>
% 121.84/16.12 ((
% 121.84/16.12 (setunionsingleton1) =>
% 121.84/16.12 ((
% 121.84/16.12 (setunionsingleton2) =>
% 121.84/16.12 ((
% 121.84/16.12 (setunionsingleton) =>
% 121.84/16.12 ((
% 121.84/16.12 (singletonprop) =>
% 121.84/16.12 ((
% 121.84/16.12 (ex1E1) =>
% 121.84/16.12 ((
% 121.84/16.12 (ex1I) =>
% 121.84/16.12 ((
% 121.84/16.12 (ex1I2) =>
% 121.84/16.12 ((
% 121.84/16.12 (singletonsuniq) =>
% 121.84/16.12 ((
% 121.84/16.12 (setukpairinjL1) =>
% 121.84/16.12 ((
% 121.84/16.12 (kfstsingleton) =>
% 121.84/16.12 ((
% 121.84/16.12 (theprop) =>
% 121.84/16.12 ((
% 121.84/16.12 (kfstpairEq) =>
% 121.84/16.12 ((
% 121.84/16.12 (cartprodfstin) =>
% 121.84/16.12 ((
% 121.84/16.12 (setukpairinjL2) =>
% 121.84/16.12 ((
% 121.84/16.12 (setukpairinjL) =>
% 121.84/16.12 ((
% 121.84/16.12 (setukpairinjR11) =>
% 121.84/16.12 ((
% 121.84/16.12 (setukpairinjR12) =>
% 121.84/16.12 ((
% 121.84/16.12 (setukpairinjR1) =>
% 121.84/16.12 ((
% 121.84/16.12 (upairequniteq) =>
% 121.84/16.12 ((
% 121.84/16.12 (setukpairinjR2) =>
% 121.84/16.12 ((
% 121.84/16.12 (setukpairinjR) =>
% 121.84/16.12 ((
% 121.84/16.12 (ksndsingleton) =>
% 121.84/16.12 ((
% 121.84/16.12 (ksndpairEq) =>
% 121.84/16.12 ((
% 121.84/16.12 (kpairsurjEq) =>
% 121.84/16.12 ((
% 121.84/16.12 (cartprodsndin) =>
% 121.84/16.12 ((
% 121.84/16.12 (cartprodpairmemEL) =>
% 121.84/16.12 ((
% 121.84/16.12 (cartprodpairmemER) =>
% 121.84/16.12 ((
% 121.84/16.12 (cartprodmempaircEq) =>
% 121.84/16.12 ((
% 121.84/16.12 (cartprodfstpairEq) =>
% 121.84/16.12 ((
% 121.84/16.12 (cartprodsndpairEq) =>
% 121.84/16.12 ((
% 121.84/16.12 (cartprodpairsurjEq) =>
% 121.84/16.12 ((
% 121.84/16.12 (dpsetconstrI) =>
% 121.84/16.12 ((
% 121.84/16.12 (dpsetconstrSub) =>
% 121.84/16.12 ((
% 121.84/16.12 (setOfPairsIsBReln) =>
% 121.84/16.12 ((
% 121.84/16.12 (dpsetconstrERa) =>
% 121.84/16.12 ((
% 121.84/16.12 (dpsetconstrEL1) =>
% 121.84/16.12 ((
% 121.84/16.12 (dpsetconstrEL2) =>
% 121.84/16.12 ((
% 121.84/16.12 (dpsetconstrER) =>
% 121.84/16.12 ((
% 121.84/16.12 (funcImageSingleton) =>
% 121.84/16.12 ((
% 121.84/16.12 (apProp) =>
% 121.84/16.12 ((
% 121.84/16.12 (app) =>
% 121.84/16.12 ((
% 121.84/16.12 (infuncsetfunc) =>
% 121.84/16.12 ((
% 121.84/16.12 (ap2p) =>
% 121.84/16.12 ((
% 121.84/16.12 (funcinfuncset) =>
% 121.84/16.12 ((
% 121.84/16.12 (lamProp) =>
% 121.84/16.12 ((
% 121.84/16.12 (lamp) =>
% 121.84/16.12 ((
% 121.84/16.12 (lam2p) =>
% 121.84/16.12 ((
% 121.84/16.12 (brelnall1) =>
% 121.84/16.12 ((
% 121.84/16.12 (brelnall2) =>
% 121.84/16.12 ((
% 121.84/16.12 (ex1E2) =>
% 121.84/16.12 ((
% 121.84/16.12 (funcGraphProp1) =>
% 121.84/16.12 ((
% 121.84/16.12 (funcGraphProp3) =>
% 121.84/16.12 ((
% 121.84/16.12 (funcGraphProp2) =>
% 121.84/16.12 ((
% 121.84/16.12 (funcextLem) =>
% 121.84/16.12 ((
% 121.84/16.12 (funcGraphProp4) =>
% 121.84/16.12 ((
% 121.84/16.12 (subbreln) =>
% 121.84/16.12 ((
% 121.84/16.12 (eqbreln) =>
% 121.84/16.12 ((
% 121.84/16.12 (funcext) =>
% 121.84/16.12 ((
% 121.84/16.12 (funcext2) =>
% 121.84/16.12 ((
% 121.84/16.12 (ap2apEq1) =>
% 121.84/16.12 ((
% 121.84/16.12 (ap2apEq2) =>
% 121.84/16.12 ((
% 121.84/16.12 (beta1) =>
% 121.84/16.12 ((
% 121.84/16.12 (eta1) =>
% 121.84/16.12 ((
% 121.84/16.12 (lam2lamEq) =>
% 121.84/16.12 ((
% 121.84/16.12 (beta2) =>
% 121.84/16.12 ((
% 121.84/16.12 (eta2) =>
% 121.84/16.12 ((
% 121.84/16.12 (iffalseProp1) =>
% 121.84/16.12 ((
% 121.84/16.12 (iffalseProp2) =>
% 121.84/16.12 ((
% 121.84/16.12 (iftrueProp1) =>
% 121.84/16.12 ((
% 121.84/16.12 (iftrueProp2) =>
% 121.84/16.12 ((
% 121.84/16.12 (ifSingleton) =>
% 121.84/16.12 ((
% 121.84/16.12 (ifp) =>
% 121.84/16.12 ((
% 121.84/16.12 (theeq) =>
% 121.84/16.12 ((
% 121.84/16.12 (iftrue) =>
% 121.84/16.12 ((
% 121.84/16.12 (iffalse) =>
% 121.84/16.12 ((
% 121.84/16.12 (iftrueorfalse) =>
% 121.84/16.12 ((
% 121.84/16.12 (binintersectT_lem) =>
% 121.84/16.12 ((
% 121.84/16.12 (binunionT_lem) =>
% 121.84/16.12 ((
% 121.84/16.12 (powersetT_lem) =>
% 121.84/16.12 ((
% 121.84/16.12 (setminusT_lem) =>
% 121.84/16.12 ((
% 121.84/16.12 (complementT_lem) =>
% 121.84/16.12 ((
% 121.84/16.12 (setextT) =>
% 121.84/16.12 ((
% 121.84/16.12 (subsetTI) =>
% 121.84/16.12 ((
% 121.84/16.12 (powersetTI1) =>
% 121.84/16.12 ((
% 121.84/16.12 (powersetTE1) =>
% 121.84/16.12 ((
% 121.84/16.12 (complementTI1) =>
% 121.84/16.12 ((
% 121.84/16.12 (complementTE1) =>
% 121.84/16.12 ((
% 121.84/16.12 (binintersectTELcontra) =>
% 121.84/16.12 ((
% 121.84/16.12 (binintersectTERcontra) =>
% 121.84/16.12 ((
% 121.84/16.12 (contrasubsetT) =>
% 121.84/16.12 ((
% 121.84/16.12 (contrasubsetT1) =>
% 121.84/16.12 ((
% 121.84/16.12 (contrasubsetT2) =>
% 121.84/16.12 ((
% 121.84/16.12 (contrasubsetT3) =>
% 121.84/16.12 ((
% 121.84/16.12 (doubleComplementI1) =>
% 121.84/16.12 ((
% 121.84/16.12 (doubleComplementE1) =>
% 121.84/16.12 ((
% 121.84/16.12 (doubleComplementSub1) =>
% 121.84/16.12 ((
% 121.84/16.12 (doubleComplementSub2) =>
% 121.84/16.12 ((
% 121.84/16.12 (doubleComplementEq) =>
% 121.84/16.12 ((
% 121.84/16.12 (complementTnotintersectT) =>
% 121.84/16.12 ((
% 121.84/16.12 (complementImpComplementIntersect) =>
% 121.84/16.12 ((
% 121.84/16.12 (complementSubsetComplementIntersect) =>
% 121.84/16.12 ((
% 121.84/16.12 (complementInPowersetComplementIntersect) =>
% 121.84/16.12 ((
% 121.84/16.12 (contraSubsetComplement) =>
% 121.84/16.12 ((
% 121.84/16.12 (complementTcontraSubset) =>
% 121.84/16.12 ((
% 121.84/16.12 (binunionTILcontra) =>
% 121.84/16.12 ((
% 121.84/16.12 (binunionTIRcontra) =>
% 121.84/16.12 ((
% 121.84/16.12 (inIntersectImpInUnion) =>
% 121.84/16.12 ((
% 121.84/16.12 (inIntersectImpInUnion2) =>
% 121.84/16.12 ((
% 121.84/16.12 (inIntersectImpInIntersectUnions) =>
% 121.84/16.12 ((
% 121.84/16.12 (intersectInPowersetIntersectUnions) =>
% 121.84/16.12 ((
% 121.84/16.12 (inComplementUnionImpNotIn1) =>
% 121.84/16.12 ((
% 121.84/16.12 (inComplementUnionImpInComplement1) =>
% 121.84/16.12 ((
% 121.84/16.12 (binunionTE) =>
% 121.84/16.12 ((
% 121.84/16.12 (binunionTEcontra) =>
% 121.84/16.12 ((
% 121.84/16.12 (demorgan2a1) =>
% 121.84/16.12 ((
% 121.84/16.12 (complementUnionInPowersetComplement) =>
% 121.84/16.12 ((
% 121.84/16.13 (demorgan2a2) =>
% 121.84/16.13 ((
% 121.84/16.13 (demorgan1a) =>
% 121.84/16.13 ((
% 121.84/16.13 (demorgan1b) =>
% 121.84/16.13 ((
% 121.84/16.13 (demorgan1) =>
% 121.84/16.13 ((
% 121.84/16.13 (demorgan2a) =>
% 121.84/16.13 ((
% 121.84/16.13 (demorgan2b2) =>
% 121.84/16.13 ((
% 121.84/16.13 (demorgan2b) =>
% 121.84/16.13 ((
% 121.84/16.13 (demorgan2) =>
% 121.84/16.13 ((
% 121.84/16.13 (woz13rule0) =>
% 121.84/16.13 ((
% 121.84/16.13 (woz13rule1) =>
% 121.84/16.13 ((
% 121.84/16.13 (woz13rule2) =>
% 121.84/16.13 ((
% 121.84/16.13 (woz13rule3) =>
% 121.84/16.13 ((
% 121.84/16.13 (woz13rule4) =>
% 121.84/16.13 ((
% 121.84/16.13 (woz1_1) =>
% 121.84/16.13 ((
% 121.84/16.13 (woz1_2) =>
% 121.84/16.13 ((
% 121.84/16.13 (woz1_3) =>
% 121.84/16.13 ((
% 121.84/16.13 (woz1_4) =>
% 121.84/16.13 ((
% 121.84/16.13 (woz1_5) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1all2) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1SetBreln1) =>
% 121.84/16.13 ((
% 121.84/16.13 (choice2fnsingleton) =>
% 121.84/16.13 ((
% 121.84/16.13 (setOfPairsIsBReln1) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1all1) =>
% 121.84/16.13 ((
% 121.84/16.13 (subbreln1) =>
% 121.84/16.13 ((
% 121.84/16.13 (eqbreln1) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1invprop) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1invI) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1invE) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1compprop) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1compI) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1compE) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1compEex) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1unionprop) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1unionIL) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1unionIR) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1unionI) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1unionE) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1unionEcases) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1unionCommutes) =>
% 121.84/16.13 ((
% 121.84/16.13 (woz2Ex) =>
% 121.84/16.13 ((
% 121.84/16.13 (woz2W) =>
% 121.84/16.13 ((
% 121.84/16.13 (woz2A) =>
% 121.84/16.13 ((
% 121.84/16.13 (woz2B) =>
% 121.84/16.13 ((
% 121.84/16.13 (image1Ex) =>
% 121.84/16.13 ((
% 121.84/16.13 (image1Ex1) =>
% 121.84/16.13 ((
% 121.84/16.13 (image1Equiv) =>
% 121.84/16.13 ((
% 121.84/16.13 (image1E) =>
% 121.84/16.13 ((
% 121.84/16.13 (image1I) =>
% 121.84/16.13 ((
% 121.84/16.13 (injFuncInInjFuncSet) =>
% 121.84/16.13 ((
% 121.84/16.13 (!!) @ (
% 121.84/16.13 (('#B') @ (
% 121.84/16.13 !!) @
% 121.84/16.13 (
% 121.84/16.13 (
% 121.84/16.13 ('#B') @ (
% 121.84/16.13 (
% 121.84/16.13 ('#B') @ (
% 121.84/16.13 !!))) @
% 121.84/16.13 (
% 121.84/16.13 (
% 121.84/16.13 ('#S') @ (
% 121.84/16.13 (
% 121.84/16.13 ('#B') @ (
% 121.84/16.13 '#S') @
% 121.84/16.13 (
% 121.84/16.13 (
% 121.84/16.13 ('#B') @ (
% 121.84/16.13 (
% 121.84/16.13 ('#B') @ (
% 121.84/16.13 '#S'))) @
% 121.84/16.13 (
% 121.84/16.13 (
% 121.84/16.13 ('#B') @ (
% 121.84/16.13 (
% 121.84/16.13 ('#B') @ (
% 121.84/16.13 (
% 121.84/16.13 ('#B') @ (
% 121.84/16.13 =>))))) @
% 121.84/16.13 (
% 121.84/16.13 (
% 121.84/16.13 ('#B') @ (
% 121.84/16.13 (
% 121.84/16.13 ('#B') @ (
% 121.84/16.13 (
% 121.84/16.13 ('#C') @ in)))) @
% 121.84/16.13 injFuncSet)))))))) @
% 121.84/16.13 (
% 121.84/16.13 (
% 121.84/16.13 ('#B') @ (
% 121.84/16.13 (
% 121.84/16.13 ('#B') @ (
% 121.84/16.13 (
% 121.84/16.13 ('#C') @ in)))) @
% 121.84/16.13 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 121.84/16.13 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1015])).
% 121.84/16.13 thf(zip_derived_cl1039, plain,
% 121.84/16.13 (~ (((powersetI1) =>
% 121.84/16.13 (((powersetE1) =>
% 121.84/16.13 (((inPowerset) =>
% 121.84/16.13 (((powersetsubset) =>
% 121.84/16.13 (((sepInPowerset) =>
% 121.84/16.13 (((sepSubset) =>
% 121.84/16.13 (((binunionIL) =>
% 121.84/16.13 (((upairset2IR) =>
% 121.84/16.13 (((binunionIR) =>
% 121.84/16.13 (((binunionEcases) =>
% 121.84/16.13 (((binunionE) =>
% 121.84/16.13 (((binunionLsub) =>
% 121.84/16.13 (((binunionRsub) =>
% 121.84/16.13 (((binintersectI) =>
% 121.84/16.13 (((binintersectSubset5) =>
% 121.84/16.13 (((binintersectEL) =>
% 121.84/16.13 (((binintersectLsub) =>
% 121.84/16.13 (((binintersectSubset2) =>
% 121.84/16.13 (((binintersectSubset3) =>
% 121.84/16.13 (((binintersectER) =>
% 121.84/16.13 (((disjointsetsI1) =>
% 121.84/16.13 (((binintersectRsub) =>
% 121.84/16.13 (((binintersectSubset4) =>
% 121.84/16.13 (((binintersectSubset1) =>
% 121.84/16.13 (((bs114d) =>
% 121.84/16.13 (((setminusI) =>
% 121.84/16.13 (((setminusEL) =>
% 121.84/16.13 (((setminusER) =>
% 121.84/16.13 (((setminusSubset2) =>
% 121.84/16.13 (((setminusERneg) =>
% 121.84/16.13 ((
% 121.84/16.13 (setminusELneg) =>
% 121.84/16.13 ((
% 121.84/16.13 (setminusILneg) =>
% 121.84/16.13 ((
% 121.84/16.13 (setminusIRneg) =>
% 121.84/16.13 ((
% 121.84/16.13 (setminusLsub) =>
% 121.84/16.13 ((
% 121.84/16.13 (setminusSubset1) =>
% 121.84/16.13 ((
% 121.84/16.13 (symdiffE) =>
% 121.84/16.13 ((
% 121.84/16.13 (symdiffI1) =>
% 121.84/16.13 ((
% 121.84/16.13 (symdiffI2) =>
% 121.84/16.13 ((
% 121.84/16.13 (symdiffIneg1) =>
% 121.84/16.13 ((
% 121.84/16.13 (symdiffIneg2) =>
% 121.84/16.13 ((
% 121.84/16.13 (secondinupair) =>
% 121.84/16.13 ((
% 121.84/16.13 (setukpairIL) =>
% 121.84/16.13 ((
% 121.84/16.13 (setukpairIR) =>
% 121.84/16.13 ((
% 121.84/16.13 (kpairiskpair) =>
% 121.84/16.13 ((
% 121.84/16.13 (kpairp) =>
% 121.84/16.13 ((
% 121.84/16.13 (singletonsubset) =>
% 121.84/16.13 ((
% 121.84/16.13 (singletoninpowerset) =>
% 121.84/16.13 ((
% 121.84/16.13 (singletoninpowunion) =>
% 121.84/16.13 ((
% 121.84/16.13 (upairset2E) =>
% 121.84/16.13 ((
% 121.84/16.13 (upairsubunion) =>
% 121.84/16.13 ((
% 121.84/16.13 (upairinpowunion) =>
% 121.84/16.13 ((
% 121.84/16.13 (ubforcartprodlem1) =>
% 121.84/16.13 ((
% 121.84/16.13 (ubforcartprodlem2) =>
% 121.84/16.13 ((
% 121.84/16.13 (ubforcartprodlem3) =>
% 121.84/16.13 ((
% 121.84/16.13 (cartprodpairin) =>
% 121.84/16.13 ((
% 121.84/16.13 (cartprodmempair1) =>
% 121.84/16.13 ((
% 121.84/16.13 (cartprodmempair) =>
% 121.84/16.13 ((
% 121.84/16.13 (setunionE2) =>
% 121.84/16.13 ((
% 121.84/16.13 (setunionsingleton1) =>
% 121.84/16.13 ((
% 121.84/16.13 (setunionsingleton2) =>
% 121.84/16.13 ((
% 121.84/16.13 (setunionsingleton) =>
% 121.84/16.13 ((
% 121.84/16.13 (singletonprop) =>
% 121.84/16.13 ((
% 121.84/16.13 (ex1E1) =>
% 121.84/16.13 ((
% 121.84/16.13 (ex1I) =>
% 121.84/16.13 ((
% 121.84/16.13 (ex1I2) =>
% 121.84/16.13 ((
% 121.84/16.13 (singletonsuniq) =>
% 121.84/16.13 ((
% 121.84/16.13 (setukpairinjL1) =>
% 121.84/16.13 ((
% 121.84/16.13 (kfstsingleton) =>
% 121.84/16.13 ((
% 121.84/16.13 (theprop) =>
% 121.84/16.13 ((
% 121.84/16.13 (kfstpairEq) =>
% 121.84/16.13 ((
% 121.84/16.13 (cartprodfstin) =>
% 121.84/16.13 ((
% 121.84/16.13 (setukpairinjL2) =>
% 121.84/16.13 ((
% 121.84/16.13 (setukpairinjL) =>
% 121.84/16.13 ((
% 121.84/16.13 (setukpairinjR11) =>
% 121.84/16.13 ((
% 121.84/16.13 (setukpairinjR12) =>
% 121.84/16.13 ((
% 121.84/16.13 (setukpairinjR1) =>
% 121.84/16.13 ((
% 121.84/16.13 (upairequniteq) =>
% 121.84/16.13 ((
% 121.84/16.13 (setukpairinjR2) =>
% 121.84/16.13 ((
% 121.84/16.13 (setukpairinjR) =>
% 121.84/16.13 ((
% 121.84/16.13 (ksndsingleton) =>
% 121.84/16.13 ((
% 121.84/16.13 (ksndpairEq) =>
% 121.84/16.13 ((
% 121.84/16.13 (kpairsurjEq) =>
% 121.84/16.13 ((
% 121.84/16.13 (cartprodsndin) =>
% 121.84/16.13 ((
% 121.84/16.13 (cartprodpairmemEL) =>
% 121.84/16.13 ((
% 121.84/16.13 (cartprodpairmemER) =>
% 121.84/16.13 ((
% 121.84/16.13 (cartprodmempaircEq) =>
% 121.84/16.13 ((
% 121.84/16.13 (cartprodfstpairEq) =>
% 121.84/16.13 ((
% 121.84/16.13 (cartprodsndpairEq) =>
% 121.84/16.13 ((
% 121.84/16.13 (cartprodpairsurjEq) =>
% 121.84/16.13 ((
% 121.84/16.13 (dpsetconstrI) =>
% 121.84/16.13 ((
% 121.84/16.13 (dpsetconstrSub) =>
% 121.84/16.13 ((
% 121.84/16.13 (setOfPairsIsBReln) =>
% 121.84/16.13 ((
% 121.84/16.13 (dpsetconstrERa) =>
% 121.84/16.13 ((
% 121.84/16.13 (dpsetconstrEL1) =>
% 121.84/16.13 ((
% 121.84/16.13 (dpsetconstrEL2) =>
% 121.84/16.13 ((
% 121.84/16.13 (dpsetconstrER) =>
% 121.84/16.13 ((
% 121.84/16.13 (funcImageSingleton) =>
% 121.84/16.13 ((
% 121.84/16.13 (apProp) =>
% 121.84/16.13 ((
% 121.84/16.13 (app) =>
% 121.84/16.13 ((
% 121.84/16.13 (infuncsetfunc) =>
% 121.84/16.13 ((
% 121.84/16.13 (ap2p) =>
% 121.84/16.13 ((
% 121.84/16.13 (funcinfuncset) =>
% 121.84/16.13 ((
% 121.84/16.13 (lamProp) =>
% 121.84/16.13 ((
% 121.84/16.13 (lamp) =>
% 121.84/16.13 ((
% 121.84/16.13 (lam2p) =>
% 121.84/16.13 ((
% 121.84/16.13 (brelnall1) =>
% 121.84/16.13 ((
% 121.84/16.13 (brelnall2) =>
% 121.84/16.13 ((
% 121.84/16.13 (ex1E2) =>
% 121.84/16.13 ((
% 121.84/16.13 (funcGraphProp1) =>
% 121.84/16.13 ((
% 121.84/16.13 (funcGraphProp3) =>
% 121.84/16.13 ((
% 121.84/16.13 (funcGraphProp2) =>
% 121.84/16.13 ((
% 121.84/16.13 (funcextLem) =>
% 121.84/16.13 ((
% 121.84/16.13 (funcGraphProp4) =>
% 121.84/16.13 ((
% 121.84/16.13 (subbreln) =>
% 121.84/16.13 ((
% 121.84/16.13 (eqbreln) =>
% 121.84/16.13 ((
% 121.84/16.13 (funcext) =>
% 121.84/16.13 ((
% 121.84/16.13 (funcext2) =>
% 121.84/16.13 ((
% 121.84/16.13 (ap2apEq1) =>
% 121.84/16.13 ((
% 121.84/16.13 (ap2apEq2) =>
% 121.84/16.13 ((
% 121.84/16.13 (beta1) =>
% 121.84/16.13 ((
% 121.84/16.13 (eta1) =>
% 121.84/16.13 ((
% 121.84/16.13 (lam2lamEq) =>
% 121.84/16.13 ((
% 121.84/16.13 (beta2) =>
% 121.84/16.13 ((
% 121.84/16.13 (eta2) =>
% 121.84/16.13 ((
% 121.84/16.13 (iffalseProp1) =>
% 121.84/16.13 ((
% 121.84/16.13 (iffalseProp2) =>
% 121.84/16.13 ((
% 121.84/16.13 (iftrueProp1) =>
% 121.84/16.13 ((
% 121.84/16.13 (iftrueProp2) =>
% 121.84/16.13 ((
% 121.84/16.13 (ifSingleton) =>
% 121.84/16.13 ((
% 121.84/16.13 (ifp) =>
% 121.84/16.13 ((
% 121.84/16.13 (theeq) =>
% 121.84/16.13 ((
% 121.84/16.13 (iftrue) =>
% 121.84/16.13 ((
% 121.84/16.13 (iffalse) =>
% 121.84/16.13 ((
% 121.84/16.13 (iftrueorfalse) =>
% 121.84/16.13 ((
% 121.84/16.13 (binintersectT_lem) =>
% 121.84/16.13 ((
% 121.84/16.13 (binunionT_lem) =>
% 121.84/16.13 ((
% 121.84/16.13 (powersetT_lem) =>
% 121.84/16.13 ((
% 121.84/16.13 (setminusT_lem) =>
% 121.84/16.13 ((
% 121.84/16.13 (complementT_lem) =>
% 121.84/16.13 ((
% 121.84/16.13 (setextT) =>
% 121.84/16.13 ((
% 121.84/16.13 (subsetTI) =>
% 121.84/16.13 ((
% 121.84/16.13 (powersetTI1) =>
% 121.84/16.13 ((
% 121.84/16.13 (powersetTE1) =>
% 121.84/16.13 ((
% 121.84/16.13 (complementTI1) =>
% 121.84/16.13 ((
% 121.84/16.13 (complementTE1) =>
% 121.84/16.13 ((
% 121.84/16.13 (binintersectTELcontra) =>
% 121.84/16.13 ((
% 121.84/16.13 (binintersectTERcontra) =>
% 121.84/16.13 ((
% 121.84/16.13 (contrasubsetT) =>
% 121.84/16.13 ((
% 121.84/16.13 (contrasubsetT1) =>
% 121.84/16.13 ((
% 121.84/16.13 (contrasubsetT2) =>
% 121.84/16.13 ((
% 121.84/16.13 (contrasubsetT3) =>
% 121.84/16.13 ((
% 121.84/16.13 (doubleComplementI1) =>
% 121.84/16.13 ((
% 121.84/16.13 (doubleComplementE1) =>
% 121.84/16.13 ((
% 121.84/16.13 (doubleComplementSub1) =>
% 121.84/16.13 ((
% 121.84/16.13 (doubleComplementSub2) =>
% 121.84/16.13 ((
% 121.84/16.13 (doubleComplementEq) =>
% 121.84/16.13 ((
% 121.84/16.13 (complementTnotintersectT) =>
% 121.84/16.13 ((
% 121.84/16.13 (complementImpComplementIntersect) =>
% 121.84/16.13 ((
% 121.84/16.13 (complementSubsetComplementIntersect) =>
% 121.84/16.13 ((
% 121.84/16.13 (complementInPowersetComplementIntersect) =>
% 121.84/16.13 ((
% 121.84/16.13 (contraSubsetComplement) =>
% 121.84/16.13 ((
% 121.84/16.13 (complementTcontraSubset) =>
% 121.84/16.13 ((
% 121.84/16.13 (binunionTILcontra) =>
% 121.84/16.13 ((
% 121.84/16.13 (binunionTIRcontra) =>
% 121.84/16.13 ((
% 121.84/16.13 (inIntersectImpInUnion) =>
% 121.84/16.13 ((
% 121.84/16.13 (inIntersectImpInUnion2) =>
% 121.84/16.13 ((
% 121.84/16.13 (inIntersectImpInIntersectUnions) =>
% 121.84/16.13 ((
% 121.84/16.13 (intersectInPowersetIntersectUnions) =>
% 121.84/16.13 ((
% 121.84/16.13 (inComplementUnionImpNotIn1) =>
% 121.84/16.13 ((
% 121.84/16.13 (inComplementUnionImpInComplement1) =>
% 121.84/16.13 ((
% 121.84/16.13 (binunionTE) =>
% 121.84/16.13 ((
% 121.84/16.13 (binunionTEcontra) =>
% 121.84/16.13 ((
% 121.84/16.13 (demorgan2a1) =>
% 121.84/16.13 ((
% 121.84/16.13 (complementUnionInPowersetComplement) =>
% 121.84/16.13 ((
% 121.84/16.13 (demorgan2a2) =>
% 121.84/16.13 ((
% 121.84/16.13 (demorgan1a) =>
% 121.84/16.13 ((
% 121.84/16.13 (demorgan1b) =>
% 121.84/16.13 ((
% 121.84/16.13 (demorgan1) =>
% 121.84/16.13 ((
% 121.84/16.13 (demorgan2a) =>
% 121.84/16.13 ((
% 121.84/16.13 (demorgan2b2) =>
% 121.84/16.13 ((
% 121.84/16.13 (demorgan2b) =>
% 121.84/16.13 ((
% 121.84/16.13 (demorgan2) =>
% 121.84/16.13 ((
% 121.84/16.13 (woz13rule0) =>
% 121.84/16.13 ((
% 121.84/16.13 (woz13rule1) =>
% 121.84/16.13 ((
% 121.84/16.13 (woz13rule2) =>
% 121.84/16.13 ((
% 121.84/16.13 (woz13rule3) =>
% 121.84/16.13 ((
% 121.84/16.13 (woz13rule4) =>
% 121.84/16.13 ((
% 121.84/16.13 (woz1_1) =>
% 121.84/16.13 ((
% 121.84/16.13 (woz1_2) =>
% 121.84/16.13 ((
% 121.84/16.13 (woz1_3) =>
% 121.84/16.13 ((
% 121.84/16.13 (woz1_4) =>
% 121.84/16.13 ((
% 121.84/16.13 (woz1_5) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1all2) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1SetBreln1) =>
% 121.84/16.13 ((
% 121.84/16.13 (choice2fnsingleton) =>
% 121.84/16.13 ((
% 121.84/16.13 (setOfPairsIsBReln1) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1all1) =>
% 121.84/16.13 ((
% 121.84/16.13 (subbreln1) =>
% 121.84/16.13 ((
% 121.84/16.13 (eqbreln1) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1invprop) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1invI) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1invE) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1compprop) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1compI) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1compE) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1compEex) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1unionprop) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1unionIL) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1unionIR) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1unionI) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1unionE) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1unionEcases) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1unionCommutes) =>
% 121.84/16.13 ((
% 121.84/16.13 (woz2Ex) =>
% 121.84/16.13 ((
% 121.84/16.13 (woz2W) =>
% 121.84/16.13 ((
% 121.84/16.13 (woz2A) =>
% 121.84/16.13 ((
% 121.84/16.13 (woz2B) =>
% 121.84/16.13 ((
% 121.84/16.13 (image1Ex) =>
% 121.84/16.13 ((
% 121.84/16.13 (image1Ex1) =>
% 121.84/16.13 ((
% 121.84/16.13 (image1Equiv) =>
% 121.84/16.13 ((
% 121.84/16.13 (image1E) =>
% 121.84/16.13 ((
% 121.84/16.13 (image1I) =>
% 121.84/16.13 ((
% 121.84/16.13 (injFuncInInjFuncSet) =>
% 121.84/16.13 ((
% 121.84/16.13 (!!) @ (
% 121.84/16.13 (('#B') @ (
% 121.84/16.13 !!) @
% 121.84/16.13 (
% 121.84/16.13 (
% 121.84/16.13 ('#B') @ (
% 121.84/16.13 (
% 121.84/16.13 ('#B') @ (
% 121.84/16.13 !!))) @
% 121.84/16.13 (
% 121.84/16.13 (
% 121.84/16.13 ('#S') @ (
% 121.84/16.13 (
% 121.84/16.13 ('#B') @ (
% 121.84/16.13 '#S') @
% 121.84/16.13 (
% 121.84/16.13 (
% 121.84/16.13 ('#B') @ (
% 121.84/16.13 (
% 121.84/16.13 ('#B') @ (
% 121.84/16.13 '#S'))) @
% 121.84/16.13 (
% 121.84/16.13 (
% 121.84/16.13 ('#B') @ (
% 121.84/16.13 (
% 121.84/16.13 ('#B') @ (
% 121.84/16.13 (
% 121.84/16.13 ('#B') @ (
% 121.84/16.13 =>))))) @
% 121.84/16.13 (
% 121.84/16.13 (
% 121.84/16.13 ('#B') @ (
% 121.84/16.13 (
% 121.84/16.13 ('#B') @ (
% 121.84/16.13 (
% 121.84/16.13 ('#C') @ in)))) @
% 121.84/16.13 injFuncSet)))))))) @
% 121.84/16.13 (
% 121.84/16.13 (
% 121.84/16.13 ('#B') @ (
% 121.84/16.13 (
% 121.84/16.13 ('#B') @ (
% 121.84/16.13 (
% 121.84/16.13 ('#C') @ in)))) @
% 121.84/16.13 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 121.84/16.13 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1027])).
% 121.84/16.13 thf(zip_derived_cl1055, plain,
% 121.84/16.13 (~ (((powersetE1) =>
% 121.84/16.13 (((inPowerset) =>
% 121.84/16.13 (((powersetsubset) =>
% 121.84/16.13 (((sepInPowerset) =>
% 121.84/16.13 (((sepSubset) =>
% 121.84/16.13 (((binunionIL) =>
% 121.84/16.13 (((upairset2IR) =>
% 121.84/16.13 (((binunionIR) =>
% 121.84/16.13 (((binunionEcases) =>
% 121.84/16.13 (((binunionE) =>
% 121.84/16.13 (((binunionLsub) =>
% 121.84/16.13 (((binunionRsub) =>
% 121.84/16.13 (((binintersectI) =>
% 121.84/16.13 (((binintersectSubset5) =>
% 121.84/16.13 (((binintersectEL) =>
% 121.84/16.13 (((binintersectLsub) =>
% 121.84/16.13 (((binintersectSubset2) =>
% 121.84/16.13 (((binintersectSubset3) =>
% 121.84/16.13 (((binintersectER) =>
% 121.84/16.13 (((disjointsetsI1) =>
% 121.84/16.13 (((binintersectRsub) =>
% 121.84/16.13 (((binintersectSubset4) =>
% 121.84/16.13 (((binintersectSubset1) =>
% 121.84/16.13 (((bs114d) =>
% 121.84/16.13 (((setminusI) =>
% 121.84/16.13 (((setminusEL) =>
% 121.84/16.13 (((setminusER) =>
% 121.84/16.13 (((setminusSubset2) =>
% 121.84/16.13 (((setminusERneg) =>
% 121.84/16.13 (((setminusELneg) =>
% 121.84/16.13 ((
% 121.84/16.13 (setminusILneg) =>
% 121.84/16.13 ((
% 121.84/16.13 (setminusIRneg) =>
% 121.84/16.13 ((
% 121.84/16.13 (setminusLsub) =>
% 121.84/16.13 ((
% 121.84/16.13 (setminusSubset1) =>
% 121.84/16.13 ((
% 121.84/16.13 (symdiffE) =>
% 121.84/16.13 ((
% 121.84/16.13 (symdiffI1) =>
% 121.84/16.13 ((
% 121.84/16.13 (symdiffI2) =>
% 121.84/16.13 ((
% 121.84/16.13 (symdiffIneg1) =>
% 121.84/16.13 ((
% 121.84/16.13 (symdiffIneg2) =>
% 121.84/16.13 ((
% 121.84/16.13 (secondinupair) =>
% 121.84/16.13 ((
% 121.84/16.13 (setukpairIL) =>
% 121.84/16.13 ((
% 121.84/16.13 (setukpairIR) =>
% 121.84/16.13 ((
% 121.84/16.13 (kpairiskpair) =>
% 121.84/16.13 ((
% 121.84/16.13 (kpairp) =>
% 121.84/16.13 ((
% 121.84/16.13 (singletonsubset) =>
% 121.84/16.13 ((
% 121.84/16.13 (singletoninpowerset) =>
% 121.84/16.13 ((
% 121.84/16.13 (singletoninpowunion) =>
% 121.84/16.13 ((
% 121.84/16.13 (upairset2E) =>
% 121.84/16.13 ((
% 121.84/16.13 (upairsubunion) =>
% 121.84/16.13 ((
% 121.84/16.13 (upairinpowunion) =>
% 121.84/16.13 ((
% 121.84/16.13 (ubforcartprodlem1) =>
% 121.84/16.13 ((
% 121.84/16.13 (ubforcartprodlem2) =>
% 121.84/16.13 ((
% 121.84/16.13 (ubforcartprodlem3) =>
% 121.84/16.13 ((
% 121.84/16.13 (cartprodpairin) =>
% 121.84/16.13 ((
% 121.84/16.13 (cartprodmempair1) =>
% 121.84/16.13 ((
% 121.84/16.13 (cartprodmempair) =>
% 121.84/16.13 ((
% 121.84/16.13 (setunionE2) =>
% 121.84/16.13 ((
% 121.84/16.13 (setunionsingleton1) =>
% 121.84/16.13 ((
% 121.84/16.13 (setunionsingleton2) =>
% 121.84/16.13 ((
% 121.84/16.13 (setunionsingleton) =>
% 121.84/16.13 ((
% 121.84/16.13 (singletonprop) =>
% 121.84/16.13 ((
% 121.84/16.13 (ex1E1) =>
% 121.84/16.13 ((
% 121.84/16.13 (ex1I) =>
% 121.84/16.13 ((
% 121.84/16.13 (ex1I2) =>
% 121.84/16.13 ((
% 121.84/16.13 (singletonsuniq) =>
% 121.84/16.13 ((
% 121.84/16.13 (setukpairinjL1) =>
% 121.84/16.13 ((
% 121.84/16.13 (kfstsingleton) =>
% 121.84/16.13 ((
% 121.84/16.13 (theprop) =>
% 121.84/16.13 ((
% 121.84/16.13 (kfstpairEq) =>
% 121.84/16.13 ((
% 121.84/16.13 (cartprodfstin) =>
% 121.84/16.13 ((
% 121.84/16.13 (setukpairinjL2) =>
% 121.84/16.13 ((
% 121.84/16.13 (setukpairinjL) =>
% 121.84/16.13 ((
% 121.84/16.13 (setukpairinjR11) =>
% 121.84/16.13 ((
% 121.84/16.13 (setukpairinjR12) =>
% 121.84/16.13 ((
% 121.84/16.13 (setukpairinjR1) =>
% 121.84/16.13 ((
% 121.84/16.13 (upairequniteq) =>
% 121.84/16.13 ((
% 121.84/16.13 (setukpairinjR2) =>
% 121.84/16.13 ((
% 121.84/16.13 (setukpairinjR) =>
% 121.84/16.13 ((
% 121.84/16.13 (ksndsingleton) =>
% 121.84/16.13 ((
% 121.84/16.13 (ksndpairEq) =>
% 121.84/16.13 ((
% 121.84/16.13 (kpairsurjEq) =>
% 121.84/16.13 ((
% 121.84/16.13 (cartprodsndin) =>
% 121.84/16.13 ((
% 121.84/16.13 (cartprodpairmemEL) =>
% 121.84/16.13 ((
% 121.84/16.13 (cartprodpairmemER) =>
% 121.84/16.13 ((
% 121.84/16.13 (cartprodmempaircEq) =>
% 121.84/16.13 ((
% 121.84/16.13 (cartprodfstpairEq) =>
% 121.84/16.13 ((
% 121.84/16.13 (cartprodsndpairEq) =>
% 121.84/16.13 ((
% 121.84/16.13 (cartprodpairsurjEq) =>
% 121.84/16.13 ((
% 121.84/16.13 (dpsetconstrI) =>
% 121.84/16.13 ((
% 121.84/16.13 (dpsetconstrSub) =>
% 121.84/16.13 ((
% 121.84/16.13 (setOfPairsIsBReln) =>
% 121.84/16.13 ((
% 121.84/16.13 (dpsetconstrERa) =>
% 121.84/16.13 ((
% 121.84/16.13 (dpsetconstrEL1) =>
% 121.84/16.13 ((
% 121.84/16.13 (dpsetconstrEL2) =>
% 121.84/16.13 ((
% 121.84/16.13 (dpsetconstrER) =>
% 121.84/16.13 ((
% 121.84/16.13 (funcImageSingleton) =>
% 121.84/16.13 ((
% 121.84/16.13 (apProp) =>
% 121.84/16.13 ((
% 121.84/16.13 (app) =>
% 121.84/16.13 ((
% 121.84/16.13 (infuncsetfunc) =>
% 121.84/16.13 ((
% 121.84/16.13 (ap2p) =>
% 121.84/16.13 ((
% 121.84/16.13 (funcinfuncset) =>
% 121.84/16.13 ((
% 121.84/16.13 (lamProp) =>
% 121.84/16.13 ((
% 121.84/16.13 (lamp) =>
% 121.84/16.13 ((
% 121.84/16.13 (lam2p) =>
% 121.84/16.13 ((
% 121.84/16.13 (brelnall1) =>
% 121.84/16.13 ((
% 121.84/16.13 (brelnall2) =>
% 121.84/16.13 ((
% 121.84/16.13 (ex1E2) =>
% 121.84/16.13 ((
% 121.84/16.13 (funcGraphProp1) =>
% 121.84/16.13 ((
% 121.84/16.13 (funcGraphProp3) =>
% 121.84/16.13 ((
% 121.84/16.13 (funcGraphProp2) =>
% 121.84/16.13 ((
% 121.84/16.13 (funcextLem) =>
% 121.84/16.13 ((
% 121.84/16.13 (funcGraphProp4) =>
% 121.84/16.13 ((
% 121.84/16.13 (subbreln) =>
% 121.84/16.13 ((
% 121.84/16.13 (eqbreln) =>
% 121.84/16.13 ((
% 121.84/16.13 (funcext) =>
% 121.84/16.13 ((
% 121.84/16.13 (funcext2) =>
% 121.84/16.13 ((
% 121.84/16.13 (ap2apEq1) =>
% 121.84/16.13 ((
% 121.84/16.13 (ap2apEq2) =>
% 121.84/16.13 ((
% 121.84/16.13 (beta1) =>
% 121.84/16.13 ((
% 121.84/16.13 (eta1) =>
% 121.84/16.13 ((
% 121.84/16.13 (lam2lamEq) =>
% 121.84/16.13 ((
% 121.84/16.13 (beta2) =>
% 121.84/16.13 ((
% 121.84/16.13 (eta2) =>
% 121.84/16.13 ((
% 121.84/16.13 (iffalseProp1) =>
% 121.84/16.13 ((
% 121.84/16.13 (iffalseProp2) =>
% 121.84/16.13 ((
% 121.84/16.13 (iftrueProp1) =>
% 121.84/16.13 ((
% 121.84/16.13 (iftrueProp2) =>
% 121.84/16.13 ((
% 121.84/16.13 (ifSingleton) =>
% 121.84/16.13 ((
% 121.84/16.13 (ifp) =>
% 121.84/16.13 ((
% 121.84/16.13 (theeq) =>
% 121.84/16.13 ((
% 121.84/16.13 (iftrue) =>
% 121.84/16.13 ((
% 121.84/16.13 (iffalse) =>
% 121.84/16.13 ((
% 121.84/16.13 (iftrueorfalse) =>
% 121.84/16.13 ((
% 121.84/16.13 (binintersectT_lem) =>
% 121.84/16.13 ((
% 121.84/16.13 (binunionT_lem) =>
% 121.84/16.13 ((
% 121.84/16.13 (powersetT_lem) =>
% 121.84/16.13 ((
% 121.84/16.13 (setminusT_lem) =>
% 121.84/16.13 ((
% 121.84/16.13 (complementT_lem) =>
% 121.84/16.13 ((
% 121.84/16.13 (setextT) =>
% 121.84/16.13 ((
% 121.84/16.13 (subsetTI) =>
% 121.84/16.13 ((
% 121.84/16.13 (powersetTI1) =>
% 121.84/16.13 ((
% 121.84/16.13 (powersetTE1) =>
% 121.84/16.13 ((
% 121.84/16.13 (complementTI1) =>
% 121.84/16.13 ((
% 121.84/16.13 (complementTE1) =>
% 121.84/16.13 ((
% 121.84/16.13 (binintersectTELcontra) =>
% 121.84/16.13 ((
% 121.84/16.13 (binintersectTERcontra) =>
% 121.84/16.13 ((
% 121.84/16.13 (contrasubsetT) =>
% 121.84/16.13 ((
% 121.84/16.13 (contrasubsetT1) =>
% 121.84/16.13 ((
% 121.84/16.13 (contrasubsetT2) =>
% 121.84/16.13 ((
% 121.84/16.13 (contrasubsetT3) =>
% 121.84/16.13 ((
% 121.84/16.13 (doubleComplementI1) =>
% 121.84/16.13 ((
% 121.84/16.13 (doubleComplementE1) =>
% 121.84/16.13 ((
% 121.84/16.13 (doubleComplementSub1) =>
% 121.84/16.13 ((
% 121.84/16.13 (doubleComplementSub2) =>
% 121.84/16.13 ((
% 121.84/16.13 (doubleComplementEq) =>
% 121.84/16.13 ((
% 121.84/16.13 (complementTnotintersectT) =>
% 121.84/16.13 ((
% 121.84/16.13 (complementImpComplementIntersect) =>
% 121.84/16.13 ((
% 121.84/16.13 (complementSubsetComplementIntersect) =>
% 121.84/16.13 ((
% 121.84/16.13 (complementInPowersetComplementIntersect) =>
% 121.84/16.13 ((
% 121.84/16.13 (contraSubsetComplement) =>
% 121.84/16.13 ((
% 121.84/16.13 (complementTcontraSubset) =>
% 121.84/16.13 ((
% 121.84/16.13 (binunionTILcontra) =>
% 121.84/16.13 ((
% 121.84/16.13 (binunionTIRcontra) =>
% 121.84/16.13 ((
% 121.84/16.13 (inIntersectImpInUnion) =>
% 121.84/16.13 ((
% 121.84/16.13 (inIntersectImpInUnion2) =>
% 121.84/16.13 ((
% 121.84/16.13 (inIntersectImpInIntersectUnions) =>
% 121.84/16.13 ((
% 121.84/16.13 (intersectInPowersetIntersectUnions) =>
% 121.84/16.13 ((
% 121.84/16.13 (inComplementUnionImpNotIn1) =>
% 121.84/16.13 ((
% 121.84/16.13 (inComplementUnionImpInComplement1) =>
% 121.84/16.13 ((
% 121.84/16.13 (binunionTE) =>
% 121.84/16.13 ((
% 121.84/16.13 (binunionTEcontra) =>
% 121.84/16.13 ((
% 121.84/16.13 (demorgan2a1) =>
% 121.84/16.13 ((
% 121.84/16.13 (complementUnionInPowersetComplement) =>
% 121.84/16.13 ((
% 121.84/16.13 (demorgan2a2) =>
% 121.84/16.13 ((
% 121.84/16.13 (demorgan1a) =>
% 121.84/16.13 ((
% 121.84/16.13 (demorgan1b) =>
% 121.84/16.13 ((
% 121.84/16.13 (demorgan1) =>
% 121.84/16.13 ((
% 121.84/16.13 (demorgan2a) =>
% 121.84/16.13 ((
% 121.84/16.13 (demorgan2b2) =>
% 121.84/16.13 ((
% 121.84/16.13 (demorgan2b) =>
% 121.84/16.13 ((
% 121.84/16.13 (demorgan2) =>
% 121.84/16.13 ((
% 121.84/16.13 (woz13rule0) =>
% 121.84/16.13 ((
% 121.84/16.13 (woz13rule1) =>
% 121.84/16.13 ((
% 121.84/16.13 (woz13rule2) =>
% 121.84/16.13 ((
% 121.84/16.13 (woz13rule3) =>
% 121.84/16.13 ((
% 121.84/16.13 (woz13rule4) =>
% 121.84/16.13 ((
% 121.84/16.13 (woz1_1) =>
% 121.84/16.13 ((
% 121.84/16.13 (woz1_2) =>
% 121.84/16.13 ((
% 121.84/16.13 (woz1_3) =>
% 121.84/16.13 ((
% 121.84/16.13 (woz1_4) =>
% 121.84/16.13 ((
% 121.84/16.13 (woz1_5) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1all2) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1SetBreln1) =>
% 121.84/16.13 ((
% 121.84/16.13 (choice2fnsingleton) =>
% 121.84/16.13 ((
% 121.84/16.13 (setOfPairsIsBReln1) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1all1) =>
% 121.84/16.13 ((
% 121.84/16.13 (subbreln1) =>
% 121.84/16.13 ((
% 121.84/16.13 (eqbreln1) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1invprop) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1invI) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1invE) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1compprop) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1compI) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1compE) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1compEex) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1unionprop) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1unionIL) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1unionIR) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1unionI) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1unionE) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1unionEcases) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1unionCommutes) =>
% 121.84/16.13 ((
% 121.84/16.13 (woz2Ex) =>
% 121.84/16.13 ((
% 121.84/16.13 (woz2W) =>
% 121.84/16.13 ((
% 121.84/16.13 (woz2A) =>
% 121.84/16.13 ((
% 121.84/16.13 (woz2B) =>
% 121.84/16.13 ((
% 121.84/16.13 (image1Ex) =>
% 121.84/16.13 ((
% 121.84/16.13 (image1Ex1) =>
% 121.84/16.13 ((
% 121.84/16.13 (image1Equiv) =>
% 121.84/16.13 ((
% 121.84/16.13 (image1E) =>
% 121.84/16.13 ((
% 121.84/16.13 (image1I) =>
% 121.84/16.13 ((
% 121.84/16.13 (injFuncInInjFuncSet) =>
% 121.84/16.13 ((
% 121.84/16.13 (!!) @ (
% 121.84/16.13 (('#B') @ (
% 121.84/16.13 !!) @
% 121.84/16.13 (
% 121.84/16.13 (
% 121.84/16.13 ('#B') @ (
% 121.84/16.13 (
% 121.84/16.13 ('#B') @ (
% 121.84/16.13 !!))) @
% 121.84/16.13 (
% 121.84/16.13 (
% 121.84/16.13 ('#S') @ (
% 121.84/16.13 (
% 121.84/16.13 ('#B') @ (
% 121.84/16.13 '#S') @
% 121.84/16.13 (
% 121.84/16.13 (
% 121.84/16.13 ('#B') @ (
% 121.84/16.13 (
% 121.84/16.13 ('#B') @ (
% 121.84/16.13 '#S'))) @
% 121.84/16.13 (
% 121.84/16.13 (
% 121.84/16.13 ('#B') @ (
% 121.84/16.13 (
% 121.84/16.13 ('#B') @ (
% 121.84/16.13 (
% 121.84/16.13 ('#B') @ (
% 121.84/16.13 =>))))) @
% 121.84/16.13 (
% 121.84/16.13 (
% 121.84/16.13 ('#B') @ (
% 121.84/16.13 (
% 121.84/16.13 ('#B') @ (
% 121.84/16.13 (
% 121.84/16.13 ('#C') @ in)))) @
% 121.84/16.13 injFuncSet)))))))) @
% 121.84/16.13 (
% 121.84/16.13 (
% 121.84/16.13 ('#B') @ (
% 121.84/16.13 (
% 121.84/16.13 ('#B') @ (
% 121.84/16.13 (
% 121.84/16.13 ('#C') @ in)))) @
% 121.84/16.13 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 121.84/16.13 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1039])).
% 121.84/16.13 thf(zip_derived_cl1067, plain,
% 121.84/16.13 (~ (((inPowerset) =>
% 121.84/16.13 (((powersetsubset) =>
% 121.84/16.13 (((sepInPowerset) =>
% 121.84/16.13 (((sepSubset) =>
% 121.84/16.13 (((binunionIL) =>
% 121.84/16.13 (((upairset2IR) =>
% 121.84/16.13 (((binunionIR) =>
% 121.84/16.13 (((binunionEcases) =>
% 121.84/16.13 (((binunionE) =>
% 121.84/16.13 (((binunionLsub) =>
% 121.84/16.13 (((binunionRsub) =>
% 121.84/16.13 (((binintersectI) =>
% 121.84/16.13 (((binintersectSubset5) =>
% 121.84/16.13 (((binintersectEL) =>
% 121.84/16.13 (((binintersectLsub) =>
% 121.84/16.13 (((binintersectSubset2) =>
% 121.84/16.13 (((binintersectSubset3) =>
% 121.84/16.13 (((binintersectER) =>
% 121.84/16.13 (((disjointsetsI1) =>
% 121.84/16.13 (((binintersectRsub) =>
% 121.84/16.13 (((binintersectSubset4) =>
% 121.84/16.13 (((binintersectSubset1) =>
% 121.84/16.13 (((bs114d) =>
% 121.84/16.13 (((setminusI) =>
% 121.84/16.13 (((setminusEL) =>
% 121.84/16.13 (((setminusER) =>
% 121.84/16.13 (((setminusSubset2) =>
% 121.84/16.13 (((setminusERneg) =>
% 121.84/16.13 (((setminusELneg) =>
% 121.84/16.13 (((setminusILneg) =>
% 121.84/16.13 ((
% 121.84/16.13 (setminusIRneg) =>
% 121.84/16.13 ((
% 121.84/16.13 (setminusLsub) =>
% 121.84/16.13 ((
% 121.84/16.13 (setminusSubset1) =>
% 121.84/16.13 ((
% 121.84/16.13 (symdiffE) =>
% 121.84/16.13 ((
% 121.84/16.13 (symdiffI1) =>
% 121.84/16.13 ((
% 121.84/16.13 (symdiffI2) =>
% 121.84/16.13 ((
% 121.84/16.13 (symdiffIneg1) =>
% 121.84/16.13 ((
% 121.84/16.13 (symdiffIneg2) =>
% 121.84/16.13 ((
% 121.84/16.13 (secondinupair) =>
% 121.84/16.13 ((
% 121.84/16.13 (setukpairIL) =>
% 121.84/16.13 ((
% 121.84/16.13 (setukpairIR) =>
% 121.84/16.13 ((
% 121.84/16.13 (kpairiskpair) =>
% 121.84/16.13 ((
% 121.84/16.13 (kpairp) =>
% 121.84/16.13 ((
% 121.84/16.13 (singletonsubset) =>
% 121.84/16.13 ((
% 121.84/16.13 (singletoninpowerset) =>
% 121.84/16.13 ((
% 121.84/16.13 (singletoninpowunion) =>
% 121.84/16.13 ((
% 121.84/16.13 (upairset2E) =>
% 121.84/16.13 ((
% 121.84/16.13 (upairsubunion) =>
% 121.84/16.13 ((
% 121.84/16.13 (upairinpowunion) =>
% 121.84/16.13 ((
% 121.84/16.13 (ubforcartprodlem1) =>
% 121.84/16.13 ((
% 121.84/16.13 (ubforcartprodlem2) =>
% 121.84/16.13 ((
% 121.84/16.13 (ubforcartprodlem3) =>
% 121.84/16.13 ((
% 121.84/16.13 (cartprodpairin) =>
% 121.84/16.13 ((
% 121.84/16.13 (cartprodmempair1) =>
% 121.84/16.13 ((
% 121.84/16.13 (cartprodmempair) =>
% 121.84/16.13 ((
% 121.84/16.13 (setunionE2) =>
% 121.84/16.13 ((
% 121.84/16.13 (setunionsingleton1) =>
% 121.84/16.13 ((
% 121.84/16.13 (setunionsingleton2) =>
% 121.84/16.13 ((
% 121.84/16.13 (setunionsingleton) =>
% 121.84/16.13 ((
% 121.84/16.13 (singletonprop) =>
% 121.84/16.13 ((
% 121.84/16.13 (ex1E1) =>
% 121.84/16.13 ((
% 121.84/16.13 (ex1I) =>
% 121.84/16.13 ((
% 121.84/16.13 (ex1I2) =>
% 121.84/16.13 ((
% 121.84/16.13 (singletonsuniq) =>
% 121.84/16.13 ((
% 121.84/16.13 (setukpairinjL1) =>
% 121.84/16.13 ((
% 121.84/16.13 (kfstsingleton) =>
% 121.84/16.13 ((
% 121.84/16.13 (theprop) =>
% 121.84/16.13 ((
% 121.84/16.13 (kfstpairEq) =>
% 121.84/16.13 ((
% 121.84/16.13 (cartprodfstin) =>
% 121.84/16.13 ((
% 121.84/16.13 (setukpairinjL2) =>
% 121.84/16.13 ((
% 121.84/16.13 (setukpairinjL) =>
% 121.84/16.13 ((
% 121.84/16.13 (setukpairinjR11) =>
% 121.84/16.13 ((
% 121.84/16.13 (setukpairinjR12) =>
% 121.84/16.13 ((
% 121.84/16.13 (setukpairinjR1) =>
% 121.84/16.13 ((
% 121.84/16.13 (upairequniteq) =>
% 121.84/16.13 ((
% 121.84/16.13 (setukpairinjR2) =>
% 121.84/16.13 ((
% 121.84/16.13 (setukpairinjR) =>
% 121.84/16.13 ((
% 121.84/16.13 (ksndsingleton) =>
% 121.84/16.13 ((
% 121.84/16.13 (ksndpairEq) =>
% 121.84/16.13 ((
% 121.84/16.13 (kpairsurjEq) =>
% 121.84/16.13 ((
% 121.84/16.13 (cartprodsndin) =>
% 121.84/16.13 ((
% 121.84/16.13 (cartprodpairmemEL) =>
% 121.84/16.13 ((
% 121.84/16.13 (cartprodpairmemER) =>
% 121.84/16.13 ((
% 121.84/16.13 (cartprodmempaircEq) =>
% 121.84/16.13 ((
% 121.84/16.13 (cartprodfstpairEq) =>
% 121.84/16.13 ((
% 121.84/16.13 (cartprodsndpairEq) =>
% 121.84/16.13 ((
% 121.84/16.13 (cartprodpairsurjEq) =>
% 121.84/16.13 ((
% 121.84/16.13 (dpsetconstrI) =>
% 121.84/16.13 ((
% 121.84/16.13 (dpsetconstrSub) =>
% 121.84/16.13 ((
% 121.84/16.13 (setOfPairsIsBReln) =>
% 121.84/16.13 ((
% 121.84/16.13 (dpsetconstrERa) =>
% 121.84/16.13 ((
% 121.84/16.13 (dpsetconstrEL1) =>
% 121.84/16.13 ((
% 121.84/16.13 (dpsetconstrEL2) =>
% 121.84/16.13 ((
% 121.84/16.13 (dpsetconstrER) =>
% 121.84/16.13 ((
% 121.84/16.13 (funcImageSingleton) =>
% 121.84/16.13 ((
% 121.84/16.13 (apProp) =>
% 121.84/16.13 ((
% 121.84/16.13 (app) =>
% 121.84/16.13 ((
% 121.84/16.13 (infuncsetfunc) =>
% 121.84/16.13 ((
% 121.84/16.13 (ap2p) =>
% 121.84/16.13 ((
% 121.84/16.13 (funcinfuncset) =>
% 121.84/16.13 ((
% 121.84/16.13 (lamProp) =>
% 121.84/16.13 ((
% 121.84/16.13 (lamp) =>
% 121.84/16.13 ((
% 121.84/16.13 (lam2p) =>
% 121.84/16.13 ((
% 121.84/16.13 (brelnall1) =>
% 121.84/16.13 ((
% 121.84/16.13 (brelnall2) =>
% 121.84/16.13 ((
% 121.84/16.13 (ex1E2) =>
% 121.84/16.13 ((
% 121.84/16.13 (funcGraphProp1) =>
% 121.84/16.13 ((
% 121.84/16.13 (funcGraphProp3) =>
% 121.84/16.13 ((
% 121.84/16.13 (funcGraphProp2) =>
% 121.84/16.13 ((
% 121.84/16.13 (funcextLem) =>
% 121.84/16.13 ((
% 121.84/16.13 (funcGraphProp4) =>
% 121.84/16.13 ((
% 121.84/16.13 (subbreln) =>
% 121.84/16.13 ((
% 121.84/16.13 (eqbreln) =>
% 121.84/16.13 ((
% 121.84/16.13 (funcext) =>
% 121.84/16.13 ((
% 121.84/16.13 (funcext2) =>
% 121.84/16.13 ((
% 121.84/16.13 (ap2apEq1) =>
% 121.84/16.13 ((
% 121.84/16.13 (ap2apEq2) =>
% 121.84/16.13 ((
% 121.84/16.13 (beta1) =>
% 121.84/16.13 ((
% 121.84/16.13 (eta1) =>
% 121.84/16.13 ((
% 121.84/16.13 (lam2lamEq) =>
% 121.84/16.13 ((
% 121.84/16.13 (beta2) =>
% 121.84/16.13 ((
% 121.84/16.13 (eta2) =>
% 121.84/16.13 ((
% 121.84/16.13 (iffalseProp1) =>
% 121.84/16.13 ((
% 121.84/16.13 (iffalseProp2) =>
% 121.84/16.13 ((
% 121.84/16.13 (iftrueProp1) =>
% 121.84/16.13 ((
% 121.84/16.13 (iftrueProp2) =>
% 121.84/16.13 ((
% 121.84/16.13 (ifSingleton) =>
% 121.84/16.13 ((
% 121.84/16.13 (ifp) =>
% 121.84/16.13 ((
% 121.84/16.13 (theeq) =>
% 121.84/16.13 ((
% 121.84/16.13 (iftrue) =>
% 121.84/16.13 ((
% 121.84/16.13 (iffalse) =>
% 121.84/16.13 ((
% 121.84/16.13 (iftrueorfalse) =>
% 121.84/16.13 ((
% 121.84/16.13 (binintersectT_lem) =>
% 121.84/16.13 ((
% 121.84/16.13 (binunionT_lem) =>
% 121.84/16.13 ((
% 121.84/16.13 (powersetT_lem) =>
% 121.84/16.13 ((
% 121.84/16.13 (setminusT_lem) =>
% 121.84/16.13 ((
% 121.84/16.13 (complementT_lem) =>
% 121.84/16.13 ((
% 121.84/16.13 (setextT) =>
% 121.84/16.13 ((
% 121.84/16.13 (subsetTI) =>
% 121.84/16.13 ((
% 121.84/16.13 (powersetTI1) =>
% 121.84/16.13 ((
% 121.84/16.13 (powersetTE1) =>
% 121.84/16.13 ((
% 121.84/16.13 (complementTI1) =>
% 121.84/16.13 ((
% 121.84/16.13 (complementTE1) =>
% 121.84/16.13 ((
% 121.84/16.13 (binintersectTELcontra) =>
% 121.84/16.13 ((
% 121.84/16.13 (binintersectTERcontra) =>
% 121.84/16.13 ((
% 121.84/16.13 (contrasubsetT) =>
% 121.84/16.13 ((
% 121.84/16.13 (contrasubsetT1) =>
% 121.84/16.13 ((
% 121.84/16.13 (contrasubsetT2) =>
% 121.84/16.13 ((
% 121.84/16.13 (contrasubsetT3) =>
% 121.84/16.13 ((
% 121.84/16.13 (doubleComplementI1) =>
% 121.84/16.13 ((
% 121.84/16.13 (doubleComplementE1) =>
% 121.84/16.13 ((
% 121.84/16.13 (doubleComplementSub1) =>
% 121.84/16.13 ((
% 121.84/16.13 (doubleComplementSub2) =>
% 121.84/16.13 ((
% 121.84/16.13 (doubleComplementEq) =>
% 121.84/16.13 ((
% 121.84/16.13 (complementTnotintersectT) =>
% 121.84/16.13 ((
% 121.84/16.13 (complementImpComplementIntersect) =>
% 121.84/16.13 ((
% 121.84/16.13 (complementSubsetComplementIntersect) =>
% 121.84/16.13 ((
% 121.84/16.13 (complementInPowersetComplementIntersect) =>
% 121.84/16.13 ((
% 121.84/16.13 (contraSubsetComplement) =>
% 121.84/16.13 ((
% 121.84/16.13 (complementTcontraSubset) =>
% 121.84/16.13 ((
% 121.84/16.13 (binunionTILcontra) =>
% 121.84/16.13 ((
% 121.84/16.13 (binunionTIRcontra) =>
% 121.84/16.13 ((
% 121.84/16.13 (inIntersectImpInUnion) =>
% 121.84/16.13 ((
% 121.84/16.13 (inIntersectImpInUnion2) =>
% 121.84/16.13 ((
% 121.84/16.13 (inIntersectImpInIntersectUnions) =>
% 121.84/16.13 ((
% 121.84/16.13 (intersectInPowersetIntersectUnions) =>
% 121.84/16.13 ((
% 121.84/16.13 (inComplementUnionImpNotIn1) =>
% 121.84/16.13 ((
% 121.84/16.13 (inComplementUnionImpInComplement1) =>
% 121.84/16.13 ((
% 121.84/16.13 (binunionTE) =>
% 121.84/16.13 ((
% 121.84/16.13 (binunionTEcontra) =>
% 121.84/16.13 ((
% 121.84/16.13 (demorgan2a1) =>
% 121.84/16.13 ((
% 121.84/16.13 (complementUnionInPowersetComplement) =>
% 121.84/16.13 ((
% 121.84/16.13 (demorgan2a2) =>
% 121.84/16.13 ((
% 121.84/16.13 (demorgan1a) =>
% 121.84/16.13 ((
% 121.84/16.13 (demorgan1b) =>
% 121.84/16.13 ((
% 121.84/16.13 (demorgan1) =>
% 121.84/16.13 ((
% 121.84/16.13 (demorgan2a) =>
% 121.84/16.13 ((
% 121.84/16.13 (demorgan2b2) =>
% 121.84/16.13 ((
% 121.84/16.13 (demorgan2b) =>
% 121.84/16.13 ((
% 121.84/16.13 (demorgan2) =>
% 121.84/16.13 ((
% 121.84/16.13 (woz13rule0) =>
% 121.84/16.13 ((
% 121.84/16.13 (woz13rule1) =>
% 121.84/16.13 ((
% 121.84/16.13 (woz13rule2) =>
% 121.84/16.13 ((
% 121.84/16.13 (woz13rule3) =>
% 121.84/16.13 ((
% 121.84/16.13 (woz13rule4) =>
% 121.84/16.13 ((
% 121.84/16.13 (woz1_1) =>
% 121.84/16.13 ((
% 121.84/16.13 (woz1_2) =>
% 121.84/16.13 ((
% 121.84/16.13 (woz1_3) =>
% 121.84/16.13 ((
% 121.84/16.13 (woz1_4) =>
% 121.84/16.13 ((
% 121.84/16.13 (woz1_5) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1all2) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1SetBreln1) =>
% 121.84/16.13 ((
% 121.84/16.13 (choice2fnsingleton) =>
% 121.84/16.13 ((
% 121.84/16.13 (setOfPairsIsBReln1) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1all1) =>
% 121.84/16.13 ((
% 121.84/16.13 (subbreln1) =>
% 121.84/16.13 ((
% 121.84/16.13 (eqbreln1) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1invprop) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1invI) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1invE) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1compprop) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1compI) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1compE) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1compEex) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1unionprop) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1unionIL) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1unionIR) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1unionI) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1unionE) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1unionEcases) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1unionCommutes) =>
% 121.84/16.13 ((
% 121.84/16.13 (woz2Ex) =>
% 121.84/16.13 ((
% 121.84/16.13 (woz2W) =>
% 121.84/16.13 ((
% 121.84/16.13 (woz2A) =>
% 121.84/16.13 ((
% 121.84/16.13 (woz2B) =>
% 121.84/16.13 ((
% 121.84/16.13 (image1Ex) =>
% 121.84/16.13 ((
% 121.84/16.13 (image1Ex1) =>
% 121.84/16.13 ((
% 121.84/16.13 (image1Equiv) =>
% 121.84/16.13 ((
% 121.84/16.13 (image1E) =>
% 121.84/16.13 ((
% 121.84/16.13 (image1I) =>
% 121.84/16.13 ((
% 121.84/16.13 (injFuncInInjFuncSet) =>
% 121.84/16.13 ((
% 121.84/16.13 (!!) @ (
% 121.84/16.13 (('#B') @ (
% 121.84/16.13 !!) @
% 121.84/16.13 (
% 121.84/16.13 (
% 121.84/16.13 ('#B') @ (
% 121.84/16.13 (
% 121.84/16.13 ('#B') @ (
% 121.84/16.13 !!))) @
% 121.84/16.13 (
% 121.84/16.13 (
% 121.84/16.13 ('#S') @ (
% 121.84/16.13 (
% 121.84/16.13 ('#B') @ (
% 121.84/16.13 '#S') @
% 121.84/16.13 (
% 121.84/16.13 (
% 121.84/16.13 ('#B') @ (
% 121.84/16.13 (
% 121.84/16.13 ('#B') @ (
% 121.84/16.13 '#S'))) @
% 121.84/16.13 (
% 121.84/16.13 (
% 121.84/16.13 ('#B') @ (
% 121.84/16.13 (
% 121.84/16.13 ('#B') @ (
% 121.84/16.13 (
% 121.84/16.13 ('#B') @ (
% 121.84/16.13 =>))))) @
% 121.84/16.13 (
% 121.84/16.13 (
% 121.84/16.13 ('#B') @ (
% 121.84/16.13 (
% 121.84/16.13 ('#B') @ (
% 121.84/16.13 (
% 121.84/16.13 ('#C') @ in)))) @
% 121.84/16.13 injFuncSet)))))))) @
% 121.84/16.13 (
% 121.84/16.13 (
% 121.84/16.13 ('#B') @ (
% 121.84/16.13 (
% 121.84/16.13 ('#B') @ (
% 121.84/16.13 (
% 121.84/16.13 ('#C') @ in)))) @
% 121.84/16.13 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 121.84/16.13 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1055])).
% 121.84/16.13 thf(zip_derived_cl1074, plain,
% 121.84/16.13 (~ (((powersetsubset) =>
% 121.84/16.13 (((sepInPowerset) =>
% 121.84/16.13 (((sepSubset) =>
% 121.84/16.13 (((binunionIL) =>
% 121.84/16.13 (((upairset2IR) =>
% 121.84/16.13 (((binunionIR) =>
% 121.84/16.13 (((binunionEcases) =>
% 121.84/16.13 (((binunionE) =>
% 121.84/16.13 (((binunionLsub) =>
% 121.84/16.13 (((binunionRsub) =>
% 121.84/16.13 (((binintersectI) =>
% 121.84/16.13 (((binintersectSubset5) =>
% 121.84/16.13 (((binintersectEL) =>
% 121.84/16.13 (((binintersectLsub) =>
% 121.84/16.13 (((binintersectSubset2) =>
% 121.84/16.13 (((binintersectSubset3) =>
% 121.84/16.13 (((binintersectER) =>
% 121.84/16.13 (((disjointsetsI1) =>
% 121.84/16.13 (((binintersectRsub) =>
% 121.84/16.13 (((binintersectSubset4) =>
% 121.84/16.13 (((binintersectSubset1) =>
% 121.84/16.13 (((bs114d) =>
% 121.84/16.13 (((setminusI) =>
% 121.84/16.13 (((setminusEL) =>
% 121.84/16.13 (((setminusER) =>
% 121.84/16.13 (((setminusSubset2) =>
% 121.84/16.13 (((setminusERneg) =>
% 121.84/16.13 (((setminusELneg) =>
% 121.84/16.13 (((setminusILneg) =>
% 121.84/16.13 (((setminusIRneg) =>
% 121.84/16.13 ((
% 121.84/16.13 (setminusLsub) =>
% 121.84/16.13 ((
% 121.84/16.13 (setminusSubset1) =>
% 121.84/16.13 ((
% 121.84/16.13 (symdiffE) =>
% 121.84/16.13 ((
% 121.84/16.13 (symdiffI1) =>
% 121.84/16.13 ((
% 121.84/16.13 (symdiffI2) =>
% 121.84/16.13 ((
% 121.84/16.13 (symdiffIneg1) =>
% 121.84/16.13 ((
% 121.84/16.13 (symdiffIneg2) =>
% 121.84/16.13 ((
% 121.84/16.13 (secondinupair) =>
% 121.84/16.13 ((
% 121.84/16.13 (setukpairIL) =>
% 121.84/16.13 ((
% 121.84/16.13 (setukpairIR) =>
% 121.84/16.13 ((
% 121.84/16.13 (kpairiskpair) =>
% 121.84/16.13 ((
% 121.84/16.13 (kpairp) =>
% 121.84/16.13 ((
% 121.84/16.13 (singletonsubset) =>
% 121.84/16.13 ((
% 121.84/16.13 (singletoninpowerset) =>
% 121.84/16.13 ((
% 121.84/16.13 (singletoninpowunion) =>
% 121.84/16.13 ((
% 121.84/16.13 (upairset2E) =>
% 121.84/16.13 ((
% 121.84/16.13 (upairsubunion) =>
% 121.84/16.13 ((
% 121.84/16.13 (upairinpowunion) =>
% 121.84/16.13 ((
% 121.84/16.13 (ubforcartprodlem1) =>
% 121.84/16.13 ((
% 121.84/16.13 (ubforcartprodlem2) =>
% 121.84/16.13 ((
% 121.84/16.13 (ubforcartprodlem3) =>
% 121.84/16.13 ((
% 121.84/16.13 (cartprodpairin) =>
% 121.84/16.13 ((
% 121.84/16.13 (cartprodmempair1) =>
% 121.84/16.13 ((
% 121.84/16.13 (cartprodmempair) =>
% 121.84/16.13 ((
% 121.84/16.13 (setunionE2) =>
% 121.84/16.13 ((
% 121.84/16.13 (setunionsingleton1) =>
% 121.84/16.13 ((
% 121.84/16.13 (setunionsingleton2) =>
% 121.84/16.13 ((
% 121.84/16.13 (setunionsingleton) =>
% 121.84/16.13 ((
% 121.84/16.13 (singletonprop) =>
% 121.84/16.13 ((
% 121.84/16.13 (ex1E1) =>
% 121.84/16.13 ((
% 121.84/16.13 (ex1I) =>
% 121.84/16.13 ((
% 121.84/16.13 (ex1I2) =>
% 121.84/16.13 ((
% 121.84/16.13 (singletonsuniq) =>
% 121.84/16.13 ((
% 121.84/16.13 (setukpairinjL1) =>
% 121.84/16.13 ((
% 121.84/16.13 (kfstsingleton) =>
% 121.84/16.13 ((
% 121.84/16.13 (theprop) =>
% 121.84/16.13 ((
% 121.84/16.13 (kfstpairEq) =>
% 121.84/16.13 ((
% 121.84/16.13 (cartprodfstin) =>
% 121.84/16.13 ((
% 121.84/16.13 (setukpairinjL2) =>
% 121.84/16.13 ((
% 121.84/16.13 (setukpairinjL) =>
% 121.84/16.13 ((
% 121.84/16.13 (setukpairinjR11) =>
% 121.84/16.13 ((
% 121.84/16.13 (setukpairinjR12) =>
% 121.84/16.13 ((
% 121.84/16.13 (setukpairinjR1) =>
% 121.84/16.13 ((
% 121.84/16.13 (upairequniteq) =>
% 121.84/16.13 ((
% 121.84/16.13 (setukpairinjR2) =>
% 121.84/16.13 ((
% 121.84/16.13 (setukpairinjR) =>
% 121.84/16.13 ((
% 121.84/16.13 (ksndsingleton) =>
% 121.84/16.13 ((
% 121.84/16.13 (ksndpairEq) =>
% 121.84/16.13 ((
% 121.84/16.13 (kpairsurjEq) =>
% 121.84/16.13 ((
% 121.84/16.13 (cartprodsndin) =>
% 121.84/16.13 ((
% 121.84/16.13 (cartprodpairmemEL) =>
% 121.84/16.13 ((
% 121.84/16.13 (cartprodpairmemER) =>
% 121.84/16.13 ((
% 121.84/16.13 (cartprodmempaircEq) =>
% 121.84/16.13 ((
% 121.84/16.13 (cartprodfstpairEq) =>
% 121.84/16.13 ((
% 121.84/16.13 (cartprodsndpairEq) =>
% 121.84/16.13 ((
% 121.84/16.13 (cartprodpairsurjEq) =>
% 121.84/16.13 ((
% 121.84/16.13 (dpsetconstrI) =>
% 121.84/16.13 ((
% 121.84/16.13 (dpsetconstrSub) =>
% 121.84/16.13 ((
% 121.84/16.13 (setOfPairsIsBReln) =>
% 121.84/16.13 ((
% 121.84/16.13 (dpsetconstrERa) =>
% 121.84/16.13 ((
% 121.84/16.13 (dpsetconstrEL1) =>
% 121.84/16.13 ((
% 121.84/16.13 (dpsetconstrEL2) =>
% 121.84/16.13 ((
% 121.84/16.13 (dpsetconstrER) =>
% 121.84/16.13 ((
% 121.84/16.13 (funcImageSingleton) =>
% 121.84/16.13 ((
% 121.84/16.13 (apProp) =>
% 121.84/16.13 ((
% 121.84/16.13 (app) =>
% 121.84/16.13 ((
% 121.84/16.13 (infuncsetfunc) =>
% 121.84/16.13 ((
% 121.84/16.13 (ap2p) =>
% 121.84/16.13 ((
% 121.84/16.13 (funcinfuncset) =>
% 121.84/16.13 ((
% 121.84/16.13 (lamProp) =>
% 121.84/16.13 ((
% 121.84/16.13 (lamp) =>
% 121.84/16.13 ((
% 121.84/16.13 (lam2p) =>
% 121.84/16.13 ((
% 121.84/16.13 (brelnall1) =>
% 121.84/16.13 ((
% 121.84/16.13 (brelnall2) =>
% 121.84/16.13 ((
% 121.84/16.13 (ex1E2) =>
% 121.84/16.13 ((
% 121.84/16.13 (funcGraphProp1) =>
% 121.84/16.13 ((
% 121.84/16.13 (funcGraphProp3) =>
% 121.84/16.13 ((
% 121.84/16.13 (funcGraphProp2) =>
% 121.84/16.13 ((
% 121.84/16.13 (funcextLem) =>
% 121.84/16.13 ((
% 121.84/16.13 (funcGraphProp4) =>
% 121.84/16.13 ((
% 121.84/16.13 (subbreln) =>
% 121.84/16.13 ((
% 121.84/16.13 (eqbreln) =>
% 121.84/16.13 ((
% 121.84/16.13 (funcext) =>
% 121.84/16.13 ((
% 121.84/16.13 (funcext2) =>
% 121.84/16.13 ((
% 121.84/16.13 (ap2apEq1) =>
% 121.84/16.13 ((
% 121.84/16.13 (ap2apEq2) =>
% 121.84/16.13 ((
% 121.84/16.13 (beta1) =>
% 121.84/16.13 ((
% 121.84/16.13 (eta1) =>
% 121.84/16.13 ((
% 121.84/16.13 (lam2lamEq) =>
% 121.84/16.13 ((
% 121.84/16.13 (beta2) =>
% 121.84/16.13 ((
% 121.84/16.13 (eta2) =>
% 121.84/16.13 ((
% 121.84/16.13 (iffalseProp1) =>
% 121.84/16.13 ((
% 121.84/16.13 (iffalseProp2) =>
% 121.84/16.13 ((
% 121.84/16.13 (iftrueProp1) =>
% 121.84/16.13 ((
% 121.84/16.13 (iftrueProp2) =>
% 121.84/16.13 ((
% 121.84/16.13 (ifSingleton) =>
% 121.84/16.13 ((
% 121.84/16.13 (ifp) =>
% 121.84/16.13 ((
% 121.84/16.13 (theeq) =>
% 121.84/16.13 ((
% 121.84/16.13 (iftrue) =>
% 121.84/16.13 ((
% 121.84/16.13 (iffalse) =>
% 121.84/16.13 ((
% 121.84/16.13 (iftrueorfalse) =>
% 121.84/16.13 ((
% 121.84/16.13 (binintersectT_lem) =>
% 121.84/16.13 ((
% 121.84/16.13 (binunionT_lem) =>
% 121.84/16.13 ((
% 121.84/16.13 (powersetT_lem) =>
% 121.84/16.13 ((
% 121.84/16.13 (setminusT_lem) =>
% 121.84/16.13 ((
% 121.84/16.13 (complementT_lem) =>
% 121.84/16.13 ((
% 121.84/16.13 (setextT) =>
% 121.84/16.13 ((
% 121.84/16.13 (subsetTI) =>
% 121.84/16.13 ((
% 121.84/16.13 (powersetTI1) =>
% 121.84/16.13 ((
% 121.84/16.13 (powersetTE1) =>
% 121.84/16.13 ((
% 121.84/16.13 (complementTI1) =>
% 121.84/16.13 ((
% 121.84/16.13 (complementTE1) =>
% 121.84/16.13 ((
% 121.84/16.13 (binintersectTELcontra) =>
% 121.84/16.13 ((
% 121.84/16.13 (binintersectTERcontra) =>
% 121.84/16.13 ((
% 121.84/16.13 (contrasubsetT) =>
% 121.84/16.13 ((
% 121.84/16.13 (contrasubsetT1) =>
% 121.84/16.13 ((
% 121.84/16.13 (contrasubsetT2) =>
% 121.84/16.13 ((
% 121.84/16.13 (contrasubsetT3) =>
% 121.84/16.13 ((
% 121.84/16.13 (doubleComplementI1) =>
% 121.84/16.13 ((
% 121.84/16.13 (doubleComplementE1) =>
% 121.84/16.13 ((
% 121.84/16.13 (doubleComplementSub1) =>
% 121.84/16.13 ((
% 121.84/16.13 (doubleComplementSub2) =>
% 121.84/16.13 ((
% 121.84/16.13 (doubleComplementEq) =>
% 121.84/16.13 ((
% 121.84/16.13 (complementTnotintersectT) =>
% 121.84/16.13 ((
% 121.84/16.13 (complementImpComplementIntersect) =>
% 121.84/16.13 ((
% 121.84/16.13 (complementSubsetComplementIntersect) =>
% 121.84/16.13 ((
% 121.84/16.13 (complementInPowersetComplementIntersect) =>
% 121.84/16.13 ((
% 121.84/16.13 (contraSubsetComplement) =>
% 121.84/16.13 ((
% 121.84/16.13 (complementTcontraSubset) =>
% 121.84/16.13 ((
% 121.84/16.13 (binunionTILcontra) =>
% 121.84/16.13 ((
% 121.84/16.13 (binunionTIRcontra) =>
% 121.84/16.13 ((
% 121.84/16.13 (inIntersectImpInUnion) =>
% 121.84/16.13 ((
% 121.84/16.13 (inIntersectImpInUnion2) =>
% 121.84/16.13 ((
% 121.84/16.13 (inIntersectImpInIntersectUnions) =>
% 121.84/16.13 ((
% 121.84/16.13 (intersectInPowersetIntersectUnions) =>
% 121.84/16.13 ((
% 121.84/16.13 (inComplementUnionImpNotIn1) =>
% 121.84/16.13 ((
% 121.84/16.13 (inComplementUnionImpInComplement1) =>
% 121.84/16.13 ((
% 121.84/16.13 (binunionTE) =>
% 121.84/16.13 ((
% 121.84/16.13 (binunionTEcontra) =>
% 121.84/16.13 ((
% 121.84/16.13 (demorgan2a1) =>
% 121.84/16.13 ((
% 121.84/16.13 (complementUnionInPowersetComplement) =>
% 121.84/16.13 ((
% 121.84/16.13 (demorgan2a2) =>
% 121.84/16.13 ((
% 121.84/16.13 (demorgan1a) =>
% 121.84/16.13 ((
% 121.84/16.13 (demorgan1b) =>
% 121.84/16.13 ((
% 121.84/16.13 (demorgan1) =>
% 121.84/16.13 ((
% 121.84/16.13 (demorgan2a) =>
% 121.84/16.13 ((
% 121.84/16.13 (demorgan2b2) =>
% 121.84/16.13 ((
% 121.84/16.13 (demorgan2b) =>
% 121.84/16.13 ((
% 121.84/16.13 (demorgan2) =>
% 121.84/16.13 ((
% 121.84/16.13 (woz13rule0) =>
% 121.84/16.13 ((
% 121.84/16.13 (woz13rule1) =>
% 121.84/16.13 ((
% 121.84/16.13 (woz13rule2) =>
% 121.84/16.13 ((
% 121.84/16.13 (woz13rule3) =>
% 121.84/16.13 ((
% 121.84/16.13 (woz13rule4) =>
% 121.84/16.13 ((
% 121.84/16.13 (woz1_1) =>
% 121.84/16.13 ((
% 121.84/16.13 (woz1_2) =>
% 121.84/16.13 ((
% 121.84/16.13 (woz1_3) =>
% 121.84/16.13 ((
% 121.84/16.13 (woz1_4) =>
% 121.84/16.13 ((
% 121.84/16.13 (woz1_5) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1all2) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1SetBreln1) =>
% 121.84/16.13 ((
% 121.84/16.13 (choice2fnsingleton) =>
% 121.84/16.13 ((
% 121.84/16.13 (setOfPairsIsBReln1) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1all1) =>
% 121.84/16.13 ((
% 121.84/16.13 (subbreln1) =>
% 121.84/16.13 ((
% 121.84/16.13 (eqbreln1) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1invprop) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1invI) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1invE) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1compprop) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1compI) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1compE) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1compEex) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1unionprop) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1unionIL) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1unionIR) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1unionI) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1unionE) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1unionEcases) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1unionCommutes) =>
% 121.84/16.13 ((
% 121.84/16.13 (woz2Ex) =>
% 121.84/16.13 ((
% 121.84/16.13 (woz2W) =>
% 121.84/16.13 ((
% 121.84/16.13 (woz2A) =>
% 121.84/16.13 ((
% 121.84/16.13 (woz2B) =>
% 121.84/16.13 ((
% 121.84/16.13 (image1Ex) =>
% 121.84/16.13 ((
% 121.84/16.13 (image1Ex1) =>
% 121.84/16.13 ((
% 121.84/16.13 (image1Equiv) =>
% 121.84/16.13 ((
% 121.84/16.13 (image1E) =>
% 121.84/16.13 ((
% 121.84/16.13 (image1I) =>
% 121.84/16.13 ((
% 121.84/16.13 (injFuncInInjFuncSet) =>
% 121.84/16.13 ((
% 121.84/16.13 (!!) @ (
% 121.84/16.13 (('#B') @ (
% 121.84/16.13 !!) @
% 121.84/16.13 (
% 121.84/16.13 (
% 121.84/16.13 ('#B') @ (
% 121.84/16.13 (
% 121.84/16.13 ('#B') @ (
% 121.84/16.13 !!))) @
% 121.84/16.13 (
% 121.84/16.13 (
% 121.84/16.13 ('#S') @ (
% 121.84/16.13 (
% 121.84/16.13 ('#B') @ (
% 121.84/16.13 '#S') @
% 121.84/16.13 (
% 121.84/16.13 (
% 121.84/16.13 ('#B') @ (
% 121.84/16.13 (
% 121.84/16.13 ('#B') @ (
% 121.84/16.13 '#S'))) @
% 121.84/16.13 (
% 121.84/16.13 (
% 121.84/16.13 ('#B') @ (
% 121.84/16.13 (
% 121.84/16.13 ('#B') @ (
% 121.84/16.13 (
% 121.84/16.13 ('#B') @ (
% 121.84/16.13 =>))))) @
% 121.84/16.13 (
% 121.84/16.13 (
% 121.84/16.13 ('#B') @ (
% 121.84/16.13 (
% 121.84/16.13 ('#B') @ (
% 121.84/16.13 (
% 121.84/16.13 ('#C') @ in)))) @
% 121.84/16.13 injFuncSet)))))))) @
% 121.84/16.13 (
% 121.84/16.13 (
% 121.84/16.13 ('#B') @ (
% 121.84/16.13 (
% 121.84/16.13 ('#B') @ (
% 121.84/16.13 (
% 121.84/16.13 ('#C') @ in)))) @
% 121.84/16.13 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 121.84/16.13 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1067])).
% 121.84/16.13 thf(zip_derived_cl1082, plain,
% 121.84/16.13 (~ (((sepInPowerset) =>
% 121.84/16.13 (((sepSubset) =>
% 121.84/16.13 (((binunionIL) =>
% 121.84/16.13 (((upairset2IR) =>
% 121.84/16.13 (((binunionIR) =>
% 121.84/16.13 (((binunionEcases) =>
% 121.84/16.13 (((binunionE) =>
% 121.84/16.13 (((binunionLsub) =>
% 121.84/16.13 (((binunionRsub) =>
% 121.84/16.13 (((binintersectI) =>
% 121.84/16.13 (((binintersectSubset5) =>
% 121.84/16.13 (((binintersectEL) =>
% 121.84/16.13 (((binintersectLsub) =>
% 121.84/16.13 (((binintersectSubset2) =>
% 121.84/16.13 (((binintersectSubset3) =>
% 121.84/16.13 (((binintersectER) =>
% 121.84/16.13 (((disjointsetsI1) =>
% 121.84/16.13 (((binintersectRsub) =>
% 121.84/16.13 (((binintersectSubset4) =>
% 121.84/16.13 (((binintersectSubset1) =>
% 121.84/16.13 (((bs114d) =>
% 121.84/16.13 (((setminusI) =>
% 121.84/16.13 (((setminusEL) =>
% 121.84/16.13 (((setminusER) =>
% 121.84/16.13 (((setminusSubset2) =>
% 121.84/16.13 (((setminusERneg) =>
% 121.84/16.13 (((setminusELneg) =>
% 121.84/16.13 (((setminusILneg) =>
% 121.84/16.13 (((setminusIRneg) =>
% 121.84/16.13 (((setminusLsub) =>
% 121.84/16.13 ((
% 121.84/16.13 (setminusSubset1) =>
% 121.84/16.13 ((
% 121.84/16.13 (symdiffE) =>
% 121.84/16.13 ((
% 121.84/16.13 (symdiffI1) =>
% 121.84/16.13 ((
% 121.84/16.13 (symdiffI2) =>
% 121.84/16.13 ((
% 121.84/16.13 (symdiffIneg1) =>
% 121.84/16.13 ((
% 121.84/16.13 (symdiffIneg2) =>
% 121.84/16.13 ((
% 121.84/16.13 (secondinupair) =>
% 121.84/16.13 ((
% 121.84/16.13 (setukpairIL) =>
% 121.84/16.13 ((
% 121.84/16.13 (setukpairIR) =>
% 121.84/16.13 ((
% 121.84/16.13 (kpairiskpair) =>
% 121.84/16.13 ((
% 121.84/16.13 (kpairp) =>
% 121.84/16.13 ((
% 121.84/16.13 (singletonsubset) =>
% 121.84/16.13 ((
% 121.84/16.13 (singletoninpowerset) =>
% 121.84/16.13 ((
% 121.84/16.13 (singletoninpowunion) =>
% 121.84/16.13 ((
% 121.84/16.13 (upairset2E) =>
% 121.84/16.13 ((
% 121.84/16.13 (upairsubunion) =>
% 121.84/16.13 ((
% 121.84/16.13 (upairinpowunion) =>
% 121.84/16.13 ((
% 121.84/16.13 (ubforcartprodlem1) =>
% 121.84/16.13 ((
% 121.84/16.13 (ubforcartprodlem2) =>
% 121.84/16.13 ((
% 121.84/16.13 (ubforcartprodlem3) =>
% 121.84/16.13 ((
% 121.84/16.13 (cartprodpairin) =>
% 121.84/16.13 ((
% 121.84/16.13 (cartprodmempair1) =>
% 121.84/16.13 ((
% 121.84/16.13 (cartprodmempair) =>
% 121.84/16.13 ((
% 121.84/16.13 (setunionE2) =>
% 121.84/16.13 ((
% 121.84/16.13 (setunionsingleton1) =>
% 121.84/16.13 ((
% 121.84/16.13 (setunionsingleton2) =>
% 121.84/16.13 ((
% 121.84/16.13 (setunionsingleton) =>
% 121.84/16.13 ((
% 121.84/16.13 (singletonprop) =>
% 121.84/16.13 ((
% 121.84/16.13 (ex1E1) =>
% 121.84/16.13 ((
% 121.84/16.13 (ex1I) =>
% 121.84/16.13 ((
% 121.84/16.13 (ex1I2) =>
% 121.84/16.13 ((
% 121.84/16.13 (singletonsuniq) =>
% 121.84/16.13 ((
% 121.84/16.13 (setukpairinjL1) =>
% 121.84/16.13 ((
% 121.84/16.13 (kfstsingleton) =>
% 121.84/16.13 ((
% 121.84/16.13 (theprop) =>
% 121.84/16.13 ((
% 121.84/16.13 (kfstpairEq) =>
% 121.84/16.13 ((
% 121.84/16.13 (cartprodfstin) =>
% 121.84/16.13 ((
% 121.84/16.13 (setukpairinjL2) =>
% 121.84/16.13 ((
% 121.84/16.13 (setukpairinjL) =>
% 121.84/16.13 ((
% 121.84/16.13 (setukpairinjR11) =>
% 121.84/16.13 ((
% 121.84/16.13 (setukpairinjR12) =>
% 121.84/16.13 ((
% 121.84/16.13 (setukpairinjR1) =>
% 121.84/16.13 ((
% 121.84/16.13 (upairequniteq) =>
% 121.84/16.13 ((
% 121.84/16.13 (setukpairinjR2) =>
% 121.84/16.13 ((
% 121.84/16.13 (setukpairinjR) =>
% 121.84/16.13 ((
% 121.84/16.13 (ksndsingleton) =>
% 121.84/16.13 ((
% 121.84/16.13 (ksndpairEq) =>
% 121.84/16.13 ((
% 121.84/16.13 (kpairsurjEq) =>
% 121.84/16.13 ((
% 121.84/16.13 (cartprodsndin) =>
% 121.84/16.13 ((
% 121.84/16.13 (cartprodpairmemEL) =>
% 121.84/16.13 ((
% 121.84/16.13 (cartprodpairmemER) =>
% 121.84/16.13 ((
% 121.84/16.13 (cartprodmempaircEq) =>
% 121.84/16.13 ((
% 121.84/16.13 (cartprodfstpairEq) =>
% 121.84/16.13 ((
% 121.84/16.13 (cartprodsndpairEq) =>
% 121.84/16.13 ((
% 121.84/16.13 (cartprodpairsurjEq) =>
% 121.84/16.13 ((
% 121.84/16.13 (dpsetconstrI) =>
% 121.84/16.13 ((
% 121.84/16.13 (dpsetconstrSub) =>
% 121.84/16.13 ((
% 121.84/16.13 (setOfPairsIsBReln) =>
% 121.84/16.13 ((
% 121.84/16.13 (dpsetconstrERa) =>
% 121.84/16.13 ((
% 121.84/16.13 (dpsetconstrEL1) =>
% 121.84/16.13 ((
% 121.84/16.13 (dpsetconstrEL2) =>
% 121.84/16.13 ((
% 121.84/16.13 (dpsetconstrER) =>
% 121.84/16.13 ((
% 121.84/16.13 (funcImageSingleton) =>
% 121.84/16.13 ((
% 121.84/16.13 (apProp) =>
% 121.84/16.13 ((
% 121.84/16.13 (app) =>
% 121.84/16.13 ((
% 121.84/16.13 (infuncsetfunc) =>
% 121.84/16.13 ((
% 121.84/16.13 (ap2p) =>
% 121.84/16.13 ((
% 121.84/16.13 (funcinfuncset) =>
% 121.84/16.13 ((
% 121.84/16.13 (lamProp) =>
% 121.84/16.13 ((
% 121.84/16.13 (lamp) =>
% 121.84/16.13 ((
% 121.84/16.13 (lam2p) =>
% 121.84/16.13 ((
% 121.84/16.13 (brelnall1) =>
% 121.84/16.13 ((
% 121.84/16.13 (brelnall2) =>
% 121.84/16.13 ((
% 121.84/16.13 (ex1E2) =>
% 121.84/16.13 ((
% 121.84/16.13 (funcGraphProp1) =>
% 121.84/16.13 ((
% 121.84/16.13 (funcGraphProp3) =>
% 121.84/16.13 ((
% 121.84/16.13 (funcGraphProp2) =>
% 121.84/16.13 ((
% 121.84/16.13 (funcextLem) =>
% 121.84/16.13 ((
% 121.84/16.13 (funcGraphProp4) =>
% 121.84/16.13 ((
% 121.84/16.13 (subbreln) =>
% 121.84/16.13 ((
% 121.84/16.13 (eqbreln) =>
% 121.84/16.13 ((
% 121.84/16.13 (funcext) =>
% 121.84/16.13 ((
% 121.84/16.13 (funcext2) =>
% 121.84/16.13 ((
% 121.84/16.13 (ap2apEq1) =>
% 121.84/16.13 ((
% 121.84/16.13 (ap2apEq2) =>
% 121.84/16.13 ((
% 121.84/16.13 (beta1) =>
% 121.84/16.13 ((
% 121.84/16.13 (eta1) =>
% 121.84/16.13 ((
% 121.84/16.13 (lam2lamEq) =>
% 121.84/16.13 ((
% 121.84/16.13 (beta2) =>
% 121.84/16.13 ((
% 121.84/16.13 (eta2) =>
% 121.84/16.13 ((
% 121.84/16.13 (iffalseProp1) =>
% 121.84/16.13 ((
% 121.84/16.13 (iffalseProp2) =>
% 121.84/16.13 ((
% 121.84/16.13 (iftrueProp1) =>
% 121.84/16.13 ((
% 121.84/16.13 (iftrueProp2) =>
% 121.84/16.13 ((
% 121.84/16.13 (ifSingleton) =>
% 121.84/16.13 ((
% 121.84/16.13 (ifp) =>
% 121.84/16.13 ((
% 121.84/16.13 (theeq) =>
% 121.84/16.13 ((
% 121.84/16.13 (iftrue) =>
% 121.84/16.13 ((
% 121.84/16.13 (iffalse) =>
% 121.84/16.13 ((
% 121.84/16.13 (iftrueorfalse) =>
% 121.84/16.13 ((
% 121.84/16.13 (binintersectT_lem) =>
% 121.84/16.13 ((
% 121.84/16.13 (binunionT_lem) =>
% 121.84/16.13 ((
% 121.84/16.13 (powersetT_lem) =>
% 121.84/16.13 ((
% 121.84/16.13 (setminusT_lem) =>
% 121.84/16.13 ((
% 121.84/16.13 (complementT_lem) =>
% 121.84/16.13 ((
% 121.84/16.13 (setextT) =>
% 121.84/16.13 ((
% 121.84/16.13 (subsetTI) =>
% 121.84/16.13 ((
% 121.84/16.13 (powersetTI1) =>
% 121.84/16.13 ((
% 121.84/16.13 (powersetTE1) =>
% 121.84/16.13 ((
% 121.84/16.13 (complementTI1) =>
% 121.84/16.13 ((
% 121.84/16.13 (complementTE1) =>
% 121.84/16.13 ((
% 121.84/16.13 (binintersectTELcontra) =>
% 121.84/16.13 ((
% 121.84/16.13 (binintersectTERcontra) =>
% 121.84/16.13 ((
% 121.84/16.13 (contrasubsetT) =>
% 121.84/16.13 ((
% 121.84/16.13 (contrasubsetT1) =>
% 121.84/16.13 ((
% 121.84/16.13 (contrasubsetT2) =>
% 121.84/16.13 ((
% 121.84/16.13 (contrasubsetT3) =>
% 121.84/16.13 ((
% 121.84/16.13 (doubleComplementI1) =>
% 121.84/16.13 ((
% 121.84/16.13 (doubleComplementE1) =>
% 121.84/16.13 ((
% 121.84/16.13 (doubleComplementSub1) =>
% 121.84/16.13 ((
% 121.84/16.13 (doubleComplementSub2) =>
% 121.84/16.13 ((
% 121.84/16.13 (doubleComplementEq) =>
% 121.84/16.13 ((
% 121.84/16.13 (complementTnotintersectT) =>
% 121.84/16.13 ((
% 121.84/16.13 (complementImpComplementIntersect) =>
% 121.84/16.13 ((
% 121.84/16.13 (complementSubsetComplementIntersect) =>
% 121.84/16.13 ((
% 121.84/16.13 (complementInPowersetComplementIntersect) =>
% 121.84/16.13 ((
% 121.84/16.13 (contraSubsetComplement) =>
% 121.84/16.13 ((
% 121.84/16.13 (complementTcontraSubset) =>
% 121.84/16.13 ((
% 121.84/16.13 (binunionTILcontra) =>
% 121.84/16.13 ((
% 121.84/16.13 (binunionTIRcontra) =>
% 121.84/16.13 ((
% 121.84/16.13 (inIntersectImpInUnion) =>
% 121.84/16.13 ((
% 121.84/16.13 (inIntersectImpInUnion2) =>
% 121.84/16.13 ((
% 121.84/16.13 (inIntersectImpInIntersectUnions) =>
% 121.84/16.13 ((
% 121.84/16.13 (intersectInPowersetIntersectUnions) =>
% 121.84/16.13 ((
% 121.84/16.13 (inComplementUnionImpNotIn1) =>
% 121.84/16.13 ((
% 121.84/16.13 (inComplementUnionImpInComplement1) =>
% 121.84/16.13 ((
% 121.84/16.13 (binunionTE) =>
% 121.84/16.13 ((
% 121.84/16.13 (binunionTEcontra) =>
% 121.84/16.13 ((
% 121.84/16.13 (demorgan2a1) =>
% 121.84/16.13 ((
% 121.84/16.13 (complementUnionInPowersetComplement) =>
% 121.84/16.13 ((
% 121.84/16.13 (demorgan2a2) =>
% 121.84/16.13 ((
% 121.84/16.13 (demorgan1a) =>
% 121.84/16.13 ((
% 121.84/16.13 (demorgan1b) =>
% 121.84/16.13 ((
% 121.84/16.13 (demorgan1) =>
% 121.84/16.13 ((
% 121.84/16.13 (demorgan2a) =>
% 121.84/16.13 ((
% 121.84/16.13 (demorgan2b2) =>
% 121.84/16.13 ((
% 121.84/16.13 (demorgan2b) =>
% 121.84/16.13 ((
% 121.84/16.13 (demorgan2) =>
% 121.84/16.13 ((
% 121.84/16.13 (woz13rule0) =>
% 121.84/16.13 ((
% 121.84/16.13 (woz13rule1) =>
% 121.84/16.13 ((
% 121.84/16.13 (woz13rule2) =>
% 121.84/16.13 ((
% 121.84/16.13 (woz13rule3) =>
% 121.84/16.13 ((
% 121.84/16.13 (woz13rule4) =>
% 121.84/16.13 ((
% 121.84/16.13 (woz1_1) =>
% 121.84/16.13 ((
% 121.84/16.13 (woz1_2) =>
% 121.84/16.13 ((
% 121.84/16.13 (woz1_3) =>
% 121.84/16.13 ((
% 121.84/16.13 (woz1_4) =>
% 121.84/16.13 ((
% 121.84/16.13 (woz1_5) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1all2) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1SetBreln1) =>
% 121.84/16.13 ((
% 121.84/16.13 (choice2fnsingleton) =>
% 121.84/16.13 ((
% 121.84/16.13 (setOfPairsIsBReln1) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1all1) =>
% 121.84/16.13 ((
% 121.84/16.13 (subbreln1) =>
% 121.84/16.13 ((
% 121.84/16.13 (eqbreln1) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1invprop) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1invI) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1invE) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1compprop) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1compI) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1compE) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1compEex) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1unionprop) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1unionIL) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1unionIR) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1unionI) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1unionE) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1unionEcases) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1unionCommutes) =>
% 121.84/16.13 ((
% 121.84/16.13 (woz2Ex) =>
% 121.84/16.13 ((
% 121.84/16.13 (woz2W) =>
% 121.84/16.13 ((
% 121.84/16.13 (woz2A) =>
% 121.84/16.13 ((
% 121.84/16.13 (woz2B) =>
% 121.84/16.13 ((
% 121.84/16.13 (image1Ex) =>
% 121.84/16.13 ((
% 121.84/16.13 (image1Ex1) =>
% 121.84/16.13 ((
% 121.84/16.13 (image1Equiv) =>
% 121.84/16.13 ((
% 121.84/16.13 (image1E) =>
% 121.84/16.13 ((
% 121.84/16.13 (image1I) =>
% 121.84/16.13 ((
% 121.84/16.13 (injFuncInInjFuncSet) =>
% 121.84/16.13 ((
% 121.84/16.13 (!!) @ (
% 121.84/16.13 (('#B') @ (
% 121.84/16.13 !!) @
% 121.84/16.13 (
% 121.84/16.13 (
% 121.84/16.13 ('#B') @ (
% 121.84/16.13 (
% 121.84/16.13 ('#B') @ (
% 121.84/16.13 !!))) @
% 121.84/16.13 (
% 121.84/16.13 (
% 121.84/16.13 ('#S') @ (
% 121.84/16.13 (
% 121.84/16.13 ('#B') @ (
% 121.84/16.13 '#S') @
% 121.84/16.13 (
% 121.84/16.13 (
% 121.84/16.13 ('#B') @ (
% 121.84/16.13 (
% 121.84/16.13 ('#B') @ (
% 121.84/16.13 '#S'))) @
% 121.84/16.13 (
% 121.84/16.13 (
% 121.84/16.13 ('#B') @ (
% 121.84/16.13 (
% 121.84/16.13 ('#B') @ (
% 121.84/16.13 (
% 121.84/16.13 ('#B') @ (
% 121.84/16.13 =>))))) @
% 121.84/16.13 (
% 121.84/16.13 (
% 121.84/16.13 ('#B') @ (
% 121.84/16.13 (
% 121.84/16.13 ('#B') @ (
% 121.84/16.13 (
% 121.84/16.13 ('#C') @ in)))) @
% 121.84/16.13 injFuncSet)))))))) @
% 121.84/16.13 (
% 121.84/16.13 (
% 121.84/16.13 ('#B') @ (
% 121.84/16.13 (
% 121.84/16.13 ('#B') @ (
% 121.84/16.13 (
% 121.84/16.13 ('#C') @ in)))) @
% 121.84/16.13 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 121.84/16.13 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1074])).
% 121.84/16.13 thf(zip_derived_cl1090, plain,
% 121.84/16.13 (~ (((sepSubset) =>
% 121.84/16.13 (((binunionIL) =>
% 121.84/16.13 (((upairset2IR) =>
% 121.84/16.13 (((binunionIR) =>
% 121.84/16.13 (((binunionEcases) =>
% 121.84/16.13 (((binunionE) =>
% 121.84/16.13 (((binunionLsub) =>
% 121.84/16.13 (((binunionRsub) =>
% 121.84/16.13 (((binintersectI) =>
% 121.84/16.13 (((binintersectSubset5) =>
% 121.84/16.13 (((binintersectEL) =>
% 121.84/16.13 (((binintersectLsub) =>
% 121.84/16.13 (((binintersectSubset2) =>
% 121.84/16.13 (((binintersectSubset3) =>
% 121.84/16.13 (((binintersectER) =>
% 121.84/16.13 (((disjointsetsI1) =>
% 121.84/16.13 (((binintersectRsub) =>
% 121.84/16.13 (((binintersectSubset4) =>
% 121.84/16.13 (((binintersectSubset1) =>
% 121.84/16.13 (((bs114d) =>
% 121.84/16.13 (((setminusI) =>
% 121.84/16.13 (((setminusEL) =>
% 121.84/16.13 (((setminusER) =>
% 121.84/16.13 (((setminusSubset2) =>
% 121.84/16.13 (((setminusERneg) =>
% 121.84/16.13 (((setminusELneg) =>
% 121.84/16.13 (((setminusILneg) =>
% 121.84/16.13 (((setminusIRneg) =>
% 121.84/16.13 (((setminusLsub) =>
% 121.84/16.13 (((setminusSubset1) =>
% 121.84/16.13 ((
% 121.84/16.13 (symdiffE) =>
% 121.84/16.13 ((
% 121.84/16.13 (symdiffI1) =>
% 121.84/16.13 ((
% 121.84/16.13 (symdiffI2) =>
% 121.84/16.13 ((
% 121.84/16.13 (symdiffIneg1) =>
% 121.84/16.13 ((
% 121.84/16.13 (symdiffIneg2) =>
% 121.84/16.13 ((
% 121.84/16.13 (secondinupair) =>
% 121.84/16.13 ((
% 121.84/16.13 (setukpairIL) =>
% 121.84/16.13 ((
% 121.84/16.13 (setukpairIR) =>
% 121.84/16.13 ((
% 121.84/16.13 (kpairiskpair) =>
% 121.84/16.13 ((
% 121.84/16.13 (kpairp) =>
% 121.84/16.13 ((
% 121.84/16.13 (singletonsubset) =>
% 121.84/16.13 ((
% 121.84/16.13 (singletoninpowerset) =>
% 121.84/16.13 ((
% 121.84/16.13 (singletoninpowunion) =>
% 121.84/16.13 ((
% 121.84/16.13 (upairset2E) =>
% 121.84/16.13 ((
% 121.84/16.13 (upairsubunion) =>
% 121.84/16.13 ((
% 121.84/16.13 (upairinpowunion) =>
% 121.84/16.13 ((
% 121.84/16.13 (ubforcartprodlem1) =>
% 121.84/16.13 ((
% 121.84/16.13 (ubforcartprodlem2) =>
% 121.84/16.13 ((
% 121.84/16.13 (ubforcartprodlem3) =>
% 121.84/16.13 ((
% 121.84/16.13 (cartprodpairin) =>
% 121.84/16.13 ((
% 121.84/16.13 (cartprodmempair1) =>
% 121.84/16.13 ((
% 121.84/16.13 (cartprodmempair) =>
% 121.84/16.13 ((
% 121.84/16.13 (setunionE2) =>
% 121.84/16.13 ((
% 121.84/16.13 (setunionsingleton1) =>
% 121.84/16.13 ((
% 121.84/16.13 (setunionsingleton2) =>
% 121.84/16.13 ((
% 121.84/16.13 (setunionsingleton) =>
% 121.84/16.13 ((
% 121.84/16.13 (singletonprop) =>
% 121.84/16.13 ((
% 121.84/16.13 (ex1E1) =>
% 121.84/16.13 ((
% 121.84/16.13 (ex1I) =>
% 121.84/16.13 ((
% 121.84/16.13 (ex1I2) =>
% 121.84/16.13 ((
% 121.84/16.13 (singletonsuniq) =>
% 121.84/16.13 ((
% 121.84/16.13 (setukpairinjL1) =>
% 121.84/16.13 ((
% 121.84/16.13 (kfstsingleton) =>
% 121.84/16.13 ((
% 121.84/16.13 (theprop) =>
% 121.84/16.13 ((
% 121.84/16.13 (kfstpairEq) =>
% 121.84/16.13 ((
% 121.84/16.13 (cartprodfstin) =>
% 121.84/16.13 ((
% 121.84/16.13 (setukpairinjL2) =>
% 121.84/16.13 ((
% 121.84/16.13 (setukpairinjL) =>
% 121.84/16.13 ((
% 121.84/16.13 (setukpairinjR11) =>
% 121.84/16.13 ((
% 121.84/16.13 (setukpairinjR12) =>
% 121.84/16.13 ((
% 121.84/16.13 (setukpairinjR1) =>
% 121.84/16.13 ((
% 121.84/16.13 (upairequniteq) =>
% 121.84/16.13 ((
% 121.84/16.13 (setukpairinjR2) =>
% 121.84/16.13 ((
% 121.84/16.13 (setukpairinjR) =>
% 121.84/16.13 ((
% 121.84/16.13 (ksndsingleton) =>
% 121.84/16.13 ((
% 121.84/16.13 (ksndpairEq) =>
% 121.84/16.13 ((
% 121.84/16.13 (kpairsurjEq) =>
% 121.84/16.13 ((
% 121.84/16.13 (cartprodsndin) =>
% 121.84/16.13 ((
% 121.84/16.13 (cartprodpairmemEL) =>
% 121.84/16.13 ((
% 121.84/16.13 (cartprodpairmemER) =>
% 121.84/16.13 ((
% 121.84/16.13 (cartprodmempaircEq) =>
% 121.84/16.13 ((
% 121.84/16.13 (cartprodfstpairEq) =>
% 121.84/16.13 ((
% 121.84/16.13 (cartprodsndpairEq) =>
% 121.84/16.13 ((
% 121.84/16.13 (cartprodpairsurjEq) =>
% 121.84/16.13 ((
% 121.84/16.13 (dpsetconstrI) =>
% 121.84/16.13 ((
% 121.84/16.13 (dpsetconstrSub) =>
% 121.84/16.13 ((
% 121.84/16.13 (setOfPairsIsBReln) =>
% 121.84/16.13 ((
% 121.84/16.13 (dpsetconstrERa) =>
% 121.84/16.13 ((
% 121.84/16.13 (dpsetconstrEL1) =>
% 121.84/16.13 ((
% 121.84/16.13 (dpsetconstrEL2) =>
% 121.84/16.13 ((
% 121.84/16.13 (dpsetconstrER) =>
% 121.84/16.13 ((
% 121.84/16.13 (funcImageSingleton) =>
% 121.84/16.13 ((
% 121.84/16.13 (apProp) =>
% 121.84/16.13 ((
% 121.84/16.13 (app) =>
% 121.84/16.13 ((
% 121.84/16.13 (infuncsetfunc) =>
% 121.84/16.13 ((
% 121.84/16.13 (ap2p) =>
% 121.84/16.13 ((
% 121.84/16.13 (funcinfuncset) =>
% 121.84/16.13 ((
% 121.84/16.13 (lamProp) =>
% 121.84/16.13 ((
% 121.84/16.13 (lamp) =>
% 121.84/16.13 ((
% 121.84/16.13 (lam2p) =>
% 121.84/16.13 ((
% 121.84/16.13 (brelnall1) =>
% 121.84/16.13 ((
% 121.84/16.13 (brelnall2) =>
% 121.84/16.13 ((
% 121.84/16.13 (ex1E2) =>
% 121.84/16.13 ((
% 121.84/16.13 (funcGraphProp1) =>
% 121.84/16.13 ((
% 121.84/16.13 (funcGraphProp3) =>
% 121.84/16.13 ((
% 121.84/16.13 (funcGraphProp2) =>
% 121.84/16.13 ((
% 121.84/16.13 (funcextLem) =>
% 121.84/16.13 ((
% 121.84/16.13 (funcGraphProp4) =>
% 121.84/16.13 ((
% 121.84/16.13 (subbreln) =>
% 121.84/16.13 ((
% 121.84/16.13 (eqbreln) =>
% 121.84/16.13 ((
% 121.84/16.13 (funcext) =>
% 121.84/16.13 ((
% 121.84/16.13 (funcext2) =>
% 121.84/16.13 ((
% 121.84/16.13 (ap2apEq1) =>
% 121.84/16.13 ((
% 121.84/16.13 (ap2apEq2) =>
% 121.84/16.13 ((
% 121.84/16.13 (beta1) =>
% 121.84/16.13 ((
% 121.84/16.13 (eta1) =>
% 121.84/16.13 ((
% 121.84/16.13 (lam2lamEq) =>
% 121.84/16.13 ((
% 121.84/16.13 (beta2) =>
% 121.84/16.13 ((
% 121.84/16.13 (eta2) =>
% 121.84/16.13 ((
% 121.84/16.13 (iffalseProp1) =>
% 121.84/16.13 ((
% 121.84/16.13 (iffalseProp2) =>
% 121.84/16.13 ((
% 121.84/16.13 (iftrueProp1) =>
% 121.84/16.13 ((
% 121.84/16.13 (iftrueProp2) =>
% 121.84/16.13 ((
% 121.84/16.13 (ifSingleton) =>
% 121.84/16.13 ((
% 121.84/16.13 (ifp) =>
% 121.84/16.13 ((
% 121.84/16.13 (theeq) =>
% 121.84/16.13 ((
% 121.84/16.13 (iftrue) =>
% 121.84/16.13 ((
% 121.84/16.13 (iffalse) =>
% 121.84/16.13 ((
% 121.84/16.13 (iftrueorfalse) =>
% 121.84/16.13 ((
% 121.84/16.13 (binintersectT_lem) =>
% 121.84/16.13 ((
% 121.84/16.13 (binunionT_lem) =>
% 121.84/16.13 ((
% 121.84/16.13 (powersetT_lem) =>
% 121.84/16.13 ((
% 121.84/16.13 (setminusT_lem) =>
% 121.84/16.13 ((
% 121.84/16.13 (complementT_lem) =>
% 121.84/16.13 ((
% 121.84/16.13 (setextT) =>
% 121.84/16.13 ((
% 121.84/16.13 (subsetTI) =>
% 121.84/16.13 ((
% 121.84/16.13 (powersetTI1) =>
% 121.84/16.13 ((
% 121.84/16.13 (powersetTE1) =>
% 121.84/16.13 ((
% 121.84/16.13 (complementTI1) =>
% 121.84/16.13 ((
% 121.84/16.13 (complementTE1) =>
% 121.84/16.13 ((
% 121.84/16.13 (binintersectTELcontra) =>
% 121.84/16.13 ((
% 121.84/16.13 (binintersectTERcontra) =>
% 121.84/16.13 ((
% 121.84/16.13 (contrasubsetT) =>
% 121.84/16.13 ((
% 121.84/16.13 (contrasubsetT1) =>
% 121.84/16.13 ((
% 121.84/16.13 (contrasubsetT2) =>
% 121.84/16.13 ((
% 121.84/16.13 (contrasubsetT3) =>
% 121.84/16.13 ((
% 121.84/16.13 (doubleComplementI1) =>
% 121.84/16.13 ((
% 121.84/16.13 (doubleComplementE1) =>
% 121.84/16.13 ((
% 121.84/16.13 (doubleComplementSub1) =>
% 121.84/16.13 ((
% 121.84/16.13 (doubleComplementSub2) =>
% 121.84/16.13 ((
% 121.84/16.13 (doubleComplementEq) =>
% 121.84/16.13 ((
% 121.84/16.13 (complementTnotintersectT) =>
% 121.84/16.13 ((
% 121.84/16.13 (complementImpComplementIntersect) =>
% 121.84/16.13 ((
% 121.84/16.13 (complementSubsetComplementIntersect) =>
% 121.84/16.13 ((
% 121.84/16.13 (complementInPowersetComplementIntersect) =>
% 121.84/16.13 ((
% 121.84/16.13 (contraSubsetComplement) =>
% 121.84/16.13 ((
% 121.84/16.13 (complementTcontraSubset) =>
% 121.84/16.13 ((
% 121.84/16.13 (binunionTILcontra) =>
% 121.84/16.13 ((
% 121.84/16.13 (binunionTIRcontra) =>
% 121.84/16.13 ((
% 121.84/16.13 (inIntersectImpInUnion) =>
% 121.84/16.13 ((
% 121.84/16.13 (inIntersectImpInUnion2) =>
% 121.84/16.13 ((
% 121.84/16.13 (inIntersectImpInIntersectUnions) =>
% 121.84/16.13 ((
% 121.84/16.13 (intersectInPowersetIntersectUnions) =>
% 121.84/16.13 ((
% 121.84/16.13 (inComplementUnionImpNotIn1) =>
% 121.84/16.13 ((
% 121.84/16.13 (inComplementUnionImpInComplement1) =>
% 121.84/16.13 ((
% 121.84/16.13 (binunionTE) =>
% 121.84/16.13 ((
% 121.84/16.13 (binunionTEcontra) =>
% 121.84/16.13 ((
% 121.84/16.13 (demorgan2a1) =>
% 121.84/16.13 ((
% 121.84/16.13 (complementUnionInPowersetComplement) =>
% 121.84/16.13 ((
% 121.84/16.13 (demorgan2a2) =>
% 121.84/16.13 ((
% 121.84/16.13 (demorgan1a) =>
% 121.84/16.13 ((
% 121.84/16.13 (demorgan1b) =>
% 121.84/16.13 ((
% 121.84/16.13 (demorgan1) =>
% 121.84/16.13 ((
% 121.84/16.13 (demorgan2a) =>
% 121.84/16.13 ((
% 121.84/16.13 (demorgan2b2) =>
% 121.84/16.13 ((
% 121.84/16.13 (demorgan2b) =>
% 121.84/16.13 ((
% 121.84/16.13 (demorgan2) =>
% 121.84/16.13 ((
% 121.84/16.13 (woz13rule0) =>
% 121.84/16.13 ((
% 121.84/16.13 (woz13rule1) =>
% 121.84/16.13 ((
% 121.84/16.13 (woz13rule2) =>
% 121.84/16.13 ((
% 121.84/16.13 (woz13rule3) =>
% 121.84/16.13 ((
% 121.84/16.13 (woz13rule4) =>
% 121.84/16.13 ((
% 121.84/16.13 (woz1_1) =>
% 121.84/16.13 ((
% 121.84/16.13 (woz1_2) =>
% 121.84/16.13 ((
% 121.84/16.13 (woz1_3) =>
% 121.84/16.13 ((
% 121.84/16.13 (woz1_4) =>
% 121.84/16.13 ((
% 121.84/16.13 (woz1_5) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1all2) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1SetBreln1) =>
% 121.84/16.13 ((
% 121.84/16.13 (choice2fnsingleton) =>
% 121.84/16.13 ((
% 121.84/16.13 (setOfPairsIsBReln1) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1all1) =>
% 121.84/16.13 ((
% 121.84/16.13 (subbreln1) =>
% 121.84/16.13 ((
% 121.84/16.13 (eqbreln1) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1invprop) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1invI) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1invE) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1compprop) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1compI) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1compE) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1compEex) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1unionprop) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1unionIL) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1unionIR) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1unionI) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1unionE) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1unionEcases) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1unionCommutes) =>
% 121.84/16.13 ((
% 121.84/16.13 (woz2Ex) =>
% 121.84/16.13 ((
% 121.84/16.13 (woz2W) =>
% 121.84/16.13 ((
% 121.84/16.13 (woz2A) =>
% 121.84/16.13 ((
% 121.84/16.13 (woz2B) =>
% 121.84/16.13 ((
% 121.84/16.13 (image1Ex) =>
% 121.84/16.13 ((
% 121.84/16.13 (image1Ex1) =>
% 121.84/16.13 ((
% 121.84/16.13 (image1Equiv) =>
% 121.84/16.13 ((
% 121.84/16.13 (image1E) =>
% 121.84/16.13 ((
% 121.84/16.13 (image1I) =>
% 121.84/16.13 ((
% 121.84/16.13 (injFuncInInjFuncSet) =>
% 121.84/16.13 ((
% 121.84/16.13 (!!) @ (
% 121.84/16.13 (('#B') @ (
% 121.84/16.13 !!) @
% 121.84/16.13 (
% 121.84/16.13 (
% 121.84/16.13 ('#B') @ (
% 121.84/16.13 (
% 121.84/16.13 ('#B') @ (
% 121.84/16.13 !!))) @
% 121.84/16.13 (
% 121.84/16.13 (
% 121.84/16.13 ('#S') @ (
% 121.84/16.13 (
% 121.84/16.13 ('#B') @ (
% 121.84/16.13 '#S') @
% 121.84/16.13 (
% 121.84/16.13 (
% 121.84/16.13 ('#B') @ (
% 121.84/16.13 (
% 121.84/16.13 ('#B') @ (
% 121.84/16.13 '#S'))) @
% 121.84/16.13 (
% 121.84/16.13 (
% 121.84/16.13 ('#B') @ (
% 121.84/16.13 (
% 121.84/16.13 ('#B') @ (
% 121.84/16.13 (
% 121.84/16.13 ('#B') @ (
% 121.84/16.13 =>))))) @
% 121.84/16.13 (
% 121.84/16.13 (
% 121.84/16.13 ('#B') @ (
% 121.84/16.13 (
% 121.84/16.13 ('#B') @ (
% 121.84/16.13 (
% 121.84/16.13 ('#C') @ in)))) @
% 121.84/16.13 injFuncSet)))))))) @
% 121.84/16.13 (
% 121.84/16.13 (
% 121.84/16.13 ('#B') @ (
% 121.84/16.13 (
% 121.84/16.13 ('#B') @ (
% 121.84/16.13 (
% 121.84/16.13 ('#C') @ in)))) @
% 121.84/16.13 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 121.84/16.13 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1082])).
% 121.84/16.13 thf(zip_derived_cl1096, plain,
% 121.84/16.13 (~ (((binunionIL) =>
% 121.84/16.13 (((upairset2IR) =>
% 121.84/16.13 (((binunionIR) =>
% 121.84/16.13 (((binunionEcases) =>
% 121.84/16.13 (((binunionE) =>
% 121.84/16.13 (((binunionLsub) =>
% 121.84/16.13 (((binunionRsub) =>
% 121.84/16.13 (((binintersectI) =>
% 121.84/16.13 (((binintersectSubset5) =>
% 121.84/16.13 (((binintersectEL) =>
% 121.84/16.13 (((binintersectLsub) =>
% 121.84/16.13 (((binintersectSubset2) =>
% 121.84/16.13 (((binintersectSubset3) =>
% 121.84/16.13 (((binintersectER) =>
% 121.84/16.13 (((disjointsetsI1) =>
% 121.84/16.13 (((binintersectRsub) =>
% 121.84/16.13 (((binintersectSubset4) =>
% 121.84/16.13 (((binintersectSubset1) =>
% 121.84/16.13 (((bs114d) =>
% 121.84/16.13 (((setminusI) =>
% 121.84/16.13 (((setminusEL) =>
% 121.84/16.13 (((setminusER) =>
% 121.84/16.13 (((setminusSubset2) =>
% 121.84/16.13 (((setminusERneg) =>
% 121.84/16.13 (((setminusELneg) =>
% 121.84/16.13 (((setminusILneg) =>
% 121.84/16.13 (((setminusIRneg) =>
% 121.84/16.13 (((setminusLsub) =>
% 121.84/16.13 (((setminusSubset1) =>
% 121.84/16.13 (((symdiffE) =>
% 121.84/16.13 ((
% 121.84/16.13 (symdiffI1) =>
% 121.84/16.13 ((
% 121.84/16.13 (symdiffI2) =>
% 121.84/16.13 ((
% 121.84/16.13 (symdiffIneg1) =>
% 121.84/16.13 ((
% 121.84/16.13 (symdiffIneg2) =>
% 121.84/16.13 ((
% 121.84/16.13 (secondinupair) =>
% 121.84/16.13 ((
% 121.84/16.13 (setukpairIL) =>
% 121.84/16.13 ((
% 121.84/16.13 (setukpairIR) =>
% 121.84/16.13 ((
% 121.84/16.13 (kpairiskpair) =>
% 121.84/16.13 ((
% 121.84/16.13 (kpairp) =>
% 121.84/16.13 ((
% 121.84/16.13 (singletonsubset) =>
% 121.84/16.13 ((
% 121.84/16.13 (singletoninpowerset) =>
% 121.84/16.13 ((
% 121.84/16.13 (singletoninpowunion) =>
% 121.84/16.13 ((
% 121.84/16.13 (upairset2E) =>
% 121.84/16.13 ((
% 121.84/16.13 (upairsubunion) =>
% 121.84/16.13 ((
% 121.84/16.13 (upairinpowunion) =>
% 121.84/16.13 ((
% 121.84/16.13 (ubforcartprodlem1) =>
% 121.84/16.13 ((
% 121.84/16.13 (ubforcartprodlem2) =>
% 121.84/16.13 ((
% 121.84/16.13 (ubforcartprodlem3) =>
% 121.84/16.13 ((
% 121.84/16.13 (cartprodpairin) =>
% 121.84/16.13 ((
% 121.84/16.13 (cartprodmempair1) =>
% 121.84/16.13 ((
% 121.84/16.13 (cartprodmempair) =>
% 121.84/16.13 ((
% 121.84/16.13 (setunionE2) =>
% 121.84/16.13 ((
% 121.84/16.13 (setunionsingleton1) =>
% 121.84/16.13 ((
% 121.84/16.13 (setunionsingleton2) =>
% 121.84/16.13 ((
% 121.84/16.13 (setunionsingleton) =>
% 121.84/16.13 ((
% 121.84/16.13 (singletonprop) =>
% 121.84/16.13 ((
% 121.84/16.13 (ex1E1) =>
% 121.84/16.13 ((
% 121.84/16.13 (ex1I) =>
% 121.84/16.13 ((
% 121.84/16.13 (ex1I2) =>
% 121.84/16.13 ((
% 121.84/16.13 (singletonsuniq) =>
% 121.84/16.13 ((
% 121.84/16.13 (setukpairinjL1) =>
% 121.84/16.13 ((
% 121.84/16.13 (kfstsingleton) =>
% 121.84/16.13 ((
% 121.84/16.13 (theprop) =>
% 121.84/16.13 ((
% 121.84/16.13 (kfstpairEq) =>
% 121.84/16.13 ((
% 121.84/16.13 (cartprodfstin) =>
% 121.84/16.13 ((
% 121.84/16.13 (setukpairinjL2) =>
% 121.84/16.13 ((
% 121.84/16.13 (setukpairinjL) =>
% 121.84/16.13 ((
% 121.84/16.13 (setukpairinjR11) =>
% 121.84/16.13 ((
% 121.84/16.13 (setukpairinjR12) =>
% 121.84/16.13 ((
% 121.84/16.13 (setukpairinjR1) =>
% 121.84/16.13 ((
% 121.84/16.13 (upairequniteq) =>
% 121.84/16.13 ((
% 121.84/16.13 (setukpairinjR2) =>
% 121.84/16.13 ((
% 121.84/16.13 (setukpairinjR) =>
% 121.84/16.13 ((
% 121.84/16.13 (ksndsingleton) =>
% 121.84/16.13 ((
% 121.84/16.13 (ksndpairEq) =>
% 121.84/16.13 ((
% 121.84/16.13 (kpairsurjEq) =>
% 121.84/16.13 ((
% 121.84/16.13 (cartprodsndin) =>
% 121.84/16.13 ((
% 121.84/16.13 (cartprodpairmemEL) =>
% 121.84/16.13 ((
% 121.84/16.13 (cartprodpairmemER) =>
% 121.84/16.13 ((
% 121.84/16.13 (cartprodmempaircEq) =>
% 121.84/16.13 ((
% 121.84/16.13 (cartprodfstpairEq) =>
% 121.84/16.13 ((
% 121.84/16.13 (cartprodsndpairEq) =>
% 121.84/16.13 ((
% 121.84/16.13 (cartprodpairsurjEq) =>
% 121.84/16.13 ((
% 121.84/16.13 (dpsetconstrI) =>
% 121.84/16.13 ((
% 121.84/16.13 (dpsetconstrSub) =>
% 121.84/16.13 ((
% 121.84/16.13 (setOfPairsIsBReln) =>
% 121.84/16.13 ((
% 121.84/16.13 (dpsetconstrERa) =>
% 121.84/16.13 ((
% 121.84/16.13 (dpsetconstrEL1) =>
% 121.84/16.13 ((
% 121.84/16.13 (dpsetconstrEL2) =>
% 121.84/16.13 ((
% 121.84/16.13 (dpsetconstrER) =>
% 121.84/16.13 ((
% 121.84/16.13 (funcImageSingleton) =>
% 121.84/16.13 ((
% 121.84/16.13 (apProp) =>
% 121.84/16.13 ((
% 121.84/16.13 (app) =>
% 121.84/16.13 ((
% 121.84/16.13 (infuncsetfunc) =>
% 121.84/16.13 ((
% 121.84/16.13 (ap2p) =>
% 121.84/16.13 ((
% 121.84/16.13 (funcinfuncset) =>
% 121.84/16.13 ((
% 121.84/16.13 (lamProp) =>
% 121.84/16.13 ((
% 121.84/16.13 (lamp) =>
% 121.84/16.13 ((
% 121.84/16.13 (lam2p) =>
% 121.84/16.13 ((
% 121.84/16.13 (brelnall1) =>
% 121.84/16.13 ((
% 121.84/16.13 (brelnall2) =>
% 121.84/16.13 ((
% 121.84/16.13 (ex1E2) =>
% 121.84/16.13 ((
% 121.84/16.13 (funcGraphProp1) =>
% 121.84/16.13 ((
% 121.84/16.13 (funcGraphProp3) =>
% 121.84/16.13 ((
% 121.84/16.13 (funcGraphProp2) =>
% 121.84/16.13 ((
% 121.84/16.13 (funcextLem) =>
% 121.84/16.13 ((
% 121.84/16.13 (funcGraphProp4) =>
% 121.84/16.13 ((
% 121.84/16.13 (subbreln) =>
% 121.84/16.13 ((
% 121.84/16.13 (eqbreln) =>
% 121.84/16.13 ((
% 121.84/16.13 (funcext) =>
% 121.84/16.13 ((
% 121.84/16.13 (funcext2) =>
% 121.84/16.13 ((
% 121.84/16.13 (ap2apEq1) =>
% 121.84/16.13 ((
% 121.84/16.13 (ap2apEq2) =>
% 121.84/16.13 ((
% 121.84/16.13 (beta1) =>
% 121.84/16.13 ((
% 121.84/16.13 (eta1) =>
% 121.84/16.13 ((
% 121.84/16.13 (lam2lamEq) =>
% 121.84/16.13 ((
% 121.84/16.13 (beta2) =>
% 121.84/16.13 ((
% 121.84/16.13 (eta2) =>
% 121.84/16.13 ((
% 121.84/16.13 (iffalseProp1) =>
% 121.84/16.13 ((
% 121.84/16.13 (iffalseProp2) =>
% 121.84/16.13 ((
% 121.84/16.13 (iftrueProp1) =>
% 121.84/16.13 ((
% 121.84/16.13 (iftrueProp2) =>
% 121.84/16.13 ((
% 121.84/16.13 (ifSingleton) =>
% 121.84/16.13 ((
% 121.84/16.13 (ifp) =>
% 121.84/16.13 ((
% 121.84/16.13 (theeq) =>
% 121.84/16.13 ((
% 121.84/16.13 (iftrue) =>
% 121.84/16.13 ((
% 121.84/16.13 (iffalse) =>
% 121.84/16.13 ((
% 121.84/16.13 (iftrueorfalse) =>
% 121.84/16.13 ((
% 121.84/16.13 (binintersectT_lem) =>
% 121.84/16.13 ((
% 121.84/16.13 (binunionT_lem) =>
% 121.84/16.13 ((
% 121.84/16.13 (powersetT_lem) =>
% 121.84/16.13 ((
% 121.84/16.13 (setminusT_lem) =>
% 121.84/16.13 ((
% 121.84/16.13 (complementT_lem) =>
% 121.84/16.13 ((
% 121.84/16.13 (setextT) =>
% 121.84/16.13 ((
% 121.84/16.13 (subsetTI) =>
% 121.84/16.13 ((
% 121.84/16.13 (powersetTI1) =>
% 121.84/16.13 ((
% 121.84/16.13 (powersetTE1) =>
% 121.84/16.13 ((
% 121.84/16.13 (complementTI1) =>
% 121.84/16.13 ((
% 121.84/16.13 (complementTE1) =>
% 121.84/16.13 ((
% 121.84/16.13 (binintersectTELcontra) =>
% 121.84/16.13 ((
% 121.84/16.13 (binintersectTERcontra) =>
% 121.84/16.13 ((
% 121.84/16.13 (contrasubsetT) =>
% 121.84/16.13 ((
% 121.84/16.13 (contrasubsetT1) =>
% 121.84/16.13 ((
% 121.84/16.13 (contrasubsetT2) =>
% 121.84/16.13 ((
% 121.84/16.13 (contrasubsetT3) =>
% 121.84/16.13 ((
% 121.84/16.13 (doubleComplementI1) =>
% 121.84/16.13 ((
% 121.84/16.13 (doubleComplementE1) =>
% 121.84/16.13 ((
% 121.84/16.13 (doubleComplementSub1) =>
% 121.84/16.13 ((
% 121.84/16.13 (doubleComplementSub2) =>
% 121.84/16.13 ((
% 121.84/16.13 (doubleComplementEq) =>
% 121.84/16.13 ((
% 121.84/16.13 (complementTnotintersectT) =>
% 121.84/16.13 ((
% 121.84/16.13 (complementImpComplementIntersect) =>
% 121.84/16.13 ((
% 121.84/16.13 (complementSubsetComplementIntersect) =>
% 121.84/16.13 ((
% 121.84/16.13 (complementInPowersetComplementIntersect) =>
% 121.84/16.13 ((
% 121.84/16.13 (contraSubsetComplement) =>
% 121.84/16.13 ((
% 121.84/16.13 (complementTcontraSubset) =>
% 121.84/16.13 ((
% 121.84/16.13 (binunionTILcontra) =>
% 121.84/16.13 ((
% 121.84/16.13 (binunionTIRcontra) =>
% 121.84/16.13 ((
% 121.84/16.13 (inIntersectImpInUnion) =>
% 121.84/16.13 ((
% 121.84/16.13 (inIntersectImpInUnion2) =>
% 121.84/16.13 ((
% 121.84/16.13 (inIntersectImpInIntersectUnions) =>
% 121.84/16.13 ((
% 121.84/16.13 (intersectInPowersetIntersectUnions) =>
% 121.84/16.13 ((
% 121.84/16.13 (inComplementUnionImpNotIn1) =>
% 121.84/16.13 ((
% 121.84/16.13 (inComplementUnionImpInComplement1) =>
% 121.84/16.13 ((
% 121.84/16.13 (binunionTE) =>
% 121.84/16.13 ((
% 121.84/16.13 (binunionTEcontra) =>
% 121.84/16.13 ((
% 121.84/16.13 (demorgan2a1) =>
% 121.84/16.13 ((
% 121.84/16.13 (complementUnionInPowersetComplement) =>
% 121.84/16.13 ((
% 121.84/16.13 (demorgan2a2) =>
% 121.84/16.13 ((
% 121.84/16.13 (demorgan1a) =>
% 121.84/16.13 ((
% 121.84/16.13 (demorgan1b) =>
% 121.84/16.13 ((
% 121.84/16.13 (demorgan1) =>
% 121.84/16.13 ((
% 121.84/16.13 (demorgan2a) =>
% 121.84/16.13 ((
% 121.84/16.13 (demorgan2b2) =>
% 121.84/16.13 ((
% 121.84/16.13 (demorgan2b) =>
% 121.84/16.13 ((
% 121.84/16.13 (demorgan2) =>
% 121.84/16.13 ((
% 121.84/16.13 (woz13rule0) =>
% 121.84/16.13 ((
% 121.84/16.13 (woz13rule1) =>
% 121.84/16.13 ((
% 121.84/16.13 (woz13rule2) =>
% 121.84/16.13 ((
% 121.84/16.13 (woz13rule3) =>
% 121.84/16.13 ((
% 121.84/16.13 (woz13rule4) =>
% 121.84/16.13 ((
% 121.84/16.13 (woz1_1) =>
% 121.84/16.13 ((
% 121.84/16.13 (woz1_2) =>
% 121.84/16.13 ((
% 121.84/16.13 (woz1_3) =>
% 121.84/16.13 ((
% 121.84/16.13 (woz1_4) =>
% 121.84/16.13 ((
% 121.84/16.13 (woz1_5) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1all2) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1SetBreln1) =>
% 121.84/16.13 ((
% 121.84/16.13 (choice2fnsingleton) =>
% 121.84/16.13 ((
% 121.84/16.13 (setOfPairsIsBReln1) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1all1) =>
% 121.84/16.13 ((
% 121.84/16.13 (subbreln1) =>
% 121.84/16.13 ((
% 121.84/16.13 (eqbreln1) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1invprop) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1invI) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1invE) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1compprop) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1compI) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1compE) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1compEex) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1unionprop) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1unionIL) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1unionIR) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1unionI) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1unionE) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1unionEcases) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1unionCommutes) =>
% 121.84/16.13 ((
% 121.84/16.13 (woz2Ex) =>
% 121.84/16.13 ((
% 121.84/16.13 (woz2W) =>
% 121.84/16.13 ((
% 121.84/16.13 (woz2A) =>
% 121.84/16.13 ((
% 121.84/16.13 (woz2B) =>
% 121.84/16.13 ((
% 121.84/16.13 (image1Ex) =>
% 121.84/16.13 ((
% 121.84/16.13 (image1Ex1) =>
% 121.84/16.13 ((
% 121.84/16.13 (image1Equiv) =>
% 121.84/16.13 ((
% 121.84/16.13 (image1E) =>
% 121.84/16.13 ((
% 121.84/16.13 (image1I) =>
% 121.84/16.13 ((
% 121.84/16.13 (injFuncInInjFuncSet) =>
% 121.84/16.13 ((
% 121.84/16.13 (!!) @ (
% 121.84/16.13 (('#B') @ (
% 121.84/16.13 !!) @
% 121.84/16.13 (
% 121.84/16.13 (
% 121.84/16.13 ('#B') @ (
% 121.84/16.13 (
% 121.84/16.13 ('#B') @ (
% 121.84/16.13 !!))) @
% 121.84/16.13 (
% 121.84/16.13 (
% 121.84/16.13 ('#S') @ (
% 121.84/16.13 (
% 121.84/16.13 ('#B') @ (
% 121.84/16.13 '#S') @
% 121.84/16.13 (
% 121.84/16.13 (
% 121.84/16.13 ('#B') @ (
% 121.84/16.13 (
% 121.84/16.13 ('#B') @ (
% 121.84/16.13 '#S'))) @
% 121.84/16.13 (
% 121.84/16.13 (
% 121.84/16.13 ('#B') @ (
% 121.84/16.13 (
% 121.84/16.13 ('#B') @ (
% 121.84/16.13 (
% 121.84/16.13 ('#B') @ (
% 121.84/16.13 =>))))) @
% 121.84/16.13 (
% 121.84/16.13 (
% 121.84/16.13 ('#B') @ (
% 121.84/16.13 (
% 121.84/16.13 ('#B') @ (
% 121.84/16.13 (
% 121.84/16.13 ('#C') @ in)))) @
% 121.84/16.13 injFuncSet)))))))) @
% 121.84/16.13 (
% 121.84/16.13 (
% 121.84/16.13 ('#B') @ (
% 121.84/16.13 (
% 121.84/16.13 ('#B') @ (
% 121.84/16.13 (
% 121.84/16.13 ('#C') @ in)))) @
% 121.84/16.13 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 121.84/16.13 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1090])).
% 121.84/16.13 thf(zip_derived_cl1102, plain,
% 121.84/16.13 (~ (((upairset2IR) =>
% 121.84/16.13 (((binunionIR) =>
% 121.84/16.13 (((binunionEcases) =>
% 121.84/16.13 (((binunionE) =>
% 121.84/16.13 (((binunionLsub) =>
% 121.84/16.13 (((binunionRsub) =>
% 121.84/16.13 (((binintersectI) =>
% 121.84/16.13 (((binintersectSubset5) =>
% 121.84/16.13 (((binintersectEL) =>
% 121.84/16.13 (((binintersectLsub) =>
% 121.84/16.13 (((binintersectSubset2) =>
% 121.84/16.13 (((binintersectSubset3) =>
% 121.84/16.13 (((binintersectER) =>
% 121.84/16.13 (((disjointsetsI1) =>
% 121.84/16.13 (((binintersectRsub) =>
% 121.84/16.13 (((binintersectSubset4) =>
% 121.84/16.13 (((binintersectSubset1) =>
% 121.84/16.13 (((bs114d) =>
% 121.84/16.13 (((setminusI) =>
% 121.84/16.13 (((setminusEL) =>
% 121.84/16.13 (((setminusER) =>
% 121.84/16.13 (((setminusSubset2) =>
% 121.84/16.13 (((setminusERneg) =>
% 121.84/16.13 (((setminusELneg) =>
% 121.84/16.13 (((setminusILneg) =>
% 121.84/16.13 (((setminusIRneg) =>
% 121.84/16.13 (((setminusLsub) =>
% 121.84/16.13 (((setminusSubset1) =>
% 121.84/16.13 (((symdiffE) =>
% 121.84/16.13 (((symdiffI1) =>
% 121.84/16.13 ((
% 121.84/16.13 (symdiffI2) =>
% 121.84/16.13 ((
% 121.84/16.13 (symdiffIneg1) =>
% 121.84/16.13 ((
% 121.84/16.13 (symdiffIneg2) =>
% 121.84/16.13 ((
% 121.84/16.13 (secondinupair) =>
% 121.84/16.13 ((
% 121.84/16.13 (setukpairIL) =>
% 121.84/16.13 ((
% 121.84/16.13 (setukpairIR) =>
% 121.84/16.13 ((
% 121.84/16.13 (kpairiskpair) =>
% 121.84/16.13 ((
% 121.84/16.13 (kpairp) =>
% 121.84/16.13 ((
% 121.84/16.13 (singletonsubset) =>
% 121.84/16.13 ((
% 121.84/16.13 (singletoninpowerset) =>
% 121.84/16.13 ((
% 121.84/16.13 (singletoninpowunion) =>
% 121.84/16.13 ((
% 121.84/16.13 (upairset2E) =>
% 121.84/16.13 ((
% 121.84/16.13 (upairsubunion) =>
% 121.84/16.13 ((
% 121.84/16.13 (upairinpowunion) =>
% 121.84/16.13 ((
% 121.84/16.13 (ubforcartprodlem1) =>
% 121.84/16.13 ((
% 121.84/16.13 (ubforcartprodlem2) =>
% 121.84/16.13 ((
% 121.84/16.13 (ubforcartprodlem3) =>
% 121.84/16.13 ((
% 121.84/16.13 (cartprodpairin) =>
% 121.84/16.13 ((
% 121.84/16.13 (cartprodmempair1) =>
% 121.84/16.13 ((
% 121.84/16.13 (cartprodmempair) =>
% 121.84/16.13 ((
% 121.84/16.13 (setunionE2) =>
% 121.84/16.13 ((
% 121.84/16.13 (setunionsingleton1) =>
% 121.84/16.13 ((
% 121.84/16.13 (setunionsingleton2) =>
% 121.84/16.13 ((
% 121.84/16.13 (setunionsingleton) =>
% 121.84/16.13 ((
% 121.84/16.13 (singletonprop) =>
% 121.84/16.13 ((
% 121.84/16.13 (ex1E1) =>
% 121.84/16.13 ((
% 121.84/16.13 (ex1I) =>
% 121.84/16.13 ((
% 121.84/16.13 (ex1I2) =>
% 121.84/16.13 ((
% 121.84/16.13 (singletonsuniq) =>
% 121.84/16.13 ((
% 121.84/16.13 (setukpairinjL1) =>
% 121.84/16.13 ((
% 121.84/16.13 (kfstsingleton) =>
% 121.84/16.13 ((
% 121.84/16.13 (theprop) =>
% 121.84/16.13 ((
% 121.84/16.13 (kfstpairEq) =>
% 121.84/16.13 ((
% 121.84/16.13 (cartprodfstin) =>
% 121.84/16.13 ((
% 121.84/16.13 (setukpairinjL2) =>
% 121.84/16.13 ((
% 121.84/16.13 (setukpairinjL) =>
% 121.84/16.13 ((
% 121.84/16.13 (setukpairinjR11) =>
% 121.84/16.13 ((
% 121.84/16.13 (setukpairinjR12) =>
% 121.84/16.13 ((
% 121.84/16.13 (setukpairinjR1) =>
% 121.84/16.13 ((
% 121.84/16.13 (upairequniteq) =>
% 121.84/16.13 ((
% 121.84/16.13 (setukpairinjR2) =>
% 121.84/16.13 ((
% 121.84/16.13 (setukpairinjR) =>
% 121.84/16.13 ((
% 121.84/16.13 (ksndsingleton) =>
% 121.84/16.13 ((
% 121.84/16.13 (ksndpairEq) =>
% 121.84/16.13 ((
% 121.84/16.13 (kpairsurjEq) =>
% 121.84/16.13 ((
% 121.84/16.13 (cartprodsndin) =>
% 121.84/16.13 ((
% 121.84/16.13 (cartprodpairmemEL) =>
% 121.84/16.13 ((
% 121.84/16.13 (cartprodpairmemER) =>
% 121.84/16.13 ((
% 121.84/16.13 (cartprodmempaircEq) =>
% 121.84/16.13 ((
% 121.84/16.13 (cartprodfstpairEq) =>
% 121.84/16.13 ((
% 121.84/16.13 (cartprodsndpairEq) =>
% 121.84/16.13 ((
% 121.84/16.13 (cartprodpairsurjEq) =>
% 121.84/16.13 ((
% 121.84/16.13 (dpsetconstrI) =>
% 121.84/16.13 ((
% 121.84/16.13 (dpsetconstrSub) =>
% 121.84/16.13 ((
% 121.84/16.13 (setOfPairsIsBReln) =>
% 121.84/16.13 ((
% 121.84/16.13 (dpsetconstrERa) =>
% 121.84/16.13 ((
% 121.84/16.13 (dpsetconstrEL1) =>
% 121.84/16.13 ((
% 121.84/16.13 (dpsetconstrEL2) =>
% 121.84/16.13 ((
% 121.84/16.13 (dpsetconstrER) =>
% 121.84/16.13 ((
% 121.84/16.13 (funcImageSingleton) =>
% 121.84/16.13 ((
% 121.84/16.13 (apProp) =>
% 121.84/16.13 ((
% 121.84/16.13 (app) =>
% 121.84/16.13 ((
% 121.84/16.13 (infuncsetfunc) =>
% 121.84/16.13 ((
% 121.84/16.13 (ap2p) =>
% 121.84/16.13 ((
% 121.84/16.13 (funcinfuncset) =>
% 121.84/16.13 ((
% 121.84/16.13 (lamProp) =>
% 121.84/16.13 ((
% 121.84/16.13 (lamp) =>
% 121.84/16.13 ((
% 121.84/16.13 (lam2p) =>
% 121.84/16.13 ((
% 121.84/16.13 (brelnall1) =>
% 121.84/16.13 ((
% 121.84/16.13 (brelnall2) =>
% 121.84/16.13 ((
% 121.84/16.13 (ex1E2) =>
% 121.84/16.13 ((
% 121.84/16.13 (funcGraphProp1) =>
% 121.84/16.13 ((
% 121.84/16.13 (funcGraphProp3) =>
% 121.84/16.13 ((
% 121.84/16.13 (funcGraphProp2) =>
% 121.84/16.13 ((
% 121.84/16.13 (funcextLem) =>
% 121.84/16.13 ((
% 121.84/16.13 (funcGraphProp4) =>
% 121.84/16.13 ((
% 121.84/16.13 (subbreln) =>
% 121.84/16.13 ((
% 121.84/16.13 (eqbreln) =>
% 121.84/16.13 ((
% 121.84/16.13 (funcext) =>
% 121.84/16.13 ((
% 121.84/16.13 (funcext2) =>
% 121.84/16.13 ((
% 121.84/16.13 (ap2apEq1) =>
% 121.84/16.13 ((
% 121.84/16.13 (ap2apEq2) =>
% 121.84/16.13 ((
% 121.84/16.13 (beta1) =>
% 121.84/16.13 ((
% 121.84/16.13 (eta1) =>
% 121.84/16.13 ((
% 121.84/16.13 (lam2lamEq) =>
% 121.84/16.13 ((
% 121.84/16.13 (beta2) =>
% 121.84/16.13 ((
% 121.84/16.13 (eta2) =>
% 121.84/16.13 ((
% 121.84/16.13 (iffalseProp1) =>
% 121.84/16.13 ((
% 121.84/16.13 (iffalseProp2) =>
% 121.84/16.13 ((
% 121.84/16.13 (iftrueProp1) =>
% 121.84/16.13 ((
% 121.84/16.13 (iftrueProp2) =>
% 121.84/16.13 ((
% 121.84/16.13 (ifSingleton) =>
% 121.84/16.13 ((
% 121.84/16.13 (ifp) =>
% 121.84/16.13 ((
% 121.84/16.13 (theeq) =>
% 121.84/16.13 ((
% 121.84/16.13 (iftrue) =>
% 121.84/16.13 ((
% 121.84/16.13 (iffalse) =>
% 121.84/16.13 ((
% 121.84/16.13 (iftrueorfalse) =>
% 121.84/16.13 ((
% 121.84/16.13 (binintersectT_lem) =>
% 121.84/16.13 ((
% 121.84/16.13 (binunionT_lem) =>
% 121.84/16.13 ((
% 121.84/16.13 (powersetT_lem) =>
% 121.84/16.13 ((
% 121.84/16.13 (setminusT_lem) =>
% 121.84/16.13 ((
% 121.84/16.13 (complementT_lem) =>
% 121.84/16.13 ((
% 121.84/16.13 (setextT) =>
% 121.84/16.13 ((
% 121.84/16.13 (subsetTI) =>
% 121.84/16.13 ((
% 121.84/16.13 (powersetTI1) =>
% 121.84/16.13 ((
% 121.84/16.13 (powersetTE1) =>
% 121.84/16.13 ((
% 121.84/16.13 (complementTI1) =>
% 121.84/16.13 ((
% 121.84/16.13 (complementTE1) =>
% 121.84/16.13 ((
% 121.84/16.13 (binintersectTELcontra) =>
% 121.84/16.13 ((
% 121.84/16.13 (binintersectTERcontra) =>
% 121.84/16.13 ((
% 121.84/16.13 (contrasubsetT) =>
% 121.84/16.13 ((
% 121.84/16.13 (contrasubsetT1) =>
% 121.84/16.13 ((
% 121.84/16.13 (contrasubsetT2) =>
% 121.84/16.13 ((
% 121.84/16.13 (contrasubsetT3) =>
% 121.84/16.13 ((
% 121.84/16.13 (doubleComplementI1) =>
% 121.84/16.13 ((
% 121.84/16.13 (doubleComplementE1) =>
% 121.84/16.13 ((
% 121.84/16.13 (doubleComplementSub1) =>
% 121.84/16.13 ((
% 121.84/16.13 (doubleComplementSub2) =>
% 121.84/16.13 ((
% 121.84/16.13 (doubleComplementEq) =>
% 121.84/16.13 ((
% 121.84/16.13 (complementTnotintersectT) =>
% 121.84/16.13 ((
% 121.84/16.13 (complementImpComplementIntersect) =>
% 121.84/16.13 ((
% 121.84/16.13 (complementSubsetComplementIntersect) =>
% 121.84/16.13 ((
% 121.84/16.13 (complementInPowersetComplementIntersect) =>
% 121.84/16.13 ((
% 121.84/16.13 (contraSubsetComplement) =>
% 121.84/16.13 ((
% 121.84/16.13 (complementTcontraSubset) =>
% 121.84/16.13 ((
% 121.84/16.13 (binunionTILcontra) =>
% 121.84/16.13 ((
% 121.84/16.13 (binunionTIRcontra) =>
% 121.84/16.13 ((
% 121.84/16.13 (inIntersectImpInUnion) =>
% 121.84/16.13 ((
% 121.84/16.13 (inIntersectImpInUnion2) =>
% 121.84/16.13 ((
% 121.84/16.13 (inIntersectImpInIntersectUnions) =>
% 121.84/16.13 ((
% 121.84/16.13 (intersectInPowersetIntersectUnions) =>
% 121.84/16.13 ((
% 121.84/16.13 (inComplementUnionImpNotIn1) =>
% 121.84/16.13 ((
% 121.84/16.13 (inComplementUnionImpInComplement1) =>
% 121.84/16.13 ((
% 121.84/16.13 (binunionTE) =>
% 121.84/16.13 ((
% 121.84/16.13 (binunionTEcontra) =>
% 121.84/16.13 ((
% 121.84/16.13 (demorgan2a1) =>
% 121.84/16.13 ((
% 121.84/16.13 (complementUnionInPowersetComplement) =>
% 121.84/16.13 ((
% 121.84/16.13 (demorgan2a2) =>
% 121.84/16.13 ((
% 121.84/16.13 (demorgan1a) =>
% 121.84/16.13 ((
% 121.84/16.13 (demorgan1b) =>
% 121.84/16.13 ((
% 121.84/16.13 (demorgan1) =>
% 121.84/16.13 ((
% 121.84/16.13 (demorgan2a) =>
% 121.84/16.13 ((
% 121.84/16.13 (demorgan2b2) =>
% 121.84/16.13 ((
% 121.84/16.13 (demorgan2b) =>
% 121.84/16.13 ((
% 121.84/16.13 (demorgan2) =>
% 121.84/16.13 ((
% 121.84/16.13 (woz13rule0) =>
% 121.84/16.13 ((
% 121.84/16.13 (woz13rule1) =>
% 121.84/16.13 ((
% 121.84/16.13 (woz13rule2) =>
% 121.84/16.13 ((
% 121.84/16.13 (woz13rule3) =>
% 121.84/16.13 ((
% 121.84/16.13 (woz13rule4) =>
% 121.84/16.13 ((
% 121.84/16.13 (woz1_1) =>
% 121.84/16.13 ((
% 121.84/16.13 (woz1_2) =>
% 121.84/16.13 ((
% 121.84/16.13 (woz1_3) =>
% 121.84/16.13 ((
% 121.84/16.13 (woz1_4) =>
% 121.84/16.13 ((
% 121.84/16.13 (woz1_5) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1all2) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1SetBreln1) =>
% 121.84/16.13 ((
% 121.84/16.13 (choice2fnsingleton) =>
% 121.84/16.13 ((
% 121.84/16.13 (setOfPairsIsBReln1) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1all1) =>
% 121.84/16.13 ((
% 121.84/16.13 (subbreln1) =>
% 121.84/16.13 ((
% 121.84/16.13 (eqbreln1) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1invprop) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1invI) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1invE) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1compprop) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1compI) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1compE) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1compEex) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1unionprop) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1unionIL) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1unionIR) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1unionI) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1unionE) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1unionEcases) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1unionCommutes) =>
% 121.84/16.13 ((
% 121.84/16.13 (woz2Ex) =>
% 121.84/16.13 ((
% 121.84/16.13 (woz2W) =>
% 121.84/16.13 ((
% 121.84/16.13 (woz2A) =>
% 121.84/16.13 ((
% 121.84/16.13 (woz2B) =>
% 121.84/16.13 ((
% 121.84/16.13 (image1Ex) =>
% 121.84/16.13 ((
% 121.84/16.13 (image1Ex1) =>
% 121.84/16.13 ((
% 121.84/16.13 (image1Equiv) =>
% 121.84/16.13 ((
% 121.84/16.13 (image1E) =>
% 121.84/16.13 ((
% 121.84/16.13 (image1I) =>
% 121.84/16.13 ((
% 121.84/16.13 (injFuncInInjFuncSet) =>
% 121.84/16.13 ((
% 121.84/16.13 (!!) @ (
% 121.84/16.13 (('#B') @ (
% 121.84/16.13 !!) @
% 121.84/16.13 (
% 121.84/16.13 (
% 121.84/16.13 ('#B') @ (
% 121.84/16.13 (
% 121.84/16.13 ('#B') @ (
% 121.84/16.13 !!))) @
% 121.84/16.13 (
% 121.84/16.13 (
% 121.84/16.13 ('#S') @ (
% 121.84/16.13 (
% 121.84/16.13 ('#B') @ (
% 121.84/16.13 '#S') @
% 121.84/16.13 (
% 121.84/16.13 (
% 121.84/16.13 ('#B') @ (
% 121.84/16.13 (
% 121.84/16.13 ('#B') @ (
% 121.84/16.13 '#S'))) @
% 121.84/16.13 (
% 121.84/16.13 (
% 121.84/16.13 ('#B') @ (
% 121.84/16.13 (
% 121.84/16.13 ('#B') @ (
% 121.84/16.13 (
% 121.84/16.13 ('#B') @ (
% 121.84/16.13 =>))))) @
% 121.84/16.13 (
% 121.84/16.13 (
% 121.84/16.13 ('#B') @ (
% 121.84/16.13 (
% 121.84/16.13 ('#B') @ (
% 121.84/16.13 (
% 121.84/16.13 ('#C') @ in)))) @
% 121.84/16.13 injFuncSet)))))))) @
% 121.84/16.13 (
% 121.84/16.13 (
% 121.84/16.13 ('#B') @ (
% 121.84/16.13 (
% 121.84/16.13 ('#B') @ (
% 121.84/16.13 (
% 121.84/16.13 ('#C') @ in)))) @
% 121.84/16.13 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 121.84/16.13 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1096])).
% 121.84/16.13 thf(zip_derived_cl1109, plain,
% 121.84/16.13 (~ (((binunionIR) =>
% 121.84/16.13 (((binunionEcases) =>
% 121.84/16.13 (((binunionE) =>
% 121.84/16.13 (((binunionLsub) =>
% 121.84/16.13 (((binunionRsub) =>
% 121.84/16.13 (((binintersectI) =>
% 121.84/16.13 (((binintersectSubset5) =>
% 121.84/16.13 (((binintersectEL) =>
% 121.84/16.13 (((binintersectLsub) =>
% 121.84/16.13 (((binintersectSubset2) =>
% 121.84/16.13 (((binintersectSubset3) =>
% 121.84/16.13 (((binintersectER) =>
% 121.84/16.13 (((disjointsetsI1) =>
% 121.84/16.13 (((binintersectRsub) =>
% 121.84/16.13 (((binintersectSubset4) =>
% 121.84/16.13 (((binintersectSubset1) =>
% 121.84/16.13 (((bs114d) =>
% 121.84/16.13 (((setminusI) =>
% 121.84/16.13 (((setminusEL) =>
% 121.84/16.13 (((setminusER) =>
% 121.84/16.13 (((setminusSubset2) =>
% 121.84/16.13 (((setminusERneg) =>
% 121.84/16.13 (((setminusELneg) =>
% 121.84/16.13 (((setminusILneg) =>
% 121.84/16.13 (((setminusIRneg) =>
% 121.84/16.13 (((setminusLsub) =>
% 121.84/16.13 (((setminusSubset1) =>
% 121.84/16.13 (((symdiffE) =>
% 121.84/16.13 (((symdiffI1) =>
% 121.84/16.13 (((symdiffI2) =>
% 121.84/16.13 ((
% 121.84/16.13 (symdiffIneg1) =>
% 121.84/16.13 ((
% 121.84/16.13 (symdiffIneg2) =>
% 121.84/16.13 ((
% 121.84/16.13 (secondinupair) =>
% 121.84/16.13 ((
% 121.84/16.13 (setukpairIL) =>
% 121.84/16.13 ((
% 121.84/16.13 (setukpairIR) =>
% 121.84/16.13 ((
% 121.84/16.13 (kpairiskpair) =>
% 121.84/16.13 ((
% 121.84/16.13 (kpairp) =>
% 121.84/16.13 ((
% 121.84/16.13 (singletonsubset) =>
% 121.84/16.13 ((
% 121.84/16.13 (singletoninpowerset) =>
% 121.84/16.13 ((
% 121.84/16.13 (singletoninpowunion) =>
% 121.84/16.13 ((
% 121.84/16.13 (upairset2E) =>
% 121.84/16.13 ((
% 121.84/16.13 (upairsubunion) =>
% 121.84/16.13 ((
% 121.84/16.13 (upairinpowunion) =>
% 121.84/16.13 ((
% 121.84/16.13 (ubforcartprodlem1) =>
% 121.84/16.13 ((
% 121.84/16.13 (ubforcartprodlem2) =>
% 121.84/16.13 ((
% 121.84/16.13 (ubforcartprodlem3) =>
% 121.84/16.13 ((
% 121.84/16.13 (cartprodpairin) =>
% 121.84/16.13 ((
% 121.84/16.13 (cartprodmempair1) =>
% 121.84/16.13 ((
% 121.84/16.13 (cartprodmempair) =>
% 121.84/16.13 ((
% 121.84/16.13 (setunionE2) =>
% 121.84/16.13 ((
% 121.84/16.13 (setunionsingleton1) =>
% 121.84/16.13 ((
% 121.84/16.13 (setunionsingleton2) =>
% 121.84/16.13 ((
% 121.84/16.13 (setunionsingleton) =>
% 121.84/16.13 ((
% 121.84/16.13 (singletonprop) =>
% 121.84/16.13 ((
% 121.84/16.13 (ex1E1) =>
% 121.84/16.13 ((
% 121.84/16.13 (ex1I) =>
% 121.84/16.13 ((
% 121.84/16.13 (ex1I2) =>
% 121.84/16.13 ((
% 121.84/16.13 (singletonsuniq) =>
% 121.84/16.13 ((
% 121.84/16.13 (setukpairinjL1) =>
% 121.84/16.13 ((
% 121.84/16.13 (kfstsingleton) =>
% 121.84/16.13 ((
% 121.84/16.13 (theprop) =>
% 121.84/16.13 ((
% 121.84/16.13 (kfstpairEq) =>
% 121.84/16.13 ((
% 121.84/16.13 (cartprodfstin) =>
% 121.84/16.13 ((
% 121.84/16.13 (setukpairinjL2) =>
% 121.84/16.13 ((
% 121.84/16.13 (setukpairinjL) =>
% 121.84/16.13 ((
% 121.84/16.13 (setukpairinjR11) =>
% 121.84/16.13 ((
% 121.84/16.13 (setukpairinjR12) =>
% 121.84/16.13 ((
% 121.84/16.13 (setukpairinjR1) =>
% 121.84/16.13 ((
% 121.84/16.13 (upairequniteq) =>
% 121.84/16.13 ((
% 121.84/16.13 (setukpairinjR2) =>
% 121.84/16.13 ((
% 121.84/16.13 (setukpairinjR) =>
% 121.84/16.13 ((
% 121.84/16.13 (ksndsingleton) =>
% 121.84/16.13 ((
% 121.84/16.13 (ksndpairEq) =>
% 121.84/16.13 ((
% 121.84/16.13 (kpairsurjEq) =>
% 121.84/16.13 ((
% 121.84/16.13 (cartprodsndin) =>
% 121.84/16.13 ((
% 121.84/16.13 (cartprodpairmemEL) =>
% 121.84/16.13 ((
% 121.84/16.13 (cartprodpairmemER) =>
% 121.84/16.13 ((
% 121.84/16.13 (cartprodmempaircEq) =>
% 121.84/16.13 ((
% 121.84/16.13 (cartprodfstpairEq) =>
% 121.84/16.13 ((
% 121.84/16.13 (cartprodsndpairEq) =>
% 121.84/16.13 ((
% 121.84/16.13 (cartprodpairsurjEq) =>
% 121.84/16.13 ((
% 121.84/16.13 (dpsetconstrI) =>
% 121.84/16.13 ((
% 121.84/16.13 (dpsetconstrSub) =>
% 121.84/16.13 ((
% 121.84/16.13 (setOfPairsIsBReln) =>
% 121.84/16.13 ((
% 121.84/16.13 (dpsetconstrERa) =>
% 121.84/16.13 ((
% 121.84/16.13 (dpsetconstrEL1) =>
% 121.84/16.13 ((
% 121.84/16.13 (dpsetconstrEL2) =>
% 121.84/16.13 ((
% 121.84/16.13 (dpsetconstrER) =>
% 121.84/16.13 ((
% 121.84/16.13 (funcImageSingleton) =>
% 121.84/16.13 ((
% 121.84/16.13 (apProp) =>
% 121.84/16.13 ((
% 121.84/16.13 (app) =>
% 121.84/16.13 ((
% 121.84/16.13 (infuncsetfunc) =>
% 121.84/16.13 ((
% 121.84/16.13 (ap2p) =>
% 121.84/16.13 ((
% 121.84/16.13 (funcinfuncset) =>
% 121.84/16.13 ((
% 121.84/16.13 (lamProp) =>
% 121.84/16.13 ((
% 121.84/16.13 (lamp) =>
% 121.84/16.13 ((
% 121.84/16.13 (lam2p) =>
% 121.84/16.13 ((
% 121.84/16.13 (brelnall1) =>
% 121.84/16.13 ((
% 121.84/16.13 (brelnall2) =>
% 121.84/16.13 ((
% 121.84/16.13 (ex1E2) =>
% 121.84/16.13 ((
% 121.84/16.13 (funcGraphProp1) =>
% 121.84/16.13 ((
% 121.84/16.13 (funcGraphProp3) =>
% 121.84/16.13 ((
% 121.84/16.13 (funcGraphProp2) =>
% 121.84/16.13 ((
% 121.84/16.13 (funcextLem) =>
% 121.84/16.13 ((
% 121.84/16.13 (funcGraphProp4) =>
% 121.84/16.13 ((
% 121.84/16.13 (subbreln) =>
% 121.84/16.13 ((
% 121.84/16.13 (eqbreln) =>
% 121.84/16.13 ((
% 121.84/16.13 (funcext) =>
% 121.84/16.13 ((
% 121.84/16.13 (funcext2) =>
% 121.84/16.13 ((
% 121.84/16.13 (ap2apEq1) =>
% 121.84/16.13 ((
% 121.84/16.13 (ap2apEq2) =>
% 121.84/16.13 ((
% 121.84/16.13 (beta1) =>
% 121.84/16.13 ((
% 121.84/16.13 (eta1) =>
% 121.84/16.13 ((
% 121.84/16.13 (lam2lamEq) =>
% 121.84/16.13 ((
% 121.84/16.13 (beta2) =>
% 121.84/16.13 ((
% 121.84/16.13 (eta2) =>
% 121.84/16.13 ((
% 121.84/16.13 (iffalseProp1) =>
% 121.84/16.13 ((
% 121.84/16.13 (iffalseProp2) =>
% 121.84/16.13 ((
% 121.84/16.13 (iftrueProp1) =>
% 121.84/16.13 ((
% 121.84/16.13 (iftrueProp2) =>
% 121.84/16.13 ((
% 121.84/16.13 (ifSingleton) =>
% 121.84/16.13 ((
% 121.84/16.13 (ifp) =>
% 121.84/16.13 ((
% 121.84/16.13 (theeq) =>
% 121.84/16.13 ((
% 121.84/16.13 (iftrue) =>
% 121.84/16.13 ((
% 121.84/16.13 (iffalse) =>
% 121.84/16.13 ((
% 121.84/16.13 (iftrueorfalse) =>
% 121.84/16.13 ((
% 121.84/16.13 (binintersectT_lem) =>
% 121.84/16.13 ((
% 121.84/16.13 (binunionT_lem) =>
% 121.84/16.13 ((
% 121.84/16.13 (powersetT_lem) =>
% 121.84/16.13 ((
% 121.84/16.13 (setminusT_lem) =>
% 121.84/16.13 ((
% 121.84/16.13 (complementT_lem) =>
% 121.84/16.13 ((
% 121.84/16.13 (setextT) =>
% 121.84/16.13 ((
% 121.84/16.13 (subsetTI) =>
% 121.84/16.13 ((
% 121.84/16.13 (powersetTI1) =>
% 121.84/16.13 ((
% 121.84/16.13 (powersetTE1) =>
% 121.84/16.13 ((
% 121.84/16.13 (complementTI1) =>
% 121.84/16.13 ((
% 121.84/16.13 (complementTE1) =>
% 121.84/16.13 ((
% 121.84/16.13 (binintersectTELcontra) =>
% 121.84/16.13 ((
% 121.84/16.13 (binintersectTERcontra) =>
% 121.84/16.13 ((
% 121.84/16.13 (contrasubsetT) =>
% 121.84/16.13 ((
% 121.84/16.13 (contrasubsetT1) =>
% 121.84/16.13 ((
% 121.84/16.13 (contrasubsetT2) =>
% 121.84/16.13 ((
% 121.84/16.13 (contrasubsetT3) =>
% 121.84/16.13 ((
% 121.84/16.13 (doubleComplementI1) =>
% 121.84/16.13 ((
% 121.84/16.13 (doubleComplementE1) =>
% 121.84/16.13 ((
% 121.84/16.13 (doubleComplementSub1) =>
% 121.84/16.13 ((
% 121.84/16.13 (doubleComplementSub2) =>
% 121.84/16.13 ((
% 121.84/16.13 (doubleComplementEq) =>
% 121.84/16.13 ((
% 121.84/16.13 (complementTnotintersectT) =>
% 121.84/16.13 ((
% 121.84/16.13 (complementImpComplementIntersect) =>
% 121.84/16.13 ((
% 121.84/16.13 (complementSubsetComplementIntersect) =>
% 121.84/16.13 ((
% 121.84/16.13 (complementInPowersetComplementIntersect) =>
% 121.84/16.13 ((
% 121.84/16.13 (contraSubsetComplement) =>
% 121.84/16.13 ((
% 121.84/16.13 (complementTcontraSubset) =>
% 121.84/16.13 ((
% 121.84/16.13 (binunionTILcontra) =>
% 121.84/16.13 ((
% 121.84/16.13 (binunionTIRcontra) =>
% 121.84/16.13 ((
% 121.84/16.13 (inIntersectImpInUnion) =>
% 121.84/16.13 ((
% 121.84/16.13 (inIntersectImpInUnion2) =>
% 121.84/16.13 ((
% 121.84/16.13 (inIntersectImpInIntersectUnions) =>
% 121.84/16.13 ((
% 121.84/16.13 (intersectInPowersetIntersectUnions) =>
% 121.84/16.13 ((
% 121.84/16.13 (inComplementUnionImpNotIn1) =>
% 121.84/16.13 ((
% 121.84/16.13 (inComplementUnionImpInComplement1) =>
% 121.84/16.13 ((
% 121.84/16.13 (binunionTE) =>
% 121.84/16.13 ((
% 121.84/16.13 (binunionTEcontra) =>
% 121.84/16.13 ((
% 121.84/16.13 (demorgan2a1) =>
% 121.84/16.13 ((
% 121.84/16.13 (complementUnionInPowersetComplement) =>
% 121.84/16.13 ((
% 121.84/16.13 (demorgan2a2) =>
% 121.84/16.13 ((
% 121.84/16.13 (demorgan1a) =>
% 121.84/16.13 ((
% 121.84/16.13 (demorgan1b) =>
% 121.84/16.13 ((
% 121.84/16.13 (demorgan1) =>
% 121.84/16.13 ((
% 121.84/16.13 (demorgan2a) =>
% 121.84/16.13 ((
% 121.84/16.13 (demorgan2b2) =>
% 121.84/16.13 ((
% 121.84/16.13 (demorgan2b) =>
% 121.84/16.13 ((
% 121.84/16.13 (demorgan2) =>
% 121.84/16.13 ((
% 121.84/16.13 (woz13rule0) =>
% 121.84/16.13 ((
% 121.84/16.13 (woz13rule1) =>
% 121.84/16.13 ((
% 121.84/16.13 (woz13rule2) =>
% 121.84/16.13 ((
% 121.84/16.13 (woz13rule3) =>
% 121.84/16.13 ((
% 121.84/16.13 (woz13rule4) =>
% 121.84/16.13 ((
% 121.84/16.13 (woz1_1) =>
% 121.84/16.13 ((
% 121.84/16.13 (woz1_2) =>
% 121.84/16.13 ((
% 121.84/16.13 (woz1_3) =>
% 121.84/16.13 ((
% 121.84/16.13 (woz1_4) =>
% 121.84/16.13 ((
% 121.84/16.13 (woz1_5) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1all2) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1SetBreln1) =>
% 121.84/16.13 ((
% 121.84/16.13 (choice2fnsingleton) =>
% 121.84/16.13 ((
% 121.84/16.13 (setOfPairsIsBReln1) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1all1) =>
% 121.84/16.13 ((
% 121.84/16.13 (subbreln1) =>
% 121.84/16.13 ((
% 121.84/16.13 (eqbreln1) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1invprop) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1invI) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1invE) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1compprop) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1compI) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1compE) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1compEex) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1unionprop) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1unionIL) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1unionIR) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1unionI) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1unionE) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1unionEcases) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1unionCommutes) =>
% 121.84/16.13 ((
% 121.84/16.13 (woz2Ex) =>
% 121.84/16.13 ((
% 121.84/16.13 (woz2W) =>
% 121.84/16.13 ((
% 121.84/16.13 (woz2A) =>
% 121.84/16.13 ((
% 121.84/16.13 (woz2B) =>
% 121.84/16.13 ((
% 121.84/16.13 (image1Ex) =>
% 121.84/16.13 ((
% 121.84/16.13 (image1Ex1) =>
% 121.84/16.13 ((
% 121.84/16.13 (image1Equiv) =>
% 121.84/16.13 ((
% 121.84/16.13 (image1E) =>
% 121.84/16.13 ((
% 121.84/16.13 (image1I) =>
% 121.84/16.13 ((
% 121.84/16.13 (injFuncInInjFuncSet) =>
% 121.84/16.13 ((
% 121.84/16.13 (!!) @ (
% 121.84/16.13 (('#B') @ (
% 121.84/16.13 !!) @
% 121.84/16.13 (
% 121.84/16.13 (
% 121.84/16.13 ('#B') @ (
% 121.84/16.13 (
% 121.84/16.13 ('#B') @ (
% 121.84/16.13 !!))) @
% 121.84/16.13 (
% 121.84/16.13 (
% 121.84/16.13 ('#S') @ (
% 121.84/16.13 (
% 121.84/16.13 ('#B') @ (
% 121.84/16.13 '#S') @
% 121.84/16.13 (
% 121.84/16.13 (
% 121.84/16.13 ('#B') @ (
% 121.84/16.13 (
% 121.84/16.13 ('#B') @ (
% 121.84/16.13 '#S'))) @
% 121.84/16.13 (
% 121.84/16.13 (
% 121.84/16.13 ('#B') @ (
% 121.84/16.13 (
% 121.84/16.13 ('#B') @ (
% 121.84/16.13 (
% 121.84/16.13 ('#B') @ (
% 121.84/16.13 =>))))) @
% 121.84/16.13 (
% 121.84/16.13 (
% 121.84/16.13 ('#B') @ (
% 121.84/16.13 (
% 121.84/16.13 ('#B') @ (
% 121.84/16.13 (
% 121.84/16.13 ('#C') @ in)))) @
% 121.84/16.13 injFuncSet)))))))) @
% 121.84/16.13 (
% 121.84/16.13 (
% 121.84/16.13 ('#B') @ (
% 121.84/16.13 (
% 121.84/16.13 ('#B') @ (
% 121.84/16.13 (
% 121.84/16.13 ('#C') @ in)))) @
% 121.84/16.13 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 121.84/16.13 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1102])).
% 121.84/16.13 thf(zip_derived_cl1115, plain,
% 121.84/16.13 (~ (((binunionEcases) =>
% 121.84/16.13 (((binunionE) =>
% 121.84/16.13 (((binunionLsub) =>
% 121.84/16.13 (((binunionRsub) =>
% 121.84/16.13 (((binintersectI) =>
% 121.84/16.13 (((binintersectSubset5) =>
% 121.84/16.13 (((binintersectEL) =>
% 121.84/16.13 (((binintersectLsub) =>
% 121.84/16.13 (((binintersectSubset2) =>
% 121.84/16.13 (((binintersectSubset3) =>
% 121.84/16.13 (((binintersectER) =>
% 121.84/16.13 (((disjointsetsI1) =>
% 121.84/16.13 (((binintersectRsub) =>
% 121.84/16.13 (((binintersectSubset4) =>
% 121.84/16.13 (((binintersectSubset1) =>
% 121.84/16.13 (((bs114d) =>
% 121.84/16.13 (((setminusI) =>
% 121.84/16.13 (((setminusEL) =>
% 121.84/16.13 (((setminusER) =>
% 121.84/16.13 (((setminusSubset2) =>
% 121.84/16.13 (((setminusERneg) =>
% 121.84/16.13 (((setminusELneg) =>
% 121.84/16.13 (((setminusILneg) =>
% 121.84/16.13 (((setminusIRneg) =>
% 121.84/16.13 (((setminusLsub) =>
% 121.84/16.13 (((setminusSubset1) =>
% 121.84/16.13 (((symdiffE) =>
% 121.84/16.13 (((symdiffI1) =>
% 121.84/16.13 (((symdiffI2) =>
% 121.84/16.13 (((symdiffIneg1) =>
% 121.84/16.13 ((
% 121.84/16.13 (symdiffIneg2) =>
% 121.84/16.13 ((
% 121.84/16.13 (secondinupair) =>
% 121.84/16.13 ((
% 121.84/16.13 (setukpairIL) =>
% 121.84/16.13 ((
% 121.84/16.13 (setukpairIR) =>
% 121.84/16.13 ((
% 121.84/16.13 (kpairiskpair) =>
% 121.84/16.13 ((
% 121.84/16.13 (kpairp) =>
% 121.84/16.13 ((
% 121.84/16.13 (singletonsubset) =>
% 121.84/16.13 ((
% 121.84/16.13 (singletoninpowerset) =>
% 121.84/16.13 ((
% 121.84/16.13 (singletoninpowunion) =>
% 121.84/16.13 ((
% 121.84/16.13 (upairset2E) =>
% 121.84/16.13 ((
% 121.84/16.13 (upairsubunion) =>
% 121.84/16.13 ((
% 121.84/16.13 (upairinpowunion) =>
% 121.84/16.13 ((
% 121.84/16.13 (ubforcartprodlem1) =>
% 121.84/16.13 ((
% 121.84/16.13 (ubforcartprodlem2) =>
% 121.84/16.13 ((
% 121.84/16.13 (ubforcartprodlem3) =>
% 121.84/16.13 ((
% 121.84/16.13 (cartprodpairin) =>
% 121.84/16.13 ((
% 121.84/16.13 (cartprodmempair1) =>
% 121.84/16.13 ((
% 121.84/16.13 (cartprodmempair) =>
% 121.84/16.13 ((
% 121.84/16.13 (setunionE2) =>
% 121.84/16.13 ((
% 121.84/16.13 (setunionsingleton1) =>
% 121.84/16.13 ((
% 121.84/16.13 (setunionsingleton2) =>
% 121.84/16.13 ((
% 121.84/16.13 (setunionsingleton) =>
% 121.84/16.13 ((
% 121.84/16.13 (singletonprop) =>
% 121.84/16.13 ((
% 121.84/16.13 (ex1E1) =>
% 121.84/16.13 ((
% 121.84/16.13 (ex1I) =>
% 121.84/16.13 ((
% 121.84/16.13 (ex1I2) =>
% 121.84/16.13 ((
% 121.84/16.13 (singletonsuniq) =>
% 121.84/16.13 ((
% 121.84/16.13 (setukpairinjL1) =>
% 121.84/16.13 ((
% 121.84/16.13 (kfstsingleton) =>
% 121.84/16.13 ((
% 121.84/16.13 (theprop) =>
% 121.84/16.13 ((
% 121.84/16.13 (kfstpairEq) =>
% 121.84/16.13 ((
% 121.84/16.13 (cartprodfstin) =>
% 121.84/16.13 ((
% 121.84/16.13 (setukpairinjL2) =>
% 121.84/16.13 ((
% 121.84/16.13 (setukpairinjL) =>
% 121.84/16.13 ((
% 121.84/16.13 (setukpairinjR11) =>
% 121.84/16.13 ((
% 121.84/16.13 (setukpairinjR12) =>
% 121.84/16.13 ((
% 121.84/16.13 (setukpairinjR1) =>
% 121.84/16.13 ((
% 121.84/16.13 (upairequniteq) =>
% 121.84/16.13 ((
% 121.84/16.13 (setukpairinjR2) =>
% 121.84/16.13 ((
% 121.84/16.13 (setukpairinjR) =>
% 121.84/16.13 ((
% 121.84/16.13 (ksndsingleton) =>
% 121.84/16.13 ((
% 121.84/16.13 (ksndpairEq) =>
% 121.84/16.13 ((
% 121.84/16.13 (kpairsurjEq) =>
% 121.84/16.13 ((
% 121.84/16.13 (cartprodsndin) =>
% 121.84/16.13 ((
% 121.84/16.13 (cartprodpairmemEL) =>
% 121.84/16.13 ((
% 121.84/16.13 (cartprodpairmemER) =>
% 121.84/16.13 ((
% 121.84/16.13 (cartprodmempaircEq) =>
% 121.84/16.13 ((
% 121.84/16.13 (cartprodfstpairEq) =>
% 121.84/16.13 ((
% 121.84/16.13 (cartprodsndpairEq) =>
% 121.84/16.13 ((
% 121.84/16.13 (cartprodpairsurjEq) =>
% 121.84/16.13 ((
% 121.84/16.13 (dpsetconstrI) =>
% 121.84/16.13 ((
% 121.84/16.13 (dpsetconstrSub) =>
% 121.84/16.13 ((
% 121.84/16.13 (setOfPairsIsBReln) =>
% 121.84/16.13 ((
% 121.84/16.13 (dpsetconstrERa) =>
% 121.84/16.13 ((
% 121.84/16.13 (dpsetconstrEL1) =>
% 121.84/16.13 ((
% 121.84/16.13 (dpsetconstrEL2) =>
% 121.84/16.13 ((
% 121.84/16.13 (dpsetconstrER) =>
% 121.84/16.13 ((
% 121.84/16.13 (funcImageSingleton) =>
% 121.84/16.13 ((
% 121.84/16.13 (apProp) =>
% 121.84/16.13 ((
% 121.84/16.13 (app) =>
% 121.84/16.13 ((
% 121.84/16.13 (infuncsetfunc) =>
% 121.84/16.13 ((
% 121.84/16.13 (ap2p) =>
% 121.84/16.13 ((
% 121.84/16.13 (funcinfuncset) =>
% 121.84/16.13 ((
% 121.84/16.13 (lamProp) =>
% 121.84/16.13 ((
% 121.84/16.13 (lamp) =>
% 121.84/16.13 ((
% 121.84/16.13 (lam2p) =>
% 121.84/16.13 ((
% 121.84/16.13 (brelnall1) =>
% 121.84/16.13 ((
% 121.84/16.13 (brelnall2) =>
% 121.84/16.13 ((
% 121.84/16.13 (ex1E2) =>
% 121.84/16.13 ((
% 121.84/16.13 (funcGraphProp1) =>
% 121.84/16.13 ((
% 121.84/16.13 (funcGraphProp3) =>
% 121.84/16.13 ((
% 121.84/16.13 (funcGraphProp2) =>
% 121.84/16.13 ((
% 121.84/16.13 (funcextLem) =>
% 121.84/16.13 ((
% 121.84/16.13 (funcGraphProp4) =>
% 121.84/16.13 ((
% 121.84/16.13 (subbreln) =>
% 121.84/16.13 ((
% 121.84/16.13 (eqbreln) =>
% 121.84/16.13 ((
% 121.84/16.13 (funcext) =>
% 121.84/16.13 ((
% 121.84/16.13 (funcext2) =>
% 121.84/16.13 ((
% 121.84/16.13 (ap2apEq1) =>
% 121.84/16.13 ((
% 121.84/16.13 (ap2apEq2) =>
% 121.84/16.13 ((
% 121.84/16.13 (beta1) =>
% 121.84/16.13 ((
% 121.84/16.13 (eta1) =>
% 121.84/16.13 ((
% 121.84/16.13 (lam2lamEq) =>
% 121.84/16.13 ((
% 121.84/16.13 (beta2) =>
% 121.84/16.13 ((
% 121.84/16.13 (eta2) =>
% 121.84/16.13 ((
% 121.84/16.13 (iffalseProp1) =>
% 121.84/16.13 ((
% 121.84/16.13 (iffalseProp2) =>
% 121.84/16.13 ((
% 121.84/16.13 (iftrueProp1) =>
% 121.84/16.13 ((
% 121.84/16.13 (iftrueProp2) =>
% 121.84/16.13 ((
% 121.84/16.13 (ifSingleton) =>
% 121.84/16.13 ((
% 121.84/16.13 (ifp) =>
% 121.84/16.13 ((
% 121.84/16.13 (theeq) =>
% 121.84/16.13 ((
% 121.84/16.13 (iftrue) =>
% 121.84/16.13 ((
% 121.84/16.13 (iffalse) =>
% 121.84/16.13 ((
% 121.84/16.13 (iftrueorfalse) =>
% 121.84/16.13 ((
% 121.84/16.13 (binintersectT_lem) =>
% 121.84/16.13 ((
% 121.84/16.13 (binunionT_lem) =>
% 121.84/16.13 ((
% 121.84/16.13 (powersetT_lem) =>
% 121.84/16.13 ((
% 121.84/16.13 (setminusT_lem) =>
% 121.84/16.13 ((
% 121.84/16.13 (complementT_lem) =>
% 121.84/16.13 ((
% 121.84/16.13 (setextT) =>
% 121.84/16.13 ((
% 121.84/16.13 (subsetTI) =>
% 121.84/16.13 ((
% 121.84/16.13 (powersetTI1) =>
% 121.84/16.13 ((
% 121.84/16.13 (powersetTE1) =>
% 121.84/16.13 ((
% 121.84/16.13 (complementTI1) =>
% 121.84/16.13 ((
% 121.84/16.13 (complementTE1) =>
% 121.84/16.13 ((
% 121.84/16.13 (binintersectTELcontra) =>
% 121.84/16.13 ((
% 121.84/16.13 (binintersectTERcontra) =>
% 121.84/16.13 ((
% 121.84/16.13 (contrasubsetT) =>
% 121.84/16.13 ((
% 121.84/16.13 (contrasubsetT1) =>
% 121.84/16.13 ((
% 121.84/16.13 (contrasubsetT2) =>
% 121.84/16.13 ((
% 121.84/16.13 (contrasubsetT3) =>
% 121.84/16.13 ((
% 121.84/16.13 (doubleComplementI1) =>
% 121.84/16.13 ((
% 121.84/16.13 (doubleComplementE1) =>
% 121.84/16.13 ((
% 121.84/16.13 (doubleComplementSub1) =>
% 121.84/16.13 ((
% 121.84/16.13 (doubleComplementSub2) =>
% 121.84/16.13 ((
% 121.84/16.13 (doubleComplementEq) =>
% 121.84/16.13 ((
% 121.84/16.13 (complementTnotintersectT) =>
% 121.84/16.13 ((
% 121.84/16.13 (complementImpComplementIntersect) =>
% 121.84/16.13 ((
% 121.84/16.13 (complementSubsetComplementIntersect) =>
% 121.84/16.13 ((
% 121.84/16.13 (complementInPowersetComplementIntersect) =>
% 121.84/16.13 ((
% 121.84/16.13 (contraSubsetComplement) =>
% 121.84/16.13 ((
% 121.84/16.13 (complementTcontraSubset) =>
% 121.84/16.13 ((
% 121.84/16.13 (binunionTILcontra) =>
% 121.84/16.13 ((
% 121.84/16.13 (binunionTIRcontra) =>
% 121.84/16.13 ((
% 121.84/16.13 (inIntersectImpInUnion) =>
% 121.84/16.13 ((
% 121.84/16.13 (inIntersectImpInUnion2) =>
% 121.84/16.13 ((
% 121.84/16.13 (inIntersectImpInIntersectUnions) =>
% 121.84/16.13 ((
% 121.84/16.13 (intersectInPowersetIntersectUnions) =>
% 121.84/16.13 ((
% 121.84/16.13 (inComplementUnionImpNotIn1) =>
% 121.84/16.13 ((
% 121.84/16.13 (inComplementUnionImpInComplement1) =>
% 121.84/16.13 ((
% 121.84/16.13 (binunionTE) =>
% 121.84/16.13 ((
% 121.84/16.13 (binunionTEcontra) =>
% 121.84/16.13 ((
% 121.84/16.13 (demorgan2a1) =>
% 121.84/16.13 ((
% 121.84/16.13 (complementUnionInPowersetComplement) =>
% 121.84/16.13 ((
% 121.84/16.13 (demorgan2a2) =>
% 121.84/16.13 ((
% 121.84/16.13 (demorgan1a) =>
% 121.84/16.13 ((
% 121.84/16.13 (demorgan1b) =>
% 121.84/16.13 ((
% 121.84/16.13 (demorgan1) =>
% 121.84/16.13 ((
% 121.84/16.13 (demorgan2a) =>
% 121.84/16.13 ((
% 121.84/16.13 (demorgan2b2) =>
% 121.84/16.13 ((
% 121.84/16.13 (demorgan2b) =>
% 121.84/16.13 ((
% 121.84/16.13 (demorgan2) =>
% 121.84/16.13 ((
% 121.84/16.13 (woz13rule0) =>
% 121.84/16.13 ((
% 121.84/16.13 (woz13rule1) =>
% 121.84/16.13 ((
% 121.84/16.13 (woz13rule2) =>
% 121.84/16.13 ((
% 121.84/16.13 (woz13rule3) =>
% 121.84/16.13 ((
% 121.84/16.13 (woz13rule4) =>
% 121.84/16.13 ((
% 121.84/16.13 (woz1_1) =>
% 121.84/16.13 ((
% 121.84/16.13 (woz1_2) =>
% 121.84/16.13 ((
% 121.84/16.13 (woz1_3) =>
% 121.84/16.13 ((
% 121.84/16.13 (woz1_4) =>
% 121.84/16.13 ((
% 121.84/16.13 (woz1_5) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1all2) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1SetBreln1) =>
% 121.84/16.13 ((
% 121.84/16.13 (choice2fnsingleton) =>
% 121.84/16.13 ((
% 121.84/16.13 (setOfPairsIsBReln1) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1all1) =>
% 121.84/16.13 ((
% 121.84/16.13 (subbreln1) =>
% 121.84/16.13 ((
% 121.84/16.13 (eqbreln1) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1invprop) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1invI) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1invE) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1compprop) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1compI) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1compE) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1compEex) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1unionprop) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1unionIL) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1unionIR) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1unionI) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1unionE) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1unionEcases) =>
% 121.84/16.13 ((
% 121.84/16.13 (breln1unionCommutes) =>
% 121.84/16.13 ((
% 121.84/16.13 (woz2Ex) =>
% 121.84/16.13 ((
% 121.84/16.13 (woz2W) =>
% 121.84/16.13 ((
% 121.84/16.13 (woz2A) =>
% 121.84/16.13 ((
% 121.84/16.13 (woz2B) =>
% 121.84/16.13 ((
% 121.84/16.13 (image1Ex) =>
% 121.84/16.13 ((
% 121.84/16.13 (image1Ex1) =>
% 121.84/16.13 ((
% 121.84/16.13 (image1Equiv) =>
% 121.84/16.13 ((
% 121.84/16.13 (image1E) =>
% 121.84/16.13 ((
% 121.84/16.13 (image1I) =>
% 121.84/16.13 ((
% 121.84/16.13 (injFuncInInjFuncSet) =>
% 121.84/16.13 ((
% 121.84/16.13 (!!) @ (
% 121.84/16.13 (('#B') @ (
% 121.84/16.13 !!) @
% 121.84/16.13 (
% 121.84/16.13 (
% 121.84/16.13 ('#B') @ (
% 121.84/16.13 (
% 121.84/16.13 ('#B') @ (
% 121.84/16.13 !!))) @
% 121.84/16.13 (
% 121.84/16.13 (
% 121.84/16.13 ('#S') @ (
% 121.84/16.13 (
% 121.84/16.13 ('#B') @ (
% 121.84/16.13 '#S') @
% 121.84/16.13 (
% 121.84/16.13 (
% 121.84/16.13 ('#B') @ (
% 121.84/16.13 (
% 121.84/16.13 ('#B') @ (
% 121.84/16.13 '#S'))) @
% 121.84/16.13 (
% 121.84/16.13 (
% 121.84/16.13 ('#B') @ (
% 121.84/16.13 (
% 121.84/16.13 ('#B') @ (
% 121.84/16.13 (
% 121.84/16.13 ('#B') @ (
% 121.84/16.13 =>))))) @
% 121.84/16.13 (
% 121.84/16.13 (
% 121.84/16.13 ('#B') @ (
% 121.84/16.13 (
% 121.84/16.13 ('#B') @ (
% 121.84/16.13 (
% 121.84/16.13 ('#C') @ in)))) @
% 121.84/16.13 injFuncSet)))))))) @
% 121.84/16.13 (
% 121.84/16.13 (
% 121.84/16.13 ('#B') @ (
% 121.84/16.13 (
% 121.84/16.13 ('#B') @ (
% 121.84/16.13 (
% 121.84/16.13 ('#C') @ in)))) @
% 121.84/16.13 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 121.84/16.13 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1109])).
% 121.84/16.13 thf(zip_derived_cl1121, plain,
% 121.84/16.13 (~ (((binunionE) =>
% 121.84/16.13 (((binunionLsub) =>
% 121.84/16.13 (((binunionRsub) =>
% 121.84/16.13 (((binintersectI) =>
% 121.84/16.13 (((binintersectSubset5) =>
% 121.84/16.13 (((binintersectEL) =>
% 121.84/16.13 (((binintersectLsub) =>
% 121.84/16.13 (((binintersectSubset2) =>
% 121.84/16.13 (((binintersectSubset3) =>
% 121.84/16.13 (((binintersectER) =>
% 121.84/16.13 (((disjointsetsI1) =>
% 121.84/16.13 (((binintersectRsub) =>
% 121.84/16.13 (((binintersectSubset4) =>
% 121.84/16.13 (((binintersectSubset1) =>
% 121.84/16.13 (((bs114d) =>
% 121.84/16.13 (((setminusI) =>
% 121.84/16.13 (((setminusEL) =>
% 121.84/16.13 (((setminusER) =>
% 121.84/16.13 (((setminusSubset2) =>
% 121.84/16.13 (((setminusERneg) =>
% 121.84/16.13 (((setminusELneg) =>
% 121.84/16.13 (((setminusILneg) =>
% 121.84/16.13 (((setminusIRneg) =>
% 121.84/16.13 (((setminusLsub) =>
% 121.84/16.13 (((setminusSubset1) =>
% 121.84/16.13 (((symdiffE) =>
% 121.84/16.13 (((symdiffI1) =>
% 121.84/16.13 (((symdiffI2) =>
% 121.84/16.13 (((symdiffIneg1) =>
% 121.84/16.13 (((symdiffIneg2) =>
% 121.84/16.13 ((
% 121.84/16.13 (secondinupair) =>
% 121.84/16.13 ((
% 121.84/16.13 (setukpairIL) =>
% 121.84/16.13 ((
% 121.84/16.13 (setukpairIR) =>
% 121.84/16.13 ((
% 121.84/16.13 (kpairiskpair) =>
% 121.84/16.13 ((
% 121.84/16.13 (kpairp) =>
% 121.84/16.13 ((
% 121.84/16.13 (singletonsubset) =>
% 121.84/16.13 ((
% 121.84/16.13 (singletoninpowerset) =>
% 121.84/16.13 ((
% 121.84/16.13 (singletoninpowunion) =>
% 121.84/16.13 ((
% 121.84/16.13 (upairset2E) =>
% 121.84/16.13 ((
% 121.84/16.13 (upairsubunion) =>
% 121.84/16.13 ((
% 121.84/16.13 (upairinpowunion) =>
% 121.84/16.13 ((
% 121.84/16.13 (ubforcartprodlem1) =>
% 121.84/16.13 ((
% 121.84/16.13 (ubforcartprodlem2) =>
% 121.84/16.13 ((
% 121.84/16.13 (ubforcartprodlem3) =>
% 121.84/16.13 ((
% 121.84/16.13 (cartprodpairin) =>
% 121.84/16.13 ((
% 121.84/16.13 (cartprodmempair1) =>
% 121.84/16.13 ((
% 121.84/16.13 (cartprodmempair) =>
% 121.84/16.13 ((
% 121.84/16.13 (setunionE2) =>
% 121.84/16.13 ((
% 121.84/16.13 (setunionsingleton1) =>
% 121.84/16.13 ((
% 121.84/16.13 (setunionsingleton2) =>
% 121.84/16.13 ((
% 121.84/16.13 (setunionsingleton) =>
% 121.84/16.13 ((
% 121.84/16.13 (singletonprop) =>
% 121.84/16.13 ((
% 121.84/16.13 (ex1E1) =>
% 121.84/16.13 ((
% 121.84/16.13 (ex1I) =>
% 121.84/16.13 ((
% 121.84/16.13 (ex1I2) =>
% 121.84/16.13 ((
% 121.84/16.13 (singletonsuniq) =>
% 121.84/16.13 ((
% 121.84/16.13 (setukpairinjL1) =>
% 121.84/16.13 ((
% 121.84/16.13 (kfstsingleton) =>
% 121.84/16.13 ((
% 121.84/16.13 (theprop) =>
% 121.84/16.13 ((
% 121.84/16.13 (kfstpairEq) =>
% 121.84/16.13 ((
% 121.84/16.13 (cartprodfstin) =>
% 121.84/16.13 ((
% 121.84/16.13 (setukpairinjL2) =>
% 121.84/16.13 ((
% 121.84/16.13 (setukpairinjL) =>
% 121.84/16.13 ((
% 121.84/16.13 (setukpairinjR11) =>
% 121.84/16.13 ((
% 121.84/16.13 (setukpairinjR12) =>
% 121.84/16.13 ((
% 121.84/16.13 (setukpairinjR1) =>
% 121.84/16.13 ((
% 121.84/16.13 (upairequniteq) =>
% 121.84/16.13 ((
% 121.84/16.13 (setukpairinjR2) =>
% 121.84/16.13 ((
% 121.84/16.13 (setukpairinjR) =>
% 121.84/16.13 ((
% 121.84/16.13 (ksndsingleton) =>
% 121.84/16.13 ((
% 121.84/16.13 (ksndpairEq) =>
% 121.84/16.13 ((
% 121.84/16.13 (kpairsurjEq) =>
% 121.84/16.13 ((
% 121.84/16.13 (cartprodsndin) =>
% 121.84/16.13 ((
% 121.84/16.13 (cartprodpairmemEL) =>
% 121.84/16.13 ((
% 121.84/16.13 (cartprodpairmemER) =>
% 121.84/16.13 ((
% 121.84/16.13 (cartprodmempaircEq) =>
% 121.84/16.13 ((
% 121.84/16.13 (cartprodfstpairEq) =>
% 121.84/16.13 ((
% 121.84/16.13 (cartprodsndpairEq) =>
% 121.84/16.13 ((
% 121.84/16.13 (cartprodpairsurjEq) =>
% 121.84/16.13 ((
% 121.84/16.13 (dpsetconstrI) =>
% 121.84/16.13 ((
% 121.84/16.13 (dpsetconstrSub) =>
% 121.84/16.13 ((
% 121.84/16.13 (setOfPairsIsBReln) =>
% 121.84/16.13 ((
% 121.84/16.13 (dpsetconstrERa) =>
% 121.84/16.13 ((
% 121.84/16.13 (dpsetconstrEL1) =>
% 121.84/16.13 ((
% 121.84/16.13 (dpsetconstrEL2) =>
% 121.84/16.13 ((
% 121.84/16.13 (dpsetconstrER) =>
% 121.84/16.13 ((
% 121.84/16.13 (funcImageSingleton) =>
% 121.84/16.13 ((
% 121.84/16.13 (apProp) =>
% 121.84/16.13 ((
% 121.84/16.13 (app) =>
% 121.84/16.13 ((
% 121.84/16.13 (infuncsetfunc) =>
% 121.84/16.13 ((
% 121.84/16.13 (ap2p) =>
% 121.84/16.13 ((
% 121.84/16.13 (funcinfuncset) =>
% 121.84/16.13 ((
% 121.84/16.13 (lamProp) =>
% 121.84/16.13 ((
% 121.84/16.13 (lamp) =>
% 121.84/16.13 ((
% 121.84/16.13 (lam2p) =>
% 121.84/16.13 ((
% 121.84/16.13 (brelnall1) =>
% 121.84/16.13 ((
% 121.84/16.13 (brelnall2) =>
% 121.84/16.13 ((
% 121.84/16.13 (ex1E2) =>
% 121.84/16.13 ((
% 121.84/16.13 (funcGraphProp1) =>
% 121.84/16.13 ((
% 121.84/16.13 (funcGraphProp3) =>
% 121.84/16.13 ((
% 121.84/16.13 (funcGraphProp2) =>
% 121.84/16.13 ((
% 121.84/16.13 (funcextLem) =>
% 121.84/16.13 ((
% 121.84/16.13 (funcGraphProp4) =>
% 121.84/16.13 ((
% 121.84/16.13 (subbreln) =>
% 121.84/16.13 ((
% 121.84/16.13 (eqbreln) =>
% 121.84/16.13 ((
% 121.84/16.13 (funcext) =>
% 121.84/16.13 ((
% 121.84/16.13 (funcext2) =>
% 121.84/16.13 ((
% 121.84/16.13 (ap2apEq1) =>
% 121.84/16.13 ((
% 121.84/16.13 (ap2apEq2) =>
% 121.84/16.13 ((
% 121.84/16.13 (beta1) =>
% 121.84/16.13 ((
% 121.84/16.13 (eta1) =>
% 121.84/16.13 ((
% 121.84/16.13 (lam2lamEq) =>
% 121.84/16.13 ((
% 121.84/16.13 (beta2) =>
% 121.84/16.13 ((
% 121.84/16.13 (eta2) =>
% 121.84/16.13 ((
% 121.84/16.13 (iffalseProp1) =>
% 121.84/16.13 ((
% 121.84/16.13 (iffalseProp2) =>
% 121.84/16.13 ((
% 121.84/16.13 (iftrueProp1) =>
% 121.84/16.13 ((
% 121.84/16.13 (iftrueProp2) =>
% 121.84/16.13 ((
% 121.84/16.13 (ifSingleton) =>
% 121.84/16.13 ((
% 121.84/16.13 (ifp) =>
% 121.84/16.13 ((
% 121.84/16.13 (theeq) =>
% 121.84/16.13 ((
% 121.84/16.13 (iftrue) =>
% 121.84/16.13 ((
% 121.84/16.13 (iffalse) =>
% 121.84/16.13 ((
% 121.84/16.13 (iftrueorfalse) =>
% 121.84/16.13 ((
% 121.84/16.13 (binintersectT_lem) =>
% 121.84/16.13 ((
% 121.84/16.13 (binunionT_lem) =>
% 121.84/16.13 ((
% 121.84/16.13 (powersetT_lem) =>
% 121.84/16.13 ((
% 121.84/16.13 (setminusT_lem) =>
% 121.84/16.13 ((
% 121.84/16.13 (complementT_lem) =>
% 121.84/16.13 ((
% 121.84/16.13 (setextT) =>
% 121.84/16.13 ((
% 121.84/16.13 (subsetTI) =>
% 121.84/16.13 ((
% 121.84/16.13 (powersetTI1) =>
% 121.84/16.13 ((
% 121.84/16.13 (powersetTE1) =>
% 121.84/16.13 ((
% 121.84/16.13 (complementTI1) =>
% 121.84/16.13 ((
% 121.84/16.13 (complementTE1) =>
% 121.84/16.13 ((
% 121.84/16.13 (binintersectTELcontra) =>
% 121.84/16.13 ((
% 121.84/16.13 (binintersectTERcontra) =>
% 121.84/16.13 ((
% 121.84/16.13 (contrasubsetT) =>
% 121.84/16.13 ((
% 121.84/16.13 (contrasubsetT1) =>
% 121.84/16.13 ((
% 121.84/16.13 (contrasubsetT2) =>
% 121.84/16.13 ((
% 121.84/16.13 (contrasubsetT3) =>
% 121.84/16.13 ((
% 121.84/16.13 (doubleComplementI1) =>
% 121.84/16.13 ((
% 121.84/16.13 (doubleComplementE1) =>
% 121.84/16.13 ((
% 121.84/16.13 (doubleComplementSub1) =>
% 121.84/16.13 ((
% 121.84/16.13 (doubleComplementSub2) =>
% 121.84/16.13 ((
% 121.84/16.13 (doubleComplementEq) =>
% 121.84/16.13 ((
% 121.84/16.13 (complementTnotintersectT) =>
% 121.84/16.13 ((
% 121.84/16.13 (complementImpComplementIntersect) =>
% 121.84/16.13 ((
% 121.84/16.13 (complementSubsetComplementIntersect) =>
% 121.84/16.13 ((
% 121.84/16.13 (complementInPowersetComplementIntersect) =>
% 121.84/16.13 ((
% 121.84/16.13 (contraSubsetComplement) =>
% 121.84/16.13 ((
% 121.84/16.13 (complementTcontraSubset) =>
% 121.84/16.13 ((
% 121.84/16.13 (binunionTILcontra) =>
% 121.84/16.13 ((
% 121.84/16.13 (binunionTIRcontra) =>
% 121.84/16.13 ((
% 121.84/16.13 (inIntersectImpInUnion) =>
% 121.84/16.13 ((
% 121.84/16.13 (inIntersectImpInUnion2) =>
% 121.84/16.13 ((
% 122.46/16.15 (inIntersectImpInIntersectUnions) =>
% 122.46/16.15 ((
% 122.46/16.15 (intersectInPowersetIntersectUnions) =>
% 122.46/16.15 ((
% 122.46/16.15 (inComplementUnionImpNotIn1) =>
% 122.46/16.15 ((
% 122.46/16.15 (inComplementUnionImpInComplement1) =>
% 122.46/16.15 ((
% 122.46/16.15 (binunionTE) =>
% 122.46/16.15 ((
% 122.46/16.15 (binunionTEcontra) =>
% 122.46/16.15 ((
% 122.46/16.15 (demorgan2a1) =>
% 122.46/16.15 ((
% 122.46/16.15 (complementUnionInPowersetComplement) =>
% 122.46/16.15 ((
% 122.46/16.15 (demorgan2a2) =>
% 122.46/16.15 ((
% 122.46/16.15 (demorgan1a) =>
% 122.46/16.15 ((
% 122.46/16.15 (demorgan1b) =>
% 122.46/16.15 ((
% 122.46/16.15 (demorgan1) =>
% 122.46/16.15 ((
% 122.46/16.15 (demorgan2a) =>
% 122.46/16.15 ((
% 122.46/16.15 (demorgan2b2) =>
% 122.46/16.15 ((
% 122.46/16.15 (demorgan2b) =>
% 122.46/16.15 ((
% 122.46/16.15 (demorgan2) =>
% 122.46/16.15 ((
% 122.46/16.15 (woz13rule0) =>
% 122.46/16.15 ((
% 122.46/16.15 (woz13rule1) =>
% 122.46/16.15 ((
% 122.46/16.15 (woz13rule2) =>
% 122.46/16.15 ((
% 122.46/16.15 (woz13rule3) =>
% 122.46/16.15 ((
% 122.46/16.15 (woz13rule4) =>
% 122.46/16.15 ((
% 122.46/16.15 (woz1_1) =>
% 122.46/16.15 ((
% 122.46/16.15 (woz1_2) =>
% 122.46/16.15 ((
% 122.46/16.15 (woz1_3) =>
% 122.46/16.15 ((
% 122.46/16.15 (woz1_4) =>
% 122.46/16.15 ((
% 122.46/16.15 (woz1_5) =>
% 122.46/16.15 ((
% 122.46/16.15 (breln1all2) =>
% 122.46/16.15 ((
% 122.46/16.15 (breln1SetBreln1) =>
% 122.46/16.15 ((
% 122.46/16.15 (choice2fnsingleton) =>
% 122.46/16.15 ((
% 122.46/16.15 (setOfPairsIsBReln1) =>
% 122.46/16.15 ((
% 122.46/16.15 (breln1all1) =>
% 122.46/16.15 ((
% 122.46/16.15 (subbreln1) =>
% 122.46/16.15 ((
% 122.46/16.15 (eqbreln1) =>
% 122.46/16.15 ((
% 122.46/16.15 (breln1invprop) =>
% 122.46/16.15 ((
% 122.46/16.15 (breln1invI) =>
% 122.46/16.15 ((
% 122.46/16.15 (breln1invE) =>
% 122.46/16.15 ((
% 122.46/16.15 (breln1compprop) =>
% 122.46/16.15 ((
% 122.46/16.15 (breln1compI) =>
% 122.46/16.15 ((
% 122.46/16.15 (breln1compE) =>
% 122.46/16.15 ((
% 122.46/16.15 (breln1compEex) =>
% 122.46/16.15 ((
% 122.46/16.15 (breln1unionprop) =>
% 122.46/16.15 ((
% 122.46/16.15 (breln1unionIL) =>
% 122.46/16.15 ((
% 122.46/16.15 (breln1unionIR) =>
% 122.46/16.15 ((
% 122.46/16.15 (breln1unionI) =>
% 122.46/16.15 ((
% 122.46/16.15 (breln1unionE) =>
% 122.46/16.15 ((
% 122.46/16.15 (breln1unionEcases) =>
% 122.46/16.15 ((
% 122.46/16.15 (breln1unionCommutes) =>
% 122.46/16.15 ((
% 122.46/16.15 (woz2Ex) =>
% 122.46/16.15 ((
% 122.46/16.15 (woz2W) =>
% 122.46/16.15 ((
% 122.46/16.15 (woz2A) =>
% 122.46/16.15 ((
% 122.46/16.15 (woz2B) =>
% 122.46/16.15 ((
% 122.46/16.15 (image1Ex) =>
% 122.46/16.15 ((
% 122.46/16.15 (image1Ex1) =>
% 122.46/16.15 ((
% 122.46/16.15 (image1Equiv) =>
% 122.46/16.15 ((
% 122.46/16.15 (image1E) =>
% 122.46/16.15 ((
% 122.46/16.15 (image1I) =>
% 122.46/16.15 ((
% 122.46/16.15 (injFuncInInjFuncSet) =>
% 122.46/16.15 ((
% 122.46/16.15 (!!) @ (
% 122.46/16.15 (('#B') @ (
% 122.46/16.15 !!) @
% 122.46/16.15 (
% 122.46/16.15 (
% 122.46/16.15 ('#B') @ (
% 122.46/16.15 (
% 122.46/16.15 ('#B') @ (
% 122.46/16.15 !!))) @
% 122.46/16.15 (
% 122.46/16.15 (
% 122.46/16.15 ('#S') @ (
% 122.46/16.15 (
% 122.46/16.15 ('#B') @ (
% 122.46/16.15 '#S') @
% 122.46/16.15 (
% 122.46/16.15 (
% 122.46/16.15 ('#B') @ (
% 122.46/16.15 (
% 122.46/16.15 ('#B') @ (
% 122.46/16.15 '#S'))) @
% 122.46/16.15 (
% 122.46/16.15 (
% 122.46/16.15 ('#B') @ (
% 122.46/16.15 (
% 122.46/16.15 ('#B') @ (
% 122.46/16.15 (
% 122.46/16.15 ('#B') @ (
% 122.46/16.15 =>))))) @
% 122.46/16.15 (
% 122.46/16.15 (
% 122.46/16.15 ('#B') @ (
% 122.46/16.15 (
% 122.46/16.15 ('#B') @ (
% 122.46/16.15 (
% 122.46/16.15 ('#C') @ in)))) @
% 122.46/16.15 injFuncSet)))))))) @
% 122.46/16.15 (
% 122.46/16.15 (
% 122.46/16.15 ('#B') @ (
% 122.46/16.15 (
% 122.46/16.15 ('#B') @ (
% 122.46/16.15 (
% 122.46/16.15 ('#C') @ in)))) @
% 122.46/16.15 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.46/16.15 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1115])).
% 122.46/16.15 thf(zip_derived_cl1128, plain,
% 122.46/16.15 (~ (((binunionLsub) =>
% 122.46/16.15 (((binunionRsub) =>
% 122.46/16.15 (((binintersectI) =>
% 122.46/16.15 (((binintersectSubset5) =>
% 122.46/16.15 (((binintersectEL) =>
% 122.46/16.15 (((binintersectLsub) =>
% 122.46/16.15 (((binintersectSubset2) =>
% 122.46/16.15 (((binintersectSubset3) =>
% 122.46/16.15 (((binintersectER) =>
% 122.46/16.15 (((disjointsetsI1) =>
% 122.46/16.15 (((binintersectRsub) =>
% 122.46/16.15 (((binintersectSubset4) =>
% 122.46/16.15 (((binintersectSubset1) =>
% 122.46/16.15 (((bs114d) =>
% 122.46/16.15 (((setminusI) =>
% 122.46/16.15 (((setminusEL) =>
% 122.46/16.15 (((setminusER) =>
% 122.46/16.15 (((setminusSubset2) =>
% 122.46/16.15 (((setminusERneg) =>
% 122.46/16.15 (((setminusELneg) =>
% 122.46/16.15 (((setminusILneg) =>
% 122.46/16.15 (((setminusIRneg) =>
% 122.46/16.15 (((setminusLsub) =>
% 122.46/16.15 (((setminusSubset1) =>
% 122.46/16.15 (((symdiffE) =>
% 122.46/16.15 (((symdiffI1) =>
% 122.46/16.15 (((symdiffI2) =>
% 122.46/16.15 (((symdiffIneg1) =>
% 122.46/16.15 (((symdiffIneg2) =>
% 122.46/16.15 (((secondinupair) =>
% 122.46/16.15 ((
% 122.46/16.15 (setukpairIL) =>
% 122.46/16.15 ((
% 122.46/16.15 (setukpairIR) =>
% 122.46/16.15 ((
% 122.46/16.15 (kpairiskpair) =>
% 122.46/16.15 ((
% 122.46/16.15 (kpairp) =>
% 122.46/16.15 ((
% 122.46/16.15 (singletonsubset) =>
% 122.46/16.15 ((
% 122.46/16.15 (singletoninpowerset) =>
% 122.46/16.15 ((
% 122.46/16.15 (singletoninpowunion) =>
% 122.46/16.15 ((
% 122.46/16.15 (upairset2E) =>
% 122.46/16.15 ((
% 122.46/16.15 (upairsubunion) =>
% 122.46/16.15 ((
% 122.46/16.15 (upairinpowunion) =>
% 122.46/16.15 ((
% 122.46/16.15 (ubforcartprodlem1) =>
% 122.46/16.15 ((
% 122.46/16.15 (ubforcartprodlem2) =>
% 122.46/16.15 ((
% 122.46/16.15 (ubforcartprodlem3) =>
% 122.46/16.15 ((
% 122.46/16.15 (cartprodpairin) =>
% 122.46/16.15 ((
% 122.46/16.15 (cartprodmempair1) =>
% 122.46/16.15 ((
% 122.46/16.15 (cartprodmempair) =>
% 122.46/16.15 ((
% 122.46/16.15 (setunionE2) =>
% 122.46/16.15 ((
% 122.46/16.15 (setunionsingleton1) =>
% 122.46/16.15 ((
% 122.46/16.15 (setunionsingleton2) =>
% 122.46/16.15 ((
% 122.46/16.15 (setunionsingleton) =>
% 122.46/16.15 ((
% 122.46/16.15 (singletonprop) =>
% 122.46/16.15 ((
% 122.46/16.15 (ex1E1) =>
% 122.46/16.15 ((
% 122.46/16.15 (ex1I) =>
% 122.46/16.15 ((
% 122.46/16.15 (ex1I2) =>
% 122.46/16.15 ((
% 122.46/16.15 (singletonsuniq) =>
% 122.46/16.15 ((
% 122.46/16.15 (setukpairinjL1) =>
% 122.46/16.15 ((
% 122.46/16.15 (kfstsingleton) =>
% 122.46/16.15 ((
% 122.46/16.15 (theprop) =>
% 122.46/16.15 ((
% 122.46/16.15 (kfstpairEq) =>
% 122.46/16.15 ((
% 122.46/16.15 (cartprodfstin) =>
% 122.46/16.15 ((
% 122.46/16.15 (setukpairinjL2) =>
% 122.46/16.15 ((
% 122.46/16.15 (setukpairinjL) =>
% 122.46/16.15 ((
% 122.46/16.15 (setukpairinjR11) =>
% 122.46/16.15 ((
% 122.46/16.15 (setukpairinjR12) =>
% 122.46/16.15 ((
% 122.46/16.15 (setukpairinjR1) =>
% 122.46/16.15 ((
% 122.46/16.15 (upairequniteq) =>
% 122.46/16.15 ((
% 122.46/16.15 (setukpairinjR2) =>
% 122.46/16.15 ((
% 122.46/16.15 (setukpairinjR) =>
% 122.46/16.15 ((
% 122.46/16.15 (ksndsingleton) =>
% 122.46/16.15 ((
% 122.46/16.15 (ksndpairEq) =>
% 122.46/16.15 ((
% 122.46/16.15 (kpairsurjEq) =>
% 122.46/16.15 ((
% 122.46/16.15 (cartprodsndin) =>
% 122.46/16.15 ((
% 122.46/16.15 (cartprodpairmemEL) =>
% 122.46/16.15 ((
% 122.46/16.15 (cartprodpairmemER) =>
% 122.46/16.15 ((
% 122.46/16.15 (cartprodmempaircEq) =>
% 122.46/16.15 ((
% 122.46/16.15 (cartprodfstpairEq) =>
% 122.46/16.15 ((
% 122.46/16.15 (cartprodsndpairEq) =>
% 122.46/16.15 ((
% 122.46/16.15 (cartprodpairsurjEq) =>
% 122.46/16.15 ((
% 122.46/16.15 (dpsetconstrI) =>
% 122.46/16.15 ((
% 122.46/16.15 (dpsetconstrSub) =>
% 122.46/16.15 ((
% 122.46/16.15 (setOfPairsIsBReln) =>
% 122.46/16.15 ((
% 122.46/16.15 (dpsetconstrERa) =>
% 122.46/16.15 ((
% 122.46/16.15 (dpsetconstrEL1) =>
% 122.46/16.15 ((
% 122.46/16.15 (dpsetconstrEL2) =>
% 122.46/16.15 ((
% 122.46/16.15 (dpsetconstrER) =>
% 122.46/16.15 ((
% 122.46/16.15 (funcImageSingleton) =>
% 122.46/16.15 ((
% 122.46/16.15 (apProp) =>
% 122.46/16.15 ((
% 122.46/16.15 (app) =>
% 122.46/16.15 ((
% 122.46/16.15 (infuncsetfunc) =>
% 122.46/16.15 ((
% 122.46/16.15 (ap2p) =>
% 122.46/16.15 ((
% 122.46/16.15 (funcinfuncset) =>
% 122.46/16.15 ((
% 122.46/16.15 (lamProp) =>
% 122.46/16.15 ((
% 122.46/16.15 (lamp) =>
% 122.46/16.15 ((
% 122.46/16.15 (lam2p) =>
% 122.46/16.15 ((
% 122.46/16.15 (brelnall1) =>
% 122.46/16.15 ((
% 122.46/16.15 (brelnall2) =>
% 122.46/16.15 ((
% 122.46/16.15 (ex1E2) =>
% 122.46/16.15 ((
% 122.46/16.15 (funcGraphProp1) =>
% 122.46/16.15 ((
% 122.46/16.15 (funcGraphProp3) =>
% 122.46/16.15 ((
% 122.46/16.15 (funcGraphProp2) =>
% 122.46/16.15 ((
% 122.46/16.15 (funcextLem) =>
% 122.46/16.15 ((
% 122.46/16.15 (funcGraphProp4) =>
% 122.46/16.15 ((
% 122.46/16.15 (subbreln) =>
% 122.46/16.15 ((
% 122.46/16.15 (eqbreln) =>
% 122.46/16.15 ((
% 122.46/16.15 (funcext) =>
% 122.46/16.15 ((
% 122.46/16.15 (funcext2) =>
% 122.46/16.15 ((
% 122.46/16.15 (ap2apEq1) =>
% 122.46/16.15 ((
% 122.46/16.15 (ap2apEq2) =>
% 122.46/16.15 ((
% 122.46/16.15 (beta1) =>
% 122.46/16.15 ((
% 122.46/16.15 (eta1) =>
% 122.46/16.15 ((
% 122.46/16.15 (lam2lamEq) =>
% 122.46/16.15 ((
% 122.46/16.15 (beta2) =>
% 122.46/16.15 ((
% 122.46/16.15 (eta2) =>
% 122.46/16.15 ((
% 122.46/16.15 (iffalseProp1) =>
% 122.46/16.15 ((
% 122.46/16.15 (iffalseProp2) =>
% 122.46/16.15 ((
% 122.46/16.15 (iftrueProp1) =>
% 122.46/16.15 ((
% 122.46/16.15 (iftrueProp2) =>
% 122.46/16.15 ((
% 122.46/16.15 (ifSingleton) =>
% 122.46/16.15 ((
% 122.46/16.15 (ifp) =>
% 122.46/16.15 ((
% 122.46/16.15 (theeq) =>
% 122.46/16.15 ((
% 122.46/16.15 (iftrue) =>
% 122.46/16.15 ((
% 122.46/16.15 (iffalse) =>
% 122.46/16.15 ((
% 122.46/16.15 (iftrueorfalse) =>
% 122.46/16.15 ((
% 122.46/16.15 (binintersectT_lem) =>
% 122.46/16.15 ((
% 122.46/16.15 (binunionT_lem) =>
% 122.46/16.15 ((
% 122.46/16.15 (powersetT_lem) =>
% 122.46/16.15 ((
% 122.46/16.15 (setminusT_lem) =>
% 122.46/16.15 ((
% 122.46/16.15 (complementT_lem) =>
% 122.46/16.15 ((
% 122.46/16.15 (setextT) =>
% 122.46/16.15 ((
% 122.46/16.15 (subsetTI) =>
% 122.46/16.15 ((
% 122.46/16.15 (powersetTI1) =>
% 122.46/16.15 ((
% 122.46/16.15 (powersetTE1) =>
% 122.46/16.15 ((
% 122.46/16.15 (complementTI1) =>
% 122.46/16.15 ((
% 122.46/16.15 (complementTE1) =>
% 122.46/16.15 ((
% 122.46/16.15 (binintersectTELcontra) =>
% 122.46/16.15 ((
% 122.46/16.15 (binintersectTERcontra) =>
% 122.46/16.15 ((
% 122.46/16.15 (contrasubsetT) =>
% 122.46/16.15 ((
% 122.46/16.15 (contrasubsetT1) =>
% 122.46/16.15 ((
% 122.46/16.15 (contrasubsetT2) =>
% 122.46/16.15 ((
% 122.46/16.15 (contrasubsetT3) =>
% 122.46/16.15 ((
% 122.46/16.15 (doubleComplementI1) =>
% 122.46/16.15 ((
% 122.46/16.15 (doubleComplementE1) =>
% 122.46/16.15 ((
% 122.46/16.15 (doubleComplementSub1) =>
% 122.46/16.15 ((
% 122.46/16.15 (doubleComplementSub2) =>
% 122.46/16.15 ((
% 122.46/16.15 (doubleComplementEq) =>
% 122.46/16.15 ((
% 122.46/16.15 (complementTnotintersectT) =>
% 122.46/16.15 ((
% 122.46/16.15 (complementImpComplementIntersect) =>
% 122.46/16.15 ((
% 122.46/16.15 (complementSubsetComplementIntersect) =>
% 122.46/16.15 ((
% 122.46/16.15 (complementInPowersetComplementIntersect) =>
% 122.46/16.15 ((
% 122.46/16.15 (contraSubsetComplement) =>
% 122.46/16.15 ((
% 122.46/16.15 (complementTcontraSubset) =>
% 122.46/16.15 ((
% 122.46/16.15 (binunionTILcontra) =>
% 122.46/16.15 ((
% 122.46/16.15 (binunionTIRcontra) =>
% 122.46/16.15 ((
% 122.46/16.15 (inIntersectImpInUnion) =>
% 122.46/16.15 ((
% 122.46/16.15 (inIntersectImpInUnion2) =>
% 122.46/16.15 ((
% 122.46/16.15 (inIntersectImpInIntersectUnions) =>
% 122.46/16.15 ((
% 122.46/16.15 (intersectInPowersetIntersectUnions) =>
% 122.46/16.15 ((
% 122.46/16.15 (inComplementUnionImpNotIn1) =>
% 122.46/16.15 ((
% 122.46/16.15 (inComplementUnionImpInComplement1) =>
% 122.46/16.15 ((
% 122.46/16.15 (binunionTE) =>
% 122.46/16.15 ((
% 122.46/16.15 (binunionTEcontra) =>
% 122.46/16.15 ((
% 122.46/16.15 (demorgan2a1) =>
% 122.46/16.15 ((
% 122.46/16.15 (complementUnionInPowersetComplement) =>
% 122.46/16.15 ((
% 122.46/16.15 (demorgan2a2) =>
% 122.46/16.15 ((
% 122.46/16.15 (demorgan1a) =>
% 122.46/16.15 ((
% 122.46/16.15 (demorgan1b) =>
% 122.46/16.15 ((
% 122.46/16.15 (demorgan1) =>
% 122.46/16.15 ((
% 122.46/16.15 (demorgan2a) =>
% 122.46/16.15 ((
% 122.46/16.15 (demorgan2b2) =>
% 122.46/16.15 ((
% 122.46/16.15 (demorgan2b) =>
% 122.46/16.15 ((
% 122.46/16.15 (demorgan2) =>
% 122.46/16.15 ((
% 122.46/16.15 (woz13rule0) =>
% 122.46/16.15 ((
% 122.46/16.15 (woz13rule1) =>
% 122.46/16.15 ((
% 122.46/16.15 (woz13rule2) =>
% 122.46/16.15 ((
% 122.46/16.15 (woz13rule3) =>
% 122.46/16.15 ((
% 122.46/16.15 (woz13rule4) =>
% 122.46/16.15 ((
% 122.46/16.15 (woz1_1) =>
% 122.46/16.15 ((
% 122.46/16.15 (woz1_2) =>
% 122.46/16.15 ((
% 122.46/16.15 (woz1_3) =>
% 122.46/16.15 ((
% 122.46/16.15 (woz1_4) =>
% 122.46/16.15 ((
% 122.46/16.15 (woz1_5) =>
% 122.46/16.15 ((
% 122.46/16.15 (breln1all2) =>
% 122.46/16.15 ((
% 122.46/16.15 (breln1SetBreln1) =>
% 122.46/16.15 ((
% 122.46/16.15 (choice2fnsingleton) =>
% 122.46/16.15 ((
% 122.46/16.15 (setOfPairsIsBReln1) =>
% 122.46/16.15 ((
% 122.46/16.15 (breln1all1) =>
% 122.46/16.15 ((
% 122.46/16.15 (subbreln1) =>
% 122.46/16.15 ((
% 122.46/16.15 (eqbreln1) =>
% 122.46/16.15 ((
% 122.46/16.15 (breln1invprop) =>
% 122.46/16.15 ((
% 122.46/16.15 (breln1invI) =>
% 122.46/16.15 ((
% 122.46/16.15 (breln1invE) =>
% 122.46/16.15 ((
% 122.46/16.15 (breln1compprop) =>
% 122.46/16.15 ((
% 122.46/16.15 (breln1compI) =>
% 122.46/16.15 ((
% 122.46/16.15 (breln1compE) =>
% 122.46/16.15 ((
% 122.46/16.15 (breln1compEex) =>
% 122.46/16.15 ((
% 122.46/16.15 (breln1unionprop) =>
% 122.46/16.15 ((
% 122.46/16.15 (breln1unionIL) =>
% 122.46/16.15 ((
% 122.46/16.15 (breln1unionIR) =>
% 122.46/16.15 ((
% 122.46/16.15 (breln1unionI) =>
% 122.46/16.15 ((
% 122.46/16.15 (breln1unionE) =>
% 122.46/16.15 ((
% 122.46/16.15 (breln1unionEcases) =>
% 122.46/16.15 ((
% 122.46/16.15 (breln1unionCommutes) =>
% 122.46/16.15 ((
% 122.46/16.15 (woz2Ex) =>
% 122.46/16.15 ((
% 122.46/16.15 (woz2W) =>
% 122.46/16.15 ((
% 122.46/16.15 (woz2A) =>
% 122.46/16.15 ((
% 122.46/16.15 (woz2B) =>
% 122.46/16.15 ((
% 122.46/16.15 (image1Ex) =>
% 122.46/16.15 ((
% 122.46/16.15 (image1Ex1) =>
% 122.46/16.15 ((
% 122.46/16.15 (image1Equiv) =>
% 122.46/16.15 ((
% 122.46/16.15 (image1E) =>
% 122.46/16.15 ((
% 122.46/16.15 (image1I) =>
% 122.46/16.15 ((
% 122.46/16.15 (injFuncInInjFuncSet) =>
% 122.46/16.15 ((
% 122.46/16.15 (!!) @ (
% 122.46/16.15 (('#B') @ (
% 122.46/16.15 !!) @
% 122.46/16.15 (
% 122.46/16.15 (
% 122.46/16.15 ('#B') @ (
% 122.46/16.15 (
% 122.46/16.15 ('#B') @ (
% 122.46/16.15 !!))) @
% 122.46/16.15 (
% 122.46/16.15 (
% 122.46/16.15 ('#S') @ (
% 122.46/16.15 (
% 122.46/16.15 ('#B') @ (
% 122.46/16.15 '#S') @
% 122.46/16.15 (
% 122.46/16.15 (
% 122.46/16.15 ('#B') @ (
% 122.46/16.15 (
% 122.46/16.15 ('#B') @ (
% 122.46/16.15 '#S'))) @
% 122.46/16.15 (
% 122.46/16.15 (
% 122.46/16.15 ('#B') @ (
% 122.46/16.15 (
% 122.46/16.15 ('#B') @ (
% 122.46/16.15 (
% 122.46/16.15 ('#B') @ (
% 122.46/16.15 =>))))) @
% 122.46/16.15 (
% 122.46/16.15 (
% 122.46/16.15 ('#B') @ (
% 122.46/16.15 (
% 122.46/16.15 ('#B') @ (
% 122.46/16.15 (
% 122.46/16.15 ('#C') @ in)))) @
% 122.46/16.15 injFuncSet)))))))) @
% 122.46/16.15 (
% 122.46/16.15 (
% 122.46/16.15 ('#B') @ (
% 122.46/16.15 (
% 122.46/16.15 ('#B') @ (
% 122.46/16.15 (
% 122.46/16.15 ('#C') @ in)))) @
% 122.46/16.15 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.46/16.15 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1121])).
% 122.46/16.15 thf(zip_derived_cl1135, plain,
% 122.46/16.15 (~ (((binunionRsub) =>
% 122.46/16.15 (((binintersectI) =>
% 122.46/16.15 (((binintersectSubset5) =>
% 122.46/16.15 (((binintersectEL) =>
% 122.46/16.15 (((binintersectLsub) =>
% 122.46/16.15 (((binintersectSubset2) =>
% 122.46/16.15 (((binintersectSubset3) =>
% 122.46/16.15 (((binintersectER) =>
% 122.46/16.15 (((disjointsetsI1) =>
% 122.46/16.15 (((binintersectRsub) =>
% 122.46/16.15 (((binintersectSubset4) =>
% 122.46/16.15 (((binintersectSubset1) =>
% 122.46/16.15 (((bs114d) =>
% 122.46/16.15 (((setminusI) =>
% 122.46/16.15 (((setminusEL) =>
% 122.46/16.15 (((setminusER) =>
% 122.46/16.15 (((setminusSubset2) =>
% 122.46/16.15 (((setminusERneg) =>
% 122.46/16.15 (((setminusELneg) =>
% 122.46/16.15 (((setminusILneg) =>
% 122.46/16.15 (((setminusIRneg) =>
% 122.46/16.15 (((setminusLsub) =>
% 122.46/16.15 (((setminusSubset1) =>
% 122.46/16.15 (((symdiffE) =>
% 122.46/16.15 (((symdiffI1) =>
% 122.46/16.15 (((symdiffI2) =>
% 122.46/16.15 (((symdiffIneg1) =>
% 122.46/16.15 (((symdiffIneg2) =>
% 122.46/16.15 (((secondinupair) =>
% 122.46/16.15 (((setukpairIL) =>
% 122.46/16.15 ((
% 122.46/16.15 (setukpairIR) =>
% 122.46/16.15 ((
% 122.46/16.15 (kpairiskpair) =>
% 122.46/16.15 ((
% 122.46/16.15 (kpairp) =>
% 122.46/16.15 ((
% 122.46/16.15 (singletonsubset) =>
% 122.46/16.15 ((
% 122.46/16.15 (singletoninpowerset) =>
% 122.46/16.15 ((
% 122.46/16.15 (singletoninpowunion) =>
% 122.46/16.15 ((
% 122.46/16.15 (upairset2E) =>
% 122.46/16.15 ((
% 122.46/16.15 (upairsubunion) =>
% 122.46/16.15 ((
% 122.46/16.15 (upairinpowunion) =>
% 122.46/16.15 ((
% 122.46/16.15 (ubforcartprodlem1) =>
% 122.46/16.15 ((
% 122.46/16.15 (ubforcartprodlem2) =>
% 122.46/16.15 ((
% 122.46/16.15 (ubforcartprodlem3) =>
% 122.46/16.15 ((
% 122.46/16.15 (cartprodpairin) =>
% 122.46/16.15 ((
% 122.46/16.15 (cartprodmempair1) =>
% 122.46/16.15 ((
% 122.46/16.15 (cartprodmempair) =>
% 122.46/16.15 ((
% 122.46/16.15 (setunionE2) =>
% 122.46/16.15 ((
% 122.46/16.15 (setunionsingleton1) =>
% 122.46/16.15 ((
% 122.46/16.15 (setunionsingleton2) =>
% 122.46/16.15 ((
% 122.46/16.15 (setunionsingleton) =>
% 122.46/16.15 ((
% 122.46/16.15 (singletonprop) =>
% 122.46/16.15 ((
% 122.46/16.15 (ex1E1) =>
% 122.46/16.15 ((
% 122.46/16.15 (ex1I) =>
% 122.46/16.15 ((
% 122.46/16.15 (ex1I2) =>
% 122.46/16.15 ((
% 122.46/16.15 (singletonsuniq) =>
% 122.46/16.15 ((
% 122.46/16.15 (setukpairinjL1) =>
% 122.46/16.15 ((
% 122.46/16.15 (kfstsingleton) =>
% 122.46/16.15 ((
% 122.46/16.15 (theprop) =>
% 122.46/16.15 ((
% 122.46/16.15 (kfstpairEq) =>
% 122.46/16.15 ((
% 122.46/16.15 (cartprodfstin) =>
% 122.46/16.15 ((
% 122.46/16.15 (setukpairinjL2) =>
% 122.46/16.15 ((
% 122.46/16.15 (setukpairinjL) =>
% 122.46/16.15 ((
% 122.46/16.15 (setukpairinjR11) =>
% 122.46/16.15 ((
% 122.46/16.15 (setukpairinjR12) =>
% 122.46/16.15 ((
% 122.46/16.15 (setukpairinjR1) =>
% 122.46/16.15 ((
% 122.46/16.15 (upairequniteq) =>
% 122.46/16.15 ((
% 122.46/16.15 (setukpairinjR2) =>
% 122.46/16.15 ((
% 122.46/16.15 (setukpairinjR) =>
% 122.46/16.15 ((
% 122.46/16.15 (ksndsingleton) =>
% 122.46/16.15 ((
% 122.46/16.15 (ksndpairEq) =>
% 122.46/16.15 ((
% 122.46/16.15 (kpairsurjEq) =>
% 122.46/16.15 ((
% 122.46/16.15 (cartprodsndin) =>
% 122.46/16.15 ((
% 122.46/16.15 (cartprodpairmemEL) =>
% 122.46/16.15 ((
% 122.46/16.15 (cartprodpairmemER) =>
% 122.46/16.15 ((
% 122.46/16.15 (cartprodmempaircEq) =>
% 122.46/16.15 ((
% 122.46/16.15 (cartprodfstpairEq) =>
% 122.46/16.15 ((
% 122.46/16.15 (cartprodsndpairEq) =>
% 122.46/16.15 ((
% 122.46/16.15 (cartprodpairsurjEq) =>
% 122.46/16.15 ((
% 122.46/16.15 (dpsetconstrI) =>
% 122.46/16.15 ((
% 122.46/16.15 (dpsetconstrSub) =>
% 122.46/16.15 ((
% 122.46/16.15 (setOfPairsIsBReln) =>
% 122.46/16.15 ((
% 122.46/16.15 (dpsetconstrERa) =>
% 122.46/16.15 ((
% 122.46/16.15 (dpsetconstrEL1) =>
% 122.46/16.15 ((
% 122.46/16.15 (dpsetconstrEL2) =>
% 122.46/16.15 ((
% 122.46/16.15 (dpsetconstrER) =>
% 122.46/16.15 ((
% 122.46/16.15 (funcImageSingleton) =>
% 122.46/16.15 ((
% 122.46/16.15 (apProp) =>
% 122.46/16.15 ((
% 122.46/16.15 (app) =>
% 122.46/16.15 ((
% 122.46/16.15 (infuncsetfunc) =>
% 122.46/16.15 ((
% 122.46/16.15 (ap2p) =>
% 122.46/16.15 ((
% 122.46/16.15 (funcinfuncset) =>
% 122.46/16.15 ((
% 122.46/16.15 (lamProp) =>
% 122.46/16.15 ((
% 122.46/16.15 (lamp) =>
% 122.46/16.15 ((
% 122.46/16.15 (lam2p) =>
% 122.46/16.15 ((
% 122.46/16.15 (brelnall1) =>
% 122.46/16.15 ((
% 122.46/16.15 (brelnall2) =>
% 122.46/16.15 ((
% 122.46/16.15 (ex1E2) =>
% 122.46/16.15 ((
% 122.46/16.15 (funcGraphProp1) =>
% 122.46/16.15 ((
% 122.46/16.15 (funcGraphProp3) =>
% 122.46/16.15 ((
% 122.46/16.15 (funcGraphProp2) =>
% 122.46/16.15 ((
% 122.46/16.15 (funcextLem) =>
% 122.46/16.15 ((
% 122.46/16.15 (funcGraphProp4) =>
% 122.46/16.15 ((
% 122.46/16.15 (subbreln) =>
% 122.46/16.15 ((
% 122.46/16.15 (eqbreln) =>
% 122.46/16.15 ((
% 122.46/16.15 (funcext) =>
% 122.46/16.15 ((
% 122.46/16.15 (funcext2) =>
% 122.46/16.15 ((
% 122.46/16.15 (ap2apEq1) =>
% 122.46/16.15 ((
% 122.46/16.15 (ap2apEq2) =>
% 122.46/16.15 ((
% 122.46/16.15 (beta1) =>
% 122.46/16.15 ((
% 122.46/16.15 (eta1) =>
% 122.46/16.15 ((
% 122.46/16.15 (lam2lamEq) =>
% 122.46/16.15 ((
% 122.46/16.15 (beta2) =>
% 122.46/16.15 ((
% 122.46/16.15 (eta2) =>
% 122.46/16.15 ((
% 122.46/16.15 (iffalseProp1) =>
% 122.46/16.15 ((
% 122.46/16.15 (iffalseProp2) =>
% 122.46/16.15 ((
% 122.46/16.15 (iftrueProp1) =>
% 122.46/16.15 ((
% 122.46/16.15 (iftrueProp2) =>
% 122.46/16.15 ((
% 122.46/16.15 (ifSingleton) =>
% 122.46/16.15 ((
% 122.46/16.15 (ifp) =>
% 122.46/16.15 ((
% 122.46/16.15 (theeq) =>
% 122.46/16.15 ((
% 122.46/16.15 (iftrue) =>
% 122.46/16.15 ((
% 122.46/16.15 (iffalse) =>
% 122.46/16.15 ((
% 122.46/16.15 (iftrueorfalse) =>
% 122.46/16.15 ((
% 122.46/16.15 (binintersectT_lem) =>
% 122.46/16.15 ((
% 122.46/16.15 (binunionT_lem) =>
% 122.46/16.15 ((
% 122.46/16.15 (powersetT_lem) =>
% 122.46/16.15 ((
% 122.46/16.15 (setminusT_lem) =>
% 122.46/16.15 ((
% 122.46/16.15 (complementT_lem) =>
% 122.46/16.15 ((
% 122.46/16.15 (setextT) =>
% 122.46/16.15 ((
% 122.46/16.15 (subsetTI) =>
% 122.46/16.15 ((
% 122.46/16.15 (powersetTI1) =>
% 122.46/16.15 ((
% 122.46/16.15 (powersetTE1) =>
% 122.46/16.15 ((
% 122.46/16.15 (complementTI1) =>
% 122.46/16.15 ((
% 122.46/16.15 (complementTE1) =>
% 122.46/16.15 ((
% 122.46/16.15 (binintersectTELcontra) =>
% 122.46/16.15 ((
% 122.46/16.15 (binintersectTERcontra) =>
% 122.46/16.15 ((
% 122.46/16.15 (contrasubsetT) =>
% 122.46/16.15 ((
% 122.46/16.15 (contrasubsetT1) =>
% 122.46/16.15 ((
% 122.46/16.15 (contrasubsetT2) =>
% 122.46/16.15 ((
% 122.46/16.15 (contrasubsetT3) =>
% 122.46/16.15 ((
% 122.46/16.15 (doubleComplementI1) =>
% 122.46/16.15 ((
% 122.46/16.15 (doubleComplementE1) =>
% 122.46/16.15 ((
% 122.46/16.15 (doubleComplementSub1) =>
% 122.46/16.15 ((
% 122.46/16.15 (doubleComplementSub2) =>
% 122.46/16.15 ((
% 122.46/16.15 (doubleComplementEq) =>
% 122.46/16.15 ((
% 122.46/16.15 (complementTnotintersectT) =>
% 122.46/16.15 ((
% 122.46/16.15 (complementImpComplementIntersect) =>
% 122.46/16.15 ((
% 122.46/16.15 (complementSubsetComplementIntersect) =>
% 122.46/16.15 ((
% 122.46/16.15 (complementInPowersetComplementIntersect) =>
% 122.46/16.15 ((
% 122.46/16.15 (contraSubsetComplement) =>
% 122.46/16.15 ((
% 122.46/16.15 (complementTcontraSubset) =>
% 122.46/16.15 ((
% 122.46/16.15 (binunionTILcontra) =>
% 122.46/16.15 ((
% 122.46/16.15 (binunionTIRcontra) =>
% 122.46/16.15 ((
% 122.46/16.15 (inIntersectImpInUnion) =>
% 122.46/16.15 ((
% 122.46/16.15 (inIntersectImpInUnion2) =>
% 122.46/16.15 ((
% 122.46/16.15 (inIntersectImpInIntersectUnions) =>
% 122.46/16.15 ((
% 122.46/16.15 (intersectInPowersetIntersectUnions) =>
% 122.46/16.15 ((
% 122.46/16.15 (inComplementUnionImpNotIn1) =>
% 122.46/16.15 ((
% 122.46/16.15 (inComplementUnionImpInComplement1) =>
% 122.46/16.15 ((
% 122.46/16.15 (binunionTE) =>
% 122.46/16.15 ((
% 122.46/16.15 (binunionTEcontra) =>
% 122.46/16.15 ((
% 122.46/16.15 (demorgan2a1) =>
% 122.46/16.15 ((
% 122.46/16.15 (complementUnionInPowersetComplement) =>
% 122.46/16.15 ((
% 122.46/16.15 (demorgan2a2) =>
% 122.46/16.15 ((
% 122.46/16.15 (demorgan1a) =>
% 122.46/16.15 ((
% 122.46/16.15 (demorgan1b) =>
% 122.46/16.15 ((
% 122.46/16.15 (demorgan1) =>
% 122.46/16.15 ((
% 122.46/16.15 (demorgan2a) =>
% 122.46/16.15 ((
% 122.46/16.15 (demorgan2b2) =>
% 122.46/16.15 ((
% 122.46/16.15 (demorgan2b) =>
% 122.46/16.15 ((
% 122.46/16.15 (demorgan2) =>
% 122.46/16.15 ((
% 122.46/16.15 (woz13rule0) =>
% 122.46/16.15 ((
% 122.46/16.15 (woz13rule1) =>
% 122.46/16.15 ((
% 122.46/16.15 (woz13rule2) =>
% 122.46/16.15 ((
% 122.46/16.15 (woz13rule3) =>
% 122.46/16.15 ((
% 122.46/16.15 (woz13rule4) =>
% 122.46/16.15 ((
% 122.46/16.15 (woz1_1) =>
% 122.46/16.15 ((
% 122.46/16.15 (woz1_2) =>
% 122.46/16.15 ((
% 122.46/16.15 (woz1_3) =>
% 122.46/16.15 ((
% 122.46/16.15 (woz1_4) =>
% 122.46/16.15 ((
% 122.46/16.15 (woz1_5) =>
% 122.46/16.15 ((
% 122.46/16.15 (breln1all2) =>
% 122.46/16.15 ((
% 122.46/16.15 (breln1SetBreln1) =>
% 122.46/16.15 ((
% 122.46/16.15 (choice2fnsingleton) =>
% 122.46/16.15 ((
% 122.46/16.15 (setOfPairsIsBReln1) =>
% 122.46/16.15 ((
% 122.46/16.15 (breln1all1) =>
% 122.46/16.15 ((
% 122.46/16.15 (subbreln1) =>
% 122.46/16.15 ((
% 122.46/16.15 (eqbreln1) =>
% 122.46/16.15 ((
% 122.46/16.15 (breln1invprop) =>
% 122.46/16.15 ((
% 122.46/16.15 (breln1invI) =>
% 122.46/16.15 ((
% 122.46/16.15 (breln1invE) =>
% 122.46/16.15 ((
% 122.46/16.15 (breln1compprop) =>
% 122.46/16.15 ((
% 122.46/16.15 (breln1compI) =>
% 122.46/16.15 ((
% 122.46/16.15 (breln1compE) =>
% 122.46/16.15 ((
% 122.46/16.15 (breln1compEex) =>
% 122.46/16.15 ((
% 122.46/16.15 (breln1unionprop) =>
% 122.46/16.15 ((
% 122.46/16.15 (breln1unionIL) =>
% 122.46/16.15 ((
% 122.46/16.15 (breln1unionIR) =>
% 122.46/16.15 ((
% 122.46/16.15 (breln1unionI) =>
% 122.46/16.15 ((
% 122.46/16.15 (breln1unionE) =>
% 122.46/16.15 ((
% 122.46/16.15 (breln1unionEcases) =>
% 122.46/16.15 ((
% 122.46/16.15 (breln1unionCommutes) =>
% 122.46/16.15 ((
% 122.46/16.15 (woz2Ex) =>
% 122.46/16.15 ((
% 122.46/16.15 (woz2W) =>
% 122.46/16.15 ((
% 122.46/16.15 (woz2A) =>
% 122.46/16.15 ((
% 122.46/16.15 (woz2B) =>
% 122.46/16.15 ((
% 122.46/16.15 (image1Ex) =>
% 122.46/16.15 ((
% 122.46/16.15 (image1Ex1) =>
% 122.46/16.15 ((
% 122.46/16.15 (image1Equiv) =>
% 122.46/16.15 ((
% 122.46/16.15 (image1E) =>
% 122.46/16.15 ((
% 122.46/16.15 (image1I) =>
% 122.46/16.15 ((
% 122.46/16.15 (injFuncInInjFuncSet) =>
% 122.46/16.15 ((
% 122.46/16.15 (!!) @ (
% 122.46/16.15 (('#B') @ (
% 122.46/16.15 !!) @
% 122.46/16.15 (
% 122.46/16.15 (
% 122.46/16.15 ('#B') @ (
% 122.46/16.15 (
% 122.46/16.15 ('#B') @ (
% 122.46/16.15 !!))) @
% 122.46/16.15 (
% 122.46/16.15 (
% 122.46/16.15 ('#S') @ (
% 122.46/16.15 (
% 122.46/16.15 ('#B') @ (
% 122.46/16.15 '#S') @
% 122.46/16.15 (
% 122.46/16.15 (
% 122.46/16.15 ('#B') @ (
% 122.46/16.15 (
% 122.46/16.15 ('#B') @ (
% 122.46/16.15 '#S'))) @
% 122.46/16.15 (
% 122.46/16.15 (
% 122.46/16.15 ('#B') @ (
% 122.46/16.15 (
% 122.46/16.15 ('#B') @ (
% 122.46/16.15 (
% 122.46/16.15 ('#B') @ (
% 122.46/16.15 =>))))) @
% 122.46/16.15 (
% 122.46/16.15 (
% 122.46/16.15 ('#B') @ (
% 122.46/16.15 (
% 122.46/16.15 ('#B') @ (
% 122.46/16.15 (
% 122.46/16.15 ('#C') @ in)))) @
% 122.46/16.15 injFuncSet)))))))) @
% 122.46/16.15 (
% 122.46/16.15 (
% 122.46/16.15 ('#B') @ (
% 122.46/16.15 (
% 122.46/16.15 ('#B') @ (
% 122.46/16.15 (
% 122.46/16.15 ('#C') @ in)))) @
% 122.46/16.15 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.46/16.15 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1128])).
% 122.46/16.15 thf(zip_derived_cl1142, plain,
% 122.46/16.15 (~ (((binintersectI) =>
% 122.46/16.15 (((binintersectSubset5) =>
% 122.46/16.15 (((binintersectEL) =>
% 122.46/16.15 (((binintersectLsub) =>
% 122.46/16.15 (((binintersectSubset2) =>
% 122.46/16.15 (((binintersectSubset3) =>
% 122.46/16.15 (((binintersectER) =>
% 122.46/16.15 (((disjointsetsI1) =>
% 122.46/16.15 (((binintersectRsub) =>
% 122.46/16.15 (((binintersectSubset4) =>
% 122.46/16.15 (((binintersectSubset1) =>
% 122.46/16.15 (((bs114d) =>
% 122.46/16.15 (((setminusI) =>
% 122.46/16.15 (((setminusEL) =>
% 122.46/16.15 (((setminusER) =>
% 122.46/16.15 (((setminusSubset2) =>
% 122.46/16.15 (((setminusERneg) =>
% 122.46/16.15 (((setminusELneg) =>
% 122.46/16.15 (((setminusILneg) =>
% 122.46/16.15 (((setminusIRneg) =>
% 122.46/16.15 (((setminusLsub) =>
% 122.46/16.15 (((setminusSubset1) =>
% 122.46/16.15 (((symdiffE) =>
% 122.46/16.15 (((symdiffI1) =>
% 122.46/16.15 (((symdiffI2) =>
% 122.46/16.15 (((symdiffIneg1) =>
% 122.46/16.15 (((symdiffIneg2) =>
% 122.46/16.15 (((secondinupair) =>
% 122.46/16.15 (((setukpairIL) =>
% 122.46/16.15 (((setukpairIR) =>
% 122.46/16.15 ((
% 122.46/16.15 (kpairiskpair) =>
% 122.46/16.15 ((
% 122.46/16.15 (kpairp) =>
% 122.46/16.15 ((
% 122.46/16.15 (singletonsubset) =>
% 122.46/16.15 ((
% 122.46/16.15 (singletoninpowerset) =>
% 122.46/16.15 ((
% 122.46/16.15 (singletoninpowunion) =>
% 122.46/16.15 ((
% 122.46/16.15 (upairset2E) =>
% 122.46/16.15 ((
% 122.46/16.15 (upairsubunion) =>
% 122.46/16.15 ((
% 122.46/16.15 (upairinpowunion) =>
% 122.46/16.15 ((
% 122.46/16.15 (ubforcartprodlem1) =>
% 122.46/16.15 ((
% 122.46/16.15 (ubforcartprodlem2) =>
% 122.46/16.15 ((
% 122.46/16.15 (ubforcartprodlem3) =>
% 122.46/16.15 ((
% 122.46/16.15 (cartprodpairin) =>
% 122.46/16.15 ((
% 122.46/16.15 (cartprodmempair1) =>
% 122.46/16.15 ((
% 122.46/16.15 (cartprodmempair) =>
% 122.46/16.15 ((
% 122.46/16.15 (setunionE2) =>
% 122.46/16.15 ((
% 122.46/16.15 (setunionsingleton1) =>
% 122.46/16.15 ((
% 122.46/16.15 (setunionsingleton2) =>
% 122.46/16.15 ((
% 122.46/16.15 (setunionsingleton) =>
% 122.46/16.15 ((
% 122.46/16.15 (singletonprop) =>
% 122.46/16.15 ((
% 122.46/16.15 (ex1E1) =>
% 122.46/16.15 ((
% 122.46/16.15 (ex1I) =>
% 122.46/16.15 ((
% 122.46/16.15 (ex1I2) =>
% 122.46/16.15 ((
% 122.46/16.15 (singletonsuniq) =>
% 122.46/16.15 ((
% 122.46/16.15 (setukpairinjL1) =>
% 122.46/16.15 ((
% 122.46/16.15 (kfstsingleton) =>
% 122.46/16.15 ((
% 122.46/16.15 (theprop) =>
% 122.46/16.15 ((
% 122.46/16.15 (kfstpairEq) =>
% 122.46/16.15 ((
% 122.46/16.15 (cartprodfstin) =>
% 122.46/16.15 ((
% 122.46/16.15 (setukpairinjL2) =>
% 122.46/16.15 ((
% 122.46/16.15 (setukpairinjL) =>
% 122.46/16.15 ((
% 122.46/16.15 (setukpairinjR11) =>
% 122.46/16.15 ((
% 122.46/16.15 (setukpairinjR12) =>
% 122.46/16.15 ((
% 122.46/16.15 (setukpairinjR1) =>
% 122.46/16.15 ((
% 122.46/16.15 (upairequniteq) =>
% 122.46/16.15 ((
% 122.46/16.15 (setukpairinjR2) =>
% 122.46/16.15 ((
% 122.46/16.15 (setukpairinjR) =>
% 122.46/16.15 ((
% 122.46/16.15 (ksndsingleton) =>
% 122.46/16.15 ((
% 122.46/16.15 (ksndpairEq) =>
% 122.46/16.15 ((
% 122.46/16.15 (kpairsurjEq) =>
% 122.46/16.15 ((
% 122.46/16.15 (cartprodsndin) =>
% 122.46/16.15 ((
% 122.46/16.15 (cartprodpairmemEL) =>
% 122.46/16.15 ((
% 122.46/16.15 (cartprodpairmemER) =>
% 122.46/16.15 ((
% 122.46/16.15 (cartprodmempaircEq) =>
% 122.46/16.15 ((
% 122.46/16.15 (cartprodfstpairEq) =>
% 122.46/16.15 ((
% 122.46/16.15 (cartprodsndpairEq) =>
% 122.46/16.15 ((
% 122.46/16.15 (cartprodpairsurjEq) =>
% 122.46/16.15 ((
% 122.46/16.15 (dpsetconstrI) =>
% 122.46/16.15 ((
% 122.46/16.15 (dpsetconstrSub) =>
% 122.46/16.15 ((
% 122.46/16.15 (setOfPairsIsBReln) =>
% 122.46/16.15 ((
% 122.46/16.15 (dpsetconstrERa) =>
% 122.46/16.15 ((
% 122.46/16.15 (dpsetconstrEL1) =>
% 122.46/16.15 ((
% 122.46/16.15 (dpsetconstrEL2) =>
% 122.46/16.15 ((
% 122.46/16.15 (dpsetconstrER) =>
% 122.46/16.15 ((
% 122.46/16.15 (funcImageSingleton) =>
% 122.46/16.15 ((
% 122.46/16.15 (apProp) =>
% 122.46/16.15 ((
% 122.46/16.15 (app) =>
% 122.46/16.15 ((
% 122.46/16.15 (infuncsetfunc) =>
% 122.46/16.15 ((
% 122.46/16.15 (ap2p) =>
% 122.46/16.15 ((
% 122.46/16.15 (funcinfuncset) =>
% 122.46/16.15 ((
% 122.46/16.15 (lamProp) =>
% 122.46/16.15 ((
% 122.46/16.15 (lamp) =>
% 122.46/16.15 ((
% 122.46/16.15 (lam2p) =>
% 122.46/16.15 ((
% 122.46/16.15 (brelnall1) =>
% 122.46/16.15 ((
% 122.46/16.15 (brelnall2) =>
% 122.46/16.15 ((
% 122.46/16.15 (ex1E2) =>
% 122.46/16.15 ((
% 122.46/16.15 (funcGraphProp1) =>
% 122.46/16.15 ((
% 122.46/16.15 (funcGraphProp3) =>
% 122.46/16.15 ((
% 122.46/16.15 (funcGraphProp2) =>
% 122.46/16.15 ((
% 122.46/16.15 (funcextLem) =>
% 122.46/16.15 ((
% 122.46/16.15 (funcGraphProp4) =>
% 122.46/16.15 ((
% 122.46/16.15 (subbreln) =>
% 122.46/16.15 ((
% 122.46/16.15 (eqbreln) =>
% 122.46/16.15 ((
% 122.46/16.15 (funcext) =>
% 122.46/16.15 ((
% 122.46/16.15 (funcext2) =>
% 122.46/16.15 ((
% 122.46/16.15 (ap2apEq1) =>
% 122.46/16.15 ((
% 122.46/16.15 (ap2apEq2) =>
% 122.46/16.15 ((
% 122.46/16.15 (beta1) =>
% 122.46/16.15 ((
% 122.46/16.15 (eta1) =>
% 122.46/16.15 ((
% 122.46/16.15 (lam2lamEq) =>
% 122.46/16.15 ((
% 122.46/16.15 (beta2) =>
% 122.46/16.15 ((
% 122.46/16.15 (eta2) =>
% 122.46/16.15 ((
% 122.46/16.15 (iffalseProp1) =>
% 122.46/16.15 ((
% 122.46/16.15 (iffalseProp2) =>
% 122.46/16.15 ((
% 122.46/16.15 (iftrueProp1) =>
% 122.46/16.15 ((
% 122.46/16.15 (iftrueProp2) =>
% 122.46/16.15 ((
% 122.46/16.15 (ifSingleton) =>
% 122.46/16.15 ((
% 122.46/16.15 (ifp) =>
% 122.46/16.15 ((
% 122.46/16.15 (theeq) =>
% 122.46/16.15 ((
% 122.46/16.15 (iftrue) =>
% 122.46/16.15 ((
% 122.46/16.15 (iffalse) =>
% 122.46/16.15 ((
% 122.46/16.15 (iftrueorfalse) =>
% 122.46/16.15 ((
% 122.46/16.15 (binintersectT_lem) =>
% 122.46/16.15 ((
% 122.46/16.15 (binunionT_lem) =>
% 122.46/16.15 ((
% 122.46/16.15 (powersetT_lem) =>
% 122.46/16.15 ((
% 122.46/16.15 (setminusT_lem) =>
% 122.46/16.15 ((
% 122.46/16.15 (complementT_lem) =>
% 122.46/16.15 ((
% 122.46/16.15 (setextT) =>
% 122.46/16.15 ((
% 122.46/16.15 (subsetTI) =>
% 122.46/16.15 ((
% 122.46/16.15 (powersetTI1) =>
% 122.46/16.15 ((
% 122.46/16.15 (powersetTE1) =>
% 122.46/16.15 ((
% 122.46/16.15 (complementTI1) =>
% 122.46/16.15 ((
% 122.46/16.15 (complementTE1) =>
% 122.46/16.15 ((
% 122.46/16.15 (binintersectTELcontra) =>
% 122.46/16.15 ((
% 122.46/16.15 (binintersectTERcontra) =>
% 122.46/16.15 ((
% 122.46/16.15 (contrasubsetT) =>
% 122.46/16.15 ((
% 122.46/16.15 (contrasubsetT1) =>
% 122.46/16.15 ((
% 122.46/16.15 (contrasubsetT2) =>
% 122.46/16.15 ((
% 122.46/16.15 (contrasubsetT3) =>
% 122.46/16.15 ((
% 122.46/16.15 (doubleComplementI1) =>
% 122.46/16.15 ((
% 122.46/16.15 (doubleComplementE1) =>
% 122.46/16.15 ((
% 122.46/16.15 (doubleComplementSub1) =>
% 122.46/16.15 ((
% 122.46/16.15 (doubleComplementSub2) =>
% 122.46/16.15 ((
% 122.46/16.15 (doubleComplementEq) =>
% 122.46/16.15 ((
% 122.46/16.15 (complementTnotintersectT) =>
% 122.46/16.15 ((
% 122.46/16.15 (complementImpComplementIntersect) =>
% 122.46/16.15 ((
% 122.46/16.15 (complementSubsetComplementIntersect) =>
% 122.46/16.15 ((
% 122.46/16.15 (complementInPowersetComplementIntersect) =>
% 122.46/16.15 ((
% 122.46/16.15 (contraSubsetComplement) =>
% 122.46/16.15 ((
% 122.46/16.15 (complementTcontraSubset) =>
% 122.46/16.15 ((
% 122.46/16.15 (binunionTILcontra) =>
% 122.46/16.15 ((
% 122.46/16.15 (binunionTIRcontra) =>
% 122.46/16.15 ((
% 122.46/16.15 (inIntersectImpInUnion) =>
% 122.46/16.15 ((
% 122.46/16.15 (inIntersectImpInUnion2) =>
% 122.46/16.15 ((
% 122.46/16.15 (inIntersectImpInIntersectUnions) =>
% 122.46/16.15 ((
% 122.46/16.15 (intersectInPowersetIntersectUnions) =>
% 122.46/16.15 ((
% 122.46/16.15 (inComplementUnionImpNotIn1) =>
% 122.46/16.15 ((
% 122.46/16.15 (inComplementUnionImpInComplement1) =>
% 122.46/16.15 ((
% 122.46/16.15 (binunionTE) =>
% 122.46/16.15 ((
% 122.46/16.15 (binunionTEcontra) =>
% 122.46/16.15 ((
% 122.46/16.15 (demorgan2a1) =>
% 122.46/16.15 ((
% 122.46/16.15 (complementUnionInPowersetComplement) =>
% 122.46/16.15 ((
% 122.46/16.15 (demorgan2a2) =>
% 122.46/16.15 ((
% 122.46/16.15 (demorgan1a) =>
% 122.46/16.15 ((
% 122.46/16.15 (demorgan1b) =>
% 122.46/16.15 ((
% 122.46/16.15 (demorgan1) =>
% 122.46/16.15 ((
% 122.46/16.15 (demorgan2a) =>
% 122.46/16.15 ((
% 122.46/16.15 (demorgan2b2) =>
% 122.46/16.15 ((
% 122.46/16.15 (demorgan2b) =>
% 122.46/16.15 ((
% 122.46/16.15 (demorgan2) =>
% 122.46/16.15 ((
% 122.46/16.15 (woz13rule0) =>
% 122.46/16.15 ((
% 122.46/16.15 (woz13rule1) =>
% 122.46/16.15 ((
% 122.46/16.15 (woz13rule2) =>
% 122.46/16.15 ((
% 122.46/16.15 (woz13rule3) =>
% 122.46/16.15 ((
% 122.46/16.15 (woz13rule4) =>
% 122.46/16.15 ((
% 122.46/16.15 (woz1_1) =>
% 122.46/16.15 ((
% 122.46/16.15 (woz1_2) =>
% 122.46/16.15 ((
% 122.46/16.15 (woz1_3) =>
% 122.46/16.15 ((
% 122.46/16.15 (woz1_4) =>
% 122.46/16.15 ((
% 122.46/16.15 (woz1_5) =>
% 122.46/16.15 ((
% 122.46/16.15 (breln1all2) =>
% 122.46/16.15 ((
% 122.46/16.15 (breln1SetBreln1) =>
% 122.46/16.15 ((
% 122.46/16.15 (choice2fnsingleton) =>
% 122.46/16.15 ((
% 122.46/16.15 (setOfPairsIsBReln1) =>
% 122.46/16.15 ((
% 122.46/16.15 (breln1all1) =>
% 122.46/16.15 ((
% 122.46/16.15 (subbreln1) =>
% 122.46/16.15 ((
% 122.46/16.15 (eqbreln1) =>
% 122.46/16.15 ((
% 122.46/16.15 (breln1invprop) =>
% 122.46/16.15 ((
% 122.46/16.15 (breln1invI) =>
% 122.46/16.15 ((
% 122.46/16.15 (breln1invE) =>
% 122.46/16.15 ((
% 122.46/16.15 (breln1compprop) =>
% 122.46/16.15 ((
% 122.46/16.15 (breln1compI) =>
% 122.46/16.15 ((
% 122.46/16.15 (breln1compE) =>
% 122.46/16.15 ((
% 122.46/16.15 (breln1compEex) =>
% 122.46/16.15 ((
% 122.46/16.15 (breln1unionprop) =>
% 122.46/16.15 ((
% 122.46/16.15 (breln1unionIL) =>
% 122.46/16.15 ((
% 122.46/16.15 (breln1unionIR) =>
% 122.46/16.15 ((
% 122.46/16.15 (breln1unionI) =>
% 122.46/16.15 ((
% 122.46/16.15 (breln1unionE) =>
% 122.46/16.15 ((
% 122.46/16.15 (breln1unionEcases) =>
% 122.46/16.15 ((
% 122.46/16.15 (breln1unionCommutes) =>
% 122.46/16.15 ((
% 122.46/16.15 (woz2Ex) =>
% 122.46/16.15 ((
% 122.46/16.15 (woz2W) =>
% 122.46/16.15 ((
% 122.46/16.15 (woz2A) =>
% 122.46/16.15 ((
% 122.46/16.15 (woz2B) =>
% 122.46/16.15 ((
% 122.46/16.15 (image1Ex) =>
% 122.46/16.15 ((
% 122.46/16.15 (image1Ex1) =>
% 122.46/16.15 ((
% 122.46/16.15 (image1Equiv) =>
% 122.46/16.15 ((
% 122.46/16.15 (image1E) =>
% 122.46/16.15 ((
% 122.46/16.15 (image1I) =>
% 122.46/16.15 ((
% 122.46/16.15 (injFuncInInjFuncSet) =>
% 122.46/16.15 ((
% 122.46/16.15 (!!) @ (
% 122.46/16.15 (('#B') @ (
% 122.46/16.15 !!) @
% 122.46/16.15 (
% 122.46/16.15 (
% 122.46/16.15 ('#B') @ (
% 122.46/16.15 (
% 122.46/16.15 ('#B') @ (
% 122.46/16.15 !!))) @
% 122.46/16.15 (
% 122.46/16.15 (
% 122.46/16.15 ('#S') @ (
% 122.46/16.15 (
% 122.46/16.15 ('#B') @ (
% 122.46/16.15 '#S') @
% 122.46/16.15 (
% 122.46/16.15 (
% 122.46/16.15 ('#B') @ (
% 122.46/16.15 (
% 122.46/16.15 ('#B') @ (
% 122.46/16.15 '#S'))) @
% 122.46/16.15 (
% 122.46/16.15 (
% 122.46/16.15 ('#B') @ (
% 122.46/16.15 (
% 122.46/16.15 ('#B') @ (
% 122.46/16.15 (
% 122.46/16.15 ('#B') @ (
% 122.46/16.15 =>))))) @
% 122.46/16.15 (
% 122.46/16.15 (
% 122.46/16.15 ('#B') @ (
% 122.46/16.15 (
% 122.46/16.15 ('#B') @ (
% 122.46/16.15 (
% 122.46/16.15 ('#C') @ in)))) @
% 122.46/16.15 injFuncSet)))))))) @
% 122.46/16.15 (
% 122.46/16.15 (
% 122.46/16.15 ('#B') @ (
% 122.46/16.15 (
% 122.46/16.15 ('#B') @ (
% 122.46/16.15 (
% 122.46/16.15 ('#C') @ in)))) @
% 122.46/16.15 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.46/16.15 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1135])).
% 122.46/16.15 thf(zip_derived_cl1150, plain,
% 122.46/16.15 (~ (((binintersectSubset5) =>
% 122.46/16.15 (((binintersectEL) =>
% 122.46/16.15 (((binintersectLsub) =>
% 122.46/16.15 (((binintersectSubset2) =>
% 122.46/16.15 (((binintersectSubset3) =>
% 122.46/16.15 (((binintersectER) =>
% 122.46/16.15 (((disjointsetsI1) =>
% 122.46/16.15 (((binintersectRsub) =>
% 122.46/16.15 (((binintersectSubset4) =>
% 122.46/16.15 (((binintersectSubset1) =>
% 122.46/16.15 (((bs114d) =>
% 122.46/16.15 (((setminusI) =>
% 122.46/16.15 (((setminusEL) =>
% 122.46/16.15 (((setminusER) =>
% 122.46/16.15 (((setminusSubset2) =>
% 122.46/16.15 (((setminusERneg) =>
% 122.46/16.15 (((setminusELneg) =>
% 122.46/16.15 (((setminusILneg) =>
% 122.46/16.15 (((setminusIRneg) =>
% 122.46/16.15 (((setminusLsub) =>
% 122.46/16.15 (((setminusSubset1) =>
% 122.46/16.15 (((symdiffE) =>
% 122.46/16.15 (((symdiffI1) =>
% 122.46/16.15 (((symdiffI2) =>
% 122.46/16.15 (((symdiffIneg1) =>
% 122.46/16.15 (((symdiffIneg2) =>
% 122.46/16.15 (((secondinupair) =>
% 122.46/16.15 (((setukpairIL) =>
% 122.46/16.15 (((setukpairIR) =>
% 122.46/16.15 (((kpairiskpair) =>
% 122.46/16.15 ((
% 122.46/16.15 (kpairp) =>
% 122.46/16.15 ((
% 122.46/16.15 (singletonsubset) =>
% 122.46/16.15 ((
% 122.46/16.15 (singletoninpowerset) =>
% 122.46/16.15 ((
% 122.46/16.15 (singletoninpowunion) =>
% 122.46/16.15 ((
% 122.46/16.15 (upairset2E) =>
% 122.46/16.15 ((
% 122.46/16.15 (upairsubunion) =>
% 122.46/16.15 ((
% 122.46/16.15 (upairinpowunion) =>
% 122.46/16.15 ((
% 122.46/16.15 (ubforcartprodlem1) =>
% 122.46/16.15 ((
% 122.46/16.15 (ubforcartprodlem2) =>
% 122.46/16.15 ((
% 122.46/16.15 (ubforcartprodlem3) =>
% 122.46/16.15 ((
% 122.46/16.15 (cartprodpairin) =>
% 122.46/16.15 ((
% 122.46/16.15 (cartprodmempair1) =>
% 122.46/16.15 ((
% 122.46/16.15 (cartprodmempair) =>
% 122.46/16.15 ((
% 122.46/16.15 (setunionE2) =>
% 122.46/16.15 ((
% 122.46/16.15 (setunionsingleton1) =>
% 122.46/16.15 ((
% 122.46/16.15 (setunionsingleton2) =>
% 122.46/16.15 ((
% 122.46/16.15 (setunionsingleton) =>
% 122.46/16.15 ((
% 122.46/16.15 (singletonprop) =>
% 122.46/16.15 ((
% 122.46/16.15 (ex1E1) =>
% 122.46/16.15 ((
% 122.46/16.15 (ex1I) =>
% 122.46/16.15 ((
% 122.46/16.15 (ex1I2) =>
% 122.46/16.15 ((
% 122.46/16.15 (singletonsuniq) =>
% 122.46/16.15 ((
% 122.46/16.15 (setukpairinjL1) =>
% 122.46/16.15 ((
% 122.46/16.15 (kfstsingleton) =>
% 122.46/16.15 ((
% 122.46/16.15 (theprop) =>
% 122.46/16.15 ((
% 122.46/16.15 (kfstpairEq) =>
% 122.46/16.15 ((
% 122.46/16.15 (cartprodfstin) =>
% 122.46/16.15 ((
% 122.46/16.15 (setukpairinjL2) =>
% 122.46/16.15 ((
% 122.46/16.15 (setukpairinjL) =>
% 122.46/16.15 ((
% 122.46/16.15 (setukpairinjR11) =>
% 122.46/16.15 ((
% 122.46/16.15 (setukpairinjR12) =>
% 122.46/16.15 ((
% 122.46/16.15 (setukpairinjR1) =>
% 122.46/16.15 ((
% 122.46/16.15 (upairequniteq) =>
% 122.46/16.15 ((
% 122.46/16.15 (setukpairinjR2) =>
% 122.46/16.15 ((
% 122.46/16.15 (setukpairinjR) =>
% 122.46/16.15 ((
% 122.46/16.15 (ksndsingleton) =>
% 122.46/16.15 ((
% 122.46/16.15 (ksndpairEq) =>
% 122.46/16.15 ((
% 122.46/16.15 (kpairsurjEq) =>
% 122.46/16.15 ((
% 122.46/16.15 (cartprodsndin) =>
% 122.46/16.15 ((
% 122.46/16.15 (cartprodpairmemEL) =>
% 122.46/16.15 ((
% 122.46/16.15 (cartprodpairmemER) =>
% 122.46/16.15 ((
% 122.46/16.15 (cartprodmempaircEq) =>
% 122.46/16.15 ((
% 122.46/16.15 (cartprodfstpairEq) =>
% 122.46/16.15 ((
% 122.46/16.15 (cartprodsndpairEq) =>
% 122.46/16.15 ((
% 122.46/16.15 (cartprodpairsurjEq) =>
% 122.46/16.15 ((
% 122.46/16.15 (dpsetconstrI) =>
% 122.46/16.15 ((
% 122.46/16.15 (dpsetconstrSub) =>
% 122.46/16.15 ((
% 122.46/16.15 (setOfPairsIsBReln) =>
% 122.46/16.15 ((
% 122.46/16.15 (dpsetconstrERa) =>
% 122.46/16.15 ((
% 122.46/16.15 (dpsetconstrEL1) =>
% 122.46/16.15 ((
% 122.46/16.15 (dpsetconstrEL2) =>
% 122.46/16.15 ((
% 122.46/16.15 (dpsetconstrER) =>
% 122.46/16.15 ((
% 122.46/16.15 (funcImageSingleton) =>
% 122.46/16.15 ((
% 122.46/16.15 (apProp) =>
% 122.46/16.15 ((
% 122.46/16.15 (app) =>
% 122.46/16.15 ((
% 122.46/16.15 (infuncsetfunc) =>
% 122.46/16.15 ((
% 122.46/16.15 (ap2p) =>
% 122.46/16.15 ((
% 122.46/16.15 (funcinfuncset) =>
% 122.46/16.15 ((
% 122.46/16.15 (lamProp) =>
% 122.46/16.15 ((
% 122.46/16.15 (lamp) =>
% 122.46/16.15 ((
% 122.46/16.15 (lam2p) =>
% 122.46/16.15 ((
% 122.46/16.15 (brelnall1) =>
% 122.46/16.15 ((
% 122.46/16.15 (brelnall2) =>
% 122.46/16.15 ((
% 122.46/16.15 (ex1E2) =>
% 122.46/16.15 ((
% 122.46/16.15 (funcGraphProp1) =>
% 122.46/16.15 ((
% 122.46/16.15 (funcGraphProp3) =>
% 122.46/16.15 ((
% 122.46/16.15 (funcGraphProp2) =>
% 122.46/16.15 ((
% 122.46/16.15 (funcextLem) =>
% 122.46/16.15 ((
% 122.46/16.15 (funcGraphProp4) =>
% 122.46/16.15 ((
% 122.46/16.15 (subbreln) =>
% 122.46/16.15 ((
% 122.46/16.15 (eqbreln) =>
% 122.46/16.15 ((
% 122.46/16.15 (funcext) =>
% 122.46/16.15 ((
% 122.46/16.15 (funcext2) =>
% 122.46/16.15 ((
% 122.46/16.15 (ap2apEq1) =>
% 122.46/16.15 ((
% 122.46/16.15 (ap2apEq2) =>
% 122.46/16.15 ((
% 122.46/16.15 (beta1) =>
% 122.46/16.15 ((
% 122.46/16.15 (eta1) =>
% 122.46/16.15 ((
% 122.46/16.15 (lam2lamEq) =>
% 122.46/16.15 ((
% 122.46/16.15 (beta2) =>
% 122.46/16.15 ((
% 122.46/16.15 (eta2) =>
% 122.46/16.15 ((
% 122.46/16.15 (iffalseProp1) =>
% 122.46/16.15 ((
% 122.46/16.15 (iffalseProp2) =>
% 122.46/16.15 ((
% 122.46/16.15 (iftrueProp1) =>
% 122.46/16.15 ((
% 122.46/16.15 (iftrueProp2) =>
% 122.46/16.15 ((
% 122.46/16.15 (ifSingleton) =>
% 122.46/16.15 ((
% 122.46/16.15 (ifp) =>
% 122.46/16.15 ((
% 122.46/16.15 (theeq) =>
% 122.46/16.15 ((
% 122.46/16.15 (iftrue) =>
% 122.46/16.15 ((
% 122.46/16.15 (iffalse) =>
% 122.46/16.15 ((
% 122.46/16.15 (iftrueorfalse) =>
% 122.46/16.15 ((
% 122.46/16.15 (binintersectT_lem) =>
% 122.46/16.15 ((
% 122.46/16.15 (binunionT_lem) =>
% 122.46/16.15 ((
% 122.46/16.15 (powersetT_lem) =>
% 122.46/16.15 ((
% 122.46/16.15 (setminusT_lem) =>
% 122.46/16.15 ((
% 122.46/16.15 (complementT_lem) =>
% 122.46/16.15 ((
% 122.46/16.15 (setextT) =>
% 122.46/16.15 ((
% 122.46/16.15 (subsetTI) =>
% 122.46/16.15 ((
% 122.46/16.15 (powersetTI1) =>
% 122.46/16.15 ((
% 122.46/16.15 (powersetTE1) =>
% 122.46/16.15 ((
% 122.46/16.15 (complementTI1) =>
% 122.46/16.15 ((
% 122.46/16.15 (complementTE1) =>
% 122.46/16.15 ((
% 122.46/16.15 (binintersectTELcontra) =>
% 122.46/16.15 ((
% 122.46/16.15 (binintersectTERcontra) =>
% 122.46/16.15 ((
% 122.46/16.15 (contrasubsetT) =>
% 122.46/16.15 ((
% 122.46/16.15 (contrasubsetT1) =>
% 122.46/16.15 ((
% 122.46/16.15 (contrasubsetT2) =>
% 122.46/16.15 ((
% 122.46/16.15 (contrasubsetT3) =>
% 122.46/16.15 ((
% 122.46/16.15 (doubleComplementI1) =>
% 122.46/16.15 ((
% 122.46/16.15 (doubleComplementE1) =>
% 122.46/16.15 ((
% 122.46/16.15 (doubleComplementSub1) =>
% 122.46/16.15 ((
% 122.46/16.15 (doubleComplementSub2) =>
% 122.46/16.15 ((
% 122.46/16.15 (doubleComplementEq) =>
% 122.46/16.15 ((
% 122.46/16.15 (complementTnotintersectT) =>
% 122.46/16.15 ((
% 122.46/16.15 (complementImpComplementIntersect) =>
% 122.46/16.15 ((
% 122.46/16.15 (complementSubsetComplementIntersect) =>
% 122.46/16.15 ((
% 122.46/16.15 (complementInPowersetComplementIntersect) =>
% 122.46/16.15 ((
% 122.46/16.15 (contraSubsetComplement) =>
% 122.46/16.15 ((
% 122.46/16.15 (complementTcontraSubset) =>
% 122.46/16.15 ((
% 122.46/16.15 (binunionTILcontra) =>
% 122.46/16.15 ((
% 122.46/16.15 (binunionTIRcontra) =>
% 122.46/16.15 ((
% 122.46/16.15 (inIntersectImpInUnion) =>
% 122.46/16.15 ((
% 122.46/16.15 (inIntersectImpInUnion2) =>
% 122.46/16.15 ((
% 122.46/16.15 (inIntersectImpInIntersectUnions) =>
% 122.46/16.15 ((
% 122.46/16.15 (intersectInPowersetIntersectUnions) =>
% 122.46/16.15 ((
% 122.46/16.15 (inComplementUnionImpNotIn1) =>
% 122.46/16.15 ((
% 122.46/16.15 (inComplementUnionImpInComplement1) =>
% 122.46/16.15 ((
% 122.46/16.15 (binunionTE) =>
% 122.46/16.15 ((
% 122.46/16.15 (binunionTEcontra) =>
% 122.46/16.15 ((
% 122.46/16.15 (demorgan2a1) =>
% 122.46/16.15 ((
% 122.46/16.15 (complementUnionInPowersetComplement) =>
% 122.46/16.15 ((
% 122.46/16.15 (demorgan2a2) =>
% 122.46/16.15 ((
% 122.46/16.15 (demorgan1a) =>
% 122.46/16.15 ((
% 122.46/16.15 (demorgan1b) =>
% 122.46/16.15 ((
% 122.46/16.15 (demorgan1) =>
% 122.46/16.15 ((
% 122.46/16.15 (demorgan2a) =>
% 122.46/16.15 ((
% 122.46/16.15 (demorgan2b2) =>
% 122.46/16.15 ((
% 122.46/16.15 (demorgan2b) =>
% 122.46/16.15 ((
% 122.46/16.15 (demorgan2) =>
% 122.46/16.15 ((
% 122.46/16.15 (woz13rule0) =>
% 122.46/16.15 ((
% 122.46/16.15 (woz13rule1) =>
% 122.46/16.15 ((
% 122.46/16.15 (woz13rule2) =>
% 122.46/16.15 ((
% 122.46/16.15 (woz13rule3) =>
% 122.46/16.15 ((
% 122.46/16.15 (woz13rule4) =>
% 122.46/16.15 ((
% 122.46/16.15 (woz1_1) =>
% 122.46/16.15 ((
% 122.46/16.15 (woz1_2) =>
% 122.46/16.15 ((
% 122.46/16.15 (woz1_3) =>
% 122.46/16.15 ((
% 122.46/16.15 (woz1_4) =>
% 122.46/16.15 ((
% 122.46/16.15 (woz1_5) =>
% 122.46/16.15 ((
% 122.46/16.15 (breln1all2) =>
% 122.46/16.15 ((
% 122.46/16.15 (breln1SetBreln1) =>
% 122.46/16.15 ((
% 122.46/16.15 (choice2fnsingleton) =>
% 122.46/16.15 ((
% 122.46/16.15 (setOfPairsIsBReln1) =>
% 122.46/16.15 ((
% 122.46/16.15 (breln1all1) =>
% 122.46/16.15 ((
% 122.46/16.15 (subbreln1) =>
% 122.46/16.15 ((
% 122.46/16.15 (eqbreln1) =>
% 122.46/16.15 ((
% 122.46/16.15 (breln1invprop) =>
% 122.46/16.15 ((
% 122.46/16.15 (breln1invI) =>
% 122.46/16.15 ((
% 122.46/16.15 (breln1invE) =>
% 122.46/16.15 ((
% 122.46/16.15 (breln1compprop) =>
% 122.46/16.15 ((
% 122.46/16.15 (breln1compI) =>
% 122.46/16.15 ((
% 122.46/16.15 (breln1compE) =>
% 122.46/16.15 ((
% 122.46/16.15 (breln1compEex) =>
% 122.46/16.15 ((
% 122.46/16.15 (breln1unionprop) =>
% 122.46/16.15 ((
% 122.46/16.15 (breln1unionIL) =>
% 122.46/16.15 ((
% 122.46/16.15 (breln1unionIR) =>
% 122.46/16.15 ((
% 122.46/16.15 (breln1unionI) =>
% 122.46/16.15 ((
% 122.46/16.15 (breln1unionE) =>
% 122.46/16.15 ((
% 122.46/16.15 (breln1unionEcases) =>
% 122.46/16.15 ((
% 122.46/16.15 (breln1unionCommutes) =>
% 122.46/16.15 ((
% 122.46/16.15 (woz2Ex) =>
% 122.46/16.15 ((
% 122.46/16.15 (woz2W) =>
% 122.46/16.15 ((
% 122.46/16.15 (woz2A) =>
% 122.46/16.15 ((
% 122.46/16.15 (woz2B) =>
% 122.46/16.15 ((
% 122.46/16.15 (image1Ex) =>
% 122.46/16.15 ((
% 122.46/16.15 (image1Ex1) =>
% 122.46/16.15 ((
% 122.46/16.15 (image1Equiv) =>
% 122.46/16.15 ((
% 122.46/16.15 (image1E) =>
% 122.46/16.15 ((
% 122.46/16.15 (image1I) =>
% 122.46/16.15 ((
% 122.46/16.15 (injFuncInInjFuncSet) =>
% 122.46/16.15 ((
% 122.46/16.15 (!!) @ (
% 122.46/16.15 (('#B') @ (
% 122.46/16.15 !!) @
% 122.46/16.15 (
% 122.46/16.15 (
% 122.46/16.15 ('#B') @ (
% 122.46/16.15 (
% 122.46/16.15 ('#B') @ (
% 122.46/16.15 !!))) @
% 122.46/16.15 (
% 122.46/16.15 (
% 122.46/16.15 ('#S') @ (
% 122.46/16.15 (
% 122.46/16.15 ('#B') @ (
% 122.46/16.15 '#S') @
% 122.46/16.15 (
% 122.46/16.15 (
% 122.46/16.15 ('#B') @ (
% 122.46/16.15 (
% 122.46/16.15 ('#B') @ (
% 122.46/16.15 '#S'))) @
% 122.46/16.15 (
% 122.46/16.15 (
% 122.46/16.15 ('#B') @ (
% 122.46/16.15 (
% 122.46/16.15 ('#B') @ (
% 122.46/16.15 (
% 122.46/16.15 ('#B') @ (
% 122.46/16.15 =>))))) @
% 122.46/16.15 (
% 122.46/16.15 (
% 122.46/16.15 ('#B') @ (
% 122.46/16.15 (
% 122.46/16.15 ('#B') @ (
% 122.46/16.15 (
% 122.46/16.15 ('#C') @ in)))) @
% 122.46/16.15 injFuncSet)))))))) @
% 122.46/16.15 (
% 122.46/16.15 (
% 122.46/16.15 ('#B') @ (
% 122.46/16.15 (
% 122.46/16.15 ('#B') @ (
% 122.46/16.15 (
% 122.46/16.15 ('#C') @ in)))) @
% 122.46/16.15 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.46/16.15 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1142])).
% 122.46/16.15 thf(zip_derived_cl1158, plain,
% 122.46/16.15 (~ (((binintersectEL) =>
% 122.46/16.15 (((binintersectLsub) =>
% 122.46/16.15 (((binintersectSubset2) =>
% 122.46/16.15 (((binintersectSubset3) =>
% 122.46/16.15 (((binintersectER) =>
% 122.46/16.15 (((disjointsetsI1) =>
% 122.46/16.15 (((binintersectRsub) =>
% 122.46/16.15 (((binintersectSubset4) =>
% 122.46/16.15 (((binintersectSubset1) =>
% 122.46/16.15 (((bs114d) =>
% 122.46/16.15 (((setminusI) =>
% 122.46/16.15 (((setminusEL) =>
% 122.46/16.15 (((setminusER) =>
% 122.46/16.15 (((setminusSubset2) =>
% 122.46/16.15 (((setminusERneg) =>
% 122.46/16.15 (((setminusELneg) =>
% 122.46/16.15 (((setminusILneg) =>
% 122.46/16.15 (((setminusIRneg) =>
% 122.46/16.15 (((setminusLsub) =>
% 122.46/16.15 (((setminusSubset1) =>
% 122.46/16.15 (((symdiffE) =>
% 122.46/16.15 (((symdiffI1) =>
% 122.46/16.15 (((symdiffI2) =>
% 122.46/16.15 (((symdiffIneg1) =>
% 122.46/16.15 (((symdiffIneg2) =>
% 122.46/16.15 (((secondinupair) =>
% 122.46/16.15 (((setukpairIL) =>
% 122.46/16.15 (((setukpairIR) =>
% 122.46/16.15 (((kpairiskpair) =>
% 122.46/16.15 (((kpairp) =>
% 122.46/16.15 ((
% 122.46/16.15 (singletonsubset) =>
% 122.46/16.15 ((
% 122.46/16.15 (singletoninpowerset) =>
% 122.46/16.15 ((
% 122.46/16.15 (singletoninpowunion) =>
% 122.46/16.15 ((
% 122.46/16.15 (upairset2E) =>
% 122.46/16.15 ((
% 122.46/16.15 (upairsubunion) =>
% 122.46/16.15 ((
% 122.46/16.15 (upairinpowunion) =>
% 122.46/16.15 ((
% 122.46/16.15 (ubforcartprodlem1) =>
% 122.46/16.15 ((
% 122.46/16.15 (ubforcartprodlem2) =>
% 122.46/16.15 ((
% 122.46/16.15 (ubforcartprodlem3) =>
% 122.46/16.15 ((
% 122.46/16.15 (cartprodpairin) =>
% 122.46/16.15 ((
% 122.46/16.15 (cartprodmempair1) =>
% 122.46/16.15 ((
% 122.46/16.15 (cartprodmempair) =>
% 122.46/16.15 ((
% 122.46/16.15 (setunionE2) =>
% 122.46/16.15 ((
% 122.46/16.15 (setunionsingleton1) =>
% 122.46/16.15 ((
% 122.46/16.15 (setunionsingleton2) =>
% 122.46/16.15 ((
% 122.46/16.15 (setunionsingleton) =>
% 122.46/16.15 ((
% 122.46/16.15 (singletonprop) =>
% 122.46/16.15 ((
% 122.46/16.15 (ex1E1) =>
% 122.46/16.15 ((
% 122.46/16.15 (ex1I) =>
% 122.46/16.15 ((
% 122.46/16.15 (ex1I2) =>
% 122.46/16.15 ((
% 122.46/16.15 (singletonsuniq) =>
% 122.46/16.15 ((
% 122.46/16.15 (setukpairinjL1) =>
% 122.46/16.15 ((
% 122.46/16.15 (kfstsingleton) =>
% 122.46/16.15 ((
% 122.46/16.15 (theprop) =>
% 122.46/16.15 ((
% 122.46/16.15 (kfstpairEq) =>
% 122.46/16.15 ((
% 122.46/16.15 (cartprodfstin) =>
% 122.46/16.15 ((
% 122.46/16.15 (setukpairinjL2) =>
% 122.46/16.15 ((
% 122.46/16.15 (setukpairinjL) =>
% 122.46/16.15 ((
% 122.46/16.15 (setukpairinjR11) =>
% 122.46/16.15 ((
% 122.46/16.15 (setukpairinjR12) =>
% 122.46/16.15 ((
% 122.46/16.15 (setukpairinjR1) =>
% 122.46/16.15 ((
% 122.46/16.15 (upairequniteq) =>
% 122.46/16.15 ((
% 122.46/16.15 (setukpairinjR2) =>
% 122.46/16.15 ((
% 122.46/16.15 (setukpairinjR) =>
% 122.46/16.15 ((
% 122.46/16.15 (ksndsingleton) =>
% 122.46/16.15 ((
% 122.46/16.15 (ksndpairEq) =>
% 122.46/16.15 ((
% 122.46/16.15 (kpairsurjEq) =>
% 122.46/16.15 ((
% 122.46/16.15 (cartprodsndin) =>
% 122.46/16.15 ((
% 122.46/16.15 (cartprodpairmemEL) =>
% 122.46/16.15 ((
% 122.46/16.15 (cartprodpairmemER) =>
% 122.46/16.15 ((
% 122.46/16.15 (cartprodmempaircEq) =>
% 122.46/16.15 ((
% 122.46/16.15 (cartprodfstpairEq) =>
% 122.46/16.15 ((
% 122.46/16.15 (cartprodsndpairEq) =>
% 122.46/16.15 ((
% 122.46/16.15 (cartprodpairsurjEq) =>
% 122.46/16.15 ((
% 122.46/16.15 (dpsetconstrI) =>
% 122.46/16.15 ((
% 122.46/16.15 (dpsetconstrSub) =>
% 122.46/16.15 ((
% 122.46/16.15 (setOfPairsIsBReln) =>
% 122.46/16.15 ((
% 122.46/16.15 (dpsetconstrERa) =>
% 122.46/16.15 ((
% 122.46/16.15 (dpsetconstrEL1) =>
% 122.46/16.15 ((
% 122.46/16.15 (dpsetconstrEL2) =>
% 122.46/16.15 ((
% 122.46/16.15 (dpsetconstrER) =>
% 122.46/16.15 ((
% 122.46/16.15 (funcImageSingleton) =>
% 122.46/16.15 ((
% 122.46/16.15 (apProp) =>
% 122.46/16.15 ((
% 122.46/16.15 (app) =>
% 122.46/16.15 ((
% 122.46/16.15 (infuncsetfunc) =>
% 122.46/16.15 ((
% 122.46/16.15 (ap2p) =>
% 122.46/16.15 ((
% 122.46/16.15 (funcinfuncset) =>
% 122.46/16.15 ((
% 122.46/16.15 (lamProp) =>
% 122.46/16.15 ((
% 122.46/16.15 (lamp) =>
% 122.46/16.15 ((
% 122.46/16.15 (lam2p) =>
% 122.46/16.15 ((
% 122.46/16.15 (brelnall1) =>
% 122.46/16.15 ((
% 122.46/16.15 (brelnall2) =>
% 122.46/16.15 ((
% 122.46/16.15 (ex1E2) =>
% 122.46/16.15 ((
% 122.46/16.15 (funcGraphProp1) =>
% 122.46/16.15 ((
% 122.46/16.15 (funcGraphProp3) =>
% 122.46/16.15 ((
% 122.46/16.15 (funcGraphProp2) =>
% 122.46/16.15 ((
% 122.46/16.15 (funcextLem) =>
% 122.46/16.15 ((
% 122.46/16.15 (funcGraphProp4) =>
% 122.46/16.15 ((
% 122.46/16.15 (subbreln) =>
% 122.46/16.15 ((
% 122.46/16.15 (eqbreln) =>
% 122.46/16.15 ((
% 122.46/16.15 (funcext) =>
% 122.46/16.15 ((
% 122.46/16.15 (funcext2) =>
% 122.46/16.15 ((
% 122.46/16.15 (ap2apEq1) =>
% 122.46/16.15 ((
% 122.46/16.15 (ap2apEq2) =>
% 122.46/16.15 ((
% 122.46/16.15 (beta1) =>
% 122.46/16.15 ((
% 122.46/16.15 (eta1) =>
% 122.46/16.15 ((
% 122.46/16.15 (lam2lamEq) =>
% 122.46/16.15 ((
% 122.46/16.15 (beta2) =>
% 122.46/16.15 ((
% 122.46/16.15 (eta2) =>
% 122.46/16.15 ((
% 122.46/16.15 (iffalseProp1) =>
% 122.46/16.15 ((
% 122.46/16.15 (iffalseProp2) =>
% 122.46/16.15 ((
% 122.46/16.15 (iftrueProp1) =>
% 122.46/16.15 ((
% 122.46/16.15 (iftrueProp2) =>
% 122.46/16.15 ((
% 122.46/16.15 (ifSingleton) =>
% 122.46/16.15 ((
% 122.46/16.15 (ifp) =>
% 122.46/16.15 ((
% 122.46/16.15 (theeq) =>
% 122.46/16.15 ((
% 122.46/16.15 (iftrue) =>
% 122.46/16.15 ((
% 122.46/16.15 (iffalse) =>
% 122.46/16.15 ((
% 122.46/16.15 (iftrueorfalse) =>
% 122.46/16.15 ((
% 122.46/16.15 (binintersectT_lem) =>
% 122.46/16.15 ((
% 122.46/16.15 (binunionT_lem) =>
% 122.46/16.15 ((
% 122.46/16.15 (powersetT_lem) =>
% 122.46/16.15 ((
% 122.46/16.15 (setminusT_lem) =>
% 122.46/16.15 ((
% 122.46/16.15 (complementT_lem) =>
% 122.46/16.15 ((
% 122.46/16.15 (setextT) =>
% 122.46/16.15 ((
% 122.46/16.15 (subsetTI) =>
% 122.46/16.15 ((
% 122.46/16.15 (powersetTI1) =>
% 122.46/16.15 ((
% 122.46/16.15 (powersetTE1) =>
% 122.46/16.15 ((
% 122.46/16.15 (complementTI1) =>
% 122.46/16.15 ((
% 122.46/16.15 (complementTE1) =>
% 122.46/16.15 ((
% 122.46/16.15 (binintersectTELcontra) =>
% 122.46/16.15 ((
% 122.46/16.15 (binintersectTERcontra) =>
% 122.46/16.15 ((
% 122.46/16.15 (contrasubsetT) =>
% 122.46/16.15 ((
% 122.46/16.15 (contrasubsetT1) =>
% 122.46/16.15 ((
% 122.46/16.15 (contrasubsetT2) =>
% 122.46/16.15 ((
% 122.46/16.15 (contrasubsetT3) =>
% 122.46/16.15 ((
% 122.46/16.15 (doubleComplementI1) =>
% 122.46/16.15 ((
% 122.46/16.15 (doubleComplementE1) =>
% 122.46/16.15 ((
% 122.46/16.15 (doubleComplementSub1) =>
% 122.46/16.15 ((
% 122.46/16.15 (doubleComplementSub2) =>
% 122.46/16.15 ((
% 122.46/16.15 (doubleComplementEq) =>
% 122.46/16.15 ((
% 122.46/16.15 (complementTnotintersectT) =>
% 122.46/16.15 ((
% 122.46/16.15 (complementImpComplementIntersect) =>
% 122.46/16.15 ((
% 122.46/16.15 (complementSubsetComplementIntersect) =>
% 122.46/16.15 ((
% 122.46/16.15 (complementInPowersetComplementIntersect) =>
% 122.46/16.15 ((
% 122.46/16.15 (contraSubsetComplement) =>
% 122.46/16.15 ((
% 122.46/16.15 (complementTcontraSubset) =>
% 122.46/16.15 ((
% 122.46/16.15 (binunionTILcontra) =>
% 122.46/16.15 ((
% 122.46/16.15 (binunionTIRcontra) =>
% 122.46/16.15 ((
% 122.46/16.15 (inIntersectImpInUnion) =>
% 122.46/16.15 ((
% 122.46/16.15 (inIntersectImpInUnion2) =>
% 122.46/16.15 ((
% 122.46/16.15 (inIntersectImpInIntersectUnions) =>
% 122.46/16.15 ((
% 122.46/16.15 (intersectInPowersetIntersectUnions) =>
% 122.46/16.15 ((
% 122.46/16.15 (inComplementUnionImpNotIn1) =>
% 122.46/16.15 ((
% 122.46/16.15 (inComplementUnionImpInComplement1) =>
% 122.46/16.15 ((
% 122.46/16.15 (binunionTE) =>
% 122.46/16.15 ((
% 122.46/16.15 (binunionTEcontra) =>
% 122.46/16.15 ((
% 122.46/16.15 (demorgan2a1) =>
% 122.46/16.15 ((
% 122.46/16.15 (complementUnionInPowersetComplement) =>
% 122.46/16.15 ((
% 122.46/16.15 (demorgan2a2) =>
% 122.46/16.15 ((
% 122.46/16.15 (demorgan1a) =>
% 122.46/16.15 ((
% 122.46/16.15 (demorgan1b) =>
% 122.46/16.15 ((
% 122.46/16.15 (demorgan1) =>
% 122.46/16.15 ((
% 122.46/16.15 (demorgan2a) =>
% 122.46/16.15 ((
% 122.46/16.15 (demorgan2b2) =>
% 122.46/16.15 ((
% 122.46/16.15 (demorgan2b) =>
% 122.46/16.15 ((
% 122.46/16.15 (demorgan2) =>
% 122.46/16.15 ((
% 122.46/16.15 (woz13rule0) =>
% 122.46/16.15 ((
% 122.46/16.15 (woz13rule1) =>
% 122.46/16.15 ((
% 122.46/16.15 (woz13rule2) =>
% 122.46/16.15 ((
% 122.46/16.15 (woz13rule3) =>
% 122.46/16.15 ((
% 122.46/16.15 (woz13rule4) =>
% 122.46/16.15 ((
% 122.46/16.15 (woz1_1) =>
% 122.46/16.15 ((
% 122.46/16.15 (woz1_2) =>
% 122.46/16.15 ((
% 122.46/16.15 (woz1_3) =>
% 122.46/16.15 ((
% 122.46/16.15 (woz1_4) =>
% 122.46/16.15 ((
% 122.46/16.15 (woz1_5) =>
% 122.46/16.15 ((
% 122.46/16.15 (breln1all2) =>
% 122.46/16.15 ((
% 122.46/16.15 (breln1SetBreln1) =>
% 122.46/16.15 ((
% 122.46/16.15 (choice2fnsingleton) =>
% 122.46/16.15 ((
% 122.46/16.15 (setOfPairsIsBReln1) =>
% 122.46/16.15 ((
% 122.46/16.15 (breln1all1) =>
% 122.46/16.15 ((
% 122.46/16.15 (subbreln1) =>
% 122.46/16.15 ((
% 122.46/16.15 (eqbreln1) =>
% 122.46/16.15 ((
% 122.46/16.15 (breln1invprop) =>
% 122.46/16.15 ((
% 122.46/16.15 (breln1invI) =>
% 122.46/16.15 ((
% 122.46/16.15 (breln1invE) =>
% 122.46/16.15 ((
% 122.46/16.15 (breln1compprop) =>
% 122.46/16.15 ((
% 122.46/16.15 (breln1compI) =>
% 122.46/16.15 ((
% 122.46/16.15 (breln1compE) =>
% 122.46/16.15 ((
% 122.46/16.15 (breln1compEex) =>
% 122.46/16.15 ((
% 122.46/16.15 (breln1unionprop) =>
% 122.46/16.15 ((
% 122.46/16.15 (breln1unionIL) =>
% 122.46/16.15 ((
% 122.46/16.15 (breln1unionIR) =>
% 122.46/16.15 ((
% 122.46/16.15 (breln1unionI) =>
% 122.46/16.15 ((
% 122.46/16.15 (breln1unionE) =>
% 122.46/16.15 ((
% 122.46/16.15 (breln1unionEcases) =>
% 122.46/16.15 ((
% 122.46/16.15 (breln1unionCommutes) =>
% 122.46/16.15 ((
% 122.46/16.15 (woz2Ex) =>
% 122.46/16.15 ((
% 122.46/16.15 (woz2W) =>
% 122.46/16.15 ((
% 122.46/16.15 (woz2A) =>
% 122.46/16.15 ((
% 122.46/16.15 (woz2B) =>
% 122.46/16.15 ((
% 122.46/16.15 (image1Ex) =>
% 122.46/16.15 ((
% 122.46/16.15 (image1Ex1) =>
% 122.46/16.15 ((
% 122.46/16.15 (image1Equiv) =>
% 122.46/16.15 ((
% 122.46/16.15 (image1E) =>
% 122.46/16.15 ((
% 122.46/16.15 (image1I) =>
% 122.46/16.15 ((
% 122.46/16.15 (injFuncInInjFuncSet) =>
% 122.46/16.15 ((
% 122.46/16.15 (!!) @ (
% 122.46/16.15 (('#B') @ (
% 122.46/16.15 !!) @
% 122.46/16.15 (
% 122.46/16.15 (
% 122.46/16.15 ('#B') @ (
% 122.46/16.15 (
% 122.46/16.15 ('#B') @ (
% 122.46/16.15 !!))) @
% 122.46/16.15 (
% 122.46/16.15 (
% 122.46/16.15 ('#S') @ (
% 122.46/16.15 (
% 122.46/16.15 ('#B') @ (
% 122.46/16.15 '#S') @
% 122.46/16.15 (
% 122.46/16.15 (
% 122.46/16.15 ('#B') @ (
% 122.46/16.15 (
% 122.46/16.15 ('#B') @ (
% 122.46/16.15 '#S'))) @
% 122.46/16.15 (
% 122.46/16.15 (
% 122.46/16.15 ('#B') @ (
% 122.46/16.15 (
% 122.46/16.15 ('#B') @ (
% 122.46/16.15 (
% 122.46/16.15 ('#B') @ (
% 122.46/16.15 =>))))) @
% 122.46/16.15 (
% 122.46/16.15 (
% 122.46/16.15 ('#B') @ (
% 122.46/16.15 (
% 122.46/16.15 ('#B') @ (
% 122.46/16.15 (
% 122.46/16.15 ('#C') @ in)))) @
% 122.46/16.15 injFuncSet)))))))) @
% 122.46/16.15 (
% 122.46/16.15 (
% 122.46/16.15 ('#B') @ (
% 122.46/16.15 (
% 122.46/16.15 ('#B') @ (
% 122.46/16.15 (
% 122.46/16.15 ('#C') @ in)))) @
% 122.46/16.15 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.46/16.15 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1150])).
% 122.46/16.15 thf(zip_derived_cl1166, plain,
% 122.46/16.15 (~ (((binintersectLsub) =>
% 122.46/16.15 (((binintersectSubset2) =>
% 122.46/16.15 (((binintersectSubset3) =>
% 122.46/16.15 (((binintersectER) =>
% 122.46/16.15 (((disjointsetsI1) =>
% 122.46/16.15 (((binintersectRsub) =>
% 122.46/16.15 (((binintersectSubset4) =>
% 122.46/16.15 (((binintersectSubset1) =>
% 122.46/16.15 (((bs114d) =>
% 122.46/16.15 (((setminusI) =>
% 122.46/16.15 (((setminusEL) =>
% 122.46/16.15 (((setminusER) =>
% 122.46/16.15 (((setminusSubset2) =>
% 122.46/16.15 (((setminusERneg) =>
% 122.46/16.15 (((setminusELneg) =>
% 122.46/16.15 (((setminusILneg) =>
% 122.46/16.15 (((setminusIRneg) =>
% 122.46/16.15 (((setminusLsub) =>
% 122.46/16.15 (((setminusSubset1) =>
% 122.46/16.15 (((symdiffE) =>
% 122.46/16.15 (((symdiffI1) =>
% 122.46/16.15 (((symdiffI2) =>
% 122.46/16.15 (((symdiffIneg1) =>
% 122.46/16.15 (((symdiffIneg2) =>
% 122.46/16.15 (((secondinupair) =>
% 122.46/16.15 (((setukpairIL) =>
% 122.46/16.15 (((setukpairIR) =>
% 122.46/16.15 (((kpairiskpair) =>
% 122.46/16.15 (((kpairp) =>
% 122.46/16.15 (((singletonsubset) =>
% 122.46/16.15 ((
% 122.46/16.15 (singletoninpowerset) =>
% 122.46/16.15 ((
% 122.46/16.15 (singletoninpowunion) =>
% 122.46/16.15 ((
% 122.46/16.15 (upairset2E) =>
% 122.46/16.15 ((
% 122.46/16.15 (upairsubunion) =>
% 122.46/16.15 ((
% 122.46/16.15 (upairinpowunion) =>
% 122.46/16.15 ((
% 122.46/16.15 (ubforcartprodlem1) =>
% 122.46/16.15 ((
% 122.46/16.15 (ubforcartprodlem2) =>
% 122.46/16.15 ((
% 122.46/16.15 (ubforcartprodlem3) =>
% 122.46/16.15 ((
% 122.46/16.15 (cartprodpairin) =>
% 122.46/16.15 ((
% 122.46/16.15 (cartprodmempair1) =>
% 122.46/16.15 ((
% 122.46/16.15 (cartprodmempair) =>
% 122.46/16.15 ((
% 122.46/16.15 (setunionE2) =>
% 122.46/16.15 ((
% 122.46/16.15 (setunionsingleton1) =>
% 122.46/16.15 ((
% 122.46/16.15 (setunionsingleton2) =>
% 122.46/16.15 ((
% 122.46/16.15 (setunionsingleton) =>
% 122.46/16.15 ((
% 122.46/16.15 (singletonprop) =>
% 122.46/16.15 ((
% 122.46/16.15 (ex1E1) =>
% 122.46/16.15 ((
% 122.46/16.15 (ex1I) =>
% 122.46/16.15 ((
% 122.46/16.15 (ex1I2) =>
% 122.46/16.15 ((
% 122.46/16.15 (singletonsuniq) =>
% 122.46/16.15 ((
% 122.46/16.15 (setukpairinjL1) =>
% 122.46/16.15 ((
% 122.46/16.15 (kfstsingleton) =>
% 122.46/16.15 ((
% 122.46/16.15 (theprop) =>
% 122.46/16.15 ((
% 122.46/16.15 (kfstpairEq) =>
% 122.46/16.15 ((
% 122.46/16.15 (cartprodfstin) =>
% 122.46/16.15 ((
% 122.46/16.15 (setukpairinjL2) =>
% 122.46/16.15 ((
% 122.46/16.15 (setukpairinjL) =>
% 122.46/16.15 ((
% 122.46/16.15 (setukpairinjR11) =>
% 122.46/16.15 ((
% 122.46/16.15 (setukpairinjR12) =>
% 122.46/16.15 ((
% 122.46/16.15 (setukpairinjR1) =>
% 122.46/16.15 ((
% 122.46/16.15 (upairequniteq) =>
% 122.46/16.15 ((
% 122.46/16.15 (setukpairinjR2) =>
% 122.46/16.15 ((
% 122.46/16.15 (setukpairinjR) =>
% 122.46/16.15 ((
% 122.46/16.15 (ksndsingleton) =>
% 122.46/16.15 ((
% 122.46/16.15 (ksndpairEq) =>
% 122.46/16.15 ((
% 122.46/16.15 (kpairsurjEq) =>
% 122.46/16.15 ((
% 122.46/16.15 (cartprodsndin) =>
% 122.46/16.15 ((
% 122.46/16.15 (cartprodpairmemEL) =>
% 122.46/16.15 ((
% 122.46/16.15 (cartprodpairmemER) =>
% 122.46/16.15 ((
% 122.46/16.15 (cartprodmempaircEq) =>
% 122.46/16.15 ((
% 122.46/16.15 (cartprodfstpairEq) =>
% 122.46/16.15 ((
% 122.46/16.15 (cartprodsndpairEq) =>
% 122.46/16.15 ((
% 122.46/16.15 (cartprodpairsurjEq) =>
% 122.46/16.15 ((
% 122.46/16.15 (dpsetconstrI) =>
% 122.46/16.15 ((
% 122.46/16.15 (dpsetconstrSub) =>
% 122.46/16.15 ((
% 122.46/16.15 (setOfPairsIsBReln) =>
% 122.46/16.15 ((
% 122.46/16.15 (dpsetconstrERa) =>
% 122.46/16.15 ((
% 122.46/16.15 (dpsetconstrEL1) =>
% 122.46/16.15 ((
% 122.46/16.15 (dpsetconstrEL2) =>
% 122.46/16.15 ((
% 122.46/16.15 (dpsetconstrER) =>
% 122.46/16.15 ((
% 122.46/16.15 (funcImageSingleton) =>
% 122.46/16.15 ((
% 122.46/16.15 (apProp) =>
% 122.46/16.15 ((
% 122.46/16.15 (app) =>
% 122.46/16.15 ((
% 122.46/16.15 (infuncsetfunc) =>
% 122.46/16.15 ((
% 122.46/16.15 (ap2p) =>
% 122.46/16.15 ((
% 122.46/16.15 (funcinfuncset) =>
% 122.46/16.15 ((
% 122.46/16.15 (lamProp) =>
% 122.46/16.15 ((
% 122.46/16.15 (lamp) =>
% 122.46/16.15 ((
% 122.46/16.15 (lam2p) =>
% 122.46/16.15 ((
% 122.46/16.15 (brelnall1) =>
% 122.46/16.15 ((
% 122.46/16.15 (brelnall2) =>
% 122.46/16.15 ((
% 122.46/16.15 (ex1E2) =>
% 122.46/16.15 ((
% 122.46/16.15 (funcGraphProp1) =>
% 122.46/16.15 ((
% 122.46/16.15 (funcGraphProp3) =>
% 122.46/16.15 ((
% 122.46/16.15 (funcGraphProp2) =>
% 122.46/16.15 ((
% 122.46/16.15 (funcextLem) =>
% 122.46/16.15 ((
% 122.46/16.15 (funcGraphProp4) =>
% 122.46/16.15 ((
% 122.46/16.15 (subbreln) =>
% 122.46/16.15 ((
% 122.46/16.15 (eqbreln) =>
% 122.46/16.15 ((
% 122.46/16.15 (funcext) =>
% 122.46/16.15 ((
% 122.46/16.15 (funcext2) =>
% 122.46/16.15 ((
% 122.46/16.15 (ap2apEq1) =>
% 122.46/16.15 ((
% 122.46/16.15 (ap2apEq2) =>
% 122.46/16.15 ((
% 122.46/16.15 (beta1) =>
% 122.46/16.15 ((
% 122.46/16.15 (eta1) =>
% 122.46/16.15 ((
% 122.46/16.15 (lam2lamEq) =>
% 122.46/16.15 ((
% 122.46/16.15 (beta2) =>
% 122.46/16.15 ((
% 122.46/16.15 (eta2) =>
% 122.46/16.15 ((
% 122.46/16.15 (iffalseProp1) =>
% 122.46/16.15 ((
% 122.46/16.15 (iffalseProp2) =>
% 122.46/16.15 ((
% 122.46/16.15 (iftrueProp1) =>
% 122.46/16.15 ((
% 122.46/16.15 (iftrueProp2) =>
% 122.46/16.15 ((
% 122.46/16.15 (ifSingleton) =>
% 122.46/16.15 ((
% 122.46/16.15 (ifp) =>
% 122.46/16.15 ((
% 122.46/16.15 (theeq) =>
% 122.46/16.15 ((
% 122.46/16.15 (iftrue) =>
% 122.46/16.15 ((
% 122.46/16.15 (iffalse) =>
% 122.46/16.15 ((
% 122.46/16.15 (iftrueorfalse) =>
% 122.46/16.15 ((
% 122.46/16.15 (binintersectT_lem) =>
% 122.46/16.15 ((
% 122.46/16.15 (binunionT_lem) =>
% 122.46/16.15 ((
% 122.46/16.15 (powersetT_lem) =>
% 122.46/16.15 ((
% 122.46/16.15 (setminusT_lem) =>
% 122.46/16.15 ((
% 122.46/16.15 (complementT_lem) =>
% 122.46/16.15 ((
% 122.46/16.15 (setextT) =>
% 122.46/16.15 ((
% 122.46/16.15 (subsetTI) =>
% 122.46/16.15 ((
% 122.46/16.15 (powersetTI1) =>
% 122.46/16.15 ((
% 122.46/16.15 (powersetTE1) =>
% 122.46/16.15 ((
% 122.46/16.15 (complementTI1) =>
% 122.46/16.15 ((
% 122.46/16.15 (complementTE1) =>
% 122.46/16.15 ((
% 122.46/16.15 (binintersectTELcontra) =>
% 122.46/16.15 ((
% 122.46/16.15 (binintersectTERcontra) =>
% 122.46/16.15 ((
% 122.46/16.15 (contrasubsetT) =>
% 122.46/16.15 ((
% 122.46/16.15 (contrasubsetT1) =>
% 122.46/16.15 ((
% 122.46/16.15 (contrasubsetT2) =>
% 122.46/16.15 ((
% 122.46/16.15 (contrasubsetT3) =>
% 122.46/16.15 ((
% 122.46/16.15 (doubleComplementI1) =>
% 122.46/16.15 ((
% 122.46/16.15 (doubleComplementE1) =>
% 122.46/16.15 ((
% 122.46/16.15 (doubleComplementSub1) =>
% 122.46/16.15 ((
% 122.46/16.15 (doubleComplementSub2) =>
% 122.46/16.15 ((
% 122.46/16.15 (doubleComplementEq) =>
% 122.46/16.15 ((
% 122.46/16.15 (complementTnotintersectT) =>
% 122.46/16.15 ((
% 122.46/16.15 (complementImpComplementIntersect) =>
% 122.46/16.15 ((
% 122.46/16.15 (complementSubsetComplementIntersect) =>
% 122.46/16.15 ((
% 122.46/16.15 (complementInPowersetComplementIntersect) =>
% 122.46/16.15 ((
% 122.46/16.15 (contraSubsetComplement) =>
% 122.46/16.15 ((
% 122.46/16.15 (complementTcontraSubset) =>
% 122.46/16.15 ((
% 122.46/16.15 (binunionTILcontra) =>
% 122.46/16.15 ((
% 122.46/16.15 (binunionTIRcontra) =>
% 122.46/16.15 ((
% 122.46/16.15 (inIntersectImpInUnion) =>
% 122.46/16.15 ((
% 122.46/16.15 (inIntersectImpInUnion2) =>
% 122.46/16.15 ((
% 122.46/16.15 (inIntersectImpInIntersectUnions) =>
% 122.46/16.15 ((
% 122.46/16.15 (intersectInPowersetIntersectUnions) =>
% 122.46/16.15 ((
% 122.46/16.15 (inComplementUnionImpNotIn1) =>
% 122.46/16.15 ((
% 122.46/16.15 (inComplementUnionImpInComplement1) =>
% 122.46/16.15 ((
% 122.46/16.15 (binunionTE) =>
% 122.46/16.15 ((
% 122.46/16.15 (binunionTEcontra) =>
% 122.46/16.15 ((
% 122.46/16.15 (demorgan2a1) =>
% 122.46/16.15 ((
% 122.46/16.15 (complementUnionInPowersetComplement) =>
% 122.46/16.15 ((
% 122.46/16.15 (demorgan2a2) =>
% 122.46/16.15 ((
% 122.46/16.15 (demorgan1a) =>
% 122.46/16.15 ((
% 122.46/16.15 (demorgan1b) =>
% 122.46/16.15 ((
% 122.46/16.15 (demorgan1) =>
% 122.46/16.15 ((
% 122.46/16.15 (demorgan2a) =>
% 122.46/16.15 ((
% 122.46/16.15 (demorgan2b2) =>
% 122.46/16.15 ((
% 122.46/16.15 (demorgan2b) =>
% 122.46/16.15 ((
% 122.46/16.15 (demorgan2) =>
% 122.46/16.15 ((
% 122.46/16.15 (woz13rule0) =>
% 122.46/16.15 ((
% 122.46/16.15 (woz13rule1) =>
% 122.46/16.15 ((
% 122.46/16.15 (woz13rule2) =>
% 122.46/16.15 ((
% 122.46/16.15 (woz13rule3) =>
% 122.46/16.15 ((
% 122.46/16.15 (woz13rule4) =>
% 122.46/16.15 ((
% 122.46/16.15 (woz1_1) =>
% 122.46/16.15 ((
% 122.46/16.15 (woz1_2) =>
% 122.46/16.15 ((
% 122.46/16.15 (woz1_3) =>
% 122.46/16.15 ((
% 122.46/16.15 (woz1_4) =>
% 122.46/16.15 ((
% 122.46/16.15 (woz1_5) =>
% 122.46/16.15 ((
% 122.46/16.15 (breln1all2) =>
% 122.46/16.15 ((
% 122.46/16.15 (breln1SetBreln1) =>
% 122.46/16.15 ((
% 122.46/16.15 (choice2fnsingleton) =>
% 122.46/16.15 ((
% 122.46/16.15 (setOfPairsIsBReln1) =>
% 122.46/16.15 ((
% 122.46/16.15 (breln1all1) =>
% 122.46/16.15 ((
% 122.46/16.15 (subbreln1) =>
% 122.46/16.15 ((
% 122.46/16.15 (eqbreln1) =>
% 122.46/16.15 ((
% 122.46/16.15 (breln1invprop) =>
% 122.46/16.15 ((
% 122.46/16.15 (breln1invI) =>
% 122.46/16.15 ((
% 122.46/16.15 (breln1invE) =>
% 122.46/16.15 ((
% 122.46/16.15 (breln1compprop) =>
% 122.46/16.15 ((
% 122.46/16.15 (breln1compI) =>
% 122.46/16.15 ((
% 122.46/16.15 (breln1compE) =>
% 122.46/16.15 ((
% 122.46/16.15 (breln1compEex) =>
% 122.46/16.15 ((
% 122.46/16.15 (breln1unionprop) =>
% 122.46/16.15 ((
% 122.46/16.15 (breln1unionIL) =>
% 122.46/16.15 ((
% 122.46/16.15 (breln1unionIR) =>
% 122.46/16.15 ((
% 122.46/16.15 (breln1unionI) =>
% 122.46/16.15 ((
% 122.46/16.15 (breln1unionE) =>
% 122.46/16.15 ((
% 122.46/16.15 (breln1unionEcases) =>
% 122.46/16.15 ((
% 122.46/16.15 (breln1unionCommutes) =>
% 122.46/16.15 ((
% 122.46/16.15 (woz2Ex) =>
% 122.46/16.15 ((
% 122.46/16.15 (woz2W) =>
% 122.46/16.15 ((
% 122.46/16.15 (woz2A) =>
% 122.46/16.15 ((
% 122.46/16.15 (woz2B) =>
% 122.46/16.15 ((
% 122.46/16.15 (image1Ex) =>
% 122.46/16.15 ((
% 122.46/16.15 (image1Ex1) =>
% 122.46/16.15 ((
% 122.46/16.15 (image1Equiv) =>
% 122.46/16.15 ((
% 122.46/16.15 (image1E) =>
% 122.46/16.15 ((
% 122.46/16.15 (image1I) =>
% 122.46/16.15 ((
% 122.46/16.15 (injFuncInInjFuncSet) =>
% 122.46/16.15 ((
% 122.46/16.15 (!!) @ (
% 122.46/16.15 (('#B') @ (
% 122.46/16.15 !!) @
% 122.46/16.15 (
% 122.46/16.15 (
% 122.46/16.15 ('#B') @ (
% 122.46/16.15 (
% 122.46/16.15 ('#B') @ (
% 122.46/16.15 !!))) @
% 122.46/16.15 (
% 122.46/16.15 (
% 122.46/16.15 ('#S') @ (
% 122.46/16.15 (
% 122.46/16.15 ('#B') @ (
% 122.46/16.15 '#S') @
% 122.46/16.15 (
% 122.46/16.15 (
% 122.46/16.15 ('#B') @ (
% 122.46/16.15 (
% 122.46/16.15 ('#B') @ (
% 122.46/16.15 '#S'))) @
% 122.46/16.15 (
% 122.46/16.15 (
% 122.46/16.15 ('#B') @ (
% 122.46/16.15 (
% 122.46/16.15 ('#B') @ (
% 122.46/16.15 (
% 122.46/16.15 ('#B') @ (
% 122.46/16.15 =>))))) @
% 122.46/16.15 (
% 122.46/16.15 (
% 122.46/16.15 ('#B') @ (
% 122.46/16.15 (
% 122.46/16.15 ('#B') @ (
% 122.46/16.15 (
% 122.46/16.15 ('#C') @ in)))) @
% 122.46/16.15 injFuncSet)))))))) @
% 122.46/16.15 (
% 122.46/16.15 (
% 122.46/16.15 ('#B') @ (
% 122.46/16.15 (
% 122.46/16.15 ('#B') @ (
% 122.46/16.15 (
% 122.46/16.15 ('#C') @ in)))) @
% 122.46/16.15 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.46/16.15 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1158])).
% 122.46/16.15 thf(zip_derived_cl1174, plain,
% 122.46/16.15 (~ (((binintersectSubset2) =>
% 122.46/16.15 (((binintersectSubset3) =>
% 122.46/16.15 (((binintersectER) =>
% 122.46/16.15 (((disjointsetsI1) =>
% 122.46/16.15 (((binintersectRsub) =>
% 122.46/16.15 (((binintersectSubset4) =>
% 122.46/16.15 (((binintersectSubset1) =>
% 122.46/16.15 (((bs114d) =>
% 122.46/16.15 (((setminusI) =>
% 122.46/16.15 (((setminusEL) =>
% 122.46/16.15 (((setminusER) =>
% 122.46/16.15 (((setminusSubset2) =>
% 122.46/16.15 (((setminusERneg) =>
% 122.46/16.15 (((setminusELneg) =>
% 122.46/16.15 (((setminusILneg) =>
% 122.46/16.15 (((setminusIRneg) =>
% 122.46/16.15 (((setminusLsub) =>
% 122.46/16.15 (((setminusSubset1) =>
% 122.46/16.15 (((symdiffE) =>
% 122.46/16.15 (((symdiffI1) =>
% 122.46/16.15 (((symdiffI2) =>
% 122.46/16.15 (((symdiffIneg1) =>
% 122.46/16.15 (((symdiffIneg2) =>
% 122.46/16.15 (((secondinupair) =>
% 122.46/16.15 (((setukpairIL) =>
% 122.46/16.15 (((setukpairIR) =>
% 122.46/16.15 (((kpairiskpair) =>
% 122.46/16.15 (((kpairp) =>
% 122.46/16.15 (((singletonsubset) =>
% 122.46/16.15 (((singletoninpowerset) =>
% 122.46/16.15 ((
% 122.46/16.15 (singletoninpowunion) =>
% 122.46/16.15 ((
% 122.46/16.15 (upairset2E) =>
% 122.46/16.15 ((
% 122.46/16.15 (upairsubunion) =>
% 122.46/16.15 ((
% 122.46/16.15 (upairinpowunion) =>
% 122.46/16.15 ((
% 122.46/16.15 (ubforcartprodlem1) =>
% 122.46/16.15 ((
% 122.46/16.15 (ubforcartprodlem2) =>
% 122.46/16.15 ((
% 122.46/16.15 (ubforcartprodlem3) =>
% 122.46/16.15 ((
% 122.46/16.15 (cartprodpairin) =>
% 122.46/16.15 ((
% 122.46/16.15 (cartprodmempair1) =>
% 122.46/16.15 ((
% 122.46/16.15 (cartprodmempair) =>
% 122.46/16.15 ((
% 122.46/16.15 (setunionE2) =>
% 122.46/16.15 ((
% 122.46/16.15 (setunionsingleton1) =>
% 122.46/16.15 ((
% 122.46/16.15 (setunionsingleton2) =>
% 122.46/16.15 ((
% 122.46/16.15 (setunionsingleton) =>
% 122.46/16.15 ((
% 122.46/16.15 (singletonprop) =>
% 122.46/16.15 ((
% 122.46/16.15 (ex1E1) =>
% 122.46/16.15 ((
% 122.46/16.15 (ex1I) =>
% 122.46/16.15 ((
% 122.46/16.15 (ex1I2) =>
% 122.46/16.15 ((
% 122.46/16.15 (singletonsuniq) =>
% 122.46/16.15 ((
% 122.46/16.15 (setukpairinjL1) =>
% 122.46/16.15 ((
% 122.46/16.15 (kfstsingleton) =>
% 122.46/16.15 ((
% 122.46/16.15 (theprop) =>
% 122.46/16.15 ((
% 122.46/16.15 (kfstpairEq) =>
% 122.46/16.15 ((
% 122.46/16.15 (cartprodfstin) =>
% 122.46/16.15 ((
% 122.46/16.15 (setukpairinjL2) =>
% 122.46/16.15 ((
% 122.46/16.15 (setukpairinjL) =>
% 122.46/16.15 ((
% 122.46/16.15 (setukpairinjR11) =>
% 122.46/16.15 ((
% 122.46/16.15 (setukpairinjR12) =>
% 122.46/16.15 ((
% 122.46/16.15 (setukpairinjR1) =>
% 122.46/16.15 ((
% 122.46/16.15 (upairequniteq) =>
% 122.46/16.15 ((
% 122.46/16.15 (setukpairinjR2) =>
% 122.46/16.15 ((
% 122.46/16.15 (setukpairinjR) =>
% 122.46/16.15 ((
% 122.46/16.15 (ksndsingleton) =>
% 122.46/16.15 ((
% 122.46/16.15 (ksndpairEq) =>
% 122.46/16.15 ((
% 122.46/16.15 (kpairsurjEq) =>
% 122.46/16.15 ((
% 122.46/16.15 (cartprodsndin) =>
% 122.46/16.15 ((
% 122.46/16.15 (cartprodpairmemEL) =>
% 122.46/16.15 ((
% 122.46/16.15 (cartprodpairmemER) =>
% 122.46/16.15 ((
% 122.46/16.15 (cartprodmempaircEq) =>
% 122.46/16.15 ((
% 122.46/16.15 (cartprodfstpairEq) =>
% 122.46/16.15 ((
% 122.46/16.15 (cartprodsndpairEq) =>
% 122.46/16.15 ((
% 122.46/16.15 (cartprodpairsurjEq) =>
% 122.46/16.15 ((
% 122.46/16.15 (dpsetconstrI) =>
% 122.46/16.15 ((
% 122.46/16.15 (dpsetconstrSub) =>
% 122.46/16.15 ((
% 122.46/16.15 (setOfPairsIsBReln) =>
% 122.46/16.15 ((
% 122.46/16.15 (dpsetconstrERa) =>
% 122.46/16.15 ((
% 122.46/16.15 (dpsetconstrEL1) =>
% 122.46/16.15 ((
% 122.46/16.15 (dpsetconstrEL2) =>
% 122.46/16.15 ((
% 122.46/16.15 (dpsetconstrER) =>
% 122.46/16.15 ((
% 122.46/16.15 (funcImageSingleton) =>
% 122.46/16.15 ((
% 122.46/16.15 (apProp) =>
% 122.46/16.15 ((
% 122.46/16.15 (app) =>
% 122.46/16.15 ((
% 122.46/16.15 (infuncsetfunc) =>
% 122.46/16.15 ((
% 122.46/16.15 (ap2p) =>
% 122.46/16.15 ((
% 122.46/16.15 (funcinfuncset) =>
% 122.46/16.15 ((
% 122.46/16.15 (lamProp) =>
% 122.46/16.15 ((
% 122.46/16.15 (lamp) =>
% 122.46/16.15 ((
% 122.46/16.15 (lam2p) =>
% 122.46/16.15 ((
% 122.46/16.15 (brelnall1) =>
% 122.46/16.15 ((
% 122.46/16.15 (brelnall2) =>
% 122.46/16.15 ((
% 122.46/16.15 (ex1E2) =>
% 122.46/16.15 ((
% 122.46/16.15 (funcGraphProp1) =>
% 122.46/16.15 ((
% 122.46/16.15 (funcGraphProp3) =>
% 122.46/16.15 ((
% 122.46/16.15 (funcGraphProp2) =>
% 122.46/16.15 ((
% 122.46/16.15 (funcextLem) =>
% 122.46/16.15 ((
% 122.46/16.15 (funcGraphProp4) =>
% 122.46/16.15 ((
% 122.46/16.15 (subbreln) =>
% 122.46/16.15 ((
% 122.46/16.15 (eqbreln) =>
% 122.46/16.15 ((
% 122.46/16.15 (funcext) =>
% 122.46/16.15 ((
% 122.46/16.15 (funcext2) =>
% 122.46/16.15 ((
% 122.46/16.15 (ap2apEq1) =>
% 122.46/16.15 ((
% 122.46/16.15 (ap2apEq2) =>
% 122.46/16.15 ((
% 122.46/16.15 (beta1) =>
% 122.46/16.15 ((
% 122.46/16.15 (eta1) =>
% 122.46/16.15 ((
% 122.46/16.15 (lam2lamEq) =>
% 122.46/16.15 ((
% 122.46/16.15 (beta2) =>
% 122.46/16.15 ((
% 122.46/16.15 (eta2) =>
% 122.46/16.15 ((
% 122.46/16.15 (iffalseProp1) =>
% 122.46/16.15 ((
% 122.46/16.15 (iffalseProp2) =>
% 122.46/16.15 ((
% 122.46/16.15 (iftrueProp1) =>
% 122.46/16.15 ((
% 122.46/16.15 (iftrueProp2) =>
% 122.46/16.15 ((
% 122.46/16.15 (ifSingleton) =>
% 122.46/16.15 ((
% 122.46/16.15 (ifp) =>
% 122.46/16.15 ((
% 122.46/16.15 (theeq) =>
% 122.46/16.15 ((
% 122.46/16.15 (iftrue) =>
% 122.46/16.15 ((
% 122.46/16.15 (iffalse) =>
% 122.46/16.15 ((
% 122.46/16.15 (iftrueorfalse) =>
% 122.46/16.15 ((
% 122.46/16.15 (binintersectT_lem) =>
% 122.46/16.15 ((
% 122.46/16.15 (binunionT_lem) =>
% 122.46/16.15 ((
% 122.46/16.15 (powersetT_lem) =>
% 122.46/16.15 ((
% 122.46/16.15 (setminusT_lem) =>
% 122.46/16.15 ((
% 122.46/16.15 (complementT_lem) =>
% 122.46/16.15 ((
% 122.46/16.15 (setextT) =>
% 122.46/16.15 ((
% 122.46/16.15 (subsetTI) =>
% 122.46/16.15 ((
% 122.46/16.15 (powersetTI1) =>
% 122.46/16.15 ((
% 122.46/16.15 (powersetTE1) =>
% 122.46/16.15 ((
% 122.46/16.15 (complementTI1) =>
% 122.46/16.15 ((
% 122.46/16.15 (complementTE1) =>
% 122.46/16.15 ((
% 122.46/16.15 (binintersectTELcontra) =>
% 122.46/16.15 ((
% 122.46/16.15 (binintersectTERcontra) =>
% 122.46/16.15 ((
% 122.46/16.15 (contrasubsetT) =>
% 122.46/16.15 ((
% 122.46/16.15 (contrasubsetT1) =>
% 122.46/16.15 ((
% 122.46/16.15 (contrasubsetT2) =>
% 122.46/16.15 ((
% 122.46/16.15 (contrasubsetT3) =>
% 122.46/16.15 ((
% 122.46/16.15 (doubleComplementI1) =>
% 122.46/16.15 ((
% 122.46/16.15 (doubleComplementE1) =>
% 122.46/16.15 ((
% 122.46/16.15 (doubleComplementSub1) =>
% 122.46/16.15 ((
% 122.46/16.15 (doubleComplementSub2) =>
% 122.46/16.15 ((
% 122.46/16.15 (doubleComplementEq) =>
% 122.46/16.15 ((
% 122.46/16.15 (complementTnotintersectT) =>
% 122.46/16.15 ((
% 122.46/16.15 (complementImpComplementIntersect) =>
% 122.46/16.15 ((
% 122.46/16.15 (complementSubsetComplementIntersect) =>
% 122.46/16.15 ((
% 122.46/16.15 (complementInPowersetComplementIntersect) =>
% 122.46/16.15 ((
% 122.46/16.15 (contraSubsetComplement) =>
% 122.46/16.15 ((
% 122.46/16.15 (complementTcontraSubset) =>
% 122.46/16.15 ((
% 122.46/16.15 (binunionTILcontra) =>
% 122.46/16.15 ((
% 122.46/16.15 (binunionTIRcontra) =>
% 122.46/16.15 ((
% 122.46/16.15 (inIntersectImpInUnion) =>
% 122.46/16.15 ((
% 122.46/16.15 (inIntersectImpInUnion2) =>
% 122.46/16.15 ((
% 122.46/16.15 (inIntersectImpInIntersectUnions) =>
% 122.46/16.15 ((
% 122.46/16.15 (intersectInPowersetIntersectUnions) =>
% 122.46/16.15 ((
% 122.46/16.15 (inComplementUnionImpNotIn1) =>
% 122.46/16.15 ((
% 122.46/16.15 (inComplementUnionImpInComplement1) =>
% 122.46/16.15 ((
% 122.46/16.15 (binunionTE) =>
% 122.46/16.15 ((
% 122.46/16.15 (binunionTEcontra) =>
% 122.46/16.15 ((
% 122.46/16.15 (demorgan2a1) =>
% 122.46/16.15 ((
% 122.46/16.15 (complementUnionInPowersetComplement) =>
% 122.46/16.15 ((
% 122.46/16.15 (demorgan2a2) =>
% 122.46/16.15 ((
% 122.46/16.15 (demorgan1a) =>
% 122.46/16.15 ((
% 122.46/16.15 (demorgan1b) =>
% 122.46/16.15 ((
% 122.46/16.15 (demorgan1) =>
% 122.46/16.15 ((
% 122.46/16.15 (demorgan2a) =>
% 122.46/16.15 ((
% 122.46/16.15 (demorgan2b2) =>
% 122.46/16.15 ((
% 122.46/16.15 (demorgan2b) =>
% 122.46/16.15 ((
% 122.46/16.15 (demorgan2) =>
% 122.46/16.15 ((
% 122.46/16.15 (woz13rule0) =>
% 122.46/16.15 ((
% 122.46/16.15 (woz13rule1) =>
% 122.46/16.15 ((
% 122.46/16.15 (woz13rule2) =>
% 122.46/16.15 ((
% 122.46/16.15 (woz13rule3) =>
% 122.46/16.15 ((
% 122.46/16.15 (woz13rule4) =>
% 122.46/16.15 ((
% 122.46/16.15 (woz1_1) =>
% 122.46/16.15 ((
% 122.46/16.15 (woz1_2) =>
% 122.46/16.15 ((
% 122.46/16.15 (woz1_3) =>
% 122.46/16.15 ((
% 122.46/16.15 (woz1_4) =>
% 122.46/16.15 ((
% 122.46/16.15 (woz1_5) =>
% 122.46/16.15 ((
% 122.46/16.15 (breln1all2) =>
% 122.46/16.15 ((
% 122.46/16.15 (breln1SetBreln1) =>
% 122.46/16.15 ((
% 122.46/16.15 (choice2fnsingleton) =>
% 122.46/16.15 ((
% 122.46/16.15 (setOfPairsIsBReln1) =>
% 122.46/16.15 ((
% 122.46/16.15 (breln1all1) =>
% 122.46/16.15 ((
% 122.46/16.15 (subbreln1) =>
% 122.46/16.15 ((
% 122.46/16.15 (eqbreln1) =>
% 122.46/16.15 ((
% 122.46/16.15 (breln1invprop) =>
% 122.46/16.15 ((
% 122.46/16.15 (breln1invI) =>
% 122.46/16.15 ((
% 122.46/16.15 (breln1invE) =>
% 122.46/16.15 ((
% 122.46/16.15 (breln1compprop) =>
% 122.46/16.15 ((
% 122.46/16.15 (breln1compI) =>
% 122.46/16.15 ((
% 122.46/16.15 (breln1compE) =>
% 122.46/16.15 ((
% 122.46/16.15 (breln1compEex) =>
% 122.46/16.15 ((
% 122.46/16.15 (breln1unionprop) =>
% 122.46/16.15 ((
% 122.46/16.15 (breln1unionIL) =>
% 122.46/16.15 ((
% 122.46/16.15 (breln1unionIR) =>
% 122.46/16.15 ((
% 122.46/16.15 (breln1unionI) =>
% 122.46/16.15 ((
% 122.46/16.15 (breln1unionE) =>
% 122.46/16.15 ((
% 122.46/16.15 (breln1unionEcases) =>
% 122.46/16.15 ((
% 122.46/16.15 (breln1unionCommutes) =>
% 122.46/16.15 ((
% 122.46/16.15 (woz2Ex) =>
% 122.46/16.15 ((
% 122.46/16.15 (woz2W) =>
% 122.46/16.15 ((
% 122.46/16.15 (woz2A) =>
% 122.46/16.15 ((
% 122.46/16.15 (woz2B) =>
% 122.46/16.15 ((
% 122.46/16.15 (image1Ex) =>
% 122.46/16.15 ((
% 122.46/16.15 (image1Ex1) =>
% 122.46/16.15 ((
% 122.46/16.15 (image1Equiv) =>
% 122.46/16.15 ((
% 122.46/16.15 (image1E) =>
% 122.46/16.15 ((
% 122.46/16.15 (image1I) =>
% 122.46/16.15 ((
% 122.46/16.15 (injFuncInInjFuncSet) =>
% 122.46/16.15 ((
% 122.46/16.15 (!!) @ (
% 122.46/16.15 (('#B') @ (
% 122.46/16.15 !!) @
% 122.46/16.15 (
% 122.46/16.15 (
% 122.46/16.15 ('#B') @ (
% 122.46/16.15 (
% 122.46/16.15 ('#B') @ (
% 122.46/16.15 !!))) @
% 122.46/16.15 (
% 122.46/16.15 (
% 122.46/16.15 ('#S') @ (
% 122.46/16.15 (
% 122.46/16.15 ('#B') @ (
% 122.46/16.15 '#S') @
% 122.46/16.15 (
% 122.46/16.15 (
% 122.46/16.15 ('#B') @ (
% 122.46/16.15 (
% 122.46/16.15 ('#B') @ (
% 122.46/16.15 '#S'))) @
% 122.46/16.15 (
% 122.46/16.15 (
% 122.46/16.15 ('#B') @ (
% 122.46/16.15 (
% 122.46/16.15 ('#B') @ (
% 122.46/16.15 (
% 122.46/16.15 ('#B') @ (
% 122.46/16.15 =>))))) @
% 122.46/16.15 (
% 122.46/16.15 (
% 122.46/16.15 ('#B') @ (
% 122.46/16.15 (
% 122.46/16.15 ('#B') @ (
% 122.46/16.15 (
% 122.46/16.15 ('#C') @ in)))) @
% 122.46/16.15 injFuncSet)))))))) @
% 122.46/16.15 (
% 122.46/16.15 (
% 122.46/16.15 ('#B') @ (
% 122.46/16.15 (
% 122.46/16.15 ('#B') @ (
% 122.46/16.15 (
% 122.46/16.15 ('#C') @ in)))) @
% 122.46/16.15 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.46/16.15 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1166])).
% 122.46/16.15 thf(zip_derived_cl1183, plain,
% 122.46/16.15 (~ (((binintersectSubset3) =>
% 122.46/16.15 (((binintersectER) =>
% 122.46/16.15 (((disjointsetsI1) =>
% 122.46/16.15 (((binintersectRsub) =>
% 122.46/16.15 (((binintersectSubset4) =>
% 122.46/16.15 (((binintersectSubset1) =>
% 122.46/16.15 (((bs114d) =>
% 122.46/16.15 (((setminusI) =>
% 122.46/16.15 (((setminusEL) =>
% 122.46/16.15 (((setminusER) =>
% 122.46/16.15 (((setminusSubset2) =>
% 122.46/16.15 (((setminusERneg) =>
% 122.46/16.15 (((setminusELneg) =>
% 122.46/16.15 (((setminusILneg) =>
% 122.46/16.15 (((setminusIRneg) =>
% 122.46/16.15 (((setminusLsub) =>
% 122.46/16.15 (((setminusSubset1) =>
% 122.46/16.15 (((symdiffE) =>
% 122.46/16.15 (((symdiffI1) =>
% 122.46/16.15 (((symdiffI2) =>
% 122.46/16.15 (((symdiffIneg1) =>
% 122.46/16.15 (((symdiffIneg2) =>
% 122.46/16.15 (((secondinupair) =>
% 122.46/16.15 (((setukpairIL) =>
% 122.46/16.15 (((setukpairIR) =>
% 122.46/16.15 (((kpairiskpair) =>
% 122.46/16.15 (((kpairp) =>
% 122.46/16.15 (((singletonsubset) =>
% 122.46/16.15 (((singletoninpowerset) =>
% 122.46/16.15 (((singletoninpowunion) =>
% 122.46/16.15 ((
% 122.46/16.15 (upairset2E) =>
% 122.46/16.15 ((
% 122.46/16.15 (upairsubunion) =>
% 122.46/16.15 ((
% 122.46/16.15 (upairinpowunion) =>
% 122.46/16.15 ((
% 122.46/16.15 (ubforcartprodlem1) =>
% 122.46/16.15 ((
% 122.46/16.15 (ubforcartprodlem2) =>
% 122.46/16.15 ((
% 122.46/16.15 (ubforcartprodlem3) =>
% 122.46/16.15 ((
% 122.46/16.15 (cartprodpairin) =>
% 122.46/16.15 ((
% 122.46/16.15 (cartprodmempair1) =>
% 122.46/16.15 ((
% 122.46/16.15 (cartprodmempair) =>
% 122.46/16.15 ((
% 122.46/16.15 (setunionE2) =>
% 122.46/16.15 ((
% 122.46/16.15 (setunionsingleton1) =>
% 122.46/16.15 ((
% 122.46/16.15 (setunionsingleton2) =>
% 122.46/16.15 ((
% 122.46/16.15 (setunionsingleton) =>
% 122.46/16.15 ((
% 122.46/16.15 (singletonprop) =>
% 122.46/16.15 ((
% 122.46/16.15 (ex1E1) =>
% 122.46/16.15 ((
% 122.46/16.15 (ex1I) =>
% 122.46/16.15 ((
% 122.46/16.15 (ex1I2) =>
% 122.46/16.15 ((
% 122.46/16.15 (singletonsuniq) =>
% 122.46/16.15 ((
% 122.46/16.15 (setukpairinjL1) =>
% 122.46/16.15 ((
% 122.46/16.15 (kfstsingleton) =>
% 122.46/16.15 ((
% 122.46/16.15 (theprop) =>
% 122.46/16.15 ((
% 122.46/16.15 (kfstpairEq) =>
% 122.46/16.15 ((
% 122.46/16.15 (cartprodfstin) =>
% 122.46/16.15 ((
% 122.46/16.15 (setukpairinjL2) =>
% 122.46/16.15 ((
% 122.46/16.15 (setukpairinjL) =>
% 122.46/16.15 ((
% 122.46/16.15 (setukpairinjR11) =>
% 122.46/16.15 ((
% 122.46/16.15 (setukpairinjR12) =>
% 122.46/16.15 ((
% 122.46/16.15 (setukpairinjR1) =>
% 122.46/16.15 ((
% 122.46/16.15 (upairequniteq) =>
% 122.46/16.15 ((
% 122.46/16.15 (setukpairinjR2) =>
% 122.46/16.15 ((
% 122.46/16.15 (setukpairinjR) =>
% 122.46/16.15 ((
% 122.46/16.15 (ksndsingleton) =>
% 122.46/16.15 ((
% 122.46/16.15 (ksndpairEq) =>
% 122.46/16.15 ((
% 122.46/16.15 (kpairsurjEq) =>
% 122.46/16.15 ((
% 122.46/16.15 (cartprodsndin) =>
% 122.46/16.15 ((
% 122.46/16.15 (cartprodpairmemEL) =>
% 122.46/16.15 ((
% 122.46/16.15 (cartprodpairmemER) =>
% 122.46/16.15 ((
% 122.46/16.15 (cartprodmempaircEq) =>
% 122.46/16.15 ((
% 122.46/16.15 (cartprodfstpairEq) =>
% 122.46/16.15 ((
% 122.46/16.15 (cartprodsndpairEq) =>
% 122.46/16.15 ((
% 122.46/16.15 (cartprodpairsurjEq) =>
% 122.46/16.15 ((
% 122.46/16.15 (dpsetconstrI) =>
% 122.46/16.15 ((
% 122.46/16.15 (dpsetconstrSub) =>
% 122.46/16.15 ((
% 122.46/16.15 (setOfPairsIsBReln) =>
% 122.46/16.15 ((
% 122.46/16.15 (dpsetconstrERa) =>
% 122.46/16.15 ((
% 122.46/16.15 (dpsetconstrEL1) =>
% 122.46/16.15 ((
% 122.46/16.15 (dpsetconstrEL2) =>
% 122.46/16.15 ((
% 122.46/16.15 (dpsetconstrER) =>
% 122.46/16.15 ((
% 122.46/16.15 (funcImageSingleton) =>
% 122.46/16.15 ((
% 122.46/16.15 (apProp) =>
% 122.46/16.15 ((
% 122.46/16.15 (app) =>
% 122.46/16.15 ((
% 122.46/16.15 (infuncsetfunc) =>
% 122.46/16.15 ((
% 122.46/16.15 (ap2p) =>
% 122.46/16.15 ((
% 122.46/16.15 (funcinfuncset) =>
% 122.46/16.15 ((
% 122.46/16.15 (lamProp) =>
% 122.46/16.15 ((
% 122.46/16.15 (lamp) =>
% 122.46/16.15 ((
% 122.46/16.15 (lam2p) =>
% 122.46/16.15 ((
% 122.46/16.15 (brelnall1) =>
% 122.46/16.15 ((
% 122.46/16.15 (brelnall2) =>
% 122.46/16.15 ((
% 122.46/16.15 (ex1E2) =>
% 122.46/16.15 ((
% 122.46/16.15 (funcGraphProp1) =>
% 122.46/16.15 ((
% 122.46/16.15 (funcGraphProp3) =>
% 122.46/16.15 ((
% 122.46/16.15 (funcGraphProp2) =>
% 122.46/16.15 ((
% 122.46/16.15 (funcextLem) =>
% 122.46/16.15 ((
% 122.46/16.15 (funcGraphProp4) =>
% 122.46/16.15 ((
% 122.46/16.15 (subbreln) =>
% 122.46/16.15 ((
% 122.46/16.15 (eqbreln) =>
% 122.46/16.15 ((
% 122.46/16.15 (funcext) =>
% 122.46/16.15 ((
% 122.46/16.15 (funcext2) =>
% 122.46/16.15 ((
% 122.46/16.15 (ap2apEq1) =>
% 122.46/16.15 ((
% 122.46/16.15 (ap2apEq2) =>
% 122.46/16.15 ((
% 122.46/16.15 (beta1) =>
% 122.46/16.15 ((
% 122.46/16.15 (eta1) =>
% 122.46/16.15 ((
% 122.46/16.15 (lam2lamEq) =>
% 122.46/16.15 ((
% 122.46/16.15 (beta2) =>
% 122.46/16.15 ((
% 122.46/16.15 (eta2) =>
% 122.46/16.15 ((
% 122.46/16.15 (iffalseProp1) =>
% 122.46/16.15 ((
% 122.46/16.15 (iffalseProp2) =>
% 122.46/16.15 ((
% 122.46/16.15 (iftrueProp1) =>
% 122.46/16.15 ((
% 122.46/16.15 (iftrueProp2) =>
% 122.46/16.15 ((
% 122.46/16.15 (ifSingleton) =>
% 122.46/16.15 ((
% 122.46/16.15 (ifp) =>
% 122.46/16.15 ((
% 122.46/16.15 (theeq) =>
% 122.46/16.15 ((
% 122.46/16.15 (iftrue) =>
% 122.46/16.15 ((
% 122.46/16.15 (iffalse) =>
% 122.46/16.15 ((
% 122.46/16.15 (iftrueorfalse) =>
% 122.46/16.15 ((
% 122.46/16.15 (binintersectT_lem) =>
% 122.46/16.15 ((
% 122.46/16.15 (binunionT_lem) =>
% 122.46/16.15 ((
% 122.46/16.15 (powersetT_lem) =>
% 122.46/16.15 ((
% 122.46/16.15 (setminusT_lem) =>
% 122.46/16.15 ((
% 122.46/16.15 (complementT_lem) =>
% 122.46/16.15 ((
% 122.46/16.15 (setextT) =>
% 122.46/16.15 ((
% 122.46/16.15 (subsetTI) =>
% 122.46/16.15 ((
% 122.46/16.15 (powersetTI1) =>
% 122.46/16.15 ((
% 122.46/16.15 (powersetTE1) =>
% 122.46/16.15 ((
% 122.46/16.15 (complementTI1) =>
% 122.46/16.15 ((
% 122.46/16.15 (complementTE1) =>
% 122.46/16.15 ((
% 122.46/16.15 (binintersectTELcontra) =>
% 122.46/16.15 ((
% 122.46/16.15 (binintersectTERcontra) =>
% 122.46/16.15 ((
% 122.46/16.15 (contrasubsetT) =>
% 122.46/16.15 ((
% 122.46/16.15 (contrasubsetT1) =>
% 122.46/16.15 ((
% 122.46/16.15 (contrasubsetT2) =>
% 122.46/16.15 ((
% 122.46/16.15 (contrasubsetT3) =>
% 122.46/16.15 ((
% 122.46/16.15 (doubleComplementI1) =>
% 122.46/16.15 ((
% 122.46/16.15 (doubleComplementE1) =>
% 122.46/16.15 ((
% 122.46/16.15 (doubleComplementSub1) =>
% 122.46/16.15 ((
% 122.46/16.15 (doubleComplementSub2) =>
% 122.46/16.15 ((
% 122.46/16.15 (doubleComplementEq) =>
% 122.46/16.15 ((
% 122.46/16.15 (complementTnotintersectT) =>
% 122.46/16.15 ((
% 122.46/16.15 (complementImpComplementIntersect) =>
% 122.46/16.15 ((
% 122.46/16.15 (complementSubsetComplementIntersect) =>
% 122.46/16.15 ((
% 122.46/16.15 (complementInPowersetComplementIntersect) =>
% 122.46/16.15 ((
% 122.46/16.15 (contraSubsetComplement) =>
% 122.46/16.15 ((
% 122.46/16.15 (complementTcontraSubset) =>
% 122.46/16.15 ((
% 122.46/16.15 (binunionTILcontra) =>
% 122.46/16.15 ((
% 122.46/16.15 (binunionTIRcontra) =>
% 122.46/16.15 ((
% 122.46/16.15 (inIntersectImpInUnion) =>
% 122.46/16.15 ((
% 122.46/16.15 (inIntersectImpInUnion2) =>
% 122.46/16.15 ((
% 122.46/16.15 (inIntersectImpInIntersectUnions) =>
% 122.46/16.15 ((
% 122.46/16.15 (intersectInPowersetIntersectUnions) =>
% 122.46/16.15 ((
% 122.46/16.15 (inComplementUnionImpNotIn1) =>
% 122.46/16.15 ((
% 122.46/16.15 (inComplementUnionImpInComplement1) =>
% 122.46/16.15 ((
% 122.46/16.15 (binunionTE) =>
% 122.46/16.15 ((
% 122.46/16.15 (binunionTEcontra) =>
% 122.46/16.15 ((
% 122.46/16.15 (demorgan2a1) =>
% 122.46/16.15 ((
% 122.46/16.15 (complementUnionInPowersetComplement) =>
% 122.46/16.15 ((
% 122.46/16.15 (demorgan2a2) =>
% 122.46/16.15 ((
% 122.46/16.15 (demorgan1a) =>
% 122.46/16.15 ((
% 122.46/16.15 (demorgan1b) =>
% 122.46/16.15 ((
% 122.46/16.15 (demorgan1) =>
% 122.46/16.15 ((
% 122.46/16.15 (demorgan2a) =>
% 122.46/16.15 ((
% 122.46/16.15 (demorgan2b2) =>
% 122.46/16.15 ((
% 122.46/16.15 (demorgan2b) =>
% 122.46/16.15 ((
% 122.46/16.15 (demorgan2) =>
% 122.46/16.15 ((
% 122.46/16.15 (woz13rule0) =>
% 122.46/16.15 ((
% 122.46/16.15 (woz13rule1) =>
% 122.46/16.15 ((
% 122.46/16.15 (woz13rule2) =>
% 122.46/16.15 ((
% 122.46/16.15 (woz13rule3) =>
% 122.46/16.15 ((
% 122.46/16.15 (woz13rule4) =>
% 122.46/16.15 ((
% 122.46/16.15 (woz1_1) =>
% 122.46/16.15 ((
% 122.46/16.15 (woz1_2) =>
% 122.46/16.15 ((
% 122.46/16.15 (woz1_3) =>
% 122.46/16.15 ((
% 122.46/16.15 (woz1_4) =>
% 122.46/16.15 ((
% 122.46/16.15 (woz1_5) =>
% 122.46/16.15 ((
% 122.46/16.15 (breln1all2) =>
% 122.46/16.15 ((
% 122.46/16.15 (breln1SetBreln1) =>
% 122.46/16.15 ((
% 122.46/16.15 (choice2fnsingleton) =>
% 122.46/16.15 ((
% 122.46/16.15 (setOfPairsIsBReln1) =>
% 122.46/16.15 ((
% 122.46/16.15 (breln1all1) =>
% 122.46/16.15 ((
% 122.46/16.15 (subbreln1) =>
% 122.46/16.15 ((
% 122.46/16.15 (eqbreln1) =>
% 122.46/16.15 ((
% 122.46/16.15 (breln1invprop) =>
% 122.46/16.15 ((
% 122.46/16.15 (breln1invI) =>
% 122.46/16.15 ((
% 122.46/16.15 (breln1invE) =>
% 122.46/16.15 ((
% 122.46/16.15 (breln1compprop) =>
% 122.46/16.15 ((
% 122.46/16.15 (breln1compI) =>
% 122.46/16.15 ((
% 122.46/16.15 (breln1compE) =>
% 122.46/16.15 ((
% 122.46/16.15 (breln1compEex) =>
% 122.46/16.15 ((
% 122.46/16.15 (breln1unionprop) =>
% 122.46/16.15 ((
% 122.46/16.15 (breln1unionIL) =>
% 122.46/16.15 ((
% 122.46/16.15 (breln1unionIR) =>
% 122.46/16.15 ((
% 122.46/16.15 (breln1unionI) =>
% 122.46/16.15 ((
% 122.46/16.15 (breln1unionE) =>
% 122.46/16.15 ((
% 122.46/16.15 (breln1unionEcases) =>
% 122.46/16.15 ((
% 122.46/16.15 (breln1unionCommutes) =>
% 122.46/16.15 ((
% 122.46/16.15 (woz2Ex) =>
% 122.46/16.15 ((
% 122.46/16.15 (woz2W) =>
% 122.46/16.15 ((
% 122.46/16.15 (woz2A) =>
% 122.46/16.15 ((
% 122.46/16.15 (woz2B) =>
% 122.46/16.15 ((
% 122.46/16.15 (image1Ex) =>
% 122.46/16.15 ((
% 122.46/16.15 (image1Ex1) =>
% 122.46/16.16 ((
% 122.46/16.16 (image1Equiv) =>
% 122.46/16.16 ((
% 122.46/16.16 (image1E) =>
% 122.46/16.16 ((
% 122.46/16.16 (image1I) =>
% 122.46/16.16 ((
% 122.46/16.16 (injFuncInInjFuncSet) =>
% 122.46/16.16 ((
% 122.46/16.16 (!!) @ (
% 122.46/16.16 (('#B') @ (
% 122.46/16.16 !!) @
% 122.46/16.16 (
% 122.46/16.16 (
% 122.46/16.16 ('#B') @ (
% 122.46/16.16 (
% 122.46/16.16 ('#B') @ (
% 122.46/16.16 !!))) @
% 122.46/16.16 (
% 122.46/16.16 (
% 122.46/16.16 ('#S') @ (
% 122.46/16.16 (
% 122.46/16.16 ('#B') @ (
% 122.46/16.16 '#S') @
% 122.46/16.16 (
% 122.46/16.16 (
% 122.46/16.16 ('#B') @ (
% 122.46/16.16 (
% 122.46/16.16 ('#B') @ (
% 122.46/16.16 '#S'))) @
% 122.46/16.16 (
% 122.46/16.16 (
% 122.46/16.16 ('#B') @ (
% 122.46/16.16 (
% 122.46/16.16 ('#B') @ (
% 122.46/16.16 (
% 122.46/16.16 ('#B') @ (
% 122.46/16.16 =>))))) @
% 122.46/16.16 (
% 122.46/16.16 (
% 122.46/16.16 ('#B') @ (
% 122.46/16.16 (
% 122.46/16.16 ('#B') @ (
% 122.46/16.16 (
% 122.46/16.16 ('#C') @ in)))) @
% 122.46/16.16 injFuncSet)))))))) @
% 122.46/16.16 (
% 122.46/16.16 (
% 122.46/16.16 ('#B') @ (
% 122.46/16.16 (
% 122.46/16.16 ('#B') @ (
% 122.46/16.16 (
% 122.46/16.16 ('#C') @ in)))) @
% 122.46/16.16 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.46/16.16 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1174])).
% 122.46/16.16 thf(zip_derived_cl1193, plain,
% 122.46/16.16 (~ (((binintersectER) =>
% 122.46/16.16 (((disjointsetsI1) =>
% 122.46/16.16 (((binintersectRsub) =>
% 122.46/16.16 (((binintersectSubset4) =>
% 122.46/16.16 (((binintersectSubset1) =>
% 122.46/16.16 (((bs114d) =>
% 122.46/16.16 (((setminusI) =>
% 122.46/16.16 (((setminusEL) =>
% 122.46/16.16 (((setminusER) =>
% 122.46/16.16 (((setminusSubset2) =>
% 122.46/16.16 (((setminusERneg) =>
% 122.46/16.16 (((setminusELneg) =>
% 122.46/16.16 (((setminusILneg) =>
% 122.46/16.16 (((setminusIRneg) =>
% 122.46/16.16 (((setminusLsub) =>
% 122.46/16.16 (((setminusSubset1) =>
% 122.46/16.16 (((symdiffE) =>
% 122.46/16.16 (((symdiffI1) =>
% 122.46/16.16 (((symdiffI2) =>
% 122.46/16.16 (((symdiffIneg1) =>
% 122.46/16.16 (((symdiffIneg2) =>
% 122.46/16.16 (((secondinupair) =>
% 122.46/16.16 (((setukpairIL) =>
% 122.46/16.16 (((setukpairIR) =>
% 122.46/16.16 (((kpairiskpair) =>
% 122.46/16.16 (((kpairp) =>
% 122.46/16.16 (((singletonsubset) =>
% 122.46/16.16 (((singletoninpowerset) =>
% 122.46/16.16 (((singletoninpowunion) =>
% 122.46/16.16 (((upairset2E) =>
% 122.46/16.16 ((
% 122.46/16.16 (upairsubunion) =>
% 122.46/16.16 ((
% 122.46/16.16 (upairinpowunion) =>
% 122.46/16.16 ((
% 122.46/16.16 (ubforcartprodlem1) =>
% 122.46/16.16 ((
% 122.46/16.16 (ubforcartprodlem2) =>
% 122.46/16.16 ((
% 122.46/16.16 (ubforcartprodlem3) =>
% 122.46/16.16 ((
% 122.46/16.16 (cartprodpairin) =>
% 122.46/16.16 ((
% 122.46/16.16 (cartprodmempair1) =>
% 122.46/16.16 ((
% 122.46/16.16 (cartprodmempair) =>
% 122.46/16.16 ((
% 122.46/16.16 (setunionE2) =>
% 122.46/16.16 ((
% 122.46/16.16 (setunionsingleton1) =>
% 122.46/16.16 ((
% 122.46/16.16 (setunionsingleton2) =>
% 122.46/16.16 ((
% 122.46/16.16 (setunionsingleton) =>
% 122.46/16.16 ((
% 122.46/16.16 (singletonprop) =>
% 122.46/16.16 ((
% 122.46/16.16 (ex1E1) =>
% 122.46/16.16 ((
% 122.46/16.16 (ex1I) =>
% 122.46/16.16 ((
% 122.46/16.16 (ex1I2) =>
% 122.46/16.16 ((
% 122.46/16.16 (singletonsuniq) =>
% 122.46/16.16 ((
% 122.46/16.16 (setukpairinjL1) =>
% 122.46/16.16 ((
% 122.46/16.16 (kfstsingleton) =>
% 122.46/16.16 ((
% 122.46/16.16 (theprop) =>
% 122.46/16.16 ((
% 122.46/16.16 (kfstpairEq) =>
% 122.46/16.16 ((
% 122.46/16.16 (cartprodfstin) =>
% 122.46/16.16 ((
% 122.46/16.16 (setukpairinjL2) =>
% 122.46/16.16 ((
% 122.46/16.16 (setukpairinjL) =>
% 122.46/16.16 ((
% 122.46/16.16 (setukpairinjR11) =>
% 122.46/16.16 ((
% 122.46/16.16 (setukpairinjR12) =>
% 122.46/16.16 ((
% 122.46/16.16 (setukpairinjR1) =>
% 122.46/16.16 ((
% 122.46/16.16 (upairequniteq) =>
% 122.46/16.16 ((
% 122.46/16.16 (setukpairinjR2) =>
% 122.46/16.16 ((
% 122.46/16.16 (setukpairinjR) =>
% 122.46/16.16 ((
% 122.46/16.16 (ksndsingleton) =>
% 122.46/16.16 ((
% 122.46/16.16 (ksndpairEq) =>
% 122.46/16.16 ((
% 122.46/16.16 (kpairsurjEq) =>
% 122.46/16.16 ((
% 122.46/16.16 (cartprodsndin) =>
% 122.46/16.16 ((
% 122.46/16.16 (cartprodpairmemEL) =>
% 122.46/16.16 ((
% 122.46/16.16 (cartprodpairmemER) =>
% 122.46/16.16 ((
% 122.46/16.16 (cartprodmempaircEq) =>
% 122.46/16.16 ((
% 122.46/16.16 (cartprodfstpairEq) =>
% 122.46/16.16 ((
% 122.46/16.16 (cartprodsndpairEq) =>
% 122.46/16.16 ((
% 122.46/16.16 (cartprodpairsurjEq) =>
% 122.46/16.16 ((
% 122.46/16.16 (dpsetconstrI) =>
% 122.46/16.16 ((
% 122.46/16.16 (dpsetconstrSub) =>
% 122.46/16.16 ((
% 122.46/16.16 (setOfPairsIsBReln) =>
% 122.46/16.16 ((
% 122.46/16.16 (dpsetconstrERa) =>
% 122.46/16.16 ((
% 122.46/16.16 (dpsetconstrEL1) =>
% 122.46/16.16 ((
% 122.46/16.16 (dpsetconstrEL2) =>
% 122.46/16.16 ((
% 122.46/16.16 (dpsetconstrER) =>
% 122.46/16.16 ((
% 122.46/16.16 (funcImageSingleton) =>
% 122.46/16.16 ((
% 122.46/16.16 (apProp) =>
% 122.46/16.16 ((
% 122.46/16.16 (app) =>
% 122.46/16.16 ((
% 122.46/16.16 (infuncsetfunc) =>
% 122.46/16.16 ((
% 122.46/16.16 (ap2p) =>
% 122.46/16.16 ((
% 122.46/16.16 (funcinfuncset) =>
% 122.46/16.16 ((
% 122.46/16.16 (lamProp) =>
% 122.46/16.16 ((
% 122.46/16.16 (lamp) =>
% 122.46/16.16 ((
% 122.46/16.16 (lam2p) =>
% 122.46/16.16 ((
% 122.46/16.16 (brelnall1) =>
% 122.46/16.16 ((
% 122.46/16.16 (brelnall2) =>
% 122.46/16.16 ((
% 122.46/16.16 (ex1E2) =>
% 122.46/16.16 ((
% 122.46/16.16 (funcGraphProp1) =>
% 122.46/16.16 ((
% 122.46/16.16 (funcGraphProp3) =>
% 122.46/16.16 ((
% 122.46/16.16 (funcGraphProp2) =>
% 122.46/16.16 ((
% 122.46/16.16 (funcextLem) =>
% 122.46/16.16 ((
% 122.46/16.16 (funcGraphProp4) =>
% 122.46/16.16 ((
% 122.46/16.16 (subbreln) =>
% 122.46/16.16 ((
% 122.46/16.16 (eqbreln) =>
% 122.46/16.16 ((
% 122.46/16.16 (funcext) =>
% 122.46/16.16 ((
% 122.46/16.16 (funcext2) =>
% 122.46/16.16 ((
% 122.46/16.16 (ap2apEq1) =>
% 122.46/16.16 ((
% 122.46/16.16 (ap2apEq2) =>
% 122.46/16.16 ((
% 122.46/16.16 (beta1) =>
% 122.46/16.16 ((
% 122.46/16.16 (eta1) =>
% 122.46/16.16 ((
% 122.46/16.16 (lam2lamEq) =>
% 122.46/16.16 ((
% 122.46/16.16 (beta2) =>
% 122.46/16.16 ((
% 122.46/16.16 (eta2) =>
% 122.46/16.16 ((
% 122.46/16.16 (iffalseProp1) =>
% 122.46/16.16 ((
% 122.46/16.16 (iffalseProp2) =>
% 122.46/16.16 ((
% 122.46/16.16 (iftrueProp1) =>
% 122.46/16.16 ((
% 122.46/16.16 (iftrueProp2) =>
% 122.46/16.16 ((
% 122.46/16.16 (ifSingleton) =>
% 122.46/16.16 ((
% 122.46/16.16 (ifp) =>
% 122.46/16.16 ((
% 122.46/16.16 (theeq) =>
% 122.46/16.16 ((
% 122.46/16.16 (iftrue) =>
% 122.46/16.16 ((
% 122.46/16.16 (iffalse) =>
% 122.46/16.16 ((
% 122.46/16.16 (iftrueorfalse) =>
% 122.46/16.16 ((
% 122.46/16.16 (binintersectT_lem) =>
% 122.46/16.16 ((
% 122.46/16.16 (binunionT_lem) =>
% 122.46/16.16 ((
% 122.46/16.16 (powersetT_lem) =>
% 122.46/16.16 ((
% 122.46/16.16 (setminusT_lem) =>
% 122.46/16.16 ((
% 122.46/16.16 (complementT_lem) =>
% 122.46/16.16 ((
% 122.46/16.16 (setextT) =>
% 122.46/16.16 ((
% 122.46/16.16 (subsetTI) =>
% 122.46/16.16 ((
% 122.46/16.16 (powersetTI1) =>
% 122.46/16.16 ((
% 122.46/16.16 (powersetTE1) =>
% 122.46/16.16 ((
% 122.46/16.16 (complementTI1) =>
% 122.46/16.16 ((
% 122.46/16.16 (complementTE1) =>
% 122.46/16.16 ((
% 122.46/16.16 (binintersectTELcontra) =>
% 122.46/16.16 ((
% 122.46/16.16 (binintersectTERcontra) =>
% 122.46/16.16 ((
% 122.46/16.16 (contrasubsetT) =>
% 122.46/16.16 ((
% 122.46/16.16 (contrasubsetT1) =>
% 122.46/16.16 ((
% 122.46/16.16 (contrasubsetT2) =>
% 122.46/16.16 ((
% 122.46/16.16 (contrasubsetT3) =>
% 122.46/16.16 ((
% 122.46/16.16 (doubleComplementI1) =>
% 122.46/16.16 ((
% 122.46/16.16 (doubleComplementE1) =>
% 122.46/16.16 ((
% 122.46/16.16 (doubleComplementSub1) =>
% 122.46/16.16 ((
% 122.46/16.16 (doubleComplementSub2) =>
% 122.46/16.16 ((
% 122.46/16.16 (doubleComplementEq) =>
% 122.46/16.16 ((
% 122.46/16.16 (complementTnotintersectT) =>
% 122.46/16.16 ((
% 122.46/16.16 (complementImpComplementIntersect) =>
% 122.46/16.16 ((
% 122.46/16.16 (complementSubsetComplementIntersect) =>
% 122.46/16.16 ((
% 122.46/16.16 (complementInPowersetComplementIntersect) =>
% 122.46/16.16 ((
% 122.46/16.16 (contraSubsetComplement) =>
% 122.46/16.16 ((
% 122.46/16.16 (complementTcontraSubset) =>
% 122.46/16.16 ((
% 122.46/16.16 (binunionTILcontra) =>
% 122.46/16.16 ((
% 122.46/16.16 (binunionTIRcontra) =>
% 122.46/16.16 ((
% 122.46/16.16 (inIntersectImpInUnion) =>
% 122.46/16.16 ((
% 122.46/16.16 (inIntersectImpInUnion2) =>
% 122.46/16.16 ((
% 122.46/16.16 (inIntersectImpInIntersectUnions) =>
% 122.46/16.16 ((
% 122.46/16.16 (intersectInPowersetIntersectUnions) =>
% 122.46/16.16 ((
% 122.46/16.16 (inComplementUnionImpNotIn1) =>
% 122.46/16.16 ((
% 122.46/16.16 (inComplementUnionImpInComplement1) =>
% 122.46/16.16 ((
% 122.46/16.16 (binunionTE) =>
% 122.46/16.16 ((
% 122.46/16.16 (binunionTEcontra) =>
% 122.46/16.16 ((
% 122.46/16.16 (demorgan2a1) =>
% 122.46/16.16 ((
% 122.46/16.16 (complementUnionInPowersetComplement) =>
% 122.46/16.16 ((
% 122.46/16.16 (demorgan2a2) =>
% 122.46/16.16 ((
% 122.46/16.16 (demorgan1a) =>
% 122.46/16.16 ((
% 122.46/16.16 (demorgan1b) =>
% 122.46/16.16 ((
% 122.46/16.16 (demorgan1) =>
% 122.46/16.16 ((
% 122.46/16.16 (demorgan2a) =>
% 122.46/16.16 ((
% 122.46/16.16 (demorgan2b2) =>
% 122.46/16.16 ((
% 122.46/16.16 (demorgan2b) =>
% 122.46/16.16 ((
% 122.46/16.16 (demorgan2) =>
% 122.46/16.16 ((
% 122.46/16.16 (woz13rule0) =>
% 122.46/16.16 ((
% 122.46/16.16 (woz13rule1) =>
% 122.46/16.16 ((
% 122.46/16.16 (woz13rule2) =>
% 122.46/16.16 ((
% 122.46/16.16 (woz13rule3) =>
% 122.46/16.16 ((
% 122.46/16.16 (woz13rule4) =>
% 122.46/16.16 ((
% 122.46/16.16 (woz1_1) =>
% 122.46/16.16 ((
% 122.46/16.16 (woz1_2) =>
% 122.46/16.16 ((
% 122.46/16.16 (woz1_3) =>
% 122.46/16.16 ((
% 122.46/16.16 (woz1_4) =>
% 122.46/16.16 ((
% 122.46/16.16 (woz1_5) =>
% 122.46/16.16 ((
% 122.46/16.16 (breln1all2) =>
% 122.46/16.16 ((
% 122.46/16.16 (breln1SetBreln1) =>
% 122.46/16.16 ((
% 122.46/16.16 (choice2fnsingleton) =>
% 122.46/16.16 ((
% 122.46/16.16 (setOfPairsIsBReln1) =>
% 122.46/16.16 ((
% 122.46/16.16 (breln1all1) =>
% 122.46/16.16 ((
% 122.46/16.16 (subbreln1) =>
% 122.46/16.16 ((
% 122.46/16.16 (eqbreln1) =>
% 122.46/16.16 ((
% 122.46/16.16 (breln1invprop) =>
% 122.46/16.16 ((
% 122.46/16.16 (breln1invI) =>
% 122.46/16.16 ((
% 122.46/16.16 (breln1invE) =>
% 122.46/16.16 ((
% 122.46/16.16 (breln1compprop) =>
% 122.46/16.16 ((
% 122.46/16.16 (breln1compI) =>
% 122.46/16.16 ((
% 122.46/16.16 (breln1compE) =>
% 122.46/16.16 ((
% 122.46/16.16 (breln1compEex) =>
% 122.46/16.16 ((
% 122.46/16.16 (breln1unionprop) =>
% 122.46/16.16 ((
% 122.46/16.16 (breln1unionIL) =>
% 122.46/16.16 ((
% 122.46/16.16 (breln1unionIR) =>
% 122.46/16.16 ((
% 122.46/16.16 (breln1unionI) =>
% 122.46/16.16 ((
% 122.46/16.16 (breln1unionE) =>
% 122.46/16.16 ((
% 122.46/16.16 (breln1unionEcases) =>
% 122.46/16.16 ((
% 122.46/16.16 (breln1unionCommutes) =>
% 122.46/16.16 ((
% 122.46/16.16 (woz2Ex) =>
% 122.46/16.16 ((
% 122.46/16.16 (woz2W) =>
% 122.46/16.16 ((
% 122.46/16.16 (woz2A) =>
% 122.46/16.16 ((
% 122.46/16.16 (woz2B) =>
% 122.46/16.16 ((
% 122.46/16.16 (image1Ex) =>
% 122.46/16.16 ((
% 122.46/16.16 (image1Ex1) =>
% 122.46/16.16 ((
% 122.46/16.16 (image1Equiv) =>
% 122.46/16.16 ((
% 122.46/16.16 (image1E) =>
% 122.46/16.16 ((
% 122.46/16.16 (image1I) =>
% 122.46/16.16 ((
% 122.46/16.16 (injFuncInInjFuncSet) =>
% 122.46/16.16 ((
% 122.46/16.16 (!!) @ (
% 122.46/16.16 (('#B') @ (
% 122.46/16.16 !!) @
% 122.46/16.16 (
% 122.46/16.16 (
% 122.46/16.16 ('#B') @ (
% 122.46/16.16 (
% 122.46/16.16 ('#B') @ (
% 122.46/16.16 !!))) @
% 122.46/16.16 (
% 122.46/16.16 (
% 122.46/16.16 ('#S') @ (
% 122.46/16.16 (
% 122.46/16.16 ('#B') @ (
% 122.46/16.16 '#S') @
% 122.46/16.16 (
% 122.46/16.16 (
% 122.46/16.16 ('#B') @ (
% 122.46/16.16 (
% 122.46/16.16 ('#B') @ (
% 122.46/16.16 '#S'))) @
% 122.46/16.16 (
% 122.46/16.16 (
% 122.46/16.16 ('#B') @ (
% 122.46/16.16 (
% 122.46/16.16 ('#B') @ (
% 122.46/16.16 (
% 122.46/16.16 ('#B') @ (
% 122.46/16.16 =>))))) @
% 122.46/16.16 (
% 122.46/16.16 (
% 122.46/16.16 ('#B') @ (
% 122.46/16.16 (
% 122.46/16.16 ('#B') @ (
% 122.46/16.16 (
% 122.46/16.16 ('#C') @ in)))) @
% 122.46/16.16 injFuncSet)))))))) @
% 122.46/16.16 (
% 122.46/16.16 (
% 122.46/16.16 ('#B') @ (
% 122.46/16.16 (
% 122.46/16.16 ('#B') @ (
% 122.46/16.16 (
% 122.46/16.16 ('#C') @ in)))) @
% 122.46/16.16 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.46/16.16 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1183])).
% 122.46/16.16 thf(zip_derived_cl1206, plain,
% 122.46/16.16 (~ (((disjointsetsI1) =>
% 122.46/16.16 (((binintersectRsub) =>
% 122.46/16.16 (((binintersectSubset4) =>
% 122.46/16.16 (((binintersectSubset1) =>
% 122.46/16.16 (((bs114d) =>
% 122.46/16.16 (((setminusI) =>
% 122.46/16.16 (((setminusEL) =>
% 122.46/16.16 (((setminusER) =>
% 122.46/16.16 (((setminusSubset2) =>
% 122.46/16.16 (((setminusERneg) =>
% 122.46/16.16 (((setminusELneg) =>
% 122.46/16.16 (((setminusILneg) =>
% 122.46/16.16 (((setminusIRneg) =>
% 122.46/16.16 (((setminusLsub) =>
% 122.46/16.16 (((setminusSubset1) =>
% 122.46/16.16 (((symdiffE) =>
% 122.46/16.16 (((symdiffI1) =>
% 122.46/16.16 (((symdiffI2) =>
% 122.46/16.16 (((symdiffIneg1) =>
% 122.46/16.16 (((symdiffIneg2) =>
% 122.46/16.16 (((secondinupair) =>
% 122.46/16.16 (((setukpairIL) =>
% 122.46/16.16 (((setukpairIR) =>
% 122.46/16.16 (((kpairiskpair) =>
% 122.46/16.16 (((kpairp) =>
% 122.46/16.16 (((singletonsubset) =>
% 122.46/16.16 (((singletoninpowerset) =>
% 122.46/16.16 (((singletoninpowunion) =>
% 122.46/16.16 (((upairset2E) =>
% 122.46/16.16 (((upairsubunion) =>
% 122.46/16.16 ((
% 122.46/16.16 (upairinpowunion) =>
% 122.46/16.16 ((
% 122.46/16.16 (ubforcartprodlem1) =>
% 122.46/16.16 ((
% 122.46/16.16 (ubforcartprodlem2) =>
% 122.46/16.16 ((
% 122.46/16.16 (ubforcartprodlem3) =>
% 122.46/16.16 ((
% 122.46/16.16 (cartprodpairin) =>
% 122.46/16.16 ((
% 122.46/16.16 (cartprodmempair1) =>
% 122.46/16.16 ((
% 122.46/16.16 (cartprodmempair) =>
% 122.46/16.16 ((
% 122.46/16.16 (setunionE2) =>
% 122.46/16.16 ((
% 122.46/16.16 (setunionsingleton1) =>
% 122.46/16.16 ((
% 122.46/16.16 (setunionsingleton2) =>
% 122.46/16.16 ((
% 122.46/16.16 (setunionsingleton) =>
% 122.46/16.16 ((
% 122.46/16.16 (singletonprop) =>
% 122.46/16.16 ((
% 122.46/16.16 (ex1E1) =>
% 122.46/16.16 ((
% 122.46/16.16 (ex1I) =>
% 122.46/16.16 ((
% 122.46/16.16 (ex1I2) =>
% 122.46/16.16 ((
% 122.46/16.16 (singletonsuniq) =>
% 122.46/16.16 ((
% 122.46/16.16 (setukpairinjL1) =>
% 122.46/16.16 ((
% 122.46/16.16 (kfstsingleton) =>
% 122.46/16.16 ((
% 122.46/16.16 (theprop) =>
% 122.46/16.16 ((
% 122.46/16.16 (kfstpairEq) =>
% 122.46/16.16 ((
% 122.46/16.16 (cartprodfstin) =>
% 122.46/16.16 ((
% 122.46/16.16 (setukpairinjL2) =>
% 122.46/16.16 ((
% 122.46/16.16 (setukpairinjL) =>
% 122.46/16.16 ((
% 122.46/16.16 (setukpairinjR11) =>
% 122.46/16.16 ((
% 122.46/16.16 (setukpairinjR12) =>
% 122.46/16.16 ((
% 122.46/16.16 (setukpairinjR1) =>
% 122.46/16.16 ((
% 122.46/16.16 (upairequniteq) =>
% 122.46/16.16 ((
% 122.46/16.16 (setukpairinjR2) =>
% 122.46/16.16 ((
% 122.46/16.16 (setukpairinjR) =>
% 122.46/16.16 ((
% 122.46/16.16 (ksndsingleton) =>
% 122.46/16.16 ((
% 122.46/16.16 (ksndpairEq) =>
% 122.46/16.16 ((
% 122.46/16.16 (kpairsurjEq) =>
% 122.46/16.16 ((
% 122.46/16.16 (cartprodsndin) =>
% 122.46/16.16 ((
% 122.46/16.16 (cartprodpairmemEL) =>
% 122.46/16.16 ((
% 122.46/16.16 (cartprodpairmemER) =>
% 122.46/16.16 ((
% 122.46/16.16 (cartprodmempaircEq) =>
% 122.46/16.16 ((
% 122.46/16.16 (cartprodfstpairEq) =>
% 122.46/16.16 ((
% 122.46/16.16 (cartprodsndpairEq) =>
% 122.46/16.16 ((
% 122.46/16.16 (cartprodpairsurjEq) =>
% 122.46/16.16 ((
% 122.46/16.16 (dpsetconstrI) =>
% 122.46/16.16 ((
% 122.46/16.16 (dpsetconstrSub) =>
% 122.46/16.16 ((
% 122.46/16.16 (setOfPairsIsBReln) =>
% 122.46/16.16 ((
% 122.46/16.16 (dpsetconstrERa) =>
% 122.46/16.16 ((
% 122.46/16.16 (dpsetconstrEL1) =>
% 122.46/16.16 ((
% 122.46/16.16 (dpsetconstrEL2) =>
% 122.46/16.16 ((
% 122.46/16.16 (dpsetconstrER) =>
% 122.46/16.16 ((
% 122.46/16.16 (funcImageSingleton) =>
% 122.46/16.16 ((
% 122.46/16.16 (apProp) =>
% 122.46/16.16 ((
% 122.46/16.16 (app) =>
% 122.46/16.16 ((
% 122.46/16.16 (infuncsetfunc) =>
% 122.46/16.16 ((
% 122.46/16.16 (ap2p) =>
% 122.46/16.16 ((
% 122.46/16.16 (funcinfuncset) =>
% 122.46/16.16 ((
% 122.46/16.16 (lamProp) =>
% 122.46/16.16 ((
% 122.46/16.16 (lamp) =>
% 122.46/16.16 ((
% 122.46/16.16 (lam2p) =>
% 122.46/16.16 ((
% 122.46/16.16 (brelnall1) =>
% 122.46/16.16 ((
% 122.46/16.16 (brelnall2) =>
% 122.46/16.16 ((
% 122.46/16.16 (ex1E2) =>
% 122.46/16.16 ((
% 122.46/16.16 (funcGraphProp1) =>
% 122.46/16.16 ((
% 122.46/16.16 (funcGraphProp3) =>
% 122.46/16.16 ((
% 122.46/16.16 (funcGraphProp2) =>
% 122.46/16.16 ((
% 122.46/16.16 (funcextLem) =>
% 122.46/16.16 ((
% 122.46/16.16 (funcGraphProp4) =>
% 122.46/16.16 ((
% 122.46/16.16 (subbreln) =>
% 122.46/16.16 ((
% 122.46/16.16 (eqbreln) =>
% 122.46/16.16 ((
% 122.46/16.16 (funcext) =>
% 122.46/16.16 ((
% 122.46/16.16 (funcext2) =>
% 122.46/16.16 ((
% 122.46/16.16 (ap2apEq1) =>
% 122.46/16.16 ((
% 122.46/16.16 (ap2apEq2) =>
% 122.46/16.16 ((
% 122.46/16.16 (beta1) =>
% 122.46/16.16 ((
% 122.46/16.16 (eta1) =>
% 122.46/16.16 ((
% 122.46/16.16 (lam2lamEq) =>
% 122.46/16.16 ((
% 122.46/16.16 (beta2) =>
% 122.46/16.16 ((
% 122.46/16.16 (eta2) =>
% 122.46/16.16 ((
% 122.46/16.16 (iffalseProp1) =>
% 122.46/16.16 ((
% 122.46/16.16 (iffalseProp2) =>
% 122.46/16.16 ((
% 122.46/16.16 (iftrueProp1) =>
% 122.46/16.16 ((
% 122.46/16.16 (iftrueProp2) =>
% 122.46/16.16 ((
% 122.46/16.16 (ifSingleton) =>
% 122.46/16.16 ((
% 122.46/16.16 (ifp) =>
% 122.46/16.16 ((
% 122.46/16.16 (theeq) =>
% 122.46/16.16 ((
% 122.46/16.16 (iftrue) =>
% 122.46/16.16 ((
% 122.46/16.16 (iffalse) =>
% 122.46/16.16 ((
% 122.46/16.16 (iftrueorfalse) =>
% 122.46/16.16 ((
% 122.46/16.16 (binintersectT_lem) =>
% 122.46/16.16 ((
% 122.46/16.16 (binunionT_lem) =>
% 122.46/16.16 ((
% 122.46/16.16 (powersetT_lem) =>
% 122.46/16.16 ((
% 122.46/16.16 (setminusT_lem) =>
% 122.46/16.16 ((
% 122.46/16.16 (complementT_lem) =>
% 122.46/16.16 ((
% 122.46/16.16 (setextT) =>
% 122.46/16.16 ((
% 122.46/16.16 (subsetTI) =>
% 122.46/16.16 ((
% 122.46/16.16 (powersetTI1) =>
% 122.46/16.16 ((
% 122.46/16.16 (powersetTE1) =>
% 122.46/16.16 ((
% 122.46/16.16 (complementTI1) =>
% 122.46/16.16 ((
% 122.46/16.16 (complementTE1) =>
% 122.46/16.16 ((
% 122.46/16.16 (binintersectTELcontra) =>
% 122.46/16.16 ((
% 122.46/16.16 (binintersectTERcontra) =>
% 122.46/16.16 ((
% 122.46/16.16 (contrasubsetT) =>
% 122.46/16.16 ((
% 122.46/16.16 (contrasubsetT1) =>
% 122.46/16.16 ((
% 122.46/16.16 (contrasubsetT2) =>
% 122.46/16.16 ((
% 122.46/16.16 (contrasubsetT3) =>
% 122.46/16.16 ((
% 122.46/16.16 (doubleComplementI1) =>
% 122.46/16.16 ((
% 122.46/16.16 (doubleComplementE1) =>
% 122.46/16.16 ((
% 122.46/16.16 (doubleComplementSub1) =>
% 122.46/16.16 ((
% 122.46/16.16 (doubleComplementSub2) =>
% 122.46/16.16 ((
% 122.46/16.16 (doubleComplementEq) =>
% 122.46/16.16 ((
% 122.46/16.16 (complementTnotintersectT) =>
% 122.46/16.16 ((
% 122.46/16.16 (complementImpComplementIntersect) =>
% 122.46/16.16 ((
% 122.46/16.16 (complementSubsetComplementIntersect) =>
% 122.46/16.16 ((
% 122.46/16.16 (complementInPowersetComplementIntersect) =>
% 122.46/16.16 ((
% 122.46/16.16 (contraSubsetComplement) =>
% 122.46/16.16 ((
% 122.46/16.16 (complementTcontraSubset) =>
% 122.46/16.16 ((
% 122.46/16.16 (binunionTILcontra) =>
% 122.46/16.16 ((
% 122.46/16.16 (binunionTIRcontra) =>
% 122.46/16.16 ((
% 122.46/16.16 (inIntersectImpInUnion) =>
% 122.46/16.16 ((
% 122.46/16.16 (inIntersectImpInUnion2) =>
% 122.46/16.16 ((
% 122.46/16.16 (inIntersectImpInIntersectUnions) =>
% 122.46/16.16 ((
% 122.46/16.16 (intersectInPowersetIntersectUnions) =>
% 122.46/16.16 ((
% 122.46/16.16 (inComplementUnionImpNotIn1) =>
% 122.46/16.16 ((
% 122.46/16.16 (inComplementUnionImpInComplement1) =>
% 122.46/16.16 ((
% 122.46/16.16 (binunionTE) =>
% 122.46/16.16 ((
% 122.46/16.16 (binunionTEcontra) =>
% 122.46/16.16 ((
% 122.46/16.16 (demorgan2a1) =>
% 122.46/16.16 ((
% 122.46/16.16 (complementUnionInPowersetComplement) =>
% 122.46/16.16 ((
% 122.46/16.16 (demorgan2a2) =>
% 122.46/16.16 ((
% 122.46/16.16 (demorgan1a) =>
% 122.46/16.16 ((
% 122.46/16.16 (demorgan1b) =>
% 122.46/16.16 ((
% 122.46/16.16 (demorgan1) =>
% 122.46/16.16 ((
% 122.46/16.16 (demorgan2a) =>
% 122.46/16.16 ((
% 122.46/16.16 (demorgan2b2) =>
% 122.46/16.16 ((
% 122.46/16.16 (demorgan2b) =>
% 122.46/16.16 ((
% 122.46/16.16 (demorgan2) =>
% 122.46/16.16 ((
% 122.46/16.16 (woz13rule0) =>
% 122.46/16.16 ((
% 122.46/16.16 (woz13rule1) =>
% 122.46/16.16 ((
% 122.46/16.16 (woz13rule2) =>
% 122.46/16.16 ((
% 122.46/16.16 (woz13rule3) =>
% 122.46/16.16 ((
% 122.46/16.16 (woz13rule4) =>
% 122.46/16.16 ((
% 122.46/16.16 (woz1_1) =>
% 122.46/16.16 ((
% 122.46/16.16 (woz1_2) =>
% 122.46/16.16 ((
% 122.46/16.16 (woz1_3) =>
% 122.46/16.16 ((
% 122.46/16.16 (woz1_4) =>
% 122.46/16.16 ((
% 122.46/16.16 (woz1_5) =>
% 122.46/16.16 ((
% 122.46/16.16 (breln1all2) =>
% 122.46/16.16 ((
% 122.46/16.16 (breln1SetBreln1) =>
% 122.46/16.16 ((
% 122.46/16.16 (choice2fnsingleton) =>
% 122.46/16.16 ((
% 122.46/16.16 (setOfPairsIsBReln1) =>
% 122.46/16.16 ((
% 122.46/16.16 (breln1all1) =>
% 122.46/16.16 ((
% 122.46/16.16 (subbreln1) =>
% 122.46/16.16 ((
% 122.46/16.16 (eqbreln1) =>
% 122.46/16.16 ((
% 122.46/16.16 (breln1invprop) =>
% 122.46/16.16 ((
% 122.46/16.16 (breln1invI) =>
% 122.46/16.16 ((
% 122.46/16.16 (breln1invE) =>
% 122.46/16.16 ((
% 122.46/16.16 (breln1compprop) =>
% 122.46/16.16 ((
% 122.46/16.16 (breln1compI) =>
% 122.46/16.16 ((
% 122.46/16.16 (breln1compE) =>
% 122.46/16.16 ((
% 122.46/16.16 (breln1compEex) =>
% 122.46/16.16 ((
% 122.46/16.16 (breln1unionprop) =>
% 122.46/16.16 ((
% 122.46/16.16 (breln1unionIL) =>
% 122.46/16.16 ((
% 122.46/16.16 (breln1unionIR) =>
% 122.46/16.16 ((
% 122.46/16.16 (breln1unionI) =>
% 122.46/16.16 ((
% 122.46/16.16 (breln1unionE) =>
% 122.46/16.16 ((
% 122.46/16.16 (breln1unionEcases) =>
% 122.46/16.16 ((
% 122.46/16.16 (breln1unionCommutes) =>
% 122.46/16.16 ((
% 122.46/16.16 (woz2Ex) =>
% 122.46/16.16 ((
% 122.46/16.16 (woz2W) =>
% 122.46/16.16 ((
% 122.46/16.16 (woz2A) =>
% 122.46/16.16 ((
% 122.46/16.16 (woz2B) =>
% 122.46/16.16 ((
% 122.46/16.16 (image1Ex) =>
% 122.46/16.16 ((
% 122.46/16.16 (image1Ex1) =>
% 122.46/16.16 ((
% 122.46/16.16 (image1Equiv) =>
% 122.46/16.16 ((
% 122.46/16.16 (image1E) =>
% 122.46/16.16 ((
% 122.46/16.16 (image1I) =>
% 122.46/16.16 ((
% 122.46/16.16 (injFuncInInjFuncSet) =>
% 122.46/16.16 ((
% 122.46/16.16 (!!) @ (
% 122.46/16.16 (('#B') @ (
% 122.46/16.16 !!) @
% 122.46/16.16 (
% 122.46/16.16 (
% 122.46/16.16 ('#B') @ (
% 122.46/16.16 (
% 122.46/16.16 ('#B') @ (
% 122.46/16.16 !!))) @
% 122.46/16.16 (
% 122.46/16.16 (
% 122.46/16.16 ('#S') @ (
% 122.46/16.16 (
% 122.46/16.16 ('#B') @ (
% 122.46/16.16 '#S') @
% 122.46/16.16 (
% 122.46/16.16 (
% 122.46/16.16 ('#B') @ (
% 122.46/16.16 (
% 122.46/16.16 ('#B') @ (
% 122.46/16.16 '#S'))) @
% 122.46/16.16 (
% 122.46/16.16 (
% 122.46/16.16 ('#B') @ (
% 122.46/16.16 (
% 122.46/16.16 ('#B') @ (
% 122.46/16.16 (
% 122.46/16.16 ('#B') @ (
% 122.46/16.16 =>))))) @
% 122.46/16.16 (
% 122.46/16.16 (
% 122.46/16.16 ('#B') @ (
% 122.46/16.16 (
% 122.46/16.16 ('#B') @ (
% 122.46/16.16 (
% 122.46/16.16 ('#C') @ in)))) @
% 122.46/16.16 injFuncSet)))))))) @
% 122.46/16.16 (
% 122.46/16.16 (
% 122.46/16.16 ('#B') @ (
% 122.46/16.16 (
% 122.46/16.16 ('#B') @ (
% 122.46/16.16 (
% 122.46/16.16 ('#C') @ in)))) @
% 122.46/16.16 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.46/16.16 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1193])).
% 122.46/16.16 thf(zip_derived_cl1216, plain,
% 122.46/16.16 (~ (((binintersectRsub) =>
% 122.46/16.16 (((binintersectSubset4) =>
% 122.46/16.16 (((binintersectSubset1) =>
% 122.46/16.16 (((bs114d) =>
% 122.46/16.16 (((setminusI) =>
% 122.46/16.16 (((setminusEL) =>
% 122.46/16.16 (((setminusER) =>
% 122.46/16.16 (((setminusSubset2) =>
% 122.46/16.16 (((setminusERneg) =>
% 122.46/16.16 (((setminusELneg) =>
% 122.46/16.16 (((setminusILneg) =>
% 122.46/16.16 (((setminusIRneg) =>
% 122.46/16.16 (((setminusLsub) =>
% 122.46/16.16 (((setminusSubset1) =>
% 122.46/16.16 (((symdiffE) =>
% 122.46/16.16 (((symdiffI1) =>
% 122.46/16.16 (((symdiffI2) =>
% 122.46/16.16 (((symdiffIneg1) =>
% 122.46/16.16 (((symdiffIneg2) =>
% 122.46/16.16 (((secondinupair) =>
% 122.46/16.16 (((setukpairIL) =>
% 122.46/16.16 (((setukpairIR) =>
% 122.46/16.16 (((kpairiskpair) =>
% 122.46/16.16 (((kpairp) =>
% 122.46/16.16 (((singletonsubset) =>
% 122.46/16.16 (((singletoninpowerset) =>
% 122.46/16.16 (((singletoninpowunion) =>
% 122.46/16.16 (((upairset2E) =>
% 122.46/16.16 (((upairsubunion) =>
% 122.46/16.16 (((upairinpowunion) =>
% 122.46/16.16 ((
% 122.46/16.16 (ubforcartprodlem1) =>
% 122.46/16.16 ((
% 122.46/16.16 (ubforcartprodlem2) =>
% 122.46/16.16 ((
% 122.46/16.16 (ubforcartprodlem3) =>
% 122.46/16.16 ((
% 122.46/16.16 (cartprodpairin) =>
% 122.46/16.16 ((
% 122.46/16.16 (cartprodmempair1) =>
% 122.46/16.16 ((
% 122.46/16.16 (cartprodmempair) =>
% 122.46/16.16 ((
% 122.46/16.16 (setunionE2) =>
% 122.46/16.16 ((
% 122.46/16.16 (setunionsingleton1) =>
% 122.46/16.16 ((
% 122.46/16.16 (setunionsingleton2) =>
% 122.46/16.16 ((
% 122.46/16.16 (setunionsingleton) =>
% 122.46/16.16 ((
% 122.46/16.16 (singletonprop) =>
% 122.46/16.16 ((
% 122.46/16.16 (ex1E1) =>
% 122.46/16.16 ((
% 122.46/16.16 (ex1I) =>
% 122.46/16.16 ((
% 122.46/16.16 (ex1I2) =>
% 122.46/16.16 ((
% 122.46/16.16 (singletonsuniq) =>
% 122.46/16.16 ((
% 122.46/16.16 (setukpairinjL1) =>
% 122.46/16.16 ((
% 122.46/16.16 (kfstsingleton) =>
% 122.46/16.16 ((
% 122.46/16.16 (theprop) =>
% 122.46/16.16 ((
% 122.46/16.16 (kfstpairEq) =>
% 122.46/16.16 ((
% 122.46/16.16 (cartprodfstin) =>
% 122.46/16.16 ((
% 122.46/16.16 (setukpairinjL2) =>
% 122.46/16.16 ((
% 122.46/16.16 (setukpairinjL) =>
% 122.46/16.16 ((
% 122.46/16.16 (setukpairinjR11) =>
% 122.46/16.16 ((
% 122.46/16.16 (setukpairinjR12) =>
% 122.46/16.16 ((
% 122.46/16.16 (setukpairinjR1) =>
% 122.46/16.16 ((
% 122.46/16.16 (upairequniteq) =>
% 122.46/16.16 ((
% 122.46/16.16 (setukpairinjR2) =>
% 122.46/16.16 ((
% 122.46/16.16 (setukpairinjR) =>
% 122.46/16.16 ((
% 122.46/16.16 (ksndsingleton) =>
% 122.46/16.16 ((
% 122.46/16.16 (ksndpairEq) =>
% 122.46/16.16 ((
% 122.46/16.16 (kpairsurjEq) =>
% 122.46/16.16 ((
% 122.46/16.16 (cartprodsndin) =>
% 122.46/16.16 ((
% 122.46/16.16 (cartprodpairmemEL) =>
% 122.46/16.16 ((
% 122.46/16.16 (cartprodpairmemER) =>
% 122.46/16.16 ((
% 122.46/16.16 (cartprodmempaircEq) =>
% 122.46/16.16 ((
% 122.46/16.16 (cartprodfstpairEq) =>
% 122.46/16.16 ((
% 122.46/16.16 (cartprodsndpairEq) =>
% 122.46/16.16 ((
% 122.46/16.16 (cartprodpairsurjEq) =>
% 122.46/16.16 ((
% 122.46/16.16 (dpsetconstrI) =>
% 122.46/16.16 ((
% 122.46/16.16 (dpsetconstrSub) =>
% 122.46/16.16 ((
% 122.46/16.16 (setOfPairsIsBReln) =>
% 122.46/16.16 ((
% 122.46/16.16 (dpsetconstrERa) =>
% 122.46/16.16 ((
% 122.46/16.16 (dpsetconstrEL1) =>
% 122.46/16.16 ((
% 122.46/16.16 (dpsetconstrEL2) =>
% 122.46/16.16 ((
% 122.46/16.16 (dpsetconstrER) =>
% 122.46/16.16 ((
% 122.46/16.16 (funcImageSingleton) =>
% 122.46/16.16 ((
% 122.46/16.16 (apProp) =>
% 122.46/16.16 ((
% 122.46/16.16 (app) =>
% 122.46/16.16 ((
% 122.46/16.16 (infuncsetfunc) =>
% 122.46/16.16 ((
% 122.46/16.16 (ap2p) =>
% 122.46/16.16 ((
% 122.46/16.16 (funcinfuncset) =>
% 122.46/16.16 ((
% 122.46/16.16 (lamProp) =>
% 122.46/16.16 ((
% 122.46/16.16 (lamp) =>
% 122.46/16.16 ((
% 122.46/16.16 (lam2p) =>
% 122.46/16.16 ((
% 122.46/16.16 (brelnall1) =>
% 122.46/16.16 ((
% 122.46/16.16 (brelnall2) =>
% 122.46/16.16 ((
% 122.46/16.16 (ex1E2) =>
% 122.46/16.16 ((
% 122.46/16.16 (funcGraphProp1) =>
% 122.46/16.16 ((
% 122.46/16.16 (funcGraphProp3) =>
% 122.46/16.16 ((
% 122.46/16.16 (funcGraphProp2) =>
% 122.46/16.16 ((
% 122.46/16.16 (funcextLem) =>
% 122.46/16.16 ((
% 122.46/16.16 (funcGraphProp4) =>
% 122.46/16.16 ((
% 122.46/16.16 (subbreln) =>
% 122.46/16.16 ((
% 122.46/16.16 (eqbreln) =>
% 122.46/16.16 ((
% 122.46/16.16 (funcext) =>
% 122.46/16.16 ((
% 122.46/16.16 (funcext2) =>
% 122.46/16.16 ((
% 122.46/16.16 (ap2apEq1) =>
% 122.46/16.16 ((
% 122.46/16.16 (ap2apEq2) =>
% 122.46/16.16 ((
% 122.46/16.16 (beta1) =>
% 122.46/16.16 ((
% 122.46/16.16 (eta1) =>
% 122.46/16.16 ((
% 122.46/16.16 (lam2lamEq) =>
% 122.46/16.16 ((
% 122.46/16.16 (beta2) =>
% 122.46/16.16 ((
% 122.46/16.16 (eta2) =>
% 122.46/16.16 ((
% 122.46/16.16 (iffalseProp1) =>
% 122.46/16.16 ((
% 122.46/16.16 (iffalseProp2) =>
% 122.46/16.16 ((
% 122.46/16.16 (iftrueProp1) =>
% 122.46/16.16 ((
% 122.46/16.16 (iftrueProp2) =>
% 122.46/16.16 ((
% 122.46/16.16 (ifSingleton) =>
% 122.46/16.16 ((
% 122.46/16.16 (ifp) =>
% 122.46/16.16 ((
% 122.46/16.16 (theeq) =>
% 122.46/16.16 ((
% 122.46/16.16 (iftrue) =>
% 122.46/16.16 ((
% 122.46/16.16 (iffalse) =>
% 122.46/16.16 ((
% 122.46/16.16 (iftrueorfalse) =>
% 122.46/16.16 ((
% 122.46/16.16 (binintersectT_lem) =>
% 122.46/16.16 ((
% 122.46/16.16 (binunionT_lem) =>
% 122.46/16.16 ((
% 122.46/16.16 (powersetT_lem) =>
% 122.46/16.16 ((
% 122.46/16.16 (setminusT_lem) =>
% 122.46/16.16 ((
% 122.46/16.16 (complementT_lem) =>
% 122.46/16.16 ((
% 122.46/16.16 (setextT) =>
% 122.46/16.16 ((
% 122.46/16.16 (subsetTI) =>
% 122.46/16.16 ((
% 122.46/16.16 (powersetTI1) =>
% 122.46/16.16 ((
% 122.46/16.16 (powersetTE1) =>
% 122.46/16.16 ((
% 122.46/16.16 (complementTI1) =>
% 122.46/16.16 ((
% 122.46/16.16 (complementTE1) =>
% 122.46/16.16 ((
% 122.46/16.16 (binintersectTELcontra) =>
% 122.46/16.16 ((
% 122.46/16.16 (binintersectTERcontra) =>
% 122.46/16.16 ((
% 122.46/16.16 (contrasubsetT) =>
% 122.46/16.16 ((
% 122.46/16.16 (contrasubsetT1) =>
% 122.46/16.16 ((
% 122.46/16.16 (contrasubsetT2) =>
% 122.46/16.16 ((
% 122.46/16.16 (contrasubsetT3) =>
% 122.46/16.16 ((
% 122.46/16.16 (doubleComplementI1) =>
% 122.46/16.16 ((
% 122.46/16.16 (doubleComplementE1) =>
% 122.46/16.16 ((
% 122.46/16.16 (doubleComplementSub1) =>
% 122.46/16.16 ((
% 122.46/16.16 (doubleComplementSub2) =>
% 122.46/16.16 ((
% 122.46/16.16 (doubleComplementEq) =>
% 122.46/16.16 ((
% 122.46/16.16 (complementTnotintersectT) =>
% 122.46/16.16 ((
% 122.46/16.16 (complementImpComplementIntersect) =>
% 122.46/16.16 ((
% 122.46/16.16 (complementSubsetComplementIntersect) =>
% 122.46/16.16 ((
% 122.46/16.16 (complementInPowersetComplementIntersect) =>
% 122.46/16.16 ((
% 122.46/16.16 (contraSubsetComplement) =>
% 122.46/16.16 ((
% 122.46/16.16 (complementTcontraSubset) =>
% 122.46/16.16 ((
% 122.46/16.16 (binunionTILcontra) =>
% 122.46/16.16 ((
% 122.46/16.16 (binunionTIRcontra) =>
% 122.46/16.16 ((
% 122.46/16.16 (inIntersectImpInUnion) =>
% 122.46/16.16 ((
% 122.46/16.16 (inIntersectImpInUnion2) =>
% 122.46/16.16 ((
% 122.46/16.16 (inIntersectImpInIntersectUnions) =>
% 122.46/16.16 ((
% 122.46/16.16 (intersectInPowersetIntersectUnions) =>
% 122.46/16.16 ((
% 122.46/16.16 (inComplementUnionImpNotIn1) =>
% 122.46/16.16 ((
% 122.46/16.16 (inComplementUnionImpInComplement1) =>
% 122.46/16.16 ((
% 122.46/16.16 (binunionTE) =>
% 122.46/16.16 ((
% 122.46/16.16 (binunionTEcontra) =>
% 122.46/16.16 ((
% 122.46/16.16 (demorgan2a1) =>
% 122.46/16.16 ((
% 122.46/16.16 (complementUnionInPowersetComplement) =>
% 122.46/16.16 ((
% 122.46/16.16 (demorgan2a2) =>
% 122.46/16.16 ((
% 122.46/16.16 (demorgan1a) =>
% 122.46/16.16 ((
% 122.46/16.16 (demorgan1b) =>
% 122.46/16.16 ((
% 122.46/16.16 (demorgan1) =>
% 122.46/16.16 ((
% 122.46/16.16 (demorgan2a) =>
% 122.46/16.16 ((
% 122.46/16.16 (demorgan2b2) =>
% 122.46/16.16 ((
% 122.46/16.16 (demorgan2b) =>
% 122.46/16.16 ((
% 122.46/16.16 (demorgan2) =>
% 122.46/16.16 ((
% 122.46/16.16 (woz13rule0) =>
% 122.46/16.16 ((
% 122.46/16.16 (woz13rule1) =>
% 122.46/16.16 ((
% 122.46/16.16 (woz13rule2) =>
% 122.46/16.16 ((
% 122.46/16.16 (woz13rule3) =>
% 122.46/16.16 ((
% 122.46/16.16 (woz13rule4) =>
% 122.46/16.16 ((
% 122.46/16.16 (woz1_1) =>
% 122.46/16.16 ((
% 122.46/16.16 (woz1_2) =>
% 122.46/16.16 ((
% 122.46/16.16 (woz1_3) =>
% 122.46/16.16 ((
% 122.46/16.16 (woz1_4) =>
% 122.46/16.16 ((
% 122.46/16.16 (woz1_5) =>
% 122.46/16.16 ((
% 122.46/16.16 (breln1all2) =>
% 122.46/16.16 ((
% 122.46/16.16 (breln1SetBreln1) =>
% 122.46/16.16 ((
% 122.46/16.16 (choice2fnsingleton) =>
% 122.46/16.16 ((
% 122.46/16.16 (setOfPairsIsBReln1) =>
% 122.46/16.16 ((
% 122.46/16.16 (breln1all1) =>
% 122.46/16.16 ((
% 122.46/16.16 (subbreln1) =>
% 122.46/16.16 ((
% 122.46/16.16 (eqbreln1) =>
% 122.46/16.16 ((
% 122.46/16.16 (breln1invprop) =>
% 122.46/16.16 ((
% 122.46/16.16 (breln1invI) =>
% 122.46/16.16 ((
% 122.46/16.16 (breln1invE) =>
% 122.46/16.16 ((
% 122.46/16.16 (breln1compprop) =>
% 122.46/16.16 ((
% 122.46/16.16 (breln1compI) =>
% 122.46/16.16 ((
% 122.46/16.16 (breln1compE) =>
% 122.46/16.16 ((
% 122.46/16.16 (breln1compEex) =>
% 122.46/16.16 ((
% 122.46/16.16 (breln1unionprop) =>
% 122.46/16.16 ((
% 122.46/16.16 (breln1unionIL) =>
% 122.46/16.16 ((
% 122.46/16.16 (breln1unionIR) =>
% 122.46/16.16 ((
% 122.46/16.16 (breln1unionI) =>
% 122.46/16.16 ((
% 122.46/16.16 (breln1unionE) =>
% 122.46/16.16 ((
% 122.46/16.16 (breln1unionEcases) =>
% 122.46/16.16 ((
% 122.46/16.16 (breln1unionCommutes) =>
% 122.46/16.16 ((
% 122.46/16.16 (woz2Ex) =>
% 122.46/16.16 ((
% 122.46/16.16 (woz2W) =>
% 122.46/16.16 ((
% 122.46/16.16 (woz2A) =>
% 122.46/16.16 ((
% 122.46/16.16 (woz2B) =>
% 122.46/16.16 ((
% 122.46/16.16 (image1Ex) =>
% 122.46/16.16 ((
% 122.46/16.16 (image1Ex1) =>
% 122.46/16.16 ((
% 122.46/16.16 (image1Equiv) =>
% 122.46/16.16 ((
% 122.46/16.16 (image1E) =>
% 122.46/16.16 ((
% 122.46/16.16 (image1I) =>
% 122.46/16.16 ((
% 122.46/16.16 (injFuncInInjFuncSet) =>
% 122.46/16.16 ((
% 122.46/16.16 (!!) @ (
% 122.46/16.16 (('#B') @ (
% 122.46/16.16 !!) @
% 122.46/16.16 (
% 122.46/16.16 (
% 122.46/16.16 ('#B') @ (
% 122.46/16.16 (
% 122.46/16.16 ('#B') @ (
% 122.46/16.16 !!))) @
% 122.46/16.16 (
% 122.46/16.16 (
% 122.46/16.16 ('#S') @ (
% 122.46/16.16 (
% 122.46/16.16 ('#B') @ (
% 122.46/16.16 '#S') @
% 122.46/16.16 (
% 122.46/16.16 (
% 122.46/16.16 ('#B') @ (
% 122.46/16.16 (
% 122.46/16.16 ('#B') @ (
% 122.46/16.16 '#S'))) @
% 122.46/16.16 (
% 122.46/16.16 (
% 122.46/16.16 ('#B') @ (
% 122.46/16.16 (
% 122.46/16.16 ('#B') @ (
% 122.46/16.16 (
% 122.46/16.16 ('#B') @ (
% 122.46/16.16 =>))))) @
% 122.46/16.16 (
% 122.46/16.16 (
% 122.46/16.16 ('#B') @ (
% 122.46/16.16 (
% 122.46/16.16 ('#B') @ (
% 122.46/16.16 (
% 122.46/16.16 ('#C') @ in)))) @
% 122.46/16.16 injFuncSet)))))))) @
% 122.46/16.16 (
% 122.46/16.16 (
% 122.46/16.16 ('#B') @ (
% 122.46/16.16 (
% 122.46/16.16 ('#B') @ (
% 122.46/16.16 (
% 122.46/16.16 ('#C') @ in)))) @
% 122.46/16.16 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.46/16.16 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1206])).
% 122.46/16.16 thf(zip_derived_cl1223, plain,
% 122.46/16.16 (~ (((binintersectSubset4) =>
% 122.46/16.16 (((binintersectSubset1) =>
% 122.46/16.16 (((bs114d) =>
% 122.46/16.16 (((setminusI) =>
% 122.46/16.16 (((setminusEL) =>
% 122.46/16.16 (((setminusER) =>
% 122.46/16.16 (((setminusSubset2) =>
% 122.46/16.16 (((setminusERneg) =>
% 122.46/16.16 (((setminusELneg) =>
% 122.46/16.16 (((setminusILneg) =>
% 122.46/16.16 (((setminusIRneg) =>
% 122.46/16.16 (((setminusLsub) =>
% 122.46/16.16 (((setminusSubset1) =>
% 122.46/16.16 (((symdiffE) =>
% 122.46/16.16 (((symdiffI1) =>
% 122.46/16.16 (((symdiffI2) =>
% 122.46/16.16 (((symdiffIneg1) =>
% 122.46/16.16 (((symdiffIneg2) =>
% 122.46/16.16 (((secondinupair) =>
% 122.46/16.16 (((setukpairIL) =>
% 122.46/16.16 (((setukpairIR) =>
% 122.46/16.16 (((kpairiskpair) =>
% 122.46/16.16 (((kpairp) =>
% 122.46/16.16 (((singletonsubset) =>
% 122.46/16.16 (((singletoninpowerset) =>
% 122.46/16.16 (((singletoninpowunion) =>
% 122.46/16.16 (((upairset2E) =>
% 122.46/16.16 (((upairsubunion) =>
% 122.46/16.16 (((upairinpowunion) =>
% 122.46/16.16 (((ubforcartprodlem1) =>
% 122.46/16.16 ((
% 122.46/16.16 (ubforcartprodlem2) =>
% 122.46/16.16 ((
% 122.46/16.16 (ubforcartprodlem3) =>
% 122.46/16.16 ((
% 122.46/16.16 (cartprodpairin) =>
% 122.46/16.16 ((
% 122.46/16.16 (cartprodmempair1) =>
% 122.46/16.16 ((
% 122.46/16.16 (cartprodmempair) =>
% 122.46/16.16 ((
% 122.46/16.16 (setunionE2) =>
% 122.46/16.16 ((
% 122.46/16.16 (setunionsingleton1) =>
% 122.46/16.16 ((
% 122.46/16.16 (setunionsingleton2) =>
% 122.46/16.16 ((
% 122.46/16.16 (setunionsingleton) =>
% 122.46/16.16 ((
% 122.46/16.16 (singletonprop) =>
% 122.46/16.16 ((
% 122.46/16.16 (ex1E1) =>
% 122.46/16.16 ((
% 122.46/16.16 (ex1I) =>
% 122.46/16.16 ((
% 122.46/16.16 (ex1I2) =>
% 122.46/16.16 ((
% 122.46/16.16 (singletonsuniq) =>
% 122.46/16.16 ((
% 122.46/16.16 (setukpairinjL1) =>
% 122.46/16.16 ((
% 122.46/16.16 (kfstsingleton) =>
% 122.46/16.16 ((
% 122.46/16.16 (theprop) =>
% 122.46/16.16 ((
% 122.46/16.16 (kfstpairEq) =>
% 122.46/16.16 ((
% 122.46/16.16 (cartprodfstin) =>
% 122.46/16.16 ((
% 122.46/16.16 (setukpairinjL2) =>
% 122.46/16.16 ((
% 122.46/16.16 (setukpairinjL) =>
% 122.46/16.16 ((
% 122.46/16.16 (setukpairinjR11) =>
% 122.46/16.16 ((
% 122.46/16.16 (setukpairinjR12) =>
% 122.46/16.16 ((
% 122.46/16.16 (setukpairinjR1) =>
% 122.46/16.16 ((
% 122.46/16.16 (upairequniteq) =>
% 122.46/16.16 ((
% 122.46/16.16 (setukpairinjR2) =>
% 122.46/16.16 ((
% 122.46/16.16 (setukpairinjR) =>
% 122.46/16.16 ((
% 122.46/16.16 (ksndsingleton) =>
% 122.46/16.16 ((
% 122.46/16.16 (ksndpairEq) =>
% 122.46/16.16 ((
% 122.46/16.16 (kpairsurjEq) =>
% 122.46/16.16 ((
% 122.46/16.16 (cartprodsndin) =>
% 122.46/16.16 ((
% 122.46/16.16 (cartprodpairmemEL) =>
% 122.46/16.16 ((
% 122.46/16.16 (cartprodpairmemER) =>
% 122.46/16.16 ((
% 122.46/16.16 (cartprodmempaircEq) =>
% 122.46/16.16 ((
% 122.46/16.16 (cartprodfstpairEq) =>
% 122.46/16.16 ((
% 122.46/16.16 (cartprodsndpairEq) =>
% 122.46/16.16 ((
% 122.46/16.16 (cartprodpairsurjEq) =>
% 122.46/16.16 ((
% 122.46/16.16 (dpsetconstrI) =>
% 122.46/16.16 ((
% 122.46/16.16 (dpsetconstrSub) =>
% 122.46/16.16 ((
% 122.46/16.16 (setOfPairsIsBReln) =>
% 122.46/16.16 ((
% 122.46/16.16 (dpsetconstrERa) =>
% 122.46/16.16 ((
% 122.46/16.16 (dpsetconstrEL1) =>
% 122.46/16.16 ((
% 122.46/16.16 (dpsetconstrEL2) =>
% 122.46/16.16 ((
% 122.46/16.16 (dpsetconstrER) =>
% 122.46/16.16 ((
% 122.46/16.16 (funcImageSingleton) =>
% 122.46/16.16 ((
% 122.46/16.16 (apProp) =>
% 122.46/16.16 ((
% 122.46/16.16 (app) =>
% 122.46/16.16 ((
% 122.46/16.16 (infuncsetfunc) =>
% 122.46/16.16 ((
% 122.46/16.16 (ap2p) =>
% 122.46/16.16 ((
% 122.46/16.16 (funcinfuncset) =>
% 122.46/16.16 ((
% 122.46/16.16 (lamProp) =>
% 122.46/16.16 ((
% 122.46/16.16 (lamp) =>
% 122.46/16.16 ((
% 122.46/16.16 (lam2p) =>
% 122.46/16.16 ((
% 122.46/16.16 (brelnall1) =>
% 122.46/16.16 ((
% 122.46/16.16 (brelnall2) =>
% 122.46/16.16 ((
% 122.46/16.16 (ex1E2) =>
% 122.46/16.16 ((
% 122.46/16.16 (funcGraphProp1) =>
% 122.46/16.16 ((
% 122.46/16.16 (funcGraphProp3) =>
% 122.46/16.16 ((
% 122.46/16.16 (funcGraphProp2) =>
% 122.46/16.16 ((
% 122.46/16.16 (funcextLem) =>
% 122.46/16.16 ((
% 122.46/16.16 (funcGraphProp4) =>
% 122.46/16.16 ((
% 122.46/16.16 (subbreln) =>
% 122.46/16.16 ((
% 122.46/16.16 (eqbreln) =>
% 122.46/16.16 ((
% 122.46/16.16 (funcext) =>
% 122.46/16.16 ((
% 122.46/16.16 (funcext2) =>
% 122.46/16.16 ((
% 122.46/16.16 (ap2apEq1) =>
% 122.46/16.16 ((
% 122.46/16.16 (ap2apEq2) =>
% 122.46/16.16 ((
% 122.46/16.16 (beta1) =>
% 122.46/16.16 ((
% 122.46/16.16 (eta1) =>
% 122.46/16.16 ((
% 122.46/16.16 (lam2lamEq) =>
% 122.46/16.16 ((
% 122.46/16.16 (beta2) =>
% 122.46/16.16 ((
% 122.46/16.16 (eta2) =>
% 122.46/16.16 ((
% 122.46/16.16 (iffalseProp1) =>
% 122.46/16.16 ((
% 122.46/16.16 (iffalseProp2) =>
% 122.46/16.16 ((
% 122.46/16.16 (iftrueProp1) =>
% 122.46/16.16 ((
% 122.46/16.16 (iftrueProp2) =>
% 122.46/16.16 ((
% 122.46/16.16 (ifSingleton) =>
% 122.46/16.16 ((
% 122.46/16.16 (ifp) =>
% 122.46/16.16 ((
% 122.46/16.16 (theeq) =>
% 122.46/16.16 ((
% 122.46/16.16 (iftrue) =>
% 122.46/16.16 ((
% 122.46/16.16 (iffalse) =>
% 122.46/16.16 ((
% 122.46/16.16 (iftrueorfalse) =>
% 122.46/16.16 ((
% 122.46/16.16 (binintersectT_lem) =>
% 122.46/16.16 ((
% 122.46/16.16 (binunionT_lem) =>
% 122.46/16.16 ((
% 122.46/16.16 (powersetT_lem) =>
% 122.46/16.16 ((
% 122.46/16.16 (setminusT_lem) =>
% 122.46/16.16 ((
% 122.46/16.16 (complementT_lem) =>
% 122.46/16.16 ((
% 122.46/16.16 (setextT) =>
% 122.46/16.16 ((
% 122.46/16.16 (subsetTI) =>
% 122.46/16.16 ((
% 122.46/16.16 (powersetTI1) =>
% 122.46/16.16 ((
% 122.46/16.16 (powersetTE1) =>
% 122.46/16.16 ((
% 122.46/16.16 (complementTI1) =>
% 122.46/16.16 ((
% 122.46/16.16 (complementTE1) =>
% 122.46/16.16 ((
% 122.46/16.16 (binintersectTELcontra) =>
% 122.46/16.16 ((
% 122.46/16.16 (binintersectTERcontra) =>
% 122.46/16.16 ((
% 122.46/16.16 (contrasubsetT) =>
% 122.46/16.16 ((
% 122.46/16.16 (contrasubsetT1) =>
% 122.46/16.16 ((
% 122.46/16.16 (contrasubsetT2) =>
% 122.46/16.16 ((
% 122.46/16.16 (contrasubsetT3) =>
% 122.46/16.16 ((
% 122.46/16.16 (doubleComplementI1) =>
% 122.46/16.16 ((
% 122.46/16.16 (doubleComplementE1) =>
% 122.46/16.16 ((
% 122.46/16.16 (doubleComplementSub1) =>
% 122.46/16.16 ((
% 122.46/16.16 (doubleComplementSub2) =>
% 122.46/16.16 ((
% 122.46/16.16 (doubleComplementEq) =>
% 122.46/16.16 ((
% 122.46/16.16 (complementTnotintersectT) =>
% 122.46/16.16 ((
% 122.46/16.16 (complementImpComplementIntersect) =>
% 122.46/16.16 ((
% 122.46/16.16 (complementSubsetComplementIntersect) =>
% 122.46/16.16 ((
% 122.46/16.16 (complementInPowersetComplementIntersect) =>
% 122.46/16.16 ((
% 122.46/16.16 (contraSubsetComplement) =>
% 122.46/16.16 ((
% 122.46/16.16 (complementTcontraSubset) =>
% 122.46/16.16 ((
% 122.46/16.16 (binunionTILcontra) =>
% 122.46/16.16 ((
% 122.46/16.16 (binunionTIRcontra) =>
% 122.46/16.16 ((
% 122.46/16.16 (inIntersectImpInUnion) =>
% 122.46/16.16 ((
% 122.46/16.16 (inIntersectImpInUnion2) =>
% 122.46/16.16 ((
% 122.46/16.16 (inIntersectImpInIntersectUnions) =>
% 122.46/16.16 ((
% 122.46/16.16 (intersectInPowersetIntersectUnions) =>
% 122.46/16.16 ((
% 122.46/16.16 (inComplementUnionImpNotIn1) =>
% 122.46/16.16 ((
% 122.46/16.16 (inComplementUnionImpInComplement1) =>
% 122.46/16.16 ((
% 122.46/16.16 (binunionTE) =>
% 122.46/16.16 ((
% 122.46/16.16 (binunionTEcontra) =>
% 122.46/16.16 ((
% 122.46/16.16 (demorgan2a1) =>
% 122.46/16.16 ((
% 122.46/16.16 (complementUnionInPowersetComplement) =>
% 122.46/16.16 ((
% 122.46/16.16 (demorgan2a2) =>
% 122.46/16.16 ((
% 122.46/16.16 (demorgan1a) =>
% 122.46/16.16 ((
% 122.46/16.16 (demorgan1b) =>
% 122.46/16.16 ((
% 122.46/16.16 (demorgan1) =>
% 122.46/16.16 ((
% 122.46/16.16 (demorgan2a) =>
% 122.46/16.16 ((
% 122.46/16.16 (demorgan2b2) =>
% 122.46/16.16 ((
% 122.46/16.16 (demorgan2b) =>
% 122.46/16.16 ((
% 122.46/16.16 (demorgan2) =>
% 122.46/16.16 ((
% 122.46/16.16 (woz13rule0) =>
% 122.46/16.16 ((
% 122.46/16.16 (woz13rule1) =>
% 122.46/16.16 ((
% 122.46/16.16 (woz13rule2) =>
% 122.46/16.16 ((
% 122.46/16.16 (woz13rule3) =>
% 122.46/16.16 ((
% 122.46/16.16 (woz13rule4) =>
% 122.46/16.16 ((
% 122.46/16.16 (woz1_1) =>
% 122.46/16.16 ((
% 122.46/16.16 (woz1_2) =>
% 122.46/16.16 ((
% 122.46/16.16 (woz1_3) =>
% 122.46/16.16 ((
% 122.46/16.16 (woz1_4) =>
% 122.46/16.16 ((
% 122.46/16.16 (woz1_5) =>
% 122.46/16.16 ((
% 122.46/16.16 (breln1all2) =>
% 122.46/16.16 ((
% 122.46/16.16 (breln1SetBreln1) =>
% 122.46/16.16 ((
% 122.46/16.16 (choice2fnsingleton) =>
% 122.46/16.16 ((
% 122.46/16.16 (setOfPairsIsBReln1) =>
% 122.46/16.16 ((
% 122.46/16.16 (breln1all1) =>
% 122.46/16.16 ((
% 122.46/16.16 (subbreln1) =>
% 122.46/16.16 ((
% 122.46/16.16 (eqbreln1) =>
% 122.46/16.16 ((
% 122.46/16.16 (breln1invprop) =>
% 122.46/16.16 ((
% 122.46/16.16 (breln1invI) =>
% 122.46/16.16 ((
% 122.46/16.16 (breln1invE) =>
% 122.46/16.16 ((
% 122.46/16.16 (breln1compprop) =>
% 122.46/16.16 ((
% 122.46/16.16 (breln1compI) =>
% 122.46/16.16 ((
% 122.46/16.16 (breln1compE) =>
% 122.46/16.16 ((
% 122.46/16.16 (breln1compEex) =>
% 122.46/16.16 ((
% 122.46/16.16 (breln1unionprop) =>
% 122.46/16.16 ((
% 122.46/16.16 (breln1unionIL) =>
% 122.46/16.16 ((
% 122.46/16.16 (breln1unionIR) =>
% 122.46/16.16 ((
% 122.46/16.16 (breln1unionI) =>
% 122.46/16.16 ((
% 122.46/16.16 (breln1unionE) =>
% 122.46/16.16 ((
% 122.46/16.16 (breln1unionEcases) =>
% 122.46/16.16 ((
% 122.46/16.16 (breln1unionCommutes) =>
% 122.46/16.16 ((
% 122.46/16.16 (woz2Ex) =>
% 122.46/16.16 ((
% 122.46/16.16 (woz2W) =>
% 122.46/16.16 ((
% 122.46/16.16 (woz2A) =>
% 122.46/16.16 ((
% 122.46/16.16 (woz2B) =>
% 122.46/16.16 ((
% 122.46/16.16 (image1Ex) =>
% 122.46/16.16 ((
% 122.46/16.16 (image1Ex1) =>
% 122.46/16.16 ((
% 122.46/16.16 (image1Equiv) =>
% 122.46/16.16 ((
% 122.46/16.16 (image1E) =>
% 122.46/16.16 ((
% 122.46/16.16 (image1I) =>
% 122.46/16.16 ((
% 122.46/16.16 (injFuncInInjFuncSet) =>
% 122.46/16.16 ((
% 122.46/16.16 (!!) @ (
% 122.46/16.16 (('#B') @ (
% 122.46/16.16 !!) @
% 122.46/16.16 (
% 122.46/16.16 (
% 122.46/16.16 ('#B') @ (
% 122.46/16.16 (
% 122.46/16.16 ('#B') @ (
% 122.46/16.16 !!))) @
% 122.46/16.16 (
% 122.46/16.16 (
% 122.46/16.16 ('#S') @ (
% 122.46/16.16 (
% 122.46/16.16 ('#B') @ (
% 122.46/16.16 '#S') @
% 122.46/16.16 (
% 122.46/16.16 (
% 122.46/16.16 ('#B') @ (
% 122.46/16.16 (
% 122.46/16.16 ('#B') @ (
% 122.46/16.16 '#S'))) @
% 122.46/16.16 (
% 122.46/16.16 (
% 122.46/16.16 ('#B') @ (
% 122.46/16.16 (
% 122.46/16.16 ('#B') @ (
% 122.46/16.16 (
% 122.46/16.16 ('#B') @ (
% 122.46/16.16 =>))))) @
% 122.46/16.16 (
% 122.46/16.16 (
% 122.46/16.16 ('#B') @ (
% 122.46/16.16 (
% 122.46/16.16 ('#B') @ (
% 122.46/16.16 (
% 122.46/16.16 ('#C') @ in)))) @
% 122.46/16.16 injFuncSet)))))))) @
% 122.46/16.16 (
% 122.46/16.16 (
% 122.46/16.16 ('#B') @ (
% 122.46/16.16 (
% 122.46/16.16 ('#B') @ (
% 122.46/16.16 (
% 122.46/16.16 ('#C') @ in)))) @
% 122.46/16.16 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.46/16.16 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1216])).
% 122.46/16.16 thf(zip_derived_cl1231, plain,
% 122.46/16.16 (~ (((binintersectSubset1) =>
% 122.46/16.16 (((bs114d) =>
% 122.46/16.16 (((setminusI) =>
% 122.46/16.16 (((setminusEL) =>
% 122.46/16.16 (((setminusER) =>
% 122.46/16.16 (((setminusSubset2) =>
% 122.46/16.16 (((setminusERneg) =>
% 122.46/16.16 (((setminusELneg) =>
% 122.46/16.16 (((setminusILneg) =>
% 122.46/16.16 (((setminusIRneg) =>
% 122.46/16.16 (((setminusLsub) =>
% 122.46/16.16 (((setminusSubset1) =>
% 122.46/16.16 (((symdiffE) =>
% 122.46/16.16 (((symdiffI1) =>
% 122.46/16.16 (((symdiffI2) =>
% 122.46/16.16 (((symdiffIneg1) =>
% 122.46/16.16 (((symdiffIneg2) =>
% 122.46/16.16 (((secondinupair) =>
% 122.46/16.16 (((setukpairIL) =>
% 122.46/16.16 (((setukpairIR) =>
% 122.46/16.16 (((kpairiskpair) =>
% 122.46/16.16 (((kpairp) =>
% 122.46/16.16 (((singletonsubset) =>
% 122.46/16.16 (((singletoninpowerset) =>
% 122.46/16.16 (((singletoninpowunion) =>
% 122.46/16.16 (((upairset2E) =>
% 122.46/16.16 (((upairsubunion) =>
% 122.46/16.16 (((upairinpowunion) =>
% 122.46/16.16 (((ubforcartprodlem1) =>
% 122.46/16.16 (((ubforcartprodlem2) =>
% 122.46/16.16 ((
% 122.46/16.16 (ubforcartprodlem3) =>
% 122.46/16.16 ((
% 122.46/16.16 (cartprodpairin) =>
% 122.46/16.16 ((
% 122.46/16.16 (cartprodmempair1) =>
% 122.46/16.16 ((
% 122.46/16.16 (cartprodmempair) =>
% 122.46/16.16 ((
% 122.46/16.16 (setunionE2) =>
% 122.46/16.16 ((
% 122.46/16.16 (setunionsingleton1) =>
% 122.46/16.16 ((
% 122.46/16.16 (setunionsingleton2) =>
% 122.46/16.16 ((
% 122.46/16.16 (setunionsingleton) =>
% 122.46/16.16 ((
% 122.46/16.16 (singletonprop) =>
% 122.46/16.16 ((
% 122.46/16.16 (ex1E1) =>
% 122.46/16.16 ((
% 122.46/16.16 (ex1I) =>
% 122.46/16.16 ((
% 122.46/16.16 (ex1I2) =>
% 122.46/16.16 ((
% 122.46/16.16 (singletonsuniq) =>
% 122.46/16.16 ((
% 122.46/16.16 (setukpairinjL1) =>
% 122.46/16.16 ((
% 122.46/16.16 (kfstsingleton) =>
% 122.46/16.16 ((
% 122.46/16.16 (theprop) =>
% 122.46/16.16 ((
% 122.46/16.16 (kfstpairEq) =>
% 122.46/16.16 ((
% 122.46/16.16 (cartprodfstin) =>
% 122.46/16.16 ((
% 122.46/16.16 (setukpairinjL2) =>
% 122.46/16.16 ((
% 122.46/16.16 (setukpairinjL) =>
% 122.46/16.16 ((
% 122.46/16.16 (setukpairinjR11) =>
% 122.46/16.16 ((
% 122.46/16.16 (setukpairinjR12) =>
% 122.46/16.16 ((
% 122.46/16.16 (setukpairinjR1) =>
% 122.46/16.16 ((
% 122.46/16.16 (upairequniteq) =>
% 122.46/16.16 ((
% 122.46/16.16 (setukpairinjR2) =>
% 122.46/16.16 ((
% 122.46/16.16 (setukpairinjR) =>
% 122.46/16.16 ((
% 122.46/16.16 (ksndsingleton) =>
% 122.46/16.16 ((
% 122.46/16.16 (ksndpairEq) =>
% 122.46/16.16 ((
% 122.46/16.16 (kpairsurjEq) =>
% 122.46/16.16 ((
% 122.46/16.16 (cartprodsndin) =>
% 122.46/16.16 ((
% 122.46/16.16 (cartprodpairmemEL) =>
% 122.46/16.16 ((
% 122.46/16.16 (cartprodpairmemER) =>
% 122.46/16.16 ((
% 122.46/16.16 (cartprodmempaircEq) =>
% 122.46/16.16 ((
% 122.46/16.16 (cartprodfstpairEq) =>
% 122.46/16.16 ((
% 122.46/16.16 (cartprodsndpairEq) =>
% 122.46/16.16 ((
% 122.46/16.16 (cartprodpairsurjEq) =>
% 122.46/16.16 ((
% 122.46/16.16 (dpsetconstrI) =>
% 122.46/16.16 ((
% 122.46/16.16 (dpsetconstrSub) =>
% 122.46/16.16 ((
% 122.46/16.16 (setOfPairsIsBReln) =>
% 122.46/16.16 ((
% 122.46/16.16 (dpsetconstrERa) =>
% 122.46/16.16 ((
% 122.46/16.16 (dpsetconstrEL1) =>
% 122.46/16.16 ((
% 122.46/16.16 (dpsetconstrEL2) =>
% 122.46/16.16 ((
% 122.46/16.16 (dpsetconstrER) =>
% 122.46/16.16 ((
% 122.46/16.16 (funcImageSingleton) =>
% 122.46/16.16 ((
% 122.46/16.16 (apProp) =>
% 122.46/16.16 ((
% 122.46/16.16 (app) =>
% 122.46/16.16 ((
% 122.46/16.16 (infuncsetfunc) =>
% 122.46/16.16 ((
% 122.46/16.16 (ap2p) =>
% 122.46/16.16 ((
% 122.46/16.16 (funcinfuncset) =>
% 122.46/16.16 ((
% 122.46/16.16 (lamProp) =>
% 122.46/16.16 ((
% 122.46/16.16 (lamp) =>
% 122.46/16.16 ((
% 122.46/16.16 (lam2p) =>
% 122.46/16.16 ((
% 122.46/16.16 (brelnall1) =>
% 122.46/16.16 ((
% 122.46/16.16 (brelnall2) =>
% 122.46/16.16 ((
% 122.46/16.16 (ex1E2) =>
% 122.46/16.16 ((
% 122.46/16.16 (funcGraphProp1) =>
% 122.46/16.16 ((
% 122.46/16.16 (funcGraphProp3) =>
% 122.46/16.16 ((
% 122.46/16.16 (funcGraphProp2) =>
% 122.46/16.16 ((
% 122.46/16.16 (funcextLem) =>
% 122.46/16.16 ((
% 122.46/16.16 (funcGraphProp4) =>
% 122.46/16.16 ((
% 122.46/16.16 (subbreln) =>
% 122.46/16.16 ((
% 122.46/16.16 (eqbreln) =>
% 122.46/16.16 ((
% 122.46/16.16 (funcext) =>
% 122.46/16.16 ((
% 122.46/16.16 (funcext2) =>
% 122.46/16.16 ((
% 122.46/16.16 (ap2apEq1) =>
% 122.46/16.16 ((
% 122.46/16.16 (ap2apEq2) =>
% 122.46/16.16 ((
% 122.46/16.16 (beta1) =>
% 122.46/16.16 ((
% 122.46/16.16 (eta1) =>
% 122.46/16.16 ((
% 122.46/16.16 (lam2lamEq) =>
% 122.46/16.16 ((
% 122.46/16.16 (beta2) =>
% 122.46/16.16 ((
% 122.46/16.16 (eta2) =>
% 122.46/16.16 ((
% 122.46/16.16 (iffalseProp1) =>
% 122.46/16.16 ((
% 122.46/16.16 (iffalseProp2) =>
% 122.46/16.16 ((
% 122.46/16.16 (iftrueProp1) =>
% 122.46/16.16 ((
% 122.46/16.16 (iftrueProp2) =>
% 122.46/16.16 ((
% 122.46/16.16 (ifSingleton) =>
% 122.46/16.16 ((
% 122.46/16.16 (ifp) =>
% 122.46/16.16 ((
% 122.46/16.16 (theeq) =>
% 122.46/16.16 ((
% 122.46/16.16 (iftrue) =>
% 122.46/16.16 ((
% 122.46/16.16 (iffalse) =>
% 122.46/16.16 ((
% 122.46/16.16 (iftrueorfalse) =>
% 122.46/16.16 ((
% 122.46/16.16 (binintersectT_lem) =>
% 122.46/16.16 ((
% 122.46/16.16 (binunionT_lem) =>
% 122.46/16.16 ((
% 122.46/16.16 (powersetT_lem) =>
% 122.46/16.16 ((
% 122.46/16.16 (setminusT_lem) =>
% 122.46/16.16 ((
% 122.46/16.16 (complementT_lem) =>
% 122.46/16.16 ((
% 122.46/16.16 (setextT) =>
% 122.46/16.16 ((
% 122.46/16.16 (subsetTI) =>
% 122.46/16.16 ((
% 122.46/16.16 (powersetTI1) =>
% 122.46/16.16 ((
% 122.46/16.16 (powersetTE1) =>
% 122.46/16.16 ((
% 122.46/16.16 (complementTI1) =>
% 122.46/16.16 ((
% 122.46/16.16 (complementTE1) =>
% 122.46/16.16 ((
% 122.46/16.16 (binintersectTELcontra) =>
% 122.46/16.16 ((
% 122.46/16.16 (binintersectTERcontra) =>
% 122.46/16.16 ((
% 122.46/16.16 (contrasubsetT) =>
% 122.46/16.16 ((
% 122.46/16.16 (contrasubsetT1) =>
% 122.46/16.16 ((
% 122.46/16.16 (contrasubsetT2) =>
% 122.46/16.16 ((
% 122.46/16.16 (contrasubsetT3) =>
% 122.46/16.16 ((
% 122.46/16.16 (doubleComplementI1) =>
% 122.46/16.16 ((
% 122.46/16.16 (doubleComplementE1) =>
% 122.46/16.16 ((
% 122.46/16.16 (doubleComplementSub1) =>
% 122.46/16.16 ((
% 122.46/16.16 (doubleComplementSub2) =>
% 122.46/16.16 ((
% 122.46/16.16 (doubleComplementEq) =>
% 122.46/16.16 ((
% 122.46/16.16 (complementTnotintersectT) =>
% 122.46/16.16 ((
% 122.46/16.16 (complementImpComplementIntersect) =>
% 122.46/16.16 ((
% 122.46/16.16 (complementSubsetComplementIntersect) =>
% 122.46/16.16 ((
% 122.46/16.16 (complementInPowersetComplementIntersect) =>
% 122.46/16.16 ((
% 122.46/16.16 (contraSubsetComplement) =>
% 122.46/16.16 ((
% 122.46/16.16 (complementTcontraSubset) =>
% 122.46/16.16 ((
% 122.46/16.16 (binunionTILcontra) =>
% 122.46/16.16 ((
% 122.46/16.16 (binunionTIRcontra) =>
% 122.46/16.16 ((
% 122.46/16.16 (inIntersectImpInUnion) =>
% 122.46/16.16 ((
% 122.46/16.16 (inIntersectImpInUnion2) =>
% 122.46/16.16 ((
% 122.46/16.16 (inIntersectImpInIntersectUnions) =>
% 122.46/16.16 ((
% 122.46/16.16 (intersectInPowersetIntersectUnions) =>
% 122.46/16.16 ((
% 122.46/16.16 (inComplementUnionImpNotIn1) =>
% 122.46/16.16 ((
% 122.46/16.16 (inComplementUnionImpInComplement1) =>
% 122.46/16.16 ((
% 122.46/16.16 (binunionTE) =>
% 122.46/16.16 ((
% 122.46/16.16 (binunionTEcontra) =>
% 122.46/16.16 ((
% 122.46/16.16 (demorgan2a1) =>
% 122.46/16.16 ((
% 122.46/16.16 (complementUnionInPowersetComplement) =>
% 122.46/16.16 ((
% 122.46/16.16 (demorgan2a2) =>
% 122.46/16.16 ((
% 122.46/16.16 (demorgan1a) =>
% 122.46/16.16 ((
% 122.46/16.16 (demorgan1b) =>
% 122.46/16.16 ((
% 122.46/16.16 (demorgan1) =>
% 122.46/16.16 ((
% 122.46/16.16 (demorgan2a) =>
% 122.46/16.16 ((
% 122.46/16.16 (demorgan2b2) =>
% 122.46/16.16 ((
% 122.46/16.16 (demorgan2b) =>
% 122.46/16.16 ((
% 122.46/16.16 (demorgan2) =>
% 122.46/16.16 ((
% 122.46/16.16 (woz13rule0) =>
% 122.46/16.16 ((
% 122.46/16.16 (woz13rule1) =>
% 122.46/16.16 ((
% 122.46/16.16 (woz13rule2) =>
% 122.46/16.16 ((
% 122.46/16.16 (woz13rule3) =>
% 122.46/16.16 ((
% 122.46/16.16 (woz13rule4) =>
% 122.46/16.16 ((
% 122.46/16.16 (woz1_1) =>
% 122.46/16.16 ((
% 122.46/16.16 (woz1_2) =>
% 122.46/16.16 ((
% 122.46/16.16 (woz1_3) =>
% 122.46/16.16 ((
% 122.46/16.16 (woz1_4) =>
% 122.46/16.16 ((
% 122.46/16.16 (woz1_5) =>
% 122.46/16.16 ((
% 122.46/16.16 (breln1all2) =>
% 122.46/16.16 ((
% 122.46/16.16 (breln1SetBreln1) =>
% 122.46/16.16 ((
% 122.46/16.16 (choice2fnsingleton) =>
% 122.46/16.16 ((
% 122.46/16.16 (setOfPairsIsBReln1) =>
% 122.46/16.16 ((
% 122.46/16.16 (breln1all1) =>
% 122.46/16.16 ((
% 122.46/16.16 (subbreln1) =>
% 122.46/16.16 ((
% 122.46/16.16 (eqbreln1) =>
% 122.46/16.16 ((
% 122.46/16.16 (breln1invprop) =>
% 122.46/16.16 ((
% 122.46/16.16 (breln1invI) =>
% 122.46/16.16 ((
% 122.46/16.16 (breln1invE) =>
% 122.46/16.16 ((
% 122.46/16.16 (breln1compprop) =>
% 122.46/16.16 ((
% 122.46/16.16 (breln1compI) =>
% 122.46/16.16 ((
% 122.46/16.16 (breln1compE) =>
% 122.46/16.16 ((
% 122.46/16.16 (breln1compEex) =>
% 122.46/16.16 ((
% 122.46/16.16 (breln1unionprop) =>
% 122.46/16.16 ((
% 122.46/16.16 (breln1unionIL) =>
% 122.46/16.16 ((
% 122.46/16.16 (breln1unionIR) =>
% 122.46/16.16 ((
% 122.46/16.16 (breln1unionI) =>
% 122.46/16.16 ((
% 122.46/16.16 (breln1unionE) =>
% 122.46/16.16 ((
% 122.46/16.16 (breln1unionEcases) =>
% 122.46/16.16 ((
% 122.46/16.16 (breln1unionCommutes) =>
% 122.46/16.16 ((
% 122.46/16.16 (woz2Ex) =>
% 122.46/16.16 ((
% 122.46/16.16 (woz2W) =>
% 122.46/16.16 ((
% 122.46/16.16 (woz2A) =>
% 122.46/16.16 ((
% 122.46/16.16 (woz2B) =>
% 122.46/16.16 ((
% 122.46/16.16 (image1Ex) =>
% 122.46/16.16 ((
% 122.46/16.16 (image1Ex1) =>
% 122.46/16.16 ((
% 122.46/16.16 (image1Equiv) =>
% 122.46/16.16 ((
% 122.46/16.16 (image1E) =>
% 122.46/16.16 ((
% 122.46/16.16 (image1I) =>
% 122.46/16.16 ((
% 122.46/16.16 (injFuncInInjFuncSet) =>
% 122.46/16.16 ((
% 122.46/16.16 (!!) @ (
% 122.46/16.16 (('#B') @ (
% 122.46/16.16 !!) @
% 122.46/16.16 (
% 122.46/16.16 (
% 122.46/16.16 ('#B') @ (
% 122.46/16.16 (
% 122.46/16.16 ('#B') @ (
% 122.46/16.16 !!))) @
% 122.46/16.16 (
% 122.46/16.16 (
% 122.46/16.16 ('#S') @ (
% 122.46/16.16 (
% 122.46/16.16 ('#B') @ (
% 122.46/16.16 '#S') @
% 122.46/16.16 (
% 122.46/16.16 (
% 122.46/16.16 ('#B') @ (
% 122.46/16.16 (
% 122.46/16.16 ('#B') @ (
% 122.46/16.16 '#S'))) @
% 122.46/16.16 (
% 122.46/16.16 (
% 122.46/16.16 ('#B') @ (
% 122.46/16.16 (
% 122.46/16.16 ('#B') @ (
% 122.46/16.16 (
% 122.46/16.16 ('#B') @ (
% 122.46/16.16 =>))))) @
% 122.46/16.16 (
% 122.46/16.16 (
% 122.46/16.16 ('#B') @ (
% 122.46/16.16 (
% 122.46/16.16 ('#B') @ (
% 122.46/16.16 (
% 122.46/16.16 ('#C') @ in)))) @
% 122.46/16.16 injFuncSet)))))))) @
% 122.46/16.16 (
% 122.46/16.16 (
% 122.46/16.16 ('#B') @ (
% 122.46/16.16 (
% 122.46/16.16 ('#B') @ (
% 122.46/16.16 (
% 122.46/16.16 ('#C') @ in)))) @
% 122.46/16.16 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.46/16.16 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1223])).
% 122.46/16.16 thf(zip_derived_cl1239, plain,
% 122.46/16.16 (~ (((bs114d) =>
% 122.46/16.16 (((setminusI) =>
% 122.46/16.16 (((setminusEL) =>
% 122.46/16.16 (((setminusER) =>
% 122.46/16.16 (((setminusSubset2) =>
% 122.46/16.16 (((setminusERneg) =>
% 122.46/16.16 (((setminusELneg) =>
% 122.46/16.16 (((setminusILneg) =>
% 122.46/16.16 (((setminusIRneg) =>
% 122.46/16.16 (((setminusLsub) =>
% 122.46/16.16 (((setminusSubset1) =>
% 122.46/16.16 (((symdiffE) =>
% 122.46/16.16 (((symdiffI1) =>
% 122.46/16.16 (((symdiffI2) =>
% 122.46/16.16 (((symdiffIneg1) =>
% 122.46/16.16 (((symdiffIneg2) =>
% 122.46/16.16 (((secondinupair) =>
% 122.46/16.16 (((setukpairIL) =>
% 122.46/16.16 (((setukpairIR) =>
% 122.46/16.16 (((kpairiskpair) =>
% 122.46/16.16 (((kpairp) =>
% 122.46/16.16 (((singletonsubset) =>
% 122.46/16.16 (((singletoninpowerset) =>
% 122.46/16.16 (((singletoninpowunion) =>
% 122.46/16.16 (((upairset2E) =>
% 122.46/16.16 (((upairsubunion) =>
% 122.46/16.16 (((upairinpowunion) =>
% 122.46/16.16 (((ubforcartprodlem1) =>
% 122.46/16.16 (((ubforcartprodlem2) =>
% 122.46/16.16 (((ubforcartprodlem3) =>
% 122.46/16.16 ((
% 122.46/16.16 (cartprodpairin) =>
% 122.46/16.16 ((
% 122.46/16.16 (cartprodmempair1) =>
% 122.46/16.16 ((
% 122.46/16.16 (cartprodmempair) =>
% 122.46/16.16 ((
% 122.46/16.16 (setunionE2) =>
% 122.46/16.16 ((
% 122.46/16.16 (setunionsingleton1) =>
% 122.46/16.16 ((
% 122.46/16.16 (setunionsingleton2) =>
% 122.46/16.16 ((
% 122.46/16.16 (setunionsingleton) =>
% 122.46/16.16 ((
% 122.46/16.16 (singletonprop) =>
% 122.46/16.16 ((
% 122.46/16.16 (ex1E1) =>
% 122.46/16.16 ((
% 122.46/16.16 (ex1I) =>
% 122.46/16.16 ((
% 122.46/16.16 (ex1I2) =>
% 122.46/16.16 ((
% 122.46/16.16 (singletonsuniq) =>
% 122.46/16.16 ((
% 122.46/16.16 (setukpairinjL1) =>
% 122.46/16.16 ((
% 122.46/16.16 (kfstsingleton) =>
% 122.46/16.16 ((
% 122.46/16.16 (theprop) =>
% 122.46/16.16 ((
% 122.46/16.16 (kfstpairEq) =>
% 122.46/16.16 ((
% 122.46/16.16 (cartprodfstin) =>
% 122.46/16.16 ((
% 122.46/16.16 (setukpairinjL2) =>
% 122.46/16.16 ((
% 122.46/16.16 (setukpairinjL) =>
% 122.46/16.16 ((
% 122.46/16.16 (setukpairinjR11) =>
% 122.46/16.16 ((
% 122.46/16.16 (setukpairinjR12) =>
% 122.46/16.16 ((
% 122.46/16.16 (setukpairinjR1) =>
% 122.46/16.16 ((
% 122.46/16.16 (upairequniteq) =>
% 122.46/16.16 ((
% 122.46/16.16 (setukpairinjR2) =>
% 122.46/16.16 ((
% 122.46/16.16 (setukpairinjR) =>
% 122.46/16.16 ((
% 122.46/16.16 (ksndsingleton) =>
% 122.46/16.16 ((
% 122.46/16.16 (ksndpairEq) =>
% 122.46/16.16 ((
% 122.46/16.16 (kpairsurjEq) =>
% 122.46/16.16 ((
% 122.46/16.16 (cartprodsndin) =>
% 122.46/16.16 ((
% 122.46/16.16 (cartprodpairmemEL) =>
% 122.46/16.16 ((
% 122.46/16.16 (cartprodpairmemER) =>
% 122.46/16.16 ((
% 122.46/16.16 (cartprodmempaircEq) =>
% 122.46/16.16 ((
% 122.46/16.16 (cartprodfstpairEq) =>
% 122.46/16.16 ((
% 122.46/16.16 (cartprodsndpairEq) =>
% 122.46/16.16 ((
% 122.46/16.16 (cartprodpairsurjEq) =>
% 122.46/16.16 ((
% 122.46/16.16 (dpsetconstrI) =>
% 122.46/16.16 ((
% 122.46/16.16 (dpsetconstrSub) =>
% 122.46/16.16 ((
% 122.46/16.16 (setOfPairsIsBReln) =>
% 122.46/16.16 ((
% 122.46/16.16 (dpsetconstrERa) =>
% 122.46/16.16 ((
% 122.46/16.16 (dpsetconstrEL1) =>
% 122.46/16.16 ((
% 122.46/16.16 (dpsetconstrEL2) =>
% 122.46/16.16 ((
% 122.46/16.16 (dpsetconstrER) =>
% 122.46/16.16 ((
% 122.46/16.16 (funcImageSingleton) =>
% 122.46/16.16 ((
% 122.46/16.16 (apProp) =>
% 122.46/16.16 ((
% 122.46/16.16 (app) =>
% 122.46/16.16 ((
% 122.46/16.16 (infuncsetfunc) =>
% 122.46/16.16 ((
% 122.46/16.16 (ap2p) =>
% 122.46/16.16 ((
% 122.46/16.16 (funcinfuncset) =>
% 122.46/16.16 ((
% 122.46/16.16 (lamProp) =>
% 122.46/16.16 ((
% 122.46/16.16 (lamp) =>
% 122.46/16.16 ((
% 122.46/16.16 (lam2p) =>
% 122.46/16.16 ((
% 122.46/16.16 (brelnall1) =>
% 122.46/16.16 ((
% 122.46/16.16 (brelnall2) =>
% 122.46/16.16 ((
% 122.46/16.16 (ex1E2) =>
% 122.46/16.16 ((
% 122.46/16.16 (funcGraphProp1) =>
% 122.46/16.16 ((
% 122.46/16.16 (funcGraphProp3) =>
% 122.46/16.16 ((
% 122.46/16.16 (funcGraphProp2) =>
% 122.46/16.16 ((
% 122.46/16.16 (funcextLem) =>
% 122.46/16.16 ((
% 122.46/16.16 (funcGraphProp4) =>
% 122.46/16.16 ((
% 122.46/16.16 (subbreln) =>
% 122.46/16.16 ((
% 122.46/16.16 (eqbreln) =>
% 122.46/16.16 ((
% 122.46/16.16 (funcext) =>
% 122.46/16.16 ((
% 122.46/16.16 (funcext2) =>
% 122.46/16.16 ((
% 122.46/16.16 (ap2apEq1) =>
% 122.46/16.16 ((
% 122.46/16.16 (ap2apEq2) =>
% 122.46/16.16 ((
% 122.46/16.16 (beta1) =>
% 122.46/16.16 ((
% 122.46/16.16 (eta1) =>
% 122.46/16.16 ((
% 122.46/16.16 (lam2lamEq) =>
% 122.46/16.16 ((
% 122.46/16.16 (beta2) =>
% 122.46/16.16 ((
% 122.46/16.16 (eta2) =>
% 122.46/16.16 ((
% 122.46/16.16 (iffalseProp1) =>
% 122.46/16.16 ((
% 122.46/16.16 (iffalseProp2) =>
% 122.46/16.16 ((
% 122.46/16.16 (iftrueProp1) =>
% 122.46/16.16 ((
% 122.46/16.16 (iftrueProp2) =>
% 122.46/16.16 ((
% 122.46/16.16 (ifSingleton) =>
% 122.46/16.16 ((
% 122.46/16.16 (ifp) =>
% 122.46/16.16 ((
% 122.46/16.16 (theeq) =>
% 122.46/16.16 ((
% 122.46/16.16 (iftrue) =>
% 122.46/16.16 ((
% 122.46/16.16 (iffalse) =>
% 122.46/16.16 ((
% 122.46/16.16 (iftrueorfalse) =>
% 122.46/16.16 ((
% 122.46/16.16 (binintersectT_lem) =>
% 122.46/16.16 ((
% 122.46/16.16 (binunionT_lem) =>
% 122.46/16.16 ((
% 122.46/16.16 (powersetT_lem) =>
% 122.46/16.16 ((
% 122.46/16.16 (setminusT_lem) =>
% 122.46/16.16 ((
% 122.46/16.16 (complementT_lem) =>
% 122.46/16.16 ((
% 122.46/16.16 (setextT) =>
% 122.46/16.16 ((
% 122.46/16.16 (subsetTI) =>
% 122.46/16.16 ((
% 122.46/16.16 (powersetTI1) =>
% 122.46/16.16 ((
% 122.46/16.16 (powersetTE1) =>
% 122.46/16.16 ((
% 122.46/16.16 (complementTI1) =>
% 122.46/16.16 ((
% 122.46/16.16 (complementTE1) =>
% 122.46/16.16 ((
% 122.46/16.16 (binintersectTELcontra) =>
% 122.46/16.16 ((
% 122.46/16.16 (binintersectTERcontra) =>
% 122.46/16.16 ((
% 122.46/16.16 (contrasubsetT) =>
% 122.46/16.16 ((
% 122.46/16.16 (contrasubsetT1) =>
% 122.46/16.16 ((
% 122.46/16.16 (contrasubsetT2) =>
% 122.46/16.16 ((
% 122.46/16.16 (contrasubsetT3) =>
% 122.46/16.16 ((
% 122.46/16.16 (doubleComplementI1) =>
% 122.46/16.16 ((
% 122.46/16.16 (doubleComplementE1) =>
% 122.46/16.16 ((
% 122.46/16.16 (doubleComplementSub1) =>
% 122.46/16.16 ((
% 122.46/16.16 (doubleComplementSub2) =>
% 122.46/16.16 ((
% 122.46/16.16 (doubleComplementEq) =>
% 122.46/16.16 ((
% 122.46/16.16 (complementTnotintersectT) =>
% 122.46/16.16 ((
% 122.46/16.16 (complementImpComplementIntersect) =>
% 122.46/16.16 ((
% 122.46/16.16 (complementSubsetComplementIntersect) =>
% 122.46/16.16 ((
% 122.46/16.16 (complementInPowersetComplementIntersect) =>
% 122.46/16.16 ((
% 122.46/16.16 (contraSubsetComplement) =>
% 122.46/16.16 ((
% 122.46/16.16 (complementTcontraSubset) =>
% 122.46/16.16 ((
% 122.46/16.16 (binunionTILcontra) =>
% 122.46/16.16 ((
% 122.46/16.16 (binunionTIRcontra) =>
% 122.46/16.16 ((
% 122.46/16.16 (inIntersectImpInUnion) =>
% 122.46/16.16 ((
% 122.46/16.16 (inIntersectImpInUnion2) =>
% 122.46/16.16 ((
% 122.46/16.16 (inIntersectImpInIntersectUnions) =>
% 122.46/16.16 ((
% 122.46/16.16 (intersectInPowersetIntersectUnions) =>
% 122.46/16.16 ((
% 122.46/16.16 (inComplementUnionImpNotIn1) =>
% 122.46/16.16 ((
% 122.46/16.16 (inComplementUnionImpInComplement1) =>
% 122.46/16.16 ((
% 122.46/16.16 (binunionTE) =>
% 122.46/16.16 ((
% 122.46/16.16 (binunionTEcontra) =>
% 122.46/16.16 ((
% 122.46/16.16 (demorgan2a1) =>
% 122.46/16.16 ((
% 122.46/16.16 (complementUnionInPowersetComplement) =>
% 122.46/16.16 ((
% 122.46/16.16 (demorgan2a2) =>
% 122.46/16.16 ((
% 122.46/16.16 (demorgan1a) =>
% 122.46/16.16 ((
% 122.46/16.16 (demorgan1b) =>
% 122.46/16.16 ((
% 122.46/16.16 (demorgan1) =>
% 122.46/16.16 ((
% 122.46/16.16 (demorgan2a) =>
% 122.46/16.16 ((
% 122.46/16.16 (demorgan2b2) =>
% 122.46/16.16 ((
% 122.46/16.16 (demorgan2b) =>
% 122.46/16.16 ((
% 122.46/16.16 (demorgan2) =>
% 122.46/16.16 ((
% 122.46/16.16 (woz13rule0) =>
% 122.46/16.16 ((
% 122.46/16.16 (woz13rule1) =>
% 122.46/16.16 ((
% 122.46/16.16 (woz13rule2) =>
% 122.46/16.16 ((
% 122.46/16.16 (woz13rule3) =>
% 122.46/16.16 ((
% 122.46/16.16 (woz13rule4) =>
% 122.46/16.16 ((
% 122.46/16.16 (woz1_1) =>
% 122.46/16.16 ((
% 122.46/16.16 (woz1_2) =>
% 122.46/16.16 ((
% 122.46/16.16 (woz1_3) =>
% 122.46/16.16 ((
% 122.46/16.16 (woz1_4) =>
% 122.46/16.16 ((
% 122.46/16.16 (woz1_5) =>
% 122.46/16.16 ((
% 122.46/16.16 (breln1all2) =>
% 122.46/16.16 ((
% 122.46/16.16 (breln1SetBreln1) =>
% 122.46/16.16 ((
% 122.46/16.16 (choice2fnsingleton) =>
% 122.46/16.16 ((
% 122.46/16.16 (setOfPairsIsBReln1) =>
% 122.46/16.16 ((
% 122.46/16.16 (breln1all1) =>
% 122.46/16.16 ((
% 122.46/16.16 (subbreln1) =>
% 122.46/16.16 ((
% 122.46/16.16 (eqbreln1) =>
% 122.46/16.16 ((
% 122.46/16.16 (breln1invprop) =>
% 122.46/16.16 ((
% 122.46/16.16 (breln1invI) =>
% 122.46/16.16 ((
% 122.46/16.16 (breln1invE) =>
% 122.46/16.16 ((
% 122.46/16.16 (breln1compprop) =>
% 122.46/16.16 ((
% 122.46/16.16 (breln1compI) =>
% 122.46/16.16 ((
% 122.46/16.16 (breln1compE) =>
% 122.46/16.16 ((
% 122.46/16.16 (breln1compEex) =>
% 122.46/16.16 ((
% 122.46/16.16 (breln1unionprop) =>
% 122.46/16.16 ((
% 122.46/16.16 (breln1unionIL) =>
% 122.46/16.16 ((
% 122.46/16.16 (breln1unionIR) =>
% 122.46/16.16 ((
% 122.46/16.16 (breln1unionI) =>
% 122.46/16.16 ((
% 122.46/16.16 (breln1unionE) =>
% 122.46/16.16 ((
% 122.46/16.16 (breln1unionEcases) =>
% 122.46/16.16 ((
% 122.46/16.16 (breln1unionCommutes) =>
% 122.46/16.16 ((
% 122.46/16.16 (woz2Ex) =>
% 122.46/16.16 ((
% 122.46/16.16 (woz2W) =>
% 122.46/16.16 ((
% 122.46/16.16 (woz2A) =>
% 122.46/16.16 ((
% 122.46/16.16 (woz2B) =>
% 122.46/16.16 ((
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% 122.46/16.16 ((
% 122.46/16.16 (image1Ex1) =>
% 122.46/16.16 ((
% 122.46/16.16 (image1Equiv) =>
% 122.46/16.16 ((
% 122.46/16.16 (image1E) =>
% 122.46/16.16 ((
% 122.46/16.16 (image1I) =>
% 122.46/16.16 ((
% 122.46/16.16 (injFuncInInjFuncSet) =>
% 122.46/16.16 ((
% 122.46/16.16 (!!) @ (
% 122.46/16.16 (('#B') @ (
% 122.46/16.16 !!) @
% 122.46/16.16 (
% 122.46/16.16 (
% 122.46/16.16 ('#B') @ (
% 122.46/16.16 (
% 122.46/16.16 ('#B') @ (
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% 122.46/16.16 (
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% 122.46/16.16 (
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% 122.46/16.16 (
% 122.46/16.16 ('#B') @ (
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% 122.46/16.16 =>))))) @
% 122.46/16.16 (
% 122.46/16.16 (
% 122.46/16.16 ('#B') @ (
% 122.46/16.16 (
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% 122.46/16.16 injFuncSet)))))))) @
% 122.46/16.16 (
% 122.46/16.16 (
% 122.46/16.16 ('#B') @ (
% 122.46/16.16 (
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% 122.46/16.16 (
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% 122.46/16.16 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.46/16.16 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1231])).
% 122.46/16.16 thf(zip_derived_cl1247, plain,
% 122.46/16.16 (~ (((setminusI) =>
% 122.46/16.16 (((setminusEL) =>
% 122.46/16.16 (((setminusER) =>
% 122.46/16.16 (((setminusSubset2) =>
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% 122.46/16.16 (((setminusELneg) =>
% 122.46/16.16 (((setminusILneg) =>
% 122.46/16.16 (((setminusIRneg) =>
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% 122.46/16.16 (((setminusSubset1) =>
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% 122.46/16.16 (((symdiffI1) =>
% 122.46/16.16 (((symdiffI2) =>
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% 122.46/16.16 (((symdiffIneg2) =>
% 122.46/16.16 (((secondinupair) =>
% 122.46/16.16 (((setukpairIL) =>
% 122.46/16.16 (((setukpairIR) =>
% 122.46/16.16 (((kpairiskpair) =>
% 122.46/16.16 (((kpairp) =>
% 122.46/16.16 (((singletonsubset) =>
% 122.46/16.16 (((singletoninpowerset) =>
% 122.46/16.16 (((singletoninpowunion) =>
% 122.46/16.16 (((upairset2E) =>
% 122.46/16.16 (((upairsubunion) =>
% 122.46/16.16 (((upairinpowunion) =>
% 122.46/16.16 (((ubforcartprodlem1) =>
% 122.46/16.16 (((ubforcartprodlem2) =>
% 122.46/16.16 (((ubforcartprodlem3) =>
% 122.46/16.16 (((cartprodpairin) =>
% 122.46/16.16 ((
% 122.46/16.16 (cartprodmempair1) =>
% 122.46/16.16 ((
% 122.46/16.16 (cartprodmempair) =>
% 122.46/16.16 ((
% 122.46/16.16 (setunionE2) =>
% 122.46/16.16 ((
% 122.46/16.16 (setunionsingleton1) =>
% 122.46/16.16 ((
% 122.46/16.16 (setunionsingleton2) =>
% 122.46/16.16 ((
% 122.46/16.16 (setunionsingleton) =>
% 122.46/16.16 ((
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% 122.46/16.16 ((
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% 122.46/16.16 ((
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% 122.46/16.16 ((
% 122.46/16.16 (ex1I2) =>
% 122.46/16.16 ((
% 122.46/16.16 (singletonsuniq) =>
% 122.46/16.16 ((
% 122.46/16.16 (setukpairinjL1) =>
% 122.46/16.16 ((
% 122.46/16.16 (kfstsingleton) =>
% 122.46/16.16 ((
% 122.46/16.16 (theprop) =>
% 122.46/16.16 ((
% 122.46/16.16 (kfstpairEq) =>
% 122.46/16.16 ((
% 122.46/16.16 (cartprodfstin) =>
% 122.46/16.16 ((
% 122.46/16.16 (setukpairinjL2) =>
% 122.46/16.16 ((
% 122.46/16.16 (setukpairinjL) =>
% 122.46/16.16 ((
% 122.46/16.16 (setukpairinjR11) =>
% 122.46/16.16 ((
% 122.46/16.16 (setukpairinjR12) =>
% 122.46/16.16 ((
% 122.46/16.16 (setukpairinjR1) =>
% 122.46/16.16 ((
% 122.46/16.16 (upairequniteq) =>
% 122.46/16.16 ((
% 122.46/16.16 (setukpairinjR2) =>
% 122.46/16.16 ((
% 122.46/16.16 (setukpairinjR) =>
% 122.46/16.16 ((
% 122.46/16.16 (ksndsingleton) =>
% 122.46/16.16 ((
% 122.46/16.16 (ksndpairEq) =>
% 122.46/16.16 ((
% 122.46/16.16 (kpairsurjEq) =>
% 122.46/16.16 ((
% 122.46/16.16 (cartprodsndin) =>
% 122.46/16.16 ((
% 122.46/16.16 (cartprodpairmemEL) =>
% 122.46/16.16 ((
% 122.46/16.16 (cartprodpairmemER) =>
% 122.46/16.16 ((
% 122.46/16.16 (cartprodmempaircEq) =>
% 122.46/16.16 ((
% 122.46/16.16 (cartprodfstpairEq) =>
% 122.46/16.16 ((
% 122.46/16.16 (cartprodsndpairEq) =>
% 122.46/16.16 ((
% 122.46/16.16 (cartprodpairsurjEq) =>
% 122.46/16.16 ((
% 122.46/16.16 (dpsetconstrI) =>
% 122.46/16.16 ((
% 122.46/16.16 (dpsetconstrSub) =>
% 122.46/16.16 ((
% 122.46/16.16 (setOfPairsIsBReln) =>
% 122.46/16.16 ((
% 122.46/16.16 (dpsetconstrERa) =>
% 122.46/16.16 ((
% 122.46/16.16 (dpsetconstrEL1) =>
% 122.46/16.16 ((
% 122.46/16.16 (dpsetconstrEL2) =>
% 122.46/16.16 ((
% 122.46/16.16 (dpsetconstrER) =>
% 122.46/16.16 ((
% 122.46/16.16 (funcImageSingleton) =>
% 122.46/16.16 ((
% 122.46/16.16 (apProp) =>
% 122.46/16.16 ((
% 122.46/16.16 (app) =>
% 122.46/16.16 ((
% 122.46/16.16 (infuncsetfunc) =>
% 122.46/16.16 ((
% 122.46/16.16 (ap2p) =>
% 122.46/16.16 ((
% 122.46/16.16 (funcinfuncset) =>
% 122.46/16.16 ((
% 122.46/16.16 (lamProp) =>
% 122.46/16.16 ((
% 122.46/16.16 (lamp) =>
% 122.46/16.16 ((
% 122.46/16.16 (lam2p) =>
% 122.46/16.16 ((
% 122.46/16.16 (brelnall1) =>
% 122.46/16.16 ((
% 122.46/16.16 (brelnall2) =>
% 122.46/16.16 ((
% 122.46/16.16 (ex1E2) =>
% 122.46/16.16 ((
% 122.46/16.16 (funcGraphProp1) =>
% 122.46/16.16 ((
% 122.46/16.16 (funcGraphProp3) =>
% 122.46/16.16 ((
% 122.46/16.16 (funcGraphProp2) =>
% 122.46/16.16 ((
% 122.46/16.16 (funcextLem) =>
% 122.46/16.16 ((
% 122.46/16.16 (funcGraphProp4) =>
% 122.46/16.16 ((
% 122.46/16.16 (subbreln) =>
% 122.46/16.16 ((
% 122.46/16.16 (eqbreln) =>
% 122.46/16.16 ((
% 122.46/16.16 (funcext) =>
% 122.46/16.16 ((
% 122.46/16.16 (funcext2) =>
% 122.46/16.16 ((
% 122.46/16.16 (ap2apEq1) =>
% 122.46/16.16 ((
% 122.46/16.16 (ap2apEq2) =>
% 122.46/16.16 ((
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% 122.46/16.16 ((
% 122.46/16.16 (eta1) =>
% 122.46/16.16 ((
% 122.46/16.16 (lam2lamEq) =>
% 122.46/16.16 ((
% 122.46/16.16 (beta2) =>
% 122.46/16.16 ((
% 122.46/16.16 (eta2) =>
% 122.46/16.16 ((
% 122.46/16.16 (iffalseProp1) =>
% 122.46/16.16 ((
% 122.46/16.16 (iffalseProp2) =>
% 122.46/16.16 ((
% 122.46/16.16 (iftrueProp1) =>
% 122.46/16.16 ((
% 122.46/16.16 (iftrueProp2) =>
% 122.46/16.16 ((
% 122.46/16.16 (ifSingleton) =>
% 122.46/16.16 ((
% 122.46/16.16 (ifp) =>
% 122.46/16.16 ((
% 122.46/16.16 (theeq) =>
% 122.46/16.16 ((
% 122.46/16.16 (iftrue) =>
% 122.46/16.16 ((
% 122.46/16.16 (iffalse) =>
% 122.46/16.16 ((
% 122.46/16.16 (iftrueorfalse) =>
% 122.46/16.16 ((
% 122.46/16.16 (binintersectT_lem) =>
% 122.46/16.16 ((
% 122.46/16.16 (binunionT_lem) =>
% 122.46/16.16 ((
% 122.46/16.16 (powersetT_lem) =>
% 122.46/16.16 ((
% 122.46/16.16 (setminusT_lem) =>
% 122.46/16.16 ((
% 122.46/16.16 (complementT_lem) =>
% 122.46/16.16 ((
% 122.46/16.16 (setextT) =>
% 122.46/16.16 ((
% 122.46/16.16 (subsetTI) =>
% 122.46/16.16 ((
% 122.46/16.16 (powersetTI1) =>
% 122.46/16.16 ((
% 122.46/16.16 (powersetTE1) =>
% 122.46/16.16 ((
% 122.46/16.16 (complementTI1) =>
% 122.46/16.16 ((
% 122.46/16.16 (complementTE1) =>
% 122.46/16.16 ((
% 122.46/16.16 (binintersectTELcontra) =>
% 122.46/16.16 ((
% 122.46/16.16 (binintersectTERcontra) =>
% 122.46/16.16 ((
% 122.46/16.16 (contrasubsetT) =>
% 122.46/16.16 ((
% 122.46/16.16 (contrasubsetT1) =>
% 122.46/16.16 ((
% 122.46/16.16 (contrasubsetT2) =>
% 122.46/16.16 ((
% 122.46/16.16 (contrasubsetT3) =>
% 122.46/16.16 ((
% 122.46/16.16 (doubleComplementI1) =>
% 122.46/16.16 ((
% 122.46/16.16 (doubleComplementE1) =>
% 122.46/16.16 ((
% 122.46/16.16 (doubleComplementSub1) =>
% 122.46/16.16 ((
% 122.46/16.16 (doubleComplementSub2) =>
% 122.46/16.16 ((
% 122.46/16.16 (doubleComplementEq) =>
% 122.46/16.16 ((
% 122.46/16.16 (complementTnotintersectT) =>
% 122.46/16.16 ((
% 122.46/16.16 (complementImpComplementIntersect) =>
% 122.46/16.16 ((
% 122.46/16.16 (complementSubsetComplementIntersect) =>
% 122.46/16.16 ((
% 122.46/16.16 (complementInPowersetComplementIntersect) =>
% 122.46/16.16 ((
% 122.46/16.16 (contraSubsetComplement) =>
% 122.46/16.16 ((
% 122.46/16.16 (complementTcontraSubset) =>
% 122.46/16.16 ((
% 122.46/16.16 (binunionTILcontra) =>
% 122.46/16.16 ((
% 122.46/16.16 (binunionTIRcontra) =>
% 122.46/16.16 ((
% 122.46/16.16 (inIntersectImpInUnion) =>
% 122.46/16.16 ((
% 122.46/16.16 (inIntersectImpInUnion2) =>
% 122.46/16.16 ((
% 122.46/16.16 (inIntersectImpInIntersectUnions) =>
% 122.46/16.16 ((
% 122.46/16.16 (intersectInPowersetIntersectUnions) =>
% 122.46/16.16 ((
% 122.46/16.16 (inComplementUnionImpNotIn1) =>
% 122.46/16.16 ((
% 122.46/16.16 (inComplementUnionImpInComplement1) =>
% 122.46/16.16 ((
% 122.46/16.16 (binunionTE) =>
% 122.46/16.16 ((
% 122.46/16.16 (binunionTEcontra) =>
% 122.46/16.16 ((
% 122.46/16.16 (demorgan2a1) =>
% 122.46/16.16 ((
% 122.46/16.16 (complementUnionInPowersetComplement) =>
% 122.46/16.16 ((
% 122.46/16.16 (demorgan2a2) =>
% 122.46/16.16 ((
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% 122.46/16.16 ((
% 122.46/16.16 (demorgan1b) =>
% 122.46/16.16 ((
% 122.46/16.16 (demorgan1) =>
% 122.46/16.16 ((
% 122.46/16.16 (demorgan2a) =>
% 122.46/16.16 ((
% 122.46/16.16 (demorgan2b2) =>
% 122.46/16.16 ((
% 122.46/16.16 (demorgan2b) =>
% 122.46/16.16 ((
% 122.46/16.16 (demorgan2) =>
% 122.46/16.16 ((
% 122.46/16.16 (woz13rule0) =>
% 122.46/16.16 ((
% 122.46/16.16 (woz13rule1) =>
% 122.46/16.16 ((
% 122.46/16.16 (woz13rule2) =>
% 122.46/16.16 ((
% 122.46/16.16 (woz13rule3) =>
% 122.46/16.16 ((
% 122.46/16.16 (woz13rule4) =>
% 122.46/16.16 ((
% 122.46/16.16 (woz1_1) =>
% 122.46/16.16 ((
% 122.46/16.16 (woz1_2) =>
% 122.46/16.16 ((
% 122.46/16.16 (woz1_3) =>
% 122.46/16.16 ((
% 122.46/16.16 (woz1_4) =>
% 122.46/16.16 ((
% 122.46/16.16 (woz1_5) =>
% 122.46/16.16 ((
% 122.46/16.16 (breln1all2) =>
% 122.46/16.16 ((
% 122.46/16.16 (breln1SetBreln1) =>
% 122.46/16.16 ((
% 122.46/16.16 (choice2fnsingleton) =>
% 122.46/16.16 ((
% 122.46/16.16 (setOfPairsIsBReln1) =>
% 122.46/16.16 ((
% 122.46/16.16 (breln1all1) =>
% 122.46/16.16 ((
% 122.46/16.16 (subbreln1) =>
% 122.46/16.16 ((
% 122.46/16.16 (eqbreln1) =>
% 122.46/16.16 ((
% 122.46/16.16 (breln1invprop) =>
% 122.46/16.16 ((
% 122.46/16.16 (breln1invI) =>
% 122.46/16.16 ((
% 122.46/16.16 (breln1invE) =>
% 122.46/16.16 ((
% 122.46/16.16 (breln1compprop) =>
% 122.46/16.16 ((
% 122.46/16.16 (breln1compI) =>
% 122.46/16.16 ((
% 122.46/16.16 (breln1compE) =>
% 122.46/16.16 ((
% 122.46/16.16 (breln1compEex) =>
% 122.46/16.16 ((
% 122.46/16.16 (breln1unionprop) =>
% 122.46/16.16 ((
% 122.46/16.16 (breln1unionIL) =>
% 122.46/16.16 ((
% 122.46/16.16 (breln1unionIR) =>
% 122.46/16.16 ((
% 122.46/16.16 (breln1unionI) =>
% 122.46/16.16 ((
% 122.46/16.16 (breln1unionE) =>
% 122.46/16.16 ((
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% 122.46/16.16 ((
% 122.46/16.16 (breln1unionCommutes) =>
% 122.46/16.16 ((
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% 122.46/16.16 ((
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% 122.46/16.16 ((
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% 122.46/16.16 ((
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% 122.46/16.16 ((
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% 122.46/16.16 ((
% 122.46/16.16 (image1Ex1) =>
% 122.46/16.16 ((
% 122.46/16.16 (image1Equiv) =>
% 122.46/16.16 ((
% 122.46/16.16 (image1E) =>
% 122.46/16.16 ((
% 122.46/16.16 (image1I) =>
% 122.46/16.16 ((
% 122.46/16.16 (injFuncInInjFuncSet) =>
% 122.46/16.16 ((
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% 122.46/16.16 (('#B') @ (
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% 122.46/16.16 (
% 122.46/16.16 (
% 122.46/16.16 ('#B') @ (
% 122.46/16.16 (
% 122.46/16.16 ('#B') @ (
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% 122.46/16.16 (
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% 122.46/16.16 (
% 122.46/16.16 (
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% 122.46/16.16 injFuncSet)))))))) @
% 122.46/16.16 (
% 122.46/16.16 (
% 122.46/16.16 ('#B') @ (
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% 122.46/16.16 (
% 122.46/16.16 ('#C') @ in)))) @
% 122.46/16.16 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.46/16.16 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1239])).
% 122.46/16.16 thf(zip_derived_cl1255, plain,
% 122.46/16.16 (~ (((setminusEL) =>
% 122.46/16.16 (((setminusER) =>
% 122.46/16.16 (((setminusSubset2) =>
% 122.46/16.16 (((setminusERneg) =>
% 122.46/16.16 (((setminusELneg) =>
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% 122.46/16.16 (((setminusIRneg) =>
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% 122.46/16.16 (((setminusSubset1) =>
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% 122.46/16.16 (((symdiffI1) =>
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% 122.46/16.16 (((symdiffIneg2) =>
% 122.46/16.16 (((secondinupair) =>
% 122.46/16.16 (((setukpairIL) =>
% 122.46/16.16 (((setukpairIR) =>
% 122.46/16.16 (((kpairiskpair) =>
% 122.46/16.16 (((kpairp) =>
% 122.46/16.16 (((singletonsubset) =>
% 122.46/16.16 (((singletoninpowerset) =>
% 122.46/16.16 (((singletoninpowunion) =>
% 122.46/16.16 (((upairset2E) =>
% 122.46/16.16 (((upairsubunion) =>
% 122.46/16.16 (((upairinpowunion) =>
% 122.46/16.16 (((ubforcartprodlem1) =>
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% 122.46/16.16 (((ubforcartprodlem3) =>
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% 122.46/16.16 (((cartprodmempair1) =>
% 122.46/16.16 ((
% 122.46/16.16 (cartprodmempair) =>
% 122.46/16.16 ((
% 122.46/16.16 (setunionE2) =>
% 122.46/16.16 ((
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% 122.46/16.16 ((
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% 122.46/16.16 ((
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% 122.46/16.16 ((
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% 122.46/16.16 ((
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% 122.46/16.16 ((
% 122.46/16.16 (setukpairinjL1) =>
% 122.46/16.16 ((
% 122.46/16.16 (kfstsingleton) =>
% 122.46/16.16 ((
% 122.46/16.16 (theprop) =>
% 122.46/16.16 ((
% 122.46/16.16 (kfstpairEq) =>
% 122.46/16.16 ((
% 122.46/16.16 (cartprodfstin) =>
% 122.46/16.16 ((
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% 122.46/16.16 ((
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% 122.46/16.16 ((
% 122.46/16.16 (setukpairinjR11) =>
% 122.46/16.16 ((
% 122.46/16.16 (setukpairinjR12) =>
% 122.46/16.16 ((
% 122.46/16.16 (setukpairinjR1) =>
% 122.46/16.16 ((
% 122.46/16.16 (upairequniteq) =>
% 122.46/16.16 ((
% 122.46/16.16 (setukpairinjR2) =>
% 122.46/16.16 ((
% 122.46/16.16 (setukpairinjR) =>
% 122.46/16.16 ((
% 122.46/16.16 (ksndsingleton) =>
% 122.46/16.16 ((
% 122.46/16.16 (ksndpairEq) =>
% 122.46/16.16 ((
% 122.46/16.16 (kpairsurjEq) =>
% 122.46/16.16 ((
% 122.46/16.16 (cartprodsndin) =>
% 122.46/16.16 ((
% 122.46/16.16 (cartprodpairmemEL) =>
% 122.46/16.16 ((
% 122.46/16.16 (cartprodpairmemER) =>
% 122.46/16.16 ((
% 122.46/16.16 (cartprodmempaircEq) =>
% 122.46/16.16 ((
% 122.46/16.16 (cartprodfstpairEq) =>
% 122.46/16.16 ((
% 122.46/16.16 (cartprodsndpairEq) =>
% 122.46/16.16 ((
% 122.46/16.16 (cartprodpairsurjEq) =>
% 122.46/16.16 ((
% 122.46/16.16 (dpsetconstrI) =>
% 122.46/16.16 ((
% 122.46/16.16 (dpsetconstrSub) =>
% 122.46/16.16 ((
% 122.46/16.16 (setOfPairsIsBReln) =>
% 122.46/16.16 ((
% 122.46/16.16 (dpsetconstrERa) =>
% 122.46/16.16 ((
% 122.46/16.16 (dpsetconstrEL1) =>
% 122.46/16.16 ((
% 122.46/16.16 (dpsetconstrEL2) =>
% 122.46/16.16 ((
% 122.46/16.16 (dpsetconstrER) =>
% 122.46/16.16 ((
% 122.46/16.16 (funcImageSingleton) =>
% 122.46/16.16 ((
% 122.46/16.16 (apProp) =>
% 122.46/16.16 ((
% 122.46/16.16 (app) =>
% 122.46/16.16 ((
% 122.46/16.16 (infuncsetfunc) =>
% 122.46/16.16 ((
% 122.46/16.16 (ap2p) =>
% 122.46/16.16 ((
% 122.46/16.16 (funcinfuncset) =>
% 122.46/16.16 ((
% 122.46/16.16 (lamProp) =>
% 122.46/16.16 ((
% 122.46/16.16 (lamp) =>
% 122.46/16.16 ((
% 122.46/16.16 (lam2p) =>
% 122.46/16.16 ((
% 122.46/16.16 (brelnall1) =>
% 122.46/16.16 ((
% 122.46/16.16 (brelnall2) =>
% 122.46/16.16 ((
% 122.46/16.16 (ex1E2) =>
% 122.46/16.16 ((
% 122.46/16.16 (funcGraphProp1) =>
% 122.46/16.16 ((
% 122.46/16.16 (funcGraphProp3) =>
% 122.46/16.16 ((
% 122.46/16.16 (funcGraphProp2) =>
% 122.46/16.16 ((
% 122.46/16.16 (funcextLem) =>
% 122.46/16.16 ((
% 122.46/16.16 (funcGraphProp4) =>
% 122.46/16.16 ((
% 122.46/16.16 (subbreln) =>
% 122.46/16.16 ((
% 122.46/16.16 (eqbreln) =>
% 122.46/16.16 ((
% 122.46/16.16 (funcext) =>
% 122.46/16.16 ((
% 122.46/16.16 (funcext2) =>
% 122.46/16.16 ((
% 122.46/16.16 (ap2apEq1) =>
% 122.46/16.16 ((
% 122.46/16.16 (ap2apEq2) =>
% 122.46/16.16 ((
% 122.46/16.16 (beta1) =>
% 122.46/16.16 ((
% 122.46/16.16 (eta1) =>
% 122.46/16.16 ((
% 122.46/16.16 (lam2lamEq) =>
% 122.46/16.16 ((
% 122.46/16.16 (beta2) =>
% 122.46/16.16 ((
% 122.46/16.16 (eta2) =>
% 122.46/16.16 ((
% 122.46/16.16 (iffalseProp1) =>
% 122.46/16.16 ((
% 122.46/16.16 (iffalseProp2) =>
% 122.46/16.16 ((
% 122.46/16.16 (iftrueProp1) =>
% 122.46/16.16 ((
% 122.46/16.16 (iftrueProp2) =>
% 122.46/16.16 ((
% 122.46/16.16 (ifSingleton) =>
% 122.46/16.16 ((
% 122.46/16.16 (ifp) =>
% 122.46/16.16 ((
% 122.46/16.16 (theeq) =>
% 122.46/16.16 ((
% 122.46/16.16 (iftrue) =>
% 122.46/16.16 ((
% 122.46/16.16 (iffalse) =>
% 122.46/16.16 ((
% 122.46/16.16 (iftrueorfalse) =>
% 122.46/16.16 ((
% 122.46/16.16 (binintersectT_lem) =>
% 122.46/16.16 ((
% 122.46/16.16 (binunionT_lem) =>
% 122.46/16.16 ((
% 122.46/16.16 (powersetT_lem) =>
% 122.46/16.16 ((
% 122.46/16.16 (setminusT_lem) =>
% 122.46/16.16 ((
% 122.46/16.16 (complementT_lem) =>
% 122.46/16.16 ((
% 122.46/16.16 (setextT) =>
% 122.46/16.16 ((
% 122.46/16.16 (subsetTI) =>
% 122.46/16.16 ((
% 122.46/16.16 (powersetTI1) =>
% 122.46/16.16 ((
% 122.46/16.16 (powersetTE1) =>
% 122.46/16.16 ((
% 122.46/16.16 (complementTI1) =>
% 122.46/16.16 ((
% 122.46/16.16 (complementTE1) =>
% 122.46/16.16 ((
% 122.46/16.16 (binintersectTELcontra) =>
% 122.46/16.16 ((
% 122.46/16.16 (binintersectTERcontra) =>
% 122.46/16.16 ((
% 122.46/16.16 (contrasubsetT) =>
% 122.46/16.16 ((
% 122.46/16.16 (contrasubsetT1) =>
% 122.46/16.16 ((
% 122.46/16.16 (contrasubsetT2) =>
% 122.46/16.16 ((
% 122.46/16.16 (contrasubsetT3) =>
% 122.46/16.16 ((
% 122.46/16.16 (doubleComplementI1) =>
% 122.46/16.16 ((
% 122.46/16.16 (doubleComplementE1) =>
% 122.46/16.16 ((
% 122.46/16.16 (doubleComplementSub1) =>
% 122.46/16.16 ((
% 122.46/16.16 (doubleComplementSub2) =>
% 122.46/16.16 ((
% 122.46/16.16 (doubleComplementEq) =>
% 122.46/16.16 ((
% 122.46/16.16 (complementTnotintersectT) =>
% 122.46/16.16 ((
% 122.46/16.16 (complementImpComplementIntersect) =>
% 122.46/16.16 ((
% 122.46/16.16 (complementSubsetComplementIntersect) =>
% 122.46/16.16 ((
% 122.46/16.16 (complementInPowersetComplementIntersect) =>
% 122.46/16.16 ((
% 122.46/16.16 (contraSubsetComplement) =>
% 122.46/16.16 ((
% 122.46/16.16 (complementTcontraSubset) =>
% 122.46/16.16 ((
% 122.46/16.16 (binunionTILcontra) =>
% 122.46/16.16 ((
% 122.46/16.16 (binunionTIRcontra) =>
% 122.46/16.16 ((
% 122.46/16.16 (inIntersectImpInUnion) =>
% 122.46/16.16 ((
% 122.46/16.16 (inIntersectImpInUnion2) =>
% 122.46/16.16 ((
% 122.46/16.16 (inIntersectImpInIntersectUnions) =>
% 122.46/16.16 ((
% 122.46/16.16 (intersectInPowersetIntersectUnions) =>
% 122.46/16.16 ((
% 122.46/16.16 (inComplementUnionImpNotIn1) =>
% 122.46/16.16 ((
% 122.46/16.16 (inComplementUnionImpInComplement1) =>
% 122.46/16.16 ((
% 122.46/16.16 (binunionTE) =>
% 122.46/16.16 ((
% 122.46/16.16 (binunionTEcontra) =>
% 122.46/16.16 ((
% 122.46/16.16 (demorgan2a1) =>
% 122.46/16.16 ((
% 122.46/16.16 (complementUnionInPowersetComplement) =>
% 122.46/16.16 ((
% 122.46/16.16 (demorgan2a2) =>
% 122.46/16.16 ((
% 122.46/16.16 (demorgan1a) =>
% 122.46/16.16 ((
% 122.46/16.16 (demorgan1b) =>
% 122.46/16.16 ((
% 122.46/16.16 (demorgan1) =>
% 122.46/16.16 ((
% 122.46/16.16 (demorgan2a) =>
% 122.46/16.16 ((
% 122.46/16.16 (demorgan2b2) =>
% 122.46/16.16 ((
% 122.46/16.16 (demorgan2b) =>
% 122.46/16.16 ((
% 122.46/16.16 (demorgan2) =>
% 122.46/16.16 ((
% 122.46/16.16 (woz13rule0) =>
% 122.46/16.16 ((
% 122.46/16.16 (woz13rule1) =>
% 122.46/16.16 ((
% 122.46/16.16 (woz13rule2) =>
% 122.46/16.16 ((
% 122.46/16.16 (woz13rule3) =>
% 122.46/16.16 ((
% 122.46/16.16 (woz13rule4) =>
% 122.46/16.16 ((
% 122.46/16.16 (woz1_1) =>
% 122.46/16.16 ((
% 122.46/16.16 (woz1_2) =>
% 122.46/16.16 ((
% 122.46/16.16 (woz1_3) =>
% 122.46/16.16 ((
% 122.46/16.16 (woz1_4) =>
% 122.46/16.16 ((
% 122.46/16.16 (woz1_5) =>
% 122.46/16.16 ((
% 122.46/16.16 (breln1all2) =>
% 122.46/16.16 ((
% 122.46/16.16 (breln1SetBreln1) =>
% 122.46/16.16 ((
% 122.46/16.16 (choice2fnsingleton) =>
% 122.46/16.16 ((
% 122.46/16.16 (setOfPairsIsBReln1) =>
% 122.46/16.16 ((
% 122.46/16.16 (breln1all1) =>
% 122.46/16.16 ((
% 122.46/16.16 (subbreln1) =>
% 122.46/16.16 ((
% 122.46/16.16 (eqbreln1) =>
% 122.46/16.16 ((
% 122.46/16.16 (breln1invprop) =>
% 122.46/16.16 ((
% 122.46/16.16 (breln1invI) =>
% 122.46/16.16 ((
% 122.46/16.16 (breln1invE) =>
% 122.46/16.16 ((
% 122.46/16.16 (breln1compprop) =>
% 122.46/16.16 ((
% 122.46/16.16 (breln1compI) =>
% 122.46/16.16 ((
% 122.46/16.16 (breln1compE) =>
% 122.46/16.16 ((
% 122.46/16.16 (breln1compEex) =>
% 122.46/16.16 ((
% 122.46/16.16 (breln1unionprop) =>
% 122.46/16.16 ((
% 122.46/16.16 (breln1unionIL) =>
% 122.46/16.16 ((
% 122.46/16.16 (breln1unionIR) =>
% 122.46/16.16 ((
% 122.46/16.16 (breln1unionI) =>
% 122.46/16.16 ((
% 122.46/16.16 (breln1unionE) =>
% 122.46/16.16 ((
% 122.46/16.16 (breln1unionEcases) =>
% 122.46/16.16 ((
% 122.46/16.16 (breln1unionCommutes) =>
% 122.46/16.16 ((
% 122.46/16.16 (woz2Ex) =>
% 122.46/16.16 ((
% 122.46/16.16 (woz2W) =>
% 122.46/16.16 ((
% 122.46/16.16 (woz2A) =>
% 122.46/16.16 ((
% 122.46/16.16 (woz2B) =>
% 122.46/16.16 ((
% 122.46/16.16 (image1Ex) =>
% 122.46/16.16 ((
% 122.46/16.16 (image1Ex1) =>
% 122.46/16.16 ((
% 122.46/16.16 (image1Equiv) =>
% 122.46/16.16 ((
% 122.46/16.16 (image1E) =>
% 122.46/16.16 ((
% 122.46/16.16 (image1I) =>
% 122.46/16.16 ((
% 122.46/16.16 (injFuncInInjFuncSet) =>
% 122.46/16.16 ((
% 122.46/16.16 (!!) @ (
% 122.46/16.16 (('#B') @ (
% 122.46/16.16 !!) @
% 122.46/16.16 (
% 122.46/16.16 (
% 122.46/16.16 ('#B') @ (
% 122.46/16.16 (
% 122.46/16.16 ('#B') @ (
% 122.46/16.16 !!))) @
% 122.46/16.16 (
% 122.46/16.16 (
% 122.46/16.16 ('#S') @ (
% 122.46/16.16 (
% 122.46/16.16 ('#B') @ (
% 122.46/16.16 '#S') @
% 122.46/16.16 (
% 122.46/16.16 (
% 122.46/16.16 ('#B') @ (
% 122.46/16.16 (
% 122.46/16.16 ('#B') @ (
% 122.46/16.16 '#S'))) @
% 122.46/16.16 (
% 122.46/16.16 (
% 122.46/16.16 ('#B') @ (
% 122.46/16.16 (
% 122.46/16.16 ('#B') @ (
% 122.46/16.16 (
% 122.46/16.16 ('#B') @ (
% 122.46/16.16 =>))))) @
% 122.46/16.16 (
% 122.46/16.16 (
% 122.46/16.16 ('#B') @ (
% 122.46/16.16 (
% 122.46/16.16 ('#B') @ (
% 122.46/16.16 (
% 122.46/16.16 ('#C') @ in)))) @
% 122.46/16.16 injFuncSet)))))))) @
% 122.46/16.16 (
% 122.46/16.16 (
% 122.46/16.16 ('#B') @ (
% 122.46/16.16 (
% 122.46/16.16 ('#B') @ (
% 122.46/16.16 (
% 122.46/16.16 ('#C') @ in)))) @
% 122.46/16.16 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.46/16.16 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1247])).
% 122.46/16.16 thf(zip_derived_cl1264, plain,
% 122.46/16.16 (~ (((setminusER) =>
% 122.46/16.16 (((setminusSubset2) =>
% 122.46/16.16 (((setminusERneg) =>
% 122.46/16.16 (((setminusELneg) =>
% 122.46/16.16 (((setminusILneg) =>
% 122.46/16.16 (((setminusIRneg) =>
% 122.46/16.16 (((setminusLsub) =>
% 122.46/16.16 (((setminusSubset1) =>
% 122.46/16.16 (((symdiffE) =>
% 122.46/16.16 (((symdiffI1) =>
% 122.46/16.16 (((symdiffI2) =>
% 122.46/16.16 (((symdiffIneg1) =>
% 122.46/16.16 (((symdiffIneg2) =>
% 122.46/16.16 (((secondinupair) =>
% 122.46/16.16 (((setukpairIL) =>
% 122.46/16.16 (((setukpairIR) =>
% 122.46/16.16 (((kpairiskpair) =>
% 122.46/16.16 (((kpairp) =>
% 122.46/16.16 (((singletonsubset) =>
% 122.46/16.16 (((singletoninpowerset) =>
% 122.46/16.16 (((singletoninpowunion) =>
% 122.46/16.16 (((upairset2E) =>
% 122.46/16.16 (((upairsubunion) =>
% 122.46/16.16 (((upairinpowunion) =>
% 122.46/16.16 (((ubforcartprodlem1) =>
% 122.46/16.16 (((ubforcartprodlem2) =>
% 122.46/16.16 (((ubforcartprodlem3) =>
% 122.46/16.16 (((cartprodpairin) =>
% 122.46/16.16 (((cartprodmempair1) =>
% 122.46/16.16 (((cartprodmempair) =>
% 122.46/16.16 ((
% 122.46/16.16 (setunionE2) =>
% 122.46/16.16 ((
% 122.46/16.16 (setunionsingleton1) =>
% 122.46/16.16 ((
% 122.46/16.16 (setunionsingleton2) =>
% 122.46/16.16 ((
% 122.46/16.16 (setunionsingleton) =>
% 122.46/16.16 ((
% 122.46/16.16 (singletonprop) =>
% 122.46/16.16 ((
% 122.46/16.16 (ex1E1) =>
% 122.46/16.16 ((
% 122.46/16.16 (ex1I) =>
% 122.46/16.16 ((
% 122.46/16.16 (ex1I2) =>
% 122.46/16.16 ((
% 122.46/16.16 (singletonsuniq) =>
% 122.46/16.16 ((
% 122.46/16.16 (setukpairinjL1) =>
% 122.46/16.16 ((
% 122.46/16.16 (kfstsingleton) =>
% 122.46/16.16 ((
% 122.46/16.16 (theprop) =>
% 122.46/16.16 ((
% 122.46/16.16 (kfstpairEq) =>
% 122.46/16.16 ((
% 122.46/16.16 (cartprodfstin) =>
% 122.46/16.16 ((
% 122.46/16.16 (setukpairinjL2) =>
% 122.46/16.16 ((
% 122.46/16.16 (setukpairinjL) =>
% 122.46/16.16 ((
% 122.46/16.16 (setukpairinjR11) =>
% 122.46/16.16 ((
% 122.46/16.16 (setukpairinjR12) =>
% 122.46/16.16 ((
% 122.46/16.16 (setukpairinjR1) =>
% 122.46/16.16 ((
% 122.46/16.16 (upairequniteq) =>
% 122.46/16.16 ((
% 122.46/16.16 (setukpairinjR2) =>
% 122.46/16.16 ((
% 122.46/16.16 (setukpairinjR) =>
% 122.46/16.16 ((
% 122.46/16.16 (ksndsingleton) =>
% 122.46/16.16 ((
% 122.46/16.16 (ksndpairEq) =>
% 122.46/16.16 ((
% 122.46/16.16 (kpairsurjEq) =>
% 122.46/16.16 ((
% 122.46/16.16 (cartprodsndin) =>
% 122.46/16.16 ((
% 122.46/16.16 (cartprodpairmemEL) =>
% 122.46/16.16 ((
% 122.46/16.16 (cartprodpairmemER) =>
% 122.46/16.16 ((
% 122.46/16.16 (cartprodmempaircEq) =>
% 122.46/16.16 ((
% 122.46/16.16 (cartprodfstpairEq) =>
% 122.46/16.16 ((
% 122.46/16.16 (cartprodsndpairEq) =>
% 122.46/16.16 ((
% 122.46/16.16 (cartprodpairsurjEq) =>
% 122.46/16.16 ((
% 122.46/16.16 (dpsetconstrI) =>
% 122.46/16.16 ((
% 122.46/16.16 (dpsetconstrSub) =>
% 122.46/16.16 ((
% 122.46/16.16 (setOfPairsIsBReln) =>
% 122.46/16.16 ((
% 122.46/16.16 (dpsetconstrERa) =>
% 122.46/16.16 ((
% 122.46/16.16 (dpsetconstrEL1) =>
% 122.46/16.16 ((
% 122.46/16.16 (dpsetconstrEL2) =>
% 122.46/16.16 ((
% 122.46/16.16 (dpsetconstrER) =>
% 122.46/16.17 ((
% 122.46/16.17 (funcImageSingleton) =>
% 122.46/16.17 ((
% 122.46/16.17 (apProp) =>
% 122.46/16.17 ((
% 122.46/16.17 (app) =>
% 122.46/16.17 ((
% 122.46/16.17 (infuncsetfunc) =>
% 122.46/16.17 ((
% 122.46/16.17 (ap2p) =>
% 122.46/16.17 ((
% 122.46/16.17 (funcinfuncset) =>
% 122.46/16.17 ((
% 122.46/16.17 (lamProp) =>
% 122.46/16.17 ((
% 122.46/16.17 (lamp) =>
% 122.46/16.17 ((
% 122.46/16.17 (lam2p) =>
% 122.46/16.17 ((
% 122.46/16.17 (brelnall1) =>
% 122.46/16.17 ((
% 122.46/16.17 (brelnall2) =>
% 122.46/16.17 ((
% 122.46/16.17 (ex1E2) =>
% 122.46/16.17 ((
% 122.46/16.17 (funcGraphProp1) =>
% 122.46/16.17 ((
% 122.46/16.17 (funcGraphProp3) =>
% 122.46/16.17 ((
% 122.46/16.17 (funcGraphProp2) =>
% 122.46/16.17 ((
% 122.46/16.17 (funcextLem) =>
% 122.46/16.17 ((
% 122.46/16.17 (funcGraphProp4) =>
% 122.46/16.17 ((
% 122.46/16.17 (subbreln) =>
% 122.46/16.17 ((
% 122.46/16.17 (eqbreln) =>
% 122.46/16.17 ((
% 122.46/16.17 (funcext) =>
% 122.46/16.17 ((
% 122.46/16.17 (funcext2) =>
% 122.46/16.17 ((
% 122.46/16.17 (ap2apEq1) =>
% 122.46/16.17 ((
% 122.46/16.17 (ap2apEq2) =>
% 122.46/16.17 ((
% 122.46/16.17 (beta1) =>
% 122.46/16.17 ((
% 122.46/16.17 (eta1) =>
% 122.46/16.17 ((
% 122.46/16.17 (lam2lamEq) =>
% 122.46/16.17 ((
% 122.46/16.17 (beta2) =>
% 122.46/16.17 ((
% 122.46/16.17 (eta2) =>
% 122.46/16.17 ((
% 122.46/16.17 (iffalseProp1) =>
% 122.46/16.17 ((
% 122.46/16.17 (iffalseProp2) =>
% 122.46/16.17 ((
% 122.46/16.17 (iftrueProp1) =>
% 122.46/16.17 ((
% 122.46/16.17 (iftrueProp2) =>
% 122.46/16.17 ((
% 122.46/16.17 (ifSingleton) =>
% 122.46/16.17 ((
% 122.46/16.17 (ifp) =>
% 122.46/16.17 ((
% 122.46/16.17 (theeq) =>
% 122.46/16.17 ((
% 122.46/16.17 (iftrue) =>
% 122.46/16.17 ((
% 122.46/16.17 (iffalse) =>
% 122.46/16.17 ((
% 122.46/16.17 (iftrueorfalse) =>
% 122.46/16.17 ((
% 122.46/16.17 (binintersectT_lem) =>
% 122.46/16.17 ((
% 122.46/16.17 (binunionT_lem) =>
% 122.46/16.17 ((
% 122.46/16.17 (powersetT_lem) =>
% 122.46/16.17 ((
% 122.46/16.17 (setminusT_lem) =>
% 122.46/16.17 ((
% 122.46/16.17 (complementT_lem) =>
% 122.46/16.17 ((
% 122.46/16.17 (setextT) =>
% 122.46/16.17 ((
% 122.46/16.17 (subsetTI) =>
% 122.46/16.17 ((
% 122.46/16.17 (powersetTI1) =>
% 122.46/16.17 ((
% 122.46/16.17 (powersetTE1) =>
% 122.46/16.17 ((
% 122.46/16.17 (complementTI1) =>
% 122.46/16.17 ((
% 122.46/16.17 (complementTE1) =>
% 122.46/16.17 ((
% 122.46/16.17 (binintersectTELcontra) =>
% 122.46/16.17 ((
% 122.46/16.17 (binintersectTERcontra) =>
% 122.46/16.17 ((
% 122.46/16.17 (contrasubsetT) =>
% 122.46/16.17 ((
% 122.46/16.17 (contrasubsetT1) =>
% 122.46/16.17 ((
% 122.46/16.17 (contrasubsetT2) =>
% 122.46/16.17 ((
% 122.46/16.17 (contrasubsetT3) =>
% 122.46/16.17 ((
% 122.46/16.17 (doubleComplementI1) =>
% 122.46/16.17 ((
% 122.46/16.17 (doubleComplementE1) =>
% 122.46/16.17 ((
% 122.46/16.17 (doubleComplementSub1) =>
% 122.46/16.17 ((
% 122.46/16.17 (doubleComplementSub2) =>
% 122.46/16.17 ((
% 122.46/16.17 (doubleComplementEq) =>
% 122.46/16.17 ((
% 122.46/16.17 (complementTnotintersectT) =>
% 122.46/16.17 ((
% 122.46/16.17 (complementImpComplementIntersect) =>
% 122.46/16.17 ((
% 122.46/16.17 (complementSubsetComplementIntersect) =>
% 122.46/16.17 ((
% 122.46/16.17 (complementInPowersetComplementIntersect) =>
% 122.46/16.17 ((
% 122.46/16.17 (contraSubsetComplement) =>
% 122.46/16.17 ((
% 122.46/16.17 (complementTcontraSubset) =>
% 122.46/16.17 ((
% 122.46/16.17 (binunionTILcontra) =>
% 122.46/16.17 ((
% 122.46/16.17 (binunionTIRcontra) =>
% 122.46/16.17 ((
% 122.46/16.17 (inIntersectImpInUnion) =>
% 122.46/16.17 ((
% 122.46/16.17 (inIntersectImpInUnion2) =>
% 122.46/16.17 ((
% 122.46/16.17 (inIntersectImpInIntersectUnions) =>
% 122.46/16.17 ((
% 122.46/16.17 (intersectInPowersetIntersectUnions) =>
% 122.46/16.17 ((
% 122.46/16.17 (inComplementUnionImpNotIn1) =>
% 122.46/16.17 ((
% 122.46/16.17 (inComplementUnionImpInComplement1) =>
% 122.46/16.17 ((
% 122.46/16.17 (binunionTE) =>
% 122.46/16.17 ((
% 122.46/16.17 (binunionTEcontra) =>
% 122.46/16.17 ((
% 122.46/16.17 (demorgan2a1) =>
% 122.46/16.17 ((
% 122.46/16.17 (complementUnionInPowersetComplement) =>
% 122.46/16.17 ((
% 122.46/16.17 (demorgan2a2) =>
% 122.46/16.17 ((
% 122.46/16.17 (demorgan1a) =>
% 122.46/16.17 ((
% 122.46/16.17 (demorgan1b) =>
% 122.46/16.17 ((
% 122.46/16.17 (demorgan1) =>
% 122.46/16.17 ((
% 122.46/16.17 (demorgan2a) =>
% 122.46/16.17 ((
% 122.46/16.17 (demorgan2b2) =>
% 122.46/16.17 ((
% 122.46/16.17 (demorgan2b) =>
% 122.46/16.17 ((
% 122.46/16.17 (demorgan2) =>
% 122.46/16.17 ((
% 122.46/16.17 (woz13rule0) =>
% 122.46/16.17 ((
% 122.46/16.17 (woz13rule1) =>
% 122.46/16.17 ((
% 122.46/16.17 (woz13rule2) =>
% 122.46/16.17 ((
% 122.46/16.17 (woz13rule3) =>
% 122.46/16.17 ((
% 122.46/16.17 (woz13rule4) =>
% 122.46/16.17 ((
% 122.46/16.17 (woz1_1) =>
% 122.46/16.17 ((
% 122.46/16.17 (woz1_2) =>
% 122.46/16.17 ((
% 122.46/16.17 (woz1_3) =>
% 122.46/16.17 ((
% 122.46/16.17 (woz1_4) =>
% 122.46/16.17 ((
% 122.46/16.17 (woz1_5) =>
% 122.46/16.17 ((
% 122.46/16.17 (breln1all2) =>
% 122.46/16.17 ((
% 122.46/16.17 (breln1SetBreln1) =>
% 122.46/16.17 ((
% 122.46/16.17 (choice2fnsingleton) =>
% 122.46/16.17 ((
% 122.46/16.17 (setOfPairsIsBReln1) =>
% 122.46/16.17 ((
% 122.46/16.17 (breln1all1) =>
% 122.46/16.17 ((
% 122.46/16.17 (subbreln1) =>
% 122.46/16.17 ((
% 122.46/16.17 (eqbreln1) =>
% 122.46/16.17 ((
% 122.46/16.17 (breln1invprop) =>
% 122.46/16.17 ((
% 122.46/16.17 (breln1invI) =>
% 122.46/16.17 ((
% 122.46/16.17 (breln1invE) =>
% 122.46/16.17 ((
% 122.46/16.17 (breln1compprop) =>
% 122.46/16.17 ((
% 122.46/16.17 (breln1compI) =>
% 122.46/16.17 ((
% 122.46/16.17 (breln1compE) =>
% 122.46/16.17 ((
% 122.46/16.17 (breln1compEex) =>
% 122.46/16.17 ((
% 122.46/16.17 (breln1unionprop) =>
% 122.46/16.17 ((
% 122.46/16.17 (breln1unionIL) =>
% 122.46/16.17 ((
% 122.46/16.17 (breln1unionIR) =>
% 122.46/16.17 ((
% 122.46/16.17 (breln1unionI) =>
% 122.46/16.17 ((
% 122.46/16.17 (breln1unionE) =>
% 122.46/16.17 ((
% 122.46/16.17 (breln1unionEcases) =>
% 122.46/16.17 ((
% 122.46/16.17 (breln1unionCommutes) =>
% 122.46/16.17 ((
% 122.46/16.17 (woz2Ex) =>
% 122.46/16.17 ((
% 122.46/16.17 (woz2W) =>
% 122.46/16.17 ((
% 122.46/16.17 (woz2A) =>
% 122.46/16.17 ((
% 122.46/16.17 (woz2B) =>
% 122.46/16.17 ((
% 122.46/16.17 (image1Ex) =>
% 122.46/16.17 ((
% 122.46/16.17 (image1Ex1) =>
% 122.46/16.17 ((
% 122.46/16.17 (image1Equiv) =>
% 122.46/16.17 ((
% 122.46/16.17 (image1E) =>
% 122.46/16.17 ((
% 122.46/16.17 (image1I) =>
% 122.46/16.17 ((
% 122.46/16.17 (injFuncInInjFuncSet) =>
% 122.46/16.17 ((
% 122.46/16.17 (!!) @ (
% 122.46/16.17 (('#B') @ (
% 122.46/16.17 !!) @
% 122.46/16.17 (
% 122.46/16.17 (
% 122.46/16.17 ('#B') @ (
% 122.46/16.17 (
% 122.46/16.17 ('#B') @ (
% 122.46/16.17 !!))) @
% 122.46/16.17 (
% 122.46/16.17 (
% 122.46/16.17 ('#S') @ (
% 122.46/16.17 (
% 122.46/16.17 ('#B') @ (
% 122.46/16.17 '#S') @
% 122.46/16.17 (
% 122.46/16.17 (
% 122.46/16.17 ('#B') @ (
% 122.46/16.17 (
% 122.46/16.17 ('#B') @ (
% 122.46/16.17 '#S'))) @
% 122.46/16.17 (
% 122.46/16.17 (
% 122.46/16.17 ('#B') @ (
% 122.46/16.17 (
% 122.46/16.17 ('#B') @ (
% 122.46/16.17 (
% 122.46/16.17 ('#B') @ (
% 122.46/16.17 =>))))) @
% 122.46/16.17 (
% 122.46/16.17 (
% 122.46/16.17 ('#B') @ (
% 122.46/16.17 (
% 122.46/16.17 ('#B') @ (
% 122.46/16.17 (
% 122.46/16.17 ('#C') @ in)))) @
% 122.46/16.17 injFuncSet)))))))) @
% 122.46/16.17 (
% 122.46/16.17 (
% 122.46/16.17 ('#B') @ (
% 122.46/16.17 (
% 122.46/16.17 ('#B') @ (
% 122.46/16.17 (
% 122.46/16.17 ('#C') @ in)))) @
% 122.46/16.17 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.46/16.17 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1255])).
% 122.46/16.17 thf(zip_derived_cl1272, plain,
% 122.46/16.17 (~ (((setminusSubset2) =>
% 122.46/16.17 (((setminusERneg) =>
% 122.46/16.17 (((setminusELneg) =>
% 122.46/16.17 (((setminusILneg) =>
% 122.46/16.17 (((setminusIRneg) =>
% 122.46/16.17 (((setminusLsub) =>
% 122.46/16.17 (((setminusSubset1) =>
% 122.46/16.17 (((symdiffE) =>
% 122.46/16.17 (((symdiffI1) =>
% 122.46/16.17 (((symdiffI2) =>
% 122.46/16.17 (((symdiffIneg1) =>
% 122.46/16.17 (((symdiffIneg2) =>
% 122.46/16.17 (((secondinupair) =>
% 122.46/16.17 (((setukpairIL) =>
% 122.46/16.17 (((setukpairIR) =>
% 122.46/16.17 (((kpairiskpair) =>
% 122.46/16.17 (((kpairp) =>
% 122.46/16.17 (((singletonsubset) =>
% 122.46/16.18 (((singletoninpowerset) =>
% 122.46/16.18 (((singletoninpowunion) =>
% 122.46/16.18 (((upairset2E) =>
% 122.46/16.18 (((upairsubunion) =>
% 122.46/16.18 (((upairinpowunion) =>
% 122.46/16.18 (((ubforcartprodlem1) =>
% 122.46/16.18 (((ubforcartprodlem2) =>
% 122.46/16.18 (((ubforcartprodlem3) =>
% 122.46/16.18 (((cartprodpairin) =>
% 122.46/16.18 (((cartprodmempair1) =>
% 122.46/16.18 (((cartprodmempair) =>
% 122.46/16.18 (((setunionE2) =>
% 122.46/16.18 ((
% 122.46/16.18 (setunionsingleton1) =>
% 122.46/16.18 ((
% 122.46/16.18 (setunionsingleton2) =>
% 122.46/16.18 ((
% 122.46/16.18 (setunionsingleton) =>
% 122.46/16.18 ((
% 122.46/16.18 (singletonprop) =>
% 122.46/16.18 ((
% 122.46/16.18 (ex1E1) =>
% 122.46/16.18 ((
% 122.46/16.18 (ex1I) =>
% 122.46/16.18 ((
% 122.46/16.18 (ex1I2) =>
% 122.46/16.18 ((
% 122.46/16.18 (singletonsuniq) =>
% 122.46/16.18 ((
% 122.46/16.18 (setukpairinjL1) =>
% 122.46/16.18 ((
% 122.46/16.18 (kfstsingleton) =>
% 122.46/16.18 ((
% 122.46/16.18 (theprop) =>
% 122.46/16.18 ((
% 122.46/16.18 (kfstpairEq) =>
% 122.46/16.18 ((
% 122.46/16.18 (cartprodfstin) =>
% 122.46/16.18 ((
% 122.46/16.18 (setukpairinjL2) =>
% 122.46/16.18 ((
% 122.46/16.18 (setukpairinjL) =>
% 122.46/16.18 ((
% 122.46/16.18 (setukpairinjR11) =>
% 122.46/16.18 ((
% 122.46/16.18 (setukpairinjR12) =>
% 122.46/16.18 ((
% 122.46/16.18 (setukpairinjR1) =>
% 122.46/16.18 ((
% 122.46/16.18 (upairequniteq) =>
% 122.46/16.18 ((
% 122.46/16.18 (setukpairinjR2) =>
% 122.46/16.18 ((
% 122.46/16.18 (setukpairinjR) =>
% 122.46/16.18 ((
% 122.46/16.18 (ksndsingleton) =>
% 122.46/16.18 ((
% 122.46/16.18 (ksndpairEq) =>
% 122.46/16.18 ((
% 122.46/16.18 (kpairsurjEq) =>
% 122.46/16.18 ((
% 122.46/16.18 (cartprodsndin) =>
% 122.46/16.18 ((
% 122.46/16.18 (cartprodpairmemEL) =>
% 122.46/16.18 ((
% 122.46/16.18 (cartprodpairmemER) =>
% 122.46/16.18 ((
% 122.46/16.18 (cartprodmempaircEq) =>
% 122.46/16.18 ((
% 122.46/16.18 (cartprodfstpairEq) =>
% 122.46/16.18 ((
% 122.46/16.18 (cartprodsndpairEq) =>
% 122.46/16.18 ((
% 122.46/16.18 (cartprodpairsurjEq) =>
% 122.46/16.18 ((
% 122.46/16.18 (dpsetconstrI) =>
% 122.46/16.18 ((
% 122.46/16.18 (dpsetconstrSub) =>
% 122.46/16.18 ((
% 122.46/16.18 (setOfPairsIsBReln) =>
% 122.46/16.18 ((
% 122.46/16.18 (dpsetconstrERa) =>
% 122.46/16.18 ((
% 122.46/16.18 (dpsetconstrEL1) =>
% 122.46/16.18 ((
% 122.46/16.18 (dpsetconstrEL2) =>
% 122.46/16.18 ((
% 122.46/16.18 (dpsetconstrER) =>
% 122.46/16.18 ((
% 122.46/16.18 (funcImageSingleton) =>
% 122.46/16.18 ((
% 122.46/16.18 (apProp) =>
% 122.46/16.18 ((
% 122.46/16.18 (app) =>
% 122.46/16.18 ((
% 122.46/16.18 (infuncsetfunc) =>
% 122.46/16.18 ((
% 122.46/16.18 (ap2p) =>
% 122.46/16.18 ((
% 122.46/16.18 (funcinfuncset) =>
% 122.46/16.18 ((
% 122.46/16.18 (lamProp) =>
% 122.46/16.18 ((
% 122.46/16.18 (lamp) =>
% 122.46/16.18 ((
% 122.46/16.18 (lam2p) =>
% 122.46/16.18 ((
% 122.46/16.18 (brelnall1) =>
% 122.46/16.18 ((
% 122.46/16.18 (brelnall2) =>
% 122.46/16.18 ((
% 122.46/16.18 (ex1E2) =>
% 122.46/16.18 ((
% 122.46/16.18 (funcGraphProp1) =>
% 122.46/16.18 ((
% 122.46/16.18 (funcGraphProp3) =>
% 122.46/16.18 ((
% 122.46/16.18 (funcGraphProp2) =>
% 122.46/16.18 ((
% 122.46/16.18 (funcextLem) =>
% 122.46/16.18 ((
% 122.46/16.18 (funcGraphProp4) =>
% 122.46/16.18 ((
% 122.46/16.18 (subbreln) =>
% 122.46/16.18 ((
% 122.46/16.18 (eqbreln) =>
% 122.46/16.18 ((
% 122.46/16.18 (funcext) =>
% 122.46/16.18 ((
% 122.46/16.18 (funcext2) =>
% 122.46/16.18 ((
% 122.46/16.18 (ap2apEq1) =>
% 122.46/16.18 ((
% 122.46/16.18 (ap2apEq2) =>
% 122.46/16.18 ((
% 122.46/16.18 (beta1) =>
% 122.46/16.18 ((
% 122.46/16.18 (eta1) =>
% 122.46/16.18 ((
% 122.46/16.18 (lam2lamEq) =>
% 122.46/16.18 ((
% 122.46/16.18 (beta2) =>
% 122.46/16.18 ((
% 122.46/16.18 (eta2) =>
% 122.46/16.18 ((
% 122.46/16.18 (iffalseProp1) =>
% 122.46/16.18 ((
% 122.46/16.18 (iffalseProp2) =>
% 122.46/16.18 ((
% 122.46/16.18 (iftrueProp1) =>
% 122.46/16.18 ((
% 122.46/16.18 (iftrueProp2) =>
% 122.46/16.18 ((
% 122.46/16.18 (ifSingleton) =>
% 122.46/16.18 ((
% 122.46/16.18 (ifp) =>
% 122.46/16.18 ((
% 122.46/16.18 (theeq) =>
% 122.46/16.18 ((
% 122.46/16.18 (iftrue) =>
% 122.46/16.18 ((
% 122.46/16.18 (iffalse) =>
% 122.46/16.18 ((
% 122.46/16.18 (iftrueorfalse) =>
% 122.46/16.18 ((
% 122.46/16.18 (binintersectT_lem) =>
% 122.46/16.18 ((
% 122.46/16.18 (binunionT_lem) =>
% 122.46/16.18 ((
% 122.46/16.18 (powersetT_lem) =>
% 122.46/16.18 ((
% 122.46/16.18 (setminusT_lem) =>
% 122.46/16.18 ((
% 122.46/16.18 (complementT_lem) =>
% 122.46/16.18 ((
% 122.46/16.18 (setextT) =>
% 122.46/16.18 ((
% 122.46/16.18 (subsetTI) =>
% 122.46/16.18 ((
% 122.46/16.18 (powersetTI1) =>
% 122.46/16.18 ((
% 122.46/16.18 (powersetTE1) =>
% 122.46/16.18 ((
% 122.46/16.18 (complementTI1) =>
% 122.46/16.18 ((
% 122.46/16.18 (complementTE1) =>
% 122.46/16.18 ((
% 122.46/16.18 (binintersectTELcontra) =>
% 122.46/16.18 ((
% 122.46/16.18 (binintersectTERcontra) =>
% 122.46/16.18 ((
% 122.46/16.18 (contrasubsetT) =>
% 122.46/16.18 ((
% 122.46/16.18 (contrasubsetT1) =>
% 122.46/16.18 ((
% 122.46/16.18 (contrasubsetT2) =>
% 122.46/16.18 ((
% 122.46/16.18 (contrasubsetT3) =>
% 122.46/16.18 ((
% 122.46/16.18 (doubleComplementI1) =>
% 122.46/16.18 ((
% 122.46/16.18 (doubleComplementE1) =>
% 122.46/16.18 ((
% 122.46/16.18 (doubleComplementSub1) =>
% 122.46/16.18 ((
% 122.46/16.18 (doubleComplementSub2) =>
% 122.46/16.18 ((
% 122.46/16.18 (doubleComplementEq) =>
% 122.46/16.18 ((
% 122.46/16.18 (complementTnotintersectT) =>
% 122.46/16.18 ((
% 122.46/16.18 (complementImpComplementIntersect) =>
% 122.46/16.18 ((
% 122.46/16.18 (complementSubsetComplementIntersect) =>
% 122.46/16.18 ((
% 122.46/16.18 (complementInPowersetComplementIntersect) =>
% 122.46/16.18 ((
% 122.46/16.18 (contraSubsetComplement) =>
% 122.46/16.18 ((
% 122.46/16.18 (complementTcontraSubset) =>
% 122.46/16.18 ((
% 122.46/16.18 (binunionTILcontra) =>
% 122.46/16.18 ((
% 122.46/16.18 (binunionTIRcontra) =>
% 122.46/16.18 ((
% 122.46/16.18 (inIntersectImpInUnion) =>
% 122.46/16.18 ((
% 122.46/16.18 (inIntersectImpInUnion2) =>
% 122.46/16.18 ((
% 122.46/16.18 (inIntersectImpInIntersectUnions) =>
% 122.46/16.18 ((
% 122.46/16.18 (intersectInPowersetIntersectUnions) =>
% 122.46/16.18 ((
% 122.46/16.18 (inComplementUnionImpNotIn1) =>
% 122.46/16.18 ((
% 122.46/16.18 (inComplementUnionImpInComplement1) =>
% 122.46/16.18 ((
% 122.46/16.18 (binunionTE) =>
% 122.46/16.18 ((
% 122.46/16.18 (binunionTEcontra) =>
% 122.46/16.18 ((
% 122.46/16.18 (demorgan2a1) =>
% 122.46/16.18 ((
% 122.46/16.18 (complementUnionInPowersetComplement) =>
% 122.46/16.18 ((
% 122.46/16.18 (demorgan2a2) =>
% 122.46/16.18 ((
% 122.46/16.18 (demorgan1a) =>
% 122.46/16.18 ((
% 122.46/16.18 (demorgan1b) =>
% 122.46/16.18 ((
% 122.46/16.18 (demorgan1) =>
% 122.46/16.18 ((
% 122.46/16.18 (demorgan2a) =>
% 122.46/16.18 ((
% 122.46/16.18 (demorgan2b2) =>
% 122.46/16.18 ((
% 122.46/16.18 (demorgan2b) =>
% 122.46/16.18 ((
% 122.46/16.18 (demorgan2) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz13rule0) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz13rule1) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz13rule2) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz13rule3) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz13rule4) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz1_1) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz1_2) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz1_3) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz1_4) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz1_5) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1all2) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1SetBreln1) =>
% 122.46/16.18 ((
% 122.46/16.18 (choice2fnsingleton) =>
% 122.46/16.18 ((
% 122.46/16.18 (setOfPairsIsBReln1) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1all1) =>
% 122.46/16.18 ((
% 122.46/16.18 (subbreln1) =>
% 122.46/16.18 ((
% 122.46/16.18 (eqbreln1) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1invprop) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1invI) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1invE) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1compprop) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1compI) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1compE) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1compEex) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1unionprop) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1unionIL) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1unionIR) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1unionI) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1unionE) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1unionEcases) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1unionCommutes) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz2Ex) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz2W) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz2A) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz2B) =>
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% 122.46/16.18 ((
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% 122.46/16.18 ((
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% 122.46/16.18 ((
% 122.46/16.18 (image1E) =>
% 122.46/16.18 ((
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% 122.46/16.18 ((
% 122.46/16.18 (injFuncInInjFuncSet) =>
% 122.46/16.18 ((
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% 122.46/16.18 (
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% 122.46/16.18 injFuncSet)))))))) @
% 122.46/16.18 (
% 122.46/16.18 (
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% 122.46/16.18 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.46/16.18 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1264])).
% 122.46/16.18 thf(zip_derived_cl1280, plain,
% 122.46/16.18 (~ (((setminusERneg) =>
% 122.46/16.18 (((setminusELneg) =>
% 122.46/16.18 (((setminusILneg) =>
% 122.46/16.18 (((setminusIRneg) =>
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% 122.46/16.18 (((setukpairIL) =>
% 122.46/16.18 (((setukpairIR) =>
% 122.46/16.18 (((kpairiskpair) =>
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% 122.46/16.18 (((singletoninpowerset) =>
% 122.46/16.18 (((singletoninpowunion) =>
% 122.46/16.18 (((upairset2E) =>
% 122.46/16.18 (((upairsubunion) =>
% 122.46/16.18 (((upairinpowunion) =>
% 122.46/16.18 (((ubforcartprodlem1) =>
% 122.46/16.18 (((ubforcartprodlem2) =>
% 122.46/16.18 (((ubforcartprodlem3) =>
% 122.46/16.18 (((cartprodpairin) =>
% 122.46/16.18 (((cartprodmempair1) =>
% 122.46/16.18 (((cartprodmempair) =>
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% 122.46/16.18 (((setunionsingleton1) =>
% 122.46/16.18 ((
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% 122.46/16.18 ((
% 122.46/16.18 (setunionsingleton) =>
% 122.46/16.18 ((
% 122.46/16.18 (singletonprop) =>
% 122.46/16.18 ((
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% 122.46/16.18 ((
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% 122.46/16.18 ((
% 122.46/16.18 (ex1I2) =>
% 122.46/16.18 ((
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% 122.46/16.18 ((
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% 122.46/16.18 ((
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% 122.46/16.18 ((
% 122.46/16.18 (theprop) =>
% 122.46/16.18 ((
% 122.46/16.18 (kfstpairEq) =>
% 122.46/16.18 ((
% 122.46/16.18 (cartprodfstin) =>
% 122.46/16.18 ((
% 122.46/16.18 (setukpairinjL2) =>
% 122.46/16.18 ((
% 122.46/16.18 (setukpairinjL) =>
% 122.46/16.18 ((
% 122.46/16.18 (setukpairinjR11) =>
% 122.46/16.18 ((
% 122.46/16.18 (setukpairinjR12) =>
% 122.46/16.18 ((
% 122.46/16.18 (setukpairinjR1) =>
% 122.46/16.18 ((
% 122.46/16.18 (upairequniteq) =>
% 122.46/16.18 ((
% 122.46/16.18 (setukpairinjR2) =>
% 122.46/16.18 ((
% 122.46/16.18 (setukpairinjR) =>
% 122.46/16.18 ((
% 122.46/16.18 (ksndsingleton) =>
% 122.46/16.18 ((
% 122.46/16.18 (ksndpairEq) =>
% 122.46/16.18 ((
% 122.46/16.18 (kpairsurjEq) =>
% 122.46/16.18 ((
% 122.46/16.18 (cartprodsndin) =>
% 122.46/16.18 ((
% 122.46/16.18 (cartprodpairmemEL) =>
% 122.46/16.18 ((
% 122.46/16.18 (cartprodpairmemER) =>
% 122.46/16.18 ((
% 122.46/16.18 (cartprodmempaircEq) =>
% 122.46/16.18 ((
% 122.46/16.18 (cartprodfstpairEq) =>
% 122.46/16.18 ((
% 122.46/16.18 (cartprodsndpairEq) =>
% 122.46/16.18 ((
% 122.46/16.18 (cartprodpairsurjEq) =>
% 122.46/16.18 ((
% 122.46/16.18 (dpsetconstrI) =>
% 122.46/16.18 ((
% 122.46/16.18 (dpsetconstrSub) =>
% 122.46/16.18 ((
% 122.46/16.18 (setOfPairsIsBReln) =>
% 122.46/16.18 ((
% 122.46/16.18 (dpsetconstrERa) =>
% 122.46/16.18 ((
% 122.46/16.18 (dpsetconstrEL1) =>
% 122.46/16.18 ((
% 122.46/16.18 (dpsetconstrEL2) =>
% 122.46/16.18 ((
% 122.46/16.18 (dpsetconstrER) =>
% 122.46/16.18 ((
% 122.46/16.18 (funcImageSingleton) =>
% 122.46/16.18 ((
% 122.46/16.18 (apProp) =>
% 122.46/16.18 ((
% 122.46/16.18 (app) =>
% 122.46/16.18 ((
% 122.46/16.18 (infuncsetfunc) =>
% 122.46/16.18 ((
% 122.46/16.18 (ap2p) =>
% 122.46/16.18 ((
% 122.46/16.18 (funcinfuncset) =>
% 122.46/16.18 ((
% 122.46/16.18 (lamProp) =>
% 122.46/16.18 ((
% 122.46/16.18 (lamp) =>
% 122.46/16.18 ((
% 122.46/16.18 (lam2p) =>
% 122.46/16.18 ((
% 122.46/16.18 (brelnall1) =>
% 122.46/16.18 ((
% 122.46/16.18 (brelnall2) =>
% 122.46/16.18 ((
% 122.46/16.18 (ex1E2) =>
% 122.46/16.18 ((
% 122.46/16.18 (funcGraphProp1) =>
% 122.46/16.18 ((
% 122.46/16.18 (funcGraphProp3) =>
% 122.46/16.18 ((
% 122.46/16.18 (funcGraphProp2) =>
% 122.46/16.18 ((
% 122.46/16.18 (funcextLem) =>
% 122.46/16.18 ((
% 122.46/16.18 (funcGraphProp4) =>
% 122.46/16.18 ((
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% 122.46/16.18 ((
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% 122.46/16.18 ((
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% 122.46/16.18 ((
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% 122.46/16.18 ((
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% 122.46/16.18 ((
% 122.46/16.18 (ap2apEq2) =>
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% 122.46/16.18 ((
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% 122.46/16.18 ((
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% 122.46/16.18 ((
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% 122.46/16.18 ((
% 122.46/16.18 (iffalseProp2) =>
% 122.46/16.18 ((
% 122.46/16.18 (iftrueProp1) =>
% 122.46/16.18 ((
% 122.46/16.18 (iftrueProp2) =>
% 122.46/16.18 ((
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% 122.46/16.18 ((
% 122.46/16.18 (ifp) =>
% 122.46/16.18 ((
% 122.46/16.18 (theeq) =>
% 122.46/16.18 ((
% 122.46/16.18 (iftrue) =>
% 122.46/16.18 ((
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% 122.46/16.18 ((
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% 122.46/16.18 ((
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% 122.46/16.18 ((
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% 122.46/16.18 ((
% 122.46/16.18 (powersetT_lem) =>
% 122.46/16.18 ((
% 122.46/16.18 (setminusT_lem) =>
% 122.46/16.18 ((
% 122.46/16.18 (complementT_lem) =>
% 122.46/16.18 ((
% 122.46/16.18 (setextT) =>
% 122.46/16.18 ((
% 122.46/16.18 (subsetTI) =>
% 122.46/16.18 ((
% 122.46/16.18 (powersetTI1) =>
% 122.46/16.18 ((
% 122.46/16.18 (powersetTE1) =>
% 122.46/16.18 ((
% 122.46/16.18 (complementTI1) =>
% 122.46/16.18 ((
% 122.46/16.18 (complementTE1) =>
% 122.46/16.18 ((
% 122.46/16.18 (binintersectTELcontra) =>
% 122.46/16.18 ((
% 122.46/16.18 (binintersectTERcontra) =>
% 122.46/16.18 ((
% 122.46/16.18 (contrasubsetT) =>
% 122.46/16.18 ((
% 122.46/16.18 (contrasubsetT1) =>
% 122.46/16.18 ((
% 122.46/16.18 (contrasubsetT2) =>
% 122.46/16.18 ((
% 122.46/16.18 (contrasubsetT3) =>
% 122.46/16.18 ((
% 122.46/16.18 (doubleComplementI1) =>
% 122.46/16.18 ((
% 122.46/16.18 (doubleComplementE1) =>
% 122.46/16.18 ((
% 122.46/16.18 (doubleComplementSub1) =>
% 122.46/16.18 ((
% 122.46/16.18 (doubleComplementSub2) =>
% 122.46/16.18 ((
% 122.46/16.18 (doubleComplementEq) =>
% 122.46/16.18 ((
% 122.46/16.18 (complementTnotintersectT) =>
% 122.46/16.18 ((
% 122.46/16.18 (complementImpComplementIntersect) =>
% 122.46/16.18 ((
% 122.46/16.18 (complementSubsetComplementIntersect) =>
% 122.46/16.18 ((
% 122.46/16.18 (complementInPowersetComplementIntersect) =>
% 122.46/16.18 ((
% 122.46/16.18 (contraSubsetComplement) =>
% 122.46/16.18 ((
% 122.46/16.18 (complementTcontraSubset) =>
% 122.46/16.18 ((
% 122.46/16.18 (binunionTILcontra) =>
% 122.46/16.18 ((
% 122.46/16.18 (binunionTIRcontra) =>
% 122.46/16.18 ((
% 122.46/16.18 (inIntersectImpInUnion) =>
% 122.46/16.18 ((
% 122.46/16.18 (inIntersectImpInUnion2) =>
% 122.46/16.18 ((
% 122.46/16.18 (inIntersectImpInIntersectUnions) =>
% 122.46/16.18 ((
% 122.46/16.18 (intersectInPowersetIntersectUnions) =>
% 122.46/16.18 ((
% 122.46/16.18 (inComplementUnionImpNotIn1) =>
% 122.46/16.18 ((
% 122.46/16.18 (inComplementUnionImpInComplement1) =>
% 122.46/16.18 ((
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% 122.46/16.18 ((
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% 122.46/16.18 ((
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% 122.46/16.18 ((
% 122.46/16.18 (complementUnionInPowersetComplement) =>
% 122.46/16.18 ((
% 122.46/16.18 (demorgan2a2) =>
% 122.46/16.18 ((
% 122.46/16.18 (demorgan1a) =>
% 122.46/16.18 ((
% 122.46/16.18 (demorgan1b) =>
% 122.46/16.18 ((
% 122.46/16.18 (demorgan1) =>
% 122.46/16.18 ((
% 122.46/16.18 (demorgan2a) =>
% 122.46/16.18 ((
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% 122.46/16.18 ((
% 122.46/16.18 (demorgan2b) =>
% 122.46/16.18 ((
% 122.46/16.18 (demorgan2) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz13rule0) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz13rule1) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz13rule2) =>
% 122.46/16.18 ((
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% 122.46/16.18 ((
% 122.46/16.18 (woz13rule4) =>
% 122.46/16.18 ((
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% 122.46/16.18 ((
% 122.46/16.18 (woz1_2) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz1_3) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz1_4) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz1_5) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1all2) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1SetBreln1) =>
% 122.46/16.18 ((
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% 122.46/16.18 ((
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% 122.46/16.18 ((
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% 122.46/16.18 ((
% 122.46/16.18 (eqbreln1) =>
% 122.46/16.18 ((
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% 122.46/16.18 ((
% 122.46/16.18 (breln1invI) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1invE) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1compprop) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1compI) =>
% 122.46/16.18 ((
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% 122.46/16.18 ((
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% 122.46/16.18 ((
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% 122.46/16.18 ((
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% 122.46/16.18 ((
% 122.46/16.18 (breln1unionIR) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1unionI) =>
% 122.46/16.18 ((
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% 122.46/16.18 ((
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% 122.46/16.18 ((
% 122.46/16.18 (breln1unionCommutes) =>
% 122.46/16.18 ((
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% 122.46/16.18 ((
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% 122.46/16.18 ((
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% 122.46/16.18 ((
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% 122.46/16.18 ((
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% 122.46/16.18 ((
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% 122.46/16.18 ((
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% 122.46/16.18 ((
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% 122.46/16.18 ((
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% 122.46/16.18 ((
% 122.46/16.18 (injFuncInInjFuncSet) =>
% 122.46/16.18 ((
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% 122.46/16.18 injFuncSet)))))))) @
% 122.46/16.18 (
% 122.46/16.18 (
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% 122.46/16.18 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1272])).
% 122.46/16.18 thf(zip_derived_cl1288, plain,
% 122.46/16.18 (~ (((setminusELneg) =>
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% 122.46/16.18 (((setminusIRneg) =>
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% 122.46/16.18 (((setukpairIR) =>
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% 122.46/16.18 (((singletoninpowerset) =>
% 122.46/16.18 (((singletoninpowunion) =>
% 122.46/16.18 (((upairset2E) =>
% 122.46/16.18 (((upairsubunion) =>
% 122.46/16.18 (((upairinpowunion) =>
% 122.46/16.18 (((ubforcartprodlem1) =>
% 122.46/16.18 (((ubforcartprodlem2) =>
% 122.46/16.18 (((ubforcartprodlem3) =>
% 122.46/16.18 (((cartprodpairin) =>
% 122.46/16.18 (((cartprodmempair1) =>
% 122.46/16.18 (((cartprodmempair) =>
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% 122.46/16.18 (((setunionsingleton2) =>
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% 122.46/16.18 ((
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% 122.46/16.18 ((
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% 122.46/16.18 ((
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% 122.46/16.18 ((
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% 122.46/16.18 ((
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% 122.46/16.18 ((
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% 122.46/16.18 ((
% 122.46/16.18 (kfstpairEq) =>
% 122.46/16.18 ((
% 122.46/16.18 (cartprodfstin) =>
% 122.46/16.18 ((
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% 122.46/16.18 ((
% 122.46/16.18 (setukpairinjL) =>
% 122.46/16.18 ((
% 122.46/16.18 (setukpairinjR11) =>
% 122.46/16.18 ((
% 122.46/16.18 (setukpairinjR12) =>
% 122.46/16.18 ((
% 122.46/16.18 (setukpairinjR1) =>
% 122.46/16.18 ((
% 122.46/16.18 (upairequniteq) =>
% 122.46/16.18 ((
% 122.46/16.18 (setukpairinjR2) =>
% 122.46/16.18 ((
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% 122.46/16.18 ((
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% 122.46/16.18 ((
% 122.46/16.18 (kpairsurjEq) =>
% 122.46/16.18 ((
% 122.46/16.18 (cartprodsndin) =>
% 122.46/16.18 ((
% 122.46/16.18 (cartprodpairmemEL) =>
% 122.46/16.18 ((
% 122.46/16.18 (cartprodpairmemER) =>
% 122.46/16.18 ((
% 122.46/16.18 (cartprodmempaircEq) =>
% 122.46/16.18 ((
% 122.46/16.18 (cartprodfstpairEq) =>
% 122.46/16.18 ((
% 122.46/16.18 (cartprodsndpairEq) =>
% 122.46/16.18 ((
% 122.46/16.18 (cartprodpairsurjEq) =>
% 122.46/16.18 ((
% 122.46/16.18 (dpsetconstrI) =>
% 122.46/16.18 ((
% 122.46/16.18 (dpsetconstrSub) =>
% 122.46/16.18 ((
% 122.46/16.18 (setOfPairsIsBReln) =>
% 122.46/16.18 ((
% 122.46/16.18 (dpsetconstrERa) =>
% 122.46/16.18 ((
% 122.46/16.18 (dpsetconstrEL1) =>
% 122.46/16.18 ((
% 122.46/16.18 (dpsetconstrEL2) =>
% 122.46/16.18 ((
% 122.46/16.18 (dpsetconstrER) =>
% 122.46/16.18 ((
% 122.46/16.18 (funcImageSingleton) =>
% 122.46/16.18 ((
% 122.46/16.18 (apProp) =>
% 122.46/16.18 ((
% 122.46/16.18 (app) =>
% 122.46/16.18 ((
% 122.46/16.18 (infuncsetfunc) =>
% 122.46/16.18 ((
% 122.46/16.18 (ap2p) =>
% 122.46/16.18 ((
% 122.46/16.18 (funcinfuncset) =>
% 122.46/16.18 ((
% 122.46/16.18 (lamProp) =>
% 122.46/16.18 ((
% 122.46/16.18 (lamp) =>
% 122.46/16.18 ((
% 122.46/16.18 (lam2p) =>
% 122.46/16.18 ((
% 122.46/16.18 (brelnall1) =>
% 122.46/16.18 ((
% 122.46/16.18 (brelnall2) =>
% 122.46/16.18 ((
% 122.46/16.18 (ex1E2) =>
% 122.46/16.18 ((
% 122.46/16.18 (funcGraphProp1) =>
% 122.46/16.18 ((
% 122.46/16.18 (funcGraphProp3) =>
% 122.46/16.18 ((
% 122.46/16.18 (funcGraphProp2) =>
% 122.46/16.18 ((
% 122.46/16.18 (funcextLem) =>
% 122.46/16.18 ((
% 122.46/16.18 (funcGraphProp4) =>
% 122.46/16.18 ((
% 122.46/16.18 (subbreln) =>
% 122.46/16.18 ((
% 122.46/16.18 (eqbreln) =>
% 122.46/16.18 ((
% 122.46/16.18 (funcext) =>
% 122.46/16.18 ((
% 122.46/16.18 (funcext2) =>
% 122.46/16.18 ((
% 122.46/16.18 (ap2apEq1) =>
% 122.46/16.18 ((
% 122.46/16.18 (ap2apEq2) =>
% 122.46/16.18 ((
% 122.46/16.18 (beta1) =>
% 122.46/16.18 ((
% 122.46/16.18 (eta1) =>
% 122.46/16.18 ((
% 122.46/16.18 (lam2lamEq) =>
% 122.46/16.18 ((
% 122.46/16.18 (beta2) =>
% 122.46/16.18 ((
% 122.46/16.18 (eta2) =>
% 122.46/16.18 ((
% 122.46/16.18 (iffalseProp1) =>
% 122.46/16.18 ((
% 122.46/16.18 (iffalseProp2) =>
% 122.46/16.18 ((
% 122.46/16.18 (iftrueProp1) =>
% 122.46/16.18 ((
% 122.46/16.18 (iftrueProp2) =>
% 122.46/16.18 ((
% 122.46/16.18 (ifSingleton) =>
% 122.46/16.18 ((
% 122.46/16.18 (ifp) =>
% 122.46/16.18 ((
% 122.46/16.18 (theeq) =>
% 122.46/16.18 ((
% 122.46/16.18 (iftrue) =>
% 122.46/16.18 ((
% 122.46/16.18 (iffalse) =>
% 122.46/16.18 ((
% 122.46/16.18 (iftrueorfalse) =>
% 122.46/16.18 ((
% 122.46/16.18 (binintersectT_lem) =>
% 122.46/16.18 ((
% 122.46/16.18 (binunionT_lem) =>
% 122.46/16.18 ((
% 122.46/16.18 (powersetT_lem) =>
% 122.46/16.18 ((
% 122.46/16.18 (setminusT_lem) =>
% 122.46/16.18 ((
% 122.46/16.18 (complementT_lem) =>
% 122.46/16.18 ((
% 122.46/16.18 (setextT) =>
% 122.46/16.18 ((
% 122.46/16.18 (subsetTI) =>
% 122.46/16.18 ((
% 122.46/16.18 (powersetTI1) =>
% 122.46/16.18 ((
% 122.46/16.18 (powersetTE1) =>
% 122.46/16.18 ((
% 122.46/16.18 (complementTI1) =>
% 122.46/16.18 ((
% 122.46/16.18 (complementTE1) =>
% 122.46/16.18 ((
% 122.46/16.18 (binintersectTELcontra) =>
% 122.46/16.18 ((
% 122.46/16.18 (binintersectTERcontra) =>
% 122.46/16.18 ((
% 122.46/16.18 (contrasubsetT) =>
% 122.46/16.18 ((
% 122.46/16.18 (contrasubsetT1) =>
% 122.46/16.18 ((
% 122.46/16.18 (contrasubsetT2) =>
% 122.46/16.18 ((
% 122.46/16.18 (contrasubsetT3) =>
% 122.46/16.18 ((
% 122.46/16.18 (doubleComplementI1) =>
% 122.46/16.18 ((
% 122.46/16.18 (doubleComplementE1) =>
% 122.46/16.18 ((
% 122.46/16.18 (doubleComplementSub1) =>
% 122.46/16.18 ((
% 122.46/16.18 (doubleComplementSub2) =>
% 122.46/16.18 ((
% 122.46/16.18 (doubleComplementEq) =>
% 122.46/16.18 ((
% 122.46/16.18 (complementTnotintersectT) =>
% 122.46/16.18 ((
% 122.46/16.18 (complementImpComplementIntersect) =>
% 122.46/16.18 ((
% 122.46/16.18 (complementSubsetComplementIntersect) =>
% 122.46/16.18 ((
% 122.46/16.18 (complementInPowersetComplementIntersect) =>
% 122.46/16.18 ((
% 122.46/16.18 (contraSubsetComplement) =>
% 122.46/16.18 ((
% 122.46/16.18 (complementTcontraSubset) =>
% 122.46/16.18 ((
% 122.46/16.18 (binunionTILcontra) =>
% 122.46/16.18 ((
% 122.46/16.18 (binunionTIRcontra) =>
% 122.46/16.18 ((
% 122.46/16.18 (inIntersectImpInUnion) =>
% 122.46/16.18 ((
% 122.46/16.18 (inIntersectImpInUnion2) =>
% 122.46/16.18 ((
% 122.46/16.18 (inIntersectImpInIntersectUnions) =>
% 122.46/16.18 ((
% 122.46/16.18 (intersectInPowersetIntersectUnions) =>
% 122.46/16.18 ((
% 122.46/16.18 (inComplementUnionImpNotIn1) =>
% 122.46/16.18 ((
% 122.46/16.18 (inComplementUnionImpInComplement1) =>
% 122.46/16.18 ((
% 122.46/16.18 (binunionTE) =>
% 122.46/16.18 ((
% 122.46/16.18 (binunionTEcontra) =>
% 122.46/16.18 ((
% 122.46/16.18 (demorgan2a1) =>
% 122.46/16.18 ((
% 122.46/16.18 (complementUnionInPowersetComplement) =>
% 122.46/16.18 ((
% 122.46/16.18 (demorgan2a2) =>
% 122.46/16.18 ((
% 122.46/16.18 (demorgan1a) =>
% 122.46/16.18 ((
% 122.46/16.18 (demorgan1b) =>
% 122.46/16.18 ((
% 122.46/16.18 (demorgan1) =>
% 122.46/16.18 ((
% 122.46/16.18 (demorgan2a) =>
% 122.46/16.18 ((
% 122.46/16.18 (demorgan2b2) =>
% 122.46/16.18 ((
% 122.46/16.18 (demorgan2b) =>
% 122.46/16.18 ((
% 122.46/16.18 (demorgan2) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz13rule0) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz13rule1) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz13rule2) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz13rule3) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz13rule4) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz1_1) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz1_2) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz1_3) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz1_4) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz1_5) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1all2) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1SetBreln1) =>
% 122.46/16.18 ((
% 122.46/16.18 (choice2fnsingleton) =>
% 122.46/16.18 ((
% 122.46/16.18 (setOfPairsIsBReln1) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1all1) =>
% 122.46/16.18 ((
% 122.46/16.18 (subbreln1) =>
% 122.46/16.18 ((
% 122.46/16.18 (eqbreln1) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1invprop) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1invI) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1invE) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1compprop) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1compI) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1compE) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1compEex) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1unionprop) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1unionIL) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1unionIR) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1unionI) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1unionE) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1unionEcases) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1unionCommutes) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz2Ex) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz2W) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz2A) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz2B) =>
% 122.46/16.18 ((
% 122.46/16.18 (image1Ex) =>
% 122.46/16.18 ((
% 122.46/16.18 (image1Ex1) =>
% 122.46/16.18 ((
% 122.46/16.18 (image1Equiv) =>
% 122.46/16.18 ((
% 122.46/16.18 (image1E) =>
% 122.46/16.18 ((
% 122.46/16.18 (image1I) =>
% 122.46/16.18 ((
% 122.46/16.18 (injFuncInInjFuncSet) =>
% 122.46/16.18 ((
% 122.46/16.18 (!!) @ (
% 122.46/16.18 (('#B') @ (
% 122.46/16.18 !!) @
% 122.46/16.18 (
% 122.46/16.18 (
% 122.46/16.18 ('#B') @ (
% 122.46/16.18 (
% 122.46/16.18 ('#B') @ (
% 122.46/16.18 !!))) @
% 122.46/16.18 (
% 122.46/16.18 (
% 122.46/16.18 ('#S') @ (
% 122.46/16.18 (
% 122.46/16.18 ('#B') @ (
% 122.46/16.18 '#S') @
% 122.46/16.18 (
% 122.46/16.18 (
% 122.46/16.18 ('#B') @ (
% 122.46/16.18 (
% 122.46/16.18 ('#B') @ (
% 122.46/16.18 '#S'))) @
% 122.46/16.18 (
% 122.46/16.18 (
% 122.46/16.18 ('#B') @ (
% 122.46/16.18 (
% 122.46/16.18 ('#B') @ (
% 122.46/16.18 (
% 122.46/16.18 ('#B') @ (
% 122.46/16.18 =>))))) @
% 122.46/16.18 (
% 122.46/16.18 (
% 122.46/16.18 ('#B') @ (
% 122.46/16.18 (
% 122.46/16.18 ('#B') @ (
% 122.46/16.18 (
% 122.46/16.18 ('#C') @ in)))) @
% 122.46/16.18 injFuncSet)))))))) @
% 122.46/16.18 (
% 122.46/16.18 (
% 122.46/16.18 ('#B') @ (
% 122.46/16.18 (
% 122.46/16.18 ('#B') @ (
% 122.46/16.18 (
% 122.46/16.18 ('#C') @ in)))) @
% 122.46/16.18 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.46/16.18 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1280])).
% 122.46/16.18 thf(zip_derived_cl1296, plain,
% 122.46/16.18 (~ (((setminusILneg) =>
% 122.46/16.18 (((setminusIRneg) =>
% 122.46/16.18 (((setminusLsub) =>
% 122.46/16.18 (((setminusSubset1) =>
% 122.46/16.18 (((symdiffE) =>
% 122.46/16.18 (((symdiffI1) =>
% 122.46/16.18 (((symdiffI2) =>
% 122.46/16.18 (((symdiffIneg1) =>
% 122.46/16.18 (((symdiffIneg2) =>
% 122.46/16.18 (((secondinupair) =>
% 122.46/16.18 (((setukpairIL) =>
% 122.46/16.18 (((setukpairIR) =>
% 122.46/16.18 (((kpairiskpair) =>
% 122.46/16.18 (((kpairp) =>
% 122.46/16.18 (((singletonsubset) =>
% 122.46/16.18 (((singletoninpowerset) =>
% 122.46/16.18 (((singletoninpowunion) =>
% 122.46/16.18 (((upairset2E) =>
% 122.46/16.18 (((upairsubunion) =>
% 122.46/16.18 (((upairinpowunion) =>
% 122.46/16.18 (((ubforcartprodlem1) =>
% 122.46/16.18 (((ubforcartprodlem2) =>
% 122.46/16.18 (((ubforcartprodlem3) =>
% 122.46/16.18 (((cartprodpairin) =>
% 122.46/16.18 (((cartprodmempair1) =>
% 122.46/16.18 (((cartprodmempair) =>
% 122.46/16.18 (((setunionE2) =>
% 122.46/16.18 (((setunionsingleton1) =>
% 122.46/16.18 (((setunionsingleton2) =>
% 122.46/16.18 (((setunionsingleton) =>
% 122.46/16.18 ((
% 122.46/16.18 (singletonprop) =>
% 122.46/16.18 ((
% 122.46/16.18 (ex1E1) =>
% 122.46/16.18 ((
% 122.46/16.18 (ex1I) =>
% 122.46/16.18 ((
% 122.46/16.18 (ex1I2) =>
% 122.46/16.18 ((
% 122.46/16.18 (singletonsuniq) =>
% 122.46/16.18 ((
% 122.46/16.18 (setukpairinjL1) =>
% 122.46/16.18 ((
% 122.46/16.18 (kfstsingleton) =>
% 122.46/16.18 ((
% 122.46/16.18 (theprop) =>
% 122.46/16.18 ((
% 122.46/16.18 (kfstpairEq) =>
% 122.46/16.18 ((
% 122.46/16.18 (cartprodfstin) =>
% 122.46/16.18 ((
% 122.46/16.18 (setukpairinjL2) =>
% 122.46/16.18 ((
% 122.46/16.18 (setukpairinjL) =>
% 122.46/16.18 ((
% 122.46/16.18 (setukpairinjR11) =>
% 122.46/16.18 ((
% 122.46/16.18 (setukpairinjR12) =>
% 122.46/16.18 ((
% 122.46/16.18 (setukpairinjR1) =>
% 122.46/16.18 ((
% 122.46/16.18 (upairequniteq) =>
% 122.46/16.18 ((
% 122.46/16.18 (setukpairinjR2) =>
% 122.46/16.18 ((
% 122.46/16.18 (setukpairinjR) =>
% 122.46/16.18 ((
% 122.46/16.18 (ksndsingleton) =>
% 122.46/16.18 ((
% 122.46/16.18 (ksndpairEq) =>
% 122.46/16.18 ((
% 122.46/16.18 (kpairsurjEq) =>
% 122.46/16.18 ((
% 122.46/16.18 (cartprodsndin) =>
% 122.46/16.18 ((
% 122.46/16.18 (cartprodpairmemEL) =>
% 122.46/16.18 ((
% 122.46/16.18 (cartprodpairmemER) =>
% 122.46/16.18 ((
% 122.46/16.18 (cartprodmempaircEq) =>
% 122.46/16.18 ((
% 122.46/16.18 (cartprodfstpairEq) =>
% 122.46/16.18 ((
% 122.46/16.18 (cartprodsndpairEq) =>
% 122.46/16.18 ((
% 122.46/16.18 (cartprodpairsurjEq) =>
% 122.46/16.18 ((
% 122.46/16.18 (dpsetconstrI) =>
% 122.46/16.18 ((
% 122.46/16.18 (dpsetconstrSub) =>
% 122.46/16.18 ((
% 122.46/16.18 (setOfPairsIsBReln) =>
% 122.46/16.18 ((
% 122.46/16.18 (dpsetconstrERa) =>
% 122.46/16.18 ((
% 122.46/16.18 (dpsetconstrEL1) =>
% 122.46/16.18 ((
% 122.46/16.18 (dpsetconstrEL2) =>
% 122.46/16.18 ((
% 122.46/16.18 (dpsetconstrER) =>
% 122.46/16.18 ((
% 122.46/16.18 (funcImageSingleton) =>
% 122.46/16.18 ((
% 122.46/16.18 (apProp) =>
% 122.46/16.18 ((
% 122.46/16.18 (app) =>
% 122.46/16.18 ((
% 122.46/16.18 (infuncsetfunc) =>
% 122.46/16.18 ((
% 122.46/16.18 (ap2p) =>
% 122.46/16.18 ((
% 122.46/16.18 (funcinfuncset) =>
% 122.46/16.18 ((
% 122.46/16.18 (lamProp) =>
% 122.46/16.18 ((
% 122.46/16.18 (lamp) =>
% 122.46/16.18 ((
% 122.46/16.18 (lam2p) =>
% 122.46/16.18 ((
% 122.46/16.18 (brelnall1) =>
% 122.46/16.18 ((
% 122.46/16.18 (brelnall2) =>
% 122.46/16.18 ((
% 122.46/16.18 (ex1E2) =>
% 122.46/16.18 ((
% 122.46/16.18 (funcGraphProp1) =>
% 122.46/16.18 ((
% 122.46/16.18 (funcGraphProp3) =>
% 122.46/16.18 ((
% 122.46/16.18 (funcGraphProp2) =>
% 122.46/16.18 ((
% 122.46/16.18 (funcextLem) =>
% 122.46/16.18 ((
% 122.46/16.18 (funcGraphProp4) =>
% 122.46/16.18 ((
% 122.46/16.18 (subbreln) =>
% 122.46/16.18 ((
% 122.46/16.18 (eqbreln) =>
% 122.46/16.18 ((
% 122.46/16.18 (funcext) =>
% 122.46/16.18 ((
% 122.46/16.18 (funcext2) =>
% 122.46/16.18 ((
% 122.46/16.18 (ap2apEq1) =>
% 122.46/16.18 ((
% 122.46/16.18 (ap2apEq2) =>
% 122.46/16.18 ((
% 122.46/16.18 (beta1) =>
% 122.46/16.18 ((
% 122.46/16.18 (eta1) =>
% 122.46/16.18 ((
% 122.46/16.18 (lam2lamEq) =>
% 122.46/16.18 ((
% 122.46/16.18 (beta2) =>
% 122.46/16.18 ((
% 122.46/16.18 (eta2) =>
% 122.46/16.18 ((
% 122.46/16.18 (iffalseProp1) =>
% 122.46/16.18 ((
% 122.46/16.18 (iffalseProp2) =>
% 122.46/16.18 ((
% 122.46/16.18 (iftrueProp1) =>
% 122.46/16.18 ((
% 122.46/16.18 (iftrueProp2) =>
% 122.46/16.18 ((
% 122.46/16.18 (ifSingleton) =>
% 122.46/16.18 ((
% 122.46/16.18 (ifp) =>
% 122.46/16.18 ((
% 122.46/16.18 (theeq) =>
% 122.46/16.18 ((
% 122.46/16.18 (iftrue) =>
% 122.46/16.18 ((
% 122.46/16.18 (iffalse) =>
% 122.46/16.18 ((
% 122.46/16.18 (iftrueorfalse) =>
% 122.46/16.18 ((
% 122.46/16.18 (binintersectT_lem) =>
% 122.46/16.18 ((
% 122.46/16.18 (binunionT_lem) =>
% 122.46/16.18 ((
% 122.46/16.18 (powersetT_lem) =>
% 122.46/16.18 ((
% 122.46/16.18 (setminusT_lem) =>
% 122.46/16.18 ((
% 122.46/16.18 (complementT_lem) =>
% 122.46/16.18 ((
% 122.46/16.18 (setextT) =>
% 122.46/16.18 ((
% 122.46/16.18 (subsetTI) =>
% 122.46/16.18 ((
% 122.46/16.18 (powersetTI1) =>
% 122.46/16.18 ((
% 122.46/16.18 (powersetTE1) =>
% 122.46/16.18 ((
% 122.46/16.18 (complementTI1) =>
% 122.46/16.18 ((
% 122.46/16.18 (complementTE1) =>
% 122.46/16.18 ((
% 122.46/16.18 (binintersectTELcontra) =>
% 122.46/16.18 ((
% 122.46/16.18 (binintersectTERcontra) =>
% 122.46/16.18 ((
% 122.46/16.18 (contrasubsetT) =>
% 122.46/16.18 ((
% 122.46/16.18 (contrasubsetT1) =>
% 122.46/16.18 ((
% 122.46/16.18 (contrasubsetT2) =>
% 122.46/16.18 ((
% 122.46/16.18 (contrasubsetT3) =>
% 122.46/16.18 ((
% 122.46/16.18 (doubleComplementI1) =>
% 122.46/16.18 ((
% 122.46/16.18 (doubleComplementE1) =>
% 122.46/16.18 ((
% 122.46/16.18 (doubleComplementSub1) =>
% 122.46/16.18 ((
% 122.46/16.18 (doubleComplementSub2) =>
% 122.46/16.18 ((
% 122.46/16.18 (doubleComplementEq) =>
% 122.46/16.18 ((
% 122.46/16.18 (complementTnotintersectT) =>
% 122.46/16.18 ((
% 122.46/16.18 (complementImpComplementIntersect) =>
% 122.46/16.18 ((
% 122.46/16.18 (complementSubsetComplementIntersect) =>
% 122.46/16.18 ((
% 122.46/16.18 (complementInPowersetComplementIntersect) =>
% 122.46/16.18 ((
% 122.46/16.18 (contraSubsetComplement) =>
% 122.46/16.18 ((
% 122.46/16.18 (complementTcontraSubset) =>
% 122.46/16.18 ((
% 122.46/16.18 (binunionTILcontra) =>
% 122.46/16.18 ((
% 122.46/16.18 (binunionTIRcontra) =>
% 122.46/16.18 ((
% 122.46/16.18 (inIntersectImpInUnion) =>
% 122.46/16.18 ((
% 122.46/16.18 (inIntersectImpInUnion2) =>
% 122.46/16.18 ((
% 122.46/16.18 (inIntersectImpInIntersectUnions) =>
% 122.46/16.18 ((
% 122.46/16.18 (intersectInPowersetIntersectUnions) =>
% 122.46/16.18 ((
% 122.46/16.18 (inComplementUnionImpNotIn1) =>
% 122.46/16.18 ((
% 122.46/16.18 (inComplementUnionImpInComplement1) =>
% 122.46/16.18 ((
% 122.46/16.18 (binunionTE) =>
% 122.46/16.18 ((
% 122.46/16.18 (binunionTEcontra) =>
% 122.46/16.18 ((
% 122.46/16.18 (demorgan2a1) =>
% 122.46/16.18 ((
% 122.46/16.18 (complementUnionInPowersetComplement) =>
% 122.46/16.18 ((
% 122.46/16.18 (demorgan2a2) =>
% 122.46/16.18 ((
% 122.46/16.18 (demorgan1a) =>
% 122.46/16.18 ((
% 122.46/16.18 (demorgan1b) =>
% 122.46/16.18 ((
% 122.46/16.18 (demorgan1) =>
% 122.46/16.18 ((
% 122.46/16.18 (demorgan2a) =>
% 122.46/16.18 ((
% 122.46/16.18 (demorgan2b2) =>
% 122.46/16.18 ((
% 122.46/16.18 (demorgan2b) =>
% 122.46/16.18 ((
% 122.46/16.18 (demorgan2) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz13rule0) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz13rule1) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz13rule2) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz13rule3) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz13rule4) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz1_1) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz1_2) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz1_3) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz1_4) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz1_5) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1all2) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1SetBreln1) =>
% 122.46/16.18 ((
% 122.46/16.18 (choice2fnsingleton) =>
% 122.46/16.18 ((
% 122.46/16.18 (setOfPairsIsBReln1) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1all1) =>
% 122.46/16.18 ((
% 122.46/16.18 (subbreln1) =>
% 122.46/16.18 ((
% 122.46/16.18 (eqbreln1) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1invprop) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1invI) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1invE) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1compprop) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1compI) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1compE) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1compEex) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1unionprop) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1unionIL) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1unionIR) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1unionI) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1unionE) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1unionEcases) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1unionCommutes) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz2Ex) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz2W) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz2A) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz2B) =>
% 122.46/16.18 ((
% 122.46/16.18 (image1Ex) =>
% 122.46/16.18 ((
% 122.46/16.18 (image1Ex1) =>
% 122.46/16.18 ((
% 122.46/16.18 (image1Equiv) =>
% 122.46/16.18 ((
% 122.46/16.18 (image1E) =>
% 122.46/16.18 ((
% 122.46/16.18 (image1I) =>
% 122.46/16.18 ((
% 122.46/16.18 (injFuncInInjFuncSet) =>
% 122.46/16.18 ((
% 122.46/16.18 (!!) @ (
% 122.46/16.18 (('#B') @ (
% 122.46/16.18 !!) @
% 122.46/16.18 (
% 122.46/16.18 (
% 122.46/16.18 ('#B') @ (
% 122.46/16.18 (
% 122.46/16.18 ('#B') @ (
% 122.46/16.18 !!))) @
% 122.46/16.18 (
% 122.46/16.18 (
% 122.46/16.18 ('#S') @ (
% 122.46/16.18 (
% 122.46/16.18 ('#B') @ (
% 122.46/16.18 '#S') @
% 122.46/16.18 (
% 122.46/16.18 (
% 122.46/16.18 ('#B') @ (
% 122.46/16.18 (
% 122.46/16.18 ('#B') @ (
% 122.46/16.18 '#S'))) @
% 122.46/16.18 (
% 122.46/16.18 (
% 122.46/16.18 ('#B') @ (
% 122.46/16.18 (
% 122.46/16.18 ('#B') @ (
% 122.46/16.18 (
% 122.46/16.18 ('#B') @ (
% 122.46/16.18 =>))))) @
% 122.46/16.18 (
% 122.46/16.18 (
% 122.46/16.18 ('#B') @ (
% 122.46/16.18 (
% 122.46/16.18 ('#B') @ (
% 122.46/16.18 (
% 122.46/16.18 ('#C') @ in)))) @
% 122.46/16.18 injFuncSet)))))))) @
% 122.46/16.18 (
% 122.46/16.18 (
% 122.46/16.18 ('#B') @ (
% 122.46/16.18 (
% 122.46/16.18 ('#B') @ (
% 122.46/16.18 (
% 122.46/16.18 ('#C') @ in)))) @
% 122.46/16.18 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.46/16.18 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1288])).
% 122.46/16.18 thf(zip_derived_cl1305, plain,
% 122.46/16.18 (~ (((setminusIRneg) =>
% 122.46/16.18 (((setminusLsub) =>
% 122.46/16.18 (((setminusSubset1) =>
% 122.46/16.18 (((symdiffE) =>
% 122.46/16.18 (((symdiffI1) =>
% 122.46/16.18 (((symdiffI2) =>
% 122.46/16.18 (((symdiffIneg1) =>
% 122.46/16.18 (((symdiffIneg2) =>
% 122.46/16.18 (((secondinupair) =>
% 122.46/16.18 (((setukpairIL) =>
% 122.46/16.18 (((setukpairIR) =>
% 122.46/16.18 (((kpairiskpair) =>
% 122.46/16.18 (((kpairp) =>
% 122.46/16.18 (((singletonsubset) =>
% 122.46/16.18 (((singletoninpowerset) =>
% 122.46/16.18 (((singletoninpowunion) =>
% 122.46/16.18 (((upairset2E) =>
% 122.46/16.18 (((upairsubunion) =>
% 122.46/16.18 (((upairinpowunion) =>
% 122.46/16.18 (((ubforcartprodlem1) =>
% 122.46/16.18 (((ubforcartprodlem2) =>
% 122.46/16.18 (((ubforcartprodlem3) =>
% 122.46/16.18 (((cartprodpairin) =>
% 122.46/16.18 (((cartprodmempair1) =>
% 122.46/16.18 (((cartprodmempair) =>
% 122.46/16.18 (((setunionE2) =>
% 122.46/16.18 (((setunionsingleton1) =>
% 122.46/16.18 (((setunionsingleton2) =>
% 122.46/16.18 (((setunionsingleton) =>
% 122.46/16.18 (((singletonprop) =>
% 122.46/16.18 ((
% 122.46/16.18 (ex1E1) =>
% 122.46/16.18 ((
% 122.46/16.18 (ex1I) =>
% 122.46/16.18 ((
% 122.46/16.18 (ex1I2) =>
% 122.46/16.18 ((
% 122.46/16.18 (singletonsuniq) =>
% 122.46/16.18 ((
% 122.46/16.18 (setukpairinjL1) =>
% 122.46/16.18 ((
% 122.46/16.18 (kfstsingleton) =>
% 122.46/16.18 ((
% 122.46/16.18 (theprop) =>
% 122.46/16.18 ((
% 122.46/16.18 (kfstpairEq) =>
% 122.46/16.18 ((
% 122.46/16.18 (cartprodfstin) =>
% 122.46/16.18 ((
% 122.46/16.18 (setukpairinjL2) =>
% 122.46/16.18 ((
% 122.46/16.18 (setukpairinjL) =>
% 122.46/16.18 ((
% 122.46/16.18 (setukpairinjR11) =>
% 122.46/16.18 ((
% 122.46/16.18 (setukpairinjR12) =>
% 122.46/16.18 ((
% 122.46/16.18 (setukpairinjR1) =>
% 122.46/16.18 ((
% 122.46/16.18 (upairequniteq) =>
% 122.46/16.18 ((
% 122.46/16.18 (setukpairinjR2) =>
% 122.46/16.18 ((
% 122.46/16.18 (setukpairinjR) =>
% 122.46/16.18 ((
% 122.46/16.18 (ksndsingleton) =>
% 122.46/16.18 ((
% 122.46/16.18 (ksndpairEq) =>
% 122.46/16.18 ((
% 122.46/16.18 (kpairsurjEq) =>
% 122.46/16.18 ((
% 122.46/16.18 (cartprodsndin) =>
% 122.46/16.18 ((
% 122.46/16.18 (cartprodpairmemEL) =>
% 122.46/16.18 ((
% 122.46/16.18 (cartprodpairmemER) =>
% 122.46/16.18 ((
% 122.46/16.18 (cartprodmempaircEq) =>
% 122.46/16.18 ((
% 122.46/16.18 (cartprodfstpairEq) =>
% 122.46/16.18 ((
% 122.46/16.18 (cartprodsndpairEq) =>
% 122.46/16.18 ((
% 122.46/16.18 (cartprodpairsurjEq) =>
% 122.46/16.18 ((
% 122.46/16.18 (dpsetconstrI) =>
% 122.46/16.18 ((
% 122.46/16.18 (dpsetconstrSub) =>
% 122.46/16.18 ((
% 122.46/16.18 (setOfPairsIsBReln) =>
% 122.46/16.18 ((
% 122.46/16.18 (dpsetconstrERa) =>
% 122.46/16.18 ((
% 122.46/16.18 (dpsetconstrEL1) =>
% 122.46/16.18 ((
% 122.46/16.18 (dpsetconstrEL2) =>
% 122.46/16.18 ((
% 122.46/16.18 (dpsetconstrER) =>
% 122.46/16.18 ((
% 122.46/16.18 (funcImageSingleton) =>
% 122.46/16.18 ((
% 122.46/16.18 (apProp) =>
% 122.46/16.18 ((
% 122.46/16.18 (app) =>
% 122.46/16.18 ((
% 122.46/16.18 (infuncsetfunc) =>
% 122.46/16.18 ((
% 122.46/16.18 (ap2p) =>
% 122.46/16.18 ((
% 122.46/16.18 (funcinfuncset) =>
% 122.46/16.18 ((
% 122.46/16.18 (lamProp) =>
% 122.46/16.18 ((
% 122.46/16.18 (lamp) =>
% 122.46/16.18 ((
% 122.46/16.18 (lam2p) =>
% 122.46/16.18 ((
% 122.46/16.18 (brelnall1) =>
% 122.46/16.18 ((
% 122.46/16.18 (brelnall2) =>
% 122.46/16.18 ((
% 122.46/16.18 (ex1E2) =>
% 122.46/16.18 ((
% 122.46/16.18 (funcGraphProp1) =>
% 122.46/16.18 ((
% 122.46/16.18 (funcGraphProp3) =>
% 122.46/16.18 ((
% 122.46/16.18 (funcGraphProp2) =>
% 122.46/16.18 ((
% 122.46/16.18 (funcextLem) =>
% 122.46/16.18 ((
% 122.46/16.18 (funcGraphProp4) =>
% 122.46/16.18 ((
% 122.46/16.18 (subbreln) =>
% 122.46/16.18 ((
% 122.46/16.18 (eqbreln) =>
% 122.46/16.18 ((
% 122.46/16.18 (funcext) =>
% 122.46/16.18 ((
% 122.46/16.18 (funcext2) =>
% 122.46/16.18 ((
% 122.46/16.18 (ap2apEq1) =>
% 122.46/16.18 ((
% 122.46/16.18 (ap2apEq2) =>
% 122.46/16.18 ((
% 122.46/16.18 (beta1) =>
% 122.46/16.18 ((
% 122.46/16.18 (eta1) =>
% 122.46/16.18 ((
% 122.46/16.18 (lam2lamEq) =>
% 122.46/16.18 ((
% 122.46/16.18 (beta2) =>
% 122.46/16.18 ((
% 122.46/16.18 (eta2) =>
% 122.46/16.18 ((
% 122.46/16.18 (iffalseProp1) =>
% 122.46/16.18 ((
% 122.46/16.18 (iffalseProp2) =>
% 122.46/16.18 ((
% 122.46/16.18 (iftrueProp1) =>
% 122.46/16.18 ((
% 122.46/16.18 (iftrueProp2) =>
% 122.46/16.18 ((
% 122.46/16.18 (ifSingleton) =>
% 122.46/16.18 ((
% 122.46/16.18 (ifp) =>
% 122.46/16.18 ((
% 122.46/16.18 (theeq) =>
% 122.46/16.18 ((
% 122.46/16.18 (iftrue) =>
% 122.46/16.18 ((
% 122.46/16.18 (iffalse) =>
% 122.46/16.18 ((
% 122.46/16.18 (iftrueorfalse) =>
% 122.46/16.18 ((
% 122.46/16.18 (binintersectT_lem) =>
% 122.46/16.18 ((
% 122.46/16.18 (binunionT_lem) =>
% 122.46/16.18 ((
% 122.46/16.18 (powersetT_lem) =>
% 122.46/16.18 ((
% 122.46/16.18 (setminusT_lem) =>
% 122.46/16.18 ((
% 122.46/16.18 (complementT_lem) =>
% 122.46/16.18 ((
% 122.46/16.18 (setextT) =>
% 122.46/16.18 ((
% 122.46/16.18 (subsetTI) =>
% 122.46/16.18 ((
% 122.46/16.18 (powersetTI1) =>
% 122.46/16.18 ((
% 122.46/16.18 (powersetTE1) =>
% 122.46/16.18 ((
% 122.46/16.18 (complementTI1) =>
% 122.46/16.18 ((
% 122.46/16.18 (complementTE1) =>
% 122.46/16.18 ((
% 122.46/16.18 (binintersectTELcontra) =>
% 122.46/16.18 ((
% 122.46/16.18 (binintersectTERcontra) =>
% 122.46/16.18 ((
% 122.46/16.18 (contrasubsetT) =>
% 122.46/16.18 ((
% 122.46/16.18 (contrasubsetT1) =>
% 122.46/16.18 ((
% 122.46/16.18 (contrasubsetT2) =>
% 122.46/16.18 ((
% 122.46/16.18 (contrasubsetT3) =>
% 122.46/16.18 ((
% 122.46/16.18 (doubleComplementI1) =>
% 122.46/16.18 ((
% 122.46/16.18 (doubleComplementE1) =>
% 122.46/16.18 ((
% 122.46/16.18 (doubleComplementSub1) =>
% 122.46/16.18 ((
% 122.46/16.18 (doubleComplementSub2) =>
% 122.46/16.18 ((
% 122.46/16.18 (doubleComplementEq) =>
% 122.46/16.18 ((
% 122.46/16.18 (complementTnotintersectT) =>
% 122.46/16.18 ((
% 122.46/16.18 (complementImpComplementIntersect) =>
% 122.46/16.18 ((
% 122.46/16.18 (complementSubsetComplementIntersect) =>
% 122.46/16.18 ((
% 122.46/16.18 (complementInPowersetComplementIntersect) =>
% 122.46/16.18 ((
% 122.46/16.18 (contraSubsetComplement) =>
% 122.46/16.18 ((
% 122.46/16.18 (complementTcontraSubset) =>
% 122.46/16.18 ((
% 122.46/16.18 (binunionTILcontra) =>
% 122.46/16.18 ((
% 122.46/16.18 (binunionTIRcontra) =>
% 122.46/16.18 ((
% 122.46/16.18 (inIntersectImpInUnion) =>
% 122.46/16.18 ((
% 122.46/16.18 (inIntersectImpInUnion2) =>
% 122.46/16.18 ((
% 122.46/16.18 (inIntersectImpInIntersectUnions) =>
% 122.46/16.18 ((
% 122.46/16.18 (intersectInPowersetIntersectUnions) =>
% 122.46/16.18 ((
% 122.46/16.18 (inComplementUnionImpNotIn1) =>
% 122.46/16.18 ((
% 122.46/16.18 (inComplementUnionImpInComplement1) =>
% 122.46/16.18 ((
% 122.46/16.18 (binunionTE) =>
% 122.46/16.18 ((
% 122.46/16.18 (binunionTEcontra) =>
% 122.46/16.18 ((
% 122.46/16.18 (demorgan2a1) =>
% 122.46/16.18 ((
% 122.46/16.18 (complementUnionInPowersetComplement) =>
% 122.46/16.18 ((
% 122.46/16.18 (demorgan2a2) =>
% 122.46/16.18 ((
% 122.46/16.18 (demorgan1a) =>
% 122.46/16.18 ((
% 122.46/16.18 (demorgan1b) =>
% 122.46/16.18 ((
% 122.46/16.18 (demorgan1) =>
% 122.46/16.18 ((
% 122.46/16.18 (demorgan2a) =>
% 122.46/16.18 ((
% 122.46/16.18 (demorgan2b2) =>
% 122.46/16.18 ((
% 122.46/16.18 (demorgan2b) =>
% 122.46/16.18 ((
% 122.46/16.18 (demorgan2) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz13rule0) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz13rule1) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz13rule2) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz13rule3) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz13rule4) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz1_1) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz1_2) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz1_3) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz1_4) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz1_5) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1all2) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1SetBreln1) =>
% 122.46/16.18 ((
% 122.46/16.18 (choice2fnsingleton) =>
% 122.46/16.18 ((
% 122.46/16.18 (setOfPairsIsBReln1) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1all1) =>
% 122.46/16.18 ((
% 122.46/16.18 (subbreln1) =>
% 122.46/16.18 ((
% 122.46/16.18 (eqbreln1) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1invprop) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1invI) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1invE) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1compprop) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1compI) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1compE) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1compEex) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1unionprop) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1unionIL) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1unionIR) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1unionI) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1unionE) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1unionEcases) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1unionCommutes) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz2Ex) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz2W) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz2A) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz2B) =>
% 122.46/16.18 ((
% 122.46/16.18 (image1Ex) =>
% 122.46/16.18 ((
% 122.46/16.18 (image1Ex1) =>
% 122.46/16.18 ((
% 122.46/16.18 (image1Equiv) =>
% 122.46/16.18 ((
% 122.46/16.18 (image1E) =>
% 122.46/16.18 ((
% 122.46/16.18 (image1I) =>
% 122.46/16.18 ((
% 122.46/16.18 (injFuncInInjFuncSet) =>
% 122.46/16.18 ((
% 122.46/16.18 (!!) @ (
% 122.46/16.18 (('#B') @ (
% 122.46/16.18 !!) @
% 122.46/16.18 (
% 122.46/16.18 (
% 122.46/16.18 ('#B') @ (
% 122.46/16.18 (
% 122.46/16.18 ('#B') @ (
% 122.46/16.18 !!))) @
% 122.46/16.18 (
% 122.46/16.18 (
% 122.46/16.18 ('#S') @ (
% 122.46/16.18 (
% 122.46/16.18 ('#B') @ (
% 122.46/16.18 '#S') @
% 122.46/16.18 (
% 122.46/16.18 (
% 122.46/16.18 ('#B') @ (
% 122.46/16.18 (
% 122.46/16.18 ('#B') @ (
% 122.46/16.18 '#S'))) @
% 122.46/16.18 (
% 122.46/16.18 (
% 122.46/16.18 ('#B') @ (
% 122.46/16.18 (
% 122.46/16.18 ('#B') @ (
% 122.46/16.18 (
% 122.46/16.18 ('#B') @ (
% 122.46/16.18 =>))))) @
% 122.46/16.18 (
% 122.46/16.18 (
% 122.46/16.18 ('#B') @ (
% 122.46/16.18 (
% 122.46/16.18 ('#B') @ (
% 122.46/16.18 (
% 122.46/16.18 ('#C') @ in)))) @
% 122.46/16.18 injFuncSet)))))))) @
% 122.46/16.18 (
% 122.46/16.18 (
% 122.46/16.18 ('#B') @ (
% 122.46/16.18 (
% 122.46/16.18 ('#B') @ (
% 122.46/16.18 (
% 122.46/16.18 ('#C') @ in)))) @
% 122.46/16.18 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.46/16.18 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1296])).
% 122.46/16.18 thf(zip_derived_cl1313, plain,
% 122.46/16.18 (~ (((setminusLsub) =>
% 122.46/16.18 (((setminusSubset1) =>
% 122.46/16.18 (((symdiffE) =>
% 122.46/16.18 (((symdiffI1) =>
% 122.46/16.18 (((symdiffI2) =>
% 122.46/16.18 (((symdiffIneg1) =>
% 122.46/16.18 (((symdiffIneg2) =>
% 122.46/16.18 (((secondinupair) =>
% 122.46/16.18 (((setukpairIL) =>
% 122.46/16.18 (((setukpairIR) =>
% 122.46/16.18 (((kpairiskpair) =>
% 122.46/16.18 (((kpairp) =>
% 122.46/16.18 (((singletonsubset) =>
% 122.46/16.18 (((singletoninpowerset) =>
% 122.46/16.18 (((singletoninpowunion) =>
% 122.46/16.18 (((upairset2E) =>
% 122.46/16.18 (((upairsubunion) =>
% 122.46/16.18 (((upairinpowunion) =>
% 122.46/16.18 (((ubforcartprodlem1) =>
% 122.46/16.18 (((ubforcartprodlem2) =>
% 122.46/16.18 (((ubforcartprodlem3) =>
% 122.46/16.18 (((cartprodpairin) =>
% 122.46/16.18 (((cartprodmempair1) =>
% 122.46/16.18 (((cartprodmempair) =>
% 122.46/16.18 (((setunionE2) =>
% 122.46/16.18 (((setunionsingleton1) =>
% 122.46/16.18 (((setunionsingleton2) =>
% 122.46/16.18 (((setunionsingleton) =>
% 122.46/16.18 (((singletonprop) =>
% 122.46/16.18 (((ex1E1) =>
% 122.46/16.18 ((
% 122.46/16.18 (ex1I) =>
% 122.46/16.18 ((
% 122.46/16.18 (ex1I2) =>
% 122.46/16.18 ((
% 122.46/16.18 (singletonsuniq) =>
% 122.46/16.18 ((
% 122.46/16.18 (setukpairinjL1) =>
% 122.46/16.18 ((
% 122.46/16.18 (kfstsingleton) =>
% 122.46/16.18 ((
% 122.46/16.18 (theprop) =>
% 122.46/16.18 ((
% 122.46/16.18 (kfstpairEq) =>
% 122.46/16.18 ((
% 122.46/16.18 (cartprodfstin) =>
% 122.46/16.18 ((
% 122.46/16.18 (setukpairinjL2) =>
% 122.46/16.18 ((
% 122.46/16.18 (setukpairinjL) =>
% 122.46/16.18 ((
% 122.46/16.18 (setukpairinjR11) =>
% 122.46/16.18 ((
% 122.46/16.18 (setukpairinjR12) =>
% 122.46/16.18 ((
% 122.46/16.18 (setukpairinjR1) =>
% 122.46/16.18 ((
% 122.46/16.18 (upairequniteq) =>
% 122.46/16.18 ((
% 122.46/16.18 (setukpairinjR2) =>
% 122.46/16.18 ((
% 122.46/16.18 (setukpairinjR) =>
% 122.46/16.18 ((
% 122.46/16.18 (ksndsingleton) =>
% 122.46/16.18 ((
% 122.46/16.18 (ksndpairEq) =>
% 122.46/16.18 ((
% 122.46/16.18 (kpairsurjEq) =>
% 122.46/16.18 ((
% 122.46/16.18 (cartprodsndin) =>
% 122.46/16.18 ((
% 122.46/16.18 (cartprodpairmemEL) =>
% 122.46/16.18 ((
% 122.46/16.18 (cartprodpairmemER) =>
% 122.46/16.18 ((
% 122.46/16.18 (cartprodmempaircEq) =>
% 122.46/16.18 ((
% 122.46/16.18 (cartprodfstpairEq) =>
% 122.46/16.18 ((
% 122.46/16.18 (cartprodsndpairEq) =>
% 122.46/16.18 ((
% 122.46/16.18 (cartprodpairsurjEq) =>
% 122.46/16.18 ((
% 122.46/16.18 (dpsetconstrI) =>
% 122.46/16.18 ((
% 122.46/16.18 (dpsetconstrSub) =>
% 122.46/16.18 ((
% 122.46/16.18 (setOfPairsIsBReln) =>
% 122.46/16.18 ((
% 122.46/16.18 (dpsetconstrERa) =>
% 122.46/16.18 ((
% 122.46/16.18 (dpsetconstrEL1) =>
% 122.46/16.18 ((
% 122.46/16.18 (dpsetconstrEL2) =>
% 122.46/16.18 ((
% 122.46/16.18 (dpsetconstrER) =>
% 122.46/16.18 ((
% 122.46/16.18 (funcImageSingleton) =>
% 122.46/16.18 ((
% 122.46/16.18 (apProp) =>
% 122.46/16.18 ((
% 122.46/16.18 (app) =>
% 122.46/16.18 ((
% 122.46/16.18 (infuncsetfunc) =>
% 122.46/16.18 ((
% 122.46/16.18 (ap2p) =>
% 122.46/16.18 ((
% 122.46/16.18 (funcinfuncset) =>
% 122.46/16.18 ((
% 122.46/16.18 (lamProp) =>
% 122.46/16.18 ((
% 122.46/16.18 (lamp) =>
% 122.46/16.18 ((
% 122.46/16.18 (lam2p) =>
% 122.46/16.18 ((
% 122.46/16.18 (brelnall1) =>
% 122.46/16.18 ((
% 122.46/16.18 (brelnall2) =>
% 122.46/16.18 ((
% 122.46/16.18 (ex1E2) =>
% 122.46/16.18 ((
% 122.46/16.18 (funcGraphProp1) =>
% 122.46/16.18 ((
% 122.46/16.18 (funcGraphProp3) =>
% 122.46/16.18 ((
% 122.46/16.18 (funcGraphProp2) =>
% 122.46/16.18 ((
% 122.46/16.18 (funcextLem) =>
% 122.46/16.18 ((
% 122.46/16.18 (funcGraphProp4) =>
% 122.46/16.18 ((
% 122.46/16.18 (subbreln) =>
% 122.46/16.18 ((
% 122.46/16.18 (eqbreln) =>
% 122.46/16.18 ((
% 122.46/16.18 (funcext) =>
% 122.46/16.18 ((
% 122.46/16.18 (funcext2) =>
% 122.46/16.18 ((
% 122.46/16.18 (ap2apEq1) =>
% 122.46/16.18 ((
% 122.46/16.18 (ap2apEq2) =>
% 122.46/16.18 ((
% 122.46/16.18 (beta1) =>
% 122.46/16.18 ((
% 122.46/16.18 (eta1) =>
% 122.46/16.18 ((
% 122.46/16.18 (lam2lamEq) =>
% 122.46/16.18 ((
% 122.46/16.18 (beta2) =>
% 122.46/16.18 ((
% 122.46/16.18 (eta2) =>
% 122.46/16.18 ((
% 122.46/16.18 (iffalseProp1) =>
% 122.46/16.18 ((
% 122.46/16.18 (iffalseProp2) =>
% 122.46/16.18 ((
% 122.46/16.18 (iftrueProp1) =>
% 122.46/16.18 ((
% 122.46/16.18 (iftrueProp2) =>
% 122.46/16.18 ((
% 122.46/16.18 (ifSingleton) =>
% 122.46/16.18 ((
% 122.46/16.18 (ifp) =>
% 122.46/16.18 ((
% 122.46/16.18 (theeq) =>
% 122.46/16.18 ((
% 122.46/16.18 (iftrue) =>
% 122.46/16.18 ((
% 122.46/16.18 (iffalse) =>
% 122.46/16.18 ((
% 122.46/16.18 (iftrueorfalse) =>
% 122.46/16.18 ((
% 122.46/16.18 (binintersectT_lem) =>
% 122.46/16.18 ((
% 122.46/16.18 (binunionT_lem) =>
% 122.46/16.18 ((
% 122.46/16.18 (powersetT_lem) =>
% 122.46/16.18 ((
% 122.46/16.18 (setminusT_lem) =>
% 122.46/16.18 ((
% 122.46/16.18 (complementT_lem) =>
% 122.46/16.18 ((
% 122.46/16.18 (setextT) =>
% 122.46/16.18 ((
% 122.46/16.18 (subsetTI) =>
% 122.46/16.18 ((
% 122.46/16.18 (powersetTI1) =>
% 122.46/16.18 ((
% 122.46/16.18 (powersetTE1) =>
% 122.46/16.18 ((
% 122.46/16.18 (complementTI1) =>
% 122.46/16.18 ((
% 122.46/16.18 (complementTE1) =>
% 122.46/16.18 ((
% 122.46/16.18 (binintersectTELcontra) =>
% 122.46/16.18 ((
% 122.46/16.18 (binintersectTERcontra) =>
% 122.46/16.18 ((
% 122.46/16.18 (contrasubsetT) =>
% 122.46/16.18 ((
% 122.46/16.18 (contrasubsetT1) =>
% 122.46/16.18 ((
% 122.46/16.18 (contrasubsetT2) =>
% 122.46/16.18 ((
% 122.46/16.18 (contrasubsetT3) =>
% 122.46/16.18 ((
% 122.46/16.18 (doubleComplementI1) =>
% 122.46/16.18 ((
% 122.46/16.18 (doubleComplementE1) =>
% 122.46/16.18 ((
% 122.46/16.18 (doubleComplementSub1) =>
% 122.46/16.18 ((
% 122.46/16.18 (doubleComplementSub2) =>
% 122.46/16.18 ((
% 122.46/16.18 (doubleComplementEq) =>
% 122.46/16.18 ((
% 122.46/16.18 (complementTnotintersectT) =>
% 122.46/16.18 ((
% 122.46/16.18 (complementImpComplementIntersect) =>
% 122.46/16.18 ((
% 122.46/16.18 (complementSubsetComplementIntersect) =>
% 122.46/16.18 ((
% 122.46/16.18 (complementInPowersetComplementIntersect) =>
% 122.46/16.18 ((
% 122.46/16.18 (contraSubsetComplement) =>
% 122.46/16.18 ((
% 122.46/16.18 (complementTcontraSubset) =>
% 122.46/16.18 ((
% 122.46/16.18 (binunionTILcontra) =>
% 122.46/16.18 ((
% 122.46/16.18 (binunionTIRcontra) =>
% 122.46/16.18 ((
% 122.46/16.18 (inIntersectImpInUnion) =>
% 122.46/16.18 ((
% 122.46/16.18 (inIntersectImpInUnion2) =>
% 122.46/16.18 ((
% 122.46/16.18 (inIntersectImpInIntersectUnions) =>
% 122.46/16.18 ((
% 122.46/16.18 (intersectInPowersetIntersectUnions) =>
% 122.46/16.18 ((
% 122.46/16.18 (inComplementUnionImpNotIn1) =>
% 122.46/16.18 ((
% 122.46/16.18 (inComplementUnionImpInComplement1) =>
% 122.46/16.18 ((
% 122.46/16.18 (binunionTE) =>
% 122.46/16.18 ((
% 122.46/16.18 (binunionTEcontra) =>
% 122.46/16.18 ((
% 122.46/16.18 (demorgan2a1) =>
% 122.46/16.18 ((
% 122.46/16.18 (complementUnionInPowersetComplement) =>
% 122.46/16.18 ((
% 122.46/16.18 (demorgan2a2) =>
% 122.46/16.18 ((
% 122.46/16.18 (demorgan1a) =>
% 122.46/16.18 ((
% 122.46/16.18 (demorgan1b) =>
% 122.46/16.18 ((
% 122.46/16.18 (demorgan1) =>
% 122.46/16.18 ((
% 122.46/16.18 (demorgan2a) =>
% 122.46/16.18 ((
% 122.46/16.18 (demorgan2b2) =>
% 122.46/16.18 ((
% 122.46/16.18 (demorgan2b) =>
% 122.46/16.18 ((
% 122.46/16.18 (demorgan2) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz13rule0) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz13rule1) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz13rule2) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz13rule3) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz13rule4) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz1_1) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz1_2) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz1_3) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz1_4) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz1_5) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1all2) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1SetBreln1) =>
% 122.46/16.18 ((
% 122.46/16.18 (choice2fnsingleton) =>
% 122.46/16.18 ((
% 122.46/16.18 (setOfPairsIsBReln1) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1all1) =>
% 122.46/16.18 ((
% 122.46/16.18 (subbreln1) =>
% 122.46/16.18 ((
% 122.46/16.18 (eqbreln1) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1invprop) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1invI) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1invE) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1compprop) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1compI) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1compE) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1compEex) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1unionprop) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1unionIL) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1unionIR) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1unionI) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1unionE) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1unionEcases) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1unionCommutes) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz2Ex) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz2W) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz2A) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz2B) =>
% 122.46/16.18 ((
% 122.46/16.18 (image1Ex) =>
% 122.46/16.18 ((
% 122.46/16.18 (image1Ex1) =>
% 122.46/16.18 ((
% 122.46/16.18 (image1Equiv) =>
% 122.46/16.18 ((
% 122.46/16.18 (image1E) =>
% 122.46/16.18 ((
% 122.46/16.18 (image1I) =>
% 122.46/16.18 ((
% 122.46/16.18 (injFuncInInjFuncSet) =>
% 122.46/16.18 ((
% 122.46/16.18 (!!) @ (
% 122.46/16.18 (('#B') @ (
% 122.46/16.18 !!) @
% 122.46/16.18 (
% 122.46/16.18 (
% 122.46/16.18 ('#B') @ (
% 122.46/16.18 (
% 122.46/16.18 ('#B') @ (
% 122.46/16.18 !!))) @
% 122.46/16.18 (
% 122.46/16.18 (
% 122.46/16.18 ('#S') @ (
% 122.46/16.18 (
% 122.46/16.18 ('#B') @ (
% 122.46/16.18 '#S') @
% 122.46/16.18 (
% 122.46/16.18 (
% 122.46/16.18 ('#B') @ (
% 122.46/16.18 (
% 122.46/16.18 ('#B') @ (
% 122.46/16.18 '#S'))) @
% 122.46/16.18 (
% 122.46/16.18 (
% 122.46/16.18 ('#B') @ (
% 122.46/16.18 (
% 122.46/16.18 ('#B') @ (
% 122.46/16.18 (
% 122.46/16.18 ('#B') @ (
% 122.46/16.18 =>))))) @
% 122.46/16.18 (
% 122.46/16.18 (
% 122.46/16.18 ('#B') @ (
% 122.46/16.18 (
% 122.46/16.18 ('#B') @ (
% 122.46/16.18 (
% 122.46/16.18 ('#C') @ in)))) @
% 122.46/16.18 injFuncSet)))))))) @
% 122.46/16.18 (
% 122.46/16.18 (
% 122.46/16.18 ('#B') @ (
% 122.46/16.18 (
% 122.46/16.18 ('#B') @ (
% 122.46/16.18 (
% 122.46/16.18 ('#C') @ in)))) @
% 122.46/16.18 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.46/16.18 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1305])).
% 122.46/16.18 thf(zip_derived_cl1321, plain,
% 122.46/16.18 (~ (((setminusSubset1) =>
% 122.46/16.18 (((symdiffE) =>
% 122.46/16.18 (((symdiffI1) =>
% 122.46/16.18 (((symdiffI2) =>
% 122.46/16.18 (((symdiffIneg1) =>
% 122.46/16.18 (((symdiffIneg2) =>
% 122.46/16.18 (((secondinupair) =>
% 122.46/16.18 (((setukpairIL) =>
% 122.46/16.18 (((setukpairIR) =>
% 122.46/16.18 (((kpairiskpair) =>
% 122.46/16.18 (((kpairp) =>
% 122.46/16.18 (((singletonsubset) =>
% 122.46/16.18 (((singletoninpowerset) =>
% 122.46/16.18 (((singletoninpowunion) =>
% 122.46/16.18 (((upairset2E) =>
% 122.46/16.18 (((upairsubunion) =>
% 122.46/16.18 (((upairinpowunion) =>
% 122.46/16.18 (((ubforcartprodlem1) =>
% 122.46/16.18 (((ubforcartprodlem2) =>
% 122.46/16.18 (((ubforcartprodlem3) =>
% 122.46/16.18 (((cartprodpairin) =>
% 122.46/16.18 (((cartprodmempair1) =>
% 122.46/16.18 (((cartprodmempair) =>
% 122.46/16.18 (((setunionE2) =>
% 122.46/16.18 (((setunionsingleton1) =>
% 122.46/16.18 (((setunionsingleton2) =>
% 122.46/16.18 (((setunionsingleton) =>
% 122.46/16.18 (((singletonprop) =>
% 122.46/16.18 (((ex1E1) =>
% 122.46/16.18 (((ex1I) =>
% 122.46/16.18 ((
% 122.46/16.18 (ex1I2) =>
% 122.46/16.18 ((
% 122.46/16.18 (singletonsuniq) =>
% 122.46/16.18 ((
% 122.46/16.18 (setukpairinjL1) =>
% 122.46/16.18 ((
% 122.46/16.18 (kfstsingleton) =>
% 122.46/16.18 ((
% 122.46/16.18 (theprop) =>
% 122.46/16.18 ((
% 122.46/16.18 (kfstpairEq) =>
% 122.46/16.18 ((
% 122.46/16.18 (cartprodfstin) =>
% 122.46/16.18 ((
% 122.46/16.18 (setukpairinjL2) =>
% 122.46/16.18 ((
% 122.46/16.18 (setukpairinjL) =>
% 122.46/16.18 ((
% 122.46/16.18 (setukpairinjR11) =>
% 122.46/16.18 ((
% 122.46/16.18 (setukpairinjR12) =>
% 122.46/16.18 ((
% 122.46/16.18 (setukpairinjR1) =>
% 122.46/16.18 ((
% 122.46/16.18 (upairequniteq) =>
% 122.46/16.18 ((
% 122.46/16.18 (setukpairinjR2) =>
% 122.46/16.18 ((
% 122.46/16.18 (setukpairinjR) =>
% 122.46/16.18 ((
% 122.46/16.18 (ksndsingleton) =>
% 122.46/16.18 ((
% 122.46/16.18 (ksndpairEq) =>
% 122.46/16.18 ((
% 122.46/16.18 (kpairsurjEq) =>
% 122.46/16.18 ((
% 122.46/16.18 (cartprodsndin) =>
% 122.46/16.18 ((
% 122.46/16.18 (cartprodpairmemEL) =>
% 122.46/16.18 ((
% 122.46/16.18 (cartprodpairmemER) =>
% 122.46/16.18 ((
% 122.46/16.18 (cartprodmempaircEq) =>
% 122.46/16.18 ((
% 122.46/16.18 (cartprodfstpairEq) =>
% 122.46/16.18 ((
% 122.46/16.18 (cartprodsndpairEq) =>
% 122.46/16.18 ((
% 122.46/16.18 (cartprodpairsurjEq) =>
% 122.46/16.18 ((
% 122.46/16.18 (dpsetconstrI) =>
% 122.46/16.18 ((
% 122.46/16.18 (dpsetconstrSub) =>
% 122.46/16.18 ((
% 122.46/16.18 (setOfPairsIsBReln) =>
% 122.46/16.18 ((
% 122.46/16.18 (dpsetconstrERa) =>
% 122.46/16.18 ((
% 122.46/16.18 (dpsetconstrEL1) =>
% 122.46/16.18 ((
% 122.46/16.18 (dpsetconstrEL2) =>
% 122.46/16.18 ((
% 122.46/16.18 (dpsetconstrER) =>
% 122.46/16.18 ((
% 122.46/16.18 (funcImageSingleton) =>
% 122.46/16.18 ((
% 122.46/16.18 (apProp) =>
% 122.46/16.18 ((
% 122.46/16.18 (app) =>
% 122.46/16.18 ((
% 122.46/16.18 (infuncsetfunc) =>
% 122.46/16.18 ((
% 122.46/16.18 (ap2p) =>
% 122.46/16.18 ((
% 122.46/16.18 (funcinfuncset) =>
% 122.46/16.18 ((
% 122.46/16.18 (lamProp) =>
% 122.46/16.18 ((
% 122.46/16.18 (lamp) =>
% 122.46/16.18 ((
% 122.46/16.18 (lam2p) =>
% 122.46/16.18 ((
% 122.46/16.18 (brelnall1) =>
% 122.46/16.18 ((
% 122.46/16.18 (brelnall2) =>
% 122.46/16.18 ((
% 122.46/16.18 (ex1E2) =>
% 122.46/16.18 ((
% 122.46/16.18 (funcGraphProp1) =>
% 122.46/16.18 ((
% 122.46/16.18 (funcGraphProp3) =>
% 122.46/16.18 ((
% 122.46/16.18 (funcGraphProp2) =>
% 122.46/16.18 ((
% 122.46/16.18 (funcextLem) =>
% 122.46/16.18 ((
% 122.46/16.18 (funcGraphProp4) =>
% 122.46/16.18 ((
% 122.46/16.18 (subbreln) =>
% 122.46/16.18 ((
% 122.46/16.18 (eqbreln) =>
% 122.46/16.18 ((
% 122.46/16.18 (funcext) =>
% 122.46/16.18 ((
% 122.46/16.18 (funcext2) =>
% 122.46/16.18 ((
% 122.46/16.18 (ap2apEq1) =>
% 122.46/16.18 ((
% 122.46/16.18 (ap2apEq2) =>
% 122.46/16.18 ((
% 122.46/16.18 (beta1) =>
% 122.46/16.18 ((
% 122.46/16.18 (eta1) =>
% 122.46/16.18 ((
% 122.46/16.18 (lam2lamEq) =>
% 122.46/16.18 ((
% 122.46/16.18 (beta2) =>
% 122.46/16.18 ((
% 122.46/16.18 (eta2) =>
% 122.46/16.18 ((
% 122.46/16.18 (iffalseProp1) =>
% 122.46/16.18 ((
% 122.46/16.18 (iffalseProp2) =>
% 122.46/16.18 ((
% 122.46/16.18 (iftrueProp1) =>
% 122.46/16.18 ((
% 122.46/16.18 (iftrueProp2) =>
% 122.46/16.18 ((
% 122.46/16.18 (ifSingleton) =>
% 122.46/16.18 ((
% 122.46/16.18 (ifp) =>
% 122.46/16.18 ((
% 122.46/16.18 (theeq) =>
% 122.46/16.18 ((
% 122.46/16.18 (iftrue) =>
% 122.46/16.18 ((
% 122.46/16.18 (iffalse) =>
% 122.46/16.18 ((
% 122.46/16.18 (iftrueorfalse) =>
% 122.46/16.18 ((
% 122.46/16.18 (binintersectT_lem) =>
% 122.46/16.18 ((
% 122.46/16.18 (binunionT_lem) =>
% 122.46/16.18 ((
% 122.46/16.18 (powersetT_lem) =>
% 122.46/16.18 ((
% 122.46/16.18 (setminusT_lem) =>
% 122.46/16.18 ((
% 122.46/16.18 (complementT_lem) =>
% 122.46/16.18 ((
% 122.46/16.18 (setextT) =>
% 122.46/16.18 ((
% 122.46/16.18 (subsetTI) =>
% 122.46/16.18 ((
% 122.46/16.18 (powersetTI1) =>
% 122.46/16.18 ((
% 122.46/16.18 (powersetTE1) =>
% 122.46/16.18 ((
% 122.46/16.18 (complementTI1) =>
% 122.46/16.18 ((
% 122.46/16.18 (complementTE1) =>
% 122.46/16.18 ((
% 122.46/16.18 (binintersectTELcontra) =>
% 122.46/16.18 ((
% 122.46/16.18 (binintersectTERcontra) =>
% 122.46/16.18 ((
% 122.46/16.18 (contrasubsetT) =>
% 122.46/16.18 ((
% 122.46/16.18 (contrasubsetT1) =>
% 122.46/16.18 ((
% 122.46/16.18 (contrasubsetT2) =>
% 122.46/16.18 ((
% 122.46/16.18 (contrasubsetT3) =>
% 122.46/16.18 ((
% 122.46/16.18 (doubleComplementI1) =>
% 122.46/16.18 ((
% 122.46/16.18 (doubleComplementE1) =>
% 122.46/16.18 ((
% 122.46/16.18 (doubleComplementSub1) =>
% 122.46/16.18 ((
% 122.46/16.18 (doubleComplementSub2) =>
% 122.46/16.18 ((
% 122.46/16.18 (doubleComplementEq) =>
% 122.46/16.18 ((
% 122.46/16.18 (complementTnotintersectT) =>
% 122.46/16.18 ((
% 122.46/16.18 (complementImpComplementIntersect) =>
% 122.46/16.18 ((
% 122.46/16.18 (complementSubsetComplementIntersect) =>
% 122.46/16.18 ((
% 122.46/16.18 (complementInPowersetComplementIntersect) =>
% 122.46/16.18 ((
% 122.46/16.18 (contraSubsetComplement) =>
% 122.46/16.18 ((
% 122.46/16.18 (complementTcontraSubset) =>
% 122.46/16.18 ((
% 122.46/16.18 (binunionTILcontra) =>
% 122.46/16.18 ((
% 122.46/16.18 (binunionTIRcontra) =>
% 122.46/16.18 ((
% 122.46/16.18 (inIntersectImpInUnion) =>
% 122.46/16.18 ((
% 122.46/16.18 (inIntersectImpInUnion2) =>
% 122.46/16.18 ((
% 122.46/16.18 (inIntersectImpInIntersectUnions) =>
% 122.46/16.18 ((
% 122.46/16.18 (intersectInPowersetIntersectUnions) =>
% 122.46/16.18 ((
% 122.46/16.18 (inComplementUnionImpNotIn1) =>
% 122.46/16.18 ((
% 122.46/16.18 (inComplementUnionImpInComplement1) =>
% 122.46/16.18 ((
% 122.46/16.18 (binunionTE) =>
% 122.46/16.18 ((
% 122.46/16.18 (binunionTEcontra) =>
% 122.46/16.18 ((
% 122.46/16.18 (demorgan2a1) =>
% 122.46/16.18 ((
% 122.46/16.18 (complementUnionInPowersetComplement) =>
% 122.46/16.18 ((
% 122.46/16.18 (demorgan2a2) =>
% 122.46/16.18 ((
% 122.46/16.18 (demorgan1a) =>
% 122.46/16.18 ((
% 122.46/16.18 (demorgan1b) =>
% 122.46/16.18 ((
% 122.46/16.18 (demorgan1) =>
% 122.46/16.18 ((
% 122.46/16.18 (demorgan2a) =>
% 122.46/16.18 ((
% 122.46/16.18 (demorgan2b2) =>
% 122.46/16.18 ((
% 122.46/16.18 (demorgan2b) =>
% 122.46/16.18 ((
% 122.46/16.18 (demorgan2) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz13rule0) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz13rule1) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz13rule2) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz13rule3) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz13rule4) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz1_1) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz1_2) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz1_3) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz1_4) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz1_5) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1all2) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1SetBreln1) =>
% 122.46/16.18 ((
% 122.46/16.18 (choice2fnsingleton) =>
% 122.46/16.18 ((
% 122.46/16.18 (setOfPairsIsBReln1) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1all1) =>
% 122.46/16.18 ((
% 122.46/16.18 (subbreln1) =>
% 122.46/16.18 ((
% 122.46/16.18 (eqbreln1) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1invprop) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1invI) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1invE) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1compprop) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1compI) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1compE) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1compEex) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1unionprop) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1unionIL) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1unionIR) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1unionI) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1unionE) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1unionEcases) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1unionCommutes) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz2Ex) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz2W) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz2A) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz2B) =>
% 122.46/16.18 ((
% 122.46/16.18 (image1Ex) =>
% 122.46/16.18 ((
% 122.46/16.18 (image1Ex1) =>
% 122.46/16.18 ((
% 122.46/16.18 (image1Equiv) =>
% 122.46/16.18 ((
% 122.46/16.18 (image1E) =>
% 122.46/16.18 ((
% 122.46/16.18 (image1I) =>
% 122.46/16.18 ((
% 122.46/16.18 (injFuncInInjFuncSet) =>
% 122.46/16.18 ((
% 122.46/16.18 (!!) @ (
% 122.46/16.18 (('#B') @ (
% 122.46/16.18 !!) @
% 122.46/16.18 (
% 122.46/16.18 (
% 122.46/16.18 ('#B') @ (
% 122.46/16.18 (
% 122.46/16.18 ('#B') @ (
% 122.46/16.18 !!))) @
% 122.46/16.18 (
% 122.46/16.18 (
% 122.46/16.18 ('#S') @ (
% 122.46/16.18 (
% 122.46/16.18 ('#B') @ (
% 122.46/16.18 '#S') @
% 122.46/16.18 (
% 122.46/16.18 (
% 122.46/16.18 ('#B') @ (
% 122.46/16.18 (
% 122.46/16.18 ('#B') @ (
% 122.46/16.18 '#S'))) @
% 122.46/16.18 (
% 122.46/16.18 (
% 122.46/16.18 ('#B') @ (
% 122.46/16.18 (
% 122.46/16.18 ('#B') @ (
% 122.46/16.18 (
% 122.46/16.18 ('#B') @ (
% 122.46/16.18 =>))))) @
% 122.46/16.18 (
% 122.46/16.18 (
% 122.46/16.18 ('#B') @ (
% 122.46/16.18 (
% 122.46/16.18 ('#B') @ (
% 122.46/16.18 (
% 122.46/16.18 ('#C') @ in)))) @
% 122.46/16.18 injFuncSet)))))))) @
% 122.46/16.18 (
% 122.46/16.18 (
% 122.46/16.18 ('#B') @ (
% 122.46/16.18 (
% 122.46/16.18 ('#B') @ (
% 122.46/16.18 (
% 122.46/16.18 ('#C') @ in)))) @
% 122.46/16.18 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.46/16.18 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1313])).
% 122.46/16.18 thf(zip_derived_cl1329, plain,
% 122.46/16.18 (~ (((symdiffE) =>
% 122.46/16.18 (((symdiffI1) =>
% 122.46/16.18 (((symdiffI2) =>
% 122.46/16.18 (((symdiffIneg1) =>
% 122.46/16.18 (((symdiffIneg2) =>
% 122.46/16.18 (((secondinupair) =>
% 122.46/16.18 (((setukpairIL) =>
% 122.46/16.18 (((setukpairIR) =>
% 122.46/16.18 (((kpairiskpair) =>
% 122.46/16.18 (((kpairp) =>
% 122.46/16.18 (((singletonsubset) =>
% 122.46/16.18 (((singletoninpowerset) =>
% 122.46/16.18 (((singletoninpowunion) =>
% 122.46/16.18 (((upairset2E) =>
% 122.46/16.18 (((upairsubunion) =>
% 122.46/16.18 (((upairinpowunion) =>
% 122.46/16.18 (((ubforcartprodlem1) =>
% 122.46/16.18 (((ubforcartprodlem2) =>
% 122.46/16.18 (((ubforcartprodlem3) =>
% 122.46/16.18 (((cartprodpairin) =>
% 122.46/16.18 (((cartprodmempair1) =>
% 122.46/16.18 (((cartprodmempair) =>
% 122.46/16.18 (((setunionE2) =>
% 122.46/16.18 (((setunionsingleton1) =>
% 122.46/16.18 (((setunionsingleton2) =>
% 122.46/16.18 (((setunionsingleton) =>
% 122.46/16.18 (((singletonprop) =>
% 122.46/16.18 (((ex1E1) =>
% 122.46/16.18 (((ex1I) =>
% 122.46/16.18 (((ex1I2) =>
% 122.46/16.18 ((
% 122.46/16.18 (singletonsuniq) =>
% 122.46/16.18 ((
% 122.46/16.18 (setukpairinjL1) =>
% 122.46/16.18 ((
% 122.46/16.18 (kfstsingleton) =>
% 122.46/16.18 ((
% 122.46/16.18 (theprop) =>
% 122.46/16.18 ((
% 122.46/16.18 (kfstpairEq) =>
% 122.46/16.18 ((
% 122.46/16.18 (cartprodfstin) =>
% 122.46/16.18 ((
% 122.46/16.18 (setukpairinjL2) =>
% 122.46/16.18 ((
% 122.46/16.18 (setukpairinjL) =>
% 122.46/16.18 ((
% 122.46/16.18 (setukpairinjR11) =>
% 122.46/16.18 ((
% 122.46/16.18 (setukpairinjR12) =>
% 122.46/16.18 ((
% 122.46/16.18 (setukpairinjR1) =>
% 122.46/16.18 ((
% 122.46/16.18 (upairequniteq) =>
% 122.46/16.18 ((
% 122.46/16.18 (setukpairinjR2) =>
% 122.46/16.18 ((
% 122.46/16.18 (setukpairinjR) =>
% 122.46/16.18 ((
% 122.46/16.18 (ksndsingleton) =>
% 122.46/16.18 ((
% 122.46/16.18 (ksndpairEq) =>
% 122.46/16.18 ((
% 122.46/16.18 (kpairsurjEq) =>
% 122.46/16.18 ((
% 122.46/16.18 (cartprodsndin) =>
% 122.46/16.18 ((
% 122.46/16.18 (cartprodpairmemEL) =>
% 122.46/16.18 ((
% 122.46/16.18 (cartprodpairmemER) =>
% 122.46/16.18 ((
% 122.46/16.18 (cartprodmempaircEq) =>
% 122.46/16.18 ((
% 122.46/16.18 (cartprodfstpairEq) =>
% 122.46/16.18 ((
% 122.46/16.18 (cartprodsndpairEq) =>
% 122.46/16.18 ((
% 122.46/16.18 (cartprodpairsurjEq) =>
% 122.46/16.18 ((
% 122.46/16.18 (dpsetconstrI) =>
% 122.46/16.18 ((
% 122.46/16.18 (dpsetconstrSub) =>
% 122.46/16.18 ((
% 122.46/16.18 (setOfPairsIsBReln) =>
% 122.46/16.18 ((
% 122.46/16.18 (dpsetconstrERa) =>
% 122.46/16.18 ((
% 122.46/16.18 (dpsetconstrEL1) =>
% 122.46/16.18 ((
% 122.46/16.18 (dpsetconstrEL2) =>
% 122.46/16.18 ((
% 122.46/16.18 (dpsetconstrER) =>
% 122.46/16.18 ((
% 122.46/16.18 (funcImageSingleton) =>
% 122.46/16.18 ((
% 122.46/16.18 (apProp) =>
% 122.46/16.18 ((
% 122.46/16.18 (app) =>
% 122.46/16.18 ((
% 122.46/16.18 (infuncsetfunc) =>
% 122.46/16.18 ((
% 122.46/16.18 (ap2p) =>
% 122.46/16.18 ((
% 122.46/16.18 (funcinfuncset) =>
% 122.46/16.18 ((
% 122.46/16.18 (lamProp) =>
% 122.46/16.18 ((
% 122.46/16.18 (lamp) =>
% 122.46/16.18 ((
% 122.46/16.18 (lam2p) =>
% 122.46/16.18 ((
% 122.46/16.18 (brelnall1) =>
% 122.46/16.18 ((
% 122.46/16.18 (brelnall2) =>
% 122.46/16.18 ((
% 122.46/16.18 (ex1E2) =>
% 122.46/16.18 ((
% 122.46/16.18 (funcGraphProp1) =>
% 122.46/16.18 ((
% 122.46/16.18 (funcGraphProp3) =>
% 122.46/16.18 ((
% 122.46/16.18 (funcGraphProp2) =>
% 122.46/16.18 ((
% 122.46/16.18 (funcextLem) =>
% 122.46/16.18 ((
% 122.46/16.18 (funcGraphProp4) =>
% 122.46/16.18 ((
% 122.46/16.18 (subbreln) =>
% 122.46/16.18 ((
% 122.46/16.18 (eqbreln) =>
% 122.46/16.18 ((
% 122.46/16.18 (funcext) =>
% 122.46/16.18 ((
% 122.46/16.18 (funcext2) =>
% 122.46/16.18 ((
% 122.46/16.18 (ap2apEq1) =>
% 122.46/16.18 ((
% 122.46/16.18 (ap2apEq2) =>
% 122.46/16.18 ((
% 122.46/16.18 (beta1) =>
% 122.46/16.18 ((
% 122.46/16.18 (eta1) =>
% 122.46/16.18 ((
% 122.46/16.18 (lam2lamEq) =>
% 122.46/16.18 ((
% 122.46/16.18 (beta2) =>
% 122.46/16.18 ((
% 122.46/16.18 (eta2) =>
% 122.46/16.18 ((
% 122.46/16.18 (iffalseProp1) =>
% 122.46/16.18 ((
% 122.46/16.18 (iffalseProp2) =>
% 122.46/16.18 ((
% 122.46/16.18 (iftrueProp1) =>
% 122.46/16.18 ((
% 122.46/16.18 (iftrueProp2) =>
% 122.46/16.18 ((
% 122.46/16.18 (ifSingleton) =>
% 122.46/16.18 ((
% 122.46/16.18 (ifp) =>
% 122.46/16.18 ((
% 122.46/16.18 (theeq) =>
% 122.46/16.18 ((
% 122.46/16.18 (iftrue) =>
% 122.46/16.18 ((
% 122.46/16.18 (iffalse) =>
% 122.46/16.18 ((
% 122.46/16.18 (iftrueorfalse) =>
% 122.46/16.18 ((
% 122.46/16.18 (binintersectT_lem) =>
% 122.46/16.18 ((
% 122.46/16.18 (binunionT_lem) =>
% 122.46/16.18 ((
% 122.46/16.18 (powersetT_lem) =>
% 122.46/16.18 ((
% 122.46/16.18 (setminusT_lem) =>
% 122.46/16.18 ((
% 122.46/16.18 (complementT_lem) =>
% 122.46/16.18 ((
% 122.46/16.18 (setextT) =>
% 122.46/16.18 ((
% 122.46/16.18 (subsetTI) =>
% 122.46/16.18 ((
% 122.46/16.18 (powersetTI1) =>
% 122.46/16.18 ((
% 122.46/16.18 (powersetTE1) =>
% 122.46/16.18 ((
% 122.46/16.18 (complementTI1) =>
% 122.46/16.18 ((
% 122.46/16.18 (complementTE1) =>
% 122.46/16.18 ((
% 122.46/16.18 (binintersectTELcontra) =>
% 122.46/16.18 ((
% 122.46/16.18 (binintersectTERcontra) =>
% 122.46/16.18 ((
% 122.46/16.18 (contrasubsetT) =>
% 122.46/16.18 ((
% 122.46/16.18 (contrasubsetT1) =>
% 122.46/16.18 ((
% 122.46/16.18 (contrasubsetT2) =>
% 122.46/16.18 ((
% 122.46/16.18 (contrasubsetT3) =>
% 122.46/16.18 ((
% 122.46/16.18 (doubleComplementI1) =>
% 122.46/16.18 ((
% 122.46/16.18 (doubleComplementE1) =>
% 122.46/16.18 ((
% 122.46/16.18 (doubleComplementSub1) =>
% 122.46/16.18 ((
% 122.46/16.18 (doubleComplementSub2) =>
% 122.46/16.18 ((
% 122.46/16.18 (doubleComplementEq) =>
% 122.46/16.18 ((
% 122.46/16.18 (complementTnotintersectT) =>
% 122.46/16.18 ((
% 122.46/16.18 (complementImpComplementIntersect) =>
% 122.46/16.18 ((
% 122.46/16.18 (complementSubsetComplementIntersect) =>
% 122.46/16.18 ((
% 122.46/16.18 (complementInPowersetComplementIntersect) =>
% 122.46/16.18 ((
% 122.46/16.18 (contraSubsetComplement) =>
% 122.46/16.18 ((
% 122.46/16.18 (complementTcontraSubset) =>
% 122.46/16.18 ((
% 122.46/16.18 (binunionTILcontra) =>
% 122.46/16.18 ((
% 122.46/16.18 (binunionTIRcontra) =>
% 122.46/16.18 ((
% 122.46/16.18 (inIntersectImpInUnion) =>
% 122.46/16.18 ((
% 122.46/16.18 (inIntersectImpInUnion2) =>
% 122.46/16.18 ((
% 122.46/16.18 (inIntersectImpInIntersectUnions) =>
% 122.46/16.18 ((
% 122.46/16.18 (intersectInPowersetIntersectUnions) =>
% 122.46/16.18 ((
% 122.46/16.18 (inComplementUnionImpNotIn1) =>
% 122.46/16.18 ((
% 122.46/16.18 (inComplementUnionImpInComplement1) =>
% 122.46/16.18 ((
% 122.46/16.18 (binunionTE) =>
% 122.46/16.18 ((
% 122.46/16.18 (binunionTEcontra) =>
% 122.46/16.18 ((
% 122.46/16.18 (demorgan2a1) =>
% 122.46/16.18 ((
% 122.46/16.18 (complementUnionInPowersetComplement) =>
% 122.46/16.18 ((
% 122.46/16.18 (demorgan2a2) =>
% 122.46/16.18 ((
% 122.46/16.18 (demorgan1a) =>
% 122.46/16.18 ((
% 122.46/16.18 (demorgan1b) =>
% 122.46/16.18 ((
% 122.46/16.18 (demorgan1) =>
% 122.46/16.18 ((
% 122.46/16.18 (demorgan2a) =>
% 122.46/16.18 ((
% 122.46/16.18 (demorgan2b2) =>
% 122.46/16.18 ((
% 122.46/16.18 (demorgan2b) =>
% 122.46/16.18 ((
% 122.46/16.18 (demorgan2) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz13rule0) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz13rule1) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz13rule2) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz13rule3) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz13rule4) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz1_1) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz1_2) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz1_3) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz1_4) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz1_5) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1all2) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1SetBreln1) =>
% 122.46/16.18 ((
% 122.46/16.18 (choice2fnsingleton) =>
% 122.46/16.18 ((
% 122.46/16.18 (setOfPairsIsBReln1) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1all1) =>
% 122.46/16.18 ((
% 122.46/16.18 (subbreln1) =>
% 122.46/16.18 ((
% 122.46/16.18 (eqbreln1) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1invprop) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1invI) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1invE) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1compprop) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1compI) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1compE) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1compEex) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1unionprop) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1unionIL) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1unionIR) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1unionI) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1unionE) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1unionEcases) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1unionCommutes) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz2Ex) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz2W) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz2A) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz2B) =>
% 122.46/16.18 ((
% 122.46/16.18 (image1Ex) =>
% 122.46/16.18 ((
% 122.46/16.18 (image1Ex1) =>
% 122.46/16.18 ((
% 122.46/16.18 (image1Equiv) =>
% 122.46/16.18 ((
% 122.46/16.18 (image1E) =>
% 122.46/16.18 ((
% 122.46/16.18 (image1I) =>
% 122.46/16.18 ((
% 122.46/16.18 (injFuncInInjFuncSet) =>
% 122.46/16.18 ((
% 122.46/16.18 (!!) @ (
% 122.46/16.18 (('#B') @ (
% 122.46/16.18 !!) @
% 122.46/16.18 (
% 122.46/16.18 (
% 122.46/16.18 ('#B') @ (
% 122.46/16.18 (
% 122.46/16.18 ('#B') @ (
% 122.46/16.18 !!))) @
% 122.46/16.18 (
% 122.46/16.18 (
% 122.46/16.18 ('#S') @ (
% 122.46/16.18 (
% 122.46/16.18 ('#B') @ (
% 122.46/16.18 '#S') @
% 122.46/16.18 (
% 122.46/16.18 (
% 122.46/16.18 ('#B') @ (
% 122.46/16.18 (
% 122.46/16.18 ('#B') @ (
% 122.46/16.18 '#S'))) @
% 122.46/16.18 (
% 122.46/16.18 (
% 122.46/16.18 ('#B') @ (
% 122.46/16.18 (
% 122.46/16.18 ('#B') @ (
% 122.46/16.18 (
% 122.46/16.18 ('#B') @ (
% 122.46/16.18 =>))))) @
% 122.46/16.18 (
% 122.46/16.18 (
% 122.46/16.18 ('#B') @ (
% 122.46/16.18 (
% 122.46/16.18 ('#B') @ (
% 122.46/16.18 (
% 122.46/16.18 ('#C') @ in)))) @
% 122.46/16.18 injFuncSet)))))))) @
% 122.46/16.18 (
% 122.46/16.18 (
% 122.46/16.18 ('#B') @ (
% 122.46/16.18 (
% 122.46/16.18 ('#B') @ (
% 122.46/16.18 (
% 122.46/16.18 ('#C') @ in)))) @
% 122.46/16.18 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.46/16.18 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1321])).
% 122.46/16.18 thf(zip_derived_cl1338, plain,
% 122.46/16.18 (~ (((symdiffI1) =>
% 122.46/16.18 (((symdiffI2) =>
% 122.46/16.18 (((symdiffIneg1) =>
% 122.46/16.18 (((symdiffIneg2) =>
% 122.46/16.18 (((secondinupair) =>
% 122.46/16.18 (((setukpairIL) =>
% 122.46/16.18 (((setukpairIR) =>
% 122.46/16.18 (((kpairiskpair) =>
% 122.46/16.18 (((kpairp) =>
% 122.46/16.18 (((singletonsubset) =>
% 122.46/16.18 (((singletoninpowerset) =>
% 122.46/16.18 (((singletoninpowunion) =>
% 122.46/16.18 (((upairset2E) =>
% 122.46/16.18 (((upairsubunion) =>
% 122.46/16.18 (((upairinpowunion) =>
% 122.46/16.18 (((ubforcartprodlem1) =>
% 122.46/16.18 (((ubforcartprodlem2) =>
% 122.46/16.18 (((ubforcartprodlem3) =>
% 122.46/16.18 (((cartprodpairin) =>
% 122.46/16.18 (((cartprodmempair1) =>
% 122.46/16.18 (((cartprodmempair) =>
% 122.46/16.18 (((setunionE2) =>
% 122.46/16.18 (((setunionsingleton1) =>
% 122.46/16.18 (((setunionsingleton2) =>
% 122.46/16.18 (((setunionsingleton) =>
% 122.46/16.18 (((singletonprop) =>
% 122.46/16.18 (((ex1E1) =>
% 122.46/16.18 (((ex1I) =>
% 122.46/16.18 (((ex1I2) =>
% 122.46/16.18 (((singletonsuniq) =>
% 122.46/16.18 ((
% 122.46/16.18 (setukpairinjL1) =>
% 122.46/16.18 ((
% 122.46/16.18 (kfstsingleton) =>
% 122.46/16.18 ((
% 122.46/16.18 (theprop) =>
% 122.46/16.18 ((
% 122.46/16.18 (kfstpairEq) =>
% 122.46/16.18 ((
% 122.46/16.18 (cartprodfstin) =>
% 122.46/16.18 ((
% 122.46/16.18 (setukpairinjL2) =>
% 122.46/16.18 ((
% 122.46/16.18 (setukpairinjL) =>
% 122.46/16.18 ((
% 122.46/16.18 (setukpairinjR11) =>
% 122.46/16.18 ((
% 122.46/16.18 (setukpairinjR12) =>
% 122.46/16.18 ((
% 122.46/16.18 (setukpairinjR1) =>
% 122.46/16.18 ((
% 122.46/16.18 (upairequniteq) =>
% 122.46/16.18 ((
% 122.46/16.18 (setukpairinjR2) =>
% 122.46/16.18 ((
% 122.46/16.18 (setukpairinjR) =>
% 122.46/16.18 ((
% 122.46/16.18 (ksndsingleton) =>
% 122.46/16.18 ((
% 122.46/16.18 (ksndpairEq) =>
% 122.46/16.18 ((
% 122.46/16.18 (kpairsurjEq) =>
% 122.46/16.18 ((
% 122.46/16.18 (cartprodsndin) =>
% 122.46/16.18 ((
% 122.46/16.18 (cartprodpairmemEL) =>
% 122.46/16.18 ((
% 122.46/16.18 (cartprodpairmemER) =>
% 122.46/16.18 ((
% 122.46/16.18 (cartprodmempaircEq) =>
% 122.46/16.18 ((
% 122.46/16.18 (cartprodfstpairEq) =>
% 122.46/16.18 ((
% 122.46/16.18 (cartprodsndpairEq) =>
% 122.46/16.18 ((
% 122.46/16.18 (cartprodpairsurjEq) =>
% 122.46/16.18 ((
% 122.46/16.18 (dpsetconstrI) =>
% 122.46/16.18 ((
% 122.46/16.18 (dpsetconstrSub) =>
% 122.46/16.18 ((
% 122.46/16.18 (setOfPairsIsBReln) =>
% 122.46/16.18 ((
% 122.46/16.18 (dpsetconstrERa) =>
% 122.46/16.18 ((
% 122.46/16.18 (dpsetconstrEL1) =>
% 122.46/16.18 ((
% 122.46/16.18 (dpsetconstrEL2) =>
% 122.46/16.18 ((
% 122.46/16.18 (dpsetconstrER) =>
% 122.46/16.18 ((
% 122.46/16.18 (funcImageSingleton) =>
% 122.46/16.18 ((
% 122.46/16.18 (apProp) =>
% 122.46/16.18 ((
% 122.46/16.18 (app) =>
% 122.46/16.18 ((
% 122.46/16.18 (infuncsetfunc) =>
% 122.46/16.18 ((
% 122.46/16.18 (ap2p) =>
% 122.46/16.18 ((
% 122.46/16.18 (funcinfuncset) =>
% 122.46/16.18 ((
% 122.46/16.18 (lamProp) =>
% 122.46/16.18 ((
% 122.46/16.18 (lamp) =>
% 122.46/16.18 ((
% 122.46/16.18 (lam2p) =>
% 122.46/16.18 ((
% 122.46/16.18 (brelnall1) =>
% 122.46/16.18 ((
% 122.46/16.18 (brelnall2) =>
% 122.46/16.18 ((
% 122.46/16.18 (ex1E2) =>
% 122.46/16.18 ((
% 122.46/16.18 (funcGraphProp1) =>
% 122.46/16.18 ((
% 122.46/16.18 (funcGraphProp3) =>
% 122.46/16.18 ((
% 122.46/16.18 (funcGraphProp2) =>
% 122.46/16.18 ((
% 122.46/16.18 (funcextLem) =>
% 122.46/16.18 ((
% 122.46/16.18 (funcGraphProp4) =>
% 122.46/16.18 ((
% 122.46/16.18 (subbreln) =>
% 122.46/16.18 ((
% 122.46/16.18 (eqbreln) =>
% 122.46/16.18 ((
% 122.46/16.18 (funcext) =>
% 122.46/16.18 ((
% 122.46/16.18 (funcext2) =>
% 122.46/16.18 ((
% 122.46/16.18 (ap2apEq1) =>
% 122.46/16.18 ((
% 122.46/16.18 (ap2apEq2) =>
% 122.46/16.18 ((
% 122.46/16.18 (beta1) =>
% 122.46/16.18 ((
% 122.46/16.18 (eta1) =>
% 122.46/16.18 ((
% 122.46/16.18 (lam2lamEq) =>
% 122.46/16.18 ((
% 122.46/16.18 (beta2) =>
% 122.46/16.18 ((
% 122.46/16.18 (eta2) =>
% 122.46/16.18 ((
% 122.46/16.18 (iffalseProp1) =>
% 122.46/16.18 ((
% 122.46/16.18 (iffalseProp2) =>
% 122.46/16.18 ((
% 122.46/16.18 (iftrueProp1) =>
% 122.46/16.18 ((
% 122.46/16.18 (iftrueProp2) =>
% 122.46/16.18 ((
% 122.46/16.18 (ifSingleton) =>
% 122.46/16.18 ((
% 122.46/16.18 (ifp) =>
% 122.46/16.18 ((
% 122.46/16.18 (theeq) =>
% 122.46/16.18 ((
% 122.46/16.18 (iftrue) =>
% 122.46/16.18 ((
% 122.46/16.18 (iffalse) =>
% 122.46/16.18 ((
% 122.46/16.18 (iftrueorfalse) =>
% 122.46/16.18 ((
% 122.46/16.18 (binintersectT_lem) =>
% 122.46/16.18 ((
% 122.46/16.18 (binunionT_lem) =>
% 122.46/16.18 ((
% 122.46/16.18 (powersetT_lem) =>
% 122.46/16.18 ((
% 122.46/16.18 (setminusT_lem) =>
% 122.46/16.18 ((
% 122.46/16.18 (complementT_lem) =>
% 122.46/16.18 ((
% 122.46/16.18 (setextT) =>
% 122.46/16.18 ((
% 122.46/16.18 (subsetTI) =>
% 122.46/16.18 ((
% 122.46/16.18 (powersetTI1) =>
% 122.46/16.18 ((
% 122.46/16.18 (powersetTE1) =>
% 122.46/16.18 ((
% 122.46/16.18 (complementTI1) =>
% 122.46/16.18 ((
% 122.46/16.18 (complementTE1) =>
% 122.46/16.18 ((
% 122.46/16.18 (binintersectTELcontra) =>
% 122.46/16.18 ((
% 122.46/16.18 (binintersectTERcontra) =>
% 122.46/16.18 ((
% 122.46/16.18 (contrasubsetT) =>
% 122.46/16.18 ((
% 122.46/16.18 (contrasubsetT1) =>
% 122.46/16.18 ((
% 122.46/16.18 (contrasubsetT2) =>
% 122.46/16.18 ((
% 122.46/16.18 (contrasubsetT3) =>
% 122.46/16.18 ((
% 122.46/16.18 (doubleComplementI1) =>
% 122.46/16.18 ((
% 122.46/16.18 (doubleComplementE1) =>
% 122.46/16.18 ((
% 122.46/16.18 (doubleComplementSub1) =>
% 122.46/16.18 ((
% 122.46/16.18 (doubleComplementSub2) =>
% 122.46/16.18 ((
% 122.46/16.18 (doubleComplementEq) =>
% 122.46/16.18 ((
% 122.46/16.18 (complementTnotintersectT) =>
% 122.46/16.18 ((
% 122.46/16.18 (complementImpComplementIntersect) =>
% 122.46/16.18 ((
% 122.46/16.18 (complementSubsetComplementIntersect) =>
% 122.46/16.18 ((
% 122.46/16.18 (complementInPowersetComplementIntersect) =>
% 122.46/16.18 ((
% 122.46/16.18 (contraSubsetComplement) =>
% 122.46/16.18 ((
% 122.46/16.18 (complementTcontraSubset) =>
% 122.46/16.18 ((
% 122.46/16.18 (binunionTILcontra) =>
% 122.46/16.18 ((
% 122.46/16.18 (binunionTIRcontra) =>
% 122.46/16.18 ((
% 122.46/16.18 (inIntersectImpInUnion) =>
% 122.46/16.18 ((
% 122.46/16.18 (inIntersectImpInUnion2) =>
% 122.46/16.18 ((
% 122.46/16.18 (inIntersectImpInIntersectUnions) =>
% 122.46/16.18 ((
% 122.46/16.18 (intersectInPowersetIntersectUnions) =>
% 122.46/16.18 ((
% 122.46/16.18 (inComplementUnionImpNotIn1) =>
% 122.46/16.18 ((
% 122.46/16.18 (inComplementUnionImpInComplement1) =>
% 122.46/16.18 ((
% 122.46/16.18 (binunionTE) =>
% 122.46/16.18 ((
% 122.46/16.18 (binunionTEcontra) =>
% 122.46/16.18 ((
% 122.46/16.18 (demorgan2a1) =>
% 122.46/16.18 ((
% 122.46/16.18 (complementUnionInPowersetComplement) =>
% 122.46/16.18 ((
% 122.46/16.18 (demorgan2a2) =>
% 122.46/16.18 ((
% 122.46/16.18 (demorgan1a) =>
% 122.46/16.18 ((
% 122.46/16.18 (demorgan1b) =>
% 122.46/16.18 ((
% 122.46/16.18 (demorgan1) =>
% 122.46/16.18 ((
% 122.46/16.18 (demorgan2a) =>
% 122.46/16.18 ((
% 122.46/16.18 (demorgan2b2) =>
% 122.46/16.18 ((
% 122.46/16.18 (demorgan2b) =>
% 122.46/16.18 ((
% 122.46/16.18 (demorgan2) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz13rule0) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz13rule1) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz13rule2) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz13rule3) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz13rule4) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz1_1) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz1_2) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz1_3) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz1_4) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz1_5) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1all2) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1SetBreln1) =>
% 122.46/16.18 ((
% 122.46/16.18 (choice2fnsingleton) =>
% 122.46/16.18 ((
% 122.46/16.18 (setOfPairsIsBReln1) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1all1) =>
% 122.46/16.18 ((
% 122.46/16.18 (subbreln1) =>
% 122.46/16.18 ((
% 122.46/16.18 (eqbreln1) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1invprop) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1invI) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1invE) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1compprop) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1compI) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1compE) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1compEex) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1unionprop) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1unionIL) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1unionIR) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1unionI) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1unionE) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1unionEcases) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1unionCommutes) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz2Ex) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz2W) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz2A) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz2B) =>
% 122.46/16.18 ((
% 122.46/16.18 (image1Ex) =>
% 122.46/16.18 ((
% 122.46/16.18 (image1Ex1) =>
% 122.46/16.18 ((
% 122.46/16.18 (image1Equiv) =>
% 122.46/16.18 ((
% 122.46/16.18 (image1E) =>
% 122.46/16.18 ((
% 122.46/16.18 (image1I) =>
% 122.46/16.18 ((
% 122.46/16.18 (injFuncInInjFuncSet) =>
% 122.46/16.18 ((
% 122.46/16.18 (!!) @ (
% 122.46/16.18 (('#B') @ (
% 122.46/16.18 !!) @
% 122.46/16.18 (
% 122.46/16.18 (
% 122.46/16.18 ('#B') @ (
% 122.46/16.18 (
% 122.46/16.18 ('#B') @ (
% 122.46/16.18 !!))) @
% 122.46/16.18 (
% 122.46/16.18 (
% 122.46/16.18 ('#S') @ (
% 122.46/16.18 (
% 122.46/16.18 ('#B') @ (
% 122.46/16.18 '#S') @
% 122.46/16.18 (
% 122.46/16.18 (
% 122.46/16.18 ('#B') @ (
% 122.46/16.18 (
% 122.46/16.18 ('#B') @ (
% 122.46/16.18 '#S'))) @
% 122.46/16.18 (
% 122.46/16.18 (
% 122.46/16.18 ('#B') @ (
% 122.46/16.18 (
% 122.46/16.18 ('#B') @ (
% 122.46/16.18 (
% 122.46/16.18 ('#B') @ (
% 122.46/16.18 =>))))) @
% 122.46/16.18 (
% 122.46/16.18 (
% 122.46/16.18 ('#B') @ (
% 122.46/16.18 (
% 122.46/16.18 ('#B') @ (
% 122.46/16.18 (
% 122.46/16.18 ('#C') @ in)))) @
% 122.46/16.18 injFuncSet)))))))) @
% 122.46/16.18 (
% 122.46/16.18 (
% 122.46/16.18 ('#B') @ (
% 122.46/16.18 (
% 122.46/16.18 ('#B') @ (
% 122.46/16.18 (
% 122.46/16.18 ('#C') @ in)))) @
% 122.46/16.18 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.46/16.18 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1329])).
% 122.46/16.18 thf(zip_derived_cl1347, plain,
% 122.46/16.18 (~ (((symdiffI2) =>
% 122.46/16.18 (((symdiffIneg1) =>
% 122.46/16.18 (((symdiffIneg2) =>
% 122.46/16.18 (((secondinupair) =>
% 122.46/16.18 (((setukpairIL) =>
% 122.46/16.18 (((setukpairIR) =>
% 122.46/16.18 (((kpairiskpair) =>
% 122.46/16.18 (((kpairp) =>
% 122.46/16.18 (((singletonsubset) =>
% 122.46/16.18 (((singletoninpowerset) =>
% 122.46/16.18 (((singletoninpowunion) =>
% 122.46/16.18 (((upairset2E) =>
% 122.46/16.18 (((upairsubunion) =>
% 122.46/16.18 (((upairinpowunion) =>
% 122.46/16.18 (((ubforcartprodlem1) =>
% 122.46/16.18 (((ubforcartprodlem2) =>
% 122.46/16.18 (((ubforcartprodlem3) =>
% 122.46/16.18 (((cartprodpairin) =>
% 122.46/16.18 (((cartprodmempair1) =>
% 122.46/16.18 (((cartprodmempair) =>
% 122.46/16.18 (((setunionE2) =>
% 122.46/16.18 (((setunionsingleton1) =>
% 122.46/16.18 (((setunionsingleton2) =>
% 122.46/16.18 (((setunionsingleton) =>
% 122.46/16.18 (((singletonprop) =>
% 122.46/16.18 (((ex1E1) =>
% 122.46/16.18 (((ex1I) =>
% 122.46/16.18 (((ex1I2) =>
% 122.46/16.18 (((singletonsuniq) =>
% 122.46/16.18 (((setukpairinjL1) =>
% 122.46/16.18 ((
% 122.46/16.18 (kfstsingleton) =>
% 122.46/16.18 ((
% 122.46/16.18 (theprop) =>
% 122.46/16.18 ((
% 122.46/16.18 (kfstpairEq) =>
% 122.46/16.18 ((
% 122.46/16.18 (cartprodfstin) =>
% 122.46/16.18 ((
% 122.46/16.18 (setukpairinjL2) =>
% 122.46/16.18 ((
% 122.46/16.18 (setukpairinjL) =>
% 122.46/16.18 ((
% 122.46/16.18 (setukpairinjR11) =>
% 122.46/16.18 ((
% 122.46/16.18 (setukpairinjR12) =>
% 122.46/16.18 ((
% 122.46/16.18 (setukpairinjR1) =>
% 122.46/16.18 ((
% 122.46/16.18 (upairequniteq) =>
% 122.46/16.18 ((
% 122.46/16.18 (setukpairinjR2) =>
% 122.46/16.18 ((
% 122.46/16.18 (setukpairinjR) =>
% 122.46/16.18 ((
% 122.46/16.18 (ksndsingleton) =>
% 122.46/16.18 ((
% 122.46/16.18 (ksndpairEq) =>
% 122.46/16.18 ((
% 122.46/16.18 (kpairsurjEq) =>
% 122.46/16.18 ((
% 122.46/16.18 (cartprodsndin) =>
% 122.46/16.18 ((
% 122.46/16.18 (cartprodpairmemEL) =>
% 122.46/16.18 ((
% 122.46/16.18 (cartprodpairmemER) =>
% 122.46/16.18 ((
% 122.46/16.18 (cartprodmempaircEq) =>
% 122.46/16.18 ((
% 122.46/16.18 (cartprodfstpairEq) =>
% 122.46/16.18 ((
% 122.46/16.18 (cartprodsndpairEq) =>
% 122.46/16.18 ((
% 122.46/16.18 (cartprodpairsurjEq) =>
% 122.46/16.18 ((
% 122.46/16.18 (dpsetconstrI) =>
% 122.46/16.18 ((
% 122.46/16.18 (dpsetconstrSub) =>
% 122.46/16.18 ((
% 122.46/16.18 (setOfPairsIsBReln) =>
% 122.46/16.18 ((
% 122.46/16.18 (dpsetconstrERa) =>
% 122.46/16.18 ((
% 122.46/16.18 (dpsetconstrEL1) =>
% 122.46/16.18 ((
% 122.46/16.18 (dpsetconstrEL2) =>
% 122.46/16.18 ((
% 122.46/16.18 (dpsetconstrER) =>
% 122.46/16.18 ((
% 122.46/16.18 (funcImageSingleton) =>
% 122.46/16.18 ((
% 122.46/16.18 (apProp) =>
% 122.46/16.18 ((
% 122.46/16.18 (app) =>
% 122.46/16.18 ((
% 122.46/16.18 (infuncsetfunc) =>
% 122.46/16.18 ((
% 122.46/16.18 (ap2p) =>
% 122.46/16.18 ((
% 122.46/16.18 (funcinfuncset) =>
% 122.46/16.18 ((
% 122.46/16.18 (lamProp) =>
% 122.46/16.18 ((
% 122.46/16.18 (lamp) =>
% 122.46/16.18 ((
% 122.46/16.18 (lam2p) =>
% 122.46/16.18 ((
% 122.46/16.18 (brelnall1) =>
% 122.46/16.18 ((
% 122.46/16.18 (brelnall2) =>
% 122.46/16.18 ((
% 122.46/16.18 (ex1E2) =>
% 122.46/16.18 ((
% 122.46/16.18 (funcGraphProp1) =>
% 122.46/16.18 ((
% 122.46/16.18 (funcGraphProp3) =>
% 122.46/16.18 ((
% 122.46/16.18 (funcGraphProp2) =>
% 122.46/16.18 ((
% 122.46/16.18 (funcextLem) =>
% 122.46/16.18 ((
% 122.46/16.18 (funcGraphProp4) =>
% 122.46/16.18 ((
% 122.46/16.18 (subbreln) =>
% 122.46/16.18 ((
% 122.46/16.18 (eqbreln) =>
% 122.46/16.18 ((
% 122.46/16.18 (funcext) =>
% 122.46/16.18 ((
% 122.46/16.18 (funcext2) =>
% 122.46/16.18 ((
% 122.46/16.18 (ap2apEq1) =>
% 122.46/16.18 ((
% 122.46/16.18 (ap2apEq2) =>
% 122.46/16.18 ((
% 122.46/16.18 (beta1) =>
% 122.46/16.18 ((
% 122.46/16.18 (eta1) =>
% 122.46/16.18 ((
% 122.46/16.18 (lam2lamEq) =>
% 122.46/16.18 ((
% 122.46/16.18 (beta2) =>
% 122.46/16.18 ((
% 122.46/16.18 (eta2) =>
% 122.46/16.18 ((
% 122.46/16.18 (iffalseProp1) =>
% 122.46/16.18 ((
% 122.46/16.18 (iffalseProp2) =>
% 122.46/16.18 ((
% 122.46/16.18 (iftrueProp1) =>
% 122.46/16.18 ((
% 122.46/16.18 (iftrueProp2) =>
% 122.46/16.18 ((
% 122.46/16.18 (ifSingleton) =>
% 122.46/16.18 ((
% 122.46/16.18 (ifp) =>
% 122.46/16.18 ((
% 122.46/16.18 (theeq) =>
% 122.46/16.18 ((
% 122.46/16.18 (iftrue) =>
% 122.46/16.18 ((
% 122.46/16.18 (iffalse) =>
% 122.46/16.18 ((
% 122.46/16.18 (iftrueorfalse) =>
% 122.46/16.18 ((
% 122.46/16.18 (binintersectT_lem) =>
% 122.46/16.18 ((
% 122.46/16.18 (binunionT_lem) =>
% 122.46/16.18 ((
% 122.46/16.18 (powersetT_lem) =>
% 122.46/16.18 ((
% 122.46/16.18 (setminusT_lem) =>
% 122.46/16.18 ((
% 122.46/16.18 (complementT_lem) =>
% 122.46/16.18 ((
% 122.46/16.18 (setextT) =>
% 122.46/16.18 ((
% 122.46/16.18 (subsetTI) =>
% 122.46/16.18 ((
% 122.46/16.18 (powersetTI1) =>
% 122.46/16.18 ((
% 122.46/16.18 (powersetTE1) =>
% 122.46/16.18 ((
% 122.46/16.18 (complementTI1) =>
% 122.46/16.18 ((
% 122.46/16.18 (complementTE1) =>
% 122.46/16.18 ((
% 122.46/16.18 (binintersectTELcontra) =>
% 122.46/16.18 ((
% 122.46/16.18 (binintersectTERcontra) =>
% 122.46/16.18 ((
% 122.46/16.18 (contrasubsetT) =>
% 122.46/16.18 ((
% 122.46/16.18 (contrasubsetT1) =>
% 122.46/16.18 ((
% 122.46/16.18 (contrasubsetT2) =>
% 122.46/16.18 ((
% 122.46/16.18 (contrasubsetT3) =>
% 122.46/16.18 ((
% 122.46/16.18 (doubleComplementI1) =>
% 122.46/16.18 ((
% 122.46/16.18 (doubleComplementE1) =>
% 122.46/16.18 ((
% 122.46/16.18 (doubleComplementSub1) =>
% 122.46/16.18 ((
% 122.46/16.18 (doubleComplementSub2) =>
% 122.46/16.18 ((
% 122.46/16.18 (doubleComplementEq) =>
% 122.46/16.18 ((
% 122.46/16.18 (complementTnotintersectT) =>
% 122.46/16.18 ((
% 122.46/16.18 (complementImpComplementIntersect) =>
% 122.46/16.18 ((
% 122.46/16.18 (complementSubsetComplementIntersect) =>
% 122.46/16.18 ((
% 122.46/16.18 (complementInPowersetComplementIntersect) =>
% 122.46/16.18 ((
% 122.46/16.18 (contraSubsetComplement) =>
% 122.46/16.18 ((
% 122.46/16.18 (complementTcontraSubset) =>
% 122.46/16.18 ((
% 122.46/16.18 (binunionTILcontra) =>
% 122.46/16.18 ((
% 122.46/16.18 (binunionTIRcontra) =>
% 122.46/16.18 ((
% 122.46/16.18 (inIntersectImpInUnion) =>
% 122.46/16.18 ((
% 122.46/16.18 (inIntersectImpInUnion2) =>
% 122.46/16.18 ((
% 122.46/16.18 (inIntersectImpInIntersectUnions) =>
% 122.46/16.18 ((
% 122.46/16.18 (intersectInPowersetIntersectUnions) =>
% 122.46/16.18 ((
% 122.46/16.18 (inComplementUnionImpNotIn1) =>
% 122.46/16.18 ((
% 122.46/16.18 (inComplementUnionImpInComplement1) =>
% 122.46/16.18 ((
% 122.46/16.18 (binunionTE) =>
% 122.46/16.18 ((
% 122.46/16.18 (binunionTEcontra) =>
% 122.46/16.18 ((
% 122.46/16.18 (demorgan2a1) =>
% 122.46/16.18 ((
% 122.46/16.18 (complementUnionInPowersetComplement) =>
% 122.46/16.18 ((
% 122.46/16.18 (demorgan2a2) =>
% 122.46/16.18 ((
% 122.46/16.18 (demorgan1a) =>
% 122.46/16.18 ((
% 122.46/16.18 (demorgan1b) =>
% 122.46/16.18 ((
% 122.46/16.18 (demorgan1) =>
% 122.46/16.18 ((
% 122.46/16.18 (demorgan2a) =>
% 122.46/16.18 ((
% 122.46/16.18 (demorgan2b2) =>
% 122.46/16.18 ((
% 122.46/16.18 (demorgan2b) =>
% 122.46/16.18 ((
% 122.46/16.18 (demorgan2) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz13rule0) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz13rule1) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz13rule2) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz13rule3) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz13rule4) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz1_1) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz1_2) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz1_3) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz1_4) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz1_5) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1all2) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1SetBreln1) =>
% 122.46/16.18 ((
% 122.46/16.18 (choice2fnsingleton) =>
% 122.46/16.18 ((
% 122.46/16.18 (setOfPairsIsBReln1) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1all1) =>
% 122.46/16.18 ((
% 122.46/16.18 (subbreln1) =>
% 122.46/16.18 ((
% 122.46/16.18 (eqbreln1) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1invprop) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1invI) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1invE) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1compprop) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1compI) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1compE) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1compEex) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1unionprop) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1unionIL) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1unionIR) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1unionI) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1unionE) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1unionEcases) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1unionCommutes) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz2Ex) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz2W) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz2A) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz2B) =>
% 122.46/16.18 ((
% 122.46/16.18 (image1Ex) =>
% 122.46/16.18 ((
% 122.46/16.18 (image1Ex1) =>
% 122.46/16.18 ((
% 122.46/16.18 (image1Equiv) =>
% 122.46/16.18 ((
% 122.46/16.18 (image1E) =>
% 122.46/16.18 ((
% 122.46/16.18 (image1I) =>
% 122.46/16.18 ((
% 122.46/16.18 (injFuncInInjFuncSet) =>
% 122.46/16.18 ((
% 122.46/16.18 (!!) @ (
% 122.46/16.18 (('#B') @ (
% 122.46/16.18 !!) @
% 122.46/16.18 (
% 122.46/16.18 (
% 122.46/16.18 ('#B') @ (
% 122.46/16.18 (
% 122.46/16.18 ('#B') @ (
% 122.46/16.18 !!))) @
% 122.46/16.18 (
% 122.46/16.18 (
% 122.46/16.18 ('#S') @ (
% 122.46/16.18 (
% 122.46/16.18 ('#B') @ (
% 122.46/16.18 '#S') @
% 122.46/16.18 (
% 122.46/16.18 (
% 122.46/16.18 ('#B') @ (
% 122.46/16.18 (
% 122.46/16.18 ('#B') @ (
% 122.46/16.18 '#S'))) @
% 122.46/16.18 (
% 122.46/16.18 (
% 122.46/16.18 ('#B') @ (
% 122.46/16.18 (
% 122.46/16.18 ('#B') @ (
% 122.46/16.18 (
% 122.46/16.18 ('#B') @ (
% 122.46/16.18 =>))))) @
% 122.46/16.18 (
% 122.46/16.18 (
% 122.46/16.18 ('#B') @ (
% 122.46/16.18 (
% 122.46/16.18 ('#B') @ (
% 122.46/16.18 (
% 122.46/16.18 ('#C') @ in)))) @
% 122.46/16.18 injFuncSet)))))))) @
% 122.46/16.18 (
% 122.46/16.18 (
% 122.46/16.18 ('#B') @ (
% 122.46/16.18 (
% 122.46/16.18 ('#B') @ (
% 122.46/16.18 (
% 122.46/16.18 ('#C') @ in)))) @
% 122.46/16.18 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.46/16.18 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1338])).
% 122.46/16.18 thf(zip_derived_cl1354, plain,
% 122.46/16.18 (~ (((symdiffIneg1) =>
% 122.46/16.18 (((symdiffIneg2) =>
% 122.46/16.18 (((secondinupair) =>
% 122.46/16.18 (((setukpairIL) =>
% 122.46/16.18 (((setukpairIR) =>
% 122.46/16.18 (((kpairiskpair) =>
% 122.46/16.18 (((kpairp) =>
% 122.46/16.18 (((singletonsubset) =>
% 122.46/16.18 (((singletoninpowerset) =>
% 122.46/16.18 (((singletoninpowunion) =>
% 122.46/16.18 (((upairset2E) =>
% 122.46/16.18 (((upairsubunion) =>
% 122.46/16.18 (((upairinpowunion) =>
% 122.46/16.18 (((ubforcartprodlem1) =>
% 122.46/16.18 (((ubforcartprodlem2) =>
% 122.46/16.18 (((ubforcartprodlem3) =>
% 122.46/16.18 (((cartprodpairin) =>
% 122.46/16.18 (((cartprodmempair1) =>
% 122.46/16.18 (((cartprodmempair) =>
% 122.46/16.18 (((setunionE2) =>
% 122.46/16.18 (((setunionsingleton1) =>
% 122.46/16.18 (((setunionsingleton2) =>
% 122.46/16.18 (((setunionsingleton) =>
% 122.46/16.18 (((singletonprop) =>
% 122.46/16.18 (((ex1E1) =>
% 122.46/16.18 (((ex1I) =>
% 122.46/16.18 (((ex1I2) =>
% 122.46/16.18 (((singletonsuniq) =>
% 122.46/16.18 (((setukpairinjL1) =>
% 122.46/16.18 (((kfstsingleton) =>
% 122.46/16.18 ((
% 122.46/16.18 (theprop) =>
% 122.46/16.18 ((
% 122.46/16.18 (kfstpairEq) =>
% 122.46/16.18 ((
% 122.46/16.18 (cartprodfstin) =>
% 122.46/16.18 ((
% 122.46/16.18 (setukpairinjL2) =>
% 122.46/16.18 ((
% 122.46/16.18 (setukpairinjL) =>
% 122.46/16.18 ((
% 122.46/16.18 (setukpairinjR11) =>
% 122.46/16.18 ((
% 122.46/16.18 (setukpairinjR12) =>
% 122.46/16.18 ((
% 122.46/16.18 (setukpairinjR1) =>
% 122.46/16.18 ((
% 122.46/16.18 (upairequniteq) =>
% 122.46/16.18 ((
% 122.46/16.18 (setukpairinjR2) =>
% 122.46/16.18 ((
% 122.46/16.18 (setukpairinjR) =>
% 122.46/16.18 ((
% 122.46/16.18 (ksndsingleton) =>
% 122.46/16.18 ((
% 122.46/16.18 (ksndpairEq) =>
% 122.46/16.18 ((
% 122.46/16.18 (kpairsurjEq) =>
% 122.46/16.18 ((
% 122.46/16.18 (cartprodsndin) =>
% 122.46/16.18 ((
% 122.46/16.18 (cartprodpairmemEL) =>
% 122.46/16.18 ((
% 122.46/16.18 (cartprodpairmemER) =>
% 122.46/16.18 ((
% 122.46/16.18 (cartprodmempaircEq) =>
% 122.46/16.18 ((
% 122.46/16.18 (cartprodfstpairEq) =>
% 122.46/16.18 ((
% 122.46/16.18 (cartprodsndpairEq) =>
% 122.46/16.18 ((
% 122.46/16.18 (cartprodpairsurjEq) =>
% 122.46/16.18 ((
% 122.46/16.18 (dpsetconstrI) =>
% 122.46/16.18 ((
% 122.46/16.18 (dpsetconstrSub) =>
% 122.46/16.18 ((
% 122.46/16.18 (setOfPairsIsBReln) =>
% 122.46/16.18 ((
% 122.46/16.18 (dpsetconstrERa) =>
% 122.46/16.18 ((
% 122.46/16.18 (dpsetconstrEL1) =>
% 122.46/16.18 ((
% 122.46/16.18 (dpsetconstrEL2) =>
% 122.46/16.18 ((
% 122.46/16.18 (dpsetconstrER) =>
% 122.46/16.18 ((
% 122.46/16.18 (funcImageSingleton) =>
% 122.46/16.18 ((
% 122.46/16.18 (apProp) =>
% 122.46/16.18 ((
% 122.46/16.18 (app) =>
% 122.46/16.18 ((
% 122.46/16.18 (infuncsetfunc) =>
% 122.46/16.18 ((
% 122.46/16.18 (ap2p) =>
% 122.46/16.18 ((
% 122.46/16.18 (funcinfuncset) =>
% 122.46/16.18 ((
% 122.46/16.18 (lamProp) =>
% 122.46/16.18 ((
% 122.46/16.18 (lamp) =>
% 122.46/16.18 ((
% 122.46/16.18 (lam2p) =>
% 122.46/16.18 ((
% 122.46/16.18 (brelnall1) =>
% 122.46/16.18 ((
% 122.46/16.18 (brelnall2) =>
% 122.46/16.18 ((
% 122.46/16.18 (ex1E2) =>
% 122.46/16.18 ((
% 122.46/16.18 (funcGraphProp1) =>
% 122.46/16.18 ((
% 122.46/16.18 (funcGraphProp3) =>
% 122.46/16.18 ((
% 122.46/16.18 (funcGraphProp2) =>
% 122.46/16.18 ((
% 122.46/16.18 (funcextLem) =>
% 122.46/16.18 ((
% 122.46/16.18 (funcGraphProp4) =>
% 122.46/16.18 ((
% 122.46/16.18 (subbreln) =>
% 122.46/16.18 ((
% 122.46/16.18 (eqbreln) =>
% 122.46/16.18 ((
% 122.46/16.18 (funcext) =>
% 122.46/16.18 ((
% 122.46/16.18 (funcext2) =>
% 122.46/16.18 ((
% 122.46/16.18 (ap2apEq1) =>
% 122.46/16.18 ((
% 122.46/16.18 (ap2apEq2) =>
% 122.46/16.18 ((
% 122.46/16.18 (beta1) =>
% 122.46/16.18 ((
% 122.46/16.18 (eta1) =>
% 122.46/16.18 ((
% 122.46/16.18 (lam2lamEq) =>
% 122.46/16.18 ((
% 122.46/16.18 (beta2) =>
% 122.46/16.18 ((
% 122.46/16.18 (eta2) =>
% 122.46/16.18 ((
% 122.46/16.18 (iffalseProp1) =>
% 122.46/16.18 ((
% 122.46/16.18 (iffalseProp2) =>
% 122.46/16.18 ((
% 122.46/16.18 (iftrueProp1) =>
% 122.46/16.18 ((
% 122.46/16.18 (iftrueProp2) =>
% 122.46/16.18 ((
% 122.46/16.18 (ifSingleton) =>
% 122.46/16.18 ((
% 122.46/16.18 (ifp) =>
% 122.46/16.18 ((
% 122.46/16.18 (theeq) =>
% 122.46/16.18 ((
% 122.46/16.18 (iftrue) =>
% 122.46/16.18 ((
% 122.46/16.18 (iffalse) =>
% 122.46/16.18 ((
% 122.46/16.18 (iftrueorfalse) =>
% 122.46/16.18 ((
% 122.46/16.18 (binintersectT_lem) =>
% 122.46/16.18 ((
% 122.46/16.18 (binunionT_lem) =>
% 122.46/16.18 ((
% 122.46/16.18 (powersetT_lem) =>
% 122.46/16.18 ((
% 122.46/16.18 (setminusT_lem) =>
% 122.46/16.18 ((
% 122.46/16.18 (complementT_lem) =>
% 122.46/16.18 ((
% 122.46/16.18 (setextT) =>
% 122.46/16.18 ((
% 122.46/16.18 (subsetTI) =>
% 122.46/16.18 ((
% 122.46/16.18 (powersetTI1) =>
% 122.46/16.18 ((
% 122.46/16.18 (powersetTE1) =>
% 122.46/16.18 ((
% 122.46/16.18 (complementTI1) =>
% 122.46/16.18 ((
% 122.46/16.18 (complementTE1) =>
% 122.46/16.18 ((
% 122.46/16.18 (binintersectTELcontra) =>
% 122.46/16.18 ((
% 122.46/16.18 (binintersectTERcontra) =>
% 122.46/16.18 ((
% 122.46/16.18 (contrasubsetT) =>
% 122.46/16.18 ((
% 122.46/16.18 (contrasubsetT1) =>
% 122.46/16.18 ((
% 122.46/16.18 (contrasubsetT2) =>
% 122.46/16.18 ((
% 122.46/16.18 (contrasubsetT3) =>
% 122.46/16.18 ((
% 122.46/16.18 (doubleComplementI1) =>
% 122.46/16.18 ((
% 122.46/16.18 (doubleComplementE1) =>
% 122.46/16.18 ((
% 122.46/16.18 (doubleComplementSub1) =>
% 122.46/16.18 ((
% 122.46/16.18 (doubleComplementSub2) =>
% 122.46/16.18 ((
% 122.46/16.18 (doubleComplementEq) =>
% 122.46/16.18 ((
% 122.46/16.18 (complementTnotintersectT) =>
% 122.46/16.18 ((
% 122.46/16.18 (complementImpComplementIntersect) =>
% 122.46/16.18 ((
% 122.46/16.18 (complementSubsetComplementIntersect) =>
% 122.46/16.18 ((
% 122.46/16.18 (complementInPowersetComplementIntersect) =>
% 122.46/16.18 ((
% 122.46/16.18 (contraSubsetComplement) =>
% 122.46/16.18 ((
% 122.46/16.18 (complementTcontraSubset) =>
% 122.46/16.18 ((
% 122.46/16.18 (binunionTILcontra) =>
% 122.46/16.18 ((
% 122.46/16.18 (binunionTIRcontra) =>
% 122.46/16.18 ((
% 122.46/16.18 (inIntersectImpInUnion) =>
% 122.46/16.18 ((
% 122.46/16.18 (inIntersectImpInUnion2) =>
% 122.46/16.18 ((
% 122.46/16.18 (inIntersectImpInIntersectUnions) =>
% 122.46/16.18 ((
% 122.46/16.18 (intersectInPowersetIntersectUnions) =>
% 122.46/16.18 ((
% 122.46/16.18 (inComplementUnionImpNotIn1) =>
% 122.46/16.18 ((
% 122.46/16.18 (inComplementUnionImpInComplement1) =>
% 122.46/16.18 ((
% 122.46/16.18 (binunionTE) =>
% 122.46/16.18 ((
% 122.46/16.18 (binunionTEcontra) =>
% 122.46/16.18 ((
% 122.46/16.18 (demorgan2a1) =>
% 122.46/16.18 ((
% 122.46/16.18 (complementUnionInPowersetComplement) =>
% 122.46/16.18 ((
% 122.46/16.18 (demorgan2a2) =>
% 122.46/16.18 ((
% 122.46/16.18 (demorgan1a) =>
% 122.46/16.18 ((
% 122.46/16.18 (demorgan1b) =>
% 122.46/16.18 ((
% 122.46/16.18 (demorgan1) =>
% 122.46/16.18 ((
% 122.46/16.18 (demorgan2a) =>
% 122.46/16.18 ((
% 122.46/16.18 (demorgan2b2) =>
% 122.46/16.18 ((
% 122.46/16.18 (demorgan2b) =>
% 122.46/16.18 ((
% 122.46/16.18 (demorgan2) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz13rule0) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz13rule1) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz13rule2) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz13rule3) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz13rule4) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz1_1) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz1_2) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz1_3) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz1_4) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz1_5) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1all2) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1SetBreln1) =>
% 122.46/16.18 ((
% 122.46/16.18 (choice2fnsingleton) =>
% 122.46/16.18 ((
% 122.46/16.18 (setOfPairsIsBReln1) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1all1) =>
% 122.46/16.18 ((
% 122.46/16.18 (subbreln1) =>
% 122.46/16.18 ((
% 122.46/16.18 (eqbreln1) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1invprop) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1invI) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1invE) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1compprop) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1compI) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1compE) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1compEex) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1unionprop) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1unionIL) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1unionIR) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1unionI) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1unionE) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1unionEcases) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1unionCommutes) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz2Ex) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz2W) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz2A) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz2B) =>
% 122.46/16.18 ((
% 122.46/16.18 (image1Ex) =>
% 122.46/16.18 ((
% 122.46/16.18 (image1Ex1) =>
% 122.46/16.18 ((
% 122.46/16.18 (image1Equiv) =>
% 122.46/16.18 ((
% 122.46/16.18 (image1E) =>
% 122.46/16.18 ((
% 122.46/16.18 (image1I) =>
% 122.46/16.18 ((
% 122.46/16.18 (injFuncInInjFuncSet) =>
% 122.46/16.18 ((
% 122.46/16.18 (!!) @ (
% 122.46/16.18 (('#B') @ (
% 122.46/16.18 !!) @
% 122.46/16.18 (
% 122.46/16.18 (
% 122.46/16.18 ('#B') @ (
% 122.46/16.18 (
% 122.46/16.18 ('#B') @ (
% 122.46/16.18 !!))) @
% 122.46/16.18 (
% 122.46/16.18 (
% 122.46/16.18 ('#S') @ (
% 122.46/16.18 (
% 122.46/16.18 ('#B') @ (
% 122.46/16.18 '#S') @
% 122.46/16.18 (
% 122.46/16.18 (
% 122.46/16.18 ('#B') @ (
% 122.46/16.18 (
% 122.46/16.18 ('#B') @ (
% 122.46/16.18 '#S'))) @
% 122.46/16.18 (
% 122.46/16.18 (
% 122.46/16.18 ('#B') @ (
% 122.46/16.18 (
% 122.46/16.18 ('#B') @ (
% 122.46/16.18 (
% 122.46/16.18 ('#B') @ (
% 122.46/16.18 =>))))) @
% 122.46/16.18 (
% 122.46/16.18 (
% 122.46/16.18 ('#B') @ (
% 122.46/16.18 (
% 122.46/16.18 ('#B') @ (
% 122.46/16.18 (
% 122.46/16.18 ('#C') @ in)))) @
% 122.46/16.18 injFuncSet)))))))) @
% 122.46/16.18 (
% 122.46/16.18 (
% 122.46/16.18 ('#B') @ (
% 122.46/16.18 (
% 122.46/16.18 ('#B') @ (
% 122.46/16.18 (
% 122.46/16.18 ('#C') @ in)))) @
% 122.46/16.18 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.46/16.18 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1347])).
% 122.46/16.18 thf(zip_derived_cl1361, plain,
% 122.46/16.18 (~ (((symdiffIneg2) =>
% 122.46/16.18 (((secondinupair) =>
% 122.46/16.18 (((setukpairIL) =>
% 122.46/16.18 (((setukpairIR) =>
% 122.46/16.18 (((kpairiskpair) =>
% 122.46/16.18 (((kpairp) =>
% 122.46/16.18 (((singletonsubset) =>
% 122.46/16.18 (((singletoninpowerset) =>
% 122.46/16.18 (((singletoninpowunion) =>
% 122.46/16.18 (((upairset2E) =>
% 122.46/16.18 (((upairsubunion) =>
% 122.46/16.18 (((upairinpowunion) =>
% 122.46/16.18 (((ubforcartprodlem1) =>
% 122.46/16.18 (((ubforcartprodlem2) =>
% 122.46/16.18 (((ubforcartprodlem3) =>
% 122.46/16.18 (((cartprodpairin) =>
% 122.46/16.18 (((cartprodmempair1) =>
% 122.46/16.18 (((cartprodmempair) =>
% 122.46/16.18 (((setunionE2) =>
% 122.46/16.18 (((setunionsingleton1) =>
% 122.46/16.18 (((setunionsingleton2) =>
% 122.46/16.18 (((setunionsingleton) =>
% 122.46/16.18 (((singletonprop) =>
% 122.46/16.18 (((ex1E1) =>
% 122.46/16.18 (((ex1I) =>
% 122.46/16.18 (((ex1I2) =>
% 122.46/16.18 (((singletonsuniq) =>
% 122.46/16.18 (((setukpairinjL1) =>
% 122.46/16.18 (((kfstsingleton) =>
% 122.46/16.18 (((theprop) =>
% 122.46/16.18 ((
% 122.46/16.18 (kfstpairEq) =>
% 122.46/16.18 ((
% 122.46/16.18 (cartprodfstin) =>
% 122.46/16.18 ((
% 122.46/16.18 (setukpairinjL2) =>
% 122.46/16.18 ((
% 122.46/16.18 (setukpairinjL) =>
% 122.46/16.18 ((
% 122.46/16.18 (setukpairinjR11) =>
% 122.46/16.18 ((
% 122.46/16.18 (setukpairinjR12) =>
% 122.46/16.18 ((
% 122.46/16.18 (setukpairinjR1) =>
% 122.46/16.18 ((
% 122.46/16.18 (upairequniteq) =>
% 122.46/16.18 ((
% 122.46/16.18 (setukpairinjR2) =>
% 122.46/16.18 ((
% 122.46/16.18 (setukpairinjR) =>
% 122.46/16.18 ((
% 122.46/16.18 (ksndsingleton) =>
% 122.46/16.18 ((
% 122.46/16.18 (ksndpairEq) =>
% 122.46/16.18 ((
% 122.46/16.18 (kpairsurjEq) =>
% 122.46/16.18 ((
% 122.46/16.18 (cartprodsndin) =>
% 122.46/16.18 ((
% 122.46/16.18 (cartprodpairmemEL) =>
% 122.46/16.18 ((
% 122.46/16.18 (cartprodpairmemER) =>
% 122.46/16.18 ((
% 122.46/16.18 (cartprodmempaircEq) =>
% 122.46/16.18 ((
% 122.46/16.18 (cartprodfstpairEq) =>
% 122.46/16.18 ((
% 122.46/16.18 (cartprodsndpairEq) =>
% 122.46/16.18 ((
% 122.46/16.18 (cartprodpairsurjEq) =>
% 122.46/16.18 ((
% 122.46/16.18 (dpsetconstrI) =>
% 122.46/16.18 ((
% 122.46/16.18 (dpsetconstrSub) =>
% 122.46/16.18 ((
% 122.46/16.18 (setOfPairsIsBReln) =>
% 122.46/16.18 ((
% 122.46/16.18 (dpsetconstrERa) =>
% 122.46/16.18 ((
% 122.46/16.18 (dpsetconstrEL1) =>
% 122.46/16.18 ((
% 122.46/16.18 (dpsetconstrEL2) =>
% 122.46/16.18 ((
% 122.46/16.18 (dpsetconstrER) =>
% 122.46/16.18 ((
% 122.46/16.18 (funcImageSingleton) =>
% 122.46/16.18 ((
% 122.46/16.18 (apProp) =>
% 122.46/16.18 ((
% 122.46/16.18 (app) =>
% 122.46/16.18 ((
% 122.46/16.18 (infuncsetfunc) =>
% 122.46/16.18 ((
% 122.46/16.18 (ap2p) =>
% 122.46/16.18 ((
% 122.46/16.18 (funcinfuncset) =>
% 122.46/16.18 ((
% 122.46/16.18 (lamProp) =>
% 122.46/16.18 ((
% 122.46/16.18 (lamp) =>
% 122.46/16.18 ((
% 122.46/16.18 (lam2p) =>
% 122.46/16.18 ((
% 122.46/16.18 (brelnall1) =>
% 122.46/16.18 ((
% 122.46/16.18 (brelnall2) =>
% 122.46/16.18 ((
% 122.46/16.18 (ex1E2) =>
% 122.46/16.18 ((
% 122.46/16.18 (funcGraphProp1) =>
% 122.46/16.18 ((
% 122.46/16.18 (funcGraphProp3) =>
% 122.46/16.18 ((
% 122.46/16.18 (funcGraphProp2) =>
% 122.46/16.18 ((
% 122.46/16.18 (funcextLem) =>
% 122.46/16.18 ((
% 122.46/16.18 (funcGraphProp4) =>
% 122.46/16.18 ((
% 122.46/16.18 (subbreln) =>
% 122.46/16.18 ((
% 122.46/16.18 (eqbreln) =>
% 122.46/16.18 ((
% 122.46/16.18 (funcext) =>
% 122.46/16.18 ((
% 122.46/16.18 (funcext2) =>
% 122.46/16.18 ((
% 122.46/16.18 (ap2apEq1) =>
% 122.46/16.18 ((
% 122.46/16.18 (ap2apEq2) =>
% 122.46/16.18 ((
% 122.46/16.18 (beta1) =>
% 122.46/16.18 ((
% 122.46/16.18 (eta1) =>
% 122.46/16.18 ((
% 122.46/16.18 (lam2lamEq) =>
% 122.46/16.18 ((
% 122.46/16.18 (beta2) =>
% 122.46/16.18 ((
% 122.46/16.18 (eta2) =>
% 122.46/16.18 ((
% 122.46/16.18 (iffalseProp1) =>
% 122.46/16.18 ((
% 122.46/16.18 (iffalseProp2) =>
% 122.46/16.18 ((
% 122.46/16.18 (iftrueProp1) =>
% 122.46/16.18 ((
% 122.46/16.18 (iftrueProp2) =>
% 122.46/16.18 ((
% 122.46/16.18 (ifSingleton) =>
% 122.46/16.18 ((
% 122.46/16.18 (ifp) =>
% 122.46/16.18 ((
% 122.46/16.18 (theeq) =>
% 122.46/16.18 ((
% 122.46/16.18 (iftrue) =>
% 122.46/16.18 ((
% 122.46/16.18 (iffalse) =>
% 122.46/16.18 ((
% 122.46/16.18 (iftrueorfalse) =>
% 122.46/16.18 ((
% 122.46/16.18 (binintersectT_lem) =>
% 122.46/16.18 ((
% 122.46/16.18 (binunionT_lem) =>
% 122.46/16.18 ((
% 122.46/16.18 (powersetT_lem) =>
% 122.46/16.18 ((
% 122.46/16.18 (setminusT_lem) =>
% 122.46/16.18 ((
% 122.46/16.18 (complementT_lem) =>
% 122.46/16.18 ((
% 122.46/16.18 (setextT) =>
% 122.46/16.18 ((
% 122.46/16.18 (subsetTI) =>
% 122.46/16.18 ((
% 122.46/16.18 (powersetTI1) =>
% 122.46/16.18 ((
% 122.46/16.18 (powersetTE1) =>
% 122.46/16.18 ((
% 122.46/16.18 (complementTI1) =>
% 122.46/16.18 ((
% 122.46/16.18 (complementTE1) =>
% 122.46/16.18 ((
% 122.46/16.18 (binintersectTELcontra) =>
% 122.46/16.18 ((
% 122.46/16.18 (binintersectTERcontra) =>
% 122.46/16.18 ((
% 122.46/16.18 (contrasubsetT) =>
% 122.46/16.18 ((
% 122.46/16.18 (contrasubsetT1) =>
% 122.46/16.18 ((
% 122.46/16.18 (contrasubsetT2) =>
% 122.46/16.18 ((
% 122.46/16.18 (contrasubsetT3) =>
% 122.46/16.18 ((
% 122.46/16.18 (doubleComplementI1) =>
% 122.46/16.18 ((
% 122.46/16.18 (doubleComplementE1) =>
% 122.46/16.18 ((
% 122.46/16.18 (doubleComplementSub1) =>
% 122.46/16.18 ((
% 122.46/16.18 (doubleComplementSub2) =>
% 122.46/16.18 ((
% 122.46/16.18 (doubleComplementEq) =>
% 122.46/16.18 ((
% 122.46/16.18 (complementTnotintersectT) =>
% 122.46/16.18 ((
% 122.46/16.18 (complementImpComplementIntersect) =>
% 122.46/16.18 ((
% 122.46/16.18 (complementSubsetComplementIntersect) =>
% 122.46/16.18 ((
% 122.46/16.18 (complementInPowersetComplementIntersect) =>
% 122.46/16.18 ((
% 122.46/16.18 (contraSubsetComplement) =>
% 122.46/16.18 ((
% 122.46/16.18 (complementTcontraSubset) =>
% 122.46/16.18 ((
% 122.46/16.18 (binunionTILcontra) =>
% 122.46/16.18 ((
% 122.46/16.18 (binunionTIRcontra) =>
% 122.46/16.18 ((
% 122.46/16.18 (inIntersectImpInUnion) =>
% 122.46/16.18 ((
% 122.46/16.18 (inIntersectImpInUnion2) =>
% 122.46/16.18 ((
% 122.46/16.18 (inIntersectImpInIntersectUnions) =>
% 122.46/16.18 ((
% 122.46/16.18 (intersectInPowersetIntersectUnions) =>
% 122.46/16.18 ((
% 122.46/16.18 (inComplementUnionImpNotIn1) =>
% 122.46/16.18 ((
% 122.46/16.18 (inComplementUnionImpInComplement1) =>
% 122.46/16.18 ((
% 122.46/16.18 (binunionTE) =>
% 122.46/16.18 ((
% 122.46/16.18 (binunionTEcontra) =>
% 122.46/16.18 ((
% 122.46/16.18 (demorgan2a1) =>
% 122.46/16.18 ((
% 122.46/16.18 (complementUnionInPowersetComplement) =>
% 122.46/16.18 ((
% 122.46/16.18 (demorgan2a2) =>
% 122.46/16.18 ((
% 122.46/16.18 (demorgan1a) =>
% 122.46/16.18 ((
% 122.46/16.18 (demorgan1b) =>
% 122.46/16.18 ((
% 122.46/16.18 (demorgan1) =>
% 122.46/16.18 ((
% 122.46/16.18 (demorgan2a) =>
% 122.46/16.18 ((
% 122.46/16.18 (demorgan2b2) =>
% 122.46/16.18 ((
% 122.46/16.18 (demorgan2b) =>
% 122.46/16.18 ((
% 122.46/16.18 (demorgan2) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz13rule0) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz13rule1) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz13rule2) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz13rule3) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz13rule4) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz1_1) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz1_2) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz1_3) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz1_4) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz1_5) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1all2) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1SetBreln1) =>
% 122.46/16.18 ((
% 122.46/16.18 (choice2fnsingleton) =>
% 122.46/16.18 ((
% 122.46/16.18 (setOfPairsIsBReln1) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1all1) =>
% 122.46/16.18 ((
% 122.46/16.18 (subbreln1) =>
% 122.46/16.18 ((
% 122.46/16.18 (eqbreln1) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1invprop) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1invI) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1invE) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1compprop) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1compI) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1compE) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1compEex) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1unionprop) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1unionIL) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1unionIR) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1unionI) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1unionE) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1unionEcases) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1unionCommutes) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz2Ex) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz2W) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz2A) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz2B) =>
% 122.46/16.18 ((
% 122.46/16.18 (image1Ex) =>
% 122.46/16.18 ((
% 122.46/16.18 (image1Ex1) =>
% 122.46/16.18 ((
% 122.46/16.18 (image1Equiv) =>
% 122.46/16.18 ((
% 122.46/16.18 (image1E) =>
% 122.46/16.18 ((
% 122.46/16.18 (image1I) =>
% 122.46/16.18 ((
% 122.46/16.18 (injFuncInInjFuncSet) =>
% 122.46/16.18 ((
% 122.46/16.18 (!!) @ (
% 122.46/16.18 (('#B') @ (
% 122.46/16.18 !!) @
% 122.46/16.18 (
% 122.46/16.18 (
% 122.46/16.18 ('#B') @ (
% 122.46/16.18 (
% 122.46/16.18 ('#B') @ (
% 122.46/16.18 !!))) @
% 122.46/16.18 (
% 122.46/16.18 (
% 122.46/16.18 ('#S') @ (
% 122.46/16.18 (
% 122.46/16.18 ('#B') @ (
% 122.46/16.18 '#S') @
% 122.46/16.18 (
% 122.46/16.18 (
% 122.46/16.18 ('#B') @ (
% 122.46/16.18 (
% 122.46/16.18 ('#B') @ (
% 122.46/16.18 '#S'))) @
% 122.46/16.18 (
% 122.46/16.18 (
% 122.46/16.18 ('#B') @ (
% 122.46/16.18 (
% 122.46/16.18 ('#B') @ (
% 122.46/16.18 (
% 122.46/16.18 ('#B') @ (
% 122.46/16.18 =>))))) @
% 122.46/16.18 (
% 122.46/16.18 (
% 122.46/16.18 ('#B') @ (
% 122.46/16.18 (
% 122.46/16.18 ('#B') @ (
% 122.46/16.18 (
% 122.46/16.18 ('#C') @ in)))) @
% 122.46/16.18 injFuncSet)))))))) @
% 122.46/16.18 (
% 122.46/16.18 (
% 122.46/16.18 ('#B') @ (
% 122.46/16.18 (
% 122.46/16.18 ('#B') @ (
% 122.46/16.18 (
% 122.46/16.18 ('#C') @ in)))) @
% 122.46/16.18 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.46/16.18 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1354])).
% 122.46/16.18 thf(zip_derived_cl1369, plain,
% 122.46/16.18 (~ (((secondinupair) =>
% 122.46/16.18 (((setukpairIL) =>
% 122.46/16.18 (((setukpairIR) =>
% 122.46/16.18 (((kpairiskpair) =>
% 122.46/16.18 (((kpairp) =>
% 122.46/16.18 (((singletonsubset) =>
% 122.46/16.18 (((singletoninpowerset) =>
% 122.46/16.18 (((singletoninpowunion) =>
% 122.46/16.18 (((upairset2E) =>
% 122.46/16.18 (((upairsubunion) =>
% 122.46/16.18 (((upairinpowunion) =>
% 122.46/16.18 (((ubforcartprodlem1) =>
% 122.46/16.18 (((ubforcartprodlem2) =>
% 122.46/16.18 (((ubforcartprodlem3) =>
% 122.46/16.18 (((cartprodpairin) =>
% 122.46/16.18 (((cartprodmempair1) =>
% 122.46/16.18 (((cartprodmempair) =>
% 122.46/16.18 (((setunionE2) =>
% 122.46/16.18 (((setunionsingleton1) =>
% 122.46/16.18 (((setunionsingleton2) =>
% 122.46/16.18 (((setunionsingleton) =>
% 122.46/16.18 (((singletonprop) =>
% 122.46/16.18 (((ex1E1) =>
% 122.46/16.18 (((ex1I) =>
% 122.46/16.18 (((ex1I2) =>
% 122.46/16.18 (((singletonsuniq) =>
% 122.46/16.18 (((setukpairinjL1) =>
% 122.46/16.18 (((kfstsingleton) =>
% 122.46/16.18 (((theprop) =>
% 122.46/16.18 (((kfstpairEq) =>
% 122.46/16.18 ((
% 122.46/16.18 (cartprodfstin) =>
% 122.46/16.18 ((
% 122.46/16.18 (setukpairinjL2) =>
% 122.46/16.18 ((
% 122.46/16.18 (setukpairinjL) =>
% 122.46/16.18 ((
% 122.46/16.18 (setukpairinjR11) =>
% 122.46/16.18 ((
% 122.46/16.18 (setukpairinjR12) =>
% 122.46/16.18 ((
% 122.46/16.18 (setukpairinjR1) =>
% 122.46/16.18 ((
% 122.46/16.18 (upairequniteq) =>
% 122.46/16.18 ((
% 122.46/16.18 (setukpairinjR2) =>
% 122.46/16.18 ((
% 122.46/16.18 (setukpairinjR) =>
% 122.46/16.18 ((
% 122.46/16.18 (ksndsingleton) =>
% 122.46/16.18 ((
% 122.46/16.18 (ksndpairEq) =>
% 122.46/16.18 ((
% 122.46/16.18 (kpairsurjEq) =>
% 122.46/16.18 ((
% 122.46/16.18 (cartprodsndin) =>
% 122.46/16.18 ((
% 122.46/16.18 (cartprodpairmemEL) =>
% 122.46/16.18 ((
% 122.46/16.18 (cartprodpairmemER) =>
% 122.46/16.18 ((
% 122.46/16.18 (cartprodmempaircEq) =>
% 122.46/16.18 ((
% 122.46/16.18 (cartprodfstpairEq) =>
% 122.46/16.18 ((
% 122.46/16.18 (cartprodsndpairEq) =>
% 122.46/16.18 ((
% 122.46/16.18 (cartprodpairsurjEq) =>
% 122.46/16.18 ((
% 122.46/16.18 (dpsetconstrI) =>
% 122.46/16.18 ((
% 122.46/16.18 (dpsetconstrSub) =>
% 122.46/16.18 ((
% 122.46/16.18 (setOfPairsIsBReln) =>
% 122.46/16.18 ((
% 122.46/16.18 (dpsetconstrERa) =>
% 122.46/16.18 ((
% 122.46/16.18 (dpsetconstrEL1) =>
% 122.46/16.18 ((
% 122.46/16.18 (dpsetconstrEL2) =>
% 122.46/16.18 ((
% 122.46/16.18 (dpsetconstrER) =>
% 122.46/16.18 ((
% 122.46/16.18 (funcImageSingleton) =>
% 122.46/16.18 ((
% 122.46/16.18 (apProp) =>
% 122.46/16.18 ((
% 122.46/16.18 (app) =>
% 122.46/16.18 ((
% 122.46/16.18 (infuncsetfunc) =>
% 122.46/16.18 ((
% 122.46/16.18 (ap2p) =>
% 122.46/16.18 ((
% 122.46/16.18 (funcinfuncset) =>
% 122.46/16.18 ((
% 122.46/16.18 (lamProp) =>
% 122.46/16.18 ((
% 122.46/16.18 (lamp) =>
% 122.46/16.18 ((
% 122.46/16.18 (lam2p) =>
% 122.46/16.18 ((
% 122.46/16.18 (brelnall1) =>
% 122.46/16.18 ((
% 122.46/16.18 (brelnall2) =>
% 122.46/16.18 ((
% 122.46/16.18 (ex1E2) =>
% 122.46/16.18 ((
% 122.46/16.18 (funcGraphProp1) =>
% 122.46/16.18 ((
% 122.46/16.18 (funcGraphProp3) =>
% 122.46/16.18 ((
% 122.46/16.18 (funcGraphProp2) =>
% 122.46/16.18 ((
% 122.46/16.18 (funcextLem) =>
% 122.46/16.18 ((
% 122.46/16.18 (funcGraphProp4) =>
% 122.46/16.18 ((
% 122.46/16.18 (subbreln) =>
% 122.46/16.18 ((
% 122.46/16.18 (eqbreln) =>
% 122.46/16.18 ((
% 122.46/16.18 (funcext) =>
% 122.46/16.18 ((
% 122.46/16.18 (funcext2) =>
% 122.46/16.18 ((
% 122.46/16.18 (ap2apEq1) =>
% 122.46/16.18 ((
% 122.46/16.18 (ap2apEq2) =>
% 122.46/16.18 ((
% 122.46/16.18 (beta1) =>
% 122.46/16.18 ((
% 122.46/16.18 (eta1) =>
% 122.46/16.18 ((
% 122.46/16.18 (lam2lamEq) =>
% 122.46/16.18 ((
% 122.46/16.18 (beta2) =>
% 122.46/16.18 ((
% 122.46/16.18 (eta2) =>
% 122.46/16.18 ((
% 122.46/16.18 (iffalseProp1) =>
% 122.46/16.18 ((
% 122.46/16.18 (iffalseProp2) =>
% 122.46/16.18 ((
% 122.46/16.18 (iftrueProp1) =>
% 122.46/16.18 ((
% 122.46/16.18 (iftrueProp2) =>
% 122.46/16.18 ((
% 122.46/16.18 (ifSingleton) =>
% 122.46/16.18 ((
% 122.46/16.18 (ifp) =>
% 122.46/16.18 ((
% 122.46/16.18 (theeq) =>
% 122.46/16.18 ((
% 122.46/16.18 (iftrue) =>
% 122.46/16.18 ((
% 122.46/16.18 (iffalse) =>
% 122.46/16.18 ((
% 122.46/16.18 (iftrueorfalse) =>
% 122.46/16.18 ((
% 122.46/16.18 (binintersectT_lem) =>
% 122.46/16.18 ((
% 122.46/16.18 (binunionT_lem) =>
% 122.46/16.18 ((
% 122.46/16.18 (powersetT_lem) =>
% 122.46/16.18 ((
% 122.46/16.18 (setminusT_lem) =>
% 122.46/16.18 ((
% 122.46/16.18 (complementT_lem) =>
% 122.46/16.18 ((
% 122.46/16.18 (setextT) =>
% 122.46/16.18 ((
% 122.46/16.18 (subsetTI) =>
% 122.46/16.18 ((
% 122.46/16.18 (powersetTI1) =>
% 122.46/16.18 ((
% 122.46/16.18 (powersetTE1) =>
% 122.46/16.18 ((
% 122.46/16.18 (complementTI1) =>
% 122.46/16.18 ((
% 122.46/16.18 (complementTE1) =>
% 122.46/16.18 ((
% 122.46/16.18 (binintersectTELcontra) =>
% 122.46/16.18 ((
% 122.46/16.18 (binintersectTERcontra) =>
% 122.46/16.18 ((
% 122.46/16.18 (contrasubsetT) =>
% 122.46/16.18 ((
% 122.46/16.18 (contrasubsetT1) =>
% 122.46/16.18 ((
% 122.46/16.18 (contrasubsetT2) =>
% 122.46/16.18 ((
% 122.46/16.18 (contrasubsetT3) =>
% 122.46/16.18 ((
% 122.46/16.18 (doubleComplementI1) =>
% 122.46/16.18 ((
% 122.46/16.18 (doubleComplementE1) =>
% 122.46/16.18 ((
% 122.46/16.18 (doubleComplementSub1) =>
% 122.46/16.18 ((
% 122.46/16.18 (doubleComplementSub2) =>
% 122.46/16.18 ((
% 122.46/16.18 (doubleComplementEq) =>
% 122.46/16.18 ((
% 122.46/16.18 (complementTnotintersectT) =>
% 122.46/16.18 ((
% 122.46/16.18 (complementImpComplementIntersect) =>
% 122.46/16.18 ((
% 122.46/16.18 (complementSubsetComplementIntersect) =>
% 122.46/16.18 ((
% 122.46/16.18 (complementInPowersetComplementIntersect) =>
% 122.46/16.18 ((
% 122.46/16.18 (contraSubsetComplement) =>
% 122.46/16.18 ((
% 122.46/16.18 (complementTcontraSubset) =>
% 122.46/16.18 ((
% 122.46/16.18 (binunionTILcontra) =>
% 122.46/16.18 ((
% 122.46/16.18 (binunionTIRcontra) =>
% 122.46/16.18 ((
% 122.46/16.18 (inIntersectImpInUnion) =>
% 122.46/16.18 ((
% 122.46/16.18 (inIntersectImpInUnion2) =>
% 122.46/16.18 ((
% 122.46/16.18 (inIntersectImpInIntersectUnions) =>
% 122.46/16.18 ((
% 122.46/16.18 (intersectInPowersetIntersectUnions) =>
% 122.46/16.18 ((
% 122.46/16.18 (inComplementUnionImpNotIn1) =>
% 122.46/16.18 ((
% 122.46/16.18 (inComplementUnionImpInComplement1) =>
% 122.46/16.18 ((
% 122.46/16.18 (binunionTE) =>
% 122.46/16.18 ((
% 122.46/16.18 (binunionTEcontra) =>
% 122.46/16.18 ((
% 122.46/16.18 (demorgan2a1) =>
% 122.46/16.18 ((
% 122.46/16.18 (complementUnionInPowersetComplement) =>
% 122.46/16.18 ((
% 122.46/16.18 (demorgan2a2) =>
% 122.46/16.18 ((
% 122.46/16.18 (demorgan1a) =>
% 122.46/16.18 ((
% 122.46/16.18 (demorgan1b) =>
% 122.46/16.18 ((
% 122.46/16.18 (demorgan1) =>
% 122.46/16.18 ((
% 122.46/16.18 (demorgan2a) =>
% 122.46/16.18 ((
% 122.46/16.18 (demorgan2b2) =>
% 122.46/16.18 ((
% 122.46/16.18 (demorgan2b) =>
% 122.46/16.18 ((
% 122.46/16.18 (demorgan2) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz13rule0) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz13rule1) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz13rule2) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz13rule3) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz13rule4) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz1_1) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz1_2) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz1_3) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz1_4) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz1_5) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1all2) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1SetBreln1) =>
% 122.46/16.18 ((
% 122.46/16.18 (choice2fnsingleton) =>
% 122.46/16.18 ((
% 122.46/16.18 (setOfPairsIsBReln1) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1all1) =>
% 122.46/16.18 ((
% 122.46/16.18 (subbreln1) =>
% 122.46/16.18 ((
% 122.46/16.18 (eqbreln1) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1invprop) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1invI) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1invE) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1compprop) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1compI) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1compE) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1compEex) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1unionprop) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1unionIL) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1unionIR) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1unionI) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1unionE) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1unionEcases) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1unionCommutes) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz2Ex) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz2W) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz2A) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz2B) =>
% 122.46/16.18 ((
% 122.46/16.18 (image1Ex) =>
% 122.46/16.18 ((
% 122.46/16.18 (image1Ex1) =>
% 122.46/16.18 ((
% 122.46/16.18 (image1Equiv) =>
% 122.46/16.18 ((
% 122.46/16.18 (image1E) =>
% 122.46/16.18 ((
% 122.46/16.18 (image1I) =>
% 122.46/16.18 ((
% 122.46/16.18 (injFuncInInjFuncSet) =>
% 122.46/16.18 ((
% 122.46/16.18 (!!) @ (
% 122.46/16.18 (('#B') @ (
% 122.46/16.18 !!) @
% 122.46/16.18 (
% 122.46/16.18 (
% 122.46/16.18 ('#B') @ (
% 122.46/16.18 (
% 122.46/16.18 ('#B') @ (
% 122.46/16.18 !!))) @
% 122.46/16.18 (
% 122.46/16.18 (
% 122.46/16.18 ('#S') @ (
% 122.46/16.18 (
% 122.46/16.18 ('#B') @ (
% 122.46/16.18 '#S') @
% 122.46/16.18 (
% 122.46/16.18 (
% 122.46/16.18 ('#B') @ (
% 122.46/16.18 (
% 122.46/16.18 ('#B') @ (
% 122.46/16.18 '#S'))) @
% 122.46/16.18 (
% 122.46/16.18 (
% 122.46/16.18 ('#B') @ (
% 122.46/16.18 (
% 122.46/16.18 ('#B') @ (
% 122.46/16.18 (
% 122.46/16.18 ('#B') @ (
% 122.46/16.18 =>))))) @
% 122.46/16.18 (
% 122.46/16.18 (
% 122.46/16.18 ('#B') @ (
% 122.46/16.18 (
% 122.46/16.18 ('#B') @ (
% 122.46/16.18 (
% 122.46/16.18 ('#C') @ in)))) @
% 122.46/16.18 injFuncSet)))))))) @
% 122.46/16.18 (
% 122.46/16.18 (
% 122.46/16.18 ('#B') @ (
% 122.46/16.18 (
% 122.46/16.18 ('#B') @ (
% 122.46/16.18 (
% 122.46/16.18 ('#C') @ in)))) @
% 122.46/16.18 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.46/16.18 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1361])).
% 122.46/16.18 thf(zip_derived_cl1377, plain,
% 122.46/16.18 (~ (((setukpairIL) =>
% 122.46/16.18 (((setukpairIR) =>
% 122.46/16.18 (((kpairiskpair) =>
% 122.46/16.18 (((kpairp) =>
% 122.46/16.18 (((singletonsubset) =>
% 122.46/16.18 (((singletoninpowerset) =>
% 122.46/16.18 (((singletoninpowunion) =>
% 122.46/16.18 (((upairset2E) =>
% 122.46/16.18 (((upairsubunion) =>
% 122.46/16.18 (((upairinpowunion) =>
% 122.46/16.18 (((ubforcartprodlem1) =>
% 122.46/16.18 (((ubforcartprodlem2) =>
% 122.46/16.18 (((ubforcartprodlem3) =>
% 122.46/16.18 (((cartprodpairin) =>
% 122.46/16.18 (((cartprodmempair1) =>
% 122.46/16.18 (((cartprodmempair) =>
% 122.46/16.18 (((setunionE2) =>
% 122.46/16.18 (((setunionsingleton1) =>
% 122.46/16.18 (((setunionsingleton2) =>
% 122.46/16.18 (((setunionsingleton) =>
% 122.46/16.18 (((singletonprop) =>
% 122.46/16.18 (((ex1E1) =>
% 122.46/16.18 (((ex1I) =>
% 122.46/16.18 (((ex1I2) =>
% 122.46/16.18 (((singletonsuniq) =>
% 122.46/16.18 (((setukpairinjL1) =>
% 122.46/16.18 (((kfstsingleton) =>
% 122.46/16.18 (((theprop) =>
% 122.46/16.18 (((kfstpairEq) =>
% 122.46/16.18 (((cartprodfstin) =>
% 122.46/16.18 ((
% 122.46/16.18 (setukpairinjL2) =>
% 122.46/16.18 ((
% 122.46/16.18 (setukpairinjL) =>
% 122.46/16.18 ((
% 122.46/16.18 (setukpairinjR11) =>
% 122.46/16.18 ((
% 122.46/16.18 (setukpairinjR12) =>
% 122.46/16.18 ((
% 122.46/16.18 (setukpairinjR1) =>
% 122.46/16.18 ((
% 122.46/16.18 (upairequniteq) =>
% 122.46/16.18 ((
% 122.46/16.18 (setukpairinjR2) =>
% 122.46/16.18 ((
% 122.46/16.18 (setukpairinjR) =>
% 122.46/16.18 ((
% 122.46/16.18 (ksndsingleton) =>
% 122.46/16.18 ((
% 122.46/16.18 (ksndpairEq) =>
% 122.46/16.18 ((
% 122.46/16.18 (kpairsurjEq) =>
% 122.46/16.18 ((
% 122.46/16.18 (cartprodsndin) =>
% 122.46/16.18 ((
% 122.46/16.18 (cartprodpairmemEL) =>
% 122.46/16.18 ((
% 122.46/16.18 (cartprodpairmemER) =>
% 122.46/16.18 ((
% 122.46/16.18 (cartprodmempaircEq) =>
% 122.46/16.18 ((
% 122.46/16.18 (cartprodfstpairEq) =>
% 122.46/16.18 ((
% 122.46/16.18 (cartprodsndpairEq) =>
% 122.46/16.18 ((
% 122.46/16.18 (cartprodpairsurjEq) =>
% 122.46/16.18 ((
% 122.46/16.18 (dpsetconstrI) =>
% 122.46/16.18 ((
% 122.46/16.18 (dpsetconstrSub) =>
% 122.46/16.18 ((
% 122.46/16.18 (setOfPairsIsBReln) =>
% 122.46/16.18 ((
% 122.46/16.18 (dpsetconstrERa) =>
% 122.46/16.18 ((
% 122.46/16.18 (dpsetconstrEL1) =>
% 122.46/16.18 ((
% 122.46/16.18 (dpsetconstrEL2) =>
% 122.46/16.18 ((
% 122.46/16.18 (dpsetconstrER) =>
% 122.46/16.18 ((
% 122.46/16.18 (funcImageSingleton) =>
% 122.46/16.18 ((
% 122.46/16.18 (apProp) =>
% 122.46/16.18 ((
% 122.46/16.18 (app) =>
% 122.46/16.18 ((
% 122.46/16.18 (infuncsetfunc) =>
% 122.46/16.18 ((
% 122.46/16.18 (ap2p) =>
% 122.46/16.18 ((
% 122.46/16.18 (funcinfuncset) =>
% 122.46/16.18 ((
% 122.46/16.18 (lamProp) =>
% 122.46/16.18 ((
% 122.46/16.18 (lamp) =>
% 122.46/16.18 ((
% 122.46/16.18 (lam2p) =>
% 122.46/16.18 ((
% 122.46/16.18 (brelnall1) =>
% 122.46/16.18 ((
% 122.46/16.18 (brelnall2) =>
% 122.46/16.18 ((
% 122.46/16.18 (ex1E2) =>
% 122.46/16.18 ((
% 122.46/16.18 (funcGraphProp1) =>
% 122.46/16.18 ((
% 122.46/16.18 (funcGraphProp3) =>
% 122.46/16.18 ((
% 122.46/16.18 (funcGraphProp2) =>
% 122.46/16.18 ((
% 122.46/16.18 (funcextLem) =>
% 122.46/16.18 ((
% 122.46/16.18 (funcGraphProp4) =>
% 122.46/16.18 ((
% 122.46/16.18 (subbreln) =>
% 122.46/16.18 ((
% 122.46/16.18 (eqbreln) =>
% 122.46/16.18 ((
% 122.46/16.18 (funcext) =>
% 122.46/16.18 ((
% 122.46/16.18 (funcext2) =>
% 122.46/16.18 ((
% 122.46/16.18 (ap2apEq1) =>
% 122.46/16.18 ((
% 122.46/16.18 (ap2apEq2) =>
% 122.46/16.18 ((
% 122.46/16.18 (beta1) =>
% 122.46/16.18 ((
% 122.46/16.18 (eta1) =>
% 122.46/16.18 ((
% 122.46/16.18 (lam2lamEq) =>
% 122.46/16.18 ((
% 122.46/16.18 (beta2) =>
% 122.46/16.18 ((
% 122.46/16.18 (eta2) =>
% 122.46/16.18 ((
% 122.46/16.18 (iffalseProp1) =>
% 122.46/16.18 ((
% 122.46/16.18 (iffalseProp2) =>
% 122.46/16.18 ((
% 122.46/16.18 (iftrueProp1) =>
% 122.46/16.18 ((
% 122.46/16.18 (iftrueProp2) =>
% 122.46/16.18 ((
% 122.46/16.18 (ifSingleton) =>
% 122.46/16.18 ((
% 122.46/16.18 (ifp) =>
% 122.46/16.18 ((
% 122.46/16.18 (theeq) =>
% 122.46/16.18 ((
% 122.46/16.18 (iftrue) =>
% 122.46/16.18 ((
% 122.46/16.18 (iffalse) =>
% 122.46/16.18 ((
% 122.46/16.18 (iftrueorfalse) =>
% 122.46/16.18 ((
% 122.46/16.18 (binintersectT_lem) =>
% 122.46/16.18 ((
% 122.46/16.18 (binunionT_lem) =>
% 122.46/16.18 ((
% 122.46/16.18 (powersetT_lem) =>
% 122.46/16.18 ((
% 122.46/16.18 (setminusT_lem) =>
% 122.46/16.18 ((
% 122.46/16.18 (complementT_lem) =>
% 122.46/16.18 ((
% 122.46/16.18 (setextT) =>
% 122.46/16.18 ((
% 122.46/16.18 (subsetTI) =>
% 122.46/16.18 ((
% 122.46/16.18 (powersetTI1) =>
% 122.46/16.18 ((
% 122.46/16.18 (powersetTE1) =>
% 122.46/16.18 ((
% 122.46/16.18 (complementTI1) =>
% 122.46/16.18 ((
% 122.46/16.18 (complementTE1) =>
% 122.46/16.18 ((
% 122.46/16.18 (binintersectTELcontra) =>
% 122.46/16.18 ((
% 122.46/16.18 (binintersectTERcontra) =>
% 122.46/16.18 ((
% 122.46/16.18 (contrasubsetT) =>
% 122.46/16.18 ((
% 122.46/16.18 (contrasubsetT1) =>
% 122.46/16.18 ((
% 122.46/16.18 (contrasubsetT2) =>
% 122.46/16.18 ((
% 122.46/16.18 (contrasubsetT3) =>
% 122.46/16.18 ((
% 122.46/16.18 (doubleComplementI1) =>
% 122.46/16.18 ((
% 122.46/16.18 (doubleComplementE1) =>
% 122.46/16.18 ((
% 122.46/16.18 (doubleComplementSub1) =>
% 122.46/16.18 ((
% 122.46/16.18 (doubleComplementSub2) =>
% 122.46/16.18 ((
% 122.46/16.18 (doubleComplementEq) =>
% 122.46/16.18 ((
% 122.46/16.18 (complementTnotintersectT) =>
% 122.46/16.18 ((
% 122.46/16.18 (complementImpComplementIntersect) =>
% 122.46/16.18 ((
% 122.46/16.18 (complementSubsetComplementIntersect) =>
% 122.46/16.18 ((
% 122.46/16.18 (complementInPowersetComplementIntersect) =>
% 122.46/16.18 ((
% 122.46/16.18 (contraSubsetComplement) =>
% 122.46/16.18 ((
% 122.46/16.18 (complementTcontraSubset) =>
% 122.46/16.18 ((
% 122.46/16.18 (binunionTILcontra) =>
% 122.46/16.18 ((
% 122.46/16.18 (binunionTIRcontra) =>
% 122.46/16.18 ((
% 122.46/16.18 (inIntersectImpInUnion) =>
% 122.46/16.18 ((
% 122.46/16.18 (inIntersectImpInUnion2) =>
% 122.46/16.18 ((
% 122.46/16.18 (inIntersectImpInIntersectUnions) =>
% 122.46/16.18 ((
% 122.46/16.18 (intersectInPowersetIntersectUnions) =>
% 122.46/16.18 ((
% 122.46/16.18 (inComplementUnionImpNotIn1) =>
% 122.46/16.18 ((
% 122.46/16.18 (inComplementUnionImpInComplement1) =>
% 122.46/16.18 ((
% 122.46/16.18 (binunionTE) =>
% 122.46/16.18 ((
% 122.46/16.18 (binunionTEcontra) =>
% 122.46/16.18 ((
% 122.46/16.18 (demorgan2a1) =>
% 122.46/16.18 ((
% 122.46/16.18 (complementUnionInPowersetComplement) =>
% 122.46/16.18 ((
% 122.46/16.18 (demorgan2a2) =>
% 122.46/16.18 ((
% 122.46/16.18 (demorgan1a) =>
% 122.46/16.18 ((
% 122.46/16.18 (demorgan1b) =>
% 122.46/16.18 ((
% 122.46/16.18 (demorgan1) =>
% 122.46/16.18 ((
% 122.46/16.18 (demorgan2a) =>
% 122.46/16.18 ((
% 122.46/16.18 (demorgan2b2) =>
% 122.46/16.18 ((
% 122.46/16.18 (demorgan2b) =>
% 122.46/16.18 ((
% 122.46/16.18 (demorgan2) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz13rule0) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz13rule1) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz13rule2) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz13rule3) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz13rule4) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz1_1) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz1_2) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz1_3) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz1_4) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz1_5) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1all2) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1SetBreln1) =>
% 122.46/16.18 ((
% 122.46/16.18 (choice2fnsingleton) =>
% 122.46/16.18 ((
% 122.46/16.18 (setOfPairsIsBReln1) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1all1) =>
% 122.46/16.18 ((
% 122.46/16.18 (subbreln1) =>
% 122.46/16.18 ((
% 122.46/16.18 (eqbreln1) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1invprop) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1invI) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1invE) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1compprop) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1compI) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1compE) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1compEex) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1unionprop) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1unionIL) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1unionIR) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1unionI) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1unionE) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1unionEcases) =>
% 122.46/16.18 ((
% 122.46/16.18 (breln1unionCommutes) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz2Ex) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz2W) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz2A) =>
% 122.46/16.18 ((
% 122.46/16.18 (woz2B) =>
% 122.46/16.18 ((
% 122.46/16.18 (image1Ex) =>
% 122.46/16.18 ((
% 122.46/16.18 (image1Ex1) =>
% 122.46/16.18 ((
% 122.46/16.18 (image1Equiv) =>
% 122.46/16.18 ((
% 122.46/16.18 (image1E) =>
% 122.46/16.18 ((
% 122.46/16.18 (image1I) =>
% 122.46/16.18 ((
% 122.46/16.18 (injFuncInInjFuncSet) =>
% 122.46/16.18 ((
% 122.46/16.18 (!!) @ (
% 122.46/16.18 (('#B') @ (
% 122.46/16.18 !!) @
% 122.46/16.18 (
% 122.46/16.18 (
% 122.46/16.18 ('#B') @ (
% 122.46/16.19 (
% 122.46/16.19 ('#B') @ (
% 122.46/16.19 !!))) @
% 122.46/16.19 (
% 122.46/16.19 (
% 122.46/16.19 ('#S') @ (
% 122.46/16.19 (
% 122.46/16.19 ('#B') @ (
% 122.46/16.19 '#S') @
% 122.46/16.19 (
% 122.46/16.19 (
% 122.46/16.19 ('#B') @ (
% 122.46/16.19 (
% 122.46/16.19 ('#B') @ (
% 122.46/16.19 '#S'))) @
% 122.46/16.19 (
% 122.46/16.19 (
% 122.46/16.19 ('#B') @ (
% 122.46/16.19 (
% 122.46/16.19 ('#B') @ (
% 122.46/16.19 (
% 122.46/16.19 ('#B') @ (
% 122.46/16.19 =>))))) @
% 122.46/16.19 (
% 122.46/16.19 (
% 122.46/16.19 ('#B') @ (
% 122.46/16.19 (
% 122.46/16.19 ('#B') @ (
% 122.46/16.19 (
% 122.46/16.19 ('#C') @ in)))) @
% 122.46/16.19 injFuncSet)))))))) @
% 122.46/16.19 (
% 122.46/16.19 (
% 122.46/16.19 ('#B') @ (
% 122.46/16.19 (
% 122.46/16.19 ('#B') @ (
% 122.46/16.19 (
% 122.46/16.19 ('#C') @ in)))) @
% 122.46/16.19 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.46/16.19 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1369])).
% 122.46/16.19 thf(zip_derived_cl1386, plain,
% 122.46/16.19 (~ (((setukpairIR) =>
% 122.46/16.19 (((kpairiskpair) =>
% 122.46/16.19 (((kpairp) =>
% 122.46/16.19 (((singletonsubset) =>
% 122.46/16.19 (((singletoninpowerset) =>
% 122.46/16.19 (((singletoninpowunion) =>
% 122.46/16.19 (((upairset2E) =>
% 122.46/16.19 (((upairsubunion) =>
% 122.46/16.19 (((upairinpowunion) =>
% 122.46/16.19 (((ubforcartprodlem1) =>
% 122.46/16.19 (((ubforcartprodlem2) =>
% 122.46/16.19 (((ubforcartprodlem3) =>
% 122.46/16.19 (((cartprodpairin) =>
% 122.46/16.19 (((cartprodmempair1) =>
% 122.46/16.19 (((cartprodmempair) =>
% 122.46/16.19 (((setunionE2) =>
% 122.46/16.19 (((setunionsingleton1) =>
% 122.46/16.19 (((setunionsingleton2) =>
% 122.46/16.19 (((setunionsingleton) =>
% 122.46/16.19 (((singletonprop) =>
% 122.46/16.19 (((ex1E1) =>
% 122.46/16.19 (((ex1I) =>
% 122.46/16.19 (((ex1I2) =>
% 122.46/16.19 (((singletonsuniq) =>
% 122.46/16.19 (((setukpairinjL1) =>
% 122.46/16.19 (((kfstsingleton) =>
% 122.46/16.19 (((theprop) =>
% 122.46/16.19 (((kfstpairEq) =>
% 122.46/16.19 (((cartprodfstin) =>
% 122.46/16.19 (((setukpairinjL2) =>
% 122.46/16.19 ((
% 122.46/16.19 (setukpairinjL) =>
% 122.46/16.19 ((
% 122.46/16.19 (setukpairinjR11) =>
% 122.46/16.19 ((
% 122.46/16.19 (setukpairinjR12) =>
% 122.46/16.19 ((
% 122.46/16.19 (setukpairinjR1) =>
% 122.46/16.19 ((
% 122.46/16.19 (upairequniteq) =>
% 122.46/16.19 ((
% 122.46/16.19 (setukpairinjR2) =>
% 122.46/16.19 ((
% 122.46/16.19 (setukpairinjR) =>
% 122.46/16.19 ((
% 122.46/16.19 (ksndsingleton) =>
% 122.46/16.19 ((
% 122.46/16.19 (ksndpairEq) =>
% 122.46/16.19 ((
% 122.46/16.19 (kpairsurjEq) =>
% 122.46/16.19 ((
% 122.46/16.19 (cartprodsndin) =>
% 122.46/16.19 ((
% 122.46/16.19 (cartprodpairmemEL) =>
% 122.46/16.19 ((
% 122.46/16.19 (cartprodpairmemER) =>
% 122.46/16.19 ((
% 122.46/16.19 (cartprodmempaircEq) =>
% 122.46/16.19 ((
% 122.46/16.19 (cartprodfstpairEq) =>
% 122.46/16.19 ((
% 122.46/16.19 (cartprodsndpairEq) =>
% 122.46/16.19 ((
% 122.46/16.19 (cartprodpairsurjEq) =>
% 122.46/16.19 ((
% 122.46/16.19 (dpsetconstrI) =>
% 122.46/16.19 ((
% 122.46/16.19 (dpsetconstrSub) =>
% 122.46/16.19 ((
% 122.46/16.19 (setOfPairsIsBReln) =>
% 122.46/16.19 ((
% 122.46/16.19 (dpsetconstrERa) =>
% 122.46/16.19 ((
% 122.46/16.19 (dpsetconstrEL1) =>
% 122.46/16.19 ((
% 122.46/16.19 (dpsetconstrEL2) =>
% 122.46/16.19 ((
% 122.46/16.19 (dpsetconstrER) =>
% 122.46/16.19 ((
% 122.46/16.19 (funcImageSingleton) =>
% 122.46/16.19 ((
% 122.46/16.19 (apProp) =>
% 122.46/16.19 ((
% 122.46/16.19 (app) =>
% 122.46/16.19 ((
% 122.46/16.19 (infuncsetfunc) =>
% 122.46/16.19 ((
% 122.46/16.19 (ap2p) =>
% 122.46/16.19 ((
% 122.46/16.19 (funcinfuncset) =>
% 122.46/16.19 ((
% 122.46/16.19 (lamProp) =>
% 122.46/16.19 ((
% 122.46/16.19 (lamp) =>
% 122.46/16.19 ((
% 122.46/16.19 (lam2p) =>
% 122.46/16.19 ((
% 122.46/16.19 (brelnall1) =>
% 122.46/16.19 ((
% 122.46/16.19 (brelnall2) =>
% 122.46/16.19 ((
% 122.46/16.19 (ex1E2) =>
% 122.46/16.19 ((
% 122.46/16.19 (funcGraphProp1) =>
% 122.46/16.19 ((
% 122.46/16.19 (funcGraphProp3) =>
% 122.46/16.19 ((
% 122.46/16.19 (funcGraphProp2) =>
% 122.46/16.19 ((
% 122.46/16.19 (funcextLem) =>
% 122.46/16.19 ((
% 122.46/16.19 (funcGraphProp4) =>
% 122.46/16.19 ((
% 122.46/16.19 (subbreln) =>
% 122.46/16.19 ((
% 122.46/16.19 (eqbreln) =>
% 122.46/16.19 ((
% 122.46/16.19 (funcext) =>
% 122.46/16.19 ((
% 122.46/16.19 (funcext2) =>
% 122.46/16.19 ((
% 122.46/16.19 (ap2apEq1) =>
% 122.46/16.19 ((
% 122.46/16.19 (ap2apEq2) =>
% 122.46/16.19 ((
% 122.46/16.19 (beta1) =>
% 122.46/16.19 ((
% 122.46/16.19 (eta1) =>
% 122.46/16.19 ((
% 122.46/16.19 (lam2lamEq) =>
% 122.46/16.19 ((
% 122.46/16.19 (beta2) =>
% 122.46/16.19 ((
% 122.46/16.19 (eta2) =>
% 122.46/16.19 ((
% 122.46/16.19 (iffalseProp1) =>
% 122.46/16.19 ((
% 122.46/16.19 (iffalseProp2) =>
% 122.46/16.19 ((
% 122.46/16.19 (iftrueProp1) =>
% 122.46/16.19 ((
% 122.46/16.19 (iftrueProp2) =>
% 122.46/16.19 ((
% 122.46/16.19 (ifSingleton) =>
% 122.46/16.19 ((
% 122.46/16.19 (ifp) =>
% 122.46/16.19 ((
% 122.46/16.19 (theeq) =>
% 122.46/16.19 ((
% 122.46/16.19 (iftrue) =>
% 122.46/16.19 ((
% 122.46/16.19 (iffalse) =>
% 122.46/16.19 ((
% 122.46/16.19 (iftrueorfalse) =>
% 122.46/16.19 ((
% 122.46/16.19 (binintersectT_lem) =>
% 122.46/16.19 ((
% 122.46/16.19 (binunionT_lem) =>
% 122.46/16.19 ((
% 122.46/16.19 (powersetT_lem) =>
% 122.46/16.19 ((
% 122.46/16.19 (setminusT_lem) =>
% 122.46/16.19 ((
% 122.46/16.19 (complementT_lem) =>
% 122.46/16.19 ((
% 122.46/16.19 (setextT) =>
% 122.46/16.19 ((
% 122.46/16.19 (subsetTI) =>
% 122.46/16.19 ((
% 122.46/16.19 (powersetTI1) =>
% 122.46/16.19 ((
% 122.46/16.19 (powersetTE1) =>
% 122.46/16.19 ((
% 122.46/16.19 (complementTI1) =>
% 122.46/16.19 ((
% 122.46/16.19 (complementTE1) =>
% 122.46/16.19 ((
% 122.46/16.19 (binintersectTELcontra) =>
% 122.46/16.19 ((
% 122.46/16.19 (binintersectTERcontra) =>
% 122.46/16.19 ((
% 122.46/16.19 (contrasubsetT) =>
% 122.46/16.19 ((
% 122.46/16.19 (contrasubsetT1) =>
% 122.46/16.19 ((
% 122.46/16.19 (contrasubsetT2) =>
% 122.46/16.19 ((
% 122.46/16.19 (contrasubsetT3) =>
% 122.46/16.19 ((
% 122.46/16.19 (doubleComplementI1) =>
% 122.46/16.19 ((
% 122.46/16.19 (doubleComplementE1) =>
% 122.46/16.19 ((
% 122.46/16.19 (doubleComplementSub1) =>
% 122.46/16.19 ((
% 122.46/16.19 (doubleComplementSub2) =>
% 122.46/16.19 ((
% 122.46/16.19 (doubleComplementEq) =>
% 122.46/16.19 ((
% 122.46/16.19 (complementTnotintersectT) =>
% 122.46/16.19 ((
% 122.46/16.19 (complementImpComplementIntersect) =>
% 122.46/16.19 ((
% 122.46/16.19 (complementSubsetComplementIntersect) =>
% 122.46/16.19 ((
% 122.46/16.19 (complementInPowersetComplementIntersect) =>
% 122.46/16.19 ((
% 122.46/16.19 (contraSubsetComplement) =>
% 122.46/16.19 ((
% 122.46/16.19 (complementTcontraSubset) =>
% 122.46/16.19 ((
% 122.46/16.19 (binunionTILcontra) =>
% 122.46/16.19 ((
% 122.46/16.19 (binunionTIRcontra) =>
% 122.46/16.19 ((
% 122.46/16.19 (inIntersectImpInUnion) =>
% 122.46/16.19 ((
% 122.46/16.19 (inIntersectImpInUnion2) =>
% 122.46/16.19 ((
% 122.46/16.19 (inIntersectImpInIntersectUnions) =>
% 122.46/16.19 ((
% 122.46/16.19 (intersectInPowersetIntersectUnions) =>
% 122.46/16.19 ((
% 122.46/16.19 (inComplementUnionImpNotIn1) =>
% 122.46/16.19 ((
% 122.46/16.19 (inComplementUnionImpInComplement1) =>
% 122.46/16.19 ((
% 122.46/16.19 (binunionTE) =>
% 122.46/16.19 ((
% 122.46/16.19 (binunionTEcontra) =>
% 122.46/16.19 ((
% 122.46/16.19 (demorgan2a1) =>
% 122.46/16.19 ((
% 122.46/16.19 (complementUnionInPowersetComplement) =>
% 122.46/16.19 ((
% 122.46/16.19 (demorgan2a2) =>
% 122.46/16.19 ((
% 122.46/16.19 (demorgan1a) =>
% 122.46/16.19 ((
% 122.46/16.19 (demorgan1b) =>
% 122.46/16.19 ((
% 122.46/16.19 (demorgan1) =>
% 122.46/16.19 ((
% 122.46/16.19 (demorgan2a) =>
% 122.46/16.19 ((
% 122.46/16.19 (demorgan2b2) =>
% 122.46/16.19 ((
% 122.46/16.19 (demorgan2b) =>
% 122.46/16.19 ((
% 122.46/16.19 (demorgan2) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz13rule0) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz13rule1) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz13rule2) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz13rule3) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz13rule4) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz1_1) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz1_2) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz1_3) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz1_4) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz1_5) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1all2) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1SetBreln1) =>
% 122.46/16.19 ((
% 122.46/16.19 (choice2fnsingleton) =>
% 122.46/16.19 ((
% 122.46/16.19 (setOfPairsIsBReln1) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1all1) =>
% 122.46/16.19 ((
% 122.46/16.19 (subbreln1) =>
% 122.46/16.19 ((
% 122.46/16.19 (eqbreln1) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1invprop) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1invI) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1invE) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1compprop) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1compI) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1compE) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1compEex) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1unionprop) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1unionIL) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1unionIR) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1unionI) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1unionE) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1unionEcases) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1unionCommutes) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz2Ex) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz2W) =>
% 122.46/16.19 ((
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% 122.46/16.19 ((
% 122.46/16.19 (woz2B) =>
% 122.46/16.19 ((
% 122.46/16.19 (image1Ex) =>
% 122.46/16.19 ((
% 122.46/16.19 (image1Ex1) =>
% 122.46/16.19 ((
% 122.46/16.19 (image1Equiv) =>
% 122.46/16.19 ((
% 122.46/16.19 (image1E) =>
% 122.46/16.19 ((
% 122.46/16.19 (image1I) =>
% 122.46/16.19 ((
% 122.46/16.19 (injFuncInInjFuncSet) =>
% 122.46/16.19 ((
% 122.46/16.19 (!!) @ (
% 122.46/16.19 (('#B') @ (
% 122.46/16.19 !!) @
% 122.46/16.19 (
% 122.46/16.19 (
% 122.46/16.19 ('#B') @ (
% 122.46/16.19 (
% 122.46/16.19 ('#B') @ (
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% 122.46/16.19 (
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% 122.46/16.19 ('#B') @ (
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% 122.46/16.19 (
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% 122.46/16.19 (
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% 122.46/16.19 (
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% 122.46/16.19 =>))))) @
% 122.46/16.19 (
% 122.46/16.19 (
% 122.46/16.19 ('#B') @ (
% 122.46/16.19 (
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% 122.46/16.19 injFuncSet)))))))) @
% 122.46/16.19 (
% 122.46/16.19 (
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% 122.46/16.19 (
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% 122.46/16.19 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.46/16.19 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1377])).
% 122.46/16.19 thf(zip_derived_cl1396, plain,
% 122.46/16.19 (~ (((kpairiskpair) =>
% 122.46/16.19 (((kpairp) =>
% 122.46/16.19 (((singletonsubset) =>
% 122.46/16.19 (((singletoninpowerset) =>
% 122.46/16.19 (((singletoninpowunion) =>
% 122.46/16.19 (((upairset2E) =>
% 122.46/16.19 (((upairsubunion) =>
% 122.46/16.19 (((upairinpowunion) =>
% 122.46/16.19 (((ubforcartprodlem1) =>
% 122.46/16.19 (((ubforcartprodlem2) =>
% 122.46/16.19 (((ubforcartprodlem3) =>
% 122.46/16.19 (((cartprodpairin) =>
% 122.46/16.19 (((cartprodmempair1) =>
% 122.46/16.19 (((cartprodmempair) =>
% 122.46/16.19 (((setunionE2) =>
% 122.46/16.19 (((setunionsingleton1) =>
% 122.46/16.19 (((setunionsingleton2) =>
% 122.46/16.19 (((setunionsingleton) =>
% 122.46/16.19 (((singletonprop) =>
% 122.46/16.19 (((ex1E1) =>
% 122.46/16.19 (((ex1I) =>
% 122.46/16.19 (((ex1I2) =>
% 122.46/16.19 (((singletonsuniq) =>
% 122.46/16.19 (((setukpairinjL1) =>
% 122.46/16.19 (((kfstsingleton) =>
% 122.46/16.19 (((theprop) =>
% 122.46/16.19 (((kfstpairEq) =>
% 122.46/16.19 (((cartprodfstin) =>
% 122.46/16.19 (((setukpairinjL2) =>
% 122.46/16.19 (((setukpairinjL) =>
% 122.46/16.19 ((
% 122.46/16.19 (setukpairinjR11) =>
% 122.46/16.19 ((
% 122.46/16.19 (setukpairinjR12) =>
% 122.46/16.19 ((
% 122.46/16.19 (setukpairinjR1) =>
% 122.46/16.19 ((
% 122.46/16.19 (upairequniteq) =>
% 122.46/16.19 ((
% 122.46/16.19 (setukpairinjR2) =>
% 122.46/16.19 ((
% 122.46/16.19 (setukpairinjR) =>
% 122.46/16.19 ((
% 122.46/16.19 (ksndsingleton) =>
% 122.46/16.19 ((
% 122.46/16.19 (ksndpairEq) =>
% 122.46/16.19 ((
% 122.46/16.19 (kpairsurjEq) =>
% 122.46/16.19 ((
% 122.46/16.19 (cartprodsndin) =>
% 122.46/16.19 ((
% 122.46/16.19 (cartprodpairmemEL) =>
% 122.46/16.19 ((
% 122.46/16.19 (cartprodpairmemER) =>
% 122.46/16.19 ((
% 122.46/16.19 (cartprodmempaircEq) =>
% 122.46/16.19 ((
% 122.46/16.19 (cartprodfstpairEq) =>
% 122.46/16.19 ((
% 122.46/16.19 (cartprodsndpairEq) =>
% 122.46/16.19 ((
% 122.46/16.19 (cartprodpairsurjEq) =>
% 122.46/16.19 ((
% 122.46/16.19 (dpsetconstrI) =>
% 122.46/16.19 ((
% 122.46/16.19 (dpsetconstrSub) =>
% 122.46/16.19 ((
% 122.46/16.19 (setOfPairsIsBReln) =>
% 122.46/16.19 ((
% 122.46/16.19 (dpsetconstrERa) =>
% 122.46/16.19 ((
% 122.46/16.19 (dpsetconstrEL1) =>
% 122.46/16.19 ((
% 122.46/16.19 (dpsetconstrEL2) =>
% 122.46/16.19 ((
% 122.46/16.19 (dpsetconstrER) =>
% 122.46/16.19 ((
% 122.46/16.19 (funcImageSingleton) =>
% 122.46/16.19 ((
% 122.46/16.19 (apProp) =>
% 122.46/16.19 ((
% 122.46/16.19 (app) =>
% 122.46/16.19 ((
% 122.46/16.19 (infuncsetfunc) =>
% 122.46/16.19 ((
% 122.46/16.19 (ap2p) =>
% 122.46/16.19 ((
% 122.46/16.19 (funcinfuncset) =>
% 122.46/16.19 ((
% 122.46/16.19 (lamProp) =>
% 122.46/16.19 ((
% 122.46/16.19 (lamp) =>
% 122.46/16.19 ((
% 122.46/16.19 (lam2p) =>
% 122.46/16.19 ((
% 122.46/16.19 (brelnall1) =>
% 122.46/16.19 ((
% 122.46/16.19 (brelnall2) =>
% 122.46/16.19 ((
% 122.46/16.19 (ex1E2) =>
% 122.46/16.19 ((
% 122.46/16.19 (funcGraphProp1) =>
% 122.46/16.19 ((
% 122.46/16.19 (funcGraphProp3) =>
% 122.46/16.19 ((
% 122.46/16.19 (funcGraphProp2) =>
% 122.46/16.19 ((
% 122.46/16.19 (funcextLem) =>
% 122.46/16.19 ((
% 122.46/16.19 (funcGraphProp4) =>
% 122.46/16.19 ((
% 122.46/16.19 (subbreln) =>
% 122.46/16.19 ((
% 122.46/16.19 (eqbreln) =>
% 122.46/16.19 ((
% 122.46/16.19 (funcext) =>
% 122.46/16.19 ((
% 122.46/16.19 (funcext2) =>
% 122.46/16.19 ((
% 122.46/16.19 (ap2apEq1) =>
% 122.46/16.19 ((
% 122.46/16.19 (ap2apEq2) =>
% 122.46/16.19 ((
% 122.46/16.19 (beta1) =>
% 122.46/16.19 ((
% 122.46/16.19 (eta1) =>
% 122.46/16.19 ((
% 122.46/16.19 (lam2lamEq) =>
% 122.46/16.19 ((
% 122.46/16.19 (beta2) =>
% 122.46/16.19 ((
% 122.46/16.19 (eta2) =>
% 122.46/16.19 ((
% 122.46/16.19 (iffalseProp1) =>
% 122.46/16.19 ((
% 122.46/16.19 (iffalseProp2) =>
% 122.46/16.19 ((
% 122.46/16.19 (iftrueProp1) =>
% 122.46/16.19 ((
% 122.46/16.19 (iftrueProp2) =>
% 122.46/16.19 ((
% 122.46/16.19 (ifSingleton) =>
% 122.46/16.19 ((
% 122.46/16.19 (ifp) =>
% 122.46/16.19 ((
% 122.46/16.19 (theeq) =>
% 122.46/16.19 ((
% 122.46/16.19 (iftrue) =>
% 122.46/16.19 ((
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% 122.46/16.19 ((
% 122.46/16.19 (iftrueorfalse) =>
% 122.46/16.19 ((
% 122.46/16.19 (binintersectT_lem) =>
% 122.46/16.19 ((
% 122.46/16.19 (binunionT_lem) =>
% 122.46/16.19 ((
% 122.46/16.19 (powersetT_lem) =>
% 122.46/16.19 ((
% 122.46/16.19 (setminusT_lem) =>
% 122.46/16.19 ((
% 122.46/16.19 (complementT_lem) =>
% 122.46/16.19 ((
% 122.46/16.19 (setextT) =>
% 122.46/16.19 ((
% 122.46/16.19 (subsetTI) =>
% 122.46/16.19 ((
% 122.46/16.19 (powersetTI1) =>
% 122.46/16.19 ((
% 122.46/16.19 (powersetTE1) =>
% 122.46/16.19 ((
% 122.46/16.19 (complementTI1) =>
% 122.46/16.19 ((
% 122.46/16.19 (complementTE1) =>
% 122.46/16.19 ((
% 122.46/16.19 (binintersectTELcontra) =>
% 122.46/16.19 ((
% 122.46/16.19 (binintersectTERcontra) =>
% 122.46/16.19 ((
% 122.46/16.19 (contrasubsetT) =>
% 122.46/16.19 ((
% 122.46/16.19 (contrasubsetT1) =>
% 122.46/16.19 ((
% 122.46/16.19 (contrasubsetT2) =>
% 122.46/16.19 ((
% 122.46/16.19 (contrasubsetT3) =>
% 122.46/16.19 ((
% 122.46/16.19 (doubleComplementI1) =>
% 122.46/16.19 ((
% 122.46/16.19 (doubleComplementE1) =>
% 122.46/16.19 ((
% 122.46/16.19 (doubleComplementSub1) =>
% 122.46/16.19 ((
% 122.46/16.19 (doubleComplementSub2) =>
% 122.46/16.19 ((
% 122.46/16.19 (doubleComplementEq) =>
% 122.46/16.19 ((
% 122.46/16.19 (complementTnotintersectT) =>
% 122.46/16.19 ((
% 122.46/16.19 (complementImpComplementIntersect) =>
% 122.46/16.19 ((
% 122.46/16.19 (complementSubsetComplementIntersect) =>
% 122.46/16.19 ((
% 122.46/16.19 (complementInPowersetComplementIntersect) =>
% 122.46/16.19 ((
% 122.46/16.19 (contraSubsetComplement) =>
% 122.46/16.19 ((
% 122.46/16.19 (complementTcontraSubset) =>
% 122.46/16.19 ((
% 122.46/16.19 (binunionTILcontra) =>
% 122.46/16.19 ((
% 122.46/16.19 (binunionTIRcontra) =>
% 122.46/16.19 ((
% 122.46/16.19 (inIntersectImpInUnion) =>
% 122.46/16.19 ((
% 122.46/16.19 (inIntersectImpInUnion2) =>
% 122.46/16.19 ((
% 122.46/16.19 (inIntersectImpInIntersectUnions) =>
% 122.46/16.19 ((
% 122.46/16.19 (intersectInPowersetIntersectUnions) =>
% 122.46/16.19 ((
% 122.46/16.19 (inComplementUnionImpNotIn1) =>
% 122.46/16.19 ((
% 122.46/16.19 (inComplementUnionImpInComplement1) =>
% 122.46/16.19 ((
% 122.46/16.19 (binunionTE) =>
% 122.46/16.19 ((
% 122.46/16.19 (binunionTEcontra) =>
% 122.46/16.19 ((
% 122.46/16.19 (demorgan2a1) =>
% 122.46/16.19 ((
% 122.46/16.19 (complementUnionInPowersetComplement) =>
% 122.46/16.19 ((
% 122.46/16.19 (demorgan2a2) =>
% 122.46/16.19 ((
% 122.46/16.19 (demorgan1a) =>
% 122.46/16.19 ((
% 122.46/16.19 (demorgan1b) =>
% 122.46/16.19 ((
% 122.46/16.19 (demorgan1) =>
% 122.46/16.19 ((
% 122.46/16.19 (demorgan2a) =>
% 122.46/16.19 ((
% 122.46/16.19 (demorgan2b2) =>
% 122.46/16.19 ((
% 122.46/16.19 (demorgan2b) =>
% 122.46/16.19 ((
% 122.46/16.19 (demorgan2) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz13rule0) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz13rule1) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz13rule2) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz13rule3) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz13rule4) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz1_1) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz1_2) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz1_3) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz1_4) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz1_5) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1all2) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1SetBreln1) =>
% 122.46/16.19 ((
% 122.46/16.19 (choice2fnsingleton) =>
% 122.46/16.19 ((
% 122.46/16.19 (setOfPairsIsBReln1) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1all1) =>
% 122.46/16.19 ((
% 122.46/16.19 (subbreln1) =>
% 122.46/16.19 ((
% 122.46/16.19 (eqbreln1) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1invprop) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1invI) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1invE) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1compprop) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1compI) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1compE) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1compEex) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1unionprop) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1unionIL) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1unionIR) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1unionI) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1unionE) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1unionEcases) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1unionCommutes) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz2Ex) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz2W) =>
% 122.46/16.19 ((
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% 122.46/16.19 ((
% 122.46/16.19 (woz2B) =>
% 122.46/16.19 ((
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% 122.46/16.19 ((
% 122.46/16.19 (image1Ex1) =>
% 122.46/16.19 ((
% 122.46/16.19 (image1Equiv) =>
% 122.46/16.19 ((
% 122.46/16.19 (image1E) =>
% 122.46/16.19 ((
% 122.46/16.19 (image1I) =>
% 122.46/16.19 ((
% 122.46/16.19 (injFuncInInjFuncSet) =>
% 122.46/16.19 ((
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% 122.46/16.19 injFuncSet)))))))) @
% 122.46/16.19 (
% 122.46/16.19 (
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% 122.46/16.19 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1386])).
% 122.46/16.19 thf(zip_derived_cl1407, plain,
% 122.46/16.19 (~ (((kpairp) =>
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% 122.46/16.19 (((singletoninpowerset) =>
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% 122.46/16.19 (((upairsubunion) =>
% 122.46/16.19 (((upairinpowunion) =>
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% 122.46/16.19 (((setunionsingleton) =>
% 122.46/16.19 (((singletonprop) =>
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% 122.46/16.19 (((kfstsingleton) =>
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% 122.46/16.19 ((
% 122.46/16.19 (setukpairinjR12) =>
% 122.46/16.19 ((
% 122.46/16.19 (setukpairinjR1) =>
% 122.46/16.19 ((
% 122.46/16.19 (upairequniteq) =>
% 122.46/16.19 ((
% 122.46/16.19 (setukpairinjR2) =>
% 122.46/16.19 ((
% 122.46/16.19 (setukpairinjR) =>
% 122.46/16.19 ((
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% 122.46/16.19 ((
% 122.46/16.19 (ksndpairEq) =>
% 122.46/16.19 ((
% 122.46/16.19 (kpairsurjEq) =>
% 122.46/16.19 ((
% 122.46/16.19 (cartprodsndin) =>
% 122.46/16.19 ((
% 122.46/16.19 (cartprodpairmemEL) =>
% 122.46/16.19 ((
% 122.46/16.19 (cartprodpairmemER) =>
% 122.46/16.19 ((
% 122.46/16.19 (cartprodmempaircEq) =>
% 122.46/16.19 ((
% 122.46/16.19 (cartprodfstpairEq) =>
% 122.46/16.19 ((
% 122.46/16.19 (cartprodsndpairEq) =>
% 122.46/16.19 ((
% 122.46/16.19 (cartprodpairsurjEq) =>
% 122.46/16.19 ((
% 122.46/16.19 (dpsetconstrI) =>
% 122.46/16.19 ((
% 122.46/16.19 (dpsetconstrSub) =>
% 122.46/16.19 ((
% 122.46/16.19 (setOfPairsIsBReln) =>
% 122.46/16.19 ((
% 122.46/16.19 (dpsetconstrERa) =>
% 122.46/16.19 ((
% 122.46/16.19 (dpsetconstrEL1) =>
% 122.46/16.19 ((
% 122.46/16.19 (dpsetconstrEL2) =>
% 122.46/16.19 ((
% 122.46/16.19 (dpsetconstrER) =>
% 122.46/16.19 ((
% 122.46/16.19 (funcImageSingleton) =>
% 122.46/16.19 ((
% 122.46/16.19 (apProp) =>
% 122.46/16.19 ((
% 122.46/16.19 (app) =>
% 122.46/16.19 ((
% 122.46/16.19 (infuncsetfunc) =>
% 122.46/16.19 ((
% 122.46/16.19 (ap2p) =>
% 122.46/16.19 ((
% 122.46/16.19 (funcinfuncset) =>
% 122.46/16.19 ((
% 122.46/16.19 (lamProp) =>
% 122.46/16.19 ((
% 122.46/16.19 (lamp) =>
% 122.46/16.19 ((
% 122.46/16.19 (lam2p) =>
% 122.46/16.19 ((
% 122.46/16.19 (brelnall1) =>
% 122.46/16.19 ((
% 122.46/16.19 (brelnall2) =>
% 122.46/16.19 ((
% 122.46/16.19 (ex1E2) =>
% 122.46/16.19 ((
% 122.46/16.19 (funcGraphProp1) =>
% 122.46/16.19 ((
% 122.46/16.19 (funcGraphProp3) =>
% 122.46/16.19 ((
% 122.46/16.19 (funcGraphProp2) =>
% 122.46/16.19 ((
% 122.46/16.19 (funcextLem) =>
% 122.46/16.19 ((
% 122.46/16.19 (funcGraphProp4) =>
% 122.46/16.19 ((
% 122.46/16.19 (subbreln) =>
% 122.46/16.19 ((
% 122.46/16.19 (eqbreln) =>
% 122.46/16.19 ((
% 122.46/16.19 (funcext) =>
% 122.46/16.19 ((
% 122.46/16.19 (funcext2) =>
% 122.46/16.19 ((
% 122.46/16.19 (ap2apEq1) =>
% 122.46/16.19 ((
% 122.46/16.19 (ap2apEq2) =>
% 122.46/16.19 ((
% 122.46/16.19 (beta1) =>
% 122.46/16.19 ((
% 122.46/16.19 (eta1) =>
% 122.46/16.19 ((
% 122.46/16.19 (lam2lamEq) =>
% 122.46/16.19 ((
% 122.46/16.19 (beta2) =>
% 122.46/16.19 ((
% 122.46/16.19 (eta2) =>
% 122.46/16.19 ((
% 122.46/16.19 (iffalseProp1) =>
% 122.46/16.19 ((
% 122.46/16.19 (iffalseProp2) =>
% 122.46/16.19 ((
% 122.46/16.19 (iftrueProp1) =>
% 122.46/16.19 ((
% 122.46/16.19 (iftrueProp2) =>
% 122.46/16.19 ((
% 122.46/16.19 (ifSingleton) =>
% 122.46/16.19 ((
% 122.46/16.19 (ifp) =>
% 122.46/16.19 ((
% 122.46/16.19 (theeq) =>
% 122.46/16.19 ((
% 122.46/16.19 (iftrue) =>
% 122.46/16.19 ((
% 122.46/16.19 (iffalse) =>
% 122.46/16.19 ((
% 122.46/16.19 (iftrueorfalse) =>
% 122.46/16.19 ((
% 122.46/16.19 (binintersectT_lem) =>
% 122.46/16.19 ((
% 122.46/16.19 (binunionT_lem) =>
% 122.46/16.19 ((
% 122.46/16.19 (powersetT_lem) =>
% 122.46/16.19 ((
% 122.46/16.19 (setminusT_lem) =>
% 122.46/16.19 ((
% 122.46/16.19 (complementT_lem) =>
% 122.46/16.19 ((
% 122.46/16.19 (setextT) =>
% 122.46/16.19 ((
% 122.46/16.19 (subsetTI) =>
% 122.46/16.19 ((
% 122.46/16.19 (powersetTI1) =>
% 122.46/16.19 ((
% 122.46/16.19 (powersetTE1) =>
% 122.46/16.19 ((
% 122.46/16.19 (complementTI1) =>
% 122.46/16.19 ((
% 122.46/16.19 (complementTE1) =>
% 122.46/16.19 ((
% 122.46/16.19 (binintersectTELcontra) =>
% 122.46/16.19 ((
% 122.46/16.19 (binintersectTERcontra) =>
% 122.46/16.19 ((
% 122.46/16.19 (contrasubsetT) =>
% 122.46/16.19 ((
% 122.46/16.19 (contrasubsetT1) =>
% 122.46/16.19 ((
% 122.46/16.19 (contrasubsetT2) =>
% 122.46/16.19 ((
% 122.46/16.19 (contrasubsetT3) =>
% 122.46/16.19 ((
% 122.46/16.19 (doubleComplementI1) =>
% 122.46/16.19 ((
% 122.46/16.19 (doubleComplementE1) =>
% 122.46/16.19 ((
% 122.46/16.19 (doubleComplementSub1) =>
% 122.46/16.19 ((
% 122.46/16.19 (doubleComplementSub2) =>
% 122.46/16.19 ((
% 122.46/16.19 (doubleComplementEq) =>
% 122.46/16.19 ((
% 122.46/16.19 (complementTnotintersectT) =>
% 122.46/16.19 ((
% 122.46/16.19 (complementImpComplementIntersect) =>
% 122.46/16.19 ((
% 122.46/16.19 (complementSubsetComplementIntersect) =>
% 122.46/16.19 ((
% 122.46/16.19 (complementInPowersetComplementIntersect) =>
% 122.46/16.19 ((
% 122.46/16.19 (contraSubsetComplement) =>
% 122.46/16.19 ((
% 122.46/16.19 (complementTcontraSubset) =>
% 122.46/16.19 ((
% 122.46/16.19 (binunionTILcontra) =>
% 122.46/16.19 ((
% 122.46/16.19 (binunionTIRcontra) =>
% 122.46/16.19 ((
% 122.46/16.19 (inIntersectImpInUnion) =>
% 122.46/16.19 ((
% 122.46/16.19 (inIntersectImpInUnion2) =>
% 122.46/16.19 ((
% 122.46/16.19 (inIntersectImpInIntersectUnions) =>
% 122.46/16.19 ((
% 122.46/16.19 (intersectInPowersetIntersectUnions) =>
% 122.46/16.19 ((
% 122.46/16.19 (inComplementUnionImpNotIn1) =>
% 122.46/16.19 ((
% 122.46/16.19 (inComplementUnionImpInComplement1) =>
% 122.46/16.19 ((
% 122.46/16.19 (binunionTE) =>
% 122.46/16.19 ((
% 122.46/16.19 (binunionTEcontra) =>
% 122.46/16.19 ((
% 122.46/16.19 (demorgan2a1) =>
% 122.46/16.19 ((
% 122.46/16.19 (complementUnionInPowersetComplement) =>
% 122.46/16.19 ((
% 122.46/16.19 (demorgan2a2) =>
% 122.46/16.19 ((
% 122.46/16.19 (demorgan1a) =>
% 122.46/16.19 ((
% 122.46/16.19 (demorgan1b) =>
% 122.46/16.19 ((
% 122.46/16.19 (demorgan1) =>
% 122.46/16.19 ((
% 122.46/16.19 (demorgan2a) =>
% 122.46/16.19 ((
% 122.46/16.19 (demorgan2b2) =>
% 122.46/16.19 ((
% 122.46/16.19 (demorgan2b) =>
% 122.46/16.19 ((
% 122.46/16.19 (demorgan2) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz13rule0) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz13rule1) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz13rule2) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz13rule3) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz13rule4) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz1_1) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz1_2) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz1_3) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz1_4) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz1_5) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1all2) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1SetBreln1) =>
% 122.46/16.19 ((
% 122.46/16.19 (choice2fnsingleton) =>
% 122.46/16.19 ((
% 122.46/16.19 (setOfPairsIsBReln1) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1all1) =>
% 122.46/16.19 ((
% 122.46/16.19 (subbreln1) =>
% 122.46/16.19 ((
% 122.46/16.19 (eqbreln1) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1invprop) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1invI) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1invE) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1compprop) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1compI) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1compE) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1compEex) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1unionprop) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1unionIL) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1unionIR) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1unionI) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1unionE) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1unionEcases) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1unionCommutes) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz2Ex) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz2W) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz2A) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz2B) =>
% 122.46/16.19 ((
% 122.46/16.19 (image1Ex) =>
% 122.46/16.19 ((
% 122.46/16.19 (image1Ex1) =>
% 122.46/16.19 ((
% 122.46/16.19 (image1Equiv) =>
% 122.46/16.19 ((
% 122.46/16.19 (image1E) =>
% 122.46/16.19 ((
% 122.46/16.19 (image1I) =>
% 122.46/16.19 ((
% 122.46/16.19 (injFuncInInjFuncSet) =>
% 122.46/16.19 ((
% 122.46/16.19 (!!) @ (
% 122.46/16.19 (('#B') @ (
% 122.46/16.19 !!) @
% 122.46/16.19 (
% 122.46/16.19 (
% 122.46/16.19 ('#B') @ (
% 122.46/16.19 (
% 122.46/16.19 ('#B') @ (
% 122.46/16.19 !!))) @
% 122.46/16.19 (
% 122.46/16.19 (
% 122.46/16.19 ('#S') @ (
% 122.46/16.19 (
% 122.46/16.19 ('#B') @ (
% 122.46/16.19 '#S') @
% 122.46/16.19 (
% 122.46/16.19 (
% 122.46/16.19 ('#B') @ (
% 122.46/16.19 (
% 122.46/16.19 ('#B') @ (
% 122.46/16.19 '#S'))) @
% 122.46/16.19 (
% 122.46/16.19 (
% 122.46/16.19 ('#B') @ (
% 122.46/16.19 (
% 122.46/16.19 ('#B') @ (
% 122.46/16.19 (
% 122.46/16.19 ('#B') @ (
% 122.46/16.19 =>))))) @
% 122.46/16.19 (
% 122.46/16.19 (
% 122.46/16.19 ('#B') @ (
% 122.46/16.19 (
% 122.46/16.19 ('#B') @ (
% 122.46/16.19 (
% 122.46/16.19 ('#C') @ in)))) @
% 122.46/16.19 injFuncSet)))))))) @
% 122.46/16.19 (
% 122.46/16.19 (
% 122.46/16.19 ('#B') @ (
% 122.46/16.19 (
% 122.46/16.19 ('#B') @ (
% 122.46/16.19 (
% 122.46/16.19 ('#C') @ in)))) @
% 122.46/16.19 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.46/16.19 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1396])).
% 122.46/16.19 thf(zip_derived_cl1420, plain,
% 122.46/16.19 (~ (((singletonsubset) =>
% 122.46/16.19 (((singletoninpowerset) =>
% 122.46/16.19 (((singletoninpowunion) =>
% 122.46/16.19 (((upairset2E) =>
% 122.46/16.19 (((upairsubunion) =>
% 122.46/16.19 (((upairinpowunion) =>
% 122.46/16.19 (((ubforcartprodlem1) =>
% 122.46/16.19 (((ubforcartprodlem2) =>
% 122.46/16.19 (((ubforcartprodlem3) =>
% 122.46/16.19 (((cartprodpairin) =>
% 122.46/16.19 (((cartprodmempair1) =>
% 122.46/16.19 (((cartprodmempair) =>
% 122.46/16.19 (((setunionE2) =>
% 122.46/16.19 (((setunionsingleton1) =>
% 122.46/16.19 (((setunionsingleton2) =>
% 122.46/16.19 (((setunionsingleton) =>
% 122.46/16.19 (((singletonprop) =>
% 122.46/16.19 (((ex1E1) =>
% 122.46/16.19 (((ex1I) =>
% 122.46/16.19 (((ex1I2) =>
% 122.46/16.19 (((singletonsuniq) =>
% 122.46/16.19 (((setukpairinjL1) =>
% 122.46/16.19 (((kfstsingleton) =>
% 122.46/16.19 (((theprop) =>
% 122.46/16.19 (((kfstpairEq) =>
% 122.46/16.19 (((cartprodfstin) =>
% 122.46/16.19 (((setukpairinjL2) =>
% 122.46/16.19 (((setukpairinjL) =>
% 122.46/16.19 (((setukpairinjR11) =>
% 122.46/16.19 (((setukpairinjR12) =>
% 122.46/16.19 ((
% 122.46/16.19 (setukpairinjR1) =>
% 122.46/16.19 ((
% 122.46/16.19 (upairequniteq) =>
% 122.46/16.19 ((
% 122.46/16.19 (setukpairinjR2) =>
% 122.46/16.19 ((
% 122.46/16.19 (setukpairinjR) =>
% 122.46/16.19 ((
% 122.46/16.19 (ksndsingleton) =>
% 122.46/16.19 ((
% 122.46/16.19 (ksndpairEq) =>
% 122.46/16.19 ((
% 122.46/16.19 (kpairsurjEq) =>
% 122.46/16.19 ((
% 122.46/16.19 (cartprodsndin) =>
% 122.46/16.19 ((
% 122.46/16.19 (cartprodpairmemEL) =>
% 122.46/16.19 ((
% 122.46/16.19 (cartprodpairmemER) =>
% 122.46/16.19 ((
% 122.46/16.19 (cartprodmempaircEq) =>
% 122.46/16.19 ((
% 122.46/16.19 (cartprodfstpairEq) =>
% 122.46/16.19 ((
% 122.46/16.19 (cartprodsndpairEq) =>
% 122.46/16.19 ((
% 122.46/16.19 (cartprodpairsurjEq) =>
% 122.46/16.19 ((
% 122.46/16.19 (dpsetconstrI) =>
% 122.46/16.19 ((
% 122.46/16.19 (dpsetconstrSub) =>
% 122.46/16.19 ((
% 122.46/16.19 (setOfPairsIsBReln) =>
% 122.46/16.19 ((
% 122.46/16.19 (dpsetconstrERa) =>
% 122.46/16.19 ((
% 122.46/16.19 (dpsetconstrEL1) =>
% 122.46/16.19 ((
% 122.46/16.19 (dpsetconstrEL2) =>
% 122.46/16.19 ((
% 122.46/16.19 (dpsetconstrER) =>
% 122.46/16.19 ((
% 122.46/16.19 (funcImageSingleton) =>
% 122.46/16.19 ((
% 122.46/16.19 (apProp) =>
% 122.46/16.19 ((
% 122.46/16.19 (app) =>
% 122.46/16.19 ((
% 122.46/16.19 (infuncsetfunc) =>
% 122.46/16.19 ((
% 122.46/16.19 (ap2p) =>
% 122.46/16.19 ((
% 122.46/16.19 (funcinfuncset) =>
% 122.46/16.19 ((
% 122.46/16.19 (lamProp) =>
% 122.46/16.19 ((
% 122.46/16.19 (lamp) =>
% 122.46/16.19 ((
% 122.46/16.19 (lam2p) =>
% 122.46/16.19 ((
% 122.46/16.19 (brelnall1) =>
% 122.46/16.19 ((
% 122.46/16.19 (brelnall2) =>
% 122.46/16.19 ((
% 122.46/16.19 (ex1E2) =>
% 122.46/16.19 ((
% 122.46/16.19 (funcGraphProp1) =>
% 122.46/16.19 ((
% 122.46/16.19 (funcGraphProp3) =>
% 122.46/16.19 ((
% 122.46/16.19 (funcGraphProp2) =>
% 122.46/16.19 ((
% 122.46/16.19 (funcextLem) =>
% 122.46/16.19 ((
% 122.46/16.19 (funcGraphProp4) =>
% 122.46/16.19 ((
% 122.46/16.19 (subbreln) =>
% 122.46/16.19 ((
% 122.46/16.19 (eqbreln) =>
% 122.46/16.19 ((
% 122.46/16.19 (funcext) =>
% 122.46/16.19 ((
% 122.46/16.19 (funcext2) =>
% 122.46/16.19 ((
% 122.46/16.19 (ap2apEq1) =>
% 122.46/16.19 ((
% 122.46/16.19 (ap2apEq2) =>
% 122.46/16.19 ((
% 122.46/16.19 (beta1) =>
% 122.46/16.19 ((
% 122.46/16.19 (eta1) =>
% 122.46/16.19 ((
% 122.46/16.19 (lam2lamEq) =>
% 122.46/16.19 ((
% 122.46/16.19 (beta2) =>
% 122.46/16.19 ((
% 122.46/16.19 (eta2) =>
% 122.46/16.19 ((
% 122.46/16.19 (iffalseProp1) =>
% 122.46/16.19 ((
% 122.46/16.19 (iffalseProp2) =>
% 122.46/16.19 ((
% 122.46/16.19 (iftrueProp1) =>
% 122.46/16.19 ((
% 122.46/16.19 (iftrueProp2) =>
% 122.46/16.19 ((
% 122.46/16.19 (ifSingleton) =>
% 122.46/16.19 ((
% 122.46/16.19 (ifp) =>
% 122.46/16.19 ((
% 122.46/16.19 (theeq) =>
% 122.46/16.19 ((
% 122.46/16.19 (iftrue) =>
% 122.46/16.19 ((
% 122.46/16.19 (iffalse) =>
% 122.46/16.19 ((
% 122.46/16.19 (iftrueorfalse) =>
% 122.46/16.19 ((
% 122.46/16.19 (binintersectT_lem) =>
% 122.46/16.19 ((
% 122.46/16.19 (binunionT_lem) =>
% 122.46/16.19 ((
% 122.46/16.19 (powersetT_lem) =>
% 122.46/16.19 ((
% 122.46/16.19 (setminusT_lem) =>
% 122.46/16.19 ((
% 122.46/16.19 (complementT_lem) =>
% 122.46/16.19 ((
% 122.46/16.19 (setextT) =>
% 122.46/16.19 ((
% 122.46/16.19 (subsetTI) =>
% 122.46/16.19 ((
% 122.46/16.19 (powersetTI1) =>
% 122.46/16.19 ((
% 122.46/16.19 (powersetTE1) =>
% 122.46/16.19 ((
% 122.46/16.19 (complementTI1) =>
% 122.46/16.19 ((
% 122.46/16.19 (complementTE1) =>
% 122.46/16.19 ((
% 122.46/16.19 (binintersectTELcontra) =>
% 122.46/16.19 ((
% 122.46/16.19 (binintersectTERcontra) =>
% 122.46/16.19 ((
% 122.46/16.19 (contrasubsetT) =>
% 122.46/16.19 ((
% 122.46/16.19 (contrasubsetT1) =>
% 122.46/16.19 ((
% 122.46/16.19 (contrasubsetT2) =>
% 122.46/16.19 ((
% 122.46/16.19 (contrasubsetT3) =>
% 122.46/16.19 ((
% 122.46/16.19 (doubleComplementI1) =>
% 122.46/16.19 ((
% 122.46/16.19 (doubleComplementE1) =>
% 122.46/16.19 ((
% 122.46/16.19 (doubleComplementSub1) =>
% 122.46/16.19 ((
% 122.46/16.19 (doubleComplementSub2) =>
% 122.46/16.19 ((
% 122.46/16.19 (doubleComplementEq) =>
% 122.46/16.19 ((
% 122.46/16.19 (complementTnotintersectT) =>
% 122.46/16.19 ((
% 122.46/16.19 (complementImpComplementIntersect) =>
% 122.46/16.19 ((
% 122.46/16.19 (complementSubsetComplementIntersect) =>
% 122.46/16.19 ((
% 122.46/16.19 (complementInPowersetComplementIntersect) =>
% 122.46/16.19 ((
% 122.46/16.19 (contraSubsetComplement) =>
% 122.46/16.19 ((
% 122.46/16.19 (complementTcontraSubset) =>
% 122.46/16.19 ((
% 122.46/16.19 (binunionTILcontra) =>
% 122.46/16.19 ((
% 122.46/16.19 (binunionTIRcontra) =>
% 122.46/16.19 ((
% 122.46/16.19 (inIntersectImpInUnion) =>
% 122.46/16.19 ((
% 122.46/16.19 (inIntersectImpInUnion2) =>
% 122.46/16.19 ((
% 122.46/16.19 (inIntersectImpInIntersectUnions) =>
% 122.46/16.19 ((
% 122.46/16.19 (intersectInPowersetIntersectUnions) =>
% 122.46/16.19 ((
% 122.46/16.19 (inComplementUnionImpNotIn1) =>
% 122.46/16.19 ((
% 122.46/16.19 (inComplementUnionImpInComplement1) =>
% 122.46/16.19 ((
% 122.46/16.19 (binunionTE) =>
% 122.46/16.19 ((
% 122.46/16.19 (binunionTEcontra) =>
% 122.46/16.19 ((
% 122.46/16.19 (demorgan2a1) =>
% 122.46/16.19 ((
% 122.46/16.19 (complementUnionInPowersetComplement) =>
% 122.46/16.19 ((
% 122.46/16.19 (demorgan2a2) =>
% 122.46/16.19 ((
% 122.46/16.19 (demorgan1a) =>
% 122.46/16.19 ((
% 122.46/16.19 (demorgan1b) =>
% 122.46/16.19 ((
% 122.46/16.19 (demorgan1) =>
% 122.46/16.19 ((
% 122.46/16.19 (demorgan2a) =>
% 122.46/16.19 ((
% 122.46/16.19 (demorgan2b2) =>
% 122.46/16.19 ((
% 122.46/16.19 (demorgan2b) =>
% 122.46/16.19 ((
% 122.46/16.19 (demorgan2) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz13rule0) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz13rule1) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz13rule2) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz13rule3) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz13rule4) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz1_1) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz1_2) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz1_3) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz1_4) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz1_5) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1all2) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1SetBreln1) =>
% 122.46/16.19 ((
% 122.46/16.19 (choice2fnsingleton) =>
% 122.46/16.19 ((
% 122.46/16.19 (setOfPairsIsBReln1) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1all1) =>
% 122.46/16.19 ((
% 122.46/16.19 (subbreln1) =>
% 122.46/16.19 ((
% 122.46/16.19 (eqbreln1) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1invprop) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1invI) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1invE) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1compprop) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1compI) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1compE) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1compEex) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1unionprop) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1unionIL) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1unionIR) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1unionI) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1unionE) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1unionEcases) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1unionCommutes) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz2Ex) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz2W) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz2A) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz2B) =>
% 122.46/16.19 ((
% 122.46/16.19 (image1Ex) =>
% 122.46/16.19 ((
% 122.46/16.19 (image1Ex1) =>
% 122.46/16.19 ((
% 122.46/16.19 (image1Equiv) =>
% 122.46/16.19 ((
% 122.46/16.19 (image1E) =>
% 122.46/16.19 ((
% 122.46/16.19 (image1I) =>
% 122.46/16.19 ((
% 122.46/16.19 (injFuncInInjFuncSet) =>
% 122.46/16.19 ((
% 122.46/16.19 (!!) @ (
% 122.46/16.19 (('#B') @ (
% 122.46/16.19 !!) @
% 122.46/16.19 (
% 122.46/16.19 (
% 122.46/16.19 ('#B') @ (
% 122.46/16.19 (
% 122.46/16.19 ('#B') @ (
% 122.46/16.19 !!))) @
% 122.46/16.19 (
% 122.46/16.19 (
% 122.46/16.19 ('#S') @ (
% 122.46/16.19 (
% 122.46/16.19 ('#B') @ (
% 122.46/16.19 '#S') @
% 122.46/16.19 (
% 122.46/16.19 (
% 122.46/16.19 ('#B') @ (
% 122.46/16.19 (
% 122.46/16.19 ('#B') @ (
% 122.46/16.19 '#S'))) @
% 122.46/16.19 (
% 122.46/16.19 (
% 122.46/16.19 ('#B') @ (
% 122.46/16.19 (
% 122.46/16.19 ('#B') @ (
% 122.46/16.19 (
% 122.46/16.19 ('#B') @ (
% 122.46/16.19 =>))))) @
% 122.46/16.19 (
% 122.46/16.19 (
% 122.46/16.19 ('#B') @ (
% 122.46/16.19 (
% 122.46/16.19 ('#B') @ (
% 122.46/16.19 (
% 122.46/16.19 ('#C') @ in)))) @
% 122.46/16.19 injFuncSet)))))))) @
% 122.46/16.19 (
% 122.46/16.19 (
% 122.46/16.19 ('#B') @ (
% 122.46/16.19 (
% 122.46/16.19 ('#B') @ (
% 122.46/16.19 (
% 122.46/16.19 ('#C') @ in)))) @
% 122.46/16.19 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.46/16.19 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1407])).
% 122.46/16.19 thf(zip_derived_cl1433, plain,
% 122.46/16.19 (~ (((singletoninpowerset) =>
% 122.46/16.19 (((singletoninpowunion) =>
% 122.46/16.19 (((upairset2E) =>
% 122.46/16.19 (((upairsubunion) =>
% 122.46/16.19 (((upairinpowunion) =>
% 122.46/16.19 (((ubforcartprodlem1) =>
% 122.46/16.19 (((ubforcartprodlem2) =>
% 122.46/16.19 (((ubforcartprodlem3) =>
% 122.46/16.19 (((cartprodpairin) =>
% 122.46/16.19 (((cartprodmempair1) =>
% 122.46/16.19 (((cartprodmempair) =>
% 122.46/16.19 (((setunionE2) =>
% 122.46/16.19 (((setunionsingleton1) =>
% 122.46/16.19 (((setunionsingleton2) =>
% 122.46/16.19 (((setunionsingleton) =>
% 122.46/16.19 (((singletonprop) =>
% 122.46/16.19 (((ex1E1) =>
% 122.46/16.19 (((ex1I) =>
% 122.46/16.19 (((ex1I2) =>
% 122.46/16.19 (((singletonsuniq) =>
% 122.46/16.19 (((setukpairinjL1) =>
% 122.46/16.19 (((kfstsingleton) =>
% 122.46/16.19 (((theprop) =>
% 122.46/16.19 (((kfstpairEq) =>
% 122.46/16.19 (((cartprodfstin) =>
% 122.46/16.19 (((setukpairinjL2) =>
% 122.46/16.19 (((setukpairinjL) =>
% 122.46/16.19 (((setukpairinjR11) =>
% 122.46/16.19 (((setukpairinjR12) =>
% 122.46/16.19 (((setukpairinjR1) =>
% 122.46/16.19 ((
% 122.46/16.19 (upairequniteq) =>
% 122.46/16.19 ((
% 122.46/16.19 (setukpairinjR2) =>
% 122.46/16.19 ((
% 122.46/16.19 (setukpairinjR) =>
% 122.46/16.19 ((
% 122.46/16.19 (ksndsingleton) =>
% 122.46/16.19 ((
% 122.46/16.19 (ksndpairEq) =>
% 122.46/16.19 ((
% 122.46/16.19 (kpairsurjEq) =>
% 122.46/16.19 ((
% 122.46/16.19 (cartprodsndin) =>
% 122.46/16.19 ((
% 122.46/16.19 (cartprodpairmemEL) =>
% 122.46/16.19 ((
% 122.46/16.19 (cartprodpairmemER) =>
% 122.46/16.19 ((
% 122.46/16.19 (cartprodmempaircEq) =>
% 122.46/16.19 ((
% 122.46/16.19 (cartprodfstpairEq) =>
% 122.46/16.19 ((
% 122.46/16.19 (cartprodsndpairEq) =>
% 122.46/16.19 ((
% 122.46/16.19 (cartprodpairsurjEq) =>
% 122.46/16.19 ((
% 122.46/16.19 (dpsetconstrI) =>
% 122.46/16.19 ((
% 122.46/16.19 (dpsetconstrSub) =>
% 122.46/16.19 ((
% 122.46/16.19 (setOfPairsIsBReln) =>
% 122.46/16.19 ((
% 122.46/16.19 (dpsetconstrERa) =>
% 122.46/16.19 ((
% 122.46/16.19 (dpsetconstrEL1) =>
% 122.46/16.19 ((
% 122.46/16.19 (dpsetconstrEL2) =>
% 122.46/16.19 ((
% 122.46/16.19 (dpsetconstrER) =>
% 122.46/16.19 ((
% 122.46/16.19 (funcImageSingleton) =>
% 122.46/16.19 ((
% 122.46/16.19 (apProp) =>
% 122.46/16.19 ((
% 122.46/16.19 (app) =>
% 122.46/16.19 ((
% 122.46/16.19 (infuncsetfunc) =>
% 122.46/16.19 ((
% 122.46/16.19 (ap2p) =>
% 122.46/16.19 ((
% 122.46/16.19 (funcinfuncset) =>
% 122.46/16.19 ((
% 122.46/16.19 (lamProp) =>
% 122.46/16.19 ((
% 122.46/16.19 (lamp) =>
% 122.46/16.19 ((
% 122.46/16.19 (lam2p) =>
% 122.46/16.19 ((
% 122.46/16.19 (brelnall1) =>
% 122.46/16.19 ((
% 122.46/16.19 (brelnall2) =>
% 122.46/16.19 ((
% 122.46/16.19 (ex1E2) =>
% 122.46/16.19 ((
% 122.46/16.19 (funcGraphProp1) =>
% 122.46/16.19 ((
% 122.46/16.19 (funcGraphProp3) =>
% 122.46/16.19 ((
% 122.46/16.19 (funcGraphProp2) =>
% 122.46/16.19 ((
% 122.46/16.19 (funcextLem) =>
% 122.46/16.19 ((
% 122.46/16.19 (funcGraphProp4) =>
% 122.46/16.19 ((
% 122.46/16.19 (subbreln) =>
% 122.46/16.19 ((
% 122.46/16.19 (eqbreln) =>
% 122.46/16.19 ((
% 122.46/16.19 (funcext) =>
% 122.46/16.19 ((
% 122.46/16.19 (funcext2) =>
% 122.46/16.19 ((
% 122.46/16.19 (ap2apEq1) =>
% 122.46/16.19 ((
% 122.46/16.19 (ap2apEq2) =>
% 122.46/16.19 ((
% 122.46/16.19 (beta1) =>
% 122.46/16.19 ((
% 122.46/16.19 (eta1) =>
% 122.46/16.19 ((
% 122.46/16.19 (lam2lamEq) =>
% 122.46/16.19 ((
% 122.46/16.19 (beta2) =>
% 122.46/16.19 ((
% 122.46/16.19 (eta2) =>
% 122.46/16.19 ((
% 122.46/16.19 (iffalseProp1) =>
% 122.46/16.19 ((
% 122.46/16.19 (iffalseProp2) =>
% 122.46/16.19 ((
% 122.46/16.19 (iftrueProp1) =>
% 122.46/16.19 ((
% 122.46/16.19 (iftrueProp2) =>
% 122.46/16.19 ((
% 122.46/16.19 (ifSingleton) =>
% 122.46/16.19 ((
% 122.46/16.19 (ifp) =>
% 122.46/16.19 ((
% 122.46/16.19 (theeq) =>
% 122.46/16.19 ((
% 122.46/16.19 (iftrue) =>
% 122.46/16.19 ((
% 122.46/16.19 (iffalse) =>
% 122.46/16.19 ((
% 122.46/16.19 (iftrueorfalse) =>
% 122.46/16.19 ((
% 122.46/16.19 (binintersectT_lem) =>
% 122.46/16.19 ((
% 122.46/16.19 (binunionT_lem) =>
% 122.46/16.19 ((
% 122.46/16.19 (powersetT_lem) =>
% 122.46/16.19 ((
% 122.46/16.19 (setminusT_lem) =>
% 122.46/16.19 ((
% 122.46/16.19 (complementT_lem) =>
% 122.46/16.19 ((
% 122.46/16.19 (setextT) =>
% 122.46/16.19 ((
% 122.46/16.19 (subsetTI) =>
% 122.46/16.19 ((
% 122.46/16.19 (powersetTI1) =>
% 122.46/16.19 ((
% 122.46/16.19 (powersetTE1) =>
% 122.46/16.19 ((
% 122.46/16.19 (complementTI1) =>
% 122.46/16.19 ((
% 122.46/16.19 (complementTE1) =>
% 122.46/16.19 ((
% 122.46/16.19 (binintersectTELcontra) =>
% 122.46/16.19 ((
% 122.46/16.19 (binintersectTERcontra) =>
% 122.46/16.19 ((
% 122.46/16.19 (contrasubsetT) =>
% 122.46/16.19 ((
% 122.46/16.19 (contrasubsetT1) =>
% 122.46/16.19 ((
% 122.46/16.19 (contrasubsetT2) =>
% 122.46/16.19 ((
% 122.46/16.19 (contrasubsetT3) =>
% 122.46/16.19 ((
% 122.46/16.19 (doubleComplementI1) =>
% 122.46/16.19 ((
% 122.46/16.19 (doubleComplementE1) =>
% 122.46/16.19 ((
% 122.46/16.19 (doubleComplementSub1) =>
% 122.46/16.19 ((
% 122.46/16.19 (doubleComplementSub2) =>
% 122.46/16.19 ((
% 122.46/16.19 (doubleComplementEq) =>
% 122.46/16.19 ((
% 122.46/16.19 (complementTnotintersectT) =>
% 122.46/16.19 ((
% 122.46/16.19 (complementImpComplementIntersect) =>
% 122.46/16.19 ((
% 122.46/16.19 (complementSubsetComplementIntersect) =>
% 122.46/16.19 ((
% 122.46/16.19 (complementInPowersetComplementIntersect) =>
% 122.46/16.19 ((
% 122.46/16.19 (contraSubsetComplement) =>
% 122.46/16.19 ((
% 122.46/16.19 (complementTcontraSubset) =>
% 122.46/16.19 ((
% 122.46/16.19 (binunionTILcontra) =>
% 122.46/16.19 ((
% 122.46/16.19 (binunionTIRcontra) =>
% 122.46/16.19 ((
% 122.46/16.19 (inIntersectImpInUnion) =>
% 122.46/16.19 ((
% 122.46/16.19 (inIntersectImpInUnion2) =>
% 122.46/16.19 ((
% 122.46/16.19 (inIntersectImpInIntersectUnions) =>
% 122.46/16.19 ((
% 122.46/16.19 (intersectInPowersetIntersectUnions) =>
% 122.46/16.19 ((
% 122.46/16.19 (inComplementUnionImpNotIn1) =>
% 122.46/16.19 ((
% 122.46/16.19 (inComplementUnionImpInComplement1) =>
% 122.46/16.19 ((
% 122.46/16.19 (binunionTE) =>
% 122.46/16.19 ((
% 122.46/16.19 (binunionTEcontra) =>
% 122.46/16.19 ((
% 122.46/16.19 (demorgan2a1) =>
% 122.46/16.19 ((
% 122.46/16.19 (complementUnionInPowersetComplement) =>
% 122.46/16.19 ((
% 122.46/16.19 (demorgan2a2) =>
% 122.46/16.19 ((
% 122.46/16.19 (demorgan1a) =>
% 122.46/16.19 ((
% 122.46/16.19 (demorgan1b) =>
% 122.46/16.19 ((
% 122.46/16.19 (demorgan1) =>
% 122.46/16.19 ((
% 122.46/16.19 (demorgan2a) =>
% 122.46/16.19 ((
% 122.46/16.19 (demorgan2b2) =>
% 122.46/16.19 ((
% 122.46/16.19 (demorgan2b) =>
% 122.46/16.19 ((
% 122.46/16.19 (demorgan2) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz13rule0) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz13rule1) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz13rule2) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz13rule3) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz13rule4) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz1_1) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz1_2) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz1_3) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz1_4) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz1_5) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1all2) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1SetBreln1) =>
% 122.46/16.19 ((
% 122.46/16.19 (choice2fnsingleton) =>
% 122.46/16.19 ((
% 122.46/16.19 (setOfPairsIsBReln1) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1all1) =>
% 122.46/16.19 ((
% 122.46/16.19 (subbreln1) =>
% 122.46/16.19 ((
% 122.46/16.19 (eqbreln1) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1invprop) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1invI) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1invE) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1compprop) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1compI) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1compE) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1compEex) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1unionprop) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1unionIL) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1unionIR) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1unionI) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1unionE) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1unionEcases) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1unionCommutes) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz2Ex) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz2W) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz2A) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz2B) =>
% 122.46/16.19 ((
% 122.46/16.19 (image1Ex) =>
% 122.46/16.19 ((
% 122.46/16.19 (image1Ex1) =>
% 122.46/16.19 ((
% 122.46/16.19 (image1Equiv) =>
% 122.46/16.19 ((
% 122.46/16.19 (image1E) =>
% 122.46/16.19 ((
% 122.46/16.19 (image1I) =>
% 122.46/16.19 ((
% 122.46/16.19 (injFuncInInjFuncSet) =>
% 122.46/16.19 ((
% 122.46/16.19 (!!) @ (
% 122.46/16.19 (('#B') @ (
% 122.46/16.19 !!) @
% 122.46/16.19 (
% 122.46/16.19 (
% 122.46/16.19 ('#B') @ (
% 122.46/16.19 (
% 122.46/16.19 ('#B') @ (
% 122.46/16.19 !!))) @
% 122.46/16.19 (
% 122.46/16.19 (
% 122.46/16.19 ('#S') @ (
% 122.46/16.19 (
% 122.46/16.19 ('#B') @ (
% 122.46/16.19 '#S') @
% 122.46/16.19 (
% 122.46/16.19 (
% 122.46/16.19 ('#B') @ (
% 122.46/16.19 (
% 122.46/16.19 ('#B') @ (
% 122.46/16.19 '#S'))) @
% 122.46/16.19 (
% 122.46/16.19 (
% 122.46/16.19 ('#B') @ (
% 122.46/16.19 (
% 122.46/16.19 ('#B') @ (
% 122.46/16.19 (
% 122.46/16.19 ('#B') @ (
% 122.46/16.19 =>))))) @
% 122.46/16.19 (
% 122.46/16.19 (
% 122.46/16.19 ('#B') @ (
% 122.46/16.19 (
% 122.46/16.19 ('#B') @ (
% 122.46/16.19 (
% 122.46/16.19 ('#C') @ in)))) @
% 122.46/16.19 injFuncSet)))))))) @
% 122.46/16.19 (
% 122.46/16.19 (
% 122.46/16.19 ('#B') @ (
% 122.46/16.19 (
% 122.46/16.19 ('#B') @ (
% 122.46/16.19 (
% 122.46/16.19 ('#C') @ in)))) @
% 122.46/16.19 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.46/16.19 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1420])).
% 122.46/16.19 thf(zip_derived_cl1444, plain,
% 122.46/16.19 (~ (((singletoninpowunion) =>
% 122.46/16.19 (((upairset2E) =>
% 122.46/16.19 (((upairsubunion) =>
% 122.46/16.19 (((upairinpowunion) =>
% 122.46/16.19 (((ubforcartprodlem1) =>
% 122.46/16.19 (((ubforcartprodlem2) =>
% 122.46/16.19 (((ubforcartprodlem3) =>
% 122.46/16.19 (((cartprodpairin) =>
% 122.46/16.19 (((cartprodmempair1) =>
% 122.46/16.19 (((cartprodmempair) =>
% 122.46/16.19 (((setunionE2) =>
% 122.46/16.19 (((setunionsingleton1) =>
% 122.46/16.19 (((setunionsingleton2) =>
% 122.46/16.19 (((setunionsingleton) =>
% 122.46/16.19 (((singletonprop) =>
% 122.46/16.19 (((ex1E1) =>
% 122.46/16.19 (((ex1I) =>
% 122.46/16.19 (((ex1I2) =>
% 122.46/16.19 (((singletonsuniq) =>
% 122.46/16.19 (((setukpairinjL1) =>
% 122.46/16.19 (((kfstsingleton) =>
% 122.46/16.19 (((theprop) =>
% 122.46/16.19 (((kfstpairEq) =>
% 122.46/16.19 (((cartprodfstin) =>
% 122.46/16.19 (((setukpairinjL2) =>
% 122.46/16.19 (((setukpairinjL) =>
% 122.46/16.19 (((setukpairinjR11) =>
% 122.46/16.19 (((setukpairinjR12) =>
% 122.46/16.19 (((setukpairinjR1) =>
% 122.46/16.19 (((upairequniteq) =>
% 122.46/16.19 ((
% 122.46/16.19 (setukpairinjR2) =>
% 122.46/16.19 ((
% 122.46/16.19 (setukpairinjR) =>
% 122.46/16.19 ((
% 122.46/16.19 (ksndsingleton) =>
% 122.46/16.19 ((
% 122.46/16.19 (ksndpairEq) =>
% 122.46/16.19 ((
% 122.46/16.19 (kpairsurjEq) =>
% 122.46/16.19 ((
% 122.46/16.19 (cartprodsndin) =>
% 122.46/16.19 ((
% 122.46/16.19 (cartprodpairmemEL) =>
% 122.46/16.19 ((
% 122.46/16.19 (cartprodpairmemER) =>
% 122.46/16.19 ((
% 122.46/16.19 (cartprodmempaircEq) =>
% 122.46/16.19 ((
% 122.46/16.19 (cartprodfstpairEq) =>
% 122.46/16.19 ((
% 122.46/16.19 (cartprodsndpairEq) =>
% 122.46/16.19 ((
% 122.46/16.19 (cartprodpairsurjEq) =>
% 122.46/16.19 ((
% 122.46/16.19 (dpsetconstrI) =>
% 122.46/16.19 ((
% 122.46/16.19 (dpsetconstrSub) =>
% 122.46/16.19 ((
% 122.46/16.19 (setOfPairsIsBReln) =>
% 122.46/16.19 ((
% 122.46/16.19 (dpsetconstrERa) =>
% 122.46/16.19 ((
% 122.46/16.19 (dpsetconstrEL1) =>
% 122.46/16.19 ((
% 122.46/16.19 (dpsetconstrEL2) =>
% 122.46/16.19 ((
% 122.46/16.19 (dpsetconstrER) =>
% 122.46/16.19 ((
% 122.46/16.19 (funcImageSingleton) =>
% 122.46/16.19 ((
% 122.46/16.19 (apProp) =>
% 122.46/16.19 ((
% 122.46/16.19 (app) =>
% 122.46/16.19 ((
% 122.46/16.19 (infuncsetfunc) =>
% 122.46/16.19 ((
% 122.46/16.19 (ap2p) =>
% 122.46/16.19 ((
% 122.46/16.19 (funcinfuncset) =>
% 122.46/16.19 ((
% 122.46/16.19 (lamProp) =>
% 122.46/16.19 ((
% 122.46/16.19 (lamp) =>
% 122.46/16.19 ((
% 122.46/16.19 (lam2p) =>
% 122.46/16.19 ((
% 122.46/16.19 (brelnall1) =>
% 122.46/16.19 ((
% 122.46/16.19 (brelnall2) =>
% 122.46/16.19 ((
% 122.46/16.19 (ex1E2) =>
% 122.46/16.19 ((
% 122.46/16.19 (funcGraphProp1) =>
% 122.46/16.19 ((
% 122.46/16.19 (funcGraphProp3) =>
% 122.46/16.19 ((
% 122.46/16.19 (funcGraphProp2) =>
% 122.46/16.19 ((
% 122.46/16.19 (funcextLem) =>
% 122.46/16.19 ((
% 122.46/16.19 (funcGraphProp4) =>
% 122.46/16.19 ((
% 122.46/16.19 (subbreln) =>
% 122.46/16.19 ((
% 122.46/16.19 (eqbreln) =>
% 122.46/16.19 ((
% 122.46/16.19 (funcext) =>
% 122.46/16.19 ((
% 122.46/16.19 (funcext2) =>
% 122.46/16.19 ((
% 122.46/16.19 (ap2apEq1) =>
% 122.46/16.19 ((
% 122.46/16.19 (ap2apEq2) =>
% 122.46/16.19 ((
% 122.46/16.19 (beta1) =>
% 122.46/16.19 ((
% 122.46/16.19 (eta1) =>
% 122.46/16.19 ((
% 122.46/16.19 (lam2lamEq) =>
% 122.46/16.19 ((
% 122.46/16.19 (beta2) =>
% 122.46/16.19 ((
% 122.46/16.19 (eta2) =>
% 122.46/16.19 ((
% 122.46/16.19 (iffalseProp1) =>
% 122.46/16.19 ((
% 122.46/16.19 (iffalseProp2) =>
% 122.46/16.19 ((
% 122.46/16.19 (iftrueProp1) =>
% 122.46/16.19 ((
% 122.46/16.19 (iftrueProp2) =>
% 122.46/16.19 ((
% 122.46/16.19 (ifSingleton) =>
% 122.46/16.19 ((
% 122.46/16.19 (ifp) =>
% 122.46/16.19 ((
% 122.46/16.19 (theeq) =>
% 122.46/16.19 ((
% 122.46/16.19 (iftrue) =>
% 122.46/16.19 ((
% 122.46/16.19 (iffalse) =>
% 122.46/16.19 ((
% 122.46/16.19 (iftrueorfalse) =>
% 122.46/16.19 ((
% 122.46/16.19 (binintersectT_lem) =>
% 122.46/16.19 ((
% 122.46/16.19 (binunionT_lem) =>
% 122.46/16.19 ((
% 122.46/16.19 (powersetT_lem) =>
% 122.46/16.19 ((
% 122.46/16.19 (setminusT_lem) =>
% 122.46/16.19 ((
% 122.46/16.19 (complementT_lem) =>
% 122.46/16.19 ((
% 122.46/16.19 (setextT) =>
% 122.46/16.19 ((
% 122.46/16.19 (subsetTI) =>
% 122.46/16.19 ((
% 122.46/16.19 (powersetTI1) =>
% 122.46/16.19 ((
% 122.46/16.19 (powersetTE1) =>
% 122.46/16.19 ((
% 122.46/16.19 (complementTI1) =>
% 122.46/16.19 ((
% 122.46/16.19 (complementTE1) =>
% 122.46/16.19 ((
% 122.46/16.19 (binintersectTELcontra) =>
% 122.46/16.19 ((
% 122.46/16.19 (binintersectTERcontra) =>
% 122.46/16.19 ((
% 122.46/16.19 (contrasubsetT) =>
% 122.46/16.19 ((
% 122.46/16.19 (contrasubsetT1) =>
% 122.46/16.19 ((
% 122.46/16.19 (contrasubsetT2) =>
% 122.46/16.19 ((
% 122.46/16.19 (contrasubsetT3) =>
% 122.46/16.19 ((
% 122.46/16.19 (doubleComplementI1) =>
% 122.46/16.19 ((
% 122.46/16.19 (doubleComplementE1) =>
% 122.46/16.19 ((
% 122.46/16.19 (doubleComplementSub1) =>
% 122.46/16.19 ((
% 122.46/16.19 (doubleComplementSub2) =>
% 122.46/16.19 ((
% 122.46/16.19 (doubleComplementEq) =>
% 122.46/16.19 ((
% 122.46/16.19 (complementTnotintersectT) =>
% 122.46/16.19 ((
% 122.46/16.19 (complementImpComplementIntersect) =>
% 122.46/16.19 ((
% 122.46/16.19 (complementSubsetComplementIntersect) =>
% 122.46/16.19 ((
% 122.46/16.19 (complementInPowersetComplementIntersect) =>
% 122.46/16.19 ((
% 122.46/16.19 (contraSubsetComplement) =>
% 122.46/16.19 ((
% 122.46/16.19 (complementTcontraSubset) =>
% 122.46/16.19 ((
% 122.46/16.19 (binunionTILcontra) =>
% 122.46/16.19 ((
% 122.46/16.19 (binunionTIRcontra) =>
% 122.46/16.19 ((
% 122.46/16.19 (inIntersectImpInUnion) =>
% 122.46/16.19 ((
% 122.46/16.19 (inIntersectImpInUnion2) =>
% 122.46/16.19 ((
% 122.46/16.19 (inIntersectImpInIntersectUnions) =>
% 122.46/16.19 ((
% 122.46/16.19 (intersectInPowersetIntersectUnions) =>
% 122.46/16.19 ((
% 122.46/16.19 (inComplementUnionImpNotIn1) =>
% 122.46/16.19 ((
% 122.46/16.19 (inComplementUnionImpInComplement1) =>
% 122.46/16.19 ((
% 122.46/16.19 (binunionTE) =>
% 122.46/16.19 ((
% 122.46/16.19 (binunionTEcontra) =>
% 122.46/16.19 ((
% 122.46/16.19 (demorgan2a1) =>
% 122.46/16.19 ((
% 122.46/16.19 (complementUnionInPowersetComplement) =>
% 122.46/16.19 ((
% 122.46/16.19 (demorgan2a2) =>
% 122.46/16.19 ((
% 122.46/16.19 (demorgan1a) =>
% 122.46/16.19 ((
% 122.46/16.19 (demorgan1b) =>
% 122.46/16.19 ((
% 122.46/16.19 (demorgan1) =>
% 122.46/16.19 ((
% 122.46/16.19 (demorgan2a) =>
% 122.46/16.19 ((
% 122.46/16.19 (demorgan2b2) =>
% 122.46/16.19 ((
% 122.46/16.19 (demorgan2b) =>
% 122.46/16.19 ((
% 122.46/16.19 (demorgan2) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz13rule0) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz13rule1) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz13rule2) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz13rule3) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz13rule4) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz1_1) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz1_2) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz1_3) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz1_4) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz1_5) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1all2) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1SetBreln1) =>
% 122.46/16.19 ((
% 122.46/16.19 (choice2fnsingleton) =>
% 122.46/16.19 ((
% 122.46/16.19 (setOfPairsIsBReln1) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1all1) =>
% 122.46/16.19 ((
% 122.46/16.19 (subbreln1) =>
% 122.46/16.19 ((
% 122.46/16.19 (eqbreln1) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1invprop) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1invI) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1invE) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1compprop) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1compI) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1compE) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1compEex) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1unionprop) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1unionIL) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1unionIR) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1unionI) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1unionE) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1unionEcases) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1unionCommutes) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz2Ex) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz2W) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz2A) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz2B) =>
% 122.46/16.19 ((
% 122.46/16.19 (image1Ex) =>
% 122.46/16.19 ((
% 122.46/16.19 (image1Ex1) =>
% 122.46/16.19 ((
% 122.46/16.19 (image1Equiv) =>
% 122.46/16.19 ((
% 122.46/16.19 (image1E) =>
% 122.46/16.19 ((
% 122.46/16.19 (image1I) =>
% 122.46/16.19 ((
% 122.46/16.19 (injFuncInInjFuncSet) =>
% 122.46/16.19 ((
% 122.46/16.19 (!!) @ (
% 122.46/16.19 (('#B') @ (
% 122.46/16.19 !!) @
% 122.46/16.19 (
% 122.46/16.19 (
% 122.46/16.19 ('#B') @ (
% 122.46/16.19 (
% 122.46/16.19 ('#B') @ (
% 122.46/16.19 !!))) @
% 122.46/16.19 (
% 122.46/16.19 (
% 122.46/16.19 ('#S') @ (
% 122.46/16.19 (
% 122.46/16.19 ('#B') @ (
% 122.46/16.19 '#S') @
% 122.46/16.19 (
% 122.46/16.19 (
% 122.46/16.19 ('#B') @ (
% 122.46/16.19 (
% 122.46/16.19 ('#B') @ (
% 122.46/16.19 '#S'))) @
% 122.46/16.19 (
% 122.46/16.19 (
% 122.46/16.19 ('#B') @ (
% 122.46/16.19 (
% 122.46/16.19 ('#B') @ (
% 122.46/16.19 (
% 122.46/16.19 ('#B') @ (
% 122.46/16.19 =>))))) @
% 122.46/16.19 (
% 122.46/16.19 (
% 122.46/16.19 ('#B') @ (
% 122.46/16.19 (
% 122.46/16.19 ('#B') @ (
% 122.46/16.19 (
% 122.46/16.19 ('#C') @ in)))) @
% 122.46/16.19 injFuncSet)))))))) @
% 122.46/16.19 (
% 122.46/16.19 (
% 122.46/16.19 ('#B') @ (
% 122.46/16.19 (
% 122.46/16.19 ('#B') @ (
% 122.46/16.19 (
% 122.46/16.19 ('#C') @ in)))) @
% 122.46/16.19 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.46/16.19 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1433])).
% 122.46/16.19 thf(zip_derived_cl1452, plain,
% 122.46/16.19 (~ (((upairset2E) =>
% 122.46/16.19 (((upairsubunion) =>
% 122.46/16.19 (((upairinpowunion) =>
% 122.46/16.19 (((ubforcartprodlem1) =>
% 122.46/16.19 (((ubforcartprodlem2) =>
% 122.46/16.19 (((ubforcartprodlem3) =>
% 122.46/16.19 (((cartprodpairin) =>
% 122.46/16.19 (((cartprodmempair1) =>
% 122.46/16.19 (((cartprodmempair) =>
% 122.46/16.19 (((setunionE2) =>
% 122.46/16.19 (((setunionsingleton1) =>
% 122.46/16.19 (((setunionsingleton2) =>
% 122.46/16.19 (((setunionsingleton) =>
% 122.46/16.19 (((singletonprop) =>
% 122.46/16.19 (((ex1E1) =>
% 122.46/16.19 (((ex1I) =>
% 122.46/16.19 (((ex1I2) =>
% 122.46/16.19 (((singletonsuniq) =>
% 122.46/16.19 (((setukpairinjL1) =>
% 122.46/16.19 (((kfstsingleton) =>
% 122.46/16.19 (((theprop) =>
% 122.46/16.19 (((kfstpairEq) =>
% 122.46/16.19 (((cartprodfstin) =>
% 122.46/16.19 (((setukpairinjL2) =>
% 122.46/16.19 (((setukpairinjL) =>
% 122.46/16.19 (((setukpairinjR11) =>
% 122.46/16.19 (((setukpairinjR12) =>
% 122.46/16.19 (((setukpairinjR1) =>
% 122.46/16.19 (((upairequniteq) =>
% 122.46/16.19 (((setukpairinjR2) =>
% 122.46/16.19 ((
% 122.46/16.19 (setukpairinjR) =>
% 122.46/16.19 ((
% 122.46/16.19 (ksndsingleton) =>
% 122.46/16.19 ((
% 122.46/16.19 (ksndpairEq) =>
% 122.46/16.19 ((
% 122.46/16.19 (kpairsurjEq) =>
% 122.46/16.19 ((
% 122.46/16.19 (cartprodsndin) =>
% 122.46/16.19 ((
% 122.46/16.19 (cartprodpairmemEL) =>
% 122.46/16.19 ((
% 122.46/16.19 (cartprodpairmemER) =>
% 122.46/16.19 ((
% 122.46/16.19 (cartprodmempaircEq) =>
% 122.46/16.19 ((
% 122.46/16.19 (cartprodfstpairEq) =>
% 122.46/16.19 ((
% 122.46/16.19 (cartprodsndpairEq) =>
% 122.46/16.19 ((
% 122.46/16.19 (cartprodpairsurjEq) =>
% 122.46/16.19 ((
% 122.46/16.19 (dpsetconstrI) =>
% 122.46/16.19 ((
% 122.46/16.19 (dpsetconstrSub) =>
% 122.46/16.19 ((
% 122.46/16.19 (setOfPairsIsBReln) =>
% 122.46/16.19 ((
% 122.46/16.19 (dpsetconstrERa) =>
% 122.46/16.19 ((
% 122.46/16.19 (dpsetconstrEL1) =>
% 122.46/16.19 ((
% 122.46/16.19 (dpsetconstrEL2) =>
% 122.46/16.19 ((
% 122.46/16.19 (dpsetconstrER) =>
% 122.46/16.19 ((
% 122.46/16.19 (funcImageSingleton) =>
% 122.46/16.19 ((
% 122.46/16.19 (apProp) =>
% 122.46/16.19 ((
% 122.46/16.19 (app) =>
% 122.46/16.19 ((
% 122.46/16.19 (infuncsetfunc) =>
% 122.46/16.19 ((
% 122.46/16.19 (ap2p) =>
% 122.46/16.19 ((
% 122.46/16.19 (funcinfuncset) =>
% 122.46/16.19 ((
% 122.46/16.19 (lamProp) =>
% 122.46/16.19 ((
% 122.46/16.19 (lamp) =>
% 122.46/16.19 ((
% 122.46/16.19 (lam2p) =>
% 122.46/16.19 ((
% 122.46/16.19 (brelnall1) =>
% 122.46/16.19 ((
% 122.46/16.19 (brelnall2) =>
% 122.46/16.19 ((
% 122.46/16.19 (ex1E2) =>
% 122.46/16.19 ((
% 122.46/16.19 (funcGraphProp1) =>
% 122.46/16.19 ((
% 122.46/16.19 (funcGraphProp3) =>
% 122.46/16.19 ((
% 122.46/16.19 (funcGraphProp2) =>
% 122.46/16.19 ((
% 122.46/16.19 (funcextLem) =>
% 122.46/16.19 ((
% 122.46/16.19 (funcGraphProp4) =>
% 122.46/16.19 ((
% 122.46/16.19 (subbreln) =>
% 122.46/16.19 ((
% 122.46/16.19 (eqbreln) =>
% 122.46/16.19 ((
% 122.46/16.19 (funcext) =>
% 122.46/16.19 ((
% 122.46/16.19 (funcext2) =>
% 122.46/16.19 ((
% 122.46/16.19 (ap2apEq1) =>
% 122.46/16.19 ((
% 122.46/16.19 (ap2apEq2) =>
% 122.46/16.19 ((
% 122.46/16.19 (beta1) =>
% 122.46/16.19 ((
% 122.46/16.19 (eta1) =>
% 122.46/16.19 ((
% 122.46/16.19 (lam2lamEq) =>
% 122.46/16.19 ((
% 122.46/16.19 (beta2) =>
% 122.46/16.19 ((
% 122.46/16.19 (eta2) =>
% 122.46/16.19 ((
% 122.46/16.19 (iffalseProp1) =>
% 122.46/16.19 ((
% 122.46/16.19 (iffalseProp2) =>
% 122.46/16.19 ((
% 122.46/16.19 (iftrueProp1) =>
% 122.46/16.19 ((
% 122.46/16.19 (iftrueProp2) =>
% 122.46/16.19 ((
% 122.46/16.19 (ifSingleton) =>
% 122.46/16.19 ((
% 122.46/16.19 (ifp) =>
% 122.46/16.19 ((
% 122.46/16.19 (theeq) =>
% 122.46/16.19 ((
% 122.46/16.19 (iftrue) =>
% 122.46/16.19 ((
% 122.46/16.19 (iffalse) =>
% 122.46/16.19 ((
% 122.46/16.19 (iftrueorfalse) =>
% 122.46/16.19 ((
% 122.46/16.19 (binintersectT_lem) =>
% 122.46/16.19 ((
% 122.46/16.19 (binunionT_lem) =>
% 122.46/16.19 ((
% 122.46/16.19 (powersetT_lem) =>
% 122.46/16.19 ((
% 122.46/16.19 (setminusT_lem) =>
% 122.46/16.19 ((
% 122.46/16.19 (complementT_lem) =>
% 122.46/16.19 ((
% 122.46/16.19 (setextT) =>
% 122.46/16.19 ((
% 122.46/16.19 (subsetTI) =>
% 122.46/16.19 ((
% 122.46/16.19 (powersetTI1) =>
% 122.46/16.19 ((
% 122.46/16.19 (powersetTE1) =>
% 122.46/16.19 ((
% 122.46/16.19 (complementTI1) =>
% 122.46/16.19 ((
% 122.46/16.19 (complementTE1) =>
% 122.46/16.19 ((
% 122.46/16.19 (binintersectTELcontra) =>
% 122.46/16.19 ((
% 122.46/16.19 (binintersectTERcontra) =>
% 122.46/16.19 ((
% 122.46/16.19 (contrasubsetT) =>
% 122.46/16.19 ((
% 122.46/16.19 (contrasubsetT1) =>
% 122.46/16.19 ((
% 122.46/16.19 (contrasubsetT2) =>
% 122.46/16.19 ((
% 122.46/16.19 (contrasubsetT3) =>
% 122.46/16.19 ((
% 122.46/16.19 (doubleComplementI1) =>
% 122.46/16.19 ((
% 122.46/16.19 (doubleComplementE1) =>
% 122.46/16.19 ((
% 122.46/16.19 (doubleComplementSub1) =>
% 122.46/16.19 ((
% 122.46/16.19 (doubleComplementSub2) =>
% 122.46/16.19 ((
% 122.46/16.19 (doubleComplementEq) =>
% 122.46/16.19 ((
% 122.46/16.19 (complementTnotintersectT) =>
% 122.46/16.19 ((
% 122.46/16.19 (complementImpComplementIntersect) =>
% 122.46/16.19 ((
% 122.46/16.19 (complementSubsetComplementIntersect) =>
% 122.46/16.19 ((
% 122.46/16.19 (complementInPowersetComplementIntersect) =>
% 122.46/16.19 ((
% 122.46/16.19 (contraSubsetComplement) =>
% 122.46/16.19 ((
% 122.46/16.19 (complementTcontraSubset) =>
% 122.46/16.19 ((
% 122.46/16.19 (binunionTILcontra) =>
% 122.46/16.19 ((
% 122.46/16.19 (binunionTIRcontra) =>
% 122.46/16.19 ((
% 122.46/16.19 (inIntersectImpInUnion) =>
% 122.46/16.19 ((
% 122.46/16.19 (inIntersectImpInUnion2) =>
% 122.46/16.19 ((
% 122.46/16.19 (inIntersectImpInIntersectUnions) =>
% 122.46/16.19 ((
% 122.46/16.19 (intersectInPowersetIntersectUnions) =>
% 122.46/16.19 ((
% 122.46/16.19 (inComplementUnionImpNotIn1) =>
% 122.46/16.19 ((
% 122.46/16.19 (inComplementUnionImpInComplement1) =>
% 122.46/16.19 ((
% 122.46/16.19 (binunionTE) =>
% 122.46/16.19 ((
% 122.46/16.19 (binunionTEcontra) =>
% 122.46/16.19 ((
% 122.46/16.19 (demorgan2a1) =>
% 122.46/16.19 ((
% 122.46/16.19 (complementUnionInPowersetComplement) =>
% 122.46/16.19 ((
% 122.46/16.19 (demorgan2a2) =>
% 122.46/16.19 ((
% 122.46/16.19 (demorgan1a) =>
% 122.46/16.19 ((
% 122.46/16.19 (demorgan1b) =>
% 122.46/16.19 ((
% 122.46/16.19 (demorgan1) =>
% 122.46/16.19 ((
% 122.46/16.19 (demorgan2a) =>
% 122.46/16.19 ((
% 122.46/16.19 (demorgan2b2) =>
% 122.46/16.19 ((
% 122.46/16.19 (demorgan2b) =>
% 122.46/16.19 ((
% 122.46/16.19 (demorgan2) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz13rule0) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz13rule1) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz13rule2) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz13rule3) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz13rule4) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz1_1) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz1_2) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz1_3) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz1_4) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz1_5) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1all2) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1SetBreln1) =>
% 122.46/16.19 ((
% 122.46/16.19 (choice2fnsingleton) =>
% 122.46/16.19 ((
% 122.46/16.19 (setOfPairsIsBReln1) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1all1) =>
% 122.46/16.19 ((
% 122.46/16.19 (subbreln1) =>
% 122.46/16.19 ((
% 122.46/16.19 (eqbreln1) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1invprop) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1invI) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1invE) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1compprop) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1compI) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1compE) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1compEex) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1unionprop) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1unionIL) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1unionIR) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1unionI) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1unionE) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1unionEcases) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1unionCommutes) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz2Ex) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz2W) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz2A) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz2B) =>
% 122.46/16.19 ((
% 122.46/16.19 (image1Ex) =>
% 122.46/16.19 ((
% 122.46/16.19 (image1Ex1) =>
% 122.46/16.19 ((
% 122.46/16.19 (image1Equiv) =>
% 122.46/16.19 ((
% 122.46/16.19 (image1E) =>
% 122.46/16.19 ((
% 122.46/16.19 (image1I) =>
% 122.46/16.19 ((
% 122.46/16.19 (injFuncInInjFuncSet) =>
% 122.46/16.19 ((
% 122.46/16.19 (!!) @ (
% 122.46/16.19 (('#B') @ (
% 122.46/16.19 !!) @
% 122.46/16.19 (
% 122.46/16.19 (
% 122.46/16.19 ('#B') @ (
% 122.46/16.19 (
% 122.46/16.19 ('#B') @ (
% 122.46/16.19 !!))) @
% 122.46/16.19 (
% 122.46/16.19 (
% 122.46/16.19 ('#S') @ (
% 122.46/16.19 (
% 122.46/16.19 ('#B') @ (
% 122.46/16.19 '#S') @
% 122.46/16.19 (
% 122.46/16.19 (
% 122.46/16.19 ('#B') @ (
% 122.46/16.19 (
% 122.46/16.19 ('#B') @ (
% 122.46/16.19 '#S'))) @
% 122.46/16.19 (
% 122.46/16.19 (
% 122.46/16.19 ('#B') @ (
% 122.46/16.19 (
% 122.46/16.19 ('#B') @ (
% 122.46/16.19 (
% 122.46/16.19 ('#B') @ (
% 122.46/16.19 =>))))) @
% 122.46/16.19 (
% 122.46/16.19 (
% 122.46/16.19 ('#B') @ (
% 122.46/16.19 (
% 122.46/16.19 ('#B') @ (
% 122.46/16.19 (
% 122.46/16.19 ('#C') @ in)))) @
% 122.46/16.19 injFuncSet)))))))) @
% 122.46/16.19 (
% 122.46/16.19 (
% 122.46/16.19 ('#B') @ (
% 122.46/16.19 (
% 122.46/16.19 ('#B') @ (
% 122.46/16.19 (
% 122.46/16.19 ('#C') @ in)))) @
% 122.46/16.19 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.46/16.19 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1444])).
% 122.46/16.19 thf(zip_derived_cl1459, plain,
% 122.46/16.19 (~ (((upairsubunion) =>
% 122.46/16.19 (((upairinpowunion) =>
% 122.46/16.19 (((ubforcartprodlem1) =>
% 122.46/16.19 (((ubforcartprodlem2) =>
% 122.46/16.19 (((ubforcartprodlem3) =>
% 122.46/16.19 (((cartprodpairin) =>
% 122.46/16.19 (((cartprodmempair1) =>
% 122.46/16.19 (((cartprodmempair) =>
% 122.46/16.19 (((setunionE2) =>
% 122.46/16.19 (((setunionsingleton1) =>
% 122.46/16.19 (((setunionsingleton2) =>
% 122.46/16.19 (((setunionsingleton) =>
% 122.46/16.19 (((singletonprop) =>
% 122.46/16.19 (((ex1E1) =>
% 122.46/16.19 (((ex1I) =>
% 122.46/16.19 (((ex1I2) =>
% 122.46/16.19 (((singletonsuniq) =>
% 122.46/16.19 (((setukpairinjL1) =>
% 122.46/16.19 (((kfstsingleton) =>
% 122.46/16.19 (((theprop) =>
% 122.46/16.19 (((kfstpairEq) =>
% 122.46/16.19 (((cartprodfstin) =>
% 122.46/16.19 (((setukpairinjL2) =>
% 122.46/16.19 (((setukpairinjL) =>
% 122.46/16.19 (((setukpairinjR11) =>
% 122.46/16.19 (((setukpairinjR12) =>
% 122.46/16.19 (((setukpairinjR1) =>
% 122.46/16.19 (((upairequniteq) =>
% 122.46/16.19 (((setukpairinjR2) =>
% 122.46/16.19 (((setukpairinjR) =>
% 122.46/16.19 ((
% 122.46/16.19 (ksndsingleton) =>
% 122.46/16.19 ((
% 122.46/16.19 (ksndpairEq) =>
% 122.46/16.19 ((
% 122.46/16.19 (kpairsurjEq) =>
% 122.46/16.19 ((
% 122.46/16.19 (cartprodsndin) =>
% 122.46/16.19 ((
% 122.46/16.19 (cartprodpairmemEL) =>
% 122.46/16.19 ((
% 122.46/16.19 (cartprodpairmemER) =>
% 122.46/16.19 ((
% 122.46/16.19 (cartprodmempaircEq) =>
% 122.46/16.19 ((
% 122.46/16.19 (cartprodfstpairEq) =>
% 122.46/16.19 ((
% 122.46/16.19 (cartprodsndpairEq) =>
% 122.46/16.19 ((
% 122.46/16.19 (cartprodpairsurjEq) =>
% 122.46/16.19 ((
% 122.46/16.19 (dpsetconstrI) =>
% 122.46/16.19 ((
% 122.46/16.19 (dpsetconstrSub) =>
% 122.46/16.19 ((
% 122.46/16.19 (setOfPairsIsBReln) =>
% 122.46/16.19 ((
% 122.46/16.19 (dpsetconstrERa) =>
% 122.46/16.19 ((
% 122.46/16.19 (dpsetconstrEL1) =>
% 122.46/16.19 ((
% 122.46/16.19 (dpsetconstrEL2) =>
% 122.46/16.19 ((
% 122.46/16.19 (dpsetconstrER) =>
% 122.46/16.19 ((
% 122.46/16.19 (funcImageSingleton) =>
% 122.46/16.19 ((
% 122.46/16.19 (apProp) =>
% 122.46/16.19 ((
% 122.46/16.19 (app) =>
% 122.46/16.19 ((
% 122.46/16.19 (infuncsetfunc) =>
% 122.46/16.19 ((
% 122.46/16.19 (ap2p) =>
% 122.46/16.19 ((
% 122.46/16.19 (funcinfuncset) =>
% 122.46/16.19 ((
% 122.46/16.19 (lamProp) =>
% 122.46/16.19 ((
% 122.46/16.19 (lamp) =>
% 122.46/16.19 ((
% 122.46/16.19 (lam2p) =>
% 122.46/16.19 ((
% 122.46/16.19 (brelnall1) =>
% 122.46/16.19 ((
% 122.46/16.19 (brelnall2) =>
% 122.46/16.19 ((
% 122.46/16.19 (ex1E2) =>
% 122.46/16.19 ((
% 122.46/16.19 (funcGraphProp1) =>
% 122.46/16.19 ((
% 122.46/16.19 (funcGraphProp3) =>
% 122.46/16.19 ((
% 122.46/16.19 (funcGraphProp2) =>
% 122.46/16.19 ((
% 122.46/16.19 (funcextLem) =>
% 122.46/16.19 ((
% 122.46/16.19 (funcGraphProp4) =>
% 122.46/16.19 ((
% 122.46/16.19 (subbreln) =>
% 122.46/16.19 ((
% 122.46/16.19 (eqbreln) =>
% 122.46/16.19 ((
% 122.46/16.19 (funcext) =>
% 122.46/16.19 ((
% 122.46/16.19 (funcext2) =>
% 122.46/16.19 ((
% 122.46/16.19 (ap2apEq1) =>
% 122.46/16.19 ((
% 122.46/16.19 (ap2apEq2) =>
% 122.46/16.19 ((
% 122.46/16.19 (beta1) =>
% 122.46/16.19 ((
% 122.46/16.19 (eta1) =>
% 122.46/16.19 ((
% 122.46/16.19 (lam2lamEq) =>
% 122.46/16.19 ((
% 122.46/16.19 (beta2) =>
% 122.46/16.19 ((
% 122.46/16.19 (eta2) =>
% 122.46/16.19 ((
% 122.46/16.19 (iffalseProp1) =>
% 122.46/16.19 ((
% 122.46/16.19 (iffalseProp2) =>
% 122.46/16.19 ((
% 122.46/16.19 (iftrueProp1) =>
% 122.46/16.19 ((
% 122.46/16.19 (iftrueProp2) =>
% 122.46/16.19 ((
% 122.46/16.19 (ifSingleton) =>
% 122.46/16.19 ((
% 122.46/16.19 (ifp) =>
% 122.46/16.19 ((
% 122.46/16.19 (theeq) =>
% 122.46/16.19 ((
% 122.46/16.19 (iftrue) =>
% 122.46/16.19 ((
% 122.46/16.19 (iffalse) =>
% 122.46/16.19 ((
% 122.46/16.19 (iftrueorfalse) =>
% 122.46/16.19 ((
% 122.46/16.19 (binintersectT_lem) =>
% 122.46/16.19 ((
% 122.46/16.19 (binunionT_lem) =>
% 122.46/16.19 ((
% 122.46/16.19 (powersetT_lem) =>
% 122.46/16.19 ((
% 122.46/16.19 (setminusT_lem) =>
% 122.46/16.19 ((
% 122.46/16.19 (complementT_lem) =>
% 122.46/16.19 ((
% 122.46/16.19 (setextT) =>
% 122.46/16.19 ((
% 122.46/16.19 (subsetTI) =>
% 122.46/16.19 ((
% 122.46/16.19 (powersetTI1) =>
% 122.46/16.19 ((
% 122.46/16.19 (powersetTE1) =>
% 122.46/16.19 ((
% 122.46/16.19 (complementTI1) =>
% 122.46/16.19 ((
% 122.46/16.19 (complementTE1) =>
% 122.46/16.19 ((
% 122.46/16.19 (binintersectTELcontra) =>
% 122.46/16.19 ((
% 122.46/16.19 (binintersectTERcontra) =>
% 122.46/16.19 ((
% 122.46/16.19 (contrasubsetT) =>
% 122.46/16.19 ((
% 122.46/16.19 (contrasubsetT1) =>
% 122.46/16.19 ((
% 122.46/16.19 (contrasubsetT2) =>
% 122.46/16.19 ((
% 122.46/16.19 (contrasubsetT3) =>
% 122.46/16.19 ((
% 122.46/16.19 (doubleComplementI1) =>
% 122.46/16.19 ((
% 122.46/16.19 (doubleComplementE1) =>
% 122.46/16.19 ((
% 122.46/16.19 (doubleComplementSub1) =>
% 122.46/16.19 ((
% 122.46/16.19 (doubleComplementSub2) =>
% 122.46/16.19 ((
% 122.46/16.19 (doubleComplementEq) =>
% 122.46/16.19 ((
% 122.46/16.19 (complementTnotintersectT) =>
% 122.46/16.19 ((
% 122.46/16.19 (complementImpComplementIntersect) =>
% 122.46/16.19 ((
% 122.46/16.19 (complementSubsetComplementIntersect) =>
% 122.46/16.19 ((
% 122.46/16.19 (complementInPowersetComplementIntersect) =>
% 122.46/16.19 ((
% 122.46/16.19 (contraSubsetComplement) =>
% 122.46/16.19 ((
% 122.46/16.19 (complementTcontraSubset) =>
% 122.46/16.19 ((
% 122.46/16.19 (binunionTILcontra) =>
% 122.46/16.19 ((
% 122.46/16.19 (binunionTIRcontra) =>
% 122.46/16.19 ((
% 122.46/16.19 (inIntersectImpInUnion) =>
% 122.46/16.19 ((
% 122.46/16.19 (inIntersectImpInUnion2) =>
% 122.46/16.19 ((
% 122.46/16.19 (inIntersectImpInIntersectUnions) =>
% 122.46/16.19 ((
% 122.46/16.19 (intersectInPowersetIntersectUnions) =>
% 122.46/16.19 ((
% 122.46/16.19 (inComplementUnionImpNotIn1) =>
% 122.46/16.19 ((
% 122.46/16.19 (inComplementUnionImpInComplement1) =>
% 122.46/16.19 ((
% 122.46/16.19 (binunionTE) =>
% 122.46/16.19 ((
% 122.46/16.19 (binunionTEcontra) =>
% 122.46/16.19 ((
% 122.46/16.19 (demorgan2a1) =>
% 122.46/16.19 ((
% 122.46/16.19 (complementUnionInPowersetComplement) =>
% 122.46/16.19 ((
% 122.46/16.19 (demorgan2a2) =>
% 122.46/16.19 ((
% 122.46/16.19 (demorgan1a) =>
% 122.46/16.19 ((
% 122.46/16.19 (demorgan1b) =>
% 122.46/16.19 ((
% 122.46/16.19 (demorgan1) =>
% 122.46/16.19 ((
% 122.46/16.19 (demorgan2a) =>
% 122.46/16.19 ((
% 122.46/16.19 (demorgan2b2) =>
% 122.46/16.19 ((
% 122.46/16.19 (demorgan2b) =>
% 122.46/16.19 ((
% 122.46/16.19 (demorgan2) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz13rule0) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz13rule1) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz13rule2) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz13rule3) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz13rule4) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz1_1) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz1_2) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz1_3) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz1_4) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz1_5) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1all2) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1SetBreln1) =>
% 122.46/16.19 ((
% 122.46/16.19 (choice2fnsingleton) =>
% 122.46/16.19 ((
% 122.46/16.19 (setOfPairsIsBReln1) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1all1) =>
% 122.46/16.19 ((
% 122.46/16.19 (subbreln1) =>
% 122.46/16.19 ((
% 122.46/16.19 (eqbreln1) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1invprop) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1invI) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1invE) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1compprop) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1compI) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1compE) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1compEex) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1unionprop) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1unionIL) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1unionIR) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1unionI) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1unionE) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1unionEcases) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1unionCommutes) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz2Ex) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz2W) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz2A) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz2B) =>
% 122.46/16.19 ((
% 122.46/16.19 (image1Ex) =>
% 122.46/16.19 ((
% 122.46/16.19 (image1Ex1) =>
% 122.46/16.19 ((
% 122.46/16.19 (image1Equiv) =>
% 122.46/16.19 ((
% 122.46/16.19 (image1E) =>
% 122.46/16.19 ((
% 122.46/16.19 (image1I) =>
% 122.46/16.19 ((
% 122.46/16.19 (injFuncInInjFuncSet) =>
% 122.46/16.19 ((
% 122.46/16.19 (!!) @ (
% 122.46/16.19 (('#B') @ (
% 122.46/16.19 !!) @
% 122.46/16.19 (
% 122.46/16.19 (
% 122.46/16.19 ('#B') @ (
% 122.46/16.19 (
% 122.46/16.19 ('#B') @ (
% 122.46/16.19 !!))) @
% 122.46/16.19 (
% 122.46/16.19 (
% 122.46/16.19 ('#S') @ (
% 122.46/16.19 (
% 122.46/16.19 ('#B') @ (
% 122.46/16.19 '#S') @
% 122.46/16.19 (
% 122.46/16.19 (
% 122.46/16.19 ('#B') @ (
% 122.46/16.19 (
% 122.46/16.19 ('#B') @ (
% 122.46/16.19 '#S'))) @
% 122.46/16.19 (
% 122.46/16.19 (
% 122.46/16.19 ('#B') @ (
% 122.46/16.19 (
% 122.46/16.19 ('#B') @ (
% 122.46/16.19 (
% 122.46/16.19 ('#B') @ (
% 122.46/16.19 =>))))) @
% 122.46/16.19 (
% 122.46/16.19 (
% 122.46/16.19 ('#B') @ (
% 122.46/16.19 (
% 122.46/16.19 ('#B') @ (
% 122.46/16.19 (
% 122.46/16.19 ('#C') @ in)))) @
% 122.46/16.19 injFuncSet)))))))) @
% 122.46/16.19 (
% 122.46/16.19 (
% 122.46/16.19 ('#B') @ (
% 122.46/16.19 (
% 122.46/16.19 ('#B') @ (
% 122.46/16.19 (
% 122.46/16.19 ('#C') @ in)))) @
% 122.46/16.19 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.46/16.19 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1452])).
% 122.46/16.19 thf(zip_derived_cl1466, plain,
% 122.46/16.19 (~ (((upairinpowunion) =>
% 122.46/16.19 (((ubforcartprodlem1) =>
% 122.46/16.19 (((ubforcartprodlem2) =>
% 122.46/16.19 (((ubforcartprodlem3) =>
% 122.46/16.19 (((cartprodpairin) =>
% 122.46/16.19 (((cartprodmempair1) =>
% 122.46/16.19 (((cartprodmempair) =>
% 122.46/16.19 (((setunionE2) =>
% 122.46/16.19 (((setunionsingleton1) =>
% 122.46/16.19 (((setunionsingleton2) =>
% 122.46/16.19 (((setunionsingleton) =>
% 122.46/16.19 (((singletonprop) =>
% 122.46/16.19 (((ex1E1) =>
% 122.46/16.19 (((ex1I) =>
% 122.46/16.19 (((ex1I2) =>
% 122.46/16.19 (((singletonsuniq) =>
% 122.46/16.19 (((setukpairinjL1) =>
% 122.46/16.19 (((kfstsingleton) =>
% 122.46/16.19 (((theprop) =>
% 122.46/16.19 (((kfstpairEq) =>
% 122.46/16.19 (((cartprodfstin) =>
% 122.46/16.19 (((setukpairinjL2) =>
% 122.46/16.19 (((setukpairinjL) =>
% 122.46/16.19 (((setukpairinjR11) =>
% 122.46/16.19 (((setukpairinjR12) =>
% 122.46/16.19 (((setukpairinjR1) =>
% 122.46/16.19 (((upairequniteq) =>
% 122.46/16.19 (((setukpairinjR2) =>
% 122.46/16.19 (((setukpairinjR) =>
% 122.46/16.19 (((ksndsingleton) =>
% 122.46/16.19 ((
% 122.46/16.19 (ksndpairEq) =>
% 122.46/16.19 ((
% 122.46/16.19 (kpairsurjEq) =>
% 122.46/16.19 ((
% 122.46/16.19 (cartprodsndin) =>
% 122.46/16.19 ((
% 122.46/16.19 (cartprodpairmemEL) =>
% 122.46/16.19 ((
% 122.46/16.19 (cartprodpairmemER) =>
% 122.46/16.19 ((
% 122.46/16.19 (cartprodmempaircEq) =>
% 122.46/16.19 ((
% 122.46/16.19 (cartprodfstpairEq) =>
% 122.46/16.19 ((
% 122.46/16.19 (cartprodsndpairEq) =>
% 122.46/16.19 ((
% 122.46/16.19 (cartprodpairsurjEq) =>
% 122.46/16.19 ((
% 122.46/16.19 (dpsetconstrI) =>
% 122.46/16.19 ((
% 122.46/16.19 (dpsetconstrSub) =>
% 122.46/16.19 ((
% 122.46/16.19 (setOfPairsIsBReln) =>
% 122.46/16.19 ((
% 122.46/16.19 (dpsetconstrERa) =>
% 122.46/16.19 ((
% 122.46/16.19 (dpsetconstrEL1) =>
% 122.46/16.19 ((
% 122.46/16.19 (dpsetconstrEL2) =>
% 122.46/16.19 ((
% 122.46/16.19 (dpsetconstrER) =>
% 122.46/16.19 ((
% 122.46/16.19 (funcImageSingleton) =>
% 122.46/16.19 ((
% 122.46/16.19 (apProp) =>
% 122.46/16.19 ((
% 122.46/16.19 (app) =>
% 122.46/16.19 ((
% 122.46/16.19 (infuncsetfunc) =>
% 122.46/16.19 ((
% 122.46/16.19 (ap2p) =>
% 122.46/16.19 ((
% 122.46/16.19 (funcinfuncset) =>
% 122.46/16.19 ((
% 122.46/16.19 (lamProp) =>
% 122.46/16.19 ((
% 122.46/16.19 (lamp) =>
% 122.46/16.19 ((
% 122.46/16.19 (lam2p) =>
% 122.46/16.19 ((
% 122.46/16.19 (brelnall1) =>
% 122.46/16.19 ((
% 122.46/16.19 (brelnall2) =>
% 122.46/16.19 ((
% 122.46/16.19 (ex1E2) =>
% 122.46/16.19 ((
% 122.46/16.19 (funcGraphProp1) =>
% 122.46/16.19 ((
% 122.46/16.19 (funcGraphProp3) =>
% 122.46/16.19 ((
% 122.46/16.19 (funcGraphProp2) =>
% 122.46/16.19 ((
% 122.46/16.19 (funcextLem) =>
% 122.46/16.19 ((
% 122.46/16.19 (funcGraphProp4) =>
% 122.46/16.19 ((
% 122.46/16.19 (subbreln) =>
% 122.46/16.19 ((
% 122.46/16.19 (eqbreln) =>
% 122.46/16.19 ((
% 122.46/16.19 (funcext) =>
% 122.46/16.19 ((
% 122.46/16.19 (funcext2) =>
% 122.46/16.19 ((
% 122.46/16.19 (ap2apEq1) =>
% 122.46/16.19 ((
% 122.46/16.19 (ap2apEq2) =>
% 122.46/16.19 ((
% 122.46/16.19 (beta1) =>
% 122.46/16.19 ((
% 122.46/16.19 (eta1) =>
% 122.46/16.19 ((
% 122.46/16.19 (lam2lamEq) =>
% 122.46/16.19 ((
% 122.46/16.19 (beta2) =>
% 122.46/16.19 ((
% 122.46/16.19 (eta2) =>
% 122.46/16.19 ((
% 122.46/16.19 (iffalseProp1) =>
% 122.46/16.19 ((
% 122.46/16.19 (iffalseProp2) =>
% 122.46/16.19 ((
% 122.46/16.19 (iftrueProp1) =>
% 122.46/16.19 ((
% 122.46/16.19 (iftrueProp2) =>
% 122.46/16.19 ((
% 122.46/16.19 (ifSingleton) =>
% 122.46/16.19 ((
% 122.46/16.19 (ifp) =>
% 122.46/16.19 ((
% 122.46/16.19 (theeq) =>
% 122.46/16.19 ((
% 122.46/16.19 (iftrue) =>
% 122.46/16.19 ((
% 122.46/16.19 (iffalse) =>
% 122.46/16.19 ((
% 122.46/16.19 (iftrueorfalse) =>
% 122.46/16.19 ((
% 122.46/16.19 (binintersectT_lem) =>
% 122.46/16.19 ((
% 122.46/16.19 (binunionT_lem) =>
% 122.46/16.19 ((
% 122.46/16.19 (powersetT_lem) =>
% 122.46/16.19 ((
% 122.46/16.19 (setminusT_lem) =>
% 122.46/16.19 ((
% 122.46/16.19 (complementT_lem) =>
% 122.46/16.19 ((
% 122.46/16.19 (setextT) =>
% 122.46/16.19 ((
% 122.46/16.19 (subsetTI) =>
% 122.46/16.19 ((
% 122.46/16.19 (powersetTI1) =>
% 122.46/16.19 ((
% 122.46/16.19 (powersetTE1) =>
% 122.46/16.19 ((
% 122.46/16.19 (complementTI1) =>
% 122.46/16.19 ((
% 122.46/16.19 (complementTE1) =>
% 122.46/16.19 ((
% 122.46/16.19 (binintersectTELcontra) =>
% 122.46/16.19 ((
% 122.46/16.19 (binintersectTERcontra) =>
% 122.46/16.19 ((
% 122.46/16.19 (contrasubsetT) =>
% 122.46/16.19 ((
% 122.46/16.19 (contrasubsetT1) =>
% 122.46/16.19 ((
% 122.46/16.19 (contrasubsetT2) =>
% 122.46/16.19 ((
% 122.46/16.19 (contrasubsetT3) =>
% 122.46/16.19 ((
% 122.46/16.19 (doubleComplementI1) =>
% 122.46/16.19 ((
% 122.46/16.19 (doubleComplementE1) =>
% 122.46/16.19 ((
% 122.46/16.19 (doubleComplementSub1) =>
% 122.46/16.19 ((
% 122.46/16.19 (doubleComplementSub2) =>
% 122.46/16.19 ((
% 122.46/16.19 (doubleComplementEq) =>
% 122.46/16.19 ((
% 122.46/16.19 (complementTnotintersectT) =>
% 122.46/16.19 ((
% 122.46/16.19 (complementImpComplementIntersect) =>
% 122.46/16.19 ((
% 122.46/16.19 (complementSubsetComplementIntersect) =>
% 122.46/16.19 ((
% 122.46/16.19 (complementInPowersetComplementIntersect) =>
% 122.46/16.19 ((
% 122.46/16.19 (contraSubsetComplement) =>
% 122.46/16.19 ((
% 122.46/16.19 (complementTcontraSubset) =>
% 122.46/16.19 ((
% 122.46/16.19 (binunionTILcontra) =>
% 122.46/16.19 ((
% 122.46/16.19 (binunionTIRcontra) =>
% 122.46/16.19 ((
% 122.46/16.19 (inIntersectImpInUnion) =>
% 122.46/16.19 ((
% 122.46/16.19 (inIntersectImpInUnion2) =>
% 122.46/16.19 ((
% 122.46/16.19 (inIntersectImpInIntersectUnions) =>
% 122.46/16.19 ((
% 122.46/16.19 (intersectInPowersetIntersectUnions) =>
% 122.46/16.19 ((
% 122.46/16.19 (inComplementUnionImpNotIn1) =>
% 122.46/16.19 ((
% 122.46/16.19 (inComplementUnionImpInComplement1) =>
% 122.46/16.19 ((
% 122.46/16.19 (binunionTE) =>
% 122.46/16.19 ((
% 122.46/16.19 (binunionTEcontra) =>
% 122.46/16.19 ((
% 122.46/16.19 (demorgan2a1) =>
% 122.46/16.19 ((
% 122.46/16.19 (complementUnionInPowersetComplement) =>
% 122.46/16.19 ((
% 122.46/16.19 (demorgan2a2) =>
% 122.46/16.19 ((
% 122.46/16.19 (demorgan1a) =>
% 122.46/16.19 ((
% 122.46/16.19 (demorgan1b) =>
% 122.46/16.19 ((
% 122.46/16.19 (demorgan1) =>
% 122.46/16.19 ((
% 122.46/16.19 (demorgan2a) =>
% 122.46/16.19 ((
% 122.46/16.19 (demorgan2b2) =>
% 122.46/16.19 ((
% 122.46/16.19 (demorgan2b) =>
% 122.46/16.19 ((
% 122.46/16.19 (demorgan2) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz13rule0) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz13rule1) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz13rule2) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz13rule3) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz13rule4) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz1_1) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz1_2) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz1_3) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz1_4) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz1_5) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1all2) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1SetBreln1) =>
% 122.46/16.19 ((
% 122.46/16.19 (choice2fnsingleton) =>
% 122.46/16.19 ((
% 122.46/16.19 (setOfPairsIsBReln1) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1all1) =>
% 122.46/16.19 ((
% 122.46/16.19 (subbreln1) =>
% 122.46/16.19 ((
% 122.46/16.19 (eqbreln1) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1invprop) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1invI) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1invE) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1compprop) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1compI) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1compE) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1compEex) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1unionprop) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1unionIL) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1unionIR) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1unionI) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1unionE) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1unionEcases) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1unionCommutes) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz2Ex) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz2W) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz2A) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz2B) =>
% 122.46/16.19 ((
% 122.46/16.19 (image1Ex) =>
% 122.46/16.19 ((
% 122.46/16.19 (image1Ex1) =>
% 122.46/16.19 ((
% 122.46/16.19 (image1Equiv) =>
% 122.46/16.19 ((
% 122.46/16.19 (image1E) =>
% 122.46/16.19 ((
% 122.46/16.19 (image1I) =>
% 122.46/16.19 ((
% 122.46/16.19 (injFuncInInjFuncSet) =>
% 122.46/16.19 ((
% 122.46/16.19 (!!) @ (
% 122.46/16.19 (('#B') @ (
% 122.46/16.19 !!) @
% 122.46/16.19 (
% 122.46/16.19 (
% 122.46/16.19 ('#B') @ (
% 122.46/16.19 (
% 122.46/16.19 ('#B') @ (
% 122.46/16.19 !!))) @
% 122.46/16.19 (
% 122.46/16.19 (
% 122.46/16.19 ('#S') @ (
% 122.46/16.19 (
% 122.46/16.19 ('#B') @ (
% 122.46/16.19 '#S') @
% 122.46/16.19 (
% 122.46/16.19 (
% 122.46/16.19 ('#B') @ (
% 122.46/16.19 (
% 122.46/16.19 ('#B') @ (
% 122.46/16.19 '#S'))) @
% 122.46/16.19 (
% 122.46/16.19 (
% 122.46/16.19 ('#B') @ (
% 122.46/16.19 (
% 122.46/16.19 ('#B') @ (
% 122.46/16.19 (
% 122.46/16.19 ('#B') @ (
% 122.46/16.19 =>))))) @
% 122.46/16.19 (
% 122.46/16.19 (
% 122.46/16.19 ('#B') @ (
% 122.46/16.19 (
% 122.46/16.19 ('#B') @ (
% 122.46/16.19 (
% 122.46/16.19 ('#C') @ in)))) @
% 122.46/16.19 injFuncSet)))))))) @
% 122.46/16.19 (
% 122.46/16.19 (
% 122.46/16.19 ('#B') @ (
% 122.46/16.19 (
% 122.46/16.19 ('#B') @ (
% 122.46/16.19 (
% 122.46/16.19 ('#C') @ in)))) @
% 122.46/16.19 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.46/16.19 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1459])).
% 122.46/16.19 thf(zip_derived_cl1473, plain,
% 122.46/16.19 (~ (((ubforcartprodlem1) =>
% 122.46/16.19 (((ubforcartprodlem2) =>
% 122.46/16.19 (((ubforcartprodlem3) =>
% 122.46/16.19 (((cartprodpairin) =>
% 122.46/16.19 (((cartprodmempair1) =>
% 122.46/16.19 (((cartprodmempair) =>
% 122.46/16.19 (((setunionE2) =>
% 122.46/16.19 (((setunionsingleton1) =>
% 122.46/16.19 (((setunionsingleton2) =>
% 122.46/16.19 (((setunionsingleton) =>
% 122.46/16.19 (((singletonprop) =>
% 122.46/16.19 (((ex1E1) =>
% 122.46/16.19 (((ex1I) =>
% 122.46/16.19 (((ex1I2) =>
% 122.46/16.19 (((singletonsuniq) =>
% 122.46/16.19 (((setukpairinjL1) =>
% 122.46/16.19 (((kfstsingleton) =>
% 122.46/16.19 (((theprop) =>
% 122.46/16.19 (((kfstpairEq) =>
% 122.46/16.19 (((cartprodfstin) =>
% 122.46/16.19 (((setukpairinjL2) =>
% 122.46/16.19 (((setukpairinjL) =>
% 122.46/16.19 (((setukpairinjR11) =>
% 122.46/16.19 (((setukpairinjR12) =>
% 122.46/16.19 (((setukpairinjR1) =>
% 122.46/16.19 (((upairequniteq) =>
% 122.46/16.19 (((setukpairinjR2) =>
% 122.46/16.19 (((setukpairinjR) =>
% 122.46/16.19 (((ksndsingleton) =>
% 122.46/16.19 (((ksndpairEq) =>
% 122.46/16.19 ((
% 122.46/16.19 (kpairsurjEq) =>
% 122.46/16.19 ((
% 122.46/16.19 (cartprodsndin) =>
% 122.46/16.19 ((
% 122.46/16.19 (cartprodpairmemEL) =>
% 122.46/16.19 ((
% 122.46/16.19 (cartprodpairmemER) =>
% 122.46/16.19 ((
% 122.46/16.19 (cartprodmempaircEq) =>
% 122.46/16.19 ((
% 122.46/16.19 (cartprodfstpairEq) =>
% 122.46/16.19 ((
% 122.46/16.19 (cartprodsndpairEq) =>
% 122.46/16.19 ((
% 122.46/16.19 (cartprodpairsurjEq) =>
% 122.46/16.19 ((
% 122.46/16.19 (dpsetconstrI) =>
% 122.46/16.19 ((
% 122.46/16.19 (dpsetconstrSub) =>
% 122.46/16.19 ((
% 122.46/16.19 (setOfPairsIsBReln) =>
% 122.46/16.19 ((
% 122.46/16.19 (dpsetconstrERa) =>
% 122.46/16.19 ((
% 122.46/16.19 (dpsetconstrEL1) =>
% 122.46/16.19 ((
% 122.46/16.19 (dpsetconstrEL2) =>
% 122.46/16.19 ((
% 122.46/16.19 (dpsetconstrER) =>
% 122.46/16.19 ((
% 122.46/16.19 (funcImageSingleton) =>
% 122.46/16.19 ((
% 122.46/16.19 (apProp) =>
% 122.46/16.19 ((
% 122.46/16.19 (app) =>
% 122.46/16.19 ((
% 122.46/16.19 (infuncsetfunc) =>
% 122.46/16.19 ((
% 122.46/16.19 (ap2p) =>
% 122.46/16.19 ((
% 122.46/16.19 (funcinfuncset) =>
% 122.46/16.19 ((
% 122.46/16.19 (lamProp) =>
% 122.46/16.19 ((
% 122.46/16.19 (lamp) =>
% 122.46/16.19 ((
% 122.46/16.19 (lam2p) =>
% 122.46/16.19 ((
% 122.46/16.19 (brelnall1) =>
% 122.46/16.19 ((
% 122.46/16.19 (brelnall2) =>
% 122.46/16.19 ((
% 122.46/16.19 (ex1E2) =>
% 122.46/16.19 ((
% 122.46/16.19 (funcGraphProp1) =>
% 122.46/16.19 ((
% 122.46/16.19 (funcGraphProp3) =>
% 122.46/16.19 ((
% 122.46/16.19 (funcGraphProp2) =>
% 122.46/16.19 ((
% 122.46/16.19 (funcextLem) =>
% 122.46/16.19 ((
% 122.46/16.19 (funcGraphProp4) =>
% 122.46/16.19 ((
% 122.46/16.19 (subbreln) =>
% 122.46/16.19 ((
% 122.46/16.19 (eqbreln) =>
% 122.46/16.19 ((
% 122.46/16.19 (funcext) =>
% 122.46/16.19 ((
% 122.46/16.19 (funcext2) =>
% 122.46/16.19 ((
% 122.46/16.19 (ap2apEq1) =>
% 122.46/16.19 ((
% 122.46/16.19 (ap2apEq2) =>
% 122.46/16.19 ((
% 122.46/16.19 (beta1) =>
% 122.46/16.19 ((
% 122.46/16.19 (eta1) =>
% 122.46/16.19 ((
% 122.46/16.19 (lam2lamEq) =>
% 122.46/16.19 ((
% 122.46/16.19 (beta2) =>
% 122.46/16.19 ((
% 122.46/16.19 (eta2) =>
% 122.46/16.19 ((
% 122.46/16.19 (iffalseProp1) =>
% 122.46/16.19 ((
% 122.46/16.19 (iffalseProp2) =>
% 122.46/16.19 ((
% 122.46/16.19 (iftrueProp1) =>
% 122.46/16.19 ((
% 122.46/16.19 (iftrueProp2) =>
% 122.46/16.19 ((
% 122.46/16.19 (ifSingleton) =>
% 122.46/16.19 ((
% 122.46/16.19 (ifp) =>
% 122.46/16.19 ((
% 122.46/16.19 (theeq) =>
% 122.46/16.19 ((
% 122.46/16.19 (iftrue) =>
% 122.46/16.19 ((
% 122.46/16.19 (iffalse) =>
% 122.46/16.19 ((
% 122.46/16.19 (iftrueorfalse) =>
% 122.46/16.19 ((
% 122.46/16.19 (binintersectT_lem) =>
% 122.46/16.19 ((
% 122.46/16.19 (binunionT_lem) =>
% 122.46/16.19 ((
% 122.46/16.19 (powersetT_lem) =>
% 122.46/16.19 ((
% 122.46/16.19 (setminusT_lem) =>
% 122.46/16.19 ((
% 122.46/16.19 (complementT_lem) =>
% 122.46/16.19 ((
% 122.46/16.19 (setextT) =>
% 122.46/16.19 ((
% 122.46/16.19 (subsetTI) =>
% 122.46/16.19 ((
% 122.46/16.19 (powersetTI1) =>
% 122.46/16.19 ((
% 122.46/16.19 (powersetTE1) =>
% 122.46/16.19 ((
% 122.46/16.19 (complementTI1) =>
% 122.46/16.19 ((
% 122.46/16.19 (complementTE1) =>
% 122.46/16.19 ((
% 122.46/16.19 (binintersectTELcontra) =>
% 122.46/16.19 ((
% 122.46/16.19 (binintersectTERcontra) =>
% 122.46/16.19 ((
% 122.46/16.19 (contrasubsetT) =>
% 122.46/16.19 ((
% 122.46/16.19 (contrasubsetT1) =>
% 122.46/16.19 ((
% 122.46/16.19 (contrasubsetT2) =>
% 122.46/16.19 ((
% 122.46/16.19 (contrasubsetT3) =>
% 122.46/16.19 ((
% 122.46/16.19 (doubleComplementI1) =>
% 122.46/16.19 ((
% 122.46/16.19 (doubleComplementE1) =>
% 122.46/16.19 ((
% 122.46/16.19 (doubleComplementSub1) =>
% 122.46/16.19 ((
% 122.46/16.19 (doubleComplementSub2) =>
% 122.46/16.19 ((
% 122.46/16.19 (doubleComplementEq) =>
% 122.46/16.19 ((
% 122.46/16.19 (complementTnotintersectT) =>
% 122.46/16.19 ((
% 122.46/16.19 (complementImpComplementIntersect) =>
% 122.46/16.19 ((
% 122.46/16.19 (complementSubsetComplementIntersect) =>
% 122.46/16.19 ((
% 122.46/16.19 (complementInPowersetComplementIntersect) =>
% 122.46/16.19 ((
% 122.46/16.19 (contraSubsetComplement) =>
% 122.46/16.19 ((
% 122.46/16.19 (complementTcontraSubset) =>
% 122.46/16.19 ((
% 122.46/16.19 (binunionTILcontra) =>
% 122.46/16.19 ((
% 122.46/16.19 (binunionTIRcontra) =>
% 122.46/16.19 ((
% 122.46/16.19 (inIntersectImpInUnion) =>
% 122.46/16.19 ((
% 122.46/16.19 (inIntersectImpInUnion2) =>
% 122.46/16.19 ((
% 122.46/16.19 (inIntersectImpInIntersectUnions) =>
% 122.46/16.19 ((
% 122.46/16.19 (intersectInPowersetIntersectUnions) =>
% 122.46/16.19 ((
% 122.46/16.19 (inComplementUnionImpNotIn1) =>
% 122.46/16.19 ((
% 122.46/16.19 (inComplementUnionImpInComplement1) =>
% 122.46/16.19 ((
% 122.46/16.19 (binunionTE) =>
% 122.46/16.19 ((
% 122.46/16.19 (binunionTEcontra) =>
% 122.46/16.19 ((
% 122.46/16.19 (demorgan2a1) =>
% 122.46/16.19 ((
% 122.46/16.19 (complementUnionInPowersetComplement) =>
% 122.46/16.19 ((
% 122.46/16.19 (demorgan2a2) =>
% 122.46/16.19 ((
% 122.46/16.19 (demorgan1a) =>
% 122.46/16.19 ((
% 122.46/16.19 (demorgan1b) =>
% 122.46/16.19 ((
% 122.46/16.19 (demorgan1) =>
% 122.46/16.19 ((
% 122.46/16.19 (demorgan2a) =>
% 122.46/16.19 ((
% 122.46/16.19 (demorgan2b2) =>
% 122.46/16.19 ((
% 122.46/16.19 (demorgan2b) =>
% 122.46/16.19 ((
% 122.46/16.19 (demorgan2) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz13rule0) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz13rule1) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz13rule2) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz13rule3) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz13rule4) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz1_1) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz1_2) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz1_3) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz1_4) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz1_5) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1all2) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1SetBreln1) =>
% 122.46/16.19 ((
% 122.46/16.19 (choice2fnsingleton) =>
% 122.46/16.19 ((
% 122.46/16.19 (setOfPairsIsBReln1) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1all1) =>
% 122.46/16.19 ((
% 122.46/16.19 (subbreln1) =>
% 122.46/16.19 ((
% 122.46/16.19 (eqbreln1) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1invprop) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1invI) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1invE) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1compprop) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1compI) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1compE) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1compEex) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1unionprop) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1unionIL) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1unionIR) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1unionI) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1unionE) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1unionEcases) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1unionCommutes) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz2Ex) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz2W) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz2A) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz2B) =>
% 122.46/16.19 ((
% 122.46/16.19 (image1Ex) =>
% 122.46/16.19 ((
% 122.46/16.19 (image1Ex1) =>
% 122.46/16.19 ((
% 122.46/16.19 (image1Equiv) =>
% 122.46/16.19 ((
% 122.46/16.19 (image1E) =>
% 122.46/16.19 ((
% 122.46/16.19 (image1I) =>
% 122.46/16.19 ((
% 122.46/16.19 (injFuncInInjFuncSet) =>
% 122.46/16.19 ((
% 122.46/16.19 (!!) @ (
% 122.46/16.19 (('#B') @ (
% 122.46/16.19 !!) @
% 122.46/16.19 (
% 122.46/16.19 (
% 122.46/16.19 ('#B') @ (
% 122.46/16.19 (
% 122.46/16.19 ('#B') @ (
% 122.46/16.19 !!))) @
% 122.46/16.19 (
% 122.46/16.19 (
% 122.46/16.19 ('#S') @ (
% 122.46/16.19 (
% 122.46/16.19 ('#B') @ (
% 122.46/16.19 '#S') @
% 122.46/16.19 (
% 122.46/16.19 (
% 122.46/16.19 ('#B') @ (
% 122.46/16.19 (
% 122.46/16.19 ('#B') @ (
% 122.46/16.19 '#S'))) @
% 122.46/16.19 (
% 122.46/16.19 (
% 122.46/16.19 ('#B') @ (
% 122.46/16.19 (
% 122.46/16.19 ('#B') @ (
% 122.46/16.19 (
% 122.46/16.19 ('#B') @ (
% 122.46/16.19 =>))))) @
% 122.46/16.19 (
% 122.46/16.19 (
% 122.46/16.19 ('#B') @ (
% 122.46/16.19 (
% 122.46/16.19 ('#B') @ (
% 122.46/16.19 (
% 122.46/16.19 ('#C') @ in)))) @
% 122.46/16.19 injFuncSet)))))))) @
% 122.46/16.19 (
% 122.46/16.19 (
% 122.46/16.19 ('#B') @ (
% 122.46/16.19 (
% 122.46/16.19 ('#B') @ (
% 122.46/16.19 (
% 122.46/16.19 ('#C') @ in)))) @
% 122.46/16.19 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.46/16.19 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1466])).
% 122.46/16.19 thf(zip_derived_cl1480, plain,
% 122.46/16.19 (~ (((ubforcartprodlem2) =>
% 122.46/16.19 (((ubforcartprodlem3) =>
% 122.46/16.19 (((cartprodpairin) =>
% 122.46/16.19 (((cartprodmempair1) =>
% 122.46/16.19 (((cartprodmempair) =>
% 122.46/16.19 (((setunionE2) =>
% 122.46/16.19 (((setunionsingleton1) =>
% 122.46/16.19 (((setunionsingleton2) =>
% 122.46/16.19 (((setunionsingleton) =>
% 122.46/16.19 (((singletonprop) =>
% 122.46/16.19 (((ex1E1) =>
% 122.46/16.19 (((ex1I) =>
% 122.46/16.19 (((ex1I2) =>
% 122.46/16.19 (((singletonsuniq) =>
% 122.46/16.19 (((setukpairinjL1) =>
% 122.46/16.19 (((kfstsingleton) =>
% 122.46/16.19 (((theprop) =>
% 122.46/16.19 (((kfstpairEq) =>
% 122.46/16.19 (((cartprodfstin) =>
% 122.46/16.19 (((setukpairinjL2) =>
% 122.46/16.19 (((setukpairinjL) =>
% 122.46/16.19 (((setukpairinjR11) =>
% 122.46/16.19 (((setukpairinjR12) =>
% 122.46/16.19 (((setukpairinjR1) =>
% 122.46/16.19 (((upairequniteq) =>
% 122.46/16.19 (((setukpairinjR2) =>
% 122.46/16.19 (((setukpairinjR) =>
% 122.46/16.19 (((ksndsingleton) =>
% 122.46/16.19 (((ksndpairEq) =>
% 122.46/16.19 (((kpairsurjEq) =>
% 122.46/16.19 ((
% 122.46/16.19 (cartprodsndin) =>
% 122.46/16.19 ((
% 122.46/16.19 (cartprodpairmemEL) =>
% 122.46/16.19 ((
% 122.46/16.19 (cartprodpairmemER) =>
% 122.46/16.19 ((
% 122.46/16.19 (cartprodmempaircEq) =>
% 122.46/16.19 ((
% 122.46/16.19 (cartprodfstpairEq) =>
% 122.46/16.19 ((
% 122.46/16.19 (cartprodsndpairEq) =>
% 122.46/16.19 ((
% 122.46/16.19 (cartprodpairsurjEq) =>
% 122.46/16.19 ((
% 122.46/16.19 (dpsetconstrI) =>
% 122.46/16.19 ((
% 122.46/16.19 (dpsetconstrSub) =>
% 122.46/16.19 ((
% 122.46/16.19 (setOfPairsIsBReln) =>
% 122.46/16.19 ((
% 122.46/16.19 (dpsetconstrERa) =>
% 122.46/16.19 ((
% 122.46/16.19 (dpsetconstrEL1) =>
% 122.46/16.19 ((
% 122.46/16.19 (dpsetconstrEL2) =>
% 122.46/16.19 ((
% 122.46/16.19 (dpsetconstrER) =>
% 122.46/16.19 ((
% 122.46/16.19 (funcImageSingleton) =>
% 122.46/16.19 ((
% 122.46/16.19 (apProp) =>
% 122.46/16.19 ((
% 122.46/16.19 (app) =>
% 122.46/16.19 ((
% 122.46/16.19 (infuncsetfunc) =>
% 122.46/16.19 ((
% 122.46/16.19 (ap2p) =>
% 122.46/16.19 ((
% 122.46/16.19 (funcinfuncset) =>
% 122.46/16.19 ((
% 122.46/16.19 (lamProp) =>
% 122.46/16.19 ((
% 122.46/16.19 (lamp) =>
% 122.46/16.19 ((
% 122.46/16.19 (lam2p) =>
% 122.46/16.19 ((
% 122.46/16.19 (brelnall1) =>
% 122.46/16.19 ((
% 122.46/16.19 (brelnall2) =>
% 122.46/16.19 ((
% 122.46/16.19 (ex1E2) =>
% 122.46/16.19 ((
% 122.46/16.19 (funcGraphProp1) =>
% 122.46/16.19 ((
% 122.46/16.19 (funcGraphProp3) =>
% 122.46/16.19 ((
% 122.46/16.19 (funcGraphProp2) =>
% 122.46/16.19 ((
% 122.46/16.19 (funcextLem) =>
% 122.46/16.19 ((
% 122.46/16.19 (funcGraphProp4) =>
% 122.46/16.19 ((
% 122.46/16.19 (subbreln) =>
% 122.46/16.19 ((
% 122.46/16.19 (eqbreln) =>
% 122.46/16.19 ((
% 122.46/16.19 (funcext) =>
% 122.46/16.19 ((
% 122.46/16.19 (funcext2) =>
% 122.46/16.19 ((
% 122.46/16.19 (ap2apEq1) =>
% 122.46/16.19 ((
% 122.46/16.19 (ap2apEq2) =>
% 122.46/16.19 ((
% 122.46/16.19 (beta1) =>
% 122.46/16.19 ((
% 122.46/16.19 (eta1) =>
% 122.46/16.19 ((
% 122.46/16.19 (lam2lamEq) =>
% 122.46/16.19 ((
% 122.46/16.19 (beta2) =>
% 122.46/16.19 ((
% 122.46/16.19 (eta2) =>
% 122.46/16.19 ((
% 122.46/16.19 (iffalseProp1) =>
% 122.46/16.19 ((
% 122.46/16.19 (iffalseProp2) =>
% 122.46/16.19 ((
% 122.46/16.19 (iftrueProp1) =>
% 122.46/16.19 ((
% 122.46/16.19 (iftrueProp2) =>
% 122.46/16.19 ((
% 122.46/16.19 (ifSingleton) =>
% 122.46/16.19 ((
% 122.46/16.19 (ifp) =>
% 122.46/16.19 ((
% 122.46/16.19 (theeq) =>
% 122.46/16.19 ((
% 122.46/16.19 (iftrue) =>
% 122.46/16.19 ((
% 122.46/16.19 (iffalse) =>
% 122.46/16.19 ((
% 122.46/16.19 (iftrueorfalse) =>
% 122.46/16.19 ((
% 122.46/16.19 (binintersectT_lem) =>
% 122.46/16.19 ((
% 122.46/16.19 (binunionT_lem) =>
% 122.46/16.19 ((
% 122.46/16.19 (powersetT_lem) =>
% 122.46/16.19 ((
% 122.46/16.19 (setminusT_lem) =>
% 122.46/16.19 ((
% 122.46/16.19 (complementT_lem) =>
% 122.46/16.19 ((
% 122.46/16.19 (setextT) =>
% 122.46/16.19 ((
% 122.46/16.19 (subsetTI) =>
% 122.46/16.19 ((
% 122.46/16.19 (powersetTI1) =>
% 122.46/16.19 ((
% 122.46/16.19 (powersetTE1) =>
% 122.46/16.19 ((
% 122.46/16.19 (complementTI1) =>
% 122.46/16.19 ((
% 122.46/16.19 (complementTE1) =>
% 122.46/16.19 ((
% 122.46/16.19 (binintersectTELcontra) =>
% 122.46/16.19 ((
% 122.46/16.19 (binintersectTERcontra) =>
% 122.46/16.19 ((
% 122.46/16.19 (contrasubsetT) =>
% 122.46/16.19 ((
% 122.46/16.19 (contrasubsetT1) =>
% 122.46/16.19 ((
% 122.46/16.19 (contrasubsetT2) =>
% 122.46/16.19 ((
% 122.46/16.19 (contrasubsetT3) =>
% 122.46/16.19 ((
% 122.46/16.19 (doubleComplementI1) =>
% 122.46/16.19 ((
% 122.46/16.19 (doubleComplementE1) =>
% 122.46/16.19 ((
% 122.46/16.19 (doubleComplementSub1) =>
% 122.46/16.19 ((
% 122.46/16.19 (doubleComplementSub2) =>
% 122.46/16.19 ((
% 122.46/16.19 (doubleComplementEq) =>
% 122.46/16.19 ((
% 122.46/16.19 (complementTnotintersectT) =>
% 122.46/16.19 ((
% 122.46/16.19 (complementImpComplementIntersect) =>
% 122.46/16.19 ((
% 122.46/16.19 (complementSubsetComplementIntersect) =>
% 122.46/16.19 ((
% 122.46/16.19 (complementInPowersetComplementIntersect) =>
% 122.46/16.19 ((
% 122.46/16.19 (contraSubsetComplement) =>
% 122.46/16.19 ((
% 122.46/16.19 (complementTcontraSubset) =>
% 122.46/16.19 ((
% 122.46/16.19 (binunionTILcontra) =>
% 122.46/16.19 ((
% 122.46/16.19 (binunionTIRcontra) =>
% 122.46/16.19 ((
% 122.46/16.19 (inIntersectImpInUnion) =>
% 122.46/16.19 ((
% 122.46/16.19 (inIntersectImpInUnion2) =>
% 122.46/16.19 ((
% 122.46/16.19 (inIntersectImpInIntersectUnions) =>
% 122.46/16.19 ((
% 122.46/16.19 (intersectInPowersetIntersectUnions) =>
% 122.46/16.19 ((
% 122.46/16.19 (inComplementUnionImpNotIn1) =>
% 122.46/16.19 ((
% 122.46/16.19 (inComplementUnionImpInComplement1) =>
% 122.46/16.19 ((
% 122.46/16.19 (binunionTE) =>
% 122.46/16.19 ((
% 122.46/16.19 (binunionTEcontra) =>
% 122.46/16.19 ((
% 122.46/16.19 (demorgan2a1) =>
% 122.46/16.19 ((
% 122.46/16.19 (complementUnionInPowersetComplement) =>
% 122.46/16.19 ((
% 122.46/16.19 (demorgan2a2) =>
% 122.46/16.19 ((
% 122.46/16.19 (demorgan1a) =>
% 122.46/16.19 ((
% 122.46/16.19 (demorgan1b) =>
% 122.46/16.19 ((
% 122.46/16.19 (demorgan1) =>
% 122.46/16.19 ((
% 122.46/16.19 (demorgan2a) =>
% 122.46/16.19 ((
% 122.46/16.19 (demorgan2b2) =>
% 122.46/16.19 ((
% 122.46/16.19 (demorgan2b) =>
% 122.46/16.19 ((
% 122.46/16.19 (demorgan2) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz13rule0) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz13rule1) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz13rule2) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz13rule3) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz13rule4) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz1_1) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz1_2) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz1_3) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz1_4) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz1_5) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1all2) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1SetBreln1) =>
% 122.46/16.19 ((
% 122.46/16.19 (choice2fnsingleton) =>
% 122.46/16.19 ((
% 122.46/16.19 (setOfPairsIsBReln1) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1all1) =>
% 122.46/16.19 ((
% 122.46/16.19 (subbreln1) =>
% 122.46/16.19 ((
% 122.46/16.19 (eqbreln1) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1invprop) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1invI) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1invE) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1compprop) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1compI) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1compE) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1compEex) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1unionprop) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1unionIL) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1unionIR) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1unionI) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1unionE) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1unionEcases) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1unionCommutes) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz2Ex) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz2W) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz2A) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz2B) =>
% 122.46/16.19 ((
% 122.46/16.19 (image1Ex) =>
% 122.46/16.19 ((
% 122.46/16.19 (image1Ex1) =>
% 122.46/16.19 ((
% 122.46/16.19 (image1Equiv) =>
% 122.46/16.19 ((
% 122.46/16.19 (image1E) =>
% 122.46/16.19 ((
% 122.46/16.19 (image1I) =>
% 122.46/16.19 ((
% 122.46/16.19 (injFuncInInjFuncSet) =>
% 122.46/16.19 ((
% 122.46/16.19 (!!) @ (
% 122.46/16.19 (('#B') @ (
% 122.46/16.19 !!) @
% 122.46/16.19 (
% 122.46/16.19 (
% 122.46/16.19 ('#B') @ (
% 122.46/16.19 (
% 122.46/16.19 ('#B') @ (
% 122.46/16.19 !!))) @
% 122.46/16.19 (
% 122.46/16.19 (
% 122.46/16.19 ('#S') @ (
% 122.46/16.19 (
% 122.46/16.19 ('#B') @ (
% 122.46/16.19 '#S') @
% 122.46/16.19 (
% 122.46/16.19 (
% 122.46/16.19 ('#B') @ (
% 122.46/16.19 (
% 122.46/16.19 ('#B') @ (
% 122.46/16.19 '#S'))) @
% 122.46/16.19 (
% 122.46/16.19 (
% 122.46/16.19 ('#B') @ (
% 122.46/16.19 (
% 122.46/16.19 ('#B') @ (
% 122.46/16.19 (
% 122.46/16.19 ('#B') @ (
% 122.46/16.19 =>))))) @
% 122.46/16.19 (
% 122.46/16.19 (
% 122.46/16.19 ('#B') @ (
% 122.46/16.19 (
% 122.46/16.19 ('#B') @ (
% 122.46/16.19 (
% 122.46/16.19 ('#C') @ in)))) @
% 122.46/16.19 injFuncSet)))))))) @
% 122.46/16.19 (
% 122.46/16.19 (
% 122.46/16.19 ('#B') @ (
% 122.46/16.19 (
% 122.46/16.19 ('#B') @ (
% 122.46/16.19 (
% 122.46/16.19 ('#C') @ in)))) @
% 122.46/16.19 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.46/16.19 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1473])).
% 122.46/16.19 thf(zip_derived_cl1488, plain,
% 122.46/16.19 (~ (((ubforcartprodlem3) =>
% 122.46/16.19 (((cartprodpairin) =>
% 122.46/16.19 (((cartprodmempair1) =>
% 122.46/16.19 (((cartprodmempair) =>
% 122.46/16.19 (((setunionE2) =>
% 122.46/16.19 (((setunionsingleton1) =>
% 122.46/16.19 (((setunionsingleton2) =>
% 122.46/16.19 (((setunionsingleton) =>
% 122.46/16.19 (((singletonprop) =>
% 122.46/16.19 (((ex1E1) =>
% 122.46/16.19 (((ex1I) =>
% 122.46/16.19 (((ex1I2) =>
% 122.46/16.19 (((singletonsuniq) =>
% 122.46/16.19 (((setukpairinjL1) =>
% 122.46/16.19 (((kfstsingleton) =>
% 122.46/16.19 (((theprop) =>
% 122.46/16.19 (((kfstpairEq) =>
% 122.46/16.19 (((cartprodfstin) =>
% 122.46/16.19 (((setukpairinjL2) =>
% 122.46/16.19 (((setukpairinjL) =>
% 122.46/16.19 (((setukpairinjR11) =>
% 122.46/16.19 (((setukpairinjR12) =>
% 122.46/16.19 (((setukpairinjR1) =>
% 122.46/16.19 (((upairequniteq) =>
% 122.46/16.19 (((setukpairinjR2) =>
% 122.46/16.19 (((setukpairinjR) =>
% 122.46/16.19 (((ksndsingleton) =>
% 122.46/16.19 (((ksndpairEq) =>
% 122.46/16.19 (((kpairsurjEq) =>
% 122.46/16.19 (((cartprodsndin) =>
% 122.46/16.19 ((
% 122.46/16.19 (cartprodpairmemEL) =>
% 122.46/16.19 ((
% 122.46/16.19 (cartprodpairmemER) =>
% 122.46/16.19 ((
% 122.46/16.19 (cartprodmempaircEq) =>
% 122.46/16.19 ((
% 122.46/16.19 (cartprodfstpairEq) =>
% 122.46/16.19 ((
% 122.46/16.19 (cartprodsndpairEq) =>
% 122.46/16.19 ((
% 122.46/16.19 (cartprodpairsurjEq) =>
% 122.46/16.19 ((
% 122.46/16.19 (dpsetconstrI) =>
% 122.46/16.19 ((
% 122.46/16.19 (dpsetconstrSub) =>
% 122.46/16.19 ((
% 122.46/16.19 (setOfPairsIsBReln) =>
% 122.46/16.19 ((
% 122.46/16.19 (dpsetconstrERa) =>
% 122.46/16.19 ((
% 122.46/16.19 (dpsetconstrEL1) =>
% 122.46/16.19 ((
% 122.46/16.19 (dpsetconstrEL2) =>
% 122.46/16.19 ((
% 122.46/16.19 (dpsetconstrER) =>
% 122.46/16.19 ((
% 122.46/16.19 (funcImageSingleton) =>
% 122.46/16.19 ((
% 122.46/16.19 (apProp) =>
% 122.46/16.19 ((
% 122.46/16.19 (app) =>
% 122.46/16.19 ((
% 122.46/16.19 (infuncsetfunc) =>
% 122.46/16.19 ((
% 122.46/16.19 (ap2p) =>
% 122.46/16.19 ((
% 122.46/16.19 (funcinfuncset) =>
% 122.46/16.19 ((
% 122.46/16.19 (lamProp) =>
% 122.46/16.19 ((
% 122.46/16.19 (lamp) =>
% 122.46/16.19 ((
% 122.46/16.19 (lam2p) =>
% 122.46/16.19 ((
% 122.46/16.19 (brelnall1) =>
% 122.46/16.19 ((
% 122.46/16.19 (brelnall2) =>
% 122.46/16.19 ((
% 122.46/16.19 (ex1E2) =>
% 122.46/16.19 ((
% 122.46/16.19 (funcGraphProp1) =>
% 122.46/16.19 ((
% 122.46/16.19 (funcGraphProp3) =>
% 122.46/16.19 ((
% 122.46/16.19 (funcGraphProp2) =>
% 122.46/16.19 ((
% 122.46/16.19 (funcextLem) =>
% 122.46/16.19 ((
% 122.46/16.19 (funcGraphProp4) =>
% 122.46/16.19 ((
% 122.46/16.19 (subbreln) =>
% 122.46/16.19 ((
% 122.46/16.19 (eqbreln) =>
% 122.46/16.19 ((
% 122.46/16.19 (funcext) =>
% 122.46/16.19 ((
% 122.46/16.19 (funcext2) =>
% 122.46/16.19 ((
% 122.46/16.19 (ap2apEq1) =>
% 122.46/16.19 ((
% 122.46/16.19 (ap2apEq2) =>
% 122.46/16.19 ((
% 122.46/16.19 (beta1) =>
% 122.46/16.19 ((
% 122.46/16.19 (eta1) =>
% 122.46/16.19 ((
% 122.46/16.19 (lam2lamEq) =>
% 122.46/16.19 ((
% 122.46/16.19 (beta2) =>
% 122.46/16.19 ((
% 122.46/16.19 (eta2) =>
% 122.46/16.19 ((
% 122.46/16.19 (iffalseProp1) =>
% 122.46/16.19 ((
% 122.46/16.19 (iffalseProp2) =>
% 122.46/16.19 ((
% 122.46/16.19 (iftrueProp1) =>
% 122.46/16.19 ((
% 122.46/16.19 (iftrueProp2) =>
% 122.46/16.19 ((
% 122.46/16.19 (ifSingleton) =>
% 122.46/16.19 ((
% 122.46/16.19 (ifp) =>
% 122.46/16.19 ((
% 122.46/16.19 (theeq) =>
% 122.46/16.19 ((
% 122.46/16.19 (iftrue) =>
% 122.46/16.19 ((
% 122.46/16.19 (iffalse) =>
% 122.46/16.19 ((
% 122.46/16.19 (iftrueorfalse) =>
% 122.46/16.19 ((
% 122.46/16.19 (binintersectT_lem) =>
% 122.46/16.19 ((
% 122.46/16.19 (binunionT_lem) =>
% 122.46/16.19 ((
% 122.46/16.19 (powersetT_lem) =>
% 122.46/16.19 ((
% 122.46/16.19 (setminusT_lem) =>
% 122.46/16.19 ((
% 122.46/16.19 (complementT_lem) =>
% 122.46/16.19 ((
% 122.46/16.19 (setextT) =>
% 122.46/16.19 ((
% 122.46/16.19 (subsetTI) =>
% 122.46/16.19 ((
% 122.46/16.19 (powersetTI1) =>
% 122.46/16.19 ((
% 122.46/16.19 (powersetTE1) =>
% 122.46/16.19 ((
% 122.46/16.19 (complementTI1) =>
% 122.46/16.19 ((
% 122.46/16.19 (complementTE1) =>
% 122.46/16.19 ((
% 122.46/16.19 (binintersectTELcontra) =>
% 122.46/16.19 ((
% 122.46/16.19 (binintersectTERcontra) =>
% 122.46/16.19 ((
% 122.46/16.19 (contrasubsetT) =>
% 122.46/16.19 ((
% 122.46/16.19 (contrasubsetT1) =>
% 122.46/16.19 ((
% 122.46/16.19 (contrasubsetT2) =>
% 122.46/16.19 ((
% 122.46/16.19 (contrasubsetT3) =>
% 122.46/16.19 ((
% 122.46/16.19 (doubleComplementI1) =>
% 122.46/16.19 ((
% 122.46/16.19 (doubleComplementE1) =>
% 122.46/16.19 ((
% 122.46/16.19 (doubleComplementSub1) =>
% 122.46/16.19 ((
% 122.46/16.19 (doubleComplementSub2) =>
% 122.46/16.19 ((
% 122.46/16.19 (doubleComplementEq) =>
% 122.46/16.19 ((
% 122.46/16.19 (complementTnotintersectT) =>
% 122.46/16.19 ((
% 122.46/16.19 (complementImpComplementIntersect) =>
% 122.46/16.19 ((
% 122.46/16.19 (complementSubsetComplementIntersect) =>
% 122.46/16.19 ((
% 122.46/16.19 (complementInPowersetComplementIntersect) =>
% 122.46/16.19 ((
% 122.46/16.19 (contraSubsetComplement) =>
% 122.46/16.19 ((
% 122.46/16.19 (complementTcontraSubset) =>
% 122.46/16.19 ((
% 122.46/16.19 (binunionTILcontra) =>
% 122.46/16.19 ((
% 122.46/16.19 (binunionTIRcontra) =>
% 122.46/16.19 ((
% 122.46/16.19 (inIntersectImpInUnion) =>
% 122.46/16.19 ((
% 122.46/16.19 (inIntersectImpInUnion2) =>
% 122.46/16.19 ((
% 122.46/16.19 (inIntersectImpInIntersectUnions) =>
% 122.46/16.19 ((
% 122.46/16.19 (intersectInPowersetIntersectUnions) =>
% 122.46/16.19 ((
% 122.46/16.19 (inComplementUnionImpNotIn1) =>
% 122.46/16.19 ((
% 122.46/16.19 (inComplementUnionImpInComplement1) =>
% 122.46/16.19 ((
% 122.46/16.19 (binunionTE) =>
% 122.46/16.19 ((
% 122.46/16.19 (binunionTEcontra) =>
% 122.46/16.19 ((
% 122.46/16.19 (demorgan2a1) =>
% 122.46/16.19 ((
% 122.46/16.19 (complementUnionInPowersetComplement) =>
% 122.46/16.19 ((
% 122.46/16.19 (demorgan2a2) =>
% 122.46/16.19 ((
% 122.46/16.19 (demorgan1a) =>
% 122.46/16.19 ((
% 122.46/16.19 (demorgan1b) =>
% 122.46/16.19 ((
% 122.46/16.19 (demorgan1) =>
% 122.46/16.19 ((
% 122.46/16.19 (demorgan2a) =>
% 122.46/16.19 ((
% 122.46/16.19 (demorgan2b2) =>
% 122.46/16.19 ((
% 122.46/16.19 (demorgan2b) =>
% 122.46/16.19 ((
% 122.46/16.19 (demorgan2) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz13rule0) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz13rule1) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz13rule2) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz13rule3) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz13rule4) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz1_1) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz1_2) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz1_3) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz1_4) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz1_5) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1all2) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1SetBreln1) =>
% 122.46/16.19 ((
% 122.46/16.19 (choice2fnsingleton) =>
% 122.46/16.19 ((
% 122.46/16.19 (setOfPairsIsBReln1) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1all1) =>
% 122.46/16.19 ((
% 122.46/16.19 (subbreln1) =>
% 122.46/16.19 ((
% 122.46/16.19 (eqbreln1) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1invprop) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1invI) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1invE) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1compprop) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1compI) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1compE) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1compEex) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1unionprop) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1unionIL) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1unionIR) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1unionI) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1unionE) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1unionEcases) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1unionCommutes) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz2Ex) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz2W) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz2A) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz2B) =>
% 122.46/16.19 ((
% 122.46/16.19 (image1Ex) =>
% 122.46/16.19 ((
% 122.46/16.19 (image1Ex1) =>
% 122.46/16.19 ((
% 122.46/16.19 (image1Equiv) =>
% 122.46/16.19 ((
% 122.46/16.19 (image1E) =>
% 122.46/16.19 ((
% 122.46/16.19 (image1I) =>
% 122.46/16.19 ((
% 122.46/16.19 (injFuncInInjFuncSet) =>
% 122.46/16.19 ((
% 122.46/16.19 (!!) @ (
% 122.46/16.19 (('#B') @ (
% 122.46/16.19 !!) @
% 122.46/16.19 (
% 122.46/16.19 (
% 122.46/16.19 ('#B') @ (
% 122.46/16.19 (
% 122.46/16.19 ('#B') @ (
% 122.46/16.19 !!))) @
% 122.46/16.19 (
% 122.46/16.19 (
% 122.46/16.19 ('#S') @ (
% 122.46/16.19 (
% 122.46/16.19 ('#B') @ (
% 122.46/16.19 '#S') @
% 122.46/16.19 (
% 122.46/16.19 (
% 122.46/16.19 ('#B') @ (
% 122.46/16.19 (
% 122.46/16.19 ('#B') @ (
% 122.46/16.19 '#S'))) @
% 122.46/16.19 (
% 122.46/16.19 (
% 122.46/16.19 ('#B') @ (
% 122.46/16.19 (
% 122.46/16.19 ('#B') @ (
% 122.46/16.19 (
% 122.46/16.19 ('#B') @ (
% 122.46/16.19 =>))))) @
% 122.46/16.19 (
% 122.46/16.19 (
% 122.46/16.19 ('#B') @ (
% 122.46/16.19 (
% 122.46/16.19 ('#B') @ (
% 122.46/16.19 (
% 122.46/16.19 ('#C') @ in)))) @
% 122.46/16.19 injFuncSet)))))))) @
% 122.46/16.19 (
% 122.46/16.19 (
% 122.46/16.19 ('#B') @ (
% 122.46/16.19 (
% 122.46/16.19 ('#B') @ (
% 122.46/16.19 (
% 122.46/16.19 ('#C') @ in)))) @
% 122.46/16.19 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.46/16.19 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1480])).
% 122.46/16.19 thf(zip_derived_cl1496, plain,
% 122.46/16.19 (~ (((cartprodpairin) =>
% 122.46/16.19 (((cartprodmempair1) =>
% 122.46/16.19 (((cartprodmempair) =>
% 122.46/16.19 (((setunionE2) =>
% 122.46/16.19 (((setunionsingleton1) =>
% 122.46/16.19 (((setunionsingleton2) =>
% 122.46/16.19 (((setunionsingleton) =>
% 122.46/16.19 (((singletonprop) =>
% 122.46/16.19 (((ex1E1) =>
% 122.46/16.19 (((ex1I) =>
% 122.46/16.19 (((ex1I2) =>
% 122.46/16.19 (((singletonsuniq) =>
% 122.46/16.19 (((setukpairinjL1) =>
% 122.46/16.19 (((kfstsingleton) =>
% 122.46/16.19 (((theprop) =>
% 122.46/16.19 (((kfstpairEq) =>
% 122.46/16.19 (((cartprodfstin) =>
% 122.46/16.19 (((setukpairinjL2) =>
% 122.46/16.19 (((setukpairinjL) =>
% 122.46/16.19 (((setukpairinjR11) =>
% 122.46/16.19 (((setukpairinjR12) =>
% 122.46/16.19 (((setukpairinjR1) =>
% 122.46/16.19 (((upairequniteq) =>
% 122.46/16.19 (((setukpairinjR2) =>
% 122.46/16.19 (((setukpairinjR) =>
% 122.46/16.19 (((ksndsingleton) =>
% 122.46/16.19 (((ksndpairEq) =>
% 122.46/16.19 (((kpairsurjEq) =>
% 122.46/16.19 (((cartprodsndin) =>
% 122.46/16.19 (((cartprodpairmemEL) =>
% 122.46/16.19 ((
% 122.46/16.19 (cartprodpairmemER) =>
% 122.46/16.19 ((
% 122.46/16.19 (cartprodmempaircEq) =>
% 122.46/16.19 ((
% 122.46/16.19 (cartprodfstpairEq) =>
% 122.46/16.19 ((
% 122.46/16.19 (cartprodsndpairEq) =>
% 122.46/16.19 ((
% 122.46/16.19 (cartprodpairsurjEq) =>
% 122.46/16.19 ((
% 122.46/16.19 (dpsetconstrI) =>
% 122.46/16.19 ((
% 122.46/16.19 (dpsetconstrSub) =>
% 122.46/16.19 ((
% 122.46/16.19 (setOfPairsIsBReln) =>
% 122.46/16.19 ((
% 122.46/16.19 (dpsetconstrERa) =>
% 122.46/16.19 ((
% 122.46/16.19 (dpsetconstrEL1) =>
% 122.46/16.19 ((
% 122.46/16.19 (dpsetconstrEL2) =>
% 122.46/16.19 ((
% 122.46/16.19 (dpsetconstrER) =>
% 122.46/16.19 ((
% 122.46/16.19 (funcImageSingleton) =>
% 122.46/16.19 ((
% 122.46/16.19 (apProp) =>
% 122.46/16.19 ((
% 122.46/16.19 (app) =>
% 122.46/16.19 ((
% 122.46/16.19 (infuncsetfunc) =>
% 122.46/16.19 ((
% 122.46/16.19 (ap2p) =>
% 122.46/16.19 ((
% 122.46/16.19 (funcinfuncset) =>
% 122.46/16.19 ((
% 122.46/16.19 (lamProp) =>
% 122.46/16.19 ((
% 122.46/16.19 (lamp) =>
% 122.46/16.19 ((
% 122.46/16.19 (lam2p) =>
% 122.46/16.19 ((
% 122.46/16.19 (brelnall1) =>
% 122.46/16.19 ((
% 122.46/16.19 (brelnall2) =>
% 122.46/16.19 ((
% 122.46/16.19 (ex1E2) =>
% 122.46/16.19 ((
% 122.46/16.19 (funcGraphProp1) =>
% 122.46/16.19 ((
% 122.46/16.19 (funcGraphProp3) =>
% 122.46/16.19 ((
% 122.46/16.19 (funcGraphProp2) =>
% 122.46/16.19 ((
% 122.46/16.19 (funcextLem) =>
% 122.46/16.19 ((
% 122.46/16.19 (funcGraphProp4) =>
% 122.46/16.19 ((
% 122.46/16.19 (subbreln) =>
% 122.46/16.19 ((
% 122.46/16.19 (eqbreln) =>
% 122.46/16.19 ((
% 122.46/16.19 (funcext) =>
% 122.46/16.19 ((
% 122.46/16.19 (funcext2) =>
% 122.46/16.19 ((
% 122.46/16.19 (ap2apEq1) =>
% 122.46/16.19 ((
% 122.46/16.19 (ap2apEq2) =>
% 122.46/16.19 ((
% 122.46/16.19 (beta1) =>
% 122.46/16.19 ((
% 122.46/16.19 (eta1) =>
% 122.46/16.19 ((
% 122.46/16.19 (lam2lamEq) =>
% 122.46/16.19 ((
% 122.46/16.19 (beta2) =>
% 122.46/16.19 ((
% 122.46/16.19 (eta2) =>
% 122.46/16.19 ((
% 122.46/16.19 (iffalseProp1) =>
% 122.46/16.19 ((
% 122.46/16.19 (iffalseProp2) =>
% 122.46/16.19 ((
% 122.46/16.19 (iftrueProp1) =>
% 122.46/16.19 ((
% 122.46/16.19 (iftrueProp2) =>
% 122.46/16.19 ((
% 122.46/16.19 (ifSingleton) =>
% 122.46/16.19 ((
% 122.46/16.19 (ifp) =>
% 122.46/16.19 ((
% 122.46/16.19 (theeq) =>
% 122.46/16.19 ((
% 122.46/16.19 (iftrue) =>
% 122.46/16.19 ((
% 122.46/16.19 (iffalse) =>
% 122.46/16.19 ((
% 122.46/16.19 (iftrueorfalse) =>
% 122.46/16.19 ((
% 122.46/16.19 (binintersectT_lem) =>
% 122.46/16.19 ((
% 122.46/16.19 (binunionT_lem) =>
% 122.46/16.19 ((
% 122.46/16.19 (powersetT_lem) =>
% 122.46/16.19 ((
% 122.46/16.19 (setminusT_lem) =>
% 122.46/16.19 ((
% 122.46/16.19 (complementT_lem) =>
% 122.46/16.19 ((
% 122.46/16.19 (setextT) =>
% 122.46/16.19 ((
% 122.46/16.19 (subsetTI) =>
% 122.46/16.19 ((
% 122.46/16.19 (powersetTI1) =>
% 122.46/16.19 ((
% 122.46/16.19 (powersetTE1) =>
% 122.46/16.19 ((
% 122.46/16.19 (complementTI1) =>
% 122.46/16.19 ((
% 122.46/16.19 (complementTE1) =>
% 122.46/16.19 ((
% 122.46/16.19 (binintersectTELcontra) =>
% 122.46/16.19 ((
% 122.46/16.19 (binintersectTERcontra) =>
% 122.46/16.19 ((
% 122.46/16.19 (contrasubsetT) =>
% 122.46/16.19 ((
% 122.46/16.19 (contrasubsetT1) =>
% 122.46/16.19 ((
% 122.46/16.19 (contrasubsetT2) =>
% 122.46/16.19 ((
% 122.46/16.19 (contrasubsetT3) =>
% 122.46/16.19 ((
% 122.46/16.19 (doubleComplementI1) =>
% 122.46/16.19 ((
% 122.46/16.19 (doubleComplementE1) =>
% 122.46/16.19 ((
% 122.46/16.19 (doubleComplementSub1) =>
% 122.46/16.19 ((
% 122.46/16.19 (doubleComplementSub2) =>
% 122.46/16.19 ((
% 122.46/16.19 (doubleComplementEq) =>
% 122.46/16.19 ((
% 122.46/16.19 (complementTnotintersectT) =>
% 122.46/16.19 ((
% 122.46/16.19 (complementImpComplementIntersect) =>
% 122.46/16.19 ((
% 122.46/16.19 (complementSubsetComplementIntersect) =>
% 122.46/16.19 ((
% 122.46/16.19 (complementInPowersetComplementIntersect) =>
% 122.46/16.19 ((
% 122.46/16.19 (contraSubsetComplement) =>
% 122.46/16.19 ((
% 122.46/16.19 (complementTcontraSubset) =>
% 122.46/16.19 ((
% 122.46/16.19 (binunionTILcontra) =>
% 122.46/16.19 ((
% 122.46/16.19 (binunionTIRcontra) =>
% 122.46/16.19 ((
% 122.46/16.19 (inIntersectImpInUnion) =>
% 122.46/16.19 ((
% 122.46/16.19 (inIntersectImpInUnion2) =>
% 122.46/16.19 ((
% 122.46/16.19 (inIntersectImpInIntersectUnions) =>
% 122.46/16.19 ((
% 122.46/16.19 (intersectInPowersetIntersectUnions) =>
% 122.46/16.19 ((
% 122.46/16.19 (inComplementUnionImpNotIn1) =>
% 122.46/16.19 ((
% 122.46/16.19 (inComplementUnionImpInComplement1) =>
% 122.46/16.19 ((
% 122.46/16.19 (binunionTE) =>
% 122.46/16.19 ((
% 122.46/16.19 (binunionTEcontra) =>
% 122.46/16.19 ((
% 122.46/16.19 (demorgan2a1) =>
% 122.46/16.19 ((
% 122.46/16.19 (complementUnionInPowersetComplement) =>
% 122.46/16.19 ((
% 122.46/16.19 (demorgan2a2) =>
% 122.46/16.19 ((
% 122.46/16.19 (demorgan1a) =>
% 122.46/16.19 ((
% 122.46/16.19 (demorgan1b) =>
% 122.46/16.19 ((
% 122.46/16.19 (demorgan1) =>
% 122.46/16.19 ((
% 122.46/16.19 (demorgan2a) =>
% 122.46/16.19 ((
% 122.46/16.19 (demorgan2b2) =>
% 122.46/16.19 ((
% 122.46/16.19 (demorgan2b) =>
% 122.46/16.19 ((
% 122.46/16.19 (demorgan2) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz13rule0) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz13rule1) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz13rule2) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz13rule3) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz13rule4) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz1_1) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz1_2) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz1_3) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz1_4) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz1_5) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1all2) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1SetBreln1) =>
% 122.46/16.19 ((
% 122.46/16.19 (choice2fnsingleton) =>
% 122.46/16.19 ((
% 122.46/16.19 (setOfPairsIsBReln1) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1all1) =>
% 122.46/16.19 ((
% 122.46/16.19 (subbreln1) =>
% 122.46/16.19 ((
% 122.46/16.19 (eqbreln1) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1invprop) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1invI) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1invE) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1compprop) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1compI) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1compE) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1compEex) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1unionprop) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1unionIL) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1unionIR) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1unionI) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1unionE) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1unionEcases) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1unionCommutes) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz2Ex) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz2W) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz2A) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz2B) =>
% 122.46/16.19 ((
% 122.46/16.19 (image1Ex) =>
% 122.46/16.19 ((
% 122.46/16.19 (image1Ex1) =>
% 122.46/16.19 ((
% 122.46/16.19 (image1Equiv) =>
% 122.46/16.19 ((
% 122.46/16.19 (image1E) =>
% 122.46/16.19 ((
% 122.46/16.19 (image1I) =>
% 122.46/16.19 ((
% 122.46/16.19 (injFuncInInjFuncSet) =>
% 122.46/16.19 ((
% 122.46/16.19 (!!) @ (
% 122.46/16.19 (('#B') @ (
% 122.46/16.19 !!) @
% 122.46/16.19 (
% 122.46/16.19 (
% 122.46/16.19 ('#B') @ (
% 122.46/16.19 (
% 122.46/16.19 ('#B') @ (
% 122.46/16.19 !!))) @
% 122.46/16.19 (
% 122.46/16.19 (
% 122.46/16.19 ('#S') @ (
% 122.46/16.19 (
% 122.46/16.19 ('#B') @ (
% 122.46/16.19 '#S') @
% 122.46/16.19 (
% 122.46/16.19 (
% 122.46/16.19 ('#B') @ (
% 122.46/16.19 (
% 122.46/16.19 ('#B') @ (
% 122.46/16.19 '#S'))) @
% 122.46/16.19 (
% 122.46/16.19 (
% 122.46/16.19 ('#B') @ (
% 122.46/16.19 (
% 122.46/16.19 ('#B') @ (
% 122.46/16.19 (
% 122.46/16.19 ('#B') @ (
% 122.46/16.19 =>))))) @
% 122.46/16.19 (
% 122.46/16.19 (
% 122.46/16.19 ('#B') @ (
% 122.46/16.19 (
% 122.46/16.19 ('#B') @ (
% 122.46/16.19 (
% 122.46/16.19 ('#C') @ in)))) @
% 122.46/16.19 injFuncSet)))))))) @
% 122.46/16.19 (
% 122.46/16.19 (
% 122.46/16.19 ('#B') @ (
% 122.46/16.19 (
% 122.46/16.19 ('#B') @ (
% 122.46/16.19 (
% 122.46/16.19 ('#C') @ in)))) @
% 122.46/16.19 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.46/16.19 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1488])).
% 122.46/16.19 thf(zip_derived_cl1505, plain,
% 122.46/16.19 (~ (((cartprodmempair1) =>
% 122.46/16.19 (((cartprodmempair) =>
% 122.46/16.19 (((setunionE2) =>
% 122.46/16.19 (((setunionsingleton1) =>
% 122.46/16.19 (((setunionsingleton2) =>
% 122.46/16.19 (((setunionsingleton) =>
% 122.46/16.19 (((singletonprop) =>
% 122.46/16.19 (((ex1E1) =>
% 122.46/16.19 (((ex1I) =>
% 122.46/16.19 (((ex1I2) =>
% 122.46/16.19 (((singletonsuniq) =>
% 122.46/16.19 (((setukpairinjL1) =>
% 122.46/16.19 (((kfstsingleton) =>
% 122.46/16.19 (((theprop) =>
% 122.46/16.19 (((kfstpairEq) =>
% 122.46/16.19 (((cartprodfstin) =>
% 122.46/16.19 (((setukpairinjL2) =>
% 122.46/16.19 (((setukpairinjL) =>
% 122.46/16.19 (((setukpairinjR11) =>
% 122.46/16.19 (((setukpairinjR12) =>
% 122.46/16.19 (((setukpairinjR1) =>
% 122.46/16.19 (((upairequniteq) =>
% 122.46/16.19 (((setukpairinjR2) =>
% 122.46/16.19 (((setukpairinjR) =>
% 122.46/16.19 (((ksndsingleton) =>
% 122.46/16.19 (((ksndpairEq) =>
% 122.46/16.19 (((kpairsurjEq) =>
% 122.46/16.19 (((cartprodsndin) =>
% 122.46/16.19 (((cartprodpairmemEL) =>
% 122.46/16.19 (((cartprodpairmemER) =>
% 122.46/16.19 ((
% 122.46/16.19 (cartprodmempaircEq) =>
% 122.46/16.19 ((
% 122.46/16.19 (cartprodfstpairEq) =>
% 122.46/16.19 ((
% 122.46/16.19 (cartprodsndpairEq) =>
% 122.46/16.19 ((
% 122.46/16.19 (cartprodpairsurjEq) =>
% 122.46/16.19 ((
% 122.46/16.19 (dpsetconstrI) =>
% 122.46/16.19 ((
% 122.46/16.19 (dpsetconstrSub) =>
% 122.46/16.19 ((
% 122.46/16.19 (setOfPairsIsBReln) =>
% 122.46/16.19 ((
% 122.46/16.19 (dpsetconstrERa) =>
% 122.46/16.19 ((
% 122.46/16.19 (dpsetconstrEL1) =>
% 122.46/16.19 ((
% 122.46/16.19 (dpsetconstrEL2) =>
% 122.46/16.19 ((
% 122.46/16.19 (dpsetconstrER) =>
% 122.46/16.19 ((
% 122.46/16.19 (funcImageSingleton) =>
% 122.46/16.19 ((
% 122.46/16.19 (apProp) =>
% 122.46/16.19 ((
% 122.46/16.19 (app) =>
% 122.46/16.19 ((
% 122.46/16.19 (infuncsetfunc) =>
% 122.46/16.19 ((
% 122.46/16.19 (ap2p) =>
% 122.46/16.19 ((
% 122.46/16.19 (funcinfuncset) =>
% 122.46/16.19 ((
% 122.46/16.19 (lamProp) =>
% 122.46/16.19 ((
% 122.46/16.19 (lamp) =>
% 122.46/16.19 ((
% 122.46/16.19 (lam2p) =>
% 122.46/16.19 ((
% 122.46/16.19 (brelnall1) =>
% 122.46/16.19 ((
% 122.46/16.19 (brelnall2) =>
% 122.46/16.19 ((
% 122.46/16.19 (ex1E2) =>
% 122.46/16.19 ((
% 122.46/16.19 (funcGraphProp1) =>
% 122.46/16.19 ((
% 122.46/16.19 (funcGraphProp3) =>
% 122.46/16.19 ((
% 122.46/16.19 (funcGraphProp2) =>
% 122.46/16.19 ((
% 122.46/16.19 (funcextLem) =>
% 122.46/16.19 ((
% 122.46/16.19 (funcGraphProp4) =>
% 122.46/16.19 ((
% 122.46/16.19 (subbreln) =>
% 122.46/16.19 ((
% 122.46/16.19 (eqbreln) =>
% 122.46/16.19 ((
% 122.46/16.19 (funcext) =>
% 122.46/16.19 ((
% 122.46/16.19 (funcext2) =>
% 122.46/16.19 ((
% 122.46/16.19 (ap2apEq1) =>
% 122.46/16.19 ((
% 122.46/16.19 (ap2apEq2) =>
% 122.46/16.19 ((
% 122.46/16.19 (beta1) =>
% 122.46/16.19 ((
% 122.46/16.19 (eta1) =>
% 122.46/16.19 ((
% 122.46/16.19 (lam2lamEq) =>
% 122.46/16.19 ((
% 122.46/16.19 (beta2) =>
% 122.46/16.19 ((
% 122.46/16.19 (eta2) =>
% 122.46/16.19 ((
% 122.46/16.19 (iffalseProp1) =>
% 122.46/16.19 ((
% 122.46/16.19 (iffalseProp2) =>
% 122.46/16.19 ((
% 122.46/16.19 (iftrueProp1) =>
% 122.46/16.19 ((
% 122.46/16.19 (iftrueProp2) =>
% 122.46/16.19 ((
% 122.46/16.19 (ifSingleton) =>
% 122.46/16.19 ((
% 122.46/16.19 (ifp) =>
% 122.46/16.19 ((
% 122.46/16.19 (theeq) =>
% 122.46/16.19 ((
% 122.46/16.19 (iftrue) =>
% 122.46/16.19 ((
% 122.46/16.19 (iffalse) =>
% 122.46/16.19 ((
% 122.46/16.19 (iftrueorfalse) =>
% 122.46/16.19 ((
% 122.46/16.19 (binintersectT_lem) =>
% 122.46/16.19 ((
% 122.46/16.19 (binunionT_lem) =>
% 122.46/16.19 ((
% 122.46/16.19 (powersetT_lem) =>
% 122.46/16.19 ((
% 122.46/16.19 (setminusT_lem) =>
% 122.46/16.19 ((
% 122.46/16.19 (complementT_lem) =>
% 122.46/16.19 ((
% 122.46/16.19 (setextT) =>
% 122.46/16.19 ((
% 122.46/16.19 (subsetTI) =>
% 122.46/16.19 ((
% 122.46/16.19 (powersetTI1) =>
% 122.46/16.19 ((
% 122.46/16.19 (powersetTE1) =>
% 122.46/16.19 ((
% 122.46/16.19 (complementTI1) =>
% 122.46/16.19 ((
% 122.46/16.19 (complementTE1) =>
% 122.46/16.19 ((
% 122.46/16.19 (binintersectTELcontra) =>
% 122.46/16.19 ((
% 122.46/16.19 (binintersectTERcontra) =>
% 122.46/16.19 ((
% 122.46/16.19 (contrasubsetT) =>
% 122.46/16.19 ((
% 122.46/16.19 (contrasubsetT1) =>
% 122.46/16.19 ((
% 122.46/16.19 (contrasubsetT2) =>
% 122.46/16.19 ((
% 122.46/16.19 (contrasubsetT3) =>
% 122.46/16.19 ((
% 122.46/16.19 (doubleComplementI1) =>
% 122.46/16.19 ((
% 122.46/16.19 (doubleComplementE1) =>
% 122.46/16.19 ((
% 122.46/16.19 (doubleComplementSub1) =>
% 122.46/16.19 ((
% 122.46/16.19 (doubleComplementSub2) =>
% 122.46/16.19 ((
% 122.46/16.19 (doubleComplementEq) =>
% 122.46/16.19 ((
% 122.46/16.19 (complementTnotintersectT) =>
% 122.46/16.19 ((
% 122.46/16.19 (complementImpComplementIntersect) =>
% 122.46/16.19 ((
% 122.46/16.19 (complementSubsetComplementIntersect) =>
% 122.46/16.19 ((
% 122.46/16.19 (complementInPowersetComplementIntersect) =>
% 122.46/16.19 ((
% 122.46/16.19 (contraSubsetComplement) =>
% 122.46/16.19 ((
% 122.46/16.19 (complementTcontraSubset) =>
% 122.46/16.19 ((
% 122.46/16.19 (binunionTILcontra) =>
% 122.46/16.19 ((
% 122.46/16.19 (binunionTIRcontra) =>
% 122.46/16.19 ((
% 122.46/16.19 (inIntersectImpInUnion) =>
% 122.46/16.19 ((
% 122.46/16.19 (inIntersectImpInUnion2) =>
% 122.46/16.19 ((
% 122.46/16.19 (inIntersectImpInIntersectUnions) =>
% 122.46/16.19 ((
% 122.46/16.19 (intersectInPowersetIntersectUnions) =>
% 122.46/16.19 ((
% 122.46/16.19 (inComplementUnionImpNotIn1) =>
% 122.46/16.19 ((
% 122.46/16.19 (inComplementUnionImpInComplement1) =>
% 122.46/16.19 ((
% 122.46/16.19 (binunionTE) =>
% 122.46/16.19 ((
% 122.46/16.19 (binunionTEcontra) =>
% 122.46/16.19 ((
% 122.46/16.19 (demorgan2a1) =>
% 122.46/16.19 ((
% 122.46/16.19 (complementUnionInPowersetComplement) =>
% 122.46/16.19 ((
% 122.46/16.19 (demorgan2a2) =>
% 122.46/16.19 ((
% 122.46/16.19 (demorgan1a) =>
% 122.46/16.19 ((
% 122.46/16.19 (demorgan1b) =>
% 122.46/16.19 ((
% 122.46/16.19 (demorgan1) =>
% 122.46/16.19 ((
% 122.46/16.19 (demorgan2a) =>
% 122.46/16.19 ((
% 122.46/16.19 (demorgan2b2) =>
% 122.46/16.19 ((
% 122.46/16.19 (demorgan2b) =>
% 122.46/16.19 ((
% 122.46/16.19 (demorgan2) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz13rule0) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz13rule1) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz13rule2) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz13rule3) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz13rule4) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz1_1) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz1_2) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz1_3) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz1_4) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz1_5) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1all2) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1SetBreln1) =>
% 122.46/16.19 ((
% 122.46/16.19 (choice2fnsingleton) =>
% 122.46/16.19 ((
% 122.46/16.19 (setOfPairsIsBReln1) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1all1) =>
% 122.46/16.19 ((
% 122.46/16.19 (subbreln1) =>
% 122.46/16.19 ((
% 122.46/16.19 (eqbreln1) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1invprop) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1invI) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1invE) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1compprop) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1compI) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1compE) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1compEex) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1unionprop) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1unionIL) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1unionIR) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1unionI) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1unionE) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1unionEcases) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1unionCommutes) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz2Ex) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz2W) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz2A) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz2B) =>
% 122.46/16.19 ((
% 122.46/16.19 (image1Ex) =>
% 122.46/16.19 ((
% 122.46/16.19 (image1Ex1) =>
% 122.46/16.19 ((
% 122.46/16.19 (image1Equiv) =>
% 122.46/16.19 ((
% 122.46/16.19 (image1E) =>
% 122.46/16.19 ((
% 122.46/16.19 (image1I) =>
% 122.46/16.19 ((
% 122.46/16.19 (injFuncInInjFuncSet) =>
% 122.46/16.19 ((
% 122.46/16.19 (!!) @ (
% 122.46/16.19 (('#B') @ (
% 122.46/16.19 !!) @
% 122.46/16.19 (
% 122.46/16.19 (
% 122.46/16.19 ('#B') @ (
% 122.46/16.19 (
% 122.46/16.19 ('#B') @ (
% 122.46/16.19 !!))) @
% 122.46/16.19 (
% 122.46/16.19 (
% 122.46/16.19 ('#S') @ (
% 122.46/16.19 (
% 122.46/16.19 ('#B') @ (
% 122.46/16.19 '#S') @
% 122.46/16.19 (
% 122.46/16.19 (
% 122.46/16.19 ('#B') @ (
% 122.46/16.19 (
% 122.46/16.19 ('#B') @ (
% 122.46/16.19 '#S'))) @
% 122.46/16.19 (
% 122.46/16.19 (
% 122.46/16.19 ('#B') @ (
% 122.46/16.19 (
% 122.46/16.19 ('#B') @ (
% 122.46/16.19 (
% 122.46/16.19 ('#B') @ (
% 122.46/16.19 =>))))) @
% 122.46/16.19 (
% 122.46/16.19 (
% 122.46/16.19 ('#B') @ (
% 122.46/16.19 (
% 122.46/16.19 ('#B') @ (
% 122.46/16.19 (
% 122.46/16.19 ('#C') @ in)))) @
% 122.46/16.19 injFuncSet)))))))) @
% 122.46/16.19 (
% 122.46/16.19 (
% 122.46/16.19 ('#B') @ (
% 122.46/16.19 (
% 122.46/16.19 ('#B') @ (
% 122.46/16.19 (
% 122.46/16.19 ('#C') @ in)))) @
% 122.46/16.19 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.46/16.19 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1496])).
% 122.46/16.19 thf(zip_derived_cl1515, plain,
% 122.46/16.19 (~ (((cartprodmempair) =>
% 122.46/16.19 (((setunionE2) =>
% 122.46/16.19 (((setunionsingleton1) =>
% 122.46/16.19 (((setunionsingleton2) =>
% 122.46/16.19 (((setunionsingleton) =>
% 122.46/16.19 (((singletonprop) =>
% 122.46/16.19 (((ex1E1) =>
% 122.46/16.19 (((ex1I) =>
% 122.46/16.19 (((ex1I2) =>
% 122.46/16.19 (((singletonsuniq) =>
% 122.46/16.19 (((setukpairinjL1) =>
% 122.46/16.19 (((kfstsingleton) =>
% 122.46/16.19 (((theprop) =>
% 122.46/16.19 (((kfstpairEq) =>
% 122.46/16.19 (((cartprodfstin) =>
% 122.46/16.19 (((setukpairinjL2) =>
% 122.46/16.19 (((setukpairinjL) =>
% 122.46/16.19 (((setukpairinjR11) =>
% 122.46/16.19 (((setukpairinjR12) =>
% 122.46/16.19 (((setukpairinjR1) =>
% 122.46/16.19 (((upairequniteq) =>
% 122.46/16.19 (((setukpairinjR2) =>
% 122.46/16.19 (((setukpairinjR) =>
% 122.46/16.19 (((ksndsingleton) =>
% 122.46/16.19 (((ksndpairEq) =>
% 122.46/16.19 (((kpairsurjEq) =>
% 122.46/16.19 (((cartprodsndin) =>
% 122.46/16.19 (((cartprodpairmemEL) =>
% 122.46/16.19 (((cartprodpairmemER) =>
% 122.46/16.19 (((cartprodmempaircEq) =>
% 122.46/16.19 ((
% 122.46/16.19 (cartprodfstpairEq) =>
% 122.46/16.19 ((
% 122.46/16.19 (cartprodsndpairEq) =>
% 122.46/16.19 ((
% 122.46/16.19 (cartprodpairsurjEq) =>
% 122.46/16.19 ((
% 122.46/16.19 (dpsetconstrI) =>
% 122.46/16.19 ((
% 122.46/16.19 (dpsetconstrSub) =>
% 122.46/16.19 ((
% 122.46/16.19 (setOfPairsIsBReln) =>
% 122.46/16.19 ((
% 122.46/16.19 (dpsetconstrERa) =>
% 122.46/16.19 ((
% 122.46/16.19 (dpsetconstrEL1) =>
% 122.46/16.19 ((
% 122.46/16.19 (dpsetconstrEL2) =>
% 122.46/16.19 ((
% 122.46/16.19 (dpsetconstrER) =>
% 122.46/16.19 ((
% 122.46/16.19 (funcImageSingleton) =>
% 122.46/16.19 ((
% 122.46/16.19 (apProp) =>
% 122.46/16.19 ((
% 122.46/16.19 (app) =>
% 122.46/16.19 ((
% 122.46/16.19 (infuncsetfunc) =>
% 122.46/16.19 ((
% 122.46/16.19 (ap2p) =>
% 122.46/16.19 ((
% 122.46/16.19 (funcinfuncset) =>
% 122.46/16.19 ((
% 122.46/16.19 (lamProp) =>
% 122.46/16.19 ((
% 122.46/16.19 (lamp) =>
% 122.46/16.19 ((
% 122.46/16.19 (lam2p) =>
% 122.46/16.19 ((
% 122.46/16.19 (brelnall1) =>
% 122.46/16.19 ((
% 122.46/16.19 (brelnall2) =>
% 122.46/16.19 ((
% 122.46/16.19 (ex1E2) =>
% 122.46/16.19 ((
% 122.46/16.19 (funcGraphProp1) =>
% 122.46/16.19 ((
% 122.46/16.19 (funcGraphProp3) =>
% 122.46/16.19 ((
% 122.46/16.19 (funcGraphProp2) =>
% 122.46/16.19 ((
% 122.46/16.19 (funcextLem) =>
% 122.46/16.19 ((
% 122.46/16.19 (funcGraphProp4) =>
% 122.46/16.19 ((
% 122.46/16.19 (subbreln) =>
% 122.46/16.19 ((
% 122.46/16.19 (eqbreln) =>
% 122.46/16.19 ((
% 122.46/16.19 (funcext) =>
% 122.46/16.19 ((
% 122.46/16.19 (funcext2) =>
% 122.46/16.19 ((
% 122.46/16.19 (ap2apEq1) =>
% 122.46/16.19 ((
% 122.46/16.19 (ap2apEq2) =>
% 122.46/16.19 ((
% 122.46/16.19 (beta1) =>
% 122.46/16.19 ((
% 122.46/16.19 (eta1) =>
% 122.46/16.19 ((
% 122.46/16.19 (lam2lamEq) =>
% 122.46/16.19 ((
% 122.46/16.19 (beta2) =>
% 122.46/16.19 ((
% 122.46/16.19 (eta2) =>
% 122.46/16.19 ((
% 122.46/16.19 (iffalseProp1) =>
% 122.46/16.19 ((
% 122.46/16.19 (iffalseProp2) =>
% 122.46/16.19 ((
% 122.46/16.19 (iftrueProp1) =>
% 122.46/16.19 ((
% 122.46/16.19 (iftrueProp2) =>
% 122.46/16.19 ((
% 122.46/16.19 (ifSingleton) =>
% 122.46/16.19 ((
% 122.46/16.19 (ifp) =>
% 122.46/16.19 ((
% 122.46/16.19 (theeq) =>
% 122.46/16.19 ((
% 122.46/16.19 (iftrue) =>
% 122.46/16.19 ((
% 122.46/16.19 (iffalse) =>
% 122.46/16.19 ((
% 122.46/16.19 (iftrueorfalse) =>
% 122.46/16.19 ((
% 122.46/16.19 (binintersectT_lem) =>
% 122.46/16.19 ((
% 122.46/16.19 (binunionT_lem) =>
% 122.46/16.19 ((
% 122.46/16.19 (powersetT_lem) =>
% 122.46/16.19 ((
% 122.46/16.19 (setminusT_lem) =>
% 122.46/16.19 ((
% 122.46/16.19 (complementT_lem) =>
% 122.46/16.19 ((
% 122.46/16.19 (setextT) =>
% 122.46/16.19 ((
% 122.46/16.19 (subsetTI) =>
% 122.46/16.19 ((
% 122.46/16.19 (powersetTI1) =>
% 122.46/16.19 ((
% 122.46/16.19 (powersetTE1) =>
% 122.46/16.19 ((
% 122.46/16.19 (complementTI1) =>
% 122.46/16.19 ((
% 122.46/16.19 (complementTE1) =>
% 122.46/16.19 ((
% 122.46/16.19 (binintersectTELcontra) =>
% 122.46/16.19 ((
% 122.46/16.19 (binintersectTERcontra) =>
% 122.46/16.19 ((
% 122.46/16.19 (contrasubsetT) =>
% 122.46/16.19 ((
% 122.46/16.19 (contrasubsetT1) =>
% 122.46/16.19 ((
% 122.46/16.19 (contrasubsetT2) =>
% 122.46/16.19 ((
% 122.46/16.19 (contrasubsetT3) =>
% 122.46/16.19 ((
% 122.46/16.19 (doubleComplementI1) =>
% 122.46/16.19 ((
% 122.46/16.19 (doubleComplementE1) =>
% 122.46/16.19 ((
% 122.46/16.19 (doubleComplementSub1) =>
% 122.46/16.19 ((
% 122.46/16.19 (doubleComplementSub2) =>
% 122.46/16.19 ((
% 122.46/16.19 (doubleComplementEq) =>
% 122.46/16.19 ((
% 122.46/16.19 (complementTnotintersectT) =>
% 122.46/16.19 ((
% 122.46/16.19 (complementImpComplementIntersect) =>
% 122.46/16.19 ((
% 122.46/16.19 (complementSubsetComplementIntersect) =>
% 122.46/16.19 ((
% 122.46/16.19 (complementInPowersetComplementIntersect) =>
% 122.46/16.19 ((
% 122.46/16.19 (contraSubsetComplement) =>
% 122.46/16.19 ((
% 122.46/16.19 (complementTcontraSubset) =>
% 122.46/16.19 ((
% 122.46/16.19 (binunionTILcontra) =>
% 122.46/16.19 ((
% 122.46/16.19 (binunionTIRcontra) =>
% 122.46/16.19 ((
% 122.46/16.19 (inIntersectImpInUnion) =>
% 122.46/16.19 ((
% 122.46/16.19 (inIntersectImpInUnion2) =>
% 122.46/16.19 ((
% 122.46/16.19 (inIntersectImpInIntersectUnions) =>
% 122.46/16.19 ((
% 122.46/16.19 (intersectInPowersetIntersectUnions) =>
% 122.46/16.19 ((
% 122.46/16.19 (inComplementUnionImpNotIn1) =>
% 122.46/16.19 ((
% 122.46/16.19 (inComplementUnionImpInComplement1) =>
% 122.46/16.19 ((
% 122.46/16.19 (binunionTE) =>
% 122.46/16.19 ((
% 122.46/16.19 (binunionTEcontra) =>
% 122.46/16.19 ((
% 122.46/16.19 (demorgan2a1) =>
% 122.46/16.19 ((
% 122.46/16.19 (complementUnionInPowersetComplement) =>
% 122.46/16.19 ((
% 122.46/16.19 (demorgan2a2) =>
% 122.46/16.19 ((
% 122.46/16.19 (demorgan1a) =>
% 122.46/16.19 ((
% 122.46/16.19 (demorgan1b) =>
% 122.46/16.19 ((
% 122.46/16.19 (demorgan1) =>
% 122.46/16.19 ((
% 122.46/16.19 (demorgan2a) =>
% 122.46/16.19 ((
% 122.46/16.19 (demorgan2b2) =>
% 122.46/16.19 ((
% 122.46/16.19 (demorgan2b) =>
% 122.46/16.19 ((
% 122.46/16.19 (demorgan2) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz13rule0) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz13rule1) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz13rule2) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz13rule3) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz13rule4) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz1_1) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz1_2) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz1_3) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz1_4) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz1_5) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1all2) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1SetBreln1) =>
% 122.46/16.19 ((
% 122.46/16.19 (choice2fnsingleton) =>
% 122.46/16.19 ((
% 122.46/16.19 (setOfPairsIsBReln1) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1all1) =>
% 122.46/16.19 ((
% 122.46/16.19 (subbreln1) =>
% 122.46/16.19 ((
% 122.46/16.19 (eqbreln1) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1invprop) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1invI) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1invE) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1compprop) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1compI) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1compE) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1compEex) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1unionprop) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1unionIL) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1unionIR) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1unionI) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1unionE) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1unionEcases) =>
% 122.46/16.19 ((
% 122.46/16.19 (breln1unionCommutes) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz2Ex) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz2W) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz2A) =>
% 122.46/16.19 ((
% 122.46/16.19 (woz2B) =>
% 122.46/16.19 ((
% 122.46/16.19 (image1Ex) =>
% 122.46/16.19 ((
% 122.46/16.19 (image1Ex1) =>
% 122.46/16.19 ((
% 122.46/16.19 (image1Equiv) =>
% 122.46/16.19 ((
% 122.46/16.19 (image1E) =>
% 122.46/16.19 ((
% 122.46/16.19 (image1I) =>
% 122.46/16.19 ((
% 122.46/16.19 (injFuncInInjFuncSet) =>
% 122.46/16.19 ((
% 122.46/16.19 (!!) @ (
% 122.46/16.19 (('#B') @ (
% 122.46/16.20 !!) @
% 122.46/16.20 (
% 122.46/16.20 (
% 122.46/16.20 ('#B') @ (
% 122.46/16.20 (
% 122.46/16.20 ('#B') @ (
% 122.46/16.20 !!))) @
% 122.46/16.20 (
% 122.46/16.20 (
% 122.46/16.20 ('#S') @ (
% 122.46/16.20 (
% 122.46/16.20 ('#B') @ (
% 122.46/16.20 '#S') @
% 122.46/16.20 (
% 122.46/16.20 (
% 122.46/16.20 ('#B') @ (
% 122.46/16.20 (
% 122.46/16.20 ('#B') @ (
% 122.46/16.20 '#S'))) @
% 122.46/16.20 (
% 122.46/16.20 (
% 122.46/16.20 ('#B') @ (
% 122.46/16.20 (
% 122.46/16.20 ('#B') @ (
% 122.46/16.20 (
% 122.46/16.20 ('#B') @ (
% 122.46/16.20 =>))))) @
% 122.46/16.20 (
% 122.46/16.20 (
% 122.46/16.20 ('#B') @ (
% 122.46/16.20 (
% 122.46/16.20 ('#B') @ (
% 122.46/16.20 (
% 122.46/16.20 ('#C') @ in)))) @
% 122.46/16.20 injFuncSet)))))))) @
% 122.46/16.20 (
% 122.46/16.20 (
% 122.46/16.20 ('#B') @ (
% 122.46/16.20 (
% 122.46/16.20 ('#B') @ (
% 122.46/16.20 (
% 122.46/16.20 ('#C') @ in)))) @
% 122.46/16.20 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.46/16.20 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1505])).
% 122.46/16.20 thf(zip_derived_cl1525, plain,
% 122.46/16.20 (~ (((setunionE2) =>
% 122.46/16.20 (((setunionsingleton1) =>
% 122.46/16.20 (((setunionsingleton2) =>
% 122.46/16.20 (((setunionsingleton) =>
% 122.46/16.20 (((singletonprop) =>
% 122.46/16.20 (((ex1E1) =>
% 122.46/16.20 (((ex1I) =>
% 122.46/16.20 (((ex1I2) =>
% 122.46/16.20 (((singletonsuniq) =>
% 122.46/16.20 (((setukpairinjL1) =>
% 122.46/16.20 (((kfstsingleton) =>
% 122.46/16.20 (((theprop) =>
% 122.46/16.20 (((kfstpairEq) =>
% 122.46/16.20 (((cartprodfstin) =>
% 122.46/16.20 (((setukpairinjL2) =>
% 122.46/16.20 (((setukpairinjL) =>
% 122.46/16.20 (((setukpairinjR11) =>
% 122.46/16.20 (((setukpairinjR12) =>
% 122.46/16.20 (((setukpairinjR1) =>
% 122.46/16.20 (((upairequniteq) =>
% 122.46/16.20 (((setukpairinjR2) =>
% 122.46/16.20 (((setukpairinjR) =>
% 122.46/16.20 (((ksndsingleton) =>
% 122.46/16.20 (((ksndpairEq) =>
% 122.46/16.20 (((kpairsurjEq) =>
% 122.46/16.20 (((cartprodsndin) =>
% 122.46/16.20 (((cartprodpairmemEL) =>
% 122.46/16.20 (((cartprodpairmemER) =>
% 122.46/16.20 (((cartprodmempaircEq) =>
% 122.46/16.20 (((cartprodfstpairEq) =>
% 122.46/16.20 ((
% 122.46/16.20 (cartprodsndpairEq) =>
% 122.46/16.20 ((
% 122.46/16.20 (cartprodpairsurjEq) =>
% 122.46/16.20 ((
% 122.46/16.20 (dpsetconstrI) =>
% 122.46/16.20 ((
% 122.46/16.20 (dpsetconstrSub) =>
% 122.46/16.20 ((
% 122.46/16.20 (setOfPairsIsBReln) =>
% 122.46/16.20 ((
% 122.46/16.20 (dpsetconstrERa) =>
% 122.46/16.20 ((
% 122.46/16.20 (dpsetconstrEL1) =>
% 122.46/16.20 ((
% 122.46/16.20 (dpsetconstrEL2) =>
% 122.46/16.20 ((
% 122.46/16.20 (dpsetconstrER) =>
% 122.46/16.20 ((
% 122.46/16.20 (funcImageSingleton) =>
% 122.46/16.20 ((
% 122.46/16.20 (apProp) =>
% 122.46/16.20 ((
% 122.46/16.20 (app) =>
% 122.46/16.20 ((
% 122.46/16.20 (infuncsetfunc) =>
% 122.46/16.20 ((
% 122.46/16.20 (ap2p) =>
% 122.46/16.20 ((
% 122.46/16.20 (funcinfuncset) =>
% 122.46/16.20 ((
% 122.46/16.20 (lamProp) =>
% 122.46/16.20 ((
% 122.46/16.20 (lamp) =>
% 122.46/16.20 ((
% 122.46/16.20 (lam2p) =>
% 122.46/16.20 ((
% 122.46/16.20 (brelnall1) =>
% 122.46/16.20 ((
% 122.46/16.20 (brelnall2) =>
% 122.46/16.20 ((
% 122.46/16.20 (ex1E2) =>
% 122.46/16.20 ((
% 122.46/16.20 (funcGraphProp1) =>
% 122.46/16.20 ((
% 122.46/16.20 (funcGraphProp3) =>
% 122.46/16.20 ((
% 122.46/16.20 (funcGraphProp2) =>
% 122.46/16.20 ((
% 122.46/16.20 (funcextLem) =>
% 122.46/16.20 ((
% 122.46/16.20 (funcGraphProp4) =>
% 122.46/16.20 ((
% 122.46/16.20 (subbreln) =>
% 122.46/16.20 ((
% 122.46/16.20 (eqbreln) =>
% 122.46/16.20 ((
% 122.46/16.20 (funcext) =>
% 122.46/16.20 ((
% 122.46/16.20 (funcext2) =>
% 122.46/16.20 ((
% 122.46/16.20 (ap2apEq1) =>
% 122.46/16.20 ((
% 122.46/16.20 (ap2apEq2) =>
% 122.46/16.20 ((
% 122.46/16.20 (beta1) =>
% 122.46/16.20 ((
% 122.46/16.20 (eta1) =>
% 122.46/16.20 ((
% 122.46/16.20 (lam2lamEq) =>
% 122.46/16.20 ((
% 122.46/16.20 (beta2) =>
% 122.46/16.20 ((
% 122.46/16.20 (eta2) =>
% 122.46/16.20 ((
% 122.46/16.20 (iffalseProp1) =>
% 122.46/16.20 ((
% 122.46/16.20 (iffalseProp2) =>
% 122.46/16.20 ((
% 122.46/16.20 (iftrueProp1) =>
% 122.46/16.20 ((
% 122.46/16.20 (iftrueProp2) =>
% 122.46/16.20 ((
% 122.46/16.20 (ifSingleton) =>
% 122.46/16.20 ((
% 122.46/16.20 (ifp) =>
% 122.46/16.20 ((
% 122.46/16.20 (theeq) =>
% 122.46/16.20 ((
% 122.46/16.20 (iftrue) =>
% 122.46/16.20 ((
% 122.46/16.20 (iffalse) =>
% 122.46/16.20 ((
% 122.46/16.20 (iftrueorfalse) =>
% 122.46/16.20 ((
% 122.46/16.20 (binintersectT_lem) =>
% 122.46/16.20 ((
% 122.46/16.20 (binunionT_lem) =>
% 122.46/16.20 ((
% 122.46/16.20 (powersetT_lem) =>
% 122.46/16.20 ((
% 122.46/16.20 (setminusT_lem) =>
% 122.46/16.20 ((
% 122.46/16.20 (complementT_lem) =>
% 122.46/16.20 ((
% 122.46/16.20 (setextT) =>
% 122.46/16.20 ((
% 122.46/16.20 (subsetTI) =>
% 122.46/16.20 ((
% 122.46/16.20 (powersetTI1) =>
% 122.46/16.20 ((
% 122.46/16.20 (powersetTE1) =>
% 122.46/16.20 ((
% 122.46/16.20 (complementTI1) =>
% 122.46/16.20 ((
% 122.46/16.20 (complementTE1) =>
% 122.46/16.20 ((
% 122.46/16.20 (binintersectTELcontra) =>
% 122.46/16.20 ((
% 122.46/16.20 (binintersectTERcontra) =>
% 122.46/16.20 ((
% 122.46/16.20 (contrasubsetT) =>
% 122.46/16.20 ((
% 122.46/16.20 (contrasubsetT1) =>
% 122.46/16.20 ((
% 122.46/16.20 (contrasubsetT2) =>
% 122.46/16.20 ((
% 122.46/16.20 (contrasubsetT3) =>
% 122.46/16.20 ((
% 122.46/16.20 (doubleComplementI1) =>
% 122.46/16.20 ((
% 122.46/16.20 (doubleComplementE1) =>
% 122.46/16.20 ((
% 122.46/16.20 (doubleComplementSub1) =>
% 122.46/16.20 ((
% 122.46/16.20 (doubleComplementSub2) =>
% 122.46/16.20 ((
% 122.46/16.20 (doubleComplementEq) =>
% 122.46/16.20 ((
% 122.46/16.20 (complementTnotintersectT) =>
% 122.46/16.20 ((
% 122.46/16.20 (complementImpComplementIntersect) =>
% 122.46/16.20 ((
% 122.46/16.20 (complementSubsetComplementIntersect) =>
% 122.46/16.20 ((
% 122.46/16.20 (complementInPowersetComplementIntersect) =>
% 122.46/16.20 ((
% 122.46/16.20 (contraSubsetComplement) =>
% 122.46/16.20 ((
% 122.46/16.20 (complementTcontraSubset) =>
% 122.46/16.20 ((
% 122.46/16.20 (binunionTILcontra) =>
% 122.46/16.20 ((
% 122.46/16.20 (binunionTIRcontra) =>
% 122.46/16.20 ((
% 122.46/16.20 (inIntersectImpInUnion) =>
% 122.46/16.20 ((
% 122.46/16.20 (inIntersectImpInUnion2) =>
% 122.46/16.20 ((
% 122.46/16.20 (inIntersectImpInIntersectUnions) =>
% 122.46/16.20 ((
% 122.46/16.20 (intersectInPowersetIntersectUnions) =>
% 122.46/16.20 ((
% 122.46/16.20 (inComplementUnionImpNotIn1) =>
% 122.46/16.20 ((
% 122.46/16.20 (inComplementUnionImpInComplement1) =>
% 122.46/16.20 ((
% 122.46/16.20 (binunionTE) =>
% 122.46/16.20 ((
% 122.46/16.20 (binunionTEcontra) =>
% 122.46/16.20 ((
% 122.46/16.20 (demorgan2a1) =>
% 122.46/16.20 ((
% 122.46/16.20 (complementUnionInPowersetComplement) =>
% 122.46/16.20 ((
% 122.46/16.20 (demorgan2a2) =>
% 122.46/16.20 ((
% 122.46/16.20 (demorgan1a) =>
% 122.46/16.20 ((
% 122.46/16.20 (demorgan1b) =>
% 122.46/16.20 ((
% 122.46/16.20 (demorgan1) =>
% 122.46/16.20 ((
% 122.46/16.20 (demorgan2a) =>
% 122.46/16.20 ((
% 122.46/16.20 (demorgan2b2) =>
% 122.46/16.20 ((
% 122.46/16.20 (demorgan2b) =>
% 122.46/16.20 ((
% 122.46/16.20 (demorgan2) =>
% 122.46/16.20 ((
% 122.46/16.20 (woz13rule0) =>
% 122.46/16.20 ((
% 122.46/16.20 (woz13rule1) =>
% 122.46/16.20 ((
% 122.46/16.20 (woz13rule2) =>
% 122.46/16.20 ((
% 122.46/16.20 (woz13rule3) =>
% 122.46/16.20 ((
% 122.46/16.20 (woz13rule4) =>
% 122.46/16.20 ((
% 122.46/16.20 (woz1_1) =>
% 122.46/16.20 ((
% 122.46/16.20 (woz1_2) =>
% 122.46/16.20 ((
% 122.46/16.20 (woz1_3) =>
% 122.46/16.20 ((
% 122.46/16.20 (woz1_4) =>
% 122.46/16.20 ((
% 122.46/16.20 (woz1_5) =>
% 122.46/16.20 ((
% 122.46/16.20 (breln1all2) =>
% 122.46/16.20 ((
% 122.46/16.20 (breln1SetBreln1) =>
% 122.46/16.20 ((
% 122.46/16.20 (choice2fnsingleton) =>
% 122.46/16.20 ((
% 122.46/16.20 (setOfPairsIsBReln1) =>
% 122.46/16.20 ((
% 122.46/16.20 (breln1all1) =>
% 122.46/16.20 ((
% 122.46/16.20 (subbreln1) =>
% 122.46/16.20 ((
% 122.46/16.20 (eqbreln1) =>
% 122.46/16.20 ((
% 122.46/16.20 (breln1invprop) =>
% 122.46/16.20 ((
% 122.46/16.20 (breln1invI) =>
% 122.46/16.20 ((
% 122.46/16.20 (breln1invE) =>
% 122.46/16.20 ((
% 122.46/16.20 (breln1compprop) =>
% 122.46/16.20 ((
% 122.46/16.20 (breln1compI) =>
% 122.46/16.20 ((
% 122.46/16.20 (breln1compE) =>
% 122.46/16.20 ((
% 122.46/16.20 (breln1compEex) =>
% 122.46/16.20 ((
% 122.46/16.20 (breln1unionprop) =>
% 122.46/16.20 ((
% 122.46/16.20 (breln1unionIL) =>
% 122.46/16.20 ((
% 122.46/16.20 (breln1unionIR) =>
% 122.46/16.20 ((
% 122.46/16.20 (breln1unionI) =>
% 122.46/16.20 ((
% 122.46/16.20 (breln1unionE) =>
% 122.46/16.20 ((
% 122.46/16.20 (breln1unionEcases) =>
% 122.46/16.20 ((
% 122.46/16.20 (breln1unionCommutes) =>
% 122.46/16.20 ((
% 122.46/16.20 (woz2Ex) =>
% 122.46/16.20 ((
% 122.46/16.20 (woz2W) =>
% 122.46/16.20 ((
% 122.46/16.20 (woz2A) =>
% 122.46/16.20 ((
% 122.46/16.20 (woz2B) =>
% 122.46/16.20 ((
% 122.46/16.20 (image1Ex) =>
% 122.46/16.20 ((
% 122.46/16.20 (image1Ex1) =>
% 122.46/16.20 ((
% 122.46/16.20 (image1Equiv) =>
% 122.46/16.20 ((
% 122.46/16.20 (image1E) =>
% 122.46/16.20 ((
% 122.46/16.20 (image1I) =>
% 122.46/16.20 ((
% 122.46/16.20 (injFuncInInjFuncSet) =>
% 122.46/16.20 ((
% 122.46/16.20 (!!) @ (
% 122.46/16.20 (('#B') @ (
% 122.46/16.20 !!) @
% 122.46/16.20 (
% 122.46/16.20 (
% 122.46/16.20 ('#B') @ (
% 122.46/16.20 (
% 122.46/16.20 ('#B') @ (
% 122.46/16.20 !!))) @
% 122.46/16.20 (
% 122.46/16.20 (
% 122.46/16.20 ('#S') @ (
% 122.46/16.20 (
% 122.46/16.20 ('#B') @ (
% 122.46/16.20 '#S') @
% 122.46/16.20 (
% 122.46/16.20 (
% 122.46/16.20 ('#B') @ (
% 122.46/16.20 (
% 122.46/16.20 ('#B') @ (
% 122.46/16.20 '#S'))) @
% 122.46/16.20 (
% 122.46/16.20 (
% 122.46/16.20 ('#B') @ (
% 122.46/16.20 (
% 122.46/16.20 ('#B') @ (
% 122.46/16.20 (
% 122.46/16.20 ('#B') @ (
% 122.46/16.20 =>))))) @
% 122.46/16.20 (
% 122.46/16.20 (
% 122.46/16.20 ('#B') @ (
% 122.46/16.20 (
% 122.46/16.20 ('#B') @ (
% 122.46/16.20 (
% 122.46/16.20 ('#C') @ in)))) @
% 122.46/16.20 injFuncSet)))))))) @
% 122.46/16.20 (
% 122.46/16.20 (
% 122.46/16.20 ('#B') @ (
% 122.46/16.20 (
% 122.46/16.20 ('#B') @ (
% 122.46/16.20 (
% 122.46/16.20 ('#C') @ in)))) @
% 122.46/16.20 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.46/16.20 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1515])).
% 122.46/16.20 thf(zip_derived_cl1535, plain,
% 122.46/16.20 (~ (((setunionsingleton1) =>
% 122.46/16.20 (((setunionsingleton2) =>
% 122.46/16.20 (((setunionsingleton) =>
% 122.46/16.20 (((singletonprop) =>
% 122.46/16.20 (((ex1E1) =>
% 122.46/16.20 (((ex1I) =>
% 122.46/16.20 (((ex1I2) =>
% 122.46/16.20 (((singletonsuniq) =>
% 122.46/16.20 (((setukpairinjL1) =>
% 122.46/16.20 (((kfstsingleton) =>
% 122.46/16.20 (((theprop) =>
% 122.46/16.20 (((kfstpairEq) =>
% 122.46/16.20 (((cartprodfstin) =>
% 122.46/16.20 (((setukpairinjL2) =>
% 122.46/16.20 (((setukpairinjL) =>
% 122.46/16.20 (((setukpairinjR11) =>
% 122.46/16.20 (((setukpairinjR12) =>
% 122.46/16.20 (((setukpairinjR1) =>
% 122.46/16.20 (((upairequniteq) =>
% 122.46/16.20 (((setukpairinjR2) =>
% 122.46/16.20 (((setukpairinjR) =>
% 122.46/16.20 (((ksndsingleton) =>
% 122.46/16.20 (((ksndpairEq) =>
% 122.46/16.20 (((kpairsurjEq) =>
% 122.46/16.20 (((cartprodsndin) =>
% 122.46/16.20 (((cartprodpairmemEL) =>
% 122.46/16.20 (((cartprodpairmemER) =>
% 122.46/16.20 (((cartprodmempaircEq) =>
% 122.46/16.20 (((cartprodfstpairEq) =>
% 122.46/16.20 (((cartprodsndpairEq) =>
% 122.46/16.20 ((
% 122.46/16.20 (cartprodpairsurjEq) =>
% 122.46/16.20 ((
% 122.46/16.20 (dpsetconstrI) =>
% 122.46/16.20 ((
% 122.46/16.20 (dpsetconstrSub) =>
% 122.46/16.20 ((
% 122.46/16.20 (setOfPairsIsBReln) =>
% 122.46/16.20 ((
% 122.46/16.20 (dpsetconstrERa) =>
% 122.46/16.20 ((
% 122.46/16.20 (dpsetconstrEL1) =>
% 122.46/16.20 ((
% 122.46/16.20 (dpsetconstrEL2) =>
% 122.46/16.20 ((
% 122.46/16.20 (dpsetconstrER) =>
% 122.46/16.20 ((
% 122.46/16.20 (funcImageSingleton) =>
% 122.46/16.20 ((
% 122.46/16.20 (apProp) =>
% 122.46/16.20 ((
% 122.46/16.20 (app) =>
% 122.46/16.20 ((
% 122.46/16.20 (infuncsetfunc) =>
% 122.46/16.20 ((
% 122.46/16.20 (ap2p) =>
% 122.46/16.20 ((
% 122.46/16.20 (funcinfuncset) =>
% 122.46/16.20 ((
% 122.46/16.20 (lamProp) =>
% 122.46/16.20 ((
% 122.46/16.20 (lamp) =>
% 122.46/16.20 ((
% 122.46/16.20 (lam2p) =>
% 122.46/16.20 ((
% 122.46/16.20 (brelnall1) =>
% 122.46/16.20 ((
% 122.46/16.20 (brelnall2) =>
% 122.46/16.20 ((
% 122.46/16.20 (ex1E2) =>
% 122.46/16.20 ((
% 122.46/16.20 (funcGraphProp1) =>
% 122.46/16.20 ((
% 122.46/16.20 (funcGraphProp3) =>
% 122.46/16.20 ((
% 122.46/16.20 (funcGraphProp2) =>
% 122.46/16.20 ((
% 122.46/16.20 (funcextLem) =>
% 122.46/16.20 ((
% 122.46/16.20 (funcGraphProp4) =>
% 122.46/16.20 ((
% 122.46/16.20 (subbreln) =>
% 122.46/16.20 ((
% 122.46/16.20 (eqbreln) =>
% 122.46/16.20 ((
% 122.46/16.20 (funcext) =>
% 122.46/16.20 ((
% 122.46/16.20 (funcext2) =>
% 122.46/16.20 ((
% 122.46/16.20 (ap2apEq1) =>
% 122.46/16.20 ((
% 122.46/16.20 (ap2apEq2) =>
% 122.46/16.20 ((
% 122.46/16.20 (beta1) =>
% 122.46/16.20 ((
% 122.46/16.20 (eta1) =>
% 122.46/16.20 ((
% 122.46/16.20 (lam2lamEq) =>
% 122.46/16.20 ((
% 122.46/16.20 (beta2) =>
% 122.46/16.20 ((
% 122.46/16.20 (eta2) =>
% 122.46/16.20 ((
% 122.46/16.20 (iffalseProp1) =>
% 122.46/16.20 ((
% 122.46/16.20 (iffalseProp2) =>
% 122.46/16.20 ((
% 122.46/16.20 (iftrueProp1) =>
% 122.46/16.20 ((
% 122.46/16.20 (iftrueProp2) =>
% 122.46/16.20 ((
% 122.46/16.20 (ifSingleton) =>
% 122.46/16.20 ((
% 122.46/16.20 (ifp) =>
% 122.46/16.20 ((
% 122.46/16.20 (theeq) =>
% 122.46/16.20 ((
% 122.46/16.20 (iftrue) =>
% 122.46/16.20 ((
% 122.46/16.20 (iffalse) =>
% 122.46/16.20 ((
% 122.46/16.20 (iftrueorfalse) =>
% 122.46/16.20 ((
% 122.46/16.20 (binintersectT_lem) =>
% 122.46/16.20 ((
% 122.46/16.20 (binunionT_lem) =>
% 122.46/16.20 ((
% 122.46/16.20 (powersetT_lem) =>
% 122.46/16.20 ((
% 122.46/16.20 (setminusT_lem) =>
% 122.46/16.20 ((
% 122.46/16.20 (complementT_lem) =>
% 122.46/16.20 ((
% 122.46/16.20 (setextT) =>
% 122.46/16.20 ((
% 122.46/16.20 (subsetTI) =>
% 122.46/16.20 ((
% 122.46/16.20 (powersetTI1) =>
% 122.46/16.20 ((
% 122.46/16.20 (powersetTE1) =>
% 122.46/16.20 ((
% 122.46/16.20 (complementTI1) =>
% 122.46/16.20 ((
% 122.46/16.20 (complementTE1) =>
% 122.46/16.20 ((
% 122.46/16.20 (binintersectTELcontra) =>
% 122.46/16.20 ((
% 122.46/16.20 (binintersectTERcontra) =>
% 122.46/16.20 ((
% 122.46/16.20 (contrasubsetT) =>
% 122.46/16.20 ((
% 122.46/16.20 (contrasubsetT1) =>
% 122.46/16.20 ((
% 122.46/16.20 (contrasubsetT2) =>
% 122.46/16.20 ((
% 122.46/16.20 (contrasubsetT3) =>
% 122.46/16.20 ((
% 122.46/16.20 (doubleComplementI1) =>
% 122.46/16.20 ((
% 122.46/16.20 (doubleComplementE1) =>
% 122.46/16.20 ((
% 122.46/16.20 (doubleComplementSub1) =>
% 122.46/16.20 ((
% 122.46/16.20 (doubleComplementSub2) =>
% 122.46/16.20 ((
% 122.46/16.20 (doubleComplementEq) =>
% 122.46/16.20 ((
% 122.46/16.20 (complementTnotintersectT) =>
% 122.46/16.20 ((
% 122.46/16.20 (complementImpComplementIntersect) =>
% 122.46/16.20 ((
% 122.46/16.20 (complementSubsetComplementIntersect) =>
% 122.46/16.20 ((
% 122.46/16.20 (complementInPowersetComplementIntersect) =>
% 122.46/16.20 ((
% 122.46/16.20 (contraSubsetComplement) =>
% 122.46/16.20 ((
% 122.46/16.20 (complementTcontraSubset) =>
% 122.46/16.20 ((
% 122.46/16.20 (binunionTILcontra) =>
% 122.46/16.20 ((
% 122.46/16.20 (binunionTIRcontra) =>
% 122.46/16.20 ((
% 122.46/16.20 (inIntersectImpInUnion) =>
% 122.46/16.20 ((
% 122.46/16.20 (inIntersectImpInUnion2) =>
% 122.46/16.20 ((
% 122.46/16.20 (inIntersectImpInIntersectUnions) =>
% 122.46/16.20 ((
% 122.46/16.20 (intersectInPowersetIntersectUnions) =>
% 122.46/16.20 ((
% 122.46/16.20 (inComplementUnionImpNotIn1) =>
% 122.46/16.20 ((
% 122.46/16.20 (inComplementUnionImpInComplement1) =>
% 122.46/16.20 ((
% 122.46/16.20 (binunionTE) =>
% 122.46/16.20 ((
% 122.46/16.20 (binunionTEcontra) =>
% 122.46/16.20 ((
% 122.46/16.20 (demorgan2a1) =>
% 122.46/16.20 ((
% 122.46/16.20 (complementUnionInPowersetComplement) =>
% 122.46/16.20 ((
% 122.46/16.20 (demorgan2a2) =>
% 122.46/16.20 ((
% 122.46/16.20 (demorgan1a) =>
% 122.46/16.20 ((
% 122.46/16.20 (demorgan1b) =>
% 122.46/16.20 ((
% 122.46/16.20 (demorgan1) =>
% 122.46/16.20 ((
% 122.46/16.20 (demorgan2a) =>
% 122.46/16.20 ((
% 122.46/16.20 (demorgan2b2) =>
% 122.46/16.20 ((
% 122.46/16.20 (demorgan2b) =>
% 122.46/16.20 ((
% 122.46/16.20 (demorgan2) =>
% 122.46/16.20 ((
% 122.46/16.20 (woz13rule0) =>
% 122.46/16.20 ((
% 122.46/16.20 (woz13rule1) =>
% 122.46/16.20 ((
% 122.46/16.20 (woz13rule2) =>
% 122.46/16.20 ((
% 122.46/16.20 (woz13rule3) =>
% 122.46/16.20 ((
% 122.46/16.20 (woz13rule4) =>
% 122.46/16.20 ((
% 122.46/16.20 (woz1_1) =>
% 122.46/16.20 ((
% 122.46/16.20 (woz1_2) =>
% 122.46/16.20 ((
% 122.46/16.20 (woz1_3) =>
% 122.46/16.20 ((
% 122.46/16.20 (woz1_4) =>
% 122.46/16.20 ((
% 122.46/16.20 (woz1_5) =>
% 122.46/16.20 ((
% 122.46/16.20 (breln1all2) =>
% 122.46/16.20 ((
% 122.46/16.20 (breln1SetBreln1) =>
% 122.46/16.20 ((
% 122.46/16.20 (choice2fnsingleton) =>
% 122.46/16.20 ((
% 122.46/16.20 (setOfPairsIsBReln1) =>
% 122.46/16.20 ((
% 122.46/16.20 (breln1all1) =>
% 122.46/16.20 ((
% 122.46/16.20 (subbreln1) =>
% 122.46/16.20 ((
% 122.46/16.20 (eqbreln1) =>
% 122.46/16.20 ((
% 122.46/16.20 (breln1invprop) =>
% 122.46/16.20 ((
% 122.46/16.20 (breln1invI) =>
% 122.46/16.20 ((
% 122.46/16.20 (breln1invE) =>
% 122.46/16.20 ((
% 122.46/16.20 (breln1compprop) =>
% 122.46/16.20 ((
% 122.46/16.20 (breln1compI) =>
% 122.46/16.20 ((
% 122.46/16.20 (breln1compE) =>
% 122.46/16.20 ((
% 122.46/16.20 (breln1compEex) =>
% 122.46/16.20 ((
% 122.46/16.20 (breln1unionprop) =>
% 122.46/16.20 ((
% 122.46/16.20 (breln1unionIL) =>
% 122.46/16.20 ((
% 122.46/16.20 (breln1unionIR) =>
% 122.46/16.20 ((
% 122.46/16.20 (breln1unionI) =>
% 122.46/16.20 ((
% 122.46/16.20 (breln1unionE) =>
% 122.46/16.20 ((
% 122.46/16.20 (breln1unionEcases) =>
% 122.46/16.20 ((
% 122.46/16.20 (breln1unionCommutes) =>
% 122.46/16.20 ((
% 122.46/16.20 (woz2Ex) =>
% 122.46/16.20 ((
% 122.46/16.20 (woz2W) =>
% 122.46/16.20 ((
% 122.46/16.20 (woz2A) =>
% 122.46/16.20 ((
% 122.46/16.20 (woz2B) =>
% 122.46/16.20 ((
% 122.46/16.20 (image1Ex) =>
% 122.46/16.20 ((
% 122.46/16.20 (image1Ex1) =>
% 122.46/16.20 ((
% 122.46/16.20 (image1Equiv) =>
% 122.46/16.20 ((
% 122.46/16.20 (image1E) =>
% 122.46/16.20 ((
% 122.46/16.20 (image1I) =>
% 122.46/16.20 ((
% 122.46/16.20 (injFuncInInjFuncSet) =>
% 122.46/16.20 ((
% 122.46/16.20 (!!) @ (
% 122.46/16.20 (('#B') @ (
% 122.46/16.20 !!) @
% 122.46/16.20 (
% 122.46/16.20 (
% 122.46/16.20 ('#B') @ (
% 122.46/16.20 (
% 122.46/16.20 ('#B') @ (
% 122.46/16.20 !!))) @
% 122.46/16.20 (
% 122.46/16.20 (
% 122.46/16.20 ('#S') @ (
% 122.46/16.20 (
% 122.46/16.20 ('#B') @ (
% 122.46/16.20 '#S') @
% 122.46/16.20 (
% 122.46/16.20 (
% 122.46/16.20 ('#B') @ (
% 122.46/16.20 (
% 122.46/16.20 ('#B') @ (
% 122.46/16.20 '#S'))) @
% 122.46/16.20 (
% 122.46/16.20 (
% 122.46/16.20 ('#B') @ (
% 122.46/16.20 (
% 122.46/16.20 ('#B') @ (
% 122.46/16.20 (
% 122.46/16.20 ('#B') @ (
% 122.46/16.20 =>))))) @
% 122.46/16.20 (
% 122.46/16.20 (
% 122.46/16.20 ('#B') @ (
% 122.46/16.20 (
% 122.46/16.20 ('#B') @ (
% 122.46/16.20 (
% 122.46/16.20 ('#C') @ in)))) @
% 122.46/16.20 injFuncSet)))))))) @
% 122.46/16.20 (
% 122.46/16.20 (
% 122.46/16.20 ('#B') @ (
% 122.46/16.20 (
% 122.46/16.20 ('#B') @ (
% 122.46/16.20 (
% 122.46/16.20 ('#C') @ in)))) @
% 122.46/16.20 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.46/16.20 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1525])).
% 122.46/16.20 thf(zip_derived_cl1545, plain,
% 122.46/16.20 (~ (((setunionsingleton2) =>
% 122.46/16.20 (((setunionsingleton) =>
% 122.46/16.20 (((singletonprop) =>
% 122.46/16.20 (((ex1E1) =>
% 122.46/16.20 (((ex1I) =>
% 122.46/16.20 (((ex1I2) =>
% 122.46/16.20 (((singletonsuniq) =>
% 122.46/16.20 (((setukpairinjL1) =>
% 122.46/16.20 (((kfstsingleton) =>
% 122.46/16.20 (((theprop) =>
% 122.46/16.20 (((kfstpairEq) =>
% 122.46/16.20 (((cartprodfstin) =>
% 122.46/16.20 (((setukpairinjL2) =>
% 122.46/16.20 (((setukpairinjL) =>
% 122.46/16.20 (((setukpairinjR11) =>
% 122.46/16.20 (((setukpairinjR12) =>
% 122.46/16.20 (((setukpairinjR1) =>
% 122.46/16.20 (((upairequniteq) =>
% 122.46/16.20 (((setukpairinjR2) =>
% 122.46/16.20 (((setukpairinjR) =>
% 122.46/16.20 (((ksndsingleton) =>
% 122.46/16.20 (((ksndpairEq) =>
% 122.46/16.20 (((kpairsurjEq) =>
% 122.46/16.20 (((cartprodsndin) =>
% 122.46/16.20 (((cartprodpairmemEL) =>
% 122.46/16.20 (((cartprodpairmemER) =>
% 122.46/16.20 (((cartprodmempaircEq) =>
% 122.46/16.20 (((cartprodfstpairEq) =>
% 122.46/16.20 (((cartprodsndpairEq) =>
% 122.46/16.20 (((cartprodpairsurjEq) =>
% 122.46/16.20 ((
% 122.46/16.20 (dpsetconstrI) =>
% 122.46/16.20 ((
% 122.46/16.20 (dpsetconstrSub) =>
% 122.46/16.20 ((
% 122.46/16.20 (setOfPairsIsBReln) =>
% 122.46/16.20 ((
% 122.46/16.20 (dpsetconstrERa) =>
% 122.46/16.20 ((
% 122.46/16.20 (dpsetconstrEL1) =>
% 122.46/16.20 ((
% 122.46/16.20 (dpsetconstrEL2) =>
% 122.46/16.20 ((
% 122.46/16.20 (dpsetconstrER) =>
% 122.46/16.20 ((
% 122.46/16.20 (funcImageSingleton) =>
% 122.46/16.20 ((
% 122.46/16.20 (apProp) =>
% 122.46/16.20 ((
% 122.46/16.20 (app) =>
% 122.46/16.20 ((
% 122.46/16.20 (infuncsetfunc) =>
% 122.46/16.20 ((
% 122.46/16.20 (ap2p) =>
% 122.46/16.20 ((
% 122.46/16.20 (funcinfuncset) =>
% 122.46/16.20 ((
% 122.46/16.20 (lamProp) =>
% 122.46/16.20 ((
% 122.46/16.20 (lamp) =>
% 122.46/16.20 ((
% 122.46/16.20 (lam2p) =>
% 122.46/16.20 ((
% 122.46/16.20 (brelnall1) =>
% 122.46/16.20 ((
% 122.46/16.20 (brelnall2) =>
% 122.46/16.20 ((
% 122.46/16.20 (ex1E2) =>
% 122.46/16.20 ((
% 122.46/16.20 (funcGraphProp1) =>
% 122.46/16.20 ((
% 122.46/16.20 (funcGraphProp3) =>
% 122.46/16.20 ((
% 122.46/16.20 (funcGraphProp2) =>
% 122.46/16.20 ((
% 122.46/16.20 (funcextLem) =>
% 122.46/16.20 ((
% 122.46/16.20 (funcGraphProp4) =>
% 122.46/16.20 ((
% 122.46/16.20 (subbreln) =>
% 122.46/16.20 ((
% 122.46/16.20 (eqbreln) =>
% 122.46/16.20 ((
% 122.46/16.20 (funcext) =>
% 122.46/16.20 ((
% 122.46/16.20 (funcext2) =>
% 122.46/16.20 ((
% 122.46/16.20 (ap2apEq1) =>
% 122.46/16.20 ((
% 122.46/16.20 (ap2apEq2) =>
% 122.46/16.20 ((
% 122.46/16.20 (beta1) =>
% 122.46/16.20 ((
% 122.46/16.20 (eta1) =>
% 122.46/16.20 ((
% 122.46/16.20 (lam2lamEq) =>
% 122.46/16.20 ((
% 122.46/16.20 (beta2) =>
% 122.46/16.20 ((
% 122.46/16.20 (eta2) =>
% 122.46/16.20 ((
% 122.46/16.20 (iffalseProp1) =>
% 122.46/16.20 ((
% 122.46/16.20 (iffalseProp2) =>
% 122.46/16.20 ((
% 122.46/16.20 (iftrueProp1) =>
% 122.46/16.20 ((
% 122.46/16.20 (iftrueProp2) =>
% 122.46/16.20 ((
% 122.46/16.20 (ifSingleton) =>
% 122.46/16.20 ((
% 122.46/16.20 (ifp) =>
% 122.46/16.20 ((
% 122.46/16.20 (theeq) =>
% 122.46/16.20 ((
% 122.46/16.20 (iftrue) =>
% 122.46/16.20 ((
% 122.46/16.20 (iffalse) =>
% 122.46/16.20 ((
% 122.46/16.20 (iftrueorfalse) =>
% 122.46/16.20 ((
% 122.46/16.20 (binintersectT_lem) =>
% 122.46/16.20 ((
% 122.46/16.20 (binunionT_lem) =>
% 122.46/16.20 ((
% 122.46/16.20 (powersetT_lem) =>
% 122.46/16.20 ((
% 122.46/16.20 (setminusT_lem) =>
% 122.46/16.20 ((
% 122.46/16.20 (complementT_lem) =>
% 122.46/16.20 ((
% 122.46/16.20 (setextT) =>
% 122.46/16.20 ((
% 122.46/16.20 (subsetTI) =>
% 122.46/16.20 ((
% 122.46/16.20 (powersetTI1) =>
% 122.46/16.20 ((
% 122.46/16.20 (powersetTE1) =>
% 122.46/16.20 ((
% 122.46/16.20 (complementTI1) =>
% 122.46/16.20 ((
% 122.46/16.20 (complementTE1) =>
% 122.46/16.20 ((
% 122.46/16.20 (binintersectTELcontra) =>
% 122.46/16.20 ((
% 122.46/16.20 (binintersectTERcontra) =>
% 122.46/16.20 ((
% 122.46/16.20 (contrasubsetT) =>
% 122.46/16.20 ((
% 122.46/16.20 (contrasubsetT1) =>
% 122.46/16.20 ((
% 122.46/16.20 (contrasubsetT2) =>
% 122.46/16.20 ((
% 122.46/16.20 (contrasubsetT3) =>
% 122.46/16.20 ((
% 122.46/16.20 (doubleComplementI1) =>
% 122.46/16.20 ((
% 122.46/16.20 (doubleComplementE1) =>
% 122.46/16.20 ((
% 122.46/16.20 (doubleComplementSub1) =>
% 122.46/16.20 ((
% 122.46/16.20 (doubleComplementSub2) =>
% 122.46/16.20 ((
% 122.46/16.20 (doubleComplementEq) =>
% 122.46/16.20 ((
% 122.46/16.20 (complementTnotintersectT) =>
% 122.46/16.20 ((
% 122.46/16.20 (complementImpComplementIntersect) =>
% 122.46/16.20 ((
% 122.46/16.20 (complementSubsetComplementIntersect) =>
% 122.46/16.20 ((
% 122.46/16.20 (complementInPowersetComplementIntersect) =>
% 122.46/16.20 ((
% 122.46/16.20 (contraSubsetComplement) =>
% 122.46/16.20 ((
% 122.46/16.20 (complementTcontraSubset) =>
% 122.46/16.20 ((
% 122.46/16.20 (binunionTILcontra) =>
% 122.46/16.20 ((
% 122.46/16.20 (binunionTIRcontra) =>
% 122.46/16.20 ((
% 122.46/16.20 (inIntersectImpInUnion) =>
% 122.46/16.20 ((
% 122.46/16.20 (inIntersectImpInUnion2) =>
% 122.46/16.20 ((
% 122.46/16.20 (inIntersectImpInIntersectUnions) =>
% 122.46/16.20 ((
% 122.46/16.20 (intersectInPowersetIntersectUnions) =>
% 122.46/16.20 ((
% 122.46/16.20 (inComplementUnionImpNotIn1) =>
% 122.46/16.20 ((
% 122.46/16.20 (inComplementUnionImpInComplement1) =>
% 122.46/16.20 ((
% 122.46/16.20 (binunionTE) =>
% 122.46/16.20 ((
% 122.46/16.20 (binunionTEcontra) =>
% 122.46/16.20 ((
% 122.46/16.20 (demorgan2a1) =>
% 122.46/16.20 ((
% 122.46/16.20 (complementUnionInPowersetComplement) =>
% 122.46/16.20 ((
% 122.46/16.20 (demorgan2a2) =>
% 122.46/16.20 ((
% 122.46/16.20 (demorgan1a) =>
% 122.46/16.20 ((
% 122.46/16.20 (demorgan1b) =>
% 122.46/16.20 ((
% 122.46/16.20 (demorgan1) =>
% 122.46/16.20 ((
% 122.46/16.20 (demorgan2a) =>
% 122.46/16.20 ((
% 122.46/16.20 (demorgan2b2) =>
% 122.46/16.20 ((
% 122.46/16.20 (demorgan2b) =>
% 122.46/16.20 ((
% 122.46/16.20 (demorgan2) =>
% 122.46/16.20 ((
% 122.46/16.20 (woz13rule0) =>
% 122.46/16.20 ((
% 122.46/16.20 (woz13rule1) =>
% 122.46/16.20 ((
% 122.46/16.20 (woz13rule2) =>
% 122.46/16.20 ((
% 122.46/16.20 (woz13rule3) =>
% 122.46/16.20 ((
% 122.46/16.20 (woz13rule4) =>
% 122.46/16.20 ((
% 122.46/16.20 (woz1_1) =>
% 122.46/16.20 ((
% 122.46/16.20 (woz1_2) =>
% 122.46/16.20 ((
% 122.46/16.20 (woz1_3) =>
% 122.46/16.20 ((
% 122.46/16.20 (woz1_4) =>
% 122.46/16.20 ((
% 122.46/16.20 (woz1_5) =>
% 122.46/16.20 ((
% 122.46/16.20 (breln1all2) =>
% 122.46/16.20 ((
% 122.46/16.20 (breln1SetBreln1) =>
% 122.46/16.20 ((
% 122.46/16.20 (choice2fnsingleton) =>
% 122.46/16.20 ((
% 122.46/16.20 (setOfPairsIsBReln1) =>
% 122.46/16.20 ((
% 122.46/16.20 (breln1all1) =>
% 122.46/16.20 ((
% 122.46/16.20 (subbreln1) =>
% 122.46/16.20 ((
% 122.46/16.20 (eqbreln1) =>
% 122.46/16.20 ((
% 122.46/16.20 (breln1invprop) =>
% 122.46/16.20 ((
% 122.46/16.20 (breln1invI) =>
% 122.46/16.20 ((
% 122.46/16.20 (breln1invE) =>
% 122.46/16.20 ((
% 122.46/16.20 (breln1compprop) =>
% 122.46/16.20 ((
% 122.46/16.20 (breln1compI) =>
% 122.46/16.20 ((
% 122.46/16.20 (breln1compE) =>
% 122.46/16.20 ((
% 122.46/16.20 (breln1compEex) =>
% 122.46/16.20 ((
% 122.46/16.20 (breln1unionprop) =>
% 122.46/16.20 ((
% 122.46/16.20 (breln1unionIL) =>
% 122.46/16.20 ((
% 122.46/16.20 (breln1unionIR) =>
% 122.46/16.20 ((
% 122.46/16.20 (breln1unionI) =>
% 122.46/16.20 ((
% 122.46/16.20 (breln1unionE) =>
% 122.46/16.20 ((
% 122.46/16.20 (breln1unionEcases) =>
% 122.46/16.20 ((
% 122.46/16.20 (breln1unionCommutes) =>
% 122.46/16.20 ((
% 122.46/16.20 (woz2Ex) =>
% 122.46/16.20 ((
% 122.46/16.20 (woz2W) =>
% 122.46/16.20 ((
% 122.46/16.20 (woz2A) =>
% 122.46/16.20 ((
% 122.46/16.20 (woz2B) =>
% 122.46/16.20 ((
% 122.84/16.20 (image1Ex) =>
% 122.84/16.20 ((
% 122.84/16.20 (image1Ex1) =>
% 122.84/16.20 ((
% 122.84/16.20 (image1Equiv) =>
% 122.84/16.20 ((
% 122.84/16.20 (image1E) =>
% 122.84/16.20 ((
% 122.84/16.20 (image1I) =>
% 122.84/16.20 ((
% 122.84/16.20 (injFuncInInjFuncSet) =>
% 122.84/16.20 ((
% 122.84/16.20 (!!) @ (
% 122.84/16.20 (('#B') @ (
% 122.84/16.20 !!) @
% 122.84/16.20 (
% 122.84/16.20 (
% 122.84/16.20 ('#B') @ (
% 122.84/16.20 (
% 122.84/16.20 ('#B') @ (
% 122.84/16.20 !!))) @
% 122.84/16.20 (
% 122.84/16.20 (
% 122.84/16.20 ('#S') @ (
% 122.84/16.20 (
% 122.84/16.20 ('#B') @ (
% 122.84/16.20 '#S') @
% 122.84/16.20 (
% 122.84/16.20 (
% 122.84/16.20 ('#B') @ (
% 122.84/16.20 (
% 122.84/16.20 ('#B') @ (
% 122.84/16.20 '#S'))) @
% 122.84/16.20 (
% 122.84/16.20 (
% 122.84/16.20 ('#B') @ (
% 122.84/16.20 (
% 122.84/16.20 ('#B') @ (
% 122.84/16.20 (
% 122.84/16.20 ('#B') @ (
% 122.84/16.20 =>))))) @
% 122.84/16.20 (
% 122.84/16.20 (
% 122.84/16.20 ('#B') @ (
% 122.84/16.20 (
% 122.84/16.20 ('#B') @ (
% 122.84/16.20 (
% 122.84/16.20 ('#C') @ in)))) @
% 122.84/16.20 injFuncSet)))))))) @
% 122.84/16.20 (
% 122.84/16.20 (
% 122.84/16.20 ('#B') @ (
% 122.84/16.20 (
% 122.84/16.20 ('#B') @ (
% 122.84/16.20 (
% 122.84/16.20 ('#C') @ in)))) @
% 122.84/16.20 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.84/16.20 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1535])).
% 122.84/16.20 thf(zip_derived_cl1555, plain,
% 122.84/16.20 (~ (((setunionsingleton) =>
% 122.84/16.20 (((singletonprop) =>
% 122.84/16.20 (((ex1E1) =>
% 122.84/16.20 (((ex1I) =>
% 122.84/16.20 (((ex1I2) =>
% 122.84/16.20 (((singletonsuniq) =>
% 122.84/16.20 (((setukpairinjL1) =>
% 122.84/16.20 (((kfstsingleton) =>
% 122.84/16.20 (((theprop) =>
% 122.84/16.20 (((kfstpairEq) =>
% 122.84/16.20 (((cartprodfstin) =>
% 122.84/16.20 (((setukpairinjL2) =>
% 122.84/16.20 (((setukpairinjL) =>
% 122.84/16.20 (((setukpairinjR11) =>
% 122.84/16.20 (((setukpairinjR12) =>
% 122.84/16.20 (((setukpairinjR1) =>
% 122.84/16.20 (((upairequniteq) =>
% 122.84/16.20 (((setukpairinjR2) =>
% 122.84/16.20 (((setukpairinjR) =>
% 122.84/16.20 (((ksndsingleton) =>
% 122.84/16.20 (((ksndpairEq) =>
% 122.84/16.20 (((kpairsurjEq) =>
% 122.84/16.20 (((cartprodsndin) =>
% 122.84/16.20 (((cartprodpairmemEL) =>
% 122.84/16.20 (((cartprodpairmemER) =>
% 122.84/16.20 (((cartprodmempaircEq) =>
% 122.84/16.20 (((cartprodfstpairEq) =>
% 122.84/16.20 (((cartprodsndpairEq) =>
% 122.84/16.20 (((cartprodpairsurjEq) =>
% 122.84/16.20 (((dpsetconstrI) =>
% 122.84/16.20 ((
% 122.84/16.20 (dpsetconstrSub) =>
% 122.84/16.20 ((
% 122.84/16.20 (setOfPairsIsBReln) =>
% 122.84/16.20 ((
% 122.84/16.20 (dpsetconstrERa) =>
% 122.84/16.20 ((
% 122.84/16.20 (dpsetconstrEL1) =>
% 122.84/16.20 ((
% 122.84/16.20 (dpsetconstrEL2) =>
% 122.84/16.20 ((
% 122.84/16.20 (dpsetconstrER) =>
% 122.84/16.20 ((
% 122.84/16.20 (funcImageSingleton) =>
% 122.84/16.20 ((
% 122.84/16.20 (apProp) =>
% 122.84/16.20 ((
% 122.84/16.20 (app) =>
% 122.84/16.20 ((
% 122.84/16.20 (infuncsetfunc) =>
% 122.84/16.20 ((
% 122.84/16.20 (ap2p) =>
% 122.84/16.20 ((
% 122.84/16.20 (funcinfuncset) =>
% 122.84/16.20 ((
% 122.84/16.20 (lamProp) =>
% 122.84/16.20 ((
% 122.84/16.20 (lamp) =>
% 122.84/16.20 ((
% 122.84/16.20 (lam2p) =>
% 122.84/16.20 ((
% 122.84/16.20 (brelnall1) =>
% 122.84/16.20 ((
% 122.84/16.20 (brelnall2) =>
% 122.84/16.20 ((
% 122.84/16.20 (ex1E2) =>
% 122.84/16.20 ((
% 122.84/16.20 (funcGraphProp1) =>
% 122.84/16.20 ((
% 122.84/16.20 (funcGraphProp3) =>
% 122.84/16.20 ((
% 122.84/16.20 (funcGraphProp2) =>
% 122.84/16.20 ((
% 122.84/16.20 (funcextLem) =>
% 122.84/16.20 ((
% 122.84/16.20 (funcGraphProp4) =>
% 122.84/16.20 ((
% 122.84/16.20 (subbreln) =>
% 122.84/16.20 ((
% 122.84/16.20 (eqbreln) =>
% 122.84/16.20 ((
% 122.84/16.20 (funcext) =>
% 122.84/16.20 ((
% 122.84/16.20 (funcext2) =>
% 122.84/16.20 ((
% 122.84/16.20 (ap2apEq1) =>
% 122.84/16.20 ((
% 122.84/16.20 (ap2apEq2) =>
% 122.84/16.20 ((
% 122.84/16.20 (beta1) =>
% 122.84/16.20 ((
% 122.84/16.20 (eta1) =>
% 122.84/16.20 ((
% 122.84/16.20 (lam2lamEq) =>
% 122.84/16.20 ((
% 122.84/16.20 (beta2) =>
% 122.84/16.20 ((
% 122.84/16.20 (eta2) =>
% 122.84/16.20 ((
% 122.84/16.20 (iffalseProp1) =>
% 122.84/16.20 ((
% 122.84/16.20 (iffalseProp2) =>
% 122.84/16.20 ((
% 122.84/16.20 (iftrueProp1) =>
% 122.84/16.20 ((
% 122.84/16.20 (iftrueProp2) =>
% 122.84/16.20 ((
% 122.84/16.20 (ifSingleton) =>
% 122.84/16.20 ((
% 122.84/16.20 (ifp) =>
% 122.84/16.20 ((
% 122.84/16.20 (theeq) =>
% 122.84/16.20 ((
% 122.84/16.20 (iftrue) =>
% 122.84/16.20 ((
% 122.84/16.20 (iffalse) =>
% 122.84/16.20 ((
% 122.84/16.20 (iftrueorfalse) =>
% 122.84/16.20 ((
% 122.84/16.20 (binintersectT_lem) =>
% 122.84/16.20 ((
% 122.84/16.20 (binunionT_lem) =>
% 122.84/16.20 ((
% 122.84/16.20 (powersetT_lem) =>
% 122.84/16.20 ((
% 122.84/16.20 (setminusT_lem) =>
% 122.84/16.20 ((
% 122.84/16.20 (complementT_lem) =>
% 122.84/16.20 ((
% 122.84/16.20 (setextT) =>
% 122.84/16.20 ((
% 122.84/16.20 (subsetTI) =>
% 122.84/16.20 ((
% 122.84/16.20 (powersetTI1) =>
% 122.84/16.20 ((
% 122.84/16.20 (powersetTE1) =>
% 122.84/16.20 ((
% 122.84/16.20 (complementTI1) =>
% 122.84/16.20 ((
% 122.84/16.20 (complementTE1) =>
% 122.84/16.20 ((
% 122.84/16.20 (binintersectTELcontra) =>
% 122.84/16.20 ((
% 122.84/16.20 (binintersectTERcontra) =>
% 122.84/16.20 ((
% 122.84/16.20 (contrasubsetT) =>
% 122.84/16.20 ((
% 122.84/16.20 (contrasubsetT1) =>
% 122.84/16.20 ((
% 122.84/16.20 (contrasubsetT2) =>
% 122.84/16.20 ((
% 122.84/16.20 (contrasubsetT3) =>
% 122.84/16.20 ((
% 122.84/16.20 (doubleComplementI1) =>
% 122.84/16.20 ((
% 122.84/16.20 (doubleComplementE1) =>
% 122.84/16.20 ((
% 122.84/16.20 (doubleComplementSub1) =>
% 122.84/16.20 ((
% 122.84/16.20 (doubleComplementSub2) =>
% 122.84/16.20 ((
% 122.84/16.20 (doubleComplementEq) =>
% 122.84/16.20 ((
% 122.84/16.20 (complementTnotintersectT) =>
% 122.84/16.20 ((
% 122.84/16.20 (complementImpComplementIntersect) =>
% 122.84/16.20 ((
% 122.84/16.20 (complementSubsetComplementIntersect) =>
% 122.84/16.20 ((
% 122.84/16.20 (complementInPowersetComplementIntersect) =>
% 122.84/16.20 ((
% 122.84/16.20 (contraSubsetComplement) =>
% 122.84/16.20 ((
% 122.84/16.20 (complementTcontraSubset) =>
% 122.84/16.20 ((
% 122.84/16.20 (binunionTILcontra) =>
% 122.84/16.20 ((
% 122.84/16.20 (binunionTIRcontra) =>
% 122.84/16.20 ((
% 122.84/16.20 (inIntersectImpInUnion) =>
% 122.84/16.20 ((
% 122.84/16.20 (inIntersectImpInUnion2) =>
% 122.84/16.20 ((
% 122.84/16.20 (inIntersectImpInIntersectUnions) =>
% 122.84/16.20 ((
% 122.84/16.20 (intersectInPowersetIntersectUnions) =>
% 122.84/16.20 ((
% 122.84/16.20 (inComplementUnionImpNotIn1) =>
% 122.84/16.20 ((
% 122.84/16.20 (inComplementUnionImpInComplement1) =>
% 122.84/16.20 ((
% 122.84/16.20 (binunionTE) =>
% 122.84/16.20 ((
% 122.84/16.20 (binunionTEcontra) =>
% 122.84/16.20 ((
% 122.84/16.20 (demorgan2a1) =>
% 122.84/16.20 ((
% 122.84/16.20 (complementUnionInPowersetComplement) =>
% 122.84/16.20 ((
% 122.84/16.20 (demorgan2a2) =>
% 122.84/16.20 ((
% 122.84/16.20 (demorgan1a) =>
% 122.84/16.20 ((
% 122.84/16.20 (demorgan1b) =>
% 122.84/16.20 ((
% 122.84/16.20 (demorgan1) =>
% 122.84/16.20 ((
% 122.84/16.20 (demorgan2a) =>
% 122.84/16.20 ((
% 122.84/16.20 (demorgan2b2) =>
% 122.84/16.20 ((
% 122.84/16.20 (demorgan2b) =>
% 122.84/16.20 ((
% 122.84/16.20 (demorgan2) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz13rule0) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz13rule1) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz13rule2) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz13rule3) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz13rule4) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz1_1) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz1_2) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz1_3) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz1_4) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz1_5) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1all2) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1SetBreln1) =>
% 122.84/16.20 ((
% 122.84/16.20 (choice2fnsingleton) =>
% 122.84/16.20 ((
% 122.84/16.20 (setOfPairsIsBReln1) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1all1) =>
% 122.84/16.20 ((
% 122.84/16.20 (subbreln1) =>
% 122.84/16.20 ((
% 122.84/16.20 (eqbreln1) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1invprop) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1invI) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1invE) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1compprop) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1compI) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1compE) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1compEex) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1unionprop) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1unionIL) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1unionIR) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1unionI) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1unionE) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1unionEcases) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1unionCommutes) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz2Ex) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz2W) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz2A) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz2B) =>
% 122.84/16.20 ((
% 122.84/16.20 (image1Ex) =>
% 122.84/16.20 ((
% 122.84/16.20 (image1Ex1) =>
% 122.84/16.20 ((
% 122.84/16.20 (image1Equiv) =>
% 122.84/16.20 ((
% 122.84/16.20 (image1E) =>
% 122.84/16.20 ((
% 122.84/16.20 (image1I) =>
% 122.84/16.20 ((
% 122.84/16.20 (injFuncInInjFuncSet) =>
% 122.84/16.20 ((
% 122.84/16.20 (!!) @ (
% 122.84/16.20 (('#B') @ (
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% 122.84/16.20 (
% 122.84/16.20 (
% 122.84/16.20 ('#B') @ (
% 122.84/16.20 (
% 122.84/16.20 ('#B') @ (
% 122.84/16.20 !!))) @
% 122.84/16.20 (
% 122.84/16.20 (
% 122.84/16.20 ('#S') @ (
% 122.84/16.20 (
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% 122.84/16.20 (
% 122.84/16.20 (
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% 122.84/16.20 (
% 122.84/16.20 ('#B') @ (
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% 122.84/16.20 (
% 122.84/16.20 (
% 122.84/16.20 ('#B') @ (
% 122.84/16.20 (
% 122.84/16.20 ('#B') @ (
% 122.84/16.20 (
% 122.84/16.20 ('#B') @ (
% 122.84/16.20 =>))))) @
% 122.84/16.20 (
% 122.84/16.20 (
% 122.84/16.20 ('#B') @ (
% 122.84/16.20 (
% 122.84/16.20 ('#B') @ (
% 122.84/16.20 (
% 122.84/16.20 ('#C') @ in)))) @
% 122.84/16.20 injFuncSet)))))))) @
% 122.84/16.20 (
% 122.84/16.20 (
% 122.84/16.20 ('#B') @ (
% 122.84/16.20 (
% 122.84/16.20 ('#B') @ (
% 122.84/16.20 (
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% 122.84/16.20 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.84/16.20 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1545])).
% 122.84/16.20 thf(zip_derived_cl1565, plain,
% 122.84/16.20 (~ (((singletonprop) =>
% 122.84/16.20 (((ex1E1) =>
% 122.84/16.20 (((ex1I) =>
% 122.84/16.20 (((ex1I2) =>
% 122.84/16.20 (((singletonsuniq) =>
% 122.84/16.20 (((setukpairinjL1) =>
% 122.84/16.20 (((kfstsingleton) =>
% 122.84/16.20 (((theprop) =>
% 122.84/16.20 (((kfstpairEq) =>
% 122.84/16.20 (((cartprodfstin) =>
% 122.84/16.20 (((setukpairinjL2) =>
% 122.84/16.20 (((setukpairinjL) =>
% 122.84/16.20 (((setukpairinjR11) =>
% 122.84/16.20 (((setukpairinjR12) =>
% 122.84/16.20 (((setukpairinjR1) =>
% 122.84/16.20 (((upairequniteq) =>
% 122.84/16.20 (((setukpairinjR2) =>
% 122.84/16.20 (((setukpairinjR) =>
% 122.84/16.20 (((ksndsingleton) =>
% 122.84/16.20 (((ksndpairEq) =>
% 122.84/16.20 (((kpairsurjEq) =>
% 122.84/16.20 (((cartprodsndin) =>
% 122.84/16.20 (((cartprodpairmemEL) =>
% 122.84/16.20 (((cartprodpairmemER) =>
% 122.84/16.20 (((cartprodmempaircEq) =>
% 122.84/16.20 (((cartprodfstpairEq) =>
% 122.84/16.20 (((cartprodsndpairEq) =>
% 122.84/16.20 (((cartprodpairsurjEq) =>
% 122.84/16.20 (((dpsetconstrI) =>
% 122.84/16.20 (((dpsetconstrSub) =>
% 122.84/16.20 ((
% 122.84/16.20 (setOfPairsIsBReln) =>
% 122.84/16.20 ((
% 122.84/16.20 (dpsetconstrERa) =>
% 122.84/16.20 ((
% 122.84/16.20 (dpsetconstrEL1) =>
% 122.84/16.20 ((
% 122.84/16.20 (dpsetconstrEL2) =>
% 122.84/16.20 ((
% 122.84/16.20 (dpsetconstrER) =>
% 122.84/16.20 ((
% 122.84/16.20 (funcImageSingleton) =>
% 122.84/16.20 ((
% 122.84/16.20 (apProp) =>
% 122.84/16.20 ((
% 122.84/16.20 (app) =>
% 122.84/16.20 ((
% 122.84/16.20 (infuncsetfunc) =>
% 122.84/16.20 ((
% 122.84/16.20 (ap2p) =>
% 122.84/16.20 ((
% 122.84/16.20 (funcinfuncset) =>
% 122.84/16.20 ((
% 122.84/16.20 (lamProp) =>
% 122.84/16.20 ((
% 122.84/16.20 (lamp) =>
% 122.84/16.20 ((
% 122.84/16.20 (lam2p) =>
% 122.84/16.20 ((
% 122.84/16.20 (brelnall1) =>
% 122.84/16.20 ((
% 122.84/16.20 (brelnall2) =>
% 122.84/16.20 ((
% 122.84/16.20 (ex1E2) =>
% 122.84/16.20 ((
% 122.84/16.20 (funcGraphProp1) =>
% 122.84/16.20 ((
% 122.84/16.20 (funcGraphProp3) =>
% 122.84/16.20 ((
% 122.84/16.20 (funcGraphProp2) =>
% 122.84/16.20 ((
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% 122.84/16.20 ((
% 122.84/16.20 (funcGraphProp4) =>
% 122.84/16.20 ((
% 122.84/16.20 (subbreln) =>
% 122.84/16.20 ((
% 122.84/16.20 (eqbreln) =>
% 122.84/16.20 ((
% 122.84/16.20 (funcext) =>
% 122.84/16.20 ((
% 122.84/16.20 (funcext2) =>
% 122.84/16.20 ((
% 122.84/16.20 (ap2apEq1) =>
% 122.84/16.20 ((
% 122.84/16.20 (ap2apEq2) =>
% 122.84/16.20 ((
% 122.84/16.20 (beta1) =>
% 122.84/16.20 ((
% 122.84/16.20 (eta1) =>
% 122.84/16.20 ((
% 122.84/16.20 (lam2lamEq) =>
% 122.84/16.20 ((
% 122.84/16.20 (beta2) =>
% 122.84/16.20 ((
% 122.84/16.20 (eta2) =>
% 122.84/16.20 ((
% 122.84/16.20 (iffalseProp1) =>
% 122.84/16.20 ((
% 122.84/16.20 (iffalseProp2) =>
% 122.84/16.20 ((
% 122.84/16.20 (iftrueProp1) =>
% 122.84/16.20 ((
% 122.84/16.20 (iftrueProp2) =>
% 122.84/16.20 ((
% 122.84/16.20 (ifSingleton) =>
% 122.84/16.20 ((
% 122.84/16.20 (ifp) =>
% 122.84/16.20 ((
% 122.84/16.20 (theeq) =>
% 122.84/16.20 ((
% 122.84/16.20 (iftrue) =>
% 122.84/16.20 ((
% 122.84/16.20 (iffalse) =>
% 122.84/16.20 ((
% 122.84/16.20 (iftrueorfalse) =>
% 122.84/16.20 ((
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% 122.84/16.20 ((
% 122.84/16.20 (binunionT_lem) =>
% 122.84/16.20 ((
% 122.84/16.20 (powersetT_lem) =>
% 122.84/16.20 ((
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% 122.84/16.20 ((
% 122.84/16.20 (complementT_lem) =>
% 122.84/16.20 ((
% 122.84/16.20 (setextT) =>
% 122.84/16.20 ((
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% 122.84/16.20 ((
% 122.84/16.20 (powersetTI1) =>
% 122.84/16.20 ((
% 122.84/16.20 (powersetTE1) =>
% 122.84/16.20 ((
% 122.84/16.20 (complementTI1) =>
% 122.84/16.20 ((
% 122.84/16.20 (complementTE1) =>
% 122.84/16.20 ((
% 122.84/16.20 (binintersectTELcontra) =>
% 122.84/16.20 ((
% 122.84/16.20 (binintersectTERcontra) =>
% 122.84/16.20 ((
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% 122.84/16.20 ((
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% 122.84/16.20 ((
% 122.84/16.20 (contrasubsetT2) =>
% 122.84/16.20 ((
% 122.84/16.20 (contrasubsetT3) =>
% 122.84/16.20 ((
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% 122.84/16.20 ((
% 122.84/16.20 (doubleComplementE1) =>
% 122.84/16.20 ((
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% 122.84/16.20 ((
% 122.84/16.20 (doubleComplementSub2) =>
% 122.84/16.20 ((
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% 122.84/16.20 ((
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% 122.84/16.20 ((
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% 122.84/16.20 ((
% 122.84/16.20 (complementSubsetComplementIntersect) =>
% 122.84/16.20 ((
% 122.84/16.20 (complementInPowersetComplementIntersect) =>
% 122.84/16.20 ((
% 122.84/16.20 (contraSubsetComplement) =>
% 122.84/16.20 ((
% 122.84/16.20 (complementTcontraSubset) =>
% 122.84/16.20 ((
% 122.84/16.20 (binunionTILcontra) =>
% 122.84/16.20 ((
% 122.84/16.20 (binunionTIRcontra) =>
% 122.84/16.20 ((
% 122.84/16.20 (inIntersectImpInUnion) =>
% 122.84/16.20 ((
% 122.84/16.20 (inIntersectImpInUnion2) =>
% 122.84/16.20 ((
% 122.84/16.20 (inIntersectImpInIntersectUnions) =>
% 122.84/16.20 ((
% 122.84/16.20 (intersectInPowersetIntersectUnions) =>
% 122.84/16.20 ((
% 122.84/16.20 (inComplementUnionImpNotIn1) =>
% 122.84/16.20 ((
% 122.84/16.20 (inComplementUnionImpInComplement1) =>
% 122.84/16.20 ((
% 122.84/16.20 (binunionTE) =>
% 122.84/16.20 ((
% 122.84/16.20 (binunionTEcontra) =>
% 122.84/16.20 ((
% 122.84/16.20 (demorgan2a1) =>
% 122.84/16.20 ((
% 122.84/16.20 (complementUnionInPowersetComplement) =>
% 122.84/16.20 ((
% 122.84/16.20 (demorgan2a2) =>
% 122.84/16.20 ((
% 122.84/16.20 (demorgan1a) =>
% 122.84/16.20 ((
% 122.84/16.20 (demorgan1b) =>
% 122.84/16.20 ((
% 122.84/16.20 (demorgan1) =>
% 122.84/16.20 ((
% 122.84/16.20 (demorgan2a) =>
% 122.84/16.20 ((
% 122.84/16.20 (demorgan2b2) =>
% 122.84/16.20 ((
% 122.84/16.20 (demorgan2b) =>
% 122.84/16.20 ((
% 122.84/16.20 (demorgan2) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz13rule0) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz13rule1) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz13rule2) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz13rule3) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz13rule4) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz1_1) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz1_2) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz1_3) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz1_4) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz1_5) =>
% 122.84/16.20 ((
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% 122.84/16.20 ((
% 122.84/16.20 (breln1SetBreln1) =>
% 122.84/16.20 ((
% 122.84/16.20 (choice2fnsingleton) =>
% 122.84/16.20 ((
% 122.84/16.20 (setOfPairsIsBReln1) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1all1) =>
% 122.84/16.20 ((
% 122.84/16.20 (subbreln1) =>
% 122.84/16.20 ((
% 122.84/16.20 (eqbreln1) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1invprop) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1invI) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1invE) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1compprop) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1compI) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1compE) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1compEex) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1unionprop) =>
% 122.84/16.20 ((
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% 122.84/16.20 ((
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% 122.84/16.20 ((
% 122.84/16.20 (breln1unionI) =>
% 122.84/16.20 ((
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% 122.84/16.20 ((
% 122.84/16.20 (breln1unionEcases) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1unionCommutes) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz2Ex) =>
% 122.84/16.20 ((
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% 122.84/16.20 ((
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% 122.84/16.20 ((
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% 122.84/16.20 ((
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% 122.84/16.20 ((
% 122.84/16.20 (image1Ex1) =>
% 122.84/16.20 ((
% 122.84/16.20 (image1Equiv) =>
% 122.84/16.20 ((
% 122.84/16.20 (image1E) =>
% 122.84/16.20 ((
% 122.84/16.20 (image1I) =>
% 122.84/16.20 ((
% 122.84/16.20 (injFuncInInjFuncSet) =>
% 122.84/16.20 ((
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% 122.84/16.20 injFuncSet)))))))) @
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% 122.84/16.20 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.84/16.20 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1555])).
% 122.84/16.20 thf(zip_derived_cl1574, plain,
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% 122.84/16.20 (((ex1I2) =>
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% 122.84/16.20 (((setukpairinjR1) =>
% 122.84/16.20 (((upairequniteq) =>
% 122.84/16.20 (((setukpairinjR2) =>
% 122.84/16.20 (((setukpairinjR) =>
% 122.84/16.20 (((ksndsingleton) =>
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% 122.84/16.20 (((cartprodpairmemER) =>
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% 122.84/16.20 ((
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% 122.84/16.20 ((
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% 122.84/16.20 ((
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% 122.84/16.20 ((
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% 122.84/16.20 ((
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% 122.84/16.20 ((
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% 122.84/16.20 ((
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% 122.84/16.20 ((
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% 122.84/16.20 ((
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% 122.84/16.20 ((
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% 122.84/16.20 ((
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% 122.84/16.20 ((
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% 122.84/16.20 ((
% 122.84/16.20 (contrasubsetT2) =>
% 122.84/16.20 ((
% 122.84/16.20 (contrasubsetT3) =>
% 122.84/16.20 ((
% 122.84/16.20 (doubleComplementI1) =>
% 122.84/16.20 ((
% 122.84/16.20 (doubleComplementE1) =>
% 122.84/16.20 ((
% 122.84/16.20 (doubleComplementSub1) =>
% 122.84/16.20 ((
% 122.84/16.20 (doubleComplementSub2) =>
% 122.84/16.20 ((
% 122.84/16.20 (doubleComplementEq) =>
% 122.84/16.20 ((
% 122.84/16.20 (complementTnotintersectT) =>
% 122.84/16.20 ((
% 122.84/16.20 (complementImpComplementIntersect) =>
% 122.84/16.20 ((
% 122.84/16.20 (complementSubsetComplementIntersect) =>
% 122.84/16.20 ((
% 122.84/16.20 (complementInPowersetComplementIntersect) =>
% 122.84/16.20 ((
% 122.84/16.20 (contraSubsetComplement) =>
% 122.84/16.20 ((
% 122.84/16.20 (complementTcontraSubset) =>
% 122.84/16.20 ((
% 122.84/16.20 (binunionTILcontra) =>
% 122.84/16.20 ((
% 122.84/16.20 (binunionTIRcontra) =>
% 122.84/16.20 ((
% 122.84/16.20 (inIntersectImpInUnion) =>
% 122.84/16.20 ((
% 122.84/16.20 (inIntersectImpInUnion2) =>
% 122.84/16.20 ((
% 122.84/16.20 (inIntersectImpInIntersectUnions) =>
% 122.84/16.20 ((
% 122.84/16.20 (intersectInPowersetIntersectUnions) =>
% 122.84/16.20 ((
% 122.84/16.20 (inComplementUnionImpNotIn1) =>
% 122.84/16.20 ((
% 122.84/16.20 (inComplementUnionImpInComplement1) =>
% 122.84/16.20 ((
% 122.84/16.20 (binunionTE) =>
% 122.84/16.20 ((
% 122.84/16.20 (binunionTEcontra) =>
% 122.84/16.20 ((
% 122.84/16.20 (demorgan2a1) =>
% 122.84/16.20 ((
% 122.84/16.20 (complementUnionInPowersetComplement) =>
% 122.84/16.20 ((
% 122.84/16.20 (demorgan2a2) =>
% 122.84/16.20 ((
% 122.84/16.20 (demorgan1a) =>
% 122.84/16.20 ((
% 122.84/16.20 (demorgan1b) =>
% 122.84/16.20 ((
% 122.84/16.20 (demorgan1) =>
% 122.84/16.20 ((
% 122.84/16.20 (demorgan2a) =>
% 122.84/16.20 ((
% 122.84/16.20 (demorgan2b2) =>
% 122.84/16.20 ((
% 122.84/16.20 (demorgan2b) =>
% 122.84/16.20 ((
% 122.84/16.20 (demorgan2) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz13rule0) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz13rule1) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz13rule2) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz13rule3) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz13rule4) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz1_1) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz1_2) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz1_3) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz1_4) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz1_5) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1all2) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1SetBreln1) =>
% 122.84/16.20 ((
% 122.84/16.20 (choice2fnsingleton) =>
% 122.84/16.20 ((
% 122.84/16.20 (setOfPairsIsBReln1) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1all1) =>
% 122.84/16.20 ((
% 122.84/16.20 (subbreln1) =>
% 122.84/16.20 ((
% 122.84/16.20 (eqbreln1) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1invprop) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1invI) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1invE) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1compprop) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1compI) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1compE) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1compEex) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1unionprop) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1unionIL) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1unionIR) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1unionI) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1unionE) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1unionEcases) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1unionCommutes) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz2Ex) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz2W) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz2A) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz2B) =>
% 122.84/16.20 ((
% 122.84/16.20 (image1Ex) =>
% 122.84/16.20 ((
% 122.84/16.20 (image1Ex1) =>
% 122.84/16.20 ((
% 122.84/16.20 (image1Equiv) =>
% 122.84/16.20 ((
% 122.84/16.20 (image1E) =>
% 122.84/16.20 ((
% 122.84/16.20 (image1I) =>
% 122.84/16.20 ((
% 122.84/16.20 (injFuncInInjFuncSet) =>
% 122.84/16.20 ((
% 122.84/16.20 (!!) @ (
% 122.84/16.20 (('#B') @ (
% 122.84/16.20 !!) @
% 122.84/16.20 (
% 122.84/16.20 (
% 122.84/16.20 ('#B') @ (
% 122.84/16.20 (
% 122.84/16.20 ('#B') @ (
% 122.84/16.20 !!))) @
% 122.84/16.20 (
% 122.84/16.20 (
% 122.84/16.20 ('#S') @ (
% 122.84/16.20 (
% 122.84/16.20 ('#B') @ (
% 122.84/16.20 '#S') @
% 122.84/16.20 (
% 122.84/16.20 (
% 122.84/16.20 ('#B') @ (
% 122.84/16.20 (
% 122.84/16.20 ('#B') @ (
% 122.84/16.20 '#S'))) @
% 122.84/16.20 (
% 122.84/16.20 (
% 122.84/16.20 ('#B') @ (
% 122.84/16.20 (
% 122.84/16.20 ('#B') @ (
% 122.84/16.20 (
% 122.84/16.20 ('#B') @ (
% 122.84/16.20 =>))))) @
% 122.84/16.20 (
% 122.84/16.20 (
% 122.84/16.20 ('#B') @ (
% 122.84/16.20 (
% 122.84/16.20 ('#B') @ (
% 122.84/16.20 (
% 122.84/16.20 ('#C') @ in)))) @
% 122.84/16.20 injFuncSet)))))))) @
% 122.84/16.20 (
% 122.84/16.20 (
% 122.84/16.20 ('#B') @ (
% 122.84/16.20 (
% 122.84/16.20 ('#B') @ (
% 122.84/16.20 (
% 122.84/16.20 ('#C') @ in)))) @
% 122.84/16.20 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.84/16.20 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1565])).
% 122.84/16.20 thf(zip_derived_cl1582, plain,
% 122.84/16.20 (~ (((ex1I) =>
% 122.84/16.20 (((ex1I2) =>
% 122.84/16.20 (((singletonsuniq) =>
% 122.84/16.20 (((setukpairinjL1) =>
% 122.84/16.20 (((kfstsingleton) =>
% 122.84/16.20 (((theprop) =>
% 122.84/16.20 (((kfstpairEq) =>
% 122.84/16.20 (((cartprodfstin) =>
% 122.84/16.20 (((setukpairinjL2) =>
% 122.84/16.20 (((setukpairinjL) =>
% 122.84/16.20 (((setukpairinjR11) =>
% 122.84/16.20 (((setukpairinjR12) =>
% 122.84/16.20 (((setukpairinjR1) =>
% 122.84/16.20 (((upairequniteq) =>
% 122.84/16.20 (((setukpairinjR2) =>
% 122.84/16.20 (((setukpairinjR) =>
% 122.84/16.20 (((ksndsingleton) =>
% 122.84/16.20 (((ksndpairEq) =>
% 122.84/16.20 (((kpairsurjEq) =>
% 122.84/16.20 (((cartprodsndin) =>
% 122.84/16.20 (((cartprodpairmemEL) =>
% 122.84/16.20 (((cartprodpairmemER) =>
% 122.84/16.20 (((cartprodmempaircEq) =>
% 122.84/16.20 (((cartprodfstpairEq) =>
% 122.84/16.20 (((cartprodsndpairEq) =>
% 122.84/16.20 (((cartprodpairsurjEq) =>
% 122.84/16.20 (((dpsetconstrI) =>
% 122.84/16.20 (((dpsetconstrSub) =>
% 122.84/16.20 (((setOfPairsIsBReln) =>
% 122.84/16.20 (((dpsetconstrERa) =>
% 122.84/16.20 ((
% 122.84/16.20 (dpsetconstrEL1) =>
% 122.84/16.20 ((
% 122.84/16.20 (dpsetconstrEL2) =>
% 122.84/16.20 ((
% 122.84/16.20 (dpsetconstrER) =>
% 122.84/16.20 ((
% 122.84/16.20 (funcImageSingleton) =>
% 122.84/16.20 ((
% 122.84/16.20 (apProp) =>
% 122.84/16.20 ((
% 122.84/16.20 (app) =>
% 122.84/16.20 ((
% 122.84/16.20 (infuncsetfunc) =>
% 122.84/16.20 ((
% 122.84/16.20 (ap2p) =>
% 122.84/16.20 ((
% 122.84/16.20 (funcinfuncset) =>
% 122.84/16.20 ((
% 122.84/16.20 (lamProp) =>
% 122.84/16.20 ((
% 122.84/16.20 (lamp) =>
% 122.84/16.20 ((
% 122.84/16.20 (lam2p) =>
% 122.84/16.20 ((
% 122.84/16.20 (brelnall1) =>
% 122.84/16.20 ((
% 122.84/16.20 (brelnall2) =>
% 122.84/16.20 ((
% 122.84/16.20 (ex1E2) =>
% 122.84/16.20 ((
% 122.84/16.20 (funcGraphProp1) =>
% 122.84/16.20 ((
% 122.84/16.20 (funcGraphProp3) =>
% 122.84/16.20 ((
% 122.84/16.20 (funcGraphProp2) =>
% 122.84/16.20 ((
% 122.84/16.20 (funcextLem) =>
% 122.84/16.20 ((
% 122.84/16.20 (funcGraphProp4) =>
% 122.84/16.20 ((
% 122.84/16.20 (subbreln) =>
% 122.84/16.20 ((
% 122.84/16.20 (eqbreln) =>
% 122.84/16.20 ((
% 122.84/16.20 (funcext) =>
% 122.84/16.20 ((
% 122.84/16.20 (funcext2) =>
% 122.84/16.20 ((
% 122.84/16.20 (ap2apEq1) =>
% 122.84/16.20 ((
% 122.84/16.20 (ap2apEq2) =>
% 122.84/16.20 ((
% 122.84/16.20 (beta1) =>
% 122.84/16.20 ((
% 122.84/16.20 (eta1) =>
% 122.84/16.20 ((
% 122.84/16.20 (lam2lamEq) =>
% 122.84/16.20 ((
% 122.84/16.20 (beta2) =>
% 122.84/16.20 ((
% 122.84/16.20 (eta2) =>
% 122.84/16.20 ((
% 122.84/16.20 (iffalseProp1) =>
% 122.84/16.20 ((
% 122.84/16.20 (iffalseProp2) =>
% 122.84/16.20 ((
% 122.84/16.20 (iftrueProp1) =>
% 122.84/16.20 ((
% 122.84/16.20 (iftrueProp2) =>
% 122.84/16.20 ((
% 122.84/16.20 (ifSingleton) =>
% 122.84/16.20 ((
% 122.84/16.20 (ifp) =>
% 122.84/16.20 ((
% 122.84/16.20 (theeq) =>
% 122.84/16.20 ((
% 122.84/16.20 (iftrue) =>
% 122.84/16.20 ((
% 122.84/16.20 (iffalse) =>
% 122.84/16.20 ((
% 122.84/16.20 (iftrueorfalse) =>
% 122.84/16.20 ((
% 122.84/16.20 (binintersectT_lem) =>
% 122.84/16.20 ((
% 122.84/16.20 (binunionT_lem) =>
% 122.84/16.20 ((
% 122.84/16.20 (powersetT_lem) =>
% 122.84/16.20 ((
% 122.84/16.20 (setminusT_lem) =>
% 122.84/16.20 ((
% 122.84/16.20 (complementT_lem) =>
% 122.84/16.20 ((
% 122.84/16.20 (setextT) =>
% 122.84/16.20 ((
% 122.84/16.20 (subsetTI) =>
% 122.84/16.20 ((
% 122.84/16.20 (powersetTI1) =>
% 122.84/16.20 ((
% 122.84/16.20 (powersetTE1) =>
% 122.84/16.20 ((
% 122.84/16.20 (complementTI1) =>
% 122.84/16.20 ((
% 122.84/16.20 (complementTE1) =>
% 122.84/16.20 ((
% 122.84/16.20 (binintersectTELcontra) =>
% 122.84/16.20 ((
% 122.84/16.20 (binintersectTERcontra) =>
% 122.84/16.20 ((
% 122.84/16.20 (contrasubsetT) =>
% 122.84/16.20 ((
% 122.84/16.20 (contrasubsetT1) =>
% 122.84/16.20 ((
% 122.84/16.20 (contrasubsetT2) =>
% 122.84/16.20 ((
% 122.84/16.20 (contrasubsetT3) =>
% 122.84/16.20 ((
% 122.84/16.20 (doubleComplementI1) =>
% 122.84/16.20 ((
% 122.84/16.20 (doubleComplementE1) =>
% 122.84/16.20 ((
% 122.84/16.20 (doubleComplementSub1) =>
% 122.84/16.20 ((
% 122.84/16.20 (doubleComplementSub2) =>
% 122.84/16.20 ((
% 122.84/16.20 (doubleComplementEq) =>
% 122.84/16.20 ((
% 122.84/16.20 (complementTnotintersectT) =>
% 122.84/16.20 ((
% 122.84/16.20 (complementImpComplementIntersect) =>
% 122.84/16.20 ((
% 122.84/16.20 (complementSubsetComplementIntersect) =>
% 122.84/16.20 ((
% 122.84/16.20 (complementInPowersetComplementIntersect) =>
% 122.84/16.20 ((
% 122.84/16.20 (contraSubsetComplement) =>
% 122.84/16.20 ((
% 122.84/16.20 (complementTcontraSubset) =>
% 122.84/16.20 ((
% 122.84/16.20 (binunionTILcontra) =>
% 122.84/16.20 ((
% 122.84/16.20 (binunionTIRcontra) =>
% 122.84/16.20 ((
% 122.84/16.20 (inIntersectImpInUnion) =>
% 122.84/16.20 ((
% 122.84/16.20 (inIntersectImpInUnion2) =>
% 122.84/16.20 ((
% 122.84/16.20 (inIntersectImpInIntersectUnions) =>
% 122.84/16.20 ((
% 122.84/16.20 (intersectInPowersetIntersectUnions) =>
% 122.84/16.20 ((
% 122.84/16.20 (inComplementUnionImpNotIn1) =>
% 122.84/16.20 ((
% 122.84/16.20 (inComplementUnionImpInComplement1) =>
% 122.84/16.20 ((
% 122.84/16.20 (binunionTE) =>
% 122.84/16.20 ((
% 122.84/16.20 (binunionTEcontra) =>
% 122.84/16.20 ((
% 122.84/16.20 (demorgan2a1) =>
% 122.84/16.20 ((
% 122.84/16.20 (complementUnionInPowersetComplement) =>
% 122.84/16.20 ((
% 122.84/16.20 (demorgan2a2) =>
% 122.84/16.20 ((
% 122.84/16.20 (demorgan1a) =>
% 122.84/16.20 ((
% 122.84/16.20 (demorgan1b) =>
% 122.84/16.20 ((
% 122.84/16.20 (demorgan1) =>
% 122.84/16.20 ((
% 122.84/16.20 (demorgan2a) =>
% 122.84/16.20 ((
% 122.84/16.20 (demorgan2b2) =>
% 122.84/16.20 ((
% 122.84/16.20 (demorgan2b) =>
% 122.84/16.20 ((
% 122.84/16.20 (demorgan2) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz13rule0) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz13rule1) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz13rule2) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz13rule3) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz13rule4) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz1_1) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz1_2) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz1_3) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz1_4) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz1_5) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1all2) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1SetBreln1) =>
% 122.84/16.20 ((
% 122.84/16.20 (choice2fnsingleton) =>
% 122.84/16.20 ((
% 122.84/16.20 (setOfPairsIsBReln1) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1all1) =>
% 122.84/16.20 ((
% 122.84/16.20 (subbreln1) =>
% 122.84/16.20 ((
% 122.84/16.20 (eqbreln1) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1invprop) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1invI) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1invE) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1compprop) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1compI) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1compE) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1compEex) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1unionprop) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1unionIL) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1unionIR) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1unionI) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1unionE) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1unionEcases) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1unionCommutes) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz2Ex) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz2W) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz2A) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz2B) =>
% 122.84/16.20 ((
% 122.84/16.20 (image1Ex) =>
% 122.84/16.20 ((
% 122.84/16.20 (image1Ex1) =>
% 122.84/16.20 ((
% 122.84/16.20 (image1Equiv) =>
% 122.84/16.20 ((
% 122.84/16.20 (image1E) =>
% 122.84/16.20 ((
% 122.84/16.20 (image1I) =>
% 122.84/16.20 ((
% 122.84/16.20 (injFuncInInjFuncSet) =>
% 122.84/16.20 ((
% 122.84/16.20 (!!) @ (
% 122.84/16.20 (('#B') @ (
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% 122.84/16.20 (
% 122.84/16.20 (
% 122.84/16.20 ('#B') @ (
% 122.84/16.20 (
% 122.84/16.20 ('#B') @ (
% 122.84/16.20 !!))) @
% 122.84/16.20 (
% 122.84/16.20 (
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% 122.84/16.20 (
% 122.84/16.20 (
% 122.84/16.20 ('#B') @ (
% 122.84/16.20 (
% 122.84/16.20 ('#B') @ (
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% 122.84/16.20 (
% 122.84/16.20 (
% 122.84/16.20 ('#B') @ (
% 122.84/16.20 (
% 122.84/16.20 ('#B') @ (
% 122.84/16.20 (
% 122.84/16.20 ('#B') @ (
% 122.84/16.20 =>))))) @
% 122.84/16.20 (
% 122.84/16.20 (
% 122.84/16.20 ('#B') @ (
% 122.84/16.20 (
% 122.84/16.20 ('#B') @ (
% 122.84/16.20 (
% 122.84/16.20 ('#C') @ in)))) @
% 122.84/16.20 injFuncSet)))))))) @
% 122.84/16.20 (
% 122.84/16.20 (
% 122.84/16.20 ('#B') @ (
% 122.84/16.20 (
% 122.84/16.20 ('#B') @ (
% 122.84/16.20 (
% 122.84/16.20 ('#C') @ in)))) @
% 122.84/16.20 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.84/16.20 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1574])).
% 122.84/16.20 thf(zip_derived_cl1591, plain,
% 122.84/16.20 (~ (((ex1I2) =>
% 122.84/16.20 (((singletonsuniq) =>
% 122.84/16.20 (((setukpairinjL1) =>
% 122.84/16.20 (((kfstsingleton) =>
% 122.84/16.20 (((theprop) =>
% 122.84/16.20 (((kfstpairEq) =>
% 122.84/16.20 (((cartprodfstin) =>
% 122.84/16.20 (((setukpairinjL2) =>
% 122.84/16.20 (((setukpairinjL) =>
% 122.84/16.20 (((setukpairinjR11) =>
% 122.84/16.20 (((setukpairinjR12) =>
% 122.84/16.20 (((setukpairinjR1) =>
% 122.84/16.20 (((upairequniteq) =>
% 122.84/16.20 (((setukpairinjR2) =>
% 122.84/16.20 (((setukpairinjR) =>
% 122.84/16.20 (((ksndsingleton) =>
% 122.84/16.20 (((ksndpairEq) =>
% 122.84/16.20 (((kpairsurjEq) =>
% 122.84/16.20 (((cartprodsndin) =>
% 122.84/16.20 (((cartprodpairmemEL) =>
% 122.84/16.20 (((cartprodpairmemER) =>
% 122.84/16.20 (((cartprodmempaircEq) =>
% 122.84/16.20 (((cartprodfstpairEq) =>
% 122.84/16.20 (((cartprodsndpairEq) =>
% 122.84/16.20 (((cartprodpairsurjEq) =>
% 122.84/16.20 (((dpsetconstrI) =>
% 122.84/16.20 (((dpsetconstrSub) =>
% 122.84/16.20 (((setOfPairsIsBReln) =>
% 122.84/16.20 (((dpsetconstrERa) =>
% 122.84/16.20 (((dpsetconstrEL1) =>
% 122.84/16.20 ((
% 122.84/16.20 (dpsetconstrEL2) =>
% 122.84/16.20 ((
% 122.84/16.20 (dpsetconstrER) =>
% 122.84/16.20 ((
% 122.84/16.20 (funcImageSingleton) =>
% 122.84/16.20 ((
% 122.84/16.20 (apProp) =>
% 122.84/16.20 ((
% 122.84/16.20 (app) =>
% 122.84/16.20 ((
% 122.84/16.20 (infuncsetfunc) =>
% 122.84/16.20 ((
% 122.84/16.20 (ap2p) =>
% 122.84/16.20 ((
% 122.84/16.20 (funcinfuncset) =>
% 122.84/16.20 ((
% 122.84/16.20 (lamProp) =>
% 122.84/16.20 ((
% 122.84/16.20 (lamp) =>
% 122.84/16.20 ((
% 122.84/16.20 (lam2p) =>
% 122.84/16.20 ((
% 122.84/16.20 (brelnall1) =>
% 122.84/16.20 ((
% 122.84/16.20 (brelnall2) =>
% 122.84/16.20 ((
% 122.84/16.20 (ex1E2) =>
% 122.84/16.20 ((
% 122.84/16.20 (funcGraphProp1) =>
% 122.84/16.20 ((
% 122.84/16.20 (funcGraphProp3) =>
% 122.84/16.20 ((
% 122.84/16.20 (funcGraphProp2) =>
% 122.84/16.20 ((
% 122.84/16.20 (funcextLem) =>
% 122.84/16.20 ((
% 122.84/16.20 (funcGraphProp4) =>
% 122.84/16.20 ((
% 122.84/16.20 (subbreln) =>
% 122.84/16.20 ((
% 122.84/16.20 (eqbreln) =>
% 122.84/16.20 ((
% 122.84/16.20 (funcext) =>
% 122.84/16.20 ((
% 122.84/16.20 (funcext2) =>
% 122.84/16.20 ((
% 122.84/16.20 (ap2apEq1) =>
% 122.84/16.20 ((
% 122.84/16.20 (ap2apEq2) =>
% 122.84/16.20 ((
% 122.84/16.20 (beta1) =>
% 122.84/16.20 ((
% 122.84/16.20 (eta1) =>
% 122.84/16.20 ((
% 122.84/16.20 (lam2lamEq) =>
% 122.84/16.20 ((
% 122.84/16.20 (beta2) =>
% 122.84/16.20 ((
% 122.84/16.20 (eta2) =>
% 122.84/16.20 ((
% 122.84/16.20 (iffalseProp1) =>
% 122.84/16.20 ((
% 122.84/16.20 (iffalseProp2) =>
% 122.84/16.20 ((
% 122.84/16.20 (iftrueProp1) =>
% 122.84/16.20 ((
% 122.84/16.20 (iftrueProp2) =>
% 122.84/16.20 ((
% 122.84/16.20 (ifSingleton) =>
% 122.84/16.20 ((
% 122.84/16.20 (ifp) =>
% 122.84/16.20 ((
% 122.84/16.20 (theeq) =>
% 122.84/16.20 ((
% 122.84/16.20 (iftrue) =>
% 122.84/16.20 ((
% 122.84/16.20 (iffalse) =>
% 122.84/16.20 ((
% 122.84/16.20 (iftrueorfalse) =>
% 122.84/16.20 ((
% 122.84/16.20 (binintersectT_lem) =>
% 122.84/16.20 ((
% 122.84/16.20 (binunionT_lem) =>
% 122.84/16.20 ((
% 122.84/16.20 (powersetT_lem) =>
% 122.84/16.20 ((
% 122.84/16.20 (setminusT_lem) =>
% 122.84/16.20 ((
% 122.84/16.20 (complementT_lem) =>
% 122.84/16.20 ((
% 122.84/16.20 (setextT) =>
% 122.84/16.20 ((
% 122.84/16.20 (subsetTI) =>
% 122.84/16.20 ((
% 122.84/16.20 (powersetTI1) =>
% 122.84/16.20 ((
% 122.84/16.20 (powersetTE1) =>
% 122.84/16.20 ((
% 122.84/16.20 (complementTI1) =>
% 122.84/16.20 ((
% 122.84/16.20 (complementTE1) =>
% 122.84/16.20 ((
% 122.84/16.20 (binintersectTELcontra) =>
% 122.84/16.20 ((
% 122.84/16.20 (binintersectTERcontra) =>
% 122.84/16.20 ((
% 122.84/16.20 (contrasubsetT) =>
% 122.84/16.20 ((
% 122.84/16.20 (contrasubsetT1) =>
% 122.84/16.20 ((
% 122.84/16.20 (contrasubsetT2) =>
% 122.84/16.20 ((
% 122.84/16.20 (contrasubsetT3) =>
% 122.84/16.20 ((
% 122.84/16.20 (doubleComplementI1) =>
% 122.84/16.20 ((
% 122.84/16.20 (doubleComplementE1) =>
% 122.84/16.20 ((
% 122.84/16.20 (doubleComplementSub1) =>
% 122.84/16.20 ((
% 122.84/16.20 (doubleComplementSub2) =>
% 122.84/16.20 ((
% 122.84/16.20 (doubleComplementEq) =>
% 122.84/16.20 ((
% 122.84/16.20 (complementTnotintersectT) =>
% 122.84/16.20 ((
% 122.84/16.20 (complementImpComplementIntersect) =>
% 122.84/16.20 ((
% 122.84/16.20 (complementSubsetComplementIntersect) =>
% 122.84/16.20 ((
% 122.84/16.20 (complementInPowersetComplementIntersect) =>
% 122.84/16.20 ((
% 122.84/16.20 (contraSubsetComplement) =>
% 122.84/16.20 ((
% 122.84/16.20 (complementTcontraSubset) =>
% 122.84/16.20 ((
% 122.84/16.20 (binunionTILcontra) =>
% 122.84/16.20 ((
% 122.84/16.20 (binunionTIRcontra) =>
% 122.84/16.20 ((
% 122.84/16.20 (inIntersectImpInUnion) =>
% 122.84/16.20 ((
% 122.84/16.20 (inIntersectImpInUnion2) =>
% 122.84/16.20 ((
% 122.84/16.20 (inIntersectImpInIntersectUnions) =>
% 122.84/16.20 ((
% 122.84/16.20 (intersectInPowersetIntersectUnions) =>
% 122.84/16.20 ((
% 122.84/16.20 (inComplementUnionImpNotIn1) =>
% 122.84/16.20 ((
% 122.84/16.20 (inComplementUnionImpInComplement1) =>
% 122.84/16.20 ((
% 122.84/16.20 (binunionTE) =>
% 122.84/16.20 ((
% 122.84/16.20 (binunionTEcontra) =>
% 122.84/16.20 ((
% 122.84/16.20 (demorgan2a1) =>
% 122.84/16.20 ((
% 122.84/16.20 (complementUnionInPowersetComplement) =>
% 122.84/16.20 ((
% 122.84/16.20 (demorgan2a2) =>
% 122.84/16.20 ((
% 122.84/16.20 (demorgan1a) =>
% 122.84/16.20 ((
% 122.84/16.20 (demorgan1b) =>
% 122.84/16.20 ((
% 122.84/16.20 (demorgan1) =>
% 122.84/16.20 ((
% 122.84/16.20 (demorgan2a) =>
% 122.84/16.20 ((
% 122.84/16.20 (demorgan2b2) =>
% 122.84/16.20 ((
% 122.84/16.20 (demorgan2b) =>
% 122.84/16.20 ((
% 122.84/16.20 (demorgan2) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz13rule0) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz13rule1) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz13rule2) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz13rule3) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz13rule4) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz1_1) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz1_2) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz1_3) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz1_4) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz1_5) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1all2) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1SetBreln1) =>
% 122.84/16.20 ((
% 122.84/16.20 (choice2fnsingleton) =>
% 122.84/16.20 ((
% 122.84/16.20 (setOfPairsIsBReln1) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1all1) =>
% 122.84/16.20 ((
% 122.84/16.20 (subbreln1) =>
% 122.84/16.20 ((
% 122.84/16.20 (eqbreln1) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1invprop) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1invI) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1invE) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1compprop) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1compI) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1compE) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1compEex) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1unionprop) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1unionIL) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1unionIR) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1unionI) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1unionE) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1unionEcases) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1unionCommutes) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz2Ex) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz2W) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz2A) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz2B) =>
% 122.84/16.20 ((
% 122.84/16.20 (image1Ex) =>
% 122.84/16.20 ((
% 122.84/16.20 (image1Ex1) =>
% 122.84/16.20 ((
% 122.84/16.20 (image1Equiv) =>
% 122.84/16.20 ((
% 122.84/16.20 (image1E) =>
% 122.84/16.20 ((
% 122.84/16.20 (image1I) =>
% 122.84/16.20 ((
% 122.84/16.20 (injFuncInInjFuncSet) =>
% 122.84/16.20 ((
% 122.84/16.20 (!!) @ (
% 122.84/16.20 (('#B') @ (
% 122.84/16.20 !!) @
% 122.84/16.20 (
% 122.84/16.20 (
% 122.84/16.20 ('#B') @ (
% 122.84/16.20 (
% 122.84/16.20 ('#B') @ (
% 122.84/16.20 !!))) @
% 122.84/16.20 (
% 122.84/16.20 (
% 122.84/16.20 ('#S') @ (
% 122.84/16.20 (
% 122.84/16.20 ('#B') @ (
% 122.84/16.20 '#S') @
% 122.84/16.20 (
% 122.84/16.20 (
% 122.84/16.20 ('#B') @ (
% 122.84/16.20 (
% 122.84/16.20 ('#B') @ (
% 122.84/16.20 '#S'))) @
% 122.84/16.20 (
% 122.84/16.20 (
% 122.84/16.20 ('#B') @ (
% 122.84/16.20 (
% 122.84/16.20 ('#B') @ (
% 122.84/16.20 (
% 122.84/16.20 ('#B') @ (
% 122.84/16.20 =>))))) @
% 122.84/16.20 (
% 122.84/16.20 (
% 122.84/16.20 ('#B') @ (
% 122.84/16.20 (
% 122.84/16.20 ('#B') @ (
% 122.84/16.20 (
% 122.84/16.20 ('#C') @ in)))) @
% 122.84/16.20 injFuncSet)))))))) @
% 122.84/16.20 (
% 122.84/16.20 (
% 122.84/16.20 ('#B') @ (
% 122.84/16.20 (
% 122.84/16.20 ('#B') @ (
% 122.84/16.20 (
% 122.84/16.20 ('#C') @ in)))) @
% 122.84/16.20 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.84/16.20 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1582])).
% 122.84/16.20 thf(zip_derived_cl1599, plain,
% 122.84/16.20 (~ (((singletonsuniq) =>
% 122.84/16.20 (((setukpairinjL1) =>
% 122.84/16.20 (((kfstsingleton) =>
% 122.84/16.20 (((theprop) =>
% 122.84/16.20 (((kfstpairEq) =>
% 122.84/16.20 (((cartprodfstin) =>
% 122.84/16.20 (((setukpairinjL2) =>
% 122.84/16.20 (((setukpairinjL) =>
% 122.84/16.20 (((setukpairinjR11) =>
% 122.84/16.20 (((setukpairinjR12) =>
% 122.84/16.20 (((setukpairinjR1) =>
% 122.84/16.20 (((upairequniteq) =>
% 122.84/16.20 (((setukpairinjR2) =>
% 122.84/16.20 (((setukpairinjR) =>
% 122.84/16.20 (((ksndsingleton) =>
% 122.84/16.20 (((ksndpairEq) =>
% 122.84/16.20 (((kpairsurjEq) =>
% 122.84/16.20 (((cartprodsndin) =>
% 122.84/16.20 (((cartprodpairmemEL) =>
% 122.84/16.20 (((cartprodpairmemER) =>
% 122.84/16.20 (((cartprodmempaircEq) =>
% 122.84/16.20 (((cartprodfstpairEq) =>
% 122.84/16.20 (((cartprodsndpairEq) =>
% 122.84/16.20 (((cartprodpairsurjEq) =>
% 122.84/16.20 (((dpsetconstrI) =>
% 122.84/16.20 (((dpsetconstrSub) =>
% 122.84/16.20 (((setOfPairsIsBReln) =>
% 122.84/16.20 (((dpsetconstrERa) =>
% 122.84/16.20 (((dpsetconstrEL1) =>
% 122.84/16.20 (((dpsetconstrEL2) =>
% 122.84/16.20 ((
% 122.84/16.20 (dpsetconstrER) =>
% 122.84/16.20 ((
% 122.84/16.20 (funcImageSingleton) =>
% 122.84/16.20 ((
% 122.84/16.20 (apProp) =>
% 122.84/16.20 ((
% 122.84/16.20 (app) =>
% 122.84/16.20 ((
% 122.84/16.20 (infuncsetfunc) =>
% 122.84/16.20 ((
% 122.84/16.20 (ap2p) =>
% 122.84/16.20 ((
% 122.84/16.20 (funcinfuncset) =>
% 122.84/16.20 ((
% 122.84/16.20 (lamProp) =>
% 122.84/16.20 ((
% 122.84/16.20 (lamp) =>
% 122.84/16.20 ((
% 122.84/16.20 (lam2p) =>
% 122.84/16.20 ((
% 122.84/16.20 (brelnall1) =>
% 122.84/16.20 ((
% 122.84/16.20 (brelnall2) =>
% 122.84/16.20 ((
% 122.84/16.20 (ex1E2) =>
% 122.84/16.20 ((
% 122.84/16.20 (funcGraphProp1) =>
% 122.84/16.20 ((
% 122.84/16.20 (funcGraphProp3) =>
% 122.84/16.20 ((
% 122.84/16.20 (funcGraphProp2) =>
% 122.84/16.20 ((
% 122.84/16.20 (funcextLem) =>
% 122.84/16.20 ((
% 122.84/16.20 (funcGraphProp4) =>
% 122.84/16.20 ((
% 122.84/16.20 (subbreln) =>
% 122.84/16.20 ((
% 122.84/16.20 (eqbreln) =>
% 122.84/16.20 ((
% 122.84/16.20 (funcext) =>
% 122.84/16.20 ((
% 122.84/16.20 (funcext2) =>
% 122.84/16.20 ((
% 122.84/16.20 (ap2apEq1) =>
% 122.84/16.20 ((
% 122.84/16.20 (ap2apEq2) =>
% 122.84/16.20 ((
% 122.84/16.20 (beta1) =>
% 122.84/16.20 ((
% 122.84/16.20 (eta1) =>
% 122.84/16.20 ((
% 122.84/16.20 (lam2lamEq) =>
% 122.84/16.20 ((
% 122.84/16.20 (beta2) =>
% 122.84/16.20 ((
% 122.84/16.20 (eta2) =>
% 122.84/16.20 ((
% 122.84/16.20 (iffalseProp1) =>
% 122.84/16.20 ((
% 122.84/16.20 (iffalseProp2) =>
% 122.84/16.20 ((
% 122.84/16.20 (iftrueProp1) =>
% 122.84/16.20 ((
% 122.84/16.20 (iftrueProp2) =>
% 122.84/16.20 ((
% 122.84/16.20 (ifSingleton) =>
% 122.84/16.20 ((
% 122.84/16.20 (ifp) =>
% 122.84/16.20 ((
% 122.84/16.20 (theeq) =>
% 122.84/16.20 ((
% 122.84/16.20 (iftrue) =>
% 122.84/16.20 ((
% 122.84/16.20 (iffalse) =>
% 122.84/16.20 ((
% 122.84/16.20 (iftrueorfalse) =>
% 122.84/16.20 ((
% 122.84/16.20 (binintersectT_lem) =>
% 122.84/16.20 ((
% 122.84/16.20 (binunionT_lem) =>
% 122.84/16.20 ((
% 122.84/16.20 (powersetT_lem) =>
% 122.84/16.20 ((
% 122.84/16.20 (setminusT_lem) =>
% 122.84/16.20 ((
% 122.84/16.20 (complementT_lem) =>
% 122.84/16.20 ((
% 122.84/16.20 (setextT) =>
% 122.84/16.20 ((
% 122.84/16.20 (subsetTI) =>
% 122.84/16.20 ((
% 122.84/16.20 (powersetTI1) =>
% 122.84/16.20 ((
% 122.84/16.20 (powersetTE1) =>
% 122.84/16.20 ((
% 122.84/16.20 (complementTI1) =>
% 122.84/16.20 ((
% 122.84/16.20 (complementTE1) =>
% 122.84/16.20 ((
% 122.84/16.20 (binintersectTELcontra) =>
% 122.84/16.20 ((
% 122.84/16.20 (binintersectTERcontra) =>
% 122.84/16.20 ((
% 122.84/16.20 (contrasubsetT) =>
% 122.84/16.20 ((
% 122.84/16.20 (contrasubsetT1) =>
% 122.84/16.20 ((
% 122.84/16.20 (contrasubsetT2) =>
% 122.84/16.20 ((
% 122.84/16.20 (contrasubsetT3) =>
% 122.84/16.20 ((
% 122.84/16.20 (doubleComplementI1) =>
% 122.84/16.20 ((
% 122.84/16.20 (doubleComplementE1) =>
% 122.84/16.20 ((
% 122.84/16.20 (doubleComplementSub1) =>
% 122.84/16.20 ((
% 122.84/16.20 (doubleComplementSub2) =>
% 122.84/16.20 ((
% 122.84/16.20 (doubleComplementEq) =>
% 122.84/16.20 ((
% 122.84/16.20 (complementTnotintersectT) =>
% 122.84/16.20 ((
% 122.84/16.20 (complementImpComplementIntersect) =>
% 122.84/16.20 ((
% 122.84/16.20 (complementSubsetComplementIntersect) =>
% 122.84/16.20 ((
% 122.84/16.20 (complementInPowersetComplementIntersect) =>
% 122.84/16.20 ((
% 122.84/16.20 (contraSubsetComplement) =>
% 122.84/16.20 ((
% 122.84/16.20 (complementTcontraSubset) =>
% 122.84/16.20 ((
% 122.84/16.20 (binunionTILcontra) =>
% 122.84/16.20 ((
% 122.84/16.20 (binunionTIRcontra) =>
% 122.84/16.20 ((
% 122.84/16.20 (inIntersectImpInUnion) =>
% 122.84/16.20 ((
% 122.84/16.20 (inIntersectImpInUnion2) =>
% 122.84/16.20 ((
% 122.84/16.20 (inIntersectImpInIntersectUnions) =>
% 122.84/16.20 ((
% 122.84/16.20 (intersectInPowersetIntersectUnions) =>
% 122.84/16.20 ((
% 122.84/16.20 (inComplementUnionImpNotIn1) =>
% 122.84/16.20 ((
% 122.84/16.20 (inComplementUnionImpInComplement1) =>
% 122.84/16.20 ((
% 122.84/16.20 (binunionTE) =>
% 122.84/16.20 ((
% 122.84/16.20 (binunionTEcontra) =>
% 122.84/16.20 ((
% 122.84/16.20 (demorgan2a1) =>
% 122.84/16.20 ((
% 122.84/16.20 (complementUnionInPowersetComplement) =>
% 122.84/16.20 ((
% 122.84/16.20 (demorgan2a2) =>
% 122.84/16.20 ((
% 122.84/16.20 (demorgan1a) =>
% 122.84/16.20 ((
% 122.84/16.20 (demorgan1b) =>
% 122.84/16.20 ((
% 122.84/16.20 (demorgan1) =>
% 122.84/16.20 ((
% 122.84/16.20 (demorgan2a) =>
% 122.84/16.20 ((
% 122.84/16.20 (demorgan2b2) =>
% 122.84/16.20 ((
% 122.84/16.20 (demorgan2b) =>
% 122.84/16.20 ((
% 122.84/16.20 (demorgan2) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz13rule0) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz13rule1) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz13rule2) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz13rule3) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz13rule4) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz1_1) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz1_2) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz1_3) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz1_4) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz1_5) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1all2) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1SetBreln1) =>
% 122.84/16.20 ((
% 122.84/16.20 (choice2fnsingleton) =>
% 122.84/16.20 ((
% 122.84/16.20 (setOfPairsIsBReln1) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1all1) =>
% 122.84/16.20 ((
% 122.84/16.20 (subbreln1) =>
% 122.84/16.20 ((
% 122.84/16.20 (eqbreln1) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1invprop) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1invI) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1invE) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1compprop) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1compI) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1compE) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1compEex) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1unionprop) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1unionIL) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1unionIR) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1unionI) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1unionE) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1unionEcases) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1unionCommutes) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz2Ex) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz2W) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz2A) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz2B) =>
% 122.84/16.20 ((
% 122.84/16.20 (image1Ex) =>
% 122.84/16.20 ((
% 122.84/16.20 (image1Ex1) =>
% 122.84/16.20 ((
% 122.84/16.20 (image1Equiv) =>
% 122.84/16.20 ((
% 122.84/16.20 (image1E) =>
% 122.84/16.20 ((
% 122.84/16.20 (image1I) =>
% 122.84/16.20 ((
% 122.84/16.20 (injFuncInInjFuncSet) =>
% 122.84/16.20 ((
% 122.84/16.20 (!!) @ (
% 122.84/16.20 (('#B') @ (
% 122.84/16.20 !!) @
% 122.84/16.20 (
% 122.84/16.20 (
% 122.84/16.20 ('#B') @ (
% 122.84/16.20 (
% 122.84/16.20 ('#B') @ (
% 122.84/16.20 !!))) @
% 122.84/16.20 (
% 122.84/16.20 (
% 122.84/16.20 ('#S') @ (
% 122.84/16.20 (
% 122.84/16.20 ('#B') @ (
% 122.84/16.20 '#S') @
% 122.84/16.20 (
% 122.84/16.20 (
% 122.84/16.20 ('#B') @ (
% 122.84/16.20 (
% 122.84/16.20 ('#B') @ (
% 122.84/16.20 '#S'))) @
% 122.84/16.20 (
% 122.84/16.20 (
% 122.84/16.20 ('#B') @ (
% 122.84/16.20 (
% 122.84/16.20 ('#B') @ (
% 122.84/16.20 (
% 122.84/16.20 ('#B') @ (
% 122.84/16.20 =>))))) @
% 122.84/16.20 (
% 122.84/16.20 (
% 122.84/16.20 ('#B') @ (
% 122.84/16.20 (
% 122.84/16.20 ('#B') @ (
% 122.84/16.20 (
% 122.84/16.20 ('#C') @ in)))) @
% 122.84/16.20 injFuncSet)))))))) @
% 122.84/16.20 (
% 122.84/16.20 (
% 122.84/16.20 ('#B') @ (
% 122.84/16.20 (
% 122.84/16.20 ('#B') @ (
% 122.84/16.20 (
% 122.84/16.20 ('#C') @ in)))) @
% 122.84/16.20 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.84/16.20 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1591])).
% 122.84/16.20 thf(zip_derived_cl1607, plain,
% 122.84/16.20 (~ (((setukpairinjL1) =>
% 122.84/16.20 (((kfstsingleton) =>
% 122.84/16.20 (((theprop) =>
% 122.84/16.20 (((kfstpairEq) =>
% 122.84/16.20 (((cartprodfstin) =>
% 122.84/16.20 (((setukpairinjL2) =>
% 122.84/16.20 (((setukpairinjL) =>
% 122.84/16.20 (((setukpairinjR11) =>
% 122.84/16.20 (((setukpairinjR12) =>
% 122.84/16.20 (((setukpairinjR1) =>
% 122.84/16.20 (((upairequniteq) =>
% 122.84/16.20 (((setukpairinjR2) =>
% 122.84/16.20 (((setukpairinjR) =>
% 122.84/16.20 (((ksndsingleton) =>
% 122.84/16.20 (((ksndpairEq) =>
% 122.84/16.20 (((kpairsurjEq) =>
% 122.84/16.20 (((cartprodsndin) =>
% 122.84/16.20 (((cartprodpairmemEL) =>
% 122.84/16.20 (((cartprodpairmemER) =>
% 122.84/16.20 (((cartprodmempaircEq) =>
% 122.84/16.20 (((cartprodfstpairEq) =>
% 122.84/16.20 (((cartprodsndpairEq) =>
% 122.84/16.20 (((cartprodpairsurjEq) =>
% 122.84/16.20 (((dpsetconstrI) =>
% 122.84/16.20 (((dpsetconstrSub) =>
% 122.84/16.20 (((setOfPairsIsBReln) =>
% 122.84/16.20 (((dpsetconstrERa) =>
% 122.84/16.20 (((dpsetconstrEL1) =>
% 122.84/16.20 (((dpsetconstrEL2) =>
% 122.84/16.20 (((dpsetconstrER) =>
% 122.84/16.20 ((
% 122.84/16.20 (funcImageSingleton) =>
% 122.84/16.20 ((
% 122.84/16.20 (apProp) =>
% 122.84/16.20 ((
% 122.84/16.20 (app) =>
% 122.84/16.20 ((
% 122.84/16.20 (infuncsetfunc) =>
% 122.84/16.20 ((
% 122.84/16.20 (ap2p) =>
% 122.84/16.20 ((
% 122.84/16.20 (funcinfuncset) =>
% 122.84/16.20 ((
% 122.84/16.20 (lamProp) =>
% 122.84/16.20 ((
% 122.84/16.20 (lamp) =>
% 122.84/16.20 ((
% 122.84/16.20 (lam2p) =>
% 122.84/16.20 ((
% 122.84/16.20 (brelnall1) =>
% 122.84/16.20 ((
% 122.84/16.20 (brelnall2) =>
% 122.84/16.20 ((
% 122.84/16.20 (ex1E2) =>
% 122.84/16.20 ((
% 122.84/16.20 (funcGraphProp1) =>
% 122.84/16.20 ((
% 122.84/16.20 (funcGraphProp3) =>
% 122.84/16.20 ((
% 122.84/16.20 (funcGraphProp2) =>
% 122.84/16.20 ((
% 122.84/16.20 (funcextLem) =>
% 122.84/16.20 ((
% 122.84/16.20 (funcGraphProp4) =>
% 122.84/16.20 ((
% 122.84/16.20 (subbreln) =>
% 122.84/16.20 ((
% 122.84/16.20 (eqbreln) =>
% 122.84/16.20 ((
% 122.84/16.20 (funcext) =>
% 122.84/16.20 ((
% 122.84/16.20 (funcext2) =>
% 122.84/16.20 ((
% 122.84/16.20 (ap2apEq1) =>
% 122.84/16.20 ((
% 122.84/16.20 (ap2apEq2) =>
% 122.84/16.20 ((
% 122.84/16.20 (beta1) =>
% 122.84/16.20 ((
% 122.84/16.20 (eta1) =>
% 122.84/16.20 ((
% 122.84/16.20 (lam2lamEq) =>
% 122.84/16.20 ((
% 122.84/16.20 (beta2) =>
% 122.84/16.20 ((
% 122.84/16.20 (eta2) =>
% 122.84/16.20 ((
% 122.84/16.20 (iffalseProp1) =>
% 122.84/16.20 ((
% 122.84/16.20 (iffalseProp2) =>
% 122.84/16.20 ((
% 122.84/16.20 (iftrueProp1) =>
% 122.84/16.20 ((
% 122.84/16.20 (iftrueProp2) =>
% 122.84/16.20 ((
% 122.84/16.20 (ifSingleton) =>
% 122.84/16.20 ((
% 122.84/16.20 (ifp) =>
% 122.84/16.20 ((
% 122.84/16.20 (theeq) =>
% 122.84/16.20 ((
% 122.84/16.20 (iftrue) =>
% 122.84/16.20 ((
% 122.84/16.20 (iffalse) =>
% 122.84/16.20 ((
% 122.84/16.20 (iftrueorfalse) =>
% 122.84/16.20 ((
% 122.84/16.20 (binintersectT_lem) =>
% 122.84/16.20 ((
% 122.84/16.20 (binunionT_lem) =>
% 122.84/16.20 ((
% 122.84/16.20 (powersetT_lem) =>
% 122.84/16.20 ((
% 122.84/16.20 (setminusT_lem) =>
% 122.84/16.20 ((
% 122.84/16.20 (complementT_lem) =>
% 122.84/16.20 ((
% 122.84/16.20 (setextT) =>
% 122.84/16.20 ((
% 122.84/16.20 (subsetTI) =>
% 122.84/16.20 ((
% 122.84/16.20 (powersetTI1) =>
% 122.84/16.20 ((
% 122.84/16.20 (powersetTE1) =>
% 122.84/16.20 ((
% 122.84/16.20 (complementTI1) =>
% 122.84/16.20 ((
% 122.84/16.20 (complementTE1) =>
% 122.84/16.20 ((
% 122.84/16.20 (binintersectTELcontra) =>
% 122.84/16.20 ((
% 122.84/16.20 (binintersectTERcontra) =>
% 122.84/16.20 ((
% 122.84/16.20 (contrasubsetT) =>
% 122.84/16.20 ((
% 122.84/16.20 (contrasubsetT1) =>
% 122.84/16.20 ((
% 122.84/16.20 (contrasubsetT2) =>
% 122.84/16.20 ((
% 122.84/16.20 (contrasubsetT3) =>
% 122.84/16.20 ((
% 122.84/16.20 (doubleComplementI1) =>
% 122.84/16.20 ((
% 122.84/16.20 (doubleComplementE1) =>
% 122.84/16.20 ((
% 122.84/16.20 (doubleComplementSub1) =>
% 122.84/16.20 ((
% 122.84/16.20 (doubleComplementSub2) =>
% 122.84/16.20 ((
% 122.84/16.20 (doubleComplementEq) =>
% 122.84/16.20 ((
% 122.84/16.20 (complementTnotintersectT) =>
% 122.84/16.20 ((
% 122.84/16.20 (complementImpComplementIntersect) =>
% 122.84/16.20 ((
% 122.84/16.20 (complementSubsetComplementIntersect) =>
% 122.84/16.20 ((
% 122.84/16.20 (complementInPowersetComplementIntersect) =>
% 122.84/16.20 ((
% 122.84/16.20 (contraSubsetComplement) =>
% 122.84/16.20 ((
% 122.84/16.20 (complementTcontraSubset) =>
% 122.84/16.20 ((
% 122.84/16.20 (binunionTILcontra) =>
% 122.84/16.20 ((
% 122.84/16.20 (binunionTIRcontra) =>
% 122.84/16.20 ((
% 122.84/16.20 (inIntersectImpInUnion) =>
% 122.84/16.20 ((
% 122.84/16.20 (inIntersectImpInUnion2) =>
% 122.84/16.20 ((
% 122.84/16.20 (inIntersectImpInIntersectUnions) =>
% 122.84/16.20 ((
% 122.84/16.20 (intersectInPowersetIntersectUnions) =>
% 122.84/16.20 ((
% 122.84/16.20 (inComplementUnionImpNotIn1) =>
% 122.84/16.20 ((
% 122.84/16.20 (inComplementUnionImpInComplement1) =>
% 122.84/16.20 ((
% 122.84/16.20 (binunionTE) =>
% 122.84/16.20 ((
% 122.84/16.20 (binunionTEcontra) =>
% 122.84/16.20 ((
% 122.84/16.20 (demorgan2a1) =>
% 122.84/16.20 ((
% 122.84/16.20 (complementUnionInPowersetComplement) =>
% 122.84/16.20 ((
% 122.84/16.20 (demorgan2a2) =>
% 122.84/16.20 ((
% 122.84/16.20 (demorgan1a) =>
% 122.84/16.20 ((
% 122.84/16.20 (demorgan1b) =>
% 122.84/16.20 ((
% 122.84/16.20 (demorgan1) =>
% 122.84/16.20 ((
% 122.84/16.20 (demorgan2a) =>
% 122.84/16.20 ((
% 122.84/16.20 (demorgan2b2) =>
% 122.84/16.20 ((
% 122.84/16.20 (demorgan2b) =>
% 122.84/16.20 ((
% 122.84/16.20 (demorgan2) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz13rule0) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz13rule1) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz13rule2) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz13rule3) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz13rule4) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz1_1) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz1_2) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz1_3) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz1_4) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz1_5) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1all2) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1SetBreln1) =>
% 122.84/16.20 ((
% 122.84/16.20 (choice2fnsingleton) =>
% 122.84/16.20 ((
% 122.84/16.20 (setOfPairsIsBReln1) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1all1) =>
% 122.84/16.20 ((
% 122.84/16.20 (subbreln1) =>
% 122.84/16.20 ((
% 122.84/16.20 (eqbreln1) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1invprop) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1invI) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1invE) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1compprop) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1compI) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1compE) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1compEex) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1unionprop) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1unionIL) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1unionIR) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1unionI) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1unionE) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1unionEcases) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1unionCommutes) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz2Ex) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz2W) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz2A) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz2B) =>
% 122.84/16.20 ((
% 122.84/16.20 (image1Ex) =>
% 122.84/16.20 ((
% 122.84/16.20 (image1Ex1) =>
% 122.84/16.20 ((
% 122.84/16.20 (image1Equiv) =>
% 122.84/16.20 ((
% 122.84/16.20 (image1E) =>
% 122.84/16.20 ((
% 122.84/16.20 (image1I) =>
% 122.84/16.20 ((
% 122.84/16.20 (injFuncInInjFuncSet) =>
% 122.84/16.20 ((
% 122.84/16.20 (!!) @ (
% 122.84/16.20 (('#B') @ (
% 122.84/16.20 !!) @
% 122.84/16.20 (
% 122.84/16.20 (
% 122.84/16.20 ('#B') @ (
% 122.84/16.20 (
% 122.84/16.20 ('#B') @ (
% 122.84/16.20 !!))) @
% 122.84/16.20 (
% 122.84/16.20 (
% 122.84/16.20 ('#S') @ (
% 122.84/16.20 (
% 122.84/16.20 ('#B') @ (
% 122.84/16.20 '#S') @
% 122.84/16.20 (
% 122.84/16.20 (
% 122.84/16.20 ('#B') @ (
% 122.84/16.20 (
% 122.84/16.20 ('#B') @ (
% 122.84/16.20 '#S'))) @
% 122.84/16.20 (
% 122.84/16.20 (
% 122.84/16.20 ('#B') @ (
% 122.84/16.20 (
% 122.84/16.20 ('#B') @ (
% 122.84/16.20 (
% 122.84/16.20 ('#B') @ (
% 122.84/16.20 =>))))) @
% 122.84/16.20 (
% 122.84/16.20 (
% 122.84/16.20 ('#B') @ (
% 122.84/16.20 (
% 122.84/16.20 ('#B') @ (
% 122.84/16.20 (
% 122.84/16.20 ('#C') @ in)))) @
% 122.84/16.20 injFuncSet)))))))) @
% 122.84/16.20 (
% 122.84/16.20 (
% 122.84/16.20 ('#B') @ (
% 122.84/16.20 (
% 122.84/16.20 ('#B') @ (
% 122.84/16.20 (
% 122.84/16.20 ('#C') @ in)))) @
% 122.84/16.20 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.84/16.20 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1599])).
% 122.84/16.20 thf(zip_derived_cl1615, plain,
% 122.84/16.20 (~ (((kfstsingleton) =>
% 122.84/16.20 (((theprop) =>
% 122.84/16.20 (((kfstpairEq) =>
% 122.84/16.20 (((cartprodfstin) =>
% 122.84/16.20 (((setukpairinjL2) =>
% 122.84/16.20 (((setukpairinjL) =>
% 122.84/16.20 (((setukpairinjR11) =>
% 122.84/16.20 (((setukpairinjR12) =>
% 122.84/16.20 (((setukpairinjR1) =>
% 122.84/16.20 (((upairequniteq) =>
% 122.84/16.20 (((setukpairinjR2) =>
% 122.84/16.20 (((setukpairinjR) =>
% 122.84/16.20 (((ksndsingleton) =>
% 122.84/16.20 (((ksndpairEq) =>
% 122.84/16.20 (((kpairsurjEq) =>
% 122.84/16.20 (((cartprodsndin) =>
% 122.84/16.20 (((cartprodpairmemEL) =>
% 122.84/16.20 (((cartprodpairmemER) =>
% 122.84/16.20 (((cartprodmempaircEq) =>
% 122.84/16.20 (((cartprodfstpairEq) =>
% 122.84/16.20 (((cartprodsndpairEq) =>
% 122.84/16.20 (((cartprodpairsurjEq) =>
% 122.84/16.20 (((dpsetconstrI) =>
% 122.84/16.20 (((dpsetconstrSub) =>
% 122.84/16.20 (((setOfPairsIsBReln) =>
% 122.84/16.20 (((dpsetconstrERa) =>
% 122.84/16.20 (((dpsetconstrEL1) =>
% 122.84/16.20 (((dpsetconstrEL2) =>
% 122.84/16.20 (((dpsetconstrER) =>
% 122.84/16.20 (((funcImageSingleton) =>
% 122.84/16.20 ((
% 122.84/16.20 (apProp) =>
% 122.84/16.20 ((
% 122.84/16.20 (app) =>
% 122.84/16.20 ((
% 122.84/16.20 (infuncsetfunc) =>
% 122.84/16.20 ((
% 122.84/16.20 (ap2p) =>
% 122.84/16.20 ((
% 122.84/16.20 (funcinfuncset) =>
% 122.84/16.20 ((
% 122.84/16.20 (lamProp) =>
% 122.84/16.20 ((
% 122.84/16.20 (lamp) =>
% 122.84/16.20 ((
% 122.84/16.20 (lam2p) =>
% 122.84/16.20 ((
% 122.84/16.20 (brelnall1) =>
% 122.84/16.20 ((
% 122.84/16.20 (brelnall2) =>
% 122.84/16.20 ((
% 122.84/16.20 (ex1E2) =>
% 122.84/16.20 ((
% 122.84/16.20 (funcGraphProp1) =>
% 122.84/16.20 ((
% 122.84/16.20 (funcGraphProp3) =>
% 122.84/16.20 ((
% 122.84/16.20 (funcGraphProp2) =>
% 122.84/16.20 ((
% 122.84/16.20 (funcextLem) =>
% 122.84/16.20 ((
% 122.84/16.20 (funcGraphProp4) =>
% 122.84/16.20 ((
% 122.84/16.20 (subbreln) =>
% 122.84/16.20 ((
% 122.84/16.20 (eqbreln) =>
% 122.84/16.20 ((
% 122.84/16.20 (funcext) =>
% 122.84/16.20 ((
% 122.84/16.20 (funcext2) =>
% 122.84/16.20 ((
% 122.84/16.20 (ap2apEq1) =>
% 122.84/16.20 ((
% 122.84/16.20 (ap2apEq2) =>
% 122.84/16.20 ((
% 122.84/16.20 (beta1) =>
% 122.84/16.20 ((
% 122.84/16.20 (eta1) =>
% 122.84/16.20 ((
% 122.84/16.20 (lam2lamEq) =>
% 122.84/16.20 ((
% 122.84/16.20 (beta2) =>
% 122.84/16.20 ((
% 122.84/16.20 (eta2) =>
% 122.84/16.20 ((
% 122.84/16.20 (iffalseProp1) =>
% 122.84/16.20 ((
% 122.84/16.20 (iffalseProp2) =>
% 122.84/16.20 ((
% 122.84/16.20 (iftrueProp1) =>
% 122.84/16.20 ((
% 122.84/16.20 (iftrueProp2) =>
% 122.84/16.20 ((
% 122.84/16.20 (ifSingleton) =>
% 122.84/16.20 ((
% 122.84/16.20 (ifp) =>
% 122.84/16.20 ((
% 122.84/16.20 (theeq) =>
% 122.84/16.20 ((
% 122.84/16.20 (iftrue) =>
% 122.84/16.20 ((
% 122.84/16.20 (iffalse) =>
% 122.84/16.20 ((
% 122.84/16.20 (iftrueorfalse) =>
% 122.84/16.20 ((
% 122.84/16.20 (binintersectT_lem) =>
% 122.84/16.20 ((
% 122.84/16.20 (binunionT_lem) =>
% 122.84/16.20 ((
% 122.84/16.20 (powersetT_lem) =>
% 122.84/16.20 ((
% 122.84/16.20 (setminusT_lem) =>
% 122.84/16.20 ((
% 122.84/16.20 (complementT_lem) =>
% 122.84/16.20 ((
% 122.84/16.20 (setextT) =>
% 122.84/16.20 ((
% 122.84/16.20 (subsetTI) =>
% 122.84/16.20 ((
% 122.84/16.20 (powersetTI1) =>
% 122.84/16.20 ((
% 122.84/16.20 (powersetTE1) =>
% 122.84/16.20 ((
% 122.84/16.20 (complementTI1) =>
% 122.84/16.20 ((
% 122.84/16.20 (complementTE1) =>
% 122.84/16.20 ((
% 122.84/16.20 (binintersectTELcontra) =>
% 122.84/16.20 ((
% 122.84/16.20 (binintersectTERcontra) =>
% 122.84/16.20 ((
% 122.84/16.20 (contrasubsetT) =>
% 122.84/16.20 ((
% 122.84/16.20 (contrasubsetT1) =>
% 122.84/16.20 ((
% 122.84/16.20 (contrasubsetT2) =>
% 122.84/16.20 ((
% 122.84/16.20 (contrasubsetT3) =>
% 122.84/16.20 ((
% 122.84/16.20 (doubleComplementI1) =>
% 122.84/16.20 ((
% 122.84/16.20 (doubleComplementE1) =>
% 122.84/16.20 ((
% 122.84/16.20 (doubleComplementSub1) =>
% 122.84/16.20 ((
% 122.84/16.20 (doubleComplementSub2) =>
% 122.84/16.20 ((
% 122.84/16.20 (doubleComplementEq) =>
% 122.84/16.20 ((
% 122.84/16.20 (complementTnotintersectT) =>
% 122.84/16.20 ((
% 122.84/16.20 (complementImpComplementIntersect) =>
% 122.84/16.20 ((
% 122.84/16.20 (complementSubsetComplementIntersect) =>
% 122.84/16.20 ((
% 122.84/16.20 (complementInPowersetComplementIntersect) =>
% 122.84/16.20 ((
% 122.84/16.20 (contraSubsetComplement) =>
% 122.84/16.20 ((
% 122.84/16.20 (complementTcontraSubset) =>
% 122.84/16.20 ((
% 122.84/16.20 (binunionTILcontra) =>
% 122.84/16.20 ((
% 122.84/16.20 (binunionTIRcontra) =>
% 122.84/16.20 ((
% 122.84/16.20 (inIntersectImpInUnion) =>
% 122.84/16.20 ((
% 122.84/16.20 (inIntersectImpInUnion2) =>
% 122.84/16.20 ((
% 122.84/16.20 (inIntersectImpInIntersectUnions) =>
% 122.84/16.20 ((
% 122.84/16.20 (intersectInPowersetIntersectUnions) =>
% 122.84/16.20 ((
% 122.84/16.20 (inComplementUnionImpNotIn1) =>
% 122.84/16.20 ((
% 122.84/16.20 (inComplementUnionImpInComplement1) =>
% 122.84/16.20 ((
% 122.84/16.20 (binunionTE) =>
% 122.84/16.20 ((
% 122.84/16.20 (binunionTEcontra) =>
% 122.84/16.20 ((
% 122.84/16.20 (demorgan2a1) =>
% 122.84/16.20 ((
% 122.84/16.20 (complementUnionInPowersetComplement) =>
% 122.84/16.20 ((
% 122.84/16.20 (demorgan2a2) =>
% 122.84/16.20 ((
% 122.84/16.20 (demorgan1a) =>
% 122.84/16.20 ((
% 122.84/16.20 (demorgan1b) =>
% 122.84/16.20 ((
% 122.84/16.20 (demorgan1) =>
% 122.84/16.20 ((
% 122.84/16.20 (demorgan2a) =>
% 122.84/16.20 ((
% 122.84/16.20 (demorgan2b2) =>
% 122.84/16.20 ((
% 122.84/16.20 (demorgan2b) =>
% 122.84/16.20 ((
% 122.84/16.20 (demorgan2) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz13rule0) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz13rule1) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz13rule2) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz13rule3) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz13rule4) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz1_1) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz1_2) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz1_3) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz1_4) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz1_5) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1all2) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1SetBreln1) =>
% 122.84/16.20 ((
% 122.84/16.20 (choice2fnsingleton) =>
% 122.84/16.20 ((
% 122.84/16.20 (setOfPairsIsBReln1) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1all1) =>
% 122.84/16.20 ((
% 122.84/16.20 (subbreln1) =>
% 122.84/16.20 ((
% 122.84/16.20 (eqbreln1) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1invprop) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1invI) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1invE) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1compprop) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1compI) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1compE) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1compEex) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1unionprop) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1unionIL) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1unionIR) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1unionI) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1unionE) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1unionEcases) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1unionCommutes) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz2Ex) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz2W) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz2A) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz2B) =>
% 122.84/16.20 ((
% 122.84/16.20 (image1Ex) =>
% 122.84/16.20 ((
% 122.84/16.20 (image1Ex1) =>
% 122.84/16.20 ((
% 122.84/16.20 (image1Equiv) =>
% 122.84/16.20 ((
% 122.84/16.20 (image1E) =>
% 122.84/16.20 ((
% 122.84/16.20 (image1I) =>
% 122.84/16.20 ((
% 122.84/16.20 (injFuncInInjFuncSet) =>
% 122.84/16.20 ((
% 122.84/16.20 (!!) @ (
% 122.84/16.20 (('#B') @ (
% 122.84/16.20 !!) @
% 122.84/16.20 (
% 122.84/16.20 (
% 122.84/16.20 ('#B') @ (
% 122.84/16.20 (
% 122.84/16.20 ('#B') @ (
% 122.84/16.20 !!))) @
% 122.84/16.20 (
% 122.84/16.20 (
% 122.84/16.20 ('#S') @ (
% 122.84/16.20 (
% 122.84/16.20 ('#B') @ (
% 122.84/16.20 '#S') @
% 122.84/16.20 (
% 122.84/16.20 (
% 122.84/16.20 ('#B') @ (
% 122.84/16.20 (
% 122.84/16.20 ('#B') @ (
% 122.84/16.20 '#S'))) @
% 122.84/16.20 (
% 122.84/16.20 (
% 122.84/16.20 ('#B') @ (
% 122.84/16.20 (
% 122.84/16.20 ('#B') @ (
% 122.84/16.20 (
% 122.84/16.20 ('#B') @ (
% 122.84/16.20 =>))))) @
% 122.84/16.20 (
% 122.84/16.20 (
% 122.84/16.20 ('#B') @ (
% 122.84/16.20 (
% 122.84/16.20 ('#B') @ (
% 122.84/16.20 (
% 122.84/16.20 ('#C') @ in)))) @
% 122.84/16.20 injFuncSet)))))))) @
% 122.84/16.20 (
% 122.84/16.20 (
% 122.84/16.20 ('#B') @ (
% 122.84/16.20 (
% 122.84/16.20 ('#B') @ (
% 122.84/16.20 (
% 122.84/16.20 ('#C') @ in)))) @
% 122.84/16.20 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.84/16.20 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1607])).
% 122.84/16.20 thf(zip_derived_cl1625, plain,
% 122.84/16.20 (~ (((theprop) =>
% 122.84/16.20 (((kfstpairEq) =>
% 122.84/16.20 (((cartprodfstin) =>
% 122.84/16.20 (((setukpairinjL2) =>
% 122.84/16.20 (((setukpairinjL) =>
% 122.84/16.20 (((setukpairinjR11) =>
% 122.84/16.20 (((setukpairinjR12) =>
% 122.84/16.20 (((setukpairinjR1) =>
% 122.84/16.20 (((upairequniteq) =>
% 122.84/16.20 (((setukpairinjR2) =>
% 122.84/16.20 (((setukpairinjR) =>
% 122.84/16.20 (((ksndsingleton) =>
% 122.84/16.20 (((ksndpairEq) =>
% 122.84/16.20 (((kpairsurjEq) =>
% 122.84/16.20 (((cartprodsndin) =>
% 122.84/16.20 (((cartprodpairmemEL) =>
% 122.84/16.20 (((cartprodpairmemER) =>
% 122.84/16.20 (((cartprodmempaircEq) =>
% 122.84/16.20 (((cartprodfstpairEq) =>
% 122.84/16.20 (((cartprodsndpairEq) =>
% 122.84/16.20 (((cartprodpairsurjEq) =>
% 122.84/16.20 (((dpsetconstrI) =>
% 122.84/16.20 (((dpsetconstrSub) =>
% 122.84/16.20 (((setOfPairsIsBReln) =>
% 122.84/16.20 (((dpsetconstrERa) =>
% 122.84/16.20 (((dpsetconstrEL1) =>
% 122.84/16.20 (((dpsetconstrEL2) =>
% 122.84/16.20 (((dpsetconstrER) =>
% 122.84/16.20 (((funcImageSingleton) =>
% 122.84/16.20 (((apProp) =>
% 122.84/16.20 ((
% 122.84/16.20 (app) =>
% 122.84/16.20 ((
% 122.84/16.20 (infuncsetfunc) =>
% 122.84/16.20 ((
% 122.84/16.20 (ap2p) =>
% 122.84/16.20 ((
% 122.84/16.20 (funcinfuncset) =>
% 122.84/16.20 ((
% 122.84/16.20 (lamProp) =>
% 122.84/16.20 ((
% 122.84/16.20 (lamp) =>
% 122.84/16.20 ((
% 122.84/16.20 (lam2p) =>
% 122.84/16.20 ((
% 122.84/16.20 (brelnall1) =>
% 122.84/16.20 ((
% 122.84/16.20 (brelnall2) =>
% 122.84/16.20 ((
% 122.84/16.20 (ex1E2) =>
% 122.84/16.20 ((
% 122.84/16.20 (funcGraphProp1) =>
% 122.84/16.20 ((
% 122.84/16.20 (funcGraphProp3) =>
% 122.84/16.20 ((
% 122.84/16.20 (funcGraphProp2) =>
% 122.84/16.20 ((
% 122.84/16.20 (funcextLem) =>
% 122.84/16.20 ((
% 122.84/16.20 (funcGraphProp4) =>
% 122.84/16.20 ((
% 122.84/16.20 (subbreln) =>
% 122.84/16.20 ((
% 122.84/16.20 (eqbreln) =>
% 122.84/16.20 ((
% 122.84/16.20 (funcext) =>
% 122.84/16.20 ((
% 122.84/16.20 (funcext2) =>
% 122.84/16.20 ((
% 122.84/16.20 (ap2apEq1) =>
% 122.84/16.20 ((
% 122.84/16.20 (ap2apEq2) =>
% 122.84/16.20 ((
% 122.84/16.20 (beta1) =>
% 122.84/16.20 ((
% 122.84/16.20 (eta1) =>
% 122.84/16.20 ((
% 122.84/16.20 (lam2lamEq) =>
% 122.84/16.20 ((
% 122.84/16.20 (beta2) =>
% 122.84/16.20 ((
% 122.84/16.20 (eta2) =>
% 122.84/16.20 ((
% 122.84/16.20 (iffalseProp1) =>
% 122.84/16.20 ((
% 122.84/16.20 (iffalseProp2) =>
% 122.84/16.20 ((
% 122.84/16.20 (iftrueProp1) =>
% 122.84/16.20 ((
% 122.84/16.20 (iftrueProp2) =>
% 122.84/16.20 ((
% 122.84/16.20 (ifSingleton) =>
% 122.84/16.20 ((
% 122.84/16.20 (ifp) =>
% 122.84/16.20 ((
% 122.84/16.20 (theeq) =>
% 122.84/16.20 ((
% 122.84/16.20 (iftrue) =>
% 122.84/16.20 ((
% 122.84/16.20 (iffalse) =>
% 122.84/16.20 ((
% 122.84/16.20 (iftrueorfalse) =>
% 122.84/16.20 ((
% 122.84/16.20 (binintersectT_lem) =>
% 122.84/16.20 ((
% 122.84/16.20 (binunionT_lem) =>
% 122.84/16.20 ((
% 122.84/16.20 (powersetT_lem) =>
% 122.84/16.20 ((
% 122.84/16.20 (setminusT_lem) =>
% 122.84/16.20 ((
% 122.84/16.20 (complementT_lem) =>
% 122.84/16.20 ((
% 122.84/16.20 (setextT) =>
% 122.84/16.20 ((
% 122.84/16.20 (subsetTI) =>
% 122.84/16.20 ((
% 122.84/16.20 (powersetTI1) =>
% 122.84/16.20 ((
% 122.84/16.20 (powersetTE1) =>
% 122.84/16.20 ((
% 122.84/16.20 (complementTI1) =>
% 122.84/16.20 ((
% 122.84/16.20 (complementTE1) =>
% 122.84/16.20 ((
% 122.84/16.20 (binintersectTELcontra) =>
% 122.84/16.20 ((
% 122.84/16.20 (binintersectTERcontra) =>
% 122.84/16.20 ((
% 122.84/16.20 (contrasubsetT) =>
% 122.84/16.20 ((
% 122.84/16.20 (contrasubsetT1) =>
% 122.84/16.20 ((
% 122.84/16.20 (contrasubsetT2) =>
% 122.84/16.20 ((
% 122.84/16.20 (contrasubsetT3) =>
% 122.84/16.20 ((
% 122.84/16.20 (doubleComplementI1) =>
% 122.84/16.20 ((
% 122.84/16.20 (doubleComplementE1) =>
% 122.84/16.20 ((
% 122.84/16.20 (doubleComplementSub1) =>
% 122.84/16.20 ((
% 122.84/16.20 (doubleComplementSub2) =>
% 122.84/16.20 ((
% 122.84/16.20 (doubleComplementEq) =>
% 122.84/16.20 ((
% 122.84/16.20 (complementTnotintersectT) =>
% 122.84/16.20 ((
% 122.84/16.20 (complementImpComplementIntersect) =>
% 122.84/16.20 ((
% 122.84/16.20 (complementSubsetComplementIntersect) =>
% 122.84/16.20 ((
% 122.84/16.20 (complementInPowersetComplementIntersect) =>
% 122.84/16.20 ((
% 122.84/16.20 (contraSubsetComplement) =>
% 122.84/16.20 ((
% 122.84/16.20 (complementTcontraSubset) =>
% 122.84/16.20 ((
% 122.84/16.20 (binunionTILcontra) =>
% 122.84/16.20 ((
% 122.84/16.20 (binunionTIRcontra) =>
% 122.84/16.20 ((
% 122.84/16.20 (inIntersectImpInUnion) =>
% 122.84/16.20 ((
% 122.84/16.20 (inIntersectImpInUnion2) =>
% 122.84/16.20 ((
% 122.84/16.20 (inIntersectImpInIntersectUnions) =>
% 122.84/16.20 ((
% 122.84/16.20 (intersectInPowersetIntersectUnions) =>
% 122.84/16.20 ((
% 122.84/16.20 (inComplementUnionImpNotIn1) =>
% 122.84/16.20 ((
% 122.84/16.20 (inComplementUnionImpInComplement1) =>
% 122.84/16.20 ((
% 122.84/16.20 (binunionTE) =>
% 122.84/16.20 ((
% 122.84/16.20 (binunionTEcontra) =>
% 122.84/16.20 ((
% 122.84/16.20 (demorgan2a1) =>
% 122.84/16.20 ((
% 122.84/16.20 (complementUnionInPowersetComplement) =>
% 122.84/16.20 ((
% 122.84/16.20 (demorgan2a2) =>
% 122.84/16.20 ((
% 122.84/16.20 (demorgan1a) =>
% 122.84/16.20 ((
% 122.84/16.20 (demorgan1b) =>
% 122.84/16.20 ((
% 122.84/16.20 (demorgan1) =>
% 122.84/16.20 ((
% 122.84/16.20 (demorgan2a) =>
% 122.84/16.20 ((
% 122.84/16.20 (demorgan2b2) =>
% 122.84/16.20 ((
% 122.84/16.20 (demorgan2b) =>
% 122.84/16.20 ((
% 122.84/16.20 (demorgan2) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz13rule0) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz13rule1) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz13rule2) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz13rule3) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz13rule4) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz1_1) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz1_2) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz1_3) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz1_4) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz1_5) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1all2) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1SetBreln1) =>
% 122.84/16.20 ((
% 122.84/16.20 (choice2fnsingleton) =>
% 122.84/16.20 ((
% 122.84/16.20 (setOfPairsIsBReln1) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1all1) =>
% 122.84/16.20 ((
% 122.84/16.20 (subbreln1) =>
% 122.84/16.20 ((
% 122.84/16.20 (eqbreln1) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1invprop) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1invI) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1invE) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1compprop) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1compI) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1compE) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1compEex) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1unionprop) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1unionIL) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1unionIR) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1unionI) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1unionE) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1unionEcases) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1unionCommutes) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz2Ex) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz2W) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz2A) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz2B) =>
% 122.84/16.20 ((
% 122.84/16.20 (image1Ex) =>
% 122.84/16.20 ((
% 122.84/16.20 (image1Ex1) =>
% 122.84/16.20 ((
% 122.84/16.20 (image1Equiv) =>
% 122.84/16.20 ((
% 122.84/16.20 (image1E) =>
% 122.84/16.20 ((
% 122.84/16.20 (image1I) =>
% 122.84/16.20 ((
% 122.84/16.20 (injFuncInInjFuncSet) =>
% 122.84/16.20 ((
% 122.84/16.20 (!!) @ (
% 122.84/16.20 (('#B') @ (
% 122.84/16.20 !!) @
% 122.84/16.20 (
% 122.84/16.20 (
% 122.84/16.20 ('#B') @ (
% 122.84/16.20 (
% 122.84/16.20 ('#B') @ (
% 122.84/16.20 !!))) @
% 122.84/16.20 (
% 122.84/16.20 (
% 122.84/16.20 ('#S') @ (
% 122.84/16.20 (
% 122.84/16.20 ('#B') @ (
% 122.84/16.20 '#S') @
% 122.84/16.20 (
% 122.84/16.20 (
% 122.84/16.20 ('#B') @ (
% 122.84/16.20 (
% 122.84/16.20 ('#B') @ (
% 122.84/16.20 '#S'))) @
% 122.84/16.20 (
% 122.84/16.20 (
% 122.84/16.20 ('#B') @ (
% 122.84/16.20 (
% 122.84/16.20 ('#B') @ (
% 122.84/16.20 (
% 122.84/16.20 ('#B') @ (
% 122.84/16.20 =>))))) @
% 122.84/16.20 (
% 122.84/16.20 (
% 122.84/16.20 ('#B') @ (
% 122.84/16.20 (
% 122.84/16.20 ('#B') @ (
% 122.84/16.20 (
% 122.84/16.20 ('#C') @ in)))) @
% 122.84/16.20 injFuncSet)))))))) @
% 122.84/16.20 (
% 122.84/16.20 (
% 122.84/16.20 ('#B') @ (
% 122.84/16.20 (
% 122.84/16.20 ('#B') @ (
% 122.84/16.20 (
% 122.84/16.20 ('#C') @ in)))) @
% 122.84/16.20 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.84/16.20 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1615])).
% 122.84/16.20 thf(zip_derived_cl1637, plain,
% 122.84/16.20 (~ (((kfstpairEq) =>
% 122.84/16.20 (((cartprodfstin) =>
% 122.84/16.20 (((setukpairinjL2) =>
% 122.84/16.20 (((setukpairinjL) =>
% 122.84/16.20 (((setukpairinjR11) =>
% 122.84/16.20 (((setukpairinjR12) =>
% 122.84/16.20 (((setukpairinjR1) =>
% 122.84/16.20 (((upairequniteq) =>
% 122.84/16.20 (((setukpairinjR2) =>
% 122.84/16.20 (((setukpairinjR) =>
% 122.84/16.20 (((ksndsingleton) =>
% 122.84/16.20 (((ksndpairEq) =>
% 122.84/16.20 (((kpairsurjEq) =>
% 122.84/16.20 (((cartprodsndin) =>
% 122.84/16.20 (((cartprodpairmemEL) =>
% 122.84/16.20 (((cartprodpairmemER) =>
% 122.84/16.20 (((cartprodmempaircEq) =>
% 122.84/16.20 (((cartprodfstpairEq) =>
% 122.84/16.20 (((cartprodsndpairEq) =>
% 122.84/16.20 (((cartprodpairsurjEq) =>
% 122.84/16.20 (((dpsetconstrI) =>
% 122.84/16.20 (((dpsetconstrSub) =>
% 122.84/16.20 (((setOfPairsIsBReln) =>
% 122.84/16.20 (((dpsetconstrERa) =>
% 122.84/16.20 (((dpsetconstrEL1) =>
% 122.84/16.20 (((dpsetconstrEL2) =>
% 122.84/16.20 (((dpsetconstrER) =>
% 122.84/16.20 (((funcImageSingleton) =>
% 122.84/16.20 (((apProp) =>
% 122.84/16.20 (((app) =>
% 122.84/16.20 ((
% 122.84/16.20 (infuncsetfunc) =>
% 122.84/16.20 ((
% 122.84/16.20 (ap2p) =>
% 122.84/16.20 ((
% 122.84/16.20 (funcinfuncset) =>
% 122.84/16.20 ((
% 122.84/16.20 (lamProp) =>
% 122.84/16.20 ((
% 122.84/16.20 (lamp) =>
% 122.84/16.20 ((
% 122.84/16.20 (lam2p) =>
% 122.84/16.20 ((
% 122.84/16.20 (brelnall1) =>
% 122.84/16.20 ((
% 122.84/16.20 (brelnall2) =>
% 122.84/16.20 ((
% 122.84/16.20 (ex1E2) =>
% 122.84/16.20 ((
% 122.84/16.20 (funcGraphProp1) =>
% 122.84/16.20 ((
% 122.84/16.20 (funcGraphProp3) =>
% 122.84/16.20 ((
% 122.84/16.20 (funcGraphProp2) =>
% 122.84/16.20 ((
% 122.84/16.20 (funcextLem) =>
% 122.84/16.20 ((
% 122.84/16.20 (funcGraphProp4) =>
% 122.84/16.20 ((
% 122.84/16.20 (subbreln) =>
% 122.84/16.20 ((
% 122.84/16.20 (eqbreln) =>
% 122.84/16.20 ((
% 122.84/16.20 (funcext) =>
% 122.84/16.20 ((
% 122.84/16.20 (funcext2) =>
% 122.84/16.20 ((
% 122.84/16.20 (ap2apEq1) =>
% 122.84/16.20 ((
% 122.84/16.20 (ap2apEq2) =>
% 122.84/16.20 ((
% 122.84/16.20 (beta1) =>
% 122.84/16.20 ((
% 122.84/16.20 (eta1) =>
% 122.84/16.20 ((
% 122.84/16.20 (lam2lamEq) =>
% 122.84/16.20 ((
% 122.84/16.20 (beta2) =>
% 122.84/16.20 ((
% 122.84/16.20 (eta2) =>
% 122.84/16.20 ((
% 122.84/16.20 (iffalseProp1) =>
% 122.84/16.20 ((
% 122.84/16.20 (iffalseProp2) =>
% 122.84/16.20 ((
% 122.84/16.20 (iftrueProp1) =>
% 122.84/16.20 ((
% 122.84/16.20 (iftrueProp2) =>
% 122.84/16.20 ((
% 122.84/16.20 (ifSingleton) =>
% 122.84/16.20 ((
% 122.84/16.20 (ifp) =>
% 122.84/16.20 ((
% 122.84/16.20 (theeq) =>
% 122.84/16.20 ((
% 122.84/16.20 (iftrue) =>
% 122.84/16.20 ((
% 122.84/16.20 (iffalse) =>
% 122.84/16.20 ((
% 122.84/16.20 (iftrueorfalse) =>
% 122.84/16.20 ((
% 122.84/16.20 (binintersectT_lem) =>
% 122.84/16.20 ((
% 122.84/16.20 (binunionT_lem) =>
% 122.84/16.20 ((
% 122.84/16.20 (powersetT_lem) =>
% 122.84/16.20 ((
% 122.84/16.20 (setminusT_lem) =>
% 122.84/16.20 ((
% 122.84/16.20 (complementT_lem) =>
% 122.84/16.20 ((
% 122.84/16.20 (setextT) =>
% 122.84/16.20 ((
% 122.84/16.20 (subsetTI) =>
% 122.84/16.20 ((
% 122.84/16.20 (powersetTI1) =>
% 122.84/16.20 ((
% 122.84/16.20 (powersetTE1) =>
% 122.84/16.20 ((
% 122.84/16.20 (complementTI1) =>
% 122.84/16.20 ((
% 122.84/16.20 (complementTE1) =>
% 122.84/16.20 ((
% 122.84/16.20 (binintersectTELcontra) =>
% 122.84/16.20 ((
% 122.84/16.20 (binintersectTERcontra) =>
% 122.84/16.20 ((
% 122.84/16.20 (contrasubsetT) =>
% 122.84/16.20 ((
% 122.84/16.20 (contrasubsetT1) =>
% 122.84/16.20 ((
% 122.84/16.20 (contrasubsetT2) =>
% 122.84/16.20 ((
% 122.84/16.20 (contrasubsetT3) =>
% 122.84/16.20 ((
% 122.84/16.20 (doubleComplementI1) =>
% 122.84/16.20 ((
% 122.84/16.20 (doubleComplementE1) =>
% 122.84/16.20 ((
% 122.84/16.20 (doubleComplementSub1) =>
% 122.84/16.20 ((
% 122.84/16.20 (doubleComplementSub2) =>
% 122.84/16.20 ((
% 122.84/16.20 (doubleComplementEq) =>
% 122.84/16.20 ((
% 122.84/16.20 (complementTnotintersectT) =>
% 122.84/16.20 ((
% 122.84/16.20 (complementImpComplementIntersect) =>
% 122.84/16.20 ((
% 122.84/16.20 (complementSubsetComplementIntersect) =>
% 122.84/16.20 ((
% 122.84/16.20 (complementInPowersetComplementIntersect) =>
% 122.84/16.20 ((
% 122.84/16.20 (contraSubsetComplement) =>
% 122.84/16.20 ((
% 122.84/16.20 (complementTcontraSubset) =>
% 122.84/16.20 ((
% 122.84/16.20 (binunionTILcontra) =>
% 122.84/16.20 ((
% 122.84/16.20 (binunionTIRcontra) =>
% 122.84/16.20 ((
% 122.84/16.20 (inIntersectImpInUnion) =>
% 122.84/16.20 ((
% 122.84/16.20 (inIntersectImpInUnion2) =>
% 122.84/16.20 ((
% 122.84/16.20 (inIntersectImpInIntersectUnions) =>
% 122.84/16.20 ((
% 122.84/16.20 (intersectInPowersetIntersectUnions) =>
% 122.84/16.20 ((
% 122.84/16.20 (inComplementUnionImpNotIn1) =>
% 122.84/16.20 ((
% 122.84/16.20 (inComplementUnionImpInComplement1) =>
% 122.84/16.20 ((
% 122.84/16.20 (binunionTE) =>
% 122.84/16.20 ((
% 122.84/16.20 (binunionTEcontra) =>
% 122.84/16.20 ((
% 122.84/16.20 (demorgan2a1) =>
% 122.84/16.20 ((
% 122.84/16.20 (complementUnionInPowersetComplement) =>
% 122.84/16.20 ((
% 122.84/16.20 (demorgan2a2) =>
% 122.84/16.20 ((
% 122.84/16.20 (demorgan1a) =>
% 122.84/16.20 ((
% 122.84/16.20 (demorgan1b) =>
% 122.84/16.20 ((
% 122.84/16.20 (demorgan1) =>
% 122.84/16.20 ((
% 122.84/16.20 (demorgan2a) =>
% 122.84/16.20 ((
% 122.84/16.20 (demorgan2b2) =>
% 122.84/16.20 ((
% 122.84/16.20 (demorgan2b) =>
% 122.84/16.20 ((
% 122.84/16.20 (demorgan2) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz13rule0) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz13rule1) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz13rule2) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz13rule3) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz13rule4) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz1_1) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz1_2) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz1_3) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz1_4) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz1_5) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1all2) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1SetBreln1) =>
% 122.84/16.20 ((
% 122.84/16.20 (choice2fnsingleton) =>
% 122.84/16.20 ((
% 122.84/16.20 (setOfPairsIsBReln1) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1all1) =>
% 122.84/16.20 ((
% 122.84/16.20 (subbreln1) =>
% 122.84/16.20 ((
% 122.84/16.20 (eqbreln1) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1invprop) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1invI) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1invE) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1compprop) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1compI) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1compE) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1compEex) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1unionprop) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1unionIL) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1unionIR) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1unionI) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1unionE) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1unionEcases) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1unionCommutes) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz2Ex) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz2W) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz2A) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz2B) =>
% 122.84/16.20 ((
% 122.84/16.20 (image1Ex) =>
% 122.84/16.20 ((
% 122.84/16.20 (image1Ex1) =>
% 122.84/16.20 ((
% 122.84/16.20 (image1Equiv) =>
% 122.84/16.20 ((
% 122.84/16.20 (image1E) =>
% 122.84/16.20 ((
% 122.84/16.20 (image1I) =>
% 122.84/16.20 ((
% 122.84/16.20 (injFuncInInjFuncSet) =>
% 122.84/16.20 ((
% 122.84/16.20 (!!) @ (
% 122.84/16.20 (('#B') @ (
% 122.84/16.20 !!) @
% 122.84/16.20 (
% 122.84/16.20 (
% 122.84/16.20 ('#B') @ (
% 122.84/16.20 (
% 122.84/16.20 ('#B') @ (
% 122.84/16.20 !!))) @
% 122.84/16.20 (
% 122.84/16.20 (
% 122.84/16.20 ('#S') @ (
% 122.84/16.20 (
% 122.84/16.20 ('#B') @ (
% 122.84/16.20 '#S') @
% 122.84/16.20 (
% 122.84/16.20 (
% 122.84/16.20 ('#B') @ (
% 122.84/16.20 (
% 122.84/16.20 ('#B') @ (
% 122.84/16.20 '#S'))) @
% 122.84/16.20 (
% 122.84/16.20 (
% 122.84/16.20 ('#B') @ (
% 122.84/16.20 (
% 122.84/16.20 ('#B') @ (
% 122.84/16.20 (
% 122.84/16.20 ('#B') @ (
% 122.84/16.20 =>))))) @
% 122.84/16.20 (
% 122.84/16.20 (
% 122.84/16.20 ('#B') @ (
% 122.84/16.20 (
% 122.84/16.20 ('#B') @ (
% 122.84/16.20 (
% 122.84/16.20 ('#C') @ in)))) @
% 122.84/16.20 injFuncSet)))))))) @
% 122.84/16.20 (
% 122.84/16.20 (
% 122.84/16.20 ('#B') @ (
% 122.84/16.20 (
% 122.84/16.20 ('#B') @ (
% 122.84/16.20 (
% 122.84/16.20 ('#C') @ in)))) @
% 122.84/16.20 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.84/16.20 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1625])).
% 122.84/16.20 thf(zip_derived_cl1649, plain,
% 122.84/16.20 (~ (((cartprodfstin) =>
% 122.84/16.20 (((setukpairinjL2) =>
% 122.84/16.20 (((setukpairinjL) =>
% 122.84/16.20 (((setukpairinjR11) =>
% 122.84/16.20 (((setukpairinjR12) =>
% 122.84/16.20 (((setukpairinjR1) =>
% 122.84/16.20 (((upairequniteq) =>
% 122.84/16.20 (((setukpairinjR2) =>
% 122.84/16.20 (((setukpairinjR) =>
% 122.84/16.20 (((ksndsingleton) =>
% 122.84/16.20 (((ksndpairEq) =>
% 122.84/16.20 (((kpairsurjEq) =>
% 122.84/16.20 (((cartprodsndin) =>
% 122.84/16.20 (((cartprodpairmemEL) =>
% 122.84/16.20 (((cartprodpairmemER) =>
% 122.84/16.20 (((cartprodmempaircEq) =>
% 122.84/16.20 (((cartprodfstpairEq) =>
% 122.84/16.20 (((cartprodsndpairEq) =>
% 122.84/16.20 (((cartprodpairsurjEq) =>
% 122.84/16.20 (((dpsetconstrI) =>
% 122.84/16.20 (((dpsetconstrSub) =>
% 122.84/16.20 (((setOfPairsIsBReln) =>
% 122.84/16.20 (((dpsetconstrERa) =>
% 122.84/16.20 (((dpsetconstrEL1) =>
% 122.84/16.20 (((dpsetconstrEL2) =>
% 122.84/16.20 (((dpsetconstrER) =>
% 122.84/16.20 (((funcImageSingleton) =>
% 122.84/16.20 (((apProp) =>
% 122.84/16.20 (((app) =>
% 122.84/16.20 (((infuncsetfunc) =>
% 122.84/16.20 ((
% 122.84/16.20 (ap2p) =>
% 122.84/16.20 ((
% 122.84/16.20 (funcinfuncset) =>
% 122.84/16.20 ((
% 122.84/16.20 (lamProp) =>
% 122.84/16.20 ((
% 122.84/16.20 (lamp) =>
% 122.84/16.20 ((
% 122.84/16.20 (lam2p) =>
% 122.84/16.20 ((
% 122.84/16.20 (brelnall1) =>
% 122.84/16.20 ((
% 122.84/16.20 (brelnall2) =>
% 122.84/16.20 ((
% 122.84/16.20 (ex1E2) =>
% 122.84/16.20 ((
% 122.84/16.20 (funcGraphProp1) =>
% 122.84/16.20 ((
% 122.84/16.20 (funcGraphProp3) =>
% 122.84/16.20 ((
% 122.84/16.20 (funcGraphProp2) =>
% 122.84/16.20 ((
% 122.84/16.20 (funcextLem) =>
% 122.84/16.20 ((
% 122.84/16.20 (funcGraphProp4) =>
% 122.84/16.20 ((
% 122.84/16.20 (subbreln) =>
% 122.84/16.20 ((
% 122.84/16.20 (eqbreln) =>
% 122.84/16.20 ((
% 122.84/16.20 (funcext) =>
% 122.84/16.20 ((
% 122.84/16.20 (funcext2) =>
% 122.84/16.20 ((
% 122.84/16.20 (ap2apEq1) =>
% 122.84/16.20 ((
% 122.84/16.20 (ap2apEq2) =>
% 122.84/16.20 ((
% 122.84/16.20 (beta1) =>
% 122.84/16.20 ((
% 122.84/16.20 (eta1) =>
% 122.84/16.20 ((
% 122.84/16.20 (lam2lamEq) =>
% 122.84/16.20 ((
% 122.84/16.20 (beta2) =>
% 122.84/16.20 ((
% 122.84/16.20 (eta2) =>
% 122.84/16.20 ((
% 122.84/16.20 (iffalseProp1) =>
% 122.84/16.20 ((
% 122.84/16.20 (iffalseProp2) =>
% 122.84/16.20 ((
% 122.84/16.20 (iftrueProp1) =>
% 122.84/16.20 ((
% 122.84/16.20 (iftrueProp2) =>
% 122.84/16.20 ((
% 122.84/16.20 (ifSingleton) =>
% 122.84/16.20 ((
% 122.84/16.20 (ifp) =>
% 122.84/16.20 ((
% 122.84/16.20 (theeq) =>
% 122.84/16.20 ((
% 122.84/16.20 (iftrue) =>
% 122.84/16.20 ((
% 122.84/16.20 (iffalse) =>
% 122.84/16.20 ((
% 122.84/16.20 (iftrueorfalse) =>
% 122.84/16.20 ((
% 122.84/16.20 (binintersectT_lem) =>
% 122.84/16.20 ((
% 122.84/16.20 (binunionT_lem) =>
% 122.84/16.20 ((
% 122.84/16.20 (powersetT_lem) =>
% 122.84/16.20 ((
% 122.84/16.20 (setminusT_lem) =>
% 122.84/16.20 ((
% 122.84/16.20 (complementT_lem) =>
% 122.84/16.20 ((
% 122.84/16.20 (setextT) =>
% 122.84/16.20 ((
% 122.84/16.20 (subsetTI) =>
% 122.84/16.20 ((
% 122.84/16.20 (powersetTI1) =>
% 122.84/16.20 ((
% 122.84/16.20 (powersetTE1) =>
% 122.84/16.20 ((
% 122.84/16.20 (complementTI1) =>
% 122.84/16.20 ((
% 122.84/16.20 (complementTE1) =>
% 122.84/16.20 ((
% 122.84/16.20 (binintersectTELcontra) =>
% 122.84/16.20 ((
% 122.84/16.20 (binintersectTERcontra) =>
% 122.84/16.20 ((
% 122.84/16.20 (contrasubsetT) =>
% 122.84/16.20 ((
% 122.84/16.20 (contrasubsetT1) =>
% 122.84/16.20 ((
% 122.84/16.20 (contrasubsetT2) =>
% 122.84/16.20 ((
% 122.84/16.20 (contrasubsetT3) =>
% 122.84/16.20 ((
% 122.84/16.20 (doubleComplementI1) =>
% 122.84/16.20 ((
% 122.84/16.20 (doubleComplementE1) =>
% 122.84/16.20 ((
% 122.84/16.20 (doubleComplementSub1) =>
% 122.84/16.20 ((
% 122.84/16.20 (doubleComplementSub2) =>
% 122.84/16.20 ((
% 122.84/16.20 (doubleComplementEq) =>
% 122.84/16.20 ((
% 122.84/16.20 (complementTnotintersectT) =>
% 122.84/16.20 ((
% 122.84/16.20 (complementImpComplementIntersect) =>
% 122.84/16.20 ((
% 122.84/16.20 (complementSubsetComplementIntersect) =>
% 122.84/16.20 ((
% 122.84/16.20 (complementInPowersetComplementIntersect) =>
% 122.84/16.20 ((
% 122.84/16.20 (contraSubsetComplement) =>
% 122.84/16.20 ((
% 122.84/16.20 (complementTcontraSubset) =>
% 122.84/16.20 ((
% 122.84/16.20 (binunionTILcontra) =>
% 122.84/16.20 ((
% 122.84/16.20 (binunionTIRcontra) =>
% 122.84/16.20 ((
% 122.84/16.20 (inIntersectImpInUnion) =>
% 122.84/16.20 ((
% 122.84/16.20 (inIntersectImpInUnion2) =>
% 122.84/16.20 ((
% 122.84/16.20 (inIntersectImpInIntersectUnions) =>
% 122.84/16.20 ((
% 122.84/16.20 (intersectInPowersetIntersectUnions) =>
% 122.84/16.20 ((
% 122.84/16.20 (inComplementUnionImpNotIn1) =>
% 122.84/16.20 ((
% 122.84/16.20 (inComplementUnionImpInComplement1) =>
% 122.84/16.20 ((
% 122.84/16.20 (binunionTE) =>
% 122.84/16.20 ((
% 122.84/16.20 (binunionTEcontra) =>
% 122.84/16.20 ((
% 122.84/16.20 (demorgan2a1) =>
% 122.84/16.20 ((
% 122.84/16.20 (complementUnionInPowersetComplement) =>
% 122.84/16.20 ((
% 122.84/16.20 (demorgan2a2) =>
% 122.84/16.20 ((
% 122.84/16.20 (demorgan1a) =>
% 122.84/16.20 ((
% 122.84/16.20 (demorgan1b) =>
% 122.84/16.20 ((
% 122.84/16.20 (demorgan1) =>
% 122.84/16.20 ((
% 122.84/16.20 (demorgan2a) =>
% 122.84/16.20 ((
% 122.84/16.20 (demorgan2b2) =>
% 122.84/16.20 ((
% 122.84/16.20 (demorgan2b) =>
% 122.84/16.20 ((
% 122.84/16.20 (demorgan2) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz13rule0) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz13rule1) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz13rule2) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz13rule3) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz13rule4) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz1_1) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz1_2) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz1_3) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz1_4) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz1_5) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1all2) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1SetBreln1) =>
% 122.84/16.20 ((
% 122.84/16.20 (choice2fnsingleton) =>
% 122.84/16.20 ((
% 122.84/16.20 (setOfPairsIsBReln1) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1all1) =>
% 122.84/16.20 ((
% 122.84/16.20 (subbreln1) =>
% 122.84/16.20 ((
% 122.84/16.20 (eqbreln1) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1invprop) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1invI) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1invE) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1compprop) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1compI) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1compE) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1compEex) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1unionprop) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1unionIL) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1unionIR) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1unionI) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1unionE) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1unionEcases) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1unionCommutes) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz2Ex) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz2W) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz2A) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz2B) =>
% 122.84/16.20 ((
% 122.84/16.20 (image1Ex) =>
% 122.84/16.20 ((
% 122.84/16.20 (image1Ex1) =>
% 122.84/16.20 ((
% 122.84/16.20 (image1Equiv) =>
% 122.84/16.20 ((
% 122.84/16.20 (image1E) =>
% 122.84/16.20 ((
% 122.84/16.20 (image1I) =>
% 122.84/16.20 ((
% 122.84/16.20 (injFuncInInjFuncSet) =>
% 122.84/16.20 ((
% 122.84/16.20 (!!) @ (
% 122.84/16.20 (('#B') @ (
% 122.84/16.20 !!) @
% 122.84/16.20 (
% 122.84/16.20 (
% 122.84/16.20 ('#B') @ (
% 122.84/16.20 (
% 122.84/16.20 ('#B') @ (
% 122.84/16.20 !!))) @
% 122.84/16.20 (
% 122.84/16.20 (
% 122.84/16.20 ('#S') @ (
% 122.84/16.20 (
% 122.84/16.20 ('#B') @ (
% 122.84/16.20 '#S') @
% 122.84/16.20 (
% 122.84/16.20 (
% 122.84/16.20 ('#B') @ (
% 122.84/16.20 (
% 122.84/16.20 ('#B') @ (
% 122.84/16.20 '#S'))) @
% 122.84/16.20 (
% 122.84/16.20 (
% 122.84/16.20 ('#B') @ (
% 122.84/16.20 (
% 122.84/16.20 ('#B') @ (
% 122.84/16.20 (
% 122.84/16.20 ('#B') @ (
% 122.84/16.20 =>))))) @
% 122.84/16.20 (
% 122.84/16.20 (
% 122.84/16.20 ('#B') @ (
% 122.84/16.20 (
% 122.84/16.20 ('#B') @ (
% 122.84/16.20 (
% 122.84/16.20 ('#C') @ in)))) @
% 122.84/16.20 injFuncSet)))))))) @
% 122.84/16.20 (
% 122.84/16.20 (
% 122.84/16.20 ('#B') @ (
% 122.84/16.20 (
% 122.84/16.20 ('#B') @ (
% 122.84/16.20 (
% 122.84/16.20 ('#C') @ in)))) @
% 122.84/16.20 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.84/16.20 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1637])).
% 122.84/16.20 thf(zip_derived_cl1664, plain,
% 122.84/16.20 (~ (((setukpairinjL2) =>
% 122.84/16.20 (((setukpairinjL) =>
% 122.84/16.20 (((setukpairinjR11) =>
% 122.84/16.20 (((setukpairinjR12) =>
% 122.84/16.20 (((setukpairinjR1) =>
% 122.84/16.20 (((upairequniteq) =>
% 122.84/16.20 (((setukpairinjR2) =>
% 122.84/16.20 (((setukpairinjR) =>
% 122.84/16.20 (((ksndsingleton) =>
% 122.84/16.20 (((ksndpairEq) =>
% 122.84/16.20 (((kpairsurjEq) =>
% 122.84/16.20 (((cartprodsndin) =>
% 122.84/16.20 (((cartprodpairmemEL) =>
% 122.84/16.20 (((cartprodpairmemER) =>
% 122.84/16.20 (((cartprodmempaircEq) =>
% 122.84/16.20 (((cartprodfstpairEq) =>
% 122.84/16.20 (((cartprodsndpairEq) =>
% 122.84/16.20 (((cartprodpairsurjEq) =>
% 122.84/16.20 (((dpsetconstrI) =>
% 122.84/16.20 (((dpsetconstrSub) =>
% 122.84/16.20 (((setOfPairsIsBReln) =>
% 122.84/16.20 (((dpsetconstrERa) =>
% 122.84/16.20 (((dpsetconstrEL1) =>
% 122.84/16.20 (((dpsetconstrEL2) =>
% 122.84/16.20 (((dpsetconstrER) =>
% 122.84/16.20 (((funcImageSingleton) =>
% 122.84/16.20 (((apProp) =>
% 122.84/16.20 (((app) =>
% 122.84/16.20 (((infuncsetfunc) =>
% 122.84/16.20 (((ap2p) =>
% 122.84/16.20 ((
% 122.84/16.20 (funcinfuncset) =>
% 122.84/16.20 ((
% 122.84/16.20 (lamProp) =>
% 122.84/16.20 ((
% 122.84/16.20 (lamp) =>
% 122.84/16.20 ((
% 122.84/16.20 (lam2p) =>
% 122.84/16.20 ((
% 122.84/16.20 (brelnall1) =>
% 122.84/16.20 ((
% 122.84/16.20 (brelnall2) =>
% 122.84/16.20 ((
% 122.84/16.20 (ex1E2) =>
% 122.84/16.20 ((
% 122.84/16.20 (funcGraphProp1) =>
% 122.84/16.20 ((
% 122.84/16.20 (funcGraphProp3) =>
% 122.84/16.20 ((
% 122.84/16.20 (funcGraphProp2) =>
% 122.84/16.20 ((
% 122.84/16.20 (funcextLem) =>
% 122.84/16.20 ((
% 122.84/16.20 (funcGraphProp4) =>
% 122.84/16.20 ((
% 122.84/16.20 (subbreln) =>
% 122.84/16.20 ((
% 122.84/16.20 (eqbreln) =>
% 122.84/16.20 ((
% 122.84/16.20 (funcext) =>
% 122.84/16.20 ((
% 122.84/16.20 (funcext2) =>
% 122.84/16.20 ((
% 122.84/16.20 (ap2apEq1) =>
% 122.84/16.20 ((
% 122.84/16.20 (ap2apEq2) =>
% 122.84/16.20 ((
% 122.84/16.20 (beta1) =>
% 122.84/16.20 ((
% 122.84/16.20 (eta1) =>
% 122.84/16.20 ((
% 122.84/16.20 (lam2lamEq) =>
% 122.84/16.20 ((
% 122.84/16.20 (beta2) =>
% 122.84/16.20 ((
% 122.84/16.20 (eta2) =>
% 122.84/16.20 ((
% 122.84/16.20 (iffalseProp1) =>
% 122.84/16.20 ((
% 122.84/16.20 (iffalseProp2) =>
% 122.84/16.20 ((
% 122.84/16.20 (iftrueProp1) =>
% 122.84/16.20 ((
% 122.84/16.20 (iftrueProp2) =>
% 122.84/16.20 ((
% 122.84/16.20 (ifSingleton) =>
% 122.84/16.20 ((
% 122.84/16.20 (ifp) =>
% 122.84/16.20 ((
% 122.84/16.20 (theeq) =>
% 122.84/16.20 ((
% 122.84/16.20 (iftrue) =>
% 122.84/16.20 ((
% 122.84/16.20 (iffalse) =>
% 122.84/16.20 ((
% 122.84/16.20 (iftrueorfalse) =>
% 122.84/16.20 ((
% 122.84/16.20 (binintersectT_lem) =>
% 122.84/16.20 ((
% 122.84/16.20 (binunionT_lem) =>
% 122.84/16.20 ((
% 122.84/16.20 (powersetT_lem) =>
% 122.84/16.20 ((
% 122.84/16.20 (setminusT_lem) =>
% 122.84/16.20 ((
% 122.84/16.20 (complementT_lem) =>
% 122.84/16.20 ((
% 122.84/16.20 (setextT) =>
% 122.84/16.20 ((
% 122.84/16.20 (subsetTI) =>
% 122.84/16.20 ((
% 122.84/16.20 (powersetTI1) =>
% 122.84/16.20 ((
% 122.84/16.20 (powersetTE1) =>
% 122.84/16.20 ((
% 122.84/16.20 (complementTI1) =>
% 122.84/16.20 ((
% 122.84/16.20 (complementTE1) =>
% 122.84/16.20 ((
% 122.84/16.20 (binintersectTELcontra) =>
% 122.84/16.20 ((
% 122.84/16.20 (binintersectTERcontra) =>
% 122.84/16.20 ((
% 122.84/16.20 (contrasubsetT) =>
% 122.84/16.20 ((
% 122.84/16.20 (contrasubsetT1) =>
% 122.84/16.20 ((
% 122.84/16.20 (contrasubsetT2) =>
% 122.84/16.20 ((
% 122.84/16.20 (contrasubsetT3) =>
% 122.84/16.20 ((
% 122.84/16.20 (doubleComplementI1) =>
% 122.84/16.20 ((
% 122.84/16.20 (doubleComplementE1) =>
% 122.84/16.20 ((
% 122.84/16.20 (doubleComplementSub1) =>
% 122.84/16.20 ((
% 122.84/16.20 (doubleComplementSub2) =>
% 122.84/16.20 ((
% 122.84/16.20 (doubleComplementEq) =>
% 122.84/16.20 ((
% 122.84/16.20 (complementTnotintersectT) =>
% 122.84/16.20 ((
% 122.84/16.20 (complementImpComplementIntersect) =>
% 122.84/16.20 ((
% 122.84/16.20 (complementSubsetComplementIntersect) =>
% 122.84/16.20 ((
% 122.84/16.20 (complementInPowersetComplementIntersect) =>
% 122.84/16.20 ((
% 122.84/16.20 (contraSubsetComplement) =>
% 122.84/16.20 ((
% 122.84/16.20 (complementTcontraSubset) =>
% 122.84/16.20 ((
% 122.84/16.20 (binunionTILcontra) =>
% 122.84/16.20 ((
% 122.84/16.20 (binunionTIRcontra) =>
% 122.84/16.20 ((
% 122.84/16.20 (inIntersectImpInUnion) =>
% 122.84/16.20 ((
% 122.84/16.20 (inIntersectImpInUnion2) =>
% 122.84/16.20 ((
% 122.84/16.20 (inIntersectImpInIntersectUnions) =>
% 122.84/16.20 ((
% 122.84/16.20 (intersectInPowersetIntersectUnions) =>
% 122.84/16.20 ((
% 122.84/16.20 (inComplementUnionImpNotIn1) =>
% 122.84/16.20 ((
% 122.84/16.20 (inComplementUnionImpInComplement1) =>
% 122.84/16.20 ((
% 122.84/16.20 (binunionTE) =>
% 122.84/16.20 ((
% 122.84/16.20 (binunionTEcontra) =>
% 122.84/16.20 ((
% 122.84/16.20 (demorgan2a1) =>
% 122.84/16.20 ((
% 122.84/16.20 (complementUnionInPowersetComplement) =>
% 122.84/16.20 ((
% 122.84/16.20 (demorgan2a2) =>
% 122.84/16.20 ((
% 122.84/16.20 (demorgan1a) =>
% 122.84/16.20 ((
% 122.84/16.20 (demorgan1b) =>
% 122.84/16.20 ((
% 122.84/16.20 (demorgan1) =>
% 122.84/16.20 ((
% 122.84/16.20 (demorgan2a) =>
% 122.84/16.20 ((
% 122.84/16.20 (demorgan2b2) =>
% 122.84/16.20 ((
% 122.84/16.20 (demorgan2b) =>
% 122.84/16.20 ((
% 122.84/16.20 (demorgan2) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz13rule0) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz13rule1) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz13rule2) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz13rule3) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz13rule4) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz1_1) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz1_2) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz1_3) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz1_4) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz1_5) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1all2) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1SetBreln1) =>
% 122.84/16.20 ((
% 122.84/16.20 (choice2fnsingleton) =>
% 122.84/16.20 ((
% 122.84/16.20 (setOfPairsIsBReln1) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1all1) =>
% 122.84/16.20 ((
% 122.84/16.20 (subbreln1) =>
% 122.84/16.20 ((
% 122.84/16.20 (eqbreln1) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1invprop) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1invI) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1invE) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1compprop) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1compI) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1compE) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1compEex) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1unionprop) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1unionIL) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1unionIR) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1unionI) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1unionE) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1unionEcases) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1unionCommutes) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz2Ex) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz2W) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz2A) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz2B) =>
% 122.84/16.20 ((
% 122.84/16.20 (image1Ex) =>
% 122.84/16.20 ((
% 122.84/16.20 (image1Ex1) =>
% 122.84/16.20 ((
% 122.84/16.20 (image1Equiv) =>
% 122.84/16.20 ((
% 122.84/16.20 (image1E) =>
% 122.84/16.20 ((
% 122.84/16.20 (image1I) =>
% 122.84/16.20 ((
% 122.84/16.20 (injFuncInInjFuncSet) =>
% 122.84/16.20 ((
% 122.84/16.20 (!!) @ (
% 122.84/16.20 (('#B') @ (
% 122.84/16.20 !!) @
% 122.84/16.20 (
% 122.84/16.20 (
% 122.84/16.20 ('#B') @ (
% 122.84/16.20 (
% 122.84/16.20 ('#B') @ (
% 122.84/16.20 !!))) @
% 122.84/16.20 (
% 122.84/16.20 (
% 122.84/16.20 ('#S') @ (
% 122.84/16.20 (
% 122.84/16.20 ('#B') @ (
% 122.84/16.20 '#S') @
% 122.84/16.20 (
% 122.84/16.20 (
% 122.84/16.20 ('#B') @ (
% 122.84/16.20 (
% 122.84/16.20 ('#B') @ (
% 122.84/16.20 '#S'))) @
% 122.84/16.20 (
% 122.84/16.20 (
% 122.84/16.20 ('#B') @ (
% 122.84/16.20 (
% 122.84/16.20 ('#B') @ (
% 122.84/16.20 (
% 122.84/16.20 ('#B') @ (
% 122.84/16.20 =>))))) @
% 122.84/16.20 (
% 122.84/16.20 (
% 122.84/16.20 ('#B') @ (
% 122.84/16.20 (
% 122.84/16.20 ('#B') @ (
% 122.84/16.20 (
% 122.84/16.20 ('#C') @ in)))) @
% 122.84/16.20 injFuncSet)))))))) @
% 122.84/16.20 (
% 122.84/16.20 (
% 122.84/16.20 ('#B') @ (
% 122.84/16.20 (
% 122.84/16.20 ('#B') @ (
% 122.84/16.20 (
% 122.84/16.20 ('#C') @ in)))) @
% 122.84/16.20 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.84/16.20 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1649])).
% 122.84/16.20 thf(zip_derived_cl1678, plain,
% 122.84/16.20 (~ (((setukpairinjL) =>
% 122.84/16.20 (((setukpairinjR11) =>
% 122.84/16.20 (((setukpairinjR12) =>
% 122.84/16.20 (((setukpairinjR1) =>
% 122.84/16.20 (((upairequniteq) =>
% 122.84/16.20 (((setukpairinjR2) =>
% 122.84/16.20 (((setukpairinjR) =>
% 122.84/16.20 (((ksndsingleton) =>
% 122.84/16.20 (((ksndpairEq) =>
% 122.84/16.20 (((kpairsurjEq) =>
% 122.84/16.20 (((cartprodsndin) =>
% 122.84/16.20 (((cartprodpairmemEL) =>
% 122.84/16.20 (((cartprodpairmemER) =>
% 122.84/16.20 (((cartprodmempaircEq) =>
% 122.84/16.20 (((cartprodfstpairEq) =>
% 122.84/16.20 (((cartprodsndpairEq) =>
% 122.84/16.20 (((cartprodpairsurjEq) =>
% 122.84/16.20 (((dpsetconstrI) =>
% 122.84/16.20 (((dpsetconstrSub) =>
% 122.84/16.20 (((setOfPairsIsBReln) =>
% 122.84/16.20 (((dpsetconstrERa) =>
% 122.84/16.20 (((dpsetconstrEL1) =>
% 122.84/16.20 (((dpsetconstrEL2) =>
% 122.84/16.20 (((dpsetconstrER) =>
% 122.84/16.20 (((funcImageSingleton) =>
% 122.84/16.20 (((apProp) =>
% 122.84/16.20 (((app) =>
% 122.84/16.20 (((infuncsetfunc) =>
% 122.84/16.20 (((ap2p) =>
% 122.84/16.20 (((funcinfuncset) =>
% 122.84/16.20 ((
% 122.84/16.20 (lamProp) =>
% 122.84/16.20 ((
% 122.84/16.20 (lamp) =>
% 122.84/16.20 ((
% 122.84/16.20 (lam2p) =>
% 122.84/16.20 ((
% 122.84/16.20 (brelnall1) =>
% 122.84/16.20 ((
% 122.84/16.20 (brelnall2) =>
% 122.84/16.20 ((
% 122.84/16.20 (ex1E2) =>
% 122.84/16.20 ((
% 122.84/16.20 (funcGraphProp1) =>
% 122.84/16.20 ((
% 122.84/16.20 (funcGraphProp3) =>
% 122.84/16.20 ((
% 122.84/16.20 (funcGraphProp2) =>
% 122.84/16.20 ((
% 122.84/16.20 (funcextLem) =>
% 122.84/16.20 ((
% 122.84/16.20 (funcGraphProp4) =>
% 122.84/16.20 ((
% 122.84/16.20 (subbreln) =>
% 122.84/16.20 ((
% 122.84/16.20 (eqbreln) =>
% 122.84/16.20 ((
% 122.84/16.20 (funcext) =>
% 122.84/16.20 ((
% 122.84/16.20 (funcext2) =>
% 122.84/16.20 ((
% 122.84/16.20 (ap2apEq1) =>
% 122.84/16.20 ((
% 122.84/16.20 (ap2apEq2) =>
% 122.84/16.20 ((
% 122.84/16.20 (beta1) =>
% 122.84/16.20 ((
% 122.84/16.20 (eta1) =>
% 122.84/16.20 ((
% 122.84/16.20 (lam2lamEq) =>
% 122.84/16.20 ((
% 122.84/16.20 (beta2) =>
% 122.84/16.20 ((
% 122.84/16.20 (eta2) =>
% 122.84/16.20 ((
% 122.84/16.20 (iffalseProp1) =>
% 122.84/16.20 ((
% 122.84/16.20 (iffalseProp2) =>
% 122.84/16.20 ((
% 122.84/16.20 (iftrueProp1) =>
% 122.84/16.20 ((
% 122.84/16.20 (iftrueProp2) =>
% 122.84/16.20 ((
% 122.84/16.20 (ifSingleton) =>
% 122.84/16.20 ((
% 122.84/16.20 (ifp) =>
% 122.84/16.20 ((
% 122.84/16.20 (theeq) =>
% 122.84/16.20 ((
% 122.84/16.20 (iftrue) =>
% 122.84/16.20 ((
% 122.84/16.20 (iffalse) =>
% 122.84/16.20 ((
% 122.84/16.20 (iftrueorfalse) =>
% 122.84/16.20 ((
% 122.84/16.20 (binintersectT_lem) =>
% 122.84/16.20 ((
% 122.84/16.20 (binunionT_lem) =>
% 122.84/16.20 ((
% 122.84/16.20 (powersetT_lem) =>
% 122.84/16.20 ((
% 122.84/16.20 (setminusT_lem) =>
% 122.84/16.20 ((
% 122.84/16.20 (complementT_lem) =>
% 122.84/16.20 ((
% 122.84/16.20 (setextT) =>
% 122.84/16.20 ((
% 122.84/16.20 (subsetTI) =>
% 122.84/16.20 ((
% 122.84/16.20 (powersetTI1) =>
% 122.84/16.20 ((
% 122.84/16.20 (powersetTE1) =>
% 122.84/16.20 ((
% 122.84/16.20 (complementTI1) =>
% 122.84/16.20 ((
% 122.84/16.20 (complementTE1) =>
% 122.84/16.20 ((
% 122.84/16.20 (binintersectTELcontra) =>
% 122.84/16.20 ((
% 122.84/16.20 (binintersectTERcontra) =>
% 122.84/16.20 ((
% 122.84/16.20 (contrasubsetT) =>
% 122.84/16.20 ((
% 122.84/16.20 (contrasubsetT1) =>
% 122.84/16.20 ((
% 122.84/16.20 (contrasubsetT2) =>
% 122.84/16.20 ((
% 122.84/16.20 (contrasubsetT3) =>
% 122.84/16.20 ((
% 122.84/16.20 (doubleComplementI1) =>
% 122.84/16.20 ((
% 122.84/16.20 (doubleComplementE1) =>
% 122.84/16.20 ((
% 122.84/16.20 (doubleComplementSub1) =>
% 122.84/16.20 ((
% 122.84/16.20 (doubleComplementSub2) =>
% 122.84/16.20 ((
% 122.84/16.20 (doubleComplementEq) =>
% 122.84/16.20 ((
% 122.84/16.20 (complementTnotintersectT) =>
% 122.84/16.20 ((
% 122.84/16.20 (complementImpComplementIntersect) =>
% 122.84/16.20 ((
% 122.84/16.20 (complementSubsetComplementIntersect) =>
% 122.84/16.20 ((
% 122.84/16.20 (complementInPowersetComplementIntersect) =>
% 122.84/16.20 ((
% 122.84/16.20 (contraSubsetComplement) =>
% 122.84/16.20 ((
% 122.84/16.20 (complementTcontraSubset) =>
% 122.84/16.20 ((
% 122.84/16.20 (binunionTILcontra) =>
% 122.84/16.20 ((
% 122.84/16.20 (binunionTIRcontra) =>
% 122.84/16.20 ((
% 122.84/16.20 (inIntersectImpInUnion) =>
% 122.84/16.20 ((
% 122.84/16.20 (inIntersectImpInUnion2) =>
% 122.84/16.20 ((
% 122.84/16.20 (inIntersectImpInIntersectUnions) =>
% 122.84/16.20 ((
% 122.84/16.20 (intersectInPowersetIntersectUnions) =>
% 122.84/16.20 ((
% 122.84/16.20 (inComplementUnionImpNotIn1) =>
% 122.84/16.20 ((
% 122.84/16.20 (inComplementUnionImpInComplement1) =>
% 122.84/16.20 ((
% 122.84/16.20 (binunionTE) =>
% 122.84/16.20 ((
% 122.84/16.20 (binunionTEcontra) =>
% 122.84/16.20 ((
% 122.84/16.20 (demorgan2a1) =>
% 122.84/16.20 ((
% 122.84/16.20 (complementUnionInPowersetComplement) =>
% 122.84/16.20 ((
% 122.84/16.20 (demorgan2a2) =>
% 122.84/16.20 ((
% 122.84/16.20 (demorgan1a) =>
% 122.84/16.20 ((
% 122.84/16.20 (demorgan1b) =>
% 122.84/16.20 ((
% 122.84/16.20 (demorgan1) =>
% 122.84/16.20 ((
% 122.84/16.20 (demorgan2a) =>
% 122.84/16.20 ((
% 122.84/16.20 (demorgan2b2) =>
% 122.84/16.20 ((
% 122.84/16.20 (demorgan2b) =>
% 122.84/16.20 ((
% 122.84/16.20 (demorgan2) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz13rule0) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz13rule1) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz13rule2) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz13rule3) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz13rule4) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz1_1) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz1_2) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz1_3) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz1_4) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz1_5) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1all2) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1SetBreln1) =>
% 122.84/16.20 ((
% 122.84/16.20 (choice2fnsingleton) =>
% 122.84/16.20 ((
% 122.84/16.20 (setOfPairsIsBReln1) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1all1) =>
% 122.84/16.20 ((
% 122.84/16.20 (subbreln1) =>
% 122.84/16.20 ((
% 122.84/16.20 (eqbreln1) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1invprop) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1invI) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1invE) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1compprop) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1compI) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1compE) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1compEex) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1unionprop) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1unionIL) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1unionIR) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1unionI) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1unionE) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1unionEcases) =>
% 122.84/16.20 ((
% 122.84/16.20 (breln1unionCommutes) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz2Ex) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz2W) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz2A) =>
% 122.84/16.20 ((
% 122.84/16.20 (woz2B) =>
% 122.84/16.20 ((
% 122.84/16.20 (image1Ex) =>
% 122.84/16.20 ((
% 122.84/16.20 (image1Ex1) =>
% 122.84/16.20 ((
% 122.84/16.20 (image1Equiv) =>
% 122.84/16.20 ((
% 122.84/16.20 (image1E) =>
% 122.84/16.20 ((
% 122.84/16.20 (image1I) =>
% 122.84/16.20 ((
% 122.84/16.20 (injFuncInInjFuncSet) =>
% 122.84/16.20 ((
% 122.84/16.20 (!!) @ (
% 122.84/16.20 (('#B') @ (
% 122.84/16.20 !!) @
% 122.84/16.20 (
% 122.84/16.20 (
% 122.84/16.20 ('#B') @ (
% 122.84/16.20 (
% 122.84/16.20 ('#B') @ (
% 122.84/16.20 !!))) @
% 122.84/16.20 (
% 122.84/16.20 (
% 122.84/16.20 ('#S') @ (
% 122.84/16.20 (
% 122.84/16.20 ('#B') @ (
% 122.84/16.20 '#S') @
% 122.84/16.20 (
% 122.84/16.20 (
% 122.84/16.20 ('#B') @ (
% 122.84/16.20 (
% 122.84/16.20 ('#B') @ (
% 122.84/16.20 '#S'))) @
% 122.84/16.20 (
% 122.84/16.20 (
% 122.84/16.20 ('#B') @ (
% 122.84/16.20 (
% 122.84/16.20 ('#B') @ (
% 122.84/16.20 (
% 122.84/16.20 ('#B') @ (
% 122.84/16.20 =>))))) @
% 122.84/16.20 (
% 122.84/16.20 (
% 122.84/16.20 ('#B') @ (
% 122.84/16.20 (
% 122.84/16.20 ('#B') @ (
% 122.84/16.20 (
% 122.84/16.20 ('#C') @ in)))) @
% 122.84/16.20 injFuncSet)))))))) @
% 122.84/16.20 (
% 122.84/16.20 (
% 122.84/16.20 ('#B') @ (
% 122.84/16.20 (
% 122.84/16.20 ('#B') @ (
% 122.84/16.20 (
% 122.84/16.20 ('#C') @ in)))) @
% 122.84/16.20 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.84/16.20 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1664])).
% 122.84/16.20 thf(zip_derived_cl1695, plain,
% 122.84/16.20 (~ (((setukpairinjR11) =>
% 122.84/16.20 (((setukpairinjR12) =>
% 122.84/16.20 (((setukpairinjR1) =>
% 122.84/16.20 (((upairequniteq) =>
% 122.84/16.21 (((setukpairinjR2) =>
% 122.84/16.21 (((setukpairinjR) =>
% 122.84/16.21 (((ksndsingleton) =>
% 122.84/16.21 (((ksndpairEq) =>
% 122.84/16.21 (((kpairsurjEq) =>
% 122.84/16.21 (((cartprodsndin) =>
% 122.84/16.21 (((cartprodpairmemEL) =>
% 122.84/16.21 (((cartprodpairmemER) =>
% 122.84/16.21 (((cartprodmempaircEq) =>
% 122.84/16.21 (((cartprodfstpairEq) =>
% 122.84/16.21 (((cartprodsndpairEq) =>
% 122.84/16.21 (((cartprodpairsurjEq) =>
% 122.84/16.21 (((dpsetconstrI) =>
% 122.84/16.21 (((dpsetconstrSub) =>
% 122.84/16.21 (((setOfPairsIsBReln) =>
% 122.84/16.21 (((dpsetconstrERa) =>
% 122.84/16.21 (((dpsetconstrEL1) =>
% 122.84/16.21 (((dpsetconstrEL2) =>
% 122.84/16.21 (((dpsetconstrER) =>
% 122.84/16.21 (((funcImageSingleton) =>
% 122.84/16.21 (((apProp) =>
% 122.84/16.21 (((app) =>
% 122.84/16.21 (((infuncsetfunc) =>
% 122.84/16.21 (((ap2p) =>
% 122.84/16.21 (((funcinfuncset) =>
% 122.84/16.21 (((lamProp) =>
% 122.84/16.21 ((
% 122.84/16.21 (lamp) =>
% 122.84/16.21 ((
% 122.84/16.21 (lam2p) =>
% 122.84/16.21 ((
% 122.84/16.21 (brelnall1) =>
% 122.84/16.21 ((
% 122.84/16.21 (brelnall2) =>
% 122.84/16.21 ((
% 122.84/16.21 (ex1E2) =>
% 122.84/16.21 ((
% 122.84/16.21 (funcGraphProp1) =>
% 122.84/16.21 ((
% 122.84/16.21 (funcGraphProp3) =>
% 122.84/16.21 ((
% 122.84/16.21 (funcGraphProp2) =>
% 122.84/16.21 ((
% 122.84/16.21 (funcextLem) =>
% 122.84/16.21 ((
% 122.84/16.21 (funcGraphProp4) =>
% 122.84/16.21 ((
% 122.84/16.21 (subbreln) =>
% 122.84/16.21 ((
% 122.84/16.21 (eqbreln) =>
% 122.84/16.21 ((
% 122.84/16.21 (funcext) =>
% 122.84/16.21 ((
% 122.84/16.21 (funcext2) =>
% 122.84/16.21 ((
% 122.84/16.21 (ap2apEq1) =>
% 122.84/16.21 ((
% 122.84/16.21 (ap2apEq2) =>
% 122.84/16.21 ((
% 122.84/16.21 (beta1) =>
% 122.84/16.21 ((
% 122.84/16.21 (eta1) =>
% 122.84/16.21 ((
% 122.84/16.21 (lam2lamEq) =>
% 122.84/16.21 ((
% 122.84/16.21 (beta2) =>
% 122.84/16.21 ((
% 122.84/16.21 (eta2) =>
% 122.84/16.21 ((
% 122.84/16.21 (iffalseProp1) =>
% 122.84/16.21 ((
% 122.84/16.21 (iffalseProp2) =>
% 122.84/16.21 ((
% 122.84/16.21 (iftrueProp1) =>
% 122.84/16.21 ((
% 122.84/16.21 (iftrueProp2) =>
% 122.84/16.21 ((
% 122.84/16.21 (ifSingleton) =>
% 122.84/16.21 ((
% 122.84/16.21 (ifp) =>
% 122.84/16.21 ((
% 122.84/16.21 (theeq) =>
% 122.84/16.21 ((
% 122.84/16.21 (iftrue) =>
% 122.84/16.21 ((
% 122.84/16.21 (iffalse) =>
% 122.84/16.21 ((
% 122.84/16.21 (iftrueorfalse) =>
% 122.84/16.21 ((
% 122.84/16.21 (binintersectT_lem) =>
% 122.84/16.21 ((
% 122.84/16.21 (binunionT_lem) =>
% 122.84/16.21 ((
% 122.84/16.21 (powersetT_lem) =>
% 122.84/16.21 ((
% 122.84/16.21 (setminusT_lem) =>
% 122.84/16.21 ((
% 122.84/16.21 (complementT_lem) =>
% 122.84/16.21 ((
% 122.84/16.21 (setextT) =>
% 122.84/16.21 ((
% 122.84/16.21 (subsetTI) =>
% 122.84/16.21 ((
% 122.84/16.21 (powersetTI1) =>
% 122.84/16.21 ((
% 122.84/16.21 (powersetTE1) =>
% 122.84/16.21 ((
% 122.84/16.21 (complementTI1) =>
% 122.84/16.21 ((
% 122.84/16.21 (complementTE1) =>
% 122.84/16.21 ((
% 122.84/16.21 (binintersectTELcontra) =>
% 122.84/16.21 ((
% 122.84/16.21 (binintersectTERcontra) =>
% 122.84/16.21 ((
% 122.84/16.21 (contrasubsetT) =>
% 122.84/16.21 ((
% 122.84/16.21 (contrasubsetT1) =>
% 122.84/16.21 ((
% 122.84/16.21 (contrasubsetT2) =>
% 122.84/16.21 ((
% 122.84/16.21 (contrasubsetT3) =>
% 122.84/16.21 ((
% 122.84/16.21 (doubleComplementI1) =>
% 122.84/16.21 ((
% 122.84/16.21 (doubleComplementE1) =>
% 122.84/16.21 ((
% 122.84/16.21 (doubleComplementSub1) =>
% 122.84/16.21 ((
% 122.84/16.21 (doubleComplementSub2) =>
% 122.84/16.21 ((
% 122.84/16.21 (doubleComplementEq) =>
% 122.84/16.21 ((
% 122.84/16.21 (complementTnotintersectT) =>
% 122.84/16.21 ((
% 122.84/16.21 (complementImpComplementIntersect) =>
% 122.84/16.21 ((
% 122.84/16.21 (complementSubsetComplementIntersect) =>
% 122.84/16.21 ((
% 122.84/16.21 (complementInPowersetComplementIntersect) =>
% 122.84/16.21 ((
% 122.84/16.21 (contraSubsetComplement) =>
% 122.84/16.21 ((
% 122.84/16.21 (complementTcontraSubset) =>
% 122.84/16.21 ((
% 122.84/16.21 (binunionTILcontra) =>
% 122.84/16.21 ((
% 122.84/16.21 (binunionTIRcontra) =>
% 122.84/16.21 ((
% 122.84/16.21 (inIntersectImpInUnion) =>
% 122.84/16.21 ((
% 122.84/16.21 (inIntersectImpInUnion2) =>
% 122.84/16.21 ((
% 122.84/16.21 (inIntersectImpInIntersectUnions) =>
% 122.84/16.21 ((
% 122.84/16.21 (intersectInPowersetIntersectUnions) =>
% 122.84/16.21 ((
% 122.84/16.21 (inComplementUnionImpNotIn1) =>
% 122.84/16.21 ((
% 122.84/16.21 (inComplementUnionImpInComplement1) =>
% 122.84/16.21 ((
% 122.84/16.21 (binunionTE) =>
% 122.84/16.21 ((
% 122.84/16.21 (binunionTEcontra) =>
% 122.84/16.21 ((
% 122.84/16.21 (demorgan2a1) =>
% 122.84/16.21 ((
% 122.84/16.21 (complementUnionInPowersetComplement) =>
% 122.84/16.21 ((
% 122.84/16.21 (demorgan2a2) =>
% 122.84/16.21 ((
% 122.84/16.21 (demorgan1a) =>
% 122.84/16.21 ((
% 122.84/16.21 (demorgan1b) =>
% 122.84/16.21 ((
% 122.84/16.21 (demorgan1) =>
% 122.84/16.21 ((
% 122.84/16.21 (demorgan2a) =>
% 122.84/16.21 ((
% 122.84/16.21 (demorgan2b2) =>
% 122.84/16.21 ((
% 122.84/16.21 (demorgan2b) =>
% 122.84/16.21 ((
% 122.84/16.21 (demorgan2) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz13rule0) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz13rule1) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz13rule2) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz13rule3) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz13rule4) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz1_1) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz1_2) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz1_3) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz1_4) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz1_5) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1all2) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1SetBreln1) =>
% 122.84/16.21 ((
% 122.84/16.21 (choice2fnsingleton) =>
% 122.84/16.21 ((
% 122.84/16.21 (setOfPairsIsBReln1) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1all1) =>
% 122.84/16.21 ((
% 122.84/16.21 (subbreln1) =>
% 122.84/16.21 ((
% 122.84/16.21 (eqbreln1) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1invprop) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1invI) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1invE) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1compprop) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1compI) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1compE) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1compEex) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1unionprop) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1unionIL) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1unionIR) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1unionI) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1unionE) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1unionEcases) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1unionCommutes) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz2Ex) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz2W) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz2A) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz2B) =>
% 122.84/16.21 ((
% 122.84/16.21 (image1Ex) =>
% 122.84/16.21 ((
% 122.84/16.21 (image1Ex1) =>
% 122.84/16.21 ((
% 122.84/16.21 (image1Equiv) =>
% 122.84/16.21 ((
% 122.84/16.21 (image1E) =>
% 122.84/16.21 ((
% 122.84/16.21 (image1I) =>
% 122.84/16.21 ((
% 122.84/16.21 (injFuncInInjFuncSet) =>
% 122.84/16.21 ((
% 122.84/16.21 (!!) @ (
% 122.84/16.21 (('#B') @ (
% 122.84/16.21 !!) @
% 122.84/16.21 (
% 122.84/16.21 (
% 122.84/16.21 ('#B') @ (
% 122.84/16.21 (
% 122.84/16.21 ('#B') @ (
% 122.84/16.21 !!))) @
% 122.84/16.21 (
% 122.84/16.21 (
% 122.84/16.21 ('#S') @ (
% 122.84/16.21 (
% 122.84/16.21 ('#B') @ (
% 122.84/16.21 '#S') @
% 122.84/16.21 (
% 122.84/16.21 (
% 122.84/16.21 ('#B') @ (
% 122.84/16.21 (
% 122.84/16.21 ('#B') @ (
% 122.84/16.21 '#S'))) @
% 122.84/16.21 (
% 122.84/16.21 (
% 122.84/16.21 ('#B') @ (
% 122.84/16.21 (
% 122.84/16.21 ('#B') @ (
% 122.84/16.21 (
% 122.84/16.21 ('#B') @ (
% 122.84/16.21 =>))))) @
% 122.84/16.21 (
% 122.84/16.21 (
% 122.84/16.21 ('#B') @ (
% 122.84/16.21 (
% 122.84/16.21 ('#B') @ (
% 122.84/16.21 (
% 122.84/16.21 ('#C') @ in)))) @
% 122.84/16.21 injFuncSet)))))))) @
% 122.84/16.21 (
% 122.84/16.21 (
% 122.84/16.21 ('#B') @ (
% 122.84/16.21 (
% 122.84/16.21 ('#B') @ (
% 122.84/16.21 (
% 122.84/16.21 ('#C') @ in)))) @
% 122.84/16.21 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.84/16.21 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1678])).
% 122.84/16.21 thf(zip_derived_cl1711, plain,
% 122.84/16.21 (~ (((setukpairinjR12) =>
% 122.84/16.21 (((setukpairinjR1) =>
% 122.84/16.21 (((upairequniteq) =>
% 122.84/16.21 (((setukpairinjR2) =>
% 122.84/16.21 (((setukpairinjR) =>
% 122.84/16.21 (((ksndsingleton) =>
% 122.84/16.21 (((ksndpairEq) =>
% 122.84/16.21 (((kpairsurjEq) =>
% 122.84/16.21 (((cartprodsndin) =>
% 122.84/16.21 (((cartprodpairmemEL) =>
% 122.84/16.21 (((cartprodpairmemER) =>
% 122.84/16.21 (((cartprodmempaircEq) =>
% 122.84/16.21 (((cartprodfstpairEq) =>
% 122.84/16.21 (((cartprodsndpairEq) =>
% 122.84/16.21 (((cartprodpairsurjEq) =>
% 122.84/16.21 (((dpsetconstrI) =>
% 122.84/16.21 (((dpsetconstrSub) =>
% 122.84/16.21 (((setOfPairsIsBReln) =>
% 122.84/16.21 (((dpsetconstrERa) =>
% 122.84/16.21 (((dpsetconstrEL1) =>
% 122.84/16.21 (((dpsetconstrEL2) =>
% 122.84/16.21 (((dpsetconstrER) =>
% 122.84/16.21 (((funcImageSingleton) =>
% 122.84/16.21 (((apProp) =>
% 122.84/16.21 (((app) =>
% 122.84/16.21 (((infuncsetfunc) =>
% 122.84/16.21 (((ap2p) =>
% 122.84/16.21 (((funcinfuncset) =>
% 122.84/16.21 (((lamProp) =>
% 122.84/16.21 (((lamp) =>
% 122.84/16.21 ((
% 122.84/16.21 (lam2p) =>
% 122.84/16.21 ((
% 122.84/16.21 (brelnall1) =>
% 122.84/16.21 ((
% 122.84/16.21 (brelnall2) =>
% 122.84/16.21 ((
% 122.84/16.21 (ex1E2) =>
% 122.84/16.21 ((
% 122.84/16.21 (funcGraphProp1) =>
% 122.84/16.21 ((
% 122.84/16.21 (funcGraphProp3) =>
% 122.84/16.21 ((
% 122.84/16.21 (funcGraphProp2) =>
% 122.84/16.21 ((
% 122.84/16.21 (funcextLem) =>
% 122.84/16.21 ((
% 122.84/16.21 (funcGraphProp4) =>
% 122.84/16.21 ((
% 122.84/16.21 (subbreln) =>
% 122.84/16.21 ((
% 122.84/16.21 (eqbreln) =>
% 122.84/16.21 ((
% 122.84/16.21 (funcext) =>
% 122.84/16.21 ((
% 122.84/16.21 (funcext2) =>
% 122.84/16.21 ((
% 122.84/16.21 (ap2apEq1) =>
% 122.84/16.21 ((
% 122.84/16.21 (ap2apEq2) =>
% 122.84/16.21 ((
% 122.84/16.21 (beta1) =>
% 122.84/16.21 ((
% 122.84/16.21 (eta1) =>
% 122.84/16.21 ((
% 122.84/16.21 (lam2lamEq) =>
% 122.84/16.21 ((
% 122.84/16.21 (beta2) =>
% 122.84/16.21 ((
% 122.84/16.21 (eta2) =>
% 122.84/16.21 ((
% 122.84/16.21 (iffalseProp1) =>
% 122.84/16.21 ((
% 122.84/16.21 (iffalseProp2) =>
% 122.84/16.21 ((
% 122.84/16.21 (iftrueProp1) =>
% 122.84/16.21 ((
% 122.84/16.21 (iftrueProp2) =>
% 122.84/16.21 ((
% 122.84/16.21 (ifSingleton) =>
% 122.84/16.21 ((
% 122.84/16.21 (ifp) =>
% 122.84/16.21 ((
% 122.84/16.21 (theeq) =>
% 122.84/16.21 ((
% 122.84/16.21 (iftrue) =>
% 122.84/16.21 ((
% 122.84/16.21 (iffalse) =>
% 122.84/16.21 ((
% 122.84/16.21 (iftrueorfalse) =>
% 122.84/16.21 ((
% 122.84/16.21 (binintersectT_lem) =>
% 122.84/16.21 ((
% 122.84/16.21 (binunionT_lem) =>
% 122.84/16.21 ((
% 122.84/16.21 (powersetT_lem) =>
% 122.84/16.21 ((
% 122.84/16.21 (setminusT_lem) =>
% 122.84/16.21 ((
% 122.84/16.21 (complementT_lem) =>
% 122.84/16.21 ((
% 122.84/16.21 (setextT) =>
% 122.84/16.21 ((
% 122.84/16.21 (subsetTI) =>
% 122.84/16.21 ((
% 122.84/16.21 (powersetTI1) =>
% 122.84/16.21 ((
% 122.84/16.21 (powersetTE1) =>
% 122.84/16.21 ((
% 122.84/16.21 (complementTI1) =>
% 122.84/16.21 ((
% 122.84/16.21 (complementTE1) =>
% 122.84/16.21 ((
% 122.84/16.21 (binintersectTELcontra) =>
% 122.84/16.21 ((
% 122.84/16.21 (binintersectTERcontra) =>
% 122.84/16.21 ((
% 122.84/16.21 (contrasubsetT) =>
% 122.84/16.21 ((
% 122.84/16.21 (contrasubsetT1) =>
% 122.84/16.21 ((
% 122.84/16.21 (contrasubsetT2) =>
% 122.84/16.21 ((
% 122.84/16.21 (contrasubsetT3) =>
% 122.84/16.21 ((
% 122.84/16.21 (doubleComplementI1) =>
% 122.84/16.21 ((
% 122.84/16.21 (doubleComplementE1) =>
% 122.84/16.21 ((
% 122.84/16.21 (doubleComplementSub1) =>
% 122.84/16.21 ((
% 122.84/16.21 (doubleComplementSub2) =>
% 122.84/16.21 ((
% 122.84/16.21 (doubleComplementEq) =>
% 122.84/16.21 ((
% 122.84/16.21 (complementTnotintersectT) =>
% 122.84/16.21 ((
% 122.84/16.21 (complementImpComplementIntersect) =>
% 122.84/16.21 ((
% 122.84/16.21 (complementSubsetComplementIntersect) =>
% 122.84/16.21 ((
% 122.84/16.21 (complementInPowersetComplementIntersect) =>
% 122.84/16.21 ((
% 122.84/16.21 (contraSubsetComplement) =>
% 122.84/16.21 ((
% 122.84/16.21 (complementTcontraSubset) =>
% 122.84/16.21 ((
% 122.84/16.21 (binunionTILcontra) =>
% 122.84/16.21 ((
% 122.84/16.21 (binunionTIRcontra) =>
% 122.84/16.21 ((
% 122.84/16.21 (inIntersectImpInUnion) =>
% 122.84/16.21 ((
% 122.84/16.21 (inIntersectImpInUnion2) =>
% 122.84/16.21 ((
% 122.84/16.21 (inIntersectImpInIntersectUnions) =>
% 122.84/16.21 ((
% 122.84/16.21 (intersectInPowersetIntersectUnions) =>
% 122.84/16.21 ((
% 122.84/16.21 (inComplementUnionImpNotIn1) =>
% 122.84/16.21 ((
% 122.84/16.21 (inComplementUnionImpInComplement1) =>
% 122.84/16.21 ((
% 122.84/16.21 (binunionTE) =>
% 122.84/16.21 ((
% 122.84/16.21 (binunionTEcontra) =>
% 122.84/16.21 ((
% 122.84/16.21 (demorgan2a1) =>
% 122.84/16.21 ((
% 122.84/16.21 (complementUnionInPowersetComplement) =>
% 122.84/16.21 ((
% 122.84/16.21 (demorgan2a2) =>
% 122.84/16.21 ((
% 122.84/16.21 (demorgan1a) =>
% 122.84/16.21 ((
% 122.84/16.21 (demorgan1b) =>
% 122.84/16.21 ((
% 122.84/16.21 (demorgan1) =>
% 122.84/16.21 ((
% 122.84/16.21 (demorgan2a) =>
% 122.84/16.21 ((
% 122.84/16.21 (demorgan2b2) =>
% 122.84/16.21 ((
% 122.84/16.21 (demorgan2b) =>
% 122.84/16.21 ((
% 122.84/16.21 (demorgan2) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz13rule0) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz13rule1) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz13rule2) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz13rule3) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz13rule4) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz1_1) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz1_2) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz1_3) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz1_4) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz1_5) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1all2) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1SetBreln1) =>
% 122.84/16.21 ((
% 122.84/16.21 (choice2fnsingleton) =>
% 122.84/16.21 ((
% 122.84/16.21 (setOfPairsIsBReln1) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1all1) =>
% 122.84/16.21 ((
% 122.84/16.21 (subbreln1) =>
% 122.84/16.21 ((
% 122.84/16.21 (eqbreln1) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1invprop) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1invI) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1invE) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1compprop) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1compI) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1compE) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1compEex) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1unionprop) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1unionIL) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1unionIR) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1unionI) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1unionE) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1unionEcases) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1unionCommutes) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz2Ex) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz2W) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz2A) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz2B) =>
% 122.84/16.21 ((
% 122.84/16.21 (image1Ex) =>
% 122.84/16.21 ((
% 122.84/16.21 (image1Ex1) =>
% 122.84/16.21 ((
% 122.84/16.21 (image1Equiv) =>
% 122.84/16.21 ((
% 122.84/16.21 (image1E) =>
% 122.84/16.21 ((
% 122.84/16.21 (image1I) =>
% 122.84/16.21 ((
% 122.84/16.21 (injFuncInInjFuncSet) =>
% 122.84/16.21 ((
% 122.84/16.21 (!!) @ (
% 122.84/16.21 (('#B') @ (
% 122.84/16.21 !!) @
% 122.84/16.21 (
% 122.84/16.21 (
% 122.84/16.21 ('#B') @ (
% 122.84/16.21 (
% 122.84/16.21 ('#B') @ (
% 122.84/16.21 !!))) @
% 122.84/16.21 (
% 122.84/16.21 (
% 122.84/16.21 ('#S') @ (
% 122.84/16.21 (
% 122.84/16.21 ('#B') @ (
% 122.84/16.21 '#S') @
% 122.84/16.21 (
% 122.84/16.21 (
% 122.84/16.21 ('#B') @ (
% 122.84/16.21 (
% 122.84/16.21 ('#B') @ (
% 122.84/16.21 '#S'))) @
% 122.84/16.21 (
% 122.84/16.21 (
% 122.84/16.21 ('#B') @ (
% 122.84/16.21 (
% 122.84/16.21 ('#B') @ (
% 122.84/16.21 (
% 122.84/16.21 ('#B') @ (
% 122.84/16.21 =>))))) @
% 122.84/16.21 (
% 122.84/16.21 (
% 122.84/16.21 ('#B') @ (
% 122.84/16.21 (
% 122.84/16.21 ('#B') @ (
% 122.84/16.21 (
% 122.84/16.21 ('#C') @ in)))) @
% 122.84/16.21 injFuncSet)))))))) @
% 122.84/16.21 (
% 122.84/16.21 (
% 122.84/16.21 ('#B') @ (
% 122.84/16.21 (
% 122.84/16.21 ('#B') @ (
% 122.84/16.21 (
% 122.84/16.21 ('#C') @ in)))) @
% 122.84/16.21 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.84/16.21 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1695])).
% 122.84/16.21 thf(zip_derived_cl1725, plain,
% 122.84/16.21 (~ (((setukpairinjR1) =>
% 122.84/16.21 (((upairequniteq) =>
% 122.84/16.21 (((setukpairinjR2) =>
% 122.84/16.21 (((setukpairinjR) =>
% 122.84/16.21 (((ksndsingleton) =>
% 122.84/16.21 (((ksndpairEq) =>
% 122.84/16.21 (((kpairsurjEq) =>
% 122.84/16.21 (((cartprodsndin) =>
% 122.84/16.21 (((cartprodpairmemEL) =>
% 122.84/16.21 (((cartprodpairmemER) =>
% 122.84/16.21 (((cartprodmempaircEq) =>
% 122.84/16.21 (((cartprodfstpairEq) =>
% 122.84/16.21 (((cartprodsndpairEq) =>
% 122.84/16.21 (((cartprodpairsurjEq) =>
% 122.84/16.21 (((dpsetconstrI) =>
% 122.84/16.21 (((dpsetconstrSub) =>
% 122.84/16.21 (((setOfPairsIsBReln) =>
% 122.84/16.21 (((dpsetconstrERa) =>
% 122.84/16.21 (((dpsetconstrEL1) =>
% 122.84/16.21 (((dpsetconstrEL2) =>
% 122.84/16.21 (((dpsetconstrER) =>
% 122.84/16.21 (((funcImageSingleton) =>
% 122.84/16.21 (((apProp) =>
% 122.84/16.21 (((app) =>
% 122.84/16.21 (((infuncsetfunc) =>
% 122.84/16.21 (((ap2p) =>
% 122.84/16.21 (((funcinfuncset) =>
% 122.84/16.21 (((lamProp) =>
% 122.84/16.21 (((lamp) =>
% 122.84/16.21 (((lam2p) =>
% 122.84/16.21 ((
% 122.84/16.21 (brelnall1) =>
% 122.84/16.21 ((
% 122.84/16.21 (brelnall2) =>
% 122.84/16.21 ((
% 122.84/16.21 (ex1E2) =>
% 122.84/16.21 ((
% 122.84/16.21 (funcGraphProp1) =>
% 122.84/16.21 ((
% 122.84/16.21 (funcGraphProp3) =>
% 122.84/16.21 ((
% 122.84/16.21 (funcGraphProp2) =>
% 122.84/16.21 ((
% 122.84/16.21 (funcextLem) =>
% 122.84/16.21 ((
% 122.84/16.21 (funcGraphProp4) =>
% 122.84/16.21 ((
% 122.84/16.21 (subbreln) =>
% 122.84/16.21 ((
% 122.84/16.21 (eqbreln) =>
% 122.84/16.21 ((
% 122.84/16.21 (funcext) =>
% 122.84/16.21 ((
% 122.84/16.21 (funcext2) =>
% 122.84/16.21 ((
% 122.84/16.21 (ap2apEq1) =>
% 122.84/16.21 ((
% 122.84/16.21 (ap2apEq2) =>
% 122.84/16.21 ((
% 122.84/16.21 (beta1) =>
% 122.84/16.21 ((
% 122.84/16.21 (eta1) =>
% 122.84/16.21 ((
% 122.84/16.21 (lam2lamEq) =>
% 122.84/16.21 ((
% 122.84/16.21 (beta2) =>
% 122.84/16.21 ((
% 122.84/16.21 (eta2) =>
% 122.84/16.21 ((
% 122.84/16.21 (iffalseProp1) =>
% 122.84/16.21 ((
% 122.84/16.21 (iffalseProp2) =>
% 122.84/16.21 ((
% 122.84/16.21 (iftrueProp1) =>
% 122.84/16.21 ((
% 122.84/16.21 (iftrueProp2) =>
% 122.84/16.21 ((
% 122.84/16.21 (ifSingleton) =>
% 122.84/16.21 ((
% 122.84/16.21 (ifp) =>
% 122.84/16.21 ((
% 122.84/16.21 (theeq) =>
% 122.84/16.21 ((
% 122.84/16.21 (iftrue) =>
% 122.84/16.21 ((
% 122.84/16.21 (iffalse) =>
% 122.84/16.21 ((
% 122.84/16.21 (iftrueorfalse) =>
% 122.84/16.21 ((
% 122.84/16.21 (binintersectT_lem) =>
% 122.84/16.21 ((
% 122.84/16.21 (binunionT_lem) =>
% 122.84/16.21 ((
% 122.84/16.21 (powersetT_lem) =>
% 122.84/16.21 ((
% 122.84/16.21 (setminusT_lem) =>
% 122.84/16.21 ((
% 122.84/16.21 (complementT_lem) =>
% 122.84/16.21 ((
% 122.84/16.21 (setextT) =>
% 122.84/16.21 ((
% 122.84/16.21 (subsetTI) =>
% 122.84/16.21 ((
% 122.84/16.21 (powersetTI1) =>
% 122.84/16.21 ((
% 122.84/16.21 (powersetTE1) =>
% 122.84/16.21 ((
% 122.84/16.21 (complementTI1) =>
% 122.84/16.21 ((
% 122.84/16.21 (complementTE1) =>
% 122.84/16.21 ((
% 122.84/16.21 (binintersectTELcontra) =>
% 122.84/16.21 ((
% 122.84/16.21 (binintersectTERcontra) =>
% 122.84/16.21 ((
% 122.84/16.21 (contrasubsetT) =>
% 122.84/16.21 ((
% 122.84/16.21 (contrasubsetT1) =>
% 122.84/16.21 ((
% 122.84/16.21 (contrasubsetT2) =>
% 122.84/16.21 ((
% 122.84/16.21 (contrasubsetT3) =>
% 122.84/16.21 ((
% 122.84/16.21 (doubleComplementI1) =>
% 122.84/16.21 ((
% 122.84/16.21 (doubleComplementE1) =>
% 122.84/16.21 ((
% 122.84/16.21 (doubleComplementSub1) =>
% 122.84/16.21 ((
% 122.84/16.21 (doubleComplementSub2) =>
% 122.84/16.21 ((
% 122.84/16.21 (doubleComplementEq) =>
% 122.84/16.21 ((
% 122.84/16.21 (complementTnotintersectT) =>
% 122.84/16.21 ((
% 122.84/16.21 (complementImpComplementIntersect) =>
% 122.84/16.21 ((
% 122.84/16.21 (complementSubsetComplementIntersect) =>
% 122.84/16.21 ((
% 122.84/16.21 (complementInPowersetComplementIntersect) =>
% 122.84/16.21 ((
% 122.84/16.21 (contraSubsetComplement) =>
% 122.84/16.21 ((
% 122.84/16.21 (complementTcontraSubset) =>
% 122.84/16.21 ((
% 122.84/16.21 (binunionTILcontra) =>
% 122.84/16.21 ((
% 122.84/16.21 (binunionTIRcontra) =>
% 122.84/16.21 ((
% 122.84/16.21 (inIntersectImpInUnion) =>
% 122.84/16.21 ((
% 122.84/16.21 (inIntersectImpInUnion2) =>
% 122.84/16.21 ((
% 122.84/16.21 (inIntersectImpInIntersectUnions) =>
% 122.84/16.21 ((
% 122.84/16.21 (intersectInPowersetIntersectUnions) =>
% 122.84/16.21 ((
% 122.84/16.21 (inComplementUnionImpNotIn1) =>
% 122.84/16.21 ((
% 122.84/16.21 (inComplementUnionImpInComplement1) =>
% 122.84/16.21 ((
% 122.84/16.21 (binunionTE) =>
% 122.84/16.21 ((
% 122.84/16.21 (binunionTEcontra) =>
% 122.84/16.21 ((
% 122.84/16.21 (demorgan2a1) =>
% 122.84/16.21 ((
% 122.84/16.21 (complementUnionInPowersetComplement) =>
% 122.84/16.21 ((
% 122.84/16.21 (demorgan2a2) =>
% 122.84/16.21 ((
% 122.84/16.21 (demorgan1a) =>
% 122.84/16.21 ((
% 122.84/16.21 (demorgan1b) =>
% 122.84/16.21 ((
% 122.84/16.21 (demorgan1) =>
% 122.84/16.21 ((
% 122.84/16.21 (demorgan2a) =>
% 122.84/16.21 ((
% 122.84/16.21 (demorgan2b2) =>
% 122.84/16.21 ((
% 122.84/16.21 (demorgan2b) =>
% 122.84/16.21 ((
% 122.84/16.21 (demorgan2) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz13rule0) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz13rule1) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz13rule2) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz13rule3) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz13rule4) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz1_1) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz1_2) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz1_3) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz1_4) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz1_5) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1all2) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1SetBreln1) =>
% 122.84/16.21 ((
% 122.84/16.21 (choice2fnsingleton) =>
% 122.84/16.21 ((
% 122.84/16.21 (setOfPairsIsBReln1) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1all1) =>
% 122.84/16.21 ((
% 122.84/16.21 (subbreln1) =>
% 122.84/16.21 ((
% 122.84/16.21 (eqbreln1) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1invprop) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1invI) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1invE) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1compprop) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1compI) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1compE) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1compEex) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1unionprop) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1unionIL) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1unionIR) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1unionI) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1unionE) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1unionEcases) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1unionCommutes) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz2Ex) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz2W) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz2A) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz2B) =>
% 122.84/16.21 ((
% 122.84/16.21 (image1Ex) =>
% 122.84/16.21 ((
% 122.84/16.21 (image1Ex1) =>
% 122.84/16.21 ((
% 122.84/16.21 (image1Equiv) =>
% 122.84/16.21 ((
% 122.84/16.21 (image1E) =>
% 122.84/16.21 ((
% 122.84/16.21 (image1I) =>
% 122.84/16.21 ((
% 122.84/16.21 (injFuncInInjFuncSet) =>
% 122.84/16.21 ((
% 122.84/16.21 (!!) @ (
% 122.84/16.21 (('#B') @ (
% 122.84/16.21 !!) @
% 122.84/16.21 (
% 122.84/16.21 (
% 122.84/16.21 ('#B') @ (
% 122.84/16.21 (
% 122.84/16.21 ('#B') @ (
% 122.84/16.21 !!))) @
% 122.84/16.21 (
% 122.84/16.21 (
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% 122.84/16.21 (
% 122.84/16.21 ('#B') @ (
% 122.84/16.21 '#S') @
% 122.84/16.21 (
% 122.84/16.21 (
% 122.84/16.21 ('#B') @ (
% 122.84/16.21 (
% 122.84/16.21 ('#B') @ (
% 122.84/16.21 '#S'))) @
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% 122.84/16.21 (
% 122.84/16.21 ('#B') @ (
% 122.84/16.21 (
% 122.84/16.21 ('#B') @ (
% 122.84/16.21 (
% 122.84/16.21 ('#B') @ (
% 122.84/16.21 =>))))) @
% 122.84/16.21 (
% 122.84/16.21 (
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% 122.84/16.21 injFuncSet)))))))) @
% 122.84/16.21 (
% 122.84/16.21 (
% 122.84/16.21 ('#B') @ (
% 122.84/16.21 (
% 122.84/16.21 ('#B') @ (
% 122.84/16.21 (
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% 122.84/16.21 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.84/16.21 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1711])).
% 122.84/16.21 thf(zip_derived_cl1738, plain,
% 122.84/16.21 (~ (((upairequniteq) =>
% 122.84/16.21 (((setukpairinjR2) =>
% 122.84/16.21 (((setukpairinjR) =>
% 122.84/16.21 (((ksndsingleton) =>
% 122.84/16.21 (((ksndpairEq) =>
% 122.84/16.21 (((kpairsurjEq) =>
% 122.84/16.21 (((cartprodsndin) =>
% 122.84/16.21 (((cartprodpairmemEL) =>
% 122.84/16.21 (((cartprodpairmemER) =>
% 122.84/16.21 (((cartprodmempaircEq) =>
% 122.84/16.21 (((cartprodfstpairEq) =>
% 122.84/16.21 (((cartprodsndpairEq) =>
% 122.84/16.21 (((cartprodpairsurjEq) =>
% 122.84/16.21 (((dpsetconstrI) =>
% 122.84/16.21 (((dpsetconstrSub) =>
% 122.84/16.21 (((setOfPairsIsBReln) =>
% 122.84/16.21 (((dpsetconstrERa) =>
% 122.84/16.21 (((dpsetconstrEL1) =>
% 122.84/16.21 (((dpsetconstrEL2) =>
% 122.84/16.21 (((dpsetconstrER) =>
% 122.84/16.21 (((funcImageSingleton) =>
% 122.84/16.21 (((apProp) =>
% 122.84/16.21 (((app) =>
% 122.84/16.21 (((infuncsetfunc) =>
% 122.84/16.21 (((ap2p) =>
% 122.84/16.21 (((funcinfuncset) =>
% 122.84/16.21 (((lamProp) =>
% 122.84/16.21 (((lamp) =>
% 122.84/16.21 (((lam2p) =>
% 122.84/16.21 (((brelnall1) =>
% 122.84/16.21 ((
% 122.84/16.21 (brelnall2) =>
% 122.84/16.21 ((
% 122.84/16.21 (ex1E2) =>
% 122.84/16.21 ((
% 122.84/16.21 (funcGraphProp1) =>
% 122.84/16.21 ((
% 122.84/16.21 (funcGraphProp3) =>
% 122.84/16.21 ((
% 122.84/16.21 (funcGraphProp2) =>
% 122.84/16.21 ((
% 122.84/16.21 (funcextLem) =>
% 122.84/16.21 ((
% 122.84/16.21 (funcGraphProp4) =>
% 122.84/16.21 ((
% 122.84/16.21 (subbreln) =>
% 122.84/16.21 ((
% 122.84/16.21 (eqbreln) =>
% 122.84/16.21 ((
% 122.84/16.21 (funcext) =>
% 122.84/16.21 ((
% 122.84/16.21 (funcext2) =>
% 122.84/16.21 ((
% 122.84/16.21 (ap2apEq1) =>
% 122.84/16.21 ((
% 122.84/16.21 (ap2apEq2) =>
% 122.84/16.21 ((
% 122.84/16.21 (beta1) =>
% 122.84/16.21 ((
% 122.84/16.21 (eta1) =>
% 122.84/16.21 ((
% 122.84/16.21 (lam2lamEq) =>
% 122.84/16.21 ((
% 122.84/16.21 (beta2) =>
% 122.84/16.21 ((
% 122.84/16.21 (eta2) =>
% 122.84/16.21 ((
% 122.84/16.21 (iffalseProp1) =>
% 122.84/16.21 ((
% 122.84/16.21 (iffalseProp2) =>
% 122.84/16.21 ((
% 122.84/16.21 (iftrueProp1) =>
% 122.84/16.21 ((
% 122.84/16.21 (iftrueProp2) =>
% 122.84/16.21 ((
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% 122.84/16.21 ((
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% 122.84/16.21 ((
% 122.84/16.21 (theeq) =>
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% 122.84/16.21 ((
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% 122.84/16.21 ((
% 122.84/16.21 (iftrueorfalse) =>
% 122.84/16.21 ((
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% 122.84/16.21 ((
% 122.84/16.21 (binunionT_lem) =>
% 122.84/16.21 ((
% 122.84/16.21 (powersetT_lem) =>
% 122.84/16.21 ((
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% 122.84/16.21 ((
% 122.84/16.21 (complementT_lem) =>
% 122.84/16.21 ((
% 122.84/16.21 (setextT) =>
% 122.84/16.21 ((
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% 122.84/16.21 ((
% 122.84/16.21 (powersetTI1) =>
% 122.84/16.21 ((
% 122.84/16.21 (powersetTE1) =>
% 122.84/16.21 ((
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% 122.84/16.21 ((
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% 122.84/16.21 ((
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% 122.84/16.21 ((
% 122.84/16.21 (binintersectTERcontra) =>
% 122.84/16.21 ((
% 122.84/16.21 (contrasubsetT) =>
% 122.84/16.21 ((
% 122.84/16.21 (contrasubsetT1) =>
% 122.84/16.21 ((
% 122.84/16.21 (contrasubsetT2) =>
% 122.84/16.21 ((
% 122.84/16.21 (contrasubsetT3) =>
% 122.84/16.21 ((
% 122.84/16.21 (doubleComplementI1) =>
% 122.84/16.21 ((
% 122.84/16.21 (doubleComplementE1) =>
% 122.84/16.21 ((
% 122.84/16.21 (doubleComplementSub1) =>
% 122.84/16.21 ((
% 122.84/16.21 (doubleComplementSub2) =>
% 122.84/16.21 ((
% 122.84/16.21 (doubleComplementEq) =>
% 122.84/16.21 ((
% 122.84/16.21 (complementTnotintersectT) =>
% 122.84/16.21 ((
% 122.84/16.21 (complementImpComplementIntersect) =>
% 122.84/16.21 ((
% 122.84/16.21 (complementSubsetComplementIntersect) =>
% 122.84/16.21 ((
% 122.84/16.21 (complementInPowersetComplementIntersect) =>
% 122.84/16.21 ((
% 122.84/16.21 (contraSubsetComplement) =>
% 122.84/16.21 ((
% 122.84/16.21 (complementTcontraSubset) =>
% 122.84/16.21 ((
% 122.84/16.21 (binunionTILcontra) =>
% 122.84/16.21 ((
% 122.84/16.21 (binunionTIRcontra) =>
% 122.84/16.21 ((
% 122.84/16.21 (inIntersectImpInUnion) =>
% 122.84/16.21 ((
% 122.84/16.21 (inIntersectImpInUnion2) =>
% 122.84/16.21 ((
% 122.84/16.21 (inIntersectImpInIntersectUnions) =>
% 122.84/16.21 ((
% 122.84/16.21 (intersectInPowersetIntersectUnions) =>
% 122.84/16.21 ((
% 122.84/16.21 (inComplementUnionImpNotIn1) =>
% 122.84/16.21 ((
% 122.84/16.21 (inComplementUnionImpInComplement1) =>
% 122.84/16.21 ((
% 122.84/16.21 (binunionTE) =>
% 122.84/16.21 ((
% 122.84/16.21 (binunionTEcontra) =>
% 122.84/16.21 ((
% 122.84/16.21 (demorgan2a1) =>
% 122.84/16.21 ((
% 122.84/16.21 (complementUnionInPowersetComplement) =>
% 122.84/16.21 ((
% 122.84/16.21 (demorgan2a2) =>
% 122.84/16.21 ((
% 122.84/16.21 (demorgan1a) =>
% 122.84/16.21 ((
% 122.84/16.21 (demorgan1b) =>
% 122.84/16.21 ((
% 122.84/16.21 (demorgan1) =>
% 122.84/16.21 ((
% 122.84/16.21 (demorgan2a) =>
% 122.84/16.21 ((
% 122.84/16.21 (demorgan2b2) =>
% 122.84/16.21 ((
% 122.84/16.21 (demorgan2b) =>
% 122.84/16.21 ((
% 122.84/16.21 (demorgan2) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz13rule0) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz13rule1) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz13rule2) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz13rule3) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz13rule4) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz1_1) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz1_2) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz1_3) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz1_4) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz1_5) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1all2) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1SetBreln1) =>
% 122.84/16.21 ((
% 122.84/16.21 (choice2fnsingleton) =>
% 122.84/16.21 ((
% 122.84/16.21 (setOfPairsIsBReln1) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1all1) =>
% 122.84/16.21 ((
% 122.84/16.21 (subbreln1) =>
% 122.84/16.21 ((
% 122.84/16.21 (eqbreln1) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1invprop) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1invI) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1invE) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1compprop) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1compI) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1compE) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1compEex) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1unionprop) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1unionIL) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1unionIR) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1unionI) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1unionE) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1unionEcases) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1unionCommutes) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz2Ex) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz2W) =>
% 122.84/16.21 ((
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% 122.84/16.21 ((
% 122.84/16.21 (woz2B) =>
% 122.84/16.21 ((
% 122.84/16.21 (image1Ex) =>
% 122.84/16.21 ((
% 122.84/16.21 (image1Ex1) =>
% 122.84/16.21 ((
% 122.84/16.21 (image1Equiv) =>
% 122.84/16.21 ((
% 122.84/16.21 (image1E) =>
% 122.84/16.21 ((
% 122.84/16.21 (image1I) =>
% 122.84/16.21 ((
% 122.84/16.21 (injFuncInInjFuncSet) =>
% 122.84/16.21 ((
% 122.84/16.21 (!!) @ (
% 122.84/16.21 (('#B') @ (
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% 122.84/16.21 (
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% 122.84/16.21 injFuncSet)))))))) @
% 122.84/16.21 (
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% 122.84/16.21 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1725])).
% 122.84/16.21 thf(zip_derived_cl1749, plain,
% 122.84/16.21 (~ (((setukpairinjR2) =>
% 122.84/16.21 (((setukpairinjR) =>
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% 122.84/16.21 (((cartprodpairmemER) =>
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% 122.84/16.21 (((cartprodsndpairEq) =>
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% 122.84/16.21 (((dpsetconstrERa) =>
% 122.84/16.21 (((dpsetconstrEL1) =>
% 122.84/16.21 (((dpsetconstrEL2) =>
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% 122.84/16.21 (((lam2p) =>
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% 122.84/16.21 (((brelnall2) =>
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% 122.84/16.21 ((
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% 122.84/16.21 ((
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% 122.84/16.21 ((
% 122.84/16.21 (funcGraphProp2) =>
% 122.84/16.21 ((
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% 122.84/16.21 ((
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% 122.84/16.21 ((
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% 122.84/16.21 ((
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% 122.84/16.21 ((
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% 122.84/16.21 ((
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% 122.84/16.21 ((
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% 122.84/16.21 ((
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% 122.84/16.21 ((
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% 122.84/16.21 ((
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% 122.84/16.21 ((
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% 122.84/16.21 ((
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% 122.84/16.21 ((
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% 122.84/16.21 ((
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% 122.84/16.21 ((
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% 122.84/16.21 ((
% 122.84/16.21 (powersetT_lem) =>
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% 122.84/16.21 ((
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% 122.84/16.21 ((
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% 122.84/16.21 ((
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% 122.84/16.21 ((
% 122.84/16.21 (powersetTE1) =>
% 122.84/16.21 ((
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% 122.84/16.21 ((
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% 122.84/16.21 ((
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% 122.84/16.21 ((
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% 122.84/16.21 ((
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% 122.84/16.21 ((
% 122.84/16.21 (contrasubsetT2) =>
% 122.84/16.21 ((
% 122.84/16.21 (contrasubsetT3) =>
% 122.84/16.21 ((
% 122.84/16.21 (doubleComplementI1) =>
% 122.84/16.21 ((
% 122.84/16.21 (doubleComplementE1) =>
% 122.84/16.21 ((
% 122.84/16.21 (doubleComplementSub1) =>
% 122.84/16.21 ((
% 122.84/16.21 (doubleComplementSub2) =>
% 122.84/16.21 ((
% 122.84/16.21 (doubleComplementEq) =>
% 122.84/16.21 ((
% 122.84/16.21 (complementTnotintersectT) =>
% 122.84/16.21 ((
% 122.84/16.21 (complementImpComplementIntersect) =>
% 122.84/16.21 ((
% 122.84/16.21 (complementSubsetComplementIntersect) =>
% 122.84/16.21 ((
% 122.84/16.21 (complementInPowersetComplementIntersect) =>
% 122.84/16.21 ((
% 122.84/16.21 (contraSubsetComplement) =>
% 122.84/16.21 ((
% 122.84/16.21 (complementTcontraSubset) =>
% 122.84/16.21 ((
% 122.84/16.21 (binunionTILcontra) =>
% 122.84/16.21 ((
% 122.84/16.21 (binunionTIRcontra) =>
% 122.84/16.21 ((
% 122.84/16.21 (inIntersectImpInUnion) =>
% 122.84/16.21 ((
% 122.84/16.21 (inIntersectImpInUnion2) =>
% 122.84/16.21 ((
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% 122.84/16.21 ((
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% 122.84/16.21 ((
% 122.84/16.21 (inComplementUnionImpInComplement1) =>
% 122.84/16.21 ((
% 122.84/16.21 (binunionTE) =>
% 122.84/16.21 ((
% 122.84/16.21 (binunionTEcontra) =>
% 122.84/16.21 ((
% 122.84/16.21 (demorgan2a1) =>
% 122.84/16.21 ((
% 122.84/16.21 (complementUnionInPowersetComplement) =>
% 122.84/16.21 ((
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% 122.84/16.21 ((
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% 122.84/16.21 ((
% 122.84/16.21 (demorgan1b) =>
% 122.84/16.21 ((
% 122.84/16.21 (demorgan1) =>
% 122.84/16.21 ((
% 122.84/16.21 (demorgan2a) =>
% 122.84/16.21 ((
% 122.84/16.21 (demorgan2b2) =>
% 122.84/16.21 ((
% 122.84/16.21 (demorgan2b) =>
% 122.84/16.21 ((
% 122.84/16.21 (demorgan2) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz13rule0) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz13rule1) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz13rule2) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz13rule3) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz13rule4) =>
% 122.84/16.21 ((
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% 122.84/16.21 ((
% 122.84/16.21 (woz1_2) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz1_3) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz1_4) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz1_5) =>
% 122.84/16.21 ((
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% 122.84/16.21 ((
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% 122.84/16.21 ((
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% 122.84/16.21 ((
% 122.84/16.21 (setOfPairsIsBReln1) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1all1) =>
% 122.84/16.21 ((
% 122.84/16.21 (subbreln1) =>
% 122.84/16.21 ((
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% 122.84/16.21 ((
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% 122.84/16.21 ((
% 122.84/16.21 (breln1invI) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1invE) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1compprop) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1compI) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1compE) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1compEex) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1unionprop) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1unionIL) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1unionIR) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1unionI) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1unionE) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1unionEcases) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1unionCommutes) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz2Ex) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz2W) =>
% 122.84/16.21 ((
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% 122.84/16.21 ((
% 122.84/16.21 (woz2B) =>
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% 122.84/16.21 ((
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% 122.84/16.21 ((
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% 122.84/16.21 ((
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% 122.84/16.21 ((
% 122.84/16.21 (image1I) =>
% 122.84/16.21 ((
% 122.84/16.21 (injFuncInInjFuncSet) =>
% 122.84/16.21 ((
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% 122.84/16.21 (
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% 122.84/16.21 (
% 122.84/16.21 ('#B') @ (
% 122.84/16.21 !!))) @
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% 122.84/16.21 injFuncSet)))))))) @
% 122.84/16.21 (
% 122.84/16.21 (
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% 122.84/16.21 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.84/16.21 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1738])).
% 122.84/16.21 thf(zip_derived_cl1760, plain,
% 122.84/16.21 (~ (((setukpairinjR) =>
% 122.84/16.21 (((ksndsingleton) =>
% 122.84/16.21 (((ksndpairEq) =>
% 122.84/16.21 (((kpairsurjEq) =>
% 122.84/16.21 (((cartprodsndin) =>
% 122.84/16.21 (((cartprodpairmemEL) =>
% 122.84/16.21 (((cartprodpairmemER) =>
% 122.84/16.21 (((cartprodmempaircEq) =>
% 122.84/16.21 (((cartprodfstpairEq) =>
% 122.84/16.21 (((cartprodsndpairEq) =>
% 122.84/16.21 (((cartprodpairsurjEq) =>
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% 122.84/16.21 (((dpsetconstrSub) =>
% 122.84/16.21 (((setOfPairsIsBReln) =>
% 122.84/16.21 (((dpsetconstrERa) =>
% 122.84/16.21 (((dpsetconstrEL1) =>
% 122.84/16.21 (((dpsetconstrEL2) =>
% 122.84/16.21 (((dpsetconstrER) =>
% 122.84/16.21 (((funcImageSingleton) =>
% 122.84/16.21 (((apProp) =>
% 122.84/16.21 (((app) =>
% 122.84/16.21 (((infuncsetfunc) =>
% 122.84/16.21 (((ap2p) =>
% 122.84/16.21 (((funcinfuncset) =>
% 122.84/16.21 (((lamProp) =>
% 122.84/16.21 (((lamp) =>
% 122.84/16.21 (((lam2p) =>
% 122.84/16.21 (((brelnall1) =>
% 122.84/16.21 (((brelnall2) =>
% 122.84/16.21 (((ex1E2) =>
% 122.84/16.21 ((
% 122.84/16.21 (funcGraphProp1) =>
% 122.84/16.21 ((
% 122.84/16.21 (funcGraphProp3) =>
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% 122.84/16.21 (funcGraphProp2) =>
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% 122.84/16.21 ((
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% 122.84/16.21 ((
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% 122.84/16.21 ((
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% 122.84/16.21 ((
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% 122.84/16.21 ((
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% 122.84/16.21 ((
% 122.84/16.21 (ap2apEq2) =>
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% 122.84/16.21 ((
% 122.84/16.21 (eta1) =>
% 122.84/16.21 ((
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% 122.84/16.21 ((
% 122.84/16.21 (beta2) =>
% 122.84/16.21 ((
% 122.84/16.21 (eta2) =>
% 122.84/16.21 ((
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% 122.84/16.21 ((
% 122.84/16.21 (iffalseProp2) =>
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% 122.84/16.21 (iftrueProp1) =>
% 122.84/16.21 ((
% 122.84/16.21 (iftrueProp2) =>
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% 122.84/16.21 ((
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% 122.84/16.21 (theeq) =>
% 122.84/16.21 ((
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% 122.84/16.21 ((
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% 122.84/16.21 ((
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% 122.84/16.21 ((
% 122.84/16.21 (powersetT_lem) =>
% 122.84/16.21 ((
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% 122.84/16.21 ((
% 122.84/16.21 (complementT_lem) =>
% 122.84/16.21 ((
% 122.84/16.21 (setextT) =>
% 122.84/16.21 ((
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% 122.84/16.21 ((
% 122.84/16.21 (powersetTI1) =>
% 122.84/16.21 ((
% 122.84/16.21 (powersetTE1) =>
% 122.84/16.21 ((
% 122.84/16.21 (complementTI1) =>
% 122.84/16.21 ((
% 122.84/16.21 (complementTE1) =>
% 122.84/16.21 ((
% 122.84/16.21 (binintersectTELcontra) =>
% 122.84/16.21 ((
% 122.84/16.21 (binintersectTERcontra) =>
% 122.84/16.21 ((
% 122.84/16.21 (contrasubsetT) =>
% 122.84/16.21 ((
% 122.84/16.21 (contrasubsetT1) =>
% 122.84/16.21 ((
% 122.84/16.21 (contrasubsetT2) =>
% 122.84/16.21 ((
% 122.84/16.21 (contrasubsetT3) =>
% 122.84/16.21 ((
% 122.84/16.21 (doubleComplementI1) =>
% 122.84/16.21 ((
% 122.84/16.21 (doubleComplementE1) =>
% 122.84/16.21 ((
% 122.84/16.21 (doubleComplementSub1) =>
% 122.84/16.21 ((
% 122.84/16.21 (doubleComplementSub2) =>
% 122.84/16.21 ((
% 122.84/16.21 (doubleComplementEq) =>
% 122.84/16.21 ((
% 122.84/16.21 (complementTnotintersectT) =>
% 122.84/16.21 ((
% 122.84/16.21 (complementImpComplementIntersect) =>
% 122.84/16.21 ((
% 122.84/16.21 (complementSubsetComplementIntersect) =>
% 122.84/16.21 ((
% 122.84/16.21 (complementInPowersetComplementIntersect) =>
% 122.84/16.21 ((
% 122.84/16.21 (contraSubsetComplement) =>
% 122.84/16.21 ((
% 122.84/16.21 (complementTcontraSubset) =>
% 122.84/16.21 ((
% 122.84/16.21 (binunionTILcontra) =>
% 122.84/16.21 ((
% 122.84/16.21 (binunionTIRcontra) =>
% 122.84/16.21 ((
% 122.84/16.21 (inIntersectImpInUnion) =>
% 122.84/16.21 ((
% 122.84/16.21 (inIntersectImpInUnion2) =>
% 122.84/16.21 ((
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% 122.84/16.21 ((
% 122.84/16.21 (intersectInPowersetIntersectUnions) =>
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% 122.84/16.21 (inComplementUnionImpNotIn1) =>
% 122.84/16.21 ((
% 122.84/16.21 (inComplementUnionImpInComplement1) =>
% 122.84/16.21 ((
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% 122.84/16.21 ((
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% 122.84/16.21 ((
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% 122.84/16.21 ((
% 122.84/16.21 (complementUnionInPowersetComplement) =>
% 122.84/16.21 ((
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% 122.84/16.21 ((
% 122.84/16.21 (demorgan1a) =>
% 122.84/16.21 ((
% 122.84/16.21 (demorgan1b) =>
% 122.84/16.21 ((
% 122.84/16.21 (demorgan1) =>
% 122.84/16.21 ((
% 122.84/16.21 (demorgan2a) =>
% 122.84/16.21 ((
% 122.84/16.21 (demorgan2b2) =>
% 122.84/16.21 ((
% 122.84/16.21 (demorgan2b) =>
% 122.84/16.21 ((
% 122.84/16.21 (demorgan2) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz13rule0) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz13rule1) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz13rule2) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz13rule3) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz13rule4) =>
% 122.84/16.21 ((
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% 122.84/16.21 ((
% 122.84/16.21 (woz1_2) =>
% 122.84/16.21 ((
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% 122.84/16.21 ((
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% 122.84/16.21 ((
% 122.84/16.21 (woz1_5) =>
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% 122.84/16.21 (breln1all2) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1SetBreln1) =>
% 122.84/16.21 ((
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% 122.84/16.21 ((
% 122.84/16.21 (setOfPairsIsBReln1) =>
% 122.84/16.21 ((
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% 122.84/16.21 ((
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% 122.84/16.21 ((
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% 122.84/16.21 ((
% 122.84/16.21 (breln1invprop) =>
% 122.84/16.21 ((
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% 122.84/16.21 ((
% 122.84/16.21 (breln1invE) =>
% 122.84/16.21 ((
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% 122.84/16.21 ((
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% 122.84/16.21 ((
% 122.84/16.21 (breln1compE) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1compEex) =>
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% 122.84/16.21 (breln1unionprop) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1unionIL) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1unionIR) =>
% 122.84/16.21 ((
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% 122.84/16.21 ((
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% 122.84/16.21 ((
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% 122.84/16.21 ((
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% 122.84/16.21 ((
% 122.84/16.21 (image1Ex1) =>
% 122.84/16.21 ((
% 122.84/16.21 (image1Equiv) =>
% 122.84/16.21 ((
% 122.84/16.21 (image1E) =>
% 122.84/16.21 ((
% 122.84/16.21 (image1I) =>
% 122.84/16.21 ((
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% 122.84/16.21 ((
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% 122.84/16.21 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1749])).
% 122.84/16.21 thf(zip_derived_cl1770, plain,
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% 122.84/16.21 ((
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% 122.84/16.21 ((
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% 122.84/16.21 (iffalseProp2) =>
% 122.84/16.21 ((
% 122.84/16.21 (iftrueProp1) =>
% 122.84/16.21 ((
% 122.84/16.21 (iftrueProp2) =>
% 122.84/16.21 ((
% 122.84/16.21 (ifSingleton) =>
% 122.84/16.21 ((
% 122.84/16.21 (ifp) =>
% 122.84/16.21 ((
% 122.84/16.21 (theeq) =>
% 122.84/16.21 ((
% 122.84/16.21 (iftrue) =>
% 122.84/16.21 ((
% 122.84/16.21 (iffalse) =>
% 122.84/16.21 ((
% 122.84/16.21 (iftrueorfalse) =>
% 122.84/16.21 ((
% 122.84/16.21 (binintersectT_lem) =>
% 122.84/16.21 ((
% 122.84/16.21 (binunionT_lem) =>
% 122.84/16.21 ((
% 122.84/16.21 (powersetT_lem) =>
% 122.84/16.21 ((
% 122.84/16.21 (setminusT_lem) =>
% 122.84/16.21 ((
% 122.84/16.21 (complementT_lem) =>
% 122.84/16.21 ((
% 122.84/16.21 (setextT) =>
% 122.84/16.21 ((
% 122.84/16.21 (subsetTI) =>
% 122.84/16.21 ((
% 122.84/16.21 (powersetTI1) =>
% 122.84/16.21 ((
% 122.84/16.21 (powersetTE1) =>
% 122.84/16.21 ((
% 122.84/16.21 (complementTI1) =>
% 122.84/16.21 ((
% 122.84/16.21 (complementTE1) =>
% 122.84/16.21 ((
% 122.84/16.21 (binintersectTELcontra) =>
% 122.84/16.21 ((
% 122.84/16.21 (binintersectTERcontra) =>
% 122.84/16.21 ((
% 122.84/16.21 (contrasubsetT) =>
% 122.84/16.21 ((
% 122.84/16.21 (contrasubsetT1) =>
% 122.84/16.21 ((
% 122.84/16.21 (contrasubsetT2) =>
% 122.84/16.21 ((
% 122.84/16.21 (contrasubsetT3) =>
% 122.84/16.21 ((
% 122.84/16.21 (doubleComplementI1) =>
% 122.84/16.21 ((
% 122.84/16.21 (doubleComplementE1) =>
% 122.84/16.21 ((
% 122.84/16.21 (doubleComplementSub1) =>
% 122.84/16.21 ((
% 122.84/16.21 (doubleComplementSub2) =>
% 122.84/16.21 ((
% 122.84/16.21 (doubleComplementEq) =>
% 122.84/16.21 ((
% 122.84/16.21 (complementTnotintersectT) =>
% 122.84/16.21 ((
% 122.84/16.21 (complementImpComplementIntersect) =>
% 122.84/16.21 ((
% 122.84/16.21 (complementSubsetComplementIntersect) =>
% 122.84/16.21 ((
% 122.84/16.21 (complementInPowersetComplementIntersect) =>
% 122.84/16.21 ((
% 122.84/16.21 (contraSubsetComplement) =>
% 122.84/16.21 ((
% 122.84/16.21 (complementTcontraSubset) =>
% 122.84/16.21 ((
% 122.84/16.21 (binunionTILcontra) =>
% 122.84/16.21 ((
% 122.84/16.21 (binunionTIRcontra) =>
% 122.84/16.21 ((
% 122.84/16.21 (inIntersectImpInUnion) =>
% 122.84/16.21 ((
% 122.84/16.21 (inIntersectImpInUnion2) =>
% 122.84/16.21 ((
% 122.84/16.21 (inIntersectImpInIntersectUnions) =>
% 122.84/16.21 ((
% 122.84/16.21 (intersectInPowersetIntersectUnions) =>
% 122.84/16.21 ((
% 122.84/16.21 (inComplementUnionImpNotIn1) =>
% 122.84/16.21 ((
% 122.84/16.21 (inComplementUnionImpInComplement1) =>
% 122.84/16.21 ((
% 122.84/16.21 (binunionTE) =>
% 122.84/16.21 ((
% 122.84/16.21 (binunionTEcontra) =>
% 122.84/16.21 ((
% 122.84/16.21 (demorgan2a1) =>
% 122.84/16.21 ((
% 122.84/16.21 (complementUnionInPowersetComplement) =>
% 122.84/16.21 ((
% 122.84/16.21 (demorgan2a2) =>
% 122.84/16.21 ((
% 122.84/16.21 (demorgan1a) =>
% 122.84/16.21 ((
% 122.84/16.21 (demorgan1b) =>
% 122.84/16.21 ((
% 122.84/16.21 (demorgan1) =>
% 122.84/16.21 ((
% 122.84/16.21 (demorgan2a) =>
% 122.84/16.21 ((
% 122.84/16.21 (demorgan2b2) =>
% 122.84/16.21 ((
% 122.84/16.21 (demorgan2b) =>
% 122.84/16.21 ((
% 122.84/16.21 (demorgan2) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz13rule0) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz13rule1) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz13rule2) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz13rule3) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz13rule4) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz1_1) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz1_2) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz1_3) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz1_4) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz1_5) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1all2) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1SetBreln1) =>
% 122.84/16.21 ((
% 122.84/16.21 (choice2fnsingleton) =>
% 122.84/16.21 ((
% 122.84/16.21 (setOfPairsIsBReln1) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1all1) =>
% 122.84/16.21 ((
% 122.84/16.21 (subbreln1) =>
% 122.84/16.21 ((
% 122.84/16.21 (eqbreln1) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1invprop) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1invI) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1invE) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1compprop) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1compI) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1compE) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1compEex) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1unionprop) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1unionIL) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1unionIR) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1unionI) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1unionE) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1unionEcases) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1unionCommutes) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz2Ex) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz2W) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz2A) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz2B) =>
% 122.84/16.21 ((
% 122.84/16.21 (image1Ex) =>
% 122.84/16.21 ((
% 122.84/16.21 (image1Ex1) =>
% 122.84/16.21 ((
% 122.84/16.21 (image1Equiv) =>
% 122.84/16.21 ((
% 122.84/16.21 (image1E) =>
% 122.84/16.21 ((
% 122.84/16.21 (image1I) =>
% 122.84/16.21 ((
% 122.84/16.21 (injFuncInInjFuncSet) =>
% 122.84/16.21 ((
% 122.84/16.21 (!!) @ (
% 122.84/16.21 (('#B') @ (
% 122.84/16.21 !!) @
% 122.84/16.21 (
% 122.84/16.21 (
% 122.84/16.21 ('#B') @ (
% 122.84/16.21 (
% 122.84/16.21 ('#B') @ (
% 122.84/16.21 !!))) @
% 122.84/16.21 (
% 122.84/16.21 (
% 122.84/16.21 ('#S') @ (
% 122.84/16.21 (
% 122.84/16.21 ('#B') @ (
% 122.84/16.21 '#S') @
% 122.84/16.21 (
% 122.84/16.21 (
% 122.84/16.21 ('#B') @ (
% 122.84/16.21 (
% 122.84/16.21 ('#B') @ (
% 122.84/16.21 '#S'))) @
% 122.84/16.21 (
% 122.84/16.21 (
% 122.84/16.21 ('#B') @ (
% 122.84/16.21 (
% 122.84/16.21 ('#B') @ (
% 122.84/16.21 (
% 122.84/16.21 ('#B') @ (
% 122.84/16.21 =>))))) @
% 122.84/16.21 (
% 122.84/16.21 (
% 122.84/16.21 ('#B') @ (
% 122.84/16.21 (
% 122.84/16.21 ('#B') @ (
% 122.84/16.21 (
% 122.84/16.21 ('#C') @ in)))) @
% 122.84/16.21 injFuncSet)))))))) @
% 122.84/16.21 (
% 122.84/16.21 (
% 122.84/16.21 ('#B') @ (
% 122.84/16.21 (
% 122.84/16.21 ('#B') @ (
% 122.84/16.21 (
% 122.84/16.21 ('#C') @ in)))) @
% 122.84/16.21 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.84/16.21 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1760])).
% 122.84/16.21 thf(zip_derived_cl1779, plain,
% 122.84/16.21 (~ (((ksndpairEq) =>
% 122.84/16.21 (((kpairsurjEq) =>
% 122.84/16.21 (((cartprodsndin) =>
% 122.84/16.21 (((cartprodpairmemEL) =>
% 122.84/16.21 (((cartprodpairmemER) =>
% 122.84/16.21 (((cartprodmempaircEq) =>
% 122.84/16.21 (((cartprodfstpairEq) =>
% 122.84/16.21 (((cartprodsndpairEq) =>
% 122.84/16.21 (((cartprodpairsurjEq) =>
% 122.84/16.21 (((dpsetconstrI) =>
% 122.84/16.21 (((dpsetconstrSub) =>
% 122.84/16.21 (((setOfPairsIsBReln) =>
% 122.84/16.21 (((dpsetconstrERa) =>
% 122.84/16.21 (((dpsetconstrEL1) =>
% 122.84/16.21 (((dpsetconstrEL2) =>
% 122.84/16.21 (((dpsetconstrER) =>
% 122.84/16.21 (((funcImageSingleton) =>
% 122.84/16.21 (((apProp) =>
% 122.84/16.21 (((app) =>
% 122.84/16.21 (((infuncsetfunc) =>
% 122.84/16.21 (((ap2p) =>
% 122.84/16.21 (((funcinfuncset) =>
% 122.84/16.21 (((lamProp) =>
% 122.84/16.21 (((lamp) =>
% 122.84/16.21 (((lam2p) =>
% 122.84/16.21 (((brelnall1) =>
% 122.84/16.21 (((brelnall2) =>
% 122.84/16.21 (((ex1E2) =>
% 122.84/16.21 (((funcGraphProp1) =>
% 122.84/16.21 (((funcGraphProp3) =>
% 122.84/16.21 ((
% 122.84/16.21 (funcGraphProp2) =>
% 122.84/16.21 ((
% 122.84/16.21 (funcextLem) =>
% 122.84/16.21 ((
% 122.84/16.21 (funcGraphProp4) =>
% 122.84/16.21 ((
% 122.84/16.21 (subbreln) =>
% 122.84/16.21 ((
% 122.84/16.21 (eqbreln) =>
% 122.84/16.21 ((
% 122.84/16.21 (funcext) =>
% 122.84/16.21 ((
% 122.84/16.21 (funcext2) =>
% 122.84/16.21 ((
% 122.84/16.21 (ap2apEq1) =>
% 122.84/16.21 ((
% 122.84/16.21 (ap2apEq2) =>
% 122.84/16.21 ((
% 122.84/16.21 (beta1) =>
% 122.84/16.21 ((
% 122.84/16.21 (eta1) =>
% 122.84/16.21 ((
% 122.84/16.21 (lam2lamEq) =>
% 122.84/16.21 ((
% 122.84/16.21 (beta2) =>
% 122.84/16.21 ((
% 122.84/16.21 (eta2) =>
% 122.84/16.21 ((
% 122.84/16.21 (iffalseProp1) =>
% 122.84/16.21 ((
% 122.84/16.21 (iffalseProp2) =>
% 122.84/16.21 ((
% 122.84/16.21 (iftrueProp1) =>
% 122.84/16.21 ((
% 122.84/16.21 (iftrueProp2) =>
% 122.84/16.21 ((
% 122.84/16.21 (ifSingleton) =>
% 122.84/16.21 ((
% 122.84/16.21 (ifp) =>
% 122.84/16.21 ((
% 122.84/16.21 (theeq) =>
% 122.84/16.21 ((
% 122.84/16.21 (iftrue) =>
% 122.84/16.21 ((
% 122.84/16.21 (iffalse) =>
% 122.84/16.21 ((
% 122.84/16.21 (iftrueorfalse) =>
% 122.84/16.21 ((
% 122.84/16.21 (binintersectT_lem) =>
% 122.84/16.21 ((
% 122.84/16.21 (binunionT_lem) =>
% 122.84/16.21 ((
% 122.84/16.21 (powersetT_lem) =>
% 122.84/16.21 ((
% 122.84/16.21 (setminusT_lem) =>
% 122.84/16.21 ((
% 122.84/16.21 (complementT_lem) =>
% 122.84/16.21 ((
% 122.84/16.21 (setextT) =>
% 122.84/16.21 ((
% 122.84/16.21 (subsetTI) =>
% 122.84/16.21 ((
% 122.84/16.21 (powersetTI1) =>
% 122.84/16.21 ((
% 122.84/16.21 (powersetTE1) =>
% 122.84/16.21 ((
% 122.84/16.21 (complementTI1) =>
% 122.84/16.21 ((
% 122.84/16.21 (complementTE1) =>
% 122.84/16.21 ((
% 122.84/16.21 (binintersectTELcontra) =>
% 122.84/16.21 ((
% 122.84/16.21 (binintersectTERcontra) =>
% 122.84/16.21 ((
% 122.84/16.21 (contrasubsetT) =>
% 122.84/16.21 ((
% 122.84/16.21 (contrasubsetT1) =>
% 122.84/16.21 ((
% 122.84/16.21 (contrasubsetT2) =>
% 122.84/16.21 ((
% 122.84/16.21 (contrasubsetT3) =>
% 122.84/16.21 ((
% 122.84/16.21 (doubleComplementI1) =>
% 122.84/16.21 ((
% 122.84/16.21 (doubleComplementE1) =>
% 122.84/16.21 ((
% 122.84/16.21 (doubleComplementSub1) =>
% 122.84/16.21 ((
% 122.84/16.21 (doubleComplementSub2) =>
% 122.84/16.21 ((
% 122.84/16.21 (doubleComplementEq) =>
% 122.84/16.21 ((
% 122.84/16.21 (complementTnotintersectT) =>
% 122.84/16.21 ((
% 122.84/16.21 (complementImpComplementIntersect) =>
% 122.84/16.21 ((
% 122.84/16.21 (complementSubsetComplementIntersect) =>
% 122.84/16.21 ((
% 122.84/16.21 (complementInPowersetComplementIntersect) =>
% 122.84/16.21 ((
% 122.84/16.21 (contraSubsetComplement) =>
% 122.84/16.21 ((
% 122.84/16.21 (complementTcontraSubset) =>
% 122.84/16.21 ((
% 122.84/16.21 (binunionTILcontra) =>
% 122.84/16.21 ((
% 122.84/16.21 (binunionTIRcontra) =>
% 122.84/16.21 ((
% 122.84/16.21 (inIntersectImpInUnion) =>
% 122.84/16.21 ((
% 122.84/16.21 (inIntersectImpInUnion2) =>
% 122.84/16.21 ((
% 122.84/16.21 (inIntersectImpInIntersectUnions) =>
% 122.84/16.21 ((
% 122.84/16.21 (intersectInPowersetIntersectUnions) =>
% 122.84/16.21 ((
% 122.84/16.21 (inComplementUnionImpNotIn1) =>
% 122.84/16.21 ((
% 122.84/16.21 (inComplementUnionImpInComplement1) =>
% 122.84/16.21 ((
% 122.84/16.21 (binunionTE) =>
% 122.84/16.21 ((
% 122.84/16.21 (binunionTEcontra) =>
% 122.84/16.21 ((
% 122.84/16.21 (demorgan2a1) =>
% 122.84/16.21 ((
% 122.84/16.21 (complementUnionInPowersetComplement) =>
% 122.84/16.21 ((
% 122.84/16.21 (demorgan2a2) =>
% 122.84/16.21 ((
% 122.84/16.21 (demorgan1a) =>
% 122.84/16.21 ((
% 122.84/16.21 (demorgan1b) =>
% 122.84/16.21 ((
% 122.84/16.21 (demorgan1) =>
% 122.84/16.21 ((
% 122.84/16.21 (demorgan2a) =>
% 122.84/16.21 ((
% 122.84/16.21 (demorgan2b2) =>
% 122.84/16.21 ((
% 122.84/16.21 (demorgan2b) =>
% 122.84/16.21 ((
% 122.84/16.21 (demorgan2) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz13rule0) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz13rule1) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz13rule2) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz13rule3) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz13rule4) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz1_1) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz1_2) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz1_3) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz1_4) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz1_5) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1all2) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1SetBreln1) =>
% 122.84/16.21 ((
% 122.84/16.21 (choice2fnsingleton) =>
% 122.84/16.21 ((
% 122.84/16.21 (setOfPairsIsBReln1) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1all1) =>
% 122.84/16.21 ((
% 122.84/16.21 (subbreln1) =>
% 122.84/16.21 ((
% 122.84/16.21 (eqbreln1) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1invprop) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1invI) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1invE) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1compprop) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1compI) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1compE) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1compEex) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1unionprop) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1unionIL) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1unionIR) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1unionI) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1unionE) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1unionEcases) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1unionCommutes) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz2Ex) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz2W) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz2A) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz2B) =>
% 122.84/16.21 ((
% 122.84/16.21 (image1Ex) =>
% 122.84/16.21 ((
% 122.84/16.21 (image1Ex1) =>
% 122.84/16.21 ((
% 122.84/16.21 (image1Equiv) =>
% 122.84/16.21 ((
% 122.84/16.21 (image1E) =>
% 122.84/16.21 ((
% 122.84/16.21 (image1I) =>
% 122.84/16.21 ((
% 122.84/16.21 (injFuncInInjFuncSet) =>
% 122.84/16.21 ((
% 122.84/16.21 (!!) @ (
% 122.84/16.21 (('#B') @ (
% 122.84/16.21 !!) @
% 122.84/16.21 (
% 122.84/16.21 (
% 122.84/16.21 ('#B') @ (
% 122.84/16.21 (
% 122.84/16.21 ('#B') @ (
% 122.84/16.21 !!))) @
% 122.84/16.21 (
% 122.84/16.21 (
% 122.84/16.21 ('#S') @ (
% 122.84/16.21 (
% 122.84/16.21 ('#B') @ (
% 122.84/16.21 '#S') @
% 122.84/16.21 (
% 122.84/16.21 (
% 122.84/16.21 ('#B') @ (
% 122.84/16.21 (
% 122.84/16.21 ('#B') @ (
% 122.84/16.21 '#S'))) @
% 122.84/16.21 (
% 122.84/16.21 (
% 122.84/16.21 ('#B') @ (
% 122.84/16.21 (
% 122.84/16.21 ('#B') @ (
% 122.84/16.21 (
% 122.84/16.21 ('#B') @ (
% 122.84/16.21 =>))))) @
% 122.84/16.21 (
% 122.84/16.21 (
% 122.84/16.21 ('#B') @ (
% 122.84/16.21 (
% 122.84/16.21 ('#B') @ (
% 122.84/16.21 (
% 122.84/16.21 ('#C') @ in)))) @
% 122.84/16.21 injFuncSet)))))))) @
% 122.84/16.21 (
% 122.84/16.21 (
% 122.84/16.21 ('#B') @ (
% 122.84/16.21 (
% 122.84/16.21 ('#B') @ (
% 122.84/16.21 (
% 122.84/16.21 ('#C') @ in)))) @
% 122.84/16.21 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.84/16.21 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1770])).
% 122.84/16.21 thf(zip_derived_cl1787, plain,
% 122.84/16.21 (~ (((kpairsurjEq) =>
% 122.84/16.21 (((cartprodsndin) =>
% 122.84/16.21 (((cartprodpairmemEL) =>
% 122.84/16.21 (((cartprodpairmemER) =>
% 122.84/16.21 (((cartprodmempaircEq) =>
% 122.84/16.21 (((cartprodfstpairEq) =>
% 122.84/16.21 (((cartprodsndpairEq) =>
% 122.84/16.21 (((cartprodpairsurjEq) =>
% 122.84/16.21 (((dpsetconstrI) =>
% 122.84/16.21 (((dpsetconstrSub) =>
% 122.84/16.21 (((setOfPairsIsBReln) =>
% 122.84/16.21 (((dpsetconstrERa) =>
% 122.84/16.21 (((dpsetconstrEL1) =>
% 122.84/16.21 (((dpsetconstrEL2) =>
% 122.84/16.21 (((dpsetconstrER) =>
% 122.84/16.21 (((funcImageSingleton) =>
% 122.84/16.21 (((apProp) =>
% 122.84/16.21 (((app) =>
% 122.84/16.21 (((infuncsetfunc) =>
% 122.84/16.21 (((ap2p) =>
% 122.84/16.21 (((funcinfuncset) =>
% 122.84/16.21 (((lamProp) =>
% 122.84/16.21 (((lamp) =>
% 122.84/16.21 (((lam2p) =>
% 122.84/16.21 (((brelnall1) =>
% 122.84/16.21 (((brelnall2) =>
% 122.84/16.21 (((ex1E2) =>
% 122.84/16.21 (((funcGraphProp1) =>
% 122.84/16.21 (((funcGraphProp3) =>
% 122.84/16.21 (((funcGraphProp2) =>
% 122.84/16.21 ((
% 122.84/16.21 (funcextLem) =>
% 122.84/16.21 ((
% 122.84/16.21 (funcGraphProp4) =>
% 122.84/16.21 ((
% 122.84/16.21 (subbreln) =>
% 122.84/16.21 ((
% 122.84/16.21 (eqbreln) =>
% 122.84/16.21 ((
% 122.84/16.21 (funcext) =>
% 122.84/16.21 ((
% 122.84/16.21 (funcext2) =>
% 122.84/16.21 ((
% 122.84/16.21 (ap2apEq1) =>
% 122.84/16.21 ((
% 122.84/16.21 (ap2apEq2) =>
% 122.84/16.21 ((
% 122.84/16.21 (beta1) =>
% 122.84/16.21 ((
% 122.84/16.21 (eta1) =>
% 122.84/16.21 ((
% 122.84/16.21 (lam2lamEq) =>
% 122.84/16.21 ((
% 122.84/16.21 (beta2) =>
% 122.84/16.21 ((
% 122.84/16.21 (eta2) =>
% 122.84/16.21 ((
% 122.84/16.21 (iffalseProp1) =>
% 122.84/16.21 ((
% 122.84/16.21 (iffalseProp2) =>
% 122.84/16.21 ((
% 122.84/16.21 (iftrueProp1) =>
% 122.84/16.21 ((
% 122.84/16.21 (iftrueProp2) =>
% 122.84/16.21 ((
% 122.84/16.21 (ifSingleton) =>
% 122.84/16.21 ((
% 122.84/16.21 (ifp) =>
% 122.84/16.21 ((
% 122.84/16.21 (theeq) =>
% 122.84/16.21 ((
% 122.84/16.21 (iftrue) =>
% 122.84/16.21 ((
% 122.84/16.21 (iffalse) =>
% 122.84/16.21 ((
% 122.84/16.21 (iftrueorfalse) =>
% 122.84/16.21 ((
% 122.84/16.21 (binintersectT_lem) =>
% 122.84/16.21 ((
% 122.84/16.21 (binunionT_lem) =>
% 122.84/16.21 ((
% 122.84/16.21 (powersetT_lem) =>
% 122.84/16.21 ((
% 122.84/16.21 (setminusT_lem) =>
% 122.84/16.21 ((
% 122.84/16.21 (complementT_lem) =>
% 122.84/16.21 ((
% 122.84/16.21 (setextT) =>
% 122.84/16.21 ((
% 122.84/16.21 (subsetTI) =>
% 122.84/16.21 ((
% 122.84/16.21 (powersetTI1) =>
% 122.84/16.21 ((
% 122.84/16.21 (powersetTE1) =>
% 122.84/16.21 ((
% 122.84/16.21 (complementTI1) =>
% 122.84/16.21 ((
% 122.84/16.21 (complementTE1) =>
% 122.84/16.21 ((
% 122.84/16.21 (binintersectTELcontra) =>
% 122.84/16.21 ((
% 122.84/16.21 (binintersectTERcontra) =>
% 122.84/16.21 ((
% 122.84/16.21 (contrasubsetT) =>
% 122.84/16.21 ((
% 122.84/16.21 (contrasubsetT1) =>
% 122.84/16.21 ((
% 122.84/16.21 (contrasubsetT2) =>
% 122.84/16.21 ((
% 122.84/16.21 (contrasubsetT3) =>
% 122.84/16.21 ((
% 122.84/16.21 (doubleComplementI1) =>
% 122.84/16.21 ((
% 122.84/16.21 (doubleComplementE1) =>
% 122.84/16.21 ((
% 122.84/16.21 (doubleComplementSub1) =>
% 122.84/16.21 ((
% 122.84/16.21 (doubleComplementSub2) =>
% 122.84/16.21 ((
% 122.84/16.21 (doubleComplementEq) =>
% 122.84/16.21 ((
% 122.84/16.21 (complementTnotintersectT) =>
% 122.84/16.21 ((
% 122.84/16.21 (complementImpComplementIntersect) =>
% 122.84/16.21 ((
% 122.84/16.21 (complementSubsetComplementIntersect) =>
% 122.84/16.21 ((
% 122.84/16.21 (complementInPowersetComplementIntersect) =>
% 122.84/16.21 ((
% 122.84/16.21 (contraSubsetComplement) =>
% 122.84/16.21 ((
% 122.84/16.21 (complementTcontraSubset) =>
% 122.84/16.21 ((
% 122.84/16.21 (binunionTILcontra) =>
% 122.84/16.21 ((
% 122.84/16.21 (binunionTIRcontra) =>
% 122.84/16.21 ((
% 122.84/16.21 (inIntersectImpInUnion) =>
% 122.84/16.21 ((
% 122.84/16.21 (inIntersectImpInUnion2) =>
% 122.84/16.21 ((
% 122.84/16.21 (inIntersectImpInIntersectUnions) =>
% 122.84/16.21 ((
% 122.84/16.21 (intersectInPowersetIntersectUnions) =>
% 122.84/16.21 ((
% 122.84/16.21 (inComplementUnionImpNotIn1) =>
% 122.84/16.21 ((
% 122.84/16.21 (inComplementUnionImpInComplement1) =>
% 122.84/16.21 ((
% 122.84/16.21 (binunionTE) =>
% 122.84/16.21 ((
% 122.84/16.21 (binunionTEcontra) =>
% 122.84/16.21 ((
% 122.84/16.21 (demorgan2a1) =>
% 122.84/16.21 ((
% 122.84/16.21 (complementUnionInPowersetComplement) =>
% 122.84/16.21 ((
% 122.84/16.21 (demorgan2a2) =>
% 122.84/16.21 ((
% 122.84/16.21 (demorgan1a) =>
% 122.84/16.21 ((
% 122.84/16.21 (demorgan1b) =>
% 122.84/16.21 ((
% 122.84/16.21 (demorgan1) =>
% 122.84/16.21 ((
% 122.84/16.21 (demorgan2a) =>
% 122.84/16.21 ((
% 122.84/16.21 (demorgan2b2) =>
% 122.84/16.21 ((
% 122.84/16.21 (demorgan2b) =>
% 122.84/16.21 ((
% 122.84/16.21 (demorgan2) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz13rule0) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz13rule1) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz13rule2) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz13rule3) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz13rule4) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz1_1) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz1_2) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz1_3) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz1_4) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz1_5) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1all2) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1SetBreln1) =>
% 122.84/16.21 ((
% 122.84/16.21 (choice2fnsingleton) =>
% 122.84/16.21 ((
% 122.84/16.21 (setOfPairsIsBReln1) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1all1) =>
% 122.84/16.21 ((
% 122.84/16.21 (subbreln1) =>
% 122.84/16.21 ((
% 122.84/16.21 (eqbreln1) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1invprop) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1invI) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1invE) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1compprop) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1compI) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1compE) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1compEex) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1unionprop) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1unionIL) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1unionIR) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1unionI) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1unionE) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1unionEcases) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1unionCommutes) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz2Ex) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz2W) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz2A) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz2B) =>
% 122.84/16.21 ((
% 122.84/16.21 (image1Ex) =>
% 122.84/16.21 ((
% 122.84/16.21 (image1Ex1) =>
% 122.84/16.21 ((
% 122.84/16.21 (image1Equiv) =>
% 122.84/16.21 ((
% 122.84/16.21 (image1E) =>
% 122.84/16.21 ((
% 122.84/16.21 (image1I) =>
% 122.84/16.21 ((
% 122.84/16.21 (injFuncInInjFuncSet) =>
% 122.84/16.21 ((
% 122.84/16.21 (!!) @ (
% 122.84/16.21 (('#B') @ (
% 122.84/16.21 !!) @
% 122.84/16.21 (
% 122.84/16.21 (
% 122.84/16.21 ('#B') @ (
% 122.84/16.21 (
% 122.84/16.21 ('#B') @ (
% 122.84/16.21 !!))) @
% 122.84/16.21 (
% 122.84/16.21 (
% 122.84/16.21 ('#S') @ (
% 122.84/16.21 (
% 122.84/16.21 ('#B') @ (
% 122.84/16.21 '#S') @
% 122.84/16.21 (
% 122.84/16.21 (
% 122.84/16.21 ('#B') @ (
% 122.84/16.21 (
% 122.84/16.21 ('#B') @ (
% 122.84/16.21 '#S'))) @
% 122.84/16.21 (
% 122.84/16.21 (
% 122.84/16.21 ('#B') @ (
% 122.84/16.21 (
% 122.84/16.21 ('#B') @ (
% 122.84/16.21 (
% 122.84/16.21 ('#B') @ (
% 122.84/16.21 =>))))) @
% 122.84/16.21 (
% 122.84/16.21 (
% 122.84/16.21 ('#B') @ (
% 122.84/16.21 (
% 122.84/16.21 ('#B') @ (
% 122.84/16.21 (
% 122.84/16.21 ('#C') @ in)))) @
% 122.84/16.21 injFuncSet)))))))) @
% 122.84/16.21 (
% 122.84/16.21 (
% 122.84/16.21 ('#B') @ (
% 122.84/16.21 (
% 122.84/16.21 ('#B') @ (
% 122.84/16.21 (
% 122.84/16.21 ('#C') @ in)))) @
% 122.84/16.21 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.84/16.21 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1779])).
% 122.84/16.21 thf(zip_derived_cl1796, plain,
% 122.84/16.21 (~ (((cartprodsndin) =>
% 122.84/16.21 (((cartprodpairmemEL) =>
% 122.84/16.21 (((cartprodpairmemER) =>
% 122.84/16.21 (((cartprodmempaircEq) =>
% 122.84/16.21 (((cartprodfstpairEq) =>
% 122.84/16.21 (((cartprodsndpairEq) =>
% 122.84/16.21 (((cartprodpairsurjEq) =>
% 122.84/16.21 (((dpsetconstrI) =>
% 122.84/16.21 (((dpsetconstrSub) =>
% 122.84/16.21 (((setOfPairsIsBReln) =>
% 122.84/16.21 (((dpsetconstrERa) =>
% 122.84/16.21 (((dpsetconstrEL1) =>
% 122.84/16.21 (((dpsetconstrEL2) =>
% 122.84/16.21 (((dpsetconstrER) =>
% 122.84/16.21 (((funcImageSingleton) =>
% 122.84/16.21 (((apProp) =>
% 122.84/16.21 (((app) =>
% 122.84/16.21 (((infuncsetfunc) =>
% 122.84/16.21 (((ap2p) =>
% 122.84/16.21 (((funcinfuncset) =>
% 122.84/16.21 (((lamProp) =>
% 122.84/16.21 (((lamp) =>
% 122.84/16.21 (((lam2p) =>
% 122.84/16.21 (((brelnall1) =>
% 122.84/16.21 (((brelnall2) =>
% 122.84/16.21 (((ex1E2) =>
% 122.84/16.21 (((funcGraphProp1) =>
% 122.84/16.21 (((funcGraphProp3) =>
% 122.84/16.21 (((funcGraphProp2) =>
% 122.84/16.21 (((funcextLem) =>
% 122.84/16.21 ((
% 122.84/16.21 (funcGraphProp4) =>
% 122.84/16.21 ((
% 122.84/16.21 (subbreln) =>
% 122.84/16.21 ((
% 122.84/16.21 (eqbreln) =>
% 122.84/16.21 ((
% 122.84/16.21 (funcext) =>
% 122.84/16.21 ((
% 122.84/16.21 (funcext2) =>
% 122.84/16.21 ((
% 122.84/16.21 (ap2apEq1) =>
% 122.84/16.21 ((
% 122.84/16.21 (ap2apEq2) =>
% 122.84/16.21 ((
% 122.84/16.21 (beta1) =>
% 122.84/16.21 ((
% 122.84/16.21 (eta1) =>
% 122.84/16.21 ((
% 122.84/16.21 (lam2lamEq) =>
% 122.84/16.21 ((
% 122.84/16.21 (beta2) =>
% 122.84/16.21 ((
% 122.84/16.21 (eta2) =>
% 122.84/16.21 ((
% 122.84/16.21 (iffalseProp1) =>
% 122.84/16.21 ((
% 122.84/16.21 (iffalseProp2) =>
% 122.84/16.21 ((
% 122.84/16.21 (iftrueProp1) =>
% 122.84/16.21 ((
% 122.84/16.21 (iftrueProp2) =>
% 122.84/16.21 ((
% 122.84/16.21 (ifSingleton) =>
% 122.84/16.21 ((
% 122.84/16.21 (ifp) =>
% 122.84/16.21 ((
% 122.84/16.21 (theeq) =>
% 122.84/16.21 ((
% 122.84/16.21 (iftrue) =>
% 122.84/16.21 ((
% 122.84/16.21 (iffalse) =>
% 122.84/16.21 ((
% 122.84/16.21 (iftrueorfalse) =>
% 122.84/16.21 ((
% 122.84/16.21 (binintersectT_lem) =>
% 122.84/16.21 ((
% 122.84/16.21 (binunionT_lem) =>
% 122.84/16.21 ((
% 122.84/16.21 (powersetT_lem) =>
% 122.84/16.21 ((
% 122.84/16.21 (setminusT_lem) =>
% 122.84/16.21 ((
% 122.84/16.21 (complementT_lem) =>
% 122.84/16.21 ((
% 122.84/16.21 (setextT) =>
% 122.84/16.21 ((
% 122.84/16.21 (subsetTI) =>
% 122.84/16.21 ((
% 122.84/16.21 (powersetTI1) =>
% 122.84/16.21 ((
% 122.84/16.21 (powersetTE1) =>
% 122.84/16.21 ((
% 122.84/16.21 (complementTI1) =>
% 122.84/16.21 ((
% 122.84/16.21 (complementTE1) =>
% 122.84/16.21 ((
% 122.84/16.21 (binintersectTELcontra) =>
% 122.84/16.21 ((
% 122.84/16.21 (binintersectTERcontra) =>
% 122.84/16.21 ((
% 122.84/16.21 (contrasubsetT) =>
% 122.84/16.21 ((
% 122.84/16.21 (contrasubsetT1) =>
% 122.84/16.21 ((
% 122.84/16.21 (contrasubsetT2) =>
% 122.84/16.21 ((
% 122.84/16.21 (contrasubsetT3) =>
% 122.84/16.21 ((
% 122.84/16.21 (doubleComplementI1) =>
% 122.84/16.21 ((
% 122.84/16.21 (doubleComplementE1) =>
% 122.84/16.21 ((
% 122.84/16.21 (doubleComplementSub1) =>
% 122.84/16.21 ((
% 122.84/16.21 (doubleComplementSub2) =>
% 122.84/16.21 ((
% 122.84/16.21 (doubleComplementEq) =>
% 122.84/16.21 ((
% 122.84/16.21 (complementTnotintersectT) =>
% 122.84/16.21 ((
% 122.84/16.21 (complementImpComplementIntersect) =>
% 122.84/16.21 ((
% 122.84/16.21 (complementSubsetComplementIntersect) =>
% 122.84/16.21 ((
% 122.84/16.21 (complementInPowersetComplementIntersect) =>
% 122.84/16.21 ((
% 122.84/16.21 (contraSubsetComplement) =>
% 122.84/16.21 ((
% 122.84/16.21 (complementTcontraSubset) =>
% 122.84/16.21 ((
% 122.84/16.21 (binunionTILcontra) =>
% 122.84/16.21 ((
% 122.84/16.21 (binunionTIRcontra) =>
% 122.84/16.21 ((
% 122.84/16.21 (inIntersectImpInUnion) =>
% 122.84/16.21 ((
% 122.84/16.21 (inIntersectImpInUnion2) =>
% 122.84/16.21 ((
% 122.84/16.21 (inIntersectImpInIntersectUnions) =>
% 122.84/16.21 ((
% 122.84/16.21 (intersectInPowersetIntersectUnions) =>
% 122.84/16.21 ((
% 122.84/16.21 (inComplementUnionImpNotIn1) =>
% 122.84/16.21 ((
% 122.84/16.21 (inComplementUnionImpInComplement1) =>
% 122.84/16.21 ((
% 122.84/16.21 (binunionTE) =>
% 122.84/16.21 ((
% 122.84/16.21 (binunionTEcontra) =>
% 122.84/16.21 ((
% 122.84/16.21 (demorgan2a1) =>
% 122.84/16.21 ((
% 122.84/16.21 (complementUnionInPowersetComplement) =>
% 122.84/16.21 ((
% 122.84/16.21 (demorgan2a2) =>
% 122.84/16.21 ((
% 122.84/16.21 (demorgan1a) =>
% 122.84/16.21 ((
% 122.84/16.21 (demorgan1b) =>
% 122.84/16.21 ((
% 122.84/16.21 (demorgan1) =>
% 122.84/16.21 ((
% 122.84/16.21 (demorgan2a) =>
% 122.84/16.21 ((
% 122.84/16.21 (demorgan2b2) =>
% 122.84/16.21 ((
% 122.84/16.21 (demorgan2b) =>
% 122.84/16.21 ((
% 122.84/16.21 (demorgan2) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz13rule0) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz13rule1) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz13rule2) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz13rule3) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz13rule4) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz1_1) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz1_2) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz1_3) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz1_4) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz1_5) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1all2) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1SetBreln1) =>
% 122.84/16.21 ((
% 122.84/16.21 (choice2fnsingleton) =>
% 122.84/16.21 ((
% 122.84/16.21 (setOfPairsIsBReln1) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1all1) =>
% 122.84/16.21 ((
% 122.84/16.21 (subbreln1) =>
% 122.84/16.21 ((
% 122.84/16.21 (eqbreln1) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1invprop) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1invI) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1invE) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1compprop) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1compI) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1compE) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1compEex) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1unionprop) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1unionIL) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1unionIR) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1unionI) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1unionE) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1unionEcases) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1unionCommutes) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz2Ex) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz2W) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz2A) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz2B) =>
% 122.84/16.21 ((
% 122.84/16.21 (image1Ex) =>
% 122.84/16.21 ((
% 122.84/16.21 (image1Ex1) =>
% 122.84/16.21 ((
% 122.84/16.21 (image1Equiv) =>
% 122.84/16.21 ((
% 122.84/16.21 (image1E) =>
% 122.84/16.21 ((
% 122.84/16.21 (image1I) =>
% 122.84/16.21 ((
% 122.84/16.21 (injFuncInInjFuncSet) =>
% 122.84/16.21 ((
% 122.84/16.21 (!!) @ (
% 122.84/16.21 (('#B') @ (
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% 122.84/16.21 (
% 122.84/16.21 ('#B') @ (
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% 122.84/16.21 ('#B') @ (
% 122.84/16.21 =>))))) @
% 122.84/16.21 (
% 122.84/16.21 (
% 122.84/16.21 ('#B') @ (
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% 122.84/16.21 ('#B') @ (
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% 122.84/16.21 injFuncSet)))))))) @
% 122.84/16.21 (
% 122.84/16.21 (
% 122.84/16.21 ('#B') @ (
% 122.84/16.21 (
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% 122.84/16.21 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.84/16.21 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1787])).
% 122.84/16.21 thf(zip_derived_cl1807, plain,
% 122.84/16.21 (~ (((cartprodpairmemEL) =>
% 122.84/16.21 (((cartprodpairmemER) =>
% 122.84/16.21 (((cartprodmempaircEq) =>
% 122.84/16.21 (((cartprodfstpairEq) =>
% 122.84/16.21 (((cartprodsndpairEq) =>
% 122.84/16.21 (((cartprodpairsurjEq) =>
% 122.84/16.21 (((dpsetconstrI) =>
% 122.84/16.21 (((dpsetconstrSub) =>
% 122.84/16.21 (((setOfPairsIsBReln) =>
% 122.84/16.21 (((dpsetconstrERa) =>
% 122.84/16.21 (((dpsetconstrEL1) =>
% 122.84/16.21 (((dpsetconstrEL2) =>
% 122.84/16.21 (((dpsetconstrER) =>
% 122.84/16.21 (((funcImageSingleton) =>
% 122.84/16.21 (((apProp) =>
% 122.84/16.21 (((app) =>
% 122.84/16.21 (((infuncsetfunc) =>
% 122.84/16.21 (((ap2p) =>
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% 122.84/16.21 (((lamProp) =>
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% 122.84/16.21 (((lam2p) =>
% 122.84/16.21 (((brelnall1) =>
% 122.84/16.21 (((brelnall2) =>
% 122.84/16.21 (((ex1E2) =>
% 122.84/16.21 (((funcGraphProp1) =>
% 122.84/16.21 (((funcGraphProp3) =>
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% 122.84/16.21 ((
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% 122.84/16.21 ((
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% 122.84/16.21 ((
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% 122.84/16.21 ((
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% 122.84/16.21 ((
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% 122.84/16.21 ((
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% 122.84/16.21 ((
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% 122.84/16.21 ((
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% 122.84/16.21 ((
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% 122.84/16.21 ((
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% 122.84/16.21 ((
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% 122.84/16.21 ((
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% 122.84/16.21 ((
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% 122.84/16.21 ((
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% 122.84/16.21 ((
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% 122.84/16.21 ((
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% 122.84/16.21 ((
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% 122.84/16.21 ((
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% 122.84/16.21 ((
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% 122.84/16.21 ((
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% 122.84/16.21 ((
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% 122.84/16.21 ((
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% 122.84/16.21 ((
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% 122.84/16.21 ((
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% 122.84/16.21 ((
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% 122.84/16.21 ((
% 122.84/16.21 (complementInPowersetComplementIntersect) =>
% 122.84/16.21 ((
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% 122.84/16.21 ((
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% 122.84/16.21 ((
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% 122.84/16.21 ((
% 122.84/16.21 (binunionTIRcontra) =>
% 122.84/16.21 ((
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% 122.84/16.21 ((
% 122.84/16.21 (inIntersectImpInUnion2) =>
% 122.84/16.21 ((
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% 122.84/16.21 ((
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% 122.84/16.21 ((
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% 122.84/16.21 ((
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% 122.84/16.21 ((
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% 122.84/16.21 ((
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% 122.84/16.21 ((
% 122.84/16.21 (complementUnionInPowersetComplement) =>
% 122.84/16.21 ((
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% 122.84/16.21 ((
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% 122.84/16.21 ((
% 122.84/16.21 (demorgan1b) =>
% 122.84/16.21 ((
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% 122.84/16.21 ((
% 122.84/16.21 (demorgan2a) =>
% 122.84/16.21 ((
% 122.84/16.21 (demorgan2b2) =>
% 122.84/16.21 ((
% 122.84/16.21 (demorgan2b) =>
% 122.84/16.21 ((
% 122.84/16.21 (demorgan2) =>
% 122.84/16.21 ((
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% 122.84/16.21 ((
% 122.84/16.21 (woz13rule1) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz13rule2) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz13rule3) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz13rule4) =>
% 122.84/16.21 ((
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% 122.84/16.21 ((
% 122.84/16.21 (woz1_2) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz1_3) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz1_4) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz1_5) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1all2) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1SetBreln1) =>
% 122.84/16.21 ((
% 122.84/16.21 (choice2fnsingleton) =>
% 122.84/16.21 ((
% 122.84/16.21 (setOfPairsIsBReln1) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1all1) =>
% 122.84/16.21 ((
% 122.84/16.21 (subbreln1) =>
% 122.84/16.21 ((
% 122.84/16.21 (eqbreln1) =>
% 122.84/16.21 ((
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% 122.84/16.21 ((
% 122.84/16.21 (breln1invI) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1invE) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1compprop) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1compI) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1compE) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1compEex) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1unionprop) =>
% 122.84/16.21 ((
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% 122.84/16.21 ((
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% 122.84/16.21 ((
% 122.84/16.21 (breln1unionI) =>
% 122.84/16.21 ((
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% 122.84/16.21 ((
% 122.84/16.21 (breln1unionEcases) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1unionCommutes) =>
% 122.84/16.21 ((
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% 122.84/16.21 ((
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% 122.84/16.21 ((
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% 122.84/16.21 ((
% 122.84/16.21 (image1Ex) =>
% 122.84/16.21 ((
% 122.84/16.21 (image1Ex1) =>
% 122.84/16.21 ((
% 122.84/16.21 (image1Equiv) =>
% 122.84/16.21 ((
% 122.84/16.21 (image1E) =>
% 122.84/16.21 ((
% 122.84/16.21 (image1I) =>
% 122.84/16.21 ((
% 122.84/16.21 (injFuncInInjFuncSet) =>
% 122.84/16.21 ((
% 122.84/16.21 (!!) @ (
% 122.84/16.21 (('#B') @ (
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% 122.84/16.21 (
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% 122.84/16.21 (
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% 122.84/16.21 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1796])).
% 122.84/16.21 thf(zip_derived_cl1816, plain,
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% 122.84/16.21 ((
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% 122.84/16.21 ((
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% 122.84/16.21 ((
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% 122.84/16.21 ((
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% 122.84/16.21 ((
% 122.84/16.21 (inIntersectImpInUnion2) =>
% 122.84/16.21 ((
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% 122.84/16.21 ((
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% 122.84/16.21 ((
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% 122.84/16.21 ((
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% 122.84/16.21 ((
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% 122.84/16.21 ((
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% 122.84/16.21 ((
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% 122.84/16.21 ((
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% 122.84/16.21 ((
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% 122.84/16.21 ((
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% 122.84/16.21 ((
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% 122.84/16.21 ((
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% 122.84/16.21 ((
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% 122.84/16.21 ((
% 122.84/16.21 (woz1_5) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1all2) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1SetBreln1) =>
% 122.84/16.21 ((
% 122.84/16.21 (choice2fnsingleton) =>
% 122.84/16.21 ((
% 122.84/16.21 (setOfPairsIsBReln1) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1all1) =>
% 122.84/16.21 ((
% 122.84/16.21 (subbreln1) =>
% 122.84/16.21 ((
% 122.84/16.21 (eqbreln1) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1invprop) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1invI) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1invE) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1compprop) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1compI) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1compE) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1compEex) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1unionprop) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1unionIL) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1unionIR) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1unionI) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1unionE) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1unionEcases) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1unionCommutes) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz2Ex) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz2W) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz2A) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz2B) =>
% 122.84/16.21 ((
% 122.84/16.21 (image1Ex) =>
% 122.84/16.21 ((
% 122.84/16.21 (image1Ex1) =>
% 122.84/16.21 ((
% 122.84/16.21 (image1Equiv) =>
% 122.84/16.21 ((
% 122.84/16.21 (image1E) =>
% 122.84/16.21 ((
% 122.84/16.21 (image1I) =>
% 122.84/16.21 ((
% 122.84/16.21 (injFuncInInjFuncSet) =>
% 122.84/16.21 ((
% 122.84/16.21 (!!) @ (
% 122.84/16.21 (('#B') @ (
% 122.84/16.21 !!) @
% 122.84/16.21 (
% 122.84/16.21 (
% 122.84/16.21 ('#B') @ (
% 122.84/16.21 (
% 122.84/16.21 ('#B') @ (
% 122.84/16.21 !!))) @
% 122.84/16.21 (
% 122.84/16.21 (
% 122.84/16.21 ('#S') @ (
% 122.84/16.21 (
% 122.84/16.21 ('#B') @ (
% 122.84/16.21 '#S') @
% 122.84/16.21 (
% 122.84/16.21 (
% 122.84/16.21 ('#B') @ (
% 122.84/16.21 (
% 122.84/16.21 ('#B') @ (
% 122.84/16.21 '#S'))) @
% 122.84/16.21 (
% 122.84/16.21 (
% 122.84/16.21 ('#B') @ (
% 122.84/16.21 (
% 122.84/16.21 ('#B') @ (
% 122.84/16.21 (
% 122.84/16.21 ('#B') @ (
% 122.84/16.21 =>))))) @
% 122.84/16.21 (
% 122.84/16.21 (
% 122.84/16.21 ('#B') @ (
% 122.84/16.21 (
% 122.84/16.21 ('#B') @ (
% 122.84/16.21 (
% 122.84/16.21 ('#C') @ in)))) @
% 122.84/16.21 injFuncSet)))))))) @
% 122.84/16.21 (
% 122.84/16.21 (
% 122.84/16.21 ('#B') @ (
% 122.84/16.21 (
% 122.84/16.21 ('#B') @ (
% 122.84/16.21 (
% 122.84/16.21 ('#C') @ in)))) @
% 122.84/16.21 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.84/16.21 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1807])).
% 122.84/16.21 thf(zip_derived_cl1825, plain,
% 122.84/16.21 (~ (((cartprodmempaircEq) =>
% 122.84/16.21 (((cartprodfstpairEq) =>
% 122.84/16.21 (((cartprodsndpairEq) =>
% 122.84/16.21 (((cartprodpairsurjEq) =>
% 122.84/16.21 (((dpsetconstrI) =>
% 122.84/16.21 (((dpsetconstrSub) =>
% 122.84/16.21 (((setOfPairsIsBReln) =>
% 122.84/16.21 (((dpsetconstrERa) =>
% 122.84/16.21 (((dpsetconstrEL1) =>
% 122.84/16.21 (((dpsetconstrEL2) =>
% 122.84/16.21 (((dpsetconstrER) =>
% 122.84/16.21 (((funcImageSingleton) =>
% 122.84/16.21 (((apProp) =>
% 122.84/16.21 (((app) =>
% 122.84/16.21 (((infuncsetfunc) =>
% 122.84/16.21 (((ap2p) =>
% 122.84/16.21 (((funcinfuncset) =>
% 122.84/16.21 (((lamProp) =>
% 122.84/16.21 (((lamp) =>
% 122.84/16.21 (((lam2p) =>
% 122.84/16.21 (((brelnall1) =>
% 122.84/16.21 (((brelnall2) =>
% 122.84/16.21 (((ex1E2) =>
% 122.84/16.21 (((funcGraphProp1) =>
% 122.84/16.21 (((funcGraphProp3) =>
% 122.84/16.21 (((funcGraphProp2) =>
% 122.84/16.21 (((funcextLem) =>
% 122.84/16.21 (((funcGraphProp4) =>
% 122.84/16.21 (((subbreln) =>
% 122.84/16.21 (((eqbreln) =>
% 122.84/16.21 ((
% 122.84/16.21 (funcext) =>
% 122.84/16.21 ((
% 122.84/16.21 (funcext2) =>
% 122.84/16.21 ((
% 122.84/16.21 (ap2apEq1) =>
% 122.84/16.21 ((
% 122.84/16.21 (ap2apEq2) =>
% 122.84/16.21 ((
% 122.84/16.21 (beta1) =>
% 122.84/16.21 ((
% 122.84/16.21 (eta1) =>
% 122.84/16.21 ((
% 122.84/16.21 (lam2lamEq) =>
% 122.84/16.21 ((
% 122.84/16.21 (beta2) =>
% 122.84/16.21 ((
% 122.84/16.21 (eta2) =>
% 122.84/16.21 ((
% 122.84/16.21 (iffalseProp1) =>
% 122.84/16.21 ((
% 122.84/16.21 (iffalseProp2) =>
% 122.84/16.21 ((
% 122.84/16.21 (iftrueProp1) =>
% 122.84/16.21 ((
% 122.84/16.21 (iftrueProp2) =>
% 122.84/16.21 ((
% 122.84/16.21 (ifSingleton) =>
% 122.84/16.21 ((
% 122.84/16.21 (ifp) =>
% 122.84/16.21 ((
% 122.84/16.21 (theeq) =>
% 122.84/16.21 ((
% 122.84/16.21 (iftrue) =>
% 122.84/16.21 ((
% 122.84/16.21 (iffalse) =>
% 122.84/16.21 ((
% 122.84/16.21 (iftrueorfalse) =>
% 122.84/16.21 ((
% 122.84/16.21 (binintersectT_lem) =>
% 122.84/16.21 ((
% 122.84/16.21 (binunionT_lem) =>
% 122.84/16.21 ((
% 122.84/16.21 (powersetT_lem) =>
% 122.84/16.21 ((
% 122.84/16.21 (setminusT_lem) =>
% 122.84/16.21 ((
% 122.84/16.21 (complementT_lem) =>
% 122.84/16.21 ((
% 122.84/16.21 (setextT) =>
% 122.84/16.21 ((
% 122.84/16.21 (subsetTI) =>
% 122.84/16.21 ((
% 122.84/16.21 (powersetTI1) =>
% 122.84/16.21 ((
% 122.84/16.21 (powersetTE1) =>
% 122.84/16.21 ((
% 122.84/16.21 (complementTI1) =>
% 122.84/16.21 ((
% 122.84/16.21 (complementTE1) =>
% 122.84/16.21 ((
% 122.84/16.21 (binintersectTELcontra) =>
% 122.84/16.21 ((
% 122.84/16.21 (binintersectTERcontra) =>
% 122.84/16.21 ((
% 122.84/16.21 (contrasubsetT) =>
% 122.84/16.21 ((
% 122.84/16.21 (contrasubsetT1) =>
% 122.84/16.21 ((
% 122.84/16.21 (contrasubsetT2) =>
% 122.84/16.21 ((
% 122.84/16.21 (contrasubsetT3) =>
% 122.84/16.21 ((
% 122.84/16.21 (doubleComplementI1) =>
% 122.84/16.21 ((
% 122.84/16.21 (doubleComplementE1) =>
% 122.84/16.21 ((
% 122.84/16.21 (doubleComplementSub1) =>
% 122.84/16.21 ((
% 122.84/16.21 (doubleComplementSub2) =>
% 122.84/16.21 ((
% 122.84/16.21 (doubleComplementEq) =>
% 122.84/16.21 ((
% 122.84/16.21 (complementTnotintersectT) =>
% 122.84/16.21 ((
% 122.84/16.21 (complementImpComplementIntersect) =>
% 122.84/16.21 ((
% 122.84/16.21 (complementSubsetComplementIntersect) =>
% 122.84/16.21 ((
% 122.84/16.21 (complementInPowersetComplementIntersect) =>
% 122.84/16.21 ((
% 122.84/16.21 (contraSubsetComplement) =>
% 122.84/16.21 ((
% 122.84/16.21 (complementTcontraSubset) =>
% 122.84/16.21 ((
% 122.84/16.21 (binunionTILcontra) =>
% 122.84/16.21 ((
% 122.84/16.21 (binunionTIRcontra) =>
% 122.84/16.21 ((
% 122.84/16.21 (inIntersectImpInUnion) =>
% 122.84/16.21 ((
% 122.84/16.21 (inIntersectImpInUnion2) =>
% 122.84/16.21 ((
% 122.84/16.21 (inIntersectImpInIntersectUnions) =>
% 122.84/16.21 ((
% 122.84/16.21 (intersectInPowersetIntersectUnions) =>
% 122.84/16.21 ((
% 122.84/16.21 (inComplementUnionImpNotIn1) =>
% 122.84/16.21 ((
% 122.84/16.21 (inComplementUnionImpInComplement1) =>
% 122.84/16.21 ((
% 122.84/16.21 (binunionTE) =>
% 122.84/16.21 ((
% 122.84/16.21 (binunionTEcontra) =>
% 122.84/16.21 ((
% 122.84/16.21 (demorgan2a1) =>
% 122.84/16.21 ((
% 122.84/16.21 (complementUnionInPowersetComplement) =>
% 122.84/16.21 ((
% 122.84/16.21 (demorgan2a2) =>
% 122.84/16.21 ((
% 122.84/16.21 (demorgan1a) =>
% 122.84/16.21 ((
% 122.84/16.21 (demorgan1b) =>
% 122.84/16.21 ((
% 122.84/16.21 (demorgan1) =>
% 122.84/16.21 ((
% 122.84/16.21 (demorgan2a) =>
% 122.84/16.21 ((
% 122.84/16.21 (demorgan2b2) =>
% 122.84/16.21 ((
% 122.84/16.21 (demorgan2b) =>
% 122.84/16.21 ((
% 122.84/16.21 (demorgan2) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz13rule0) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz13rule1) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz13rule2) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz13rule3) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz13rule4) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz1_1) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz1_2) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz1_3) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz1_4) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz1_5) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1all2) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1SetBreln1) =>
% 122.84/16.21 ((
% 122.84/16.21 (choice2fnsingleton) =>
% 122.84/16.21 ((
% 122.84/16.21 (setOfPairsIsBReln1) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1all1) =>
% 122.84/16.21 ((
% 122.84/16.21 (subbreln1) =>
% 122.84/16.21 ((
% 122.84/16.21 (eqbreln1) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1invprop) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1invI) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1invE) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1compprop) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1compI) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1compE) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1compEex) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1unionprop) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1unionIL) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1unionIR) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1unionI) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1unionE) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1unionEcases) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1unionCommutes) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz2Ex) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz2W) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz2A) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz2B) =>
% 122.84/16.21 ((
% 122.84/16.21 (image1Ex) =>
% 122.84/16.21 ((
% 122.84/16.21 (image1Ex1) =>
% 122.84/16.21 ((
% 122.84/16.21 (image1Equiv) =>
% 122.84/16.21 ((
% 122.84/16.21 (image1E) =>
% 122.84/16.21 ((
% 122.84/16.21 (image1I) =>
% 122.84/16.21 ((
% 122.84/16.21 (injFuncInInjFuncSet) =>
% 122.84/16.21 ((
% 122.84/16.21 (!!) @ (
% 122.84/16.21 (('#B') @ (
% 122.84/16.21 !!) @
% 122.84/16.21 (
% 122.84/16.21 (
% 122.84/16.21 ('#B') @ (
% 122.84/16.21 (
% 122.84/16.21 ('#B') @ (
% 122.84/16.21 !!))) @
% 122.84/16.21 (
% 122.84/16.21 (
% 122.84/16.21 ('#S') @ (
% 122.84/16.21 (
% 122.84/16.21 ('#B') @ (
% 122.84/16.21 '#S') @
% 122.84/16.21 (
% 122.84/16.21 (
% 122.84/16.21 ('#B') @ (
% 122.84/16.21 (
% 122.84/16.21 ('#B') @ (
% 122.84/16.21 '#S'))) @
% 122.84/16.21 (
% 122.84/16.21 (
% 122.84/16.21 ('#B') @ (
% 122.84/16.21 (
% 122.84/16.21 ('#B') @ (
% 122.84/16.21 (
% 122.84/16.21 ('#B') @ (
% 122.84/16.21 =>))))) @
% 122.84/16.21 (
% 122.84/16.21 (
% 122.84/16.21 ('#B') @ (
% 122.84/16.21 (
% 122.84/16.21 ('#B') @ (
% 122.84/16.21 (
% 122.84/16.21 ('#C') @ in)))) @
% 122.84/16.21 injFuncSet)))))))) @
% 122.84/16.21 (
% 122.84/16.21 (
% 122.84/16.21 ('#B') @ (
% 122.84/16.21 (
% 122.84/16.21 ('#B') @ (
% 122.84/16.21 (
% 122.84/16.21 ('#C') @ in)))) @
% 122.84/16.21 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.84/16.21 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1816])).
% 122.84/16.21 thf(zip_derived_cl1833, plain,
% 122.84/16.21 (~ (((cartprodfstpairEq) =>
% 122.84/16.21 (((cartprodsndpairEq) =>
% 122.84/16.21 (((cartprodpairsurjEq) =>
% 122.84/16.21 (((dpsetconstrI) =>
% 122.84/16.21 (((dpsetconstrSub) =>
% 122.84/16.21 (((setOfPairsIsBReln) =>
% 122.84/16.21 (((dpsetconstrERa) =>
% 122.84/16.21 (((dpsetconstrEL1) =>
% 122.84/16.21 (((dpsetconstrEL2) =>
% 122.84/16.21 (((dpsetconstrER) =>
% 122.84/16.21 (((funcImageSingleton) =>
% 122.84/16.21 (((apProp) =>
% 122.84/16.21 (((app) =>
% 122.84/16.21 (((infuncsetfunc) =>
% 122.84/16.21 (((ap2p) =>
% 122.84/16.21 (((funcinfuncset) =>
% 122.84/16.21 (((lamProp) =>
% 122.84/16.21 (((lamp) =>
% 122.84/16.21 (((lam2p) =>
% 122.84/16.21 (((brelnall1) =>
% 122.84/16.21 (((brelnall2) =>
% 122.84/16.21 (((ex1E2) =>
% 122.84/16.21 (((funcGraphProp1) =>
% 122.84/16.21 (((funcGraphProp3) =>
% 122.84/16.21 (((funcGraphProp2) =>
% 122.84/16.21 (((funcextLem) =>
% 122.84/16.21 (((funcGraphProp4) =>
% 122.84/16.21 (((subbreln) =>
% 122.84/16.21 (((eqbreln) =>
% 122.84/16.21 (((funcext) =>
% 122.84/16.21 ((
% 122.84/16.21 (funcext2) =>
% 122.84/16.21 ((
% 122.84/16.21 (ap2apEq1) =>
% 122.84/16.21 ((
% 122.84/16.21 (ap2apEq2) =>
% 122.84/16.21 ((
% 122.84/16.21 (beta1) =>
% 122.84/16.21 ((
% 122.84/16.21 (eta1) =>
% 122.84/16.21 ((
% 122.84/16.21 (lam2lamEq) =>
% 122.84/16.21 ((
% 122.84/16.21 (beta2) =>
% 122.84/16.21 ((
% 122.84/16.21 (eta2) =>
% 122.84/16.21 ((
% 122.84/16.21 (iffalseProp1) =>
% 122.84/16.21 ((
% 122.84/16.21 (iffalseProp2) =>
% 122.84/16.21 ((
% 122.84/16.21 (iftrueProp1) =>
% 122.84/16.21 ((
% 122.84/16.21 (iftrueProp2) =>
% 122.84/16.21 ((
% 122.84/16.21 (ifSingleton) =>
% 122.84/16.21 ((
% 122.84/16.21 (ifp) =>
% 122.84/16.21 ((
% 122.84/16.21 (theeq) =>
% 122.84/16.21 ((
% 122.84/16.21 (iftrue) =>
% 122.84/16.21 ((
% 122.84/16.21 (iffalse) =>
% 122.84/16.21 ((
% 122.84/16.21 (iftrueorfalse) =>
% 122.84/16.21 ((
% 122.84/16.21 (binintersectT_lem) =>
% 122.84/16.21 ((
% 122.84/16.21 (binunionT_lem) =>
% 122.84/16.21 ((
% 122.84/16.21 (powersetT_lem) =>
% 122.84/16.21 ((
% 122.84/16.21 (setminusT_lem) =>
% 122.84/16.21 ((
% 122.84/16.21 (complementT_lem) =>
% 122.84/16.21 ((
% 122.84/16.21 (setextT) =>
% 122.84/16.21 ((
% 122.84/16.21 (subsetTI) =>
% 122.84/16.21 ((
% 122.84/16.21 (powersetTI1) =>
% 122.84/16.21 ((
% 122.84/16.21 (powersetTE1) =>
% 122.84/16.21 ((
% 122.84/16.21 (complementTI1) =>
% 122.84/16.21 ((
% 122.84/16.21 (complementTE1) =>
% 122.84/16.21 ((
% 122.84/16.21 (binintersectTELcontra) =>
% 122.84/16.21 ((
% 122.84/16.21 (binintersectTERcontra) =>
% 122.84/16.21 ((
% 122.84/16.21 (contrasubsetT) =>
% 122.84/16.21 ((
% 122.84/16.21 (contrasubsetT1) =>
% 122.84/16.21 ((
% 122.84/16.21 (contrasubsetT2) =>
% 122.84/16.21 ((
% 122.84/16.21 (contrasubsetT3) =>
% 122.84/16.21 ((
% 122.84/16.21 (doubleComplementI1) =>
% 122.84/16.21 ((
% 122.84/16.21 (doubleComplementE1) =>
% 122.84/16.21 ((
% 122.84/16.21 (doubleComplementSub1) =>
% 122.84/16.21 ((
% 122.84/16.21 (doubleComplementSub2) =>
% 122.84/16.21 ((
% 122.84/16.21 (doubleComplementEq) =>
% 122.84/16.21 ((
% 122.84/16.21 (complementTnotintersectT) =>
% 122.84/16.21 ((
% 122.84/16.21 (complementImpComplementIntersect) =>
% 122.84/16.21 ((
% 122.84/16.21 (complementSubsetComplementIntersect) =>
% 122.84/16.21 ((
% 122.84/16.21 (complementInPowersetComplementIntersect) =>
% 122.84/16.21 ((
% 122.84/16.21 (contraSubsetComplement) =>
% 122.84/16.21 ((
% 122.84/16.21 (complementTcontraSubset) =>
% 122.84/16.21 ((
% 122.84/16.21 (binunionTILcontra) =>
% 122.84/16.21 ((
% 122.84/16.21 (binunionTIRcontra) =>
% 122.84/16.21 ((
% 122.84/16.21 (inIntersectImpInUnion) =>
% 122.84/16.21 ((
% 122.84/16.21 (inIntersectImpInUnion2) =>
% 122.84/16.21 ((
% 122.84/16.21 (inIntersectImpInIntersectUnions) =>
% 122.84/16.21 ((
% 122.84/16.21 (intersectInPowersetIntersectUnions) =>
% 122.84/16.21 ((
% 122.84/16.21 (inComplementUnionImpNotIn1) =>
% 122.84/16.21 ((
% 122.84/16.21 (inComplementUnionImpInComplement1) =>
% 122.84/16.21 ((
% 122.84/16.21 (binunionTE) =>
% 122.84/16.21 ((
% 122.84/16.21 (binunionTEcontra) =>
% 122.84/16.21 ((
% 122.84/16.21 (demorgan2a1) =>
% 122.84/16.21 ((
% 122.84/16.21 (complementUnionInPowersetComplement) =>
% 122.84/16.21 ((
% 122.84/16.21 (demorgan2a2) =>
% 122.84/16.21 ((
% 122.84/16.21 (demorgan1a) =>
% 122.84/16.21 ((
% 122.84/16.21 (demorgan1b) =>
% 122.84/16.21 ((
% 122.84/16.21 (demorgan1) =>
% 122.84/16.21 ((
% 122.84/16.21 (demorgan2a) =>
% 122.84/16.21 ((
% 122.84/16.21 (demorgan2b2) =>
% 122.84/16.21 ((
% 122.84/16.21 (demorgan2b) =>
% 122.84/16.21 ((
% 122.84/16.21 (demorgan2) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz13rule0) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz13rule1) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz13rule2) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz13rule3) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz13rule4) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz1_1) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz1_2) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz1_3) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz1_4) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz1_5) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1all2) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1SetBreln1) =>
% 122.84/16.21 ((
% 122.84/16.21 (choice2fnsingleton) =>
% 122.84/16.21 ((
% 122.84/16.21 (setOfPairsIsBReln1) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1all1) =>
% 122.84/16.21 ((
% 122.84/16.21 (subbreln1) =>
% 122.84/16.21 ((
% 122.84/16.21 (eqbreln1) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1invprop) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1invI) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1invE) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1compprop) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1compI) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1compE) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1compEex) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1unionprop) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1unionIL) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1unionIR) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1unionI) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1unionE) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1unionEcases) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1unionCommutes) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz2Ex) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz2W) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz2A) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz2B) =>
% 122.84/16.21 ((
% 122.84/16.21 (image1Ex) =>
% 122.84/16.21 ((
% 122.84/16.21 (image1Ex1) =>
% 122.84/16.21 ((
% 122.84/16.21 (image1Equiv) =>
% 122.84/16.21 ((
% 122.84/16.21 (image1E) =>
% 122.84/16.21 ((
% 122.84/16.21 (image1I) =>
% 122.84/16.21 ((
% 122.84/16.21 (injFuncInInjFuncSet) =>
% 122.84/16.21 ((
% 122.84/16.21 (!!) @ (
% 122.84/16.21 (('#B') @ (
% 122.84/16.21 !!) @
% 122.84/16.21 (
% 122.84/16.21 (
% 122.84/16.21 ('#B') @ (
% 122.84/16.21 (
% 122.84/16.21 ('#B') @ (
% 122.84/16.21 !!))) @
% 122.84/16.21 (
% 122.84/16.21 (
% 122.84/16.21 ('#S') @ (
% 122.84/16.21 (
% 122.84/16.21 ('#B') @ (
% 122.84/16.21 '#S') @
% 122.84/16.21 (
% 122.84/16.21 (
% 122.84/16.21 ('#B') @ (
% 122.84/16.21 (
% 122.84/16.21 ('#B') @ (
% 122.84/16.21 '#S'))) @
% 122.84/16.21 (
% 122.84/16.21 (
% 122.84/16.21 ('#B') @ (
% 122.84/16.21 (
% 122.84/16.21 ('#B') @ (
% 122.84/16.21 (
% 122.84/16.21 ('#B') @ (
% 122.84/16.21 =>))))) @
% 122.84/16.21 (
% 122.84/16.21 (
% 122.84/16.21 ('#B') @ (
% 122.84/16.21 (
% 122.84/16.21 ('#B') @ (
% 122.84/16.21 (
% 122.84/16.21 ('#C') @ in)))) @
% 122.84/16.21 injFuncSet)))))))) @
% 122.84/16.21 (
% 122.84/16.21 (
% 122.84/16.21 ('#B') @ (
% 122.84/16.21 (
% 122.84/16.21 ('#B') @ (
% 122.84/16.21 (
% 122.84/16.21 ('#C') @ in)))) @
% 122.84/16.21 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.84/16.21 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1825])).
% 122.84/16.21 thf(zip_derived_cl1840, plain,
% 122.84/16.21 (~ (((cartprodsndpairEq) =>
% 122.84/16.21 (((cartprodpairsurjEq) =>
% 122.84/16.21 (((dpsetconstrI) =>
% 122.84/16.21 (((dpsetconstrSub) =>
% 122.84/16.21 (((setOfPairsIsBReln) =>
% 122.84/16.21 (((dpsetconstrERa) =>
% 122.84/16.21 (((dpsetconstrEL1) =>
% 122.84/16.21 (((dpsetconstrEL2) =>
% 122.84/16.21 (((dpsetconstrER) =>
% 122.84/16.21 (((funcImageSingleton) =>
% 122.84/16.21 (((apProp) =>
% 122.84/16.21 (((app) =>
% 122.84/16.21 (((infuncsetfunc) =>
% 122.84/16.21 (((ap2p) =>
% 122.84/16.21 (((funcinfuncset) =>
% 122.84/16.21 (((lamProp) =>
% 122.84/16.21 (((lamp) =>
% 122.84/16.21 (((lam2p) =>
% 122.84/16.21 (((brelnall1) =>
% 122.84/16.21 (((brelnall2) =>
% 122.84/16.21 (((ex1E2) =>
% 122.84/16.21 (((funcGraphProp1) =>
% 122.84/16.21 (((funcGraphProp3) =>
% 122.84/16.21 (((funcGraphProp2) =>
% 122.84/16.21 (((funcextLem) =>
% 122.84/16.21 (((funcGraphProp4) =>
% 122.84/16.21 (((subbreln) =>
% 122.84/16.21 (((eqbreln) =>
% 122.84/16.21 (((funcext) =>
% 122.84/16.21 (((funcext2) =>
% 122.84/16.21 ((
% 122.84/16.21 (ap2apEq1) =>
% 122.84/16.21 ((
% 122.84/16.21 (ap2apEq2) =>
% 122.84/16.21 ((
% 122.84/16.21 (beta1) =>
% 122.84/16.21 ((
% 122.84/16.21 (eta1) =>
% 122.84/16.21 ((
% 122.84/16.21 (lam2lamEq) =>
% 122.84/16.21 ((
% 122.84/16.21 (beta2) =>
% 122.84/16.21 ((
% 122.84/16.21 (eta2) =>
% 122.84/16.21 ((
% 122.84/16.21 (iffalseProp1) =>
% 122.84/16.21 ((
% 122.84/16.21 (iffalseProp2) =>
% 122.84/16.21 ((
% 122.84/16.21 (iftrueProp1) =>
% 122.84/16.21 ((
% 122.84/16.21 (iftrueProp2) =>
% 122.84/16.21 ((
% 122.84/16.21 (ifSingleton) =>
% 122.84/16.21 ((
% 122.84/16.21 (ifp) =>
% 122.84/16.21 ((
% 122.84/16.21 (theeq) =>
% 122.84/16.21 ((
% 122.84/16.21 (iftrue) =>
% 122.84/16.21 ((
% 122.84/16.21 (iffalse) =>
% 122.84/16.21 ((
% 122.84/16.21 (iftrueorfalse) =>
% 122.84/16.21 ((
% 122.84/16.21 (binintersectT_lem) =>
% 122.84/16.21 ((
% 122.84/16.21 (binunionT_lem) =>
% 122.84/16.21 ((
% 122.84/16.21 (powersetT_lem) =>
% 122.84/16.21 ((
% 122.84/16.21 (setminusT_lem) =>
% 122.84/16.21 ((
% 122.84/16.21 (complementT_lem) =>
% 122.84/16.21 ((
% 122.84/16.21 (setextT) =>
% 122.84/16.21 ((
% 122.84/16.21 (subsetTI) =>
% 122.84/16.21 ((
% 122.84/16.21 (powersetTI1) =>
% 122.84/16.21 ((
% 122.84/16.21 (powersetTE1) =>
% 122.84/16.21 ((
% 122.84/16.21 (complementTI1) =>
% 122.84/16.21 ((
% 122.84/16.21 (complementTE1) =>
% 122.84/16.21 ((
% 122.84/16.21 (binintersectTELcontra) =>
% 122.84/16.21 ((
% 122.84/16.21 (binintersectTERcontra) =>
% 122.84/16.21 ((
% 122.84/16.21 (contrasubsetT) =>
% 122.84/16.21 ((
% 122.84/16.21 (contrasubsetT1) =>
% 122.84/16.21 ((
% 122.84/16.21 (contrasubsetT2) =>
% 122.84/16.21 ((
% 122.84/16.21 (contrasubsetT3) =>
% 122.84/16.21 ((
% 122.84/16.21 (doubleComplementI1) =>
% 122.84/16.21 ((
% 122.84/16.21 (doubleComplementE1) =>
% 122.84/16.21 ((
% 122.84/16.21 (doubleComplementSub1) =>
% 122.84/16.21 ((
% 122.84/16.21 (doubleComplementSub2) =>
% 122.84/16.21 ((
% 122.84/16.21 (doubleComplementEq) =>
% 122.84/16.21 ((
% 122.84/16.21 (complementTnotintersectT) =>
% 122.84/16.21 ((
% 122.84/16.21 (complementImpComplementIntersect) =>
% 122.84/16.21 ((
% 122.84/16.21 (complementSubsetComplementIntersect) =>
% 122.84/16.21 ((
% 122.84/16.21 (complementInPowersetComplementIntersect) =>
% 122.84/16.21 ((
% 122.84/16.21 (contraSubsetComplement) =>
% 122.84/16.21 ((
% 122.84/16.21 (complementTcontraSubset) =>
% 122.84/16.21 ((
% 122.84/16.21 (binunionTILcontra) =>
% 122.84/16.21 ((
% 122.84/16.21 (binunionTIRcontra) =>
% 122.84/16.21 ((
% 122.84/16.21 (inIntersectImpInUnion) =>
% 122.84/16.21 ((
% 122.84/16.21 (inIntersectImpInUnion2) =>
% 122.84/16.21 ((
% 122.84/16.21 (inIntersectImpInIntersectUnions) =>
% 122.84/16.21 ((
% 122.84/16.21 (intersectInPowersetIntersectUnions) =>
% 122.84/16.21 ((
% 122.84/16.21 (inComplementUnionImpNotIn1) =>
% 122.84/16.21 ((
% 122.84/16.21 (inComplementUnionImpInComplement1) =>
% 122.84/16.21 ((
% 122.84/16.21 (binunionTE) =>
% 122.84/16.21 ((
% 122.84/16.21 (binunionTEcontra) =>
% 122.84/16.21 ((
% 122.84/16.21 (demorgan2a1) =>
% 122.84/16.21 ((
% 122.84/16.21 (complementUnionInPowersetComplement) =>
% 122.84/16.21 ((
% 122.84/16.21 (demorgan2a2) =>
% 122.84/16.21 ((
% 122.84/16.21 (demorgan1a) =>
% 122.84/16.21 ((
% 122.84/16.21 (demorgan1b) =>
% 122.84/16.21 ((
% 122.84/16.21 (demorgan1) =>
% 122.84/16.21 ((
% 122.84/16.21 (demorgan2a) =>
% 122.84/16.21 ((
% 122.84/16.21 (demorgan2b2) =>
% 122.84/16.21 ((
% 122.84/16.21 (demorgan2b) =>
% 122.84/16.21 ((
% 122.84/16.21 (demorgan2) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz13rule0) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz13rule1) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz13rule2) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz13rule3) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz13rule4) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz1_1) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz1_2) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz1_3) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz1_4) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz1_5) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1all2) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1SetBreln1) =>
% 122.84/16.21 ((
% 122.84/16.21 (choice2fnsingleton) =>
% 122.84/16.21 ((
% 122.84/16.21 (setOfPairsIsBReln1) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1all1) =>
% 122.84/16.21 ((
% 122.84/16.21 (subbreln1) =>
% 122.84/16.21 ((
% 122.84/16.21 (eqbreln1) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1invprop) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1invI) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1invE) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1compprop) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1compI) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1compE) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1compEex) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1unionprop) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1unionIL) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1unionIR) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1unionI) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1unionE) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1unionEcases) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1unionCommutes) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz2Ex) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz2W) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz2A) =>
% 122.84/16.21 ((
% 122.84/16.21 (woz2B) =>
% 122.84/16.21 ((
% 122.84/16.21 (image1Ex) =>
% 122.84/16.21 ((
% 122.84/16.21 (image1Ex1) =>
% 122.84/16.21 ((
% 122.84/16.21 (image1Equiv) =>
% 122.84/16.21 ((
% 122.84/16.21 (image1E) =>
% 122.84/16.21 ((
% 122.84/16.21 (image1I) =>
% 122.84/16.21 ((
% 122.84/16.21 (injFuncInInjFuncSet) =>
% 122.84/16.21 ((
% 122.84/16.21 (!!) @ (
% 122.84/16.21 (('#B') @ (
% 122.84/16.21 !!) @
% 122.84/16.21 (
% 122.84/16.21 (
% 122.84/16.21 ('#B') @ (
% 122.84/16.21 (
% 122.84/16.21 ('#B') @ (
% 122.84/16.21 !!))) @
% 122.84/16.21 (
% 122.84/16.21 (
% 122.84/16.21 ('#S') @ (
% 122.84/16.21 (
% 122.84/16.21 ('#B') @ (
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% 122.84/16.21 (
% 122.84/16.21 (
% 122.84/16.21 ('#B') @ (
% 122.84/16.21 (
% 122.84/16.21 ('#B') @ (
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% 122.84/16.21 (
% 122.84/16.21 (
% 122.84/16.21 ('#B') @ (
% 122.84/16.21 (
% 122.84/16.21 ('#B') @ (
% 122.84/16.21 (
% 122.84/16.21 ('#B') @ (
% 122.84/16.21 =>))))) @
% 122.84/16.21 (
% 122.84/16.21 (
% 122.84/16.21 ('#B') @ (
% 122.84/16.21 (
% 122.84/16.21 ('#B') @ (
% 122.84/16.21 (
% 122.84/16.21 ('#C') @ in)))) @
% 122.84/16.21 injFuncSet)))))))) @
% 122.84/16.21 (
% 122.84/16.21 (
% 122.84/16.21 ('#B') @ (
% 122.84/16.21 (
% 122.84/16.21 ('#B') @ (
% 122.84/16.21 (
% 122.84/16.21 ('#C') @ in)))) @
% 122.84/16.21 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.84/16.21 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1833])).
% 122.84/16.21 thf(zip_derived_cl1848, plain,
% 122.84/16.21 (~ (((cartprodpairsurjEq) =>
% 122.84/16.21 (((dpsetconstrI) =>
% 122.84/16.21 (((dpsetconstrSub) =>
% 122.84/16.21 (((setOfPairsIsBReln) =>
% 122.84/16.21 (((dpsetconstrERa) =>
% 122.84/16.21 (((dpsetconstrEL1) =>
% 122.84/16.21 (((dpsetconstrEL2) =>
% 122.84/16.21 (((dpsetconstrER) =>
% 122.84/16.21 (((funcImageSingleton) =>
% 122.84/16.21 (((apProp) =>
% 122.84/16.21 (((app) =>
% 122.84/16.21 (((infuncsetfunc) =>
% 122.84/16.21 (((ap2p) =>
% 122.84/16.21 (((funcinfuncset) =>
% 122.84/16.21 (((lamProp) =>
% 122.84/16.21 (((lamp) =>
% 122.84/16.21 (((lam2p) =>
% 122.84/16.21 (((brelnall1) =>
% 122.84/16.21 (((brelnall2) =>
% 122.84/16.21 (((ex1E2) =>
% 122.84/16.21 (((funcGraphProp1) =>
% 122.84/16.21 (((funcGraphProp3) =>
% 122.84/16.21 (((funcGraphProp2) =>
% 122.84/16.21 (((funcextLem) =>
% 122.84/16.21 (((funcGraphProp4) =>
% 122.84/16.21 (((subbreln) =>
% 122.84/16.21 (((eqbreln) =>
% 122.84/16.21 (((funcext) =>
% 122.84/16.21 (((funcext2) =>
% 122.84/16.21 (((ap2apEq1) =>
% 122.84/16.21 ((
% 122.84/16.21 (ap2apEq2) =>
% 122.84/16.21 ((
% 122.84/16.21 (beta1) =>
% 122.84/16.21 ((
% 122.84/16.21 (eta1) =>
% 122.84/16.21 ((
% 122.84/16.21 (lam2lamEq) =>
% 122.84/16.21 ((
% 122.84/16.21 (beta2) =>
% 122.84/16.21 ((
% 122.84/16.21 (eta2) =>
% 122.84/16.21 ((
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% 122.84/16.21 ((
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% 122.84/16.21 ((
% 122.84/16.21 (iftrueProp1) =>
% 122.84/16.21 ((
% 122.84/16.21 (iftrueProp2) =>
% 122.84/16.21 ((
% 122.84/16.21 (ifSingleton) =>
% 122.84/16.21 ((
% 122.84/16.21 (ifp) =>
% 122.84/16.21 ((
% 122.84/16.21 (theeq) =>
% 122.84/16.21 ((
% 122.84/16.21 (iftrue) =>
% 122.84/16.21 ((
% 122.84/16.21 (iffalse) =>
% 122.84/16.21 ((
% 122.84/16.21 (iftrueorfalse) =>
% 122.84/16.21 ((
% 122.84/16.21 (binintersectT_lem) =>
% 122.84/16.21 ((
% 122.84/16.21 (binunionT_lem) =>
% 122.84/16.21 ((
% 122.84/16.21 (powersetT_lem) =>
% 122.84/16.21 ((
% 122.84/16.21 (setminusT_lem) =>
% 122.84/16.21 ((
% 122.84/16.21 (complementT_lem) =>
% 122.84/16.21 ((
% 122.84/16.21 (setextT) =>
% 122.84/16.21 ((
% 122.84/16.21 (subsetTI) =>
% 122.84/16.21 ((
% 122.84/16.21 (powersetTI1) =>
% 122.84/16.21 ((
% 122.84/16.21 (powersetTE1) =>
% 122.84/16.21 ((
% 122.84/16.21 (complementTI1) =>
% 122.84/16.21 ((
% 122.84/16.21 (complementTE1) =>
% 122.84/16.21 ((
% 122.84/16.21 (binintersectTELcontra) =>
% 122.84/16.21 ((
% 122.84/16.21 (binintersectTERcontra) =>
% 122.84/16.21 ((
% 122.84/16.21 (contrasubsetT) =>
% 122.84/16.21 ((
% 122.84/16.21 (contrasubsetT1) =>
% 122.84/16.21 ((
% 122.84/16.21 (contrasubsetT2) =>
% 122.84/16.21 ((
% 122.84/16.21 (contrasubsetT3) =>
% 122.84/16.21 ((
% 122.84/16.21 (doubleComplementI1) =>
% 122.84/16.21 ((
% 122.84/16.21 (doubleComplementE1) =>
% 122.84/16.21 ((
% 122.84/16.21 (doubleComplementSub1) =>
% 122.84/16.21 ((
% 122.84/16.21 (doubleComplementSub2) =>
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% 122.84/16.21 ((
% 122.84/16.21 (complementInPowersetComplementIntersect) =>
% 122.84/16.21 ((
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% 122.84/16.21 ((
% 122.84/16.21 (complementTcontraSubset) =>
% 122.84/16.21 ((
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% 122.84/16.21 ((
% 122.84/16.21 (binunionTIRcontra) =>
% 122.84/16.21 ((
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% 122.84/16.21 ((
% 122.84/16.21 (inIntersectImpInUnion2) =>
% 122.84/16.21 ((
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% 122.84/16.21 (inComplementUnionImpInComplement1) =>
% 122.84/16.21 ((
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% 122.84/16.21 ((
% 122.84/16.21 (binunionTEcontra) =>
% 122.84/16.21 ((
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% 122.84/16.21 ((
% 122.84/16.21 (complementUnionInPowersetComplement) =>
% 122.84/16.21 ((
% 122.84/16.21 (demorgan2a2) =>
% 122.84/16.21 ((
% 122.84/16.21 (demorgan1a) =>
% 122.84/16.21 ((
% 122.84/16.21 (demorgan1b) =>
% 122.84/16.21 ((
% 122.84/16.21 (demorgan1) =>
% 122.84/16.21 ((
% 122.84/16.21 (demorgan2a) =>
% 122.84/16.21 ((
% 122.84/16.21 (demorgan2b2) =>
% 122.84/16.21 ((
% 122.84/16.21 (demorgan2b) =>
% 122.84/16.21 ((
% 122.84/16.21 (demorgan2) =>
% 122.84/16.21 ((
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% 122.84/16.21 ((
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% 122.84/16.21 ((
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% 122.84/16.21 ((
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% 122.84/16.21 (setOfPairsIsBReln1) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1all1) =>
% 122.84/16.21 ((
% 122.84/16.21 (subbreln1) =>
% 122.84/16.21 ((
% 122.84/16.21 (eqbreln1) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1invprop) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1invI) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1invE) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1compprop) =>
% 122.84/16.21 ((
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% 122.84/16.21 ((
% 122.84/16.21 (breln1compE) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1compEex) =>
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% 122.84/16.21 ((
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% 122.84/16.21 ((
% 122.84/16.21 (breln1unionIR) =>
% 122.84/16.21 ((
% 122.84/16.21 (breln1unionI) =>
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% 122.84/16.21 (breln1unionEcases) =>
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% 122.84/16.21 ((
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% 122.84/16.21 (injFuncInInjFuncSet) =>
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% 122.84/16.21 (
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% 122.84/16.21 injFuncSet)))))))) @
% 122.84/16.21 (
% 122.84/16.21 (
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% 122.84/16.21 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.84/16.21 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1840])).
% 122.84/16.21 thf(zip_derived_cl1856, plain,
% 122.84/16.21 (~ (((dpsetconstrI) =>
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% 122.84/16.21 (((dpsetconstrER) =>
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% 122.84/16.21 (((infuncsetfunc) =>
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% 122.84/16.21 ((
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% 122.84/16.21 ((
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% 122.84/16.21 ((
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% 122.84/16.21 ((
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% 122.84/16.21 ((
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% 122.84/16.21 ((
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% 122.84/16.21 ((
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% 122.84/16.21 ((
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% 122.84/16.21 ((
% 122.84/16.21 (binunionTIRcontra) =>
% 122.84/16.21 ((
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% 122.84/16.21 ((
% 122.84/16.21 (inIntersectImpInUnion2) =>
% 122.84/16.21 ((
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% 122.84/16.21 ((
% 122.84/16.21 (intersectInPowersetIntersectUnions) =>
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% 122.84/16.21 (inComplementUnionImpNotIn1) =>
% 122.84/16.21 ((
% 122.84/16.21 (inComplementUnionImpInComplement1) =>
% 122.84/16.21 ((
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% 122.84/16.21 ((
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% 122.84/16.21 ((
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% 122.84/16.21 ((
% 122.84/16.21 (complementUnionInPowersetComplement) =>
% 122.84/16.21 ((
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% 122.84/16.21 ((
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% 122.84/16.21 ((
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% 122.84/16.21 ((
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% 122.84/16.21 ((
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% 122.84/16.21 ((
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% 122.84/16.21 ((
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% 122.84/16.21 ((
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% 122.84/16.21 ((
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% 122.84/16.21 ((
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% 122.84/16.21 ((
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% 122.84/16.21 ((
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% 122.84/16.21 ((
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% 122.84/16.21 ((
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% 122.84/16.21 ((
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% 122.84/16.21 ((
% 122.84/16.21 (woz1_5) =>
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% 122.84/16.21 ((
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% 122.84/16.21 ((
% 122.84/16.21 (breln1all1) =>
% 122.84/16.21 ((
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% 122.84/16.21 ((
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% 122.84/16.21 ((
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% 122.84/16.21 ((
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% 122.84/16.21 ((
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% 122.84/16.21 ((
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% 122.84/16.21 ((
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% 122.84/16.21 ((
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% 122.84/16.21 ((
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% 122.84/16.21 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1848])).
% 122.84/16.21 thf(zip_derived_cl1865, plain,
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% 122.84/16.21 ((
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% 122.84/16.21 ((
% 122.84/16.21 (contrasubsetT3) =>
% 122.84/16.21 ((
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% 122.84/16.21 ((
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% 122.84/16.21 ((
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% 122.84/16.21 ((
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% 122.84/16.21 ((
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% 122.84/16.21 ((
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% 122.84/16.21 ((
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% 122.84/16.21 ((
% 122.84/16.21 (demorgan1b) =>
% 122.84/16.21 ((
% 122.84/16.21 (demorgan1) =>
% 122.84/16.21 ((
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% 122.84/16.21 ((
% 122.84/16.21 (demorgan2b2) =>
% 122.84/16.21 ((
% 122.84/16.21 (demorgan2b) =>
% 122.84/16.21 ((
% 122.84/16.21 (demorgan2) =>
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% 122.84/16.21 ((
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% 122.84/16.21 ((
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% 122.84/16.21 ((
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% 122.84/16.21 ((
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% 122.84/16.21 ((
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% 122.84/16.21 ((
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% 122.84/16.21 ((
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% 122.84/16.21 ((
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% 122.84/16.21 (
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% 122.84/16.21 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1856])).
% 122.84/16.22 thf(zip_derived_cl1874, plain,
% 122.84/16.22 (~ (((setOfPairsIsBReln) =>
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% 122.84/16.22 (((dpsetconstrEL2) =>
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% 122.84/16.22 ((
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% 122.84/16.22 ((
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% 122.84/16.22 ((
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% 122.84/16.22 ((
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% 122.84/16.22 ((
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% 122.84/16.22 ((
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% 122.84/16.22 ((
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% 122.84/16.22 ((
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% 122.84/16.22 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1865])).
% 122.84/16.22 thf(zip_derived_cl1883, plain,
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% 122.84/16.22 ((
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% 122.84/16.22 ((
% 122.84/16.22 (contrasubsetT3) =>
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% 122.84/16.22 ((
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% 122.84/16.22 ((
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% 122.84/16.22 ((
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% 122.84/16.22 ((
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% 122.84/16.22 ((
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% 122.84/16.22 ((
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% 122.84/16.22 ((
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% 122.84/16.22 ((
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% 122.84/16.22 ((
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% 122.84/16.22 ((
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% 122.84/16.22 ((
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% 122.84/16.22 ((
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% 122.84/16.22 ((
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% 122.84/16.22 ((
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% 122.84/16.22 (breln1unionI) =>
% 122.84/16.22 ((
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% 122.84/16.22 (breln1unionEcases) =>
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% 122.84/16.22 ((
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% 122.84/16.22 ((
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% 122.84/16.22 ((
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% 122.84/16.22 (
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% 122.84/16.22 (
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% 122.84/16.22 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1874])).
% 122.84/16.22 thf(zip_derived_cl1893, plain,
% 122.84/16.22 (~ (((dpsetconstrEL1) =>
% 122.84/16.22 (((dpsetconstrEL2) =>
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% 122.84/16.22 ((
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% 122.84/16.22 ((
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% 122.84/16.22 ((
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% 122.84/16.22 ((
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% 122.84/16.22 ((
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% 122.84/16.22 ((
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% 122.84/16.22 ((
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% 122.84/16.22 ((
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% 122.84/16.22 ((
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% 122.84/16.22 ((
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% 122.84/16.22 ((
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% 122.84/16.22 ((
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% 122.84/16.22 (image1E) =>
% 122.84/16.22 ((
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% 122.84/16.22 ((
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% 122.84/16.22 ((
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% 122.84/16.22 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1883])).
% 122.84/16.22 thf(zip_derived_cl1903, plain,
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% 122.84/16.22 (((beta2) =>
% 122.84/16.22 (((eta2) =>
% 122.84/16.22 ((
% 122.84/16.22 (iffalseProp1) =>
% 122.84/16.22 ((
% 122.84/16.22 (iffalseProp2) =>
% 122.84/16.22 ((
% 122.84/16.22 (iftrueProp1) =>
% 122.84/16.22 ((
% 122.84/16.22 (iftrueProp2) =>
% 122.84/16.22 ((
% 122.84/16.22 (ifSingleton) =>
% 122.84/16.22 ((
% 122.84/16.22 (ifp) =>
% 122.84/16.22 ((
% 122.84/16.22 (theeq) =>
% 122.84/16.22 ((
% 122.84/16.22 (iftrue) =>
% 122.84/16.22 ((
% 122.84/16.22 (iffalse) =>
% 122.84/16.22 ((
% 122.84/16.22 (iftrueorfalse) =>
% 122.84/16.22 ((
% 122.84/16.22 (binintersectT_lem) =>
% 122.84/16.22 ((
% 122.84/16.22 (binunionT_lem) =>
% 122.84/16.22 ((
% 122.84/16.22 (powersetT_lem) =>
% 122.84/16.22 ((
% 122.84/16.22 (setminusT_lem) =>
% 122.84/16.22 ((
% 122.84/16.22 (complementT_lem) =>
% 122.84/16.22 ((
% 122.84/16.22 (setextT) =>
% 122.84/16.22 ((
% 122.84/16.22 (subsetTI) =>
% 122.84/16.22 ((
% 122.84/16.22 (powersetTI1) =>
% 122.84/16.22 ((
% 122.84/16.22 (powersetTE1) =>
% 122.84/16.22 ((
% 122.84/16.22 (complementTI1) =>
% 122.84/16.22 ((
% 122.84/16.22 (complementTE1) =>
% 122.84/16.22 ((
% 122.84/16.22 (binintersectTELcontra) =>
% 122.84/16.22 ((
% 122.84/16.22 (binintersectTERcontra) =>
% 122.84/16.22 ((
% 122.84/16.22 (contrasubsetT) =>
% 122.84/16.22 ((
% 122.84/16.22 (contrasubsetT1) =>
% 122.84/16.22 ((
% 122.84/16.22 (contrasubsetT2) =>
% 122.84/16.22 ((
% 122.84/16.22 (contrasubsetT3) =>
% 122.84/16.22 ((
% 122.84/16.22 (doubleComplementI1) =>
% 122.84/16.22 ((
% 122.84/16.22 (doubleComplementE1) =>
% 122.84/16.22 ((
% 122.84/16.22 (doubleComplementSub1) =>
% 122.84/16.22 ((
% 122.84/16.22 (doubleComplementSub2) =>
% 122.84/16.22 ((
% 122.84/16.22 (doubleComplementEq) =>
% 122.84/16.22 ((
% 122.84/16.22 (complementTnotintersectT) =>
% 122.84/16.22 ((
% 122.84/16.22 (complementImpComplementIntersect) =>
% 122.84/16.22 ((
% 122.84/16.22 (complementSubsetComplementIntersect) =>
% 122.84/16.22 ((
% 122.84/16.22 (complementInPowersetComplementIntersect) =>
% 122.84/16.22 ((
% 122.84/16.22 (contraSubsetComplement) =>
% 122.84/16.22 ((
% 122.84/16.22 (complementTcontraSubset) =>
% 122.84/16.22 ((
% 122.84/16.22 (binunionTILcontra) =>
% 122.84/16.22 ((
% 122.84/16.22 (binunionTIRcontra) =>
% 122.84/16.22 ((
% 122.84/16.22 (inIntersectImpInUnion) =>
% 122.84/16.22 ((
% 122.84/16.22 (inIntersectImpInUnion2) =>
% 122.84/16.22 ((
% 122.84/16.22 (inIntersectImpInIntersectUnions) =>
% 122.84/16.22 ((
% 122.84/16.22 (intersectInPowersetIntersectUnions) =>
% 122.84/16.22 ((
% 122.84/16.22 (inComplementUnionImpNotIn1) =>
% 122.84/16.22 ((
% 122.84/16.22 (inComplementUnionImpInComplement1) =>
% 122.84/16.22 ((
% 122.84/16.22 (binunionTE) =>
% 122.84/16.22 ((
% 122.84/16.22 (binunionTEcontra) =>
% 122.84/16.22 ((
% 122.84/16.22 (demorgan2a1) =>
% 122.84/16.22 ((
% 122.84/16.22 (complementUnionInPowersetComplement) =>
% 122.84/16.22 ((
% 122.84/16.22 (demorgan2a2) =>
% 122.84/16.22 ((
% 122.84/16.22 (demorgan1a) =>
% 122.84/16.22 ((
% 122.84/16.22 (demorgan1b) =>
% 122.84/16.22 ((
% 122.84/16.22 (demorgan1) =>
% 122.84/16.22 ((
% 122.84/16.22 (demorgan2a) =>
% 122.84/16.22 ((
% 122.84/16.22 (demorgan2b2) =>
% 122.84/16.22 ((
% 122.84/16.22 (demorgan2b) =>
% 122.84/16.22 ((
% 122.84/16.22 (demorgan2) =>
% 122.84/16.22 ((
% 122.84/16.22 (woz13rule0) =>
% 122.84/16.22 ((
% 122.84/16.22 (woz13rule1) =>
% 122.84/16.22 ((
% 122.84/16.22 (woz13rule2) =>
% 122.84/16.22 ((
% 122.84/16.22 (woz13rule3) =>
% 122.84/16.22 ((
% 122.84/16.22 (woz13rule4) =>
% 122.84/16.22 ((
% 122.84/16.22 (woz1_1) =>
% 122.84/16.22 ((
% 122.84/16.22 (woz1_2) =>
% 122.84/16.22 ((
% 122.84/16.22 (woz1_3) =>
% 122.84/16.22 ((
% 122.84/16.22 (woz1_4) =>
% 122.84/16.22 ((
% 122.84/16.22 (woz1_5) =>
% 122.84/16.22 ((
% 122.84/16.22 (breln1all2) =>
% 122.84/16.22 ((
% 122.84/16.22 (breln1SetBreln1) =>
% 122.84/16.22 ((
% 122.84/16.22 (choice2fnsingleton) =>
% 122.84/16.22 ((
% 122.84/16.22 (setOfPairsIsBReln1) =>
% 122.84/16.22 ((
% 122.84/16.22 (breln1all1) =>
% 122.84/16.22 ((
% 122.84/16.22 (subbreln1) =>
% 122.84/16.22 ((
% 122.84/16.22 (eqbreln1) =>
% 122.84/16.22 ((
% 122.84/16.22 (breln1invprop) =>
% 122.84/16.22 ((
% 122.84/16.22 (breln1invI) =>
% 122.84/16.22 ((
% 122.84/16.22 (breln1invE) =>
% 122.84/16.22 ((
% 122.84/16.22 (breln1compprop) =>
% 122.84/16.22 ((
% 122.84/16.22 (breln1compI) =>
% 122.84/16.22 ((
% 122.84/16.22 (breln1compE) =>
% 122.84/16.22 ((
% 122.84/16.22 (breln1compEex) =>
% 122.84/16.22 ((
% 122.84/16.22 (breln1unionprop) =>
% 122.84/16.22 ((
% 122.84/16.22 (breln1unionIL) =>
% 122.84/16.22 ((
% 122.84/16.22 (breln1unionIR) =>
% 122.84/16.22 ((
% 122.84/16.22 (breln1unionI) =>
% 122.84/16.22 ((
% 122.84/16.22 (breln1unionE) =>
% 122.84/16.22 ((
% 122.84/16.22 (breln1unionEcases) =>
% 122.84/16.22 ((
% 122.84/16.22 (breln1unionCommutes) =>
% 122.84/16.22 ((
% 122.84/16.22 (woz2Ex) =>
% 122.84/16.22 ((
% 122.84/16.22 (woz2W) =>
% 122.84/16.22 ((
% 122.84/16.22 (woz2A) =>
% 122.84/16.22 ((
% 122.84/16.22 (woz2B) =>
% 122.84/16.22 ((
% 122.84/16.22 (image1Ex) =>
% 122.84/16.22 ((
% 122.84/16.22 (image1Ex1) =>
% 122.84/16.22 ((
% 122.84/16.22 (image1Equiv) =>
% 122.84/16.22 ((
% 122.84/16.22 (image1E) =>
% 122.84/16.22 ((
% 122.84/16.22 (image1I) =>
% 122.84/16.22 ((
% 122.84/16.22 (injFuncInInjFuncSet) =>
% 122.84/16.22 ((
% 122.84/16.22 (!!) @ (
% 122.84/16.22 (('#B') @ (
% 122.84/16.22 !!) @
% 122.84/16.22 (
% 122.84/16.22 (
% 122.84/16.22 ('#B') @ (
% 122.84/16.22 (
% 122.84/16.22 ('#B') @ (
% 122.84/16.22 !!))) @
% 122.84/16.22 (
% 122.84/16.22 (
% 122.84/16.22 ('#S') @ (
% 122.84/16.22 (
% 122.84/16.22 ('#B') @ (
% 122.84/16.22 '#S') @
% 122.84/16.22 (
% 122.84/16.22 (
% 122.84/16.22 ('#B') @ (
% 122.84/16.22 (
% 122.84/16.22 ('#B') @ (
% 122.84/16.22 '#S'))) @
% 122.84/16.22 (
% 122.84/16.22 (
% 122.84/16.22 ('#B') @ (
% 122.84/16.22 (
% 122.84/16.22 ('#B') @ (
% 122.84/16.22 (
% 122.84/16.22 ('#B') @ (
% 122.84/16.22 =>))))) @
% 122.84/16.22 (
% 122.84/16.22 (
% 122.84/16.22 ('#B') @ (
% 122.84/16.22 (
% 122.84/16.22 ('#B') @ (
% 122.84/16.22 (
% 122.84/16.22 ('#C') @ in)))) @
% 122.84/16.22 injFuncSet)))))))) @
% 122.84/16.22 (
% 122.84/16.22 (
% 122.84/16.22 ('#B') @ (
% 122.84/16.22 (
% 122.84/16.22 ('#B') @ (
% 122.84/16.22 (
% 122.84/16.22 ('#C') @ in)))) @
% 122.84/16.22 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.84/16.22 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1893])).
% 122.84/16.22 thf(zip_derived_cl1914, plain,
% 122.84/16.22 (~ (((dpsetconstrER) =>
% 122.84/16.22 (((funcImageSingleton) =>
% 122.84/16.22 (((apProp) =>
% 122.84/16.22 (((app) =>
% 122.84/16.22 (((infuncsetfunc) =>
% 122.84/16.22 (((ap2p) =>
% 122.84/16.22 (((funcinfuncset) =>
% 122.84/16.22 (((lamProp) =>
% 122.84/16.22 (((lamp) =>
% 122.84/16.22 (((lam2p) =>
% 122.84/16.22 (((brelnall1) =>
% 122.84/16.22 (((brelnall2) =>
% 122.84/16.22 (((ex1E2) =>
% 122.84/16.22 (((funcGraphProp1) =>
% 122.84/16.22 (((funcGraphProp3) =>
% 122.84/16.22 (((funcGraphProp2) =>
% 122.84/16.22 (((funcextLem) =>
% 122.84/16.22 (((funcGraphProp4) =>
% 122.84/16.22 (((subbreln) =>
% 122.84/16.22 (((eqbreln) =>
% 122.84/16.22 (((funcext) =>
% 122.84/16.22 (((funcext2) =>
% 122.84/16.22 (((ap2apEq1) =>
% 122.84/16.22 (((ap2apEq2) =>
% 122.84/16.22 (((beta1) =>
% 122.84/16.22 (((eta1) =>
% 122.84/16.22 (((lam2lamEq) =>
% 122.84/16.22 (((beta2) =>
% 122.84/16.22 (((eta2) =>
% 122.84/16.22 (((iffalseProp1) =>
% 122.84/16.22 ((
% 122.84/16.22 (iffalseProp2) =>
% 122.84/16.22 ((
% 122.84/16.22 (iftrueProp1) =>
% 122.84/16.22 ((
% 122.84/16.22 (iftrueProp2) =>
% 122.84/16.22 ((
% 122.84/16.22 (ifSingleton) =>
% 122.84/16.22 ((
% 122.84/16.22 (ifp) =>
% 122.84/16.22 ((
% 122.84/16.22 (theeq) =>
% 122.84/16.22 ((
% 122.84/16.22 (iftrue) =>
% 122.84/16.22 ((
% 122.84/16.22 (iffalse) =>
% 122.84/16.22 ((
% 122.84/16.22 (iftrueorfalse) =>
% 122.84/16.22 ((
% 122.84/16.22 (binintersectT_lem) =>
% 122.84/16.22 ((
% 122.84/16.22 (binunionT_lem) =>
% 122.84/16.22 ((
% 122.84/16.22 (powersetT_lem) =>
% 122.84/16.22 ((
% 122.84/16.22 (setminusT_lem) =>
% 122.84/16.22 ((
% 122.84/16.22 (complementT_lem) =>
% 122.84/16.22 ((
% 122.84/16.22 (setextT) =>
% 122.84/16.22 ((
% 122.84/16.22 (subsetTI) =>
% 122.84/16.22 ((
% 122.84/16.22 (powersetTI1) =>
% 122.84/16.22 ((
% 122.84/16.22 (powersetTE1) =>
% 122.84/16.22 ((
% 122.84/16.22 (complementTI1) =>
% 122.84/16.22 ((
% 122.84/16.22 (complementTE1) =>
% 122.84/16.22 ((
% 122.84/16.22 (binintersectTELcontra) =>
% 122.84/16.22 ((
% 122.84/16.22 (binintersectTERcontra) =>
% 122.84/16.22 ((
% 122.84/16.22 (contrasubsetT) =>
% 122.84/16.22 ((
% 122.84/16.22 (contrasubsetT1) =>
% 122.84/16.22 ((
% 122.84/16.22 (contrasubsetT2) =>
% 122.84/16.22 ((
% 122.84/16.22 (contrasubsetT3) =>
% 122.84/16.22 ((
% 122.84/16.22 (doubleComplementI1) =>
% 122.84/16.22 ((
% 122.84/16.22 (doubleComplementE1) =>
% 122.84/16.22 ((
% 122.84/16.22 (doubleComplementSub1) =>
% 122.84/16.22 ((
% 122.84/16.22 (doubleComplementSub2) =>
% 122.84/16.22 ((
% 122.84/16.22 (doubleComplementEq) =>
% 122.84/16.22 ((
% 122.84/16.22 (complementTnotintersectT) =>
% 122.84/16.22 ((
% 122.84/16.22 (complementImpComplementIntersect) =>
% 122.84/16.22 ((
% 122.84/16.22 (complementSubsetComplementIntersect) =>
% 122.84/16.22 ((
% 122.84/16.22 (complementInPowersetComplementIntersect) =>
% 122.84/16.22 ((
% 122.84/16.22 (contraSubsetComplement) =>
% 122.84/16.22 ((
% 122.84/16.22 (complementTcontraSubset) =>
% 122.84/16.22 ((
% 122.84/16.22 (binunionTILcontra) =>
% 122.84/16.22 ((
% 122.84/16.22 (binunionTIRcontra) =>
% 122.84/16.22 ((
% 122.84/16.22 (inIntersectImpInUnion) =>
% 122.84/16.22 ((
% 122.84/16.22 (inIntersectImpInUnion2) =>
% 122.84/16.22 ((
% 122.84/16.22 (inIntersectImpInIntersectUnions) =>
% 122.84/16.22 ((
% 122.84/16.22 (intersectInPowersetIntersectUnions) =>
% 122.84/16.22 ((
% 122.84/16.22 (inComplementUnionImpNotIn1) =>
% 122.84/16.22 ((
% 122.84/16.22 (inComplementUnionImpInComplement1) =>
% 122.84/16.22 ((
% 122.84/16.22 (binunionTE) =>
% 122.84/16.22 ((
% 122.84/16.22 (binunionTEcontra) =>
% 122.84/16.22 ((
% 122.84/16.22 (demorgan2a1) =>
% 122.84/16.22 ((
% 122.84/16.22 (complementUnionInPowersetComplement) =>
% 122.84/16.22 ((
% 122.84/16.22 (demorgan2a2) =>
% 122.84/16.22 ((
% 122.84/16.22 (demorgan1a) =>
% 122.84/16.22 ((
% 122.84/16.22 (demorgan1b) =>
% 122.84/16.22 ((
% 122.84/16.22 (demorgan1) =>
% 122.84/16.22 ((
% 122.84/16.22 (demorgan2a) =>
% 122.84/16.22 ((
% 122.84/16.22 (demorgan2b2) =>
% 122.84/16.22 ((
% 122.84/16.22 (demorgan2b) =>
% 122.84/16.22 ((
% 122.84/16.22 (demorgan2) =>
% 122.84/16.22 ((
% 122.84/16.22 (woz13rule0) =>
% 122.84/16.22 ((
% 122.84/16.22 (woz13rule1) =>
% 122.84/16.22 ((
% 122.84/16.22 (woz13rule2) =>
% 122.84/16.22 ((
% 122.84/16.22 (woz13rule3) =>
% 122.84/16.22 ((
% 122.84/16.22 (woz13rule4) =>
% 122.84/16.22 ((
% 122.84/16.22 (woz1_1) =>
% 122.84/16.22 ((
% 122.84/16.22 (woz1_2) =>
% 122.84/16.22 ((
% 122.84/16.22 (woz1_3) =>
% 122.84/16.22 ((
% 122.84/16.22 (woz1_4) =>
% 122.84/16.22 ((
% 122.84/16.22 (woz1_5) =>
% 122.84/16.22 ((
% 122.84/16.22 (breln1all2) =>
% 122.84/16.22 ((
% 122.84/16.22 (breln1SetBreln1) =>
% 122.84/16.22 ((
% 122.84/16.22 (choice2fnsingleton) =>
% 122.84/16.22 ((
% 122.84/16.22 (setOfPairsIsBReln1) =>
% 122.84/16.22 ((
% 122.84/16.22 (breln1all1) =>
% 122.84/16.22 ((
% 122.84/16.22 (subbreln1) =>
% 122.84/16.22 ((
% 122.84/16.22 (eqbreln1) =>
% 122.84/16.22 ((
% 122.84/16.22 (breln1invprop) =>
% 122.84/16.22 ((
% 122.84/16.22 (breln1invI) =>
% 122.84/16.22 ((
% 122.84/16.22 (breln1invE) =>
% 122.84/16.22 ((
% 122.84/16.22 (breln1compprop) =>
% 122.84/16.22 ((
% 122.84/16.22 (breln1compI) =>
% 122.84/16.22 ((
% 122.84/16.22 (breln1compE) =>
% 122.84/16.22 ((
% 122.84/16.22 (breln1compEex) =>
% 122.84/16.22 ((
% 122.84/16.22 (breln1unionprop) =>
% 122.84/16.22 ((
% 122.84/16.22 (breln1unionIL) =>
% 122.84/16.22 ((
% 122.84/16.22 (breln1unionIR) =>
% 122.84/16.22 ((
% 122.84/16.22 (breln1unionI) =>
% 122.84/16.22 ((
% 122.84/16.22 (breln1unionE) =>
% 122.84/16.22 ((
% 122.84/16.22 (breln1unionEcases) =>
% 122.84/16.22 ((
% 122.84/16.22 (breln1unionCommutes) =>
% 122.84/16.22 ((
% 122.84/16.22 (woz2Ex) =>
% 122.84/16.22 ((
% 122.84/16.22 (woz2W) =>
% 122.84/16.22 ((
% 122.84/16.22 (woz2A) =>
% 122.84/16.22 ((
% 122.84/16.22 (woz2B) =>
% 122.84/16.22 ((
% 122.84/16.22 (image1Ex) =>
% 122.84/16.22 ((
% 122.84/16.22 (image1Ex1) =>
% 122.84/16.22 ((
% 122.84/16.22 (image1Equiv) =>
% 122.84/16.22 ((
% 122.84/16.22 (image1E) =>
% 122.84/16.22 ((
% 122.84/16.22 (image1I) =>
% 122.84/16.22 ((
% 122.84/16.22 (injFuncInInjFuncSet) =>
% 122.84/16.22 ((
% 122.84/16.22 (!!) @ (
% 122.84/16.22 (('#B') @ (
% 122.84/16.22 !!) @
% 122.84/16.22 (
% 122.84/16.22 (
% 122.84/16.22 ('#B') @ (
% 122.84/16.22 (
% 122.84/16.22 ('#B') @ (
% 122.84/16.22 !!))) @
% 122.84/16.22 (
% 122.84/16.22 (
% 122.84/16.22 ('#S') @ (
% 122.84/16.22 (
% 122.84/16.22 ('#B') @ (
% 122.84/16.22 '#S') @
% 122.84/16.22 (
% 122.84/16.22 (
% 122.84/16.22 ('#B') @ (
% 122.84/16.22 (
% 122.84/16.22 ('#B') @ (
% 122.84/16.22 '#S'))) @
% 122.84/16.22 (
% 122.84/16.22 (
% 122.84/16.22 ('#B') @ (
% 122.84/16.22 (
% 122.84/16.22 ('#B') @ (
% 122.84/16.22 (
% 122.84/16.22 ('#B') @ (
% 122.84/16.22 =>))))) @
% 122.84/16.22 (
% 122.84/16.22 (
% 122.84/16.22 ('#B') @ (
% 122.84/16.22 (
% 122.84/16.22 ('#B') @ (
% 122.84/16.22 (
% 122.84/16.22 ('#C') @ in)))) @
% 122.84/16.22 injFuncSet)))))))) @
% 122.84/16.22 (
% 122.84/16.22 (
% 122.84/16.22 ('#B') @ (
% 122.84/16.22 (
% 122.84/16.22 ('#B') @ (
% 122.84/16.22 (
% 122.84/16.22 ('#C') @ in)))) @
% 122.84/16.22 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.84/16.22 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1903])).
% 122.84/16.22 thf(zip_derived_cl1923, plain,
% 122.84/16.22 (~ (((funcImageSingleton) =>
% 122.84/16.22 (((apProp) =>
% 122.84/16.22 (((app) =>
% 122.84/16.22 (((infuncsetfunc) =>
% 122.84/16.22 (((ap2p) =>
% 122.84/16.22 (((funcinfuncset) =>
% 122.84/16.22 (((lamProp) =>
% 122.84/16.22 (((lamp) =>
% 122.84/16.22 (((lam2p) =>
% 122.84/16.22 (((brelnall1) =>
% 122.84/16.22 (((brelnall2) =>
% 122.84/16.22 (((ex1E2) =>
% 122.84/16.22 (((funcGraphProp1) =>
% 122.84/16.22 (((funcGraphProp3) =>
% 122.84/16.22 (((funcGraphProp2) =>
% 122.84/16.22 (((funcextLem) =>
% 122.84/16.22 (((funcGraphProp4) =>
% 122.84/16.22 (((subbreln) =>
% 122.84/16.22 (((eqbreln) =>
% 122.84/16.22 (((funcext) =>
% 122.84/16.22 (((funcext2) =>
% 122.84/16.22 (((ap2apEq1) =>
% 122.84/16.22 (((ap2apEq2) =>
% 122.84/16.22 (((beta1) =>
% 122.84/16.22 (((eta1) =>
% 122.84/16.22 (((lam2lamEq) =>
% 122.84/16.22 (((beta2) =>
% 122.84/16.22 (((eta2) =>
% 122.84/16.22 (((iffalseProp1) =>
% 122.84/16.22 (((iffalseProp2) =>
% 122.84/16.22 ((
% 122.84/16.22 (iftrueProp1) =>
% 122.84/16.22 ((
% 122.84/16.22 (iftrueProp2) =>
% 122.84/16.22 ((
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% 122.84/16.22 ((
% 122.84/16.22 (ifp) =>
% 122.84/16.22 ((
% 122.84/16.22 (theeq) =>
% 122.84/16.22 ((
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% 122.84/16.22 ((
% 122.84/16.22 (binunionT_lem) =>
% 122.84/16.22 ((
% 122.84/16.22 (powersetT_lem) =>
% 122.84/16.22 ((
% 122.84/16.22 (setminusT_lem) =>
% 122.84/16.22 ((
% 122.84/16.22 (complementT_lem) =>
% 122.84/16.22 ((
% 122.84/16.22 (setextT) =>
% 122.84/16.22 ((
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% 122.84/16.22 ((
% 122.84/16.22 (powersetTI1) =>
% 122.84/16.22 ((
% 122.84/16.22 (powersetTE1) =>
% 122.84/16.22 ((
% 122.84/16.22 (complementTI1) =>
% 122.84/16.22 ((
% 122.84/16.22 (complementTE1) =>
% 122.84/16.22 ((
% 122.84/16.22 (binintersectTELcontra) =>
% 122.84/16.22 ((
% 122.84/16.22 (binintersectTERcontra) =>
% 122.84/16.22 ((
% 122.84/16.22 (contrasubsetT) =>
% 122.84/16.22 ((
% 122.84/16.22 (contrasubsetT1) =>
% 122.84/16.22 ((
% 122.84/16.22 (contrasubsetT2) =>
% 122.84/16.22 ((
% 122.84/16.22 (contrasubsetT3) =>
% 122.84/16.22 ((
% 122.84/16.22 (doubleComplementI1) =>
% 122.84/16.22 ((
% 122.84/16.22 (doubleComplementE1) =>
% 122.84/16.22 ((
% 122.84/16.22 (doubleComplementSub1) =>
% 122.84/16.22 ((
% 122.84/16.22 (doubleComplementSub2) =>
% 122.84/16.22 ((
% 122.84/16.22 (doubleComplementEq) =>
% 122.84/16.22 ((
% 122.84/16.22 (complementTnotintersectT) =>
% 122.84/16.22 ((
% 122.84/16.22 (complementImpComplementIntersect) =>
% 122.84/16.22 ((
% 122.84/16.22 (complementSubsetComplementIntersect) =>
% 122.84/16.22 ((
% 122.84/16.22 (complementInPowersetComplementIntersect) =>
% 122.84/16.22 ((
% 122.84/16.22 (contraSubsetComplement) =>
% 122.84/16.22 ((
% 122.84/16.22 (complementTcontraSubset) =>
% 122.84/16.22 ((
% 122.84/16.22 (binunionTILcontra) =>
% 122.84/16.22 ((
% 122.84/16.22 (binunionTIRcontra) =>
% 122.84/16.22 ((
% 122.84/16.22 (inIntersectImpInUnion) =>
% 122.84/16.22 ((
% 122.84/16.22 (inIntersectImpInUnion2) =>
% 122.84/16.22 ((
% 122.84/16.22 (inIntersectImpInIntersectUnions) =>
% 122.84/16.22 ((
% 122.84/16.22 (intersectInPowersetIntersectUnions) =>
% 122.84/16.22 ((
% 122.84/16.22 (inComplementUnionImpNotIn1) =>
% 122.84/16.22 ((
% 122.84/16.22 (inComplementUnionImpInComplement1) =>
% 122.84/16.22 ((
% 122.84/16.22 (binunionTE) =>
% 122.84/16.22 ((
% 122.84/16.22 (binunionTEcontra) =>
% 122.84/16.22 ((
% 122.84/16.22 (demorgan2a1) =>
% 122.84/16.22 ((
% 122.84/16.22 (complementUnionInPowersetComplement) =>
% 122.84/16.22 ((
% 122.84/16.22 (demorgan2a2) =>
% 122.84/16.22 ((
% 122.84/16.22 (demorgan1a) =>
% 122.84/16.22 ((
% 122.84/16.22 (demorgan1b) =>
% 122.84/16.22 ((
% 122.84/16.22 (demorgan1) =>
% 122.84/16.22 ((
% 122.84/16.22 (demorgan2a) =>
% 122.84/16.22 ((
% 122.84/16.22 (demorgan2b2) =>
% 122.84/16.22 ((
% 122.84/16.22 (demorgan2b) =>
% 122.84/16.22 ((
% 122.84/16.22 (demorgan2) =>
% 122.84/16.22 ((
% 122.84/16.22 (woz13rule0) =>
% 122.84/16.22 ((
% 122.84/16.22 (woz13rule1) =>
% 122.84/16.22 ((
% 122.84/16.22 (woz13rule2) =>
% 122.84/16.22 ((
% 122.84/16.22 (woz13rule3) =>
% 122.84/16.22 ((
% 122.84/16.22 (woz13rule4) =>
% 122.84/16.22 ((
% 122.84/16.22 (woz1_1) =>
% 122.84/16.22 ((
% 122.84/16.22 (woz1_2) =>
% 122.84/16.22 ((
% 122.84/16.22 (woz1_3) =>
% 122.84/16.22 ((
% 122.84/16.22 (woz1_4) =>
% 122.84/16.22 ((
% 122.84/16.22 (woz1_5) =>
% 122.84/16.22 ((
% 122.84/16.22 (breln1all2) =>
% 122.84/16.22 ((
% 122.84/16.22 (breln1SetBreln1) =>
% 122.84/16.22 ((
% 122.84/16.22 (choice2fnsingleton) =>
% 122.84/16.22 ((
% 122.84/16.22 (setOfPairsIsBReln1) =>
% 122.84/16.22 ((
% 122.84/16.22 (breln1all1) =>
% 122.84/16.22 ((
% 122.84/16.22 (subbreln1) =>
% 122.84/16.22 ((
% 122.84/16.22 (eqbreln1) =>
% 122.84/16.22 ((
% 122.84/16.22 (breln1invprop) =>
% 122.84/16.22 ((
% 122.84/16.22 (breln1invI) =>
% 122.84/16.22 ((
% 122.84/16.22 (breln1invE) =>
% 122.84/16.22 ((
% 122.84/16.22 (breln1compprop) =>
% 122.84/16.22 ((
% 122.84/16.22 (breln1compI) =>
% 122.84/16.22 ((
% 122.84/16.22 (breln1compE) =>
% 122.84/16.22 ((
% 122.84/16.22 (breln1compEex) =>
% 122.84/16.22 ((
% 122.84/16.22 (breln1unionprop) =>
% 122.84/16.22 ((
% 122.84/16.22 (breln1unionIL) =>
% 122.84/16.22 ((
% 122.84/16.22 (breln1unionIR) =>
% 122.84/16.22 ((
% 122.84/16.22 (breln1unionI) =>
% 122.84/16.22 ((
% 122.84/16.22 (breln1unionE) =>
% 122.84/16.22 ((
% 122.84/16.22 (breln1unionEcases) =>
% 122.84/16.22 ((
% 122.84/16.22 (breln1unionCommutes) =>
% 122.84/16.22 ((
% 122.84/16.22 (woz2Ex) =>
% 122.84/16.22 ((
% 122.84/16.22 (woz2W) =>
% 122.84/16.22 ((
% 122.84/16.22 (woz2A) =>
% 122.84/16.22 ((
% 122.84/16.22 (woz2B) =>
% 122.84/16.22 ((
% 122.84/16.22 (image1Ex) =>
% 122.84/16.22 ((
% 122.84/16.22 (image1Ex1) =>
% 122.84/16.22 ((
% 122.84/16.22 (image1Equiv) =>
% 122.84/16.22 ((
% 122.84/16.22 (image1E) =>
% 122.84/16.22 ((
% 122.84/16.22 (image1I) =>
% 122.84/16.22 ((
% 122.84/16.22 (injFuncInInjFuncSet) =>
% 122.84/16.22 ((
% 122.84/16.22 (!!) @ (
% 122.84/16.22 (('#B') @ (
% 122.84/16.22 !!) @
% 122.84/16.22 (
% 122.84/16.22 (
% 122.84/16.22 ('#B') @ (
% 122.84/16.22 (
% 122.84/16.22 ('#B') @ (
% 122.84/16.22 !!))) @
% 122.84/16.22 (
% 122.84/16.22 (
% 122.84/16.22 ('#S') @ (
% 122.84/16.22 (
% 122.84/16.22 ('#B') @ (
% 122.84/16.22 '#S') @
% 122.84/16.22 (
% 122.84/16.22 (
% 122.84/16.22 ('#B') @ (
% 122.84/16.22 (
% 122.84/16.22 ('#B') @ (
% 122.84/16.22 '#S'))) @
% 122.84/16.22 (
% 122.84/16.22 (
% 122.84/16.22 ('#B') @ (
% 122.84/16.22 (
% 122.84/16.22 ('#B') @ (
% 122.84/16.22 (
% 122.84/16.22 ('#B') @ (
% 122.84/16.22 =>))))) @
% 122.84/16.22 (
% 122.84/16.22 (
% 122.84/16.22 ('#B') @ (
% 122.84/16.22 (
% 122.84/16.22 ('#B') @ (
% 122.84/16.22 (
% 122.84/16.22 ('#C') @ in)))) @
% 122.84/16.22 injFuncSet)))))))) @
% 122.84/16.22 (
% 122.84/16.22 (
% 122.84/16.22 ('#B') @ (
% 122.84/16.22 (
% 122.84/16.22 ('#B') @ (
% 122.84/16.22 (
% 122.84/16.22 ('#C') @ in)))) @
% 122.84/16.22 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.84/16.22 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1914])).
% 122.84/16.22 thf(zip_derived_cl1931, plain,
% 122.84/16.22 (~ (((apProp) =>
% 122.84/16.22 (((app) =>
% 122.84/16.22 (((infuncsetfunc) =>
% 122.84/16.22 (((ap2p) =>
% 122.84/16.22 (((funcinfuncset) =>
% 122.84/16.22 (((lamProp) =>
% 122.84/16.22 (((lamp) =>
% 122.84/16.22 (((lam2p) =>
% 122.84/16.22 (((brelnall1) =>
% 122.84/16.22 (((brelnall2) =>
% 122.84/16.22 (((ex1E2) =>
% 122.84/16.22 (((funcGraphProp1) =>
% 122.84/16.22 (((funcGraphProp3) =>
% 122.84/16.22 (((funcGraphProp2) =>
% 122.84/16.22 (((funcextLem) =>
% 122.84/16.22 (((funcGraphProp4) =>
% 122.84/16.22 (((subbreln) =>
% 122.84/16.22 (((eqbreln) =>
% 122.84/16.22 (((funcext) =>
% 122.84/16.22 (((funcext2) =>
% 122.84/16.22 (((ap2apEq1) =>
% 122.84/16.22 (((ap2apEq2) =>
% 122.84/16.22 (((beta1) =>
% 122.84/16.22 (((eta1) =>
% 122.84/16.22 (((lam2lamEq) =>
% 122.84/16.22 (((beta2) =>
% 122.84/16.22 (((eta2) =>
% 122.84/16.22 (((iffalseProp1) =>
% 122.84/16.22 (((iffalseProp2) =>
% 122.84/16.22 (((iftrueProp1) =>
% 122.84/16.22 ((
% 122.84/16.22 (iftrueProp2) =>
% 122.84/16.22 ((
% 122.84/16.22 (ifSingleton) =>
% 122.84/16.22 ((
% 122.84/16.22 (ifp) =>
% 122.84/16.22 ((
% 122.84/16.22 (theeq) =>
% 122.84/16.22 ((
% 122.84/16.22 (iftrue) =>
% 122.84/16.22 ((
% 122.84/16.22 (iffalse) =>
% 122.84/16.22 ((
% 122.84/16.22 (iftrueorfalse) =>
% 122.84/16.22 ((
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% 122.84/16.22 ((
% 122.84/16.22 (binunionT_lem) =>
% 122.84/16.22 ((
% 122.84/16.22 (powersetT_lem) =>
% 122.84/16.22 ((
% 122.84/16.22 (setminusT_lem) =>
% 122.84/16.22 ((
% 122.84/16.22 (complementT_lem) =>
% 122.84/16.22 ((
% 122.84/16.22 (setextT) =>
% 122.84/16.22 ((
% 122.84/16.22 (subsetTI) =>
% 122.84/16.22 ((
% 122.84/16.22 (powersetTI1) =>
% 122.84/16.22 ((
% 122.84/16.22 (powersetTE1) =>
% 122.84/16.22 ((
% 122.84/16.22 (complementTI1) =>
% 122.84/16.22 ((
% 122.84/16.22 (complementTE1) =>
% 122.84/16.22 ((
% 122.84/16.22 (binintersectTELcontra) =>
% 122.84/16.22 ((
% 122.84/16.22 (binintersectTERcontra) =>
% 122.84/16.22 ((
% 122.84/16.22 (contrasubsetT) =>
% 122.84/16.22 ((
% 122.84/16.22 (contrasubsetT1) =>
% 122.84/16.22 ((
% 122.84/16.22 (contrasubsetT2) =>
% 122.84/16.22 ((
% 122.84/16.22 (contrasubsetT3) =>
% 122.84/16.22 ((
% 122.84/16.22 (doubleComplementI1) =>
% 122.84/16.22 ((
% 122.84/16.22 (doubleComplementE1) =>
% 122.84/16.22 ((
% 122.84/16.22 (doubleComplementSub1) =>
% 122.84/16.22 ((
% 122.84/16.22 (doubleComplementSub2) =>
% 122.84/16.22 ((
% 122.84/16.22 (doubleComplementEq) =>
% 122.84/16.22 ((
% 122.84/16.22 (complementTnotintersectT) =>
% 122.84/16.22 ((
% 122.84/16.22 (complementImpComplementIntersect) =>
% 122.84/16.22 ((
% 122.84/16.22 (complementSubsetComplementIntersect) =>
% 122.84/16.22 ((
% 122.84/16.22 (complementInPowersetComplementIntersect) =>
% 122.84/16.22 ((
% 122.84/16.22 (contraSubsetComplement) =>
% 122.84/16.22 ((
% 122.84/16.22 (complementTcontraSubset) =>
% 122.84/16.22 ((
% 122.84/16.22 (binunionTILcontra) =>
% 122.84/16.22 ((
% 122.84/16.22 (binunionTIRcontra) =>
% 122.84/16.22 ((
% 122.84/16.22 (inIntersectImpInUnion) =>
% 122.84/16.22 ((
% 122.84/16.22 (inIntersectImpInUnion2) =>
% 122.84/16.22 ((
% 122.84/16.22 (inIntersectImpInIntersectUnions) =>
% 122.84/16.22 ((
% 122.84/16.22 (intersectInPowersetIntersectUnions) =>
% 122.84/16.22 ((
% 122.84/16.22 (inComplementUnionImpNotIn1) =>
% 122.84/16.22 ((
% 122.84/16.22 (inComplementUnionImpInComplement1) =>
% 122.84/16.22 ((
% 122.84/16.22 (binunionTE) =>
% 122.84/16.22 ((
% 122.84/16.22 (binunionTEcontra) =>
% 122.84/16.22 ((
% 122.84/16.22 (demorgan2a1) =>
% 122.84/16.22 ((
% 122.84/16.22 (complementUnionInPowersetComplement) =>
% 122.84/16.22 ((
% 122.84/16.22 (demorgan2a2) =>
% 122.84/16.22 ((
% 122.84/16.22 (demorgan1a) =>
% 122.84/16.22 ((
% 122.84/16.22 (demorgan1b) =>
% 122.84/16.22 ((
% 122.84/16.22 (demorgan1) =>
% 122.84/16.22 ((
% 122.84/16.22 (demorgan2a) =>
% 122.84/16.22 ((
% 122.84/16.22 (demorgan2b2) =>
% 122.84/16.22 ((
% 122.84/16.22 (demorgan2b) =>
% 122.84/16.22 ((
% 122.84/16.22 (demorgan2) =>
% 122.84/16.22 ((
% 122.84/16.22 (woz13rule0) =>
% 122.84/16.22 ((
% 122.84/16.22 (woz13rule1) =>
% 122.84/16.22 ((
% 122.84/16.22 (woz13rule2) =>
% 122.84/16.22 ((
% 122.84/16.22 (woz13rule3) =>
% 122.84/16.22 ((
% 122.84/16.22 (woz13rule4) =>
% 122.84/16.22 ((
% 122.84/16.22 (woz1_1) =>
% 122.84/16.22 ((
% 122.84/16.22 (woz1_2) =>
% 122.84/16.22 ((
% 122.84/16.22 (woz1_3) =>
% 122.84/16.22 ((
% 122.84/16.22 (woz1_4) =>
% 122.84/16.22 ((
% 122.84/16.22 (woz1_5) =>
% 122.84/16.22 ((
% 122.84/16.22 (breln1all2) =>
% 122.84/16.22 ((
% 122.84/16.22 (breln1SetBreln1) =>
% 122.84/16.22 ((
% 122.84/16.22 (choice2fnsingleton) =>
% 122.84/16.22 ((
% 122.84/16.22 (setOfPairsIsBReln1) =>
% 122.84/16.22 ((
% 122.84/16.22 (breln1all1) =>
% 122.84/16.22 ((
% 122.84/16.22 (subbreln1) =>
% 122.84/16.22 ((
% 122.84/16.22 (eqbreln1) =>
% 122.84/16.22 ((
% 122.84/16.22 (breln1invprop) =>
% 122.84/16.22 ((
% 122.84/16.22 (breln1invI) =>
% 122.84/16.22 ((
% 122.84/16.22 (breln1invE) =>
% 122.84/16.22 ((
% 122.84/16.22 (breln1compprop) =>
% 122.84/16.22 ((
% 122.84/16.22 (breln1compI) =>
% 122.84/16.22 ((
% 122.84/16.22 (breln1compE) =>
% 122.84/16.22 ((
% 122.84/16.22 (breln1compEex) =>
% 122.84/16.22 ((
% 122.84/16.22 (breln1unionprop) =>
% 122.84/16.22 ((
% 122.84/16.22 (breln1unionIL) =>
% 122.84/16.22 ((
% 122.84/16.22 (breln1unionIR) =>
% 122.84/16.22 ((
% 122.84/16.22 (breln1unionI) =>
% 122.84/16.22 ((
% 122.84/16.22 (breln1unionE) =>
% 122.84/16.22 ((
% 122.84/16.22 (breln1unionEcases) =>
% 122.84/16.22 ((
% 122.84/16.22 (breln1unionCommutes) =>
% 122.84/16.22 ((
% 122.84/16.22 (woz2Ex) =>
% 122.84/16.22 ((
% 122.84/16.22 (woz2W) =>
% 122.84/16.22 ((
% 122.84/16.22 (woz2A) =>
% 122.84/16.22 ((
% 122.84/16.22 (woz2B) =>
% 122.84/16.22 ((
% 122.84/16.22 (image1Ex) =>
% 122.84/16.22 ((
% 122.84/16.22 (image1Ex1) =>
% 122.84/16.22 ((
% 122.84/16.22 (image1Equiv) =>
% 122.84/16.22 ((
% 122.84/16.22 (image1E) =>
% 122.84/16.22 ((
% 122.84/16.22 (image1I) =>
% 122.84/16.22 ((
% 122.84/16.22 (injFuncInInjFuncSet) =>
% 122.84/16.22 ((
% 122.84/16.22 (!!) @ (
% 122.84/16.22 (('#B') @ (
% 122.84/16.22 !!) @
% 122.84/16.22 (
% 122.84/16.22 (
% 122.84/16.22 ('#B') @ (
% 122.84/16.22 (
% 122.84/16.22 ('#B') @ (
% 122.84/16.22 !!))) @
% 122.84/16.22 (
% 122.84/16.22 (
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% 122.84/16.22 (
% 122.84/16.22 ('#B') @ (
% 122.84/16.22 '#S') @
% 122.84/16.22 (
% 122.84/16.22 (
% 122.84/16.22 ('#B') @ (
% 122.84/16.22 (
% 122.84/16.22 ('#B') @ (
% 122.84/16.22 '#S'))) @
% 122.84/16.22 (
% 122.84/16.22 (
% 122.84/16.22 ('#B') @ (
% 122.84/16.22 (
% 122.84/16.22 ('#B') @ (
% 122.84/16.22 (
% 122.84/16.22 ('#B') @ (
% 122.84/16.22 =>))))) @
% 122.84/16.22 (
% 122.84/16.22 (
% 122.84/16.22 ('#B') @ (
% 122.84/16.22 (
% 122.84/16.22 ('#B') @ (
% 122.84/16.22 (
% 122.84/16.22 ('#C') @ in)))) @
% 122.84/16.22 injFuncSet)))))))) @
% 122.84/16.22 (
% 122.84/16.22 (
% 122.84/16.22 ('#B') @ (
% 122.84/16.22 (
% 122.84/16.22 ('#B') @ (
% 122.84/16.22 (
% 122.84/16.22 ('#C') @ in)))) @
% 122.84/16.22 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.84/16.22 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1923])).
% 122.84/16.22 thf(zip_derived_cl1940, plain,
% 122.84/16.22 (~ (((app) =>
% 122.84/16.22 (((infuncsetfunc) =>
% 122.84/16.22 (((ap2p) =>
% 122.84/16.22 (((funcinfuncset) =>
% 122.84/16.22 (((lamProp) =>
% 122.84/16.22 (((lamp) =>
% 122.84/16.22 (((lam2p) =>
% 122.84/16.22 (((brelnall1) =>
% 122.84/16.22 (((brelnall2) =>
% 122.84/16.22 (((ex1E2) =>
% 122.84/16.22 (((funcGraphProp1) =>
% 122.84/16.22 (((funcGraphProp3) =>
% 122.84/16.22 (((funcGraphProp2) =>
% 122.84/16.22 (((funcextLem) =>
% 122.84/16.22 (((funcGraphProp4) =>
% 122.84/16.22 (((subbreln) =>
% 122.84/16.22 (((eqbreln) =>
% 122.84/16.22 (((funcext) =>
% 122.84/16.22 (((funcext2) =>
% 122.84/16.22 (((ap2apEq1) =>
% 122.84/16.22 (((ap2apEq2) =>
% 122.84/16.22 (((beta1) =>
% 122.84/16.22 (((eta1) =>
% 122.84/16.22 (((lam2lamEq) =>
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% 122.84/16.22 (((eta2) =>
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% 122.84/16.22 ((
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% 122.84/16.22 ((
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% 122.84/16.22 ((
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% 122.84/16.22 ((
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% 122.84/16.22 ((
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% 122.84/16.22 ((
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% 122.84/16.22 ((
% 122.84/16.22 (demorgan2b) =>
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% 122.84/16.22 (demorgan2) =>
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% 122.84/16.22 ((
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% 122.84/16.22 ((
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% 122.84/16.22 ((
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% 122.84/16.22 ((
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% 122.84/16.22 (
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% 122.84/16.22 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.84/16.22 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1931])).
% 122.84/16.22 thf(zip_derived_cl1950, plain,
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% 122.84/16.22 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1940])).
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% 122.84/16.22 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1950])).
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% 122.84/16.22 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1960])).
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% 122.84/16.22 ((
% 122.84/16.22 (complementTI1) =>
% 122.84/16.22 ((
% 122.84/16.22 (complementTE1) =>
% 122.84/16.22 ((
% 122.84/16.22 (binintersectTELcontra) =>
% 122.84/16.22 ((
% 122.84/16.22 (binintersectTERcontra) =>
% 122.84/16.22 ((
% 122.84/16.22 (contrasubsetT) =>
% 122.84/16.22 ((
% 122.84/16.22 (contrasubsetT1) =>
% 122.84/16.22 ((
% 122.84/16.22 (contrasubsetT2) =>
% 122.84/16.22 ((
% 122.84/16.22 (contrasubsetT3) =>
% 122.84/16.22 ((
% 122.84/16.22 (doubleComplementI1) =>
% 122.84/16.22 ((
% 122.84/16.22 (doubleComplementE1) =>
% 122.84/16.22 ((
% 122.84/16.22 (doubleComplementSub1) =>
% 122.84/16.22 ((
% 122.84/16.22 (doubleComplementSub2) =>
% 122.84/16.22 ((
% 122.84/16.22 (doubleComplementEq) =>
% 122.84/16.22 ((
% 122.84/16.22 (complementTnotintersectT) =>
% 122.84/16.22 ((
% 122.84/16.22 (complementImpComplementIntersect) =>
% 122.84/16.22 ((
% 122.84/16.22 (complementSubsetComplementIntersect) =>
% 122.84/16.22 ((
% 122.84/16.22 (complementInPowersetComplementIntersect) =>
% 122.84/16.22 ((
% 122.84/16.22 (contraSubsetComplement) =>
% 122.84/16.22 ((
% 122.84/16.22 (complementTcontraSubset) =>
% 122.84/16.22 ((
% 122.84/16.22 (binunionTILcontra) =>
% 122.84/16.22 ((
% 122.84/16.22 (binunionTIRcontra) =>
% 122.84/16.22 ((
% 122.84/16.22 (inIntersectImpInUnion) =>
% 122.84/16.22 ((
% 122.84/16.22 (inIntersectImpInUnion2) =>
% 122.84/16.22 ((
% 122.84/16.22 (inIntersectImpInIntersectUnions) =>
% 122.84/16.22 ((
% 122.84/16.22 (intersectInPowersetIntersectUnions) =>
% 122.84/16.22 ((
% 122.84/16.22 (inComplementUnionImpNotIn1) =>
% 122.84/16.22 ((
% 122.84/16.22 (inComplementUnionImpInComplement1) =>
% 122.84/16.22 ((
% 122.84/16.22 (binunionTE) =>
% 122.84/16.22 ((
% 122.84/16.22 (binunionTEcontra) =>
% 122.84/16.22 ((
% 122.84/16.22 (demorgan2a1) =>
% 122.84/16.22 ((
% 122.84/16.22 (complementUnionInPowersetComplement) =>
% 122.84/16.22 ((
% 122.84/16.22 (demorgan2a2) =>
% 122.84/16.22 ((
% 122.84/16.22 (demorgan1a) =>
% 122.84/16.22 ((
% 122.84/16.22 (demorgan1b) =>
% 122.84/16.22 ((
% 122.84/16.22 (demorgan1) =>
% 122.84/16.22 ((
% 122.84/16.22 (demorgan2a) =>
% 122.84/16.22 ((
% 122.84/16.22 (demorgan2b2) =>
% 122.84/16.22 ((
% 122.84/16.22 (demorgan2b) =>
% 122.84/16.22 ((
% 122.84/16.22 (demorgan2) =>
% 122.84/16.22 ((
% 122.84/16.22 (woz13rule0) =>
% 122.84/16.22 ((
% 122.84/16.22 (woz13rule1) =>
% 122.84/16.22 ((
% 122.84/16.22 (woz13rule2) =>
% 122.84/16.22 ((
% 122.84/16.22 (woz13rule3) =>
% 122.84/16.22 ((
% 122.84/16.22 (woz13rule4) =>
% 122.84/16.22 ((
% 122.84/16.22 (woz1_1) =>
% 122.84/16.22 ((
% 122.84/16.22 (woz1_2) =>
% 122.84/16.22 ((
% 122.84/16.22 (woz1_3) =>
% 122.84/16.22 ((
% 122.84/16.22 (woz1_4) =>
% 122.84/16.22 ((
% 122.84/16.22 (woz1_5) =>
% 122.84/16.22 ((
% 122.84/16.22 (breln1all2) =>
% 122.84/16.22 ((
% 122.84/16.22 (breln1SetBreln1) =>
% 122.84/16.22 ((
% 122.84/16.22 (choice2fnsingleton) =>
% 122.84/16.22 ((
% 122.84/16.22 (setOfPairsIsBReln1) =>
% 122.84/16.22 ((
% 122.84/16.22 (breln1all1) =>
% 122.84/16.22 ((
% 122.84/16.22 (subbreln1) =>
% 122.84/16.22 ((
% 122.84/16.22 (eqbreln1) =>
% 122.84/16.22 ((
% 122.84/16.22 (breln1invprop) =>
% 122.84/16.22 ((
% 122.84/16.22 (breln1invI) =>
% 122.84/16.22 ((
% 122.84/16.22 (breln1invE) =>
% 122.84/16.22 ((
% 122.84/16.22 (breln1compprop) =>
% 122.84/16.22 ((
% 122.84/16.22 (breln1compI) =>
% 122.84/16.22 ((
% 122.84/16.22 (breln1compE) =>
% 122.84/16.22 ((
% 122.84/16.22 (breln1compEex) =>
% 122.84/16.22 ((
% 122.84/16.22 (breln1unionprop) =>
% 122.84/16.22 ((
% 122.84/16.22 (breln1unionIL) =>
% 122.84/16.22 ((
% 122.84/16.22 (breln1unionIR) =>
% 122.84/16.22 ((
% 122.84/16.22 (breln1unionI) =>
% 122.84/16.22 ((
% 122.84/16.22 (breln1unionE) =>
% 122.84/16.22 ((
% 122.84/16.22 (breln1unionEcases) =>
% 122.84/16.22 ((
% 122.84/16.22 (breln1unionCommutes) =>
% 122.84/16.22 ((
% 122.84/16.22 (woz2Ex) =>
% 122.84/16.22 ((
% 122.84/16.22 (woz2W) =>
% 122.84/16.22 ((
% 122.84/16.22 (woz2A) =>
% 122.84/16.22 ((
% 122.84/16.22 (woz2B) =>
% 122.84/16.22 ((
% 122.84/16.22 (image1Ex) =>
% 122.84/16.22 ((
% 122.84/16.22 (image1Ex1) =>
% 122.84/16.22 ((
% 122.84/16.22 (image1Equiv) =>
% 122.84/16.22 ((
% 122.84/16.22 (image1E) =>
% 122.84/16.22 ((
% 122.84/16.22 (image1I) =>
% 122.84/16.22 ((
% 122.84/16.22 (injFuncInInjFuncSet) =>
% 122.84/16.22 ((
% 122.84/16.22 (!!) @ (
% 122.84/16.22 (('#B') @ (
% 122.84/16.22 !!) @
% 122.84/16.22 (
% 122.84/16.22 (
% 122.84/16.22 ('#B') @ (
% 122.84/16.22 (
% 122.84/16.22 ('#B') @ (
% 122.84/16.22 !!))) @
% 122.84/16.22 (
% 122.84/16.22 (
% 122.84/16.22 ('#S') @ (
% 122.84/16.22 (
% 122.84/16.22 ('#B') @ (
% 122.84/16.22 '#S') @
% 122.84/16.22 (
% 122.84/16.22 (
% 122.84/16.22 ('#B') @ (
% 122.84/16.22 (
% 122.84/16.22 ('#B') @ (
% 122.84/16.22 '#S'))) @
% 122.84/16.22 (
% 122.84/16.22 (
% 122.84/16.22 ('#B') @ (
% 122.84/16.22 (
% 122.84/16.22 ('#B') @ (
% 122.84/16.22 (
% 122.84/16.22 ('#B') @ (
% 122.84/16.22 =>))))) @
% 122.84/16.22 (
% 122.84/16.22 (
% 122.84/16.22 ('#B') @ (
% 122.84/16.22 (
% 122.84/16.22 ('#B') @ (
% 122.84/16.22 (
% 122.84/16.22 ('#C') @ in)))) @
% 122.84/16.22 injFuncSet)))))))) @
% 122.84/16.22 (
% 122.84/16.22 (
% 122.84/16.22 ('#B') @ (
% 122.84/16.22 (
% 122.84/16.22 ('#B') @ (
% 122.84/16.22 (
% 122.84/16.22 ('#C') @ in)))) @
% 122.84/16.22 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.84/16.22 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1971])).
% 122.84/16.22 thf(zip_derived_cl1992, plain,
% 122.84/16.22 (~ (((lamp) =>
% 122.84/16.22 (((lam2p) =>
% 122.84/16.22 (((brelnall1) =>
% 122.84/16.22 (((brelnall2) =>
% 122.84/16.22 (((ex1E2) =>
% 122.84/16.22 (((funcGraphProp1) =>
% 122.84/16.22 (((funcGraphProp3) =>
% 122.84/16.22 (((funcGraphProp2) =>
% 122.84/16.22 (((funcextLem) =>
% 122.84/16.22 (((funcGraphProp4) =>
% 122.84/16.22 (((subbreln) =>
% 122.84/16.22 (((eqbreln) =>
% 122.84/16.22 (((funcext) =>
% 122.84/16.22 (((funcext2) =>
% 122.84/16.22 (((ap2apEq1) =>
% 122.84/16.22 (((ap2apEq2) =>
% 122.84/16.22 (((beta1) =>
% 122.84/16.22 (((eta1) =>
% 122.84/16.22 (((lam2lamEq) =>
% 122.84/16.22 (((beta2) =>
% 122.84/16.22 (((eta2) =>
% 122.84/16.22 (((iffalseProp1) =>
% 122.84/16.22 (((iffalseProp2) =>
% 122.84/16.22 (((iftrueProp1) =>
% 122.84/16.22 (((iftrueProp2) =>
% 122.84/16.22 (((ifSingleton) =>
% 122.84/16.22 (((ifp) =>
% 122.84/16.22 (((theeq) =>
% 122.84/16.22 (((iftrue) =>
% 122.84/16.22 (((iffalse) =>
% 122.84/16.22 ((
% 122.84/16.22 (iftrueorfalse) =>
% 122.84/16.22 ((
% 122.84/16.22 (binintersectT_lem) =>
% 122.84/16.22 ((
% 122.84/16.22 (binunionT_lem) =>
% 122.84/16.22 ((
% 122.84/16.22 (powersetT_lem) =>
% 122.84/16.22 ((
% 122.84/16.22 (setminusT_lem) =>
% 122.84/16.22 ((
% 122.84/16.22 (complementT_lem) =>
% 122.84/16.22 ((
% 122.84/16.22 (setextT) =>
% 122.84/16.22 ((
% 122.84/16.22 (subsetTI) =>
% 122.84/16.22 ((
% 122.84/16.22 (powersetTI1) =>
% 122.84/16.22 ((
% 122.84/16.22 (powersetTE1) =>
% 122.84/16.22 ((
% 122.84/16.22 (complementTI1) =>
% 122.84/16.22 ((
% 122.84/16.22 (complementTE1) =>
% 122.84/16.22 ((
% 122.84/16.22 (binintersectTELcontra) =>
% 122.84/16.22 ((
% 122.84/16.22 (binintersectTERcontra) =>
% 122.84/16.22 ((
% 122.84/16.22 (contrasubsetT) =>
% 122.84/16.22 ((
% 122.84/16.22 (contrasubsetT1) =>
% 122.84/16.22 ((
% 122.84/16.22 (contrasubsetT2) =>
% 122.84/16.22 ((
% 122.84/16.22 (contrasubsetT3) =>
% 122.84/16.22 ((
% 122.84/16.22 (doubleComplementI1) =>
% 122.84/16.22 ((
% 122.84/16.22 (doubleComplementE1) =>
% 122.84/16.22 ((
% 122.84/16.22 (doubleComplementSub1) =>
% 122.84/16.22 ((
% 122.84/16.22 (doubleComplementSub2) =>
% 122.84/16.22 ((
% 122.84/16.22 (doubleComplementEq) =>
% 122.84/16.22 ((
% 122.84/16.22 (complementTnotintersectT) =>
% 122.84/16.22 ((
% 122.84/16.22 (complementImpComplementIntersect) =>
% 122.84/16.22 ((
% 122.84/16.22 (complementSubsetComplementIntersect) =>
% 122.84/16.22 ((
% 122.84/16.22 (complementInPowersetComplementIntersect) =>
% 122.84/16.22 ((
% 122.84/16.22 (contraSubsetComplement) =>
% 122.84/16.22 ((
% 122.84/16.22 (complementTcontraSubset) =>
% 122.84/16.22 ((
% 122.84/16.22 (binunionTILcontra) =>
% 122.84/16.22 ((
% 122.84/16.22 (binunionTIRcontra) =>
% 122.84/16.22 ((
% 122.84/16.22 (inIntersectImpInUnion) =>
% 122.84/16.22 ((
% 122.84/16.22 (inIntersectImpInUnion2) =>
% 122.84/16.22 ((
% 122.84/16.22 (inIntersectImpInIntersectUnions) =>
% 122.84/16.22 ((
% 122.84/16.22 (intersectInPowersetIntersectUnions) =>
% 122.84/16.22 ((
% 122.84/16.22 (inComplementUnionImpNotIn1) =>
% 122.84/16.22 ((
% 122.84/16.22 (inComplementUnionImpInComplement1) =>
% 122.84/16.22 ((
% 122.84/16.22 (binunionTE) =>
% 122.84/16.22 ((
% 122.84/16.22 (binunionTEcontra) =>
% 122.84/16.22 ((
% 122.84/16.22 (demorgan2a1) =>
% 122.84/16.22 ((
% 122.84/16.22 (complementUnionInPowersetComplement) =>
% 122.84/16.22 ((
% 122.84/16.22 (demorgan2a2) =>
% 122.84/16.22 ((
% 122.84/16.22 (demorgan1a) =>
% 122.84/16.22 ((
% 122.84/16.22 (demorgan1b) =>
% 122.84/16.22 ((
% 122.84/16.22 (demorgan1) =>
% 122.84/16.22 ((
% 122.84/16.22 (demorgan2a) =>
% 122.84/16.22 ((
% 122.84/16.22 (demorgan2b2) =>
% 122.84/16.22 ((
% 122.84/16.22 (demorgan2b) =>
% 122.84/16.22 ((
% 122.84/16.22 (demorgan2) =>
% 122.84/16.22 ((
% 122.84/16.22 (woz13rule0) =>
% 122.84/16.22 ((
% 122.84/16.22 (woz13rule1) =>
% 122.84/16.22 ((
% 122.84/16.22 (woz13rule2) =>
% 122.84/16.22 ((
% 122.84/16.22 (woz13rule3) =>
% 122.84/16.22 ((
% 122.84/16.22 (woz13rule4) =>
% 122.84/16.22 ((
% 122.84/16.22 (woz1_1) =>
% 122.84/16.22 ((
% 122.84/16.22 (woz1_2) =>
% 122.84/16.22 ((
% 122.84/16.22 (woz1_3) =>
% 122.84/16.22 ((
% 122.84/16.22 (woz1_4) =>
% 122.84/16.22 ((
% 122.84/16.22 (woz1_5) =>
% 122.84/16.22 ((
% 122.84/16.22 (breln1all2) =>
% 122.84/16.22 ((
% 122.84/16.22 (breln1SetBreln1) =>
% 122.84/16.22 ((
% 122.84/16.22 (choice2fnsingleton) =>
% 122.84/16.22 ((
% 122.84/16.22 (setOfPairsIsBReln1) =>
% 122.84/16.22 ((
% 122.84/16.22 (breln1all1) =>
% 122.84/16.22 ((
% 122.84/16.22 (subbreln1) =>
% 122.84/16.22 ((
% 122.84/16.22 (eqbreln1) =>
% 122.84/16.22 ((
% 122.84/16.22 (breln1invprop) =>
% 122.84/16.22 ((
% 122.84/16.22 (breln1invI) =>
% 122.84/16.22 ((
% 122.84/16.22 (breln1invE) =>
% 122.84/16.22 ((
% 122.84/16.22 (breln1compprop) =>
% 122.84/16.22 ((
% 122.84/16.22 (breln1compI) =>
% 122.84/16.22 ((
% 122.84/16.22 (breln1compE) =>
% 122.84/16.22 ((
% 122.84/16.22 (breln1compEex) =>
% 122.84/16.22 ((
% 122.84/16.22 (breln1unionprop) =>
% 122.84/16.22 ((
% 122.84/16.22 (breln1unionIL) =>
% 122.84/16.22 ((
% 122.84/16.22 (breln1unionIR) =>
% 122.84/16.22 ((
% 122.84/16.22 (breln1unionI) =>
% 122.84/16.22 ((
% 122.84/16.22 (breln1unionE) =>
% 122.84/16.22 ((
% 122.84/16.22 (breln1unionEcases) =>
% 122.84/16.22 ((
% 122.84/16.22 (breln1unionCommutes) =>
% 122.84/16.22 ((
% 122.84/16.22 (woz2Ex) =>
% 122.84/16.22 ((
% 122.84/16.22 (woz2W) =>
% 122.84/16.22 ((
% 122.84/16.22 (woz2A) =>
% 122.84/16.22 ((
% 122.84/16.22 (woz2B) =>
% 122.84/16.22 ((
% 122.84/16.22 (image1Ex) =>
% 122.84/16.22 ((
% 122.84/16.22 (image1Ex1) =>
% 122.84/16.22 ((
% 122.84/16.22 (image1Equiv) =>
% 122.84/16.22 ((
% 122.84/16.22 (image1E) =>
% 122.84/16.22 ((
% 122.84/16.22 (image1I) =>
% 122.84/16.22 ((
% 122.84/16.22 (injFuncInInjFuncSet) =>
% 122.84/16.22 ((
% 122.84/16.22 (!!) @ (
% 122.84/16.22 (('#B') @ (
% 122.84/16.22 !!) @
% 122.84/16.22 (
% 122.84/16.22 (
% 122.84/16.22 ('#B') @ (
% 122.84/16.22 (
% 122.84/16.22 ('#B') @ (
% 122.84/16.22 !!))) @
% 122.84/16.22 (
% 122.84/16.22 (
% 122.84/16.22 ('#S') @ (
% 122.84/16.22 (
% 122.84/16.22 ('#B') @ (
% 122.84/16.22 '#S') @
% 122.84/16.22 (
% 122.84/16.22 (
% 122.84/16.22 ('#B') @ (
% 122.84/16.22 (
% 122.84/16.22 ('#B') @ (
% 122.84/16.22 '#S'))) @
% 122.84/16.22 (
% 122.84/16.22 (
% 122.84/16.22 ('#B') @ (
% 122.84/16.22 (
% 122.84/16.22 ('#B') @ (
% 122.84/16.22 (
% 122.84/16.22 ('#B') @ (
% 122.84/16.22 =>))))) @
% 122.84/16.22 (
% 122.84/16.22 (
% 122.84/16.22 ('#B') @ (
% 122.84/16.22 (
% 122.84/16.22 ('#B') @ (
% 122.84/16.22 (
% 122.84/16.22 ('#C') @ in)))) @
% 122.84/16.22 injFuncSet)))))))) @
% 122.84/16.22 (
% 122.84/16.22 (
% 122.84/16.22 ('#B') @ (
% 122.84/16.22 (
% 122.84/16.22 ('#B') @ (
% 122.84/16.22 (
% 122.84/16.22 ('#C') @ in)))) @
% 122.84/16.22 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.84/16.22 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1982])).
% 122.84/16.22 thf(zip_derived_cl2002, plain,
% 122.84/16.22 (~ (((lam2p) =>
% 122.84/16.22 (((brelnall1) =>
% 122.84/16.22 (((brelnall2) =>
% 122.84/16.22 (((ex1E2) =>
% 122.84/16.22 (((funcGraphProp1) =>
% 122.84/16.22 (((funcGraphProp3) =>
% 122.84/16.22 (((funcGraphProp2) =>
% 122.84/16.22 (((funcextLem) =>
% 122.84/16.22 (((funcGraphProp4) =>
% 122.84/16.22 (((subbreln) =>
% 122.84/16.22 (((eqbreln) =>
% 122.84/16.22 (((funcext) =>
% 122.84/16.22 (((funcext2) =>
% 122.84/16.22 (((ap2apEq1) =>
% 122.84/16.22 (((ap2apEq2) =>
% 122.84/16.22 (((beta1) =>
% 122.84/16.22 (((eta1) =>
% 122.84/16.22 (((lam2lamEq) =>
% 122.84/16.22 (((beta2) =>
% 122.84/16.22 (((eta2) =>
% 122.84/16.22 (((iffalseProp1) =>
% 122.84/16.22 (((iffalseProp2) =>
% 122.84/16.22 (((iftrueProp1) =>
% 122.84/16.22 (((iftrueProp2) =>
% 122.84/16.22 (((ifSingleton) =>
% 122.84/16.22 (((ifp) =>
% 122.84/16.22 (((theeq) =>
% 122.84/16.22 (((iftrue) =>
% 122.84/16.22 (((iffalse) =>
% 122.84/16.22 (((iftrueorfalse) =>
% 122.84/16.22 ((
% 122.84/16.22 (binintersectT_lem) =>
% 122.84/16.22 ((
% 122.84/16.22 (binunionT_lem) =>
% 122.84/16.22 ((
% 122.84/16.22 (powersetT_lem) =>
% 122.84/16.22 ((
% 122.84/16.22 (setminusT_lem) =>
% 122.84/16.22 ((
% 122.84/16.22 (complementT_lem) =>
% 122.84/16.22 ((
% 122.84/16.22 (setextT) =>
% 122.84/16.22 ((
% 122.84/16.22 (subsetTI) =>
% 122.84/16.22 ((
% 122.84/16.22 (powersetTI1) =>
% 122.84/16.22 ((
% 122.84/16.22 (powersetTE1) =>
% 122.84/16.22 ((
% 122.84/16.22 (complementTI1) =>
% 122.84/16.22 ((
% 122.84/16.22 (complementTE1) =>
% 122.84/16.22 ((
% 122.84/16.22 (binintersectTELcontra) =>
% 122.84/16.22 ((
% 122.84/16.22 (binintersectTERcontra) =>
% 122.84/16.22 ((
% 122.84/16.22 (contrasubsetT) =>
% 122.84/16.22 ((
% 122.84/16.22 (contrasubsetT1) =>
% 122.84/16.22 ((
% 122.84/16.22 (contrasubsetT2) =>
% 122.84/16.22 ((
% 122.84/16.22 (contrasubsetT3) =>
% 122.84/16.22 ((
% 122.84/16.22 (doubleComplementI1) =>
% 122.84/16.22 ((
% 122.84/16.22 (doubleComplementE1) =>
% 122.84/16.22 ((
% 122.84/16.22 (doubleComplementSub1) =>
% 122.84/16.22 ((
% 122.84/16.22 (doubleComplementSub2) =>
% 122.84/16.22 ((
% 122.84/16.22 (doubleComplementEq) =>
% 122.84/16.22 ((
% 122.84/16.22 (complementTnotintersectT) =>
% 122.84/16.22 ((
% 122.84/16.22 (complementImpComplementIntersect) =>
% 122.84/16.22 ((
% 122.84/16.22 (complementSubsetComplementIntersect) =>
% 122.84/16.22 ((
% 122.84/16.22 (complementInPowersetComplementIntersect) =>
% 122.84/16.22 ((
% 122.84/16.22 (contraSubsetComplement) =>
% 122.84/16.22 ((
% 122.84/16.22 (complementTcontraSubset) =>
% 122.84/16.22 ((
% 122.84/16.22 (binunionTILcontra) =>
% 122.84/16.22 ((
% 122.84/16.22 (binunionTIRcontra) =>
% 122.84/16.22 ((
% 122.84/16.22 (inIntersectImpInUnion) =>
% 122.84/16.22 ((
% 122.84/16.22 (inIntersectImpInUnion2) =>
% 122.84/16.22 ((
% 122.84/16.22 (inIntersectImpInIntersectUnions) =>
% 122.84/16.22 ((
% 122.84/16.22 (intersectInPowersetIntersectUnions) =>
% 122.84/16.22 ((
% 122.84/16.22 (inComplementUnionImpNotIn1) =>
% 122.84/16.22 ((
% 122.84/16.22 (inComplementUnionImpInComplement1) =>
% 122.84/16.22 ((
% 122.84/16.22 (binunionTE) =>
% 122.84/16.22 ((
% 122.84/16.22 (binunionTEcontra) =>
% 122.84/16.22 ((
% 122.84/16.22 (demorgan2a1) =>
% 122.84/16.22 ((
% 122.84/16.22 (complementUnionInPowersetComplement) =>
% 122.84/16.22 ((
% 122.84/16.22 (demorgan2a2) =>
% 122.84/16.22 ((
% 122.84/16.22 (demorgan1a) =>
% 122.84/16.22 ((
% 122.84/16.22 (demorgan1b) =>
% 122.84/16.22 ((
% 122.84/16.22 (demorgan1) =>
% 122.84/16.22 ((
% 122.84/16.22 (demorgan2a) =>
% 122.84/16.22 ((
% 122.84/16.22 (demorgan2b2) =>
% 122.84/16.22 ((
% 122.84/16.22 (demorgan2b) =>
% 122.84/16.22 ((
% 122.84/16.22 (demorgan2) =>
% 122.84/16.22 ((
% 122.84/16.22 (woz13rule0) =>
% 122.84/16.22 ((
% 122.84/16.22 (woz13rule1) =>
% 122.84/16.22 ((
% 122.84/16.22 (woz13rule2) =>
% 122.84/16.22 ((
% 122.84/16.22 (woz13rule3) =>
% 122.84/16.22 ((
% 122.84/16.22 (woz13rule4) =>
% 122.84/16.22 ((
% 122.84/16.22 (woz1_1) =>
% 122.84/16.22 ((
% 122.84/16.22 (woz1_2) =>
% 122.84/16.22 ((
% 122.84/16.22 (woz1_3) =>
% 122.84/16.22 ((
% 122.84/16.22 (woz1_4) =>
% 122.84/16.22 ((
% 122.84/16.22 (woz1_5) =>
% 122.84/16.22 ((
% 122.84/16.22 (breln1all2) =>
% 122.84/16.22 ((
% 122.84/16.22 (breln1SetBreln1) =>
% 122.84/16.22 ((
% 122.84/16.22 (choice2fnsingleton) =>
% 122.84/16.22 ((
% 122.84/16.22 (setOfPairsIsBReln1) =>
% 122.84/16.22 ((
% 122.84/16.22 (breln1all1) =>
% 122.84/16.22 ((
% 122.84/16.22 (subbreln1) =>
% 122.84/16.22 ((
% 122.84/16.22 (eqbreln1) =>
% 122.84/16.22 ((
% 122.84/16.22 (breln1invprop) =>
% 122.84/16.22 ((
% 122.84/16.22 (breln1invI) =>
% 122.84/16.22 ((
% 122.84/16.22 (breln1invE) =>
% 122.84/16.22 ((
% 122.84/16.22 (breln1compprop) =>
% 122.84/16.22 ((
% 122.84/16.22 (breln1compI) =>
% 122.84/16.22 ((
% 122.84/16.22 (breln1compE) =>
% 122.84/16.22 ((
% 122.84/16.22 (breln1compEex) =>
% 122.84/16.22 ((
% 122.84/16.22 (breln1unionprop) =>
% 122.84/16.22 ((
% 122.84/16.22 (breln1unionIL) =>
% 122.84/16.22 ((
% 122.84/16.22 (breln1unionIR) =>
% 122.84/16.22 ((
% 122.84/16.22 (breln1unionI) =>
% 122.84/16.22 ((
% 122.84/16.22 (breln1unionE) =>
% 122.84/16.22 ((
% 122.84/16.22 (breln1unionEcases) =>
% 122.84/16.22 ((
% 122.84/16.22 (breln1unionCommutes) =>
% 122.84/16.22 ((
% 122.84/16.22 (woz2Ex) =>
% 122.84/16.22 ((
% 122.84/16.22 (woz2W) =>
% 122.84/16.22 ((
% 122.84/16.22 (woz2A) =>
% 122.84/16.22 ((
% 122.84/16.22 (woz2B) =>
% 122.84/16.22 ((
% 122.84/16.22 (image1Ex) =>
% 122.84/16.22 ((
% 122.84/16.22 (image1Ex1) =>
% 122.84/16.22 ((
% 122.84/16.22 (image1Equiv) =>
% 122.84/16.22 ((
% 122.84/16.22 (image1E) =>
% 122.84/16.22 ((
% 122.84/16.22 (image1I) =>
% 122.84/16.22 ((
% 122.84/16.22 (injFuncInInjFuncSet) =>
% 122.84/16.22 ((
% 122.84/16.22 (!!) @ (
% 122.84/16.22 (('#B') @ (
% 122.84/16.22 !!) @
% 122.84/16.22 (
% 122.84/16.22 (
% 122.84/16.22 ('#B') @ (
% 122.84/16.22 (
% 122.84/16.22 ('#B') @ (
% 122.84/16.22 !!))) @
% 122.84/16.22 (
% 122.84/16.22 (
% 122.84/16.22 ('#S') @ (
% 122.84/16.22 (
% 122.84/16.22 ('#B') @ (
% 122.84/16.22 '#S') @
% 122.84/16.22 (
% 122.84/16.22 (
% 122.84/16.22 ('#B') @ (
% 122.84/16.22 (
% 122.84/16.22 ('#B') @ (
% 122.84/16.22 '#S'))) @
% 122.84/16.22 (
% 122.84/16.22 (
% 122.84/16.22 ('#B') @ (
% 122.84/16.22 (
% 122.84/16.22 ('#B') @ (
% 122.84/16.22 (
% 122.84/16.22 ('#B') @ (
% 122.84/16.22 =>))))) @
% 122.84/16.22 (
% 122.84/16.22 (
% 122.84/16.22 ('#B') @ (
% 122.84/16.22 (
% 122.84/16.22 ('#B') @ (
% 122.84/16.22 (
% 122.84/16.22 ('#C') @ in)))) @
% 122.84/16.22 injFuncSet)))))))) @
% 122.84/16.22 (
% 122.84/16.22 (
% 122.84/16.22 ('#B') @ (
% 122.84/16.22 (
% 122.84/16.22 ('#B') @ (
% 122.84/16.22 (
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% 122.84/16.22 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.84/16.22 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1992])).
% 122.84/16.22 thf(zip_derived_cl2012, plain,
% 122.84/16.22 (~ (((brelnall1) =>
% 122.84/16.22 (((brelnall2) =>
% 122.84/16.22 (((ex1E2) =>
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% 122.84/16.22 (((funcGraphProp3) =>
% 122.84/16.22 (((funcGraphProp2) =>
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% 122.84/16.22 (((funcGraphProp4) =>
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% 122.84/16.22 (((eqbreln) =>
% 122.84/16.22 (((funcext) =>
% 122.84/16.22 (((funcext2) =>
% 122.84/16.22 (((ap2apEq1) =>
% 122.84/16.22 (((ap2apEq2) =>
% 122.84/16.22 (((beta1) =>
% 122.84/16.22 (((eta1) =>
% 122.84/16.22 (((lam2lamEq) =>
% 122.84/16.22 (((beta2) =>
% 122.84/16.22 (((eta2) =>
% 122.84/16.22 (((iffalseProp1) =>
% 122.84/16.22 (((iffalseProp2) =>
% 122.84/16.22 (((iftrueProp1) =>
% 122.84/16.22 (((iftrueProp2) =>
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% 122.84/16.22 (((theeq) =>
% 122.84/16.22 (((iftrue) =>
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% 122.84/16.22 (binunionT_lem) =>
% 122.84/16.22 ((
% 122.84/16.22 (powersetT_lem) =>
% 122.84/16.22 ((
% 122.84/16.22 (setminusT_lem) =>
% 122.84/16.22 ((
% 122.84/16.22 (complementT_lem) =>
% 122.84/16.22 ((
% 122.84/16.22 (setextT) =>
% 122.84/16.22 ((
% 122.84/16.22 (subsetTI) =>
% 122.84/16.22 ((
% 122.84/16.22 (powersetTI1) =>
% 122.84/16.22 ((
% 122.84/16.22 (powersetTE1) =>
% 122.84/16.22 ((
% 122.84/16.22 (complementTI1) =>
% 122.84/16.22 ((
% 122.84/16.22 (complementTE1) =>
% 122.84/16.22 ((
% 122.84/16.22 (binintersectTELcontra) =>
% 122.84/16.22 ((
% 122.84/16.22 (binintersectTERcontra) =>
% 122.84/16.22 ((
% 122.84/16.22 (contrasubsetT) =>
% 122.84/16.22 ((
% 122.84/16.22 (contrasubsetT1) =>
% 122.84/16.22 ((
% 122.84/16.22 (contrasubsetT2) =>
% 122.84/16.22 ((
% 122.84/16.22 (contrasubsetT3) =>
% 122.84/16.22 ((
% 122.84/16.22 (doubleComplementI1) =>
% 122.84/16.22 ((
% 122.84/16.22 (doubleComplementE1) =>
% 122.84/16.22 ((
% 122.84/16.22 (doubleComplementSub1) =>
% 122.84/16.22 ((
% 122.84/16.22 (doubleComplementSub2) =>
% 122.84/16.22 ((
% 122.84/16.22 (doubleComplementEq) =>
% 122.84/16.22 ((
% 122.84/16.22 (complementTnotintersectT) =>
% 122.84/16.22 ((
% 122.84/16.22 (complementImpComplementIntersect) =>
% 122.84/16.22 ((
% 122.84/16.22 (complementSubsetComplementIntersect) =>
% 122.84/16.22 ((
% 122.84/16.22 (complementInPowersetComplementIntersect) =>
% 122.84/16.22 ((
% 122.84/16.22 (contraSubsetComplement) =>
% 122.84/16.22 ((
% 122.84/16.22 (complementTcontraSubset) =>
% 122.84/16.22 ((
% 122.84/16.22 (binunionTILcontra) =>
% 122.84/16.22 ((
% 122.84/16.22 (binunionTIRcontra) =>
% 122.84/16.22 ((
% 122.84/16.22 (inIntersectImpInUnion) =>
% 122.84/16.22 ((
% 122.84/16.22 (inIntersectImpInUnion2) =>
% 122.84/16.22 ((
% 122.84/16.22 (inIntersectImpInIntersectUnions) =>
% 122.84/16.22 ((
% 122.84/16.22 (intersectInPowersetIntersectUnions) =>
% 122.84/16.22 ((
% 122.84/16.22 (inComplementUnionImpNotIn1) =>
% 122.84/16.22 ((
% 122.84/16.22 (inComplementUnionImpInComplement1) =>
% 122.84/16.22 ((
% 122.84/16.22 (binunionTE) =>
% 122.84/16.22 ((
% 122.84/16.22 (binunionTEcontra) =>
% 122.84/16.22 ((
% 122.84/16.22 (demorgan2a1) =>
% 122.84/16.22 ((
% 122.84/16.22 (complementUnionInPowersetComplement) =>
% 122.84/16.22 ((
% 122.84/16.22 (demorgan2a2) =>
% 122.84/16.22 ((
% 122.84/16.22 (demorgan1a) =>
% 122.84/16.22 ((
% 122.84/16.22 (demorgan1b) =>
% 122.84/16.22 ((
% 122.84/16.22 (demorgan1) =>
% 122.84/16.22 ((
% 122.84/16.22 (demorgan2a) =>
% 122.84/16.22 ((
% 122.84/16.22 (demorgan2b2) =>
% 122.84/16.22 ((
% 122.84/16.22 (demorgan2b) =>
% 122.84/16.22 ((
% 122.84/16.22 (demorgan2) =>
% 122.84/16.22 ((
% 122.84/16.22 (woz13rule0) =>
% 122.84/16.22 ((
% 122.84/16.22 (woz13rule1) =>
% 122.84/16.22 ((
% 122.84/16.22 (woz13rule2) =>
% 122.84/16.22 ((
% 122.84/16.22 (woz13rule3) =>
% 122.84/16.22 ((
% 122.84/16.22 (woz13rule4) =>
% 122.84/16.22 ((
% 122.84/16.22 (woz1_1) =>
% 122.84/16.22 ((
% 122.84/16.22 (woz1_2) =>
% 122.84/16.22 ((
% 122.84/16.22 (woz1_3) =>
% 122.84/16.22 ((
% 122.84/16.22 (woz1_4) =>
% 122.84/16.22 ((
% 122.84/16.22 (woz1_5) =>
% 122.84/16.22 ((
% 122.84/16.22 (breln1all2) =>
% 122.84/16.22 ((
% 122.84/16.22 (breln1SetBreln1) =>
% 122.84/16.22 ((
% 122.84/16.22 (choice2fnsingleton) =>
% 122.84/16.22 ((
% 122.84/16.22 (setOfPairsIsBReln1) =>
% 122.84/16.22 ((
% 122.84/16.22 (breln1all1) =>
% 122.84/16.22 ((
% 122.84/16.22 (subbreln1) =>
% 122.84/16.22 ((
% 122.84/16.22 (eqbreln1) =>
% 122.84/16.22 ((
% 122.84/16.22 (breln1invprop) =>
% 122.84/16.22 ((
% 122.84/16.22 (breln1invI) =>
% 122.84/16.22 ((
% 122.84/16.22 (breln1invE) =>
% 122.84/16.22 ((
% 122.84/16.22 (breln1compprop) =>
% 122.84/16.22 ((
% 122.84/16.22 (breln1compI) =>
% 122.84/16.22 ((
% 122.84/16.22 (breln1compE) =>
% 122.84/16.22 ((
% 122.84/16.22 (breln1compEex) =>
% 122.84/16.22 ((
% 122.84/16.22 (breln1unionprop) =>
% 122.84/16.22 ((
% 122.84/16.22 (breln1unionIL) =>
% 122.84/16.22 ((
% 122.84/16.22 (breln1unionIR) =>
% 122.84/16.22 ((
% 122.84/16.22 (breln1unionI) =>
% 122.84/16.22 ((
% 122.84/16.22 (breln1unionE) =>
% 122.84/16.22 ((
% 122.84/16.22 (breln1unionEcases) =>
% 122.84/16.22 ((
% 122.84/16.22 (breln1unionCommutes) =>
% 122.84/16.22 ((
% 122.84/16.22 (woz2Ex) =>
% 122.84/16.22 ((
% 122.84/16.22 (woz2W) =>
% 122.84/16.22 ((
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% 122.84/16.22 ((
% 122.84/16.22 (woz2B) =>
% 122.84/16.22 ((
% 122.84/16.22 (image1Ex) =>
% 122.84/16.22 ((
% 122.84/16.22 (image1Ex1) =>
% 122.84/16.22 ((
% 122.84/16.22 (image1Equiv) =>
% 122.84/16.22 ((
% 122.84/16.22 (image1E) =>
% 122.84/16.22 ((
% 122.84/16.22 (image1I) =>
% 122.84/16.22 ((
% 122.84/16.22 (injFuncInInjFuncSet) =>
% 122.84/16.22 ((
% 122.84/16.22 (!!) @ (
% 122.84/16.22 (('#B') @ (
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% 122.84/16.22 (
% 122.84/16.22 (
% 122.84/16.22 ('#B') @ (
% 122.84/16.22 (
% 122.84/16.22 ('#B') @ (
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% 122.84/16.22 ('#B') @ (
% 122.84/16.22 (
% 122.84/16.22 ('#B') @ (
% 122.84/16.22 (
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% 122.84/16.22 injFuncSet)))))))) @
% 122.84/16.22 (
% 122.84/16.22 (
% 122.84/16.22 ('#B') @ (
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% 122.84/16.22 ('#B') @ (
% 122.84/16.22 (
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% 122.84/16.22 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.84/16.22 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2002])).
% 122.84/16.22 thf(zip_derived_cl2021, plain,
% 122.84/16.22 (~ (((brelnall2) =>
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% 122.84/16.22 (((eta1) =>
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% 122.84/16.22 ((
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% 122.84/16.22 ((
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% 122.84/16.22 ((
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% 122.84/16.22 ((
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% 122.84/16.22 ((
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% 122.84/16.22 ((
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% 122.84/16.22 ((
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% 122.84/16.22 ((
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% 122.84/16.22 ((
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% 122.84/16.22 ((
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% 122.84/16.22 ((
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% 122.84/16.22 ((
% 122.84/16.22 (complementInPowersetComplementIntersect) =>
% 122.84/16.22 ((
% 122.84/16.22 (contraSubsetComplement) =>
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% 122.84/16.22 ((
% 122.84/16.22 (binunionTIRcontra) =>
% 122.84/16.22 ((
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% 122.84/16.22 ((
% 122.84/16.22 (inIntersectImpInUnion2) =>
% 122.84/16.22 ((
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% 122.84/16.22 ((
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% 122.84/16.22 ((
% 122.84/16.22 (inComplementUnionImpNotIn1) =>
% 122.84/16.22 ((
% 122.84/16.22 (inComplementUnionImpInComplement1) =>
% 122.84/16.22 ((
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% 122.84/16.22 ((
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% 122.84/16.22 ((
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% 122.84/16.22 ((
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% 122.84/16.22 ((
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% 122.84/16.22 ((
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% 122.84/16.22 ((
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% 122.84/16.22 ((
% 122.84/16.22 (demorgan2a) =>
% 122.84/16.22 ((
% 122.84/16.22 (demorgan2b2) =>
% 122.84/16.22 ((
% 122.84/16.22 (demorgan2b) =>
% 122.84/16.22 ((
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% 122.84/16.22 ((
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% 122.84/16.22 ((
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% 122.84/16.22 ((
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% 122.84/16.22 ((
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% 122.84/16.22 ((
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% 122.84/16.22 ((
% 122.84/16.22 (breln1all1) =>
% 122.84/16.22 ((
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% 122.84/16.22 ((
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% 122.84/16.22 ((
% 122.84/16.22 (breln1invI) =>
% 122.84/16.22 ((
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% 122.84/16.22 ((
% 122.84/16.22 (breln1compE) =>
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% 122.84/16.22 ((
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% 122.84/16.22 ((
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% 122.84/16.22 (breln1unionCommutes) =>
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% 122.84/16.22 ((
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% 122.84/16.22 ((
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% 122.84/16.22 ((
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% 122.84/16.22 ((
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% 122.84/16.22 ((
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% 122.84/16.22 ((
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% 122.84/16.22 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2012])).
% 122.84/16.22 thf(zip_derived_cl2030, plain,
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% 122.84/16.22 ((
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% 122.84/16.22 ((
% 122.84/16.22 (binunionTIRcontra) =>
% 122.84/16.22 ((
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% 122.84/16.22 ((
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% 122.84/16.22 ((
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% 122.84/16.22 (inComplementUnionImpInComplement1) =>
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% 122.84/16.22 ((
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% 122.84/16.22 (complementUnionInPowersetComplement) =>
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% 122.84/16.22 ((
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% 122.84/16.22 ((
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% 122.84/16.22 ((
% 122.84/16.22 (demorgan2a) =>
% 122.84/16.22 ((
% 122.84/16.22 (demorgan2b2) =>
% 122.84/16.22 ((
% 122.84/16.22 (demorgan2b) =>
% 122.84/16.22 ((
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% 122.84/16.22 ((
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% 122.84/16.22 ((
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% 122.84/16.22 ((
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% 122.84/16.22 ((
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% 122.84/16.22 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2021])).
% 122.84/16.22 thf(zip_derived_cl2039, plain,
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% 122.84/16.22 ((
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% 122.84/16.22 ((
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% 122.84/16.22 ((
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% 122.84/16.22 ((
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% 122.84/16.22 ((
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% 122.84/16.22 ((
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% 122.84/16.22 ((
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% 122.84/16.22 ((
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% 122.84/16.22 ((
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% 122.84/16.22 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2030])).
% 122.84/16.22 thf(zip_derived_cl2048, plain,
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% 122.84/16.22 ((
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% 122.84/16.22 ((
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% 122.84/16.22 ((
% 122.84/16.22 (demorgan2a) =>
% 122.84/16.22 ((
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% 122.84/16.22 ((
% 122.84/16.22 (demorgan2b) =>
% 122.84/16.22 ((
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% 122.84/16.22 ((
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% 122.84/16.22 ((
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% 122.84/16.22 ((
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% 122.84/16.22 ((
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% 122.84/16.22 ((
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% 122.84/16.22 ((
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% 122.84/16.22 ((
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% 122.84/16.22 ((
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% 122.84/16.22 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2039])).
% 122.84/16.22 thf(zip_derived_cl2059, plain,
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% 122.84/16.23 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2059])).
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% 122.84/16.23 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2070])).
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% 122.84/16.23 (((ap2apEq2) =>
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% 122.84/16.23 (((eta1) =>
% 122.84/16.23 (((lam2lamEq) =>
% 122.84/16.23 (((beta2) =>
% 122.84/16.23 (((eta2) =>
% 122.84/16.23 (((iffalseProp1) =>
% 122.84/16.23 (((iffalseProp2) =>
% 122.84/16.23 (((iftrueProp1) =>
% 122.84/16.23 (((iftrueProp2) =>
% 122.84/16.23 (((ifSingleton) =>
% 122.84/16.23 (((ifp) =>
% 122.84/16.23 (((theeq) =>
% 122.84/16.23 (((iftrue) =>
% 122.84/16.23 (((iffalse) =>
% 122.84/16.23 (((iftrueorfalse) =>
% 122.84/16.23 (((binintersectT_lem) =>
% 122.84/16.23 (((binunionT_lem) =>
% 122.84/16.23 (((powersetT_lem) =>
% 122.84/16.23 (((setminusT_lem) =>
% 122.84/16.23 (((complementT_lem) =>
% 122.84/16.23 (((setextT) =>
% 122.84/16.23 (((subsetTI) =>
% 122.84/16.23 (((powersetTI1) =>
% 122.84/16.23 (((powersetTE1) =>
% 122.84/16.23 ((
% 122.84/16.23 (complementTI1) =>
% 122.84/16.23 ((
% 122.84/16.23 (complementTE1) =>
% 122.84/16.23 ((
% 122.84/16.23 (binintersectTELcontra) =>
% 122.84/16.23 ((
% 122.84/16.23 (binintersectTERcontra) =>
% 122.84/16.23 ((
% 122.84/16.23 (contrasubsetT) =>
% 122.84/16.23 ((
% 122.84/16.23 (contrasubsetT1) =>
% 122.84/16.23 ((
% 122.84/16.23 (contrasubsetT2) =>
% 122.84/16.23 ((
% 122.84/16.23 (contrasubsetT3) =>
% 122.84/16.23 ((
% 122.84/16.23 (doubleComplementI1) =>
% 122.84/16.23 ((
% 122.84/16.23 (doubleComplementE1) =>
% 122.84/16.23 ((
% 122.84/16.23 (doubleComplementSub1) =>
% 122.84/16.23 ((
% 122.84/16.23 (doubleComplementSub2) =>
% 122.84/16.23 ((
% 122.84/16.23 (doubleComplementEq) =>
% 122.84/16.23 ((
% 122.84/16.23 (complementTnotintersectT) =>
% 122.84/16.23 ((
% 122.84/16.23 (complementImpComplementIntersect) =>
% 122.84/16.23 ((
% 122.84/16.23 (complementSubsetComplementIntersect) =>
% 122.84/16.23 ((
% 122.84/16.23 (complementInPowersetComplementIntersect) =>
% 122.84/16.23 ((
% 122.84/16.23 (contraSubsetComplement) =>
% 122.84/16.23 ((
% 122.84/16.23 (complementTcontraSubset) =>
% 122.84/16.23 ((
% 122.84/16.23 (binunionTILcontra) =>
% 122.84/16.23 ((
% 122.84/16.23 (binunionTIRcontra) =>
% 122.84/16.23 ((
% 122.84/16.23 (inIntersectImpInUnion) =>
% 122.84/16.23 ((
% 122.84/16.23 (inIntersectImpInUnion2) =>
% 122.84/16.23 ((
% 122.84/16.23 (inIntersectImpInIntersectUnions) =>
% 122.84/16.23 ((
% 122.84/16.23 (intersectInPowersetIntersectUnions) =>
% 122.84/16.23 ((
% 122.84/16.23 (inComplementUnionImpNotIn1) =>
% 122.84/16.23 ((
% 122.84/16.23 (inComplementUnionImpInComplement1) =>
% 122.84/16.23 ((
% 122.84/16.23 (binunionTE) =>
% 122.84/16.23 ((
% 122.84/16.23 (binunionTEcontra) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan2a1) =>
% 122.84/16.23 ((
% 122.84/16.23 (complementUnionInPowersetComplement) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan2a2) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan1a) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan1b) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan1) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan2a) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan2b2) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan2b) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan2) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz13rule0) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz13rule1) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz13rule2) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz13rule3) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz13rule4) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz1_1) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz1_2) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz1_3) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz1_4) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz1_5) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1all2) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1SetBreln1) =>
% 122.84/16.23 ((
% 122.84/16.23 (choice2fnsingleton) =>
% 122.84/16.23 ((
% 122.84/16.23 (setOfPairsIsBReln1) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1all1) =>
% 122.84/16.23 ((
% 122.84/16.23 (subbreln1) =>
% 122.84/16.23 ((
% 122.84/16.23 (eqbreln1) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1invprop) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1invI) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1invE) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1compprop) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1compI) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1compE) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1compEex) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1unionprop) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1unionIL) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1unionIR) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1unionI) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1unionE) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1unionEcases) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1unionCommutes) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz2Ex) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz2W) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz2A) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz2B) =>
% 122.84/16.23 ((
% 122.84/16.23 (image1Ex) =>
% 122.84/16.23 ((
% 122.84/16.23 (image1Ex1) =>
% 122.84/16.23 ((
% 122.84/16.23 (image1Equiv) =>
% 122.84/16.23 ((
% 122.84/16.23 (image1E) =>
% 122.84/16.23 ((
% 122.84/16.23 (image1I) =>
% 122.84/16.23 ((
% 122.84/16.23 (injFuncInInjFuncSet) =>
% 122.84/16.23 ((
% 122.84/16.23 (!!) @ (
% 122.84/16.23 (('#B') @ (
% 122.84/16.23 !!) @
% 122.84/16.23 (
% 122.84/16.23 (
% 122.84/16.23 ('#B') @ (
% 122.84/16.23 (
% 122.84/16.23 ('#B') @ (
% 122.84/16.23 !!))) @
% 122.84/16.23 (
% 122.84/16.23 (
% 122.84/16.23 ('#S') @ (
% 122.84/16.23 (
% 122.84/16.23 ('#B') @ (
% 122.84/16.23 '#S') @
% 122.84/16.23 (
% 122.84/16.23 (
% 122.84/16.23 ('#B') @ (
% 122.84/16.23 (
% 122.84/16.23 ('#B') @ (
% 122.84/16.23 '#S'))) @
% 122.84/16.23 (
% 122.84/16.23 (
% 122.84/16.23 ('#B') @ (
% 122.84/16.23 (
% 122.84/16.23 ('#B') @ (
% 122.84/16.23 (
% 122.84/16.23 ('#B') @ (
% 122.84/16.23 =>))))) @
% 122.84/16.23 (
% 122.84/16.23 (
% 122.84/16.23 ('#B') @ (
% 122.84/16.23 (
% 122.84/16.23 ('#B') @ (
% 122.84/16.23 (
% 122.84/16.23 ('#C') @ in)))) @
% 122.84/16.23 injFuncSet)))))))) @
% 122.84/16.23 (
% 122.84/16.23 (
% 122.84/16.23 ('#B') @ (
% 122.84/16.23 (
% 122.84/16.23 ('#B') @ (
% 122.84/16.23 (
% 122.84/16.23 ('#C') @ in)))) @
% 122.84/16.23 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.84/16.23 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2081])).
% 122.84/16.23 thf(zip_derived_cl2102, plain,
% 122.84/16.23 (~ (((eqbreln) =>
% 122.84/16.23 (((funcext) =>
% 122.84/16.23 (((funcext2) =>
% 122.84/16.23 (((ap2apEq1) =>
% 122.84/16.23 (((ap2apEq2) =>
% 122.84/16.23 (((beta1) =>
% 122.84/16.23 (((eta1) =>
% 122.84/16.23 (((lam2lamEq) =>
% 122.84/16.23 (((beta2) =>
% 122.84/16.23 (((eta2) =>
% 122.84/16.23 (((iffalseProp1) =>
% 122.84/16.23 (((iffalseProp2) =>
% 122.84/16.23 (((iftrueProp1) =>
% 122.84/16.23 (((iftrueProp2) =>
% 122.84/16.23 (((ifSingleton) =>
% 122.84/16.23 (((ifp) =>
% 122.84/16.23 (((theeq) =>
% 122.84/16.23 (((iftrue) =>
% 122.84/16.23 (((iffalse) =>
% 122.84/16.23 (((iftrueorfalse) =>
% 122.84/16.23 (((binintersectT_lem) =>
% 122.84/16.23 (((binunionT_lem) =>
% 122.84/16.23 (((powersetT_lem) =>
% 122.84/16.23 (((setminusT_lem) =>
% 122.84/16.23 (((complementT_lem) =>
% 122.84/16.23 (((setextT) =>
% 122.84/16.23 (((subsetTI) =>
% 122.84/16.23 (((powersetTI1) =>
% 122.84/16.23 (((powersetTE1) =>
% 122.84/16.23 (((complementTI1) =>
% 122.84/16.23 ((
% 122.84/16.23 (complementTE1) =>
% 122.84/16.23 ((
% 122.84/16.23 (binintersectTELcontra) =>
% 122.84/16.23 ((
% 122.84/16.23 (binintersectTERcontra) =>
% 122.84/16.23 ((
% 122.84/16.23 (contrasubsetT) =>
% 122.84/16.23 ((
% 122.84/16.23 (contrasubsetT1) =>
% 122.84/16.23 ((
% 122.84/16.23 (contrasubsetT2) =>
% 122.84/16.23 ((
% 122.84/16.23 (contrasubsetT3) =>
% 122.84/16.23 ((
% 122.84/16.23 (doubleComplementI1) =>
% 122.84/16.23 ((
% 122.84/16.23 (doubleComplementE1) =>
% 122.84/16.23 ((
% 122.84/16.23 (doubleComplementSub1) =>
% 122.84/16.23 ((
% 122.84/16.23 (doubleComplementSub2) =>
% 122.84/16.23 ((
% 122.84/16.23 (doubleComplementEq) =>
% 122.84/16.23 ((
% 122.84/16.23 (complementTnotintersectT) =>
% 122.84/16.23 ((
% 122.84/16.23 (complementImpComplementIntersect) =>
% 122.84/16.23 ((
% 122.84/16.23 (complementSubsetComplementIntersect) =>
% 122.84/16.23 ((
% 122.84/16.23 (complementInPowersetComplementIntersect) =>
% 122.84/16.23 ((
% 122.84/16.23 (contraSubsetComplement) =>
% 122.84/16.23 ((
% 122.84/16.23 (complementTcontraSubset) =>
% 122.84/16.23 ((
% 122.84/16.23 (binunionTILcontra) =>
% 122.84/16.23 ((
% 122.84/16.23 (binunionTIRcontra) =>
% 122.84/16.23 ((
% 122.84/16.23 (inIntersectImpInUnion) =>
% 122.84/16.23 ((
% 122.84/16.23 (inIntersectImpInUnion2) =>
% 122.84/16.23 ((
% 122.84/16.23 (inIntersectImpInIntersectUnions) =>
% 122.84/16.23 ((
% 122.84/16.23 (intersectInPowersetIntersectUnions) =>
% 122.84/16.23 ((
% 122.84/16.23 (inComplementUnionImpNotIn1) =>
% 122.84/16.23 ((
% 122.84/16.23 (inComplementUnionImpInComplement1) =>
% 122.84/16.23 ((
% 122.84/16.23 (binunionTE) =>
% 122.84/16.23 ((
% 122.84/16.23 (binunionTEcontra) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan2a1) =>
% 122.84/16.23 ((
% 122.84/16.23 (complementUnionInPowersetComplement) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan2a2) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan1a) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan1b) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan1) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan2a) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan2b2) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan2b) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan2) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz13rule0) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz13rule1) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz13rule2) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz13rule3) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz13rule4) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz1_1) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz1_2) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz1_3) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz1_4) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz1_5) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1all2) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1SetBreln1) =>
% 122.84/16.23 ((
% 122.84/16.23 (choice2fnsingleton) =>
% 122.84/16.23 ((
% 122.84/16.23 (setOfPairsIsBReln1) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1all1) =>
% 122.84/16.23 ((
% 122.84/16.23 (subbreln1) =>
% 122.84/16.23 ((
% 122.84/16.23 (eqbreln1) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1invprop) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1invI) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1invE) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1compprop) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1compI) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1compE) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1compEex) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1unionprop) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1unionIL) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1unionIR) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1unionI) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1unionE) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1unionEcases) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1unionCommutes) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz2Ex) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz2W) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz2A) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz2B) =>
% 122.84/16.23 ((
% 122.84/16.23 (image1Ex) =>
% 122.84/16.23 ((
% 122.84/16.23 (image1Ex1) =>
% 122.84/16.23 ((
% 122.84/16.23 (image1Equiv) =>
% 122.84/16.23 ((
% 122.84/16.23 (image1E) =>
% 122.84/16.23 ((
% 122.84/16.23 (image1I) =>
% 122.84/16.23 ((
% 122.84/16.23 (injFuncInInjFuncSet) =>
% 122.84/16.23 ((
% 122.84/16.23 (!!) @ (
% 122.84/16.23 (('#B') @ (
% 122.84/16.23 !!) @
% 122.84/16.23 (
% 122.84/16.23 (
% 122.84/16.23 ('#B') @ (
% 122.84/16.23 (
% 122.84/16.23 ('#B') @ (
% 122.84/16.23 !!))) @
% 122.84/16.23 (
% 122.84/16.23 (
% 122.84/16.23 ('#S') @ (
% 122.84/16.23 (
% 122.84/16.23 ('#B') @ (
% 122.84/16.23 '#S') @
% 122.84/16.23 (
% 122.84/16.23 (
% 122.84/16.23 ('#B') @ (
% 122.84/16.23 (
% 122.84/16.23 ('#B') @ (
% 122.84/16.23 '#S'))) @
% 122.84/16.23 (
% 122.84/16.23 (
% 122.84/16.23 ('#B') @ (
% 122.84/16.23 (
% 122.84/16.23 ('#B') @ (
% 122.84/16.23 (
% 122.84/16.23 ('#B') @ (
% 122.84/16.23 =>))))) @
% 122.84/16.23 (
% 122.84/16.23 (
% 122.84/16.23 ('#B') @ (
% 122.84/16.23 (
% 122.84/16.23 ('#B') @ (
% 122.84/16.23 (
% 122.84/16.23 ('#C') @ in)))) @
% 122.84/16.23 injFuncSet)))))))) @
% 122.84/16.23 (
% 122.84/16.23 (
% 122.84/16.23 ('#B') @ (
% 122.84/16.23 (
% 122.84/16.23 ('#B') @ (
% 122.84/16.23 (
% 122.84/16.23 ('#C') @ in)))) @
% 122.84/16.23 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.84/16.23 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2091])).
% 122.84/16.23 thf(zip_derived_cl2115, plain,
% 122.84/16.23 (~ (((funcext) =>
% 122.84/16.23 (((funcext2) =>
% 122.84/16.23 (((ap2apEq1) =>
% 122.84/16.23 (((ap2apEq2) =>
% 122.84/16.23 (((beta1) =>
% 122.84/16.23 (((eta1) =>
% 122.84/16.23 (((lam2lamEq) =>
% 122.84/16.23 (((beta2) =>
% 122.84/16.23 (((eta2) =>
% 122.84/16.23 (((iffalseProp1) =>
% 122.84/16.23 (((iffalseProp2) =>
% 122.84/16.23 (((iftrueProp1) =>
% 122.84/16.23 (((iftrueProp2) =>
% 122.84/16.23 (((ifSingleton) =>
% 122.84/16.23 (((ifp) =>
% 122.84/16.23 (((theeq) =>
% 122.84/16.23 (((iftrue) =>
% 122.84/16.23 (((iffalse) =>
% 122.84/16.23 (((iftrueorfalse) =>
% 122.84/16.23 (((binintersectT_lem) =>
% 122.84/16.23 (((binunionT_lem) =>
% 122.84/16.23 (((powersetT_lem) =>
% 122.84/16.23 (((setminusT_lem) =>
% 122.84/16.23 (((complementT_lem) =>
% 122.84/16.23 (((setextT) =>
% 122.84/16.23 (((subsetTI) =>
% 122.84/16.23 (((powersetTI1) =>
% 122.84/16.23 (((powersetTE1) =>
% 122.84/16.23 (((complementTI1) =>
% 122.84/16.23 (((complementTE1) =>
% 122.84/16.23 ((
% 122.84/16.23 (binintersectTELcontra) =>
% 122.84/16.23 ((
% 122.84/16.23 (binintersectTERcontra) =>
% 122.84/16.23 ((
% 122.84/16.23 (contrasubsetT) =>
% 122.84/16.23 ((
% 122.84/16.23 (contrasubsetT1) =>
% 122.84/16.23 ((
% 122.84/16.23 (contrasubsetT2) =>
% 122.84/16.23 ((
% 122.84/16.23 (contrasubsetT3) =>
% 122.84/16.23 ((
% 122.84/16.23 (doubleComplementI1) =>
% 122.84/16.23 ((
% 122.84/16.23 (doubleComplementE1) =>
% 122.84/16.23 ((
% 122.84/16.23 (doubleComplementSub1) =>
% 122.84/16.23 ((
% 122.84/16.23 (doubleComplementSub2) =>
% 122.84/16.23 ((
% 122.84/16.23 (doubleComplementEq) =>
% 122.84/16.23 ((
% 122.84/16.23 (complementTnotintersectT) =>
% 122.84/16.23 ((
% 122.84/16.23 (complementImpComplementIntersect) =>
% 122.84/16.23 ((
% 122.84/16.23 (complementSubsetComplementIntersect) =>
% 122.84/16.23 ((
% 122.84/16.23 (complementInPowersetComplementIntersect) =>
% 122.84/16.23 ((
% 122.84/16.23 (contraSubsetComplement) =>
% 122.84/16.23 ((
% 122.84/16.23 (complementTcontraSubset) =>
% 122.84/16.23 ((
% 122.84/16.23 (binunionTILcontra) =>
% 122.84/16.23 ((
% 122.84/16.23 (binunionTIRcontra) =>
% 122.84/16.23 ((
% 122.84/16.23 (inIntersectImpInUnion) =>
% 122.84/16.23 ((
% 122.84/16.23 (inIntersectImpInUnion2) =>
% 122.84/16.23 ((
% 122.84/16.23 (inIntersectImpInIntersectUnions) =>
% 122.84/16.23 ((
% 122.84/16.23 (intersectInPowersetIntersectUnions) =>
% 122.84/16.23 ((
% 122.84/16.23 (inComplementUnionImpNotIn1) =>
% 122.84/16.23 ((
% 122.84/16.23 (inComplementUnionImpInComplement1) =>
% 122.84/16.23 ((
% 122.84/16.23 (binunionTE) =>
% 122.84/16.23 ((
% 122.84/16.23 (binunionTEcontra) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan2a1) =>
% 122.84/16.23 ((
% 122.84/16.23 (complementUnionInPowersetComplement) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan2a2) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan1a) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan1b) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan1) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan2a) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan2b2) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan2b) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan2) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz13rule0) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz13rule1) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz13rule2) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz13rule3) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz13rule4) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz1_1) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz1_2) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz1_3) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz1_4) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz1_5) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1all2) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1SetBreln1) =>
% 122.84/16.23 ((
% 122.84/16.23 (choice2fnsingleton) =>
% 122.84/16.23 ((
% 122.84/16.23 (setOfPairsIsBReln1) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1all1) =>
% 122.84/16.23 ((
% 122.84/16.23 (subbreln1) =>
% 122.84/16.23 ((
% 122.84/16.23 (eqbreln1) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1invprop) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1invI) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1invE) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1compprop) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1compI) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1compE) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1compEex) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1unionprop) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1unionIL) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1unionIR) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1unionI) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1unionE) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1unionEcases) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1unionCommutes) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz2Ex) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz2W) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz2A) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz2B) =>
% 122.84/16.23 ((
% 122.84/16.23 (image1Ex) =>
% 122.84/16.23 ((
% 122.84/16.23 (image1Ex1) =>
% 122.84/16.23 ((
% 122.84/16.23 (image1Equiv) =>
% 122.84/16.23 ((
% 122.84/16.23 (image1E) =>
% 122.84/16.23 ((
% 122.84/16.23 (image1I) =>
% 122.84/16.23 ((
% 122.84/16.23 (injFuncInInjFuncSet) =>
% 122.84/16.23 ((
% 122.84/16.23 (!!) @ (
% 122.84/16.23 (('#B') @ (
% 122.84/16.23 !!) @
% 122.84/16.23 (
% 122.84/16.23 (
% 122.84/16.23 ('#B') @ (
% 122.84/16.23 (
% 122.84/16.23 ('#B') @ (
% 122.84/16.23 !!))) @
% 122.84/16.23 (
% 122.84/16.23 (
% 122.84/16.23 ('#S') @ (
% 122.84/16.23 (
% 122.84/16.23 ('#B') @ (
% 122.84/16.23 '#S') @
% 122.84/16.23 (
% 122.84/16.23 (
% 122.84/16.23 ('#B') @ (
% 122.84/16.23 (
% 122.84/16.23 ('#B') @ (
% 122.84/16.23 '#S'))) @
% 122.84/16.23 (
% 122.84/16.23 (
% 122.84/16.23 ('#B') @ (
% 122.84/16.23 (
% 122.84/16.23 ('#B') @ (
% 122.84/16.23 (
% 122.84/16.23 ('#B') @ (
% 122.84/16.23 =>))))) @
% 122.84/16.23 (
% 122.84/16.23 (
% 122.84/16.23 ('#B') @ (
% 122.84/16.23 (
% 122.84/16.23 ('#B') @ (
% 122.84/16.23 (
% 122.84/16.23 ('#C') @ in)))) @
% 122.84/16.23 injFuncSet)))))))) @
% 122.84/16.23 (
% 122.84/16.23 (
% 122.84/16.23 ('#B') @ (
% 122.84/16.23 (
% 122.84/16.23 ('#B') @ (
% 122.84/16.23 (
% 122.84/16.23 ('#C') @ in)))) @
% 122.84/16.23 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.84/16.23 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2102])).
% 122.84/16.23 thf(zip_derived_cl2130, plain,
% 122.84/16.23 (~ (((funcext2) =>
% 122.84/16.23 (((ap2apEq1) =>
% 122.84/16.23 (((ap2apEq2) =>
% 122.84/16.23 (((beta1) =>
% 122.84/16.23 (((eta1) =>
% 122.84/16.23 (((lam2lamEq) =>
% 122.84/16.23 (((beta2) =>
% 122.84/16.23 (((eta2) =>
% 122.84/16.23 (((iffalseProp1) =>
% 122.84/16.23 (((iffalseProp2) =>
% 122.84/16.23 (((iftrueProp1) =>
% 122.84/16.23 (((iftrueProp2) =>
% 122.84/16.23 (((ifSingleton) =>
% 122.84/16.23 (((ifp) =>
% 122.84/16.23 (((theeq) =>
% 122.84/16.23 (((iftrue) =>
% 122.84/16.23 (((iffalse) =>
% 122.84/16.23 (((iftrueorfalse) =>
% 122.84/16.23 (((binintersectT_lem) =>
% 122.84/16.23 (((binunionT_lem) =>
% 122.84/16.23 (((powersetT_lem) =>
% 122.84/16.23 (((setminusT_lem) =>
% 122.84/16.23 (((complementT_lem) =>
% 122.84/16.23 (((setextT) =>
% 122.84/16.23 (((subsetTI) =>
% 122.84/16.23 (((powersetTI1) =>
% 122.84/16.23 (((powersetTE1) =>
% 122.84/16.23 (((complementTI1) =>
% 122.84/16.23 (((complementTE1) =>
% 122.84/16.23 (((binintersectTELcontra) =>
% 122.84/16.23 ((
% 122.84/16.23 (binintersectTERcontra) =>
% 122.84/16.23 ((
% 122.84/16.23 (contrasubsetT) =>
% 122.84/16.23 ((
% 122.84/16.23 (contrasubsetT1) =>
% 122.84/16.23 ((
% 122.84/16.23 (contrasubsetT2) =>
% 122.84/16.23 ((
% 122.84/16.23 (contrasubsetT3) =>
% 122.84/16.23 ((
% 122.84/16.23 (doubleComplementI1) =>
% 122.84/16.23 ((
% 122.84/16.23 (doubleComplementE1) =>
% 122.84/16.23 ((
% 122.84/16.23 (doubleComplementSub1) =>
% 122.84/16.23 ((
% 122.84/16.23 (doubleComplementSub2) =>
% 122.84/16.23 ((
% 122.84/16.23 (doubleComplementEq) =>
% 122.84/16.23 ((
% 122.84/16.23 (complementTnotintersectT) =>
% 122.84/16.23 ((
% 122.84/16.23 (complementImpComplementIntersect) =>
% 122.84/16.23 ((
% 122.84/16.23 (complementSubsetComplementIntersect) =>
% 122.84/16.23 ((
% 122.84/16.23 (complementInPowersetComplementIntersect) =>
% 122.84/16.23 ((
% 122.84/16.23 (contraSubsetComplement) =>
% 122.84/16.23 ((
% 122.84/16.23 (complementTcontraSubset) =>
% 122.84/16.23 ((
% 122.84/16.23 (binunionTILcontra) =>
% 122.84/16.23 ((
% 122.84/16.23 (binunionTIRcontra) =>
% 122.84/16.23 ((
% 122.84/16.23 (inIntersectImpInUnion) =>
% 122.84/16.23 ((
% 122.84/16.23 (inIntersectImpInUnion2) =>
% 122.84/16.23 ((
% 122.84/16.23 (inIntersectImpInIntersectUnions) =>
% 122.84/16.23 ((
% 122.84/16.23 (intersectInPowersetIntersectUnions) =>
% 122.84/16.23 ((
% 122.84/16.23 (inComplementUnionImpNotIn1) =>
% 122.84/16.23 ((
% 122.84/16.23 (inComplementUnionImpInComplement1) =>
% 122.84/16.23 ((
% 122.84/16.23 (binunionTE) =>
% 122.84/16.23 ((
% 122.84/16.23 (binunionTEcontra) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan2a1) =>
% 122.84/16.23 ((
% 122.84/16.23 (complementUnionInPowersetComplement) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan2a2) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan1a) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan1b) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan1) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan2a) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan2b2) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan2b) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan2) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz13rule0) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz13rule1) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz13rule2) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz13rule3) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz13rule4) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz1_1) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz1_2) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz1_3) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz1_4) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz1_5) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1all2) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1SetBreln1) =>
% 122.84/16.23 ((
% 122.84/16.23 (choice2fnsingleton) =>
% 122.84/16.23 ((
% 122.84/16.23 (setOfPairsIsBReln1) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1all1) =>
% 122.84/16.23 ((
% 122.84/16.23 (subbreln1) =>
% 122.84/16.23 ((
% 122.84/16.23 (eqbreln1) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1invprop) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1invI) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1invE) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1compprop) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1compI) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1compE) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1compEex) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1unionprop) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1unionIL) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1unionIR) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1unionI) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1unionE) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1unionEcases) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1unionCommutes) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz2Ex) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz2W) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz2A) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz2B) =>
% 122.84/16.23 ((
% 122.84/16.23 (image1Ex) =>
% 122.84/16.23 ((
% 122.84/16.23 (image1Ex1) =>
% 122.84/16.23 ((
% 122.84/16.23 (image1Equiv) =>
% 122.84/16.23 ((
% 122.84/16.23 (image1E) =>
% 122.84/16.23 ((
% 122.84/16.23 (image1I) =>
% 122.84/16.23 ((
% 122.84/16.23 (injFuncInInjFuncSet) =>
% 122.84/16.23 ((
% 122.84/16.23 (!!) @ (
% 122.84/16.23 (('#B') @ (
% 122.84/16.23 !!) @
% 122.84/16.23 (
% 122.84/16.23 (
% 122.84/16.23 ('#B') @ (
% 122.84/16.23 (
% 122.84/16.23 ('#B') @ (
% 122.84/16.23 !!))) @
% 122.84/16.23 (
% 122.84/16.23 (
% 122.84/16.23 ('#S') @ (
% 122.84/16.23 (
% 122.84/16.23 ('#B') @ (
% 122.84/16.23 '#S') @
% 122.84/16.23 (
% 122.84/16.23 (
% 122.84/16.23 ('#B') @ (
% 122.84/16.23 (
% 122.84/16.23 ('#B') @ (
% 122.84/16.23 '#S'))) @
% 122.84/16.23 (
% 122.84/16.23 (
% 122.84/16.23 ('#B') @ (
% 122.84/16.23 (
% 122.84/16.23 ('#B') @ (
% 122.84/16.23 (
% 122.84/16.23 ('#B') @ (
% 122.84/16.23 =>))))) @
% 122.84/16.23 (
% 122.84/16.23 (
% 122.84/16.23 ('#B') @ (
% 122.84/16.23 (
% 122.84/16.23 ('#B') @ (
% 122.84/16.23 (
% 122.84/16.23 ('#C') @ in)))) @
% 122.84/16.23 injFuncSet)))))))) @
% 122.84/16.23 (
% 122.84/16.23 (
% 122.84/16.23 ('#B') @ (
% 122.84/16.23 (
% 122.84/16.23 ('#B') @ (
% 122.84/16.23 (
% 122.84/16.23 ('#C') @ in)))) @
% 122.84/16.23 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.84/16.23 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2115])).
% 122.84/16.23 thf(zip_derived_cl2146, plain,
% 122.84/16.23 (~ (((ap2apEq1) =>
% 122.84/16.23 (((ap2apEq2) =>
% 122.84/16.23 (((beta1) =>
% 122.84/16.23 (((eta1) =>
% 122.84/16.23 (((lam2lamEq) =>
% 122.84/16.23 (((beta2) =>
% 122.84/16.23 (((eta2) =>
% 122.84/16.23 (((iffalseProp1) =>
% 122.84/16.23 (((iffalseProp2) =>
% 122.84/16.23 (((iftrueProp1) =>
% 122.84/16.23 (((iftrueProp2) =>
% 122.84/16.23 (((ifSingleton) =>
% 122.84/16.23 (((ifp) =>
% 122.84/16.23 (((theeq) =>
% 122.84/16.23 (((iftrue) =>
% 122.84/16.23 (((iffalse) =>
% 122.84/16.23 (((iftrueorfalse) =>
% 122.84/16.23 (((binintersectT_lem) =>
% 122.84/16.23 (((binunionT_lem) =>
% 122.84/16.23 (((powersetT_lem) =>
% 122.84/16.23 (((setminusT_lem) =>
% 122.84/16.23 (((complementT_lem) =>
% 122.84/16.23 (((setextT) =>
% 122.84/16.23 (((subsetTI) =>
% 122.84/16.23 (((powersetTI1) =>
% 122.84/16.23 (((powersetTE1) =>
% 122.84/16.23 (((complementTI1) =>
% 122.84/16.23 (((complementTE1) =>
% 122.84/16.23 (((binintersectTELcontra) =>
% 122.84/16.23 (((binintersectTERcontra) =>
% 122.84/16.23 ((
% 122.84/16.23 (contrasubsetT) =>
% 122.84/16.23 ((
% 122.84/16.23 (contrasubsetT1) =>
% 122.84/16.23 ((
% 122.84/16.23 (contrasubsetT2) =>
% 122.84/16.23 ((
% 122.84/16.23 (contrasubsetT3) =>
% 122.84/16.23 ((
% 122.84/16.23 (doubleComplementI1) =>
% 122.84/16.23 ((
% 122.84/16.23 (doubleComplementE1) =>
% 122.84/16.23 ((
% 122.84/16.23 (doubleComplementSub1) =>
% 122.84/16.23 ((
% 122.84/16.23 (doubleComplementSub2) =>
% 122.84/16.23 ((
% 122.84/16.23 (doubleComplementEq) =>
% 122.84/16.23 ((
% 122.84/16.23 (complementTnotintersectT) =>
% 122.84/16.23 ((
% 122.84/16.23 (complementImpComplementIntersect) =>
% 122.84/16.23 ((
% 122.84/16.23 (complementSubsetComplementIntersect) =>
% 122.84/16.23 ((
% 122.84/16.23 (complementInPowersetComplementIntersect) =>
% 122.84/16.23 ((
% 122.84/16.23 (contraSubsetComplement) =>
% 122.84/16.23 ((
% 122.84/16.23 (complementTcontraSubset) =>
% 122.84/16.23 ((
% 122.84/16.23 (binunionTILcontra) =>
% 122.84/16.23 ((
% 122.84/16.23 (binunionTIRcontra) =>
% 122.84/16.23 ((
% 122.84/16.23 (inIntersectImpInUnion) =>
% 122.84/16.23 ((
% 122.84/16.23 (inIntersectImpInUnion2) =>
% 122.84/16.23 ((
% 122.84/16.23 (inIntersectImpInIntersectUnions) =>
% 122.84/16.23 ((
% 122.84/16.23 (intersectInPowersetIntersectUnions) =>
% 122.84/16.23 ((
% 122.84/16.23 (inComplementUnionImpNotIn1) =>
% 122.84/16.23 ((
% 122.84/16.23 (inComplementUnionImpInComplement1) =>
% 122.84/16.23 ((
% 122.84/16.23 (binunionTE) =>
% 122.84/16.23 ((
% 122.84/16.23 (binunionTEcontra) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan2a1) =>
% 122.84/16.23 ((
% 122.84/16.23 (complementUnionInPowersetComplement) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan2a2) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan1a) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan1b) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan1) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan2a) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan2b2) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan2b) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan2) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz13rule0) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz13rule1) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz13rule2) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz13rule3) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz13rule4) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz1_1) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz1_2) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz1_3) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz1_4) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz1_5) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1all2) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1SetBreln1) =>
% 122.84/16.23 ((
% 122.84/16.23 (choice2fnsingleton) =>
% 122.84/16.23 ((
% 122.84/16.23 (setOfPairsIsBReln1) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1all1) =>
% 122.84/16.23 ((
% 122.84/16.23 (subbreln1) =>
% 122.84/16.23 ((
% 122.84/16.23 (eqbreln1) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1invprop) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1invI) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1invE) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1compprop) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1compI) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1compE) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1compEex) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1unionprop) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1unionIL) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1unionIR) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1unionI) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1unionE) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1unionEcases) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1unionCommutes) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz2Ex) =>
% 122.84/16.23 ((
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% 122.84/16.23 ((
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% 122.84/16.23 ((
% 122.84/16.23 (woz2B) =>
% 122.84/16.23 ((
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% 122.84/16.23 ((
% 122.84/16.23 (image1Ex1) =>
% 122.84/16.23 ((
% 122.84/16.23 (image1Equiv) =>
% 122.84/16.23 ((
% 122.84/16.23 (image1E) =>
% 122.84/16.23 ((
% 122.84/16.23 (image1I) =>
% 122.84/16.23 ((
% 122.84/16.23 (injFuncInInjFuncSet) =>
% 122.84/16.23 ((
% 122.84/16.23 (!!) @ (
% 122.84/16.23 (('#B') @ (
% 122.84/16.23 !!) @
% 122.84/16.23 (
% 122.84/16.23 (
% 122.84/16.23 ('#B') @ (
% 122.84/16.23 (
% 122.84/16.23 ('#B') @ (
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% 122.84/16.23 thf(zip_derived_cl2163, plain,
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% 122.84/16.23 (((lam2lamEq) =>
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% 122.84/16.23 (((complementT_lem) =>
% 122.84/16.23 (((setextT) =>
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% 122.84/16.23 (((powersetTE1) =>
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% 122.84/16.23 (((complementTE1) =>
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% 122.84/16.23 (((binintersectTERcontra) =>
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% 122.84/16.23 ((
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% 122.84/16.23 ((
% 122.84/16.23 (contrasubsetT2) =>
% 122.84/16.23 ((
% 122.84/16.23 (contrasubsetT3) =>
% 122.84/16.23 ((
% 122.84/16.23 (doubleComplementI1) =>
% 122.84/16.23 ((
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% 122.84/16.23 ((
% 122.84/16.23 (doubleComplementSub1) =>
% 122.84/16.23 ((
% 122.84/16.23 (doubleComplementSub2) =>
% 122.84/16.23 ((
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% 122.84/16.23 ((
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% 122.84/16.23 ((
% 122.84/16.23 (complementImpComplementIntersect) =>
% 122.84/16.23 ((
% 122.84/16.23 (complementSubsetComplementIntersect) =>
% 122.84/16.23 ((
% 122.84/16.23 (complementInPowersetComplementIntersect) =>
% 122.84/16.23 ((
% 122.84/16.23 (contraSubsetComplement) =>
% 122.84/16.23 ((
% 122.84/16.23 (complementTcontraSubset) =>
% 122.84/16.23 ((
% 122.84/16.23 (binunionTILcontra) =>
% 122.84/16.23 ((
% 122.84/16.23 (binunionTIRcontra) =>
% 122.84/16.23 ((
% 122.84/16.23 (inIntersectImpInUnion) =>
% 122.84/16.23 ((
% 122.84/16.23 (inIntersectImpInUnion2) =>
% 122.84/16.23 ((
% 122.84/16.23 (inIntersectImpInIntersectUnions) =>
% 122.84/16.23 ((
% 122.84/16.23 (intersectInPowersetIntersectUnions) =>
% 122.84/16.23 ((
% 122.84/16.23 (inComplementUnionImpNotIn1) =>
% 122.84/16.23 ((
% 122.84/16.23 (inComplementUnionImpInComplement1) =>
% 122.84/16.23 ((
% 122.84/16.23 (binunionTE) =>
% 122.84/16.23 ((
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% 122.84/16.23 ((
% 122.84/16.23 (demorgan2a1) =>
% 122.84/16.23 ((
% 122.84/16.23 (complementUnionInPowersetComplement) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan2a2) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan1a) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan1b) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan1) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan2a) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan2b2) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan2b) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan2) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz13rule0) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz13rule1) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz13rule2) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz13rule3) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz13rule4) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz1_1) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz1_2) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz1_3) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz1_4) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz1_5) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1all2) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1SetBreln1) =>
% 122.84/16.23 ((
% 122.84/16.23 (choice2fnsingleton) =>
% 122.84/16.23 ((
% 122.84/16.23 (setOfPairsIsBReln1) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1all1) =>
% 122.84/16.23 ((
% 122.84/16.23 (subbreln1) =>
% 122.84/16.23 ((
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% 122.84/16.23 ((
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% 122.84/16.23 ((
% 122.84/16.23 (breln1invI) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1invE) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1compprop) =>
% 122.84/16.23 ((
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% 122.84/16.23 ((
% 122.84/16.23 (breln1compE) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1compEex) =>
% 122.84/16.23 ((
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% 122.84/16.23 ((
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% 122.84/16.23 ((
% 122.84/16.23 (breln1unionIR) =>
% 122.84/16.23 ((
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% 122.84/16.23 ((
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% 122.84/16.23 ((
% 122.84/16.23 (breln1unionEcases) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1unionCommutes) =>
% 122.84/16.23 ((
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% 122.84/16.23 ((
% 122.84/16.23 (woz2W) =>
% 122.84/16.23 ((
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% 122.84/16.23 ((
% 122.84/16.23 (woz2B) =>
% 122.84/16.23 ((
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% 122.84/16.23 ((
% 122.84/16.23 (image1Ex1) =>
% 122.84/16.23 ((
% 122.84/16.23 (image1Equiv) =>
% 122.84/16.23 ((
% 122.84/16.23 (image1E) =>
% 122.84/16.23 ((
% 122.84/16.23 (image1I) =>
% 122.84/16.23 ((
% 122.84/16.23 (injFuncInInjFuncSet) =>
% 122.84/16.23 ((
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% 122.84/16.23 (
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% 122.84/16.23 (
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% 122.84/16.23 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2146])).
% 122.84/16.23 thf(zip_derived_cl2181, plain,
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% 122.84/16.23 (((iftrueorfalse) =>
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% 122.84/16.23 (((binunionT_lem) =>
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% 122.84/16.23 (((complementT_lem) =>
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% 122.84/16.23 ((
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% 122.84/16.23 ((
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% 122.84/16.23 ((
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% 122.84/16.23 ((
% 122.84/16.23 (complementSubsetComplementIntersect) =>
% 122.84/16.23 ((
% 122.84/16.23 (complementInPowersetComplementIntersect) =>
% 122.84/16.23 ((
% 122.84/16.23 (contraSubsetComplement) =>
% 122.84/16.23 ((
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% 122.84/16.23 ((
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% 122.84/16.23 ((
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% 122.84/16.23 ((
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% 122.84/16.23 ((
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% 122.84/16.23 ((
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% 122.84/16.23 ((
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% 122.84/16.23 ((
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% 122.84/16.23 ((
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% 122.84/16.23 ((
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% 122.84/16.23 ((
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% 122.84/16.23 ((
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% 122.84/16.23 ((
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% 122.84/16.23 ((
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% 122.84/16.23 ((
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% 122.84/16.23 ((
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% 122.84/16.23 ((
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% 122.84/16.23 ((
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% 122.84/16.23 ('#C') @ in)))) @
% 122.84/16.23 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.84/16.23 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2163])).
% 122.84/16.23 thf(zip_derived_cl2198, plain,
% 122.84/16.23 (~ (((eta1) =>
% 122.84/16.23 (((lam2lamEq) =>
% 122.84/16.23 (((beta2) =>
% 122.84/16.23 (((eta2) =>
% 122.84/16.23 (((iffalseProp1) =>
% 122.84/16.23 (((iffalseProp2) =>
% 122.84/16.23 (((iftrueProp1) =>
% 122.84/16.23 (((iftrueProp2) =>
% 122.84/16.23 (((ifSingleton) =>
% 122.84/16.23 (((ifp) =>
% 122.84/16.23 (((theeq) =>
% 122.84/16.23 (((iftrue) =>
% 122.84/16.23 (((iffalse) =>
% 122.84/16.23 (((iftrueorfalse) =>
% 122.84/16.23 (((binintersectT_lem) =>
% 122.84/16.23 (((binunionT_lem) =>
% 122.84/16.23 (((powersetT_lem) =>
% 122.84/16.23 (((setminusT_lem) =>
% 122.84/16.23 (((complementT_lem) =>
% 122.84/16.23 (((setextT) =>
% 122.84/16.23 (((subsetTI) =>
% 122.84/16.23 (((powersetTI1) =>
% 122.84/16.23 (((powersetTE1) =>
% 122.84/16.23 (((complementTI1) =>
% 122.84/16.23 (((complementTE1) =>
% 122.84/16.23 (((binintersectTELcontra) =>
% 122.84/16.23 (((binintersectTERcontra) =>
% 122.84/16.23 (((contrasubsetT) =>
% 122.84/16.23 (((contrasubsetT1) =>
% 122.84/16.23 (((contrasubsetT2) =>
% 122.84/16.23 ((
% 122.84/16.23 (contrasubsetT3) =>
% 122.84/16.23 ((
% 122.84/16.23 (doubleComplementI1) =>
% 122.84/16.23 ((
% 122.84/16.23 (doubleComplementE1) =>
% 122.84/16.23 ((
% 122.84/16.23 (doubleComplementSub1) =>
% 122.84/16.23 ((
% 122.84/16.23 (doubleComplementSub2) =>
% 122.84/16.23 ((
% 122.84/16.23 (doubleComplementEq) =>
% 122.84/16.23 ((
% 122.84/16.23 (complementTnotintersectT) =>
% 122.84/16.23 ((
% 122.84/16.23 (complementImpComplementIntersect) =>
% 122.84/16.23 ((
% 122.84/16.23 (complementSubsetComplementIntersect) =>
% 122.84/16.23 ((
% 122.84/16.23 (complementInPowersetComplementIntersect) =>
% 122.84/16.23 ((
% 122.84/16.23 (contraSubsetComplement) =>
% 122.84/16.23 ((
% 122.84/16.23 (complementTcontraSubset) =>
% 122.84/16.23 ((
% 122.84/16.23 (binunionTILcontra) =>
% 122.84/16.23 ((
% 122.84/16.23 (binunionTIRcontra) =>
% 122.84/16.23 ((
% 122.84/16.23 (inIntersectImpInUnion) =>
% 122.84/16.23 ((
% 122.84/16.23 (inIntersectImpInUnion2) =>
% 122.84/16.23 ((
% 122.84/16.23 (inIntersectImpInIntersectUnions) =>
% 122.84/16.23 ((
% 122.84/16.23 (intersectInPowersetIntersectUnions) =>
% 122.84/16.23 ((
% 122.84/16.23 (inComplementUnionImpNotIn1) =>
% 122.84/16.23 ((
% 122.84/16.23 (inComplementUnionImpInComplement1) =>
% 122.84/16.23 ((
% 122.84/16.23 (binunionTE) =>
% 122.84/16.23 ((
% 122.84/16.23 (binunionTEcontra) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan2a1) =>
% 122.84/16.23 ((
% 122.84/16.23 (complementUnionInPowersetComplement) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan2a2) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan1a) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan1b) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan1) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan2a) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan2b2) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan2b) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan2) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz13rule0) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz13rule1) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz13rule2) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz13rule3) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz13rule4) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz1_1) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz1_2) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz1_3) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz1_4) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz1_5) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1all2) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1SetBreln1) =>
% 122.84/16.23 ((
% 122.84/16.23 (choice2fnsingleton) =>
% 122.84/16.23 ((
% 122.84/16.23 (setOfPairsIsBReln1) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1all1) =>
% 122.84/16.23 ((
% 122.84/16.23 (subbreln1) =>
% 122.84/16.23 ((
% 122.84/16.23 (eqbreln1) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1invprop) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1invI) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1invE) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1compprop) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1compI) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1compE) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1compEex) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1unionprop) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1unionIL) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1unionIR) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1unionI) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1unionE) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1unionEcases) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1unionCommutes) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz2Ex) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz2W) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz2A) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz2B) =>
% 122.84/16.23 ((
% 122.84/16.23 (image1Ex) =>
% 122.84/16.23 ((
% 122.84/16.23 (image1Ex1) =>
% 122.84/16.23 ((
% 122.84/16.23 (image1Equiv) =>
% 122.84/16.23 ((
% 122.84/16.23 (image1E) =>
% 122.84/16.23 ((
% 122.84/16.23 (image1I) =>
% 122.84/16.23 ((
% 122.84/16.23 (injFuncInInjFuncSet) =>
% 122.84/16.23 ((
% 122.84/16.23 (!!) @ (
% 122.84/16.23 (('#B') @ (
% 122.84/16.23 !!) @
% 122.84/16.23 (
% 122.84/16.23 (
% 122.84/16.23 ('#B') @ (
% 122.84/16.23 (
% 122.84/16.23 ('#B') @ (
% 122.84/16.23 !!))) @
% 122.84/16.23 (
% 122.84/16.23 (
% 122.84/16.23 ('#S') @ (
% 122.84/16.23 (
% 122.84/16.23 ('#B') @ (
% 122.84/16.23 '#S') @
% 122.84/16.23 (
% 122.84/16.23 (
% 122.84/16.23 ('#B') @ (
% 122.84/16.23 (
% 122.84/16.23 ('#B') @ (
% 122.84/16.23 '#S'))) @
% 122.84/16.23 (
% 122.84/16.23 (
% 122.84/16.23 ('#B') @ (
% 122.84/16.23 (
% 122.84/16.23 ('#B') @ (
% 122.84/16.23 (
% 122.84/16.23 ('#B') @ (
% 122.84/16.23 =>))))) @
% 122.84/16.23 (
% 122.84/16.23 (
% 122.84/16.23 ('#B') @ (
% 122.84/16.23 (
% 122.84/16.23 ('#B') @ (
% 122.84/16.23 (
% 122.84/16.23 ('#C') @ in)))) @
% 122.84/16.23 injFuncSet)))))))) @
% 122.84/16.23 (
% 122.84/16.23 (
% 122.84/16.23 ('#B') @ (
% 122.84/16.23 (
% 122.84/16.23 ('#B') @ (
% 122.84/16.23 (
% 122.84/16.23 ('#C') @ in)))) @
% 122.84/16.23 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.84/16.23 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2181])).
% 122.84/16.23 thf(zip_derived_cl2213, plain,
% 122.84/16.23 (~ (((lam2lamEq) =>
% 122.84/16.23 (((beta2) =>
% 122.84/16.23 (((eta2) =>
% 122.84/16.23 (((iffalseProp1) =>
% 122.84/16.23 (((iffalseProp2) =>
% 122.84/16.23 (((iftrueProp1) =>
% 122.84/16.23 (((iftrueProp2) =>
% 122.84/16.23 (((ifSingleton) =>
% 122.84/16.23 (((ifp) =>
% 122.84/16.23 (((theeq) =>
% 122.84/16.23 (((iftrue) =>
% 122.84/16.23 (((iffalse) =>
% 122.84/16.23 (((iftrueorfalse) =>
% 122.84/16.23 (((binintersectT_lem) =>
% 122.84/16.23 (((binunionT_lem) =>
% 122.84/16.23 (((powersetT_lem) =>
% 122.84/16.23 (((setminusT_lem) =>
% 122.84/16.23 (((complementT_lem) =>
% 122.84/16.23 (((setextT) =>
% 122.84/16.23 (((subsetTI) =>
% 122.84/16.23 (((powersetTI1) =>
% 122.84/16.23 (((powersetTE1) =>
% 122.84/16.23 (((complementTI1) =>
% 122.84/16.23 (((complementTE1) =>
% 122.84/16.23 (((binintersectTELcontra) =>
% 122.84/16.23 (((binintersectTERcontra) =>
% 122.84/16.23 (((contrasubsetT) =>
% 122.84/16.23 (((contrasubsetT1) =>
% 122.84/16.23 (((contrasubsetT2) =>
% 122.84/16.23 (((contrasubsetT3) =>
% 122.84/16.23 ((
% 122.84/16.23 (doubleComplementI1) =>
% 122.84/16.23 ((
% 122.84/16.23 (doubleComplementE1) =>
% 122.84/16.23 ((
% 122.84/16.23 (doubleComplementSub1) =>
% 122.84/16.23 ((
% 122.84/16.23 (doubleComplementSub2) =>
% 122.84/16.23 ((
% 122.84/16.23 (doubleComplementEq) =>
% 122.84/16.23 ((
% 122.84/16.23 (complementTnotintersectT) =>
% 122.84/16.23 ((
% 122.84/16.23 (complementImpComplementIntersect) =>
% 122.84/16.23 ((
% 122.84/16.23 (complementSubsetComplementIntersect) =>
% 122.84/16.23 ((
% 122.84/16.23 (complementInPowersetComplementIntersect) =>
% 122.84/16.23 ((
% 122.84/16.23 (contraSubsetComplement) =>
% 122.84/16.23 ((
% 122.84/16.23 (complementTcontraSubset) =>
% 122.84/16.23 ((
% 122.84/16.23 (binunionTILcontra) =>
% 122.84/16.23 ((
% 122.84/16.23 (binunionTIRcontra) =>
% 122.84/16.23 ((
% 122.84/16.23 (inIntersectImpInUnion) =>
% 122.84/16.23 ((
% 122.84/16.23 (inIntersectImpInUnion2) =>
% 122.84/16.23 ((
% 122.84/16.23 (inIntersectImpInIntersectUnions) =>
% 122.84/16.23 ((
% 122.84/16.23 (intersectInPowersetIntersectUnions) =>
% 122.84/16.23 ((
% 122.84/16.23 (inComplementUnionImpNotIn1) =>
% 122.84/16.23 ((
% 122.84/16.23 (inComplementUnionImpInComplement1) =>
% 122.84/16.23 ((
% 122.84/16.23 (binunionTE) =>
% 122.84/16.23 ((
% 122.84/16.23 (binunionTEcontra) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan2a1) =>
% 122.84/16.23 ((
% 122.84/16.23 (complementUnionInPowersetComplement) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan2a2) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan1a) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan1b) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan1) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan2a) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan2b2) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan2b) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan2) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz13rule0) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz13rule1) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz13rule2) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz13rule3) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz13rule4) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz1_1) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz1_2) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz1_3) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz1_4) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz1_5) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1all2) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1SetBreln1) =>
% 122.84/16.23 ((
% 122.84/16.23 (choice2fnsingleton) =>
% 122.84/16.23 ((
% 122.84/16.23 (setOfPairsIsBReln1) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1all1) =>
% 122.84/16.23 ((
% 122.84/16.23 (subbreln1) =>
% 122.84/16.23 ((
% 122.84/16.23 (eqbreln1) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1invprop) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1invI) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1invE) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1compprop) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1compI) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1compE) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1compEex) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1unionprop) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1unionIL) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1unionIR) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1unionI) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1unionE) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1unionEcases) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1unionCommutes) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz2Ex) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz2W) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz2A) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz2B) =>
% 122.84/16.23 ((
% 122.84/16.23 (image1Ex) =>
% 122.84/16.23 ((
% 122.84/16.23 (image1Ex1) =>
% 122.84/16.23 ((
% 122.84/16.23 (image1Equiv) =>
% 122.84/16.23 ((
% 122.84/16.23 (image1E) =>
% 122.84/16.23 ((
% 122.84/16.23 (image1I) =>
% 122.84/16.23 ((
% 122.84/16.23 (injFuncInInjFuncSet) =>
% 122.84/16.23 ((
% 122.84/16.23 (!!) @ (
% 122.84/16.23 (('#B') @ (
% 122.84/16.23 !!) @
% 122.84/16.23 (
% 122.84/16.23 (
% 122.84/16.23 ('#B') @ (
% 122.84/16.23 (
% 122.84/16.23 ('#B') @ (
% 122.84/16.23 !!))) @
% 122.84/16.23 (
% 122.84/16.23 (
% 122.84/16.23 ('#S') @ (
% 122.84/16.23 (
% 122.84/16.23 ('#B') @ (
% 122.84/16.23 '#S') @
% 122.84/16.23 (
% 122.84/16.23 (
% 122.84/16.23 ('#B') @ (
% 122.84/16.23 (
% 122.84/16.23 ('#B') @ (
% 122.84/16.23 '#S'))) @
% 122.84/16.23 (
% 122.84/16.23 (
% 122.84/16.23 ('#B') @ (
% 122.84/16.23 (
% 122.84/16.23 ('#B') @ (
% 122.84/16.23 (
% 122.84/16.23 ('#B') @ (
% 122.84/16.23 =>))))) @
% 122.84/16.23 (
% 122.84/16.23 (
% 122.84/16.23 ('#B') @ (
% 122.84/16.23 (
% 122.84/16.23 ('#B') @ (
% 122.84/16.23 (
% 122.84/16.23 ('#C') @ in)))) @
% 122.84/16.23 injFuncSet)))))))) @
% 122.84/16.23 (
% 122.84/16.23 (
% 122.84/16.23 ('#B') @ (
% 122.84/16.23 (
% 122.84/16.23 ('#B') @ (
% 122.84/16.23 (
% 122.84/16.23 ('#C') @ in)))) @
% 122.84/16.23 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.84/16.23 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2198])).
% 122.84/16.23 thf(zip_derived_cl2228, plain,
% 122.84/16.23 (~ (((beta2) =>
% 122.84/16.23 (((eta2) =>
% 122.84/16.23 (((iffalseProp1) =>
% 122.84/16.23 (((iffalseProp2) =>
% 122.84/16.23 (((iftrueProp1) =>
% 122.84/16.23 (((iftrueProp2) =>
% 122.84/16.23 (((ifSingleton) =>
% 122.84/16.23 (((ifp) =>
% 122.84/16.23 (((theeq) =>
% 122.84/16.23 (((iftrue) =>
% 122.84/16.23 (((iffalse) =>
% 122.84/16.23 (((iftrueorfalse) =>
% 122.84/16.23 (((binintersectT_lem) =>
% 122.84/16.23 (((binunionT_lem) =>
% 122.84/16.23 (((powersetT_lem) =>
% 122.84/16.23 (((setminusT_lem) =>
% 122.84/16.23 (((complementT_lem) =>
% 122.84/16.23 (((setextT) =>
% 122.84/16.23 (((subsetTI) =>
% 122.84/16.23 (((powersetTI1) =>
% 122.84/16.23 (((powersetTE1) =>
% 122.84/16.23 (((complementTI1) =>
% 122.84/16.23 (((complementTE1) =>
% 122.84/16.23 (((binintersectTELcontra) =>
% 122.84/16.23 (((binintersectTERcontra) =>
% 122.84/16.23 (((contrasubsetT) =>
% 122.84/16.23 (((contrasubsetT1) =>
% 122.84/16.23 (((contrasubsetT2) =>
% 122.84/16.23 (((contrasubsetT3) =>
% 122.84/16.23 (((doubleComplementI1) =>
% 122.84/16.23 ((
% 122.84/16.23 (doubleComplementE1) =>
% 122.84/16.23 ((
% 122.84/16.23 (doubleComplementSub1) =>
% 122.84/16.23 ((
% 122.84/16.23 (doubleComplementSub2) =>
% 122.84/16.23 ((
% 122.84/16.23 (doubleComplementEq) =>
% 122.84/16.23 ((
% 122.84/16.23 (complementTnotintersectT) =>
% 122.84/16.23 ((
% 122.84/16.23 (complementImpComplementIntersect) =>
% 122.84/16.23 ((
% 122.84/16.23 (complementSubsetComplementIntersect) =>
% 122.84/16.23 ((
% 122.84/16.23 (complementInPowersetComplementIntersect) =>
% 122.84/16.23 ((
% 122.84/16.23 (contraSubsetComplement) =>
% 122.84/16.23 ((
% 122.84/16.23 (complementTcontraSubset) =>
% 122.84/16.23 ((
% 122.84/16.23 (binunionTILcontra) =>
% 122.84/16.23 ((
% 122.84/16.23 (binunionTIRcontra) =>
% 122.84/16.23 ((
% 122.84/16.23 (inIntersectImpInUnion) =>
% 122.84/16.23 ((
% 122.84/16.23 (inIntersectImpInUnion2) =>
% 122.84/16.23 ((
% 122.84/16.23 (inIntersectImpInIntersectUnions) =>
% 122.84/16.23 ((
% 122.84/16.23 (intersectInPowersetIntersectUnions) =>
% 122.84/16.23 ((
% 122.84/16.23 (inComplementUnionImpNotIn1) =>
% 122.84/16.23 ((
% 122.84/16.23 (inComplementUnionImpInComplement1) =>
% 122.84/16.23 ((
% 122.84/16.23 (binunionTE) =>
% 122.84/16.23 ((
% 122.84/16.23 (binunionTEcontra) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan2a1) =>
% 122.84/16.23 ((
% 122.84/16.23 (complementUnionInPowersetComplement) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan2a2) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan1a) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan1b) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan1) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan2a) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan2b2) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan2b) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan2) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz13rule0) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz13rule1) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz13rule2) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz13rule3) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz13rule4) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz1_1) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz1_2) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz1_3) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz1_4) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz1_5) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1all2) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1SetBreln1) =>
% 122.84/16.23 ((
% 122.84/16.23 (choice2fnsingleton) =>
% 122.84/16.23 ((
% 122.84/16.23 (setOfPairsIsBReln1) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1all1) =>
% 122.84/16.23 ((
% 122.84/16.23 (subbreln1) =>
% 122.84/16.23 ((
% 122.84/16.23 (eqbreln1) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1invprop) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1invI) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1invE) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1compprop) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1compI) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1compE) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1compEex) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1unionprop) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1unionIL) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1unionIR) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1unionI) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1unionE) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1unionEcases) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1unionCommutes) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz2Ex) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz2W) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz2A) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz2B) =>
% 122.84/16.23 ((
% 122.84/16.23 (image1Ex) =>
% 122.84/16.23 ((
% 122.84/16.23 (image1Ex1) =>
% 122.84/16.23 ((
% 122.84/16.23 (image1Equiv) =>
% 122.84/16.23 ((
% 122.84/16.23 (image1E) =>
% 122.84/16.23 ((
% 122.84/16.23 (image1I) =>
% 122.84/16.23 ((
% 122.84/16.23 (injFuncInInjFuncSet) =>
% 122.84/16.23 ((
% 122.84/16.23 (!!) @ (
% 122.84/16.23 (('#B') @ (
% 122.84/16.23 !!) @
% 122.84/16.23 (
% 122.84/16.23 (
% 122.84/16.23 ('#B') @ (
% 122.84/16.23 (
% 122.84/16.23 ('#B') @ (
% 122.84/16.23 !!))) @
% 122.84/16.23 (
% 122.84/16.23 (
% 122.84/16.23 ('#S') @ (
% 122.84/16.23 (
% 122.84/16.23 ('#B') @ (
% 122.84/16.23 '#S') @
% 122.84/16.23 (
% 122.84/16.23 (
% 122.84/16.23 ('#B') @ (
% 122.84/16.23 (
% 122.84/16.23 ('#B') @ (
% 122.84/16.23 '#S'))) @
% 122.84/16.23 (
% 122.84/16.23 (
% 122.84/16.23 ('#B') @ (
% 122.84/16.23 (
% 122.84/16.23 ('#B') @ (
% 122.84/16.23 (
% 122.84/16.23 ('#B') @ (
% 122.84/16.23 =>))))) @
% 122.84/16.23 (
% 122.84/16.23 (
% 122.84/16.23 ('#B') @ (
% 122.84/16.23 (
% 122.84/16.23 ('#B') @ (
% 122.84/16.23 (
% 122.84/16.23 ('#C') @ in)))) @
% 122.84/16.23 injFuncSet)))))))) @
% 122.84/16.23 (
% 122.84/16.23 (
% 122.84/16.23 ('#B') @ (
% 122.84/16.23 (
% 122.84/16.23 ('#B') @ (
% 122.84/16.23 (
% 122.84/16.23 ('#C') @ in)))) @
% 122.84/16.23 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.84/16.23 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2213])).
% 122.84/16.23 thf(zip_derived_cl2244, plain,
% 122.84/16.23 (~ (((eta2) =>
% 122.84/16.23 (((iffalseProp1) =>
% 122.84/16.23 (((iffalseProp2) =>
% 122.84/16.23 (((iftrueProp1) =>
% 122.84/16.23 (((iftrueProp2) =>
% 122.84/16.23 (((ifSingleton) =>
% 122.84/16.23 (((ifp) =>
% 122.84/16.23 (((theeq) =>
% 122.84/16.23 (((iftrue) =>
% 122.84/16.23 (((iffalse) =>
% 122.84/16.23 (((iftrueorfalse) =>
% 122.84/16.23 (((binintersectT_lem) =>
% 122.84/16.23 (((binunionT_lem) =>
% 122.84/16.23 (((powersetT_lem) =>
% 122.84/16.23 (((setminusT_lem) =>
% 122.84/16.23 (((complementT_lem) =>
% 122.84/16.23 (((setextT) =>
% 122.84/16.23 (((subsetTI) =>
% 122.84/16.23 (((powersetTI1) =>
% 122.84/16.23 (((powersetTE1) =>
% 122.84/16.23 (((complementTI1) =>
% 122.84/16.23 (((complementTE1) =>
% 122.84/16.23 (((binintersectTELcontra) =>
% 122.84/16.23 (((binintersectTERcontra) =>
% 122.84/16.23 (((contrasubsetT) =>
% 122.84/16.23 (((contrasubsetT1) =>
% 122.84/16.23 (((contrasubsetT2) =>
% 122.84/16.23 (((contrasubsetT3) =>
% 122.84/16.23 (((doubleComplementI1) =>
% 122.84/16.23 (((doubleComplementE1) =>
% 122.84/16.23 ((
% 122.84/16.23 (doubleComplementSub1) =>
% 122.84/16.23 ((
% 122.84/16.23 (doubleComplementSub2) =>
% 122.84/16.23 ((
% 122.84/16.23 (doubleComplementEq) =>
% 122.84/16.23 ((
% 122.84/16.23 (complementTnotintersectT) =>
% 122.84/16.23 ((
% 122.84/16.23 (complementImpComplementIntersect) =>
% 122.84/16.23 ((
% 122.84/16.23 (complementSubsetComplementIntersect) =>
% 122.84/16.23 ((
% 122.84/16.23 (complementInPowersetComplementIntersect) =>
% 122.84/16.23 ((
% 122.84/16.23 (contraSubsetComplement) =>
% 122.84/16.23 ((
% 122.84/16.23 (complementTcontraSubset) =>
% 122.84/16.23 ((
% 122.84/16.23 (binunionTILcontra) =>
% 122.84/16.23 ((
% 122.84/16.23 (binunionTIRcontra) =>
% 122.84/16.23 ((
% 122.84/16.23 (inIntersectImpInUnion) =>
% 122.84/16.23 ((
% 122.84/16.23 (inIntersectImpInUnion2) =>
% 122.84/16.23 ((
% 122.84/16.23 (inIntersectImpInIntersectUnions) =>
% 122.84/16.23 ((
% 122.84/16.23 (intersectInPowersetIntersectUnions) =>
% 122.84/16.23 ((
% 122.84/16.23 (inComplementUnionImpNotIn1) =>
% 122.84/16.23 ((
% 122.84/16.23 (inComplementUnionImpInComplement1) =>
% 122.84/16.23 ((
% 122.84/16.23 (binunionTE) =>
% 122.84/16.23 ((
% 122.84/16.23 (binunionTEcontra) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan2a1) =>
% 122.84/16.23 ((
% 122.84/16.23 (complementUnionInPowersetComplement) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan2a2) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan1a) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan1b) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan1) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan2a) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan2b2) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan2b) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan2) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz13rule0) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz13rule1) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz13rule2) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz13rule3) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz13rule4) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz1_1) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz1_2) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz1_3) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz1_4) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz1_5) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1all2) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1SetBreln1) =>
% 122.84/16.23 ((
% 122.84/16.23 (choice2fnsingleton) =>
% 122.84/16.23 ((
% 122.84/16.23 (setOfPairsIsBReln1) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1all1) =>
% 122.84/16.23 ((
% 122.84/16.23 (subbreln1) =>
% 122.84/16.23 ((
% 122.84/16.23 (eqbreln1) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1invprop) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1invI) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1invE) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1compprop) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1compI) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1compE) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1compEex) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1unionprop) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1unionIL) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1unionIR) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1unionI) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1unionE) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1unionEcases) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1unionCommutes) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz2Ex) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz2W) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz2A) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz2B) =>
% 122.84/16.23 ((
% 122.84/16.23 (image1Ex) =>
% 122.84/16.23 ((
% 122.84/16.23 (image1Ex1) =>
% 122.84/16.23 ((
% 122.84/16.23 (image1Equiv) =>
% 122.84/16.23 ((
% 122.84/16.23 (image1E) =>
% 122.84/16.23 ((
% 122.84/16.23 (image1I) =>
% 122.84/16.23 ((
% 122.84/16.23 (injFuncInInjFuncSet) =>
% 122.84/16.23 ((
% 122.84/16.23 (!!) @ (
% 122.84/16.23 (('#B') @ (
% 122.84/16.23 !!) @
% 122.84/16.23 (
% 122.84/16.23 (
% 122.84/16.23 ('#B') @ (
% 122.84/16.23 (
% 122.84/16.23 ('#B') @ (
% 122.84/16.23 !!))) @
% 122.84/16.23 (
% 122.84/16.23 (
% 122.84/16.23 ('#S') @ (
% 122.84/16.23 (
% 122.84/16.23 ('#B') @ (
% 122.84/16.23 '#S') @
% 122.84/16.23 (
% 122.84/16.23 (
% 122.84/16.23 ('#B') @ (
% 122.84/16.23 (
% 122.84/16.23 ('#B') @ (
% 122.84/16.23 '#S'))) @
% 122.84/16.23 (
% 122.84/16.23 (
% 122.84/16.23 ('#B') @ (
% 122.84/16.23 (
% 122.84/16.23 ('#B') @ (
% 122.84/16.23 (
% 122.84/16.23 ('#B') @ (
% 122.84/16.23 =>))))) @
% 122.84/16.23 (
% 122.84/16.23 (
% 122.84/16.23 ('#B') @ (
% 122.84/16.23 (
% 122.84/16.23 ('#B') @ (
% 122.84/16.23 (
% 122.84/16.23 ('#C') @ in)))) @
% 122.84/16.23 injFuncSet)))))))) @
% 122.84/16.23 (
% 122.84/16.23 (
% 122.84/16.23 ('#B') @ (
% 122.84/16.23 (
% 122.84/16.23 ('#B') @ (
% 122.84/16.23 (
% 122.84/16.23 ('#C') @ in)))) @
% 122.84/16.23 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.84/16.23 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2228])).
% 122.84/16.23 thf(zip_derived_cl2261, plain,
% 122.84/16.23 (~ (((iffalseProp1) =>
% 122.84/16.23 (((iffalseProp2) =>
% 122.84/16.23 (((iftrueProp1) =>
% 122.84/16.23 (((iftrueProp2) =>
% 122.84/16.23 (((ifSingleton) =>
% 122.84/16.23 (((ifp) =>
% 122.84/16.23 (((theeq) =>
% 122.84/16.23 (((iftrue) =>
% 122.84/16.23 (((iffalse) =>
% 122.84/16.23 (((iftrueorfalse) =>
% 122.84/16.23 (((binintersectT_lem) =>
% 122.84/16.23 (((binunionT_lem) =>
% 122.84/16.23 (((powersetT_lem) =>
% 122.84/16.23 (((setminusT_lem) =>
% 122.84/16.23 (((complementT_lem) =>
% 122.84/16.23 (((setextT) =>
% 122.84/16.23 (((subsetTI) =>
% 122.84/16.23 (((powersetTI1) =>
% 122.84/16.23 (((powersetTE1) =>
% 122.84/16.23 (((complementTI1) =>
% 122.84/16.23 (((complementTE1) =>
% 122.84/16.23 (((binintersectTELcontra) =>
% 122.84/16.23 (((binintersectTERcontra) =>
% 122.84/16.23 (((contrasubsetT) =>
% 122.84/16.23 (((contrasubsetT1) =>
% 122.84/16.23 (((contrasubsetT2) =>
% 122.84/16.23 (((contrasubsetT3) =>
% 122.84/16.23 (((doubleComplementI1) =>
% 122.84/16.23 (((doubleComplementE1) =>
% 122.84/16.23 (((doubleComplementSub1) =>
% 122.84/16.23 ((
% 122.84/16.23 (doubleComplementSub2) =>
% 122.84/16.23 ((
% 122.84/16.23 (doubleComplementEq) =>
% 122.84/16.23 ((
% 122.84/16.23 (complementTnotintersectT) =>
% 122.84/16.23 ((
% 122.84/16.23 (complementImpComplementIntersect) =>
% 122.84/16.23 ((
% 122.84/16.23 (complementSubsetComplementIntersect) =>
% 122.84/16.23 ((
% 122.84/16.23 (complementInPowersetComplementIntersect) =>
% 122.84/16.23 ((
% 122.84/16.23 (contraSubsetComplement) =>
% 122.84/16.23 ((
% 122.84/16.23 (complementTcontraSubset) =>
% 122.84/16.23 ((
% 122.84/16.23 (binunionTILcontra) =>
% 122.84/16.23 ((
% 122.84/16.23 (binunionTIRcontra) =>
% 122.84/16.23 ((
% 122.84/16.23 (inIntersectImpInUnion) =>
% 122.84/16.23 ((
% 122.84/16.23 (inIntersectImpInUnion2) =>
% 122.84/16.23 ((
% 122.84/16.23 (inIntersectImpInIntersectUnions) =>
% 122.84/16.23 ((
% 122.84/16.23 (intersectInPowersetIntersectUnions) =>
% 122.84/16.23 ((
% 122.84/16.23 (inComplementUnionImpNotIn1) =>
% 122.84/16.23 ((
% 122.84/16.23 (inComplementUnionImpInComplement1) =>
% 122.84/16.23 ((
% 122.84/16.23 (binunionTE) =>
% 122.84/16.23 ((
% 122.84/16.23 (binunionTEcontra) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan2a1) =>
% 122.84/16.23 ((
% 122.84/16.23 (complementUnionInPowersetComplement) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan2a2) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan1a) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan1b) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan1) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan2a) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan2b2) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan2b) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan2) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz13rule0) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz13rule1) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz13rule2) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz13rule3) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz13rule4) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz1_1) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz1_2) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz1_3) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz1_4) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz1_5) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1all2) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1SetBreln1) =>
% 122.84/16.23 ((
% 122.84/16.23 (choice2fnsingleton) =>
% 122.84/16.23 ((
% 122.84/16.23 (setOfPairsIsBReln1) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1all1) =>
% 122.84/16.23 ((
% 122.84/16.23 (subbreln1) =>
% 122.84/16.23 ((
% 122.84/16.23 (eqbreln1) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1invprop) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1invI) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1invE) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1compprop) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1compI) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1compE) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1compEex) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1unionprop) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1unionIL) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1unionIR) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1unionI) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1unionE) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1unionEcases) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1unionCommutes) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz2Ex) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz2W) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz2A) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz2B) =>
% 122.84/16.23 ((
% 122.84/16.23 (image1Ex) =>
% 122.84/16.23 ((
% 122.84/16.23 (image1Ex1) =>
% 122.84/16.23 ((
% 122.84/16.23 (image1Equiv) =>
% 122.84/16.23 ((
% 122.84/16.23 (image1E) =>
% 122.84/16.23 ((
% 122.84/16.23 (image1I) =>
% 122.84/16.23 ((
% 122.84/16.23 (injFuncInInjFuncSet) =>
% 122.84/16.23 ((
% 122.84/16.23 (!!) @ (
% 122.84/16.23 (('#B') @ (
% 122.84/16.23 !!) @
% 122.84/16.23 (
% 122.84/16.23 (
% 122.84/16.23 ('#B') @ (
% 122.84/16.23 (
% 122.84/16.23 ('#B') @ (
% 122.84/16.23 !!))) @
% 122.84/16.23 (
% 122.84/16.23 (
% 122.84/16.23 ('#S') @ (
% 122.84/16.23 (
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% 122.84/16.23 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2244])).
% 122.84/16.23 thf(zip_derived_cl2279, plain,
% 122.84/16.23 (~ (((iffalseProp2) =>
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% 122.84/16.23 (((iftrueProp2) =>
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% 122.84/16.23 (((setminusT_lem) =>
% 122.84/16.23 (((complementT_lem) =>
% 122.84/16.23 (((setextT) =>
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% 122.84/16.23 ((
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% 122.84/16.23 ((
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% 122.84/16.23 ((
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% 122.84/16.23 ((
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% 122.84/16.23 ((
% 122.84/16.23 (inComplementUnionImpNotIn1) =>
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% 122.84/16.23 (inComplementUnionImpInComplement1) =>
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% 122.84/16.23 ((
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% 122.84/16.23 ((
% 122.84/16.23 (complementUnionInPowersetComplement) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan2a2) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan1a) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan1b) =>
% 122.84/16.23 ((
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% 122.84/16.23 ((
% 122.84/16.23 (demorgan2a) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan2b2) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan2b) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan2) =>
% 122.84/16.23 ((
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% 122.84/16.23 ((
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% 122.84/16.23 ((
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% 122.84/16.23 ((
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% 122.84/16.23 ((
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% 122.84/16.23 ((
% 122.84/16.23 (setOfPairsIsBReln1) =>
% 122.84/16.23 ((
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% 122.84/16.23 ((
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% 122.84/16.23 ((
% 122.84/16.23 (eqbreln1) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1invprop) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1invI) =>
% 122.84/16.23 ((
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% 122.84/16.23 ((
% 122.84/16.23 (breln1unionprop) =>
% 122.84/16.23 ((
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% 122.84/16.23 ((
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% 122.84/16.23 ((
% 122.84/16.23 (breln1unionI) =>
% 122.84/16.23 ((
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% 122.84/16.23 (breln1unionEcases) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1unionCommutes) =>
% 122.84/16.23 ((
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% 122.84/16.23 ((
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% 122.84/16.23 ((
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% 122.84/16.23 ((
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% 122.84/16.23 ((
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% 122.84/16.23 ((
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% 122.84/16.23 (
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% 122.84/16.23 (
% 122.84/16.23 ('#B') @ (
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% 122.84/16.23 (
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% 122.84/16.23 ('#B') @ (
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% 122.84/16.23 (
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% 122.84/16.23 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.84/16.23 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2261])).
% 122.84/16.23 thf(zip_derived_cl2299, plain,
% 122.84/16.23 (~ (((iftrueProp1) =>
% 122.84/16.23 (((iftrueProp2) =>
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% 122.84/16.23 (((ifp) =>
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% 122.84/16.23 (((powersetT_lem) =>
% 122.84/16.23 (((setminusT_lem) =>
% 122.84/16.23 (((complementT_lem) =>
% 122.84/16.23 (((setextT) =>
% 122.84/16.23 (((subsetTI) =>
% 122.84/16.23 (((powersetTI1) =>
% 122.84/16.23 (((powersetTE1) =>
% 122.84/16.23 (((complementTI1) =>
% 122.84/16.23 (((complementTE1) =>
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% 122.84/16.23 (((binintersectTERcontra) =>
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% 122.84/16.23 (((contrasubsetT1) =>
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% 122.84/16.23 (((contrasubsetT3) =>
% 122.84/16.23 (((doubleComplementI1) =>
% 122.84/16.23 (((doubleComplementE1) =>
% 122.84/16.23 (((doubleComplementSub1) =>
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% 122.84/16.23 (((doubleComplementEq) =>
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% 122.84/16.23 ((
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% 122.84/16.23 ((
% 122.84/16.23 (complementSubsetComplementIntersect) =>
% 122.84/16.23 ((
% 122.84/16.23 (complementInPowersetComplementIntersect) =>
% 122.84/16.23 ((
% 122.84/16.23 (contraSubsetComplement) =>
% 122.84/16.23 ((
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% 122.84/16.23 ((
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% 122.84/16.23 ((
% 122.84/16.23 (binunionTIRcontra) =>
% 122.84/16.23 ((
% 122.84/16.23 (inIntersectImpInUnion) =>
% 122.84/16.23 ((
% 122.84/16.23 (inIntersectImpInUnion2) =>
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% 122.84/16.23 ((
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% 122.84/16.23 ((
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% 122.84/16.23 ((
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% 122.84/16.23 ((
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% 122.84/16.23 ((
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% 122.84/16.23 ((
% 122.84/16.23 (demorgan2b) =>
% 122.84/16.23 ((
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% 122.84/16.23 ((
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% 122.84/16.23 ((
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% 122.84/16.23 ((
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% 122.84/16.23 ((
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% 122.84/16.23 ((
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% 122.84/16.23 ((
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% 122.84/16.23 ((
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% 122.84/16.23 ((
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% 122.84/16.23 ((
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% 122.84/16.23 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2279])).
% 122.84/16.23 thf(zip_derived_cl2321, plain,
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% 122.84/16.23 ((
% 122.84/16.23 (complementSubsetComplementIntersect) =>
% 122.84/16.23 ((
% 122.84/16.23 (complementInPowersetComplementIntersect) =>
% 122.84/16.23 ((
% 122.84/16.23 (contraSubsetComplement) =>
% 122.84/16.23 ((
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% 122.84/16.23 ((
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% 122.84/16.23 ((
% 122.84/16.23 (inIntersectImpInUnion2) =>
% 122.84/16.23 ((
% 122.84/16.23 (inIntersectImpInIntersectUnions) =>
% 122.84/16.23 ((
% 122.84/16.23 (intersectInPowersetIntersectUnions) =>
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% 122.84/16.23 (inComplementUnionImpNotIn1) =>
% 122.84/16.23 ((
% 122.84/16.23 (inComplementUnionImpInComplement1) =>
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% 122.84/16.23 ((
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% 122.84/16.23 ((
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% 122.84/16.23 ((
% 122.84/16.23 (complementUnionInPowersetComplement) =>
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% 122.84/16.23 ((
% 122.84/16.23 (demorgan1a) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan1b) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan1) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan2a) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan2b2) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan2b) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan2) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz13rule0) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz13rule1) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz13rule2) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz13rule3) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz13rule4) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz1_1) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz1_2) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz1_3) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz1_4) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz1_5) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1all2) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1SetBreln1) =>
% 122.84/16.23 ((
% 122.84/16.23 (choice2fnsingleton) =>
% 122.84/16.23 ((
% 122.84/16.23 (setOfPairsIsBReln1) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1all1) =>
% 122.84/16.23 ((
% 122.84/16.23 (subbreln1) =>
% 122.84/16.23 ((
% 122.84/16.23 (eqbreln1) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1invprop) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1invI) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1invE) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1compprop) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1compI) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1compE) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1compEex) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1unionprop) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1unionIL) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1unionIR) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1unionI) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1unionE) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1unionEcases) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1unionCommutes) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz2Ex) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz2W) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz2A) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz2B) =>
% 122.84/16.23 ((
% 122.84/16.23 (image1Ex) =>
% 122.84/16.23 ((
% 122.84/16.23 (image1Ex1) =>
% 122.84/16.23 ((
% 122.84/16.23 (image1Equiv) =>
% 122.84/16.23 ((
% 122.84/16.23 (image1E) =>
% 122.84/16.23 ((
% 122.84/16.23 (image1I) =>
% 122.84/16.23 ((
% 122.84/16.23 (injFuncInInjFuncSet) =>
% 122.84/16.23 ((
% 122.84/16.23 (!!) @ (
% 122.84/16.23 (('#B') @ (
% 122.84/16.23 !!) @
% 122.84/16.23 (
% 122.84/16.23 (
% 122.84/16.23 ('#B') @ (
% 122.84/16.23 (
% 122.84/16.23 ('#B') @ (
% 122.84/16.23 !!))) @
% 122.84/16.23 (
% 122.84/16.23 (
% 122.84/16.23 ('#S') @ (
% 122.84/16.23 (
% 122.84/16.23 ('#B') @ (
% 122.84/16.23 '#S') @
% 122.84/16.23 (
% 122.84/16.23 (
% 122.84/16.23 ('#B') @ (
% 122.84/16.23 (
% 122.84/16.23 ('#B') @ (
% 122.84/16.23 '#S'))) @
% 122.84/16.23 (
% 122.84/16.23 (
% 122.84/16.23 ('#B') @ (
% 122.84/16.23 (
% 122.84/16.23 ('#B') @ (
% 122.84/16.23 (
% 122.84/16.23 ('#B') @ (
% 122.84/16.23 =>))))) @
% 122.84/16.23 (
% 122.84/16.23 (
% 122.84/16.23 ('#B') @ (
% 122.84/16.23 (
% 122.84/16.23 ('#B') @ (
% 122.84/16.23 (
% 122.84/16.23 ('#C') @ in)))) @
% 122.84/16.23 injFuncSet)))))))) @
% 122.84/16.23 (
% 122.84/16.23 (
% 122.84/16.23 ('#B') @ (
% 122.84/16.23 (
% 122.84/16.23 ('#B') @ (
% 122.84/16.23 (
% 122.84/16.23 ('#C') @ in)))) @
% 122.84/16.23 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.84/16.23 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2299])).
% 122.84/16.23 thf(zip_derived_cl2337, plain,
% 122.84/16.23 (~ (((ifSingleton) =>
% 122.84/16.23 (((ifp) =>
% 122.84/16.23 (((theeq) =>
% 122.84/16.23 (((iftrue) =>
% 122.84/16.23 (((iffalse) =>
% 122.84/16.23 (((iftrueorfalse) =>
% 122.84/16.23 (((binintersectT_lem) =>
% 122.84/16.23 (((binunionT_lem) =>
% 122.84/16.23 (((powersetT_lem) =>
% 122.84/16.23 (((setminusT_lem) =>
% 122.84/16.23 (((complementT_lem) =>
% 122.84/16.23 (((setextT) =>
% 122.84/16.23 (((subsetTI) =>
% 122.84/16.23 (((powersetTI1) =>
% 122.84/16.23 (((powersetTE1) =>
% 122.84/16.23 (((complementTI1) =>
% 122.84/16.23 (((complementTE1) =>
% 122.84/16.23 (((binintersectTELcontra) =>
% 122.84/16.23 (((binintersectTERcontra) =>
% 122.84/16.23 (((contrasubsetT) =>
% 122.84/16.23 (((contrasubsetT1) =>
% 122.84/16.23 (((contrasubsetT2) =>
% 122.84/16.23 (((contrasubsetT3) =>
% 122.84/16.23 (((doubleComplementI1) =>
% 122.84/16.23 (((doubleComplementE1) =>
% 122.84/16.23 (((doubleComplementSub1) =>
% 122.84/16.23 (((doubleComplementSub2) =>
% 122.84/16.23 (((doubleComplementEq) =>
% 122.84/16.23 (((complementTnotintersectT) =>
% 122.84/16.23 (((complementImpComplementIntersect) =>
% 122.84/16.23 ((
% 122.84/16.23 (complementSubsetComplementIntersect) =>
% 122.84/16.23 ((
% 122.84/16.23 (complementInPowersetComplementIntersect) =>
% 122.84/16.23 ((
% 122.84/16.23 (contraSubsetComplement) =>
% 122.84/16.23 ((
% 122.84/16.23 (complementTcontraSubset) =>
% 122.84/16.23 ((
% 122.84/16.23 (binunionTILcontra) =>
% 122.84/16.23 ((
% 122.84/16.23 (binunionTIRcontra) =>
% 122.84/16.23 ((
% 122.84/16.23 (inIntersectImpInUnion) =>
% 122.84/16.23 ((
% 122.84/16.23 (inIntersectImpInUnion2) =>
% 122.84/16.23 ((
% 122.84/16.23 (inIntersectImpInIntersectUnions) =>
% 122.84/16.23 ((
% 122.84/16.23 (intersectInPowersetIntersectUnions) =>
% 122.84/16.23 ((
% 122.84/16.23 (inComplementUnionImpNotIn1) =>
% 122.84/16.23 ((
% 122.84/16.23 (inComplementUnionImpInComplement1) =>
% 122.84/16.23 ((
% 122.84/16.23 (binunionTE) =>
% 122.84/16.23 ((
% 122.84/16.23 (binunionTEcontra) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan2a1) =>
% 122.84/16.23 ((
% 122.84/16.23 (complementUnionInPowersetComplement) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan2a2) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan1a) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan1b) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan1) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan2a) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan2b2) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan2b) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan2) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz13rule0) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz13rule1) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz13rule2) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz13rule3) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz13rule4) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz1_1) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz1_2) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz1_3) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz1_4) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz1_5) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1all2) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1SetBreln1) =>
% 122.84/16.23 ((
% 122.84/16.23 (choice2fnsingleton) =>
% 122.84/16.23 ((
% 122.84/16.23 (setOfPairsIsBReln1) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1all1) =>
% 122.84/16.23 ((
% 122.84/16.23 (subbreln1) =>
% 122.84/16.23 ((
% 122.84/16.23 (eqbreln1) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1invprop) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1invI) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1invE) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1compprop) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1compI) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1compE) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1compEex) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1unionprop) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1unionIL) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1unionIR) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1unionI) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1unionE) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1unionEcases) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1unionCommutes) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz2Ex) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz2W) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz2A) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz2B) =>
% 122.84/16.23 ((
% 122.84/16.23 (image1Ex) =>
% 122.84/16.23 ((
% 122.84/16.23 (image1Ex1) =>
% 122.84/16.23 ((
% 122.84/16.23 (image1Equiv) =>
% 122.84/16.23 ((
% 122.84/16.23 (image1E) =>
% 122.84/16.23 ((
% 122.84/16.23 (image1I) =>
% 122.84/16.23 ((
% 122.84/16.23 (injFuncInInjFuncSet) =>
% 122.84/16.23 ((
% 122.84/16.23 (!!) @ (
% 122.84/16.23 (('#B') @ (
% 122.84/16.23 !!) @
% 122.84/16.23 (
% 122.84/16.23 (
% 122.84/16.23 ('#B') @ (
% 122.84/16.23 (
% 122.84/16.23 ('#B') @ (
% 122.84/16.23 !!))) @
% 122.84/16.23 (
% 122.84/16.23 (
% 122.84/16.23 ('#S') @ (
% 122.84/16.23 (
% 122.84/16.23 ('#B') @ (
% 122.84/16.23 '#S') @
% 122.84/16.23 (
% 122.84/16.23 (
% 122.84/16.23 ('#B') @ (
% 122.84/16.23 (
% 122.84/16.23 ('#B') @ (
% 122.84/16.23 '#S'))) @
% 122.84/16.23 (
% 122.84/16.23 (
% 122.84/16.23 ('#B') @ (
% 122.84/16.23 (
% 122.84/16.23 ('#B') @ (
% 122.84/16.23 (
% 122.84/16.23 ('#B') @ (
% 122.84/16.23 =>))))) @
% 122.84/16.23 (
% 122.84/16.23 (
% 122.84/16.23 ('#B') @ (
% 122.84/16.23 (
% 122.84/16.23 ('#B') @ (
% 122.84/16.23 (
% 122.84/16.23 ('#C') @ in)))) @
% 122.84/16.23 injFuncSet)))))))) @
% 122.84/16.23 (
% 122.84/16.23 (
% 122.84/16.23 ('#B') @ (
% 122.84/16.23 (
% 122.84/16.23 ('#B') @ (
% 122.84/16.23 (
% 122.84/16.23 ('#C') @ in)))) @
% 122.84/16.23 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.84/16.23 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2321])).
% 122.84/16.23 thf(zip_derived_cl2353, plain,
% 122.84/16.23 (~ (((ifp) =>
% 122.84/16.23 (((theeq) =>
% 122.84/16.23 (((iftrue) =>
% 122.84/16.23 (((iffalse) =>
% 122.84/16.23 (((iftrueorfalse) =>
% 122.84/16.23 (((binintersectT_lem) =>
% 122.84/16.23 (((binunionT_lem) =>
% 122.84/16.23 (((powersetT_lem) =>
% 122.84/16.23 (((setminusT_lem) =>
% 122.84/16.23 (((complementT_lem) =>
% 122.84/16.23 (((setextT) =>
% 122.84/16.23 (((subsetTI) =>
% 122.84/16.23 (((powersetTI1) =>
% 122.84/16.23 (((powersetTE1) =>
% 122.84/16.23 (((complementTI1) =>
% 122.84/16.23 (((complementTE1) =>
% 122.84/16.23 (((binintersectTELcontra) =>
% 122.84/16.23 (((binintersectTERcontra) =>
% 122.84/16.23 (((contrasubsetT) =>
% 122.84/16.23 (((contrasubsetT1) =>
% 122.84/16.23 (((contrasubsetT2) =>
% 122.84/16.23 (((contrasubsetT3) =>
% 122.84/16.23 (((doubleComplementI1) =>
% 122.84/16.23 (((doubleComplementE1) =>
% 122.84/16.23 (((doubleComplementSub1) =>
% 122.84/16.23 (((doubleComplementSub2) =>
% 122.84/16.23 (((doubleComplementEq) =>
% 122.84/16.23 (((complementTnotintersectT) =>
% 122.84/16.23 (((complementImpComplementIntersect) =>
% 122.84/16.23 (((complementSubsetComplementIntersect) =>
% 122.84/16.23 ((
% 122.84/16.23 (complementInPowersetComplementIntersect) =>
% 122.84/16.23 ((
% 122.84/16.23 (contraSubsetComplement) =>
% 122.84/16.23 ((
% 122.84/16.23 (complementTcontraSubset) =>
% 122.84/16.23 ((
% 122.84/16.23 (binunionTILcontra) =>
% 122.84/16.23 ((
% 122.84/16.23 (binunionTIRcontra) =>
% 122.84/16.23 ((
% 122.84/16.23 (inIntersectImpInUnion) =>
% 122.84/16.23 ((
% 122.84/16.23 (inIntersectImpInUnion2) =>
% 122.84/16.23 ((
% 122.84/16.23 (inIntersectImpInIntersectUnions) =>
% 122.84/16.23 ((
% 122.84/16.23 (intersectInPowersetIntersectUnions) =>
% 122.84/16.23 ((
% 122.84/16.23 (inComplementUnionImpNotIn1) =>
% 122.84/16.23 ((
% 122.84/16.23 (inComplementUnionImpInComplement1) =>
% 122.84/16.23 ((
% 122.84/16.23 (binunionTE) =>
% 122.84/16.23 ((
% 122.84/16.23 (binunionTEcontra) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan2a1) =>
% 122.84/16.23 ((
% 122.84/16.23 (complementUnionInPowersetComplement) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan2a2) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan1a) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan1b) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan1) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan2a) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan2b2) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan2b) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan2) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz13rule0) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz13rule1) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz13rule2) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz13rule3) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz13rule4) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz1_1) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz1_2) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz1_3) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz1_4) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz1_5) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1all2) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1SetBreln1) =>
% 122.84/16.23 ((
% 122.84/16.23 (choice2fnsingleton) =>
% 122.84/16.23 ((
% 122.84/16.23 (setOfPairsIsBReln1) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1all1) =>
% 122.84/16.23 ((
% 122.84/16.23 (subbreln1) =>
% 122.84/16.23 ((
% 122.84/16.23 (eqbreln1) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1invprop) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1invI) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1invE) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1compprop) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1compI) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1compE) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1compEex) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1unionprop) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1unionIL) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1unionIR) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1unionI) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1unionE) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1unionEcases) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1unionCommutes) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz2Ex) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz2W) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz2A) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz2B) =>
% 122.84/16.23 ((
% 122.84/16.23 (image1Ex) =>
% 122.84/16.23 ((
% 122.84/16.23 (image1Ex1) =>
% 122.84/16.23 ((
% 122.84/16.23 (image1Equiv) =>
% 122.84/16.23 ((
% 122.84/16.23 (image1E) =>
% 122.84/16.23 ((
% 122.84/16.23 (image1I) =>
% 122.84/16.23 ((
% 122.84/16.23 (injFuncInInjFuncSet) =>
% 122.84/16.23 ((
% 122.84/16.23 (!!) @ (
% 122.84/16.23 (('#B') @ (
% 122.84/16.23 !!) @
% 122.84/16.23 (
% 122.84/16.23 (
% 122.84/16.23 ('#B') @ (
% 122.84/16.23 (
% 122.84/16.23 ('#B') @ (
% 122.84/16.23 !!))) @
% 122.84/16.23 (
% 122.84/16.23 (
% 122.84/16.23 ('#S') @ (
% 122.84/16.23 (
% 122.84/16.23 ('#B') @ (
% 122.84/16.23 '#S') @
% 122.84/16.23 (
% 122.84/16.23 (
% 122.84/16.23 ('#B') @ (
% 122.84/16.23 (
% 122.84/16.23 ('#B') @ (
% 122.84/16.23 '#S'))) @
% 122.84/16.23 (
% 122.84/16.23 (
% 122.84/16.23 ('#B') @ (
% 122.84/16.23 (
% 122.84/16.23 ('#B') @ (
% 122.84/16.23 (
% 122.84/16.23 ('#B') @ (
% 122.84/16.23 =>))))) @
% 122.84/16.23 (
% 122.84/16.23 (
% 122.84/16.23 ('#B') @ (
% 122.84/16.23 (
% 122.84/16.23 ('#B') @ (
% 122.84/16.23 (
% 122.84/16.23 ('#C') @ in)))) @
% 122.84/16.23 injFuncSet)))))))) @
% 122.84/16.23 (
% 122.84/16.23 (
% 122.84/16.23 ('#B') @ (
% 122.84/16.23 (
% 122.84/16.23 ('#B') @ (
% 122.84/16.23 (
% 122.84/16.23 ('#C') @ in)))) @
% 122.84/16.23 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.84/16.23 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2337])).
% 122.84/16.23 thf(zip_derived_cl2374, plain,
% 122.84/16.23 (~ (((theeq) =>
% 122.84/16.23 (((iftrue) =>
% 122.84/16.23 (((iffalse) =>
% 122.84/16.23 (((iftrueorfalse) =>
% 122.84/16.23 (((binintersectT_lem) =>
% 122.84/16.23 (((binunionT_lem) =>
% 122.84/16.23 (((powersetT_lem) =>
% 122.84/16.23 (((setminusT_lem) =>
% 122.84/16.23 (((complementT_lem) =>
% 122.84/16.23 (((setextT) =>
% 122.84/16.23 (((subsetTI) =>
% 122.84/16.23 (((powersetTI1) =>
% 122.84/16.23 (((powersetTE1) =>
% 122.84/16.23 (((complementTI1) =>
% 122.84/16.23 (((complementTE1) =>
% 122.84/16.23 (((binintersectTELcontra) =>
% 122.84/16.23 (((binintersectTERcontra) =>
% 122.84/16.23 (((contrasubsetT) =>
% 122.84/16.23 (((contrasubsetT1) =>
% 122.84/16.23 (((contrasubsetT2) =>
% 122.84/16.23 (((contrasubsetT3) =>
% 122.84/16.23 (((doubleComplementI1) =>
% 122.84/16.23 (((doubleComplementE1) =>
% 122.84/16.23 (((doubleComplementSub1) =>
% 122.84/16.23 (((doubleComplementSub2) =>
% 122.84/16.23 (((doubleComplementEq) =>
% 122.84/16.23 (((complementTnotintersectT) =>
% 122.84/16.23 (((complementImpComplementIntersect) =>
% 122.84/16.23 (((complementSubsetComplementIntersect) =>
% 122.84/16.23 (((complementInPowersetComplementIntersect) =>
% 122.84/16.23 ((
% 122.84/16.23 (contraSubsetComplement) =>
% 122.84/16.23 ((
% 122.84/16.23 (complementTcontraSubset) =>
% 122.84/16.23 ((
% 122.84/16.23 (binunionTILcontra) =>
% 122.84/16.23 ((
% 122.84/16.23 (binunionTIRcontra) =>
% 122.84/16.23 ((
% 122.84/16.23 (inIntersectImpInUnion) =>
% 122.84/16.23 ((
% 122.84/16.23 (inIntersectImpInUnion2) =>
% 122.84/16.23 ((
% 122.84/16.23 (inIntersectImpInIntersectUnions) =>
% 122.84/16.23 ((
% 122.84/16.23 (intersectInPowersetIntersectUnions) =>
% 122.84/16.23 ((
% 122.84/16.23 (inComplementUnionImpNotIn1) =>
% 122.84/16.23 ((
% 122.84/16.23 (inComplementUnionImpInComplement1) =>
% 122.84/16.23 ((
% 122.84/16.23 (binunionTE) =>
% 122.84/16.23 ((
% 122.84/16.23 (binunionTEcontra) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan2a1) =>
% 122.84/16.23 ((
% 122.84/16.23 (complementUnionInPowersetComplement) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan2a2) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan1a) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan1b) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan1) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan2a) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan2b2) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan2b) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan2) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz13rule0) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz13rule1) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz13rule2) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz13rule3) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz13rule4) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz1_1) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz1_2) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz1_3) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz1_4) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz1_5) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1all2) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1SetBreln1) =>
% 122.84/16.23 ((
% 122.84/16.23 (choice2fnsingleton) =>
% 122.84/16.23 ((
% 122.84/16.23 (setOfPairsIsBReln1) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1all1) =>
% 122.84/16.23 ((
% 122.84/16.23 (subbreln1) =>
% 122.84/16.23 ((
% 122.84/16.23 (eqbreln1) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1invprop) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1invI) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1invE) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1compprop) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1compI) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1compE) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1compEex) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1unionprop) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1unionIL) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1unionIR) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1unionI) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1unionE) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1unionEcases) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1unionCommutes) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz2Ex) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz2W) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz2A) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz2B) =>
% 122.84/16.23 ((
% 122.84/16.23 (image1Ex) =>
% 122.84/16.23 ((
% 122.84/16.23 (image1Ex1) =>
% 122.84/16.23 ((
% 122.84/16.23 (image1Equiv) =>
% 122.84/16.23 ((
% 122.84/16.23 (image1E) =>
% 122.84/16.23 ((
% 122.84/16.23 (image1I) =>
% 122.84/16.23 ((
% 122.84/16.23 (injFuncInInjFuncSet) =>
% 122.84/16.23 ((
% 122.84/16.23 (!!) @ (
% 122.84/16.23 (('#B') @ (
% 122.84/16.23 !!) @
% 122.84/16.23 (
% 122.84/16.23 (
% 122.84/16.23 ('#B') @ (
% 122.84/16.23 (
% 122.84/16.23 ('#B') @ (
% 122.84/16.23 !!))) @
% 122.84/16.23 (
% 122.84/16.23 (
% 122.84/16.23 ('#S') @ (
% 122.84/16.23 (
% 122.84/16.23 ('#B') @ (
% 122.84/16.23 '#S') @
% 122.84/16.23 (
% 122.84/16.23 (
% 122.84/16.23 ('#B') @ (
% 122.84/16.23 (
% 122.84/16.23 ('#B') @ (
% 122.84/16.23 '#S'))) @
% 122.84/16.23 (
% 122.84/16.23 (
% 122.84/16.23 ('#B') @ (
% 122.84/16.23 (
% 122.84/16.23 ('#B') @ (
% 122.84/16.23 (
% 122.84/16.23 ('#B') @ (
% 122.84/16.23 =>))))) @
% 122.84/16.23 (
% 122.84/16.23 (
% 122.84/16.23 ('#B') @ (
% 122.84/16.23 (
% 122.84/16.23 ('#B') @ (
% 122.84/16.23 (
% 122.84/16.23 ('#C') @ in)))) @
% 122.84/16.23 injFuncSet)))))))) @
% 122.84/16.23 (
% 122.84/16.23 (
% 122.84/16.23 ('#B') @ (
% 122.84/16.23 (
% 122.84/16.23 ('#B') @ (
% 122.84/16.23 (
% 122.84/16.23 ('#C') @ in)))) @
% 122.84/16.23 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.84/16.23 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2353])).
% 122.84/16.23 thf(zip_derived_cl2392, plain,
% 122.84/16.23 (~ (((iftrue) =>
% 122.84/16.23 (((iffalse) =>
% 122.84/16.23 (((iftrueorfalse) =>
% 122.84/16.23 (((binintersectT_lem) =>
% 122.84/16.23 (((binunionT_lem) =>
% 122.84/16.23 (((powersetT_lem) =>
% 122.84/16.23 (((setminusT_lem) =>
% 122.84/16.23 (((complementT_lem) =>
% 122.84/16.23 (((setextT) =>
% 122.84/16.23 (((subsetTI) =>
% 122.84/16.23 (((powersetTI1) =>
% 122.84/16.23 (((powersetTE1) =>
% 122.84/16.23 (((complementTI1) =>
% 122.84/16.23 (((complementTE1) =>
% 122.84/16.23 (((binintersectTELcontra) =>
% 122.84/16.23 (((binintersectTERcontra) =>
% 122.84/16.23 (((contrasubsetT) =>
% 122.84/16.23 (((contrasubsetT1) =>
% 122.84/16.23 (((contrasubsetT2) =>
% 122.84/16.23 (((contrasubsetT3) =>
% 122.84/16.23 (((doubleComplementI1) =>
% 122.84/16.23 (((doubleComplementE1) =>
% 122.84/16.23 (((doubleComplementSub1) =>
% 122.84/16.23 (((doubleComplementSub2) =>
% 122.84/16.23 (((doubleComplementEq) =>
% 122.84/16.23 (((complementTnotintersectT) =>
% 122.84/16.23 (((complementImpComplementIntersect) =>
% 122.84/16.23 (((complementSubsetComplementIntersect) =>
% 122.84/16.23 (((complementInPowersetComplementIntersect) =>
% 122.84/16.23 (((contraSubsetComplement) =>
% 122.84/16.23 ((
% 122.84/16.23 (complementTcontraSubset) =>
% 122.84/16.23 ((
% 122.84/16.23 (binunionTILcontra) =>
% 122.84/16.23 ((
% 122.84/16.23 (binunionTIRcontra) =>
% 122.84/16.23 ((
% 122.84/16.23 (inIntersectImpInUnion) =>
% 122.84/16.23 ((
% 122.84/16.23 (inIntersectImpInUnion2) =>
% 122.84/16.23 ((
% 122.84/16.23 (inIntersectImpInIntersectUnions) =>
% 122.84/16.23 ((
% 122.84/16.23 (intersectInPowersetIntersectUnions) =>
% 122.84/16.23 ((
% 122.84/16.23 (inComplementUnionImpNotIn1) =>
% 122.84/16.23 ((
% 122.84/16.23 (inComplementUnionImpInComplement1) =>
% 122.84/16.23 ((
% 122.84/16.23 (binunionTE) =>
% 122.84/16.23 ((
% 122.84/16.23 (binunionTEcontra) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan2a1) =>
% 122.84/16.23 ((
% 122.84/16.23 (complementUnionInPowersetComplement) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan2a2) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan1a) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan1b) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan1) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan2a) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan2b2) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan2b) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan2) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz13rule0) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz13rule1) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz13rule2) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz13rule3) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz13rule4) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz1_1) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz1_2) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz1_3) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz1_4) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz1_5) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1all2) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1SetBreln1) =>
% 122.84/16.23 ((
% 122.84/16.23 (choice2fnsingleton) =>
% 122.84/16.23 ((
% 122.84/16.23 (setOfPairsIsBReln1) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1all1) =>
% 122.84/16.23 ((
% 122.84/16.23 (subbreln1) =>
% 122.84/16.23 ((
% 122.84/16.23 (eqbreln1) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1invprop) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1invI) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1invE) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1compprop) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1compI) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1compE) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1compEex) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1unionprop) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1unionIL) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1unionIR) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1unionI) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1unionE) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1unionEcases) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1unionCommutes) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz2Ex) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz2W) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz2A) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz2B) =>
% 122.84/16.23 ((
% 122.84/16.23 (image1Ex) =>
% 122.84/16.23 ((
% 122.84/16.23 (image1Ex1) =>
% 122.84/16.23 ((
% 122.84/16.23 (image1Equiv) =>
% 122.84/16.23 ((
% 122.84/16.23 (image1E) =>
% 122.84/16.23 ((
% 122.84/16.23 (image1I) =>
% 122.84/16.23 ((
% 122.84/16.23 (injFuncInInjFuncSet) =>
% 122.84/16.23 ((
% 122.84/16.23 (!!) @ (
% 122.84/16.23 (('#B') @ (
% 122.84/16.23 !!) @
% 122.84/16.23 (
% 122.84/16.23 (
% 122.84/16.23 ('#B') @ (
% 122.84/16.23 (
% 122.84/16.23 ('#B') @ (
% 122.84/16.23 !!))) @
% 122.84/16.23 (
% 122.84/16.23 (
% 122.84/16.23 ('#S') @ (
% 122.84/16.23 (
% 122.84/16.23 ('#B') @ (
% 122.84/16.23 '#S') @
% 122.84/16.23 (
% 122.84/16.23 (
% 122.84/16.23 ('#B') @ (
% 122.84/16.23 (
% 122.84/16.23 ('#B') @ (
% 122.84/16.23 '#S'))) @
% 122.84/16.23 (
% 122.84/16.23 (
% 122.84/16.23 ('#B') @ (
% 122.84/16.23 (
% 122.84/16.23 ('#B') @ (
% 122.84/16.23 (
% 122.84/16.23 ('#B') @ (
% 122.84/16.23 =>))))) @
% 122.84/16.23 (
% 122.84/16.23 (
% 122.84/16.23 ('#B') @ (
% 122.84/16.23 (
% 122.84/16.23 ('#B') @ (
% 122.84/16.23 (
% 122.84/16.23 ('#C') @ in)))) @
% 122.84/16.23 injFuncSet)))))))) @
% 122.84/16.23 (
% 122.84/16.23 (
% 122.84/16.23 ('#B') @ (
% 122.84/16.23 (
% 122.84/16.23 ('#B') @ (
% 122.84/16.23 (
% 122.84/16.23 ('#C') @ in)))) @
% 122.84/16.23 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.84/16.23 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2374])).
% 122.84/16.23 thf(zip_derived_cl2408, plain,
% 122.84/16.23 (~ (((iffalse) =>
% 122.84/16.23 (((iftrueorfalse) =>
% 122.84/16.23 (((binintersectT_lem) =>
% 122.84/16.23 (((binunionT_lem) =>
% 122.84/16.23 (((powersetT_lem) =>
% 122.84/16.23 (((setminusT_lem) =>
% 122.84/16.23 (((complementT_lem) =>
% 122.84/16.23 (((setextT) =>
% 122.84/16.23 (((subsetTI) =>
% 122.84/16.23 (((powersetTI1) =>
% 122.84/16.23 (((powersetTE1) =>
% 122.84/16.23 (((complementTI1) =>
% 122.84/16.23 (((complementTE1) =>
% 122.84/16.23 (((binintersectTELcontra) =>
% 122.84/16.23 (((binintersectTERcontra) =>
% 122.84/16.23 (((contrasubsetT) =>
% 122.84/16.23 (((contrasubsetT1) =>
% 122.84/16.23 (((contrasubsetT2) =>
% 122.84/16.23 (((contrasubsetT3) =>
% 122.84/16.23 (((doubleComplementI1) =>
% 122.84/16.23 (((doubleComplementE1) =>
% 122.84/16.23 (((doubleComplementSub1) =>
% 122.84/16.23 (((doubleComplementSub2) =>
% 122.84/16.23 (((doubleComplementEq) =>
% 122.84/16.23 (((complementTnotintersectT) =>
% 122.84/16.23 (((complementImpComplementIntersect) =>
% 122.84/16.23 (((complementSubsetComplementIntersect) =>
% 122.84/16.23 (((complementInPowersetComplementIntersect) =>
% 122.84/16.23 (((contraSubsetComplement) =>
% 122.84/16.23 (((complementTcontraSubset) =>
% 122.84/16.23 ((
% 122.84/16.23 (binunionTILcontra) =>
% 122.84/16.23 ((
% 122.84/16.23 (binunionTIRcontra) =>
% 122.84/16.23 ((
% 122.84/16.23 (inIntersectImpInUnion) =>
% 122.84/16.23 ((
% 122.84/16.23 (inIntersectImpInUnion2) =>
% 122.84/16.23 ((
% 122.84/16.23 (inIntersectImpInIntersectUnions) =>
% 122.84/16.23 ((
% 122.84/16.23 (intersectInPowersetIntersectUnions) =>
% 122.84/16.23 ((
% 122.84/16.23 (inComplementUnionImpNotIn1) =>
% 122.84/16.23 ((
% 122.84/16.23 (inComplementUnionImpInComplement1) =>
% 122.84/16.23 ((
% 122.84/16.23 (binunionTE) =>
% 122.84/16.23 ((
% 122.84/16.23 (binunionTEcontra) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan2a1) =>
% 122.84/16.23 ((
% 122.84/16.23 (complementUnionInPowersetComplement) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan2a2) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan1a) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan1b) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan1) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan2a) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan2b2) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan2b) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan2) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz13rule0) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz13rule1) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz13rule2) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz13rule3) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz13rule4) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz1_1) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz1_2) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz1_3) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz1_4) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz1_5) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1all2) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1SetBreln1) =>
% 122.84/16.23 ((
% 122.84/16.23 (choice2fnsingleton) =>
% 122.84/16.23 ((
% 122.84/16.23 (setOfPairsIsBReln1) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1all1) =>
% 122.84/16.23 ((
% 122.84/16.23 (subbreln1) =>
% 122.84/16.23 ((
% 122.84/16.23 (eqbreln1) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1invprop) =>
% 122.84/16.23 ((
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% 122.84/16.23 ((
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% 122.84/16.23 ((
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% 122.84/16.23 ((
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% 122.84/16.23 (breln1unionCommutes) =>
% 122.84/16.23 ((
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% 122.84/16.23 ((
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% 122.84/16.23 ((
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% 122.84/16.23 ((
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% 122.84/16.23 ((
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% 122.84/16.23 ((
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% 122.84/16.23 ((
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% 122.84/16.23 ((
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% 122.84/16.23 ((
% 122.84/16.23 (demorgan1b) =>
% 122.84/16.23 ((
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% 122.84/16.23 ((
% 122.84/16.23 (demorgan2a) =>
% 122.84/16.23 ((
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% 122.84/16.23 ((
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% 122.84/16.23 ((
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% 122.84/16.23 ((
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% 122.84/16.23 ((
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% 122.84/16.23 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2408])).
% 122.84/16.23 thf(zip_derived_cl2442, plain,
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% 122.84/16.23 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2427])).
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% 122.84/16.23 (inComplementUnionImpNotIn1) =>
% 122.84/16.23 ((
% 122.84/16.23 (inComplementUnionImpInComplement1) =>
% 122.84/16.23 ((
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% 122.84/16.23 ((
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% 122.84/16.23 ((
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% 122.84/16.23 ((
% 122.84/16.23 (complementUnionInPowersetComplement) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan2a2) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan1a) =>
% 122.84/16.23 ((
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% 122.84/16.23 ((
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% 122.84/16.23 ((
% 122.84/16.23 (demorgan2a) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan2b2) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan2b) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan2) =>
% 122.84/16.23 ((
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% 122.84/16.23 ((
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% 122.84/16.23 ((
% 122.84/16.23 (woz13rule2) =>
% 122.84/16.23 ((
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% 122.84/16.23 ((
% 122.84/16.23 (woz13rule4) =>
% 122.84/16.23 ((
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% 122.84/16.23 ((
% 122.84/16.23 (woz1_2) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz1_3) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz1_4) =>
% 122.84/16.23 ((
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% 122.84/16.23 ((
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% 122.84/16.23 ((
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% 122.84/16.23 ((
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% 122.84/16.23 ((
% 122.84/16.23 (setOfPairsIsBReln1) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1all1) =>
% 122.84/16.23 ((
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% 122.84/16.23 ((
% 122.84/16.23 (eqbreln1) =>
% 122.84/16.23 ((
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% 122.84/16.23 ((
% 122.84/16.23 (breln1invI) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1invE) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1compprop) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1compI) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1compE) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1compEex) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1unionprop) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1unionIL) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1unionIR) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1unionI) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1unionE) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1unionEcases) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1unionCommutes) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz2Ex) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz2W) =>
% 122.84/16.23 ((
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% 122.84/16.23 ((
% 122.84/16.23 (woz2B) =>
% 122.84/16.23 ((
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% 122.84/16.23 ((
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% 122.84/16.23 ((
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% 122.84/16.23 ((
% 122.84/16.23 (image1E) =>
% 122.84/16.23 ((
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% 122.84/16.23 ((
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% 122.84/16.23 ((
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% 122.84/16.23 (
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% 122.84/16.23 (
% 122.84/16.23 ('#B') @ (
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% 122.84/16.23 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.84/16.23 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2442])).
% 122.84/16.23 thf(zip_derived_cl2465, plain,
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% 122.84/16.23 (((powersetTE1) =>
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% 122.84/16.23 (((binintersectTERcontra) =>
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% 122.84/16.23 (((doubleComplementSub1) =>
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% 122.84/16.23 (((doubleComplementEq) =>
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% 122.84/16.23 ((
% 122.84/16.23 (intersectInPowersetIntersectUnions) =>
% 122.84/16.23 ((
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% 122.84/16.23 ((
% 122.84/16.23 (inComplementUnionImpInComplement1) =>
% 122.84/16.23 ((
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% 122.84/16.23 ((
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% 122.84/16.23 ((
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% 122.84/16.23 ((
% 122.84/16.23 (complementUnionInPowersetComplement) =>
% 122.84/16.23 ((
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% 122.84/16.23 ((
% 122.84/16.23 (demorgan1a) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan1b) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan1) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan2a) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan2b2) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan2b) =>
% 122.84/16.23 ((
% 122.84/16.23 (demorgan2) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz13rule0) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz13rule1) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz13rule2) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz13rule3) =>
% 122.84/16.23 ((
% 122.84/16.23 (woz13rule4) =>
% 122.84/16.23 ((
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% 122.84/16.23 ((
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% 122.84/16.23 ((
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% 122.84/16.23 ((
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% 122.84/16.23 ((
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% 122.84/16.23 ((
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% 122.84/16.23 ((
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% 122.84/16.23 ((
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% 122.84/16.23 ((
% 122.84/16.23 (breln1all1) =>
% 122.84/16.23 ((
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% 122.84/16.23 ((
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% 122.84/16.23 ((
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% 122.84/16.23 ((
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% 122.84/16.23 ((
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% 122.84/16.23 ((
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% 122.84/16.23 ((
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% 122.84/16.23 ((
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% 122.84/16.23 ((
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% 122.84/16.23 ((
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% 122.84/16.23 ((
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% 122.84/16.23 ((
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% 122.84/16.23 ((
% 122.84/16.23 (breln1unionE) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1unionEcases) =>
% 122.84/16.23 ((
% 122.84/16.23 (breln1unionCommutes) =>
% 122.84/16.23 ((
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% 122.84/16.23 ((
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% 122.84/16.23 ((
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% 122.84/16.23 ((
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% 122.84/16.23 ((
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% 122.84/16.23 ((
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% 122.84/16.23 ((
% 122.84/16.23 (image1E) =>
% 122.84/16.23 ((
% 122.84/16.23 (image1I) =>
% 122.84/16.23 ((
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% 122.84/16.23 ((
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% 122.84/16.23 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2454])).
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% 122.84/16.24 (((doubleComplementE1) =>
% 122.84/16.24 (((doubleComplementSub1) =>
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% 122.84/16.24 (((complementSubsetComplementIntersect) =>
% 122.84/16.24 (((complementInPowersetComplementIntersect) =>
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% 122.84/16.24 ((
% 122.84/16.24 (intersectInPowersetIntersectUnions) =>
% 122.84/16.24 ((
% 122.84/16.24 (inComplementUnionImpNotIn1) =>
% 122.84/16.24 ((
% 122.84/16.24 (inComplementUnionImpInComplement1) =>
% 122.84/16.24 ((
% 122.84/16.24 (binunionTE) =>
% 122.84/16.24 ((
% 122.84/16.24 (binunionTEcontra) =>
% 122.84/16.24 ((
% 122.84/16.24 (demorgan2a1) =>
% 122.84/16.24 ((
% 122.84/16.24 (complementUnionInPowersetComplement) =>
% 122.84/16.24 ((
% 122.84/16.24 (demorgan2a2) =>
% 122.84/16.24 ((
% 122.84/16.24 (demorgan1a) =>
% 122.84/16.24 ((
% 122.84/16.24 (demorgan1b) =>
% 122.84/16.24 ((
% 122.84/16.24 (demorgan1) =>
% 122.84/16.24 ((
% 122.84/16.24 (demorgan2a) =>
% 122.84/16.24 ((
% 122.84/16.24 (demorgan2b2) =>
% 122.84/16.24 ((
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% 122.84/16.24 ((
% 122.84/16.24 (breln1unionIR) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionI) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionE) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionEcases) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionCommutes) =>
% 122.84/16.24 ((
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% 122.84/16.24 ((
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% 122.84/16.24 ((
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% 122.84/16.24 ((
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% 122.84/16.24 ('#C') @ in)))) @
% 122.84/16.24 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.84/16.24 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2465])).
% 122.84/16.24 thf(zip_derived_cl2485, plain,
% 122.84/16.24 (~ (((complementT_lem) =>
% 122.84/16.24 (((setextT) =>
% 122.84/16.24 (((subsetTI) =>
% 122.84/16.24 (((powersetTI1) =>
% 122.84/16.24 (((powersetTE1) =>
% 122.84/16.24 (((complementTI1) =>
% 122.84/16.24 (((complementTE1) =>
% 122.84/16.24 (((binintersectTELcontra) =>
% 122.84/16.24 (((binintersectTERcontra) =>
% 122.84/16.24 (((contrasubsetT) =>
% 122.84/16.24 (((contrasubsetT1) =>
% 122.84/16.24 (((contrasubsetT2) =>
% 122.84/16.24 (((contrasubsetT3) =>
% 122.84/16.24 (((doubleComplementI1) =>
% 122.84/16.24 (((doubleComplementE1) =>
% 122.84/16.24 (((doubleComplementSub1) =>
% 122.84/16.24 (((doubleComplementSub2) =>
% 122.84/16.24 (((doubleComplementEq) =>
% 122.84/16.24 (((complementTnotintersectT) =>
% 122.84/16.24 (((complementImpComplementIntersect) =>
% 122.84/16.24 (((complementSubsetComplementIntersect) =>
% 122.84/16.24 (((complementInPowersetComplementIntersect) =>
% 122.84/16.24 (((contraSubsetComplement) =>
% 122.84/16.24 (((complementTcontraSubset) =>
% 122.84/16.24 (((binunionTILcontra) =>
% 122.84/16.24 (((binunionTIRcontra) =>
% 122.84/16.24 (((inIntersectImpInUnion) =>
% 122.84/16.24 (((inIntersectImpInUnion2) =>
% 122.84/16.24 (((inIntersectImpInIntersectUnions) =>
% 122.84/16.24 (((intersectInPowersetIntersectUnions) =>
% 122.84/16.24 ((
% 122.84/16.24 (inComplementUnionImpNotIn1) =>
% 122.84/16.24 ((
% 122.84/16.24 (inComplementUnionImpInComplement1) =>
% 122.84/16.24 ((
% 122.84/16.24 (binunionTE) =>
% 122.84/16.24 ((
% 122.84/16.24 (binunionTEcontra) =>
% 122.84/16.24 ((
% 122.84/16.24 (demorgan2a1) =>
% 122.84/16.24 ((
% 122.84/16.24 (complementUnionInPowersetComplement) =>
% 122.84/16.24 ((
% 122.84/16.24 (demorgan2a2) =>
% 122.84/16.24 ((
% 122.84/16.24 (demorgan1a) =>
% 122.84/16.24 ((
% 122.84/16.24 (demorgan1b) =>
% 122.84/16.24 ((
% 122.84/16.24 (demorgan1) =>
% 122.84/16.24 ((
% 122.84/16.24 (demorgan2a) =>
% 122.84/16.24 ((
% 122.84/16.24 (demorgan2b2) =>
% 122.84/16.24 ((
% 122.84/16.24 (demorgan2b) =>
% 122.84/16.24 ((
% 122.84/16.24 (demorgan2) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz13rule0) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz13rule1) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz13rule2) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz13rule3) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz13rule4) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz1_1) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz1_2) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz1_3) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz1_4) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz1_5) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1all2) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1SetBreln1) =>
% 122.84/16.24 ((
% 122.84/16.24 (choice2fnsingleton) =>
% 122.84/16.24 ((
% 122.84/16.24 (setOfPairsIsBReln1) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1all1) =>
% 122.84/16.24 ((
% 122.84/16.24 (subbreln1) =>
% 122.84/16.24 ((
% 122.84/16.24 (eqbreln1) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1invprop) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1invI) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1invE) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1compprop) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1compI) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1compE) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1compEex) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionprop) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionIL) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionIR) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionI) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionE) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionEcases) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionCommutes) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz2Ex) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz2W) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz2A) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz2B) =>
% 122.84/16.24 ((
% 122.84/16.24 (image1Ex) =>
% 122.84/16.24 ((
% 122.84/16.24 (image1Ex1) =>
% 122.84/16.24 ((
% 122.84/16.24 (image1Equiv) =>
% 122.84/16.24 ((
% 122.84/16.24 (image1E) =>
% 122.84/16.24 ((
% 122.84/16.24 (image1I) =>
% 122.84/16.24 ((
% 122.84/16.24 (injFuncInInjFuncSet) =>
% 122.84/16.24 ((
% 122.84/16.24 (!!) @ (
% 122.84/16.24 (('#B') @ (
% 122.84/16.24 !!) @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 !!))) @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#S') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 '#S') @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 '#S'))) @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 =>))))) @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#C') @ in)))) @
% 122.84/16.24 injFuncSet)))))))) @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#C') @ in)))) @
% 122.84/16.24 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.84/16.24 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2476])).
% 122.84/16.24 thf(zip_derived_cl2495, plain,
% 122.84/16.24 (~ (((setextT) =>
% 122.84/16.24 (((subsetTI) =>
% 122.84/16.24 (((powersetTI1) =>
% 122.84/16.24 (((powersetTE1) =>
% 122.84/16.24 (((complementTI1) =>
% 122.84/16.24 (((complementTE1) =>
% 122.84/16.24 (((binintersectTELcontra) =>
% 122.84/16.24 (((binintersectTERcontra) =>
% 122.84/16.24 (((contrasubsetT) =>
% 122.84/16.24 (((contrasubsetT1) =>
% 122.84/16.24 (((contrasubsetT2) =>
% 122.84/16.24 (((contrasubsetT3) =>
% 122.84/16.24 (((doubleComplementI1) =>
% 122.84/16.24 (((doubleComplementE1) =>
% 122.84/16.24 (((doubleComplementSub1) =>
% 122.84/16.24 (((doubleComplementSub2) =>
% 122.84/16.24 (((doubleComplementEq) =>
% 122.84/16.24 (((complementTnotintersectT) =>
% 122.84/16.24 (((complementImpComplementIntersect) =>
% 122.84/16.24 (((complementSubsetComplementIntersect) =>
% 122.84/16.24 (((complementInPowersetComplementIntersect) =>
% 122.84/16.24 (((contraSubsetComplement) =>
% 122.84/16.24 (((complementTcontraSubset) =>
% 122.84/16.24 (((binunionTILcontra) =>
% 122.84/16.24 (((binunionTIRcontra) =>
% 122.84/16.24 (((inIntersectImpInUnion) =>
% 122.84/16.24 (((inIntersectImpInUnion2) =>
% 122.84/16.24 (((inIntersectImpInIntersectUnions) =>
% 122.84/16.24 (((intersectInPowersetIntersectUnions) =>
% 122.84/16.24 (((inComplementUnionImpNotIn1) =>
% 122.84/16.24 ((
% 122.84/16.24 (inComplementUnionImpInComplement1) =>
% 122.84/16.24 ((
% 122.84/16.24 (binunionTE) =>
% 122.84/16.24 ((
% 122.84/16.24 (binunionTEcontra) =>
% 122.84/16.24 ((
% 122.84/16.24 (demorgan2a1) =>
% 122.84/16.24 ((
% 122.84/16.24 (complementUnionInPowersetComplement) =>
% 122.84/16.24 ((
% 122.84/16.24 (demorgan2a2) =>
% 122.84/16.24 ((
% 122.84/16.24 (demorgan1a) =>
% 122.84/16.24 ((
% 122.84/16.24 (demorgan1b) =>
% 122.84/16.24 ((
% 122.84/16.24 (demorgan1) =>
% 122.84/16.24 ((
% 122.84/16.24 (demorgan2a) =>
% 122.84/16.24 ((
% 122.84/16.24 (demorgan2b2) =>
% 122.84/16.24 ((
% 122.84/16.24 (demorgan2b) =>
% 122.84/16.24 ((
% 122.84/16.24 (demorgan2) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz13rule0) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz13rule1) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz13rule2) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz13rule3) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz13rule4) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz1_1) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz1_2) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz1_3) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz1_4) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz1_5) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1all2) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1SetBreln1) =>
% 122.84/16.24 ((
% 122.84/16.24 (choice2fnsingleton) =>
% 122.84/16.24 ((
% 122.84/16.24 (setOfPairsIsBReln1) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1all1) =>
% 122.84/16.24 ((
% 122.84/16.24 (subbreln1) =>
% 122.84/16.24 ((
% 122.84/16.24 (eqbreln1) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1invprop) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1invI) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1invE) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1compprop) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1compI) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1compE) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1compEex) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionprop) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionIL) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionIR) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionI) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionE) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionEcases) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionCommutes) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz2Ex) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz2W) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz2A) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz2B) =>
% 122.84/16.24 ((
% 122.84/16.24 (image1Ex) =>
% 122.84/16.24 ((
% 122.84/16.24 (image1Ex1) =>
% 122.84/16.24 ((
% 122.84/16.24 (image1Equiv) =>
% 122.84/16.24 ((
% 122.84/16.24 (image1E) =>
% 122.84/16.24 ((
% 122.84/16.24 (image1I) =>
% 122.84/16.24 ((
% 122.84/16.24 (injFuncInInjFuncSet) =>
% 122.84/16.24 ((
% 122.84/16.24 (!!) @ (
% 122.84/16.24 (('#B') @ (
% 122.84/16.24 !!) @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 !!))) @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#S') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 '#S') @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 '#S'))) @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 =>))))) @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#C') @ in)))) @
% 122.84/16.24 injFuncSet)))))))) @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#C') @ in)))) @
% 122.84/16.24 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.84/16.24 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2485])).
% 122.84/16.24 thf(zip_derived_cl2506, plain,
% 122.84/16.24 (~ (((subsetTI) =>
% 122.84/16.24 (((powersetTI1) =>
% 122.84/16.24 (((powersetTE1) =>
% 122.84/16.24 (((complementTI1) =>
% 122.84/16.24 (((complementTE1) =>
% 122.84/16.24 (((binintersectTELcontra) =>
% 122.84/16.24 (((binintersectTERcontra) =>
% 122.84/16.24 (((contrasubsetT) =>
% 122.84/16.24 (((contrasubsetT1) =>
% 122.84/16.24 (((contrasubsetT2) =>
% 122.84/16.24 (((contrasubsetT3) =>
% 122.84/16.24 (((doubleComplementI1) =>
% 122.84/16.24 (((doubleComplementE1) =>
% 122.84/16.24 (((doubleComplementSub1) =>
% 122.84/16.24 (((doubleComplementSub2) =>
% 122.84/16.24 (((doubleComplementEq) =>
% 122.84/16.24 (((complementTnotintersectT) =>
% 122.84/16.24 (((complementImpComplementIntersect) =>
% 122.84/16.24 (((complementSubsetComplementIntersect) =>
% 122.84/16.24 (((complementInPowersetComplementIntersect) =>
% 122.84/16.24 (((contraSubsetComplement) =>
% 122.84/16.24 (((complementTcontraSubset) =>
% 122.84/16.24 (((binunionTILcontra) =>
% 122.84/16.24 (((binunionTIRcontra) =>
% 122.84/16.24 (((inIntersectImpInUnion) =>
% 122.84/16.24 (((inIntersectImpInUnion2) =>
% 122.84/16.24 (((inIntersectImpInIntersectUnions) =>
% 122.84/16.24 (((intersectInPowersetIntersectUnions) =>
% 122.84/16.24 (((inComplementUnionImpNotIn1) =>
% 122.84/16.24 (((inComplementUnionImpInComplement1) =>
% 122.84/16.24 ((
% 122.84/16.24 (binunionTE) =>
% 122.84/16.24 ((
% 122.84/16.24 (binunionTEcontra) =>
% 122.84/16.24 ((
% 122.84/16.24 (demorgan2a1) =>
% 122.84/16.24 ((
% 122.84/16.24 (complementUnionInPowersetComplement) =>
% 122.84/16.24 ((
% 122.84/16.24 (demorgan2a2) =>
% 122.84/16.24 ((
% 122.84/16.24 (demorgan1a) =>
% 122.84/16.24 ((
% 122.84/16.24 (demorgan1b) =>
% 122.84/16.24 ((
% 122.84/16.24 (demorgan1) =>
% 122.84/16.24 ((
% 122.84/16.24 (demorgan2a) =>
% 122.84/16.24 ((
% 122.84/16.24 (demorgan2b2) =>
% 122.84/16.24 ((
% 122.84/16.24 (demorgan2b) =>
% 122.84/16.24 ((
% 122.84/16.24 (demorgan2) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz13rule0) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz13rule1) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz13rule2) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz13rule3) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz13rule4) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz1_1) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz1_2) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz1_3) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz1_4) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz1_5) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1all2) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1SetBreln1) =>
% 122.84/16.24 ((
% 122.84/16.24 (choice2fnsingleton) =>
% 122.84/16.24 ((
% 122.84/16.24 (setOfPairsIsBReln1) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1all1) =>
% 122.84/16.24 ((
% 122.84/16.24 (subbreln1) =>
% 122.84/16.24 ((
% 122.84/16.24 (eqbreln1) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1invprop) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1invI) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1invE) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1compprop) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1compI) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1compE) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1compEex) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionprop) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionIL) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionIR) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionI) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionE) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionEcases) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionCommutes) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz2Ex) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz2W) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz2A) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz2B) =>
% 122.84/16.24 ((
% 122.84/16.24 (image1Ex) =>
% 122.84/16.24 ((
% 122.84/16.24 (image1Ex1) =>
% 122.84/16.24 ((
% 122.84/16.24 (image1Equiv) =>
% 122.84/16.24 ((
% 122.84/16.24 (image1E) =>
% 122.84/16.24 ((
% 122.84/16.24 (image1I) =>
% 122.84/16.24 ((
% 122.84/16.24 (injFuncInInjFuncSet) =>
% 122.84/16.24 ((
% 122.84/16.24 (!!) @ (
% 122.84/16.24 (('#B') @ (
% 122.84/16.24 !!) @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
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% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#S') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 '#S') @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 '#S'))) @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 =>))))) @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#C') @ in)))) @
% 122.84/16.24 injFuncSet)))))))) @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#C') @ in)))) @
% 122.84/16.24 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.84/16.24 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2495])).
% 122.84/16.24 thf(zip_derived_cl2518, plain,
% 122.84/16.24 (~ (((powersetTI1) =>
% 122.84/16.24 (((powersetTE1) =>
% 122.84/16.24 (((complementTI1) =>
% 122.84/16.24 (((complementTE1) =>
% 122.84/16.24 (((binintersectTELcontra) =>
% 122.84/16.24 (((binintersectTERcontra) =>
% 122.84/16.24 (((contrasubsetT) =>
% 122.84/16.24 (((contrasubsetT1) =>
% 122.84/16.24 (((contrasubsetT2) =>
% 122.84/16.24 (((contrasubsetT3) =>
% 122.84/16.24 (((doubleComplementI1) =>
% 122.84/16.24 (((doubleComplementE1) =>
% 122.84/16.24 (((doubleComplementSub1) =>
% 122.84/16.24 (((doubleComplementSub2) =>
% 122.84/16.24 (((doubleComplementEq) =>
% 122.84/16.24 (((complementTnotintersectT) =>
% 122.84/16.24 (((complementImpComplementIntersect) =>
% 122.84/16.24 (((complementSubsetComplementIntersect) =>
% 122.84/16.24 (((complementInPowersetComplementIntersect) =>
% 122.84/16.24 (((contraSubsetComplement) =>
% 122.84/16.24 (((complementTcontraSubset) =>
% 122.84/16.24 (((binunionTILcontra) =>
% 122.84/16.24 (((binunionTIRcontra) =>
% 122.84/16.24 (((inIntersectImpInUnion) =>
% 122.84/16.24 (((inIntersectImpInUnion2) =>
% 122.84/16.24 (((inIntersectImpInIntersectUnions) =>
% 122.84/16.24 (((intersectInPowersetIntersectUnions) =>
% 122.84/16.24 (((inComplementUnionImpNotIn1) =>
% 122.84/16.24 (((inComplementUnionImpInComplement1) =>
% 122.84/16.24 (((binunionTE) =>
% 122.84/16.24 ((
% 122.84/16.24 (binunionTEcontra) =>
% 122.84/16.24 ((
% 122.84/16.24 (demorgan2a1) =>
% 122.84/16.24 ((
% 122.84/16.24 (complementUnionInPowersetComplement) =>
% 122.84/16.24 ((
% 122.84/16.24 (demorgan2a2) =>
% 122.84/16.24 ((
% 122.84/16.24 (demorgan1a) =>
% 122.84/16.24 ((
% 122.84/16.24 (demorgan1b) =>
% 122.84/16.24 ((
% 122.84/16.24 (demorgan1) =>
% 122.84/16.24 ((
% 122.84/16.24 (demorgan2a) =>
% 122.84/16.24 ((
% 122.84/16.24 (demorgan2b2) =>
% 122.84/16.24 ((
% 122.84/16.24 (demorgan2b) =>
% 122.84/16.24 ((
% 122.84/16.24 (demorgan2) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz13rule0) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz13rule1) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz13rule2) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz13rule3) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz13rule4) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz1_1) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz1_2) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz1_3) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz1_4) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz1_5) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1all2) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1SetBreln1) =>
% 122.84/16.24 ((
% 122.84/16.24 (choice2fnsingleton) =>
% 122.84/16.24 ((
% 122.84/16.24 (setOfPairsIsBReln1) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1all1) =>
% 122.84/16.24 ((
% 122.84/16.24 (subbreln1) =>
% 122.84/16.24 ((
% 122.84/16.24 (eqbreln1) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1invprop) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1invI) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1invE) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1compprop) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1compI) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1compE) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1compEex) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionprop) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionIL) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionIR) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionI) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionE) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionEcases) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionCommutes) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz2Ex) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz2W) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz2A) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz2B) =>
% 122.84/16.24 ((
% 122.84/16.24 (image1Ex) =>
% 122.84/16.24 ((
% 122.84/16.24 (image1Ex1) =>
% 122.84/16.24 ((
% 122.84/16.24 (image1Equiv) =>
% 122.84/16.24 ((
% 122.84/16.24 (image1E) =>
% 122.84/16.24 ((
% 122.84/16.24 (image1I) =>
% 122.84/16.24 ((
% 122.84/16.24 (injFuncInInjFuncSet) =>
% 122.84/16.24 ((
% 122.84/16.24 (!!) @ (
% 122.84/16.24 (('#B') @ (
% 122.84/16.24 !!) @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 !!))) @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#S') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 '#S') @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 '#S'))) @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 =>))))) @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#C') @ in)))) @
% 122.84/16.24 injFuncSet)))))))) @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#C') @ in)))) @
% 122.84/16.24 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.84/16.24 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2506])).
% 122.84/16.24 thf(zip_derived_cl2527, plain,
% 122.84/16.24 (~ (((powersetTE1) =>
% 122.84/16.24 (((complementTI1) =>
% 122.84/16.24 (((complementTE1) =>
% 122.84/16.24 (((binintersectTELcontra) =>
% 122.84/16.24 (((binintersectTERcontra) =>
% 122.84/16.24 (((contrasubsetT) =>
% 122.84/16.24 (((contrasubsetT1) =>
% 122.84/16.24 (((contrasubsetT2) =>
% 122.84/16.24 (((contrasubsetT3) =>
% 122.84/16.24 (((doubleComplementI1) =>
% 122.84/16.24 (((doubleComplementE1) =>
% 122.84/16.24 (((doubleComplementSub1) =>
% 122.84/16.24 (((doubleComplementSub2) =>
% 122.84/16.24 (((doubleComplementEq) =>
% 122.84/16.24 (((complementTnotintersectT) =>
% 122.84/16.24 (((complementImpComplementIntersect) =>
% 122.84/16.24 (((complementSubsetComplementIntersect) =>
% 122.84/16.24 (((complementInPowersetComplementIntersect) =>
% 122.84/16.24 (((contraSubsetComplement) =>
% 122.84/16.24 (((complementTcontraSubset) =>
% 122.84/16.24 (((binunionTILcontra) =>
% 122.84/16.24 (((binunionTIRcontra) =>
% 122.84/16.24 (((inIntersectImpInUnion) =>
% 122.84/16.24 (((inIntersectImpInUnion2) =>
% 122.84/16.24 (((inIntersectImpInIntersectUnions) =>
% 122.84/16.24 (((intersectInPowersetIntersectUnions) =>
% 122.84/16.24 (((inComplementUnionImpNotIn1) =>
% 122.84/16.24 (((inComplementUnionImpInComplement1) =>
% 122.84/16.24 (((binunionTE) =>
% 122.84/16.24 (((binunionTEcontra) =>
% 122.84/16.24 ((
% 122.84/16.24 (demorgan2a1) =>
% 122.84/16.24 ((
% 122.84/16.24 (complementUnionInPowersetComplement) =>
% 122.84/16.24 ((
% 122.84/16.24 (demorgan2a2) =>
% 122.84/16.24 ((
% 122.84/16.24 (demorgan1a) =>
% 122.84/16.24 ((
% 122.84/16.24 (demorgan1b) =>
% 122.84/16.24 ((
% 122.84/16.24 (demorgan1) =>
% 122.84/16.24 ((
% 122.84/16.24 (demorgan2a) =>
% 122.84/16.24 ((
% 122.84/16.24 (demorgan2b2) =>
% 122.84/16.24 ((
% 122.84/16.24 (demorgan2b) =>
% 122.84/16.24 ((
% 122.84/16.24 (demorgan2) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz13rule0) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz13rule1) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz13rule2) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz13rule3) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz13rule4) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz1_1) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz1_2) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz1_3) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz1_4) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz1_5) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1all2) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1SetBreln1) =>
% 122.84/16.24 ((
% 122.84/16.24 (choice2fnsingleton) =>
% 122.84/16.24 ((
% 122.84/16.24 (setOfPairsIsBReln1) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1all1) =>
% 122.84/16.24 ((
% 122.84/16.24 (subbreln1) =>
% 122.84/16.24 ((
% 122.84/16.24 (eqbreln1) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1invprop) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1invI) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1invE) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1compprop) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1compI) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1compE) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1compEex) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionprop) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionIL) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionIR) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionI) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionE) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionEcases) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionCommutes) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz2Ex) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz2W) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz2A) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz2B) =>
% 122.84/16.24 ((
% 122.84/16.24 (image1Ex) =>
% 122.84/16.24 ((
% 122.84/16.24 (image1Ex1) =>
% 122.84/16.24 ((
% 122.84/16.24 (image1Equiv) =>
% 122.84/16.24 ((
% 122.84/16.24 (image1E) =>
% 122.84/16.24 ((
% 122.84/16.24 (image1I) =>
% 122.84/16.24 ((
% 122.84/16.24 (injFuncInInjFuncSet) =>
% 122.84/16.24 ((
% 122.84/16.24 (!!) @ (
% 122.84/16.24 (('#B') @ (
% 122.84/16.24 !!) @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 !!))) @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#S') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 '#S') @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 '#S'))) @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 =>))))) @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#C') @ in)))) @
% 122.84/16.24 injFuncSet)))))))) @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#C') @ in)))) @
% 122.84/16.24 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.84/16.24 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2518])).
% 122.84/16.24 thf(zip_derived_cl2535, plain,
% 122.84/16.24 (~ (((complementTI1) =>
% 122.84/16.24 (((complementTE1) =>
% 122.84/16.24 (((binintersectTELcontra) =>
% 122.84/16.24 (((binintersectTERcontra) =>
% 122.84/16.24 (((contrasubsetT) =>
% 122.84/16.24 (((contrasubsetT1) =>
% 122.84/16.24 (((contrasubsetT2) =>
% 122.84/16.24 (((contrasubsetT3) =>
% 122.84/16.24 (((doubleComplementI1) =>
% 122.84/16.24 (((doubleComplementE1) =>
% 122.84/16.24 (((doubleComplementSub1) =>
% 122.84/16.24 (((doubleComplementSub2) =>
% 122.84/16.24 (((doubleComplementEq) =>
% 122.84/16.24 (((complementTnotintersectT) =>
% 122.84/16.24 (((complementImpComplementIntersect) =>
% 122.84/16.24 (((complementSubsetComplementIntersect) =>
% 122.84/16.24 (((complementInPowersetComplementIntersect) =>
% 122.84/16.24 (((contraSubsetComplement) =>
% 122.84/16.24 (((complementTcontraSubset) =>
% 122.84/16.24 (((binunionTILcontra) =>
% 122.84/16.24 (((binunionTIRcontra) =>
% 122.84/16.24 (((inIntersectImpInUnion) =>
% 122.84/16.24 (((inIntersectImpInUnion2) =>
% 122.84/16.24 (((inIntersectImpInIntersectUnions) =>
% 122.84/16.24 (((intersectInPowersetIntersectUnions) =>
% 122.84/16.24 (((inComplementUnionImpNotIn1) =>
% 122.84/16.24 (((inComplementUnionImpInComplement1) =>
% 122.84/16.24 (((binunionTE) =>
% 122.84/16.24 (((binunionTEcontra) =>
% 122.84/16.24 (((demorgan2a1) =>
% 122.84/16.24 ((
% 122.84/16.24 (complementUnionInPowersetComplement) =>
% 122.84/16.24 ((
% 122.84/16.24 (demorgan2a2) =>
% 122.84/16.24 ((
% 122.84/16.24 (demorgan1a) =>
% 122.84/16.24 ((
% 122.84/16.24 (demorgan1b) =>
% 122.84/16.24 ((
% 122.84/16.24 (demorgan1) =>
% 122.84/16.24 ((
% 122.84/16.24 (demorgan2a) =>
% 122.84/16.24 ((
% 122.84/16.24 (demorgan2b2) =>
% 122.84/16.24 ((
% 122.84/16.24 (demorgan2b) =>
% 122.84/16.24 ((
% 122.84/16.24 (demorgan2) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz13rule0) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz13rule1) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz13rule2) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz13rule3) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz13rule4) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz1_1) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz1_2) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz1_3) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz1_4) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz1_5) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1all2) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1SetBreln1) =>
% 122.84/16.24 ((
% 122.84/16.24 (choice2fnsingleton) =>
% 122.84/16.24 ((
% 122.84/16.24 (setOfPairsIsBReln1) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1all1) =>
% 122.84/16.24 ((
% 122.84/16.24 (subbreln1) =>
% 122.84/16.24 ((
% 122.84/16.24 (eqbreln1) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1invprop) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1invI) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1invE) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1compprop) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1compI) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1compE) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1compEex) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionprop) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionIL) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionIR) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionI) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionE) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionEcases) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionCommutes) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz2Ex) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz2W) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz2A) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz2B) =>
% 122.84/16.24 ((
% 122.84/16.24 (image1Ex) =>
% 122.84/16.24 ((
% 122.84/16.24 (image1Ex1) =>
% 122.84/16.24 ((
% 122.84/16.24 (image1Equiv) =>
% 122.84/16.24 ((
% 122.84/16.24 (image1E) =>
% 122.84/16.24 ((
% 122.84/16.24 (image1I) =>
% 122.84/16.24 ((
% 122.84/16.24 (injFuncInInjFuncSet) =>
% 122.84/16.24 ((
% 122.84/16.24 (!!) @ (
% 122.84/16.24 (('#B') @ (
% 122.84/16.24 !!) @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 !!))) @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#S') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 '#S') @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 '#S'))) @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 =>))))) @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#C') @ in)))) @
% 122.84/16.24 injFuncSet)))))))) @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#C') @ in)))) @
% 122.84/16.24 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.84/16.24 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2527])).
% 122.84/16.24 thf(zip_derived_cl2543, plain,
% 122.84/16.24 (~ (((complementTE1) =>
% 122.84/16.24 (((binintersectTELcontra) =>
% 122.84/16.24 (((binintersectTERcontra) =>
% 122.84/16.24 (((contrasubsetT) =>
% 122.84/16.24 (((contrasubsetT1) =>
% 122.84/16.24 (((contrasubsetT2) =>
% 122.84/16.24 (((contrasubsetT3) =>
% 122.84/16.24 (((doubleComplementI1) =>
% 122.84/16.24 (((doubleComplementE1) =>
% 122.84/16.24 (((doubleComplementSub1) =>
% 122.84/16.24 (((doubleComplementSub2) =>
% 122.84/16.24 (((doubleComplementEq) =>
% 122.84/16.24 (((complementTnotintersectT) =>
% 122.84/16.24 (((complementImpComplementIntersect) =>
% 122.84/16.24 (((complementSubsetComplementIntersect) =>
% 122.84/16.24 (((complementInPowersetComplementIntersect) =>
% 122.84/16.24 (((contraSubsetComplement) =>
% 122.84/16.24 (((complementTcontraSubset) =>
% 122.84/16.24 (((binunionTILcontra) =>
% 122.84/16.24 (((binunionTIRcontra) =>
% 122.84/16.24 (((inIntersectImpInUnion) =>
% 122.84/16.24 (((inIntersectImpInUnion2) =>
% 122.84/16.24 (((inIntersectImpInIntersectUnions) =>
% 122.84/16.24 (((intersectInPowersetIntersectUnions) =>
% 122.84/16.24 (((inComplementUnionImpNotIn1) =>
% 122.84/16.24 (((inComplementUnionImpInComplement1) =>
% 122.84/16.24 (((binunionTE) =>
% 122.84/16.24 (((binunionTEcontra) =>
% 122.84/16.24 (((demorgan2a1) =>
% 122.84/16.24 (((complementUnionInPowersetComplement) =>
% 122.84/16.24 ((
% 122.84/16.24 (demorgan2a2) =>
% 122.84/16.24 ((
% 122.84/16.24 (demorgan1a) =>
% 122.84/16.24 ((
% 122.84/16.24 (demorgan1b) =>
% 122.84/16.24 ((
% 122.84/16.24 (demorgan1) =>
% 122.84/16.24 ((
% 122.84/16.24 (demorgan2a) =>
% 122.84/16.24 ((
% 122.84/16.24 (demorgan2b2) =>
% 122.84/16.24 ((
% 122.84/16.24 (demorgan2b) =>
% 122.84/16.24 ((
% 122.84/16.24 (demorgan2) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz13rule0) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz13rule1) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz13rule2) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz13rule3) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz13rule4) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz1_1) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz1_2) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz1_3) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz1_4) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz1_5) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1all2) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1SetBreln1) =>
% 122.84/16.24 ((
% 122.84/16.24 (choice2fnsingleton) =>
% 122.84/16.24 ((
% 122.84/16.24 (setOfPairsIsBReln1) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1all1) =>
% 122.84/16.24 ((
% 122.84/16.24 (subbreln1) =>
% 122.84/16.24 ((
% 122.84/16.24 (eqbreln1) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1invprop) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1invI) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1invE) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1compprop) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1compI) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1compE) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1compEex) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionprop) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionIL) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionIR) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionI) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionE) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionEcases) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionCommutes) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz2Ex) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz2W) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz2A) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz2B) =>
% 122.84/16.24 ((
% 122.84/16.24 (image1Ex) =>
% 122.84/16.24 ((
% 122.84/16.24 (image1Ex1) =>
% 122.84/16.24 ((
% 122.84/16.24 (image1Equiv) =>
% 122.84/16.24 ((
% 122.84/16.24 (image1E) =>
% 122.84/16.24 ((
% 122.84/16.24 (image1I) =>
% 122.84/16.24 ((
% 122.84/16.24 (injFuncInInjFuncSet) =>
% 122.84/16.24 ((
% 122.84/16.24 (!!) @ (
% 122.84/16.24 (('#B') @ (
% 122.84/16.24 !!) @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 !!))) @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#S') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 '#S') @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 '#S'))) @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 =>))))) @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#C') @ in)))) @
% 122.84/16.24 injFuncSet)))))))) @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#C') @ in)))) @
% 122.84/16.24 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.84/16.24 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2535])).
% 122.84/16.24 thf(zip_derived_cl2551, plain,
% 122.84/16.24 (~ (((binintersectTELcontra) =>
% 122.84/16.24 (((binintersectTERcontra) =>
% 122.84/16.24 (((contrasubsetT) =>
% 122.84/16.24 (((contrasubsetT1) =>
% 122.84/16.24 (((contrasubsetT2) =>
% 122.84/16.24 (((contrasubsetT3) =>
% 122.84/16.24 (((doubleComplementI1) =>
% 122.84/16.24 (((doubleComplementE1) =>
% 122.84/16.24 (((doubleComplementSub1) =>
% 122.84/16.24 (((doubleComplementSub2) =>
% 122.84/16.24 (((doubleComplementEq) =>
% 122.84/16.24 (((complementTnotintersectT) =>
% 122.84/16.24 (((complementImpComplementIntersect) =>
% 122.84/16.24 (((complementSubsetComplementIntersect) =>
% 122.84/16.24 (((complementInPowersetComplementIntersect) =>
% 122.84/16.24 (((contraSubsetComplement) =>
% 122.84/16.24 (((complementTcontraSubset) =>
% 122.84/16.24 (((binunionTILcontra) =>
% 122.84/16.24 (((binunionTIRcontra) =>
% 122.84/16.24 (((inIntersectImpInUnion) =>
% 122.84/16.24 (((inIntersectImpInUnion2) =>
% 122.84/16.24 (((inIntersectImpInIntersectUnions) =>
% 122.84/16.24 (((intersectInPowersetIntersectUnions) =>
% 122.84/16.24 (((inComplementUnionImpNotIn1) =>
% 122.84/16.24 (((inComplementUnionImpInComplement1) =>
% 122.84/16.24 (((binunionTE) =>
% 122.84/16.24 (((binunionTEcontra) =>
% 122.84/16.24 (((demorgan2a1) =>
% 122.84/16.24 (((complementUnionInPowersetComplement) =>
% 122.84/16.24 (((demorgan2a2) =>
% 122.84/16.24 ((
% 122.84/16.24 (demorgan1a) =>
% 122.84/16.24 ((
% 122.84/16.24 (demorgan1b) =>
% 122.84/16.24 ((
% 122.84/16.24 (demorgan1) =>
% 122.84/16.24 ((
% 122.84/16.24 (demorgan2a) =>
% 122.84/16.24 ((
% 122.84/16.24 (demorgan2b2) =>
% 122.84/16.24 ((
% 122.84/16.24 (demorgan2b) =>
% 122.84/16.24 ((
% 122.84/16.24 (demorgan2) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz13rule0) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz13rule1) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz13rule2) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz13rule3) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz13rule4) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz1_1) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz1_2) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz1_3) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz1_4) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz1_5) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1all2) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1SetBreln1) =>
% 122.84/16.24 ((
% 122.84/16.24 (choice2fnsingleton) =>
% 122.84/16.24 ((
% 122.84/16.24 (setOfPairsIsBReln1) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1all1) =>
% 122.84/16.24 ((
% 122.84/16.24 (subbreln1) =>
% 122.84/16.24 ((
% 122.84/16.24 (eqbreln1) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1invprop) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1invI) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1invE) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1compprop) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1compI) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1compE) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1compEex) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionprop) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionIL) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionIR) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionI) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionE) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionEcases) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionCommutes) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz2Ex) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz2W) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz2A) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz2B) =>
% 122.84/16.24 ((
% 122.84/16.24 (image1Ex) =>
% 122.84/16.24 ((
% 122.84/16.24 (image1Ex1) =>
% 122.84/16.24 ((
% 122.84/16.24 (image1Equiv) =>
% 122.84/16.24 ((
% 122.84/16.24 (image1E) =>
% 122.84/16.24 ((
% 122.84/16.24 (image1I) =>
% 122.84/16.24 ((
% 122.84/16.24 (injFuncInInjFuncSet) =>
% 122.84/16.24 ((
% 122.84/16.24 (!!) @ (
% 122.84/16.24 (('#B') @ (
% 122.84/16.24 !!) @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
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% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#S') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 '#S') @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
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% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
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% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#C') @ in)))) @
% 122.84/16.24 injFuncSet)))))))) @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#C') @ in)))) @
% 122.84/16.24 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.84/16.24 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2543])).
% 122.84/16.24 thf(zip_derived_cl2560, plain,
% 122.84/16.24 (~ (((binintersectTERcontra) =>
% 122.84/16.24 (((contrasubsetT) =>
% 122.84/16.24 (((contrasubsetT1) =>
% 122.84/16.24 (((contrasubsetT2) =>
% 122.84/16.24 (((contrasubsetT3) =>
% 122.84/16.24 (((doubleComplementI1) =>
% 122.84/16.24 (((doubleComplementE1) =>
% 122.84/16.24 (((doubleComplementSub1) =>
% 122.84/16.24 (((doubleComplementSub2) =>
% 122.84/16.24 (((doubleComplementEq) =>
% 122.84/16.24 (((complementTnotintersectT) =>
% 122.84/16.24 (((complementImpComplementIntersect) =>
% 122.84/16.24 (((complementSubsetComplementIntersect) =>
% 122.84/16.24 (((complementInPowersetComplementIntersect) =>
% 122.84/16.24 (((contraSubsetComplement) =>
% 122.84/16.24 (((complementTcontraSubset) =>
% 122.84/16.24 (((binunionTILcontra) =>
% 122.84/16.24 (((binunionTIRcontra) =>
% 122.84/16.24 (((inIntersectImpInUnion) =>
% 122.84/16.24 (((inIntersectImpInUnion2) =>
% 122.84/16.24 (((inIntersectImpInIntersectUnions) =>
% 122.84/16.24 (((intersectInPowersetIntersectUnions) =>
% 122.84/16.24 (((inComplementUnionImpNotIn1) =>
% 122.84/16.24 (((inComplementUnionImpInComplement1) =>
% 122.84/16.24 (((binunionTE) =>
% 122.84/16.24 (((binunionTEcontra) =>
% 122.84/16.24 (((demorgan2a1) =>
% 122.84/16.24 (((complementUnionInPowersetComplement) =>
% 122.84/16.24 (((demorgan2a2) =>
% 122.84/16.24 (((demorgan1a) =>
% 122.84/16.24 ((
% 122.84/16.24 (demorgan1b) =>
% 122.84/16.24 ((
% 122.84/16.24 (demorgan1) =>
% 122.84/16.24 ((
% 122.84/16.24 (demorgan2a) =>
% 122.84/16.24 ((
% 122.84/16.24 (demorgan2b2) =>
% 122.84/16.24 ((
% 122.84/16.24 (demorgan2b) =>
% 122.84/16.24 ((
% 122.84/16.24 (demorgan2) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz13rule0) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz13rule1) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz13rule2) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz13rule3) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz13rule4) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz1_1) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz1_2) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz1_3) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz1_4) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz1_5) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1all2) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1SetBreln1) =>
% 122.84/16.24 ((
% 122.84/16.24 (choice2fnsingleton) =>
% 122.84/16.24 ((
% 122.84/16.24 (setOfPairsIsBReln1) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1all1) =>
% 122.84/16.24 ((
% 122.84/16.24 (subbreln1) =>
% 122.84/16.24 ((
% 122.84/16.24 (eqbreln1) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1invprop) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1invI) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1invE) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1compprop) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1compI) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1compE) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1compEex) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionprop) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionIL) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionIR) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionI) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionE) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionEcases) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionCommutes) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz2Ex) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz2W) =>
% 122.84/16.24 ((
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% 122.84/16.24 ((
% 122.84/16.24 (woz2B) =>
% 122.84/16.24 ((
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% 122.84/16.24 ((
% 122.84/16.24 (image1Ex1) =>
% 122.84/16.24 ((
% 122.84/16.24 (image1Equiv) =>
% 122.84/16.24 ((
% 122.84/16.24 (image1E) =>
% 122.84/16.24 ((
% 122.84/16.24 (image1I) =>
% 122.84/16.24 ((
% 122.84/16.24 (injFuncInInjFuncSet) =>
% 122.84/16.24 ((
% 122.84/16.24 (!!) @ (
% 122.84/16.24 (('#B') @ (
% 122.84/16.24 !!) @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 !!))) @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#S') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 '#S') @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 '#S'))) @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 =>))))) @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#C') @ in)))) @
% 122.84/16.24 injFuncSet)))))))) @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#C') @ in)))) @
% 122.84/16.24 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.84/16.24 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2551])).
% 122.84/16.24 thf(zip_derived_cl2570, plain,
% 122.84/16.24 (~ (((contrasubsetT) =>
% 122.84/16.24 (((contrasubsetT1) =>
% 122.84/16.24 (((contrasubsetT2) =>
% 122.84/16.24 (((contrasubsetT3) =>
% 122.84/16.24 (((doubleComplementI1) =>
% 122.84/16.24 (((doubleComplementE1) =>
% 122.84/16.24 (((doubleComplementSub1) =>
% 122.84/16.24 (((doubleComplementSub2) =>
% 122.84/16.24 (((doubleComplementEq) =>
% 122.84/16.24 (((complementTnotintersectT) =>
% 122.84/16.24 (((complementImpComplementIntersect) =>
% 122.84/16.24 (((complementSubsetComplementIntersect) =>
% 122.84/16.24 (((complementInPowersetComplementIntersect) =>
% 122.84/16.24 (((contraSubsetComplement) =>
% 122.84/16.24 (((complementTcontraSubset) =>
% 122.84/16.24 (((binunionTILcontra) =>
% 122.84/16.24 (((binunionTIRcontra) =>
% 122.84/16.24 (((inIntersectImpInUnion) =>
% 122.84/16.24 (((inIntersectImpInUnion2) =>
% 122.84/16.24 (((inIntersectImpInIntersectUnions) =>
% 122.84/16.24 (((intersectInPowersetIntersectUnions) =>
% 122.84/16.24 (((inComplementUnionImpNotIn1) =>
% 122.84/16.24 (((inComplementUnionImpInComplement1) =>
% 122.84/16.24 (((binunionTE) =>
% 122.84/16.24 (((binunionTEcontra) =>
% 122.84/16.24 (((demorgan2a1) =>
% 122.84/16.24 (((complementUnionInPowersetComplement) =>
% 122.84/16.24 (((demorgan2a2) =>
% 122.84/16.24 (((demorgan1a) =>
% 122.84/16.24 (((demorgan1b) =>
% 122.84/16.24 ((
% 122.84/16.24 (demorgan1) =>
% 122.84/16.24 ((
% 122.84/16.24 (demorgan2a) =>
% 122.84/16.24 ((
% 122.84/16.24 (demorgan2b2) =>
% 122.84/16.24 ((
% 122.84/16.24 (demorgan2b) =>
% 122.84/16.24 ((
% 122.84/16.24 (demorgan2) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz13rule0) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz13rule1) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz13rule2) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz13rule3) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz13rule4) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz1_1) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz1_2) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz1_3) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz1_4) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz1_5) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1all2) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1SetBreln1) =>
% 122.84/16.24 ((
% 122.84/16.24 (choice2fnsingleton) =>
% 122.84/16.24 ((
% 122.84/16.24 (setOfPairsIsBReln1) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1all1) =>
% 122.84/16.24 ((
% 122.84/16.24 (subbreln1) =>
% 122.84/16.24 ((
% 122.84/16.24 (eqbreln1) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1invprop) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1invI) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1invE) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1compprop) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1compI) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1compE) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1compEex) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionprop) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionIL) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionIR) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionI) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionE) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionEcases) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionCommutes) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz2Ex) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz2W) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz2A) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz2B) =>
% 122.84/16.24 ((
% 122.84/16.24 (image1Ex) =>
% 122.84/16.24 ((
% 122.84/16.24 (image1Ex1) =>
% 122.84/16.24 ((
% 122.84/16.24 (image1Equiv) =>
% 122.84/16.24 ((
% 122.84/16.24 (image1E) =>
% 122.84/16.24 ((
% 122.84/16.24 (image1I) =>
% 122.84/16.24 ((
% 122.84/16.24 (injFuncInInjFuncSet) =>
% 122.84/16.24 ((
% 122.84/16.24 (!!) @ (
% 122.84/16.24 (('#B') @ (
% 122.84/16.24 !!) @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 !!))) @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#S') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 '#S') @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 '#S'))) @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 =>))))) @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#C') @ in)))) @
% 122.84/16.24 injFuncSet)))))))) @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#C') @ in)))) @
% 122.84/16.24 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.84/16.24 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2560])).
% 122.84/16.24 thf(zip_derived_cl2581, plain,
% 122.84/16.24 (~ (((contrasubsetT1) =>
% 122.84/16.24 (((contrasubsetT2) =>
% 122.84/16.24 (((contrasubsetT3) =>
% 122.84/16.24 (((doubleComplementI1) =>
% 122.84/16.24 (((doubleComplementE1) =>
% 122.84/16.24 (((doubleComplementSub1) =>
% 122.84/16.24 (((doubleComplementSub2) =>
% 122.84/16.24 (((doubleComplementEq) =>
% 122.84/16.24 (((complementTnotintersectT) =>
% 122.84/16.24 (((complementImpComplementIntersect) =>
% 122.84/16.24 (((complementSubsetComplementIntersect) =>
% 122.84/16.24 (((complementInPowersetComplementIntersect) =>
% 122.84/16.24 (((contraSubsetComplement) =>
% 122.84/16.24 (((complementTcontraSubset) =>
% 122.84/16.24 (((binunionTILcontra) =>
% 122.84/16.24 (((binunionTIRcontra) =>
% 122.84/16.24 (((inIntersectImpInUnion) =>
% 122.84/16.24 (((inIntersectImpInUnion2) =>
% 122.84/16.24 (((inIntersectImpInIntersectUnions) =>
% 122.84/16.24 (((intersectInPowersetIntersectUnions) =>
% 122.84/16.24 (((inComplementUnionImpNotIn1) =>
% 122.84/16.24 (((inComplementUnionImpInComplement1) =>
% 122.84/16.24 (((binunionTE) =>
% 122.84/16.24 (((binunionTEcontra) =>
% 122.84/16.24 (((demorgan2a1) =>
% 122.84/16.24 (((complementUnionInPowersetComplement) =>
% 122.84/16.24 (((demorgan2a2) =>
% 122.84/16.24 (((demorgan1a) =>
% 122.84/16.24 (((demorgan1b) =>
% 122.84/16.24 (((demorgan1) =>
% 122.84/16.24 ((
% 122.84/16.24 (demorgan2a) =>
% 122.84/16.24 ((
% 122.84/16.24 (demorgan2b2) =>
% 122.84/16.24 ((
% 122.84/16.24 (demorgan2b) =>
% 122.84/16.24 ((
% 122.84/16.24 (demorgan2) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz13rule0) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz13rule1) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz13rule2) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz13rule3) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz13rule4) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz1_1) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz1_2) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz1_3) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz1_4) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz1_5) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1all2) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1SetBreln1) =>
% 122.84/16.24 ((
% 122.84/16.24 (choice2fnsingleton) =>
% 122.84/16.24 ((
% 122.84/16.24 (setOfPairsIsBReln1) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1all1) =>
% 122.84/16.24 ((
% 122.84/16.24 (subbreln1) =>
% 122.84/16.24 ((
% 122.84/16.24 (eqbreln1) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1invprop) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1invI) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1invE) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1compprop) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1compI) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1compE) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1compEex) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionprop) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionIL) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionIR) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionI) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionE) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionEcases) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionCommutes) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz2Ex) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz2W) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz2A) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz2B) =>
% 122.84/16.24 ((
% 122.84/16.24 (image1Ex) =>
% 122.84/16.24 ((
% 122.84/16.24 (image1Ex1) =>
% 122.84/16.24 ((
% 122.84/16.24 (image1Equiv) =>
% 122.84/16.24 ((
% 122.84/16.24 (image1E) =>
% 122.84/16.24 ((
% 122.84/16.24 (image1I) =>
% 122.84/16.24 ((
% 122.84/16.24 (injFuncInInjFuncSet) =>
% 122.84/16.24 ((
% 122.84/16.24 (!!) @ (
% 122.84/16.24 (('#B') @ (
% 122.84/16.24 !!) @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 !!))) @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#S') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 '#S') @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 '#S'))) @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 =>))))) @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#C') @ in)))) @
% 122.84/16.24 injFuncSet)))))))) @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#C') @ in)))) @
% 122.84/16.24 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.84/16.24 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2570])).
% 122.84/16.24 thf(zip_derived_cl2594, plain,
% 122.84/16.24 (~ (((contrasubsetT2) =>
% 122.84/16.24 (((contrasubsetT3) =>
% 122.84/16.24 (((doubleComplementI1) =>
% 122.84/16.24 (((doubleComplementE1) =>
% 122.84/16.24 (((doubleComplementSub1) =>
% 122.84/16.24 (((doubleComplementSub2) =>
% 122.84/16.24 (((doubleComplementEq) =>
% 122.84/16.24 (((complementTnotintersectT) =>
% 122.84/16.24 (((complementImpComplementIntersect) =>
% 122.84/16.24 (((complementSubsetComplementIntersect) =>
% 122.84/16.24 (((complementInPowersetComplementIntersect) =>
% 122.84/16.24 (((contraSubsetComplement) =>
% 122.84/16.24 (((complementTcontraSubset) =>
% 122.84/16.24 (((binunionTILcontra) =>
% 122.84/16.24 (((binunionTIRcontra) =>
% 122.84/16.24 (((inIntersectImpInUnion) =>
% 122.84/16.24 (((inIntersectImpInUnion2) =>
% 122.84/16.24 (((inIntersectImpInIntersectUnions) =>
% 122.84/16.24 (((intersectInPowersetIntersectUnions) =>
% 122.84/16.24 (((inComplementUnionImpNotIn1) =>
% 122.84/16.24 (((inComplementUnionImpInComplement1) =>
% 122.84/16.24 (((binunionTE) =>
% 122.84/16.24 (((binunionTEcontra) =>
% 122.84/16.24 (((demorgan2a1) =>
% 122.84/16.24 (((complementUnionInPowersetComplement) =>
% 122.84/16.24 (((demorgan2a2) =>
% 122.84/16.24 (((demorgan1a) =>
% 122.84/16.24 (((demorgan1b) =>
% 122.84/16.24 (((demorgan1) =>
% 122.84/16.24 (((demorgan2a) =>
% 122.84/16.24 ((
% 122.84/16.24 (demorgan2b2) =>
% 122.84/16.24 ((
% 122.84/16.24 (demorgan2b) =>
% 122.84/16.24 ((
% 122.84/16.24 (demorgan2) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz13rule0) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz13rule1) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz13rule2) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz13rule3) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz13rule4) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz1_1) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz1_2) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz1_3) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz1_4) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz1_5) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1all2) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1SetBreln1) =>
% 122.84/16.24 ((
% 122.84/16.24 (choice2fnsingleton) =>
% 122.84/16.24 ((
% 122.84/16.24 (setOfPairsIsBReln1) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1all1) =>
% 122.84/16.24 ((
% 122.84/16.24 (subbreln1) =>
% 122.84/16.24 ((
% 122.84/16.24 (eqbreln1) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1invprop) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1invI) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1invE) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1compprop) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1compI) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1compE) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1compEex) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionprop) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionIL) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionIR) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionI) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionE) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionEcases) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionCommutes) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz2Ex) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz2W) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz2A) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz2B) =>
% 122.84/16.24 ((
% 122.84/16.24 (image1Ex) =>
% 122.84/16.24 ((
% 122.84/16.24 (image1Ex1) =>
% 122.84/16.24 ((
% 122.84/16.24 (image1Equiv) =>
% 122.84/16.24 ((
% 122.84/16.24 (image1E) =>
% 122.84/16.24 ((
% 122.84/16.24 (image1I) =>
% 122.84/16.24 ((
% 122.84/16.24 (injFuncInInjFuncSet) =>
% 122.84/16.24 ((
% 122.84/16.24 (!!) @ (
% 122.84/16.24 (('#B') @ (
% 122.84/16.24 !!) @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 !!))) @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#S') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 '#S') @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 '#S'))) @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 =>))))) @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#C') @ in)))) @
% 122.84/16.24 injFuncSet)))))))) @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#C') @ in)))) @
% 122.84/16.24 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.84/16.24 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2581])).
% 122.84/16.24 thf(zip_derived_cl2610, plain,
% 122.84/16.24 (~ (((contrasubsetT3) =>
% 122.84/16.24 (((doubleComplementI1) =>
% 122.84/16.24 (((doubleComplementE1) =>
% 122.84/16.24 (((doubleComplementSub1) =>
% 122.84/16.24 (((doubleComplementSub2) =>
% 122.84/16.24 (((doubleComplementEq) =>
% 122.84/16.24 (((complementTnotintersectT) =>
% 122.84/16.24 (((complementImpComplementIntersect) =>
% 122.84/16.24 (((complementSubsetComplementIntersect) =>
% 122.84/16.24 (((complementInPowersetComplementIntersect) =>
% 122.84/16.24 (((contraSubsetComplement) =>
% 122.84/16.24 (((complementTcontraSubset) =>
% 122.84/16.24 (((binunionTILcontra) =>
% 122.84/16.24 (((binunionTIRcontra) =>
% 122.84/16.24 (((inIntersectImpInUnion) =>
% 122.84/16.24 (((inIntersectImpInUnion2) =>
% 122.84/16.24 (((inIntersectImpInIntersectUnions) =>
% 122.84/16.24 (((intersectInPowersetIntersectUnions) =>
% 122.84/16.24 (((inComplementUnionImpNotIn1) =>
% 122.84/16.24 (((inComplementUnionImpInComplement1) =>
% 122.84/16.24 (((binunionTE) =>
% 122.84/16.24 (((binunionTEcontra) =>
% 122.84/16.24 (((demorgan2a1) =>
% 122.84/16.24 (((complementUnionInPowersetComplement) =>
% 122.84/16.24 (((demorgan2a2) =>
% 122.84/16.24 (((demorgan1a) =>
% 122.84/16.24 (((demorgan1b) =>
% 122.84/16.24 (((demorgan1) =>
% 122.84/16.24 (((demorgan2a) =>
% 122.84/16.24 (((demorgan2b2) =>
% 122.84/16.24 ((
% 122.84/16.24 (demorgan2b) =>
% 122.84/16.24 ((
% 122.84/16.24 (demorgan2) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz13rule0) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz13rule1) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz13rule2) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz13rule3) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz13rule4) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz1_1) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz1_2) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz1_3) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz1_4) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz1_5) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1all2) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1SetBreln1) =>
% 122.84/16.24 ((
% 122.84/16.24 (choice2fnsingleton) =>
% 122.84/16.24 ((
% 122.84/16.24 (setOfPairsIsBReln1) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1all1) =>
% 122.84/16.24 ((
% 122.84/16.24 (subbreln1) =>
% 122.84/16.24 ((
% 122.84/16.24 (eqbreln1) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1invprop) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1invI) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1invE) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1compprop) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1compI) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1compE) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1compEex) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionprop) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionIL) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionIR) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionI) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionE) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionEcases) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionCommutes) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz2Ex) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz2W) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz2A) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz2B) =>
% 122.84/16.24 ((
% 122.84/16.24 (image1Ex) =>
% 122.84/16.24 ((
% 122.84/16.24 (image1Ex1) =>
% 122.84/16.24 ((
% 122.84/16.24 (image1Equiv) =>
% 122.84/16.24 ((
% 122.84/16.24 (image1E) =>
% 122.84/16.24 ((
% 122.84/16.24 (image1I) =>
% 122.84/16.24 ((
% 122.84/16.24 (injFuncInInjFuncSet) =>
% 122.84/16.24 ((
% 122.84/16.24 (!!) @ (
% 122.84/16.24 (('#B') @ (
% 122.84/16.24 !!) @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 !!))) @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#S') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 '#S') @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 '#S'))) @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 =>))))) @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#C') @ in)))) @
% 122.84/16.24 injFuncSet)))))))) @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#C') @ in)))) @
% 122.84/16.24 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.84/16.24 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2594])).
% 122.84/16.24 thf(zip_derived_cl2629, plain,
% 122.84/16.24 (~ (((doubleComplementI1) =>
% 122.84/16.24 (((doubleComplementE1) =>
% 122.84/16.24 (((doubleComplementSub1) =>
% 122.84/16.24 (((doubleComplementSub2) =>
% 122.84/16.24 (((doubleComplementEq) =>
% 122.84/16.24 (((complementTnotintersectT) =>
% 122.84/16.24 (((complementImpComplementIntersect) =>
% 122.84/16.24 (((complementSubsetComplementIntersect) =>
% 122.84/16.24 (((complementInPowersetComplementIntersect) =>
% 122.84/16.24 (((contraSubsetComplement) =>
% 122.84/16.24 (((complementTcontraSubset) =>
% 122.84/16.24 (((binunionTILcontra) =>
% 122.84/16.24 (((binunionTIRcontra) =>
% 122.84/16.24 (((inIntersectImpInUnion) =>
% 122.84/16.24 (((inIntersectImpInUnion2) =>
% 122.84/16.24 (((inIntersectImpInIntersectUnions) =>
% 122.84/16.24 (((intersectInPowersetIntersectUnions) =>
% 122.84/16.24 (((inComplementUnionImpNotIn1) =>
% 122.84/16.24 (((inComplementUnionImpInComplement1) =>
% 122.84/16.24 (((binunionTE) =>
% 122.84/16.24 (((binunionTEcontra) =>
% 122.84/16.24 (((demorgan2a1) =>
% 122.84/16.24 (((complementUnionInPowersetComplement) =>
% 122.84/16.24 (((demorgan2a2) =>
% 122.84/16.24 (((demorgan1a) =>
% 122.84/16.24 (((demorgan1b) =>
% 122.84/16.24 (((demorgan1) =>
% 122.84/16.24 (((demorgan2a) =>
% 122.84/16.24 (((demorgan2b2) =>
% 122.84/16.24 (((demorgan2b) =>
% 122.84/16.24 ((
% 122.84/16.24 (demorgan2) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz13rule0) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz13rule1) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz13rule2) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz13rule3) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz13rule4) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz1_1) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz1_2) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz1_3) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz1_4) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz1_5) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1all2) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1SetBreln1) =>
% 122.84/16.24 ((
% 122.84/16.24 (choice2fnsingleton) =>
% 122.84/16.24 ((
% 122.84/16.24 (setOfPairsIsBReln1) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1all1) =>
% 122.84/16.24 ((
% 122.84/16.24 (subbreln1) =>
% 122.84/16.24 ((
% 122.84/16.24 (eqbreln1) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1invprop) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1invI) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1invE) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1compprop) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1compI) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1compE) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1compEex) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionprop) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionIL) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionIR) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionI) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionE) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionEcases) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionCommutes) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz2Ex) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz2W) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz2A) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz2B) =>
% 122.84/16.24 ((
% 122.84/16.24 (image1Ex) =>
% 122.84/16.24 ((
% 122.84/16.24 (image1Ex1) =>
% 122.84/16.24 ((
% 122.84/16.24 (image1Equiv) =>
% 122.84/16.24 ((
% 122.84/16.24 (image1E) =>
% 122.84/16.24 ((
% 122.84/16.24 (image1I) =>
% 122.84/16.24 ((
% 122.84/16.24 (injFuncInInjFuncSet) =>
% 122.84/16.24 ((
% 122.84/16.24 (!!) @ (
% 122.84/16.24 (('#B') @ (
% 122.84/16.24 !!) @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 !!))) @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#S') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 '#S') @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 '#S'))) @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 =>))))) @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#C') @ in)))) @
% 122.84/16.24 injFuncSet)))))))) @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#C') @ in)))) @
% 122.84/16.24 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.84/16.24 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2610])).
% 122.84/16.24 thf(zip_derived_cl2648, plain,
% 122.84/16.24 (~ (((doubleComplementE1) =>
% 122.84/16.24 (((doubleComplementSub1) =>
% 122.84/16.24 (((doubleComplementSub2) =>
% 122.84/16.24 (((doubleComplementEq) =>
% 122.84/16.24 (((complementTnotintersectT) =>
% 122.84/16.24 (((complementImpComplementIntersect) =>
% 122.84/16.24 (((complementSubsetComplementIntersect) =>
% 122.84/16.24 (((complementInPowersetComplementIntersect) =>
% 122.84/16.24 (((contraSubsetComplement) =>
% 122.84/16.24 (((complementTcontraSubset) =>
% 122.84/16.24 (((binunionTILcontra) =>
% 122.84/16.24 (((binunionTIRcontra) =>
% 122.84/16.24 (((inIntersectImpInUnion) =>
% 122.84/16.24 (((inIntersectImpInUnion2) =>
% 122.84/16.24 (((inIntersectImpInIntersectUnions) =>
% 122.84/16.24 (((intersectInPowersetIntersectUnions) =>
% 122.84/16.24 (((inComplementUnionImpNotIn1) =>
% 122.84/16.24 (((inComplementUnionImpInComplement1) =>
% 122.84/16.24 (((binunionTE) =>
% 122.84/16.24 (((binunionTEcontra) =>
% 122.84/16.24 (((demorgan2a1) =>
% 122.84/16.24 (((complementUnionInPowersetComplement) =>
% 122.84/16.24 (((demorgan2a2) =>
% 122.84/16.24 (((demorgan1a) =>
% 122.84/16.24 (((demorgan1b) =>
% 122.84/16.24 (((demorgan1) =>
% 122.84/16.24 (((demorgan2a) =>
% 122.84/16.24 (((demorgan2b2) =>
% 122.84/16.24 (((demorgan2b) =>
% 122.84/16.24 (((demorgan2) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz13rule0) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz13rule1) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz13rule2) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz13rule3) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz13rule4) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz1_1) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz1_2) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz1_3) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz1_4) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz1_5) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1all2) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1SetBreln1) =>
% 122.84/16.24 ((
% 122.84/16.24 (choice2fnsingleton) =>
% 122.84/16.24 ((
% 122.84/16.24 (setOfPairsIsBReln1) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1all1) =>
% 122.84/16.24 ((
% 122.84/16.24 (subbreln1) =>
% 122.84/16.24 ((
% 122.84/16.24 (eqbreln1) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1invprop) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1invI) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1invE) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1compprop) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1compI) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1compE) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1compEex) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionprop) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionIL) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionIR) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionI) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionE) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionEcases) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionCommutes) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz2Ex) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz2W) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz2A) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz2B) =>
% 122.84/16.24 ((
% 122.84/16.24 (image1Ex) =>
% 122.84/16.24 ((
% 122.84/16.24 (image1Ex1) =>
% 122.84/16.24 ((
% 122.84/16.24 (image1Equiv) =>
% 122.84/16.24 ((
% 122.84/16.24 (image1E) =>
% 122.84/16.24 ((
% 122.84/16.24 (image1I) =>
% 122.84/16.24 ((
% 122.84/16.24 (injFuncInInjFuncSet) =>
% 122.84/16.24 ((
% 122.84/16.24 (!!) @ (
% 122.84/16.24 (('#B') @ (
% 122.84/16.24 !!) @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 !!))) @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#S') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 '#S') @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 '#S'))) @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 =>))))) @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#C') @ in)))) @
% 122.84/16.24 injFuncSet)))))))) @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#C') @ in)))) @
% 122.84/16.24 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.84/16.24 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2629])).
% 122.84/16.24 thf(zip_derived_cl2665, plain,
% 122.84/16.24 (~ (((doubleComplementSub1) =>
% 122.84/16.24 (((doubleComplementSub2) =>
% 122.84/16.24 (((doubleComplementEq) =>
% 122.84/16.24 (((complementTnotintersectT) =>
% 122.84/16.24 (((complementImpComplementIntersect) =>
% 122.84/16.24 (((complementSubsetComplementIntersect) =>
% 122.84/16.24 (((complementInPowersetComplementIntersect) =>
% 122.84/16.24 (((contraSubsetComplement) =>
% 122.84/16.24 (((complementTcontraSubset) =>
% 122.84/16.24 (((binunionTILcontra) =>
% 122.84/16.24 (((binunionTIRcontra) =>
% 122.84/16.24 (((inIntersectImpInUnion) =>
% 122.84/16.24 (((inIntersectImpInUnion2) =>
% 122.84/16.24 (((inIntersectImpInIntersectUnions) =>
% 122.84/16.24 (((intersectInPowersetIntersectUnions) =>
% 122.84/16.24 (((inComplementUnionImpNotIn1) =>
% 122.84/16.24 (((inComplementUnionImpInComplement1) =>
% 122.84/16.24 (((binunionTE) =>
% 122.84/16.24 (((binunionTEcontra) =>
% 122.84/16.24 (((demorgan2a1) =>
% 122.84/16.24 (((complementUnionInPowersetComplement) =>
% 122.84/16.24 (((demorgan2a2) =>
% 122.84/16.24 (((demorgan1a) =>
% 122.84/16.24 (((demorgan1b) =>
% 122.84/16.24 (((demorgan1) =>
% 122.84/16.24 (((demorgan2a) =>
% 122.84/16.24 (((demorgan2b2) =>
% 122.84/16.24 (((demorgan2b) =>
% 122.84/16.24 (((demorgan2) =>
% 122.84/16.24 (((woz13rule0) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz13rule1) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz13rule2) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz13rule3) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz13rule4) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz1_1) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz1_2) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz1_3) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz1_4) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz1_5) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1all2) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1SetBreln1) =>
% 122.84/16.24 ((
% 122.84/16.24 (choice2fnsingleton) =>
% 122.84/16.24 ((
% 122.84/16.24 (setOfPairsIsBReln1) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1all1) =>
% 122.84/16.24 ((
% 122.84/16.24 (subbreln1) =>
% 122.84/16.24 ((
% 122.84/16.24 (eqbreln1) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1invprop) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1invI) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1invE) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1compprop) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1compI) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1compE) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1compEex) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionprop) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionIL) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionIR) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionI) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionE) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionEcases) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionCommutes) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz2Ex) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz2W) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz2A) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz2B) =>
% 122.84/16.24 ((
% 122.84/16.24 (image1Ex) =>
% 122.84/16.24 ((
% 122.84/16.24 (image1Ex1) =>
% 122.84/16.24 ((
% 122.84/16.24 (image1Equiv) =>
% 122.84/16.24 ((
% 122.84/16.24 (image1E) =>
% 122.84/16.24 ((
% 122.84/16.24 (image1I) =>
% 122.84/16.24 ((
% 122.84/16.24 (injFuncInInjFuncSet) =>
% 122.84/16.24 ((
% 122.84/16.24 (!!) @ (
% 122.84/16.24 (('#B') @ (
% 122.84/16.24 !!) @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 !!))) @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#S') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 '#S') @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 '#S'))) @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 =>))))) @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#C') @ in)))) @
% 122.84/16.24 injFuncSet)))))))) @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#C') @ in)))) @
% 122.84/16.24 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.84/16.24 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2648])).
% 122.84/16.24 thf(zip_derived_cl2680, plain,
% 122.84/16.24 (~ (((doubleComplementSub2) =>
% 122.84/16.24 (((doubleComplementEq) =>
% 122.84/16.24 (((complementTnotintersectT) =>
% 122.84/16.24 (((complementImpComplementIntersect) =>
% 122.84/16.24 (((complementSubsetComplementIntersect) =>
% 122.84/16.24 (((complementInPowersetComplementIntersect) =>
% 122.84/16.24 (((contraSubsetComplement) =>
% 122.84/16.24 (((complementTcontraSubset) =>
% 122.84/16.24 (((binunionTILcontra) =>
% 122.84/16.24 (((binunionTIRcontra) =>
% 122.84/16.24 (((inIntersectImpInUnion) =>
% 122.84/16.24 (((inIntersectImpInUnion2) =>
% 122.84/16.24 (((inIntersectImpInIntersectUnions) =>
% 122.84/16.24 (((intersectInPowersetIntersectUnions) =>
% 122.84/16.24 (((inComplementUnionImpNotIn1) =>
% 122.84/16.24 (((inComplementUnionImpInComplement1) =>
% 122.84/16.24 (((binunionTE) =>
% 122.84/16.24 (((binunionTEcontra) =>
% 122.84/16.24 (((demorgan2a1) =>
% 122.84/16.24 (((complementUnionInPowersetComplement) =>
% 122.84/16.24 (((demorgan2a2) =>
% 122.84/16.24 (((demorgan1a) =>
% 122.84/16.24 (((demorgan1b) =>
% 122.84/16.24 (((demorgan1) =>
% 122.84/16.24 (((demorgan2a) =>
% 122.84/16.24 (((demorgan2b2) =>
% 122.84/16.24 (((demorgan2b) =>
% 122.84/16.24 (((demorgan2) =>
% 122.84/16.24 (((woz13rule0) =>
% 122.84/16.24 (((woz13rule1) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz13rule2) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz13rule3) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz13rule4) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz1_1) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz1_2) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz1_3) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz1_4) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz1_5) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1all2) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1SetBreln1) =>
% 122.84/16.24 ((
% 122.84/16.24 (choice2fnsingleton) =>
% 122.84/16.24 ((
% 122.84/16.24 (setOfPairsIsBReln1) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1all1) =>
% 122.84/16.24 ((
% 122.84/16.24 (subbreln1) =>
% 122.84/16.24 ((
% 122.84/16.24 (eqbreln1) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1invprop) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1invI) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1invE) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1compprop) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1compI) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1compE) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1compEex) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionprop) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionIL) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionIR) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionI) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionE) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionEcases) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionCommutes) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz2Ex) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz2W) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz2A) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz2B) =>
% 122.84/16.24 ((
% 122.84/16.24 (image1Ex) =>
% 122.84/16.24 ((
% 122.84/16.24 (image1Ex1) =>
% 122.84/16.24 ((
% 122.84/16.24 (image1Equiv) =>
% 122.84/16.24 ((
% 122.84/16.24 (image1E) =>
% 122.84/16.24 ((
% 122.84/16.24 (image1I) =>
% 122.84/16.24 ((
% 122.84/16.24 (injFuncInInjFuncSet) =>
% 122.84/16.24 ((
% 122.84/16.24 (!!) @ (
% 122.84/16.24 (('#B') @ (
% 122.84/16.24 !!) @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 !!))) @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#S') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 '#S') @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 '#S'))) @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 =>))))) @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#C') @ in)))) @
% 122.84/16.24 injFuncSet)))))))) @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#C') @ in)))) @
% 122.84/16.24 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.84/16.24 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2665])).
% 122.84/16.24 thf(zip_derived_cl2692, plain,
% 122.84/16.24 (~ (((doubleComplementEq) =>
% 122.84/16.24 (((complementTnotintersectT) =>
% 122.84/16.24 (((complementImpComplementIntersect) =>
% 122.84/16.24 (((complementSubsetComplementIntersect) =>
% 122.84/16.24 (((complementInPowersetComplementIntersect) =>
% 122.84/16.24 (((contraSubsetComplement) =>
% 122.84/16.24 (((complementTcontraSubset) =>
% 122.84/16.24 (((binunionTILcontra) =>
% 122.84/16.24 (((binunionTIRcontra) =>
% 122.84/16.24 (((inIntersectImpInUnion) =>
% 122.84/16.24 (((inIntersectImpInUnion2) =>
% 122.84/16.24 (((inIntersectImpInIntersectUnions) =>
% 122.84/16.24 (((intersectInPowersetIntersectUnions) =>
% 122.84/16.24 (((inComplementUnionImpNotIn1) =>
% 122.84/16.24 (((inComplementUnionImpInComplement1) =>
% 122.84/16.24 (((binunionTE) =>
% 122.84/16.24 (((binunionTEcontra) =>
% 122.84/16.24 (((demorgan2a1) =>
% 122.84/16.24 (((complementUnionInPowersetComplement) =>
% 122.84/16.24 (((demorgan2a2) =>
% 122.84/16.24 (((demorgan1a) =>
% 122.84/16.24 (((demorgan1b) =>
% 122.84/16.24 (((demorgan1) =>
% 122.84/16.24 (((demorgan2a) =>
% 122.84/16.24 (((demorgan2b2) =>
% 122.84/16.24 (((demorgan2b) =>
% 122.84/16.24 (((demorgan2) =>
% 122.84/16.24 (((woz13rule0) =>
% 122.84/16.24 (((woz13rule1) =>
% 122.84/16.24 (((woz13rule2) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz13rule3) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz13rule4) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz1_1) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz1_2) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz1_3) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz1_4) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz1_5) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1all2) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1SetBreln1) =>
% 122.84/16.24 ((
% 122.84/16.24 (choice2fnsingleton) =>
% 122.84/16.24 ((
% 122.84/16.24 (setOfPairsIsBReln1) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1all1) =>
% 122.84/16.24 ((
% 122.84/16.24 (subbreln1) =>
% 122.84/16.24 ((
% 122.84/16.24 (eqbreln1) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1invprop) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1invI) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1invE) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1compprop) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1compI) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1compE) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1compEex) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionprop) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionIL) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionIR) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionI) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionE) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionEcases) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionCommutes) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz2Ex) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz2W) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz2A) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz2B) =>
% 122.84/16.24 ((
% 122.84/16.24 (image1Ex) =>
% 122.84/16.24 ((
% 122.84/16.24 (image1Ex1) =>
% 122.84/16.24 ((
% 122.84/16.24 (image1Equiv) =>
% 122.84/16.24 ((
% 122.84/16.24 (image1E) =>
% 122.84/16.24 ((
% 122.84/16.24 (image1I) =>
% 122.84/16.24 ((
% 122.84/16.24 (injFuncInInjFuncSet) =>
% 122.84/16.24 ((
% 122.84/16.24 (!!) @ (
% 122.84/16.24 (('#B') @ (
% 122.84/16.24 !!) @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 !!))) @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#S') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 '#S') @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 '#S'))) @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 =>))))) @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#C') @ in)))) @
% 122.84/16.24 injFuncSet)))))))) @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#C') @ in)))) @
% 122.84/16.24 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.84/16.24 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2680])).
% 122.84/16.24 thf(zip_derived_cl2704, plain,
% 122.84/16.24 (~ (((complementTnotintersectT) =>
% 122.84/16.24 (((complementImpComplementIntersect) =>
% 122.84/16.24 (((complementSubsetComplementIntersect) =>
% 122.84/16.24 (((complementInPowersetComplementIntersect) =>
% 122.84/16.24 (((contraSubsetComplement) =>
% 122.84/16.24 (((complementTcontraSubset) =>
% 122.84/16.24 (((binunionTILcontra) =>
% 122.84/16.24 (((binunionTIRcontra) =>
% 122.84/16.24 (((inIntersectImpInUnion) =>
% 122.84/16.24 (((inIntersectImpInUnion2) =>
% 122.84/16.24 (((inIntersectImpInIntersectUnions) =>
% 122.84/16.24 (((intersectInPowersetIntersectUnions) =>
% 122.84/16.24 (((inComplementUnionImpNotIn1) =>
% 122.84/16.24 (((inComplementUnionImpInComplement1) =>
% 122.84/16.24 (((binunionTE) =>
% 122.84/16.24 (((binunionTEcontra) =>
% 122.84/16.24 (((demorgan2a1) =>
% 122.84/16.24 (((complementUnionInPowersetComplement) =>
% 122.84/16.24 (((demorgan2a2) =>
% 122.84/16.24 (((demorgan1a) =>
% 122.84/16.24 (((demorgan1b) =>
% 122.84/16.24 (((demorgan1) =>
% 122.84/16.24 (((demorgan2a) =>
% 122.84/16.24 (((demorgan2b2) =>
% 122.84/16.24 (((demorgan2b) =>
% 122.84/16.24 (((demorgan2) =>
% 122.84/16.24 (((woz13rule0) =>
% 122.84/16.24 (((woz13rule1) =>
% 122.84/16.24 (((woz13rule2) =>
% 122.84/16.24 (((woz13rule3) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz13rule4) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz1_1) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz1_2) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz1_3) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz1_4) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz1_5) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1all2) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1SetBreln1) =>
% 122.84/16.24 ((
% 122.84/16.24 (choice2fnsingleton) =>
% 122.84/16.24 ((
% 122.84/16.24 (setOfPairsIsBReln1) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1all1) =>
% 122.84/16.24 ((
% 122.84/16.24 (subbreln1) =>
% 122.84/16.24 ((
% 122.84/16.24 (eqbreln1) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1invprop) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1invI) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1invE) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1compprop) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1compI) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1compE) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1compEex) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionprop) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionIL) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionIR) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionI) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionE) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionEcases) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionCommutes) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz2Ex) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz2W) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz2A) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz2B) =>
% 122.84/16.24 ((
% 122.84/16.24 (image1Ex) =>
% 122.84/16.24 ((
% 122.84/16.24 (image1Ex1) =>
% 122.84/16.24 ((
% 122.84/16.24 (image1Equiv) =>
% 122.84/16.24 ((
% 122.84/16.24 (image1E) =>
% 122.84/16.24 ((
% 122.84/16.24 (image1I) =>
% 122.84/16.24 ((
% 122.84/16.24 (injFuncInInjFuncSet) =>
% 122.84/16.24 ((
% 122.84/16.24 (!!) @ (
% 122.84/16.24 (('#B') @ (
% 122.84/16.24 !!) @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 !!))) @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#S') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 '#S') @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 '#S'))) @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 =>))))) @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#C') @ in)))) @
% 122.84/16.24 injFuncSet)))))))) @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#C') @ in)))) @
% 122.84/16.24 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.84/16.24 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2692])).
% 122.84/16.24 thf(zip_derived_cl2716, plain,
% 122.84/16.24 (~ (((complementImpComplementIntersect) =>
% 122.84/16.24 (((complementSubsetComplementIntersect) =>
% 122.84/16.24 (((complementInPowersetComplementIntersect) =>
% 122.84/16.24 (((contraSubsetComplement) =>
% 122.84/16.24 (((complementTcontraSubset) =>
% 122.84/16.24 (((binunionTILcontra) =>
% 122.84/16.24 (((binunionTIRcontra) =>
% 122.84/16.24 (((inIntersectImpInUnion) =>
% 122.84/16.24 (((inIntersectImpInUnion2) =>
% 122.84/16.24 (((inIntersectImpInIntersectUnions) =>
% 122.84/16.24 (((intersectInPowersetIntersectUnions) =>
% 122.84/16.24 (((inComplementUnionImpNotIn1) =>
% 122.84/16.24 (((inComplementUnionImpInComplement1) =>
% 122.84/16.24 (((binunionTE) =>
% 122.84/16.24 (((binunionTEcontra) =>
% 122.84/16.24 (((demorgan2a1) =>
% 122.84/16.24 (((complementUnionInPowersetComplement) =>
% 122.84/16.24 (((demorgan2a2) =>
% 122.84/16.24 (((demorgan1a) =>
% 122.84/16.24 (((demorgan1b) =>
% 122.84/16.24 (((demorgan1) =>
% 122.84/16.24 (((demorgan2a) =>
% 122.84/16.24 (((demorgan2b2) =>
% 122.84/16.24 (((demorgan2b) =>
% 122.84/16.24 (((demorgan2) =>
% 122.84/16.24 (((woz13rule0) =>
% 122.84/16.24 (((woz13rule1) =>
% 122.84/16.24 (((woz13rule2) =>
% 122.84/16.24 (((woz13rule3) =>
% 122.84/16.24 (((woz13rule4) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz1_1) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz1_2) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz1_3) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz1_4) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz1_5) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1all2) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1SetBreln1) =>
% 122.84/16.24 ((
% 122.84/16.24 (choice2fnsingleton) =>
% 122.84/16.24 ((
% 122.84/16.24 (setOfPairsIsBReln1) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1all1) =>
% 122.84/16.24 ((
% 122.84/16.24 (subbreln1) =>
% 122.84/16.24 ((
% 122.84/16.24 (eqbreln1) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1invprop) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1invI) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1invE) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1compprop) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1compI) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1compE) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1compEex) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionprop) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionIL) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionIR) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionI) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionE) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionEcases) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionCommutes) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz2Ex) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz2W) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz2A) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz2B) =>
% 122.84/16.24 ((
% 122.84/16.24 (image1Ex) =>
% 122.84/16.24 ((
% 122.84/16.24 (image1Ex1) =>
% 122.84/16.24 ((
% 122.84/16.24 (image1Equiv) =>
% 122.84/16.24 ((
% 122.84/16.24 (image1E) =>
% 122.84/16.24 ((
% 122.84/16.24 (image1I) =>
% 122.84/16.24 ((
% 122.84/16.24 (injFuncInInjFuncSet) =>
% 122.84/16.24 ((
% 122.84/16.24 (!!) @ (
% 122.84/16.24 (('#B') @ (
% 122.84/16.24 !!) @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 !!))) @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#S') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 '#S') @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 '#S'))) @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 =>))))) @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#C') @ in)))) @
% 122.84/16.24 injFuncSet)))))))) @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#C') @ in)))) @
% 122.84/16.24 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.84/16.24 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2704])).
% 122.84/16.24 thf(zip_derived_cl2728, plain,
% 122.84/16.24 (~ (((complementSubsetComplementIntersect) =>
% 122.84/16.24 (((complementInPowersetComplementIntersect) =>
% 122.84/16.24 (((contraSubsetComplement) =>
% 122.84/16.24 (((complementTcontraSubset) =>
% 122.84/16.24 (((binunionTILcontra) =>
% 122.84/16.24 (((binunionTIRcontra) =>
% 122.84/16.24 (((inIntersectImpInUnion) =>
% 122.84/16.24 (((inIntersectImpInUnion2) =>
% 122.84/16.24 (((inIntersectImpInIntersectUnions) =>
% 122.84/16.24 (((intersectInPowersetIntersectUnions) =>
% 122.84/16.24 (((inComplementUnionImpNotIn1) =>
% 122.84/16.24 (((inComplementUnionImpInComplement1) =>
% 122.84/16.24 (((binunionTE) =>
% 122.84/16.24 (((binunionTEcontra) =>
% 122.84/16.24 (((demorgan2a1) =>
% 122.84/16.24 (((complementUnionInPowersetComplement) =>
% 122.84/16.24 (((demorgan2a2) =>
% 122.84/16.24 (((demorgan1a) =>
% 122.84/16.24 (((demorgan1b) =>
% 122.84/16.24 (((demorgan1) =>
% 122.84/16.24 (((demorgan2a) =>
% 122.84/16.24 (((demorgan2b2) =>
% 122.84/16.24 (((demorgan2b) =>
% 122.84/16.24 (((demorgan2) =>
% 122.84/16.24 (((woz13rule0) =>
% 122.84/16.24 (((woz13rule1) =>
% 122.84/16.24 (((woz13rule2) =>
% 122.84/16.24 (((woz13rule3) =>
% 122.84/16.24 (((woz13rule4) =>
% 122.84/16.24 (((woz1_1) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz1_2) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz1_3) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz1_4) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz1_5) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1all2) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1SetBreln1) =>
% 122.84/16.24 ((
% 122.84/16.24 (choice2fnsingleton) =>
% 122.84/16.24 ((
% 122.84/16.24 (setOfPairsIsBReln1) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1all1) =>
% 122.84/16.24 ((
% 122.84/16.24 (subbreln1) =>
% 122.84/16.24 ((
% 122.84/16.24 (eqbreln1) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1invprop) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1invI) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1invE) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1compprop) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1compI) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1compE) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1compEex) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionprop) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionIL) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionIR) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionI) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionE) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionEcases) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionCommutes) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz2Ex) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz2W) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz2A) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz2B) =>
% 122.84/16.24 ((
% 122.84/16.24 (image1Ex) =>
% 122.84/16.24 ((
% 122.84/16.24 (image1Ex1) =>
% 122.84/16.24 ((
% 122.84/16.24 (image1Equiv) =>
% 122.84/16.24 ((
% 122.84/16.24 (image1E) =>
% 122.84/16.24 ((
% 122.84/16.24 (image1I) =>
% 122.84/16.24 ((
% 122.84/16.24 (injFuncInInjFuncSet) =>
% 122.84/16.24 ((
% 122.84/16.24 (!!) @ (
% 122.84/16.24 (('#B') @ (
% 122.84/16.24 !!) @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 !!))) @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#S') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 '#S') @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 '#S'))) @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 =>))))) @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#C') @ in)))) @
% 122.84/16.24 injFuncSet)))))))) @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#C') @ in)))) @
% 122.84/16.24 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.84/16.24 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2716])).
% 122.84/16.24 thf(zip_derived_cl2738, plain,
% 122.84/16.24 (~ (((complementInPowersetComplementIntersect) =>
% 122.84/16.24 (((contraSubsetComplement) =>
% 122.84/16.24 (((complementTcontraSubset) =>
% 122.84/16.24 (((binunionTILcontra) =>
% 122.84/16.24 (((binunionTIRcontra) =>
% 122.84/16.24 (((inIntersectImpInUnion) =>
% 122.84/16.24 (((inIntersectImpInUnion2) =>
% 122.84/16.24 (((inIntersectImpInIntersectUnions) =>
% 122.84/16.24 (((intersectInPowersetIntersectUnions) =>
% 122.84/16.24 (((inComplementUnionImpNotIn1) =>
% 122.84/16.24 (((inComplementUnionImpInComplement1) =>
% 122.84/16.24 (((binunionTE) =>
% 122.84/16.24 (((binunionTEcontra) =>
% 122.84/16.24 (((demorgan2a1) =>
% 122.84/16.24 (((complementUnionInPowersetComplement) =>
% 122.84/16.24 (((demorgan2a2) =>
% 122.84/16.24 (((demorgan1a) =>
% 122.84/16.24 (((demorgan1b) =>
% 122.84/16.24 (((demorgan1) =>
% 122.84/16.24 (((demorgan2a) =>
% 122.84/16.24 (((demorgan2b2) =>
% 122.84/16.24 (((demorgan2b) =>
% 122.84/16.24 (((demorgan2) =>
% 122.84/16.24 (((woz13rule0) =>
% 122.84/16.24 (((woz13rule1) =>
% 122.84/16.24 (((woz13rule2) =>
% 122.84/16.24 (((woz13rule3) =>
% 122.84/16.24 (((woz13rule4) =>
% 122.84/16.24 (((woz1_1) =>
% 122.84/16.24 (((woz1_2) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz1_3) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz1_4) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz1_5) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1all2) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1SetBreln1) =>
% 122.84/16.24 ((
% 122.84/16.24 (choice2fnsingleton) =>
% 122.84/16.24 ((
% 122.84/16.24 (setOfPairsIsBReln1) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1all1) =>
% 122.84/16.24 ((
% 122.84/16.24 (subbreln1) =>
% 122.84/16.24 ((
% 122.84/16.24 (eqbreln1) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1invprop) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1invI) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1invE) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1compprop) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1compI) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1compE) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1compEex) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionprop) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionIL) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionIR) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionI) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionE) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionEcases) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionCommutes) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz2Ex) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz2W) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz2A) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz2B) =>
% 122.84/16.24 ((
% 122.84/16.24 (image1Ex) =>
% 122.84/16.24 ((
% 122.84/16.24 (image1Ex1) =>
% 122.84/16.24 ((
% 122.84/16.24 (image1Equiv) =>
% 122.84/16.24 ((
% 122.84/16.24 (image1E) =>
% 122.84/16.24 ((
% 122.84/16.24 (image1I) =>
% 122.84/16.24 ((
% 122.84/16.24 (injFuncInInjFuncSet) =>
% 122.84/16.24 ((
% 122.84/16.24 (!!) @ (
% 122.84/16.24 (('#B') @ (
% 122.84/16.24 !!) @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 !!))) @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#S') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 '#S') @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 '#S'))) @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 =>))))) @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#C') @ in)))) @
% 122.84/16.24 injFuncSet)))))))) @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#C') @ in)))) @
% 122.84/16.24 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.84/16.24 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2728])).
% 122.84/16.24 thf(zip_derived_cl2746, plain,
% 122.84/16.24 (~ (((contraSubsetComplement) =>
% 122.84/16.24 (((complementTcontraSubset) =>
% 122.84/16.24 (((binunionTILcontra) =>
% 122.84/16.24 (((binunionTIRcontra) =>
% 122.84/16.24 (((inIntersectImpInUnion) =>
% 122.84/16.24 (((inIntersectImpInUnion2) =>
% 122.84/16.24 (((inIntersectImpInIntersectUnions) =>
% 122.84/16.24 (((intersectInPowersetIntersectUnions) =>
% 122.84/16.24 (((inComplementUnionImpNotIn1) =>
% 122.84/16.24 (((inComplementUnionImpInComplement1) =>
% 122.84/16.24 (((binunionTE) =>
% 122.84/16.24 (((binunionTEcontra) =>
% 122.84/16.24 (((demorgan2a1) =>
% 122.84/16.24 (((complementUnionInPowersetComplement) =>
% 122.84/16.24 (((demorgan2a2) =>
% 122.84/16.24 (((demorgan1a) =>
% 122.84/16.24 (((demorgan1b) =>
% 122.84/16.24 (((demorgan1) =>
% 122.84/16.24 (((demorgan2a) =>
% 122.84/16.24 (((demorgan2b2) =>
% 122.84/16.24 (((demorgan2b) =>
% 122.84/16.24 (((demorgan2) =>
% 122.84/16.24 (((woz13rule0) =>
% 122.84/16.24 (((woz13rule1) =>
% 122.84/16.24 (((woz13rule2) =>
% 122.84/16.24 (((woz13rule3) =>
% 122.84/16.24 (((woz13rule4) =>
% 122.84/16.24 (((woz1_1) =>
% 122.84/16.24 (((woz1_2) =>
% 122.84/16.24 (((woz1_3) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz1_4) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz1_5) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1all2) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1SetBreln1) =>
% 122.84/16.24 ((
% 122.84/16.24 (choice2fnsingleton) =>
% 122.84/16.24 ((
% 122.84/16.24 (setOfPairsIsBReln1) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1all1) =>
% 122.84/16.24 ((
% 122.84/16.24 (subbreln1) =>
% 122.84/16.24 ((
% 122.84/16.24 (eqbreln1) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1invprop) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1invI) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1invE) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1compprop) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1compI) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1compE) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1compEex) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionprop) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionIL) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionIR) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionI) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionE) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionEcases) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionCommutes) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz2Ex) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz2W) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz2A) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz2B) =>
% 122.84/16.24 ((
% 122.84/16.24 (image1Ex) =>
% 122.84/16.24 ((
% 122.84/16.24 (image1Ex1) =>
% 122.84/16.24 ((
% 122.84/16.24 (image1Equiv) =>
% 122.84/16.24 ((
% 122.84/16.24 (image1E) =>
% 122.84/16.24 ((
% 122.84/16.24 (image1I) =>
% 122.84/16.24 ((
% 122.84/16.24 (injFuncInInjFuncSet) =>
% 122.84/16.24 ((
% 122.84/16.24 (!!) @ (
% 122.84/16.24 (('#B') @ (
% 122.84/16.24 !!) @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 !!))) @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#S') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 '#S') @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 '#S'))) @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 =>))))) @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#C') @ in)))) @
% 122.84/16.24 injFuncSet)))))))) @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#C') @ in)))) @
% 122.84/16.24 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.84/16.24 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2738])).
% 122.84/16.24 thf(zip_derived_cl2754, plain,
% 122.84/16.24 (~ (((complementTcontraSubset) =>
% 122.84/16.24 (((binunionTILcontra) =>
% 122.84/16.24 (((binunionTIRcontra) =>
% 122.84/16.24 (((inIntersectImpInUnion) =>
% 122.84/16.24 (((inIntersectImpInUnion2) =>
% 122.84/16.24 (((inIntersectImpInIntersectUnions) =>
% 122.84/16.24 (((intersectInPowersetIntersectUnions) =>
% 122.84/16.24 (((inComplementUnionImpNotIn1) =>
% 122.84/16.24 (((inComplementUnionImpInComplement1) =>
% 122.84/16.24 (((binunionTE) =>
% 122.84/16.24 (((binunionTEcontra) =>
% 122.84/16.24 (((demorgan2a1) =>
% 122.84/16.24 (((complementUnionInPowersetComplement) =>
% 122.84/16.24 (((demorgan2a2) =>
% 122.84/16.24 (((demorgan1a) =>
% 122.84/16.24 (((demorgan1b) =>
% 122.84/16.24 (((demorgan1) =>
% 122.84/16.24 (((demorgan2a) =>
% 122.84/16.24 (((demorgan2b2) =>
% 122.84/16.24 (((demorgan2b) =>
% 122.84/16.24 (((demorgan2) =>
% 122.84/16.24 (((woz13rule0) =>
% 122.84/16.24 (((woz13rule1) =>
% 122.84/16.24 (((woz13rule2) =>
% 122.84/16.24 (((woz13rule3) =>
% 122.84/16.24 (((woz13rule4) =>
% 122.84/16.24 (((woz1_1) =>
% 122.84/16.24 (((woz1_2) =>
% 122.84/16.24 (((woz1_3) =>
% 122.84/16.24 (((woz1_4) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz1_5) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1all2) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1SetBreln1) =>
% 122.84/16.24 ((
% 122.84/16.24 (choice2fnsingleton) =>
% 122.84/16.24 ((
% 122.84/16.24 (setOfPairsIsBReln1) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1all1) =>
% 122.84/16.24 ((
% 122.84/16.24 (subbreln1) =>
% 122.84/16.24 ((
% 122.84/16.24 (eqbreln1) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1invprop) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1invI) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1invE) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1compprop) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1compI) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1compE) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1compEex) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionprop) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionIL) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionIR) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionI) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionE) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionEcases) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionCommutes) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz2Ex) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz2W) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz2A) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz2B) =>
% 122.84/16.24 ((
% 122.84/16.24 (image1Ex) =>
% 122.84/16.24 ((
% 122.84/16.24 (image1Ex1) =>
% 122.84/16.24 ((
% 122.84/16.24 (image1Equiv) =>
% 122.84/16.24 ((
% 122.84/16.24 (image1E) =>
% 122.84/16.24 ((
% 122.84/16.24 (image1I) =>
% 122.84/16.24 ((
% 122.84/16.24 (injFuncInInjFuncSet) =>
% 122.84/16.24 ((
% 122.84/16.24 (!!) @ (
% 122.84/16.24 (('#B') @ (
% 122.84/16.24 !!) @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 !!))) @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#S') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 '#S') @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 '#S'))) @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 =>))))) @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#C') @ in)))) @
% 122.84/16.24 injFuncSet)))))))) @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#C') @ in)))) @
% 122.84/16.24 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.84/16.24 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2746])).
% 122.84/16.24 thf(zip_derived_cl2762, plain,
% 122.84/16.24 (~ (((binunionTILcontra) =>
% 122.84/16.24 (((binunionTIRcontra) =>
% 122.84/16.24 (((inIntersectImpInUnion) =>
% 122.84/16.24 (((inIntersectImpInUnion2) =>
% 122.84/16.24 (((inIntersectImpInIntersectUnions) =>
% 122.84/16.24 (((intersectInPowersetIntersectUnions) =>
% 122.84/16.24 (((inComplementUnionImpNotIn1) =>
% 122.84/16.24 (((inComplementUnionImpInComplement1) =>
% 122.84/16.24 (((binunionTE) =>
% 122.84/16.24 (((binunionTEcontra) =>
% 122.84/16.24 (((demorgan2a1) =>
% 122.84/16.24 (((complementUnionInPowersetComplement) =>
% 122.84/16.24 (((demorgan2a2) =>
% 122.84/16.24 (((demorgan1a) =>
% 122.84/16.24 (((demorgan1b) =>
% 122.84/16.24 (((demorgan1) =>
% 122.84/16.24 (((demorgan2a) =>
% 122.84/16.24 (((demorgan2b2) =>
% 122.84/16.24 (((demorgan2b) =>
% 122.84/16.24 (((demorgan2) =>
% 122.84/16.24 (((woz13rule0) =>
% 122.84/16.24 (((woz13rule1) =>
% 122.84/16.24 (((woz13rule2) =>
% 122.84/16.24 (((woz13rule3) =>
% 122.84/16.24 (((woz13rule4) =>
% 122.84/16.24 (((woz1_1) =>
% 122.84/16.24 (((woz1_2) =>
% 122.84/16.24 (((woz1_3) =>
% 122.84/16.24 (((woz1_4) =>
% 122.84/16.24 (((woz1_5) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1all2) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1SetBreln1) =>
% 122.84/16.24 ((
% 122.84/16.24 (choice2fnsingleton) =>
% 122.84/16.24 ((
% 122.84/16.24 (setOfPairsIsBReln1) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1all1) =>
% 122.84/16.24 ((
% 122.84/16.24 (subbreln1) =>
% 122.84/16.24 ((
% 122.84/16.24 (eqbreln1) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1invprop) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1invI) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1invE) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1compprop) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1compI) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1compE) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1compEex) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionprop) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionIL) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionIR) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionI) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionE) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionEcases) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionCommutes) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz2Ex) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz2W) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz2A) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz2B) =>
% 122.84/16.24 ((
% 122.84/16.24 (image1Ex) =>
% 122.84/16.24 ((
% 122.84/16.24 (image1Ex1) =>
% 122.84/16.24 ((
% 122.84/16.24 (image1Equiv) =>
% 122.84/16.24 ((
% 122.84/16.24 (image1E) =>
% 122.84/16.24 ((
% 122.84/16.24 (image1I) =>
% 122.84/16.24 ((
% 122.84/16.24 (injFuncInInjFuncSet) =>
% 122.84/16.24 ((
% 122.84/16.24 (!!) @ (
% 122.84/16.24 (('#B') @ (
% 122.84/16.24 !!) @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 !!))) @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#S') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 '#S') @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 '#S'))) @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 =>))))) @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#C') @ in)))) @
% 122.84/16.24 injFuncSet)))))))) @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#C') @ in)))) @
% 122.84/16.24 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.84/16.24 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2754])).
% 122.84/16.24 thf(zip_derived_cl2771, plain,
% 122.84/16.24 (~ (((binunionTIRcontra) =>
% 122.84/16.24 (((inIntersectImpInUnion) =>
% 122.84/16.24 (((inIntersectImpInUnion2) =>
% 122.84/16.24 (((inIntersectImpInIntersectUnions) =>
% 122.84/16.24 (((intersectInPowersetIntersectUnions) =>
% 122.84/16.24 (((inComplementUnionImpNotIn1) =>
% 122.84/16.24 (((inComplementUnionImpInComplement1) =>
% 122.84/16.24 (((binunionTE) =>
% 122.84/16.24 (((binunionTEcontra) =>
% 122.84/16.24 (((demorgan2a1) =>
% 122.84/16.24 (((complementUnionInPowersetComplement) =>
% 122.84/16.24 (((demorgan2a2) =>
% 122.84/16.24 (((demorgan1a) =>
% 122.84/16.24 (((demorgan1b) =>
% 122.84/16.24 (((demorgan1) =>
% 122.84/16.24 (((demorgan2a) =>
% 122.84/16.24 (((demorgan2b2) =>
% 122.84/16.24 (((demorgan2b) =>
% 122.84/16.24 (((demorgan2) =>
% 122.84/16.24 (((woz13rule0) =>
% 122.84/16.24 (((woz13rule1) =>
% 122.84/16.24 (((woz13rule2) =>
% 122.84/16.24 (((woz13rule3) =>
% 122.84/16.24 (((woz13rule4) =>
% 122.84/16.24 (((woz1_1) =>
% 122.84/16.24 (((woz1_2) =>
% 122.84/16.24 (((woz1_3) =>
% 122.84/16.24 (((woz1_4) =>
% 122.84/16.24 (((woz1_5) =>
% 122.84/16.24 (((breln1all2) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1SetBreln1) =>
% 122.84/16.24 ((
% 122.84/16.24 (choice2fnsingleton) =>
% 122.84/16.24 ((
% 122.84/16.24 (setOfPairsIsBReln1) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1all1) =>
% 122.84/16.24 ((
% 122.84/16.24 (subbreln1) =>
% 122.84/16.24 ((
% 122.84/16.24 (eqbreln1) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1invprop) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1invI) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1invE) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1compprop) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1compI) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1compE) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1compEex) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionprop) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionIL) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionIR) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionI) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionE) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionEcases) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionCommutes) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz2Ex) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz2W) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz2A) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz2B) =>
% 122.84/16.24 ((
% 122.84/16.24 (image1Ex) =>
% 122.84/16.24 ((
% 122.84/16.24 (image1Ex1) =>
% 122.84/16.24 ((
% 122.84/16.24 (image1Equiv) =>
% 122.84/16.24 ((
% 122.84/16.24 (image1E) =>
% 122.84/16.24 ((
% 122.84/16.24 (image1I) =>
% 122.84/16.24 ((
% 122.84/16.24 (injFuncInInjFuncSet) =>
% 122.84/16.24 ((
% 122.84/16.24 (!!) @ (
% 122.84/16.24 (('#B') @ (
% 122.84/16.24 !!) @
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% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
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% 122.84/16.24 (
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% 122.84/16.24 injFuncSet)))))))) @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
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% 122.84/16.24 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.84/16.24 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2762])).
% 122.84/16.24 thf(zip_derived_cl2781, plain,
% 122.84/16.24 (~ (((inIntersectImpInUnion) =>
% 122.84/16.24 (((inIntersectImpInUnion2) =>
% 122.84/16.24 (((inIntersectImpInIntersectUnions) =>
% 122.84/16.24 (((intersectInPowersetIntersectUnions) =>
% 122.84/16.24 (((inComplementUnionImpNotIn1) =>
% 122.84/16.24 (((inComplementUnionImpInComplement1) =>
% 122.84/16.24 (((binunionTE) =>
% 122.84/16.24 (((binunionTEcontra) =>
% 122.84/16.24 (((demorgan2a1) =>
% 122.84/16.24 (((complementUnionInPowersetComplement) =>
% 122.84/16.24 (((demorgan2a2) =>
% 122.84/16.24 (((demorgan1a) =>
% 122.84/16.24 (((demorgan1b) =>
% 122.84/16.24 (((demorgan1) =>
% 122.84/16.24 (((demorgan2a) =>
% 122.84/16.24 (((demorgan2b2) =>
% 122.84/16.24 (((demorgan2b) =>
% 122.84/16.24 (((demorgan2) =>
% 122.84/16.24 (((woz13rule0) =>
% 122.84/16.24 (((woz13rule1) =>
% 122.84/16.24 (((woz13rule2) =>
% 122.84/16.24 (((woz13rule3) =>
% 122.84/16.24 (((woz13rule4) =>
% 122.84/16.24 (((woz1_1) =>
% 122.84/16.24 (((woz1_2) =>
% 122.84/16.24 (((woz1_3) =>
% 122.84/16.24 (((woz1_4) =>
% 122.84/16.24 (((woz1_5) =>
% 122.84/16.24 (((breln1all2) =>
% 122.84/16.24 (((breln1SetBreln1) =>
% 122.84/16.24 ((
% 122.84/16.24 (choice2fnsingleton) =>
% 122.84/16.24 ((
% 122.84/16.24 (setOfPairsIsBReln1) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1all1) =>
% 122.84/16.24 ((
% 122.84/16.24 (subbreln1) =>
% 122.84/16.24 ((
% 122.84/16.24 (eqbreln1) =>
% 122.84/16.24 ((
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% 122.84/16.24 ((
% 122.84/16.24 (breln1invI) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1invE) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1compprop) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1compI) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1compE) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1compEex) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionprop) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionIL) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionIR) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionI) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionE) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionEcases) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionCommutes) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz2Ex) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz2W) =>
% 122.84/16.24 ((
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% 122.84/16.24 ((
% 122.84/16.24 (woz2B) =>
% 122.84/16.24 ((
% 122.84/16.24 (image1Ex) =>
% 122.84/16.24 ((
% 122.84/16.24 (image1Ex1) =>
% 122.84/16.24 ((
% 122.84/16.24 (image1Equiv) =>
% 122.84/16.24 ((
% 122.84/16.24 (image1E) =>
% 122.84/16.24 ((
% 122.84/16.24 (image1I) =>
% 122.84/16.24 ((
% 122.84/16.24 (injFuncInInjFuncSet) =>
% 122.84/16.24 ((
% 122.84/16.24 (!!) @ (
% 122.84/16.24 (('#B') @ (
% 122.84/16.24 !!) @
% 122.84/16.24 (
% 122.84/16.24 (
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% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
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% 122.84/16.24 (
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% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
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% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
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% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 =>))))) @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
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% 122.84/16.24 (
% 122.84/16.24 (
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% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
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% 122.84/16.24 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.84/16.24 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2771])).
% 122.84/16.24 thf(zip_derived_cl2792, plain,
% 122.84/16.24 (~ (((inIntersectImpInUnion2) =>
% 122.84/16.24 (((inIntersectImpInIntersectUnions) =>
% 122.84/16.24 (((intersectInPowersetIntersectUnions) =>
% 122.84/16.24 (((inComplementUnionImpNotIn1) =>
% 122.84/16.24 (((inComplementUnionImpInComplement1) =>
% 122.84/16.24 (((binunionTE) =>
% 122.84/16.24 (((binunionTEcontra) =>
% 122.84/16.24 (((demorgan2a1) =>
% 122.84/16.24 (((complementUnionInPowersetComplement) =>
% 122.84/16.24 (((demorgan2a2) =>
% 122.84/16.24 (((demorgan1a) =>
% 122.84/16.24 (((demorgan1b) =>
% 122.84/16.24 (((demorgan1) =>
% 122.84/16.24 (((demorgan2a) =>
% 122.84/16.24 (((demorgan2b2) =>
% 122.84/16.24 (((demorgan2b) =>
% 122.84/16.24 (((demorgan2) =>
% 122.84/16.24 (((woz13rule0) =>
% 122.84/16.24 (((woz13rule1) =>
% 122.84/16.24 (((woz13rule2) =>
% 122.84/16.24 (((woz13rule3) =>
% 122.84/16.24 (((woz13rule4) =>
% 122.84/16.24 (((woz1_1) =>
% 122.84/16.24 (((woz1_2) =>
% 122.84/16.24 (((woz1_3) =>
% 122.84/16.24 (((woz1_4) =>
% 122.84/16.24 (((woz1_5) =>
% 122.84/16.24 (((breln1all2) =>
% 122.84/16.24 (((breln1SetBreln1) =>
% 122.84/16.24 (((choice2fnsingleton) =>
% 122.84/16.24 ((
% 122.84/16.24 (setOfPairsIsBReln1) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1all1) =>
% 122.84/16.24 ((
% 122.84/16.24 (subbreln1) =>
% 122.84/16.24 ((
% 122.84/16.24 (eqbreln1) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1invprop) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1invI) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1invE) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1compprop) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1compI) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1compE) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1compEex) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionprop) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionIL) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionIR) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionI) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionE) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionEcases) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionCommutes) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz2Ex) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz2W) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz2A) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz2B) =>
% 122.84/16.24 ((
% 122.84/16.24 (image1Ex) =>
% 122.84/16.24 ((
% 122.84/16.24 (image1Ex1) =>
% 122.84/16.24 ((
% 122.84/16.24 (image1Equiv) =>
% 122.84/16.24 ((
% 122.84/16.24 (image1E) =>
% 122.84/16.24 ((
% 122.84/16.24 (image1I) =>
% 122.84/16.24 ((
% 122.84/16.24 (injFuncInInjFuncSet) =>
% 122.84/16.24 ((
% 122.84/16.24 (!!) @ (
% 122.84/16.24 (('#B') @ (
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% 122.84/16.24 (
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% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
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% 122.84/16.24 (
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% 122.84/16.24 (
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% 122.84/16.24 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.84/16.24 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2781])).
% 122.84/16.24 thf(zip_derived_cl2803, plain,
% 122.84/16.24 (~ (((inIntersectImpInIntersectUnions) =>
% 122.84/16.24 (((intersectInPowersetIntersectUnions) =>
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% 122.84/16.24 (((inComplementUnionImpInComplement1) =>
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% 122.84/16.24 (((binunionTEcontra) =>
% 122.84/16.24 (((demorgan2a1) =>
% 122.84/16.24 (((complementUnionInPowersetComplement) =>
% 122.84/16.24 (((demorgan2a2) =>
% 122.84/16.24 (((demorgan1a) =>
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% 122.84/16.24 (((demorgan1) =>
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% 122.84/16.24 (((woz1_3) =>
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% 122.84/16.24 ((
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% 122.84/16.24 ((
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% 122.84/16.24 ((
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% 122.84/16.24 ((
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% 122.84/16.24 ((
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% 122.84/16.24 ((
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% 122.84/16.24 ((
% 122.84/16.24 (breln1compE) =>
% 122.84/16.24 ((
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% 122.84/16.24 ((
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% 122.84/16.24 ((
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% 122.84/16.24 ((
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% 122.84/16.24 ((
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% 122.84/16.24 ((
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% 122.84/16.24 ((
% 122.84/16.24 (breln1unionEcases) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionCommutes) =>
% 122.84/16.24 ((
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% 122.84/16.24 ((
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% 122.84/16.24 ((
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% 122.84/16.24 ((
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% 122.84/16.24 ((
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% 122.84/16.24 ((
% 122.84/16.24 (image1Ex1) =>
% 122.84/16.24 ((
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% 122.84/16.24 ((
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% 122.84/16.24 ((
% 122.84/16.24 (image1I) =>
% 122.84/16.24 ((
% 122.84/16.24 (injFuncInInjFuncSet) =>
% 122.84/16.24 ((
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% 122.84/16.24 (('#B') @ (
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% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
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% 122.84/16.24 ('#B') @ (
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% 122.84/16.24 (
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% 122.84/16.24 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.84/16.24 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2792])).
% 122.84/16.24 thf(zip_derived_cl2813, plain,
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% 122.84/16.24 (((inComplementUnionImpInComplement1) =>
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% 122.84/16.24 (((binunionTEcontra) =>
% 122.84/16.24 (((demorgan2a1) =>
% 122.84/16.24 (((complementUnionInPowersetComplement) =>
% 122.84/16.24 (((demorgan2a2) =>
% 122.84/16.24 (((demorgan1a) =>
% 122.84/16.24 (((demorgan1b) =>
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% 122.84/16.24 ((
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% 122.84/16.24 ((
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% 122.84/16.24 ((
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% 122.84/16.24 ((
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% 122.84/16.24 ((
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% 122.84/16.24 ((
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% 122.84/16.24 ((
% 122.84/16.24 (breln1unionIR) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionI) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionE) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionEcases) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionCommutes) =>
% 122.84/16.24 ((
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% 122.84/16.24 ((
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% 122.84/16.24 ((
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% 122.84/16.24 ((
% 122.84/16.24 (woz2B) =>
% 122.84/16.24 ((
% 122.84/16.24 (image1Ex) =>
% 122.84/16.24 ((
% 122.84/16.24 (image1Ex1) =>
% 122.84/16.24 ((
% 122.84/16.24 (image1Equiv) =>
% 122.84/16.24 ((
% 122.84/16.24 (image1E) =>
% 122.84/16.24 ((
% 122.84/16.24 (image1I) =>
% 122.84/16.24 ((
% 122.84/16.24 (injFuncInInjFuncSet) =>
% 122.84/16.24 ((
% 122.84/16.24 (!!) @ (
% 122.84/16.24 (('#B') @ (
% 122.84/16.24 !!) @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
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% 122.84/16.24 (
% 122.84/16.24 ('#S') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 '#S') @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 '#S'))) @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 =>))))) @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#C') @ in)))) @
% 122.84/16.24 injFuncSet)))))))) @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#C') @ in)))) @
% 122.84/16.24 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.84/16.24 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2803])).
% 122.84/16.24 thf(zip_derived_cl2823, plain,
% 122.84/16.24 (~ (((inComplementUnionImpNotIn1) =>
% 122.84/16.24 (((inComplementUnionImpInComplement1) =>
% 122.84/16.24 (((binunionTE) =>
% 122.84/16.24 (((binunionTEcontra) =>
% 122.84/16.24 (((demorgan2a1) =>
% 122.84/16.24 (((complementUnionInPowersetComplement) =>
% 122.84/16.24 (((demorgan2a2) =>
% 122.84/16.24 (((demorgan1a) =>
% 122.84/16.24 (((demorgan1b) =>
% 122.84/16.24 (((demorgan1) =>
% 122.84/16.24 (((demorgan2a) =>
% 122.84/16.24 (((demorgan2b2) =>
% 122.84/16.24 (((demorgan2b) =>
% 122.84/16.24 (((demorgan2) =>
% 122.84/16.24 (((woz13rule0) =>
% 122.84/16.24 (((woz13rule1) =>
% 122.84/16.24 (((woz13rule2) =>
% 122.84/16.24 (((woz13rule3) =>
% 122.84/16.24 (((woz13rule4) =>
% 122.84/16.24 (((woz1_1) =>
% 122.84/16.24 (((woz1_2) =>
% 122.84/16.24 (((woz1_3) =>
% 122.84/16.24 (((woz1_4) =>
% 122.84/16.24 (((woz1_5) =>
% 122.84/16.24 (((breln1all2) =>
% 122.84/16.24 (((breln1SetBreln1) =>
% 122.84/16.24 (((choice2fnsingleton) =>
% 122.84/16.24 (((setOfPairsIsBReln1) =>
% 122.84/16.24 (((breln1all1) =>
% 122.84/16.24 (((subbreln1) =>
% 122.84/16.24 ((
% 122.84/16.24 (eqbreln1) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1invprop) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1invI) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1invE) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1compprop) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1compI) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1compE) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1compEex) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionprop) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionIL) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionIR) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionI) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionE) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionEcases) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionCommutes) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz2Ex) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz2W) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz2A) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz2B) =>
% 122.84/16.24 ((
% 122.84/16.24 (image1Ex) =>
% 122.84/16.24 ((
% 122.84/16.24 (image1Ex1) =>
% 122.84/16.24 ((
% 122.84/16.24 (image1Equiv) =>
% 122.84/16.24 ((
% 122.84/16.24 (image1E) =>
% 122.84/16.24 ((
% 122.84/16.24 (image1I) =>
% 122.84/16.24 ((
% 122.84/16.24 (injFuncInInjFuncSet) =>
% 122.84/16.24 ((
% 122.84/16.24 (!!) @ (
% 122.84/16.24 (('#B') @ (
% 122.84/16.24 !!) @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 !!))) @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#S') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 '#S') @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 '#S'))) @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 =>))))) @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#C') @ in)))) @
% 122.84/16.24 injFuncSet)))))))) @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#C') @ in)))) @
% 122.84/16.24 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.84/16.24 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2813])).
% 122.84/16.24 thf(zip_derived_cl2834, plain,
% 122.84/16.24 (~ (((inComplementUnionImpInComplement1) =>
% 122.84/16.24 (((binunionTE) =>
% 122.84/16.24 (((binunionTEcontra) =>
% 122.84/16.24 (((demorgan2a1) =>
% 122.84/16.24 (((complementUnionInPowersetComplement) =>
% 122.84/16.24 (((demorgan2a2) =>
% 122.84/16.24 (((demorgan1a) =>
% 122.84/16.24 (((demorgan1b) =>
% 122.84/16.24 (((demorgan1) =>
% 122.84/16.24 (((demorgan2a) =>
% 122.84/16.24 (((demorgan2b2) =>
% 122.84/16.24 (((demorgan2b) =>
% 122.84/16.24 (((demorgan2) =>
% 122.84/16.24 (((woz13rule0) =>
% 122.84/16.24 (((woz13rule1) =>
% 122.84/16.24 (((woz13rule2) =>
% 122.84/16.24 (((woz13rule3) =>
% 122.84/16.24 (((woz13rule4) =>
% 122.84/16.24 (((woz1_1) =>
% 122.84/16.24 (((woz1_2) =>
% 122.84/16.24 (((woz1_3) =>
% 122.84/16.24 (((woz1_4) =>
% 122.84/16.24 (((woz1_5) =>
% 122.84/16.24 (((breln1all2) =>
% 122.84/16.24 (((breln1SetBreln1) =>
% 122.84/16.24 (((choice2fnsingleton) =>
% 122.84/16.24 (((setOfPairsIsBReln1) =>
% 122.84/16.24 (((breln1all1) =>
% 122.84/16.24 (((subbreln1) =>
% 122.84/16.24 (((eqbreln1) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1invprop) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1invI) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1invE) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1compprop) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1compI) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1compE) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1compEex) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionprop) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionIL) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionIR) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionI) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionE) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionEcases) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionCommutes) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz2Ex) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz2W) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz2A) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz2B) =>
% 122.84/16.24 ((
% 122.84/16.24 (image1Ex) =>
% 122.84/16.24 ((
% 122.84/16.24 (image1Ex1) =>
% 122.84/16.24 ((
% 122.84/16.24 (image1Equiv) =>
% 122.84/16.24 ((
% 122.84/16.24 (image1E) =>
% 122.84/16.24 ((
% 122.84/16.24 (image1I) =>
% 122.84/16.24 ((
% 122.84/16.24 (injFuncInInjFuncSet) =>
% 122.84/16.24 ((
% 122.84/16.24 (!!) @ (
% 122.84/16.24 (('#B') @ (
% 122.84/16.24 !!) @
% 122.84/16.24 (
% 122.84/16.24 (
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% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 !!))) @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#S') @ (
% 122.84/16.24 (
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% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 '#S'))) @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 =>))))) @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
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% 122.84/16.24 injFuncSet)))))))) @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#C') @ in)))) @
% 122.84/16.24 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.84/16.24 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2823])).
% 122.84/16.24 thf(zip_derived_cl2845, plain,
% 122.84/16.24 (~ (((binunionTE) =>
% 122.84/16.24 (((binunionTEcontra) =>
% 122.84/16.24 (((demorgan2a1) =>
% 122.84/16.24 (((complementUnionInPowersetComplement) =>
% 122.84/16.24 (((demorgan2a2) =>
% 122.84/16.24 (((demorgan1a) =>
% 122.84/16.24 (((demorgan1b) =>
% 122.84/16.24 (((demorgan1) =>
% 122.84/16.24 (((demorgan2a) =>
% 122.84/16.24 (((demorgan2b2) =>
% 122.84/16.24 (((demorgan2b) =>
% 122.84/16.24 (((demorgan2) =>
% 122.84/16.24 (((woz13rule0) =>
% 122.84/16.24 (((woz13rule1) =>
% 122.84/16.24 (((woz13rule2) =>
% 122.84/16.24 (((woz13rule3) =>
% 122.84/16.24 (((woz13rule4) =>
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% 122.84/16.24 (((woz1_3) =>
% 122.84/16.24 (((woz1_4) =>
% 122.84/16.24 (((woz1_5) =>
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% 122.84/16.24 ((
% 122.84/16.24 (breln1invI) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1invE) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1compprop) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1compI) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1compE) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1compEex) =>
% 122.84/16.24 ((
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% 122.84/16.24 ((
% 122.84/16.24 (breln1unionIL) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionIR) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionI) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionE) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionEcases) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionCommutes) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz2Ex) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz2W) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz2A) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz2B) =>
% 122.84/16.24 ((
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% 122.84/16.24 ((
% 122.84/16.24 (image1Ex1) =>
% 122.84/16.24 ((
% 122.84/16.24 (image1Equiv) =>
% 122.84/16.24 ((
% 122.84/16.24 (image1E) =>
% 122.84/16.24 ((
% 122.84/16.24 (image1I) =>
% 122.84/16.24 ((
% 122.84/16.24 (injFuncInInjFuncSet) =>
% 122.84/16.24 ((
% 122.84/16.24 (!!) @ (
% 122.84/16.24 (('#B') @ (
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% 122.84/16.24 (
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% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
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% 122.84/16.24 (
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% 122.84/16.24 ('#B') @ (
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% 122.84/16.24 ('#B') @ (
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% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
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% 122.84/16.24 ('#B') @ (
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% 122.84/16.24 injFuncSet)))))))) @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
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% 122.84/16.24 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.84/16.24 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2834])).
% 122.84/16.24 thf(zip_derived_cl2857, plain,
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% 122.84/16.24 (((demorgan2a1) =>
% 122.84/16.24 (((complementUnionInPowersetComplement) =>
% 122.84/16.24 (((demorgan2a2) =>
% 122.84/16.24 (((demorgan1a) =>
% 122.84/16.24 (((demorgan1b) =>
% 122.84/16.24 (((demorgan1) =>
% 122.84/16.24 (((demorgan2a) =>
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% 122.84/16.24 (((woz13rule4) =>
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% 122.84/16.24 (((woz1_3) =>
% 122.84/16.24 (((woz1_4) =>
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% 122.84/16.24 (((setOfPairsIsBReln1) =>
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% 122.84/16.24 ((
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% 122.84/16.24 ((
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% 122.84/16.24 ((
% 122.84/16.24 (breln1compE) =>
% 122.84/16.24 ((
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% 122.84/16.24 ((
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% 122.84/16.24 ((
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% 122.84/16.24 ((
% 122.84/16.24 (breln1unionI) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionE) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionEcases) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionCommutes) =>
% 122.84/16.24 ((
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% 122.84/16.24 ((
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% 122.84/16.24 ((
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% 122.84/16.24 ((
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% 122.84/16.24 ((
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% 122.84/16.24 ((
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% 122.84/16.24 ((
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% 122.84/16.24 ((
% 122.84/16.24 (image1E) =>
% 122.84/16.24 ((
% 122.84/16.24 (image1I) =>
% 122.84/16.24 ((
% 122.84/16.24 (injFuncInInjFuncSet) =>
% 122.84/16.24 ((
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% 122.84/16.24 (('#B') @ (
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% 122.84/16.24 (
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% 122.84/16.24 '#S') @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 '#S'))) @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 =>))))) @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#C') @ in)))) @
% 122.84/16.24 injFuncSet)))))))) @
% 122.84/16.24 (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#B') @ (
% 122.84/16.24 (
% 122.84/16.24 ('#C') @ in)))) @
% 122.84/16.24 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.84/16.24 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2845])).
% 122.84/16.24 thf(zip_derived_cl2869, plain,
% 122.84/16.24 (~ (((demorgan2a1) =>
% 122.84/16.24 (((complementUnionInPowersetComplement) =>
% 122.84/16.24 (((demorgan2a2) =>
% 122.84/16.24 (((demorgan1a) =>
% 122.84/16.24 (((demorgan1b) =>
% 122.84/16.24 (((demorgan1) =>
% 122.84/16.24 (((demorgan2a) =>
% 122.84/16.24 (((demorgan2b2) =>
% 122.84/16.24 (((demorgan2b) =>
% 122.84/16.24 (((demorgan2) =>
% 122.84/16.24 (((woz13rule0) =>
% 122.84/16.24 (((woz13rule1) =>
% 122.84/16.24 (((woz13rule2) =>
% 122.84/16.24 (((woz13rule3) =>
% 122.84/16.24 (((woz13rule4) =>
% 122.84/16.24 (((woz1_1) =>
% 122.84/16.24 (((woz1_2) =>
% 122.84/16.24 (((woz1_3) =>
% 122.84/16.24 (((woz1_4) =>
% 122.84/16.24 (((woz1_5) =>
% 122.84/16.24 (((breln1all2) =>
% 122.84/16.24 (((breln1SetBreln1) =>
% 122.84/16.24 (((choice2fnsingleton) =>
% 122.84/16.24 (((setOfPairsIsBReln1) =>
% 122.84/16.24 (((breln1all1) =>
% 122.84/16.24 (((subbreln1) =>
% 122.84/16.24 (((eqbreln1) =>
% 122.84/16.24 (((breln1invprop) =>
% 122.84/16.24 (((breln1invI) =>
% 122.84/16.24 (((breln1invE) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1compprop) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1compI) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1compE) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1compEex) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionprop) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionIL) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionIR) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionI) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionE) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionEcases) =>
% 122.84/16.24 ((
% 122.84/16.24 (breln1unionCommutes) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz2Ex) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz2W) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz2A) =>
% 122.84/16.24 ((
% 122.84/16.24 (woz2B) =>
% 122.84/16.24 ((
% 122.84/16.24 (image1Ex) =>
% 122.84/16.24 ((
% 122.84/16.24 (image1Ex1) =>
% 122.84/16.24 ((
% 122.84/16.24 (image1Equiv) =>
% 122.84/16.24 ((
% 122.84/16.24 (image1E) =>
% 122.84/16.24 ((
% 122.84/16.25 (image1I) =>
% 122.84/16.25 ((
% 122.84/16.25 (injFuncInInjFuncSet) =>
% 122.84/16.25 ((
% 122.84/16.25 (!!) @ (
% 122.84/16.25 (('#B') @ (
% 122.84/16.25 !!) @
% 122.84/16.25 (
% 122.84/16.25 (
% 122.84/16.25 ('#B') @ (
% 122.84/16.25 (
% 122.84/16.25 ('#B') @ (
% 122.84/16.25 !!))) @
% 122.84/16.25 (
% 122.84/16.25 (
% 122.84/16.25 ('#S') @ (
% 122.84/16.25 (
% 122.84/16.25 ('#B') @ (
% 122.84/16.25 '#S') @
% 122.84/16.25 (
% 122.84/16.25 (
% 122.84/16.25 ('#B') @ (
% 122.84/16.25 (
% 122.84/16.25 ('#B') @ (
% 122.84/16.25 '#S'))) @
% 122.84/16.25 (
% 122.84/16.25 (
% 122.84/16.25 ('#B') @ (
% 122.84/16.25 (
% 122.84/16.25 ('#B') @ (
% 122.84/16.25 (
% 122.84/16.25 ('#B') @ (
% 122.84/16.25 =>))))) @
% 122.84/16.25 (
% 122.84/16.25 (
% 122.84/16.25 ('#B') @ (
% 122.84/16.25 (
% 122.84/16.25 ('#B') @ (
% 122.84/16.25 (
% 122.84/16.25 ('#C') @ in)))) @
% 122.84/16.25 injFuncSet)))))))) @
% 122.84/16.25 (
% 122.84/16.25 (
% 122.84/16.25 ('#B') @ (
% 122.84/16.25 (
% 122.84/16.25 ('#B') @ (
% 122.84/16.25 (
% 122.84/16.25 ('#C') @ in)))) @
% 122.84/16.25 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.84/16.25 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2857])).
% 122.84/16.25 thf(zip_derived_cl2881, plain,
% 122.84/16.25 (~ (((complementUnionInPowersetComplement) =>
% 122.84/16.25 (((demorgan2a2) =>
% 122.84/16.25 (((demorgan1a) =>
% 122.84/16.25 (((demorgan1b) =>
% 122.84/16.25 (((demorgan1) =>
% 122.84/16.25 (((demorgan2a) =>
% 122.84/16.25 (((demorgan2b2) =>
% 122.84/16.25 (((demorgan2b) =>
% 122.84/16.25 (((demorgan2) =>
% 122.84/16.25 (((woz13rule0) =>
% 122.84/16.25 (((woz13rule1) =>
% 122.84/16.25 (((woz13rule2) =>
% 122.84/16.25 (((woz13rule3) =>
% 122.84/16.25 (((woz13rule4) =>
% 122.84/16.25 (((woz1_1) =>
% 122.84/16.25 (((woz1_2) =>
% 122.84/16.25 (((woz1_3) =>
% 122.84/16.25 (((woz1_4) =>
% 122.84/16.25 (((woz1_5) =>
% 122.84/16.25 (((breln1all2) =>
% 122.84/16.25 (((breln1SetBreln1) =>
% 122.84/16.25 (((choice2fnsingleton) =>
% 122.84/16.25 (((setOfPairsIsBReln1) =>
% 122.84/16.25 (((breln1all1) =>
% 122.84/16.25 (((subbreln1) =>
% 122.84/16.25 (((eqbreln1) =>
% 122.84/16.25 (((breln1invprop) =>
% 122.84/16.25 (((breln1invI) =>
% 122.84/16.25 (((breln1invE) =>
% 122.84/16.25 (((breln1compprop) =>
% 122.84/16.25 ((
% 122.84/16.25 (breln1compI) =>
% 122.84/16.25 ((
% 122.84/16.25 (breln1compE) =>
% 122.84/16.25 ((
% 122.84/16.25 (breln1compEex) =>
% 122.84/16.25 ((
% 122.84/16.25 (breln1unionprop) =>
% 122.84/16.25 ((
% 122.84/16.25 (breln1unionIL) =>
% 122.84/16.25 ((
% 122.84/16.25 (breln1unionIR) =>
% 122.84/16.25 ((
% 122.84/16.25 (breln1unionI) =>
% 122.84/16.25 ((
% 122.84/16.25 (breln1unionE) =>
% 122.84/16.25 ((
% 122.84/16.25 (breln1unionEcases) =>
% 122.84/16.25 ((
% 122.84/16.25 (breln1unionCommutes) =>
% 122.84/16.25 ((
% 122.84/16.25 (woz2Ex) =>
% 122.84/16.25 ((
% 122.84/16.25 (woz2W) =>
% 122.84/16.25 ((
% 122.84/16.25 (woz2A) =>
% 122.84/16.25 ((
% 122.84/16.25 (woz2B) =>
% 122.84/16.25 ((
% 122.84/16.25 (image1Ex) =>
% 122.84/16.25 ((
% 122.84/16.25 (image1Ex1) =>
% 122.84/16.25 ((
% 122.84/16.25 (image1Equiv) =>
% 122.84/16.25 ((
% 122.84/16.25 (image1E) =>
% 122.84/16.25 ((
% 122.84/16.25 (image1I) =>
% 122.84/16.25 ((
% 122.84/16.25 (injFuncInInjFuncSet) =>
% 122.84/16.25 ((
% 122.84/16.25 (!!) @ (
% 122.84/16.25 (('#B') @ (
% 122.84/16.25 !!) @
% 122.84/16.25 (
% 122.84/16.25 (
% 122.84/16.25 ('#B') @ (
% 122.84/16.25 (
% 122.84/16.25 ('#B') @ (
% 122.84/16.25 !!))) @
% 122.84/16.25 (
% 122.84/16.25 (
% 122.84/16.25 ('#S') @ (
% 122.84/16.25 (
% 122.84/16.25 ('#B') @ (
% 122.84/16.25 '#S') @
% 122.84/16.25 (
% 122.84/16.25 (
% 122.84/16.25 ('#B') @ (
% 122.84/16.25 (
% 122.84/16.25 ('#B') @ (
% 122.84/16.25 '#S'))) @
% 122.84/16.25 (
% 122.84/16.25 (
% 122.84/16.25 ('#B') @ (
% 122.84/16.25 (
% 122.84/16.25 ('#B') @ (
% 122.84/16.25 (
% 122.84/16.25 ('#B') @ (
% 122.84/16.25 =>))))) @
% 122.84/16.25 (
% 122.84/16.25 (
% 122.84/16.25 ('#B') @ (
% 122.84/16.25 (
% 122.84/16.25 ('#B') @ (
% 122.84/16.25 (
% 122.84/16.25 ('#C') @ in)))) @
% 122.84/16.25 injFuncSet)))))))) @
% 122.84/16.25 (
% 122.84/16.25 (
% 122.84/16.25 ('#B') @ (
% 122.84/16.25 (
% 122.84/16.25 ('#B') @ (
% 122.84/16.25 (
% 122.84/16.25 ('#C') @ in)))) @
% 122.84/16.25 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.84/16.25 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2869])).
% 122.84/16.25 thf(zip_derived_cl2893, plain,
% 122.84/16.25 (~ (((demorgan2a2) =>
% 122.84/16.25 (((demorgan1a) =>
% 122.84/16.25 (((demorgan1b) =>
% 122.84/16.25 (((demorgan1) =>
% 122.84/16.25 (((demorgan2a) =>
% 122.84/16.25 (((demorgan2b2) =>
% 122.84/16.25 (((demorgan2b) =>
% 122.84/16.25 (((demorgan2) =>
% 122.84/16.25 (((woz13rule0) =>
% 122.84/16.25 (((woz13rule1) =>
% 122.84/16.25 (((woz13rule2) =>
% 122.84/16.25 (((woz13rule3) =>
% 122.84/16.25 (((woz13rule4) =>
% 122.84/16.25 (((woz1_1) =>
% 122.84/16.25 (((woz1_2) =>
% 122.84/16.25 (((woz1_3) =>
% 122.84/16.25 (((woz1_4) =>
% 122.84/16.25 (((woz1_5) =>
% 122.84/16.25 (((breln1all2) =>
% 122.84/16.25 (((breln1SetBreln1) =>
% 122.84/16.25 (((choice2fnsingleton) =>
% 122.84/16.25 (((setOfPairsIsBReln1) =>
% 122.84/16.25 (((breln1all1) =>
% 122.84/16.25 (((subbreln1) =>
% 122.84/16.25 (((eqbreln1) =>
% 122.84/16.25 (((breln1invprop) =>
% 122.84/16.25 (((breln1invI) =>
% 122.84/16.25 (((breln1invE) =>
% 122.84/16.25 (((breln1compprop) =>
% 122.84/16.25 (((breln1compI) =>
% 122.84/16.25 ((
% 122.84/16.25 (breln1compE) =>
% 122.84/16.25 ((
% 122.84/16.25 (breln1compEex) =>
% 122.84/16.25 ((
% 122.84/16.25 (breln1unionprop) =>
% 122.84/16.25 ((
% 122.84/16.25 (breln1unionIL) =>
% 122.84/16.25 ((
% 122.84/16.25 (breln1unionIR) =>
% 122.84/16.25 ((
% 122.84/16.25 (breln1unionI) =>
% 122.84/16.25 ((
% 122.84/16.25 (breln1unionE) =>
% 122.84/16.25 ((
% 122.84/16.25 (breln1unionEcases) =>
% 122.84/16.25 ((
% 122.84/16.25 (breln1unionCommutes) =>
% 122.84/16.25 ((
% 122.84/16.25 (woz2Ex) =>
% 122.84/16.25 ((
% 122.84/16.25 (woz2W) =>
% 122.84/16.25 ((
% 122.84/16.25 (woz2A) =>
% 122.84/16.25 ((
% 122.84/16.25 (woz2B) =>
% 122.84/16.25 ((
% 122.84/16.25 (image1Ex) =>
% 122.84/16.25 ((
% 122.84/16.25 (image1Ex1) =>
% 122.84/16.25 ((
% 122.84/16.25 (image1Equiv) =>
% 122.84/16.25 ((
% 122.84/16.25 (image1E) =>
% 122.84/16.25 ((
% 122.84/16.25 (image1I) =>
% 122.84/16.25 ((
% 122.84/16.25 (injFuncInInjFuncSet) =>
% 122.84/16.25 ((
% 122.84/16.25 (!!) @ (
% 122.84/16.25 (('#B') @ (
% 122.84/16.25 !!) @
% 122.84/16.25 (
% 122.84/16.25 (
% 122.84/16.25 ('#B') @ (
% 122.84/16.25 (
% 122.84/16.25 ('#B') @ (
% 122.84/16.25 !!))) @
% 122.84/16.25 (
% 122.84/16.25 (
% 122.84/16.25 ('#S') @ (
% 122.84/16.25 (
% 122.84/16.25 ('#B') @ (
% 122.84/16.25 '#S') @
% 122.84/16.25 (
% 122.84/16.25 (
% 122.84/16.25 ('#B') @ (
% 122.84/16.25 (
% 122.84/16.25 ('#B') @ (
% 122.84/16.25 '#S'))) @
% 122.84/16.25 (
% 122.84/16.25 (
% 122.84/16.25 ('#B') @ (
% 122.84/16.25 (
% 122.84/16.25 ('#B') @ (
% 122.84/16.25 (
% 122.84/16.25 ('#B') @ (
% 122.84/16.25 =>))))) @
% 122.84/16.25 (
% 122.84/16.25 (
% 122.84/16.25 ('#B') @ (
% 122.84/16.25 (
% 122.84/16.25 ('#B') @ (
% 122.84/16.25 (
% 122.84/16.25 ('#C') @ in)))) @
% 122.84/16.25 injFuncSet)))))))) @
% 122.84/16.25 (
% 122.84/16.25 (
% 122.84/16.25 ('#B') @ (
% 122.84/16.25 (
% 122.84/16.25 ('#B') @ (
% 122.84/16.25 (
% 122.84/16.25 ('#C') @ in)))) @
% 122.84/16.25 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.84/16.25 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2881])).
% 122.84/16.25 thf(zip_derived_cl2906, plain,
% 122.84/16.25 (~ (((demorgan1a) =>
% 122.84/16.25 (((demorgan1b) =>
% 122.84/16.25 (((demorgan1) =>
% 122.84/16.25 (((demorgan2a) =>
% 122.84/16.25 (((demorgan2b2) =>
% 122.84/16.25 (((demorgan2b) =>
% 122.84/16.25 (((demorgan2) =>
% 122.84/16.25 (((woz13rule0) =>
% 122.84/16.25 (((woz13rule1) =>
% 122.84/16.25 (((woz13rule2) =>
% 122.84/16.25 (((woz13rule3) =>
% 122.84/16.25 (((woz13rule4) =>
% 122.84/16.25 (((woz1_1) =>
% 122.84/16.25 (((woz1_2) =>
% 122.84/16.25 (((woz1_3) =>
% 122.84/16.25 (((woz1_4) =>
% 122.84/16.25 (((woz1_5) =>
% 122.84/16.25 (((breln1all2) =>
% 122.84/16.25 (((breln1SetBreln1) =>
% 122.84/16.25 (((choice2fnsingleton) =>
% 122.84/16.25 (((setOfPairsIsBReln1) =>
% 122.84/16.25 (((breln1all1) =>
% 122.84/16.25 (((subbreln1) =>
% 122.84/16.25 (((eqbreln1) =>
% 122.84/16.25 (((breln1invprop) =>
% 122.84/16.25 (((breln1invI) =>
% 122.84/16.25 (((breln1invE) =>
% 122.84/16.25 (((breln1compprop) =>
% 122.84/16.25 (((breln1compI) =>
% 122.84/16.25 (((breln1compE) =>
% 122.84/16.25 ((
% 122.84/16.25 (breln1compEex) =>
% 122.84/16.25 ((
% 122.84/16.25 (breln1unionprop) =>
% 122.84/16.25 ((
% 122.84/16.25 (breln1unionIL) =>
% 122.84/16.25 ((
% 122.84/16.25 (breln1unionIR) =>
% 122.84/16.25 ((
% 122.84/16.25 (breln1unionI) =>
% 122.84/16.25 ((
% 122.84/16.25 (breln1unionE) =>
% 122.84/16.25 ((
% 122.84/16.25 (breln1unionEcases) =>
% 122.84/16.25 ((
% 122.84/16.25 (breln1unionCommutes) =>
% 122.84/16.25 ((
% 122.84/16.25 (woz2Ex) =>
% 122.84/16.25 ((
% 122.84/16.25 (woz2W) =>
% 122.84/16.25 ((
% 122.84/16.25 (woz2A) =>
% 122.84/16.25 ((
% 122.84/16.25 (woz2B) =>
% 122.84/16.25 ((
% 122.84/16.25 (image1Ex) =>
% 122.84/16.25 ((
% 122.84/16.25 (image1Ex1) =>
% 122.84/16.25 ((
% 122.84/16.25 (image1Equiv) =>
% 122.84/16.25 ((
% 122.84/16.25 (image1E) =>
% 122.84/16.25 ((
% 122.84/16.25 (image1I) =>
% 122.84/16.25 ((
% 122.84/16.25 (injFuncInInjFuncSet) =>
% 122.84/16.25 ((
% 122.84/16.25 (!!) @ (
% 122.84/16.25 (('#B') @ (
% 122.84/16.25 !!) @
% 122.84/16.25 (
% 122.84/16.25 (
% 122.84/16.25 ('#B') @ (
% 122.84/16.25 (
% 122.84/16.25 ('#B') @ (
% 122.84/16.25 !!))) @
% 122.84/16.25 (
% 122.84/16.25 (
% 122.84/16.25 ('#S') @ (
% 122.84/16.25 (
% 122.84/16.25 ('#B') @ (
% 122.84/16.25 '#S') @
% 122.84/16.25 (
% 122.84/16.25 (
% 122.84/16.25 ('#B') @ (
% 122.84/16.25 (
% 122.84/16.25 ('#B') @ (
% 122.84/16.25 '#S'))) @
% 122.84/16.25 (
% 122.84/16.25 (
% 122.84/16.25 ('#B') @ (
% 122.84/16.25 (
% 122.84/16.25 ('#B') @ (
% 122.84/16.25 (
% 122.84/16.25 ('#B') @ (
% 122.84/16.25 =>))))) @
% 122.84/16.25 (
% 122.84/16.25 (
% 122.84/16.25 ('#B') @ (
% 122.84/16.25 (
% 122.84/16.25 ('#B') @ (
% 122.84/16.25 (
% 122.84/16.25 ('#C') @ in)))) @
% 122.84/16.25 injFuncSet)))))))) @
% 122.84/16.25 (
% 122.84/16.25 (
% 122.84/16.25 ('#B') @ (
% 122.84/16.25 (
% 122.84/16.25 ('#B') @ (
% 122.84/16.25 (
% 122.84/16.25 ('#C') @ in)))) @
% 122.84/16.25 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.84/16.25 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2893])).
% 122.84/16.25 thf(zip_derived_cl2920, plain,
% 122.84/16.25 (~ (((demorgan1b) =>
% 122.84/16.25 (((demorgan1) =>
% 122.84/16.25 (((demorgan2a) =>
% 122.84/16.25 (((demorgan2b2) =>
% 122.84/16.25 (((demorgan2b) =>
% 122.84/16.25 (((demorgan2) =>
% 122.84/16.25 (((woz13rule0) =>
% 122.84/16.25 (((woz13rule1) =>
% 122.84/16.25 (((woz13rule2) =>
% 122.84/16.25 (((woz13rule3) =>
% 122.84/16.25 (((woz13rule4) =>
% 122.84/16.25 (((woz1_1) =>
% 122.84/16.25 (((woz1_2) =>
% 122.84/16.25 (((woz1_3) =>
% 122.84/16.25 (((woz1_4) =>
% 122.84/16.25 (((woz1_5) =>
% 122.84/16.25 (((breln1all2) =>
% 122.84/16.25 (((breln1SetBreln1) =>
% 122.84/16.25 (((choice2fnsingleton) =>
% 122.84/16.25 (((setOfPairsIsBReln1) =>
% 122.84/16.25 (((breln1all1) =>
% 122.84/16.25 (((subbreln1) =>
% 122.84/16.25 (((eqbreln1) =>
% 122.84/16.25 (((breln1invprop) =>
% 122.84/16.25 (((breln1invI) =>
% 122.84/16.25 (((breln1invE) =>
% 122.84/16.25 (((breln1compprop) =>
% 122.84/16.25 (((breln1compI) =>
% 122.84/16.25 (((breln1compE) =>
% 122.84/16.25 (((breln1compEex) =>
% 122.84/16.25 ((
% 122.84/16.25 (breln1unionprop) =>
% 122.84/16.25 ((
% 122.84/16.25 (breln1unionIL) =>
% 122.84/16.25 ((
% 122.84/16.25 (breln1unionIR) =>
% 122.84/16.25 ((
% 122.84/16.25 (breln1unionI) =>
% 122.84/16.25 ((
% 122.84/16.25 (breln1unionE) =>
% 122.84/16.25 ((
% 122.84/16.25 (breln1unionEcases) =>
% 122.84/16.25 ((
% 122.84/16.25 (breln1unionCommutes) =>
% 122.84/16.25 ((
% 122.84/16.25 (woz2Ex) =>
% 122.84/16.25 ((
% 122.84/16.25 (woz2W) =>
% 122.84/16.25 ((
% 122.84/16.25 (woz2A) =>
% 122.84/16.25 ((
% 122.84/16.25 (woz2B) =>
% 122.84/16.25 ((
% 122.84/16.25 (image1Ex) =>
% 122.84/16.25 ((
% 122.84/16.25 (image1Ex1) =>
% 122.84/16.25 ((
% 122.84/16.25 (image1Equiv) =>
% 122.84/16.25 ((
% 122.84/16.25 (image1E) =>
% 122.84/16.25 ((
% 122.84/16.25 (image1I) =>
% 122.84/16.25 ((
% 122.84/16.25 (injFuncInInjFuncSet) =>
% 122.84/16.25 ((
% 122.84/16.25 (!!) @ (
% 122.84/16.25 (('#B') @ (
% 122.84/16.25 !!) @
% 122.84/16.25 (
% 122.84/16.25 (
% 122.84/16.25 ('#B') @ (
% 122.84/16.25 (
% 122.84/16.25 ('#B') @ (
% 122.84/16.25 !!))) @
% 122.84/16.25 (
% 122.84/16.25 (
% 122.84/16.25 ('#S') @ (
% 122.84/16.25 (
% 122.84/16.25 ('#B') @ (
% 122.84/16.25 '#S') @
% 122.84/16.25 (
% 122.84/16.25 (
% 122.84/16.25 ('#B') @ (
% 122.84/16.25 (
% 122.84/16.25 ('#B') @ (
% 122.84/16.25 '#S'))) @
% 122.84/16.25 (
% 122.84/16.25 (
% 122.84/16.25 ('#B') @ (
% 122.84/16.25 (
% 122.84/16.25 ('#B') @ (
% 122.84/16.25 (
% 122.84/16.25 ('#B') @ (
% 122.84/16.25 =>))))) @
% 122.84/16.25 (
% 122.84/16.25 (
% 122.84/16.25 ('#B') @ (
% 122.84/16.25 (
% 122.84/16.25 ('#B') @ (
% 122.84/16.25 (
% 122.84/16.25 ('#C') @ in)))) @
% 122.84/16.25 injFuncSet)))))))) @
% 122.84/16.25 (
% 122.84/16.25 (
% 122.84/16.25 ('#B') @ (
% 122.84/16.25 (
% 122.84/16.25 ('#B') @ (
% 122.84/16.25 (
% 122.84/16.25 ('#C') @ in)))) @
% 122.84/16.25 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.84/16.25 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2906])).
% 122.84/16.25 thf(zip_derived_cl2933, plain,
% 122.84/16.25 (~ (((demorgan1) =>
% 122.84/16.25 (((demorgan2a) =>
% 122.84/16.25 (((demorgan2b2) =>
% 122.84/16.25 (((demorgan2b) =>
% 122.84/16.25 (((demorgan2) =>
% 122.84/16.25 (((woz13rule0) =>
% 122.84/16.25 (((woz13rule1) =>
% 122.84/16.25 (((woz13rule2) =>
% 122.84/16.25 (((woz13rule3) =>
% 122.84/16.25 (((woz13rule4) =>
% 122.84/16.25 (((woz1_1) =>
% 122.84/16.25 (((woz1_2) =>
% 122.84/16.25 (((woz1_3) =>
% 122.84/16.25 (((woz1_4) =>
% 122.84/16.25 (((woz1_5) =>
% 122.84/16.25 (((breln1all2) =>
% 122.84/16.25 (((breln1SetBreln1) =>
% 122.84/16.25 (((choice2fnsingleton) =>
% 122.84/16.25 (((setOfPairsIsBReln1) =>
% 122.84/16.25 (((breln1all1) =>
% 122.84/16.25 (((subbreln1) =>
% 122.84/16.25 (((eqbreln1) =>
% 122.84/16.25 (((breln1invprop) =>
% 122.84/16.25 (((breln1invI) =>
% 122.84/16.25 (((breln1invE) =>
% 122.84/16.25 (((breln1compprop) =>
% 122.84/16.25 (((breln1compI) =>
% 122.84/16.25 (((breln1compE) =>
% 122.84/16.25 (((breln1compEex) =>
% 122.84/16.25 (((breln1unionprop) =>
% 122.84/16.25 ((
% 122.84/16.25 (breln1unionIL) =>
% 122.84/16.25 ((
% 122.84/16.25 (breln1unionIR) =>
% 122.84/16.25 ((
% 122.84/16.25 (breln1unionI) =>
% 122.84/16.25 ((
% 122.84/16.25 (breln1unionE) =>
% 122.84/16.25 ((
% 122.84/16.25 (breln1unionEcases) =>
% 122.84/16.25 ((
% 122.84/16.25 (breln1unionCommutes) =>
% 122.84/16.25 ((
% 122.84/16.25 (woz2Ex) =>
% 122.84/16.25 ((
% 122.84/16.25 (woz2W) =>
% 122.84/16.25 ((
% 122.84/16.25 (woz2A) =>
% 122.84/16.25 ((
% 122.84/16.25 (woz2B) =>
% 122.84/16.25 ((
% 122.84/16.25 (image1Ex) =>
% 122.84/16.25 ((
% 122.84/16.25 (image1Ex1) =>
% 122.84/16.25 ((
% 122.84/16.25 (image1Equiv) =>
% 122.84/16.25 ((
% 122.84/16.25 (image1E) =>
% 122.84/16.25 ((
% 122.84/16.25 (image1I) =>
% 122.84/16.25 ((
% 122.84/16.25 (injFuncInInjFuncSet) =>
% 122.84/16.25 ((
% 122.84/16.25 (!!) @ (
% 122.84/16.25 (('#B') @ (
% 122.84/16.25 !!) @
% 122.84/16.25 (
% 122.84/16.25 (
% 122.84/16.25 ('#B') @ (
% 122.84/16.25 (
% 122.84/16.25 ('#B') @ (
% 122.84/16.25 !!))) @
% 122.84/16.25 (
% 122.84/16.25 (
% 122.84/16.25 ('#S') @ (
% 122.84/16.25 (
% 122.84/16.25 ('#B') @ (
% 122.84/16.25 '#S') @
% 122.84/16.25 (
% 122.84/16.25 (
% 122.84/16.25 ('#B') @ (
% 122.84/16.25 (
% 122.84/16.25 ('#B') @ (
% 122.84/16.25 '#S'))) @
% 122.84/16.25 (
% 122.84/16.25 (
% 122.84/16.25 ('#B') @ (
% 122.84/16.25 (
% 122.84/16.25 ('#B') @ (
% 122.84/16.25 (
% 122.84/16.25 ('#B') @ (
% 122.84/16.25 =>))))) @
% 122.84/16.25 (
% 122.84/16.25 (
% 122.84/16.25 ('#B') @ (
% 122.84/16.25 (
% 122.84/16.25 ('#B') @ (
% 122.84/16.25 (
% 122.84/16.25 ('#C') @ in)))) @
% 122.84/16.25 injFuncSet)))))))) @
% 122.84/16.25 (
% 122.84/16.25 (
% 122.84/16.25 ('#B') @ (
% 122.84/16.25 (
% 122.84/16.25 ('#B') @ (
% 122.84/16.25 (
% 122.84/16.25 ('#C') @ in)))) @
% 122.84/16.25 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.84/16.25 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2920])).
% 122.84/16.25 thf(zip_derived_cl2946, plain,
% 122.84/16.25 (~ (((demorgan2a) =>
% 122.84/16.25 (((demorgan2b2) =>
% 122.84/16.25 (((demorgan2b) =>
% 122.84/16.25 (((demorgan2) =>
% 122.84/16.25 (((woz13rule0) =>
% 122.84/16.25 (((woz13rule1) =>
% 122.84/16.25 (((woz13rule2) =>
% 122.84/16.25 (((woz13rule3) =>
% 122.84/16.25 (((woz13rule4) =>
% 122.84/16.25 (((woz1_1) =>
% 122.84/16.25 (((woz1_2) =>
% 122.84/16.25 (((woz1_3) =>
% 122.84/16.25 (((woz1_4) =>
% 122.84/16.25 (((woz1_5) =>
% 122.84/16.25 (((breln1all2) =>
% 122.84/16.25 (((breln1SetBreln1) =>
% 122.84/16.25 (((choice2fnsingleton) =>
% 122.84/16.25 (((setOfPairsIsBReln1) =>
% 122.84/16.25 (((breln1all1) =>
% 122.84/16.25 (((subbreln1) =>
% 122.84/16.25 (((eqbreln1) =>
% 122.84/16.25 (((breln1invprop) =>
% 122.84/16.25 (((breln1invI) =>
% 122.84/16.25 (((breln1invE) =>
% 122.84/16.25 (((breln1compprop) =>
% 122.84/16.25 (((breln1compI) =>
% 122.84/16.25 (((breln1compE) =>
% 122.84/16.25 (((breln1compEex) =>
% 122.84/16.25 (((breln1unionprop) =>
% 122.84/16.25 (((breln1unionIL) =>
% 122.84/16.25 ((
% 122.84/16.25 (breln1unionIR) =>
% 122.84/16.25 ((
% 122.84/16.25 (breln1unionI) =>
% 122.84/16.25 ((
% 122.84/16.25 (breln1unionE) =>
% 122.84/16.25 ((
% 122.84/16.25 (breln1unionEcases) =>
% 122.84/16.25 ((
% 122.84/16.25 (breln1unionCommutes) =>
% 122.84/16.25 ((
% 122.84/16.25 (woz2Ex) =>
% 122.84/16.25 ((
% 122.84/16.25 (woz2W) =>
% 122.84/16.25 ((
% 122.84/16.25 (woz2A) =>
% 122.84/16.25 ((
% 122.84/16.25 (woz2B) =>
% 122.84/16.25 ((
% 122.84/16.25 (image1Ex) =>
% 122.84/16.25 ((
% 122.84/16.25 (image1Ex1) =>
% 122.84/16.25 ((
% 122.84/16.25 (image1Equiv) =>
% 122.84/16.25 ((
% 122.84/16.25 (image1E) =>
% 122.84/16.25 ((
% 122.84/16.25 (image1I) =>
% 122.84/16.25 ((
% 122.84/16.25 (injFuncInInjFuncSet) =>
% 122.84/16.25 ((
% 122.84/16.25 (!!) @ (
% 122.84/16.25 (('#B') @ (
% 122.84/16.25 !!) @
% 122.84/16.25 (
% 122.84/16.25 (
% 122.84/16.25 ('#B') @ (
% 122.84/16.25 (
% 122.84/16.25 ('#B') @ (
% 122.84/16.25 !!))) @
% 122.84/16.25 (
% 122.84/16.25 (
% 122.84/16.25 ('#S') @ (
% 122.84/16.25 (
% 122.84/16.25 ('#B') @ (
% 122.84/16.25 '#S') @
% 122.84/16.25 (
% 122.84/16.25 (
% 122.84/16.25 ('#B') @ (
% 122.84/16.25 (
% 122.84/16.25 ('#B') @ (
% 122.84/16.25 '#S'))) @
% 122.84/16.25 (
% 122.84/16.25 (
% 122.84/16.25 ('#B') @ (
% 122.84/16.25 (
% 122.84/16.25 ('#B') @ (
% 122.84/16.25 (
% 122.84/16.25 ('#B') @ (
% 122.84/16.25 =>))))) @
% 122.84/16.25 (
% 122.84/16.25 (
% 122.84/16.25 ('#B') @ (
% 122.84/16.25 (
% 122.84/16.25 ('#B') @ (
% 122.84/16.25 (
% 122.84/16.25 ('#C') @ in)))) @
% 122.84/16.25 injFuncSet)))))))) @
% 122.84/16.25 (
% 122.84/16.25 (
% 122.84/16.25 ('#B') @ (
% 122.84/16.25 (
% 122.84/16.25 ('#B') @ (
% 122.84/16.25 (
% 122.84/16.25 ('#C') @ in)))) @
% 122.84/16.25 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.84/16.25 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2933])).
% 122.84/16.25 thf(zip_derived_cl2958, plain,
% 122.84/16.25 (~ (((demorgan2b2) =>
% 122.84/16.25 (((demorgan2b) =>
% 122.84/16.25 (((demorgan2) =>
% 122.84/16.25 (((woz13rule0) =>
% 122.84/16.25 (((woz13rule1) =>
% 122.84/16.25 (((woz13rule2) =>
% 122.84/16.25 (((woz13rule3) =>
% 122.84/16.25 (((woz13rule4) =>
% 122.84/16.25 (((woz1_1) =>
% 122.84/16.25 (((woz1_2) =>
% 122.84/16.25 (((woz1_3) =>
% 122.84/16.25 (((woz1_4) =>
% 122.84/16.25 (((woz1_5) =>
% 122.84/16.25 (((breln1all2) =>
% 122.84/16.25 (((breln1SetBreln1) =>
% 122.84/16.25 (((choice2fnsingleton) =>
% 122.84/16.25 (((setOfPairsIsBReln1) =>
% 122.84/16.25 (((breln1all1) =>
% 122.84/16.25 (((subbreln1) =>
% 122.84/16.25 (((eqbreln1) =>
% 122.84/16.25 (((breln1invprop) =>
% 122.84/16.25 (((breln1invI) =>
% 122.84/16.25 (((breln1invE) =>
% 122.84/16.25 (((breln1compprop) =>
% 122.84/16.25 (((breln1compI) =>
% 122.84/16.25 (((breln1compE) =>
% 122.84/16.25 (((breln1compEex) =>
% 122.84/16.25 (((breln1unionprop) =>
% 122.84/16.25 (((breln1unionIL) =>
% 122.84/16.25 (((breln1unionIR) =>
% 122.84/16.25 ((
% 122.84/16.25 (breln1unionI) =>
% 122.84/16.25 ((
% 122.84/16.25 (breln1unionE) =>
% 122.84/16.25 ((
% 122.84/16.25 (breln1unionEcases) =>
% 122.84/16.25 ((
% 122.84/16.25 (breln1unionCommutes) =>
% 122.84/16.25 ((
% 122.84/16.25 (woz2Ex) =>
% 122.84/16.25 ((
% 122.84/16.25 (woz2W) =>
% 122.84/16.25 ((
% 122.84/16.25 (woz2A) =>
% 122.84/16.25 ((
% 122.84/16.25 (woz2B) =>
% 122.84/16.25 ((
% 122.84/16.25 (image1Ex) =>
% 122.84/16.25 ((
% 122.84/16.25 (image1Ex1) =>
% 122.84/16.25 ((
% 122.84/16.25 (image1Equiv) =>
% 122.84/16.25 ((
% 122.84/16.25 (image1E) =>
% 122.84/16.25 ((
% 122.84/16.25 (image1I) =>
% 122.84/16.25 ((
% 122.84/16.25 (injFuncInInjFuncSet) =>
% 122.84/16.25 ((
% 122.84/16.25 (!!) @ (
% 122.84/16.25 (('#B') @ (
% 122.84/16.25 !!) @
% 122.84/16.25 (
% 122.84/16.25 (
% 122.84/16.25 ('#B') @ (
% 122.84/16.25 (
% 122.84/16.25 ('#B') @ (
% 122.84/16.25 !!))) @
% 122.84/16.25 (
% 122.84/16.25 (
% 122.84/16.25 ('#S') @ (
% 122.84/16.25 (
% 122.84/16.25 ('#B') @ (
% 122.84/16.25 '#S') @
% 122.84/16.25 (
% 122.84/16.25 (
% 122.84/16.25 ('#B') @ (
% 122.84/16.25 (
% 122.84/16.25 ('#B') @ (
% 122.84/16.25 '#S'))) @
% 122.84/16.25 (
% 122.84/16.25 (
% 122.84/16.25 ('#B') @ (
% 122.84/16.25 (
% 122.84/16.25 ('#B') @ (
% 122.84/16.25 (
% 122.84/16.25 ('#B') @ (
% 122.84/16.25 =>))))) @
% 122.84/16.25 (
% 122.84/16.25 (
% 122.84/16.25 ('#B') @ (
% 122.84/16.25 (
% 122.84/16.25 ('#B') @ (
% 122.84/16.25 (
% 122.84/16.25 ('#C') @ in)))) @
% 122.84/16.25 injFuncSet)))))))) @
% 122.84/16.25 (
% 122.84/16.25 (
% 122.84/16.25 ('#B') @ (
% 122.84/16.25 (
% 122.84/16.25 ('#B') @ (
% 122.84/16.25 (
% 122.84/16.25 ('#C') @ in)))) @
% 122.84/16.25 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.84/16.25 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2946])).
% 122.84/16.25 thf(zip_derived_cl2970, plain,
% 122.84/16.25 (~ (((demorgan2b) =>
% 122.84/16.25 (((demorgan2) =>
% 122.84/16.25 (((woz13rule0) =>
% 122.84/16.25 (((woz13rule1) =>
% 122.84/16.25 (((woz13rule2) =>
% 122.84/16.25 (((woz13rule3) =>
% 122.84/16.25 (((woz13rule4) =>
% 122.84/16.25 (((woz1_1) =>
% 122.84/16.25 (((woz1_2) =>
% 122.84/16.25 (((woz1_3) =>
% 122.84/16.25 (((woz1_4) =>
% 122.84/16.25 (((woz1_5) =>
% 122.84/16.25 (((breln1all2) =>
% 122.84/16.25 (((breln1SetBreln1) =>
% 122.84/16.25 (((choice2fnsingleton) =>
% 122.84/16.25 (((setOfPairsIsBReln1) =>
% 122.84/16.25 (((breln1all1) =>
% 122.84/16.25 (((subbreln1) =>
% 122.84/16.25 (((eqbreln1) =>
% 122.84/16.25 (((breln1invprop) =>
% 122.84/16.25 (((breln1invI) =>
% 122.84/16.25 (((breln1invE) =>
% 122.84/16.25 (((breln1compprop) =>
% 122.84/16.25 (((breln1compI) =>
% 122.84/16.25 (((breln1compE) =>
% 122.84/16.25 (((breln1compEex) =>
% 122.84/16.25 (((breln1unionprop) =>
% 122.84/16.25 (((breln1unionIL) =>
% 122.84/16.25 (((breln1unionIR) =>
% 122.84/16.25 (((breln1unionI) =>
% 122.84/16.25 ((
% 122.84/16.25 (breln1unionE) =>
% 122.84/16.25 ((
% 122.84/16.25 (breln1unionEcases) =>
% 122.84/16.25 ((
% 122.84/16.25 (breln1unionCommutes) =>
% 122.84/16.25 ((
% 122.84/16.25 (woz2Ex) =>
% 122.84/16.25 ((
% 122.84/16.25 (woz2W) =>
% 122.84/16.25 ((
% 122.84/16.25 (woz2A) =>
% 122.84/16.25 ((
% 122.84/16.25 (woz2B) =>
% 122.84/16.25 ((
% 122.84/16.25 (image1Ex) =>
% 122.84/16.25 ((
% 122.84/16.25 (image1Ex1) =>
% 122.84/16.25 ((
% 122.84/16.25 (image1Equiv) =>
% 122.84/16.25 ((
% 122.84/16.25 (image1E) =>
% 122.84/16.25 ((
% 122.84/16.25 (image1I) =>
% 122.84/16.25 ((
% 122.84/16.25 (injFuncInInjFuncSet) =>
% 122.84/16.25 ((
% 122.84/16.25 (!!) @ (
% 122.84/16.25 (('#B') @ (
% 122.84/16.25 !!) @
% 122.84/16.25 (
% 122.84/16.25 (
% 122.84/16.25 ('#B') @ (
% 122.84/16.25 (
% 122.84/16.25 ('#B') @ (
% 122.84/16.25 !!))) @
% 122.84/16.25 (
% 122.84/16.25 (
% 122.84/16.25 ('#S') @ (
% 122.84/16.25 (
% 122.84/16.25 ('#B') @ (
% 122.84/16.25 '#S') @
% 122.84/16.25 (
% 122.84/16.25 (
% 122.84/16.25 ('#B') @ (
% 122.84/16.25 (
% 122.84/16.25 ('#B') @ (
% 122.84/16.25 '#S'))) @
% 122.84/16.25 (
% 122.84/16.25 (
% 122.84/16.25 ('#B') @ (
% 122.84/16.25 (
% 122.84/16.25 ('#B') @ (
% 122.84/16.25 (
% 122.84/16.25 ('#B') @ (
% 122.84/16.25 =>))))) @
% 122.84/16.25 (
% 122.84/16.25 (
% 122.84/16.25 ('#B') @ (
% 122.84/16.25 (
% 122.84/16.25 ('#B') @ (
% 122.84/16.25 (
% 122.84/16.25 ('#C') @ in)))) @
% 122.84/16.25 injFuncSet)))))))) @
% 122.84/16.25 (
% 122.84/16.25 (
% 122.84/16.25 ('#B') @ (
% 122.84/16.25 (
% 122.84/16.25 ('#B') @ (
% 122.84/16.25 (
% 122.84/16.25 ('#C') @ in)))) @
% 122.84/16.25 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.84/16.25 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2958])).
% 122.84/16.25 thf(zip_derived_cl2982, plain,
% 122.84/16.25 (~ (((demorgan2) =>
% 122.84/16.25 (((woz13rule0) =>
% 122.84/16.25 (((woz13rule1) =>
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% 122.84/16.25 (injFuncInInjFuncSet) =>
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% 122.84/16.25 (dsetconstr @ (funcSet @ '#sk47' @ '#sk48') @
% 122.84/16.25 (injective @ '#sk47' @ '#sk48')))),
% 122.84/16.25 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3617])).
% 122.84/16.25 thf(zip_derived_cl3627, plain,
% 122.84/16.25 (~ (in @
% 122.84/16.25 ('#sk12' @ (funcSet @ '#sk47' @ '#sk48') @
% 122.84/16.25 (dsetconstr @ (funcSet @ '#sk47' @ '#sk48') @
% 122.84/16.25 (injective @ '#sk47' @ '#sk48'))) @
% 122.84/16.25 (funcSet @ '#sk47' @ '#sk48'))),
% 122.84/16.25 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3617])).
% 122.84/16.25 thf(zip_derived_cl88, plain, ( (dsetconstrEL)),
% 122.84/16.25 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl79])).
% 122.84/16.25 thf(dsetconstrEL, axiom, (dsetconstrEL) =>
% 122.84/16.25 ((((!!) @ (^[Y0 : $i]:
% 122.84/16.25 (((!!) @ (^[Y1 : $i > $o]:
% 122.84/16.25 (((!!) @ (^[Y2 : $i]:
% 122.84/16.25 (((in @ Y2 @
% 122.84/16.25 (dsetconstr @ Y0 @
% 122.84/16.25 (^[Y3 : $i]: (Y1 @ Y3)))) =>
% 122.84/16.25 (in @ Y2 @ Y0))))))))))))
% 122.84/16.25 = ($true))).
% 122.84/16.25 thf('5', plain,
% 122.84/16.25 (( dsetconstrEL ) <=>
% 122.84/16.25 ( ![X5:$i,X7:( $i > $o ),X9:$i]:
% 122.84/16.25 ( ( in @ X9 @ ( dsetconstr @ X5 @ ( ^[V_1:$i]: ( X7 @ V_1 ) ) ) ) =>
% 122.84/16.25 ( in @ X9 @ X5 ) ) )),
% 122.84/16.25 inference('rw.lit', [status(esa)], [dsetconstrEL])).
% 122.84/16.25 thf(zip_derived_cl103, plain,
% 122.84/16.25 ( (((!!) @ (^[Y0 : $i]:
% 122.84/16.25 (((!!) @ (^[Y1 : $i > $o]:
% 122.84/16.25 (((!!) @ (^[Y2 : $i]:
% 122.84/16.25 (((in @ Y2 @
% 122.84/16.25 (dsetconstr @ Y0 @
% 122.84/16.25 (^[Y3 : $i]: (Y1 @ Y3)))) =>
% 122.84/16.25 (in @ Y2 @ Y0))))))))))))),
% 122.84/16.25 inference('rw_clause', [status(thm)], [zip_derived_cl88, '5'])).
% 122.84/16.25 thf(zip_derived_cl119, plain,
% 122.84/16.25 ( (((!!) @ ((('#B') @ (!!) @
% 122.84/16.25 ((('#B') @ ((('#B') @ (!!))) @
% 122.84/16.25 ((('#S') @ ((('#B') @ ('#C') @
% 122.84/16.25 ((('#B') @ ((('#B') @ ('#S'))) @
% 122.84/16.25 ((('#B') @ ((('#B') @ ((('#B') @ (=>))))) @
% 122.84/16.25 ((('#B') @ ((('#B') @ ((('#C') @ in)))) @
% 122.84/16.25 dsetconstr)))))))) @
% 122.84/16.25 ((('#C') @ in))))))))))),
% 122.84/16.25 inference('comb-normalize', [status(thm)], [zip_derived_cl103])).
% 122.84/16.25 thf(zip_derived_cl120, plain,
% 122.84/16.25 (![X2 : $i]:
% 122.84/16.25 (((!!) @ ((('#B') @ (!!) @
% 122.84/16.25 ((('#C') @ ((('#B') @ ('#S') @
% 122.84/16.25 ((('#B') @ ((('#B') @ (=>))) @
% 122.84/16.25 ((('#B') @ ((('#C') @ in)) @
% 122.84/16.25 (dsetconstr @ X2))))))) @
% 122.84/16.25 ((('#C') @ in @ X2))))))))),
% 122.84/16.25 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl119])).
% 122.84/16.25 thf(zip_derived_cl137, plain,
% 122.84/16.25 (![X2 : $i, X4 : $i > $o]:
% 122.84/16.25 (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 122.84/16.25 ((('#C') @ in @ (dsetconstr @ X2 @ X4))))) @
% 122.84/16.25 ((('#C') @ in @ X2))))))),
% 122.84/16.25 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl120])).
% 122.84/16.25 thf(zip_derived_cl152, plain,
% 122.84/16.25 (![X2 : $i, X4 : $i > $o, X6 : $i]:
% 122.84/16.25 (((in @ X6 @ (dsetconstr @ X2 @ X4)) => (in @ X6 @ X2)))),
% 122.84/16.25 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl137])).
% 122.84/16.25 thf(zip_derived_cl167, plain,
% 122.84/16.25 (![X2 : $i, X4 : $i > $o, X6 : $i]:
% 122.84/16.25 (~ (in @ X6 @ (dsetconstr @ X2 @ X4)) | (in @ X6 @ X2))),
% 122.84/16.25 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl152])).
% 122.84/16.25 thf(zip_derived_cl3741, plain, ($false),
% 122.84/16.25 inference('eprover', [status(thm)],
% 122.84/16.25 [zip_derived_cl3626, zip_derived_cl3627, zip_derived_cl167])).
% 122.84/16.25
% 122.84/16.25 % SZS output end Refutation
% 122.84/16.25
% 122.84/16.25
% 122.84/16.25 % /export/starexec/sandbox2/solver/bin/lams/30_b.l.sh running for 90s
% 122.84/16.25 % Terminating...
% 123.25/16.37 % Runner terminated.
% 123.25/16.37 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------