%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SEU801^1 : TPTP v8.1.2. Released v3.7.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.00nMOSpSN3 true
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 19:17:53 EDT 2023
% Result : Theorem 97.06s 13.32s
% Output : Refutation 99.84s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEU801^1 : TPTP v8.1.2. Released v3.7.0.
% 0.00/0.15 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.00nMOSpSN3 true
% 0.14/0.35 % Computer : n013.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Wed Aug 23 12:31:17 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.14/0.36 % Running portfolio for 300 s
% 0.14/0.36 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.36 % Number of cores: 8
% 0.14/0.36 % Python version: Python 3.6.8
% 0.22/0.36 % Running in HO mode
% 0.22/0.64 % Total configuration time : 828
% 0.22/0.64 % Estimated wc time : 1656
% 0.22/0.64 % Estimated cpu time (8 cpus) : 207.0
% 0.22/0.70 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s
% 1.05/0.75 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s
% 1.05/0.76 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s
% 1.05/0.76 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s
% 1.05/0.76 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s
% 1.05/0.77 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s
% 1.05/0.77 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 1.41/0.80 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s
% 97.06/13.32 % Solved by lams/40_b.comb.sh.
% 97.06/13.32 % done 372 iterations in 12.199s
% 97.06/13.32 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 97.06/13.32 % SZS output start Refutation
% 97.06/13.32 thf(setadjoinAx_type, type, setadjoinAx: $o).
% 97.06/13.32 thf(cartprodfstpairEq_type, type, cartprodfstpairEq: $o).
% 97.06/13.32 thf(notdexE_type, type, notdexE: $o).
% 97.06/13.32 thf(setunionAx_type, type, setunionAx: $o).
% 97.06/13.32 thf(setminusELneg_type, type, setminusELneg: $o).
% 97.06/13.32 thf(breln1unionEcases_type, type, breln1unionEcases: $o).
% 97.06/13.32 thf(powersetE_type, type, powersetE: $o).
% 97.06/13.32 thf(woz1_1_type, type, woz1_1: $o).
% 97.06/13.32 thf(omegaSAx_type, type, omegaSAx: $o).
% 97.06/13.32 thf(breln1unionI_type, type, breln1unionI: $o).
% 97.06/13.32 thf(complementSubsetComplementIntersect_type, type, complementSubsetComplementIntersect:
% 97.06/13.32 $o).
% 97.06/13.32 thf(exuI1_type, type, exuI1: $o).
% 97.06/13.32 thf(exuI2_type, type, exuI2: $o).
% 97.06/13.32 thf(notequalI2_type, type, notequalI2: $o).
% 97.06/13.32 thf(kfstsingleton_type, type, kfstsingleton: $o).
% 97.06/13.32 thf(kpairiskpair_type, type, kpairiskpair: $o).
% 97.06/13.32 thf(upairsubunion_type, type, upairsubunion: $o).
% 97.06/13.32 thf(binunionTE_type, type, binunionTE: $o).
% 97.06/13.32 thf(binunionTEcontra_type, type, binunionTEcontra: $o).
% 97.06/13.32 thf(powerset__Cong_type, type, powerset__Cong: $o).
% 97.06/13.32 thf(setukpairinjR2_type, type, setukpairinjR2: $o).
% 97.06/13.32 thf(singletonsuniq_type, type, singletonsuniq: $o).
% 97.06/13.32 thf(setminusILneg_type, type, setminusILneg: $o).
% 97.06/13.32 thf(wellorderingAx_type, type, wellorderingAx: $o).
% 97.06/13.32 thf(kpairsurjEq_type, type, kpairsurjEq: $o).
% 97.06/13.32 thf(funcextLem_type, type, funcextLem: $o).
% 97.06/13.32 thf(setadjoinSub2_type, type, setadjoinSub2: $o).
% 97.06/13.32 thf(binintersectSubset5_type, type, binintersectSubset5: $o).
% 97.06/13.32 thf(upairinpowunion_type, type, upairinpowunion: $o).
% 97.06/13.32 thf(eta1_type, type, eta1: $o).
% 97.06/13.32 thf(complementTnotintersectT_type, type, complementTnotintersectT: $o).
% 97.06/13.32 thf(setoftrueEq_type, type, setoftrueEq: $o).
% 97.06/13.32 thf(apProp_type, type, apProp: $o).
% 97.06/13.32 thf(setextT_type, type, setextT: $o).
% 97.06/13.32 thf(inIntersectImpInIntersectUnions_type, type, inIntersectImpInIntersectUnions:
% 97.06/13.32 $o).
% 97.06/13.32 thf(emptyset__Cong_type, type, emptyset__Cong: $o).
% 97.06/13.32 thf(cartprodmempaircEq_type, type, cartprodmempaircEq: $o).
% 97.06/13.32 thf(breln1invprop_type, type, breln1invprop: $o).
% 97.06/13.32 thf(lamProp_type, type, lamProp: $o).
% 97.06/13.32 thf(dpsetconstrSub_type, type, dpsetconstrSub: $o).
% 97.06/13.32 thf(ex1E1_type, type, ex1E1: $o).
% 97.06/13.32 thf(sepInPowerset_type, type, sepInPowerset: $o).
% 97.06/13.32 thf(setukpairIR_type, type, setukpairIR: $o).
% 97.06/13.32 thf(brelnall1_type, type, brelnall1: $o).
% 97.06/13.32 thf(binunionE_type, type, binunionE: $o).
% 97.06/13.32 thf(setext_type, type, setext: $o).
% 97.06/13.32 thf(complementTcontraSubset_type, type, complementTcontraSubset: $o).
% 97.06/13.32 thf(emptyinPowerset_type, type, emptyinPowerset: $o).
% 97.06/13.32 thf(binintersectTELcontra_type, type, binintersectTELcontra: $o).
% 97.06/13.32 thf(ubforcartprodlem1_type, type, ubforcartprodlem1: $o).
% 97.06/13.32 thf(iftrue_type, type, iftrue: $o).
% 97.06/13.32 thf(woz13rule4_type, type, woz13rule4: $o).
% 97.06/13.32 thf(descr__Cong_type, type, descr__Cong: $o).
% 97.06/13.32 thf(funcGraphProp2_type, type, funcGraphProp2: $o).
% 97.06/13.32 thf(theprop_type, type, theprop: $o).
% 97.06/13.32 thf(image1I_type, type, image1I: $o).
% 97.06/13.32 thf(binintersectSubset1_type, type, binintersectSubset1: $o).
% 97.06/13.32 thf(in_type, type, in: $i > $i > $o).
% 97.06/13.32 thf(cartprodsndpairEq_type, type, cartprodsndpairEq: $o).
% 97.06/13.32 thf(quantDeMorgan1_type, type, quantDeMorgan1: $o).
% 97.06/13.32 thf(setukpairinjL2_type, type, setukpairinjL2: $o).
% 97.06/13.32 thf(demorgan1_type, type, demorgan1: $o).
% 97.06/13.32 thf(setadjoinIR_type, type, setadjoinIR: $o).
% 97.06/13.32 thf(complementInPowersetComplementIntersect_type, type, complementInPowersetComplementIntersect:
% 97.06/13.32 $o).
% 97.06/13.32 thf(inIntersectImpInUnion_type, type, inIntersectImpInUnion: $o).
% 97.06/13.32 thf(breln1SetBreln1_type, type, breln1SetBreln1: $o).
% 97.06/13.32 thf(setadjoin__Cong_type, type, setadjoin__Cong: $o).
% 97.06/13.32 thf(ksndpairEq_type, type, ksndpairEq: $o).
% 97.06/13.32 thf(ex1I2_type, type, ex1I2: $o).
% 97.06/13.32 thf(symdiffI2_type, type, symdiffI2: $o).
% 97.06/13.32 thf(ap2apEq2_type, type, ap2apEq2: $o).
% 97.06/13.32 thf(ifSingleton_type, type, ifSingleton: $o).
% 97.06/13.32 thf(upairset2IR_type, type, upairset2IR: $o).
% 97.06/13.32 thf(iftrueProp1_type, type, iftrueProp1: $o).
% 97.06/13.32 thf(complementTI1_type, type, complementTI1: $o).
% 97.06/13.32 thf(subsetE_type, type, subsetE: $o).
% 97.06/13.32 thf(prop2set2propI_type, type, prop2set2propI: $o).
% 97.06/13.32 thf(doubleComplementSub2_type, type, doubleComplementSub2: $o).
% 97.06/13.32 thf(complementUnionInPowersetComplement_type, type, complementUnionInPowersetComplement:
% 98.80/13.32 $o).
% 98.80/13.32 thf(iffalse_type, type, iffalse: $o).
% 98.80/13.32 thf(dsetconstrEL_type, type, dsetconstrEL: $o).
% 98.80/13.32 thf(setbeta_type, type, setbeta: $o).
% 98.80/13.32 thf(eqinunit_type, type, eqinunit: $o).
% 98.80/13.32 thf(upairsetIL_type, type, upairsetIL: $o).
% 98.80/13.32 thf(powersetI1_type, type, powersetI1: $o).
% 98.80/13.32 thf(cartprodfstin_type, type, cartprodfstin: $o).
% 98.80/13.32 thf(lamp_type, type, lamp: $o).
% 98.80/13.32 thf(iffalseProp1_type, type, iffalseProp1: $o).
% 98.80/13.32 thf(breln1invI_type, type, breln1invI: $o).
% 98.80/13.32 thf(binintersectSubset3_type, type, binintersectSubset3: $o).
% 98.80/13.32 thf(breln1unionE_type, type, breln1unionE: $o).
% 98.80/13.32 thf(ksndsingleton_type, type, ksndsingleton: $o).
% 98.80/13.32 thf(setminusIRneg_type, type, setminusIRneg: $o).
% 98.80/13.32 thf('#sk12_type', type, '#sk12': $i > $i > $i).
% 98.80/13.32 thf(lam2lamEq_type, type, lam2lamEq: $o).
% 98.80/13.32 thf(powersetAx_type, type, powersetAx: $o).
% 98.80/13.32 thf(woz2Ex_type, type, woz2Ex: $o).
% 98.80/13.32 thf(eta2_type, type, eta2: $o).
% 98.80/13.32 thf(binintersectSubset4_type, type, binintersectSubset4: $o).
% 98.80/13.32 thf(singletoninpowunion_type, type, singletoninpowunion: $o).
% 98.80/13.32 thf(image1Ex_type, type, image1Ex: $o).
% 98.80/13.32 thf(powersetI_type, type, powersetI: $o).
% 98.80/13.32 thf(cartprodmempair_type, type, cartprodmempair: $o).
% 98.80/13.32 thf(powersetTE1_type, type, powersetTE1: $o).
% 98.80/13.32 thf(upairsetIR_type, type, upairsetIR: $o).
% 98.80/13.32 thf(cartprodpairsurjEq_type, type, cartprodpairsurjEq: $o).
% 98.80/13.32 thf(lam2p_type, type, lam2p: $o).
% 98.80/13.32 thf(contraSubsetComplement_type, type, contraSubsetComplement: $o).
% 98.80/13.32 thf(doubleComplementSub1_type, type, doubleComplementSub1: $o).
% 98.80/13.32 thf(cartprodpairmemEL_type, type, cartprodpairmemEL: $o).
% 98.80/13.32 thf(setOfPairsIsBReln1_type, type, setOfPairsIsBReln1: $o).
% 98.80/13.32 thf(inCongP_type, type, inCongP: $o).
% 98.80/13.32 thf(setukpairinjR11_type, type, setukpairinjR11: $o).
% 98.80/13.32 thf(setadjoinSub_type, type, setadjoinSub: $o).
% 98.80/13.32 thf(exuE3e_type, type, exuE3e: $o).
% 98.80/13.32 thf(emptysetE_type, type, emptysetE: $o).
% 98.80/13.32 thf(woz13rule2_type, type, woz13rule2: $o).
% 98.80/13.32 thf(binintersectSubset2_type, type, binintersectSubset2: $o).
% 98.80/13.32 thf(image1E_type, type, image1E: $o).
% 98.80/13.32 thf(setunionI_type, type, setunionI: $o).
% 98.80/13.32 thf(breln1unionIR_type, type, breln1unionIR: $o).
% 98.80/13.32 thf(binintersectTERcontra_type, type, binintersectTERcontra: $o).
% 98.80/13.32 thf(setunion__Cong_type, type, setunion__Cong: $o).
% 98.80/13.32 thf(injFuncSetFuncInj_type, type, injFuncSetFuncInj: $o).
% 98.80/13.32 thf(prop2setI_type, type, prop2setI: $o).
% 98.80/13.32 thf(nonemptyImpWitness_type, type, nonemptyImpWitness: $o).
% 98.80/13.32 thf(setminusER_type, type, setminusER: $o).
% 98.80/13.32 thf(exuE2_type, type, exuE2: $o).
% 98.80/13.32 thf(woz1_2_type, type, woz1_2: $o).
% 98.80/13.32 thf(emptyset_type, type, emptyset: $i).
% 98.80/13.32 thf(setukpairinjR12_type, type, setukpairinjR12: $o).
% 98.80/13.32 thf(funcGraphProp1_type, type, funcGraphProp1: $o).
% 98.80/13.32 thf(powersetsubset_type, type, powersetsubset: $o).
% 98.80/13.32 thf(upairequniteq_type, type, upairequniteq: $o).
% 98.80/13.32 thf(dpsetconstrEL1_type, type, dpsetconstrEL1: $o).
% 98.80/13.32 thf(injFuncInInjFuncSet_type, type, injFuncInInjFuncSet: $o).
% 98.80/13.32 thf(subPowSU_type, type, subPowSU: $o).
% 98.80/13.32 thf(breln1compprop_type, type, breln1compprop: $o).
% 98.80/13.32 thf(woz2B_type, type, woz2B: $o).
% 98.80/13.32 thf(notequalI1_type, type, notequalI1: $o).
% 98.80/13.32 thf(demorgan2b_type, type, demorgan2b: $o).
% 98.80/13.32 thf(notinemptyset_type, type, notinemptyset: $o).
% 98.80/13.32 thf(nonemptyI1_type, type, nonemptyI1: $o).
% 98.80/13.32 thf(breln1unionIL_type, type, breln1unionIL: $o).
% 98.80/13.32 thf(subsetTrans_type, type, subsetTrans: $o).
% 98.80/13.32 thf(setukpairinjR_type, type, setukpairinjR: $o).
% 98.80/13.32 thf(infuncsetfunc_type, type, infuncsetfunc: $o).
% 98.80/13.32 thf(kpairp_type, type, kpairp: $o).
% 98.80/13.32 thf(setukpairinjR1_type, type, setukpairinjR1: $o).
% 98.80/13.32 thf(setminusI_type, type, setminusI: $o).
% 98.80/13.32 thf(binunionIL_type, type, binunionIL: $o).
% 98.80/13.32 thf(setOfPairsIsBReln_type, type, setOfPairsIsBReln: $o).
% 98.80/13.32 thf(setukpairinjL1_type, type, setukpairinjL1: $o).
% 98.80/13.32 thf(setunionsingleton_type, type, setunionsingleton: $o).
% 98.80/13.32 thf(powersetTI1_type, type, powersetTI1: $o).
% 98.80/13.32 thf(subsetE2_type, type, subsetE2: $o).
% 98.80/13.32 thf(image1Ex1_type, type, image1Ex1: $o).
% 98.80/13.32 thf(singletonsswitch_type, type, singletonsswitch: $o).
% 98.80/13.32 thf('#sk47_type', type, '#sk47': $i).
% 98.80/13.32 thf(ubforcartprodlem3_type, type, ubforcartprodlem3: $o).
% 98.80/13.32 thf(setextsub_type, type, setextsub: $o).
% 98.80/13.32 thf(binunionLsub_type, type, binunionLsub: $o).
% 98.80/13.32 thf(contrasubsetT1_type, type, contrasubsetT1: $o).
% 98.80/13.32 thf(setunionsingleton1_type, type, setunionsingleton1: $o).
% 98.80/13.32 thf(breln1compE_type, type, breln1compE: $o).
% 98.80/13.32 thf(emptysetsubset_type, type, emptysetsubset: $o).
% 98.80/13.32 thf(quantDeMorgan3_type, type, quantDeMorgan3: $o).
% 98.80/13.32 thf(dpsetconstrERa_type, type, dpsetconstrERa: $o).
% 98.80/13.32 thf(setunionE_type, type, setunionE: $o).
% 98.80/13.32 thf(setminusSubset1_type, type, setminusSubset1: $o).
% 98.80/13.32 thf(complementT_lem_type, type, complementT_lem: $o).
% 98.80/13.32 thf(binintersectT_lem_type, type, binintersectT_lem: $o).
% 98.80/13.32 thf(emptyinunitempty_type, type, emptyinunitempty: $o).
% 98.80/13.32 thf(binunionIR_type, type, binunionIR: $o).
% 98.80/13.32 thf(injFuncSetFuncIn_type, type, injFuncSetFuncIn: $o).
% 98.80/13.32 thf(setadjoinE_type, type, setadjoinE: $o).
% 98.80/13.32 thf(doubleComplementEq_type, type, doubleComplementEq: $o).
% 98.80/13.32 thf(eqbreln1_type, type, eqbreln1: $o).
% 98.80/13.32 thf(cartprodpairmemER_type, type, cartprodpairmemER: $o).
% 98.80/13.32 thf(dpsetconstrER_type, type, dpsetconstrER: $o).
% 98.80/13.32 thf(doubleComplementE1_type, type, doubleComplementE1: $o).
% 98.80/13.32 thf(setadjoinIL_type, type, setadjoinIL: $o).
% 98.80/13.32 thf(exuE1_type, type, exuE1: $o).
% 98.80/13.32 thf(ubforcartprodlem2_type, type, ubforcartprodlem2: $o).
% 98.80/13.32 thf(binintersectRsub_type, type, binintersectRsub: $o).
% 98.80/13.32 thf(setminusLsub_type, type, setminusLsub: $o).
% 98.80/13.32 thf(notinsingleton_type, type, notinsingleton: $o).
% 98.80/13.32 thf(intersectInPowersetIntersectUnions_type, type, intersectInPowersetIntersectUnions:
% 98.80/13.32 $o).
% 98.80/13.32 thf(dpsetconstrEL2_type, type, dpsetconstrEL2: $o).
% 98.80/13.32 thf(eqimpsubset2_type, type, eqimpsubset2: $o).
% 98.80/13.32 thf(exuEu_type, type, exuEu: $o).
% 98.80/13.32 thf(emptysetimpfalse_type, type, emptysetimpfalse: $o).
% 98.80/13.32 thf(upairsetE_type, type, upairsetE: $o).
% 98.80/13.32 thf(omega0Ax_type, type, omega0Ax: $o).
% 98.80/13.32 thf(breln1invE_type, type, breln1invE: $o).
% 98.80/13.32 thf(breln1unionCommutes_type, type, breln1unionCommutes: $o).
% 98.80/13.32 thf(funcGraphProp3_type, type, funcGraphProp3: $o).
% 98.80/13.32 thf(app_type, type, app: $o).
% 98.80/13.32 thf(funcImageSingleton_type, type, funcImageSingleton: $o).
% 98.80/13.32 thf(dpsetconstrI_type, type, dpsetconstrI: $o).
% 98.80/13.32 thf(notsubsetI_type, type, notsubsetI: $o).
% 98.80/13.32 thf(powersetT_lem_type, type, powersetT_lem: $o).
% 98.80/13.32 thf(woz2W_type, type, woz2W: $o).
% 98.80/13.32 thf(iffalseProp2_type, type, iffalseProp2: $o).
% 98.80/13.32 thf(quantDeMorgan4_type, type, quantDeMorgan4: $o).
% 98.80/13.32 thf(setextAx_type, type, setextAx: $o).
% 98.80/13.32 thf(breln1all1_type, type, breln1all1: $o).
% 98.80/13.32 thf(choice2fnsingleton_type, type, choice2fnsingleton: $o).
% 98.80/13.32 thf(breln1compI_type, type, breln1compI: $o).
% 98.80/13.32 thf(demorgan2a1_type, type, demorgan2a1: $o).
% 98.80/13.32 thf(powersetE1_type, type, powersetE1: $o).
% 98.80/13.32 thf(bs114d_type, type, bs114d: $o).
% 98.80/13.32 thf(complementTE1_type, type, complementTE1: $o).
% 98.80/13.32 thf(noeltsimpempty_type, type, noeltsimpempty: $o).
% 98.80/13.32 thf(breln1all2_type, type, breln1all2: $o).
% 98.80/13.32 thf(contrasubsetT2_type, type, contrasubsetT2: $o).
% 98.80/13.32 thf(surjective_type, type, surjective: $i > $i > $i > $o).
% 98.80/13.32 thf(inIntersectImpInUnion2_type, type, inIntersectImpInUnion2: $o).
% 98.80/13.32 thf(demorgan2b2_type, type, demorgan2b2: $o).
% 98.80/13.32 thf(binintersectLsub_type, type, binintersectLsub: $o).
% 98.80/13.32 thf(subsetI1_type, type, subsetI1: $o).
% 98.80/13.32 thf(symdiffE_type, type, symdiffE: $o).
% 98.80/13.32 thf(woz13rule1_type, type, woz13rule1: $o).
% 98.80/13.32 thf(breln1unionprop_type, type, breln1unionprop: $o).
% 98.80/13.32 thf(descrp_type, type, descrp: $o).
% 98.80/13.32 thf(dsetconstr__Cong_type, type, dsetconstr__Cong: $o).
% 98.80/13.32 thf(foundationAx_type, type, foundationAx: $o).
% 98.80/13.32 thf(brelnall2_type, type, brelnall2: $o).
% 98.80/13.32 thf(emptysetAx_type, type, emptysetAx: $o).
% 98.80/13.32 thf(emptyI_type, type, emptyI: $o).
% 98.80/13.32 thf(setadjoinOr_type, type, setadjoinOr: $o).
% 98.80/13.32 thf(binintersectEL_type, type, binintersectEL: $o).
% 98.80/13.32 thf(emptyE1_type, type, emptyE1: $o).
% 98.80/13.32 thf(demorgan2a_type, type, demorgan2a: $o).
% 98.80/13.32 thf(woz1_3_type, type, woz1_3: $o).
% 98.80/13.32 thf(emptyInPowerset_type, type, emptyInPowerset: $o).
% 98.80/13.32 thf(vacuousDall_type, type, vacuousDall: $o).
% 98.80/13.32 thf(dsetconstr_type, type, dsetconstr: $i > ($i > $o) > $i).
% 98.80/13.32 thf(dsetconstrER_type, type, dsetconstrER: $o).
% 98.80/13.32 thf(demorgan1a_type, type, demorgan1a: $o).
% 98.80/13.32 thf(ifp_type, type, ifp: $o).
% 98.80/13.32 thf(funcSet_type, type, funcSet: $i > $i > $i).
% 98.80/13.32 thf(binintersectI_type, type, binintersectI: $o).
% 98.80/13.32 thf(beta1_type, type, beta1: $o).
% 98.80/13.32 thf(funcext2_type, type, funcext2: $o).
% 98.80/13.32 thf(subbreln_type, type, subbreln: $o).
% 98.80/13.32 thf(cartprodpairin_type, type, cartprodpairin: $o).
% 98.80/13.32 thf('#sk49_type', type, '#sk49': $i).
% 98.80/13.32 thf(cartprodmempair1_type, type, cartprodmempair1: $o).
% 98.80/13.32 thf(subbreln1_type, type, subbreln1: $o).
% 98.80/13.32 thf(demorgan2a2_type, type, demorgan2a2: $o).
% 98.80/13.32 thf(image1Equiv_type, type, image1Equiv: $o).
% 98.80/13.32 thf(subsetTI_type, type, subsetTI: $o).
% 98.80/13.32 thf(setminusT_lem_type, type, setminusT_lem: $o).
% 98.80/13.32 thf(ap2p_type, type, ap2p: $o).
% 98.80/13.32 thf(doubleComplementI1_type, type, doubleComplementI1: $o).
% 98.80/13.32 thf(binunionT_lem_type, type, binunionT_lem: $o).
% 98.80/13.32 thf(symdiffI1_type, type, symdiffI1: $o).
% 98.80/13.32 thf(woz1_4_type, type, woz1_4: $o).
% 98.80/13.32 thf(kfstpairEq_type, type, kfstpairEq: $o).
% 98.80/13.32 thf(subsetI2_type, type, subsetI2: $o).
% 98.80/13.32 thf(symdiffIneg1_type, type, symdiffIneg1: $o).
% 98.80/13.32 thf(theeq_type, type, theeq: $o).
% 98.80/13.32 thf(setminusERneg_type, type, setminusERneg: $o).
% 98.80/13.32 thf(symdiffIneg2_type, type, symdiffIneg2: $o).
% 98.80/13.32 thf(binunionTIRcontra_type, type, binunionTIRcontra: $o).
% 98.80/13.32 thf(omega__Cong_type, type, omega__Cong: $o).
% 98.80/13.32 thf(demorgan1b_type, type, demorgan1b: $o).
% 98.80/13.32 thf(subsetRefl_type, type, subsetRefl: $o).
% 98.80/13.32 thf(uniqinunit_type, type, uniqinunit: $o).
% 98.80/13.32 thf(eqbreln_type, type, eqbreln: $o).
% 98.80/13.32 thf(inComplementUnionImpNotIn1_type, type, inComplementUnionImpNotIn1: $o).
% 98.80/13.32 thf(funcinfuncset_type, type, funcinfuncset: $o).
% 98.80/13.32 thf(breln1compEex_type, type, breln1compEex: $o).
% 98.80/13.32 thf(contrasubsetT_type, type, contrasubsetT: $o).
% 98.80/13.32 thf(setminusSubset2_type, type, setminusSubset2: $o).
% 98.80/13.32 thf(prop2setE_type, type, prop2setE: $o).
% 98.80/13.32 thf(binunionEcases_type, type, binunionEcases: $o).
% 98.80/13.32 thf(omega_type, type, omega: $i).
% 98.80/13.32 thf(nonemptyI_type, type, nonemptyI: $o).
% 98.80/13.32 thf(disjointsetsI1_type, type, disjointsetsI1: $o).
% 98.80/13.32 thf(woz2A_type, type, woz2A: $o).
% 98.80/13.32 thf(exuE3u_type, type, exuE3u: $o).
% 98.80/13.32 thf(setminusEL_type, type, setminusEL: $o).
% 98.80/13.32 thf(funcGraphProp4_type, type, funcGraphProp4: $o).
% 98.80/13.32 thf(woz1_5_type, type, woz1_5: $o).
% 98.80/13.32 thf(demorgan2_type, type, demorgan2: $o).
% 98.80/13.32 thf(setunionsingleton2_type, type, setunionsingleton2: $o).
% 98.80/13.32 thf(sepSubset_type, type, sepSubset: $o).
% 98.80/13.32 thf(inComplementUnionImpInComplement1_type, type, inComplementUnionImpInComplement1:
% 98.80/13.32 $o).
% 98.80/13.32 thf(funcext_type, type, funcext: $o).
% 98.80/13.32 thf(surjFuncSet_type, type, surjFuncSet: $i > $i > $i).
% 98.80/13.32 thf(upairset2E_type, type, upairset2E: $o).
% 98.80/13.32 thf(eqimpsubset1_type, type, eqimpsubset1: $o).
% 98.80/13.32 thf(exuI3_type, type, exuI3: $o).
% 98.80/13.32 thf(notdallE_type, type, notdallE: $o).
% 98.80/13.32 thf(iftrueProp2_type, type, iftrueProp2: $o).
% 98.80/13.32 thf(binintersectER_type, type, binintersectER: $o).
% 98.80/13.32 thf(woz13rule0_type, type, woz13rule0: $o).
% 98.80/13.32 thf(dsetconstrI_type, type, dsetconstrI: $o).
% 98.80/13.32 thf(beta2_type, type, beta2: $o).
% 98.80/13.32 thf(setadjoin_type, type, setadjoin: $i > $i > $i).
% 98.80/13.32 thf(exu__Cong_type, type, exu__Cong: $o).
% 98.80/13.32 thf(cartprodsndin_type, type, cartprodsndin: $o).
% 98.80/13.32 thf(iftrueorfalse_type, type, iftrueorfalse: $o).
% 98.80/13.32 thf(quantDeMorgan2_type, type, quantDeMorgan2: $o).
% 98.80/13.32 thf(ex1I_type, type, ex1I: $o).
% 98.80/13.32 thf(secondinupair_type, type, secondinupair: $o).
% 98.80/13.32 thf(singletonprop_type, type, singletonprop: $o).
% 98.80/13.32 thf(singletonsubset_type, type, singletonsubset: $o).
% 98.80/13.32 thf(singletoninpowerset_type, type, singletoninpowerset: $o).
% 98.80/13.32 thf(subsetemptysetimpeq_type, type, subsetemptysetimpeq: $o).
% 98.80/13.32 thf(ex1E2_type, type, ex1E2: $o).
% 98.80/13.32 thf(replAx_type, type, replAx: $o).
% 98.80/13.32 thf(nonemptyE1_type, type, nonemptyE1: $o).
% 98.80/13.32 thf(omegaIndAx_type, type, omegaIndAx: $o).
% 98.80/13.32 thf(setukpairIL_type, type, setukpairIL: $o).
% 98.80/13.32 thf(setunionE2_type, type, setunionE2: $o).
% 98.80/13.32 thf(inPowerset_type, type, inPowerset: $o).
% 98.80/13.32 thf(binunionTILcontra_type, type, binunionTILcontra: $o).
% 98.80/13.32 thf(ap2apEq1_type, type, ap2apEq1: $o).
% 98.80/13.32 thf(contrasubsetT3_type, type, contrasubsetT3: $o).
% 98.80/13.32 thf(woz13rule3_type, type, woz13rule3: $o).
% 98.80/13.32 thf(complementImpComplementIntersect_type, type, complementImpComplementIntersect:
% 98.80/13.32 $o).
% 98.80/13.32 thf(in__Cong_type, type, in__Cong: $o).
% 98.80/13.32 thf(setukpairinjL_type, type, setukpairinjL: $o).
% 98.80/13.32 thf(binunionRsub_type, type, binunionRsub: $o).
% 98.80/13.32 thf(subset2powerset_type, type, subset2powerset: $o).
% 98.80/13.32 thf(s_comb_type, type, '#S': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > (A > B) > A > C)).
% 98.80/13.32 thf(c_comb_type, type, '#C': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > B > A > C)).
% 98.80/13.32 thf(b_comb_type, type, '#B': !>[A:$tType, B:$tType, C:$tType]: ((A > B) > (C > A) > C > B)).
% 98.80/13.32 thf(k_comb_type, type, '#K': !>[A:$tType, B:$tType]: (B > A > B)).
% 98.80/13.32 thf(i_comb_type, type, '#I': !>[A:$tType]: (A > A)).
% 98.80/13.32 thf(surjFuncSetFuncIn, conjecture,
% 98.80/13.32 (( setextAx ) =>
% 98.80/13.32 ( ( emptysetAx ) =>
% 98.80/13.32 ( ( setadjoinAx ) =>
% 98.80/13.32 ( ( powersetAx ) =>
% 98.80/13.32 ( ( setunionAx ) =>
% 98.80/13.32 ( ( omega0Ax ) =>
% 98.80/13.32 ( ( omegaSAx ) =>
% 98.80/13.32 ( ( omegaIndAx ) =>
% 98.80/13.32 ( ( replAx ) =>
% 98.80/13.32 ( ( foundationAx ) =>
% 98.80/13.32 ( ( wellorderingAx ) =>
% 98.80/13.32 ( ( descrp ) =>
% 98.80/13.32 ( ( dsetconstrI ) =>
% 98.80/13.32 ( ( dsetconstrEL ) =>
% 98.80/13.32 ( ( dsetconstrER ) =>
% 98.80/13.32 ( ( exuE1 ) =>
% 98.80/13.32 ( ( prop2setE ) =>
% 98.80/13.32 ( ( emptysetE ) =>
% 98.80/13.32 ( ( emptysetimpfalse ) =>
% 98.80/13.32 ( ( notinemptyset ) =>
% 98.80/13.32 ( ( exuE3e ) =>
% 98.80/13.32 ( ( setext ) =>
% 98.80/13.32 ( ( emptyI ) =>
% 98.80/13.32 ( ( noeltsimpempty ) =>
% 98.80/13.32 ( ( setbeta ) =>
% 98.80/13.32 ( ( nonemptyE1 ) =>
% 98.80/13.32 ( ( nonemptyI ) =>
% 98.80/13.32 ( ( nonemptyI1 ) =>
% 98.80/13.32 ( ( setadjoinIL ) =>
% 98.80/13.32 ( ( emptyinunitempty ) =>
% 98.80/13.32 ( ( setadjoinIR ) =>
% 98.80/13.32 ( ( setadjoinE ) =>
% 98.80/13.32 ( (
% 98.80/13.32 setadjoinOr ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 setoftrueEq ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 powersetI ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 emptyinPowerset ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 emptyInPowerset ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 powersetE ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 setunionI ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 setunionE ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 subPowSU ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 exuE2 ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 nonemptyImpWitness ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 uniqinunit ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 notinsingleton ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 eqinunit ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 singletonsswitch ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 upairsetE ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 upairsetIL ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 upairsetIR ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 emptyE1 ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 vacuousDall ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 quantDeMorgan1 ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 quantDeMorgan2 ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 quantDeMorgan3 ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 quantDeMorgan4 ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 prop2setI ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 prop2set2propI ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 notdexE ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 notdallE ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 exuI1 ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 exuI3 ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 exuI2 ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 inCongP ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 in__Cong ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 exuE3u ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 exu__Cong ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 emptyset__Cong ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 setadjoin__Cong ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 powerset__Cong ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 setunion__Cong ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 omega__Cong ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 exuEu ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 descr__Cong ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 dsetconstr__Cong ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 subsetI1 ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 eqimpsubset2 ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 eqimpsubset1 ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 subsetI2 ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 emptysetsubset ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 subsetE ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 subsetE2 ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 notsubsetI ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 notequalI1 ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 notequalI2 ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 subsetRefl ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 subsetTrans ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 setadjoinSub ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 setadjoinSub2 ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 subset2powerset ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 setextsub ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 subsetemptysetimpeq ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 powersetI1 ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 powersetE1 ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 inPowerset ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 powersetsubset ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 sepInPowerset ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 sepSubset ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 binunionIL ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 upairset2IR ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 binunionIR ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 binunionEcases ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 binunionE ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 binunionLsub ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 binunionRsub ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 binintersectI ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 binintersectSubset5 ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 binintersectEL ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 binintersectLsub ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 binintersectSubset2 ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 binintersectSubset3 ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 binintersectER ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 disjointsetsI1 ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 binintersectRsub ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 binintersectSubset4 ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 binintersectSubset1 ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 bs114d ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 setminusI ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 setminusEL ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 setminusER ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 setminusSubset2 ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 setminusERneg ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 setminusELneg ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 setminusILneg ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 setminusIRneg ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 setminusLsub ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 setminusSubset1 ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 symdiffE ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 symdiffI1 ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 symdiffI2 ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 symdiffIneg1 ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 symdiffIneg2 ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 secondinupair ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 setukpairIL ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 setukpairIR ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 kpairiskpair ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 kpairp ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 singletonsubset ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 singletoninpowerset ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 singletoninpowunion ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 upairset2E ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 upairsubunion ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 upairinpowunion ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 ubforcartprodlem1 ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 ubforcartprodlem2 ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 ubforcartprodlem3 ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 cartprodpairin ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 cartprodmempair1 ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 cartprodmempair ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 setunionE2 ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 setunionsingleton1 ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 setunionsingleton2 ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 setunionsingleton ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 singletonprop ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 ex1E1 ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 ex1I ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 ex1I2 ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 singletonsuniq ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 setukpairinjL1 ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 kfstsingleton ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 theprop ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 kfstpairEq ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 cartprodfstin ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 setukpairinjL2 ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 setukpairinjL ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 setukpairinjR11 ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 setukpairinjR12 ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 setukpairinjR1 ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 upairequniteq ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 setukpairinjR2 ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 setukpairinjR ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 ksndsingleton ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 ksndpairEq ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 kpairsurjEq ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 cartprodsndin ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 cartprodpairmemEL ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 cartprodpairmemER ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 cartprodmempaircEq ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 cartprodfstpairEq ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 cartprodsndpairEq ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 cartprodpairsurjEq ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 dpsetconstrI ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 dpsetconstrSub ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 setOfPairsIsBReln ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 dpsetconstrERa ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 dpsetconstrEL1 ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 dpsetconstrEL2 ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 dpsetconstrER ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 funcImageSingleton ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 apProp ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 app ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 infuncsetfunc ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 ap2p ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 funcinfuncset ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 lamProp ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 lamp ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 lam2p ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 brelnall1 ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 brelnall2 ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 ex1E2 ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 funcGraphProp1 ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 funcGraphProp3 ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 funcGraphProp2 ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 funcextLem ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 funcGraphProp4 ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 subbreln ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 eqbreln ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 funcext ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 funcext2 ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 ap2apEq1 ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 ap2apEq2 ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 beta1 ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 eta1 ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 lam2lamEq ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 beta2 ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 eta2 ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 iffalseProp1 ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 iffalseProp2 ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 iftrueProp1 ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 iftrueProp2 ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 ifSingleton ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 ifp ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 theeq ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 iftrue ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 iffalse ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 iftrueorfalse ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 binintersectT_lem ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 binunionT_lem ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 powersetT_lem ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 setminusT_lem ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 complementT_lem ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 setextT ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 subsetTI ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 powersetTI1 ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 powersetTE1 ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 complementTI1 ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 complementTE1 ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 binintersectTELcontra ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 binintersectTERcontra ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 contrasubsetT ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 contrasubsetT1 ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 contrasubsetT2 ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 contrasubsetT3 ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 doubleComplementI1 ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 doubleComplementE1 ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 doubleComplementSub1 ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 doubleComplementSub2 ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 doubleComplementEq ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 complementTnotintersectT ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 complementImpComplementIntersect ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 complementSubsetComplementIntersect ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 complementInPowersetComplementIntersect ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 contraSubsetComplement ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 complementTcontraSubset ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 binunionTILcontra ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 binunionTIRcontra ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 inIntersectImpInUnion ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 inIntersectImpInUnion2 ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 inIntersectImpInIntersectUnions ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 intersectInPowersetIntersectUnions ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 inComplementUnionImpNotIn1 ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 inComplementUnionImpInComplement1 ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 binunionTE ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 binunionTEcontra ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 demorgan2a1 ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 complementUnionInPowersetComplement ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 demorgan2a2 ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 demorgan1a ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 demorgan1b ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 demorgan1 ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 demorgan2a ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 demorgan2b2 ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 demorgan2b ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 demorgan2 ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 woz13rule0 ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 woz13rule1 ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 woz13rule2 ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 woz13rule3 ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 woz13rule4 ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 woz1_1 ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 woz1_2 ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 woz1_3 ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 woz1_4 ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 woz1_5 ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 breln1all2 ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 breln1SetBreln1 ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 choice2fnsingleton ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 setOfPairsIsBReln1 ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 breln1all1 ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 subbreln1 ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 eqbreln1 ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 breln1invprop ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 breln1invI ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 breln1invE ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 breln1compprop ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 breln1compI ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 breln1compE ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 breln1compEex ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 breln1unionprop ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 breln1unionIL ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 breln1unionIR ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 breln1unionI ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 breln1unionE ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 breln1unionEcases ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 breln1unionCommutes ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 woz2Ex ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 woz2W ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 woz2A ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 woz2B ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 image1Ex ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 image1Ex1 ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 image1Equiv ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 image1E ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 image1I ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 injFuncInInjFuncSet ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 injFuncSetFuncIn ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 injFuncSetFuncInj ) =>
% 98.80/13.32 (
% 98.80/13.32 ![
% 98.80/13.32 A:$i,B:$i,
% 98.80/13.32 Xf:$i]:
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 in @
% 98.80/13.32 Xf @
% 98.80/13.32 (
% 98.80/13.32 surjFuncSet
% 98.80/13.32 @
% 98.80/13.32 A @ B ) ) =>
% 98.80/13.32 (
% 98.80/13.32 in @
% 98.80/13.32 Xf @
% 98.80/13.32 (
% 98.80/13.32 funcSet @
% 98.80/13.32 A @ B ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 98.80/13.32 thf(zf_stmt_0, negated_conjecture,
% 98.80/13.32 (~( ( setextAx ) =>
% 98.80/13.32 ( ( emptysetAx ) =>
% 98.80/13.32 ( ( setadjoinAx ) =>
% 98.80/13.32 ( ( powersetAx ) =>
% 98.80/13.32 ( ( setunionAx ) =>
% 98.80/13.32 ( ( omega0Ax ) =>
% 98.80/13.32 ( ( omegaSAx ) =>
% 98.80/13.32 ( ( omegaIndAx ) =>
% 98.80/13.32 ( ( replAx ) =>
% 98.80/13.32 ( ( foundationAx ) =>
% 98.80/13.32 ( ( wellorderingAx ) =>
% 98.80/13.32 ( ( descrp ) =>
% 98.80/13.32 ( ( dsetconstrI ) =>
% 98.80/13.32 ( ( dsetconstrEL ) =>
% 98.80/13.32 ( ( dsetconstrER ) =>
% 98.80/13.32 ( ( exuE1 ) =>
% 98.80/13.32 ( ( prop2setE ) =>
% 98.80/13.32 ( ( emptysetE ) =>
% 98.80/13.32 ( ( emptysetimpfalse ) =>
% 98.80/13.32 ( ( notinemptyset ) =>
% 98.80/13.32 ( ( exuE3e ) =>
% 98.80/13.32 ( ( setext ) =>
% 98.80/13.32 ( ( emptyI ) =>
% 98.80/13.32 ( ( noeltsimpempty ) =>
% 98.80/13.32 ( ( setbeta ) =>
% 98.80/13.32 ( ( nonemptyE1 ) =>
% 98.80/13.32 ( ( nonemptyI ) =>
% 98.80/13.32 ( ( nonemptyI1 ) =>
% 98.80/13.32 ( ( setadjoinIL ) =>
% 98.80/13.32 ( ( emptyinunitempty ) =>
% 98.80/13.32 ( ( setadjoinIR ) =>
% 98.80/13.32 ( (
% 98.80/13.32 setadjoinE ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 setadjoinOr ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 setoftrueEq ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 powersetI ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 emptyinPowerset ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 emptyInPowerset ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 powersetE ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 setunionI ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 setunionE ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 subPowSU ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 exuE2 ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 nonemptyImpWitness ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 uniqinunit ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 notinsingleton ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 eqinunit ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 singletonsswitch ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 upairsetE ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 upairsetIL ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 upairsetIR ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 emptyE1 ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 vacuousDall ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 quantDeMorgan1 ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 quantDeMorgan2 ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 quantDeMorgan3 ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 quantDeMorgan4 ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 prop2setI ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 prop2set2propI ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 notdexE ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 notdallE ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 exuI1 ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 exuI3 ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 exuI2 ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 inCongP ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 in__Cong ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 exuE3u ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 exu__Cong ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 emptyset__Cong ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 setadjoin__Cong ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 powerset__Cong ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 setunion__Cong ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 omega__Cong ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 exuEu ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 descr__Cong ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 dsetconstr__Cong ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 subsetI1 ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 eqimpsubset2 ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 eqimpsubset1 ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 subsetI2 ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 emptysetsubset ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 subsetE ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 subsetE2 ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 notsubsetI ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 notequalI1 ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 notequalI2 ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 subsetRefl ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 subsetTrans ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 setadjoinSub ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 setadjoinSub2 ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 subset2powerset ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 setextsub ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 subsetemptysetimpeq ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 powersetI1 ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 powersetE1 ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 inPowerset ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 powersetsubset ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 sepInPowerset ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 sepSubset ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 binunionIL ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 upairset2IR ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 binunionIR ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 binunionEcases ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 binunionE ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 binunionLsub ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 binunionRsub ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 binintersectI ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 binintersectSubset5 ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 binintersectEL ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 binintersectLsub ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 binintersectSubset2 ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 binintersectSubset3 ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 binintersectER ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 disjointsetsI1 ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 binintersectRsub ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 binintersectSubset4 ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 binintersectSubset1 ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 bs114d ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 setminusI ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 setminusEL ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 setminusER ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 setminusSubset2 ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 setminusERneg ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 setminusELneg ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 setminusILneg ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 setminusIRneg ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 setminusLsub ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 setminusSubset1 ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 symdiffE ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 symdiffI1 ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 symdiffI2 ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 symdiffIneg1 ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 symdiffIneg2 ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 secondinupair ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 setukpairIL ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 setukpairIR ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 kpairiskpair ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 kpairp ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 singletonsubset ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 singletoninpowerset ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 singletoninpowunion ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 upairset2E ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 upairsubunion ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 upairinpowunion ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 ubforcartprodlem1 ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 ubforcartprodlem2 ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 ubforcartprodlem3 ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 cartprodpairin ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 cartprodmempair1 ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 cartprodmempair ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 setunionE2 ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 setunionsingleton1 ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 setunionsingleton2 ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 setunionsingleton ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 singletonprop ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 ex1E1 ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 ex1I ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 ex1I2 ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 singletonsuniq ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 setukpairinjL1 ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 kfstsingleton ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 theprop ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 kfstpairEq ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 cartprodfstin ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 setukpairinjL2 ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 setukpairinjL ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 setukpairinjR11 ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 setukpairinjR12 ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 setukpairinjR1 ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 upairequniteq ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 setukpairinjR2 ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 setukpairinjR ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 ksndsingleton ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 ksndpairEq ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 kpairsurjEq ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 cartprodsndin ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 cartprodpairmemEL ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 cartprodpairmemER ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 cartprodmempaircEq ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 cartprodfstpairEq ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 cartprodsndpairEq ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 cartprodpairsurjEq ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 dpsetconstrI ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 dpsetconstrSub ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 setOfPairsIsBReln ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 dpsetconstrERa ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 dpsetconstrEL1 ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 dpsetconstrEL2 ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 dpsetconstrER ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 funcImageSingleton ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 apProp ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 app ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 infuncsetfunc ) =>
% 98.80/13.32 (
% 98.80/13.32 (
% 98.80/13.32 ap2p ) =>
% 98.80/13.33 (
% 98.80/13.33 (
% 98.80/13.33 funcinfuncset ) =>
% 98.80/13.33 (
% 98.80/13.33 (
% 98.80/13.33 lamProp ) =>
% 98.80/13.33 (
% 98.80/13.33 (
% 98.80/13.33 lamp ) =>
% 98.80/13.33 (
% 98.80/13.33 (
% 98.80/13.33 lam2p ) =>
% 98.80/13.33 (
% 98.80/13.33 (
% 98.80/13.33 brelnall1 ) =>
% 98.80/13.33 (
% 98.80/13.33 (
% 98.80/13.33 brelnall2 ) =>
% 98.80/13.33 (
% 98.80/13.33 (
% 98.80/13.33 ex1E2 ) =>
% 98.80/13.33 (
% 98.80/13.33 (
% 98.80/13.33 funcGraphProp1 ) =>
% 98.80/13.33 (
% 98.80/13.33 (
% 98.80/13.33 funcGraphProp3 ) =>
% 98.80/13.33 (
% 98.80/13.33 (
% 98.80/13.33 funcGraphProp2 ) =>
% 98.80/13.33 (
% 98.80/13.33 (
% 98.80/13.33 funcextLem ) =>
% 98.80/13.33 (
% 98.80/13.33 (
% 98.80/13.33 funcGraphProp4 ) =>
% 98.80/13.33 (
% 98.80/13.33 (
% 98.80/13.33 subbreln ) =>
% 98.80/13.33 (
% 98.80/13.33 (
% 98.80/13.33 eqbreln ) =>
% 98.80/13.33 (
% 98.80/13.33 (
% 98.80/13.33 funcext ) =>
% 98.80/13.33 (
% 98.80/13.33 (
% 98.80/13.33 funcext2 ) =>
% 98.80/13.33 (
% 98.80/13.33 (
% 98.80/13.33 ap2apEq1 ) =>
% 98.80/13.33 (
% 98.80/13.33 (
% 98.80/13.33 ap2apEq2 ) =>
% 98.80/13.33 (
% 98.80/13.33 (
% 98.80/13.33 beta1 ) =>
% 98.80/13.33 (
% 98.80/13.33 (
% 98.80/13.33 eta1 ) =>
% 98.80/13.33 (
% 98.80/13.33 (
% 98.80/13.33 lam2lamEq ) =>
% 98.80/13.33 (
% 98.80/13.33 (
% 98.80/13.33 beta2 ) =>
% 98.80/13.33 (
% 98.80/13.33 (
% 98.80/13.33 eta2 ) =>
% 98.80/13.33 (
% 98.80/13.33 (
% 98.80/13.33 iffalseProp1 ) =>
% 98.80/13.33 (
% 98.80/13.33 (
% 98.80/13.33 iffalseProp2 ) =>
% 98.80/13.33 (
% 98.80/13.33 (
% 98.80/13.33 iftrueProp1 ) =>
% 98.80/13.33 (
% 98.80/13.33 (
% 98.80/13.33 iftrueProp2 ) =>
% 98.80/13.33 (
% 98.80/13.33 (
% 98.80/13.33 ifSingleton ) =>
% 98.80/13.33 (
% 98.80/13.33 (
% 98.80/13.33 ifp ) =>
% 98.80/13.33 (
% 98.80/13.33 (
% 98.80/13.33 theeq ) =>
% 98.80/13.33 (
% 98.80/13.33 (
% 98.80/13.33 iftrue ) =>
% 98.80/13.33 (
% 98.80/13.33 (
% 98.80/13.33 iffalse ) =>
% 98.80/13.33 (
% 98.80/13.33 (
% 98.80/13.33 iftrueorfalse ) =>
% 98.80/13.33 (
% 98.80/13.33 (
% 98.80/13.33 binintersectT_lem ) =>
% 98.80/13.33 (
% 98.80/13.33 (
% 98.80/13.33 binunionT_lem ) =>
% 98.80/13.33 (
% 98.80/13.33 (
% 98.80/13.33 powersetT_lem ) =>
% 98.80/13.33 (
% 98.80/13.33 (
% 98.80/13.33 setminusT_lem ) =>
% 98.80/13.33 (
% 98.80/13.33 (
% 98.80/13.33 complementT_lem ) =>
% 98.80/13.33 (
% 98.80/13.33 (
% 98.80/13.33 setextT ) =>
% 98.80/13.33 (
% 98.80/13.33 (
% 98.80/13.33 subsetTI ) =>
% 98.80/13.33 (
% 98.80/13.33 (
% 98.80/13.33 powersetTI1 ) =>
% 98.80/13.33 (
% 98.80/13.33 (
% 98.80/13.33 powersetTE1 ) =>
% 98.80/13.33 (
% 98.80/13.33 (
% 98.80/13.33 complementTI1 ) =>
% 98.80/13.33 (
% 98.80/13.33 (
% 98.80/13.33 complementTE1 ) =>
% 98.80/13.33 (
% 98.80/13.33 (
% 98.80/13.33 binintersectTELcontra ) =>
% 98.80/13.33 (
% 98.80/13.33 (
% 98.80/13.33 binintersectTERcontra ) =>
% 98.80/13.33 (
% 98.80/13.33 (
% 98.80/13.33 contrasubsetT ) =>
% 98.80/13.33 (
% 98.80/13.33 (
% 98.80/13.33 contrasubsetT1 ) =>
% 98.80/13.33 (
% 98.80/13.33 (
% 98.80/13.33 contrasubsetT2 ) =>
% 98.80/13.33 (
% 98.80/13.33 (
% 98.80/13.33 contrasubsetT3 ) =>
% 98.80/13.33 (
% 98.80/13.33 (
% 98.80/13.33 doubleComplementI1 ) =>
% 98.80/13.33 (
% 98.80/13.33 (
% 98.80/13.33 doubleComplementE1 ) =>
% 98.80/13.33 (
% 98.80/13.33 (
% 98.80/13.33 doubleComplementSub1 ) =>
% 98.80/13.33 (
% 98.80/13.33 (
% 98.80/13.33 doubleComplementSub2 ) =>
% 98.80/13.33 (
% 98.80/13.33 (
% 98.80/13.33 doubleComplementEq ) =>
% 98.80/13.33 (
% 98.80/13.33 (
% 98.80/13.33 complementTnotintersectT ) =>
% 98.80/13.33 (
% 98.80/13.33 (
% 98.80/13.33 complementImpComplementIntersect ) =>
% 98.80/13.33 (
% 98.80/13.33 (
% 98.80/13.33 complementSubsetComplementIntersect ) =>
% 98.80/13.33 (
% 98.80/13.33 (
% 98.80/13.33 complementInPowersetComplementIntersect ) =>
% 98.80/13.33 (
% 98.80/13.33 (
% 98.80/13.33 contraSubsetComplement ) =>
% 98.80/13.33 (
% 98.80/13.33 (
% 98.80/13.33 complementTcontraSubset ) =>
% 98.80/13.33 (
% 98.80/13.33 (
% 98.80/13.33 binunionTILcontra ) =>
% 98.80/13.33 (
% 98.80/13.33 (
% 98.80/13.33 binunionTIRcontra ) =>
% 98.80/13.33 (
% 98.80/13.33 (
% 98.80/13.33 inIntersectImpInUnion ) =>
% 98.80/13.33 (
% 98.80/13.33 (
% 98.80/13.33 inIntersectImpInUnion2 ) =>
% 98.80/13.33 (
% 98.80/13.33 (
% 98.80/13.33 inIntersectImpInIntersectUnions ) =>
% 98.80/13.33 (
% 98.80/13.33 (
% 98.80/13.33 intersectInPowersetIntersectUnions ) =>
% 98.80/13.33 (
% 98.80/13.33 (
% 98.80/13.33 inComplementUnionImpNotIn1 ) =>
% 98.80/13.33 (
% 98.80/13.33 (
% 98.80/13.33 inComplementUnionImpInComplement1 ) =>
% 98.80/13.33 (
% 98.80/13.33 (
% 98.80/13.33 binunionTE ) =>
% 98.80/13.33 (
% 98.80/13.33 (
% 98.80/13.33 binunionTEcontra ) =>
% 98.80/13.33 (
% 98.80/13.33 (
% 98.80/13.33 demorgan2a1 ) =>
% 98.80/13.33 (
% 98.80/13.33 (
% 98.80/13.33 complementUnionInPowersetComplement ) =>
% 98.80/13.33 (
% 98.80/13.33 (
% 98.80/13.33 demorgan2a2 ) =>
% 98.80/13.33 (
% 98.80/13.33 (
% 98.80/13.33 demorgan1a ) =>
% 98.80/13.33 (
% 98.80/13.33 (
% 98.80/13.33 demorgan1b ) =>
% 98.80/13.33 (
% 98.80/13.33 (
% 98.80/13.33 demorgan1 ) =>
% 98.80/13.33 (
% 98.80/13.33 (
% 98.80/13.33 demorgan2a ) =>
% 98.80/13.33 (
% 98.80/13.33 (
% 98.80/13.33 demorgan2b2 ) =>
% 98.80/13.33 (
% 98.80/13.33 (
% 98.80/13.33 demorgan2b ) =>
% 98.80/13.33 (
% 98.80/13.33 (
% 98.80/13.33 demorgan2 ) =>
% 98.80/13.33 (
% 98.80/13.33 (
% 98.80/13.33 woz13rule0 ) =>
% 98.80/13.33 (
% 98.80/13.33 (
% 98.80/13.33 woz13rule1 ) =>
% 98.80/13.33 (
% 98.80/13.33 (
% 98.80/13.33 woz13rule2 ) =>
% 98.80/13.33 (
% 98.80/13.33 (
% 98.80/13.33 woz13rule3 ) =>
% 98.80/13.33 (
% 98.80/13.33 (
% 98.80/13.33 woz13rule4 ) =>
% 98.80/13.33 (
% 98.80/13.33 (
% 98.80/13.33 woz1_1 ) =>
% 98.80/13.33 (
% 98.80/13.33 (
% 98.80/13.33 woz1_2 ) =>
% 98.80/13.33 (
% 98.80/13.33 (
% 98.80/13.33 woz1_3 ) =>
% 98.80/13.33 (
% 98.80/13.33 (
% 98.80/13.33 woz1_4 ) =>
% 98.80/13.33 (
% 98.80/13.33 (
% 98.80/13.33 woz1_5 ) =>
% 98.80/13.33 (
% 98.80/13.33 (
% 98.80/13.33 breln1all2 ) =>
% 98.80/13.33 (
% 98.80/13.33 (
% 98.80/13.33 breln1SetBreln1 ) =>
% 98.80/13.33 (
% 98.80/13.33 (
% 98.80/13.33 choice2fnsingleton ) =>
% 98.80/13.33 (
% 98.80/13.33 (
% 98.80/13.33 setOfPairsIsBReln1 ) =>
% 98.80/13.33 (
% 98.80/13.33 (
% 98.80/13.33 breln1all1 ) =>
% 98.80/13.33 (
% 98.80/13.33 (
% 98.80/13.33 subbreln1 ) =>
% 98.80/13.33 (
% 98.80/13.33 (
% 98.80/13.33 eqbreln1 ) =>
% 98.80/13.33 (
% 98.80/13.33 (
% 98.80/13.33 breln1invprop ) =>
% 98.80/13.33 (
% 98.80/13.33 (
% 98.80/13.33 breln1invI ) =>
% 98.80/13.33 (
% 98.80/13.33 (
% 98.80/13.33 breln1invE ) =>
% 98.80/13.33 (
% 98.80/13.33 (
% 98.80/13.33 breln1compprop ) =>
% 98.80/13.33 (
% 98.80/13.33 (
% 98.80/13.33 breln1compI ) =>
% 98.80/13.33 (
% 98.80/13.33 (
% 98.80/13.33 breln1compE ) =>
% 98.80/13.33 (
% 98.80/13.33 (
% 98.80/13.33 breln1compEex ) =>
% 98.80/13.33 (
% 98.80/13.33 (
% 98.80/13.33 breln1unionprop ) =>
% 98.80/13.33 (
% 98.80/13.33 (
% 98.80/13.33 breln1unionIL ) =>
% 98.80/13.33 (
% 98.80/13.33 (
% 98.80/13.33 breln1unionIR ) =>
% 98.80/13.33 (
% 98.80/13.33 (
% 98.80/13.33 breln1unionI ) =>
% 98.80/13.33 (
% 98.80/13.33 (
% 98.80/13.33 breln1unionE ) =>
% 98.80/13.33 (
% 98.80/13.33 (
% 98.80/13.33 breln1unionEcases ) =>
% 98.80/13.33 (
% 98.80/13.33 (
% 98.80/13.33 breln1unionCommutes ) =>
% 98.80/13.33 (
% 98.80/13.33 (
% 98.80/13.33 woz2Ex ) =>
% 98.80/13.33 (
% 98.80/13.33 (
% 98.80/13.33 woz2W ) =>
% 98.80/13.33 (
% 98.80/13.33 (
% 98.80/13.33 woz2A ) =>
% 98.80/13.33 (
% 98.80/13.33 (
% 98.80/13.33 woz2B ) =>
% 98.80/13.33 (
% 98.80/13.33 (
% 98.80/13.33 image1Ex ) =>
% 98.80/13.33 (
% 98.80/13.33 (
% 98.80/13.33 image1Ex1 ) =>
% 98.80/13.33 (
% 98.80/13.33 (
% 98.80/13.33 image1Equiv ) =>
% 98.80/13.33 (
% 98.80/13.33 (
% 98.80/13.33 image1E ) =>
% 98.80/13.33 (
% 98.80/13.33 (
% 98.80/13.33 image1I ) =>
% 98.80/13.33 (
% 98.80/13.33 (
% 98.80/13.33 injFuncInInjFuncSet ) =>
% 98.80/13.33 (
% 98.80/13.33 (
% 98.80/13.33 injFuncSetFuncIn ) =>
% 98.80/13.33 (
% 98.80/13.33 (
% 98.80/13.33 injFuncSetFuncInj ) =>
% 98.80/13.33 (
% 98.80/13.33 ![
% 98.80/13.33 A:$i,
% 98.80/13.33 B:$i,
% 98.80/13.33 Xf:$i]:
% 98.80/13.33 (
% 98.80/13.33 (
% 98.80/13.33 in @
% 98.80/13.33 Xf @
% 98.80/13.33 (
% 98.80/13.33 surjFuncSet
% 98.80/13.33 @
% 98.80/13.33 A @ B ) ) =>
% 98.80/13.33 (
% 98.80/13.33 in @
% 98.80/13.33 Xf @
% 98.80/13.33 (
% 98.80/13.33 funcSet @
% 98.80/13.33 A @ B ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )),
% 98.80/13.33 inference('cnf.neg', [status(esa)], [surjFuncSetFuncIn])).
% 98.80/13.33 thf(zip_derived_cl0, plain,
% 98.80/13.33 (~ (((setextAx) =>
% 98.80/13.33 (((emptysetAx) =>
% 98.80/13.33 (((setadjoinAx) =>
% 98.80/13.33 (((powersetAx) =>
% 98.80/13.33 (((setunionAx) =>
% 98.80/13.33 (((omega0Ax) =>
% 98.80/13.33 (((omegaSAx) =>
% 98.80/13.33 (((omegaIndAx) =>
% 98.80/13.33 (((replAx) =>
% 98.80/13.33 (((foundationAx) =>
% 98.80/13.33 (((wellorderingAx) =>
% 98.80/13.33 (((descrp) =>
% 98.80/13.33 (((dsetconstrI) =>
% 98.80/13.33 (((dsetconstrEL) =>
% 98.80/13.33 (((dsetconstrER) =>
% 98.80/13.33 (((exuE1) =>
% 98.80/13.33 (((prop2setE) =>
% 98.80/13.33 (((emptysetE) =>
% 98.80/13.33 (((emptysetimpfalse) =>
% 98.80/13.33 (((notinemptyset) =>
% 98.80/13.33 (((exuE3e) =>
% 98.80/13.33 (((setext) =>
% 98.80/13.33 (((emptyI) =>
% 98.80/13.33 (((noeltsimpempty) =>
% 98.80/13.33 (((setbeta) =>
% 98.80/13.33 (((nonemptyE1) =>
% 98.80/13.33 (((nonemptyI) =>
% 98.80/13.33 (((nonemptyI1) =>
% 98.80/13.33 (((setadjoinIL) =>
% 98.80/13.33 (((emptyinunitempty) =>
% 98.80/13.33 ((
% 98.80/13.33 (setadjoinIR) =>
% 98.80/13.33 ((
% 98.80/13.33 (setadjoinE) =>
% 98.80/13.33 ((
% 98.80/13.33 (setadjoinOr) =>
% 98.80/13.33 ((
% 98.80/13.33 (setoftrueEq) =>
% 98.80/13.33 ((
% 98.80/13.33 (powersetI) =>
% 98.80/13.33 ((
% 98.80/13.33 (emptyinPowerset) =>
% 98.80/13.33 ((
% 98.80/13.33 (emptyInPowerset) =>
% 98.80/13.33 ((
% 98.80/13.33 (powersetE) =>
% 98.80/13.33 ((
% 98.80/13.33 (setunionI) =>
% 98.80/13.33 ((
% 98.80/13.33 (setunionE) =>
% 98.80/13.33 ((
% 98.80/13.33 (subPowSU) =>
% 98.80/13.33 ((
% 98.80/13.33 (exuE2) =>
% 98.80/13.33 ((
% 98.80/13.33 (nonemptyImpWitness) =>
% 98.80/13.33 ((
% 98.80/13.33 (uniqinunit) =>
% 98.80/13.33 ((
% 98.80/13.33 (notinsingleton) =>
% 98.80/13.33 ((
% 98.80/13.33 (eqinunit) =>
% 98.80/13.33 ((
% 98.80/13.33 (singletonsswitch) =>
% 98.80/13.33 ((
% 98.80/13.33 (upairsetE) =>
% 98.80/13.33 ((
% 98.80/13.33 (upairsetIL) =>
% 98.80/13.33 ((
% 98.80/13.33 (upairsetIR) =>
% 98.80/13.33 ((
% 98.80/13.33 (emptyE1) =>
% 98.80/13.33 ((
% 98.80/13.33 (vacuousDall) =>
% 98.80/13.33 ((
% 98.80/13.33 (quantDeMorgan1) =>
% 98.80/13.33 ((
% 98.80/13.33 (quantDeMorgan2) =>
% 98.80/13.33 ((
% 98.80/13.33 (quantDeMorgan3) =>
% 98.80/13.33 ((
% 98.80/13.33 (quantDeMorgan4) =>
% 98.80/13.33 ((
% 98.80/13.33 (prop2setI) =>
% 98.80/13.33 ((
% 98.80/13.33 (prop2set2propI) =>
% 98.80/13.33 ((
% 98.80/13.33 (notdexE) =>
% 98.80/13.33 ((
% 98.80/13.33 (notdallE) =>
% 98.80/13.33 ((
% 98.80/13.33 (exuI1) =>
% 98.80/13.33 ((
% 98.80/13.33 (exuI3) =>
% 98.80/13.33 ((
% 98.80/13.33 (exuI2) =>
% 98.80/13.33 ((
% 98.80/13.33 (inCongP) =>
% 98.80/13.33 ((
% 98.80/13.33 (in__Cong) =>
% 98.80/13.33 ((
% 98.80/13.33 (exuE3u) =>
% 98.80/13.33 ((
% 98.80/13.33 (exu__Cong) =>
% 98.80/13.33 ((
% 98.80/13.33 (emptyset__Cong) =>
% 98.80/13.33 ((
% 98.80/13.33 (setadjoin__Cong) =>
% 98.80/13.33 ((
% 98.80/13.33 (powerset__Cong) =>
% 98.80/13.33 ((
% 98.80/13.33 (setunion__Cong) =>
% 98.80/13.33 ((
% 98.80/13.33 (omega__Cong) =>
% 98.80/13.33 ((
% 98.80/13.33 (exuEu) =>
% 98.80/13.33 ((
% 98.80/13.33 (descr__Cong) =>
% 98.80/13.33 ((
% 98.80/13.33 (dsetconstr__Cong) =>
% 98.80/13.33 ((
% 98.80/13.33 (subsetI1) =>
% 98.80/13.33 ((
% 98.80/13.33 (eqimpsubset2) =>
% 98.80/13.33 ((
% 98.80/13.33 (eqimpsubset1) =>
% 98.80/13.33 ((
% 98.80/13.33 (subsetI2) =>
% 98.80/13.33 ((
% 98.80/13.33 (emptysetsubset) =>
% 98.80/13.33 ((
% 98.80/13.33 (subsetE) =>
% 98.80/13.33 ((
% 98.80/13.33 (subsetE2) =>
% 98.80/13.33 ((
% 98.80/13.33 (notsubsetI) =>
% 98.80/13.33 ((
% 98.80/13.33 (notequalI1) =>
% 98.80/13.33 ((
% 98.80/13.33 (notequalI2) =>
% 98.80/13.33 ((
% 98.80/13.33 (subsetRefl) =>
% 98.80/13.33 ((
% 98.80/13.33 (subsetTrans) =>
% 98.80/13.33 ((
% 98.80/13.33 (setadjoinSub) =>
% 98.80/13.33 ((
% 98.80/13.33 (setadjoinSub2) =>
% 98.80/13.33 ((
% 98.80/13.33 (subset2powerset) =>
% 98.80/13.33 ((
% 98.80/13.33 (setextsub) =>
% 98.80/13.33 ((
% 98.80/13.33 (subsetemptysetimpeq) =>
% 98.80/13.33 ((
% 98.80/13.33 (powersetI1) =>
% 98.80/13.33 ((
% 98.80/13.33 (powersetE1) =>
% 98.80/13.33 ((
% 98.80/13.33 (inPowerset) =>
% 98.80/13.33 ((
% 98.80/13.33 (powersetsubset) =>
% 98.80/13.33 ((
% 98.80/13.33 (sepInPowerset) =>
% 98.80/13.33 ((
% 98.80/13.33 (sepSubset) =>
% 98.80/13.33 ((
% 98.80/13.33 (binunionIL) =>
% 98.80/13.33 ((
% 98.80/13.33 (upairset2IR) =>
% 98.80/13.33 ((
% 98.80/13.33 (binunionIR) =>
% 98.80/13.33 ((
% 98.80/13.33 (binunionEcases) =>
% 98.80/13.33 ((
% 98.80/13.33 (binunionE) =>
% 98.80/13.33 ((
% 98.80/13.33 (binunionLsub) =>
% 98.80/13.33 ((
% 98.80/13.33 (binunionRsub) =>
% 98.80/13.33 ((
% 98.80/13.33 (binintersectI) =>
% 98.80/13.33 ((
% 98.80/13.33 (binintersectSubset5) =>
% 98.80/13.33 ((
% 98.80/13.33 (binintersectEL) =>
% 98.80/13.33 ((
% 98.80/13.33 (binintersectLsub) =>
% 98.80/13.33 ((
% 98.80/13.33 (binintersectSubset2) =>
% 98.80/13.33 ((
% 98.80/13.33 (binintersectSubset3) =>
% 98.80/13.33 ((
% 98.80/13.33 (binintersectER) =>
% 98.80/13.33 ((
% 98.80/13.33 (disjointsetsI1) =>
% 98.80/13.33 ((
% 98.80/13.33 (binintersectRsub) =>
% 98.80/13.33 ((
% 98.80/13.33 (binintersectSubset4) =>
% 98.80/13.33 ((
% 98.80/13.33 (binintersectSubset1) =>
% 98.80/13.33 ((
% 98.80/13.33 (bs114d) =>
% 98.80/13.33 ((
% 98.80/13.33 (setminusI) =>
% 98.80/13.33 ((
% 98.80/13.33 (setminusEL) =>
% 98.80/13.33 ((
% 98.80/13.33 (setminusER) =>
% 98.80/13.33 ((
% 98.80/13.33 (setminusSubset2) =>
% 98.80/13.33 ((
% 98.80/13.33 (setminusERneg) =>
% 98.80/13.33 ((
% 98.80/13.33 (setminusELneg) =>
% 98.80/13.33 ((
% 98.80/13.33 (setminusILneg) =>
% 98.80/13.33 ((
% 98.80/13.33 (setminusIRneg) =>
% 98.80/13.33 ((
% 98.80/13.33 (setminusLsub) =>
% 98.80/13.33 ((
% 98.80/13.33 (setminusSubset1) =>
% 98.80/13.33 ((
% 98.80/13.33 (symdiffE) =>
% 98.80/13.33 ((
% 98.80/13.33 (symdiffI1) =>
% 98.80/13.33 ((
% 98.80/13.33 (symdiffI2) =>
% 98.80/13.33 ((
% 98.80/13.33 (symdiffIneg1) =>
% 98.80/13.33 ((
% 98.80/13.33 (symdiffIneg2) =>
% 98.80/13.33 ((
% 98.80/13.33 (secondinupair) =>
% 98.80/13.33 ((
% 98.80/13.33 (setukpairIL) =>
% 98.80/13.33 ((
% 98.80/13.33 (setukpairIR) =>
% 98.80/13.33 ((
% 98.80/13.33 (kpairiskpair) =>
% 98.80/13.33 ((
% 98.80/13.33 (kpairp) =>
% 98.80/13.33 ((
% 98.80/13.33 (singletonsubset) =>
% 98.80/13.33 ((
% 98.80/13.33 (singletoninpowerset) =>
% 98.80/13.33 ((
% 98.80/13.33 (singletoninpowunion) =>
% 98.80/13.33 ((
% 98.80/13.33 (upairset2E) =>
% 98.80/13.33 ((
% 98.80/13.33 (upairsubunion) =>
% 98.80/13.33 ((
% 98.80/13.33 (upairinpowunion) =>
% 98.80/13.33 ((
% 98.80/13.33 (ubforcartprodlem1) =>
% 98.80/13.33 ((
% 98.80/13.33 (ubforcartprodlem2) =>
% 98.80/13.33 ((
% 98.80/13.33 (ubforcartprodlem3) =>
% 98.80/13.33 ((
% 98.80/13.33 (cartprodpairin) =>
% 98.80/13.33 ((
% 98.80/13.33 (cartprodmempair1) =>
% 98.80/13.33 ((
% 98.80/13.33 (cartprodmempair) =>
% 98.80/13.33 ((
% 98.80/13.33 (setunionE2) =>
% 98.80/13.33 ((
% 98.80/13.33 (setunionsingleton1) =>
% 98.80/13.33 ((
% 98.80/13.33 (setunionsingleton2) =>
% 98.80/13.33 ((
% 98.80/13.33 (setunionsingleton) =>
% 98.80/13.33 ((
% 98.80/13.33 (singletonprop) =>
% 98.80/13.33 ((
% 98.80/13.33 (ex1E1) =>
% 98.80/13.33 ((
% 98.80/13.33 (ex1I) =>
% 98.80/13.33 ((
% 98.80/13.33 (ex1I2) =>
% 98.80/13.33 ((
% 98.80/13.33 (singletonsuniq) =>
% 98.80/13.33 ((
% 98.80/13.33 (setukpairinjL1) =>
% 98.80/13.33 ((
% 98.80/13.33 (kfstsingleton) =>
% 98.80/13.33 ((
% 98.80/13.33 (theprop) =>
% 98.80/13.33 ((
% 98.80/13.33 (kfstpairEq) =>
% 98.80/13.33 ((
% 98.80/13.33 (cartprodfstin) =>
% 98.80/13.33 ((
% 98.80/13.33 (setukpairinjL2) =>
% 98.80/13.33 ((
% 98.80/13.33 (setukpairinjL) =>
% 98.80/13.33 ((
% 98.80/13.33 (setukpairinjR11) =>
% 98.80/13.33 ((
% 98.80/13.33 (setukpairinjR12) =>
% 98.80/13.33 ((
% 98.80/13.33 (setukpairinjR1) =>
% 98.80/13.33 ((
% 98.80/13.33 (upairequniteq) =>
% 98.80/13.33 ((
% 98.80/13.33 (setukpairinjR2) =>
% 98.80/13.33 ((
% 98.80/13.33 (setukpairinjR) =>
% 98.80/13.33 ((
% 98.80/13.33 (ksndsingleton) =>
% 98.80/13.33 ((
% 98.80/13.33 (ksndpairEq) =>
% 98.80/13.33 ((
% 98.80/13.33 (kpairsurjEq) =>
% 98.80/13.33 ((
% 98.80/13.33 (cartprodsndin) =>
% 98.80/13.33 ((
% 98.80/13.33 (cartprodpairmemEL) =>
% 98.80/13.33 ((
% 98.80/13.33 (cartprodpairmemER) =>
% 98.80/13.33 ((
% 98.80/13.33 (cartprodmempaircEq) =>
% 98.80/13.33 ((
% 98.80/13.33 (cartprodfstpairEq) =>
% 98.80/13.33 ((
% 98.80/13.33 (cartprodsndpairEq) =>
% 98.80/13.33 ((
% 98.80/13.33 (cartprodpairsurjEq) =>
% 98.80/13.33 ((
% 98.80/13.33 (dpsetconstrI) =>
% 98.80/13.33 ((
% 98.80/13.33 (dpsetconstrSub) =>
% 98.80/13.33 ((
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% 98.80/13.33 ((
% 98.80/13.33 (setunionE2) =>
% 98.80/13.33 ((
% 98.80/13.33 (setunionsingleton1) =>
% 98.80/13.33 ((
% 98.80/13.33 (setunionsingleton2) =>
% 98.80/13.33 ((
% 98.80/13.33 (setunionsingleton) =>
% 98.80/13.33 ((
% 98.80/13.33 (singletonprop) =>
% 98.80/13.33 ((
% 98.80/13.33 (ex1E1) =>
% 98.80/13.33 ((
% 98.80/13.33 (ex1I) =>
% 98.80/13.33 ((
% 98.80/13.33 (ex1I2) =>
% 98.80/13.33 ((
% 98.80/13.33 (singletonsuniq) =>
% 98.80/13.33 ((
% 98.80/13.33 (setukpairinjL1) =>
% 98.80/13.33 ((
% 98.80/13.33 (kfstsingleton) =>
% 98.80/13.33 ((
% 98.80/13.33 (theprop) =>
% 98.80/13.33 ((
% 98.80/13.33 (kfstpairEq) =>
% 98.80/13.33 ((
% 98.80/13.33 (cartprodfstin) =>
% 98.80/13.33 ((
% 98.80/13.33 (setukpairinjL2) =>
% 98.80/13.33 ((
% 98.80/13.33 (setukpairinjL) =>
% 98.80/13.33 ((
% 98.80/13.33 (setukpairinjR11) =>
% 98.80/13.33 ((
% 98.80/13.33 (setukpairinjR12) =>
% 98.80/13.33 ((
% 98.80/13.33 (setukpairinjR1) =>
% 98.80/13.33 ((
% 98.80/13.33 (upairequniteq) =>
% 98.80/13.33 ((
% 98.80/13.33 (setukpairinjR2) =>
% 98.80/13.33 ((
% 98.80/13.33 (setukpairinjR) =>
% 98.80/13.33 ((
% 98.80/13.33 (ksndsingleton) =>
% 98.80/13.33 ((
% 98.80/13.33 (ksndpairEq) =>
% 98.80/13.33 ((
% 98.80/13.33 (kpairsurjEq) =>
% 98.80/13.33 ((
% 98.80/13.33 (cartprodsndin) =>
% 98.80/13.33 ((
% 98.80/13.33 (cartprodpairmemEL) =>
% 98.80/13.33 ((
% 98.80/13.33 (cartprodpairmemER) =>
% 98.80/13.33 ((
% 98.80/13.33 (cartprodmempaircEq) =>
% 98.80/13.33 ((
% 98.80/13.33 (cartprodfstpairEq) =>
% 98.80/13.33 ((
% 98.80/13.33 (cartprodsndpairEq) =>
% 98.80/13.33 ((
% 98.80/13.33 (cartprodpairsurjEq) =>
% 98.80/13.33 ((
% 98.80/13.33 (dpsetconstrI) =>
% 98.80/13.33 ((
% 98.80/13.33 (dpsetconstrSub) =>
% 98.80/13.33 ((
% 98.80/13.33 (setOfPairsIsBReln) =>
% 98.80/13.33 ((
% 98.80/13.33 (dpsetconstrERa) =>
% 98.80/13.33 ((
% 98.80/13.33 (dpsetconstrEL1) =>
% 98.80/13.33 ((
% 98.80/13.33 (dpsetconstrEL2) =>
% 98.80/13.33 ((
% 98.80/13.33 (dpsetconstrER) =>
% 98.80/13.33 ((
% 98.80/13.33 (funcImageSingleton) =>
% 98.80/13.33 ((
% 98.80/13.33 (apProp) =>
% 98.80/13.33 ((
% 98.80/13.33 (app) =>
% 98.80/13.33 ((
% 98.80/13.33 (infuncsetfunc) =>
% 98.80/13.33 ((
% 98.80/13.33 (ap2p) =>
% 98.80/13.33 ((
% 98.80/13.33 (funcinfuncset) =>
% 98.80/13.33 ((
% 98.80/13.33 (lamProp) =>
% 98.80/13.33 ((
% 98.80/13.33 (lamp) =>
% 98.80/13.33 ((
% 98.80/13.33 (lam2p) =>
% 98.80/13.33 ((
% 98.80/13.33 (brelnall1) =>
% 98.80/13.33 ((
% 98.80/13.33 (brelnall2) =>
% 98.80/13.33 ((
% 98.80/13.33 (ex1E2) =>
% 98.80/13.33 ((
% 98.80/13.33 (funcGraphProp1) =>
% 98.80/13.33 ((
% 98.80/13.33 (funcGraphProp3) =>
% 98.80/13.33 ((
% 98.80/13.33 (funcGraphProp2) =>
% 98.80/13.33 ((
% 98.80/13.33 (funcextLem) =>
% 98.80/13.33 ((
% 98.80/13.33 (funcGraphProp4) =>
% 98.80/13.33 ((
% 98.80/13.33 (subbreln) =>
% 98.80/13.33 ((
% 98.80/13.33 (eqbreln) =>
% 98.80/13.33 ((
% 98.80/13.33 (funcext) =>
% 98.80/13.33 ((
% 98.80/13.33 (funcext2) =>
% 98.80/13.33 ((
% 98.80/13.33 (ap2apEq1) =>
% 98.80/13.33 ((
% 98.80/13.33 (ap2apEq2) =>
% 98.80/13.33 ((
% 98.80/13.33 (beta1) =>
% 98.80/13.33 ((
% 98.80/13.33 (eta1) =>
% 98.80/13.33 ((
% 98.80/13.33 (lam2lamEq) =>
% 98.80/13.33 ((
% 98.80/13.33 (beta2) =>
% 98.80/13.33 ((
% 98.80/13.33 (eta2) =>
% 98.80/13.33 ((
% 98.80/13.33 (iffalseProp1) =>
% 98.80/13.33 ((
% 98.80/13.33 (iffalseProp2) =>
% 98.80/13.33 ((
% 98.80/13.33 (iftrueProp1) =>
% 98.80/13.33 ((
% 98.80/13.33 (iftrueProp2) =>
% 98.80/13.33 ((
% 98.80/13.33 (ifSingleton) =>
% 98.80/13.33 ((
% 98.80/13.33 (ifp) =>
% 98.80/13.33 ((
% 98.80/13.33 (theeq) =>
% 98.80/13.33 ((
% 98.80/13.33 (iftrue) =>
% 98.80/13.33 ((
% 98.80/13.33 (iffalse) =>
% 98.80/13.33 ((
% 98.80/13.33 (iftrueorfalse) =>
% 98.80/13.33 ((
% 98.80/13.33 (binintersectT_lem) =>
% 98.80/13.33 ((
% 98.80/13.33 (binunionT_lem) =>
% 98.80/13.33 ((
% 98.80/13.33 (powersetT_lem) =>
% 98.80/13.33 ((
% 98.80/13.33 (setminusT_lem) =>
% 98.80/13.33 ((
% 98.80/13.33 (complementT_lem) =>
% 98.80/13.33 ((
% 98.80/13.33 (setextT) =>
% 98.80/13.33 ((
% 98.80/13.33 (subsetTI) =>
% 98.80/13.33 ((
% 98.80/13.33 (powersetTI1) =>
% 98.80/13.33 ((
% 98.80/13.33 (powersetTE1) =>
% 98.80/13.33 ((
% 98.80/13.33 (complementTI1) =>
% 98.80/13.33 ((
% 98.80/13.33 (complementTE1) =>
% 98.80/13.33 ((
% 98.80/13.33 (binintersectTELcontra) =>
% 98.80/13.33 ((
% 98.80/13.33 (binintersectTERcontra) =>
% 98.80/13.33 ((
% 98.80/13.33 (contrasubsetT) =>
% 98.80/13.33 ((
% 98.80/13.33 (contrasubsetT1) =>
% 98.80/13.33 ((
% 98.80/13.33 (contrasubsetT2) =>
% 98.80/13.33 ((
% 98.80/13.33 (contrasubsetT3) =>
% 98.80/13.33 ((
% 98.80/13.33 (doubleComplementI1) =>
% 98.80/13.33 ((
% 98.80/13.33 (doubleComplementE1) =>
% 98.80/13.33 ((
% 98.80/13.33 (doubleComplementSub1) =>
% 98.80/13.33 ((
% 98.80/13.33 (doubleComplementSub2) =>
% 98.80/13.33 ((
% 98.80/13.33 (doubleComplementEq) =>
% 98.80/13.33 ((
% 98.80/13.33 (complementTnotintersectT) =>
% 98.80/13.33 ((
% 98.80/13.33 (complementImpComplementIntersect) =>
% 98.80/13.33 ((
% 98.80/13.33 (complementSubsetComplementIntersect) =>
% 98.80/13.33 ((
% 98.80/13.33 (complementInPowersetComplementIntersect) =>
% 98.80/13.33 ((
% 98.80/13.33 (contraSubsetComplement) =>
% 98.80/13.33 ((
% 98.80/13.33 (complementTcontraSubset) =>
% 98.80/13.33 ((
% 98.80/13.33 (binunionTILcontra) =>
% 98.80/13.33 ((
% 98.80/13.33 (binunionTIRcontra) =>
% 98.80/13.33 ((
% 98.80/13.33 (inIntersectImpInUnion) =>
% 98.80/13.33 ((
% 98.80/13.33 (inIntersectImpInUnion2) =>
% 98.80/13.33 ((
% 98.80/13.33 (inIntersectImpInIntersectUnions) =>
% 98.80/13.33 ((
% 98.80/13.33 (intersectInPowersetIntersectUnions) =>
% 98.80/13.33 ((
% 98.80/13.33 (inComplementUnionImpNotIn1) =>
% 98.80/13.33 ((
% 98.80/13.33 (inComplementUnionImpInComplement1) =>
% 98.80/13.33 ((
% 98.80/13.33 (binunionTE) =>
% 98.80/13.33 ((
% 98.80/13.33 (binunionTEcontra) =>
% 98.80/13.33 ((
% 98.80/13.33 (demorgan2a1) =>
% 98.80/13.33 ((
% 98.80/13.33 (complementUnionInPowersetComplement) =>
% 98.80/13.33 ((
% 98.80/13.33 (demorgan2a2) =>
% 98.80/13.33 ((
% 98.80/13.33 (demorgan1a) =>
% 98.80/13.33 ((
% 98.80/13.33 (demorgan1b) =>
% 98.80/13.33 ((
% 98.80/13.33 (demorgan1) =>
% 98.80/13.33 ((
% 98.80/13.33 (demorgan2a) =>
% 98.80/13.33 ((
% 98.80/13.33 (demorgan2b2) =>
% 98.80/13.33 ((
% 98.80/13.33 (demorgan2b) =>
% 98.80/13.33 ((
% 98.80/13.33 (demorgan2) =>
% 98.80/13.33 ((
% 98.80/13.33 (woz13rule0) =>
% 98.80/13.33 ((
% 98.80/13.33 (woz13rule1) =>
% 98.80/13.33 ((
% 98.80/13.33 (woz13rule2) =>
% 98.80/13.33 ((
% 98.80/13.33 (woz13rule3) =>
% 98.80/13.33 ((
% 98.80/13.33 (woz13rule4) =>
% 98.80/13.33 ((
% 98.80/13.33 (woz1_1) =>
% 98.80/13.33 ((
% 98.80/13.33 (woz1_2) =>
% 98.80/13.33 ((
% 98.80/13.33 (woz1_3) =>
% 98.80/13.33 ((
% 98.80/13.33 (woz1_4) =>
% 98.80/13.33 ((
% 98.80/13.33 (woz1_5) =>
% 98.80/13.33 ((
% 98.80/13.33 (breln1all2) =>
% 98.80/13.33 ((
% 98.80/13.33 (breln1SetBreln1) =>
% 98.80/13.33 ((
% 98.80/13.33 (choice2fnsingleton) =>
% 98.80/13.33 ((
% 98.80/13.33 (setOfPairsIsBReln1) =>
% 98.80/13.33 ((
% 98.80/13.33 (breln1all1) =>
% 98.80/13.33 ((
% 98.80/13.33 (subbreln1) =>
% 98.80/13.33 ((
% 98.80/13.33 (eqbreln1) =>
% 98.80/13.33 ((
% 98.80/13.33 (breln1invprop) =>
% 98.80/13.33 ((
% 98.80/13.33 (breln1invI) =>
% 98.80/13.33 ((
% 98.80/13.33 (breln1invE) =>
% 98.80/13.33 ((
% 98.80/13.33 (breln1compprop) =>
% 98.80/13.33 ((
% 98.80/13.33 (breln1compI) =>
% 98.80/13.33 ((
% 98.80/13.33 (breln1compE) =>
% 98.80/13.33 ((
% 98.80/13.33 (breln1compEex) =>
% 98.80/13.33 ((
% 98.80/13.33 (breln1unionprop) =>
% 98.80/13.33 ((
% 98.80/13.33 (breln1unionIL) =>
% 98.80/13.33 ((
% 98.80/13.33 (breln1unionIR) =>
% 98.80/13.33 ((
% 98.80/13.33 (breln1unionI) =>
% 98.80/13.33 ((
% 98.80/13.33 (breln1unionE) =>
% 98.80/13.33 ((
% 98.80/13.33 (breln1unionEcases) =>
% 98.80/13.33 ((
% 98.80/13.33 (breln1unionCommutes) =>
% 98.80/13.33 ((
% 98.80/13.33 (woz2Ex) =>
% 98.80/13.33 ((
% 98.80/13.33 (woz2W) =>
% 98.80/13.33 ((
% 98.80/13.33 (woz2A) =>
% 98.80/13.33 ((
% 98.80/13.33 (woz2B) =>
% 98.80/13.33 ((
% 98.80/13.33 (image1Ex) =>
% 98.80/13.33 ((
% 98.80/13.33 (image1Ex1) =>
% 98.80/13.33 ((
% 98.80/13.33 (image1Equiv) =>
% 98.80/13.33 ((
% 98.80/13.33 (image1E) =>
% 98.80/13.33 ((
% 98.80/13.33 (image1I) =>
% 98.80/13.33 ((
% 98.80/13.33 (injFuncInInjFuncSet) =>
% 98.80/13.33 ((
% 98.80/13.33 (injFuncSetFuncIn) =>
% 98.80/13.33 ((
% 98.80/13.33 (injFuncSetFuncInj) =>
% 98.80/13.33 ((
% 98.80/13.33 (!!) @ (
% 98.80/13.33 (('#B') @ (
% 98.80/13.33 !!) @
% 98.80/13.33 (
% 98.80/13.33 (
% 98.80/13.33 ('#B') @ (
% 98.80/13.33 (
% 98.80/13.33 ('#B') @ (
% 98.80/13.33 !!))) @
% 98.80/13.33 (
% 98.80/13.33 (
% 98.80/13.33 ('#S') @ (
% 98.80/13.33 (
% 98.80/13.33 ('#B') @ (
% 98.80/13.33 '#S') @
% 98.80/13.33 (
% 98.80/13.33 (
% 98.80/13.33 ('#B') @ (
% 98.80/13.33 (
% 98.80/13.33 ('#B') @ (
% 98.80/13.33 '#S'))) @
% 98.80/13.33 (
% 98.80/13.33 (
% 98.80/13.33 ('#B') @ (
% 98.80/13.33 (
% 98.80/13.33 ('#B') @ (
% 98.80/13.33 (
% 98.80/13.33 ('#B') @ (
% 98.80/13.33 =>))))) @
% 98.80/13.33 (
% 98.80/13.33 (
% 98.80/13.33 ('#B') @ (
% 98.80/13.33 (
% 98.80/13.33 ('#B') @ (
% 98.80/13.33 (
% 98.80/13.33 ('#C') @ in)))) @
% 98.80/13.33 surjFuncSet)))))))) @
% 98.80/13.33 (
% 98.80/13.33 (
% 98.80/13.33 ('#B') @ (
% 98.80/13.33 (
% 98.80/13.33 ('#B') @ (
% 98.80/13.33 (
% 98.80/13.33 ('#C') @ in)))) @
% 98.80/13.33 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.80/13.33 inference('lams2combs', [status(thm)], [zip_derived_cl0])).
% 98.80/13.33 thf(omega0Ax, axiom,(( omega0Ax ) = ((in @ emptyset @ omega)))).
% 98.80/13.33 thf('0', plain, (( omega0Ax ) = ( in @ emptyset @ omega )),
% 98.80/13.33 define([status(thm)])).
% 98.80/13.33 thf(emptyinunitempty, axiom,(( emptyinunitempty ) =
% 98.80/13.33 ((in @ emptyset @ (setadjoin @ emptyset @ emptyset))))).
% 98.80/13.33 thf('1', plain,
% 98.80/13.33 (( emptyinunitempty ) =
% 98.80/13.33 ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )),
% 98.80/13.33 define([status(thm)])).
% 98.80/13.33 thf(emptyset__Cong, axiom,(( emptyset__Cong ) =
% 98.80/13.33 ((((emptyset) = (emptyset)))))).
% 98.80/13.33 thf('2', plain, (( emptyset__Cong ) = ( ( emptyset ) = ( emptyset ) )),
% 98.80/13.33 define([status(thm)])).
% 98.80/13.33 thf(omega__Cong, axiom,(( omega__Cong ) = ((((omega) = (omega)))))).
% 98.80/13.33 thf('3', plain, (( omega__Cong ) = ( ( omega ) = ( omega ) )),
% 98.80/13.33 define([status(thm)])).
% 98.80/13.33 thf(zip_derived_cl2, plain,
% 98.80/13.33 (~ (((setextAx) =>
% 98.80/13.33 (((emptysetAx) =>
% 98.80/13.33 (((setadjoinAx) =>
% 98.80/13.33 (((powersetAx) =>
% 98.80/13.33 (((setunionAx) =>
% 98.80/13.33 (((in @ emptyset @ omega) =>
% 98.80/13.33 (((omegaSAx) =>
% 98.80/13.33 (((omegaIndAx) =>
% 98.80/13.33 (((replAx) =>
% 98.80/13.33 (((foundationAx) =>
% 98.80/13.33 (((wellorderingAx) =>
% 98.80/13.33 (((descrp) =>
% 98.80/13.33 (((dsetconstrI) =>
% 98.80/13.33 (((dsetconstrEL) =>
% 98.80/13.33 (((dsetconstrER) =>
% 98.80/13.33 (((exuE1) =>
% 98.80/13.33 (((prop2setE) =>
% 98.80/13.33 (((emptysetE) =>
% 98.80/13.33 (((emptysetimpfalse) =>
% 98.80/13.33 (((notinemptyset) =>
% 98.80/13.33 (((exuE3e) =>
% 98.80/13.33 (((setext) =>
% 98.80/13.33 (((emptyI) =>
% 98.80/13.33 (((noeltsimpempty) =>
% 98.80/13.33 (((setbeta) =>
% 98.80/13.33 (((nonemptyE1) =>
% 98.80/13.33 (((nonemptyI) =>
% 98.80/13.33 (((nonemptyI1) =>
% 98.80/13.33 (((setadjoinIL) =>
% 98.80/13.33 (((in @
% 98.80/13.33 emptyset @
% 98.80/13.33 (setadjoin @
% 98.80/13.33 emptyset @
% 98.80/13.33 emptyset)) =>
% 98.80/13.33 ((
% 98.80/13.33 (setadjoinIR) =>
% 98.80/13.33 ((
% 98.80/13.33 (setadjoinE) =>
% 98.80/13.33 ((
% 98.80/13.33 (setadjoinOr) =>
% 98.80/13.33 ((
% 98.80/13.33 (setoftrueEq) =>
% 98.80/13.33 ((
% 98.80/13.33 (powersetI) =>
% 98.80/13.33 ((
% 98.80/13.33 (emptyinPowerset) =>
% 98.80/13.33 ((
% 98.80/13.33 (emptyInPowerset) =>
% 98.80/13.33 ((
% 98.80/13.33 (powersetE) =>
% 98.80/13.33 ((
% 98.80/13.33 (setunionI) =>
% 98.80/13.33 ((
% 98.80/13.33 (setunionE) =>
% 98.80/13.33 ((
% 98.80/13.33 (subPowSU) =>
% 98.80/13.33 ((
% 98.80/13.33 (exuE2) =>
% 98.80/13.33 ((
% 98.80/13.33 (nonemptyImpWitness) =>
% 98.80/13.33 ((
% 98.80/13.33 (uniqinunit) =>
% 98.80/13.33 ((
% 98.80/13.33 (notinsingleton) =>
% 98.80/13.33 ((
% 98.80/13.33 (eqinunit) =>
% 98.80/13.33 ((
% 98.80/13.33 (singletonsswitch) =>
% 98.80/13.33 ((
% 98.80/13.33 (upairsetE) =>
% 98.80/13.33 ((
% 98.80/13.33 (upairsetIL) =>
% 98.80/13.33 ((
% 98.80/13.33 (upairsetIR) =>
% 98.80/13.33 ((
% 98.80/13.33 (emptyE1) =>
% 98.80/13.33 ((
% 98.80/13.33 (vacuousDall) =>
% 98.80/13.33 ((
% 98.80/13.33 (quantDeMorgan1) =>
% 98.80/13.33 ((
% 98.80/13.33 (quantDeMorgan2) =>
% 98.80/13.33 ((
% 98.80/13.33 (quantDeMorgan3) =>
% 98.80/13.33 ((
% 98.80/13.33 (quantDeMorgan4) =>
% 98.80/13.33 ((
% 98.80/13.33 (prop2setI) =>
% 98.80/13.33 ((
% 98.80/13.33 (prop2set2propI) =>
% 98.80/13.33 ((
% 98.80/13.33 (notdexE) =>
% 98.80/13.33 ((
% 98.80/13.33 (notdallE) =>
% 98.80/13.33 ((
% 98.80/13.33 (exuI1) =>
% 98.80/13.33 ((
% 98.80/13.33 (exuI3) =>
% 98.80/13.33 ((
% 98.80/13.33 (exuI2) =>
% 98.80/13.33 ((
% 98.80/13.33 (inCongP) =>
% 98.80/13.33 ((
% 98.80/13.33 (in__Cong) =>
% 98.80/13.33 ((
% 98.80/13.33 (exuE3u) =>
% 98.80/13.33 ((
% 98.80/13.33 (exu__Cong) =>
% 98.80/13.33 ((
% 98.80/13.33 ((
% 98.80/13.33 (emptyset) =
% 98.80/13.33 (emptyset))) =>
% 98.80/13.33 ((
% 98.80/13.33 (setadjoin__Cong) =>
% 98.80/13.33 ((
% 98.80/13.33 (powerset__Cong) =>
% 98.80/13.33 ((
% 98.80/13.33 (setunion__Cong) =>
% 98.80/13.33 ((
% 98.80/13.33 ((
% 98.80/13.33 (omega) =
% 98.80/13.33 (omega))) =>
% 98.80/13.33 ((
% 98.80/13.33 (exuEu) =>
% 98.80/13.33 ((
% 98.80/13.33 (descr__Cong) =>
% 98.80/13.33 ((
% 98.80/13.33 (dsetconstr__Cong) =>
% 98.80/13.33 ((
% 98.80/13.33 (subsetI1) =>
% 98.80/13.33 ((
% 98.80/13.33 (eqimpsubset2) =>
% 98.80/13.33 ((
% 98.80/13.33 (eqimpsubset1) =>
% 98.80/13.33 ((
% 98.80/13.33 (subsetI2) =>
% 98.80/13.33 ((
% 98.80/13.33 (emptysetsubset) =>
% 98.80/13.33 ((
% 98.80/13.33 (subsetE) =>
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% 98.80/13.34 ('#B') @ (
% 98.80/13.34 (
% 98.80/13.34 ('#C') @ in)))) @
% 98.80/13.34 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.80/13.34 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl25])).
% 98.80/13.34 thf(zip_derived_cl40, plain,
% 98.80/13.34 (~ (((omegaIndAx) =>
% 98.80/13.34 (((replAx) =>
% 98.80/13.34 (((foundationAx) =>
% 98.80/13.34 (((wellorderingAx) =>
% 98.80/13.34 (((descrp) =>
% 98.80/13.34 (((dsetconstrI) =>
% 98.80/13.34 (((dsetconstrEL) =>
% 98.80/13.34 (((dsetconstrER) =>
% 98.80/13.34 (((exuE1) =>
% 98.80/13.34 (((prop2setE) =>
% 98.80/13.34 (((emptysetE) =>
% 98.80/13.34 (((emptysetimpfalse) =>
% 98.80/13.34 (((notinemptyset) =>
% 98.80/13.34 (((exuE3e) =>
% 98.80/13.34 (((setext) =>
% 98.80/13.34 (((emptyI) =>
% 98.80/13.34 (((noeltsimpempty) =>
% 98.80/13.34 (((setbeta) =>
% 98.80/13.34 (((nonemptyE1) =>
% 98.80/13.34 (((nonemptyI) =>
% 98.80/13.34 (((nonemptyI1) =>
% 98.80/13.34 (((setadjoinIL) =>
% 98.80/13.34 (((in @ emptyset @
% 98.80/13.34 (setadjoin @ emptyset @
% 98.80/13.34 emptyset)) =>
% 98.80/13.34 (((setadjoinIR) =>
% 98.80/13.34 (((setadjoinE) =>
% 98.80/13.34 (((setadjoinOr) =>
% 98.80/13.34 (((setoftrueEq) =>
% 98.80/13.34 (((powersetI) =>
% 98.80/13.34 (((emptyinPowerset) =>
% 98.80/13.34 (((emptyInPowerset) =>
% 98.80/13.34 ((
% 98.80/13.34 (powersetE) =>
% 98.80/13.34 ((
% 98.80/13.34 (setunionI) =>
% 98.80/13.34 ((
% 98.80/13.34 (setunionE) =>
% 98.80/13.34 ((
% 98.80/13.34 (subPowSU) =>
% 98.80/13.34 ((
% 98.80/13.34 (exuE2) =>
% 98.80/13.34 ((
% 98.80/13.34 (nonemptyImpWitness) =>
% 98.80/13.34 ((
% 98.80/13.34 (uniqinunit) =>
% 98.80/13.34 ((
% 98.80/13.34 (notinsingleton) =>
% 98.80/13.34 ((
% 98.80/13.34 (eqinunit) =>
% 98.80/13.34 ((
% 98.80/13.34 (singletonsswitch) =>
% 98.80/13.34 ((
% 98.80/13.34 (upairsetE) =>
% 98.80/13.34 ((
% 98.80/13.34 (upairsetIL) =>
% 98.80/13.34 ((
% 98.80/13.34 (upairsetIR) =>
% 98.80/13.34 ((
% 98.80/13.34 (emptyE1) =>
% 98.80/13.34 ((
% 98.80/13.34 (vacuousDall) =>
% 98.80/13.34 ((
% 98.80/13.34 (quantDeMorgan1) =>
% 98.80/13.34 ((
% 98.80/13.34 (quantDeMorgan2) =>
% 98.80/13.34 ((
% 98.80/13.34 (quantDeMorgan3) =>
% 98.80/13.34 ((
% 98.80/13.34 (quantDeMorgan4) =>
% 98.80/13.34 ((
% 98.80/13.34 (prop2setI) =>
% 98.80/13.34 ((
% 98.80/13.34 (prop2set2propI) =>
% 98.80/13.34 ((
% 98.80/13.34 (notdexE) =>
% 98.80/13.34 ((
% 98.80/13.34 (notdallE) =>
% 98.80/13.34 ((
% 98.80/13.34 (exuI1) =>
% 98.80/13.34 ((
% 98.80/13.34 (exuI3) =>
% 98.80/13.34 ((
% 98.80/13.34 (exuI2) =>
% 98.80/13.34 ((
% 98.80/13.34 (inCongP) =>
% 98.80/13.34 ((
% 98.80/13.34 (in__Cong) =>
% 98.80/13.34 ((
% 98.80/13.34 (exuE3u) =>
% 98.80/13.34 ((
% 98.80/13.34 (exu__Cong) =>
% 98.80/13.34 ((
% 98.80/13.34 (setadjoin__Cong) =>
% 98.80/13.34 ((
% 98.80/13.34 (powerset__Cong) =>
% 98.80/13.34 ((
% 98.80/13.34 (setunion__Cong) =>
% 98.80/13.34 ((
% 98.80/13.34 (exuEu) =>
% 98.80/13.34 ((
% 98.80/13.34 (descr__Cong) =>
% 98.80/13.34 ((
% 98.80/13.34 (dsetconstr__Cong) =>
% 98.80/13.34 ((
% 98.80/13.34 (subsetI1) =>
% 98.80/13.34 ((
% 98.80/13.34 (eqimpsubset2) =>
% 98.80/13.34 ((
% 98.80/13.34 (eqimpsubset1) =>
% 98.80/13.34 ((
% 98.80/13.34 (subsetI2) =>
% 98.80/13.34 ((
% 98.80/13.34 (emptysetsubset) =>
% 98.80/13.34 ((
% 98.80/13.34 (subsetE) =>
% 98.80/13.34 ((
% 98.80/13.34 (subsetE2) =>
% 98.80/13.34 ((
% 98.80/13.34 (notsubsetI) =>
% 98.80/13.34 ((
% 98.80/13.34 (notequalI1) =>
% 98.80/13.34 ((
% 98.80/13.34 (notequalI2) =>
% 98.80/13.34 ((
% 98.80/13.34 (subsetRefl) =>
% 98.80/13.34 ((
% 98.80/13.34 (subsetTrans) =>
% 98.80/13.34 ((
% 98.80/13.34 (setadjoinSub) =>
% 98.80/13.34 ((
% 98.80/13.34 (setadjoinSub2) =>
% 98.80/13.34 ((
% 98.80/13.34 (subset2powerset) =>
% 98.80/13.34 ((
% 98.80/13.34 (setextsub) =>
% 98.80/13.34 ((
% 98.80/13.34 (subsetemptysetimpeq) =>
% 98.80/13.34 ((
% 98.80/13.34 (powersetI1) =>
% 98.80/13.34 ((
% 98.80/13.34 (powersetE1) =>
% 98.80/13.34 ((
% 98.80/13.34 (inPowerset) =>
% 98.80/13.34 ((
% 98.80/13.34 (powersetsubset) =>
% 98.80/13.34 ((
% 98.80/13.34 (sepInPowerset) =>
% 98.80/13.34 ((
% 98.80/13.34 (sepSubset) =>
% 98.80/13.34 ((
% 98.80/13.34 (binunionIL) =>
% 98.80/13.34 ((
% 98.80/13.34 (upairset2IR) =>
% 98.80/13.34 ((
% 98.80/13.34 (binunionIR) =>
% 98.80/13.34 ((
% 98.80/13.34 (binunionEcases) =>
% 98.80/13.34 ((
% 98.80/13.34 (binunionE) =>
% 98.80/13.34 ((
% 98.80/13.34 (binunionLsub) =>
% 98.80/13.34 ((
% 98.80/13.34 (binunionRsub) =>
% 98.80/13.34 ((
% 98.80/13.34 (binintersectI) =>
% 98.80/13.34 ((
% 98.80/13.34 (binintersectSubset5) =>
% 98.80/13.34 ((
% 98.80/13.34 (binintersectEL) =>
% 98.80/13.34 ((
% 98.80/13.34 (binintersectLsub) =>
% 98.80/13.34 ((
% 98.80/13.34 (binintersectSubset2) =>
% 98.80/13.34 ((
% 98.80/13.34 (binintersectSubset3) =>
% 98.80/13.34 ((
% 98.80/13.34 (binintersectER) =>
% 98.80/13.34 ((
% 98.80/13.34 (disjointsetsI1) =>
% 98.80/13.34 ((
% 98.80/13.34 (binintersectRsub) =>
% 98.80/13.34 ((
% 98.80/13.34 (binintersectSubset4) =>
% 98.80/13.34 ((
% 98.80/13.34 (binintersectSubset1) =>
% 98.80/13.34 ((
% 98.80/13.34 (bs114d) =>
% 98.80/13.34 ((
% 98.80/13.34 (setminusI) =>
% 98.80/13.34 ((
% 98.80/13.34 (setminusEL) =>
% 98.80/13.34 ((
% 98.80/13.34 (setminusER) =>
% 98.80/13.34 ((
% 98.80/13.34 (setminusSubset2) =>
% 98.80/13.34 ((
% 98.80/13.34 (setminusERneg) =>
% 98.80/13.34 ((
% 98.80/13.34 (setminusELneg) =>
% 98.80/13.34 ((
% 98.80/13.34 (setminusILneg) =>
% 98.80/13.34 ((
% 98.80/13.34 (setminusIRneg) =>
% 98.80/13.34 ((
% 98.80/13.34 (setminusLsub) =>
% 98.80/13.34 ((
% 98.80/13.34 (setminusSubset1) =>
% 98.80/13.34 ((
% 98.80/13.34 (symdiffE) =>
% 98.80/13.34 ((
% 98.80/13.34 (symdiffI1) =>
% 98.80/13.34 ((
% 98.80/13.34 (symdiffI2) =>
% 98.80/13.34 ((
% 98.80/13.34 (symdiffIneg1) =>
% 98.80/13.34 ((
% 98.80/13.34 (symdiffIneg2) =>
% 98.80/13.34 ((
% 98.80/13.34 (secondinupair) =>
% 98.80/13.34 ((
% 98.80/13.34 (setukpairIL) =>
% 98.80/13.34 ((
% 98.80/13.34 (setukpairIR) =>
% 98.80/13.34 ((
% 98.80/13.34 (kpairiskpair) =>
% 98.80/13.34 ((
% 98.80/13.34 (kpairp) =>
% 98.80/13.34 ((
% 98.80/13.34 (singletonsubset) =>
% 98.80/13.34 ((
% 98.80/13.34 (singletoninpowerset) =>
% 98.80/13.34 ((
% 98.80/13.34 (singletoninpowunion) =>
% 98.80/13.34 ((
% 98.80/13.34 (upairset2E) =>
% 98.80/13.34 ((
% 98.80/13.34 (upairsubunion) =>
% 98.80/13.34 ((
% 98.80/13.34 (upairinpowunion) =>
% 98.80/13.34 ((
% 98.80/13.34 (ubforcartprodlem1) =>
% 98.80/13.34 ((
% 98.80/13.34 (ubforcartprodlem2) =>
% 98.80/13.34 ((
% 98.80/13.34 (ubforcartprodlem3) =>
% 98.80/13.34 ((
% 98.80/13.34 (cartprodpairin) =>
% 98.80/13.34 ((
% 98.80/13.34 (cartprodmempair1) =>
% 98.80/13.34 ((
% 98.80/13.34 (cartprodmempair) =>
% 98.80/13.34 ((
% 98.80/13.34 (setunionE2) =>
% 98.80/13.34 ((
% 98.80/13.34 (setunionsingleton1) =>
% 98.80/13.34 ((
% 98.80/13.34 (setunionsingleton2) =>
% 98.80/13.34 ((
% 98.80/13.34 (setunionsingleton) =>
% 98.80/13.34 ((
% 98.80/13.34 (singletonprop) =>
% 98.80/13.34 ((
% 98.80/13.34 (ex1E1) =>
% 98.80/13.34 ((
% 98.80/13.34 (ex1I) =>
% 98.80/13.34 ((
% 98.80/13.34 (ex1I2) =>
% 98.80/13.34 ((
% 98.80/13.34 (singletonsuniq) =>
% 98.80/13.34 ((
% 98.80/13.34 (setukpairinjL1) =>
% 98.80/13.34 ((
% 98.80/13.34 (kfstsingleton) =>
% 98.80/13.34 ((
% 98.80/13.34 (theprop) =>
% 98.80/13.34 ((
% 98.80/13.34 (kfstpairEq) =>
% 98.80/13.34 ((
% 98.80/13.34 (cartprodfstin) =>
% 98.80/13.34 ((
% 98.80/13.34 (setukpairinjL2) =>
% 98.80/13.34 ((
% 98.80/13.34 (setukpairinjL) =>
% 98.80/13.34 ((
% 98.80/13.34 (setukpairinjR11) =>
% 98.80/13.34 ((
% 98.80/13.34 (setukpairinjR12) =>
% 98.80/13.34 ((
% 98.80/13.34 (setukpairinjR1) =>
% 98.80/13.34 ((
% 98.80/13.34 (upairequniteq) =>
% 98.80/13.34 ((
% 98.80/13.34 (setukpairinjR2) =>
% 98.80/13.34 ((
% 98.80/13.34 (setukpairinjR) =>
% 98.80/13.34 ((
% 98.80/13.34 (ksndsingleton) =>
% 98.80/13.34 ((
% 98.80/13.34 (ksndpairEq) =>
% 98.80/13.34 ((
% 98.80/13.34 (kpairsurjEq) =>
% 98.80/13.34 ((
% 98.80/13.34 (cartprodsndin) =>
% 98.80/13.34 ((
% 98.80/13.34 (cartprodpairmemEL) =>
% 98.80/13.34 ((
% 98.80/13.34 (cartprodpairmemER) =>
% 98.80/13.34 ((
% 98.80/13.34 (cartprodmempaircEq) =>
% 98.80/13.34 ((
% 98.80/13.34 (cartprodfstpairEq) =>
% 98.80/13.34 ((
% 98.80/13.34 (cartprodsndpairEq) =>
% 98.80/13.34 ((
% 98.80/13.34 (cartprodpairsurjEq) =>
% 98.80/13.34 ((
% 98.80/13.34 (dpsetconstrI) =>
% 98.80/13.34 ((
% 98.80/13.34 (dpsetconstrSub) =>
% 98.80/13.34 ((
% 98.80/13.34 (setOfPairsIsBReln) =>
% 98.80/13.34 ((
% 98.80/13.34 (dpsetconstrERa) =>
% 98.80/13.34 ((
% 98.80/13.34 (dpsetconstrEL1) =>
% 98.80/13.34 ((
% 98.80/13.34 (dpsetconstrEL2) =>
% 98.80/13.34 ((
% 98.80/13.34 (dpsetconstrER) =>
% 98.80/13.34 ((
% 98.80/13.34 (funcImageSingleton) =>
% 98.80/13.34 ((
% 98.80/13.34 (apProp) =>
% 98.80/13.34 ((
% 98.80/13.34 (app) =>
% 98.80/13.34 ((
% 98.80/13.34 (infuncsetfunc) =>
% 98.80/13.34 ((
% 98.80/13.34 (ap2p) =>
% 98.80/13.34 ((
% 98.80/13.34 (funcinfuncset) =>
% 98.80/13.34 ((
% 98.80/13.34 (lamProp) =>
% 98.80/13.34 ((
% 98.80/13.34 (lamp) =>
% 98.80/13.34 ((
% 98.80/13.34 (lam2p) =>
% 98.80/13.34 ((
% 98.80/13.34 (brelnall1) =>
% 98.80/13.34 ((
% 98.80/13.34 (brelnall2) =>
% 98.80/13.34 ((
% 98.80/13.34 (ex1E2) =>
% 98.80/13.34 ((
% 98.80/13.34 (funcGraphProp1) =>
% 98.80/13.34 ((
% 98.80/13.34 (funcGraphProp3) =>
% 98.80/13.34 ((
% 98.80/13.34 (funcGraphProp2) =>
% 98.80/13.34 ((
% 98.80/13.34 (funcextLem) =>
% 98.80/13.34 ((
% 98.80/13.34 (funcGraphProp4) =>
% 98.80/13.34 ((
% 98.80/13.34 (subbreln) =>
% 98.80/13.34 ((
% 98.80/13.34 (eqbreln) =>
% 98.80/13.34 ((
% 98.80/13.34 (funcext) =>
% 98.80/13.34 ((
% 98.80/13.34 (funcext2) =>
% 98.80/13.34 ((
% 98.80/13.34 (ap2apEq1) =>
% 98.80/13.34 ((
% 98.80/13.34 (ap2apEq2) =>
% 98.80/13.34 ((
% 98.80/13.34 (beta1) =>
% 98.80/13.34 ((
% 98.80/13.34 (eta1) =>
% 98.80/13.34 ((
% 98.80/13.34 (lam2lamEq) =>
% 98.80/13.34 ((
% 98.80/13.34 (beta2) =>
% 98.80/13.34 ((
% 98.80/13.34 (eta2) =>
% 98.80/13.34 ((
% 98.80/13.34 (iffalseProp1) =>
% 98.80/13.34 ((
% 98.80/13.34 (iffalseProp2) =>
% 98.80/13.34 ((
% 98.80/13.34 (iftrueProp1) =>
% 98.80/13.34 ((
% 98.80/13.34 (iftrueProp2) =>
% 98.80/13.34 ((
% 98.80/13.34 (ifSingleton) =>
% 98.80/13.34 ((
% 98.80/13.34 (ifp) =>
% 98.80/13.34 ((
% 98.80/13.34 (theeq) =>
% 98.80/13.34 ((
% 98.80/13.34 (iftrue) =>
% 98.80/13.34 ((
% 98.80/13.34 (iffalse) =>
% 98.80/13.34 ((
% 98.80/13.34 (iftrueorfalse) =>
% 98.80/13.34 ((
% 98.80/13.34 (binintersectT_lem) =>
% 98.80/13.34 ((
% 98.80/13.34 (binunionT_lem) =>
% 98.80/13.34 ((
% 98.80/13.34 (powersetT_lem) =>
% 98.80/13.34 ((
% 98.80/13.34 (setminusT_lem) =>
% 98.80/13.34 ((
% 98.80/13.34 (complementT_lem) =>
% 98.80/13.34 ((
% 98.80/13.34 (setextT) =>
% 98.80/13.34 ((
% 98.80/13.34 (subsetTI) =>
% 98.80/13.34 ((
% 98.80/13.34 (powersetTI1) =>
% 98.80/13.34 ((
% 98.80/13.34 (powersetTE1) =>
% 98.80/13.34 ((
% 98.80/13.34 (complementTI1) =>
% 98.80/13.34 ((
% 98.80/13.34 (complementTE1) =>
% 98.80/13.34 ((
% 98.80/13.34 (binintersectTELcontra) =>
% 98.80/13.34 ((
% 98.80/13.34 (binintersectTERcontra) =>
% 98.80/13.34 ((
% 98.80/13.34 (contrasubsetT) =>
% 98.80/13.34 ((
% 98.80/13.34 (contrasubsetT1) =>
% 98.80/13.34 ((
% 98.80/13.34 (contrasubsetT2) =>
% 98.80/13.34 ((
% 98.80/13.34 (contrasubsetT3) =>
% 98.80/13.34 ((
% 98.80/13.34 (doubleComplementI1) =>
% 98.80/13.34 ((
% 98.80/13.34 (doubleComplementE1) =>
% 98.80/13.34 ((
% 98.80/13.34 (doubleComplementSub1) =>
% 98.80/13.34 ((
% 98.80/13.34 (doubleComplementSub2) =>
% 98.80/13.34 ((
% 98.80/13.34 (doubleComplementEq) =>
% 98.80/13.34 ((
% 98.80/13.34 (complementTnotintersectT) =>
% 98.80/13.34 ((
% 98.80/13.34 (complementImpComplementIntersect) =>
% 98.80/13.34 ((
% 98.80/13.34 (complementSubsetComplementIntersect) =>
% 98.80/13.34 ((
% 98.80/13.34 (complementInPowersetComplementIntersect) =>
% 98.80/13.34 ((
% 98.80/13.34 (contraSubsetComplement) =>
% 98.80/13.34 ((
% 98.80/13.34 (complementTcontraSubset) =>
% 98.80/13.34 ((
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% 98.80/13.34 ((
% 98.80/13.34 (binunionTIRcontra) =>
% 98.80/13.34 ((
% 98.80/13.34 (inIntersectImpInUnion) =>
% 98.80/13.34 ((
% 98.80/13.34 (inIntersectImpInUnion2) =>
% 98.80/13.34 ((
% 98.80/13.34 (inIntersectImpInIntersectUnions) =>
% 98.80/13.34 ((
% 98.80/13.34 (intersectInPowersetIntersectUnions) =>
% 98.80/13.34 ((
% 98.80/13.34 (inComplementUnionImpNotIn1) =>
% 98.80/13.34 ((
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% 98.80/13.34 ((
% 98.80/13.34 (binunionTE) =>
% 98.80/13.34 ((
% 98.80/13.34 (binunionTEcontra) =>
% 98.80/13.34 ((
% 98.80/13.34 (demorgan2a1) =>
% 98.80/13.34 ((
% 98.80/13.34 (complementUnionInPowersetComplement) =>
% 98.80/13.34 ((
% 98.80/13.34 (demorgan2a2) =>
% 98.80/13.34 ((
% 98.80/13.34 (demorgan1a) =>
% 98.80/13.34 ((
% 98.80/13.34 (demorgan1b) =>
% 98.80/13.34 ((
% 98.80/13.34 (demorgan1) =>
% 98.80/13.34 ((
% 98.80/13.34 (demorgan2a) =>
% 98.80/13.34 ((
% 98.80/13.34 (demorgan2b2) =>
% 98.80/13.34 ((
% 98.80/13.34 (demorgan2b) =>
% 98.80/13.34 ((
% 98.80/13.34 (demorgan2) =>
% 98.80/13.34 ((
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% 98.80/13.34 ((
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% 98.80/13.34 (woz1_5) =>
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% 98.80/13.34 (breln1all2) =>
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% 98.80/13.34 (breln1SetBreln1) =>
% 98.80/13.34 ((
% 98.80/13.34 (choice2fnsingleton) =>
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% 98.80/13.34 (breln1compI) =>
% 98.80/13.34 ((
% 98.80/13.34 (breln1compE) =>
% 98.80/13.34 ((
% 98.80/13.34 (breln1compEex) =>
% 98.80/13.34 ((
% 98.80/13.34 (breln1unionprop) =>
% 98.80/13.34 ((
% 98.80/13.34 (breln1unionIL) =>
% 98.80/13.34 ((
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% 98.80/13.34 ((
% 98.80/13.34 (breln1unionE) =>
% 98.80/13.34 ((
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% 98.80/13.34 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl33])).
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% 98.80/13.34 ((
% 98.80/13.34 (powerset__Cong) =>
% 98.80/13.34 ((
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% 98.80/13.34 ((
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% 98.80/13.34 ((
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% 98.80/13.34 ((
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% 98.80/13.34 ((
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% 98.80/13.34 ((
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% 98.80/13.34 ((
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% 98.80/13.34 ((
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% 98.80/13.34 ((
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% 98.80/13.34 ((
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% 98.80/13.34 ((
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% 98.80/13.34 ((
% 98.80/13.34 (setminusIRneg) =>
% 98.80/13.34 ((
% 98.80/13.34 (setminusLsub) =>
% 98.80/13.34 ((
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% 98.80/13.34 ((
% 98.80/13.34 (symdiffE) =>
% 98.80/13.34 ((
% 98.80/13.34 (symdiffI1) =>
% 98.80/13.34 ((
% 98.80/13.34 (symdiffI2) =>
% 98.80/13.34 ((
% 98.80/13.34 (symdiffIneg1) =>
% 98.80/13.34 ((
% 98.80/13.34 (symdiffIneg2) =>
% 98.80/13.34 ((
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% 98.80/13.34 (inIntersectImpInIntersectUnions) =>
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% 98.80/13.34 (intersectInPowersetIntersectUnions) =>
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% 98.80/13.34 (demorgan2b) =>
% 98.80/13.34 ((
% 98.80/13.34 (demorgan2) =>
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% 98.80/13.34 ((
% 98.80/13.34 (woz13rule2) =>
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% 98.80/13.34 (woz13rule3) =>
% 98.80/13.34 ((
% 98.80/13.34 (woz13rule4) =>
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% 98.80/13.34 (breln1SetBreln1) =>
% 98.80/13.34 ((
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% 98.80/13.34 (breln1invE) =>
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% 98.80/13.34 (breln1compE) =>
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% 98.80/13.34 (breln1compEex) =>
% 98.80/13.34 ((
% 98.80/13.34 (breln1unionprop) =>
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% 98.80/13.34 (breln1unionI) =>
% 98.80/13.34 ((
% 98.80/13.34 (breln1unionE) =>
% 98.80/13.34 ((
% 98.80/13.34 (breln1unionEcases) =>
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% 98.80/13.34 (breln1unionCommutes) =>
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% 98.80/13.34 ((
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% 98.80/13.34 ((
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% 98.80/13.34 ((
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% 98.80/13.34 ((
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% 98.80/13.34 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl40])).
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% 98.80/13.34 (setadjoin__Cong) =>
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% 98.80/13.34 (powerset__Cong) =>
% 98.80/13.34 ((
% 98.80/13.34 (setunion__Cong) =>
% 98.80/13.34 ((
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% 98.80/13.34 ((
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% 98.80/13.34 ((
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% 98.80/13.34 ((
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% 98.80/13.34 ((
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% 98.80/13.34 ((
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% 98.80/13.34 ((
% 98.80/13.34 (setminusILneg) =>
% 98.80/13.34 ((
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% 98.80/13.34 ((
% 98.80/13.34 (setminusLsub) =>
% 98.80/13.34 ((
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% 98.80/13.34 ((
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% 98.80/13.34 ((
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% 98.80/13.34 ((
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% 98.80/13.34 ((
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% 98.80/13.34 ((
% 98.80/13.34 (lamp) =>
% 98.80/13.34 ((
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% 98.80/13.34 ((
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% 98.80/13.34 ((
% 98.80/13.34 (funcGraphProp3) =>
% 98.80/13.34 ((
% 98.80/13.34 (funcGraphProp2) =>
% 98.80/13.34 ((
% 98.80/13.34 (funcextLem) =>
% 98.80/13.34 ((
% 98.80/13.34 (funcGraphProp4) =>
% 98.80/13.34 ((
% 98.80/13.34 (subbreln) =>
% 98.80/13.34 ((
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% 98.80/13.34 ((
% 98.80/13.34 (funcext2) =>
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% 98.80/13.34 ((
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% 98.80/13.34 ((
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% 98.80/13.34 ((
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% 98.80/13.34 (contrasubsetT2) =>
% 98.80/13.34 ((
% 98.80/13.34 (contrasubsetT3) =>
% 98.80/13.34 ((
% 98.80/13.34 (doubleComplementI1) =>
% 98.80/13.34 ((
% 98.80/13.34 (doubleComplementE1) =>
% 98.80/13.34 ((
% 98.80/13.34 (doubleComplementSub1) =>
% 98.80/13.34 ((
% 98.80/13.34 (doubleComplementSub2) =>
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% 98.80/13.34 (doubleComplementEq) =>
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% 98.80/13.34 (complementTnotintersectT) =>
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% 98.80/13.34 (complementImpComplementIntersect) =>
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% 98.80/13.34 (complementSubsetComplementIntersect) =>
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% 98.80/13.34 (contraSubsetComplement) =>
% 98.80/13.34 ((
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% 98.80/13.34 ((
% 98.80/13.34 (binunionTIRcontra) =>
% 98.80/13.34 ((
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% 98.80/13.34 ((
% 98.80/13.34 (inIntersectImpInUnion2) =>
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% 98.80/13.34 (inIntersectImpInIntersectUnions) =>
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% 98.80/13.34 (intersectInPowersetIntersectUnions) =>
% 98.80/13.34 ((
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% 98.80/13.34 ((
% 98.80/13.34 (inComplementUnionImpInComplement1) =>
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% 98.80/13.34 ((
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% 98.80/13.34 ((
% 98.80/13.34 (demorgan1b) =>
% 98.80/13.34 ((
% 98.80/13.34 (demorgan1) =>
% 99.06/13.34 ((
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% 99.06/13.34 ((
% 99.06/13.34 (demorgan2b2) =>
% 99.06/13.34 ((
% 99.06/13.34 (demorgan2b) =>
% 99.06/13.34 ((
% 99.06/13.34 (demorgan2) =>
% 99.06/13.34 ((
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% 99.06/13.34 ((
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% 99.06/13.34 ((
% 99.06/13.34 (woz13rule2) =>
% 99.06/13.34 ((
% 99.06/13.34 (woz13rule3) =>
% 99.06/13.34 ((
% 99.06/13.34 (woz13rule4) =>
% 99.06/13.34 ((
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% 99.06/13.34 ((
% 99.06/13.34 (woz1_2) =>
% 99.06/13.34 ((
% 99.06/13.34 (woz1_3) =>
% 99.06/13.34 ((
% 99.06/13.34 (woz1_4) =>
% 99.06/13.34 ((
% 99.06/13.34 (woz1_5) =>
% 99.06/13.34 ((
% 99.06/13.34 (breln1all2) =>
% 99.06/13.34 ((
% 99.06/13.34 (breln1SetBreln1) =>
% 99.06/13.34 ((
% 99.06/13.34 (choice2fnsingleton) =>
% 99.06/13.34 ((
% 99.06/13.34 (setOfPairsIsBReln1) =>
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% 99.06/13.34 ((
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% 99.06/13.34 ((
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% 99.06/13.34 ((
% 99.06/13.34 (breln1invprop) =>
% 99.06/13.34 ((
% 99.06/13.34 (breln1invI) =>
% 99.06/13.34 ((
% 99.06/13.34 (breln1invE) =>
% 99.06/13.34 ((
% 99.06/13.34 (breln1compprop) =>
% 99.06/13.34 ((
% 99.06/13.34 (breln1compI) =>
% 99.06/13.34 ((
% 99.06/13.34 (breln1compE) =>
% 99.06/13.34 ((
% 99.06/13.34 (breln1compEex) =>
% 99.06/13.34 ((
% 99.06/13.34 (breln1unionprop) =>
% 99.06/13.34 ((
% 99.06/13.34 (breln1unionIL) =>
% 99.06/13.34 ((
% 99.06/13.34 (breln1unionIR) =>
% 99.06/13.34 ((
% 99.06/13.34 (breln1unionI) =>
% 99.06/13.34 ((
% 99.06/13.34 (breln1unionE) =>
% 99.06/13.34 ((
% 99.06/13.34 (breln1unionEcases) =>
% 99.06/13.34 ((
% 99.06/13.34 (breln1unionCommutes) =>
% 99.06/13.34 ((
% 99.06/13.34 (woz2Ex) =>
% 99.06/13.34 ((
% 99.06/13.34 (woz2W) =>
% 99.06/13.34 ((
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% 99.06/13.34 ((
% 99.06/13.34 (woz2B) =>
% 99.06/13.34 ((
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% 99.06/13.34 ((
% 99.06/13.34 (image1Ex1) =>
% 99.06/13.34 ((
% 99.06/13.34 (image1Equiv) =>
% 99.06/13.34 ((
% 99.06/13.34 (image1E) =>
% 99.06/13.34 ((
% 99.06/13.34 (image1I) =>
% 99.06/13.34 ((
% 99.06/13.34 (injFuncInInjFuncSet) =>
% 99.06/13.34 ((
% 99.06/13.34 (injFuncSetFuncIn) =>
% 99.06/13.34 ((
% 99.06/13.34 (injFuncSetFuncInj) =>
% 99.06/13.34 ((
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% 99.06/13.34 (('#B') @ (
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% 99.06/13.34 (
% 99.06/13.34 (
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% 99.06/13.34 (
% 99.06/13.34 ('#B') @ (
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% 99.06/13.34 (
% 99.06/13.34 (
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% 99.06/13.34 (
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% 99.06/13.34 (
% 99.06/13.34 (
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% 99.06/13.34 (
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% 99.06/13.34 (
% 99.06/13.34 (
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% 99.06/13.34 (
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% 99.06/13.34 surjFuncSet)))))))) @
% 99.06/13.34 (
% 99.06/13.34 (
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% 99.06/13.34 (
% 99.06/13.34 ('#B') @ (
% 99.06/13.34 (
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% 99.06/13.34 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.06/13.34 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl52])).
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% 99.06/13.34 ((
% 99.06/13.34 (quantDeMorgan3) =>
% 99.06/13.34 ((
% 99.06/13.34 (quantDeMorgan4) =>
% 99.06/13.34 ((
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% 99.06/13.34 ((
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% 99.06/13.34 ((
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% 99.06/13.34 ((
% 99.06/13.34 (exu__Cong) =>
% 99.06/13.34 ((
% 99.06/13.34 (setadjoin__Cong) =>
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% 99.06/13.34 (powerset__Cong) =>
% 99.06/13.34 ((
% 99.06/13.34 (setunion__Cong) =>
% 99.06/13.34 ((
% 99.06/13.34 (exuEu) =>
% 99.06/13.34 ((
% 99.06/13.34 (descr__Cong) =>
% 99.06/13.34 ((
% 99.06/13.34 (dsetconstr__Cong) =>
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% 99.06/13.34 ((
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% 99.06/13.34 ((
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% 99.06/13.34 ((
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% 99.06/13.34 ((
% 99.06/13.34 (binintersectSubset4) =>
% 99.06/13.34 ((
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% 99.06/13.34 ((
% 99.06/13.34 (bs114d) =>
% 99.06/13.34 ((
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% 99.06/13.34 ((
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% 99.06/13.34 ((
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% 99.06/13.34 ((
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% 99.06/13.34 ((
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% 99.06/13.34 ((
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% 99.06/13.34 ((
% 99.06/13.34 (setminusILneg) =>
% 99.06/13.34 ((
% 99.06/13.34 (setminusIRneg) =>
% 99.06/13.34 ((
% 99.06/13.34 (setminusLsub) =>
% 99.06/13.34 ((
% 99.06/13.34 (setminusSubset1) =>
% 99.06/13.34 ((
% 99.06/13.34 (symdiffE) =>
% 99.06/13.34 ((
% 99.06/13.34 (symdiffI1) =>
% 99.06/13.34 ((
% 99.06/13.34 (symdiffI2) =>
% 99.06/13.34 ((
% 99.06/13.34 (symdiffIneg1) =>
% 99.06/13.34 ((
% 99.06/13.34 (symdiffIneg2) =>
% 99.06/13.34 ((
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% 99.06/13.34 ((
% 99.06/13.34 (setukpairIL) =>
% 99.06/13.34 ((
% 99.06/13.34 (setukpairIR) =>
% 99.06/13.34 ((
% 99.06/13.34 (kpairiskpair) =>
% 99.06/13.34 ((
% 99.06/13.34 (kpairp) =>
% 99.06/13.34 ((
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% 99.06/13.34 ((
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% 99.06/13.34 ((
% 99.06/13.34 (singletoninpowunion) =>
% 99.06/13.34 ((
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% 99.06/13.34 ((
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% 99.06/13.34 ((
% 99.06/13.34 (upairinpowunion) =>
% 99.06/13.34 ((
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% 99.06/13.34 ((
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% 99.06/13.34 ((
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% 99.06/13.34 ((
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% 99.06/13.34 ((
% 99.06/13.34 (cartprodpairmemER) =>
% 99.06/13.34 ((
% 99.06/13.34 (cartprodmempaircEq) =>
% 99.06/13.34 ((
% 99.06/13.34 (cartprodfstpairEq) =>
% 99.06/13.34 ((
% 99.06/13.34 (cartprodsndpairEq) =>
% 99.06/13.34 ((
% 99.06/13.34 (cartprodpairsurjEq) =>
% 99.06/13.34 ((
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% 99.06/13.34 ((
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% 99.06/13.34 (dpsetconstrEL2) =>
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% 99.06/13.34 (funcImageSingleton) =>
% 99.06/13.34 ((
% 99.06/13.34 (apProp) =>
% 99.06/13.34 ((
% 99.06/13.34 (app) =>
% 99.06/13.34 ((
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% 99.06/13.34 ((
% 99.06/13.34 (ap2p) =>
% 99.06/13.34 ((
% 99.06/13.34 (funcinfuncset) =>
% 99.06/13.34 ((
% 99.06/13.34 (lamProp) =>
% 99.06/13.34 ((
% 99.06/13.34 (lamp) =>
% 99.06/13.34 ((
% 99.06/13.34 (lam2p) =>
% 99.06/13.34 ((
% 99.06/13.34 (brelnall1) =>
% 99.06/13.34 ((
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% 99.06/13.34 ((
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% 99.06/13.34 ((
% 99.06/13.34 (funcGraphProp3) =>
% 99.06/13.34 ((
% 99.06/13.34 (funcGraphProp2) =>
% 99.06/13.34 ((
% 99.06/13.34 (funcextLem) =>
% 99.06/13.34 ((
% 99.06/13.34 (funcGraphProp4) =>
% 99.06/13.34 ((
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% 99.06/13.34 ((
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% 99.06/13.34 ((
% 99.06/13.34 (funcext2) =>
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% 99.06/13.34 ((
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% 99.06/13.34 ((
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% 99.06/13.34 ((
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% 99.06/13.34 ((
% 99.06/13.34 (iffalseProp2) =>
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% 99.06/13.34 ((
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% 99.06/13.34 ((
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% 99.06/13.34 ((
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% 99.06/13.34 ((
% 99.06/13.34 (contrasubsetT2) =>
% 99.06/13.34 ((
% 99.06/13.34 (contrasubsetT3) =>
% 99.06/13.34 ((
% 99.06/13.34 (doubleComplementI1) =>
% 99.06/13.34 ((
% 99.06/13.34 (doubleComplementE1) =>
% 99.06/13.34 ((
% 99.06/13.34 (doubleComplementSub1) =>
% 99.06/13.34 ((
% 99.06/13.34 (doubleComplementSub2) =>
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% 99.06/13.34 (doubleComplementEq) =>
% 99.06/13.34 ((
% 99.06/13.34 (complementTnotintersectT) =>
% 99.06/13.34 ((
% 99.06/13.34 (complementImpComplementIntersect) =>
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% 99.06/13.34 (complementSubsetComplementIntersect) =>
% 99.06/13.34 ((
% 99.06/13.34 (complementInPowersetComplementIntersect) =>
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% 99.06/13.34 (contraSubsetComplement) =>
% 99.06/13.34 ((
% 99.06/13.34 (complementTcontraSubset) =>
% 99.06/13.34 ((
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% 99.06/13.34 ((
% 99.06/13.34 (binunionTIRcontra) =>
% 99.06/13.34 ((
% 99.06/13.34 (inIntersectImpInUnion) =>
% 99.06/13.34 ((
% 99.06/13.34 (inIntersectImpInUnion2) =>
% 99.06/13.34 ((
% 99.06/13.34 (inIntersectImpInIntersectUnions) =>
% 99.06/13.34 ((
% 99.06/13.34 (intersectInPowersetIntersectUnions) =>
% 99.06/13.34 ((
% 99.06/13.34 (inComplementUnionImpNotIn1) =>
% 99.06/13.34 ((
% 99.06/13.34 (inComplementUnionImpInComplement1) =>
% 99.06/13.34 ((
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% 99.06/13.34 ((
% 99.06/13.34 (binunionTEcontra) =>
% 99.06/13.34 ((
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% 99.06/13.34 ((
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% 99.06/13.34 ((
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% 99.06/13.34 ((
% 99.06/13.34 (demorgan1a) =>
% 99.06/13.34 ((
% 99.06/13.34 (demorgan1b) =>
% 99.06/13.34 ((
% 99.06/13.34 (demorgan1) =>
% 99.06/13.34 ((
% 99.06/13.34 (demorgan2a) =>
% 99.06/13.34 ((
% 99.06/13.34 (demorgan2b2) =>
% 99.06/13.34 ((
% 99.06/13.34 (demorgan2b) =>
% 99.06/13.34 ((
% 99.06/13.34 (demorgan2) =>
% 99.06/13.34 ((
% 99.06/13.34 (woz13rule0) =>
% 99.06/13.34 ((
% 99.06/13.34 (woz13rule1) =>
% 99.06/13.34 ((
% 99.06/13.34 (woz13rule2) =>
% 99.06/13.34 ((
% 99.06/13.34 (woz13rule3) =>
% 99.06/13.34 ((
% 99.06/13.34 (woz13rule4) =>
% 99.06/13.34 ((
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% 99.06/13.34 ((
% 99.06/13.34 (woz1_2) =>
% 99.06/13.34 ((
% 99.06/13.34 (woz1_3) =>
% 99.06/13.34 ((
% 99.06/13.34 (woz1_4) =>
% 99.06/13.34 ((
% 99.06/13.34 (woz1_5) =>
% 99.06/13.34 ((
% 99.06/13.34 (breln1all2) =>
% 99.06/13.34 ((
% 99.06/13.34 (breln1SetBreln1) =>
% 99.06/13.34 ((
% 99.06/13.34 (choice2fnsingleton) =>
% 99.06/13.34 ((
% 99.06/13.34 (setOfPairsIsBReln1) =>
% 99.06/13.34 ((
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% 99.06/13.34 ((
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% 99.06/13.34 ((
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% 99.06/13.34 ((
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% 99.06/13.34 ((
% 99.06/13.34 (breln1invI) =>
% 99.06/13.34 ((
% 99.06/13.34 (breln1invE) =>
% 99.06/13.34 ((
% 99.06/13.34 (breln1compprop) =>
% 99.06/13.34 ((
% 99.06/13.34 (breln1compI) =>
% 99.06/13.34 ((
% 99.06/13.34 (breln1compE) =>
% 99.06/13.34 ((
% 99.06/13.34 (breln1compEex) =>
% 99.06/13.34 ((
% 99.06/13.34 (breln1unionprop) =>
% 99.06/13.34 ((
% 99.06/13.34 (breln1unionIL) =>
% 99.06/13.34 ((
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% 99.06/13.34 ((
% 99.06/13.34 (breln1unionI) =>
% 99.06/13.34 ((
% 99.06/13.34 (breln1unionE) =>
% 99.06/13.34 ((
% 99.06/13.34 (breln1unionEcases) =>
% 99.06/13.34 ((
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% 99.06/13.34 ((
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% 99.06/13.34 ((
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% 99.06/13.34 ((
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% 99.06/13.34 ((
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% 99.06/13.34 ((
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% 99.06/13.34 ((
% 99.06/13.34 (image1Ex1) =>
% 99.06/13.34 ((
% 99.06/13.34 (image1Equiv) =>
% 99.06/13.34 ((
% 99.06/13.34 (image1E) =>
% 99.06/13.34 ((
% 99.06/13.34 (image1I) =>
% 99.06/13.34 ((
% 99.06/13.34 (injFuncInInjFuncSet) =>
% 99.06/13.34 ((
% 99.06/13.34 (injFuncSetFuncIn) =>
% 99.06/13.34 ((
% 99.06/13.34 (injFuncSetFuncInj) =>
% 99.06/13.34 ((
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% 99.06/13.34 (
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% 99.06/13.34 (
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% 99.06/13.34 (
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% 99.06/13.34 (
% 99.06/13.34 (
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% 99.06/13.34 (
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% 99.06/13.34 surjFuncSet)))))))) @
% 99.06/13.34 (
% 99.06/13.34 (
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% 99.06/13.34 (
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% 99.06/13.34 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
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% 99.06/13.34 ((
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% 99.06/13.34 ((
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% 99.06/13.34 ((
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% 99.06/13.34 ((
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% 99.06/13.34 ((
% 99.06/13.34 (exu__Cong) =>
% 99.06/13.34 ((
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% 99.06/13.34 (powerset__Cong) =>
% 99.06/13.34 ((
% 99.06/13.34 (setunion__Cong) =>
% 99.06/13.34 ((
% 99.06/13.34 (exuEu) =>
% 99.06/13.34 ((
% 99.06/13.34 (descr__Cong) =>
% 99.06/13.34 ((
% 99.06/13.34 (dsetconstr__Cong) =>
% 99.06/13.34 ((
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% 99.06/13.34 ((
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% 99.06/13.34 (binintersectSubset2) =>
% 99.06/13.34 ((
% 99.06/13.34 (binintersectSubset3) =>
% 99.06/13.34 ((
% 99.06/13.34 (binintersectER) =>
% 99.06/13.34 ((
% 99.06/13.34 (disjointsetsI1) =>
% 99.06/13.34 ((
% 99.06/13.34 (binintersectRsub) =>
% 99.06/13.34 ((
% 99.06/13.34 (binintersectSubset4) =>
% 99.06/13.34 ((
% 99.06/13.34 (binintersectSubset1) =>
% 99.06/13.34 ((
% 99.06/13.34 (bs114d) =>
% 99.06/13.34 ((
% 99.06/13.34 (setminusI) =>
% 99.06/13.34 ((
% 99.06/13.34 (setminusEL) =>
% 99.06/13.34 ((
% 99.06/13.34 (setminusER) =>
% 99.06/13.34 ((
% 99.06/13.34 (setminusSubset2) =>
% 99.06/13.34 ((
% 99.06/13.34 (setminusERneg) =>
% 99.06/13.34 ((
% 99.06/13.34 (setminusELneg) =>
% 99.06/13.34 ((
% 99.06/13.34 (setminusILneg) =>
% 99.06/13.34 ((
% 99.06/13.34 (setminusIRneg) =>
% 99.06/13.34 ((
% 99.06/13.34 (setminusLsub) =>
% 99.06/13.34 ((
% 99.06/13.34 (setminusSubset1) =>
% 99.06/13.34 ((
% 99.06/13.34 (symdiffE) =>
% 99.06/13.34 ((
% 99.06/13.34 (symdiffI1) =>
% 99.06/13.34 ((
% 99.06/13.34 (symdiffI2) =>
% 99.06/13.34 ((
% 99.06/13.34 (symdiffIneg1) =>
% 99.06/13.34 ((
% 99.06/13.34 (symdiffIneg2) =>
% 99.06/13.34 ((
% 99.06/13.34 (secondinupair) =>
% 99.06/13.34 ((
% 99.06/13.34 (setukpairIL) =>
% 99.06/13.34 ((
% 99.06/13.34 (setukpairIR) =>
% 99.06/13.34 ((
% 99.06/13.34 (kpairiskpair) =>
% 99.06/13.34 ((
% 99.06/13.34 (kpairp) =>
% 99.06/13.34 ((
% 99.06/13.34 (singletonsubset) =>
% 99.06/13.34 ((
% 99.06/13.34 (singletoninpowerset) =>
% 99.06/13.34 ((
% 99.06/13.34 (singletoninpowunion) =>
% 99.06/13.34 ((
% 99.06/13.34 (upairset2E) =>
% 99.06/13.34 ((
% 99.06/13.34 (upairsubunion) =>
% 99.06/13.34 ((
% 99.06/13.34 (upairinpowunion) =>
% 99.06/13.34 ((
% 99.06/13.34 (ubforcartprodlem1) =>
% 99.06/13.34 ((
% 99.06/13.34 (ubforcartprodlem2) =>
% 99.06/13.34 ((
% 99.06/13.34 (ubforcartprodlem3) =>
% 99.06/13.34 ((
% 99.06/13.34 (cartprodpairin) =>
% 99.06/13.34 ((
% 99.06/13.34 (cartprodmempair1) =>
% 99.06/13.34 ((
% 99.06/13.34 (cartprodmempair) =>
% 99.06/13.34 ((
% 99.06/13.34 (setunionE2) =>
% 99.06/13.34 ((
% 99.06/13.34 (setunionsingleton1) =>
% 99.06/13.34 ((
% 99.06/13.34 (setunionsingleton2) =>
% 99.06/13.34 ((
% 99.06/13.34 (setunionsingleton) =>
% 99.06/13.34 ((
% 99.06/13.34 (singletonprop) =>
% 99.06/13.34 ((
% 99.06/13.34 (ex1E1) =>
% 99.06/13.34 ((
% 99.06/13.34 (ex1I) =>
% 99.06/13.34 ((
% 99.06/13.34 (ex1I2) =>
% 99.06/13.34 ((
% 99.06/13.34 (singletonsuniq) =>
% 99.06/13.34 ((
% 99.06/13.34 (setukpairinjL1) =>
% 99.06/13.34 ((
% 99.06/13.34 (kfstsingleton) =>
% 99.06/13.34 ((
% 99.06/13.34 (theprop) =>
% 99.06/13.34 ((
% 99.06/13.34 (kfstpairEq) =>
% 99.06/13.34 ((
% 99.06/13.34 (cartprodfstin) =>
% 99.06/13.34 ((
% 99.06/13.34 (setukpairinjL2) =>
% 99.06/13.34 ((
% 99.06/13.34 (setukpairinjL) =>
% 99.06/13.34 ((
% 99.06/13.34 (setukpairinjR11) =>
% 99.06/13.34 ((
% 99.06/13.34 (setukpairinjR12) =>
% 99.06/13.34 ((
% 99.06/13.34 (setukpairinjR1) =>
% 99.06/13.34 ((
% 99.06/13.34 (upairequniteq) =>
% 99.06/13.34 ((
% 99.06/13.34 (setukpairinjR2) =>
% 99.06/13.34 ((
% 99.06/13.34 (setukpairinjR) =>
% 99.06/13.34 ((
% 99.06/13.34 (ksndsingleton) =>
% 99.06/13.34 ((
% 99.06/13.34 (ksndpairEq) =>
% 99.06/13.34 ((
% 99.06/13.34 (kpairsurjEq) =>
% 99.06/13.34 ((
% 99.06/13.34 (cartprodsndin) =>
% 99.06/13.34 ((
% 99.06/13.34 (cartprodpairmemEL) =>
% 99.06/13.34 ((
% 99.06/13.34 (cartprodpairmemER) =>
% 99.06/13.34 ((
% 99.06/13.34 (cartprodmempaircEq) =>
% 99.06/13.34 ((
% 99.06/13.34 (cartprodfstpairEq) =>
% 99.06/13.34 ((
% 99.06/13.34 (cartprodsndpairEq) =>
% 99.06/13.34 ((
% 99.06/13.34 (cartprodpairsurjEq) =>
% 99.06/13.34 ((
% 99.06/13.34 (dpsetconstrI) =>
% 99.06/13.34 ((
% 99.06/13.34 (dpsetconstrSub) =>
% 99.06/13.34 ((
% 99.06/13.34 (setOfPairsIsBReln) =>
% 99.06/13.34 ((
% 99.06/13.34 (dpsetconstrERa) =>
% 99.06/13.34 ((
% 99.06/13.34 (dpsetconstrEL1) =>
% 99.06/13.34 ((
% 99.06/13.34 (dpsetconstrEL2) =>
% 99.06/13.34 ((
% 99.06/13.34 (dpsetconstrER) =>
% 99.06/13.34 ((
% 99.06/13.34 (funcImageSingleton) =>
% 99.06/13.34 ((
% 99.06/13.34 (apProp) =>
% 99.06/13.34 ((
% 99.06/13.34 (app) =>
% 99.06/13.34 ((
% 99.06/13.34 (infuncsetfunc) =>
% 99.06/13.34 ((
% 99.06/13.34 (ap2p) =>
% 99.06/13.34 ((
% 99.06/13.34 (funcinfuncset) =>
% 99.06/13.34 ((
% 99.06/13.34 (lamProp) =>
% 99.06/13.34 ((
% 99.06/13.34 (lamp) =>
% 99.06/13.34 ((
% 99.06/13.34 (lam2p) =>
% 99.06/13.34 ((
% 99.06/13.34 (brelnall1) =>
% 99.06/13.34 ((
% 99.06/13.34 (brelnall2) =>
% 99.06/13.34 ((
% 99.06/13.34 (ex1E2) =>
% 99.06/13.34 ((
% 99.06/13.34 (funcGraphProp1) =>
% 99.06/13.34 ((
% 99.06/13.34 (funcGraphProp3) =>
% 99.06/13.34 ((
% 99.06/13.34 (funcGraphProp2) =>
% 99.06/13.34 ((
% 99.06/13.34 (funcextLem) =>
% 99.06/13.34 ((
% 99.06/13.34 (funcGraphProp4) =>
% 99.06/13.34 ((
% 99.06/13.34 (subbreln) =>
% 99.06/13.34 ((
% 99.06/13.34 (eqbreln) =>
% 99.06/13.34 ((
% 99.06/13.34 (funcext) =>
% 99.06/13.34 ((
% 99.06/13.34 (funcext2) =>
% 99.06/13.34 ((
% 99.06/13.34 (ap2apEq1) =>
% 99.06/13.34 ((
% 99.06/13.34 (ap2apEq2) =>
% 99.06/13.34 ((
% 99.06/13.34 (beta1) =>
% 99.06/13.34 ((
% 99.06/13.34 (eta1) =>
% 99.06/13.34 ((
% 99.06/13.34 (lam2lamEq) =>
% 99.06/13.34 ((
% 99.06/13.34 (beta2) =>
% 99.06/13.34 ((
% 99.06/13.34 (eta2) =>
% 99.06/13.34 ((
% 99.06/13.34 (iffalseProp1) =>
% 99.06/13.34 ((
% 99.06/13.34 (iffalseProp2) =>
% 99.06/13.34 ((
% 99.06/13.34 (iftrueProp1) =>
% 99.06/13.34 ((
% 99.06/13.34 (iftrueProp2) =>
% 99.06/13.34 ((
% 99.06/13.34 (ifSingleton) =>
% 99.06/13.34 ((
% 99.06/13.34 (ifp) =>
% 99.06/13.34 ((
% 99.06/13.34 (theeq) =>
% 99.06/13.34 ((
% 99.06/13.34 (iftrue) =>
% 99.06/13.34 ((
% 99.06/13.34 (iffalse) =>
% 99.06/13.34 ((
% 99.06/13.34 (iftrueorfalse) =>
% 99.06/13.34 ((
% 99.06/13.34 (binintersectT_lem) =>
% 99.06/13.34 ((
% 99.06/13.34 (binunionT_lem) =>
% 99.06/13.34 ((
% 99.06/13.34 (powersetT_lem) =>
% 99.06/13.34 ((
% 99.06/13.34 (setminusT_lem) =>
% 99.06/13.34 ((
% 99.06/13.34 (complementT_lem) =>
% 99.06/13.34 ((
% 99.06/13.34 (setextT) =>
% 99.06/13.34 ((
% 99.06/13.34 (subsetTI) =>
% 99.06/13.34 ((
% 99.06/13.34 (powersetTI1) =>
% 99.06/13.34 ((
% 99.06/13.34 (powersetTE1) =>
% 99.06/13.34 ((
% 99.06/13.34 (complementTI1) =>
% 99.06/13.34 ((
% 99.06/13.34 (complementTE1) =>
% 99.06/13.34 ((
% 99.06/13.34 (binintersectTELcontra) =>
% 99.06/13.34 ((
% 99.06/13.34 (binintersectTERcontra) =>
% 99.06/13.34 ((
% 99.06/13.34 (contrasubsetT) =>
% 99.06/13.34 ((
% 99.06/13.34 (contrasubsetT1) =>
% 99.06/13.34 ((
% 99.06/13.34 (contrasubsetT2) =>
% 99.06/13.34 ((
% 99.06/13.34 (contrasubsetT3) =>
% 99.06/13.34 ((
% 99.06/13.34 (doubleComplementI1) =>
% 99.06/13.34 ((
% 99.06/13.34 (doubleComplementE1) =>
% 99.06/13.34 ((
% 99.06/13.34 (doubleComplementSub1) =>
% 99.06/13.34 ((
% 99.06/13.34 (doubleComplementSub2) =>
% 99.06/13.34 ((
% 99.06/13.34 (doubleComplementEq) =>
% 99.06/13.34 ((
% 99.06/13.34 (complementTnotintersectT) =>
% 99.06/13.34 ((
% 99.06/13.34 (complementImpComplementIntersect) =>
% 99.06/13.34 ((
% 99.06/13.34 (complementSubsetComplementIntersect) =>
% 99.06/13.34 ((
% 99.06/13.34 (complementInPowersetComplementIntersect) =>
% 99.06/13.34 ((
% 99.06/13.34 (contraSubsetComplement) =>
% 99.06/13.34 ((
% 99.06/13.34 (complementTcontraSubset) =>
% 99.06/13.34 ((
% 99.06/13.34 (binunionTILcontra) =>
% 99.06/13.34 ((
% 99.06/13.34 (binunionTIRcontra) =>
% 99.06/13.34 ((
% 99.06/13.34 (inIntersectImpInUnion) =>
% 99.06/13.34 ((
% 99.06/13.34 (inIntersectImpInUnion2) =>
% 99.06/13.34 ((
% 99.06/13.34 (inIntersectImpInIntersectUnions) =>
% 99.06/13.34 ((
% 99.06/13.34 (intersectInPowersetIntersectUnions) =>
% 99.06/13.34 ((
% 99.06/13.34 (inComplementUnionImpNotIn1) =>
% 99.06/13.34 ((
% 99.06/13.34 (inComplementUnionImpInComplement1) =>
% 99.06/13.34 ((
% 99.06/13.34 (binunionTE) =>
% 99.06/13.34 ((
% 99.06/13.34 (binunionTEcontra) =>
% 99.06/13.34 ((
% 99.06/13.34 (demorgan2a1) =>
% 99.06/13.34 ((
% 99.06/13.34 (complementUnionInPowersetComplement) =>
% 99.06/13.34 ((
% 99.06/13.34 (demorgan2a2) =>
% 99.06/13.34 ((
% 99.06/13.34 (demorgan1a) =>
% 99.06/13.34 ((
% 99.06/13.34 (demorgan1b) =>
% 99.06/13.34 ((
% 99.06/13.34 (demorgan1) =>
% 99.06/13.34 ((
% 99.06/13.34 (demorgan2a) =>
% 99.06/13.34 ((
% 99.06/13.34 (demorgan2b2) =>
% 99.06/13.34 ((
% 99.06/13.34 (demorgan2b) =>
% 99.06/13.34 ((
% 99.06/13.34 (demorgan2) =>
% 99.06/13.34 ((
% 99.06/13.34 (woz13rule0) =>
% 99.06/13.34 ((
% 99.06/13.34 (woz13rule1) =>
% 99.06/13.34 ((
% 99.06/13.34 (woz13rule2) =>
% 99.06/13.34 ((
% 99.06/13.34 (woz13rule3) =>
% 99.06/13.34 ((
% 99.06/13.34 (woz13rule4) =>
% 99.06/13.34 ((
% 99.06/13.34 (woz1_1) =>
% 99.06/13.34 ((
% 99.06/13.34 (woz1_2) =>
% 99.06/13.34 ((
% 99.06/13.34 (woz1_3) =>
% 99.06/13.34 ((
% 99.06/13.34 (woz1_4) =>
% 99.06/13.34 ((
% 99.06/13.34 (woz1_5) =>
% 99.06/13.34 ((
% 99.06/13.34 (breln1all2) =>
% 99.06/13.34 ((
% 99.06/13.34 (breln1SetBreln1) =>
% 99.06/13.34 ((
% 99.06/13.35 (choice2fnsingleton) =>
% 99.06/13.35 ((
% 99.06/13.35 (setOfPairsIsBReln1) =>
% 99.06/13.35 ((
% 99.06/13.35 (breln1all1) =>
% 99.06/13.35 ((
% 99.06/13.35 (subbreln1) =>
% 99.06/13.35 ((
% 99.06/13.35 (eqbreln1) =>
% 99.06/13.35 ((
% 99.06/13.35 (breln1invprop) =>
% 99.06/13.35 ((
% 99.06/13.35 (breln1invI) =>
% 99.06/13.35 ((
% 99.06/13.35 (breln1invE) =>
% 99.06/13.35 ((
% 99.06/13.35 (breln1compprop) =>
% 99.06/13.35 ((
% 99.06/13.35 (breln1compI) =>
% 99.06/13.35 ((
% 99.06/13.35 (breln1compE) =>
% 99.06/13.35 ((
% 99.06/13.35 (breln1compEex) =>
% 99.06/13.35 ((
% 99.06/13.35 (breln1unionprop) =>
% 99.06/13.35 ((
% 99.06/13.35 (breln1unionIL) =>
% 99.06/13.35 ((
% 99.06/13.35 (breln1unionIR) =>
% 99.06/13.35 ((
% 99.06/13.35 (breln1unionI) =>
% 99.06/13.35 ((
% 99.06/13.35 (breln1unionE) =>
% 99.06/13.35 ((
% 99.06/13.35 (breln1unionEcases) =>
% 99.06/13.35 ((
% 99.06/13.35 (breln1unionCommutes) =>
% 99.06/13.35 ((
% 99.06/13.35 (woz2Ex) =>
% 99.06/13.35 ((
% 99.06/13.35 (woz2W) =>
% 99.06/13.35 ((
% 99.06/13.35 (woz2A) =>
% 99.06/13.35 ((
% 99.06/13.35 (woz2B) =>
% 99.06/13.35 ((
% 99.06/13.35 (image1Ex) =>
% 99.06/13.35 ((
% 99.06/13.35 (image1Ex1) =>
% 99.06/13.35 ((
% 99.06/13.35 (image1Equiv) =>
% 99.06/13.35 ((
% 99.06/13.35 (image1E) =>
% 99.06/13.35 ((
% 99.06/13.35 (image1I) =>
% 99.06/13.35 ((
% 99.06/13.35 (injFuncInInjFuncSet) =>
% 99.06/13.35 ((
% 99.06/13.35 (injFuncSetFuncIn) =>
% 99.06/13.35 ((
% 99.06/13.35 (injFuncSetFuncInj) =>
% 99.06/13.35 ((
% 99.06/13.35 (!!) @ (
% 99.06/13.35 (('#B') @ (
% 99.06/13.35 !!) @
% 99.06/13.35 (
% 99.06/13.35 (
% 99.06/13.35 ('#B') @ (
% 99.06/13.35 (
% 99.06/13.35 ('#B') @ (
% 99.06/13.35 !!))) @
% 99.06/13.35 (
% 99.06/13.35 (
% 99.06/13.35 ('#S') @ (
% 99.06/13.35 (
% 99.06/13.35 ('#B') @ (
% 99.06/13.35 '#S') @
% 99.06/13.35 (
% 99.06/13.35 (
% 99.06/13.35 ('#B') @ (
% 99.06/13.35 (
% 99.06/13.35 ('#B') @ (
% 99.06/13.35 '#S'))) @
% 99.06/13.35 (
% 99.06/13.35 (
% 99.06/13.35 ('#B') @ (
% 99.06/13.35 (
% 99.06/13.35 ('#B') @ (
% 99.06/13.35 (
% 99.06/13.35 ('#B') @ (
% 99.06/13.35 =>))))) @
% 99.06/13.35 (
% 99.06/13.35 (
% 99.06/13.35 ('#B') @ (
% 99.06/13.35 (
% 99.06/13.35 ('#B') @ (
% 99.06/13.35 (
% 99.06/13.35 ('#C') @ in)))) @
% 99.06/13.35 surjFuncSet)))))))) @
% 99.06/13.35 (
% 99.06/13.35 (
% 99.06/13.35 ('#B') @ (
% 99.06/13.35 (
% 99.06/13.35 ('#B') @ (
% 99.06/13.35 (
% 99.06/13.35 ('#C') @ in)))) @
% 99.06/13.35 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.06/13.35 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl64])).
% 99.06/13.35 thf(zip_derived_cl79, plain,
% 99.06/13.35 (~ (((dsetconstrEL) =>
% 99.06/13.35 (((dsetconstrER) =>
% 99.06/13.35 (((exuE1) =>
% 99.06/13.35 (((prop2setE) =>
% 99.06/13.35 (((emptysetE) =>
% 99.06/13.35 (((emptysetimpfalse) =>
% 99.06/13.35 (((notinemptyset) =>
% 99.06/13.35 (((exuE3e) =>
% 99.06/13.35 (((setext) =>
% 99.06/13.35 (((emptyI) =>
% 99.06/13.35 (((noeltsimpempty) =>
% 99.06/13.35 (((setbeta) =>
% 99.06/13.35 (((nonemptyE1) =>
% 99.06/13.35 (((nonemptyI) =>
% 99.06/13.35 (((nonemptyI1) =>
% 99.06/13.35 (((setadjoinIL) =>
% 99.06/13.35 (((in @ emptyset @
% 99.06/13.35 (setadjoin @ emptyset @ emptyset)) =>
% 99.06/13.35 (((setadjoinIR) =>
% 99.06/13.35 (((setadjoinE) =>
% 99.06/13.35 (((setadjoinOr) =>
% 99.06/13.35 (((setoftrueEq) =>
% 99.06/13.35 (((powersetI) =>
% 99.06/13.35 (((emptyinPowerset) =>
% 99.06/13.35 (((emptyInPowerset) =>
% 99.06/13.35 (((powersetE) =>
% 99.06/13.35 (((setunionI) =>
% 99.06/13.35 (((setunionE) =>
% 99.06/13.35 (((subPowSU) =>
% 99.06/13.35 (((exuE2) =>
% 99.06/13.35 (((nonemptyImpWitness) =>
% 99.06/13.35 ((
% 99.06/13.35 (uniqinunit) =>
% 99.06/13.35 ((
% 99.06/13.35 (notinsingleton) =>
% 99.06/13.35 ((
% 99.06/13.35 (eqinunit) =>
% 99.06/13.35 ((
% 99.06/13.35 (singletonsswitch) =>
% 99.06/13.35 ((
% 99.06/13.35 (upairsetE) =>
% 99.06/13.35 ((
% 99.06/13.35 (upairsetIL) =>
% 99.06/13.35 ((
% 99.06/13.35 (upairsetIR) =>
% 99.06/13.35 ((
% 99.06/13.35 (emptyE1) =>
% 99.06/13.35 ((
% 99.06/13.35 (vacuousDall) =>
% 99.06/13.35 ((
% 99.06/13.35 (quantDeMorgan1) =>
% 99.06/13.35 ((
% 99.06/13.35 (quantDeMorgan2) =>
% 99.06/13.35 ((
% 99.06/13.35 (quantDeMorgan3) =>
% 99.06/13.35 ((
% 99.06/13.35 (quantDeMorgan4) =>
% 99.06/13.35 ((
% 99.06/13.35 (prop2setI) =>
% 99.06/13.35 ((
% 99.06/13.35 (prop2set2propI) =>
% 99.06/13.35 ((
% 99.06/13.35 (notdexE) =>
% 99.06/13.35 ((
% 99.06/13.35 (notdallE) =>
% 99.06/13.35 ((
% 99.06/13.35 (exuI1) =>
% 99.06/13.35 ((
% 99.06/13.35 (exuI3) =>
% 99.06/13.35 ((
% 99.06/13.35 (exuI2) =>
% 99.06/13.35 ((
% 99.06/13.35 (inCongP) =>
% 99.06/13.35 ((
% 99.06/13.35 (in__Cong) =>
% 99.06/13.35 ((
% 99.06/13.35 (exuE3u) =>
% 99.06/13.35 ((
% 99.06/13.35 (exu__Cong) =>
% 99.06/13.35 ((
% 99.06/13.35 (setadjoin__Cong) =>
% 99.06/13.35 ((
% 99.06/13.35 (powerset__Cong) =>
% 99.06/13.35 ((
% 99.06/13.35 (setunion__Cong) =>
% 99.06/13.35 ((
% 99.06/13.35 (exuEu) =>
% 99.06/13.35 ((
% 99.06/13.35 (descr__Cong) =>
% 99.06/13.35 ((
% 99.06/13.35 (dsetconstr__Cong) =>
% 99.06/13.35 ((
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% 99.06/13.35 ((
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% 99.06/13.35 (
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% 99.06/13.35 surjFuncSet)))))))) @
% 99.06/13.35 (
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% 99.06/13.35 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.06/13.35 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl79])).
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% 99.06/13.35 ((
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% 99.06/13.35 ((
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% 99.06/13.35 ((
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% 99.06/13.35 ((
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% 99.06/13.35 ((
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% 99.06/13.35 ((
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% 99.06/13.35 ((
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% 99.06/13.35 ((
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% 99.06/13.35 ((
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% 99.06/13.35 ((
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% 99.06/13.35 ((
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% 99.06/13.35 ((
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% 99.06/13.35 ((
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% 99.06/13.35 ((
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% 99.06/13.35 ((
% 99.06/13.35 (setminusSubset1) =>
% 99.06/13.35 ((
% 99.06/13.35 (symdiffE) =>
% 99.06/13.35 ((
% 99.06/13.35 (symdiffI1) =>
% 99.06/13.35 ((
% 99.06/13.35 (symdiffI2) =>
% 99.06/13.35 ((
% 99.06/13.35 (symdiffIneg1) =>
% 99.06/13.35 ((
% 99.06/13.35 (symdiffIneg2) =>
% 99.06/13.35 ((
% 99.06/13.35 (secondinupair) =>
% 99.06/13.35 ((
% 99.06/13.35 (setukpairIL) =>
% 99.06/13.35 ((
% 99.06/13.35 (setukpairIR) =>
% 99.06/13.35 ((
% 99.06/13.35 (kpairiskpair) =>
% 99.06/13.35 ((
% 99.06/13.35 (kpairp) =>
% 99.06/13.35 ((
% 99.06/13.35 (singletonsubset) =>
% 99.06/13.35 ((
% 99.06/13.35 (singletoninpowerset) =>
% 99.06/13.35 ((
% 99.06/13.35 (singletoninpowunion) =>
% 99.06/13.35 ((
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% 99.06/13.35 ((
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% 99.06/13.35 ((
% 99.06/13.35 (upairinpowunion) =>
% 99.06/13.35 ((
% 99.06/13.35 (ubforcartprodlem1) =>
% 99.06/13.35 ((
% 99.06/13.35 (ubforcartprodlem2) =>
% 99.06/13.35 ((
% 99.06/13.35 (ubforcartprodlem3) =>
% 99.06/13.35 ((
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% 99.06/13.35 ((
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% 99.06/13.35 ((
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% 99.06/13.35 ((
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% 99.06/13.35 ((
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% 99.06/13.35 ((
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% 99.06/13.35 ((
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% 99.06/13.35 ((
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% 99.06/13.35 ((
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% 99.06/13.35 ((
% 99.06/13.35 (ksndpairEq) =>
% 99.06/13.35 ((
% 99.06/13.35 (kpairsurjEq) =>
% 99.06/13.35 ((
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% 99.06/13.35 ((
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% 99.06/13.35 ((
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% 99.06/13.35 ((
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% 99.06/13.35 ((
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% 99.06/13.35 ((
% 99.06/13.35 (demorgan1a) =>
% 99.06/13.35 ((
% 99.06/13.35 (demorgan1b) =>
% 99.06/13.35 ((
% 99.06/13.35 (demorgan1) =>
% 99.06/13.35 ((
% 99.06/13.35 (demorgan2a) =>
% 99.06/13.35 ((
% 99.06/13.35 (demorgan2b2) =>
% 99.06/13.35 ((
% 99.06/13.35 (demorgan2b) =>
% 99.06/13.35 ((
% 99.06/13.35 (demorgan2) =>
% 99.06/13.35 ((
% 99.06/13.35 (woz13rule0) =>
% 99.06/13.35 ((
% 99.06/13.35 (woz13rule1) =>
% 99.06/13.35 ((
% 99.06/13.35 (woz13rule2) =>
% 99.06/13.35 ((
% 99.06/13.35 (woz13rule3) =>
% 99.06/13.35 ((
% 99.06/13.35 (woz13rule4) =>
% 99.06/13.35 ((
% 99.06/13.35 (woz1_1) =>
% 99.06/13.35 ((
% 99.06/13.35 (woz1_2) =>
% 99.06/13.35 ((
% 99.06/13.35 (woz1_3) =>
% 99.06/13.35 ((
% 99.06/13.35 (woz1_4) =>
% 99.06/13.35 ((
% 99.06/13.35 (woz1_5) =>
% 99.06/13.35 ((
% 99.06/13.35 (breln1all2) =>
% 99.06/13.35 ((
% 99.06/13.35 (breln1SetBreln1) =>
% 99.06/13.35 ((
% 99.06/13.35 (choice2fnsingleton) =>
% 99.06/13.35 ((
% 99.06/13.35 (setOfPairsIsBReln1) =>
% 99.06/13.35 ((
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% 99.06/13.35 ((
% 99.06/13.35 (subbreln1) =>
% 99.06/13.35 ((
% 99.06/13.35 (eqbreln1) =>
% 99.06/13.35 ((
% 99.06/13.35 (breln1invprop) =>
% 99.06/13.35 ((
% 99.06/13.35 (breln1invI) =>
% 99.06/13.35 ((
% 99.06/13.35 (breln1invE) =>
% 99.06/13.35 ((
% 99.06/13.35 (breln1compprop) =>
% 99.06/13.35 ((
% 99.06/13.35 (breln1compI) =>
% 99.06/13.35 ((
% 99.06/13.35 (breln1compE) =>
% 99.06/13.35 ((
% 99.06/13.35 (breln1compEex) =>
% 99.06/13.35 ((
% 99.06/13.35 (breln1unionprop) =>
% 99.06/13.35 ((
% 99.06/13.35 (breln1unionIL) =>
% 99.06/13.35 ((
% 99.06/13.35 (breln1unionIR) =>
% 99.06/13.35 ((
% 99.06/13.35 (breln1unionI) =>
% 99.06/13.35 ((
% 99.06/13.35 (breln1unionE) =>
% 99.06/13.35 ((
% 99.06/13.35 (breln1unionEcases) =>
% 99.06/13.35 ((
% 99.06/13.35 (breln1unionCommutes) =>
% 99.06/13.35 ((
% 99.06/13.35 (woz2Ex) =>
% 99.06/13.35 ((
% 99.06/13.35 (woz2W) =>
% 99.06/13.35 ((
% 99.06/13.35 (woz2A) =>
% 99.06/13.35 ((
% 99.06/13.35 (woz2B) =>
% 99.06/13.35 ((
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% 99.06/13.35 ((
% 99.06/13.35 (image1Ex1) =>
% 99.06/13.35 ((
% 99.06/13.35 (image1Equiv) =>
% 99.06/13.35 ((
% 99.06/13.35 (image1E) =>
% 99.06/13.35 ((
% 99.06/13.35 (image1I) =>
% 99.06/13.35 ((
% 99.06/13.35 (injFuncInInjFuncSet) =>
% 99.06/13.35 ((
% 99.06/13.35 (injFuncSetFuncIn) =>
% 99.06/13.35 ((
% 99.06/13.35 (injFuncSetFuncInj) =>
% 99.06/13.35 ((
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% 99.06/13.35 (
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% 99.06/13.35 (
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% 99.06/13.35 (
% 99.06/13.35 (
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% 99.06/13.35 (
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% 99.06/13.35 surjFuncSet)))))))) @
% 99.06/13.35 (
% 99.06/13.35 (
% 99.06/13.35 ('#B') @ (
% 99.06/13.35 (
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% 99.06/13.35 (
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% 99.06/13.35 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
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% 99.06/13.35 ((
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% 99.06/13.35 ((
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% 99.06/13.35 ((
% 99.06/13.35 (quantDeMorgan4) =>
% 99.06/13.35 ((
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% 99.06/13.35 ((
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% 99.06/13.35 ((
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% 99.06/13.35 ((
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% 99.06/13.35 ((
% 99.06/13.35 (exuI3) =>
% 99.06/13.35 ((
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% 99.06/13.35 ((
% 99.06/13.35 (inCongP) =>
% 99.06/13.35 ((
% 99.06/13.35 (in__Cong) =>
% 99.06/13.35 ((
% 99.06/13.35 (exuE3u) =>
% 99.06/13.35 ((
% 99.06/13.35 (exu__Cong) =>
% 99.06/13.35 ((
% 99.06/13.35 (setadjoin__Cong) =>
% 99.06/13.35 ((
% 99.06/13.35 (powerset__Cong) =>
% 99.06/13.35 ((
% 99.06/13.35 (setunion__Cong) =>
% 99.06/13.35 ((
% 99.06/13.35 (exuEu) =>
% 99.06/13.35 ((
% 99.06/13.35 (descr__Cong) =>
% 99.06/13.35 ((
% 99.06/13.35 (dsetconstr__Cong) =>
% 99.06/13.35 ((
% 99.06/13.35 (subsetI1) =>
% 99.06/13.35 ((
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% 99.06/13.35 ((
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% 99.06/13.35 ((
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% 99.06/13.35 ((
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% 99.06/13.35 ((
% 99.06/13.35 (subsetE) =>
% 99.06/13.35 ((
% 99.06/13.35 (subsetE2) =>
% 99.06/13.35 ((
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% 99.06/13.35 ((
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% 99.06/13.35 ((
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% 99.06/13.35 ((
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% 99.06/13.35 ((
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% 99.06/13.35 ((
% 99.06/13.35 (powersetE1) =>
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% 99.06/13.35 ((
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% 99.06/13.35 ((
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% 99.06/13.35 ((
% 99.06/13.35 (upairset2IR) =>
% 99.06/13.35 ((
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% 99.06/13.35 ((
% 99.06/13.35 (binunionEcases) =>
% 99.06/13.35 ((
% 99.06/13.35 (binunionE) =>
% 99.06/13.35 ((
% 99.06/13.35 (binunionLsub) =>
% 99.06/13.35 ((
% 99.06/13.35 (binunionRsub) =>
% 99.06/13.35 ((
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% 99.06/13.35 ((
% 99.06/13.35 (binintersectSubset5) =>
% 99.06/13.35 ((
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% 99.06/13.35 ((
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% 99.06/13.35 ((
% 99.06/13.35 (binintersectSubset3) =>
% 99.06/13.35 ((
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% 99.06/13.35 ((
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% 99.06/13.35 ((
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% 99.06/13.35 ((
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% 99.06/13.35 ((
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% 99.06/13.35 ((
% 99.06/13.35 (setminusEL) =>
% 99.06/13.35 ((
% 99.06/13.35 (setminusER) =>
% 99.06/13.35 ((
% 99.06/13.35 (setminusSubset2) =>
% 99.06/13.35 ((
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% 99.06/13.35 ((
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% 99.06/13.35 ((
% 99.06/13.35 (setminusILneg) =>
% 99.06/13.35 ((
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% 99.06/13.35 ((
% 99.06/13.35 (setminusLsub) =>
% 99.06/13.35 ((
% 99.06/13.35 (setminusSubset1) =>
% 99.06/13.35 ((
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% 99.06/13.35 ((
% 99.06/13.35 (symdiffI1) =>
% 99.06/13.35 ((
% 99.06/13.35 (symdiffI2) =>
% 99.06/13.35 ((
% 99.06/13.35 (symdiffIneg1) =>
% 99.06/13.35 ((
% 99.06/13.35 (symdiffIneg2) =>
% 99.06/13.35 ((
% 99.06/13.35 (secondinupair) =>
% 99.06/13.35 ((
% 99.06/13.35 (setukpairIL) =>
% 99.06/13.35 ((
% 99.06/13.35 (setukpairIR) =>
% 99.06/13.35 ((
% 99.06/13.35 (kpairiskpair) =>
% 99.06/13.35 ((
% 99.06/13.35 (kpairp) =>
% 99.06/13.35 ((
% 99.06/13.35 (singletonsubset) =>
% 99.06/13.35 ((
% 99.06/13.35 (singletoninpowerset) =>
% 99.06/13.35 ((
% 99.06/13.35 (singletoninpowunion) =>
% 99.06/13.35 ((
% 99.06/13.35 (upairset2E) =>
% 99.06/13.35 ((
% 99.06/13.35 (upairsubunion) =>
% 99.06/13.35 ((
% 99.06/13.35 (upairinpowunion) =>
% 99.06/13.35 ((
% 99.06/13.35 (ubforcartprodlem1) =>
% 99.06/13.35 ((
% 99.06/13.35 (ubforcartprodlem2) =>
% 99.06/13.35 ((
% 99.06/13.35 (ubforcartprodlem3) =>
% 99.06/13.35 ((
% 99.06/13.35 (cartprodpairin) =>
% 99.06/13.35 ((
% 99.06/13.35 (cartprodmempair1) =>
% 99.06/13.35 ((
% 99.06/13.35 (cartprodmempair) =>
% 99.06/13.35 ((
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% 99.06/13.35 ((
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% 99.06/13.35 ((
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% 99.06/13.35 ((
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% 99.06/13.35 ((
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% 99.06/13.35 ((
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% 99.06/13.35 ((
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% 99.06/13.35 ((
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% 99.06/13.35 ((
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% 99.06/13.35 ((
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% 99.06/13.35 ((
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% 99.06/13.35 ((
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% 99.06/13.35 ((
% 99.06/13.35 (kpairsurjEq) =>
% 99.06/13.35 ((
% 99.06/13.35 (cartprodsndin) =>
% 99.06/13.35 ((
% 99.06/13.35 (cartprodpairmemEL) =>
% 99.06/13.35 ((
% 99.06/13.35 (cartprodpairmemER) =>
% 99.06/13.35 ((
% 99.06/13.35 (cartprodmempaircEq) =>
% 99.06/13.35 ((
% 99.06/13.35 (cartprodfstpairEq) =>
% 99.06/13.35 ((
% 99.06/13.35 (cartprodsndpairEq) =>
% 99.06/13.35 ((
% 99.06/13.35 (cartprodpairsurjEq) =>
% 99.06/13.35 ((
% 99.06/13.35 (dpsetconstrI) =>
% 99.06/13.35 ((
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% 99.06/13.35 ((
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% 99.06/13.35 ((
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% 99.06/13.35 ((
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% 99.06/13.35 ((
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% 99.06/13.35 ((
% 99.06/13.35 (complementTI1) =>
% 99.06/13.35 ((
% 99.06/13.35 (complementTE1) =>
% 99.06/13.35 ((
% 99.06/13.35 (binintersectTELcontra) =>
% 99.06/13.35 ((
% 99.06/13.35 (binintersectTERcontra) =>
% 99.06/13.35 ((
% 99.06/13.35 (contrasubsetT) =>
% 99.06/13.35 ((
% 99.06/13.35 (contrasubsetT1) =>
% 99.06/13.35 ((
% 99.06/13.35 (contrasubsetT2) =>
% 99.06/13.35 ((
% 99.06/13.35 (contrasubsetT3) =>
% 99.06/13.35 ((
% 99.06/13.35 (doubleComplementI1) =>
% 99.06/13.35 ((
% 99.06/13.35 (doubleComplementE1) =>
% 99.06/13.35 ((
% 99.06/13.35 (doubleComplementSub1) =>
% 99.06/13.35 ((
% 99.06/13.35 (doubleComplementSub2) =>
% 99.06/13.35 ((
% 99.06/13.35 (doubleComplementEq) =>
% 99.06/13.35 ((
% 99.06/13.35 (complementTnotintersectT) =>
% 99.06/13.35 ((
% 99.06/13.35 (complementImpComplementIntersect) =>
% 99.06/13.35 ((
% 99.06/13.35 (complementSubsetComplementIntersect) =>
% 99.06/13.35 ((
% 99.06/13.35 (complementInPowersetComplementIntersect) =>
% 99.06/13.35 ((
% 99.06/13.35 (contraSubsetComplement) =>
% 99.06/13.35 ((
% 99.06/13.35 (complementTcontraSubset) =>
% 99.06/13.35 ((
% 99.06/13.35 (binunionTILcontra) =>
% 99.06/13.35 ((
% 99.06/13.35 (binunionTIRcontra) =>
% 99.06/13.35 ((
% 99.06/13.35 (inIntersectImpInUnion) =>
% 99.06/13.35 ((
% 99.06/13.35 (inIntersectImpInUnion2) =>
% 99.06/13.35 ((
% 99.06/13.35 (inIntersectImpInIntersectUnions) =>
% 99.06/13.35 ((
% 99.06/13.35 (intersectInPowersetIntersectUnions) =>
% 99.06/13.35 ((
% 99.06/13.35 (inComplementUnionImpNotIn1) =>
% 99.06/13.35 ((
% 99.06/13.35 (inComplementUnionImpInComplement1) =>
% 99.06/13.35 ((
% 99.06/13.35 (binunionTE) =>
% 99.06/13.35 ((
% 99.06/13.35 (binunionTEcontra) =>
% 99.06/13.35 ((
% 99.06/13.35 (demorgan2a1) =>
% 99.06/13.35 ((
% 99.06/13.35 (complementUnionInPowersetComplement) =>
% 99.06/13.35 ((
% 99.06/13.35 (demorgan2a2) =>
% 99.06/13.35 ((
% 99.06/13.35 (demorgan1a) =>
% 99.06/13.35 ((
% 99.06/13.35 (demorgan1b) =>
% 99.06/13.35 ((
% 99.06/13.35 (demorgan1) =>
% 99.06/13.35 ((
% 99.06/13.35 (demorgan2a) =>
% 99.06/13.35 ((
% 99.06/13.35 (demorgan2b2) =>
% 99.06/13.35 ((
% 99.06/13.35 (demorgan2b) =>
% 99.06/13.35 ((
% 99.06/13.35 (demorgan2) =>
% 99.06/13.35 ((
% 99.06/13.35 (woz13rule0) =>
% 99.06/13.35 ((
% 99.06/13.35 (woz13rule1) =>
% 99.06/13.35 ((
% 99.06/13.35 (woz13rule2) =>
% 99.06/13.35 ((
% 99.06/13.35 (woz13rule3) =>
% 99.06/13.35 ((
% 99.06/13.35 (woz13rule4) =>
% 99.06/13.35 ((
% 99.06/13.35 (woz1_1) =>
% 99.06/13.35 ((
% 99.06/13.35 (woz1_2) =>
% 99.06/13.35 ((
% 99.06/13.35 (woz1_3) =>
% 99.06/13.35 ((
% 99.06/13.35 (woz1_4) =>
% 99.06/13.35 ((
% 99.06/13.35 (woz1_5) =>
% 99.06/13.35 ((
% 99.06/13.35 (breln1all2) =>
% 99.06/13.35 ((
% 99.06/13.35 (breln1SetBreln1) =>
% 99.06/13.35 ((
% 99.06/13.35 (choice2fnsingleton) =>
% 99.06/13.35 ((
% 99.06/13.35 (setOfPairsIsBReln1) =>
% 99.06/13.35 ((
% 99.06/13.35 (breln1all1) =>
% 99.06/13.35 ((
% 99.06/13.35 (subbreln1) =>
% 99.06/13.35 ((
% 99.06/13.35 (eqbreln1) =>
% 99.06/13.35 ((
% 99.06/13.35 (breln1invprop) =>
% 99.06/13.35 ((
% 99.06/13.35 (breln1invI) =>
% 99.06/13.35 ((
% 99.06/13.35 (breln1invE) =>
% 99.06/13.35 ((
% 99.06/13.35 (breln1compprop) =>
% 99.06/13.35 ((
% 99.06/13.35 (breln1compI) =>
% 99.06/13.35 ((
% 99.06/13.35 (breln1compE) =>
% 99.06/13.35 ((
% 99.06/13.35 (breln1compEex) =>
% 99.06/13.35 ((
% 99.06/13.35 (breln1unionprop) =>
% 99.06/13.35 ((
% 99.06/13.35 (breln1unionIL) =>
% 99.06/13.35 ((
% 99.06/13.35 (breln1unionIR) =>
% 99.06/13.35 ((
% 99.06/13.35 (breln1unionI) =>
% 99.06/13.35 ((
% 99.06/13.35 (breln1unionE) =>
% 99.06/13.35 ((
% 99.06/13.35 (breln1unionEcases) =>
% 99.06/13.35 ((
% 99.06/13.35 (breln1unionCommutes) =>
% 99.06/13.35 ((
% 99.06/13.35 (woz2Ex) =>
% 99.06/13.35 ((
% 99.06/13.35 (woz2W) =>
% 99.06/13.35 ((
% 99.06/13.35 (woz2A) =>
% 99.06/13.35 ((
% 99.06/13.35 (woz2B) =>
% 99.06/13.35 ((
% 99.06/13.35 (image1Ex) =>
% 99.06/13.35 ((
% 99.06/13.35 (image1Ex1) =>
% 99.06/13.35 ((
% 99.06/13.35 (image1Equiv) =>
% 99.06/13.35 ((
% 99.06/13.35 (image1E) =>
% 99.06/13.35 ((
% 99.06/13.35 (image1I) =>
% 99.06/13.35 ((
% 99.06/13.35 (injFuncInInjFuncSet) =>
% 99.06/13.35 ((
% 99.06/13.35 (injFuncSetFuncIn) =>
% 99.06/13.35 ((
% 99.06/13.35 (injFuncSetFuncInj) =>
% 99.06/13.35 ((
% 99.06/13.35 (!!) @ (
% 99.06/13.35 (('#B') @ (
% 99.06/13.35 !!) @
% 99.06/13.35 (
% 99.06/13.35 (
% 99.06/13.35 ('#B') @ (
% 99.06/13.35 (
% 99.06/13.35 ('#B') @ (
% 99.06/13.35 !!))) @
% 99.06/13.35 (
% 99.06/13.35 (
% 99.06/13.35 ('#S') @ (
% 99.06/13.35 (
% 99.06/13.35 ('#B') @ (
% 99.06/13.35 '#S') @
% 99.06/13.35 (
% 99.06/13.35 (
% 99.06/13.35 ('#B') @ (
% 99.06/13.35 (
% 99.06/13.35 ('#B') @ (
% 99.06/13.35 '#S'))) @
% 99.06/13.35 (
% 99.06/13.35 (
% 99.06/13.35 ('#B') @ (
% 99.06/13.35 (
% 99.06/13.35 ('#B') @ (
% 99.06/13.35 (
% 99.06/13.35 ('#B') @ (
% 99.06/13.35 =>))))) @
% 99.06/13.35 (
% 99.06/13.35 (
% 99.06/13.35 ('#B') @ (
% 99.06/13.35 (
% 99.06/13.35 ('#B') @ (
% 99.06/13.35 (
% 99.06/13.35 ('#C') @ in)))) @
% 99.06/13.35 surjFuncSet)))))))) @
% 99.06/13.35 (
% 99.06/13.35 (
% 99.06/13.35 ('#B') @ (
% 99.06/13.35 (
% 99.06/13.35 ('#B') @ (
% 99.06/13.35 (
% 99.06/13.35 ('#C') @ in)))) @
% 99.06/13.35 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.06/13.35 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl123])).
% 99.06/13.35 thf(zip_derived_cl158, plain,
% 99.06/13.35 (~ (((emptysetimpfalse) =>
% 99.06/13.35 (((notinemptyset) =>
% 99.06/13.35 (((exuE3e) =>
% 99.06/13.35 (((setext) =>
% 99.06/13.35 (((emptyI) =>
% 99.06/13.35 (((noeltsimpempty) =>
% 99.06/13.35 (((setbeta) =>
% 99.06/13.35 (((nonemptyE1) =>
% 99.06/13.35 (((nonemptyI) =>
% 99.06/13.35 (((nonemptyI1) =>
% 99.06/13.35 (((setadjoinIL) =>
% 99.06/13.35 (((in @ emptyset @
% 99.06/13.35 (setadjoin @ emptyset @ emptyset)) =>
% 99.06/13.35 (((setadjoinIR) =>
% 99.06/13.35 (((setadjoinE) =>
% 99.06/13.35 (((setadjoinOr) =>
% 99.06/13.35 (((setoftrueEq) =>
% 99.06/13.35 (((powersetI) =>
% 99.06/13.35 (((emptyinPowerset) =>
% 99.06/13.35 (((emptyInPowerset) =>
% 99.06/13.35 (((powersetE) =>
% 99.06/13.35 (((setunionI) =>
% 99.06/13.35 (((setunionE) =>
% 99.06/13.35 (((subPowSU) =>
% 99.06/13.35 (((exuE2) =>
% 99.06/13.35 (((nonemptyImpWitness) =>
% 99.06/13.35 (((uniqinunit) =>
% 99.06/13.35 (((notinsingleton) =>
% 99.06/13.35 (((eqinunit) =>
% 99.06/13.35 (((singletonsswitch) =>
% 99.06/13.35 (((upairsetE) =>
% 99.06/13.35 ((
% 99.06/13.35 (upairsetIL) =>
% 99.06/13.35 ((
% 99.06/13.35 (upairsetIR) =>
% 99.06/13.35 ((
% 99.06/13.35 (emptyE1) =>
% 99.06/13.35 ((
% 99.06/13.35 (vacuousDall) =>
% 99.06/13.35 ((
% 99.06/13.35 (quantDeMorgan1) =>
% 99.06/13.35 ((
% 99.06/13.35 (quantDeMorgan2) =>
% 99.06/13.35 ((
% 99.06/13.35 (quantDeMorgan3) =>
% 99.06/13.35 ((
% 99.06/13.35 (quantDeMorgan4) =>
% 99.06/13.35 ((
% 99.06/13.35 (prop2setI) =>
% 99.06/13.35 ((
% 99.06/13.35 (prop2set2propI) =>
% 99.06/13.35 ((
% 99.06/13.35 (notdexE) =>
% 99.06/13.35 ((
% 99.06/13.35 (notdallE) =>
% 99.06/13.35 ((
% 99.06/13.35 (exuI1) =>
% 99.06/13.35 ((
% 99.06/13.35 (exuI3) =>
% 99.06/13.35 ((
% 99.06/13.35 (exuI2) =>
% 99.06/13.35 ((
% 99.06/13.35 (inCongP) =>
% 99.06/13.35 ((
% 99.06/13.35 (in__Cong) =>
% 99.06/13.35 ((
% 99.06/13.35 (exuE3u) =>
% 99.06/13.35 ((
% 99.06/13.35 (exu__Cong) =>
% 99.06/13.35 ((
% 99.06/13.35 (setadjoin__Cong) =>
% 99.06/13.35 ((
% 99.06/13.35 (powerset__Cong) =>
% 99.06/13.35 ((
% 99.06/13.35 (setunion__Cong) =>
% 99.06/13.35 ((
% 99.06/13.35 (exuEu) =>
% 99.06/13.35 ((
% 99.06/13.35 (descr__Cong) =>
% 99.06/13.35 ((
% 99.06/13.35 (dsetconstr__Cong) =>
% 99.06/13.35 ((
% 99.06/13.35 (subsetI1) =>
% 99.06/13.35 ((
% 99.06/13.35 (eqimpsubset2) =>
% 99.06/13.35 ((
% 99.06/13.35 (eqimpsubset1) =>
% 99.06/13.35 ((
% 99.06/13.35 (subsetI2) =>
% 99.06/13.35 ((
% 99.06/13.35 (emptysetsubset) =>
% 99.06/13.35 ((
% 99.06/13.35 (subsetE) =>
% 99.06/13.35 ((
% 99.06/13.35 (subsetE2) =>
% 99.06/13.35 ((
% 99.06/13.35 (notsubsetI) =>
% 99.06/13.35 ((
% 99.06/13.35 (notequalI1) =>
% 99.06/13.35 ((
% 99.06/13.35 (notequalI2) =>
% 99.06/13.35 ((
% 99.06/13.35 (subsetRefl) =>
% 99.06/13.35 ((
% 99.06/13.35 (subsetTrans) =>
% 99.06/13.35 ((
% 99.06/13.35 (setadjoinSub) =>
% 99.06/13.35 ((
% 99.06/13.35 (setadjoinSub2) =>
% 99.06/13.35 ((
% 99.06/13.35 (subset2powerset) =>
% 99.06/13.35 ((
% 99.06/13.35 (setextsub) =>
% 99.06/13.35 ((
% 99.06/13.35 (subsetemptysetimpeq) =>
% 99.06/13.35 ((
% 99.06/13.35 (powersetI1) =>
% 99.06/13.35 ((
% 99.06/13.35 (powersetE1) =>
% 99.06/13.35 ((
% 99.06/13.35 (inPowerset) =>
% 99.06/13.35 ((
% 99.06/13.35 (powersetsubset) =>
% 99.06/13.35 ((
% 99.06/13.35 (sepInPowerset) =>
% 99.06/13.35 ((
% 99.06/13.35 (sepSubset) =>
% 99.06/13.35 ((
% 99.06/13.35 (binunionIL) =>
% 99.06/13.35 ((
% 99.06/13.35 (upairset2IR) =>
% 99.06/13.35 ((
% 99.06/13.35 (binunionIR) =>
% 99.06/13.35 ((
% 99.06/13.35 (binunionEcases) =>
% 99.06/13.35 ((
% 99.06/13.35 (binunionE) =>
% 99.06/13.35 ((
% 99.06/13.35 (binunionLsub) =>
% 99.06/13.35 ((
% 99.06/13.35 (binunionRsub) =>
% 99.06/13.35 ((
% 99.06/13.35 (binintersectI) =>
% 99.06/13.35 ((
% 99.06/13.35 (binintersectSubset5) =>
% 99.06/13.35 ((
% 99.06/13.35 (binintersectEL) =>
% 99.06/13.35 ((
% 99.06/13.35 (binintersectLsub) =>
% 99.06/13.35 ((
% 99.06/13.35 (binintersectSubset2) =>
% 99.06/13.35 ((
% 99.06/13.35 (binintersectSubset3) =>
% 99.06/13.35 ((
% 99.06/13.35 (binintersectER) =>
% 99.06/13.35 ((
% 99.06/13.35 (disjointsetsI1) =>
% 99.06/13.35 ((
% 99.06/13.35 (binintersectRsub) =>
% 99.06/13.35 ((
% 99.06/13.35 (binintersectSubset4) =>
% 99.06/13.35 ((
% 99.06/13.35 (binintersectSubset1) =>
% 99.06/13.35 ((
% 99.06/13.35 (bs114d) =>
% 99.06/13.35 ((
% 99.06/13.35 (setminusI) =>
% 99.06/13.35 ((
% 99.06/13.35 (setminusEL) =>
% 99.06/13.35 ((
% 99.06/13.35 (setminusER) =>
% 99.06/13.35 ((
% 99.06/13.35 (setminusSubset2) =>
% 99.06/13.35 ((
% 99.06/13.35 (setminusERneg) =>
% 99.06/13.35 ((
% 99.06/13.35 (setminusELneg) =>
% 99.06/13.35 ((
% 99.06/13.35 (setminusILneg) =>
% 99.06/13.35 ((
% 99.06/13.35 (setminusIRneg) =>
% 99.06/13.35 ((
% 99.06/13.35 (setminusLsub) =>
% 99.06/13.35 ((
% 99.06/13.35 (setminusSubset1) =>
% 99.06/13.35 ((
% 99.06/13.35 (symdiffE) =>
% 99.06/13.35 ((
% 99.06/13.35 (symdiffI1) =>
% 99.06/13.35 ((
% 99.06/13.35 (symdiffI2) =>
% 99.06/13.35 ((
% 99.06/13.35 (symdiffIneg1) =>
% 99.06/13.35 ((
% 99.06/13.35 (symdiffIneg2) =>
% 99.06/13.35 ((
% 99.06/13.35 (secondinupair) =>
% 99.06/13.35 ((
% 99.06/13.35 (setukpairIL) =>
% 99.06/13.35 ((
% 99.06/13.35 (setukpairIR) =>
% 99.06/13.35 ((
% 99.06/13.35 (kpairiskpair) =>
% 99.06/13.35 ((
% 99.06/13.35 (kpairp) =>
% 99.06/13.35 ((
% 99.06/13.35 (singletonsubset) =>
% 99.06/13.35 ((
% 99.06/13.35 (singletoninpowerset) =>
% 99.06/13.35 ((
% 99.06/13.35 (singletoninpowunion) =>
% 99.06/13.35 ((
% 99.06/13.35 (upairset2E) =>
% 99.06/13.35 ((
% 99.06/13.35 (upairsubunion) =>
% 99.06/13.35 ((
% 99.06/13.35 (upairinpowunion) =>
% 99.06/13.35 ((
% 99.06/13.35 (ubforcartprodlem1) =>
% 99.06/13.35 ((
% 99.06/13.35 (ubforcartprodlem2) =>
% 99.06/13.35 ((
% 99.06/13.35 (ubforcartprodlem3) =>
% 99.06/13.35 ((
% 99.06/13.35 (cartprodpairin) =>
% 99.06/13.35 ((
% 99.06/13.35 (cartprodmempair1) =>
% 99.06/13.35 ((
% 99.06/13.35 (cartprodmempair) =>
% 99.06/13.35 ((
% 99.06/13.35 (setunionE2) =>
% 99.06/13.35 ((
% 99.06/13.35 (setunionsingleton1) =>
% 99.06/13.35 ((
% 99.06/13.35 (setunionsingleton2) =>
% 99.06/13.35 ((
% 99.06/13.35 (setunionsingleton) =>
% 99.06/13.35 ((
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% 99.06/13.35 ((
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% 99.06/13.35 ((
% 99.06/13.35 (ex1I) =>
% 99.06/13.35 ((
% 99.06/13.35 (ex1I2) =>
% 99.06/13.35 ((
% 99.06/13.35 (singletonsuniq) =>
% 99.06/13.35 ((
% 99.06/13.35 (setukpairinjL1) =>
% 99.06/13.35 ((
% 99.06/13.35 (kfstsingleton) =>
% 99.06/13.35 ((
% 99.06/13.35 (theprop) =>
% 99.06/13.35 ((
% 99.06/13.35 (kfstpairEq) =>
% 99.06/13.35 ((
% 99.06/13.35 (cartprodfstin) =>
% 99.06/13.35 ((
% 99.06/13.35 (setukpairinjL2) =>
% 99.06/13.35 ((
% 99.06/13.35 (setukpairinjL) =>
% 99.06/13.35 ((
% 99.06/13.35 (setukpairinjR11) =>
% 99.06/13.35 ((
% 99.06/13.35 (setukpairinjR12) =>
% 99.06/13.35 ((
% 99.06/13.35 (setukpairinjR1) =>
% 99.06/13.35 ((
% 99.06/13.35 (upairequniteq) =>
% 99.06/13.35 ((
% 99.06/13.35 (setukpairinjR2) =>
% 99.06/13.35 ((
% 99.06/13.35 (setukpairinjR) =>
% 99.06/13.35 ((
% 99.06/13.35 (ksndsingleton) =>
% 99.06/13.35 ((
% 99.06/13.35 (ksndpairEq) =>
% 99.06/13.35 ((
% 99.06/13.35 (kpairsurjEq) =>
% 99.06/13.35 ((
% 99.06/13.35 (cartprodsndin) =>
% 99.06/13.35 ((
% 99.06/13.35 (cartprodpairmemEL) =>
% 99.06/13.35 ((
% 99.06/13.35 (cartprodpairmemER) =>
% 99.06/13.35 ((
% 99.06/13.35 (cartprodmempaircEq) =>
% 99.06/13.35 ((
% 99.06/13.35 (cartprodfstpairEq) =>
% 99.06/13.35 ((
% 99.06/13.35 (cartprodsndpairEq) =>
% 99.06/13.35 ((
% 99.06/13.35 (cartprodpairsurjEq) =>
% 99.06/13.35 ((
% 99.06/13.35 (dpsetconstrI) =>
% 99.06/13.35 ((
% 99.06/13.35 (dpsetconstrSub) =>
% 99.06/13.35 ((
% 99.06/13.35 (setOfPairsIsBReln) =>
% 99.06/13.35 ((
% 99.06/13.35 (dpsetconstrERa) =>
% 99.06/13.35 ((
% 99.06/13.35 (dpsetconstrEL1) =>
% 99.06/13.35 ((
% 99.06/13.35 (dpsetconstrEL2) =>
% 99.06/13.35 ((
% 99.06/13.35 (dpsetconstrER) =>
% 99.06/13.35 ((
% 99.06/13.35 (funcImageSingleton) =>
% 99.06/13.35 ((
% 99.06/13.35 (apProp) =>
% 99.06/13.35 ((
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% 99.06/13.35 ((
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% 99.06/13.35 ((
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% 99.06/13.35 ((
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% 99.06/13.35 ((
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% 99.06/13.35 ((
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% 99.06/13.35 ((
% 99.06/13.35 (lam2p) =>
% 99.06/13.35 ((
% 99.06/13.35 (brelnall1) =>
% 99.06/13.35 ((
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% 99.06/13.35 ((
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% 99.06/13.35 ((
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% 99.06/13.35 ((
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% 99.06/13.35 ((
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% 99.06/13.35 ((
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% 99.06/13.35 ((
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% 99.06/13.35 (woz13rule2) =>
% 99.06/13.35 ((
% 99.06/13.35 (woz13rule3) =>
% 99.06/13.35 ((
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% 99.06/13.35 (woz1_2) =>
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% 99.06/13.35 ((
% 99.06/13.35 (woz1_4) =>
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% 99.06/13.35 (woz1_5) =>
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% 99.06/13.35 ((
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% 99.06/13.35 ((
% 99.06/13.35 (breln1compprop) =>
% 99.06/13.35 ((
% 99.06/13.35 (breln1compI) =>
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% 99.06/13.35 ((
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% 99.06/13.35 ((
% 99.06/13.35 (breln1unionE) =>
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% 99.06/13.35 ((
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% 99.06/13.35 ((
% 99.06/13.35 (image1E) =>
% 99.06/13.35 ((
% 99.06/13.35 (image1I) =>
% 99.06/13.35 ((
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% 99.06/13.35 ((
% 99.06/13.35 (injFuncSetFuncIn) =>
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% 99.06/13.35 ((
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% 99.06/13.35 ((
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% 99.06/13.35 ((
% 99.06/13.35 (ubforcartprodlem2) =>
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% 99.06/13.35 (cartprodpairmemEL) =>
% 99.06/13.35 ((
% 99.06/13.35 (cartprodpairmemER) =>
% 99.06/13.35 ((
% 99.06/13.35 (cartprodmempaircEq) =>
% 99.06/13.35 ((
% 99.06/13.35 (cartprodfstpairEq) =>
% 99.06/13.35 ((
% 99.06/13.35 (cartprodsndpairEq) =>
% 99.06/13.35 ((
% 99.06/13.35 (cartprodpairsurjEq) =>
% 99.06/13.35 ((
% 99.06/13.35 (dpsetconstrI) =>
% 99.06/13.35 ((
% 99.06/13.35 (dpsetconstrSub) =>
% 99.06/13.35 ((
% 99.06/13.35 (setOfPairsIsBReln) =>
% 99.06/13.35 ((
% 99.06/13.35 (dpsetconstrERa) =>
% 99.06/13.35 ((
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% 99.06/13.35 ((
% 99.06/13.35 (dpsetconstrEL2) =>
% 99.06/13.35 ((
% 99.06/13.35 (dpsetconstrER) =>
% 99.06/13.35 ((
% 99.06/13.35 (funcImageSingleton) =>
% 99.06/13.35 ((
% 99.06/13.35 (apProp) =>
% 99.06/13.35 ((
% 99.06/13.35 (app) =>
% 99.06/13.35 ((
% 99.06/13.35 (infuncsetfunc) =>
% 99.06/13.35 ((
% 99.06/13.35 (ap2p) =>
% 99.06/13.35 ((
% 99.06/13.35 (funcinfuncset) =>
% 99.06/13.35 ((
% 99.06/13.35 (lamProp) =>
% 99.06/13.35 ((
% 99.06/13.35 (lamp) =>
% 99.06/13.35 ((
% 99.06/13.35 (lam2p) =>
% 99.06/13.35 ((
% 99.06/13.35 (brelnall1) =>
% 99.06/13.35 ((
% 99.06/13.35 (brelnall2) =>
% 99.06/13.35 ((
% 99.06/13.35 (ex1E2) =>
% 99.06/13.35 ((
% 99.06/13.35 (funcGraphProp1) =>
% 99.06/13.35 ((
% 99.06/13.35 (funcGraphProp3) =>
% 99.06/13.35 ((
% 99.06/13.35 (funcGraphProp2) =>
% 99.06/13.35 ((
% 99.06/13.35 (funcextLem) =>
% 99.06/13.35 ((
% 99.06/13.35 (funcGraphProp4) =>
% 99.06/13.35 ((
% 99.06/13.35 (subbreln) =>
% 99.06/13.35 ((
% 99.06/13.35 (eqbreln) =>
% 99.06/13.35 ((
% 99.06/13.35 (funcext) =>
% 99.06/13.35 ((
% 99.06/13.35 (funcext2) =>
% 99.06/13.35 ((
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% 99.06/13.35 ((
% 99.06/13.35 (ap2apEq2) =>
% 99.06/13.35 ((
% 99.06/13.35 (beta1) =>
% 99.06/13.35 ((
% 99.06/13.35 (eta1) =>
% 99.06/13.35 ((
% 99.06/13.35 (lam2lamEq) =>
% 99.06/13.35 ((
% 99.06/13.35 (beta2) =>
% 99.06/13.35 ((
% 99.06/13.35 (eta2) =>
% 99.06/13.35 ((
% 99.06/13.35 (iffalseProp1) =>
% 99.06/13.35 ((
% 99.06/13.35 (iffalseProp2) =>
% 99.06/13.35 ((
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% 99.06/13.35 ((
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% 99.06/13.35 ((
% 99.06/13.35 (ifp) =>
% 99.06/13.35 ((
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% 99.06/13.35 ((
% 99.06/13.35 (iftrue) =>
% 99.06/13.35 ((
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% 99.06/13.35 ((
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% 99.06/13.35 ((
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% 99.06/13.35 ((
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% 99.06/13.35 ((
% 99.06/13.35 (powersetTE1) =>
% 99.06/13.35 ((
% 99.06/13.35 (complementTI1) =>
% 99.06/13.35 ((
% 99.06/13.35 (complementTE1) =>
% 99.06/13.35 ((
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% 99.06/13.35 ((
% 99.06/13.35 (binintersectTERcontra) =>
% 99.06/13.35 ((
% 99.06/13.35 (contrasubsetT) =>
% 99.06/13.35 ((
% 99.06/13.35 (contrasubsetT1) =>
% 99.06/13.35 ((
% 99.06/13.35 (contrasubsetT2) =>
% 99.06/13.35 ((
% 99.06/13.35 (contrasubsetT3) =>
% 99.06/13.35 ((
% 99.06/13.35 (doubleComplementI1) =>
% 99.06/13.35 ((
% 99.06/13.35 (doubleComplementE1) =>
% 99.06/13.35 ((
% 99.06/13.35 (doubleComplementSub1) =>
% 99.06/13.35 ((
% 99.06/13.35 (doubleComplementSub2) =>
% 99.06/13.35 ((
% 99.06/13.35 (doubleComplementEq) =>
% 99.06/13.35 ((
% 99.06/13.35 (complementTnotintersectT) =>
% 99.06/13.35 ((
% 99.06/13.35 (complementImpComplementIntersect) =>
% 99.06/13.35 ((
% 99.06/13.35 (complementSubsetComplementIntersect) =>
% 99.06/13.35 ((
% 99.06/13.35 (complementInPowersetComplementIntersect) =>
% 99.06/13.35 ((
% 99.06/13.35 (contraSubsetComplement) =>
% 99.06/13.35 ((
% 99.06/13.35 (complementTcontraSubset) =>
% 99.06/13.35 ((
% 99.06/13.35 (binunionTILcontra) =>
% 99.06/13.35 ((
% 99.06/13.35 (binunionTIRcontra) =>
% 99.06/13.35 ((
% 99.06/13.35 (inIntersectImpInUnion) =>
% 99.06/13.35 ((
% 99.06/13.35 (inIntersectImpInUnion2) =>
% 99.06/13.35 ((
% 99.06/13.35 (inIntersectImpInIntersectUnions) =>
% 99.06/13.35 ((
% 99.06/13.35 (intersectInPowersetIntersectUnions) =>
% 99.06/13.35 ((
% 99.06/13.35 (inComplementUnionImpNotIn1) =>
% 99.06/13.35 ((
% 99.06/13.35 (inComplementUnionImpInComplement1) =>
% 99.06/13.35 ((
% 99.06/13.35 (binunionTE) =>
% 99.06/13.35 ((
% 99.06/13.35 (binunionTEcontra) =>
% 99.06/13.35 ((
% 99.06/13.35 (demorgan2a1) =>
% 99.06/13.35 ((
% 99.06/13.35 (complementUnionInPowersetComplement) =>
% 99.06/13.35 ((
% 99.06/13.35 (demorgan2a2) =>
% 99.06/13.35 ((
% 99.06/13.35 (demorgan1a) =>
% 99.06/13.35 ((
% 99.06/13.35 (demorgan1b) =>
% 99.06/13.35 ((
% 99.06/13.35 (demorgan1) =>
% 99.06/13.35 ((
% 99.06/13.35 (demorgan2a) =>
% 99.06/13.35 ((
% 99.06/13.35 (demorgan2b2) =>
% 99.06/13.35 ((
% 99.06/13.35 (demorgan2b) =>
% 99.06/13.35 ((
% 99.06/13.35 (demorgan2) =>
% 99.06/13.35 ((
% 99.06/13.35 (woz13rule0) =>
% 99.06/13.35 ((
% 99.06/13.35 (woz13rule1) =>
% 99.06/13.35 ((
% 99.06/13.35 (woz13rule2) =>
% 99.06/13.35 ((
% 99.06/13.35 (woz13rule3) =>
% 99.06/13.35 ((
% 99.06/13.35 (woz13rule4) =>
% 99.06/13.35 ((
% 99.06/13.35 (woz1_1) =>
% 99.06/13.35 ((
% 99.06/13.35 (woz1_2) =>
% 99.06/13.35 ((
% 99.06/13.35 (woz1_3) =>
% 99.06/13.35 ((
% 99.06/13.35 (woz1_4) =>
% 99.06/13.35 ((
% 99.06/13.35 (woz1_5) =>
% 99.06/13.35 ((
% 99.06/13.35 (breln1all2) =>
% 99.06/13.35 ((
% 99.06/13.35 (breln1SetBreln1) =>
% 99.06/13.35 ((
% 99.06/13.35 (choice2fnsingleton) =>
% 99.06/13.35 ((
% 99.06/13.35 (setOfPairsIsBReln1) =>
% 99.06/13.35 ((
% 99.06/13.35 (breln1all1) =>
% 99.06/13.35 ((
% 99.06/13.35 (subbreln1) =>
% 99.06/13.35 ((
% 99.06/13.35 (eqbreln1) =>
% 99.06/13.35 ((
% 99.06/13.35 (breln1invprop) =>
% 99.06/13.35 ((
% 99.06/13.35 (breln1invI) =>
% 99.06/13.35 ((
% 99.06/13.35 (breln1invE) =>
% 99.06/13.35 ((
% 99.06/13.35 (breln1compprop) =>
% 99.06/13.35 ((
% 99.06/13.35 (breln1compI) =>
% 99.06/13.35 ((
% 99.06/13.35 (breln1compE) =>
% 99.06/13.35 ((
% 99.06/13.35 (breln1compEex) =>
% 99.06/13.35 ((
% 99.06/13.35 (breln1unionprop) =>
% 99.06/13.35 ((
% 99.06/13.35 (breln1unionIL) =>
% 99.06/13.35 ((
% 99.06/13.35 (breln1unionIR) =>
% 99.06/13.35 ((
% 99.06/13.35 (breln1unionI) =>
% 99.06/13.35 ((
% 99.06/13.35 (breln1unionE) =>
% 99.06/13.35 ((
% 99.06/13.35 (breln1unionEcases) =>
% 99.06/13.35 ((
% 99.06/13.35 (breln1unionCommutes) =>
% 99.06/13.35 ((
% 99.06/13.35 (woz2Ex) =>
% 99.06/13.35 ((
% 99.06/13.35 (woz2W) =>
% 99.06/13.35 ((
% 99.06/13.35 (woz2A) =>
% 99.06/13.35 ((
% 99.06/13.35 (woz2B) =>
% 99.06/13.35 ((
% 99.06/13.35 (image1Ex) =>
% 99.06/13.35 ((
% 99.06/13.35 (image1Ex1) =>
% 99.06/13.35 ((
% 99.06/13.35 (image1Equiv) =>
% 99.06/13.35 ((
% 99.06/13.35 (image1E) =>
% 99.06/13.35 ((
% 99.06/13.35 (image1I) =>
% 99.06/13.35 ((
% 99.06/13.35 (injFuncInInjFuncSet) =>
% 99.06/13.35 ((
% 99.06/13.35 (injFuncSetFuncIn) =>
% 99.06/13.35 ((
% 99.06/13.35 (injFuncSetFuncInj) =>
% 99.06/13.35 ((
% 99.06/13.35 (!!) @ (
% 99.06/13.35 (('#B') @ (
% 99.06/13.35 !!) @
% 99.06/13.35 (
% 99.06/13.35 (
% 99.06/13.35 ('#B') @ (
% 99.06/13.35 (
% 99.06/13.35 ('#B') @ (
% 99.06/13.35 !!))) @
% 99.06/13.35 (
% 99.06/13.35 (
% 99.06/13.35 ('#S') @ (
% 99.06/13.35 (
% 99.06/13.35 ('#B') @ (
% 99.06/13.35 '#S') @
% 99.06/13.35 (
% 99.06/13.35 (
% 99.06/13.35 ('#B') @ (
% 99.06/13.35 (
% 99.06/13.35 ('#B') @ (
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% 99.06/13.35 (
% 99.06/13.35 (
% 99.06/13.35 ('#B') @ (
% 99.06/13.35 (
% 99.06/13.35 ('#B') @ (
% 99.06/13.35 (
% 99.06/13.35 ('#B') @ (
% 99.06/13.35 =>))))) @
% 99.06/13.35 (
% 99.06/13.35 (
% 99.06/13.35 ('#B') @ (
% 99.06/13.35 (
% 99.06/13.35 ('#B') @ (
% 99.06/13.35 (
% 99.06/13.35 ('#C') @ in)))) @
% 99.06/13.35 surjFuncSet)))))))) @
% 99.06/13.35 (
% 99.06/13.35 (
% 99.06/13.35 ('#B') @ (
% 99.06/13.35 (
% 99.06/13.35 ('#B') @ (
% 99.06/13.35 (
% 99.06/13.35 ('#C') @ in)))) @
% 99.06/13.35 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.06/13.35 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl158])).
% 99.06/13.35 thf(zip_derived_cl189, plain,
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% 99.06/13.35 (((noeltsimpempty) =>
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% 99.06/13.35 (((nonemptyI1) =>
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% 99.06/13.35 (((in @ emptyset @
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% 99.06/13.35 (((setadjoinIR) =>
% 99.06/13.35 (((setadjoinE) =>
% 99.06/13.35 (((setadjoinOr) =>
% 99.06/13.35 (((setoftrueEq) =>
% 99.06/13.35 (((powersetI) =>
% 99.06/13.35 (((emptyinPowerset) =>
% 99.06/13.35 (((emptyInPowerset) =>
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% 99.06/13.35 (((setunionI) =>
% 99.06/13.35 (((setunionE) =>
% 99.06/13.35 (((subPowSU) =>
% 99.06/13.35 (((exuE2) =>
% 99.06/13.35 (((nonemptyImpWitness) =>
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% 99.06/13.35 (((upairsetIL) =>
% 99.06/13.35 (((upairsetIR) =>
% 99.06/13.35 ((
% 99.06/13.35 (emptyE1) =>
% 99.06/13.35 ((
% 99.06/13.35 (vacuousDall) =>
% 99.06/13.35 ((
% 99.06/13.35 (quantDeMorgan1) =>
% 99.06/13.35 ((
% 99.06/13.35 (quantDeMorgan2) =>
% 99.06/13.35 ((
% 99.06/13.35 (quantDeMorgan3) =>
% 99.06/13.35 ((
% 99.06/13.35 (quantDeMorgan4) =>
% 99.06/13.35 ((
% 99.06/13.35 (prop2setI) =>
% 99.06/13.35 ((
% 99.06/13.35 (prop2set2propI) =>
% 99.06/13.35 ((
% 99.06/13.35 (notdexE) =>
% 99.06/13.35 ((
% 99.06/13.35 (notdallE) =>
% 99.06/13.35 ((
% 99.06/13.35 (exuI1) =>
% 99.06/13.35 ((
% 99.06/13.35 (exuI3) =>
% 99.06/13.35 ((
% 99.06/13.35 (exuI2) =>
% 99.06/13.35 ((
% 99.06/13.35 (inCongP) =>
% 99.06/13.35 ((
% 99.06/13.35 (in__Cong) =>
% 99.06/13.35 ((
% 99.06/13.35 (exuE3u) =>
% 99.06/13.35 ((
% 99.06/13.35 (exu__Cong) =>
% 99.06/13.35 ((
% 99.06/13.35 (setadjoin__Cong) =>
% 99.06/13.35 ((
% 99.06/13.35 (powerset__Cong) =>
% 99.06/13.35 ((
% 99.06/13.35 (setunion__Cong) =>
% 99.06/13.35 ((
% 99.06/13.35 (exuEu) =>
% 99.06/13.35 ((
% 99.06/13.35 (descr__Cong) =>
% 99.06/13.35 ((
% 99.06/13.35 (dsetconstr__Cong) =>
% 99.06/13.35 ((
% 99.06/13.35 (subsetI1) =>
% 99.06/13.35 ((
% 99.06/13.35 (eqimpsubset2) =>
% 99.06/13.35 ((
% 99.06/13.35 (eqimpsubset1) =>
% 99.06/13.35 ((
% 99.06/13.35 (subsetI2) =>
% 99.06/13.35 ((
% 99.06/13.35 (emptysetsubset) =>
% 99.06/13.35 ((
% 99.06/13.35 (subsetE) =>
% 99.06/13.35 ((
% 99.06/13.35 (subsetE2) =>
% 99.06/13.35 ((
% 99.06/13.35 (notsubsetI) =>
% 99.06/13.35 ((
% 99.06/13.35 (notequalI1) =>
% 99.06/13.35 ((
% 99.06/13.35 (notequalI2) =>
% 99.06/13.35 ((
% 99.06/13.35 (subsetRefl) =>
% 99.06/13.35 ((
% 99.06/13.35 (subsetTrans) =>
% 99.06/13.35 ((
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% 99.06/13.35 ((
% 99.06/13.35 (setadjoinSub2) =>
% 99.06/13.35 ((
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% 99.06/13.35 ((
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% 99.06/13.35 ((
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% 99.06/13.35 ((
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% 99.06/13.35 ((
% 99.06/13.35 (powersetE1) =>
% 99.06/13.35 ((
% 99.06/13.35 (inPowerset) =>
% 99.06/13.35 ((
% 99.06/13.35 (powersetsubset) =>
% 99.06/13.35 ((
% 99.06/13.35 (sepInPowerset) =>
% 99.06/13.35 ((
% 99.06/13.35 (sepSubset) =>
% 99.06/13.35 ((
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% 99.06/13.35 ((
% 99.06/13.35 (upairset2IR) =>
% 99.06/13.35 ((
% 99.06/13.35 (binunionIR) =>
% 99.06/13.35 ((
% 99.06/13.35 (binunionEcases) =>
% 99.06/13.35 ((
% 99.06/13.35 (binunionE) =>
% 99.06/13.35 ((
% 99.06/13.35 (binunionLsub) =>
% 99.06/13.35 ((
% 99.06/13.35 (binunionRsub) =>
% 99.06/13.35 ((
% 99.06/13.35 (binintersectI) =>
% 99.06/13.35 ((
% 99.06/13.35 (binintersectSubset5) =>
% 99.06/13.35 ((
% 99.06/13.35 (binintersectEL) =>
% 99.06/13.35 ((
% 99.06/13.35 (binintersectLsub) =>
% 99.06/13.35 ((
% 99.06/13.35 (binintersectSubset2) =>
% 99.06/13.35 ((
% 99.06/13.35 (binintersectSubset3) =>
% 99.06/13.35 ((
% 99.06/13.35 (binintersectER) =>
% 99.06/13.35 ((
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% 99.06/13.35 ((
% 99.06/13.35 (binintersectRsub) =>
% 99.06/13.35 ((
% 99.06/13.35 (binintersectSubset4) =>
% 99.06/13.35 ((
% 99.06/13.35 (binintersectSubset1) =>
% 99.06/13.35 ((
% 99.06/13.35 (bs114d) =>
% 99.06/13.35 ((
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% 99.06/13.35 ((
% 99.06/13.35 (setminusEL) =>
% 99.06/13.35 ((
% 99.06/13.35 (setminusER) =>
% 99.06/13.35 ((
% 99.06/13.35 (setminusSubset2) =>
% 99.06/13.35 ((
% 99.06/13.35 (setminusERneg) =>
% 99.06/13.35 ((
% 99.06/13.35 (setminusELneg) =>
% 99.06/13.35 ((
% 99.06/13.35 (setminusILneg) =>
% 99.06/13.35 ((
% 99.06/13.35 (setminusIRneg) =>
% 99.06/13.35 ((
% 99.06/13.35 (setminusLsub) =>
% 99.06/13.35 ((
% 99.06/13.35 (setminusSubset1) =>
% 99.06/13.35 ((
% 99.06/13.35 (symdiffE) =>
% 99.06/13.35 ((
% 99.06/13.35 (symdiffI1) =>
% 99.06/13.35 ((
% 99.06/13.35 (symdiffI2) =>
% 99.06/13.35 ((
% 99.06/13.35 (symdiffIneg1) =>
% 99.06/13.35 ((
% 99.06/13.35 (symdiffIneg2) =>
% 99.06/13.35 ((
% 99.06/13.35 (secondinupair) =>
% 99.06/13.35 ((
% 99.06/13.35 (setukpairIL) =>
% 99.06/13.35 ((
% 99.06/13.35 (setukpairIR) =>
% 99.06/13.35 ((
% 99.06/13.35 (kpairiskpair) =>
% 99.06/13.35 ((
% 99.06/13.35 (kpairp) =>
% 99.06/13.35 ((
% 99.06/13.35 (singletonsubset) =>
% 99.06/13.35 ((
% 99.06/13.35 (singletoninpowerset) =>
% 99.06/13.35 ((
% 99.06/13.35 (singletoninpowunion) =>
% 99.06/13.35 ((
% 99.06/13.35 (upairset2E) =>
% 99.06/13.35 ((
% 99.06/13.35 (upairsubunion) =>
% 99.06/13.35 ((
% 99.06/13.35 (upairinpowunion) =>
% 99.06/13.35 ((
% 99.06/13.35 (ubforcartprodlem1) =>
% 99.06/13.35 ((
% 99.06/13.35 (ubforcartprodlem2) =>
% 99.06/13.35 ((
% 99.06/13.35 (ubforcartprodlem3) =>
% 99.06/13.35 ((
% 99.06/13.35 (cartprodpairin) =>
% 99.06/13.35 ((
% 99.06/13.35 (cartprodmempair1) =>
% 99.06/13.35 ((
% 99.06/13.35 (cartprodmempair) =>
% 99.06/13.35 ((
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% 99.06/13.35 ((
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% 99.06/13.35 ((
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% 99.06/13.35 ((
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% 99.06/13.35 ((
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% 99.06/13.35 (setukpairinjL2) =>
% 99.06/13.35 ((
% 99.06/13.35 (setukpairinjL) =>
% 99.06/13.35 ((
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% 99.06/13.35 ((
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% 99.06/13.35 ((
% 99.06/13.35 (cartprodpairmemER) =>
% 99.06/13.35 ((
% 99.06/13.35 (cartprodmempaircEq) =>
% 99.06/13.35 ((
% 99.06/13.35 (cartprodfstpairEq) =>
% 99.06/13.35 ((
% 99.06/13.35 (cartprodsndpairEq) =>
% 99.06/13.35 ((
% 99.06/13.35 (cartprodpairsurjEq) =>
% 99.06/13.35 ((
% 99.06/13.35 (dpsetconstrI) =>
% 99.06/13.35 ((
% 99.06/13.35 (dpsetconstrSub) =>
% 99.06/13.35 ((
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% 99.06/13.35 ((
% 99.06/13.35 (dpsetconstrEL2) =>
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% 99.06/13.35 (dpsetconstrER) =>
% 99.06/13.35 ((
% 99.06/13.35 (funcImageSingleton) =>
% 99.06/13.35 ((
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% 99.06/13.35 ((
% 99.06/13.35 (app) =>
% 99.06/13.35 ((
% 99.06/13.35 (infuncsetfunc) =>
% 99.06/13.35 ((
% 99.06/13.35 (ap2p) =>
% 99.06/13.35 ((
% 99.06/13.35 (funcinfuncset) =>
% 99.06/13.35 ((
% 99.06/13.35 (lamProp) =>
% 99.06/13.35 ((
% 99.06/13.35 (lamp) =>
% 99.06/13.35 ((
% 99.06/13.35 (lam2p) =>
% 99.06/13.35 ((
% 99.06/13.35 (brelnall1) =>
% 99.06/13.35 ((
% 99.06/13.35 (brelnall2) =>
% 99.06/13.35 ((
% 99.06/13.35 (ex1E2) =>
% 99.06/13.35 ((
% 99.06/13.35 (funcGraphProp1) =>
% 99.06/13.35 ((
% 99.06/13.35 (funcGraphProp3) =>
% 99.06/13.35 ((
% 99.06/13.35 (funcGraphProp2) =>
% 99.06/13.35 ((
% 99.06/13.35 (funcextLem) =>
% 99.06/13.35 ((
% 99.06/13.35 (funcGraphProp4) =>
% 99.06/13.35 ((
% 99.06/13.35 (subbreln) =>
% 99.06/13.35 ((
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% 99.06/13.35 (funcext2) =>
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% 99.06/13.35 (ap2apEq2) =>
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% 99.06/13.35 ((
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% 99.06/13.35 (lam2lamEq) =>
% 99.06/13.35 ((
% 99.06/13.35 (beta2) =>
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% 99.06/13.35 ((
% 99.06/13.35 (iffalseProp2) =>
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% 99.06/13.35 ((
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% 99.06/13.35 ((
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% 99.06/13.35 (iftrue) =>
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% 99.06/13.35 ((
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% 99.06/13.35 ((
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% 99.06/13.35 ((
% 99.06/13.35 (complementTE1) =>
% 99.06/13.35 ((
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% 99.06/13.35 ((
% 99.06/13.35 (binintersectTERcontra) =>
% 99.06/13.35 ((
% 99.06/13.35 (contrasubsetT) =>
% 99.06/13.35 ((
% 99.06/13.35 (contrasubsetT1) =>
% 99.06/13.35 ((
% 99.06/13.35 (contrasubsetT2) =>
% 99.06/13.35 ((
% 99.06/13.35 (contrasubsetT3) =>
% 99.06/13.35 ((
% 99.06/13.35 (doubleComplementI1) =>
% 99.06/13.35 ((
% 99.06/13.35 (doubleComplementE1) =>
% 99.06/13.35 ((
% 99.06/13.35 (doubleComplementSub1) =>
% 99.06/13.35 ((
% 99.06/13.35 (doubleComplementSub2) =>
% 99.06/13.35 ((
% 99.06/13.35 (doubleComplementEq) =>
% 99.06/13.35 ((
% 99.06/13.35 (complementTnotintersectT) =>
% 99.06/13.35 ((
% 99.06/13.35 (complementImpComplementIntersect) =>
% 99.06/13.35 ((
% 99.06/13.35 (complementSubsetComplementIntersect) =>
% 99.06/13.35 ((
% 99.06/13.35 (complementInPowersetComplementIntersect) =>
% 99.06/13.35 ((
% 99.06/13.35 (contraSubsetComplement) =>
% 99.06/13.35 ((
% 99.06/13.35 (complementTcontraSubset) =>
% 99.06/13.35 ((
% 99.06/13.35 (binunionTILcontra) =>
% 99.06/13.35 ((
% 99.06/13.35 (binunionTIRcontra) =>
% 99.06/13.35 ((
% 99.06/13.35 (inIntersectImpInUnion) =>
% 99.06/13.35 ((
% 99.06/13.35 (inIntersectImpInUnion2) =>
% 99.06/13.35 ((
% 99.06/13.35 (inIntersectImpInIntersectUnions) =>
% 99.06/13.35 ((
% 99.06/13.35 (intersectInPowersetIntersectUnions) =>
% 99.06/13.35 ((
% 99.06/13.35 (inComplementUnionImpNotIn1) =>
% 99.06/13.35 ((
% 99.06/13.35 (inComplementUnionImpInComplement1) =>
% 99.06/13.35 ((
% 99.06/13.35 (binunionTE) =>
% 99.06/13.35 ((
% 99.06/13.35 (binunionTEcontra) =>
% 99.06/13.35 ((
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% 99.06/13.35 ((
% 99.06/13.35 (complementUnionInPowersetComplement) =>
% 99.06/13.35 ((
% 99.06/13.35 (demorgan2a2) =>
% 99.06/13.35 ((
% 99.06/13.35 (demorgan1a) =>
% 99.06/13.35 ((
% 99.06/13.35 (demorgan1b) =>
% 99.06/13.35 ((
% 99.06/13.35 (demorgan1) =>
% 99.06/13.35 ((
% 99.06/13.35 (demorgan2a) =>
% 99.06/13.35 ((
% 99.06/13.35 (demorgan2b2) =>
% 99.06/13.35 ((
% 99.06/13.35 (demorgan2b) =>
% 99.06/13.35 ((
% 99.06/13.35 (demorgan2) =>
% 99.06/13.35 ((
% 99.06/13.35 (woz13rule0) =>
% 99.06/13.35 ((
% 99.06/13.35 (woz13rule1) =>
% 99.06/13.35 ((
% 99.06/13.35 (woz13rule2) =>
% 99.06/13.35 ((
% 99.06/13.35 (woz13rule3) =>
% 99.06/13.35 ((
% 99.06/13.35 (woz13rule4) =>
% 99.06/13.35 ((
% 99.06/13.35 (woz1_1) =>
% 99.06/13.35 ((
% 99.06/13.35 (woz1_2) =>
% 99.06/13.35 ((
% 99.06/13.35 (woz1_3) =>
% 99.06/13.35 ((
% 99.06/13.35 (woz1_4) =>
% 99.06/13.35 ((
% 99.06/13.35 (woz1_5) =>
% 99.06/13.35 ((
% 99.06/13.35 (breln1all2) =>
% 99.06/13.35 ((
% 99.06/13.35 (breln1SetBreln1) =>
% 99.06/13.35 ((
% 99.06/13.35 (choice2fnsingleton) =>
% 99.06/13.35 ((
% 99.06/13.35 (setOfPairsIsBReln1) =>
% 99.06/13.35 ((
% 99.06/13.35 (breln1all1) =>
% 99.06/13.35 ((
% 99.06/13.35 (subbreln1) =>
% 99.06/13.35 ((
% 99.06/13.35 (eqbreln1) =>
% 99.06/13.35 ((
% 99.06/13.35 (breln1invprop) =>
% 99.06/13.35 ((
% 99.06/13.35 (breln1invI) =>
% 99.06/13.35 ((
% 99.06/13.35 (breln1invE) =>
% 99.06/13.35 ((
% 99.06/13.35 (breln1compprop) =>
% 99.06/13.35 ((
% 99.06/13.35 (breln1compI) =>
% 99.06/13.35 ((
% 99.06/13.35 (breln1compE) =>
% 99.06/13.35 ((
% 99.06/13.35 (breln1compEex) =>
% 99.06/13.35 ((
% 99.06/13.35 (breln1unionprop) =>
% 99.06/13.35 ((
% 99.06/13.35 (breln1unionIL) =>
% 99.06/13.35 ((
% 99.06/13.35 (breln1unionIR) =>
% 99.06/13.35 ((
% 99.06/13.35 (breln1unionI) =>
% 99.06/13.35 ((
% 99.06/13.35 (breln1unionE) =>
% 99.06/13.35 ((
% 99.06/13.35 (breln1unionEcases) =>
% 99.06/13.35 ((
% 99.06/13.35 (breln1unionCommutes) =>
% 99.06/13.35 ((
% 99.06/13.35 (woz2Ex) =>
% 99.06/13.35 ((
% 99.06/13.35 (woz2W) =>
% 99.06/13.35 ((
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% 99.06/13.35 ((
% 99.06/13.35 (woz2B) =>
% 99.06/13.35 ((
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% 99.06/13.35 ((
% 99.06/13.35 (image1Ex1) =>
% 99.06/13.35 ((
% 99.06/13.35 (image1Equiv) =>
% 99.06/13.35 ((
% 99.06/13.35 (image1E) =>
% 99.06/13.35 ((
% 99.06/13.35 (image1I) =>
% 99.06/13.35 ((
% 99.06/13.35 (injFuncInInjFuncSet) =>
% 99.06/13.35 ((
% 99.06/13.35 (injFuncSetFuncIn) =>
% 99.06/13.35 ((
% 99.06/13.35 (injFuncSetFuncInj) =>
% 99.06/13.35 ((
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% 99.06/13.35 (
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% 99.06/13.35 (
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% 99.06/13.35 (
% 99.06/13.35 (
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% 99.06/13.35 (
% 99.06/13.35 (
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% 99.06/13.35 (
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% 99.06/13.35 (
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% 99.06/13.35 (
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% 99.06/13.35 surjFuncSet)))))))) @
% 99.06/13.35 (
% 99.06/13.35 (
% 99.06/13.35 ('#B') @ (
% 99.06/13.35 (
% 99.06/13.35 ('#B') @ (
% 99.06/13.35 (
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% 99.06/13.35 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.06/13.35 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl174])).
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% 99.06/13.35 ((
% 99.06/13.35 (quantDeMorgan2) =>
% 99.06/13.35 ((
% 99.06/13.35 (quantDeMorgan3) =>
% 99.06/13.35 ((
% 99.06/13.35 (quantDeMorgan4) =>
% 99.06/13.35 ((
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% 99.06/13.35 ((
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% 99.06/13.35 ((
% 99.06/13.35 (notdallE) =>
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% 99.06/13.35 ((
% 99.06/13.35 (exuI3) =>
% 99.06/13.35 ((
% 99.06/13.35 (exuI2) =>
% 99.06/13.35 ((
% 99.06/13.35 (inCongP) =>
% 99.06/13.35 ((
% 99.06/13.35 (in__Cong) =>
% 99.06/13.35 ((
% 99.06/13.35 (exuE3u) =>
% 99.06/13.35 ((
% 99.06/13.35 (exu__Cong) =>
% 99.06/13.35 ((
% 99.06/13.35 (setadjoin__Cong) =>
% 99.06/13.35 ((
% 99.06/13.35 (powerset__Cong) =>
% 99.06/13.35 ((
% 99.06/13.35 (setunion__Cong) =>
% 99.06/13.35 ((
% 99.06/13.35 (exuEu) =>
% 99.06/13.35 ((
% 99.06/13.35 (descr__Cong) =>
% 99.06/13.35 ((
% 99.06/13.35 (dsetconstr__Cong) =>
% 99.06/13.35 ((
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% 99.06/13.35 ((
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% 99.06/13.35 ((
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% 99.06/13.35 ((
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% 99.06/13.35 ((
% 99.06/13.35 (subsetE2) =>
% 99.06/13.35 ((
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% 99.06/13.35 ((
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% 99.06/13.35 ((
% 99.06/13.35 (notequalI2) =>
% 99.06/13.35 ((
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% 99.06/13.35 ((
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% 99.06/13.35 ((
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% 99.06/13.35 ((
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% 99.06/13.35 ((
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% 99.06/13.35 ((
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% 99.06/13.35 ((
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% 99.06/13.35 ((
% 99.06/13.35 (binunionIR) =>
% 99.06/13.35 ((
% 99.06/13.35 (binunionEcases) =>
% 99.06/13.35 ((
% 99.06/13.35 (binunionE) =>
% 99.06/13.35 ((
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% 99.06/13.35 ((
% 99.06/13.35 (binunionRsub) =>
% 99.06/13.35 ((
% 99.06/13.35 (binintersectI) =>
% 99.06/13.35 ((
% 99.06/13.35 (binintersectSubset5) =>
% 99.06/13.35 ((
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% 99.06/13.35 ((
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% 99.06/13.35 ((
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% 99.06/13.35 ((
% 99.06/13.35 (binintersectSubset3) =>
% 99.06/13.35 ((
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% 99.06/13.35 ((
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% 99.06/13.35 ((
% 99.06/13.35 (binintersectSubset1) =>
% 99.06/13.35 ((
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% 99.06/13.35 ((
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% 99.06/13.35 ((
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% 99.06/13.35 ((
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% 99.06/13.35 ((
% 99.06/13.35 (setminusERneg) =>
% 99.06/13.35 ((
% 99.06/13.35 (setminusELneg) =>
% 99.06/13.35 ((
% 99.06/13.35 (setminusILneg) =>
% 99.06/13.35 ((
% 99.06/13.35 (setminusIRneg) =>
% 99.06/13.35 ((
% 99.06/13.35 (setminusLsub) =>
% 99.06/13.35 ((
% 99.06/13.35 (setminusSubset1) =>
% 99.06/13.35 ((
% 99.06/13.35 (symdiffE) =>
% 99.06/13.35 ((
% 99.06/13.35 (symdiffI1) =>
% 99.06/13.35 ((
% 99.06/13.35 (symdiffI2) =>
% 99.06/13.35 ((
% 99.06/13.35 (symdiffIneg1) =>
% 99.06/13.35 ((
% 99.06/13.35 (symdiffIneg2) =>
% 99.06/13.35 ((
% 99.06/13.35 (secondinupair) =>
% 99.06/13.35 ((
% 99.06/13.35 (setukpairIL) =>
% 99.06/13.35 ((
% 99.06/13.35 (setukpairIR) =>
% 99.06/13.35 ((
% 99.06/13.35 (kpairiskpair) =>
% 99.06/13.35 ((
% 99.06/13.35 (kpairp) =>
% 99.06/13.35 ((
% 99.06/13.35 (singletonsubset) =>
% 99.06/13.35 ((
% 99.06/13.35 (singletoninpowerset) =>
% 99.06/13.35 ((
% 99.06/13.35 (singletoninpowunion) =>
% 99.06/13.35 ((
% 99.06/13.35 (upairset2E) =>
% 99.06/13.35 ((
% 99.06/13.35 (upairsubunion) =>
% 99.06/13.35 ((
% 99.06/13.35 (upairinpowunion) =>
% 99.06/13.35 ((
% 99.06/13.35 (ubforcartprodlem1) =>
% 99.06/13.35 ((
% 99.06/13.35 (ubforcartprodlem2) =>
% 99.06/13.35 ((
% 99.06/13.35 (ubforcartprodlem3) =>
% 99.06/13.35 ((
% 99.06/13.35 (cartprodpairin) =>
% 99.06/13.35 ((
% 99.06/13.35 (cartprodmempair1) =>
% 99.06/13.35 ((
% 99.06/13.35 (cartprodmempair) =>
% 99.06/13.35 ((
% 99.06/13.35 (setunionE2) =>
% 99.06/13.35 ((
% 99.06/13.35 (setunionsingleton1) =>
% 99.06/13.35 ((
% 99.06/13.35 (setunionsingleton2) =>
% 99.06/13.35 ((
% 99.06/13.35 (setunionsingleton) =>
% 99.06/13.35 ((
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% 99.06/13.35 ((
% 99.06/13.35 (ex1E1) =>
% 99.06/13.35 ((
% 99.06/13.35 (ex1I) =>
% 99.06/13.35 ((
% 99.06/13.35 (ex1I2) =>
% 99.06/13.35 ((
% 99.06/13.35 (singletonsuniq) =>
% 99.06/13.35 ((
% 99.06/13.35 (setukpairinjL1) =>
% 99.06/13.35 ((
% 99.06/13.35 (kfstsingleton) =>
% 99.06/13.35 ((
% 99.06/13.35 (theprop) =>
% 99.06/13.35 ((
% 99.06/13.35 (kfstpairEq) =>
% 99.06/13.35 ((
% 99.06/13.35 (cartprodfstin) =>
% 99.06/13.35 ((
% 99.06/13.35 (setukpairinjL2) =>
% 99.06/13.35 ((
% 99.06/13.35 (setukpairinjL) =>
% 99.06/13.35 ((
% 99.06/13.35 (setukpairinjR11) =>
% 99.06/13.35 ((
% 99.06/13.35 (setukpairinjR12) =>
% 99.06/13.35 ((
% 99.06/13.35 (setukpairinjR1) =>
% 99.06/13.35 ((
% 99.06/13.35 (upairequniteq) =>
% 99.06/13.35 ((
% 99.06/13.35 (setukpairinjR2) =>
% 99.06/13.35 ((
% 99.06/13.35 (setukpairinjR) =>
% 99.06/13.35 ((
% 99.06/13.35 (ksndsingleton) =>
% 99.06/13.35 ((
% 99.06/13.35 (ksndpairEq) =>
% 99.06/13.35 ((
% 99.06/13.35 (kpairsurjEq) =>
% 99.06/13.35 ((
% 99.06/13.35 (cartprodsndin) =>
% 99.06/13.35 ((
% 99.06/13.35 (cartprodpairmemEL) =>
% 99.06/13.35 ((
% 99.06/13.35 (cartprodpairmemER) =>
% 99.06/13.35 ((
% 99.06/13.35 (cartprodmempaircEq) =>
% 99.06/13.35 ((
% 99.06/13.35 (cartprodfstpairEq) =>
% 99.06/13.35 ((
% 99.06/13.35 (cartprodsndpairEq) =>
% 99.06/13.35 ((
% 99.06/13.35 (cartprodpairsurjEq) =>
% 99.06/13.35 ((
% 99.06/13.35 (dpsetconstrI) =>
% 99.06/13.35 ((
% 99.06/13.35 (dpsetconstrSub) =>
% 99.06/13.35 ((
% 99.06/13.35 (setOfPairsIsBReln) =>
% 99.06/13.35 ((
% 99.06/13.35 (dpsetconstrERa) =>
% 99.06/13.35 ((
% 99.06/13.35 (dpsetconstrEL1) =>
% 99.06/13.35 ((
% 99.06/13.35 (dpsetconstrEL2) =>
% 99.06/13.35 ((
% 99.06/13.35 (dpsetconstrER) =>
% 99.06/13.35 ((
% 99.06/13.35 (funcImageSingleton) =>
% 99.06/13.35 ((
% 99.06/13.35 (apProp) =>
% 99.06/13.35 ((
% 99.06/13.35 (app) =>
% 99.06/13.35 ((
% 99.06/13.35 (infuncsetfunc) =>
% 99.06/13.35 ((
% 99.06/13.35 (ap2p) =>
% 99.06/13.35 ((
% 99.06/13.35 (funcinfuncset) =>
% 99.06/13.35 ((
% 99.06/13.35 (lamProp) =>
% 99.06/13.35 ((
% 99.06/13.35 (lamp) =>
% 99.06/13.35 ((
% 99.06/13.35 (lam2p) =>
% 99.06/13.35 ((
% 99.06/13.35 (brelnall1) =>
% 99.06/13.35 ((
% 99.06/13.35 (brelnall2) =>
% 99.06/13.35 ((
% 99.06/13.35 (ex1E2) =>
% 99.06/13.35 ((
% 99.06/13.35 (funcGraphProp1) =>
% 99.06/13.35 ((
% 99.06/13.35 (funcGraphProp3) =>
% 99.06/13.36 ((
% 99.06/13.36 (funcGraphProp2) =>
% 99.06/13.36 ((
% 99.06/13.36 (funcextLem) =>
% 99.06/13.36 ((
% 99.06/13.36 (funcGraphProp4) =>
% 99.06/13.36 ((
% 99.06/13.36 (subbreln) =>
% 99.06/13.36 ((
% 99.06/13.36 (eqbreln) =>
% 99.06/13.36 ((
% 99.06/13.36 (funcext) =>
% 99.06/13.36 ((
% 99.06/13.36 (funcext2) =>
% 99.06/13.36 ((
% 99.06/13.36 (ap2apEq1) =>
% 99.06/13.36 ((
% 99.06/13.36 (ap2apEq2) =>
% 99.06/13.36 ((
% 99.06/13.36 (beta1) =>
% 99.06/13.36 ((
% 99.06/13.36 (eta1) =>
% 99.06/13.36 ((
% 99.06/13.36 (lam2lamEq) =>
% 99.06/13.36 ((
% 99.06/13.36 (beta2) =>
% 99.06/13.36 ((
% 99.06/13.36 (eta2) =>
% 99.06/13.36 ((
% 99.06/13.36 (iffalseProp1) =>
% 99.06/13.36 ((
% 99.06/13.36 (iffalseProp2) =>
% 99.06/13.36 ((
% 99.06/13.36 (iftrueProp1) =>
% 99.06/13.36 ((
% 99.06/13.36 (iftrueProp2) =>
% 99.06/13.36 ((
% 99.06/13.36 (ifSingleton) =>
% 99.06/13.36 ((
% 99.06/13.36 (ifp) =>
% 99.06/13.36 ((
% 99.06/13.36 (theeq) =>
% 99.06/13.36 ((
% 99.06/13.36 (iftrue) =>
% 99.06/13.36 ((
% 99.06/13.36 (iffalse) =>
% 99.06/13.36 ((
% 99.06/13.36 (iftrueorfalse) =>
% 99.06/13.36 ((
% 99.06/13.36 (binintersectT_lem) =>
% 99.06/13.36 ((
% 99.06/13.36 (binunionT_lem) =>
% 99.06/13.36 ((
% 99.06/13.36 (powersetT_lem) =>
% 99.06/13.36 ((
% 99.06/13.36 (setminusT_lem) =>
% 99.06/13.36 ((
% 99.06/13.36 (complementT_lem) =>
% 99.06/13.36 ((
% 99.06/13.36 (setextT) =>
% 99.06/13.36 ((
% 99.06/13.36 (subsetTI) =>
% 99.06/13.36 ((
% 99.06/13.36 (powersetTI1) =>
% 99.06/13.36 ((
% 99.06/13.36 (powersetTE1) =>
% 99.06/13.36 ((
% 99.06/13.36 (complementTI1) =>
% 99.06/13.36 ((
% 99.06/13.36 (complementTE1) =>
% 99.06/13.36 ((
% 99.06/13.36 (binintersectTELcontra) =>
% 99.06/13.36 ((
% 99.06/13.36 (binintersectTERcontra) =>
% 99.06/13.36 ((
% 99.06/13.36 (contrasubsetT) =>
% 99.06/13.36 ((
% 99.06/13.36 (contrasubsetT1) =>
% 99.06/13.36 ((
% 99.06/13.36 (contrasubsetT2) =>
% 99.06/13.36 ((
% 99.06/13.36 (contrasubsetT3) =>
% 99.06/13.36 ((
% 99.06/13.36 (doubleComplementI1) =>
% 99.06/13.36 ((
% 99.06/13.36 (doubleComplementE1) =>
% 99.06/13.36 ((
% 99.06/13.36 (doubleComplementSub1) =>
% 99.06/13.36 ((
% 99.06/13.36 (doubleComplementSub2) =>
% 99.06/13.36 ((
% 99.06/13.36 (doubleComplementEq) =>
% 99.06/13.36 ((
% 99.06/13.36 (complementTnotintersectT) =>
% 99.06/13.36 ((
% 99.06/13.36 (complementImpComplementIntersect) =>
% 99.06/13.36 ((
% 99.06/13.36 (complementSubsetComplementIntersect) =>
% 99.06/13.36 ((
% 99.06/13.36 (complementInPowersetComplementIntersect) =>
% 99.06/13.36 ((
% 99.06/13.36 (contraSubsetComplement) =>
% 99.06/13.36 ((
% 99.06/13.36 (complementTcontraSubset) =>
% 99.06/13.36 ((
% 99.06/13.36 (binunionTILcontra) =>
% 99.06/13.36 ((
% 99.06/13.36 (binunionTIRcontra) =>
% 99.06/13.36 ((
% 99.06/13.36 (inIntersectImpInUnion) =>
% 99.06/13.36 ((
% 99.06/13.36 (inIntersectImpInUnion2) =>
% 99.06/13.36 ((
% 99.06/13.36 (inIntersectImpInIntersectUnions) =>
% 99.06/13.36 ((
% 99.06/13.36 (intersectInPowersetIntersectUnions) =>
% 99.06/13.36 ((
% 99.06/13.36 (inComplementUnionImpNotIn1) =>
% 99.06/13.36 ((
% 99.06/13.36 (inComplementUnionImpInComplement1) =>
% 99.06/13.36 ((
% 99.06/13.36 (binunionTE) =>
% 99.06/13.36 ((
% 99.06/13.36 (binunionTEcontra) =>
% 99.06/13.36 ((
% 99.06/13.36 (demorgan2a1) =>
% 99.06/13.36 ((
% 99.06/13.36 (complementUnionInPowersetComplement) =>
% 99.06/13.36 ((
% 99.06/13.36 (demorgan2a2) =>
% 99.06/13.36 ((
% 99.06/13.36 (demorgan1a) =>
% 99.06/13.36 ((
% 99.06/13.36 (demorgan1b) =>
% 99.06/13.36 ((
% 99.06/13.36 (demorgan1) =>
% 99.06/13.36 ((
% 99.06/13.36 (demorgan2a) =>
% 99.06/13.36 ((
% 99.06/13.36 (demorgan2b2) =>
% 99.06/13.36 ((
% 99.06/13.36 (demorgan2b) =>
% 99.06/13.36 ((
% 99.06/13.36 (demorgan2) =>
% 99.06/13.36 ((
% 99.06/13.36 (woz13rule0) =>
% 99.06/13.36 ((
% 99.06/13.36 (woz13rule1) =>
% 99.06/13.36 ((
% 99.06/13.36 (woz13rule2) =>
% 99.06/13.36 ((
% 99.06/13.36 (woz13rule3) =>
% 99.06/13.36 ((
% 99.06/13.36 (woz13rule4) =>
% 99.06/13.36 ((
% 99.06/13.36 (woz1_1) =>
% 99.06/13.36 ((
% 99.06/13.36 (woz1_2) =>
% 99.06/13.36 ((
% 99.06/13.36 (woz1_3) =>
% 99.06/13.36 ((
% 99.06/13.36 (woz1_4) =>
% 99.06/13.36 ((
% 99.06/13.36 (woz1_5) =>
% 99.06/13.36 ((
% 99.06/13.36 (breln1all2) =>
% 99.06/13.36 ((
% 99.06/13.36 (breln1SetBreln1) =>
% 99.06/13.36 ((
% 99.06/13.36 (choice2fnsingleton) =>
% 99.06/13.36 ((
% 99.06/13.36 (setOfPairsIsBReln1) =>
% 99.06/13.36 ((
% 99.06/13.36 (breln1all1) =>
% 99.06/13.36 ((
% 99.06/13.36 (subbreln1) =>
% 99.06/13.36 ((
% 99.06/13.36 (eqbreln1) =>
% 99.06/13.36 ((
% 99.06/13.36 (breln1invprop) =>
% 99.06/13.36 ((
% 99.06/13.36 (breln1invI) =>
% 99.06/13.36 ((
% 99.06/13.36 (breln1invE) =>
% 99.06/13.36 ((
% 99.06/13.36 (breln1compprop) =>
% 99.06/13.36 ((
% 99.06/13.36 (breln1compI) =>
% 99.06/13.36 ((
% 99.06/13.36 (breln1compE) =>
% 99.06/13.36 ((
% 99.06/13.36 (breln1compEex) =>
% 99.06/13.36 ((
% 99.06/13.36 (breln1unionprop) =>
% 99.06/13.36 ((
% 99.06/13.36 (breln1unionIL) =>
% 99.06/13.36 ((
% 99.06/13.36 (breln1unionIR) =>
% 99.06/13.36 ((
% 99.06/13.36 (breln1unionI) =>
% 99.06/13.36 ((
% 99.06/13.36 (breln1unionE) =>
% 99.06/13.36 ((
% 99.06/13.36 (breln1unionEcases) =>
% 99.06/13.36 ((
% 99.06/13.36 (breln1unionCommutes) =>
% 99.06/13.36 ((
% 99.06/13.36 (woz2Ex) =>
% 99.06/13.36 ((
% 99.06/13.36 (woz2W) =>
% 99.06/13.36 ((
% 99.06/13.36 (woz2A) =>
% 99.06/13.36 ((
% 99.06/13.36 (woz2B) =>
% 99.06/13.36 ((
% 99.06/13.36 (image1Ex) =>
% 99.06/13.36 ((
% 99.06/13.36 (image1Ex1) =>
% 99.06/13.36 ((
% 99.06/13.36 (image1Equiv) =>
% 99.06/13.36 ((
% 99.06/13.36 (image1E) =>
% 99.06/13.36 ((
% 99.06/13.36 (image1I) =>
% 99.06/13.36 ((
% 99.06/13.36 (injFuncInInjFuncSet) =>
% 99.06/13.36 ((
% 99.06/13.36 (injFuncSetFuncIn) =>
% 99.06/13.36 ((
% 99.06/13.36 (injFuncSetFuncInj) =>
% 99.06/13.36 ((
% 99.06/13.36 (!!) @ (
% 99.06/13.36 (('#B') @ (
% 99.06/13.36 !!) @
% 99.06/13.36 (
% 99.06/13.36 (
% 99.06/13.36 ('#B') @ (
% 99.06/13.36 (
% 99.06/13.36 ('#B') @ (
% 99.06/13.36 !!))) @
% 99.06/13.36 (
% 99.06/13.36 (
% 99.06/13.36 ('#S') @ (
% 99.06/13.36 (
% 99.06/13.36 ('#B') @ (
% 99.06/13.36 '#S') @
% 99.06/13.36 (
% 99.06/13.36 (
% 99.06/13.36 ('#B') @ (
% 99.06/13.36 (
% 99.06/13.36 ('#B') @ (
% 99.06/13.36 '#S'))) @
% 99.06/13.36 (
% 99.06/13.36 (
% 99.06/13.36 ('#B') @ (
% 99.06/13.36 (
% 99.06/13.36 ('#B') @ (
% 99.06/13.36 (
% 99.06/13.36 ('#B') @ (
% 99.06/13.36 =>))))) @
% 99.06/13.36 (
% 99.06/13.36 (
% 99.06/13.36 ('#B') @ (
% 99.06/13.36 (
% 99.06/13.36 ('#B') @ (
% 99.06/13.36 (
% 99.06/13.36 ('#C') @ in)))) @
% 99.06/13.36 surjFuncSet)))))))) @
% 99.06/13.36 (
% 99.06/13.36 (
% 99.06/13.36 ('#B') @ (
% 99.06/13.36 (
% 99.06/13.36 ('#B') @ (
% 99.06/13.36 (
% 99.06/13.36 ('#C') @ in)))) @
% 99.06/13.36 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.06/13.36 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl189])).
% 99.06/13.36 thf(zip_derived_cl222, plain,
% 99.06/13.36 (~ (((emptyI) =>
% 99.06/13.36 (((noeltsimpempty) =>
% 99.06/13.36 (((setbeta) =>
% 99.06/13.36 (((nonemptyE1) =>
% 99.06/13.36 (((nonemptyI) =>
% 99.06/13.36 (((nonemptyI1) =>
% 99.06/13.36 (((setadjoinIL) =>
% 99.06/13.36 (((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) =>
% 99.06/13.36 (((setadjoinIR) =>
% 99.06/13.36 (((setadjoinE) =>
% 99.06/13.36 (((setadjoinOr) =>
% 99.06/13.36 (((setoftrueEq) =>
% 99.06/13.36 (((powersetI) =>
% 99.06/13.36 (((emptyinPowerset) =>
% 99.06/13.36 (((emptyInPowerset) =>
% 99.06/13.36 (((powersetE) =>
% 99.06/13.36 (((setunionI) =>
% 99.06/13.36 (((setunionE) =>
% 99.06/13.36 (((subPowSU) =>
% 99.06/13.36 (((exuE2) =>
% 99.06/13.36 (((nonemptyImpWitness) =>
% 99.06/13.36 (((uniqinunit) =>
% 99.06/13.36 (((notinsingleton) =>
% 99.06/13.36 (((eqinunit) =>
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% 99.06/13.36 (((upairsetIR) =>
% 99.06/13.36 (((emptyE1) =>
% 99.06/13.36 (((vacuousDall) =>
% 99.06/13.36 ((
% 99.06/13.36 (quantDeMorgan1) =>
% 99.06/13.36 ((
% 99.06/13.36 (quantDeMorgan2) =>
% 99.06/13.36 ((
% 99.06/13.36 (quantDeMorgan3) =>
% 99.06/13.36 ((
% 99.06/13.36 (quantDeMorgan4) =>
% 99.06/13.36 ((
% 99.06/13.36 (prop2setI) =>
% 99.06/13.36 ((
% 99.06/13.36 (prop2set2propI) =>
% 99.06/13.36 ((
% 99.06/13.36 (notdexE) =>
% 99.06/13.36 ((
% 99.06/13.36 (notdallE) =>
% 99.06/13.36 ((
% 99.06/13.36 (exuI1) =>
% 99.06/13.36 ((
% 99.06/13.36 (exuI3) =>
% 99.06/13.36 ((
% 99.06/13.36 (exuI2) =>
% 99.06/13.36 ((
% 99.06/13.36 (inCongP) =>
% 99.06/13.36 ((
% 99.06/13.36 (in__Cong) =>
% 99.06/13.36 ((
% 99.06/13.36 (exuE3u) =>
% 99.06/13.36 ((
% 99.06/13.36 (exu__Cong) =>
% 99.06/13.36 ((
% 99.06/13.36 (setadjoin__Cong) =>
% 99.06/13.36 ((
% 99.06/13.36 (powerset__Cong) =>
% 99.06/13.36 ((
% 99.06/13.36 (setunion__Cong) =>
% 99.06/13.36 ((
% 99.06/13.36 (exuEu) =>
% 99.06/13.36 ((
% 99.06/13.36 (descr__Cong) =>
% 99.06/13.36 ((
% 99.06/13.36 (dsetconstr__Cong) =>
% 99.06/13.36 ((
% 99.06/13.36 (subsetI1) =>
% 99.06/13.36 ((
% 99.06/13.36 (eqimpsubset2) =>
% 99.06/13.36 ((
% 99.06/13.36 (eqimpsubset1) =>
% 99.06/13.36 ((
% 99.06/13.36 (subsetI2) =>
% 99.06/13.36 ((
% 99.06/13.36 (emptysetsubset) =>
% 99.06/13.36 ((
% 99.06/13.36 (subsetE) =>
% 99.06/13.36 ((
% 99.06/13.36 (subsetE2) =>
% 99.06/13.36 ((
% 99.06/13.36 (notsubsetI) =>
% 99.06/13.36 ((
% 99.06/13.36 (notequalI1) =>
% 99.06/13.36 ((
% 99.06/13.36 (notequalI2) =>
% 99.06/13.36 ((
% 99.06/13.36 (subsetRefl) =>
% 99.06/13.36 ((
% 99.06/13.36 (subsetTrans) =>
% 99.06/13.36 ((
% 99.06/13.36 (setadjoinSub) =>
% 99.06/13.36 ((
% 99.06/13.36 (setadjoinSub2) =>
% 99.06/13.36 ((
% 99.06/13.36 (subset2powerset) =>
% 99.06/13.36 ((
% 99.06/13.36 (setextsub) =>
% 99.06/13.36 ((
% 99.06/13.36 (subsetemptysetimpeq) =>
% 99.06/13.36 ((
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% 99.06/13.36 ((
% 99.06/13.36 (powersetE1) =>
% 99.06/13.36 ((
% 99.06/13.36 (inPowerset) =>
% 99.06/13.36 ((
% 99.06/13.36 (powersetsubset) =>
% 99.06/13.36 ((
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% 99.06/13.36 ((
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% 99.06/13.36 ((
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% 99.06/13.36 ((
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% 99.06/13.36 ((
% 99.06/13.36 (binunionRsub) =>
% 99.06/13.36 ((
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% 99.06/13.36 ((
% 99.06/13.36 (binintersectSubset5) =>
% 99.06/13.36 ((
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% 99.06/13.36 ((
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% 99.06/13.36 ((
% 99.06/13.36 (binintersectSubset2) =>
% 99.06/13.36 ((
% 99.06/13.36 (binintersectSubset3) =>
% 99.06/13.36 ((
% 99.06/13.36 (binintersectER) =>
% 99.06/13.36 ((
% 99.06/13.36 (disjointsetsI1) =>
% 99.06/13.36 ((
% 99.06/13.36 (binintersectRsub) =>
% 99.06/13.36 ((
% 99.06/13.36 (binintersectSubset4) =>
% 99.06/13.36 ((
% 99.06/13.36 (binintersectSubset1) =>
% 99.06/13.36 ((
% 99.06/13.36 (bs114d) =>
% 99.06/13.36 ((
% 99.06/13.36 (setminusI) =>
% 99.06/13.36 ((
% 99.06/13.36 (setminusEL) =>
% 99.06/13.36 ((
% 99.06/13.36 (setminusER) =>
% 99.06/13.36 ((
% 99.06/13.36 (setminusSubset2) =>
% 99.06/13.36 ((
% 99.06/13.36 (setminusERneg) =>
% 99.06/13.36 ((
% 99.06/13.36 (setminusELneg) =>
% 99.06/13.36 ((
% 99.06/13.36 (setminusILneg) =>
% 99.06/13.36 ((
% 99.06/13.36 (setminusIRneg) =>
% 99.06/13.36 ((
% 99.06/13.36 (setminusLsub) =>
% 99.06/13.36 ((
% 99.06/13.36 (setminusSubset1) =>
% 99.06/13.36 ((
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% 99.06/13.36 ((
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% 99.06/13.36 ((
% 99.06/13.36 (symdiffI2) =>
% 99.06/13.36 ((
% 99.06/13.36 (symdiffIneg1) =>
% 99.06/13.36 ((
% 99.06/13.36 (symdiffIneg2) =>
% 99.06/13.36 ((
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% 99.06/13.36 ((
% 99.06/13.36 (setukpairIL) =>
% 99.06/13.36 ((
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% 99.06/13.36 ((
% 99.06/13.36 (kpairiskpair) =>
% 99.06/13.36 ((
% 99.06/13.36 (kpairp) =>
% 99.06/13.36 ((
% 99.06/13.36 (singletonsubset) =>
% 99.06/13.36 ((
% 99.06/13.36 (singletoninpowerset) =>
% 99.06/13.36 ((
% 99.06/13.36 (singletoninpowunion) =>
% 99.06/13.36 ((
% 99.06/13.36 (upairset2E) =>
% 99.06/13.36 ((
% 99.06/13.36 (upairsubunion) =>
% 99.06/13.36 ((
% 99.06/13.36 (upairinpowunion) =>
% 99.06/13.36 ((
% 99.06/13.36 (ubforcartprodlem1) =>
% 99.06/13.36 ((
% 99.06/13.36 (ubforcartprodlem2) =>
% 99.06/13.36 ((
% 99.06/13.36 (ubforcartprodlem3) =>
% 99.06/13.36 ((
% 99.06/13.36 (cartprodpairin) =>
% 99.06/13.36 ((
% 99.06/13.36 (cartprodmempair1) =>
% 99.06/13.36 ((
% 99.06/13.36 (cartprodmempair) =>
% 99.06/13.36 ((
% 99.06/13.36 (setunionE2) =>
% 99.06/13.36 ((
% 99.06/13.36 (setunionsingleton1) =>
% 99.06/13.36 ((
% 99.06/13.36 (setunionsingleton2) =>
% 99.06/13.36 ((
% 99.06/13.36 (setunionsingleton) =>
% 99.06/13.36 ((
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% 99.06/13.36 ((
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% 99.06/13.36 ((
% 99.06/13.36 (ex1I) =>
% 99.06/13.36 ((
% 99.06/13.36 (ex1I2) =>
% 99.06/13.36 ((
% 99.06/13.36 (singletonsuniq) =>
% 99.06/13.36 ((
% 99.06/13.36 (setukpairinjL1) =>
% 99.06/13.36 ((
% 99.06/13.36 (kfstsingleton) =>
% 99.06/13.36 ((
% 99.06/13.36 (theprop) =>
% 99.06/13.36 ((
% 99.06/13.36 (kfstpairEq) =>
% 99.06/13.36 ((
% 99.06/13.36 (cartprodfstin) =>
% 99.06/13.36 ((
% 99.06/13.36 (setukpairinjL2) =>
% 99.06/13.36 ((
% 99.06/13.36 (setukpairinjL) =>
% 99.06/13.36 ((
% 99.06/13.36 (setukpairinjR11) =>
% 99.06/13.36 ((
% 99.06/13.36 (setukpairinjR12) =>
% 99.06/13.36 ((
% 99.06/13.36 (setukpairinjR1) =>
% 99.06/13.36 ((
% 99.06/13.36 (upairequniteq) =>
% 99.06/13.36 ((
% 99.06/13.36 (setukpairinjR2) =>
% 99.06/13.36 ((
% 99.06/13.36 (setukpairinjR) =>
% 99.06/13.36 ((
% 99.06/13.36 (ksndsingleton) =>
% 99.06/13.36 ((
% 99.06/13.36 (ksndpairEq) =>
% 99.06/13.36 ((
% 99.06/13.36 (kpairsurjEq) =>
% 99.06/13.36 ((
% 99.06/13.36 (cartprodsndin) =>
% 99.06/13.36 ((
% 99.06/13.36 (cartprodpairmemEL) =>
% 99.06/13.36 ((
% 99.06/13.36 (cartprodpairmemER) =>
% 99.06/13.36 ((
% 99.06/13.36 (cartprodmempaircEq) =>
% 99.06/13.36 ((
% 99.06/13.36 (cartprodfstpairEq) =>
% 99.06/13.36 ((
% 99.06/13.36 (cartprodsndpairEq) =>
% 99.06/13.36 ((
% 99.06/13.36 (cartprodpairsurjEq) =>
% 99.06/13.36 ((
% 99.06/13.36 (dpsetconstrI) =>
% 99.06/13.36 ((
% 99.06/13.36 (dpsetconstrSub) =>
% 99.06/13.36 ((
% 99.06/13.36 (setOfPairsIsBReln) =>
% 99.06/13.36 ((
% 99.06/13.36 (dpsetconstrERa) =>
% 99.06/13.36 ((
% 99.06/13.36 (dpsetconstrEL1) =>
% 99.06/13.36 ((
% 99.06/13.36 (dpsetconstrEL2) =>
% 99.06/13.36 ((
% 99.06/13.36 (dpsetconstrER) =>
% 99.06/13.36 ((
% 99.06/13.36 (funcImageSingleton) =>
% 99.06/13.36 ((
% 99.06/13.36 (apProp) =>
% 99.06/13.36 ((
% 99.06/13.36 (app) =>
% 99.06/13.36 ((
% 99.06/13.36 (infuncsetfunc) =>
% 99.06/13.36 ((
% 99.06/13.36 (ap2p) =>
% 99.06/13.36 ((
% 99.06/13.36 (funcinfuncset) =>
% 99.06/13.36 ((
% 99.06/13.36 (lamProp) =>
% 99.06/13.36 ((
% 99.06/13.36 (lamp) =>
% 99.06/13.36 ((
% 99.06/13.36 (lam2p) =>
% 99.06/13.36 ((
% 99.06/13.36 (brelnall1) =>
% 99.06/13.36 ((
% 99.06/13.36 (brelnall2) =>
% 99.06/13.36 ((
% 99.06/13.36 (ex1E2) =>
% 99.06/13.36 ((
% 99.06/13.36 (funcGraphProp1) =>
% 99.06/13.36 ((
% 99.06/13.36 (funcGraphProp3) =>
% 99.06/13.36 ((
% 99.06/13.36 (funcGraphProp2) =>
% 99.06/13.36 ((
% 99.06/13.36 (funcextLem) =>
% 99.06/13.36 ((
% 99.06/13.36 (funcGraphProp4) =>
% 99.06/13.36 ((
% 99.06/13.36 (subbreln) =>
% 99.06/13.36 ((
% 99.06/13.36 (eqbreln) =>
% 99.06/13.36 ((
% 99.06/13.36 (funcext) =>
% 99.06/13.36 ((
% 99.06/13.36 (funcext2) =>
% 99.06/13.36 ((
% 99.06/13.36 (ap2apEq1) =>
% 99.06/13.36 ((
% 99.06/13.36 (ap2apEq2) =>
% 99.06/13.36 ((
% 99.06/13.36 (beta1) =>
% 99.06/13.36 ((
% 99.06/13.36 (eta1) =>
% 99.06/13.36 ((
% 99.06/13.36 (lam2lamEq) =>
% 99.06/13.36 ((
% 99.06/13.36 (beta2) =>
% 99.06/13.36 ((
% 99.06/13.36 (eta2) =>
% 99.06/13.36 ((
% 99.06/13.36 (iffalseProp1) =>
% 99.06/13.36 ((
% 99.06/13.36 (iffalseProp2) =>
% 99.06/13.36 ((
% 99.06/13.36 (iftrueProp1) =>
% 99.06/13.36 ((
% 99.06/13.36 (iftrueProp2) =>
% 99.06/13.36 ((
% 99.06/13.36 (ifSingleton) =>
% 99.06/13.36 ((
% 99.06/13.36 (ifp) =>
% 99.06/13.36 ((
% 99.06/13.36 (theeq) =>
% 99.06/13.36 ((
% 99.06/13.36 (iftrue) =>
% 99.06/13.36 ((
% 99.06/13.36 (iffalse) =>
% 99.06/13.36 ((
% 99.06/13.36 (iftrueorfalse) =>
% 99.06/13.36 ((
% 99.06/13.36 (binintersectT_lem) =>
% 99.06/13.36 ((
% 99.06/13.36 (binunionT_lem) =>
% 99.06/13.36 ((
% 99.06/13.36 (powersetT_lem) =>
% 99.06/13.36 ((
% 99.06/13.36 (setminusT_lem) =>
% 99.06/13.36 ((
% 99.06/13.36 (complementT_lem) =>
% 99.06/13.36 ((
% 99.06/13.36 (setextT) =>
% 99.06/13.36 ((
% 99.06/13.36 (subsetTI) =>
% 99.06/13.36 ((
% 99.06/13.36 (powersetTI1) =>
% 99.06/13.36 ((
% 99.06/13.36 (powersetTE1) =>
% 99.06/13.36 ((
% 99.06/13.36 (complementTI1) =>
% 99.06/13.36 ((
% 99.06/13.36 (complementTE1) =>
% 99.06/13.36 ((
% 99.06/13.36 (binintersectTELcontra) =>
% 99.06/13.36 ((
% 99.06/13.36 (binintersectTERcontra) =>
% 99.06/13.36 ((
% 99.06/13.36 (contrasubsetT) =>
% 99.06/13.36 ((
% 99.06/13.36 (contrasubsetT1) =>
% 99.06/13.36 ((
% 99.06/13.36 (contrasubsetT2) =>
% 99.06/13.36 ((
% 99.06/13.36 (contrasubsetT3) =>
% 99.06/13.36 ((
% 99.06/13.36 (doubleComplementI1) =>
% 99.06/13.36 ((
% 99.06/13.36 (doubleComplementE1) =>
% 99.06/13.36 ((
% 99.06/13.36 (doubleComplementSub1) =>
% 99.06/13.36 ((
% 99.06/13.36 (doubleComplementSub2) =>
% 99.06/13.36 ((
% 99.06/13.36 (doubleComplementEq) =>
% 99.06/13.36 ((
% 99.06/13.36 (complementTnotintersectT) =>
% 99.06/13.36 ((
% 99.06/13.36 (complementImpComplementIntersect) =>
% 99.06/13.36 ((
% 99.06/13.36 (complementSubsetComplementIntersect) =>
% 99.06/13.36 ((
% 99.06/13.36 (complementInPowersetComplementIntersect) =>
% 99.06/13.36 ((
% 99.06/13.36 (contraSubsetComplement) =>
% 99.06/13.36 ((
% 99.06/13.36 (complementTcontraSubset) =>
% 99.06/13.36 ((
% 99.06/13.36 (binunionTILcontra) =>
% 99.06/13.36 ((
% 99.06/13.36 (binunionTIRcontra) =>
% 99.06/13.36 ((
% 99.06/13.36 (inIntersectImpInUnion) =>
% 99.06/13.36 ((
% 99.06/13.36 (inIntersectImpInUnion2) =>
% 99.06/13.36 ((
% 99.06/13.36 (inIntersectImpInIntersectUnions) =>
% 99.06/13.36 ((
% 99.06/13.36 (intersectInPowersetIntersectUnions) =>
% 99.06/13.36 ((
% 99.06/13.36 (inComplementUnionImpNotIn1) =>
% 99.06/13.36 ((
% 99.06/13.36 (inComplementUnionImpInComplement1) =>
% 99.06/13.36 ((
% 99.06/13.36 (binunionTE) =>
% 99.06/13.36 ((
% 99.06/13.36 (binunionTEcontra) =>
% 99.06/13.36 ((
% 99.06/13.36 (demorgan2a1) =>
% 99.06/13.36 ((
% 99.06/13.36 (complementUnionInPowersetComplement) =>
% 99.06/13.36 ((
% 99.06/13.36 (demorgan2a2) =>
% 99.06/13.36 ((
% 99.06/13.36 (demorgan1a) =>
% 99.06/13.36 ((
% 99.06/13.36 (demorgan1b) =>
% 99.06/13.36 ((
% 99.06/13.36 (demorgan1) =>
% 99.06/13.36 ((
% 99.06/13.36 (demorgan2a) =>
% 99.06/13.36 ((
% 99.06/13.36 (demorgan2b2) =>
% 99.06/13.36 ((
% 99.06/13.36 (demorgan2b) =>
% 99.06/13.36 ((
% 99.06/13.36 (demorgan2) =>
% 99.06/13.36 ((
% 99.06/13.36 (woz13rule0) =>
% 99.06/13.36 ((
% 99.06/13.36 (woz13rule1) =>
% 99.06/13.36 ((
% 99.06/13.36 (woz13rule2) =>
% 99.06/13.36 ((
% 99.06/13.36 (woz13rule3) =>
% 99.06/13.36 ((
% 99.06/13.36 (woz13rule4) =>
% 99.06/13.36 ((
% 99.06/13.36 (woz1_1) =>
% 99.06/13.36 ((
% 99.06/13.36 (woz1_2) =>
% 99.06/13.36 ((
% 99.06/13.36 (woz1_3) =>
% 99.06/13.36 ((
% 99.06/13.36 (woz1_4) =>
% 99.06/13.36 ((
% 99.06/13.36 (woz1_5) =>
% 99.06/13.36 ((
% 99.06/13.36 (breln1all2) =>
% 99.06/13.36 ((
% 99.06/13.36 (breln1SetBreln1) =>
% 99.06/13.36 ((
% 99.06/13.36 (choice2fnsingleton) =>
% 99.06/13.36 ((
% 99.06/13.36 (setOfPairsIsBReln1) =>
% 99.06/13.36 ((
% 99.06/13.36 (breln1all1) =>
% 99.06/13.36 ((
% 99.06/13.36 (subbreln1) =>
% 99.06/13.36 ((
% 99.06/13.36 (eqbreln1) =>
% 99.06/13.36 ((
% 99.06/13.36 (breln1invprop) =>
% 99.06/13.36 ((
% 99.06/13.36 (breln1invI) =>
% 99.06/13.36 ((
% 99.06/13.36 (breln1invE) =>
% 99.06/13.36 ((
% 99.06/13.36 (breln1compprop) =>
% 99.06/13.36 ((
% 99.06/13.36 (breln1compI) =>
% 99.06/13.36 ((
% 99.06/13.36 (breln1compE) =>
% 99.06/13.36 ((
% 99.06/13.36 (breln1compEex) =>
% 99.06/13.36 ((
% 99.06/13.36 (breln1unionprop) =>
% 99.06/13.36 ((
% 99.06/13.36 (breln1unionIL) =>
% 99.06/13.36 ((
% 99.06/13.36 (breln1unionIR) =>
% 99.06/13.36 ((
% 99.06/13.36 (breln1unionI) =>
% 99.06/13.36 ((
% 99.06/13.36 (breln1unionE) =>
% 99.06/13.36 ((
% 99.06/13.36 (breln1unionEcases) =>
% 99.06/13.36 ((
% 99.06/13.36 (breln1unionCommutes) =>
% 99.06/13.36 ((
% 99.06/13.36 (woz2Ex) =>
% 99.06/13.36 ((
% 99.06/13.36 (woz2W) =>
% 99.06/13.36 ((
% 99.06/13.36 (woz2A) =>
% 99.06/13.36 ((
% 99.06/13.36 (woz2B) =>
% 99.06/13.36 ((
% 99.06/13.36 (image1Ex) =>
% 99.06/13.36 ((
% 99.06/13.36 (image1Ex1) =>
% 99.06/13.36 ((
% 99.06/13.36 (image1Equiv) =>
% 99.06/13.36 ((
% 99.06/13.36 (image1E) =>
% 99.06/13.36 ((
% 99.06/13.36 (image1I) =>
% 99.06/13.36 ((
% 99.06/13.36 (injFuncInInjFuncSet) =>
% 99.06/13.36 ((
% 99.06/13.36 (injFuncSetFuncIn) =>
% 99.06/13.36 ((
% 99.06/13.36 (injFuncSetFuncInj) =>
% 99.06/13.36 ((
% 99.06/13.36 (!!) @ (
% 99.06/13.36 (('#B') @ (
% 99.06/13.36 !!) @
% 99.06/13.36 (
% 99.06/13.36 (
% 99.06/13.36 ('#B') @ (
% 99.06/13.36 (
% 99.06/13.36 ('#B') @ (
% 99.06/13.36 !!))) @
% 99.06/13.36 (
% 99.06/13.36 (
% 99.06/13.36 ('#S') @ (
% 99.06/13.36 (
% 99.06/13.36 ('#B') @ (
% 99.06/13.36 '#S') @
% 99.06/13.36 (
% 99.06/13.36 (
% 99.06/13.36 ('#B') @ (
% 99.06/13.36 (
% 99.06/13.36 ('#B') @ (
% 99.06/13.36 '#S'))) @
% 99.06/13.36 (
% 99.06/13.36 (
% 99.06/13.36 ('#B') @ (
% 99.06/13.36 (
% 99.06/13.36 ('#B') @ (
% 99.06/13.36 (
% 99.06/13.36 ('#B') @ (
% 99.06/13.36 =>))))) @
% 99.06/13.36 (
% 99.06/13.36 (
% 99.06/13.36 ('#B') @ (
% 99.06/13.36 (
% 99.06/13.36 ('#B') @ (
% 99.06/13.36 (
% 99.06/13.36 ('#C') @ in)))) @
% 99.06/13.36 surjFuncSet)))))))) @
% 99.06/13.36 (
% 99.06/13.36 (
% 99.06/13.36 ('#B') @ (
% 99.06/13.36 (
% 99.06/13.36 ('#B') @ (
% 99.06/13.36 (
% 99.06/13.36 ('#C') @ in)))) @
% 99.06/13.36 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.06/13.36 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl206])).
% 99.06/13.36 thf(zip_derived_cl236, plain,
% 99.06/13.36 (~ (((noeltsimpempty) =>
% 99.06/13.36 (((setbeta) =>
% 99.06/13.36 (((nonemptyE1) =>
% 99.06/13.36 (((nonemptyI) =>
% 99.06/13.36 (((nonemptyI1) =>
% 99.06/13.36 (((setadjoinIL) =>
% 99.06/13.36 (((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) =>
% 99.06/13.36 (((setadjoinIR) =>
% 99.06/13.36 (((setadjoinE) =>
% 99.06/13.36 (((setadjoinOr) =>
% 99.06/13.36 (((setoftrueEq) =>
% 99.06/13.36 (((powersetI) =>
% 99.06/13.36 (((emptyinPowerset) =>
% 99.06/13.36 (((emptyInPowerset) =>
% 99.06/13.36 (((powersetE) =>
% 99.06/13.36 (((setunionI) =>
% 99.06/13.36 (((setunionE) =>
% 99.06/13.36 (((subPowSU) =>
% 99.06/13.36 (((exuE2) =>
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% 99.06/13.36 (((notinsingleton) =>
% 99.06/13.36 (((eqinunit) =>
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% 99.06/13.36 (((upairsetIL) =>
% 99.06/13.36 (((upairsetIR) =>
% 99.06/13.36 (((emptyE1) =>
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% 99.06/13.36 (((quantDeMorgan1) =>
% 99.06/13.36 ((
% 99.06/13.36 (quantDeMorgan2) =>
% 99.06/13.36 ((
% 99.06/13.36 (quantDeMorgan3) =>
% 99.06/13.36 ((
% 99.06/13.36 (quantDeMorgan4) =>
% 99.06/13.36 ((
% 99.06/13.36 (prop2setI) =>
% 99.06/13.36 ((
% 99.06/13.36 (prop2set2propI) =>
% 99.06/13.36 ((
% 99.06/13.36 (notdexE) =>
% 99.06/13.36 ((
% 99.06/13.36 (notdallE) =>
% 99.06/13.36 ((
% 99.06/13.36 (exuI1) =>
% 99.06/13.36 ((
% 99.06/13.36 (exuI3) =>
% 99.06/13.36 ((
% 99.06/13.36 (exuI2) =>
% 99.06/13.36 ((
% 99.06/13.36 (inCongP) =>
% 99.06/13.36 ((
% 99.06/13.36 (in__Cong) =>
% 99.06/13.36 ((
% 99.06/13.36 (exuE3u) =>
% 99.06/13.36 ((
% 99.06/13.36 (exu__Cong) =>
% 99.06/13.36 ((
% 99.06/13.36 (setadjoin__Cong) =>
% 99.06/13.36 ((
% 99.06/13.36 (powerset__Cong) =>
% 99.06/13.36 ((
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% 99.06/13.36 (cartprodpairmemER) =>
% 99.06/13.36 ((
% 99.06/13.36 (cartprodmempaircEq) =>
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% 99.06/13.36 ((
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% 99.06/13.36 ((
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% 99.06/13.36 ((
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% 99.06/13.36 (funcGraphProp3) =>
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% 99.06/13.36 ((
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% 99.06/13.36 ((
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% 99.06/13.36 ((
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% 99.06/13.36 ((
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% 99.06/13.36 ((
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% 99.06/13.36 ((
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% 99.06/13.36 ((
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% 99.06/13.36 ((
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% 99.06/13.36 ((
% 99.06/13.36 (woz13rule3) =>
% 99.06/13.36 ((
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% 99.06/13.36 (woz1_5) =>
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% 99.06/13.36 ((
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% 99.06/13.36 ((
% 99.06/13.36 (breln1compprop) =>
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% 99.06/13.36 ((
% 99.06/13.36 (breln1compEex) =>
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% 99.06/13.36 ((
% 99.06/13.36 (breln1unionE) =>
% 99.06/13.36 ((
% 99.06/13.36 (breln1unionEcases) =>
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% 99.06/13.36 ((
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% 99.06/13.36 ((
% 99.06/13.36 (image1Ex1) =>
% 99.06/13.36 ((
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% 99.06/13.36 ((
% 99.06/13.36 (image1E) =>
% 99.06/13.36 ((
% 99.06/13.36 (image1I) =>
% 99.06/13.36 ((
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% 99.06/13.36 ((
% 99.06/13.36 (injFuncSetFuncIn) =>
% 99.06/13.36 ((
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% 99.06/13.36 (
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% 99.06/13.36 ((
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% 99.06/13.36 ((
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% 99.06/13.36 ((
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% 99.06/13.36 ((
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% 99.06/13.36 ((
% 99.06/13.36 (ubforcartprodlem2) =>
% 99.06/13.36 ((
% 99.06/13.36 (ubforcartprodlem3) =>
% 99.06/13.36 ((
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% 99.06/13.36 ((
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% 99.06/13.36 ((
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% 99.06/13.36 ((
% 99.06/13.36 (ubforcartprodlem3) =>
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% 99.06/13.36 ((
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% 99.06/13.36 ((
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% 99.06/13.36 ((
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% 99.06/13.36 ((
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% 99.06/13.36 ((
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% 99.06/13.36 ((
% 99.06/13.36 (ubforcartprodlem3) =>
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% 99.06/13.36 ((
% 99.06/13.36 (cartprodmempair) =>
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% 99.20/13.37 ((
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% 99.20/13.37 ((
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% 99.20/13.37 ((
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% 99.20/13.37 ((
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% 99.20/13.37 ((
% 99.20/13.37 (breln1compE) =>
% 99.20/13.37 ((
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% 99.20/13.37 ((
% 99.20/13.37 (breln1unionI) =>
% 99.20/13.37 ((
% 99.20/13.37 (breln1unionE) =>
% 99.20/13.37 ((
% 99.20/13.37 (breln1unionEcases) =>
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% 99.20/13.37 ((
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% 99.20/13.37 ((
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% 99.20/13.37 ((
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% 99.20/13.37 ((
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% 99.20/13.37 ((
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% 99.20/13.37 ((
% 99.20/13.37 (injFuncSetFuncIn) =>
% 99.20/13.37 ((
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% 99.20/13.37 (
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% 99.20/13.37 ((
% 99.20/13.37 (ubforcartprodlem2) =>
% 99.20/13.37 ((
% 99.20/13.37 (ubforcartprodlem3) =>
% 99.20/13.37 ((
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% 99.20/13.37 ((
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% 99.20/13.37 ((
% 99.20/13.37 (cartprodmempair) =>
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% 99.20/13.37 ((
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% 99.20/13.37 ((
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% 99.20/13.37 (setunionsingleton) =>
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% 99.20/13.37 ((
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% 99.20/13.37 ((
% 99.20/13.37 (lam2p) =>
% 99.20/13.37 ((
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% 99.20/13.37 ((
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% 99.20/13.37 ((
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% 99.20/13.37 (funcGraphProp3) =>
% 99.20/13.37 ((
% 99.20/13.37 (funcGraphProp2) =>
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% 99.20/13.37 ((
% 99.20/13.37 (funcGraphProp4) =>
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% 99.20/13.37 (doubleComplementSub2) =>
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% 99.20/13.37 ((
% 99.20/13.37 (demorgan2a) =>
% 99.20/13.37 ((
% 99.20/13.37 (demorgan2b2) =>
% 99.20/13.37 ((
% 99.20/13.37 (demorgan2b) =>
% 99.20/13.37 ((
% 99.20/13.37 (demorgan2) =>
% 99.20/13.37 ((
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% 99.20/13.37 ((
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% 99.20/13.37 ((
% 99.20/13.37 (woz13rule2) =>
% 99.20/13.37 ((
% 99.20/13.37 (woz13rule3) =>
% 99.20/13.37 ((
% 99.20/13.37 (woz13rule4) =>
% 99.20/13.37 ((
% 99.20/13.37 (woz1_1) =>
% 99.20/13.37 ((
% 99.20/13.37 (woz1_2) =>
% 99.20/13.37 ((
% 99.20/13.37 (woz1_3) =>
% 99.20/13.37 ((
% 99.20/13.37 (woz1_4) =>
% 99.20/13.37 ((
% 99.20/13.37 (woz1_5) =>
% 99.20/13.37 ((
% 99.20/13.37 (breln1all2) =>
% 99.20/13.37 ((
% 99.20/13.37 (breln1SetBreln1) =>
% 99.20/13.37 ((
% 99.20/13.37 (choice2fnsingleton) =>
% 99.20/13.37 ((
% 99.20/13.37 (setOfPairsIsBReln1) =>
% 99.20/13.37 ((
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% 99.20/13.37 ((
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% 99.20/13.37 ((
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% 99.20/13.37 ((
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% 99.20/13.37 ((
% 99.20/13.37 (breln1invI) =>
% 99.20/13.37 ((
% 99.20/13.37 (breln1invE) =>
% 99.20/13.37 ((
% 99.20/13.37 (breln1compprop) =>
% 99.20/13.37 ((
% 99.20/13.37 (breln1compI) =>
% 99.20/13.37 ((
% 99.20/13.37 (breln1compE) =>
% 99.20/13.37 ((
% 99.20/13.37 (breln1compEex) =>
% 99.20/13.37 ((
% 99.20/13.37 (breln1unionprop) =>
% 99.20/13.37 ((
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% 99.20/13.37 ((
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% 99.20/13.37 ((
% 99.20/13.37 (breln1unionI) =>
% 99.20/13.37 ((
% 99.20/13.37 (breln1unionE) =>
% 99.20/13.37 ((
% 99.20/13.37 (breln1unionEcases) =>
% 99.20/13.37 ((
% 99.20/13.37 (breln1unionCommutes) =>
% 99.20/13.37 ((
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% 99.20/13.37 ((
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% 99.20/13.37 ((
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% 99.20/13.37 ((
% 99.20/13.37 (woz2B) =>
% 99.20/13.37 ((
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% 99.20/13.37 ((
% 99.20/13.37 (image1Ex1) =>
% 99.20/13.37 ((
% 99.20/13.37 (image1Equiv) =>
% 99.20/13.37 ((
% 99.20/13.37 (image1E) =>
% 99.20/13.37 ((
% 99.20/13.37 (image1I) =>
% 99.20/13.37 ((
% 99.20/13.37 (injFuncInInjFuncSet) =>
% 99.20/13.37 ((
% 99.20/13.37 (injFuncSetFuncIn) =>
% 99.20/13.37 ((
% 99.20/13.37 (injFuncSetFuncInj) =>
% 99.20/13.37 ((
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% 99.20/13.37 (
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% 99.20/13.37 (
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% 99.20/13.37 surjFuncSet)))))))) @
% 99.20/13.37 (
% 99.20/13.37 (
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% 99.20/13.37 (
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% 99.20/13.37 (
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% 99.20/13.37 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
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% 99.20/13.37 ((
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% 99.20/13.37 ((
% 99.20/13.37 (exuE3u) =>
% 99.20/13.37 ((
% 99.20/13.37 (exu__Cong) =>
% 99.20/13.37 ((
% 99.20/13.37 (setadjoin__Cong) =>
% 99.20/13.37 ((
% 99.20/13.37 (powerset__Cong) =>
% 99.20/13.37 ((
% 99.20/13.37 (setunion__Cong) =>
% 99.20/13.37 ((
% 99.20/13.37 (exuEu) =>
% 99.20/13.37 ((
% 99.20/13.37 (descr__Cong) =>
% 99.20/13.37 ((
% 99.20/13.37 (dsetconstr__Cong) =>
% 99.20/13.37 ((
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% 99.20/13.37 ((
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% 99.20/13.37 ((
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% 99.20/13.37 ((
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% 99.20/13.37 ((
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% 99.20/13.37 ((
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% 99.20/13.37 ((
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% 99.20/13.37 ((
% 99.20/13.37 (binintersectSubset3) =>
% 99.20/13.37 ((
% 99.20/13.37 (binintersectER) =>
% 99.20/13.37 ((
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% 99.20/13.37 ((
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% 99.20/13.37 ((
% 99.20/13.37 (binintersectSubset4) =>
% 99.20/13.37 ((
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% 99.20/13.37 ((
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% 99.20/13.37 ((
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% 99.20/13.37 ((
% 99.20/13.37 (setminusEL) =>
% 99.20/13.37 ((
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% 99.20/13.37 ((
% 99.20/13.37 (setminusSubset2) =>
% 99.20/13.37 ((
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% 99.20/13.37 ((
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% 99.20/13.37 ((
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% 99.20/13.37 ((
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% 99.20/13.37 ((
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% 99.20/13.37 ((
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% 99.20/13.37 ((
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% 99.20/13.37 ((
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% 99.20/13.37 ((
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% 99.20/13.37 ((
% 99.20/13.37 (setukpairIR) =>
% 99.20/13.37 ((
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% 99.20/13.37 ((
% 99.20/13.37 (kpairp) =>
% 99.20/13.37 ((
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% 99.20/13.37 ((
% 99.20/13.37 (singletoninpowerset) =>
% 99.20/13.37 ((
% 99.20/13.37 (singletoninpowunion) =>
% 99.20/13.37 ((
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% 99.20/13.37 ((
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% 99.20/13.37 ((
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% 99.20/13.37 ((
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% 99.20/13.37 ((
% 99.20/13.37 (ubforcartprodlem2) =>
% 99.20/13.37 ((
% 99.20/13.37 (ubforcartprodlem3) =>
% 99.20/13.37 ((
% 99.20/13.37 (cartprodpairin) =>
% 99.20/13.37 ((
% 99.20/13.37 (cartprodmempair1) =>
% 99.20/13.37 ((
% 99.20/13.37 (cartprodmempair) =>
% 99.20/13.37 ((
% 99.20/13.37 (setunionE2) =>
% 99.20/13.37 ((
% 99.20/13.37 (setunionsingleton1) =>
% 99.20/13.37 ((
% 99.20/13.37 (setunionsingleton2) =>
% 99.20/13.37 ((
% 99.20/13.37 (setunionsingleton) =>
% 99.20/13.37 ((
% 99.20/13.37 (singletonprop) =>
% 99.20/13.37 ((
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% 99.20/13.37 ((
% 99.20/13.37 (ex1I) =>
% 99.20/13.37 ((
% 99.20/13.37 (ex1I2) =>
% 99.20/13.37 ((
% 99.20/13.37 (singletonsuniq) =>
% 99.20/13.37 ((
% 99.20/13.37 (setukpairinjL1) =>
% 99.20/13.37 ((
% 99.20/13.37 (kfstsingleton) =>
% 99.20/13.37 ((
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% 99.20/13.37 ((
% 99.20/13.37 (kfstpairEq) =>
% 99.20/13.37 ((
% 99.20/13.37 (cartprodfstin) =>
% 99.20/13.37 ((
% 99.20/13.37 (setukpairinjL2) =>
% 99.20/13.37 ((
% 99.20/13.37 (setukpairinjL) =>
% 99.20/13.37 ((
% 99.20/13.37 (setukpairinjR11) =>
% 99.20/13.37 ((
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% 99.20/13.37 ((
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% 99.20/13.37 ((
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% 99.20/13.37 ((
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% 99.20/13.37 ((
% 99.20/13.37 (cartprodpairmemER) =>
% 99.20/13.37 ((
% 99.20/13.37 (cartprodmempaircEq) =>
% 99.20/13.37 ((
% 99.20/13.37 (cartprodfstpairEq) =>
% 99.20/13.37 ((
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% 99.20/13.37 (cartprodpairsurjEq) =>
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% 99.20/13.37 ((
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% 99.20/13.37 ((
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% 99.20/13.37 ((
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% 99.20/13.37 ((
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% 99.20/13.37 ((
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% 99.20/13.37 ((
% 99.20/13.37 (funcGraphProp3) =>
% 99.20/13.37 ((
% 99.20/13.37 (funcGraphProp2) =>
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% 99.20/13.37 ((
% 99.20/13.37 (funcGraphProp4) =>
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% 99.20/13.37 ((
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% 99.20/13.37 ((
% 99.20/13.37 (contrasubsetT3) =>
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% 99.20/13.37 (doubleComplementSub2) =>
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% 99.20/13.37 (complementTnotintersectT) =>
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% 99.20/13.37 ((
% 99.20/13.37 (inIntersectImpInUnion2) =>
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% 99.20/13.37 (intersectInPowersetIntersectUnions) =>
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% 99.20/13.37 (inComplementUnionImpInComplement1) =>
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% 99.20/13.37 ((
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% 99.20/13.37 ((
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% 99.20/13.37 ((
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% 99.20/13.37 ((
% 99.20/13.37 (demorgan2a) =>
% 99.20/13.37 ((
% 99.20/13.37 (demorgan2b2) =>
% 99.20/13.37 ((
% 99.20/13.37 (demorgan2b) =>
% 99.20/13.37 ((
% 99.20/13.37 (demorgan2) =>
% 99.20/13.37 ((
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% 99.20/13.37 ((
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% 99.20/13.37 ((
% 99.20/13.37 (woz13rule2) =>
% 99.20/13.37 ((
% 99.20/13.37 (woz13rule3) =>
% 99.20/13.37 ((
% 99.20/13.37 (woz13rule4) =>
% 99.20/13.37 ((
% 99.20/13.37 (woz1_1) =>
% 99.20/13.37 ((
% 99.20/13.37 (woz1_2) =>
% 99.20/13.37 ((
% 99.20/13.37 (woz1_3) =>
% 99.20/13.37 ((
% 99.20/13.37 (woz1_4) =>
% 99.20/13.37 ((
% 99.20/13.37 (woz1_5) =>
% 99.20/13.37 ((
% 99.20/13.37 (breln1all2) =>
% 99.20/13.37 ((
% 99.20/13.37 (breln1SetBreln1) =>
% 99.20/13.37 ((
% 99.20/13.37 (choice2fnsingleton) =>
% 99.20/13.37 ((
% 99.20/13.37 (setOfPairsIsBReln1) =>
% 99.20/13.37 ((
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% 99.20/13.37 ((
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% 99.20/13.37 ((
% 99.20/13.37 (eqbreln1) =>
% 99.20/13.37 ((
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% 99.20/13.37 ((
% 99.20/13.37 (breln1invI) =>
% 99.20/13.37 ((
% 99.20/13.37 (breln1invE) =>
% 99.20/13.37 ((
% 99.20/13.37 (breln1compprop) =>
% 99.20/13.37 ((
% 99.20/13.37 (breln1compI) =>
% 99.20/13.37 ((
% 99.20/13.37 (breln1compE) =>
% 99.20/13.37 ((
% 99.20/13.37 (breln1compEex) =>
% 99.20/13.37 ((
% 99.20/13.37 (breln1unionprop) =>
% 99.20/13.37 ((
% 99.20/13.37 (breln1unionIL) =>
% 99.20/13.37 ((
% 99.20/13.37 (breln1unionIR) =>
% 99.20/13.37 ((
% 99.20/13.37 (breln1unionI) =>
% 99.20/13.37 ((
% 99.20/13.37 (breln1unionE) =>
% 99.20/13.37 ((
% 99.20/13.37 (breln1unionEcases) =>
% 99.20/13.37 ((
% 99.20/13.37 (breln1unionCommutes) =>
% 99.20/13.37 ((
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% 99.20/13.37 ((
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% 99.20/13.37 ((
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% 99.20/13.37 ((
% 99.20/13.37 (woz2B) =>
% 99.20/13.37 ((
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% 99.20/13.37 ((
% 99.20/13.37 (image1Ex1) =>
% 99.20/13.37 ((
% 99.20/13.37 (image1Equiv) =>
% 99.20/13.37 ((
% 99.20/13.37 (image1E) =>
% 99.20/13.37 ((
% 99.20/13.37 (image1I) =>
% 99.20/13.37 ((
% 99.20/13.37 (injFuncInInjFuncSet) =>
% 99.20/13.37 ((
% 99.20/13.37 (injFuncSetFuncIn) =>
% 99.20/13.37 ((
% 99.20/13.37 (injFuncSetFuncInj) =>
% 99.20/13.37 ((
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% 99.20/13.37 (
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% 99.20/13.37 (
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% 99.20/13.37 surjFuncSet)))))))) @
% 99.20/13.37 (
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% 99.20/13.37 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
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% 99.20/13.37 ((
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% 99.20/13.37 ((
% 99.20/13.37 (exu__Cong) =>
% 99.20/13.37 ((
% 99.20/13.37 (setadjoin__Cong) =>
% 99.20/13.37 ((
% 99.20/13.37 (powerset__Cong) =>
% 99.20/13.37 ((
% 99.20/13.37 (setunion__Cong) =>
% 99.20/13.37 ((
% 99.20/13.37 (exuEu) =>
% 99.20/13.37 ((
% 99.20/13.37 (descr__Cong) =>
% 99.20/13.37 ((
% 99.20/13.37 (dsetconstr__Cong) =>
% 99.20/13.37 ((
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% 99.20/13.37 ((
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% 99.20/13.37 ((
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% 99.20/13.37 ((
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% 99.20/13.37 ((
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% 99.20/13.37 ((
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% 99.20/13.37 ((
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% 99.20/13.37 ((
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% 99.20/13.37 ((
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% 99.20/13.37 ((
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% 99.20/13.37 ((
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% 99.20/13.37 ((
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% 99.20/13.37 ((
% 99.20/13.37 (binintersectSubset3) =>
% 99.20/13.37 ((
% 99.20/13.37 (binintersectER) =>
% 99.20/13.37 ((
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% 99.20/13.37 ((
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% 99.20/13.37 ((
% 99.20/13.37 (binintersectSubset4) =>
% 99.20/13.37 ((
% 99.20/13.37 (binintersectSubset1) =>
% 99.20/13.37 ((
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% 99.20/13.37 ((
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% 99.20/13.37 ((
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% 99.20/13.37 ((
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% 99.20/13.37 ((
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% 99.20/13.37 ((
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% 99.20/13.37 ((
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% 99.20/13.37 ((
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% 99.20/13.37 ((
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% 99.20/13.37 ((
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% 99.20/13.37 ((
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% 99.20/13.37 ((
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% 99.20/13.37 ((
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% 99.20/13.37 ((
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% 99.20/13.37 ((
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% 99.20/13.37 ((
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% 99.20/13.37 ((
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% 99.20/13.37 ((
% 99.20/13.37 (setukpairIR) =>
% 99.20/13.37 ((
% 99.20/13.37 (kpairiskpair) =>
% 99.20/13.37 ((
% 99.20/13.37 (kpairp) =>
% 99.20/13.37 ((
% 99.20/13.37 (singletonsubset) =>
% 99.20/13.37 ((
% 99.20/13.37 (singletoninpowerset) =>
% 99.20/13.37 ((
% 99.20/13.37 (singletoninpowunion) =>
% 99.20/13.37 ((
% 99.20/13.37 (upairset2E) =>
% 99.20/13.37 ((
% 99.20/13.37 (upairsubunion) =>
% 99.20/13.37 ((
% 99.20/13.37 (upairinpowunion) =>
% 99.20/13.37 ((
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% 99.20/13.37 ((
% 99.20/13.37 (ubforcartprodlem2) =>
% 99.20/13.37 ((
% 99.20/13.37 (ubforcartprodlem3) =>
% 99.20/13.37 ((
% 99.20/13.37 (cartprodpairin) =>
% 99.20/13.37 ((
% 99.20/13.37 (cartprodmempair1) =>
% 99.20/13.37 ((
% 99.20/13.37 (cartprodmempair) =>
% 99.20/13.37 ((
% 99.20/13.37 (setunionE2) =>
% 99.20/13.37 ((
% 99.20/13.37 (setunionsingleton1) =>
% 99.20/13.37 ((
% 99.20/13.37 (setunionsingleton2) =>
% 99.20/13.37 ((
% 99.20/13.37 (setunionsingleton) =>
% 99.20/13.37 ((
% 99.20/13.37 (singletonprop) =>
% 99.20/13.37 ((
% 99.20/13.37 (ex1E1) =>
% 99.20/13.37 ((
% 99.20/13.37 (ex1I) =>
% 99.20/13.37 ((
% 99.20/13.37 (ex1I2) =>
% 99.20/13.37 ((
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% 99.20/13.37 ((
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% 99.20/13.37 (cartprodpairmemER) =>
% 99.20/13.37 ((
% 99.20/13.37 (cartprodmempaircEq) =>
% 99.20/13.37 ((
% 99.20/13.37 (cartprodfstpairEq) =>
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% 99.20/13.37 (cartprodpairsurjEq) =>
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% 99.20/13.37 ((
% 99.20/13.37 (lamp) =>
% 99.20/13.37 ((
% 99.20/13.37 (lam2p) =>
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% 99.20/13.37 ((
% 99.20/13.37 (funcGraphProp3) =>
% 99.20/13.37 ((
% 99.20/13.37 (funcGraphProp2) =>
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% 99.20/13.37 ((
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% 99.20/13.37 ((
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% 99.20/13.37 ((
% 99.20/13.37 (contrasubsetT3) =>
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% 99.20/13.37 ((
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% 99.20/13.37 (complementTnotintersectT) =>
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% 99.20/13.37 ((
% 99.20/13.37 (inIntersectImpInUnion2) =>
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% 99.20/13.37 (intersectInPowersetIntersectUnions) =>
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% 99.20/13.37 ((
% 99.20/13.37 (demorgan2a) =>
% 99.20/13.37 ((
% 99.20/13.37 (demorgan2b2) =>
% 99.20/13.37 ((
% 99.20/13.37 (demorgan2b) =>
% 99.20/13.37 ((
% 99.20/13.37 (demorgan2) =>
% 99.20/13.37 ((
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% 99.20/13.37 ((
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% 99.20/13.37 ((
% 99.20/13.37 (woz13rule2) =>
% 99.20/13.37 ((
% 99.20/13.37 (woz13rule3) =>
% 99.20/13.37 ((
% 99.20/13.37 (woz13rule4) =>
% 99.20/13.37 ((
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% 99.20/13.37 ((
% 99.20/13.37 (woz1_2) =>
% 99.20/13.37 ((
% 99.20/13.37 (woz1_3) =>
% 99.20/13.37 ((
% 99.20/13.37 (woz1_4) =>
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% 99.20/13.37 (woz1_5) =>
% 99.20/13.37 ((
% 99.20/13.37 (breln1all2) =>
% 99.20/13.37 ((
% 99.20/13.37 (breln1SetBreln1) =>
% 99.20/13.37 ((
% 99.20/13.37 (choice2fnsingleton) =>
% 99.20/13.37 ((
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% 99.20/13.37 ((
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% 99.20/13.37 ((
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% 99.20/13.37 ((
% 99.20/13.37 (breln1invE) =>
% 99.20/13.37 ((
% 99.20/13.37 (breln1compprop) =>
% 99.20/13.37 ((
% 99.20/13.37 (breln1compI) =>
% 99.20/13.37 ((
% 99.20/13.37 (breln1compE) =>
% 99.20/13.37 ((
% 99.20/13.37 (breln1compEex) =>
% 99.20/13.37 ((
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% 99.20/13.37 ((
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% 99.20/13.37 ((
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% 99.20/13.37 ((
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% 99.20/13.37 ((
% 99.20/13.37 (breln1unionE) =>
% 99.20/13.37 ((
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% 99.20/13.37 ((
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% 99.20/13.37 ((
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% 99.20/13.37 ((
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% 99.20/13.37 ((
% 99.20/13.37 (image1I) =>
% 99.20/13.37 ((
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% 99.20/13.37 ((
% 99.20/13.37 (injFuncSetFuncIn) =>
% 99.20/13.37 ((
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% 99.20/13.37 (
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% 99.20/13.37 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
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% 99.20/13.37 (powerset__Cong) =>
% 99.20/13.37 ((
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% 99.20/13.37 ((
% 99.20/13.37 (exuEu) =>
% 99.20/13.37 ((
% 99.20/13.37 (descr__Cong) =>
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% 99.20/13.37 ((
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% 99.20/13.37 ((
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% 99.20/13.37 ((
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% 99.20/13.37 ((
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% 99.20/13.37 ((
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% 99.20/13.37 ((
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% 99.20/13.37 ((
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% 99.20/13.37 ((
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% 99.20/13.37 ((
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% 99.20/13.37 ((
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% 99.20/13.37 ((
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% 99.20/13.37 ((
% 99.20/13.37 (cartprodfstin) =>
% 99.20/13.37 ((
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% 99.20/13.37 ((
% 99.20/13.37 (setukpairinjL) =>
% 99.20/13.37 ((
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% 99.20/13.37 (kpairsurjEq) =>
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% 99.20/13.37 ((
% 99.20/13.37 (cartprodpairmemEL) =>
% 99.20/13.37 ((
% 99.20/13.37 (cartprodpairmemER) =>
% 99.20/13.37 ((
% 99.20/13.37 (cartprodmempaircEq) =>
% 99.20/13.37 ((
% 99.20/13.37 (cartprodfstpairEq) =>
% 99.20/13.37 ((
% 99.20/13.37 (cartprodsndpairEq) =>
% 99.20/13.37 ((
% 99.20/13.37 (cartprodpairsurjEq) =>
% 99.20/13.37 ((
% 99.20/13.37 (dpsetconstrI) =>
% 99.20/13.37 ((
% 99.20/13.37 (dpsetconstrSub) =>
% 99.20/13.37 ((
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% 99.20/13.37 (dpsetconstrEL2) =>
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% 99.20/13.37 ((
% 99.20/13.37 (funcImageSingleton) =>
% 99.20/13.37 ((
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% 99.20/13.37 ((
% 99.20/13.37 (app) =>
% 99.20/13.37 ((
% 99.20/13.37 (infuncsetfunc) =>
% 99.20/13.37 ((
% 99.20/13.37 (ap2p) =>
% 99.20/13.37 ((
% 99.20/13.37 (funcinfuncset) =>
% 99.20/13.37 ((
% 99.20/13.37 (lamProp) =>
% 99.20/13.37 ((
% 99.20/13.37 (lamp) =>
% 99.20/13.37 ((
% 99.20/13.37 (lam2p) =>
% 99.20/13.37 ((
% 99.20/13.37 (brelnall1) =>
% 99.20/13.37 ((
% 99.20/13.37 (brelnall2) =>
% 99.20/13.37 ((
% 99.20/13.37 (ex1E2) =>
% 99.20/13.37 ((
% 99.20/13.37 (funcGraphProp1) =>
% 99.20/13.37 ((
% 99.20/13.37 (funcGraphProp3) =>
% 99.20/13.37 ((
% 99.20/13.37 (funcGraphProp2) =>
% 99.20/13.37 ((
% 99.20/13.37 (funcextLem) =>
% 99.20/13.37 ((
% 99.20/13.37 (funcGraphProp4) =>
% 99.20/13.37 ((
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% 99.20/13.37 ((
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% 99.20/13.37 ((
% 99.20/13.37 (eta1) =>
% 99.20/13.37 ((
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% 99.20/13.37 (beta2) =>
% 99.20/13.37 ((
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% 99.20/13.37 ((
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% 99.20/13.37 ((
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% 99.20/13.37 ((
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% 99.20/13.37 ((
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% 99.20/13.37 ((
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% 99.20/13.37 ((
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% 99.20/13.37 ((
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% 99.20/13.37 ((
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% 99.20/13.37 ((
% 99.20/13.37 (complementTE1) =>
% 99.20/13.37 ((
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% 99.20/13.37 ((
% 99.20/13.37 (binintersectTERcontra) =>
% 99.20/13.37 ((
% 99.20/13.37 (contrasubsetT) =>
% 99.20/13.37 ((
% 99.20/13.37 (contrasubsetT1) =>
% 99.20/13.37 ((
% 99.20/13.37 (contrasubsetT2) =>
% 99.20/13.37 ((
% 99.20/13.37 (contrasubsetT3) =>
% 99.20/13.37 ((
% 99.20/13.37 (doubleComplementI1) =>
% 99.20/13.37 ((
% 99.20/13.37 (doubleComplementE1) =>
% 99.20/13.37 ((
% 99.20/13.37 (doubleComplementSub1) =>
% 99.20/13.37 ((
% 99.20/13.37 (doubleComplementSub2) =>
% 99.20/13.37 ((
% 99.20/13.37 (doubleComplementEq) =>
% 99.20/13.37 ((
% 99.20/13.37 (complementTnotintersectT) =>
% 99.20/13.37 ((
% 99.20/13.37 (complementImpComplementIntersect) =>
% 99.20/13.37 ((
% 99.20/13.37 (complementSubsetComplementIntersect) =>
% 99.20/13.37 ((
% 99.20/13.37 (complementInPowersetComplementIntersect) =>
% 99.20/13.37 ((
% 99.20/13.37 (contraSubsetComplement) =>
% 99.20/13.37 ((
% 99.20/13.37 (complementTcontraSubset) =>
% 99.20/13.37 ((
% 99.20/13.37 (binunionTILcontra) =>
% 99.20/13.37 ((
% 99.20/13.37 (binunionTIRcontra) =>
% 99.20/13.37 ((
% 99.20/13.37 (inIntersectImpInUnion) =>
% 99.20/13.37 ((
% 99.20/13.37 (inIntersectImpInUnion2) =>
% 99.20/13.37 ((
% 99.20/13.37 (inIntersectImpInIntersectUnions) =>
% 99.20/13.37 ((
% 99.20/13.37 (intersectInPowersetIntersectUnions) =>
% 99.20/13.37 ((
% 99.20/13.37 (inComplementUnionImpNotIn1) =>
% 99.20/13.37 ((
% 99.20/13.37 (inComplementUnionImpInComplement1) =>
% 99.20/13.37 ((
% 99.20/13.37 (binunionTE) =>
% 99.20/13.37 ((
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% 99.20/13.37 ((
% 99.20/13.37 (demorgan2a1) =>
% 99.20/13.37 ((
% 99.20/13.37 (complementUnionInPowersetComplement) =>
% 99.20/13.37 ((
% 99.20/13.37 (demorgan2a2) =>
% 99.20/13.37 ((
% 99.20/13.37 (demorgan1a) =>
% 99.20/13.37 ((
% 99.20/13.37 (demorgan1b) =>
% 99.20/13.37 ((
% 99.20/13.37 (demorgan1) =>
% 99.20/13.37 ((
% 99.20/13.37 (demorgan2a) =>
% 99.20/13.37 ((
% 99.20/13.37 (demorgan2b2) =>
% 99.20/13.37 ((
% 99.20/13.37 (demorgan2b) =>
% 99.20/13.37 ((
% 99.20/13.37 (demorgan2) =>
% 99.20/13.37 ((
% 99.20/13.37 (woz13rule0) =>
% 99.20/13.37 ((
% 99.20/13.37 (woz13rule1) =>
% 99.20/13.37 ((
% 99.20/13.37 (woz13rule2) =>
% 99.20/13.37 ((
% 99.20/13.37 (woz13rule3) =>
% 99.20/13.37 ((
% 99.20/13.37 (woz13rule4) =>
% 99.20/13.37 ((
% 99.20/13.37 (woz1_1) =>
% 99.20/13.37 ((
% 99.20/13.37 (woz1_2) =>
% 99.20/13.37 ((
% 99.20/13.37 (woz1_3) =>
% 99.20/13.37 ((
% 99.20/13.37 (woz1_4) =>
% 99.20/13.37 ((
% 99.20/13.37 (woz1_5) =>
% 99.20/13.37 ((
% 99.20/13.37 (breln1all2) =>
% 99.20/13.37 ((
% 99.20/13.37 (breln1SetBreln1) =>
% 99.20/13.37 ((
% 99.20/13.37 (choice2fnsingleton) =>
% 99.20/13.37 ((
% 99.20/13.37 (setOfPairsIsBReln1) =>
% 99.20/13.37 ((
% 99.20/13.37 (breln1all1) =>
% 99.20/13.37 ((
% 99.20/13.37 (subbreln1) =>
% 99.20/13.37 ((
% 99.20/13.37 (eqbreln1) =>
% 99.20/13.37 ((
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% 99.20/13.37 ((
% 99.20/13.37 (breln1invI) =>
% 99.20/13.37 ((
% 99.20/13.37 (breln1invE) =>
% 99.20/13.37 ((
% 99.20/13.37 (breln1compprop) =>
% 99.20/13.37 ((
% 99.20/13.37 (breln1compI) =>
% 99.20/13.37 ((
% 99.20/13.37 (breln1compE) =>
% 99.20/13.37 ((
% 99.20/13.37 (breln1compEex) =>
% 99.20/13.37 ((
% 99.20/13.37 (breln1unionprop) =>
% 99.20/13.37 ((
% 99.20/13.37 (breln1unionIL) =>
% 99.20/13.37 ((
% 99.20/13.37 (breln1unionIR) =>
% 99.20/13.37 ((
% 99.20/13.37 (breln1unionI) =>
% 99.20/13.37 ((
% 99.20/13.37 (breln1unionE) =>
% 99.20/13.37 ((
% 99.20/13.37 (breln1unionEcases) =>
% 99.20/13.37 ((
% 99.20/13.37 (breln1unionCommutes) =>
% 99.20/13.37 ((
% 99.20/13.37 (woz2Ex) =>
% 99.20/13.37 ((
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% 99.20/13.37 ((
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% 99.20/13.37 ((
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% 99.20/13.37 ((
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% 99.20/13.37 ((
% 99.20/13.37 (image1Ex1) =>
% 99.20/13.37 ((
% 99.20/13.37 (image1Equiv) =>
% 99.20/13.37 ((
% 99.20/13.37 (image1E) =>
% 99.20/13.37 ((
% 99.20/13.37 (image1I) =>
% 99.20/13.37 ((
% 99.20/13.37 (injFuncInInjFuncSet) =>
% 99.20/13.37 ((
% 99.20/13.37 (injFuncSetFuncIn) =>
% 99.20/13.37 ((
% 99.20/13.37 (injFuncSetFuncInj) =>
% 99.20/13.37 ((
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% 99.20/13.37 (('#B') @ (
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% 99.20/13.37 (
% 99.20/13.37 (
% 99.20/13.37 ('#B') @ (
% 99.20/13.37 (
% 99.20/13.37 ('#B') @ (
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% 99.20/13.37 (
% 99.20/13.37 (
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% 99.20/13.37 (
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% 99.20/13.37 (
% 99.20/13.37 (
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% 99.20/13.37 ('#B') @ (
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% 99.20/13.37 (
% 99.20/13.37 (
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% 99.20/13.37 (
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% 99.20/13.37 (
% 99.20/13.37 ('#B') @ (
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% 99.20/13.37 (
% 99.20/13.37 (
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% 99.20/13.37 (
% 99.20/13.37 ('#B') @ (
% 99.20/13.37 (
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% 99.20/13.37 surjFuncSet)))))))) @
% 99.20/13.37 (
% 99.20/13.37 (
% 99.20/13.37 ('#B') @ (
% 99.20/13.37 (
% 99.20/13.37 ('#B') @ (
% 99.20/13.37 (
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% 99.20/13.37 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.20/13.37 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl376])).
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% 99.20/13.37 (((quantDeMorgan4) =>
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% 99.20/13.37 (((exu__Cong) =>
% 99.20/13.37 ((
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% 99.20/13.37 ((
% 99.20/13.37 (powerset__Cong) =>
% 99.20/13.37 ((
% 99.20/13.37 (setunion__Cong) =>
% 99.20/13.37 ((
% 99.20/13.37 (exuEu) =>
% 99.20/13.37 ((
% 99.20/13.37 (descr__Cong) =>
% 99.20/13.37 ((
% 99.20/13.37 (dsetconstr__Cong) =>
% 99.20/13.37 ((
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% 99.20/13.37 ((
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% 99.20/13.37 ((
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% 99.20/13.37 ((
% 99.20/13.37 (subsetE2) =>
% 99.20/13.37 ((
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% 99.20/13.37 ((
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% 99.20/13.37 ((
% 99.20/13.37 (notequalI2) =>
% 99.20/13.37 ((
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% 99.20/13.37 ((
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% 99.20/13.37 ((
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% 99.20/13.37 ((
% 99.20/13.37 (sepSubset) =>
% 99.20/13.37 ((
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% 99.20/13.37 ((
% 99.20/13.37 (upairset2IR) =>
% 99.20/13.37 ((
% 99.20/13.37 (binunionIR) =>
% 99.20/13.37 ((
% 99.20/13.37 (binunionEcases) =>
% 99.20/13.37 ((
% 99.20/13.37 (binunionE) =>
% 99.20/13.37 ((
% 99.20/13.37 (binunionLsub) =>
% 99.20/13.37 ((
% 99.20/13.37 (binunionRsub) =>
% 99.20/13.37 ((
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% 99.20/13.37 ((
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% 99.20/13.37 ((
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% 99.20/13.37 ((
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% 99.20/13.37 ((
% 99.20/13.37 (binintersectSubset2) =>
% 99.20/13.37 ((
% 99.20/13.37 (binintersectSubset3) =>
% 99.20/13.37 ((
% 99.20/13.37 (binintersectER) =>
% 99.20/13.37 ((
% 99.20/13.37 (disjointsetsI1) =>
% 99.20/13.37 ((
% 99.20/13.37 (binintersectRsub) =>
% 99.20/13.37 ((
% 99.20/13.37 (binintersectSubset4) =>
% 99.20/13.37 ((
% 99.20/13.37 (binintersectSubset1) =>
% 99.20/13.37 ((
% 99.20/13.37 (bs114d) =>
% 99.20/13.37 ((
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% 99.20/13.37 ((
% 99.20/13.37 (setminusEL) =>
% 99.20/13.37 ((
% 99.20/13.37 (setminusER) =>
% 99.20/13.37 ((
% 99.20/13.37 (setminusSubset2) =>
% 99.20/13.37 ((
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% 99.20/13.37 ((
% 99.20/13.37 (setminusELneg) =>
% 99.20/13.37 ((
% 99.20/13.37 (setminusILneg) =>
% 99.20/13.37 ((
% 99.20/13.37 (setminusIRneg) =>
% 99.20/13.37 ((
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% 99.20/13.37 ((
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% 99.20/13.37 ((
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% 99.20/13.37 ((
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% 99.20/13.37 ((
% 99.20/13.37 (symdiffI2) =>
% 99.20/13.37 ((
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% 99.20/13.37 (kpairp) =>
% 99.20/13.37 ((
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% 99.20/13.37 ((
% 99.20/13.37 (singletoninpowerset) =>
% 99.20/13.37 ((
% 99.20/13.37 (singletoninpowunion) =>
% 99.20/13.37 ((
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% 99.20/13.37 ((
% 99.20/13.37 (upairsubunion) =>
% 99.20/13.37 ((
% 99.20/13.37 (upairinpowunion) =>
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% 99.20/13.37 ((
% 99.20/13.37 (ubforcartprodlem2) =>
% 99.20/13.37 ((
% 99.20/13.37 (ubforcartprodlem3) =>
% 99.20/13.37 ((
% 99.20/13.37 (cartprodpairin) =>
% 99.20/13.37 ((
% 99.20/13.37 (cartprodmempair1) =>
% 99.20/13.37 ((
% 99.20/13.37 (cartprodmempair) =>
% 99.20/13.37 ((
% 99.20/13.37 (setunionE2) =>
% 99.20/13.37 ((
% 99.20/13.37 (setunionsingleton1) =>
% 99.20/13.37 ((
% 99.20/13.37 (setunionsingleton2) =>
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% 99.20/13.37 ((
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% 99.20/13.37 ((
% 99.20/13.37 (ex1I2) =>
% 99.20/13.37 ((
% 99.20/13.37 (singletonsuniq) =>
% 99.20/13.37 ((
% 99.20/13.37 (setukpairinjL1) =>
% 99.20/13.37 ((
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% 99.20/13.37 ((
% 99.20/13.37 (theprop) =>
% 99.20/13.37 ((
% 99.20/13.37 (kfstpairEq) =>
% 99.20/13.37 ((
% 99.20/13.37 (cartprodfstin) =>
% 99.20/13.37 ((
% 99.20/13.37 (setukpairinjL2) =>
% 99.20/13.37 ((
% 99.20/13.37 (setukpairinjL) =>
% 99.20/13.37 ((
% 99.20/13.37 (setukpairinjR11) =>
% 99.20/13.37 ((
% 99.20/13.37 (setukpairinjR12) =>
% 99.20/13.37 ((
% 99.20/13.37 (setukpairinjR1) =>
% 99.20/13.37 ((
% 99.20/13.37 (upairequniteq) =>
% 99.20/13.37 ((
% 99.20/13.37 (setukpairinjR2) =>
% 99.20/13.37 ((
% 99.20/13.37 (setukpairinjR) =>
% 99.20/13.37 ((
% 99.20/13.37 (ksndsingleton) =>
% 99.20/13.37 ((
% 99.20/13.37 (ksndpairEq) =>
% 99.20/13.37 ((
% 99.20/13.37 (kpairsurjEq) =>
% 99.20/13.37 ((
% 99.20/13.37 (cartprodsndin) =>
% 99.20/13.37 ((
% 99.20/13.37 (cartprodpairmemEL) =>
% 99.20/13.37 ((
% 99.20/13.37 (cartprodpairmemER) =>
% 99.20/13.37 ((
% 99.20/13.37 (cartprodmempaircEq) =>
% 99.20/13.37 ((
% 99.20/13.37 (cartprodfstpairEq) =>
% 99.20/13.37 ((
% 99.20/13.37 (cartprodsndpairEq) =>
% 99.20/13.37 ((
% 99.20/13.37 (cartprodpairsurjEq) =>
% 99.20/13.37 ((
% 99.20/13.37 (dpsetconstrI) =>
% 99.20/13.37 ((
% 99.20/13.37 (dpsetconstrSub) =>
% 99.20/13.37 ((
% 99.20/13.37 (setOfPairsIsBReln) =>
% 99.20/13.37 ((
% 99.20/13.37 (dpsetconstrERa) =>
% 99.20/13.37 ((
% 99.20/13.37 (dpsetconstrEL1) =>
% 99.20/13.37 ((
% 99.20/13.37 (dpsetconstrEL2) =>
% 99.20/13.37 ((
% 99.20/13.37 (dpsetconstrER) =>
% 99.20/13.37 ((
% 99.20/13.37 (funcImageSingleton) =>
% 99.20/13.37 ((
% 99.20/13.37 (apProp) =>
% 99.20/13.37 ((
% 99.20/13.37 (app) =>
% 99.20/13.37 ((
% 99.20/13.37 (infuncsetfunc) =>
% 99.20/13.37 ((
% 99.20/13.37 (ap2p) =>
% 99.20/13.37 ((
% 99.20/13.37 (funcinfuncset) =>
% 99.20/13.37 ((
% 99.20/13.37 (lamProp) =>
% 99.20/13.37 ((
% 99.20/13.37 (lamp) =>
% 99.20/13.37 ((
% 99.20/13.37 (lam2p) =>
% 99.20/13.37 ((
% 99.20/13.37 (brelnall1) =>
% 99.20/13.37 ((
% 99.20/13.37 (brelnall2) =>
% 99.20/13.37 ((
% 99.20/13.37 (ex1E2) =>
% 99.20/13.37 ((
% 99.20/13.37 (funcGraphProp1) =>
% 99.20/13.37 ((
% 99.20/13.37 (funcGraphProp3) =>
% 99.20/13.37 ((
% 99.20/13.37 (funcGraphProp2) =>
% 99.20/13.37 ((
% 99.20/13.37 (funcextLem) =>
% 99.20/13.37 ((
% 99.20/13.37 (funcGraphProp4) =>
% 99.20/13.37 ((
% 99.20/13.37 (subbreln) =>
% 99.20/13.37 ((
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% 99.20/13.37 ((
% 99.20/13.37 (funcext) =>
% 99.20/13.37 ((
% 99.20/13.37 (funcext2) =>
% 99.20/13.37 ((
% 99.20/13.37 (ap2apEq1) =>
% 99.20/13.37 ((
% 99.20/13.37 (ap2apEq2) =>
% 99.20/13.37 ((
% 99.20/13.37 (beta1) =>
% 99.20/13.37 ((
% 99.20/13.37 (eta1) =>
% 99.20/13.37 ((
% 99.20/13.37 (lam2lamEq) =>
% 99.20/13.37 ((
% 99.20/13.37 (beta2) =>
% 99.20/13.37 ((
% 99.20/13.37 (eta2) =>
% 99.20/13.37 ((
% 99.20/13.37 (iffalseProp1) =>
% 99.20/13.37 ((
% 99.20/13.37 (iffalseProp2) =>
% 99.20/13.37 ((
% 99.20/13.37 (iftrueProp1) =>
% 99.20/13.37 ((
% 99.20/13.37 (iftrueProp2) =>
% 99.20/13.37 ((
% 99.20/13.37 (ifSingleton) =>
% 99.20/13.37 ((
% 99.20/13.37 (ifp) =>
% 99.20/13.37 ((
% 99.20/13.37 (theeq) =>
% 99.20/13.37 ((
% 99.20/13.37 (iftrue) =>
% 99.20/13.37 ((
% 99.20/13.37 (iffalse) =>
% 99.20/13.37 ((
% 99.20/13.37 (iftrueorfalse) =>
% 99.20/13.37 ((
% 99.20/13.37 (binintersectT_lem) =>
% 99.20/13.37 ((
% 99.20/13.37 (binunionT_lem) =>
% 99.20/13.37 ((
% 99.20/13.37 (powersetT_lem) =>
% 99.20/13.37 ((
% 99.20/13.37 (setminusT_lem) =>
% 99.20/13.37 ((
% 99.20/13.37 (complementT_lem) =>
% 99.20/13.37 ((
% 99.20/13.37 (setextT) =>
% 99.20/13.37 ((
% 99.20/13.37 (subsetTI) =>
% 99.20/13.37 ((
% 99.20/13.37 (powersetTI1) =>
% 99.20/13.37 ((
% 99.20/13.37 (powersetTE1) =>
% 99.20/13.37 ((
% 99.20/13.37 (complementTI1) =>
% 99.20/13.37 ((
% 99.20/13.37 (complementTE1) =>
% 99.20/13.37 ((
% 99.20/13.37 (binintersectTELcontra) =>
% 99.20/13.37 ((
% 99.20/13.37 (binintersectTERcontra) =>
% 99.20/13.37 ((
% 99.20/13.37 (contrasubsetT) =>
% 99.20/13.37 ((
% 99.20/13.37 (contrasubsetT1) =>
% 99.20/13.37 ((
% 99.20/13.37 (contrasubsetT2) =>
% 99.20/13.37 ((
% 99.20/13.37 (contrasubsetT3) =>
% 99.20/13.37 ((
% 99.20/13.37 (doubleComplementI1) =>
% 99.20/13.37 ((
% 99.20/13.37 (doubleComplementE1) =>
% 99.20/13.37 ((
% 99.20/13.37 (doubleComplementSub1) =>
% 99.20/13.37 ((
% 99.20/13.37 (doubleComplementSub2) =>
% 99.20/13.37 ((
% 99.20/13.37 (doubleComplementEq) =>
% 99.20/13.37 ((
% 99.20/13.37 (complementTnotintersectT) =>
% 99.20/13.37 ((
% 99.20/13.37 (complementImpComplementIntersect) =>
% 99.20/13.37 ((
% 99.20/13.37 (complementSubsetComplementIntersect) =>
% 99.20/13.37 ((
% 99.20/13.37 (complementInPowersetComplementIntersect) =>
% 99.20/13.37 ((
% 99.20/13.37 (contraSubsetComplement) =>
% 99.20/13.37 ((
% 99.20/13.37 (complementTcontraSubset) =>
% 99.20/13.37 ((
% 99.20/13.37 (binunionTILcontra) =>
% 99.20/13.37 ((
% 99.20/13.37 (binunionTIRcontra) =>
% 99.20/13.37 ((
% 99.20/13.37 (inIntersectImpInUnion) =>
% 99.20/13.37 ((
% 99.20/13.37 (inIntersectImpInUnion2) =>
% 99.20/13.37 ((
% 99.20/13.37 (inIntersectImpInIntersectUnions) =>
% 99.20/13.37 ((
% 99.20/13.37 (intersectInPowersetIntersectUnions) =>
% 99.20/13.37 ((
% 99.20/13.37 (inComplementUnionImpNotIn1) =>
% 99.20/13.37 ((
% 99.20/13.37 (inComplementUnionImpInComplement1) =>
% 99.20/13.37 ((
% 99.20/13.37 (binunionTE) =>
% 99.20/13.37 ((
% 99.20/13.37 (binunionTEcontra) =>
% 99.20/13.37 ((
% 99.20/13.37 (demorgan2a1) =>
% 99.20/13.37 ((
% 99.20/13.37 (complementUnionInPowersetComplement) =>
% 99.20/13.37 ((
% 99.20/13.37 (demorgan2a2) =>
% 99.20/13.37 ((
% 99.20/13.37 (demorgan1a) =>
% 99.20/13.37 ((
% 99.20/13.37 (demorgan1b) =>
% 99.20/13.37 ((
% 99.20/13.37 (demorgan1) =>
% 99.20/13.37 ((
% 99.20/13.37 (demorgan2a) =>
% 99.20/13.37 ((
% 99.20/13.37 (demorgan2b2) =>
% 99.20/13.37 ((
% 99.20/13.37 (demorgan2b) =>
% 99.20/13.37 ((
% 99.20/13.37 (demorgan2) =>
% 99.20/13.37 ((
% 99.20/13.37 (woz13rule0) =>
% 99.20/13.37 ((
% 99.20/13.37 (woz13rule1) =>
% 99.20/13.37 ((
% 99.20/13.37 (woz13rule2) =>
% 99.20/13.37 ((
% 99.20/13.37 (woz13rule3) =>
% 99.20/13.37 ((
% 99.20/13.37 (woz13rule4) =>
% 99.20/13.37 ((
% 99.20/13.37 (woz1_1) =>
% 99.20/13.37 ((
% 99.20/13.37 (woz1_2) =>
% 99.20/13.37 ((
% 99.20/13.37 (woz1_3) =>
% 99.20/13.37 ((
% 99.20/13.37 (woz1_4) =>
% 99.20/13.37 ((
% 99.20/13.37 (woz1_5) =>
% 99.20/13.37 ((
% 99.20/13.37 (breln1all2) =>
% 99.20/13.37 ((
% 99.20/13.37 (breln1SetBreln1) =>
% 99.20/13.37 ((
% 99.20/13.37 (choice2fnsingleton) =>
% 99.20/13.37 ((
% 99.20/13.37 (setOfPairsIsBReln1) =>
% 99.20/13.37 ((
% 99.20/13.37 (breln1all1) =>
% 99.20/13.37 ((
% 99.20/13.37 (subbreln1) =>
% 99.20/13.37 ((
% 99.20/13.37 (eqbreln1) =>
% 99.20/13.37 ((
% 99.20/13.37 (breln1invprop) =>
% 99.20/13.37 ((
% 99.20/13.37 (breln1invI) =>
% 99.20/13.37 ((
% 99.20/13.37 (breln1invE) =>
% 99.20/13.37 ((
% 99.20/13.37 (breln1compprop) =>
% 99.20/13.37 ((
% 99.20/13.37 (breln1compI) =>
% 99.20/13.37 ((
% 99.20/13.37 (breln1compE) =>
% 99.20/13.37 ((
% 99.20/13.37 (breln1compEex) =>
% 99.20/13.37 ((
% 99.20/13.37 (breln1unionprop) =>
% 99.20/13.37 ((
% 99.20/13.37 (breln1unionIL) =>
% 99.20/13.37 ((
% 99.20/13.37 (breln1unionIR) =>
% 99.20/13.37 ((
% 99.20/13.37 (breln1unionI) =>
% 99.20/13.37 ((
% 99.20/13.37 (breln1unionE) =>
% 99.20/13.37 ((
% 99.20/13.37 (breln1unionEcases) =>
% 99.20/13.37 ((
% 99.20/13.37 (breln1unionCommutes) =>
% 99.20/13.37 ((
% 99.20/13.37 (woz2Ex) =>
% 99.20/13.37 ((
% 99.20/13.37 (woz2W) =>
% 99.20/13.37 ((
% 99.20/13.37 (woz2A) =>
% 99.20/13.37 ((
% 99.20/13.37 (woz2B) =>
% 99.20/13.37 ((
% 99.20/13.37 (image1Ex) =>
% 99.20/13.37 ((
% 99.20/13.37 (image1Ex1) =>
% 99.20/13.37 ((
% 99.20/13.37 (image1Equiv) =>
% 99.20/13.37 ((
% 99.20/13.37 (image1E) =>
% 99.20/13.37 ((
% 99.20/13.37 (image1I) =>
% 99.20/13.37 ((
% 99.20/13.37 (injFuncInInjFuncSet) =>
% 99.20/13.37 ((
% 99.20/13.37 (injFuncSetFuncIn) =>
% 99.20/13.37 ((
% 99.20/13.37 (injFuncSetFuncInj) =>
% 99.20/13.37 ((
% 99.20/13.37 (!!) @ (
% 99.20/13.37 (('#B') @ (
% 99.20/13.37 !!) @
% 99.20/13.37 (
% 99.20/13.37 (
% 99.20/13.37 ('#B') @ (
% 99.20/13.37 (
% 99.20/13.37 ('#B') @ (
% 99.20/13.37 !!))) @
% 99.20/13.37 (
% 99.20/13.37 (
% 99.20/13.37 ('#S') @ (
% 99.20/13.37 (
% 99.20/13.37 ('#B') @ (
% 99.20/13.37 '#S') @
% 99.20/13.37 (
% 99.20/13.37 (
% 99.20/13.37 ('#B') @ (
% 99.20/13.37 (
% 99.20/13.37 ('#B') @ (
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% 99.20/13.37 (
% 99.20/13.37 (
% 99.20/13.37 ('#B') @ (
% 99.20/13.37 (
% 99.20/13.37 ('#B') @ (
% 99.20/13.37 (
% 99.20/13.37 ('#B') @ (
% 99.20/13.37 =>))))) @
% 99.20/13.37 (
% 99.20/13.37 (
% 99.20/13.37 ('#B') @ (
% 99.20/13.37 (
% 99.20/13.37 ('#B') @ (
% 99.20/13.37 (
% 99.20/13.37 ('#C') @ in)))) @
% 99.20/13.37 surjFuncSet)))))))) @
% 99.20/13.37 (
% 99.20/13.37 (
% 99.20/13.37 ('#B') @ (
% 99.20/13.37 (
% 99.20/13.37 ('#B') @ (
% 99.20/13.37 (
% 99.20/13.37 ('#C') @ in)))) @
% 99.20/13.37 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.20/13.37 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl384])).
% 99.20/13.37 thf(zip_derived_cl400, plain,
% 99.20/13.37 (~ (((setunionI) =>
% 99.20/13.37 (((setunionE) =>
% 99.20/13.37 (((subPowSU) =>
% 99.20/13.37 (((exuE2) =>
% 99.20/13.37 (((nonemptyImpWitness) =>
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% 99.20/13.37 (((eqinunit) =>
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% 99.20/13.37 (((upairsetIR) =>
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% 99.20/13.37 (((quantDeMorgan1) =>
% 99.20/13.37 (((quantDeMorgan2) =>
% 99.20/13.37 (((quantDeMorgan3) =>
% 99.20/13.37 (((quantDeMorgan4) =>
% 99.20/13.37 (((prop2setI) =>
% 99.20/13.37 (((prop2set2propI) =>
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% 99.20/13.37 (((notdallE) =>
% 99.20/13.37 (((exuI1) =>
% 99.20/13.37 (((exuI3) =>
% 99.20/13.37 (((exuI2) =>
% 99.20/13.37 (((inCongP) =>
% 99.20/13.37 (((in__Cong) =>
% 99.20/13.37 (((exuE3u) =>
% 99.20/13.37 (((exu__Cong) =>
% 99.20/13.37 (((setadjoin__Cong) =>
% 99.20/13.37 ((
% 99.20/13.37 (powerset__Cong) =>
% 99.20/13.37 ((
% 99.20/13.37 (setunion__Cong) =>
% 99.20/13.37 ((
% 99.20/13.37 (exuEu) =>
% 99.20/13.37 ((
% 99.20/13.37 (descr__Cong) =>
% 99.20/13.37 ((
% 99.20/13.37 (dsetconstr__Cong) =>
% 99.20/13.37 ((
% 99.20/13.37 (subsetI1) =>
% 99.20/13.37 ((
% 99.20/13.37 (eqimpsubset2) =>
% 99.20/13.37 ((
% 99.20/13.37 (eqimpsubset1) =>
% 99.20/13.37 ((
% 99.20/13.37 (subsetI2) =>
% 99.20/13.37 ((
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% 99.20/13.37 ((
% 99.20/13.37 (subsetE) =>
% 99.20/13.37 ((
% 99.20/13.37 (subsetE2) =>
% 99.20/13.37 ((
% 99.20/13.37 (notsubsetI) =>
% 99.20/13.37 ((
% 99.20/13.37 (notequalI1) =>
% 99.20/13.37 ((
% 99.20/13.37 (notequalI2) =>
% 99.20/13.37 ((
% 99.20/13.37 (subsetRefl) =>
% 99.20/13.37 ((
% 99.20/13.37 (subsetTrans) =>
% 99.20/13.37 ((
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% 99.20/13.37 ((
% 99.20/13.37 (setadjoinSub2) =>
% 99.20/13.37 ((
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% 99.20/13.37 ((
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% 99.20/13.37 ((
% 99.20/13.37 (powersetE1) =>
% 99.20/13.37 ((
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% 99.20/13.37 ((
% 99.20/13.37 (powersetsubset) =>
% 99.20/13.37 ((
% 99.20/13.37 (sepInPowerset) =>
% 99.20/13.37 ((
% 99.20/13.37 (sepSubset) =>
% 99.20/13.37 ((
% 99.20/13.37 (binunionIL) =>
% 99.20/13.37 ((
% 99.20/13.37 (upairset2IR) =>
% 99.20/13.37 ((
% 99.20/13.37 (binunionIR) =>
% 99.20/13.37 ((
% 99.20/13.37 (binunionEcases) =>
% 99.20/13.37 ((
% 99.20/13.37 (binunionE) =>
% 99.20/13.37 ((
% 99.20/13.37 (binunionLsub) =>
% 99.20/13.37 ((
% 99.20/13.37 (binunionRsub) =>
% 99.20/13.37 ((
% 99.20/13.37 (binintersectI) =>
% 99.20/13.37 ((
% 99.20/13.37 (binintersectSubset5) =>
% 99.20/13.37 ((
% 99.20/13.37 (binintersectEL) =>
% 99.20/13.37 ((
% 99.20/13.37 (binintersectLsub) =>
% 99.20/13.37 ((
% 99.20/13.37 (binintersectSubset2) =>
% 99.20/13.37 ((
% 99.20/13.37 (binintersectSubset3) =>
% 99.20/13.37 ((
% 99.20/13.37 (binintersectER) =>
% 99.20/13.37 ((
% 99.20/13.37 (disjointsetsI1) =>
% 99.20/13.37 ((
% 99.20/13.37 (binintersectRsub) =>
% 99.20/13.37 ((
% 99.20/13.37 (binintersectSubset4) =>
% 99.20/13.37 ((
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% 99.20/13.37 ((
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% 99.20/13.37 ((
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% 99.20/13.37 ((
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% 99.20/13.37 (setminusILneg) =>
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% 99.20/13.37 ((
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% 99.20/13.37 ((
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% 99.20/13.37 ((
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% 99.20/13.37 ((
% 99.20/13.37 (cartprodmempair) =>
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% 99.20/13.37 ((
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% 99.20/13.37 ((
% 99.20/13.37 (setunionsingleton2) =>
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% 99.20/13.37 ((
% 99.20/13.37 (ex1I2) =>
% 99.20/13.37 ((
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% 99.20/13.37 ((
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% 99.20/13.37 ((
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% 99.20/13.37 ((
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% 99.20/13.37 ((
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% 99.20/13.37 ((
% 99.20/13.37 (cartprodfstin) =>
% 99.20/13.37 ((
% 99.20/13.37 (setukpairinjL2) =>
% 99.20/13.37 ((
% 99.20/13.37 (setukpairinjL) =>
% 99.20/13.37 ((
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% 99.20/13.37 ((
% 99.20/13.37 (setukpairinjR12) =>
% 99.20/13.37 ((
% 99.20/13.37 (setukpairinjR1) =>
% 99.20/13.37 ((
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% 99.20/13.37 (setukpairinjR) =>
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% 99.20/13.37 ((
% 99.20/13.37 (kpairsurjEq) =>
% 99.20/13.37 ((
% 99.20/13.37 (cartprodsndin) =>
% 99.20/13.37 ((
% 99.20/13.37 (cartprodpairmemEL) =>
% 99.20/13.37 ((
% 99.20/13.37 (cartprodpairmemER) =>
% 99.20/13.37 ((
% 99.20/13.37 (cartprodmempaircEq) =>
% 99.20/13.37 ((
% 99.20/13.37 (cartprodfstpairEq) =>
% 99.20/13.37 ((
% 99.20/13.37 (cartprodsndpairEq) =>
% 99.20/13.37 ((
% 99.20/13.37 (cartprodpairsurjEq) =>
% 99.20/13.37 ((
% 99.20/13.37 (dpsetconstrI) =>
% 99.20/13.37 ((
% 99.20/13.37 (dpsetconstrSub) =>
% 99.20/13.37 ((
% 99.20/13.37 (setOfPairsIsBReln) =>
% 99.20/13.37 ((
% 99.20/13.37 (dpsetconstrERa) =>
% 99.20/13.37 ((
% 99.20/13.37 (dpsetconstrEL1) =>
% 99.20/13.37 ((
% 99.20/13.37 (dpsetconstrEL2) =>
% 99.20/13.37 ((
% 99.20/13.37 (dpsetconstrER) =>
% 99.20/13.37 ((
% 99.20/13.37 (funcImageSingleton) =>
% 99.20/13.37 ((
% 99.20/13.37 (apProp) =>
% 99.20/13.37 ((
% 99.20/13.37 (app) =>
% 99.20/13.37 ((
% 99.20/13.37 (infuncsetfunc) =>
% 99.20/13.37 ((
% 99.20/13.37 (ap2p) =>
% 99.20/13.37 ((
% 99.20/13.37 (funcinfuncset) =>
% 99.20/13.37 ((
% 99.20/13.37 (lamProp) =>
% 99.20/13.37 ((
% 99.20/13.37 (lamp) =>
% 99.20/13.37 ((
% 99.20/13.37 (lam2p) =>
% 99.20/13.37 ((
% 99.20/13.37 (brelnall1) =>
% 99.20/13.37 ((
% 99.20/13.37 (brelnall2) =>
% 99.20/13.37 ((
% 99.20/13.37 (ex1E2) =>
% 99.20/13.37 ((
% 99.20/13.37 (funcGraphProp1) =>
% 99.20/13.37 ((
% 99.20/13.37 (funcGraphProp3) =>
% 99.20/13.37 ((
% 99.20/13.37 (funcGraphProp2) =>
% 99.20/13.37 ((
% 99.20/13.37 (funcextLem) =>
% 99.20/13.37 ((
% 99.20/13.37 (funcGraphProp4) =>
% 99.20/13.37 ((
% 99.20/13.37 (subbreln) =>
% 99.20/13.37 ((
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% 99.20/13.37 ((
% 99.20/13.37 (funcext) =>
% 99.20/13.37 ((
% 99.20/13.37 (funcext2) =>
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% 99.20/13.37 ((
% 99.20/13.37 (ap2apEq2) =>
% 99.20/13.37 ((
% 99.20/13.37 (beta1) =>
% 99.20/13.37 ((
% 99.20/13.37 (eta1) =>
% 99.20/13.37 ((
% 99.20/13.37 (lam2lamEq) =>
% 99.20/13.37 ((
% 99.20/13.37 (beta2) =>
% 99.20/13.37 ((
% 99.20/13.37 (eta2) =>
% 99.20/13.37 ((
% 99.20/13.37 (iffalseProp1) =>
% 99.20/13.37 ((
% 99.20/13.37 (iffalseProp2) =>
% 99.20/13.37 ((
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% 99.20/13.37 ((
% 99.20/13.37 (iftrueProp2) =>
% 99.20/13.37 ((
% 99.20/13.37 (ifSingleton) =>
% 99.20/13.37 ((
% 99.20/13.37 (ifp) =>
% 99.20/13.37 ((
% 99.20/13.37 (theeq) =>
% 99.20/13.37 ((
% 99.20/13.37 (iftrue) =>
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% 99.20/13.37 ((
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% 99.20/13.37 ((
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% 99.20/13.37 ((
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% 99.20/13.37 (setminusT_lem) =>
% 99.20/13.37 ((
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% 99.20/13.37 ((
% 99.20/13.37 (setextT) =>
% 99.20/13.37 ((
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% 99.20/13.37 ((
% 99.20/13.37 (powersetTI1) =>
% 99.20/13.37 ((
% 99.20/13.37 (powersetTE1) =>
% 99.20/13.37 ((
% 99.20/13.37 (complementTI1) =>
% 99.20/13.37 ((
% 99.20/13.37 (complementTE1) =>
% 99.20/13.37 ((
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% 99.20/13.37 ((
% 99.20/13.37 (binintersectTERcontra) =>
% 99.20/13.37 ((
% 99.20/13.37 (contrasubsetT) =>
% 99.20/13.37 ((
% 99.20/13.37 (contrasubsetT1) =>
% 99.20/13.37 ((
% 99.20/13.37 (contrasubsetT2) =>
% 99.20/13.37 ((
% 99.20/13.37 (contrasubsetT3) =>
% 99.20/13.37 ((
% 99.20/13.37 (doubleComplementI1) =>
% 99.20/13.37 ((
% 99.20/13.37 (doubleComplementE1) =>
% 99.20/13.37 ((
% 99.20/13.37 (doubleComplementSub1) =>
% 99.20/13.37 ((
% 99.20/13.37 (doubleComplementSub2) =>
% 99.20/13.37 ((
% 99.20/13.37 (doubleComplementEq) =>
% 99.20/13.37 ((
% 99.20/13.37 (complementTnotintersectT) =>
% 99.20/13.37 ((
% 99.20/13.37 (complementImpComplementIntersect) =>
% 99.20/13.37 ((
% 99.20/13.37 (complementSubsetComplementIntersect) =>
% 99.20/13.37 ((
% 99.20/13.37 (complementInPowersetComplementIntersect) =>
% 99.20/13.37 ((
% 99.20/13.37 (contraSubsetComplement) =>
% 99.20/13.37 ((
% 99.20/13.37 (complementTcontraSubset) =>
% 99.20/13.37 ((
% 99.20/13.37 (binunionTILcontra) =>
% 99.20/13.37 ((
% 99.20/13.37 (binunionTIRcontra) =>
% 99.20/13.37 ((
% 99.20/13.37 (inIntersectImpInUnion) =>
% 99.20/13.37 ((
% 99.20/13.37 (inIntersectImpInUnion2) =>
% 99.20/13.37 ((
% 99.20/13.37 (inIntersectImpInIntersectUnions) =>
% 99.20/13.37 ((
% 99.20/13.37 (intersectInPowersetIntersectUnions) =>
% 99.20/13.37 ((
% 99.20/13.37 (inComplementUnionImpNotIn1) =>
% 99.20/13.37 ((
% 99.20/13.37 (inComplementUnionImpInComplement1) =>
% 99.20/13.37 ((
% 99.20/13.37 (binunionTE) =>
% 99.20/13.37 ((
% 99.20/13.37 (binunionTEcontra) =>
% 99.20/13.37 ((
% 99.20/13.37 (demorgan2a1) =>
% 99.20/13.37 ((
% 99.20/13.37 (complementUnionInPowersetComplement) =>
% 99.20/13.37 ((
% 99.20/13.37 (demorgan2a2) =>
% 99.20/13.37 ((
% 99.20/13.37 (demorgan1a) =>
% 99.20/13.37 ((
% 99.20/13.37 (demorgan1b) =>
% 99.20/13.37 ((
% 99.20/13.37 (demorgan1) =>
% 99.20/13.37 ((
% 99.20/13.37 (demorgan2a) =>
% 99.20/13.37 ((
% 99.20/13.37 (demorgan2b2) =>
% 99.20/13.37 ((
% 99.20/13.37 (demorgan2b) =>
% 99.20/13.37 ((
% 99.20/13.37 (demorgan2) =>
% 99.20/13.37 ((
% 99.20/13.37 (woz13rule0) =>
% 99.20/13.37 ((
% 99.20/13.37 (woz13rule1) =>
% 99.20/13.37 ((
% 99.20/13.37 (woz13rule2) =>
% 99.20/13.37 ((
% 99.20/13.37 (woz13rule3) =>
% 99.20/13.37 ((
% 99.20/13.37 (woz13rule4) =>
% 99.20/13.37 ((
% 99.20/13.37 (woz1_1) =>
% 99.20/13.37 ((
% 99.20/13.37 (woz1_2) =>
% 99.20/13.37 ((
% 99.20/13.37 (woz1_3) =>
% 99.20/13.37 ((
% 99.20/13.37 (woz1_4) =>
% 99.20/13.37 ((
% 99.20/13.37 (woz1_5) =>
% 99.20/13.37 ((
% 99.20/13.37 (breln1all2) =>
% 99.20/13.37 ((
% 99.20/13.37 (breln1SetBreln1) =>
% 99.20/13.37 ((
% 99.20/13.37 (choice2fnsingleton) =>
% 99.20/13.37 ((
% 99.20/13.37 (setOfPairsIsBReln1) =>
% 99.20/13.37 ((
% 99.20/13.37 (breln1all1) =>
% 99.20/13.37 ((
% 99.20/13.37 (subbreln1) =>
% 99.20/13.37 ((
% 99.20/13.37 (eqbreln1) =>
% 99.20/13.37 ((
% 99.20/13.37 (breln1invprop) =>
% 99.20/13.37 ((
% 99.20/13.37 (breln1invI) =>
% 99.20/13.37 ((
% 99.20/13.37 (breln1invE) =>
% 99.20/13.37 ((
% 99.20/13.37 (breln1compprop) =>
% 99.20/13.37 ((
% 99.20/13.37 (breln1compI) =>
% 99.20/13.37 ((
% 99.20/13.37 (breln1compE) =>
% 99.20/13.37 ((
% 99.20/13.37 (breln1compEex) =>
% 99.20/13.37 ((
% 99.20/13.37 (breln1unionprop) =>
% 99.20/13.37 ((
% 99.20/13.37 (breln1unionIL) =>
% 99.20/13.37 ((
% 99.20/13.37 (breln1unionIR) =>
% 99.20/13.37 ((
% 99.20/13.37 (breln1unionI) =>
% 99.20/13.37 ((
% 99.20/13.37 (breln1unionE) =>
% 99.20/13.37 ((
% 99.20/13.37 (breln1unionEcases) =>
% 99.20/13.37 ((
% 99.20/13.37 (breln1unionCommutes) =>
% 99.20/13.37 ((
% 99.20/13.37 (woz2Ex) =>
% 99.20/13.37 ((
% 99.20/13.37 (woz2W) =>
% 99.20/13.37 ((
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% 99.20/13.37 ((
% 99.20/13.37 (woz2B) =>
% 99.20/13.37 ((
% 99.20/13.37 (image1Ex) =>
% 99.20/13.37 ((
% 99.20/13.37 (image1Ex1) =>
% 99.20/13.37 ((
% 99.20/13.37 (image1Equiv) =>
% 99.20/13.37 ((
% 99.20/13.37 (image1E) =>
% 99.20/13.37 ((
% 99.20/13.37 (image1I) =>
% 99.20/13.37 ((
% 99.20/13.37 (injFuncInInjFuncSet) =>
% 99.20/13.37 ((
% 99.20/13.37 (injFuncSetFuncIn) =>
% 99.20/13.37 ((
% 99.20/13.37 (injFuncSetFuncInj) =>
% 99.20/13.37 ((
% 99.20/13.37 (!!) @ (
% 99.20/13.37 (('#B') @ (
% 99.20/13.37 !!) @
% 99.20/13.37 (
% 99.20/13.37 (
% 99.20/13.37 ('#B') @ (
% 99.20/13.37 (
% 99.20/13.37 ('#B') @ (
% 99.20/13.37 !!))) @
% 99.20/13.37 (
% 99.20/13.37 (
% 99.20/13.37 ('#S') @ (
% 99.20/13.37 (
% 99.20/13.37 ('#B') @ (
% 99.20/13.37 '#S') @
% 99.20/13.37 (
% 99.20/13.37 (
% 99.20/13.37 ('#B') @ (
% 99.20/13.37 (
% 99.20/13.37 ('#B') @ (
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% 99.20/13.37 (
% 99.20/13.37 (
% 99.20/13.37 ('#B') @ (
% 99.20/13.37 (
% 99.20/13.37 ('#B') @ (
% 99.20/13.37 (
% 99.20/13.37 ('#B') @ (
% 99.20/13.37 =>))))) @
% 99.20/13.37 (
% 99.20/13.37 (
% 99.20/13.37 ('#B') @ (
% 99.20/13.37 (
% 99.20/13.37 ('#B') @ (
% 99.20/13.37 (
% 99.20/13.37 ('#C') @ in)))) @
% 99.20/13.37 surjFuncSet)))))))) @
% 99.20/13.37 (
% 99.20/13.37 (
% 99.20/13.37 ('#B') @ (
% 99.20/13.37 (
% 99.20/13.37 ('#B') @ (
% 99.20/13.37 (
% 99.20/13.37 ('#C') @ in)))) @
% 99.20/13.37 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.20/13.37 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl392])).
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% 99.20/13.37 (~ (((setunionE) =>
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% 99.20/13.37 (((nonemptyImpWitness) =>
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% 99.20/13.37 (((upairsetIR) =>
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% 99.20/13.37 (((quantDeMorgan1) =>
% 99.20/13.37 (((quantDeMorgan2) =>
% 99.20/13.37 (((quantDeMorgan3) =>
% 99.20/13.37 (((quantDeMorgan4) =>
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% 99.20/13.37 (((notdallE) =>
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% 99.20/13.37 (((exuI3) =>
% 99.20/13.37 (((exuI2) =>
% 99.20/13.37 (((inCongP) =>
% 99.20/13.37 (((in__Cong) =>
% 99.20/13.37 (((exuE3u) =>
% 99.20/13.37 (((exu__Cong) =>
% 99.20/13.37 (((setadjoin__Cong) =>
% 99.20/13.37 (((powerset__Cong) =>
% 99.20/13.37 ((
% 99.20/13.37 (setunion__Cong) =>
% 99.20/13.37 ((
% 99.20/13.37 (exuEu) =>
% 99.20/13.37 ((
% 99.20/13.37 (descr__Cong) =>
% 99.20/13.37 ((
% 99.20/13.37 (dsetconstr__Cong) =>
% 99.20/13.37 ((
% 99.20/13.37 (subsetI1) =>
% 99.20/13.37 ((
% 99.20/13.37 (eqimpsubset2) =>
% 99.20/13.37 ((
% 99.20/13.37 (eqimpsubset1) =>
% 99.20/13.37 ((
% 99.20/13.37 (subsetI2) =>
% 99.20/13.37 ((
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% 99.20/13.37 ((
% 99.20/13.37 (subsetE) =>
% 99.20/13.37 ((
% 99.20/13.37 (subsetE2) =>
% 99.20/13.37 ((
% 99.20/13.37 (notsubsetI) =>
% 99.20/13.37 ((
% 99.20/13.37 (notequalI1) =>
% 99.20/13.37 ((
% 99.20/13.37 (notequalI2) =>
% 99.20/13.37 ((
% 99.20/13.37 (subsetRefl) =>
% 99.20/13.37 ((
% 99.20/13.37 (subsetTrans) =>
% 99.20/13.37 ((
% 99.20/13.37 (setadjoinSub) =>
% 99.20/13.37 ((
% 99.20/13.37 (setadjoinSub2) =>
% 99.20/13.37 ((
% 99.20/13.37 (subset2powerset) =>
% 99.20/13.37 ((
% 99.20/13.37 (setextsub) =>
% 99.20/13.37 ((
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% 99.20/13.37 ((
% 99.20/13.37 (powersetE1) =>
% 99.20/13.37 ((
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% 99.20/13.37 ((
% 99.20/13.37 (powersetsubset) =>
% 99.20/13.37 ((
% 99.20/13.37 (sepInPowerset) =>
% 99.20/13.37 ((
% 99.20/13.37 (sepSubset) =>
% 99.20/13.37 ((
% 99.20/13.37 (binunionIL) =>
% 99.20/13.37 ((
% 99.20/13.37 (upairset2IR) =>
% 99.20/13.37 ((
% 99.20/13.37 (binunionIR) =>
% 99.20/13.37 ((
% 99.20/13.37 (binunionEcases) =>
% 99.20/13.37 ((
% 99.20/13.37 (binunionE) =>
% 99.20/13.37 ((
% 99.20/13.37 (binunionLsub) =>
% 99.20/13.37 ((
% 99.20/13.37 (binunionRsub) =>
% 99.20/13.37 ((
% 99.20/13.37 (binintersectI) =>
% 99.20/13.37 ((
% 99.20/13.37 (binintersectSubset5) =>
% 99.20/13.37 ((
% 99.20/13.37 (binintersectEL) =>
% 99.20/13.37 ((
% 99.20/13.37 (binintersectLsub) =>
% 99.20/13.37 ((
% 99.20/13.37 (binintersectSubset2) =>
% 99.20/13.37 ((
% 99.20/13.37 (binintersectSubset3) =>
% 99.20/13.37 ((
% 99.20/13.37 (binintersectER) =>
% 99.20/13.37 ((
% 99.20/13.37 (disjointsetsI1) =>
% 99.20/13.37 ((
% 99.20/13.37 (binintersectRsub) =>
% 99.20/13.37 ((
% 99.20/13.37 (binintersectSubset4) =>
% 99.20/13.37 ((
% 99.20/13.37 (binintersectSubset1) =>
% 99.20/13.37 ((
% 99.20/13.37 (bs114d) =>
% 99.20/13.37 ((
% 99.20/13.37 (setminusI) =>
% 99.20/13.37 ((
% 99.20/13.37 (setminusEL) =>
% 99.20/13.37 ((
% 99.20/13.37 (setminusER) =>
% 99.20/13.37 ((
% 99.20/13.37 (setminusSubset2) =>
% 99.20/13.37 ((
% 99.20/13.37 (setminusERneg) =>
% 99.20/13.37 ((
% 99.20/13.37 (setminusELneg) =>
% 99.20/13.37 ((
% 99.20/13.37 (setminusILneg) =>
% 99.20/13.37 ((
% 99.20/13.37 (setminusIRneg) =>
% 99.20/13.37 ((
% 99.20/13.37 (setminusLsub) =>
% 99.20/13.37 ((
% 99.20/13.37 (setminusSubset1) =>
% 99.20/13.37 ((
% 99.20/13.37 (symdiffE) =>
% 99.20/13.37 ((
% 99.20/13.37 (symdiffI1) =>
% 99.20/13.37 ((
% 99.20/13.37 (symdiffI2) =>
% 99.20/13.37 ((
% 99.20/13.37 (symdiffIneg1) =>
% 99.20/13.37 ((
% 99.20/13.37 (symdiffIneg2) =>
% 99.20/13.37 ((
% 99.20/13.37 (secondinupair) =>
% 99.20/13.37 ((
% 99.20/13.37 (setukpairIL) =>
% 99.20/13.37 ((
% 99.20/13.37 (setukpairIR) =>
% 99.20/13.37 ((
% 99.20/13.37 (kpairiskpair) =>
% 99.20/13.37 ((
% 99.20/13.37 (kpairp) =>
% 99.20/13.37 ((
% 99.20/13.37 (singletonsubset) =>
% 99.20/13.37 ((
% 99.20/13.37 (singletoninpowerset) =>
% 99.20/13.37 ((
% 99.20/13.37 (singletoninpowunion) =>
% 99.20/13.37 ((
% 99.20/13.37 (upairset2E) =>
% 99.20/13.37 ((
% 99.20/13.37 (upairsubunion) =>
% 99.20/13.37 ((
% 99.20/13.37 (upairinpowunion) =>
% 99.20/13.37 ((
% 99.20/13.37 (ubforcartprodlem1) =>
% 99.20/13.37 ((
% 99.20/13.37 (ubforcartprodlem2) =>
% 99.20/13.37 ((
% 99.20/13.37 (ubforcartprodlem3) =>
% 99.20/13.37 ((
% 99.20/13.37 (cartprodpairin) =>
% 99.20/13.37 ((
% 99.20/13.37 (cartprodmempair1) =>
% 99.20/13.37 ((
% 99.20/13.37 (cartprodmempair) =>
% 99.20/13.37 ((
% 99.20/13.37 (setunionE2) =>
% 99.20/13.37 ((
% 99.20/13.37 (setunionsingleton1) =>
% 99.20/13.37 ((
% 99.20/13.37 (setunionsingleton2) =>
% 99.20/13.37 ((
% 99.20/13.37 (setunionsingleton) =>
% 99.20/13.37 ((
% 99.20/13.37 (singletonprop) =>
% 99.20/13.37 ((
% 99.20/13.37 (ex1E1) =>
% 99.20/13.37 ((
% 99.20/13.37 (ex1I) =>
% 99.20/13.37 ((
% 99.20/13.37 (ex1I2) =>
% 99.20/13.37 ((
% 99.20/13.37 (singletonsuniq) =>
% 99.20/13.37 ((
% 99.20/13.37 (setukpairinjL1) =>
% 99.20/13.37 ((
% 99.20/13.37 (kfstsingleton) =>
% 99.20/13.37 ((
% 99.20/13.37 (theprop) =>
% 99.20/13.37 ((
% 99.20/13.37 (kfstpairEq) =>
% 99.20/13.37 ((
% 99.20/13.37 (cartprodfstin) =>
% 99.20/13.37 ((
% 99.20/13.37 (setukpairinjL2) =>
% 99.20/13.37 ((
% 99.20/13.37 (setukpairinjL) =>
% 99.20/13.37 ((
% 99.20/13.37 (setukpairinjR11) =>
% 99.20/13.37 ((
% 99.20/13.37 (setukpairinjR12) =>
% 99.20/13.37 ((
% 99.20/13.37 (setukpairinjR1) =>
% 99.20/13.37 ((
% 99.20/13.37 (upairequniteq) =>
% 99.20/13.37 ((
% 99.20/13.37 (setukpairinjR2) =>
% 99.20/13.37 ((
% 99.20/13.37 (setukpairinjR) =>
% 99.20/13.37 ((
% 99.20/13.37 (ksndsingleton) =>
% 99.20/13.37 ((
% 99.20/13.37 (ksndpairEq) =>
% 99.20/13.37 ((
% 99.20/13.37 (kpairsurjEq) =>
% 99.20/13.37 ((
% 99.20/13.37 (cartprodsndin) =>
% 99.20/13.37 ((
% 99.20/13.37 (cartprodpairmemEL) =>
% 99.20/13.37 ((
% 99.20/13.37 (cartprodpairmemER) =>
% 99.20/13.37 ((
% 99.20/13.37 (cartprodmempaircEq) =>
% 99.20/13.37 ((
% 99.20/13.37 (cartprodfstpairEq) =>
% 99.20/13.37 ((
% 99.20/13.37 (cartprodsndpairEq) =>
% 99.20/13.37 ((
% 99.20/13.37 (cartprodpairsurjEq) =>
% 99.20/13.37 ((
% 99.20/13.37 (dpsetconstrI) =>
% 99.20/13.37 ((
% 99.20/13.37 (dpsetconstrSub) =>
% 99.20/13.37 ((
% 99.20/13.37 (setOfPairsIsBReln) =>
% 99.20/13.37 ((
% 99.20/13.37 (dpsetconstrERa) =>
% 99.20/13.37 ((
% 99.20/13.37 (dpsetconstrEL1) =>
% 99.20/13.37 ((
% 99.20/13.37 (dpsetconstrEL2) =>
% 99.20/13.37 ((
% 99.20/13.37 (dpsetconstrER) =>
% 99.20/13.37 ((
% 99.20/13.37 (funcImageSingleton) =>
% 99.20/13.37 ((
% 99.20/13.37 (apProp) =>
% 99.20/13.37 ((
% 99.20/13.37 (app) =>
% 99.20/13.37 ((
% 99.20/13.37 (infuncsetfunc) =>
% 99.20/13.37 ((
% 99.20/13.37 (ap2p) =>
% 99.20/13.37 ((
% 99.20/13.37 (funcinfuncset) =>
% 99.20/13.37 ((
% 99.20/13.37 (lamProp) =>
% 99.20/13.37 ((
% 99.20/13.37 (lamp) =>
% 99.20/13.37 ((
% 99.20/13.37 (lam2p) =>
% 99.20/13.37 ((
% 99.20/13.37 (brelnall1) =>
% 99.20/13.37 ((
% 99.20/13.37 (brelnall2) =>
% 99.20/13.37 ((
% 99.20/13.37 (ex1E2) =>
% 99.20/13.37 ((
% 99.20/13.37 (funcGraphProp1) =>
% 99.20/13.37 ((
% 99.20/13.37 (funcGraphProp3) =>
% 99.20/13.37 ((
% 99.20/13.37 (funcGraphProp2) =>
% 99.20/13.37 ((
% 99.20/13.37 (funcextLem) =>
% 99.20/13.37 ((
% 99.20/13.37 (funcGraphProp4) =>
% 99.20/13.37 ((
% 99.20/13.37 (subbreln) =>
% 99.20/13.37 ((
% 99.20/13.37 (eqbreln) =>
% 99.20/13.37 ((
% 99.20/13.37 (funcext) =>
% 99.20/13.37 ((
% 99.20/13.37 (funcext2) =>
% 99.20/13.37 ((
% 99.20/13.37 (ap2apEq1) =>
% 99.20/13.37 ((
% 99.20/13.37 (ap2apEq2) =>
% 99.20/13.37 ((
% 99.20/13.37 (beta1) =>
% 99.20/13.37 ((
% 99.20/13.37 (eta1) =>
% 99.20/13.37 ((
% 99.20/13.37 (lam2lamEq) =>
% 99.20/13.37 ((
% 99.20/13.37 (beta2) =>
% 99.20/13.37 ((
% 99.20/13.37 (eta2) =>
% 99.20/13.37 ((
% 99.20/13.37 (iffalseProp1) =>
% 99.20/13.37 ((
% 99.20/13.37 (iffalseProp2) =>
% 99.20/13.37 ((
% 99.20/13.37 (iftrueProp1) =>
% 99.20/13.37 ((
% 99.20/13.37 (iftrueProp2) =>
% 99.20/13.37 ((
% 99.20/13.37 (ifSingleton) =>
% 99.20/13.37 ((
% 99.20/13.37 (ifp) =>
% 99.20/13.37 ((
% 99.20/13.37 (theeq) =>
% 99.20/13.37 ((
% 99.20/13.37 (iftrue) =>
% 99.20/13.37 ((
% 99.20/13.37 (iffalse) =>
% 99.20/13.37 ((
% 99.20/13.37 (iftrueorfalse) =>
% 99.20/13.37 ((
% 99.20/13.37 (binintersectT_lem) =>
% 99.20/13.37 ((
% 99.20/13.37 (binunionT_lem) =>
% 99.20/13.37 ((
% 99.20/13.37 (powersetT_lem) =>
% 99.20/13.37 ((
% 99.20/13.37 (setminusT_lem) =>
% 99.20/13.37 ((
% 99.20/13.37 (complementT_lem) =>
% 99.20/13.37 ((
% 99.20/13.37 (setextT) =>
% 99.20/13.37 ((
% 99.20/13.37 (subsetTI) =>
% 99.20/13.37 ((
% 99.20/13.37 (powersetTI1) =>
% 99.20/13.37 ((
% 99.20/13.37 (powersetTE1) =>
% 99.20/13.37 ((
% 99.20/13.37 (complementTI1) =>
% 99.20/13.37 ((
% 99.20/13.37 (complementTE1) =>
% 99.20/13.37 ((
% 99.20/13.37 (binintersectTELcontra) =>
% 99.20/13.37 ((
% 99.20/13.37 (binintersectTERcontra) =>
% 99.20/13.37 ((
% 99.20/13.37 (contrasubsetT) =>
% 99.20/13.37 ((
% 99.20/13.37 (contrasubsetT1) =>
% 99.20/13.37 ((
% 99.20/13.37 (contrasubsetT2) =>
% 99.20/13.37 ((
% 99.20/13.37 (contrasubsetT3) =>
% 99.20/13.37 ((
% 99.20/13.37 (doubleComplementI1) =>
% 99.20/13.37 ((
% 99.20/13.37 (doubleComplementE1) =>
% 99.20/13.37 ((
% 99.20/13.37 (doubleComplementSub1) =>
% 99.20/13.37 ((
% 99.20/13.37 (doubleComplementSub2) =>
% 99.20/13.37 ((
% 99.20/13.37 (doubleComplementEq) =>
% 99.20/13.37 ((
% 99.20/13.37 (complementTnotintersectT) =>
% 99.20/13.37 ((
% 99.20/13.37 (complementImpComplementIntersect) =>
% 99.20/13.37 ((
% 99.20/13.37 (complementSubsetComplementIntersect) =>
% 99.20/13.37 ((
% 99.20/13.37 (complementInPowersetComplementIntersect) =>
% 99.20/13.37 ((
% 99.20/13.37 (contraSubsetComplement) =>
% 99.20/13.37 ((
% 99.20/13.37 (complementTcontraSubset) =>
% 99.20/13.37 ((
% 99.20/13.37 (binunionTILcontra) =>
% 99.20/13.37 ((
% 99.20/13.37 (binunionTIRcontra) =>
% 99.20/13.37 ((
% 99.20/13.37 (inIntersectImpInUnion) =>
% 99.20/13.37 ((
% 99.20/13.37 (inIntersectImpInUnion2) =>
% 99.20/13.37 ((
% 99.20/13.37 (inIntersectImpInIntersectUnions) =>
% 99.20/13.37 ((
% 99.20/13.37 (intersectInPowersetIntersectUnions) =>
% 99.20/13.37 ((
% 99.20/13.37 (inComplementUnionImpNotIn1) =>
% 99.20/13.37 ((
% 99.20/13.37 (inComplementUnionImpInComplement1) =>
% 99.20/13.37 ((
% 99.20/13.37 (binunionTE) =>
% 99.20/13.37 ((
% 99.20/13.37 (binunionTEcontra) =>
% 99.20/13.37 ((
% 99.20/13.37 (demorgan2a1) =>
% 99.20/13.37 ((
% 99.20/13.37 (complementUnionInPowersetComplement) =>
% 99.20/13.38 ((
% 99.20/13.38 (demorgan2a2) =>
% 99.20/13.38 ((
% 99.20/13.38 (demorgan1a) =>
% 99.20/13.38 ((
% 99.20/13.38 (demorgan1b) =>
% 99.20/13.38 ((
% 99.20/13.38 (demorgan1) =>
% 99.20/13.38 ((
% 99.20/13.38 (demorgan2a) =>
% 99.20/13.38 ((
% 99.20/13.38 (demorgan2b2) =>
% 99.20/13.38 ((
% 99.20/13.38 (demorgan2b) =>
% 99.20/13.38 ((
% 99.20/13.38 (demorgan2) =>
% 99.20/13.38 ((
% 99.20/13.38 (woz13rule0) =>
% 99.20/13.38 ((
% 99.20/13.38 (woz13rule1) =>
% 99.20/13.38 ((
% 99.20/13.38 (woz13rule2) =>
% 99.20/13.38 ((
% 99.20/13.38 (woz13rule3) =>
% 99.20/13.38 ((
% 99.20/13.38 (woz13rule4) =>
% 99.20/13.38 ((
% 99.20/13.38 (woz1_1) =>
% 99.20/13.38 ((
% 99.20/13.38 (woz1_2) =>
% 99.20/13.38 ((
% 99.20/13.38 (woz1_3) =>
% 99.20/13.38 ((
% 99.20/13.38 (woz1_4) =>
% 99.20/13.38 ((
% 99.20/13.38 (woz1_5) =>
% 99.20/13.38 ((
% 99.20/13.38 (breln1all2) =>
% 99.20/13.38 ((
% 99.20/13.38 (breln1SetBreln1) =>
% 99.20/13.38 ((
% 99.20/13.38 (choice2fnsingleton) =>
% 99.20/13.38 ((
% 99.20/13.38 (setOfPairsIsBReln1) =>
% 99.20/13.38 ((
% 99.20/13.38 (breln1all1) =>
% 99.20/13.38 ((
% 99.20/13.38 (subbreln1) =>
% 99.20/13.38 ((
% 99.20/13.38 (eqbreln1) =>
% 99.20/13.38 ((
% 99.20/13.38 (breln1invprop) =>
% 99.20/13.38 ((
% 99.20/13.38 (breln1invI) =>
% 99.20/13.38 ((
% 99.20/13.38 (breln1invE) =>
% 99.20/13.38 ((
% 99.20/13.38 (breln1compprop) =>
% 99.20/13.38 ((
% 99.20/13.38 (breln1compI) =>
% 99.20/13.38 ((
% 99.20/13.38 (breln1compE) =>
% 99.20/13.38 ((
% 99.20/13.38 (breln1compEex) =>
% 99.20/13.38 ((
% 99.20/13.38 (breln1unionprop) =>
% 99.20/13.38 ((
% 99.20/13.38 (breln1unionIL) =>
% 99.20/13.38 ((
% 99.20/13.38 (breln1unionIR) =>
% 99.20/13.38 ((
% 99.20/13.38 (breln1unionI) =>
% 99.20/13.38 ((
% 99.20/13.38 (breln1unionE) =>
% 99.20/13.38 ((
% 99.20/13.38 (breln1unionEcases) =>
% 99.20/13.38 ((
% 99.20/13.38 (breln1unionCommutes) =>
% 99.20/13.38 ((
% 99.20/13.38 (woz2Ex) =>
% 99.20/13.38 ((
% 99.20/13.38 (woz2W) =>
% 99.20/13.38 ((
% 99.20/13.38 (woz2A) =>
% 99.20/13.38 ((
% 99.20/13.38 (woz2B) =>
% 99.20/13.38 ((
% 99.20/13.38 (image1Ex) =>
% 99.20/13.38 ((
% 99.20/13.38 (image1Ex1) =>
% 99.20/13.38 ((
% 99.20/13.38 (image1Equiv) =>
% 99.20/13.38 ((
% 99.20/13.38 (image1E) =>
% 99.20/13.38 ((
% 99.20/13.38 (image1I) =>
% 99.20/13.38 ((
% 99.20/13.38 (injFuncInInjFuncSet) =>
% 99.20/13.38 ((
% 99.20/13.38 (injFuncSetFuncIn) =>
% 99.20/13.38 ((
% 99.20/13.38 (injFuncSetFuncInj) =>
% 99.20/13.38 ((
% 99.20/13.38 (!!) @ (
% 99.20/13.38 (('#B') @ (
% 99.20/13.38 !!) @
% 99.20/13.38 (
% 99.20/13.38 (
% 99.20/13.38 ('#B') @ (
% 99.20/13.38 (
% 99.20/13.38 ('#B') @ (
% 99.20/13.38 !!))) @
% 99.20/13.38 (
% 99.20/13.38 (
% 99.20/13.38 ('#S') @ (
% 99.20/13.38 (
% 99.20/13.38 ('#B') @ (
% 99.20/13.38 '#S') @
% 99.20/13.38 (
% 99.20/13.38 (
% 99.20/13.38 ('#B') @ (
% 99.20/13.38 (
% 99.20/13.38 ('#B') @ (
% 99.20/13.38 '#S'))) @
% 99.20/13.38 (
% 99.20/13.38 (
% 99.20/13.38 ('#B') @ (
% 99.20/13.38 (
% 99.20/13.38 ('#B') @ (
% 99.20/13.38 (
% 99.20/13.38 ('#B') @ (
% 99.20/13.38 =>))))) @
% 99.20/13.38 (
% 99.20/13.38 (
% 99.20/13.38 ('#B') @ (
% 99.20/13.38 (
% 99.20/13.38 ('#B') @ (
% 99.20/13.38 (
% 99.20/13.38 ('#C') @ in)))) @
% 99.20/13.38 surjFuncSet)))))))) @
% 99.20/13.38 (
% 99.20/13.38 (
% 99.20/13.38 ('#B') @ (
% 99.20/13.38 (
% 99.20/13.38 ('#B') @ (
% 99.20/13.38 (
% 99.20/13.38 ('#C') @ in)))) @
% 99.20/13.38 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.20/13.38 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl400])).
% 99.20/13.38 thf(zip_derived_cl417, plain,
% 99.20/13.38 (~ (((subPowSU) =>
% 99.20/13.38 (((exuE2) =>
% 99.20/13.38 (((nonemptyImpWitness) =>
% 99.20/13.38 (((uniqinunit) =>
% 99.20/13.38 (((notinsingleton) =>
% 99.20/13.38 (((eqinunit) =>
% 99.20/13.38 (((singletonsswitch) =>
% 99.20/13.38 (((upairsetE) =>
% 99.20/13.38 (((upairsetIL) =>
% 99.20/13.38 (((upairsetIR) =>
% 99.20/13.38 (((emptyE1) =>
% 99.20/13.38 (((vacuousDall) =>
% 99.20/13.38 (((quantDeMorgan1) =>
% 99.20/13.38 (((quantDeMorgan2) =>
% 99.20/13.38 (((quantDeMorgan3) =>
% 99.20/13.38 (((quantDeMorgan4) =>
% 99.20/13.38 (((prop2setI) =>
% 99.20/13.38 (((prop2set2propI) =>
% 99.20/13.38 (((notdexE) =>
% 99.20/13.38 (((notdallE) =>
% 99.20/13.38 (((exuI1) =>
% 99.20/13.38 (((exuI3) =>
% 99.20/13.38 (((exuI2) =>
% 99.20/13.38 (((inCongP) =>
% 99.20/13.38 (((in__Cong) =>
% 99.20/13.38 (((exuE3u) =>
% 99.20/13.38 (((exu__Cong) =>
% 99.20/13.38 (((setadjoin__Cong) =>
% 99.20/13.38 (((powerset__Cong) =>
% 99.20/13.38 (((setunion__Cong) =>
% 99.20/13.38 ((
% 99.20/13.38 (exuEu) =>
% 99.20/13.38 ((
% 99.20/13.38 (descr__Cong) =>
% 99.20/13.38 ((
% 99.20/13.38 (dsetconstr__Cong) =>
% 99.20/13.38 ((
% 99.20/13.38 (subsetI1) =>
% 99.20/13.38 ((
% 99.20/13.38 (eqimpsubset2) =>
% 99.20/13.38 ((
% 99.20/13.38 (eqimpsubset1) =>
% 99.20/13.38 ((
% 99.20/13.38 (subsetI2) =>
% 99.20/13.38 ((
% 99.20/13.38 (emptysetsubset) =>
% 99.20/13.38 ((
% 99.20/13.38 (subsetE) =>
% 99.20/13.38 ((
% 99.20/13.38 (subsetE2) =>
% 99.20/13.38 ((
% 99.20/13.38 (notsubsetI) =>
% 99.20/13.38 ((
% 99.20/13.38 (notequalI1) =>
% 99.20/13.38 ((
% 99.20/13.38 (notequalI2) =>
% 99.20/13.38 ((
% 99.20/13.38 (subsetRefl) =>
% 99.20/13.38 ((
% 99.20/13.38 (subsetTrans) =>
% 99.20/13.38 ((
% 99.20/13.38 (setadjoinSub) =>
% 99.20/13.38 ((
% 99.20/13.38 (setadjoinSub2) =>
% 99.20/13.38 ((
% 99.20/13.38 (subset2powerset) =>
% 99.20/13.38 ((
% 99.20/13.38 (setextsub) =>
% 99.20/13.38 ((
% 99.20/13.38 (subsetemptysetimpeq) =>
% 99.20/13.38 ((
% 99.20/13.38 (powersetI1) =>
% 99.20/13.38 ((
% 99.20/13.38 (powersetE1) =>
% 99.20/13.38 ((
% 99.20/13.38 (inPowerset) =>
% 99.20/13.38 ((
% 99.20/13.38 (powersetsubset) =>
% 99.20/13.38 ((
% 99.20/13.38 (sepInPowerset) =>
% 99.20/13.38 ((
% 99.20/13.38 (sepSubset) =>
% 99.20/13.38 ((
% 99.20/13.38 (binunionIL) =>
% 99.20/13.38 ((
% 99.20/13.38 (upairset2IR) =>
% 99.20/13.38 ((
% 99.20/13.38 (binunionIR) =>
% 99.20/13.38 ((
% 99.20/13.38 (binunionEcases) =>
% 99.20/13.38 ((
% 99.20/13.38 (binunionE) =>
% 99.20/13.38 ((
% 99.20/13.38 (binunionLsub) =>
% 99.20/13.38 ((
% 99.20/13.38 (binunionRsub) =>
% 99.20/13.38 ((
% 99.20/13.38 (binintersectI) =>
% 99.20/13.38 ((
% 99.20/13.38 (binintersectSubset5) =>
% 99.20/13.38 ((
% 99.20/13.38 (binintersectEL) =>
% 99.20/13.38 ((
% 99.20/13.38 (binintersectLsub) =>
% 99.20/13.38 ((
% 99.20/13.38 (binintersectSubset2) =>
% 99.20/13.38 ((
% 99.20/13.38 (binintersectSubset3) =>
% 99.20/13.38 ((
% 99.20/13.38 (binintersectER) =>
% 99.20/13.38 ((
% 99.20/13.38 (disjointsetsI1) =>
% 99.20/13.38 ((
% 99.20/13.38 (binintersectRsub) =>
% 99.20/13.38 ((
% 99.20/13.38 (binintersectSubset4) =>
% 99.20/13.38 ((
% 99.20/13.38 (binintersectSubset1) =>
% 99.20/13.38 ((
% 99.20/13.38 (bs114d) =>
% 99.20/13.38 ((
% 99.20/13.38 (setminusI) =>
% 99.20/13.38 ((
% 99.20/13.38 (setminusEL) =>
% 99.20/13.38 ((
% 99.20/13.38 (setminusER) =>
% 99.20/13.38 ((
% 99.20/13.38 (setminusSubset2) =>
% 99.20/13.38 ((
% 99.20/13.38 (setminusERneg) =>
% 99.20/13.38 ((
% 99.20/13.38 (setminusELneg) =>
% 99.20/13.38 ((
% 99.20/13.38 (setminusILneg) =>
% 99.20/13.38 ((
% 99.20/13.38 (setminusIRneg) =>
% 99.20/13.38 ((
% 99.20/13.38 (setminusLsub) =>
% 99.20/13.38 ((
% 99.20/13.38 (setminusSubset1) =>
% 99.20/13.38 ((
% 99.20/13.38 (symdiffE) =>
% 99.20/13.38 ((
% 99.20/13.38 (symdiffI1) =>
% 99.20/13.38 ((
% 99.20/13.38 (symdiffI2) =>
% 99.20/13.38 ((
% 99.20/13.38 (symdiffIneg1) =>
% 99.20/13.38 ((
% 99.20/13.38 (symdiffIneg2) =>
% 99.20/13.38 ((
% 99.20/13.38 (secondinupair) =>
% 99.20/13.38 ((
% 99.20/13.38 (setukpairIL) =>
% 99.20/13.38 ((
% 99.20/13.38 (setukpairIR) =>
% 99.20/13.38 ((
% 99.20/13.38 (kpairiskpair) =>
% 99.20/13.38 ((
% 99.20/13.38 (kpairp) =>
% 99.20/13.38 ((
% 99.20/13.38 (singletonsubset) =>
% 99.20/13.38 ((
% 99.20/13.38 (singletoninpowerset) =>
% 99.20/13.38 ((
% 99.20/13.38 (singletoninpowunion) =>
% 99.20/13.38 ((
% 99.20/13.38 (upairset2E) =>
% 99.20/13.38 ((
% 99.20/13.38 (upairsubunion) =>
% 99.20/13.38 ((
% 99.20/13.38 (upairinpowunion) =>
% 99.20/13.38 ((
% 99.20/13.38 (ubforcartprodlem1) =>
% 99.20/13.38 ((
% 99.20/13.38 (ubforcartprodlem2) =>
% 99.20/13.38 ((
% 99.20/13.38 (ubforcartprodlem3) =>
% 99.20/13.38 ((
% 99.20/13.38 (cartprodpairin) =>
% 99.20/13.38 ((
% 99.20/13.38 (cartprodmempair1) =>
% 99.20/13.38 ((
% 99.20/13.38 (cartprodmempair) =>
% 99.20/13.38 ((
% 99.20/13.38 (setunionE2) =>
% 99.20/13.38 ((
% 99.20/13.38 (setunionsingleton1) =>
% 99.20/13.38 ((
% 99.20/13.38 (setunionsingleton2) =>
% 99.20/13.38 ((
% 99.20/13.38 (setunionsingleton) =>
% 99.20/13.38 ((
% 99.20/13.38 (singletonprop) =>
% 99.20/13.38 ((
% 99.20/13.38 (ex1E1) =>
% 99.20/13.38 ((
% 99.20/13.38 (ex1I) =>
% 99.20/13.38 ((
% 99.20/13.38 (ex1I2) =>
% 99.20/13.38 ((
% 99.20/13.38 (singletonsuniq) =>
% 99.20/13.38 ((
% 99.20/13.38 (setukpairinjL1) =>
% 99.20/13.38 ((
% 99.20/13.38 (kfstsingleton) =>
% 99.20/13.38 ((
% 99.20/13.38 (theprop) =>
% 99.20/13.38 ((
% 99.20/13.38 (kfstpairEq) =>
% 99.20/13.38 ((
% 99.20/13.38 (cartprodfstin) =>
% 99.20/13.38 ((
% 99.20/13.38 (setukpairinjL2) =>
% 99.20/13.38 ((
% 99.20/13.38 (setukpairinjL) =>
% 99.20/13.38 ((
% 99.20/13.38 (setukpairinjR11) =>
% 99.20/13.38 ((
% 99.20/13.38 (setukpairinjR12) =>
% 99.20/13.38 ((
% 99.20/13.38 (setukpairinjR1) =>
% 99.20/13.38 ((
% 99.20/13.38 (upairequniteq) =>
% 99.20/13.38 ((
% 99.20/13.38 (setukpairinjR2) =>
% 99.20/13.38 ((
% 99.20/13.38 (setukpairinjR) =>
% 99.20/13.38 ((
% 99.20/13.38 (ksndsingleton) =>
% 99.20/13.38 ((
% 99.20/13.38 (ksndpairEq) =>
% 99.20/13.38 ((
% 99.20/13.38 (kpairsurjEq) =>
% 99.20/13.38 ((
% 99.20/13.38 (cartprodsndin) =>
% 99.20/13.38 ((
% 99.20/13.38 (cartprodpairmemEL) =>
% 99.20/13.38 ((
% 99.20/13.38 (cartprodpairmemER) =>
% 99.20/13.38 ((
% 99.20/13.38 (cartprodmempaircEq) =>
% 99.20/13.38 ((
% 99.20/13.38 (cartprodfstpairEq) =>
% 99.20/13.38 ((
% 99.20/13.38 (cartprodsndpairEq) =>
% 99.20/13.38 ((
% 99.20/13.38 (cartprodpairsurjEq) =>
% 99.20/13.38 ((
% 99.20/13.38 (dpsetconstrI) =>
% 99.20/13.38 ((
% 99.20/13.38 (dpsetconstrSub) =>
% 99.20/13.38 ((
% 99.20/13.38 (setOfPairsIsBReln) =>
% 99.20/13.38 ((
% 99.20/13.38 (dpsetconstrERa) =>
% 99.20/13.38 ((
% 99.20/13.38 (dpsetconstrEL1) =>
% 99.20/13.38 ((
% 99.20/13.38 (dpsetconstrEL2) =>
% 99.20/13.38 ((
% 99.20/13.38 (dpsetconstrER) =>
% 99.20/13.38 ((
% 99.20/13.38 (funcImageSingleton) =>
% 99.20/13.38 ((
% 99.20/13.38 (apProp) =>
% 99.20/13.38 ((
% 99.20/13.38 (app) =>
% 99.20/13.38 ((
% 99.20/13.38 (infuncsetfunc) =>
% 99.20/13.38 ((
% 99.20/13.38 (ap2p) =>
% 99.20/13.38 ((
% 99.20/13.38 (funcinfuncset) =>
% 99.20/13.38 ((
% 99.20/13.38 (lamProp) =>
% 99.20/13.38 ((
% 99.20/13.38 (lamp) =>
% 99.20/13.38 ((
% 99.20/13.38 (lam2p) =>
% 99.20/13.38 ((
% 99.20/13.38 (brelnall1) =>
% 99.20/13.38 ((
% 99.20/13.38 (brelnall2) =>
% 99.20/13.38 ((
% 99.20/13.38 (ex1E2) =>
% 99.20/13.38 ((
% 99.20/13.38 (funcGraphProp1) =>
% 99.20/13.38 ((
% 99.20/13.38 (funcGraphProp3) =>
% 99.20/13.38 ((
% 99.20/13.38 (funcGraphProp2) =>
% 99.20/13.38 ((
% 99.20/13.38 (funcextLem) =>
% 99.20/13.38 ((
% 99.20/13.38 (funcGraphProp4) =>
% 99.20/13.38 ((
% 99.20/13.38 (subbreln) =>
% 99.20/13.38 ((
% 99.20/13.38 (eqbreln) =>
% 99.20/13.38 ((
% 99.20/13.38 (funcext) =>
% 99.20/13.38 ((
% 99.20/13.38 (funcext2) =>
% 99.20/13.38 ((
% 99.20/13.38 (ap2apEq1) =>
% 99.20/13.38 ((
% 99.20/13.38 (ap2apEq2) =>
% 99.20/13.38 ((
% 99.20/13.38 (beta1) =>
% 99.20/13.38 ((
% 99.20/13.38 (eta1) =>
% 99.20/13.38 ((
% 99.20/13.38 (lam2lamEq) =>
% 99.20/13.38 ((
% 99.20/13.38 (beta2) =>
% 99.20/13.38 ((
% 99.20/13.38 (eta2) =>
% 99.20/13.38 ((
% 99.20/13.38 (iffalseProp1) =>
% 99.20/13.38 ((
% 99.20/13.38 (iffalseProp2) =>
% 99.20/13.38 ((
% 99.20/13.38 (iftrueProp1) =>
% 99.20/13.38 ((
% 99.20/13.38 (iftrueProp2) =>
% 99.20/13.38 ((
% 99.20/13.38 (ifSingleton) =>
% 99.20/13.38 ((
% 99.20/13.38 (ifp) =>
% 99.20/13.38 ((
% 99.20/13.38 (theeq) =>
% 99.20/13.38 ((
% 99.20/13.38 (iftrue) =>
% 99.20/13.38 ((
% 99.20/13.38 (iffalse) =>
% 99.20/13.38 ((
% 99.20/13.38 (iftrueorfalse) =>
% 99.20/13.38 ((
% 99.20/13.38 (binintersectT_lem) =>
% 99.20/13.38 ((
% 99.20/13.38 (binunionT_lem) =>
% 99.20/13.38 ((
% 99.20/13.38 (powersetT_lem) =>
% 99.20/13.38 ((
% 99.20/13.38 (setminusT_lem) =>
% 99.20/13.38 ((
% 99.20/13.38 (complementT_lem) =>
% 99.20/13.38 ((
% 99.20/13.38 (setextT) =>
% 99.20/13.38 ((
% 99.20/13.38 (subsetTI) =>
% 99.20/13.38 ((
% 99.20/13.38 (powersetTI1) =>
% 99.20/13.38 ((
% 99.20/13.38 (powersetTE1) =>
% 99.20/13.38 ((
% 99.20/13.38 (complementTI1) =>
% 99.20/13.38 ((
% 99.20/13.38 (complementTE1) =>
% 99.20/13.38 ((
% 99.20/13.38 (binintersectTELcontra) =>
% 99.20/13.38 ((
% 99.20/13.38 (binintersectTERcontra) =>
% 99.20/13.38 ((
% 99.20/13.38 (contrasubsetT) =>
% 99.20/13.38 ((
% 99.20/13.38 (contrasubsetT1) =>
% 99.20/13.38 ((
% 99.20/13.38 (contrasubsetT2) =>
% 99.20/13.38 ((
% 99.20/13.38 (contrasubsetT3) =>
% 99.20/13.38 ((
% 99.20/13.38 (doubleComplementI1) =>
% 99.20/13.38 ((
% 99.20/13.38 (doubleComplementE1) =>
% 99.20/13.38 ((
% 99.20/13.38 (doubleComplementSub1) =>
% 99.20/13.38 ((
% 99.20/13.38 (doubleComplementSub2) =>
% 99.20/13.38 ((
% 99.20/13.38 (doubleComplementEq) =>
% 99.20/13.38 ((
% 99.20/13.38 (complementTnotintersectT) =>
% 99.20/13.38 ((
% 99.20/13.38 (complementImpComplementIntersect) =>
% 99.20/13.38 ((
% 99.20/13.38 (complementSubsetComplementIntersect) =>
% 99.20/13.38 ((
% 99.20/13.38 (complementInPowersetComplementIntersect) =>
% 99.20/13.38 ((
% 99.20/13.38 (contraSubsetComplement) =>
% 99.20/13.38 ((
% 99.20/13.38 (complementTcontraSubset) =>
% 99.20/13.38 ((
% 99.20/13.38 (binunionTILcontra) =>
% 99.20/13.38 ((
% 99.20/13.38 (binunionTIRcontra) =>
% 99.20/13.38 ((
% 99.20/13.38 (inIntersectImpInUnion) =>
% 99.20/13.38 ((
% 99.20/13.38 (inIntersectImpInUnion2) =>
% 99.20/13.38 ((
% 99.20/13.38 (inIntersectImpInIntersectUnions) =>
% 99.20/13.38 ((
% 99.20/13.38 (intersectInPowersetIntersectUnions) =>
% 99.20/13.38 ((
% 99.20/13.38 (inComplementUnionImpNotIn1) =>
% 99.20/13.38 ((
% 99.20/13.38 (inComplementUnionImpInComplement1) =>
% 99.20/13.38 ((
% 99.20/13.38 (binunionTE) =>
% 99.20/13.38 ((
% 99.20/13.38 (binunionTEcontra) =>
% 99.20/13.38 ((
% 99.20/13.38 (demorgan2a1) =>
% 99.20/13.38 ((
% 99.20/13.38 (complementUnionInPowersetComplement) =>
% 99.20/13.38 ((
% 99.20/13.38 (demorgan2a2) =>
% 99.20/13.38 ((
% 99.20/13.38 (demorgan1a) =>
% 99.20/13.38 ((
% 99.20/13.38 (demorgan1b) =>
% 99.20/13.38 ((
% 99.20/13.38 (demorgan1) =>
% 99.20/13.38 ((
% 99.20/13.38 (demorgan2a) =>
% 99.20/13.38 ((
% 99.20/13.38 (demorgan2b2) =>
% 99.20/13.38 ((
% 99.20/13.38 (demorgan2b) =>
% 99.20/13.38 ((
% 99.20/13.38 (demorgan2) =>
% 99.20/13.38 ((
% 99.20/13.38 (woz13rule0) =>
% 99.20/13.38 ((
% 99.20/13.38 (woz13rule1) =>
% 99.20/13.38 ((
% 99.20/13.38 (woz13rule2) =>
% 99.20/13.38 ((
% 99.20/13.38 (woz13rule3) =>
% 99.20/13.38 ((
% 99.20/13.38 (woz13rule4) =>
% 99.20/13.38 ((
% 99.20/13.38 (woz1_1) =>
% 99.20/13.38 ((
% 99.20/13.38 (woz1_2) =>
% 99.20/13.38 ((
% 99.20/13.38 (woz1_3) =>
% 99.20/13.38 ((
% 99.20/13.38 (woz1_4) =>
% 99.20/13.38 ((
% 99.20/13.38 (woz1_5) =>
% 99.20/13.38 ((
% 99.20/13.38 (breln1all2) =>
% 99.20/13.38 ((
% 99.20/13.38 (breln1SetBreln1) =>
% 99.20/13.38 ((
% 99.20/13.38 (choice2fnsingleton) =>
% 99.20/13.38 ((
% 99.20/13.38 (setOfPairsIsBReln1) =>
% 99.20/13.38 ((
% 99.20/13.38 (breln1all1) =>
% 99.20/13.38 ((
% 99.20/13.38 (subbreln1) =>
% 99.20/13.38 ((
% 99.20/13.38 (eqbreln1) =>
% 99.20/13.38 ((
% 99.20/13.38 (breln1invprop) =>
% 99.20/13.38 ((
% 99.20/13.38 (breln1invI) =>
% 99.20/13.38 ((
% 99.20/13.38 (breln1invE) =>
% 99.20/13.38 ((
% 99.20/13.38 (breln1compprop) =>
% 99.20/13.38 ((
% 99.20/13.38 (breln1compI) =>
% 99.20/13.38 ((
% 99.20/13.38 (breln1compE) =>
% 99.20/13.38 ((
% 99.20/13.38 (breln1compEex) =>
% 99.20/13.38 ((
% 99.20/13.38 (breln1unionprop) =>
% 99.20/13.38 ((
% 99.20/13.38 (breln1unionIL) =>
% 99.20/13.38 ((
% 99.20/13.38 (breln1unionIR) =>
% 99.20/13.38 ((
% 99.20/13.38 (breln1unionI) =>
% 99.20/13.38 ((
% 99.20/13.38 (breln1unionE) =>
% 99.20/13.38 ((
% 99.20/13.38 (breln1unionEcases) =>
% 99.20/13.38 ((
% 99.20/13.38 (breln1unionCommutes) =>
% 99.20/13.38 ((
% 99.20/13.38 (woz2Ex) =>
% 99.20/13.38 ((
% 99.20/13.38 (woz2W) =>
% 99.20/13.38 ((
% 99.20/13.38 (woz2A) =>
% 99.20/13.38 ((
% 99.20/13.38 (woz2B) =>
% 99.20/13.38 ((
% 99.20/13.38 (image1Ex) =>
% 99.20/13.38 ((
% 99.20/13.38 (image1Ex1) =>
% 99.20/13.38 ((
% 99.20/13.38 (image1Equiv) =>
% 99.20/13.38 ((
% 99.20/13.38 (image1E) =>
% 99.20/13.38 ((
% 99.20/13.38 (image1I) =>
% 99.20/13.38 ((
% 99.20/13.38 (injFuncInInjFuncSet) =>
% 99.20/13.38 ((
% 99.20/13.38 (injFuncSetFuncIn) =>
% 99.20/13.38 ((
% 99.20/13.38 (injFuncSetFuncInj) =>
% 99.20/13.38 ((
% 99.20/13.38 (!!) @ (
% 99.20/13.38 (('#B') @ (
% 99.20/13.38 !!) @
% 99.20/13.38 (
% 99.20/13.38 (
% 99.20/13.38 ('#B') @ (
% 99.20/13.38 (
% 99.20/13.38 ('#B') @ (
% 99.20/13.38 !!))) @
% 99.20/13.38 (
% 99.20/13.38 (
% 99.20/13.38 ('#S') @ (
% 99.20/13.38 (
% 99.20/13.38 ('#B') @ (
% 99.20/13.38 '#S') @
% 99.20/13.38 (
% 99.20/13.38 (
% 99.20/13.38 ('#B') @ (
% 99.20/13.38 (
% 99.20/13.38 ('#B') @ (
% 99.20/13.38 '#S'))) @
% 99.20/13.38 (
% 99.20/13.38 (
% 99.20/13.38 ('#B') @ (
% 99.20/13.38 (
% 99.20/13.38 ('#B') @ (
% 99.20/13.38 (
% 99.20/13.38 ('#B') @ (
% 99.20/13.38 =>))))) @
% 99.20/13.38 (
% 99.20/13.38 (
% 99.20/13.38 ('#B') @ (
% 99.20/13.38 (
% 99.20/13.38 ('#B') @ (
% 99.20/13.38 (
% 99.20/13.38 ('#C') @ in)))) @
% 99.20/13.38 surjFuncSet)))))))) @
% 99.20/13.38 (
% 99.20/13.38 (
% 99.20/13.38 ('#B') @ (
% 99.20/13.38 (
% 99.20/13.38 ('#B') @ (
% 99.20/13.38 (
% 99.20/13.38 ('#C') @ in)))) @
% 99.20/13.38 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.20/13.38 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl408])).
% 99.20/13.38 thf(zip_derived_cl428, plain,
% 99.20/13.38 (~ (((exuE2) =>
% 99.20/13.38 (((nonemptyImpWitness) =>
% 99.20/13.38 (((uniqinunit) =>
% 99.20/13.38 (((notinsingleton) =>
% 99.20/13.38 (((eqinunit) =>
% 99.20/13.38 (((singletonsswitch) =>
% 99.20/13.38 (((upairsetE) =>
% 99.20/13.38 (((upairsetIL) =>
% 99.20/13.38 (((upairsetIR) =>
% 99.20/13.38 (((emptyE1) =>
% 99.20/13.38 (((vacuousDall) =>
% 99.20/13.38 (((quantDeMorgan1) =>
% 99.20/13.38 (((quantDeMorgan2) =>
% 99.20/13.38 (((quantDeMorgan3) =>
% 99.20/13.38 (((quantDeMorgan4) =>
% 99.20/13.38 (((prop2setI) =>
% 99.20/13.38 (((prop2set2propI) =>
% 99.20/13.38 (((notdexE) =>
% 99.20/13.38 (((notdallE) =>
% 99.20/13.38 (((exuI1) =>
% 99.20/13.38 (((exuI3) =>
% 99.20/13.38 (((exuI2) =>
% 99.20/13.38 (((inCongP) =>
% 99.20/13.38 (((in__Cong) =>
% 99.20/13.38 (((exuE3u) =>
% 99.20/13.38 (((exu__Cong) =>
% 99.20/13.38 (((setadjoin__Cong) =>
% 99.20/13.38 (((powerset__Cong) =>
% 99.20/13.38 (((setunion__Cong) =>
% 99.20/13.38 (((exuEu) =>
% 99.20/13.38 ((
% 99.20/13.38 (descr__Cong) =>
% 99.20/13.38 ((
% 99.20/13.38 (dsetconstr__Cong) =>
% 99.20/13.38 ((
% 99.20/13.38 (subsetI1) =>
% 99.20/13.38 ((
% 99.20/13.38 (eqimpsubset2) =>
% 99.20/13.38 ((
% 99.20/13.38 (eqimpsubset1) =>
% 99.20/13.38 ((
% 99.20/13.38 (subsetI2) =>
% 99.20/13.38 ((
% 99.20/13.38 (emptysetsubset) =>
% 99.20/13.38 ((
% 99.20/13.38 (subsetE) =>
% 99.20/13.38 ((
% 99.20/13.38 (subsetE2) =>
% 99.20/13.38 ((
% 99.20/13.38 (notsubsetI) =>
% 99.20/13.38 ((
% 99.20/13.38 (notequalI1) =>
% 99.20/13.38 ((
% 99.20/13.38 (notequalI2) =>
% 99.20/13.38 ((
% 99.20/13.38 (subsetRefl) =>
% 99.20/13.38 ((
% 99.20/13.38 (subsetTrans) =>
% 99.20/13.38 ((
% 99.20/13.38 (setadjoinSub) =>
% 99.20/13.38 ((
% 99.20/13.38 (setadjoinSub2) =>
% 99.20/13.38 ((
% 99.20/13.38 (subset2powerset) =>
% 99.20/13.38 ((
% 99.20/13.38 (setextsub) =>
% 99.20/13.38 ((
% 99.20/13.38 (subsetemptysetimpeq) =>
% 99.20/13.38 ((
% 99.20/13.38 (powersetI1) =>
% 99.20/13.38 ((
% 99.20/13.38 (powersetE1) =>
% 99.20/13.38 ((
% 99.20/13.38 (inPowerset) =>
% 99.20/13.38 ((
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% 99.20/13.38 ((
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% 99.20/13.38 ((
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% 99.20/13.38 ((
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% 99.20/13.38 (binunionRsub) =>
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% 99.20/13.38 ((
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% 99.20/13.38 ((
% 99.20/13.38 (binintersectSubset3) =>
% 99.20/13.38 ((
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% 99.20/13.38 ((
% 99.20/13.38 (binintersectRsub) =>
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% 99.20/13.38 (binintersectSubset4) =>
% 99.20/13.38 ((
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% 99.20/13.38 ((
% 99.20/13.38 (bs114d) =>
% 99.20/13.38 ((
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% 99.20/13.38 ((
% 99.20/13.38 (setminusEL) =>
% 99.20/13.38 ((
% 99.20/13.38 (setminusER) =>
% 99.20/13.38 ((
% 99.20/13.38 (setminusSubset2) =>
% 99.20/13.38 ((
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% 99.20/13.38 ((
% 99.20/13.38 (setminusELneg) =>
% 99.20/13.38 ((
% 99.20/13.38 (setminusILneg) =>
% 99.20/13.38 ((
% 99.20/13.38 (setminusIRneg) =>
% 99.20/13.38 ((
% 99.20/13.38 (setminusLsub) =>
% 99.20/13.38 ((
% 99.20/13.38 (setminusSubset1) =>
% 99.20/13.38 ((
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% 99.20/13.38 ((
% 99.20/13.38 (symdiffI2) =>
% 99.20/13.38 ((
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% 99.20/13.38 ((
% 99.20/13.38 (symdiffIneg2) =>
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% 99.20/13.38 ((
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% 99.20/13.38 ((
% 99.20/13.38 (kpairp) =>
% 99.20/13.38 ((
% 99.20/13.38 (singletonsubset) =>
% 99.20/13.38 ((
% 99.20/13.38 (singletoninpowerset) =>
% 99.20/13.38 ((
% 99.20/13.38 (singletoninpowunion) =>
% 99.20/13.38 ((
% 99.20/13.38 (upairset2E) =>
% 99.20/13.38 ((
% 99.20/13.38 (upairsubunion) =>
% 99.20/13.38 ((
% 99.20/13.38 (upairinpowunion) =>
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% 99.20/13.38 ((
% 99.20/13.38 (ubforcartprodlem2) =>
% 99.20/13.38 ((
% 99.20/13.38 (ubforcartprodlem3) =>
% 99.20/13.38 ((
% 99.20/13.38 (cartprodpairin) =>
% 99.20/13.38 ((
% 99.20/13.38 (cartprodmempair1) =>
% 99.20/13.38 ((
% 99.20/13.38 (cartprodmempair) =>
% 99.20/13.38 ((
% 99.20/13.38 (setunionE2) =>
% 99.20/13.38 ((
% 99.20/13.38 (setunionsingleton1) =>
% 99.20/13.38 ((
% 99.20/13.38 (setunionsingleton2) =>
% 99.20/13.38 ((
% 99.20/13.38 (setunionsingleton) =>
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% 99.20/13.38 ((
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% 99.20/13.38 ((
% 99.20/13.38 (ex1I) =>
% 99.20/13.38 ((
% 99.20/13.38 (ex1I2) =>
% 99.20/13.38 ((
% 99.20/13.38 (singletonsuniq) =>
% 99.20/13.38 ((
% 99.20/13.38 (setukpairinjL1) =>
% 99.20/13.38 ((
% 99.20/13.38 (kfstsingleton) =>
% 99.20/13.38 ((
% 99.20/13.38 (theprop) =>
% 99.20/13.38 ((
% 99.20/13.38 (kfstpairEq) =>
% 99.20/13.38 ((
% 99.20/13.38 (cartprodfstin) =>
% 99.20/13.38 ((
% 99.20/13.38 (setukpairinjL2) =>
% 99.20/13.38 ((
% 99.20/13.38 (setukpairinjL) =>
% 99.20/13.38 ((
% 99.20/13.38 (setukpairinjR11) =>
% 99.20/13.38 ((
% 99.20/13.38 (setukpairinjR12) =>
% 99.20/13.38 ((
% 99.20/13.38 (setukpairinjR1) =>
% 99.20/13.38 ((
% 99.20/13.38 (upairequniteq) =>
% 99.20/13.38 ((
% 99.20/13.38 (setukpairinjR2) =>
% 99.20/13.38 ((
% 99.20/13.38 (setukpairinjR) =>
% 99.20/13.38 ((
% 99.20/13.38 (ksndsingleton) =>
% 99.20/13.38 ((
% 99.20/13.38 (ksndpairEq) =>
% 99.20/13.38 ((
% 99.20/13.38 (kpairsurjEq) =>
% 99.20/13.38 ((
% 99.20/13.38 (cartprodsndin) =>
% 99.20/13.38 ((
% 99.20/13.38 (cartprodpairmemEL) =>
% 99.20/13.38 ((
% 99.20/13.38 (cartprodpairmemER) =>
% 99.20/13.38 ((
% 99.20/13.38 (cartprodmempaircEq) =>
% 99.20/13.38 ((
% 99.20/13.38 (cartprodfstpairEq) =>
% 99.20/13.38 ((
% 99.20/13.38 (cartprodsndpairEq) =>
% 99.20/13.38 ((
% 99.20/13.38 (cartprodpairsurjEq) =>
% 99.20/13.38 ((
% 99.20/13.38 (dpsetconstrI) =>
% 99.20/13.38 ((
% 99.20/13.38 (dpsetconstrSub) =>
% 99.20/13.38 ((
% 99.20/13.38 (setOfPairsIsBReln) =>
% 99.20/13.38 ((
% 99.20/13.38 (dpsetconstrERa) =>
% 99.20/13.38 ((
% 99.20/13.38 (dpsetconstrEL1) =>
% 99.20/13.38 ((
% 99.20/13.38 (dpsetconstrEL2) =>
% 99.20/13.38 ((
% 99.20/13.38 (dpsetconstrER) =>
% 99.20/13.38 ((
% 99.20/13.38 (funcImageSingleton) =>
% 99.20/13.38 ((
% 99.20/13.38 (apProp) =>
% 99.20/13.38 ((
% 99.20/13.38 (app) =>
% 99.20/13.38 ((
% 99.20/13.38 (infuncsetfunc) =>
% 99.20/13.38 ((
% 99.20/13.38 (ap2p) =>
% 99.20/13.38 ((
% 99.20/13.38 (funcinfuncset) =>
% 99.20/13.38 ((
% 99.20/13.38 (lamProp) =>
% 99.20/13.38 ((
% 99.20/13.38 (lamp) =>
% 99.20/13.38 ((
% 99.20/13.38 (lam2p) =>
% 99.20/13.38 ((
% 99.20/13.38 (brelnall1) =>
% 99.20/13.38 ((
% 99.20/13.38 (brelnall2) =>
% 99.20/13.38 ((
% 99.20/13.38 (ex1E2) =>
% 99.20/13.38 ((
% 99.20/13.38 (funcGraphProp1) =>
% 99.20/13.38 ((
% 99.20/13.38 (funcGraphProp3) =>
% 99.20/13.38 ((
% 99.20/13.38 (funcGraphProp2) =>
% 99.20/13.38 ((
% 99.20/13.38 (funcextLem) =>
% 99.20/13.38 ((
% 99.20/13.38 (funcGraphProp4) =>
% 99.20/13.38 ((
% 99.20/13.38 (subbreln) =>
% 99.20/13.38 ((
% 99.20/13.38 (eqbreln) =>
% 99.20/13.38 ((
% 99.20/13.38 (funcext) =>
% 99.20/13.38 ((
% 99.20/13.38 (funcext2) =>
% 99.20/13.38 ((
% 99.20/13.38 (ap2apEq1) =>
% 99.20/13.38 ((
% 99.20/13.38 (ap2apEq2) =>
% 99.20/13.38 ((
% 99.20/13.38 (beta1) =>
% 99.20/13.38 ((
% 99.20/13.38 (eta1) =>
% 99.20/13.38 ((
% 99.20/13.38 (lam2lamEq) =>
% 99.20/13.38 ((
% 99.20/13.38 (beta2) =>
% 99.20/13.38 ((
% 99.20/13.38 (eta2) =>
% 99.20/13.38 ((
% 99.20/13.38 (iffalseProp1) =>
% 99.20/13.38 ((
% 99.20/13.38 (iffalseProp2) =>
% 99.20/13.38 ((
% 99.20/13.38 (iftrueProp1) =>
% 99.20/13.38 ((
% 99.20/13.38 (iftrueProp2) =>
% 99.20/13.38 ((
% 99.20/13.38 (ifSingleton) =>
% 99.20/13.38 ((
% 99.20/13.38 (ifp) =>
% 99.20/13.38 ((
% 99.20/13.38 (theeq) =>
% 99.20/13.38 ((
% 99.20/13.38 (iftrue) =>
% 99.20/13.38 ((
% 99.20/13.38 (iffalse) =>
% 99.20/13.38 ((
% 99.20/13.38 (iftrueorfalse) =>
% 99.20/13.38 ((
% 99.20/13.38 (binintersectT_lem) =>
% 99.20/13.38 ((
% 99.20/13.38 (binunionT_lem) =>
% 99.20/13.38 ((
% 99.20/13.38 (powersetT_lem) =>
% 99.20/13.38 ((
% 99.20/13.38 (setminusT_lem) =>
% 99.20/13.38 ((
% 99.20/13.38 (complementT_lem) =>
% 99.20/13.38 ((
% 99.20/13.38 (setextT) =>
% 99.20/13.38 ((
% 99.20/13.38 (subsetTI) =>
% 99.20/13.38 ((
% 99.20/13.38 (powersetTI1) =>
% 99.20/13.38 ((
% 99.20/13.38 (powersetTE1) =>
% 99.20/13.38 ((
% 99.20/13.38 (complementTI1) =>
% 99.20/13.38 ((
% 99.20/13.38 (complementTE1) =>
% 99.20/13.38 ((
% 99.20/13.38 (binintersectTELcontra) =>
% 99.20/13.38 ((
% 99.20/13.38 (binintersectTERcontra) =>
% 99.20/13.38 ((
% 99.20/13.38 (contrasubsetT) =>
% 99.20/13.38 ((
% 99.20/13.38 (contrasubsetT1) =>
% 99.20/13.38 ((
% 99.20/13.38 (contrasubsetT2) =>
% 99.20/13.38 ((
% 99.20/13.38 (contrasubsetT3) =>
% 99.20/13.38 ((
% 99.20/13.38 (doubleComplementI1) =>
% 99.20/13.38 ((
% 99.20/13.38 (doubleComplementE1) =>
% 99.20/13.38 ((
% 99.20/13.38 (doubleComplementSub1) =>
% 99.20/13.38 ((
% 99.20/13.38 (doubleComplementSub2) =>
% 99.20/13.38 ((
% 99.20/13.38 (doubleComplementEq) =>
% 99.20/13.38 ((
% 99.20/13.38 (complementTnotintersectT) =>
% 99.20/13.38 ((
% 99.20/13.38 (complementImpComplementIntersect) =>
% 99.20/13.38 ((
% 99.20/13.38 (complementSubsetComplementIntersect) =>
% 99.20/13.38 ((
% 99.20/13.38 (complementInPowersetComplementIntersect) =>
% 99.20/13.38 ((
% 99.20/13.38 (contraSubsetComplement) =>
% 99.20/13.38 ((
% 99.20/13.38 (complementTcontraSubset) =>
% 99.20/13.38 ((
% 99.20/13.38 (binunionTILcontra) =>
% 99.20/13.38 ((
% 99.20/13.38 (binunionTIRcontra) =>
% 99.20/13.38 ((
% 99.20/13.38 (inIntersectImpInUnion) =>
% 99.20/13.38 ((
% 99.20/13.38 (inIntersectImpInUnion2) =>
% 99.20/13.38 ((
% 99.20/13.38 (inIntersectImpInIntersectUnions) =>
% 99.20/13.38 ((
% 99.20/13.38 (intersectInPowersetIntersectUnions) =>
% 99.20/13.38 ((
% 99.20/13.38 (inComplementUnionImpNotIn1) =>
% 99.20/13.38 ((
% 99.20/13.38 (inComplementUnionImpInComplement1) =>
% 99.20/13.38 ((
% 99.20/13.38 (binunionTE) =>
% 99.20/13.38 ((
% 99.20/13.38 (binunionTEcontra) =>
% 99.20/13.38 ((
% 99.20/13.38 (demorgan2a1) =>
% 99.20/13.38 ((
% 99.20/13.38 (complementUnionInPowersetComplement) =>
% 99.20/13.38 ((
% 99.20/13.38 (demorgan2a2) =>
% 99.20/13.38 ((
% 99.20/13.38 (demorgan1a) =>
% 99.20/13.38 ((
% 99.20/13.38 (demorgan1b) =>
% 99.20/13.38 ((
% 99.20/13.38 (demorgan1) =>
% 99.20/13.38 ((
% 99.20/13.38 (demorgan2a) =>
% 99.20/13.38 ((
% 99.20/13.38 (demorgan2b2) =>
% 99.20/13.38 ((
% 99.20/13.38 (demorgan2b) =>
% 99.20/13.38 ((
% 99.20/13.38 (demorgan2) =>
% 99.20/13.38 ((
% 99.20/13.38 (woz13rule0) =>
% 99.20/13.38 ((
% 99.20/13.38 (woz13rule1) =>
% 99.20/13.38 ((
% 99.20/13.38 (woz13rule2) =>
% 99.20/13.38 ((
% 99.20/13.38 (woz13rule3) =>
% 99.20/13.38 ((
% 99.20/13.38 (woz13rule4) =>
% 99.20/13.38 ((
% 99.20/13.38 (woz1_1) =>
% 99.20/13.38 ((
% 99.20/13.38 (woz1_2) =>
% 99.20/13.38 ((
% 99.20/13.38 (woz1_3) =>
% 99.20/13.38 ((
% 99.20/13.38 (woz1_4) =>
% 99.20/13.38 ((
% 99.20/13.38 (woz1_5) =>
% 99.20/13.38 ((
% 99.20/13.38 (breln1all2) =>
% 99.20/13.38 ((
% 99.20/13.38 (breln1SetBreln1) =>
% 99.20/13.38 ((
% 99.20/13.38 (choice2fnsingleton) =>
% 99.20/13.38 ((
% 99.20/13.38 (setOfPairsIsBReln1) =>
% 99.20/13.38 ((
% 99.20/13.38 (breln1all1) =>
% 99.20/13.38 ((
% 99.20/13.38 (subbreln1) =>
% 99.20/13.38 ((
% 99.20/13.38 (eqbreln1) =>
% 99.20/13.38 ((
% 99.20/13.38 (breln1invprop) =>
% 99.20/13.38 ((
% 99.20/13.38 (breln1invI) =>
% 99.20/13.38 ((
% 99.20/13.38 (breln1invE) =>
% 99.20/13.38 ((
% 99.20/13.38 (breln1compprop) =>
% 99.20/13.38 ((
% 99.20/13.38 (breln1compI) =>
% 99.20/13.38 ((
% 99.20/13.38 (breln1compE) =>
% 99.20/13.38 ((
% 99.20/13.38 (breln1compEex) =>
% 99.20/13.38 ((
% 99.20/13.38 (breln1unionprop) =>
% 99.20/13.38 ((
% 99.20/13.38 (breln1unionIL) =>
% 99.20/13.38 ((
% 99.20/13.38 (breln1unionIR) =>
% 99.20/13.38 ((
% 99.20/13.38 (breln1unionI) =>
% 99.20/13.38 ((
% 99.20/13.38 (breln1unionE) =>
% 99.20/13.38 ((
% 99.20/13.38 (breln1unionEcases) =>
% 99.20/13.38 ((
% 99.20/13.38 (breln1unionCommutes) =>
% 99.20/13.38 ((
% 99.20/13.38 (woz2Ex) =>
% 99.20/13.38 ((
% 99.20/13.38 (woz2W) =>
% 99.20/13.38 ((
% 99.20/13.38 (woz2A) =>
% 99.20/13.38 ((
% 99.20/13.38 (woz2B) =>
% 99.20/13.38 ((
% 99.20/13.38 (image1Ex) =>
% 99.20/13.38 ((
% 99.20/13.38 (image1Ex1) =>
% 99.20/13.38 ((
% 99.20/13.38 (image1Equiv) =>
% 99.20/13.38 ((
% 99.20/13.38 (image1E) =>
% 99.20/13.38 ((
% 99.20/13.38 (image1I) =>
% 99.20/13.38 ((
% 99.20/13.38 (injFuncInInjFuncSet) =>
% 99.20/13.38 ((
% 99.20/13.38 (injFuncSetFuncIn) =>
% 99.20/13.38 ((
% 99.20/13.38 (injFuncSetFuncInj) =>
% 99.20/13.38 ((
% 99.20/13.38 (!!) @ (
% 99.20/13.38 (('#B') @ (
% 99.20/13.38 !!) @
% 99.20/13.38 (
% 99.20/13.38 (
% 99.20/13.38 ('#B') @ (
% 99.20/13.38 (
% 99.20/13.38 ('#B') @ (
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% 99.20/13.38 (
% 99.20/13.38 (
% 99.20/13.38 ('#S') @ (
% 99.20/13.38 (
% 99.20/13.38 ('#B') @ (
% 99.20/13.38 '#S') @
% 99.20/13.38 (
% 99.20/13.38 (
% 99.20/13.38 ('#B') @ (
% 99.20/13.38 (
% 99.20/13.38 ('#B') @ (
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% 99.20/13.38 (
% 99.20/13.38 (
% 99.20/13.38 ('#B') @ (
% 99.20/13.38 (
% 99.20/13.38 ('#B') @ (
% 99.20/13.38 (
% 99.20/13.38 ('#B') @ (
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% 99.20/13.38 (
% 99.20/13.38 (
% 99.20/13.38 ('#B') @ (
% 99.20/13.38 (
% 99.20/13.38 ('#B') @ (
% 99.20/13.38 (
% 99.20/13.38 ('#C') @ in)))) @
% 99.20/13.38 surjFuncSet)))))))) @
% 99.20/13.38 (
% 99.20/13.38 (
% 99.20/13.38 ('#B') @ (
% 99.20/13.38 (
% 99.20/13.38 ('#B') @ (
% 99.20/13.38 (
% 99.20/13.38 ('#C') @ in)))) @
% 99.20/13.38 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.20/13.38 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl417])).
% 99.20/13.38 thf(zip_derived_cl439, plain,
% 99.20/13.38 (~ (((nonemptyImpWitness) =>
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% 99.20/13.38 (((upairsetIR) =>
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% 99.20/13.38 (((quantDeMorgan1) =>
% 99.20/13.38 (((quantDeMorgan2) =>
% 99.20/13.38 (((quantDeMorgan3) =>
% 99.20/13.38 (((quantDeMorgan4) =>
% 99.20/13.38 (((prop2setI) =>
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% 99.20/13.38 (((notdallE) =>
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% 99.20/13.38 (((exuI2) =>
% 99.20/13.38 (((inCongP) =>
% 99.20/13.38 (((in__Cong) =>
% 99.20/13.38 (((exuE3u) =>
% 99.20/13.38 (((exu__Cong) =>
% 99.20/13.38 (((setadjoin__Cong) =>
% 99.20/13.38 (((powerset__Cong) =>
% 99.20/13.38 (((setunion__Cong) =>
% 99.20/13.38 (((exuEu) =>
% 99.20/13.38 (((descr__Cong) =>
% 99.20/13.38 ((
% 99.20/13.38 (dsetconstr__Cong) =>
% 99.20/13.38 ((
% 99.20/13.38 (subsetI1) =>
% 99.20/13.38 ((
% 99.20/13.38 (eqimpsubset2) =>
% 99.20/13.38 ((
% 99.20/13.38 (eqimpsubset1) =>
% 99.20/13.38 ((
% 99.20/13.38 (subsetI2) =>
% 99.20/13.38 ((
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% 99.20/13.38 ((
% 99.20/13.38 (subsetE) =>
% 99.20/13.38 ((
% 99.20/13.38 (subsetE2) =>
% 99.20/13.38 ((
% 99.20/13.38 (notsubsetI) =>
% 99.20/13.38 ((
% 99.20/13.38 (notequalI1) =>
% 99.20/13.38 ((
% 99.20/13.38 (notequalI2) =>
% 99.20/13.38 ((
% 99.20/13.38 (subsetRefl) =>
% 99.20/13.38 ((
% 99.20/13.38 (subsetTrans) =>
% 99.20/13.38 ((
% 99.20/13.38 (setadjoinSub) =>
% 99.20/13.38 ((
% 99.20/13.38 (setadjoinSub2) =>
% 99.20/13.38 ((
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% 99.20/13.38 (cartprodmempaircEq) =>
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% 99.20/13.38 ((
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% 99.20/13.38 ((
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% 99.20/13.38 ((
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% 99.20/13.38 (((exuEu) =>
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% 99.20/13.38 ((
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% 99.20/13.38 ((
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% 99.20/13.38 ((
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% 99.20/13.38 ((
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% 99.20/13.38 (setukpairinjL) =>
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% 99.20/13.38 (kpairsurjEq) =>
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% 99.20/13.38 (cartprodsndin) =>
% 99.20/13.38 ((
% 99.20/13.38 (cartprodpairmemEL) =>
% 99.20/13.38 ((
% 99.20/13.38 (cartprodpairmemER) =>
% 99.20/13.38 ((
% 99.20/13.38 (cartprodmempaircEq) =>
% 99.20/13.38 ((
% 99.20/13.38 (cartprodfstpairEq) =>
% 99.20/13.38 ((
% 99.20/13.38 (cartprodsndpairEq) =>
% 99.20/13.38 ((
% 99.20/13.38 (cartprodpairsurjEq) =>
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% 99.20/13.38 ((
% 99.20/13.38 (dpsetconstrSub) =>
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% 99.20/13.38 ((
% 99.20/13.38 (lamp) =>
% 99.20/13.38 ((
% 99.20/13.38 (lam2p) =>
% 99.20/13.38 ((
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% 99.20/13.38 ((
% 99.20/13.38 (brelnall2) =>
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% 99.20/13.38 ((
% 99.20/13.38 (funcGraphProp3) =>
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% 99.20/13.38 (funcGraphProp2) =>
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% 99.20/13.38 ((
% 99.20/13.38 (funcGraphProp4) =>
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% 99.20/13.38 ((
% 99.20/13.38 (contrasubsetT2) =>
% 99.20/13.38 ((
% 99.20/13.38 (contrasubsetT3) =>
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% 99.20/13.38 ((
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% 99.20/13.38 (complementTnotintersectT) =>
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% 99.20/13.38 (complementTcontraSubset) =>
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% 99.20/13.38 ((
% 99.20/13.38 (binunionTIRcontra) =>
% 99.20/13.38 ((
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% 99.20/13.38 ((
% 99.20/13.38 (inIntersectImpInUnion2) =>
% 99.20/13.38 ((
% 99.20/13.38 (inIntersectImpInIntersectUnions) =>
% 99.20/13.38 ((
% 99.20/13.38 (intersectInPowersetIntersectUnions) =>
% 99.20/13.38 ((
% 99.20/13.38 (inComplementUnionImpNotIn1) =>
% 99.20/13.38 ((
% 99.20/13.38 (inComplementUnionImpInComplement1) =>
% 99.20/13.38 ((
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% 99.20/13.38 ((
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% 99.20/13.38 ((
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% 99.20/13.38 ((
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% 99.20/13.38 ((
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% 99.20/13.38 ((
% 99.20/13.38 (demorgan2a) =>
% 99.20/13.38 ((
% 99.20/13.38 (demorgan2b2) =>
% 99.20/13.38 ((
% 99.20/13.38 (demorgan2b) =>
% 99.20/13.38 ((
% 99.20/13.38 (demorgan2) =>
% 99.20/13.38 ((
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% 99.20/13.38 ((
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% 99.20/13.38 ((
% 99.20/13.38 (woz13rule2) =>
% 99.20/13.38 ((
% 99.20/13.38 (woz13rule3) =>
% 99.20/13.38 ((
% 99.20/13.38 (woz13rule4) =>
% 99.20/13.38 ((
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% 99.20/13.38 ((
% 99.20/13.38 (woz1_2) =>
% 99.20/13.38 ((
% 99.20/13.38 (woz1_3) =>
% 99.20/13.38 ((
% 99.20/13.38 (woz1_4) =>
% 99.20/13.38 ((
% 99.20/13.38 (woz1_5) =>
% 99.20/13.38 ((
% 99.20/13.38 (breln1all2) =>
% 99.20/13.38 ((
% 99.20/13.38 (breln1SetBreln1) =>
% 99.20/13.38 ((
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% 99.20/13.38 ((
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% 99.20/13.38 ((
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% 99.20/13.38 ((
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% 99.20/13.38 ((
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% 99.20/13.38 ((
% 99.20/13.38 (breln1invE) =>
% 99.20/13.38 ((
% 99.20/13.38 (breln1compprop) =>
% 99.20/13.38 ((
% 99.20/13.38 (breln1compI) =>
% 99.20/13.38 ((
% 99.20/13.38 (breln1compE) =>
% 99.20/13.38 ((
% 99.20/13.38 (breln1compEex) =>
% 99.20/13.38 ((
% 99.20/13.38 (breln1unionprop) =>
% 99.20/13.38 ((
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% 99.20/13.38 ((
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% 99.20/13.38 ((
% 99.20/13.38 (breln1unionI) =>
% 99.20/13.38 ((
% 99.20/13.38 (breln1unionE) =>
% 99.20/13.38 ((
% 99.20/13.38 (breln1unionEcases) =>
% 99.20/13.38 ((
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% 99.20/13.38 ((
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% 99.20/13.38 ((
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% 99.20/13.38 ((
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% 99.20/13.38 (woz2B) =>
% 99.20/13.38 ((
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% 99.20/13.38 ((
% 99.20/13.38 (image1Ex1) =>
% 99.20/13.38 ((
% 99.20/13.38 (image1Equiv) =>
% 99.20/13.38 ((
% 99.20/13.38 (image1E) =>
% 99.20/13.38 ((
% 99.20/13.38 (image1I) =>
% 99.20/13.38 ((
% 99.20/13.38 (injFuncInInjFuncSet) =>
% 99.20/13.38 ((
% 99.20/13.38 (injFuncSetFuncIn) =>
% 99.20/13.38 ((
% 99.20/13.38 (injFuncSetFuncInj) =>
% 99.20/13.38 ((
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% 99.20/13.38 (
% 99.20/13.38 (
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% 99.20/13.38 (
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% 99.20/13.38 (
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% 99.20/13.38 (
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% 99.20/13.38 (
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% 99.20/13.38 surjFuncSet)))))))) @
% 99.20/13.38 (
% 99.20/13.38 (
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% 99.20/13.38 (
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% 99.20/13.38 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
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% 99.20/13.38 (((in__Cong) =>
% 99.20/13.38 (((exuE3u) =>
% 99.20/13.38 (((exu__Cong) =>
% 99.20/13.38 (((setadjoin__Cong) =>
% 99.20/13.38 (((powerset__Cong) =>
% 99.20/13.38 (((setunion__Cong) =>
% 99.20/13.38 (((exuEu) =>
% 99.20/13.38 (((descr__Cong) =>
% 99.20/13.38 (((dsetconstr__Cong) =>
% 99.20/13.38 (((subsetI1) =>
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% 99.20/13.38 (((eqimpsubset1) =>
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% 99.20/13.38 ((
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% 99.20/13.38 (setukpairinjL) =>
% 99.20/13.38 ((
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% 99.20/13.38 (kpairsurjEq) =>
% 99.20/13.38 ((
% 99.20/13.38 (cartprodsndin) =>
% 99.20/13.38 ((
% 99.20/13.38 (cartprodpairmemEL) =>
% 99.20/13.38 ((
% 99.20/13.38 (cartprodpairmemER) =>
% 99.20/13.38 ((
% 99.20/13.38 (cartprodmempaircEq) =>
% 99.20/13.38 ((
% 99.20/13.38 (cartprodfstpairEq) =>
% 99.20/13.38 ((
% 99.20/13.38 (cartprodsndpairEq) =>
% 99.20/13.38 ((
% 99.20/13.38 (cartprodpairsurjEq) =>
% 99.20/13.38 ((
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% 99.20/13.38 ((
% 99.20/13.38 (dpsetconstrSub) =>
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% 99.20/13.38 (dpsetconstrEL2) =>
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% 99.20/13.38 ((
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% 99.20/13.38 (app) =>
% 99.20/13.38 ((
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% 99.20/13.38 (ap2p) =>
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% 99.20/13.38 (funcinfuncset) =>
% 99.20/13.38 ((
% 99.20/13.38 (lamProp) =>
% 99.20/13.38 ((
% 99.20/13.38 (lamp) =>
% 99.20/13.38 ((
% 99.20/13.38 (lam2p) =>
% 99.20/13.38 ((
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% 99.20/13.38 ((
% 99.20/13.38 (brelnall2) =>
% 99.20/13.38 ((
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% 99.20/13.38 (funcGraphProp1) =>
% 99.20/13.38 ((
% 99.20/13.38 (funcGraphProp3) =>
% 99.20/13.38 ((
% 99.20/13.38 (funcGraphProp2) =>
% 99.20/13.38 ((
% 99.20/13.38 (funcextLem) =>
% 99.20/13.38 ((
% 99.20/13.38 (funcGraphProp4) =>
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% 99.20/13.38 ((
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% 99.20/13.38 ((
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% 99.20/13.38 ((
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% 99.20/13.38 ((
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% 99.20/13.38 (beta2) =>
% 99.20/13.38 ((
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% 99.20/13.38 ((
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% 99.20/13.38 ((
% 99.20/13.38 (iffalseProp2) =>
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% 99.20/13.38 ((
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% 99.20/13.38 ((
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% 99.20/13.38 ((
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% 99.20/13.38 ((
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% 99.20/13.38 ((
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% 99.20/13.38 ((
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% 99.20/13.38 ((
% 99.20/13.38 (contrasubsetT2) =>
% 99.20/13.38 ((
% 99.20/13.38 (contrasubsetT3) =>
% 99.20/13.38 ((
% 99.20/13.38 (doubleComplementI1) =>
% 99.20/13.38 ((
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% 99.20/13.38 ((
% 99.20/13.38 (doubleComplementSub2) =>
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% 99.20/13.38 (doubleComplementEq) =>
% 99.20/13.38 ((
% 99.20/13.38 (complementTnotintersectT) =>
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% 99.20/13.38 (complementImpComplementIntersect) =>
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% 99.20/13.38 (complementSubsetComplementIntersect) =>
% 99.20/13.38 ((
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% 99.20/13.38 ((
% 99.20/13.38 (contraSubsetComplement) =>
% 99.20/13.38 ((
% 99.20/13.38 (complementTcontraSubset) =>
% 99.20/13.38 ((
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% 99.20/13.38 ((
% 99.20/13.38 (binunionTIRcontra) =>
% 99.20/13.38 ((
% 99.20/13.38 (inIntersectImpInUnion) =>
% 99.20/13.38 ((
% 99.20/13.38 (inIntersectImpInUnion2) =>
% 99.20/13.38 ((
% 99.20/13.38 (inIntersectImpInIntersectUnions) =>
% 99.20/13.38 ((
% 99.20/13.38 (intersectInPowersetIntersectUnions) =>
% 99.20/13.38 ((
% 99.20/13.38 (inComplementUnionImpNotIn1) =>
% 99.20/13.38 ((
% 99.20/13.38 (inComplementUnionImpInComplement1) =>
% 99.20/13.38 ((
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% 99.20/13.38 ((
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% 99.20/13.38 ((
% 99.20/13.38 (complementUnionInPowersetComplement) =>
% 99.20/13.38 ((
% 99.20/13.38 (demorgan2a2) =>
% 99.20/13.38 ((
% 99.20/13.38 (demorgan1a) =>
% 99.20/13.38 ((
% 99.20/13.38 (demorgan1b) =>
% 99.20/13.38 ((
% 99.20/13.38 (demorgan1) =>
% 99.20/13.38 ((
% 99.20/13.38 (demorgan2a) =>
% 99.20/13.38 ((
% 99.20/13.38 (demorgan2b2) =>
% 99.20/13.38 ((
% 99.20/13.38 (demorgan2b) =>
% 99.20/13.38 ((
% 99.20/13.38 (demorgan2) =>
% 99.20/13.38 ((
% 99.20/13.38 (woz13rule0) =>
% 99.20/13.38 ((
% 99.20/13.38 (woz13rule1) =>
% 99.20/13.38 ((
% 99.20/13.38 (woz13rule2) =>
% 99.20/13.38 ((
% 99.20/13.38 (woz13rule3) =>
% 99.20/13.38 ((
% 99.20/13.38 (woz13rule4) =>
% 99.20/13.38 ((
% 99.20/13.38 (woz1_1) =>
% 99.20/13.38 ((
% 99.20/13.38 (woz1_2) =>
% 99.20/13.38 ((
% 99.20/13.38 (woz1_3) =>
% 99.20/13.38 ((
% 99.20/13.38 (woz1_4) =>
% 99.20/13.38 ((
% 99.20/13.38 (woz1_5) =>
% 99.20/13.38 ((
% 99.20/13.38 (breln1all2) =>
% 99.20/13.38 ((
% 99.20/13.38 (breln1SetBreln1) =>
% 99.20/13.38 ((
% 99.20/13.38 (choice2fnsingleton) =>
% 99.20/13.38 ((
% 99.20/13.38 (setOfPairsIsBReln1) =>
% 99.20/13.38 ((
% 99.20/13.38 (breln1all1) =>
% 99.20/13.38 ((
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% 99.20/13.38 ((
% 99.20/13.38 (eqbreln1) =>
% 99.20/13.38 ((
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% 99.20/13.38 ((
% 99.20/13.38 (breln1invI) =>
% 99.20/13.38 ((
% 99.20/13.38 (breln1invE) =>
% 99.20/13.38 ((
% 99.20/13.38 (breln1compprop) =>
% 99.20/13.38 ((
% 99.20/13.38 (breln1compI) =>
% 99.20/13.38 ((
% 99.20/13.38 (breln1compE) =>
% 99.20/13.38 ((
% 99.20/13.38 (breln1compEex) =>
% 99.20/13.38 ((
% 99.20/13.38 (breln1unionprop) =>
% 99.20/13.38 ((
% 99.20/13.38 (breln1unionIL) =>
% 99.20/13.38 ((
% 99.20/13.38 (breln1unionIR) =>
% 99.20/13.38 ((
% 99.20/13.38 (breln1unionI) =>
% 99.20/13.38 ((
% 99.20/13.38 (breln1unionE) =>
% 99.20/13.38 ((
% 99.20/13.38 (breln1unionEcases) =>
% 99.20/13.38 ((
% 99.20/13.38 (breln1unionCommutes) =>
% 99.20/13.38 ((
% 99.20/13.38 (woz2Ex) =>
% 99.20/13.38 ((
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% 99.20/13.38 ((
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% 99.20/13.38 ((
% 99.20/13.38 (woz2B) =>
% 99.20/13.38 ((
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% 99.20/13.38 ((
% 99.20/13.38 (image1Ex1) =>
% 99.20/13.38 ((
% 99.20/13.38 (image1Equiv) =>
% 99.20/13.38 ((
% 99.20/13.38 (image1E) =>
% 99.20/13.38 ((
% 99.20/13.38 (image1I) =>
% 99.20/13.38 ((
% 99.20/13.38 (injFuncInInjFuncSet) =>
% 99.20/13.38 ((
% 99.20/13.38 (injFuncSetFuncIn) =>
% 99.20/13.38 ((
% 99.20/13.38 (injFuncSetFuncInj) =>
% 99.20/13.38 ((
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% 99.20/13.38 (('#B') @ (
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% 99.20/13.38 (
% 99.20/13.38 (
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% 99.20/13.38 (
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% 99.20/13.38 (
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% 99.20/13.38 (
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% 99.20/13.38 (
% 99.20/13.38 (
% 99.20/13.38 ('#B') @ (
% 99.20/13.38 (
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% 99.20/13.38 (
% 99.20/13.38 (
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% 99.20/13.38 (
% 99.20/13.38 ('#B') @ (
% 99.20/13.38 (
% 99.20/13.38 ('#B') @ (
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% 99.20/13.38 (
% 99.20/13.38 (
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% 99.20/13.38 (
% 99.20/13.38 ('#B') @ (
% 99.20/13.38 (
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% 99.20/13.38 surjFuncSet)))))))) @
% 99.20/13.38 (
% 99.20/13.38 (
% 99.20/13.38 ('#B') @ (
% 99.20/13.38 (
% 99.20/13.38 ('#B') @ (
% 99.20/13.38 (
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% 99.20/13.38 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.20/13.38 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl467])).
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% 99.20/13.38 (((quantDeMorgan2) =>
% 99.20/13.38 (((quantDeMorgan3) =>
% 99.20/13.38 (((quantDeMorgan4) =>
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% 99.20/13.38 (((notdallE) =>
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% 99.20/13.38 (((exuI3) =>
% 99.20/13.38 (((exuI2) =>
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% 99.20/13.38 (((in__Cong) =>
% 99.20/13.38 (((exuE3u) =>
% 99.20/13.38 (((exu__Cong) =>
% 99.20/13.38 (((setadjoin__Cong) =>
% 99.20/13.38 (((powerset__Cong) =>
% 99.20/13.38 (((setunion__Cong) =>
% 99.20/13.38 (((exuEu) =>
% 99.20/13.38 (((descr__Cong) =>
% 99.20/13.38 (((dsetconstr__Cong) =>
% 99.20/13.38 (((subsetI1) =>
% 99.20/13.38 (((eqimpsubset2) =>
% 99.20/13.38 (((eqimpsubset1) =>
% 99.20/13.38 (((subsetI2) =>
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% 99.20/13.38 ((
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% 99.20/13.38 ((
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% 99.20/13.38 ((
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% 99.20/13.38 ((
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% 99.20/13.38 ((
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% 99.20/13.38 ((
% 99.20/13.38 (cartprodfstin) =>
% 99.20/13.38 ((
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% 99.20/13.38 ((
% 99.20/13.38 (setukpairinjL) =>
% 99.20/13.38 ((
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% 99.20/13.38 ((
% 99.20/13.38 (setukpairinjR12) =>
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% 99.20/13.38 (setukpairinjR1) =>
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% 99.20/13.38 ((
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% 99.20/13.38 (kpairsurjEq) =>
% 99.20/13.38 ((
% 99.20/13.38 (cartprodsndin) =>
% 99.20/13.38 ((
% 99.20/13.38 (cartprodpairmemEL) =>
% 99.20/13.38 ((
% 99.20/13.38 (cartprodpairmemER) =>
% 99.20/13.38 ((
% 99.20/13.38 (cartprodmempaircEq) =>
% 99.20/13.38 ((
% 99.20/13.38 (cartprodfstpairEq) =>
% 99.20/13.38 ((
% 99.20/13.38 (cartprodsndpairEq) =>
% 99.20/13.38 ((
% 99.20/13.38 (cartprodpairsurjEq) =>
% 99.20/13.38 ((
% 99.20/13.38 (dpsetconstrI) =>
% 99.20/13.38 ((
% 99.20/13.38 (dpsetconstrSub) =>
% 99.20/13.38 ((
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% 99.20/13.38 (dpsetconstrERa) =>
% 99.20/13.38 ((
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% 99.20/13.38 ((
% 99.20/13.38 (dpsetconstrEL2) =>
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% 99.20/13.38 (dpsetconstrER) =>
% 99.20/13.38 ((
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% 99.20/13.38 ((
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% 99.20/13.38 ((
% 99.20/13.38 (app) =>
% 99.20/13.38 ((
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% 99.20/13.38 ((
% 99.20/13.38 (ap2p) =>
% 99.20/13.38 ((
% 99.20/13.38 (funcinfuncset) =>
% 99.20/13.38 ((
% 99.20/13.38 (lamProp) =>
% 99.20/13.38 ((
% 99.20/13.38 (lamp) =>
% 99.20/13.38 ((
% 99.20/13.38 (lam2p) =>
% 99.20/13.38 ((
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% 99.20/13.38 ((
% 99.20/13.38 (brelnall2) =>
% 99.20/13.38 ((
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% 99.20/13.38 ((
% 99.20/13.38 (funcGraphProp1) =>
% 99.20/13.38 ((
% 99.20/13.38 (funcGraphProp3) =>
% 99.20/13.38 ((
% 99.20/13.38 (funcGraphProp2) =>
% 99.20/13.38 ((
% 99.20/13.38 (funcextLem) =>
% 99.20/13.38 ((
% 99.20/13.38 (funcGraphProp4) =>
% 99.20/13.38 ((
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% 99.20/13.38 ((
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% 99.20/13.38 ((
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% 99.20/13.38 ((
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% 99.20/13.38 ((
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% 99.20/13.38 ((
% 99.20/13.38 (lam2lamEq) =>
% 99.20/13.38 ((
% 99.20/13.38 (beta2) =>
% 99.20/13.38 ((
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% 99.20/13.38 ((
% 99.20/13.38 (iffalseProp1) =>
% 99.20/13.38 ((
% 99.20/13.38 (iffalseProp2) =>
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% 99.20/13.38 ((
% 99.20/13.38 (iftrueProp2) =>
% 99.20/13.38 ((
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% 99.20/13.38 ((
% 99.20/13.38 (ifp) =>
% 99.20/13.38 ((
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% 99.20/13.38 ((
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% 99.20/13.38 ((
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% 99.20/13.38 ((
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% 99.20/13.38 ((
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% 99.20/13.38 ((
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% 99.20/13.38 ((
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% 99.20/13.38 ((
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% 99.20/13.38 ((
% 99.20/13.38 (contrasubsetT2) =>
% 99.20/13.38 ((
% 99.20/13.38 (contrasubsetT3) =>
% 99.20/13.38 ((
% 99.20/13.38 (doubleComplementI1) =>
% 99.20/13.38 ((
% 99.20/13.38 (doubleComplementE1) =>
% 99.20/13.38 ((
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% 99.20/13.38 ((
% 99.20/13.38 (doubleComplementSub2) =>
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% 99.20/13.38 (doubleComplementEq) =>
% 99.20/13.38 ((
% 99.20/13.38 (complementTnotintersectT) =>
% 99.20/13.38 ((
% 99.20/13.38 (complementImpComplementIntersect) =>
% 99.20/13.38 ((
% 99.20/13.38 (complementSubsetComplementIntersect) =>
% 99.20/13.38 ((
% 99.20/13.38 (complementInPowersetComplementIntersect) =>
% 99.20/13.38 ((
% 99.20/13.38 (contraSubsetComplement) =>
% 99.20/13.38 ((
% 99.20/13.38 (complementTcontraSubset) =>
% 99.20/13.38 ((
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% 99.20/13.38 ((
% 99.20/13.38 (binunionTIRcontra) =>
% 99.20/13.38 ((
% 99.20/13.38 (inIntersectImpInUnion) =>
% 99.20/13.38 ((
% 99.20/13.38 (inIntersectImpInUnion2) =>
% 99.20/13.38 ((
% 99.20/13.38 (inIntersectImpInIntersectUnions) =>
% 99.20/13.38 ((
% 99.20/13.38 (intersectInPowersetIntersectUnions) =>
% 99.20/13.38 ((
% 99.20/13.38 (inComplementUnionImpNotIn1) =>
% 99.20/13.38 ((
% 99.20/13.38 (inComplementUnionImpInComplement1) =>
% 99.20/13.38 ((
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% 99.20/13.38 ((
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% 99.20/13.38 ((
% 99.20/13.38 (complementUnionInPowersetComplement) =>
% 99.20/13.38 ((
% 99.20/13.38 (demorgan2a2) =>
% 99.20/13.38 ((
% 99.20/13.38 (demorgan1a) =>
% 99.20/13.38 ((
% 99.20/13.38 (demorgan1b) =>
% 99.20/13.38 ((
% 99.20/13.38 (demorgan1) =>
% 99.20/13.38 ((
% 99.20/13.38 (demorgan2a) =>
% 99.20/13.38 ((
% 99.20/13.38 (demorgan2b2) =>
% 99.20/13.38 ((
% 99.20/13.38 (demorgan2b) =>
% 99.20/13.38 ((
% 99.20/13.38 (demorgan2) =>
% 99.20/13.38 ((
% 99.20/13.38 (woz13rule0) =>
% 99.20/13.38 ((
% 99.20/13.38 (woz13rule1) =>
% 99.20/13.38 ((
% 99.20/13.38 (woz13rule2) =>
% 99.20/13.38 ((
% 99.20/13.38 (woz13rule3) =>
% 99.20/13.38 ((
% 99.20/13.38 (woz13rule4) =>
% 99.20/13.38 ((
% 99.20/13.38 (woz1_1) =>
% 99.20/13.38 ((
% 99.20/13.38 (woz1_2) =>
% 99.20/13.38 ((
% 99.20/13.38 (woz1_3) =>
% 99.20/13.38 ((
% 99.20/13.38 (woz1_4) =>
% 99.20/13.38 ((
% 99.20/13.38 (woz1_5) =>
% 99.20/13.38 ((
% 99.20/13.38 (breln1all2) =>
% 99.20/13.38 ((
% 99.20/13.38 (breln1SetBreln1) =>
% 99.20/13.38 ((
% 99.20/13.38 (choice2fnsingleton) =>
% 99.20/13.38 ((
% 99.20/13.38 (setOfPairsIsBReln1) =>
% 99.20/13.38 ((
% 99.20/13.38 (breln1all1) =>
% 99.20/13.38 ((
% 99.20/13.38 (subbreln1) =>
% 99.20/13.38 ((
% 99.20/13.38 (eqbreln1) =>
% 99.20/13.38 ((
% 99.20/13.38 (breln1invprop) =>
% 99.20/13.38 ((
% 99.20/13.38 (breln1invI) =>
% 99.20/13.38 ((
% 99.20/13.38 (breln1invE) =>
% 99.20/13.38 ((
% 99.20/13.38 (breln1compprop) =>
% 99.20/13.38 ((
% 99.20/13.38 (breln1compI) =>
% 99.20/13.38 ((
% 99.20/13.38 (breln1compE) =>
% 99.20/13.38 ((
% 99.20/13.38 (breln1compEex) =>
% 99.20/13.38 ((
% 99.20/13.38 (breln1unionprop) =>
% 99.20/13.38 ((
% 99.20/13.38 (breln1unionIL) =>
% 99.20/13.38 ((
% 99.20/13.38 (breln1unionIR) =>
% 99.20/13.38 ((
% 99.20/13.38 (breln1unionI) =>
% 99.20/13.38 ((
% 99.20/13.38 (breln1unionE) =>
% 99.20/13.38 ((
% 99.20/13.38 (breln1unionEcases) =>
% 99.20/13.38 ((
% 99.20/13.38 (breln1unionCommutes) =>
% 99.20/13.38 ((
% 99.20/13.38 (woz2Ex) =>
% 99.20/13.38 ((
% 99.20/13.38 (woz2W) =>
% 99.20/13.38 ((
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% 99.20/13.38 ((
% 99.20/13.38 (woz2B) =>
% 99.20/13.38 ((
% 99.20/13.38 (image1Ex) =>
% 99.20/13.38 ((
% 99.20/13.38 (image1Ex1) =>
% 99.20/13.38 ((
% 99.20/13.38 (image1Equiv) =>
% 99.20/13.38 ((
% 99.20/13.38 (image1E) =>
% 99.20/13.38 ((
% 99.20/13.38 (image1I) =>
% 99.20/13.38 ((
% 99.20/13.38 (injFuncInInjFuncSet) =>
% 99.20/13.38 ((
% 99.20/13.38 (injFuncSetFuncIn) =>
% 99.20/13.38 ((
% 99.20/13.38 (injFuncSetFuncInj) =>
% 99.20/13.38 ((
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% 99.20/13.38 (('#B') @ (
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% 99.20/13.38 (
% 99.20/13.38 (
% 99.20/13.38 ('#B') @ (
% 99.20/13.38 (
% 99.20/13.38 ('#B') @ (
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% 99.20/13.38 (
% 99.20/13.38 (
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% 99.20/13.38 (
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% 99.20/13.38 (
% 99.20/13.38 (
% 99.20/13.38 ('#B') @ (
% 99.20/13.38 (
% 99.20/13.38 ('#B') @ (
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% 99.20/13.38 (
% 99.20/13.38 (
% 99.20/13.38 ('#B') @ (
% 99.20/13.38 (
% 99.20/13.38 ('#B') @ (
% 99.20/13.38 (
% 99.20/13.38 ('#B') @ (
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% 99.20/13.38 (
% 99.20/13.38 (
% 99.20/13.38 ('#B') @ (
% 99.20/13.38 (
% 99.20/13.38 ('#B') @ (
% 99.20/13.38 (
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% 99.20/13.38 surjFuncSet)))))))) @
% 99.20/13.38 (
% 99.20/13.38 (
% 99.20/13.38 ('#B') @ (
% 99.20/13.38 (
% 99.20/13.38 ('#B') @ (
% 99.20/13.38 (
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% 99.20/13.38 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.20/13.38 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl475])).
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% 99.20/13.38 (((quantDeMorgan2) =>
% 99.20/13.38 (((quantDeMorgan3) =>
% 99.20/13.38 (((quantDeMorgan4) =>
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% 99.20/13.38 (((notdallE) =>
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% 99.20/13.38 (((exuI3) =>
% 99.20/13.38 (((exuI2) =>
% 99.20/13.38 (((inCongP) =>
% 99.20/13.38 (((in__Cong) =>
% 99.20/13.38 (((exuE3u) =>
% 99.20/13.38 (((exu__Cong) =>
% 99.20/13.38 (((setadjoin__Cong) =>
% 99.20/13.38 (((powerset__Cong) =>
% 99.20/13.38 (((setunion__Cong) =>
% 99.20/13.38 (((exuEu) =>
% 99.20/13.38 (((descr__Cong) =>
% 99.20/13.38 (((dsetconstr__Cong) =>
% 99.20/13.38 (((subsetI1) =>
% 99.20/13.38 (((eqimpsubset2) =>
% 99.20/13.38 (((eqimpsubset1) =>
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% 99.20/13.38 (singletoninpowerset) =>
% 99.20/13.38 ((
% 99.20/13.38 (singletoninpowunion) =>
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% 99.20/13.38 ((
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% 99.20/13.38 ((
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% 99.20/13.38 ((
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% 99.20/13.38 ((
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% 99.20/13.38 ((
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% 99.20/13.38 ((
% 99.20/13.38 (kfstpairEq) =>
% 99.20/13.38 ((
% 99.20/13.38 (cartprodfstin) =>
% 99.20/13.38 ((
% 99.20/13.38 (setukpairinjL2) =>
% 99.20/13.38 ((
% 99.20/13.38 (setukpairinjL) =>
% 99.20/13.38 ((
% 99.20/13.38 (setukpairinjR11) =>
% 99.20/13.38 ((
% 99.20/13.38 (setukpairinjR12) =>
% 99.20/13.38 ((
% 99.20/13.38 (setukpairinjR1) =>
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% 99.20/13.38 (setukpairinjR) =>
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% 99.20/13.38 (ksndsingleton) =>
% 99.20/13.38 ((
% 99.20/13.38 (ksndpairEq) =>
% 99.20/13.38 ((
% 99.20/13.38 (kpairsurjEq) =>
% 99.20/13.38 ((
% 99.20/13.38 (cartprodsndin) =>
% 99.20/13.38 ((
% 99.20/13.38 (cartprodpairmemEL) =>
% 99.20/13.38 ((
% 99.20/13.38 (cartprodpairmemER) =>
% 99.20/13.38 ((
% 99.20/13.38 (cartprodmempaircEq) =>
% 99.20/13.38 ((
% 99.20/13.38 (cartprodfstpairEq) =>
% 99.20/13.38 ((
% 99.20/13.38 (cartprodsndpairEq) =>
% 99.20/13.38 ((
% 99.20/13.38 (cartprodpairsurjEq) =>
% 99.20/13.38 ((
% 99.20/13.38 (dpsetconstrI) =>
% 99.20/13.38 ((
% 99.20/13.38 (dpsetconstrSub) =>
% 99.20/13.38 ((
% 99.20/13.38 (setOfPairsIsBReln) =>
% 99.20/13.38 ((
% 99.20/13.38 (dpsetconstrERa) =>
% 99.20/13.38 ((
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% 99.20/13.38 ((
% 99.20/13.38 (dpsetconstrEL2) =>
% 99.20/13.38 ((
% 99.20/13.38 (dpsetconstrER) =>
% 99.20/13.38 ((
% 99.20/13.38 (funcImageSingleton) =>
% 99.20/13.38 ((
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% 99.20/13.38 ((
% 99.20/13.38 (app) =>
% 99.20/13.38 ((
% 99.20/13.38 (infuncsetfunc) =>
% 99.20/13.38 ((
% 99.20/13.38 (ap2p) =>
% 99.20/13.38 ((
% 99.20/13.38 (funcinfuncset) =>
% 99.20/13.38 ((
% 99.20/13.38 (lamProp) =>
% 99.20/13.38 ((
% 99.20/13.38 (lamp) =>
% 99.20/13.38 ((
% 99.20/13.38 (lam2p) =>
% 99.20/13.38 ((
% 99.20/13.38 (brelnall1) =>
% 99.20/13.38 ((
% 99.20/13.38 (brelnall2) =>
% 99.20/13.38 ((
% 99.20/13.38 (ex1E2) =>
% 99.20/13.38 ((
% 99.20/13.38 (funcGraphProp1) =>
% 99.20/13.38 ((
% 99.20/13.38 (funcGraphProp3) =>
% 99.20/13.38 ((
% 99.20/13.38 (funcGraphProp2) =>
% 99.20/13.38 ((
% 99.20/13.38 (funcextLem) =>
% 99.20/13.38 ((
% 99.20/13.38 (funcGraphProp4) =>
% 99.20/13.38 ((
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% 99.20/13.38 ((
% 99.20/13.38 (ap2apEq2) =>
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% 99.20/13.38 ((
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% 99.20/13.38 ((
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% 99.20/13.38 (beta2) =>
% 99.20/13.38 ((
% 99.20/13.38 (eta2) =>
% 99.20/13.38 ((
% 99.20/13.38 (iffalseProp1) =>
% 99.20/13.38 ((
% 99.20/13.38 (iffalseProp2) =>
% 99.20/13.38 ((
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% 99.20/13.38 ((
% 99.20/13.38 (iftrueProp2) =>
% 99.20/13.38 ((
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% 99.20/13.38 ((
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% 99.20/13.38 ((
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% 99.20/13.38 ((
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% 99.20/13.38 ((
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% 99.20/13.38 ((
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% 99.20/13.38 ((
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% 99.20/13.38 ((
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% 99.20/13.38 ((
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% 99.20/13.38 ((
% 99.20/13.38 (contrasubsetT2) =>
% 99.20/13.38 ((
% 99.20/13.38 (contrasubsetT3) =>
% 99.20/13.38 ((
% 99.20/13.38 (doubleComplementI1) =>
% 99.20/13.38 ((
% 99.20/13.38 (doubleComplementE1) =>
% 99.20/13.38 ((
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% 99.20/13.38 ((
% 99.20/13.38 (doubleComplementSub2) =>
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% 99.20/13.38 (doubleComplementEq) =>
% 99.20/13.38 ((
% 99.20/13.38 (complementTnotintersectT) =>
% 99.20/13.38 ((
% 99.20/13.38 (complementImpComplementIntersect) =>
% 99.20/13.38 ((
% 99.20/13.38 (complementSubsetComplementIntersect) =>
% 99.20/13.38 ((
% 99.20/13.38 (complementInPowersetComplementIntersect) =>
% 99.20/13.38 ((
% 99.20/13.38 (contraSubsetComplement) =>
% 99.20/13.38 ((
% 99.20/13.38 (complementTcontraSubset) =>
% 99.20/13.38 ((
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% 99.20/13.38 ((
% 99.20/13.38 (binunionTIRcontra) =>
% 99.20/13.38 ((
% 99.20/13.38 (inIntersectImpInUnion) =>
% 99.20/13.38 ((
% 99.20/13.38 (inIntersectImpInUnion2) =>
% 99.20/13.38 ((
% 99.20/13.38 (inIntersectImpInIntersectUnions) =>
% 99.20/13.38 ((
% 99.20/13.38 (intersectInPowersetIntersectUnions) =>
% 99.20/13.38 ((
% 99.20/13.38 (inComplementUnionImpNotIn1) =>
% 99.20/13.38 ((
% 99.20/13.38 (inComplementUnionImpInComplement1) =>
% 99.20/13.38 ((
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% 99.20/13.38 ((
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% 99.20/13.38 ((
% 99.20/13.38 (complementUnionInPowersetComplement) =>
% 99.20/13.38 ((
% 99.20/13.38 (demorgan2a2) =>
% 99.20/13.38 ((
% 99.20/13.38 (demorgan1a) =>
% 99.20/13.38 ((
% 99.20/13.38 (demorgan1b) =>
% 99.20/13.38 ((
% 99.20/13.38 (demorgan1) =>
% 99.20/13.38 ((
% 99.20/13.38 (demorgan2a) =>
% 99.20/13.38 ((
% 99.20/13.38 (demorgan2b2) =>
% 99.20/13.38 ((
% 99.20/13.38 (demorgan2b) =>
% 99.20/13.38 ((
% 99.20/13.38 (demorgan2) =>
% 99.20/13.38 ((
% 99.20/13.38 (woz13rule0) =>
% 99.20/13.38 ((
% 99.20/13.38 (woz13rule1) =>
% 99.20/13.38 ((
% 99.20/13.38 (woz13rule2) =>
% 99.20/13.38 ((
% 99.20/13.38 (woz13rule3) =>
% 99.20/13.38 ((
% 99.20/13.38 (woz13rule4) =>
% 99.20/13.38 ((
% 99.20/13.38 (woz1_1) =>
% 99.20/13.38 ((
% 99.20/13.38 (woz1_2) =>
% 99.20/13.38 ((
% 99.20/13.38 (woz1_3) =>
% 99.20/13.38 ((
% 99.20/13.38 (woz1_4) =>
% 99.20/13.38 ((
% 99.20/13.38 (woz1_5) =>
% 99.20/13.38 ((
% 99.20/13.38 (breln1all2) =>
% 99.20/13.38 ((
% 99.20/13.38 (breln1SetBreln1) =>
% 99.20/13.38 ((
% 99.20/13.38 (choice2fnsingleton) =>
% 99.20/13.38 ((
% 99.20/13.38 (setOfPairsIsBReln1) =>
% 99.20/13.38 ((
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% 99.20/13.38 ((
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% 99.20/13.38 ((
% 99.20/13.38 (eqbreln1) =>
% 99.20/13.38 ((
% 99.20/13.38 (breln1invprop) =>
% 99.20/13.38 ((
% 99.20/13.38 (breln1invI) =>
% 99.20/13.38 ((
% 99.20/13.38 (breln1invE) =>
% 99.20/13.38 ((
% 99.20/13.38 (breln1compprop) =>
% 99.20/13.38 ((
% 99.20/13.38 (breln1compI) =>
% 99.20/13.38 ((
% 99.20/13.38 (breln1compE) =>
% 99.20/13.38 ((
% 99.20/13.38 (breln1compEex) =>
% 99.20/13.38 ((
% 99.20/13.38 (breln1unionprop) =>
% 99.20/13.38 ((
% 99.20/13.38 (breln1unionIL) =>
% 99.20/13.38 ((
% 99.20/13.38 (breln1unionIR) =>
% 99.20/13.38 ((
% 99.20/13.38 (breln1unionI) =>
% 99.20/13.38 ((
% 99.20/13.38 (breln1unionE) =>
% 99.20/13.38 ((
% 99.20/13.38 (breln1unionEcases) =>
% 99.20/13.38 ((
% 99.20/13.38 (breln1unionCommutes) =>
% 99.20/13.38 ((
% 99.20/13.38 (woz2Ex) =>
% 99.20/13.38 ((
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% 99.20/13.38 ((
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% 99.20/13.38 ((
% 99.20/13.38 (woz2B) =>
% 99.20/13.38 ((
% 99.20/13.38 (image1Ex) =>
% 99.20/13.38 ((
% 99.20/13.38 (image1Ex1) =>
% 99.20/13.38 ((
% 99.20/13.38 (image1Equiv) =>
% 99.20/13.38 ((
% 99.20/13.38 (image1E) =>
% 99.20/13.38 ((
% 99.20/13.38 (image1I) =>
% 99.20/13.38 ((
% 99.20/13.38 (injFuncInInjFuncSet) =>
% 99.20/13.38 ((
% 99.20/13.38 (injFuncSetFuncIn) =>
% 99.20/13.38 ((
% 99.20/13.38 (injFuncSetFuncInj) =>
% 99.20/13.38 ((
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% 99.20/13.38 (('#B') @ (
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% 99.20/13.38 (
% 99.20/13.38 (
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% 99.20/13.38 (
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% 99.20/13.38 (
% 99.20/13.38 (
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% 99.20/13.38 (
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% 99.20/13.38 (
% 99.20/13.38 (
% 99.20/13.38 ('#B') @ (
% 99.20/13.38 (
% 99.20/13.38 ('#B') @ (
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% 99.20/13.38 (
% 99.20/13.38 (
% 99.20/13.38 ('#B') @ (
% 99.20/13.38 (
% 99.20/13.38 ('#B') @ (
% 99.20/13.38 (
% 99.20/13.38 ('#B') @ (
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% 99.20/13.38 (
% 99.20/13.38 (
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% 99.20/13.38 (
% 99.20/13.38 ('#B') @ (
% 99.20/13.38 (
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% 99.20/13.38 surjFuncSet)))))))) @
% 99.20/13.38 (
% 99.20/13.38 (
% 99.20/13.38 ('#B') @ (
% 99.20/13.38 (
% 99.20/13.38 ('#B') @ (
% 99.20/13.38 (
% 99.20/13.38 ('#C') @ in)))) @
% 99.20/13.38 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.20/13.38 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl485])).
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% 99.20/13.38 (((quantDeMorgan2) =>
% 99.20/13.38 (((quantDeMorgan3) =>
% 99.20/13.38 (((quantDeMorgan4) =>
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% 99.20/13.38 (((notdallE) =>
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% 99.20/13.38 (((exuI3) =>
% 99.20/13.38 (((exuI2) =>
% 99.20/13.38 (((inCongP) =>
% 99.20/13.38 (((in__Cong) =>
% 99.20/13.38 (((exuE3u) =>
% 99.20/13.38 (((exu__Cong) =>
% 99.20/13.38 (((setadjoin__Cong) =>
% 99.20/13.38 (((powerset__Cong) =>
% 99.20/13.38 (((setunion__Cong) =>
% 99.20/13.38 (((exuEu) =>
% 99.20/13.38 (((descr__Cong) =>
% 99.20/13.38 (((dsetconstr__Cong) =>
% 99.20/13.38 (((subsetI1) =>
% 99.20/13.38 (((eqimpsubset2) =>
% 99.20/13.38 (((eqimpsubset1) =>
% 99.20/13.38 (((subsetI2) =>
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% 99.20/13.38 (((subsetE) =>
% 99.20/13.38 ((
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% 99.20/13.38 ((
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% 99.20/13.39 ((
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% 99.20/13.39 ((
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% 99.20/13.39 ((
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% 99.20/13.39 ((
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% 99.20/13.39 (kpairsurjEq) =>
% 99.20/13.39 ((
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% 99.20/13.39 ((
% 99.20/13.39 (cartprodpairmemEL) =>
% 99.20/13.39 ((
% 99.20/13.39 (cartprodpairmemER) =>
% 99.20/13.39 ((
% 99.20/13.39 (cartprodmempaircEq) =>
% 99.20/13.39 ((
% 99.20/13.39 (cartprodfstpairEq) =>
% 99.20/13.39 ((
% 99.20/13.39 (cartprodsndpairEq) =>
% 99.20/13.39 ((
% 99.20/13.39 (cartprodpairsurjEq) =>
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% 99.20/13.39 ((
% 99.20/13.39 (dpsetconstrSub) =>
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% 99.20/13.39 (dpsetconstrEL2) =>
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% 99.20/13.39 ((
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% 99.20/13.39 ((
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% 99.20/13.39 (app) =>
% 99.20/13.39 ((
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% 99.20/13.39 ((
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% 99.20/13.39 ((
% 99.20/13.39 (funcinfuncset) =>
% 99.20/13.39 ((
% 99.20/13.39 (lamProp) =>
% 99.20/13.39 ((
% 99.20/13.39 (lamp) =>
% 99.20/13.39 ((
% 99.20/13.39 (lam2p) =>
% 99.20/13.39 ((
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% 99.20/13.39 ((
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% 99.20/13.39 ((
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% 99.20/13.39 (funcGraphProp1) =>
% 99.20/13.39 ((
% 99.20/13.39 (funcGraphProp3) =>
% 99.20/13.39 ((
% 99.20/13.39 (funcGraphProp2) =>
% 99.20/13.39 ((
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% 99.20/13.39 ((
% 99.20/13.39 (funcGraphProp4) =>
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% 99.20/13.39 ((
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% 99.20/13.39 ((
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% 99.20/13.39 ((
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% 99.20/13.39 (beta2) =>
% 99.20/13.39 ((
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% 99.20/13.39 ((
% 99.20/13.39 (iffalseProp1) =>
% 99.20/13.39 ((
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% 99.20/13.39 ((
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% 99.20/13.39 ((
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% 99.20/13.39 ((
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% 99.20/13.39 ((
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% 99.20/13.39 ((
% 99.20/13.39 (contrasubsetT2) =>
% 99.20/13.39 ((
% 99.20/13.39 (contrasubsetT3) =>
% 99.20/13.39 ((
% 99.20/13.39 (doubleComplementI1) =>
% 99.20/13.39 ((
% 99.20/13.39 (doubleComplementE1) =>
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% 99.20/13.39 ((
% 99.20/13.39 (doubleComplementSub2) =>
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% 99.20/13.39 (doubleComplementEq) =>
% 99.20/13.39 ((
% 99.20/13.39 (complementTnotintersectT) =>
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% 99.20/13.39 (complementImpComplementIntersect) =>
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% 99.20/13.39 (complementSubsetComplementIntersect) =>
% 99.20/13.39 ((
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% 99.20/13.39 ((
% 99.20/13.39 (contraSubsetComplement) =>
% 99.20/13.39 ((
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% 99.20/13.39 ((
% 99.20/13.39 (binunionTIRcontra) =>
% 99.20/13.39 ((
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% 99.20/13.39 ((
% 99.20/13.39 (inIntersectImpInUnion2) =>
% 99.20/13.39 ((
% 99.20/13.39 (inIntersectImpInIntersectUnions) =>
% 99.20/13.39 ((
% 99.20/13.39 (intersectInPowersetIntersectUnions) =>
% 99.20/13.39 ((
% 99.20/13.39 (inComplementUnionImpNotIn1) =>
% 99.20/13.39 ((
% 99.20/13.39 (inComplementUnionImpInComplement1) =>
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% 99.20/13.39 ((
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% 99.20/13.39 ((
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% 99.20/13.39 ((
% 99.20/13.39 (demorgan1b) =>
% 99.20/13.39 ((
% 99.20/13.39 (demorgan1) =>
% 99.20/13.39 ((
% 99.20/13.39 (demorgan2a) =>
% 99.20/13.39 ((
% 99.20/13.39 (demorgan2b2) =>
% 99.20/13.39 ((
% 99.20/13.39 (demorgan2b) =>
% 99.20/13.39 ((
% 99.20/13.39 (demorgan2) =>
% 99.20/13.39 ((
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% 99.20/13.39 ((
% 99.20/13.39 (woz13rule1) =>
% 99.20/13.39 ((
% 99.20/13.39 (woz13rule2) =>
% 99.20/13.39 ((
% 99.20/13.39 (woz13rule3) =>
% 99.20/13.39 ((
% 99.20/13.39 (woz13rule4) =>
% 99.20/13.39 ((
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% 99.20/13.39 ((
% 99.20/13.39 (woz1_2) =>
% 99.20/13.39 ((
% 99.20/13.39 (woz1_3) =>
% 99.20/13.39 ((
% 99.20/13.39 (woz1_4) =>
% 99.20/13.39 ((
% 99.20/13.39 (woz1_5) =>
% 99.20/13.39 ((
% 99.20/13.39 (breln1all2) =>
% 99.20/13.39 ((
% 99.20/13.39 (breln1SetBreln1) =>
% 99.20/13.39 ((
% 99.20/13.39 (choice2fnsingleton) =>
% 99.20/13.39 ((
% 99.20/13.39 (setOfPairsIsBReln1) =>
% 99.20/13.39 ((
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% 99.20/13.39 ((
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% 99.20/13.39 ((
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% 99.20/13.39 ((
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% 99.20/13.39 ((
% 99.20/13.39 (breln1invE) =>
% 99.20/13.39 ((
% 99.20/13.39 (breln1compprop) =>
% 99.20/13.39 ((
% 99.20/13.39 (breln1compI) =>
% 99.20/13.39 ((
% 99.20/13.39 (breln1compE) =>
% 99.20/13.39 ((
% 99.20/13.39 (breln1compEex) =>
% 99.20/13.39 ((
% 99.20/13.39 (breln1unionprop) =>
% 99.20/13.39 ((
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% 99.20/13.39 ((
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% 99.20/13.39 ((
% 99.20/13.39 (breln1unionI) =>
% 99.20/13.39 ((
% 99.20/13.39 (breln1unionE) =>
% 99.20/13.39 ((
% 99.20/13.39 (breln1unionEcases) =>
% 99.20/13.39 ((
% 99.20/13.39 (breln1unionCommutes) =>
% 99.20/13.39 ((
% 99.20/13.39 (woz2Ex) =>
% 99.20/13.39 ((
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% 99.20/13.39 ((
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% 99.20/13.39 ((
% 99.20/13.39 (image1Ex1) =>
% 99.20/13.39 ((
% 99.20/13.39 (image1Equiv) =>
% 99.20/13.39 ((
% 99.20/13.39 (image1E) =>
% 99.20/13.39 ((
% 99.20/13.39 (image1I) =>
% 99.20/13.39 ((
% 99.20/13.39 (injFuncInInjFuncSet) =>
% 99.20/13.39 ((
% 99.20/13.39 (injFuncSetFuncIn) =>
% 99.20/13.39 ((
% 99.20/13.39 (injFuncSetFuncInj) =>
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% 99.20/13.39 (
% 99.20/13.39 (
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% 99.20/13.39 (
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% 99.20/13.39 (
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% 99.20/13.39 (
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% 99.20/13.39 (
% 99.20/13.39 (
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% 99.20/13.39 (
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% 99.20/13.39 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
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% 99.20/13.39 (((exuE3u) =>
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% 99.20/13.39 (((powerset__Cong) =>
% 99.20/13.39 (((setunion__Cong) =>
% 99.20/13.39 (((exuEu) =>
% 99.20/13.39 (((descr__Cong) =>
% 99.20/13.39 (((dsetconstr__Cong) =>
% 99.20/13.39 (((subsetI1) =>
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% 99.20/13.39 ((
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% 99.20/13.39 ((
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% 99.20/13.39 ((
% 99.20/13.39 (cartprodpairmemER) =>
% 99.20/13.39 ((
% 99.20/13.39 (cartprodmempaircEq) =>
% 99.20/13.39 ((
% 99.20/13.39 (cartprodfstpairEq) =>
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% 99.20/13.39 (lamp) =>
% 99.20/13.39 ((
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% 99.20/13.39 ((
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% 99.20/13.39 ((
% 99.20/13.39 (funcGraphProp3) =>
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% 99.20/13.39 (funcGraphProp2) =>
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% 99.20/13.39 (funcGraphProp4) =>
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% 99.20/13.39 ((
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% 99.20/13.39 ((
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% 99.20/13.39 ((
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% 99.20/13.39 ((
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% 99.20/13.39 ((
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% 99.20/13.39 ((
% 99.20/13.39 (breln1compE) =>
% 99.20/13.39 ((
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% 99.20/13.39 ((
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% 99.20/13.39 ((
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% 99.20/13.39 ((
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% 99.20/13.39 ((
% 99.20/13.39 (image1E) =>
% 99.20/13.39 ((
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% 99.20/13.39 ((
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% 99.20/13.39 ((
% 99.20/13.39 (injFuncSetFuncIn) =>
% 99.20/13.39 ((
% 99.20/13.39 (injFuncSetFuncInj) =>
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% 99.20/13.39 (
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% 99.20/13.39 (
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% 99.20/13.39 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
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% 99.20/13.39 (((exuE3u) =>
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% 99.20/13.39 (((powerset__Cong) =>
% 99.20/13.39 (((setunion__Cong) =>
% 99.20/13.39 (((exuEu) =>
% 99.20/13.39 (((descr__Cong) =>
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% 99.20/13.39 ((
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% 99.20/13.39 ((
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% 99.20/13.39 ((
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% 99.20/13.39 ((
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% 99.20/13.39 ((
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% 99.20/13.39 (setukpairinjR11) =>
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% 99.20/13.39 (setukpairinjR1) =>
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% 99.20/13.39 (kpairsurjEq) =>
% 99.20/13.39 ((
% 99.20/13.39 (cartprodsndin) =>
% 99.20/13.39 ((
% 99.20/13.39 (cartprodpairmemEL) =>
% 99.20/13.39 ((
% 99.20/13.39 (cartprodpairmemER) =>
% 99.20/13.39 ((
% 99.20/13.39 (cartprodmempaircEq) =>
% 99.20/13.39 ((
% 99.20/13.39 (cartprodfstpairEq) =>
% 99.20/13.39 ((
% 99.20/13.39 (cartprodsndpairEq) =>
% 99.20/13.39 ((
% 99.20/13.39 (cartprodpairsurjEq) =>
% 99.20/13.39 ((
% 99.20/13.39 (dpsetconstrI) =>
% 99.20/13.39 ((
% 99.20/13.39 (dpsetconstrSub) =>
% 99.20/13.39 ((
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% 99.20/13.39 (dpsetconstrERa) =>
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% 99.20/13.39 ((
% 99.20/13.39 (dpsetconstrEL2) =>
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% 99.20/13.39 (dpsetconstrER) =>
% 99.20/13.39 ((
% 99.20/13.39 (funcImageSingleton) =>
% 99.20/13.39 ((
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% 99.20/13.39 ((
% 99.20/13.39 (app) =>
% 99.20/13.39 ((
% 99.20/13.39 (infuncsetfunc) =>
% 99.20/13.39 ((
% 99.20/13.39 (ap2p) =>
% 99.20/13.39 ((
% 99.20/13.39 (funcinfuncset) =>
% 99.20/13.39 ((
% 99.20/13.39 (lamProp) =>
% 99.20/13.39 ((
% 99.20/13.39 (lamp) =>
% 99.20/13.39 ((
% 99.20/13.39 (lam2p) =>
% 99.20/13.39 ((
% 99.20/13.39 (brelnall1) =>
% 99.20/13.39 ((
% 99.20/13.39 (brelnall2) =>
% 99.20/13.39 ((
% 99.20/13.39 (ex1E2) =>
% 99.20/13.39 ((
% 99.20/13.39 (funcGraphProp1) =>
% 99.20/13.39 ((
% 99.20/13.39 (funcGraphProp3) =>
% 99.20/13.39 ((
% 99.20/13.39 (funcGraphProp2) =>
% 99.20/13.39 ((
% 99.20/13.39 (funcextLem) =>
% 99.20/13.39 ((
% 99.20/13.39 (funcGraphProp4) =>
% 99.20/13.39 ((
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% 99.20/13.39 ((
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% 99.20/13.39 ((
% 99.20/13.39 (lam2lamEq) =>
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% 99.20/13.39 (beta2) =>
% 99.20/13.39 ((
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% 99.20/13.39 ((
% 99.20/13.39 (iffalseProp1) =>
% 99.20/13.39 ((
% 99.20/13.39 (iffalseProp2) =>
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% 99.20/13.39 ((
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% 99.20/13.39 ((
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% 99.20/13.39 ((
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% 99.20/13.39 ((
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% 99.20/13.39 ((
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% 99.20/13.39 ((
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% 99.20/13.39 ((
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% 99.20/13.39 ((
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% 99.20/13.39 ((
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% 99.20/13.39 ((
% 99.20/13.39 (contrasubsetT2) =>
% 99.20/13.39 ((
% 99.20/13.39 (contrasubsetT3) =>
% 99.20/13.39 ((
% 99.20/13.39 (doubleComplementI1) =>
% 99.20/13.39 ((
% 99.20/13.39 (doubleComplementE1) =>
% 99.20/13.39 ((
% 99.20/13.39 (doubleComplementSub1) =>
% 99.20/13.39 ((
% 99.20/13.39 (doubleComplementSub2) =>
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% 99.20/13.39 (doubleComplementEq) =>
% 99.20/13.39 ((
% 99.20/13.39 (complementTnotintersectT) =>
% 99.20/13.39 ((
% 99.20/13.39 (complementImpComplementIntersect) =>
% 99.20/13.39 ((
% 99.20/13.39 (complementSubsetComplementIntersect) =>
% 99.20/13.39 ((
% 99.20/13.39 (complementInPowersetComplementIntersect) =>
% 99.20/13.39 ((
% 99.20/13.39 (contraSubsetComplement) =>
% 99.20/13.39 ((
% 99.20/13.39 (complementTcontraSubset) =>
% 99.20/13.39 ((
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% 99.20/13.39 ((
% 99.20/13.39 (binunionTIRcontra) =>
% 99.20/13.39 ((
% 99.20/13.39 (inIntersectImpInUnion) =>
% 99.20/13.39 ((
% 99.20/13.39 (inIntersectImpInUnion2) =>
% 99.20/13.39 ((
% 99.20/13.39 (inIntersectImpInIntersectUnions) =>
% 99.20/13.39 ((
% 99.20/13.39 (intersectInPowersetIntersectUnions) =>
% 99.20/13.39 ((
% 99.20/13.39 (inComplementUnionImpNotIn1) =>
% 99.20/13.39 ((
% 99.20/13.39 (inComplementUnionImpInComplement1) =>
% 99.20/13.39 ((
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% 99.20/13.39 ((
% 99.20/13.39 (complementUnionInPowersetComplement) =>
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% 99.20/13.39 ((
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% 99.20/13.39 ((
% 99.20/13.39 (demorgan1b) =>
% 99.20/13.39 ((
% 99.20/13.39 (demorgan1) =>
% 99.20/13.39 ((
% 99.20/13.39 (demorgan2a) =>
% 99.20/13.39 ((
% 99.20/13.39 (demorgan2b2) =>
% 99.20/13.39 ((
% 99.20/13.39 (demorgan2b) =>
% 99.20/13.39 ((
% 99.20/13.39 (demorgan2) =>
% 99.20/13.39 ((
% 99.20/13.39 (woz13rule0) =>
% 99.20/13.39 ((
% 99.20/13.39 (woz13rule1) =>
% 99.20/13.39 ((
% 99.20/13.39 (woz13rule2) =>
% 99.20/13.39 ((
% 99.20/13.39 (woz13rule3) =>
% 99.20/13.39 ((
% 99.20/13.39 (woz13rule4) =>
% 99.20/13.39 ((
% 99.20/13.39 (woz1_1) =>
% 99.20/13.39 ((
% 99.20/13.39 (woz1_2) =>
% 99.20/13.39 ((
% 99.20/13.39 (woz1_3) =>
% 99.20/13.39 ((
% 99.20/13.39 (woz1_4) =>
% 99.20/13.39 ((
% 99.20/13.39 (woz1_5) =>
% 99.20/13.39 ((
% 99.20/13.39 (breln1all2) =>
% 99.20/13.39 ((
% 99.20/13.39 (breln1SetBreln1) =>
% 99.20/13.39 ((
% 99.20/13.39 (choice2fnsingleton) =>
% 99.20/13.39 ((
% 99.20/13.39 (setOfPairsIsBReln1) =>
% 99.20/13.39 ((
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% 99.20/13.39 ((
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% 99.20/13.39 ((
% 99.20/13.39 (eqbreln1) =>
% 99.20/13.39 ((
% 99.20/13.39 (breln1invprop) =>
% 99.20/13.39 ((
% 99.20/13.39 (breln1invI) =>
% 99.20/13.39 ((
% 99.20/13.39 (breln1invE) =>
% 99.20/13.39 ((
% 99.20/13.39 (breln1compprop) =>
% 99.20/13.39 ((
% 99.20/13.39 (breln1compI) =>
% 99.20/13.39 ((
% 99.20/13.39 (breln1compE) =>
% 99.20/13.39 ((
% 99.20/13.39 (breln1compEex) =>
% 99.20/13.39 ((
% 99.20/13.39 (breln1unionprop) =>
% 99.20/13.39 ((
% 99.20/13.39 (breln1unionIL) =>
% 99.20/13.39 ((
% 99.20/13.39 (breln1unionIR) =>
% 99.20/13.39 ((
% 99.20/13.39 (breln1unionI) =>
% 99.20/13.39 ((
% 99.20/13.39 (breln1unionE) =>
% 99.20/13.39 ((
% 99.20/13.39 (breln1unionEcases) =>
% 99.20/13.39 ((
% 99.20/13.39 (breln1unionCommutes) =>
% 99.20/13.39 ((
% 99.20/13.39 (woz2Ex) =>
% 99.20/13.39 ((
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% 99.20/13.39 ((
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% 99.20/13.39 ((
% 99.20/13.39 (woz2B) =>
% 99.20/13.39 ((
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% 99.20/13.39 ((
% 99.20/13.39 (image1Ex1) =>
% 99.20/13.39 ((
% 99.20/13.39 (image1Equiv) =>
% 99.20/13.39 ((
% 99.20/13.39 (image1E) =>
% 99.20/13.39 ((
% 99.20/13.39 (image1I) =>
% 99.20/13.39 ((
% 99.20/13.39 (injFuncInInjFuncSet) =>
% 99.20/13.39 ((
% 99.20/13.39 (injFuncSetFuncIn) =>
% 99.20/13.39 ((
% 99.20/13.39 (injFuncSetFuncInj) =>
% 99.20/13.39 ((
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% 99.20/13.39 (
% 99.20/13.39 (
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% 99.20/13.39 (
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% 99.20/13.39 (
% 99.20/13.39 (
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% 99.20/13.39 (
% 99.20/13.39 (
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% 99.20/13.39 (
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% 99.20/13.39 (
% 99.20/13.39 (
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% 99.20/13.39 surjFuncSet)))))))) @
% 99.20/13.39 (
% 99.20/13.39 (
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% 99.20/13.39 (
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% 99.20/13.39 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.20/13.39 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl517])).
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% 99.20/13.39 (((exuE3u) =>
% 99.20/13.39 (((exu__Cong) =>
% 99.20/13.39 (((setadjoin__Cong) =>
% 99.20/13.39 (((powerset__Cong) =>
% 99.20/13.39 (((setunion__Cong) =>
% 99.20/13.39 (((exuEu) =>
% 99.20/13.39 (((descr__Cong) =>
% 99.20/13.39 (((dsetconstr__Cong) =>
% 99.20/13.39 (((subsetI1) =>
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% 99.20/13.39 ((
% 99.20/13.39 (subsetTrans) =>
% 99.20/13.39 ((
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% 99.20/13.39 ((
% 99.20/13.39 (setadjoinSub2) =>
% 99.20/13.39 ((
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% 99.20/13.39 ((
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% 99.20/13.39 (powersetE1) =>
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% 99.20/13.39 ((
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% 99.20/13.39 ((
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% 99.20/13.39 ((
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% 99.20/13.39 (setukpairinjL2) =>
% 99.20/13.39 ((
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% 99.20/13.39 (setukpairinjR1) =>
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% 99.20/13.39 (kpairsurjEq) =>
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% 99.20/13.39 (cartprodsndin) =>
% 99.20/13.39 ((
% 99.20/13.39 (cartprodpairmemEL) =>
% 99.20/13.39 ((
% 99.20/13.39 (cartprodpairmemER) =>
% 99.20/13.39 ((
% 99.20/13.39 (cartprodmempaircEq) =>
% 99.20/13.39 ((
% 99.20/13.39 (cartprodfstpairEq) =>
% 99.20/13.39 ((
% 99.20/13.39 (cartprodsndpairEq) =>
% 99.20/13.39 ((
% 99.20/13.39 (cartprodpairsurjEq) =>
% 99.20/13.39 ((
% 99.20/13.39 (dpsetconstrI) =>
% 99.20/13.39 ((
% 99.20/13.39 (dpsetconstrSub) =>
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% 99.20/13.39 (dpsetconstrERa) =>
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% 99.20/13.39 (dpsetconstrEL2) =>
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% 99.20/13.39 (dpsetconstrER) =>
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% 99.20/13.39 ((
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% 99.20/13.39 (app) =>
% 99.20/13.39 ((
% 99.20/13.39 (infuncsetfunc) =>
% 99.20/13.39 ((
% 99.20/13.39 (ap2p) =>
% 99.20/13.39 ((
% 99.20/13.39 (funcinfuncset) =>
% 99.20/13.39 ((
% 99.20/13.39 (lamProp) =>
% 99.20/13.39 ((
% 99.20/13.39 (lamp) =>
% 99.20/13.39 ((
% 99.20/13.39 (lam2p) =>
% 99.20/13.39 ((
% 99.20/13.39 (brelnall1) =>
% 99.20/13.39 ((
% 99.20/13.39 (brelnall2) =>
% 99.20/13.39 ((
% 99.20/13.39 (ex1E2) =>
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% 99.20/13.39 (funcGraphProp1) =>
% 99.20/13.39 ((
% 99.20/13.39 (funcGraphProp3) =>
% 99.20/13.39 ((
% 99.20/13.39 (funcGraphProp2) =>
% 99.20/13.39 ((
% 99.20/13.39 (funcextLem) =>
% 99.20/13.39 ((
% 99.20/13.39 (funcGraphProp4) =>
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% 99.20/13.39 ((
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% 99.20/13.39 ((
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% 99.20/13.39 ((
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% 99.20/13.39 ((
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% 99.20/13.39 ((
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% 99.20/13.39 ((
% 99.20/13.39 (contrasubsetT2) =>
% 99.20/13.39 ((
% 99.20/13.39 (contrasubsetT3) =>
% 99.20/13.39 ((
% 99.20/13.39 (doubleComplementI1) =>
% 99.20/13.39 ((
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% 99.20/13.39 ((
% 99.20/13.39 (doubleComplementSub2) =>
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% 99.20/13.39 ((
% 99.20/13.39 (complementTnotintersectT) =>
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% 99.20/13.39 (complementImpComplementIntersect) =>
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% 99.20/13.39 (complementSubsetComplementIntersect) =>
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% 99.20/13.39 (contraSubsetComplement) =>
% 99.20/13.39 ((
% 99.20/13.39 (complementTcontraSubset) =>
% 99.20/13.39 ((
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% 99.20/13.39 ((
% 99.20/13.39 (binunionTIRcontra) =>
% 99.20/13.39 ((
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% 99.20/13.39 ((
% 99.20/13.39 (inIntersectImpInUnion2) =>
% 99.20/13.39 ((
% 99.20/13.39 (inIntersectImpInIntersectUnions) =>
% 99.20/13.39 ((
% 99.20/13.39 (intersectInPowersetIntersectUnions) =>
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% 99.20/13.39 (inComplementUnionImpNotIn1) =>
% 99.20/13.39 ((
% 99.20/13.39 (inComplementUnionImpInComplement1) =>
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% 99.20/13.39 ((
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% 99.20/13.39 ((
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% 99.20/13.39 ((
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% 99.20/13.39 (demorgan1) =>
% 99.20/13.39 ((
% 99.20/13.39 (demorgan2a) =>
% 99.20/13.39 ((
% 99.20/13.39 (demorgan2b2) =>
% 99.20/13.39 ((
% 99.20/13.39 (demorgan2b) =>
% 99.20/13.39 ((
% 99.20/13.39 (demorgan2) =>
% 99.20/13.39 ((
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% 99.20/13.39 ((
% 99.20/13.39 (woz13rule1) =>
% 99.20/13.39 ((
% 99.20/13.39 (woz13rule2) =>
% 99.20/13.39 ((
% 99.20/13.39 (woz13rule3) =>
% 99.20/13.39 ((
% 99.20/13.39 (woz13rule4) =>
% 99.20/13.39 ((
% 99.20/13.39 (woz1_1) =>
% 99.20/13.39 ((
% 99.20/13.39 (woz1_2) =>
% 99.20/13.39 ((
% 99.20/13.39 (woz1_3) =>
% 99.20/13.39 ((
% 99.20/13.39 (woz1_4) =>
% 99.20/13.39 ((
% 99.20/13.39 (woz1_5) =>
% 99.20/13.39 ((
% 99.20/13.39 (breln1all2) =>
% 99.20/13.39 ((
% 99.20/13.39 (breln1SetBreln1) =>
% 99.20/13.39 ((
% 99.20/13.39 (choice2fnsingleton) =>
% 99.20/13.39 ((
% 99.20/13.39 (setOfPairsIsBReln1) =>
% 99.20/13.39 ((
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% 99.20/13.39 ((
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% 99.20/13.39 ((
% 99.20/13.39 (eqbreln1) =>
% 99.20/13.39 ((
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% 99.20/13.39 ((
% 99.20/13.39 (breln1invI) =>
% 99.20/13.39 ((
% 99.20/13.39 (breln1invE) =>
% 99.20/13.39 ((
% 99.20/13.39 (breln1compprop) =>
% 99.20/13.39 ((
% 99.20/13.39 (breln1compI) =>
% 99.20/13.39 ((
% 99.20/13.39 (breln1compE) =>
% 99.20/13.39 ((
% 99.20/13.39 (breln1compEex) =>
% 99.20/13.39 ((
% 99.20/13.39 (breln1unionprop) =>
% 99.20/13.39 ((
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% 99.20/13.39 ((
% 99.20/13.39 (breln1unionIR) =>
% 99.20/13.39 ((
% 99.20/13.39 (breln1unionI) =>
% 99.20/13.39 ((
% 99.20/13.39 (breln1unionE) =>
% 99.20/13.39 ((
% 99.20/13.39 (breln1unionEcases) =>
% 99.20/13.39 ((
% 99.20/13.39 (breln1unionCommutes) =>
% 99.20/13.39 ((
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% 99.20/13.39 ((
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% 99.20/13.39 ((
% 99.20/13.39 (image1Ex1) =>
% 99.20/13.39 ((
% 99.20/13.39 (image1Equiv) =>
% 99.20/13.39 ((
% 99.20/13.39 (image1E) =>
% 99.20/13.39 ((
% 99.20/13.39 (image1I) =>
% 99.20/13.39 ((
% 99.20/13.39 (injFuncInInjFuncSet) =>
% 99.20/13.39 ((
% 99.20/13.39 (injFuncSetFuncIn) =>
% 99.20/13.39 ((
% 99.20/13.39 (injFuncSetFuncInj) =>
% 99.20/13.39 ((
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% 99.20/13.39 (
% 99.20/13.39 (
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% 99.20/13.39 (
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% 99.20/13.39 (
% 99.20/13.39 (
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% 99.20/13.39 (
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% 99.20/13.39 surjFuncSet)))))))) @
% 99.20/13.39 (
% 99.20/13.39 (
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% 99.20/13.39 (
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% 99.20/13.39 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.20/13.39 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl528])).
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% 99.20/13.39 (((exuE3u) =>
% 99.20/13.39 (((exu__Cong) =>
% 99.20/13.39 (((setadjoin__Cong) =>
% 99.20/13.39 (((powerset__Cong) =>
% 99.20/13.39 (((setunion__Cong) =>
% 99.20/13.39 (((exuEu) =>
% 99.20/13.39 (((descr__Cong) =>
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% 99.20/13.39 (setadjoinSub2) =>
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% 99.20/13.39 ((
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% 99.20/13.39 ((
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% 99.20/13.39 ((
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% 99.20/13.39 ((
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% 99.20/13.39 ((
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% 99.20/13.39 ((
% 99.20/13.39 (binunionRsub) =>
% 99.20/13.39 ((
% 99.20/13.39 (binintersectI) =>
% 99.20/13.39 ((
% 99.20/13.39 (binintersectSubset5) =>
% 99.20/13.39 ((
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% 99.20/13.39 ((
% 99.20/13.39 (binintersectLsub) =>
% 99.20/13.39 ((
% 99.20/13.39 (binintersectSubset2) =>
% 99.20/13.39 ((
% 99.20/13.39 (binintersectSubset3) =>
% 99.20/13.39 ((
% 99.20/13.39 (binintersectER) =>
% 99.20/13.39 ((
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% 99.20/13.39 ((
% 99.20/13.39 (binintersectRsub) =>
% 99.20/13.39 ((
% 99.20/13.39 (binintersectSubset4) =>
% 99.20/13.39 ((
% 99.20/13.39 (binintersectSubset1) =>
% 99.20/13.39 ((
% 99.20/13.39 (bs114d) =>
% 99.20/13.39 ((
% 99.20/13.39 (setminusI) =>
% 99.20/13.39 ((
% 99.20/13.39 (setminusEL) =>
% 99.20/13.39 ((
% 99.20/13.39 (setminusER) =>
% 99.20/13.39 ((
% 99.20/13.39 (setminusSubset2) =>
% 99.20/13.39 ((
% 99.20/13.39 (setminusERneg) =>
% 99.20/13.39 ((
% 99.20/13.39 (setminusELneg) =>
% 99.20/13.39 ((
% 99.20/13.39 (setminusILneg) =>
% 99.20/13.39 ((
% 99.20/13.39 (setminusIRneg) =>
% 99.20/13.39 ((
% 99.20/13.39 (setminusLsub) =>
% 99.20/13.39 ((
% 99.20/13.39 (setminusSubset1) =>
% 99.20/13.39 ((
% 99.20/13.39 (symdiffE) =>
% 99.20/13.39 ((
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% 99.20/13.39 ((
% 99.20/13.39 (symdiffI2) =>
% 99.20/13.39 ((
% 99.20/13.39 (symdiffIneg1) =>
% 99.20/13.39 ((
% 99.20/13.39 (symdiffIneg2) =>
% 99.20/13.39 ((
% 99.20/13.39 (secondinupair) =>
% 99.20/13.39 ((
% 99.20/13.39 (setukpairIL) =>
% 99.20/13.39 ((
% 99.20/13.39 (setukpairIR) =>
% 99.20/13.39 ((
% 99.20/13.39 (kpairiskpair) =>
% 99.20/13.39 ((
% 99.20/13.39 (kpairp) =>
% 99.20/13.39 ((
% 99.20/13.39 (singletonsubset) =>
% 99.20/13.39 ((
% 99.20/13.39 (singletoninpowerset) =>
% 99.20/13.39 ((
% 99.20/13.39 (singletoninpowunion) =>
% 99.20/13.39 ((
% 99.20/13.39 (upairset2E) =>
% 99.20/13.39 ((
% 99.20/13.39 (upairsubunion) =>
% 99.20/13.39 ((
% 99.20/13.39 (upairinpowunion) =>
% 99.20/13.39 ((
% 99.20/13.39 (ubforcartprodlem1) =>
% 99.20/13.39 ((
% 99.20/13.39 (ubforcartprodlem2) =>
% 99.20/13.39 ((
% 99.20/13.39 (ubforcartprodlem3) =>
% 99.20/13.39 ((
% 99.20/13.39 (cartprodpairin) =>
% 99.20/13.39 ((
% 99.20/13.39 (cartprodmempair1) =>
% 99.20/13.39 ((
% 99.20/13.39 (cartprodmempair) =>
% 99.20/13.39 ((
% 99.20/13.39 (setunionE2) =>
% 99.20/13.39 ((
% 99.20/13.39 (setunionsingleton1) =>
% 99.20/13.39 ((
% 99.20/13.39 (setunionsingleton2) =>
% 99.20/13.39 ((
% 99.20/13.39 (setunionsingleton) =>
% 99.20/13.39 ((
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% 99.20/13.39 ((
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% 99.20/13.39 ((
% 99.20/13.39 (ex1I) =>
% 99.20/13.39 ((
% 99.20/13.39 (ex1I2) =>
% 99.20/13.39 ((
% 99.20/13.39 (singletonsuniq) =>
% 99.20/13.39 ((
% 99.20/13.39 (setukpairinjL1) =>
% 99.20/13.39 ((
% 99.20/13.39 (kfstsingleton) =>
% 99.20/13.39 ((
% 99.20/13.39 (theprop) =>
% 99.20/13.39 ((
% 99.20/13.39 (kfstpairEq) =>
% 99.20/13.39 ((
% 99.20/13.39 (cartprodfstin) =>
% 99.20/13.39 ((
% 99.20/13.39 (setukpairinjL2) =>
% 99.20/13.39 ((
% 99.20/13.39 (setukpairinjL) =>
% 99.20/13.39 ((
% 99.20/13.39 (setukpairinjR11) =>
% 99.20/13.39 ((
% 99.20/13.39 (setukpairinjR12) =>
% 99.20/13.39 ((
% 99.20/13.39 (setukpairinjR1) =>
% 99.20/13.39 ((
% 99.20/13.39 (upairequniteq) =>
% 99.20/13.39 ((
% 99.20/13.39 (setukpairinjR2) =>
% 99.20/13.39 ((
% 99.20/13.39 (setukpairinjR) =>
% 99.20/13.39 ((
% 99.20/13.39 (ksndsingleton) =>
% 99.20/13.39 ((
% 99.20/13.39 (ksndpairEq) =>
% 99.20/13.39 ((
% 99.20/13.39 (kpairsurjEq) =>
% 99.20/13.39 ((
% 99.20/13.39 (cartprodsndin) =>
% 99.20/13.39 ((
% 99.20/13.39 (cartprodpairmemEL) =>
% 99.20/13.39 ((
% 99.20/13.39 (cartprodpairmemER) =>
% 99.20/13.39 ((
% 99.20/13.39 (cartprodmempaircEq) =>
% 99.20/13.39 ((
% 99.20/13.39 (cartprodfstpairEq) =>
% 99.20/13.39 ((
% 99.20/13.39 (cartprodsndpairEq) =>
% 99.20/13.39 ((
% 99.20/13.39 (cartprodpairsurjEq) =>
% 99.20/13.39 ((
% 99.20/13.39 (dpsetconstrI) =>
% 99.20/13.39 ((
% 99.20/13.39 (dpsetconstrSub) =>
% 99.20/13.39 ((
% 99.20/13.39 (setOfPairsIsBReln) =>
% 99.20/13.39 ((
% 99.20/13.39 (dpsetconstrERa) =>
% 99.20/13.39 ((
% 99.20/13.39 (dpsetconstrEL1) =>
% 99.20/13.39 ((
% 99.20/13.39 (dpsetconstrEL2) =>
% 99.20/13.39 ((
% 99.20/13.39 (dpsetconstrER) =>
% 99.20/13.39 ((
% 99.20/13.39 (funcImageSingleton) =>
% 99.20/13.39 ((
% 99.20/13.39 (apProp) =>
% 99.20/13.39 ((
% 99.20/13.39 (app) =>
% 99.20/13.39 ((
% 99.20/13.39 (infuncsetfunc) =>
% 99.20/13.39 ((
% 99.20/13.39 (ap2p) =>
% 99.20/13.39 ((
% 99.20/13.39 (funcinfuncset) =>
% 99.20/13.39 ((
% 99.20/13.39 (lamProp) =>
% 99.20/13.39 ((
% 99.20/13.39 (lamp) =>
% 99.20/13.39 ((
% 99.20/13.39 (lam2p) =>
% 99.20/13.39 ((
% 99.20/13.39 (brelnall1) =>
% 99.20/13.39 ((
% 99.20/13.39 (brelnall2) =>
% 99.20/13.39 ((
% 99.20/13.39 (ex1E2) =>
% 99.20/13.39 ((
% 99.20/13.39 (funcGraphProp1) =>
% 99.20/13.39 ((
% 99.20/13.39 (funcGraphProp3) =>
% 99.20/13.39 ((
% 99.20/13.39 (funcGraphProp2) =>
% 99.20/13.39 ((
% 99.20/13.39 (funcextLem) =>
% 99.20/13.39 ((
% 99.20/13.39 (funcGraphProp4) =>
% 99.20/13.39 ((
% 99.20/13.39 (subbreln) =>
% 99.20/13.39 ((
% 99.20/13.39 (eqbreln) =>
% 99.20/13.39 ((
% 99.20/13.39 (funcext) =>
% 99.20/13.39 ((
% 99.20/13.39 (funcext2) =>
% 99.20/13.39 ((
% 99.20/13.39 (ap2apEq1) =>
% 99.20/13.39 ((
% 99.20/13.39 (ap2apEq2) =>
% 99.20/13.39 ((
% 99.20/13.39 (beta1) =>
% 99.20/13.39 ((
% 99.20/13.39 (eta1) =>
% 99.20/13.39 ((
% 99.20/13.39 (lam2lamEq) =>
% 99.20/13.39 ((
% 99.20/13.39 (beta2) =>
% 99.20/13.39 ((
% 99.20/13.39 (eta2) =>
% 99.20/13.39 ((
% 99.20/13.39 (iffalseProp1) =>
% 99.20/13.39 ((
% 99.20/13.39 (iffalseProp2) =>
% 99.20/13.39 ((
% 99.20/13.39 (iftrueProp1) =>
% 99.20/13.39 ((
% 99.20/13.39 (iftrueProp2) =>
% 99.20/13.39 ((
% 99.20/13.39 (ifSingleton) =>
% 99.20/13.39 ((
% 99.20/13.39 (ifp) =>
% 99.20/13.39 ((
% 99.20/13.39 (theeq) =>
% 99.20/13.39 ((
% 99.20/13.39 (iftrue) =>
% 99.20/13.39 ((
% 99.20/13.39 (iffalse) =>
% 99.20/13.39 ((
% 99.20/13.39 (iftrueorfalse) =>
% 99.20/13.39 ((
% 99.20/13.39 (binintersectT_lem) =>
% 99.20/13.39 ((
% 99.20/13.39 (binunionT_lem) =>
% 99.20/13.39 ((
% 99.20/13.39 (powersetT_lem) =>
% 99.20/13.39 ((
% 99.20/13.39 (setminusT_lem) =>
% 99.20/13.39 ((
% 99.20/13.39 (complementT_lem) =>
% 99.20/13.39 ((
% 99.20/13.39 (setextT) =>
% 99.20/13.39 ((
% 99.20/13.39 (subsetTI) =>
% 99.20/13.39 ((
% 99.20/13.39 (powersetTI1) =>
% 99.20/13.39 ((
% 99.20/13.39 (powersetTE1) =>
% 99.20/13.39 ((
% 99.20/13.39 (complementTI1) =>
% 99.20/13.39 ((
% 99.20/13.39 (complementTE1) =>
% 99.20/13.39 ((
% 99.20/13.39 (binintersectTELcontra) =>
% 99.20/13.39 ((
% 99.20/13.39 (binintersectTERcontra) =>
% 99.20/13.39 ((
% 99.20/13.39 (contrasubsetT) =>
% 99.20/13.39 ((
% 99.20/13.39 (contrasubsetT1) =>
% 99.20/13.39 ((
% 99.20/13.39 (contrasubsetT2) =>
% 99.20/13.39 ((
% 99.20/13.39 (contrasubsetT3) =>
% 99.20/13.39 ((
% 99.20/13.39 (doubleComplementI1) =>
% 99.20/13.39 ((
% 99.20/13.39 (doubleComplementE1) =>
% 99.20/13.39 ((
% 99.20/13.39 (doubleComplementSub1) =>
% 99.20/13.39 ((
% 99.20/13.39 (doubleComplementSub2) =>
% 99.20/13.39 ((
% 99.20/13.39 (doubleComplementEq) =>
% 99.20/13.39 ((
% 99.20/13.39 (complementTnotintersectT) =>
% 99.20/13.39 ((
% 99.20/13.39 (complementImpComplementIntersect) =>
% 99.20/13.39 ((
% 99.20/13.39 (complementSubsetComplementIntersect) =>
% 99.20/13.39 ((
% 99.20/13.39 (complementInPowersetComplementIntersect) =>
% 99.20/13.39 ((
% 99.20/13.39 (contraSubsetComplement) =>
% 99.20/13.39 ((
% 99.20/13.39 (complementTcontraSubset) =>
% 99.20/13.39 ((
% 99.20/13.39 (binunionTILcontra) =>
% 99.20/13.39 ((
% 99.20/13.39 (binunionTIRcontra) =>
% 99.20/13.39 ((
% 99.20/13.39 (inIntersectImpInUnion) =>
% 99.20/13.39 ((
% 99.20/13.39 (inIntersectImpInUnion2) =>
% 99.20/13.39 ((
% 99.20/13.39 (inIntersectImpInIntersectUnions) =>
% 99.20/13.39 ((
% 99.20/13.39 (intersectInPowersetIntersectUnions) =>
% 99.20/13.39 ((
% 99.20/13.39 (inComplementUnionImpNotIn1) =>
% 99.20/13.39 ((
% 99.20/13.39 (inComplementUnionImpInComplement1) =>
% 99.20/13.39 ((
% 99.20/13.39 (binunionTE) =>
% 99.20/13.39 ((
% 99.20/13.39 (binunionTEcontra) =>
% 99.20/13.39 ((
% 99.20/13.39 (demorgan2a1) =>
% 99.20/13.39 ((
% 99.20/13.39 (complementUnionInPowersetComplement) =>
% 99.20/13.39 ((
% 99.20/13.39 (demorgan2a2) =>
% 99.20/13.39 ((
% 99.20/13.39 (demorgan1a) =>
% 99.20/13.39 ((
% 99.20/13.39 (demorgan1b) =>
% 99.20/13.39 ((
% 99.20/13.39 (demorgan1) =>
% 99.20/13.39 ((
% 99.20/13.39 (demorgan2a) =>
% 99.20/13.39 ((
% 99.20/13.39 (demorgan2b2) =>
% 99.20/13.39 ((
% 99.20/13.39 (demorgan2b) =>
% 99.20/13.39 ((
% 99.20/13.39 (demorgan2) =>
% 99.20/13.39 ((
% 99.20/13.39 (woz13rule0) =>
% 99.20/13.39 ((
% 99.20/13.39 (woz13rule1) =>
% 99.20/13.39 ((
% 99.20/13.39 (woz13rule2) =>
% 99.20/13.39 ((
% 99.20/13.39 (woz13rule3) =>
% 99.20/13.39 ((
% 99.20/13.39 (woz13rule4) =>
% 99.20/13.39 ((
% 99.20/13.39 (woz1_1) =>
% 99.20/13.39 ((
% 99.20/13.39 (woz1_2) =>
% 99.20/13.39 ((
% 99.20/13.39 (woz1_3) =>
% 99.20/13.39 ((
% 99.20/13.39 (woz1_4) =>
% 99.20/13.39 ((
% 99.20/13.39 (woz1_5) =>
% 99.20/13.39 ((
% 99.20/13.39 (breln1all2) =>
% 99.20/13.39 ((
% 99.20/13.39 (breln1SetBreln1) =>
% 99.20/13.39 ((
% 99.20/13.39 (choice2fnsingleton) =>
% 99.20/13.39 ((
% 99.20/13.39 (setOfPairsIsBReln1) =>
% 99.20/13.39 ((
% 99.20/13.39 (breln1all1) =>
% 99.20/13.39 ((
% 99.20/13.39 (subbreln1) =>
% 99.20/13.39 ((
% 99.20/13.39 (eqbreln1) =>
% 99.20/13.39 ((
% 99.20/13.39 (breln1invprop) =>
% 99.20/13.39 ((
% 99.20/13.39 (breln1invI) =>
% 99.20/13.39 ((
% 99.20/13.39 (breln1invE) =>
% 99.20/13.39 ((
% 99.20/13.39 (breln1compprop) =>
% 99.20/13.39 ((
% 99.20/13.39 (breln1compI) =>
% 99.20/13.39 ((
% 99.20/13.39 (breln1compE) =>
% 99.20/13.39 ((
% 99.20/13.39 (breln1compEex) =>
% 99.20/13.39 ((
% 99.20/13.39 (breln1unionprop) =>
% 99.20/13.39 ((
% 99.20/13.39 (breln1unionIL) =>
% 99.20/13.39 ((
% 99.20/13.39 (breln1unionIR) =>
% 99.20/13.39 ((
% 99.20/13.39 (breln1unionI) =>
% 99.20/13.39 ((
% 99.20/13.39 (breln1unionE) =>
% 99.20/13.39 ((
% 99.20/13.39 (breln1unionEcases) =>
% 99.20/13.39 ((
% 99.20/13.39 (breln1unionCommutes) =>
% 99.20/13.39 ((
% 99.20/13.39 (woz2Ex) =>
% 99.20/13.39 ((
% 99.20/13.39 (woz2W) =>
% 99.20/13.39 ((
% 99.20/13.39 (woz2A) =>
% 99.20/13.39 ((
% 99.20/13.39 (woz2B) =>
% 99.20/13.39 ((
% 99.20/13.39 (image1Ex) =>
% 99.20/13.39 ((
% 99.20/13.39 (image1Ex1) =>
% 99.20/13.39 ((
% 99.20/13.39 (image1Equiv) =>
% 99.20/13.39 ((
% 99.20/13.39 (image1E) =>
% 99.20/13.39 ((
% 99.20/13.39 (image1I) =>
% 99.20/13.39 ((
% 99.20/13.39 (injFuncInInjFuncSet) =>
% 99.20/13.39 ((
% 99.20/13.39 (injFuncSetFuncIn) =>
% 99.20/13.39 ((
% 99.20/13.39 (injFuncSetFuncInj) =>
% 99.20/13.39 ((
% 99.20/13.39 (!!) @ (
% 99.20/13.39 (('#B') @ (
% 99.20/13.39 !!) @
% 99.20/13.39 (
% 99.20/13.39 (
% 99.20/13.39 ('#B') @ (
% 99.20/13.39 (
% 99.20/13.39 ('#B') @ (
% 99.20/13.39 !!))) @
% 99.20/13.39 (
% 99.20/13.39 (
% 99.20/13.39 ('#S') @ (
% 99.20/13.39 (
% 99.20/13.39 ('#B') @ (
% 99.20/13.39 '#S') @
% 99.20/13.39 (
% 99.20/13.39 (
% 99.20/13.39 ('#B') @ (
% 99.20/13.39 (
% 99.20/13.39 ('#B') @ (
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% 99.20/13.39 (
% 99.20/13.39 (
% 99.20/13.39 ('#B') @ (
% 99.20/13.39 (
% 99.20/13.39 ('#B') @ (
% 99.20/13.39 (
% 99.20/13.39 ('#B') @ (
% 99.20/13.39 =>))))) @
% 99.20/13.39 (
% 99.20/13.39 (
% 99.20/13.39 ('#B') @ (
% 99.20/13.39 (
% 99.20/13.39 ('#B') @ (
% 99.20/13.39 (
% 99.20/13.39 ('#C') @ in)))) @
% 99.20/13.39 surjFuncSet)))))))) @
% 99.20/13.39 (
% 99.20/13.39 (
% 99.20/13.39 ('#B') @ (
% 99.20/13.39 (
% 99.20/13.39 ('#B') @ (
% 99.20/13.39 (
% 99.20/13.39 ('#C') @ in)))) @
% 99.20/13.39 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.20/13.39 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl537])).
% 99.20/13.39 thf(zip_derived_cl553, plain,
% 99.20/13.39 (~ (((quantDeMorgan3) =>
% 99.20/13.39 (((quantDeMorgan4) =>
% 99.20/13.39 (((prop2setI) =>
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% 99.20/13.39 (((notdallE) =>
% 99.20/13.39 (((exuI1) =>
% 99.20/13.39 (((exuI3) =>
% 99.20/13.39 (((exuI2) =>
% 99.20/13.39 (((inCongP) =>
% 99.20/13.39 (((in__Cong) =>
% 99.20/13.39 (((exuE3u) =>
% 99.20/13.39 (((exu__Cong) =>
% 99.20/13.39 (((setadjoin__Cong) =>
% 99.20/13.39 (((powerset__Cong) =>
% 99.20/13.39 (((setunion__Cong) =>
% 99.20/13.39 (((exuEu) =>
% 99.20/13.39 (((descr__Cong) =>
% 99.20/13.39 (((dsetconstr__Cong) =>
% 99.20/13.39 (((subsetI1) =>
% 99.20/13.39 (((eqimpsubset2) =>
% 99.20/13.39 (((eqimpsubset1) =>
% 99.20/13.39 (((subsetI2) =>
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% 99.20/13.39 (((subsetE) =>
% 99.20/13.39 (((subsetE2) =>
% 99.20/13.39 (((notsubsetI) =>
% 99.20/13.39 (((notequalI1) =>
% 99.20/13.39 (((notequalI2) =>
% 99.20/13.39 (((subsetRefl) =>
% 99.20/13.39 ((
% 99.20/13.39 (subsetTrans) =>
% 99.20/13.39 ((
% 99.20/13.39 (setadjoinSub) =>
% 99.20/13.39 ((
% 99.20/13.39 (setadjoinSub2) =>
% 99.20/13.39 ((
% 99.20/13.39 (subset2powerset) =>
% 99.20/13.39 ((
% 99.20/13.39 (setextsub) =>
% 99.20/13.39 ((
% 99.20/13.39 (subsetemptysetimpeq) =>
% 99.20/13.39 ((
% 99.20/13.39 (powersetI1) =>
% 99.20/13.39 ((
% 99.20/13.39 (powersetE1) =>
% 99.20/13.39 ((
% 99.20/13.39 (inPowerset) =>
% 99.20/13.39 ((
% 99.20/13.39 (powersetsubset) =>
% 99.20/13.39 ((
% 99.20/13.39 (sepInPowerset) =>
% 99.20/13.39 ((
% 99.20/13.39 (sepSubset) =>
% 99.20/13.39 ((
% 99.20/13.39 (binunionIL) =>
% 99.20/13.39 ((
% 99.20/13.39 (upairset2IR) =>
% 99.20/13.39 ((
% 99.20/13.39 (binunionIR) =>
% 99.20/13.39 ((
% 99.20/13.39 (binunionEcases) =>
% 99.20/13.39 ((
% 99.20/13.39 (binunionE) =>
% 99.20/13.39 ((
% 99.20/13.39 (binunionLsub) =>
% 99.20/13.39 ((
% 99.20/13.39 (binunionRsub) =>
% 99.20/13.39 ((
% 99.20/13.39 (binintersectI) =>
% 99.20/13.39 ((
% 99.20/13.39 (binintersectSubset5) =>
% 99.20/13.39 ((
% 99.20/13.39 (binintersectEL) =>
% 99.20/13.39 ((
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% 99.20/13.39 (binintersectSubset2) =>
% 99.20/13.39 ((
% 99.20/13.39 (binintersectSubset3) =>
% 99.20/13.39 ((
% 99.20/13.39 (binintersectER) =>
% 99.20/13.39 ((
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% 99.20/13.39 ((
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% 99.20/13.39 ((
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% 99.20/13.39 ((
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% 99.20/13.39 ((
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% 99.20/13.39 ((
% 99.20/13.39 (setminusEL) =>
% 99.20/13.39 ((
% 99.20/13.39 (setminusER) =>
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% 99.20/13.39 (setminusSubset2) =>
% 99.20/13.39 ((
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% 99.20/13.39 (setminusELneg) =>
% 99.20/13.39 ((
% 99.20/13.39 (setminusILneg) =>
% 99.20/13.39 ((
% 99.20/13.39 (setminusIRneg) =>
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% 99.20/13.39 ((
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% 99.20/13.39 ((
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% 99.20/13.39 ((
% 99.20/13.39 (symdiffI2) =>
% 99.20/13.39 ((
% 99.20/13.39 (symdiffIneg1) =>
% 99.20/13.39 ((
% 99.20/13.39 (symdiffIneg2) =>
% 99.20/13.39 ((
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% 99.20/13.39 ((
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% 99.20/13.39 ((
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% 99.20/13.39 ((
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% 99.20/13.39 ((
% 99.20/13.39 (kpairp) =>
% 99.20/13.39 ((
% 99.20/13.39 (singletonsubset) =>
% 99.20/13.39 ((
% 99.20/13.39 (singletoninpowerset) =>
% 99.20/13.39 ((
% 99.20/13.39 (singletoninpowunion) =>
% 99.20/13.39 ((
% 99.20/13.39 (upairset2E) =>
% 99.20/13.39 ((
% 99.20/13.39 (upairsubunion) =>
% 99.20/13.39 ((
% 99.20/13.39 (upairinpowunion) =>
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% 99.20/13.39 ((
% 99.20/13.39 (ubforcartprodlem2) =>
% 99.20/13.39 ((
% 99.20/13.39 (ubforcartprodlem3) =>
% 99.20/13.39 ((
% 99.20/13.39 (cartprodpairin) =>
% 99.20/13.39 ((
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% 99.20/13.39 ((
% 99.20/13.39 (cartprodmempair) =>
% 99.20/13.39 ((
% 99.20/13.39 (setunionE2) =>
% 99.20/13.39 ((
% 99.20/13.39 (setunionsingleton1) =>
% 99.20/13.39 ((
% 99.20/13.39 (setunionsingleton2) =>
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% 99.20/13.39 ((
% 99.20/13.39 (ex1I) =>
% 99.20/13.39 ((
% 99.20/13.39 (ex1I2) =>
% 99.20/13.39 ((
% 99.20/13.39 (singletonsuniq) =>
% 99.20/13.39 ((
% 99.20/13.39 (setukpairinjL1) =>
% 99.20/13.39 ((
% 99.20/13.39 (kfstsingleton) =>
% 99.20/13.39 ((
% 99.20/13.39 (theprop) =>
% 99.20/13.39 ((
% 99.20/13.39 (kfstpairEq) =>
% 99.20/13.39 ((
% 99.20/13.39 (cartprodfstin) =>
% 99.20/13.39 ((
% 99.20/13.39 (setukpairinjL2) =>
% 99.20/13.39 ((
% 99.20/13.39 (setukpairinjL) =>
% 99.20/13.39 ((
% 99.20/13.39 (setukpairinjR11) =>
% 99.20/13.39 ((
% 99.20/13.39 (setukpairinjR12) =>
% 99.20/13.39 ((
% 99.20/13.39 (setukpairinjR1) =>
% 99.20/13.39 ((
% 99.20/13.39 (upairequniteq) =>
% 99.20/13.39 ((
% 99.20/13.39 (setukpairinjR2) =>
% 99.20/13.39 ((
% 99.20/13.39 (setukpairinjR) =>
% 99.20/13.39 ((
% 99.20/13.39 (ksndsingleton) =>
% 99.20/13.39 ((
% 99.20/13.39 (ksndpairEq) =>
% 99.20/13.39 ((
% 99.20/13.39 (kpairsurjEq) =>
% 99.20/13.39 ((
% 99.20/13.39 (cartprodsndin) =>
% 99.20/13.39 ((
% 99.20/13.39 (cartprodpairmemEL) =>
% 99.20/13.39 ((
% 99.20/13.39 (cartprodpairmemER) =>
% 99.20/13.39 ((
% 99.20/13.39 (cartprodmempaircEq) =>
% 99.20/13.39 ((
% 99.20/13.39 (cartprodfstpairEq) =>
% 99.20/13.39 ((
% 99.20/13.39 (cartprodsndpairEq) =>
% 99.20/13.39 ((
% 99.20/13.39 (cartprodpairsurjEq) =>
% 99.20/13.39 ((
% 99.20/13.39 (dpsetconstrI) =>
% 99.20/13.39 ((
% 99.20/13.39 (dpsetconstrSub) =>
% 99.20/13.39 ((
% 99.20/13.39 (setOfPairsIsBReln) =>
% 99.20/13.39 ((
% 99.20/13.39 (dpsetconstrERa) =>
% 99.20/13.39 ((
% 99.20/13.39 (dpsetconstrEL1) =>
% 99.20/13.39 ((
% 99.20/13.39 (dpsetconstrEL2) =>
% 99.20/13.39 ((
% 99.20/13.39 (dpsetconstrER) =>
% 99.20/13.39 ((
% 99.20/13.39 (funcImageSingleton) =>
% 99.20/13.39 ((
% 99.20/13.39 (apProp) =>
% 99.20/13.39 ((
% 99.20/13.39 (app) =>
% 99.20/13.39 ((
% 99.20/13.39 (infuncsetfunc) =>
% 99.20/13.39 ((
% 99.20/13.39 (ap2p) =>
% 99.20/13.39 ((
% 99.20/13.39 (funcinfuncset) =>
% 99.20/13.39 ((
% 99.20/13.39 (lamProp) =>
% 99.20/13.39 ((
% 99.20/13.39 (lamp) =>
% 99.20/13.39 ((
% 99.20/13.39 (lam2p) =>
% 99.20/13.39 ((
% 99.20/13.39 (brelnall1) =>
% 99.20/13.39 ((
% 99.20/13.39 (brelnall2) =>
% 99.20/13.39 ((
% 99.20/13.39 (ex1E2) =>
% 99.20/13.39 ((
% 99.20/13.39 (funcGraphProp1) =>
% 99.20/13.39 ((
% 99.20/13.39 (funcGraphProp3) =>
% 99.20/13.39 ((
% 99.20/13.39 (funcGraphProp2) =>
% 99.20/13.39 ((
% 99.20/13.39 (funcextLem) =>
% 99.20/13.39 ((
% 99.20/13.39 (funcGraphProp4) =>
% 99.20/13.39 ((
% 99.20/13.39 (subbreln) =>
% 99.20/13.39 ((
% 99.20/13.39 (eqbreln) =>
% 99.20/13.39 ((
% 99.20/13.39 (funcext) =>
% 99.20/13.39 ((
% 99.20/13.39 (funcext2) =>
% 99.20/13.39 ((
% 99.20/13.39 (ap2apEq1) =>
% 99.20/13.39 ((
% 99.20/13.39 (ap2apEq2) =>
% 99.20/13.39 ((
% 99.20/13.39 (beta1) =>
% 99.20/13.39 ((
% 99.20/13.39 (eta1) =>
% 99.20/13.39 ((
% 99.20/13.39 (lam2lamEq) =>
% 99.20/13.39 ((
% 99.20/13.39 (beta2) =>
% 99.20/13.39 ((
% 99.20/13.39 (eta2) =>
% 99.20/13.39 ((
% 99.20/13.39 (iffalseProp1) =>
% 99.20/13.39 ((
% 99.20/13.39 (iffalseProp2) =>
% 99.20/13.39 ((
% 99.20/13.39 (iftrueProp1) =>
% 99.20/13.39 ((
% 99.20/13.39 (iftrueProp2) =>
% 99.20/13.39 ((
% 99.20/13.39 (ifSingleton) =>
% 99.20/13.39 ((
% 99.20/13.39 (ifp) =>
% 99.20/13.39 ((
% 99.20/13.39 (theeq) =>
% 99.20/13.39 ((
% 99.20/13.39 (iftrue) =>
% 99.20/13.39 ((
% 99.20/13.39 (iffalse) =>
% 99.20/13.39 ((
% 99.20/13.39 (iftrueorfalse) =>
% 99.20/13.39 ((
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% 99.20/13.39 ((
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% 99.20/13.39 (powersetT_lem) =>
% 99.20/13.39 ((
% 99.20/13.39 (setminusT_lem) =>
% 99.20/13.39 ((
% 99.20/13.39 (complementT_lem) =>
% 99.20/13.39 ((
% 99.20/13.39 (setextT) =>
% 99.20/13.39 ((
% 99.20/13.39 (subsetTI) =>
% 99.20/13.39 ((
% 99.20/13.39 (powersetTI1) =>
% 99.20/13.39 ((
% 99.20/13.39 (powersetTE1) =>
% 99.20/13.39 ((
% 99.20/13.39 (complementTI1) =>
% 99.20/13.39 ((
% 99.20/13.39 (complementTE1) =>
% 99.20/13.39 ((
% 99.20/13.39 (binintersectTELcontra) =>
% 99.20/13.39 ((
% 99.20/13.39 (binintersectTERcontra) =>
% 99.20/13.39 ((
% 99.20/13.39 (contrasubsetT) =>
% 99.20/13.39 ((
% 99.20/13.39 (contrasubsetT1) =>
% 99.20/13.39 ((
% 99.20/13.39 (contrasubsetT2) =>
% 99.20/13.39 ((
% 99.20/13.39 (contrasubsetT3) =>
% 99.20/13.39 ((
% 99.20/13.39 (doubleComplementI1) =>
% 99.20/13.39 ((
% 99.20/13.39 (doubleComplementE1) =>
% 99.20/13.39 ((
% 99.20/13.39 (doubleComplementSub1) =>
% 99.20/13.39 ((
% 99.20/13.39 (doubleComplementSub2) =>
% 99.20/13.39 ((
% 99.20/13.39 (doubleComplementEq) =>
% 99.20/13.39 ((
% 99.20/13.39 (complementTnotintersectT) =>
% 99.20/13.39 ((
% 99.20/13.39 (complementImpComplementIntersect) =>
% 99.20/13.39 ((
% 99.20/13.39 (complementSubsetComplementIntersect) =>
% 99.20/13.39 ((
% 99.20/13.39 (complementInPowersetComplementIntersect) =>
% 99.20/13.39 ((
% 99.20/13.39 (contraSubsetComplement) =>
% 99.20/13.39 ((
% 99.20/13.39 (complementTcontraSubset) =>
% 99.20/13.39 ((
% 99.20/13.39 (binunionTILcontra) =>
% 99.20/13.39 ((
% 99.20/13.39 (binunionTIRcontra) =>
% 99.20/13.39 ((
% 99.20/13.39 (inIntersectImpInUnion) =>
% 99.20/13.39 ((
% 99.20/13.39 (inIntersectImpInUnion2) =>
% 99.20/13.39 ((
% 99.20/13.39 (inIntersectImpInIntersectUnions) =>
% 99.20/13.39 ((
% 99.20/13.39 (intersectInPowersetIntersectUnions) =>
% 99.20/13.39 ((
% 99.20/13.39 (inComplementUnionImpNotIn1) =>
% 99.20/13.39 ((
% 99.20/13.39 (inComplementUnionImpInComplement1) =>
% 99.20/13.39 ((
% 99.20/13.39 (binunionTE) =>
% 99.20/13.39 ((
% 99.20/13.39 (binunionTEcontra) =>
% 99.20/13.39 ((
% 99.20/13.39 (demorgan2a1) =>
% 99.20/13.39 ((
% 99.20/13.39 (complementUnionInPowersetComplement) =>
% 99.20/13.39 ((
% 99.20/13.39 (demorgan2a2) =>
% 99.20/13.39 ((
% 99.20/13.39 (demorgan1a) =>
% 99.20/13.39 ((
% 99.20/13.39 (demorgan1b) =>
% 99.20/13.39 ((
% 99.20/13.39 (demorgan1) =>
% 99.20/13.39 ((
% 99.20/13.39 (demorgan2a) =>
% 99.20/13.39 ((
% 99.20/13.39 (demorgan2b2) =>
% 99.20/13.39 ((
% 99.20/13.39 (demorgan2b) =>
% 99.20/13.39 ((
% 99.20/13.39 (demorgan2) =>
% 99.20/13.39 ((
% 99.20/13.39 (woz13rule0) =>
% 99.20/13.39 ((
% 99.20/13.39 (woz13rule1) =>
% 99.20/13.39 ((
% 99.20/13.39 (woz13rule2) =>
% 99.20/13.39 ((
% 99.20/13.39 (woz13rule3) =>
% 99.20/13.39 ((
% 99.20/13.39 (woz13rule4) =>
% 99.20/13.39 ((
% 99.20/13.39 (woz1_1) =>
% 99.20/13.39 ((
% 99.20/13.39 (woz1_2) =>
% 99.20/13.39 ((
% 99.20/13.39 (woz1_3) =>
% 99.20/13.39 ((
% 99.20/13.39 (woz1_4) =>
% 99.20/13.39 ((
% 99.20/13.39 (woz1_5) =>
% 99.20/13.39 ((
% 99.20/13.39 (breln1all2) =>
% 99.20/13.39 ((
% 99.20/13.39 (breln1SetBreln1) =>
% 99.20/13.39 ((
% 99.20/13.39 (choice2fnsingleton) =>
% 99.20/13.39 ((
% 99.20/13.39 (setOfPairsIsBReln1) =>
% 99.20/13.39 ((
% 99.20/13.39 (breln1all1) =>
% 99.20/13.39 ((
% 99.20/13.39 (subbreln1) =>
% 99.20/13.39 ((
% 99.20/13.39 (eqbreln1) =>
% 99.20/13.39 ((
% 99.20/13.39 (breln1invprop) =>
% 99.20/13.39 ((
% 99.20/13.39 (breln1invI) =>
% 99.20/13.39 ((
% 99.20/13.39 (breln1invE) =>
% 99.20/13.39 ((
% 99.20/13.39 (breln1compprop) =>
% 99.20/13.39 ((
% 99.20/13.39 (breln1compI) =>
% 99.20/13.39 ((
% 99.20/13.39 (breln1compE) =>
% 99.20/13.39 ((
% 99.20/13.39 (breln1compEex) =>
% 99.20/13.39 ((
% 99.20/13.39 (breln1unionprop) =>
% 99.20/13.39 ((
% 99.20/13.39 (breln1unionIL) =>
% 99.20/13.39 ((
% 99.20/13.39 (breln1unionIR) =>
% 99.20/13.39 ((
% 99.20/13.39 (breln1unionI) =>
% 99.20/13.39 ((
% 99.20/13.39 (breln1unionE) =>
% 99.20/13.39 ((
% 99.20/13.39 (breln1unionEcases) =>
% 99.20/13.39 ((
% 99.20/13.39 (breln1unionCommutes) =>
% 99.20/13.39 ((
% 99.20/13.39 (woz2Ex) =>
% 99.20/13.39 ((
% 99.20/13.39 (woz2W) =>
% 99.20/13.39 ((
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% 99.20/13.39 ((
% 99.20/13.39 (woz2B) =>
% 99.20/13.39 ((
% 99.20/13.39 (image1Ex) =>
% 99.20/13.39 ((
% 99.20/13.39 (image1Ex1) =>
% 99.20/13.39 ((
% 99.20/13.39 (image1Equiv) =>
% 99.20/13.39 ((
% 99.20/13.39 (image1E) =>
% 99.20/13.39 ((
% 99.20/13.39 (image1I) =>
% 99.20/13.39 ((
% 99.20/13.39 (injFuncInInjFuncSet) =>
% 99.20/13.39 ((
% 99.20/13.39 (injFuncSetFuncIn) =>
% 99.20/13.39 ((
% 99.20/13.39 (injFuncSetFuncInj) =>
% 99.20/13.39 ((
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% 99.20/13.39 (('#B') @ (
% 99.20/13.39 !!) @
% 99.20/13.39 (
% 99.20/13.39 (
% 99.20/13.39 ('#B') @ (
% 99.20/13.39 (
% 99.20/13.39 ('#B') @ (
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% 99.20/13.39 (
% 99.20/13.39 (
% 99.20/13.39 ('#S') @ (
% 99.20/13.39 (
% 99.20/13.39 ('#B') @ (
% 99.20/13.39 '#S') @
% 99.20/13.39 (
% 99.20/13.39 (
% 99.20/13.39 ('#B') @ (
% 99.20/13.39 (
% 99.20/13.39 ('#B') @ (
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% 99.20/13.39 (
% 99.20/13.39 (
% 99.20/13.39 ('#B') @ (
% 99.20/13.39 (
% 99.20/13.39 ('#B') @ (
% 99.20/13.39 (
% 99.20/13.39 ('#B') @ (
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% 99.20/13.39 (
% 99.20/13.39 (
% 99.20/13.39 ('#B') @ (
% 99.20/13.39 (
% 99.20/13.39 ('#B') @ (
% 99.20/13.39 (
% 99.20/13.39 ('#C') @ in)))) @
% 99.20/13.39 surjFuncSet)))))))) @
% 99.20/13.39 (
% 99.20/13.39 (
% 99.20/13.39 ('#B') @ (
% 99.20/13.39 (
% 99.20/13.39 ('#B') @ (
% 99.20/13.39 (
% 99.20/13.39 ('#C') @ in)))) @
% 99.20/13.39 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.20/13.39 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl546])).
% 99.20/13.39 thf(zip_derived_cl561, plain,
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% 99.20/13.39 (((prop2setI) =>
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% 99.20/13.39 (((in__Cong) =>
% 99.20/13.39 (((exuE3u) =>
% 99.20/13.39 (((exu__Cong) =>
% 99.20/13.39 (((setadjoin__Cong) =>
% 99.20/13.39 (((powerset__Cong) =>
% 99.20/13.39 (((setunion__Cong) =>
% 99.20/13.39 (((exuEu) =>
% 99.20/13.39 (((descr__Cong) =>
% 99.20/13.39 (((dsetconstr__Cong) =>
% 99.20/13.39 (((subsetI1) =>
% 99.20/13.39 (((eqimpsubset2) =>
% 99.20/13.39 (((eqimpsubset1) =>
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% 99.20/13.39 (((subsetE) =>
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% 99.20/13.39 (((notequalI1) =>
% 99.20/13.39 (((notequalI2) =>
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% 99.20/13.39 ((
% 99.20/13.39 (setadjoinSub2) =>
% 99.20/13.39 ((
% 99.20/13.39 (subset2powerset) =>
% 99.20/13.39 ((
% 99.20/13.39 (setextsub) =>
% 99.20/13.39 ((
% 99.20/13.39 (subsetemptysetimpeq) =>
% 99.20/13.39 ((
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% 99.20/13.39 ((
% 99.20/13.39 (powersetE1) =>
% 99.20/13.39 ((
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% 99.20/13.39 ((
% 99.20/13.39 (powersetsubset) =>
% 99.20/13.39 ((
% 99.20/13.39 (sepInPowerset) =>
% 99.20/13.39 ((
% 99.20/13.39 (sepSubset) =>
% 99.20/13.39 ((
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% 99.20/13.39 ((
% 99.20/13.39 (upairset2IR) =>
% 99.20/13.39 ((
% 99.20/13.39 (binunionIR) =>
% 99.20/13.39 ((
% 99.20/13.39 (binunionEcases) =>
% 99.20/13.39 ((
% 99.20/13.39 (binunionE) =>
% 99.20/13.39 ((
% 99.20/13.39 (binunionLsub) =>
% 99.20/13.39 ((
% 99.20/13.39 (binunionRsub) =>
% 99.20/13.39 ((
% 99.20/13.39 (binintersectI) =>
% 99.20/13.39 ((
% 99.20/13.39 (binintersectSubset5) =>
% 99.20/13.39 ((
% 99.20/13.39 (binintersectEL) =>
% 99.20/13.39 ((
% 99.20/13.39 (binintersectLsub) =>
% 99.20/13.39 ((
% 99.20/13.39 (binintersectSubset2) =>
% 99.20/13.39 ((
% 99.20/13.39 (binintersectSubset3) =>
% 99.20/13.39 ((
% 99.20/13.39 (binintersectER) =>
% 99.20/13.39 ((
% 99.20/13.39 (disjointsetsI1) =>
% 99.20/13.39 ((
% 99.20/13.39 (binintersectRsub) =>
% 99.20/13.39 ((
% 99.20/13.39 (binintersectSubset4) =>
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% 99.20/13.39 (cartprodpairmemER) =>
% 99.20/13.39 ((
% 99.20/13.39 (cartprodmempaircEq) =>
% 99.20/13.39 ((
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% 99.20/13.39 (cartprodsndpairEq) =>
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% 99.20/13.39 (cartprodpairsurjEq) =>
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% 99.20/13.39 ((
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% 99.20/13.39 ((
% 99.20/13.39 (ap2p) =>
% 99.20/13.39 ((
% 99.20/13.39 (funcinfuncset) =>
% 99.20/13.39 ((
% 99.20/13.39 (lamProp) =>
% 99.20/13.39 ((
% 99.20/13.39 (lamp) =>
% 99.20/13.39 ((
% 99.20/13.39 (lam2p) =>
% 99.20/13.39 ((
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% 99.20/13.39 ((
% 99.20/13.39 (brelnall2) =>
% 99.20/13.39 ((
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% 99.20/13.39 ((
% 99.20/13.39 (funcGraphProp3) =>
% 99.20/13.39 ((
% 99.20/13.39 (funcGraphProp2) =>
% 99.20/13.39 ((
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% 99.20/13.39 ((
% 99.20/13.39 (funcGraphProp4) =>
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% 99.20/13.39 ((
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% 99.20/13.39 ((
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% 99.20/13.39 ((
% 99.20/13.39 (contrasubsetT2) =>
% 99.20/13.39 ((
% 99.20/13.39 (contrasubsetT3) =>
% 99.20/13.39 ((
% 99.20/13.39 (doubleComplementI1) =>
% 99.20/13.39 ((
% 99.20/13.39 (doubleComplementE1) =>
% 99.20/13.39 ((
% 99.20/13.39 (doubleComplementSub1) =>
% 99.20/13.39 ((
% 99.20/13.39 (doubleComplementSub2) =>
% 99.20/13.39 ((
% 99.20/13.39 (doubleComplementEq) =>
% 99.20/13.39 ((
% 99.20/13.39 (complementTnotintersectT) =>
% 99.20/13.39 ((
% 99.20/13.39 (complementImpComplementIntersect) =>
% 99.20/13.39 ((
% 99.20/13.39 (complementSubsetComplementIntersect) =>
% 99.20/13.39 ((
% 99.20/13.39 (complementInPowersetComplementIntersect) =>
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% 99.20/13.39 (contraSubsetComplement) =>
% 99.20/13.39 ((
% 99.20/13.39 (complementTcontraSubset) =>
% 99.20/13.39 ((
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% 99.20/13.39 ((
% 99.20/13.39 (binunionTIRcontra) =>
% 99.20/13.39 ((
% 99.20/13.39 (inIntersectImpInUnion) =>
% 99.20/13.39 ((
% 99.20/13.39 (inIntersectImpInUnion2) =>
% 99.20/13.39 ((
% 99.20/13.39 (inIntersectImpInIntersectUnions) =>
% 99.20/13.39 ((
% 99.20/13.39 (intersectInPowersetIntersectUnions) =>
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% 99.20/13.39 (inComplementUnionImpNotIn1) =>
% 99.20/13.39 ((
% 99.20/13.39 (inComplementUnionImpInComplement1) =>
% 99.20/13.39 ((
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% 99.20/13.39 ((
% 99.20/13.39 (binunionTEcontra) =>
% 99.20/13.39 ((
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% 99.20/13.39 ((
% 99.20/13.39 (complementUnionInPowersetComplement) =>
% 99.20/13.39 ((
% 99.20/13.39 (demorgan2a2) =>
% 99.20/13.39 ((
% 99.20/13.39 (demorgan1a) =>
% 99.20/13.39 ((
% 99.20/13.39 (demorgan1b) =>
% 99.20/13.39 ((
% 99.20/13.39 (demorgan1) =>
% 99.20/13.39 ((
% 99.20/13.39 (demorgan2a) =>
% 99.20/13.39 ((
% 99.20/13.39 (demorgan2b2) =>
% 99.20/13.39 ((
% 99.20/13.39 (demorgan2b) =>
% 99.20/13.39 ((
% 99.20/13.39 (demorgan2) =>
% 99.20/13.39 ((
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% 99.20/13.39 ((
% 99.20/13.39 (woz13rule1) =>
% 99.20/13.39 ((
% 99.20/13.39 (woz13rule2) =>
% 99.20/13.39 ((
% 99.20/13.39 (woz13rule3) =>
% 99.20/13.39 ((
% 99.20/13.39 (woz13rule4) =>
% 99.20/13.39 ((
% 99.20/13.39 (woz1_1) =>
% 99.20/13.39 ((
% 99.20/13.39 (woz1_2) =>
% 99.20/13.39 ((
% 99.20/13.39 (woz1_3) =>
% 99.20/13.39 ((
% 99.20/13.39 (woz1_4) =>
% 99.20/13.39 ((
% 99.20/13.39 (woz1_5) =>
% 99.20/13.39 ((
% 99.20/13.39 (breln1all2) =>
% 99.20/13.39 ((
% 99.20/13.39 (breln1SetBreln1) =>
% 99.20/13.39 ((
% 99.20/13.39 (choice2fnsingleton) =>
% 99.20/13.39 ((
% 99.20/13.39 (setOfPairsIsBReln1) =>
% 99.20/13.39 ((
% 99.20/13.39 (breln1all1) =>
% 99.20/13.39 ((
% 99.20/13.39 (subbreln1) =>
% 99.20/13.39 ((
% 99.20/13.39 (eqbreln1) =>
% 99.20/13.39 ((
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% 99.20/13.39 ((
% 99.20/13.39 (breln1invI) =>
% 99.20/13.39 ((
% 99.20/13.39 (breln1invE) =>
% 99.20/13.39 ((
% 99.20/13.39 (breln1compprop) =>
% 99.20/13.39 ((
% 99.20/13.39 (breln1compI) =>
% 99.20/13.39 ((
% 99.20/13.39 (breln1compE) =>
% 99.20/13.39 ((
% 99.20/13.39 (breln1compEex) =>
% 99.20/13.39 ((
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% 99.20/13.39 ((
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% 99.20/13.39 ((
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% 99.20/13.39 ((
% 99.20/13.39 (breln1unionI) =>
% 99.20/13.39 ((
% 99.20/13.39 (breln1unionE) =>
% 99.20/13.39 ((
% 99.20/13.39 (breln1unionEcases) =>
% 99.20/13.39 ((
% 99.20/13.39 (breln1unionCommutes) =>
% 99.20/13.39 ((
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% 99.20/13.39 ((
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% 99.20/13.39 ((
% 99.20/13.39 (image1Ex1) =>
% 99.20/13.39 ((
% 99.20/13.39 (image1Equiv) =>
% 99.20/13.39 ((
% 99.20/13.39 (image1E) =>
% 99.20/13.39 ((
% 99.20/13.39 (image1I) =>
% 99.20/13.39 ((
% 99.20/13.39 (injFuncInInjFuncSet) =>
% 99.20/13.39 ((
% 99.20/13.39 (injFuncSetFuncIn) =>
% 99.20/13.39 ((
% 99.20/13.39 (injFuncSetFuncInj) =>
% 99.20/13.39 ((
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% 99.20/13.39 (('#B') @ (
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% 99.20/13.39 (
% 99.20/13.39 (
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% 99.20/13.39 (
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% 99.20/13.39 (
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% 99.20/13.39 (
% 99.20/13.39 (
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% 99.20/13.39 (
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% 99.20/13.39 (
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% 99.20/13.39 (
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% 99.20/13.39 surjFuncSet)))))))) @
% 99.20/13.39 (
% 99.20/13.39 (
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% 99.20/13.39 (
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% 99.20/13.39 (
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% 99.20/13.39 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.20/13.39 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl570])).
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% 99.20/13.39 (((setadjoin__Cong) =>
% 99.20/13.39 (((powerset__Cong) =>
% 99.20/13.39 (((setunion__Cong) =>
% 99.20/13.39 (((exuEu) =>
% 99.20/13.39 (((descr__Cong) =>
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% 99.20/13.39 ((
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% 99.20/13.39 ((
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% 99.20/13.39 ((
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% 99.20/13.39 ((
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% 99.20/13.39 ((
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% 99.20/13.39 ((
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% 99.20/13.39 ((
% 99.20/13.39 (binunionRsub) =>
% 99.20/13.39 ((
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% 99.20/13.39 ((
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% 99.20/13.39 ((
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% 99.20/13.39 ((
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% 99.20/13.39 ((
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% 99.20/13.39 ((
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% 99.20/13.39 ((
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% 99.20/13.39 ((
% 99.20/13.39 (setminusSubset2) =>
% 99.20/13.39 ((
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% 99.20/13.39 ((
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% 99.20/13.39 ((
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% 99.20/13.39 ((
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% 99.20/13.39 ((
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% 99.20/13.39 ((
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% 99.20/13.39 ((
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% 99.20/13.39 ((
% 99.20/13.39 (symdiffIneg2) =>
% 99.20/13.39 ((
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% 99.20/13.39 ((
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% 99.20/13.39 ((
% 99.20/13.39 (setukpairIR) =>
% 99.20/13.39 ((
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% 99.20/13.39 ((
% 99.20/13.39 (kpairp) =>
% 99.20/13.39 ((
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% 99.20/13.39 ((
% 99.20/13.39 (singletoninpowerset) =>
% 99.20/13.39 ((
% 99.20/13.39 (singletoninpowunion) =>
% 99.20/13.39 ((
% 99.20/13.39 (upairset2E) =>
% 99.20/13.39 ((
% 99.20/13.39 (upairsubunion) =>
% 99.20/13.39 ((
% 99.20/13.39 (upairinpowunion) =>
% 99.20/13.39 ((
% 99.20/13.39 (ubforcartprodlem1) =>
% 99.20/13.39 ((
% 99.20/13.39 (ubforcartprodlem2) =>
% 99.20/13.39 ((
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% 99.20/13.39 ((
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% 99.20/13.39 ((
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% 99.20/13.39 (cartprodpairmemER) =>
% 99.20/13.39 ((
% 99.20/13.39 (cartprodmempaircEq) =>
% 99.20/13.39 ((
% 99.20/13.39 (cartprodfstpairEq) =>
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% 99.20/13.39 (cartprodsndpairEq) =>
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% 99.20/13.39 (cartprodpairsurjEq) =>
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% 99.20/13.39 ((
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% 99.20/13.39 ((
% 99.20/13.39 (ap2p) =>
% 99.20/13.39 ((
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% 99.20/13.39 ((
% 99.20/13.39 (lamProp) =>
% 99.20/13.39 ((
% 99.20/13.39 (lamp) =>
% 99.20/13.39 ((
% 99.20/13.39 (lam2p) =>
% 99.20/13.39 ((
% 99.20/13.39 (brelnall1) =>
% 99.20/13.39 ((
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% 99.20/13.39 ((
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% 99.20/13.39 ((
% 99.20/13.39 (funcGraphProp3) =>
% 99.20/13.39 ((
% 99.20/13.39 (funcGraphProp2) =>
% 99.20/13.39 ((
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% 99.20/13.39 ((
% 99.20/13.39 (funcGraphProp4) =>
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% 99.20/13.39 ((
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% 99.20/13.39 ((
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% 99.20/13.39 ((
% 99.20/13.39 (contrasubsetT2) =>
% 99.20/13.39 ((
% 99.20/13.39 (contrasubsetT3) =>
% 99.20/13.39 ((
% 99.20/13.39 (doubleComplementI1) =>
% 99.20/13.39 ((
% 99.20/13.39 (doubleComplementE1) =>
% 99.20/13.39 ((
% 99.20/13.39 (doubleComplementSub1) =>
% 99.20/13.39 ((
% 99.20/13.39 (doubleComplementSub2) =>
% 99.20/13.39 ((
% 99.20/13.39 (doubleComplementEq) =>
% 99.20/13.39 ((
% 99.20/13.39 (complementTnotintersectT) =>
% 99.20/13.39 ((
% 99.20/13.39 (complementImpComplementIntersect) =>
% 99.20/13.39 ((
% 99.20/13.39 (complementSubsetComplementIntersect) =>
% 99.20/13.39 ((
% 99.20/13.39 (complementInPowersetComplementIntersect) =>
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% 99.20/13.39 (contraSubsetComplement) =>
% 99.20/13.39 ((
% 99.20/13.39 (complementTcontraSubset) =>
% 99.20/13.39 ((
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% 99.20/13.39 ((
% 99.20/13.39 (binunionTIRcontra) =>
% 99.20/13.39 ((
% 99.20/13.39 (inIntersectImpInUnion) =>
% 99.20/13.39 ((
% 99.20/13.39 (inIntersectImpInUnion2) =>
% 99.20/13.39 ((
% 99.20/13.39 (inIntersectImpInIntersectUnions) =>
% 99.20/13.39 ((
% 99.20/13.39 (intersectInPowersetIntersectUnions) =>
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% 99.20/13.39 (inComplementUnionImpNotIn1) =>
% 99.20/13.39 ((
% 99.20/13.39 (inComplementUnionImpInComplement1) =>
% 99.20/13.39 ((
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% 99.20/13.39 ((
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% 99.20/13.39 ((
% 99.20/13.39 (complementUnionInPowersetComplement) =>
% 99.20/13.39 ((
% 99.20/13.39 (demorgan2a2) =>
% 99.20/13.39 ((
% 99.20/13.39 (demorgan1a) =>
% 99.20/13.39 ((
% 99.20/13.39 (demorgan1b) =>
% 99.20/13.39 ((
% 99.20/13.39 (demorgan1) =>
% 99.20/13.39 ((
% 99.20/13.39 (demorgan2a) =>
% 99.20/13.39 ((
% 99.20/13.39 (demorgan2b2) =>
% 99.20/13.39 ((
% 99.20/13.39 (demorgan2b) =>
% 99.20/13.39 ((
% 99.20/13.39 (demorgan2) =>
% 99.20/13.39 ((
% 99.20/13.39 (woz13rule0) =>
% 99.20/13.39 ((
% 99.20/13.39 (woz13rule1) =>
% 99.20/13.39 ((
% 99.20/13.39 (woz13rule2) =>
% 99.20/13.39 ((
% 99.20/13.39 (woz13rule3) =>
% 99.20/13.39 ((
% 99.20/13.39 (woz13rule4) =>
% 99.20/13.39 ((
% 99.20/13.39 (woz1_1) =>
% 99.20/13.39 ((
% 99.20/13.39 (woz1_2) =>
% 99.20/13.39 ((
% 99.20/13.39 (woz1_3) =>
% 99.20/13.39 ((
% 99.20/13.39 (woz1_4) =>
% 99.20/13.39 ((
% 99.20/13.39 (woz1_5) =>
% 99.20/13.39 ((
% 99.20/13.39 (breln1all2) =>
% 99.20/13.39 ((
% 99.20/13.39 (breln1SetBreln1) =>
% 99.20/13.39 ((
% 99.20/13.39 (choice2fnsingleton) =>
% 99.20/13.39 ((
% 99.20/13.39 (setOfPairsIsBReln1) =>
% 99.20/13.39 ((
% 99.20/13.39 (breln1all1) =>
% 99.20/13.39 ((
% 99.20/13.39 (subbreln1) =>
% 99.20/13.39 ((
% 99.20/13.39 (eqbreln1) =>
% 99.20/13.39 ((
% 99.20/13.39 (breln1invprop) =>
% 99.20/13.39 ((
% 99.20/13.39 (breln1invI) =>
% 99.20/13.39 ((
% 99.20/13.39 (breln1invE) =>
% 99.20/13.39 ((
% 99.20/13.39 (breln1compprop) =>
% 99.20/13.39 ((
% 99.20/13.39 (breln1compI) =>
% 99.20/13.39 ((
% 99.20/13.39 (breln1compE) =>
% 99.20/13.39 ((
% 99.20/13.39 (breln1compEex) =>
% 99.20/13.39 ((
% 99.20/13.39 (breln1unionprop) =>
% 99.20/13.39 ((
% 99.20/13.39 (breln1unionIL) =>
% 99.20/13.39 ((
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% 99.20/13.39 ((
% 99.20/13.39 (breln1unionI) =>
% 99.20/13.39 ((
% 99.20/13.39 (breln1unionE) =>
% 99.20/13.39 ((
% 99.20/13.39 (breln1unionEcases) =>
% 99.20/13.39 ((
% 99.20/13.39 (breln1unionCommutes) =>
% 99.20/13.39 ((
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% 99.20/13.39 ((
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% 99.20/13.39 ((
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% 99.20/13.39 ((
% 99.20/13.39 (woz2B) =>
% 99.20/13.39 ((
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% 99.20/13.39 ((
% 99.20/13.39 (image1Ex1) =>
% 99.20/13.39 ((
% 99.20/13.39 (image1Equiv) =>
% 99.20/13.39 ((
% 99.20/13.39 (image1E) =>
% 99.20/13.39 ((
% 99.20/13.39 (image1I) =>
% 99.20/13.39 ((
% 99.20/13.39 (injFuncInInjFuncSet) =>
% 99.20/13.39 ((
% 99.20/13.39 (injFuncSetFuncIn) =>
% 99.20/13.39 ((
% 99.20/13.39 (injFuncSetFuncInj) =>
% 99.20/13.39 ((
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% 99.20/13.39 (
% 99.20/13.39 (
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% 99.20/13.39 (
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% 99.20/13.39 (
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% 99.20/13.39 (
% 99.20/13.39 (
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% 99.20/13.39 (
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% 99.20/13.39 (
% 99.20/13.39 (
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% 99.20/13.39 (
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% 99.20/13.39 (
% 99.20/13.39 ('#B') @ (
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% 99.20/13.39 (
% 99.20/13.39 (
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% 99.20/13.39 surjFuncSet)))))))) @
% 99.20/13.39 (
% 99.20/13.39 (
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% 99.20/13.39 (
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% 99.20/13.39 (
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% 99.20/13.39 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
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% 99.20/13.39 (((setadjoin__Cong) =>
% 99.20/13.39 (((powerset__Cong) =>
% 99.20/13.39 (((setunion__Cong) =>
% 99.20/13.39 (((exuEu) =>
% 99.20/13.39 (((descr__Cong) =>
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% 99.20/13.39 ((
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% 99.20/13.39 ((
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% 99.20/13.39 ((
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% 99.20/13.39 ((
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% 99.20/13.39 ((
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% 99.20/13.39 ((
% 99.20/13.39 (binunionE) =>
% 99.20/13.39 ((
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% 99.20/13.39 ((
% 99.20/13.39 (binunionRsub) =>
% 99.20/13.39 ((
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% 99.20/13.39 ((
% 99.20/13.39 (binintersectSubset5) =>
% 99.20/13.39 ((
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% 99.20/13.39 ((
% 99.20/13.39 (binintersectLsub) =>
% 99.20/13.39 ((
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% 99.20/13.39 ((
% 99.20/13.39 (binintersectSubset3) =>
% 99.20/13.39 ((
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% 99.20/13.39 (binintersectSubset4) =>
% 99.20/13.39 ((
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% 99.20/13.39 ((
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% 99.20/13.39 ((
% 99.20/13.39 (setminusEL) =>
% 99.20/13.39 ((
% 99.20/13.39 (setminusER) =>
% 99.20/13.39 ((
% 99.20/13.39 (setminusSubset2) =>
% 99.20/13.39 ((
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% 99.20/13.39 ((
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% 99.20/13.39 ((
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% 99.20/13.39 ((
% 99.20/13.39 (setminusIRneg) =>
% 99.20/13.39 ((
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% 99.20/13.39 ((
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% 99.20/13.39 ((
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% 99.20/13.39 ((
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% 99.20/13.39 ((
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% 99.20/13.39 ((
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% 99.20/13.39 ((
% 99.20/13.39 (symdiffIneg2) =>
% 99.20/13.39 ((
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% 99.20/13.39 ((
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% 99.20/13.39 ((
% 99.20/13.39 (setukpairIR) =>
% 99.20/13.39 ((
% 99.20/13.39 (kpairiskpair) =>
% 99.20/13.39 ((
% 99.20/13.39 (kpairp) =>
% 99.20/13.39 ((
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% 99.20/13.40 ((
% 99.20/13.40 (singletoninpowerset) =>
% 99.20/13.40 ((
% 99.20/13.40 (singletoninpowunion) =>
% 99.20/13.40 ((
% 99.20/13.40 (upairset2E) =>
% 99.20/13.40 ((
% 99.20/13.40 (upairsubunion) =>
% 99.20/13.40 ((
% 99.20/13.40 (upairinpowunion) =>
% 99.20/13.40 ((
% 99.20/13.40 (ubforcartprodlem1) =>
% 99.20/13.40 ((
% 99.20/13.40 (ubforcartprodlem2) =>
% 99.20/13.40 ((
% 99.20/13.40 (ubforcartprodlem3) =>
% 99.20/13.40 ((
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% 99.20/13.40 ((
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% 99.20/13.40 ((
% 99.20/13.40 (cartprodmempair) =>
% 99.20/13.40 ((
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% 99.20/13.40 ((
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% 99.20/13.40 ((
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% 99.20/13.40 (singletonsuniq) =>
% 99.20/13.40 ((
% 99.20/13.40 (setukpairinjL1) =>
% 99.20/13.40 ((
% 99.20/13.40 (kfstsingleton) =>
% 99.20/13.40 ((
% 99.20/13.40 (theprop) =>
% 99.20/13.40 ((
% 99.20/13.40 (kfstpairEq) =>
% 99.20/13.40 ((
% 99.20/13.40 (cartprodfstin) =>
% 99.20/13.40 ((
% 99.20/13.40 (setukpairinjL2) =>
% 99.20/13.40 ((
% 99.20/13.40 (setukpairinjL) =>
% 99.20/13.40 ((
% 99.20/13.40 (setukpairinjR11) =>
% 99.20/13.40 ((
% 99.20/13.40 (setukpairinjR12) =>
% 99.20/13.40 ((
% 99.20/13.40 (setukpairinjR1) =>
% 99.20/13.40 ((
% 99.20/13.40 (upairequniteq) =>
% 99.20/13.40 ((
% 99.20/13.40 (setukpairinjR2) =>
% 99.20/13.40 ((
% 99.20/13.40 (setukpairinjR) =>
% 99.20/13.40 ((
% 99.20/13.40 (ksndsingleton) =>
% 99.20/13.40 ((
% 99.20/13.40 (ksndpairEq) =>
% 99.20/13.40 ((
% 99.20/13.40 (kpairsurjEq) =>
% 99.20/13.40 ((
% 99.20/13.40 (cartprodsndin) =>
% 99.20/13.40 ((
% 99.20/13.40 (cartprodpairmemEL) =>
% 99.20/13.40 ((
% 99.20/13.40 (cartprodpairmemER) =>
% 99.20/13.40 ((
% 99.20/13.40 (cartprodmempaircEq) =>
% 99.20/13.40 ((
% 99.20/13.40 (cartprodfstpairEq) =>
% 99.20/13.40 ((
% 99.20/13.40 (cartprodsndpairEq) =>
% 99.20/13.40 ((
% 99.20/13.40 (cartprodpairsurjEq) =>
% 99.20/13.40 ((
% 99.20/13.40 (dpsetconstrI) =>
% 99.20/13.40 ((
% 99.20/13.40 (dpsetconstrSub) =>
% 99.20/13.40 ((
% 99.20/13.40 (setOfPairsIsBReln) =>
% 99.20/13.40 ((
% 99.20/13.40 (dpsetconstrERa) =>
% 99.20/13.40 ((
% 99.20/13.40 (dpsetconstrEL1) =>
% 99.20/13.40 ((
% 99.20/13.40 (dpsetconstrEL2) =>
% 99.20/13.40 ((
% 99.20/13.40 (dpsetconstrER) =>
% 99.20/13.40 ((
% 99.20/13.40 (funcImageSingleton) =>
% 99.20/13.40 ((
% 99.20/13.40 (apProp) =>
% 99.20/13.40 ((
% 99.20/13.40 (app) =>
% 99.20/13.40 ((
% 99.20/13.40 (infuncsetfunc) =>
% 99.20/13.40 ((
% 99.20/13.40 (ap2p) =>
% 99.20/13.40 ((
% 99.20/13.40 (funcinfuncset) =>
% 99.20/13.40 ((
% 99.20/13.40 (lamProp) =>
% 99.20/13.40 ((
% 99.20/13.40 (lamp) =>
% 99.20/13.40 ((
% 99.20/13.40 (lam2p) =>
% 99.20/13.40 ((
% 99.20/13.40 (brelnall1) =>
% 99.20/13.40 ((
% 99.20/13.40 (brelnall2) =>
% 99.20/13.40 ((
% 99.20/13.40 (ex1E2) =>
% 99.20/13.40 ((
% 99.20/13.40 (funcGraphProp1) =>
% 99.20/13.40 ((
% 99.20/13.40 (funcGraphProp3) =>
% 99.20/13.40 ((
% 99.20/13.40 (funcGraphProp2) =>
% 99.20/13.40 ((
% 99.20/13.40 (funcextLem) =>
% 99.20/13.40 ((
% 99.20/13.40 (funcGraphProp4) =>
% 99.20/13.40 ((
% 99.20/13.40 (subbreln) =>
% 99.20/13.40 ((
% 99.20/13.40 (eqbreln) =>
% 99.20/13.40 ((
% 99.20/13.40 (funcext) =>
% 99.20/13.40 ((
% 99.20/13.40 (funcext2) =>
% 99.20/13.40 ((
% 99.20/13.40 (ap2apEq1) =>
% 99.20/13.40 ((
% 99.20/13.40 (ap2apEq2) =>
% 99.20/13.40 ((
% 99.20/13.40 (beta1) =>
% 99.20/13.40 ((
% 99.20/13.40 (eta1) =>
% 99.20/13.40 ((
% 99.20/13.40 (lam2lamEq) =>
% 99.20/13.40 ((
% 99.20/13.40 (beta2) =>
% 99.20/13.40 ((
% 99.20/13.40 (eta2) =>
% 99.20/13.40 ((
% 99.20/13.40 (iffalseProp1) =>
% 99.20/13.40 ((
% 99.20/13.40 (iffalseProp2) =>
% 99.20/13.40 ((
% 99.20/13.40 (iftrueProp1) =>
% 99.20/13.40 ((
% 99.20/13.40 (iftrueProp2) =>
% 99.20/13.40 ((
% 99.20/13.40 (ifSingleton) =>
% 99.20/13.40 ((
% 99.20/13.40 (ifp) =>
% 99.20/13.40 ((
% 99.20/13.40 (theeq) =>
% 99.20/13.40 ((
% 99.20/13.40 (iftrue) =>
% 99.20/13.40 ((
% 99.20/13.40 (iffalse) =>
% 99.20/13.40 ((
% 99.20/13.40 (iftrueorfalse) =>
% 99.20/13.40 ((
% 99.20/13.40 (binintersectT_lem) =>
% 99.20/13.40 ((
% 99.20/13.40 (binunionT_lem) =>
% 99.20/13.40 ((
% 99.20/13.40 (powersetT_lem) =>
% 99.20/13.40 ((
% 99.20/13.40 (setminusT_lem) =>
% 99.20/13.40 ((
% 99.20/13.40 (complementT_lem) =>
% 99.20/13.40 ((
% 99.20/13.40 (setextT) =>
% 99.20/13.40 ((
% 99.20/13.40 (subsetTI) =>
% 99.20/13.40 ((
% 99.20/13.40 (powersetTI1) =>
% 99.20/13.40 ((
% 99.20/13.40 (powersetTE1) =>
% 99.20/13.40 ((
% 99.20/13.40 (complementTI1) =>
% 99.20/13.40 ((
% 99.20/13.40 (complementTE1) =>
% 99.20/13.40 ((
% 99.20/13.40 (binintersectTELcontra) =>
% 99.20/13.40 ((
% 99.20/13.40 (binintersectTERcontra) =>
% 99.20/13.40 ((
% 99.20/13.40 (contrasubsetT) =>
% 99.20/13.40 ((
% 99.20/13.40 (contrasubsetT1) =>
% 99.20/13.40 ((
% 99.20/13.40 (contrasubsetT2) =>
% 99.20/13.40 ((
% 99.20/13.40 (contrasubsetT3) =>
% 99.20/13.40 ((
% 99.20/13.40 (doubleComplementI1) =>
% 99.20/13.40 ((
% 99.20/13.40 (doubleComplementE1) =>
% 99.20/13.40 ((
% 99.20/13.40 (doubleComplementSub1) =>
% 99.20/13.40 ((
% 99.20/13.40 (doubleComplementSub2) =>
% 99.20/13.40 ((
% 99.20/13.40 (doubleComplementEq) =>
% 99.20/13.40 ((
% 99.20/13.40 (complementTnotintersectT) =>
% 99.20/13.40 ((
% 99.20/13.40 (complementImpComplementIntersect) =>
% 99.20/13.40 ((
% 99.20/13.40 (complementSubsetComplementIntersect) =>
% 99.20/13.40 ((
% 99.20/13.40 (complementInPowersetComplementIntersect) =>
% 99.20/13.40 ((
% 99.20/13.40 (contraSubsetComplement) =>
% 99.20/13.40 ((
% 99.20/13.40 (complementTcontraSubset) =>
% 99.20/13.40 ((
% 99.20/13.40 (binunionTILcontra) =>
% 99.20/13.40 ((
% 99.20/13.40 (binunionTIRcontra) =>
% 99.20/13.40 ((
% 99.20/13.40 (inIntersectImpInUnion) =>
% 99.20/13.40 ((
% 99.20/13.40 (inIntersectImpInUnion2) =>
% 99.20/13.40 ((
% 99.20/13.40 (inIntersectImpInIntersectUnions) =>
% 99.20/13.40 ((
% 99.20/13.40 (intersectInPowersetIntersectUnions) =>
% 99.20/13.40 ((
% 99.20/13.40 (inComplementUnionImpNotIn1) =>
% 99.20/13.40 ((
% 99.20/13.40 (inComplementUnionImpInComplement1) =>
% 99.20/13.40 ((
% 99.20/13.40 (binunionTE) =>
% 99.20/13.40 ((
% 99.20/13.40 (binunionTEcontra) =>
% 99.20/13.40 ((
% 99.20/13.40 (demorgan2a1) =>
% 99.20/13.40 ((
% 99.20/13.40 (complementUnionInPowersetComplement) =>
% 99.20/13.40 ((
% 99.20/13.40 (demorgan2a2) =>
% 99.20/13.40 ((
% 99.20/13.40 (demorgan1a) =>
% 99.20/13.40 ((
% 99.20/13.40 (demorgan1b) =>
% 99.20/13.40 ((
% 99.20/13.40 (demorgan1) =>
% 99.20/13.40 ((
% 99.20/13.40 (demorgan2a) =>
% 99.20/13.40 ((
% 99.20/13.40 (demorgan2b2) =>
% 99.20/13.40 ((
% 99.20/13.40 (demorgan2b) =>
% 99.20/13.40 ((
% 99.20/13.40 (demorgan2) =>
% 99.20/13.40 ((
% 99.20/13.40 (woz13rule0) =>
% 99.20/13.40 ((
% 99.20/13.40 (woz13rule1) =>
% 99.20/13.40 ((
% 99.20/13.40 (woz13rule2) =>
% 99.20/13.40 ((
% 99.20/13.40 (woz13rule3) =>
% 99.20/13.40 ((
% 99.20/13.40 (woz13rule4) =>
% 99.20/13.40 ((
% 99.20/13.40 (woz1_1) =>
% 99.20/13.40 ((
% 99.20/13.40 (woz1_2) =>
% 99.20/13.40 ((
% 99.20/13.40 (woz1_3) =>
% 99.20/13.40 ((
% 99.20/13.40 (woz1_4) =>
% 99.20/13.40 ((
% 99.20/13.40 (woz1_5) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1all2) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1SetBreln1) =>
% 99.20/13.40 ((
% 99.20/13.40 (choice2fnsingleton) =>
% 99.20/13.40 ((
% 99.20/13.40 (setOfPairsIsBReln1) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1all1) =>
% 99.20/13.40 ((
% 99.20/13.40 (subbreln1) =>
% 99.20/13.40 ((
% 99.20/13.40 (eqbreln1) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1invprop) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1invI) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1invE) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1compprop) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1compI) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1compE) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1compEex) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1unionprop) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1unionIL) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1unionIR) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1unionI) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1unionE) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1unionEcases) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1unionCommutes) =>
% 99.20/13.40 ((
% 99.20/13.40 (woz2Ex) =>
% 99.20/13.40 ((
% 99.20/13.40 (woz2W) =>
% 99.20/13.40 ((
% 99.20/13.40 (woz2A) =>
% 99.20/13.40 ((
% 99.20/13.40 (woz2B) =>
% 99.20/13.40 ((
% 99.20/13.40 (image1Ex) =>
% 99.20/13.40 ((
% 99.20/13.40 (image1Ex1) =>
% 99.20/13.40 ((
% 99.20/13.40 (image1Equiv) =>
% 99.20/13.40 ((
% 99.20/13.40 (image1E) =>
% 99.20/13.40 ((
% 99.20/13.40 (image1I) =>
% 99.20/13.40 ((
% 99.20/13.40 (injFuncInInjFuncSet) =>
% 99.20/13.40 ((
% 99.20/13.40 (injFuncSetFuncIn) =>
% 99.20/13.40 ((
% 99.20/13.40 (injFuncSetFuncInj) =>
% 99.20/13.40 ((
% 99.20/13.40 (!!) @ (
% 99.20/13.40 (('#B') @ (
% 99.20/13.40 !!) @
% 99.20/13.40 (
% 99.20/13.40 (
% 99.20/13.40 ('#B') @ (
% 99.20/13.40 (
% 99.20/13.40 ('#B') @ (
% 99.20/13.40 !!))) @
% 99.20/13.40 (
% 99.20/13.40 (
% 99.20/13.40 ('#S') @ (
% 99.20/13.40 (
% 99.20/13.40 ('#B') @ (
% 99.20/13.40 '#S') @
% 99.20/13.40 (
% 99.20/13.40 (
% 99.20/13.40 ('#B') @ (
% 99.20/13.40 (
% 99.20/13.40 ('#B') @ (
% 99.20/13.40 '#S'))) @
% 99.20/13.40 (
% 99.20/13.40 (
% 99.20/13.40 ('#B') @ (
% 99.20/13.40 (
% 99.20/13.40 ('#B') @ (
% 99.20/13.40 (
% 99.20/13.40 ('#B') @ (
% 99.20/13.40 =>))))) @
% 99.20/13.40 (
% 99.20/13.40 (
% 99.20/13.40 ('#B') @ (
% 99.20/13.40 (
% 99.20/13.40 ('#B') @ (
% 99.20/13.40 (
% 99.20/13.40 ('#C') @ in)))) @
% 99.20/13.40 surjFuncSet)))))))) @
% 99.20/13.40 (
% 99.20/13.40 (
% 99.20/13.40 ('#B') @ (
% 99.20/13.40 (
% 99.20/13.40 ('#B') @ (
% 99.20/13.40 (
% 99.20/13.40 ('#C') @ in)))) @
% 99.20/13.40 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.20/13.40 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl586])).
% 99.20/13.40 thf(zip_derived_cl606, plain,
% 99.20/13.40 (~ (((exuI1) =>
% 99.20/13.40 (((exuI3) =>
% 99.20/13.40 (((exuI2) =>
% 99.20/13.40 (((inCongP) =>
% 99.20/13.40 (((in__Cong) =>
% 99.20/13.40 (((exuE3u) =>
% 99.20/13.40 (((exu__Cong) =>
% 99.20/13.40 (((setadjoin__Cong) =>
% 99.20/13.40 (((powerset__Cong) =>
% 99.20/13.40 (((setunion__Cong) =>
% 99.20/13.40 (((exuEu) =>
% 99.20/13.40 (((descr__Cong) =>
% 99.20/13.40 (((dsetconstr__Cong) =>
% 99.20/13.40 (((subsetI1) =>
% 99.20/13.40 (((eqimpsubset2) =>
% 99.20/13.40 (((eqimpsubset1) =>
% 99.20/13.40 (((subsetI2) =>
% 99.20/13.40 (((emptysetsubset) =>
% 99.20/13.40 (((subsetE) =>
% 99.20/13.40 (((subsetE2) =>
% 99.20/13.40 (((notsubsetI) =>
% 99.20/13.40 (((notequalI1) =>
% 99.20/13.40 (((notequalI2) =>
% 99.20/13.40 (((subsetRefl) =>
% 99.20/13.40 (((subsetTrans) =>
% 99.20/13.40 (((setadjoinSub) =>
% 99.20/13.40 (((setadjoinSub2) =>
% 99.20/13.40 (((subset2powerset) =>
% 99.20/13.40 (((setextsub) =>
% 99.20/13.40 (((subsetemptysetimpeq) =>
% 99.20/13.40 ((
% 99.20/13.40 (powersetI1) =>
% 99.20/13.40 ((
% 99.20/13.40 (powersetE1) =>
% 99.20/13.40 ((
% 99.20/13.40 (inPowerset) =>
% 99.20/13.40 ((
% 99.20/13.40 (powersetsubset) =>
% 99.20/13.40 ((
% 99.20/13.40 (sepInPowerset) =>
% 99.20/13.40 ((
% 99.20/13.40 (sepSubset) =>
% 99.20/13.40 ((
% 99.20/13.40 (binunionIL) =>
% 99.20/13.40 ((
% 99.20/13.40 (upairset2IR) =>
% 99.20/13.40 ((
% 99.20/13.40 (binunionIR) =>
% 99.20/13.40 ((
% 99.20/13.40 (binunionEcases) =>
% 99.20/13.40 ((
% 99.20/13.40 (binunionE) =>
% 99.20/13.40 ((
% 99.20/13.40 (binunionLsub) =>
% 99.20/13.40 ((
% 99.20/13.40 (binunionRsub) =>
% 99.20/13.40 ((
% 99.20/13.40 (binintersectI) =>
% 99.20/13.40 ((
% 99.20/13.40 (binintersectSubset5) =>
% 99.20/13.40 ((
% 99.20/13.40 (binintersectEL) =>
% 99.20/13.40 ((
% 99.20/13.40 (binintersectLsub) =>
% 99.20/13.40 ((
% 99.20/13.40 (binintersectSubset2) =>
% 99.20/13.40 ((
% 99.20/13.40 (binintersectSubset3) =>
% 99.20/13.40 ((
% 99.20/13.40 (binintersectER) =>
% 99.20/13.40 ((
% 99.20/13.40 (disjointsetsI1) =>
% 99.20/13.40 ((
% 99.20/13.40 (binintersectRsub) =>
% 99.20/13.40 ((
% 99.20/13.40 (binintersectSubset4) =>
% 99.20/13.40 ((
% 99.20/13.40 (binintersectSubset1) =>
% 99.20/13.40 ((
% 99.20/13.40 (bs114d) =>
% 99.20/13.40 ((
% 99.20/13.40 (setminusI) =>
% 99.20/13.40 ((
% 99.20/13.40 (setminusEL) =>
% 99.20/13.40 ((
% 99.20/13.40 (setminusER) =>
% 99.20/13.40 ((
% 99.20/13.40 (setminusSubset2) =>
% 99.20/13.40 ((
% 99.20/13.40 (setminusERneg) =>
% 99.20/13.40 ((
% 99.20/13.40 (setminusELneg) =>
% 99.20/13.40 ((
% 99.20/13.40 (setminusILneg) =>
% 99.20/13.40 ((
% 99.20/13.40 (setminusIRneg) =>
% 99.20/13.40 ((
% 99.20/13.40 (setminusLsub) =>
% 99.20/13.40 ((
% 99.20/13.40 (setminusSubset1) =>
% 99.20/13.40 ((
% 99.20/13.40 (symdiffE) =>
% 99.20/13.40 ((
% 99.20/13.40 (symdiffI1) =>
% 99.20/13.40 ((
% 99.20/13.40 (symdiffI2) =>
% 99.20/13.40 ((
% 99.20/13.40 (symdiffIneg1) =>
% 99.20/13.40 ((
% 99.20/13.40 (symdiffIneg2) =>
% 99.20/13.40 ((
% 99.20/13.40 (secondinupair) =>
% 99.20/13.40 ((
% 99.20/13.40 (setukpairIL) =>
% 99.20/13.40 ((
% 99.20/13.40 (setukpairIR) =>
% 99.20/13.40 ((
% 99.20/13.40 (kpairiskpair) =>
% 99.20/13.40 ((
% 99.20/13.40 (kpairp) =>
% 99.20/13.40 ((
% 99.20/13.40 (singletonsubset) =>
% 99.20/13.40 ((
% 99.20/13.40 (singletoninpowerset) =>
% 99.20/13.40 ((
% 99.20/13.40 (singletoninpowunion) =>
% 99.20/13.40 ((
% 99.20/13.40 (upairset2E) =>
% 99.20/13.40 ((
% 99.20/13.40 (upairsubunion) =>
% 99.20/13.40 ((
% 99.20/13.40 (upairinpowunion) =>
% 99.20/13.40 ((
% 99.20/13.40 (ubforcartprodlem1) =>
% 99.20/13.40 ((
% 99.20/13.40 (ubforcartprodlem2) =>
% 99.20/13.40 ((
% 99.20/13.40 (ubforcartprodlem3) =>
% 99.20/13.40 ((
% 99.20/13.40 (cartprodpairin) =>
% 99.20/13.40 ((
% 99.20/13.40 (cartprodmempair1) =>
% 99.20/13.40 ((
% 99.20/13.40 (cartprodmempair) =>
% 99.20/13.40 ((
% 99.20/13.40 (setunionE2) =>
% 99.20/13.40 ((
% 99.20/13.40 (setunionsingleton1) =>
% 99.20/13.40 ((
% 99.20/13.40 (setunionsingleton2) =>
% 99.20/13.40 ((
% 99.20/13.40 (setunionsingleton) =>
% 99.20/13.40 ((
% 99.20/13.40 (singletonprop) =>
% 99.20/13.40 ((
% 99.20/13.40 (ex1E1) =>
% 99.20/13.40 ((
% 99.20/13.40 (ex1I) =>
% 99.20/13.40 ((
% 99.20/13.40 (ex1I2) =>
% 99.20/13.40 ((
% 99.20/13.40 (singletonsuniq) =>
% 99.20/13.40 ((
% 99.20/13.40 (setukpairinjL1) =>
% 99.20/13.40 ((
% 99.20/13.40 (kfstsingleton) =>
% 99.20/13.40 ((
% 99.20/13.40 (theprop) =>
% 99.20/13.40 ((
% 99.20/13.40 (kfstpairEq) =>
% 99.20/13.40 ((
% 99.20/13.40 (cartprodfstin) =>
% 99.20/13.40 ((
% 99.20/13.40 (setukpairinjL2) =>
% 99.20/13.40 ((
% 99.20/13.40 (setukpairinjL) =>
% 99.20/13.40 ((
% 99.20/13.40 (setukpairinjR11) =>
% 99.20/13.40 ((
% 99.20/13.40 (setukpairinjR12) =>
% 99.20/13.40 ((
% 99.20/13.40 (setukpairinjR1) =>
% 99.20/13.40 ((
% 99.20/13.40 (upairequniteq) =>
% 99.20/13.40 ((
% 99.20/13.40 (setukpairinjR2) =>
% 99.20/13.40 ((
% 99.20/13.40 (setukpairinjR) =>
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% 99.20/13.40 ((
% 99.20/13.40 (cartprodsndin) =>
% 99.20/13.40 ((
% 99.20/13.40 (cartprodpairmemEL) =>
% 99.20/13.40 ((
% 99.20/13.40 (cartprodpairmemER) =>
% 99.20/13.40 ((
% 99.20/13.40 (cartprodmempaircEq) =>
% 99.20/13.40 ((
% 99.20/13.40 (cartprodfstpairEq) =>
% 99.20/13.40 ((
% 99.20/13.40 (cartprodsndpairEq) =>
% 99.20/13.40 ((
% 99.20/13.40 (cartprodpairsurjEq) =>
% 99.20/13.40 ((
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% 99.20/13.40 ((
% 99.20/13.40 (dpsetconstrSub) =>
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% 99.20/13.40 ((
% 99.20/13.40 (dpsetconstrEL2) =>
% 99.20/13.40 ((
% 99.20/13.40 (dpsetconstrER) =>
% 99.20/13.40 ((
% 99.20/13.40 (funcImageSingleton) =>
% 99.20/13.40 ((
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% 99.20/13.40 ((
% 99.20/13.40 (app) =>
% 99.20/13.40 ((
% 99.20/13.40 (infuncsetfunc) =>
% 99.20/13.40 ((
% 99.20/13.40 (ap2p) =>
% 99.20/13.40 ((
% 99.20/13.40 (funcinfuncset) =>
% 99.20/13.40 ((
% 99.20/13.40 (lamProp) =>
% 99.20/13.40 ((
% 99.20/13.40 (lamp) =>
% 99.20/13.40 ((
% 99.20/13.40 (lam2p) =>
% 99.20/13.40 ((
% 99.20/13.40 (brelnall1) =>
% 99.20/13.40 ((
% 99.20/13.40 (brelnall2) =>
% 99.20/13.40 ((
% 99.20/13.40 (ex1E2) =>
% 99.20/13.40 ((
% 99.20/13.40 (funcGraphProp1) =>
% 99.20/13.40 ((
% 99.20/13.40 (funcGraphProp3) =>
% 99.20/13.40 ((
% 99.20/13.40 (funcGraphProp2) =>
% 99.20/13.40 ((
% 99.20/13.40 (funcextLem) =>
% 99.20/13.40 ((
% 99.20/13.40 (funcGraphProp4) =>
% 99.20/13.40 ((
% 99.20/13.40 (subbreln) =>
% 99.20/13.40 ((
% 99.20/13.40 (eqbreln) =>
% 99.20/13.40 ((
% 99.20/13.40 (funcext) =>
% 99.20/13.40 ((
% 99.20/13.40 (funcext2) =>
% 99.20/13.40 ((
% 99.20/13.40 (ap2apEq1) =>
% 99.20/13.40 ((
% 99.20/13.40 (ap2apEq2) =>
% 99.20/13.40 ((
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% 99.20/13.40 ((
% 99.20/13.40 (eta1) =>
% 99.20/13.40 ((
% 99.20/13.40 (lam2lamEq) =>
% 99.20/13.40 ((
% 99.20/13.40 (beta2) =>
% 99.20/13.40 ((
% 99.20/13.40 (eta2) =>
% 99.20/13.40 ((
% 99.20/13.40 (iffalseProp1) =>
% 99.20/13.40 ((
% 99.20/13.40 (iffalseProp2) =>
% 99.20/13.40 ((
% 99.20/13.40 (iftrueProp1) =>
% 99.20/13.40 ((
% 99.20/13.40 (iftrueProp2) =>
% 99.20/13.40 ((
% 99.20/13.40 (ifSingleton) =>
% 99.20/13.40 ((
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% 99.20/13.40 ((
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% 99.20/13.40 ((
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% 99.20/13.40 ((
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% 99.20/13.40 (powersetT_lem) =>
% 99.20/13.40 ((
% 99.20/13.40 (setminusT_lem) =>
% 99.20/13.40 ((
% 99.20/13.40 (complementT_lem) =>
% 99.20/13.40 ((
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% 99.20/13.40 ((
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% 99.20/13.40 ((
% 99.20/13.40 (powersetTE1) =>
% 99.20/13.40 ((
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% 99.20/13.40 ((
% 99.20/13.40 (complementTE1) =>
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% 99.20/13.40 (binintersectTELcontra) =>
% 99.20/13.40 ((
% 99.20/13.40 (binintersectTERcontra) =>
% 99.20/13.40 ((
% 99.20/13.40 (contrasubsetT) =>
% 99.20/13.40 ((
% 99.20/13.40 (contrasubsetT1) =>
% 99.20/13.40 ((
% 99.20/13.40 (contrasubsetT2) =>
% 99.20/13.40 ((
% 99.20/13.40 (contrasubsetT3) =>
% 99.20/13.40 ((
% 99.20/13.40 (doubleComplementI1) =>
% 99.20/13.40 ((
% 99.20/13.40 (doubleComplementE1) =>
% 99.20/13.40 ((
% 99.20/13.40 (doubleComplementSub1) =>
% 99.20/13.40 ((
% 99.20/13.40 (doubleComplementSub2) =>
% 99.20/13.40 ((
% 99.20/13.40 (doubleComplementEq) =>
% 99.20/13.40 ((
% 99.20/13.40 (complementTnotintersectT) =>
% 99.20/13.40 ((
% 99.20/13.40 (complementImpComplementIntersect) =>
% 99.20/13.40 ((
% 99.20/13.40 (complementSubsetComplementIntersect) =>
% 99.20/13.40 ((
% 99.20/13.40 (complementInPowersetComplementIntersect) =>
% 99.20/13.40 ((
% 99.20/13.40 (contraSubsetComplement) =>
% 99.20/13.40 ((
% 99.20/13.40 (complementTcontraSubset) =>
% 99.20/13.40 ((
% 99.20/13.40 (binunionTILcontra) =>
% 99.20/13.40 ((
% 99.20/13.40 (binunionTIRcontra) =>
% 99.20/13.40 ((
% 99.20/13.40 (inIntersectImpInUnion) =>
% 99.20/13.40 ((
% 99.20/13.40 (inIntersectImpInUnion2) =>
% 99.20/13.40 ((
% 99.20/13.40 (inIntersectImpInIntersectUnions) =>
% 99.20/13.40 ((
% 99.20/13.40 (intersectInPowersetIntersectUnions) =>
% 99.20/13.40 ((
% 99.20/13.40 (inComplementUnionImpNotIn1) =>
% 99.20/13.40 ((
% 99.20/13.40 (inComplementUnionImpInComplement1) =>
% 99.20/13.40 ((
% 99.20/13.40 (binunionTE) =>
% 99.20/13.40 ((
% 99.20/13.40 (binunionTEcontra) =>
% 99.20/13.40 ((
% 99.20/13.40 (demorgan2a1) =>
% 99.20/13.40 ((
% 99.20/13.40 (complementUnionInPowersetComplement) =>
% 99.20/13.40 ((
% 99.20/13.40 (demorgan2a2) =>
% 99.20/13.40 ((
% 99.20/13.40 (demorgan1a) =>
% 99.20/13.40 ((
% 99.20/13.40 (demorgan1b) =>
% 99.20/13.40 ((
% 99.20/13.40 (demorgan1) =>
% 99.20/13.40 ((
% 99.20/13.40 (demorgan2a) =>
% 99.20/13.40 ((
% 99.20/13.40 (demorgan2b2) =>
% 99.20/13.40 ((
% 99.20/13.40 (demorgan2b) =>
% 99.20/13.40 ((
% 99.20/13.40 (demorgan2) =>
% 99.20/13.40 ((
% 99.20/13.40 (woz13rule0) =>
% 99.20/13.40 ((
% 99.20/13.40 (woz13rule1) =>
% 99.20/13.40 ((
% 99.20/13.40 (woz13rule2) =>
% 99.20/13.40 ((
% 99.20/13.40 (woz13rule3) =>
% 99.20/13.40 ((
% 99.20/13.40 (woz13rule4) =>
% 99.20/13.40 ((
% 99.20/13.40 (woz1_1) =>
% 99.20/13.40 ((
% 99.20/13.40 (woz1_2) =>
% 99.20/13.40 ((
% 99.20/13.40 (woz1_3) =>
% 99.20/13.40 ((
% 99.20/13.40 (woz1_4) =>
% 99.20/13.40 ((
% 99.20/13.40 (woz1_5) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1all2) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1SetBreln1) =>
% 99.20/13.40 ((
% 99.20/13.40 (choice2fnsingleton) =>
% 99.20/13.40 ((
% 99.20/13.40 (setOfPairsIsBReln1) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1all1) =>
% 99.20/13.40 ((
% 99.20/13.40 (subbreln1) =>
% 99.20/13.40 ((
% 99.20/13.40 (eqbreln1) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1invprop) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1invI) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1invE) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1compprop) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1compI) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1compE) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1compEex) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1unionprop) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1unionIL) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1unionIR) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1unionI) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1unionE) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1unionEcases) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1unionCommutes) =>
% 99.20/13.40 ((
% 99.20/13.40 (woz2Ex) =>
% 99.20/13.40 ((
% 99.20/13.40 (woz2W) =>
% 99.20/13.40 ((
% 99.20/13.40 (woz2A) =>
% 99.20/13.40 ((
% 99.20/13.40 (woz2B) =>
% 99.20/13.40 ((
% 99.20/13.40 (image1Ex) =>
% 99.20/13.40 ((
% 99.20/13.40 (image1Ex1) =>
% 99.20/13.40 ((
% 99.20/13.40 (image1Equiv) =>
% 99.20/13.40 ((
% 99.20/13.40 (image1E) =>
% 99.20/13.40 ((
% 99.20/13.40 (image1I) =>
% 99.20/13.40 ((
% 99.20/13.40 (injFuncInInjFuncSet) =>
% 99.20/13.40 ((
% 99.20/13.40 (injFuncSetFuncIn) =>
% 99.20/13.40 ((
% 99.20/13.40 (injFuncSetFuncInj) =>
% 99.20/13.40 ((
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% 99.20/13.40 (('#B') @ (
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% 99.20/13.40 (
% 99.20/13.40 (
% 99.20/13.40 ('#B') @ (
% 99.20/13.40 (
% 99.20/13.40 ('#B') @ (
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% 99.20/13.40 (
% 99.20/13.40 (
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% 99.20/13.40 (
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% 99.20/13.40 (
% 99.20/13.40 (
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% 99.20/13.40 (
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% 99.20/13.40 (
% 99.20/13.40 (
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% 99.20/13.40 (
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% 99.20/13.40 (
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% 99.20/13.40 (
% 99.20/13.40 (
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% 99.20/13.40 (
% 99.20/13.40 ('#B') @ (
% 99.20/13.40 (
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% 99.20/13.40 surjFuncSet)))))))) @
% 99.20/13.40 (
% 99.20/13.40 (
% 99.20/13.40 ('#B') @ (
% 99.20/13.40 (
% 99.20/13.40 ('#B') @ (
% 99.20/13.40 (
% 99.20/13.40 ('#C') @ in)))) @
% 99.20/13.40 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.20/13.40 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl595])).
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% 99.20/13.40 (((exuI2) =>
% 99.20/13.40 (((inCongP) =>
% 99.20/13.40 (((in__Cong) =>
% 99.20/13.40 (((exuE3u) =>
% 99.20/13.40 (((exu__Cong) =>
% 99.20/13.40 (((setadjoin__Cong) =>
% 99.20/13.40 (((powerset__Cong) =>
% 99.20/13.40 (((setunion__Cong) =>
% 99.20/13.40 (((exuEu) =>
% 99.20/13.40 (((descr__Cong) =>
% 99.20/13.40 (((dsetconstr__Cong) =>
% 99.20/13.40 (((subsetI1) =>
% 99.20/13.40 (((eqimpsubset2) =>
% 99.20/13.40 (((eqimpsubset1) =>
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% 99.20/13.40 (((notequalI2) =>
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% 99.20/13.40 (((powersetI1) =>
% 99.20/13.40 ((
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% 99.20/13.40 ((
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% 99.20/13.40 ((
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% 99.20/13.40 ((
% 99.20/13.40 (sepInPowerset) =>
% 99.20/13.40 ((
% 99.20/13.40 (sepSubset) =>
% 99.20/13.40 ((
% 99.20/13.40 (binunionIL) =>
% 99.20/13.40 ((
% 99.20/13.40 (upairset2IR) =>
% 99.20/13.40 ((
% 99.20/13.40 (binunionIR) =>
% 99.20/13.40 ((
% 99.20/13.40 (binunionEcases) =>
% 99.20/13.40 ((
% 99.20/13.40 (binunionE) =>
% 99.20/13.40 ((
% 99.20/13.40 (binunionLsub) =>
% 99.20/13.40 ((
% 99.20/13.40 (binunionRsub) =>
% 99.20/13.40 ((
% 99.20/13.40 (binintersectI) =>
% 99.20/13.40 ((
% 99.20/13.40 (binintersectSubset5) =>
% 99.20/13.40 ((
% 99.20/13.40 (binintersectEL) =>
% 99.20/13.40 ((
% 99.20/13.40 (binintersectLsub) =>
% 99.20/13.40 ((
% 99.20/13.40 (binintersectSubset2) =>
% 99.20/13.40 ((
% 99.20/13.40 (binintersectSubset3) =>
% 99.20/13.40 ((
% 99.20/13.40 (binintersectER) =>
% 99.20/13.40 ((
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% 99.20/13.40 ((
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% 99.20/13.40 ((
% 99.20/13.40 (binintersectSubset4) =>
% 99.20/13.40 ((
% 99.20/13.40 (binintersectSubset1) =>
% 99.20/13.40 ((
% 99.20/13.40 (bs114d) =>
% 99.20/13.40 ((
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% 99.20/13.40 ((
% 99.20/13.40 (setminusEL) =>
% 99.20/13.40 ((
% 99.20/13.40 (setminusER) =>
% 99.20/13.40 ((
% 99.20/13.40 (setminusSubset2) =>
% 99.20/13.40 ((
% 99.20/13.40 (setminusERneg) =>
% 99.20/13.40 ((
% 99.20/13.40 (setminusELneg) =>
% 99.20/13.40 ((
% 99.20/13.40 (setminusILneg) =>
% 99.20/13.40 ((
% 99.20/13.40 (setminusIRneg) =>
% 99.20/13.40 ((
% 99.20/13.40 (setminusLsub) =>
% 99.20/13.40 ((
% 99.20/13.40 (setminusSubset1) =>
% 99.20/13.40 ((
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% 99.20/13.40 ((
% 99.20/13.40 (symdiffI1) =>
% 99.20/13.40 ((
% 99.20/13.40 (symdiffI2) =>
% 99.20/13.40 ((
% 99.20/13.40 (symdiffIneg1) =>
% 99.20/13.40 ((
% 99.20/13.40 (symdiffIneg2) =>
% 99.20/13.40 ((
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% 99.20/13.40 ((
% 99.20/13.40 (setukpairIL) =>
% 99.20/13.40 ((
% 99.20/13.40 (setukpairIR) =>
% 99.20/13.40 ((
% 99.20/13.40 (kpairiskpair) =>
% 99.20/13.40 ((
% 99.20/13.40 (kpairp) =>
% 99.20/13.40 ((
% 99.20/13.40 (singletonsubset) =>
% 99.20/13.40 ((
% 99.20/13.40 (singletoninpowerset) =>
% 99.20/13.40 ((
% 99.20/13.40 (singletoninpowunion) =>
% 99.20/13.40 ((
% 99.20/13.40 (upairset2E) =>
% 99.20/13.40 ((
% 99.20/13.40 (upairsubunion) =>
% 99.20/13.40 ((
% 99.20/13.40 (upairinpowunion) =>
% 99.20/13.40 ((
% 99.20/13.40 (ubforcartprodlem1) =>
% 99.20/13.40 ((
% 99.20/13.40 (ubforcartprodlem2) =>
% 99.20/13.40 ((
% 99.20/13.40 (ubforcartprodlem3) =>
% 99.20/13.40 ((
% 99.20/13.40 (cartprodpairin) =>
% 99.20/13.40 ((
% 99.20/13.40 (cartprodmempair1) =>
% 99.20/13.40 ((
% 99.20/13.40 (cartprodmempair) =>
% 99.20/13.40 ((
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% 99.20/13.40 ((
% 99.20/13.40 (setunionsingleton1) =>
% 99.20/13.40 ((
% 99.20/13.40 (setunionsingleton2) =>
% 99.20/13.40 ((
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% 99.20/13.40 ((
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% 99.20/13.40 ((
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% 99.20/13.40 ((
% 99.20/13.40 (ex1I2) =>
% 99.20/13.40 ((
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% 99.20/13.40 ((
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% 99.20/13.40 ((
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% 99.20/13.40 ((
% 99.20/13.40 (theprop) =>
% 99.20/13.40 ((
% 99.20/13.40 (kfstpairEq) =>
% 99.20/13.40 ((
% 99.20/13.40 (cartprodfstin) =>
% 99.20/13.40 ((
% 99.20/13.40 (setukpairinjL2) =>
% 99.20/13.40 ((
% 99.20/13.40 (setukpairinjL) =>
% 99.20/13.40 ((
% 99.20/13.40 (setukpairinjR11) =>
% 99.20/13.40 ((
% 99.20/13.40 (setukpairinjR12) =>
% 99.20/13.40 ((
% 99.20/13.40 (setukpairinjR1) =>
% 99.20/13.40 ((
% 99.20/13.40 (upairequniteq) =>
% 99.20/13.40 ((
% 99.20/13.40 (setukpairinjR2) =>
% 99.20/13.40 ((
% 99.20/13.40 (setukpairinjR) =>
% 99.20/13.40 ((
% 99.20/13.40 (ksndsingleton) =>
% 99.20/13.40 ((
% 99.20/13.40 (ksndpairEq) =>
% 99.20/13.40 ((
% 99.20/13.40 (kpairsurjEq) =>
% 99.20/13.40 ((
% 99.20/13.40 (cartprodsndin) =>
% 99.20/13.40 ((
% 99.20/13.40 (cartprodpairmemEL) =>
% 99.20/13.40 ((
% 99.20/13.40 (cartprodpairmemER) =>
% 99.20/13.40 ((
% 99.20/13.40 (cartprodmempaircEq) =>
% 99.20/13.40 ((
% 99.20/13.40 (cartprodfstpairEq) =>
% 99.20/13.40 ((
% 99.20/13.40 (cartprodsndpairEq) =>
% 99.20/13.40 ((
% 99.20/13.40 (cartprodpairsurjEq) =>
% 99.20/13.40 ((
% 99.20/13.40 (dpsetconstrI) =>
% 99.20/13.40 ((
% 99.20/13.40 (dpsetconstrSub) =>
% 99.20/13.40 ((
% 99.20/13.40 (setOfPairsIsBReln) =>
% 99.20/13.40 ((
% 99.20/13.40 (dpsetconstrERa) =>
% 99.20/13.40 ((
% 99.20/13.40 (dpsetconstrEL1) =>
% 99.20/13.40 ((
% 99.20/13.40 (dpsetconstrEL2) =>
% 99.20/13.40 ((
% 99.20/13.40 (dpsetconstrER) =>
% 99.20/13.40 ((
% 99.20/13.40 (funcImageSingleton) =>
% 99.20/13.40 ((
% 99.20/13.40 (apProp) =>
% 99.20/13.40 ((
% 99.20/13.40 (app) =>
% 99.20/13.40 ((
% 99.20/13.40 (infuncsetfunc) =>
% 99.20/13.40 ((
% 99.20/13.40 (ap2p) =>
% 99.20/13.40 ((
% 99.20/13.40 (funcinfuncset) =>
% 99.20/13.40 ((
% 99.20/13.40 (lamProp) =>
% 99.20/13.40 ((
% 99.20/13.40 (lamp) =>
% 99.20/13.40 ((
% 99.20/13.40 (lam2p) =>
% 99.20/13.40 ((
% 99.20/13.40 (brelnall1) =>
% 99.20/13.40 ((
% 99.20/13.40 (brelnall2) =>
% 99.20/13.40 ((
% 99.20/13.40 (ex1E2) =>
% 99.20/13.40 ((
% 99.20/13.40 (funcGraphProp1) =>
% 99.20/13.40 ((
% 99.20/13.40 (funcGraphProp3) =>
% 99.20/13.40 ((
% 99.20/13.40 (funcGraphProp2) =>
% 99.20/13.40 ((
% 99.20/13.40 (funcextLem) =>
% 99.20/13.40 ((
% 99.20/13.40 (funcGraphProp4) =>
% 99.20/13.40 ((
% 99.20/13.40 (subbreln) =>
% 99.20/13.40 ((
% 99.20/13.40 (eqbreln) =>
% 99.20/13.40 ((
% 99.20/13.40 (funcext) =>
% 99.20/13.40 ((
% 99.20/13.40 (funcext2) =>
% 99.20/13.40 ((
% 99.20/13.40 (ap2apEq1) =>
% 99.20/13.40 ((
% 99.20/13.40 (ap2apEq2) =>
% 99.20/13.40 ((
% 99.20/13.40 (beta1) =>
% 99.20/13.40 ((
% 99.20/13.40 (eta1) =>
% 99.20/13.40 ((
% 99.20/13.40 (lam2lamEq) =>
% 99.20/13.40 ((
% 99.20/13.40 (beta2) =>
% 99.20/13.40 ((
% 99.20/13.40 (eta2) =>
% 99.20/13.40 ((
% 99.20/13.40 (iffalseProp1) =>
% 99.20/13.40 ((
% 99.20/13.40 (iffalseProp2) =>
% 99.20/13.40 ((
% 99.20/13.40 (iftrueProp1) =>
% 99.20/13.40 ((
% 99.20/13.40 (iftrueProp2) =>
% 99.20/13.40 ((
% 99.20/13.40 (ifSingleton) =>
% 99.20/13.40 ((
% 99.20/13.40 (ifp) =>
% 99.20/13.40 ((
% 99.20/13.40 (theeq) =>
% 99.20/13.40 ((
% 99.20/13.40 (iftrue) =>
% 99.20/13.40 ((
% 99.20/13.40 (iffalse) =>
% 99.20/13.40 ((
% 99.20/13.40 (iftrueorfalse) =>
% 99.20/13.40 ((
% 99.20/13.40 (binintersectT_lem) =>
% 99.20/13.40 ((
% 99.20/13.40 (binunionT_lem) =>
% 99.20/13.40 ((
% 99.20/13.40 (powersetT_lem) =>
% 99.20/13.40 ((
% 99.20/13.40 (setminusT_lem) =>
% 99.20/13.40 ((
% 99.20/13.40 (complementT_lem) =>
% 99.20/13.40 ((
% 99.20/13.40 (setextT) =>
% 99.20/13.40 ((
% 99.20/13.40 (subsetTI) =>
% 99.20/13.40 ((
% 99.20/13.40 (powersetTI1) =>
% 99.20/13.40 ((
% 99.20/13.40 (powersetTE1) =>
% 99.20/13.40 ((
% 99.20/13.40 (complementTI1) =>
% 99.20/13.40 ((
% 99.20/13.40 (complementTE1) =>
% 99.20/13.40 ((
% 99.20/13.40 (binintersectTELcontra) =>
% 99.20/13.40 ((
% 99.20/13.40 (binintersectTERcontra) =>
% 99.20/13.40 ((
% 99.20/13.40 (contrasubsetT) =>
% 99.20/13.40 ((
% 99.20/13.40 (contrasubsetT1) =>
% 99.20/13.40 ((
% 99.20/13.40 (contrasubsetT2) =>
% 99.20/13.40 ((
% 99.20/13.40 (contrasubsetT3) =>
% 99.20/13.40 ((
% 99.20/13.40 (doubleComplementI1) =>
% 99.20/13.40 ((
% 99.20/13.40 (doubleComplementE1) =>
% 99.20/13.40 ((
% 99.20/13.40 (doubleComplementSub1) =>
% 99.20/13.40 ((
% 99.20/13.40 (doubleComplementSub2) =>
% 99.20/13.40 ((
% 99.20/13.40 (doubleComplementEq) =>
% 99.20/13.40 ((
% 99.20/13.40 (complementTnotintersectT) =>
% 99.20/13.40 ((
% 99.20/13.40 (complementImpComplementIntersect) =>
% 99.20/13.40 ((
% 99.20/13.40 (complementSubsetComplementIntersect) =>
% 99.20/13.40 ((
% 99.20/13.40 (complementInPowersetComplementIntersect) =>
% 99.20/13.40 ((
% 99.20/13.40 (contraSubsetComplement) =>
% 99.20/13.40 ((
% 99.20/13.40 (complementTcontraSubset) =>
% 99.20/13.40 ((
% 99.20/13.40 (binunionTILcontra) =>
% 99.20/13.40 ((
% 99.20/13.40 (binunionTIRcontra) =>
% 99.20/13.40 ((
% 99.20/13.40 (inIntersectImpInUnion) =>
% 99.20/13.40 ((
% 99.20/13.40 (inIntersectImpInUnion2) =>
% 99.20/13.40 ((
% 99.20/13.40 (inIntersectImpInIntersectUnions) =>
% 99.20/13.40 ((
% 99.20/13.40 (intersectInPowersetIntersectUnions) =>
% 99.20/13.40 ((
% 99.20/13.40 (inComplementUnionImpNotIn1) =>
% 99.20/13.40 ((
% 99.20/13.40 (inComplementUnionImpInComplement1) =>
% 99.20/13.40 ((
% 99.20/13.40 (binunionTE) =>
% 99.20/13.40 ((
% 99.20/13.40 (binunionTEcontra) =>
% 99.20/13.40 ((
% 99.20/13.40 (demorgan2a1) =>
% 99.20/13.40 ((
% 99.20/13.40 (complementUnionInPowersetComplement) =>
% 99.20/13.40 ((
% 99.20/13.40 (demorgan2a2) =>
% 99.20/13.40 ((
% 99.20/13.40 (demorgan1a) =>
% 99.20/13.40 ((
% 99.20/13.40 (demorgan1b) =>
% 99.20/13.40 ((
% 99.20/13.40 (demorgan1) =>
% 99.20/13.40 ((
% 99.20/13.40 (demorgan2a) =>
% 99.20/13.40 ((
% 99.20/13.40 (demorgan2b2) =>
% 99.20/13.40 ((
% 99.20/13.40 (demorgan2b) =>
% 99.20/13.40 ((
% 99.20/13.40 (demorgan2) =>
% 99.20/13.40 ((
% 99.20/13.40 (woz13rule0) =>
% 99.20/13.40 ((
% 99.20/13.40 (woz13rule1) =>
% 99.20/13.40 ((
% 99.20/13.40 (woz13rule2) =>
% 99.20/13.40 ((
% 99.20/13.40 (woz13rule3) =>
% 99.20/13.40 ((
% 99.20/13.40 (woz13rule4) =>
% 99.20/13.40 ((
% 99.20/13.40 (woz1_1) =>
% 99.20/13.40 ((
% 99.20/13.40 (woz1_2) =>
% 99.20/13.40 ((
% 99.20/13.40 (woz1_3) =>
% 99.20/13.40 ((
% 99.20/13.40 (woz1_4) =>
% 99.20/13.40 ((
% 99.20/13.40 (woz1_5) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1all2) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1SetBreln1) =>
% 99.20/13.40 ((
% 99.20/13.40 (choice2fnsingleton) =>
% 99.20/13.40 ((
% 99.20/13.40 (setOfPairsIsBReln1) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1all1) =>
% 99.20/13.40 ((
% 99.20/13.40 (subbreln1) =>
% 99.20/13.40 ((
% 99.20/13.40 (eqbreln1) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1invprop) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1invI) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1invE) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1compprop) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1compI) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1compE) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1compEex) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1unionprop) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1unionIL) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1unionIR) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1unionI) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1unionE) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1unionEcases) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1unionCommutes) =>
% 99.20/13.40 ((
% 99.20/13.40 (woz2Ex) =>
% 99.20/13.40 ((
% 99.20/13.40 (woz2W) =>
% 99.20/13.40 ((
% 99.20/13.40 (woz2A) =>
% 99.20/13.40 ((
% 99.20/13.40 (woz2B) =>
% 99.20/13.40 ((
% 99.20/13.40 (image1Ex) =>
% 99.20/13.40 ((
% 99.20/13.40 (image1Ex1) =>
% 99.20/13.40 ((
% 99.20/13.40 (image1Equiv) =>
% 99.20/13.40 ((
% 99.20/13.40 (image1E) =>
% 99.20/13.40 ((
% 99.20/13.40 (image1I) =>
% 99.20/13.40 ((
% 99.20/13.40 (injFuncInInjFuncSet) =>
% 99.20/13.40 ((
% 99.20/13.40 (injFuncSetFuncIn) =>
% 99.20/13.40 ((
% 99.20/13.40 (injFuncSetFuncInj) =>
% 99.20/13.40 ((
% 99.20/13.40 (!!) @ (
% 99.20/13.40 (('#B') @ (
% 99.20/13.40 !!) @
% 99.20/13.40 (
% 99.20/13.40 (
% 99.20/13.40 ('#B') @ (
% 99.20/13.40 (
% 99.20/13.40 ('#B') @ (
% 99.20/13.40 !!))) @
% 99.20/13.40 (
% 99.20/13.40 (
% 99.20/13.40 ('#S') @ (
% 99.20/13.40 (
% 99.20/13.40 ('#B') @ (
% 99.20/13.40 '#S') @
% 99.20/13.40 (
% 99.20/13.40 (
% 99.20/13.40 ('#B') @ (
% 99.20/13.40 (
% 99.20/13.40 ('#B') @ (
% 99.20/13.40 '#S'))) @
% 99.20/13.40 (
% 99.20/13.40 (
% 99.20/13.40 ('#B') @ (
% 99.20/13.40 (
% 99.20/13.40 ('#B') @ (
% 99.20/13.40 (
% 99.20/13.40 ('#B') @ (
% 99.20/13.40 =>))))) @
% 99.20/13.40 (
% 99.20/13.40 (
% 99.20/13.40 ('#B') @ (
% 99.20/13.40 (
% 99.20/13.40 ('#B') @ (
% 99.20/13.40 (
% 99.20/13.40 ('#C') @ in)))) @
% 99.20/13.40 surjFuncSet)))))))) @
% 99.20/13.40 (
% 99.20/13.40 (
% 99.20/13.40 ('#B') @ (
% 99.20/13.40 (
% 99.20/13.40 ('#B') @ (
% 99.20/13.40 (
% 99.20/13.40 ('#C') @ in)))) @
% 99.20/13.40 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.20/13.40 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl606])).
% 99.20/13.40 thf(zip_derived_cl630, plain,
% 99.20/13.40 (~ (((exuI2) =>
% 99.20/13.40 (((inCongP) =>
% 99.20/13.40 (((in__Cong) =>
% 99.20/13.40 (((exuE3u) =>
% 99.20/13.40 (((exu__Cong) =>
% 99.20/13.40 (((setadjoin__Cong) =>
% 99.20/13.40 (((powerset__Cong) =>
% 99.20/13.40 (((setunion__Cong) =>
% 99.20/13.40 (((exuEu) =>
% 99.20/13.40 (((descr__Cong) =>
% 99.20/13.40 (((dsetconstr__Cong) =>
% 99.20/13.40 (((subsetI1) =>
% 99.20/13.40 (((eqimpsubset2) =>
% 99.20/13.40 (((eqimpsubset1) =>
% 99.20/13.40 (((subsetI2) =>
% 99.20/13.40 (((emptysetsubset) =>
% 99.20/13.40 (((subsetE) =>
% 99.20/13.40 (((subsetE2) =>
% 99.20/13.40 (((notsubsetI) =>
% 99.20/13.40 (((notequalI1) =>
% 99.20/13.40 (((notequalI2) =>
% 99.20/13.40 (((subsetRefl) =>
% 99.20/13.40 (((subsetTrans) =>
% 99.20/13.40 (((setadjoinSub) =>
% 99.20/13.40 (((setadjoinSub2) =>
% 99.20/13.40 (((subset2powerset) =>
% 99.20/13.40 (((setextsub) =>
% 99.20/13.40 (((subsetemptysetimpeq) =>
% 99.20/13.40 (((powersetI1) =>
% 99.20/13.40 (((powersetE1) =>
% 99.20/13.40 ((
% 99.20/13.40 (inPowerset) =>
% 99.20/13.40 ((
% 99.20/13.40 (powersetsubset) =>
% 99.20/13.40 ((
% 99.20/13.40 (sepInPowerset) =>
% 99.20/13.40 ((
% 99.20/13.40 (sepSubset) =>
% 99.20/13.40 ((
% 99.20/13.40 (binunionIL) =>
% 99.20/13.40 ((
% 99.20/13.40 (upairset2IR) =>
% 99.20/13.40 ((
% 99.20/13.40 (binunionIR) =>
% 99.20/13.40 ((
% 99.20/13.40 (binunionEcases) =>
% 99.20/13.40 ((
% 99.20/13.40 (binunionE) =>
% 99.20/13.40 ((
% 99.20/13.40 (binunionLsub) =>
% 99.20/13.40 ((
% 99.20/13.40 (binunionRsub) =>
% 99.20/13.40 ((
% 99.20/13.40 (binintersectI) =>
% 99.20/13.40 ((
% 99.20/13.40 (binintersectSubset5) =>
% 99.20/13.40 ((
% 99.20/13.40 (binintersectEL) =>
% 99.20/13.40 ((
% 99.20/13.40 (binintersectLsub) =>
% 99.20/13.40 ((
% 99.20/13.40 (binintersectSubset2) =>
% 99.20/13.40 ((
% 99.20/13.40 (binintersectSubset3) =>
% 99.20/13.40 ((
% 99.20/13.40 (binintersectER) =>
% 99.20/13.40 ((
% 99.20/13.40 (disjointsetsI1) =>
% 99.20/13.40 ((
% 99.20/13.40 (binintersectRsub) =>
% 99.20/13.40 ((
% 99.20/13.40 (binintersectSubset4) =>
% 99.20/13.40 ((
% 99.20/13.40 (binintersectSubset1) =>
% 99.20/13.40 ((
% 99.20/13.40 (bs114d) =>
% 99.20/13.40 ((
% 99.20/13.40 (setminusI) =>
% 99.20/13.40 ((
% 99.20/13.40 (setminusEL) =>
% 99.20/13.40 ((
% 99.20/13.40 (setminusER) =>
% 99.20/13.40 ((
% 99.20/13.40 (setminusSubset2) =>
% 99.20/13.40 ((
% 99.20/13.40 (setminusERneg) =>
% 99.20/13.40 ((
% 99.20/13.40 (setminusELneg) =>
% 99.20/13.40 ((
% 99.20/13.40 (setminusILneg) =>
% 99.20/13.40 ((
% 99.20/13.40 (setminusIRneg) =>
% 99.20/13.40 ((
% 99.20/13.40 (setminusLsub) =>
% 99.20/13.40 ((
% 99.20/13.40 (setminusSubset1) =>
% 99.20/13.40 ((
% 99.20/13.40 (symdiffE) =>
% 99.20/13.40 ((
% 99.20/13.40 (symdiffI1) =>
% 99.20/13.40 ((
% 99.20/13.40 (symdiffI2) =>
% 99.20/13.40 ((
% 99.20/13.40 (symdiffIneg1) =>
% 99.20/13.40 ((
% 99.20/13.40 (symdiffIneg2) =>
% 99.20/13.40 ((
% 99.20/13.40 (secondinupair) =>
% 99.20/13.40 ((
% 99.20/13.40 (setukpairIL) =>
% 99.20/13.40 ((
% 99.20/13.40 (setukpairIR) =>
% 99.20/13.40 ((
% 99.20/13.40 (kpairiskpair) =>
% 99.20/13.40 ((
% 99.20/13.40 (kpairp) =>
% 99.20/13.40 ((
% 99.20/13.40 (singletonsubset) =>
% 99.20/13.40 ((
% 99.20/13.40 (singletoninpowerset) =>
% 99.20/13.40 ((
% 99.20/13.40 (singletoninpowunion) =>
% 99.20/13.40 ((
% 99.20/13.40 (upairset2E) =>
% 99.20/13.40 ((
% 99.20/13.40 (upairsubunion) =>
% 99.20/13.40 ((
% 99.20/13.40 (upairinpowunion) =>
% 99.20/13.40 ((
% 99.20/13.40 (ubforcartprodlem1) =>
% 99.20/13.40 ((
% 99.20/13.40 (ubforcartprodlem2) =>
% 99.20/13.40 ((
% 99.20/13.40 (ubforcartprodlem3) =>
% 99.20/13.40 ((
% 99.20/13.40 (cartprodpairin) =>
% 99.20/13.40 ((
% 99.20/13.40 (cartprodmempair1) =>
% 99.20/13.40 ((
% 99.20/13.40 (cartprodmempair) =>
% 99.20/13.40 ((
% 99.20/13.40 (setunionE2) =>
% 99.20/13.40 ((
% 99.20/13.40 (setunionsingleton1) =>
% 99.20/13.40 ((
% 99.20/13.40 (setunionsingleton2) =>
% 99.20/13.40 ((
% 99.20/13.40 (setunionsingleton) =>
% 99.20/13.40 ((
% 99.20/13.40 (singletonprop) =>
% 99.20/13.40 ((
% 99.20/13.40 (ex1E1) =>
% 99.20/13.40 ((
% 99.20/13.40 (ex1I) =>
% 99.20/13.40 ((
% 99.20/13.40 (ex1I2) =>
% 99.20/13.40 ((
% 99.20/13.40 (singletonsuniq) =>
% 99.20/13.40 ((
% 99.20/13.40 (setukpairinjL1) =>
% 99.20/13.40 ((
% 99.20/13.40 (kfstsingleton) =>
% 99.20/13.40 ((
% 99.20/13.40 (theprop) =>
% 99.20/13.40 ((
% 99.20/13.40 (kfstpairEq) =>
% 99.20/13.40 ((
% 99.20/13.40 (cartprodfstin) =>
% 99.20/13.40 ((
% 99.20/13.40 (setukpairinjL2) =>
% 99.20/13.40 ((
% 99.20/13.40 (setukpairinjL) =>
% 99.20/13.40 ((
% 99.20/13.40 (setukpairinjR11) =>
% 99.20/13.40 ((
% 99.20/13.40 (setukpairinjR12) =>
% 99.20/13.40 ((
% 99.20/13.40 (setukpairinjR1) =>
% 99.20/13.40 ((
% 99.20/13.40 (upairequniteq) =>
% 99.20/13.40 ((
% 99.20/13.40 (setukpairinjR2) =>
% 99.20/13.40 ((
% 99.20/13.40 (setukpairinjR) =>
% 99.20/13.40 ((
% 99.20/13.40 (ksndsingleton) =>
% 99.20/13.40 ((
% 99.20/13.40 (ksndpairEq) =>
% 99.20/13.40 ((
% 99.20/13.40 (kpairsurjEq) =>
% 99.20/13.40 ((
% 99.20/13.40 (cartprodsndin) =>
% 99.20/13.40 ((
% 99.20/13.40 (cartprodpairmemEL) =>
% 99.20/13.40 ((
% 99.20/13.40 (cartprodpairmemER) =>
% 99.20/13.40 ((
% 99.20/13.40 (cartprodmempaircEq) =>
% 99.20/13.40 ((
% 99.20/13.40 (cartprodfstpairEq) =>
% 99.20/13.40 ((
% 99.20/13.40 (cartprodsndpairEq) =>
% 99.20/13.40 ((
% 99.20/13.40 (cartprodpairsurjEq) =>
% 99.20/13.40 ((
% 99.20/13.40 (dpsetconstrI) =>
% 99.20/13.40 ((
% 99.20/13.40 (dpsetconstrSub) =>
% 99.20/13.40 ((
% 99.20/13.40 (setOfPairsIsBReln) =>
% 99.20/13.40 ((
% 99.20/13.40 (dpsetconstrERa) =>
% 99.20/13.40 ((
% 99.20/13.40 (dpsetconstrEL1) =>
% 99.20/13.40 ((
% 99.20/13.40 (dpsetconstrEL2) =>
% 99.20/13.40 ((
% 99.20/13.40 (dpsetconstrER) =>
% 99.20/13.40 ((
% 99.20/13.40 (funcImageSingleton) =>
% 99.20/13.40 ((
% 99.20/13.40 (apProp) =>
% 99.20/13.40 ((
% 99.20/13.40 (app) =>
% 99.20/13.40 ((
% 99.20/13.40 (infuncsetfunc) =>
% 99.20/13.40 ((
% 99.20/13.40 (ap2p) =>
% 99.20/13.40 ((
% 99.20/13.40 (funcinfuncset) =>
% 99.20/13.40 ((
% 99.20/13.40 (lamProp) =>
% 99.20/13.40 ((
% 99.20/13.40 (lamp) =>
% 99.20/13.40 ((
% 99.20/13.40 (lam2p) =>
% 99.20/13.40 ((
% 99.20/13.40 (brelnall1) =>
% 99.20/13.40 ((
% 99.20/13.40 (brelnall2) =>
% 99.20/13.40 ((
% 99.20/13.40 (ex1E2) =>
% 99.20/13.40 ((
% 99.20/13.40 (funcGraphProp1) =>
% 99.20/13.40 ((
% 99.20/13.40 (funcGraphProp3) =>
% 99.20/13.40 ((
% 99.20/13.40 (funcGraphProp2) =>
% 99.20/13.40 ((
% 99.20/13.40 (funcextLem) =>
% 99.20/13.40 ((
% 99.20/13.40 (funcGraphProp4) =>
% 99.20/13.40 ((
% 99.20/13.40 (subbreln) =>
% 99.20/13.40 ((
% 99.20/13.40 (eqbreln) =>
% 99.20/13.40 ((
% 99.20/13.40 (funcext) =>
% 99.20/13.40 ((
% 99.20/13.40 (funcext2) =>
% 99.20/13.40 ((
% 99.20/13.40 (ap2apEq1) =>
% 99.20/13.40 ((
% 99.20/13.40 (ap2apEq2) =>
% 99.20/13.40 ((
% 99.20/13.40 (beta1) =>
% 99.20/13.40 ((
% 99.20/13.40 (eta1) =>
% 99.20/13.40 ((
% 99.20/13.40 (lam2lamEq) =>
% 99.20/13.40 ((
% 99.20/13.40 (beta2) =>
% 99.20/13.40 ((
% 99.20/13.40 (eta2) =>
% 99.20/13.40 ((
% 99.20/13.40 (iffalseProp1) =>
% 99.20/13.40 ((
% 99.20/13.40 (iffalseProp2) =>
% 99.20/13.40 ((
% 99.20/13.40 (iftrueProp1) =>
% 99.20/13.40 ((
% 99.20/13.40 (iftrueProp2) =>
% 99.20/13.40 ((
% 99.20/13.40 (ifSingleton) =>
% 99.20/13.40 ((
% 99.20/13.40 (ifp) =>
% 99.20/13.40 ((
% 99.20/13.40 (theeq) =>
% 99.20/13.40 ((
% 99.20/13.40 (iftrue) =>
% 99.20/13.40 ((
% 99.20/13.40 (iffalse) =>
% 99.20/13.40 ((
% 99.20/13.40 (iftrueorfalse) =>
% 99.20/13.40 ((
% 99.20/13.40 (binintersectT_lem) =>
% 99.20/13.40 ((
% 99.20/13.40 (binunionT_lem) =>
% 99.20/13.40 ((
% 99.20/13.40 (powersetT_lem) =>
% 99.20/13.40 ((
% 99.20/13.40 (setminusT_lem) =>
% 99.20/13.40 ((
% 99.20/13.40 (complementT_lem) =>
% 99.20/13.40 ((
% 99.20/13.40 (setextT) =>
% 99.20/13.40 ((
% 99.20/13.40 (subsetTI) =>
% 99.20/13.40 ((
% 99.20/13.40 (powersetTI1) =>
% 99.20/13.40 ((
% 99.20/13.40 (powersetTE1) =>
% 99.20/13.40 ((
% 99.20/13.40 (complementTI1) =>
% 99.20/13.40 ((
% 99.20/13.40 (complementTE1) =>
% 99.20/13.40 ((
% 99.20/13.40 (binintersectTELcontra) =>
% 99.20/13.40 ((
% 99.20/13.40 (binintersectTERcontra) =>
% 99.20/13.40 ((
% 99.20/13.40 (contrasubsetT) =>
% 99.20/13.40 ((
% 99.20/13.40 (contrasubsetT1) =>
% 99.20/13.40 ((
% 99.20/13.40 (contrasubsetT2) =>
% 99.20/13.40 ((
% 99.20/13.40 (contrasubsetT3) =>
% 99.20/13.40 ((
% 99.20/13.40 (doubleComplementI1) =>
% 99.20/13.40 ((
% 99.20/13.40 (doubleComplementE1) =>
% 99.20/13.40 ((
% 99.20/13.40 (doubleComplementSub1) =>
% 99.20/13.40 ((
% 99.20/13.40 (doubleComplementSub2) =>
% 99.20/13.40 ((
% 99.20/13.40 (doubleComplementEq) =>
% 99.20/13.40 ((
% 99.20/13.40 (complementTnotintersectT) =>
% 99.20/13.40 ((
% 99.20/13.40 (complementImpComplementIntersect) =>
% 99.20/13.40 ((
% 99.20/13.40 (complementSubsetComplementIntersect) =>
% 99.20/13.40 ((
% 99.20/13.40 (complementInPowersetComplementIntersect) =>
% 99.20/13.40 ((
% 99.20/13.40 (contraSubsetComplement) =>
% 99.20/13.40 ((
% 99.20/13.40 (complementTcontraSubset) =>
% 99.20/13.40 ((
% 99.20/13.40 (binunionTILcontra) =>
% 99.20/13.40 ((
% 99.20/13.40 (binunionTIRcontra) =>
% 99.20/13.40 ((
% 99.20/13.40 (inIntersectImpInUnion) =>
% 99.20/13.40 ((
% 99.20/13.40 (inIntersectImpInUnion2) =>
% 99.20/13.40 ((
% 99.20/13.40 (inIntersectImpInIntersectUnions) =>
% 99.20/13.40 ((
% 99.20/13.40 (intersectInPowersetIntersectUnions) =>
% 99.20/13.40 ((
% 99.20/13.40 (inComplementUnionImpNotIn1) =>
% 99.20/13.40 ((
% 99.20/13.40 (inComplementUnionImpInComplement1) =>
% 99.20/13.40 ((
% 99.20/13.40 (binunionTE) =>
% 99.20/13.40 ((
% 99.20/13.40 (binunionTEcontra) =>
% 99.20/13.40 ((
% 99.20/13.40 (demorgan2a1) =>
% 99.20/13.40 ((
% 99.20/13.40 (complementUnionInPowersetComplement) =>
% 99.20/13.40 ((
% 99.20/13.40 (demorgan2a2) =>
% 99.20/13.40 ((
% 99.20/13.40 (demorgan1a) =>
% 99.20/13.40 ((
% 99.20/13.40 (demorgan1b) =>
% 99.20/13.40 ((
% 99.20/13.40 (demorgan1) =>
% 99.20/13.40 ((
% 99.20/13.40 (demorgan2a) =>
% 99.20/13.40 ((
% 99.20/13.40 (demorgan2b2) =>
% 99.20/13.40 ((
% 99.20/13.40 (demorgan2b) =>
% 99.20/13.40 ((
% 99.20/13.40 (demorgan2) =>
% 99.20/13.40 ((
% 99.20/13.40 (woz13rule0) =>
% 99.20/13.40 ((
% 99.20/13.40 (woz13rule1) =>
% 99.20/13.40 ((
% 99.20/13.40 (woz13rule2) =>
% 99.20/13.40 ((
% 99.20/13.40 (woz13rule3) =>
% 99.20/13.40 ((
% 99.20/13.40 (woz13rule4) =>
% 99.20/13.40 ((
% 99.20/13.40 (woz1_1) =>
% 99.20/13.40 ((
% 99.20/13.40 (woz1_2) =>
% 99.20/13.40 ((
% 99.20/13.40 (woz1_3) =>
% 99.20/13.40 ((
% 99.20/13.40 (woz1_4) =>
% 99.20/13.40 ((
% 99.20/13.40 (woz1_5) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1all2) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1SetBreln1) =>
% 99.20/13.40 ((
% 99.20/13.40 (choice2fnsingleton) =>
% 99.20/13.40 ((
% 99.20/13.40 (setOfPairsIsBReln1) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1all1) =>
% 99.20/13.40 ((
% 99.20/13.40 (subbreln1) =>
% 99.20/13.40 ((
% 99.20/13.40 (eqbreln1) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1invprop) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1invI) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1invE) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1compprop) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1compI) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1compE) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1compEex) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1unionprop) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1unionIL) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1unionIR) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1unionI) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1unionE) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1unionEcases) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1unionCommutes) =>
% 99.20/13.40 ((
% 99.20/13.40 (woz2Ex) =>
% 99.20/13.40 ((
% 99.20/13.40 (woz2W) =>
% 99.20/13.40 ((
% 99.20/13.40 (woz2A) =>
% 99.20/13.40 ((
% 99.20/13.40 (woz2B) =>
% 99.20/13.40 ((
% 99.20/13.40 (image1Ex) =>
% 99.20/13.40 ((
% 99.20/13.40 (image1Ex1) =>
% 99.20/13.40 ((
% 99.20/13.40 (image1Equiv) =>
% 99.20/13.40 ((
% 99.20/13.40 (image1E) =>
% 99.20/13.40 ((
% 99.20/13.40 (image1I) =>
% 99.20/13.40 ((
% 99.20/13.40 (injFuncInInjFuncSet) =>
% 99.20/13.40 ((
% 99.20/13.40 (injFuncSetFuncIn) =>
% 99.20/13.40 ((
% 99.20/13.40 (injFuncSetFuncInj) =>
% 99.20/13.40 ((
% 99.20/13.40 (!!) @ (
% 99.20/13.40 (('#B') @ (
% 99.20/13.40 !!) @
% 99.20/13.40 (
% 99.20/13.40 (
% 99.20/13.40 ('#B') @ (
% 99.20/13.40 (
% 99.20/13.40 ('#B') @ (
% 99.20/13.40 !!))) @
% 99.20/13.40 (
% 99.20/13.40 (
% 99.20/13.40 ('#S') @ (
% 99.20/13.40 (
% 99.20/13.40 ('#B') @ (
% 99.20/13.40 '#S') @
% 99.20/13.40 (
% 99.20/13.40 (
% 99.20/13.40 ('#B') @ (
% 99.20/13.40 (
% 99.20/13.40 ('#B') @ (
% 99.20/13.40 '#S'))) @
% 99.20/13.40 (
% 99.20/13.40 (
% 99.20/13.40 ('#B') @ (
% 99.20/13.40 (
% 99.20/13.40 ('#B') @ (
% 99.20/13.40 (
% 99.20/13.40 ('#B') @ (
% 99.20/13.40 =>))))) @
% 99.20/13.40 (
% 99.20/13.40 (
% 99.20/13.40 ('#B') @ (
% 99.20/13.40 (
% 99.20/13.40 ('#B') @ (
% 99.20/13.40 (
% 99.20/13.40 ('#C') @ in)))) @
% 99.20/13.40 surjFuncSet)))))))) @
% 99.20/13.40 (
% 99.20/13.40 (
% 99.20/13.40 ('#B') @ (
% 99.20/13.40 (
% 99.20/13.40 ('#B') @ (
% 99.20/13.40 (
% 99.20/13.40 ('#C') @ in)))) @
% 99.20/13.40 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.20/13.40 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl619])).
% 99.20/13.40 thf(zip_derived_cl640, plain,
% 99.20/13.40 (~ (((inCongP) =>
% 99.20/13.40 (((in__Cong) =>
% 99.20/13.40 (((exuE3u) =>
% 99.20/13.40 (((exu__Cong) =>
% 99.20/13.40 (((setadjoin__Cong) =>
% 99.20/13.40 (((powerset__Cong) =>
% 99.20/13.40 (((setunion__Cong) =>
% 99.20/13.40 (((exuEu) =>
% 99.20/13.40 (((descr__Cong) =>
% 99.20/13.40 (((dsetconstr__Cong) =>
% 99.20/13.40 (((subsetI1) =>
% 99.20/13.40 (((eqimpsubset2) =>
% 99.20/13.40 (((eqimpsubset1) =>
% 99.20/13.40 (((subsetI2) =>
% 99.20/13.40 (((emptysetsubset) =>
% 99.20/13.40 (((subsetE) =>
% 99.20/13.40 (((subsetE2) =>
% 99.20/13.40 (((notsubsetI) =>
% 99.20/13.40 (((notequalI1) =>
% 99.20/13.40 (((notequalI2) =>
% 99.20/13.40 (((subsetRefl) =>
% 99.20/13.40 (((subsetTrans) =>
% 99.20/13.40 (((setadjoinSub) =>
% 99.20/13.40 (((setadjoinSub2) =>
% 99.20/13.40 (((subset2powerset) =>
% 99.20/13.40 (((setextsub) =>
% 99.20/13.40 (((subsetemptysetimpeq) =>
% 99.20/13.40 (((powersetI1) =>
% 99.20/13.40 (((powersetE1) =>
% 99.20/13.40 (((inPowerset) =>
% 99.20/13.40 ((
% 99.20/13.40 (powersetsubset) =>
% 99.20/13.40 ((
% 99.20/13.40 (sepInPowerset) =>
% 99.20/13.40 ((
% 99.20/13.40 (sepSubset) =>
% 99.20/13.40 ((
% 99.20/13.40 (binunionIL) =>
% 99.20/13.40 ((
% 99.20/13.40 (upairset2IR) =>
% 99.20/13.40 ((
% 99.20/13.40 (binunionIR) =>
% 99.20/13.40 ((
% 99.20/13.40 (binunionEcases) =>
% 99.20/13.40 ((
% 99.20/13.40 (binunionE) =>
% 99.20/13.40 ((
% 99.20/13.40 (binunionLsub) =>
% 99.20/13.40 ((
% 99.20/13.40 (binunionRsub) =>
% 99.20/13.40 ((
% 99.20/13.40 (binintersectI) =>
% 99.20/13.40 ((
% 99.20/13.40 (binintersectSubset5) =>
% 99.20/13.40 ((
% 99.20/13.40 (binintersectEL) =>
% 99.20/13.40 ((
% 99.20/13.40 (binintersectLsub) =>
% 99.20/13.40 ((
% 99.20/13.40 (binintersectSubset2) =>
% 99.20/13.40 ((
% 99.20/13.40 (binintersectSubset3) =>
% 99.20/13.40 ((
% 99.20/13.40 (binintersectER) =>
% 99.20/13.40 ((
% 99.20/13.40 (disjointsetsI1) =>
% 99.20/13.40 ((
% 99.20/13.40 (binintersectRsub) =>
% 99.20/13.40 ((
% 99.20/13.40 (binintersectSubset4) =>
% 99.20/13.40 ((
% 99.20/13.40 (binintersectSubset1) =>
% 99.20/13.40 ((
% 99.20/13.40 (bs114d) =>
% 99.20/13.40 ((
% 99.20/13.40 (setminusI) =>
% 99.20/13.40 ((
% 99.20/13.40 (setminusEL) =>
% 99.20/13.40 ((
% 99.20/13.40 (setminusER) =>
% 99.20/13.40 ((
% 99.20/13.40 (setminusSubset2) =>
% 99.20/13.40 ((
% 99.20/13.40 (setminusERneg) =>
% 99.20/13.40 ((
% 99.20/13.40 (setminusELneg) =>
% 99.20/13.40 ((
% 99.20/13.40 (setminusILneg) =>
% 99.20/13.40 ((
% 99.20/13.40 (setminusIRneg) =>
% 99.20/13.40 ((
% 99.20/13.40 (setminusLsub) =>
% 99.20/13.40 ((
% 99.20/13.40 (setminusSubset1) =>
% 99.20/13.40 ((
% 99.20/13.40 (symdiffE) =>
% 99.20/13.40 ((
% 99.20/13.40 (symdiffI1) =>
% 99.20/13.40 ((
% 99.20/13.40 (symdiffI2) =>
% 99.20/13.40 ((
% 99.20/13.40 (symdiffIneg1) =>
% 99.20/13.40 ((
% 99.20/13.40 (symdiffIneg2) =>
% 99.20/13.40 ((
% 99.20/13.40 (secondinupair) =>
% 99.20/13.40 ((
% 99.20/13.40 (setukpairIL) =>
% 99.20/13.40 ((
% 99.20/13.40 (setukpairIR) =>
% 99.20/13.40 ((
% 99.20/13.40 (kpairiskpair) =>
% 99.20/13.40 ((
% 99.20/13.40 (kpairp) =>
% 99.20/13.40 ((
% 99.20/13.40 (singletonsubset) =>
% 99.20/13.40 ((
% 99.20/13.40 (singletoninpowerset) =>
% 99.20/13.40 ((
% 99.20/13.40 (singletoninpowunion) =>
% 99.20/13.40 ((
% 99.20/13.40 (upairset2E) =>
% 99.20/13.40 ((
% 99.20/13.40 (upairsubunion) =>
% 99.20/13.40 ((
% 99.20/13.40 (upairinpowunion) =>
% 99.20/13.40 ((
% 99.20/13.40 (ubforcartprodlem1) =>
% 99.20/13.40 ((
% 99.20/13.40 (ubforcartprodlem2) =>
% 99.20/13.40 ((
% 99.20/13.40 (ubforcartprodlem3) =>
% 99.20/13.40 ((
% 99.20/13.40 (cartprodpairin) =>
% 99.20/13.40 ((
% 99.20/13.40 (cartprodmempair1) =>
% 99.20/13.40 ((
% 99.20/13.40 (cartprodmempair) =>
% 99.20/13.40 ((
% 99.20/13.40 (setunionE2) =>
% 99.20/13.40 ((
% 99.20/13.40 (setunionsingleton1) =>
% 99.20/13.40 ((
% 99.20/13.40 (setunionsingleton2) =>
% 99.20/13.40 ((
% 99.20/13.40 (setunionsingleton) =>
% 99.20/13.40 ((
% 99.20/13.40 (singletonprop) =>
% 99.20/13.40 ((
% 99.20/13.40 (ex1E1) =>
% 99.20/13.40 ((
% 99.20/13.40 (ex1I) =>
% 99.20/13.40 ((
% 99.20/13.40 (ex1I2) =>
% 99.20/13.40 ((
% 99.20/13.40 (singletonsuniq) =>
% 99.20/13.40 ((
% 99.20/13.40 (setukpairinjL1) =>
% 99.20/13.40 ((
% 99.20/13.40 (kfstsingleton) =>
% 99.20/13.40 ((
% 99.20/13.40 (theprop) =>
% 99.20/13.40 ((
% 99.20/13.40 (kfstpairEq) =>
% 99.20/13.40 ((
% 99.20/13.40 (cartprodfstin) =>
% 99.20/13.40 ((
% 99.20/13.40 (setukpairinjL2) =>
% 99.20/13.40 ((
% 99.20/13.40 (setukpairinjL) =>
% 99.20/13.40 ((
% 99.20/13.40 (setukpairinjR11) =>
% 99.20/13.40 ((
% 99.20/13.40 (setukpairinjR12) =>
% 99.20/13.40 ((
% 99.20/13.40 (setukpairinjR1) =>
% 99.20/13.40 ((
% 99.20/13.40 (upairequniteq) =>
% 99.20/13.40 ((
% 99.20/13.40 (setukpairinjR2) =>
% 99.20/13.40 ((
% 99.20/13.40 (setukpairinjR) =>
% 99.20/13.40 ((
% 99.20/13.40 (ksndsingleton) =>
% 99.20/13.40 ((
% 99.20/13.40 (ksndpairEq) =>
% 99.20/13.40 ((
% 99.20/13.40 (kpairsurjEq) =>
% 99.20/13.40 ((
% 99.20/13.40 (cartprodsndin) =>
% 99.20/13.40 ((
% 99.20/13.40 (cartprodpairmemEL) =>
% 99.20/13.40 ((
% 99.20/13.40 (cartprodpairmemER) =>
% 99.20/13.40 ((
% 99.20/13.40 (cartprodmempaircEq) =>
% 99.20/13.40 ((
% 99.20/13.40 (cartprodfstpairEq) =>
% 99.20/13.40 ((
% 99.20/13.40 (cartprodsndpairEq) =>
% 99.20/13.40 ((
% 99.20/13.40 (cartprodpairsurjEq) =>
% 99.20/13.40 ((
% 99.20/13.40 (dpsetconstrI) =>
% 99.20/13.40 ((
% 99.20/13.40 (dpsetconstrSub) =>
% 99.20/13.40 ((
% 99.20/13.40 (setOfPairsIsBReln) =>
% 99.20/13.40 ((
% 99.20/13.40 (dpsetconstrERa) =>
% 99.20/13.40 ((
% 99.20/13.40 (dpsetconstrEL1) =>
% 99.20/13.40 ((
% 99.20/13.40 (dpsetconstrEL2) =>
% 99.20/13.40 ((
% 99.20/13.40 (dpsetconstrER) =>
% 99.20/13.40 ((
% 99.20/13.40 (funcImageSingleton) =>
% 99.20/13.40 ((
% 99.20/13.40 (apProp) =>
% 99.20/13.40 ((
% 99.20/13.40 (app) =>
% 99.20/13.40 ((
% 99.20/13.40 (infuncsetfunc) =>
% 99.20/13.40 ((
% 99.20/13.40 (ap2p) =>
% 99.20/13.40 ((
% 99.20/13.40 (funcinfuncset) =>
% 99.20/13.40 ((
% 99.20/13.40 (lamProp) =>
% 99.20/13.40 ((
% 99.20/13.40 (lamp) =>
% 99.20/13.40 ((
% 99.20/13.40 (lam2p) =>
% 99.20/13.40 ((
% 99.20/13.40 (brelnall1) =>
% 99.20/13.40 ((
% 99.20/13.40 (brelnall2) =>
% 99.20/13.40 ((
% 99.20/13.40 (ex1E2) =>
% 99.20/13.40 ((
% 99.20/13.40 (funcGraphProp1) =>
% 99.20/13.40 ((
% 99.20/13.40 (funcGraphProp3) =>
% 99.20/13.40 ((
% 99.20/13.40 (funcGraphProp2) =>
% 99.20/13.40 ((
% 99.20/13.40 (funcextLem) =>
% 99.20/13.40 ((
% 99.20/13.40 (funcGraphProp4) =>
% 99.20/13.40 ((
% 99.20/13.40 (subbreln) =>
% 99.20/13.40 ((
% 99.20/13.40 (eqbreln) =>
% 99.20/13.40 ((
% 99.20/13.40 (funcext) =>
% 99.20/13.40 ((
% 99.20/13.40 (funcext2) =>
% 99.20/13.40 ((
% 99.20/13.40 (ap2apEq1) =>
% 99.20/13.40 ((
% 99.20/13.40 (ap2apEq2) =>
% 99.20/13.40 ((
% 99.20/13.40 (beta1) =>
% 99.20/13.40 ((
% 99.20/13.40 (eta1) =>
% 99.20/13.40 ((
% 99.20/13.40 (lam2lamEq) =>
% 99.20/13.40 ((
% 99.20/13.40 (beta2) =>
% 99.20/13.40 ((
% 99.20/13.40 (eta2) =>
% 99.20/13.40 ((
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% 99.20/13.40 ((
% 99.20/13.40 (iffalseProp2) =>
% 99.20/13.40 ((
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% 99.20/13.40 ((
% 99.20/13.40 (iftrueProp2) =>
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% 99.20/13.40 (ifSingleton) =>
% 99.20/13.40 ((
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% 99.20/13.40 ((
% 99.20/13.40 (theeq) =>
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% 99.20/13.40 ((
% 99.20/13.40 (setminusT_lem) =>
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% 99.20/13.40 ((
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% 99.20/13.40 ((
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% 99.20/13.40 ((
% 99.20/13.40 (powersetTE1) =>
% 99.20/13.40 ((
% 99.20/13.40 (complementTI1) =>
% 99.20/13.40 ((
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% 99.20/13.40 ((
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% 99.20/13.40 ((
% 99.20/13.40 (binintersectTERcontra) =>
% 99.20/13.40 ((
% 99.20/13.40 (contrasubsetT) =>
% 99.20/13.40 ((
% 99.20/13.40 (contrasubsetT1) =>
% 99.20/13.40 ((
% 99.20/13.40 (contrasubsetT2) =>
% 99.20/13.40 ((
% 99.20/13.40 (contrasubsetT3) =>
% 99.20/13.40 ((
% 99.20/13.40 (doubleComplementI1) =>
% 99.20/13.40 ((
% 99.20/13.40 (doubleComplementE1) =>
% 99.20/13.40 ((
% 99.20/13.40 (doubleComplementSub1) =>
% 99.20/13.40 ((
% 99.20/13.40 (doubleComplementSub2) =>
% 99.20/13.40 ((
% 99.20/13.40 (doubleComplementEq) =>
% 99.20/13.40 ((
% 99.20/13.40 (complementTnotintersectT) =>
% 99.20/13.40 ((
% 99.20/13.40 (complementImpComplementIntersect) =>
% 99.20/13.40 ((
% 99.20/13.40 (complementSubsetComplementIntersect) =>
% 99.20/13.40 ((
% 99.20/13.40 (complementInPowersetComplementIntersect) =>
% 99.20/13.40 ((
% 99.20/13.40 (contraSubsetComplement) =>
% 99.20/13.40 ((
% 99.20/13.40 (complementTcontraSubset) =>
% 99.20/13.40 ((
% 99.20/13.40 (binunionTILcontra) =>
% 99.20/13.40 ((
% 99.20/13.40 (binunionTIRcontra) =>
% 99.20/13.40 ((
% 99.20/13.40 (inIntersectImpInUnion) =>
% 99.20/13.40 ((
% 99.20/13.40 (inIntersectImpInUnion2) =>
% 99.20/13.40 ((
% 99.20/13.40 (inIntersectImpInIntersectUnions) =>
% 99.20/13.40 ((
% 99.20/13.40 (intersectInPowersetIntersectUnions) =>
% 99.20/13.40 ((
% 99.20/13.40 (inComplementUnionImpNotIn1) =>
% 99.20/13.40 ((
% 99.20/13.40 (inComplementUnionImpInComplement1) =>
% 99.20/13.40 ((
% 99.20/13.40 (binunionTE) =>
% 99.20/13.40 ((
% 99.20/13.40 (binunionTEcontra) =>
% 99.20/13.40 ((
% 99.20/13.40 (demorgan2a1) =>
% 99.20/13.40 ((
% 99.20/13.40 (complementUnionInPowersetComplement) =>
% 99.20/13.40 ((
% 99.20/13.40 (demorgan2a2) =>
% 99.20/13.40 ((
% 99.20/13.40 (demorgan1a) =>
% 99.20/13.40 ((
% 99.20/13.40 (demorgan1b) =>
% 99.20/13.40 ((
% 99.20/13.40 (demorgan1) =>
% 99.20/13.40 ((
% 99.20/13.40 (demorgan2a) =>
% 99.20/13.40 ((
% 99.20/13.40 (demorgan2b2) =>
% 99.20/13.40 ((
% 99.20/13.40 (demorgan2b) =>
% 99.20/13.40 ((
% 99.20/13.40 (demorgan2) =>
% 99.20/13.40 ((
% 99.20/13.40 (woz13rule0) =>
% 99.20/13.40 ((
% 99.20/13.40 (woz13rule1) =>
% 99.20/13.40 ((
% 99.20/13.40 (woz13rule2) =>
% 99.20/13.40 ((
% 99.20/13.40 (woz13rule3) =>
% 99.20/13.40 ((
% 99.20/13.40 (woz13rule4) =>
% 99.20/13.40 ((
% 99.20/13.40 (woz1_1) =>
% 99.20/13.40 ((
% 99.20/13.40 (woz1_2) =>
% 99.20/13.40 ((
% 99.20/13.40 (woz1_3) =>
% 99.20/13.40 ((
% 99.20/13.40 (woz1_4) =>
% 99.20/13.40 ((
% 99.20/13.40 (woz1_5) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1all2) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1SetBreln1) =>
% 99.20/13.40 ((
% 99.20/13.40 (choice2fnsingleton) =>
% 99.20/13.40 ((
% 99.20/13.40 (setOfPairsIsBReln1) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1all1) =>
% 99.20/13.40 ((
% 99.20/13.40 (subbreln1) =>
% 99.20/13.40 ((
% 99.20/13.40 (eqbreln1) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1invprop) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1invI) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1invE) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1compprop) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1compI) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1compE) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1compEex) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1unionprop) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1unionIL) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1unionIR) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1unionI) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1unionE) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1unionEcases) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1unionCommutes) =>
% 99.20/13.40 ((
% 99.20/13.40 (woz2Ex) =>
% 99.20/13.40 ((
% 99.20/13.40 (woz2W) =>
% 99.20/13.40 ((
% 99.20/13.40 (woz2A) =>
% 99.20/13.40 ((
% 99.20/13.40 (woz2B) =>
% 99.20/13.40 ((
% 99.20/13.40 (image1Ex) =>
% 99.20/13.40 ((
% 99.20/13.40 (image1Ex1) =>
% 99.20/13.40 ((
% 99.20/13.40 (image1Equiv) =>
% 99.20/13.40 ((
% 99.20/13.40 (image1E) =>
% 99.20/13.40 ((
% 99.20/13.40 (image1I) =>
% 99.20/13.40 ((
% 99.20/13.40 (injFuncInInjFuncSet) =>
% 99.20/13.40 ((
% 99.20/13.40 (injFuncSetFuncIn) =>
% 99.20/13.40 ((
% 99.20/13.40 (injFuncSetFuncInj) =>
% 99.20/13.40 ((
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% 99.20/13.40 (
% 99.20/13.40 (
% 99.20/13.40 ('#B') @ (
% 99.20/13.40 (
% 99.20/13.40 ('#B') @ (
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% 99.20/13.40 (
% 99.20/13.40 (
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% 99.20/13.40 (
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% 99.20/13.40 (
% 99.20/13.40 (
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% 99.20/13.40 (
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% 99.20/13.40 (
% 99.20/13.40 (
% 99.20/13.40 ('#B') @ (
% 99.20/13.40 (
% 99.20/13.40 ('#B') @ (
% 99.20/13.40 (
% 99.20/13.40 ('#B') @ (
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% 99.20/13.40 (
% 99.20/13.40 (
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% 99.20/13.40 (
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% 99.20/13.40 surjFuncSet)))))))) @
% 99.20/13.40 (
% 99.20/13.40 (
% 99.20/13.40 ('#B') @ (
% 99.20/13.40 (
% 99.20/13.40 ('#B') @ (
% 99.20/13.40 (
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% 99.20/13.40 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.20/13.40 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl630])).
% 99.20/13.40 thf(zip_derived_cl650, plain,
% 99.20/13.40 (~ (((in__Cong) =>
% 99.20/13.40 (((exuE3u) =>
% 99.20/13.40 (((exu__Cong) =>
% 99.20/13.40 (((setadjoin__Cong) =>
% 99.20/13.40 (((powerset__Cong) =>
% 99.20/13.40 (((setunion__Cong) =>
% 99.20/13.40 (((exuEu) =>
% 99.20/13.40 (((descr__Cong) =>
% 99.20/13.40 (((dsetconstr__Cong) =>
% 99.20/13.40 (((subsetI1) =>
% 99.20/13.40 (((eqimpsubset2) =>
% 99.20/13.40 (((eqimpsubset1) =>
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% 99.20/13.40 (((subsetE) =>
% 99.20/13.40 (((subsetE2) =>
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% 99.20/13.40 (((notequalI1) =>
% 99.20/13.40 (((notequalI2) =>
% 99.20/13.40 (((subsetRefl) =>
% 99.20/13.40 (((subsetTrans) =>
% 99.20/13.40 (((setadjoinSub) =>
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% 99.20/13.40 ((
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% 99.20/13.40 ((
% 99.20/13.40 (sepSubset) =>
% 99.20/13.40 ((
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% 99.20/13.40 ((
% 99.20/13.40 (upairset2IR) =>
% 99.20/13.40 ((
% 99.20/13.40 (binunionIR) =>
% 99.20/13.40 ((
% 99.20/13.40 (binunionEcases) =>
% 99.20/13.40 ((
% 99.20/13.40 (binunionE) =>
% 99.20/13.40 ((
% 99.20/13.40 (binunionLsub) =>
% 99.20/13.40 ((
% 99.20/13.40 (binunionRsub) =>
% 99.20/13.40 ((
% 99.20/13.40 (binintersectI) =>
% 99.20/13.40 ((
% 99.20/13.40 (binintersectSubset5) =>
% 99.20/13.40 ((
% 99.20/13.40 (binintersectEL) =>
% 99.20/13.40 ((
% 99.20/13.40 (binintersectLsub) =>
% 99.20/13.40 ((
% 99.20/13.40 (binintersectSubset2) =>
% 99.20/13.40 ((
% 99.20/13.40 (binintersectSubset3) =>
% 99.20/13.40 ((
% 99.20/13.40 (binintersectER) =>
% 99.20/13.40 ((
% 99.20/13.40 (disjointsetsI1) =>
% 99.20/13.40 ((
% 99.20/13.40 (binintersectRsub) =>
% 99.20/13.40 ((
% 99.20/13.40 (binintersectSubset4) =>
% 99.20/13.40 ((
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% 99.20/13.40 ((
% 99.20/13.40 (bs114d) =>
% 99.20/13.40 ((
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% 99.20/13.40 ((
% 99.20/13.40 (setminusEL) =>
% 99.20/13.40 ((
% 99.20/13.40 (setminusER) =>
% 99.20/13.40 ((
% 99.20/13.40 (setminusSubset2) =>
% 99.20/13.40 ((
% 99.20/13.40 (setminusERneg) =>
% 99.20/13.40 ((
% 99.20/13.40 (setminusELneg) =>
% 99.20/13.40 ((
% 99.20/13.40 (setminusILneg) =>
% 99.20/13.40 ((
% 99.20/13.40 (setminusIRneg) =>
% 99.20/13.40 ((
% 99.20/13.40 (setminusLsub) =>
% 99.20/13.40 ((
% 99.20/13.40 (setminusSubset1) =>
% 99.20/13.40 ((
% 99.20/13.40 (symdiffE) =>
% 99.20/13.40 ((
% 99.20/13.40 (symdiffI1) =>
% 99.20/13.40 ((
% 99.20/13.40 (symdiffI2) =>
% 99.20/13.40 ((
% 99.20/13.40 (symdiffIneg1) =>
% 99.20/13.40 ((
% 99.20/13.40 (symdiffIneg2) =>
% 99.20/13.40 ((
% 99.20/13.40 (secondinupair) =>
% 99.20/13.40 ((
% 99.20/13.40 (setukpairIL) =>
% 99.20/13.40 ((
% 99.20/13.40 (setukpairIR) =>
% 99.20/13.40 ((
% 99.20/13.40 (kpairiskpair) =>
% 99.20/13.40 ((
% 99.20/13.40 (kpairp) =>
% 99.20/13.40 ((
% 99.20/13.40 (singletonsubset) =>
% 99.20/13.40 ((
% 99.20/13.40 (singletoninpowerset) =>
% 99.20/13.40 ((
% 99.20/13.40 (singletoninpowunion) =>
% 99.20/13.40 ((
% 99.20/13.40 (upairset2E) =>
% 99.20/13.40 ((
% 99.20/13.40 (upairsubunion) =>
% 99.20/13.40 ((
% 99.20/13.40 (upairinpowunion) =>
% 99.20/13.40 ((
% 99.20/13.40 (ubforcartprodlem1) =>
% 99.20/13.40 ((
% 99.20/13.40 (ubforcartprodlem2) =>
% 99.20/13.40 ((
% 99.20/13.40 (ubforcartprodlem3) =>
% 99.20/13.40 ((
% 99.20/13.40 (cartprodpairin) =>
% 99.20/13.40 ((
% 99.20/13.40 (cartprodmempair1) =>
% 99.20/13.40 ((
% 99.20/13.40 (cartprodmempair) =>
% 99.20/13.40 ((
% 99.20/13.40 (setunionE2) =>
% 99.20/13.40 ((
% 99.20/13.40 (setunionsingleton1) =>
% 99.20/13.40 ((
% 99.20/13.40 (setunionsingleton2) =>
% 99.20/13.40 ((
% 99.20/13.40 (setunionsingleton) =>
% 99.20/13.40 ((
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% 99.20/13.40 ((
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% 99.20/13.40 ((
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% 99.20/13.40 ((
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% 99.20/13.40 ((
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% 99.20/13.40 ((
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% 99.20/13.40 ((
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% 99.20/13.40 ((
% 99.20/13.40 (setukpairinjR11) =>
% 99.20/13.40 ((
% 99.20/13.40 (setukpairinjR12) =>
% 99.20/13.40 ((
% 99.20/13.40 (setukpairinjR1) =>
% 99.20/13.40 ((
% 99.20/13.40 (upairequniteq) =>
% 99.20/13.40 ((
% 99.20/13.40 (setukpairinjR2) =>
% 99.20/13.40 ((
% 99.20/13.40 (setukpairinjR) =>
% 99.20/13.40 ((
% 99.20/13.40 (ksndsingleton) =>
% 99.20/13.40 ((
% 99.20/13.40 (ksndpairEq) =>
% 99.20/13.40 ((
% 99.20/13.40 (kpairsurjEq) =>
% 99.20/13.40 ((
% 99.20/13.40 (cartprodsndin) =>
% 99.20/13.40 ((
% 99.20/13.40 (cartprodpairmemEL) =>
% 99.20/13.40 ((
% 99.20/13.40 (cartprodpairmemER) =>
% 99.20/13.40 ((
% 99.20/13.40 (cartprodmempaircEq) =>
% 99.20/13.40 ((
% 99.20/13.40 (cartprodfstpairEq) =>
% 99.20/13.40 ((
% 99.20/13.40 (cartprodsndpairEq) =>
% 99.20/13.40 ((
% 99.20/13.40 (cartprodpairsurjEq) =>
% 99.20/13.40 ((
% 99.20/13.40 (dpsetconstrI) =>
% 99.20/13.40 ((
% 99.20/13.40 (dpsetconstrSub) =>
% 99.20/13.40 ((
% 99.20/13.40 (setOfPairsIsBReln) =>
% 99.20/13.40 ((
% 99.20/13.40 (dpsetconstrERa) =>
% 99.20/13.40 ((
% 99.20/13.40 (dpsetconstrEL1) =>
% 99.20/13.40 ((
% 99.20/13.40 (dpsetconstrEL2) =>
% 99.20/13.40 ((
% 99.20/13.40 (dpsetconstrER) =>
% 99.20/13.40 ((
% 99.20/13.40 (funcImageSingleton) =>
% 99.20/13.40 ((
% 99.20/13.40 (apProp) =>
% 99.20/13.40 ((
% 99.20/13.40 (app) =>
% 99.20/13.40 ((
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% 99.20/13.40 ((
% 99.20/13.40 (ap2p) =>
% 99.20/13.40 ((
% 99.20/13.40 (funcinfuncset) =>
% 99.20/13.40 ((
% 99.20/13.40 (lamProp) =>
% 99.20/13.40 ((
% 99.20/13.40 (lamp) =>
% 99.20/13.40 ((
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% 99.20/13.40 ((
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% 99.20/13.40 ((
% 99.20/13.40 (brelnall2) =>
% 99.20/13.40 ((
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% 99.20/13.40 ((
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% 99.20/13.40 ((
% 99.20/13.40 (funcGraphProp3) =>
% 99.20/13.40 ((
% 99.20/13.40 (funcGraphProp2) =>
% 99.20/13.40 ((
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% 99.20/13.40 ((
% 99.20/13.40 (funcGraphProp4) =>
% 99.20/13.40 ((
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% 99.20/13.40 ((
% 99.20/13.40 (eqbreln) =>
% 99.20/13.40 ((
% 99.20/13.40 (funcext) =>
% 99.20/13.40 ((
% 99.20/13.40 (funcext2) =>
% 99.20/13.40 ((
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% 99.20/13.40 ((
% 99.20/13.40 (ap2apEq2) =>
% 99.20/13.40 ((
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% 99.20/13.40 ((
% 99.20/13.40 (eta1) =>
% 99.20/13.40 ((
% 99.20/13.40 (lam2lamEq) =>
% 99.20/13.40 ((
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% 99.20/13.40 ((
% 99.20/13.40 (eta2) =>
% 99.20/13.40 ((
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% 99.20/13.40 ((
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% 99.20/13.40 ((
% 99.20/13.40 (iftrueProp2) =>
% 99.20/13.40 ((
% 99.20/13.40 (ifSingleton) =>
% 99.20/13.40 ((
% 99.20/13.40 (ifp) =>
% 99.20/13.40 ((
% 99.20/13.40 (theeq) =>
% 99.20/13.40 ((
% 99.20/13.40 (iftrue) =>
% 99.20/13.40 ((
% 99.20/13.40 (iffalse) =>
% 99.20/13.40 ((
% 99.20/13.40 (iftrueorfalse) =>
% 99.20/13.40 ((
% 99.20/13.40 (binintersectT_lem) =>
% 99.20/13.40 ((
% 99.20/13.40 (binunionT_lem) =>
% 99.20/13.40 ((
% 99.20/13.40 (powersetT_lem) =>
% 99.20/13.40 ((
% 99.20/13.40 (setminusT_lem) =>
% 99.20/13.40 ((
% 99.20/13.40 (complementT_lem) =>
% 99.20/13.40 ((
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% 99.20/13.40 ((
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% 99.20/13.40 ((
% 99.20/13.40 (powersetTI1) =>
% 99.20/13.40 ((
% 99.20/13.40 (powersetTE1) =>
% 99.20/13.40 ((
% 99.20/13.40 (complementTI1) =>
% 99.20/13.40 ((
% 99.20/13.40 (complementTE1) =>
% 99.20/13.40 ((
% 99.20/13.40 (binintersectTELcontra) =>
% 99.20/13.40 ((
% 99.20/13.40 (binintersectTERcontra) =>
% 99.20/13.40 ((
% 99.20/13.40 (contrasubsetT) =>
% 99.20/13.40 ((
% 99.20/13.40 (contrasubsetT1) =>
% 99.20/13.40 ((
% 99.20/13.40 (contrasubsetT2) =>
% 99.20/13.40 ((
% 99.20/13.40 (contrasubsetT3) =>
% 99.20/13.40 ((
% 99.20/13.40 (doubleComplementI1) =>
% 99.20/13.40 ((
% 99.20/13.40 (doubleComplementE1) =>
% 99.20/13.40 ((
% 99.20/13.40 (doubleComplementSub1) =>
% 99.20/13.40 ((
% 99.20/13.40 (doubleComplementSub2) =>
% 99.20/13.40 ((
% 99.20/13.40 (doubleComplementEq) =>
% 99.20/13.40 ((
% 99.20/13.40 (complementTnotintersectT) =>
% 99.20/13.40 ((
% 99.20/13.40 (complementImpComplementIntersect) =>
% 99.20/13.40 ((
% 99.20/13.40 (complementSubsetComplementIntersect) =>
% 99.20/13.40 ((
% 99.20/13.40 (complementInPowersetComplementIntersect) =>
% 99.20/13.40 ((
% 99.20/13.40 (contraSubsetComplement) =>
% 99.20/13.40 ((
% 99.20/13.40 (complementTcontraSubset) =>
% 99.20/13.40 ((
% 99.20/13.40 (binunionTILcontra) =>
% 99.20/13.40 ((
% 99.20/13.40 (binunionTIRcontra) =>
% 99.20/13.40 ((
% 99.20/13.40 (inIntersectImpInUnion) =>
% 99.20/13.40 ((
% 99.20/13.40 (inIntersectImpInUnion2) =>
% 99.20/13.40 ((
% 99.20/13.40 (inIntersectImpInIntersectUnions) =>
% 99.20/13.40 ((
% 99.20/13.40 (intersectInPowersetIntersectUnions) =>
% 99.20/13.40 ((
% 99.20/13.40 (inComplementUnionImpNotIn1) =>
% 99.20/13.40 ((
% 99.20/13.40 (inComplementUnionImpInComplement1) =>
% 99.20/13.40 ((
% 99.20/13.40 (binunionTE) =>
% 99.20/13.40 ((
% 99.20/13.40 (binunionTEcontra) =>
% 99.20/13.40 ((
% 99.20/13.40 (demorgan2a1) =>
% 99.20/13.40 ((
% 99.20/13.40 (complementUnionInPowersetComplement) =>
% 99.20/13.40 ((
% 99.20/13.40 (demorgan2a2) =>
% 99.20/13.40 ((
% 99.20/13.40 (demorgan1a) =>
% 99.20/13.40 ((
% 99.20/13.40 (demorgan1b) =>
% 99.20/13.40 ((
% 99.20/13.40 (demorgan1) =>
% 99.20/13.40 ((
% 99.20/13.40 (demorgan2a) =>
% 99.20/13.40 ((
% 99.20/13.40 (demorgan2b2) =>
% 99.20/13.40 ((
% 99.20/13.40 (demorgan2b) =>
% 99.20/13.40 ((
% 99.20/13.40 (demorgan2) =>
% 99.20/13.40 ((
% 99.20/13.40 (woz13rule0) =>
% 99.20/13.40 ((
% 99.20/13.40 (woz13rule1) =>
% 99.20/13.40 ((
% 99.20/13.40 (woz13rule2) =>
% 99.20/13.40 ((
% 99.20/13.40 (woz13rule3) =>
% 99.20/13.40 ((
% 99.20/13.40 (woz13rule4) =>
% 99.20/13.40 ((
% 99.20/13.40 (woz1_1) =>
% 99.20/13.40 ((
% 99.20/13.40 (woz1_2) =>
% 99.20/13.40 ((
% 99.20/13.40 (woz1_3) =>
% 99.20/13.40 ((
% 99.20/13.40 (woz1_4) =>
% 99.20/13.40 ((
% 99.20/13.40 (woz1_5) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1all2) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1SetBreln1) =>
% 99.20/13.40 ((
% 99.20/13.40 (choice2fnsingleton) =>
% 99.20/13.40 ((
% 99.20/13.40 (setOfPairsIsBReln1) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1all1) =>
% 99.20/13.40 ((
% 99.20/13.40 (subbreln1) =>
% 99.20/13.40 ((
% 99.20/13.40 (eqbreln1) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1invprop) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1invI) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1invE) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1compprop) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1compI) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1compE) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1compEex) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1unionprop) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1unionIL) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1unionIR) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1unionI) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1unionE) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1unionEcases) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1unionCommutes) =>
% 99.20/13.40 ((
% 99.20/13.40 (woz2Ex) =>
% 99.20/13.40 ((
% 99.20/13.40 (woz2W) =>
% 99.20/13.40 ((
% 99.20/13.40 (woz2A) =>
% 99.20/13.40 ((
% 99.20/13.40 (woz2B) =>
% 99.20/13.40 ((
% 99.20/13.40 (image1Ex) =>
% 99.20/13.40 ((
% 99.20/13.40 (image1Ex1) =>
% 99.20/13.40 ((
% 99.20/13.40 (image1Equiv) =>
% 99.20/13.40 ((
% 99.20/13.40 (image1E) =>
% 99.20/13.40 ((
% 99.20/13.40 (image1I) =>
% 99.20/13.40 ((
% 99.20/13.40 (injFuncInInjFuncSet) =>
% 99.20/13.40 ((
% 99.20/13.40 (injFuncSetFuncIn) =>
% 99.20/13.40 ((
% 99.20/13.40 (injFuncSetFuncInj) =>
% 99.20/13.40 ((
% 99.20/13.40 (!!) @ (
% 99.20/13.40 (('#B') @ (
% 99.20/13.40 !!) @
% 99.20/13.40 (
% 99.20/13.40 (
% 99.20/13.40 ('#B') @ (
% 99.20/13.40 (
% 99.20/13.40 ('#B') @ (
% 99.20/13.40 !!))) @
% 99.20/13.40 (
% 99.20/13.40 (
% 99.20/13.40 ('#S') @ (
% 99.20/13.40 (
% 99.20/13.40 ('#B') @ (
% 99.20/13.40 '#S') @
% 99.20/13.40 (
% 99.20/13.40 (
% 99.20/13.40 ('#B') @ (
% 99.20/13.40 (
% 99.20/13.40 ('#B') @ (
% 99.20/13.40 '#S'))) @
% 99.20/13.40 (
% 99.20/13.40 (
% 99.20/13.40 ('#B') @ (
% 99.20/13.40 (
% 99.20/13.40 ('#B') @ (
% 99.20/13.40 (
% 99.20/13.40 ('#B') @ (
% 99.20/13.40 =>))))) @
% 99.20/13.40 (
% 99.20/13.40 (
% 99.20/13.40 ('#B') @ (
% 99.20/13.40 (
% 99.20/13.40 ('#B') @ (
% 99.20/13.40 (
% 99.20/13.40 ('#C') @ in)))) @
% 99.20/13.40 surjFuncSet)))))))) @
% 99.20/13.40 (
% 99.20/13.40 (
% 99.20/13.40 ('#B') @ (
% 99.20/13.40 (
% 99.20/13.40 ('#B') @ (
% 99.20/13.40 (
% 99.20/13.40 ('#C') @ in)))) @
% 99.20/13.40 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.20/13.40 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl640])).
% 99.20/13.40 thf(zip_derived_cl660, plain,
% 99.20/13.40 (~ (((exuE3u) =>
% 99.20/13.40 (((exu__Cong) =>
% 99.20/13.40 (((setadjoin__Cong) =>
% 99.20/13.40 (((powerset__Cong) =>
% 99.20/13.40 (((setunion__Cong) =>
% 99.20/13.40 (((exuEu) =>
% 99.20/13.40 (((descr__Cong) =>
% 99.20/13.40 (((dsetconstr__Cong) =>
% 99.20/13.40 (((subsetI1) =>
% 99.20/13.40 (((eqimpsubset2) =>
% 99.20/13.40 (((eqimpsubset1) =>
% 99.20/13.40 (((subsetI2) =>
% 99.20/13.40 (((emptysetsubset) =>
% 99.20/13.40 (((subsetE) =>
% 99.20/13.40 (((subsetE2) =>
% 99.20/13.40 (((notsubsetI) =>
% 99.20/13.40 (((notequalI1) =>
% 99.20/13.40 (((notequalI2) =>
% 99.20/13.40 (((subsetRefl) =>
% 99.20/13.40 (((subsetTrans) =>
% 99.20/13.40 (((setadjoinSub) =>
% 99.20/13.40 (((setadjoinSub2) =>
% 99.20/13.40 (((subset2powerset) =>
% 99.20/13.40 (((setextsub) =>
% 99.20/13.40 (((subsetemptysetimpeq) =>
% 99.20/13.40 (((powersetI1) =>
% 99.20/13.40 (((powersetE1) =>
% 99.20/13.40 (((inPowerset) =>
% 99.20/13.40 (((powersetsubset) =>
% 99.20/13.40 (((sepInPowerset) =>
% 99.20/13.40 ((
% 99.20/13.40 (sepSubset) =>
% 99.20/13.40 ((
% 99.20/13.40 (binunionIL) =>
% 99.20/13.40 ((
% 99.20/13.40 (upairset2IR) =>
% 99.20/13.40 ((
% 99.20/13.40 (binunionIR) =>
% 99.20/13.40 ((
% 99.20/13.40 (binunionEcases) =>
% 99.20/13.40 ((
% 99.20/13.40 (binunionE) =>
% 99.20/13.40 ((
% 99.20/13.40 (binunionLsub) =>
% 99.20/13.40 ((
% 99.20/13.40 (binunionRsub) =>
% 99.20/13.40 ((
% 99.20/13.40 (binintersectI) =>
% 99.20/13.40 ((
% 99.20/13.40 (binintersectSubset5) =>
% 99.20/13.40 ((
% 99.20/13.40 (binintersectEL) =>
% 99.20/13.40 ((
% 99.20/13.40 (binintersectLsub) =>
% 99.20/13.40 ((
% 99.20/13.40 (binintersectSubset2) =>
% 99.20/13.40 ((
% 99.20/13.40 (binintersectSubset3) =>
% 99.20/13.40 ((
% 99.20/13.40 (binintersectER) =>
% 99.20/13.40 ((
% 99.20/13.40 (disjointsetsI1) =>
% 99.20/13.40 ((
% 99.20/13.40 (binintersectRsub) =>
% 99.20/13.40 ((
% 99.20/13.40 (binintersectSubset4) =>
% 99.20/13.40 ((
% 99.20/13.40 (binintersectSubset1) =>
% 99.20/13.40 ((
% 99.20/13.40 (bs114d) =>
% 99.20/13.40 ((
% 99.20/13.40 (setminusI) =>
% 99.20/13.40 ((
% 99.20/13.40 (setminusEL) =>
% 99.20/13.40 ((
% 99.20/13.40 (setminusER) =>
% 99.20/13.40 ((
% 99.20/13.40 (setminusSubset2) =>
% 99.20/13.40 ((
% 99.20/13.40 (setminusERneg) =>
% 99.20/13.40 ((
% 99.20/13.40 (setminusELneg) =>
% 99.20/13.40 ((
% 99.20/13.40 (setminusILneg) =>
% 99.20/13.40 ((
% 99.20/13.40 (setminusIRneg) =>
% 99.20/13.40 ((
% 99.20/13.40 (setminusLsub) =>
% 99.20/13.40 ((
% 99.20/13.40 (setminusSubset1) =>
% 99.20/13.40 ((
% 99.20/13.40 (symdiffE) =>
% 99.20/13.40 ((
% 99.20/13.40 (symdiffI1) =>
% 99.20/13.40 ((
% 99.20/13.40 (symdiffI2) =>
% 99.20/13.40 ((
% 99.20/13.40 (symdiffIneg1) =>
% 99.20/13.40 ((
% 99.20/13.40 (symdiffIneg2) =>
% 99.20/13.40 ((
% 99.20/13.40 (secondinupair) =>
% 99.20/13.40 ((
% 99.20/13.40 (setukpairIL) =>
% 99.20/13.40 ((
% 99.20/13.40 (setukpairIR) =>
% 99.20/13.40 ((
% 99.20/13.40 (kpairiskpair) =>
% 99.20/13.40 ((
% 99.20/13.40 (kpairp) =>
% 99.20/13.40 ((
% 99.20/13.40 (singletonsubset) =>
% 99.20/13.40 ((
% 99.20/13.40 (singletoninpowerset) =>
% 99.20/13.40 ((
% 99.20/13.40 (singletoninpowunion) =>
% 99.20/13.40 ((
% 99.20/13.40 (upairset2E) =>
% 99.20/13.40 ((
% 99.20/13.40 (upairsubunion) =>
% 99.20/13.40 ((
% 99.20/13.40 (upairinpowunion) =>
% 99.20/13.40 ((
% 99.20/13.40 (ubforcartprodlem1) =>
% 99.20/13.40 ((
% 99.20/13.40 (ubforcartprodlem2) =>
% 99.20/13.40 ((
% 99.20/13.40 (ubforcartprodlem3) =>
% 99.20/13.40 ((
% 99.20/13.40 (cartprodpairin) =>
% 99.20/13.40 ((
% 99.20/13.40 (cartprodmempair1) =>
% 99.20/13.40 ((
% 99.20/13.40 (cartprodmempair) =>
% 99.20/13.40 ((
% 99.20/13.40 (setunionE2) =>
% 99.20/13.40 ((
% 99.20/13.40 (setunionsingleton1) =>
% 99.20/13.40 ((
% 99.20/13.40 (setunionsingleton2) =>
% 99.20/13.40 ((
% 99.20/13.40 (setunionsingleton) =>
% 99.20/13.40 ((
% 99.20/13.40 (singletonprop) =>
% 99.20/13.40 ((
% 99.20/13.40 (ex1E1) =>
% 99.20/13.40 ((
% 99.20/13.40 (ex1I) =>
% 99.20/13.40 ((
% 99.20/13.40 (ex1I2) =>
% 99.20/13.40 ((
% 99.20/13.40 (singletonsuniq) =>
% 99.20/13.40 ((
% 99.20/13.40 (setukpairinjL1) =>
% 99.20/13.40 ((
% 99.20/13.40 (kfstsingleton) =>
% 99.20/13.40 ((
% 99.20/13.40 (theprop) =>
% 99.20/13.40 ((
% 99.20/13.40 (kfstpairEq) =>
% 99.20/13.40 ((
% 99.20/13.40 (cartprodfstin) =>
% 99.20/13.40 ((
% 99.20/13.40 (setukpairinjL2) =>
% 99.20/13.40 ((
% 99.20/13.40 (setukpairinjL) =>
% 99.20/13.40 ((
% 99.20/13.40 (setukpairinjR11) =>
% 99.20/13.40 ((
% 99.20/13.40 (setukpairinjR12) =>
% 99.20/13.40 ((
% 99.20/13.40 (setukpairinjR1) =>
% 99.20/13.40 ((
% 99.20/13.40 (upairequniteq) =>
% 99.20/13.40 ((
% 99.20/13.40 (setukpairinjR2) =>
% 99.20/13.40 ((
% 99.20/13.40 (setukpairinjR) =>
% 99.20/13.40 ((
% 99.20/13.40 (ksndsingleton) =>
% 99.20/13.40 ((
% 99.20/13.40 (ksndpairEq) =>
% 99.20/13.40 ((
% 99.20/13.40 (kpairsurjEq) =>
% 99.20/13.40 ((
% 99.20/13.40 (cartprodsndin) =>
% 99.20/13.40 ((
% 99.20/13.40 (cartprodpairmemEL) =>
% 99.20/13.40 ((
% 99.20/13.40 (cartprodpairmemER) =>
% 99.20/13.40 ((
% 99.20/13.40 (cartprodmempaircEq) =>
% 99.20/13.40 ((
% 99.20/13.40 (cartprodfstpairEq) =>
% 99.20/13.40 ((
% 99.20/13.40 (cartprodsndpairEq) =>
% 99.20/13.40 ((
% 99.20/13.40 (cartprodpairsurjEq) =>
% 99.20/13.40 ((
% 99.20/13.40 (dpsetconstrI) =>
% 99.20/13.40 ((
% 99.20/13.40 (dpsetconstrSub) =>
% 99.20/13.40 ((
% 99.20/13.40 (setOfPairsIsBReln) =>
% 99.20/13.40 ((
% 99.20/13.40 (dpsetconstrERa) =>
% 99.20/13.40 ((
% 99.20/13.40 (dpsetconstrEL1) =>
% 99.20/13.40 ((
% 99.20/13.40 (dpsetconstrEL2) =>
% 99.20/13.40 ((
% 99.20/13.40 (dpsetconstrER) =>
% 99.20/13.40 ((
% 99.20/13.40 (funcImageSingleton) =>
% 99.20/13.40 ((
% 99.20/13.40 (apProp) =>
% 99.20/13.40 ((
% 99.20/13.40 (app) =>
% 99.20/13.40 ((
% 99.20/13.40 (infuncsetfunc) =>
% 99.20/13.40 ((
% 99.20/13.40 (ap2p) =>
% 99.20/13.40 ((
% 99.20/13.40 (funcinfuncset) =>
% 99.20/13.40 ((
% 99.20/13.40 (lamProp) =>
% 99.20/13.40 ((
% 99.20/13.40 (lamp) =>
% 99.20/13.40 ((
% 99.20/13.40 (lam2p) =>
% 99.20/13.40 ((
% 99.20/13.40 (brelnall1) =>
% 99.20/13.40 ((
% 99.20/13.40 (brelnall2) =>
% 99.20/13.40 ((
% 99.20/13.40 (ex1E2) =>
% 99.20/13.40 ((
% 99.20/13.40 (funcGraphProp1) =>
% 99.20/13.40 ((
% 99.20/13.40 (funcGraphProp3) =>
% 99.20/13.40 ((
% 99.20/13.40 (funcGraphProp2) =>
% 99.20/13.40 ((
% 99.20/13.40 (funcextLem) =>
% 99.20/13.40 ((
% 99.20/13.40 (funcGraphProp4) =>
% 99.20/13.40 ((
% 99.20/13.40 (subbreln) =>
% 99.20/13.40 ((
% 99.20/13.40 (eqbreln) =>
% 99.20/13.40 ((
% 99.20/13.40 (funcext) =>
% 99.20/13.40 ((
% 99.20/13.40 (funcext2) =>
% 99.20/13.40 ((
% 99.20/13.40 (ap2apEq1) =>
% 99.20/13.40 ((
% 99.20/13.40 (ap2apEq2) =>
% 99.20/13.40 ((
% 99.20/13.40 (beta1) =>
% 99.20/13.40 ((
% 99.20/13.40 (eta1) =>
% 99.20/13.40 ((
% 99.20/13.40 (lam2lamEq) =>
% 99.20/13.40 ((
% 99.20/13.40 (beta2) =>
% 99.20/13.40 ((
% 99.20/13.40 (eta2) =>
% 99.20/13.40 ((
% 99.20/13.40 (iffalseProp1) =>
% 99.20/13.40 ((
% 99.20/13.40 (iffalseProp2) =>
% 99.20/13.40 ((
% 99.20/13.40 (iftrueProp1) =>
% 99.20/13.40 ((
% 99.20/13.40 (iftrueProp2) =>
% 99.20/13.40 ((
% 99.20/13.40 (ifSingleton) =>
% 99.20/13.40 ((
% 99.20/13.40 (ifp) =>
% 99.20/13.40 ((
% 99.20/13.40 (theeq) =>
% 99.20/13.40 ((
% 99.20/13.40 (iftrue) =>
% 99.20/13.40 ((
% 99.20/13.40 (iffalse) =>
% 99.20/13.40 ((
% 99.20/13.40 (iftrueorfalse) =>
% 99.20/13.40 ((
% 99.20/13.40 (binintersectT_lem) =>
% 99.20/13.40 ((
% 99.20/13.40 (binunionT_lem) =>
% 99.20/13.40 ((
% 99.20/13.40 (powersetT_lem) =>
% 99.20/13.40 ((
% 99.20/13.40 (setminusT_lem) =>
% 99.20/13.40 ((
% 99.20/13.40 (complementT_lem) =>
% 99.20/13.40 ((
% 99.20/13.40 (setextT) =>
% 99.20/13.40 ((
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% 99.20/13.40 ((
% 99.20/13.40 (powersetTI1) =>
% 99.20/13.40 ((
% 99.20/13.40 (powersetTE1) =>
% 99.20/13.40 ((
% 99.20/13.40 (complementTI1) =>
% 99.20/13.40 ((
% 99.20/13.40 (complementTE1) =>
% 99.20/13.40 ((
% 99.20/13.40 (binintersectTELcontra) =>
% 99.20/13.40 ((
% 99.20/13.40 (binintersectTERcontra) =>
% 99.20/13.40 ((
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% 99.20/13.40 ((
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% 99.20/13.40 ((
% 99.20/13.40 (contrasubsetT2) =>
% 99.20/13.40 ((
% 99.20/13.40 (contrasubsetT3) =>
% 99.20/13.40 ((
% 99.20/13.40 (doubleComplementI1) =>
% 99.20/13.40 ((
% 99.20/13.40 (doubleComplementE1) =>
% 99.20/13.40 ((
% 99.20/13.40 (doubleComplementSub1) =>
% 99.20/13.40 ((
% 99.20/13.40 (doubleComplementSub2) =>
% 99.20/13.40 ((
% 99.20/13.40 (doubleComplementEq) =>
% 99.20/13.40 ((
% 99.20/13.40 (complementTnotintersectT) =>
% 99.20/13.40 ((
% 99.20/13.40 (complementImpComplementIntersect) =>
% 99.20/13.40 ((
% 99.20/13.40 (complementSubsetComplementIntersect) =>
% 99.20/13.40 ((
% 99.20/13.40 (complementInPowersetComplementIntersect) =>
% 99.20/13.40 ((
% 99.20/13.40 (contraSubsetComplement) =>
% 99.20/13.40 ((
% 99.20/13.40 (complementTcontraSubset) =>
% 99.20/13.40 ((
% 99.20/13.40 (binunionTILcontra) =>
% 99.20/13.40 ((
% 99.20/13.40 (binunionTIRcontra) =>
% 99.20/13.40 ((
% 99.20/13.40 (inIntersectImpInUnion) =>
% 99.20/13.40 ((
% 99.20/13.40 (inIntersectImpInUnion2) =>
% 99.20/13.40 ((
% 99.20/13.40 (inIntersectImpInIntersectUnions) =>
% 99.20/13.40 ((
% 99.20/13.40 (intersectInPowersetIntersectUnions) =>
% 99.20/13.40 ((
% 99.20/13.40 (inComplementUnionImpNotIn1) =>
% 99.20/13.40 ((
% 99.20/13.40 (inComplementUnionImpInComplement1) =>
% 99.20/13.40 ((
% 99.20/13.40 (binunionTE) =>
% 99.20/13.40 ((
% 99.20/13.40 (binunionTEcontra) =>
% 99.20/13.40 ((
% 99.20/13.40 (demorgan2a1) =>
% 99.20/13.40 ((
% 99.20/13.40 (complementUnionInPowersetComplement) =>
% 99.20/13.40 ((
% 99.20/13.40 (demorgan2a2) =>
% 99.20/13.40 ((
% 99.20/13.40 (demorgan1a) =>
% 99.20/13.40 ((
% 99.20/13.40 (demorgan1b) =>
% 99.20/13.40 ((
% 99.20/13.40 (demorgan1) =>
% 99.20/13.40 ((
% 99.20/13.40 (demorgan2a) =>
% 99.20/13.40 ((
% 99.20/13.40 (demorgan2b2) =>
% 99.20/13.40 ((
% 99.20/13.40 (demorgan2b) =>
% 99.20/13.40 ((
% 99.20/13.40 (demorgan2) =>
% 99.20/13.40 ((
% 99.20/13.40 (woz13rule0) =>
% 99.20/13.40 ((
% 99.20/13.40 (woz13rule1) =>
% 99.20/13.40 ((
% 99.20/13.40 (woz13rule2) =>
% 99.20/13.40 ((
% 99.20/13.40 (woz13rule3) =>
% 99.20/13.40 ((
% 99.20/13.40 (woz13rule4) =>
% 99.20/13.40 ((
% 99.20/13.40 (woz1_1) =>
% 99.20/13.40 ((
% 99.20/13.40 (woz1_2) =>
% 99.20/13.40 ((
% 99.20/13.40 (woz1_3) =>
% 99.20/13.40 ((
% 99.20/13.40 (woz1_4) =>
% 99.20/13.40 ((
% 99.20/13.40 (woz1_5) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1all2) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1SetBreln1) =>
% 99.20/13.40 ((
% 99.20/13.40 (choice2fnsingleton) =>
% 99.20/13.40 ((
% 99.20/13.40 (setOfPairsIsBReln1) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1all1) =>
% 99.20/13.40 ((
% 99.20/13.40 (subbreln1) =>
% 99.20/13.40 ((
% 99.20/13.40 (eqbreln1) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1invprop) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1invI) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1invE) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1compprop) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1compI) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1compE) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1compEex) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1unionprop) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1unionIL) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1unionIR) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1unionI) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1unionE) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1unionEcases) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1unionCommutes) =>
% 99.20/13.40 ((
% 99.20/13.40 (woz2Ex) =>
% 99.20/13.40 ((
% 99.20/13.40 (woz2W) =>
% 99.20/13.40 ((
% 99.20/13.40 (woz2A) =>
% 99.20/13.40 ((
% 99.20/13.40 (woz2B) =>
% 99.20/13.40 ((
% 99.20/13.40 (image1Ex) =>
% 99.20/13.40 ((
% 99.20/13.40 (image1Ex1) =>
% 99.20/13.40 ((
% 99.20/13.40 (image1Equiv) =>
% 99.20/13.40 ((
% 99.20/13.40 (image1E) =>
% 99.20/13.40 ((
% 99.20/13.40 (image1I) =>
% 99.20/13.40 ((
% 99.20/13.40 (injFuncInInjFuncSet) =>
% 99.20/13.40 ((
% 99.20/13.40 (injFuncSetFuncIn) =>
% 99.20/13.40 ((
% 99.20/13.40 (injFuncSetFuncInj) =>
% 99.20/13.40 ((
% 99.20/13.40 (!!) @ (
% 99.20/13.40 (('#B') @ (
% 99.20/13.40 !!) @
% 99.20/13.40 (
% 99.20/13.40 (
% 99.20/13.40 ('#B') @ (
% 99.20/13.40 (
% 99.20/13.40 ('#B') @ (
% 99.20/13.40 !!))) @
% 99.20/13.40 (
% 99.20/13.40 (
% 99.20/13.40 ('#S') @ (
% 99.20/13.40 (
% 99.20/13.40 ('#B') @ (
% 99.20/13.40 '#S') @
% 99.20/13.40 (
% 99.20/13.40 (
% 99.20/13.40 ('#B') @ (
% 99.20/13.40 (
% 99.20/13.40 ('#B') @ (
% 99.20/13.40 '#S'))) @
% 99.20/13.40 (
% 99.20/13.40 (
% 99.20/13.40 ('#B') @ (
% 99.20/13.40 (
% 99.20/13.40 ('#B') @ (
% 99.20/13.40 (
% 99.20/13.40 ('#B') @ (
% 99.20/13.40 =>))))) @
% 99.20/13.40 (
% 99.20/13.40 (
% 99.20/13.40 ('#B') @ (
% 99.20/13.40 (
% 99.20/13.40 ('#B') @ (
% 99.20/13.40 (
% 99.20/13.40 ('#C') @ in)))) @
% 99.20/13.40 surjFuncSet)))))))) @
% 99.20/13.40 (
% 99.20/13.40 (
% 99.20/13.40 ('#B') @ (
% 99.20/13.40 (
% 99.20/13.40 ('#B') @ (
% 99.20/13.40 (
% 99.20/13.40 ('#C') @ in)))) @
% 99.20/13.40 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.20/13.40 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl650])).
% 99.20/13.40 thf(zip_derived_cl672, plain,
% 99.20/13.40 (~ (((exu__Cong) =>
% 99.20/13.40 (((setadjoin__Cong) =>
% 99.20/13.40 (((powerset__Cong) =>
% 99.20/13.40 (((setunion__Cong) =>
% 99.20/13.40 (((exuEu) =>
% 99.20/13.40 (((descr__Cong) =>
% 99.20/13.40 (((dsetconstr__Cong) =>
% 99.20/13.40 (((subsetI1) =>
% 99.20/13.40 (((eqimpsubset2) =>
% 99.20/13.40 (((eqimpsubset1) =>
% 99.20/13.40 (((subsetI2) =>
% 99.20/13.40 (((emptysetsubset) =>
% 99.20/13.40 (((subsetE) =>
% 99.20/13.40 (((subsetE2) =>
% 99.20/13.40 (((notsubsetI) =>
% 99.20/13.40 (((notequalI1) =>
% 99.20/13.40 (((notequalI2) =>
% 99.20/13.40 (((subsetRefl) =>
% 99.20/13.40 (((subsetTrans) =>
% 99.20/13.40 (((setadjoinSub) =>
% 99.20/13.40 (((setadjoinSub2) =>
% 99.20/13.40 (((subset2powerset) =>
% 99.20/13.40 (((setextsub) =>
% 99.20/13.40 (((subsetemptysetimpeq) =>
% 99.20/13.40 (((powersetI1) =>
% 99.20/13.40 (((powersetE1) =>
% 99.20/13.40 (((inPowerset) =>
% 99.20/13.40 (((powersetsubset) =>
% 99.20/13.40 (((sepInPowerset) =>
% 99.20/13.40 (((sepSubset) =>
% 99.20/13.40 ((
% 99.20/13.40 (binunionIL) =>
% 99.20/13.40 ((
% 99.20/13.40 (upairset2IR) =>
% 99.20/13.40 ((
% 99.20/13.40 (binunionIR) =>
% 99.20/13.40 ((
% 99.20/13.40 (binunionEcases) =>
% 99.20/13.40 ((
% 99.20/13.40 (binunionE) =>
% 99.20/13.40 ((
% 99.20/13.40 (binunionLsub) =>
% 99.20/13.40 ((
% 99.20/13.40 (binunionRsub) =>
% 99.20/13.40 ((
% 99.20/13.40 (binintersectI) =>
% 99.20/13.40 ((
% 99.20/13.40 (binintersectSubset5) =>
% 99.20/13.40 ((
% 99.20/13.40 (binintersectEL) =>
% 99.20/13.40 ((
% 99.20/13.40 (binintersectLsub) =>
% 99.20/13.40 ((
% 99.20/13.40 (binintersectSubset2) =>
% 99.20/13.40 ((
% 99.20/13.40 (binintersectSubset3) =>
% 99.20/13.40 ((
% 99.20/13.40 (binintersectER) =>
% 99.20/13.40 ((
% 99.20/13.40 (disjointsetsI1) =>
% 99.20/13.40 ((
% 99.20/13.40 (binintersectRsub) =>
% 99.20/13.40 ((
% 99.20/13.40 (binintersectSubset4) =>
% 99.20/13.40 ((
% 99.20/13.40 (binintersectSubset1) =>
% 99.20/13.40 ((
% 99.20/13.40 (bs114d) =>
% 99.20/13.40 ((
% 99.20/13.40 (setminusI) =>
% 99.20/13.40 ((
% 99.20/13.40 (setminusEL) =>
% 99.20/13.40 ((
% 99.20/13.40 (setminusER) =>
% 99.20/13.40 ((
% 99.20/13.40 (setminusSubset2) =>
% 99.20/13.40 ((
% 99.20/13.40 (setminusERneg) =>
% 99.20/13.40 ((
% 99.20/13.40 (setminusELneg) =>
% 99.20/13.40 ((
% 99.20/13.40 (setminusILneg) =>
% 99.20/13.40 ((
% 99.20/13.40 (setminusIRneg) =>
% 99.20/13.40 ((
% 99.20/13.40 (setminusLsub) =>
% 99.20/13.40 ((
% 99.20/13.40 (setminusSubset1) =>
% 99.20/13.40 ((
% 99.20/13.40 (symdiffE) =>
% 99.20/13.40 ((
% 99.20/13.40 (symdiffI1) =>
% 99.20/13.40 ((
% 99.20/13.40 (symdiffI2) =>
% 99.20/13.40 ((
% 99.20/13.40 (symdiffIneg1) =>
% 99.20/13.40 ((
% 99.20/13.40 (symdiffIneg2) =>
% 99.20/13.40 ((
% 99.20/13.40 (secondinupair) =>
% 99.20/13.40 ((
% 99.20/13.40 (setukpairIL) =>
% 99.20/13.40 ((
% 99.20/13.40 (setukpairIR) =>
% 99.20/13.40 ((
% 99.20/13.40 (kpairiskpair) =>
% 99.20/13.40 ((
% 99.20/13.40 (kpairp) =>
% 99.20/13.40 ((
% 99.20/13.40 (singletonsubset) =>
% 99.20/13.40 ((
% 99.20/13.40 (singletoninpowerset) =>
% 99.20/13.40 ((
% 99.20/13.40 (singletoninpowunion) =>
% 99.20/13.40 ((
% 99.20/13.40 (upairset2E) =>
% 99.20/13.40 ((
% 99.20/13.40 (upairsubunion) =>
% 99.20/13.40 ((
% 99.20/13.40 (upairinpowunion) =>
% 99.20/13.40 ((
% 99.20/13.40 (ubforcartprodlem1) =>
% 99.20/13.40 ((
% 99.20/13.40 (ubforcartprodlem2) =>
% 99.20/13.40 ((
% 99.20/13.40 (ubforcartprodlem3) =>
% 99.20/13.40 ((
% 99.20/13.40 (cartprodpairin) =>
% 99.20/13.40 ((
% 99.20/13.40 (cartprodmempair1) =>
% 99.20/13.40 ((
% 99.20/13.40 (cartprodmempair) =>
% 99.20/13.40 ((
% 99.20/13.40 (setunionE2) =>
% 99.20/13.40 ((
% 99.20/13.40 (setunionsingleton1) =>
% 99.20/13.40 ((
% 99.20/13.40 (setunionsingleton2) =>
% 99.20/13.40 ((
% 99.20/13.40 (setunionsingleton) =>
% 99.20/13.40 ((
% 99.20/13.40 (singletonprop) =>
% 99.20/13.40 ((
% 99.20/13.40 (ex1E1) =>
% 99.20/13.40 ((
% 99.20/13.40 (ex1I) =>
% 99.20/13.40 ((
% 99.20/13.40 (ex1I2) =>
% 99.20/13.40 ((
% 99.20/13.40 (singletonsuniq) =>
% 99.20/13.40 ((
% 99.20/13.40 (setukpairinjL1) =>
% 99.20/13.40 ((
% 99.20/13.40 (kfstsingleton) =>
% 99.20/13.40 ((
% 99.20/13.40 (theprop) =>
% 99.20/13.40 ((
% 99.20/13.40 (kfstpairEq) =>
% 99.20/13.40 ((
% 99.20/13.40 (cartprodfstin) =>
% 99.20/13.40 ((
% 99.20/13.40 (setukpairinjL2) =>
% 99.20/13.40 ((
% 99.20/13.40 (setukpairinjL) =>
% 99.20/13.40 ((
% 99.20/13.40 (setukpairinjR11) =>
% 99.20/13.40 ((
% 99.20/13.40 (setukpairinjR12) =>
% 99.20/13.40 ((
% 99.20/13.40 (setukpairinjR1) =>
% 99.20/13.40 ((
% 99.20/13.40 (upairequniteq) =>
% 99.20/13.40 ((
% 99.20/13.40 (setukpairinjR2) =>
% 99.20/13.40 ((
% 99.20/13.40 (setukpairinjR) =>
% 99.20/13.40 ((
% 99.20/13.40 (ksndsingleton) =>
% 99.20/13.40 ((
% 99.20/13.40 (ksndpairEq) =>
% 99.20/13.40 ((
% 99.20/13.40 (kpairsurjEq) =>
% 99.20/13.40 ((
% 99.20/13.40 (cartprodsndin) =>
% 99.20/13.40 ((
% 99.20/13.40 (cartprodpairmemEL) =>
% 99.20/13.40 ((
% 99.20/13.40 (cartprodpairmemER) =>
% 99.20/13.40 ((
% 99.20/13.40 (cartprodmempaircEq) =>
% 99.20/13.40 ((
% 99.20/13.40 (cartprodfstpairEq) =>
% 99.20/13.40 ((
% 99.20/13.40 (cartprodsndpairEq) =>
% 99.20/13.40 ((
% 99.20/13.40 (cartprodpairsurjEq) =>
% 99.20/13.40 ((
% 99.20/13.40 (dpsetconstrI) =>
% 99.20/13.40 ((
% 99.20/13.40 (dpsetconstrSub) =>
% 99.20/13.40 ((
% 99.20/13.40 (setOfPairsIsBReln) =>
% 99.20/13.40 ((
% 99.20/13.40 (dpsetconstrERa) =>
% 99.20/13.40 ((
% 99.20/13.40 (dpsetconstrEL1) =>
% 99.20/13.40 ((
% 99.20/13.40 (dpsetconstrEL2) =>
% 99.20/13.40 ((
% 99.20/13.40 (dpsetconstrER) =>
% 99.20/13.40 ((
% 99.20/13.40 (funcImageSingleton) =>
% 99.20/13.40 ((
% 99.20/13.40 (apProp) =>
% 99.20/13.40 ((
% 99.20/13.40 (app) =>
% 99.20/13.40 ((
% 99.20/13.40 (infuncsetfunc) =>
% 99.20/13.40 ((
% 99.20/13.40 (ap2p) =>
% 99.20/13.40 ((
% 99.20/13.40 (funcinfuncset) =>
% 99.20/13.40 ((
% 99.20/13.40 (lamProp) =>
% 99.20/13.40 ((
% 99.20/13.40 (lamp) =>
% 99.20/13.40 ((
% 99.20/13.40 (lam2p) =>
% 99.20/13.40 ((
% 99.20/13.40 (brelnall1) =>
% 99.20/13.40 ((
% 99.20/13.40 (brelnall2) =>
% 99.20/13.40 ((
% 99.20/13.40 (ex1E2) =>
% 99.20/13.40 ((
% 99.20/13.40 (funcGraphProp1) =>
% 99.20/13.40 ((
% 99.20/13.40 (funcGraphProp3) =>
% 99.20/13.40 ((
% 99.20/13.40 (funcGraphProp2) =>
% 99.20/13.40 ((
% 99.20/13.40 (funcextLem) =>
% 99.20/13.40 ((
% 99.20/13.40 (funcGraphProp4) =>
% 99.20/13.40 ((
% 99.20/13.40 (subbreln) =>
% 99.20/13.40 ((
% 99.20/13.40 (eqbreln) =>
% 99.20/13.40 ((
% 99.20/13.40 (funcext) =>
% 99.20/13.40 ((
% 99.20/13.40 (funcext2) =>
% 99.20/13.40 ((
% 99.20/13.40 (ap2apEq1) =>
% 99.20/13.40 ((
% 99.20/13.40 (ap2apEq2) =>
% 99.20/13.40 ((
% 99.20/13.40 (beta1) =>
% 99.20/13.40 ((
% 99.20/13.40 (eta1) =>
% 99.20/13.40 ((
% 99.20/13.40 (lam2lamEq) =>
% 99.20/13.40 ((
% 99.20/13.40 (beta2) =>
% 99.20/13.40 ((
% 99.20/13.40 (eta2) =>
% 99.20/13.40 ((
% 99.20/13.40 (iffalseProp1) =>
% 99.20/13.40 ((
% 99.20/13.40 (iffalseProp2) =>
% 99.20/13.40 ((
% 99.20/13.40 (iftrueProp1) =>
% 99.20/13.40 ((
% 99.20/13.40 (iftrueProp2) =>
% 99.20/13.40 ((
% 99.20/13.40 (ifSingleton) =>
% 99.20/13.40 ((
% 99.20/13.40 (ifp) =>
% 99.20/13.40 ((
% 99.20/13.40 (theeq) =>
% 99.20/13.40 ((
% 99.20/13.40 (iftrue) =>
% 99.20/13.40 ((
% 99.20/13.40 (iffalse) =>
% 99.20/13.40 ((
% 99.20/13.40 (iftrueorfalse) =>
% 99.20/13.40 ((
% 99.20/13.40 (binintersectT_lem) =>
% 99.20/13.40 ((
% 99.20/13.40 (binunionT_lem) =>
% 99.20/13.40 ((
% 99.20/13.40 (powersetT_lem) =>
% 99.20/13.40 ((
% 99.20/13.40 (setminusT_lem) =>
% 99.20/13.40 ((
% 99.20/13.40 (complementT_lem) =>
% 99.20/13.40 ((
% 99.20/13.40 (setextT) =>
% 99.20/13.40 ((
% 99.20/13.40 (subsetTI) =>
% 99.20/13.40 ((
% 99.20/13.40 (powersetTI1) =>
% 99.20/13.40 ((
% 99.20/13.40 (powersetTE1) =>
% 99.20/13.40 ((
% 99.20/13.40 (complementTI1) =>
% 99.20/13.40 ((
% 99.20/13.40 (complementTE1) =>
% 99.20/13.40 ((
% 99.20/13.40 (binintersectTELcontra) =>
% 99.20/13.40 ((
% 99.20/13.40 (binintersectTERcontra) =>
% 99.20/13.40 ((
% 99.20/13.40 (contrasubsetT) =>
% 99.20/13.40 ((
% 99.20/13.40 (contrasubsetT1) =>
% 99.20/13.40 ((
% 99.20/13.40 (contrasubsetT2) =>
% 99.20/13.40 ((
% 99.20/13.40 (contrasubsetT3) =>
% 99.20/13.40 ((
% 99.20/13.40 (doubleComplementI1) =>
% 99.20/13.40 ((
% 99.20/13.40 (doubleComplementE1) =>
% 99.20/13.40 ((
% 99.20/13.40 (doubleComplementSub1) =>
% 99.20/13.40 ((
% 99.20/13.40 (doubleComplementSub2) =>
% 99.20/13.40 ((
% 99.20/13.40 (doubleComplementEq) =>
% 99.20/13.40 ((
% 99.20/13.40 (complementTnotintersectT) =>
% 99.20/13.40 ((
% 99.20/13.40 (complementImpComplementIntersect) =>
% 99.20/13.40 ((
% 99.20/13.40 (complementSubsetComplementIntersect) =>
% 99.20/13.40 ((
% 99.20/13.40 (complementInPowersetComplementIntersect) =>
% 99.20/13.40 ((
% 99.20/13.40 (contraSubsetComplement) =>
% 99.20/13.40 ((
% 99.20/13.40 (complementTcontraSubset) =>
% 99.20/13.40 ((
% 99.20/13.40 (binunionTILcontra) =>
% 99.20/13.40 ((
% 99.20/13.40 (binunionTIRcontra) =>
% 99.20/13.40 ((
% 99.20/13.40 (inIntersectImpInUnion) =>
% 99.20/13.40 ((
% 99.20/13.40 (inIntersectImpInUnion2) =>
% 99.20/13.40 ((
% 99.20/13.40 (inIntersectImpInIntersectUnions) =>
% 99.20/13.40 ((
% 99.20/13.40 (intersectInPowersetIntersectUnions) =>
% 99.20/13.40 ((
% 99.20/13.40 (inComplementUnionImpNotIn1) =>
% 99.20/13.40 ((
% 99.20/13.40 (inComplementUnionImpInComplement1) =>
% 99.20/13.40 ((
% 99.20/13.40 (binunionTE) =>
% 99.20/13.40 ((
% 99.20/13.40 (binunionTEcontra) =>
% 99.20/13.40 ((
% 99.20/13.40 (demorgan2a1) =>
% 99.20/13.40 ((
% 99.20/13.40 (complementUnionInPowersetComplement) =>
% 99.20/13.40 ((
% 99.20/13.40 (demorgan2a2) =>
% 99.20/13.40 ((
% 99.20/13.40 (demorgan1a) =>
% 99.20/13.40 ((
% 99.20/13.40 (demorgan1b) =>
% 99.20/13.40 ((
% 99.20/13.40 (demorgan1) =>
% 99.20/13.40 ((
% 99.20/13.40 (demorgan2a) =>
% 99.20/13.40 ((
% 99.20/13.40 (demorgan2b2) =>
% 99.20/13.40 ((
% 99.20/13.40 (demorgan2b) =>
% 99.20/13.40 ((
% 99.20/13.40 (demorgan2) =>
% 99.20/13.40 ((
% 99.20/13.40 (woz13rule0) =>
% 99.20/13.40 ((
% 99.20/13.40 (woz13rule1) =>
% 99.20/13.40 ((
% 99.20/13.40 (woz13rule2) =>
% 99.20/13.40 ((
% 99.20/13.40 (woz13rule3) =>
% 99.20/13.40 ((
% 99.20/13.40 (woz13rule4) =>
% 99.20/13.40 ((
% 99.20/13.40 (woz1_1) =>
% 99.20/13.40 ((
% 99.20/13.40 (woz1_2) =>
% 99.20/13.40 ((
% 99.20/13.40 (woz1_3) =>
% 99.20/13.40 ((
% 99.20/13.40 (woz1_4) =>
% 99.20/13.40 ((
% 99.20/13.40 (woz1_5) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1all2) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1SetBreln1) =>
% 99.20/13.40 ((
% 99.20/13.40 (choice2fnsingleton) =>
% 99.20/13.40 ((
% 99.20/13.40 (setOfPairsIsBReln1) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1all1) =>
% 99.20/13.40 ((
% 99.20/13.40 (subbreln1) =>
% 99.20/13.40 ((
% 99.20/13.40 (eqbreln1) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1invprop) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1invI) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1invE) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1compprop) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1compI) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1compE) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1compEex) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1unionprop) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1unionIL) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1unionIR) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1unionI) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1unionE) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1unionEcases) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1unionCommutes) =>
% 99.20/13.40 ((
% 99.20/13.40 (woz2Ex) =>
% 99.20/13.40 ((
% 99.20/13.40 (woz2W) =>
% 99.20/13.40 ((
% 99.20/13.40 (woz2A) =>
% 99.20/13.40 ((
% 99.20/13.40 (woz2B) =>
% 99.20/13.40 ((
% 99.20/13.40 (image1Ex) =>
% 99.20/13.40 ((
% 99.20/13.40 (image1Ex1) =>
% 99.20/13.40 ((
% 99.20/13.40 (image1Equiv) =>
% 99.20/13.40 ((
% 99.20/13.40 (image1E) =>
% 99.20/13.40 ((
% 99.20/13.40 (image1I) =>
% 99.20/13.40 ((
% 99.20/13.40 (injFuncInInjFuncSet) =>
% 99.20/13.40 ((
% 99.20/13.40 (injFuncSetFuncIn) =>
% 99.20/13.40 ((
% 99.20/13.40 (injFuncSetFuncInj) =>
% 99.20/13.40 ((
% 99.20/13.40 (!!) @ (
% 99.20/13.40 (('#B') @ (
% 99.20/13.40 !!) @
% 99.20/13.40 (
% 99.20/13.40 (
% 99.20/13.40 ('#B') @ (
% 99.20/13.40 (
% 99.20/13.40 ('#B') @ (
% 99.20/13.40 !!))) @
% 99.20/13.40 (
% 99.20/13.40 (
% 99.20/13.40 ('#S') @ (
% 99.20/13.40 (
% 99.20/13.40 ('#B') @ (
% 99.20/13.40 '#S') @
% 99.20/13.40 (
% 99.20/13.40 (
% 99.20/13.40 ('#B') @ (
% 99.20/13.40 (
% 99.20/13.40 ('#B') @ (
% 99.20/13.40 '#S'))) @
% 99.20/13.40 (
% 99.20/13.40 (
% 99.20/13.40 ('#B') @ (
% 99.20/13.40 (
% 99.20/13.40 ('#B') @ (
% 99.20/13.40 (
% 99.20/13.40 ('#B') @ (
% 99.20/13.40 =>))))) @
% 99.20/13.40 (
% 99.20/13.40 (
% 99.20/13.40 ('#B') @ (
% 99.20/13.40 (
% 99.20/13.40 ('#B') @ (
% 99.20/13.40 (
% 99.20/13.40 ('#C') @ in)))) @
% 99.20/13.40 surjFuncSet)))))))) @
% 99.20/13.40 (
% 99.20/13.40 (
% 99.20/13.40 ('#B') @ (
% 99.20/13.40 (
% 99.20/13.40 ('#B') @ (
% 99.20/13.40 (
% 99.20/13.40 ('#C') @ in)))) @
% 99.20/13.40 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.20/13.40 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl660])).
% 99.20/13.40 thf(zip_derived_cl685, plain,
% 99.20/13.40 (~ (((setadjoin__Cong) =>
% 99.20/13.40 (((powerset__Cong) =>
% 99.20/13.40 (((setunion__Cong) =>
% 99.20/13.40 (((exuEu) =>
% 99.20/13.40 (((descr__Cong) =>
% 99.20/13.40 (((dsetconstr__Cong) =>
% 99.20/13.40 (((subsetI1) =>
% 99.20/13.40 (((eqimpsubset2) =>
% 99.20/13.40 (((eqimpsubset1) =>
% 99.20/13.40 (((subsetI2) =>
% 99.20/13.40 (((emptysetsubset) =>
% 99.20/13.40 (((subsetE) =>
% 99.20/13.40 (((subsetE2) =>
% 99.20/13.40 (((notsubsetI) =>
% 99.20/13.40 (((notequalI1) =>
% 99.20/13.40 (((notequalI2) =>
% 99.20/13.40 (((subsetRefl) =>
% 99.20/13.40 (((subsetTrans) =>
% 99.20/13.40 (((setadjoinSub) =>
% 99.20/13.40 (((setadjoinSub2) =>
% 99.20/13.40 (((subset2powerset) =>
% 99.20/13.40 (((setextsub) =>
% 99.20/13.40 (((subsetemptysetimpeq) =>
% 99.20/13.40 (((powersetI1) =>
% 99.20/13.40 (((powersetE1) =>
% 99.20/13.40 (((inPowerset) =>
% 99.20/13.40 (((powersetsubset) =>
% 99.20/13.40 (((sepInPowerset) =>
% 99.20/13.40 (((sepSubset) =>
% 99.20/13.40 (((binunionIL) =>
% 99.20/13.40 ((
% 99.20/13.40 (upairset2IR) =>
% 99.20/13.40 ((
% 99.20/13.40 (binunionIR) =>
% 99.20/13.40 ((
% 99.20/13.40 (binunionEcases) =>
% 99.20/13.40 ((
% 99.20/13.40 (binunionE) =>
% 99.20/13.40 ((
% 99.20/13.40 (binunionLsub) =>
% 99.20/13.40 ((
% 99.20/13.40 (binunionRsub) =>
% 99.20/13.40 ((
% 99.20/13.40 (binintersectI) =>
% 99.20/13.40 ((
% 99.20/13.40 (binintersectSubset5) =>
% 99.20/13.40 ((
% 99.20/13.40 (binintersectEL) =>
% 99.20/13.40 ((
% 99.20/13.40 (binintersectLsub) =>
% 99.20/13.40 ((
% 99.20/13.40 (binintersectSubset2) =>
% 99.20/13.40 ((
% 99.20/13.40 (binintersectSubset3) =>
% 99.20/13.40 ((
% 99.20/13.40 (binintersectER) =>
% 99.20/13.40 ((
% 99.20/13.40 (disjointsetsI1) =>
% 99.20/13.40 ((
% 99.20/13.40 (binintersectRsub) =>
% 99.20/13.40 ((
% 99.20/13.40 (binintersectSubset4) =>
% 99.20/13.40 ((
% 99.20/13.40 (binintersectSubset1) =>
% 99.20/13.40 ((
% 99.20/13.40 (bs114d) =>
% 99.20/13.40 ((
% 99.20/13.40 (setminusI) =>
% 99.20/13.40 ((
% 99.20/13.40 (setminusEL) =>
% 99.20/13.40 ((
% 99.20/13.40 (setminusER) =>
% 99.20/13.40 ((
% 99.20/13.40 (setminusSubset2) =>
% 99.20/13.40 ((
% 99.20/13.40 (setminusERneg) =>
% 99.20/13.40 ((
% 99.20/13.40 (setminusELneg) =>
% 99.20/13.40 ((
% 99.20/13.40 (setminusILneg) =>
% 99.20/13.40 ((
% 99.20/13.40 (setminusIRneg) =>
% 99.20/13.40 ((
% 99.20/13.40 (setminusLsub) =>
% 99.20/13.40 ((
% 99.20/13.40 (setminusSubset1) =>
% 99.20/13.40 ((
% 99.20/13.40 (symdiffE) =>
% 99.20/13.40 ((
% 99.20/13.40 (symdiffI1) =>
% 99.20/13.40 ((
% 99.20/13.40 (symdiffI2) =>
% 99.20/13.40 ((
% 99.20/13.40 (symdiffIneg1) =>
% 99.20/13.40 ((
% 99.20/13.40 (symdiffIneg2) =>
% 99.20/13.40 ((
% 99.20/13.40 (secondinupair) =>
% 99.20/13.40 ((
% 99.20/13.40 (setukpairIL) =>
% 99.20/13.40 ((
% 99.20/13.40 (setukpairIR) =>
% 99.20/13.40 ((
% 99.20/13.40 (kpairiskpair) =>
% 99.20/13.40 ((
% 99.20/13.40 (kpairp) =>
% 99.20/13.40 ((
% 99.20/13.40 (singletonsubset) =>
% 99.20/13.40 ((
% 99.20/13.40 (singletoninpowerset) =>
% 99.20/13.40 ((
% 99.20/13.40 (singletoninpowunion) =>
% 99.20/13.40 ((
% 99.20/13.40 (upairset2E) =>
% 99.20/13.40 ((
% 99.20/13.40 (upairsubunion) =>
% 99.20/13.40 ((
% 99.20/13.40 (upairinpowunion) =>
% 99.20/13.40 ((
% 99.20/13.40 (ubforcartprodlem1) =>
% 99.20/13.40 ((
% 99.20/13.40 (ubforcartprodlem2) =>
% 99.20/13.40 ((
% 99.20/13.40 (ubforcartprodlem3) =>
% 99.20/13.40 ((
% 99.20/13.40 (cartprodpairin) =>
% 99.20/13.40 ((
% 99.20/13.40 (cartprodmempair1) =>
% 99.20/13.40 ((
% 99.20/13.40 (cartprodmempair) =>
% 99.20/13.40 ((
% 99.20/13.40 (setunionE2) =>
% 99.20/13.40 ((
% 99.20/13.40 (setunionsingleton1) =>
% 99.20/13.40 ((
% 99.20/13.40 (setunionsingleton2) =>
% 99.20/13.40 ((
% 99.20/13.40 (setunionsingleton) =>
% 99.20/13.40 ((
% 99.20/13.40 (singletonprop) =>
% 99.20/13.40 ((
% 99.20/13.40 (ex1E1) =>
% 99.20/13.40 ((
% 99.20/13.40 (ex1I) =>
% 99.20/13.40 ((
% 99.20/13.40 (ex1I2) =>
% 99.20/13.40 ((
% 99.20/13.40 (singletonsuniq) =>
% 99.20/13.40 ((
% 99.20/13.40 (setukpairinjL1) =>
% 99.20/13.40 ((
% 99.20/13.40 (kfstsingleton) =>
% 99.20/13.40 ((
% 99.20/13.40 (theprop) =>
% 99.20/13.40 ((
% 99.20/13.40 (kfstpairEq) =>
% 99.20/13.40 ((
% 99.20/13.40 (cartprodfstin) =>
% 99.20/13.40 ((
% 99.20/13.40 (setukpairinjL2) =>
% 99.20/13.40 ((
% 99.20/13.40 (setukpairinjL) =>
% 99.20/13.40 ((
% 99.20/13.40 (setukpairinjR11) =>
% 99.20/13.40 ((
% 99.20/13.40 (setukpairinjR12) =>
% 99.20/13.40 ((
% 99.20/13.40 (setukpairinjR1) =>
% 99.20/13.40 ((
% 99.20/13.40 (upairequniteq) =>
% 99.20/13.40 ((
% 99.20/13.40 (setukpairinjR2) =>
% 99.20/13.40 ((
% 99.20/13.40 (setukpairinjR) =>
% 99.20/13.40 ((
% 99.20/13.40 (ksndsingleton) =>
% 99.20/13.40 ((
% 99.20/13.40 (ksndpairEq) =>
% 99.20/13.40 ((
% 99.20/13.40 (kpairsurjEq) =>
% 99.20/13.40 ((
% 99.20/13.40 (cartprodsndin) =>
% 99.20/13.40 ((
% 99.20/13.40 (cartprodpairmemEL) =>
% 99.20/13.40 ((
% 99.20/13.40 (cartprodpairmemER) =>
% 99.20/13.40 ((
% 99.20/13.40 (cartprodmempaircEq) =>
% 99.20/13.40 ((
% 99.20/13.40 (cartprodfstpairEq) =>
% 99.20/13.40 ((
% 99.20/13.40 (cartprodsndpairEq) =>
% 99.20/13.40 ((
% 99.20/13.40 (cartprodpairsurjEq) =>
% 99.20/13.40 ((
% 99.20/13.40 (dpsetconstrI) =>
% 99.20/13.40 ((
% 99.20/13.40 (dpsetconstrSub) =>
% 99.20/13.40 ((
% 99.20/13.40 (setOfPairsIsBReln) =>
% 99.20/13.40 ((
% 99.20/13.40 (dpsetconstrERa) =>
% 99.20/13.40 ((
% 99.20/13.40 (dpsetconstrEL1) =>
% 99.20/13.40 ((
% 99.20/13.40 (dpsetconstrEL2) =>
% 99.20/13.40 ((
% 99.20/13.40 (dpsetconstrER) =>
% 99.20/13.40 ((
% 99.20/13.40 (funcImageSingleton) =>
% 99.20/13.40 ((
% 99.20/13.40 (apProp) =>
% 99.20/13.40 ((
% 99.20/13.40 (app) =>
% 99.20/13.40 ((
% 99.20/13.40 (infuncsetfunc) =>
% 99.20/13.40 ((
% 99.20/13.40 (ap2p) =>
% 99.20/13.40 ((
% 99.20/13.40 (funcinfuncset) =>
% 99.20/13.40 ((
% 99.20/13.40 (lamProp) =>
% 99.20/13.40 ((
% 99.20/13.40 (lamp) =>
% 99.20/13.40 ((
% 99.20/13.40 (lam2p) =>
% 99.20/13.40 ((
% 99.20/13.40 (brelnall1) =>
% 99.20/13.40 ((
% 99.20/13.40 (brelnall2) =>
% 99.20/13.40 ((
% 99.20/13.40 (ex1E2) =>
% 99.20/13.40 ((
% 99.20/13.40 (funcGraphProp1) =>
% 99.20/13.40 ((
% 99.20/13.40 (funcGraphProp3) =>
% 99.20/13.40 ((
% 99.20/13.40 (funcGraphProp2) =>
% 99.20/13.40 ((
% 99.20/13.40 (funcextLem) =>
% 99.20/13.40 ((
% 99.20/13.40 (funcGraphProp4) =>
% 99.20/13.40 ((
% 99.20/13.40 (subbreln) =>
% 99.20/13.40 ((
% 99.20/13.40 (eqbreln) =>
% 99.20/13.40 ((
% 99.20/13.40 (funcext) =>
% 99.20/13.40 ((
% 99.20/13.40 (funcext2) =>
% 99.20/13.40 ((
% 99.20/13.40 (ap2apEq1) =>
% 99.20/13.40 ((
% 99.20/13.40 (ap2apEq2) =>
% 99.20/13.40 ((
% 99.20/13.40 (beta1) =>
% 99.20/13.40 ((
% 99.20/13.40 (eta1) =>
% 99.20/13.40 ((
% 99.20/13.40 (lam2lamEq) =>
% 99.20/13.40 ((
% 99.20/13.40 (beta2) =>
% 99.20/13.40 ((
% 99.20/13.40 (eta2) =>
% 99.20/13.40 ((
% 99.20/13.40 (iffalseProp1) =>
% 99.20/13.40 ((
% 99.20/13.40 (iffalseProp2) =>
% 99.20/13.40 ((
% 99.20/13.40 (iftrueProp1) =>
% 99.20/13.40 ((
% 99.20/13.40 (iftrueProp2) =>
% 99.20/13.40 ((
% 99.20/13.40 (ifSingleton) =>
% 99.20/13.40 ((
% 99.20/13.40 (ifp) =>
% 99.20/13.40 ((
% 99.20/13.40 (theeq) =>
% 99.20/13.40 ((
% 99.20/13.40 (iftrue) =>
% 99.20/13.40 ((
% 99.20/13.40 (iffalse) =>
% 99.20/13.40 ((
% 99.20/13.40 (iftrueorfalse) =>
% 99.20/13.40 ((
% 99.20/13.40 (binintersectT_lem) =>
% 99.20/13.40 ((
% 99.20/13.40 (binunionT_lem) =>
% 99.20/13.40 ((
% 99.20/13.40 (powersetT_lem) =>
% 99.20/13.40 ((
% 99.20/13.40 (setminusT_lem) =>
% 99.20/13.40 ((
% 99.20/13.40 (complementT_lem) =>
% 99.20/13.40 ((
% 99.20/13.40 (setextT) =>
% 99.20/13.40 ((
% 99.20/13.40 (subsetTI) =>
% 99.20/13.40 ((
% 99.20/13.40 (powersetTI1) =>
% 99.20/13.40 ((
% 99.20/13.40 (powersetTE1) =>
% 99.20/13.40 ((
% 99.20/13.40 (complementTI1) =>
% 99.20/13.40 ((
% 99.20/13.40 (complementTE1) =>
% 99.20/13.40 ((
% 99.20/13.40 (binintersectTELcontra) =>
% 99.20/13.40 ((
% 99.20/13.40 (binintersectTERcontra) =>
% 99.20/13.40 ((
% 99.20/13.40 (contrasubsetT) =>
% 99.20/13.40 ((
% 99.20/13.40 (contrasubsetT1) =>
% 99.20/13.40 ((
% 99.20/13.40 (contrasubsetT2) =>
% 99.20/13.40 ((
% 99.20/13.40 (contrasubsetT3) =>
% 99.20/13.40 ((
% 99.20/13.40 (doubleComplementI1) =>
% 99.20/13.40 ((
% 99.20/13.40 (doubleComplementE1) =>
% 99.20/13.40 ((
% 99.20/13.40 (doubleComplementSub1) =>
% 99.20/13.40 ((
% 99.20/13.40 (doubleComplementSub2) =>
% 99.20/13.40 ((
% 99.20/13.40 (doubleComplementEq) =>
% 99.20/13.40 ((
% 99.20/13.40 (complementTnotintersectT) =>
% 99.20/13.40 ((
% 99.20/13.40 (complementImpComplementIntersect) =>
% 99.20/13.40 ((
% 99.20/13.40 (complementSubsetComplementIntersect) =>
% 99.20/13.40 ((
% 99.20/13.40 (complementInPowersetComplementIntersect) =>
% 99.20/13.40 ((
% 99.20/13.40 (contraSubsetComplement) =>
% 99.20/13.40 ((
% 99.20/13.40 (complementTcontraSubset) =>
% 99.20/13.40 ((
% 99.20/13.40 (binunionTILcontra) =>
% 99.20/13.40 ((
% 99.20/13.40 (binunionTIRcontra) =>
% 99.20/13.40 ((
% 99.20/13.40 (inIntersectImpInUnion) =>
% 99.20/13.40 ((
% 99.20/13.40 (inIntersectImpInUnion2) =>
% 99.20/13.40 ((
% 99.20/13.40 (inIntersectImpInIntersectUnions) =>
% 99.20/13.40 ((
% 99.20/13.40 (intersectInPowersetIntersectUnions) =>
% 99.20/13.40 ((
% 99.20/13.40 (inComplementUnionImpNotIn1) =>
% 99.20/13.40 ((
% 99.20/13.40 (inComplementUnionImpInComplement1) =>
% 99.20/13.40 ((
% 99.20/13.40 (binunionTE) =>
% 99.20/13.40 ((
% 99.20/13.40 (binunionTEcontra) =>
% 99.20/13.40 ((
% 99.20/13.40 (demorgan2a1) =>
% 99.20/13.40 ((
% 99.20/13.40 (complementUnionInPowersetComplement) =>
% 99.20/13.40 ((
% 99.20/13.40 (demorgan2a2) =>
% 99.20/13.40 ((
% 99.20/13.40 (demorgan1a) =>
% 99.20/13.40 ((
% 99.20/13.40 (demorgan1b) =>
% 99.20/13.40 ((
% 99.20/13.40 (demorgan1) =>
% 99.20/13.40 ((
% 99.20/13.40 (demorgan2a) =>
% 99.20/13.40 ((
% 99.20/13.40 (demorgan2b2) =>
% 99.20/13.40 ((
% 99.20/13.40 (demorgan2b) =>
% 99.20/13.40 ((
% 99.20/13.40 (demorgan2) =>
% 99.20/13.40 ((
% 99.20/13.40 (woz13rule0) =>
% 99.20/13.40 ((
% 99.20/13.40 (woz13rule1) =>
% 99.20/13.40 ((
% 99.20/13.40 (woz13rule2) =>
% 99.20/13.40 ((
% 99.20/13.40 (woz13rule3) =>
% 99.20/13.40 ((
% 99.20/13.40 (woz13rule4) =>
% 99.20/13.40 ((
% 99.20/13.40 (woz1_1) =>
% 99.20/13.40 ((
% 99.20/13.40 (woz1_2) =>
% 99.20/13.40 ((
% 99.20/13.40 (woz1_3) =>
% 99.20/13.40 ((
% 99.20/13.40 (woz1_4) =>
% 99.20/13.40 ((
% 99.20/13.40 (woz1_5) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1all2) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1SetBreln1) =>
% 99.20/13.40 ((
% 99.20/13.40 (choice2fnsingleton) =>
% 99.20/13.40 ((
% 99.20/13.40 (setOfPairsIsBReln1) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1all1) =>
% 99.20/13.40 ((
% 99.20/13.40 (subbreln1) =>
% 99.20/13.40 ((
% 99.20/13.40 (eqbreln1) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1invprop) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1invI) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1invE) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1compprop) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1compI) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1compE) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1compEex) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1unionprop) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1unionIL) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1unionIR) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1unionI) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1unionE) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1unionEcases) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1unionCommutes) =>
% 99.20/13.40 ((
% 99.20/13.40 (woz2Ex) =>
% 99.20/13.40 ((
% 99.20/13.40 (woz2W) =>
% 99.20/13.40 ((
% 99.20/13.40 (woz2A) =>
% 99.20/13.40 ((
% 99.20/13.40 (woz2B) =>
% 99.20/13.40 ((
% 99.20/13.40 (image1Ex) =>
% 99.20/13.40 ((
% 99.20/13.40 (image1Ex1) =>
% 99.20/13.40 ((
% 99.20/13.40 (image1Equiv) =>
% 99.20/13.40 ((
% 99.20/13.40 (image1E) =>
% 99.20/13.40 ((
% 99.20/13.40 (image1I) =>
% 99.20/13.40 ((
% 99.20/13.40 (injFuncInInjFuncSet) =>
% 99.20/13.40 ((
% 99.20/13.40 (injFuncSetFuncIn) =>
% 99.20/13.40 ((
% 99.20/13.40 (injFuncSetFuncInj) =>
% 99.20/13.40 ((
% 99.20/13.40 (!!) @ (
% 99.20/13.40 (('#B') @ (
% 99.20/13.40 !!) @
% 99.20/13.40 (
% 99.20/13.40 (
% 99.20/13.40 ('#B') @ (
% 99.20/13.40 (
% 99.20/13.40 ('#B') @ (
% 99.20/13.40 !!))) @
% 99.20/13.40 (
% 99.20/13.40 (
% 99.20/13.40 ('#S') @ (
% 99.20/13.40 (
% 99.20/13.40 ('#B') @ (
% 99.20/13.40 '#S') @
% 99.20/13.40 (
% 99.20/13.40 (
% 99.20/13.40 ('#B') @ (
% 99.20/13.40 (
% 99.20/13.40 ('#B') @ (
% 99.20/13.40 '#S'))) @
% 99.20/13.40 (
% 99.20/13.40 (
% 99.20/13.40 ('#B') @ (
% 99.20/13.40 (
% 99.20/13.40 ('#B') @ (
% 99.20/13.40 (
% 99.20/13.40 ('#B') @ (
% 99.20/13.40 =>))))) @
% 99.20/13.40 (
% 99.20/13.40 (
% 99.20/13.40 ('#B') @ (
% 99.20/13.40 (
% 99.20/13.40 ('#B') @ (
% 99.20/13.40 (
% 99.20/13.40 ('#C') @ in)))) @
% 99.20/13.40 surjFuncSet)))))))) @
% 99.20/13.40 (
% 99.20/13.40 (
% 99.20/13.40 ('#B') @ (
% 99.20/13.40 (
% 99.20/13.40 ('#B') @ (
% 99.20/13.40 (
% 99.20/13.40 ('#C') @ in)))) @
% 99.20/13.40 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.20/13.40 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl672])).
% 99.20/13.40 thf(zip_derived_cl699, plain,
% 99.20/13.40 (~ (((powerset__Cong) =>
% 99.20/13.40 (((setunion__Cong) =>
% 99.20/13.40 (((exuEu) =>
% 99.20/13.40 (((descr__Cong) =>
% 99.20/13.40 (((dsetconstr__Cong) =>
% 99.20/13.40 (((subsetI1) =>
% 99.20/13.40 (((eqimpsubset2) =>
% 99.20/13.40 (((eqimpsubset1) =>
% 99.20/13.40 (((subsetI2) =>
% 99.20/13.40 (((emptysetsubset) =>
% 99.20/13.40 (((subsetE) =>
% 99.20/13.40 (((subsetE2) =>
% 99.20/13.40 (((notsubsetI) =>
% 99.20/13.40 (((notequalI1) =>
% 99.20/13.40 (((notequalI2) =>
% 99.20/13.40 (((subsetRefl) =>
% 99.20/13.40 (((subsetTrans) =>
% 99.20/13.40 (((setadjoinSub) =>
% 99.20/13.40 (((setadjoinSub2) =>
% 99.20/13.40 (((subset2powerset) =>
% 99.20/13.40 (((setextsub) =>
% 99.20/13.40 (((subsetemptysetimpeq) =>
% 99.20/13.40 (((powersetI1) =>
% 99.20/13.40 (((powersetE1) =>
% 99.20/13.40 (((inPowerset) =>
% 99.20/13.40 (((powersetsubset) =>
% 99.20/13.40 (((sepInPowerset) =>
% 99.20/13.40 (((sepSubset) =>
% 99.20/13.40 (((binunionIL) =>
% 99.20/13.40 (((upairset2IR) =>
% 99.20/13.40 ((
% 99.20/13.40 (binunionIR) =>
% 99.20/13.40 ((
% 99.20/13.40 (binunionEcases) =>
% 99.20/13.40 ((
% 99.20/13.40 (binunionE) =>
% 99.20/13.40 ((
% 99.20/13.40 (binunionLsub) =>
% 99.20/13.40 ((
% 99.20/13.40 (binunionRsub) =>
% 99.20/13.40 ((
% 99.20/13.40 (binintersectI) =>
% 99.20/13.40 ((
% 99.20/13.40 (binintersectSubset5) =>
% 99.20/13.40 ((
% 99.20/13.40 (binintersectEL) =>
% 99.20/13.40 ((
% 99.20/13.40 (binintersectLsub) =>
% 99.20/13.40 ((
% 99.20/13.40 (binintersectSubset2) =>
% 99.20/13.40 ((
% 99.20/13.40 (binintersectSubset3) =>
% 99.20/13.40 ((
% 99.20/13.40 (binintersectER) =>
% 99.20/13.40 ((
% 99.20/13.40 (disjointsetsI1) =>
% 99.20/13.40 ((
% 99.20/13.40 (binintersectRsub) =>
% 99.20/13.40 ((
% 99.20/13.40 (binintersectSubset4) =>
% 99.20/13.40 ((
% 99.20/13.40 (binintersectSubset1) =>
% 99.20/13.40 ((
% 99.20/13.40 (bs114d) =>
% 99.20/13.40 ((
% 99.20/13.40 (setminusI) =>
% 99.20/13.40 ((
% 99.20/13.40 (setminusEL) =>
% 99.20/13.40 ((
% 99.20/13.40 (setminusER) =>
% 99.20/13.40 ((
% 99.20/13.40 (setminusSubset2) =>
% 99.20/13.40 ((
% 99.20/13.40 (setminusERneg) =>
% 99.20/13.40 ((
% 99.20/13.40 (setminusELneg) =>
% 99.20/13.40 ((
% 99.20/13.40 (setminusILneg) =>
% 99.20/13.40 ((
% 99.20/13.40 (setminusIRneg) =>
% 99.20/13.40 ((
% 99.20/13.40 (setminusLsub) =>
% 99.20/13.40 ((
% 99.20/13.40 (setminusSubset1) =>
% 99.20/13.40 ((
% 99.20/13.40 (symdiffE) =>
% 99.20/13.40 ((
% 99.20/13.40 (symdiffI1) =>
% 99.20/13.40 ((
% 99.20/13.40 (symdiffI2) =>
% 99.20/13.40 ((
% 99.20/13.40 (symdiffIneg1) =>
% 99.20/13.40 ((
% 99.20/13.40 (symdiffIneg2) =>
% 99.20/13.40 ((
% 99.20/13.40 (secondinupair) =>
% 99.20/13.40 ((
% 99.20/13.40 (setukpairIL) =>
% 99.20/13.40 ((
% 99.20/13.40 (setukpairIR) =>
% 99.20/13.40 ((
% 99.20/13.40 (kpairiskpair) =>
% 99.20/13.40 ((
% 99.20/13.40 (kpairp) =>
% 99.20/13.40 ((
% 99.20/13.40 (singletonsubset) =>
% 99.20/13.40 ((
% 99.20/13.40 (singletoninpowerset) =>
% 99.20/13.40 ((
% 99.20/13.40 (singletoninpowunion) =>
% 99.20/13.40 ((
% 99.20/13.40 (upairset2E) =>
% 99.20/13.40 ((
% 99.20/13.40 (upairsubunion) =>
% 99.20/13.40 ((
% 99.20/13.40 (upairinpowunion) =>
% 99.20/13.40 ((
% 99.20/13.40 (ubforcartprodlem1) =>
% 99.20/13.40 ((
% 99.20/13.40 (ubforcartprodlem2) =>
% 99.20/13.40 ((
% 99.20/13.40 (ubforcartprodlem3) =>
% 99.20/13.40 ((
% 99.20/13.40 (cartprodpairin) =>
% 99.20/13.40 ((
% 99.20/13.40 (cartprodmempair1) =>
% 99.20/13.40 ((
% 99.20/13.40 (cartprodmempair) =>
% 99.20/13.40 ((
% 99.20/13.40 (setunionE2) =>
% 99.20/13.40 ((
% 99.20/13.40 (setunionsingleton1) =>
% 99.20/13.40 ((
% 99.20/13.40 (setunionsingleton2) =>
% 99.20/13.40 ((
% 99.20/13.40 (setunionsingleton) =>
% 99.20/13.40 ((
% 99.20/13.40 (singletonprop) =>
% 99.20/13.40 ((
% 99.20/13.40 (ex1E1) =>
% 99.20/13.40 ((
% 99.20/13.40 (ex1I) =>
% 99.20/13.40 ((
% 99.20/13.40 (ex1I2) =>
% 99.20/13.40 ((
% 99.20/13.40 (singletonsuniq) =>
% 99.20/13.40 ((
% 99.20/13.40 (setukpairinjL1) =>
% 99.20/13.40 ((
% 99.20/13.40 (kfstsingleton) =>
% 99.20/13.40 ((
% 99.20/13.40 (theprop) =>
% 99.20/13.40 ((
% 99.20/13.40 (kfstpairEq) =>
% 99.20/13.40 ((
% 99.20/13.40 (cartprodfstin) =>
% 99.20/13.40 ((
% 99.20/13.40 (setukpairinjL2) =>
% 99.20/13.40 ((
% 99.20/13.40 (setukpairinjL) =>
% 99.20/13.40 ((
% 99.20/13.40 (setukpairinjR11) =>
% 99.20/13.40 ((
% 99.20/13.40 (setukpairinjR12) =>
% 99.20/13.40 ((
% 99.20/13.40 (setukpairinjR1) =>
% 99.20/13.40 ((
% 99.20/13.40 (upairequniteq) =>
% 99.20/13.40 ((
% 99.20/13.40 (setukpairinjR2) =>
% 99.20/13.40 ((
% 99.20/13.40 (setukpairinjR) =>
% 99.20/13.40 ((
% 99.20/13.40 (ksndsingleton) =>
% 99.20/13.40 ((
% 99.20/13.40 (ksndpairEq) =>
% 99.20/13.40 ((
% 99.20/13.40 (kpairsurjEq) =>
% 99.20/13.40 ((
% 99.20/13.40 (cartprodsndin) =>
% 99.20/13.40 ((
% 99.20/13.40 (cartprodpairmemEL) =>
% 99.20/13.40 ((
% 99.20/13.40 (cartprodpairmemER) =>
% 99.20/13.40 ((
% 99.20/13.40 (cartprodmempaircEq) =>
% 99.20/13.40 ((
% 99.20/13.40 (cartprodfstpairEq) =>
% 99.20/13.40 ((
% 99.20/13.40 (cartprodsndpairEq) =>
% 99.20/13.40 ((
% 99.20/13.40 (cartprodpairsurjEq) =>
% 99.20/13.40 ((
% 99.20/13.40 (dpsetconstrI) =>
% 99.20/13.40 ((
% 99.20/13.40 (dpsetconstrSub) =>
% 99.20/13.40 ((
% 99.20/13.40 (setOfPairsIsBReln) =>
% 99.20/13.40 ((
% 99.20/13.40 (dpsetconstrERa) =>
% 99.20/13.40 ((
% 99.20/13.40 (dpsetconstrEL1) =>
% 99.20/13.40 ((
% 99.20/13.40 (dpsetconstrEL2) =>
% 99.20/13.40 ((
% 99.20/13.40 (dpsetconstrER) =>
% 99.20/13.40 ((
% 99.20/13.40 (funcImageSingleton) =>
% 99.20/13.40 ((
% 99.20/13.40 (apProp) =>
% 99.20/13.40 ((
% 99.20/13.40 (app) =>
% 99.20/13.40 ((
% 99.20/13.40 (infuncsetfunc) =>
% 99.20/13.40 ((
% 99.20/13.40 (ap2p) =>
% 99.20/13.40 ((
% 99.20/13.40 (funcinfuncset) =>
% 99.20/13.40 ((
% 99.20/13.40 (lamProp) =>
% 99.20/13.40 ((
% 99.20/13.40 (lamp) =>
% 99.20/13.40 ((
% 99.20/13.40 (lam2p) =>
% 99.20/13.40 ((
% 99.20/13.40 (brelnall1) =>
% 99.20/13.40 ((
% 99.20/13.40 (brelnall2) =>
% 99.20/13.40 ((
% 99.20/13.40 (ex1E2) =>
% 99.20/13.40 ((
% 99.20/13.40 (funcGraphProp1) =>
% 99.20/13.40 ((
% 99.20/13.40 (funcGraphProp3) =>
% 99.20/13.40 ((
% 99.20/13.40 (funcGraphProp2) =>
% 99.20/13.40 ((
% 99.20/13.40 (funcextLem) =>
% 99.20/13.40 ((
% 99.20/13.40 (funcGraphProp4) =>
% 99.20/13.40 ((
% 99.20/13.40 (subbreln) =>
% 99.20/13.40 ((
% 99.20/13.40 (eqbreln) =>
% 99.20/13.40 ((
% 99.20/13.40 (funcext) =>
% 99.20/13.40 ((
% 99.20/13.40 (funcext2) =>
% 99.20/13.40 ((
% 99.20/13.40 (ap2apEq1) =>
% 99.20/13.40 ((
% 99.20/13.40 (ap2apEq2) =>
% 99.20/13.40 ((
% 99.20/13.40 (beta1) =>
% 99.20/13.40 ((
% 99.20/13.40 (eta1) =>
% 99.20/13.40 ((
% 99.20/13.40 (lam2lamEq) =>
% 99.20/13.40 ((
% 99.20/13.40 (beta2) =>
% 99.20/13.40 ((
% 99.20/13.40 (eta2) =>
% 99.20/13.40 ((
% 99.20/13.40 (iffalseProp1) =>
% 99.20/13.40 ((
% 99.20/13.40 (iffalseProp2) =>
% 99.20/13.40 ((
% 99.20/13.40 (iftrueProp1) =>
% 99.20/13.40 ((
% 99.20/13.40 (iftrueProp2) =>
% 99.20/13.40 ((
% 99.20/13.40 (ifSingleton) =>
% 99.20/13.40 ((
% 99.20/13.40 (ifp) =>
% 99.20/13.40 ((
% 99.20/13.40 (theeq) =>
% 99.20/13.40 ((
% 99.20/13.40 (iftrue) =>
% 99.20/13.40 ((
% 99.20/13.40 (iffalse) =>
% 99.20/13.40 ((
% 99.20/13.40 (iftrueorfalse) =>
% 99.20/13.40 ((
% 99.20/13.40 (binintersectT_lem) =>
% 99.20/13.40 ((
% 99.20/13.40 (binunionT_lem) =>
% 99.20/13.40 ((
% 99.20/13.40 (powersetT_lem) =>
% 99.20/13.40 ((
% 99.20/13.40 (setminusT_lem) =>
% 99.20/13.40 ((
% 99.20/13.40 (complementT_lem) =>
% 99.20/13.40 ((
% 99.20/13.40 (setextT) =>
% 99.20/13.40 ((
% 99.20/13.40 (subsetTI) =>
% 99.20/13.40 ((
% 99.20/13.40 (powersetTI1) =>
% 99.20/13.40 ((
% 99.20/13.40 (powersetTE1) =>
% 99.20/13.40 ((
% 99.20/13.40 (complementTI1) =>
% 99.20/13.40 ((
% 99.20/13.40 (complementTE1) =>
% 99.20/13.40 ((
% 99.20/13.40 (binintersectTELcontra) =>
% 99.20/13.40 ((
% 99.20/13.40 (binintersectTERcontra) =>
% 99.20/13.40 ((
% 99.20/13.40 (contrasubsetT) =>
% 99.20/13.40 ((
% 99.20/13.40 (contrasubsetT1) =>
% 99.20/13.40 ((
% 99.20/13.40 (contrasubsetT2) =>
% 99.20/13.40 ((
% 99.20/13.40 (contrasubsetT3) =>
% 99.20/13.40 ((
% 99.20/13.40 (doubleComplementI1) =>
% 99.20/13.40 ((
% 99.20/13.40 (doubleComplementE1) =>
% 99.20/13.40 ((
% 99.20/13.40 (doubleComplementSub1) =>
% 99.20/13.40 ((
% 99.20/13.40 (doubleComplementSub2) =>
% 99.20/13.40 ((
% 99.20/13.40 (doubleComplementEq) =>
% 99.20/13.40 ((
% 99.20/13.40 (complementTnotintersectT) =>
% 99.20/13.40 ((
% 99.20/13.40 (complementImpComplementIntersect) =>
% 99.20/13.40 ((
% 99.20/13.40 (complementSubsetComplementIntersect) =>
% 99.20/13.40 ((
% 99.20/13.40 (complementInPowersetComplementIntersect) =>
% 99.20/13.40 ((
% 99.20/13.40 (contraSubsetComplement) =>
% 99.20/13.40 ((
% 99.20/13.40 (complementTcontraSubset) =>
% 99.20/13.40 ((
% 99.20/13.40 (binunionTILcontra) =>
% 99.20/13.40 ((
% 99.20/13.40 (binunionTIRcontra) =>
% 99.20/13.40 ((
% 99.20/13.40 (inIntersectImpInUnion) =>
% 99.20/13.40 ((
% 99.20/13.40 (inIntersectImpInUnion2) =>
% 99.20/13.40 ((
% 99.20/13.40 (inIntersectImpInIntersectUnions) =>
% 99.20/13.40 ((
% 99.20/13.40 (intersectInPowersetIntersectUnions) =>
% 99.20/13.40 ((
% 99.20/13.40 (inComplementUnionImpNotIn1) =>
% 99.20/13.40 ((
% 99.20/13.40 (inComplementUnionImpInComplement1) =>
% 99.20/13.40 ((
% 99.20/13.40 (binunionTE) =>
% 99.20/13.40 ((
% 99.20/13.40 (binunionTEcontra) =>
% 99.20/13.40 ((
% 99.20/13.40 (demorgan2a1) =>
% 99.20/13.40 ((
% 99.20/13.40 (complementUnionInPowersetComplement) =>
% 99.20/13.40 ((
% 99.20/13.40 (demorgan2a2) =>
% 99.20/13.40 ((
% 99.20/13.40 (demorgan1a) =>
% 99.20/13.40 ((
% 99.20/13.40 (demorgan1b) =>
% 99.20/13.40 ((
% 99.20/13.40 (demorgan1) =>
% 99.20/13.40 ((
% 99.20/13.40 (demorgan2a) =>
% 99.20/13.40 ((
% 99.20/13.40 (demorgan2b2) =>
% 99.20/13.40 ((
% 99.20/13.40 (demorgan2b) =>
% 99.20/13.40 ((
% 99.20/13.40 (demorgan2) =>
% 99.20/13.40 ((
% 99.20/13.40 (woz13rule0) =>
% 99.20/13.40 ((
% 99.20/13.40 (woz13rule1) =>
% 99.20/13.40 ((
% 99.20/13.40 (woz13rule2) =>
% 99.20/13.40 ((
% 99.20/13.40 (woz13rule3) =>
% 99.20/13.40 ((
% 99.20/13.40 (woz13rule4) =>
% 99.20/13.40 ((
% 99.20/13.40 (woz1_1) =>
% 99.20/13.40 ((
% 99.20/13.40 (woz1_2) =>
% 99.20/13.40 ((
% 99.20/13.40 (woz1_3) =>
% 99.20/13.40 ((
% 99.20/13.40 (woz1_4) =>
% 99.20/13.40 ((
% 99.20/13.40 (woz1_5) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1all2) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1SetBreln1) =>
% 99.20/13.40 ((
% 99.20/13.40 (choice2fnsingleton) =>
% 99.20/13.40 ((
% 99.20/13.40 (setOfPairsIsBReln1) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1all1) =>
% 99.20/13.40 ((
% 99.20/13.40 (subbreln1) =>
% 99.20/13.40 ((
% 99.20/13.40 (eqbreln1) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1invprop) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1invI) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1invE) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1compprop) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1compI) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1compE) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1compEex) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1unionprop) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1unionIL) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1unionIR) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1unionI) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1unionE) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1unionEcases) =>
% 99.20/13.40 ((
% 99.20/13.40 (breln1unionCommutes) =>
% 99.20/13.40 ((
% 99.20/13.40 (woz2Ex) =>
% 99.20/13.40 ((
% 99.20/13.40 (woz2W) =>
% 99.20/13.40 ((
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% 99.20/13.40 ((
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% 99.20/13.40 ((
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% 99.20/13.40 ((
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% 99.20/13.40 ((
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% 99.20/13.40 ((
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% 99.20/13.40 ((
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% 99.20/13.40 ((
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% 99.20/13.40 ((
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% 99.20/13.40 ((
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% 99.20/13.40 ((
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% 99.20/13.40 ((
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% 99.20/13.40 ((
% 99.20/13.40 (ubforcartprodlem3) =>
% 99.20/13.40 ((
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% 99.20/13.40 ((
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% 99.20/13.40 ((
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% 99.20/13.40 ((
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% 99.20/13.40 ((
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% 99.20/13.40 ((
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% 99.20/13.40 ((
% 99.20/13.40 (kpairsurjEq) =>
% 99.20/13.40 ((
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% 99.20/13.40 ((
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% 99.20/13.40 ((
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% 99.20/13.40 ((
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% 99.20/13.40 ((
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% 99.20/13.40 ((
% 99.20/13.40 (cartprodsndpairEq) =>
% 99.20/13.40 ((
% 99.20/13.40 (cartprodpairsurjEq) =>
% 99.20/13.40 ((
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% 99.20/13.40 ((
% 99.20/13.40 (dpsetconstrSub) =>
% 99.20/13.40 ((
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% 99.20/13.40 (dpsetconstrEL2) =>
% 99.20/13.40 ((
% 99.20/13.40 (dpsetconstrER) =>
% 99.20/13.40 ((
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% 99.20/13.40 ((
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% 99.20/13.40 ((
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% 99.20/13.41 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl699])).
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
% 99.20/13.41 (symdiffIneg2) =>
% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
% 99.20/13.41 (ubforcartprodlem2) =>
% 99.20/13.41 ((
% 99.20/13.41 (ubforcartprodlem3) =>
% 99.20/13.41 ((
% 99.20/13.41 (cartprodpairin) =>
% 99.20/13.41 ((
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% 99.20/13.41 ((
% 99.20/13.41 (cartprodmempair) =>
% 99.20/13.41 ((
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% 99.20/13.41 ((
% 99.20/13.41 (setunionsingleton1) =>
% 99.20/13.41 ((
% 99.20/13.41 (setunionsingleton2) =>
% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
% 99.20/13.41 (setukpairinjL) =>
% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
% 99.20/13.41 (upairequniteq) =>
% 99.20/13.41 ((
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% 99.20/13.41 ((
% 99.20/13.41 (setukpairinjR) =>
% 99.20/13.41 ((
% 99.20/13.41 (ksndsingleton) =>
% 99.20/13.41 ((
% 99.20/13.41 (ksndpairEq) =>
% 99.20/13.41 ((
% 99.20/13.41 (kpairsurjEq) =>
% 99.20/13.41 ((
% 99.20/13.41 (cartprodsndin) =>
% 99.20/13.41 ((
% 99.20/13.41 (cartprodpairmemEL) =>
% 99.20/13.41 ((
% 99.20/13.41 (cartprodpairmemER) =>
% 99.20/13.41 ((
% 99.20/13.41 (cartprodmempaircEq) =>
% 99.20/13.41 ((
% 99.20/13.41 (cartprodfstpairEq) =>
% 99.20/13.41 ((
% 99.20/13.41 (cartprodsndpairEq) =>
% 99.20/13.41 ((
% 99.20/13.41 (cartprodpairsurjEq) =>
% 99.20/13.41 ((
% 99.20/13.41 (dpsetconstrI) =>
% 99.20/13.41 ((
% 99.20/13.41 (dpsetconstrSub) =>
% 99.20/13.41 ((
% 99.20/13.41 (setOfPairsIsBReln) =>
% 99.20/13.41 ((
% 99.20/13.41 (dpsetconstrERa) =>
% 99.20/13.41 ((
% 99.20/13.41 (dpsetconstrEL1) =>
% 99.20/13.41 ((
% 99.20/13.41 (dpsetconstrEL2) =>
% 99.20/13.41 ((
% 99.20/13.41 (dpsetconstrER) =>
% 99.20/13.41 ((
% 99.20/13.41 (funcImageSingleton) =>
% 99.20/13.41 ((
% 99.20/13.41 (apProp) =>
% 99.20/13.41 ((
% 99.20/13.41 (app) =>
% 99.20/13.41 ((
% 99.20/13.41 (infuncsetfunc) =>
% 99.20/13.41 ((
% 99.20/13.41 (ap2p) =>
% 99.20/13.41 ((
% 99.20/13.41 (funcinfuncset) =>
% 99.20/13.41 ((
% 99.20/13.41 (lamProp) =>
% 99.20/13.41 ((
% 99.20/13.41 (lamp) =>
% 99.20/13.41 ((
% 99.20/13.41 (lam2p) =>
% 99.20/13.41 ((
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% 99.20/13.41 ((
% 99.20/13.41 (brelnall2) =>
% 99.20/13.41 ((
% 99.20/13.41 (ex1E2) =>
% 99.20/13.41 ((
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% 99.20/13.41 ((
% 99.20/13.41 (funcGraphProp3) =>
% 99.20/13.41 ((
% 99.20/13.41 (funcGraphProp2) =>
% 99.20/13.41 ((
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% 99.20/13.41 ((
% 99.20/13.41 (funcGraphProp4) =>
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% 99.20/13.41 ((
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% 99.20/13.41 ((
% 99.20/13.41 (funcext) =>
% 99.20/13.41 ((
% 99.20/13.41 (funcext2) =>
% 99.20/13.41 ((
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% 99.20/13.41 ((
% 99.20/13.41 (ap2apEq2) =>
% 99.20/13.41 ((
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% 99.20/13.41 ((
% 99.20/13.41 (eta1) =>
% 99.20/13.41 ((
% 99.20/13.41 (lam2lamEq) =>
% 99.20/13.41 ((
% 99.20/13.41 (beta2) =>
% 99.20/13.41 ((
% 99.20/13.41 (eta2) =>
% 99.20/13.41 ((
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% 99.20/13.41 ((
% 99.20/13.41 (iffalseProp2) =>
% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
% 99.20/13.41 (contrasubsetT2) =>
% 99.20/13.41 ((
% 99.20/13.41 (contrasubsetT3) =>
% 99.20/13.41 ((
% 99.20/13.41 (doubleComplementI1) =>
% 99.20/13.41 ((
% 99.20/13.41 (doubleComplementE1) =>
% 99.20/13.41 ((
% 99.20/13.41 (doubleComplementSub1) =>
% 99.20/13.41 ((
% 99.20/13.41 (doubleComplementSub2) =>
% 99.20/13.41 ((
% 99.20/13.41 (doubleComplementEq) =>
% 99.20/13.41 ((
% 99.20/13.41 (complementTnotintersectT) =>
% 99.20/13.41 ((
% 99.20/13.41 (complementImpComplementIntersect) =>
% 99.20/13.41 ((
% 99.20/13.41 (complementSubsetComplementIntersect) =>
% 99.20/13.41 ((
% 99.20/13.41 (complementInPowersetComplementIntersect) =>
% 99.20/13.41 ((
% 99.20/13.41 (contraSubsetComplement) =>
% 99.20/13.41 ((
% 99.20/13.41 (complementTcontraSubset) =>
% 99.20/13.41 ((
% 99.20/13.41 (binunionTILcontra) =>
% 99.20/13.41 ((
% 99.20/13.41 (binunionTIRcontra) =>
% 99.20/13.41 ((
% 99.20/13.41 (inIntersectImpInUnion) =>
% 99.20/13.41 ((
% 99.20/13.41 (inIntersectImpInUnion2) =>
% 99.20/13.41 ((
% 99.20/13.41 (inIntersectImpInIntersectUnions) =>
% 99.20/13.41 ((
% 99.20/13.41 (intersectInPowersetIntersectUnions) =>
% 99.20/13.41 ((
% 99.20/13.41 (inComplementUnionImpNotIn1) =>
% 99.20/13.41 ((
% 99.20/13.41 (inComplementUnionImpInComplement1) =>
% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
% 99.20/13.41 (demorgan2a1) =>
% 99.20/13.41 ((
% 99.20/13.41 (complementUnionInPowersetComplement) =>
% 99.20/13.41 ((
% 99.20/13.41 (demorgan2a2) =>
% 99.20/13.41 ((
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% 99.20/13.41 ((
% 99.20/13.41 (demorgan1b) =>
% 99.20/13.41 ((
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% 99.20/13.41 ((
% 99.20/13.41 (demorgan2a) =>
% 99.20/13.41 ((
% 99.20/13.41 (demorgan2b2) =>
% 99.20/13.41 ((
% 99.20/13.41 (demorgan2b) =>
% 99.20/13.41 ((
% 99.20/13.41 (demorgan2) =>
% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
% 99.20/13.41 (woz13rule4) =>
% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
% 99.20/13.41 (woz1_3) =>
% 99.20/13.41 ((
% 99.20/13.41 (woz1_4) =>
% 99.20/13.41 ((
% 99.20/13.41 (woz1_5) =>
% 99.20/13.41 ((
% 99.20/13.41 (breln1all2) =>
% 99.20/13.41 ((
% 99.20/13.41 (breln1SetBreln1) =>
% 99.20/13.41 ((
% 99.20/13.41 (choice2fnsingleton) =>
% 99.20/13.41 ((
% 99.20/13.41 (setOfPairsIsBReln1) =>
% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
% 99.20/13.41 (eqbreln1) =>
% 99.20/13.41 ((
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% 99.20/13.41 ((
% 99.20/13.41 (breln1invI) =>
% 99.20/13.41 ((
% 99.20/13.41 (breln1invE) =>
% 99.20/13.41 ((
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% 99.20/13.41 ((
% 99.20/13.41 (breln1compI) =>
% 99.20/13.41 ((
% 99.20/13.41 (breln1compE) =>
% 99.20/13.41 ((
% 99.20/13.41 (breln1compEex) =>
% 99.20/13.41 ((
% 99.20/13.41 (breln1unionprop) =>
% 99.20/13.41 ((
% 99.20/13.41 (breln1unionIL) =>
% 99.20/13.41 ((
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% 99.20/13.41 ((
% 99.20/13.41 (breln1unionI) =>
% 99.20/13.41 ((
% 99.20/13.41 (breln1unionE) =>
% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
% 99.20/13.41 (injFuncSetFuncIn) =>
% 99.20/13.41 ((
% 99.20/13.41 (injFuncSetFuncInj) =>
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% 99.20/13.41 (
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% 99.20/13.41 (
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% 99.20/13.41 (
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% 99.20/13.41 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
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% 99.20/13.41 (((dsetconstr__Cong) =>
% 99.20/13.41 (((subsetI1) =>
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% 99.20/13.41 (bs114d) =>
% 99.20/13.41 ((
% 99.20/13.41 (setminusI) =>
% 99.20/13.41 ((
% 99.20/13.41 (setminusEL) =>
% 99.20/13.41 ((
% 99.20/13.41 (setminusER) =>
% 99.20/13.41 ((
% 99.20/13.41 (setminusSubset2) =>
% 99.20/13.41 ((
% 99.20/13.41 (setminusERneg) =>
% 99.20/13.41 ((
% 99.20/13.41 (setminusELneg) =>
% 99.20/13.41 ((
% 99.20/13.41 (setminusILneg) =>
% 99.20/13.41 ((
% 99.20/13.41 (setminusIRneg) =>
% 99.20/13.41 ((
% 99.20/13.41 (setminusLsub) =>
% 99.20/13.41 ((
% 99.20/13.41 (setminusSubset1) =>
% 99.20/13.41 ((
% 99.20/13.41 (symdiffE) =>
% 99.20/13.41 ((
% 99.20/13.41 (symdiffI1) =>
% 99.20/13.41 ((
% 99.20/13.41 (symdiffI2) =>
% 99.20/13.41 ((
% 99.20/13.41 (symdiffIneg1) =>
% 99.20/13.41 ((
% 99.20/13.41 (symdiffIneg2) =>
% 99.20/13.41 ((
% 99.20/13.41 (secondinupair) =>
% 99.20/13.41 ((
% 99.20/13.41 (setukpairIL) =>
% 99.20/13.41 ((
% 99.20/13.41 (setukpairIR) =>
% 99.20/13.41 ((
% 99.20/13.41 (kpairiskpair) =>
% 99.20/13.41 ((
% 99.20/13.41 (kpairp) =>
% 99.20/13.41 ((
% 99.20/13.41 (singletonsubset) =>
% 99.20/13.41 ((
% 99.20/13.41 (singletoninpowerset) =>
% 99.20/13.41 ((
% 99.20/13.41 (singletoninpowunion) =>
% 99.20/13.41 ((
% 99.20/13.41 (upairset2E) =>
% 99.20/13.41 ((
% 99.20/13.41 (upairsubunion) =>
% 99.20/13.41 ((
% 99.20/13.41 (upairinpowunion) =>
% 99.20/13.41 ((
% 99.20/13.41 (ubforcartprodlem1) =>
% 99.20/13.41 ((
% 99.20/13.41 (ubforcartprodlem2) =>
% 99.20/13.41 ((
% 99.20/13.41 (ubforcartprodlem3) =>
% 99.20/13.41 ((
% 99.20/13.41 (cartprodpairin) =>
% 99.20/13.41 ((
% 99.20/13.41 (cartprodmempair1) =>
% 99.20/13.41 ((
% 99.20/13.41 (cartprodmempair) =>
% 99.20/13.41 ((
% 99.20/13.41 (setunionE2) =>
% 99.20/13.41 ((
% 99.20/13.41 (setunionsingleton1) =>
% 99.20/13.41 ((
% 99.20/13.41 (setunionsingleton2) =>
% 99.20/13.41 ((
% 99.20/13.41 (setunionsingleton) =>
% 99.20/13.41 ((
% 99.20/13.41 (singletonprop) =>
% 99.20/13.41 ((
% 99.20/13.41 (ex1E1) =>
% 99.20/13.41 ((
% 99.20/13.41 (ex1I) =>
% 99.20/13.41 ((
% 99.20/13.41 (ex1I2) =>
% 99.20/13.41 ((
% 99.20/13.41 (singletonsuniq) =>
% 99.20/13.41 ((
% 99.20/13.41 (setukpairinjL1) =>
% 99.20/13.41 ((
% 99.20/13.41 (kfstsingleton) =>
% 99.20/13.41 ((
% 99.20/13.41 (theprop) =>
% 99.20/13.41 ((
% 99.20/13.41 (kfstpairEq) =>
% 99.20/13.41 ((
% 99.20/13.41 (cartprodfstin) =>
% 99.20/13.41 ((
% 99.20/13.41 (setukpairinjL2) =>
% 99.20/13.41 ((
% 99.20/13.41 (setukpairinjL) =>
% 99.20/13.41 ((
% 99.20/13.41 (setukpairinjR11) =>
% 99.20/13.41 ((
% 99.20/13.41 (setukpairinjR12) =>
% 99.20/13.41 ((
% 99.20/13.41 (setukpairinjR1) =>
% 99.20/13.41 ((
% 99.20/13.41 (upairequniteq) =>
% 99.20/13.41 ((
% 99.20/13.41 (setukpairinjR2) =>
% 99.20/13.41 ((
% 99.20/13.41 (setukpairinjR) =>
% 99.20/13.41 ((
% 99.20/13.41 (ksndsingleton) =>
% 99.20/13.41 ((
% 99.20/13.41 (ksndpairEq) =>
% 99.20/13.41 ((
% 99.20/13.41 (kpairsurjEq) =>
% 99.20/13.41 ((
% 99.20/13.41 (cartprodsndin) =>
% 99.20/13.41 ((
% 99.20/13.41 (cartprodpairmemEL) =>
% 99.20/13.41 ((
% 99.20/13.41 (cartprodpairmemER) =>
% 99.20/13.41 ((
% 99.20/13.41 (cartprodmempaircEq) =>
% 99.20/13.41 ((
% 99.20/13.41 (cartprodfstpairEq) =>
% 99.20/13.41 ((
% 99.20/13.41 (cartprodsndpairEq) =>
% 99.20/13.41 ((
% 99.20/13.41 (cartprodpairsurjEq) =>
% 99.20/13.41 ((
% 99.20/13.41 (dpsetconstrI) =>
% 99.20/13.41 ((
% 99.20/13.41 (dpsetconstrSub) =>
% 99.20/13.41 ((
% 99.20/13.41 (setOfPairsIsBReln) =>
% 99.20/13.41 ((
% 99.20/13.41 (dpsetconstrERa) =>
% 99.20/13.41 ((
% 99.20/13.41 (dpsetconstrEL1) =>
% 99.20/13.41 ((
% 99.20/13.41 (dpsetconstrEL2) =>
% 99.20/13.41 ((
% 99.20/13.41 (dpsetconstrER) =>
% 99.20/13.41 ((
% 99.20/13.41 (funcImageSingleton) =>
% 99.20/13.41 ((
% 99.20/13.41 (apProp) =>
% 99.20/13.41 ((
% 99.20/13.41 (app) =>
% 99.20/13.41 ((
% 99.20/13.41 (infuncsetfunc) =>
% 99.20/13.41 ((
% 99.20/13.41 (ap2p) =>
% 99.20/13.41 ((
% 99.20/13.41 (funcinfuncset) =>
% 99.20/13.41 ((
% 99.20/13.41 (lamProp) =>
% 99.20/13.41 ((
% 99.20/13.41 (lamp) =>
% 99.20/13.41 ((
% 99.20/13.41 (lam2p) =>
% 99.20/13.41 ((
% 99.20/13.41 (brelnall1) =>
% 99.20/13.41 ((
% 99.20/13.41 (brelnall2) =>
% 99.20/13.41 ((
% 99.20/13.41 (ex1E2) =>
% 99.20/13.41 ((
% 99.20/13.41 (funcGraphProp1) =>
% 99.20/13.41 ((
% 99.20/13.41 (funcGraphProp3) =>
% 99.20/13.41 ((
% 99.20/13.41 (funcGraphProp2) =>
% 99.20/13.41 ((
% 99.20/13.41 (funcextLem) =>
% 99.20/13.41 ((
% 99.20/13.41 (funcGraphProp4) =>
% 99.20/13.41 ((
% 99.20/13.41 (subbreln) =>
% 99.20/13.41 ((
% 99.20/13.41 (eqbreln) =>
% 99.20/13.41 ((
% 99.20/13.41 (funcext) =>
% 99.20/13.41 ((
% 99.20/13.41 (funcext2) =>
% 99.20/13.41 ((
% 99.20/13.41 (ap2apEq1) =>
% 99.20/13.41 ((
% 99.20/13.41 (ap2apEq2) =>
% 99.20/13.41 ((
% 99.20/13.41 (beta1) =>
% 99.20/13.41 ((
% 99.20/13.41 (eta1) =>
% 99.20/13.41 ((
% 99.20/13.41 (lam2lamEq) =>
% 99.20/13.41 ((
% 99.20/13.41 (beta2) =>
% 99.20/13.41 ((
% 99.20/13.41 (eta2) =>
% 99.20/13.41 ((
% 99.20/13.41 (iffalseProp1) =>
% 99.20/13.41 ((
% 99.20/13.41 (iffalseProp2) =>
% 99.20/13.41 ((
% 99.20/13.41 (iftrueProp1) =>
% 99.20/13.41 ((
% 99.20/13.41 (iftrueProp2) =>
% 99.20/13.41 ((
% 99.20/13.41 (ifSingleton) =>
% 99.20/13.41 ((
% 99.20/13.41 (ifp) =>
% 99.20/13.41 ((
% 99.20/13.41 (theeq) =>
% 99.20/13.41 ((
% 99.20/13.41 (iftrue) =>
% 99.20/13.41 ((
% 99.20/13.41 (iffalse) =>
% 99.20/13.41 ((
% 99.20/13.41 (iftrueorfalse) =>
% 99.20/13.41 ((
% 99.20/13.41 (binintersectT_lem) =>
% 99.20/13.41 ((
% 99.20/13.41 (binunionT_lem) =>
% 99.20/13.41 ((
% 99.20/13.41 (powersetT_lem) =>
% 99.20/13.41 ((
% 99.20/13.41 (setminusT_lem) =>
% 99.20/13.41 ((
% 99.20/13.41 (complementT_lem) =>
% 99.20/13.41 ((
% 99.20/13.41 (setextT) =>
% 99.20/13.41 ((
% 99.20/13.41 (subsetTI) =>
% 99.20/13.41 ((
% 99.20/13.41 (powersetTI1) =>
% 99.20/13.41 ((
% 99.20/13.41 (powersetTE1) =>
% 99.20/13.41 ((
% 99.20/13.41 (complementTI1) =>
% 99.20/13.41 ((
% 99.20/13.41 (complementTE1) =>
% 99.20/13.41 ((
% 99.20/13.41 (binintersectTELcontra) =>
% 99.20/13.41 ((
% 99.20/13.41 (binintersectTERcontra) =>
% 99.20/13.41 ((
% 99.20/13.41 (contrasubsetT) =>
% 99.20/13.41 ((
% 99.20/13.41 (contrasubsetT1) =>
% 99.20/13.41 ((
% 99.20/13.41 (contrasubsetT2) =>
% 99.20/13.41 ((
% 99.20/13.41 (contrasubsetT3) =>
% 99.20/13.41 ((
% 99.20/13.41 (doubleComplementI1) =>
% 99.20/13.41 ((
% 99.20/13.41 (doubleComplementE1) =>
% 99.20/13.41 ((
% 99.20/13.41 (doubleComplementSub1) =>
% 99.20/13.41 ((
% 99.20/13.41 (doubleComplementSub2) =>
% 99.20/13.41 ((
% 99.20/13.41 (doubleComplementEq) =>
% 99.20/13.41 ((
% 99.20/13.41 (complementTnotintersectT) =>
% 99.20/13.41 ((
% 99.20/13.41 (complementImpComplementIntersect) =>
% 99.20/13.41 ((
% 99.20/13.41 (complementSubsetComplementIntersect) =>
% 99.20/13.41 ((
% 99.20/13.41 (complementInPowersetComplementIntersect) =>
% 99.20/13.41 ((
% 99.20/13.41 (contraSubsetComplement) =>
% 99.20/13.41 ((
% 99.20/13.41 (complementTcontraSubset) =>
% 99.20/13.41 ((
% 99.20/13.41 (binunionTILcontra) =>
% 99.20/13.41 ((
% 99.20/13.41 (binunionTIRcontra) =>
% 99.20/13.41 ((
% 99.20/13.41 (inIntersectImpInUnion) =>
% 99.20/13.41 ((
% 99.20/13.41 (inIntersectImpInUnion2) =>
% 99.20/13.41 ((
% 99.20/13.41 (inIntersectImpInIntersectUnions) =>
% 99.20/13.41 ((
% 99.20/13.41 (intersectInPowersetIntersectUnions) =>
% 99.20/13.41 ((
% 99.20/13.41 (inComplementUnionImpNotIn1) =>
% 99.20/13.41 ((
% 99.20/13.41 (inComplementUnionImpInComplement1) =>
% 99.20/13.41 ((
% 99.20/13.41 (binunionTE) =>
% 99.20/13.41 ((
% 99.20/13.41 (binunionTEcontra) =>
% 99.20/13.41 ((
% 99.20/13.41 (demorgan2a1) =>
% 99.20/13.41 ((
% 99.20/13.41 (complementUnionInPowersetComplement) =>
% 99.20/13.41 ((
% 99.20/13.41 (demorgan2a2) =>
% 99.20/13.41 ((
% 99.20/13.41 (demorgan1a) =>
% 99.20/13.41 ((
% 99.20/13.41 (demorgan1b) =>
% 99.20/13.41 ((
% 99.20/13.41 (demorgan1) =>
% 99.20/13.41 ((
% 99.20/13.41 (demorgan2a) =>
% 99.20/13.41 ((
% 99.20/13.41 (demorgan2b2) =>
% 99.20/13.41 ((
% 99.20/13.41 (demorgan2b) =>
% 99.20/13.41 ((
% 99.20/13.41 (demorgan2) =>
% 99.20/13.41 ((
% 99.20/13.41 (woz13rule0) =>
% 99.20/13.41 ((
% 99.20/13.41 (woz13rule1) =>
% 99.20/13.41 ((
% 99.20/13.41 (woz13rule2) =>
% 99.20/13.41 ((
% 99.20/13.41 (woz13rule3) =>
% 99.20/13.41 ((
% 99.20/13.41 (woz13rule4) =>
% 99.20/13.41 ((
% 99.20/13.41 (woz1_1) =>
% 99.20/13.41 ((
% 99.20/13.41 (woz1_2) =>
% 99.20/13.41 ((
% 99.20/13.41 (woz1_3) =>
% 99.20/13.41 ((
% 99.20/13.41 (woz1_4) =>
% 99.20/13.41 ((
% 99.20/13.41 (woz1_5) =>
% 99.20/13.41 ((
% 99.20/13.41 (breln1all2) =>
% 99.20/13.41 ((
% 99.20/13.41 (breln1SetBreln1) =>
% 99.20/13.41 ((
% 99.20/13.41 (choice2fnsingleton) =>
% 99.20/13.41 ((
% 99.20/13.41 (setOfPairsIsBReln1) =>
% 99.20/13.41 ((
% 99.20/13.41 (breln1all1) =>
% 99.20/13.41 ((
% 99.20/13.41 (subbreln1) =>
% 99.20/13.41 ((
% 99.20/13.41 (eqbreln1) =>
% 99.20/13.41 ((
% 99.20/13.41 (breln1invprop) =>
% 99.20/13.41 ((
% 99.20/13.41 (breln1invI) =>
% 99.20/13.41 ((
% 99.20/13.41 (breln1invE) =>
% 99.20/13.41 ((
% 99.20/13.41 (breln1compprop) =>
% 99.20/13.41 ((
% 99.20/13.41 (breln1compI) =>
% 99.20/13.41 ((
% 99.20/13.41 (breln1compE) =>
% 99.20/13.41 ((
% 99.20/13.41 (breln1compEex) =>
% 99.20/13.41 ((
% 99.20/13.41 (breln1unionprop) =>
% 99.20/13.41 ((
% 99.20/13.41 (breln1unionIL) =>
% 99.20/13.41 ((
% 99.20/13.41 (breln1unionIR) =>
% 99.20/13.41 ((
% 99.20/13.41 (breln1unionI) =>
% 99.20/13.41 ((
% 99.20/13.41 (breln1unionE) =>
% 99.20/13.41 ((
% 99.20/13.41 (breln1unionEcases) =>
% 99.20/13.41 ((
% 99.20/13.41 (breln1unionCommutes) =>
% 99.20/13.41 ((
% 99.20/13.41 (woz2Ex) =>
% 99.20/13.41 ((
% 99.20/13.41 (woz2W) =>
% 99.20/13.41 ((
% 99.20/13.41 (woz2A) =>
% 99.20/13.41 ((
% 99.20/13.41 (woz2B) =>
% 99.20/13.41 ((
% 99.20/13.41 (image1Ex) =>
% 99.20/13.41 ((
% 99.20/13.41 (image1Ex1) =>
% 99.20/13.41 ((
% 99.20/13.41 (image1Equiv) =>
% 99.20/13.41 ((
% 99.20/13.41 (image1E) =>
% 99.20/13.41 ((
% 99.20/13.41 (image1I) =>
% 99.20/13.41 ((
% 99.20/13.41 (injFuncInInjFuncSet) =>
% 99.20/13.41 ((
% 99.20/13.41 (injFuncSetFuncIn) =>
% 99.20/13.41 ((
% 99.20/13.41 (injFuncSetFuncInj) =>
% 99.20/13.41 ((
% 99.20/13.41 (!!) @ (
% 99.20/13.41 (('#B') @ (
% 99.20/13.41 !!) @
% 99.20/13.41 (
% 99.20/13.41 (
% 99.20/13.41 ('#B') @ (
% 99.20/13.41 (
% 99.20/13.41 ('#B') @ (
% 99.20/13.41 !!))) @
% 99.20/13.41 (
% 99.20/13.41 (
% 99.20/13.41 ('#S') @ (
% 99.20/13.41 (
% 99.20/13.41 ('#B') @ (
% 99.20/13.41 '#S') @
% 99.20/13.41 (
% 99.20/13.41 (
% 99.20/13.41 ('#B') @ (
% 99.20/13.41 (
% 99.20/13.41 ('#B') @ (
% 99.20/13.41 '#S'))) @
% 99.20/13.41 (
% 99.20/13.41 (
% 99.20/13.41 ('#B') @ (
% 99.20/13.41 (
% 99.20/13.41 ('#B') @ (
% 99.20/13.41 (
% 99.20/13.41 ('#B') @ (
% 99.20/13.41 =>))))) @
% 99.20/13.41 (
% 99.20/13.41 (
% 99.20/13.41 ('#B') @ (
% 99.20/13.41 (
% 99.20/13.41 ('#B') @ (
% 99.20/13.41 (
% 99.20/13.41 ('#C') @ in)))) @
% 99.20/13.41 surjFuncSet)))))))) @
% 99.20/13.41 (
% 99.20/13.41 (
% 99.20/13.41 ('#B') @ (
% 99.20/13.41 (
% 99.20/13.41 ('#B') @ (
% 99.20/13.41 (
% 99.20/13.41 ('#C') @ in)))) @
% 99.20/13.41 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.20/13.41 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl749])).
% 99.20/13.41 thf(zip_derived_cl789, plain,
% 99.20/13.41 (~ (((subsetI1) =>
% 99.20/13.41 (((eqimpsubset2) =>
% 99.20/13.41 (((eqimpsubset1) =>
% 99.20/13.41 (((subsetI2) =>
% 99.20/13.41 (((emptysetsubset) =>
% 99.20/13.41 (((subsetE) =>
% 99.20/13.41 (((subsetE2) =>
% 99.20/13.41 (((notsubsetI) =>
% 99.20/13.41 (((notequalI1) =>
% 99.20/13.41 (((notequalI2) =>
% 99.20/13.41 (((subsetRefl) =>
% 99.20/13.41 (((subsetTrans) =>
% 99.20/13.41 (((setadjoinSub) =>
% 99.20/13.41 (((setadjoinSub2) =>
% 99.20/13.41 (((subset2powerset) =>
% 99.20/13.41 (((setextsub) =>
% 99.20/13.41 (((subsetemptysetimpeq) =>
% 99.20/13.41 (((powersetI1) =>
% 99.20/13.41 (((powersetE1) =>
% 99.20/13.41 (((inPowerset) =>
% 99.20/13.41 (((powersetsubset) =>
% 99.20/13.41 (((sepInPowerset) =>
% 99.20/13.41 (((sepSubset) =>
% 99.20/13.41 (((binunionIL) =>
% 99.20/13.41 (((upairset2IR) =>
% 99.20/13.41 (((binunionIR) =>
% 99.20/13.41 (((binunionEcases) =>
% 99.20/13.41 (((binunionE) =>
% 99.20/13.41 (((binunionLsub) =>
% 99.20/13.41 (((binunionRsub) =>
% 99.20/13.41 ((
% 99.20/13.41 (binintersectI) =>
% 99.20/13.41 ((
% 99.20/13.41 (binintersectSubset5) =>
% 99.20/13.41 ((
% 99.20/13.41 (binintersectEL) =>
% 99.20/13.41 ((
% 99.20/13.41 (binintersectLsub) =>
% 99.20/13.41 ((
% 99.20/13.41 (binintersectSubset2) =>
% 99.20/13.41 ((
% 99.20/13.41 (binintersectSubset3) =>
% 99.20/13.41 ((
% 99.20/13.41 (binintersectER) =>
% 99.20/13.41 ((
% 99.20/13.41 (disjointsetsI1) =>
% 99.20/13.41 ((
% 99.20/13.41 (binintersectRsub) =>
% 99.20/13.41 ((
% 99.20/13.41 (binintersectSubset4) =>
% 99.20/13.41 ((
% 99.20/13.41 (binintersectSubset1) =>
% 99.20/13.41 ((
% 99.20/13.41 (bs114d) =>
% 99.20/13.41 ((
% 99.20/13.41 (setminusI) =>
% 99.20/13.41 ((
% 99.20/13.41 (setminusEL) =>
% 99.20/13.41 ((
% 99.20/13.41 (setminusER) =>
% 99.20/13.41 ((
% 99.20/13.41 (setminusSubset2) =>
% 99.20/13.41 ((
% 99.20/13.41 (setminusERneg) =>
% 99.20/13.41 ((
% 99.20/13.41 (setminusELneg) =>
% 99.20/13.41 ((
% 99.20/13.41 (setminusILneg) =>
% 99.20/13.41 ((
% 99.20/13.41 (setminusIRneg) =>
% 99.20/13.41 ((
% 99.20/13.41 (setminusLsub) =>
% 99.20/13.41 ((
% 99.20/13.41 (setminusSubset1) =>
% 99.20/13.41 ((
% 99.20/13.41 (symdiffE) =>
% 99.20/13.41 ((
% 99.20/13.41 (symdiffI1) =>
% 99.20/13.41 ((
% 99.20/13.41 (symdiffI2) =>
% 99.20/13.41 ((
% 99.20/13.41 (symdiffIneg1) =>
% 99.20/13.41 ((
% 99.20/13.41 (symdiffIneg2) =>
% 99.20/13.41 ((
% 99.20/13.41 (secondinupair) =>
% 99.20/13.41 ((
% 99.20/13.41 (setukpairIL) =>
% 99.20/13.41 ((
% 99.20/13.41 (setukpairIR) =>
% 99.20/13.41 ((
% 99.20/13.41 (kpairiskpair) =>
% 99.20/13.41 ((
% 99.20/13.41 (kpairp) =>
% 99.20/13.41 ((
% 99.20/13.41 (singletonsubset) =>
% 99.20/13.41 ((
% 99.20/13.41 (singletoninpowerset) =>
% 99.20/13.41 ((
% 99.20/13.41 (singletoninpowunion) =>
% 99.20/13.41 ((
% 99.20/13.41 (upairset2E) =>
% 99.20/13.41 ((
% 99.20/13.41 (upairsubunion) =>
% 99.20/13.41 ((
% 99.20/13.41 (upairinpowunion) =>
% 99.20/13.41 ((
% 99.20/13.41 (ubforcartprodlem1) =>
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% 99.20/13.41 (cartprodsndpairEq) =>
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% 99.20/13.41 ((
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% 99.20/13.41 (lamProp) =>
% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
% 99.20/13.41 (brelnall2) =>
% 99.20/13.41 ((
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% 99.20/13.41 ((
% 99.20/13.41 (funcGraphProp1) =>
% 99.20/13.41 ((
% 99.20/13.41 (funcGraphProp3) =>
% 99.20/13.41 ((
% 99.20/13.41 (funcGraphProp2) =>
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% 99.20/13.41 ((
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% 99.20/13.41 ((
% 99.20/13.41 (contrasubsetT2) =>
% 99.20/13.41 ((
% 99.20/13.41 (contrasubsetT3) =>
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% 99.20/13.41 (doubleComplementEq) =>
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% 99.20/13.41 ((
% 99.20/13.41 (binunionTIRcontra) =>
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
% 99.20/13.41 (demorgan2a) =>
% 99.20/13.41 ((
% 99.20/13.41 (demorgan2b2) =>
% 99.20/13.41 ((
% 99.20/13.41 (demorgan2b) =>
% 99.20/13.41 ((
% 99.20/13.41 (demorgan2) =>
% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 (woz13rule3) =>
% 99.20/13.41 ((
% 99.20/13.41 (woz13rule4) =>
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% 99.20/13.41 ((
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% 99.20/13.41 ((
% 99.20/13.41 (woz1_4) =>
% 99.20/13.41 ((
% 99.20/13.41 (woz1_5) =>
% 99.20/13.41 ((
% 99.20/13.41 (breln1all2) =>
% 99.20/13.41 ((
% 99.20/13.41 (breln1SetBreln1) =>
% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
% 99.20/13.41 (breln1compE) =>
% 99.20/13.41 ((
% 99.20/13.41 (breln1compEex) =>
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 (
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% 99.20/13.41 (binintersectSubset3) =>
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
% 99.20/13.41 (ubforcartprodlem3) =>
% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
% 99.20/13.41 (cartprodmempair) =>
% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
% 99.20/13.41 (setunionsingleton2) =>
% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
% 99.20/13.41 (cartprodpairmemER) =>
% 99.20/13.41 ((
% 99.20/13.41 (cartprodmempaircEq) =>
% 99.20/13.41 ((
% 99.20/13.41 (cartprodfstpairEq) =>
% 99.20/13.41 ((
% 99.20/13.41 (cartprodsndpairEq) =>
% 99.20/13.41 ((
% 99.20/13.41 (cartprodpairsurjEq) =>
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% 99.20/13.41 ((
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% 99.20/13.41 (funcImageSingleton) =>
% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
% 99.20/13.41 (infuncsetfunc) =>
% 99.20/13.41 ((
% 99.20/13.41 (ap2p) =>
% 99.20/13.41 ((
% 99.20/13.41 (funcinfuncset) =>
% 99.20/13.41 ((
% 99.20/13.41 (lamProp) =>
% 99.20/13.41 ((
% 99.20/13.41 (lamp) =>
% 99.20/13.41 ((
% 99.20/13.41 (lam2p) =>
% 99.20/13.41 ((
% 99.20/13.41 (brelnall1) =>
% 99.20/13.41 ((
% 99.20/13.41 (brelnall2) =>
% 99.20/13.41 ((
% 99.20/13.41 (ex1E2) =>
% 99.20/13.41 ((
% 99.20/13.41 (funcGraphProp1) =>
% 99.20/13.41 ((
% 99.20/13.41 (funcGraphProp3) =>
% 99.20/13.41 ((
% 99.20/13.41 (funcGraphProp2) =>
% 99.20/13.41 ((
% 99.20/13.41 (funcextLem) =>
% 99.20/13.41 ((
% 99.20/13.41 (funcGraphProp4) =>
% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
% 99.20/13.41 (funcext) =>
% 99.20/13.41 ((
% 99.20/13.41 (funcext2) =>
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% 99.20/13.41 ((
% 99.20/13.41 (ap2apEq2) =>
% 99.20/13.41 ((
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% 99.20/13.41 ((
% 99.20/13.41 (eta1) =>
% 99.20/13.41 ((
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% 99.20/13.41 ((
% 99.20/13.41 (beta2) =>
% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
% 99.20/13.41 (iffalseProp2) =>
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% 99.20/13.41 ((
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% 99.20/13.41 ((
% 99.20/13.41 (binintersectTERcontra) =>
% 99.20/13.41 ((
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% 99.20/13.41 ((
% 99.20/13.41 (contrasubsetT1) =>
% 99.20/13.41 ((
% 99.20/13.41 (contrasubsetT2) =>
% 99.20/13.41 ((
% 99.20/13.41 (contrasubsetT3) =>
% 99.20/13.41 ((
% 99.20/13.41 (doubleComplementI1) =>
% 99.20/13.41 ((
% 99.20/13.41 (doubleComplementE1) =>
% 99.20/13.41 ((
% 99.20/13.41 (doubleComplementSub1) =>
% 99.20/13.41 ((
% 99.20/13.41 (doubleComplementSub2) =>
% 99.20/13.41 ((
% 99.20/13.41 (doubleComplementEq) =>
% 99.20/13.41 ((
% 99.20/13.41 (complementTnotintersectT) =>
% 99.20/13.41 ((
% 99.20/13.41 (complementImpComplementIntersect) =>
% 99.20/13.41 ((
% 99.20/13.41 (complementSubsetComplementIntersect) =>
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% 99.20/13.41 (complementInPowersetComplementIntersect) =>
% 99.20/13.41 ((
% 99.20/13.41 (contraSubsetComplement) =>
% 99.20/13.41 ((
% 99.20/13.41 (complementTcontraSubset) =>
% 99.20/13.41 ((
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% 99.20/13.41 ((
% 99.20/13.41 (binunionTIRcontra) =>
% 99.20/13.41 ((
% 99.20/13.41 (inIntersectImpInUnion) =>
% 99.20/13.41 ((
% 99.20/13.41 (inIntersectImpInUnion2) =>
% 99.20/13.41 ((
% 99.20/13.41 (inIntersectImpInIntersectUnions) =>
% 99.20/13.41 ((
% 99.20/13.41 (intersectInPowersetIntersectUnions) =>
% 99.20/13.41 ((
% 99.20/13.41 (inComplementUnionImpNotIn1) =>
% 99.20/13.41 ((
% 99.20/13.41 (inComplementUnionImpInComplement1) =>
% 99.20/13.41 ((
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% 99.20/13.41 ((
% 99.20/13.41 (binunionTEcontra) =>
% 99.20/13.41 ((
% 99.20/13.41 (demorgan2a1) =>
% 99.20/13.41 ((
% 99.20/13.41 (complementUnionInPowersetComplement) =>
% 99.20/13.41 ((
% 99.20/13.41 (demorgan2a2) =>
% 99.20/13.41 ((
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% 99.20/13.41 ((
% 99.20/13.41 (demorgan1b) =>
% 99.20/13.41 ((
% 99.20/13.41 (demorgan1) =>
% 99.20/13.41 ((
% 99.20/13.41 (demorgan2a) =>
% 99.20/13.41 ((
% 99.20/13.41 (demorgan2b2) =>
% 99.20/13.41 ((
% 99.20/13.41 (demorgan2b) =>
% 99.20/13.41 ((
% 99.20/13.41 (demorgan2) =>
% 99.20/13.41 ((
% 99.20/13.41 (woz13rule0) =>
% 99.20/13.41 ((
% 99.20/13.41 (woz13rule1) =>
% 99.20/13.41 ((
% 99.20/13.41 (woz13rule2) =>
% 99.20/13.41 ((
% 99.20/13.41 (woz13rule3) =>
% 99.20/13.41 ((
% 99.20/13.41 (woz13rule4) =>
% 99.20/13.41 ((
% 99.20/13.41 (woz1_1) =>
% 99.20/13.41 ((
% 99.20/13.41 (woz1_2) =>
% 99.20/13.41 ((
% 99.20/13.41 (woz1_3) =>
% 99.20/13.41 ((
% 99.20/13.41 (woz1_4) =>
% 99.20/13.41 ((
% 99.20/13.41 (woz1_5) =>
% 99.20/13.41 ((
% 99.20/13.41 (breln1all2) =>
% 99.20/13.41 ((
% 99.20/13.41 (breln1SetBreln1) =>
% 99.20/13.41 ((
% 99.20/13.41 (choice2fnsingleton) =>
% 99.20/13.41 ((
% 99.20/13.41 (setOfPairsIsBReln1) =>
% 99.20/13.41 ((
% 99.20/13.41 (breln1all1) =>
% 99.20/13.41 ((
% 99.20/13.41 (subbreln1) =>
% 99.20/13.41 ((
% 99.20/13.41 (eqbreln1) =>
% 99.20/13.41 ((
% 99.20/13.41 (breln1invprop) =>
% 99.20/13.41 ((
% 99.20/13.41 (breln1invI) =>
% 99.20/13.41 ((
% 99.20/13.41 (breln1invE) =>
% 99.20/13.41 ((
% 99.20/13.41 (breln1compprop) =>
% 99.20/13.41 ((
% 99.20/13.41 (breln1compI) =>
% 99.20/13.41 ((
% 99.20/13.41 (breln1compE) =>
% 99.20/13.41 ((
% 99.20/13.41 (breln1compEex) =>
% 99.20/13.41 ((
% 99.20/13.41 (breln1unionprop) =>
% 99.20/13.41 ((
% 99.20/13.41 (breln1unionIL) =>
% 99.20/13.41 ((
% 99.20/13.41 (breln1unionIR) =>
% 99.20/13.41 ((
% 99.20/13.41 (breln1unionI) =>
% 99.20/13.41 ((
% 99.20/13.41 (breln1unionE) =>
% 99.20/13.41 ((
% 99.20/13.41 (breln1unionEcases) =>
% 99.20/13.41 ((
% 99.20/13.41 (breln1unionCommutes) =>
% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
% 99.20/13.41 (woz2B) =>
% 99.20/13.41 ((
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% 99.20/13.41 ((
% 99.20/13.41 (image1Ex1) =>
% 99.20/13.41 ((
% 99.20/13.41 (image1Equiv) =>
% 99.20/13.41 ((
% 99.20/13.41 (image1E) =>
% 99.20/13.41 ((
% 99.20/13.41 (image1I) =>
% 99.20/13.41 ((
% 99.20/13.41 (injFuncInInjFuncSet) =>
% 99.20/13.41 ((
% 99.20/13.41 (injFuncSetFuncIn) =>
% 99.20/13.41 ((
% 99.20/13.41 (injFuncSetFuncInj) =>
% 99.20/13.41 ((
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% 99.20/13.41 (('#B') @ (
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% 99.20/13.41 (
% 99.20/13.41 (
% 99.20/13.41 ('#B') @ (
% 99.20/13.41 (
% 99.20/13.41 ('#B') @ (
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% 99.20/13.41 (
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% 99.20/13.41 (
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% 99.20/13.41 (
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% 99.20/13.41 (
% 99.20/13.41 (
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% 99.20/13.41 (
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% 99.20/13.41 (
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% 99.20/13.41 (
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% 99.20/13.41 (
% 99.20/13.41 ('#B') @ (
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% 99.20/13.41 surjFuncSet)))))))) @
% 99.20/13.41 (
% 99.20/13.41 (
% 99.20/13.41 ('#B') @ (
% 99.20/13.41 (
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% 99.20/13.41 (
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% 99.20/13.41 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
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% 99.20/13.41 ((
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% 99.20/13.41 ((
% 99.20/13.41 (binintersectSubset3) =>
% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
% 99.20/13.41 (binintersectSubset1) =>
% 99.20/13.41 ((
% 99.20/13.41 (bs114d) =>
% 99.20/13.41 ((
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% 99.20/13.41 ((
% 99.20/13.41 (setminusEL) =>
% 99.20/13.41 ((
% 99.20/13.41 (setminusER) =>
% 99.20/13.41 ((
% 99.20/13.41 (setminusSubset2) =>
% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
% 99.20/13.41 (setminusILneg) =>
% 99.20/13.41 ((
% 99.20/13.41 (setminusIRneg) =>
% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
% 99.20/13.41 (symdiffIneg2) =>
% 99.20/13.41 ((
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% 99.20/13.41 ((
% 99.20/13.41 (setukpairIR) =>
% 99.20/13.41 ((
% 99.20/13.41 (kpairiskpair) =>
% 99.20/13.41 ((
% 99.20/13.41 (kpairp) =>
% 99.20/13.41 ((
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% 99.20/13.41 ((
% 99.20/13.41 (singletoninpowerset) =>
% 99.20/13.41 ((
% 99.20/13.41 (singletoninpowunion) =>
% 99.20/13.41 ((
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% 99.20/13.41 ((
% 99.20/13.41 (upairsubunion) =>
% 99.20/13.41 ((
% 99.20/13.41 (upairinpowunion) =>
% 99.20/13.41 ((
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% 99.20/13.41 ((
% 99.20/13.41 (ubforcartprodlem2) =>
% 99.20/13.41 ((
% 99.20/13.41 (ubforcartprodlem3) =>
% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
% 99.20/13.41 (cartprodmempair) =>
% 99.20/13.41 ((
% 99.20/13.41 (setunionE2) =>
% 99.20/13.41 ((
% 99.20/13.41 (setunionsingleton1) =>
% 99.20/13.41 ((
% 99.20/13.41 (setunionsingleton2) =>
% 99.20/13.41 ((
% 99.20/13.41 (setunionsingleton) =>
% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
% 99.20/13.41 (ex1I) =>
% 99.20/13.41 ((
% 99.20/13.41 (ex1I2) =>
% 99.20/13.41 ((
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% 99.20/13.41 ((
% 99.20/13.41 (setukpairinjL1) =>
% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
% 99.20/13.41 (kfstpairEq) =>
% 99.20/13.41 ((
% 99.20/13.41 (cartprodfstin) =>
% 99.20/13.41 ((
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% 99.20/13.41 ((
% 99.20/13.41 (setukpairinjL) =>
% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
% 99.20/13.41 (kpairsurjEq) =>
% 99.20/13.41 ((
% 99.20/13.41 (cartprodsndin) =>
% 99.20/13.41 ((
% 99.20/13.41 (cartprodpairmemEL) =>
% 99.20/13.41 ((
% 99.20/13.41 (cartprodpairmemER) =>
% 99.20/13.41 ((
% 99.20/13.41 (cartprodmempaircEq) =>
% 99.20/13.41 ((
% 99.20/13.41 (cartprodfstpairEq) =>
% 99.20/13.41 ((
% 99.20/13.41 (cartprodsndpairEq) =>
% 99.20/13.41 ((
% 99.20/13.41 (cartprodpairsurjEq) =>
% 99.20/13.41 ((
% 99.20/13.41 (dpsetconstrI) =>
% 99.20/13.41 ((
% 99.20/13.41 (dpsetconstrSub) =>
% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
% 99.20/13.41 (dpsetconstrEL1) =>
% 99.20/13.41 ((
% 99.20/13.41 (dpsetconstrEL2) =>
% 99.20/13.41 ((
% 99.20/13.41 (dpsetconstrER) =>
% 99.20/13.41 ((
% 99.20/13.41 (funcImageSingleton) =>
% 99.20/13.41 ((
% 99.20/13.41 (apProp) =>
% 99.20/13.41 ((
% 99.20/13.41 (app) =>
% 99.20/13.41 ((
% 99.20/13.41 (infuncsetfunc) =>
% 99.20/13.41 ((
% 99.20/13.41 (ap2p) =>
% 99.20/13.41 ((
% 99.20/13.41 (funcinfuncset) =>
% 99.20/13.41 ((
% 99.20/13.41 (lamProp) =>
% 99.20/13.41 ((
% 99.20/13.41 (lamp) =>
% 99.20/13.41 ((
% 99.20/13.41 (lam2p) =>
% 99.20/13.41 ((
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% 99.20/13.41 ((
% 99.20/13.41 (brelnall2) =>
% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
% 99.20/13.41 (funcGraphProp3) =>
% 99.20/13.41 ((
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% 99.20/13.41 ((
% 99.20/13.41 (contrasubsetT2) =>
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% 99.20/13.41 ((
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% 99.20/13.41 ((
% 99.20/13.41 (demorgan2b) =>
% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 (woz1_5) =>
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
% 99.20/13.41 (breln1compEex) =>
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 (
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
% 99.20/13.41 (cartprodsndpairEq) =>
% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
% 99.20/13.41 (lamp) =>
% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
% 99.20/13.41 (contrasubsetT2) =>
% 99.20/13.41 ((
% 99.20/13.41 (contrasubsetT3) =>
% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
% 99.20/13.41 (doubleComplementSub1) =>
% 99.20/13.41 ((
% 99.20/13.41 (doubleComplementSub2) =>
% 99.20/13.41 ((
% 99.20/13.41 (doubleComplementEq) =>
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% 99.20/13.41 ((
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% 99.20/13.41 ((
% 99.20/13.41 (inIntersectImpInUnion2) =>
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% 99.20/13.41 (inIntersectImpInIntersectUnions) =>
% 99.20/13.41 ((
% 99.20/13.41 (intersectInPowersetIntersectUnions) =>
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
% 99.20/13.41 (demorgan1b) =>
% 99.20/13.41 ((
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% 99.20/13.41 ((
% 99.20/13.41 (demorgan2a) =>
% 99.20/13.41 ((
% 99.20/13.41 (demorgan2b2) =>
% 99.20/13.41 ((
% 99.20/13.41 (demorgan2b) =>
% 99.20/13.41 ((
% 99.20/13.41 (demorgan2) =>
% 99.20/13.41 ((
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% 99.20/13.41 ((
% 99.20/13.41 (woz13rule1) =>
% 99.20/13.41 ((
% 99.20/13.41 (woz13rule2) =>
% 99.20/13.41 ((
% 99.20/13.41 (woz13rule3) =>
% 99.20/13.41 ((
% 99.20/13.41 (woz13rule4) =>
% 99.20/13.41 ((
% 99.20/13.41 (woz1_1) =>
% 99.20/13.41 ((
% 99.20/13.41 (woz1_2) =>
% 99.20/13.41 ((
% 99.20/13.41 (woz1_3) =>
% 99.20/13.41 ((
% 99.20/13.41 (woz1_4) =>
% 99.20/13.41 ((
% 99.20/13.41 (woz1_5) =>
% 99.20/13.41 ((
% 99.20/13.41 (breln1all2) =>
% 99.20/13.41 ((
% 99.20/13.41 (breln1SetBreln1) =>
% 99.20/13.41 ((
% 99.20/13.41 (choice2fnsingleton) =>
% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
% 99.20/13.41 (eqbreln1) =>
% 99.20/13.41 ((
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% 99.20/13.41 ((
% 99.20/13.41 (breln1invI) =>
% 99.20/13.41 ((
% 99.20/13.41 (breln1invE) =>
% 99.20/13.41 ((
% 99.20/13.41 (breln1compprop) =>
% 99.20/13.41 ((
% 99.20/13.41 (breln1compI) =>
% 99.20/13.41 ((
% 99.20/13.41 (breln1compE) =>
% 99.20/13.41 ((
% 99.20/13.41 (breln1compEex) =>
% 99.20/13.41 ((
% 99.20/13.41 (breln1unionprop) =>
% 99.20/13.41 ((
% 99.20/13.41 (breln1unionIL) =>
% 99.20/13.41 ((
% 99.20/13.41 (breln1unionIR) =>
% 99.20/13.41 ((
% 99.20/13.41 (breln1unionI) =>
% 99.20/13.41 ((
% 99.20/13.41 (breln1unionE) =>
% 99.20/13.41 ((
% 99.20/13.41 (breln1unionEcases) =>
% 99.20/13.41 ((
% 99.20/13.41 (breln1unionCommutes) =>
% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
% 99.20/13.41 (woz2B) =>
% 99.20/13.41 ((
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% 99.20/13.41 ((
% 99.20/13.41 (image1Ex1) =>
% 99.20/13.41 ((
% 99.20/13.41 (image1Equiv) =>
% 99.20/13.41 ((
% 99.20/13.41 (image1E) =>
% 99.20/13.41 ((
% 99.20/13.41 (image1I) =>
% 99.20/13.41 ((
% 99.20/13.41 (injFuncInInjFuncSet) =>
% 99.20/13.41 ((
% 99.20/13.41 (injFuncSetFuncIn) =>
% 99.20/13.41 ((
% 99.20/13.41 (injFuncSetFuncInj) =>
% 99.20/13.41 ((
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% 99.20/13.41 (
% 99.20/13.41 (
% 99.20/13.41 ('#B') @ (
% 99.20/13.41 (
% 99.20/13.41 ('#B') @ (
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% 99.20/13.41 (
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% 99.20/13.41 (
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% 99.20/13.41 (
% 99.20/13.41 (
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% 99.20/13.41 (
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% 99.20/13.41 (
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% 99.20/13.41 (
% 99.20/13.41 (
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% 99.20/13.41 (
% 99.20/13.41 ('#B') @ (
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% 99.20/13.41 surjFuncSet)))))))) @
% 99.20/13.41 (
% 99.20/13.41 (
% 99.20/13.41 ('#B') @ (
% 99.20/13.41 (
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% 99.20/13.41 (
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% 99.20/13.41 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.20/13.41 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl824])).
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% 99.20/13.41 (((notequalI2) =>
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% 99.20/13.41 (((powersetE1) =>
% 99.20/13.41 (((inPowerset) =>
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% 99.20/13.41 (((sepSubset) =>
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% 99.20/13.41 (((upairset2IR) =>
% 99.20/13.41 (((binunionIR) =>
% 99.20/13.41 (((binunionEcases) =>
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% 99.20/13.41 (((binunionRsub) =>
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% 99.20/13.41 (((binintersectLsub) =>
% 99.20/13.41 ((
% 99.20/13.41 (binintersectSubset2) =>
% 99.20/13.41 ((
% 99.20/13.41 (binintersectSubset3) =>
% 99.20/13.41 ((
% 99.20/13.41 (binintersectER) =>
% 99.20/13.41 ((
% 99.20/13.41 (disjointsetsI1) =>
% 99.20/13.41 ((
% 99.20/13.41 (binintersectRsub) =>
% 99.20/13.41 ((
% 99.20/13.41 (binintersectSubset4) =>
% 99.20/13.41 ((
% 99.20/13.41 (binintersectSubset1) =>
% 99.20/13.41 ((
% 99.20/13.41 (bs114d) =>
% 99.20/13.41 ((
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% 99.20/13.41 ((
% 99.20/13.41 (setminusEL) =>
% 99.20/13.41 ((
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% 99.20/13.41 ((
% 99.20/13.41 (setminusSubset2) =>
% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
% 99.20/13.41 (setminusILneg) =>
% 99.20/13.41 ((
% 99.20/13.41 (setminusIRneg) =>
% 99.20/13.41 ((
% 99.20/13.41 (setminusLsub) =>
% 99.20/13.41 ((
% 99.20/13.41 (setminusSubset1) =>
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
% 99.20/13.41 (symdiffIneg2) =>
% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
% 99.20/13.41 (kpairiskpair) =>
% 99.20/13.41 ((
% 99.20/13.41 (kpairp) =>
% 99.20/13.41 ((
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% 99.20/13.41 ((
% 99.20/13.41 (singletoninpowerset) =>
% 99.20/13.41 ((
% 99.20/13.41 (singletoninpowunion) =>
% 99.20/13.41 ((
% 99.20/13.41 (upairset2E) =>
% 99.20/13.41 ((
% 99.20/13.41 (upairsubunion) =>
% 99.20/13.41 ((
% 99.20/13.41 (upairinpowunion) =>
% 99.20/13.41 ((
% 99.20/13.41 (ubforcartprodlem1) =>
% 99.20/13.41 ((
% 99.20/13.41 (ubforcartprodlem2) =>
% 99.20/13.41 ((
% 99.20/13.41 (ubforcartprodlem3) =>
% 99.20/13.41 ((
% 99.20/13.41 (cartprodpairin) =>
% 99.20/13.41 ((
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% 99.20/13.41 ((
% 99.20/13.41 (cartprodmempair) =>
% 99.20/13.41 ((
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% 99.20/13.41 ((
% 99.20/13.41 (setunionsingleton1) =>
% 99.20/13.41 ((
% 99.20/13.41 (setunionsingleton2) =>
% 99.20/13.41 ((
% 99.20/13.41 (setunionsingleton) =>
% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
% 99.20/13.41 (ex1I2) =>
% 99.20/13.41 ((
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% 99.20/13.41 ((
% 99.20/13.41 (setukpairinjL1) =>
% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
% 99.20/13.41 (kfstpairEq) =>
% 99.20/13.41 ((
% 99.20/13.41 (cartprodfstin) =>
% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
% 99.20/13.41 (kpairsurjEq) =>
% 99.20/13.41 ((
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% 99.20/13.41 ((
% 99.20/13.41 (cartprodpairmemEL) =>
% 99.20/13.41 ((
% 99.20/13.41 (cartprodpairmemER) =>
% 99.20/13.41 ((
% 99.20/13.41 (cartprodmempaircEq) =>
% 99.20/13.41 ((
% 99.20/13.41 (cartprodfstpairEq) =>
% 99.20/13.41 ((
% 99.20/13.41 (cartprodsndpairEq) =>
% 99.20/13.41 ((
% 99.20/13.41 (cartprodpairsurjEq) =>
% 99.20/13.41 ((
% 99.20/13.41 (dpsetconstrI) =>
% 99.20/13.41 ((
% 99.20/13.41 (dpsetconstrSub) =>
% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
% 99.20/13.41 (dpsetconstrEL2) =>
% 99.20/13.41 ((
% 99.20/13.41 (dpsetconstrER) =>
% 99.20/13.41 ((
% 99.20/13.41 (funcImageSingleton) =>
% 99.20/13.41 ((
% 99.20/13.41 (apProp) =>
% 99.20/13.41 ((
% 99.20/13.41 (app) =>
% 99.20/13.41 ((
% 99.20/13.41 (infuncsetfunc) =>
% 99.20/13.41 ((
% 99.20/13.41 (ap2p) =>
% 99.20/13.41 ((
% 99.20/13.41 (funcinfuncset) =>
% 99.20/13.41 ((
% 99.20/13.41 (lamProp) =>
% 99.20/13.41 ((
% 99.20/13.41 (lamp) =>
% 99.20/13.41 ((
% 99.20/13.41 (lam2p) =>
% 99.20/13.41 ((
% 99.20/13.41 (brelnall1) =>
% 99.20/13.41 ((
% 99.20/13.41 (brelnall2) =>
% 99.20/13.41 ((
% 99.20/13.41 (ex1E2) =>
% 99.20/13.41 ((
% 99.20/13.41 (funcGraphProp1) =>
% 99.20/13.41 ((
% 99.20/13.41 (funcGraphProp3) =>
% 99.20/13.41 ((
% 99.20/13.41 (funcGraphProp2) =>
% 99.20/13.41 ((
% 99.20/13.41 (funcextLem) =>
% 99.20/13.41 ((
% 99.20/13.41 (funcGraphProp4) =>
% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
% 99.20/13.41 (funcext) =>
% 99.20/13.41 ((
% 99.20/13.41 (funcext2) =>
% 99.20/13.41 ((
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% 99.20/13.41 ((
% 99.20/13.41 (ap2apEq2) =>
% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
% 99.20/13.41 (lam2lamEq) =>
% 99.20/13.41 ((
% 99.20/13.41 (beta2) =>
% 99.20/13.41 ((
% 99.20/13.41 (eta2) =>
% 99.20/13.41 ((
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% 99.20/13.41 ((
% 99.20/13.41 (iffalseProp2) =>
% 99.20/13.41 ((
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% 99.20/13.41 ((
% 99.20/13.41 (iftrueProp2) =>
% 99.20/13.41 ((
% 99.20/13.41 (ifSingleton) =>
% 99.20/13.41 ((
% 99.20/13.41 (ifp) =>
% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
% 99.20/13.41 (iffalse) =>
% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
% 99.20/13.41 (binunionT_lem) =>
% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
% 99.20/13.41 (powersetTI1) =>
% 99.20/13.41 ((
% 99.20/13.41 (powersetTE1) =>
% 99.20/13.41 ((
% 99.20/13.41 (complementTI1) =>
% 99.20/13.41 ((
% 99.20/13.41 (complementTE1) =>
% 99.20/13.41 ((
% 99.20/13.41 (binintersectTELcontra) =>
% 99.20/13.41 ((
% 99.20/13.41 (binintersectTERcontra) =>
% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
% 99.20/13.41 (contrasubsetT2) =>
% 99.20/13.41 ((
% 99.20/13.41 (contrasubsetT3) =>
% 99.20/13.41 ((
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% 99.20/13.41 ((
% 99.20/13.41 (doubleComplementE1) =>
% 99.20/13.41 ((
% 99.20/13.41 (doubleComplementSub1) =>
% 99.20/13.41 ((
% 99.20/13.41 (doubleComplementSub2) =>
% 99.20/13.41 ((
% 99.20/13.41 (doubleComplementEq) =>
% 99.20/13.41 ((
% 99.20/13.41 (complementTnotintersectT) =>
% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
% 99.20/13.41 (contraSubsetComplement) =>
% 99.20/13.41 ((
% 99.20/13.41 (complementTcontraSubset) =>
% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 (cartprodsndpairEq) =>
% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
% 99.20/13.41 (breln1invE) =>
% 99.20/13.41 ((
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% 99.20/13.41 ((
% 99.20/13.41 (breln1compI) =>
% 99.20/13.41 ((
% 99.20/13.41 (breln1compE) =>
% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 (
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% 99.20/13.41 (
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% 99.20/13.41 (
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% 99.20/13.41 surjFuncSet)))))))) @
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
% 99.20/13.41 (setminusSubset1) =>
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
% 99.20/13.41 (singletoninpowunion) =>
% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
% 99.20/13.41 (upairinpowunion) =>
% 99.20/13.41 ((
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% 99.20/13.41 ((
% 99.20/13.41 (ubforcartprodlem2) =>
% 99.20/13.41 ((
% 99.20/13.41 (ubforcartprodlem3) =>
% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
% 99.20/13.41 (ex1I2) =>
% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 (ksndpairEq) =>
% 99.20/13.41 ((
% 99.20/13.41 (kpairsurjEq) =>
% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
% 99.20/13.41 (cartprodpairmemER) =>
% 99.20/13.41 ((
% 99.20/13.41 (cartprodmempaircEq) =>
% 99.20/13.41 ((
% 99.20/13.41 (cartprodfstpairEq) =>
% 99.20/13.41 ((
% 99.20/13.41 (cartprodsndpairEq) =>
% 99.20/13.41 ((
% 99.20/13.41 (cartprodpairsurjEq) =>
% 99.20/13.41 ((
% 99.20/13.41 (dpsetconstrI) =>
% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
% 99.20/13.41 (app) =>
% 99.20/13.41 ((
% 99.20/13.41 (infuncsetfunc) =>
% 99.20/13.41 ((
% 99.20/13.41 (ap2p) =>
% 99.20/13.41 ((
% 99.20/13.41 (funcinfuncset) =>
% 99.20/13.41 ((
% 99.20/13.41 (lamProp) =>
% 99.20/13.41 ((
% 99.20/13.41 (lamp) =>
% 99.20/13.41 ((
% 99.20/13.41 (lam2p) =>
% 99.20/13.41 ((
% 99.20/13.41 (brelnall1) =>
% 99.20/13.41 ((
% 99.20/13.41 (brelnall2) =>
% 99.20/13.41 ((
% 99.20/13.41 (ex1E2) =>
% 99.20/13.41 ((
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% 99.20/13.41 ((
% 99.20/13.41 (funcGraphProp3) =>
% 99.20/13.41 ((
% 99.20/13.41 (funcGraphProp2) =>
% 99.20/13.41 ((
% 99.20/13.41 (funcextLem) =>
% 99.20/13.41 ((
% 99.20/13.41 (funcGraphProp4) =>
% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
% 99.20/13.41 (funcext2) =>
% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
% 99.20/13.41 (iffalseProp2) =>
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
% 99.20/13.41 (complementTE1) =>
% 99.20/13.41 ((
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% 99.20/13.41 ((
% 99.20/13.41 (binintersectTERcontra) =>
% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
% 99.20/13.41 (contrasubsetT2) =>
% 99.20/13.41 ((
% 99.20/13.41 (contrasubsetT3) =>
% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
% 99.20/13.41 (doubleComplementSub2) =>
% 99.20/13.41 ((
% 99.20/13.41 (doubleComplementEq) =>
% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
% 99.20/13.41 (binunionTIRcontra) =>
% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
% 99.20/13.41 (inComplementUnionImpInComplement1) =>
% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
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% 99.20/13.41 ((
% 99.20/13.41 (injFuncSetFuncIn) =>
% 99.20/13.41 ((
% 99.20/13.41 (injFuncSetFuncInj) =>
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% 99.20/13.42 ((
% 99.20/13.42 (cartprodpairmemEL) =>
% 99.20/13.42 ((
% 99.20/13.42 (cartprodpairmemER) =>
% 99.20/13.42 ((
% 99.20/13.42 (cartprodmempaircEq) =>
% 99.20/13.42 ((
% 99.20/13.42 (cartprodfstpairEq) =>
% 99.20/13.42 ((
% 99.20/13.42 (cartprodsndpairEq) =>
% 99.20/13.42 ((
% 99.20/13.42 (cartprodpairsurjEq) =>
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% 99.20/13.42 ((
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% 99.20/13.42 (dpsetconstrEL2) =>
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% 99.20/13.42 (dpsetconstrER) =>
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% 99.20/13.42 ((
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% 99.20/13.42 ((
% 99.20/13.42 (app) =>
% 99.20/13.42 ((
% 99.20/13.42 (infuncsetfunc) =>
% 99.20/13.42 ((
% 99.20/13.42 (ap2p) =>
% 99.20/13.42 ((
% 99.20/13.42 (funcinfuncset) =>
% 99.20/13.42 ((
% 99.20/13.42 (lamProp) =>
% 99.20/13.42 ((
% 99.20/13.42 (lamp) =>
% 99.20/13.42 ((
% 99.20/13.42 (lam2p) =>
% 99.20/13.42 ((
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% 99.20/13.42 ((
% 99.20/13.42 (brelnall2) =>
% 99.20/13.42 ((
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% 99.20/13.42 ((
% 99.20/13.42 (funcGraphProp1) =>
% 99.20/13.42 ((
% 99.20/13.42 (funcGraphProp3) =>
% 99.20/13.42 ((
% 99.20/13.42 (funcGraphProp2) =>
% 99.20/13.42 ((
% 99.20/13.42 (funcextLem) =>
% 99.20/13.42 ((
% 99.20/13.42 (funcGraphProp4) =>
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% 99.20/13.42 ((
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% 99.20/13.42 ((
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% 99.20/13.42 ((
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% 99.20/13.42 ((
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% 99.20/13.42 ((
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% 99.20/13.42 ((
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% 99.20/13.42 (iffalseProp2) =>
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% 99.20/13.42 ((
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% 99.20/13.42 ((
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% 99.20/13.42 ((
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% 99.20/13.42 ((
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% 99.20/13.42 ((
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% 99.20/13.42 ((
% 99.20/13.42 (contrasubsetT2) =>
% 99.20/13.42 ((
% 99.20/13.42 (contrasubsetT3) =>
% 99.20/13.42 ((
% 99.20/13.42 (doubleComplementI1) =>
% 99.20/13.42 ((
% 99.20/13.42 (doubleComplementE1) =>
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% 99.20/13.42 (doubleComplementSub1) =>
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% 99.20/13.42 (doubleComplementEq) =>
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% 99.20/13.42 (complementImpComplementIntersect) =>
% 99.20/13.42 ((
% 99.20/13.42 (complementSubsetComplementIntersect) =>
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% 99.20/13.42 (complementInPowersetComplementIntersect) =>
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% 99.20/13.42 (contraSubsetComplement) =>
% 99.20/13.42 ((
% 99.20/13.42 (complementTcontraSubset) =>
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% 99.20/13.42 ((
% 99.20/13.42 (binunionTIRcontra) =>
% 99.20/13.42 ((
% 99.20/13.42 (inIntersectImpInUnion) =>
% 99.20/13.42 ((
% 99.20/13.42 (inIntersectImpInUnion2) =>
% 99.20/13.42 ((
% 99.20/13.42 (inIntersectImpInIntersectUnions) =>
% 99.20/13.42 ((
% 99.20/13.42 (intersectInPowersetIntersectUnions) =>
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% 99.20/13.42 (inComplementUnionImpNotIn1) =>
% 99.20/13.42 ((
% 99.20/13.42 (inComplementUnionImpInComplement1) =>
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% 99.20/13.42 ((
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% 99.20/13.42 ((
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% 99.20/13.42 ((
% 99.20/13.42 (demorgan2a2) =>
% 99.20/13.42 ((
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% 99.20/13.42 ((
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% 99.20/13.42 ((
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% 99.20/13.42 ((
% 99.20/13.42 (demorgan2a) =>
% 99.20/13.42 ((
% 99.20/13.42 (demorgan2b2) =>
% 99.20/13.42 ((
% 99.20/13.42 (demorgan2b) =>
% 99.20/13.42 ((
% 99.20/13.42 (demorgan2) =>
% 99.20/13.42 ((
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% 99.20/13.42 ((
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% 99.20/13.42 ((
% 99.20/13.42 (woz13rule2) =>
% 99.20/13.42 ((
% 99.20/13.42 (woz13rule3) =>
% 99.20/13.42 ((
% 99.20/13.42 (woz13rule4) =>
% 99.20/13.42 ((
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% 99.20/13.42 ((
% 99.20/13.42 (woz1_2) =>
% 99.20/13.42 ((
% 99.20/13.42 (woz1_3) =>
% 99.20/13.42 ((
% 99.20/13.42 (woz1_4) =>
% 99.20/13.42 ((
% 99.20/13.42 (woz1_5) =>
% 99.20/13.42 ((
% 99.20/13.42 (breln1all2) =>
% 99.20/13.42 ((
% 99.20/13.42 (breln1SetBreln1) =>
% 99.20/13.42 ((
% 99.20/13.42 (choice2fnsingleton) =>
% 99.20/13.42 ((
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% 99.20/13.42 ((
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% 99.20/13.42 ((
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% 99.20/13.42 ((
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% 99.20/13.42 ((
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% 99.20/13.42 ((
% 99.20/13.42 (breln1invI) =>
% 99.20/13.42 ((
% 99.20/13.42 (breln1invE) =>
% 99.20/13.42 ((
% 99.20/13.42 (breln1compprop) =>
% 99.20/13.42 ((
% 99.20/13.42 (breln1compI) =>
% 99.20/13.42 ((
% 99.20/13.42 (breln1compE) =>
% 99.20/13.42 ((
% 99.20/13.42 (breln1compEex) =>
% 99.20/13.42 ((
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% 99.20/13.42 ((
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% 99.20/13.42 ((
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% 99.20/13.42 ((
% 99.20/13.42 (breln1unionI) =>
% 99.20/13.42 ((
% 99.20/13.42 (breln1unionE) =>
% 99.20/13.42 ((
% 99.20/13.42 (breln1unionEcases) =>
% 99.20/13.42 ((
% 99.20/13.42 (breln1unionCommutes) =>
% 99.20/13.42 ((
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% 99.20/13.42 ((
% 99.20/13.42 (woz2W) =>
% 99.20/13.42 ((
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% 99.20/13.42 ((
% 99.20/13.42 (woz2B) =>
% 99.20/13.42 ((
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% 99.20/13.42 ((
% 99.20/13.42 (image1Ex1) =>
% 99.20/13.42 ((
% 99.20/13.42 (image1Equiv) =>
% 99.20/13.42 ((
% 99.20/13.42 (image1E) =>
% 99.20/13.42 ((
% 99.20/13.42 (image1I) =>
% 99.20/13.42 ((
% 99.20/13.42 (injFuncInInjFuncSet) =>
% 99.20/13.42 ((
% 99.20/13.42 (injFuncSetFuncIn) =>
% 99.20/13.42 ((
% 99.20/13.42 (injFuncSetFuncInj) =>
% 99.20/13.42 ((
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% 99.20/13.42 (
% 99.20/13.42 (
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% 99.20/13.42 (
% 99.20/13.42 ('#B') @ (
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% 99.20/13.42 (
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% 99.20/13.42 (
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% 99.20/13.42 (
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% 99.20/13.42 surjFuncSet)))))))) @
% 99.20/13.42 (
% 99.20/13.42 (
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% 99.20/13.42 (
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% 99.20/13.42 (
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% 99.20/13.42 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
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% 99.20/13.42 (((binintersectEL) =>
% 99.20/13.42 (((binintersectLsub) =>
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% 99.20/13.42 (((binintersectRsub) =>
% 99.20/13.42 ((
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% 99.20/13.42 ((
% 99.20/13.42 (binintersectSubset1) =>
% 99.20/13.42 ((
% 99.20/13.42 (bs114d) =>
% 99.20/13.42 ((
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% 99.20/13.42 ((
% 99.20/13.42 (setminusEL) =>
% 99.20/13.42 ((
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% 99.20/13.42 ((
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% 99.20/13.42 ((
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% 99.20/13.42 ((
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% 99.20/13.42 ((
% 99.20/13.42 (setminusIRneg) =>
% 99.20/13.42 ((
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% 99.20/13.42 ((
% 99.20/13.42 (setminusSubset1) =>
% 99.20/13.42 ((
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% 99.20/13.42 ((
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% 99.20/13.42 ((
% 99.20/13.42 (symdiffI2) =>
% 99.20/13.42 ((
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% 99.20/13.42 ((
% 99.20/13.42 (symdiffIneg2) =>
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% 99.20/13.42 ((
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% 99.20/13.42 ((
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% 99.20/13.42 ((
% 99.20/13.42 (ubforcartprodlem3) =>
% 99.20/13.42 ((
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% 99.20/13.42 ((
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% 99.20/13.42 ((
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% 99.20/13.42 ((
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% 99.20/13.42 ((
% 99.20/13.42 (ex1I2) =>
% 99.20/13.42 ((
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% 99.20/13.42 ((
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% 99.20/13.42 ((
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% 99.20/13.42 ((
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% 99.20/13.42 ((
% 99.20/13.42 (kfstpairEq) =>
% 99.20/13.42 ((
% 99.20/13.42 (cartprodfstin) =>
% 99.20/13.42 ((
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% 99.20/13.42 ((
% 99.20/13.42 (setukpairinjL) =>
% 99.20/13.42 ((
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% 99.20/13.42 (kpairsurjEq) =>
% 99.20/13.42 ((
% 99.20/13.42 (cartprodsndin) =>
% 99.20/13.42 ((
% 99.20/13.42 (cartprodpairmemEL) =>
% 99.20/13.42 ((
% 99.20/13.42 (cartprodpairmemER) =>
% 99.20/13.42 ((
% 99.20/13.42 (cartprodmempaircEq) =>
% 99.20/13.42 ((
% 99.20/13.42 (cartprodfstpairEq) =>
% 99.20/13.42 ((
% 99.20/13.42 (cartprodsndpairEq) =>
% 99.20/13.42 ((
% 99.20/13.42 (cartprodpairsurjEq) =>
% 99.20/13.42 ((
% 99.20/13.42 (dpsetconstrI) =>
% 99.20/13.42 ((
% 99.20/13.42 (dpsetconstrSub) =>
% 99.20/13.42 ((
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% 99.20/13.42 ((
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% 99.20/13.42 ((
% 99.20/13.42 (dpsetconstrEL2) =>
% 99.20/13.42 ((
% 99.20/13.42 (dpsetconstrER) =>
% 99.20/13.42 ((
% 99.20/13.42 (funcImageSingleton) =>
% 99.20/13.42 ((
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% 99.20/13.42 ((
% 99.20/13.42 (app) =>
% 99.20/13.42 ((
% 99.20/13.42 (infuncsetfunc) =>
% 99.20/13.42 ((
% 99.20/13.42 (ap2p) =>
% 99.20/13.42 ((
% 99.20/13.42 (funcinfuncset) =>
% 99.20/13.42 ((
% 99.20/13.42 (lamProp) =>
% 99.20/13.42 ((
% 99.20/13.42 (lamp) =>
% 99.20/13.42 ((
% 99.20/13.42 (lam2p) =>
% 99.20/13.42 ((
% 99.20/13.42 (brelnall1) =>
% 99.20/13.42 ((
% 99.20/13.42 (brelnall2) =>
% 99.20/13.42 ((
% 99.20/13.42 (ex1E2) =>
% 99.20/13.42 ((
% 99.20/13.42 (funcGraphProp1) =>
% 99.20/13.42 ((
% 99.20/13.42 (funcGraphProp3) =>
% 99.20/13.42 ((
% 99.20/13.42 (funcGraphProp2) =>
% 99.20/13.42 ((
% 99.20/13.42 (funcextLem) =>
% 99.20/13.42 ((
% 99.20/13.42 (funcGraphProp4) =>
% 99.20/13.42 ((
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% 99.20/13.42 ((
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% 99.20/13.42 ((
% 99.20/13.42 (funcext) =>
% 99.20/13.42 ((
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% 99.20/13.42 (ap2apEq1) =>
% 99.20/13.42 ((
% 99.20/13.42 (ap2apEq2) =>
% 99.20/13.42 ((
% 99.20/13.42 (beta1) =>
% 99.20/13.42 ((
% 99.20/13.42 (eta1) =>
% 99.20/13.42 ((
% 99.20/13.42 (lam2lamEq) =>
% 99.20/13.42 ((
% 99.20/13.42 (beta2) =>
% 99.20/13.42 ((
% 99.20/13.42 (eta2) =>
% 99.20/13.42 ((
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% 99.20/13.42 ((
% 99.20/13.42 (iffalseProp2) =>
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% 99.20/13.42 ((
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% 99.20/13.42 ((
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% 99.20/13.42 ((
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% 99.20/13.42 ((
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% 99.20/13.42 ((
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% 99.20/13.42 ((
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% 99.20/13.42 ((
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% 99.20/13.42 ((
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% 99.20/13.42 ((
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% 99.20/13.42 ((
% 99.20/13.42 (powersetTI1) =>
% 99.20/13.42 ((
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% 99.20/13.42 ((
% 99.20/13.42 (complementTI1) =>
% 99.20/13.42 ((
% 99.20/13.42 (complementTE1) =>
% 99.20/13.42 ((
% 99.20/13.42 (binintersectTELcontra) =>
% 99.20/13.42 ((
% 99.20/13.42 (binintersectTERcontra) =>
% 99.20/13.42 ((
% 99.20/13.42 (contrasubsetT) =>
% 99.20/13.42 ((
% 99.20/13.42 (contrasubsetT1) =>
% 99.20/13.42 ((
% 99.20/13.42 (contrasubsetT2) =>
% 99.20/13.42 ((
% 99.20/13.42 (contrasubsetT3) =>
% 99.20/13.42 ((
% 99.20/13.42 (doubleComplementI1) =>
% 99.20/13.42 ((
% 99.20/13.42 (doubleComplementE1) =>
% 99.20/13.42 ((
% 99.20/13.42 (doubleComplementSub1) =>
% 99.20/13.42 ((
% 99.20/13.42 (doubleComplementSub2) =>
% 99.20/13.42 ((
% 99.20/13.42 (doubleComplementEq) =>
% 99.20/13.42 ((
% 99.20/13.42 (complementTnotintersectT) =>
% 99.20/13.42 ((
% 99.20/13.42 (complementImpComplementIntersect) =>
% 99.20/13.42 ((
% 99.20/13.42 (complementSubsetComplementIntersect) =>
% 99.20/13.42 ((
% 99.20/13.42 (complementInPowersetComplementIntersect) =>
% 99.20/13.42 ((
% 99.20/13.42 (contraSubsetComplement) =>
% 99.20/13.42 ((
% 99.20/13.42 (complementTcontraSubset) =>
% 99.20/13.42 ((
% 99.20/13.42 (binunionTILcontra) =>
% 99.20/13.42 ((
% 99.20/13.42 (binunionTIRcontra) =>
% 99.20/13.42 ((
% 99.20/13.42 (inIntersectImpInUnion) =>
% 99.20/13.42 ((
% 99.20/13.42 (inIntersectImpInUnion2) =>
% 99.20/13.42 ((
% 99.20/13.42 (inIntersectImpInIntersectUnions) =>
% 99.20/13.42 ((
% 99.20/13.42 (intersectInPowersetIntersectUnions) =>
% 99.20/13.42 ((
% 99.20/13.42 (inComplementUnionImpNotIn1) =>
% 99.20/13.42 ((
% 99.20/13.42 (inComplementUnionImpInComplement1) =>
% 99.20/13.42 ((
% 99.20/13.42 (binunionTE) =>
% 99.20/13.42 ((
% 99.20/13.42 (binunionTEcontra) =>
% 99.20/13.42 ((
% 99.20/13.42 (demorgan2a1) =>
% 99.20/13.42 ((
% 99.20/13.42 (complementUnionInPowersetComplement) =>
% 99.20/13.42 ((
% 99.20/13.42 (demorgan2a2) =>
% 99.20/13.42 ((
% 99.20/13.42 (demorgan1a) =>
% 99.20/13.42 ((
% 99.20/13.42 (demorgan1b) =>
% 99.20/13.42 ((
% 99.20/13.42 (demorgan1) =>
% 99.20/13.42 ((
% 99.20/13.42 (demorgan2a) =>
% 99.20/13.42 ((
% 99.20/13.42 (demorgan2b2) =>
% 99.20/13.42 ((
% 99.20/13.42 (demorgan2b) =>
% 99.20/13.42 ((
% 99.20/13.42 (demorgan2) =>
% 99.20/13.42 ((
% 99.20/13.42 (woz13rule0) =>
% 99.20/13.42 ((
% 99.20/13.42 (woz13rule1) =>
% 99.20/13.42 ((
% 99.20/13.42 (woz13rule2) =>
% 99.20/13.42 ((
% 99.20/13.42 (woz13rule3) =>
% 99.20/13.42 ((
% 99.20/13.42 (woz13rule4) =>
% 99.20/13.42 ((
% 99.20/13.42 (woz1_1) =>
% 99.20/13.42 ((
% 99.20/13.42 (woz1_2) =>
% 99.20/13.42 ((
% 99.20/13.42 (woz1_3) =>
% 99.20/13.42 ((
% 99.20/13.42 (woz1_4) =>
% 99.20/13.42 ((
% 99.20/13.42 (woz1_5) =>
% 99.20/13.42 ((
% 99.20/13.42 (breln1all2) =>
% 99.20/13.42 ((
% 99.20/13.42 (breln1SetBreln1) =>
% 99.20/13.42 ((
% 99.20/13.42 (choice2fnsingleton) =>
% 99.20/13.42 ((
% 99.20/13.42 (setOfPairsIsBReln1) =>
% 99.20/13.42 ((
% 99.20/13.42 (breln1all1) =>
% 99.20/13.42 ((
% 99.20/13.42 (subbreln1) =>
% 99.20/13.42 ((
% 99.20/13.42 (eqbreln1) =>
% 99.20/13.42 ((
% 99.20/13.42 (breln1invprop) =>
% 99.20/13.42 ((
% 99.20/13.42 (breln1invI) =>
% 99.20/13.42 ((
% 99.20/13.42 (breln1invE) =>
% 99.20/13.42 ((
% 99.20/13.42 (breln1compprop) =>
% 99.20/13.42 ((
% 99.20/13.42 (breln1compI) =>
% 99.20/13.42 ((
% 99.20/13.42 (breln1compE) =>
% 99.20/13.42 ((
% 99.20/13.42 (breln1compEex) =>
% 99.20/13.42 ((
% 99.20/13.42 (breln1unionprop) =>
% 99.20/13.42 ((
% 99.20/13.42 (breln1unionIL) =>
% 99.20/13.42 ((
% 99.20/13.42 (breln1unionIR) =>
% 99.20/13.42 ((
% 99.20/13.42 (breln1unionI) =>
% 99.20/13.42 ((
% 99.20/13.42 (breln1unionE) =>
% 99.20/13.42 ((
% 99.20/13.42 (breln1unionEcases) =>
% 99.20/13.42 ((
% 99.20/13.42 (breln1unionCommutes) =>
% 99.20/13.42 ((
% 99.20/13.42 (woz2Ex) =>
% 99.20/13.42 ((
% 99.20/13.42 (woz2W) =>
% 99.20/13.42 ((
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% 99.20/13.42 ((
% 99.20/13.42 (woz2B) =>
% 99.20/13.42 ((
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% 99.20/13.42 ((
% 99.20/13.42 (image1Ex1) =>
% 99.20/13.42 ((
% 99.20/13.42 (image1Equiv) =>
% 99.20/13.42 ((
% 99.20/13.42 (image1E) =>
% 99.20/13.42 ((
% 99.20/13.42 (image1I) =>
% 99.20/13.42 ((
% 99.20/13.42 (injFuncInInjFuncSet) =>
% 99.20/13.42 ((
% 99.20/13.42 (injFuncSetFuncIn) =>
% 99.20/13.42 ((
% 99.20/13.42 (injFuncSetFuncInj) =>
% 99.20/13.42 ((
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% 99.20/13.42 (('#B') @ (
% 99.20/13.42 !!) @
% 99.20/13.42 (
% 99.20/13.42 (
% 99.20/13.42 ('#B') @ (
% 99.20/13.42 (
% 99.20/13.42 ('#B') @ (
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% 99.20/13.42 (
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% 99.20/13.42 (
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% 99.20/13.42 (
% 99.20/13.42 (
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% 99.20/13.42 (
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% 99.20/13.42 (
% 99.20/13.42 (
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% 99.20/13.42 (
% 99.20/13.42 ('#B') @ (
% 99.20/13.42 (
% 99.20/13.42 ('#B') @ (
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% 99.20/13.42 (
% 99.20/13.42 (
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% 99.20/13.42 (
% 99.20/13.42 ('#B') @ (
% 99.20/13.42 (
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% 99.20/13.42 surjFuncSet)))))))) @
% 99.20/13.42 (
% 99.20/13.42 (
% 99.20/13.42 ('#B') @ (
% 99.20/13.42 (
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% 99.20/13.42 (
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% 99.20/13.42 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.20/13.42 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl909])).
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% 99.20/13.42 (((binintersectEL) =>
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% 99.20/13.42 (((binintersectSubset2) =>
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% 99.20/13.42 (((binintersectSubset4) =>
% 99.20/13.42 ((
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% 99.20/13.42 ((
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% 99.20/13.42 ((
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% 99.20/13.42 ((
% 99.20/13.42 (setminusEL) =>
% 99.20/13.42 ((
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% 99.20/13.42 ((
% 99.20/13.42 (setminusSubset2) =>
% 99.20/13.42 ((
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% 99.20/13.42 ((
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% 99.20/13.42 ((
% 99.20/13.42 (setminusILneg) =>
% 99.20/13.42 ((
% 99.20/13.42 (setminusIRneg) =>
% 99.20/13.42 ((
% 99.20/13.42 (setminusLsub) =>
% 99.20/13.42 ((
% 99.20/13.42 (setminusSubset1) =>
% 99.20/13.42 ((
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% 99.20/13.42 ((
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% 99.20/13.42 ((
% 99.20/13.42 (symdiffI2) =>
% 99.20/13.42 ((
% 99.20/13.42 (symdiffIneg1) =>
% 99.20/13.42 ((
% 99.20/13.42 (symdiffIneg2) =>
% 99.20/13.42 ((
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% 99.20/13.42 ((
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% 99.20/13.42 ((
% 99.20/13.42 (setukpairIR) =>
% 99.20/13.42 ((
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% 99.20/13.42 ((
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% 99.20/13.42 ((
% 99.20/13.42 (singletoninpowerset) =>
% 99.20/13.42 ((
% 99.20/13.42 (singletoninpowunion) =>
% 99.20/13.42 ((
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% 99.20/13.42 ((
% 99.20/13.42 (upairsubunion) =>
% 99.20/13.42 ((
% 99.20/13.42 (upairinpowunion) =>
% 99.20/13.42 ((
% 99.20/13.42 (ubforcartprodlem1) =>
% 99.20/13.42 ((
% 99.20/13.42 (ubforcartprodlem2) =>
% 99.20/13.42 ((
% 99.20/13.42 (ubforcartprodlem3) =>
% 99.20/13.42 ((
% 99.20/13.42 (cartprodpairin) =>
% 99.20/13.42 ((
% 99.20/13.42 (cartprodmempair1) =>
% 99.20/13.42 ((
% 99.20/13.42 (cartprodmempair) =>
% 99.20/13.42 ((
% 99.20/13.42 (setunionE2) =>
% 99.20/13.42 ((
% 99.20/13.42 (setunionsingleton1) =>
% 99.20/13.42 ((
% 99.20/13.42 (setunionsingleton2) =>
% 99.20/13.42 ((
% 99.20/13.42 (setunionsingleton) =>
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% 99.20/13.42 ((
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% 99.20/13.42 ((
% 99.20/13.42 (ex1I) =>
% 99.20/13.42 ((
% 99.20/13.42 (ex1I2) =>
% 99.20/13.42 ((
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% 99.20/13.42 ((
% 99.20/13.42 (setukpairinjL1) =>
% 99.20/13.42 ((
% 99.20/13.42 (kfstsingleton) =>
% 99.20/13.42 ((
% 99.20/13.42 (theprop) =>
% 99.20/13.42 ((
% 99.20/13.42 (kfstpairEq) =>
% 99.20/13.42 ((
% 99.20/13.42 (cartprodfstin) =>
% 99.20/13.42 ((
% 99.20/13.42 (setukpairinjL2) =>
% 99.20/13.42 ((
% 99.20/13.42 (setukpairinjL) =>
% 99.20/13.42 ((
% 99.20/13.42 (setukpairinjR11) =>
% 99.20/13.42 ((
% 99.20/13.42 (setukpairinjR12) =>
% 99.20/13.42 ((
% 99.20/13.42 (setukpairinjR1) =>
% 99.20/13.42 ((
% 99.20/13.42 (upairequniteq) =>
% 99.20/13.42 ((
% 99.20/13.42 (setukpairinjR2) =>
% 99.20/13.42 ((
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% 99.20/13.42 ((
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% 99.20/13.42 ((
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% 99.20/13.42 ((
% 99.20/13.42 (cartprodpairmemER) =>
% 99.20/13.42 ((
% 99.20/13.42 (cartprodmempaircEq) =>
% 99.20/13.42 ((
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% 99.20/13.42 (cartprodsndpairEq) =>
% 99.20/13.42 ((
% 99.20/13.42 (cartprodpairsurjEq) =>
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% 99.20/13.42 ((
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% 99.20/13.42 ((
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% 99.20/13.42 ((
% 99.20/13.42 (funcinfuncset) =>
% 99.20/13.42 ((
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% 99.20/13.42 ((
% 99.20/13.42 (lamp) =>
% 99.20/13.42 ((
% 99.20/13.42 (lam2p) =>
% 99.20/13.42 ((
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% 99.20/13.42 ((
% 99.20/13.42 (brelnall2) =>
% 99.20/13.42 ((
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% 99.20/13.42 ((
% 99.20/13.42 (funcGraphProp1) =>
% 99.20/13.42 ((
% 99.20/13.42 (funcGraphProp3) =>
% 99.20/13.42 ((
% 99.20/13.42 (funcGraphProp2) =>
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% 99.20/13.42 ((
% 99.20/13.42 (funcGraphProp4) =>
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% 99.20/13.42 ((
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% 99.20/13.42 ((
% 99.20/13.42 (contrasubsetT2) =>
% 99.20/13.42 ((
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% 99.20/13.42 ((
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% 99.20/13.42 (doubleComplementEq) =>
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% 99.20/13.42 ((
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% 99.20/13.42 ((
% 99.20/13.42 (binunionTIRcontra) =>
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% 99.20/13.42 (inIntersectImpInUnion2) =>
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% 99.20/13.42 (inIntersectImpInIntersectUnions) =>
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% 99.20/13.42 ((
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% 99.20/13.42 ((
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% 99.20/13.42 ((
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% 99.20/13.42 ((
% 99.20/13.42 (demorgan2a) =>
% 99.20/13.42 ((
% 99.20/13.42 (demorgan2b2) =>
% 99.20/13.42 ((
% 99.20/13.42 (demorgan2b) =>
% 99.20/13.42 ((
% 99.20/13.42 (demorgan2) =>
% 99.20/13.42 ((
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% 99.20/13.42 ((
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% 99.20/13.42 ((
% 99.20/13.42 (woz13rule2) =>
% 99.20/13.42 ((
% 99.20/13.42 (woz13rule3) =>
% 99.20/13.42 ((
% 99.20/13.42 (woz13rule4) =>
% 99.20/13.42 ((
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% 99.20/13.42 ((
% 99.20/13.42 (woz1_2) =>
% 99.20/13.42 ((
% 99.20/13.42 (woz1_3) =>
% 99.20/13.42 ((
% 99.20/13.42 (woz1_4) =>
% 99.20/13.42 ((
% 99.20/13.42 (woz1_5) =>
% 99.20/13.42 ((
% 99.20/13.42 (breln1all2) =>
% 99.20/13.42 ((
% 99.20/13.42 (breln1SetBreln1) =>
% 99.20/13.42 ((
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% 99.20/13.42 ((
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% 99.20/13.42 ((
% 99.20/13.42 (breln1invI) =>
% 99.20/13.42 ((
% 99.20/13.42 (breln1invE) =>
% 99.20/13.42 ((
% 99.20/13.42 (breln1compprop) =>
% 99.20/13.42 ((
% 99.20/13.42 (breln1compI) =>
% 99.20/13.42 ((
% 99.20/13.42 (breln1compE) =>
% 99.20/13.42 ((
% 99.20/13.42 (breln1compEex) =>
% 99.20/13.42 ((
% 99.57/13.42 (breln1unionprop) =>
% 99.57/13.42 ((
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% 99.57/13.42 ((
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% 99.57/13.42 ((
% 99.57/13.42 (breln1unionI) =>
% 99.57/13.42 ((
% 99.57/13.42 (breln1unionE) =>
% 99.57/13.42 ((
% 99.57/13.42 (breln1unionEcases) =>
% 99.57/13.42 ((
% 99.57/13.42 (breln1unionCommutes) =>
% 99.57/13.42 ((
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% 99.57/13.42 ((
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% 99.57/13.42 ((
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% 99.57/13.42 ((
% 99.57/13.42 (woz2B) =>
% 99.57/13.42 ((
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% 99.57/13.42 ((
% 99.57/13.42 (image1Ex1) =>
% 99.57/13.42 ((
% 99.57/13.42 (image1Equiv) =>
% 99.57/13.42 ((
% 99.57/13.42 (image1E) =>
% 99.57/13.42 ((
% 99.57/13.42 (image1I) =>
% 99.57/13.42 ((
% 99.57/13.42 (injFuncInInjFuncSet) =>
% 99.57/13.42 ((
% 99.57/13.42 (injFuncSetFuncIn) =>
% 99.57/13.42 ((
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% 99.57/13.42 ((
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% 99.57/13.42 (
% 99.57/13.42 (
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% 99.57/13.42 surjFuncSet)))))))) @
% 99.57/13.42 (
% 99.57/13.42 (
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% 99.57/13.42 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
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% 99.57/13.42 ((
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% 99.57/13.42 ((
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% 99.57/13.42 ((
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% 99.57/13.42 ((
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% 99.57/13.42 ((
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% 99.57/13.42 ((
% 99.57/13.42 (symdiffIneg2) =>
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% 99.57/13.42 ((
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% 99.57/13.42 ((
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% 99.57/13.42 ((
% 99.57/13.42 (ubforcartprodlem3) =>
% 99.57/13.42 ((
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% 99.57/13.42 ((
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% 99.57/13.42 ((
% 99.57/13.42 (cartprodmempair) =>
% 99.57/13.42 ((
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% 99.57/13.42 ((
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% 99.57/13.42 ((
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% 99.57/13.42 ((
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% 99.57/13.42 ((
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% 99.57/13.42 ((
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% 99.57/13.42 ((
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% 99.57/13.42 ((
% 99.57/13.42 (setukpairinjR12) =>
% 99.57/13.42 ((
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% 99.57/13.42 ((
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% 99.57/13.42 ((
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% 99.57/13.42 ((
% 99.57/13.42 (setukpairinjR) =>
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% 99.57/13.42 ((
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% 99.57/13.42 (cartprodpairmemER) =>
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% 99.57/13.42 (cartprodfstpairEq) =>
% 99.57/13.42 ((
% 99.57/13.42 (cartprodsndpairEq) =>
% 99.57/13.42 ((
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% 99.57/13.42 ((
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% 99.57/13.42 ((
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% 99.57/13.42 ((
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% 99.57/13.42 ((
% 99.57/13.42 (dpsetconstrER) =>
% 99.57/13.42 ((
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% 99.57/13.42 ((
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% 99.57/13.42 ((
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% 99.57/13.42 ((
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% 99.57/13.42 ((
% 99.57/13.42 (lamp) =>
% 99.57/13.42 ((
% 99.57/13.42 (lam2p) =>
% 99.57/13.42 ((
% 99.57/13.42 (brelnall1) =>
% 99.57/13.42 ((
% 99.57/13.42 (brelnall2) =>
% 99.57/13.42 ((
% 99.57/13.42 (ex1E2) =>
% 99.57/13.42 ((
% 99.57/13.42 (funcGraphProp1) =>
% 99.57/13.42 ((
% 99.57/13.42 (funcGraphProp3) =>
% 99.57/13.42 ((
% 99.57/13.42 (funcGraphProp2) =>
% 99.57/13.42 ((
% 99.57/13.42 (funcextLem) =>
% 99.57/13.42 ((
% 99.57/13.42 (funcGraphProp4) =>
% 99.57/13.42 ((
% 99.57/13.42 (subbreln) =>
% 99.57/13.42 ((
% 99.57/13.42 (eqbreln) =>
% 99.57/13.42 ((
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% 99.57/13.42 (doubleComplementEq) =>
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% 99.57/13.42 ((
% 99.57/13.42 (complementSubsetComplementIntersect) =>
% 99.57/13.42 ((
% 99.57/13.42 (complementInPowersetComplementIntersect) =>
% 99.57/13.42 ((
% 99.57/13.42 (contraSubsetComplement) =>
% 99.57/13.42 ((
% 99.57/13.42 (complementTcontraSubset) =>
% 99.57/13.42 ((
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% 99.57/13.42 ((
% 99.57/13.42 (binunionTIRcontra) =>
% 99.57/13.42 ((
% 99.57/13.42 (inIntersectImpInUnion) =>
% 99.57/13.42 ((
% 99.57/13.42 (inIntersectImpInUnion2) =>
% 99.57/13.42 ((
% 99.57/13.42 (inIntersectImpInIntersectUnions) =>
% 99.57/13.42 ((
% 99.57/13.42 (intersectInPowersetIntersectUnions) =>
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% 99.57/13.42 (inComplementUnionImpNotIn1) =>
% 99.57/13.42 ((
% 99.57/13.42 (inComplementUnionImpInComplement1) =>
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% 99.57/13.42 ((
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% 99.57/13.42 ((
% 99.57/13.42 (demorgan2a1) =>
% 99.57/13.42 ((
% 99.57/13.42 (complementUnionInPowersetComplement) =>
% 99.57/13.42 ((
% 99.57/13.42 (demorgan2a2) =>
% 99.57/13.42 ((
% 99.57/13.42 (demorgan1a) =>
% 99.57/13.42 ((
% 99.57/13.42 (demorgan1b) =>
% 99.57/13.42 ((
% 99.57/13.42 (demorgan1) =>
% 99.57/13.42 ((
% 99.57/13.42 (demorgan2a) =>
% 99.57/13.42 ((
% 99.57/13.42 (demorgan2b2) =>
% 99.57/13.42 ((
% 99.57/13.42 (demorgan2b) =>
% 99.57/13.42 ((
% 99.57/13.42 (demorgan2) =>
% 99.57/13.42 ((
% 99.57/13.42 (woz13rule0) =>
% 99.57/13.42 ((
% 99.57/13.42 (woz13rule1) =>
% 99.57/13.42 ((
% 99.57/13.42 (woz13rule2) =>
% 99.57/13.42 ((
% 99.57/13.42 (woz13rule3) =>
% 99.57/13.42 ((
% 99.57/13.42 (woz13rule4) =>
% 99.57/13.42 ((
% 99.57/13.42 (woz1_1) =>
% 99.57/13.42 ((
% 99.57/13.42 (woz1_2) =>
% 99.57/13.42 ((
% 99.57/13.42 (woz1_3) =>
% 99.57/13.42 ((
% 99.57/13.42 (woz1_4) =>
% 99.57/13.42 ((
% 99.57/13.42 (woz1_5) =>
% 99.57/13.42 ((
% 99.57/13.42 (breln1all2) =>
% 99.57/13.42 ((
% 99.57/13.42 (breln1SetBreln1) =>
% 99.57/13.42 ((
% 99.57/13.42 (choice2fnsingleton) =>
% 99.57/13.42 ((
% 99.57/13.42 (setOfPairsIsBReln1) =>
% 99.57/13.42 ((
% 99.57/13.42 (breln1all1) =>
% 99.57/13.42 ((
% 99.57/13.42 (subbreln1) =>
% 99.57/13.42 ((
% 99.57/13.42 (eqbreln1) =>
% 99.57/13.42 ((
% 99.57/13.42 (breln1invprop) =>
% 99.57/13.42 ((
% 99.57/13.42 (breln1invI) =>
% 99.57/13.42 ((
% 99.57/13.42 (breln1invE) =>
% 99.57/13.42 ((
% 99.57/13.42 (breln1compprop) =>
% 99.57/13.42 ((
% 99.57/13.42 (breln1compI) =>
% 99.57/13.42 ((
% 99.57/13.42 (breln1compE) =>
% 99.57/13.42 ((
% 99.57/13.42 (breln1compEex) =>
% 99.57/13.42 ((
% 99.57/13.42 (breln1unionprop) =>
% 99.57/13.42 ((
% 99.57/13.42 (breln1unionIL) =>
% 99.57/13.42 ((
% 99.57/13.42 (breln1unionIR) =>
% 99.57/13.42 ((
% 99.57/13.42 (breln1unionI) =>
% 99.57/13.42 ((
% 99.57/13.42 (breln1unionE) =>
% 99.57/13.42 ((
% 99.57/13.42 (breln1unionEcases) =>
% 99.57/13.42 ((
% 99.57/13.42 (breln1unionCommutes) =>
% 99.57/13.42 ((
% 99.57/13.42 (woz2Ex) =>
% 99.57/13.42 ((
% 99.57/13.42 (woz2W) =>
% 99.57/13.42 ((
% 99.57/13.42 (woz2A) =>
% 99.57/13.42 ((
% 99.57/13.42 (woz2B) =>
% 99.57/13.42 ((
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% 99.57/13.42 ((
% 99.57/13.42 (image1Ex1) =>
% 99.57/13.42 ((
% 99.57/13.42 (image1Equiv) =>
% 99.57/13.42 ((
% 99.57/13.42 (image1E) =>
% 99.57/13.42 ((
% 99.57/13.42 (image1I) =>
% 99.57/13.42 ((
% 99.57/13.42 (injFuncInInjFuncSet) =>
% 99.57/13.42 ((
% 99.57/13.42 (injFuncSetFuncIn) =>
% 99.57/13.42 ((
% 99.57/13.42 (injFuncSetFuncInj) =>
% 99.57/13.42 ((
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% 99.57/13.42 (('#B') @ (
% 99.57/13.42 !!) @
% 99.57/13.42 (
% 99.57/13.42 (
% 99.57/13.42 ('#B') @ (
% 99.57/13.42 (
% 99.57/13.42 ('#B') @ (
% 99.57/13.42 !!))) @
% 99.57/13.42 (
% 99.57/13.42 (
% 99.57/13.42 ('#S') @ (
% 99.57/13.42 (
% 99.57/13.42 ('#B') @ (
% 99.57/13.42 '#S') @
% 99.57/13.42 (
% 99.57/13.42 (
% 99.57/13.42 ('#B') @ (
% 99.57/13.42 (
% 99.57/13.42 ('#B') @ (
% 99.57/13.42 '#S'))) @
% 99.57/13.42 (
% 99.57/13.42 (
% 99.57/13.42 ('#B') @ (
% 99.57/13.42 (
% 99.57/13.42 ('#B') @ (
% 99.57/13.42 (
% 99.57/13.42 ('#B') @ (
% 99.57/13.42 =>))))) @
% 99.57/13.42 (
% 99.57/13.42 (
% 99.57/13.42 ('#B') @ (
% 99.57/13.42 (
% 99.57/13.42 ('#B') @ (
% 99.57/13.42 (
% 99.57/13.42 ('#C') @ in)))) @
% 99.57/13.42 surjFuncSet)))))))) @
% 99.57/13.42 (
% 99.57/13.42 (
% 99.57/13.42 ('#B') @ (
% 99.57/13.42 (
% 99.57/13.42 ('#B') @ (
% 99.57/13.42 (
% 99.57/13.42 ('#C') @ in)))) @
% 99.57/13.42 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.57/13.42 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl952])).
% 99.57/13.42 thf(zip_derived_cl984, plain,
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% 99.57/13.42 (((subset2powerset) =>
% 99.57/13.42 (((setextsub) =>
% 99.57/13.42 (((subsetemptysetimpeq) =>
% 99.57/13.42 (((powersetI1) =>
% 99.57/13.42 (((powersetE1) =>
% 99.57/13.42 (((inPowerset) =>
% 99.57/13.42 (((powersetsubset) =>
% 99.57/13.42 (((sepInPowerset) =>
% 99.57/13.42 (((sepSubset) =>
% 99.57/13.42 (((binunionIL) =>
% 99.57/13.42 (((upairset2IR) =>
% 99.57/13.42 (((binunionIR) =>
% 99.57/13.42 (((binunionEcases) =>
% 99.57/13.42 (((binunionE) =>
% 99.57/13.42 (((binunionLsub) =>
% 99.57/13.42 (((binunionRsub) =>
% 99.57/13.42 (((binintersectI) =>
% 99.57/13.42 (((binintersectSubset5) =>
% 99.57/13.42 (((binintersectEL) =>
% 99.57/13.42 (((binintersectLsub) =>
% 99.57/13.42 (((binintersectSubset2) =>
% 99.57/13.42 (((binintersectSubset3) =>
% 99.57/13.42 (((binintersectER) =>
% 99.57/13.42 (((disjointsetsI1) =>
% 99.57/13.42 (((binintersectRsub) =>
% 99.57/13.42 (((binintersectSubset4) =>
% 99.57/13.42 (((binintersectSubset1) =>
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% 99.57/13.42 (((setminusI) =>
% 99.57/13.42 ((
% 99.57/13.42 (setminusEL) =>
% 99.57/13.42 ((
% 99.57/13.42 (setminusER) =>
% 99.57/13.42 ((
% 99.57/13.42 (setminusSubset2) =>
% 99.57/13.42 ((
% 99.57/13.42 (setminusERneg) =>
% 99.57/13.42 ((
% 99.57/13.42 (setminusELneg) =>
% 99.57/13.42 ((
% 99.57/13.42 (setminusILneg) =>
% 99.57/13.42 ((
% 99.57/13.42 (setminusIRneg) =>
% 99.57/13.42 ((
% 99.57/13.42 (setminusLsub) =>
% 99.57/13.42 ((
% 99.57/13.42 (setminusSubset1) =>
% 99.57/13.42 ((
% 99.57/13.42 (symdiffE) =>
% 99.57/13.42 ((
% 99.57/13.42 (symdiffI1) =>
% 99.57/13.42 ((
% 99.57/13.42 (symdiffI2) =>
% 99.57/13.42 ((
% 99.57/13.42 (symdiffIneg1) =>
% 99.57/13.42 ((
% 99.57/13.42 (symdiffIneg2) =>
% 99.57/13.42 ((
% 99.57/13.42 (secondinupair) =>
% 99.57/13.42 ((
% 99.57/13.42 (setukpairIL) =>
% 99.57/13.42 ((
% 99.57/13.42 (setukpairIR) =>
% 99.57/13.42 ((
% 99.57/13.42 (kpairiskpair) =>
% 99.57/13.42 ((
% 99.57/13.42 (kpairp) =>
% 99.57/13.42 ((
% 99.57/13.42 (singletonsubset) =>
% 99.57/13.42 ((
% 99.57/13.42 (singletoninpowerset) =>
% 99.57/13.42 ((
% 99.57/13.42 (singletoninpowunion) =>
% 99.57/13.42 ((
% 99.57/13.42 (upairset2E) =>
% 99.57/13.42 ((
% 99.57/13.42 (upairsubunion) =>
% 99.57/13.42 ((
% 99.57/13.42 (upairinpowunion) =>
% 99.57/13.42 ((
% 99.57/13.42 (ubforcartprodlem1) =>
% 99.57/13.42 ((
% 99.57/13.42 (ubforcartprodlem2) =>
% 99.57/13.42 ((
% 99.57/13.42 (ubforcartprodlem3) =>
% 99.57/13.42 ((
% 99.57/13.42 (cartprodpairin) =>
% 99.57/13.42 ((
% 99.57/13.42 (cartprodmempair1) =>
% 99.57/13.42 ((
% 99.57/13.42 (cartprodmempair) =>
% 99.57/13.42 ((
% 99.57/13.42 (setunionE2) =>
% 99.57/13.42 ((
% 99.57/13.42 (setunionsingleton1) =>
% 99.57/13.42 ((
% 99.57/13.42 (setunionsingleton2) =>
% 99.57/13.42 ((
% 99.57/13.42 (setunionsingleton) =>
% 99.57/13.42 ((
% 99.57/13.42 (singletonprop) =>
% 99.57/13.42 ((
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% 99.57/13.42 ((
% 99.57/13.42 (ex1I) =>
% 99.57/13.42 ((
% 99.57/13.42 (ex1I2) =>
% 99.57/13.42 ((
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% 99.57/13.42 ((
% 99.57/13.42 (setukpairinjL1) =>
% 99.57/13.42 ((
% 99.57/13.42 (kfstsingleton) =>
% 99.57/13.42 ((
% 99.57/13.42 (theprop) =>
% 99.57/13.42 ((
% 99.57/13.42 (kfstpairEq) =>
% 99.57/13.42 ((
% 99.57/13.42 (cartprodfstin) =>
% 99.57/13.42 ((
% 99.57/13.42 (setukpairinjL2) =>
% 99.57/13.42 ((
% 99.57/13.42 (setukpairinjL) =>
% 99.57/13.42 ((
% 99.57/13.42 (setukpairinjR11) =>
% 99.57/13.42 ((
% 99.57/13.42 (setukpairinjR12) =>
% 99.57/13.42 ((
% 99.57/13.42 (setukpairinjR1) =>
% 99.57/13.42 ((
% 99.57/13.42 (upairequniteq) =>
% 99.57/13.42 ((
% 99.57/13.42 (setukpairinjR2) =>
% 99.57/13.42 ((
% 99.57/13.42 (setukpairinjR) =>
% 99.57/13.42 ((
% 99.57/13.42 (ksndsingleton) =>
% 99.57/13.42 ((
% 99.57/13.42 (ksndpairEq) =>
% 99.57/13.42 ((
% 99.57/13.42 (kpairsurjEq) =>
% 99.57/13.42 ((
% 99.57/13.42 (cartprodsndin) =>
% 99.57/13.42 ((
% 99.57/13.42 (cartprodpairmemEL) =>
% 99.57/13.42 ((
% 99.57/13.42 (cartprodpairmemER) =>
% 99.57/13.42 ((
% 99.57/13.42 (cartprodmempaircEq) =>
% 99.57/13.42 ((
% 99.57/13.42 (cartprodfstpairEq) =>
% 99.57/13.42 ((
% 99.57/13.42 (cartprodsndpairEq) =>
% 99.57/13.42 ((
% 99.57/13.42 (cartprodpairsurjEq) =>
% 99.57/13.42 ((
% 99.57/13.42 (dpsetconstrI) =>
% 99.57/13.42 ((
% 99.57/13.42 (dpsetconstrSub) =>
% 99.57/13.42 ((
% 99.57/13.42 (setOfPairsIsBReln) =>
% 99.57/13.42 ((
% 99.57/13.42 (dpsetconstrERa) =>
% 99.57/13.42 ((
% 99.57/13.42 (dpsetconstrEL1) =>
% 99.57/13.42 ((
% 99.57/13.42 (dpsetconstrEL2) =>
% 99.57/13.42 ((
% 99.57/13.42 (dpsetconstrER) =>
% 99.57/13.42 ((
% 99.57/13.42 (funcImageSingleton) =>
% 99.57/13.42 ((
% 99.57/13.42 (apProp) =>
% 99.57/13.42 ((
% 99.57/13.42 (app) =>
% 99.57/13.42 ((
% 99.57/13.42 (infuncsetfunc) =>
% 99.57/13.42 ((
% 99.57/13.42 (ap2p) =>
% 99.57/13.42 ((
% 99.57/13.42 (funcinfuncset) =>
% 99.57/13.42 ((
% 99.57/13.42 (lamProp) =>
% 99.57/13.42 ((
% 99.57/13.42 (lamp) =>
% 99.57/13.42 ((
% 99.57/13.42 (lam2p) =>
% 99.57/13.42 ((
% 99.57/13.42 (brelnall1) =>
% 99.57/13.42 ((
% 99.57/13.42 (brelnall2) =>
% 99.57/13.42 ((
% 99.57/13.42 (ex1E2) =>
% 99.57/13.42 ((
% 99.57/13.42 (funcGraphProp1) =>
% 99.57/13.42 ((
% 99.57/13.42 (funcGraphProp3) =>
% 99.57/13.42 ((
% 99.57/13.42 (funcGraphProp2) =>
% 99.57/13.42 ((
% 99.57/13.42 (funcextLem) =>
% 99.57/13.42 ((
% 99.57/13.42 (funcGraphProp4) =>
% 99.57/13.42 ((
% 99.57/13.42 (subbreln) =>
% 99.57/13.42 ((
% 99.57/13.42 (eqbreln) =>
% 99.57/13.42 ((
% 99.57/13.42 (funcext) =>
% 99.57/13.42 ((
% 99.57/13.42 (funcext2) =>
% 99.57/13.42 ((
% 99.57/13.42 (ap2apEq1) =>
% 99.57/13.42 ((
% 99.57/13.42 (ap2apEq2) =>
% 99.57/13.42 ((
% 99.57/13.42 (beta1) =>
% 99.57/13.42 ((
% 99.57/13.42 (eta1) =>
% 99.57/13.42 ((
% 99.57/13.42 (lam2lamEq) =>
% 99.57/13.42 ((
% 99.57/13.42 (beta2) =>
% 99.57/13.42 ((
% 99.57/13.42 (eta2) =>
% 99.57/13.42 ((
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% 99.57/13.42 ((
% 99.57/13.42 (iffalseProp2) =>
% 99.57/13.42 ((
% 99.57/13.42 (iftrueProp1) =>
% 99.57/13.42 ((
% 99.57/13.42 (iftrueProp2) =>
% 99.57/13.42 ((
% 99.57/13.42 (ifSingleton) =>
% 99.57/13.42 ((
% 99.57/13.42 (ifp) =>
% 99.57/13.42 ((
% 99.57/13.42 (theeq) =>
% 99.57/13.42 ((
% 99.57/13.42 (iftrue) =>
% 99.57/13.42 ((
% 99.57/13.42 (iffalse) =>
% 99.57/13.42 ((
% 99.57/13.42 (iftrueorfalse) =>
% 99.57/13.42 ((
% 99.57/13.42 (binintersectT_lem) =>
% 99.57/13.42 ((
% 99.57/13.42 (binunionT_lem) =>
% 99.57/13.42 ((
% 99.57/13.42 (powersetT_lem) =>
% 99.57/13.42 ((
% 99.57/13.42 (setminusT_lem) =>
% 99.57/13.42 ((
% 99.57/13.42 (complementT_lem) =>
% 99.57/13.42 ((
% 99.57/13.42 (setextT) =>
% 99.57/13.42 ((
% 99.57/13.42 (subsetTI) =>
% 99.57/13.42 ((
% 99.57/13.42 (powersetTI1) =>
% 99.57/13.42 ((
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% 99.57/13.42 ((
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% 99.57/13.42 ((
% 99.57/13.42 (complementTE1) =>
% 99.57/13.42 ((
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% 99.57/13.42 ((
% 99.57/13.42 (binintersectTERcontra) =>
% 99.57/13.42 ((
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% 99.57/13.42 ((
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% 99.57/13.42 ((
% 99.57/13.42 (contrasubsetT2) =>
% 99.57/13.42 ((
% 99.57/13.42 (contrasubsetT3) =>
% 99.57/13.42 ((
% 99.57/13.42 (doubleComplementI1) =>
% 99.57/13.42 ((
% 99.57/13.42 (doubleComplementE1) =>
% 99.57/13.42 ((
% 99.57/13.42 (doubleComplementSub1) =>
% 99.57/13.42 ((
% 99.57/13.42 (doubleComplementSub2) =>
% 99.57/13.42 ((
% 99.57/13.42 (doubleComplementEq) =>
% 99.57/13.42 ((
% 99.57/13.42 (complementTnotintersectT) =>
% 99.57/13.42 ((
% 99.57/13.42 (complementImpComplementIntersect) =>
% 99.57/13.42 ((
% 99.57/13.42 (complementSubsetComplementIntersect) =>
% 99.57/13.42 ((
% 99.57/13.42 (complementInPowersetComplementIntersect) =>
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% 99.57/13.42 (contraSubsetComplement) =>
% 99.57/13.42 ((
% 99.57/13.42 (complementTcontraSubset) =>
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% 99.57/13.42 ((
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% 99.57/13.42 (intersectInPowersetIntersectUnions) =>
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% 99.57/13.42 (inComplementUnionImpNotIn1) =>
% 99.57/13.42 ((
% 99.57/13.42 (inComplementUnionImpInComplement1) =>
% 99.57/13.42 ((
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% 99.57/13.42 ((
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% 99.57/13.42 ((
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% 99.57/13.42 ((
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% 99.57/13.42 ((
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% 99.57/13.42 ((
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% 99.57/13.42 ((
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% 99.57/13.42 ((
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% 99.57/13.42 (breln1all2) =>
% 99.57/13.42 ((
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% 99.57/13.42 ((
% 99.57/13.42 (breln1invI) =>
% 99.57/13.42 ((
% 99.57/13.42 (breln1invE) =>
% 99.57/13.42 ((
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% 99.57/13.42 ((
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% 99.57/13.42 ((
% 99.57/13.42 (breln1compE) =>
% 99.57/13.42 ((
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% 99.57/13.42 ((
% 99.57/13.42 (breln1unionI) =>
% 99.57/13.42 ((
% 99.57/13.42 (breln1unionE) =>
% 99.57/13.42 ((
% 99.57/13.42 (breln1unionEcases) =>
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% 99.57/13.42 (breln1unionCommutes) =>
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% 99.57/13.42 ((
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% 99.57/13.42 ((
% 99.57/13.42 (image1Ex1) =>
% 99.57/13.42 ((
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% 99.57/13.42 (
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% 99.57/13.42 surjFuncSet)))))))) @
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% 99.57/13.42 (
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% 99.57/13.42 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
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% 99.57/13.42 ((
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% 99.57/13.42 ((
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% 99.57/13.42 ((
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% 99.57/13.42 ((
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% 99.57/13.42 ((
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% 99.57/13.42 ((
% 99.57/13.42 (symdiffI2) =>
% 99.57/13.42 ((
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% 99.57/13.42 ((
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% 99.57/13.42 ((
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% 99.57/13.42 ((
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% 99.57/13.42 ((
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% 99.57/13.42 ((
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% 99.57/13.42 ((
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% 99.57/13.42 ((
% 99.57/13.42 (upairinpowunion) =>
% 99.57/13.42 ((
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% 99.57/13.42 ((
% 99.57/13.42 (ubforcartprodlem2) =>
% 99.57/13.42 ((
% 99.57/13.42 (ubforcartprodlem3) =>
% 99.57/13.42 ((
% 99.57/13.42 (cartprodpairin) =>
% 99.57/13.42 ((
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% 99.57/13.42 ((
% 99.57/13.42 (cartprodmempair) =>
% 99.57/13.42 ((
% 99.57/13.42 (setunionE2) =>
% 99.57/13.42 ((
% 99.57/13.42 (setunionsingleton1) =>
% 99.57/13.42 ((
% 99.57/13.42 (setunionsingleton2) =>
% 99.57/13.42 ((
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% 99.57/13.42 ((
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% 99.57/13.42 ((
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% 99.57/13.42 ((
% 99.57/13.42 (theprop) =>
% 99.57/13.42 ((
% 99.57/13.42 (kfstpairEq) =>
% 99.57/13.42 ((
% 99.57/13.42 (cartprodfstin) =>
% 99.57/13.42 ((
% 99.57/13.42 (setukpairinjL2) =>
% 99.57/13.42 ((
% 99.57/13.42 (setukpairinjL) =>
% 99.57/13.42 ((
% 99.57/13.42 (setukpairinjR11) =>
% 99.57/13.42 ((
% 99.57/13.42 (setukpairinjR12) =>
% 99.57/13.42 ((
% 99.57/13.42 (setukpairinjR1) =>
% 99.57/13.42 ((
% 99.57/13.42 (upairequniteq) =>
% 99.57/13.42 ((
% 99.57/13.42 (setukpairinjR2) =>
% 99.57/13.42 ((
% 99.57/13.42 (setukpairinjR) =>
% 99.57/13.42 ((
% 99.57/13.42 (ksndsingleton) =>
% 99.57/13.42 ((
% 99.57/13.42 (ksndpairEq) =>
% 99.57/13.42 ((
% 99.57/13.42 (kpairsurjEq) =>
% 99.57/13.42 ((
% 99.57/13.42 (cartprodsndin) =>
% 99.57/13.42 ((
% 99.57/13.42 (cartprodpairmemEL) =>
% 99.57/13.42 ((
% 99.57/13.42 (cartprodpairmemER) =>
% 99.57/13.42 ((
% 99.57/13.42 (cartprodmempaircEq) =>
% 99.57/13.42 ((
% 99.57/13.42 (cartprodfstpairEq) =>
% 99.57/13.42 ((
% 99.57/13.42 (cartprodsndpairEq) =>
% 99.57/13.42 ((
% 99.57/13.42 (cartprodpairsurjEq) =>
% 99.57/13.42 ((
% 99.57/13.42 (dpsetconstrI) =>
% 99.57/13.42 ((
% 99.57/13.42 (dpsetconstrSub) =>
% 99.57/13.42 ((
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% 99.57/13.42 ((
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% 99.57/13.42 ((
% 99.57/13.42 (dpsetconstrEL2) =>
% 99.57/13.42 ((
% 99.57/13.42 (dpsetconstrER) =>
% 99.57/13.42 ((
% 99.57/13.42 (funcImageSingleton) =>
% 99.57/13.42 ((
% 99.57/13.42 (apProp) =>
% 99.57/13.42 ((
% 99.57/13.42 (app) =>
% 99.57/13.42 ((
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% 99.57/13.42 ((
% 99.57/13.42 (ap2p) =>
% 99.57/13.42 ((
% 99.57/13.42 (funcinfuncset) =>
% 99.57/13.42 ((
% 99.57/13.42 (lamProp) =>
% 99.57/13.42 ((
% 99.57/13.42 (lamp) =>
% 99.57/13.42 ((
% 99.57/13.42 (lam2p) =>
% 99.57/13.42 ((
% 99.57/13.42 (brelnall1) =>
% 99.57/13.42 ((
% 99.57/13.42 (brelnall2) =>
% 99.57/13.42 ((
% 99.57/13.42 (ex1E2) =>
% 99.57/13.42 ((
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% 99.57/13.42 ((
% 99.57/13.42 (funcGraphProp3) =>
% 99.57/13.42 ((
% 99.57/13.42 (funcGraphProp2) =>
% 99.57/13.42 ((
% 99.57/13.42 (funcextLem) =>
% 99.57/13.42 ((
% 99.57/13.42 (funcGraphProp4) =>
% 99.57/13.42 ((
% 99.57/13.42 (subbreln) =>
% 99.57/13.42 ((
% 99.57/13.42 (eqbreln) =>
% 99.57/13.42 ((
% 99.57/13.42 (funcext) =>
% 99.57/13.42 ((
% 99.57/13.42 (funcext2) =>
% 99.57/13.42 ((
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% 99.57/13.42 ((
% 99.57/13.42 (ap2apEq2) =>
% 99.57/13.42 ((
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% 99.57/13.42 ((
% 99.57/13.42 (eta1) =>
% 99.57/13.42 ((
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% 99.57/13.42 ((
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% 99.57/13.42 ((
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% 99.57/13.42 ((
% 99.57/13.42 (iffalseProp2) =>
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% 99.57/13.42 ((
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% 99.57/13.42 ((
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% 99.57/13.42 ((
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% 99.57/13.42 (contrasubsetT3) =>
% 99.57/13.42 ((
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% 99.57/13.42 ((
% 99.57/13.42 (doubleComplementE1) =>
% 99.57/13.42 ((
% 99.57/13.42 (doubleComplementSub1) =>
% 99.57/13.42 ((
% 99.57/13.42 (doubleComplementSub2) =>
% 99.57/13.42 ((
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% 99.57/13.42 ((
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% 99.57/13.42 ((
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% 99.57/13.42 (inComplementUnionImpInComplement1) =>
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% 99.57/13.42 ((
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% 99.57/13.42 ((
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% 99.57/13.42 ((
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% 99.57/13.42 ((
% 99.57/13.42 (setminusELneg) =>
% 99.57/13.42 ((
% 99.57/13.42 (setminusILneg) =>
% 99.57/13.42 ((
% 99.57/13.42 (setminusIRneg) =>
% 99.57/13.42 ((
% 99.57/13.42 (setminusLsub) =>
% 99.57/13.42 ((
% 99.57/13.42 (setminusSubset1) =>
% 99.57/13.42 ((
% 99.57/13.42 (symdiffE) =>
% 99.57/13.42 ((
% 99.57/13.42 (symdiffI1) =>
% 99.57/13.42 ((
% 99.57/13.42 (symdiffI2) =>
% 99.57/13.42 ((
% 99.57/13.42 (symdiffIneg1) =>
% 99.57/13.42 ((
% 99.57/13.42 (symdiffIneg2) =>
% 99.57/13.42 ((
% 99.57/13.42 (secondinupair) =>
% 99.57/13.42 ((
% 99.57/13.42 (setukpairIL) =>
% 99.57/13.42 ((
% 99.57/13.42 (setukpairIR) =>
% 99.57/13.42 ((
% 99.57/13.42 (kpairiskpair) =>
% 99.57/13.42 ((
% 99.57/13.42 (kpairp) =>
% 99.57/13.42 ((
% 99.57/13.42 (singletonsubset) =>
% 99.57/13.42 ((
% 99.57/13.42 (singletoninpowerset) =>
% 99.57/13.42 ((
% 99.57/13.42 (singletoninpowunion) =>
% 99.57/13.42 ((
% 99.57/13.42 (upairset2E) =>
% 99.57/13.42 ((
% 99.57/13.42 (upairsubunion) =>
% 99.57/13.42 ((
% 99.57/13.42 (upairinpowunion) =>
% 99.57/13.42 ((
% 99.57/13.42 (ubforcartprodlem1) =>
% 99.57/13.42 ((
% 99.57/13.42 (ubforcartprodlem2) =>
% 99.57/13.42 ((
% 99.57/13.42 (ubforcartprodlem3) =>
% 99.57/13.42 ((
% 99.57/13.42 (cartprodpairin) =>
% 99.57/13.42 ((
% 99.57/13.42 (cartprodmempair1) =>
% 99.57/13.42 ((
% 99.57/13.42 (cartprodmempair) =>
% 99.57/13.42 ((
% 99.57/13.42 (setunionE2) =>
% 99.57/13.42 ((
% 99.57/13.42 (setunionsingleton1) =>
% 99.57/13.42 ((
% 99.57/13.42 (setunionsingleton2) =>
% 99.57/13.42 ((
% 99.57/13.42 (setunionsingleton) =>
% 99.57/13.42 ((
% 99.57/13.42 (singletonprop) =>
% 99.57/13.42 ((
% 99.57/13.42 (ex1E1) =>
% 99.57/13.42 ((
% 99.57/13.42 (ex1I) =>
% 99.57/13.42 ((
% 99.57/13.42 (ex1I2) =>
% 99.57/13.42 ((
% 99.57/13.42 (singletonsuniq) =>
% 99.57/13.42 ((
% 99.57/13.42 (setukpairinjL1) =>
% 99.57/13.42 ((
% 99.57/13.42 (kfstsingleton) =>
% 99.57/13.42 ((
% 99.57/13.42 (theprop) =>
% 99.57/13.42 ((
% 99.57/13.42 (kfstpairEq) =>
% 99.57/13.42 ((
% 99.57/13.42 (cartprodfstin) =>
% 99.57/13.42 ((
% 99.57/13.42 (setukpairinjL2) =>
% 99.57/13.42 ((
% 99.57/13.42 (setukpairinjL) =>
% 99.57/13.42 ((
% 99.57/13.42 (setukpairinjR11) =>
% 99.57/13.42 ((
% 99.57/13.42 (setukpairinjR12) =>
% 99.57/13.42 ((
% 99.57/13.42 (setukpairinjR1) =>
% 99.57/13.42 ((
% 99.57/13.42 (upairequniteq) =>
% 99.57/13.42 ((
% 99.57/13.42 (setukpairinjR2) =>
% 99.57/13.42 ((
% 99.57/13.42 (setukpairinjR) =>
% 99.57/13.42 ((
% 99.57/13.42 (ksndsingleton) =>
% 99.57/13.42 ((
% 99.57/13.42 (ksndpairEq) =>
% 99.57/13.42 ((
% 99.57/13.42 (kpairsurjEq) =>
% 99.57/13.42 ((
% 99.57/13.42 (cartprodsndin) =>
% 99.57/13.42 ((
% 99.57/13.42 (cartprodpairmemEL) =>
% 99.57/13.42 ((
% 99.57/13.42 (cartprodpairmemER) =>
% 99.57/13.42 ((
% 99.57/13.42 (cartprodmempaircEq) =>
% 99.57/13.42 ((
% 99.57/13.42 (cartprodfstpairEq) =>
% 99.57/13.42 ((
% 99.57/13.42 (cartprodsndpairEq) =>
% 99.57/13.42 ((
% 99.57/13.42 (cartprodpairsurjEq) =>
% 99.57/13.42 ((
% 99.57/13.42 (dpsetconstrI) =>
% 99.57/13.42 ((
% 99.57/13.42 (dpsetconstrSub) =>
% 99.57/13.42 ((
% 99.57/13.42 (setOfPairsIsBReln) =>
% 99.57/13.42 ((
% 99.57/13.42 (dpsetconstrERa) =>
% 99.57/13.42 ((
% 99.57/13.42 (dpsetconstrEL1) =>
% 99.57/13.42 ((
% 99.57/13.42 (dpsetconstrEL2) =>
% 99.57/13.42 ((
% 99.57/13.42 (dpsetconstrER) =>
% 99.57/13.42 ((
% 99.57/13.42 (funcImageSingleton) =>
% 99.57/13.42 ((
% 99.57/13.42 (apProp) =>
% 99.57/13.42 ((
% 99.57/13.42 (app) =>
% 99.57/13.42 ((
% 99.57/13.42 (infuncsetfunc) =>
% 99.57/13.42 ((
% 99.57/13.42 (ap2p) =>
% 99.57/13.42 ((
% 99.57/13.42 (funcinfuncset) =>
% 99.57/13.42 ((
% 99.57/13.42 (lamProp) =>
% 99.57/13.42 ((
% 99.57/13.42 (lamp) =>
% 99.57/13.42 ((
% 99.57/13.42 (lam2p) =>
% 99.57/13.42 ((
% 99.57/13.42 (brelnall1) =>
% 99.57/13.42 ((
% 99.57/13.42 (brelnall2) =>
% 99.57/13.42 ((
% 99.57/13.42 (ex1E2) =>
% 99.57/13.42 ((
% 99.57/13.42 (funcGraphProp1) =>
% 99.57/13.42 ((
% 99.57/13.42 (funcGraphProp3) =>
% 99.57/13.42 ((
% 99.57/13.42 (funcGraphProp2) =>
% 99.57/13.42 ((
% 99.57/13.42 (funcextLem) =>
% 99.57/13.42 ((
% 99.57/13.42 (funcGraphProp4) =>
% 99.57/13.42 ((
% 99.57/13.42 (subbreln) =>
% 99.57/13.42 ((
% 99.57/13.42 (eqbreln) =>
% 99.57/13.42 ((
% 99.57/13.42 (funcext) =>
% 99.57/13.42 ((
% 99.57/13.42 (funcext2) =>
% 99.57/13.42 ((
% 99.57/13.42 (ap2apEq1) =>
% 99.57/13.42 ((
% 99.57/13.42 (ap2apEq2) =>
% 99.57/13.42 ((
% 99.57/13.42 (beta1) =>
% 99.57/13.42 ((
% 99.57/13.42 (eta1) =>
% 99.57/13.42 ((
% 99.57/13.42 (lam2lamEq) =>
% 99.57/13.42 ((
% 99.57/13.42 (beta2) =>
% 99.57/13.42 ((
% 99.57/13.42 (eta2) =>
% 99.57/13.42 ((
% 99.57/13.42 (iffalseProp1) =>
% 99.57/13.42 ((
% 99.57/13.42 (iffalseProp2) =>
% 99.57/13.42 ((
% 99.57/13.42 (iftrueProp1) =>
% 99.57/13.42 ((
% 99.57/13.42 (iftrueProp2) =>
% 99.57/13.42 ((
% 99.57/13.42 (ifSingleton) =>
% 99.57/13.42 ((
% 99.57/13.42 (ifp) =>
% 99.57/13.42 ((
% 99.57/13.42 (theeq) =>
% 99.57/13.42 ((
% 99.57/13.42 (iftrue) =>
% 99.57/13.42 ((
% 99.57/13.42 (iffalse) =>
% 99.57/13.42 ((
% 99.57/13.42 (iftrueorfalse) =>
% 99.57/13.42 ((
% 99.57/13.42 (binintersectT_lem) =>
% 99.57/13.42 ((
% 99.57/13.42 (binunionT_lem) =>
% 99.57/13.42 ((
% 99.57/13.42 (powersetT_lem) =>
% 99.57/13.42 ((
% 99.57/13.42 (setminusT_lem) =>
% 99.57/13.42 ((
% 99.57/13.42 (complementT_lem) =>
% 99.57/13.42 ((
% 99.57/13.42 (setextT) =>
% 99.57/13.42 ((
% 99.57/13.42 (subsetTI) =>
% 99.57/13.42 ((
% 99.57/13.42 (powersetTI1) =>
% 99.57/13.42 ((
% 99.57/13.42 (powersetTE1) =>
% 99.57/13.42 ((
% 99.57/13.42 (complementTI1) =>
% 99.57/13.42 ((
% 99.57/13.42 (complementTE1) =>
% 99.57/13.42 ((
% 99.57/13.42 (binintersectTELcontra) =>
% 99.57/13.42 ((
% 99.57/13.42 (binintersectTERcontra) =>
% 99.57/13.42 ((
% 99.57/13.42 (contrasubsetT) =>
% 99.57/13.42 ((
% 99.57/13.42 (contrasubsetT1) =>
% 99.57/13.42 ((
% 99.57/13.42 (contrasubsetT2) =>
% 99.57/13.42 ((
% 99.57/13.42 (contrasubsetT3) =>
% 99.57/13.42 ((
% 99.57/13.42 (doubleComplementI1) =>
% 99.57/13.42 ((
% 99.57/13.42 (doubleComplementE1) =>
% 99.57/13.42 ((
% 99.57/13.42 (doubleComplementSub1) =>
% 99.57/13.42 ((
% 99.57/13.42 (doubleComplementSub2) =>
% 99.57/13.42 ((
% 99.57/13.42 (doubleComplementEq) =>
% 99.57/13.42 ((
% 99.57/13.42 (complementTnotintersectT) =>
% 99.57/13.42 ((
% 99.57/13.42 (complementImpComplementIntersect) =>
% 99.57/13.42 ((
% 99.57/13.42 (complementSubsetComplementIntersect) =>
% 99.57/13.42 ((
% 99.57/13.42 (complementInPowersetComplementIntersect) =>
% 99.57/13.42 ((
% 99.57/13.42 (contraSubsetComplement) =>
% 99.57/13.42 ((
% 99.57/13.42 (complementTcontraSubset) =>
% 99.57/13.42 ((
% 99.57/13.42 (binunionTILcontra) =>
% 99.57/13.42 ((
% 99.57/13.42 (binunionTIRcontra) =>
% 99.57/13.42 ((
% 99.57/13.42 (inIntersectImpInUnion) =>
% 99.57/13.42 ((
% 99.57/13.42 (inIntersectImpInUnion2) =>
% 99.57/13.42 ((
% 99.57/13.42 (inIntersectImpInIntersectUnions) =>
% 99.57/13.42 ((
% 99.57/13.42 (intersectInPowersetIntersectUnions) =>
% 99.57/13.42 ((
% 99.57/13.42 (inComplementUnionImpNotIn1) =>
% 99.57/13.42 ((
% 99.57/13.42 (inComplementUnionImpInComplement1) =>
% 99.57/13.42 ((
% 99.57/13.42 (binunionTE) =>
% 99.57/13.42 ((
% 99.57/13.42 (binunionTEcontra) =>
% 99.57/13.42 ((
% 99.57/13.42 (demorgan2a1) =>
% 99.57/13.42 ((
% 99.57/13.42 (complementUnionInPowersetComplement) =>
% 99.57/13.42 ((
% 99.57/13.42 (demorgan2a2) =>
% 99.57/13.42 ((
% 99.57/13.42 (demorgan1a) =>
% 99.57/13.42 ((
% 99.57/13.42 (demorgan1b) =>
% 99.57/13.42 ((
% 99.57/13.42 (demorgan1) =>
% 99.57/13.42 ((
% 99.57/13.42 (demorgan2a) =>
% 99.57/13.42 ((
% 99.57/13.42 (demorgan2b2) =>
% 99.57/13.42 ((
% 99.57/13.42 (demorgan2b) =>
% 99.57/13.42 ((
% 99.57/13.42 (demorgan2) =>
% 99.57/13.42 ((
% 99.57/13.42 (woz13rule0) =>
% 99.57/13.42 ((
% 99.57/13.42 (woz13rule1) =>
% 99.57/13.42 ((
% 99.57/13.42 (woz13rule2) =>
% 99.57/13.42 ((
% 99.57/13.42 (woz13rule3) =>
% 99.57/13.42 ((
% 99.57/13.42 (woz13rule4) =>
% 99.57/13.42 ((
% 99.57/13.42 (woz1_1) =>
% 99.57/13.42 ((
% 99.57/13.42 (woz1_2) =>
% 99.57/13.42 ((
% 99.57/13.42 (woz1_3) =>
% 99.57/13.42 ((
% 99.57/13.42 (woz1_4) =>
% 99.57/13.42 ((
% 99.57/13.42 (woz1_5) =>
% 99.57/13.42 ((
% 99.57/13.42 (breln1all2) =>
% 99.57/13.42 ((
% 99.57/13.42 (breln1SetBreln1) =>
% 99.57/13.42 ((
% 99.57/13.42 (choice2fnsingleton) =>
% 99.57/13.42 ((
% 99.57/13.42 (setOfPairsIsBReln1) =>
% 99.57/13.42 ((
% 99.57/13.42 (breln1all1) =>
% 99.57/13.42 ((
% 99.57/13.42 (subbreln1) =>
% 99.57/13.42 ((
% 99.57/13.42 (eqbreln1) =>
% 99.57/13.42 ((
% 99.57/13.42 (breln1invprop) =>
% 99.57/13.42 ((
% 99.57/13.42 (breln1invI) =>
% 99.57/13.42 ((
% 99.57/13.42 (breln1invE) =>
% 99.57/13.42 ((
% 99.57/13.42 (breln1compprop) =>
% 99.57/13.42 ((
% 99.57/13.42 (breln1compI) =>
% 99.57/13.42 ((
% 99.57/13.42 (breln1compE) =>
% 99.57/13.42 ((
% 99.57/13.42 (breln1compEex) =>
% 99.57/13.42 ((
% 99.57/13.42 (breln1unionprop) =>
% 99.57/13.42 ((
% 99.57/13.42 (breln1unionIL) =>
% 99.57/13.42 ((
% 99.57/13.42 (breln1unionIR) =>
% 99.57/13.42 ((
% 99.57/13.42 (breln1unionI) =>
% 99.57/13.42 ((
% 99.57/13.42 (breln1unionE) =>
% 99.57/13.42 ((
% 99.57/13.42 (breln1unionEcases) =>
% 99.57/13.42 ((
% 99.57/13.42 (breln1unionCommutes) =>
% 99.57/13.42 ((
% 99.57/13.42 (woz2Ex) =>
% 99.57/13.42 ((
% 99.57/13.42 (woz2W) =>
% 99.57/13.42 ((
% 99.57/13.42 (woz2A) =>
% 99.57/13.42 ((
% 99.57/13.42 (woz2B) =>
% 99.57/13.42 ((
% 99.57/13.42 (image1Ex) =>
% 99.57/13.42 ((
% 99.57/13.42 (image1Ex1) =>
% 99.57/13.42 ((
% 99.57/13.42 (image1Equiv) =>
% 99.57/13.42 ((
% 99.57/13.42 (image1E) =>
% 99.57/13.42 ((
% 99.57/13.42 (image1I) =>
% 99.57/13.42 ((
% 99.57/13.42 (injFuncInInjFuncSet) =>
% 99.57/13.42 ((
% 99.57/13.42 (injFuncSetFuncIn) =>
% 99.57/13.42 ((
% 99.57/13.42 (injFuncSetFuncInj) =>
% 99.57/13.42 ((
% 99.57/13.42 (!!) @ (
% 99.57/13.42 (('#B') @ (
% 99.57/13.42 !!) @
% 99.57/13.42 (
% 99.57/13.42 (
% 99.57/13.42 ('#B') @ (
% 99.57/13.42 (
% 99.57/13.42 ('#B') @ (
% 99.57/13.42 !!))) @
% 99.57/13.42 (
% 99.57/13.42 (
% 99.57/13.42 ('#S') @ (
% 99.57/13.42 (
% 99.57/13.42 ('#B') @ (
% 99.57/13.42 '#S') @
% 99.57/13.42 (
% 99.57/13.42 (
% 99.57/13.42 ('#B') @ (
% 99.57/13.42 (
% 99.57/13.42 ('#B') @ (
% 99.57/13.42 '#S'))) @
% 99.57/13.42 (
% 99.57/13.42 (
% 99.57/13.42 ('#B') @ (
% 99.57/13.42 (
% 99.57/13.42 ('#B') @ (
% 99.57/13.42 (
% 99.57/13.42 ('#B') @ (
% 99.57/13.42 =>))))) @
% 99.57/13.42 (
% 99.57/13.42 (
% 99.57/13.42 ('#B') @ (
% 99.57/13.42 (
% 99.57/13.42 ('#B') @ (
% 99.57/13.42 (
% 99.57/13.42 ('#C') @ in)))) @
% 99.57/13.42 surjFuncSet)))))))) @
% 99.57/13.42 (
% 99.57/13.42 (
% 99.57/13.42 ('#B') @ (
% 99.57/13.42 (
% 99.57/13.42 ('#B') @ (
% 99.57/13.42 (
% 99.57/13.42 ('#C') @ in)))) @
% 99.57/13.42 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.57/13.42 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1015])).
% 99.57/13.42 thf(zip_derived_cl1039, plain,
% 99.57/13.42 (~ (((powersetI1) =>
% 99.57/13.42 (((powersetE1) =>
% 99.57/13.42 (((inPowerset) =>
% 99.57/13.42 (((powersetsubset) =>
% 99.57/13.42 (((sepInPowerset) =>
% 99.57/13.42 (((sepSubset) =>
% 99.57/13.42 (((binunionIL) =>
% 99.57/13.42 (((upairset2IR) =>
% 99.57/13.42 (((binunionIR) =>
% 99.57/13.42 (((binunionEcases) =>
% 99.57/13.42 (((binunionE) =>
% 99.57/13.42 (((binunionLsub) =>
% 99.57/13.42 (((binunionRsub) =>
% 99.57/13.42 (((binintersectI) =>
% 99.57/13.42 (((binintersectSubset5) =>
% 99.57/13.42 (((binintersectEL) =>
% 99.57/13.42 (((binintersectLsub) =>
% 99.57/13.42 (((binintersectSubset2) =>
% 99.57/13.42 (((binintersectSubset3) =>
% 99.57/13.42 (((binintersectER) =>
% 99.57/13.42 (((disjointsetsI1) =>
% 99.57/13.42 (((binintersectRsub) =>
% 99.57/13.42 (((binintersectSubset4) =>
% 99.57/13.42 (((binintersectSubset1) =>
% 99.57/13.42 (((bs114d) =>
% 99.57/13.42 (((setminusI) =>
% 99.57/13.42 (((setminusEL) =>
% 99.57/13.42 (((setminusER) =>
% 99.57/13.42 (((setminusSubset2) =>
% 99.57/13.42 (((setminusERneg) =>
% 99.57/13.42 ((
% 99.57/13.42 (setminusELneg) =>
% 99.57/13.42 ((
% 99.57/13.42 (setminusILneg) =>
% 99.57/13.42 ((
% 99.57/13.42 (setminusIRneg) =>
% 99.57/13.42 ((
% 99.57/13.42 (setminusLsub) =>
% 99.57/13.42 ((
% 99.57/13.42 (setminusSubset1) =>
% 99.57/13.42 ((
% 99.57/13.42 (symdiffE) =>
% 99.57/13.42 ((
% 99.57/13.42 (symdiffI1) =>
% 99.57/13.42 ((
% 99.57/13.42 (symdiffI2) =>
% 99.57/13.42 ((
% 99.57/13.42 (symdiffIneg1) =>
% 99.57/13.42 ((
% 99.57/13.42 (symdiffIneg2) =>
% 99.57/13.42 ((
% 99.57/13.42 (secondinupair) =>
% 99.57/13.42 ((
% 99.57/13.42 (setukpairIL) =>
% 99.57/13.42 ((
% 99.57/13.42 (setukpairIR) =>
% 99.57/13.42 ((
% 99.57/13.42 (kpairiskpair) =>
% 99.57/13.42 ((
% 99.57/13.42 (kpairp) =>
% 99.57/13.42 ((
% 99.57/13.42 (singletonsubset) =>
% 99.57/13.42 ((
% 99.57/13.42 (singletoninpowerset) =>
% 99.57/13.42 ((
% 99.57/13.42 (singletoninpowunion) =>
% 99.57/13.42 ((
% 99.57/13.42 (upairset2E) =>
% 99.57/13.42 ((
% 99.57/13.42 (upairsubunion) =>
% 99.57/13.42 ((
% 99.57/13.42 (upairinpowunion) =>
% 99.57/13.42 ((
% 99.57/13.42 (ubforcartprodlem1) =>
% 99.57/13.42 ((
% 99.57/13.42 (ubforcartprodlem2) =>
% 99.57/13.42 ((
% 99.57/13.42 (ubforcartprodlem3) =>
% 99.57/13.42 ((
% 99.57/13.42 (cartprodpairin) =>
% 99.57/13.42 ((
% 99.57/13.42 (cartprodmempair1) =>
% 99.57/13.42 ((
% 99.57/13.42 (cartprodmempair) =>
% 99.57/13.42 ((
% 99.57/13.42 (setunionE2) =>
% 99.57/13.42 ((
% 99.57/13.42 (setunionsingleton1) =>
% 99.57/13.42 ((
% 99.57/13.42 (setunionsingleton2) =>
% 99.57/13.42 ((
% 99.57/13.42 (setunionsingleton) =>
% 99.57/13.42 ((
% 99.57/13.42 (singletonprop) =>
% 99.57/13.42 ((
% 99.57/13.42 (ex1E1) =>
% 99.57/13.42 ((
% 99.57/13.42 (ex1I) =>
% 99.57/13.42 ((
% 99.57/13.42 (ex1I2) =>
% 99.57/13.42 ((
% 99.57/13.42 (singletonsuniq) =>
% 99.57/13.42 ((
% 99.57/13.42 (setukpairinjL1) =>
% 99.57/13.42 ((
% 99.57/13.42 (kfstsingleton) =>
% 99.57/13.42 ((
% 99.57/13.42 (theprop) =>
% 99.57/13.42 ((
% 99.57/13.42 (kfstpairEq) =>
% 99.57/13.42 ((
% 99.57/13.42 (cartprodfstin) =>
% 99.57/13.42 ((
% 99.57/13.42 (setukpairinjL2) =>
% 99.57/13.42 ((
% 99.57/13.42 (setukpairinjL) =>
% 99.57/13.42 ((
% 99.57/13.42 (setukpairinjR11) =>
% 99.57/13.42 ((
% 99.57/13.42 (setukpairinjR12) =>
% 99.57/13.42 ((
% 99.57/13.42 (setukpairinjR1) =>
% 99.57/13.42 ((
% 99.57/13.42 (upairequniteq) =>
% 99.57/13.42 ((
% 99.57/13.42 (setukpairinjR2) =>
% 99.57/13.42 ((
% 99.57/13.42 (setukpairinjR) =>
% 99.57/13.42 ((
% 99.57/13.42 (ksndsingleton) =>
% 99.57/13.42 ((
% 99.57/13.42 (ksndpairEq) =>
% 99.57/13.42 ((
% 99.57/13.42 (kpairsurjEq) =>
% 99.57/13.42 ((
% 99.57/13.42 (cartprodsndin) =>
% 99.57/13.42 ((
% 99.57/13.42 (cartprodpairmemEL) =>
% 99.57/13.42 ((
% 99.57/13.42 (cartprodpairmemER) =>
% 99.57/13.42 ((
% 99.57/13.42 (cartprodmempaircEq) =>
% 99.57/13.42 ((
% 99.57/13.42 (cartprodfstpairEq) =>
% 99.57/13.42 ((
% 99.57/13.42 (cartprodsndpairEq) =>
% 99.57/13.42 ((
% 99.57/13.42 (cartprodpairsurjEq) =>
% 99.57/13.42 ((
% 99.57/13.42 (dpsetconstrI) =>
% 99.57/13.42 ((
% 99.57/13.42 (dpsetconstrSub) =>
% 99.57/13.42 ((
% 99.57/13.42 (setOfPairsIsBReln) =>
% 99.57/13.42 ((
% 99.57/13.42 (dpsetconstrERa) =>
% 99.57/13.42 ((
% 99.57/13.42 (dpsetconstrEL1) =>
% 99.57/13.42 ((
% 99.57/13.42 (dpsetconstrEL2) =>
% 99.57/13.42 ((
% 99.57/13.42 (dpsetconstrER) =>
% 99.57/13.42 ((
% 99.57/13.42 (funcImageSingleton) =>
% 99.57/13.42 ((
% 99.57/13.42 (apProp) =>
% 99.57/13.42 ((
% 99.57/13.42 (app) =>
% 99.57/13.42 ((
% 99.57/13.42 (infuncsetfunc) =>
% 99.57/13.42 ((
% 99.57/13.42 (ap2p) =>
% 99.57/13.42 ((
% 99.57/13.42 (funcinfuncset) =>
% 99.57/13.42 ((
% 99.57/13.42 (lamProp) =>
% 99.57/13.42 ((
% 99.57/13.42 (lamp) =>
% 99.57/13.42 ((
% 99.57/13.42 (lam2p) =>
% 99.57/13.42 ((
% 99.57/13.42 (brelnall1) =>
% 99.57/13.42 ((
% 99.57/13.42 (brelnall2) =>
% 99.57/13.42 ((
% 99.57/13.42 (ex1E2) =>
% 99.57/13.42 ((
% 99.57/13.42 (funcGraphProp1) =>
% 99.57/13.42 ((
% 99.57/13.42 (funcGraphProp3) =>
% 99.57/13.42 ((
% 99.57/13.42 (funcGraphProp2) =>
% 99.57/13.42 ((
% 99.57/13.42 (funcextLem) =>
% 99.57/13.42 ((
% 99.57/13.42 (funcGraphProp4) =>
% 99.57/13.42 ((
% 99.57/13.42 (subbreln) =>
% 99.57/13.42 ((
% 99.57/13.42 (eqbreln) =>
% 99.57/13.42 ((
% 99.57/13.42 (funcext) =>
% 99.57/13.42 ((
% 99.57/13.42 (funcext2) =>
% 99.57/13.42 ((
% 99.57/13.42 (ap2apEq1) =>
% 99.57/13.42 ((
% 99.57/13.42 (ap2apEq2) =>
% 99.57/13.42 ((
% 99.57/13.42 (beta1) =>
% 99.57/13.42 ((
% 99.57/13.42 (eta1) =>
% 99.57/13.42 ((
% 99.57/13.42 (lam2lamEq) =>
% 99.57/13.42 ((
% 99.57/13.42 (beta2) =>
% 99.57/13.42 ((
% 99.57/13.42 (eta2) =>
% 99.57/13.42 ((
% 99.57/13.42 (iffalseProp1) =>
% 99.57/13.42 ((
% 99.57/13.42 (iffalseProp2) =>
% 99.57/13.42 ((
% 99.57/13.42 (iftrueProp1) =>
% 99.57/13.42 ((
% 99.57/13.42 (iftrueProp2) =>
% 99.57/13.42 ((
% 99.57/13.42 (ifSingleton) =>
% 99.57/13.42 ((
% 99.57/13.42 (ifp) =>
% 99.57/13.42 ((
% 99.57/13.42 (theeq) =>
% 99.57/13.42 ((
% 99.57/13.42 (iftrue) =>
% 99.57/13.42 ((
% 99.57/13.42 (iffalse) =>
% 99.57/13.42 ((
% 99.57/13.42 (iftrueorfalse) =>
% 99.57/13.42 ((
% 99.57/13.42 (binintersectT_lem) =>
% 99.57/13.42 ((
% 99.57/13.42 (binunionT_lem) =>
% 99.57/13.42 ((
% 99.57/13.42 (powersetT_lem) =>
% 99.57/13.42 ((
% 99.57/13.42 (setminusT_lem) =>
% 99.57/13.42 ((
% 99.57/13.42 (complementT_lem) =>
% 99.57/13.42 ((
% 99.57/13.42 (setextT) =>
% 99.57/13.42 ((
% 99.57/13.42 (subsetTI) =>
% 99.57/13.42 ((
% 99.57/13.42 (powersetTI1) =>
% 99.57/13.42 ((
% 99.57/13.42 (powersetTE1) =>
% 99.57/13.42 ((
% 99.57/13.42 (complementTI1) =>
% 99.57/13.42 ((
% 99.57/13.42 (complementTE1) =>
% 99.57/13.42 ((
% 99.57/13.42 (binintersectTELcontra) =>
% 99.57/13.42 ((
% 99.57/13.42 (binintersectTERcontra) =>
% 99.57/13.42 ((
% 99.57/13.42 (contrasubsetT) =>
% 99.57/13.42 ((
% 99.57/13.42 (contrasubsetT1) =>
% 99.57/13.42 ((
% 99.57/13.42 (contrasubsetT2) =>
% 99.57/13.42 ((
% 99.57/13.42 (contrasubsetT3) =>
% 99.57/13.42 ((
% 99.57/13.42 (doubleComplementI1) =>
% 99.57/13.42 ((
% 99.57/13.42 (doubleComplementE1) =>
% 99.57/13.42 ((
% 99.57/13.42 (doubleComplementSub1) =>
% 99.57/13.42 ((
% 99.57/13.42 (doubleComplementSub2) =>
% 99.57/13.42 ((
% 99.57/13.42 (doubleComplementEq) =>
% 99.57/13.42 ((
% 99.57/13.42 (complementTnotintersectT) =>
% 99.57/13.42 ((
% 99.57/13.42 (complementImpComplementIntersect) =>
% 99.57/13.42 ((
% 99.57/13.42 (complementSubsetComplementIntersect) =>
% 99.57/13.42 ((
% 99.57/13.42 (complementInPowersetComplementIntersect) =>
% 99.57/13.42 ((
% 99.57/13.42 (contraSubsetComplement) =>
% 99.57/13.42 ((
% 99.57/13.42 (complementTcontraSubset) =>
% 99.57/13.42 ((
% 99.57/13.42 (binunionTILcontra) =>
% 99.57/13.42 ((
% 99.57/13.42 (binunionTIRcontra) =>
% 99.57/13.42 ((
% 99.57/13.42 (inIntersectImpInUnion) =>
% 99.57/13.42 ((
% 99.57/13.42 (inIntersectImpInUnion2) =>
% 99.57/13.42 ((
% 99.57/13.42 (inIntersectImpInIntersectUnions) =>
% 99.57/13.42 ((
% 99.57/13.42 (intersectInPowersetIntersectUnions) =>
% 99.57/13.42 ((
% 99.57/13.42 (inComplementUnionImpNotIn1) =>
% 99.57/13.42 ((
% 99.57/13.42 (inComplementUnionImpInComplement1) =>
% 99.57/13.42 ((
% 99.57/13.42 (binunionTE) =>
% 99.57/13.42 ((
% 99.57/13.42 (binunionTEcontra) =>
% 99.57/13.42 ((
% 99.57/13.42 (demorgan2a1) =>
% 99.57/13.42 ((
% 99.57/13.42 (complementUnionInPowersetComplement) =>
% 99.57/13.42 ((
% 99.57/13.42 (demorgan2a2) =>
% 99.57/13.42 ((
% 99.57/13.42 (demorgan1a) =>
% 99.57/13.42 ((
% 99.57/13.42 (demorgan1b) =>
% 99.57/13.42 ((
% 99.57/13.42 (demorgan1) =>
% 99.57/13.42 ((
% 99.57/13.42 (demorgan2a) =>
% 99.57/13.42 ((
% 99.57/13.42 (demorgan2b2) =>
% 99.57/13.42 ((
% 99.57/13.42 (demorgan2b) =>
% 99.57/13.42 ((
% 99.57/13.42 (demorgan2) =>
% 99.57/13.42 ((
% 99.57/13.42 (woz13rule0) =>
% 99.57/13.42 ((
% 99.57/13.42 (woz13rule1) =>
% 99.57/13.42 ((
% 99.57/13.42 (woz13rule2) =>
% 99.57/13.42 ((
% 99.57/13.42 (woz13rule3) =>
% 99.57/13.42 ((
% 99.57/13.42 (woz13rule4) =>
% 99.57/13.42 ((
% 99.57/13.42 (woz1_1) =>
% 99.57/13.42 ((
% 99.57/13.42 (woz1_2) =>
% 99.57/13.42 ((
% 99.57/13.42 (woz1_3) =>
% 99.57/13.42 ((
% 99.57/13.42 (woz1_4) =>
% 99.57/13.42 ((
% 99.57/13.42 (woz1_5) =>
% 99.57/13.42 ((
% 99.57/13.42 (breln1all2) =>
% 99.57/13.42 ((
% 99.57/13.42 (breln1SetBreln1) =>
% 99.57/13.42 ((
% 99.57/13.42 (choice2fnsingleton) =>
% 99.57/13.42 ((
% 99.57/13.42 (setOfPairsIsBReln1) =>
% 99.57/13.42 ((
% 99.57/13.42 (breln1all1) =>
% 99.57/13.42 ((
% 99.57/13.42 (subbreln1) =>
% 99.57/13.42 ((
% 99.57/13.42 (eqbreln1) =>
% 99.57/13.42 ((
% 99.57/13.42 (breln1invprop) =>
% 99.57/13.42 ((
% 99.57/13.42 (breln1invI) =>
% 99.57/13.42 ((
% 99.57/13.42 (breln1invE) =>
% 99.57/13.42 ((
% 99.57/13.42 (breln1compprop) =>
% 99.57/13.42 ((
% 99.57/13.42 (breln1compI) =>
% 99.57/13.42 ((
% 99.57/13.42 (breln1compE) =>
% 99.57/13.42 ((
% 99.57/13.42 (breln1compEex) =>
% 99.57/13.42 ((
% 99.57/13.42 (breln1unionprop) =>
% 99.57/13.42 ((
% 99.57/13.42 (breln1unionIL) =>
% 99.57/13.42 ((
% 99.57/13.42 (breln1unionIR) =>
% 99.57/13.42 ((
% 99.57/13.42 (breln1unionI) =>
% 99.57/13.42 ((
% 99.57/13.42 (breln1unionE) =>
% 99.57/13.42 ((
% 99.57/13.42 (breln1unionEcases) =>
% 99.57/13.42 ((
% 99.57/13.42 (breln1unionCommutes) =>
% 99.57/13.42 ((
% 99.57/13.42 (woz2Ex) =>
% 99.57/13.42 ((
% 99.57/13.42 (woz2W) =>
% 99.57/13.42 ((
% 99.57/13.42 (woz2A) =>
% 99.57/13.42 ((
% 99.57/13.42 (woz2B) =>
% 99.57/13.42 ((
% 99.57/13.42 (image1Ex) =>
% 99.57/13.42 ((
% 99.57/13.42 (image1Ex1) =>
% 99.57/13.42 ((
% 99.57/13.42 (image1Equiv) =>
% 99.57/13.42 ((
% 99.57/13.42 (image1E) =>
% 99.57/13.42 ((
% 99.57/13.42 (image1I) =>
% 99.57/13.42 ((
% 99.57/13.42 (injFuncInInjFuncSet) =>
% 99.57/13.42 ((
% 99.57/13.42 (injFuncSetFuncIn) =>
% 99.57/13.42 ((
% 99.57/13.42 (injFuncSetFuncInj) =>
% 99.57/13.42 ((
% 99.57/13.42 (!!) @ (
% 99.57/13.42 (('#B') @ (
% 99.57/13.42 !!) @
% 99.57/13.42 (
% 99.57/13.42 (
% 99.57/13.42 ('#B') @ (
% 99.57/13.42 (
% 99.57/13.42 ('#B') @ (
% 99.57/13.42 !!))) @
% 99.57/13.42 (
% 99.57/13.42 (
% 99.57/13.42 ('#S') @ (
% 99.57/13.42 (
% 99.57/13.42 ('#B') @ (
% 99.57/13.42 '#S') @
% 99.57/13.42 (
% 99.57/13.42 (
% 99.57/13.42 ('#B') @ (
% 99.57/13.42 (
% 99.57/13.42 ('#B') @ (
% 99.57/13.42 '#S'))) @
% 99.57/13.42 (
% 99.57/13.42 (
% 99.57/13.42 ('#B') @ (
% 99.57/13.42 (
% 99.57/13.42 ('#B') @ (
% 99.57/13.42 (
% 99.57/13.42 ('#B') @ (
% 99.57/13.42 =>))))) @
% 99.57/13.42 (
% 99.57/13.42 (
% 99.57/13.42 ('#B') @ (
% 99.57/13.42 (
% 99.57/13.42 ('#B') @ (
% 99.57/13.42 (
% 99.57/13.42 ('#C') @ in)))) @
% 99.57/13.42 surjFuncSet)))))))) @
% 99.57/13.42 (
% 99.57/13.42 (
% 99.57/13.42 ('#B') @ (
% 99.57/13.42 (
% 99.57/13.42 ('#B') @ (
% 99.57/13.42 (
% 99.57/13.42 ('#C') @ in)))) @
% 99.57/13.42 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.57/13.42 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1027])).
% 99.57/13.42 thf(zip_derived_cl1055, plain,
% 99.57/13.42 (~ (((powersetE1) =>
% 99.57/13.42 (((inPowerset) =>
% 99.57/13.42 (((powersetsubset) =>
% 99.57/13.42 (((sepInPowerset) =>
% 99.57/13.42 (((sepSubset) =>
% 99.57/13.42 (((binunionIL) =>
% 99.57/13.42 (((upairset2IR) =>
% 99.57/13.42 (((binunionIR) =>
% 99.57/13.42 (((binunionEcases) =>
% 99.57/13.42 (((binunionE) =>
% 99.57/13.42 (((binunionLsub) =>
% 99.57/13.42 (((binunionRsub) =>
% 99.57/13.42 (((binintersectI) =>
% 99.57/13.42 (((binintersectSubset5) =>
% 99.57/13.42 (((binintersectEL) =>
% 99.57/13.42 (((binintersectLsub) =>
% 99.57/13.42 (((binintersectSubset2) =>
% 99.57/13.42 (((binintersectSubset3) =>
% 99.57/13.42 (((binintersectER) =>
% 99.57/13.42 (((disjointsetsI1) =>
% 99.57/13.42 (((binintersectRsub) =>
% 99.57/13.42 (((binintersectSubset4) =>
% 99.57/13.42 (((binintersectSubset1) =>
% 99.57/13.42 (((bs114d) =>
% 99.57/13.42 (((setminusI) =>
% 99.57/13.42 (((setminusEL) =>
% 99.57/13.42 (((setminusER) =>
% 99.57/13.42 (((setminusSubset2) =>
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% 99.57/13.42 (((setminusELneg) =>
% 99.57/13.42 ((
% 99.57/13.42 (setminusILneg) =>
% 99.57/13.42 ((
% 99.57/13.42 (setminusIRneg) =>
% 99.57/13.42 ((
% 99.57/13.42 (setminusLsub) =>
% 99.57/13.42 ((
% 99.57/13.42 (setminusSubset1) =>
% 99.57/13.42 ((
% 99.57/13.42 (symdiffE) =>
% 99.57/13.42 ((
% 99.57/13.42 (symdiffI1) =>
% 99.57/13.42 ((
% 99.57/13.42 (symdiffI2) =>
% 99.57/13.42 ((
% 99.57/13.42 (symdiffIneg1) =>
% 99.57/13.42 ((
% 99.57/13.42 (symdiffIneg2) =>
% 99.57/13.42 ((
% 99.57/13.42 (secondinupair) =>
% 99.57/13.42 ((
% 99.57/13.42 (setukpairIL) =>
% 99.57/13.42 ((
% 99.57/13.42 (setukpairIR) =>
% 99.57/13.42 ((
% 99.57/13.42 (kpairiskpair) =>
% 99.57/13.42 ((
% 99.57/13.42 (kpairp) =>
% 99.57/13.42 ((
% 99.57/13.42 (singletonsubset) =>
% 99.57/13.42 ((
% 99.57/13.42 (singletoninpowerset) =>
% 99.57/13.42 ((
% 99.57/13.42 (singletoninpowunion) =>
% 99.57/13.42 ((
% 99.57/13.42 (upairset2E) =>
% 99.57/13.42 ((
% 99.57/13.42 (upairsubunion) =>
% 99.57/13.42 ((
% 99.57/13.42 (upairinpowunion) =>
% 99.57/13.42 ((
% 99.57/13.42 (ubforcartprodlem1) =>
% 99.57/13.42 ((
% 99.57/13.42 (ubforcartprodlem2) =>
% 99.57/13.42 ((
% 99.57/13.42 (ubforcartprodlem3) =>
% 99.57/13.42 ((
% 99.57/13.42 (cartprodpairin) =>
% 99.57/13.42 ((
% 99.57/13.42 (cartprodmempair1) =>
% 99.57/13.42 ((
% 99.57/13.42 (cartprodmempair) =>
% 99.57/13.42 ((
% 99.57/13.42 (setunionE2) =>
% 99.57/13.42 ((
% 99.57/13.42 (setunionsingleton1) =>
% 99.57/13.42 ((
% 99.57/13.42 (setunionsingleton2) =>
% 99.57/13.42 ((
% 99.57/13.42 (setunionsingleton) =>
% 99.57/13.42 ((
% 99.57/13.42 (singletonprop) =>
% 99.57/13.42 ((
% 99.57/13.42 (ex1E1) =>
% 99.57/13.42 ((
% 99.57/13.42 (ex1I) =>
% 99.57/13.42 ((
% 99.57/13.42 (ex1I2) =>
% 99.57/13.42 ((
% 99.57/13.42 (singletonsuniq) =>
% 99.57/13.42 ((
% 99.57/13.42 (setukpairinjL1) =>
% 99.57/13.42 ((
% 99.57/13.42 (kfstsingleton) =>
% 99.57/13.42 ((
% 99.57/13.42 (theprop) =>
% 99.57/13.42 ((
% 99.57/13.42 (kfstpairEq) =>
% 99.57/13.42 ((
% 99.57/13.42 (cartprodfstin) =>
% 99.57/13.42 ((
% 99.57/13.42 (setukpairinjL2) =>
% 99.57/13.42 ((
% 99.57/13.42 (setukpairinjL) =>
% 99.57/13.42 ((
% 99.57/13.42 (setukpairinjR11) =>
% 99.57/13.42 ((
% 99.57/13.42 (setukpairinjR12) =>
% 99.57/13.42 ((
% 99.57/13.42 (setukpairinjR1) =>
% 99.57/13.42 ((
% 99.57/13.42 (upairequniteq) =>
% 99.57/13.42 ((
% 99.57/13.42 (setukpairinjR2) =>
% 99.57/13.42 ((
% 99.57/13.42 (setukpairinjR) =>
% 99.57/13.42 ((
% 99.57/13.42 (ksndsingleton) =>
% 99.57/13.42 ((
% 99.57/13.42 (ksndpairEq) =>
% 99.57/13.42 ((
% 99.57/13.42 (kpairsurjEq) =>
% 99.57/13.42 ((
% 99.57/13.42 (cartprodsndin) =>
% 99.57/13.42 ((
% 99.57/13.42 (cartprodpairmemEL) =>
% 99.57/13.42 ((
% 99.57/13.42 (cartprodpairmemER) =>
% 99.57/13.42 ((
% 99.57/13.42 (cartprodmempaircEq) =>
% 99.57/13.42 ((
% 99.57/13.42 (cartprodfstpairEq) =>
% 99.57/13.42 ((
% 99.57/13.42 (cartprodsndpairEq) =>
% 99.57/13.42 ((
% 99.57/13.42 (cartprodpairsurjEq) =>
% 99.57/13.42 ((
% 99.57/13.42 (dpsetconstrI) =>
% 99.57/13.42 ((
% 99.57/13.42 (dpsetconstrSub) =>
% 99.57/13.42 ((
% 99.57/13.42 (setOfPairsIsBReln) =>
% 99.57/13.42 ((
% 99.57/13.42 (dpsetconstrERa) =>
% 99.57/13.42 ((
% 99.57/13.42 (dpsetconstrEL1) =>
% 99.57/13.42 ((
% 99.57/13.42 (dpsetconstrEL2) =>
% 99.57/13.42 ((
% 99.57/13.42 (dpsetconstrER) =>
% 99.57/13.42 ((
% 99.57/13.42 (funcImageSingleton) =>
% 99.57/13.42 ((
% 99.57/13.42 (apProp) =>
% 99.57/13.42 ((
% 99.57/13.42 (app) =>
% 99.57/13.42 ((
% 99.57/13.42 (infuncsetfunc) =>
% 99.57/13.42 ((
% 99.57/13.42 (ap2p) =>
% 99.57/13.42 ((
% 99.57/13.42 (funcinfuncset) =>
% 99.57/13.42 ((
% 99.57/13.42 (lamProp) =>
% 99.57/13.42 ((
% 99.57/13.42 (lamp) =>
% 99.57/13.42 ((
% 99.57/13.42 (lam2p) =>
% 99.57/13.42 ((
% 99.57/13.42 (brelnall1) =>
% 99.57/13.42 ((
% 99.57/13.42 (brelnall2) =>
% 99.57/13.42 ((
% 99.57/13.42 (ex1E2) =>
% 99.57/13.42 ((
% 99.57/13.42 (funcGraphProp1) =>
% 99.57/13.42 ((
% 99.57/13.42 (funcGraphProp3) =>
% 99.57/13.42 ((
% 99.57/13.42 (funcGraphProp2) =>
% 99.57/13.42 ((
% 99.57/13.42 (funcextLem) =>
% 99.57/13.42 ((
% 99.57/13.42 (funcGraphProp4) =>
% 99.57/13.42 ((
% 99.57/13.42 (subbreln) =>
% 99.57/13.42 ((
% 99.57/13.42 (eqbreln) =>
% 99.57/13.42 ((
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% 99.57/13.43 ((
% 99.57/13.43 (demorgan2a) =>
% 99.57/13.43 ((
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% 99.57/13.43 ((
% 99.57/13.43 (demorgan2b) =>
% 99.57/13.43 ((
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% 99.57/13.43 ((
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% 99.57/13.43 ((
% 99.57/13.43 (woz13rule2) =>
% 99.57/13.43 ((
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% 99.57/13.43 ((
% 99.57/13.43 (breln1compE) =>
% 99.57/13.43 ((
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% 99.57/13.43 (breln1unionI) =>
% 99.57/13.43 ((
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% 99.57/13.43 ((
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% 99.57/13.43 ((
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% 99.57/13.43 ((
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% 99.57/13.43 ((
% 99.57/13.43 (image1I) =>
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% 99.57/13.43 (
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% 99.57/13.43 (
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% 99.57/13.43 ((
% 99.57/13.43 (singletoninpowunion) =>
% 99.57/13.43 ((
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% 99.57/13.43 ((
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% 99.57/13.43 ((
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% 99.57/13.43 ((
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% 99.57/13.43 ((
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% 99.57/13.43 ((
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% 99.57/13.43 ((
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% 99.57/13.43 ((
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% 99.57/13.43 ((
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% 99.57/13.43 ((
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% 99.57/13.43 ((
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% 99.57/13.43 ((
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% 99.57/13.43 ((
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% 99.57/13.43 ((
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% 99.57/13.43 ((
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% 99.57/13.43 ((
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% 99.57/13.43 ((
% 99.57/13.43 (setukpairinjR12) =>
% 99.57/13.43 ((
% 99.57/13.43 (setukpairinjR1) =>
% 99.57/13.43 ((
% 99.57/13.43 (upairequniteq) =>
% 99.57/13.43 ((
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% 99.57/13.43 ((
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% 99.57/13.43 ((
% 99.57/13.43 (kpairsurjEq) =>
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% 99.57/13.43 ((
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% 99.57/13.43 ((
% 99.57/13.43 (cartprodpairmemER) =>
% 99.57/13.43 ((
% 99.57/13.43 (cartprodmempaircEq) =>
% 99.57/13.43 ((
% 99.57/13.43 (cartprodfstpairEq) =>
% 99.57/13.43 ((
% 99.57/13.43 (cartprodsndpairEq) =>
% 99.57/13.43 ((
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% 99.57/13.43 ((
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% 99.57/13.43 ((
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% 99.57/13.43 ((
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% 99.57/13.43 ((
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% 99.57/13.43 ((
% 99.57/13.43 (lam2p) =>
% 99.57/13.43 ((
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% 99.57/13.43 ((
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% 99.57/13.43 ((
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% 99.57/13.43 ((
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% 99.57/13.43 ((
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% 99.57/13.43 ((
% 99.57/13.43 (funcext2) =>
% 99.57/13.43 ((
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% 99.57/13.43 ((
% 99.57/13.43 (ap2apEq2) =>
% 99.57/13.43 ((
% 99.57/13.43 (beta1) =>
% 99.57/13.43 ((
% 99.57/13.43 (eta1) =>
% 99.57/13.43 ((
% 99.57/13.43 (lam2lamEq) =>
% 99.57/13.43 ((
% 99.57/13.43 (beta2) =>
% 99.57/13.43 ((
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% 99.57/13.43 ((
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% 99.57/13.43 ((
% 99.57/13.43 (iffalseProp2) =>
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% 99.57/13.43 ((
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% 99.57/13.43 ((
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% 99.57/13.43 ((
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% 99.57/13.43 ((
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% 99.57/13.43 ((
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% 99.57/13.43 ((
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% 99.57/13.43 ((
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% 99.57/13.43 ((
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% 99.57/13.43 ((
% 99.57/13.43 (complementInPowersetComplementIntersect) =>
% 99.57/13.43 ((
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% 99.57/13.43 ((
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% 99.57/13.43 ((
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% 99.57/13.43 ((
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% 99.57/13.43 ((
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% 99.57/13.43 ((
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% 99.57/13.43 ((
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% 99.57/13.43 ((
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% 99.57/13.43 ((
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% 99.57/13.43 ((
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% 99.57/13.43 ((
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% 99.57/13.43 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1082])).
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% 99.57/13.43 (setunionsingleton) =>
% 99.57/13.43 ((
% 99.57/13.43 (singletonprop) =>
% 99.57/13.43 ((
% 99.57/13.43 (ex1E1) =>
% 99.57/13.43 ((
% 99.57/13.43 (ex1I) =>
% 99.57/13.43 ((
% 99.57/13.43 (ex1I2) =>
% 99.57/13.43 ((
% 99.57/13.43 (singletonsuniq) =>
% 99.57/13.43 ((
% 99.57/13.43 (setukpairinjL1) =>
% 99.57/13.43 ((
% 99.57/13.43 (kfstsingleton) =>
% 99.57/13.43 ((
% 99.57/13.43 (theprop) =>
% 99.57/13.43 ((
% 99.57/13.43 (kfstpairEq) =>
% 99.57/13.43 ((
% 99.57/13.43 (cartprodfstin) =>
% 99.57/13.43 ((
% 99.57/13.43 (setukpairinjL2) =>
% 99.57/13.43 ((
% 99.57/13.43 (setukpairinjL) =>
% 99.57/13.43 ((
% 99.57/13.43 (setukpairinjR11) =>
% 99.57/13.43 ((
% 99.57/13.43 (setukpairinjR12) =>
% 99.57/13.43 ((
% 99.57/13.43 (setukpairinjR1) =>
% 99.57/13.43 ((
% 99.57/13.43 (upairequniteq) =>
% 99.57/13.43 ((
% 99.57/13.43 (setukpairinjR2) =>
% 99.57/13.43 ((
% 99.57/13.43 (setukpairinjR) =>
% 99.57/13.43 ((
% 99.57/13.43 (ksndsingleton) =>
% 99.57/13.43 ((
% 99.57/13.43 (ksndpairEq) =>
% 99.57/13.43 ((
% 99.57/13.43 (kpairsurjEq) =>
% 99.57/13.43 ((
% 99.57/13.43 (cartprodsndin) =>
% 99.57/13.43 ((
% 99.57/13.43 (cartprodpairmemEL) =>
% 99.57/13.43 ((
% 99.57/13.43 (cartprodpairmemER) =>
% 99.57/13.43 ((
% 99.57/13.43 (cartprodmempaircEq) =>
% 99.57/13.43 ((
% 99.57/13.43 (cartprodfstpairEq) =>
% 99.57/13.43 ((
% 99.57/13.43 (cartprodsndpairEq) =>
% 99.57/13.43 ((
% 99.57/13.43 (cartprodpairsurjEq) =>
% 99.57/13.43 ((
% 99.57/13.43 (dpsetconstrI) =>
% 99.57/13.43 ((
% 99.57/13.43 (dpsetconstrSub) =>
% 99.57/13.43 ((
% 99.57/13.43 (setOfPairsIsBReln) =>
% 99.57/13.43 ((
% 99.57/13.43 (dpsetconstrERa) =>
% 99.57/13.43 ((
% 99.57/13.43 (dpsetconstrEL1) =>
% 99.57/13.43 ((
% 99.57/13.43 (dpsetconstrEL2) =>
% 99.57/13.43 ((
% 99.57/13.43 (dpsetconstrER) =>
% 99.57/13.43 ((
% 99.57/13.43 (funcImageSingleton) =>
% 99.57/13.43 ((
% 99.57/13.43 (apProp) =>
% 99.57/13.43 ((
% 99.57/13.43 (app) =>
% 99.57/13.43 ((
% 99.57/13.43 (infuncsetfunc) =>
% 99.57/13.43 ((
% 99.57/13.43 (ap2p) =>
% 99.57/13.43 ((
% 99.57/13.43 (funcinfuncset) =>
% 99.57/13.43 ((
% 99.57/13.43 (lamProp) =>
% 99.57/13.43 ((
% 99.57/13.43 (lamp) =>
% 99.57/13.43 ((
% 99.57/13.43 (lam2p) =>
% 99.57/13.43 ((
% 99.57/13.43 (brelnall1) =>
% 99.57/13.43 ((
% 99.57/13.43 (brelnall2) =>
% 99.57/13.43 ((
% 99.57/13.43 (ex1E2) =>
% 99.57/13.43 ((
% 99.57/13.43 (funcGraphProp1) =>
% 99.57/13.43 ((
% 99.57/13.43 (funcGraphProp3) =>
% 99.57/13.43 ((
% 99.57/13.43 (funcGraphProp2) =>
% 99.57/13.43 ((
% 99.57/13.43 (funcextLem) =>
% 99.57/13.43 ((
% 99.57/13.43 (funcGraphProp4) =>
% 99.57/13.43 ((
% 99.57/13.43 (subbreln) =>
% 99.57/13.43 ((
% 99.57/13.43 (eqbreln) =>
% 99.57/13.43 ((
% 99.57/13.43 (funcext) =>
% 99.57/13.43 ((
% 99.57/13.43 (funcext2) =>
% 99.57/13.43 ((
% 99.57/13.43 (ap2apEq1) =>
% 99.57/13.43 ((
% 99.57/13.43 (ap2apEq2) =>
% 99.57/13.43 ((
% 99.57/13.43 (beta1) =>
% 99.57/13.43 ((
% 99.57/13.43 (eta1) =>
% 99.57/13.43 ((
% 99.57/13.43 (lam2lamEq) =>
% 99.57/13.43 ((
% 99.57/13.43 (beta2) =>
% 99.57/13.43 ((
% 99.57/13.43 (eta2) =>
% 99.57/13.43 ((
% 99.57/13.43 (iffalseProp1) =>
% 99.57/13.43 ((
% 99.57/13.43 (iffalseProp2) =>
% 99.57/13.43 ((
% 99.57/13.43 (iftrueProp1) =>
% 99.57/13.43 ((
% 99.57/13.43 (iftrueProp2) =>
% 99.57/13.43 ((
% 99.57/13.43 (ifSingleton) =>
% 99.57/13.43 ((
% 99.57/13.43 (ifp) =>
% 99.57/13.43 ((
% 99.57/13.43 (theeq) =>
% 99.57/13.43 ((
% 99.57/13.43 (iftrue) =>
% 99.57/13.43 ((
% 99.57/13.43 (iffalse) =>
% 99.57/13.43 ((
% 99.57/13.43 (iftrueorfalse) =>
% 99.57/13.43 ((
% 99.57/13.43 (binintersectT_lem) =>
% 99.57/13.43 ((
% 99.57/13.43 (binunionT_lem) =>
% 99.57/13.43 ((
% 99.57/13.43 (powersetT_lem) =>
% 99.57/13.43 ((
% 99.57/13.43 (setminusT_lem) =>
% 99.57/13.43 ((
% 99.57/13.43 (complementT_lem) =>
% 99.57/13.43 ((
% 99.57/13.43 (setextT) =>
% 99.57/13.43 ((
% 99.57/13.43 (subsetTI) =>
% 99.57/13.43 ((
% 99.57/13.43 (powersetTI1) =>
% 99.57/13.43 ((
% 99.57/13.43 (powersetTE1) =>
% 99.57/13.43 ((
% 99.57/13.43 (complementTI1) =>
% 99.57/13.43 ((
% 99.57/13.43 (complementTE1) =>
% 99.57/13.43 ((
% 99.57/13.43 (binintersectTELcontra) =>
% 99.57/13.43 ((
% 99.57/13.43 (binintersectTERcontra) =>
% 99.57/13.43 ((
% 99.57/13.43 (contrasubsetT) =>
% 99.57/13.43 ((
% 99.57/13.43 (contrasubsetT1) =>
% 99.57/13.43 ((
% 99.57/13.43 (contrasubsetT2) =>
% 99.57/13.43 ((
% 99.57/13.43 (contrasubsetT3) =>
% 99.57/13.43 ((
% 99.57/13.43 (doubleComplementI1) =>
% 99.57/13.43 ((
% 99.57/13.43 (doubleComplementE1) =>
% 99.57/13.43 ((
% 99.57/13.43 (doubleComplementSub1) =>
% 99.57/13.43 ((
% 99.57/13.43 (doubleComplementSub2) =>
% 99.57/13.43 ((
% 99.57/13.43 (doubleComplementEq) =>
% 99.57/13.43 ((
% 99.57/13.43 (complementTnotintersectT) =>
% 99.57/13.43 ((
% 99.57/13.43 (complementImpComplementIntersect) =>
% 99.57/13.43 ((
% 99.57/13.43 (complementSubsetComplementIntersect) =>
% 99.57/13.43 ((
% 99.57/13.43 (complementInPowersetComplementIntersect) =>
% 99.57/13.43 ((
% 99.57/13.43 (contraSubsetComplement) =>
% 99.57/13.43 ((
% 99.57/13.43 (complementTcontraSubset) =>
% 99.57/13.43 ((
% 99.57/13.43 (binunionTILcontra) =>
% 99.57/13.43 ((
% 99.57/13.43 (binunionTIRcontra) =>
% 99.57/13.43 ((
% 99.57/13.43 (inIntersectImpInUnion) =>
% 99.57/13.43 ((
% 99.57/13.43 (inIntersectImpInUnion2) =>
% 99.57/13.43 ((
% 99.57/13.43 (inIntersectImpInIntersectUnions) =>
% 99.57/13.43 ((
% 99.57/13.43 (intersectInPowersetIntersectUnions) =>
% 99.57/13.43 ((
% 99.57/13.43 (inComplementUnionImpNotIn1) =>
% 99.57/13.43 ((
% 99.57/13.43 (inComplementUnionImpInComplement1) =>
% 99.57/13.43 ((
% 99.57/13.43 (binunionTE) =>
% 99.57/13.43 ((
% 99.57/13.43 (binunionTEcontra) =>
% 99.57/13.43 ((
% 99.57/13.43 (demorgan2a1) =>
% 99.57/13.43 ((
% 99.57/13.43 (complementUnionInPowersetComplement) =>
% 99.57/13.43 ((
% 99.57/13.43 (demorgan2a2) =>
% 99.57/13.43 ((
% 99.57/13.43 (demorgan1a) =>
% 99.57/13.43 ((
% 99.57/13.43 (demorgan1b) =>
% 99.57/13.43 ((
% 99.57/13.43 (demorgan1) =>
% 99.57/13.43 ((
% 99.57/13.43 (demorgan2a) =>
% 99.57/13.43 ((
% 99.57/13.43 (demorgan2b2) =>
% 99.57/13.43 ((
% 99.57/13.43 (demorgan2b) =>
% 99.57/13.43 ((
% 99.57/13.43 (demorgan2) =>
% 99.57/13.43 ((
% 99.57/13.43 (woz13rule0) =>
% 99.57/13.43 ((
% 99.57/13.43 (woz13rule1) =>
% 99.57/13.43 ((
% 99.57/13.43 (woz13rule2) =>
% 99.57/13.43 ((
% 99.57/13.43 (woz13rule3) =>
% 99.57/13.43 ((
% 99.57/13.43 (woz13rule4) =>
% 99.57/13.43 ((
% 99.57/13.43 (woz1_1) =>
% 99.57/13.43 ((
% 99.57/13.43 (woz1_2) =>
% 99.57/13.43 ((
% 99.57/13.43 (woz1_3) =>
% 99.57/13.43 ((
% 99.57/13.43 (woz1_4) =>
% 99.57/13.43 ((
% 99.57/13.43 (woz1_5) =>
% 99.57/13.43 ((
% 99.57/13.43 (breln1all2) =>
% 99.57/13.43 ((
% 99.57/13.43 (breln1SetBreln1) =>
% 99.57/13.43 ((
% 99.57/13.43 (choice2fnsingleton) =>
% 99.57/13.43 ((
% 99.57/13.43 (setOfPairsIsBReln1) =>
% 99.57/13.43 ((
% 99.57/13.43 (breln1all1) =>
% 99.57/13.43 ((
% 99.57/13.43 (subbreln1) =>
% 99.57/13.43 ((
% 99.57/13.43 (eqbreln1) =>
% 99.57/13.43 ((
% 99.57/13.43 (breln1invprop) =>
% 99.57/13.43 ((
% 99.57/13.43 (breln1invI) =>
% 99.57/13.43 ((
% 99.57/13.43 (breln1invE) =>
% 99.57/13.43 ((
% 99.57/13.43 (breln1compprop) =>
% 99.57/13.43 ((
% 99.57/13.43 (breln1compI) =>
% 99.57/13.43 ((
% 99.57/13.43 (breln1compE) =>
% 99.57/13.43 ((
% 99.57/13.43 (breln1compEex) =>
% 99.57/13.43 ((
% 99.57/13.43 (breln1unionprop) =>
% 99.57/13.43 ((
% 99.57/13.43 (breln1unionIL) =>
% 99.57/13.43 ((
% 99.57/13.43 (breln1unionIR) =>
% 99.57/13.43 ((
% 99.57/13.43 (breln1unionI) =>
% 99.57/13.43 ((
% 99.57/13.43 (breln1unionE) =>
% 99.57/13.43 ((
% 99.57/13.43 (breln1unionEcases) =>
% 99.57/13.43 ((
% 99.57/13.43 (breln1unionCommutes) =>
% 99.57/13.43 ((
% 99.57/13.43 (woz2Ex) =>
% 99.57/13.43 ((
% 99.57/13.43 (woz2W) =>
% 99.57/13.43 ((
% 99.57/13.43 (woz2A) =>
% 99.57/13.43 ((
% 99.57/13.43 (woz2B) =>
% 99.57/13.43 ((
% 99.57/13.43 (image1Ex) =>
% 99.57/13.43 ((
% 99.57/13.43 (image1Ex1) =>
% 99.57/13.43 ((
% 99.57/13.43 (image1Equiv) =>
% 99.57/13.43 ((
% 99.57/13.43 (image1E) =>
% 99.57/13.43 ((
% 99.57/13.43 (image1I) =>
% 99.57/13.43 ((
% 99.57/13.43 (injFuncInInjFuncSet) =>
% 99.57/13.43 ((
% 99.57/13.43 (injFuncSetFuncIn) =>
% 99.57/13.43 ((
% 99.57/13.43 (injFuncSetFuncInj) =>
% 99.57/13.43 ((
% 99.57/13.43 (!!) @ (
% 99.57/13.43 (('#B') @ (
% 99.57/13.43 !!) @
% 99.57/13.43 (
% 99.57/13.43 (
% 99.57/13.43 ('#B') @ (
% 99.57/13.43 (
% 99.57/13.43 ('#B') @ (
% 99.57/13.43 !!))) @
% 99.57/13.43 (
% 99.57/13.43 (
% 99.57/13.43 ('#S') @ (
% 99.57/13.43 (
% 99.57/13.43 ('#B') @ (
% 99.57/13.43 '#S') @
% 99.57/13.43 (
% 99.57/13.43 (
% 99.57/13.43 ('#B') @ (
% 99.57/13.43 (
% 99.57/13.43 ('#B') @ (
% 99.57/13.43 '#S'))) @
% 99.57/13.43 (
% 99.57/13.43 (
% 99.57/13.43 ('#B') @ (
% 99.57/13.43 (
% 99.57/13.43 ('#B') @ (
% 99.57/13.43 (
% 99.57/13.43 ('#B') @ (
% 99.57/13.43 =>))))) @
% 99.57/13.43 (
% 99.57/13.43 (
% 99.57/13.43 ('#B') @ (
% 99.57/13.43 (
% 99.57/13.43 ('#B') @ (
% 99.57/13.43 (
% 99.57/13.43 ('#C') @ in)))) @
% 99.57/13.43 surjFuncSet)))))))) @
% 99.57/13.43 (
% 99.57/13.43 (
% 99.57/13.43 ('#B') @ (
% 99.57/13.43 (
% 99.57/13.43 ('#B') @ (
% 99.57/13.43 (
% 99.57/13.43 ('#C') @ in)))) @
% 99.57/13.43 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.57/13.43 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1090])).
% 99.57/13.43 thf(zip_derived_cl1102, plain,
% 99.57/13.43 (~ (((upairset2IR) =>
% 99.57/13.43 (((binunionIR) =>
% 99.57/13.43 (((binunionEcases) =>
% 99.57/13.43 (((binunionE) =>
% 99.57/13.43 (((binunionLsub) =>
% 99.57/13.43 (((binunionRsub) =>
% 99.57/13.43 (((binintersectI) =>
% 99.57/13.43 (((binintersectSubset5) =>
% 99.57/13.43 (((binintersectEL) =>
% 99.57/13.43 (((binintersectLsub) =>
% 99.57/13.43 (((binintersectSubset2) =>
% 99.57/13.43 (((binintersectSubset3) =>
% 99.57/13.43 (((binintersectER) =>
% 99.57/13.43 (((disjointsetsI1) =>
% 99.57/13.43 (((binintersectRsub) =>
% 99.57/13.43 (((binintersectSubset4) =>
% 99.57/13.43 (((binintersectSubset1) =>
% 99.57/13.43 (((bs114d) =>
% 99.57/13.43 (((setminusI) =>
% 99.57/13.43 (((setminusEL) =>
% 99.57/13.43 (((setminusER) =>
% 99.57/13.43 (((setminusSubset2) =>
% 99.57/13.43 (((setminusERneg) =>
% 99.57/13.43 (((setminusELneg) =>
% 99.57/13.43 (((setminusILneg) =>
% 99.57/13.43 (((setminusIRneg) =>
% 99.57/13.43 (((setminusLsub) =>
% 99.57/13.43 (((setminusSubset1) =>
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% 99.57/13.43 (((symdiffI1) =>
% 99.57/13.43 ((
% 99.57/13.43 (symdiffI2) =>
% 99.57/13.43 ((
% 99.57/13.43 (symdiffIneg1) =>
% 99.57/13.43 ((
% 99.57/13.43 (symdiffIneg2) =>
% 99.57/13.43 ((
% 99.57/13.43 (secondinupair) =>
% 99.57/13.43 ((
% 99.57/13.43 (setukpairIL) =>
% 99.57/13.43 ((
% 99.57/13.43 (setukpairIR) =>
% 99.57/13.43 ((
% 99.57/13.43 (kpairiskpair) =>
% 99.57/13.43 ((
% 99.57/13.43 (kpairp) =>
% 99.57/13.43 ((
% 99.57/13.43 (singletonsubset) =>
% 99.57/13.43 ((
% 99.57/13.43 (singletoninpowerset) =>
% 99.57/13.43 ((
% 99.57/13.43 (singletoninpowunion) =>
% 99.57/13.43 ((
% 99.57/13.43 (upairset2E) =>
% 99.57/13.43 ((
% 99.57/13.43 (upairsubunion) =>
% 99.57/13.43 ((
% 99.57/13.43 (upairinpowunion) =>
% 99.57/13.43 ((
% 99.57/13.43 (ubforcartprodlem1) =>
% 99.57/13.43 ((
% 99.57/13.43 (ubforcartprodlem2) =>
% 99.57/13.43 ((
% 99.57/13.43 (ubforcartprodlem3) =>
% 99.57/13.43 ((
% 99.57/13.43 (cartprodpairin) =>
% 99.57/13.43 ((
% 99.57/13.43 (cartprodmempair1) =>
% 99.57/13.43 ((
% 99.57/13.43 (cartprodmempair) =>
% 99.57/13.43 ((
% 99.57/13.43 (setunionE2) =>
% 99.57/13.43 ((
% 99.57/13.43 (setunionsingleton1) =>
% 99.57/13.43 ((
% 99.57/13.43 (setunionsingleton2) =>
% 99.57/13.43 ((
% 99.57/13.43 (setunionsingleton) =>
% 99.57/13.43 ((
% 99.57/13.43 (singletonprop) =>
% 99.57/13.43 ((
% 99.57/13.43 (ex1E1) =>
% 99.57/13.43 ((
% 99.57/13.43 (ex1I) =>
% 99.57/13.43 ((
% 99.57/13.43 (ex1I2) =>
% 99.57/13.43 ((
% 99.57/13.43 (singletonsuniq) =>
% 99.57/13.43 ((
% 99.57/13.43 (setukpairinjL1) =>
% 99.57/13.43 ((
% 99.57/13.43 (kfstsingleton) =>
% 99.57/13.43 ((
% 99.57/13.43 (theprop) =>
% 99.57/13.43 ((
% 99.57/13.43 (kfstpairEq) =>
% 99.57/13.43 ((
% 99.57/13.43 (cartprodfstin) =>
% 99.57/13.43 ((
% 99.57/13.43 (setukpairinjL2) =>
% 99.57/13.43 ((
% 99.57/13.43 (setukpairinjL) =>
% 99.57/13.43 ((
% 99.57/13.43 (setukpairinjR11) =>
% 99.57/13.43 ((
% 99.57/13.43 (setukpairinjR12) =>
% 99.57/13.43 ((
% 99.57/13.43 (setukpairinjR1) =>
% 99.57/13.43 ((
% 99.57/13.43 (upairequniteq) =>
% 99.57/13.43 ((
% 99.57/13.43 (setukpairinjR2) =>
% 99.57/13.43 ((
% 99.57/13.43 (setukpairinjR) =>
% 99.57/13.43 ((
% 99.57/13.43 (ksndsingleton) =>
% 99.57/13.43 ((
% 99.57/13.43 (ksndpairEq) =>
% 99.57/13.43 ((
% 99.57/13.43 (kpairsurjEq) =>
% 99.57/13.43 ((
% 99.57/13.43 (cartprodsndin) =>
% 99.57/13.43 ((
% 99.57/13.43 (cartprodpairmemEL) =>
% 99.57/13.43 ((
% 99.57/13.43 (cartprodpairmemER) =>
% 99.57/13.43 ((
% 99.57/13.43 (cartprodmempaircEq) =>
% 99.57/13.43 ((
% 99.57/13.43 (cartprodfstpairEq) =>
% 99.57/13.43 ((
% 99.57/13.43 (cartprodsndpairEq) =>
% 99.57/13.43 ((
% 99.57/13.43 (cartprodpairsurjEq) =>
% 99.57/13.43 ((
% 99.57/13.43 (dpsetconstrI) =>
% 99.57/13.43 ((
% 99.57/13.43 (dpsetconstrSub) =>
% 99.57/13.43 ((
% 99.57/13.43 (setOfPairsIsBReln) =>
% 99.57/13.43 ((
% 99.57/13.43 (dpsetconstrERa) =>
% 99.57/13.43 ((
% 99.57/13.43 (dpsetconstrEL1) =>
% 99.57/13.43 ((
% 99.57/13.43 (dpsetconstrEL2) =>
% 99.57/13.43 ((
% 99.57/13.43 (dpsetconstrER) =>
% 99.57/13.43 ((
% 99.57/13.43 (funcImageSingleton) =>
% 99.57/13.43 ((
% 99.57/13.43 (apProp) =>
% 99.57/13.43 ((
% 99.57/13.43 (app) =>
% 99.57/13.43 ((
% 99.57/13.43 (infuncsetfunc) =>
% 99.57/13.43 ((
% 99.57/13.43 (ap2p) =>
% 99.57/13.43 ((
% 99.57/13.43 (funcinfuncset) =>
% 99.57/13.43 ((
% 99.57/13.43 (lamProp) =>
% 99.57/13.43 ((
% 99.57/13.43 (lamp) =>
% 99.57/13.43 ((
% 99.57/13.43 (lam2p) =>
% 99.57/13.43 ((
% 99.57/13.43 (brelnall1) =>
% 99.57/13.43 ((
% 99.57/13.43 (brelnall2) =>
% 99.57/13.43 ((
% 99.57/13.43 (ex1E2) =>
% 99.57/13.43 ((
% 99.57/13.43 (funcGraphProp1) =>
% 99.57/13.43 ((
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% 99.57/13.43 ((
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% 99.57/13.43 ((
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% 99.57/13.43 (woz13rule2) =>
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% 99.57/13.43 ((
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% 99.57/13.43 (contraSubsetComplement) =>
% 99.57/13.43 ((
% 99.57/13.43 (complementTcontraSubset) =>
% 99.57/13.43 ((
% 99.57/13.43 (binunionTILcontra) =>
% 99.57/13.43 ((
% 99.57/13.43 (binunionTIRcontra) =>
% 99.57/13.43 ((
% 99.57/13.43 (inIntersectImpInUnion) =>
% 99.57/13.43 ((
% 99.57/13.43 (inIntersectImpInUnion2) =>
% 99.57/13.43 ((
% 99.57/13.43 (inIntersectImpInIntersectUnions) =>
% 99.57/13.43 ((
% 99.57/13.43 (intersectInPowersetIntersectUnions) =>
% 99.57/13.43 ((
% 99.57/13.43 (inComplementUnionImpNotIn1) =>
% 99.57/13.43 ((
% 99.57/13.43 (inComplementUnionImpInComplement1) =>
% 99.57/13.43 ((
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% 99.57/13.43 ((
% 99.57/13.43 (binunionTEcontra) =>
% 99.57/13.43 ((
% 99.57/13.43 (demorgan2a1) =>
% 99.57/13.43 ((
% 99.57/13.43 (complementUnionInPowersetComplement) =>
% 99.57/13.43 ((
% 99.57/13.43 (demorgan2a2) =>
% 99.57/13.43 ((
% 99.57/13.43 (demorgan1a) =>
% 99.57/13.43 ((
% 99.57/13.43 (demorgan1b) =>
% 99.57/13.43 ((
% 99.57/13.43 (demorgan1) =>
% 99.57/13.43 ((
% 99.57/13.43 (demorgan2a) =>
% 99.57/13.43 ((
% 99.57/13.43 (demorgan2b2) =>
% 99.57/13.43 ((
% 99.57/13.43 (demorgan2b) =>
% 99.57/13.43 ((
% 99.57/13.43 (demorgan2) =>
% 99.57/13.43 ((
% 99.57/13.43 (woz13rule0) =>
% 99.57/13.43 ((
% 99.57/13.43 (woz13rule1) =>
% 99.57/13.43 ((
% 99.57/13.43 (woz13rule2) =>
% 99.57/13.43 ((
% 99.57/13.43 (woz13rule3) =>
% 99.57/13.43 ((
% 99.57/13.43 (woz13rule4) =>
% 99.57/13.43 ((
% 99.57/13.43 (woz1_1) =>
% 99.57/13.43 ((
% 99.57/13.43 (woz1_2) =>
% 99.57/13.43 ((
% 99.57/13.43 (woz1_3) =>
% 99.57/13.43 ((
% 99.57/13.43 (woz1_4) =>
% 99.57/13.43 ((
% 99.57/13.43 (woz1_5) =>
% 99.57/13.43 ((
% 99.57/13.43 (breln1all2) =>
% 99.57/13.43 ((
% 99.57/13.43 (breln1SetBreln1) =>
% 99.57/13.43 ((
% 99.57/13.43 (choice2fnsingleton) =>
% 99.57/13.43 ((
% 99.57/13.43 (setOfPairsIsBReln1) =>
% 99.57/13.43 ((
% 99.57/13.43 (breln1all1) =>
% 99.57/13.43 ((
% 99.57/13.43 (subbreln1) =>
% 99.57/13.43 ((
% 99.57/13.43 (eqbreln1) =>
% 99.57/13.43 ((
% 99.57/13.43 (breln1invprop) =>
% 99.57/13.43 ((
% 99.57/13.43 (breln1invI) =>
% 99.57/13.43 ((
% 99.57/13.43 (breln1invE) =>
% 99.57/13.43 ((
% 99.57/13.43 (breln1compprop) =>
% 99.57/13.43 ((
% 99.57/13.43 (breln1compI) =>
% 99.57/13.43 ((
% 99.57/13.43 (breln1compE) =>
% 99.57/13.43 ((
% 99.57/13.43 (breln1compEex) =>
% 99.57/13.43 ((
% 99.57/13.43 (breln1unionprop) =>
% 99.57/13.43 ((
% 99.57/13.43 (breln1unionIL) =>
% 99.57/13.43 ((
% 99.57/13.43 (breln1unionIR) =>
% 99.57/13.43 ((
% 99.57/13.43 (breln1unionI) =>
% 99.57/13.43 ((
% 99.57/13.43 (breln1unionE) =>
% 99.57/13.43 ((
% 99.57/13.43 (breln1unionEcases) =>
% 99.57/13.43 ((
% 99.57/13.43 (breln1unionCommutes) =>
% 99.57/13.43 ((
% 99.57/13.43 (woz2Ex) =>
% 99.57/13.43 ((
% 99.57/13.43 (woz2W) =>
% 99.57/13.43 ((
% 99.57/13.43 (woz2A) =>
% 99.57/13.43 ((
% 99.57/13.43 (woz2B) =>
% 99.57/13.43 ((
% 99.57/13.43 (image1Ex) =>
% 99.57/13.43 ((
% 99.57/13.43 (image1Ex1) =>
% 99.57/13.43 ((
% 99.57/13.43 (image1Equiv) =>
% 99.57/13.43 ((
% 99.57/13.43 (image1E) =>
% 99.57/13.43 ((
% 99.57/13.43 (image1I) =>
% 99.57/13.43 ((
% 99.57/13.43 (injFuncInInjFuncSet) =>
% 99.57/13.43 ((
% 99.57/13.43 (injFuncSetFuncIn) =>
% 99.57/13.43 ((
% 99.57/13.43 (injFuncSetFuncInj) =>
% 99.57/13.43 ((
% 99.57/13.43 (!!) @ (
% 99.57/13.43 (('#B') @ (
% 99.57/13.43 !!) @
% 99.57/13.43 (
% 99.57/13.43 (
% 99.57/13.43 ('#B') @ (
% 99.57/13.43 (
% 99.57/13.43 ('#B') @ (
% 99.57/13.43 !!))) @
% 99.57/13.43 (
% 99.57/13.43 (
% 99.57/13.43 ('#S') @ (
% 99.57/13.43 (
% 99.57/13.43 ('#B') @ (
% 99.57/13.43 '#S') @
% 99.57/13.43 (
% 99.57/13.43 (
% 99.57/13.43 ('#B') @ (
% 99.57/13.43 (
% 99.57/13.43 ('#B') @ (
% 99.57/13.43 '#S'))) @
% 99.57/13.43 (
% 99.57/13.43 (
% 99.57/13.43 ('#B') @ (
% 99.57/13.43 (
% 99.57/13.43 ('#B') @ (
% 99.57/13.43 (
% 99.57/13.43 ('#B') @ (
% 99.57/13.43 =>))))) @
% 99.57/13.43 (
% 99.57/13.43 (
% 99.57/13.43 ('#B') @ (
% 99.57/13.43 (
% 99.57/13.43 ('#B') @ (
% 99.57/13.43 (
% 99.57/13.43 ('#C') @ in)))) @
% 99.57/13.43 surjFuncSet)))))))) @
% 99.57/13.43 (
% 99.57/13.43 (
% 99.57/13.43 ('#B') @ (
% 99.57/13.43 (
% 99.57/13.43 ('#B') @ (
% 99.57/13.43 (
% 99.57/13.43 ('#C') @ in)))) @
% 99.57/13.43 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.57/13.43 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1102])).
% 99.57/13.43 thf(zip_derived_cl1115, plain,
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% 99.57/13.43 (((binunionE) =>
% 99.57/13.43 (((binunionLsub) =>
% 99.57/13.43 (((binunionRsub) =>
% 99.57/13.43 (((binintersectI) =>
% 99.57/13.43 (((binintersectSubset5) =>
% 99.57/13.43 (((binintersectEL) =>
% 99.57/13.43 (((binintersectLsub) =>
% 99.57/13.43 (((binintersectSubset2) =>
% 99.57/13.43 (((binintersectSubset3) =>
% 99.57/13.43 (((binintersectER) =>
% 99.57/13.43 (((disjointsetsI1) =>
% 99.57/13.43 (((binintersectRsub) =>
% 99.57/13.43 (((binintersectSubset4) =>
% 99.57/13.43 (((binintersectSubset1) =>
% 99.57/13.43 (((bs114d) =>
% 99.57/13.43 (((setminusI) =>
% 99.57/13.43 (((setminusEL) =>
% 99.57/13.43 (((setminusER) =>
% 99.57/13.43 (((setminusSubset2) =>
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% 99.57/13.43 (((setminusELneg) =>
% 99.57/13.43 (((setminusILneg) =>
% 99.57/13.43 (((setminusIRneg) =>
% 99.57/13.43 (((setminusLsub) =>
% 99.57/13.43 (((setminusSubset1) =>
% 99.57/13.43 (((symdiffE) =>
% 99.57/13.43 (((symdiffI1) =>
% 99.57/13.43 (((symdiffI2) =>
% 99.57/13.43 (((symdiffIneg1) =>
% 99.57/13.43 ((
% 99.57/13.43 (symdiffIneg2) =>
% 99.57/13.43 ((
% 99.57/13.43 (secondinupair) =>
% 99.57/13.43 ((
% 99.57/13.43 (setukpairIL) =>
% 99.57/13.43 ((
% 99.57/13.43 (setukpairIR) =>
% 99.57/13.43 ((
% 99.57/13.43 (kpairiskpair) =>
% 99.57/13.43 ((
% 99.57/13.43 (kpairp) =>
% 99.57/13.43 ((
% 99.57/13.43 (singletonsubset) =>
% 99.57/13.43 ((
% 99.57/13.43 (singletoninpowerset) =>
% 99.57/13.43 ((
% 99.57/13.43 (singletoninpowunion) =>
% 99.57/13.43 ((
% 99.57/13.43 (upairset2E) =>
% 99.57/13.43 ((
% 99.57/13.43 (upairsubunion) =>
% 99.57/13.43 ((
% 99.57/13.43 (upairinpowunion) =>
% 99.57/13.43 ((
% 99.57/13.43 (ubforcartprodlem1) =>
% 99.57/13.43 ((
% 99.57/13.43 (ubforcartprodlem2) =>
% 99.57/13.43 ((
% 99.57/13.43 (ubforcartprodlem3) =>
% 99.57/13.43 ((
% 99.57/13.43 (cartprodpairin) =>
% 99.57/13.43 ((
% 99.57/13.43 (cartprodmempair1) =>
% 99.57/13.43 ((
% 99.57/13.43 (cartprodmempair) =>
% 99.57/13.43 ((
% 99.57/13.43 (setunionE2) =>
% 99.57/13.43 ((
% 99.57/13.43 (setunionsingleton1) =>
% 99.57/13.43 ((
% 99.57/13.43 (setunionsingleton2) =>
% 99.57/13.43 ((
% 99.57/13.43 (setunionsingleton) =>
% 99.57/13.43 ((
% 99.57/13.43 (singletonprop) =>
% 99.57/13.43 ((
% 99.57/13.43 (ex1E1) =>
% 99.57/13.43 ((
% 99.57/13.43 (ex1I) =>
% 99.57/13.43 ((
% 99.57/13.43 (ex1I2) =>
% 99.57/13.43 ((
% 99.57/13.43 (singletonsuniq) =>
% 99.57/13.43 ((
% 99.57/13.43 (setukpairinjL1) =>
% 99.57/13.43 ((
% 99.57/13.43 (kfstsingleton) =>
% 99.57/13.43 ((
% 99.57/13.43 (theprop) =>
% 99.57/13.43 ((
% 99.57/13.43 (kfstpairEq) =>
% 99.57/13.43 ((
% 99.57/13.43 (cartprodfstin) =>
% 99.57/13.43 ((
% 99.57/13.43 (setukpairinjL2) =>
% 99.57/13.43 ((
% 99.57/13.43 (setukpairinjL) =>
% 99.57/13.43 ((
% 99.57/13.43 (setukpairinjR11) =>
% 99.57/13.43 ((
% 99.57/13.43 (setukpairinjR12) =>
% 99.57/13.43 ((
% 99.57/13.43 (setukpairinjR1) =>
% 99.57/13.43 ((
% 99.57/13.43 (upairequniteq) =>
% 99.57/13.43 ((
% 99.57/13.43 (setukpairinjR2) =>
% 99.57/13.43 ((
% 99.57/13.43 (setukpairinjR) =>
% 99.57/13.43 ((
% 99.57/13.43 (ksndsingleton) =>
% 99.57/13.43 ((
% 99.57/13.43 (ksndpairEq) =>
% 99.57/13.43 ((
% 99.57/13.43 (kpairsurjEq) =>
% 99.57/13.43 ((
% 99.57/13.43 (cartprodsndin) =>
% 99.57/13.43 ((
% 99.57/13.43 (cartprodpairmemEL) =>
% 99.57/13.43 ((
% 99.57/13.43 (cartprodpairmemER) =>
% 99.57/13.43 ((
% 99.57/13.43 (cartprodmempaircEq) =>
% 99.57/13.43 ((
% 99.57/13.43 (cartprodfstpairEq) =>
% 99.57/13.43 ((
% 99.57/13.43 (cartprodsndpairEq) =>
% 99.57/13.43 ((
% 99.57/13.43 (cartprodpairsurjEq) =>
% 99.57/13.43 ((
% 99.57/13.43 (dpsetconstrI) =>
% 99.57/13.43 ((
% 99.57/13.43 (dpsetconstrSub) =>
% 99.57/13.43 ((
% 99.57/13.43 (setOfPairsIsBReln) =>
% 99.57/13.43 ((
% 99.57/13.43 (dpsetconstrERa) =>
% 99.57/13.43 ((
% 99.57/13.43 (dpsetconstrEL1) =>
% 99.57/13.43 ((
% 99.57/13.43 (dpsetconstrEL2) =>
% 99.57/13.43 ((
% 99.57/13.43 (dpsetconstrER) =>
% 99.57/13.43 ((
% 99.57/13.43 (funcImageSingleton) =>
% 99.57/13.43 ((
% 99.57/13.43 (apProp) =>
% 99.57/13.43 ((
% 99.57/13.43 (app) =>
% 99.57/13.43 ((
% 99.57/13.43 (infuncsetfunc) =>
% 99.57/13.43 ((
% 99.57/13.43 (ap2p) =>
% 99.57/13.43 ((
% 99.57/13.43 (funcinfuncset) =>
% 99.57/13.43 ((
% 99.57/13.43 (lamProp) =>
% 99.57/13.43 ((
% 99.57/13.43 (lamp) =>
% 99.57/13.43 ((
% 99.57/13.43 (lam2p) =>
% 99.57/13.43 ((
% 99.57/13.43 (brelnall1) =>
% 99.57/13.43 ((
% 99.57/13.43 (brelnall2) =>
% 99.57/13.43 ((
% 99.57/13.43 (ex1E2) =>
% 99.57/13.43 ((
% 99.57/13.43 (funcGraphProp1) =>
% 99.57/13.43 ((
% 99.57/13.43 (funcGraphProp3) =>
% 99.57/13.43 ((
% 99.57/13.43 (funcGraphProp2) =>
% 99.57/13.43 ((
% 99.57/13.43 (funcextLem) =>
% 99.57/13.43 ((
% 99.57/13.43 (funcGraphProp4) =>
% 99.57/13.43 ((
% 99.57/13.43 (subbreln) =>
% 99.57/13.43 ((
% 99.57/13.43 (eqbreln) =>
% 99.57/13.43 ((
% 99.57/13.43 (funcext) =>
% 99.57/13.43 ((
% 99.57/13.43 (funcext2) =>
% 99.57/13.43 ((
% 99.57/13.43 (ap2apEq1) =>
% 99.57/13.43 ((
% 99.57/13.43 (ap2apEq2) =>
% 99.57/13.43 ((
% 99.57/13.43 (beta1) =>
% 99.57/13.43 ((
% 99.57/13.43 (eta1) =>
% 99.57/13.43 ((
% 99.57/13.43 (lam2lamEq) =>
% 99.57/13.43 ((
% 99.57/13.43 (beta2) =>
% 99.57/13.43 ((
% 99.57/13.43 (eta2) =>
% 99.57/13.43 ((
% 99.57/13.43 (iffalseProp1) =>
% 99.57/13.43 ((
% 99.57/13.43 (iffalseProp2) =>
% 99.57/13.43 ((
% 99.57/13.43 (iftrueProp1) =>
% 99.57/13.43 ((
% 99.57/13.43 (iftrueProp2) =>
% 99.57/13.43 ((
% 99.57/13.43 (ifSingleton) =>
% 99.57/13.43 ((
% 99.57/13.43 (ifp) =>
% 99.57/13.43 ((
% 99.57/13.43 (theeq) =>
% 99.57/13.43 ((
% 99.57/13.43 (iftrue) =>
% 99.57/13.43 ((
% 99.57/13.43 (iffalse) =>
% 99.57/13.43 ((
% 99.57/13.43 (iftrueorfalse) =>
% 99.57/13.43 ((
% 99.57/13.43 (binintersectT_lem) =>
% 99.57/13.43 ((
% 99.57/13.43 (binunionT_lem) =>
% 99.57/13.43 ((
% 99.57/13.43 (powersetT_lem) =>
% 99.57/13.43 ((
% 99.57/13.43 (setminusT_lem) =>
% 99.57/13.43 ((
% 99.57/13.43 (complementT_lem) =>
% 99.57/13.43 ((
% 99.57/13.43 (setextT) =>
% 99.57/13.43 ((
% 99.57/13.43 (subsetTI) =>
% 99.57/13.43 ((
% 99.57/13.43 (powersetTI1) =>
% 99.57/13.43 ((
% 99.57/13.43 (powersetTE1) =>
% 99.57/13.43 ((
% 99.57/13.43 (complementTI1) =>
% 99.57/13.43 ((
% 99.57/13.43 (complementTE1) =>
% 99.57/13.43 ((
% 99.57/13.43 (binintersectTELcontra) =>
% 99.57/13.43 ((
% 99.57/13.43 (binintersectTERcontra) =>
% 99.57/13.43 ((
% 99.57/13.43 (contrasubsetT) =>
% 99.57/13.43 ((
% 99.57/13.43 (contrasubsetT1) =>
% 99.57/13.43 ((
% 99.57/13.43 (contrasubsetT2) =>
% 99.57/13.43 ((
% 99.57/13.43 (contrasubsetT3) =>
% 99.57/13.43 ((
% 99.57/13.43 (doubleComplementI1) =>
% 99.57/13.43 ((
% 99.57/13.43 (doubleComplementE1) =>
% 99.57/13.43 ((
% 99.57/13.43 (doubleComplementSub1) =>
% 99.57/13.43 ((
% 99.57/13.43 (doubleComplementSub2) =>
% 99.57/13.43 ((
% 99.57/13.43 (doubleComplementEq) =>
% 99.57/13.43 ((
% 99.57/13.43 (complementTnotintersectT) =>
% 99.57/13.43 ((
% 99.57/13.43 (complementImpComplementIntersect) =>
% 99.57/13.43 ((
% 99.57/13.43 (complementSubsetComplementIntersect) =>
% 99.57/13.43 ((
% 99.57/13.43 (complementInPowersetComplementIntersect) =>
% 99.57/13.43 ((
% 99.57/13.43 (contraSubsetComplement) =>
% 99.57/13.43 ((
% 99.57/13.43 (complementTcontraSubset) =>
% 99.57/13.43 ((
% 99.57/13.43 (binunionTILcontra) =>
% 99.57/13.43 ((
% 99.57/13.43 (binunionTIRcontra) =>
% 99.57/13.43 ((
% 99.57/13.43 (inIntersectImpInUnion) =>
% 99.57/13.43 ((
% 99.57/13.43 (inIntersectImpInUnion2) =>
% 99.57/13.43 ((
% 99.57/13.43 (inIntersectImpInIntersectUnions) =>
% 99.57/13.43 ((
% 99.57/13.43 (intersectInPowersetIntersectUnions) =>
% 99.57/13.43 ((
% 99.57/13.43 (inComplementUnionImpNotIn1) =>
% 99.57/13.43 ((
% 99.57/13.43 (inComplementUnionImpInComplement1) =>
% 99.57/13.43 ((
% 99.57/13.43 (binunionTE) =>
% 99.57/13.43 ((
% 99.57/13.43 (binunionTEcontra) =>
% 99.57/13.43 ((
% 99.57/13.43 (demorgan2a1) =>
% 99.57/13.43 ((
% 99.57/13.43 (complementUnionInPowersetComplement) =>
% 99.57/13.43 ((
% 99.57/13.43 (demorgan2a2) =>
% 99.57/13.43 ((
% 99.57/13.43 (demorgan1a) =>
% 99.57/13.43 ((
% 99.57/13.43 (demorgan1b) =>
% 99.57/13.43 ((
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% 99.57/13.43 ((
% 99.57/13.43 (demorgan2a) =>
% 99.57/13.43 ((
% 99.57/13.43 (demorgan2b2) =>
% 99.57/13.43 ((
% 99.57/13.43 (demorgan2b) =>
% 99.57/13.43 ((
% 99.57/13.43 (demorgan2) =>
% 99.57/13.43 ((
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% 99.57/13.43 ((
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% 99.57/13.43 ((
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% 99.57/13.43 ((
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% 99.57/13.43 ((
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% 99.57/13.43 ((
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% 99.57/13.43 ((
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% 99.57/13.43 ((
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% 99.57/13.43 ((
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% 99.57/13.43 ((
% 99.57/13.43 (breln1invI) =>
% 99.57/13.43 ((
% 99.57/13.43 (breln1invE) =>
% 99.57/13.43 ((
% 99.57/13.43 (breln1compprop) =>
% 99.57/13.43 ((
% 99.57/13.43 (breln1compI) =>
% 99.57/13.43 ((
% 99.57/13.43 (breln1compE) =>
% 99.57/13.43 ((
% 99.57/13.43 (breln1compEex) =>
% 99.57/13.43 ((
% 99.57/13.43 (breln1unionprop) =>
% 99.57/13.43 ((
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% 99.57/13.43 ((
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% 99.57/13.43 ((
% 99.57/13.43 (cartprodpairmemER) =>
% 99.57/13.43 ((
% 99.57/13.43 (cartprodmempaircEq) =>
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% 99.57/13.43 (cartprodfstpairEq) =>
% 99.57/13.43 ((
% 99.57/13.43 (cartprodsndpairEq) =>
% 99.57/13.43 ((
% 99.57/13.43 (cartprodpairsurjEq) =>
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% 99.57/13.43 ((
% 99.57/13.43 (dpsetconstrSub) =>
% 99.57/13.43 ((
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% 99.57/13.43 ((
% 99.57/13.43 (dpsetconstrEL2) =>
% 99.57/13.43 ((
% 99.57/13.43 (dpsetconstrER) =>
% 99.57/13.43 ((
% 99.57/13.43 (funcImageSingleton) =>
% 99.57/13.43 ((
% 99.57/13.43 (apProp) =>
% 99.57/13.43 ((
% 99.57/13.43 (app) =>
% 99.57/13.43 ((
% 99.57/13.43 (infuncsetfunc) =>
% 99.57/13.43 ((
% 99.57/13.43 (ap2p) =>
% 99.57/13.43 ((
% 99.57/13.43 (funcinfuncset) =>
% 99.57/13.43 ((
% 99.57/13.43 (lamProp) =>
% 99.57/13.43 ((
% 99.57/13.43 (lamp) =>
% 99.57/13.43 ((
% 99.57/13.43 (lam2p) =>
% 99.57/13.43 ((
% 99.57/13.43 (brelnall1) =>
% 99.57/13.43 ((
% 99.57/13.43 (brelnall2) =>
% 99.57/13.43 ((
% 99.57/13.43 (ex1E2) =>
% 99.57/13.43 ((
% 99.57/13.43 (funcGraphProp1) =>
% 99.57/13.43 ((
% 99.57/13.43 (funcGraphProp3) =>
% 99.57/13.43 ((
% 99.57/13.43 (funcGraphProp2) =>
% 99.57/13.43 ((
% 99.57/13.43 (funcextLem) =>
% 99.57/13.43 ((
% 99.57/13.43 (funcGraphProp4) =>
% 99.57/13.43 ((
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% 99.57/13.43 ((
% 99.57/13.43 (eqbreln) =>
% 99.57/13.43 ((
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% 99.57/13.43 (funcext2) =>
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% 99.57/13.43 (ap2apEq2) =>
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% 99.57/13.43 ((
% 99.57/13.43 (eta1) =>
% 99.57/13.43 ((
% 99.57/13.43 (lam2lamEq) =>
% 99.57/13.43 ((
% 99.57/13.43 (beta2) =>
% 99.57/13.43 ((
% 99.57/13.43 (eta2) =>
% 99.57/13.43 ((
% 99.57/13.43 (iffalseProp1) =>
% 99.57/13.43 ((
% 99.57/13.43 (iffalseProp2) =>
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% 99.57/13.43 (iftrueProp1) =>
% 99.57/13.43 ((
% 99.57/13.43 (iftrueProp2) =>
% 99.57/13.43 ((
% 99.57/13.43 (ifSingleton) =>
% 99.57/13.43 ((
% 99.57/13.43 (ifp) =>
% 99.57/13.43 ((
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% 99.57/13.43 (iftrue) =>
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% 99.57/13.43 ((
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% 99.57/13.43 ((
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% 99.57/13.43 ((
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% 99.57/13.43 ((
% 99.57/13.43 (setextT) =>
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% 99.57/13.43 (subsetTI) =>
% 99.57/13.43 ((
% 99.57/13.43 (powersetTI1) =>
% 99.57/13.43 ((
% 99.57/13.43 (powersetTE1) =>
% 99.57/13.43 ((
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% 99.57/13.43 ((
% 99.57/13.43 (complementTE1) =>
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% 99.57/13.43 ((
% 99.57/13.43 (binintersectTERcontra) =>
% 99.57/13.43 ((
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% 99.57/13.43 ((
% 99.57/13.43 (contrasubsetT1) =>
% 99.57/13.43 ((
% 99.57/13.43 (contrasubsetT2) =>
% 99.57/13.43 ((
% 99.57/13.43 (contrasubsetT3) =>
% 99.57/13.43 ((
% 99.57/13.43 (doubleComplementI1) =>
% 99.57/13.43 ((
% 99.57/13.43 (doubleComplementE1) =>
% 99.57/13.43 ((
% 99.57/13.43 (doubleComplementSub1) =>
% 99.57/13.43 ((
% 99.57/13.43 (doubleComplementSub2) =>
% 99.57/13.43 ((
% 99.57/13.43 (doubleComplementEq) =>
% 99.57/13.43 ((
% 99.57/13.43 (complementTnotintersectT) =>
% 99.57/13.43 ((
% 99.57/13.43 (complementImpComplementIntersect) =>
% 99.57/13.43 ((
% 99.57/13.43 (complementSubsetComplementIntersect) =>
% 99.57/13.43 ((
% 99.57/13.43 (complementInPowersetComplementIntersect) =>
% 99.57/13.43 ((
% 99.57/13.43 (contraSubsetComplement) =>
% 99.57/13.43 ((
% 99.57/13.43 (complementTcontraSubset) =>
% 99.57/13.43 ((
% 99.57/13.43 (binunionTILcontra) =>
% 99.57/13.43 ((
% 99.57/13.43 (binunionTIRcontra) =>
% 99.57/13.43 ((
% 99.57/13.43 (inIntersectImpInUnion) =>
% 99.57/13.43 ((
% 99.57/13.43 (inIntersectImpInUnion2) =>
% 99.57/13.43 ((
% 99.57/13.43 (inIntersectImpInIntersectUnions) =>
% 99.57/13.43 ((
% 99.57/13.43 (intersectInPowersetIntersectUnions) =>
% 99.57/13.43 ((
% 99.57/13.43 (inComplementUnionImpNotIn1) =>
% 99.57/13.43 ((
% 99.57/13.43 (inComplementUnionImpInComplement1) =>
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% 99.57/13.43 (binunionTE) =>
% 99.57/13.43 ((
% 99.57/13.43 (binunionTEcontra) =>
% 99.57/13.43 ((
% 99.57/13.43 (demorgan2a1) =>
% 99.57/13.43 ((
% 99.57/13.43 (complementUnionInPowersetComplement) =>
% 99.57/13.43 ((
% 99.57/13.43 (demorgan2a2) =>
% 99.57/13.43 ((
% 99.57/13.43 (demorgan1a) =>
% 99.57/13.43 ((
% 99.57/13.43 (demorgan1b) =>
% 99.57/13.43 ((
% 99.57/13.43 (demorgan1) =>
% 99.57/13.43 ((
% 99.57/13.43 (demorgan2a) =>
% 99.57/13.43 ((
% 99.57/13.43 (demorgan2b2) =>
% 99.57/13.43 ((
% 99.57/13.43 (demorgan2b) =>
% 99.57/13.43 ((
% 99.57/13.43 (demorgan2) =>
% 99.57/13.43 ((
% 99.57/13.43 (woz13rule0) =>
% 99.57/13.43 ((
% 99.57/13.43 (woz13rule1) =>
% 99.57/13.43 ((
% 99.57/13.43 (woz13rule2) =>
% 99.57/13.43 ((
% 99.57/13.43 (woz13rule3) =>
% 99.57/13.43 ((
% 99.57/13.43 (woz13rule4) =>
% 99.57/13.43 ((
% 99.57/13.43 (woz1_1) =>
% 99.57/13.43 ((
% 99.57/13.43 (woz1_2) =>
% 99.57/13.43 ((
% 99.57/13.43 (woz1_3) =>
% 99.57/13.43 ((
% 99.57/13.43 (woz1_4) =>
% 99.57/13.43 ((
% 99.57/13.43 (woz1_5) =>
% 99.57/13.43 ((
% 99.57/13.43 (breln1all2) =>
% 99.57/13.43 ((
% 99.57/13.43 (breln1SetBreln1) =>
% 99.57/13.43 ((
% 99.57/13.43 (choice2fnsingleton) =>
% 99.57/13.43 ((
% 99.57/13.43 (setOfPairsIsBReln1) =>
% 99.57/13.43 ((
% 99.57/13.43 (breln1all1) =>
% 99.57/13.43 ((
% 99.57/13.43 (subbreln1) =>
% 99.57/13.43 ((
% 99.57/13.43 (eqbreln1) =>
% 99.57/13.43 ((
% 99.57/13.43 (breln1invprop) =>
% 99.57/13.43 ((
% 99.57/13.43 (breln1invI) =>
% 99.57/13.43 ((
% 99.57/13.43 (breln1invE) =>
% 99.57/13.43 ((
% 99.57/13.43 (breln1compprop) =>
% 99.57/13.43 ((
% 99.57/13.43 (breln1compI) =>
% 99.57/13.43 ((
% 99.57/13.43 (breln1compE) =>
% 99.57/13.43 ((
% 99.57/13.43 (breln1compEex) =>
% 99.57/13.43 ((
% 99.57/13.43 (breln1unionprop) =>
% 99.57/13.43 ((
% 99.57/13.43 (breln1unionIL) =>
% 99.57/13.43 ((
% 99.57/13.43 (breln1unionIR) =>
% 99.57/13.43 ((
% 99.57/13.43 (breln1unionI) =>
% 99.57/13.43 ((
% 99.57/13.43 (breln1unionE) =>
% 99.57/13.43 ((
% 99.57/13.43 (breln1unionEcases) =>
% 99.57/13.43 ((
% 99.57/13.43 (breln1unionCommutes) =>
% 99.57/13.43 ((
% 99.57/13.43 (woz2Ex) =>
% 99.57/13.43 ((
% 99.57/13.43 (woz2W) =>
% 99.57/13.43 ((
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% 99.57/13.43 ((
% 99.57/13.43 (woz2B) =>
% 99.57/13.43 ((
% 99.57/13.43 (image1Ex) =>
% 99.57/13.43 ((
% 99.57/13.43 (image1Ex1) =>
% 99.57/13.43 ((
% 99.57/13.43 (image1Equiv) =>
% 99.57/13.43 ((
% 99.57/13.43 (image1E) =>
% 99.57/13.43 ((
% 99.57/13.43 (image1I) =>
% 99.57/13.43 ((
% 99.57/13.43 (injFuncInInjFuncSet) =>
% 99.57/13.43 ((
% 99.57/13.43 (injFuncSetFuncIn) =>
% 99.57/13.43 ((
% 99.57/13.43 (injFuncSetFuncInj) =>
% 99.57/13.43 ((
% 99.57/13.43 (!!) @ (
% 99.57/13.43 (('#B') @ (
% 99.57/13.43 !!) @
% 99.57/13.43 (
% 99.57/13.43 (
% 99.57/13.43 ('#B') @ (
% 99.57/13.43 (
% 99.57/13.43 ('#B') @ (
% 99.57/13.43 !!))) @
% 99.57/13.43 (
% 99.57/13.43 (
% 99.57/13.43 ('#S') @ (
% 99.57/13.43 (
% 99.57/13.43 ('#B') @ (
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% 99.57/13.43 (
% 99.57/13.43 (
% 99.57/13.43 ('#B') @ (
% 99.57/13.43 (
% 99.57/13.43 ('#B') @ (
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% 99.57/13.43 (
% 99.57/13.43 (
% 99.57/13.43 ('#B') @ (
% 99.57/13.43 (
% 99.57/13.43 ('#B') @ (
% 99.57/13.43 (
% 99.57/13.43 ('#B') @ (
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% 99.57/13.43 (
% 99.57/13.43 (
% 99.57/13.43 ('#B') @ (
% 99.57/13.43 (
% 99.57/13.43 ('#B') @ (
% 99.57/13.43 (
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% 99.57/13.43 surjFuncSet)))))))) @
% 99.57/13.43 (
% 99.57/13.43 (
% 99.57/13.43 ('#B') @ (
% 99.57/13.43 (
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% 99.57/13.43 (
% 99.57/13.43 ('#C') @ in)))) @
% 99.57/13.43 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.57/13.43 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1121])).
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% 99.57/13.43 (((binintersectRsub) =>
% 99.57/13.43 (((binintersectSubset4) =>
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% 99.57/13.43 (((setminusEL) =>
% 99.57/13.43 (((setminusER) =>
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% 99.57/13.43 ((
% 99.57/13.43 (kpairp) =>
% 99.57/13.43 ((
% 99.57/13.43 (singletonsubset) =>
% 99.57/13.43 ((
% 99.57/13.43 (singletoninpowerset) =>
% 99.57/13.43 ((
% 99.57/13.43 (singletoninpowunion) =>
% 99.57/13.43 ((
% 99.57/13.43 (upairset2E) =>
% 99.57/13.43 ((
% 99.57/13.43 (upairsubunion) =>
% 99.57/13.43 ((
% 99.57/13.43 (upairinpowunion) =>
% 99.57/13.43 ((
% 99.57/13.43 (ubforcartprodlem1) =>
% 99.57/13.43 ((
% 99.57/13.43 (ubforcartprodlem2) =>
% 99.57/13.43 ((
% 99.57/13.43 (ubforcartprodlem3) =>
% 99.57/13.43 ((
% 99.57/13.43 (cartprodpairin) =>
% 99.57/13.43 ((
% 99.57/13.43 (cartprodmempair1) =>
% 99.57/13.43 ((
% 99.57/13.43 (cartprodmempair) =>
% 99.57/13.43 ((
% 99.57/13.43 (setunionE2) =>
% 99.57/13.43 ((
% 99.57/13.43 (setunionsingleton1) =>
% 99.57/13.43 ((
% 99.57/13.43 (setunionsingleton2) =>
% 99.57/13.43 ((
% 99.57/13.43 (setunionsingleton) =>
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% 99.57/13.43 ((
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% 99.57/13.43 ((
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% 99.57/13.43 ((
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% 99.57/13.43 ((
% 99.57/13.43 (kfstpairEq) =>
% 99.57/13.43 ((
% 99.57/13.43 (cartprodfstin) =>
% 99.57/13.43 ((
% 99.57/13.43 (setukpairinjL2) =>
% 99.57/13.43 ((
% 99.57/13.43 (setukpairinjL) =>
% 99.57/13.43 ((
% 99.57/13.43 (setukpairinjR11) =>
% 99.57/13.43 ((
% 99.57/13.43 (setukpairinjR12) =>
% 99.57/13.43 ((
% 99.57/13.43 (setukpairinjR1) =>
% 99.57/13.43 ((
% 99.57/13.43 (upairequniteq) =>
% 99.57/13.43 ((
% 99.57/13.43 (setukpairinjR2) =>
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% 99.57/13.43 (ksndpairEq) =>
% 99.57/13.43 ((
% 99.57/13.43 (kpairsurjEq) =>
% 99.57/13.43 ((
% 99.57/13.43 (cartprodsndin) =>
% 99.57/13.43 ((
% 99.57/13.43 (cartprodpairmemEL) =>
% 99.57/13.43 ((
% 99.57/13.43 (cartprodpairmemER) =>
% 99.57/13.43 ((
% 99.57/13.43 (cartprodmempaircEq) =>
% 99.57/13.43 ((
% 99.57/13.43 (cartprodfstpairEq) =>
% 99.57/13.43 ((
% 99.57/13.43 (cartprodsndpairEq) =>
% 99.57/13.43 ((
% 99.57/13.43 (cartprodpairsurjEq) =>
% 99.57/13.43 ((
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% 99.57/13.43 ((
% 99.57/13.43 (dpsetconstrSub) =>
% 99.57/13.43 ((
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% 99.57/13.43 ((
% 99.57/13.43 (dpsetconstrEL2) =>
% 99.57/13.43 ((
% 99.57/13.43 (dpsetconstrER) =>
% 99.57/13.43 ((
% 99.57/13.43 (funcImageSingleton) =>
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% 99.57/13.43 ((
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% 99.57/13.43 ((
% 99.57/13.43 (infuncsetfunc) =>
% 99.57/13.43 ((
% 99.57/13.43 (ap2p) =>
% 99.57/13.43 ((
% 99.57/13.43 (funcinfuncset) =>
% 99.57/13.43 ((
% 99.57/13.43 (lamProp) =>
% 99.57/13.43 ((
% 99.57/13.43 (lamp) =>
% 99.57/13.43 ((
% 99.57/13.43 (lam2p) =>
% 99.57/13.43 ((
% 99.57/13.43 (brelnall1) =>
% 99.57/13.43 ((
% 99.57/13.43 (brelnall2) =>
% 99.57/13.43 ((
% 99.57/13.43 (ex1E2) =>
% 99.57/13.43 ((
% 99.57/13.43 (funcGraphProp1) =>
% 99.57/13.43 ((
% 99.57/13.43 (funcGraphProp3) =>
% 99.57/13.43 ((
% 99.57/13.43 (funcGraphProp2) =>
% 99.57/13.43 ((
% 99.57/13.43 (funcextLem) =>
% 99.57/13.43 ((
% 99.57/13.43 (funcGraphProp4) =>
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% 99.57/13.43 ((
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% 99.57/13.43 (funcext2) =>
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% 99.57/13.43 (ap2apEq2) =>
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% 99.57/13.43 ((
% 99.57/13.43 (eta1) =>
% 99.57/13.43 ((
% 99.57/13.43 (lam2lamEq) =>
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% 99.57/13.43 ((
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% 99.57/13.43 ((
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% 99.57/13.43 ((
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% 99.57/13.43 ((
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% 99.57/13.43 ((
% 99.57/13.43 (binintersectTERcontra) =>
% 99.57/13.43 ((
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% 99.57/13.43 ((
% 99.57/13.43 (contrasubsetT1) =>
% 99.57/13.43 ((
% 99.57/13.43 (contrasubsetT2) =>
% 99.57/13.43 ((
% 99.57/13.43 (contrasubsetT3) =>
% 99.57/13.43 ((
% 99.57/13.43 (doubleComplementI1) =>
% 99.57/13.43 ((
% 99.57/13.43 (doubleComplementE1) =>
% 99.57/13.43 ((
% 99.57/13.43 (doubleComplementSub1) =>
% 99.57/13.43 ((
% 99.57/13.43 (doubleComplementSub2) =>
% 99.57/13.43 ((
% 99.57/13.43 (doubleComplementEq) =>
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% 99.57/13.43 ((
% 99.57/13.43 (complementImpComplementIntersect) =>
% 99.57/13.43 ((
% 99.57/13.43 (complementSubsetComplementIntersect) =>
% 99.57/13.43 ((
% 99.57/13.43 (complementInPowersetComplementIntersect) =>
% 99.57/13.43 ((
% 99.57/13.43 (contraSubsetComplement) =>
% 99.57/13.43 ((
% 99.57/13.43 (complementTcontraSubset) =>
% 99.57/13.43 ((
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% 99.57/13.43 ((
% 99.57/13.43 (binunionTIRcontra) =>
% 99.57/13.43 ((
% 99.57/13.43 (inIntersectImpInUnion) =>
% 99.57/13.43 ((
% 99.57/13.43 (inIntersectImpInUnion2) =>
% 99.57/13.43 ((
% 99.57/13.43 (inIntersectImpInIntersectUnions) =>
% 99.57/13.43 ((
% 99.57/13.43 (intersectInPowersetIntersectUnions) =>
% 99.57/13.43 ((
% 99.57/13.43 (inComplementUnionImpNotIn1) =>
% 99.57/13.43 ((
% 99.57/13.43 (inComplementUnionImpInComplement1) =>
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% 99.57/13.43 ((
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% 99.57/13.43 ((
% 99.57/13.43 (demorgan2a2) =>
% 99.57/13.43 ((
% 99.57/13.43 (demorgan1a) =>
% 99.57/13.43 ((
% 99.57/13.43 (demorgan1b) =>
% 99.57/13.43 ((
% 99.57/13.43 (demorgan1) =>
% 99.57/13.43 ((
% 99.57/13.43 (demorgan2a) =>
% 99.57/13.43 ((
% 99.57/13.43 (demorgan2b2) =>
% 99.57/13.43 ((
% 99.57/13.43 (demorgan2b) =>
% 99.57/13.43 ((
% 99.57/13.43 (demorgan2) =>
% 99.57/13.43 ((
% 99.57/13.43 (woz13rule0) =>
% 99.57/13.43 ((
% 99.57/13.43 (woz13rule1) =>
% 99.57/13.43 ((
% 99.57/13.43 (woz13rule2) =>
% 99.57/13.43 ((
% 99.57/13.43 (woz13rule3) =>
% 99.57/13.43 ((
% 99.57/13.43 (woz13rule4) =>
% 99.57/13.43 ((
% 99.57/13.43 (woz1_1) =>
% 99.57/13.43 ((
% 99.57/13.43 (woz1_2) =>
% 99.57/13.43 ((
% 99.57/13.43 (woz1_3) =>
% 99.57/13.43 ((
% 99.57/13.43 (woz1_4) =>
% 99.57/13.43 ((
% 99.57/13.43 (woz1_5) =>
% 99.57/13.43 ((
% 99.57/13.43 (breln1all2) =>
% 99.57/13.43 ((
% 99.57/13.43 (breln1SetBreln1) =>
% 99.57/13.43 ((
% 99.57/13.43 (choice2fnsingleton) =>
% 99.57/13.43 ((
% 99.57/13.43 (setOfPairsIsBReln1) =>
% 99.57/13.43 ((
% 99.57/13.43 (breln1all1) =>
% 99.57/13.43 ((
% 99.57/13.43 (subbreln1) =>
% 99.57/13.43 ((
% 99.57/13.43 (eqbreln1) =>
% 99.57/13.43 ((
% 99.57/13.43 (breln1invprop) =>
% 99.57/13.43 ((
% 99.57/13.43 (breln1invI) =>
% 99.57/13.43 ((
% 99.57/13.43 (breln1invE) =>
% 99.57/13.43 ((
% 99.57/13.43 (breln1compprop) =>
% 99.57/13.43 ((
% 99.57/13.43 (breln1compI) =>
% 99.57/13.43 ((
% 99.57/13.43 (breln1compE) =>
% 99.57/13.43 ((
% 99.57/13.43 (breln1compEex) =>
% 99.57/13.43 ((
% 99.57/13.43 (breln1unionprop) =>
% 99.57/13.43 ((
% 99.57/13.43 (breln1unionIL) =>
% 99.57/13.43 ((
% 99.57/13.43 (breln1unionIR) =>
% 99.57/13.43 ((
% 99.57/13.43 (breln1unionI) =>
% 99.57/13.43 ((
% 99.57/13.43 (breln1unionE) =>
% 99.57/13.43 ((
% 99.57/13.43 (breln1unionEcases) =>
% 99.57/13.43 ((
% 99.57/13.43 (breln1unionCommutes) =>
% 99.57/13.43 ((
% 99.57/13.43 (woz2Ex) =>
% 99.57/13.43 ((
% 99.57/13.43 (woz2W) =>
% 99.57/13.43 ((
% 99.57/13.43 (woz2A) =>
% 99.57/13.43 ((
% 99.57/13.43 (woz2B) =>
% 99.57/13.43 ((
% 99.57/13.43 (image1Ex) =>
% 99.57/13.43 ((
% 99.57/13.43 (image1Ex1) =>
% 99.57/13.43 ((
% 99.57/13.43 (image1Equiv) =>
% 99.57/13.43 ((
% 99.57/13.43 (image1E) =>
% 99.57/13.43 ((
% 99.57/13.43 (image1I) =>
% 99.57/13.43 ((
% 99.57/13.43 (injFuncInInjFuncSet) =>
% 99.57/13.43 ((
% 99.57/13.43 (injFuncSetFuncIn) =>
% 99.57/13.43 ((
% 99.57/13.43 (injFuncSetFuncInj) =>
% 99.57/13.43 ((
% 99.57/13.43 (!!) @ (
% 99.57/13.43 (('#B') @ (
% 99.57/13.43 !!) @
% 99.57/13.43 (
% 99.57/13.43 (
% 99.57/13.43 ('#B') @ (
% 99.57/13.43 (
% 99.57/13.43 ('#B') @ (
% 99.57/13.43 !!))) @
% 99.57/13.43 (
% 99.57/13.43 (
% 99.57/13.43 ('#S') @ (
% 99.57/13.43 (
% 99.57/13.43 ('#B') @ (
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% 99.57/13.43 (
% 99.57/13.43 (
% 99.57/13.43 ('#B') @ (
% 99.57/13.43 (
% 99.57/13.43 ('#B') @ (
% 99.57/13.43 '#S'))) @
% 99.57/13.43 (
% 99.57/13.43 (
% 99.57/13.43 ('#B') @ (
% 99.57/13.43 (
% 99.57/13.43 ('#B') @ (
% 99.57/13.43 (
% 99.57/13.43 ('#B') @ (
% 99.57/13.43 =>))))) @
% 99.57/13.43 (
% 99.57/13.43 (
% 99.57/13.43 ('#B') @ (
% 99.57/13.43 (
% 99.57/13.43 ('#B') @ (
% 99.57/13.43 (
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% 99.57/13.43 surjFuncSet)))))))) @
% 99.57/13.43 (
% 99.57/13.43 (
% 99.57/13.43 ('#B') @ (
% 99.57/13.43 (
% 99.57/13.43 ('#B') @ (
% 99.57/13.43 (
% 99.57/13.43 ('#C') @ in)))) @
% 99.57/13.43 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.57/13.43 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1128])).
% 99.57/13.43 thf(zip_derived_cl1142, plain,
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% 99.57/13.43 (((binintersectRsub) =>
% 99.57/13.43 (((binintersectSubset4) =>
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% 99.57/13.43 (((setminusEL) =>
% 99.57/13.43 (((setminusER) =>
% 99.57/13.43 (((setminusSubset2) =>
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% 99.57/13.43 (((setminusELneg) =>
% 99.57/13.43 (((setminusILneg) =>
% 99.57/13.43 (((setminusIRneg) =>
% 99.57/13.43 (((setminusLsub) =>
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% 99.57/13.43 (((symdiffI1) =>
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% 99.57/13.43 (((setukpairIR) =>
% 99.57/13.43 ((
% 99.57/13.43 (kpairiskpair) =>
% 99.57/13.43 ((
% 99.57/13.43 (kpairp) =>
% 99.57/13.43 ((
% 99.57/13.43 (singletonsubset) =>
% 99.57/13.43 ((
% 99.57/13.43 (singletoninpowerset) =>
% 99.57/13.43 ((
% 99.57/13.43 (singletoninpowunion) =>
% 99.57/13.43 ((
% 99.57/13.43 (upairset2E) =>
% 99.57/13.43 ((
% 99.57/13.43 (upairsubunion) =>
% 99.57/13.43 ((
% 99.57/13.43 (upairinpowunion) =>
% 99.57/13.43 ((
% 99.57/13.43 (ubforcartprodlem1) =>
% 99.57/13.43 ((
% 99.57/13.43 (ubforcartprodlem2) =>
% 99.57/13.43 ((
% 99.57/13.43 (ubforcartprodlem3) =>
% 99.57/13.43 ((
% 99.57/13.43 (cartprodpairin) =>
% 99.57/13.43 ((
% 99.57/13.43 (cartprodmempair1) =>
% 99.57/13.43 ((
% 99.57/13.43 (cartprodmempair) =>
% 99.57/13.43 ((
% 99.57/13.43 (setunionE2) =>
% 99.57/13.43 ((
% 99.57/13.43 (setunionsingleton1) =>
% 99.57/13.43 ((
% 99.57/13.43 (setunionsingleton2) =>
% 99.57/13.43 ((
% 99.57/13.43 (setunionsingleton) =>
% 99.57/13.43 ((
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% 99.57/13.43 ((
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% 99.57/13.43 ((
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% 99.57/13.43 ((
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% 99.57/13.43 ((
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% 99.57/13.43 ((
% 99.57/13.43 (kfstpairEq) =>
% 99.57/13.43 ((
% 99.57/13.43 (cartprodfstin) =>
% 99.57/13.43 ((
% 99.57/13.43 (setukpairinjL2) =>
% 99.57/13.43 ((
% 99.57/13.43 (setukpairinjL) =>
% 99.57/13.43 ((
% 99.57/13.43 (setukpairinjR11) =>
% 99.57/13.43 ((
% 99.57/13.43 (setukpairinjR12) =>
% 99.57/13.43 ((
% 99.57/13.43 (setukpairinjR1) =>
% 99.57/13.43 ((
% 99.57/13.43 (upairequniteq) =>
% 99.57/13.43 ((
% 99.57/13.43 (setukpairinjR2) =>
% 99.57/13.43 ((
% 99.57/13.43 (setukpairinjR) =>
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% 99.57/13.43 ((
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% 99.57/13.43 ((
% 99.57/13.43 (kpairsurjEq) =>
% 99.57/13.43 ((
% 99.57/13.43 (cartprodsndin) =>
% 99.57/13.43 ((
% 99.57/13.43 (cartprodpairmemEL) =>
% 99.57/13.43 ((
% 99.57/13.43 (cartprodpairmemER) =>
% 99.57/13.43 ((
% 99.57/13.43 (cartprodmempaircEq) =>
% 99.57/13.43 ((
% 99.57/13.43 (cartprodfstpairEq) =>
% 99.57/13.43 ((
% 99.57/13.43 (cartprodsndpairEq) =>
% 99.57/13.44 ((
% 99.57/13.44 (cartprodpairsurjEq) =>
% 99.57/13.44 ((
% 99.57/13.44 (dpsetconstrI) =>
% 99.57/13.44 ((
% 99.57/13.44 (dpsetconstrSub) =>
% 99.57/13.44 ((
% 99.57/13.44 (setOfPairsIsBReln) =>
% 99.57/13.44 ((
% 99.57/13.44 (dpsetconstrERa) =>
% 99.57/13.44 ((
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% 99.57/13.44 ((
% 99.57/13.44 (dpsetconstrEL2) =>
% 99.57/13.44 ((
% 99.57/13.44 (dpsetconstrER) =>
% 99.57/13.44 ((
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% 99.57/13.44 ((
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% 99.57/13.44 ((
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% 99.57/13.44 ((
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% 99.57/13.44 ((
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% 99.57/13.44 ((
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% 99.57/13.44 ((
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% 99.57/13.44 ((
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% 99.57/13.44 ((
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% 99.57/13.44 ((
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% 99.57/13.44 ((
% 99.57/13.44 (funcGraphProp3) =>
% 99.57/13.44 ((
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% 99.57/13.44 ((
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% 99.57/13.44 ((
% 99.57/13.44 (funcGraphProp4) =>
% 99.57/13.44 ((
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% 99.57/13.44 ((
% 99.57/13.44 (eqbreln) =>
% 99.57/13.44 ((
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% 99.57/13.44 ((
% 99.57/13.44 (funcext2) =>
% 99.57/13.44 ((
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% 99.57/13.44 ((
% 99.57/13.44 (ap2apEq2) =>
% 99.57/13.44 ((
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% 99.57/13.44 ((
% 99.57/13.44 (eta1) =>
% 99.57/13.44 ((
% 99.57/13.44 (lam2lamEq) =>
% 99.57/13.44 ((
% 99.57/13.44 (beta2) =>
% 99.57/13.44 ((
% 99.57/13.44 (eta2) =>
% 99.57/13.44 ((
% 99.57/13.44 (iffalseProp1) =>
% 99.57/13.44 ((
% 99.57/13.44 (iffalseProp2) =>
% 99.57/13.44 ((
% 99.57/13.44 (iftrueProp1) =>
% 99.57/13.44 ((
% 99.57/13.44 (iftrueProp2) =>
% 99.57/13.44 ((
% 99.57/13.44 (ifSingleton) =>
% 99.57/13.44 ((
% 99.57/13.44 (ifp) =>
% 99.57/13.44 ((
% 99.57/13.44 (theeq) =>
% 99.57/13.44 ((
% 99.57/13.44 (iftrue) =>
% 99.57/13.44 ((
% 99.57/13.44 (iffalse) =>
% 99.57/13.44 ((
% 99.57/13.44 (iftrueorfalse) =>
% 99.57/13.44 ((
% 99.57/13.44 (binintersectT_lem) =>
% 99.57/13.44 ((
% 99.57/13.44 (binunionT_lem) =>
% 99.57/13.44 ((
% 99.57/13.44 (powersetT_lem) =>
% 99.57/13.44 ((
% 99.57/13.44 (setminusT_lem) =>
% 99.57/13.44 ((
% 99.57/13.44 (complementT_lem) =>
% 99.57/13.44 ((
% 99.57/13.44 (setextT) =>
% 99.57/13.44 ((
% 99.57/13.44 (subsetTI) =>
% 99.57/13.44 ((
% 99.57/13.44 (powersetTI1) =>
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% 99.57/13.44 ((
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% 99.57/13.44 (((binintersectRsub) =>
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% 99.57/13.44 (cartprodpairmemER) =>
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% 99.57/13.44 (cartprodpairsurjEq) =>
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% 99.57/13.44 (dpsetconstrER) =>
% 99.57/13.44 ((
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% 99.57/13.44 ((
% 99.57/13.44 (apProp) =>
% 99.57/13.44 ((
% 99.57/13.44 (app) =>
% 99.57/13.44 ((
% 99.57/13.44 (infuncsetfunc) =>
% 99.57/13.44 ((
% 99.57/13.44 (ap2p) =>
% 99.57/13.44 ((
% 99.57/13.44 (funcinfuncset) =>
% 99.57/13.44 ((
% 99.57/13.44 (lamProp) =>
% 99.57/13.44 ((
% 99.57/13.44 (lamp) =>
% 99.57/13.44 ((
% 99.57/13.44 (lam2p) =>
% 99.57/13.44 ((
% 99.57/13.44 (brelnall1) =>
% 99.57/13.44 ((
% 99.57/13.44 (brelnall2) =>
% 99.57/13.44 ((
% 99.57/13.44 (ex1E2) =>
% 99.57/13.44 ((
% 99.57/13.44 (funcGraphProp1) =>
% 99.57/13.44 ((
% 99.57/13.44 (funcGraphProp3) =>
% 99.57/13.44 ((
% 99.57/13.44 (funcGraphProp2) =>
% 99.57/13.44 ((
% 99.57/13.44 (funcextLem) =>
% 99.57/13.44 ((
% 99.57/13.44 (funcGraphProp4) =>
% 99.57/13.44 ((
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% 99.57/13.44 ((
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% 99.57/13.44 (funcext2) =>
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% 99.57/13.44 (ap2apEq2) =>
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% 99.57/13.44 ((
% 99.57/13.44 (eta1) =>
% 99.57/13.44 ((
% 99.57/13.44 (lam2lamEq) =>
% 99.57/13.44 ((
% 99.57/13.44 (beta2) =>
% 99.57/13.44 ((
% 99.57/13.44 (eta2) =>
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% 99.57/13.44 (iffalseProp2) =>
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% 99.57/13.44 ((
% 99.57/13.44 (iftrueProp2) =>
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% 99.57/13.44 ((
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% 99.57/13.44 ((
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% 99.57/13.44 ((
% 99.57/13.44 (binintersectTERcontra) =>
% 99.57/13.44 ((
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% 99.57/13.44 (contrasubsetT1) =>
% 99.57/13.44 ((
% 99.57/13.44 (contrasubsetT2) =>
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% 99.57/13.44 (contrasubsetT3) =>
% 99.57/13.44 ((
% 99.57/13.44 (doubleComplementI1) =>
% 99.57/13.44 ((
% 99.57/13.44 (doubleComplementE1) =>
% 99.57/13.44 ((
% 99.57/13.44 (doubleComplementSub1) =>
% 99.57/13.44 ((
% 99.57/13.44 (doubleComplementSub2) =>
% 99.57/13.44 ((
% 99.57/13.44 (doubleComplementEq) =>
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% 99.57/13.44 (complementTnotintersectT) =>
% 99.57/13.44 ((
% 99.57/13.44 (complementImpComplementIntersect) =>
% 99.57/13.44 ((
% 99.57/13.44 (complementSubsetComplementIntersect) =>
% 99.57/13.44 ((
% 99.57/13.44 (complementInPowersetComplementIntersect) =>
% 99.57/13.44 ((
% 99.57/13.44 (contraSubsetComplement) =>
% 99.57/13.44 ((
% 99.57/13.44 (complementTcontraSubset) =>
% 99.57/13.44 ((
% 99.57/13.44 (binunionTILcontra) =>
% 99.57/13.44 ((
% 99.57/13.44 (binunionTIRcontra) =>
% 99.57/13.44 ((
% 99.57/13.44 (inIntersectImpInUnion) =>
% 99.57/13.44 ((
% 99.57/13.44 (inIntersectImpInUnion2) =>
% 99.57/13.44 ((
% 99.57/13.44 (inIntersectImpInIntersectUnions) =>
% 99.57/13.44 ((
% 99.57/13.44 (intersectInPowersetIntersectUnions) =>
% 99.57/13.44 ((
% 99.57/13.44 (inComplementUnionImpNotIn1) =>
% 99.57/13.44 ((
% 99.57/13.44 (inComplementUnionImpInComplement1) =>
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% 99.57/13.44 (binunionTE) =>
% 99.57/13.44 ((
% 99.57/13.44 (binunionTEcontra) =>
% 99.57/13.44 ((
% 99.57/13.44 (demorgan2a1) =>
% 99.57/13.44 ((
% 99.57/13.44 (complementUnionInPowersetComplement) =>
% 99.57/13.44 ((
% 99.57/13.44 (demorgan2a2) =>
% 99.57/13.44 ((
% 99.57/13.44 (demorgan1a) =>
% 99.57/13.44 ((
% 99.57/13.44 (demorgan1b) =>
% 99.57/13.44 ((
% 99.57/13.44 (demorgan1) =>
% 99.57/13.44 ((
% 99.57/13.44 (demorgan2a) =>
% 99.57/13.44 ((
% 99.57/13.44 (demorgan2b2) =>
% 99.57/13.44 ((
% 99.57/13.44 (demorgan2b) =>
% 99.57/13.44 ((
% 99.57/13.44 (demorgan2) =>
% 99.57/13.44 ((
% 99.57/13.44 (woz13rule0) =>
% 99.57/13.44 ((
% 99.57/13.44 (woz13rule1) =>
% 99.57/13.44 ((
% 99.57/13.44 (woz13rule2) =>
% 99.57/13.44 ((
% 99.57/13.44 (woz13rule3) =>
% 99.57/13.44 ((
% 99.57/13.44 (woz13rule4) =>
% 99.57/13.44 ((
% 99.57/13.44 (woz1_1) =>
% 99.57/13.44 ((
% 99.57/13.44 (woz1_2) =>
% 99.57/13.44 ((
% 99.57/13.44 (woz1_3) =>
% 99.57/13.44 ((
% 99.57/13.44 (woz1_4) =>
% 99.57/13.44 ((
% 99.57/13.44 (woz1_5) =>
% 99.57/13.44 ((
% 99.57/13.44 (breln1all2) =>
% 99.57/13.44 ((
% 99.57/13.44 (breln1SetBreln1) =>
% 99.57/13.44 ((
% 99.57/13.44 (choice2fnsingleton) =>
% 99.57/13.44 ((
% 99.57/13.44 (setOfPairsIsBReln1) =>
% 99.57/13.44 ((
% 99.57/13.44 (breln1all1) =>
% 99.57/13.44 ((
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% 99.57/13.44 ((
% 99.57/13.44 (eqbreln1) =>
% 99.57/13.44 ((
% 99.57/13.44 (breln1invprop) =>
% 99.57/13.44 ((
% 99.57/13.44 (breln1invI) =>
% 99.57/13.44 ((
% 99.57/13.44 (breln1invE) =>
% 99.57/13.44 ((
% 99.57/13.44 (breln1compprop) =>
% 99.57/13.44 ((
% 99.57/13.44 (breln1compI) =>
% 99.57/13.44 ((
% 99.57/13.44 (breln1compE) =>
% 99.57/13.44 ((
% 99.57/13.44 (breln1compEex) =>
% 99.57/13.44 ((
% 99.57/13.44 (breln1unionprop) =>
% 99.57/13.44 ((
% 99.57/13.44 (breln1unionIL) =>
% 99.57/13.44 ((
% 99.57/13.44 (breln1unionIR) =>
% 99.57/13.44 ((
% 99.57/13.44 (breln1unionI) =>
% 99.57/13.44 ((
% 99.57/13.44 (breln1unionE) =>
% 99.57/13.44 ((
% 99.57/13.44 (breln1unionEcases) =>
% 99.57/13.44 ((
% 99.57/13.44 (breln1unionCommutes) =>
% 99.57/13.44 ((
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% 99.57/13.44 ((
% 99.57/13.44 (woz2W) =>
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% 99.57/13.44 ((
% 99.57/13.44 (image1Ex1) =>
% 99.57/13.44 ((
% 99.57/13.44 (image1Equiv) =>
% 99.57/13.44 ((
% 99.57/13.44 (image1E) =>
% 99.57/13.44 ((
% 99.57/13.44 (image1I) =>
% 99.57/13.44 ((
% 99.57/13.44 (injFuncInInjFuncSet) =>
% 99.57/13.44 ((
% 99.57/13.44 (injFuncSetFuncIn) =>
% 99.57/13.44 ((
% 99.57/13.44 (injFuncSetFuncInj) =>
% 99.57/13.44 ((
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% 99.57/13.44 (
% 99.57/13.44 (
% 99.57/13.44 ('#B') @ (
% 99.57/13.44 (
% 99.57/13.44 ('#B') @ (
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% 99.57/13.44 (
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% 99.57/13.44 (
% 99.57/13.44 (
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% 99.57/13.44 (
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% 99.57/13.44 surjFuncSet)))))))) @
% 99.57/13.44 (
% 99.57/13.44 (
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% 99.57/13.44 (
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% 99.57/13.44 (
% 99.57/13.44 ('#C') @ in)))) @
% 99.57/13.44 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.57/13.44 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1158])).
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% 99.57/13.44 ((
% 99.57/13.44 (upairsubunion) =>
% 99.57/13.44 ((
% 99.57/13.44 (upairinpowunion) =>
% 99.57/13.44 ((
% 99.57/13.44 (ubforcartprodlem1) =>
% 99.57/13.44 ((
% 99.57/13.44 (ubforcartprodlem2) =>
% 99.57/13.44 ((
% 99.57/13.44 (ubforcartprodlem3) =>
% 99.57/13.44 ((
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% 99.57/13.44 ((
% 99.57/13.44 (cartprodmempair1) =>
% 99.57/13.44 ((
% 99.57/13.44 (cartprodmempair) =>
% 99.57/13.44 ((
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% 99.57/13.44 ((
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% 99.57/13.44 ((
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% 99.57/13.44 ((
% 99.57/13.44 (setunionsingleton) =>
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% 99.57/13.44 ((
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% 99.57/13.44 ((
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% 99.57/13.44 ((
% 99.57/13.44 (setukpairinjL2) =>
% 99.57/13.44 ((
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% 99.57/13.44 ((
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% 99.57/13.44 ((
% 99.57/13.44 (setukpairinjR12) =>
% 99.57/13.44 ((
% 99.57/13.44 (setukpairinjR1) =>
% 99.57/13.44 ((
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% 99.57/13.44 ((
% 99.57/13.44 (setukpairinjR2) =>
% 99.57/13.44 ((
% 99.57/13.44 (setukpairinjR) =>
% 99.57/13.44 ((
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% 99.57/13.44 ((
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% 99.57/13.44 ((
% 99.57/13.44 (kpairsurjEq) =>
% 99.57/13.44 ((
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% 99.57/13.44 ((
% 99.57/13.44 (cartprodpairmemEL) =>
% 99.57/13.44 ((
% 99.57/13.44 (cartprodpairmemER) =>
% 99.57/13.44 ((
% 99.57/13.44 (cartprodmempaircEq) =>
% 99.57/13.44 ((
% 99.57/13.44 (cartprodfstpairEq) =>
% 99.57/13.44 ((
% 99.57/13.44 (cartprodsndpairEq) =>
% 99.57/13.44 ((
% 99.57/13.44 (cartprodpairsurjEq) =>
% 99.57/13.44 ((
% 99.57/13.44 (dpsetconstrI) =>
% 99.57/13.44 ((
% 99.57/13.44 (dpsetconstrSub) =>
% 99.57/13.44 ((
% 99.57/13.44 (setOfPairsIsBReln) =>
% 99.57/13.44 ((
% 99.57/13.44 (dpsetconstrERa) =>
% 99.57/13.44 ((
% 99.57/13.44 (dpsetconstrEL1) =>
% 99.57/13.44 ((
% 99.57/13.44 (dpsetconstrEL2) =>
% 99.57/13.44 ((
% 99.57/13.44 (dpsetconstrER) =>
% 99.57/13.44 ((
% 99.57/13.44 (funcImageSingleton) =>
% 99.57/13.44 ((
% 99.57/13.44 (apProp) =>
% 99.57/13.44 ((
% 99.57/13.44 (app) =>
% 99.57/13.44 ((
% 99.57/13.44 (infuncsetfunc) =>
% 99.57/13.44 ((
% 99.57/13.44 (ap2p) =>
% 99.57/13.44 ((
% 99.57/13.44 (funcinfuncset) =>
% 99.57/13.44 ((
% 99.57/13.44 (lamProp) =>
% 99.57/13.44 ((
% 99.57/13.44 (lamp) =>
% 99.57/13.44 ((
% 99.57/13.44 (lam2p) =>
% 99.57/13.44 ((
% 99.57/13.44 (brelnall1) =>
% 99.57/13.44 ((
% 99.57/13.44 (brelnall2) =>
% 99.57/13.44 ((
% 99.57/13.44 (ex1E2) =>
% 99.57/13.44 ((
% 99.57/13.44 (funcGraphProp1) =>
% 99.57/13.44 ((
% 99.57/13.44 (funcGraphProp3) =>
% 99.57/13.44 ((
% 99.57/13.44 (funcGraphProp2) =>
% 99.57/13.44 ((
% 99.57/13.44 (funcextLem) =>
% 99.57/13.44 ((
% 99.57/13.44 (funcGraphProp4) =>
% 99.57/13.44 ((
% 99.57/13.44 (subbreln) =>
% 99.57/13.44 ((
% 99.57/13.44 (eqbreln) =>
% 99.57/13.44 ((
% 99.57/13.44 (funcext) =>
% 99.57/13.44 ((
% 99.57/13.44 (funcext2) =>
% 99.57/13.44 ((
% 99.57/13.44 (ap2apEq1) =>
% 99.57/13.44 ((
% 99.57/13.44 (ap2apEq2) =>
% 99.57/13.44 ((
% 99.57/13.44 (beta1) =>
% 99.57/13.44 ((
% 99.57/13.44 (eta1) =>
% 99.57/13.44 ((
% 99.57/13.44 (lam2lamEq) =>
% 99.57/13.44 ((
% 99.57/13.44 (beta2) =>
% 99.57/13.44 ((
% 99.57/13.44 (eta2) =>
% 99.57/13.44 ((
% 99.57/13.44 (iffalseProp1) =>
% 99.57/13.44 ((
% 99.57/13.44 (iffalseProp2) =>
% 99.57/13.44 ((
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% 99.57/13.44 ((
% 99.57/13.44 (iftrueProp2) =>
% 99.57/13.44 ((
% 99.57/13.44 (ifSingleton) =>
% 99.57/13.44 ((
% 99.57/13.44 (ifp) =>
% 99.57/13.44 ((
% 99.57/13.44 (theeq) =>
% 99.57/13.44 ((
% 99.57/13.44 (iftrue) =>
% 99.57/13.44 ((
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% 99.57/13.44 (iftrueorfalse) =>
% 99.57/13.44 ((
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% 99.57/13.44 ((
% 99.57/13.44 (binunionT_lem) =>
% 99.57/13.44 ((
% 99.57/13.44 (powersetT_lem) =>
% 99.57/13.44 ((
% 99.57/13.44 (setminusT_lem) =>
% 99.57/13.44 ((
% 99.57/13.44 (complementT_lem) =>
% 99.57/13.44 ((
% 99.57/13.44 (setextT) =>
% 99.57/13.44 ((
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% 99.57/13.44 ((
% 99.57/13.44 (powersetTI1) =>
% 99.57/13.44 ((
% 99.57/13.44 (powersetTE1) =>
% 99.57/13.44 ((
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% 99.57/13.44 ((
% 99.57/13.44 (complementTE1) =>
% 99.57/13.44 ((
% 99.57/13.44 (binintersectTELcontra) =>
% 99.57/13.44 ((
% 99.57/13.44 (binintersectTERcontra) =>
% 99.57/13.44 ((
% 99.57/13.44 (contrasubsetT) =>
% 99.57/13.44 ((
% 99.57/13.44 (contrasubsetT1) =>
% 99.57/13.44 ((
% 99.57/13.44 (contrasubsetT2) =>
% 99.57/13.44 ((
% 99.57/13.44 (contrasubsetT3) =>
% 99.57/13.44 ((
% 99.57/13.44 (doubleComplementI1) =>
% 99.57/13.44 ((
% 99.57/13.44 (doubleComplementE1) =>
% 99.57/13.44 ((
% 99.57/13.44 (doubleComplementSub1) =>
% 99.57/13.44 ((
% 99.57/13.44 (doubleComplementSub2) =>
% 99.57/13.44 ((
% 99.57/13.44 (doubleComplementEq) =>
% 99.57/13.44 ((
% 99.57/13.44 (complementTnotintersectT) =>
% 99.57/13.44 ((
% 99.57/13.44 (complementImpComplementIntersect) =>
% 99.57/13.44 ((
% 99.57/13.44 (complementSubsetComplementIntersect) =>
% 99.57/13.44 ((
% 99.57/13.44 (complementInPowersetComplementIntersect) =>
% 99.57/13.44 ((
% 99.57/13.44 (contraSubsetComplement) =>
% 99.57/13.44 ((
% 99.57/13.44 (complementTcontraSubset) =>
% 99.57/13.44 ((
% 99.57/13.44 (binunionTILcontra) =>
% 99.57/13.44 ((
% 99.57/13.44 (binunionTIRcontra) =>
% 99.57/13.44 ((
% 99.57/13.44 (inIntersectImpInUnion) =>
% 99.57/13.44 ((
% 99.57/13.44 (inIntersectImpInUnion2) =>
% 99.57/13.44 ((
% 99.57/13.44 (inIntersectImpInIntersectUnions) =>
% 99.57/13.44 ((
% 99.57/13.44 (intersectInPowersetIntersectUnions) =>
% 99.57/13.44 ((
% 99.57/13.44 (inComplementUnionImpNotIn1) =>
% 99.57/13.44 ((
% 99.57/13.44 (inComplementUnionImpInComplement1) =>
% 99.57/13.44 ((
% 99.57/13.44 (binunionTE) =>
% 99.57/13.44 ((
% 99.57/13.44 (binunionTEcontra) =>
% 99.57/13.44 ((
% 99.57/13.44 (demorgan2a1) =>
% 99.57/13.44 ((
% 99.57/13.44 (complementUnionInPowersetComplement) =>
% 99.57/13.44 ((
% 99.57/13.44 (demorgan2a2) =>
% 99.57/13.44 ((
% 99.57/13.44 (demorgan1a) =>
% 99.57/13.44 ((
% 99.57/13.44 (demorgan1b) =>
% 99.57/13.44 ((
% 99.57/13.44 (demorgan1) =>
% 99.57/13.44 ((
% 99.57/13.44 (demorgan2a) =>
% 99.57/13.44 ((
% 99.57/13.44 (demorgan2b2) =>
% 99.57/13.44 ((
% 99.57/13.44 (demorgan2b) =>
% 99.57/13.44 ((
% 99.57/13.44 (demorgan2) =>
% 99.57/13.44 ((
% 99.57/13.44 (woz13rule0) =>
% 99.57/13.44 ((
% 99.57/13.44 (woz13rule1) =>
% 99.57/13.44 ((
% 99.57/13.44 (woz13rule2) =>
% 99.57/13.44 ((
% 99.57/13.44 (woz13rule3) =>
% 99.57/13.44 ((
% 99.57/13.44 (woz13rule4) =>
% 99.57/13.44 ((
% 99.57/13.44 (woz1_1) =>
% 99.57/13.44 ((
% 99.57/13.44 (woz1_2) =>
% 99.57/13.44 ((
% 99.57/13.44 (woz1_3) =>
% 99.57/13.44 ((
% 99.57/13.44 (woz1_4) =>
% 99.57/13.44 ((
% 99.57/13.44 (woz1_5) =>
% 99.57/13.44 ((
% 99.57/13.44 (breln1all2) =>
% 99.57/13.44 ((
% 99.57/13.44 (breln1SetBreln1) =>
% 99.57/13.44 ((
% 99.57/13.44 (choice2fnsingleton) =>
% 99.57/13.44 ((
% 99.57/13.44 (setOfPairsIsBReln1) =>
% 99.57/13.44 ((
% 99.57/13.44 (breln1all1) =>
% 99.57/13.44 ((
% 99.57/13.44 (subbreln1) =>
% 99.57/13.44 ((
% 99.57/13.44 (eqbreln1) =>
% 99.57/13.44 ((
% 99.57/13.44 (breln1invprop) =>
% 99.57/13.44 ((
% 99.57/13.44 (breln1invI) =>
% 99.57/13.44 ((
% 99.57/13.44 (breln1invE) =>
% 99.57/13.44 ((
% 99.57/13.44 (breln1compprop) =>
% 99.57/13.44 ((
% 99.57/13.44 (breln1compI) =>
% 99.57/13.44 ((
% 99.57/13.44 (breln1compE) =>
% 99.57/13.44 ((
% 99.57/13.44 (breln1compEex) =>
% 99.57/13.44 ((
% 99.57/13.44 (breln1unionprop) =>
% 99.57/13.44 ((
% 99.57/13.44 (breln1unionIL) =>
% 99.57/13.44 ((
% 99.57/13.44 (breln1unionIR) =>
% 99.57/13.44 ((
% 99.57/13.44 (breln1unionI) =>
% 99.57/13.44 ((
% 99.57/13.44 (breln1unionE) =>
% 99.57/13.44 ((
% 99.57/13.44 (breln1unionEcases) =>
% 99.57/13.44 ((
% 99.57/13.44 (breln1unionCommutes) =>
% 99.57/13.44 ((
% 99.57/13.44 (woz2Ex) =>
% 99.57/13.44 ((
% 99.57/13.44 (woz2W) =>
% 99.57/13.44 ((
% 99.57/13.44 (woz2A) =>
% 99.57/13.44 ((
% 99.57/13.44 (woz2B) =>
% 99.57/13.44 ((
% 99.57/13.44 (image1Ex) =>
% 99.57/13.44 ((
% 99.57/13.44 (image1Ex1) =>
% 99.57/13.44 ((
% 99.57/13.44 (image1Equiv) =>
% 99.57/13.44 ((
% 99.57/13.44 (image1E) =>
% 99.57/13.44 ((
% 99.57/13.44 (image1I) =>
% 99.57/13.44 ((
% 99.57/13.44 (injFuncInInjFuncSet) =>
% 99.57/13.44 ((
% 99.57/13.44 (injFuncSetFuncIn) =>
% 99.57/13.44 ((
% 99.57/13.44 (injFuncSetFuncInj) =>
% 99.57/13.44 ((
% 99.57/13.44 (!!) @ (
% 99.57/13.44 (('#B') @ (
% 99.57/13.44 !!) @
% 99.57/13.44 (
% 99.57/13.44 (
% 99.57/13.44 ('#B') @ (
% 99.57/13.44 (
% 99.57/13.44 ('#B') @ (
% 99.57/13.44 !!))) @
% 99.57/13.44 (
% 99.57/13.44 (
% 99.57/13.44 ('#S') @ (
% 99.57/13.44 (
% 99.57/13.44 ('#B') @ (
% 99.57/13.44 '#S') @
% 99.57/13.44 (
% 99.57/13.44 (
% 99.57/13.44 ('#B') @ (
% 99.57/13.44 (
% 99.57/13.44 ('#B') @ (
% 99.57/13.44 '#S'))) @
% 99.57/13.44 (
% 99.57/13.44 (
% 99.57/13.44 ('#B') @ (
% 99.57/13.44 (
% 99.57/13.44 ('#B') @ (
% 99.57/13.44 (
% 99.57/13.44 ('#B') @ (
% 99.57/13.44 =>))))) @
% 99.57/13.44 (
% 99.57/13.44 (
% 99.57/13.44 ('#B') @ (
% 99.57/13.44 (
% 99.57/13.44 ('#B') @ (
% 99.57/13.44 (
% 99.57/13.44 ('#C') @ in)))) @
% 99.57/13.44 surjFuncSet)))))))) @
% 99.57/13.44 (
% 99.57/13.44 (
% 99.57/13.44 ('#B') @ (
% 99.57/13.44 (
% 99.57/13.44 ('#B') @ (
% 99.57/13.44 (
% 99.57/13.44 ('#C') @ in)))) @
% 99.57/13.44 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.57/13.44 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1166])).
% 99.57/13.44 thf(zip_derived_cl1183, plain,
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% 99.57/13.44 (((binintersectER) =>
% 99.57/13.44 (((disjointsetsI1) =>
% 99.57/13.44 (((binintersectRsub) =>
% 99.57/13.44 (((binintersectSubset4) =>
% 99.57/13.44 (((binintersectSubset1) =>
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% 99.57/13.44 (((setminusI) =>
% 99.57/13.44 (((setminusEL) =>
% 99.57/13.44 (((setminusER) =>
% 99.57/13.44 (((setminusSubset2) =>
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% 99.57/13.44 (((setminusELneg) =>
% 99.57/13.44 (((setminusILneg) =>
% 99.57/13.44 (((setminusIRneg) =>
% 99.57/13.44 (((setminusLsub) =>
% 99.57/13.44 (((setminusSubset1) =>
% 99.57/13.44 (((symdiffE) =>
% 99.57/13.44 (((symdiffI1) =>
% 99.57/13.44 (((symdiffI2) =>
% 99.57/13.44 (((symdiffIneg1) =>
% 99.57/13.44 (((symdiffIneg2) =>
% 99.57/13.44 (((secondinupair) =>
% 99.57/13.44 (((setukpairIL) =>
% 99.57/13.44 (((setukpairIR) =>
% 99.57/13.44 (((kpairiskpair) =>
% 99.57/13.44 (((kpairp) =>
% 99.57/13.44 (((singletonsubset) =>
% 99.57/13.44 (((singletoninpowerset) =>
% 99.57/13.44 (((singletoninpowunion) =>
% 99.57/13.44 ((
% 99.57/13.44 (upairset2E) =>
% 99.57/13.44 ((
% 99.57/13.44 (upairsubunion) =>
% 99.57/13.44 ((
% 99.57/13.44 (upairinpowunion) =>
% 99.57/13.44 ((
% 99.57/13.44 (ubforcartprodlem1) =>
% 99.57/13.44 ((
% 99.57/13.44 (ubforcartprodlem2) =>
% 99.57/13.44 ((
% 99.57/13.44 (ubforcartprodlem3) =>
% 99.57/13.44 ((
% 99.57/13.44 (cartprodpairin) =>
% 99.57/13.44 ((
% 99.57/13.44 (cartprodmempair1) =>
% 99.57/13.44 ((
% 99.57/13.44 (cartprodmempair) =>
% 99.57/13.44 ((
% 99.57/13.44 (setunionE2) =>
% 99.57/13.44 ((
% 99.57/13.44 (setunionsingleton1) =>
% 99.57/13.44 ((
% 99.57/13.44 (setunionsingleton2) =>
% 99.57/13.44 ((
% 99.57/13.44 (setunionsingleton) =>
% 99.57/13.44 ((
% 99.57/13.44 (singletonprop) =>
% 99.57/13.44 ((
% 99.57/13.44 (ex1E1) =>
% 99.57/13.44 ((
% 99.57/13.44 (ex1I) =>
% 99.57/13.44 ((
% 99.57/13.44 (ex1I2) =>
% 99.57/13.44 ((
% 99.57/13.44 (singletonsuniq) =>
% 99.57/13.44 ((
% 99.57/13.44 (setukpairinjL1) =>
% 99.57/13.44 ((
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% 99.57/13.44 ((
% 99.57/13.44 (theprop) =>
% 99.57/13.44 ((
% 99.57/13.44 (kfstpairEq) =>
% 99.57/13.44 ((
% 99.57/13.44 (cartprodfstin) =>
% 99.57/13.44 ((
% 99.57/13.44 (setukpairinjL2) =>
% 99.57/13.44 ((
% 99.57/13.44 (setukpairinjL) =>
% 99.57/13.44 ((
% 99.57/13.44 (setukpairinjR11) =>
% 99.57/13.44 ((
% 99.57/13.44 (setukpairinjR12) =>
% 99.57/13.44 ((
% 99.57/13.44 (setukpairinjR1) =>
% 99.57/13.44 ((
% 99.57/13.44 (upairequniteq) =>
% 99.57/13.44 ((
% 99.57/13.44 (setukpairinjR2) =>
% 99.57/13.44 ((
% 99.57/13.44 (setukpairinjR) =>
% 99.57/13.44 ((
% 99.57/13.44 (ksndsingleton) =>
% 99.57/13.44 ((
% 99.57/13.44 (ksndpairEq) =>
% 99.57/13.44 ((
% 99.57/13.44 (kpairsurjEq) =>
% 99.57/13.44 ((
% 99.57/13.44 (cartprodsndin) =>
% 99.57/13.44 ((
% 99.57/13.44 (cartprodpairmemEL) =>
% 99.57/13.44 ((
% 99.57/13.44 (cartprodpairmemER) =>
% 99.57/13.44 ((
% 99.57/13.44 (cartprodmempaircEq) =>
% 99.57/13.44 ((
% 99.57/13.44 (cartprodfstpairEq) =>
% 99.57/13.44 ((
% 99.57/13.44 (cartprodsndpairEq) =>
% 99.57/13.44 ((
% 99.57/13.44 (cartprodpairsurjEq) =>
% 99.57/13.44 ((
% 99.57/13.44 (dpsetconstrI) =>
% 99.57/13.44 ((
% 99.57/13.44 (dpsetconstrSub) =>
% 99.57/13.44 ((
% 99.57/13.44 (setOfPairsIsBReln) =>
% 99.57/13.44 ((
% 99.57/13.44 (dpsetconstrERa) =>
% 99.57/13.44 ((
% 99.57/13.44 (dpsetconstrEL1) =>
% 99.57/13.44 ((
% 99.57/13.44 (dpsetconstrEL2) =>
% 99.57/13.44 ((
% 99.57/13.44 (dpsetconstrER) =>
% 99.57/13.44 ((
% 99.57/13.44 (funcImageSingleton) =>
% 99.57/13.44 ((
% 99.57/13.44 (apProp) =>
% 99.57/13.44 ((
% 99.57/13.44 (app) =>
% 99.57/13.44 ((
% 99.57/13.44 (infuncsetfunc) =>
% 99.57/13.44 ((
% 99.57/13.44 (ap2p) =>
% 99.57/13.44 ((
% 99.57/13.44 (funcinfuncset) =>
% 99.57/13.44 ((
% 99.57/13.44 (lamProp) =>
% 99.57/13.44 ((
% 99.57/13.44 (lamp) =>
% 99.57/13.44 ((
% 99.57/13.44 (lam2p) =>
% 99.57/13.44 ((
% 99.57/13.44 (brelnall1) =>
% 99.57/13.44 ((
% 99.57/13.44 (brelnall2) =>
% 99.57/13.44 ((
% 99.57/13.44 (ex1E2) =>
% 99.57/13.44 ((
% 99.57/13.44 (funcGraphProp1) =>
% 99.57/13.44 ((
% 99.57/13.44 (funcGraphProp3) =>
% 99.57/13.44 ((
% 99.57/13.44 (funcGraphProp2) =>
% 99.57/13.44 ((
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% 99.57/13.44 ((
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% 99.57/13.44 ((
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% 99.57/13.44 ((
% 99.57/13.44 (eqbreln) =>
% 99.57/13.44 ((
% 99.57/13.44 (funcext) =>
% 99.57/13.44 ((
% 99.57/13.44 (funcext2) =>
% 99.57/13.44 ((
% 99.57/13.44 (ap2apEq1) =>
% 99.57/13.44 ((
% 99.57/13.44 (ap2apEq2) =>
% 99.57/13.44 ((
% 99.57/13.44 (beta1) =>
% 99.57/13.44 ((
% 99.57/13.44 (eta1) =>
% 99.57/13.44 ((
% 99.57/13.44 (lam2lamEq) =>
% 99.57/13.44 ((
% 99.57/13.44 (beta2) =>
% 99.57/13.44 ((
% 99.57/13.44 (eta2) =>
% 99.57/13.44 ((
% 99.57/13.44 (iffalseProp1) =>
% 99.57/13.44 ((
% 99.57/13.44 (iffalseProp2) =>
% 99.57/13.44 ((
% 99.57/13.44 (iftrueProp1) =>
% 99.57/13.44 ((
% 99.57/13.44 (iftrueProp2) =>
% 99.57/13.44 ((
% 99.57/13.44 (ifSingleton) =>
% 99.57/13.44 ((
% 99.57/13.44 (ifp) =>
% 99.57/13.44 ((
% 99.57/13.44 (theeq) =>
% 99.57/13.44 ((
% 99.57/13.44 (iftrue) =>
% 99.57/13.44 ((
% 99.57/13.44 (iffalse) =>
% 99.57/13.44 ((
% 99.57/13.44 (iftrueorfalse) =>
% 99.57/13.44 ((
% 99.57/13.44 (binintersectT_lem) =>
% 99.57/13.44 ((
% 99.57/13.44 (binunionT_lem) =>
% 99.57/13.44 ((
% 99.57/13.44 (powersetT_lem) =>
% 99.57/13.44 ((
% 99.57/13.44 (setminusT_lem) =>
% 99.57/13.44 ((
% 99.57/13.44 (complementT_lem) =>
% 99.57/13.44 ((
% 99.57/13.44 (setextT) =>
% 99.57/13.44 ((
% 99.57/13.44 (subsetTI) =>
% 99.57/13.44 ((
% 99.57/13.44 (powersetTI1) =>
% 99.57/13.44 ((
% 99.57/13.44 (powersetTE1) =>
% 99.57/13.44 ((
% 99.57/13.44 (complementTI1) =>
% 99.57/13.44 ((
% 99.57/13.44 (complementTE1) =>
% 99.57/13.44 ((
% 99.57/13.44 (binintersectTELcontra) =>
% 99.57/13.44 ((
% 99.57/13.44 (binintersectTERcontra) =>
% 99.57/13.44 ((
% 99.57/13.44 (contrasubsetT) =>
% 99.57/13.44 ((
% 99.57/13.44 (contrasubsetT1) =>
% 99.57/13.44 ((
% 99.57/13.44 (contrasubsetT2) =>
% 99.57/13.44 ((
% 99.57/13.44 (contrasubsetT3) =>
% 99.57/13.44 ((
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% 99.57/13.44 ((
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% 99.57/13.44 (doubleComplementSub2) =>
% 99.57/13.44 ((
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% 99.57/13.44 ((
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% 99.57/13.44 ((
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% 99.57/13.44 ((
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% 99.57/13.44 ((
% 99.57/13.44 (demorgan1b) =>
% 99.57/13.44 ((
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% 99.57/13.44 ((
% 99.57/13.44 (demorgan2a) =>
% 99.57/13.44 ((
% 99.57/13.44 (demorgan2b2) =>
% 99.57/13.44 ((
% 99.57/13.44 (demorgan2b) =>
% 99.57/13.44 ((
% 99.57/13.44 (demorgan2) =>
% 99.57/13.44 ((
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% 99.57/13.44 ((
% 99.57/13.44 (woz13rule1) =>
% 99.57/13.44 ((
% 99.57/13.44 (woz13rule2) =>
% 99.57/13.44 ((
% 99.57/13.44 (woz13rule3) =>
% 99.57/13.44 ((
% 99.57/13.44 (woz13rule4) =>
% 99.57/13.44 ((
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% 99.57/13.44 ((
% 99.57/13.44 (woz1_2) =>
% 99.57/13.44 ((
% 99.57/13.44 (woz1_3) =>
% 99.57/13.44 ((
% 99.57/13.44 (woz1_4) =>
% 99.57/13.44 ((
% 99.57/13.44 (woz1_5) =>
% 99.57/13.44 ((
% 99.57/13.44 (breln1all2) =>
% 99.57/13.44 ((
% 99.57/13.44 (breln1SetBreln1) =>
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% 99.57/13.44 ((
% 99.57/13.44 (setOfPairsIsBReln1) =>
% 99.57/13.44 ((
% 99.57/13.44 (breln1all1) =>
% 99.57/13.44 ((
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% 99.57/13.44 ((
% 99.57/13.44 (eqbreln1) =>
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% 99.57/13.44 ((
% 99.57/13.44 (breln1invI) =>
% 99.57/13.44 ((
% 99.57/13.44 (breln1invE) =>
% 99.57/13.44 ((
% 99.57/13.44 (breln1compprop) =>
% 99.57/13.44 ((
% 99.57/13.44 (breln1compI) =>
% 99.57/13.44 ((
% 99.57/13.44 (breln1compE) =>
% 99.57/13.44 ((
% 99.57/13.44 (breln1compEex) =>
% 99.57/13.44 ((
% 99.57/13.44 (breln1unionprop) =>
% 99.57/13.44 ((
% 99.57/13.44 (breln1unionIL) =>
% 99.57/13.44 ((
% 99.57/13.44 (breln1unionIR) =>
% 99.57/13.44 ((
% 99.57/13.44 (breln1unionI) =>
% 99.57/13.44 ((
% 99.57/13.44 (breln1unionE) =>
% 99.57/13.44 ((
% 99.57/13.44 (breln1unionEcases) =>
% 99.57/13.44 ((
% 99.57/13.44 (breln1unionCommutes) =>
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% 99.57/13.44 ((
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% 99.57/13.44 ((
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% 99.57/13.44 ((
% 99.57/13.44 (woz2B) =>
% 99.57/13.44 ((
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% 99.57/13.44 ((
% 99.57/13.44 (image1Ex1) =>
% 99.57/13.44 ((
% 99.57/13.44 (image1Equiv) =>
% 99.57/13.44 ((
% 99.57/13.44 (image1E) =>
% 99.57/13.44 ((
% 99.57/13.44 (image1I) =>
% 99.57/13.44 ((
% 99.57/13.44 (injFuncInInjFuncSet) =>
% 99.57/13.44 ((
% 99.57/13.44 (injFuncSetFuncIn) =>
% 99.57/13.44 ((
% 99.57/13.44 (injFuncSetFuncInj) =>
% 99.57/13.44 ((
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% 99.57/13.44 (('#B') @ (
% 99.57/13.44 !!) @
% 99.57/13.44 (
% 99.57/13.44 (
% 99.57/13.44 ('#B') @ (
% 99.57/13.44 (
% 99.57/13.44 ('#B') @ (
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% 99.57/13.44 (
% 99.57/13.44 (
% 99.57/13.44 ('#S') @ (
% 99.57/13.44 (
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% 99.57/13.44 (
% 99.57/13.44 (
% 99.57/13.44 ('#B') @ (
% 99.57/13.44 (
% 99.57/13.44 ('#B') @ (
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% 99.57/13.44 (
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% 99.57/13.44 (
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% 99.57/13.44 (
% 99.57/13.44 (
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% 99.57/13.44 (
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% 99.57/13.44 surjFuncSet)))))))) @
% 99.57/13.44 (
% 99.57/13.44 (
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% 99.57/13.44 (
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% 99.57/13.44 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.57/13.44 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1174])).
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% 99.57/13.44 (((setminusSubset1) =>
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% 99.57/13.44 ((
% 99.57/13.44 (upairsubunion) =>
% 99.57/13.44 ((
% 99.57/13.44 (upairinpowunion) =>
% 99.57/13.44 ((
% 99.57/13.44 (ubforcartprodlem1) =>
% 99.57/13.44 ((
% 99.57/13.44 (ubforcartprodlem2) =>
% 99.57/13.44 ((
% 99.57/13.44 (ubforcartprodlem3) =>
% 99.57/13.44 ((
% 99.57/13.44 (cartprodpairin) =>
% 99.57/13.44 ((
% 99.57/13.44 (cartprodmempair1) =>
% 99.57/13.44 ((
% 99.57/13.44 (cartprodmempair) =>
% 99.57/13.44 ((
% 99.57/13.44 (setunionE2) =>
% 99.57/13.44 ((
% 99.57/13.44 (setunionsingleton1) =>
% 99.57/13.44 ((
% 99.57/13.44 (setunionsingleton2) =>
% 99.57/13.44 ((
% 99.57/13.44 (setunionsingleton) =>
% 99.57/13.44 ((
% 99.57/13.44 (singletonprop) =>
% 99.57/13.44 ((
% 99.57/13.44 (ex1E1) =>
% 99.57/13.44 ((
% 99.57/13.44 (ex1I) =>
% 99.57/13.44 ((
% 99.57/13.44 (ex1I2) =>
% 99.57/13.44 ((
% 99.57/13.44 (singletonsuniq) =>
% 99.57/13.44 ((
% 99.57/13.44 (setukpairinjL1) =>
% 99.57/13.44 ((
% 99.57/13.44 (kfstsingleton) =>
% 99.57/13.44 ((
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% 99.57/13.44 ((
% 99.57/13.44 (kfstpairEq) =>
% 99.57/13.44 ((
% 99.57/13.44 (cartprodfstin) =>
% 99.57/13.44 ((
% 99.57/13.44 (setukpairinjL2) =>
% 99.57/13.44 ((
% 99.57/13.44 (setukpairinjL) =>
% 99.57/13.44 ((
% 99.57/13.44 (setukpairinjR11) =>
% 99.57/13.44 ((
% 99.57/13.44 (setukpairinjR12) =>
% 99.57/13.44 ((
% 99.57/13.44 (setukpairinjR1) =>
% 99.57/13.44 ((
% 99.57/13.44 (upairequniteq) =>
% 99.57/13.44 ((
% 99.57/13.44 (setukpairinjR2) =>
% 99.57/13.44 ((
% 99.57/13.44 (setukpairinjR) =>
% 99.57/13.44 ((
% 99.57/13.44 (ksndsingleton) =>
% 99.57/13.44 ((
% 99.57/13.44 (ksndpairEq) =>
% 99.57/13.44 ((
% 99.57/13.44 (kpairsurjEq) =>
% 99.57/13.44 ((
% 99.57/13.44 (cartprodsndin) =>
% 99.57/13.44 ((
% 99.57/13.44 (cartprodpairmemEL) =>
% 99.57/13.44 ((
% 99.57/13.44 (cartprodpairmemER) =>
% 99.57/13.44 ((
% 99.57/13.44 (cartprodmempaircEq) =>
% 99.57/13.44 ((
% 99.57/13.44 (cartprodfstpairEq) =>
% 99.57/13.44 ((
% 99.57/13.44 (cartprodsndpairEq) =>
% 99.57/13.44 ((
% 99.57/13.44 (cartprodpairsurjEq) =>
% 99.57/13.44 ((
% 99.57/13.44 (dpsetconstrI) =>
% 99.57/13.44 ((
% 99.57/13.44 (dpsetconstrSub) =>
% 99.57/13.44 ((
% 99.57/13.44 (setOfPairsIsBReln) =>
% 99.57/13.44 ((
% 99.57/13.44 (dpsetconstrERa) =>
% 99.57/13.44 ((
% 99.57/13.44 (dpsetconstrEL1) =>
% 99.57/13.44 ((
% 99.57/13.44 (dpsetconstrEL2) =>
% 99.57/13.44 ((
% 99.57/13.44 (dpsetconstrER) =>
% 99.57/13.44 ((
% 99.57/13.44 (funcImageSingleton) =>
% 99.57/13.44 ((
% 99.57/13.44 (apProp) =>
% 99.57/13.44 ((
% 99.57/13.44 (app) =>
% 99.57/13.44 ((
% 99.57/13.44 (infuncsetfunc) =>
% 99.57/13.44 ((
% 99.57/13.44 (ap2p) =>
% 99.57/13.44 ((
% 99.57/13.44 (funcinfuncset) =>
% 99.57/13.44 ((
% 99.57/13.44 (lamProp) =>
% 99.57/13.44 ((
% 99.57/13.44 (lamp) =>
% 99.57/13.44 ((
% 99.57/13.44 (lam2p) =>
% 99.57/13.44 ((
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% 99.57/13.44 ((
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% 99.57/13.44 ((
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% 99.57/13.44 ((
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% 99.57/13.44 ((
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% 99.57/13.44 ((
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% 99.57/13.44 ((
% 99.57/13.44 (funcext2) =>
% 99.57/13.44 ((
% 99.57/13.44 (ap2apEq1) =>
% 99.57/13.44 ((
% 99.57/13.44 (ap2apEq2) =>
% 99.57/13.44 ((
% 99.57/13.44 (beta1) =>
% 99.57/13.44 ((
% 99.57/13.44 (eta1) =>
% 99.57/13.44 ((
% 99.57/13.44 (lam2lamEq) =>
% 99.57/13.44 ((
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% 99.57/13.44 ((
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% 99.57/13.44 ((
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% 99.57/13.44 ((
% 99.57/13.44 (iffalseProp2) =>
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% 99.57/13.44 (iftrueProp1) =>
% 99.57/13.44 ((
% 99.57/13.44 (iftrueProp2) =>
% 99.57/13.44 ((
% 99.57/13.44 (ifSingleton) =>
% 99.57/13.44 ((
% 99.57/13.44 (ifp) =>
% 99.57/13.44 ((
% 99.57/13.44 (theeq) =>
% 99.57/13.44 ((
% 99.57/13.44 (iftrue) =>
% 99.57/13.44 ((
% 99.57/13.44 (iffalse) =>
% 99.57/13.44 ((
% 99.57/13.44 (iftrueorfalse) =>
% 99.57/13.44 ((
% 99.57/13.44 (binintersectT_lem) =>
% 99.57/13.44 ((
% 99.57/13.44 (binunionT_lem) =>
% 99.57/13.44 ((
% 99.57/13.44 (powersetT_lem) =>
% 99.57/13.44 ((
% 99.57/13.44 (setminusT_lem) =>
% 99.57/13.44 ((
% 99.57/13.44 (complementT_lem) =>
% 99.57/13.44 ((
% 99.57/13.44 (setextT) =>
% 99.57/13.44 ((
% 99.57/13.44 (subsetTI) =>
% 99.57/13.44 ((
% 99.57/13.44 (powersetTI1) =>
% 99.57/13.44 ((
% 99.57/13.44 (powersetTE1) =>
% 99.57/13.44 ((
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% 99.57/13.44 ((
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% 99.57/13.44 ((
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% 99.57/13.44 ((
% 99.57/13.44 (binintersectTERcontra) =>
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% 99.57/13.44 ((
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% 99.57/13.44 ((
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% 99.57/13.44 ((
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% 99.57/13.44 ((
% 99.57/13.44 (doubleComplementSub2) =>
% 99.57/13.44 ((
% 99.57/13.44 (doubleComplementEq) =>
% 99.57/13.44 ((
% 99.57/13.44 (complementTnotintersectT) =>
% 99.57/13.44 ((
% 99.57/13.44 (complementImpComplementIntersect) =>
% 99.57/13.44 ((
% 99.57/13.44 (complementSubsetComplementIntersect) =>
% 99.57/13.44 ((
% 99.57/13.44 (complementInPowersetComplementIntersect) =>
% 99.57/13.44 ((
% 99.57/13.44 (contraSubsetComplement) =>
% 99.57/13.44 ((
% 99.57/13.44 (complementTcontraSubset) =>
% 99.57/13.44 ((
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% 99.57/13.44 ((
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% 99.57/13.44 ((
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% 99.57/13.44 ((
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% 99.57/13.44 ((
% 99.57/13.44 (inComplementUnionImpInComplement1) =>
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% 99.57/13.44 ((
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% 99.57/13.44 ((
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% 99.57/13.44 ((
% 99.57/13.44 (complementUnionInPowersetComplement) =>
% 99.57/13.44 ((
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% 99.57/13.44 ((
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% 99.57/13.44 ((
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% 99.57/13.44 ((
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% 99.57/13.44 ((
% 99.57/13.44 (ubforcartprodlem3) =>
% 99.57/13.44 ((
% 99.57/13.44 (cartprodpairin) =>
% 99.57/13.44 ((
% 99.57/13.44 (cartprodmempair1) =>
% 99.57/13.44 ((
% 99.57/13.44 (cartprodmempair) =>
% 99.57/13.44 ((
% 99.57/13.44 (setunionE2) =>
% 99.57/13.44 ((
% 99.57/13.44 (setunionsingleton1) =>
% 99.57/13.44 ((
% 99.57/13.44 (setunionsingleton2) =>
% 99.57/13.44 ((
% 99.57/13.44 (setunionsingleton) =>
% 99.57/13.44 ((
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% 99.57/13.44 ((
% 99.57/13.44 (ex1E1) =>
% 99.57/13.44 ((
% 99.57/13.44 (ex1I) =>
% 99.57/13.44 ((
% 99.57/13.44 (ex1I2) =>
% 99.57/13.44 ((
% 99.57/13.44 (singletonsuniq) =>
% 99.57/13.44 ((
% 99.57/13.44 (setukpairinjL1) =>
% 99.57/13.44 ((
% 99.57/13.44 (kfstsingleton) =>
% 99.57/13.44 ((
% 99.57/13.44 (theprop) =>
% 99.57/13.44 ((
% 99.57/13.44 (kfstpairEq) =>
% 99.57/13.44 ((
% 99.57/13.44 (cartprodfstin) =>
% 99.57/13.44 ((
% 99.57/13.44 (setukpairinjL2) =>
% 99.57/13.44 ((
% 99.57/13.44 (setukpairinjL) =>
% 99.57/13.44 ((
% 99.57/13.44 (setukpairinjR11) =>
% 99.57/13.44 ((
% 99.57/13.44 (setukpairinjR12) =>
% 99.57/13.44 ((
% 99.57/13.44 (setukpairinjR1) =>
% 99.57/13.44 ((
% 99.57/13.44 (upairequniteq) =>
% 99.57/13.44 ((
% 99.57/13.44 (setukpairinjR2) =>
% 99.57/13.44 ((
% 99.57/13.44 (setukpairinjR) =>
% 99.57/13.44 ((
% 99.57/13.44 (ksndsingleton) =>
% 99.57/13.44 ((
% 99.57/13.44 (ksndpairEq) =>
% 99.57/13.44 ((
% 99.57/13.44 (kpairsurjEq) =>
% 99.57/13.44 ((
% 99.57/13.44 (cartprodsndin) =>
% 99.57/13.44 ((
% 99.57/13.44 (cartprodpairmemEL) =>
% 99.57/13.44 ((
% 99.57/13.44 (cartprodpairmemER) =>
% 99.57/13.44 ((
% 99.57/13.44 (cartprodmempaircEq) =>
% 99.57/13.44 ((
% 99.57/13.44 (cartprodfstpairEq) =>
% 99.57/13.44 ((
% 99.57/13.44 (cartprodsndpairEq) =>
% 99.57/13.44 ((
% 99.57/13.44 (cartprodpairsurjEq) =>
% 99.57/13.44 ((
% 99.57/13.44 (dpsetconstrI) =>
% 99.57/13.44 ((
% 99.57/13.44 (dpsetconstrSub) =>
% 99.57/13.44 ((
% 99.57/13.44 (setOfPairsIsBReln) =>
% 99.57/13.44 ((
% 99.57/13.44 (dpsetconstrERa) =>
% 99.57/13.44 ((
% 99.57/13.44 (dpsetconstrEL1) =>
% 99.57/13.44 ((
% 99.57/13.44 (dpsetconstrEL2) =>
% 99.57/13.44 ((
% 99.57/13.44 (dpsetconstrER) =>
% 99.57/13.44 ((
% 99.57/13.44 (funcImageSingleton) =>
% 99.57/13.44 ((
% 99.57/13.44 (apProp) =>
% 99.57/13.44 ((
% 99.57/13.44 (app) =>
% 99.57/13.44 ((
% 99.57/13.44 (infuncsetfunc) =>
% 99.57/13.44 ((
% 99.57/13.44 (ap2p) =>
% 99.57/13.44 ((
% 99.57/13.44 (funcinfuncset) =>
% 99.57/13.44 ((
% 99.57/13.44 (lamProp) =>
% 99.57/13.44 ((
% 99.57/13.44 (lamp) =>
% 99.57/13.44 ((
% 99.57/13.44 (lam2p) =>
% 99.57/13.44 ((
% 99.57/13.44 (brelnall1) =>
% 99.57/13.44 ((
% 99.57/13.44 (brelnall2) =>
% 99.57/13.44 ((
% 99.57/13.44 (ex1E2) =>
% 99.57/13.44 ((
% 99.57/13.44 (funcGraphProp1) =>
% 99.57/13.44 ((
% 99.57/13.44 (funcGraphProp3) =>
% 99.57/13.44 ((
% 99.57/13.44 (funcGraphProp2) =>
% 99.57/13.44 ((
% 99.57/13.44 (funcextLem) =>
% 99.57/13.44 ((
% 99.57/13.44 (funcGraphProp4) =>
% 99.57/13.44 ((
% 99.57/13.44 (subbreln) =>
% 99.57/13.44 ((
% 99.57/13.44 (eqbreln) =>
% 99.57/13.44 ((
% 99.57/13.44 (funcext) =>
% 99.57/13.44 ((
% 99.57/13.44 (funcext2) =>
% 99.57/13.44 ((
% 99.57/13.44 (ap2apEq1) =>
% 99.57/13.44 ((
% 99.57/13.44 (ap2apEq2) =>
% 99.57/13.44 ((
% 99.57/13.44 (beta1) =>
% 99.57/13.44 ((
% 99.57/13.44 (eta1) =>
% 99.57/13.44 ((
% 99.57/13.44 (lam2lamEq) =>
% 99.57/13.44 ((
% 99.57/13.44 (beta2) =>
% 99.57/13.44 ((
% 99.57/13.44 (eta2) =>
% 99.57/13.44 ((
% 99.57/13.44 (iffalseProp1) =>
% 99.57/13.44 ((
% 99.57/13.44 (iffalseProp2) =>
% 99.57/13.44 ((
% 99.57/13.44 (iftrueProp1) =>
% 99.57/13.44 ((
% 99.57/13.44 (iftrueProp2) =>
% 99.57/13.44 ((
% 99.57/13.44 (ifSingleton) =>
% 99.57/13.44 ((
% 99.57/13.44 (ifp) =>
% 99.57/13.44 ((
% 99.57/13.44 (theeq) =>
% 99.57/13.44 ((
% 99.57/13.44 (iftrue) =>
% 99.57/13.44 ((
% 99.57/13.44 (iffalse) =>
% 99.57/13.44 ((
% 99.57/13.44 (iftrueorfalse) =>
% 99.57/13.44 ((
% 99.57/13.44 (binintersectT_lem) =>
% 99.57/13.44 ((
% 99.57/13.44 (binunionT_lem) =>
% 99.57/13.44 ((
% 99.57/13.44 (powersetT_lem) =>
% 99.57/13.44 ((
% 99.57/13.44 (setminusT_lem) =>
% 99.57/13.44 ((
% 99.57/13.44 (complementT_lem) =>
% 99.57/13.44 ((
% 99.57/13.44 (setextT) =>
% 99.57/13.44 ((
% 99.57/13.44 (subsetTI) =>
% 99.57/13.44 ((
% 99.57/13.44 (powersetTI1) =>
% 99.57/13.44 ((
% 99.57/13.44 (powersetTE1) =>
% 99.57/13.44 ((
% 99.57/13.44 (complementTI1) =>
% 99.57/13.44 ((
% 99.57/13.44 (complementTE1) =>
% 99.57/13.44 ((
% 99.57/13.44 (binintersectTELcontra) =>
% 99.57/13.44 ((
% 99.57/13.44 (binintersectTERcontra) =>
% 99.57/13.44 ((
% 99.57/13.44 (contrasubsetT) =>
% 99.57/13.44 ((
% 99.57/13.44 (contrasubsetT1) =>
% 99.57/13.44 ((
% 99.57/13.44 (contrasubsetT2) =>
% 99.57/13.44 ((
% 99.57/13.44 (contrasubsetT3) =>
% 99.57/13.44 ((
% 99.57/13.44 (doubleComplementI1) =>
% 99.57/13.44 ((
% 99.57/13.44 (doubleComplementE1) =>
% 99.57/13.44 ((
% 99.57/13.44 (doubleComplementSub1) =>
% 99.57/13.44 ((
% 99.57/13.44 (doubleComplementSub2) =>
% 99.57/13.44 ((
% 99.57/13.44 (doubleComplementEq) =>
% 99.57/13.44 ((
% 99.57/13.44 (complementTnotintersectT) =>
% 99.57/13.44 ((
% 99.57/13.44 (complementImpComplementIntersect) =>
% 99.57/13.44 ((
% 99.57/13.44 (complementSubsetComplementIntersect) =>
% 99.57/13.44 ((
% 99.57/13.44 (complementInPowersetComplementIntersect) =>
% 99.57/13.44 ((
% 99.57/13.44 (contraSubsetComplement) =>
% 99.57/13.44 ((
% 99.57/13.44 (complementTcontraSubset) =>
% 99.57/13.44 ((
% 99.57/13.44 (binunionTILcontra) =>
% 99.57/13.44 ((
% 99.57/13.44 (binunionTIRcontra) =>
% 99.57/13.44 ((
% 99.57/13.44 (inIntersectImpInUnion) =>
% 99.57/13.44 ((
% 99.57/13.44 (inIntersectImpInUnion2) =>
% 99.57/13.44 ((
% 99.57/13.44 (inIntersectImpInIntersectUnions) =>
% 99.57/13.44 ((
% 99.57/13.44 (intersectInPowersetIntersectUnions) =>
% 99.57/13.44 ((
% 99.57/13.44 (inComplementUnionImpNotIn1) =>
% 99.57/13.44 ((
% 99.57/13.44 (inComplementUnionImpInComplement1) =>
% 99.57/13.44 ((
% 99.57/13.44 (binunionTE) =>
% 99.57/13.44 ((
% 99.57/13.44 (binunionTEcontra) =>
% 99.57/13.44 ((
% 99.57/13.44 (demorgan2a1) =>
% 99.57/13.44 ((
% 99.57/13.44 (complementUnionInPowersetComplement) =>
% 99.57/13.44 ((
% 99.57/13.44 (demorgan2a2) =>
% 99.57/13.44 ((
% 99.57/13.44 (demorgan1a) =>
% 99.57/13.44 ((
% 99.57/13.44 (demorgan1b) =>
% 99.57/13.44 ((
% 99.57/13.44 (demorgan1) =>
% 99.57/13.44 ((
% 99.57/13.44 (demorgan2a) =>
% 99.57/13.44 ((
% 99.57/13.44 (demorgan2b2) =>
% 99.57/13.44 ((
% 99.57/13.44 (demorgan2b) =>
% 99.57/13.44 ((
% 99.57/13.44 (demorgan2) =>
% 99.57/13.44 ((
% 99.57/13.44 (woz13rule0) =>
% 99.57/13.44 ((
% 99.57/13.44 (woz13rule1) =>
% 99.57/13.44 ((
% 99.57/13.44 (woz13rule2) =>
% 99.57/13.44 ((
% 99.57/13.44 (woz13rule3) =>
% 99.57/13.44 ((
% 99.57/13.44 (woz13rule4) =>
% 99.57/13.44 ((
% 99.57/13.44 (woz1_1) =>
% 99.57/13.44 ((
% 99.57/13.44 (woz1_2) =>
% 99.57/13.44 ((
% 99.57/13.44 (woz1_3) =>
% 99.57/13.44 ((
% 99.57/13.44 (woz1_4) =>
% 99.57/13.44 ((
% 99.57/13.44 (woz1_5) =>
% 99.57/13.44 ((
% 99.57/13.44 (breln1all2) =>
% 99.57/13.44 ((
% 99.57/13.44 (breln1SetBreln1) =>
% 99.57/13.44 ((
% 99.57/13.44 (choice2fnsingleton) =>
% 99.57/13.44 ((
% 99.57/13.44 (setOfPairsIsBReln1) =>
% 99.57/13.44 ((
% 99.57/13.44 (breln1all1) =>
% 99.57/13.44 ((
% 99.57/13.44 (subbreln1) =>
% 99.57/13.44 ((
% 99.57/13.44 (eqbreln1) =>
% 99.57/13.44 ((
% 99.57/13.44 (breln1invprop) =>
% 99.57/13.44 ((
% 99.57/13.44 (breln1invI) =>
% 99.57/13.44 ((
% 99.57/13.44 (breln1invE) =>
% 99.57/13.44 ((
% 99.57/13.44 (breln1compprop) =>
% 99.57/13.44 ((
% 99.57/13.44 (breln1compI) =>
% 99.57/13.44 ((
% 99.57/13.44 (breln1compE) =>
% 99.57/13.44 ((
% 99.57/13.44 (breln1compEex) =>
% 99.57/13.44 ((
% 99.57/13.44 (breln1unionprop) =>
% 99.57/13.44 ((
% 99.57/13.44 (breln1unionIL) =>
% 99.57/13.44 ((
% 99.57/13.44 (breln1unionIR) =>
% 99.57/13.44 ((
% 99.57/13.44 (breln1unionI) =>
% 99.57/13.44 ((
% 99.57/13.44 (breln1unionE) =>
% 99.57/13.44 ((
% 99.57/13.44 (breln1unionEcases) =>
% 99.57/13.44 ((
% 99.57/13.44 (breln1unionCommutes) =>
% 99.57/13.44 ((
% 99.57/13.44 (woz2Ex) =>
% 99.57/13.44 ((
% 99.57/13.44 (woz2W) =>
% 99.57/13.44 ((
% 99.57/13.44 (woz2A) =>
% 99.57/13.44 ((
% 99.57/13.44 (woz2B) =>
% 99.57/13.44 ((
% 99.57/13.44 (image1Ex) =>
% 99.57/13.44 ((
% 99.57/13.44 (image1Ex1) =>
% 99.57/13.44 ((
% 99.57/13.44 (image1Equiv) =>
% 99.57/13.44 ((
% 99.57/13.44 (image1E) =>
% 99.57/13.44 ((
% 99.57/13.44 (image1I) =>
% 99.57/13.44 ((
% 99.57/13.44 (injFuncInInjFuncSet) =>
% 99.57/13.44 ((
% 99.57/13.44 (injFuncSetFuncIn) =>
% 99.57/13.44 ((
% 99.57/13.44 (injFuncSetFuncInj) =>
% 99.57/13.44 ((
% 99.57/13.44 (!!) @ (
% 99.57/13.44 (('#B') @ (
% 99.57/13.44 !!) @
% 99.57/13.44 (
% 99.57/13.44 (
% 99.57/13.44 ('#B') @ (
% 99.57/13.44 (
% 99.57/13.44 ('#B') @ (
% 99.57/13.44 !!))) @
% 99.57/13.44 (
% 99.57/13.44 (
% 99.57/13.44 ('#S') @ (
% 99.57/13.44 (
% 99.57/13.44 ('#B') @ (
% 99.57/13.44 '#S') @
% 99.57/13.44 (
% 99.57/13.44 (
% 99.57/13.44 ('#B') @ (
% 99.57/13.44 (
% 99.57/13.44 ('#B') @ (
% 99.57/13.44 '#S'))) @
% 99.57/13.44 (
% 99.57/13.44 (
% 99.57/13.44 ('#B') @ (
% 99.57/13.44 (
% 99.57/13.44 ('#B') @ (
% 99.57/13.44 (
% 99.57/13.44 ('#B') @ (
% 99.57/13.44 =>))))) @
% 99.57/13.44 (
% 99.57/13.44 (
% 99.57/13.44 ('#B') @ (
% 99.57/13.44 (
% 99.57/13.44 ('#B') @ (
% 99.57/13.44 (
% 99.57/13.44 ('#C') @ in)))) @
% 99.57/13.44 surjFuncSet)))))))) @
% 99.57/13.44 (
% 99.57/13.44 (
% 99.57/13.44 ('#B') @ (
% 99.57/13.44 (
% 99.57/13.44 ('#B') @ (
% 99.57/13.44 (
% 99.57/13.44 ('#C') @ in)))) @
% 99.57/13.44 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.57/13.44 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1206])).
% 99.57/13.44 thf(zip_derived_cl1223, plain,
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% 99.57/13.44 (((binintersectSubset1) =>
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% 99.57/13.44 (((setminusER) =>
% 99.57/13.44 (((setminusSubset2) =>
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% 99.57/13.44 (((setminusELneg) =>
% 99.57/13.44 (((setminusILneg) =>
% 99.57/13.44 (((setminusIRneg) =>
% 99.57/13.44 (((setminusLsub) =>
% 99.57/13.44 (((setminusSubset1) =>
% 99.57/13.44 (((symdiffE) =>
% 99.57/13.44 (((symdiffI1) =>
% 99.57/13.44 (((symdiffI2) =>
% 99.57/13.44 (((symdiffIneg1) =>
% 99.57/13.44 (((symdiffIneg2) =>
% 99.57/13.44 (((secondinupair) =>
% 99.57/13.44 (((setukpairIL) =>
% 99.57/13.44 (((setukpairIR) =>
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% 99.57/13.44 (((kpairp) =>
% 99.57/13.44 (((singletonsubset) =>
% 99.57/13.44 (((singletoninpowerset) =>
% 99.57/13.44 (((singletoninpowunion) =>
% 99.57/13.44 (((upairset2E) =>
% 99.57/13.44 (((upairsubunion) =>
% 99.57/13.44 (((upairinpowunion) =>
% 99.57/13.44 (((ubforcartprodlem1) =>
% 99.57/13.44 ((
% 99.57/13.44 (ubforcartprodlem2) =>
% 99.57/13.44 ((
% 99.57/13.44 (ubforcartprodlem3) =>
% 99.57/13.44 ((
% 99.57/13.44 (cartprodpairin) =>
% 99.57/13.44 ((
% 99.57/13.44 (cartprodmempair1) =>
% 99.57/13.44 ((
% 99.57/13.44 (cartprodmempair) =>
% 99.57/13.44 ((
% 99.57/13.44 (setunionE2) =>
% 99.57/13.44 ((
% 99.57/13.44 (setunionsingleton1) =>
% 99.57/13.44 ((
% 99.57/13.44 (setunionsingleton2) =>
% 99.57/13.44 ((
% 99.57/13.44 (setunionsingleton) =>
% 99.57/13.44 ((
% 99.57/13.44 (singletonprop) =>
% 99.57/13.44 ((
% 99.57/13.44 (ex1E1) =>
% 99.57/13.44 ((
% 99.57/13.44 (ex1I) =>
% 99.57/13.44 ((
% 99.57/13.44 (ex1I2) =>
% 99.57/13.44 ((
% 99.57/13.44 (singletonsuniq) =>
% 99.57/13.44 ((
% 99.57/13.44 (setukpairinjL1) =>
% 99.57/13.44 ((
% 99.57/13.44 (kfstsingleton) =>
% 99.57/13.44 ((
% 99.57/13.44 (theprop) =>
% 99.57/13.44 ((
% 99.57/13.44 (kfstpairEq) =>
% 99.57/13.44 ((
% 99.57/13.44 (cartprodfstin) =>
% 99.57/13.44 ((
% 99.57/13.44 (setukpairinjL2) =>
% 99.57/13.44 ((
% 99.57/13.44 (setukpairinjL) =>
% 99.57/13.44 ((
% 99.57/13.44 (setukpairinjR11) =>
% 99.57/13.44 ((
% 99.57/13.44 (setukpairinjR12) =>
% 99.57/13.44 ((
% 99.57/13.44 (setukpairinjR1) =>
% 99.57/13.44 ((
% 99.57/13.44 (upairequniteq) =>
% 99.57/13.44 ((
% 99.57/13.44 (setukpairinjR2) =>
% 99.57/13.44 ((
% 99.57/13.44 (setukpairinjR) =>
% 99.57/13.44 ((
% 99.57/13.44 (ksndsingleton) =>
% 99.57/13.44 ((
% 99.57/13.44 (ksndpairEq) =>
% 99.57/13.44 ((
% 99.57/13.44 (kpairsurjEq) =>
% 99.57/13.44 ((
% 99.57/13.44 (cartprodsndin) =>
% 99.57/13.44 ((
% 99.57/13.44 (cartprodpairmemEL) =>
% 99.57/13.44 ((
% 99.57/13.44 (cartprodpairmemER) =>
% 99.57/13.44 ((
% 99.57/13.44 (cartprodmempaircEq) =>
% 99.57/13.44 ((
% 99.57/13.44 (cartprodfstpairEq) =>
% 99.57/13.44 ((
% 99.57/13.44 (cartprodsndpairEq) =>
% 99.57/13.44 ((
% 99.57/13.44 (cartprodpairsurjEq) =>
% 99.57/13.44 ((
% 99.57/13.44 (dpsetconstrI) =>
% 99.57/13.44 ((
% 99.57/13.44 (dpsetconstrSub) =>
% 99.57/13.44 ((
% 99.57/13.44 (setOfPairsIsBReln) =>
% 99.57/13.44 ((
% 99.57/13.44 (dpsetconstrERa) =>
% 99.57/13.44 ((
% 99.57/13.44 (dpsetconstrEL1) =>
% 99.57/13.44 ((
% 99.57/13.44 (dpsetconstrEL2) =>
% 99.57/13.44 ((
% 99.57/13.44 (dpsetconstrER) =>
% 99.57/13.44 ((
% 99.57/13.44 (funcImageSingleton) =>
% 99.57/13.44 ((
% 99.57/13.44 (apProp) =>
% 99.57/13.44 ((
% 99.57/13.44 (app) =>
% 99.57/13.44 ((
% 99.57/13.44 (infuncsetfunc) =>
% 99.57/13.44 ((
% 99.57/13.44 (ap2p) =>
% 99.57/13.44 ((
% 99.57/13.44 (funcinfuncset) =>
% 99.57/13.44 ((
% 99.57/13.44 (lamProp) =>
% 99.57/13.44 ((
% 99.57/13.44 (lamp) =>
% 99.57/13.44 ((
% 99.57/13.44 (lam2p) =>
% 99.57/13.44 ((
% 99.57/13.44 (brelnall1) =>
% 99.57/13.44 ((
% 99.57/13.44 (brelnall2) =>
% 99.57/13.44 ((
% 99.57/13.44 (ex1E2) =>
% 99.57/13.44 ((
% 99.57/13.44 (funcGraphProp1) =>
% 99.57/13.44 ((
% 99.57/13.44 (funcGraphProp3) =>
% 99.57/13.44 ((
% 99.57/13.44 (funcGraphProp2) =>
% 99.57/13.44 ((
% 99.57/13.44 (funcextLem) =>
% 99.57/13.44 ((
% 99.57/13.44 (funcGraphProp4) =>
% 99.57/13.44 ((
% 99.57/13.44 (subbreln) =>
% 99.57/13.44 ((
% 99.57/13.44 (eqbreln) =>
% 99.57/13.44 ((
% 99.57/13.44 (funcext) =>
% 99.57/13.44 ((
% 99.57/13.44 (funcext2) =>
% 99.57/13.44 ((
% 99.57/13.44 (ap2apEq1) =>
% 99.57/13.44 ((
% 99.57/13.44 (ap2apEq2) =>
% 99.57/13.44 ((
% 99.57/13.44 (beta1) =>
% 99.57/13.44 ((
% 99.57/13.44 (eta1) =>
% 99.57/13.44 ((
% 99.57/13.44 (lam2lamEq) =>
% 99.57/13.44 ((
% 99.57/13.44 (beta2) =>
% 99.57/13.44 ((
% 99.57/13.44 (eta2) =>
% 99.57/13.44 ((
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% 99.57/13.44 ((
% 99.57/13.44 (iffalseProp2) =>
% 99.57/13.44 ((
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% 99.57/13.44 ((
% 99.57/13.44 (iftrueProp2) =>
% 99.57/13.44 ((
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% 99.57/13.44 ((
% 99.57/13.44 (ifp) =>
% 99.57/13.44 ((
% 99.57/13.44 (theeq) =>
% 99.57/13.44 ((
% 99.57/13.44 (iftrue) =>
% 99.57/13.44 ((
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% 99.57/13.44 ((
% 99.57/13.44 (iftrueorfalse) =>
% 99.57/13.44 ((
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% 99.57/13.44 ((
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% 99.57/13.44 ((
% 99.57/13.44 (powersetT_lem) =>
% 99.57/13.44 ((
% 99.57/13.44 (setminusT_lem) =>
% 99.57/13.44 ((
% 99.57/13.44 (complementT_lem) =>
% 99.57/13.44 ((
% 99.57/13.44 (setextT) =>
% 99.57/13.44 ((
% 99.57/13.44 (subsetTI) =>
% 99.57/13.44 ((
% 99.57/13.44 (powersetTI1) =>
% 99.57/13.44 ((
% 99.57/13.44 (powersetTE1) =>
% 99.57/13.44 ((
% 99.57/13.44 (complementTI1) =>
% 99.57/13.44 ((
% 99.57/13.44 (complementTE1) =>
% 99.57/13.44 ((
% 99.57/13.44 (binintersectTELcontra) =>
% 99.57/13.44 ((
% 99.57/13.44 (binintersectTERcontra) =>
% 99.57/13.44 ((
% 99.57/13.44 (contrasubsetT) =>
% 99.57/13.44 ((
% 99.57/13.44 (contrasubsetT1) =>
% 99.57/13.44 ((
% 99.57/13.44 (contrasubsetT2) =>
% 99.57/13.44 ((
% 99.57/13.44 (contrasubsetT3) =>
% 99.57/13.44 ((
% 99.57/13.44 (doubleComplementI1) =>
% 99.57/13.44 ((
% 99.57/13.44 (doubleComplementE1) =>
% 99.57/13.44 ((
% 99.57/13.44 (doubleComplementSub1) =>
% 99.57/13.44 ((
% 99.57/13.44 (doubleComplementSub2) =>
% 99.57/13.44 ((
% 99.57/13.44 (doubleComplementEq) =>
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% 99.57/13.44 ((
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% 99.57/13.44 ((
% 99.57/13.44 (complementSubsetComplementIntersect) =>
% 99.57/13.44 ((
% 99.57/13.44 (complementInPowersetComplementIntersect) =>
% 99.57/13.44 ((
% 99.57/13.44 (contraSubsetComplement) =>
% 99.57/13.44 ((
% 99.57/13.44 (complementTcontraSubset) =>
% 99.57/13.44 ((
% 99.57/13.44 (binunionTILcontra) =>
% 99.57/13.44 ((
% 99.57/13.44 (binunionTIRcontra) =>
% 99.57/13.44 ((
% 99.57/13.44 (inIntersectImpInUnion) =>
% 99.57/13.44 ((
% 99.57/13.44 (inIntersectImpInUnion2) =>
% 99.57/13.44 ((
% 99.57/13.44 (inIntersectImpInIntersectUnions) =>
% 99.57/13.44 ((
% 99.57/13.44 (intersectInPowersetIntersectUnions) =>
% 99.57/13.44 ((
% 99.57/13.44 (inComplementUnionImpNotIn1) =>
% 99.57/13.44 ((
% 99.57/13.44 (inComplementUnionImpInComplement1) =>
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% 99.57/13.44 ((
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% 99.57/13.44 ((
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% 99.57/13.44 ((
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% 99.57/13.44 ((
% 99.57/13.44 (demorgan2a2) =>
% 99.57/13.44 ((
% 99.57/13.44 (demorgan1a) =>
% 99.57/13.44 ((
% 99.57/13.44 (demorgan1b) =>
% 99.57/13.44 ((
% 99.57/13.44 (demorgan1) =>
% 99.57/13.44 ((
% 99.57/13.44 (demorgan2a) =>
% 99.57/13.44 ((
% 99.57/13.44 (demorgan2b2) =>
% 99.57/13.44 ((
% 99.57/13.44 (demorgan2b) =>
% 99.57/13.44 ((
% 99.57/13.44 (demorgan2) =>
% 99.57/13.44 ((
% 99.57/13.44 (woz13rule0) =>
% 99.57/13.44 ((
% 99.57/13.44 (woz13rule1) =>
% 99.57/13.44 ((
% 99.57/13.44 (woz13rule2) =>
% 99.57/13.44 ((
% 99.57/13.44 (woz13rule3) =>
% 99.57/13.44 ((
% 99.57/13.44 (woz13rule4) =>
% 99.57/13.44 ((
% 99.57/13.44 (woz1_1) =>
% 99.57/13.44 ((
% 99.57/13.44 (woz1_2) =>
% 99.57/13.44 ((
% 99.57/13.44 (woz1_3) =>
% 99.57/13.44 ((
% 99.57/13.44 (woz1_4) =>
% 99.57/13.44 ((
% 99.57/13.44 (woz1_5) =>
% 99.57/13.44 ((
% 99.57/13.44 (breln1all2) =>
% 99.57/13.44 ((
% 99.57/13.44 (breln1SetBreln1) =>
% 99.57/13.44 ((
% 99.57/13.44 (choice2fnsingleton) =>
% 99.57/13.44 ((
% 99.57/13.44 (setOfPairsIsBReln1) =>
% 99.57/13.44 ((
% 99.57/13.44 (breln1all1) =>
% 99.57/13.44 ((
% 99.57/13.44 (subbreln1) =>
% 99.57/13.44 ((
% 99.57/13.44 (eqbreln1) =>
% 99.57/13.44 ((
% 99.57/13.44 (breln1invprop) =>
% 99.57/13.44 ((
% 99.57/13.44 (breln1invI) =>
% 99.57/13.44 ((
% 99.57/13.44 (breln1invE) =>
% 99.57/13.44 ((
% 99.57/13.44 (breln1compprop) =>
% 99.57/13.44 ((
% 99.57/13.44 (breln1compI) =>
% 99.57/13.44 ((
% 99.57/13.44 (breln1compE) =>
% 99.57/13.44 ((
% 99.57/13.44 (breln1compEex) =>
% 99.57/13.44 ((
% 99.57/13.44 (breln1unionprop) =>
% 99.57/13.44 ((
% 99.57/13.44 (breln1unionIL) =>
% 99.57/13.44 ((
% 99.57/13.44 (breln1unionIR) =>
% 99.57/13.44 ((
% 99.57/13.44 (breln1unionI) =>
% 99.57/13.44 ((
% 99.57/13.44 (breln1unionE) =>
% 99.57/13.44 ((
% 99.57/13.44 (breln1unionEcases) =>
% 99.57/13.44 ((
% 99.57/13.44 (breln1unionCommutes) =>
% 99.57/13.44 ((
% 99.57/13.44 (woz2Ex) =>
% 99.57/13.44 ((
% 99.57/13.44 (woz2W) =>
% 99.57/13.44 ((
% 99.57/13.44 (woz2A) =>
% 99.57/13.44 ((
% 99.57/13.44 (woz2B) =>
% 99.57/13.44 ((
% 99.57/13.44 (image1Ex) =>
% 99.57/13.44 ((
% 99.57/13.44 (image1Ex1) =>
% 99.57/13.44 ((
% 99.57/13.44 (image1Equiv) =>
% 99.57/13.44 ((
% 99.57/13.44 (image1E) =>
% 99.57/13.44 ((
% 99.57/13.44 (image1I) =>
% 99.57/13.44 ((
% 99.57/13.44 (injFuncInInjFuncSet) =>
% 99.57/13.44 ((
% 99.57/13.44 (injFuncSetFuncIn) =>
% 99.57/13.44 ((
% 99.57/13.44 (injFuncSetFuncInj) =>
% 99.57/13.44 ((
% 99.57/13.44 (!!) @ (
% 99.57/13.44 (('#B') @ (
% 99.57/13.44 !!) @
% 99.57/13.44 (
% 99.57/13.44 (
% 99.57/13.44 ('#B') @ (
% 99.57/13.44 (
% 99.57/13.44 ('#B') @ (
% 99.57/13.44 !!))) @
% 99.57/13.44 (
% 99.57/13.44 (
% 99.57/13.44 ('#S') @ (
% 99.57/13.44 (
% 99.57/13.44 ('#B') @ (
% 99.57/13.44 '#S') @
% 99.57/13.44 (
% 99.57/13.44 (
% 99.57/13.44 ('#B') @ (
% 99.57/13.44 (
% 99.57/13.44 ('#B') @ (
% 99.57/13.44 '#S'))) @
% 99.57/13.44 (
% 99.57/13.44 (
% 99.57/13.44 ('#B') @ (
% 99.57/13.44 (
% 99.57/13.44 ('#B') @ (
% 99.57/13.44 (
% 99.57/13.44 ('#B') @ (
% 99.57/13.44 =>))))) @
% 99.57/13.44 (
% 99.57/13.44 (
% 99.57/13.44 ('#B') @ (
% 99.57/13.44 (
% 99.57/13.44 ('#B') @ (
% 99.57/13.44 (
% 99.57/13.44 ('#C') @ in)))) @
% 99.57/13.44 surjFuncSet)))))))) @
% 99.57/13.44 (
% 99.57/13.44 (
% 99.57/13.44 ('#B') @ (
% 99.57/13.44 (
% 99.57/13.44 ('#B') @ (
% 99.57/13.44 (
% 99.57/13.44 ('#C') @ in)))) @
% 99.57/13.44 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.57/13.44 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1216])).
% 99.57/13.44 thf(zip_derived_cl1231, plain,
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% 99.57/13.44 (((setminusEL) =>
% 99.57/13.44 (((setminusER) =>
% 99.57/13.44 (((setminusSubset2) =>
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% 99.57/13.44 (((setminusELneg) =>
% 99.57/13.44 (((setminusILneg) =>
% 99.57/13.44 (((setminusIRneg) =>
% 99.57/13.44 (((setminusLsub) =>
% 99.57/13.44 (((setminusSubset1) =>
% 99.57/13.44 (((symdiffE) =>
% 99.57/13.44 (((symdiffI1) =>
% 99.57/13.44 (((symdiffI2) =>
% 99.57/13.44 (((symdiffIneg1) =>
% 99.57/13.44 (((symdiffIneg2) =>
% 99.57/13.44 (((secondinupair) =>
% 99.57/13.44 (((setukpairIL) =>
% 99.57/13.44 (((setukpairIR) =>
% 99.57/13.44 (((kpairiskpair) =>
% 99.57/13.44 (((kpairp) =>
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% 99.57/13.44 (((singletoninpowerset) =>
% 99.57/13.44 (((singletoninpowunion) =>
% 99.57/13.44 (((upairset2E) =>
% 99.57/13.44 (((upairsubunion) =>
% 99.57/13.44 (((upairinpowunion) =>
% 99.57/13.44 (((ubforcartprodlem1) =>
% 99.57/13.44 (((ubforcartprodlem2) =>
% 99.57/13.44 ((
% 99.57/13.44 (ubforcartprodlem3) =>
% 99.57/13.44 ((
% 99.57/13.44 (cartprodpairin) =>
% 99.57/13.44 ((
% 99.57/13.44 (cartprodmempair1) =>
% 99.57/13.44 ((
% 99.57/13.44 (cartprodmempair) =>
% 99.57/13.44 ((
% 99.57/13.44 (setunionE2) =>
% 99.57/13.44 ((
% 99.57/13.44 (setunionsingleton1) =>
% 99.57/13.44 ((
% 99.57/13.44 (setunionsingleton2) =>
% 99.57/13.44 ((
% 99.57/13.44 (setunionsingleton) =>
% 99.57/13.44 ((
% 99.57/13.44 (singletonprop) =>
% 99.57/13.44 ((
% 99.57/13.44 (ex1E1) =>
% 99.57/13.44 ((
% 99.57/13.44 (ex1I) =>
% 99.57/13.44 ((
% 99.57/13.44 (ex1I2) =>
% 99.57/13.44 ((
% 99.57/13.44 (singletonsuniq) =>
% 99.57/13.44 ((
% 99.57/13.44 (setukpairinjL1) =>
% 99.57/13.44 ((
% 99.57/13.44 (kfstsingleton) =>
% 99.57/13.44 ((
% 99.57/13.44 (theprop) =>
% 99.57/13.44 ((
% 99.57/13.44 (kfstpairEq) =>
% 99.57/13.44 ((
% 99.57/13.44 (cartprodfstin) =>
% 99.57/13.44 ((
% 99.57/13.44 (setukpairinjL2) =>
% 99.57/13.44 ((
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% 99.57/13.44 ((
% 99.57/13.44 (setukpairinjR11) =>
% 99.57/13.44 ((
% 99.57/13.44 (setukpairinjR12) =>
% 99.57/13.44 ((
% 99.57/13.44 (setukpairinjR1) =>
% 99.57/13.44 ((
% 99.57/13.44 (upairequniteq) =>
% 99.57/13.44 ((
% 99.57/13.44 (setukpairinjR2) =>
% 99.57/13.44 ((
% 99.57/13.44 (setukpairinjR) =>
% 99.57/13.44 ((
% 99.57/13.44 (ksndsingleton) =>
% 99.57/13.44 ((
% 99.57/13.44 (ksndpairEq) =>
% 99.57/13.44 ((
% 99.57/13.44 (kpairsurjEq) =>
% 99.57/13.44 ((
% 99.57/13.44 (cartprodsndin) =>
% 99.57/13.44 ((
% 99.57/13.44 (cartprodpairmemEL) =>
% 99.57/13.44 ((
% 99.57/13.44 (cartprodpairmemER) =>
% 99.57/13.44 ((
% 99.57/13.44 (cartprodmempaircEq) =>
% 99.57/13.44 ((
% 99.57/13.44 (cartprodfstpairEq) =>
% 99.57/13.44 ((
% 99.57/13.44 (cartprodsndpairEq) =>
% 99.57/13.44 ((
% 99.57/13.44 (cartprodpairsurjEq) =>
% 99.57/13.44 ((
% 99.57/13.44 (dpsetconstrI) =>
% 99.57/13.44 ((
% 99.57/13.44 (dpsetconstrSub) =>
% 99.57/13.44 ((
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% 99.57/13.44 ((
% 99.57/13.44 (dpsetconstrERa) =>
% 99.57/13.44 ((
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% 99.57/13.44 ((
% 99.57/13.44 (dpsetconstrEL2) =>
% 99.57/13.44 ((
% 99.57/13.44 (dpsetconstrER) =>
% 99.57/13.44 ((
% 99.57/13.44 (funcImageSingleton) =>
% 99.57/13.44 ((
% 99.57/13.44 (apProp) =>
% 99.57/13.44 ((
% 99.57/13.44 (app) =>
% 99.57/13.44 ((
% 99.57/13.44 (infuncsetfunc) =>
% 99.57/13.44 ((
% 99.57/13.44 (ap2p) =>
% 99.57/13.44 ((
% 99.57/13.44 (funcinfuncset) =>
% 99.57/13.44 ((
% 99.57/13.44 (lamProp) =>
% 99.57/13.44 ((
% 99.57/13.44 (lamp) =>
% 99.57/13.44 ((
% 99.57/13.44 (lam2p) =>
% 99.57/13.44 ((
% 99.57/13.44 (brelnall1) =>
% 99.57/13.44 ((
% 99.57/13.44 (brelnall2) =>
% 99.57/13.44 ((
% 99.57/13.44 (ex1E2) =>
% 99.57/13.44 ((
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% 99.57/13.44 ((
% 99.57/13.44 (funcGraphProp3) =>
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% 99.57/13.44 ((
% 99.57/13.44 (ap2apEq2) =>
% 99.57/13.44 ((
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% 99.57/13.44 ((
% 99.57/13.44 (eta1) =>
% 99.57/13.44 ((
% 99.57/13.44 (lam2lamEq) =>
% 99.57/13.44 ((
% 99.57/13.44 (beta2) =>
% 99.57/13.44 ((
% 99.57/13.44 (eta2) =>
% 99.57/13.44 ((
% 99.57/13.44 (iffalseProp1) =>
% 99.57/13.44 ((
% 99.57/13.44 (iffalseProp2) =>
% 99.57/13.44 ((
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% 99.57/13.44 ((
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% 99.57/13.44 ((
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% 99.57/13.44 ((
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% 99.57/13.44 ((
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% 99.57/13.44 ((
% 99.57/13.44 (iftrue) =>
% 99.57/13.44 ((
% 99.57/13.44 (iffalse) =>
% 99.57/13.44 ((
% 99.57/13.44 (iftrueorfalse) =>
% 99.57/13.44 ((
% 99.57/13.44 (binintersectT_lem) =>
% 99.57/13.44 ((
% 99.57/13.44 (binunionT_lem) =>
% 99.57/13.44 ((
% 99.57/13.44 (powersetT_lem) =>
% 99.57/13.44 ((
% 99.57/13.44 (setminusT_lem) =>
% 99.57/13.44 ((
% 99.57/13.44 (complementT_lem) =>
% 99.57/13.44 ((
% 99.57/13.44 (setextT) =>
% 99.57/13.44 ((
% 99.57/13.44 (subsetTI) =>
% 99.57/13.44 ((
% 99.57/13.44 (powersetTI1) =>
% 99.57/13.44 ((
% 99.57/13.44 (powersetTE1) =>
% 99.57/13.44 ((
% 99.57/13.44 (complementTI1) =>
% 99.57/13.44 ((
% 99.57/13.44 (complementTE1) =>
% 99.57/13.44 ((
% 99.57/13.44 (binintersectTELcontra) =>
% 99.57/13.44 ((
% 99.57/13.44 (binintersectTERcontra) =>
% 99.57/13.44 ((
% 99.57/13.44 (contrasubsetT) =>
% 99.57/13.44 ((
% 99.57/13.44 (contrasubsetT1) =>
% 99.57/13.44 ((
% 99.57/13.44 (contrasubsetT2) =>
% 99.57/13.44 ((
% 99.57/13.44 (contrasubsetT3) =>
% 99.57/13.44 ((
% 99.57/13.44 (doubleComplementI1) =>
% 99.57/13.44 ((
% 99.57/13.44 (doubleComplementE1) =>
% 99.57/13.44 ((
% 99.57/13.44 (doubleComplementSub1) =>
% 99.57/13.44 ((
% 99.57/13.44 (doubleComplementSub2) =>
% 99.57/13.44 ((
% 99.57/13.44 (doubleComplementEq) =>
% 99.57/13.44 ((
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% 99.57/13.44 ((
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% 99.57/13.44 ((
% 99.57/13.44 (complementSubsetComplementIntersect) =>
% 99.57/13.44 ((
% 99.57/13.44 (complementInPowersetComplementIntersect) =>
% 99.57/13.44 ((
% 99.57/13.44 (contraSubsetComplement) =>
% 99.57/13.44 ((
% 99.57/13.44 (complementTcontraSubset) =>
% 99.57/13.44 ((
% 99.57/13.44 (binunionTILcontra) =>
% 99.57/13.44 ((
% 99.57/13.44 (binunionTIRcontra) =>
% 99.57/13.44 ((
% 99.57/13.44 (inIntersectImpInUnion) =>
% 99.57/13.44 ((
% 99.57/13.44 (inIntersectImpInUnion2) =>
% 99.57/13.44 ((
% 99.57/13.44 (inIntersectImpInIntersectUnions) =>
% 99.57/13.44 ((
% 99.57/13.44 (intersectInPowersetIntersectUnions) =>
% 99.57/13.44 ((
% 99.57/13.44 (inComplementUnionImpNotIn1) =>
% 99.57/13.44 ((
% 99.57/13.44 (inComplementUnionImpInComplement1) =>
% 99.57/13.44 ((
% 99.57/13.44 (binunionTE) =>
% 99.57/13.44 ((
% 99.57/13.44 (binunionTEcontra) =>
% 99.57/13.44 ((
% 99.57/13.44 (demorgan2a1) =>
% 99.57/13.44 ((
% 99.57/13.44 (complementUnionInPowersetComplement) =>
% 99.57/13.44 ((
% 99.57/13.44 (demorgan2a2) =>
% 99.57/13.44 ((
% 99.57/13.44 (demorgan1a) =>
% 99.57/13.44 ((
% 99.57/13.44 (demorgan1b) =>
% 99.57/13.44 ((
% 99.57/13.44 (demorgan1) =>
% 99.57/13.44 ((
% 99.57/13.44 (demorgan2a) =>
% 99.57/13.44 ((
% 99.57/13.44 (demorgan2b2) =>
% 99.57/13.44 ((
% 99.57/13.44 (demorgan2b) =>
% 99.57/13.44 ((
% 99.57/13.44 (demorgan2) =>
% 99.57/13.44 ((
% 99.57/13.44 (woz13rule0) =>
% 99.57/13.44 ((
% 99.57/13.44 (woz13rule1) =>
% 99.57/13.44 ((
% 99.57/13.44 (woz13rule2) =>
% 99.57/13.44 ((
% 99.57/13.44 (woz13rule3) =>
% 99.57/13.44 ((
% 99.57/13.44 (woz13rule4) =>
% 99.57/13.44 ((
% 99.57/13.44 (woz1_1) =>
% 99.57/13.44 ((
% 99.57/13.44 (woz1_2) =>
% 99.57/13.44 ((
% 99.57/13.44 (woz1_3) =>
% 99.57/13.44 ((
% 99.57/13.44 (woz1_4) =>
% 99.57/13.44 ((
% 99.57/13.44 (woz1_5) =>
% 99.57/13.44 ((
% 99.57/13.44 (breln1all2) =>
% 99.57/13.44 ((
% 99.57/13.44 (breln1SetBreln1) =>
% 99.57/13.44 ((
% 99.57/13.44 (choice2fnsingleton) =>
% 99.57/13.44 ((
% 99.57/13.44 (setOfPairsIsBReln1) =>
% 99.57/13.44 ((
% 99.57/13.44 (breln1all1) =>
% 99.57/13.44 ((
% 99.57/13.44 (subbreln1) =>
% 99.57/13.44 ((
% 99.57/13.44 (eqbreln1) =>
% 99.57/13.44 ((
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% 99.57/13.44 ((
% 99.57/13.44 (breln1invI) =>
% 99.57/13.44 ((
% 99.57/13.44 (breln1invE) =>
% 99.57/13.44 ((
% 99.57/13.44 (breln1compprop) =>
% 99.57/13.44 ((
% 99.57/13.44 (breln1compI) =>
% 99.57/13.44 ((
% 99.57/13.44 (breln1compE) =>
% 99.57/13.44 ((
% 99.57/13.44 (breln1compEex) =>
% 99.57/13.44 ((
% 99.57/13.44 (breln1unionprop) =>
% 99.57/13.44 ((
% 99.57/13.44 (breln1unionIL) =>
% 99.57/13.44 ((
% 99.57/13.44 (breln1unionIR) =>
% 99.57/13.44 ((
% 99.57/13.44 (breln1unionI) =>
% 99.57/13.44 ((
% 99.57/13.44 (breln1unionE) =>
% 99.57/13.44 ((
% 99.57/13.44 (breln1unionEcases) =>
% 99.57/13.44 ((
% 99.57/13.44 (breln1unionCommutes) =>
% 99.57/13.44 ((
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% 99.57/13.44 ((
% 99.57/13.44 (woz2W) =>
% 99.57/13.44 ((
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% 99.57/13.44 ((
% 99.57/13.44 (woz2B) =>
% 99.57/13.44 ((
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% 99.57/13.44 ((
% 99.57/13.44 (image1Ex1) =>
% 99.57/13.44 ((
% 99.57/13.44 (image1Equiv) =>
% 99.57/13.44 ((
% 99.57/13.44 (image1E) =>
% 99.57/13.44 ((
% 99.57/13.44 (image1I) =>
% 99.57/13.44 ((
% 99.57/13.44 (injFuncInInjFuncSet) =>
% 99.57/13.44 ((
% 99.57/13.44 (injFuncSetFuncIn) =>
% 99.57/13.44 ((
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% 99.57/13.44 ((
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% 99.57/13.44 !!) @
% 99.57/13.44 (
% 99.57/13.44 (
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% 99.57/13.44 (
% 99.57/13.44 ('#B') @ (
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% 99.57/13.44 (
% 99.57/13.44 (
% 99.57/13.44 ('#S') @ (
% 99.57/13.44 (
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% 99.57/13.44 (
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% 99.57/13.44 (
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% 99.57/13.44 (
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% 99.57/13.44 (
% 99.57/13.44 (
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% 99.57/13.44 surjFuncSet)))))))) @
% 99.57/13.44 (
% 99.57/13.44 (
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% 99.57/13.44 (
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% 99.57/13.44 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.57/13.44 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1223])).
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% 99.57/13.44 (((setminusER) =>
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% 99.57/13.44 (((setminusILneg) =>
% 99.57/13.44 (((setminusIRneg) =>
% 99.57/13.44 (((setminusLsub) =>
% 99.57/13.44 (((setminusSubset1) =>
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% 99.57/13.44 (((symdiffI1) =>
% 99.57/13.44 (((symdiffI2) =>
% 99.57/13.44 (((symdiffIneg1) =>
% 99.57/13.44 (((symdiffIneg2) =>
% 99.57/13.44 (((secondinupair) =>
% 99.57/13.44 (((setukpairIL) =>
% 99.57/13.44 (((setukpairIR) =>
% 99.57/13.44 (((kpairiskpair) =>
% 99.57/13.44 (((kpairp) =>
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% 99.57/13.44 (((singletoninpowerset) =>
% 99.57/13.44 (((singletoninpowunion) =>
% 99.57/13.44 (((upairset2E) =>
% 99.57/13.44 (((upairsubunion) =>
% 99.57/13.44 (((upairinpowunion) =>
% 99.57/13.44 (((ubforcartprodlem1) =>
% 99.57/13.44 (((ubforcartprodlem2) =>
% 99.57/13.44 (((ubforcartprodlem3) =>
% 99.57/13.44 ((
% 99.57/13.44 (cartprodpairin) =>
% 99.57/13.44 ((
% 99.57/13.44 (cartprodmempair1) =>
% 99.57/13.44 ((
% 99.57/13.44 (cartprodmempair) =>
% 99.57/13.44 ((
% 99.57/13.44 (setunionE2) =>
% 99.57/13.44 ((
% 99.57/13.44 (setunionsingleton1) =>
% 99.57/13.44 ((
% 99.57/13.44 (setunionsingleton2) =>
% 99.57/13.44 ((
% 99.57/13.44 (setunionsingleton) =>
% 99.57/13.44 ((
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% 99.57/13.44 ((
% 99.57/13.44 (ex1E1) =>
% 99.57/13.44 ((
% 99.57/13.44 (ex1I) =>
% 99.57/13.44 ((
% 99.57/13.44 (ex1I2) =>
% 99.57/13.44 ((
% 99.57/13.44 (singletonsuniq) =>
% 99.57/13.44 ((
% 99.57/13.44 (setukpairinjL1) =>
% 99.57/13.44 ((
% 99.57/13.44 (kfstsingleton) =>
% 99.57/13.44 ((
% 99.57/13.44 (theprop) =>
% 99.57/13.44 ((
% 99.57/13.44 (kfstpairEq) =>
% 99.57/13.44 ((
% 99.57/13.44 (cartprodfstin) =>
% 99.57/13.44 ((
% 99.57/13.44 (setukpairinjL2) =>
% 99.57/13.44 ((
% 99.57/13.44 (setukpairinjL) =>
% 99.57/13.44 ((
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% 99.57/13.44 ((
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% 99.57/13.44 ((
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% 99.57/13.44 (upairequniteq) =>
% 99.57/13.44 ((
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% 99.57/13.44 ((
% 99.57/13.44 (setukpairinjR) =>
% 99.57/13.44 ((
% 99.57/13.44 (ksndsingleton) =>
% 99.57/13.44 ((
% 99.57/13.44 (ksndpairEq) =>
% 99.57/13.44 ((
% 99.57/13.44 (kpairsurjEq) =>
% 99.57/13.44 ((
% 99.57/13.44 (cartprodsndin) =>
% 99.57/13.44 ((
% 99.57/13.44 (cartprodpairmemEL) =>
% 99.57/13.44 ((
% 99.57/13.44 (cartprodpairmemER) =>
% 99.57/13.44 ((
% 99.57/13.44 (cartprodmempaircEq) =>
% 99.57/13.44 ((
% 99.57/13.44 (cartprodfstpairEq) =>
% 99.57/13.44 ((
% 99.57/13.44 (cartprodsndpairEq) =>
% 99.57/13.44 ((
% 99.57/13.44 (cartprodpairsurjEq) =>
% 99.57/13.44 ((
% 99.57/13.44 (dpsetconstrI) =>
% 99.57/13.44 ((
% 99.57/13.44 (dpsetconstrSub) =>
% 99.57/13.44 ((
% 99.57/13.44 (setOfPairsIsBReln) =>
% 99.57/13.44 ((
% 99.57/13.44 (dpsetconstrERa) =>
% 99.57/13.44 ((
% 99.57/13.44 (dpsetconstrEL1) =>
% 99.57/13.44 ((
% 99.57/13.44 (dpsetconstrEL2) =>
% 99.57/13.44 ((
% 99.57/13.44 (dpsetconstrER) =>
% 99.57/13.44 ((
% 99.57/13.44 (funcImageSingleton) =>
% 99.57/13.44 ((
% 99.57/13.44 (apProp) =>
% 99.57/13.44 ((
% 99.57/13.44 (app) =>
% 99.57/13.44 ((
% 99.57/13.44 (infuncsetfunc) =>
% 99.57/13.44 ((
% 99.57/13.44 (ap2p) =>
% 99.57/13.44 ((
% 99.57/13.44 (funcinfuncset) =>
% 99.57/13.44 ((
% 99.57/13.44 (lamProp) =>
% 99.57/13.44 ((
% 99.57/13.44 (lamp) =>
% 99.57/13.44 ((
% 99.57/13.44 (lam2p) =>
% 99.57/13.44 ((
% 99.57/13.44 (brelnall1) =>
% 99.57/13.44 ((
% 99.57/13.44 (brelnall2) =>
% 99.57/13.44 ((
% 99.57/13.44 (ex1E2) =>
% 99.57/13.44 ((
% 99.57/13.44 (funcGraphProp1) =>
% 99.57/13.44 ((
% 99.57/13.44 (funcGraphProp3) =>
% 99.57/13.44 ((
% 99.57/13.44 (funcGraphProp2) =>
% 99.57/13.44 ((
% 99.57/13.44 (funcextLem) =>
% 99.57/13.44 ((
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% 99.57/13.44 ((
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% 99.57/13.44 ((
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% 99.57/13.44 ((
% 99.57/13.44 (funcext2) =>
% 99.57/13.44 ((
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% 99.57/13.44 ((
% 99.57/13.44 (ap2apEq2) =>
% 99.57/13.44 ((
% 99.57/13.44 (beta1) =>
% 99.57/13.44 ((
% 99.57/13.44 (eta1) =>
% 99.57/13.44 ((
% 99.57/13.44 (lam2lamEq) =>
% 99.57/13.44 ((
% 99.57/13.44 (beta2) =>
% 99.57/13.44 ((
% 99.57/13.44 (eta2) =>
% 99.57/13.44 ((
% 99.57/13.44 (iffalseProp1) =>
% 99.57/13.44 ((
% 99.57/13.44 (iffalseProp2) =>
% 99.57/13.44 ((
% 99.57/13.44 (iftrueProp1) =>
% 99.57/13.44 ((
% 99.57/13.44 (iftrueProp2) =>
% 99.57/13.44 ((
% 99.57/13.44 (ifSingleton) =>
% 99.57/13.44 ((
% 99.57/13.44 (ifp) =>
% 99.57/13.44 ((
% 99.57/13.44 (theeq) =>
% 99.57/13.44 ((
% 99.57/13.44 (iftrue) =>
% 99.57/13.44 ((
% 99.57/13.44 (iffalse) =>
% 99.57/13.44 ((
% 99.57/13.44 (iftrueorfalse) =>
% 99.57/13.44 ((
% 99.57/13.44 (binintersectT_lem) =>
% 99.57/13.44 ((
% 99.57/13.44 (binunionT_lem) =>
% 99.57/13.44 ((
% 99.57/13.44 (powersetT_lem) =>
% 99.57/13.44 ((
% 99.57/13.44 (setminusT_lem) =>
% 99.57/13.44 ((
% 99.57/13.44 (complementT_lem) =>
% 99.57/13.44 ((
% 99.57/13.44 (setextT) =>
% 99.57/13.44 ((
% 99.57/13.44 (subsetTI) =>
% 99.57/13.44 ((
% 99.57/13.44 (powersetTI1) =>
% 99.57/13.44 ((
% 99.57/13.44 (powersetTE1) =>
% 99.57/13.44 ((
% 99.57/13.44 (complementTI1) =>
% 99.57/13.44 ((
% 99.57/13.44 (complementTE1) =>
% 99.57/13.44 ((
% 99.57/13.44 (binintersectTELcontra) =>
% 99.57/13.44 ((
% 99.57/13.44 (binintersectTERcontra) =>
% 99.57/13.44 ((
% 99.57/13.44 (contrasubsetT) =>
% 99.57/13.44 ((
% 99.57/13.44 (contrasubsetT1) =>
% 99.57/13.44 ((
% 99.57/13.44 (contrasubsetT2) =>
% 99.57/13.44 ((
% 99.57/13.44 (contrasubsetT3) =>
% 99.57/13.44 ((
% 99.57/13.44 (doubleComplementI1) =>
% 99.57/13.44 ((
% 99.57/13.44 (doubleComplementE1) =>
% 99.57/13.44 ((
% 99.57/13.44 (doubleComplementSub1) =>
% 99.57/13.44 ((
% 99.57/13.44 (doubleComplementSub2) =>
% 99.57/13.44 ((
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% 99.57/13.44 ((
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% 99.57/13.44 ((
% 99.57/13.44 (complementSubsetComplementIntersect) =>
% 99.57/13.44 ((
% 99.57/13.44 (complementInPowersetComplementIntersect) =>
% 99.57/13.44 ((
% 99.57/13.44 (contraSubsetComplement) =>
% 99.57/13.44 ((
% 99.57/13.44 (complementTcontraSubset) =>
% 99.57/13.44 ((
% 99.57/13.44 (binunionTILcontra) =>
% 99.57/13.44 ((
% 99.57/13.44 (binunionTIRcontra) =>
% 99.57/13.44 ((
% 99.57/13.44 (inIntersectImpInUnion) =>
% 99.57/13.44 ((
% 99.57/13.44 (inIntersectImpInUnion2) =>
% 99.57/13.44 ((
% 99.57/13.44 (inIntersectImpInIntersectUnions) =>
% 99.57/13.44 ((
% 99.57/13.44 (intersectInPowersetIntersectUnions) =>
% 99.57/13.44 ((
% 99.57/13.44 (inComplementUnionImpNotIn1) =>
% 99.57/13.44 ((
% 99.57/13.44 (inComplementUnionImpInComplement1) =>
% 99.57/13.44 ((
% 99.57/13.44 (binunionTE) =>
% 99.57/13.44 ((
% 99.57/13.44 (binunionTEcontra) =>
% 99.57/13.44 ((
% 99.57/13.44 (demorgan2a1) =>
% 99.57/13.44 ((
% 99.57/13.44 (complementUnionInPowersetComplement) =>
% 99.57/13.44 ((
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% 99.57/13.44 ((
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% 99.57/13.44 ((
% 99.57/13.44 (demorgan1b) =>
% 99.57/13.44 ((
% 99.57/13.44 (demorgan1) =>
% 99.57/13.44 ((
% 99.57/13.44 (demorgan2a) =>
% 99.57/13.44 ((
% 99.57/13.44 (demorgan2b2) =>
% 99.57/13.44 ((
% 99.57/13.44 (demorgan2b) =>
% 99.57/13.44 ((
% 99.57/13.44 (demorgan2) =>
% 99.57/13.44 ((
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% 99.57/13.44 ((
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% 99.57/13.45 ((
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% 99.57/13.45 ((
% 99.57/13.45 (ap2p) =>
% 99.57/13.45 ((
% 99.57/13.45 (funcinfuncset) =>
% 99.57/13.45 ((
% 99.57/13.45 (lamProp) =>
% 99.57/13.45 ((
% 99.57/13.45 (lamp) =>
% 99.57/13.45 ((
% 99.57/13.45 (lam2p) =>
% 99.57/13.45 ((
% 99.57/13.45 (brelnall1) =>
% 99.57/13.45 ((
% 99.57/13.45 (brelnall2) =>
% 99.57/13.45 ((
% 99.57/13.45 (ex1E2) =>
% 99.57/13.45 ((
% 99.57/13.45 (funcGraphProp1) =>
% 99.57/13.45 ((
% 99.57/13.45 (funcGraphProp3) =>
% 99.57/13.45 ((
% 99.57/13.45 (funcGraphProp2) =>
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% 99.57/13.45 ((
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% 99.57/13.45 ((
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% 99.57/13.45 ((
% 99.57/13.45 (contrasubsetT2) =>
% 99.57/13.45 ((
% 99.57/13.45 (contrasubsetT3) =>
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% 99.57/13.45 ((
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% 99.57/13.45 ((
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% 99.57/13.45 ((
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% 99.57/13.45 ((
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% 99.57/13.45 (demorgan1b) =>
% 99.57/13.45 ((
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% 99.57/13.45 ((
% 99.57/13.45 (demorgan2a) =>
% 99.57/13.45 ((
% 99.57/13.45 (demorgan2b2) =>
% 99.57/13.45 ((
% 99.57/13.45 (demorgan2b) =>
% 99.57/13.45 ((
% 99.57/13.45 (demorgan2) =>
% 99.57/13.45 ((
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% 99.57/13.45 ((
% 99.57/13.45 (woz13rule1) =>
% 99.57/13.45 ((
% 99.57/13.45 (woz13rule2) =>
% 99.57/13.45 ((
% 99.57/13.45 (woz13rule3) =>
% 99.57/13.45 ((
% 99.57/13.45 (woz13rule4) =>
% 99.57/13.45 ((
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% 99.57/13.45 ((
% 99.57/13.45 (woz1_2) =>
% 99.57/13.45 ((
% 99.57/13.45 (woz1_3) =>
% 99.57/13.45 ((
% 99.57/13.45 (woz1_4) =>
% 99.57/13.45 ((
% 99.57/13.45 (woz1_5) =>
% 99.57/13.45 ((
% 99.57/13.45 (breln1all2) =>
% 99.57/13.45 ((
% 99.57/13.45 (breln1SetBreln1) =>
% 99.57/13.45 ((
% 99.57/13.45 (choice2fnsingleton) =>
% 99.57/13.45 ((
% 99.57/13.45 (setOfPairsIsBReln1) =>
% 99.57/13.45 ((
% 99.57/13.45 (breln1all1) =>
% 99.57/13.45 ((
% 99.57/13.45 (subbreln1) =>
% 99.57/13.45 ((
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% 99.57/13.45 ((
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% 99.57/13.45 ((
% 99.57/13.45 (breln1invI) =>
% 99.57/13.45 ((
% 99.57/13.45 (breln1invE) =>
% 99.57/13.45 ((
% 99.57/13.45 (breln1compprop) =>
% 99.57/13.45 ((
% 99.57/13.45 (breln1compI) =>
% 99.57/13.45 ((
% 99.57/13.45 (breln1compE) =>
% 99.57/13.45 ((
% 99.57/13.45 (breln1compEex) =>
% 99.57/13.45 ((
% 99.57/13.45 (breln1unionprop) =>
% 99.57/13.45 ((
% 99.57/13.45 (breln1unionIL) =>
% 99.57/13.45 ((
% 99.57/13.45 (breln1unionIR) =>
% 99.57/13.45 ((
% 99.57/13.45 (breln1unionI) =>
% 99.57/13.45 ((
% 99.57/13.45 (breln1unionE) =>
% 99.57/13.45 ((
% 99.57/13.45 (breln1unionEcases) =>
% 99.57/13.45 ((
% 99.57/13.45 (breln1unionCommutes) =>
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% 99.57/13.45 ((
% 99.57/13.45 (woz2B) =>
% 99.57/13.45 ((
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% 99.57/13.45 ((
% 99.57/13.45 (image1Ex1) =>
% 99.57/13.45 ((
% 99.57/13.45 (image1Equiv) =>
% 99.57/13.45 ((
% 99.57/13.45 (image1E) =>
% 99.57/13.45 ((
% 99.57/13.45 (image1I) =>
% 99.57/13.45 ((
% 99.57/13.45 (injFuncInInjFuncSet) =>
% 99.57/13.45 ((
% 99.57/13.45 (injFuncSetFuncIn) =>
% 99.57/13.45 ((
% 99.57/13.45 (injFuncSetFuncInj) =>
% 99.57/13.45 ((
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% 99.57/13.45 (('#B') @ (
% 99.57/13.45 !!) @
% 99.57/13.45 (
% 99.57/13.45 (
% 99.57/13.45 ('#B') @ (
% 99.57/13.45 (
% 99.57/13.45 ('#B') @ (
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% 99.57/13.45 (
% 99.57/13.45 (
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% 99.57/13.45 (
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% 99.57/13.45 (
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% 99.57/13.45 (
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% 99.57/13.45 (
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% 99.57/13.45 (
% 99.57/13.45 (
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% 99.57/13.45 (
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% 99.57/13.45 surjFuncSet)))))))) @
% 99.57/13.45 (
% 99.57/13.45 (
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% 99.57/13.45 (
% 99.57/13.45 ('#B') @ (
% 99.57/13.45 (
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% 99.57/13.45 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.57/13.45 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1247])).
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% 99.57/13.45 ((
% 99.57/13.45 (kfstpairEq) =>
% 99.57/13.45 ((
% 99.57/13.45 (cartprodfstin) =>
% 99.57/13.45 ((
% 99.57/13.45 (setukpairinjL2) =>
% 99.57/13.45 ((
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% 99.57/13.45 ((
% 99.57/13.45 (kpairsurjEq) =>
% 99.57/13.45 ((
% 99.57/13.45 (cartprodsndin) =>
% 99.57/13.45 ((
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% 99.57/13.45 ((
% 99.57/13.45 (cartprodpairmemER) =>
% 99.57/13.45 ((
% 99.57/13.45 (cartprodmempaircEq) =>
% 99.57/13.45 ((
% 99.57/13.45 (cartprodfstpairEq) =>
% 99.57/13.45 ((
% 99.57/13.45 (cartprodsndpairEq) =>
% 99.57/13.45 ((
% 99.57/13.45 (cartprodpairsurjEq) =>
% 99.57/13.45 ((
% 99.57/13.45 (dpsetconstrI) =>
% 99.57/13.45 ((
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% 99.57/13.45 ((
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% 99.57/13.45 ((
% 99.57/13.45 (brelnall2) =>
% 99.57/13.45 ((
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% 99.57/13.45 ((
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% 99.57/13.45 ((
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% 99.57/13.45 ((
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% 99.57/13.45 ((
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% 99.57/13.45 ((
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% 99.57/13.45 ((
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% 99.57/13.45 ((
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% 99.57/13.45 ((
% 99.57/13.45 (powersetT_lem) =>
% 99.57/13.45 ((
% 99.57/13.45 (setminusT_lem) =>
% 99.57/13.45 ((
% 99.57/13.45 (complementT_lem) =>
% 99.57/13.45 ((
% 99.57/13.45 (setextT) =>
% 99.57/13.45 ((
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% 99.57/13.45 ((
% 99.57/13.45 (powersetTI1) =>
% 99.57/13.45 ((
% 99.57/13.45 (powersetTE1) =>
% 99.57/13.45 ((
% 99.57/13.45 (complementTI1) =>
% 99.57/13.45 ((
% 99.57/13.45 (complementTE1) =>
% 99.57/13.45 ((
% 99.57/13.45 (binintersectTELcontra) =>
% 99.57/13.45 ((
% 99.57/13.45 (binintersectTERcontra) =>
% 99.57/13.45 ((
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% 99.57/13.45 ((
% 99.57/13.45 (contrasubsetT1) =>
% 99.57/13.45 ((
% 99.57/13.45 (contrasubsetT2) =>
% 99.57/13.45 ((
% 99.57/13.45 (contrasubsetT3) =>
% 99.57/13.45 ((
% 99.57/13.45 (doubleComplementI1) =>
% 99.57/13.45 ((
% 99.57/13.45 (doubleComplementE1) =>
% 99.57/13.45 ((
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% 99.57/13.45 ((
% 99.57/13.45 (doubleComplementSub2) =>
% 99.57/13.45 ((
% 99.57/13.45 (doubleComplementEq) =>
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% 99.57/13.45 (complementTnotintersectT) =>
% 99.57/13.45 ((
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% 99.57/13.45 ((
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% 99.57/13.45 ((
% 99.57/13.45 (binunionTIRcontra) =>
% 99.57/13.45 ((
% 99.57/13.45 (inIntersectImpInUnion) =>
% 99.57/13.45 ((
% 99.57/13.45 (inIntersectImpInUnion2) =>
% 99.57/13.45 ((
% 99.57/13.45 (inIntersectImpInIntersectUnions) =>
% 99.57/13.45 ((
% 99.57/13.45 (intersectInPowersetIntersectUnions) =>
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% 99.57/13.45 ((
% 99.57/13.45 (cartprodfstpairEq) =>
% 99.57/13.45 ((
% 99.57/13.45 (cartprodsndpairEq) =>
% 99.57/13.45 ((
% 99.57/13.45 (cartprodpairsurjEq) =>
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% 99.57/13.45 ((
% 99.57/13.45 (setminusT_lem) =>
% 99.57/13.45 ((
% 99.57/13.45 (complementT_lem) =>
% 99.57/13.45 ((
% 99.57/13.45 (setextT) =>
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% 99.57/13.45 ((
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% 99.57/13.45 ((
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% 99.57/13.45 ((
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% 99.57/13.45 (app) =>
% 99.57/13.45 ((
% 99.57/13.45 (infuncsetfunc) =>
% 99.57/13.45 ((
% 99.57/13.45 (ap2p) =>
% 99.57/13.45 ((
% 99.57/13.45 (funcinfuncset) =>
% 99.57/13.45 ((
% 99.57/13.45 (lamProp) =>
% 99.57/13.45 ((
% 99.57/13.45 (lamp) =>
% 99.57/13.45 ((
% 99.57/13.45 (lam2p) =>
% 99.57/13.45 ((
% 99.57/13.45 (brelnall1) =>
% 99.57/13.45 ((
% 99.57/13.45 (brelnall2) =>
% 99.57/13.45 ((
% 99.57/13.45 (ex1E2) =>
% 99.57/13.45 ((
% 99.57/13.45 (funcGraphProp1) =>
% 99.57/13.45 ((
% 99.57/13.45 (funcGraphProp3) =>
% 99.57/13.45 ((
% 99.57/13.45 (funcGraphProp2) =>
% 99.57/13.45 ((
% 99.57/13.45 (funcextLem) =>
% 99.57/13.45 ((
% 99.57/13.45 (funcGraphProp4) =>
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% 99.57/13.45 ((
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% 99.57/13.45 (ap2apEq2) =>
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% 99.57/13.45 ((
% 99.57/13.45 (eta1) =>
% 99.57/13.45 ((
% 99.57/13.45 (lam2lamEq) =>
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% 99.57/13.45 ((
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% 99.57/13.45 (setextT) =>
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% 99.57/13.45 ((
% 99.57/13.45 (powersetTI1) =>
% 99.57/13.45 ((
% 99.57/13.45 (powersetTE1) =>
% 99.57/13.45 ((
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% 99.57/13.45 ((
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% 99.57/13.45 ((
% 99.57/13.45 (binintersectTERcontra) =>
% 99.57/13.45 ((
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% 99.57/13.45 ((
% 99.57/13.45 (contrasubsetT1) =>
% 99.57/13.45 ((
% 99.57/13.45 (contrasubsetT2) =>
% 99.57/13.45 ((
% 99.57/13.45 (contrasubsetT3) =>
% 99.57/13.45 ((
% 99.57/13.45 (doubleComplementI1) =>
% 99.57/13.45 ((
% 99.57/13.45 (doubleComplementE1) =>
% 99.57/13.45 ((
% 99.57/13.45 (doubleComplementSub1) =>
% 99.57/13.45 ((
% 99.57/13.45 (doubleComplementSub2) =>
% 99.57/13.45 ((
% 99.57/13.45 (doubleComplementEq) =>
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% 99.57/13.45 ((
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% 99.57/13.45 ((
% 99.57/13.45 (complementSubsetComplementIntersect) =>
% 99.57/13.45 ((
% 99.57/13.45 (complementInPowersetComplementIntersect) =>
% 99.57/13.45 ((
% 99.57/13.45 (contraSubsetComplement) =>
% 99.57/13.45 ((
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% 99.57/13.45 ((
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% 99.57/13.45 ((
% 99.57/13.45 (binunionTIRcontra) =>
% 99.57/13.45 ((
% 99.57/13.45 (inIntersectImpInUnion) =>
% 99.57/13.45 ((
% 99.57/13.45 (inIntersectImpInUnion2) =>
% 99.57/13.45 ((
% 99.57/13.45 (inIntersectImpInIntersectUnions) =>
% 99.57/13.45 ((
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% 99.57/13.45 (inComplementUnionImpNotIn1) =>
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% 99.57/13.45 ((
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% 99.57/13.45 ((
% 99.57/13.45 (complementUnionInPowersetComplement) =>
% 99.57/13.45 ((
% 99.57/13.45 (demorgan2a2) =>
% 99.57/13.45 ((
% 99.57/13.45 (demorgan1a) =>
% 99.57/13.45 ((
% 99.57/13.45 (demorgan1b) =>
% 99.57/13.45 ((
% 99.57/13.45 (demorgan1) =>
% 99.57/13.45 ((
% 99.57/13.45 (demorgan2a) =>
% 99.57/13.45 ((
% 99.57/13.45 (demorgan2b2) =>
% 99.57/13.45 ((
% 99.57/13.45 (demorgan2b) =>
% 99.57/13.45 ((
% 99.57/13.45 (demorgan2) =>
% 99.57/13.45 ((
% 99.57/13.45 (woz13rule0) =>
% 99.57/13.45 ((
% 99.57/13.45 (woz13rule1) =>
% 99.57/13.45 ((
% 99.57/13.45 (woz13rule2) =>
% 99.57/13.45 ((
% 99.57/13.45 (woz13rule3) =>
% 99.57/13.45 ((
% 99.57/13.45 (woz13rule4) =>
% 99.57/13.45 ((
% 99.57/13.45 (woz1_1) =>
% 99.57/13.45 ((
% 99.57/13.45 (woz1_2) =>
% 99.57/13.45 ((
% 99.57/13.45 (woz1_3) =>
% 99.57/13.45 ((
% 99.57/13.45 (woz1_4) =>
% 99.57/13.45 ((
% 99.57/13.45 (woz1_5) =>
% 99.57/13.45 ((
% 99.57/13.45 (breln1all2) =>
% 99.57/13.45 ((
% 99.57/13.45 (breln1SetBreln1) =>
% 99.57/13.45 ((
% 99.57/13.45 (choice2fnsingleton) =>
% 99.57/13.45 ((
% 99.57/13.45 (setOfPairsIsBReln1) =>
% 99.57/13.45 ((
% 99.57/13.45 (breln1all1) =>
% 99.57/13.45 ((
% 99.57/13.45 (subbreln1) =>
% 99.57/13.45 ((
% 99.57/13.45 (eqbreln1) =>
% 99.57/13.45 ((
% 99.57/13.45 (breln1invprop) =>
% 99.57/13.45 ((
% 99.57/13.45 (breln1invI) =>
% 99.57/13.45 ((
% 99.57/13.45 (breln1invE) =>
% 99.57/13.45 ((
% 99.57/13.45 (breln1compprop) =>
% 99.57/13.45 ((
% 99.57/13.45 (breln1compI) =>
% 99.57/13.45 ((
% 99.57/13.45 (breln1compE) =>
% 99.57/13.45 ((
% 99.57/13.45 (breln1compEex) =>
% 99.57/13.45 ((
% 99.57/13.45 (breln1unionprop) =>
% 99.57/13.45 ((
% 99.57/13.45 (breln1unionIL) =>
% 99.57/13.45 ((
% 99.57/13.45 (breln1unionIR) =>
% 99.57/13.45 ((
% 99.57/13.45 (breln1unionI) =>
% 99.57/13.45 ((
% 99.57/13.45 (breln1unionE) =>
% 99.57/13.45 ((
% 99.57/13.45 (breln1unionEcases) =>
% 99.57/13.45 ((
% 99.57/13.45 (breln1unionCommutes) =>
% 99.57/13.45 ((
% 99.57/13.45 (woz2Ex) =>
% 99.57/13.45 ((
% 99.57/13.45 (woz2W) =>
% 99.57/13.45 ((
% 99.57/13.45 (woz2A) =>
% 99.57/13.45 ((
% 99.57/13.45 (woz2B) =>
% 99.57/13.45 ((
% 99.57/13.45 (image1Ex) =>
% 99.57/13.45 ((
% 99.57/13.45 (image1Ex1) =>
% 99.57/13.45 ((
% 99.57/13.45 (image1Equiv) =>
% 99.57/13.45 ((
% 99.57/13.45 (image1E) =>
% 99.57/13.45 ((
% 99.57/13.45 (image1I) =>
% 99.57/13.45 ((
% 99.57/13.45 (injFuncInInjFuncSet) =>
% 99.57/13.45 ((
% 99.57/13.45 (injFuncSetFuncIn) =>
% 99.57/13.45 ((
% 99.57/13.45 (injFuncSetFuncInj) =>
% 99.57/13.45 ((
% 99.57/13.45 (!!) @ (
% 99.57/13.45 (('#B') @ (
% 99.57/13.45 !!) @
% 99.57/13.45 (
% 99.57/13.45 (
% 99.57/13.45 ('#B') @ (
% 99.57/13.45 (
% 99.57/13.45 ('#B') @ (
% 99.57/13.45 !!))) @
% 99.57/13.45 (
% 99.57/13.45 (
% 99.57/13.45 ('#S') @ (
% 99.57/13.45 (
% 99.57/13.45 ('#B') @ (
% 99.57/13.45 '#S') @
% 99.57/13.45 (
% 99.57/13.45 (
% 99.57/13.45 ('#B') @ (
% 99.57/13.45 (
% 99.57/13.45 ('#B') @ (
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% 99.57/13.45 (
% 99.57/13.45 (
% 99.57/13.45 ('#B') @ (
% 99.57/13.45 (
% 99.57/13.45 ('#B') @ (
% 99.57/13.45 (
% 99.57/13.45 ('#B') @ (
% 99.57/13.45 =>))))) @
% 99.57/13.45 (
% 99.57/13.45 (
% 99.57/13.45 ('#B') @ (
% 99.57/13.45 (
% 99.57/13.45 ('#B') @ (
% 99.57/13.45 (
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% 99.57/13.45 surjFuncSet)))))))) @
% 99.57/13.45 (
% 99.57/13.45 (
% 99.57/13.45 ('#B') @ (
% 99.57/13.45 (
% 99.57/13.45 ('#B') @ (
% 99.57/13.45 (
% 99.57/13.45 ('#C') @ in)))) @
% 99.57/13.45 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.57/13.45 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1280])).
% 99.57/13.45 thf(zip_derived_cl1296, plain,
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% 99.57/13.45 (((symdiffIneg2) =>
% 99.57/13.45 (((secondinupair) =>
% 99.57/13.45 (((setukpairIL) =>
% 99.57/13.45 (((setukpairIR) =>
% 99.57/13.45 (((kpairiskpair) =>
% 99.57/13.45 (((kpairp) =>
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% 99.57/13.45 (((singletoninpowerset) =>
% 99.57/13.45 (((singletoninpowunion) =>
% 99.57/13.45 (((upairset2E) =>
% 99.57/13.45 (((upairsubunion) =>
% 99.57/13.45 (((upairinpowunion) =>
% 99.57/13.45 (((ubforcartprodlem1) =>
% 99.57/13.45 (((ubforcartprodlem2) =>
% 99.57/13.45 (((ubforcartprodlem3) =>
% 99.57/13.45 (((cartprodpairin) =>
% 99.57/13.45 (((cartprodmempair1) =>
% 99.57/13.45 (((cartprodmempair) =>
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% 99.57/13.45 ((
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% 99.57/13.45 ((
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% 99.57/13.45 ((
% 99.57/13.45 (ex1I2) =>
% 99.57/13.45 ((
% 99.57/13.45 (singletonsuniq) =>
% 99.57/13.45 ((
% 99.57/13.45 (setukpairinjL1) =>
% 99.57/13.45 ((
% 99.57/13.45 (kfstsingleton) =>
% 99.57/13.45 ((
% 99.57/13.45 (theprop) =>
% 99.57/13.45 ((
% 99.57/13.45 (kfstpairEq) =>
% 99.57/13.45 ((
% 99.57/13.45 (cartprodfstin) =>
% 99.57/13.45 ((
% 99.57/13.45 (setukpairinjL2) =>
% 99.57/13.45 ((
% 99.57/13.45 (setukpairinjL) =>
% 99.57/13.45 ((
% 99.57/13.45 (setukpairinjR11) =>
% 99.57/13.45 ((
% 99.57/13.45 (setukpairinjR12) =>
% 99.57/13.45 ((
% 99.57/13.45 (setukpairinjR1) =>
% 99.57/13.45 ((
% 99.57/13.45 (upairequniteq) =>
% 99.57/13.45 ((
% 99.57/13.45 (setukpairinjR2) =>
% 99.57/13.45 ((
% 99.57/13.45 (setukpairinjR) =>
% 99.57/13.45 ((
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% 99.57/13.45 ((
% 99.57/13.45 (ksndpairEq) =>
% 99.57/13.45 ((
% 99.57/13.45 (kpairsurjEq) =>
% 99.57/13.45 ((
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% 99.57/13.45 ((
% 99.57/13.45 (cartprodpairmemEL) =>
% 99.57/13.45 ((
% 99.57/13.45 (cartprodpairmemER) =>
% 99.57/13.45 ((
% 99.57/13.45 (cartprodmempaircEq) =>
% 99.57/13.45 ((
% 99.57/13.45 (cartprodfstpairEq) =>
% 99.57/13.45 ((
% 99.57/13.45 (cartprodsndpairEq) =>
% 99.57/13.45 ((
% 99.57/13.45 (cartprodpairsurjEq) =>
% 99.57/13.45 ((
% 99.57/13.45 (dpsetconstrI) =>
% 99.57/13.45 ((
% 99.57/13.45 (dpsetconstrSub) =>
% 99.57/13.45 ((
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% 99.57/13.45 (dpsetconstrERa) =>
% 99.57/13.45 ((
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% 99.57/13.45 ((
% 99.57/13.45 (dpsetconstrEL2) =>
% 99.57/13.45 ((
% 99.57/13.45 (dpsetconstrER) =>
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% 99.57/13.45 ((
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% 99.57/13.45 ((
% 99.57/13.45 (funcinfuncset) =>
% 99.57/13.45 ((
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% 99.57/13.45 ((
% 99.57/13.45 (lamp) =>
% 99.57/13.45 ((
% 99.57/13.45 (lam2p) =>
% 99.57/13.45 ((
% 99.57/13.45 (brelnall1) =>
% 99.57/13.45 ((
% 99.57/13.45 (brelnall2) =>
% 99.57/13.45 ((
% 99.57/13.45 (ex1E2) =>
% 99.57/13.45 ((
% 99.57/13.45 (funcGraphProp1) =>
% 99.57/13.45 ((
% 99.57/13.45 (funcGraphProp3) =>
% 99.57/13.45 ((
% 99.57/13.45 (funcGraphProp2) =>
% 99.57/13.45 ((
% 99.57/13.45 (funcextLem) =>
% 99.57/13.45 ((
% 99.57/13.45 (funcGraphProp4) =>
% 99.57/13.45 ((
% 99.57/13.45 (subbreln) =>
% 99.57/13.45 ((
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% 99.57/13.45 ((
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% 99.57/13.45 ((
% 99.57/13.45 (funcext2) =>
% 99.57/13.45 ((
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% 99.57/13.45 ((
% 99.57/13.45 (ap2apEq2) =>
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% 99.57/13.45 ((
% 99.57/13.45 (eta1) =>
% 99.57/13.45 ((
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% 99.57/13.45 ((
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% 99.57/13.45 ((
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% 99.57/13.45 ((
% 99.57/13.45 (iftrueProp2) =>
% 99.57/13.45 ((
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% 99.57/13.45 ((
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% 99.57/13.45 ((
% 99.57/13.45 (theeq) =>
% 99.57/13.45 ((
% 99.57/13.45 (iftrue) =>
% 99.57/13.45 ((
% 99.57/13.45 (iffalse) =>
% 99.57/13.45 ((
% 99.57/13.45 (iftrueorfalse) =>
% 99.57/13.45 ((
% 99.57/13.45 (binintersectT_lem) =>
% 99.57/13.45 ((
% 99.57/13.45 (binunionT_lem) =>
% 99.57/13.45 ((
% 99.57/13.45 (powersetT_lem) =>
% 99.57/13.45 ((
% 99.57/13.45 (setminusT_lem) =>
% 99.57/13.45 ((
% 99.57/13.45 (complementT_lem) =>
% 99.57/13.45 ((
% 99.57/13.45 (setextT) =>
% 99.57/13.45 ((
% 99.57/13.45 (subsetTI) =>
% 99.57/13.45 ((
% 99.57/13.45 (powersetTI1) =>
% 99.57/13.45 ((
% 99.57/13.45 (powersetTE1) =>
% 99.57/13.45 ((
% 99.57/13.45 (complementTI1) =>
% 99.57/13.45 ((
% 99.57/13.45 (complementTE1) =>
% 99.57/13.45 ((
% 99.57/13.45 (binintersectTELcontra) =>
% 99.57/13.45 ((
% 99.57/13.45 (binintersectTERcontra) =>
% 99.57/13.45 ((
% 99.57/13.45 (contrasubsetT) =>
% 99.57/13.45 ((
% 99.57/13.45 (contrasubsetT1) =>
% 99.57/13.45 ((
% 99.57/13.45 (contrasubsetT2) =>
% 99.57/13.45 ((
% 99.57/13.45 (contrasubsetT3) =>
% 99.57/13.45 ((
% 99.57/13.45 (doubleComplementI1) =>
% 99.57/13.45 ((
% 99.57/13.45 (doubleComplementE1) =>
% 99.57/13.45 ((
% 99.57/13.45 (doubleComplementSub1) =>
% 99.57/13.45 ((
% 99.57/13.45 (doubleComplementSub2) =>
% 99.57/13.45 ((
% 99.57/13.45 (doubleComplementEq) =>
% 99.57/13.45 ((
% 99.57/13.45 (complementTnotintersectT) =>
% 99.57/13.45 ((
% 99.57/13.45 (complementImpComplementIntersect) =>
% 99.57/13.45 ((
% 99.57/13.45 (complementSubsetComplementIntersect) =>
% 99.57/13.45 ((
% 99.57/13.45 (complementInPowersetComplementIntersect) =>
% 99.57/13.45 ((
% 99.57/13.45 (contraSubsetComplement) =>
% 99.57/13.45 ((
% 99.57/13.45 (complementTcontraSubset) =>
% 99.57/13.45 ((
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% 99.57/13.45 ((
% 99.57/13.45 (binunionTIRcontra) =>
% 99.57/13.45 ((
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% 99.57/13.45 ((
% 99.57/13.45 (inIntersectImpInUnion2) =>
% 99.57/13.45 ((
% 99.57/13.45 (inIntersectImpInIntersectUnions) =>
% 99.57/13.45 ((
% 99.57/13.45 (intersectInPowersetIntersectUnions) =>
% 99.57/13.45 ((
% 99.57/13.45 (inComplementUnionImpNotIn1) =>
% 99.57/13.45 ((
% 99.57/13.45 (inComplementUnionImpInComplement1) =>
% 99.57/13.45 ((
% 99.57/13.45 (binunionTE) =>
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% 99.57/13.45 ((
% 99.57/13.45 (demorgan2a) =>
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% 99.57/13.45 ((
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% 99.57/13.45 ((
% 99.57/13.45 (breln1compE) =>
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% 99.57/13.45 ((
% 99.57/13.45 (breln1unionE) =>
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% 99.57/13.45 ((
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% 99.57/13.45 ((
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% 99.57/13.45 (cartprodfstin) =>
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% 99.57/13.45 ((
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% 99.57/13.45 ((
% 99.57/13.45 (cartprodpairmemER) =>
% 99.57/13.45 ((
% 99.57/13.45 (cartprodmempaircEq) =>
% 99.57/13.45 ((
% 99.57/13.45 (cartprodfstpairEq) =>
% 99.57/13.45 ((
% 99.57/13.45 (cartprodsndpairEq) =>
% 99.57/13.45 ((
% 99.57/13.45 (cartprodpairsurjEq) =>
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% 99.57/13.45 ((
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% 99.57/13.45 ((
% 99.57/13.45 (lamp) =>
% 99.57/13.45 ((
% 99.57/13.45 (lam2p) =>
% 99.57/13.45 ((
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% 99.57/13.45 ((
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% 99.57/13.45 ((
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% 99.57/13.45 ((
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% 99.57/13.45 ((
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% 99.57/13.45 ((
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% 99.57/13.45 ((
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% 99.57/13.45 ((
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% 99.57/13.45 ((
% 99.57/13.45 (complementTI1) =>
% 99.57/13.45 ((
% 99.57/13.45 (complementTE1) =>
% 99.57/13.45 ((
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% 99.57/13.45 ((
% 99.57/13.45 (binintersectTERcontra) =>
% 99.57/13.45 ((
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% 99.57/13.45 ((
% 99.57/13.45 (contrasubsetT2) =>
% 99.57/13.45 ((
% 99.57/13.45 (contrasubsetT3) =>
% 99.57/13.45 ((
% 99.57/13.45 (doubleComplementI1) =>
% 99.57/13.45 ((
% 99.57/13.45 (doubleComplementE1) =>
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% 99.57/13.45 (doubleComplementSub2) =>
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% 99.57/13.45 (eqbreln) =>
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% 99.57/13.45 ((
% 99.57/13.45 (ap2apEq2) =>
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% 99.57/13.45 ((
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% 99.57/13.45 ((
% 99.57/13.45 (lam2lamEq) =>
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% 99.57/13.45 ((
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% 99.57/13.45 ((
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% 99.57/13.45 ((
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% 99.57/13.45 ((
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% 99.57/13.45 ((
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% 99.57/13.45 ((
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% 99.57/13.45 ((
% 99.57/13.45 (binintersectTERcontra) =>
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% 99.57/13.45 ((
% 99.57/13.45 (contrasubsetT2) =>
% 99.57/13.45 ((
% 99.57/13.45 (contrasubsetT3) =>
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% 99.57/13.45 ((
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% 99.57/13.45 ((
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% 99.57/13.45 ((
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% 99.57/13.45 (contraSubsetComplement) =>
% 99.57/13.45 ((
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% 99.57/13.45 ((
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% 99.57/13.45 ((
% 99.57/13.45 (binunionTIRcontra) =>
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% 99.57/13.45 ((
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% 99.57/13.45 ((
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% 99.57/13.45 ((
% 99.57/13.45 (demorgan1b) =>
% 99.57/13.45 ((
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% 99.57/13.45 ((
% 99.57/13.45 (demorgan2a) =>
% 99.57/13.45 ((
% 99.57/13.45 (demorgan2b2) =>
% 99.57/13.45 ((
% 99.57/13.45 (demorgan2b) =>
% 99.57/13.45 ((
% 99.57/13.45 (demorgan2) =>
% 99.57/13.45 ((
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% 99.57/13.45 ((
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% 99.57/13.45 ((
% 99.57/13.45 (woz13rule2) =>
% 99.57/13.45 ((
% 99.57/13.45 (woz13rule3) =>
% 99.57/13.45 ((
% 99.57/13.45 (woz13rule4) =>
% 99.57/13.45 ((
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% 99.57/13.45 ((
% 99.57/13.45 (woz1_2) =>
% 99.57/13.45 ((
% 99.57/13.45 (woz1_3) =>
% 99.57/13.45 ((
% 99.57/13.45 (woz1_4) =>
% 99.57/13.45 ((
% 99.57/13.45 (woz1_5) =>
% 99.57/13.45 ((
% 99.57/13.45 (breln1all2) =>
% 99.57/13.45 ((
% 99.57/13.45 (breln1SetBreln1) =>
% 99.57/13.45 ((
% 99.57/13.45 (choice2fnsingleton) =>
% 99.57/13.45 ((
% 99.57/13.45 (setOfPairsIsBReln1) =>
% 99.57/13.45 ((
% 99.57/13.45 (breln1all1) =>
% 99.57/13.45 ((
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% 99.57/13.45 ((
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% 99.57/13.45 ((
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% 99.57/13.45 ((
% 99.57/13.45 (breln1invI) =>
% 99.57/13.45 ((
% 99.57/13.45 (breln1invE) =>
% 99.57/13.45 ((
% 99.57/13.45 (breln1compprop) =>
% 99.57/13.45 ((
% 99.57/13.45 (breln1compI) =>
% 99.57/13.45 ((
% 99.57/13.45 (breln1compE) =>
% 99.57/13.45 ((
% 99.57/13.45 (breln1compEex) =>
% 99.57/13.45 ((
% 99.57/13.45 (breln1unionprop) =>
% 99.57/13.45 ((
% 99.57/13.45 (breln1unionIL) =>
% 99.57/13.45 ((
% 99.57/13.45 (breln1unionIR) =>
% 99.57/13.45 ((
% 99.57/13.45 (breln1unionI) =>
% 99.57/13.45 ((
% 99.57/13.45 (breln1unionE) =>
% 99.57/13.45 ((
% 99.57/13.45 (breln1unionEcases) =>
% 99.57/13.45 ((
% 99.57/13.45 (breln1unionCommutes) =>
% 99.57/13.45 ((
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% 99.57/13.45 ((
% 99.57/13.45 (woz2W) =>
% 99.57/13.45 ((
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% 99.57/13.45 ((
% 99.57/13.45 (woz2B) =>
% 99.57/13.45 ((
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% 99.57/13.45 ((
% 99.57/13.45 (image1Ex1) =>
% 99.57/13.45 ((
% 99.57/13.45 (image1Equiv) =>
% 99.57/13.45 ((
% 99.57/13.45 (image1E) =>
% 99.57/13.45 ((
% 99.57/13.45 (image1I) =>
% 99.57/13.45 ((
% 99.57/13.45 (injFuncInInjFuncSet) =>
% 99.57/13.45 ((
% 99.57/13.45 (injFuncSetFuncIn) =>
% 99.57/13.45 ((
% 99.57/13.45 (injFuncSetFuncInj) =>
% 99.57/13.45 ((
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% 99.57/13.45 (('#B') @ (
% 99.57/13.45 !!) @
% 99.57/13.45 (
% 99.57/13.45 (
% 99.57/13.45 ('#B') @ (
% 99.57/13.45 (
% 99.57/13.45 ('#B') @ (
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% 99.57/13.45 (
% 99.57/13.45 (
% 99.57/13.45 ('#S') @ (
% 99.57/13.45 (
% 99.57/13.45 ('#B') @ (
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% 99.57/13.45 (
% 99.57/13.45 (
% 99.57/13.45 ('#B') @ (
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% 99.57/13.45 (
% 99.57/13.45 (
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% 99.57/13.45 (
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% 99.57/13.45 (
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% 99.57/13.45 (
% 99.57/13.45 (
% 99.57/13.45 ('#B') @ (
% 99.57/13.45 (
% 99.57/13.45 ('#B') @ (
% 99.57/13.45 (
% 99.57/13.45 ('#C') @ in)))) @
% 99.57/13.45 surjFuncSet)))))))) @
% 99.57/13.45 (
% 99.57/13.45 (
% 99.57/13.45 ('#B') @ (
% 99.57/13.45 (
% 99.57/13.45 ('#B') @ (
% 99.57/13.45 (
% 99.57/13.45 ('#C') @ in)))) @
% 99.57/13.45 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.57/13.45 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1313])).
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% 99.57/13.45 (((singletoninpowunion) =>
% 99.57/13.45 (((upairset2E) =>
% 99.57/13.45 (((upairsubunion) =>
% 99.57/13.45 (((upairinpowunion) =>
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% 99.57/13.45 (((ubforcartprodlem2) =>
% 99.57/13.45 (((ubforcartprodlem3) =>
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% 99.57/13.45 ((
% 99.57/13.45 (kfstpairEq) =>
% 99.57/13.45 ((
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% 99.57/13.45 ((
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% 99.57/13.45 ((
% 99.57/13.45 (setukpairinjR1) =>
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% 99.57/13.45 ((
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% 99.57/13.45 ((
% 99.57/13.45 (kpairsurjEq) =>
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% 99.57/13.45 ((
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% 99.57/13.45 (cartprodfstpairEq) =>
% 99.57/13.45 ((
% 99.57/13.45 (cartprodsndpairEq) =>
% 99.57/13.45 ((
% 99.57/13.45 (cartprodpairsurjEq) =>
% 99.57/13.45 ((
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% 99.57/13.45 (dpsetconstrSub) =>
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% 99.57/13.45 ((
% 99.57/13.45 (dpsetconstrEL2) =>
% 99.57/13.45 ((
% 99.57/13.45 (dpsetconstrER) =>
% 99.57/13.45 ((
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% 99.57/13.45 ((
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% 99.57/13.45 ((
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% 99.57/13.45 ((
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% 99.57/13.45 (funcext2) =>
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% 99.57/13.45 ((
% 99.57/13.45 (ap2apEq2) =>
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% 99.57/13.45 ((
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% 99.57/13.45 ((
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% 99.57/13.45 ((
% 99.57/13.45 (binunionT_lem) =>
% 99.57/13.45 ((
% 99.57/13.45 (powersetT_lem) =>
% 99.57/13.45 ((
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% 99.57/13.45 ((
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% 99.57/13.45 ((
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% 99.57/13.45 ((
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% 99.57/13.45 ((
% 99.57/13.45 (binintersectTERcontra) =>
% 99.57/13.45 ((
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% 99.57/13.45 ((
% 99.57/13.45 (contrasubsetT1) =>
% 99.57/13.45 ((
% 99.57/13.45 (contrasubsetT2) =>
% 99.57/13.45 ((
% 99.57/13.45 (contrasubsetT3) =>
% 99.57/13.45 ((
% 99.57/13.45 (doubleComplementI1) =>
% 99.57/13.45 ((
% 99.57/13.45 (doubleComplementE1) =>
% 99.57/13.45 ((
% 99.57/13.45 (doubleComplementSub1) =>
% 99.57/13.45 ((
% 99.57/13.45 (doubleComplementSub2) =>
% 99.57/13.45 ((
% 99.57/13.45 (doubleComplementEq) =>
% 99.57/13.45 ((
% 99.57/13.45 (complementTnotintersectT) =>
% 99.57/13.45 ((
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% 99.57/13.45 ((
% 99.57/13.45 (complementSubsetComplementIntersect) =>
% 99.57/13.45 ((
% 99.57/13.45 (complementInPowersetComplementIntersect) =>
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% 99.57/13.45 (contraSubsetComplement) =>
% 99.57/13.45 ((
% 99.57/13.45 (complementTcontraSubset) =>
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% 99.57/13.45 ((
% 99.57/13.45 (inComplementUnionImpInComplement1) =>
% 99.57/13.45 ((
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% 99.57/13.45 ((
% 99.57/13.45 (binunionTEcontra) =>
% 99.57/13.45 ((
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% 99.57/13.45 ((
% 99.57/13.45 (complementUnionInPowersetComplement) =>
% 99.57/13.45 ((
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% 99.57/13.45 ((
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% 99.57/13.45 ((
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% 99.57/13.45 (((ex1I2) =>
% 99.57/13.45 (((singletonsuniq) =>
% 99.57/13.45 (((setukpairinjL1) =>
% 99.57/13.45 ((
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% 99.57/13.45 ((
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% 99.57/13.45 ((
% 99.57/13.45 (kfstpairEq) =>
% 99.57/13.45 ((
% 99.57/13.45 (cartprodfstin) =>
% 99.57/13.45 ((
% 99.57/13.45 (setukpairinjL2) =>
% 99.57/13.45 ((
% 99.57/13.45 (setukpairinjL) =>
% 99.57/13.45 ((
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% 99.57/13.45 ((
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% 99.57/13.45 ((
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% 99.57/13.45 (kpairsurjEq) =>
% 99.57/13.45 ((
% 99.57/13.45 (cartprodsndin) =>
% 99.57/13.45 ((
% 99.57/13.45 (cartprodpairmemEL) =>
% 99.57/13.45 ((
% 99.57/13.45 (cartprodpairmemER) =>
% 99.57/13.45 ((
% 99.57/13.45 (cartprodmempaircEq) =>
% 99.57/13.45 ((
% 99.57/13.45 (cartprodfstpairEq) =>
% 99.57/13.45 ((
% 99.57/13.45 (cartprodsndpairEq) =>
% 99.57/13.45 ((
% 99.57/13.45 (cartprodpairsurjEq) =>
% 99.57/13.45 ((
% 99.57/13.45 (dpsetconstrI) =>
% 99.57/13.45 ((
% 99.57/13.45 (dpsetconstrSub) =>
% 99.57/13.45 ((
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% 99.57/13.45 ((
% 99.57/13.45 (dpsetconstrERa) =>
% 99.57/13.45 ((
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% 99.57/13.45 ((
% 99.57/13.45 (dpsetconstrEL2) =>
% 99.57/13.45 ((
% 99.57/13.45 (dpsetconstrER) =>
% 99.57/13.45 ((
% 99.57/13.45 (funcImageSingleton) =>
% 99.57/13.45 ((
% 99.57/13.45 (apProp) =>
% 99.57/13.45 ((
% 99.57/13.45 (app) =>
% 99.57/13.45 ((
% 99.57/13.45 (infuncsetfunc) =>
% 99.57/13.45 ((
% 99.57/13.45 (ap2p) =>
% 99.57/13.45 ((
% 99.57/13.45 (funcinfuncset) =>
% 99.57/13.45 ((
% 99.57/13.45 (lamProp) =>
% 99.57/13.45 ((
% 99.57/13.45 (lamp) =>
% 99.57/13.45 ((
% 99.57/13.45 (lam2p) =>
% 99.57/13.45 ((
% 99.57/13.45 (brelnall1) =>
% 99.57/13.45 ((
% 99.57/13.45 (brelnall2) =>
% 99.57/13.45 ((
% 99.57/13.45 (ex1E2) =>
% 99.57/13.45 ((
% 99.57/13.45 (funcGraphProp1) =>
% 99.57/13.45 ((
% 99.57/13.45 (funcGraphProp3) =>
% 99.57/13.45 ((
% 99.57/13.45 (funcGraphProp2) =>
% 99.57/13.45 ((
% 99.57/13.45 (funcextLem) =>
% 99.57/13.45 ((
% 99.57/13.45 (funcGraphProp4) =>
% 99.57/13.45 ((
% 99.57/13.45 (subbreln) =>
% 99.57/13.45 ((
% 99.57/13.45 (eqbreln) =>
% 99.57/13.45 ((
% 99.57/13.45 (funcext) =>
% 99.57/13.45 ((
% 99.57/13.45 (funcext2) =>
% 99.57/13.45 ((
% 99.57/13.45 (ap2apEq1) =>
% 99.57/13.45 ((
% 99.57/13.45 (ap2apEq2) =>
% 99.57/13.45 ((
% 99.57/13.45 (beta1) =>
% 99.57/13.45 ((
% 99.57/13.45 (eta1) =>
% 99.57/13.45 ((
% 99.57/13.45 (lam2lamEq) =>
% 99.57/13.45 ((
% 99.57/13.45 (beta2) =>
% 99.57/13.45 ((
% 99.57/13.45 (eta2) =>
% 99.57/13.45 ((
% 99.57/13.45 (iffalseProp1) =>
% 99.57/13.45 ((
% 99.57/13.45 (iffalseProp2) =>
% 99.57/13.45 ((
% 99.57/13.45 (iftrueProp1) =>
% 99.57/13.45 ((
% 99.57/13.45 (iftrueProp2) =>
% 99.57/13.45 ((
% 99.57/13.45 (ifSingleton) =>
% 99.57/13.45 ((
% 99.57/13.45 (ifp) =>
% 99.57/13.45 ((
% 99.57/13.45 (theeq) =>
% 99.57/13.45 ((
% 99.57/13.45 (iftrue) =>
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% 99.57/13.45 ((
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% 99.57/13.45 ((
% 99.57/13.45 (binunionT_lem) =>
% 99.57/13.45 ((
% 99.57/13.45 (powersetT_lem) =>
% 99.57/13.45 ((
% 99.57/13.45 (setminusT_lem) =>
% 99.57/13.45 ((
% 99.57/13.45 (complementT_lem) =>
% 99.57/13.45 ((
% 99.57/13.45 (setextT) =>
% 99.57/13.45 ((
% 99.57/13.45 (subsetTI) =>
% 99.57/13.45 ((
% 99.57/13.45 (powersetTI1) =>
% 99.57/13.45 ((
% 99.57/13.45 (powersetTE1) =>
% 99.57/13.45 ((
% 99.57/13.45 (complementTI1) =>
% 99.57/13.45 ((
% 99.57/13.45 (complementTE1) =>
% 99.57/13.45 ((
% 99.57/13.45 (binintersectTELcontra) =>
% 99.57/13.45 ((
% 99.57/13.45 (binintersectTERcontra) =>
% 99.57/13.45 ((
% 99.57/13.45 (contrasubsetT) =>
% 99.57/13.45 ((
% 99.57/13.45 (contrasubsetT1) =>
% 99.57/13.45 ((
% 99.57/13.45 (contrasubsetT2) =>
% 99.57/13.45 ((
% 99.57/13.45 (contrasubsetT3) =>
% 99.57/13.45 ((
% 99.57/13.45 (doubleComplementI1) =>
% 99.57/13.45 ((
% 99.57/13.45 (doubleComplementE1) =>
% 99.57/13.45 ((
% 99.57/13.45 (doubleComplementSub1) =>
% 99.57/13.45 ((
% 99.57/13.45 (doubleComplementSub2) =>
% 99.57/13.45 ((
% 99.57/13.45 (doubleComplementEq) =>
% 99.57/13.45 ((
% 99.57/13.45 (complementTnotintersectT) =>
% 99.57/13.45 ((
% 99.57/13.45 (complementImpComplementIntersect) =>
% 99.57/13.45 ((
% 99.57/13.45 (complementSubsetComplementIntersect) =>
% 99.57/13.45 ((
% 99.57/13.45 (complementInPowersetComplementIntersect) =>
% 99.57/13.45 ((
% 99.57/13.45 (contraSubsetComplement) =>
% 99.57/13.45 ((
% 99.57/13.45 (complementTcontraSubset) =>
% 99.57/13.45 ((
% 99.57/13.45 (binunionTILcontra) =>
% 99.57/13.45 ((
% 99.57/13.45 (binunionTIRcontra) =>
% 99.57/13.45 ((
% 99.57/13.45 (inIntersectImpInUnion) =>
% 99.57/13.45 ((
% 99.57/13.45 (inIntersectImpInUnion2) =>
% 99.57/13.45 ((
% 99.57/13.45 (inIntersectImpInIntersectUnions) =>
% 99.57/13.45 ((
% 99.57/13.45 (intersectInPowersetIntersectUnions) =>
% 99.57/13.45 ((
% 99.57/13.45 (inComplementUnionImpNotIn1) =>
% 99.57/13.45 ((
% 99.57/13.45 (inComplementUnionImpInComplement1) =>
% 99.57/13.45 ((
% 99.57/13.45 (binunionTE) =>
% 99.57/13.45 ((
% 99.57/13.45 (binunionTEcontra) =>
% 99.57/13.45 ((
% 99.57/13.45 (demorgan2a1) =>
% 99.57/13.45 ((
% 99.57/13.45 (complementUnionInPowersetComplement) =>
% 99.57/13.45 ((
% 99.57/13.45 (demorgan2a2) =>
% 99.57/13.45 ((
% 99.57/13.45 (demorgan1a) =>
% 99.57/13.45 ((
% 99.57/13.45 (demorgan1b) =>
% 99.57/13.45 ((
% 99.57/13.45 (demorgan1) =>
% 99.57/13.45 ((
% 99.57/13.45 (demorgan2a) =>
% 99.57/13.45 ((
% 99.57/13.45 (demorgan2b2) =>
% 99.57/13.45 ((
% 99.57/13.45 (demorgan2b) =>
% 99.57/13.45 ((
% 99.57/13.45 (demorgan2) =>
% 99.57/13.45 ((
% 99.57/13.45 (woz13rule0) =>
% 99.57/13.45 ((
% 99.57/13.45 (woz13rule1) =>
% 99.57/13.45 ((
% 99.57/13.45 (woz13rule2) =>
% 99.57/13.45 ((
% 99.57/13.45 (woz13rule3) =>
% 99.57/13.45 ((
% 99.57/13.45 (woz13rule4) =>
% 99.57/13.45 ((
% 99.57/13.45 (woz1_1) =>
% 99.57/13.45 ((
% 99.57/13.45 (woz1_2) =>
% 99.57/13.45 ((
% 99.57/13.45 (woz1_3) =>
% 99.57/13.45 ((
% 99.57/13.45 (woz1_4) =>
% 99.57/13.45 ((
% 99.57/13.45 (woz1_5) =>
% 99.57/13.45 ((
% 99.57/13.45 (breln1all2) =>
% 99.57/13.45 ((
% 99.57/13.45 (breln1SetBreln1) =>
% 99.57/13.45 ((
% 99.57/13.45 (choice2fnsingleton) =>
% 99.57/13.45 ((
% 99.57/13.45 (setOfPairsIsBReln1) =>
% 99.57/13.45 ((
% 99.57/13.45 (breln1all1) =>
% 99.57/13.45 ((
% 99.57/13.45 (subbreln1) =>
% 99.57/13.45 ((
% 99.57/13.45 (eqbreln1) =>
% 99.57/13.45 ((
% 99.57/13.45 (breln1invprop) =>
% 99.57/13.45 ((
% 99.57/13.45 (breln1invI) =>
% 99.57/13.45 ((
% 99.57/13.45 (breln1invE) =>
% 99.57/13.45 ((
% 99.57/13.45 (breln1compprop) =>
% 99.57/13.45 ((
% 99.57/13.45 (breln1compI) =>
% 99.57/13.45 ((
% 99.57/13.45 (breln1compE) =>
% 99.57/13.45 ((
% 99.57/13.45 (breln1compEex) =>
% 99.57/13.45 ((
% 99.57/13.45 (breln1unionprop) =>
% 99.57/13.45 ((
% 99.57/13.45 (breln1unionIL) =>
% 99.57/13.45 ((
% 99.57/13.45 (breln1unionIR) =>
% 99.57/13.45 ((
% 99.57/13.45 (breln1unionI) =>
% 99.57/13.45 ((
% 99.57/13.45 (breln1unionE) =>
% 99.57/13.45 ((
% 99.57/13.45 (breln1unionEcases) =>
% 99.57/13.45 ((
% 99.57/13.45 (breln1unionCommutes) =>
% 99.57/13.45 ((
% 99.57/13.45 (woz2Ex) =>
% 99.57/13.45 ((
% 99.57/13.45 (woz2W) =>
% 99.57/13.45 ((
% 99.57/13.45 (woz2A) =>
% 99.57/13.45 ((
% 99.57/13.45 (woz2B) =>
% 99.57/13.45 ((
% 99.57/13.45 (image1Ex) =>
% 99.57/13.45 ((
% 99.57/13.45 (image1Ex1) =>
% 99.57/13.45 ((
% 99.57/13.45 (image1Equiv) =>
% 99.57/13.45 ((
% 99.57/13.45 (image1E) =>
% 99.57/13.45 ((
% 99.57/13.45 (image1I) =>
% 99.57/13.45 ((
% 99.84/13.45 (injFuncInInjFuncSet) =>
% 99.84/13.45 ((
% 99.84/13.45 (injFuncSetFuncIn) =>
% 99.84/13.45 ((
% 99.84/13.45 (injFuncSetFuncInj) =>
% 99.84/13.45 ((
% 99.84/13.45 (!!) @ (
% 99.84/13.45 (('#B') @ (
% 99.84/13.45 !!) @
% 99.84/13.45 (
% 99.84/13.45 (
% 99.84/13.45 ('#B') @ (
% 99.84/13.45 (
% 99.84/13.45 ('#B') @ (
% 99.84/13.45 !!))) @
% 99.84/13.45 (
% 99.84/13.45 (
% 99.84/13.45 ('#S') @ (
% 99.84/13.45 (
% 99.84/13.45 ('#B') @ (
% 99.84/13.45 '#S') @
% 99.84/13.45 (
% 99.84/13.45 (
% 99.84/13.45 ('#B') @ (
% 99.84/13.45 (
% 99.84/13.45 ('#B') @ (
% 99.84/13.45 '#S'))) @
% 99.84/13.45 (
% 99.84/13.45 (
% 99.84/13.45 ('#B') @ (
% 99.84/13.45 (
% 99.84/13.45 ('#B') @ (
% 99.84/13.45 (
% 99.84/13.45 ('#B') @ (
% 99.84/13.45 =>))))) @
% 99.84/13.45 (
% 99.84/13.45 (
% 99.84/13.45 ('#B') @ (
% 99.84/13.45 (
% 99.84/13.45 ('#B') @ (
% 99.84/13.45 (
% 99.84/13.45 ('#C') @ in)))) @
% 99.84/13.45 surjFuncSet)))))))) @
% 99.84/13.45 (
% 99.84/13.45 (
% 99.84/13.45 ('#B') @ (
% 99.84/13.45 (
% 99.84/13.45 ('#B') @ (
% 99.84/13.45 (
% 99.84/13.45 ('#C') @ in)))) @
% 99.84/13.45 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.84/13.45 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1338])).
% 99.84/13.45 thf(zip_derived_cl1354, plain,
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% 99.84/13.45 (((setukpairIR) =>
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% 99.84/13.45 (((kpairp) =>
% 99.84/13.45 (((singletonsubset) =>
% 99.84/13.45 (((singletoninpowerset) =>
% 99.84/13.45 (((singletoninpowunion) =>
% 99.84/13.45 (((upairset2E) =>
% 99.84/13.45 (((upairsubunion) =>
% 99.84/13.45 (((upairinpowunion) =>
% 99.84/13.45 (((ubforcartprodlem1) =>
% 99.84/13.45 (((ubforcartprodlem2) =>
% 99.84/13.45 (((ubforcartprodlem3) =>
% 99.84/13.45 (((cartprodpairin) =>
% 99.84/13.45 (((cartprodmempair1) =>
% 99.84/13.45 (((cartprodmempair) =>
% 99.84/13.45 (((setunionE2) =>
% 99.84/13.45 (((setunionsingleton1) =>
% 99.84/13.45 (((setunionsingleton2) =>
% 99.84/13.45 (((setunionsingleton) =>
% 99.84/13.45 (((singletonprop) =>
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% 99.84/13.45 (((ex1I2) =>
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% 99.84/13.45 (((setukpairinjL1) =>
% 99.84/13.45 (((kfstsingleton) =>
% 99.84/13.45 ((
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% 99.84/13.45 ((
% 99.84/13.45 (kfstpairEq) =>
% 99.84/13.45 ((
% 99.84/13.45 (cartprodfstin) =>
% 99.84/13.45 ((
% 99.84/13.45 (setukpairinjL2) =>
% 99.84/13.45 ((
% 99.84/13.45 (setukpairinjL) =>
% 99.84/13.45 ((
% 99.84/13.45 (setukpairinjR11) =>
% 99.84/13.45 ((
% 99.84/13.45 (setukpairinjR12) =>
% 99.84/13.45 ((
% 99.84/13.45 (setukpairinjR1) =>
% 99.84/13.45 ((
% 99.84/13.45 (upairequniteq) =>
% 99.84/13.45 ((
% 99.84/13.45 (setukpairinjR2) =>
% 99.84/13.45 ((
% 99.84/13.45 (setukpairinjR) =>
% 99.84/13.45 ((
% 99.84/13.45 (ksndsingleton) =>
% 99.84/13.45 ((
% 99.84/13.45 (ksndpairEq) =>
% 99.84/13.45 ((
% 99.84/13.45 (kpairsurjEq) =>
% 99.84/13.45 ((
% 99.84/13.45 (cartprodsndin) =>
% 99.84/13.45 ((
% 99.84/13.45 (cartprodpairmemEL) =>
% 99.84/13.45 ((
% 99.84/13.45 (cartprodpairmemER) =>
% 99.84/13.45 ((
% 99.84/13.45 (cartprodmempaircEq) =>
% 99.84/13.45 ((
% 99.84/13.45 (cartprodfstpairEq) =>
% 99.84/13.45 ((
% 99.84/13.45 (cartprodsndpairEq) =>
% 99.84/13.45 ((
% 99.84/13.45 (cartprodpairsurjEq) =>
% 99.84/13.45 ((
% 99.84/13.45 (dpsetconstrI) =>
% 99.84/13.45 ((
% 99.84/13.45 (dpsetconstrSub) =>
% 99.84/13.45 ((
% 99.84/13.45 (setOfPairsIsBReln) =>
% 99.84/13.45 ((
% 99.84/13.45 (dpsetconstrERa) =>
% 99.84/13.45 ((
% 99.84/13.45 (dpsetconstrEL1) =>
% 99.84/13.45 ((
% 99.84/13.45 (dpsetconstrEL2) =>
% 99.84/13.45 ((
% 99.84/13.45 (dpsetconstrER) =>
% 99.84/13.45 ((
% 99.84/13.45 (funcImageSingleton) =>
% 99.84/13.45 ((
% 99.84/13.45 (apProp) =>
% 99.84/13.45 ((
% 99.84/13.45 (app) =>
% 99.84/13.45 ((
% 99.84/13.45 (infuncsetfunc) =>
% 99.84/13.45 ((
% 99.84/13.45 (ap2p) =>
% 99.84/13.45 ((
% 99.84/13.45 (funcinfuncset) =>
% 99.84/13.45 ((
% 99.84/13.45 (lamProp) =>
% 99.84/13.45 ((
% 99.84/13.45 (lamp) =>
% 99.84/13.45 ((
% 99.84/13.45 (lam2p) =>
% 99.84/13.45 ((
% 99.84/13.45 (brelnall1) =>
% 99.84/13.45 ((
% 99.84/13.45 (brelnall2) =>
% 99.84/13.45 ((
% 99.84/13.45 (ex1E2) =>
% 99.84/13.45 ((
% 99.84/13.45 (funcGraphProp1) =>
% 99.84/13.45 ((
% 99.84/13.45 (funcGraphProp3) =>
% 99.84/13.45 ((
% 99.84/13.45 (funcGraphProp2) =>
% 99.84/13.45 ((
% 99.84/13.45 (funcextLem) =>
% 99.84/13.45 ((
% 99.84/13.45 (funcGraphProp4) =>
% 99.84/13.45 ((
% 99.84/13.45 (subbreln) =>
% 99.84/13.45 ((
% 99.84/13.45 (eqbreln) =>
% 99.84/13.45 ((
% 99.84/13.45 (funcext) =>
% 99.84/13.45 ((
% 99.84/13.45 (funcext2) =>
% 99.84/13.45 ((
% 99.84/13.45 (ap2apEq1) =>
% 99.84/13.45 ((
% 99.84/13.45 (ap2apEq2) =>
% 99.84/13.45 ((
% 99.84/13.45 (beta1) =>
% 99.84/13.45 ((
% 99.84/13.45 (eta1) =>
% 99.84/13.45 ((
% 99.84/13.45 (lam2lamEq) =>
% 99.84/13.45 ((
% 99.84/13.45 (beta2) =>
% 99.84/13.45 ((
% 99.84/13.45 (eta2) =>
% 99.84/13.45 ((
% 99.84/13.45 (iffalseProp1) =>
% 99.84/13.45 ((
% 99.84/13.45 (iffalseProp2) =>
% 99.84/13.45 ((
% 99.84/13.45 (iftrueProp1) =>
% 99.84/13.45 ((
% 99.84/13.45 (iftrueProp2) =>
% 99.84/13.45 ((
% 99.84/13.45 (ifSingleton) =>
% 99.84/13.45 ((
% 99.84/13.45 (ifp) =>
% 99.84/13.45 ((
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% 99.84/13.45 ((
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% 99.84/13.45 ((
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% 99.84/13.45 ((
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% 99.84/13.45 ((
% 99.84/13.45 (binintersectT_lem) =>
% 99.84/13.45 ((
% 99.84/13.45 (binunionT_lem) =>
% 99.84/13.45 ((
% 99.84/13.45 (powersetT_lem) =>
% 99.84/13.45 ((
% 99.84/13.45 (setminusT_lem) =>
% 99.84/13.45 ((
% 99.84/13.45 (complementT_lem) =>
% 99.84/13.45 ((
% 99.84/13.45 (setextT) =>
% 99.84/13.45 ((
% 99.84/13.45 (subsetTI) =>
% 99.84/13.45 ((
% 99.84/13.45 (powersetTI1) =>
% 99.84/13.45 ((
% 99.84/13.45 (powersetTE1) =>
% 99.84/13.45 ((
% 99.84/13.45 (complementTI1) =>
% 99.84/13.45 ((
% 99.84/13.45 (complementTE1) =>
% 99.84/13.45 ((
% 99.84/13.45 (binintersectTELcontra) =>
% 99.84/13.45 ((
% 99.84/13.45 (binintersectTERcontra) =>
% 99.84/13.45 ((
% 99.84/13.45 (contrasubsetT) =>
% 99.84/13.45 ((
% 99.84/13.45 (contrasubsetT1) =>
% 99.84/13.45 ((
% 99.84/13.45 (contrasubsetT2) =>
% 99.84/13.45 ((
% 99.84/13.45 (contrasubsetT3) =>
% 99.84/13.45 ((
% 99.84/13.45 (doubleComplementI1) =>
% 99.84/13.45 ((
% 99.84/13.45 (doubleComplementE1) =>
% 99.84/13.45 ((
% 99.84/13.45 (doubleComplementSub1) =>
% 99.84/13.45 ((
% 99.84/13.45 (doubleComplementSub2) =>
% 99.84/13.45 ((
% 99.84/13.45 (doubleComplementEq) =>
% 99.84/13.45 ((
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% 99.84/13.45 ((
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% 99.84/13.45 ((
% 99.84/13.45 (complementSubsetComplementIntersect) =>
% 99.84/13.45 ((
% 99.84/13.45 (complementInPowersetComplementIntersect) =>
% 99.84/13.45 ((
% 99.84/13.45 (contraSubsetComplement) =>
% 99.84/13.45 ((
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% 99.84/13.45 ((
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% 99.84/13.45 ((
% 99.84/13.45 (binunionTIRcontra) =>
% 99.84/13.45 ((
% 99.84/13.45 (inIntersectImpInUnion) =>
% 99.84/13.45 ((
% 99.84/13.45 (inIntersectImpInUnion2) =>
% 99.84/13.45 ((
% 99.84/13.45 (inIntersectImpInIntersectUnions) =>
% 99.84/13.45 ((
% 99.84/13.45 (intersectInPowersetIntersectUnions) =>
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% 99.84/13.45 ((
% 99.84/13.45 (inComplementUnionImpInComplement1) =>
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% 99.84/13.45 ((
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% 99.84/13.45 ((
% 99.84/13.45 (complementUnionInPowersetComplement) =>
% 99.84/13.45 ((
% 99.84/13.45 (demorgan2a2) =>
% 99.84/13.45 ((
% 99.84/13.45 (demorgan1a) =>
% 99.84/13.45 ((
% 99.84/13.45 (demorgan1b) =>
% 99.84/13.45 ((
% 99.84/13.45 (demorgan1) =>
% 99.84/13.45 ((
% 99.84/13.45 (demorgan2a) =>
% 99.84/13.45 ((
% 99.84/13.45 (demorgan2b2) =>
% 99.84/13.45 ((
% 99.84/13.45 (demorgan2b) =>
% 99.84/13.45 ((
% 99.84/13.45 (demorgan2) =>
% 99.84/13.45 ((
% 99.84/13.45 (woz13rule0) =>
% 99.84/13.45 ((
% 99.84/13.45 (woz13rule1) =>
% 99.84/13.45 ((
% 99.84/13.45 (woz13rule2) =>
% 99.84/13.45 ((
% 99.84/13.45 (woz13rule3) =>
% 99.84/13.45 ((
% 99.84/13.45 (woz13rule4) =>
% 99.84/13.45 ((
% 99.84/13.45 (woz1_1) =>
% 99.84/13.45 ((
% 99.84/13.45 (woz1_2) =>
% 99.84/13.45 ((
% 99.84/13.45 (woz1_3) =>
% 99.84/13.45 ((
% 99.84/13.45 (woz1_4) =>
% 99.84/13.45 ((
% 99.84/13.45 (woz1_5) =>
% 99.84/13.45 ((
% 99.84/13.45 (breln1all2) =>
% 99.84/13.45 ((
% 99.84/13.45 (breln1SetBreln1) =>
% 99.84/13.45 ((
% 99.84/13.45 (choice2fnsingleton) =>
% 99.84/13.45 ((
% 99.84/13.45 (setOfPairsIsBReln1) =>
% 99.84/13.45 ((
% 99.84/13.45 (breln1all1) =>
% 99.84/13.45 ((
% 99.84/13.45 (subbreln1) =>
% 99.84/13.45 ((
% 99.84/13.45 (eqbreln1) =>
% 99.84/13.45 ((
% 99.84/13.45 (breln1invprop) =>
% 99.84/13.45 ((
% 99.84/13.45 (breln1invI) =>
% 99.84/13.45 ((
% 99.84/13.45 (breln1invE) =>
% 99.84/13.45 ((
% 99.84/13.45 (breln1compprop) =>
% 99.84/13.45 ((
% 99.84/13.45 (breln1compI) =>
% 99.84/13.45 ((
% 99.84/13.45 (breln1compE) =>
% 99.84/13.45 ((
% 99.84/13.45 (breln1compEex) =>
% 99.84/13.45 ((
% 99.84/13.45 (breln1unionprop) =>
% 99.84/13.45 ((
% 99.84/13.45 (breln1unionIL) =>
% 99.84/13.45 ((
% 99.84/13.45 (breln1unionIR) =>
% 99.84/13.45 ((
% 99.84/13.45 (breln1unionI) =>
% 99.84/13.45 ((
% 99.84/13.45 (breln1unionE) =>
% 99.84/13.45 ((
% 99.84/13.45 (breln1unionEcases) =>
% 99.84/13.45 ((
% 99.84/13.45 (breln1unionCommutes) =>
% 99.84/13.45 ((
% 99.84/13.45 (woz2Ex) =>
% 99.84/13.45 ((
% 99.84/13.45 (woz2W) =>
% 99.84/13.45 ((
% 99.84/13.45 (woz2A) =>
% 99.84/13.45 ((
% 99.84/13.45 (woz2B) =>
% 99.84/13.45 ((
% 99.84/13.45 (image1Ex) =>
% 99.84/13.45 ((
% 99.84/13.45 (image1Ex1) =>
% 99.84/13.45 ((
% 99.84/13.45 (image1Equiv) =>
% 99.84/13.45 ((
% 99.84/13.45 (image1E) =>
% 99.84/13.45 ((
% 99.84/13.45 (image1I) =>
% 99.84/13.45 ((
% 99.84/13.45 (injFuncInInjFuncSet) =>
% 99.84/13.45 ((
% 99.84/13.45 (injFuncSetFuncIn) =>
% 99.84/13.45 ((
% 99.84/13.45 (injFuncSetFuncInj) =>
% 99.84/13.45 ((
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% 99.84/13.45 (('#B') @ (
% 99.84/13.45 !!) @
% 99.84/13.45 (
% 99.84/13.45 (
% 99.84/13.45 ('#B') @ (
% 99.84/13.45 (
% 99.84/13.45 ('#B') @ (
% 99.84/13.45 !!))) @
% 99.84/13.45 (
% 99.84/13.45 (
% 99.84/13.45 ('#S') @ (
% 99.84/13.45 (
% 99.84/13.45 ('#B') @ (
% 99.84/13.45 '#S') @
% 99.84/13.45 (
% 99.84/13.45 (
% 99.84/13.45 ('#B') @ (
% 99.84/13.45 (
% 99.84/13.45 ('#B') @ (
% 99.84/13.45 '#S'))) @
% 99.84/13.45 (
% 99.84/13.45 (
% 99.84/13.45 ('#B') @ (
% 99.84/13.45 (
% 99.84/13.45 ('#B') @ (
% 99.84/13.45 (
% 99.84/13.45 ('#B') @ (
% 99.84/13.45 =>))))) @
% 99.84/13.45 (
% 99.84/13.45 (
% 99.84/13.45 ('#B') @ (
% 99.84/13.45 (
% 99.84/13.45 ('#B') @ (
% 99.84/13.45 (
% 99.84/13.45 ('#C') @ in)))) @
% 99.84/13.45 surjFuncSet)))))))) @
% 99.84/13.45 (
% 99.84/13.45 (
% 99.84/13.45 ('#B') @ (
% 99.84/13.45 (
% 99.84/13.45 ('#B') @ (
% 99.84/13.45 (
% 99.84/13.45 ('#C') @ in)))) @
% 99.84/13.45 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.84/13.45 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1347])).
% 99.84/13.45 thf(zip_derived_cl1361, plain,
% 99.84/13.45 (~ (((symdiffIneg2) =>
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% 99.84/13.45 (((setukpairIL) =>
% 99.84/13.45 (((setukpairIR) =>
% 99.84/13.45 (((kpairiskpair) =>
% 99.84/13.45 (((kpairp) =>
% 99.84/13.45 (((singletonsubset) =>
% 99.84/13.45 (((singletoninpowerset) =>
% 99.84/13.45 (((singletoninpowunion) =>
% 99.84/13.46 (((upairset2E) =>
% 99.84/13.46 (((upairsubunion) =>
% 99.84/13.46 (((upairinpowunion) =>
% 99.84/13.46 (((ubforcartprodlem1) =>
% 99.84/13.46 (((ubforcartprodlem2) =>
% 99.84/13.46 (((ubforcartprodlem3) =>
% 99.84/13.46 (((cartprodpairin) =>
% 99.84/13.46 (((cartprodmempair1) =>
% 99.84/13.46 (((cartprodmempair) =>
% 99.84/13.46 (((setunionE2) =>
% 99.84/13.46 (((setunionsingleton1) =>
% 99.84/13.46 (((setunionsingleton2) =>
% 99.84/13.46 (((setunionsingleton) =>
% 99.84/13.46 (((singletonprop) =>
% 99.84/13.46 (((ex1E1) =>
% 99.84/13.46 (((ex1I) =>
% 99.84/13.46 (((ex1I2) =>
% 99.84/13.46 (((singletonsuniq) =>
% 99.84/13.46 (((setukpairinjL1) =>
% 99.84/13.46 (((kfstsingleton) =>
% 99.84/13.46 (((theprop) =>
% 99.84/13.46 ((
% 99.84/13.46 (kfstpairEq) =>
% 99.84/13.46 ((
% 99.84/13.46 (cartprodfstin) =>
% 99.84/13.46 ((
% 99.84/13.46 (setukpairinjL2) =>
% 99.84/13.46 ((
% 99.84/13.46 (setukpairinjL) =>
% 99.84/13.46 ((
% 99.84/13.46 (setukpairinjR11) =>
% 99.84/13.46 ((
% 99.84/13.46 (setukpairinjR12) =>
% 99.84/13.46 ((
% 99.84/13.46 (setukpairinjR1) =>
% 99.84/13.46 ((
% 99.84/13.46 (upairequniteq) =>
% 99.84/13.46 ((
% 99.84/13.46 (setukpairinjR2) =>
% 99.84/13.46 ((
% 99.84/13.46 (setukpairinjR) =>
% 99.84/13.46 ((
% 99.84/13.46 (ksndsingleton) =>
% 99.84/13.46 ((
% 99.84/13.46 (ksndpairEq) =>
% 99.84/13.46 ((
% 99.84/13.46 (kpairsurjEq) =>
% 99.84/13.46 ((
% 99.84/13.46 (cartprodsndin) =>
% 99.84/13.46 ((
% 99.84/13.46 (cartprodpairmemEL) =>
% 99.84/13.46 ((
% 99.84/13.46 (cartprodpairmemER) =>
% 99.84/13.46 ((
% 99.84/13.46 (cartprodmempaircEq) =>
% 99.84/13.46 ((
% 99.84/13.46 (cartprodfstpairEq) =>
% 99.84/13.46 ((
% 99.84/13.46 (cartprodsndpairEq) =>
% 99.84/13.46 ((
% 99.84/13.46 (cartprodpairsurjEq) =>
% 99.84/13.46 ((
% 99.84/13.46 (dpsetconstrI) =>
% 99.84/13.46 ((
% 99.84/13.46 (dpsetconstrSub) =>
% 99.84/13.46 ((
% 99.84/13.46 (setOfPairsIsBReln) =>
% 99.84/13.46 ((
% 99.84/13.46 (dpsetconstrERa) =>
% 99.84/13.46 ((
% 99.84/13.46 (dpsetconstrEL1) =>
% 99.84/13.46 ((
% 99.84/13.46 (dpsetconstrEL2) =>
% 99.84/13.46 ((
% 99.84/13.46 (dpsetconstrER) =>
% 99.84/13.46 ((
% 99.84/13.46 (funcImageSingleton) =>
% 99.84/13.46 ((
% 99.84/13.46 (apProp) =>
% 99.84/13.46 ((
% 99.84/13.46 (app) =>
% 99.84/13.46 ((
% 99.84/13.46 (infuncsetfunc) =>
% 99.84/13.46 ((
% 99.84/13.46 (ap2p) =>
% 99.84/13.46 ((
% 99.84/13.46 (funcinfuncset) =>
% 99.84/13.46 ((
% 99.84/13.46 (lamProp) =>
% 99.84/13.46 ((
% 99.84/13.46 (lamp) =>
% 99.84/13.46 ((
% 99.84/13.46 (lam2p) =>
% 99.84/13.46 ((
% 99.84/13.46 (brelnall1) =>
% 99.84/13.46 ((
% 99.84/13.46 (brelnall2) =>
% 99.84/13.46 ((
% 99.84/13.46 (ex1E2) =>
% 99.84/13.46 ((
% 99.84/13.46 (funcGraphProp1) =>
% 99.84/13.46 ((
% 99.84/13.46 (funcGraphProp3) =>
% 99.84/13.46 ((
% 99.84/13.46 (funcGraphProp2) =>
% 99.84/13.46 ((
% 99.84/13.46 (funcextLem) =>
% 99.84/13.46 ((
% 99.84/13.46 (funcGraphProp4) =>
% 99.84/13.46 ((
% 99.84/13.46 (subbreln) =>
% 99.84/13.46 ((
% 99.84/13.46 (eqbreln) =>
% 99.84/13.46 ((
% 99.84/13.46 (funcext) =>
% 99.84/13.46 ((
% 99.84/13.46 (funcext2) =>
% 99.84/13.46 ((
% 99.84/13.46 (ap2apEq1) =>
% 99.84/13.46 ((
% 99.84/13.46 (ap2apEq2) =>
% 99.84/13.46 ((
% 99.84/13.46 (beta1) =>
% 99.84/13.46 ((
% 99.84/13.46 (eta1) =>
% 99.84/13.46 ((
% 99.84/13.46 (lam2lamEq) =>
% 99.84/13.46 ((
% 99.84/13.46 (beta2) =>
% 99.84/13.46 ((
% 99.84/13.46 (eta2) =>
% 99.84/13.46 ((
% 99.84/13.46 (iffalseProp1) =>
% 99.84/13.46 ((
% 99.84/13.46 (iffalseProp2) =>
% 99.84/13.46 ((
% 99.84/13.46 (iftrueProp1) =>
% 99.84/13.46 ((
% 99.84/13.46 (iftrueProp2) =>
% 99.84/13.46 ((
% 99.84/13.46 (ifSingleton) =>
% 99.84/13.46 ((
% 99.84/13.46 (ifp) =>
% 99.84/13.46 ((
% 99.84/13.46 (theeq) =>
% 99.84/13.46 ((
% 99.84/13.46 (iftrue) =>
% 99.84/13.46 ((
% 99.84/13.46 (iffalse) =>
% 99.84/13.46 ((
% 99.84/13.46 (iftrueorfalse) =>
% 99.84/13.46 ((
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% 99.84/13.46 ((
% 99.84/13.46 (binunionT_lem) =>
% 99.84/13.46 ((
% 99.84/13.46 (powersetT_lem) =>
% 99.84/13.46 ((
% 99.84/13.46 (setminusT_lem) =>
% 99.84/13.46 ((
% 99.84/13.46 (complementT_lem) =>
% 99.84/13.46 ((
% 99.84/13.46 (setextT) =>
% 99.84/13.46 ((
% 99.84/13.46 (subsetTI) =>
% 99.84/13.46 ((
% 99.84/13.46 (powersetTI1) =>
% 99.84/13.46 ((
% 99.84/13.46 (powersetTE1) =>
% 99.84/13.46 ((
% 99.84/13.46 (complementTI1) =>
% 99.84/13.46 ((
% 99.84/13.46 (complementTE1) =>
% 99.84/13.46 ((
% 99.84/13.46 (binintersectTELcontra) =>
% 99.84/13.46 ((
% 99.84/13.46 (binintersectTERcontra) =>
% 99.84/13.46 ((
% 99.84/13.46 (contrasubsetT) =>
% 99.84/13.46 ((
% 99.84/13.46 (contrasubsetT1) =>
% 99.84/13.46 ((
% 99.84/13.46 (contrasubsetT2) =>
% 99.84/13.46 ((
% 99.84/13.46 (contrasubsetT3) =>
% 99.84/13.46 ((
% 99.84/13.46 (doubleComplementI1) =>
% 99.84/13.46 ((
% 99.84/13.46 (doubleComplementE1) =>
% 99.84/13.46 ((
% 99.84/13.46 (doubleComplementSub1) =>
% 99.84/13.46 ((
% 99.84/13.46 (doubleComplementSub2) =>
% 99.84/13.46 ((
% 99.84/13.46 (doubleComplementEq) =>
% 99.84/13.46 ((
% 99.84/13.46 (complementTnotintersectT) =>
% 99.84/13.46 ((
% 99.84/13.46 (complementImpComplementIntersect) =>
% 99.84/13.46 ((
% 99.84/13.46 (complementSubsetComplementIntersect) =>
% 99.84/13.46 ((
% 99.84/13.46 (complementInPowersetComplementIntersect) =>
% 99.84/13.46 ((
% 99.84/13.46 (contraSubsetComplement) =>
% 99.84/13.46 ((
% 99.84/13.46 (complementTcontraSubset) =>
% 99.84/13.46 ((
% 99.84/13.46 (binunionTILcontra) =>
% 99.84/13.46 ((
% 99.84/13.46 (binunionTIRcontra) =>
% 99.84/13.46 ((
% 99.84/13.46 (inIntersectImpInUnion) =>
% 99.84/13.46 ((
% 99.84/13.46 (inIntersectImpInUnion2) =>
% 99.84/13.46 ((
% 99.84/13.46 (inIntersectImpInIntersectUnions) =>
% 99.84/13.46 ((
% 99.84/13.46 (intersectInPowersetIntersectUnions) =>
% 99.84/13.46 ((
% 99.84/13.46 (inComplementUnionImpNotIn1) =>
% 99.84/13.46 ((
% 99.84/13.46 (inComplementUnionImpInComplement1) =>
% 99.84/13.46 ((
% 99.84/13.46 (binunionTE) =>
% 99.84/13.46 ((
% 99.84/13.46 (binunionTEcontra) =>
% 99.84/13.46 ((
% 99.84/13.46 (demorgan2a1) =>
% 99.84/13.46 ((
% 99.84/13.46 (complementUnionInPowersetComplement) =>
% 99.84/13.46 ((
% 99.84/13.46 (demorgan2a2) =>
% 99.84/13.46 ((
% 99.84/13.46 (demorgan1a) =>
% 99.84/13.46 ((
% 99.84/13.46 (demorgan1b) =>
% 99.84/13.46 ((
% 99.84/13.46 (demorgan1) =>
% 99.84/13.46 ((
% 99.84/13.46 (demorgan2a) =>
% 99.84/13.46 ((
% 99.84/13.46 (demorgan2b2) =>
% 99.84/13.46 ((
% 99.84/13.46 (demorgan2b) =>
% 99.84/13.46 ((
% 99.84/13.46 (demorgan2) =>
% 99.84/13.46 ((
% 99.84/13.46 (woz13rule0) =>
% 99.84/13.46 ((
% 99.84/13.46 (woz13rule1) =>
% 99.84/13.46 ((
% 99.84/13.46 (woz13rule2) =>
% 99.84/13.46 ((
% 99.84/13.46 (woz13rule3) =>
% 99.84/13.46 ((
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% 99.84/13.46 ((
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% 99.84/13.46 ((
% 99.84/13.46 (woz1_4) =>
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% 99.84/13.46 (woz1_5) =>
% 99.84/13.46 ((
% 99.84/13.46 (breln1all2) =>
% 99.84/13.46 ((
% 99.84/13.46 (breln1SetBreln1) =>
% 99.84/13.46 ((
% 99.84/13.46 (choice2fnsingleton) =>
% 99.84/13.46 ((
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% 99.84/13.46 ((
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% 99.84/13.46 ((
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% 99.84/13.46 (ex1E2) =>
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% 99.84/13.46 (
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% 99.84/13.46 (cartprodmempaircEq) =>
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% 99.84/13.46 (cartprodfstpairEq) =>
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% 99.84/13.46 (cartprodsndpairEq) =>
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% 99.84/13.46 ((
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% 99.84/13.46 ((
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% 99.84/13.46 (kpairsurjEq) =>
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% 99.84/13.46 (cartprodsndin) =>
% 99.84/13.46 ((
% 99.84/13.46 (cartprodpairmemEL) =>
% 99.84/13.46 ((
% 99.84/13.46 (cartprodpairmemER) =>
% 99.84/13.46 ((
% 99.84/13.46 (cartprodmempaircEq) =>
% 99.84/13.46 ((
% 99.84/13.46 (cartprodfstpairEq) =>
% 99.84/13.46 ((
% 99.84/13.46 (cartprodsndpairEq) =>
% 99.84/13.46 ((
% 99.84/13.46 (cartprodpairsurjEq) =>
% 99.84/13.46 ((
% 99.84/13.46 (dpsetconstrI) =>
% 99.84/13.46 ((
% 99.84/13.46 (dpsetconstrSub) =>
% 99.84/13.46 ((
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% 99.84/13.46 ((
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% 99.84/13.46 ((
% 99.84/13.46 (dpsetconstrEL2) =>
% 99.84/13.46 ((
% 99.84/13.46 (dpsetconstrER) =>
% 99.84/13.46 ((
% 99.84/13.46 (funcImageSingleton) =>
% 99.84/13.46 ((
% 99.84/13.46 (apProp) =>
% 99.84/13.46 ((
% 99.84/13.46 (app) =>
% 99.84/13.46 ((
% 99.84/13.46 (infuncsetfunc) =>
% 99.84/13.46 ((
% 99.84/13.46 (ap2p) =>
% 99.84/13.46 ((
% 99.84/13.46 (funcinfuncset) =>
% 99.84/13.46 ((
% 99.84/13.46 (lamProp) =>
% 99.84/13.46 ((
% 99.84/13.46 (lamp) =>
% 99.84/13.46 ((
% 99.84/13.46 (lam2p) =>
% 99.84/13.46 ((
% 99.84/13.46 (brelnall1) =>
% 99.84/13.46 ((
% 99.84/13.46 (brelnall2) =>
% 99.84/13.46 ((
% 99.84/13.46 (ex1E2) =>
% 99.84/13.46 ((
% 99.84/13.46 (funcGraphProp1) =>
% 99.84/13.46 ((
% 99.84/13.46 (funcGraphProp3) =>
% 99.84/13.46 ((
% 99.84/13.46 (funcGraphProp2) =>
% 99.84/13.46 ((
% 99.84/13.46 (funcextLem) =>
% 99.84/13.46 ((
% 99.84/13.46 (funcGraphProp4) =>
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% 99.84/13.46 (ap2apEq2) =>
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% 99.84/13.46 ((
% 99.84/13.46 (eta1) =>
% 99.84/13.46 ((
% 99.84/13.46 (lam2lamEq) =>
% 99.84/13.46 ((
% 99.84/13.46 (beta2) =>
% 99.84/13.46 ((
% 99.84/13.46 (eta2) =>
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% 99.84/13.46 (iftrueProp1) =>
% 99.84/13.46 ((
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% 99.84/13.46 ((
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% 99.84/13.46 ((
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% 99.84/13.46 ((
% 99.84/13.46 (binintersectTERcontra) =>
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% 99.84/13.46 ((
% 99.84/13.46 (contrasubsetT1) =>
% 99.84/13.46 ((
% 99.84/13.46 (contrasubsetT2) =>
% 99.84/13.46 ((
% 99.84/13.46 (contrasubsetT3) =>
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% 99.84/13.46 ((
% 99.84/13.46 (doubleComplementE1) =>
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% 99.84/13.46 ((
% 99.84/13.46 (doubleComplementSub2) =>
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% 99.84/13.46 (contraSubsetComplement) =>
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% 99.84/13.46 ((
% 99.84/13.46 (binunionTIRcontra) =>
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% 99.84/13.46 (inIntersectImpInUnion2) =>
% 99.84/13.46 ((
% 99.84/13.46 (inIntersectImpInIntersectUnions) =>
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% 99.84/13.46 (inComplementUnionImpNotIn1) =>
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% 99.84/13.46 ((
% 99.84/13.46 (complementUnionInPowersetComplement) =>
% 99.84/13.46 ((
% 99.84/13.46 (demorgan2a2) =>
% 99.84/13.46 ((
% 99.84/13.46 (demorgan1a) =>
% 99.84/13.46 ((
% 99.84/13.46 (demorgan1b) =>
% 99.84/13.46 ((
% 99.84/13.46 (demorgan1) =>
% 99.84/13.46 ((
% 99.84/13.46 (demorgan2a) =>
% 99.84/13.46 ((
% 99.84/13.46 (demorgan2b2) =>
% 99.84/13.46 ((
% 99.84/13.46 (demorgan2b) =>
% 99.84/13.46 ((
% 99.84/13.46 (demorgan2) =>
% 99.84/13.46 ((
% 99.84/13.46 (woz13rule0) =>
% 99.84/13.46 ((
% 99.84/13.46 (woz13rule1) =>
% 99.84/13.46 ((
% 99.84/13.46 (woz13rule2) =>
% 99.84/13.46 ((
% 99.84/13.46 (woz13rule3) =>
% 99.84/13.46 ((
% 99.84/13.46 (woz13rule4) =>
% 99.84/13.46 ((
% 99.84/13.46 (woz1_1) =>
% 99.84/13.46 ((
% 99.84/13.46 (woz1_2) =>
% 99.84/13.46 ((
% 99.84/13.46 (woz1_3) =>
% 99.84/13.46 ((
% 99.84/13.46 (woz1_4) =>
% 99.84/13.46 ((
% 99.84/13.46 (woz1_5) =>
% 99.84/13.46 ((
% 99.84/13.46 (breln1all2) =>
% 99.84/13.46 ((
% 99.84/13.46 (breln1SetBreln1) =>
% 99.84/13.46 ((
% 99.84/13.46 (choice2fnsingleton) =>
% 99.84/13.46 ((
% 99.84/13.46 (setOfPairsIsBReln1) =>
% 99.84/13.46 ((
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% 99.84/13.46 ((
% 99.84/13.46 (subbreln1) =>
% 99.84/13.46 ((
% 99.84/13.46 (eqbreln1) =>
% 99.84/13.46 ((
% 99.84/13.46 (breln1invprop) =>
% 99.84/13.46 ((
% 99.84/13.46 (breln1invI) =>
% 99.84/13.46 ((
% 99.84/13.46 (breln1invE) =>
% 99.84/13.46 ((
% 99.84/13.46 (breln1compprop) =>
% 99.84/13.46 ((
% 99.84/13.46 (breln1compI) =>
% 99.84/13.46 ((
% 99.84/13.46 (breln1compE) =>
% 99.84/13.46 ((
% 99.84/13.46 (breln1compEex) =>
% 99.84/13.46 ((
% 99.84/13.46 (breln1unionprop) =>
% 99.84/13.46 ((
% 99.84/13.46 (breln1unionIL) =>
% 99.84/13.46 ((
% 99.84/13.46 (breln1unionIR) =>
% 99.84/13.46 ((
% 99.84/13.46 (breln1unionI) =>
% 99.84/13.46 ((
% 99.84/13.46 (breln1unionE) =>
% 99.84/13.46 ((
% 99.84/13.46 (breln1unionEcases) =>
% 99.84/13.46 ((
% 99.84/13.46 (breln1unionCommutes) =>
% 99.84/13.46 ((
% 99.84/13.46 (woz2Ex) =>
% 99.84/13.46 ((
% 99.84/13.46 (woz2W) =>
% 99.84/13.46 ((
% 99.84/13.46 (woz2A) =>
% 99.84/13.46 ((
% 99.84/13.46 (woz2B) =>
% 99.84/13.46 ((
% 99.84/13.46 (image1Ex) =>
% 99.84/13.46 ((
% 99.84/13.46 (image1Ex1) =>
% 99.84/13.46 ((
% 99.84/13.46 (image1Equiv) =>
% 99.84/13.46 ((
% 99.84/13.46 (image1E) =>
% 99.84/13.46 ((
% 99.84/13.46 (image1I) =>
% 99.84/13.46 ((
% 99.84/13.46 (injFuncInInjFuncSet) =>
% 99.84/13.46 ((
% 99.84/13.46 (injFuncSetFuncIn) =>
% 99.84/13.46 ((
% 99.84/13.46 (injFuncSetFuncInj) =>
% 99.84/13.46 ((
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% 99.84/13.46 (('#B') @ (
% 99.84/13.46 !!) @
% 99.84/13.46 (
% 99.84/13.46 (
% 99.84/13.46 ('#B') @ (
% 99.84/13.46 (
% 99.84/13.46 ('#B') @ (
% 99.84/13.46 !!))) @
% 99.84/13.46 (
% 99.84/13.46 (
% 99.84/13.46 ('#S') @ (
% 99.84/13.46 (
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% 99.84/13.46 (
% 99.84/13.46 (
% 99.84/13.46 ('#B') @ (
% 99.84/13.46 (
% 99.84/13.46 ('#B') @ (
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% 99.84/13.46 (
% 99.84/13.46 (
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% 99.84/13.46 (
% 99.84/13.46 ('#B') @ (
% 99.84/13.46 (
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% 99.84/13.46 (
% 99.84/13.46 (
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% 99.84/13.46 (
% 99.84/13.46 ('#B') @ (
% 99.84/13.46 (
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% 99.84/13.46 surjFuncSet)))))))) @
% 99.84/13.46 (
% 99.84/13.46 (
% 99.84/13.46 ('#B') @ (
% 99.84/13.46 (
% 99.84/13.46 ('#B') @ (
% 99.84/13.46 (
% 99.84/13.46 ('#C') @ in)))) @
% 99.84/13.46 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.84/13.46 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1396])).
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% 99.84/13.46 (((ubforcartprodlem2) =>
% 99.84/13.46 (((ubforcartprodlem3) =>
% 99.84/13.46 (((cartprodpairin) =>
% 99.84/13.46 (((cartprodmempair1) =>
% 99.84/13.46 (((cartprodmempair) =>
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% 99.84/13.46 (setukpairinjR1) =>
% 99.84/13.46 ((
% 99.84/13.46 (upairequniteq) =>
% 99.84/13.46 ((
% 99.84/13.46 (setukpairinjR2) =>
% 99.84/13.46 ((
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% 99.84/13.46 ((
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% 99.84/13.46 ((
% 99.84/13.46 (kpairsurjEq) =>
% 99.84/13.46 ((
% 99.84/13.46 (cartprodsndin) =>
% 99.84/13.46 ((
% 99.84/13.46 (cartprodpairmemEL) =>
% 99.84/13.46 ((
% 99.84/13.46 (cartprodpairmemER) =>
% 99.84/13.46 ((
% 99.84/13.46 (cartprodmempaircEq) =>
% 99.84/13.46 ((
% 99.84/13.46 (cartprodfstpairEq) =>
% 99.84/13.46 ((
% 99.84/13.46 (cartprodsndpairEq) =>
% 99.84/13.46 ((
% 99.84/13.46 (cartprodpairsurjEq) =>
% 99.84/13.46 ((
% 99.84/13.46 (dpsetconstrI) =>
% 99.84/13.46 ((
% 99.84/13.46 (dpsetconstrSub) =>
% 99.84/13.46 ((
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% 99.84/13.46 ((
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% 99.84/13.46 ((
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% 99.84/13.46 ((
% 99.84/13.46 (ap2p) =>
% 99.84/13.46 ((
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% 99.84/13.46 ((
% 99.84/13.46 (lamp) =>
% 99.84/13.46 ((
% 99.84/13.46 (lam2p) =>
% 99.84/13.46 ((
% 99.84/13.46 (brelnall1) =>
% 99.84/13.46 ((
% 99.84/13.46 (brelnall2) =>
% 99.84/13.46 ((
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% 99.84/13.46 ((
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% 99.84/13.46 (funcGraphProp4) =>
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% 99.84/13.46 ((
% 99.84/13.46 (funcext2) =>
% 99.84/13.46 ((
% 99.84/13.46 (ap2apEq1) =>
% 99.84/13.46 ((
% 99.84/13.46 (ap2apEq2) =>
% 99.84/13.46 ((
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% 99.84/13.46 ((
% 99.84/13.46 (eta1) =>
% 99.84/13.46 ((
% 99.84/13.46 (lam2lamEq) =>
% 99.84/13.46 ((
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% 99.84/13.46 ((
% 99.84/13.46 (eta2) =>
% 99.84/13.46 ((
% 99.84/13.46 (iffalseProp1) =>
% 99.84/13.46 ((
% 99.84/13.46 (iffalseProp2) =>
% 99.84/13.46 ((
% 99.84/13.46 (iftrueProp1) =>
% 99.84/13.46 ((
% 99.84/13.46 (iftrueProp2) =>
% 99.84/13.46 ((
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% 99.84/13.46 ((
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% 99.84/13.46 ((
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% 99.84/13.46 ((
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% 99.84/13.46 ((
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% 99.84/13.46 ((
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% 99.84/13.46 ((
% 99.84/13.46 (complementTI1) =>
% 99.84/13.46 ((
% 99.84/13.46 (complementTE1) =>
% 99.84/13.46 ((
% 99.84/13.46 (binintersectTELcontra) =>
% 99.84/13.46 ((
% 99.84/13.46 (binintersectTERcontra) =>
% 99.84/13.46 ((
% 99.84/13.46 (contrasubsetT) =>
% 99.84/13.46 ((
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% 99.84/13.46 ((
% 99.84/13.46 (contrasubsetT2) =>
% 99.84/13.46 ((
% 99.84/13.46 (contrasubsetT3) =>
% 99.84/13.46 ((
% 99.84/13.46 (doubleComplementI1) =>
% 99.84/13.46 ((
% 99.84/13.46 (doubleComplementE1) =>
% 99.84/13.46 ((
% 99.84/13.46 (doubleComplementSub1) =>
% 99.84/13.46 ((
% 99.84/13.46 (doubleComplementSub2) =>
% 99.84/13.46 ((
% 99.84/13.46 (doubleComplementEq) =>
% 99.84/13.46 ((
% 99.84/13.46 (complementTnotintersectT) =>
% 99.84/13.46 ((
% 99.84/13.46 (complementImpComplementIntersect) =>
% 99.84/13.46 ((
% 99.84/13.46 (complementSubsetComplementIntersect) =>
% 99.84/13.46 ((
% 99.84/13.46 (complementInPowersetComplementIntersect) =>
% 99.84/13.46 ((
% 99.84/13.46 (contraSubsetComplement) =>
% 99.84/13.46 ((
% 99.84/13.46 (complementTcontraSubset) =>
% 99.84/13.46 ((
% 99.84/13.46 (binunionTILcontra) =>
% 99.84/13.46 ((
% 99.84/13.46 (binunionTIRcontra) =>
% 99.84/13.46 ((
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% 99.84/13.46 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1420])).
% 99.84/13.46 thf(zip_derived_cl1444, plain,
% 99.84/13.46 (~ (((singletoninpowunion) =>
% 99.84/13.46 (((upairset2E) =>
% 99.84/13.46 (((upairsubunion) =>
% 99.84/13.46 (((upairinpowunion) =>
% 99.84/13.46 (((ubforcartprodlem1) =>
% 99.84/13.46 (((ubforcartprodlem2) =>
% 99.84/13.46 (((ubforcartprodlem3) =>
% 99.84/13.46 (((cartprodpairin) =>
% 99.84/13.46 (((cartprodmempair1) =>
% 99.84/13.46 (((cartprodmempair) =>
% 99.84/13.46 (((setunionE2) =>
% 99.84/13.46 (((setunionsingleton1) =>
% 99.84/13.46 (((setunionsingleton2) =>
% 99.84/13.46 (((setunionsingleton) =>
% 99.84/13.46 (((singletonprop) =>
% 99.84/13.46 (((ex1E1) =>
% 99.84/13.46 (((ex1I) =>
% 99.84/13.46 (((ex1I2) =>
% 99.84/13.46 (((singletonsuniq) =>
% 99.84/13.46 (((setukpairinjL1) =>
% 99.84/13.46 (((kfstsingleton) =>
% 99.84/13.46 (((theprop) =>
% 99.84/13.46 (((kfstpairEq) =>
% 99.84/13.46 (((cartprodfstin) =>
% 99.84/13.46 (((setukpairinjL2) =>
% 99.84/13.46 (((setukpairinjL) =>
% 99.84/13.46 (((setukpairinjR11) =>
% 99.84/13.46 (((setukpairinjR12) =>
% 99.84/13.46 (((setukpairinjR1) =>
% 99.84/13.46 (((upairequniteq) =>
% 99.84/13.46 ((
% 99.84/13.46 (setukpairinjR2) =>
% 99.84/13.46 ((
% 99.84/13.46 (setukpairinjR) =>
% 99.84/13.46 ((
% 99.84/13.46 (ksndsingleton) =>
% 99.84/13.46 ((
% 99.84/13.46 (ksndpairEq) =>
% 99.84/13.46 ((
% 99.84/13.46 (kpairsurjEq) =>
% 99.84/13.46 ((
% 99.84/13.46 (cartprodsndin) =>
% 99.84/13.46 ((
% 99.84/13.46 (cartprodpairmemEL) =>
% 99.84/13.46 ((
% 99.84/13.46 (cartprodpairmemER) =>
% 99.84/13.46 ((
% 99.84/13.46 (cartprodmempaircEq) =>
% 99.84/13.46 ((
% 99.84/13.46 (cartprodfstpairEq) =>
% 99.84/13.46 ((
% 99.84/13.46 (cartprodsndpairEq) =>
% 99.84/13.46 ((
% 99.84/13.46 (cartprodpairsurjEq) =>
% 99.84/13.46 ((
% 99.84/13.46 (dpsetconstrI) =>
% 99.84/13.46 ((
% 99.84/13.46 (dpsetconstrSub) =>
% 99.84/13.46 ((
% 99.84/13.46 (setOfPairsIsBReln) =>
% 99.84/13.46 ((
% 99.84/13.46 (dpsetconstrERa) =>
% 99.84/13.46 ((
% 99.84/13.46 (dpsetconstrEL1) =>
% 99.84/13.46 ((
% 99.84/13.46 (dpsetconstrEL2) =>
% 99.84/13.46 ((
% 99.84/13.46 (dpsetconstrER) =>
% 99.84/13.46 ((
% 99.84/13.46 (funcImageSingleton) =>
% 99.84/13.46 ((
% 99.84/13.46 (apProp) =>
% 99.84/13.46 ((
% 99.84/13.46 (app) =>
% 99.84/13.46 ((
% 99.84/13.46 (infuncsetfunc) =>
% 99.84/13.46 ((
% 99.84/13.46 (ap2p) =>
% 99.84/13.46 ((
% 99.84/13.46 (funcinfuncset) =>
% 99.84/13.46 ((
% 99.84/13.46 (lamProp) =>
% 99.84/13.46 ((
% 99.84/13.46 (lamp) =>
% 99.84/13.46 ((
% 99.84/13.46 (lam2p) =>
% 99.84/13.46 ((
% 99.84/13.46 (brelnall1) =>
% 99.84/13.46 ((
% 99.84/13.46 (brelnall2) =>
% 99.84/13.46 ((
% 99.84/13.46 (ex1E2) =>
% 99.84/13.46 ((
% 99.84/13.46 (funcGraphProp1) =>
% 99.84/13.46 ((
% 99.84/13.46 (funcGraphProp3) =>
% 99.84/13.46 ((
% 99.84/13.46 (funcGraphProp2) =>
% 99.84/13.46 ((
% 99.84/13.46 (funcextLem) =>
% 99.84/13.46 ((
% 99.84/13.46 (funcGraphProp4) =>
% 99.84/13.46 ((
% 99.84/13.46 (subbreln) =>
% 99.84/13.46 ((
% 99.84/13.46 (eqbreln) =>
% 99.84/13.46 ((
% 99.84/13.46 (funcext) =>
% 99.84/13.46 ((
% 99.84/13.46 (funcext2) =>
% 99.84/13.46 ((
% 99.84/13.46 (ap2apEq1) =>
% 99.84/13.46 ((
% 99.84/13.46 (ap2apEq2) =>
% 99.84/13.46 ((
% 99.84/13.46 (beta1) =>
% 99.84/13.46 ((
% 99.84/13.46 (eta1) =>
% 99.84/13.46 ((
% 99.84/13.46 (lam2lamEq) =>
% 99.84/13.46 ((
% 99.84/13.46 (beta2) =>
% 99.84/13.46 ((
% 99.84/13.46 (eta2) =>
% 99.84/13.46 ((
% 99.84/13.46 (iffalseProp1) =>
% 99.84/13.46 ((
% 99.84/13.46 (iffalseProp2) =>
% 99.84/13.46 ((
% 99.84/13.46 (iftrueProp1) =>
% 99.84/13.46 ((
% 99.84/13.46 (iftrueProp2) =>
% 99.84/13.46 ((
% 99.84/13.46 (ifSingleton) =>
% 99.84/13.46 ((
% 99.84/13.46 (ifp) =>
% 99.84/13.46 ((
% 99.84/13.46 (theeq) =>
% 99.84/13.46 ((
% 99.84/13.46 (iftrue) =>
% 99.84/13.46 ((
% 99.84/13.46 (iffalse) =>
% 99.84/13.46 ((
% 99.84/13.46 (iftrueorfalse) =>
% 99.84/13.46 ((
% 99.84/13.46 (binintersectT_lem) =>
% 99.84/13.46 ((
% 99.84/13.46 (binunionT_lem) =>
% 99.84/13.46 ((
% 99.84/13.46 (powersetT_lem) =>
% 99.84/13.46 ((
% 99.84/13.46 (setminusT_lem) =>
% 99.84/13.46 ((
% 99.84/13.46 (complementT_lem) =>
% 99.84/13.46 ((
% 99.84/13.46 (setextT) =>
% 99.84/13.46 ((
% 99.84/13.46 (subsetTI) =>
% 99.84/13.46 ((
% 99.84/13.46 (powersetTI1) =>
% 99.84/13.46 ((
% 99.84/13.46 (powersetTE1) =>
% 99.84/13.46 ((
% 99.84/13.46 (complementTI1) =>
% 99.84/13.46 ((
% 99.84/13.46 (complementTE1) =>
% 99.84/13.46 ((
% 99.84/13.46 (binintersectTELcontra) =>
% 99.84/13.46 ((
% 99.84/13.46 (binintersectTERcontra) =>
% 99.84/13.46 ((
% 99.84/13.46 (contrasubsetT) =>
% 99.84/13.46 ((
% 99.84/13.46 (contrasubsetT1) =>
% 99.84/13.46 ((
% 99.84/13.46 (contrasubsetT2) =>
% 99.84/13.46 ((
% 99.84/13.46 (contrasubsetT3) =>
% 99.84/13.46 ((
% 99.84/13.46 (doubleComplementI1) =>
% 99.84/13.46 ((
% 99.84/13.46 (doubleComplementE1) =>
% 99.84/13.46 ((
% 99.84/13.46 (doubleComplementSub1) =>
% 99.84/13.46 ((
% 99.84/13.46 (doubleComplementSub2) =>
% 99.84/13.46 ((
% 99.84/13.46 (doubleComplementEq) =>
% 99.84/13.46 ((
% 99.84/13.46 (complementTnotintersectT) =>
% 99.84/13.46 ((
% 99.84/13.46 (complementImpComplementIntersect) =>
% 99.84/13.46 ((
% 99.84/13.46 (complementSubsetComplementIntersect) =>
% 99.84/13.46 ((
% 99.84/13.46 (complementInPowersetComplementIntersect) =>
% 99.84/13.46 ((
% 99.84/13.46 (contraSubsetComplement) =>
% 99.84/13.46 ((
% 99.84/13.46 (complementTcontraSubset) =>
% 99.84/13.46 ((
% 99.84/13.46 (binunionTILcontra) =>
% 99.84/13.46 ((
% 99.84/13.46 (binunionTIRcontra) =>
% 99.84/13.46 ((
% 99.84/13.46 (inIntersectImpInUnion) =>
% 99.84/13.46 ((
% 99.84/13.46 (inIntersectImpInUnion2) =>
% 99.84/13.46 ((
% 99.84/13.46 (inIntersectImpInIntersectUnions) =>
% 99.84/13.46 ((
% 99.84/13.46 (intersectInPowersetIntersectUnions) =>
% 99.84/13.46 ((
% 99.84/13.46 (inComplementUnionImpNotIn1) =>
% 99.84/13.46 ((
% 99.84/13.46 (inComplementUnionImpInComplement1) =>
% 99.84/13.46 ((
% 99.84/13.46 (binunionTE) =>
% 99.84/13.46 ((
% 99.84/13.46 (binunionTEcontra) =>
% 99.84/13.46 ((
% 99.84/13.46 (demorgan2a1) =>
% 99.84/13.46 ((
% 99.84/13.46 (complementUnionInPowersetComplement) =>
% 99.84/13.46 ((
% 99.84/13.46 (demorgan2a2) =>
% 99.84/13.46 ((
% 99.84/13.46 (demorgan1a) =>
% 99.84/13.46 ((
% 99.84/13.46 (demorgan1b) =>
% 99.84/13.46 ((
% 99.84/13.46 (demorgan1) =>
% 99.84/13.46 ((
% 99.84/13.46 (demorgan2a) =>
% 99.84/13.46 ((
% 99.84/13.46 (demorgan2b2) =>
% 99.84/13.46 ((
% 99.84/13.46 (demorgan2b) =>
% 99.84/13.46 ((
% 99.84/13.46 (demorgan2) =>
% 99.84/13.46 ((
% 99.84/13.46 (woz13rule0) =>
% 99.84/13.46 ((
% 99.84/13.46 (woz13rule1) =>
% 99.84/13.46 ((
% 99.84/13.46 (woz13rule2) =>
% 99.84/13.46 ((
% 99.84/13.46 (woz13rule3) =>
% 99.84/13.46 ((
% 99.84/13.46 (woz13rule4) =>
% 99.84/13.46 ((
% 99.84/13.46 (woz1_1) =>
% 99.84/13.46 ((
% 99.84/13.46 (woz1_2) =>
% 99.84/13.46 ((
% 99.84/13.46 (woz1_3) =>
% 99.84/13.46 ((
% 99.84/13.46 (woz1_4) =>
% 99.84/13.46 ((
% 99.84/13.46 (woz1_5) =>
% 99.84/13.46 ((
% 99.84/13.46 (breln1all2) =>
% 99.84/13.46 ((
% 99.84/13.46 (breln1SetBreln1) =>
% 99.84/13.46 ((
% 99.84/13.46 (choice2fnsingleton) =>
% 99.84/13.46 ((
% 99.84/13.46 (setOfPairsIsBReln1) =>
% 99.84/13.46 ((
% 99.84/13.46 (breln1all1) =>
% 99.84/13.46 ((
% 99.84/13.46 (subbreln1) =>
% 99.84/13.46 ((
% 99.84/13.46 (eqbreln1) =>
% 99.84/13.46 ((
% 99.84/13.46 (breln1invprop) =>
% 99.84/13.46 ((
% 99.84/13.46 (breln1invI) =>
% 99.84/13.46 ((
% 99.84/13.46 (breln1invE) =>
% 99.84/13.46 ((
% 99.84/13.46 (breln1compprop) =>
% 99.84/13.46 ((
% 99.84/13.46 (breln1compI) =>
% 99.84/13.46 ((
% 99.84/13.46 (breln1compE) =>
% 99.84/13.46 ((
% 99.84/13.46 (breln1compEex) =>
% 99.84/13.46 ((
% 99.84/13.46 (breln1unionprop) =>
% 99.84/13.46 ((
% 99.84/13.46 (breln1unionIL) =>
% 99.84/13.46 ((
% 99.84/13.46 (breln1unionIR) =>
% 99.84/13.46 ((
% 99.84/13.46 (breln1unionI) =>
% 99.84/13.46 ((
% 99.84/13.46 (breln1unionE) =>
% 99.84/13.46 ((
% 99.84/13.46 (breln1unionEcases) =>
% 99.84/13.46 ((
% 99.84/13.46 (breln1unionCommutes) =>
% 99.84/13.46 ((
% 99.84/13.46 (woz2Ex) =>
% 99.84/13.46 ((
% 99.84/13.46 (woz2W) =>
% 99.84/13.46 ((
% 99.84/13.46 (woz2A) =>
% 99.84/13.46 ((
% 99.84/13.46 (woz2B) =>
% 99.84/13.46 ((
% 99.84/13.46 (image1Ex) =>
% 99.84/13.46 ((
% 99.84/13.46 (image1Ex1) =>
% 99.84/13.46 ((
% 99.84/13.46 (image1Equiv) =>
% 99.84/13.46 ((
% 99.84/13.46 (image1E) =>
% 99.84/13.46 ((
% 99.84/13.46 (image1I) =>
% 99.84/13.46 ((
% 99.84/13.46 (injFuncInInjFuncSet) =>
% 99.84/13.46 ((
% 99.84/13.46 (injFuncSetFuncIn) =>
% 99.84/13.46 ((
% 99.84/13.46 (injFuncSetFuncInj) =>
% 99.84/13.46 ((
% 99.84/13.46 (!!) @ (
% 99.84/13.46 (('#B') @ (
% 99.84/13.46 !!) @
% 99.84/13.46 (
% 99.84/13.46 (
% 99.84/13.46 ('#B') @ (
% 99.84/13.46 (
% 99.84/13.46 ('#B') @ (
% 99.84/13.46 !!))) @
% 99.84/13.46 (
% 99.84/13.46 (
% 99.84/13.46 ('#S') @ (
% 99.84/13.46 (
% 99.84/13.46 ('#B') @ (
% 99.84/13.46 '#S') @
% 99.84/13.46 (
% 99.84/13.46 (
% 99.84/13.46 ('#B') @ (
% 99.84/13.46 (
% 99.84/13.46 ('#B') @ (
% 99.84/13.46 '#S'))) @
% 99.84/13.46 (
% 99.84/13.46 (
% 99.84/13.46 ('#B') @ (
% 99.84/13.46 (
% 99.84/13.46 ('#B') @ (
% 99.84/13.46 (
% 99.84/13.46 ('#B') @ (
% 99.84/13.46 =>))))) @
% 99.84/13.46 (
% 99.84/13.46 (
% 99.84/13.46 ('#B') @ (
% 99.84/13.46 (
% 99.84/13.46 ('#B') @ (
% 99.84/13.46 (
% 99.84/13.46 ('#C') @ in)))) @
% 99.84/13.46 surjFuncSet)))))))) @
% 99.84/13.46 (
% 99.84/13.46 (
% 99.84/13.46 ('#B') @ (
% 99.84/13.46 (
% 99.84/13.46 ('#B') @ (
% 99.84/13.46 (
% 99.84/13.46 ('#C') @ in)))) @
% 99.84/13.46 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.84/13.46 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1433])).
% 99.84/13.46 thf(zip_derived_cl1452, plain,
% 99.84/13.46 (~ (((upairset2E) =>
% 99.84/13.46 (((upairsubunion) =>
% 99.84/13.46 (((upairinpowunion) =>
% 99.84/13.46 (((ubforcartprodlem1) =>
% 99.84/13.46 (((ubforcartprodlem2) =>
% 99.84/13.46 (((ubforcartprodlem3) =>
% 99.84/13.46 (((cartprodpairin) =>
% 99.84/13.46 (((cartprodmempair1) =>
% 99.84/13.46 (((cartprodmempair) =>
% 99.84/13.46 (((setunionE2) =>
% 99.84/13.46 (((setunionsingleton1) =>
% 99.84/13.46 (((setunionsingleton2) =>
% 99.84/13.46 (((setunionsingleton) =>
% 99.84/13.46 (((singletonprop) =>
% 99.84/13.46 (((ex1E1) =>
% 99.84/13.46 (((ex1I) =>
% 99.84/13.46 (((ex1I2) =>
% 99.84/13.46 (((singletonsuniq) =>
% 99.84/13.46 (((setukpairinjL1) =>
% 99.84/13.46 (((kfstsingleton) =>
% 99.84/13.46 (((theprop) =>
% 99.84/13.46 (((kfstpairEq) =>
% 99.84/13.46 (((cartprodfstin) =>
% 99.84/13.46 (((setukpairinjL2) =>
% 99.84/13.46 (((setukpairinjL) =>
% 99.84/13.46 (((setukpairinjR11) =>
% 99.84/13.46 (((setukpairinjR12) =>
% 99.84/13.46 (((setukpairinjR1) =>
% 99.84/13.46 (((upairequniteq) =>
% 99.84/13.46 (((setukpairinjR2) =>
% 99.84/13.46 ((
% 99.84/13.46 (setukpairinjR) =>
% 99.84/13.46 ((
% 99.84/13.46 (ksndsingleton) =>
% 99.84/13.46 ((
% 99.84/13.46 (ksndpairEq) =>
% 99.84/13.46 ((
% 99.84/13.46 (kpairsurjEq) =>
% 99.84/13.46 ((
% 99.84/13.46 (cartprodsndin) =>
% 99.84/13.46 ((
% 99.84/13.46 (cartprodpairmemEL) =>
% 99.84/13.46 ((
% 99.84/13.46 (cartprodpairmemER) =>
% 99.84/13.46 ((
% 99.84/13.46 (cartprodmempaircEq) =>
% 99.84/13.46 ((
% 99.84/13.46 (cartprodfstpairEq) =>
% 99.84/13.46 ((
% 99.84/13.46 (cartprodsndpairEq) =>
% 99.84/13.46 ((
% 99.84/13.46 (cartprodpairsurjEq) =>
% 99.84/13.46 ((
% 99.84/13.46 (dpsetconstrI) =>
% 99.84/13.46 ((
% 99.84/13.46 (dpsetconstrSub) =>
% 99.84/13.46 ((
% 99.84/13.46 (setOfPairsIsBReln) =>
% 99.84/13.46 ((
% 99.84/13.46 (dpsetconstrERa) =>
% 99.84/13.46 ((
% 99.84/13.46 (dpsetconstrEL1) =>
% 99.84/13.46 ((
% 99.84/13.46 (dpsetconstrEL2) =>
% 99.84/13.46 ((
% 99.84/13.46 (dpsetconstrER) =>
% 99.84/13.46 ((
% 99.84/13.46 (funcImageSingleton) =>
% 99.84/13.46 ((
% 99.84/13.46 (apProp) =>
% 99.84/13.46 ((
% 99.84/13.46 (app) =>
% 99.84/13.46 ((
% 99.84/13.46 (infuncsetfunc) =>
% 99.84/13.46 ((
% 99.84/13.46 (ap2p) =>
% 99.84/13.46 ((
% 99.84/13.46 (funcinfuncset) =>
% 99.84/13.46 ((
% 99.84/13.46 (lamProp) =>
% 99.84/13.46 ((
% 99.84/13.46 (lamp) =>
% 99.84/13.46 ((
% 99.84/13.46 (lam2p) =>
% 99.84/13.46 ((
% 99.84/13.46 (brelnall1) =>
% 99.84/13.46 ((
% 99.84/13.46 (brelnall2) =>
% 99.84/13.46 ((
% 99.84/13.46 (ex1E2) =>
% 99.84/13.46 ((
% 99.84/13.46 (funcGraphProp1) =>
% 99.84/13.46 ((
% 99.84/13.46 (funcGraphProp3) =>
% 99.84/13.46 ((
% 99.84/13.46 (funcGraphProp2) =>
% 99.84/13.46 ((
% 99.84/13.46 (funcextLem) =>
% 99.84/13.46 ((
% 99.84/13.46 (funcGraphProp4) =>
% 99.84/13.46 ((
% 99.84/13.46 (subbreln) =>
% 99.84/13.46 ((
% 99.84/13.46 (eqbreln) =>
% 99.84/13.46 ((
% 99.84/13.46 (funcext) =>
% 99.84/13.46 ((
% 99.84/13.46 (funcext2) =>
% 99.84/13.46 ((
% 99.84/13.46 (ap2apEq1) =>
% 99.84/13.46 ((
% 99.84/13.46 (ap2apEq2) =>
% 99.84/13.46 ((
% 99.84/13.46 (beta1) =>
% 99.84/13.46 ((
% 99.84/13.46 (eta1) =>
% 99.84/13.46 ((
% 99.84/13.46 (lam2lamEq) =>
% 99.84/13.46 ((
% 99.84/13.46 (beta2) =>
% 99.84/13.46 ((
% 99.84/13.46 (eta2) =>
% 99.84/13.46 ((
% 99.84/13.46 (iffalseProp1) =>
% 99.84/13.46 ((
% 99.84/13.46 (iffalseProp2) =>
% 99.84/13.46 ((
% 99.84/13.46 (iftrueProp1) =>
% 99.84/13.46 ((
% 99.84/13.46 (iftrueProp2) =>
% 99.84/13.46 ((
% 99.84/13.46 (ifSingleton) =>
% 99.84/13.46 ((
% 99.84/13.46 (ifp) =>
% 99.84/13.46 ((
% 99.84/13.46 (theeq) =>
% 99.84/13.46 ((
% 99.84/13.46 (iftrue) =>
% 99.84/13.46 ((
% 99.84/13.46 (iffalse) =>
% 99.84/13.46 ((
% 99.84/13.46 (iftrueorfalse) =>
% 99.84/13.46 ((
% 99.84/13.46 (binintersectT_lem) =>
% 99.84/13.46 ((
% 99.84/13.46 (binunionT_lem) =>
% 99.84/13.46 ((
% 99.84/13.46 (powersetT_lem) =>
% 99.84/13.46 ((
% 99.84/13.46 (setminusT_lem) =>
% 99.84/13.46 ((
% 99.84/13.46 (complementT_lem) =>
% 99.84/13.46 ((
% 99.84/13.46 (setextT) =>
% 99.84/13.46 ((
% 99.84/13.46 (subsetTI) =>
% 99.84/13.46 ((
% 99.84/13.46 (powersetTI1) =>
% 99.84/13.46 ((
% 99.84/13.46 (powersetTE1) =>
% 99.84/13.46 ((
% 99.84/13.46 (complementTI1) =>
% 99.84/13.46 ((
% 99.84/13.46 (complementTE1) =>
% 99.84/13.46 ((
% 99.84/13.46 (binintersectTELcontra) =>
% 99.84/13.46 ((
% 99.84/13.46 (binintersectTERcontra) =>
% 99.84/13.46 ((
% 99.84/13.46 (contrasubsetT) =>
% 99.84/13.46 ((
% 99.84/13.46 (contrasubsetT1) =>
% 99.84/13.46 ((
% 99.84/13.46 (contrasubsetT2) =>
% 99.84/13.46 ((
% 99.84/13.46 (contrasubsetT3) =>
% 99.84/13.46 ((
% 99.84/13.46 (doubleComplementI1) =>
% 99.84/13.46 ((
% 99.84/13.46 (doubleComplementE1) =>
% 99.84/13.46 ((
% 99.84/13.46 (doubleComplementSub1) =>
% 99.84/13.46 ((
% 99.84/13.46 (doubleComplementSub2) =>
% 99.84/13.46 ((
% 99.84/13.46 (doubleComplementEq) =>
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% 99.84/13.46 (complementTnotintersectT) =>
% 99.84/13.46 ((
% 99.84/13.46 (complementImpComplementIntersect) =>
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% 99.84/13.46 (complementSubsetComplementIntersect) =>
% 99.84/13.46 ((
% 99.84/13.46 (complementInPowersetComplementIntersect) =>
% 99.84/13.46 ((
% 99.84/13.46 (contraSubsetComplement) =>
% 99.84/13.46 ((
% 99.84/13.46 (complementTcontraSubset) =>
% 99.84/13.46 ((
% 99.84/13.46 (binunionTILcontra) =>
% 99.84/13.46 ((
% 99.84/13.46 (binunionTIRcontra) =>
% 99.84/13.46 ((
% 99.84/13.46 (inIntersectImpInUnion) =>
% 99.84/13.46 ((
% 99.84/13.46 (inIntersectImpInUnion2) =>
% 99.84/13.46 ((
% 99.84/13.46 (inIntersectImpInIntersectUnions) =>
% 99.84/13.46 ((
% 99.84/13.46 (intersectInPowersetIntersectUnions) =>
% 99.84/13.46 ((
% 99.84/13.46 (inComplementUnionImpNotIn1) =>
% 99.84/13.46 ((
% 99.84/13.46 (inComplementUnionImpInComplement1) =>
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% 99.84/13.46 ((
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% 99.84/13.46 ((
% 99.84/13.46 (complementUnionInPowersetComplement) =>
% 99.84/13.46 ((
% 99.84/13.46 (demorgan2a2) =>
% 99.84/13.46 ((
% 99.84/13.46 (demorgan1a) =>
% 99.84/13.46 ((
% 99.84/13.46 (demorgan1b) =>
% 99.84/13.46 ((
% 99.84/13.46 (demorgan1) =>
% 99.84/13.46 ((
% 99.84/13.46 (demorgan2a) =>
% 99.84/13.46 ((
% 99.84/13.46 (demorgan2b2) =>
% 99.84/13.46 ((
% 99.84/13.46 (demorgan2b) =>
% 99.84/13.46 ((
% 99.84/13.46 (demorgan2) =>
% 99.84/13.46 ((
% 99.84/13.46 (woz13rule0) =>
% 99.84/13.46 ((
% 99.84/13.46 (woz13rule1) =>
% 99.84/13.46 ((
% 99.84/13.46 (woz13rule2) =>
% 99.84/13.46 ((
% 99.84/13.46 (woz13rule3) =>
% 99.84/13.46 ((
% 99.84/13.46 (woz13rule4) =>
% 99.84/13.46 ((
% 99.84/13.46 (woz1_1) =>
% 99.84/13.46 ((
% 99.84/13.46 (woz1_2) =>
% 99.84/13.46 ((
% 99.84/13.46 (woz1_3) =>
% 99.84/13.46 ((
% 99.84/13.46 (woz1_4) =>
% 99.84/13.46 ((
% 99.84/13.46 (woz1_5) =>
% 99.84/13.46 ((
% 99.84/13.46 (breln1all2) =>
% 99.84/13.46 ((
% 99.84/13.46 (breln1SetBreln1) =>
% 99.84/13.46 ((
% 99.84/13.46 (choice2fnsingleton) =>
% 99.84/13.46 ((
% 99.84/13.46 (setOfPairsIsBReln1) =>
% 99.84/13.46 ((
% 99.84/13.46 (breln1all1) =>
% 99.84/13.46 ((
% 99.84/13.46 (subbreln1) =>
% 99.84/13.46 ((
% 99.84/13.46 (eqbreln1) =>
% 99.84/13.46 ((
% 99.84/13.46 (breln1invprop) =>
% 99.84/13.46 ((
% 99.84/13.46 (breln1invI) =>
% 99.84/13.46 ((
% 99.84/13.46 (breln1invE) =>
% 99.84/13.46 ((
% 99.84/13.46 (breln1compprop) =>
% 99.84/13.46 ((
% 99.84/13.46 (breln1compI) =>
% 99.84/13.46 ((
% 99.84/13.46 (breln1compE) =>
% 99.84/13.46 ((
% 99.84/13.46 (breln1compEex) =>
% 99.84/13.46 ((
% 99.84/13.46 (breln1unionprop) =>
% 99.84/13.46 ((
% 99.84/13.46 (breln1unionIL) =>
% 99.84/13.46 ((
% 99.84/13.46 (breln1unionIR) =>
% 99.84/13.46 ((
% 99.84/13.46 (breln1unionI) =>
% 99.84/13.46 ((
% 99.84/13.46 (breln1unionE) =>
% 99.84/13.46 ((
% 99.84/13.46 (breln1unionEcases) =>
% 99.84/13.46 ((
% 99.84/13.46 (breln1unionCommutes) =>
% 99.84/13.46 ((
% 99.84/13.46 (woz2Ex) =>
% 99.84/13.46 ((
% 99.84/13.46 (woz2W) =>
% 99.84/13.46 ((
% 99.84/13.46 (woz2A) =>
% 99.84/13.46 ((
% 99.84/13.46 (woz2B) =>
% 99.84/13.46 ((
% 99.84/13.46 (image1Ex) =>
% 99.84/13.46 ((
% 99.84/13.46 (image1Ex1) =>
% 99.84/13.46 ((
% 99.84/13.46 (image1Equiv) =>
% 99.84/13.46 ((
% 99.84/13.46 (image1E) =>
% 99.84/13.46 ((
% 99.84/13.46 (image1I) =>
% 99.84/13.46 ((
% 99.84/13.46 (injFuncInInjFuncSet) =>
% 99.84/13.46 ((
% 99.84/13.46 (injFuncSetFuncIn) =>
% 99.84/13.46 ((
% 99.84/13.46 (injFuncSetFuncInj) =>
% 99.84/13.46 ((
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% 99.84/13.46 (('#B') @ (
% 99.84/13.46 !!) @
% 99.84/13.46 (
% 99.84/13.46 (
% 99.84/13.46 ('#B') @ (
% 99.84/13.46 (
% 99.84/13.46 ('#B') @ (
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% 99.84/13.46 (
% 99.84/13.46 (
% 99.84/13.46 ('#S') @ (
% 99.84/13.46 (
% 99.84/13.46 ('#B') @ (
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% 99.84/13.46 (
% 99.84/13.46 (
% 99.84/13.46 ('#B') @ (
% 99.84/13.46 (
% 99.84/13.46 ('#B') @ (
% 99.84/13.46 '#S'))) @
% 99.84/13.46 (
% 99.84/13.46 (
% 99.84/13.46 ('#B') @ (
% 99.84/13.46 (
% 99.84/13.46 ('#B') @ (
% 99.84/13.46 (
% 99.84/13.46 ('#B') @ (
% 99.84/13.46 =>))))) @
% 99.84/13.46 (
% 99.84/13.46 (
% 99.84/13.46 ('#B') @ (
% 99.84/13.46 (
% 99.84/13.46 ('#B') @ (
% 99.84/13.46 (
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% 99.84/13.46 surjFuncSet)))))))) @
% 99.84/13.46 (
% 99.84/13.46 (
% 99.84/13.46 ('#B') @ (
% 99.84/13.46 (
% 99.84/13.46 ('#B') @ (
% 99.84/13.46 (
% 99.84/13.46 ('#C') @ in)))) @
% 99.84/13.46 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.84/13.46 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1444])).
% 99.84/13.46 thf(zip_derived_cl1459, plain,
% 99.84/13.46 (~ (((upairsubunion) =>
% 99.84/13.46 (((upairinpowunion) =>
% 99.84/13.46 (((ubforcartprodlem1) =>
% 99.84/13.46 (((ubforcartprodlem2) =>
% 99.84/13.46 (((ubforcartprodlem3) =>
% 99.84/13.46 (((cartprodpairin) =>
% 99.84/13.46 (((cartprodmempair1) =>
% 99.84/13.46 (((cartprodmempair) =>
% 99.84/13.46 (((setunionE2) =>
% 99.84/13.46 (((setunionsingleton1) =>
% 99.84/13.46 (((setunionsingleton2) =>
% 99.84/13.46 (((setunionsingleton) =>
% 99.84/13.46 (((singletonprop) =>
% 99.84/13.46 (((ex1E1) =>
% 99.84/13.46 (((ex1I) =>
% 99.84/13.46 (((ex1I2) =>
% 99.84/13.46 (((singletonsuniq) =>
% 99.84/13.46 (((setukpairinjL1) =>
% 99.84/13.46 (((kfstsingleton) =>
% 99.84/13.46 (((theprop) =>
% 99.84/13.46 (((kfstpairEq) =>
% 99.84/13.46 (((cartprodfstin) =>
% 99.84/13.46 (((setukpairinjL2) =>
% 99.84/13.46 (((setukpairinjL) =>
% 99.84/13.46 (((setukpairinjR11) =>
% 99.84/13.46 (((setukpairinjR12) =>
% 99.84/13.46 (((setukpairinjR1) =>
% 99.84/13.46 (((upairequniteq) =>
% 99.84/13.46 (((setukpairinjR2) =>
% 99.84/13.46 (((setukpairinjR) =>
% 99.84/13.46 ((
% 99.84/13.46 (ksndsingleton) =>
% 99.84/13.46 ((
% 99.84/13.46 (ksndpairEq) =>
% 99.84/13.46 ((
% 99.84/13.46 (kpairsurjEq) =>
% 99.84/13.46 ((
% 99.84/13.46 (cartprodsndin) =>
% 99.84/13.46 ((
% 99.84/13.46 (cartprodpairmemEL) =>
% 99.84/13.46 ((
% 99.84/13.46 (cartprodpairmemER) =>
% 99.84/13.46 ((
% 99.84/13.46 (cartprodmempaircEq) =>
% 99.84/13.46 ((
% 99.84/13.46 (cartprodfstpairEq) =>
% 99.84/13.46 ((
% 99.84/13.46 (cartprodsndpairEq) =>
% 99.84/13.46 ((
% 99.84/13.46 (cartprodpairsurjEq) =>
% 99.84/13.46 ((
% 99.84/13.46 (dpsetconstrI) =>
% 99.84/13.46 ((
% 99.84/13.46 (dpsetconstrSub) =>
% 99.84/13.46 ((
% 99.84/13.46 (setOfPairsIsBReln) =>
% 99.84/13.46 ((
% 99.84/13.46 (dpsetconstrERa) =>
% 99.84/13.46 ((
% 99.84/13.46 (dpsetconstrEL1) =>
% 99.84/13.46 ((
% 99.84/13.46 (dpsetconstrEL2) =>
% 99.84/13.46 ((
% 99.84/13.46 (dpsetconstrER) =>
% 99.84/13.46 ((
% 99.84/13.46 (funcImageSingleton) =>
% 99.84/13.46 ((
% 99.84/13.46 (apProp) =>
% 99.84/13.46 ((
% 99.84/13.46 (app) =>
% 99.84/13.46 ((
% 99.84/13.46 (infuncsetfunc) =>
% 99.84/13.46 ((
% 99.84/13.46 (ap2p) =>
% 99.84/13.46 ((
% 99.84/13.46 (funcinfuncset) =>
% 99.84/13.46 ((
% 99.84/13.46 (lamProp) =>
% 99.84/13.46 ((
% 99.84/13.46 (lamp) =>
% 99.84/13.46 ((
% 99.84/13.46 (lam2p) =>
% 99.84/13.46 ((
% 99.84/13.46 (brelnall1) =>
% 99.84/13.46 ((
% 99.84/13.46 (brelnall2) =>
% 99.84/13.46 ((
% 99.84/13.46 (ex1E2) =>
% 99.84/13.46 ((
% 99.84/13.46 (funcGraphProp1) =>
% 99.84/13.46 ((
% 99.84/13.46 (funcGraphProp3) =>
% 99.84/13.46 ((
% 99.84/13.46 (funcGraphProp2) =>
% 99.84/13.46 ((
% 99.84/13.46 (funcextLem) =>
% 99.84/13.46 ((
% 99.84/13.46 (funcGraphProp4) =>
% 99.84/13.46 ((
% 99.84/13.46 (subbreln) =>
% 99.84/13.46 ((
% 99.84/13.46 (eqbreln) =>
% 99.84/13.46 ((
% 99.84/13.46 (funcext) =>
% 99.84/13.46 ((
% 99.84/13.46 (funcext2) =>
% 99.84/13.46 ((
% 99.84/13.46 (ap2apEq1) =>
% 99.84/13.46 ((
% 99.84/13.46 (ap2apEq2) =>
% 99.84/13.46 ((
% 99.84/13.46 (beta1) =>
% 99.84/13.46 ((
% 99.84/13.46 (eta1) =>
% 99.84/13.46 ((
% 99.84/13.46 (lam2lamEq) =>
% 99.84/13.46 ((
% 99.84/13.46 (beta2) =>
% 99.84/13.46 ((
% 99.84/13.46 (eta2) =>
% 99.84/13.46 ((
% 99.84/13.46 (iffalseProp1) =>
% 99.84/13.46 ((
% 99.84/13.46 (iffalseProp2) =>
% 99.84/13.46 ((
% 99.84/13.46 (iftrueProp1) =>
% 99.84/13.46 ((
% 99.84/13.46 (iftrueProp2) =>
% 99.84/13.46 ((
% 99.84/13.46 (ifSingleton) =>
% 99.84/13.46 ((
% 99.84/13.46 (ifp) =>
% 99.84/13.46 ((
% 99.84/13.46 (theeq) =>
% 99.84/13.46 ((
% 99.84/13.46 (iftrue) =>
% 99.84/13.46 ((
% 99.84/13.46 (iffalse) =>
% 99.84/13.46 ((
% 99.84/13.46 (iftrueorfalse) =>
% 99.84/13.46 ((
% 99.84/13.46 (binintersectT_lem) =>
% 99.84/13.46 ((
% 99.84/13.46 (binunionT_lem) =>
% 99.84/13.46 ((
% 99.84/13.46 (powersetT_lem) =>
% 99.84/13.46 ((
% 99.84/13.46 (setminusT_lem) =>
% 99.84/13.46 ((
% 99.84/13.46 (complementT_lem) =>
% 99.84/13.46 ((
% 99.84/13.46 (setextT) =>
% 99.84/13.46 ((
% 99.84/13.46 (subsetTI) =>
% 99.84/13.46 ((
% 99.84/13.46 (powersetTI1) =>
% 99.84/13.46 ((
% 99.84/13.46 (powersetTE1) =>
% 99.84/13.46 ((
% 99.84/13.46 (complementTI1) =>
% 99.84/13.46 ((
% 99.84/13.46 (complementTE1) =>
% 99.84/13.46 ((
% 99.84/13.46 (binintersectTELcontra) =>
% 99.84/13.46 ((
% 99.84/13.46 (binintersectTERcontra) =>
% 99.84/13.46 ((
% 99.84/13.46 (contrasubsetT) =>
% 99.84/13.46 ((
% 99.84/13.46 (contrasubsetT1) =>
% 99.84/13.46 ((
% 99.84/13.46 (contrasubsetT2) =>
% 99.84/13.46 ((
% 99.84/13.46 (contrasubsetT3) =>
% 99.84/13.46 ((
% 99.84/13.46 (doubleComplementI1) =>
% 99.84/13.46 ((
% 99.84/13.46 (doubleComplementE1) =>
% 99.84/13.46 ((
% 99.84/13.46 (doubleComplementSub1) =>
% 99.84/13.46 ((
% 99.84/13.46 (doubleComplementSub2) =>
% 99.84/13.46 ((
% 99.84/13.46 (doubleComplementEq) =>
% 99.84/13.46 ((
% 99.84/13.46 (complementTnotintersectT) =>
% 99.84/13.46 ((
% 99.84/13.46 (complementImpComplementIntersect) =>
% 99.84/13.46 ((
% 99.84/13.46 (complementSubsetComplementIntersect) =>
% 99.84/13.46 ((
% 99.84/13.46 (complementInPowersetComplementIntersect) =>
% 99.84/13.46 ((
% 99.84/13.46 (contraSubsetComplement) =>
% 99.84/13.46 ((
% 99.84/13.46 (complementTcontraSubset) =>
% 99.84/13.46 ((
% 99.84/13.46 (binunionTILcontra) =>
% 99.84/13.46 ((
% 99.84/13.46 (binunionTIRcontra) =>
% 99.84/13.46 ((
% 99.84/13.46 (inIntersectImpInUnion) =>
% 99.84/13.46 ((
% 99.84/13.46 (inIntersectImpInUnion2) =>
% 99.84/13.46 ((
% 99.84/13.46 (inIntersectImpInIntersectUnions) =>
% 99.84/13.46 ((
% 99.84/13.46 (intersectInPowersetIntersectUnions) =>
% 99.84/13.46 ((
% 99.84/13.46 (inComplementUnionImpNotIn1) =>
% 99.84/13.46 ((
% 99.84/13.46 (inComplementUnionImpInComplement1) =>
% 99.84/13.46 ((
% 99.84/13.46 (binunionTE) =>
% 99.84/13.46 ((
% 99.84/13.46 (binunionTEcontra) =>
% 99.84/13.46 ((
% 99.84/13.46 (demorgan2a1) =>
% 99.84/13.46 ((
% 99.84/13.46 (complementUnionInPowersetComplement) =>
% 99.84/13.46 ((
% 99.84/13.46 (demorgan2a2) =>
% 99.84/13.46 ((
% 99.84/13.46 (demorgan1a) =>
% 99.84/13.46 ((
% 99.84/13.46 (demorgan1b) =>
% 99.84/13.46 ((
% 99.84/13.46 (demorgan1) =>
% 99.84/13.46 ((
% 99.84/13.46 (demorgan2a) =>
% 99.84/13.46 ((
% 99.84/13.46 (demorgan2b2) =>
% 99.84/13.46 ((
% 99.84/13.46 (demorgan2b) =>
% 99.84/13.46 ((
% 99.84/13.46 (demorgan2) =>
% 99.84/13.46 ((
% 99.84/13.46 (woz13rule0) =>
% 99.84/13.46 ((
% 99.84/13.46 (woz13rule1) =>
% 99.84/13.46 ((
% 99.84/13.46 (woz13rule2) =>
% 99.84/13.46 ((
% 99.84/13.46 (woz13rule3) =>
% 99.84/13.46 ((
% 99.84/13.46 (woz13rule4) =>
% 99.84/13.46 ((
% 99.84/13.46 (woz1_1) =>
% 99.84/13.46 ((
% 99.84/13.46 (woz1_2) =>
% 99.84/13.46 ((
% 99.84/13.46 (woz1_3) =>
% 99.84/13.46 ((
% 99.84/13.46 (woz1_4) =>
% 99.84/13.46 ((
% 99.84/13.46 (woz1_5) =>
% 99.84/13.46 ((
% 99.84/13.46 (breln1all2) =>
% 99.84/13.46 ((
% 99.84/13.46 (breln1SetBreln1) =>
% 99.84/13.46 ((
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% 99.84/13.46 ((
% 99.84/13.46 (setOfPairsIsBReln1) =>
% 99.84/13.46 ((
% 99.84/13.46 (breln1all1) =>
% 99.84/13.46 ((
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% 99.84/13.46 ((
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% 99.84/13.46 ((
% 99.84/13.46 (breln1invprop) =>
% 99.84/13.46 ((
% 99.84/13.46 (breln1invI) =>
% 99.84/13.46 ((
% 99.84/13.46 (breln1invE) =>
% 99.84/13.46 ((
% 99.84/13.46 (breln1compprop) =>
% 99.84/13.46 ((
% 99.84/13.46 (breln1compI) =>
% 99.84/13.46 ((
% 99.84/13.46 (breln1compE) =>
% 99.84/13.46 ((
% 99.84/13.46 (breln1compEex) =>
% 99.84/13.46 ((
% 99.84/13.46 (breln1unionprop) =>
% 99.84/13.46 ((
% 99.84/13.46 (breln1unionIL) =>
% 99.84/13.46 ((
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% 99.84/13.46 ((
% 99.84/13.46 (breln1unionI) =>
% 99.84/13.46 ((
% 99.84/13.46 (breln1unionE) =>
% 99.84/13.46 ((
% 99.84/13.46 (breln1unionEcases) =>
% 99.84/13.46 ((
% 99.84/13.46 (breln1unionCommutes) =>
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% 99.84/13.46 ((
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% 99.84/13.46 ((
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% 99.84/13.46 ((
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% 99.84/13.53 surjFuncSet)))))))) @
% 99.84/13.53 ((('#B') @ ((('#B') @ ((('#C') @ in)))) @
% 99.84/13.53 funcSet))))))))))))))))))))))))),
% 99.84/13.53 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3493])).
% 99.84/13.53 thf(zip_derived_cl3526, plain,
% 99.84/13.53 (~ (((image1Equiv) =>
% 99.84/13.53 (((image1E) =>
% 99.84/13.53 (((image1I) =>
% 99.84/13.53 (((injFuncInInjFuncSet) =>
% 99.84/13.53 (((injFuncSetFuncIn) =>
% 99.84/13.53 (((injFuncSetFuncInj) =>
% 99.84/13.53 (((!!) @ ((('#B') @ (!!) @
% 99.84/13.53 ((('#B') @ ((('#B') @ (!!))) @
% 99.84/13.53 ((('#S') @ ((('#B') @ ('#S') @
% 99.84/13.53 ((('#B') @ ((('#B') @ ('#S'))) @
% 99.84/13.53 ((('#B') @ ((('#B') @ (
% 99.84/13.53 (('#B') @ (=>))))) @
% 99.84/13.53 ((('#B') @ ((('#B') @ (
% 99.84/13.53 (('#C') @ in)))) @
% 99.84/13.53 surjFuncSet)))))))) @
% 99.84/13.53 ((('#B') @ ((('#B') @ ((('#C') @ in)))) @
% 99.84/13.53 funcSet))))))))))))))))))))))),
% 99.84/13.53 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3511])).
% 99.84/13.53 thf(zip_derived_cl3540, plain,
% 99.84/13.53 (~ (((image1E) =>
% 99.84/13.53 (((image1I) =>
% 99.84/13.53 (((injFuncInInjFuncSet) =>
% 99.84/13.53 (((injFuncSetFuncIn) =>
% 99.84/13.53 (((injFuncSetFuncInj) =>
% 99.84/13.53 (((!!) @ ((('#B') @ (!!) @
% 99.84/13.53 ((('#B') @ ((('#B') @ (!!))) @
% 99.84/13.53 ((('#S') @ ((('#B') @ ('#S') @
% 99.84/13.53 ((('#B') @ ((('#B') @ ('#S'))) @
% 99.84/13.53 ((('#B') @ ((('#B') @ ((
% 99.84/13.53 ('#B') @ (
% 99.84/13.53 =>))))) @
% 99.84/13.53 ((('#B') @ ((('#B') @ (
% 99.84/13.53 (('#C') @ in)))) @
% 99.84/13.53 surjFuncSet)))))))) @
% 99.84/13.53 ((('#B') @ ((('#B') @ ((('#C') @ in)))) @
% 99.84/13.53 funcSet))))))))))))))))))))),
% 99.84/13.53 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3526])).
% 99.84/13.53 thf(zip_derived_cl3554, plain,
% 99.84/13.53 (~ (((image1I) =>
% 99.84/13.53 (((injFuncInInjFuncSet) =>
% 99.84/13.53 (((injFuncSetFuncIn) =>
% 99.84/13.53 (((injFuncSetFuncInj) =>
% 99.84/13.53 (((!!) @ ((('#B') @ (!!) @
% 99.84/13.53 ((('#B') @ ((('#B') @ (!!))) @
% 99.84/13.53 ((('#S') @ ((('#B') @ ('#S') @
% 99.84/13.53 ((('#B') @ ((('#B') @ ('#S'))) @
% 99.84/13.53 ((('#B') @ ((('#B') @ ((('#B') @ (
% 99.84/13.53 =>))))) @
% 99.84/13.53 ((('#B') @ ((('#B') @ ((
% 99.84/13.53 ('#C') @ in)))) @
% 99.84/13.53 surjFuncSet)))))))) @
% 99.84/13.53 ((('#B') @ ((('#B') @ ((('#C') @ in)))) @
% 99.84/13.53 funcSet))))))))))))))))))),
% 99.84/13.53 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3540])).
% 99.84/13.53 thf(zip_derived_cl3570, plain,
% 99.84/13.53 (~ (((injFuncInInjFuncSet) =>
% 99.84/13.53 (((injFuncSetFuncIn) =>
% 99.84/13.53 (((injFuncSetFuncInj) =>
% 99.84/13.53 (((!!) @ ((('#B') @ (!!) @
% 99.84/13.53 ((('#B') @ ((('#B') @ (!!))) @
% 99.84/13.53 ((('#S') @ ((('#B') @ ('#S') @
% 99.84/13.53 ((('#B') @ ((('#B') @ ('#S'))) @
% 99.84/13.53 ((('#B') @ ((('#B') @ ((('#B') @ (
% 99.84/13.53 =>))))) @
% 99.84/13.53 ((('#B') @ ((('#B') @ ((('#C') @ in)))) @
% 99.84/13.53 surjFuncSet)))))))) @
% 99.84/13.53 ((('#B') @ ((('#B') @ ((('#C') @ in)))) @ funcSet))))))))))))))))),
% 99.84/13.53 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3554])).
% 99.84/13.53 thf(zip_derived_cl3584, plain,
% 99.84/13.53 (~ (((injFuncSetFuncIn) =>
% 99.84/13.53 (((injFuncSetFuncInj) =>
% 99.84/13.53 (((!!) @ ((('#B') @ (!!) @
% 99.84/13.53 ((('#B') @ ((('#B') @ (!!))) @
% 99.84/13.53 ((('#S') @ ((('#B') @ ('#S') @
% 99.84/13.53 ((('#B') @ ((('#B') @ ('#S'))) @
% 99.84/13.53 ((('#B') @ ((('#B') @ ((('#B') @ (=>))))) @
% 99.84/13.53 ((('#B') @ ((('#B') @ ((('#C') @ in)))) @
% 99.84/13.53 surjFuncSet)))))))) @
% 99.84/13.53 ((('#B') @ ((('#B') @ ((('#C') @ in)))) @ funcSet))))))))))))))),
% 99.84/13.53 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3570])).
% 99.84/13.53 thf(zip_derived_cl3597, plain,
% 99.84/13.53 (~ (((injFuncSetFuncInj) =>
% 99.84/13.53 (((!!) @ ((('#B') @ (!!) @
% 99.84/13.53 ((('#B') @ ((('#B') @ (!!))) @
% 99.84/13.53 ((('#S') @ ((('#B') @ ('#S') @
% 99.84/13.53 ((('#B') @ ((('#B') @ ('#S'))) @
% 99.84/13.53 ((('#B') @ ((('#B') @ ((('#B') @ (=>))))) @
% 99.84/13.53 ((('#B') @ ((('#B') @ ((('#C') @ in)))) @
% 99.84/13.53 surjFuncSet)))))))) @
% 99.84/13.53 ((('#B') @ ((('#B') @ ((('#C') @ in)))) @ funcSet))))))))))))),
% 99.84/13.53 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3584])).
% 99.84/13.53 thf(zip_derived_cl3610, plain,
% 99.84/13.53 (~ (((!!) @ ((('#B') @ (!!) @
% 99.84/13.53 ((('#B') @ ((('#B') @ (!!))) @
% 99.84/13.53 ((('#S') @ ((('#B') @ ('#S') @
% 99.84/13.53 ((('#B') @ ((('#B') @ ('#S'))) @
% 99.84/13.53 ((('#B') @ ((('#B') @ ((('#B') @ (=>))))) @
% 99.84/13.53 ((('#B') @ ((('#B') @ ((('#C') @ in)))) @
% 99.84/13.53 surjFuncSet)))))))) @
% 99.84/13.53 ((('#B') @ ((('#B') @ ((('#C') @ in)))) @ funcSet))))))))))),
% 99.84/13.53 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3597])).
% 99.84/13.53 thf(zip_derived_cl3622, plain,
% 99.84/13.53 (~ (((!!) @ ((('#B') @ (!!) @
% 99.84/13.53 ((('#S') @ ((('#B') @ ('#S') @
% 99.84/13.53 ((('#B') @ ((('#B') @ (=>))) @
% 99.84/13.53 ((('#B') @ ((('#C') @ in)) @
% 99.84/13.53 (surjFuncSet @ '#sk47'))))))) @
% 99.84/13.53 ((('#B') @ ((('#C') @ in)) @ (funcSet @ '#sk47')))))))))),
% 99.84/13.53 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl3610])).
% 99.84/13.53 thf(zip_derived_cl3633, plain,
% 99.84/13.53 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 99.84/13.53 ((('#C') @ in @
% 99.84/13.53 (surjFuncSet @ '#sk47' @ '#sk49'))))) @
% 99.84/13.53 ((('#C') @ in @ (funcSet @ '#sk47' @ '#sk49')))))))),
% 99.84/13.53 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl3622])).
% 99.84/13.53 thf(surjFuncSet, axiom,(( surjFuncSet @ (X0)@ (X1)) =
% 99.84/13.53 ((dsetconstr @ (funcSet @ X0 @ X1) @
% 99.84/13.53 (^[Y0 : $i]: (surjective @ X0 @ X1 @ Y0)))))).
% 99.84/13.53 thf('4', plain,
% 99.84/13.53 (![X1:$i,X0:$i]:
% 99.84/13.53 ( ( surjFuncSet @ X0 @ X1 ) =
% 99.84/13.53 ( dsetconstr @
% 99.84/13.53 ( funcSet @ X0 @ X1 ) @
% 99.84/13.53 ( ^[V_1:$i]: ( surjective @ X0 @ X1 @ V_1 ) ) ) )),
% 99.84/13.53 define([status(thm)])).
% 99.84/13.53 thf(zip_derived_cl3646, plain,
% 99.84/13.53 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 99.84/13.53 ((('#C') @ in @
% 99.84/13.53 (dsetconstr @ (funcSet @ '#sk47' @ '#sk49') @
% 99.84/13.53 (surjective @ '#sk47' @ '#sk49')))))) @
% 99.84/13.53 ((('#C') @ in @ (funcSet @ '#sk47' @ '#sk49')))))))),
% 99.84/13.53 inference('rw', [status(thm)], [zip_derived_cl3633, '4'])).
% 99.84/13.53 thf(zip_derived_cl3647, plain,
% 99.84/13.53 (~ (((in @
% 99.84/13.53 ('#sk12' @ (funcSet @ '#sk47' @ '#sk49') @
% 99.84/13.53 (dsetconstr @ (funcSet @ '#sk47' @ '#sk49') @
% 99.84/13.53 (surjective @ '#sk47' @ '#sk49'))) @
% 99.84/13.53 (dsetconstr @ (funcSet @ '#sk47' @ '#sk49') @
% 99.84/13.53 (surjective @ '#sk47' @ '#sk49'))) =>
% 99.84/13.53 (in @
% 99.84/13.53 ('#sk12' @ (funcSet @ '#sk47' @ '#sk49') @
% 99.84/13.53 (dsetconstr @ (funcSet @ '#sk47' @ '#sk49') @
% 99.84/13.53 (surjective @ '#sk47' @ '#sk49'))) @
% 99.84/13.53 (funcSet @ '#sk47' @ '#sk49'))))),
% 99.84/13.53 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl3646])).
% 99.84/13.53 thf(zip_derived_cl3656, plain,
% 99.84/13.53 ( (in @
% 99.84/13.53 ('#sk12' @ (funcSet @ '#sk47' @ '#sk49') @
% 99.84/13.53 (dsetconstr @ (funcSet @ '#sk47' @ '#sk49') @
% 99.84/13.53 (surjective @ '#sk47' @ '#sk49'))) @
% 99.84/13.53 (dsetconstr @ (funcSet @ '#sk47' @ '#sk49') @
% 99.84/13.53 (surjective @ '#sk47' @ '#sk49')))),
% 99.84/13.53 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3647])).
% 99.84/13.53 thf(zip_derived_cl3657, plain,
% 99.84/13.53 (~ (in @
% 99.84/13.53 ('#sk12' @ (funcSet @ '#sk47' @ '#sk49') @
% 99.84/13.53 (dsetconstr @ (funcSet @ '#sk47' @ '#sk49') @
% 99.84/13.53 (surjective @ '#sk47' @ '#sk49'))) @
% 99.84/13.53 (funcSet @ '#sk47' @ '#sk49'))),
% 99.84/13.53 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3647])).
% 99.84/13.53 thf(zip_derived_cl88, plain, ( (dsetconstrEL)),
% 99.84/13.53 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl79])).
% 99.84/13.53 thf(dsetconstrEL, axiom, (dsetconstrEL) =>
% 99.84/13.53 ((((!!) @ (^[Y0 : $i]:
% 99.84/13.53 (((!!) @ (^[Y1 : $i > $o]:
% 99.84/13.53 (((!!) @ (^[Y2 : $i]:
% 99.84/13.53 (((in @ Y2 @
% 99.84/13.53 (dsetconstr @ Y0 @
% 99.84/13.53 (^[Y3 : $i]: (Y1 @ Y3)))) =>
% 99.84/13.53 (in @ Y2 @ Y0))))))))))))
% 99.84/13.53 = ($true))).
% 99.84/13.53 thf('5', plain,
% 99.84/13.53 (( dsetconstrEL ) <=>
% 99.84/13.53 ( ![X5:$i,X7:( $i > $o ),X9:$i]:
% 99.84/13.53 ( ( in @ X9 @ ( dsetconstr @ X5 @ ( ^[V_1:$i]: ( X7 @ V_1 ) ) ) ) =>
% 99.84/13.53 ( in @ X9 @ X5 ) ) )),
% 99.84/13.53 inference('rw.lit', [status(esa)], [dsetconstrEL])).
% 99.84/13.53 thf(zip_derived_cl103, plain,
% 99.84/13.53 ( (((!!) @ (^[Y0 : $i]:
% 99.84/13.53 (((!!) @ (^[Y1 : $i > $o]:
% 99.84/13.53 (((!!) @ (^[Y2 : $i]:
% 99.84/13.53 (((in @ Y2 @
% 99.84/13.53 (dsetconstr @ Y0 @
% 99.84/13.53 (^[Y3 : $i]: (Y1 @ Y3)))) =>
% 99.84/13.53 (in @ Y2 @ Y0))))))))))))),
% 99.84/13.53 inference('rw_clause', [status(thm)], [zip_derived_cl88, '5'])).
% 99.84/13.53 thf(zip_derived_cl119, plain,
% 99.84/13.53 ( (((!!) @ ((('#B') @ (!!) @
% 99.84/13.53 ((('#B') @ ((('#B') @ (!!))) @
% 99.84/13.53 ((('#S') @ ((('#B') @ ('#C') @
% 99.84/13.53 ((('#B') @ ((('#B') @ ('#S'))) @
% 99.84/13.53 ((('#B') @ ((('#B') @ ((('#B') @ (=>))))) @
% 99.84/13.53 ((('#B') @ ((('#B') @ ((('#C') @ in)))) @
% 99.84/13.53 dsetconstr)))))))) @
% 99.84/13.53 ((('#C') @ in))))))))))),
% 99.84/13.53 inference('comb-normalize', [status(thm)], [zip_derived_cl103])).
% 99.84/13.53 thf(zip_derived_cl120, plain,
% 99.84/13.53 (![X2 : $i]:
% 99.84/13.53 (((!!) @ ((('#B') @ (!!) @
% 99.84/13.53 ((('#C') @ ((('#B') @ ('#S') @
% 99.84/13.53 ((('#B') @ ((('#B') @ (=>))) @
% 99.84/13.53 ((('#B') @ ((('#C') @ in)) @
% 99.84/13.53 (dsetconstr @ X2))))))) @
% 99.84/13.53 ((('#C') @ in @ X2))))))))),
% 99.84/13.53 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl119])).
% 99.84/13.53 thf(zip_derived_cl137, plain,
% 99.84/13.53 (![X2 : $i, X4 : $i > $o]:
% 99.84/13.53 (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 99.84/13.53 ((('#C') @ in @ (dsetconstr @ X2 @ X4))))) @
% 99.84/13.53 ((('#C') @ in @ X2))))))),
% 99.84/13.53 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl120])).
% 99.84/13.53 thf(zip_derived_cl152, plain,
% 99.84/13.53 (![X2 : $i, X4 : $i > $o, X6 : $i]:
% 99.84/13.53 (((in @ X6 @ (dsetconstr @ X2 @ X4)) => (in @ X6 @ X2)))),
% 99.84/13.53 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl137])).
% 99.84/13.53 thf(zip_derived_cl167, plain,
% 99.84/13.53 (![X2 : $i, X4 : $i > $o, X6 : $i]:
% 99.84/13.53 (~ (in @ X6 @ (dsetconstr @ X2 @ X4)) | (in @ X6 @ X2))),
% 99.84/13.53 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl152])).
% 99.84/13.53 thf(zip_derived_cl10859, plain, ($false),
% 99.84/13.53 inference('eprover', [status(thm)],
% 99.84/13.53 [zip_derived_cl3656, zip_derived_cl3657, zip_derived_cl167])).
% 99.84/13.53
% 99.84/13.53 % SZS output end Refutation
% 99.84/13.53
% 99.84/13.53
% 99.84/13.53 % /export/starexec/sandbox/solver/bin/lams/30_b.l.sh running for 90s
% 99.84/13.53 % Terminating...
% 100.43/13.65 % Runner terminated.
% 100.43/13.65 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------