0.07/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.12/0.18 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.W5JbTSVgdv true 0.18/0.39 % Computer : n029.cluster.edu 0.18/0.39 % Model : x86_64 x86_64 0.18/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.18/0.39 % Memory : 8042.1875MB 0.18/0.39 % OS : Linux 3.10.0-693.el7.x86_64 0.18/0.39 % CPULimit : 1200 0.18/0.39 % WCLimit : 120 0.18/0.39 % DateTime : Tue Jul 13 13:00:10 EDT 2021 0.18/0.39 % CPUTime : 0.18/0.39 % Running portfolio for 120 s 0.18/0.39 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p 0.18/0.39 % Number of cores: 8 0.18/0.39 % Python version: Python 3.6.8 0.18/0.40 % Running in HO mode 0.38/0.72 % Total configuration time : 828 0.38/0.72 % Estimated wc time : 983 0.38/0.72 % Estimated cpu time (8 cpus) : 122.875 0.40/0.78 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 47s 0.40/0.79 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 47s 0.40/0.79 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 47s 0.40/0.82 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 18s 0.40/0.82 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 53s 0.40/0.82 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 41s 0.40/0.82 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 24s 0.40/0.82 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 35s 0.40/0.93 % /export/starexec/sandbox2/solver/bin/lams/30_b.l.sh running for 53s 77.33/10.53 % Solved by lams/30_b.l.sh. 77.33/10.53 % running E: timeout 14 /export/starexec/sandbox2/solver/bin/lams/eprover-ho --pos-ext=all --neg-ext=all /export/starexec/sandbox2/tmp/tmp.W5JbTSVgdv/e_inputa0fbdf --cpu-limit=12 --auto -s -p 77.33/10.53 % done 306 iterations in 9.197s 77.33/10.53 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p' 77.33/10.53 % SZS output start Refutation 77.33/10.53 thf(setadjoin_type, type, setadjoin: $i > $i > $i). 77.33/10.53 thf(binintersectER_type, type, binintersectER: $o). 77.33/10.53 thf(setadjoinSub_type, type, setadjoinSub: $o). 77.33/10.53 thf(demorgan1b_type, type, demorgan1b: $o). 77.33/10.53 thf(setukpairinjR_type, type, setukpairinjR: $o). 77.33/10.53 thf(emptysetimpfalse_type, type, emptysetimpfalse: $o). 77.33/10.53 thf(vacuousDall_type, type, vacuousDall: $o). 77.33/10.53 thf(setextT_type, type, setextT: $o). 77.33/10.53 thf(setadjoinIR_type, type, setadjoinIR: $o). 77.33/10.53 thf(funcext2_type, type, funcext2: $o). 77.33/10.53 thf(ex1I2_type, type, ex1I2: $o). 77.33/10.53 thf(omega0Ax_type, type, omega0Ax: $o). 77.33/10.53 thf(subsetE_type, type, subsetE: $o). 77.33/10.53 thf(binintersectSubset3_type, type, binintersectSubset3: $o). 77.33/10.53 thf(setminusER_type, type, setminusER: $o). 77.33/10.53 thf(surjCantorThm_type, type, surjCantorThm: $o). 77.33/10.53 thf(inIntersectImpInIntersectUnions_type, type, inIntersectImpInIntersectUnions: 77.33/10.53 $o). 77.33/10.53 thf(leftInvIsSurj_type, type, leftInvIsSurj: $o). 77.33/10.53 thf(woz13rule2_type, type, woz13rule2: $o). 77.33/10.53 thf(intersectInPowersetIntersectUnions_type, type, intersectInPowersetIntersectUnions: 77.33/10.53 $o). 77.33/10.53 thf(binunionE_type, type, binunionE: $o). 77.33/10.53 thf(setadjoinSub2_type, type, setadjoinSub2: $o). 77.33/10.53 thf(powersetE_type, type, powersetE: $o). 77.33/10.53 thf(breln1all1_type, type, breln1all1: $o). 77.33/10.53 thf(funcGraphProp2_type, type, funcGraphProp2: $o). 77.33/10.53 thf(contrasubsetT_type, type, contrasubsetT: $o). 77.33/10.53 thf(woz13rule0_type, type, woz13rule0: $o). 77.33/10.53 thf(binunionRsub_type, type, binunionRsub: $o). 77.33/10.53 thf(woz1_5_type, type, woz1_5: $o). 77.33/10.53 thf(lamProp_type, type, lamProp: $o). 77.33/10.53 thf(setOfPairsIsBReln_type, type, setOfPairsIsBReln: $o). 77.33/10.53 thf(beta2_type, type, beta2: $o). 77.33/10.53 thf(breln1invprop_type, type, breln1invprop: $o). 77.33/10.53 thf(quantDeMorgan3_type, type, quantDeMorgan3: $o). 77.33/10.53 thf(powerset__Cong_type, type, powerset__Cong: $o). 77.33/10.53 thf(iffalse_type, type, iffalse: $o). 77.33/10.53 thf(singletonprop_type, type, singletonprop: $o). 77.33/10.53 thf(dpsetconstrERa_type, type, dpsetconstrERa: $o). 77.33/10.53 thf(demorgan2b_type, type, demorgan2b: $o). 77.33/10.53 thf(omegaIndAx_type, type, omegaIndAx: $o). 77.33/10.53 thf(uniqinunit_type, type, uniqinunit: $o). 77.33/10.53 thf(dsetconstr__Cong_type, type, dsetconstr__Cong: $o). 77.33/10.53 thf(exu__Cong_type, type, exu__Cong: $o). 77.33/10.53 thf(subset2powerset_type, type, subset2powerset: $o). 77.33/10.53 thf(setoftrueEq_type, type, setoftrueEq: $o). 77.33/10.53 thf(image1Ex1_type, type, image1Ex1: $o). 77.33/10.53 thf(brelnall1_type, type, brelnall1: $o). 77.33/10.53 thf(iftrueProp2_type, type, iftrueProp2: $o). 77.33/10.53 thf(upairsetIL_type, type, upairsetIL: $o). 77.33/10.53 thf(disjointsetsI1_type, type, disjointsetsI1: $o). 77.33/10.53 thf(kpairsurjEq_type, type, kpairsurjEq: $o). 77.33/10.53 thf(emptyI_type, type, emptyI: $o). 77.33/10.53 thf(setukpairIL_type, type, setukpairIL: $o). 77.33/10.53 thf(ifSingleton_type, type, ifSingleton: $o). 77.33/10.53 thf(apProp_type, type, apProp: $o). 77.33/10.53 thf(exuI3_type, type, exuI3: $o). 77.33/10.53 thf(singletonsuniq_type, type, singletonsuniq: $o). 77.33/10.53 thf(binintersectTERcontra_type, type, binintersectTERcontra: $o). 77.33/10.53 thf(brelnall2_type, type, brelnall2: $o). 77.33/10.53 thf(emptysetAx_type, type, emptysetAx: $o). 77.33/10.53 thf(setukpairIR_type, type, setukpairIR: $o). 77.33/10.53 thf(binunionTE_type, type, binunionTE: $o). 77.33/10.53 thf(complementSubsetComplementIntersect_type, type, complementSubsetComplementIntersect: 77.33/10.53 $o). 77.33/10.53 thf(complementTnotintersectT_type, type, complementTnotintersectT: $o). 77.33/10.53 thf(emptyInPowerset_type, type, emptyInPowerset: $o). 77.33/10.53 thf(setadjoinIL_type, type, setadjoinIL: $o). 77.33/10.53 thf(upairsubunion_type, type, upairsubunion: $o). 77.33/10.53 thf(cartprodsndin_type, type, cartprodsndin: $o). 77.33/10.53 thf(emptyinunitempty_type, type, emptyinunitempty: $o). 77.33/10.53 thf(upairsetIR_type, type, upairsetIR: $o). 77.33/10.53 thf(setukpairinjR12_type, type, setukpairinjR12: $o). 77.33/10.53 thf(ubforcartprodlem3_type, type, ubforcartprodlem3: $o). 77.33/10.53 thf(woz1_2_type, type, woz1_2: $o). 77.33/10.53 thf(emptyset__Cong_type, type, emptyset__Cong: $o). 77.33/10.53 thf(doubleComplementE1_type, type, doubleComplementE1: $o). 77.33/10.53 thf(binintersectTELcontra_type, type, binintersectTELcontra: $o). 77.33/10.53 thf(complementTI1_type, type, complementTI1: $o). 77.33/10.53 thf(setunionTransitive_type, type, setunionTransitive: $o). 77.33/10.53 thf(setminusI_type, type, setminusI: $o). 77.33/10.53 thf(setukpairinjL1_type, type, setukpairinjL1: $o). 77.33/10.53 thf(descrp_type, type, descrp: $o). 77.33/10.53 thf(binintersectI_type, type, binintersectI: $o). 77.33/10.53 thf(nonemptyI1_type, type, nonemptyI1: $o). 77.33/10.53 thf(foundation2_type, type, foundation2: $o). 77.33/10.53 thf(demorgan2b2_type, type, demorgan2b2: $o). 77.33/10.53 thf(emptysetsubset_type, type, emptysetsubset: $o). 77.33/10.53 thf(setunionAx_type, type, setunionAx: $o). 77.33/10.53 thf(breln1compprop_type, type, breln1compprop: $o). 77.33/10.53 thf(notsubsetI_type, type, notsubsetI: $o). 77.33/10.53 thf(image1I_type, type, image1I: $o). 77.33/10.53 thf(breln1unionCommutes_type, type, breln1unionCommutes: $o). 77.33/10.53 thf(woz2W_type, type, woz2W: $o). 77.33/10.53 thf(inComplementUnionImpInComplement1_type, type, inComplementUnionImpInComplement1: 77.33/10.53 $o). 77.33/10.53 thf(woz2A_type, type, woz2A: $o). 77.33/10.53 thf(setukpairinjL2_type, type, setukpairinjL2: $o). 77.33/10.53 thf(binintersectSubset5_type, type, binintersectSubset5: $o). 77.33/10.53 thf(upairset2IR_type, type, upairset2IR: $o). 77.33/10.53 thf(doubleComplementSub2_type, type, doubleComplementSub2: $o). 77.33/10.53 thf(breln1SetBreln1_type, type, breln1SetBreln1: $o). 77.33/10.53 thf(binunionLsub_type, type, binunionLsub: $o). 77.33/10.53 thf(ap2apEq2_type, type, ap2apEq2: $o). 77.33/10.53 thf(subsetRefl_type, type, subsetRefl: $o). 77.33/10.53 thf(omegaSclos_type, type, omegaSclos: $o). 77.33/10.53 thf(cartprodfstin_type, type, cartprodfstin: $o). 77.33/10.53 thf(nonemptyI_type, type, nonemptyI: $o). 77.33/10.53 thf(emptysetE_type, type, emptysetE: $o). 77.33/10.53 thf(sepInPowerset_type, type, sepInPowerset: $o). 77.33/10.53 thf(woz1_1_type, type, woz1_1: $o). 77.33/10.53 thf(inIntersectImpInUnion_type, type, inIntersectImpInUnion: $o). 77.33/10.53 thf(subbreln1_type, type, subbreln1: $o). 77.33/10.53 thf(breln1unionIL_type, type, breln1unionIL: $o). 77.33/10.53 thf(cartprodmempair1_type, type, cartprodmempair1: $o). 77.33/10.53 thf(setminusT_lem_type, type, setminusT_lem: $o). 77.33/10.53 thf(subsetemptysetimpeq_type, type, subsetemptysetimpeq: $o). 77.33/10.53 thf(inIntersectImpInUnion2_type, type, inIntersectImpInUnion2: $o). 77.33/10.53 thf(dpsetconstrEL2_type, type, dpsetconstrEL2: $o). 77.33/10.53 thf(powersetI_type, type, powersetI: $o). 77.33/10.53 thf(setukpairinjR2_type, type, setukpairinjR2: $o). 77.33/10.53 thf(exuE2_type, type, exuE2: $o). 77.33/10.53 thf(breln1invE_type, type, breln1invE: $o). 77.33/10.53 thf(setukpairinjR11_type, type, setukpairinjR11: $o). 77.33/10.53 thf(setOfPairsIsBReln1_type, type, setOfPairsIsBReln1: $o). 77.33/10.53 thf(exuE3e_type, type, exuE3e: $o). 77.33/10.53 thf(setminusSubset1_type, type, setminusSubset1: $o). 77.33/10.53 thf(notequalI2_type, type, notequalI2: $o). 77.33/10.53 thf(descr__Cong_type, type, descr__Cong: $o). 77.33/10.53 thf(binintTransitive_type, type, binintTransitive: $o). 77.33/10.53 thf(iffalseProp2_type, type, iffalseProp2: $o). 77.33/10.53 thf(wellorderedByIn_type, type, wellorderedByIn: $i > $o). 77.33/10.53 thf(setextAx_type, type, setextAx: $o). 77.33/10.53 thf(eqbreln1_type, type, eqbreln1: $o). 77.33/10.53 thf(quantDeMorgan1_type, type, quantDeMorgan1: $o). 77.33/10.53 thf(eqinunit_type, type, eqinunit: $o). 77.33/10.53 thf(symdiffE_type, type, symdiffE: $o). 77.33/10.53 thf(binunionTIRcontra_type, type, binunionTIRcontra: $o). 77.33/10.53 thf(upairinpowunion_type, type, upairinpowunion: $o). 77.33/10.53 thf(doubleComplementI1_type, type, doubleComplementI1: $o). 77.33/10.53 thf(injFuncInInjFuncSet_type, type, injFuncInInjFuncSet: $o). 77.50/10.53 thf('#sk1597_type', type, '#sk1597': $i). 77.50/10.53 thf(ex1E1_type, type, ex1E1: $o). 77.50/10.53 thf(binintersectSubset1_type, type, binintersectSubset1: $o). 77.50/10.53 thf(powersetAx_type, type, powersetAx: $o). 77.50/10.53 thf(contrasubsetT1_type, type, contrasubsetT1: $o). 77.50/10.53 thf(upairset2E_type, type, upairset2E: $o). 77.50/10.53 thf(kfstpairEq_type, type, kfstpairEq: $o). 77.50/10.53 thf(subsetI2_type, type, subsetI2: $o). 77.50/10.53 thf(symdiffI1_type, type, symdiffI1: $o). 77.50/10.53 thf(subsetI1_type, type, subsetI1: $o). 77.50/10.53 thf(doubleComplementSub1_type, type, doubleComplementSub1: $o). 77.50/10.53 thf(binunionTILcontra_type, type, binunionTILcontra: $o). 77.50/10.53 thf(breln1invI_type, type, breln1invI: $o). 77.50/10.53 thf(nonemptyImpWitness_type, type, nonemptyImpWitness: $o). 77.50/10.53 thf(replAx_type, type, replAx: $o). 77.50/10.53 thf(subPowSU_type, type, subPowSU: $o). 77.50/10.53 thf(setunionE_type, type, setunionE: $o). 77.50/10.53 thf(ordinal_type, type, ordinal: $i > $o). 77.50/10.53 thf(setunionsingleton_type, type, setunionsingleton: $o). 77.50/10.53 thf(setunion__Cong_type, type, setunion__Cong: $o). 77.50/10.53 thf(lam2p_type, type, lam2p: $o). 77.50/10.53 thf(bs114d_type, type, bs114d: $o). 77.50/10.53 thf(demorgan1a_type, type, demorgan1a: $o). 77.50/10.53 thf(setminusSubset2_type, type, setminusSubset2: $o). 77.50/10.53 thf(binintersectT_lem_type, type, binintersectT_lem: $o). 77.50/10.53 thf(powersetE1_type, type, powersetE1: $o). 77.50/10.53 thf(ubforcartprodlem2_type, type, ubforcartprodlem2: $o). 77.50/10.53 thf(woz13rule1_type, type, woz13rule1: $o). 77.50/10.53 thf(dpsetconstrSub_type, type, dpsetconstrSub: $o). 77.50/10.53 thf(omegaSAx_type, type, omegaSAx: $o). 77.50/10.53 thf(breln1all2_type, type, breln1all2: $o). 77.50/10.53 thf(complementTE1_type, type, complementTE1: $o). 77.50/10.53 thf(subbreln_type, type, subbreln: $o). 77.50/10.53 thf(breln1unionI_type, type, breln1unionI: $o). 77.50/10.53 thf(eqbreln_type, type, eqbreln: $o). 77.50/10.53 thf(injFuncSetFuncIn_type, type, injFuncSetFuncIn: $o). 77.50/10.53 thf(setext_type, type, setext: $o). 77.50/10.53 thf(subsetTI_type, type, subsetTI: $o). 77.50/10.53 thf(notequalI1_type, type, notequalI1: $o). 77.50/10.53 thf(woz13rule4_type, type, woz13rule4: $o). 77.50/10.53 thf(beta1_type, type, beta1: $o). 77.50/10.53 thf(funcinfuncset_type, type, funcinfuncset: $o). 77.50/10.53 thf(setextsub_type, type, setextsub: $o). 77.50/10.53 thf(kpairp_type, type, kpairp: $o). 77.50/10.53 thf(surjFuncSetFuncSurj_type, type, surjFuncSetFuncSurj: $o). 77.50/10.53 thf(notinself_type, type, notinself: $o). 77.50/10.53 thf(funcext_type, type, funcext: $o). 77.50/10.53 thf(omega__Cong_type, type, omega__Cong: $o). 77.50/10.53 thf(contraSubsetComplement_type, type, contraSubsetComplement: $o). 77.50/10.53 thf(symdiffI2_type, type, symdiffI2: $o). 77.50/10.53 thf(omega_type, type, omega: $i). 77.50/10.53 thf(dpsetconstrER_type, type, dpsetconstrER: $o). 77.50/10.53 thf(powersetTI1_type, type, powersetTI1: $o). 77.50/10.53 thf(setbeta_type, type, setbeta: $o). 77.50/10.53 thf(dsetconstrER_type, type, dsetconstrER: $o). 77.50/10.53 thf(nonemptyE1_type, type, nonemptyE1: $o). 77.50/10.53 thf(image1Equiv_type, type, image1Equiv: $o). 77.50/10.53 thf(binunionIL_type, type, binunionIL: $o). 77.50/10.53 thf(breln1compE_type, type, breln1compE: $o). 77.50/10.53 thf(prop2setE_type, type, prop2setE: $o). 77.50/10.53 thf(complementInPowersetComplementIntersect_type, type, complementInPowersetComplementIntersect: 77.50/10.53 $o). 77.50/10.53 thf(complementTcontraSubset_type, type, complementTcontraSubset: $o). 77.50/10.53 thf(prop2set2propI_type, type, prop2set2propI: $o). 77.50/10.53 thf(notdallE_type, type, notdallE: $o). 77.50/10.53 thf(eqimpsubset1_type, type, eqimpsubset1: $o). 77.50/10.53 thf(cartprodpairsurjEq_type, type, cartprodpairsurjEq: $o). 77.50/10.53 thf(ordinalMinLem1_type, type, ordinalMinLem1: $o). 77.50/10.53 thf(exuEu_type, type, exuEu: $o). 77.50/10.53 thf(dpsetconstrEL1_type, type, dpsetconstrEL1: $o). 77.50/10.53 thf(image1E_type, type, image1E: $o). 77.50/10.53 thf(singletoninpowerset_type, type, singletoninpowerset: $o). 77.50/10.53 thf(notinsingleton_type, type, notinsingleton: $o). 77.50/10.53 thf(upairsetE_type, type, upairsetE: $o). 77.50/10.53 thf(contrasubsetT3_type, type, contrasubsetT3: $o). 77.50/10.53 thf(emptyE1_type, type, emptyE1: $o). 77.50/10.53 thf(emptyinPowerset_type, type, emptyinPowerset: $o). 77.50/10.53 thf(cartprodmempair_type, type, cartprodmempair: $o). 77.50/10.53 thf(binunionEcases_type, type, binunionEcases: $o). 77.50/10.53 thf(cartprodpairmemER_type, type, cartprodpairmemER: $o). 77.50/10.53 thf(injFuncSetFuncInj_type, type, injFuncSetFuncInj: $o). 77.50/10.53 thf(dpsetconstrI_type, type, dpsetconstrI: $o). 77.50/10.53 thf(woz1_4_type, type, woz1_4: $o). 77.50/10.53 thf(peanoSinj_type, type, peanoSinj: $o). 77.50/10.53 thf(symdiffIneg1_type, type, symdiffIneg1: $o). 77.50/10.53 thf(theeq_type, type, theeq: $o). 77.50/10.53 thf(binintersectSubset4_type, type, binintersectSubset4: $o). 77.50/10.53 thf(powersetTE1_type, type, powersetTE1: $o). 77.50/10.53 thf(wellorderingAx_type, type, wellorderingAx: $o). 77.50/10.53 thf(singletoninpowunion_type, type, singletoninpowunion: $o). 77.50/10.53 thf(binintersectLsub_type, type, binintersectLsub: $o). 77.50/10.53 thf(breln1unionprop_type, type, breln1unionprop: $o). 77.50/10.53 thf(binintersectRsub_type, type, binintersectRsub: $o). 77.50/10.53 thf(powersetsubset_type, type, powersetsubset: $o). 77.50/10.53 thf(funcGraphProp4_type, type, funcGraphProp4: $o). 77.50/10.53 thf(emptyset_type, type, emptyset: $i). 77.50/10.53 thf(ubforcartprodlem1_type, type, ubforcartprodlem1: $o). 77.50/10.53 thf(woz2Ex_type, type, woz2Ex: $o). 77.50/10.53 thf(noeltsimpempty_type, type, noeltsimpempty: $o). 77.50/10.53 thf(iffalseProp1_type, type, iffalseProp1: $o). 77.50/10.53 thf(exuE1_type, type, exuE1: $o). 77.50/10.53 thf(omegaSp_type, type, omegaSp: $o). 77.50/10.53 thf(inPowerset_type, type, inPowerset: $o). 77.50/10.53 thf(in_type, type, in: $i > $i > $o). 77.50/10.53 thf(cartprodpairin_type, type, cartprodpairin: $o). 77.50/10.53 thf(setunionI_type, type, setunionI: $o). 77.50/10.53 thf(in__Cong_type, type, in__Cong: $o). 77.50/10.53 thf(binintersect_type, type, binintersect: $i > $i > $i). 77.50/10.53 thf('#sk337_type', type, '#sk337': $i > ($i > $o) > $i). 77.50/10.53 thf(setadjoinE_type, type, setadjoinE: $o). 77.50/10.53 thf(subsetTrans_type, type, subsetTrans: $o). 77.50/10.53 thf(dsetconstrEL_type, type, dsetconstrEL: $o). 77.50/10.53 thf(demorgan2a_type, type, demorgan2a: $o). 77.50/10.53 thf(woz1_3_type, type, woz1_3: $o). 77.50/10.53 thf(symdiffIneg2_type, type, symdiffIneg2: $o). 77.50/10.53 thf(choice2fnsingleton_type, type, choice2fnsingleton: $o). 77.50/10.53 thf(setminusIRneg_type, type, setminusIRneg: $o). 77.50/10.53 thf(setminusELneg_type, type, setminusELneg: $o). 77.50/10.53 thf(foundationAx_type, type, foundationAx: $o). 77.50/10.53 thf(transitivesetOp1_type, type, transitivesetOp1: $o). 77.50/10.53 thf(woz13rule3_type, type, woz13rule3: $o). 77.50/10.53 thf(sepSubset_type, type, sepSubset: $o). 77.50/10.53 thf(cartprodpairmemEL_type, type, cartprodpairmemEL: $o). 77.50/10.53 thf(woz2B_type, type, woz2B: $o). 77.50/10.53 thf(ex1E2_type, type, ex1E2: $o). 77.50/10.53 thf(exuE3u_type, type, exuE3u: $o). 77.50/10.53 thf(kpairiskpair_type, type, kpairiskpair: $o). 77.50/10.53 thf(funcextLem_type, type, funcextLem: $o). 77.50/10.53 thf(breln1unionIR_type, type, breln1unionIR: $o). 77.50/10.53 thf(powersetT_lem_type, type, powersetT_lem: $o). 77.50/10.53 thf(setadjoinOr_type, type, setadjoinOr: $o). 77.50/10.53 thf(cartprodsndpairEq_type, type, cartprodsndpairEq: $o). 77.50/10.53 thf(ap2p_type, type, ap2p: $o). 77.50/10.53 thf(exuI1_type, type, exuI1: $o). 77.50/10.53 thf(doubleComplementEq_type, type, doubleComplementEq: $o). 77.50/10.53 thf(transitivesetOp2_type, type, transitivesetOp2: $o). 77.50/10.53 thf(setukpairinjR1_type, type, setukpairinjR1: $o). 77.50/10.53 thf(breln1unionEcases_type, type, breln1unionEcases: $o). 77.50/10.53 thf(setukpairinjL_type, type, setukpairinjL: $o). 77.50/10.53 thf(quantDeMorgan2_type, type, quantDeMorgan2: $o). 77.50/10.53 thf(binunionIR_type, type, binunionIR: $o). 77.50/10.53 thf('#form1598_type', type, '#form1598': $i > $o). 77.50/10.53 thf(inCongP_type, type, inCongP: $o). 77.50/10.53 thf(setminusLsub_type, type, setminusLsub: $o). 77.50/10.53 thf(cartprodmempaircEq_type, type, cartprodmempaircEq: $o). 77.50/10.53 thf(demorgan2a2_type, type, demorgan2a2: $o). 77.50/10.53 thf(binintersectSubset2_type, type, binintersectSubset2: $o). 77.50/10.53 thf(setadjoin__Cong_type, type, setadjoin__Cong: $o). 77.50/10.53 thf(eta1_type, type, eta1: $o). 77.50/10.53 thf(eqimpsubset2_type, type, eqimpsubset2: $o). 77.50/10.53 thf(breln1compI_type, type, breln1compI: $o). 77.50/10.53 thf(demorgan2_type, type, demorgan2: $o). 77.50/10.53 thf(upairequniteq_type, type, upairequniteq: $o). 77.50/10.53 thf(setminusERneg_type, type, setminusERneg: $o). 77.50/10.53 thf(ifp_type, type, ifp: $o). 77.50/10.53 thf(breln1unionE_type, type, breln1unionE: $o). 77.50/10.53 thf('#sk1599_type', type, '#sk1599': $i). 77.50/10.53 thf(complementT_lem_type, type, complementT_lem: $o). 77.50/10.53 thf(notinself2_type, type, notinself2: $o). 77.50/10.53 thf(exuI2_type, type, exuI2: $o). 77.50/10.53 thf(powersetI1_type, type, powersetI1: $o). 77.50/10.53 thf(infuncsetfunc_type, type, infuncsetfunc: $o). 77.50/10.53 thf(iftrueProp1_type, type, iftrueProp1: $o). 77.50/10.53 thf(binunionTEcontra_type, type, binunionTEcontra: $o). 77.50/10.53 thf(complementUnionInPowersetComplement_type, type, complementUnionInPowersetComplement: 77.50/10.53 $o). 77.50/10.53 thf(cartprodfstpairEq_type, type, cartprodfstpairEq: $o). 77.50/10.53 thf(lam2lamEq_type, type, lam2lamEq: $o). 77.50/10.53 thf(iftrue_type, type, iftrue: $o). 77.50/10.53 thf(breln1compEex_type, type, breln1compEex: $o). 77.50/10.53 thf(transitiveset_type, type, transitiveset: $i > $o). 77.50/10.53 thf(complementImpComplementIntersect_type, type, complementImpComplementIntersect: 77.50/10.53 $o). 77.50/10.53 thf(setunionsingleton1_type, type, setunionsingleton1: $o). 77.50/10.53 thf(setminusILneg_type, type, setminusILneg: $o). 77.50/10.53 thf(dsetconstrI_type, type, dsetconstrI: $o). 77.50/10.53 thf(image1Ex_type, type, image1Ex: $o). 77.50/10.53 thf(ap2apEq1_type, type, ap2apEq1: $o). 77.50/10.53 thf(peano0notS_type, type, peano0notS: $o). 77.50/10.53 thf(ksndpairEq_type, type, ksndpairEq: $o). 77.50/10.53 thf(setminusEL_type, type, setminusEL: $o). 77.50/10.53 thf(singletonsubset_type, type, singletonsubset: $o). 77.50/10.53 thf(ksndsingleton_type, type, ksndsingleton: $o). 77.50/10.53 thf(theprop_type, type, theprop: $o). 77.50/10.53 thf(demorgan2a1_type, type, demorgan2a1: $o). 77.50/10.53 thf(secondinupair_type, type, secondinupair: $o). 77.50/10.53 thf(eta2_type, type, eta2: $o). 77.50/10.53 thf(ex1I_type, type, ex1I: $o). 77.50/10.53 thf(demorgan1_type, type, demorgan1: $o). 77.50/10.53 thf(funcGraphProp3_type, type, funcGraphProp3: $o). 77.50/10.53 thf(funcImageSingleton_type, type, funcImageSingleton: $o). 77.50/10.53 thf(funcGraphProp1_type, type, funcGraphProp1: $o). 77.50/10.53 thf(inComplementUnionImpNotIn1_type, type, inComplementUnionImpNotIn1: $o). 77.50/10.53 thf(subsetE2_type, type, subsetE2: $o). 77.50/10.53 thf(singletonsswitch_type, type, singletonsswitch: $o). 77.50/10.53 thf(contrasubsetT2_type, type, contrasubsetT2: $o). 77.50/10.53 thf(binintersectEL_type, type, binintersectEL: $o). 77.50/10.53 thf(setadjoinAx_type, type, setadjoinAx: $o). 77.50/10.53 thf(quantDeMorgan4_type, type, quantDeMorgan4: $o). 77.50/10.53 thf('#sk1600_type', type, '#sk1600': $i). 77.50/10.53 thf(notinemptyset_type, type, notinemptyset: $o). 77.50/10.53 thf(prop2setI_type, type, prop2setI: $o). 77.50/10.53 thf(lamp_type, type, lamp: $o). 77.50/10.53 thf(iftrueorfalse_type, type, iftrueorfalse: $o). 77.50/10.53 thf(setunionsingleton2_type, type, setunionsingleton2: $o). 77.50/10.53 thf(setunionE2_type, type, setunionE2: $o). 77.50/10.53 thf(app_type, type, app: $o). 77.50/10.53 thf(binunionT_lem_type, type, binunionT_lem: $o). 77.50/10.53 thf(surjFuncSetFuncIn_type, type, surjFuncSetFuncIn: $o). 77.50/10.53 thf(subset_type, type, subset: $i > $i > $o). 77.50/10.53 thf(notdexE_type, type, notdexE: $o). 77.50/10.53 thf(kfstsingleton_type, type, kfstsingleton: $o). 77.50/10.53 thf(ordinalTransSet, conjecture, 77.50/10.53 (( setextAx ) => 77.50/10.53 ( ( emptysetAx ) => 77.50/10.53 ( ( setadjoinAx ) => 77.50/10.53 ( ( powersetAx ) => 77.50/10.53 ( ( setunionAx ) => 77.50/10.53 ( ( omega0Ax ) => 77.50/10.53 ( ( omegaSAx ) => 77.50/10.53 ( ( omegaIndAx ) => 77.50/10.53 ( ( replAx ) => 77.50/10.53 ( ( foundationAx ) => 77.50/10.53 ( ( wellorderingAx ) => 77.50/10.53 ( ( descrp ) => 77.50/10.53 ( ( dsetconstrI ) => 77.50/10.53 ( ( dsetconstrEL ) => 77.50/10.53 ( ( dsetconstrER ) => 77.50/10.53 ( ( exuE1 ) => 77.50/10.53 ( ( prop2setE ) => 77.50/10.53 ( ( emptysetE ) => 77.50/10.53 ( ( emptysetimpfalse ) => 77.50/10.53 ( ( notinemptyset ) => 77.50/10.53 ( ( exuE3e ) => 77.50/10.53 ( ( setext ) => 77.50/10.53 ( ( emptyI ) => 77.50/10.53 ( ( noeltsimpempty ) => 77.50/10.53 ( ( setbeta ) => 77.50/10.53 ( ( nonemptyE1 ) => 77.50/10.53 ( ( nonemptyI ) => 77.50/10.53 ( ( nonemptyI1 ) => 77.50/10.53 ( ( setadjoinIL ) => 77.50/10.53 ( ( emptyinunitempty ) => 77.50/10.53 ( ( setadjoinIR ) => 77.50/10.53 ( ( setadjoinE ) => 77.50/10.53 ( ( 77.50/10.53 setadjoinOr ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 setoftrueEq ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 powersetI ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 emptyinPowerset ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 emptyInPowerset ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 powersetE ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 setunionI ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 setunionE ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 subPowSU ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 exuE2 ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 nonemptyImpWitness ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 uniqinunit ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 notinsingleton ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 eqinunit ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 singletonsswitch ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 upairsetE ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 upairsetIL ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 upairsetIR ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 emptyE1 ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 vacuousDall ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 quantDeMorgan1 ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 quantDeMorgan2 ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 quantDeMorgan3 ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 quantDeMorgan4 ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 prop2setI ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 prop2set2propI ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 notdexE ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 notdallE ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 exuI1 ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 exuI3 ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 exuI2 ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 inCongP ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 in__Cong ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 exuE3u ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 exu__Cong ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 emptyset__Cong ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 setadjoin__Cong ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 powerset__Cong ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 setunion__Cong ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 omega__Cong ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 exuEu ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 descr__Cong ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 dsetconstr__Cong ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 subsetI1 ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 eqimpsubset2 ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 eqimpsubset1 ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 subsetI2 ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 emptysetsubset ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 subsetE ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 subsetE2 ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 notsubsetI ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 notequalI1 ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 notequalI2 ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 subsetRefl ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 subsetTrans ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 setadjoinSub ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 setadjoinSub2 ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 subset2powerset ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 setextsub ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 subsetemptysetimpeq ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 powersetI1 ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 powersetE1 ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 inPowerset ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 powersetsubset ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 sepInPowerset ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 sepSubset ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 binunionIL ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 upairset2IR ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 binunionIR ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 binunionEcases ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 binunionE ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 binunionLsub ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 binunionRsub ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 binintersectI ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 binintersectSubset5 ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 binintersectEL ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 binintersectLsub ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 binintersectSubset2 ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 binintersectSubset3 ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 binintersectER ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 disjointsetsI1 ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 binintersectRsub ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 binintersectSubset4 ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 binintersectSubset1 ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 bs114d ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 setminusI ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 setminusEL ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 setminusER ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 setminusSubset2 ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 setminusERneg ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 setminusELneg ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 setminusILneg ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 setminusIRneg ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 setminusLsub ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 setminusSubset1 ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 symdiffE ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 symdiffI1 ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 symdiffI2 ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 symdiffIneg1 ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 symdiffIneg2 ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 secondinupair ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 setukpairIL ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 setukpairIR ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 kpairiskpair ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 kpairp ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 singletonsubset ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 singletoninpowerset ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 singletoninpowunion ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 upairset2E ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 upairsubunion ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 upairinpowunion ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 ubforcartprodlem1 ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 ubforcartprodlem2 ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 ubforcartprodlem3 ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 cartprodpairin ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 cartprodmempair1 ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 cartprodmempair ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 setunionE2 ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 setunionsingleton1 ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 setunionsingleton2 ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 setunionsingleton ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 singletonprop ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 ex1E1 ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 ex1I ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 ex1I2 ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 singletonsuniq ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 setukpairinjL1 ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 kfstsingleton ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 theprop ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 kfstpairEq ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 cartprodfstin ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 setukpairinjL2 ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 setukpairinjL ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 setukpairinjR11 ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 setukpairinjR12 ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 setukpairinjR1 ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 upairequniteq ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 setukpairinjR2 ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 setukpairinjR ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 ksndsingleton ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 ksndpairEq ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 kpairsurjEq ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 cartprodsndin ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 cartprodpairmemEL ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 cartprodpairmemER ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 cartprodmempaircEq ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 cartprodfstpairEq ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 cartprodsndpairEq ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 cartprodpairsurjEq ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 dpsetconstrI ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 dpsetconstrSub ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 setOfPairsIsBReln ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 dpsetconstrERa ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 dpsetconstrEL1 ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 dpsetconstrEL2 ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 dpsetconstrER ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 funcImageSingleton ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 apProp ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 app ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 infuncsetfunc ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 ap2p ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 funcinfuncset ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 lamProp ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 lamp ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 lam2p ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 brelnall1 ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 brelnall2 ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 ex1E2 ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 funcGraphProp1 ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 funcGraphProp3 ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 funcGraphProp2 ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 funcextLem ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 funcGraphProp4 ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 subbreln ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 eqbreln ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 funcext ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 funcext2 ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 ap2apEq1 ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 ap2apEq2 ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 beta1 ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 eta1 ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 lam2lamEq ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 beta2 ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 eta2 ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 iffalseProp1 ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 iffalseProp2 ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 iftrueProp1 ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 iftrueProp2 ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 ifSingleton ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 ifp ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 theeq ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 iftrue ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 iffalse ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 iftrueorfalse ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 binintersectT_lem ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 binunionT_lem ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 powersetT_lem ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 setminusT_lem ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 complementT_lem ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 setextT ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 subsetTI ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 powersetTI1 ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 powersetTE1 ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 complementTI1 ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 complementTE1 ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 binintersectTELcontra ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 binintersectTERcontra ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 contrasubsetT ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 contrasubsetT1 ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 contrasubsetT2 ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 contrasubsetT3 ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 doubleComplementI1 ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 doubleComplementE1 ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 doubleComplementSub1 ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 doubleComplementSub2 ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 doubleComplementEq ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 complementTnotintersectT ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 complementImpComplementIntersect ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 complementSubsetComplementIntersect ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 complementInPowersetComplementIntersect ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 contraSubsetComplement ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 complementTcontraSubset ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 binunionTILcontra ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 binunionTIRcontra ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 inIntersectImpInUnion ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 inIntersectImpInUnion2 ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 inIntersectImpInIntersectUnions ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 intersectInPowersetIntersectUnions ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 inComplementUnionImpNotIn1 ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 inComplementUnionImpInComplement1 ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 binunionTE ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 binunionTEcontra ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 demorgan2a1 ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 complementUnionInPowersetComplement ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 demorgan2a2 ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 demorgan1a ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 demorgan1b ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 demorgan1 ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 demorgan2a ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 demorgan2b2 ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 demorgan2b ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 demorgan2 ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 woz13rule0 ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 woz13rule1 ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 woz13rule2 ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 woz13rule3 ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 woz13rule4 ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 woz1_1 ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 woz1_2 ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 woz1_3 ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 woz1_4 ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 woz1_5 ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 breln1all2 ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 breln1SetBreln1 ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 choice2fnsingleton ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 setOfPairsIsBReln1 ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 breln1all1 ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 subbreln1 ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 eqbreln1 ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 breln1invprop ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 breln1invI ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 breln1invE ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 breln1compprop ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 breln1compI ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 breln1compE ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 breln1compEex ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 breln1unionprop ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 breln1unionIL ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 breln1unionIR ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 breln1unionI ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 breln1unionE ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 breln1unionEcases ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 breln1unionCommutes ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 woz2Ex ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 woz2W ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 woz2A ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 woz2B ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 image1Ex ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 image1Ex1 ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 image1Equiv ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 image1E ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 image1I ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 injFuncInInjFuncSet ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 injFuncSetFuncIn ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 injFuncSetFuncInj ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 surjFuncSetFuncIn ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 surjFuncSetFuncSurj ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 leftInvIsSurj ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 surjCantorThm ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 foundation2 ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 notinself ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 notinself2 ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 omegaSp ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 omegaSclos ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 peano0notS ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 peanoSinj ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 transitivesetOp1 ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 binintTransitive ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 transitivesetOp2 ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 setunionTransitive ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 ordinalMinLem1 ) => 77.50/10.53 ( 77.50/10.53 ![ 77.50/10.53 X:$i]: 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 ordinal @ 77.50/10.53 X ) => 77.50/10.53 ( 77.50/10.53 ![ 77.50/10.53 Xx:$i,A:$i]: 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 in @ A @ X ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 in @ 77.50/10.53 Xx @ A ) => 77.50/10.53 ( 77.50/10.53 in @ 77.50/10.53 Xx @ X ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))). 77.50/10.53 thf(zf_stmt_0, negated_conjecture, 77.50/10.53 (~( ( setextAx ) => 77.50/10.53 ( ( emptysetAx ) => 77.50/10.53 ( ( setadjoinAx ) => 77.50/10.53 ( ( powersetAx ) => 77.50/10.53 ( ( setunionAx ) => 77.50/10.53 ( ( omega0Ax ) => 77.50/10.53 ( ( omegaSAx ) => 77.50/10.53 ( ( omegaIndAx ) => 77.50/10.53 ( ( replAx ) => 77.50/10.53 ( ( foundationAx ) => 77.50/10.53 ( ( wellorderingAx ) => 77.50/10.53 ( ( descrp ) => 77.50/10.53 ( ( dsetconstrI ) => 77.50/10.53 ( ( dsetconstrEL ) => 77.50/10.53 ( ( dsetconstrER ) => 77.50/10.53 ( ( exuE1 ) => 77.50/10.53 ( ( prop2setE ) => 77.50/10.53 ( ( emptysetE ) => 77.50/10.53 ( ( emptysetimpfalse ) => 77.50/10.53 ( ( notinemptyset ) => 77.50/10.53 ( ( exuE3e ) => 77.50/10.53 ( ( setext ) => 77.50/10.53 ( ( emptyI ) => 77.50/10.53 ( ( noeltsimpempty ) => 77.50/10.53 ( ( setbeta ) => 77.50/10.53 ( ( nonemptyE1 ) => 77.50/10.53 ( ( nonemptyI ) => 77.50/10.53 ( ( nonemptyI1 ) => 77.50/10.53 ( ( setadjoinIL ) => 77.50/10.53 ( ( emptyinunitempty ) => 77.50/10.53 ( ( setadjoinIR ) => 77.50/10.53 ( ( 77.50/10.53 setadjoinE ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 setadjoinOr ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 setoftrueEq ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 powersetI ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 emptyinPowerset ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 emptyInPowerset ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 powersetE ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 setunionI ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 setunionE ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 subPowSU ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 exuE2 ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 nonemptyImpWitness ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 uniqinunit ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 notinsingleton ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 eqinunit ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 singletonsswitch ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 upairsetE ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 upairsetIL ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 upairsetIR ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 emptyE1 ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 vacuousDall ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 quantDeMorgan1 ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 quantDeMorgan2 ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 quantDeMorgan3 ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 quantDeMorgan4 ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 prop2setI ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 prop2set2propI ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 notdexE ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 notdallE ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 exuI1 ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 exuI3 ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 exuI2 ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 inCongP ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 in__Cong ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 exuE3u ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 exu__Cong ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 emptyset__Cong ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 setadjoin__Cong ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 powerset__Cong ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 setunion__Cong ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 omega__Cong ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 exuEu ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 descr__Cong ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 dsetconstr__Cong ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 subsetI1 ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 eqimpsubset2 ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 eqimpsubset1 ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 subsetI2 ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 emptysetsubset ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 subsetE ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 subsetE2 ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 notsubsetI ) => 77.50/10.53 ( 77.50/10.53 ( 77.50/10.53 notequalI1 ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 notequalI2 ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 subsetRefl ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 subsetTrans ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 setadjoinSub ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 setadjoinSub2 ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 subset2powerset ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 setextsub ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 subsetemptysetimpeq ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 powersetI1 ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 powersetE1 ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 inPowerset ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 powersetsubset ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 sepInPowerset ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 sepSubset ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 binunionIL ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 upairset2IR ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 binunionIR ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 binunionEcases ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 binunionE ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 binunionLsub ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 binunionRsub ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 binintersectI ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 binintersectSubset5 ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 binintersectEL ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 binintersectLsub ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 binintersectSubset2 ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 binintersectSubset3 ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 binintersectER ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 disjointsetsI1 ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 binintersectRsub ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 binintersectSubset4 ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 binintersectSubset1 ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 bs114d ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 setminusI ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 setminusEL ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 setminusER ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 setminusSubset2 ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 setminusERneg ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 setminusELneg ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 setminusILneg ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 setminusIRneg ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 setminusLsub ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 setminusSubset1 ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 symdiffE ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 symdiffI1 ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 symdiffI2 ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 symdiffIneg1 ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 symdiffIneg2 ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 secondinupair ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 setukpairIL ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 setukpairIR ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 kpairiskpair ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 kpairp ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 singletonsubset ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 singletoninpowerset ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 singletoninpowunion ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 upairset2E ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 upairsubunion ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 upairinpowunion ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 ubforcartprodlem1 ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 ubforcartprodlem2 ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 ubforcartprodlem3 ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 cartprodpairin ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 cartprodmempair1 ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 cartprodmempair ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 setunionE2 ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 setunionsingleton1 ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 setunionsingleton2 ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 setunionsingleton ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 singletonprop ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 ex1E1 ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 ex1I ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 ex1I2 ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 singletonsuniq ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 setukpairinjL1 ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 kfstsingleton ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 theprop ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 kfstpairEq ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 cartprodfstin ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 setukpairinjL2 ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 setukpairinjL ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 setukpairinjR11 ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 setukpairinjR12 ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 setukpairinjR1 ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 upairequniteq ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 setukpairinjR2 ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 setukpairinjR ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 ksndsingleton ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 ksndpairEq ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 kpairsurjEq ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 cartprodsndin ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 cartprodpairmemEL ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 cartprodpairmemER ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 cartprodmempaircEq ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 cartprodfstpairEq ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 cartprodsndpairEq ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 cartprodpairsurjEq ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 dpsetconstrI ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 dpsetconstrSub ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 setOfPairsIsBReln ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 dpsetconstrERa ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 dpsetconstrEL1 ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 dpsetconstrEL2 ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 dpsetconstrER ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 funcImageSingleton ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 apProp ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 app ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 infuncsetfunc ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 ap2p ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 funcinfuncset ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 lamProp ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 lamp ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 lam2p ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 brelnall1 ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 brelnall2 ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 ex1E2 ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 funcGraphProp1 ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 funcGraphProp3 ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 funcGraphProp2 ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 funcextLem ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 funcGraphProp4 ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 subbreln ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 eqbreln ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 funcext ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 funcext2 ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 ap2apEq1 ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 ap2apEq2 ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 beta1 ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 eta1 ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 lam2lamEq ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 beta2 ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 eta2 ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 iffalseProp1 ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 iffalseProp2 ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 iftrueProp1 ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 iftrueProp2 ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 ifSingleton ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 ifp ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 theeq ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 iftrue ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 iffalse ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 iftrueorfalse ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 binintersectT_lem ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 binunionT_lem ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 powersetT_lem ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 setminusT_lem ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 complementT_lem ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 setextT ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 subsetTI ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 powersetTI1 ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 powersetTE1 ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 complementTI1 ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 complementTE1 ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 binintersectTELcontra ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 binintersectTERcontra ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 contrasubsetT ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 contrasubsetT1 ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 contrasubsetT2 ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 contrasubsetT3 ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 doubleComplementI1 ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 doubleComplementE1 ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 doubleComplementSub1 ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 doubleComplementSub2 ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 doubleComplementEq ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 complementTnotintersectT ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 complementImpComplementIntersect ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 complementSubsetComplementIntersect ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 complementInPowersetComplementIntersect ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 contraSubsetComplement ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 complementTcontraSubset ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 binunionTILcontra ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 binunionTIRcontra ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 inIntersectImpInUnion ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 inIntersectImpInUnion2 ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 inIntersectImpInIntersectUnions ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 intersectInPowersetIntersectUnions ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 inComplementUnionImpNotIn1 ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 inComplementUnionImpInComplement1 ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 binunionTE ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 binunionTEcontra ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 demorgan2a1 ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 complementUnionInPowersetComplement ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 demorgan2a2 ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 demorgan1a ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 demorgan1b ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 demorgan1 ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 demorgan2a ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 demorgan2b2 ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 demorgan2b ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 demorgan2 ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 woz13rule0 ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 woz13rule1 ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 woz13rule2 ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 woz13rule3 ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 woz13rule4 ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 woz1_1 ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 woz1_2 ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 woz1_3 ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 woz1_4 ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 woz1_5 ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 breln1all2 ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 breln1SetBreln1 ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 choice2fnsingleton ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 setOfPairsIsBReln1 ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 breln1all1 ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 subbreln1 ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 eqbreln1 ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 breln1invprop ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 breln1invI ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 breln1invE ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 breln1compprop ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 breln1compI ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 breln1compE ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 breln1compEex ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 breln1unionprop ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 breln1unionIL ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 breln1unionIR ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 breln1unionI ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 breln1unionE ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 breln1unionEcases ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 breln1unionCommutes ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 woz2Ex ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 woz2W ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 woz2A ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 woz2B ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 image1Ex ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 image1Ex1 ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 image1Equiv ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 image1E ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 image1I ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 injFuncInInjFuncSet ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 injFuncSetFuncIn ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 injFuncSetFuncInj ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 surjFuncSetFuncIn ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 surjFuncSetFuncSurj ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 leftInvIsSurj ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 surjCantorThm ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 foundation2 ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 notinself ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 notinself2 ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 omegaSp ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 omegaSclos ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 peano0notS ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 peanoSinj ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 transitivesetOp1 ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 binintTransitive ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 transitivesetOp2 ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 setunionTransitive ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 ordinalMinLem1 ) => 77.50/10.54 ( 77.50/10.54 ![ 77.50/10.54 X:$i]: 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 ordinal @ 77.50/10.54 X ) => 77.50/10.54 ( 77.50/10.54 ![ 77.50/10.54 Xx:$i, 77.50/10.54 A:$i]: 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 in @ 77.50/10.54 A @ X ) => 77.50/10.54 ( 77.50/10.54 ( 77.50/10.54 in @ 77.50/10.54 Xx @ A ) => 77.50/10.54 ( 77.50/10.54 in @ 77.50/10.54 Xx @ X ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )), 77.50/10.54 inference('cnf.neg', [status(esa)], [ordinalTransSet])). 77.50/10.54 thf(zip_derived_cl0, plain, 77.50/10.54 (~ (((setextAx) => 77.50/10.54 (((emptysetAx) => 77.50/10.54 (((setadjoinAx) => 77.50/10.54 (((powersetAx) => 77.50/10.54 (((setunionAx) => 77.50/10.54 (((omega0Ax) => 77.50/10.54 (((omegaSAx) => 77.50/10.54 (((omegaIndAx) => 77.50/10.54 (((replAx) => 77.50/10.54 (((foundationAx) => 77.50/10.54 (((wellorderingAx) => 77.50/10.54 (((descrp) => 77.50/10.54 (((dsetconstrI) => 77.50/10.54 (((dsetconstrEL) => 77.50/10.54 (((dsetconstrER) => 77.50/10.54 (((exuE1) => 77.50/10.54 (((prop2setE) => 77.50/10.54 (((emptysetE) => 77.50/10.54 (((emptysetimpfalse) => 77.50/10.54 (((notinemptyset) => 77.50/10.54 (((exuE3e) => 77.50/10.54 (((setext) => 77.50/10.54 (((emptyI) => 77.50/10.54 (((noeltsimpempty) => 77.50/10.54 (((setbeta) => 77.50/10.54 (((nonemptyE1) => 77.50/10.54 (((nonemptyI) => 77.50/10.54 (((nonemptyI1) => 77.50/10.54 (((setadjoinIL) => 77.50/10.54 (((emptyinunitempty) => 77.50/10.54 (( 77.50/10.54 (setadjoinIR) => 77.50/10.54 (( 77.50/10.54 (setadjoinE) => 77.50/10.54 (( 77.50/10.54 (setadjoinOr) => 77.50/10.54 (( 77.50/10.54 (setoftrueEq) => 77.50/10.54 (( 77.50/10.54 (powersetI) => 77.50/10.54 (( 77.50/10.54 (emptyinPowerset) => 77.50/10.54 (( 77.50/10.54 (emptyInPowerset) => 77.50/10.54 (( 77.50/10.54 (powersetE) => 77.50/10.54 (( 77.50/10.54 (setunionI) => 77.50/10.54 (( 77.50/10.54 (setunionE) => 77.50/10.54 (( 77.50/10.54 (subPowSU) => 77.50/10.54 (( 77.50/10.54 (exuE2) => 77.50/10.54 (( 77.50/10.54 (nonemptyImpWitness) => 77.50/10.54 (( 77.50/10.54 (uniqinunit) => 77.50/10.54 (( 77.50/10.54 (notinsingleton) => 77.50/10.54 (( 77.50/10.54 (eqinunit) => 77.50/10.54 (( 77.50/10.54 (singletonsswitch) => 77.50/10.54 (( 77.50/10.54 (upairsetE) => 77.50/10.54 (( 77.50/10.54 (upairsetIL) => 77.50/10.54 (( 77.50/10.54 (upairsetIR) => 77.50/10.54 (( 77.50/10.54 (emptyE1) => 77.50/10.54 (( 77.50/10.54 (vacuousDall) => 77.50/10.54 (( 77.50/10.54 (quantDeMorgan1) => 77.50/10.54 (( 77.50/10.54 (quantDeMorgan2) => 77.50/10.54 (( 77.50/10.54 (quantDeMorgan3) => 77.50/10.54 (( 77.50/10.54 (quantDeMorgan4) => 77.50/10.54 (( 77.50/10.54 (prop2setI) => 77.50/10.54 (( 77.50/10.54 (prop2set2propI) => 77.50/10.54 (( 77.50/10.54 (notdexE) => 77.50/10.54 (( 77.50/10.54 (notdallE) => 77.50/10.54 (( 77.50/10.54 (exuI1) => 77.50/10.54 (( 77.50/10.54 (exuI3) => 77.50/10.54 (( 77.50/10.54 (exuI2) => 77.50/10.54 (( 77.50/10.54 (inCongP) => 77.50/10.54 (( 77.50/10.54 (in__Cong) => 77.50/10.54 (( 77.50/10.54 (exuE3u) => 77.50/10.54 (( 77.50/10.54 (exu__Cong) => 77.50/10.54 (( 77.50/10.54 (emptyset__Cong) => 77.50/10.54 (( 77.50/10.54 (setadjoin__Cong) => 77.50/10.54 (( 77.50/10.54 (powerset__Cong) => 77.50/10.54 (( 77.50/10.54 (setunion__Cong) => 77.50/10.54 (( 77.50/10.54 (omega__Cong) => 77.50/10.54 (( 77.50/10.54 (exuEu) => 77.50/10.54 (( 77.50/10.54 (descr__Cong) => 77.50/10.54 (( 77.50/10.54 (dsetconstr__Cong) => 77.50/10.54 (( 77.50/10.54 (subsetI1) => 77.50/10.54 (( 77.50/10.54 (eqimpsubset2) => 77.50/10.54 (( 77.50/10.54 (eqimpsubset1) => 77.50/10.54 (( 77.50/10.54 (subsetI2) => 77.50/10.54 (( 77.50/10.54 (emptysetsubset) => 77.50/10.54 (( 77.50/10.54 (subsetE) => 77.50/10.54 (( 77.50/10.54 (subsetE2) => 77.50/10.54 (( 77.50/10.54 (notsubsetI) => 77.50/10.54 (( 77.50/10.54 (notequalI1) => 77.50/10.54 (( 77.50/10.54 (notequalI2) => 77.50/10.54 (( 77.50/10.54 (subsetRefl) => 77.50/10.54 (( 77.50/10.54 (subsetTrans) => 77.50/10.54 (( 77.50/10.54 (setadjoinSub) => 77.50/10.54 (( 77.50/10.54 (setadjoinSub2) => 77.50/10.54 (( 77.50/10.54 (subset2powerset) => 77.50/10.54 (( 77.50/10.54 (setextsub) => 77.50/10.54 (( 77.50/10.54 (subsetemptysetimpeq) => 77.50/10.54 (( 77.50/10.54 (powersetI1) => 77.50/10.54 (( 77.50/10.54 (powersetE1) => 77.50/10.54 (( 77.50/10.54 (inPowerset) => 77.50/10.54 (( 77.50/10.54 (powersetsubset) => 77.50/10.54 (( 77.50/10.54 (sepInPowerset) => 77.50/10.54 (( 77.50/10.54 (sepSubset) => 77.50/10.54 (( 77.50/10.54 (binunionIL) => 77.50/10.54 (( 77.50/10.54 (upairset2IR) => 77.50/10.54 (( 77.50/10.54 (binunionIR) => 77.50/10.54 (( 77.50/10.54 (binunionEcases) => 77.50/10.54 (( 77.50/10.54 (binunionE) => 77.50/10.54 (( 77.50/10.54 (binunionLsub) => 77.50/10.54 (( 77.50/10.54 (binunionRsub) => 77.50/10.54 (( 77.50/10.54 (binintersectI) => 77.50/10.54 (( 77.50/10.54 (binintersectSubset5) => 77.50/10.54 (( 77.50/10.54 (binintersectEL) => 77.50/10.54 (( 77.50/10.54 (binintersectLsub) => 77.50/10.54 (( 77.50/10.54 (binintersectSubset2) => 77.50/10.54 (( 77.50/10.54 (binintersectSubset3) => 77.50/10.54 (( 77.50/10.54 (binintersectER) => 77.50/10.54 (( 77.50/10.54 (disjointsetsI1) => 77.50/10.54 (( 77.50/10.54 (binintersectRsub) => 77.50/10.54 (( 77.50/10.54 (binintersectSubset4) => 77.50/10.54 (( 77.50/10.54 (binintersectSubset1) => 77.50/10.54 (( 77.50/10.54 (bs114d) => 77.50/10.54 (( 77.50/10.54 (setminusI) => 77.50/10.54 (( 77.50/10.54 (setminusEL) => 77.50/10.54 (( 77.50/10.54 (setminusER) => 77.50/10.54 (( 77.50/10.54 (setminusSubset2) => 77.50/10.54 (( 77.50/10.54 (setminusERneg) => 77.50/10.54 (( 77.50/10.54 (setminusELneg) => 77.50/10.54 (( 77.50/10.54 (setminusILneg) => 77.50/10.54 (( 77.50/10.54 (setminusIRneg) => 77.50/10.54 (( 77.50/10.54 (setminusLsub) => 77.50/10.54 (( 77.50/10.54 (setminusSubset1) => 77.50/10.54 (( 77.50/10.54 (symdiffE) => 77.50/10.54 (( 77.50/10.54 (symdiffI1) => 77.50/10.54 (( 77.50/10.54 (symdiffI2) => 77.50/10.54 (( 77.50/10.54 (symdiffIneg1) => 77.50/10.54 (( 77.50/10.54 (symdiffIneg2) => 77.50/10.54 (( 77.50/10.54 (secondinupair) => 77.50/10.54 (( 77.50/10.54 (setukpairIL) => 77.50/10.54 (( 77.50/10.54 (setukpairIR) => 77.50/10.54 (( 77.50/10.54 (kpairiskpair) => 77.50/10.54 (( 77.50/10.54 (kpairp) => 77.50/10.54 (( 77.50/10.54 (singletonsubset) => 77.50/10.54 (( 77.50/10.54 (singletoninpowerset) => 77.50/10.54 (( 77.50/10.54 (singletoninpowunion) => 77.50/10.54 (( 77.50/10.54 (upairset2E) => 77.50/10.54 (( 77.50/10.54 (upairsubunion) => 77.50/10.54 (( 77.50/10.54 (upairinpowunion) => 77.50/10.54 (( 77.50/10.54 (ubforcartprodlem1) => 77.50/10.54 (( 77.50/10.54 (ubforcartprodlem2) => 77.50/10.54 (( 77.50/10.54 (ubforcartprodlem3) => 77.50/10.54 (( 77.50/10.54 (cartprodpairin) => 77.50/10.54 (( 77.50/10.54 (cartprodmempair1) => 77.50/10.54 (( 77.50/10.54 (cartprodmempair) => 77.50/10.54 (( 77.50/10.54 (setunionE2) => 77.50/10.54 (( 77.50/10.54 (setunionsingleton1) => 77.50/10.54 (( 77.50/10.54 (setunionsingleton2) => 77.50/10.54 (( 77.50/10.54 (setunionsingleton) => 77.50/10.54 (( 77.50/10.54 (singletonprop) => 77.50/10.54 (( 77.50/10.54 (ex1E1) => 77.50/10.54 (( 77.50/10.54 (ex1I) => 77.50/10.54 (( 77.50/10.54 (ex1I2) => 77.50/10.54 (( 77.50/10.54 (singletonsuniq) => 77.50/10.54 (( 77.50/10.54 (setukpairinjL1) => 77.50/10.54 (( 77.50/10.54 (kfstsingleton) => 77.50/10.54 (( 77.50/10.54 (theprop) => 77.50/10.54 (( 77.50/10.54 (kfstpairEq) => 77.50/10.54 (( 77.50/10.54 (cartprodfstin) => 77.50/10.54 (( 77.50/10.54 (setukpairinjL2) => 77.50/10.54 (( 77.50/10.54 (setukpairinjL) => 77.50/10.54 (( 77.50/10.54 (setukpairinjR11) => 77.50/10.54 (( 77.50/10.54 (setukpairinjR12) => 77.50/10.54 (( 77.50/10.54 (setukpairinjR1) => 77.50/10.54 (( 77.50/10.54 (upairequniteq) => 77.50/10.54 (( 77.50/10.54 (setukpairinjR2) => 77.50/10.54 (( 77.50/10.54 (setukpairinjR) => 77.50/10.54 (( 77.50/10.54 (ksndsingleton) => 77.50/10.54 (( 77.50/10.54 (ksndpairEq) => 77.50/10.54 (( 77.50/10.54 (kpairsurjEq) => 77.50/10.54 (( 77.50/10.54 (cartprodsndin) => 77.50/10.54 (( 77.50/10.54 (cartprodpairmemEL) => 77.50/10.54 (( 77.50/10.54 (cartprodpairmemER) => 77.50/10.54 (( 77.50/10.54 (cartprodmempaircEq) => 77.50/10.54 (( 77.50/10.54 (cartprodfstpairEq) => 77.50/10.54 (( 77.50/10.54 (cartprodsndpairEq) => 77.50/10.54 (( 77.50/10.54 (cartprodpairsurjEq) => 77.50/10.54 (( 77.50/10.54 (dpsetconstrI) => 77.50/10.54 (( 77.50/10.54 (dpsetconstrSub) => 77.50/10.54 (( 77.50/10.54 (setOfPairsIsBReln) => 77.50/10.54 (( 77.50/10.54 (dpsetconstrERa) => 77.50/10.54 (( 77.50/10.54 (dpsetconstrEL1) => 77.50/10.54 (( 77.50/10.54 (dpsetconstrEL2) => 77.50/10.54 (( 77.50/10.54 (dpsetconstrER) => 77.50/10.54 (( 77.50/10.54 (funcImageSingleton) => 77.50/10.54 (( 77.50/10.54 (apProp) => 77.50/10.54 (( 77.50/10.54 (app) => 77.50/10.54 (( 77.50/10.54 (infuncsetfunc) => 77.50/10.54 (( 77.50/10.54 (ap2p) => 77.50/10.54 (( 77.50/10.54 (funcinfuncset) => 77.50/10.54 (( 77.50/10.54 (lamProp) => 77.50/10.54 (( 77.50/10.54 (lamp) => 77.50/10.54 (( 77.50/10.54 (lam2p) => 77.50/10.54 (( 77.50/10.54 (brelnall1) => 77.50/10.54 (( 77.50/10.54 (brelnall2) => 77.50/10.54 (( 77.50/10.54 (ex1E2) => 77.50/10.54 (( 77.50/10.54 (funcGraphProp1) => 77.50/10.54 (( 77.50/10.54 (funcGraphProp3) => 77.50/10.54 (( 77.50/10.54 (funcGraphProp2) => 77.50/10.54 (( 77.50/10.54 (funcextLem) => 77.50/10.54 (( 77.50/10.54 (funcGraphProp4) => 77.50/10.54 (( 77.50/10.54 (subbreln) => 77.50/10.54 (( 77.50/10.54 (eqbreln) => 77.50/10.54 (( 77.50/10.54 (funcext) => 77.50/10.54 (( 77.50/10.54 (funcext2) => 77.50/10.54 (( 77.50/10.54 (ap2apEq1) => 77.50/10.54 (( 77.50/10.54 (ap2apEq2) => 77.50/10.54 (( 77.50/10.54 (beta1) => 77.50/10.54 (( 77.50/10.54 (eta1) => 77.50/10.54 (( 77.50/10.54 (lam2lamEq) => 77.50/10.54 (( 77.50/10.54 (beta2) => 77.50/10.54 (( 77.50/10.54 (eta2) => 77.50/10.54 (( 77.50/10.54 (iffalseProp1) => 77.50/10.54 (( 77.50/10.54 (iffalseProp2) => 77.50/10.54 (( 77.50/10.54 (iftrueProp1) => 77.50/10.54 (( 77.50/10.54 (iftrueProp2) => 77.50/10.54 (( 77.50/10.54 (ifSingleton) => 77.50/10.54 (( 77.50/10.54 (ifp) => 77.50/10.54 (( 77.50/10.54 (theeq) => 77.50/10.54 (( 77.50/10.54 (iftrue) => 77.50/10.54 (( 77.50/10.54 (iffalse) => 77.50/10.54 (( 77.50/10.54 (iftrueorfalse) => 77.50/10.54 (( 77.50/10.54 (binintersectT_lem) => 77.50/10.54 (( 77.50/10.54 (binunionT_lem) => 77.50/10.54 (( 77.50/10.54 (powersetT_lem) => 77.50/10.54 (( 77.50/10.54 (setminusT_lem) => 77.50/10.54 (( 77.50/10.54 (complementT_lem) => 77.50/10.54 (( 77.50/10.54 (setextT) => 77.50/10.54 (( 77.50/10.54 (subsetTI) => 77.50/10.54 (( 77.50/10.54 (powersetTI1) => 77.50/10.54 (( 77.50/10.54 (powersetTE1) => 77.50/10.54 (( 77.50/10.54 (complementTI1) => 77.50/10.54 (( 77.50/10.54 (complementTE1) => 77.50/10.54 (( 77.50/10.54 (binintersectTELcontra) => 77.50/10.54 (( 77.50/10.54 (binintersectTERcontra) => 77.50/10.54 (( 77.50/10.54 (contrasubsetT) => 77.50/10.54 (( 77.50/10.54 (contrasubsetT1) => 77.50/10.54 (( 77.50/10.54 (contrasubsetT2) => 77.50/10.54 (( 77.50/10.54 (contrasubsetT3) => 77.50/10.54 (( 77.50/10.54 (doubleComplementI1) => 77.50/10.54 (( 77.50/10.54 (doubleComplementE1) => 77.50/10.54 (( 77.50/10.54 (doubleComplementSub1) => 77.50/10.54 (( 77.50/10.54 (doubleComplementSub2) => 77.50/10.54 (( 77.50/10.54 (doubleComplementEq) => 77.50/10.54 (( 77.50/10.54 (complementTnotintersectT) => 77.50/10.54 (( 77.50/10.54 (complementImpComplementIntersect) => 77.50/10.54 (( 77.50/10.54 (complementSubsetComplementIntersect) => 77.50/10.54 (( 77.50/10.54 (complementInPowersetComplementIntersect) => 77.50/10.54 (( 77.50/10.54 (contraSubsetComplement) => 77.50/10.54 (( 77.50/10.54 (complementTcontraSubset) => 77.50/10.54 (( 77.50/10.54 (binunionTILcontra) => 77.50/10.54 (( 77.50/10.54 (binunionTIRcontra) => 77.50/10.54 (( 77.50/10.54 (inIntersectImpInUnion) => 77.50/10.54 (( 77.50/10.54 (inIntersectImpInUnion2) => 77.50/10.54 (( 77.50/10.54 (inIntersectImpInIntersectUnions) => 77.50/10.54 (( 77.50/10.54 (intersectInPowersetIntersectUnions) => 77.50/10.54 (( 77.50/10.54 (inComplementUnionImpNotIn1) => 77.50/10.54 (( 77.50/10.54 (inComplementUnionImpInComplement1) => 77.50/10.54 (( 77.50/10.54 (binunionTE) => 77.50/10.54 (( 77.50/10.54 (binunionTEcontra) => 77.50/10.54 (( 77.50/10.54 (demorgan2a1) => 77.50/10.54 (( 77.50/10.54 (complementUnionInPowersetComplement) => 77.50/10.54 (( 77.50/10.54 (demorgan2a2) => 77.50/10.54 (( 77.50/10.54 (demorgan1a) => 77.50/10.54 (( 77.50/10.54 (demorgan1b) => 77.50/10.54 (( 77.50/10.54 (demorgan1) => 77.50/10.54 (( 77.50/10.54 (demorgan2a) => 77.50/10.54 (( 77.50/10.54 (demorgan2b2) => 77.50/10.54 (( 77.50/10.54 (demorgan2b) => 77.50/10.54 (( 77.50/10.54 (demorgan2) => 77.50/10.54 (( 77.50/10.54 (woz13rule0) => 77.50/10.54 (( 77.50/10.54 (woz13rule1) => 77.50/10.54 (( 77.50/10.54 (woz13rule2) => 77.50/10.54 (( 77.50/10.54 (woz13rule3) => 77.50/10.54 (( 77.50/10.54 (woz13rule4) => 77.50/10.54 (( 77.50/10.54 (woz1_1) => 77.50/10.54 (( 77.50/10.54 (woz1_2) => 77.50/10.54 (( 77.50/10.54 (woz1_3) => 77.50/10.54 (( 77.50/10.54 (woz1_4) => 77.50/10.54 (( 77.50/10.54 (woz1_5) => 77.50/10.54 (( 77.50/10.54 (breln1all2) => 77.50/10.54 (( 77.50/10.54 (breln1SetBreln1) => 77.50/10.54 (( 77.50/10.54 (choice2fnsingleton) => 77.50/10.54 (( 77.50/10.54 (setOfPairsIsBReln1) => 77.50/10.54 (( 77.50/10.54 (breln1all1) => 77.50/10.54 (( 77.50/10.54 (subbreln1) => 77.50/10.54 (( 77.50/10.54 (eqbreln1) => 77.50/10.54 (( 77.50/10.54 (breln1invprop) => 77.50/10.54 (( 77.50/10.54 (breln1invI) => 77.50/10.54 (( 77.50/10.54 (breln1invE) => 77.50/10.54 (( 77.50/10.54 (breln1compprop) => 77.50/10.54 (( 77.50/10.54 (breln1compI) => 77.50/10.54 (( 77.50/10.54 (breln1compE) => 77.50/10.54 (( 77.50/10.54 (breln1compEex) => 77.50/10.54 (( 77.50/10.54 (breln1unionprop) => 77.50/10.54 (( 77.50/10.54 (breln1unionIL) => 77.50/10.54 (( 77.50/10.54 (breln1unionIR) => 77.50/10.54 (( 77.50/10.54 (breln1unionI) => 77.50/10.54 (( 77.50/10.54 (breln1unionE) => 77.50/10.54 (( 77.50/10.54 (breln1unionEcases) => 77.50/10.54 (( 77.50/10.54 (breln1unionCommutes) => 77.50/10.54 (( 77.50/10.54 (woz2Ex) => 77.50/10.54 (( 77.50/10.54 (woz2W) => 77.50/10.54 (( 77.50/10.54 (woz2A) => 77.50/10.54 (( 77.50/10.54 (woz2B) => 77.50/10.54 (( 77.50/10.54 (image1Ex) => 77.50/10.54 (( 77.50/10.54 (image1Ex1) => 77.50/10.54 (( 77.50/10.54 (image1Equiv) => 77.50/10.54 (( 77.50/10.54 (image1E) => 77.50/10.54 (( 77.50/10.54 (image1I) => 77.50/10.54 (( 77.50/10.54 (injFuncInInjFuncSet) => 77.50/10.54 (( 77.50/10.54 (injFuncSetFuncIn) => 77.50/10.54 (( 77.50/10.54 (injFuncSetFuncInj) => 77.50/10.54 (( 77.50/10.54 (surjFuncSetFuncIn) => 77.50/10.54 (( 77.50/10.54 (surjFuncSetFuncSurj) => 77.50/10.54 (( 77.50/10.54 (leftInvIsSurj) => 77.50/10.54 (( 77.50/10.54 (surjCantorThm) => 77.50/10.54 (( 77.50/10.54 (foundation2) => 77.50/10.54 (( 77.50/10.54 (notinself) => 77.50/10.54 (( 77.50/10.54 (notinself2) => 77.50/10.54 (( 77.50/10.54 (omegaSp) => 77.50/10.54 (( 77.50/10.54 (omegaSclos) => 77.50/10.54 (( 77.50/10.54 (peano0notS) => 77.50/10.54 (( 77.50/10.54 (peanoSinj) => 77.50/10.54 (( 77.50/10.54 (transitivesetOp1) => 77.50/10.54 (( 77.50/10.54 (binintTransitive) => 77.50/10.54 (( 77.50/10.54 (transitivesetOp2) => 77.50/10.54 (( 77.50/10.54 (setunionTransitive) => 77.50/10.54 (( 77.50/10.54 (ordinalMinLem1) => 77.50/10.54 (( 77.50/10.54 (!!) @ ( 77.50/10.54 ^[Y0 : $i]: 77.50/10.54 (( 77.50/10.54 (ordinal @ 77.50/10.54 Y0) => 77.50/10.54 (( 77.50/10.54 (!!) @ ( 77.50/10.54 ^[Y1 : $i]: 77.50/10.54 (( 77.50/10.54 (!!) @ ( 77.50/10.54 ^[Y2 : $i]: 77.50/10.54 (( 77.50/10.54 (in @ 77.50/10.54 Y2 @ 77.50/10.54 Y0) => 77.50/10.54 (( 77.50/10.54 (in @ 77.50/10.54 Y1 @ 77.50/10.54 Y2) => 77.50/10.54 (in @ 77.50/10.54 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 77.50/10.54 inference('cnf', [status(esa)], [zf_stmt_0])). 77.50/10.54 thf(omega0Ax, axiom,(( omega0Ax ) = ((in @ emptyset @ omega)))). 77.50/10.54 thf('0', plain, (( omega0Ax ) = ( in @ emptyset @ omega )), 77.50/10.54 define([status(thm)])). 77.50/10.54 thf(emptyinunitempty, axiom,(( emptyinunitempty ) = 77.50/10.54 ((in @ emptyset @ (setadjoin @ emptyset @ emptyset))))). 77.50/10.54 thf('1', plain, 77.50/10.54 (( emptyinunitempty ) = 77.50/10.54 ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )), 77.50/10.54 define([status(thm)])). 77.50/10.54 thf(emptyset__Cong, axiom,(( emptyset__Cong ) = 77.50/10.54 ((((emptyset) = (emptyset)))))). 77.50/10.54 thf('2', plain, (( emptyset__Cong ) = ( ( emptyset ) = ( emptyset ) )), 77.50/10.54 define([status(thm)])). 77.50/10.54 thf(omega__Cong, axiom,(( omega__Cong ) = ((((omega) = (omega)))))). 77.50/10.54 thf('3', plain, (( omega__Cong ) = ( ( omega ) = ( omega ) )), 77.50/10.54 define([status(thm)])). 77.50/10.54 thf(zip_derived_cl1, plain, 77.50/10.54 (~ (((setextAx) => 77.50/10.54 (((emptysetAx) => 77.50/10.54 (((setadjoinAx) => 77.50/10.54 (((powersetAx) => 77.50/10.54 (((setunionAx) => 77.50/10.54 (((in @ emptyset @ omega) => 77.50/10.54 (((omegaSAx) => 77.50/10.54 (((omegaIndAx) => 77.50/10.54 (((replAx) => 77.50/10.54 (((foundationAx) => 77.50/10.54 (((wellorderingAx) => 77.50/10.54 (((descrp) => 77.50/10.54 (((dsetconstrI) => 77.50/10.54 (((dsetconstrEL) => 77.50/10.54 (((dsetconstrER) => 77.50/10.54 (((exuE1) => 77.50/10.54 (((prop2setE) => 77.50/10.54 (((emptysetE) => 77.50/10.54 (((emptysetimpfalse) => 77.50/10.54 (((notinemptyset) => 77.50/10.54 (((exuE3e) => 77.50/10.54 (((setext) => 77.50/10.54 (((emptyI) => 77.50/10.54 (((noeltsimpempty) => 77.50/10.54 (((setbeta) => 77.50/10.54 (((nonemptyE1) => 77.50/10.54 (((nonemptyI) => 77.50/10.54 (((nonemptyI1) => 77.50/10.54 (((setadjoinIL) => 77.50/10.54 (((in @ 77.50/10.54 emptyset @ 77.50/10.54 (setadjoin @ 77.50/10.54 emptyset @ 77.50/10.54 emptyset)) => 77.50/10.54 (( 77.50/10.54 (setadjoinIR) => 77.50/10.54 (( 77.50/10.54 (setadjoinE) => 77.50/10.54 (( 77.50/10.54 (setadjoinOr) => 77.50/10.54 (( 77.50/10.54 (setoftrueEq) => 77.50/10.54 (( 77.50/10.54 (powersetI) => 77.50/10.54 (( 77.50/10.54 (emptyinPowerset) => 77.50/10.54 (( 77.50/10.54 (emptyInPowerset) => 77.50/10.54 (( 77.50/10.54 (powersetE) => 77.50/10.54 (( 77.50/10.54 (setunionI) => 77.50/10.54 (( 77.50/10.54 (setunionE) => 77.50/10.54 (( 77.50/10.54 (subPowSU) => 77.50/10.54 (( 77.50/10.54 (exuE2) => 77.50/10.54 (( 77.50/10.54 (nonemptyImpWitness) => 77.50/10.54 (( 77.50/10.54 (uniqinunit) => 77.50/10.54 (( 77.50/10.54 (notinsingleton) => 77.50/10.54 (( 77.50/10.54 (eqinunit) => 77.50/10.54 (( 77.50/10.54 (singletonsswitch) => 77.50/10.54 (( 77.50/10.54 (upairsetE) => 77.50/10.54 (( 77.50/10.54 (upairsetIL) => 77.50/10.54 (( 77.50/10.54 (upairsetIR) => 77.50/10.54 (( 77.50/10.54 (emptyE1) => 77.50/10.54 (( 77.50/10.54 (vacuousDall) => 77.50/10.54 (( 77.50/10.54 (quantDeMorgan1) => 77.50/10.54 (( 77.50/10.54 (quantDeMorgan2) => 77.50/10.54 (( 77.50/10.54 (quantDeMorgan3) => 77.50/10.54 (( 77.50/10.54 (quantDeMorgan4) => 77.50/10.54 (( 77.50/10.54 (prop2setI) => 77.50/10.54 (( 77.50/10.54 (prop2set2propI) => 77.50/10.54 (( 77.50/10.54 (notdexE) => 77.50/10.54 (( 77.50/10.54 (notdallE) => 77.50/10.54 (( 77.50/10.54 (exuI1) => 77.50/10.54 (( 77.50/10.54 (exuI3) => 77.50/10.54 (( 77.50/10.54 (exuI2) => 77.50/10.54 (( 77.50/10.54 (inCongP) => 77.50/10.54 (( 77.50/10.54 (in__Cong) => 77.50/10.54 (( 77.50/10.54 (exuE3u) => 77.50/10.54 (( 77.50/10.54 (exu__Cong) => 77.50/10.54 (( 77.50/10.54 (( 77.50/10.54 (emptyset) = 77.50/10.54 (emptyset))) => 77.50/10.54 (( 77.50/10.54 (setadjoin__Cong) => 77.50/10.54 (( 77.50/10.54 (powerset__Cong) => 77.50/10.54 (( 77.50/10.54 (setunion__Cong) => 77.50/10.54 (( 77.50/10.54 (( 77.50/10.54 (omega) = 77.50/10.54 (omega))) => 77.50/10.54 (( 77.50/10.54 (exuEu) => 77.50/10.54 (( 77.50/10.54 (descr__Cong) => 77.50/10.54 (( 77.50/10.54 (dsetconstr__Cong) => 77.50/10.54 (( 77.50/10.54 (subsetI1) => 77.50/10.54 (( 77.50/10.54 (eqimpsubset2) => 77.50/10.54 (( 77.50/10.54 (eqimpsubset1) => 77.50/10.54 (( 77.50/10.54 (subsetI2) => 77.50/10.54 (( 77.50/10.54 (emptysetsubset) => 77.50/10.54 (( 77.50/10.54 (subsetE) => 77.50/10.54 (( 77.50/10.54 (subsetE2) => 77.50/10.54 (( 77.50/10.54 (notsubsetI) => 77.50/10.54 (( 77.50/10.54 (notequalI1) => 77.50/10.54 (( 77.50/10.54 (notequalI2) => 77.50/10.54 (( 77.50/10.54 (subsetRefl) => 77.50/10.54 (( 77.50/10.54 (subsetTrans) => 77.50/10.54 (( 77.50/10.54 (setadjoinSub) => 77.50/10.54 (( 77.50/10.54 (setadjoinSub2) => 77.50/10.54 (( 77.50/10.54 (subset2powerset) => 77.50/10.54 (( 77.50/10.54 (setextsub) => 77.50/10.54 (( 77.50/10.54 (subsetemptysetimpeq) => 77.50/10.54 (( 77.50/10.54 (powersetI1) => 77.50/10.54 (( 77.50/10.54 (powersetE1) => 77.50/10.54 (( 77.50/10.54 (inPowerset) => 77.50/10.54 (( 77.50/10.54 (powersetsubset) => 77.50/10.54 (( 77.50/10.54 (sepInPowerset) => 77.50/10.54 (( 77.50/10.54 (sepSubset) => 77.50/10.54 (( 77.50/10.54 (binunionIL) => 77.50/10.54 (( 77.50/10.54 (upairset2IR) => 77.50/10.54 (( 77.50/10.54 (binunionIR) => 77.50/10.54 (( 77.50/10.54 (binunionEcases) => 77.50/10.54 (( 77.50/10.54 (binunionE) => 77.50/10.54 (( 77.50/10.54 (binunionLsub) => 77.50/10.54 (( 77.50/10.54 (binunionRsub) => 77.50/10.54 (( 77.50/10.54 (binintersectI) => 77.50/10.54 (( 77.50/10.54 (binintersectSubset5) => 77.50/10.54 (( 77.50/10.54 (binintersectEL) => 77.50/10.54 (( 77.50/10.54 (binintersectLsub) => 77.50/10.54 (( 77.50/10.54 (binintersectSubset2) => 77.50/10.54 (( 77.50/10.54 (binintersectSubset3) => 77.50/10.54 (( 77.50/10.54 (binintersectER) => 77.50/10.54 (( 77.50/10.54 (disjointsetsI1) => 77.50/10.54 (( 77.50/10.54 (binintersectRsub) => 77.50/10.54 (( 77.50/10.54 (binintersectSubset4) => 77.50/10.54 (( 77.50/10.54 (binintersectSubset1) => 77.50/10.54 (( 77.50/10.54 (bs114d) => 77.50/10.54 (( 77.50/10.54 (setminusI) => 77.50/10.54 (( 77.50/10.54 (setminusEL) => 77.50/10.54 (( 77.50/10.54 (setminusER) => 77.50/10.54 (( 77.50/10.54 (setminusSubset2) => 77.50/10.54 (( 77.50/10.54 (setminusERneg) => 77.50/10.54 (( 77.50/10.54 (setminusELneg) => 77.50/10.54 (( 77.50/10.54 (setminusILneg) => 77.50/10.54 (( 77.50/10.54 (setminusIRneg) => 77.50/10.54 (( 77.50/10.54 (setminusLsub) => 77.50/10.54 (( 77.50/10.54 (setminusSubset1) => 77.50/10.54 (( 77.50/10.54 (symdiffE) => 77.50/10.54 (( 77.50/10.54 (symdiffI1) => 77.50/10.54 (( 77.50/10.54 (symdiffI2) => 77.50/10.54 (( 77.50/10.54 (symdiffIneg1) => 77.50/10.54 (( 77.50/10.54 (symdiffIneg2) => 77.50/10.54 (( 77.50/10.54 (secondinupair) => 77.50/10.54 (( 77.50/10.54 (setukpairIL) => 77.50/10.54 (( 77.50/10.54 (setukpairIR) => 77.50/10.54 (( 77.50/10.54 (kpairiskpair) => 77.50/10.54 (( 77.50/10.54 (kpairp) => 77.50/10.54 (( 77.50/10.54 (singletonsubset) => 77.50/10.54 (( 77.50/10.54 (singletoninpowerset) => 77.50/10.54 (( 77.50/10.54 (singletoninpowunion) => 77.50/10.54 (( 77.50/10.54 (upairset2E) => 77.50/10.54 (( 77.50/10.54 (upairsubunion) => 77.50/10.54 (( 77.50/10.54 (upairinpowunion) => 77.50/10.54 (( 77.50/10.54 (ubforcartprodlem1) => 77.50/10.54 (( 77.50/10.54 (ubforcartprodlem2) => 77.50/10.54 (( 77.50/10.54 (ubforcartprodlem3) => 77.50/10.54 (( 77.50/10.54 (cartprodpairin) => 77.50/10.54 (( 77.50/10.54 (cartprodmempair1) => 77.50/10.54 (( 77.50/10.54 (cartprodmempair) => 77.50/10.54 (( 77.50/10.54 (setunionE2) => 77.50/10.54 (( 77.50/10.54 (setunionsingleton1) => 77.50/10.54 (( 77.50/10.54 (setunionsingleton2) => 77.50/10.54 (( 77.50/10.54 (setunionsingleton) => 77.50/10.54 (( 77.50/10.54 (singletonprop) => 77.50/10.54 (( 77.50/10.54 (ex1E1) => 77.50/10.54 (( 77.50/10.54 (ex1I) => 77.50/10.54 (( 77.50/10.54 (ex1I2) => 77.50/10.54 (( 77.50/10.54 (singletonsuniq) => 77.50/10.54 (( 77.50/10.54 (setukpairinjL1) => 77.50/10.54 (( 77.50/10.54 (kfstsingleton) => 77.50/10.54 (( 77.50/10.54 (theprop) => 77.50/10.54 (( 77.50/10.54 (kfstpairEq) => 77.50/10.54 (( 77.50/10.54 (cartprodfstin) => 77.50/10.54 (( 77.50/10.54 (setukpairinjL2) => 77.50/10.54 (( 77.50/10.54 (setukpairinjL) => 77.50/10.54 (( 77.50/10.54 (setukpairinjR11) => 77.50/10.54 (( 77.50/10.54 (setukpairinjR12) => 77.50/10.54 (( 77.50/10.54 (setukpairinjR1) => 77.50/10.54 (( 77.50/10.54 (upairequniteq) => 77.50/10.54 (( 77.50/10.54 (setukpairinjR2) => 77.50/10.54 (( 77.50/10.54 (setukpairinjR) => 77.50/10.54 (( 77.50/10.54 (ksndsingleton) => 77.50/10.54 (( 77.50/10.54 (ksndpairEq) => 77.50/10.54 (( 77.50/10.54 (kpairsurjEq) => 77.50/10.54 (( 77.50/10.54 (cartprodsndin) => 77.50/10.54 (( 77.50/10.54 (cartprodpairmemEL) => 77.50/10.54 (( 77.50/10.54 (cartprodpairmemER) => 77.50/10.54 (( 77.50/10.54 (cartprodmempaircEq) => 77.50/10.54 (( 77.50/10.54 (cartprodfstpairEq) => 77.50/10.54 (( 77.50/10.54 (cartprodsndpairEq) => 77.50/10.54 (( 77.50/10.54 (cartprodpairsurjEq) => 77.50/10.54 (( 77.50/10.54 (dpsetconstrI) => 77.50/10.54 (( 77.50/10.54 (dpsetconstrSub) => 77.50/10.54 (( 77.50/10.54 (setOfPairsIsBReln) => 77.50/10.54 (( 77.50/10.54 (dpsetconstrERa) => 77.50/10.54 (( 77.50/10.54 (dpsetconstrEL1) => 77.50/10.54 (( 77.50/10.54 (dpsetconstrEL2) => 77.50/10.54 (( 77.50/10.54 (dpsetconstrER) => 77.50/10.54 (( 77.50/10.54 (funcImageSingleton) => 77.50/10.54 (( 77.50/10.54 (apProp) => 77.50/10.54 (( 77.50/10.54 (app) => 77.50/10.54 (( 77.50/10.54 (infuncsetfunc) => 77.50/10.54 (( 77.50/10.54 (ap2p) => 77.50/10.54 (( 77.50/10.54 (funcinfuncset) => 77.50/10.54 (( 77.50/10.54 (lamProp) => 77.50/10.54 (( 77.50/10.54 (lamp) => 77.50/10.54 (( 77.50/10.54 (lam2p) => 77.50/10.54 (( 77.50/10.54 (brelnall1) => 77.50/10.54 (( 77.50/10.54 (brelnall2) => 77.50/10.54 (( 77.50/10.54 (ex1E2) => 77.50/10.54 (( 77.50/10.54 (funcGraphProp1) => 77.50/10.54 (( 77.50/10.54 (funcGraphProp3) => 77.50/10.54 (( 77.50/10.54 (funcGraphProp2) => 77.50/10.54 (( 77.50/10.54 (funcextLem) => 77.50/10.54 (( 77.50/10.54 (funcGraphProp4) => 77.50/10.54 (( 77.50/10.54 (subbreln) => 77.50/10.54 (( 77.50/10.54 (eqbreln) => 77.50/10.54 (( 77.50/10.54 (funcext) => 77.50/10.54 (( 77.50/10.54 (funcext2) => 77.50/10.54 (( 77.50/10.54 (ap2apEq1) => 77.50/10.54 (( 77.50/10.54 (ap2apEq2) => 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(powersetTE1) => 77.50/10.54 (( 77.50/10.54 (complementTI1) => 77.50/10.54 (( 77.50/10.54 (complementTE1) => 77.50/10.54 (( 77.50/10.54 (binintersectTELcontra) => 77.50/10.54 (( 77.50/10.54 (binintersectTERcontra) => 77.50/10.54 (( 77.50/10.54 (contrasubsetT) => 77.50/10.54 (( 77.50/10.54 (contrasubsetT1) => 77.50/10.54 (( 77.50/10.54 (contrasubsetT2) => 77.50/10.54 (( 77.50/10.54 (contrasubsetT3) => 77.50/10.54 (( 77.50/10.54 (doubleComplementI1) => 77.50/10.54 (( 77.50/10.54 (doubleComplementE1) => 77.50/10.54 (( 77.50/10.54 (doubleComplementSub1) => 77.50/10.54 (( 77.50/10.54 (doubleComplementSub2) => 77.50/10.54 (( 77.50/10.54 (doubleComplementEq) => 77.50/10.54 (( 77.50/10.54 (complementTnotintersectT) => 77.50/10.54 (( 77.50/10.54 (complementImpComplementIntersect) => 77.50/10.54 (( 77.50/10.54 (complementSubsetComplementIntersect) => 77.50/10.54 (( 77.50/10.54 (complementInPowersetComplementIntersect) => 77.50/10.54 (( 77.50/10.54 (contraSubsetComplement) => 77.50/10.54 (( 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(demorgan2b) => 77.50/10.54 (( 77.50/10.54 (demorgan2) => 77.50/10.54 (( 77.50/10.54 (woz13rule0) => 77.50/10.54 (( 77.50/10.54 (woz13rule1) => 77.50/10.54 (( 77.50/10.54 (woz13rule2) => 77.50/10.54 (( 77.50/10.54 (woz13rule3) => 77.50/10.54 (( 77.50/10.54 (woz13rule4) => 77.50/10.54 (( 77.50/10.54 (woz1_1) => 77.50/10.54 (( 77.50/10.54 (woz1_2) => 77.50/10.54 (( 77.50/10.54 (woz1_3) => 77.50/10.54 (( 77.50/10.54 (woz1_4) => 77.50/10.54 (( 77.50/10.54 (woz1_5) => 77.50/10.54 (( 77.50/10.54 (breln1all2) => 77.50/10.54 (( 77.50/10.54 (breln1SetBreln1) => 77.50/10.54 (( 77.50/10.54 (choice2fnsingleton) => 77.50/10.54 (( 77.50/10.54 (setOfPairsIsBReln1) => 77.50/10.54 (( 77.50/10.54 (breln1all1) => 77.50/10.54 (( 77.50/10.54 (subbreln1) => 77.50/10.54 (( 77.50/10.54 (eqbreln1) => 77.50/10.54 (( 77.50/10.54 (breln1invprop) => 77.50/10.54 (( 77.50/10.54 (breln1invI) => 77.50/10.54 (( 77.50/10.54 (breln1invE) => 77.50/10.54 (( 77.50/10.54 (breln1compprop) => 77.50/10.54 (( 77.50/10.54 (breln1compI) => 77.50/10.54 (( 77.50/10.54 (breln1compE) => 77.50/10.54 (( 77.50/10.54 (breln1compEex) => 77.50/10.54 (( 77.50/10.54 (breln1unionprop) => 77.50/10.54 (( 77.50/10.54 (breln1unionIL) => 77.50/10.54 (( 77.50/10.54 (breln1unionIR) => 77.50/10.54 (( 77.50/10.54 (breln1unionI) => 77.50/10.54 (( 77.50/10.54 (breln1unionE) => 77.50/10.54 (( 77.50/10.54 (breln1unionEcases) => 77.50/10.54 (( 77.50/10.54 (breln1unionCommutes) => 77.50/10.54 (( 77.50/10.54 (woz2Ex) => 77.50/10.54 (( 77.50/10.54 (woz2W) => 77.50/10.54 (( 77.50/10.54 (woz2A) => 77.50/10.54 (( 77.50/10.54 (woz2B) => 77.50/10.54 (( 77.50/10.54 (image1Ex) => 77.50/10.54 (( 77.50/10.54 (image1Ex1) => 77.50/10.54 (( 77.50/10.54 (image1Equiv) => 77.50/10.54 (( 77.50/10.54 (image1E) => 77.50/10.54 (( 77.50/10.54 (image1I) => 77.50/10.54 (( 77.50/10.54 (injFuncInInjFuncSet) => 77.50/10.54 (( 77.50/10.54 (injFuncSetFuncIn) => 77.50/10.54 (( 77.50/10.54 (injFuncSetFuncInj) => 77.50/10.54 (( 77.50/10.54 (surjFuncSetFuncIn) => 77.50/10.54 (( 77.50/10.54 (surjFuncSetFuncSurj) => 77.50/10.54 (( 77.50/10.54 (leftInvIsSurj) => 77.50/10.54 (( 77.50/10.54 (surjCantorThm) => 77.50/10.54 (( 77.50/10.54 (foundation2) => 77.50/10.54 (( 77.50/10.54 (notinself) => 77.50/10.54 (( 77.50/10.54 (notinself2) => 77.50/10.54 (( 77.50/10.54 (omegaSp) => 77.50/10.54 (( 77.50/10.54 (omegaSclos) => 77.50/10.54 (( 77.50/10.54 (peano0notS) => 77.50/10.54 (( 77.50/10.54 (peanoSinj) => 77.50/10.54 (( 77.50/10.54 (transitivesetOp1) => 77.50/10.54 (( 77.50/10.54 (binintTransitive) => 77.50/10.54 (( 77.50/10.54 (transitivesetOp2) => 77.50/10.54 (( 77.50/10.54 (setunionTransitive) => 77.50/10.54 (( 77.50/10.54 (ordinalMinLem1) => 77.50/10.54 (( 77.50/10.54 (!!) @ ( 77.50/10.54 ^[Y0 : $i]: 77.50/10.54 (( 77.50/10.54 (ordinal @ 77.50/10.54 Y0) => 77.50/10.54 (( 77.50/10.54 (!!) @ ( 77.50/10.54 ^[Y1 : $i]: 77.50/10.54 (( 77.50/10.54 (!!) @ ( 77.50/10.54 ^[Y2 : $i]: 77.50/10.54 (( 77.50/10.54 (in @ 77.50/10.54 Y2 @ 77.50/10.54 Y0) => 77.50/10.54 (( 77.50/10.54 (in @ 77.50/10.54 Y1 @ 77.50/10.54 Y2) => 77.50/10.54 (in @ 77.50/10.54 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 77.50/10.54 inference('rw', [status(thm)], [zip_derived_cl0, '0', '1', '2', '3'])). 77.50/10.54 thf(zip_derived_cl2, plain, 77.50/10.54 (~ (((setextAx) => 77.50/10.54 (((emptysetAx) => 77.50/10.54 (((setadjoinAx) => 77.50/10.54 (((powersetAx) => 77.50/10.54 (((setunionAx) => 77.50/10.54 (((in @ emptyset @ omega) => 77.50/10.54 (((omegaSAx) => 77.50/10.54 (((omegaIndAx) => 77.50/10.54 (((replAx) => 77.50/10.54 (((foundationAx) => 77.50/10.54 (((wellorderingAx) => 77.50/10.54 (((descrp) => 77.50/10.54 (((dsetconstrI) => 77.50/10.54 (((dsetconstrEL) => 77.50/10.54 (((dsetconstrER) => 77.50/10.54 (((exuE1) => 77.50/10.54 (((prop2setE) => 77.50/10.54 (((emptysetE) => 77.50/10.54 (((emptysetimpfalse) => 77.50/10.54 (((notinemptyset) => 77.50/10.54 (((exuE3e) => 77.50/10.54 (((setext) => 77.50/10.54 (((emptyI) => 77.50/10.54 (((noeltsimpempty) => 77.50/10.54 (((setbeta) => 77.50/10.54 (((nonemptyE1) => 77.50/10.54 (((nonemptyI) => 77.50/10.54 (((nonemptyI1) => 77.50/10.54 (((setadjoinIL) => 77.50/10.54 (((in @ 77.50/10.54 emptyset @ 77.50/10.54 (setadjoin @ 77.50/10.54 emptyset @ 77.50/10.54 emptyset)) => 77.50/10.54 (( 77.50/10.54 (setadjoinIR) => 77.50/10.54 (( 77.50/10.54 (setadjoinE) => 77.50/10.54 (( 77.50/10.54 (setadjoinOr) => 77.50/10.54 (( 77.50/10.54 (setoftrueEq) => 77.50/10.54 (( 77.50/10.54 (powersetI) => 77.50/10.54 (( 77.50/10.54 (emptyinPowerset) => 77.50/10.54 (( 77.50/10.54 (emptyInPowerset) => 77.50/10.54 (( 77.50/10.54 (powersetE) => 77.50/10.54 (( 77.50/10.54 (setunionI) => 77.50/10.54 (( 77.50/10.54 (setunionE) => 77.50/10.54 (( 77.50/10.54 (subPowSU) => 77.50/10.54 (( 77.50/10.54 (exuE2) => 77.50/10.54 (( 77.50/10.54 (nonemptyImpWitness) => 77.50/10.54 (( 77.50/10.54 (uniqinunit) => 77.50/10.54 (( 77.50/10.54 (notinsingleton) => 77.50/10.54 (( 77.50/10.54 (eqinunit) => 77.50/10.54 (( 77.50/10.54 (singletonsswitch) => 77.50/10.54 (( 77.50/10.54 (upairsetE) => 77.50/10.54 (( 77.50/10.54 (upairsetIL) => 77.50/10.54 (( 77.50/10.54 (upairsetIR) => 77.50/10.54 (( 77.50/10.54 (emptyE1) => 77.50/10.54 (( 77.50/10.54 (vacuousDall) => 77.50/10.54 (( 77.50/10.54 (quantDeMorgan1) => 77.50/10.54 (( 77.50/10.54 (quantDeMorgan2) => 77.50/10.54 (( 77.50/10.54 (quantDeMorgan3) => 77.50/10.54 (( 77.50/10.54 (quantDeMorgan4) => 77.50/10.54 (( 77.50/10.54 (prop2setI) => 77.50/10.54 (( 77.50/10.54 (prop2set2propI) => 77.50/10.54 (( 77.50/10.54 (notdexE) => 77.50/10.54 (( 77.50/10.54 (notdallE) => 77.50/10.54 (( 77.50/10.54 (exuI1) => 77.50/10.54 (( 77.50/10.54 (exuI3) => 77.50/10.54 (( 77.50/10.54 (exuI2) => 77.50/10.54 (( 77.50/10.54 (inCongP) => 77.50/10.54 (( 77.50/10.54 (in__Cong) => 77.50/10.54 (( 77.50/10.54 (exuE3u) => 77.50/10.54 (( 77.50/10.54 (exu__Cong) => 77.50/10.54 (( 77.50/10.54 (setadjoin__Cong) => 77.50/10.54 (( 77.50/10.54 (powerset__Cong) => 77.50/10.54 (( 77.50/10.54 (setunion__Cong) => 77.50/10.54 (( 77.50/10.54 (exuEu) => 77.50/10.54 (( 77.50/10.54 (descr__Cong) => 77.50/10.54 (( 77.50/10.54 (dsetconstr__Cong) => 77.50/10.54 (( 77.50/10.54 (subsetI1) => 77.50/10.54 (( 77.50/10.54 (eqimpsubset2) => 77.50/10.54 (( 77.50/10.54 (eqimpsubset1) => 77.50/10.54 (( 77.50/10.54 (subsetI2) => 77.50/10.54 (( 77.50/10.54 (emptysetsubset) => 77.50/10.54 (( 77.50/10.54 (subsetE) => 77.50/10.54 (( 77.50/10.54 (subsetE2) => 77.50/10.54 (( 77.50/10.54 (notsubsetI) => 77.50/10.54 (( 77.50/10.54 (notequalI1) => 77.50/10.54 (( 77.50/10.54 (notequalI2) => 77.50/10.54 (( 77.50/10.54 (subsetRefl) => 77.50/10.54 (( 77.50/10.54 (subsetTrans) => 77.50/10.54 (( 77.50/10.54 (setadjoinSub) => 77.50/10.54 (( 77.50/10.54 (setadjoinSub2) => 77.50/10.54 (( 77.50/10.54 (subset2powerset) => 77.50/10.54 (( 77.50/10.54 (setextsub) => 77.50/10.54 (( 77.50/10.54 (subsetemptysetimpeq) => 77.50/10.54 (( 77.50/10.54 (powersetI1) => 77.50/10.54 (( 77.50/10.54 (powersetE1) => 77.50/10.54 (( 77.50/10.54 (inPowerset) => 77.50/10.54 (( 77.50/10.54 (powersetsubset) => 77.50/10.54 (( 77.50/10.54 (sepInPowerset) => 77.50/10.54 (( 77.50/10.54 (sepSubset) => 77.50/10.54 (( 77.50/10.54 (binunionIL) => 77.50/10.54 (( 77.50/10.54 (upairset2IR) => 77.50/10.54 (( 77.50/10.54 (binunionIR) => 77.50/10.54 (( 77.50/10.54 (binunionEcases) => 77.50/10.54 (( 77.50/10.54 (binunionE) => 77.50/10.54 (( 77.50/10.54 (binunionLsub) => 77.50/10.54 (( 77.50/10.54 (binunionRsub) => 77.50/10.54 (( 77.50/10.54 (binintersectI) => 77.50/10.54 (( 77.50/10.54 (binintersectSubset5) => 77.50/10.54 (( 77.50/10.54 (binintersectEL) => 77.50/10.54 (( 77.50/10.54 (binintersectLsub) => 77.50/10.54 (( 77.50/10.54 (binintersectSubset2) => 77.50/10.54 (( 77.50/10.54 (binintersectSubset3) => 77.50/10.54 (( 77.50/10.54 (binintersectER) => 77.50/10.54 (( 77.50/10.54 (disjointsetsI1) => 77.50/10.54 (( 77.50/10.54 (binintersectRsub) => 77.50/10.54 (( 77.50/10.54 (binintersectSubset4) => 77.50/10.54 (( 77.50/10.54 (binintersectSubset1) => 77.50/10.54 (( 77.50/10.54 (bs114d) => 77.50/10.54 (( 77.50/10.54 (setminusI) => 77.50/10.54 (( 77.50/10.54 (setminusEL) => 77.50/10.54 (( 77.50/10.54 (setminusER) => 77.50/10.54 (( 77.50/10.54 (setminusSubset2) => 77.50/10.54 (( 77.50/10.54 (setminusERneg) => 77.50/10.54 (( 77.50/10.54 (setminusELneg) => 77.50/10.54 (( 77.50/10.54 (setminusILneg) => 77.50/10.54 (( 77.50/10.54 (setminusIRneg) => 77.50/10.54 (( 77.50/10.54 (setminusLsub) => 77.50/10.54 (( 77.50/10.54 (setminusSubset1) => 77.50/10.54 (( 77.50/10.54 (symdiffE) => 77.50/10.54 (( 77.50/10.54 (symdiffI1) => 77.50/10.54 (( 77.50/10.54 (symdiffI2) => 77.50/10.54 (( 77.50/10.54 (symdiffIneg1) => 77.50/10.54 (( 77.50/10.54 (symdiffIneg2) => 77.50/10.54 (( 77.50/10.54 (secondinupair) => 77.50/10.54 (( 77.50/10.54 (setukpairIL) => 77.50/10.54 (( 77.50/10.54 (setukpairIR) => 77.50/10.54 (( 77.50/10.54 (kpairiskpair) => 77.50/10.54 (( 77.50/10.54 (kpairp) => 77.50/10.54 (( 77.50/10.54 (singletonsubset) => 77.50/10.54 (( 77.50/10.54 (singletoninpowerset) => 77.50/10.54 (( 77.50/10.54 (singletoninpowunion) => 77.50/10.54 (( 77.50/10.54 (upairset2E) => 77.50/10.54 (( 77.50/10.54 (upairsubunion) => 77.50/10.54 (( 77.50/10.54 (upairinpowunion) => 77.50/10.54 (( 77.50/10.54 (ubforcartprodlem1) => 77.50/10.54 (( 77.50/10.54 (ubforcartprodlem2) => 77.50/10.54 (( 77.50/10.54 (ubforcartprodlem3) => 77.50/10.54 (( 77.50/10.54 (cartprodpairin) => 77.50/10.54 (( 77.50/10.54 (cartprodmempair1) => 77.50/10.54 (( 77.50/10.54 (cartprodmempair) => 77.50/10.54 (( 77.50/10.54 (setunionE2) => 77.50/10.54 (( 77.50/10.54 (setunionsingleton1) => 77.50/10.54 (( 77.50/10.54 (setunionsingleton2) => 77.50/10.54 (( 77.50/10.54 (setunionsingleton) => 77.50/10.54 (( 77.50/10.54 (singletonprop) => 77.50/10.54 (( 77.50/10.54 (ex1E1) => 77.50/10.54 (( 77.50/10.54 (ex1I) => 77.50/10.54 (( 77.50/10.54 (ex1I2) => 77.50/10.54 (( 77.50/10.54 (singletonsuniq) => 77.50/10.54 (( 77.50/10.54 (setukpairinjL1) => 77.50/10.54 (( 77.50/10.54 (kfstsingleton) => 77.50/10.54 (( 77.50/10.54 (theprop) => 77.50/10.54 (( 77.50/10.54 (kfstpairEq) => 77.50/10.54 (( 77.50/10.54 (cartprodfstin) => 77.50/10.54 (( 77.50/10.54 (setukpairinjL2) => 77.50/10.54 (( 77.50/10.54 (setukpairinjL) => 77.50/10.54 (( 77.50/10.54 (setukpairinjR11) => 77.50/10.54 (( 77.50/10.54 (setukpairinjR12) => 77.50/10.54 (( 77.50/10.54 (setukpairinjR1) => 77.50/10.54 (( 77.50/10.54 (upairequniteq) => 77.50/10.54 (( 77.50/10.54 (setukpairinjR2) => 77.50/10.54 (( 77.50/10.54 (setukpairinjR) => 77.50/10.54 (( 77.50/10.54 (ksndsingleton) => 77.50/10.54 (( 77.50/10.54 (ksndpairEq) => 77.50/10.54 (( 77.50/10.54 (kpairsurjEq) => 77.50/10.54 (( 77.50/10.54 (cartprodsndin) => 77.50/10.54 (( 77.50/10.54 (cartprodpairmemEL) => 77.50/10.54 (( 77.50/10.54 (cartprodpairmemER) => 77.50/10.54 (( 77.50/10.54 (cartprodmempaircEq) => 77.50/10.54 (( 77.50/10.54 (cartprodfstpairEq) => 77.50/10.54 (( 77.50/10.54 (cartprodsndpairEq) => 77.50/10.54 (( 77.50/10.54 (cartprodpairsurjEq) => 77.50/10.54 (( 77.50/10.54 (dpsetconstrI) => 77.50/10.54 (( 77.50/10.54 (dpsetconstrSub) => 77.50/10.54 (( 77.50/10.54 (setOfPairsIsBReln) => 77.50/10.54 (( 77.50/10.54 (dpsetconstrERa) => 77.50/10.54 (( 77.50/10.54 (dpsetconstrEL1) => 77.50/10.54 (( 77.50/10.54 (dpsetconstrEL2) => 77.50/10.54 (( 77.50/10.54 (dpsetconstrER) => 77.50/10.54 (( 77.50/10.54 (funcImageSingleton) => 77.50/10.54 (( 77.50/10.54 (apProp) => 77.50/10.54 (( 77.50/10.54 (app) => 77.50/10.54 (( 77.50/10.54 (infuncsetfunc) => 77.50/10.54 (( 77.50/10.54 (ap2p) => 77.50/10.54 (( 77.50/10.54 (funcinfuncset) => 77.50/10.54 (( 77.50/10.54 (lamProp) => 77.50/10.54 (( 77.50/10.54 (lamp) => 77.50/10.54 (( 77.50/10.54 (lam2p) => 77.50/10.54 (( 77.50/10.54 (brelnall1) => 77.50/10.54 (( 77.50/10.54 (brelnall2) => 77.50/10.54 (( 77.50/10.54 (ex1E2) => 77.50/10.54 (( 77.50/10.54 (funcGraphProp1) => 77.50/10.54 (( 77.50/10.54 (funcGraphProp3) => 77.50/10.54 (( 77.50/10.54 (funcGraphProp2) => 77.50/10.54 (( 77.50/10.54 (funcextLem) => 77.50/10.54 (( 77.50/10.54 (funcGraphProp4) => 77.50/10.54 (( 77.50/10.54 (subbreln) => 77.50/10.54 (( 77.50/10.54 (eqbreln) => 77.50/10.54 (( 77.50/10.54 (funcext) => 77.50/10.54 (( 77.50/10.54 (funcext2) => 77.50/10.54 (( 77.50/10.54 (ap2apEq1) => 77.50/10.54 (( 77.50/10.54 (ap2apEq2) => 77.50/10.54 (( 77.50/10.54 (beta1) => 77.50/10.54 (( 77.50/10.54 (eta1) => 77.50/10.54 (( 77.50/10.54 (lam2lamEq) => 77.50/10.54 (( 77.50/10.54 (beta2) => 77.50/10.54 (( 77.50/10.54 (eta2) => 77.50/10.54 (( 77.50/10.54 (iffalseProp1) => 77.50/10.54 (( 77.50/10.54 (iffalseProp2) => 77.50/10.54 (( 77.50/10.54 (iftrueProp1) => 77.50/10.54 (( 77.50/10.54 (iftrueProp2) => 77.50/10.54 (( 77.50/10.54 (ifSingleton) => 77.50/10.54 (( 77.50/10.54 (ifp) => 77.50/10.54 (( 77.50/10.54 (theeq) => 77.50/10.54 (( 77.50/10.54 (iftrue) => 77.50/10.54 (( 77.50/10.54 (iffalse) => 77.50/10.54 (( 77.50/10.54 (iftrueorfalse) => 77.50/10.54 (( 77.50/10.54 (binintersectT_lem) => 77.50/10.54 (( 77.50/10.54 (binunionT_lem) => 77.50/10.54 (( 77.50/10.54 (powersetT_lem) => 77.50/10.54 (( 77.50/10.54 (setminusT_lem) => 77.50/10.54 (( 77.50/10.54 (complementT_lem) => 77.50/10.54 (( 77.50/10.54 (setextT) => 77.50/10.54 (( 77.50/10.54 (subsetTI) => 77.50/10.54 (( 77.50/10.54 (powersetTI1) => 77.50/10.54 (( 77.50/10.54 (powersetTE1) => 77.50/10.54 (( 77.50/10.54 (complementTI1) => 77.50/10.54 (( 77.50/10.54 (complementTE1) => 77.50/10.54 (( 77.50/10.54 (binintersectTELcontra) => 77.50/10.54 (( 77.50/10.54 (binintersectTERcontra) => 77.50/10.54 (( 77.50/10.54 (contrasubsetT) => 77.50/10.54 (( 77.50/10.54 (contrasubsetT1) => 77.50/10.54 (( 77.50/10.54 (contrasubsetT2) => 77.50/10.54 (( 77.50/10.54 (contrasubsetT3) => 77.50/10.54 (( 77.50/10.54 (doubleComplementI1) => 77.50/10.54 (( 77.50/10.54 (doubleComplementE1) => 77.50/10.54 (( 77.50/10.54 (doubleComplementSub1) => 77.50/10.54 (( 77.50/10.54 (doubleComplementSub2) => 77.50/10.54 (( 77.50/10.54 (doubleComplementEq) => 77.50/10.54 (( 77.50/10.54 (complementTnotintersectT) => 77.50/10.54 (( 77.50/10.54 (complementImpComplementIntersect) => 77.50/10.54 (( 77.50/10.54 (complementSubsetComplementIntersect) => 77.50/10.54 (( 77.50/10.54 (complementInPowersetComplementIntersect) => 77.50/10.54 (( 77.50/10.54 (contraSubsetComplement) => 77.50/10.54 (( 77.50/10.54 (complementTcontraSubset) => 77.50/10.54 (( 77.50/10.54 (binunionTILcontra) => 77.50/10.54 (( 77.50/10.54 (binunionTIRcontra) => 77.50/10.54 (( 77.50/10.54 (inIntersectImpInUnion) => 77.50/10.54 (( 77.50/10.54 (inIntersectImpInUnion2) => 77.50/10.54 (( 77.50/10.54 (inIntersectImpInIntersectUnions) => 77.50/10.54 (( 77.50/10.54 (intersectInPowersetIntersectUnions) => 77.50/10.54 (( 77.50/10.54 (inComplementUnionImpNotIn1) => 77.50/10.54 (( 77.50/10.54 (inComplementUnionImpInComplement1) => 77.50/10.54 (( 77.50/10.54 (binunionTE) => 77.50/10.54 (( 77.50/10.54 (binunionTEcontra) => 77.50/10.54 (( 77.50/10.54 (demorgan2a1) => 77.50/10.54 (( 77.50/10.54 (complementUnionInPowersetComplement) => 77.50/10.54 (( 77.50/10.54 (demorgan2a2) => 77.50/10.54 (( 77.50/10.54 (demorgan1a) => 77.50/10.54 (( 77.50/10.54 (demorgan1b) => 77.50/10.54 (( 77.50/10.54 (demorgan1) => 77.50/10.54 (( 77.50/10.54 (demorgan2a) => 77.50/10.54 (( 77.50/10.54 (demorgan2b2) => 77.50/10.54 (( 77.50/10.54 (demorgan2b) => 77.50/10.54 (( 77.50/10.54 (demorgan2) => 77.50/10.54 (( 77.50/10.54 (woz13rule0) => 77.50/10.54 (( 77.50/10.54 (woz13rule1) => 77.50/10.54 (( 77.50/10.54 (woz13rule2) => 77.50/10.54 (( 77.50/10.54 (woz13rule3) => 77.50/10.54 (( 77.50/10.54 (woz13rule4) => 77.50/10.54 (( 77.50/10.54 (woz1_1) => 77.50/10.54 (( 77.50/10.54 (woz1_2) => 77.50/10.54 (( 77.50/10.54 (woz1_3) => 77.50/10.54 (( 77.50/10.54 (woz1_4) => 77.50/10.54 (( 77.50/10.54 (woz1_5) => 77.50/10.54 (( 77.50/10.54 (breln1all2) => 77.50/10.54 (( 77.50/10.54 (breln1SetBreln1) => 77.50/10.54 (( 77.50/10.54 (choice2fnsingleton) => 77.50/10.54 (( 77.50/10.54 (setOfPairsIsBReln1) => 77.50/10.54 (( 77.50/10.54 (breln1all1) => 77.50/10.54 (( 77.50/10.54 (subbreln1) => 77.50/10.54 (( 77.50/10.54 (eqbreln1) => 77.50/10.54 (( 77.50/10.54 (breln1invprop) => 77.50/10.54 (( 77.50/10.54 (breln1invI) => 77.50/10.54 (( 77.50/10.54 (breln1invE) => 77.50/10.54 (( 77.50/10.54 (breln1compprop) => 77.50/10.54 (( 77.50/10.54 (breln1compI) => 77.50/10.54 (( 77.50/10.54 (breln1compE) => 77.50/10.54 (( 77.50/10.54 (breln1compEex) => 77.50/10.54 (( 77.50/10.54 (breln1unionprop) => 77.50/10.54 (( 77.50/10.54 (breln1unionIL) => 77.50/10.54 (( 77.50/10.54 (breln1unionIR) => 77.50/10.54 (( 77.50/10.54 (breln1unionI) => 77.50/10.54 (( 77.50/10.54 (breln1unionE) => 77.50/10.54 (( 77.50/10.54 (breln1unionEcases) => 77.50/10.54 (( 77.50/10.54 (breln1unionCommutes) => 77.50/10.54 (( 77.50/10.54 (woz2Ex) => 77.50/10.54 (( 77.50/10.54 (woz2W) => 77.50/10.54 (( 77.50/10.54 (woz2A) => 77.50/10.54 (( 77.50/10.54 (woz2B) => 77.50/10.54 (( 77.50/10.54 (image1Ex) => 77.50/10.54 (( 77.50/10.54 (image1Ex1) => 77.50/10.54 (( 77.50/10.54 (image1Equiv) => 77.50/10.54 (( 77.50/10.54 (image1E) => 77.50/10.54 (( 77.50/10.54 (image1I) => 77.50/10.54 (( 77.50/10.54 (injFuncInInjFuncSet) => 77.50/10.54 (( 77.50/10.54 (injFuncSetFuncIn) => 77.50/10.54 (( 77.50/10.54 (injFuncSetFuncInj) => 77.50/10.54 (( 77.50/10.54 (surjFuncSetFuncIn) => 77.50/10.54 (( 77.50/10.54 (surjFuncSetFuncSurj) => 77.50/10.54 (( 77.50/10.54 (leftInvIsSurj) => 77.50/10.54 (( 77.50/10.54 (surjCantorThm) => 77.50/10.54 (( 77.50/10.54 (foundation2) => 77.50/10.54 (( 77.50/10.54 (notinself) => 77.50/10.54 (( 77.50/10.54 (notinself2) => 77.50/10.54 (( 77.50/10.54 (omegaSp) => 77.50/10.54 (( 77.50/10.54 (omegaSclos) => 77.50/10.54 (( 77.50/10.54 (peano0notS) => 77.50/10.54 (( 77.50/10.54 (peanoSinj) => 77.50/10.54 (( 77.50/10.54 (transitivesetOp1) => 77.50/10.54 (( 77.50/10.54 (binintTransitive) => 77.50/10.54 (( 77.50/10.54 (transitivesetOp2) => 77.50/10.54 (( 77.50/10.54 (setunionTransitive) => 77.50/10.54 (( 77.50/10.54 (ordinalMinLem1) => 77.50/10.54 (( 77.50/10.54 (!!) @ ( 77.50/10.54 ^[Y0 : $i]: 77.50/10.54 (( 77.50/10.54 (ordinal @ 77.50/10.54 Y0) => 77.50/10.54 (( 77.50/10.54 (!!) @ ( 77.50/10.54 ^[Y1 : $i]: 77.50/10.54 (( 77.50/10.54 (!!) @ ( 77.50/10.54 ^[Y2 : $i]: 77.50/10.54 (( 77.50/10.54 (in @ 77.50/10.54 Y2 @ 77.50/10.54 Y0) => 77.50/10.54 (( 77.50/10.54 (in @ 77.50/10.54 Y1 @ 77.50/10.54 Y2) => 77.50/10.54 (in @ 77.50/10.54 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 77.50/10.54 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl1])). 77.50/10.54 thf(zip_derived_cl4, plain, 77.50/10.54 (~ (((emptysetAx) => 77.50/10.54 (((setadjoinAx) => 77.50/10.54 (((powersetAx) => 77.50/10.54 (((setunionAx) => 77.50/10.54 (((in @ emptyset @ omega) => 77.50/10.54 (((omegaSAx) => 77.50/10.54 (((omegaIndAx) => 77.50/10.54 (((replAx) => 77.50/10.54 (((foundationAx) => 77.50/10.54 (((wellorderingAx) => 77.50/10.54 (((descrp) => 77.50/10.54 (((dsetconstrI) => 77.50/10.54 (((dsetconstrEL) => 77.50/10.54 (((dsetconstrER) => 77.50/10.54 (((exuE1) => 77.50/10.54 (((prop2setE) => 77.50/10.54 (((emptysetE) => 77.50/10.54 (((emptysetimpfalse) => 77.50/10.54 (((notinemptyset) => 77.50/10.54 (((exuE3e) => 77.50/10.54 (((setext) => 77.50/10.54 (((emptyI) => 77.50/10.54 (((noeltsimpempty) => 77.50/10.54 (((setbeta) => 77.50/10.54 (((nonemptyE1) => 77.50/10.54 (((nonemptyI) => 77.50/10.54 (((nonemptyI1) => 77.50/10.54 (((setadjoinIL) => 77.50/10.54 (((in @ 77.50/10.54 emptyset @ 77.50/10.54 (setadjoin @ 77.50/10.54 emptyset @ 77.50/10.54 emptyset)) => 77.50/10.54 (((setadjoinIR) => 77.50/10.54 (( 77.50/10.54 (setadjoinE) => 77.50/10.54 (( 77.50/10.54 (setadjoinOr) => 77.50/10.54 (( 77.50/10.54 (setoftrueEq) => 77.50/10.54 (( 77.50/10.54 (powersetI) => 77.50/10.54 (( 77.50/10.54 (emptyinPowerset) => 77.50/10.54 (( 77.50/10.54 (emptyInPowerset) => 77.50/10.54 (( 77.50/10.54 (powersetE) => 77.50/10.54 (( 77.50/10.54 (setunionI) => 77.50/10.54 (( 77.50/10.54 (setunionE) => 77.50/10.54 (( 77.50/10.54 (subPowSU) => 77.50/10.54 (( 77.50/10.54 (exuE2) => 77.50/10.54 (( 77.50/10.54 (nonemptyImpWitness) => 77.50/10.54 (( 77.50/10.54 (uniqinunit) => 77.50/10.54 (( 77.50/10.54 (notinsingleton) => 77.50/10.54 (( 77.50/10.54 (eqinunit) => 77.50/10.54 (( 77.50/10.54 (singletonsswitch) => 77.50/10.54 (( 77.50/10.54 (upairsetE) => 77.50/10.54 (( 77.50/10.54 (upairsetIL) => 77.50/10.54 (( 77.50/10.54 (upairsetIR) => 77.50/10.54 (( 77.50/10.54 (emptyE1) => 77.50/10.54 (( 77.50/10.54 (vacuousDall) => 77.50/10.54 (( 77.50/10.54 (quantDeMorgan1) => 77.50/10.54 (( 77.50/10.54 (quantDeMorgan2) => 77.50/10.54 (( 77.50/10.54 (quantDeMorgan3) => 77.50/10.54 (( 77.50/10.54 (quantDeMorgan4) => 77.50/10.54 (( 77.50/10.54 (prop2setI) => 77.50/10.54 (( 77.50/10.54 (prop2set2propI) => 77.50/10.54 (( 77.50/10.54 (notdexE) => 77.50/10.54 (( 77.50/10.54 (notdallE) => 77.50/10.54 (( 77.50/10.54 (exuI1) => 77.50/10.54 (( 77.50/10.54 (exuI3) => 77.50/10.54 (( 77.50/10.54 (exuI2) => 77.50/10.54 (( 77.50/10.54 (inCongP) => 77.50/10.54 (( 77.50/10.54 (in__Cong) => 77.50/10.54 (( 77.50/10.54 (exuE3u) => 77.50/10.54 (( 77.50/10.54 (exu__Cong) => 77.50/10.54 (( 77.50/10.54 (setadjoin__Cong) => 77.50/10.54 (( 77.50/10.54 (powerset__Cong) => 77.50/10.54 (( 77.50/10.54 (setunion__Cong) => 77.50/10.54 (( 77.50/10.54 (exuEu) => 77.50/10.54 (( 77.50/10.54 (descr__Cong) => 77.50/10.54 (( 77.50/10.54 (dsetconstr__Cong) => 77.50/10.54 (( 77.50/10.54 (subsetI1) => 77.50/10.54 (( 77.50/10.54 (eqimpsubset2) => 77.50/10.54 (( 77.50/10.54 (eqimpsubset1) => 77.50/10.54 (( 77.50/10.54 (subsetI2) => 77.50/10.54 (( 77.50/10.54 (emptysetsubset) => 77.50/10.54 (( 77.50/10.54 (subsetE) => 77.50/10.54 (( 77.50/10.54 (subsetE2) => 77.50/10.54 (( 77.50/10.54 (notsubsetI) => 77.50/10.54 (( 77.50/10.54 (notequalI1) => 77.50/10.54 (( 77.50/10.54 (notequalI2) => 77.50/10.54 (( 77.50/10.54 (subsetRefl) => 77.50/10.54 (( 77.50/10.54 (subsetTrans) => 77.50/10.54 (( 77.50/10.54 (setadjoinSub) => 77.50/10.54 (( 77.50/10.54 (setadjoinSub2) => 77.50/10.54 (( 77.50/10.54 (subset2powerset) => 77.50/10.54 (( 77.50/10.54 (setextsub) => 77.50/10.54 (( 77.50/10.54 (subsetemptysetimpeq) => 77.50/10.54 (( 77.50/10.54 (powersetI1) => 77.50/10.54 (( 77.50/10.54 (powersetE1) => 77.50/10.54 (( 77.50/10.54 (inPowerset) => 77.50/10.54 (( 77.50/10.54 (powersetsubset) => 77.50/10.54 (( 77.50/10.54 (sepInPowerset) => 77.50/10.54 (( 77.50/10.54 (sepSubset) => 77.50/10.54 (( 77.50/10.54 (binunionIL) => 77.50/10.54 (( 77.50/10.54 (upairset2IR) => 77.50/10.54 (( 77.50/10.54 (binunionIR) => 77.50/10.54 (( 77.50/10.54 (binunionEcases) => 77.50/10.54 (( 77.50/10.54 (binunionE) => 77.50/10.54 (( 77.50/10.54 (binunionLsub) => 77.50/10.54 (( 77.50/10.54 (binunionRsub) => 77.50/10.54 (( 77.50/10.54 (binintersectI) => 77.50/10.54 (( 77.50/10.54 (binintersectSubset5) => 77.50/10.54 (( 77.50/10.54 (binintersectEL) => 77.50/10.54 (( 77.50/10.54 (binintersectLsub) => 77.50/10.54 (( 77.50/10.54 (binintersectSubset2) => 77.50/10.54 (( 77.50/10.54 (binintersectSubset3) => 77.50/10.54 (( 77.50/10.54 (binintersectER) => 77.50/10.54 (( 77.50/10.54 (disjointsetsI1) => 77.50/10.54 (( 77.50/10.54 (binintersectRsub) => 77.50/10.54 (( 77.50/10.54 (binintersectSubset4) => 77.50/10.54 (( 77.50/10.54 (binintersectSubset1) => 77.50/10.54 (( 77.50/10.54 (bs114d) => 77.50/10.54 (( 77.50/10.54 (setminusI) => 77.50/10.54 (( 77.50/10.54 (setminusEL) => 77.50/10.54 (( 77.50/10.54 (setminusER) => 77.50/10.54 (( 77.50/10.54 (setminusSubset2) => 77.50/10.54 (( 77.50/10.54 (setminusERneg) => 77.50/10.54 (( 77.50/10.54 (setminusELneg) => 77.50/10.54 (( 77.50/10.54 (setminusILneg) => 77.50/10.54 (( 77.50/10.54 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77.50/10.54 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 77.50/10.54 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2])). 77.50/10.54 thf(zip_derived_cl7, plain, 77.50/10.54 (~ (((setadjoinAx) => 77.50/10.54 (((powersetAx) => 77.50/10.54 (((setunionAx) => 77.50/10.54 (((in @ emptyset @ omega) => 77.50/10.54 (((omegaSAx) => 77.50/10.54 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=> 77.50/10.54 (( 77.50/10.54 (woz13rule4) => 77.50/10.54 (( 77.50/10.54 (woz1_1) => 77.50/10.54 (( 77.50/10.54 (woz1_2) => 77.50/10.54 (( 77.50/10.54 (woz1_3) => 77.50/10.54 (( 77.50/10.54 (woz1_4) => 77.50/10.54 (( 77.50/10.54 (woz1_5) => 77.50/10.54 (( 77.50/10.54 (breln1all2) => 77.50/10.54 (( 77.50/10.54 (breln1SetBreln1) => 77.50/10.54 (( 77.50/10.54 (choice2fnsingleton) => 77.50/10.54 (( 77.50/10.54 (setOfPairsIsBReln1) => 77.50/10.54 (( 77.50/10.54 (breln1all1) => 77.50/10.54 (( 77.50/10.54 (subbreln1) => 77.50/10.54 (( 77.50/10.54 (eqbreln1) => 77.50/10.54 (( 77.50/10.54 (breln1invprop) => 77.50/10.54 (( 77.50/10.54 (breln1invI) => 77.50/10.54 (( 77.50/10.54 (breln1invE) => 77.50/10.54 (( 77.50/10.54 (breln1compprop) => 77.50/10.54 (( 77.50/10.54 (breln1compI) => 77.50/10.54 (( 77.50/10.54 (breln1compE) => 77.50/10.54 (( 77.50/10.54 (breln1compEex) => 77.50/10.54 (( 77.50/10.54 (breln1unionprop) => 77.50/10.54 (( 77.50/10.54 (breln1unionIL) => 77.50/10.54 (( 77.50/10.54 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=> 77.50/10.54 (( 77.50/10.54 (notinself2) => 77.50/10.54 (( 77.50/10.54 (omegaSp) => 77.50/10.54 (( 77.50/10.54 (omegaSclos) => 77.50/10.54 (( 77.50/10.54 (peano0notS) => 77.50/10.54 (( 77.50/10.54 (peanoSinj) => 77.50/10.54 (( 77.50/10.54 (transitivesetOp1) => 77.50/10.54 (( 77.50/10.54 (binintTransitive) => 77.50/10.54 (( 77.50/10.54 (transitivesetOp2) => 77.50/10.54 (( 77.50/10.54 (setunionTransitive) => 77.50/10.54 (( 77.50/10.54 (ordinalMinLem1) => 77.50/10.54 (( 77.50/10.54 (!!) @ ( 77.50/10.54 ^[Y0 : $i]: 77.50/10.54 (( 77.50/10.54 (ordinal @ 77.50/10.54 Y0) => 77.50/10.54 (( 77.50/10.54 (!!) @ ( 77.50/10.54 ^[Y1 : $i]: 77.50/10.54 (( 77.50/10.54 (!!) @ ( 77.50/10.54 ^[Y2 : $i]: 77.50/10.54 (( 77.50/10.54 (in @ 77.50/10.54 Y2 @ 77.50/10.54 Y0) => 77.50/10.54 (( 77.50/10.54 (in @ 77.50/10.54 Y1 @ 77.50/10.54 Y2) => 77.50/10.54 (in @ 77.50/10.54 Y1 @ 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(((wellorderingAx) => 77.50/10.54 (((descrp) => 77.50/10.54 (((dsetconstrI) => 77.50/10.54 (((dsetconstrEL) => 77.50/10.54 (((dsetconstrER) => 77.50/10.54 (((exuE1) => 77.50/10.54 (((prop2setE) => 77.50/10.54 (((emptysetE) => 77.50/10.54 (((emptysetimpfalse) => 77.50/10.54 (((notinemptyset) => 77.50/10.54 (((exuE3e) => 77.50/10.54 (((setext) => 77.50/10.54 (((emptyI) => 77.50/10.54 (((noeltsimpempty) => 77.50/10.54 (((setbeta) => 77.50/10.54 (((nonemptyE1) => 77.50/10.54 (((nonemptyI) => 77.50/10.54 (((nonemptyI1) => 77.50/10.54 (((setadjoinIL) => 77.50/10.54 (((in @ emptyset @ 77.50/10.54 (setadjoin @ 77.50/10.54 emptyset @ 77.50/10.54 emptyset)) => 77.50/10.54 (((setadjoinIR) => 77.50/10.54 (((setadjoinE) => 77.50/10.54 (((setadjoinOr) => 77.50/10.54 (((setoftrueEq) => 77.50/10.54 (( 77.50/10.54 (powersetI) => 77.50/10.54 (( 77.50/10.54 (emptyinPowerset) => 77.50/10.54 (( 77.50/10.54 (emptyInPowerset) => 77.50/10.54 (( 77.50/10.54 (powersetE) => 77.50/10.54 (( 77.50/10.54 (setunionI) => 77.50/10.54 (( 77.50/10.54 (setunionE) => 77.50/10.54 (( 77.50/10.54 (subPowSU) => 77.50/10.54 (( 77.50/10.54 (exuE2) => 77.50/10.54 (( 77.50/10.54 (nonemptyImpWitness) => 77.50/10.54 (( 77.50/10.54 (uniqinunit) => 77.50/10.54 (( 77.50/10.54 (notinsingleton) => 77.50/10.54 (( 77.50/10.54 (eqinunit) => 77.50/10.54 (( 77.50/10.54 (singletonsswitch) => 77.50/10.54 (( 77.50/10.54 (upairsetE) => 77.50/10.54 (( 77.50/10.54 (upairsetIL) => 77.50/10.54 (( 77.50/10.54 (upairsetIR) => 77.50/10.54 (( 77.50/10.54 (emptyE1) => 77.50/10.54 (( 77.50/10.54 (vacuousDall) => 77.50/10.54 (( 77.50/10.54 (quantDeMorgan1) => 77.50/10.54 (( 77.50/10.54 (quantDeMorgan2) => 77.50/10.54 (( 77.50/10.54 (quantDeMorgan3) => 77.50/10.54 (( 77.50/10.54 (quantDeMorgan4) => 77.50/10.54 (( 77.50/10.54 (prop2setI) => 77.50/10.54 (( 77.50/10.54 (prop2set2propI) => 77.50/10.54 (( 77.50/10.54 (notdexE) => 77.50/10.54 (( 77.50/10.54 (notdallE) => 77.50/10.54 (( 77.50/10.54 (exuI1) => 77.50/10.54 (( 77.50/10.54 (exuI3) => 77.50/10.54 (( 77.50/10.54 (exuI2) => 77.50/10.54 (( 77.50/10.54 (inCongP) => 77.50/10.54 (( 77.50/10.54 (in__Cong) => 77.50/10.54 (( 77.50/10.54 (exuE3u) => 77.50/10.54 (( 77.50/10.54 (exu__Cong) => 77.50/10.54 (( 77.50/10.54 (setadjoin__Cong) => 77.50/10.54 (( 77.50/10.54 (powerset__Cong) => 77.50/10.54 (( 77.50/10.54 (setunion__Cong) => 77.50/10.54 (( 77.50/10.54 (exuEu) => 77.50/10.54 (( 77.50/10.54 (descr__Cong) => 77.50/10.54 (( 77.50/10.54 (dsetconstr__Cong) => 77.50/10.54 (( 77.50/10.54 (subsetI1) => 77.50/10.54 (( 77.50/10.54 (eqimpsubset2) => 77.50/10.54 (( 77.50/10.54 (eqimpsubset1) => 77.50/10.54 (( 77.50/10.54 (subsetI2) => 77.50/10.54 (( 77.50/10.54 (emptysetsubset) => 77.50/10.54 (( 77.50/10.54 (subsetE) => 77.50/10.54 (( 77.50/10.54 (subsetE2) => 77.50/10.54 (( 77.50/10.54 (notsubsetI) => 77.50/10.54 (( 77.50/10.54 (notequalI1) => 77.50/10.54 (( 77.50/10.54 (notequalI2) => 77.50/10.54 (( 77.50/10.54 (subsetRefl) => 77.50/10.54 (( 77.50/10.54 (subsetTrans) => 77.50/10.54 (( 77.50/10.54 (setadjoinSub) => 77.50/10.54 (( 77.50/10.54 (setadjoinSub2) => 77.50/10.54 (( 77.50/10.54 (subset2powerset) => 77.50/10.54 (( 77.50/10.54 (setextsub) => 77.50/10.54 (( 77.50/10.54 (subsetemptysetimpeq) => 77.50/10.54 (( 77.50/10.54 (powersetI1) => 77.50/10.54 (( 77.50/10.54 (powersetE1) => 77.50/10.54 (( 77.50/10.54 (inPowerset) => 77.50/10.54 (( 77.50/10.54 (powersetsubset) => 77.50/10.54 (( 77.50/10.54 (sepInPowerset) => 77.50/10.54 (( 77.50/10.54 (sepSubset) => 77.50/10.54 (( 77.50/10.54 (binunionIL) => 77.50/10.54 (( 77.50/10.54 (upairset2IR) => 77.50/10.54 (( 77.50/10.54 (binunionIR) => 77.50/10.54 (( 77.50/10.54 (binunionEcases) => 77.50/10.54 (( 77.50/10.54 (binunionE) => 77.50/10.54 (( 77.50/10.54 (binunionLsub) => 77.50/10.54 (( 77.50/10.54 (binunionRsub) => 77.50/10.54 (( 77.50/10.54 (binintersectI) => 77.50/10.54 (( 77.50/10.54 (binintersectSubset5) => 77.50/10.54 (( 77.50/10.54 (binintersectEL) => 77.50/10.54 (( 77.50/10.54 (binintersectLsub) => 77.50/10.54 (( 77.50/10.54 (binintersectSubset2) => 77.50/10.54 (( 77.50/10.54 (binintersectSubset3) => 77.50/10.54 (( 77.50/10.54 (binintersectER) => 77.50/10.54 (( 77.50/10.54 (disjointsetsI1) => 77.50/10.54 (( 77.50/10.54 (binintersectRsub) => 77.50/10.54 (( 77.50/10.54 (binintersectSubset4) => 77.50/10.54 (( 77.50/10.54 (binintersectSubset1) => 77.50/10.54 (( 77.50/10.54 (bs114d) => 77.50/10.54 (( 77.50/10.54 (setminusI) => 77.50/10.54 (( 77.50/10.54 (setminusEL) => 77.50/10.54 (( 77.50/10.54 (setminusER) => 77.50/10.54 (( 77.50/10.54 (setminusSubset2) => 77.50/10.54 (( 77.50/10.54 (setminusERneg) => 77.50/10.54 (( 77.50/10.54 (setminusELneg) => 77.50/10.54 (( 77.50/10.54 (setminusILneg) => 77.50/10.54 (( 77.50/10.54 (setminusIRneg) => 77.50/10.54 (( 77.50/10.54 (setminusLsub) => 77.50/10.54 (( 77.50/10.54 (setminusSubset1) => 77.50/10.54 (( 77.50/10.54 (symdiffE) => 77.50/10.54 (( 77.50/10.54 (symdiffI1) => 77.50/10.54 (( 77.50/10.54 (symdiffI2) => 77.50/10.54 (( 77.50/10.54 (symdiffIneg1) => 77.50/10.54 (( 77.50/10.54 (symdiffIneg2) => 77.50/10.54 (( 77.50/10.54 (secondinupair) => 77.50/10.54 (( 77.50/10.54 (setukpairIL) => 77.50/10.54 (( 77.50/10.54 (setukpairIR) => 77.50/10.54 (( 77.50/10.54 (kpairiskpair) => 77.50/10.54 (( 77.50/10.54 (kpairp) => 77.50/10.54 (( 77.50/10.54 (singletonsubset) => 77.50/10.54 (( 77.50/10.54 (singletoninpowerset) => 77.50/10.54 (( 77.50/10.54 (singletoninpowunion) => 77.50/10.54 (( 77.50/10.54 (upairset2E) => 77.50/10.54 (( 77.50/10.54 (upairsubunion) => 77.50/10.54 (( 77.50/10.54 (upairinpowunion) => 77.50/10.54 (( 77.50/10.54 (ubforcartprodlem1) => 77.50/10.54 (( 77.50/10.54 (ubforcartprodlem2) => 77.50/10.54 (( 77.50/10.54 (ubforcartprodlem3) => 77.50/10.54 (( 77.50/10.54 (cartprodpairin) => 77.50/10.54 (( 77.50/10.54 (cartprodmempair1) => 77.50/10.54 (( 77.50/10.54 (cartprodmempair) => 77.50/10.54 (( 77.50/10.54 (setunionE2) => 77.50/10.54 (( 77.50/10.54 (setunionsingleton1) => 77.50/10.54 (( 77.50/10.54 (setunionsingleton2) => 77.50/10.54 (( 77.50/10.54 (setunionsingleton) => 77.50/10.54 (( 77.50/10.54 (singletonprop) => 77.50/10.54 (( 77.50/10.54 (ex1E1) => 77.50/10.54 (( 77.50/10.54 (ex1I) => 77.50/10.54 (( 77.50/10.54 (ex1I2) => 77.50/10.54 (( 77.50/10.54 (singletonsuniq) => 77.50/10.54 (( 77.50/10.54 (setukpairinjL1) => 77.50/10.54 (( 77.50/10.54 (kfstsingleton) => 77.50/10.54 (( 77.50/10.54 (theprop) => 77.50/10.54 (( 77.50/10.54 (kfstpairEq) => 77.50/10.54 (( 77.50/10.54 (cartprodfstin) => 77.50/10.54 (( 77.50/10.54 (setukpairinjL2) => 77.50/10.54 (( 77.50/10.54 (setukpairinjL) => 77.50/10.54 (( 77.50/10.54 (setukpairinjR11) => 77.50/10.54 (( 77.50/10.54 (setukpairinjR12) => 77.50/10.54 (( 77.50/10.54 (setukpairinjR1) => 77.50/10.54 (( 77.50/10.54 (upairequniteq) => 77.50/10.54 (( 77.50/10.54 (setukpairinjR2) => 77.50/10.54 (( 77.50/10.54 (setukpairinjR) => 77.50/10.54 (( 77.50/10.54 (ksndsingleton) => 77.50/10.54 (( 77.50/10.54 (ksndpairEq) => 77.50/10.54 (( 77.50/10.54 (kpairsurjEq) => 77.50/10.54 (( 77.50/10.54 (cartprodsndin) => 77.50/10.54 (( 77.50/10.54 (cartprodpairmemEL) => 77.50/10.54 (( 77.50/10.54 (cartprodpairmemER) => 77.50/10.54 (( 77.50/10.54 (cartprodmempaircEq) => 77.50/10.54 (( 77.50/10.54 (cartprodfstpairEq) => 77.50/10.54 (( 77.50/10.54 (cartprodsndpairEq) => 77.50/10.54 (( 77.50/10.54 (cartprodpairsurjEq) => 77.50/10.54 (( 77.50/10.54 (dpsetconstrI) => 77.50/10.54 (( 77.50/10.54 (dpsetconstrSub) => 77.50/10.54 (( 77.50/10.54 (setOfPairsIsBReln) => 77.50/10.54 (( 77.50/10.54 (dpsetconstrERa) => 77.50/10.54 (( 77.50/10.54 (dpsetconstrEL1) => 77.50/10.54 (( 77.50/10.54 (dpsetconstrEL2) => 77.50/10.54 (( 77.50/10.54 (dpsetconstrER) => 77.50/10.54 (( 77.50/10.54 (funcImageSingleton) => 77.50/10.54 (( 77.50/10.54 (apProp) => 77.50/10.54 (( 77.50/10.54 (app) => 77.50/10.54 (( 77.50/10.54 (infuncsetfunc) => 77.50/10.54 (( 77.50/10.54 (ap2p) => 77.50/10.54 (( 77.50/10.54 (funcinfuncset) => 77.50/10.54 (( 77.50/10.54 (lamProp) => 77.50/10.54 (( 77.50/10.54 (lamp) => 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(iftrueProp2) => 77.50/10.54 (( 77.50/10.54 (ifSingleton) => 77.50/10.54 (( 77.50/10.54 (ifp) => 77.50/10.54 (( 77.50/10.54 (theeq) => 77.50/10.54 (( 77.50/10.54 (iftrue) => 77.50/10.54 (( 77.50/10.54 (iffalse) => 77.50/10.54 (( 77.50/10.54 (iftrueorfalse) => 77.50/10.54 (( 77.50/10.54 (binintersectT_lem) => 77.50/10.54 (( 77.50/10.54 (binunionT_lem) => 77.50/10.54 (( 77.50/10.54 (powersetT_lem) => 77.50/10.54 (( 77.50/10.54 (setminusT_lem) => 77.50/10.54 (( 77.50/10.54 (complementT_lem) => 77.50/10.54 (( 77.50/10.54 (setextT) => 77.50/10.54 (( 77.50/10.54 (subsetTI) => 77.50/10.54 (( 77.50/10.54 (powersetTI1) => 77.50/10.54 (( 77.50/10.54 (powersetTE1) => 77.50/10.54 (( 77.50/10.54 (complementTI1) => 77.50/10.54 (( 77.50/10.54 (complementTE1) => 77.50/10.54 (( 77.50/10.54 (binintersectTELcontra) => 77.50/10.54 (( 77.50/10.54 (binintersectTERcontra) => 77.50/10.54 (( 77.50/10.54 (contrasubsetT) => 77.50/10.54 (( 77.50/10.54 (contrasubsetT1) => 77.50/10.54 (( 77.50/10.54 (contrasubsetT2) => 77.50/10.54 (( 77.50/10.54 (contrasubsetT3) => 77.50/10.54 (( 77.50/10.54 (doubleComplementI1) => 77.50/10.54 (( 77.50/10.54 (doubleComplementE1) => 77.50/10.54 (( 77.50/10.54 (doubleComplementSub1) => 77.50/10.54 (( 77.50/10.54 (doubleComplementSub2) => 77.50/10.54 (( 77.50/10.54 (doubleComplementEq) => 77.50/10.54 (( 77.50/10.54 (complementTnotintersectT) => 77.50/10.54 (( 77.50/10.54 (complementImpComplementIntersect) => 77.50/10.54 (( 77.50/10.54 (complementSubsetComplementIntersect) => 77.50/10.54 (( 77.50/10.54 (complementInPowersetComplementIntersect) => 77.50/10.54 (( 77.50/10.54 (contraSubsetComplement) => 77.50/10.54 (( 77.50/10.54 (complementTcontraSubset) => 77.50/10.54 (( 77.50/10.54 (binunionTILcontra) => 77.50/10.54 (( 77.50/10.54 (binunionTIRcontra) => 77.50/10.54 (( 77.50/10.54 (inIntersectImpInUnion) => 77.50/10.54 (( 77.50/10.54 (inIntersectImpInUnion2) => 77.50/10.54 (( 77.50/10.54 (inIntersectImpInIntersectUnions) => 77.50/10.54 (( 77.50/10.54 (intersectInPowersetIntersectUnions) => 77.50/10.54 (( 77.50/10.54 (inComplementUnionImpNotIn1) => 77.50/10.54 (( 77.50/10.54 (inComplementUnionImpInComplement1) => 77.50/10.54 (( 77.50/10.54 (binunionTE) => 77.50/10.54 (( 77.50/10.54 (binunionTEcontra) => 77.50/10.54 (( 77.50/10.54 (demorgan2a1) => 77.50/10.54 (( 77.50/10.54 (complementUnionInPowersetComplement) => 77.50/10.54 (( 77.50/10.54 (demorgan2a2) => 77.50/10.54 (( 77.50/10.54 (demorgan1a) => 77.50/10.54 (( 77.50/10.54 (demorgan1b) => 77.50/10.54 (( 77.50/10.54 (demorgan1) => 77.50/10.54 (( 77.50/10.54 (demorgan2a) => 77.50/10.54 (( 77.50/10.54 (demorgan2b2) => 77.50/10.54 (( 77.50/10.54 (demorgan2b) => 77.50/10.54 (( 77.50/10.54 (demorgan2) => 77.50/10.54 (( 77.50/10.54 (woz13rule0) => 77.50/10.54 (( 77.50/10.54 (woz13rule1) => 77.50/10.54 (( 77.50/10.54 (woz13rule2) => 77.50/10.54 (( 77.50/10.54 (woz13rule3) => 77.50/10.54 (( 77.50/10.54 (woz13rule4) => 77.50/10.54 (( 77.50/10.54 (woz1_1) => 77.50/10.54 (( 77.50/10.54 (woz1_2) => 77.50/10.54 (( 77.50/10.54 (woz1_3) => 77.50/10.54 (( 77.50/10.54 (woz1_4) => 77.50/10.54 (( 77.50/10.54 (woz1_5) => 77.50/10.54 (( 77.50/10.54 (breln1all2) => 77.50/10.54 (( 77.50/10.54 (breln1SetBreln1) => 77.50/10.54 (( 77.50/10.54 (choice2fnsingleton) => 77.50/10.54 (( 77.50/10.54 (setOfPairsIsBReln1) => 77.50/10.54 (( 77.50/10.54 (breln1all1) => 77.50/10.54 (( 77.50/10.54 (subbreln1) => 77.50/10.54 (( 77.50/10.54 (eqbreln1) => 77.50/10.54 (( 77.50/10.54 (breln1invprop) => 77.50/10.54 (( 77.50/10.54 (breln1invI) => 77.50/10.54 (( 77.50/10.54 (breln1invE) => 77.50/10.54 (( 77.50/10.54 (breln1compprop) => 77.50/10.54 (( 77.50/10.54 (breln1compI) => 77.50/10.54 (( 77.50/10.54 (breln1compE) => 77.50/10.54 (( 77.50/10.54 (breln1compEex) => 77.50/10.54 (( 77.50/10.54 (breln1unionprop) => 77.50/10.54 (( 77.50/10.54 (breln1unionIL) => 77.50/10.54 (( 77.50/10.54 (breln1unionIR) => 77.50/10.54 (( 77.50/10.54 (breln1unionI) => 77.50/10.54 (( 77.50/10.54 (breln1unionE) => 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Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 77.50/10.55 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl11])). 77.50/10.55 thf(zip_derived_cl21, plain, 77.50/10.55 (~ (((in @ emptyset @ omega) => 77.50/10.55 (((omegaSAx) => 77.50/10.55 (((omegaIndAx) => 77.50/10.55 (((replAx) => 77.50/10.55 (((foundationAx) => 77.50/10.55 (((wellorderingAx) => 77.50/10.55 (((descrp) => 77.50/10.55 (((dsetconstrI) => 77.50/10.55 (((dsetconstrEL) => 77.50/10.55 (((dsetconstrER) => 77.50/10.55 (((exuE1) => 77.50/10.55 (((prop2setE) => 77.50/10.55 (((emptysetE) => 77.50/10.55 (((emptysetimpfalse) => 77.50/10.55 (((notinemptyset) => 77.50/10.55 (((exuE3e) => 77.50/10.55 (((setext) => 77.50/10.55 (((emptyI) => 77.50/10.55 (((noeltsimpempty) => 77.50/10.55 (((setbeta) => 77.50/10.55 (((nonemptyE1) => 77.50/10.55 (((nonemptyI) => 77.50/10.55 (((nonemptyI1) => 77.50/10.55 (((setadjoinIL) => 77.50/10.55 (((in @ emptyset @ 77.50/10.55 (setadjoin @ 77.50/10.55 emptyset @ emptyset)) => 77.50/10.55 (((setadjoinIR) => 77.50/10.55 (((setadjoinE) => 77.50/10.55 (((setadjoinOr) => 77.50/10.55 (((setoftrueEq) => 77.50/10.55 (((powersetI) => 77.50/10.55 (( 77.50/10.55 (emptyinPowerset) => 77.50/10.55 (( 77.50/10.55 (emptyInPowerset) => 77.50/10.55 (( 77.50/10.55 (powersetE) => 77.50/10.55 (( 77.50/10.55 (setunionI) => 77.50/10.55 (( 77.50/10.55 (setunionE) => 77.50/10.55 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(symdiffIneg2) => 77.50/10.55 (( 77.50/10.55 (secondinupair) => 77.50/10.55 (( 77.50/10.55 (setukpairIL) => 77.50/10.55 (( 77.50/10.55 (setukpairIR) => 77.50/10.55 (( 77.50/10.55 (kpairiskpair) => 77.50/10.55 (( 77.50/10.55 (kpairp) => 77.50/10.55 (( 77.50/10.55 (singletonsubset) => 77.50/10.55 (( 77.50/10.55 (singletoninpowerset) => 77.50/10.55 (( 77.50/10.55 (singletoninpowunion) => 77.50/10.55 (( 77.50/10.55 (upairset2E) => 77.50/10.55 (( 77.50/10.55 (upairsubunion) => 77.50/10.55 (( 77.50/10.55 (upairinpowunion) => 77.50/10.55 (( 77.50/10.55 (ubforcartprodlem1) => 77.50/10.55 (( 77.50/10.55 (ubforcartprodlem2) => 77.50/10.55 (( 77.50/10.55 (ubforcartprodlem3) => 77.50/10.55 (( 77.50/10.55 (cartprodpairin) => 77.50/10.55 (( 77.50/10.55 (cartprodmempair1) => 77.50/10.55 (( 77.50/10.55 (cartprodmempair) => 77.50/10.55 (( 77.50/10.55 (setunionE2) => 77.50/10.55 (( 77.50/10.55 (setunionsingleton1) => 77.50/10.55 (( 77.50/10.55 (setunionsingleton2) => 77.50/10.55 (( 77.50/10.55 (setunionsingleton) => 77.50/10.55 (( 77.50/10.55 (singletonprop) => 77.50/10.55 (( 77.50/10.55 (ex1E1) => 77.50/10.55 (( 77.50/10.55 (ex1I) => 77.50/10.55 (( 77.50/10.55 (ex1I2) => 77.50/10.55 (( 77.50/10.55 (singletonsuniq) => 77.50/10.55 (( 77.50/10.55 (setukpairinjL1) => 77.50/10.55 (( 77.50/10.55 (kfstsingleton) => 77.50/10.55 (( 77.50/10.55 (theprop) => 77.50/10.55 (( 77.50/10.55 (kfstpairEq) => 77.50/10.55 (( 77.50/10.55 (cartprodfstin) => 77.50/10.55 (( 77.50/10.55 (setukpairinjL2) => 77.50/10.55 (( 77.50/10.55 (setukpairinjL) => 77.50/10.55 (( 77.50/10.55 (setukpairinjR11) => 77.50/10.55 (( 77.50/10.55 (setukpairinjR12) => 77.50/10.55 (( 77.50/10.55 (setukpairinjR1) => 77.50/10.55 (( 77.50/10.55 (upairequniteq) => 77.50/10.55 (( 77.50/10.55 (setukpairinjR2) => 77.50/10.55 (( 77.50/10.55 (setukpairinjR) => 77.50/10.55 (( 77.50/10.55 (ksndsingleton) => 77.50/10.55 (( 77.50/10.55 (ksndpairEq) => 77.50/10.55 (( 77.50/10.55 (kpairsurjEq) => 77.50/10.55 (( 77.50/10.55 (cartprodsndin) => 77.50/10.55 (( 77.50/10.55 (cartprodpairmemEL) => 77.50/10.55 (( 77.50/10.55 (cartprodpairmemER) => 77.50/10.55 (( 77.50/10.55 (cartprodmempaircEq) => 77.50/10.55 (( 77.50/10.55 (cartprodfstpairEq) => 77.50/10.55 (( 77.50/10.55 (cartprodsndpairEq) => 77.50/10.55 (( 77.50/10.55 (cartprodpairsurjEq) => 77.50/10.55 (( 77.50/10.55 (dpsetconstrI) => 77.50/10.55 (( 77.50/10.55 (dpsetconstrSub) => 77.50/10.55 (( 77.50/10.55 (setOfPairsIsBReln) => 77.50/10.55 (( 77.50/10.55 (dpsetconstrERa) => 77.50/10.55 (( 77.50/10.55 (dpsetconstrEL1) => 77.50/10.55 (( 77.50/10.55 (dpsetconstrEL2) => 77.50/10.55 (( 77.50/10.55 (dpsetconstrER) => 77.50/10.55 (( 77.50/10.55 (funcImageSingleton) => 77.50/10.55 (( 77.50/10.55 (apProp) => 77.50/10.55 (( 77.50/10.55 (app) => 77.50/10.55 (( 77.50/10.55 (infuncsetfunc) => 77.50/10.55 (( 77.50/10.55 (ap2p) => 77.50/10.55 (( 77.50/10.55 (funcinfuncset) => 77.50/10.55 (( 77.50/10.55 (lamProp) => 77.50/10.55 (( 77.50/10.55 (lamp) => 77.50/10.55 (( 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(( 77.50/10.55 (contrasubsetT3) => 77.50/10.55 (( 77.50/10.55 (doubleComplementI1) => 77.50/10.55 (( 77.50/10.55 (doubleComplementE1) => 77.50/10.55 (( 77.50/10.55 (doubleComplementSub1) => 77.50/10.55 (( 77.50/10.55 (doubleComplementSub2) => 77.50/10.55 (( 77.50/10.55 (doubleComplementEq) => 77.50/10.55 (( 77.50/10.55 (complementTnotintersectT) => 77.50/10.55 (( 77.50/10.55 (complementImpComplementIntersect) => 77.50/10.55 (( 77.50/10.55 (complementSubsetComplementIntersect) => 77.50/10.55 (( 77.50/10.55 (complementInPowersetComplementIntersect) => 77.50/10.55 (( 77.50/10.55 (contraSubsetComplement) => 77.50/10.55 (( 77.50/10.55 (complementTcontraSubset) => 77.50/10.55 (( 77.50/10.55 (binunionTILcontra) => 77.50/10.55 (( 77.50/10.55 (binunionTIRcontra) => 77.50/10.55 (( 77.50/10.55 (inIntersectImpInUnion) => 77.50/10.55 (( 77.50/10.55 (inIntersectImpInUnion2) => 77.50/10.55 (( 77.50/10.55 (inIntersectImpInIntersectUnions) => 77.50/10.55 (( 77.50/10.55 (intersectInPowersetIntersectUnions) => 77.50/10.55 (( 77.50/10.55 (inComplementUnionImpNotIn1) => 77.50/10.55 (( 77.50/10.55 (inComplementUnionImpInComplement1) => 77.50/10.55 (( 77.50/10.55 (binunionTE) => 77.50/10.55 (( 77.50/10.55 (binunionTEcontra) => 77.50/10.55 (( 77.50/10.55 (demorgan2a1) => 77.50/10.55 (( 77.50/10.55 (complementUnionInPowersetComplement) => 77.50/10.55 (( 77.50/10.55 (demorgan2a2) => 77.50/10.55 (( 77.50/10.55 (demorgan1a) => 77.50/10.55 (( 77.50/10.55 (demorgan1b) => 77.50/10.55 (( 77.50/10.55 (demorgan1) => 77.50/10.55 (( 77.50/10.55 (demorgan2a) => 77.50/10.55 (( 77.50/10.55 (demorgan2b2) => 77.50/10.55 (( 77.50/10.55 (demorgan2b) => 77.50/10.55 (( 77.50/10.55 (demorgan2) => 77.50/10.55 (( 77.50/10.55 (woz13rule0) => 77.50/10.55 (( 77.50/10.55 (woz13rule1) => 77.50/10.55 (( 77.50/10.55 (woz13rule2) => 77.50/10.55 (( 77.50/10.55 (woz13rule3) => 77.50/10.55 (( 77.50/10.55 (woz13rule4) => 77.50/10.55 (( 77.50/10.55 (woz1_1) => 77.50/10.55 (( 77.50/10.55 (woz1_2) => 77.50/10.55 (( 77.50/10.55 (woz1_3) => 77.50/10.55 (( 77.50/10.55 (woz1_4) => 77.50/10.55 (( 77.50/10.55 (woz1_5) => 77.50/10.55 (( 77.50/10.55 (breln1all2) => 77.50/10.55 (( 77.50/10.55 (breln1SetBreln1) => 77.50/10.55 (( 77.50/10.55 (choice2fnsingleton) => 77.50/10.55 (( 77.50/10.55 (setOfPairsIsBReln1) => 77.50/10.55 (( 77.50/10.55 (breln1all1) => 77.50/10.55 (( 77.50/10.55 (subbreln1) => 77.50/10.55 (( 77.50/10.55 (eqbreln1) => 77.50/10.55 (( 77.50/10.55 (breln1invprop) => 77.50/10.55 (( 77.50/10.55 (breln1invI) => 77.50/10.55 (( 77.50/10.55 (breln1invE) => 77.50/10.55 (( 77.50/10.55 (breln1compprop) => 77.50/10.55 (( 77.50/10.55 (breln1compI) => 77.50/10.55 (( 77.50/10.55 (breln1compE) => 77.50/10.55 (( 77.50/10.55 (breln1compEex) => 77.50/10.55 (( 77.50/10.55 (breln1unionprop) => 77.50/10.55 (( 77.50/10.55 (breln1unionIL) => 77.50/10.55 (( 77.50/10.55 (breln1unionIR) => 77.50/10.55 (( 77.50/10.55 (breln1unionI) => 77.50/10.55 (( 77.50/10.55 (breln1unionE) => 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77.50/10.55 (omegaSclos) => 77.50/10.55 (( 77.50/10.55 (peano0notS) => 77.50/10.55 (( 77.50/10.55 (peanoSinj) => 77.50/10.55 (( 77.50/10.55 (transitivesetOp1) => 77.50/10.55 (( 77.50/10.55 (binintTransitive) => 77.50/10.55 (( 77.50/10.55 (transitivesetOp2) => 77.50/10.55 (( 77.50/10.55 (setunionTransitive) => 77.50/10.55 (( 77.50/10.55 (ordinalMinLem1) => 77.50/10.55 (( 77.50/10.55 (!!) @ ( 77.50/10.55 ^[Y0 : $i]: 77.50/10.55 (( 77.50/10.55 (ordinal @ 77.50/10.55 Y0) => 77.50/10.55 (( 77.50/10.55 (!!) @ ( 77.50/10.55 ^[Y1 : $i]: 77.50/10.55 (( 77.50/10.55 (!!) @ ( 77.50/10.55 ^[Y2 : $i]: 77.50/10.55 (( 77.50/10.55 (in @ 77.50/10.55 Y2 @ 77.50/10.55 Y0) => 77.50/10.55 (( 77.50/10.55 (in @ 77.50/10.55 Y1 @ 77.50/10.55 Y2) => 77.50/10.55 (in @ 77.50/10.55 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 77.50/10.55 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl16])). 77.50/10.55 thf(zip_derived_cl28, plain, 77.50/10.55 (~ (((omegaSAx) => 77.50/10.55 (((omegaIndAx) => 77.50/10.55 (((replAx) => 77.50/10.55 (((foundationAx) => 77.50/10.55 (((wellorderingAx) => 77.50/10.55 (((descrp) => 77.50/10.55 (((dsetconstrI) => 77.50/10.55 (((dsetconstrEL) => 77.50/10.55 (((dsetconstrER) => 77.50/10.55 (((exuE1) => 77.50/10.55 (((prop2setE) => 77.50/10.55 (((emptysetE) => 77.50/10.55 (((emptysetimpfalse) => 77.50/10.55 (((notinemptyset) => 77.50/10.55 (((exuE3e) => 77.50/10.55 (((setext) => 77.50/10.55 (((emptyI) => 77.50/10.55 (((noeltsimpempty) => 77.50/10.55 (((setbeta) => 77.50/10.55 (((nonemptyE1) => 77.50/10.55 (((nonemptyI) => 77.50/10.55 (((nonemptyI1) => 77.50/10.55 (((setadjoinIL) => 77.50/10.55 (((in @ emptyset @ 77.50/10.55 (setadjoin @ 77.50/10.55 emptyset @ emptyset)) => 77.50/10.55 (((setadjoinIR) => 77.50/10.55 (((setadjoinE) => 77.50/10.55 (((setadjoinOr) => 77.50/10.55 (((setoftrueEq) => 77.50/10.55 (((powersetI) => 77.50/10.55 (((emptyinPowerset) => 77.50/10.55 (( 77.50/10.55 (emptyInPowerset) => 77.50/10.55 (( 77.50/10.55 (powersetE) => 77.50/10.55 (( 77.50/10.55 (setunionI) => 77.50/10.55 (( 77.50/10.55 (setunionE) => 77.50/10.55 (( 77.50/10.55 (subPowSU) => 77.50/10.55 (( 77.50/10.55 (exuE2) => 77.50/10.55 (( 77.50/10.55 (nonemptyImpWitness) => 77.50/10.55 (( 77.50/10.55 (uniqinunit) => 77.50/10.55 (( 77.50/10.55 (notinsingleton) => 77.50/10.55 (( 77.50/10.55 (eqinunit) => 77.50/10.55 (( 77.50/10.55 (singletonsswitch) => 77.50/10.55 (( 77.50/10.55 (upairsetE) => 77.50/10.55 (( 77.50/10.55 (upairsetIL) => 77.50/10.55 (( 77.50/10.55 (upairsetIR) => 77.50/10.55 (( 77.50/10.55 (emptyE1) => 77.50/10.55 (( 77.50/10.55 (vacuousDall) => 77.50/10.55 (( 77.50/10.55 (quantDeMorgan1) => 77.50/10.55 (( 77.50/10.55 (quantDeMorgan2) => 77.50/10.55 (( 77.50/10.55 (quantDeMorgan3) => 77.50/10.55 (( 77.50/10.55 (quantDeMorgan4) => 77.50/10.55 (( 77.50/10.55 (prop2setI) => 77.50/10.55 (( 77.50/10.55 (prop2set2propI) => 77.50/10.55 (( 77.50/10.55 (notdexE) => 77.50/10.55 (( 77.50/10.55 (notdallE) => 77.50/10.55 (( 77.50/10.55 (exuI1) => 77.50/10.55 (( 77.50/10.55 (exuI3) => 77.50/10.55 (( 77.50/10.55 (exuI2) => 77.50/10.55 (( 77.50/10.55 (inCongP) => 77.50/10.55 (( 77.50/10.55 (in__Cong) => 77.50/10.55 (( 77.50/10.55 (exuE3u) => 77.50/10.55 (( 77.50/10.55 (exu__Cong) => 77.50/10.55 (( 77.50/10.55 (setadjoin__Cong) => 77.50/10.55 (( 77.50/10.55 (powerset__Cong) => 77.50/10.55 (( 77.50/10.55 (setunion__Cong) => 77.50/10.55 (( 77.50/10.55 (exuEu) => 77.50/10.55 (( 77.50/10.55 (descr__Cong) => 77.50/10.55 (( 77.50/10.55 (dsetconstr__Cong) => 77.50/10.55 (( 77.50/10.55 (subsetI1) => 77.50/10.55 (( 77.50/10.55 (eqimpsubset2) => 77.50/10.55 (( 77.50/10.55 (eqimpsubset1) => 77.50/10.55 (( 77.50/10.55 (subsetI2) => 77.50/10.55 (( 77.50/10.55 (emptysetsubset) => 77.50/10.55 (( 77.50/10.55 (subsetE) => 77.50/10.55 (( 77.50/10.55 (subsetE2) => 77.50/10.55 (( 77.50/10.55 (notsubsetI) => 77.50/10.55 (( 77.50/10.55 (notequalI1) => 77.50/10.55 (( 77.50/10.55 (notequalI2) => 77.50/10.55 (( 77.50/10.55 (subsetRefl) => 77.50/10.55 (( 77.50/10.55 (subsetTrans) => 77.50/10.55 (( 77.50/10.55 (setadjoinSub) => 77.50/10.55 (( 77.50/10.55 (setadjoinSub2) => 77.50/10.55 (( 77.50/10.55 (subset2powerset) => 77.50/10.55 (( 77.50/10.55 (setextsub) => 77.50/10.55 (( 77.50/10.55 (subsetemptysetimpeq) => 77.50/10.55 (( 77.50/10.55 (powersetI1) => 77.50/10.55 (( 77.50/10.55 (powersetE1) => 77.50/10.55 (( 77.50/10.55 (inPowerset) => 77.50/10.55 (( 77.50/10.55 (powersetsubset) => 77.50/10.55 (( 77.50/10.55 (sepInPowerset) => 77.50/10.55 (( 77.50/10.55 (sepSubset) => 77.50/10.55 (( 77.50/10.55 (binunionIL) => 77.50/10.55 (( 77.50/10.55 (upairset2IR) => 77.50/10.55 (( 77.50/10.55 (binunionIR) => 77.50/10.55 (( 77.50/10.55 (binunionEcases) => 77.50/10.55 (( 77.50/10.55 (binunionE) => 77.50/10.55 (( 77.50/10.55 (binunionLsub) => 77.50/10.55 (( 77.50/10.55 (binunionRsub) => 77.50/10.55 (( 77.50/10.55 (binintersectI) => 77.50/10.55 (( 77.50/10.55 (binintersectSubset5) => 77.50/10.55 (( 77.50/10.55 (binintersectEL) => 77.50/10.55 (( 77.50/10.55 (binintersectLsub) => 77.50/10.55 (( 77.50/10.55 (binintersectSubset2) => 77.50/10.55 (( 77.50/10.55 (binintersectSubset3) => 77.50/10.55 (( 77.50/10.55 (binintersectER) => 77.50/10.55 (( 77.50/10.55 (disjointsetsI1) => 77.50/10.55 (( 77.50/10.55 (binintersectRsub) => 77.50/10.55 (( 77.50/10.55 (binintersectSubset4) => 77.50/10.55 (( 77.50/10.55 (binintersectSubset1) => 77.50/10.55 (( 77.50/10.55 (bs114d) => 77.50/10.55 (( 77.50/10.55 (setminusI) => 77.50/10.55 (( 77.50/10.55 (setminusEL) => 77.50/10.55 (( 77.50/10.55 (setminusER) => 77.50/10.55 (( 77.50/10.55 (setminusSubset2) => 77.50/10.55 (( 77.50/10.55 (setminusERneg) => 77.50/10.55 (( 77.50/10.55 (setminusELneg) => 77.50/10.55 (( 77.50/10.55 (setminusILneg) => 77.50/10.55 (( 77.50/10.55 (setminusIRneg) => 77.50/10.55 (( 77.50/10.55 (setminusLsub) => 77.50/10.55 (( 77.50/10.55 (setminusSubset1) => 77.50/10.55 (( 77.50/10.55 (symdiffE) => 77.50/10.55 (( 77.50/10.55 (symdiffI1) => 77.50/10.55 (( 77.50/10.55 (symdiffI2) => 77.50/10.55 (( 77.50/10.55 (symdiffIneg1) => 77.50/10.55 (( 77.50/10.55 (symdiffIneg2) => 77.50/10.55 (( 77.50/10.55 (secondinupair) => 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77.50/10.55 (cartprodpairmemER) => 77.50/10.55 (( 77.50/10.55 (cartprodmempaircEq) => 77.50/10.55 (( 77.50/10.55 (cartprodfstpairEq) => 77.50/10.55 (( 77.50/10.55 (cartprodsndpairEq) => 77.50/10.55 (( 77.50/10.55 (cartprodpairsurjEq) => 77.50/10.55 (( 77.50/10.55 (dpsetconstrI) => 77.50/10.55 (( 77.50/10.55 (dpsetconstrSub) => 77.50/10.55 (( 77.50/10.55 (setOfPairsIsBReln) => 77.50/10.55 (( 77.50/10.55 (dpsetconstrERa) => 77.50/10.55 (( 77.50/10.55 (dpsetconstrEL1) => 77.50/10.55 (( 77.50/10.55 (dpsetconstrEL2) => 77.50/10.55 (( 77.50/10.55 (dpsetconstrER) => 77.50/10.55 (( 77.50/10.55 (funcImageSingleton) => 77.50/10.55 (( 77.50/10.55 (apProp) => 77.50/10.55 (( 77.50/10.55 (app) => 77.50/10.55 (( 77.50/10.55 (infuncsetfunc) => 77.50/10.55 (( 77.50/10.55 (ap2p) => 77.50/10.55 (( 77.50/10.55 (funcinfuncset) => 77.50/10.55 (( 77.50/10.55 (lamProp) => 77.50/10.55 (( 77.50/10.55 (lamp) => 77.50/10.55 (( 77.50/10.55 (lam2p) => 77.50/10.55 (( 77.50/10.55 (brelnall1) => 77.50/10.55 (( 77.50/10.55 (brelnall2) => 77.50/10.55 (( 77.50/10.55 (ex1E2) => 77.50/10.55 (( 77.50/10.55 (funcGraphProp1) => 77.50/10.55 (( 77.50/10.55 (funcGraphProp3) => 77.50/10.55 (( 77.50/10.55 (funcGraphProp2) => 77.50/10.55 (( 77.50/10.55 (funcextLem) => 77.50/10.55 (( 77.50/10.55 (funcGraphProp4) => 77.50/10.55 (( 77.50/10.55 (subbreln) => 77.50/10.55 (( 77.50/10.55 (eqbreln) => 77.50/10.55 (( 77.50/10.55 (funcext) => 77.50/10.55 (( 77.50/10.55 (funcext2) => 77.50/10.55 (( 77.50/10.55 (ap2apEq1) => 77.50/10.55 (( 77.50/10.55 (ap2apEq2) => 77.50/10.55 (( 77.50/10.55 (beta1) => 77.50/10.55 (( 77.50/10.55 (eta1) => 77.50/10.55 (( 77.50/10.55 (lam2lamEq) => 77.50/10.55 (( 77.50/10.55 (beta2) => 77.50/10.55 (( 77.50/10.55 (eta2) => 77.50/10.55 (( 77.50/10.55 (iffalseProp1) => 77.50/10.55 (( 77.50/10.55 (iffalseProp2) => 77.50/10.55 (( 77.50/10.55 (iftrueProp1) => 77.50/10.55 (( 77.50/10.55 (iftrueProp2) => 77.50/10.55 (( 77.50/10.55 (ifSingleton) => 77.50/10.55 (( 77.50/10.55 (ifp) => 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(doubleComplementI1) => 77.50/10.55 (( 77.50/10.55 (doubleComplementE1) => 77.50/10.55 (( 77.50/10.55 (doubleComplementSub1) => 77.50/10.55 (( 77.50/10.55 (doubleComplementSub2) => 77.50/10.55 (( 77.50/10.55 (doubleComplementEq) => 77.50/10.55 (( 77.50/10.55 (complementTnotintersectT) => 77.50/10.55 (( 77.50/10.55 (complementImpComplementIntersect) => 77.50/10.55 (( 77.50/10.55 (complementSubsetComplementIntersect) => 77.50/10.55 (( 77.50/10.55 (complementInPowersetComplementIntersect) => 77.50/10.55 (( 77.50/10.55 (contraSubsetComplement) => 77.50/10.55 (( 77.50/10.55 (complementTcontraSubset) => 77.50/10.55 (( 77.50/10.55 (binunionTILcontra) => 77.50/10.55 (( 77.50/10.55 (binunionTIRcontra) => 77.50/10.55 (( 77.50/10.55 (inIntersectImpInUnion) => 77.50/10.55 (( 77.50/10.55 (inIntersectImpInUnion2) => 77.50/10.55 (( 77.50/10.55 (inIntersectImpInIntersectUnions) => 77.50/10.55 (( 77.50/10.55 (intersectInPowersetIntersectUnions) => 77.50/10.55 (( 77.50/10.55 (inComplementUnionImpNotIn1) => 77.50/10.55 (( 77.50/10.55 (inComplementUnionImpInComplement1) => 77.50/10.55 (( 77.50/10.55 (binunionTE) => 77.50/10.55 (( 77.50/10.55 (binunionTEcontra) => 77.50/10.55 (( 77.50/10.55 (demorgan2a1) => 77.50/10.55 (( 77.50/10.55 (complementUnionInPowersetComplement) => 77.50/10.55 (( 77.50/10.55 (demorgan2a2) => 77.50/10.55 (( 77.50/10.55 (demorgan1a) => 77.50/10.55 (( 77.50/10.55 (demorgan1b) => 77.50/10.55 (( 77.50/10.55 (demorgan1) => 77.50/10.55 (( 77.50/10.55 (demorgan2a) => 77.50/10.55 (( 77.50/10.55 (demorgan2b2) => 77.50/10.55 (( 77.50/10.55 (demorgan2b) => 77.50/10.55 (( 77.50/10.55 (demorgan2) => 77.50/10.55 (( 77.50/10.55 (woz13rule0) => 77.50/10.55 (( 77.50/10.55 (woz13rule1) => 77.50/10.55 (( 77.50/10.55 (woz13rule2) => 77.50/10.55 (( 77.50/10.55 (woz13rule3) => 77.50/10.55 (( 77.50/10.55 (woz13rule4) => 77.50/10.55 (( 77.50/10.55 (woz1_1) => 77.50/10.55 (( 77.50/10.55 (woz1_2) => 77.50/10.55 (( 77.50/10.55 (woz1_3) => 77.50/10.55 (( 77.50/10.55 (woz1_4) => 77.50/10.55 (( 77.50/10.55 (woz1_5) => 77.50/10.55 (( 77.50/10.55 (breln1all2) => 77.50/10.55 (( 77.50/10.55 (breln1SetBreln1) => 77.50/10.55 (( 77.50/10.55 (choice2fnsingleton) => 77.50/10.55 (( 77.50/10.55 (setOfPairsIsBReln1) => 77.50/10.55 (( 77.50/10.55 (breln1all1) => 77.50/10.55 (( 77.50/10.55 (subbreln1) => 77.50/10.55 (( 77.50/10.55 (eqbreln1) => 77.50/10.55 (( 77.50/10.55 (breln1invprop) => 77.50/10.55 (( 77.50/10.55 (breln1invI) => 77.50/10.55 (( 77.50/10.55 (breln1invE) => 77.50/10.55 (( 77.50/10.55 (breln1compprop) => 77.50/10.55 (( 77.50/10.55 (breln1compI) => 77.50/10.55 (( 77.50/10.55 (breln1compE) => 77.50/10.55 (( 77.50/10.55 (breln1compEex) => 77.50/10.55 (( 77.50/10.55 (breln1unionprop) => 77.50/10.55 (( 77.50/10.55 (breln1unionIL) => 77.50/10.55 (( 77.50/10.55 (breln1unionIR) => 77.50/10.55 (( 77.50/10.55 (breln1unionI) => 77.50/10.55 (( 77.50/10.55 (breln1unionE) => 77.50/10.55 (( 77.50/10.55 (breln1unionEcases) => 77.50/10.55 (( 77.50/10.55 (breln1unionCommutes) => 77.50/10.55 (( 77.50/10.55 (woz2Ex) => 77.50/10.55 (( 77.50/10.55 (woz2W) => 77.50/10.55 (( 77.50/10.55 (woz2A) => 77.50/10.55 (( 77.50/10.55 (woz2B) => 77.50/10.55 (( 77.50/10.55 (image1Ex) => 77.50/10.55 (( 77.50/10.55 (image1Ex1) => 77.50/10.55 (( 77.50/10.55 (image1Equiv) => 77.50/10.55 (( 77.50/10.55 (image1E) => 77.50/10.55 (( 77.50/10.55 (image1I) => 77.50/10.55 (( 77.50/10.55 (injFuncInInjFuncSet) => 77.50/10.55 (( 77.50/10.55 (injFuncSetFuncIn) => 77.50/10.55 (( 77.50/10.55 (injFuncSetFuncInj) => 77.50/10.55 (( 77.50/10.55 (surjFuncSetFuncIn) => 77.50/10.55 (( 77.50/10.55 (surjFuncSetFuncSurj) => 77.50/10.55 (( 77.50/10.55 (leftInvIsSurj) => 77.50/10.55 (( 77.50/10.55 (surjCantorThm) => 77.50/10.55 (( 77.50/10.55 (foundation2) => 77.50/10.55 (( 77.50/10.55 (notinself) => 77.50/10.55 (( 77.50/10.55 (notinself2) => 77.50/10.55 (( 77.50/10.55 (omegaSp) => 77.50/10.55 (( 77.50/10.55 (omegaSclos) => 77.50/10.55 (( 77.50/10.55 (peano0notS) => 77.50/10.55 (( 77.50/10.55 (peanoSinj) => 77.50/10.55 (( 77.50/10.55 (transitivesetOp1) => 77.50/10.55 (( 77.50/10.55 (binintTransitive) => 77.50/10.55 (( 77.50/10.55 (transitivesetOp2) => 77.50/10.55 (( 77.50/10.55 (setunionTransitive) => 77.50/10.55 (( 77.50/10.55 (ordinalMinLem1) => 77.50/10.55 (( 77.50/10.55 (!!) @ ( 77.50/10.55 ^[Y0 : $i]: 77.50/10.55 (( 77.50/10.55 (ordinal @ 77.50/10.55 Y0) => 77.50/10.55 (( 77.50/10.55 (!!) @ ( 77.50/10.55 ^[Y1 : $i]: 77.50/10.55 (( 77.50/10.55 (!!) @ ( 77.50/10.55 ^[Y2 : $i]: 77.50/10.55 (( 77.50/10.55 (in @ 77.50/10.55 Y2 @ 77.50/10.55 Y0) => 77.50/10.55 (( 77.50/10.55 (in @ 77.50/10.55 Y1 @ 77.50/10.55 Y2) => 77.50/10.55 (in @ 77.50/10.55 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 77.50/10.55 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl21])). 77.50/10.55 thf(zip_derived_cl34, plain, 77.50/10.55 (~ (((omegaIndAx) => 77.50/10.55 (((replAx) => 77.50/10.55 (((foundationAx) => 77.50/10.55 (((wellorderingAx) => 77.50/10.55 (((descrp) => 77.50/10.55 (((dsetconstrI) => 77.50/10.55 (((dsetconstrEL) => 77.50/10.55 (((dsetconstrER) => 77.50/10.55 (((exuE1) => 77.50/10.55 (((prop2setE) => 77.50/10.55 (((emptysetE) => 77.50/10.55 (((emptysetimpfalse) => 77.50/10.55 (((notinemptyset) => 77.50/10.55 (((exuE3e) => 77.50/10.55 (((setext) => 77.50/10.55 (((emptyI) => 77.50/10.55 (((noeltsimpempty) => 77.50/10.55 (((setbeta) => 77.50/10.55 (((nonemptyE1) => 77.50/10.55 (((nonemptyI) => 77.50/10.55 (((nonemptyI1) => 77.50/10.55 (((setadjoinIL) => 77.50/10.55 (((in @ emptyset @ 77.50/10.55 (setadjoin @ emptyset @ 77.50/10.55 emptyset)) => 77.50/10.55 (((setadjoinIR) => 77.50/10.55 (((setadjoinE) => 77.50/10.55 (((setadjoinOr) => 77.50/10.55 (((setoftrueEq) => 77.50/10.55 (((powersetI) => 77.50/10.55 (((emptyinPowerset) => 77.50/10.55 (((emptyInPowerset) => 77.50/10.55 (( 77.50/10.55 (powersetE) => 77.50/10.55 (( 77.50/10.55 (setunionI) => 77.50/10.55 (( 77.50/10.55 (setunionE) => 77.50/10.55 (( 77.50/10.55 (subPowSU) => 77.50/10.55 (( 77.50/10.55 (exuE2) => 77.50/10.55 (( 77.50/10.55 (nonemptyImpWitness) => 77.50/10.55 (( 77.50/10.55 (uniqinunit) => 77.50/10.55 (( 77.50/10.55 (notinsingleton) => 77.50/10.55 (( 77.50/10.55 (eqinunit) => 77.50/10.55 (( 77.50/10.55 (singletonsswitch) => 77.50/10.55 (( 77.50/10.55 (upairsetE) => 77.50/10.55 (( 77.50/10.55 (upairsetIL) => 77.50/10.55 (( 77.50/10.55 (upairsetIR) => 77.50/10.55 (( 77.50/10.55 (emptyE1) => 77.50/10.55 (( 77.50/10.55 (vacuousDall) => 77.50/10.55 (( 77.50/10.55 (quantDeMorgan1) => 77.50/10.55 (( 77.50/10.55 (quantDeMorgan2) => 77.50/10.55 (( 77.50/10.55 (quantDeMorgan3) => 77.50/10.55 (( 77.50/10.55 (quantDeMorgan4) => 77.50/10.55 (( 77.50/10.55 (prop2setI) => 77.50/10.55 (( 77.50/10.55 (prop2set2propI) => 77.50/10.55 (( 77.50/10.55 (notdexE) => 77.50/10.55 (( 77.50/10.55 (notdallE) => 77.50/10.55 (( 77.50/10.55 (exuI1) => 77.50/10.55 (( 77.50/10.55 (exuI3) => 77.50/10.55 (( 77.50/10.55 (exuI2) => 77.50/10.55 (( 77.50/10.55 (inCongP) => 77.50/10.55 (( 77.50/10.55 (in__Cong) => 77.50/10.55 (( 77.50/10.55 (exuE3u) => 77.50/10.55 (( 77.50/10.55 (exu__Cong) => 77.50/10.55 (( 77.50/10.55 (setadjoin__Cong) => 77.50/10.55 (( 77.50/10.55 (powerset__Cong) => 77.50/10.55 (( 77.50/10.55 (setunion__Cong) => 77.50/10.55 (( 77.50/10.55 (exuEu) => 77.50/10.55 (( 77.50/10.55 (descr__Cong) => 77.50/10.55 (( 77.50/10.55 (dsetconstr__Cong) => 77.50/10.55 (( 77.50/10.55 (subsetI1) => 77.50/10.55 (( 77.50/10.55 (eqimpsubset2) => 77.50/10.55 (( 77.50/10.55 (eqimpsubset1) => 77.50/10.55 (( 77.50/10.55 (subsetI2) => 77.50/10.55 (( 77.50/10.55 (emptysetsubset) => 77.50/10.55 (( 77.50/10.55 (subsetE) => 77.50/10.55 (( 77.50/10.55 (subsetE2) => 77.50/10.55 (( 77.50/10.55 (notsubsetI) => 77.50/10.55 (( 77.50/10.55 (notequalI1) => 77.50/10.55 (( 77.50/10.55 (notequalI2) => 77.50/10.55 (( 77.50/10.55 (subsetRefl) => 77.50/10.55 (( 77.50/10.55 (subsetTrans) => 77.50/10.55 (( 77.50/10.55 (setadjoinSub) => 77.50/10.55 (( 77.50/10.55 (setadjoinSub2) => 77.50/10.55 (( 77.50/10.55 (subset2powerset) => 77.50/10.55 (( 77.50/10.55 (setextsub) => 77.50/10.55 (( 77.50/10.55 (subsetemptysetimpeq) => 77.50/10.55 (( 77.50/10.55 (powersetI1) => 77.50/10.55 (( 77.50/10.55 (powersetE1) => 77.50/10.55 (( 77.50/10.55 (inPowerset) => 77.50/10.55 (( 77.50/10.55 (powersetsubset) => 77.50/10.55 (( 77.50/10.55 (sepInPowerset) => 77.50/10.55 (( 77.50/10.55 (sepSubset) => 77.50/10.55 (( 77.50/10.55 (binunionIL) => 77.50/10.55 (( 77.50/10.55 (upairset2IR) => 77.50/10.55 (( 77.50/10.55 (binunionIR) => 77.50/10.55 (( 77.50/10.55 (binunionEcases) => 77.50/10.55 (( 77.50/10.55 (binunionE) => 77.50/10.55 (( 77.50/10.55 (binunionLsub) => 77.50/10.55 (( 77.50/10.55 (binunionRsub) => 77.50/10.55 (( 77.50/10.55 (binintersectI) => 77.50/10.55 (( 77.50/10.55 (binintersectSubset5) => 77.50/10.55 (( 77.50/10.55 (binintersectEL) => 77.50/10.55 (( 77.50/10.55 (binintersectLsub) => 77.50/10.55 (( 77.50/10.55 (binintersectSubset2) => 77.50/10.55 (( 77.50/10.55 (binintersectSubset3) => 77.50/10.55 (( 77.50/10.55 (binintersectER) => 77.50/10.55 (( 77.50/10.55 (disjointsetsI1) => 77.50/10.55 (( 77.50/10.55 (binintersectRsub) => 77.50/10.55 (( 77.50/10.55 (binintersectSubset4) => 77.50/10.55 (( 77.50/10.55 (binintersectSubset1) => 77.50/10.55 (( 77.50/10.55 (bs114d) => 77.50/10.55 (( 77.50/10.55 (setminusI) => 77.50/10.55 (( 77.50/10.55 (setminusEL) => 77.50/10.55 (( 77.50/10.55 (setminusER) => 77.50/10.55 (( 77.50/10.55 (setminusSubset2) => 77.50/10.55 (( 77.50/10.55 (setminusERneg) => 77.50/10.55 (( 77.50/10.55 (setminusELneg) => 77.50/10.55 (( 77.50/10.55 (setminusILneg) => 77.50/10.55 (( 77.50/10.55 (setminusIRneg) => 77.50/10.55 (( 77.50/10.55 (setminusLsub) => 77.50/10.55 (( 77.50/10.55 (setminusSubset1) => 77.50/10.55 (( 77.50/10.55 (symdiffE) => 77.50/10.55 (( 77.50/10.55 (symdiffI1) => 77.50/10.55 (( 77.50/10.55 (symdiffI2) => 77.50/10.55 (( 77.50/10.55 (symdiffIneg1) => 77.50/10.55 (( 77.50/10.55 (symdiffIneg2) => 77.50/10.55 (( 77.50/10.55 (secondinupair) => 77.50/10.55 (( 77.50/10.55 (setukpairIL) => 77.50/10.55 (( 77.50/10.55 (setukpairIR) => 77.50/10.55 (( 77.50/10.55 (kpairiskpair) => 77.50/10.55 (( 77.50/10.55 (kpairp) => 77.50/10.55 (( 77.50/10.55 (singletonsubset) => 77.50/10.55 (( 77.50/10.55 (singletoninpowerset) => 77.50/10.55 (( 77.50/10.55 (singletoninpowunion) => 77.50/10.55 (( 77.50/10.55 (upairset2E) => 77.50/10.55 (( 77.50/10.55 (upairsubunion) => 77.50/10.55 (( 77.50/10.55 (upairinpowunion) => 77.50/10.55 (( 77.50/10.55 (ubforcartprodlem1) => 77.50/10.55 (( 77.50/10.55 (ubforcartprodlem2) => 77.50/10.55 (( 77.50/10.55 (ubforcartprodlem3) => 77.50/10.55 (( 77.50/10.55 (cartprodpairin) => 77.50/10.55 (( 77.50/10.55 (cartprodmempair1) => 77.50/10.55 (( 77.50/10.55 (cartprodmempair) => 77.50/10.55 (( 77.50/10.55 (setunionE2) => 77.50/10.55 (( 77.50/10.55 (setunionsingleton1) => 77.50/10.55 (( 77.50/10.55 (setunionsingleton2) => 77.50/10.55 (( 77.50/10.55 (setunionsingleton) => 77.50/10.55 (( 77.50/10.55 (singletonprop) => 77.50/10.55 (( 77.50/10.55 (ex1E1) => 77.50/10.55 (( 77.50/10.55 (ex1I) => 77.50/10.55 (( 77.50/10.55 (ex1I2) => 77.50/10.55 (( 77.50/10.55 (singletonsuniq) => 77.50/10.55 (( 77.50/10.55 (setukpairinjL1) => 77.50/10.55 (( 77.50/10.55 (kfstsingleton) => 77.50/10.55 (( 77.50/10.55 (theprop) => 77.50/10.55 (( 77.50/10.55 (kfstpairEq) => 77.50/10.55 (( 77.50/10.55 (cartprodfstin) => 77.50/10.55 (( 77.50/10.55 (setukpairinjL2) => 77.50/10.55 (( 77.50/10.55 (setukpairinjL) => 77.50/10.55 (( 77.50/10.55 (setukpairinjR11) => 77.50/10.55 (( 77.50/10.55 (setukpairinjR12) => 77.50/10.55 (( 77.50/10.55 (setukpairinjR1) => 77.50/10.55 (( 77.50/10.55 (upairequniteq) => 77.50/10.55 (( 77.50/10.55 (setukpairinjR2) => 77.50/10.55 (( 77.50/10.55 (setukpairinjR) => 77.50/10.55 (( 77.50/10.55 (ksndsingleton) => 77.50/10.55 (( 77.50/10.55 (ksndpairEq) => 77.50/10.55 (( 77.50/10.55 (kpairsurjEq) => 77.50/10.55 (( 77.50/10.55 (cartprodsndin) => 77.50/10.55 (( 77.50/10.55 (cartprodpairmemEL) => 77.50/10.55 (( 77.50/10.55 (cartprodpairmemER) => 77.50/10.55 (( 77.50/10.55 (cartprodmempaircEq) => 77.50/10.55 (( 77.50/10.55 (cartprodfstpairEq) => 77.50/10.55 (( 77.50/10.55 (cartprodsndpairEq) => 77.50/10.55 (( 77.50/10.55 (cartprodpairsurjEq) => 77.50/10.55 (( 77.50/10.55 (dpsetconstrI) => 77.50/10.55 (( 77.50/10.55 (dpsetconstrSub) => 77.50/10.55 (( 77.50/10.55 (setOfPairsIsBReln) => 77.50/10.55 (( 77.50/10.55 (dpsetconstrERa) => 77.50/10.55 (( 77.50/10.55 (dpsetconstrEL1) => 77.50/10.55 (( 77.50/10.55 (dpsetconstrEL2) => 77.50/10.55 (( 77.50/10.55 (dpsetconstrER) => 77.50/10.55 (( 77.50/10.55 (funcImageSingleton) => 77.50/10.55 (( 77.50/10.55 (apProp) => 77.50/10.55 (( 77.50/10.55 (app) => 77.50/10.55 (( 77.50/10.55 (infuncsetfunc) => 77.50/10.55 (( 77.50/10.55 (ap2p) => 77.50/10.55 (( 77.50/10.55 (funcinfuncset) => 77.50/10.55 (( 77.50/10.55 (lamProp) => 77.50/10.55 (( 77.50/10.55 (lamp) => 77.50/10.55 (( 77.50/10.55 (lam2p) => 77.50/10.55 (( 77.50/10.55 (brelnall1) => 77.50/10.55 (( 77.50/10.55 (brelnall2) => 77.50/10.55 (( 77.50/10.55 (ex1E2) => 77.50/10.55 (( 77.50/10.55 (funcGraphProp1) => 77.50/10.55 (( 77.50/10.55 (funcGraphProp3) => 77.50/10.55 (( 77.50/10.55 (funcGraphProp2) => 77.50/10.55 (( 77.50/10.55 (funcextLem) => 77.50/10.55 (( 77.50/10.55 (funcGraphProp4) => 77.50/10.55 (( 77.50/10.55 (subbreln) => 77.50/10.55 (( 77.50/10.55 (eqbreln) => 77.50/10.55 (( 77.50/10.55 (funcext) => 77.50/10.55 (( 77.50/10.55 (funcext2) => 77.50/10.55 (( 77.50/10.55 (ap2apEq1) => 77.50/10.55 (( 77.50/10.55 (ap2apEq2) => 77.50/10.55 (( 77.50/10.55 (beta1) => 77.50/10.55 (( 77.50/10.55 (eta1) => 77.50/10.55 (( 77.50/10.55 (lam2lamEq) => 77.50/10.55 (( 77.50/10.55 (beta2) => 77.50/10.55 (( 77.50/10.55 (eta2) => 77.50/10.55 (( 77.50/10.55 (iffalseProp1) => 77.50/10.55 (( 77.50/10.55 (iffalseProp2) => 77.50/10.55 (( 77.50/10.55 (iftrueProp1) => 77.50/10.55 (( 77.50/10.55 (iftrueProp2) => 77.50/10.55 (( 77.50/10.55 (ifSingleton) => 77.50/10.55 (( 77.50/10.55 (ifp) => 77.50/10.55 (( 77.50/10.55 (theeq) => 77.50/10.55 (( 77.50/10.55 (iftrue) => 77.50/10.55 (( 77.50/10.55 (iffalse) => 77.50/10.55 (( 77.50/10.55 (iftrueorfalse) => 77.50/10.55 (( 77.50/10.55 (binintersectT_lem) => 77.50/10.55 (( 77.50/10.55 (binunionT_lem) => 77.50/10.55 (( 77.50/10.55 (powersetT_lem) => 77.50/10.55 (( 77.50/10.55 (setminusT_lem) => 77.50/10.55 (( 77.50/10.55 (complementT_lem) => 77.50/10.55 (( 77.50/10.55 (setextT) => 77.50/10.55 (( 77.50/10.55 (subsetTI) => 77.50/10.55 (( 77.50/10.55 (powersetTI1) => 77.50/10.55 (( 77.50/10.55 (powersetTE1) => 77.50/10.55 (( 77.50/10.55 (complementTI1) => 77.50/10.55 (( 77.50/10.55 (complementTE1) => 77.50/10.55 (( 77.50/10.55 (binintersectTELcontra) => 77.50/10.55 (( 77.50/10.55 (binintersectTERcontra) => 77.50/10.55 (( 77.50/10.55 (contrasubsetT) => 77.50/10.55 (( 77.50/10.55 (contrasubsetT1) => 77.50/10.55 (( 77.50/10.55 (contrasubsetT2) => 77.50/10.55 (( 77.50/10.55 (contrasubsetT3) => 77.50/10.55 (( 77.50/10.55 (doubleComplementI1) => 77.50/10.55 (( 77.50/10.55 (doubleComplementE1) => 77.50/10.55 (( 77.50/10.55 (doubleComplementSub1) => 77.50/10.55 (( 77.50/10.55 (doubleComplementSub2) => 77.50/10.55 (( 77.50/10.55 (doubleComplementEq) => 77.50/10.55 (( 77.50/10.55 (complementTnotintersectT) => 77.50/10.55 (( 77.50/10.55 (complementImpComplementIntersect) => 77.50/10.55 (( 77.50/10.55 (complementSubsetComplementIntersect) => 77.50/10.55 (( 77.50/10.55 (complementInPowersetComplementIntersect) => 77.50/10.55 (( 77.50/10.55 (contraSubsetComplement) => 77.50/10.55 (( 77.50/10.55 (complementTcontraSubset) => 77.50/10.55 (( 77.50/10.55 (binunionTILcontra) => 77.50/10.55 (( 77.50/10.55 (binunionTIRcontra) => 77.50/10.55 (( 77.50/10.55 (inIntersectImpInUnion) => 77.50/10.55 (( 77.50/10.55 (inIntersectImpInUnion2) => 77.50/10.55 (( 77.50/10.55 (inIntersectImpInIntersectUnions) => 77.50/10.55 (( 77.50/10.55 (intersectInPowersetIntersectUnions) => 77.50/10.55 (( 77.50/10.55 (inComplementUnionImpNotIn1) => 77.50/10.55 (( 77.50/10.55 (inComplementUnionImpInComplement1) => 77.50/10.55 (( 77.50/10.55 (binunionTE) => 77.50/10.55 (( 77.50/10.55 (binunionTEcontra) => 77.50/10.55 (( 77.50/10.55 (demorgan2a1) => 77.50/10.55 (( 77.50/10.55 (complementUnionInPowersetComplement) => 77.50/10.55 (( 77.50/10.55 (demorgan2a2) => 77.50/10.55 (( 77.50/10.55 (demorgan1a) => 77.50/10.55 (( 77.50/10.55 (demorgan1b) => 77.50/10.55 (( 77.50/10.55 (demorgan1) => 77.50/10.55 (( 77.50/10.55 (demorgan2a) => 77.50/10.55 (( 77.50/10.55 (demorgan2b2) => 77.50/10.55 (( 77.50/10.55 (demorgan2b) => 77.50/10.55 (( 77.50/10.55 (demorgan2) => 77.50/10.55 (( 77.50/10.55 (woz13rule0) => 77.50/10.55 (( 77.50/10.55 (woz13rule1) => 77.50/10.55 (( 77.50/10.55 (woz13rule2) => 77.50/10.55 (( 77.50/10.55 (woz13rule3) => 77.50/10.55 (( 77.50/10.55 (woz13rule4) => 77.50/10.55 (( 77.50/10.55 (woz1_1) => 77.50/10.55 (( 77.50/10.55 (woz1_2) => 77.50/10.55 (( 77.50/10.55 (woz1_3) => 77.50/10.55 (( 77.50/10.55 (woz1_4) => 77.50/10.55 (( 77.50/10.55 (woz1_5) => 77.50/10.55 (( 77.50/10.55 (breln1all2) => 77.50/10.55 (( 77.50/10.55 (breln1SetBreln1) => 77.50/10.55 (( 77.50/10.55 (choice2fnsingleton) => 77.50/10.55 (( 77.50/10.55 (setOfPairsIsBReln1) => 77.50/10.55 (( 77.50/10.55 (breln1all1) => 77.50/10.55 (( 77.50/10.55 (subbreln1) => 77.50/10.55 (( 77.50/10.55 (eqbreln1) => 77.50/10.55 (( 77.50/10.55 (breln1invprop) => 77.50/10.55 (( 77.50/10.55 (breln1invI) => 77.50/10.55 (( 77.50/10.55 (breln1invE) => 77.50/10.55 (( 77.50/10.55 (breln1compprop) => 77.50/10.55 (( 77.50/10.55 (breln1compI) => 77.50/10.55 (( 77.50/10.55 (breln1compE) => 77.50/10.55 (( 77.50/10.55 (breln1compEex) => 77.50/10.55 (( 77.50/10.55 (breln1unionprop) => 77.50/10.55 (( 77.50/10.55 (breln1unionIL) => 77.50/10.55 (( 77.50/10.55 (breln1unionIR) => 77.50/10.55 (( 77.50/10.55 (breln1unionI) => 77.50/10.55 (( 77.50/10.55 (breln1unionE) => 77.50/10.55 (( 77.50/10.55 (breln1unionEcases) => 77.50/10.55 (( 77.50/10.55 (breln1unionCommutes) => 77.50/10.55 (( 77.50/10.55 (woz2Ex) => 77.50/10.55 (( 77.50/10.55 (woz2W) => 77.50/10.55 (( 77.50/10.55 (woz2A) => 77.50/10.55 (( 77.50/10.55 (woz2B) => 77.50/10.55 (( 77.50/10.55 (image1Ex) => 77.50/10.55 (( 77.50/10.55 (image1Ex1) => 77.50/10.55 (( 77.50/10.55 (image1Equiv) => 77.50/10.55 (( 77.50/10.55 (image1E) => 77.50/10.55 (( 77.50/10.55 (image1I) => 77.50/10.55 (( 77.50/10.55 (injFuncInInjFuncSet) => 77.50/10.55 (( 77.50/10.55 (injFuncSetFuncIn) => 77.50/10.55 (( 77.50/10.55 (injFuncSetFuncInj) => 77.50/10.55 (( 77.50/10.55 (surjFuncSetFuncIn) => 77.50/10.55 (( 77.50/10.55 (surjFuncSetFuncSurj) => 77.50/10.55 (( 77.50/10.55 (leftInvIsSurj) => 77.50/10.55 (( 77.50/10.55 (surjCantorThm) => 77.50/10.55 (( 77.50/10.55 (foundation2) => 77.50/10.55 (( 77.50/10.55 (notinself) => 77.50/10.55 (( 77.50/10.55 (notinself2) => 77.50/10.55 (( 77.50/10.55 (omegaSp) => 77.50/10.55 (( 77.50/10.55 (omegaSclos) => 77.50/10.55 (( 77.50/10.55 (peano0notS) => 77.50/10.55 (( 77.50/10.55 (peanoSinj) => 77.50/10.55 (( 77.50/10.55 (transitivesetOp1) => 77.50/10.55 (( 77.50/10.55 (binintTransitive) => 77.50/10.55 (( 77.50/10.55 (transitivesetOp2) => 77.50/10.55 (( 77.50/10.55 (setunionTransitive) => 77.50/10.55 (( 77.50/10.55 (ordinalMinLem1) => 77.50/10.55 (( 77.50/10.55 (!!) @ ( 77.50/10.55 ^[Y0 : $i]: 77.50/10.55 (( 77.50/10.55 (ordinal @ 77.50/10.55 Y0) => 77.50/10.55 (( 77.50/10.55 (!!) @ ( 77.50/10.55 ^[Y1 : $i]: 77.50/10.55 (( 77.50/10.55 (!!) @ ( 77.50/10.55 ^[Y2 : $i]: 77.50/10.55 (( 77.50/10.55 (in @ 77.50/10.55 Y2 @ 77.50/10.55 Y0) => 77.50/10.55 (( 77.50/10.55 (in @ 77.50/10.55 Y1 @ 77.50/10.55 Y2) => 77.50/10.55 (in @ 77.50/10.55 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 77.50/10.55 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl28])). 77.50/10.55 thf(zip_derived_cl40, plain, 77.50/10.55 (~ (((replAx) => 77.50/10.55 (((foundationAx) => 77.50/10.55 (((wellorderingAx) => 77.50/10.55 (((descrp) => 77.50/10.55 (((dsetconstrI) => 77.50/10.55 (((dsetconstrEL) => 77.50/10.55 (((dsetconstrER) => 77.50/10.55 (((exuE1) => 77.50/10.55 (((prop2setE) => 77.50/10.55 (((emptysetE) => 77.50/10.55 (((emptysetimpfalse) => 77.50/10.55 (((notinemptyset) => 77.50/10.55 (((exuE3e) => 77.50/10.55 (((setext) => 77.50/10.55 (((emptyI) => 77.50/10.55 (((noeltsimpempty) => 77.50/10.55 (((setbeta) => 77.50/10.55 (((nonemptyE1) => 77.50/10.55 (((nonemptyI) => 77.50/10.55 (((nonemptyI1) => 77.50/10.55 (((setadjoinIL) => 77.50/10.55 (((in @ emptyset @ 77.50/10.55 (setadjoin @ emptyset @ 77.50/10.55 emptyset)) => 77.50/10.55 (((setadjoinIR) => 77.50/10.55 (((setadjoinE) => 77.50/10.55 (((setadjoinOr) => 77.50/10.55 (((setoftrueEq) => 77.50/10.55 (((powersetI) => 77.50/10.55 (((emptyinPowerset) => 77.50/10.55 (((emptyInPowerset) => 77.50/10.55 (((powersetE) => 77.50/10.55 (( 77.50/10.55 (setunionI) => 77.50/10.55 (( 77.50/10.55 (setunionE) => 77.50/10.55 (( 77.50/10.55 (subPowSU) => 77.50/10.55 (( 77.50/10.55 (exuE2) => 77.50/10.55 (( 77.50/10.55 (nonemptyImpWitness) => 77.50/10.55 (( 77.50/10.55 (uniqinunit) => 77.50/10.55 (( 77.50/10.55 (notinsingleton) => 77.50/10.55 (( 77.50/10.55 (eqinunit) => 77.50/10.55 (( 77.50/10.55 (singletonsswitch) => 77.50/10.55 (( 77.50/10.55 (upairsetE) => 77.50/10.55 (( 77.50/10.55 (upairsetIL) => 77.50/10.55 (( 77.50/10.55 (upairsetIR) => 77.50/10.55 (( 77.50/10.55 (emptyE1) => 77.50/10.55 (( 77.50/10.55 (vacuousDall) => 77.50/10.55 (( 77.50/10.55 (quantDeMorgan1) => 77.50/10.55 (( 77.50/10.55 (quantDeMorgan2) => 77.50/10.55 (( 77.50/10.55 (quantDeMorgan3) => 77.50/10.55 (( 77.50/10.55 (quantDeMorgan4) => 77.50/10.55 (( 77.50/10.55 (prop2setI) => 77.50/10.55 (( 77.50/10.55 (prop2set2propI) => 77.50/10.55 (( 77.50/10.55 (notdexE) => 77.50/10.55 (( 77.50/10.55 (notdallE) => 77.50/10.55 (( 77.50/10.55 (exuI1) => 77.50/10.55 (( 77.50/10.55 (exuI3) => 77.50/10.55 (( 77.50/10.55 (exuI2) => 77.50/10.55 (( 77.50/10.55 (inCongP) => 77.50/10.55 (( 77.50/10.55 (in__Cong) => 77.50/10.55 (( 77.50/10.55 (exuE3u) => 77.50/10.55 (( 77.50/10.55 (exu__Cong) => 77.50/10.55 (( 77.50/10.55 (setadjoin__Cong) => 77.50/10.55 (( 77.50/10.55 (powerset__Cong) => 77.50/10.55 (( 77.50/10.55 (setunion__Cong) => 77.50/10.55 (( 77.50/10.55 (exuEu) => 77.50/10.55 (( 77.50/10.55 (descr__Cong) => 77.50/10.55 (( 77.50/10.55 (dsetconstr__Cong) => 77.50/10.55 (( 77.50/10.55 (subsetI1) => 77.50/10.55 (( 77.50/10.55 (eqimpsubset2) => 77.50/10.55 (( 77.50/10.55 (eqimpsubset1) => 77.50/10.55 (( 77.50/10.55 (subsetI2) => 77.50/10.55 (( 77.50/10.55 (emptysetsubset) => 77.50/10.55 (( 77.50/10.55 (subsetE) => 77.50/10.55 (( 77.50/10.55 (subsetE2) => 77.50/10.55 (( 77.50/10.55 (notsubsetI) => 77.50/10.55 (( 77.50/10.55 (notequalI1) => 77.50/10.55 (( 77.50/10.55 (notequalI2) => 77.50/10.55 (( 77.50/10.55 (subsetRefl) => 77.50/10.55 (( 77.50/10.55 (subsetTrans) => 77.50/10.55 (( 77.50/10.55 (setadjoinSub) => 77.50/10.55 (( 77.50/10.55 (setadjoinSub2) => 77.50/10.55 (( 77.50/10.55 (subset2powerset) => 77.50/10.55 (( 77.50/10.55 (setextsub) => 77.50/10.55 (( 77.50/10.55 (subsetemptysetimpeq) => 77.50/10.55 (( 77.50/10.55 (powersetI1) => 77.50/10.55 (( 77.50/10.55 (powersetE1) => 77.50/10.55 (( 77.50/10.55 (inPowerset) => 77.50/10.55 (( 77.50/10.55 (powersetsubset) => 77.50/10.55 (( 77.50/10.55 (sepInPowerset) => 77.50/10.55 (( 77.50/10.55 (sepSubset) => 77.50/10.55 (( 77.50/10.55 (binunionIL) => 77.50/10.55 (( 77.50/10.55 (upairset2IR) => 77.50/10.55 (( 77.50/10.55 (binunionIR) => 77.50/10.55 (( 77.50/10.55 (binunionEcases) => 77.50/10.55 (( 77.50/10.55 (binunionE) => 77.50/10.55 (( 77.50/10.55 (binunionLsub) => 77.50/10.55 (( 77.50/10.55 (binunionRsub) => 77.50/10.55 (( 77.50/10.55 (binintersectI) => 77.50/10.55 (( 77.50/10.55 (binintersectSubset5) => 77.50/10.55 (( 77.50/10.55 (binintersectEL) => 77.50/10.55 (( 77.50/10.55 (binintersectLsub) => 77.50/10.55 (( 77.50/10.55 (binintersectSubset2) => 77.50/10.55 (( 77.50/10.55 (binintersectSubset3) => 77.50/10.55 (( 77.50/10.55 (binintersectER) => 77.50/10.55 (( 77.50/10.55 (disjointsetsI1) => 77.50/10.55 (( 77.50/10.55 (binintersectRsub) => 77.50/10.55 (( 77.50/10.55 (binintersectSubset4) => 77.50/10.55 (( 77.50/10.55 (binintersectSubset1) => 77.50/10.55 (( 77.50/10.55 (bs114d) => 77.50/10.55 (( 77.50/10.55 (setminusI) => 77.50/10.55 (( 77.50/10.55 (setminusEL) => 77.50/10.55 (( 77.50/10.55 (setminusER) => 77.50/10.55 (( 77.50/10.55 (setminusSubset2) => 77.50/10.55 (( 77.50/10.55 (setminusERneg) => 77.50/10.55 (( 77.50/10.55 (setminusELneg) => 77.50/10.55 (( 77.50/10.55 (setminusILneg) => 77.50/10.55 (( 77.50/10.55 (setminusIRneg) => 77.50/10.55 (( 77.50/10.55 (setminusLsub) => 77.50/10.55 (( 77.50/10.55 (setminusSubset1) => 77.50/10.55 (( 77.50/10.55 (symdiffE) => 77.50/10.55 (( 77.50/10.55 (symdiffI1) => 77.50/10.55 (( 77.50/10.55 (symdiffI2) => 77.50/10.55 (( 77.50/10.55 (symdiffIneg1) => 77.50/10.55 (( 77.50/10.55 (symdiffIneg2) => 77.50/10.55 (( 77.50/10.55 (secondinupair) => 77.50/10.55 (( 77.50/10.55 (setukpairIL) => 77.50/10.55 (( 77.50/10.55 (setukpairIR) => 77.50/10.55 (( 77.50/10.55 (kpairiskpair) => 77.50/10.55 (( 77.50/10.55 (kpairp) => 77.50/10.55 (( 77.50/10.55 (singletonsubset) => 77.50/10.55 (( 77.50/10.55 (singletoninpowerset) => 77.50/10.55 (( 77.50/10.55 (singletoninpowunion) => 77.50/10.55 (( 77.50/10.55 (upairset2E) => 77.50/10.55 (( 77.50/10.55 (upairsubunion) => 77.50/10.55 (( 77.50/10.55 (upairinpowunion) => 77.50/10.55 (( 77.50/10.55 (ubforcartprodlem1) => 77.50/10.55 (( 77.50/10.55 (ubforcartprodlem2) => 77.50/10.55 (( 77.50/10.55 (ubforcartprodlem3) => 77.50/10.55 (( 77.50/10.55 (cartprodpairin) => 77.50/10.55 (( 77.50/10.55 (cartprodmempair1) => 77.50/10.55 (( 77.50/10.55 (cartprodmempair) => 77.50/10.55 (( 77.50/10.55 (setunionE2) => 77.50/10.55 (( 77.50/10.55 (setunionsingleton1) => 77.50/10.55 (( 77.50/10.55 (setunionsingleton2) => 77.50/10.55 (( 77.50/10.55 (setunionsingleton) => 77.50/10.55 (( 77.50/10.55 (singletonprop) => 77.50/10.55 (( 77.50/10.55 (ex1E1) => 77.50/10.55 (( 77.50/10.55 (ex1I) => 77.50/10.55 (( 77.50/10.55 (ex1I2) => 77.50/10.55 (( 77.50/10.55 (singletonsuniq) => 77.50/10.55 (( 77.50/10.55 (setukpairinjL1) => 77.50/10.55 (( 77.50/10.55 (kfstsingleton) => 77.50/10.55 (( 77.50/10.55 (theprop) => 77.50/10.55 (( 77.50/10.55 (kfstpairEq) => 77.50/10.55 (( 77.50/10.55 (cartprodfstin) => 77.50/10.55 (( 77.50/10.55 (setukpairinjL2) => 77.50/10.55 (( 77.50/10.55 (setukpairinjL) => 77.50/10.55 (( 77.50/10.55 (setukpairinjR11) => 77.50/10.55 (( 77.50/10.55 (setukpairinjR12) => 77.50/10.55 (( 77.50/10.55 (setukpairinjR1) => 77.50/10.55 (( 77.50/10.55 (upairequniteq) => 77.50/10.55 (( 77.50/10.55 (setukpairinjR2) => 77.50/10.55 (( 77.50/10.55 (setukpairinjR) => 77.50/10.55 (( 77.50/10.55 (ksndsingleton) => 77.50/10.55 (( 77.50/10.55 (ksndpairEq) => 77.50/10.55 (( 77.50/10.55 (kpairsurjEq) => 77.50/10.55 (( 77.50/10.55 (cartprodsndin) => 77.50/10.55 (( 77.50/10.55 (cartprodpairmemEL) => 77.50/10.55 (( 77.50/10.55 (cartprodpairmemER) => 77.50/10.55 (( 77.50/10.55 (cartprodmempaircEq) => 77.50/10.55 (( 77.50/10.55 (cartprodfstpairEq) => 77.50/10.55 (( 77.50/10.55 (cartprodsndpairEq) => 77.50/10.55 (( 77.50/10.55 (cartprodpairsurjEq) => 77.50/10.55 (( 77.50/10.55 (dpsetconstrI) => 77.50/10.55 (( 77.50/10.55 (dpsetconstrSub) => 77.50/10.55 (( 77.50/10.55 (setOfPairsIsBReln) => 77.50/10.55 (( 77.50/10.55 (dpsetconstrERa) => 77.50/10.55 (( 77.50/10.55 (dpsetconstrEL1) => 77.50/10.55 (( 77.50/10.55 (dpsetconstrEL2) => 77.50/10.55 (( 77.50/10.55 (dpsetconstrER) => 77.50/10.55 (( 77.50/10.55 (funcImageSingleton) => 77.50/10.55 (( 77.50/10.55 (apProp) => 77.50/10.55 (( 77.50/10.55 (app) => 77.50/10.55 (( 77.50/10.55 (infuncsetfunc) => 77.50/10.55 (( 77.50/10.55 (ap2p) => 77.50/10.55 (( 77.50/10.55 (funcinfuncset) => 77.50/10.55 (( 77.50/10.55 (lamProp) => 77.50/10.55 (( 77.50/10.55 (lamp) => 77.50/10.55 (( 77.50/10.55 (lam2p) => 77.50/10.55 (( 77.50/10.55 (brelnall1) => 77.50/10.55 (( 77.50/10.55 (brelnall2) => 77.50/10.55 (( 77.50/10.55 (ex1E2) => 77.50/10.55 (( 77.50/10.55 (funcGraphProp1) => 77.50/10.55 (( 77.50/10.55 (funcGraphProp3) => 77.50/10.55 (( 77.50/10.55 (funcGraphProp2) => 77.50/10.55 (( 77.50/10.55 (funcextLem) => 77.50/10.55 (( 77.50/10.55 (funcGraphProp4) => 77.50/10.55 (( 77.50/10.55 (subbreln) => 77.50/10.55 (( 77.50/10.55 (eqbreln) => 77.50/10.55 (( 77.50/10.55 (funcext) => 77.50/10.55 (( 77.50/10.55 (funcext2) => 77.50/10.55 (( 77.50/10.55 (ap2apEq1) => 77.50/10.55 (( 77.50/10.55 (ap2apEq2) => 77.50/10.55 (( 77.50/10.55 (beta1) => 77.50/10.55 (( 77.50/10.55 (eta1) => 77.50/10.55 (( 77.50/10.55 (lam2lamEq) => 77.50/10.55 (( 77.50/10.55 (beta2) => 77.50/10.55 (( 77.50/10.55 (eta2) => 77.50/10.55 (( 77.50/10.55 (iffalseProp1) => 77.50/10.55 (( 77.50/10.55 (iffalseProp2) => 77.50/10.55 (( 77.50/10.55 (iftrueProp1) => 77.50/10.55 (( 77.50/10.55 (iftrueProp2) => 77.50/10.55 (( 77.50/10.55 (ifSingleton) => 77.50/10.55 (( 77.50/10.55 (ifp) => 77.50/10.55 (( 77.50/10.55 (theeq) => 77.50/10.55 (( 77.50/10.55 (iftrue) => 77.50/10.55 (( 77.50/10.55 (iffalse) => 77.50/10.55 (( 77.50/10.55 (iftrueorfalse) => 77.50/10.55 (( 77.50/10.55 (binintersectT_lem) => 77.50/10.55 (( 77.50/10.55 (binunionT_lem) => 77.50/10.55 (( 77.50/10.55 (powersetT_lem) => 77.50/10.55 (( 77.50/10.55 (setminusT_lem) => 77.50/10.55 (( 77.50/10.55 (complementT_lem) => 77.50/10.55 (( 77.50/10.55 (setextT) => 77.50/10.55 (( 77.50/10.55 (subsetTI) => 77.50/10.55 (( 77.50/10.55 (powersetTI1) => 77.50/10.55 (( 77.50/10.55 (powersetTE1) => 77.50/10.55 (( 77.50/10.55 (complementTI1) => 77.50/10.55 (( 77.50/10.55 (complementTE1) => 77.50/10.55 (( 77.50/10.55 (binintersectTELcontra) => 77.50/10.55 (( 77.50/10.55 (binintersectTERcontra) => 77.50/10.55 (( 77.50/10.55 (contrasubsetT) => 77.50/10.55 (( 77.50/10.55 (contrasubsetT1) => 77.50/10.55 (( 77.50/10.55 (contrasubsetT2) => 77.50/10.55 (( 77.50/10.55 (contrasubsetT3) => 77.50/10.55 (( 77.50/10.55 (doubleComplementI1) => 77.50/10.55 (( 77.50/10.55 (doubleComplementE1) => 77.50/10.55 (( 77.50/10.55 (doubleComplementSub1) => 77.50/10.55 (( 77.50/10.55 (doubleComplementSub2) => 77.50/10.55 (( 77.50/10.55 (doubleComplementEq) => 77.50/10.55 (( 77.50/10.55 (complementTnotintersectT) => 77.50/10.55 (( 77.50/10.55 (complementImpComplementIntersect) => 77.50/10.55 (( 77.50/10.55 (complementSubsetComplementIntersect) => 77.50/10.55 (( 77.50/10.55 (complementInPowersetComplementIntersect) => 77.50/10.55 (( 77.50/10.55 (contraSubsetComplement) => 77.50/10.55 (( 77.50/10.55 (complementTcontraSubset) => 77.50/10.55 (( 77.50/10.55 (binunionTILcontra) => 77.50/10.55 (( 77.50/10.55 (binunionTIRcontra) => 77.50/10.55 (( 77.50/10.55 (inIntersectImpInUnion) => 77.50/10.55 (( 77.50/10.55 (inIntersectImpInUnion2) => 77.50/10.55 (( 77.50/10.55 (inIntersectImpInIntersectUnions) => 77.50/10.55 (( 77.50/10.55 (intersectInPowersetIntersectUnions) => 77.50/10.55 (( 77.50/10.55 (inComplementUnionImpNotIn1) => 77.50/10.55 (( 77.50/10.55 (inComplementUnionImpInComplement1) => 77.50/10.55 (( 77.50/10.55 (binunionTE) => 77.50/10.55 (( 77.50/10.55 (binunionTEcontra) => 77.50/10.55 (( 77.50/10.55 (demorgan2a1) => 77.50/10.55 (( 77.50/10.55 (complementUnionInPowersetComplement) => 77.50/10.55 (( 77.50/10.55 (demorgan2a2) => 77.50/10.55 (( 77.50/10.55 (demorgan1a) => 77.50/10.55 (( 77.50/10.55 (demorgan1b) => 77.50/10.55 (( 77.50/10.55 (demorgan1) => 77.50/10.55 (( 77.50/10.55 (demorgan2a) => 77.50/10.55 (( 77.50/10.55 (demorgan2b2) => 77.50/10.55 (( 77.50/10.55 (demorgan2b) => 77.50/10.55 (( 77.50/10.55 (demorgan2) => 77.50/10.55 (( 77.50/10.55 (woz13rule0) => 77.50/10.55 (( 77.50/10.55 (woz13rule1) => 77.50/10.55 (( 77.50/10.55 (woz13rule2) => 77.50/10.55 (( 77.50/10.55 (woz13rule3) => 77.50/10.55 (( 77.50/10.55 (woz13rule4) => 77.50/10.55 (( 77.50/10.55 (woz1_1) => 77.50/10.55 (( 77.50/10.55 (woz1_2) => 77.50/10.55 (( 77.50/10.55 (woz1_3) => 77.50/10.55 (( 77.50/10.55 (woz1_4) => 77.50/10.55 (( 77.50/10.55 (woz1_5) => 77.50/10.55 (( 77.50/10.55 (breln1all2) => 77.50/10.55 (( 77.50/10.55 (breln1SetBreln1) => 77.50/10.55 (( 77.50/10.55 (choice2fnsingleton) => 77.50/10.55 (( 77.50/10.55 (setOfPairsIsBReln1) => 77.50/10.55 (( 77.50/10.55 (breln1all1) => 77.50/10.55 (( 77.50/10.55 (subbreln1) => 77.50/10.55 (( 77.50/10.55 (eqbreln1) => 77.50/10.55 (( 77.50/10.55 (breln1invprop) => 77.50/10.55 (( 77.50/10.55 (breln1invI) => 77.50/10.55 (( 77.50/10.55 (breln1invE) => 77.50/10.55 (( 77.50/10.55 (breln1compprop) => 77.50/10.55 (( 77.50/10.55 (breln1compI) => 77.50/10.55 (( 77.50/10.55 (breln1compE) => 77.50/10.55 (( 77.50/10.55 (breln1compEex) => 77.50/10.55 (( 77.50/10.55 (breln1unionprop) => 77.50/10.55 (( 77.50/10.55 (breln1unionIL) => 77.50/10.55 (( 77.50/10.55 (breln1unionIR) => 77.50/10.55 (( 77.50/10.55 (breln1unionI) => 77.50/10.55 (( 77.50/10.55 (breln1unionE) => 77.50/10.55 (( 77.50/10.55 (breln1unionEcases) => 77.50/10.55 (( 77.50/10.55 (breln1unionCommutes) => 77.50/10.55 (( 77.50/10.55 (woz2Ex) => 77.50/10.55 (( 77.50/10.55 (woz2W) => 77.50/10.55 (( 77.50/10.55 (woz2A) => 77.50/10.55 (( 77.50/10.55 (woz2B) => 77.50/10.55 (( 77.50/10.55 (image1Ex) => 77.50/10.55 (( 77.50/10.55 (image1Ex1) => 77.50/10.55 (( 77.50/10.55 (image1Equiv) => 77.50/10.55 (( 77.50/10.55 (image1E) => 77.50/10.55 (( 77.50/10.55 (image1I) => 77.50/10.55 (( 77.50/10.55 (injFuncInInjFuncSet) => 77.50/10.55 (( 77.50/10.55 (injFuncSetFuncIn) => 77.50/10.55 (( 77.50/10.55 (injFuncSetFuncInj) => 77.50/10.55 (( 77.50/10.55 (surjFuncSetFuncIn) => 77.50/10.55 (( 77.50/10.55 (surjFuncSetFuncSurj) => 77.50/10.55 (( 77.50/10.55 (leftInvIsSurj) => 77.50/10.55 (( 77.50/10.55 (surjCantorThm) => 77.50/10.55 (( 77.50/10.55 (foundation2) => 77.50/10.55 (( 77.50/10.55 (notinself) => 77.50/10.55 (( 77.50/10.55 (notinself2) => 77.50/10.55 (( 77.50/10.55 (omegaSp) => 77.50/10.55 (( 77.50/10.55 (omegaSclos) => 77.50/10.55 (( 77.50/10.55 (peano0notS) => 77.50/10.55 (( 77.50/10.55 (peanoSinj) => 77.50/10.55 (( 77.50/10.55 (transitivesetOp1) => 77.50/10.55 (( 77.50/10.55 (binintTransitive) => 77.50/10.55 (( 77.50/10.55 (transitivesetOp2) => 77.50/10.55 (( 77.50/10.55 (setunionTransitive) => 77.50/10.55 (( 77.50/10.55 (ordinalMinLem1) => 77.50/10.55 (( 77.50/10.55 (!!) @ ( 77.50/10.55 ^[Y0 : $i]: 77.50/10.55 (( 77.50/10.55 (ordinal @ 77.50/10.55 Y0) => 77.50/10.55 (( 77.50/10.55 (!!) @ ( 77.50/10.55 ^[Y1 : $i]: 77.50/10.55 (( 77.50/10.55 (!!) @ ( 77.50/10.55 ^[Y2 : $i]: 77.50/10.55 (( 77.50/10.55 (in @ 77.50/10.55 Y2 @ 77.50/10.55 Y0) => 77.50/10.55 (( 77.50/10.55 (in @ 77.50/10.55 Y1 @ 77.50/10.55 Y2) => 77.50/10.55 (in @ 77.50/10.55 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 77.50/10.55 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl34])). 77.50/10.55 thf(zip_derived_cl45, plain, 77.50/10.55 (~ (((foundationAx) => 77.50/10.55 (((wellorderingAx) => 77.50/10.55 (((descrp) => 77.50/10.55 (((dsetconstrI) => 77.50/10.55 (((dsetconstrEL) => 77.50/10.55 (((dsetconstrER) => 77.50/10.55 (((exuE1) => 77.50/10.55 (((prop2setE) => 77.50/10.55 (((emptysetE) => 77.50/10.55 (((emptysetimpfalse) => 77.50/10.55 (((notinemptyset) => 77.50/10.55 (((exuE3e) => 77.50/10.55 (((setext) => 77.50/10.55 (((emptyI) => 77.50/10.55 (((noeltsimpempty) => 77.50/10.55 (((setbeta) => 77.50/10.55 (((nonemptyE1) => 77.50/10.55 (((nonemptyI) => 77.50/10.55 (((nonemptyI1) => 77.50/10.55 (((setadjoinIL) => 77.50/10.55 (((in @ emptyset @ 77.50/10.55 (setadjoin @ emptyset @ 77.50/10.55 emptyset)) => 77.50/10.55 (((setadjoinIR) => 77.50/10.55 (((setadjoinE) => 77.50/10.55 (((setadjoinOr) => 77.50/10.55 (((setoftrueEq) => 77.50/10.55 (((powersetI) => 77.50/10.55 (((emptyinPowerset) => 77.50/10.55 (((emptyInPowerset) => 77.50/10.55 (((powersetE) => 77.50/10.55 (((setunionI) => 77.50/10.55 (( 77.50/10.55 (setunionE) => 77.50/10.55 (( 77.50/10.55 (subPowSU) => 77.50/10.55 (( 77.50/10.55 (exuE2) => 77.50/10.55 (( 77.50/10.55 (nonemptyImpWitness) => 77.50/10.55 (( 77.50/10.55 (uniqinunit) => 77.50/10.55 (( 77.50/10.55 (notinsingleton) => 77.50/10.55 (( 77.50/10.55 (eqinunit) => 77.50/10.55 (( 77.50/10.55 (singletonsswitch) => 77.50/10.55 (( 77.50/10.55 (upairsetE) => 77.50/10.55 (( 77.50/10.55 (upairsetIL) => 77.50/10.55 (( 77.50/10.55 (upairsetIR) => 77.50/10.55 (( 77.50/10.55 (emptyE1) => 77.50/10.55 (( 77.50/10.55 (vacuousDall) => 77.50/10.55 (( 77.50/10.55 (quantDeMorgan1) => 77.50/10.55 (( 77.50/10.55 (quantDeMorgan2) => 77.50/10.55 (( 77.50/10.55 (quantDeMorgan3) => 77.50/10.55 (( 77.50/10.55 (quantDeMorgan4) => 77.50/10.55 (( 77.50/10.55 (prop2setI) => 77.50/10.55 (( 77.50/10.55 (prop2set2propI) => 77.50/10.55 (( 77.50/10.55 (notdexE) => 77.50/10.55 (( 77.50/10.55 (notdallE) => 77.50/10.55 (( 77.50/10.55 (exuI1) => 77.50/10.55 (( 77.50/10.55 (exuI3) => 77.50/10.55 (( 77.50/10.55 (exuI2) => 77.50/10.55 (( 77.50/10.55 (inCongP) => 77.50/10.55 (( 77.50/10.55 (in__Cong) => 77.50/10.55 (( 77.50/10.55 (exuE3u) => 77.50/10.55 (( 77.50/10.55 (exu__Cong) => 77.50/10.55 (( 77.50/10.55 (setadjoin__Cong) => 77.50/10.55 (( 77.50/10.55 (powerset__Cong) => 77.50/10.55 (( 77.50/10.55 (setunion__Cong) => 77.50/10.55 (( 77.50/10.55 (exuEu) => 77.50/10.55 (( 77.50/10.55 (descr__Cong) => 77.50/10.55 (( 77.50/10.55 (dsetconstr__Cong) => 77.50/10.55 (( 77.50/10.55 (subsetI1) => 77.50/10.55 (( 77.50/10.55 (eqimpsubset2) => 77.50/10.55 (( 77.50/10.55 (eqimpsubset1) => 77.50/10.55 (( 77.50/10.55 (subsetI2) => 77.50/10.55 (( 77.50/10.55 (emptysetsubset) => 77.50/10.55 (( 77.50/10.55 (subsetE) => 77.50/10.55 (( 77.50/10.55 (subsetE2) => 77.50/10.55 (( 77.50/10.55 (notsubsetI) => 77.50/10.55 (( 77.50/10.55 (notequalI1) => 77.50/10.55 (( 77.50/10.55 (notequalI2) => 77.50/10.55 (( 77.50/10.55 (subsetRefl) => 77.50/10.55 (( 77.50/10.55 (subsetTrans) => 77.50/10.55 (( 77.50/10.55 (setadjoinSub) => 77.50/10.55 (( 77.50/10.55 (setadjoinSub2) => 77.50/10.55 (( 77.50/10.55 (subset2powerset) => 77.50/10.55 (( 77.50/10.55 (setextsub) => 77.50/10.55 (( 77.50/10.55 (subsetemptysetimpeq) => 77.50/10.55 (( 77.50/10.55 (powersetI1) => 77.50/10.55 (( 77.50/10.55 (powersetE1) => 77.50/10.55 (( 77.50/10.55 (inPowerset) => 77.50/10.55 (( 77.50/10.55 (powersetsubset) => 77.50/10.55 (( 77.50/10.55 (sepInPowerset) => 77.50/10.55 (( 77.50/10.55 (sepSubset) => 77.50/10.55 (( 77.50/10.55 (binunionIL) => 77.50/10.55 (( 77.50/10.55 (upairset2IR) => 77.50/10.55 (( 77.50/10.55 (binunionIR) => 77.50/10.55 (( 77.50/10.55 (binunionEcases) => 77.50/10.55 (( 77.50/10.55 (binunionE) => 77.50/10.55 (( 77.50/10.55 (binunionLsub) => 77.50/10.55 (( 77.50/10.55 (binunionRsub) => 77.50/10.55 (( 77.50/10.55 (binintersectI) => 77.50/10.55 (( 77.50/10.55 (binintersectSubset5) => 77.50/10.55 (( 77.50/10.55 (binintersectEL) => 77.50/10.55 (( 77.50/10.55 (binintersectLsub) => 77.50/10.55 (( 77.50/10.55 (binintersectSubset2) => 77.50/10.55 (( 77.50/10.55 (binintersectSubset3) => 77.50/10.55 (( 77.50/10.55 (binintersectER) => 77.50/10.55 (( 77.50/10.55 (disjointsetsI1) => 77.50/10.55 (( 77.50/10.55 (binintersectRsub) => 77.50/10.55 (( 77.50/10.55 (binintersectSubset4) => 77.50/10.55 (( 77.50/10.55 (binintersectSubset1) => 77.50/10.55 (( 77.50/10.55 (bs114d) => 77.50/10.55 (( 77.50/10.55 (setminusI) => 77.50/10.55 (( 77.50/10.55 (setminusEL) => 77.50/10.55 (( 77.50/10.55 (setminusER) => 77.50/10.55 (( 77.50/10.55 (setminusSubset2) => 77.50/10.55 (( 77.50/10.55 (setminusERneg) => 77.50/10.55 (( 77.50/10.55 (setminusELneg) => 77.50/10.55 (( 77.50/10.55 (setminusILneg) => 77.50/10.55 (( 77.50/10.55 (setminusIRneg) => 77.50/10.55 (( 77.50/10.55 (setminusLsub) => 77.50/10.55 (( 77.50/10.55 (setminusSubset1) => 77.50/10.55 (( 77.50/10.55 (symdiffE) => 77.50/10.55 (( 77.50/10.55 (symdiffI1) => 77.50/10.55 (( 77.50/10.55 (symdiffI2) => 77.50/10.55 (( 77.50/10.55 (symdiffIneg1) => 77.50/10.55 (( 77.50/10.55 (symdiffIneg2) => 77.50/10.55 (( 77.50/10.55 (secondinupair) => 77.50/10.55 (( 77.50/10.55 (setukpairIL) => 77.50/10.55 (( 77.50/10.55 (setukpairIR) => 77.50/10.55 (( 77.50/10.55 (kpairiskpair) => 77.50/10.55 (( 77.50/10.55 (kpairp) => 77.50/10.55 (( 77.50/10.55 (singletonsubset) => 77.50/10.55 (( 77.50/10.55 (singletoninpowerset) => 77.50/10.55 (( 77.50/10.55 (singletoninpowunion) => 77.50/10.55 (( 77.50/10.55 (upairset2E) => 77.50/10.55 (( 77.50/10.55 (upairsubunion) => 77.50/10.55 (( 77.50/10.55 (upairinpowunion) => 77.50/10.55 (( 77.50/10.55 (ubforcartprodlem1) => 77.50/10.55 (( 77.50/10.55 (ubforcartprodlem2) => 77.50/10.55 (( 77.50/10.55 (ubforcartprodlem3) => 77.50/10.55 (( 77.50/10.55 (cartprodpairin) => 77.50/10.55 (( 77.50/10.55 (cartprodmempair1) => 77.50/10.55 (( 77.50/10.55 (cartprodmempair) => 77.50/10.55 (( 77.50/10.55 (setunionE2) => 77.50/10.55 (( 77.50/10.55 (setunionsingleton1) => 77.50/10.55 (( 77.50/10.55 (setunionsingleton2) => 77.50/10.55 (( 77.50/10.55 (setunionsingleton) => 77.50/10.55 (( 77.50/10.55 (singletonprop) => 77.50/10.55 (( 77.50/10.55 (ex1E1) => 77.50/10.55 (( 77.50/10.55 (ex1I) => 77.50/10.55 (( 77.50/10.55 (ex1I2) => 77.50/10.55 (( 77.50/10.55 (singletonsuniq) => 77.50/10.55 (( 77.50/10.55 (setukpairinjL1) => 77.50/10.55 (( 77.50/10.55 (kfstsingleton) => 77.50/10.55 (( 77.50/10.55 (theprop) => 77.50/10.55 (( 77.50/10.55 (kfstpairEq) => 77.50/10.55 (( 77.50/10.55 (cartprodfstin) => 77.50/10.55 (( 77.50/10.55 (setukpairinjL2) => 77.50/10.55 (( 77.50/10.55 (setukpairinjL) => 77.50/10.55 (( 77.50/10.55 (setukpairinjR11) => 77.50/10.55 (( 77.50/10.55 (setukpairinjR12) => 77.50/10.55 (( 77.50/10.55 (setukpairinjR1) => 77.50/10.55 (( 77.50/10.55 (upairequniteq) => 77.50/10.55 (( 77.50/10.55 (setukpairinjR2) => 77.50/10.55 (( 77.50/10.55 (setukpairinjR) => 77.50/10.55 (( 77.50/10.55 (ksndsingleton) => 77.50/10.55 (( 77.50/10.55 (ksndpairEq) => 77.50/10.55 (( 77.50/10.55 (kpairsurjEq) => 77.50/10.55 (( 77.50/10.55 (cartprodsndin) => 77.50/10.55 (( 77.50/10.55 (cartprodpairmemEL) => 77.50/10.55 (( 77.50/10.55 (cartprodpairmemER) => 77.50/10.55 (( 77.50/10.55 (cartprodmempaircEq) => 77.50/10.55 (( 77.50/10.55 (cartprodfstpairEq) => 77.50/10.55 (( 77.50/10.55 (cartprodsndpairEq) => 77.50/10.55 (( 77.50/10.55 (cartprodpairsurjEq) => 77.50/10.55 (( 77.50/10.55 (dpsetconstrI) => 77.50/10.55 (( 77.50/10.55 (dpsetconstrSub) => 77.50/10.55 (( 77.50/10.55 (setOfPairsIsBReln) => 77.50/10.55 (( 77.50/10.55 (dpsetconstrERa) => 77.50/10.55 (( 77.50/10.55 (dpsetconstrEL1) => 77.50/10.55 (( 77.50/10.55 (dpsetconstrEL2) => 77.50/10.55 (( 77.50/10.55 (dpsetconstrER) => 77.50/10.55 (( 77.50/10.55 (funcImageSingleton) => 77.50/10.55 (( 77.50/10.55 (apProp) => 77.50/10.55 (( 77.50/10.55 (app) => 77.50/10.55 (( 77.50/10.55 (infuncsetfunc) => 77.50/10.55 (( 77.50/10.55 (ap2p) => 77.50/10.55 (( 77.50/10.55 (funcinfuncset) => 77.50/10.55 (( 77.50/10.55 (lamProp) => 77.50/10.55 (( 77.50/10.55 (lamp) => 77.50/10.55 (( 77.50/10.55 (lam2p) => 77.50/10.55 (( 77.50/10.55 (brelnall1) => 77.50/10.55 (( 77.50/10.55 (brelnall2) => 77.50/10.55 (( 77.50/10.55 (ex1E2) => 77.50/10.55 (( 77.50/10.55 (funcGraphProp1) => 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77.50/10.55 (doubleComplementEq) => 77.50/10.55 (( 77.50/10.55 (complementTnotintersectT) => 77.50/10.55 (( 77.50/10.55 (complementImpComplementIntersect) => 77.50/10.55 (( 77.50/10.55 (complementSubsetComplementIntersect) => 77.50/10.55 (( 77.50/10.55 (complementInPowersetComplementIntersect) => 77.50/10.55 (( 77.50/10.55 (contraSubsetComplement) => 77.50/10.55 (( 77.50/10.55 (complementTcontraSubset) => 77.50/10.55 (( 77.50/10.55 (binunionTILcontra) => 77.50/10.55 (( 77.50/10.55 (binunionTIRcontra) => 77.50/10.55 (( 77.50/10.55 (inIntersectImpInUnion) => 77.50/10.55 (( 77.50/10.55 (inIntersectImpInUnion2) => 77.50/10.55 (( 77.50/10.55 (inIntersectImpInIntersectUnions) => 77.50/10.55 (( 77.50/10.55 (intersectInPowersetIntersectUnions) => 77.50/10.55 (( 77.50/10.55 (inComplementUnionImpNotIn1) => 77.50/10.55 (( 77.50/10.55 (inComplementUnionImpInComplement1) => 77.50/10.55 (( 77.50/10.55 (binunionTE) => 77.50/10.55 (( 77.50/10.55 (binunionTEcontra) => 77.50/10.55 (( 77.50/10.55 (demorgan2a1) => 77.50/10.55 (( 77.50/10.55 (complementUnionInPowersetComplement) => 77.50/10.55 (( 77.50/10.55 (demorgan2a2) => 77.50/10.55 (( 77.50/10.55 (demorgan1a) => 77.50/10.55 (( 77.50/10.55 (demorgan1b) => 77.50/10.55 (( 77.50/10.55 (demorgan1) => 77.50/10.55 (( 77.50/10.55 (demorgan2a) => 77.50/10.55 (( 77.50/10.55 (demorgan2b2) => 77.50/10.55 (( 77.50/10.55 (demorgan2b) => 77.50/10.55 (( 77.50/10.55 (demorgan2) => 77.50/10.55 (( 77.50/10.55 (woz13rule0) => 77.50/10.55 (( 77.50/10.55 (woz13rule1) => 77.50/10.55 (( 77.50/10.55 (woz13rule2) => 77.50/10.55 (( 77.50/10.55 (woz13rule3) => 77.50/10.55 (( 77.50/10.55 (woz13rule4) => 77.50/10.55 (( 77.50/10.55 (woz1_1) => 77.50/10.55 (( 77.50/10.55 (woz1_2) => 77.50/10.55 (( 77.50/10.55 (woz1_3) => 77.50/10.55 (( 77.50/10.55 (woz1_4) => 77.50/10.55 (( 77.50/10.55 (woz1_5) => 77.50/10.55 (( 77.50/10.55 (breln1all2) => 77.50/10.55 (( 77.50/10.55 (breln1SetBreln1) => 77.50/10.55 (( 77.50/10.55 (choice2fnsingleton) => 77.50/10.55 (( 77.50/10.55 (setOfPairsIsBReln1) => 77.50/10.55 (( 77.50/10.55 (breln1all1) => 77.50/10.55 (( 77.50/10.55 (subbreln1) => 77.50/10.55 (( 77.50/10.55 (eqbreln1) => 77.50/10.55 (( 77.50/10.55 (breln1invprop) => 77.50/10.55 (( 77.50/10.55 (breln1invI) => 77.50/10.55 (( 77.50/10.55 (breln1invE) => 77.50/10.55 (( 77.50/10.55 (breln1compprop) => 77.50/10.55 (( 77.50/10.55 (breln1compI) => 77.50/10.55 (( 77.50/10.55 (breln1compE) => 77.50/10.55 (( 77.50/10.55 (breln1compEex) => 77.50/10.55 (( 77.50/10.55 (breln1unionprop) => 77.50/10.55 (( 77.50/10.55 (breln1unionIL) => 77.50/10.55 (( 77.50/10.55 (breln1unionIR) => 77.50/10.55 (( 77.50/10.55 (breln1unionI) => 77.50/10.55 (( 77.50/10.55 (breln1unionE) => 77.50/10.55 (( 77.50/10.55 (breln1unionEcases) => 77.50/10.55 (( 77.50/10.55 (breln1unionCommutes) => 77.50/10.55 (( 77.50/10.55 (woz2Ex) => 77.50/10.55 (( 77.50/10.55 (woz2W) => 77.50/10.55 (( 77.50/10.55 (woz2A) => 77.50/10.55 (( 77.50/10.55 (woz2B) => 77.50/10.55 (( 77.50/10.55 (image1Ex) => 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(setunionTransitive) => 77.50/10.55 (( 77.50/10.55 (ordinalMinLem1) => 77.50/10.55 (( 77.50/10.55 (!!) @ ( 77.50/10.55 ^[Y0 : $i]: 77.50/10.55 (( 77.50/10.55 (ordinal @ 77.50/10.55 Y0) => 77.50/10.55 (( 77.50/10.55 (!!) @ ( 77.50/10.55 ^[Y1 : $i]: 77.50/10.55 (( 77.50/10.55 (!!) @ ( 77.50/10.55 ^[Y2 : $i]: 77.50/10.55 (( 77.50/10.55 (in @ 77.50/10.55 Y2 @ 77.50/10.55 Y0) => 77.50/10.55 (( 77.50/10.55 (in @ 77.50/10.55 Y1 @ 77.50/10.55 Y2) => 77.50/10.55 (in @ 77.50/10.55 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 77.50/10.55 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl45])). 77.50/10.55 thf(zip_derived_cl56, plain, 77.50/10.55 (~ (((descrp) => 77.50/10.55 (((dsetconstrI) => 77.50/10.55 (((dsetconstrEL) => 77.50/10.55 (((dsetconstrER) => 77.50/10.55 (((exuE1) => 77.50/10.55 (((prop2setE) => 77.50/10.55 (((emptysetE) => 77.50/10.55 (((emptysetimpfalse) => 77.50/10.55 (((notinemptyset) => 77.50/10.55 (((exuE3e) => 77.50/10.55 (((setext) => 77.50/10.55 (((emptyI) => 77.50/10.55 (((noeltsimpempty) => 77.50/10.55 (((setbeta) => 77.50/10.55 (((nonemptyE1) => 77.50/10.55 (((nonemptyI) => 77.50/10.55 (((nonemptyI1) => 77.50/10.55 (((setadjoinIL) => 77.50/10.55 (((in @ emptyset @ 77.50/10.55 (setadjoin @ emptyset @ emptyset)) => 77.50/10.55 (((setadjoinIR) => 77.50/10.55 (((setadjoinE) => 77.50/10.55 (((setadjoinOr) => 77.50/10.55 (((setoftrueEq) => 77.50/10.55 (((powersetI) => 77.50/10.55 (((emptyinPowerset) => 77.50/10.55 (((emptyInPowerset) => 77.50/10.55 (((powersetE) => 77.50/10.55 (((setunionI) => 77.50/10.55 (((setunionE) => 77.50/10.55 (((subPowSU) => 77.50/10.55 (( 77.50/10.55 (exuE2) => 77.50/10.55 (( 77.50/10.55 (nonemptyImpWitness) => 77.50/10.55 (( 77.50/10.55 (uniqinunit) => 77.50/10.55 (( 77.50/10.55 (notinsingleton) => 77.50/10.55 (( 77.50/10.55 (eqinunit) => 77.50/10.55 (( 77.50/10.55 (singletonsswitch) => 77.50/10.55 (( 77.50/10.55 (upairsetE) => 77.50/10.55 (( 77.50/10.55 (upairsetIL) => 77.50/10.55 (( 77.50/10.55 (upairsetIR) => 77.50/10.55 (( 77.50/10.55 (emptyE1) => 77.50/10.55 (( 77.50/10.55 (vacuousDall) => 77.50/10.55 (( 77.50/10.55 (quantDeMorgan1) => 77.50/10.55 (( 77.50/10.55 (quantDeMorgan2) => 77.50/10.55 (( 77.50/10.55 (quantDeMorgan3) => 77.50/10.55 (( 77.50/10.55 (quantDeMorgan4) => 77.50/10.55 (( 77.50/10.55 (prop2setI) => 77.50/10.55 (( 77.50/10.55 (prop2set2propI) => 77.50/10.55 (( 77.50/10.55 (notdexE) => 77.50/10.55 (( 77.50/10.55 (notdallE) => 77.50/10.55 (( 77.50/10.55 (exuI1) => 77.50/10.55 (( 77.50/10.55 (exuI3) => 77.50/10.55 (( 77.50/10.55 (exuI2) => 77.50/10.55 (( 77.50/10.55 (inCongP) => 77.50/10.55 (( 77.50/10.55 (in__Cong) => 77.50/10.55 (( 77.50/10.55 (exuE3u) => 77.50/10.55 (( 77.50/10.55 (exu__Cong) => 77.50/10.55 (( 77.50/10.55 (setadjoin__Cong) => 77.50/10.55 (( 77.50/10.55 (powerset__Cong) => 77.50/10.55 (( 77.50/10.55 (setunion__Cong) => 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(inPowerset) => 77.50/10.55 (( 77.50/10.55 (powersetsubset) => 77.50/10.55 (( 77.50/10.55 (sepInPowerset) => 77.50/10.55 (( 77.50/10.55 (sepSubset) => 77.50/10.55 (( 77.50/10.55 (binunionIL) => 77.50/10.55 (( 77.50/10.55 (upairset2IR) => 77.50/10.55 (( 77.50/10.55 (binunionIR) => 77.50/10.55 (( 77.50/10.55 (binunionEcases) => 77.50/10.55 (( 77.50/10.55 (binunionE) => 77.50/10.55 (( 77.50/10.55 (binunionLsub) => 77.50/10.55 (( 77.50/10.55 (binunionRsub) => 77.50/10.55 (( 77.50/10.55 (binintersectI) => 77.50/10.55 (( 77.50/10.55 (binintersectSubset5) => 77.50/10.55 (( 77.50/10.55 (binintersectEL) => 77.50/10.55 (( 77.50/10.55 (binintersectLsub) => 77.50/10.55 (( 77.50/10.55 (binintersectSubset2) => 77.50/10.55 (( 77.50/10.55 (binintersectSubset3) => 77.50/10.55 (( 77.50/10.55 (binintersectER) => 77.50/10.55 (( 77.50/10.55 (disjointsetsI1) => 77.50/10.55 (( 77.50/10.55 (binintersectRsub) => 77.50/10.55 (( 77.50/10.55 (binintersectSubset4) => 77.50/10.55 (( 77.50/10.55 (binintersectSubset1) => 77.50/10.55 (( 77.50/10.55 (bs114d) => 77.50/10.55 (( 77.50/10.55 (setminusI) => 77.50/10.55 (( 77.50/10.55 (setminusEL) => 77.50/10.55 (( 77.50/10.55 (setminusER) => 77.50/10.55 (( 77.50/10.55 (setminusSubset2) => 77.50/10.55 (( 77.50/10.55 (setminusERneg) => 77.50/10.55 (( 77.50/10.55 (setminusELneg) => 77.50/10.55 (( 77.50/10.55 (setminusILneg) => 77.50/10.55 (( 77.50/10.55 (setminusIRneg) => 77.50/10.55 (( 77.50/10.55 (setminusLsub) => 77.50/10.55 (( 77.50/10.55 (setminusSubset1) => 77.50/10.55 (( 77.50/10.55 (symdiffE) => 77.50/10.55 (( 77.50/10.55 (symdiffI1) => 77.50/10.55 (( 77.50/10.55 (symdiffI2) => 77.50/10.55 (( 77.50/10.55 (symdiffIneg1) => 77.50/10.55 (( 77.50/10.55 (symdiffIneg2) => 77.50/10.55 (( 77.50/10.55 (secondinupair) => 77.50/10.55 (( 77.50/10.55 (setukpairIL) => 77.50/10.55 (( 77.50/10.55 (setukpairIR) => 77.50/10.55 (( 77.50/10.55 (kpairiskpair) => 77.50/10.55 (( 77.50/10.55 (kpairp) => 77.50/10.55 (( 77.50/10.55 (singletonsubset) => 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77.50/10.55 (kfstsingleton) => 77.50/10.55 (( 77.50/10.55 (theprop) => 77.50/10.55 (( 77.50/10.55 (kfstpairEq) => 77.50/10.55 (( 77.50/10.55 (cartprodfstin) => 77.50/10.55 (( 77.50/10.55 (setukpairinjL2) => 77.50/10.55 (( 77.50/10.55 (setukpairinjL) => 77.50/10.55 (( 77.50/10.55 (setukpairinjR11) => 77.50/10.55 (( 77.50/10.55 (setukpairinjR12) => 77.50/10.55 (( 77.50/10.55 (setukpairinjR1) => 77.50/10.55 (( 77.50/10.55 (upairequniteq) => 77.50/10.55 (( 77.50/10.55 (setukpairinjR2) => 77.50/10.55 (( 77.50/10.55 (setukpairinjR) => 77.50/10.55 (( 77.50/10.55 (ksndsingleton) => 77.50/10.55 (( 77.50/10.55 (ksndpairEq) => 77.50/10.55 (( 77.50/10.55 (kpairsurjEq) => 77.50/10.55 (( 77.50/10.55 (cartprodsndin) => 77.50/10.55 (( 77.50/10.55 (cartprodpairmemEL) => 77.50/10.55 (( 77.50/10.55 (cartprodpairmemER) => 77.50/10.55 (( 77.50/10.55 (cartprodmempaircEq) => 77.50/10.55 (( 77.50/10.55 (cartprodfstpairEq) => 77.50/10.55 (( 77.50/10.55 (cartprodsndpairEq) => 77.50/10.55 (( 77.50/10.55 (cartprodpairsurjEq) => 77.50/10.55 (( 77.50/10.55 (dpsetconstrI) => 77.50/10.55 (( 77.50/10.55 (dpsetconstrSub) => 77.50/10.55 (( 77.50/10.55 (setOfPairsIsBReln) => 77.50/10.55 (( 77.50/10.55 (dpsetconstrERa) => 77.50/10.55 (( 77.50/10.55 (dpsetconstrEL1) => 77.50/10.55 (( 77.50/10.55 (dpsetconstrEL2) => 77.50/10.55 (( 77.50/10.55 (dpsetconstrER) => 77.50/10.55 (( 77.50/10.55 (funcImageSingleton) => 77.50/10.55 (( 77.50/10.55 (apProp) => 77.50/10.55 (( 77.50/10.55 (app) => 77.50/10.55 (( 77.50/10.55 (infuncsetfunc) => 77.50/10.55 (( 77.50/10.55 (ap2p) => 77.50/10.55 (( 77.50/10.55 (funcinfuncset) => 77.50/10.55 (( 77.50/10.55 (lamProp) => 77.50/10.55 (( 77.50/10.55 (lamp) => 77.50/10.55 (( 77.50/10.55 (lam2p) => 77.50/10.55 (( 77.50/10.55 (brelnall1) => 77.50/10.55 (( 77.50/10.55 (brelnall2) => 77.50/10.55 (( 77.50/10.55 (ex1E2) => 77.50/10.55 (( 77.50/10.55 (funcGraphProp1) => 77.50/10.55 (( 77.50/10.55 (funcGraphProp3) => 77.50/10.55 (( 77.50/10.55 (funcGraphProp2) => 77.50/10.55 (( 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77.50/10.55 (binunionT_lem) => 77.50/10.55 (( 77.50/10.55 (powersetT_lem) => 77.50/10.55 (( 77.50/10.55 (setminusT_lem) => 77.50/10.55 (( 77.50/10.55 (complementT_lem) => 77.50/10.55 (( 77.50/10.55 (setextT) => 77.50/10.55 (( 77.50/10.55 (subsetTI) => 77.50/10.55 (( 77.50/10.55 (powersetTI1) => 77.50/10.55 (( 77.50/10.55 (powersetTE1) => 77.50/10.55 (( 77.50/10.55 (complementTI1) => 77.50/10.55 (( 77.50/10.55 (complementTE1) => 77.50/10.55 (( 77.50/10.55 (binintersectTELcontra) => 77.50/10.55 (( 77.50/10.55 (binintersectTERcontra) => 77.50/10.55 (( 77.50/10.55 (contrasubsetT) => 77.50/10.55 (( 77.50/10.55 (contrasubsetT1) => 77.50/10.55 (( 77.50/10.55 (contrasubsetT2) => 77.50/10.55 (( 77.50/10.55 (contrasubsetT3) => 77.50/10.55 (( 77.50/10.55 (doubleComplementI1) => 77.50/10.55 (( 77.50/10.55 (doubleComplementE1) => 77.50/10.55 (( 77.50/10.55 (doubleComplementSub1) => 77.50/10.55 (( 77.50/10.55 (doubleComplementSub2) => 77.50/10.55 (( 77.50/10.55 (doubleComplementEq) => 77.50/10.55 (( 77.50/10.55 (complementTnotintersectT) => 77.50/10.55 (( 77.50/10.55 (complementImpComplementIntersect) => 77.50/10.55 (( 77.50/10.55 (complementSubsetComplementIntersect) => 77.50/10.55 (( 77.50/10.55 (complementInPowersetComplementIntersect) => 77.50/10.55 (( 77.50/10.55 (contraSubsetComplement) => 77.50/10.55 (( 77.50/10.55 (complementTcontraSubset) => 77.50/10.55 (( 77.50/10.55 (binunionTILcontra) => 77.50/10.55 (( 77.50/10.55 (binunionTIRcontra) => 77.50/10.55 (( 77.50/10.55 (inIntersectImpInUnion) => 77.50/10.55 (( 77.50/10.55 (inIntersectImpInUnion2) => 77.50/10.55 (( 77.50/10.55 (inIntersectImpInIntersectUnions) => 77.50/10.55 (( 77.50/10.55 (intersectInPowersetIntersectUnions) => 77.50/10.55 (( 77.50/10.55 (inComplementUnionImpNotIn1) => 77.50/10.55 (( 77.50/10.55 (inComplementUnionImpInComplement1) => 77.50/10.55 (( 77.50/10.55 (binunionTE) => 77.50/10.55 (( 77.50/10.55 (binunionTEcontra) => 77.50/10.55 (( 77.50/10.55 (demorgan2a1) => 77.50/10.55 (( 77.50/10.55 (complementUnionInPowersetComplement) => 77.50/10.55 (( 77.50/10.55 (demorgan2a2) => 77.50/10.55 (( 77.50/10.55 (demorgan1a) => 77.50/10.55 (( 77.50/10.55 (demorgan1b) => 77.50/10.55 (( 77.50/10.55 (demorgan1) => 77.50/10.55 (( 77.50/10.55 (demorgan2a) => 77.50/10.55 (( 77.50/10.55 (demorgan2b2) => 77.50/10.55 (( 77.50/10.55 (demorgan2b) => 77.50/10.55 (( 77.50/10.55 (demorgan2) => 77.50/10.55 (( 77.50/10.55 (woz13rule0) => 77.50/10.55 (( 77.50/10.55 (woz13rule1) => 77.50/10.55 (( 77.50/10.55 (woz13rule2) => 77.50/10.55 (( 77.50/10.55 (woz13rule3) => 77.50/10.55 (( 77.50/10.55 (woz13rule4) => 77.50/10.55 (( 77.50/10.55 (woz1_1) => 77.50/10.55 (( 77.50/10.55 (woz1_2) => 77.50/10.55 (( 77.50/10.55 (woz1_3) => 77.50/10.55 (( 77.50/10.55 (woz1_4) => 77.50/10.55 (( 77.50/10.55 (woz1_5) => 77.50/10.55 (( 77.50/10.55 (breln1all2) => 77.50/10.55 (( 77.50/10.55 (breln1SetBreln1) => 77.50/10.55 (( 77.50/10.55 (choice2fnsingleton) => 77.50/10.55 (( 77.50/10.55 (setOfPairsIsBReln1) => 77.50/10.55 (( 77.50/10.55 (breln1all1) => 77.50/10.55 (( 77.50/10.55 (subbreln1) => 77.50/10.55 (( 77.50/10.55 (eqbreln1) => 77.50/10.55 (( 77.50/10.55 (breln1invprop) => 77.50/10.55 (( 77.50/10.55 (breln1invI) => 77.50/10.55 (( 77.50/10.55 (breln1invE) => 77.50/10.55 (( 77.50/10.55 (breln1compprop) => 77.50/10.55 (( 77.50/10.55 (breln1compI) => 77.50/10.55 (( 77.50/10.55 (breln1compE) => 77.50/10.55 (( 77.50/10.55 (breln1compEex) => 77.50/10.55 (( 77.50/10.55 (breln1unionprop) => 77.50/10.55 (( 77.50/10.55 (breln1unionIL) => 77.50/10.55 (( 77.50/10.55 (breln1unionIR) => 77.50/10.55 (( 77.50/10.55 (breln1unionI) => 77.50/10.55 (( 77.50/10.55 (breln1unionE) => 77.50/10.55 (( 77.50/10.55 (breln1unionEcases) => 77.50/10.55 (( 77.50/10.55 (breln1unionCommutes) => 77.50/10.55 (( 77.50/10.55 (woz2Ex) => 77.50/10.55 (( 77.50/10.55 (woz2W) => 77.50/10.55 (( 77.50/10.55 (woz2A) => 77.50/10.55 (( 77.50/10.55 (woz2B) => 77.50/10.55 (( 77.50/10.55 (image1Ex) => 77.50/10.55 (( 77.50/10.55 (image1Ex1) => 77.50/10.55 (( 77.50/10.55 (image1Equiv) => 77.50/10.55 (( 77.50/10.55 (image1E) => 77.50/10.55 (( 77.50/10.55 (image1I) => 77.50/10.55 (( 77.50/10.55 (injFuncInInjFuncSet) => 77.50/10.55 (( 77.50/10.55 (injFuncSetFuncIn) => 77.50/10.55 (( 77.50/10.55 (injFuncSetFuncInj) => 77.50/10.55 (( 77.50/10.55 (surjFuncSetFuncIn) => 77.50/10.55 (( 77.50/10.55 (surjFuncSetFuncSurj) => 77.50/10.55 (( 77.50/10.55 (leftInvIsSurj) => 77.50/10.55 (( 77.50/10.55 (surjCantorThm) => 77.50/10.55 (( 77.50/10.55 (foundation2) => 77.50/10.55 (( 77.50/10.55 (notinself) => 77.50/10.55 (( 77.50/10.55 (notinself2) => 77.50/10.55 (( 77.50/10.55 (omegaSp) => 77.50/10.55 (( 77.50/10.55 (omegaSclos) => 77.50/10.55 (( 77.50/10.55 (peano0notS) => 77.50/10.55 (( 77.50/10.55 (peanoSinj) => 77.50/10.55 (( 77.50/10.55 (transitivesetOp1) => 77.50/10.55 (( 77.50/10.55 (binintTransitive) => 77.50/10.55 (( 77.50/10.55 (transitivesetOp2) => 77.50/10.55 (( 77.50/10.55 (setunionTransitive) => 77.50/10.55 (( 77.50/10.55 (ordinalMinLem1) => 77.50/10.55 (( 77.50/10.55 (!!) @ ( 77.50/10.55 ^[Y0 : $i]: 77.50/10.55 (( 77.50/10.55 (ordinal @ 77.50/10.55 Y0) => 77.50/10.55 (( 77.50/10.55 (!!) @ ( 77.50/10.55 ^[Y1 : $i]: 77.50/10.55 (( 77.50/10.55 (!!) @ ( 77.50/10.55 ^[Y2 : $i]: 77.50/10.55 (( 77.50/10.55 (in @ 77.50/10.55 Y2 @ 77.50/10.55 Y0) => 77.50/10.55 (( 77.50/10.55 (in @ 77.50/10.55 Y1 @ 77.50/10.55 Y2) => 77.50/10.55 (in @ 77.50/10.55 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 77.50/10.55 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl50])). 77.50/10.55 thf(zip_derived_cl62, plain, 77.50/10.55 (~ (((dsetconstrI) => 77.50/10.55 (((dsetconstrEL) => 77.50/10.55 (((dsetconstrER) => 77.50/10.55 (((exuE1) => 77.50/10.55 (((prop2setE) => 77.50/10.55 (((emptysetE) => 77.50/10.55 (((emptysetimpfalse) => 77.50/10.55 (((notinemptyset) => 77.50/10.55 (((exuE3e) => 77.50/10.55 (((setext) => 77.50/10.55 (((emptyI) => 77.50/10.55 (((noeltsimpempty) => 77.50/10.55 (((setbeta) => 77.50/10.55 (((nonemptyE1) => 77.50/10.55 (((nonemptyI) => 77.50/10.55 (((nonemptyI1) => 77.50/10.55 (((setadjoinIL) => 77.50/10.55 (((in @ emptyset @ 77.50/10.55 (setadjoin @ emptyset @ emptyset)) => 77.50/10.55 (((setadjoinIR) => 77.50/10.55 (((setadjoinE) => 77.50/10.55 (((setadjoinOr) => 77.50/10.55 (((setoftrueEq) => 77.50/10.55 (((powersetI) => 77.50/10.55 (((emptyinPowerset) => 77.50/10.55 (((emptyInPowerset) => 77.50/10.55 (((powersetE) => 77.50/10.55 (((setunionI) => 77.50/10.55 (((setunionE) => 77.50/10.55 (((subPowSU) => 77.50/10.55 (((exuE2) => 77.50/10.55 (( 77.50/10.55 (nonemptyImpWitness) => 77.50/10.55 (( 77.50/10.55 (uniqinunit) => 77.50/10.55 (( 77.50/10.55 (notinsingleton) => 77.50/10.55 (( 77.50/10.55 (eqinunit) => 77.50/10.55 (( 77.50/10.55 (singletonsswitch) => 77.50/10.55 (( 77.50/10.55 (upairsetE) => 77.50/10.55 (( 77.50/10.55 (upairsetIL) => 77.50/10.55 (( 77.50/10.55 (upairsetIR) => 77.50/10.55 (( 77.50/10.55 (emptyE1) => 77.50/10.55 (( 77.50/10.55 (vacuousDall) => 77.50/10.55 (( 77.50/10.55 (quantDeMorgan1) => 77.50/10.55 (( 77.50/10.55 (quantDeMorgan2) => 77.50/10.55 (( 77.50/10.55 (quantDeMorgan3) => 77.50/10.55 (( 77.50/10.55 (quantDeMorgan4) => 77.50/10.55 (( 77.50/10.55 (prop2setI) => 77.50/10.55 (( 77.50/10.55 (prop2set2propI) => 77.50/10.55 (( 77.50/10.55 (notdexE) => 77.50/10.55 (( 77.50/10.55 (notdallE) => 77.50/10.55 (( 77.50/10.55 (exuI1) => 77.50/10.55 (( 77.50/10.55 (exuI3) => 77.50/10.55 (( 77.50/10.55 (exuI2) => 77.50/10.55 (( 77.50/10.55 (inCongP) => 77.50/10.55 (( 77.50/10.55 (in__Cong) => 77.50/10.55 (( 77.50/10.55 (exuE3u) => 77.50/10.55 (( 77.50/10.55 (exu__Cong) => 77.50/10.55 (( 77.50/10.55 (setadjoin__Cong) => 77.50/10.55 (( 77.50/10.55 (powerset__Cong) => 77.50/10.55 (( 77.50/10.55 (setunion__Cong) => 77.50/10.55 (( 77.50/10.55 (exuEu) => 77.50/10.55 (( 77.50/10.55 (descr__Cong) => 77.50/10.55 (( 77.50/10.55 (dsetconstr__Cong) => 77.50/10.55 (( 77.50/10.55 (subsetI1) => 77.50/10.55 (( 77.50/10.55 (eqimpsubset2) => 77.50/10.55 (( 77.50/10.55 (eqimpsubset1) => 77.50/10.55 (( 77.50/10.55 (subsetI2) => 77.50/10.55 (( 77.50/10.55 (emptysetsubset) => 77.50/10.55 (( 77.50/10.55 (subsetE) => 77.50/10.55 (( 77.50/10.55 (subsetE2) => 77.50/10.55 (( 77.50/10.55 (notsubsetI) => 77.50/10.55 (( 77.50/10.55 (notequalI1) => 77.50/10.55 (( 77.50/10.55 (notequalI2) => 77.50/10.55 (( 77.50/10.55 (subsetRefl) => 77.50/10.55 (( 77.50/10.55 (subsetTrans) => 77.50/10.55 (( 77.50/10.55 (setadjoinSub) => 77.50/10.55 (( 77.50/10.55 (setadjoinSub2) => 77.50/10.55 (( 77.50/10.55 (subset2powerset) => 77.50/10.55 (( 77.50/10.55 (setextsub) => 77.50/10.55 (( 77.50/10.55 (subsetemptysetimpeq) => 77.50/10.55 (( 77.50/10.55 (powersetI1) => 77.50/10.55 (( 77.50/10.55 (powersetE1) => 77.50/10.55 (( 77.50/10.55 (inPowerset) => 77.50/10.55 (( 77.50/10.55 (powersetsubset) => 77.50/10.55 (( 77.50/10.55 (sepInPowerset) => 77.50/10.55 (( 77.50/10.55 (sepSubset) => 77.50/10.55 (( 77.50/10.55 (binunionIL) => 77.50/10.55 (( 77.50/10.55 (upairset2IR) => 77.50/10.55 (( 77.50/10.55 (binunionIR) => 77.50/10.55 (( 77.50/10.55 (binunionEcases) => 77.50/10.55 (( 77.50/10.55 (binunionE) => 77.50/10.55 (( 77.50/10.55 (binunionLsub) => 77.50/10.55 (( 77.50/10.55 (binunionRsub) => 77.50/10.55 (( 77.50/10.55 (binintersectI) => 77.50/10.55 (( 77.50/10.55 (binintersectSubset5) => 77.50/10.55 (( 77.50/10.55 (binintersectEL) => 77.50/10.55 (( 77.50/10.55 (binintersectLsub) => 77.50/10.55 (( 77.50/10.55 (binintersectSubset2) => 77.50/10.55 (( 77.50/10.55 (binintersectSubset3) => 77.50/10.55 (( 77.50/10.55 (binintersectER) => 77.50/10.55 (( 77.50/10.55 (disjointsetsI1) => 77.50/10.55 (( 77.50/10.55 (binintersectRsub) => 77.50/10.55 (( 77.50/10.55 (binintersectSubset4) => 77.50/10.55 (( 77.50/10.55 (binintersectSubset1) => 77.50/10.55 (( 77.50/10.55 (bs114d) => 77.50/10.55 (( 77.50/10.55 (setminusI) => 77.50/10.55 (( 77.50/10.55 (setminusEL) => 77.50/10.55 (( 77.50/10.55 (setminusER) => 77.50/10.55 (( 77.50/10.55 (setminusSubset2) => 77.50/10.55 (( 77.50/10.55 (setminusERneg) => 77.50/10.55 (( 77.50/10.55 (setminusELneg) => 77.50/10.55 (( 77.50/10.55 (setminusILneg) => 77.50/10.55 (( 77.50/10.55 (setminusIRneg) => 77.50/10.55 (( 77.50/10.55 (setminusLsub) => 77.50/10.55 (( 77.50/10.55 (setminusSubset1) => 77.50/10.55 (( 77.50/10.55 (symdiffE) => 77.50/10.55 (( 77.50/10.55 (symdiffI1) => 77.50/10.55 (( 77.50/10.55 (symdiffI2) => 77.50/10.55 (( 77.50/10.55 (symdiffIneg1) => 77.50/10.55 (( 77.50/10.55 (symdiffIneg2) => 77.50/10.55 (( 77.50/10.55 (secondinupair) => 77.50/10.55 (( 77.50/10.55 (setukpairIL) => 77.50/10.55 (( 77.50/10.55 (setukpairIR) => 77.50/10.55 (( 77.50/10.55 (kpairiskpair) => 77.50/10.55 (( 77.50/10.55 (kpairp) => 77.50/10.55 (( 77.50/10.55 (singletonsubset) => 77.50/10.55 (( 77.50/10.55 (singletoninpowerset) => 77.50/10.55 (( 77.50/10.55 (singletoninpowunion) => 77.50/10.55 (( 77.50/10.55 (upairset2E) => 77.50/10.55 (( 77.50/10.55 (upairsubunion) => 77.50/10.55 (( 77.50/10.55 (upairinpowunion) => 77.50/10.55 (( 77.50/10.55 (ubforcartprodlem1) => 77.50/10.55 (( 77.50/10.55 (ubforcartprodlem2) => 77.50/10.55 (( 77.50/10.55 (ubforcartprodlem3) => 77.50/10.55 (( 77.50/10.55 (cartprodpairin) => 77.50/10.55 (( 77.50/10.55 (cartprodmempair1) => 77.50/10.55 (( 77.50/10.55 (cartprodmempair) => 77.50/10.55 (( 77.50/10.55 (setunionE2) => 77.50/10.55 (( 77.50/10.55 (setunionsingleton1) => 77.50/10.55 (( 77.50/10.55 (setunionsingleton2) => 77.50/10.55 (( 77.50/10.55 (setunionsingleton) => 77.50/10.55 (( 77.50/10.55 (singletonprop) => 77.50/10.55 (( 77.50/10.55 (ex1E1) => 77.50/10.55 (( 77.50/10.55 (ex1I) => 77.50/10.56 (( 77.50/10.56 (ex1I2) => 77.50/10.56 (( 77.50/10.56 (singletonsuniq) => 77.50/10.56 (( 77.50/10.56 (setukpairinjL1) => 77.50/10.56 (( 77.50/10.56 (kfstsingleton) => 77.50/10.56 (( 77.50/10.56 (theprop) => 77.50/10.56 (( 77.50/10.56 (kfstpairEq) => 77.50/10.56 (( 77.50/10.56 (cartprodfstin) => 77.50/10.56 (( 77.50/10.56 (setukpairinjL2) => 77.50/10.56 (( 77.50/10.56 (setukpairinjL) => 77.50/10.56 (( 77.50/10.56 (setukpairinjR11) => 77.50/10.56 (( 77.50/10.56 (setukpairinjR12) => 77.50/10.56 (( 77.50/10.56 (setukpairinjR1) => 77.50/10.56 (( 77.50/10.56 (upairequniteq) => 77.50/10.56 (( 77.50/10.56 (setukpairinjR2) => 77.50/10.56 (( 77.50/10.56 (setukpairinjR) => 77.50/10.56 (( 77.50/10.56 (ksndsingleton) => 77.50/10.56 (( 77.50/10.56 (ksndpairEq) => 77.50/10.56 (( 77.50/10.56 (kpairsurjEq) => 77.50/10.56 (( 77.50/10.56 (cartprodsndin) => 77.50/10.56 (( 77.50/10.56 (cartprodpairmemEL) => 77.50/10.56 (( 77.50/10.56 (cartprodpairmemER) => 77.50/10.56 (( 77.50/10.56 (cartprodmempaircEq) => 77.50/10.56 (( 77.50/10.56 (cartprodfstpairEq) => 77.50/10.56 (( 77.50/10.56 (cartprodsndpairEq) => 77.50/10.56 (( 77.50/10.56 (cartprodpairsurjEq) => 77.50/10.56 (( 77.50/10.56 (dpsetconstrI) => 77.50/10.56 (( 77.50/10.56 (dpsetconstrSub) => 77.50/10.56 (( 77.50/10.56 (setOfPairsIsBReln) => 77.50/10.56 (( 77.50/10.56 (dpsetconstrERa) => 77.50/10.56 (( 77.50/10.56 (dpsetconstrEL1) => 77.50/10.56 (( 77.50/10.56 (dpsetconstrEL2) => 77.50/10.56 (( 77.50/10.56 (dpsetconstrER) => 77.50/10.56 (( 77.50/10.56 (funcImageSingleton) => 77.50/10.56 (( 77.50/10.56 (apProp) => 77.50/10.56 (( 77.50/10.56 (app) => 77.50/10.56 (( 77.50/10.56 (infuncsetfunc) => 77.50/10.56 (( 77.50/10.56 (ap2p) => 77.50/10.56 (( 77.50/10.56 (funcinfuncset) => 77.50/10.56 (( 77.50/10.56 (lamProp) => 77.50/10.56 (( 77.50/10.56 (lamp) => 77.50/10.56 (( 77.50/10.56 (lam2p) => 77.50/10.56 (( 77.50/10.56 (brelnall1) => 77.50/10.56 (( 77.50/10.56 (brelnall2) => 77.50/10.56 (( 77.50/10.56 (ex1E2) => 77.50/10.56 (( 77.50/10.56 (funcGraphProp1) => 77.50/10.56 (( 77.50/10.56 (funcGraphProp3) => 77.50/10.56 (( 77.50/10.56 (funcGraphProp2) => 77.50/10.56 (( 77.50/10.56 (funcextLem) => 77.50/10.56 (( 77.50/10.56 (funcGraphProp4) => 77.50/10.56 (( 77.50/10.56 (subbreln) => 77.50/10.56 (( 77.50/10.56 (eqbreln) => 77.50/10.56 (( 77.50/10.56 (funcext) => 77.50/10.56 (( 77.50/10.56 (funcext2) => 77.50/10.56 (( 77.50/10.56 (ap2apEq1) => 77.50/10.56 (( 77.50/10.56 (ap2apEq2) => 77.50/10.56 (( 77.50/10.56 (beta1) => 77.50/10.56 (( 77.50/10.56 (eta1) => 77.50/10.56 (( 77.50/10.56 (lam2lamEq) => 77.50/10.56 (( 77.50/10.56 (beta2) => 77.50/10.56 (( 77.50/10.56 (eta2) => 77.50/10.56 (( 77.50/10.56 (iffalseProp1) => 77.50/10.56 (( 77.50/10.56 (iffalseProp2) => 77.50/10.56 (( 77.50/10.56 (iftrueProp1) => 77.50/10.56 (( 77.50/10.56 (iftrueProp2) => 77.50/10.56 (( 77.50/10.56 (ifSingleton) => 77.50/10.56 (( 77.50/10.56 (ifp) => 77.50/10.56 (( 77.50/10.56 (theeq) => 77.50/10.56 (( 77.50/10.56 (iftrue) => 77.50/10.56 (( 77.50/10.56 (iffalse) => 77.50/10.56 (( 77.50/10.56 (iftrueorfalse) => 77.50/10.56 (( 77.50/10.56 (binintersectT_lem) => 77.50/10.56 (( 77.50/10.56 (binunionT_lem) => 77.50/10.56 (( 77.50/10.56 (powersetT_lem) => 77.50/10.56 (( 77.50/10.56 (setminusT_lem) => 77.50/10.56 (( 77.50/10.56 (complementT_lem) => 77.50/10.56 (( 77.50/10.56 (setextT) => 77.50/10.56 (( 77.50/10.56 (subsetTI) => 77.50/10.56 (( 77.50/10.56 (powersetTI1) => 77.50/10.56 (( 77.50/10.56 (powersetTE1) => 77.50/10.56 (( 77.50/10.56 (complementTI1) => 77.50/10.56 (( 77.50/10.56 (complementTE1) => 77.50/10.56 (( 77.50/10.56 (binintersectTELcontra) => 77.50/10.56 (( 77.50/10.56 (binintersectTERcontra) => 77.50/10.56 (( 77.50/10.56 (contrasubsetT) => 77.50/10.56 (( 77.50/10.56 (contrasubsetT1) => 77.50/10.56 (( 77.50/10.56 (contrasubsetT2) => 77.50/10.56 (( 77.50/10.56 (contrasubsetT3) => 77.50/10.56 (( 77.50/10.56 (doubleComplementI1) => 77.50/10.56 (( 77.50/10.56 (doubleComplementE1) => 77.50/10.56 (( 77.50/10.56 (doubleComplementSub1) => 77.50/10.56 (( 77.50/10.56 (doubleComplementSub2) => 77.50/10.56 (( 77.50/10.56 (doubleComplementEq) => 77.50/10.56 (( 77.50/10.56 (complementTnotintersectT) => 77.50/10.56 (( 77.50/10.56 (complementImpComplementIntersect) => 77.50/10.56 (( 77.50/10.56 (complementSubsetComplementIntersect) => 77.50/10.56 (( 77.50/10.56 (complementInPowersetComplementIntersect) => 77.50/10.56 (( 77.50/10.56 (contraSubsetComplement) => 77.50/10.56 (( 77.50/10.56 (complementTcontraSubset) => 77.50/10.56 (( 77.50/10.56 (binunionTILcontra) => 77.50/10.56 (( 77.50/10.56 (binunionTIRcontra) => 77.50/10.56 (( 77.50/10.56 (inIntersectImpInUnion) => 77.50/10.56 (( 77.50/10.56 (inIntersectImpInUnion2) => 77.50/10.56 (( 77.50/10.56 (inIntersectImpInIntersectUnions) => 77.50/10.56 (( 77.50/10.56 (intersectInPowersetIntersectUnions) => 77.50/10.56 (( 77.50/10.56 (inComplementUnionImpNotIn1) => 77.50/10.56 (( 77.50/10.56 (inComplementUnionImpInComplement1) => 77.50/10.56 (( 77.50/10.56 (binunionTE) => 77.50/10.56 (( 77.50/10.56 (binunionTEcontra) => 77.50/10.56 (( 77.50/10.56 (demorgan2a1) => 77.50/10.56 (( 77.50/10.56 (complementUnionInPowersetComplement) => 77.50/10.56 (( 77.50/10.56 (demorgan2a2) => 77.50/10.56 (( 77.50/10.56 (demorgan1a) => 77.50/10.56 (( 77.50/10.56 (demorgan1b) => 77.50/10.56 (( 77.50/10.56 (demorgan1) => 77.50/10.56 (( 77.50/10.56 (demorgan2a) => 77.50/10.56 (( 77.50/10.56 (demorgan2b2) => 77.50/10.56 (( 77.50/10.56 (demorgan2b) => 77.50/10.56 (( 77.50/10.56 (demorgan2) => 77.50/10.56 (( 77.50/10.56 (woz13rule0) => 77.50/10.56 (( 77.50/10.56 (woz13rule1) => 77.50/10.56 (( 77.50/10.56 (woz13rule2) => 77.50/10.56 (( 77.50/10.56 (woz13rule3) => 77.50/10.56 (( 77.50/10.56 (woz13rule4) => 77.50/10.56 (( 77.50/10.56 (woz1_1) => 77.50/10.56 (( 77.50/10.56 (woz1_2) => 77.50/10.56 (( 77.50/10.56 (woz1_3) => 77.50/10.56 (( 77.50/10.56 (woz1_4) => 77.50/10.56 (( 77.50/10.56 (woz1_5) => 77.50/10.56 (( 77.50/10.56 (breln1all2) => 77.50/10.56 (( 77.50/10.56 (breln1SetBreln1) => 77.50/10.56 (( 77.50/10.56 (choice2fnsingleton) => 77.50/10.56 (( 77.50/10.56 (setOfPairsIsBReln1) => 77.50/10.56 (( 77.50/10.56 (breln1all1) => 77.50/10.56 (( 77.50/10.56 (subbreln1) => 77.50/10.56 (( 77.50/10.56 (eqbreln1) => 77.50/10.56 (( 77.50/10.56 (breln1invprop) => 77.50/10.56 (( 77.50/10.56 (breln1invI) => 77.50/10.56 (( 77.50/10.56 (breln1invE) => 77.50/10.56 (( 77.50/10.56 (breln1compprop) => 77.50/10.56 (( 77.50/10.56 (breln1compI) => 77.50/10.56 (( 77.50/10.56 (breln1compE) => 77.50/10.56 (( 77.50/10.56 (breln1compEex) => 77.50/10.56 (( 77.50/10.56 (breln1unionprop) => 77.50/10.56 (( 77.50/10.56 (breln1unionIL) => 77.50/10.56 (( 77.50/10.56 (breln1unionIR) => 77.50/10.56 (( 77.50/10.56 (breln1unionI) => 77.50/10.56 (( 77.50/10.56 (breln1unionE) => 77.50/10.56 (( 77.50/10.56 (breln1unionEcases) => 77.50/10.56 (( 77.50/10.56 (breln1unionCommutes) => 77.50/10.56 (( 77.50/10.56 (woz2Ex) => 77.50/10.56 (( 77.50/10.56 (woz2W) => 77.50/10.56 (( 77.50/10.56 (woz2A) => 77.50/10.56 (( 77.50/10.56 (woz2B) => 77.50/10.56 (( 77.50/10.56 (image1Ex) => 77.50/10.56 (( 77.50/10.56 (image1Ex1) => 77.50/10.56 (( 77.50/10.56 (image1Equiv) => 77.50/10.56 (( 77.50/10.56 (image1E) => 77.50/10.56 (( 77.50/10.56 (image1I) => 77.50/10.56 (( 77.50/10.56 (injFuncInInjFuncSet) => 77.50/10.56 (( 77.50/10.56 (injFuncSetFuncIn) => 77.50/10.56 (( 77.50/10.56 (injFuncSetFuncInj) => 77.50/10.56 (( 77.50/10.56 (surjFuncSetFuncIn) => 77.50/10.56 (( 77.50/10.56 (surjFuncSetFuncSurj) => 77.50/10.56 (( 77.50/10.56 (leftInvIsSurj) => 77.50/10.56 (( 77.50/10.56 (surjCantorThm) => 77.50/10.56 (( 77.50/10.56 (foundation2) => 77.50/10.56 (( 77.50/10.56 (notinself) => 77.50/10.56 (( 77.50/10.56 (notinself2) => 77.50/10.56 (( 77.50/10.56 (omegaSp) => 77.50/10.56 (( 77.50/10.56 (omegaSclos) => 77.50/10.56 (( 77.50/10.56 (peano0notS) => 77.50/10.56 (( 77.50/10.56 (peanoSinj) => 77.50/10.56 (( 77.50/10.56 (transitivesetOp1) => 77.50/10.56 (( 77.50/10.56 (binintTransitive) => 77.50/10.56 (( 77.50/10.56 (transitivesetOp2) => 77.50/10.56 (( 77.50/10.56 (setunionTransitive) => 77.50/10.56 (( 77.50/10.56 (ordinalMinLem1) => 77.50/10.56 (( 77.50/10.56 (!!) @ ( 77.50/10.56 ^[Y0 : $i]: 77.50/10.56 (( 77.50/10.56 (ordinal @ 77.50/10.56 Y0) => 77.50/10.56 (( 77.50/10.56 (!!) @ ( 77.50/10.56 ^[Y1 : $i]: 77.50/10.56 (( 77.50/10.56 (!!) @ ( 77.50/10.56 ^[Y2 : $i]: 77.50/10.56 (( 77.50/10.56 (in @ 77.50/10.56 Y2 @ 77.50/10.56 Y0) => 77.50/10.56 (( 77.50/10.56 (in @ 77.50/10.56 Y1 @ 77.50/10.56 Y2) => 77.50/10.56 (in @ 77.50/10.56 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 77.50/10.56 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl56])). 77.50/10.56 thf(zip_derived_cl69, plain, 77.50/10.56 (~ (((dsetconstrEL) => 77.50/10.56 (((dsetconstrER) => 77.50/10.56 (((exuE1) => 77.50/10.56 (((prop2setE) => 77.50/10.56 (((emptysetE) => 77.50/10.56 (((emptysetimpfalse) => 77.50/10.56 (((notinemptyset) => 77.50/10.56 (((exuE3e) => 77.50/10.56 (((setext) => 77.50/10.56 (((emptyI) => 77.50/10.56 (((noeltsimpempty) => 77.50/10.56 (((setbeta) => 77.50/10.56 (((nonemptyE1) => 77.50/10.56 (((nonemptyI) => 77.50/10.56 (((nonemptyI1) => 77.50/10.56 (((setadjoinIL) => 77.50/10.56 (((in @ emptyset @ 77.50/10.56 (setadjoin @ emptyset @ emptyset)) => 77.50/10.56 (((setadjoinIR) => 77.50/10.56 (((setadjoinE) => 77.50/10.56 (((setadjoinOr) => 77.50/10.56 (((setoftrueEq) => 77.50/10.56 (((powersetI) => 77.50/10.56 (((emptyinPowerset) => 77.50/10.56 (((emptyInPowerset) => 77.50/10.56 (((powersetE) => 77.50/10.56 (((setunionI) => 77.50/10.56 (((setunionE) => 77.50/10.56 (((subPowSU) => 77.50/10.56 (((exuE2) => 77.50/10.56 (((nonemptyImpWitness) => 77.50/10.56 (( 77.50/10.56 (uniqinunit) => 77.50/10.56 (( 77.50/10.56 (notinsingleton) => 77.50/10.56 (( 77.50/10.56 (eqinunit) => 77.50/10.56 (( 77.50/10.56 (singletonsswitch) => 77.50/10.56 (( 77.50/10.56 (upairsetE) => 77.50/10.56 (( 77.50/10.56 (upairsetIL) => 77.50/10.56 (( 77.50/10.56 (upairsetIR) => 77.50/10.56 (( 77.50/10.56 (emptyE1) => 77.50/10.56 (( 77.50/10.56 (vacuousDall) => 77.50/10.56 (( 77.50/10.56 (quantDeMorgan1) => 77.50/10.56 (( 77.50/10.56 (quantDeMorgan2) => 77.50/10.56 (( 77.50/10.56 (quantDeMorgan3) => 77.50/10.56 (( 77.50/10.56 (quantDeMorgan4) => 77.50/10.56 (( 77.50/10.56 (prop2setI) => 77.50/10.56 (( 77.50/10.56 (prop2set2propI) => 77.50/10.56 (( 77.50/10.56 (notdexE) => 77.50/10.56 (( 77.50/10.56 (notdallE) => 77.50/10.56 (( 77.50/10.56 (exuI1) => 77.50/10.56 (( 77.50/10.56 (exuI3) => 77.50/10.56 (( 77.50/10.56 (exuI2) => 77.50/10.56 (( 77.50/10.56 (inCongP) => 77.50/10.56 (( 77.50/10.56 (in__Cong) => 77.50/10.56 (( 77.50/10.56 (exuE3u) => 77.50/10.56 (( 77.50/10.56 (exu__Cong) => 77.50/10.56 (( 77.50/10.56 (setadjoin__Cong) => 77.50/10.56 (( 77.50/10.56 (powerset__Cong) => 77.50/10.56 (( 77.50/10.56 (setunion__Cong) => 77.50/10.56 (( 77.50/10.56 (exuEu) => 77.50/10.56 (( 77.50/10.56 (descr__Cong) => 77.50/10.56 (( 77.50/10.56 (dsetconstr__Cong) => 77.50/10.56 (( 77.50/10.56 (subsetI1) => 77.50/10.56 (( 77.50/10.56 (eqimpsubset2) => 77.50/10.56 (( 77.50/10.56 (eqimpsubset1) => 77.50/10.56 (( 77.50/10.56 (subsetI2) => 77.50/10.56 (( 77.50/10.56 (emptysetsubset) => 77.50/10.56 (( 77.50/10.56 (subsetE) => 77.50/10.56 (( 77.50/10.56 (subsetE2) => 77.50/10.56 (( 77.50/10.56 (notsubsetI) => 77.50/10.56 (( 77.50/10.56 (notequalI1) => 77.50/10.56 (( 77.50/10.56 (notequalI2) => 77.50/10.56 (( 77.50/10.56 (subsetRefl) => 77.50/10.56 (( 77.50/10.56 (subsetTrans) => 77.50/10.56 (( 77.50/10.56 (setadjoinSub) => 77.50/10.56 (( 77.50/10.56 (setadjoinSub2) => 77.50/10.56 (( 77.50/10.56 (subset2powerset) => 77.50/10.56 (( 77.50/10.56 (setextsub) => 77.50/10.56 (( 77.50/10.56 (subsetemptysetimpeq) => 77.50/10.56 (( 77.50/10.56 (powersetI1) => 77.50/10.56 (( 77.50/10.56 (powersetE1) => 77.50/10.56 (( 77.50/10.56 (inPowerset) => 77.50/10.56 (( 77.50/10.56 (powersetsubset) => 77.50/10.56 (( 77.50/10.56 (sepInPowerset) => 77.50/10.56 (( 77.50/10.56 (sepSubset) => 77.50/10.56 (( 77.50/10.56 (binunionIL) => 77.50/10.56 (( 77.50/10.56 (upairset2IR) => 77.50/10.56 (( 77.50/10.56 (binunionIR) => 77.50/10.56 (( 77.50/10.56 (binunionEcases) => 77.50/10.56 (( 77.50/10.56 (binunionE) => 77.50/10.56 (( 77.50/10.56 (binunionLsub) => 77.50/10.56 (( 77.50/10.56 (binunionRsub) => 77.50/10.56 (( 77.50/10.56 (binintersectI) => 77.50/10.56 (( 77.50/10.56 (binintersectSubset5) => 77.50/10.56 (( 77.50/10.56 (binintersectEL) => 77.50/10.56 (( 77.50/10.56 (binintersectLsub) => 77.50/10.56 (( 77.50/10.56 (binintersectSubset2) => 77.50/10.56 (( 77.50/10.56 (binintersectSubset3) => 77.50/10.56 (( 77.50/10.56 (binintersectER) => 77.50/10.56 (( 77.50/10.56 (disjointsetsI1) => 77.50/10.56 (( 77.50/10.56 (binintersectRsub) => 77.50/10.56 (( 77.50/10.56 (binintersectSubset4) => 77.50/10.56 (( 77.50/10.56 (binintersectSubset1) => 77.50/10.56 (( 77.50/10.56 (bs114d) => 77.50/10.56 (( 77.50/10.56 (setminusI) => 77.50/10.56 (( 77.50/10.56 (setminusEL) => 77.50/10.56 (( 77.50/10.56 (setminusER) => 77.50/10.56 (( 77.50/10.56 (setminusSubset2) => 77.50/10.56 (( 77.50/10.56 (setminusERneg) => 77.50/10.56 (( 77.50/10.56 (setminusELneg) => 77.50/10.56 (( 77.50/10.56 (setminusILneg) => 77.50/10.56 (( 77.50/10.56 (setminusIRneg) => 77.50/10.56 (( 77.50/10.56 (setminusLsub) => 77.50/10.56 (( 77.50/10.56 (setminusSubset1) => 77.50/10.56 (( 77.50/10.56 (symdiffE) => 77.50/10.56 (( 77.50/10.56 (symdiffI1) => 77.50/10.56 (( 77.50/10.56 (symdiffI2) => 77.50/10.56 (( 77.50/10.56 (symdiffIneg1) => 77.50/10.56 (( 77.50/10.56 (symdiffIneg2) => 77.50/10.56 (( 77.50/10.56 (secondinupair) => 77.50/10.56 (( 77.50/10.56 (setukpairIL) => 77.50/10.56 (( 77.50/10.56 (setukpairIR) => 77.50/10.56 (( 77.50/10.56 (kpairiskpair) => 77.50/10.56 (( 77.50/10.56 (kpairp) => 77.50/10.56 (( 77.50/10.56 (singletonsubset) => 77.50/10.56 (( 77.50/10.56 (singletoninpowerset) => 77.50/10.56 (( 77.50/10.56 (singletoninpowunion) => 77.50/10.56 (( 77.50/10.56 (upairset2E) => 77.50/10.56 (( 77.50/10.56 (upairsubunion) => 77.50/10.56 (( 77.50/10.56 (upairinpowunion) => 77.50/10.56 (( 77.50/10.56 (ubforcartprodlem1) => 77.50/10.56 (( 77.50/10.56 (ubforcartprodlem2) => 77.50/10.56 (( 77.50/10.56 (ubforcartprodlem3) => 77.50/10.56 (( 77.50/10.56 (cartprodpairin) => 77.50/10.56 (( 77.50/10.56 (cartprodmempair1) => 77.50/10.56 (( 77.50/10.56 (cartprodmempair) => 77.50/10.56 (( 77.50/10.56 (setunionE2) => 77.50/10.56 (( 77.50/10.56 (setunionsingleton1) => 77.50/10.56 (( 77.50/10.56 (setunionsingleton2) => 77.50/10.56 (( 77.50/10.56 (setunionsingleton) => 77.50/10.56 (( 77.50/10.56 (singletonprop) => 77.50/10.56 (( 77.50/10.56 (ex1E1) => 77.50/10.56 (( 77.50/10.56 (ex1I) => 77.50/10.56 (( 77.50/10.56 (ex1I2) => 77.50/10.56 (( 77.50/10.56 (singletonsuniq) => 77.50/10.56 (( 77.50/10.56 (setukpairinjL1) => 77.50/10.56 (( 77.50/10.56 (kfstsingleton) => 77.50/10.56 (( 77.50/10.56 (theprop) => 77.50/10.56 (( 77.50/10.56 (kfstpairEq) => 77.50/10.56 (( 77.50/10.56 (cartprodfstin) => 77.50/10.56 (( 77.50/10.56 (setukpairinjL2) => 77.50/10.56 (( 77.50/10.56 (setukpairinjL) => 77.50/10.56 (( 77.50/10.56 (setukpairinjR11) => 77.50/10.56 (( 77.50/10.56 (setukpairinjR12) => 77.50/10.56 (( 77.50/10.56 (setukpairinjR1) => 77.50/10.56 (( 77.50/10.56 (upairequniteq) => 77.50/10.56 (( 77.50/10.56 (setukpairinjR2) => 77.50/10.56 (( 77.50/10.56 (setukpairinjR) => 77.50/10.56 (( 77.50/10.56 (ksndsingleton) => 77.50/10.56 (( 77.50/10.56 (ksndpairEq) => 77.50/10.56 (( 77.50/10.56 (kpairsurjEq) => 77.50/10.56 (( 77.50/10.56 (cartprodsndin) => 77.50/10.56 (( 77.50/10.56 (cartprodpairmemEL) => 77.50/10.56 (( 77.50/10.56 (cartprodpairmemER) => 77.50/10.56 (( 77.50/10.56 (cartprodmempaircEq) => 77.50/10.56 (( 77.50/10.56 (cartprodfstpairEq) => 77.50/10.56 (( 77.50/10.56 (cartprodsndpairEq) => 77.50/10.56 (( 77.50/10.56 (cartprodpairsurjEq) => 77.50/10.56 (( 77.50/10.56 (dpsetconstrI) => 77.50/10.56 (( 77.50/10.56 (dpsetconstrSub) => 77.50/10.56 (( 77.50/10.56 (setOfPairsIsBReln) => 77.50/10.56 (( 77.50/10.56 (dpsetconstrERa) => 77.50/10.56 (( 77.50/10.56 (dpsetconstrEL1) => 77.50/10.56 (( 77.50/10.56 (dpsetconstrEL2) => 77.50/10.56 (( 77.50/10.56 (dpsetconstrER) => 77.50/10.56 (( 77.50/10.56 (funcImageSingleton) => 77.50/10.56 (( 77.50/10.56 (apProp) => 77.50/10.56 (( 77.50/10.56 (app) => 77.50/10.56 (( 77.50/10.56 (infuncsetfunc) => 77.50/10.56 (( 77.50/10.56 (ap2p) => 77.50/10.56 (( 77.50/10.56 (funcinfuncset) => 77.50/10.56 (( 77.50/10.56 (lamProp) => 77.50/10.56 (( 77.50/10.56 (lamp) => 77.50/10.56 (( 77.50/10.56 (lam2p) => 77.50/10.56 (( 77.50/10.56 (brelnall1) => 77.50/10.56 (( 77.50/10.56 (brelnall2) => 77.50/10.56 (( 77.50/10.56 (ex1E2) => 77.50/10.56 (( 77.50/10.56 (funcGraphProp1) => 77.50/10.56 (( 77.50/10.56 (funcGraphProp3) => 77.50/10.56 (( 77.50/10.56 (funcGraphProp2) => 77.50/10.56 (( 77.50/10.56 (funcextLem) => 77.50/10.56 (( 77.50/10.56 (funcGraphProp4) => 77.50/10.56 (( 77.50/10.56 (subbreln) => 77.50/10.56 (( 77.50/10.56 (eqbreln) => 77.50/10.56 (( 77.50/10.56 (funcext) => 77.50/10.56 (( 77.50/10.56 (funcext2) => 77.50/10.56 (( 77.50/10.56 (ap2apEq1) => 77.50/10.56 (( 77.50/10.56 (ap2apEq2) => 77.50/10.56 (( 77.50/10.56 (beta1) => 77.50/10.56 (( 77.50/10.56 (eta1) => 77.50/10.56 (( 77.50/10.56 (lam2lamEq) => 77.50/10.56 (( 77.50/10.56 (beta2) => 77.50/10.56 (( 77.50/10.56 (eta2) => 77.50/10.56 (( 77.50/10.56 (iffalseProp1) => 77.50/10.56 (( 77.50/10.56 (iffalseProp2) => 77.50/10.56 (( 77.50/10.56 (iftrueProp1) => 77.50/10.56 (( 77.50/10.56 (iftrueProp2) => 77.50/10.56 (( 77.50/10.56 (ifSingleton) => 77.50/10.56 (( 77.50/10.56 (ifp) => 77.50/10.56 (( 77.50/10.56 (theeq) => 77.50/10.56 (( 77.50/10.56 (iftrue) => 77.50/10.56 (( 77.50/10.56 (iffalse) => 77.50/10.56 (( 77.50/10.56 (iftrueorfalse) => 77.50/10.56 (( 77.50/10.56 (binintersectT_lem) => 77.50/10.56 (( 77.50/10.56 (binunionT_lem) => 77.50/10.56 (( 77.50/10.56 (powersetT_lem) => 77.50/10.56 (( 77.50/10.56 (setminusT_lem) => 77.50/10.56 (( 77.50/10.56 (complementT_lem) => 77.50/10.56 (( 77.50/10.56 (setextT) => 77.50/10.56 (( 77.50/10.56 (subsetTI) => 77.50/10.56 (( 77.50/10.56 (powersetTI1) => 77.50/10.56 (( 77.50/10.56 (powersetTE1) => 77.50/10.56 (( 77.50/10.56 (complementTI1) => 77.50/10.56 (( 77.50/10.56 (complementTE1) => 77.50/10.56 (( 77.50/10.56 (binintersectTELcontra) => 77.50/10.56 (( 77.50/10.56 (binintersectTERcontra) => 77.50/10.56 (( 77.50/10.56 (contrasubsetT) => 77.50/10.56 (( 77.50/10.56 (contrasubsetT1) => 77.50/10.56 (( 77.50/10.56 (contrasubsetT2) => 77.50/10.56 (( 77.50/10.56 (contrasubsetT3) => 77.50/10.56 (( 77.50/10.56 (doubleComplementI1) => 77.50/10.56 (( 77.50/10.56 (doubleComplementE1) => 77.50/10.56 (( 77.50/10.56 (doubleComplementSub1) => 77.50/10.56 (( 77.50/10.56 (doubleComplementSub2) => 77.50/10.56 (( 77.50/10.56 (doubleComplementEq) => 77.50/10.56 (( 77.50/10.56 (complementTnotintersectT) => 77.50/10.56 (( 77.50/10.56 (complementImpComplementIntersect) => 77.50/10.56 (( 77.50/10.56 (complementSubsetComplementIntersect) => 77.50/10.56 (( 77.50/10.56 (complementInPowersetComplementIntersect) => 77.50/10.56 (( 77.50/10.56 (contraSubsetComplement) => 77.50/10.56 (( 77.50/10.56 (complementTcontraSubset) => 77.50/10.56 (( 77.50/10.56 (binunionTILcontra) => 77.50/10.56 (( 77.50/10.56 (binunionTIRcontra) => 77.50/10.56 (( 77.50/10.56 (inIntersectImpInUnion) => 77.50/10.56 (( 77.50/10.56 (inIntersectImpInUnion2) => 77.50/10.56 (( 77.50/10.56 (inIntersectImpInIntersectUnions) => 77.50/10.56 (( 77.50/10.56 (intersectInPowersetIntersectUnions) => 77.50/10.56 (( 77.50/10.56 (inComplementUnionImpNotIn1) => 77.50/10.56 (( 77.50/10.56 (inComplementUnionImpInComplement1) => 77.50/10.56 (( 77.50/10.56 (binunionTE) => 77.50/10.56 (( 77.50/10.56 (binunionTEcontra) => 77.50/10.56 (( 77.50/10.56 (demorgan2a1) => 77.50/10.56 (( 77.50/10.56 (complementUnionInPowersetComplement) => 77.50/10.56 (( 77.50/10.56 (demorgan2a2) => 77.50/10.56 (( 77.50/10.56 (demorgan1a) => 77.50/10.56 (( 77.50/10.56 (demorgan1b) => 77.50/10.56 (( 77.50/10.56 (demorgan1) => 77.50/10.56 (( 77.50/10.56 (demorgan2a) => 77.50/10.56 (( 77.50/10.56 (demorgan2b2) => 77.50/10.56 (( 77.50/10.56 (demorgan2b) => 77.50/10.56 (( 77.50/10.56 (demorgan2) => 77.50/10.56 (( 77.50/10.56 (woz13rule0) => 77.50/10.56 (( 77.50/10.56 (woz13rule1) => 77.50/10.56 (( 77.50/10.56 (woz13rule2) => 77.50/10.56 (( 77.50/10.56 (woz13rule3) => 77.50/10.56 (( 77.50/10.56 (woz13rule4) => 77.50/10.56 (( 77.50/10.56 (woz1_1) => 77.50/10.56 (( 77.50/10.56 (woz1_2) => 77.50/10.56 (( 77.50/10.56 (woz1_3) => 77.50/10.56 (( 77.50/10.56 (woz1_4) => 77.50/10.56 (( 77.50/10.56 (woz1_5) => 77.50/10.56 (( 77.50/10.56 (breln1all2) => 77.50/10.56 (( 77.50/10.56 (breln1SetBreln1) => 77.50/10.56 (( 77.50/10.56 (choice2fnsingleton) => 77.50/10.56 (( 77.50/10.56 (setOfPairsIsBReln1) => 77.50/10.56 (( 77.50/10.56 (breln1all1) => 77.50/10.56 (( 77.50/10.56 (subbreln1) => 77.50/10.56 (( 77.50/10.56 (eqbreln1) => 77.50/10.56 (( 77.50/10.56 (breln1invprop) => 77.50/10.56 (( 77.50/10.56 (breln1invI) => 77.50/10.56 (( 77.50/10.56 (breln1invE) => 77.50/10.56 (( 77.50/10.56 (breln1compprop) => 77.50/10.56 (( 77.50/10.56 (breln1compI) => 77.50/10.56 (( 77.50/10.56 (breln1compE) => 77.50/10.56 (( 77.50/10.56 (breln1compEex) => 77.50/10.56 (( 77.50/10.56 (breln1unionprop) => 77.50/10.56 (( 77.50/10.56 (breln1unionIL) => 77.50/10.56 (( 77.50/10.56 (breln1unionIR) => 77.50/10.56 (( 77.50/10.56 (breln1unionI) => 77.50/10.56 (( 77.50/10.56 (breln1unionE) => 77.50/10.56 (( 77.50/10.56 (breln1unionEcases) => 77.50/10.56 (( 77.50/10.56 (breln1unionCommutes) => 77.50/10.56 (( 77.50/10.56 (woz2Ex) => 77.50/10.56 (( 77.50/10.56 (woz2W) => 77.50/10.56 (( 77.50/10.56 (woz2A) => 77.50/10.56 (( 77.50/10.56 (woz2B) => 77.50/10.56 (( 77.50/10.56 (image1Ex) => 77.50/10.56 (( 77.50/10.56 (image1Ex1) => 77.50/10.56 (( 77.50/10.56 (image1Equiv) => 77.50/10.56 (( 77.50/10.56 (image1E) => 77.50/10.56 (( 77.50/10.56 (image1I) => 77.50/10.56 (( 77.50/10.56 (injFuncInInjFuncSet) => 77.50/10.56 (( 77.50/10.56 (injFuncSetFuncIn) => 77.50/10.56 (( 77.50/10.56 (injFuncSetFuncInj) => 77.50/10.56 (( 77.50/10.56 (surjFuncSetFuncIn) => 77.50/10.56 (( 77.50/10.56 (surjFuncSetFuncSurj) => 77.50/10.56 (( 77.50/10.56 (leftInvIsSurj) => 77.50/10.56 (( 77.50/10.56 (surjCantorThm) => 77.50/10.56 (( 77.50/10.56 (foundation2) => 77.50/10.56 (( 77.50/10.56 (notinself) => 77.50/10.56 (( 77.50/10.56 (notinself2) => 77.50/10.56 (( 77.50/10.56 (omegaSp) => 77.50/10.56 (( 77.50/10.56 (omegaSclos) => 77.50/10.56 (( 77.50/10.56 (peano0notS) => 77.50/10.56 (( 77.50/10.56 (peanoSinj) => 77.50/10.56 (( 77.50/10.56 (transitivesetOp1) => 77.50/10.56 (( 77.50/10.56 (binintTransitive) => 77.50/10.56 (( 77.50/10.56 (transitivesetOp2) => 77.50/10.56 (( 77.50/10.56 (setunionTransitive) => 77.50/10.56 (( 77.50/10.56 (ordinalMinLem1) => 77.50/10.56 (( 77.50/10.56 (!!) @ ( 77.50/10.56 ^[Y0 : $i]: 77.50/10.56 (( 77.50/10.56 (ordinal @ 77.50/10.56 Y0) => 77.50/10.56 (( 77.50/10.56 (!!) @ ( 77.50/10.56 ^[Y1 : $i]: 77.50/10.56 (( 77.50/10.56 (!!) @ ( 77.50/10.56 ^[Y2 : $i]: 77.50/10.56 (( 77.50/10.56 (in @ 77.50/10.56 Y2 @ 77.50/10.56 Y0) => 77.50/10.56 (( 77.50/10.56 (in @ 77.50/10.56 Y1 @ 77.50/10.56 Y2) => 77.50/10.56 (in @ 77.50/10.56 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 77.50/10.56 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl62])). 77.50/10.56 thf(zip_derived_cl79, plain, 77.50/10.56 (~ (((dsetconstrER) => 77.50/10.56 (((exuE1) => 77.50/10.56 (((prop2setE) => 77.50/10.56 (((emptysetE) => 77.50/10.56 (((emptysetimpfalse) => 77.50/10.56 (((notinemptyset) => 77.50/10.56 (((exuE3e) => 77.50/10.56 (((setext) => 77.50/10.56 (((emptyI) => 77.50/10.56 (((noeltsimpempty) => 77.50/10.56 (((setbeta) => 77.50/10.56 (((nonemptyE1) => 77.50/10.56 (((nonemptyI) => 77.50/10.56 (((nonemptyI1) => 77.50/10.56 (((setadjoinIL) => 77.50/10.56 (((in @ emptyset @ 77.50/10.56 (setadjoin @ emptyset @ emptyset)) => 77.50/10.56 (((setadjoinIR) => 77.50/10.56 (((setadjoinE) => 77.50/10.56 (((setadjoinOr) => 77.50/10.56 (((setoftrueEq) => 77.50/10.56 (((powersetI) => 77.50/10.56 (((emptyinPowerset) => 77.50/10.56 (((emptyInPowerset) => 77.50/10.56 (((powersetE) => 77.50/10.56 (((setunionI) => 77.50/10.56 (((setunionE) => 77.50/10.56 (((subPowSU) => 77.50/10.56 (((exuE2) => 77.50/10.56 (((nonemptyImpWitness) => 77.50/10.56 (((uniqinunit) => 77.50/10.56 (( 77.50/10.56 (notinsingleton) => 77.50/10.56 (( 77.50/10.56 (eqinunit) => 77.50/10.56 (( 77.50/10.56 (singletonsswitch) => 77.50/10.56 (( 77.50/10.56 (upairsetE) => 77.50/10.56 (( 77.50/10.56 (upairsetIL) => 77.50/10.56 (( 77.50/10.56 (upairsetIR) => 77.50/10.56 (( 77.50/10.56 (emptyE1) => 77.50/10.56 (( 77.50/10.56 (vacuousDall) => 77.50/10.56 (( 77.50/10.56 (quantDeMorgan1) => 77.50/10.56 (( 77.50/10.56 (quantDeMorgan2) => 77.50/10.56 (( 77.50/10.56 (quantDeMorgan3) => 77.50/10.56 (( 77.50/10.56 (quantDeMorgan4) => 77.50/10.56 (( 77.50/10.56 (prop2setI) => 77.50/10.56 (( 77.50/10.56 (prop2set2propI) => 77.50/10.56 (( 77.50/10.56 (notdexE) => 77.50/10.56 (( 77.50/10.56 (notdallE) => 77.50/10.56 (( 77.50/10.56 (exuI1) => 77.50/10.56 (( 77.50/10.56 (exuI3) => 77.50/10.56 (( 77.50/10.56 (exuI2) => 77.50/10.56 (( 77.50/10.56 (inCongP) => 77.50/10.56 (( 77.50/10.56 (in__Cong) => 77.50/10.56 (( 77.50/10.56 (exuE3u) => 77.50/10.56 (( 77.50/10.56 (exu__Cong) => 77.50/10.56 (( 77.50/10.56 (setadjoin__Cong) => 77.50/10.56 (( 77.50/10.56 (powerset__Cong) => 77.50/10.56 (( 77.50/10.56 (setunion__Cong) => 77.50/10.56 (( 77.50/10.56 (exuEu) => 77.50/10.56 (( 77.50/10.56 (descr__Cong) => 77.50/10.56 (( 77.50/10.56 (dsetconstr__Cong) => 77.50/10.56 (( 77.50/10.56 (subsetI1) => 77.50/10.56 (( 77.50/10.56 (eqimpsubset2) => 77.50/10.56 (( 77.50/10.56 (eqimpsubset1) => 77.50/10.56 (( 77.50/10.56 (subsetI2) => 77.50/10.56 (( 77.50/10.56 (emptysetsubset) => 77.50/10.56 (( 77.50/10.56 (subsetE) => 77.50/10.56 (( 77.50/10.56 (subsetE2) => 77.50/10.56 (( 77.50/10.56 (notsubsetI) => 77.50/10.56 (( 77.50/10.56 (notequalI1) => 77.50/10.56 (( 77.50/10.56 (notequalI2) => 77.50/10.56 (( 77.50/10.56 (subsetRefl) => 77.50/10.56 (( 77.50/10.56 (subsetTrans) => 77.50/10.56 (( 77.50/10.56 (setadjoinSub) => 77.50/10.56 (( 77.50/10.56 (setadjoinSub2) => 77.50/10.56 (( 77.50/10.56 (subset2powerset) => 77.50/10.56 (( 77.50/10.56 (setextsub) => 77.50/10.56 (( 77.50/10.56 (subsetemptysetimpeq) => 77.50/10.56 (( 77.50/10.56 (powersetI1) => 77.50/10.56 (( 77.50/10.56 (powersetE1) => 77.50/10.56 (( 77.50/10.56 (inPowerset) => 77.50/10.56 (( 77.50/10.56 (powersetsubset) => 77.50/10.56 (( 77.50/10.56 (sepInPowerset) => 77.50/10.56 (( 77.50/10.56 (sepSubset) => 77.50/10.56 (( 77.50/10.56 (binunionIL) => 77.50/10.56 (( 77.50/10.56 (upairset2IR) => 77.50/10.56 (( 77.50/10.56 (binunionIR) => 77.50/10.56 (( 77.50/10.56 (binunionEcases) => 77.50/10.56 (( 77.50/10.56 (binunionE) => 77.50/10.56 (( 77.50/10.56 (binunionLsub) => 77.50/10.56 (( 77.50/10.56 (binunionRsub) => 77.50/10.56 (( 77.50/10.56 (binintersectI) => 77.50/10.56 (( 77.50/10.56 (binintersectSubset5) => 77.50/10.56 (( 77.50/10.56 (binintersectEL) => 77.50/10.56 (( 77.50/10.56 (binintersectLsub) => 77.50/10.56 (( 77.50/10.56 (binintersectSubset2) => 77.50/10.56 (( 77.50/10.56 (binintersectSubset3) => 77.50/10.56 (( 77.50/10.56 (binintersectER) => 77.50/10.56 (( 77.50/10.56 (disjointsetsI1) => 77.50/10.56 (( 77.50/10.56 (binintersectRsub) => 77.50/10.56 (( 77.50/10.56 (binintersectSubset4) => 77.50/10.56 (( 77.50/10.56 (binintersectSubset1) => 77.50/10.56 (( 77.50/10.56 (bs114d) => 77.50/10.56 (( 77.50/10.56 (setminusI) => 77.50/10.56 (( 77.50/10.56 (setminusEL) => 77.50/10.56 (( 77.50/10.56 (setminusER) => 77.50/10.56 (( 77.50/10.56 (setminusSubset2) => 77.50/10.56 (( 77.50/10.56 (setminusERneg) => 77.50/10.56 (( 77.50/10.56 (setminusELneg) => 77.50/10.56 (( 77.50/10.56 (setminusILneg) => 77.50/10.56 (( 77.50/10.56 (setminusIRneg) => 77.50/10.56 (( 77.50/10.56 (setminusLsub) => 77.50/10.56 (( 77.50/10.56 (setminusSubset1) => 77.50/10.56 (( 77.50/10.56 (symdiffE) => 77.50/10.56 (( 77.50/10.56 (symdiffI1) => 77.50/10.56 (( 77.50/10.56 (symdiffI2) => 77.50/10.56 (( 77.50/10.56 (symdiffIneg1) => 77.50/10.56 (( 77.50/10.56 (symdiffIneg2) => 77.50/10.56 (( 77.50/10.56 (secondinupair) => 77.50/10.56 (( 77.50/10.56 (setukpairIL) => 77.50/10.56 (( 77.50/10.56 (setukpairIR) => 77.50/10.56 (( 77.50/10.56 (kpairiskpair) => 77.50/10.56 (( 77.50/10.56 (kpairp) => 77.50/10.56 (( 77.50/10.56 (singletonsubset) => 77.50/10.56 (( 77.50/10.56 (singletoninpowerset) => 77.50/10.56 (( 77.50/10.56 (singletoninpowunion) => 77.50/10.56 (( 77.50/10.56 (upairset2E) => 77.50/10.56 (( 77.50/10.56 (upairsubunion) => 77.50/10.56 (( 77.50/10.56 (upairinpowunion) => 77.50/10.56 (( 77.50/10.56 (ubforcartprodlem1) => 77.50/10.56 (( 77.50/10.56 (ubforcartprodlem2) => 77.50/10.56 (( 77.50/10.56 (ubforcartprodlem3) => 77.50/10.56 (( 77.50/10.56 (cartprodpairin) => 77.50/10.56 (( 77.50/10.56 (cartprodmempair1) => 77.50/10.56 (( 77.50/10.56 (cartprodmempair) => 77.50/10.56 (( 77.50/10.56 (setunionE2) => 77.50/10.56 (( 77.50/10.56 (setunionsingleton1) => 77.50/10.56 (( 77.50/10.56 (setunionsingleton2) => 77.50/10.56 (( 77.50/10.56 (setunionsingleton) => 77.50/10.56 (( 77.50/10.56 (singletonprop) => 77.50/10.56 (( 77.50/10.56 (ex1E1) => 77.50/10.56 (( 77.50/10.56 (ex1I) => 77.50/10.56 (( 77.50/10.56 (ex1I2) => 77.50/10.56 (( 77.50/10.56 (singletonsuniq) => 77.50/10.56 (( 77.50/10.56 (setukpairinjL1) => 77.50/10.56 (( 77.50/10.56 (kfstsingleton) => 77.50/10.56 (( 77.50/10.56 (theprop) => 77.50/10.56 (( 77.50/10.56 (kfstpairEq) => 77.50/10.56 (( 77.50/10.56 (cartprodfstin) => 77.50/10.56 (( 77.50/10.56 (setukpairinjL2) => 77.50/10.56 (( 77.50/10.56 (setukpairinjL) => 77.50/10.56 (( 77.50/10.56 (setukpairinjR11) => 77.50/10.56 (( 77.50/10.56 (setukpairinjR12) => 77.50/10.56 (( 77.50/10.56 (setukpairinjR1) => 77.50/10.56 (( 77.50/10.56 (upairequniteq) => 77.50/10.56 (( 77.50/10.56 (setukpairinjR2) => 77.50/10.56 (( 77.50/10.56 (setukpairinjR) => 77.50/10.56 (( 77.50/10.56 (ksndsingleton) => 77.50/10.56 (( 77.50/10.56 (ksndpairEq) => 77.50/10.56 (( 77.50/10.56 (kpairsurjEq) => 77.50/10.56 (( 77.50/10.56 (cartprodsndin) => 77.50/10.56 (( 77.50/10.56 (cartprodpairmemEL) => 77.50/10.56 (( 77.50/10.56 (cartprodpairmemER) => 77.50/10.56 (( 77.50/10.56 (cartprodmempaircEq) => 77.50/10.56 (( 77.50/10.56 (cartprodfstpairEq) => 77.50/10.56 (( 77.50/10.56 (cartprodsndpairEq) => 77.50/10.56 (( 77.50/10.56 (cartprodpairsurjEq) => 77.50/10.56 (( 77.50/10.56 (dpsetconstrI) => 77.50/10.56 (( 77.50/10.56 (dpsetconstrSub) => 77.50/10.56 (( 77.50/10.56 (setOfPairsIsBReln) => 77.50/10.56 (( 77.50/10.56 (dpsetconstrERa) => 77.50/10.56 (( 77.50/10.56 (dpsetconstrEL1) => 77.50/10.56 (( 77.50/10.56 (dpsetconstrEL2) => 77.50/10.56 (( 77.50/10.56 (dpsetconstrER) => 77.50/10.56 (( 77.50/10.56 (funcImageSingleton) => 77.50/10.56 (( 77.50/10.56 (apProp) => 77.50/10.56 (( 77.50/10.56 (app) => 77.50/10.56 (( 77.50/10.56 (infuncsetfunc) => 77.50/10.56 (( 77.50/10.56 (ap2p) => 77.50/10.56 (( 77.50/10.56 (funcinfuncset) => 77.50/10.56 (( 77.50/10.56 (lamProp) => 77.50/10.56 (( 77.50/10.56 (lamp) => 77.50/10.56 (( 77.50/10.56 (lam2p) => 77.50/10.56 (( 77.50/10.56 (brelnall1) => 77.50/10.56 (( 77.50/10.56 (brelnall2) => 77.50/10.56 (( 77.50/10.56 (ex1E2) => 77.50/10.56 (( 77.50/10.56 (funcGraphProp1) => 77.50/10.56 (( 77.50/10.56 (funcGraphProp3) => 77.50/10.56 (( 77.50/10.56 (funcGraphProp2) => 77.50/10.56 (( 77.50/10.56 (funcextLem) => 77.50/10.56 (( 77.50/10.56 (funcGraphProp4) => 77.50/10.56 (( 77.50/10.56 (subbreln) => 77.50/10.56 (( 77.50/10.56 (eqbreln) => 77.50/10.56 (( 77.50/10.56 (funcext) => 77.50/10.56 (( 77.50/10.56 (funcext2) => 77.50/10.56 (( 77.50/10.56 (ap2apEq1) => 77.50/10.56 (( 77.50/10.56 (ap2apEq2) => 77.50/10.56 (( 77.50/10.56 (beta1) => 77.50/10.56 (( 77.50/10.56 (eta1) => 77.50/10.56 (( 77.50/10.56 (lam2lamEq) => 77.50/10.56 (( 77.50/10.56 (beta2) => 77.50/10.56 (( 77.50/10.56 (eta2) => 77.50/10.56 (( 77.50/10.56 (iffalseProp1) => 77.50/10.56 (( 77.50/10.56 (iffalseProp2) => 77.50/10.56 (( 77.50/10.56 (iftrueProp1) => 77.50/10.56 (( 77.50/10.56 (iftrueProp2) => 77.50/10.56 (( 77.50/10.56 (ifSingleton) => 77.50/10.56 (( 77.50/10.56 (ifp) => 77.50/10.56 (( 77.50/10.56 (theeq) => 77.50/10.56 (( 77.50/10.56 (iftrue) => 77.50/10.56 (( 77.50/10.56 (iffalse) => 77.50/10.56 (( 77.50/10.56 (iftrueorfalse) => 77.50/10.56 (( 77.50/10.56 (binintersectT_lem) => 77.50/10.56 (( 77.50/10.56 (binunionT_lem) => 77.50/10.56 (( 77.50/10.56 (powersetT_lem) => 77.50/10.56 (( 77.50/10.56 (setminusT_lem) => 77.50/10.56 (( 77.50/10.56 (complementT_lem) => 77.50/10.56 (( 77.50/10.56 (setextT) => 77.50/10.56 (( 77.50/10.56 (subsetTI) => 77.50/10.56 (( 77.50/10.56 (powersetTI1) => 77.50/10.56 (( 77.50/10.56 (powersetTE1) => 77.50/10.56 (( 77.50/10.56 (complementTI1) => 77.50/10.56 (( 77.50/10.56 (complementTE1) => 77.50/10.56 (( 77.50/10.56 (binintersectTELcontra) => 77.50/10.56 (( 77.50/10.56 (binintersectTERcontra) => 77.50/10.56 (( 77.50/10.56 (contrasubsetT) => 77.50/10.56 (( 77.50/10.56 (contrasubsetT1) => 77.50/10.56 (( 77.50/10.56 (contrasubsetT2) => 77.50/10.56 (( 77.50/10.56 (contrasubsetT3) => 77.50/10.56 (( 77.50/10.56 (doubleComplementI1) => 77.50/10.56 (( 77.50/10.56 (doubleComplementE1) => 77.50/10.56 (( 77.50/10.56 (doubleComplementSub1) => 77.50/10.56 (( 77.50/10.56 (doubleComplementSub2) => 77.50/10.56 (( 77.50/10.56 (doubleComplementEq) => 77.50/10.56 (( 77.50/10.56 (complementTnotintersectT) => 77.50/10.56 (( 77.50/10.56 (complementImpComplementIntersect) => 77.50/10.56 (( 77.50/10.56 (complementSubsetComplementIntersect) => 77.50/10.56 (( 77.50/10.56 (complementInPowersetComplementIntersect) => 77.50/10.56 (( 77.50/10.56 (contraSubsetComplement) => 77.50/10.56 (( 77.50/10.56 (complementTcontraSubset) => 77.50/10.56 (( 77.50/10.56 (binunionTILcontra) => 77.50/10.56 (( 77.50/10.56 (binunionTIRcontra) => 77.50/10.56 (( 77.50/10.56 (inIntersectImpInUnion) => 77.50/10.56 (( 77.50/10.56 (inIntersectImpInUnion2) => 77.50/10.56 (( 77.50/10.56 (inIntersectImpInIntersectUnions) => 77.50/10.56 (( 77.50/10.56 (intersectInPowersetIntersectUnions) => 77.50/10.56 (( 77.50/10.56 (inComplementUnionImpNotIn1) => 77.50/10.56 (( 77.50/10.56 (inComplementUnionImpInComplement1) => 77.50/10.56 (( 77.50/10.56 (binunionTE) => 77.50/10.56 (( 77.50/10.56 (binunionTEcontra) => 77.50/10.56 (( 77.50/10.56 (demorgan2a1) => 77.50/10.56 (( 77.50/10.56 (complementUnionInPowersetComplement) => 77.50/10.56 (( 77.50/10.56 (demorgan2a2) => 77.50/10.56 (( 77.50/10.56 (demorgan1a) => 77.50/10.56 (( 77.50/10.56 (demorgan1b) => 77.50/10.56 (( 77.50/10.56 (demorgan1) => 77.50/10.56 (( 77.50/10.56 (demorgan2a) => 77.50/10.56 (( 77.50/10.56 (demorgan2b2) => 77.50/10.56 (( 77.50/10.56 (demorgan2b) => 77.50/10.56 (( 77.50/10.56 (demorgan2) => 77.50/10.56 (( 77.50/10.56 (woz13rule0) => 77.50/10.56 (( 77.50/10.56 (woz13rule1) => 77.50/10.56 (( 77.50/10.56 (woz13rule2) => 77.50/10.56 (( 77.50/10.56 (woz13rule3) => 77.50/10.56 (( 77.50/10.56 (woz13rule4) => 77.50/10.56 (( 77.50/10.56 (woz1_1) => 77.50/10.56 (( 77.50/10.56 (woz1_2) => 77.50/10.56 (( 77.50/10.56 (woz1_3) => 77.50/10.56 (( 77.50/10.56 (woz1_4) => 77.50/10.56 (( 77.50/10.56 (woz1_5) => 77.50/10.56 (( 77.50/10.56 (breln1all2) => 77.50/10.56 (( 77.50/10.56 (breln1SetBreln1) => 77.50/10.56 (( 77.50/10.56 (choice2fnsingleton) => 77.50/10.56 (( 77.50/10.56 (setOfPairsIsBReln1) => 77.50/10.56 (( 77.50/10.56 (breln1all1) => 77.50/10.56 (( 77.50/10.56 (subbreln1) => 77.50/10.56 (( 77.50/10.56 (eqbreln1) => 77.50/10.56 (( 77.50/10.56 (breln1invprop) => 77.50/10.56 (( 77.50/10.56 (breln1invI) => 77.50/10.56 (( 77.50/10.56 (breln1invE) => 77.50/10.56 (( 77.50/10.56 (breln1compprop) => 77.50/10.56 (( 77.50/10.56 (breln1compI) => 77.50/10.56 (( 77.50/10.56 (breln1compE) => 77.50/10.56 (( 77.50/10.56 (breln1compEex) => 77.50/10.56 (( 77.50/10.56 (breln1unionprop) => 77.50/10.56 (( 77.50/10.56 (breln1unionIL) => 77.50/10.56 (( 77.50/10.56 (breln1unionIR) => 77.50/10.56 (( 77.50/10.56 (breln1unionI) => 77.50/10.56 (( 77.50/10.56 (breln1unionE) => 77.50/10.56 (( 77.50/10.56 (breln1unionEcases) => 77.50/10.56 (( 77.50/10.56 (breln1unionCommutes) => 77.50/10.56 (( 77.50/10.56 (woz2Ex) => 77.50/10.56 (( 77.50/10.56 (woz2W) => 77.50/10.56 (( 77.50/10.56 (woz2A) => 77.50/10.56 (( 77.50/10.56 (woz2B) => 77.50/10.56 (( 77.50/10.56 (image1Ex) => 77.50/10.56 (( 77.50/10.56 (image1Ex1) => 77.50/10.56 (( 77.50/10.56 (image1Equiv) => 77.50/10.56 (( 77.50/10.56 (image1E) => 77.50/10.56 (( 77.50/10.56 (image1I) => 77.50/10.56 (( 77.50/10.56 (injFuncInInjFuncSet) => 77.50/10.56 (( 77.50/10.56 (injFuncSetFuncIn) => 77.50/10.56 (( 77.50/10.56 (injFuncSetFuncInj) => 77.50/10.56 (( 77.50/10.56 (surjFuncSetFuncIn) => 77.50/10.56 (( 77.50/10.56 (surjFuncSetFuncSurj) => 77.50/10.56 (( 77.50/10.56 (leftInvIsSurj) => 77.50/10.56 (( 77.50/10.56 (surjCantorThm) => 77.50/10.56 (( 77.50/10.56 (foundation2) => 77.50/10.56 (( 77.50/10.56 (notinself) => 77.50/10.56 (( 77.50/10.56 (notinself2) => 77.50/10.56 (( 77.50/10.56 (omegaSp) => 77.50/10.56 (( 77.50/10.56 (omegaSclos) => 77.50/10.56 (( 77.50/10.56 (peano0notS) => 77.50/10.56 (( 77.50/10.56 (peanoSinj) => 77.50/10.56 (( 77.50/10.56 (transitivesetOp1) => 77.50/10.56 (( 77.50/10.56 (binintTransitive) => 77.50/10.56 (( 77.50/10.56 (transitivesetOp2) => 77.50/10.56 (( 77.50/10.56 (setunionTransitive) => 77.50/10.56 (( 77.50/10.56 (ordinalMinLem1) => 77.50/10.56 (( 77.50/10.56 (!!) @ ( 77.50/10.56 ^[Y0 : $i]: 77.50/10.56 (( 77.50/10.56 (ordinal @ 77.50/10.56 Y0) => 77.50/10.56 (( 77.50/10.56 (!!) @ ( 77.50/10.56 ^[Y1 : $i]: 77.50/10.56 (( 77.50/10.56 (!!) @ ( 77.50/10.56 ^[Y2 : $i]: 77.50/10.56 (( 77.50/10.56 (in @ 77.50/10.56 Y2 @ 77.50/10.56 Y0) => 77.50/10.56 (( 77.50/10.56 (in @ 77.50/10.56 Y1 @ 77.50/10.56 Y2) => 77.50/10.56 (in @ 77.50/10.56 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 77.50/10.56 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl69])). 77.50/10.56 thf(zip_derived_cl95, plain, 77.50/10.56 (~ (((exuE1) => 77.50/10.56 (((prop2setE) => 77.50/10.56 (((emptysetE) => 77.50/10.56 (((emptysetimpfalse) => 77.50/10.56 (((notinemptyset) => 77.50/10.56 (((exuE3e) => 77.50/10.56 (((setext) => 77.50/10.56 (((emptyI) => 77.50/10.56 (((noeltsimpempty) => 77.50/10.56 (((setbeta) => 77.50/10.56 (((nonemptyE1) => 77.50/10.56 (((nonemptyI) => 77.50/10.56 (((nonemptyI1) => 77.50/10.56 (((setadjoinIL) => 77.50/10.56 (((in @ emptyset @ 77.50/10.56 (setadjoin @ emptyset @ emptyset)) => 77.50/10.56 (((setadjoinIR) => 77.50/10.56 (((setadjoinE) => 77.50/10.56 (((setadjoinOr) => 77.50/10.56 (((setoftrueEq) => 77.50/10.56 (((powersetI) => 77.50/10.56 (((emptyinPowerset) => 77.50/10.56 (((emptyInPowerset) => 77.50/10.56 (((powersetE) => 77.50/10.56 (((setunionI) => 77.50/10.56 (((setunionE) => 77.50/10.56 (((subPowSU) => 77.50/10.56 (((exuE2) => 77.50/10.56 (((nonemptyImpWitness) => 77.50/10.56 (((uniqinunit) => 77.50/10.56 (((notinsingleton) => 77.50/10.56 (( 77.50/10.56 (eqinunit) => 77.50/10.56 (( 77.50/10.56 (singletonsswitch) => 77.50/10.56 (( 77.50/10.56 (upairsetE) => 77.50/10.56 (( 77.50/10.56 (upairsetIL) => 77.50/10.56 (( 77.50/10.56 (upairsetIR) => 77.50/10.56 (( 77.50/10.56 (emptyE1) => 77.50/10.56 (( 77.50/10.56 (vacuousDall) => 77.50/10.56 (( 77.50/10.56 (quantDeMorgan1) => 77.50/10.56 (( 77.50/10.56 (quantDeMorgan2) => 77.50/10.56 (( 77.50/10.56 (quantDeMorgan3) => 77.50/10.56 (( 77.50/10.56 (quantDeMorgan4) => 77.50/10.57 (( 77.50/10.57 (prop2setI) => 77.50/10.57 (( 77.50/10.57 (prop2set2propI) => 77.50/10.57 (( 77.50/10.57 (notdexE) => 77.50/10.57 (( 77.50/10.57 (notdallE) => 77.50/10.57 (( 77.50/10.57 (exuI1) => 77.50/10.57 (( 77.50/10.57 (exuI3) => 77.50/10.57 (( 77.50/10.57 (exuI2) => 77.50/10.57 (( 77.50/10.57 (inCongP) => 77.50/10.57 (( 77.50/10.57 (in__Cong) => 77.50/10.57 (( 77.50/10.57 (exuE3u) => 77.50/10.57 (( 77.50/10.57 (exu__Cong) => 77.50/10.57 (( 77.50/10.57 (setadjoin__Cong) => 77.50/10.57 (( 77.50/10.57 (powerset__Cong) => 77.50/10.57 (( 77.50/10.57 (setunion__Cong) => 77.50/10.57 (( 77.50/10.57 (exuEu) => 77.50/10.57 (( 77.50/10.57 (descr__Cong) => 77.50/10.57 (( 77.50/10.57 (dsetconstr__Cong) => 77.50/10.57 (( 77.50/10.57 (subsetI1) => 77.50/10.57 (( 77.50/10.57 (eqimpsubset2) => 77.50/10.57 (( 77.50/10.57 (eqimpsubset1) => 77.50/10.57 (( 77.50/10.57 (subsetI2) => 77.50/10.57 (( 77.50/10.57 (emptysetsubset) => 77.50/10.57 (( 77.50/10.57 (subsetE) => 77.50/10.57 (( 77.50/10.57 (subsetE2) => 77.50/10.57 (( 77.50/10.57 (notsubsetI) => 77.50/10.57 (( 77.50/10.57 (notequalI1) => 77.50/10.57 (( 77.50/10.57 (notequalI2) => 77.50/10.57 (( 77.50/10.57 (subsetRefl) => 77.50/10.57 (( 77.50/10.57 (subsetTrans) => 77.50/10.57 (( 77.50/10.57 (setadjoinSub) => 77.50/10.57 (( 77.50/10.57 (setadjoinSub2) => 77.50/10.57 (( 77.50/10.57 (subset2powerset) => 77.50/10.57 (( 77.50/10.57 (setextsub) => 77.50/10.57 (( 77.50/10.57 (subsetemptysetimpeq) => 77.50/10.57 (( 77.50/10.57 (powersetI1) => 77.50/10.57 (( 77.50/10.57 (powersetE1) => 77.50/10.57 (( 77.50/10.57 (inPowerset) => 77.50/10.57 (( 77.50/10.57 (powersetsubset) => 77.50/10.57 (( 77.50/10.57 (sepInPowerset) => 77.50/10.57 (( 77.50/10.57 (sepSubset) => 77.50/10.57 (( 77.50/10.57 (binunionIL) => 77.50/10.57 (( 77.50/10.57 (upairset2IR) => 77.50/10.57 (( 77.50/10.57 (binunionIR) => 77.50/10.57 (( 77.50/10.57 (binunionEcases) => 77.50/10.57 (( 77.50/10.57 (binunionE) => 77.50/10.57 (( 77.50/10.57 (binunionLsub) => 77.50/10.57 (( 77.50/10.57 (binunionRsub) => 77.50/10.57 (( 77.50/10.57 (binintersectI) => 77.50/10.57 (( 77.50/10.57 (binintersectSubset5) => 77.50/10.57 (( 77.50/10.57 (binintersectEL) => 77.50/10.57 (( 77.50/10.57 (binintersectLsub) => 77.50/10.57 (( 77.50/10.57 (binintersectSubset2) => 77.50/10.57 (( 77.50/10.57 (binintersectSubset3) => 77.50/10.57 (( 77.50/10.57 (binintersectER) => 77.50/10.57 (( 77.50/10.57 (disjointsetsI1) => 77.50/10.57 (( 77.50/10.57 (binintersectRsub) => 77.50/10.57 (( 77.50/10.57 (binintersectSubset4) => 77.50/10.57 (( 77.50/10.57 (binintersectSubset1) => 77.50/10.57 (( 77.50/10.57 (bs114d) => 77.50/10.57 (( 77.50/10.57 (setminusI) => 77.50/10.57 (( 77.50/10.57 (setminusEL) => 77.50/10.57 (( 77.50/10.57 (setminusER) => 77.50/10.57 (( 77.50/10.57 (setminusSubset2) => 77.50/10.57 (( 77.50/10.57 (setminusERneg) => 77.50/10.57 (( 77.50/10.57 (setminusELneg) => 77.50/10.57 (( 77.50/10.57 (setminusILneg) => 77.50/10.57 (( 77.50/10.57 (setminusIRneg) => 77.50/10.57 (( 77.50/10.57 (setminusLsub) => 77.50/10.57 (( 77.50/10.57 (setminusSubset1) => 77.50/10.57 (( 77.50/10.57 (symdiffE) => 77.50/10.57 (( 77.50/10.57 (symdiffI1) => 77.50/10.57 (( 77.50/10.57 (symdiffI2) => 77.50/10.57 (( 77.50/10.57 (symdiffIneg1) => 77.50/10.57 (( 77.50/10.57 (symdiffIneg2) => 77.50/10.57 (( 77.50/10.57 (secondinupair) => 77.50/10.57 (( 77.50/10.57 (setukpairIL) => 77.50/10.57 (( 77.50/10.57 (setukpairIR) => 77.50/10.57 (( 77.50/10.57 (kpairiskpair) => 77.50/10.57 (( 77.50/10.57 (kpairp) => 77.50/10.57 (( 77.50/10.57 (singletonsubset) => 77.50/10.57 (( 77.50/10.57 (singletoninpowerset) => 77.50/10.57 (( 77.50/10.57 (singletoninpowunion) => 77.50/10.57 (( 77.50/10.57 (upairset2E) => 77.50/10.57 (( 77.50/10.57 (upairsubunion) => 77.50/10.57 (( 77.50/10.57 (upairinpowunion) => 77.50/10.57 (( 77.50/10.57 (ubforcartprodlem1) => 77.50/10.57 (( 77.50/10.57 (ubforcartprodlem2) => 77.50/10.57 (( 77.50/10.57 (ubforcartprodlem3) => 77.50/10.57 (( 77.50/10.57 (cartprodpairin) => 77.50/10.57 (( 77.50/10.57 (cartprodmempair1) => 77.50/10.57 (( 77.50/10.57 (cartprodmempair) => 77.50/10.57 (( 77.50/10.57 (setunionE2) => 77.50/10.57 (( 77.50/10.57 (setunionsingleton1) => 77.50/10.57 (( 77.50/10.57 (setunionsingleton2) => 77.50/10.57 (( 77.50/10.57 (setunionsingleton) => 77.50/10.57 (( 77.50/10.57 (singletonprop) => 77.50/10.57 (( 77.50/10.57 (ex1E1) => 77.50/10.57 (( 77.50/10.57 (ex1I) => 77.50/10.57 (( 77.50/10.57 (ex1I2) => 77.50/10.57 (( 77.50/10.57 (singletonsuniq) => 77.50/10.57 (( 77.50/10.57 (setukpairinjL1) => 77.50/10.57 (( 77.50/10.57 (kfstsingleton) => 77.50/10.57 (( 77.50/10.57 (theprop) => 77.50/10.57 (( 77.50/10.57 (kfstpairEq) => 77.50/10.57 (( 77.50/10.57 (cartprodfstin) => 77.50/10.57 (( 77.50/10.57 (setukpairinjL2) => 77.50/10.57 (( 77.50/10.57 (setukpairinjL) => 77.50/10.57 (( 77.50/10.57 (setukpairinjR11) => 77.50/10.57 (( 77.50/10.57 (setukpairinjR12) => 77.50/10.57 (( 77.50/10.57 (setukpairinjR1) => 77.50/10.57 (( 77.50/10.57 (upairequniteq) => 77.50/10.57 (( 77.50/10.57 (setukpairinjR2) => 77.50/10.57 (( 77.50/10.57 (setukpairinjR) => 77.50/10.57 (( 77.50/10.57 (ksndsingleton) => 77.50/10.57 (( 77.50/10.57 (ksndpairEq) => 77.50/10.57 (( 77.50/10.57 (kpairsurjEq) => 77.50/10.57 (( 77.50/10.57 (cartprodsndin) => 77.50/10.57 (( 77.50/10.57 (cartprodpairmemEL) => 77.50/10.57 (( 77.50/10.57 (cartprodpairmemER) => 77.50/10.57 (( 77.50/10.57 (cartprodmempaircEq) => 77.50/10.57 (( 77.50/10.57 (cartprodfstpairEq) => 77.50/10.57 (( 77.50/10.57 (cartprodsndpairEq) => 77.50/10.57 (( 77.50/10.57 (cartprodpairsurjEq) => 77.50/10.57 (( 77.50/10.57 (dpsetconstrI) => 77.50/10.57 (( 77.50/10.57 (dpsetconstrSub) => 77.50/10.57 (( 77.50/10.57 (setOfPairsIsBReln) => 77.50/10.57 (( 77.50/10.57 (dpsetconstrERa) => 77.50/10.57 (( 77.50/10.57 (dpsetconstrEL1) => 77.50/10.57 (( 77.50/10.57 (dpsetconstrEL2) => 77.50/10.57 (( 77.50/10.57 (dpsetconstrER) => 77.50/10.57 (( 77.50/10.57 (funcImageSingleton) => 77.50/10.57 (( 77.50/10.57 (apProp) => 77.50/10.57 (( 77.50/10.57 (app) => 77.50/10.57 (( 77.50/10.57 (infuncsetfunc) => 77.50/10.57 (( 77.50/10.57 (ap2p) => 77.50/10.57 (( 77.50/10.57 (funcinfuncset) => 77.50/10.57 (( 77.50/10.57 (lamProp) => 77.50/10.57 (( 77.50/10.57 (lamp) => 77.50/10.57 (( 77.50/10.57 (lam2p) => 77.50/10.57 (( 77.50/10.57 (brelnall1) => 77.50/10.57 (( 77.50/10.57 (brelnall2) => 77.50/10.57 (( 77.50/10.57 (ex1E2) => 77.50/10.57 (( 77.50/10.57 (funcGraphProp1) => 77.50/10.57 (( 77.50/10.57 (funcGraphProp3) => 77.50/10.57 (( 77.50/10.57 (funcGraphProp2) => 77.50/10.57 (( 77.50/10.57 (funcextLem) => 77.50/10.57 (( 77.50/10.57 (funcGraphProp4) => 77.50/10.57 (( 77.50/10.57 (subbreln) => 77.50/10.57 (( 77.50/10.57 (eqbreln) => 77.50/10.57 (( 77.50/10.57 (funcext) => 77.50/10.57 (( 77.50/10.57 (funcext2) => 77.50/10.57 (( 77.50/10.57 (ap2apEq1) => 77.50/10.57 (( 77.50/10.57 (ap2apEq2) => 77.50/10.57 (( 77.50/10.57 (beta1) => 77.50/10.57 (( 77.50/10.57 (eta1) => 77.50/10.57 (( 77.50/10.57 (lam2lamEq) => 77.50/10.57 (( 77.50/10.57 (beta2) => 77.50/10.57 (( 77.50/10.57 (eta2) => 77.50/10.57 (( 77.50/10.57 (iffalseProp1) => 77.50/10.57 (( 77.50/10.57 (iffalseProp2) => 77.50/10.57 (( 77.50/10.57 (iftrueProp1) => 77.50/10.57 (( 77.50/10.57 (iftrueProp2) => 77.50/10.57 (( 77.50/10.57 (ifSingleton) => 77.50/10.57 (( 77.50/10.57 (ifp) => 77.50/10.57 (( 77.50/10.57 (theeq) => 77.50/10.57 (( 77.50/10.57 (iftrue) => 77.50/10.57 (( 77.50/10.57 (iffalse) => 77.50/10.57 (( 77.50/10.57 (iftrueorfalse) => 77.50/10.57 (( 77.50/10.57 (binintersectT_lem) => 77.50/10.57 (( 77.50/10.57 (binunionT_lem) => 77.50/10.57 (( 77.50/10.57 (powersetT_lem) => 77.50/10.57 (( 77.50/10.57 (setminusT_lem) => 77.50/10.57 (( 77.50/10.57 (complementT_lem) => 77.50/10.57 (( 77.50/10.57 (setextT) => 77.50/10.57 (( 77.50/10.57 (subsetTI) => 77.50/10.57 (( 77.50/10.57 (powersetTI1) => 77.50/10.57 (( 77.50/10.57 (powersetTE1) => 77.50/10.57 (( 77.50/10.57 (complementTI1) => 77.50/10.57 (( 77.50/10.57 (complementTE1) => 77.50/10.57 (( 77.50/10.57 (binintersectTELcontra) => 77.50/10.57 (( 77.50/10.57 (binintersectTERcontra) => 77.50/10.57 (( 77.50/10.57 (contrasubsetT) => 77.50/10.57 (( 77.50/10.57 (contrasubsetT1) => 77.50/10.57 (( 77.50/10.57 (contrasubsetT2) => 77.50/10.57 (( 77.50/10.57 (contrasubsetT3) => 77.50/10.57 (( 77.50/10.57 (doubleComplementI1) => 77.50/10.57 (( 77.50/10.57 (doubleComplementE1) => 77.50/10.57 (( 77.50/10.57 (doubleComplementSub1) => 77.50/10.57 (( 77.50/10.57 (doubleComplementSub2) => 77.50/10.57 (( 77.50/10.57 (doubleComplementEq) => 77.50/10.57 (( 77.50/10.57 (complementTnotintersectT) => 77.50/10.57 (( 77.50/10.57 (complementImpComplementIntersect) => 77.50/10.57 (( 77.50/10.57 (complementSubsetComplementIntersect) => 77.50/10.57 (( 77.50/10.57 (complementInPowersetComplementIntersect) => 77.50/10.57 (( 77.50/10.57 (contraSubsetComplement) => 77.50/10.57 (( 77.50/10.57 (complementTcontraSubset) => 77.50/10.57 (( 77.50/10.57 (binunionTILcontra) => 77.50/10.57 (( 77.50/10.57 (binunionTIRcontra) => 77.50/10.57 (( 77.50/10.57 (inIntersectImpInUnion) => 77.50/10.57 (( 77.50/10.57 (inIntersectImpInUnion2) => 77.50/10.57 (( 77.50/10.57 (inIntersectImpInIntersectUnions) => 77.50/10.57 (( 77.50/10.57 (intersectInPowersetIntersectUnions) => 77.50/10.57 (( 77.50/10.57 (inComplementUnionImpNotIn1) => 77.50/10.57 (( 77.50/10.57 (inComplementUnionImpInComplement1) => 77.50/10.57 (( 77.50/10.57 (binunionTE) => 77.50/10.57 (( 77.50/10.57 (binunionTEcontra) => 77.50/10.57 (( 77.50/10.57 (demorgan2a1) => 77.50/10.57 (( 77.50/10.57 (complementUnionInPowersetComplement) => 77.50/10.57 (( 77.50/10.57 (demorgan2a2) => 77.50/10.57 (( 77.50/10.57 (demorgan1a) => 77.50/10.57 (( 77.50/10.57 (demorgan1b) => 77.50/10.57 (( 77.50/10.57 (demorgan1) => 77.50/10.57 (( 77.50/10.57 (demorgan2a) => 77.50/10.57 (( 77.50/10.57 (demorgan2b2) => 77.50/10.57 (( 77.50/10.57 (demorgan2b) => 77.50/10.57 (( 77.50/10.57 (demorgan2) => 77.50/10.57 (( 77.50/10.57 (woz13rule0) => 77.50/10.57 (( 77.50/10.57 (woz13rule1) => 77.50/10.57 (( 77.50/10.57 (woz13rule2) => 77.50/10.57 (( 77.50/10.57 (woz13rule3) => 77.50/10.57 (( 77.50/10.57 (woz13rule4) => 77.50/10.57 (( 77.50/10.57 (woz1_1) => 77.50/10.57 (( 77.50/10.57 (woz1_2) => 77.50/10.57 (( 77.50/10.57 (woz1_3) => 77.50/10.57 (( 77.50/10.57 (woz1_4) => 77.50/10.57 (( 77.50/10.57 (woz1_5) => 77.50/10.57 (( 77.50/10.57 (breln1all2) => 77.50/10.57 (( 77.50/10.57 (breln1SetBreln1) => 77.50/10.57 (( 77.50/10.57 (choice2fnsingleton) => 77.50/10.57 (( 77.50/10.57 (setOfPairsIsBReln1) => 77.50/10.57 (( 77.50/10.57 (breln1all1) => 77.50/10.57 (( 77.50/10.57 (subbreln1) => 77.50/10.57 (( 77.50/10.57 (eqbreln1) => 77.50/10.57 (( 77.50/10.57 (breln1invprop) => 77.50/10.57 (( 77.50/10.57 (breln1invI) => 77.50/10.57 (( 77.50/10.57 (breln1invE) => 77.50/10.57 (( 77.50/10.57 (breln1compprop) => 77.50/10.57 (( 77.50/10.57 (breln1compI) => 77.50/10.57 (( 77.50/10.57 (breln1compE) => 77.50/10.57 (( 77.50/10.57 (breln1compEex) => 77.50/10.57 (( 77.50/10.57 (breln1unionprop) => 77.50/10.57 (( 77.50/10.57 (breln1unionIL) => 77.50/10.57 (( 77.50/10.57 (breln1unionIR) => 77.50/10.57 (( 77.50/10.57 (breln1unionI) => 77.50/10.57 (( 77.50/10.57 (breln1unionE) => 77.50/10.57 (( 77.50/10.57 (breln1unionEcases) => 77.50/10.57 (( 77.50/10.57 (breln1unionCommutes) => 77.50/10.57 (( 77.50/10.57 (woz2Ex) => 77.50/10.57 (( 77.50/10.57 (woz2W) => 77.50/10.57 (( 77.50/10.57 (woz2A) => 77.50/10.57 (( 77.50/10.57 (woz2B) => 77.50/10.57 (( 77.50/10.57 (image1Ex) => 77.50/10.57 (( 77.50/10.57 (image1Ex1) => 77.50/10.57 (( 77.50/10.57 (image1Equiv) => 77.50/10.57 (( 77.50/10.57 (image1E) => 77.50/10.57 (( 77.50/10.57 (image1I) => 77.50/10.57 (( 77.50/10.57 (injFuncInInjFuncSet) => 77.50/10.57 (( 77.50/10.57 (injFuncSetFuncIn) => 77.50/10.57 (( 77.50/10.57 (injFuncSetFuncInj) => 77.50/10.57 (( 77.50/10.57 (surjFuncSetFuncIn) => 77.50/10.57 (( 77.50/10.57 (surjFuncSetFuncSurj) => 77.50/10.57 (( 77.50/10.57 (leftInvIsSurj) => 77.50/10.57 (( 77.50/10.57 (surjCantorThm) => 77.50/10.57 (( 77.50/10.57 (foundation2) => 77.50/10.57 (( 77.50/10.57 (notinself) => 77.50/10.57 (( 77.50/10.57 (notinself2) => 77.50/10.57 (( 77.50/10.57 (omegaSp) => 77.50/10.57 (( 77.50/10.57 (omegaSclos) => 77.50/10.57 (( 77.50/10.57 (peano0notS) => 77.50/10.57 (( 77.50/10.57 (peanoSinj) => 77.50/10.57 (( 77.50/10.57 (transitivesetOp1) => 77.50/10.57 (( 77.50/10.57 (binintTransitive) => 77.50/10.57 (( 77.50/10.57 (transitivesetOp2) => 77.50/10.57 (( 77.50/10.57 (setunionTransitive) => 77.50/10.57 (( 77.50/10.57 (ordinalMinLem1) => 77.50/10.57 (( 77.50/10.57 (!!) @ ( 77.50/10.57 ^[Y0 : $i]: 77.50/10.57 (( 77.50/10.57 (ordinal @ 77.50/10.57 Y0) => 77.50/10.57 (( 77.50/10.57 (!!) @ ( 77.50/10.57 ^[Y1 : $i]: 77.50/10.57 (( 77.50/10.57 (!!) @ ( 77.50/10.57 ^[Y2 : $i]: 77.50/10.57 (( 77.50/10.57 (in @ 77.50/10.57 Y2 @ 77.50/10.57 Y0) => 77.50/10.57 (( 77.50/10.57 (in @ 77.50/10.57 Y1 @ 77.50/10.57 Y2) => 77.50/10.57 (in @ 77.50/10.57 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 77.50/10.57 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl79])). 77.50/10.57 thf(zip_derived_cl115, plain, 77.50/10.57 (~ (((prop2setE) => 77.50/10.57 (((emptysetE) => 77.50/10.57 (((emptysetimpfalse) => 77.50/10.57 (((notinemptyset) => 77.50/10.57 (((exuE3e) => 77.50/10.57 (((setext) => 77.50/10.57 (((emptyI) => 77.50/10.57 (((noeltsimpempty) => 77.50/10.57 (((setbeta) => 77.50/10.57 (((nonemptyE1) => 77.50/10.57 (((nonemptyI) => 77.50/10.57 (((nonemptyI1) => 77.50/10.57 (((setadjoinIL) => 77.50/10.57 (((in @ emptyset @ 77.50/10.57 (setadjoin @ emptyset @ emptyset)) => 77.50/10.57 (((setadjoinIR) => 77.50/10.57 (((setadjoinE) => 77.50/10.57 (((setadjoinOr) => 77.50/10.57 (((setoftrueEq) => 77.50/10.57 (((powersetI) => 77.50/10.57 (((emptyinPowerset) => 77.50/10.57 (((emptyInPowerset) => 77.50/10.57 (((powersetE) => 77.50/10.57 (((setunionI) => 77.50/10.57 (((setunionE) => 77.50/10.57 (((subPowSU) => 77.50/10.57 (((exuE2) => 77.50/10.57 (((nonemptyImpWitness) => 77.50/10.57 (((uniqinunit) => 77.50/10.57 (((notinsingleton) => 77.50/10.57 (((eqinunit) => 77.50/10.57 (( 77.50/10.57 (singletonsswitch) => 77.50/10.57 (( 77.50/10.57 (upairsetE) => 77.50/10.57 (( 77.50/10.57 (upairsetIL) => 77.50/10.57 (( 77.50/10.57 (upairsetIR) => 77.50/10.57 (( 77.50/10.57 (emptyE1) => 77.50/10.57 (( 77.50/10.57 (vacuousDall) => 77.50/10.57 (( 77.50/10.57 (quantDeMorgan1) => 77.50/10.57 (( 77.50/10.57 (quantDeMorgan2) => 77.50/10.57 (( 77.50/10.57 (quantDeMorgan3) => 77.50/10.57 (( 77.50/10.57 (quantDeMorgan4) => 77.50/10.57 (( 77.50/10.57 (prop2setI) => 77.50/10.57 (( 77.50/10.57 (prop2set2propI) => 77.50/10.57 (( 77.50/10.57 (notdexE) => 77.50/10.57 (( 77.50/10.57 (notdallE) => 77.50/10.57 (( 77.50/10.57 (exuI1) => 77.50/10.57 (( 77.50/10.57 (exuI3) => 77.50/10.57 (( 77.50/10.57 (exuI2) => 77.50/10.57 (( 77.50/10.57 (inCongP) => 77.50/10.57 (( 77.50/10.57 (in__Cong) => 77.50/10.57 (( 77.50/10.57 (exuE3u) => 77.50/10.57 (( 77.50/10.57 (exu__Cong) => 77.50/10.57 (( 77.50/10.57 (setadjoin__Cong) => 77.50/10.57 (( 77.50/10.57 (powerset__Cong) => 77.50/10.57 (( 77.50/10.57 (setunion__Cong) => 77.50/10.57 (( 77.50/10.57 (exuEu) => 77.50/10.57 (( 77.50/10.57 (descr__Cong) => 77.50/10.57 (( 77.50/10.57 (dsetconstr__Cong) => 77.50/10.57 (( 77.50/10.57 (subsetI1) => 77.50/10.57 (( 77.50/10.57 (eqimpsubset2) => 77.50/10.57 (( 77.50/10.57 (eqimpsubset1) => 77.50/10.57 (( 77.50/10.57 (subsetI2) => 77.50/10.57 (( 77.50/10.57 (emptysetsubset) => 77.50/10.57 (( 77.50/10.57 (subsetE) => 77.50/10.57 (( 77.50/10.57 (subsetE2) => 77.50/10.57 (( 77.50/10.57 (notsubsetI) => 77.50/10.57 (( 77.50/10.57 (notequalI1) => 77.50/10.57 (( 77.50/10.57 (notequalI2) => 77.50/10.57 (( 77.50/10.57 (subsetRefl) => 77.50/10.57 (( 77.50/10.57 (subsetTrans) => 77.50/10.57 (( 77.50/10.57 (setadjoinSub) => 77.50/10.57 (( 77.50/10.57 (setadjoinSub2) => 77.50/10.57 (( 77.50/10.57 (subset2powerset) => 77.50/10.57 (( 77.50/10.57 (setextsub) => 77.50/10.57 (( 77.50/10.57 (subsetemptysetimpeq) => 77.50/10.57 (( 77.50/10.57 (powersetI1) => 77.50/10.57 (( 77.50/10.57 (powersetE1) => 77.50/10.57 (( 77.50/10.57 (inPowerset) => 77.50/10.57 (( 77.50/10.57 (powersetsubset) => 77.50/10.57 (( 77.50/10.57 (sepInPowerset) => 77.50/10.57 (( 77.50/10.57 (sepSubset) => 77.50/10.57 (( 77.50/10.57 (binunionIL) => 77.50/10.57 (( 77.50/10.57 (upairset2IR) => 77.50/10.57 (( 77.50/10.57 (binunionIR) => 77.50/10.57 (( 77.50/10.57 (binunionEcases) => 77.50/10.57 (( 77.50/10.57 (binunionE) => 77.50/10.57 (( 77.50/10.57 (binunionLsub) => 77.50/10.57 (( 77.50/10.57 (binunionRsub) => 77.50/10.57 (( 77.50/10.57 (binintersectI) => 77.50/10.57 (( 77.50/10.57 (binintersectSubset5) => 77.50/10.57 (( 77.50/10.57 (binintersectEL) => 77.50/10.57 (( 77.50/10.57 (binintersectLsub) => 77.50/10.57 (( 77.50/10.57 (binintersectSubset2) => 77.50/10.57 (( 77.50/10.57 (binintersectSubset3) => 77.50/10.57 (( 77.50/10.57 (binintersectER) => 77.50/10.57 (( 77.50/10.57 (disjointsetsI1) => 77.50/10.57 (( 77.50/10.57 (binintersectRsub) => 77.50/10.57 (( 77.50/10.57 (binintersectSubset4) => 77.50/10.57 (( 77.50/10.57 (binintersectSubset1) => 77.50/10.57 (( 77.50/10.57 (bs114d) => 77.50/10.57 (( 77.50/10.57 (setminusI) => 77.50/10.57 (( 77.50/10.57 (setminusEL) => 77.50/10.57 (( 77.50/10.57 (setminusER) => 77.50/10.57 (( 77.50/10.57 (setminusSubset2) => 77.50/10.57 (( 77.50/10.57 (setminusERneg) => 77.50/10.57 (( 77.50/10.57 (setminusELneg) => 77.50/10.57 (( 77.50/10.57 (setminusILneg) => 77.50/10.57 (( 77.50/10.57 (setminusIRneg) => 77.50/10.57 (( 77.50/10.57 (setminusLsub) => 77.50/10.57 (( 77.50/10.57 (setminusSubset1) => 77.50/10.57 (( 77.50/10.57 (symdiffE) => 77.50/10.57 (( 77.50/10.57 (symdiffI1) => 77.50/10.57 (( 77.50/10.57 (symdiffI2) => 77.50/10.57 (( 77.50/10.57 (symdiffIneg1) => 77.50/10.57 (( 77.50/10.57 (symdiffIneg2) => 77.50/10.57 (( 77.50/10.57 (secondinupair) => 77.50/10.57 (( 77.50/10.57 (setukpairIL) => 77.50/10.57 (( 77.50/10.57 (setukpairIR) => 77.50/10.57 (( 77.50/10.57 (kpairiskpair) => 77.50/10.57 (( 77.50/10.57 (kpairp) => 77.50/10.57 (( 77.50/10.57 (singletonsubset) => 77.50/10.57 (( 77.50/10.57 (singletoninpowerset) => 77.50/10.57 (( 77.50/10.57 (singletoninpowunion) => 77.50/10.57 (( 77.50/10.57 (upairset2E) => 77.50/10.57 (( 77.50/10.57 (upairsubunion) => 77.50/10.57 (( 77.50/10.57 (upairinpowunion) => 77.50/10.57 (( 77.50/10.57 (ubforcartprodlem1) => 77.50/10.57 (( 77.50/10.57 (ubforcartprodlem2) => 77.50/10.57 (( 77.50/10.57 (ubforcartprodlem3) => 77.50/10.57 (( 77.50/10.57 (cartprodpairin) => 77.50/10.57 (( 77.50/10.57 (cartprodmempair1) => 77.50/10.57 (( 77.50/10.57 (cartprodmempair) => 77.50/10.57 (( 77.50/10.57 (setunionE2) => 77.50/10.57 (( 77.50/10.57 (setunionsingleton1) => 77.50/10.57 (( 77.50/10.57 (setunionsingleton2) => 77.50/10.57 (( 77.50/10.57 (setunionsingleton) => 77.50/10.57 (( 77.50/10.57 (singletonprop) => 77.50/10.57 (( 77.50/10.57 (ex1E1) => 77.50/10.57 (( 77.50/10.57 (ex1I) => 77.50/10.57 (( 77.50/10.57 (ex1I2) => 77.50/10.57 (( 77.50/10.57 (singletonsuniq) => 77.50/10.57 (( 77.50/10.57 (setukpairinjL1) => 77.50/10.57 (( 77.50/10.57 (kfstsingleton) => 77.50/10.57 (( 77.50/10.57 (theprop) => 77.50/10.57 (( 77.50/10.57 (kfstpairEq) => 77.50/10.57 (( 77.50/10.57 (cartprodfstin) => 77.50/10.57 (( 77.50/10.57 (setukpairinjL2) => 77.50/10.57 (( 77.50/10.57 (setukpairinjL) => 77.50/10.57 (( 77.50/10.57 (setukpairinjR11) => 77.50/10.57 (( 77.50/10.57 (setukpairinjR12) => 77.50/10.57 (( 77.50/10.57 (setukpairinjR1) => 77.50/10.57 (( 77.50/10.57 (upairequniteq) => 77.50/10.57 (( 77.50/10.57 (setukpairinjR2) => 77.50/10.57 (( 77.50/10.57 (setukpairinjR) => 77.50/10.57 (( 77.50/10.57 (ksndsingleton) => 77.50/10.57 (( 77.50/10.57 (ksndpairEq) => 77.50/10.57 (( 77.50/10.57 (kpairsurjEq) => 77.50/10.57 (( 77.50/10.57 (cartprodsndin) => 77.50/10.57 (( 77.50/10.57 (cartprodpairmemEL) => 77.50/10.57 (( 77.50/10.57 (cartprodpairmemER) => 77.50/10.57 (( 77.50/10.57 (cartprodmempaircEq) => 77.50/10.57 (( 77.50/10.57 (cartprodfstpairEq) => 77.50/10.57 (( 77.50/10.57 (cartprodsndpairEq) => 77.50/10.57 (( 77.50/10.57 (cartprodpairsurjEq) => 77.50/10.57 (( 77.50/10.57 (dpsetconstrI) => 77.50/10.57 (( 77.50/10.57 (dpsetconstrSub) => 77.50/10.57 (( 77.50/10.57 (setOfPairsIsBReln) => 77.50/10.57 (( 77.50/10.57 (dpsetconstrERa) => 77.50/10.57 (( 77.50/10.57 (dpsetconstrEL1) => 77.50/10.57 (( 77.50/10.57 (dpsetconstrEL2) => 77.50/10.57 (( 77.50/10.57 (dpsetconstrER) => 77.50/10.57 (( 77.50/10.57 (funcImageSingleton) => 77.50/10.57 (( 77.50/10.57 (apProp) => 77.50/10.57 (( 77.50/10.57 (app) => 77.50/10.57 (( 77.50/10.57 (infuncsetfunc) => 77.50/10.57 (( 77.50/10.57 (ap2p) => 77.50/10.57 (( 77.50/10.57 (funcinfuncset) => 77.50/10.57 (( 77.50/10.57 (lamProp) => 77.50/10.57 (( 77.50/10.57 (lamp) => 77.50/10.57 (( 77.50/10.57 (lam2p) => 77.50/10.57 (( 77.50/10.57 (brelnall1) => 77.50/10.57 (( 77.50/10.57 (brelnall2) => 77.50/10.57 (( 77.50/10.57 (ex1E2) => 77.50/10.57 (( 77.50/10.57 (funcGraphProp1) => 77.50/10.57 (( 77.50/10.57 (funcGraphProp3) => 77.50/10.57 (( 77.50/10.57 (funcGraphProp2) => 77.50/10.57 (( 77.50/10.57 (funcextLem) => 77.50/10.57 (( 77.50/10.57 (funcGraphProp4) => 77.50/10.57 (( 77.50/10.57 (subbreln) => 77.50/10.57 (( 77.50/10.57 (eqbreln) => 77.50/10.57 (( 77.50/10.57 (funcext) => 77.50/10.57 (( 77.50/10.57 (funcext2) => 77.50/10.57 (( 77.50/10.57 (ap2apEq1) => 77.50/10.57 (( 77.50/10.57 (ap2apEq2) => 77.50/10.57 (( 77.50/10.57 (beta1) => 77.50/10.57 (( 77.50/10.57 (eta1) => 77.50/10.57 (( 77.50/10.57 (lam2lamEq) => 77.50/10.57 (( 77.50/10.57 (beta2) => 77.50/10.57 (( 77.50/10.57 (eta2) => 77.50/10.57 (( 77.50/10.57 (iffalseProp1) => 77.50/10.57 (( 77.50/10.57 (iffalseProp2) => 77.50/10.57 (( 77.50/10.57 (iftrueProp1) => 77.50/10.57 (( 77.50/10.57 (iftrueProp2) => 77.50/10.57 (( 77.50/10.57 (ifSingleton) => 77.50/10.57 (( 77.50/10.57 (ifp) => 77.50/10.57 (( 77.50/10.57 (theeq) => 77.50/10.57 (( 77.50/10.57 (iftrue) => 77.50/10.57 (( 77.50/10.57 (iffalse) => 77.50/10.57 (( 77.50/10.57 (iftrueorfalse) => 77.50/10.57 (( 77.50/10.57 (binintersectT_lem) => 77.50/10.57 (( 77.50/10.57 (binunionT_lem) => 77.50/10.57 (( 77.50/10.57 (powersetT_lem) => 77.50/10.57 (( 77.50/10.57 (setminusT_lem) => 77.50/10.57 (( 77.50/10.57 (complementT_lem) => 77.50/10.57 (( 77.50/10.57 (setextT) => 77.50/10.57 (( 77.50/10.57 (subsetTI) => 77.50/10.57 (( 77.50/10.57 (powersetTI1) => 77.50/10.57 (( 77.50/10.57 (powersetTE1) => 77.50/10.57 (( 77.50/10.57 (complementTI1) => 77.50/10.57 (( 77.50/10.57 (complementTE1) => 77.50/10.57 (( 77.50/10.57 (binintersectTELcontra) => 77.50/10.57 (( 77.50/10.57 (binintersectTERcontra) => 77.50/10.57 (( 77.50/10.57 (contrasubsetT) => 77.50/10.57 (( 77.50/10.57 (contrasubsetT1) => 77.50/10.57 (( 77.50/10.57 (contrasubsetT2) => 77.50/10.57 (( 77.50/10.57 (contrasubsetT3) => 77.50/10.57 (( 77.50/10.57 (doubleComplementI1) => 77.50/10.57 (( 77.50/10.57 (doubleComplementE1) => 77.50/10.57 (( 77.50/10.57 (doubleComplementSub1) => 77.50/10.57 (( 77.50/10.57 (doubleComplementSub2) => 77.50/10.57 (( 77.50/10.57 (doubleComplementEq) => 77.50/10.57 (( 77.50/10.57 (complementTnotintersectT) => 77.50/10.57 (( 77.50/10.57 (complementImpComplementIntersect) => 77.50/10.57 (( 77.50/10.57 (complementSubsetComplementIntersect) => 77.50/10.57 (( 77.50/10.57 (complementInPowersetComplementIntersect) => 77.50/10.57 (( 77.50/10.57 (contraSubsetComplement) => 77.50/10.57 (( 77.50/10.57 (complementTcontraSubset) => 77.50/10.57 (( 77.50/10.57 (binunionTILcontra) => 77.50/10.57 (( 77.50/10.57 (binunionTIRcontra) => 77.50/10.57 (( 77.50/10.57 (inIntersectImpInUnion) => 77.50/10.57 (( 77.50/10.57 (inIntersectImpInUnion2) => 77.50/10.57 (( 77.50/10.57 (inIntersectImpInIntersectUnions) => 77.50/10.57 (( 77.50/10.57 (intersectInPowersetIntersectUnions) => 77.50/10.57 (( 77.50/10.57 (inComplementUnionImpNotIn1) => 77.50/10.57 (( 77.50/10.57 (inComplementUnionImpInComplement1) => 77.50/10.57 (( 77.50/10.57 (binunionTE) => 77.50/10.57 (( 77.50/10.57 (binunionTEcontra) => 77.50/10.57 (( 77.50/10.57 (demorgan2a1) => 77.50/10.57 (( 77.50/10.57 (complementUnionInPowersetComplement) => 77.50/10.57 (( 77.50/10.57 (demorgan2a2) => 77.50/10.57 (( 77.50/10.57 (demorgan1a) => 77.50/10.57 (( 77.50/10.57 (demorgan1b) => 77.50/10.57 (( 77.50/10.57 (demorgan1) => 77.50/10.57 (( 77.50/10.57 (demorgan2a) => 77.50/10.57 (( 77.50/10.57 (demorgan2b2) => 77.50/10.57 (( 77.50/10.57 (demorgan2b) => 77.50/10.57 (( 77.50/10.57 (demorgan2) => 77.50/10.57 (( 77.50/10.57 (woz13rule0) => 77.50/10.57 (( 77.50/10.57 (woz13rule1) => 77.50/10.57 (( 77.50/10.57 (woz13rule2) => 77.50/10.57 (( 77.50/10.57 (woz13rule3) => 77.50/10.57 (( 77.50/10.57 (woz13rule4) => 77.50/10.57 (( 77.50/10.57 (woz1_1) => 77.50/10.57 (( 77.50/10.57 (woz1_2) => 77.50/10.57 (( 77.50/10.57 (woz1_3) => 77.50/10.57 (( 77.50/10.57 (woz1_4) => 77.50/10.57 (( 77.50/10.57 (woz1_5) => 77.50/10.57 (( 77.50/10.57 (breln1all2) => 77.50/10.57 (( 77.50/10.57 (breln1SetBreln1) => 77.50/10.57 (( 77.50/10.57 (choice2fnsingleton) => 77.50/10.57 (( 77.50/10.57 (setOfPairsIsBReln1) => 77.50/10.57 (( 77.50/10.57 (breln1all1) => 77.50/10.57 (( 77.50/10.57 (subbreln1) => 77.50/10.57 (( 77.50/10.57 (eqbreln1) => 77.50/10.57 (( 77.50/10.57 (breln1invprop) => 77.50/10.57 (( 77.50/10.57 (breln1invI) => 77.50/10.57 (( 77.50/10.57 (breln1invE) => 77.50/10.57 (( 77.50/10.57 (breln1compprop) => 77.50/10.57 (( 77.50/10.57 (breln1compI) => 77.50/10.57 (( 77.50/10.57 (breln1compE) => 77.50/10.57 (( 77.50/10.57 (breln1compEex) => 77.50/10.57 (( 77.50/10.57 (breln1unionprop) => 77.50/10.57 (( 77.50/10.57 (breln1unionIL) => 77.50/10.57 (( 77.50/10.57 (breln1unionIR) => 77.50/10.57 (( 77.50/10.57 (breln1unionI) => 77.50/10.57 (( 77.50/10.57 (breln1unionE) => 77.50/10.57 (( 77.50/10.57 (breln1unionEcases) => 77.50/10.57 (( 77.50/10.57 (breln1unionCommutes) => 77.50/10.57 (( 77.50/10.57 (woz2Ex) => 77.50/10.57 (( 77.50/10.57 (woz2W) => 77.50/10.57 (( 77.50/10.57 (woz2A) => 77.50/10.57 (( 77.50/10.57 (woz2B) => 77.50/10.57 (( 77.50/10.57 (image1Ex) => 77.50/10.57 (( 77.50/10.57 (image1Ex1) => 77.50/10.57 (( 77.50/10.57 (image1Equiv) => 77.50/10.57 (( 77.50/10.57 (image1E) => 77.50/10.57 (( 77.50/10.57 (image1I) => 77.50/10.57 (( 77.50/10.57 (injFuncInInjFuncSet) => 77.50/10.57 (( 77.50/10.57 (injFuncSetFuncIn) => 77.50/10.57 (( 77.50/10.57 (injFuncSetFuncInj) => 77.50/10.57 (( 77.50/10.57 (surjFuncSetFuncIn) => 77.50/10.57 (( 77.50/10.57 (surjFuncSetFuncSurj) => 77.50/10.57 (( 77.50/10.57 (leftInvIsSurj) => 77.50/10.57 (( 77.50/10.57 (surjCantorThm) => 77.50/10.57 (( 77.50/10.57 (foundation2) => 77.50/10.57 (( 77.50/10.57 (notinself) => 77.50/10.57 (( 77.50/10.57 (notinself2) => 77.50/10.57 (( 77.50/10.57 (omegaSp) => 77.50/10.57 (( 77.50/10.57 (omegaSclos) => 77.50/10.57 (( 77.50/10.57 (peano0notS) => 77.50/10.57 (( 77.50/10.57 (peanoSinj) => 77.50/10.57 (( 77.50/10.57 (transitivesetOp1) => 77.50/10.57 (( 77.50/10.57 (binintTransitive) => 77.50/10.57 (( 77.50/10.57 (transitivesetOp2) => 77.50/10.57 (( 77.50/10.57 (setunionTransitive) => 77.50/10.57 (( 77.50/10.57 (ordinalMinLem1) => 77.50/10.57 (( 77.50/10.57 (!!) @ ( 77.50/10.57 ^[Y0 : $i]: 77.50/10.57 (( 77.50/10.57 (ordinal @ 77.50/10.57 Y0) => 77.50/10.57 (( 77.50/10.57 (!!) @ ( 77.50/10.57 ^[Y1 : $i]: 77.50/10.57 (( 77.50/10.57 (!!) @ ( 77.50/10.57 ^[Y2 : $i]: 77.50/10.57 (( 77.50/10.57 (in @ 77.50/10.57 Y2 @ 77.50/10.57 Y0) => 77.50/10.57 (( 77.50/10.57 (in @ 77.50/10.57 Y1 @ 77.50/10.57 Y2) => 77.50/10.57 (in @ 77.50/10.57 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 77.50/10.57 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl95])). 77.50/10.57 thf(zip_derived_cl133, plain, 77.50/10.57 (~ (((emptysetE) => 77.50/10.57 (((emptysetimpfalse) => 77.50/10.57 (((notinemptyset) => 77.50/10.57 (((exuE3e) => 77.50/10.57 (((setext) => 77.50/10.57 (((emptyI) => 77.50/10.57 (((noeltsimpempty) => 77.50/10.57 (((setbeta) => 77.50/10.57 (((nonemptyE1) => 77.50/10.57 (((nonemptyI) => 77.50/10.57 (((nonemptyI1) => 77.50/10.57 (((setadjoinIL) => 77.50/10.57 (((in @ emptyset @ 77.50/10.57 (setadjoin @ emptyset @ emptyset)) => 77.50/10.57 (((setadjoinIR) => 77.50/10.57 (((setadjoinE) => 77.50/10.57 (((setadjoinOr) => 77.50/10.57 (((setoftrueEq) => 77.50/10.57 (((powersetI) => 77.50/10.57 (((emptyinPowerset) => 77.50/10.57 (((emptyInPowerset) => 77.50/10.57 (((powersetE) => 77.50/10.57 (((setunionI) => 77.50/10.57 (((setunionE) => 77.50/10.57 (((subPowSU) => 77.50/10.57 (((exuE2) => 77.50/10.57 (((nonemptyImpWitness) => 77.50/10.57 (((uniqinunit) => 77.50/10.57 (((notinsingleton) => 77.50/10.57 (((eqinunit) => 77.50/10.57 (((singletonsswitch) => 77.50/10.57 (( 77.50/10.57 (upairsetE) => 77.50/10.57 (( 77.50/10.57 (upairsetIL) => 77.50/10.57 (( 77.50/10.57 (upairsetIR) => 77.50/10.57 (( 77.50/10.57 (emptyE1) => 77.50/10.57 (( 77.50/10.57 (vacuousDall) => 77.50/10.57 (( 77.50/10.57 (quantDeMorgan1) => 77.50/10.57 (( 77.50/10.57 (quantDeMorgan2) => 77.50/10.57 (( 77.50/10.57 (quantDeMorgan3) => 77.50/10.57 (( 77.50/10.57 (quantDeMorgan4) => 77.50/10.57 (( 77.50/10.57 (prop2setI) => 77.50/10.57 (( 77.50/10.57 (prop2set2propI) => 77.50/10.57 (( 77.50/10.57 (notdexE) => 77.50/10.57 (( 77.50/10.57 (notdallE) => 77.50/10.57 (( 77.50/10.57 (exuI1) => 77.50/10.57 (( 77.50/10.57 (exuI3) => 77.50/10.57 (( 77.50/10.57 (exuI2) => 77.50/10.57 (( 77.50/10.57 (inCongP) => 77.50/10.57 (( 77.50/10.57 (in__Cong) => 77.50/10.57 (( 77.50/10.57 (exuE3u) => 77.50/10.57 (( 77.50/10.57 (exu__Cong) => 77.50/10.57 (( 77.50/10.57 (setadjoin__Cong) => 77.50/10.57 (( 77.50/10.57 (powerset__Cong) => 77.50/10.57 (( 77.50/10.57 (setunion__Cong) => 77.50/10.57 (( 77.50/10.57 (exuEu) => 77.50/10.57 (( 77.50/10.57 (descr__Cong) => 77.50/10.57 (( 77.50/10.57 (dsetconstr__Cong) => 77.50/10.57 (( 77.50/10.57 (subsetI1) => 77.50/10.57 (( 77.50/10.57 (eqimpsubset2) => 77.50/10.57 (( 77.50/10.57 (eqimpsubset1) => 77.50/10.57 (( 77.50/10.57 (subsetI2) => 77.50/10.57 (( 77.50/10.57 (emptysetsubset) => 77.50/10.57 (( 77.50/10.57 (subsetE) => 77.50/10.57 (( 77.50/10.57 (subsetE2) => 77.50/10.57 (( 77.50/10.57 (notsubsetI) => 77.50/10.57 (( 77.50/10.57 (notequalI1) => 77.50/10.57 (( 77.50/10.57 (notequalI2) => 77.50/10.57 (( 77.50/10.57 (subsetRefl) => 77.50/10.57 (( 77.50/10.57 (subsetTrans) => 77.50/10.57 (( 77.50/10.57 (setadjoinSub) => 77.50/10.57 (( 77.50/10.57 (setadjoinSub2) => 77.50/10.57 (( 77.50/10.57 (subset2powerset) => 77.50/10.57 (( 77.50/10.57 (setextsub) => 77.50/10.57 (( 77.50/10.57 (subsetemptysetimpeq) => 77.50/10.57 (( 77.50/10.57 (powersetI1) => 77.50/10.57 (( 77.50/10.57 (powersetE1) => 77.50/10.57 (( 77.50/10.57 (inPowerset) => 77.50/10.57 (( 77.50/10.57 (powersetsubset) => 77.50/10.57 (( 77.50/10.57 (sepInPowerset) => 77.50/10.57 (( 77.50/10.57 (sepSubset) => 77.50/10.57 (( 77.50/10.57 (binunionIL) => 77.50/10.57 (( 77.50/10.57 (upairset2IR) => 77.50/10.57 (( 77.50/10.57 (binunionIR) => 77.50/10.57 (( 77.50/10.57 (binunionEcases) => 77.50/10.57 (( 77.50/10.57 (binunionE) => 77.50/10.57 (( 77.50/10.57 (binunionLsub) => 77.50/10.57 (( 77.50/10.57 (binunionRsub) => 77.50/10.57 (( 77.50/10.57 (binintersectI) => 77.50/10.57 (( 77.50/10.57 (binintersectSubset5) => 77.50/10.57 (( 77.50/10.57 (binintersectEL) => 77.50/10.57 (( 77.50/10.57 (binintersectLsub) => 77.50/10.57 (( 77.50/10.57 (binintersectSubset2) => 77.50/10.57 (( 77.50/10.57 (binintersectSubset3) => 77.50/10.57 (( 77.50/10.57 (binintersectER) => 77.50/10.57 (( 77.50/10.57 (disjointsetsI1) => 77.50/10.57 (( 77.50/10.57 (binintersectRsub) => 77.50/10.57 (( 77.50/10.57 (binintersectSubset4) => 77.50/10.57 (( 77.50/10.57 (binintersectSubset1) => 77.50/10.57 (( 77.50/10.57 (bs114d) => 77.50/10.57 (( 77.50/10.57 (setminusI) => 77.50/10.57 (( 77.50/10.57 (setminusEL) => 77.50/10.57 (( 77.50/10.57 (setminusER) => 77.50/10.57 (( 77.50/10.57 (setminusSubset2) => 77.50/10.57 (( 77.50/10.57 (setminusERneg) => 77.50/10.57 (( 77.50/10.57 (setminusELneg) => 77.50/10.57 (( 77.50/10.57 (setminusILneg) => 77.50/10.57 (( 77.50/10.57 (setminusIRneg) => 77.50/10.57 (( 77.50/10.57 (setminusLsub) => 77.50/10.57 (( 77.50/10.57 (setminusSubset1) => 77.50/10.57 (( 77.50/10.57 (symdiffE) => 77.50/10.57 (( 77.50/10.57 (symdiffI1) => 77.50/10.57 (( 77.50/10.57 (symdiffI2) => 77.50/10.57 (( 77.50/10.57 (symdiffIneg1) => 77.50/10.57 (( 77.50/10.57 (symdiffIneg2) => 77.50/10.57 (( 77.50/10.57 (secondinupair) => 77.50/10.57 (( 77.50/10.57 (setukpairIL) => 77.50/10.57 (( 77.50/10.57 (setukpairIR) => 77.50/10.57 (( 77.50/10.57 (kpairiskpair) => 77.50/10.57 (( 77.50/10.57 (kpairp) => 77.50/10.57 (( 77.50/10.57 (singletonsubset) => 77.50/10.57 (( 77.50/10.57 (singletoninpowerset) => 77.50/10.57 (( 77.50/10.57 (singletoninpowunion) => 77.50/10.57 (( 77.50/10.57 (upairset2E) => 77.50/10.57 (( 77.50/10.57 (upairsubunion) => 77.50/10.57 (( 77.50/10.57 (upairinpowunion) => 77.50/10.57 (( 77.50/10.57 (ubforcartprodlem1) => 77.50/10.57 (( 77.50/10.57 (ubforcartprodlem2) => 77.50/10.57 (( 77.50/10.57 (ubforcartprodlem3) => 77.50/10.57 (( 77.50/10.57 (cartprodpairin) => 77.50/10.57 (( 77.50/10.57 (cartprodmempair1) => 77.50/10.57 (( 77.50/10.57 (cartprodmempair) => 77.50/10.57 (( 77.50/10.57 (setunionE2) => 77.50/10.57 (( 77.50/10.57 (setunionsingleton1) => 77.50/10.57 (( 77.50/10.57 (setunionsingleton2) => 77.50/10.57 (( 77.50/10.57 (setunionsingleton) => 77.50/10.57 (( 77.50/10.57 (singletonprop) => 77.50/10.57 (( 77.50/10.57 (ex1E1) => 77.50/10.57 (( 77.50/10.57 (ex1I) => 77.50/10.57 (( 77.50/10.57 (ex1I2) => 77.50/10.57 (( 77.50/10.57 (singletonsuniq) => 77.50/10.57 (( 77.50/10.57 (setukpairinjL1) => 77.50/10.57 (( 77.50/10.57 (kfstsingleton) => 77.50/10.57 (( 77.50/10.57 (theprop) => 77.50/10.57 (( 77.50/10.57 (kfstpairEq) => 77.50/10.57 (( 77.50/10.57 (cartprodfstin) => 77.50/10.57 (( 77.50/10.57 (setukpairinjL2) => 77.50/10.57 (( 77.50/10.57 (setukpairinjL) => 77.50/10.57 (( 77.50/10.57 (setukpairinjR11) => 77.50/10.57 (( 77.50/10.57 (setukpairinjR12) => 77.50/10.57 (( 77.50/10.57 (setukpairinjR1) => 77.50/10.57 (( 77.50/10.57 (upairequniteq) => 77.50/10.57 (( 77.50/10.57 (setukpairinjR2) => 77.50/10.57 (( 77.50/10.57 (setukpairinjR) => 77.50/10.57 (( 77.50/10.57 (ksndsingleton) => 77.50/10.57 (( 77.50/10.57 (ksndpairEq) => 77.50/10.57 (( 77.50/10.57 (kpairsurjEq) => 77.50/10.57 (( 77.50/10.57 (cartprodsndin) => 77.50/10.57 (( 77.50/10.57 (cartprodpairmemEL) => 77.50/10.57 (( 77.50/10.57 (cartprodpairmemER) => 77.50/10.57 (( 77.50/10.57 (cartprodmempaircEq) => 77.50/10.57 (( 77.50/10.57 (cartprodfstpairEq) => 77.50/10.57 (( 77.50/10.57 (cartprodsndpairEq) => 77.50/10.57 (( 77.50/10.57 (cartprodpairsurjEq) => 77.50/10.57 (( 77.50/10.57 (dpsetconstrI) => 77.50/10.57 (( 77.50/10.57 (dpsetconstrSub) => 77.50/10.57 (( 77.50/10.57 (setOfPairsIsBReln) => 77.50/10.57 (( 77.50/10.57 (dpsetconstrERa) => 77.50/10.57 (( 77.50/10.57 (dpsetconstrEL1) => 77.50/10.57 (( 77.50/10.57 (dpsetconstrEL2) => 77.50/10.57 (( 77.50/10.57 (dpsetconstrER) => 77.50/10.57 (( 77.50/10.57 (funcImageSingleton) => 77.50/10.57 (( 77.50/10.57 (apProp) => 77.50/10.57 (( 77.50/10.57 (app) => 77.50/10.57 (( 77.50/10.57 (infuncsetfunc) => 77.50/10.57 (( 77.50/10.57 (ap2p) => 77.50/10.57 (( 77.50/10.57 (funcinfuncset) => 77.50/10.57 (( 77.50/10.57 (lamProp) => 77.50/10.57 (( 77.50/10.57 (lamp) => 77.50/10.57 (( 77.50/10.57 (lam2p) => 77.50/10.57 (( 77.50/10.57 (brelnall1) => 77.50/10.57 (( 77.50/10.57 (brelnall2) => 77.50/10.57 (( 77.50/10.57 (ex1E2) => 77.50/10.57 (( 77.50/10.57 (funcGraphProp1) => 77.50/10.57 (( 77.50/10.57 (funcGraphProp3) => 77.50/10.57 (( 77.50/10.57 (funcGraphProp2) => 77.50/10.57 (( 77.50/10.57 (funcextLem) => 77.50/10.57 (( 77.50/10.57 (funcGraphProp4) => 77.50/10.57 (( 77.50/10.57 (subbreln) => 77.50/10.57 (( 77.50/10.57 (eqbreln) => 77.50/10.57 (( 77.50/10.57 (funcext) => 77.50/10.57 (( 77.50/10.57 (funcext2) => 77.50/10.57 (( 77.50/10.57 (ap2apEq1) => 77.50/10.57 (( 77.50/10.57 (ap2apEq2) => 77.50/10.57 (( 77.50/10.57 (beta1) => 77.50/10.57 (( 77.50/10.57 (eta1) => 77.50/10.57 (( 77.50/10.57 (lam2lamEq) => 77.50/10.57 (( 77.50/10.57 (beta2) => 77.50/10.57 (( 77.50/10.57 (eta2) => 77.50/10.57 (( 77.50/10.57 (iffalseProp1) => 77.50/10.57 (( 77.50/10.57 (iffalseProp2) => 77.50/10.57 (( 77.50/10.57 (iftrueProp1) => 77.50/10.57 (( 77.50/10.57 (iftrueProp2) => 77.50/10.57 (( 77.50/10.57 (ifSingleton) => 77.50/10.57 (( 77.50/10.57 (ifp) => 77.50/10.57 (( 77.50/10.57 (theeq) => 77.50/10.57 (( 77.50/10.57 (iftrue) => 77.50/10.57 (( 77.50/10.57 (iffalse) => 77.50/10.57 (( 77.50/10.57 (iftrueorfalse) => 77.50/10.57 (( 77.50/10.57 (binintersectT_lem) => 77.50/10.57 (( 77.50/10.57 (binunionT_lem) => 77.50/10.57 (( 77.50/10.57 (powersetT_lem) => 77.50/10.57 (( 77.50/10.57 (setminusT_lem) => 77.50/10.57 (( 77.50/10.57 (complementT_lem) => 77.50/10.57 (( 77.50/10.57 (setextT) => 77.50/10.57 (( 77.50/10.57 (subsetTI) => 77.50/10.57 (( 77.50/10.57 (powersetTI1) => 77.50/10.57 (( 77.50/10.57 (powersetTE1) => 77.50/10.57 (( 77.50/10.57 (complementTI1) => 77.50/10.57 (( 77.50/10.57 (complementTE1) => 77.50/10.57 (( 77.50/10.57 (binintersectTELcontra) => 77.50/10.57 (( 77.50/10.57 (binintersectTERcontra) => 77.50/10.57 (( 77.50/10.57 (contrasubsetT) => 77.50/10.57 (( 77.50/10.57 (contrasubsetT1) => 77.50/10.57 (( 77.50/10.57 (contrasubsetT2) => 77.50/10.57 (( 77.50/10.57 (contrasubsetT3) => 77.50/10.57 (( 77.50/10.57 (doubleComplementI1) => 77.50/10.57 (( 77.50/10.57 (doubleComplementE1) => 77.50/10.57 (( 77.50/10.57 (doubleComplementSub1) => 77.50/10.57 (( 77.50/10.57 (doubleComplementSub2) => 77.50/10.57 (( 77.50/10.57 (doubleComplementEq) => 77.50/10.57 (( 77.50/10.57 (complementTnotintersectT) => 77.50/10.57 (( 77.50/10.57 (complementImpComplementIntersect) => 77.50/10.57 (( 77.50/10.57 (complementSubsetComplementIntersect) => 77.50/10.57 (( 77.50/10.57 (complementInPowersetComplementIntersect) => 77.50/10.57 (( 77.50/10.57 (contraSubsetComplement) => 77.50/10.57 (( 77.50/10.57 (complementTcontraSubset) => 77.50/10.57 (( 77.50/10.57 (binunionTILcontra) => 77.50/10.57 (( 77.50/10.57 (binunionTIRcontra) => 77.50/10.57 (( 77.50/10.57 (inIntersectImpInUnion) => 77.50/10.57 (( 77.50/10.57 (inIntersectImpInUnion2) => 77.50/10.57 (( 77.50/10.57 (inIntersectImpInIntersectUnions) => 77.50/10.57 (( 77.50/10.57 (intersectInPowersetIntersectUnions) => 77.50/10.57 (( 77.50/10.57 (inComplementUnionImpNotIn1) => 77.50/10.57 (( 77.50/10.57 (inComplementUnionImpInComplement1) => 77.50/10.57 (( 77.50/10.57 (binunionTE) => 77.50/10.57 (( 77.50/10.57 (binunionTEcontra) => 77.50/10.57 (( 77.50/10.57 (demorgan2a1) => 77.50/10.57 (( 77.50/10.57 (complementUnionInPowersetComplement) => 77.50/10.57 (( 77.50/10.57 (demorgan2a2) => 77.50/10.57 (( 77.50/10.57 (demorgan1a) => 77.50/10.57 (( 77.50/10.57 (demorgan1b) => 77.50/10.57 (( 77.50/10.57 (demorgan1) => 77.50/10.57 (( 77.50/10.57 (demorgan2a) => 77.50/10.57 (( 77.50/10.57 (demorgan2b2) => 77.50/10.57 (( 77.50/10.57 (demorgan2b) => 77.50/10.57 (( 77.50/10.57 (demorgan2) => 77.50/10.57 (( 77.50/10.57 (woz13rule0) => 77.50/10.57 (( 77.50/10.57 (woz13rule1) => 77.50/10.57 (( 77.50/10.57 (woz13rule2) => 77.50/10.57 (( 77.50/10.57 (woz13rule3) => 77.50/10.57 (( 77.50/10.57 (woz13rule4) => 77.50/10.57 (( 77.50/10.57 (woz1_1) => 77.50/10.57 (( 77.50/10.57 (woz1_2) => 77.50/10.57 (( 77.50/10.57 (woz1_3) => 77.50/10.57 (( 77.50/10.57 (woz1_4) => 77.50/10.57 (( 77.50/10.57 (woz1_5) => 77.50/10.57 (( 77.50/10.57 (breln1all2) => 77.50/10.57 (( 77.50/10.57 (breln1SetBreln1) => 77.50/10.57 (( 77.50/10.57 (choice2fnsingleton) => 77.50/10.57 (( 77.50/10.57 (setOfPairsIsBReln1) => 77.50/10.57 (( 77.50/10.57 (breln1all1) => 77.50/10.57 (( 77.50/10.57 (subbreln1) => 77.50/10.57 (( 77.50/10.57 (eqbreln1) => 77.50/10.57 (( 77.50/10.57 (breln1invprop) => 77.50/10.57 (( 77.50/10.57 (breln1invI) => 77.50/10.57 (( 77.50/10.57 (breln1invE) => 77.50/10.57 (( 77.50/10.57 (breln1compprop) => 77.50/10.57 (( 77.50/10.57 (breln1compI) => 77.50/10.57 (( 77.50/10.57 (breln1compE) => 77.50/10.57 (( 77.50/10.57 (breln1compEex) => 77.50/10.57 (( 77.50/10.57 (breln1unionprop) => 77.50/10.57 (( 77.50/10.57 (breln1unionIL) => 77.50/10.57 (( 77.50/10.57 (breln1unionIR) => 77.50/10.57 (( 77.50/10.57 (breln1unionI) => 77.50/10.57 (( 77.50/10.57 (breln1unionE) => 77.50/10.57 (( 77.50/10.57 (breln1unionEcases) => 77.50/10.57 (( 77.50/10.57 (breln1unionCommutes) => 77.50/10.57 (( 77.50/10.57 (woz2Ex) => 77.50/10.57 (( 77.50/10.57 (woz2W) => 77.50/10.57 (( 77.50/10.57 (woz2A) => 77.50/10.57 (( 77.50/10.57 (woz2B) => 77.50/10.57 (( 77.50/10.57 (image1Ex) => 77.50/10.57 (( 77.50/10.57 (image1Ex1) => 77.50/10.57 (( 77.50/10.57 (image1Equiv) => 77.50/10.57 (( 77.50/10.57 (image1E) => 77.50/10.57 (( 77.50/10.57 (image1I) => 77.50/10.57 (( 77.50/10.57 (injFuncInInjFuncSet) => 77.50/10.57 (( 77.50/10.57 (injFuncSetFuncIn) => 77.50/10.57 (( 77.50/10.57 (injFuncSetFuncInj) => 77.50/10.57 (( 77.50/10.57 (surjFuncSetFuncIn) => 77.50/10.57 (( 77.50/10.57 (surjFuncSetFuncSurj) => 77.50/10.57 (( 77.50/10.57 (leftInvIsSurj) => 77.50/10.57 (( 77.50/10.57 (surjCantorThm) => 77.50/10.57 (( 77.50/10.57 (foundation2) => 77.50/10.57 (( 77.50/10.57 (notinself) => 77.50/10.57 (( 77.50/10.57 (notinself2) => 77.50/10.57 (( 77.50/10.57 (omegaSp) => 77.50/10.57 (( 77.50/10.57 (omegaSclos) => 77.50/10.57 (( 77.50/10.57 (peano0notS) => 77.50/10.57 (( 77.50/10.57 (peanoSinj) => 77.50/10.57 (( 77.50/10.57 (transitivesetOp1) => 77.50/10.57 (( 77.50/10.57 (binintTransitive) => 77.50/10.57 (( 77.50/10.57 (transitivesetOp2) => 77.50/10.57 (( 77.50/10.57 (setunionTransitive) => 77.50/10.57 (( 77.50/10.57 (ordinalMinLem1) => 77.50/10.57 (( 77.50/10.57 (!!) @ ( 77.50/10.57 ^[Y0 : $i]: 77.50/10.57 (( 77.50/10.57 (ordinal @ 77.50/10.57 Y0) => 77.50/10.57 (( 77.50/10.57 (!!) @ ( 77.50/10.57 ^[Y1 : $i]: 77.50/10.57 (( 77.50/10.57 (!!) @ ( 77.50/10.57 ^[Y2 : $i]: 77.50/10.57 (( 77.50/10.57 (in @ 77.50/10.57 Y2 @ 77.50/10.57 Y0) => 77.50/10.57 (( 77.50/10.57 (in @ 77.50/10.57 Y1 @ 77.50/10.57 Y2) => 77.50/10.57 (in @ 77.50/10.57 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 77.50/10.57 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl115])). 77.50/10.57 thf(zip_derived_cl149, plain, 77.50/10.57 (~ (((emptysetimpfalse) => 77.50/10.57 (((notinemptyset) => 77.50/10.57 (((exuE3e) => 77.50/10.57 (((setext) => 77.50/10.57 (((emptyI) => 77.50/10.57 (((noeltsimpempty) => 77.50/10.57 (((setbeta) => 77.50/10.57 (((nonemptyE1) => 77.50/10.57 (((nonemptyI) => 77.50/10.57 (((nonemptyI1) => 77.50/10.57 (((setadjoinIL) => 77.50/10.57 (((in @ emptyset @ 77.50/10.57 (setadjoin @ emptyset @ emptyset)) => 77.50/10.57 (((setadjoinIR) => 77.50/10.57 (((setadjoinE) => 77.50/10.57 (((setadjoinOr) => 77.50/10.57 (((setoftrueEq) => 77.50/10.57 (((powersetI) => 77.50/10.57 (((emptyinPowerset) => 77.50/10.57 (((emptyInPowerset) => 77.50/10.57 (((powersetE) => 77.50/10.57 (((setunionI) => 77.50/10.57 (((setunionE) => 77.50/10.57 (((subPowSU) => 77.50/10.57 (((exuE2) => 77.50/10.57 (((nonemptyImpWitness) => 77.50/10.57 (((uniqinunit) => 77.50/10.57 (((notinsingleton) => 77.50/10.57 (((eqinunit) => 77.50/10.57 (((singletonsswitch) => 77.50/10.57 (((upairsetE) => 77.50/10.57 (( 77.50/10.57 (upairsetIL) => 77.50/10.57 (( 77.50/10.57 (upairsetIR) => 77.50/10.57 (( 77.50/10.57 (emptyE1) => 77.50/10.57 (( 77.50/10.57 (vacuousDall) => 77.50/10.57 (( 77.50/10.57 (quantDeMorgan1) => 77.50/10.57 (( 77.50/10.57 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77.50/10.57 (( 77.50/10.57 (setukpairinjR12) => 77.50/10.57 (( 77.50/10.57 (setukpairinjR1) => 77.50/10.57 (( 77.50/10.57 (upairequniteq) => 77.50/10.57 (( 77.50/10.57 (setukpairinjR2) => 77.50/10.57 (( 77.50/10.57 (setukpairinjR) => 77.50/10.57 (( 77.50/10.57 (ksndsingleton) => 77.50/10.57 (( 77.50/10.57 (ksndpairEq) => 77.50/10.57 (( 77.50/10.57 (kpairsurjEq) => 77.50/10.57 (( 77.50/10.57 (cartprodsndin) => 77.50/10.57 (( 77.50/10.57 (cartprodpairmemEL) => 77.50/10.57 (( 77.50/10.57 (cartprodpairmemER) => 77.50/10.57 (( 77.50/10.57 (cartprodmempaircEq) => 77.50/10.57 (( 77.50/10.57 (cartprodfstpairEq) => 77.50/10.57 (( 77.50/10.57 (cartprodsndpairEq) => 77.50/10.57 (( 77.50/10.57 (cartprodpairsurjEq) => 77.50/10.57 (( 77.50/10.57 (dpsetconstrI) => 77.50/10.57 (( 77.50/10.57 (dpsetconstrSub) => 77.50/10.57 (( 77.50/10.57 (setOfPairsIsBReln) => 77.50/10.57 (( 77.50/10.57 (dpsetconstrERa) => 77.50/10.57 (( 77.50/10.57 (dpsetconstrEL1) => 77.50/10.57 (( 77.50/10.57 (dpsetconstrEL2) => 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77.50/10.57 Y0) => 77.50/10.57 (( 77.50/10.57 (in @ 77.50/10.57 Y1 @ 77.50/10.57 Y2) => 77.50/10.57 (in @ 77.50/10.57 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 77.50/10.57 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl133])). 77.50/10.57 thf(zip_derived_cl164, plain, 77.50/10.57 (~ (((notinemptyset) => 77.50/10.57 (((exuE3e) => 77.50/10.57 (((setext) => 77.50/10.57 (((emptyI) 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77.50/10.57 (( 77.50/10.57 (setukpairinjR11) => 77.50/10.57 (( 77.50/10.57 (setukpairinjR12) => 77.50/10.57 (( 77.50/10.57 (setukpairinjR1) => 77.50/10.57 (( 77.50/10.57 (upairequniteq) => 77.50/10.57 (( 77.50/10.57 (setukpairinjR2) => 77.50/10.57 (( 77.50/10.57 (setukpairinjR) => 77.50/10.57 (( 77.50/10.57 (ksndsingleton) => 77.50/10.57 (( 77.50/10.57 (ksndpairEq) => 77.50/10.57 (( 77.50/10.57 (kpairsurjEq) => 77.50/10.57 (( 77.50/10.57 (cartprodsndin) => 77.50/10.57 (( 77.50/10.57 (cartprodpairmemEL) => 77.50/10.57 (( 77.50/10.57 (cartprodpairmemER) => 77.50/10.57 (( 77.50/10.57 (cartprodmempaircEq) => 77.50/10.57 (( 77.50/10.57 (cartprodfstpairEq) => 77.50/10.57 (( 77.50/10.57 (cartprodsndpairEq) => 77.50/10.57 (( 77.50/10.57 (cartprodpairsurjEq) => 77.50/10.57 (( 77.50/10.57 (dpsetconstrI) => 77.50/10.57 (( 77.50/10.57 (dpsetconstrSub) => 77.50/10.57 (( 77.50/10.57 (setOfPairsIsBReln) => 77.50/10.57 (( 77.50/10.57 (dpsetconstrERa) => 77.50/10.57 (( 77.50/10.57 (dpsetconstrEL1) => 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(injFuncSetFuncInj) => 77.50/10.57 (( 77.50/10.57 (surjFuncSetFuncIn) => 77.50/10.57 (( 77.50/10.57 (surjFuncSetFuncSurj) => 77.50/10.57 (( 77.50/10.57 (leftInvIsSurj) => 77.50/10.57 (( 77.50/10.57 (surjCantorThm) => 77.50/10.57 (( 77.50/10.57 (foundation2) => 77.50/10.57 (( 77.50/10.57 (notinself) => 77.50/10.57 (( 77.50/10.57 (notinself2) => 77.50/10.57 (( 77.50/10.57 (omegaSp) => 77.50/10.57 (( 77.50/10.57 (omegaSclos) => 77.50/10.57 (( 77.50/10.57 (peano0notS) => 77.50/10.57 (( 77.50/10.57 (peanoSinj) => 77.50/10.57 (( 77.50/10.57 (transitivesetOp1) => 77.50/10.57 (( 77.50/10.57 (binintTransitive) => 77.50/10.57 (( 77.50/10.57 (transitivesetOp2) => 77.50/10.57 (( 77.50/10.57 (setunionTransitive) => 77.50/10.57 (( 77.50/10.57 (ordinalMinLem1) => 77.50/10.57 (( 77.50/10.57 (!!) @ ( 77.50/10.57 ^[Y0 : $i]: 77.50/10.57 (( 77.50/10.57 (ordinal @ 77.50/10.57 Y0) => 77.50/10.57 (( 77.50/10.57 (!!) @ ( 77.50/10.57 ^[Y1 : $i]: 77.50/10.57 (( 77.50/10.57 (!!) @ ( 77.50/10.57 ^[Y2 : $i]: 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(binunionIR) => 77.50/10.57 (( 77.50/10.57 (binunionEcases) => 77.50/10.57 (( 77.50/10.57 (binunionE) => 77.50/10.57 (( 77.50/10.57 (binunionLsub) => 77.50/10.57 (( 77.50/10.57 (binunionRsub) => 77.50/10.57 (( 77.50/10.57 (binintersectI) => 77.50/10.57 (( 77.50/10.57 (binintersectSubset5) => 77.50/10.57 (( 77.50/10.57 (binintersectEL) => 77.50/10.57 (( 77.50/10.57 (binintersectLsub) => 77.50/10.57 (( 77.50/10.57 (binintersectSubset2) => 77.50/10.57 (( 77.50/10.57 (binintersectSubset3) => 77.50/10.57 (( 77.50/10.57 (binintersectER) => 77.50/10.57 (( 77.50/10.57 (disjointsetsI1) => 77.50/10.57 (( 77.50/10.57 (binintersectRsub) => 77.50/10.57 (( 77.50/10.57 (binintersectSubset4) => 77.50/10.57 (( 77.50/10.57 (binintersectSubset1) => 77.50/10.57 (( 77.50/10.57 (bs114d) => 77.50/10.57 (( 77.50/10.57 (setminusI) => 77.50/10.57 (( 77.50/10.57 (setminusEL) => 77.50/10.57 (( 77.50/10.57 (setminusER) => 77.50/10.57 (( 77.50/10.57 (setminusSubset2) => 77.50/10.57 (( 77.50/10.57 (setminusERneg) => 77.50/10.57 (( 77.50/10.57 (setminusELneg) => 77.50/10.57 (( 77.50/10.57 (setminusILneg) => 77.50/10.57 (( 77.50/10.57 (setminusIRneg) => 77.50/10.57 (( 77.50/10.57 (setminusLsub) => 77.50/10.57 (( 77.50/10.57 (setminusSubset1) => 77.50/10.57 (( 77.50/10.57 (symdiffE) => 77.50/10.57 (( 77.50/10.57 (symdiffI1) => 77.50/10.57 (( 77.50/10.57 (symdiffI2) => 77.50/10.57 (( 77.50/10.57 (symdiffIneg1) => 77.50/10.57 (( 77.50/10.57 (symdiffIneg2) => 77.50/10.57 (( 77.50/10.57 (secondinupair) => 77.50/10.57 (( 77.50/10.57 (setukpairIL) => 77.50/10.57 (( 77.50/10.57 (setukpairIR) => 77.50/10.57 (( 77.50/10.57 (kpairiskpair) => 77.50/10.57 (( 77.50/10.57 (kpairp) => 77.50/10.57 (( 77.50/10.57 (singletonsubset) => 77.50/10.57 (( 77.50/10.57 (singletoninpowerset) => 77.50/10.57 (( 77.50/10.57 (singletoninpowunion) => 77.50/10.57 (( 77.50/10.57 (upairset2E) => 77.50/10.57 (( 77.50/10.57 (upairsubunion) => 77.50/10.57 (( 77.50/10.57 (upairinpowunion) => 77.50/10.57 (( 77.50/10.57 (ubforcartprodlem1) => 77.50/10.57 (( 77.50/10.57 (ubforcartprodlem2) => 77.50/10.57 (( 77.50/10.57 (ubforcartprodlem3) => 77.50/10.57 (( 77.50/10.57 (cartprodpairin) => 77.50/10.57 (( 77.50/10.57 (cartprodmempair1) => 77.50/10.57 (( 77.50/10.57 (cartprodmempair) => 77.50/10.57 (( 77.50/10.57 (setunionE2) => 77.50/10.57 (( 77.50/10.57 (setunionsingleton1) => 77.50/10.57 (( 77.50/10.57 (setunionsingleton2) => 77.50/10.57 (( 77.50/10.57 (setunionsingleton) => 77.50/10.57 (( 77.50/10.57 (singletonprop) => 77.50/10.57 (( 77.50/10.57 (ex1E1) => 77.50/10.57 (( 77.50/10.57 (ex1I) => 77.50/10.57 (( 77.50/10.57 (ex1I2) => 77.50/10.57 (( 77.50/10.57 (singletonsuniq) => 77.50/10.57 (( 77.50/10.57 (setukpairinjL1) => 77.50/10.57 (( 77.50/10.57 (kfstsingleton) => 77.50/10.57 (( 77.50/10.57 (theprop) => 77.50/10.57 (( 77.50/10.57 (kfstpairEq) => 77.50/10.57 (( 77.50/10.57 (cartprodfstin) => 77.50/10.57 (( 77.50/10.57 (setukpairinjL2) => 77.50/10.57 (( 77.50/10.57 (setukpairinjL) => 77.50/10.57 (( 77.50/10.57 (setukpairinjR11) => 77.50/10.57 (( 77.50/10.57 (setukpairinjR12) => 77.50/10.57 (( 77.50/10.57 (setukpairinjR1) => 77.50/10.57 (( 77.50/10.57 (upairequniteq) => 77.50/10.57 (( 77.50/10.57 (setukpairinjR2) => 77.50/10.57 (( 77.50/10.57 (setukpairinjR) => 77.50/10.57 (( 77.50/10.57 (ksndsingleton) => 77.50/10.57 (( 77.50/10.57 (ksndpairEq) => 77.50/10.57 (( 77.50/10.57 (kpairsurjEq) => 77.50/10.57 (( 77.50/10.57 (cartprodsndin) => 77.50/10.57 (( 77.50/10.57 (cartprodpairmemEL) => 77.50/10.57 (( 77.50/10.57 (cartprodpairmemER) => 77.50/10.57 (( 77.50/10.57 (cartprodmempaircEq) => 77.50/10.57 (( 77.50/10.57 (cartprodfstpairEq) => 77.50/10.57 (( 77.50/10.57 (cartprodsndpairEq) => 77.50/10.57 (( 77.50/10.57 (cartprodpairsurjEq) => 77.50/10.57 (( 77.50/10.57 (dpsetconstrI) => 77.50/10.57 (( 77.50/10.57 (dpsetconstrSub) => 77.50/10.57 (( 77.50/10.57 (setOfPairsIsBReln) => 77.50/10.57 (( 77.50/10.57 (dpsetconstrERa) => 77.50/10.57 (( 77.50/10.57 (dpsetconstrEL1) => 77.50/10.57 (( 77.50/10.57 (dpsetconstrEL2) => 77.50/10.57 (( 77.50/10.57 (dpsetconstrER) => 77.50/10.57 (( 77.50/10.57 (funcImageSingleton) => 77.50/10.57 (( 77.50/10.57 (apProp) => 77.50/10.57 (( 77.50/10.57 (app) => 77.50/10.57 (( 77.50/10.57 (infuncsetfunc) => 77.50/10.57 (( 77.50/10.57 (ap2p) => 77.50/10.57 (( 77.50/10.57 (funcinfuncset) => 77.50/10.57 (( 77.50/10.57 (lamProp) => 77.50/10.57 (( 77.50/10.57 (lamp) => 77.50/10.57 (( 77.50/10.57 (lam2p) => 77.50/10.57 (( 77.50/10.57 (brelnall1) => 77.50/10.57 (( 77.50/10.57 (brelnall2) => 77.50/10.57 (( 77.50/10.57 (ex1E2) => 77.50/10.57 (( 77.50/10.57 (funcGraphProp1) => 77.50/10.57 (( 77.50/10.57 (funcGraphProp3) => 77.50/10.57 (( 77.50/10.57 (funcGraphProp2) => 77.50/10.57 (( 77.50/10.57 (funcextLem) => 77.50/10.57 (( 77.50/10.57 (funcGraphProp4) => 77.50/10.57 (( 77.50/10.57 (subbreln) => 77.50/10.57 (( 77.50/10.57 (eqbreln) => 77.50/10.57 (( 77.50/10.57 (funcext) => 77.50/10.57 (( 77.50/10.57 (funcext2) => 77.50/10.57 (( 77.50/10.57 (ap2apEq1) => 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(powersetTI1) => 77.50/10.57 (( 77.50/10.57 (powersetTE1) => 77.50/10.57 (( 77.50/10.57 (complementTI1) => 77.50/10.57 (( 77.50/10.57 (complementTE1) => 77.50/10.57 (( 77.50/10.57 (binintersectTELcontra) => 77.50/10.57 (( 77.50/10.57 (binintersectTERcontra) => 77.50/10.57 (( 77.50/10.57 (contrasubsetT) => 77.50/10.57 (( 77.50/10.57 (contrasubsetT1) => 77.50/10.57 (( 77.50/10.57 (contrasubsetT2) => 77.50/10.57 (( 77.50/10.57 (contrasubsetT3) => 77.50/10.57 (( 77.50/10.57 (doubleComplementI1) => 77.50/10.57 (( 77.50/10.57 (doubleComplementE1) => 77.50/10.57 (( 77.50/10.57 (doubleComplementSub1) => 77.50/10.57 (( 77.50/10.57 (doubleComplementSub2) => 77.50/10.57 (( 77.50/10.57 (doubleComplementEq) => 77.50/10.57 (( 77.50/10.57 (complementTnotintersectT) => 77.50/10.57 (( 77.50/10.57 (complementImpComplementIntersect) => 77.50/10.57 (( 77.50/10.57 (complementSubsetComplementIntersect) => 77.50/10.57 (( 77.50/10.57 (complementInPowersetComplementIntersect) => 77.50/10.57 (( 77.50/10.57 (contraSubsetComplement) => 77.50/10.57 (( 77.50/10.57 (complementTcontraSubset) => 77.50/10.57 (( 77.50/10.57 (binunionTILcontra) => 77.50/10.57 (( 77.50/10.57 (binunionTIRcontra) => 77.50/10.57 (( 77.50/10.57 (inIntersectImpInUnion) => 77.50/10.57 (( 77.50/10.57 (inIntersectImpInUnion2) => 77.50/10.57 (( 77.50/10.57 (inIntersectImpInIntersectUnions) => 77.50/10.57 (( 77.50/10.57 (intersectInPowersetIntersectUnions) => 77.50/10.57 (( 77.50/10.57 (inComplementUnionImpNotIn1) => 77.50/10.57 (( 77.50/10.57 (inComplementUnionImpInComplement1) => 77.50/10.57 (( 77.50/10.57 (binunionTE) => 77.50/10.57 (( 77.50/10.57 (binunionTEcontra) => 77.50/10.57 (( 77.50/10.57 (demorgan2a1) => 77.50/10.57 (( 77.50/10.57 (complementUnionInPowersetComplement) => 77.50/10.57 (( 77.50/10.57 (demorgan2a2) => 77.50/10.57 (( 77.50/10.57 (demorgan1a) => 77.50/10.57 (( 77.50/10.57 (demorgan1b) => 77.50/10.57 (( 77.50/10.57 (demorgan1) => 77.50/10.57 (( 77.50/10.57 (demorgan2a) => 77.50/10.57 (( 77.50/10.57 (demorgan2b2) => 77.50/10.57 (( 77.50/10.57 (demorgan2b) => 77.50/10.57 (( 77.50/10.57 (demorgan2) => 77.50/10.57 (( 77.50/10.57 (woz13rule0) => 77.50/10.57 (( 77.50/10.57 (woz13rule1) => 77.50/10.57 (( 77.50/10.57 (woz13rule2) => 77.50/10.57 (( 77.50/10.57 (woz13rule3) => 77.50/10.57 (( 77.50/10.57 (woz13rule4) => 77.50/10.57 (( 77.50/10.57 (woz1_1) => 77.50/10.57 (( 77.50/10.57 (woz1_2) => 77.50/10.57 (( 77.50/10.57 (woz1_3) => 77.50/10.57 (( 77.50/10.57 (woz1_4) => 77.50/10.57 (( 77.50/10.57 (woz1_5) => 77.50/10.57 (( 77.50/10.57 (breln1all2) => 77.50/10.57 (( 77.50/10.57 (breln1SetBreln1) => 77.50/10.57 (( 77.50/10.57 (choice2fnsingleton) => 77.50/10.57 (( 77.50/10.57 (setOfPairsIsBReln1) => 77.50/10.57 (( 77.50/10.57 (breln1all1) => 77.50/10.57 (( 77.50/10.57 (subbreln1) => 77.50/10.57 (( 77.50/10.57 (eqbreln1) => 77.50/10.57 (( 77.50/10.57 (breln1invprop) => 77.50/10.57 (( 77.50/10.57 (breln1invI) => 77.50/10.57 (( 77.50/10.57 (breln1invE) => 77.50/10.57 (( 77.50/10.57 (breln1compprop) => 77.50/10.57 (( 77.50/10.57 (breln1compI) => 77.50/10.57 (( 77.50/10.57 (breln1compE) => 77.50/10.57 (( 77.50/10.57 (breln1compEex) => 77.50/10.57 (( 77.50/10.57 (breln1unionprop) => 77.50/10.57 (( 77.50/10.57 (breln1unionIL) => 77.50/10.57 (( 77.50/10.57 (breln1unionIR) => 77.50/10.57 (( 77.50/10.57 (breln1unionI) => 77.50/10.57 (( 77.50/10.57 (breln1unionE) => 77.50/10.57 (( 77.50/10.57 (breln1unionEcases) => 77.50/10.57 (( 77.50/10.57 (breln1unionCommutes) => 77.50/10.57 (( 77.50/10.57 (woz2Ex) => 77.50/10.57 (( 77.50/10.57 (woz2W) => 77.50/10.57 (( 77.50/10.57 (woz2A) => 77.50/10.57 (( 77.50/10.57 (woz2B) => 77.50/10.57 (( 77.50/10.57 (image1Ex) => 77.50/10.57 (( 77.50/10.57 (image1Ex1) => 77.50/10.57 (( 77.50/10.57 (image1Equiv) => 77.50/10.57 (( 77.50/10.57 (image1E) => 77.50/10.57 (( 77.50/10.57 (image1I) => 77.50/10.57 (( 77.50/10.57 (injFuncInInjFuncSet) => 77.50/10.57 (( 77.50/10.57 (injFuncSetFuncIn) => 77.50/10.57 (( 77.50/10.57 (injFuncSetFuncInj) => 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(in @ 77.50/10.57 Y2 @ 77.50/10.57 Y0) => 77.50/10.57 (( 77.50/10.57 (in @ 77.50/10.57 Y1 @ 77.50/10.57 Y2) => 77.50/10.57 (in @ 77.50/10.57 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 77.50/10.57 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl177])). 77.50/10.57 thf(zip_derived_cl205, plain, 77.50/10.57 (~ (((emptyI) => 77.50/10.57 (((noeltsimpempty) => 77.50/10.57 (((setbeta) => 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77.50/10.57 (setminusILneg) => 77.50/10.57 (( 77.50/10.57 (setminusIRneg) => 77.50/10.57 (( 77.50/10.57 (setminusLsub) => 77.50/10.57 (( 77.50/10.57 (setminusSubset1) => 77.50/10.57 (( 77.50/10.57 (symdiffE) => 77.50/10.57 (( 77.50/10.57 (symdiffI1) => 77.50/10.57 (( 77.50/10.57 (symdiffI2) => 77.50/10.57 (( 77.50/10.57 (symdiffIneg1) => 77.50/10.57 (( 77.50/10.57 (symdiffIneg2) => 77.50/10.57 (( 77.50/10.57 (secondinupair) => 77.50/10.57 (( 77.50/10.57 (setukpairIL) => 77.50/10.57 (( 77.50/10.57 (setukpairIR) => 77.50/10.57 (( 77.50/10.57 (kpairiskpair) => 77.50/10.57 (( 77.50/10.57 (kpairp) => 77.50/10.57 (( 77.50/10.57 (singletonsubset) => 77.50/10.57 (( 77.50/10.57 (singletoninpowerset) => 77.50/10.57 (( 77.50/10.57 (singletoninpowunion) => 77.50/10.57 (( 77.50/10.57 (upairset2E) => 77.50/10.57 (( 77.50/10.57 (upairsubunion) => 77.50/10.57 (( 77.50/10.57 (upairinpowunion) => 77.50/10.57 (( 77.50/10.57 (ubforcartprodlem1) => 77.50/10.57 (( 77.50/10.57 (ubforcartprodlem2) => 77.50/10.57 (( 77.50/10.57 (ubforcartprodlem3) => 77.50/10.57 (( 77.50/10.57 (cartprodpairin) => 77.50/10.57 (( 77.50/10.57 (cartprodmempair1) => 77.50/10.57 (( 77.50/10.57 (cartprodmempair) => 77.50/10.57 (( 77.50/10.57 (setunionE2) => 77.50/10.57 (( 77.50/10.57 (setunionsingleton1) => 77.50/10.57 (( 77.50/10.57 (setunionsingleton2) => 77.50/10.57 (( 77.50/10.57 (setunionsingleton) => 77.50/10.57 (( 77.50/10.57 (singletonprop) => 77.50/10.57 (( 77.50/10.57 (ex1E1) => 77.50/10.57 (( 77.50/10.57 (ex1I) => 77.50/10.57 (( 77.50/10.57 (ex1I2) => 77.50/10.57 (( 77.50/10.57 (singletonsuniq) => 77.50/10.57 (( 77.50/10.57 (setukpairinjL1) => 77.50/10.57 (( 77.50/10.57 (kfstsingleton) => 77.50/10.57 (( 77.50/10.57 (theprop) => 77.50/10.57 (( 77.50/10.57 (kfstpairEq) => 77.50/10.57 (( 77.50/10.57 (cartprodfstin) => 77.50/10.57 (( 77.50/10.57 (setukpairinjL2) => 77.50/10.57 (( 77.50/10.57 (setukpairinjL) => 77.50/10.57 (( 77.50/10.57 (setukpairinjR11) => 77.50/10.57 (( 77.50/10.57 (setukpairinjR12) => 77.50/10.57 (( 77.50/10.57 (setukpairinjR1) => 77.50/10.57 (( 77.50/10.57 (upairequniteq) => 77.50/10.57 (( 77.50/10.57 (setukpairinjR2) => 77.50/10.57 (( 77.50/10.57 (setukpairinjR) => 77.50/10.57 (( 77.50/10.57 (ksndsingleton) => 77.50/10.57 (( 77.50/10.57 (ksndpairEq) => 77.50/10.57 (( 77.50/10.57 (kpairsurjEq) => 77.50/10.57 (( 77.50/10.57 (cartprodsndin) => 77.50/10.57 (( 77.50/10.57 (cartprodpairmemEL) => 77.50/10.57 (( 77.50/10.57 (cartprodpairmemER) => 77.50/10.57 (( 77.50/10.57 (cartprodmempaircEq) => 77.50/10.57 (( 77.50/10.57 (cartprodfstpairEq) => 77.50/10.57 (( 77.50/10.57 (cartprodsndpairEq) => 77.50/10.57 (( 77.50/10.57 (cartprodpairsurjEq) => 77.50/10.57 (( 77.50/10.57 (dpsetconstrI) => 77.50/10.57 (( 77.50/10.57 (dpsetconstrSub) => 77.50/10.57 (( 77.50/10.57 (setOfPairsIsBReln) => 77.50/10.57 (( 77.50/10.57 (dpsetconstrERa) => 77.50/10.57 (( 77.50/10.57 (dpsetconstrEL1) => 77.50/10.57 (( 77.50/10.57 (dpsetconstrEL2) => 77.50/10.57 (( 77.50/10.57 (dpsetconstrER) => 77.50/10.57 (( 77.50/10.57 (funcImageSingleton) => 77.50/10.57 (( 77.50/10.57 (apProp) => 77.50/10.57 (( 77.50/10.57 (app) => 77.50/10.57 (( 77.50/10.57 (infuncsetfunc) => 77.50/10.57 (( 77.50/10.57 (ap2p) => 77.50/10.57 (( 77.50/10.57 (funcinfuncset) => 77.50/10.57 (( 77.50/10.57 (lamProp) => 77.50/10.57 (( 77.50/10.57 (lamp) => 77.50/10.57 (( 77.50/10.57 (lam2p) => 77.50/10.57 (( 77.50/10.57 (brelnall1) => 77.50/10.57 (( 77.50/10.57 (brelnall2) => 77.50/10.57 (( 77.50/10.57 (ex1E2) => 77.50/10.57 (( 77.50/10.57 (funcGraphProp1) => 77.50/10.57 (( 77.50/10.57 (funcGraphProp3) => 77.50/10.57 (( 77.50/10.57 (funcGraphProp2) => 77.50/10.57 (( 77.50/10.57 (funcextLem) => 77.50/10.57 (( 77.50/10.57 (funcGraphProp4) => 77.50/10.57 (( 77.50/10.57 (subbreln) => 77.50/10.57 (( 77.50/10.57 (eqbreln) => 77.50/10.57 (( 77.50/10.57 (funcext) => 77.50/10.57 (( 77.50/10.57 (funcext2) => 77.50/10.57 (( 77.50/10.57 (ap2apEq1) => 77.50/10.57 (( 77.50/10.57 (ap2apEq2) => 77.50/10.57 (( 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=> 77.50/10.57 (( 77.50/10.57 (complementTI1) => 77.50/10.57 (( 77.50/10.57 (complementTE1) => 77.50/10.57 (( 77.50/10.57 (binintersectTELcontra) => 77.50/10.57 (( 77.50/10.57 (binintersectTERcontra) => 77.50/10.57 (( 77.50/10.57 (contrasubsetT) => 77.50/10.57 (( 77.50/10.57 (contrasubsetT1) => 77.50/10.57 (( 77.50/10.57 (contrasubsetT2) => 77.50/10.57 (( 77.50/10.57 (contrasubsetT3) => 77.50/10.57 (( 77.50/10.57 (doubleComplementI1) => 77.50/10.57 (( 77.50/10.57 (doubleComplementE1) => 77.50/10.57 (( 77.50/10.57 (doubleComplementSub1) => 77.50/10.57 (( 77.50/10.57 (doubleComplementSub2) => 77.50/10.57 (( 77.50/10.57 (doubleComplementEq) => 77.50/10.57 (( 77.50/10.57 (complementTnotintersectT) => 77.50/10.57 (( 77.50/10.57 (complementImpComplementIntersect) => 77.50/10.57 (( 77.50/10.57 (complementSubsetComplementIntersect) => 77.50/10.57 (( 77.50/10.57 (complementInPowersetComplementIntersect) => 77.50/10.57 (( 77.50/10.57 (contraSubsetComplement) => 77.50/10.57 (( 77.50/10.57 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77.50/10.57 (in @ 77.50/10.57 Y1 @ 77.50/10.57 Y2) => 77.50/10.57 (in @ 77.50/10.57 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 77.50/10.57 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl191])). 77.50/10.57 thf(zip_derived_cl219, plain, 77.50/10.57 (~ (((noeltsimpempty) => 77.50/10.57 (((setbeta) => 77.50/10.57 (((nonemptyE1) => 77.50/10.57 (((nonemptyI) => 77.50/10.57 (((nonemptyI1) => 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(binunionRsub) => 77.50/10.57 (( 77.50/10.57 (binintersectI) => 77.50/10.57 (( 77.50/10.57 (binintersectSubset5) => 77.50/10.57 (( 77.50/10.57 (binintersectEL) => 77.50/10.57 (( 77.50/10.57 (binintersectLsub) => 77.50/10.57 (( 77.50/10.57 (binintersectSubset2) => 77.50/10.57 (( 77.50/10.57 (binintersectSubset3) => 77.50/10.57 (( 77.50/10.57 (binintersectER) => 77.50/10.57 (( 77.50/10.57 (disjointsetsI1) => 77.50/10.57 (( 77.50/10.57 (binintersectRsub) => 77.50/10.57 (( 77.50/10.57 (binintersectSubset4) => 77.50/10.57 (( 77.50/10.57 (binintersectSubset1) => 77.50/10.57 (( 77.50/10.57 (bs114d) => 77.50/10.57 (( 77.50/10.57 (setminusI) => 77.50/10.57 (( 77.50/10.57 (setminusEL) => 77.50/10.57 (( 77.50/10.57 (setminusER) => 77.50/10.57 (( 77.50/10.57 (setminusSubset2) => 77.50/10.57 (( 77.50/10.57 (setminusERneg) => 77.50/10.57 (( 77.50/10.57 (setminusELneg) => 77.50/10.57 (( 77.50/10.57 (setminusILneg) => 77.50/10.57 (( 77.50/10.57 (setminusIRneg) => 77.50/10.57 (( 77.50/10.57 (setminusLsub) => 77.50/10.57 (( 77.50/10.57 (setminusSubset1) => 77.50/10.57 (( 77.50/10.57 (symdiffE) => 77.50/10.57 (( 77.50/10.57 (symdiffI1) => 77.50/10.57 (( 77.50/10.57 (symdiffI2) => 77.50/10.57 (( 77.50/10.57 (symdiffIneg1) => 77.50/10.57 (( 77.50/10.57 (symdiffIneg2) => 77.50/10.57 (( 77.50/10.57 (secondinupair) => 77.50/10.57 (( 77.50/10.57 (setukpairIL) => 77.50/10.57 (( 77.50/10.57 (setukpairIR) => 77.50/10.57 (( 77.50/10.57 (kpairiskpair) => 77.50/10.57 (( 77.50/10.57 (kpairp) => 77.50/10.57 (( 77.50/10.57 (singletonsubset) => 77.50/10.57 (( 77.50/10.57 (singletoninpowerset) => 77.50/10.57 (( 77.50/10.57 (singletoninpowunion) => 77.50/10.57 (( 77.50/10.57 (upairset2E) => 77.50/10.57 (( 77.50/10.57 (upairsubunion) => 77.50/10.57 (( 77.50/10.57 (upairinpowunion) => 77.50/10.57 (( 77.50/10.57 (ubforcartprodlem1) => 77.50/10.57 (( 77.50/10.57 (ubforcartprodlem2) => 77.50/10.57 (( 77.50/10.57 (ubforcartprodlem3) => 77.50/10.57 (( 77.50/10.57 (cartprodpairin) => 77.50/10.57 (( 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(( 77.50/10.57 (setukpairinjR2) => 77.50/10.57 (( 77.50/10.57 (setukpairinjR) => 77.50/10.57 (( 77.50/10.57 (ksndsingleton) => 77.50/10.57 (( 77.50/10.57 (ksndpairEq) => 77.50/10.57 (( 77.50/10.57 (kpairsurjEq) => 77.50/10.57 (( 77.50/10.57 (cartprodsndin) => 77.50/10.57 (( 77.50/10.57 (cartprodpairmemEL) => 77.50/10.57 (( 77.50/10.57 (cartprodpairmemER) => 77.50/10.57 (( 77.50/10.57 (cartprodmempaircEq) => 77.50/10.57 (( 77.50/10.57 (cartprodfstpairEq) => 77.50/10.57 (( 77.50/10.57 (cartprodsndpairEq) => 77.50/10.57 (( 77.50/10.57 (cartprodpairsurjEq) => 77.50/10.57 (( 77.50/10.57 (dpsetconstrI) => 77.50/10.57 (( 77.78/10.57 (dpsetconstrSub) => 77.78/10.57 (( 77.78/10.57 (setOfPairsIsBReln) => 77.78/10.57 (( 77.78/10.57 (dpsetconstrERa) => 77.78/10.57 (( 77.78/10.57 (dpsetconstrEL1) => 77.78/10.57 (( 77.78/10.57 (dpsetconstrEL2) => 77.78/10.57 (( 77.78/10.57 (dpsetconstrER) => 77.78/10.57 (( 77.78/10.57 (funcImageSingleton) => 77.78/10.57 (( 77.78/10.57 (apProp) => 77.78/10.57 (( 77.78/10.57 (app) => 77.78/10.57 (( 77.78/10.57 (infuncsetfunc) => 77.78/10.57 (( 77.78/10.57 (ap2p) => 77.78/10.57 (( 77.78/10.57 (funcinfuncset) => 77.78/10.57 (( 77.78/10.57 (lamProp) => 77.78/10.57 (( 77.78/10.57 (lamp) => 77.78/10.57 (( 77.78/10.57 (lam2p) => 77.78/10.57 (( 77.78/10.57 (brelnall1) => 77.78/10.57 (( 77.78/10.57 (brelnall2) => 77.78/10.57 (( 77.78/10.57 (ex1E2) => 77.78/10.57 (( 77.78/10.57 (funcGraphProp1) => 77.78/10.57 (( 77.78/10.57 (funcGraphProp3) => 77.78/10.57 (( 77.78/10.57 (funcGraphProp2) => 77.78/10.57 (( 77.78/10.57 (funcextLem) => 77.78/10.57 (( 77.78/10.57 (funcGraphProp4) => 77.78/10.57 (( 77.78/10.57 (subbreln) => 77.78/10.57 (( 77.78/10.57 (eqbreln) => 77.78/10.57 (( 77.78/10.57 (funcext) => 77.78/10.57 (( 77.78/10.57 (funcext2) => 77.78/10.57 (( 77.78/10.58 (ap2apEq1) => 77.78/10.58 (( 77.78/10.58 (ap2apEq2) => 77.78/10.58 (( 77.78/10.58 (beta1) => 77.78/10.58 (( 77.78/10.58 (eta1) => 77.78/10.58 (( 77.78/10.58 (lam2lamEq) => 77.78/10.58 (( 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77.78/10.58 (binintersectTELcontra) => 77.78/10.58 (( 77.78/10.58 (binintersectTERcontra) => 77.78/10.58 (( 77.78/10.58 (contrasubsetT) => 77.78/10.58 (( 77.78/10.58 (contrasubsetT1) => 77.78/10.58 (( 77.78/10.58 (contrasubsetT2) => 77.78/10.58 (( 77.78/10.58 (contrasubsetT3) => 77.78/10.58 (( 77.78/10.58 (doubleComplementI1) => 77.78/10.58 (( 77.78/10.58 (doubleComplementE1) => 77.78/10.58 (( 77.78/10.58 (doubleComplementSub1) => 77.78/10.58 (( 77.78/10.58 (doubleComplementSub2) => 77.78/10.58 (( 77.78/10.58 (doubleComplementEq) => 77.78/10.58 (( 77.78/10.58 (complementTnotintersectT) => 77.78/10.58 (( 77.78/10.58 (complementImpComplementIntersect) => 77.78/10.58 (( 77.78/10.58 (complementSubsetComplementIntersect) => 77.78/10.58 (( 77.78/10.58 (complementInPowersetComplementIntersect) => 77.78/10.58 (( 77.78/10.58 (contraSubsetComplement) => 77.78/10.58 (( 77.78/10.58 (complementTcontraSubset) => 77.78/10.58 (( 77.78/10.58 (binunionTILcontra) => 77.78/10.58 (( 77.78/10.58 (binunionTIRcontra) => 77.78/10.58 (( 77.78/10.58 (inIntersectImpInUnion) => 77.78/10.58 (( 77.78/10.58 (inIntersectImpInUnion2) => 77.78/10.58 (( 77.78/10.58 (inIntersectImpInIntersectUnions) => 77.78/10.58 (( 77.78/10.58 (intersectInPowersetIntersectUnions) => 77.78/10.58 (( 77.78/10.58 (inComplementUnionImpNotIn1) => 77.78/10.58 (( 77.78/10.58 (inComplementUnionImpInComplement1) => 77.78/10.58 (( 77.78/10.58 (binunionTE) => 77.78/10.58 (( 77.78/10.58 (binunionTEcontra) => 77.78/10.58 (( 77.78/10.58 (demorgan2a1) => 77.78/10.58 (( 77.78/10.58 (complementUnionInPowersetComplement) => 77.78/10.58 (( 77.78/10.58 (demorgan2a2) => 77.78/10.58 (( 77.78/10.58 (demorgan1a) => 77.78/10.58 (( 77.78/10.58 (demorgan1b) => 77.78/10.58 (( 77.78/10.58 (demorgan1) => 77.78/10.58 (( 77.78/10.58 (demorgan2a) => 77.78/10.58 (( 77.78/10.58 (demorgan2b2) => 77.78/10.58 (( 77.78/10.58 (demorgan2b) => 77.78/10.58 (( 77.78/10.58 (demorgan2) => 77.78/10.58 (( 77.78/10.58 (woz13rule0) => 77.78/10.58 (( 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77.78/10.58 (surjCantorThm) => 77.78/10.58 (( 77.78/10.58 (foundation2) => 77.78/10.58 (( 77.78/10.58 (notinself) => 77.78/10.58 (( 77.78/10.58 (notinself2) => 77.78/10.58 (( 77.78/10.58 (omegaSp) => 77.78/10.58 (( 77.78/10.58 (omegaSclos) => 77.78/10.58 (( 77.78/10.58 (peano0notS) => 77.78/10.58 (( 77.78/10.58 (peanoSinj) => 77.78/10.58 (( 77.78/10.58 (transitivesetOp1) => 77.78/10.58 (( 77.78/10.58 (binintTransitive) => 77.78/10.58 (( 77.78/10.58 (transitivesetOp2) => 77.78/10.58 (( 77.78/10.58 (setunionTransitive) => 77.78/10.58 (( 77.78/10.58 (ordinalMinLem1) => 77.78/10.58 (( 77.78/10.58 (!!) @ ( 77.78/10.58 ^[Y0 : $i]: 77.78/10.58 (( 77.78/10.58 (ordinal @ 77.78/10.58 Y0) => 77.78/10.58 (( 77.78/10.58 (!!) @ ( 77.78/10.58 ^[Y1 : $i]: 77.78/10.58 (( 77.78/10.58 (!!) @ ( 77.78/10.58 ^[Y2 : $i]: 77.78/10.58 (( 77.78/10.58 (in @ 77.78/10.58 Y2 @ 77.78/10.58 Y0) => 77.78/10.58 (( 77.78/10.58 (in @ 77.78/10.58 Y1 @ 77.78/10.58 Y2) => 77.78/10.58 (in @ 77.78/10.58 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 77.78/10.58 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl205])). 77.78/10.58 thf(zip_derived_cl231, plain, 77.78/10.58 (~ (((setbeta) => 77.78/10.58 (((nonemptyE1) => 77.78/10.58 (((nonemptyI) => 77.78/10.58 (((nonemptyI1) => 77.78/10.58 (((setadjoinIL) => 77.78/10.58 (((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) => 77.78/10.58 (((setadjoinIR) => 77.78/10.58 (((setadjoinE) => 77.78/10.58 (((setadjoinOr) => 77.78/10.58 (((setoftrueEq) => 77.78/10.58 (((powersetI) => 77.78/10.58 (((emptyinPowerset) => 77.78/10.58 (((emptyInPowerset) => 77.78/10.58 (((powersetE) => 77.78/10.58 (((setunionI) => 77.78/10.58 (((setunionE) => 77.78/10.58 (((subPowSU) => 77.78/10.58 (((exuE2) => 77.78/10.58 (((nonemptyImpWitness) => 77.78/10.58 (((uniqinunit) => 77.78/10.58 (((notinsingleton) => 77.78/10.58 (((eqinunit) => 77.78/10.58 (((singletonsswitch) => 77.78/10.58 (((upairsetE) => 77.78/10.58 (((upairsetIL) => 77.78/10.58 (((upairsetIR) => 77.78/10.58 (((emptyE1) => 77.78/10.58 (((vacuousDall) => 77.78/10.58 (((quantDeMorgan1) => 77.78/10.58 (((quantDeMorgan2) => 77.78/10.58 (( 77.78/10.58 (quantDeMorgan3) => 77.78/10.58 (( 77.78/10.58 (quantDeMorgan4) => 77.78/10.58 (( 77.78/10.58 (prop2setI) => 77.78/10.58 (( 77.78/10.58 (prop2set2propI) => 77.78/10.58 (( 77.78/10.58 (notdexE) => 77.78/10.58 (( 77.78/10.58 (notdallE) => 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77.78/10.58 (binintersectEL) => 77.78/10.58 (( 77.78/10.58 (binintersectLsub) => 77.78/10.58 (( 77.78/10.58 (binintersectSubset2) => 77.78/10.58 (( 77.78/10.58 (binintersectSubset3) => 77.78/10.58 (( 77.78/10.58 (binintersectER) => 77.78/10.58 (( 77.78/10.58 (disjointsetsI1) => 77.78/10.58 (( 77.78/10.58 (binintersectRsub) => 77.78/10.58 (( 77.78/10.58 (binintersectSubset4) => 77.78/10.58 (( 77.78/10.58 (binintersectSubset1) => 77.78/10.58 (( 77.78/10.58 (bs114d) => 77.78/10.58 (( 77.78/10.58 (setminusI) => 77.78/10.58 (( 77.78/10.58 (setminusEL) => 77.78/10.58 (( 77.78/10.58 (setminusER) => 77.78/10.58 (( 77.78/10.58 (setminusSubset2) => 77.78/10.58 (( 77.78/10.58 (setminusERneg) => 77.78/10.58 (( 77.78/10.58 (setminusELneg) => 77.78/10.58 (( 77.78/10.58 (setminusILneg) => 77.78/10.58 (( 77.78/10.58 (setminusIRneg) => 77.78/10.58 (( 77.78/10.58 (setminusLsub) => 77.78/10.58 (( 77.78/10.58 (setminusSubset1) => 77.78/10.58 (( 77.78/10.58 (symdiffE) => 77.78/10.58 (( 77.78/10.58 (symdiffI1) => 77.78/10.58 (( 77.78/10.58 (symdiffI2) => 77.78/10.58 (( 77.78/10.58 (symdiffIneg1) => 77.78/10.58 (( 77.78/10.58 (symdiffIneg2) => 77.78/10.58 (( 77.78/10.58 (secondinupair) => 77.78/10.58 (( 77.78/10.58 (setukpairIL) => 77.78/10.58 (( 77.78/10.58 (setukpairIR) => 77.78/10.58 (( 77.78/10.58 (kpairiskpair) => 77.78/10.58 (( 77.78/10.58 (kpairp) => 77.78/10.58 (( 77.78/10.58 (singletonsubset) => 77.78/10.58 (( 77.78/10.58 (singletoninpowerset) => 77.78/10.58 (( 77.78/10.58 (singletoninpowunion) => 77.78/10.58 (( 77.78/10.58 (upairset2E) => 77.78/10.58 (( 77.78/10.58 (upairsubunion) => 77.78/10.58 (( 77.78/10.58 (upairinpowunion) => 77.78/10.58 (( 77.78/10.58 (ubforcartprodlem1) => 77.78/10.58 (( 77.78/10.58 (ubforcartprodlem2) => 77.78/10.58 (( 77.78/10.58 (ubforcartprodlem3) => 77.78/10.58 (( 77.78/10.58 (cartprodpairin) => 77.78/10.58 (( 77.78/10.58 (cartprodmempair1) => 77.78/10.58 (( 77.78/10.58 (cartprodmempair) => 77.78/10.58 (( 77.78/10.58 (setunionE2) => 77.78/10.58 (( 77.78/10.58 (setunionsingleton1) => 77.78/10.58 (( 77.78/10.58 (setunionsingleton2) => 77.78/10.58 (( 77.78/10.58 (setunionsingleton) => 77.78/10.58 (( 77.78/10.58 (singletonprop) => 77.78/10.58 (( 77.78/10.58 (ex1E1) => 77.78/10.58 (( 77.78/10.58 (ex1I) => 77.78/10.58 (( 77.78/10.58 (ex1I2) => 77.78/10.58 (( 77.78/10.58 (singletonsuniq) => 77.78/10.58 (( 77.78/10.58 (setukpairinjL1) => 77.78/10.58 (( 77.78/10.58 (kfstsingleton) => 77.78/10.58 (( 77.78/10.58 (theprop) => 77.78/10.58 (( 77.78/10.58 (kfstpairEq) => 77.78/10.58 (( 77.78/10.58 (cartprodfstin) => 77.78/10.58 (( 77.78/10.58 (setukpairinjL2) => 77.78/10.58 (( 77.78/10.58 (setukpairinjL) => 77.78/10.58 (( 77.78/10.58 (setukpairinjR11) => 77.78/10.58 (( 77.78/10.58 (setukpairinjR12) => 77.78/10.58 (( 77.78/10.58 (setukpairinjR1) => 77.78/10.58 (( 77.78/10.58 (upairequniteq) => 77.78/10.58 (( 77.78/10.58 (setukpairinjR2) => 77.78/10.58 (( 77.78/10.58 (setukpairinjR) => 77.78/10.58 (( 77.78/10.58 (ksndsingleton) => 77.78/10.58 (( 77.78/10.58 (ksndpairEq) => 77.78/10.58 (( 77.78/10.58 (kpairsurjEq) => 77.78/10.58 (( 77.78/10.58 (cartprodsndin) => 77.78/10.58 (( 77.78/10.58 (cartprodpairmemEL) => 77.78/10.58 (( 77.78/10.58 (cartprodpairmemER) => 77.78/10.58 (( 77.78/10.58 (cartprodmempaircEq) => 77.78/10.58 (( 77.78/10.58 (cartprodfstpairEq) => 77.78/10.58 (( 77.78/10.58 (cartprodsndpairEq) => 77.78/10.58 (( 77.78/10.58 (cartprodpairsurjEq) => 77.78/10.58 (( 77.78/10.58 (dpsetconstrI) => 77.78/10.58 (( 77.78/10.58 (dpsetconstrSub) => 77.78/10.58 (( 77.78/10.58 (setOfPairsIsBReln) => 77.78/10.58 (( 77.78/10.58 (dpsetconstrERa) => 77.78/10.58 (( 77.78/10.58 (dpsetconstrEL1) => 77.78/10.58 (( 77.78/10.58 (dpsetconstrEL2) => 77.78/10.58 (( 77.78/10.58 (dpsetconstrER) => 77.78/10.58 (( 77.78/10.58 (funcImageSingleton) => 77.78/10.58 (( 77.78/10.58 (apProp) => 77.78/10.58 (( 77.78/10.58 (app) => 77.78/10.58 (( 77.78/10.58 (infuncsetfunc) => 77.78/10.58 (( 77.78/10.58 (ap2p) => 77.78/10.58 (( 77.78/10.58 (funcinfuncset) => 77.78/10.58 (( 77.78/10.58 (lamProp) => 77.78/10.58 (( 77.78/10.58 (lamp) => 77.78/10.58 (( 77.78/10.58 (lam2p) => 77.78/10.58 (( 77.78/10.58 (brelnall1) => 77.78/10.58 (( 77.78/10.58 (brelnall2) => 77.78/10.58 (( 77.78/10.58 (ex1E2) => 77.78/10.58 (( 77.78/10.58 (funcGraphProp1) => 77.78/10.58 (( 77.78/10.58 (funcGraphProp3) => 77.78/10.58 (( 77.78/10.58 (funcGraphProp2) => 77.78/10.58 (( 77.78/10.58 (funcextLem) => 77.78/10.58 (( 77.78/10.58 (funcGraphProp4) => 77.78/10.58 (( 77.78/10.58 (subbreln) => 77.78/10.58 (( 77.78/10.58 (eqbreln) => 77.78/10.58 (( 77.78/10.58 (funcext) => 77.78/10.58 (( 77.78/10.58 (funcext2) => 77.78/10.58 (( 77.78/10.58 (ap2apEq1) => 77.78/10.58 (( 77.78/10.58 (ap2apEq2) => 77.78/10.58 (( 77.78/10.58 (beta1) => 77.78/10.58 (( 77.78/10.58 (eta1) => 77.78/10.58 (( 77.78/10.58 (lam2lamEq) => 77.78/10.58 (( 77.78/10.58 (beta2) => 77.78/10.58 (( 77.78/10.58 (eta2) => 77.78/10.58 (( 77.78/10.58 (iffalseProp1) => 77.78/10.58 (( 77.78/10.58 (iffalseProp2) => 77.78/10.58 (( 77.78/10.58 (iftrueProp1) => 77.78/10.58 (( 77.78/10.58 (iftrueProp2) => 77.78/10.58 (( 77.78/10.58 (ifSingleton) => 77.78/10.58 (( 77.78/10.58 (ifp) => 77.78/10.58 (( 77.78/10.58 (theeq) => 77.78/10.58 (( 77.78/10.58 (iftrue) => 77.78/10.58 (( 77.78/10.58 (iffalse) => 77.78/10.58 (( 77.78/10.58 (iftrueorfalse) => 77.78/10.58 (( 77.78/10.58 (binintersectT_lem) => 77.78/10.58 (( 77.78/10.58 (binunionT_lem) => 77.78/10.58 (( 77.78/10.58 (powersetT_lem) => 77.78/10.58 (( 77.78/10.58 (setminusT_lem) => 77.78/10.58 (( 77.78/10.58 (complementT_lem) => 77.78/10.58 (( 77.78/10.58 (setextT) => 77.78/10.58 (( 77.78/10.58 (subsetTI) => 77.78/10.58 (( 77.78/10.58 (powersetTI1) => 77.78/10.58 (( 77.78/10.58 (powersetTE1) => 77.78/10.58 (( 77.78/10.58 (complementTI1) => 77.78/10.58 (( 77.78/10.58 (complementTE1) => 77.78/10.58 (( 77.78/10.58 (binintersectTELcontra) => 77.78/10.58 (( 77.78/10.58 (binintersectTERcontra) => 77.78/10.58 (( 77.78/10.58 (contrasubsetT) => 77.78/10.58 (( 77.78/10.58 (contrasubsetT1) => 77.78/10.58 (( 77.78/10.58 (contrasubsetT2) => 77.78/10.58 (( 77.78/10.58 (contrasubsetT3) => 77.78/10.58 (( 77.78/10.58 (doubleComplementI1) => 77.78/10.58 (( 77.78/10.58 (doubleComplementE1) => 77.78/10.58 (( 77.78/10.58 (doubleComplementSub1) => 77.78/10.58 (( 77.78/10.58 (doubleComplementSub2) => 77.78/10.58 (( 77.78/10.58 (doubleComplementEq) => 77.78/10.58 (( 77.78/10.58 (complementTnotintersectT) => 77.78/10.58 (( 77.78/10.58 (complementImpComplementIntersect) => 77.78/10.58 (( 77.78/10.58 (complementSubsetComplementIntersect) => 77.78/10.58 (( 77.78/10.58 (complementInPowersetComplementIntersect) => 77.78/10.58 (( 77.78/10.58 (contraSubsetComplement) => 77.78/10.58 (( 77.78/10.58 (complementTcontraSubset) => 77.78/10.58 (( 77.78/10.58 (binunionTILcontra) => 77.78/10.58 (( 77.78/10.58 (binunionTIRcontra) => 77.78/10.58 (( 77.78/10.58 (inIntersectImpInUnion) => 77.78/10.58 (( 77.78/10.58 (inIntersectImpInUnion2) => 77.78/10.58 (( 77.78/10.58 (inIntersectImpInIntersectUnions) => 77.78/10.58 (( 77.78/10.58 (intersectInPowersetIntersectUnions) => 77.78/10.58 (( 77.78/10.58 (inComplementUnionImpNotIn1) => 77.78/10.58 (( 77.78/10.58 (inComplementUnionImpInComplement1) => 77.78/10.58 (( 77.78/10.58 (binunionTE) => 77.78/10.58 (( 77.78/10.58 (binunionTEcontra) => 77.78/10.58 (( 77.78/10.58 (demorgan2a1) => 77.78/10.58 (( 77.78/10.58 (complementUnionInPowersetComplement) => 77.78/10.58 (( 77.78/10.58 (demorgan2a2) => 77.78/10.58 (( 77.78/10.58 (demorgan1a) => 77.78/10.58 (( 77.78/10.58 (demorgan1b) => 77.78/10.58 (( 77.78/10.58 (demorgan1) => 77.78/10.58 (( 77.78/10.58 (demorgan2a) => 77.78/10.58 (( 77.78/10.58 (demorgan2b2) => 77.78/10.58 (( 77.78/10.58 (demorgan2b) => 77.78/10.58 (( 77.78/10.58 (demorgan2) => 77.78/10.58 (( 77.78/10.58 (woz13rule0) => 77.78/10.58 (( 77.78/10.58 (woz13rule1) => 77.78/10.58 (( 77.78/10.58 (woz13rule2) => 77.78/10.58 (( 77.78/10.58 (woz13rule3) => 77.78/10.58 (( 77.78/10.58 (woz13rule4) => 77.78/10.58 (( 77.78/10.58 (woz1_1) => 77.78/10.58 (( 77.78/10.58 (woz1_2) => 77.78/10.58 (( 77.78/10.58 (woz1_3) => 77.78/10.58 (( 77.78/10.58 (woz1_4) => 77.78/10.58 (( 77.78/10.58 (woz1_5) => 77.78/10.58 (( 77.78/10.58 (breln1all2) => 77.78/10.58 (( 77.78/10.58 (breln1SetBreln1) => 77.78/10.58 (( 77.78/10.58 (choice2fnsingleton) => 77.78/10.58 (( 77.78/10.58 (setOfPairsIsBReln1) => 77.78/10.58 (( 77.78/10.58 (breln1all1) => 77.78/10.58 (( 77.78/10.58 (subbreln1) => 77.78/10.58 (( 77.78/10.58 (eqbreln1) => 77.78/10.58 (( 77.78/10.58 (breln1invprop) => 77.78/10.58 (( 77.78/10.58 (breln1invI) => 77.78/10.58 (( 77.78/10.58 (breln1invE) => 77.78/10.58 (( 77.78/10.58 (breln1compprop) => 77.78/10.58 (( 77.78/10.58 (breln1compI) => 77.78/10.58 (( 77.78/10.58 (breln1compE) => 77.78/10.58 (( 77.78/10.58 (breln1compEex) => 77.78/10.58 (( 77.78/10.58 (breln1unionprop) => 77.78/10.58 (( 77.78/10.58 (breln1unionIL) => 77.78/10.58 (( 77.78/10.58 (breln1unionIR) => 77.78/10.58 (( 77.78/10.58 (breln1unionI) => 77.78/10.58 (( 77.78/10.58 (breln1unionE) => 77.78/10.58 (( 77.78/10.58 (breln1unionEcases) => 77.78/10.58 (( 77.78/10.58 (breln1unionCommutes) => 77.78/10.58 (( 77.78/10.58 (woz2Ex) => 77.78/10.58 (( 77.78/10.58 (woz2W) => 77.78/10.58 (( 77.78/10.58 (woz2A) => 77.78/10.58 (( 77.78/10.58 (woz2B) => 77.78/10.58 (( 77.78/10.58 (image1Ex) => 77.78/10.58 (( 77.78/10.58 (image1Ex1) => 77.78/10.58 (( 77.78/10.58 (image1Equiv) => 77.78/10.58 (( 77.78/10.58 (image1E) => 77.78/10.58 (( 77.78/10.58 (image1I) => 77.78/10.58 (( 77.78/10.58 (injFuncInInjFuncSet) => 77.78/10.58 (( 77.78/10.58 (injFuncSetFuncIn) => 77.78/10.58 (( 77.78/10.58 (injFuncSetFuncInj) => 77.78/10.58 (( 77.78/10.58 (surjFuncSetFuncIn) => 77.78/10.58 (( 77.78/10.58 (surjFuncSetFuncSurj) => 77.78/10.58 (( 77.78/10.58 (leftInvIsSurj) => 77.78/10.58 (( 77.78/10.58 (surjCantorThm) => 77.78/10.58 (( 77.78/10.58 (foundation2) => 77.78/10.58 (( 77.78/10.58 (notinself) => 77.78/10.58 (( 77.78/10.58 (notinself2) => 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(subsetTrans) => 77.78/10.58 (( 77.78/10.58 (setadjoinSub) => 77.78/10.58 (( 77.78/10.58 (setadjoinSub2) => 77.78/10.58 (( 77.78/10.58 (subset2powerset) => 77.78/10.58 (( 77.78/10.58 (setextsub) => 77.78/10.58 (( 77.78/10.58 (subsetemptysetimpeq) => 77.78/10.58 (( 77.78/10.58 (powersetI1) => 77.78/10.58 (( 77.78/10.58 (powersetE1) => 77.78/10.58 (( 77.78/10.58 (inPowerset) => 77.78/10.58 (( 77.78/10.58 (powersetsubset) => 77.78/10.58 (( 77.78/10.58 (sepInPowerset) => 77.78/10.58 (( 77.78/10.58 (sepSubset) => 77.78/10.58 (( 77.78/10.58 (binunionIL) => 77.78/10.58 (( 77.78/10.58 (upairset2IR) => 77.78/10.58 (( 77.78/10.58 (binunionIR) => 77.78/10.58 (( 77.78/10.58 (binunionEcases) => 77.78/10.58 (( 77.78/10.58 (binunionE) => 77.78/10.58 (( 77.78/10.58 (binunionLsub) => 77.78/10.58 (( 77.78/10.58 (binunionRsub) => 77.78/10.58 (( 77.78/10.58 (binintersectI) => 77.78/10.58 (( 77.78/10.58 (binintersectSubset5) => 77.78/10.58 (( 77.78/10.58 (binintersectEL) => 77.78/10.58 (( 77.78/10.58 (binintersectLsub) => 77.78/10.58 (( 77.78/10.58 (binintersectSubset2) => 77.78/10.58 (( 77.78/10.58 (binintersectSubset3) => 77.78/10.58 (( 77.78/10.58 (binintersectER) => 77.78/10.58 (( 77.78/10.58 (disjointsetsI1) => 77.78/10.58 (( 77.78/10.58 (binintersectRsub) => 77.78/10.58 (( 77.78/10.58 (binintersectSubset4) => 77.78/10.58 (( 77.78/10.58 (binintersectSubset1) => 77.78/10.58 (( 77.78/10.58 (bs114d) => 77.78/10.58 (( 77.78/10.58 (setminusI) => 77.78/10.58 (( 77.78/10.58 (setminusEL) => 77.78/10.58 (( 77.78/10.58 (setminusER) => 77.78/10.58 (( 77.78/10.58 (setminusSubset2) => 77.78/10.58 (( 77.78/10.58 (setminusERneg) => 77.78/10.58 (( 77.78/10.58 (setminusELneg) => 77.78/10.58 (( 77.78/10.58 (setminusILneg) => 77.78/10.58 (( 77.78/10.58 (setminusIRneg) => 77.78/10.58 (( 77.78/10.58 (setminusLsub) => 77.78/10.58 (( 77.78/10.58 (setminusSubset1) => 77.78/10.58 (( 77.78/10.58 (symdiffE) => 77.78/10.58 (( 77.78/10.58 (symdiffI1) => 77.78/10.58 (( 77.78/10.58 (symdiffI2) => 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77.78/10.58 (kpairsurjEq) => 77.78/10.58 (( 77.78/10.58 (cartprodsndin) => 77.78/10.58 (( 77.78/10.58 (cartprodpairmemEL) => 77.78/10.58 (( 77.78/10.58 (cartprodpairmemER) => 77.78/10.58 (( 77.78/10.58 (cartprodmempaircEq) => 77.78/10.58 (( 77.78/10.58 (cartprodfstpairEq) => 77.78/10.58 (( 77.78/10.58 (cartprodsndpairEq) => 77.78/10.58 (( 77.78/10.58 (cartprodpairsurjEq) => 77.78/10.58 (( 77.78/10.58 (dpsetconstrI) => 77.78/10.58 (( 77.78/10.58 (dpsetconstrSub) => 77.78/10.58 (( 77.78/10.58 (setOfPairsIsBReln) => 77.78/10.58 (( 77.78/10.58 (dpsetconstrERa) => 77.78/10.58 (( 77.78/10.58 (dpsetconstrEL1) => 77.78/10.58 (( 77.78/10.58 (dpsetconstrEL2) => 77.78/10.58 (( 77.78/10.58 (dpsetconstrER) => 77.78/10.58 (( 77.78/10.58 (funcImageSingleton) => 77.78/10.58 (( 77.78/10.58 (apProp) => 77.78/10.58 (( 77.78/10.58 (app) => 77.78/10.58 (( 77.78/10.58 (infuncsetfunc) => 77.78/10.58 (( 77.78/10.58 (ap2p) => 77.78/10.58 (( 77.78/10.58 (funcinfuncset) => 77.78/10.58 (( 77.78/10.58 (lamProp) => 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=> 77.78/10.58 (( 77.78/10.58 (breln1unionEcases) => 77.78/10.58 (( 77.78/10.58 (breln1unionCommutes) => 77.78/10.58 (( 77.78/10.58 (woz2Ex) => 77.78/10.58 (( 77.78/10.58 (woz2W) => 77.78/10.58 (( 77.78/10.58 (woz2A) => 77.78/10.58 (( 77.78/10.58 (woz2B) => 77.78/10.58 (( 77.78/10.58 (image1Ex) => 77.78/10.58 (( 77.78/10.58 (image1Ex1) => 77.78/10.58 (( 77.78/10.58 (image1Equiv) => 77.78/10.58 (( 77.78/10.58 (image1E) => 77.78/10.58 (( 77.78/10.58 (image1I) => 77.78/10.58 (( 77.78/10.58 (injFuncInInjFuncSet) => 77.78/10.58 (( 77.78/10.58 (injFuncSetFuncIn) => 77.78/10.58 (( 77.78/10.58 (injFuncSetFuncInj) => 77.78/10.58 (( 77.78/10.58 (surjFuncSetFuncIn) => 77.78/10.58 (( 77.78/10.58 (surjFuncSetFuncSurj) => 77.78/10.58 (( 77.78/10.58 (leftInvIsSurj) => 77.78/10.58 (( 77.78/10.58 (surjCantorThm) => 77.78/10.58 (( 77.78/10.58 (foundation2) => 77.78/10.58 (( 77.78/10.58 (notinself) => 77.78/10.58 (( 77.78/10.58 (notinself2) => 77.78/10.58 (( 77.78/10.58 (omegaSp) => 77.78/10.58 (( 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77.78/10.58 (( 77.78/10.58 (binintersectSubset3) => 77.78/10.58 (( 77.78/10.58 (binintersectER) => 77.78/10.58 (( 77.78/10.58 (disjointsetsI1) => 77.78/10.58 (( 77.78/10.58 (binintersectRsub) => 77.78/10.58 (( 77.78/10.58 (binintersectSubset4) => 77.78/10.58 (( 77.78/10.58 (binintersectSubset1) => 77.78/10.58 (( 77.78/10.58 (bs114d) => 77.78/10.58 (( 77.78/10.58 (setminusI) => 77.78/10.58 (( 77.78/10.58 (setminusEL) => 77.78/10.58 (( 77.78/10.58 (setminusER) => 77.78/10.58 (( 77.78/10.58 (setminusSubset2) => 77.78/10.58 (( 77.78/10.58 (setminusERneg) => 77.78/10.58 (( 77.78/10.58 (setminusELneg) => 77.78/10.58 (( 77.78/10.58 (setminusILneg) => 77.78/10.58 (( 77.78/10.58 (setminusIRneg) => 77.78/10.58 (( 77.78/10.58 (setminusLsub) => 77.78/10.58 (( 77.78/10.58 (setminusSubset1) => 77.78/10.58 (( 77.78/10.58 (symdiffE) => 77.78/10.58 (( 77.78/10.58 (symdiffI1) => 77.78/10.58 (( 77.78/10.58 (symdiffI2) => 77.78/10.58 (( 77.78/10.58 (symdiffIneg1) => 77.78/10.58 (( 77.78/10.58 (symdiffIneg2) => 77.78/10.58 (( 77.78/10.58 (secondinupair) => 77.78/10.58 (( 77.78/10.58 (setukpairIL) => 77.78/10.58 (( 77.78/10.58 (setukpairIR) => 77.78/10.58 (( 77.78/10.58 (kpairiskpair) => 77.78/10.58 (( 77.78/10.58 (kpairp) => 77.78/10.58 (( 77.78/10.58 (singletonsubset) => 77.78/10.58 (( 77.78/10.58 (singletoninpowerset) => 77.78/10.58 (( 77.78/10.58 (singletoninpowunion) => 77.78/10.58 (( 77.78/10.58 (upairset2E) => 77.78/10.58 (( 77.78/10.58 (upairsubunion) => 77.78/10.58 (( 77.78/10.58 (upairinpowunion) => 77.78/10.58 (( 77.78/10.58 (ubforcartprodlem1) => 77.78/10.58 (( 77.78/10.58 (ubforcartprodlem2) => 77.78/10.58 (( 77.78/10.58 (ubforcartprodlem3) => 77.78/10.58 (( 77.78/10.58 (cartprodpairin) => 77.78/10.58 (( 77.78/10.58 (cartprodmempair1) => 77.78/10.58 (( 77.78/10.58 (cartprodmempair) => 77.78/10.58 (( 77.78/10.58 (setunionE2) => 77.78/10.58 (( 77.78/10.58 (setunionsingleton1) => 77.78/10.58 (( 77.78/10.58 (setunionsingleton2) => 77.78/10.58 (( 77.78/10.58 (setunionsingleton) => 77.78/10.58 (( 77.78/10.58 (singletonprop) => 77.78/10.58 (( 77.78/10.58 (ex1E1) => 77.78/10.58 (( 77.78/10.58 (ex1I) => 77.78/10.58 (( 77.78/10.58 (ex1I2) => 77.78/10.58 (( 77.78/10.58 (singletonsuniq) => 77.78/10.58 (( 77.78/10.58 (setukpairinjL1) => 77.78/10.58 (( 77.78/10.58 (kfstsingleton) => 77.78/10.58 (( 77.78/10.58 (theprop) => 77.78/10.58 (( 77.78/10.58 (kfstpairEq) => 77.78/10.58 (( 77.78/10.58 (cartprodfstin) => 77.78/10.58 (( 77.78/10.58 (setukpairinjL2) => 77.78/10.58 (( 77.78/10.58 (setukpairinjL) => 77.78/10.58 (( 77.78/10.58 (setukpairinjR11) => 77.78/10.58 (( 77.78/10.58 (setukpairinjR12) => 77.78/10.58 (( 77.78/10.58 (setukpairinjR1) => 77.78/10.58 (( 77.78/10.58 (upairequniteq) => 77.78/10.58 (( 77.78/10.58 (setukpairinjR2) => 77.78/10.58 (( 77.78/10.58 (setukpairinjR) => 77.78/10.58 (( 77.78/10.58 (ksndsingleton) => 77.78/10.58 (( 77.78/10.58 (ksndpairEq) => 77.78/10.58 (( 77.78/10.58 (kpairsurjEq) => 77.78/10.58 (( 77.78/10.58 (cartprodsndin) => 77.78/10.58 (( 77.78/10.58 (cartprodpairmemEL) => 77.78/10.58 (( 77.78/10.58 (cartprodpairmemER) => 77.78/10.58 (( 77.78/10.58 (cartprodmempaircEq) => 77.78/10.58 (( 77.78/10.58 (cartprodfstpairEq) => 77.78/10.58 (( 77.78/10.58 (cartprodsndpairEq) => 77.78/10.58 (( 77.78/10.58 (cartprodpairsurjEq) => 77.78/10.58 (( 77.78/10.58 (dpsetconstrI) => 77.78/10.58 (( 77.78/10.58 (dpsetconstrSub) => 77.78/10.58 (( 77.78/10.58 (setOfPairsIsBReln) => 77.78/10.58 (( 77.78/10.58 (dpsetconstrERa) => 77.78/10.58 (( 77.78/10.58 (dpsetconstrEL1) => 77.78/10.58 (( 77.78/10.58 (dpsetconstrEL2) => 77.78/10.58 (( 77.78/10.58 (dpsetconstrER) => 77.78/10.58 (( 77.78/10.58 (funcImageSingleton) => 77.78/10.58 (( 77.78/10.58 (apProp) => 77.78/10.58 (( 77.78/10.58 (app) => 77.78/10.58 (( 77.78/10.58 (infuncsetfunc) => 77.78/10.58 (( 77.78/10.58 (ap2p) => 77.78/10.58 (( 77.78/10.58 (funcinfuncset) => 77.78/10.58 (( 77.78/10.58 (lamProp) => 77.78/10.58 (( 77.78/10.58 (lamp) => 77.78/10.58 (( 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(( 77.78/10.58 (contrasubsetT3) => 77.78/10.58 (( 77.78/10.58 (doubleComplementI1) => 77.78/10.58 (( 77.78/10.58 (doubleComplementE1) => 77.78/10.58 (( 77.78/10.58 (doubleComplementSub1) => 77.78/10.58 (( 77.78/10.58 (doubleComplementSub2) => 77.78/10.58 (( 77.78/10.58 (doubleComplementEq) => 77.78/10.58 (( 77.78/10.58 (complementTnotintersectT) => 77.78/10.58 (( 77.78/10.58 (complementImpComplementIntersect) => 77.78/10.58 (( 77.78/10.58 (complementSubsetComplementIntersect) => 77.78/10.58 (( 77.78/10.58 (complementInPowersetComplementIntersect) => 77.78/10.58 (( 77.78/10.58 (contraSubsetComplement) => 77.78/10.58 (( 77.78/10.58 (complementTcontraSubset) => 77.78/10.58 (( 77.78/10.58 (binunionTILcontra) => 77.78/10.58 (( 77.78/10.58 (binunionTIRcontra) => 77.78/10.58 (( 77.78/10.58 (inIntersectImpInUnion) => 77.78/10.58 (( 77.78/10.58 (inIntersectImpInUnion2) => 77.78/10.58 (( 77.78/10.58 (inIntersectImpInIntersectUnions) => 77.78/10.58 (( 77.78/10.58 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(woz1_2) => 77.78/10.58 (( 77.78/10.58 (woz1_3) => 77.78/10.58 (( 77.78/10.58 (woz1_4) => 77.78/10.58 (( 77.78/10.58 (woz1_5) => 77.78/10.58 (( 77.78/10.58 (breln1all2) => 77.78/10.58 (( 77.78/10.58 (breln1SetBreln1) => 77.78/10.58 (( 77.78/10.58 (choice2fnsingleton) => 77.78/10.58 (( 77.78/10.58 (setOfPairsIsBReln1) => 77.78/10.58 (( 77.78/10.58 (breln1all1) => 77.78/10.58 (( 77.78/10.58 (subbreln1) => 77.78/10.58 (( 77.78/10.58 (eqbreln1) => 77.78/10.58 (( 77.78/10.58 (breln1invprop) => 77.78/10.58 (( 77.78/10.58 (breln1invI) => 77.78/10.58 (( 77.78/10.58 (breln1invE) => 77.78/10.58 (( 77.78/10.58 (breln1compprop) => 77.78/10.58 (( 77.78/10.58 (breln1compI) => 77.78/10.58 (( 77.78/10.58 (breln1compE) => 77.78/10.58 (( 77.78/10.58 (breln1compEex) => 77.78/10.58 (( 77.78/10.58 (breln1unionprop) => 77.78/10.58 (( 77.78/10.58 (breln1unionIL) => 77.78/10.58 (( 77.78/10.58 (breln1unionIR) => 77.78/10.58 (( 77.78/10.58 (breln1unionI) => 77.78/10.58 (( 77.78/10.58 (breln1unionE) => 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77.78/10.58 (omegaSclos) => 77.78/10.58 (( 77.78/10.58 (peano0notS) => 77.78/10.58 (( 77.78/10.58 (peanoSinj) => 77.78/10.58 (( 77.78/10.58 (transitivesetOp1) => 77.78/10.58 (( 77.78/10.58 (binintTransitive) => 77.78/10.58 (( 77.78/10.58 (transitivesetOp2) => 77.78/10.58 (( 77.78/10.58 (setunionTransitive) => 77.78/10.58 (( 77.78/10.58 (ordinalMinLem1) => 77.78/10.58 (( 77.78/10.58 (!!) @ ( 77.78/10.58 ^[Y0 : $i]: 77.78/10.58 (( 77.78/10.58 (ordinal @ 77.78/10.58 Y0) => 77.78/10.58 (( 77.78/10.58 (!!) @ ( 77.78/10.58 ^[Y1 : $i]: 77.78/10.58 (( 77.78/10.58 (!!) @ ( 77.78/10.58 ^[Y2 : $i]: 77.78/10.58 (( 77.78/10.58 (in @ 77.78/10.58 Y2 @ 77.78/10.58 Y0) => 77.78/10.58 (( 77.78/10.58 (in @ 77.78/10.58 Y1 @ 77.78/10.58 Y2) => 77.78/10.58 (in @ 77.78/10.58 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 77.78/10.58 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl258])). 77.78/10.58 thf(zip_derived_cl285, plain, 77.78/10.58 (~ (((setadjoinIL) => 77.78/10.58 (((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) => 77.78/10.58 (((setadjoinIR) => 77.78/10.58 (((setadjoinE) => 77.78/10.58 (((setadjoinOr) => 77.78/10.58 (((setoftrueEq) => 77.78/10.58 (((powersetI) => 77.78/10.58 (((emptyinPowerset) => 77.78/10.58 (((emptyInPowerset) => 77.78/10.58 (((powersetE) => 77.78/10.58 (((setunionI) => 77.78/10.58 (((setunionE) => 77.78/10.58 (((subPowSU) => 77.78/10.58 (((exuE2) => 77.78/10.58 (((nonemptyImpWitness) => 77.78/10.58 (((uniqinunit) => 77.78/10.58 (((notinsingleton) => 77.78/10.58 (((eqinunit) => 77.78/10.58 (((singletonsswitch) => 77.78/10.58 (((upairsetE) => 77.78/10.58 (((upairsetIL) => 77.78/10.58 (((upairsetIR) => 77.78/10.58 (((emptyE1) => 77.78/10.58 (((vacuousDall) => 77.78/10.58 (((quantDeMorgan1) => 77.78/10.58 (((quantDeMorgan2) => 77.78/10.58 (((quantDeMorgan3) => 77.78/10.58 (((quantDeMorgan4) => 77.78/10.58 (((prop2setI) => 77.78/10.58 (((prop2set2propI) => 77.78/10.58 (( 77.78/10.58 (notdexE) => 77.78/10.58 (( 77.78/10.58 (notdallE) => 77.78/10.58 (( 77.78/10.58 (exuI1) => 77.78/10.58 (( 77.78/10.58 (exuI3) => 77.78/10.58 (( 77.78/10.58 (exuI2) => 77.78/10.58 (( 77.78/10.58 (inCongP) => 77.78/10.58 (( 77.78/10.58 (in__Cong) => 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(subset2powerset) => 77.78/10.58 (( 77.78/10.58 (setextsub) => 77.78/10.58 (( 77.78/10.58 (subsetemptysetimpeq) => 77.78/10.58 (( 77.78/10.58 (powersetI1) => 77.78/10.58 (( 77.78/10.58 (powersetE1) => 77.78/10.58 (( 77.78/10.58 (inPowerset) => 77.78/10.58 (( 77.78/10.58 (powersetsubset) => 77.78/10.58 (( 77.78/10.58 (sepInPowerset) => 77.78/10.58 (( 77.78/10.58 (sepSubset) => 77.78/10.58 (( 77.78/10.58 (binunionIL) => 77.78/10.58 (( 77.78/10.58 (upairset2IR) => 77.78/10.58 (( 77.78/10.58 (binunionIR) => 77.78/10.58 (( 77.78/10.58 (binunionEcases) => 77.78/10.58 (( 77.78/10.58 (binunionE) => 77.78/10.58 (( 77.78/10.58 (binunionLsub) => 77.78/10.58 (( 77.78/10.58 (binunionRsub) => 77.78/10.58 (( 77.78/10.58 (binintersectI) => 77.78/10.58 (( 77.78/10.58 (binintersectSubset5) => 77.78/10.58 (( 77.78/10.58 (binintersectEL) => 77.78/10.58 (( 77.78/10.58 (binintersectLsub) => 77.78/10.58 (( 77.78/10.58 (binintersectSubset2) => 77.78/10.58 (( 77.78/10.58 (binintersectSubset3) => 77.78/10.58 (( 77.78/10.58 (binintersectER) => 77.78/10.58 (( 77.78/10.58 (disjointsetsI1) => 77.78/10.58 (( 77.78/10.58 (binintersectRsub) => 77.78/10.58 (( 77.78/10.58 (binintersectSubset4) => 77.78/10.58 (( 77.78/10.58 (binintersectSubset1) => 77.78/10.58 (( 77.78/10.58 (bs114d) => 77.78/10.58 (( 77.78/10.58 (setminusI) => 77.78/10.58 (( 77.78/10.58 (setminusEL) => 77.78/10.58 (( 77.78/10.58 (setminusER) => 77.78/10.58 (( 77.78/10.58 (setminusSubset2) => 77.78/10.58 (( 77.78/10.58 (setminusERneg) => 77.78/10.58 (( 77.78/10.58 (setminusELneg) => 77.78/10.58 (( 77.78/10.58 (setminusILneg) => 77.78/10.58 (( 77.78/10.58 (setminusIRneg) => 77.78/10.58 (( 77.78/10.58 (setminusLsub) => 77.78/10.58 (( 77.78/10.58 (setminusSubset1) => 77.78/10.58 (( 77.78/10.58 (symdiffE) => 77.78/10.58 (( 77.78/10.58 (symdiffI1) => 77.78/10.58 (( 77.78/10.58 (symdiffI2) => 77.78/10.58 (( 77.78/10.58 (symdiffIneg1) => 77.78/10.58 (( 77.78/10.58 (symdiffIneg2) => 77.78/10.58 (( 77.78/10.58 (secondinupair) => 77.78/10.58 (( 77.78/10.58 (setukpairIL) => 77.78/10.58 (( 77.78/10.58 (setukpairIR) => 77.78/10.58 (( 77.78/10.58 (kpairiskpair) => 77.78/10.58 (( 77.78/10.58 (kpairp) => 77.78/10.58 (( 77.78/10.58 (singletonsubset) => 77.78/10.58 (( 77.78/10.58 (singletoninpowerset) => 77.78/10.58 (( 77.78/10.58 (singletoninpowunion) => 77.78/10.58 (( 77.78/10.58 (upairset2E) => 77.78/10.58 (( 77.78/10.58 (upairsubunion) => 77.78/10.58 (( 77.78/10.58 (upairinpowunion) => 77.78/10.58 (( 77.78/10.58 (ubforcartprodlem1) => 77.78/10.58 (( 77.78/10.58 (ubforcartprodlem2) => 77.78/10.58 (( 77.78/10.58 (ubforcartprodlem3) => 77.78/10.58 (( 77.78/10.58 (cartprodpairin) => 77.78/10.58 (( 77.78/10.58 (cartprodmempair1) => 77.78/10.58 (( 77.78/10.58 (cartprodmempair) => 77.78/10.58 (( 77.78/10.58 (setunionE2) => 77.78/10.58 (( 77.78/10.58 (setunionsingleton1) => 77.78/10.58 (( 77.78/10.58 (setunionsingleton2) => 77.78/10.58 (( 77.78/10.58 (setunionsingleton) => 77.78/10.58 (( 77.78/10.58 (singletonprop) => 77.78/10.58 (( 77.78/10.58 (ex1E1) => 77.78/10.58 (( 77.78/10.58 (ex1I) => 77.78/10.58 (( 77.78/10.58 (ex1I2) => 77.78/10.58 (( 77.78/10.58 (singletonsuniq) => 77.78/10.58 (( 77.78/10.58 (setukpairinjL1) => 77.78/10.58 (( 77.78/10.58 (kfstsingleton) => 77.78/10.58 (( 77.78/10.58 (theprop) => 77.78/10.58 (( 77.78/10.58 (kfstpairEq) => 77.78/10.58 (( 77.78/10.58 (cartprodfstin) => 77.78/10.58 (( 77.78/10.58 (setukpairinjL2) => 77.78/10.58 (( 77.78/10.58 (setukpairinjL) => 77.78/10.58 (( 77.78/10.58 (setukpairinjR11) => 77.78/10.58 (( 77.78/10.58 (setukpairinjR12) => 77.78/10.58 (( 77.78/10.58 (setukpairinjR1) => 77.78/10.58 (( 77.78/10.58 (upairequniteq) => 77.78/10.58 (( 77.78/10.58 (setukpairinjR2) => 77.78/10.58 (( 77.78/10.58 (setukpairinjR) => 77.78/10.58 (( 77.78/10.58 (ksndsingleton) => 77.78/10.58 (( 77.78/10.58 (ksndpairEq) => 77.78/10.58 (( 77.78/10.58 (kpairsurjEq) => 77.78/10.58 (( 77.78/10.58 (cartprodsndin) => 77.78/10.58 (( 77.78/10.58 (cartprodpairmemEL) => 77.78/10.58 (( 77.78/10.58 (cartprodpairmemER) => 77.78/10.58 (( 77.78/10.58 (cartprodmempaircEq) => 77.78/10.58 (( 77.78/10.58 (cartprodfstpairEq) => 77.78/10.58 (( 77.78/10.58 (cartprodsndpairEq) => 77.78/10.58 (( 77.78/10.58 (cartprodpairsurjEq) => 77.78/10.58 (( 77.78/10.58 (dpsetconstrI) => 77.78/10.58 (( 77.78/10.58 (dpsetconstrSub) => 77.78/10.58 (( 77.78/10.58 (setOfPairsIsBReln) => 77.78/10.58 (( 77.78/10.58 (dpsetconstrERa) => 77.78/10.58 (( 77.78/10.58 (dpsetconstrEL1) => 77.78/10.58 (( 77.78/10.58 (dpsetconstrEL2) => 77.78/10.58 (( 77.78/10.58 (dpsetconstrER) => 77.78/10.58 (( 77.78/10.58 (funcImageSingleton) => 77.78/10.58 (( 77.78/10.58 (apProp) => 77.78/10.58 (( 77.78/10.58 (app) => 77.78/10.58 (( 77.78/10.58 (infuncsetfunc) => 77.78/10.58 (( 77.78/10.58 (ap2p) => 77.78/10.58 (( 77.78/10.58 (funcinfuncset) => 77.78/10.58 (( 77.78/10.58 (lamProp) => 77.78/10.58 (( 77.78/10.58 (lamp) => 77.78/10.58 (( 77.78/10.58 (lam2p) => 77.78/10.58 (( 77.78/10.58 (brelnall1) => 77.78/10.58 (( 77.78/10.58 (brelnall2) => 77.78/10.58 (( 77.78/10.58 (ex1E2) => 77.78/10.58 (( 77.78/10.58 (funcGraphProp1) => 77.78/10.58 (( 77.78/10.58 (funcGraphProp3) => 77.78/10.58 (( 77.78/10.58 (funcGraphProp2) => 77.78/10.58 (( 77.78/10.58 (funcextLem) => 77.78/10.58 (( 77.78/10.58 (funcGraphProp4) => 77.78/10.58 (( 77.78/10.58 (subbreln) => 77.78/10.58 (( 77.78/10.58 (eqbreln) => 77.78/10.58 (( 77.78/10.58 (funcext) => 77.78/10.58 (( 77.78/10.58 (funcext2) => 77.78/10.58 (( 77.78/10.58 (ap2apEq1) => 77.78/10.58 (( 77.78/10.58 (ap2apEq2) => 77.78/10.58 (( 77.78/10.58 (beta1) => 77.78/10.58 (( 77.78/10.58 (eta1) => 77.78/10.58 (( 77.78/10.58 (lam2lamEq) => 77.78/10.58 (( 77.78/10.58 (beta2) => 77.78/10.58 (( 77.78/10.58 (eta2) => 77.78/10.58 (( 77.78/10.58 (iffalseProp1) => 77.78/10.58 (( 77.78/10.58 (iffalseProp2) => 77.78/10.58 (( 77.78/10.58 (iftrueProp1) => 77.78/10.58 (( 77.78/10.58 (iftrueProp2) => 77.78/10.58 (( 77.78/10.58 (ifSingleton) => 77.78/10.58 (( 77.78/10.58 (ifp) => 77.78/10.58 (( 77.78/10.58 (theeq) => 77.78/10.58 (( 77.78/10.58 (iftrue) => 77.78/10.58 (( 77.78/10.58 (iffalse) => 77.78/10.58 (( 77.78/10.58 (iftrueorfalse) => 77.78/10.58 (( 77.78/10.58 (binintersectT_lem) => 77.78/10.58 (( 77.78/10.58 (binunionT_lem) => 77.78/10.58 (( 77.78/10.58 (powersetT_lem) => 77.78/10.58 (( 77.78/10.58 (setminusT_lem) => 77.78/10.58 (( 77.78/10.58 (complementT_lem) => 77.78/10.58 (( 77.78/10.58 (setextT) => 77.78/10.58 (( 77.78/10.58 (subsetTI) => 77.78/10.58 (( 77.78/10.58 (powersetTI1) => 77.78/10.58 (( 77.78/10.58 (powersetTE1) => 77.78/10.58 (( 77.78/10.58 (complementTI1) => 77.78/10.58 (( 77.78/10.58 (complementTE1) => 77.78/10.58 (( 77.78/10.58 (binintersectTELcontra) => 77.78/10.58 (( 77.78/10.58 (binintersectTERcontra) => 77.78/10.58 (( 77.78/10.58 (contrasubsetT) => 77.78/10.58 (( 77.78/10.58 (contrasubsetT1) => 77.78/10.58 (( 77.78/10.58 (contrasubsetT2) => 77.78/10.58 (( 77.78/10.58 (contrasubsetT3) => 77.78/10.58 (( 77.78/10.58 (doubleComplementI1) => 77.78/10.58 (( 77.78/10.58 (doubleComplementE1) => 77.78/10.58 (( 77.78/10.58 (doubleComplementSub1) => 77.78/10.58 (( 77.78/10.58 (doubleComplementSub2) => 77.78/10.58 (( 77.78/10.58 (doubleComplementEq) => 77.78/10.58 (( 77.78/10.58 (complementTnotintersectT) => 77.78/10.58 (( 77.78/10.58 (complementImpComplementIntersect) => 77.78/10.58 (( 77.78/10.58 (complementSubsetComplementIntersect) => 77.78/10.58 (( 77.78/10.58 (complementInPowersetComplementIntersect) => 77.78/10.58 (( 77.78/10.58 (contraSubsetComplement) => 77.78/10.58 (( 77.78/10.58 (complementTcontraSubset) => 77.78/10.58 (( 77.78/10.58 (binunionTILcontra) => 77.78/10.58 (( 77.78/10.58 (binunionTIRcontra) => 77.78/10.58 (( 77.78/10.58 (inIntersectImpInUnion) => 77.78/10.58 (( 77.78/10.58 (inIntersectImpInUnion2) => 77.78/10.58 (( 77.78/10.58 (inIntersectImpInIntersectUnions) => 77.78/10.58 (( 77.78/10.58 (intersectInPowersetIntersectUnions) => 77.78/10.58 (( 77.78/10.58 (inComplementUnionImpNotIn1) => 77.78/10.58 (( 77.78/10.58 (inComplementUnionImpInComplement1) => 77.78/10.58 (( 77.78/10.58 (binunionTE) => 77.78/10.58 (( 77.78/10.58 (binunionTEcontra) => 77.78/10.58 (( 77.78/10.58 (demorgan2a1) => 77.78/10.58 (( 77.78/10.58 (complementUnionInPowersetComplement) => 77.78/10.58 (( 77.78/10.58 (demorgan2a2) => 77.78/10.58 (( 77.78/10.58 (demorgan1a) => 77.78/10.58 (( 77.78/10.58 (demorgan1b) => 77.78/10.58 (( 77.78/10.58 (demorgan1) => 77.78/10.58 (( 77.78/10.58 (demorgan2a) => 77.78/10.58 (( 77.78/10.58 (demorgan2b2) => 77.78/10.58 (( 77.78/10.58 (demorgan2b) => 77.78/10.58 (( 77.78/10.58 (demorgan2) => 77.78/10.58 (( 77.78/10.58 (woz13rule0) => 77.78/10.58 (( 77.78/10.58 (woz13rule1) => 77.78/10.58 (( 77.78/10.58 (woz13rule2) => 77.78/10.58 (( 77.78/10.58 (woz13rule3) => 77.78/10.58 (( 77.78/10.58 (woz13rule4) => 77.78/10.58 (( 77.78/10.58 (woz1_1) => 77.78/10.58 (( 77.78/10.58 (woz1_2) => 77.78/10.58 (( 77.78/10.58 (woz1_3) => 77.78/10.58 (( 77.78/10.58 (woz1_4) => 77.78/10.58 (( 77.78/10.58 (woz1_5) => 77.78/10.58 (( 77.78/10.58 (breln1all2) => 77.78/10.58 (( 77.78/10.58 (breln1SetBreln1) => 77.78/10.58 (( 77.78/10.58 (choice2fnsingleton) => 77.78/10.58 (( 77.78/10.58 (setOfPairsIsBReln1) => 77.78/10.58 (( 77.78/10.58 (breln1all1) => 77.78/10.58 (( 77.78/10.58 (subbreln1) => 77.78/10.58 (( 77.78/10.58 (eqbreln1) => 77.78/10.58 (( 77.78/10.58 (breln1invprop) => 77.78/10.58 (( 77.78/10.58 (breln1invI) => 77.78/10.58 (( 77.78/10.58 (breln1invE) => 77.78/10.58 (( 77.78/10.58 (breln1compprop) => 77.78/10.58 (( 77.78/10.58 (breln1compI) => 77.78/10.58 (( 77.78/10.58 (breln1compE) => 77.78/10.58 (( 77.78/10.58 (breln1compEex) => 77.78/10.58 (( 77.78/10.58 (breln1unionprop) => 77.78/10.58 (( 77.78/10.58 (breln1unionIL) => 77.78/10.58 (( 77.78/10.58 (breln1unionIR) => 77.78/10.58 (( 77.78/10.58 (breln1unionI) => 77.78/10.58 (( 77.78/10.58 (breln1unionE) => 77.78/10.58 (( 77.78/10.58 (breln1unionEcases) => 77.78/10.58 (( 77.78/10.58 (breln1unionCommutes) => 77.78/10.58 (( 77.78/10.58 (woz2Ex) => 77.78/10.58 (( 77.78/10.58 (woz2W) => 77.78/10.58 (( 77.78/10.58 (woz2A) => 77.78/10.58 (( 77.78/10.58 (woz2B) => 77.78/10.58 (( 77.78/10.58 (image1Ex) => 77.78/10.58 (( 77.78/10.58 (image1Ex1) => 77.78/10.58 (( 77.78/10.58 (image1Equiv) => 77.78/10.58 (( 77.78/10.58 (image1E) => 77.78/10.58 (( 77.78/10.58 (image1I) => 77.78/10.58 (( 77.78/10.58 (injFuncInInjFuncSet) => 77.78/10.58 (( 77.78/10.58 (injFuncSetFuncIn) => 77.78/10.58 (( 77.78/10.58 (injFuncSetFuncInj) => 77.78/10.58 (( 77.78/10.58 (surjFuncSetFuncIn) => 77.78/10.58 (( 77.78/10.58 (surjFuncSetFuncSurj) => 77.78/10.58 (( 77.78/10.58 (leftInvIsSurj) => 77.78/10.58 (( 77.78/10.58 (surjCantorThm) => 77.78/10.58 (( 77.78/10.58 (foundation2) => 77.78/10.58 (( 77.78/10.58 (notinself) => 77.78/10.58 (( 77.78/10.58 (notinself2) => 77.78/10.58 (( 77.78/10.58 (omegaSp) => 77.78/10.58 (( 77.78/10.58 (omegaSclos) => 77.78/10.58 (( 77.78/10.58 (peano0notS) => 77.78/10.58 (( 77.78/10.58 (peanoSinj) => 77.78/10.58 (( 77.78/10.58 (transitivesetOp1) => 77.78/10.58 (( 77.78/10.58 (binintTransitive) => 77.78/10.58 (( 77.78/10.58 (transitivesetOp2) => 77.78/10.58 (( 77.78/10.58 (setunionTransitive) => 77.78/10.58 (( 77.78/10.58 (ordinalMinLem1) => 77.78/10.58 (( 77.78/10.58 (!!) @ ( 77.78/10.58 ^[Y0 : $i]: 77.78/10.58 (( 77.78/10.58 (ordinal @ 77.78/10.58 Y0) => 77.78/10.58 (( 77.78/10.58 (!!) @ ( 77.78/10.58 ^[Y1 : $i]: 77.78/10.58 (( 77.78/10.58 (!!) @ ( 77.78/10.58 ^[Y2 : $i]: 77.78/10.58 (( 77.78/10.58 (in @ 77.78/10.58 Y2 @ 77.78/10.58 Y0) => 77.78/10.58 (( 77.78/10.58 (in @ 77.78/10.58 Y1 @ 77.78/10.58 Y2) => 77.78/10.58 (in @ 77.78/10.58 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 77.78/10.58 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl274])). 77.78/10.58 thf(zip_derived_cl297, plain, 77.78/10.58 (~ (((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) => 77.78/10.58 (((setadjoinIR) => 77.78/10.58 (((setadjoinE) => 77.78/10.58 (((setadjoinOr) => 77.78/10.58 (((setoftrueEq) => 77.78/10.58 (((powersetI) => 77.78/10.58 (((emptyinPowerset) => 77.78/10.58 (((emptyInPowerset) => 77.78/10.58 (((powersetE) => 77.78/10.58 (((setunionI) => 77.78/10.58 (((setunionE) => 77.78/10.58 (((subPowSU) => 77.78/10.58 (((exuE2) => 77.78/10.58 (((nonemptyImpWitness) => 77.78/10.58 (((uniqinunit) => 77.78/10.58 (((notinsingleton) => 77.78/10.58 (((eqinunit) => 77.78/10.58 (((singletonsswitch) => 77.78/10.58 (((upairsetE) => 77.78/10.58 (((upairsetIL) => 77.78/10.58 (((upairsetIR) => 77.78/10.58 (((emptyE1) => 77.78/10.58 (((vacuousDall) => 77.78/10.58 (((quantDeMorgan1) => 77.78/10.58 (((quantDeMorgan2) => 77.78/10.58 (((quantDeMorgan3) => 77.78/10.58 (((quantDeMorgan4) => 77.78/10.58 (((prop2setI) => 77.78/10.58 (((prop2set2propI) => 77.78/10.58 (((notdexE) => 77.78/10.58 (( 77.78/10.58 (notdallE) => 77.78/10.58 (( 77.78/10.58 (exuI1) => 77.78/10.58 (( 77.78/10.58 (exuI3) => 77.78/10.58 (( 77.78/10.58 (exuI2) => 77.78/10.58 (( 77.78/10.58 (inCongP) => 77.78/10.58 (( 77.78/10.58 (in__Cong) => 77.78/10.58 (( 77.78/10.58 (exuE3u) => 77.78/10.58 (( 77.78/10.58 (exu__Cong) => 77.78/10.58 (( 77.78/10.58 (setadjoin__Cong) => 77.78/10.58 (( 77.78/10.58 (powerset__Cong) => 77.78/10.58 (( 77.78/10.58 (setunion__Cong) => 77.78/10.58 (( 77.78/10.58 (exuEu) => 77.78/10.58 (( 77.78/10.58 (descr__Cong) => 77.78/10.58 (( 77.78/10.58 (dsetconstr__Cong) => 77.78/10.58 (( 77.78/10.58 (subsetI1) => 77.78/10.58 (( 77.78/10.58 (eqimpsubset2) => 77.78/10.58 (( 77.78/10.58 (eqimpsubset1) => 77.78/10.58 (( 77.78/10.58 (subsetI2) => 77.78/10.58 (( 77.78/10.58 (emptysetsubset) => 77.78/10.58 (( 77.78/10.58 (subsetE) => 77.78/10.58 (( 77.78/10.58 (subsetE2) => 77.78/10.58 (( 77.78/10.58 (notsubsetI) => 77.78/10.58 (( 77.78/10.58 (notequalI1) => 77.78/10.58 (( 77.78/10.58 (notequalI2) => 77.78/10.58 (( 77.78/10.58 (subsetRefl) => 77.78/10.58 (( 77.78/10.58 (subsetTrans) => 77.78/10.58 (( 77.78/10.58 (setadjoinSub) => 77.78/10.58 (( 77.78/10.58 (setadjoinSub2) => 77.78/10.58 (( 77.78/10.58 (subset2powerset) => 77.78/10.58 (( 77.78/10.58 (setextsub) => 77.78/10.58 (( 77.78/10.58 (subsetemptysetimpeq) => 77.78/10.58 (( 77.78/10.58 (powersetI1) => 77.78/10.58 (( 77.78/10.58 (powersetE1) => 77.78/10.58 (( 77.78/10.58 (inPowerset) => 77.78/10.58 (( 77.78/10.58 (powersetsubset) => 77.78/10.58 (( 77.78/10.58 (sepInPowerset) => 77.78/10.58 (( 77.78/10.58 (sepSubset) => 77.78/10.58 (( 77.78/10.58 (binunionIL) => 77.78/10.58 (( 77.78/10.58 (upairset2IR) => 77.78/10.58 (( 77.78/10.58 (binunionIR) => 77.78/10.58 (( 77.78/10.58 (binunionEcases) => 77.78/10.58 (( 77.78/10.58 (binunionE) => 77.78/10.58 (( 77.78/10.58 (binunionLsub) => 77.78/10.58 (( 77.78/10.58 (binunionRsub) => 77.78/10.58 (( 77.78/10.58 (binintersectI) => 77.78/10.58 (( 77.78/10.58 (binintersectSubset5) => 77.78/10.58 (( 77.78/10.58 (binintersectEL) => 77.78/10.58 (( 77.78/10.58 (binintersectLsub) => 77.78/10.58 (( 77.78/10.58 (binintersectSubset2) => 77.78/10.58 (( 77.78/10.58 (binintersectSubset3) => 77.78/10.58 (( 77.78/10.58 (binintersectER) => 77.78/10.58 (( 77.78/10.58 (disjointsetsI1) => 77.78/10.58 (( 77.78/10.58 (binintersectRsub) => 77.78/10.58 (( 77.78/10.58 (binintersectSubset4) => 77.78/10.58 (( 77.78/10.58 (binintersectSubset1) => 77.78/10.58 (( 77.78/10.58 (bs114d) => 77.78/10.58 (( 77.78/10.58 (setminusI) => 77.78/10.58 (( 77.78/10.58 (setminusEL) => 77.78/10.58 (( 77.78/10.58 (setminusER) => 77.78/10.58 (( 77.78/10.58 (setminusSubset2) => 77.78/10.58 (( 77.78/10.58 (setminusERneg) => 77.78/10.58 (( 77.78/10.58 (setminusELneg) => 77.78/10.58 (( 77.78/10.58 (setminusILneg) => 77.78/10.58 (( 77.78/10.58 (setminusIRneg) => 77.78/10.58 (( 77.78/10.58 (setminusLsub) => 77.78/10.58 (( 77.78/10.58 (setminusSubset1) => 77.78/10.58 (( 77.78/10.58 (symdiffE) => 77.78/10.58 (( 77.78/10.58 (symdiffI1) => 77.78/10.58 (( 77.78/10.58 (symdiffI2) => 77.78/10.58 (( 77.78/10.58 (symdiffIneg1) => 77.78/10.58 (( 77.78/10.58 (symdiffIneg2) => 77.78/10.58 (( 77.78/10.58 (secondinupair) => 77.78/10.58 (( 77.78/10.58 (setukpairIL) => 77.78/10.58 (( 77.78/10.58 (setukpairIR) => 77.78/10.58 (( 77.78/10.58 (kpairiskpair) => 77.78/10.58 (( 77.78/10.58 (kpairp) => 77.78/10.58 (( 77.78/10.58 (singletonsubset) => 77.78/10.58 (( 77.78/10.58 (singletoninpowerset) => 77.78/10.58 (( 77.78/10.58 (singletoninpowunion) => 77.78/10.58 (( 77.78/10.58 (upairset2E) => 77.78/10.58 (( 77.78/10.58 (upairsubunion) => 77.78/10.58 (( 77.78/10.58 (upairinpowunion) => 77.78/10.58 (( 77.78/10.58 (ubforcartprodlem1) => 77.78/10.58 (( 77.78/10.58 (ubforcartprodlem2) => 77.78/10.58 (( 77.78/10.58 (ubforcartprodlem3) => 77.78/10.58 (( 77.78/10.58 (cartprodpairin) => 77.78/10.58 (( 77.78/10.58 (cartprodmempair1) => 77.78/10.58 (( 77.78/10.58 (cartprodmempair) => 77.78/10.58 (( 77.78/10.58 (setunionE2) => 77.78/10.58 (( 77.78/10.58 (setunionsingleton1) => 77.78/10.58 (( 77.78/10.58 (setunionsingleton2) => 77.78/10.58 (( 77.78/10.58 (setunionsingleton) => 77.78/10.58 (( 77.78/10.58 (singletonprop) => 77.78/10.58 (( 77.78/10.58 (ex1E1) => 77.78/10.58 (( 77.78/10.58 (ex1I) => 77.78/10.58 (( 77.78/10.58 (ex1I2) => 77.78/10.58 (( 77.78/10.58 (singletonsuniq) => 77.78/10.58 (( 77.78/10.58 (setukpairinjL1) => 77.78/10.58 (( 77.78/10.58 (kfstsingleton) => 77.78/10.58 (( 77.78/10.58 (theprop) => 77.78/10.58 (( 77.78/10.58 (kfstpairEq) => 77.78/10.58 (( 77.78/10.58 (cartprodfstin) => 77.78/10.58 (( 77.78/10.58 (setukpairinjL2) => 77.78/10.58 (( 77.78/10.58 (setukpairinjL) => 77.78/10.58 (( 77.78/10.58 (setukpairinjR11) => 77.78/10.58 (( 77.78/10.58 (setukpairinjR12) => 77.78/10.58 (( 77.78/10.58 (setukpairinjR1) => 77.78/10.58 (( 77.78/10.58 (upairequniteq) => 77.78/10.58 (( 77.78/10.58 (setukpairinjR2) => 77.78/10.58 (( 77.78/10.58 (setukpairinjR) => 77.78/10.58 (( 77.78/10.58 (ksndsingleton) => 77.78/10.58 (( 77.78/10.58 (ksndpairEq) => 77.78/10.58 (( 77.78/10.58 (kpairsurjEq) => 77.78/10.58 (( 77.78/10.58 (cartprodsndin) => 77.78/10.58 (( 77.78/10.58 (cartprodpairmemEL) => 77.78/10.58 (( 77.78/10.58 (cartprodpairmemER) => 77.78/10.58 (( 77.78/10.58 (cartprodmempaircEq) => 77.78/10.58 (( 77.78/10.58 (cartprodfstpairEq) => 77.78/10.58 (( 77.78/10.58 (cartprodsndpairEq) => 77.78/10.58 (( 77.78/10.58 (cartprodpairsurjEq) => 77.78/10.58 (( 77.78/10.58 (dpsetconstrI) => 77.78/10.58 (( 77.78/10.58 (dpsetconstrSub) => 77.78/10.58 (( 77.78/10.58 (setOfPairsIsBReln) => 77.78/10.58 (( 77.78/10.58 (dpsetconstrERa) => 77.78/10.58 (( 77.78/10.58 (dpsetconstrEL1) => 77.78/10.58 (( 77.78/10.58 (dpsetconstrEL2) => 77.78/10.58 (( 77.78/10.58 (dpsetconstrER) => 77.78/10.58 (( 77.78/10.58 (funcImageSingleton) => 77.78/10.58 (( 77.78/10.58 (apProp) => 77.78/10.58 (( 77.78/10.58 (app) => 77.78/10.58 (( 77.78/10.58 (infuncsetfunc) => 77.78/10.58 (( 77.78/10.58 (ap2p) => 77.78/10.58 (( 77.78/10.58 (funcinfuncset) => 77.78/10.58 (( 77.78/10.58 (lamProp) => 77.78/10.58 (( 77.78/10.58 (lamp) => 77.78/10.58 (( 77.78/10.58 (lam2p) => 77.78/10.58 (( 77.78/10.58 (brelnall1) => 77.78/10.58 (( 77.78/10.58 (brelnall2) => 77.78/10.58 (( 77.78/10.58 (ex1E2) => 77.78/10.58 (( 77.78/10.58 (funcGraphProp1) => 77.78/10.58 (( 77.78/10.58 (funcGraphProp3) => 77.78/10.58 (( 77.78/10.58 (funcGraphProp2) => 77.78/10.58 (( 77.78/10.58 (funcextLem) => 77.78/10.58 (( 77.78/10.58 (funcGraphProp4) => 77.78/10.58 (( 77.78/10.58 (subbreln) => 77.78/10.58 (( 77.78/10.58 (eqbreln) => 77.78/10.58 (( 77.78/10.58 (funcext) => 77.78/10.58 (( 77.78/10.58 (funcext2) => 77.78/10.58 (( 77.78/10.58 (ap2apEq1) => 77.78/10.58 (( 77.78/10.58 (ap2apEq2) => 77.78/10.58 (( 77.78/10.58 (beta1) => 77.78/10.58 (( 77.78/10.58 (eta1) => 77.78/10.58 (( 77.78/10.58 (lam2lamEq) => 77.78/10.58 (( 77.78/10.58 (beta2) => 77.78/10.58 (( 77.78/10.58 (eta2) => 77.78/10.58 (( 77.78/10.58 (iffalseProp1) => 77.78/10.58 (( 77.78/10.58 (iffalseProp2) => 77.78/10.58 (( 77.78/10.58 (iftrueProp1) => 77.78/10.58 (( 77.78/10.58 (iftrueProp2) => 77.78/10.58 (( 77.78/10.58 (ifSingleton) => 77.78/10.58 (( 77.78/10.58 (ifp) => 77.78/10.58 (( 77.78/10.58 (theeq) => 77.78/10.58 (( 77.78/10.58 (iftrue) => 77.78/10.58 (( 77.78/10.58 (iffalse) => 77.78/10.58 (( 77.78/10.58 (iftrueorfalse) => 77.78/10.58 (( 77.78/10.58 (binintersectT_lem) => 77.78/10.58 (( 77.78/10.58 (binunionT_lem) => 77.78/10.58 (( 77.78/10.58 (powersetT_lem) => 77.78/10.58 (( 77.78/10.58 (setminusT_lem) => 77.78/10.58 (( 77.78/10.58 (complementT_lem) => 77.78/10.58 (( 77.78/10.58 (setextT) => 77.78/10.58 (( 77.78/10.58 (subsetTI) => 77.78/10.58 (( 77.78/10.58 (powersetTI1) => 77.78/10.58 (( 77.78/10.58 (powersetTE1) => 77.78/10.58 (( 77.78/10.58 (complementTI1) => 77.78/10.58 (( 77.78/10.58 (complementTE1) => 77.78/10.58 (( 77.78/10.58 (binintersectTELcontra) => 77.78/10.58 (( 77.78/10.58 (binintersectTERcontra) => 77.78/10.58 (( 77.78/10.58 (contrasubsetT) => 77.78/10.58 (( 77.78/10.58 (contrasubsetT1) => 77.78/10.58 (( 77.78/10.58 (contrasubsetT2) => 77.78/10.58 (( 77.78/10.58 (contrasubsetT3) => 77.78/10.58 (( 77.78/10.58 (doubleComplementI1) => 77.78/10.58 (( 77.78/10.58 (doubleComplementE1) => 77.78/10.58 (( 77.78/10.58 (doubleComplementSub1) => 77.78/10.58 (( 77.78/10.58 (doubleComplementSub2) => 77.78/10.58 (( 77.78/10.58 (doubleComplementEq) => 77.78/10.58 (( 77.78/10.58 (complementTnotintersectT) => 77.78/10.58 (( 77.78/10.58 (complementImpComplementIntersect) => 77.78/10.58 (( 77.78/10.58 (complementSubsetComplementIntersect) => 77.78/10.58 (( 77.78/10.58 (complementInPowersetComplementIntersect) => 77.78/10.58 (( 77.78/10.58 (contraSubsetComplement) => 77.78/10.58 (( 77.78/10.58 (complementTcontraSubset) => 77.78/10.58 (( 77.78/10.58 (binunionTILcontra) => 77.78/10.58 (( 77.78/10.58 (binunionTIRcontra) => 77.78/10.58 (( 77.78/10.58 (inIntersectImpInUnion) => 77.78/10.58 (( 77.78/10.58 (inIntersectImpInUnion2) => 77.78/10.58 (( 77.78/10.58 (inIntersectImpInIntersectUnions) => 77.78/10.58 (( 77.78/10.58 (intersectInPowersetIntersectUnions) => 77.78/10.58 (( 77.78/10.58 (inComplementUnionImpNotIn1) => 77.78/10.58 (( 77.78/10.58 (inComplementUnionImpInComplement1) => 77.78/10.58 (( 77.78/10.58 (binunionTE) => 77.78/10.58 (( 77.78/10.58 (binunionTEcontra) => 77.78/10.58 (( 77.78/10.58 (demorgan2a1) => 77.78/10.58 (( 77.78/10.58 (complementUnionInPowersetComplement) => 77.78/10.58 (( 77.78/10.58 (demorgan2a2) => 77.78/10.58 (( 77.78/10.58 (demorgan1a) => 77.78/10.58 (( 77.78/10.58 (demorgan1b) => 77.78/10.58 (( 77.78/10.58 (demorgan1) => 77.78/10.58 (( 77.78/10.58 (demorgan2a) => 77.78/10.58 (( 77.78/10.58 (demorgan2b2) => 77.78/10.58 (( 77.78/10.58 (demorgan2b) => 77.78/10.58 (( 77.78/10.58 (demorgan2) => 77.78/10.58 (( 77.78/10.58 (woz13rule0) => 77.78/10.58 (( 77.78/10.58 (woz13rule1) => 77.78/10.58 (( 77.78/10.58 (woz13rule2) => 77.78/10.58 (( 77.78/10.58 (woz13rule3) => 77.78/10.58 (( 77.78/10.58 (woz13rule4) => 77.78/10.58 (( 77.78/10.58 (woz1_1) => 77.78/10.58 (( 77.78/10.58 (woz1_2) => 77.78/10.58 (( 77.78/10.58 (woz1_3) => 77.78/10.58 (( 77.78/10.58 (woz1_4) => 77.78/10.58 (( 77.78/10.58 (woz1_5) => 77.78/10.58 (( 77.78/10.58 (breln1all2) => 77.78/10.58 (( 77.78/10.58 (breln1SetBreln1) => 77.78/10.58 (( 77.78/10.58 (choice2fnsingleton) => 77.78/10.58 (( 77.78/10.58 (setOfPairsIsBReln1) => 77.78/10.58 (( 77.78/10.58 (breln1all1) => 77.78/10.58 (( 77.78/10.58 (subbreln1) => 77.78/10.58 (( 77.78/10.58 (eqbreln1) => 77.78/10.58 (( 77.78/10.58 (breln1invprop) => 77.78/10.58 (( 77.78/10.58 (breln1invI) => 77.78/10.58 (( 77.78/10.58 (breln1invE) => 77.78/10.58 (( 77.78/10.58 (breln1compprop) => 77.78/10.58 (( 77.78/10.58 (breln1compI) => 77.78/10.58 (( 77.78/10.58 (breln1compE) => 77.78/10.58 (( 77.78/10.58 (breln1compEex) => 77.78/10.58 (( 77.78/10.58 (breln1unionprop) => 77.78/10.58 (( 77.78/10.58 (breln1unionIL) => 77.78/10.58 (( 77.78/10.58 (breln1unionIR) => 77.78/10.58 (( 77.78/10.58 (breln1unionI) => 77.78/10.58 (( 77.78/10.58 (breln1unionE) => 77.78/10.58 (( 77.78/10.58 (breln1unionEcases) => 77.78/10.58 (( 77.78/10.58 (breln1unionCommutes) => 77.78/10.58 (( 77.78/10.58 (woz2Ex) => 77.78/10.58 (( 77.78/10.58 (woz2W) => 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(binintTransitive) => 77.78/10.58 (( 77.78/10.58 (transitivesetOp2) => 77.78/10.58 (( 77.78/10.58 (setunionTransitive) => 77.78/10.58 (( 77.78/10.58 (ordinalMinLem1) => 77.78/10.58 (( 77.78/10.58 (!!) @ ( 77.78/10.58 ^[Y0 : $i]: 77.78/10.58 (( 77.78/10.58 (ordinal @ 77.78/10.58 Y0) => 77.78/10.58 (( 77.78/10.58 (!!) @ ( 77.78/10.58 ^[Y1 : $i]: 77.78/10.58 (( 77.78/10.58 (!!) @ ( 77.78/10.58 ^[Y2 : $i]: 77.78/10.58 (( 77.78/10.58 (in @ 77.78/10.58 Y2 @ 77.78/10.58 Y0) => 77.78/10.58 (( 77.78/10.58 (in @ 77.78/10.58 Y1 @ 77.78/10.58 Y2) => 77.78/10.58 (in @ 77.78/10.58 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 77.78/10.58 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl285])). 77.78/10.58 thf(zip_derived_cl305, plain, 77.78/10.58 (~ (((setadjoinIR) => 77.78/10.58 (((setadjoinE) => 77.78/10.58 (((setadjoinOr) => 77.78/10.58 (((setoftrueEq) => 77.78/10.58 (((powersetI) => 77.78/10.58 (((emptyinPowerset) => 77.78/10.58 (((emptyInPowerset) => 77.78/10.58 (((powersetE) => 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=> 77.78/10.58 (( 77.78/10.58 (powerset__Cong) => 77.78/10.58 (( 77.78/10.58 (setunion__Cong) => 77.78/10.58 (( 77.78/10.58 (exuEu) => 77.78/10.58 (( 77.78/10.58 (descr__Cong) => 77.78/10.58 (( 77.78/10.58 (dsetconstr__Cong) => 77.78/10.58 (( 77.78/10.58 (subsetI1) => 77.78/10.58 (( 77.78/10.58 (eqimpsubset2) => 77.78/10.58 (( 77.78/10.58 (eqimpsubset1) => 77.78/10.58 (( 77.78/10.58 (subsetI2) => 77.78/10.58 (( 77.78/10.58 (emptysetsubset) => 77.78/10.58 (( 77.78/10.58 (subsetE) => 77.78/10.58 (( 77.78/10.58 (subsetE2) => 77.78/10.58 (( 77.78/10.58 (notsubsetI) => 77.78/10.58 (( 77.78/10.58 (notequalI1) => 77.78/10.58 (( 77.78/10.58 (notequalI2) => 77.78/10.58 (( 77.78/10.58 (subsetRefl) => 77.78/10.58 (( 77.78/10.58 (subsetTrans) => 77.78/10.58 (( 77.78/10.58 (setadjoinSub) => 77.78/10.58 (( 77.78/10.58 (setadjoinSub2) => 77.78/10.58 (( 77.78/10.58 (subset2powerset) => 77.78/10.58 (( 77.78/10.58 (setextsub) => 77.78/10.58 (( 77.78/10.58 (subsetemptysetimpeq) => 77.78/10.58 (( 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77.78/10.58 (( 77.78/10.58 (binintersectSubset4) => 77.78/10.58 (( 77.78/10.58 (binintersectSubset1) => 77.78/10.58 (( 77.78/10.58 (bs114d) => 77.78/10.58 (( 77.78/10.58 (setminusI) => 77.78/10.58 (( 77.78/10.58 (setminusEL) => 77.78/10.58 (( 77.78/10.58 (setminusER) => 77.78/10.58 (( 77.78/10.58 (setminusSubset2) => 77.78/10.58 (( 77.78/10.58 (setminusERneg) => 77.78/10.58 (( 77.78/10.58 (setminusELneg) => 77.78/10.58 (( 77.78/10.58 (setminusILneg) => 77.78/10.58 (( 77.78/10.58 (setminusIRneg) => 77.78/10.58 (( 77.78/10.58 (setminusLsub) => 77.78/10.58 (( 77.78/10.58 (setminusSubset1) => 77.78/10.58 (( 77.78/10.58 (symdiffE) => 77.78/10.58 (( 77.78/10.58 (symdiffI1) => 77.78/10.58 (( 77.78/10.58 (symdiffI2) => 77.78/10.58 (( 77.78/10.58 (symdiffIneg1) => 77.78/10.58 (( 77.78/10.58 (symdiffIneg2) => 77.78/10.58 (( 77.78/10.58 (secondinupair) => 77.78/10.58 (( 77.78/10.58 (setukpairIL) => 77.78/10.58 (( 77.78/10.58 (setukpairIR) => 77.78/10.58 (( 77.78/10.58 (kpairiskpair) => 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77.78/10.58 (singletonsuniq) => 77.78/10.58 (( 77.78/10.58 (setukpairinjL1) => 77.78/10.58 (( 77.78/10.58 (kfstsingleton) => 77.78/10.58 (( 77.78/10.58 (theprop) => 77.78/10.58 (( 77.78/10.58 (kfstpairEq) => 77.78/10.58 (( 77.78/10.58 (cartprodfstin) => 77.78/10.58 (( 77.78/10.58 (setukpairinjL2) => 77.78/10.58 (( 77.78/10.58 (setukpairinjL) => 77.78/10.58 (( 77.78/10.58 (setukpairinjR11) => 77.78/10.58 (( 77.78/10.58 (setukpairinjR12) => 77.78/10.58 (( 77.78/10.58 (setukpairinjR1) => 77.78/10.58 (( 77.78/10.58 (upairequniteq) => 77.78/10.58 (( 77.78/10.58 (setukpairinjR2) => 77.78/10.58 (( 77.78/10.58 (setukpairinjR) => 77.78/10.58 (( 77.78/10.58 (ksndsingleton) => 77.78/10.58 (( 77.78/10.58 (ksndpairEq) => 77.78/10.58 (( 77.78/10.58 (kpairsurjEq) => 77.78/10.58 (( 77.78/10.58 (cartprodsndin) => 77.78/10.58 (( 77.78/10.58 (cartprodpairmemEL) => 77.78/10.58 (( 77.78/10.58 (cartprodpairmemER) => 77.78/10.58 (( 77.78/10.58 (cartprodmempaircEq) => 77.78/10.58 (( 77.78/10.58 (cartprodfstpairEq) => 77.78/10.58 (( 77.78/10.58 (cartprodsndpairEq) => 77.78/10.58 (( 77.78/10.58 (cartprodpairsurjEq) => 77.78/10.58 (( 77.78/10.58 (dpsetconstrI) => 77.78/10.58 (( 77.78/10.58 (dpsetconstrSub) => 77.78/10.58 (( 77.78/10.58 (setOfPairsIsBReln) => 77.78/10.58 (( 77.78/10.58 (dpsetconstrERa) => 77.78/10.58 (( 77.78/10.58 (dpsetconstrEL1) => 77.78/10.58 (( 77.78/10.58 (dpsetconstrEL2) => 77.78/10.58 (( 77.78/10.58 (dpsetconstrER) => 77.78/10.58 (( 77.78/10.58 (funcImageSingleton) => 77.78/10.58 (( 77.78/10.58 (apProp) => 77.78/10.58 (( 77.78/10.58 (app) => 77.78/10.58 (( 77.78/10.58 (infuncsetfunc) => 77.78/10.58 (( 77.78/10.58 (ap2p) => 77.78/10.58 (( 77.78/10.58 (funcinfuncset) => 77.78/10.58 (( 77.78/10.58 (lamProp) => 77.78/10.58 (( 77.78/10.58 (lamp) => 77.78/10.58 (( 77.78/10.58 (lam2p) => 77.78/10.58 (( 77.78/10.58 (brelnall1) => 77.78/10.58 (( 77.78/10.58 (brelnall2) => 77.78/10.58 (( 77.78/10.58 (ex1E2) => 77.78/10.58 (( 77.78/10.58 (funcGraphProp1) => 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77.78/10.58 (binunionTEcontra) => 77.78/10.58 (( 77.78/10.58 (demorgan2a1) => 77.78/10.58 (( 77.78/10.58 (complementUnionInPowersetComplement) => 77.78/10.58 (( 77.78/10.58 (demorgan2a2) => 77.78/10.58 (( 77.78/10.58 (demorgan1a) => 77.78/10.58 (( 77.78/10.58 (demorgan1b) => 77.78/10.58 (( 77.78/10.58 (demorgan1) => 77.78/10.58 (( 77.78/10.58 (demorgan2a) => 77.78/10.58 (( 77.78/10.58 (demorgan2b2) => 77.78/10.58 (( 77.78/10.58 (demorgan2b) => 77.78/10.58 (( 77.78/10.58 (demorgan2) => 77.78/10.58 (( 77.78/10.58 (woz13rule0) => 77.78/10.58 (( 77.78/10.58 (woz13rule1) => 77.78/10.58 (( 77.78/10.58 (woz13rule2) => 77.78/10.58 (( 77.78/10.58 (woz13rule3) => 77.78/10.58 (( 77.78/10.58 (woz13rule4) => 77.78/10.58 (( 77.78/10.58 (woz1_1) => 77.78/10.58 (( 77.78/10.58 (woz1_2) => 77.78/10.58 (( 77.78/10.58 (woz1_3) => 77.78/10.58 (( 77.78/10.58 (woz1_4) => 77.78/10.58 (( 77.78/10.58 (woz1_5) => 77.78/10.58 (( 77.78/10.58 (breln1all2) => 77.78/10.58 (( 77.78/10.58 (breln1SetBreln1) => 77.78/10.58 (( 77.78/10.58 (choice2fnsingleton) => 77.78/10.58 (( 77.78/10.58 (setOfPairsIsBReln1) => 77.78/10.58 (( 77.78/10.58 (breln1all1) => 77.78/10.58 (( 77.78/10.58 (subbreln1) => 77.78/10.58 (( 77.78/10.58 (eqbreln1) => 77.78/10.58 (( 77.78/10.58 (breln1invprop) => 77.78/10.58 (( 77.78/10.58 (breln1invI) => 77.78/10.58 (( 77.78/10.58 (breln1invE) => 77.78/10.58 (( 77.78/10.58 (breln1compprop) => 77.78/10.58 (( 77.78/10.58 (breln1compI) => 77.78/10.58 (( 77.78/10.58 (breln1compE) => 77.78/10.58 (( 77.78/10.58 (breln1compEex) => 77.78/10.58 (( 77.78/10.58 (breln1unionprop) => 77.78/10.58 (( 77.78/10.58 (breln1unionIL) => 77.78/10.58 (( 77.78/10.58 (breln1unionIR) => 77.78/10.58 (( 77.78/10.58 (breln1unionI) => 77.78/10.58 (( 77.78/10.58 (breln1unionE) => 77.78/10.58 (( 77.78/10.58 (breln1unionEcases) => 77.78/10.58 (( 77.78/10.58 (breln1unionCommutes) => 77.78/10.58 (( 77.78/10.58 (woz2Ex) => 77.78/10.58 (( 77.78/10.58 (woz2W) => 77.78/10.58 (( 77.78/10.58 (woz2A) => 77.78/10.58 (( 77.78/10.58 (woz2B) => 77.78/10.58 (( 77.78/10.58 (image1Ex) => 77.78/10.58 (( 77.78/10.58 (image1Ex1) => 77.78/10.58 (( 77.78/10.58 (image1Equiv) => 77.78/10.58 (( 77.78/10.58 (image1E) => 77.78/10.58 (( 77.78/10.58 (image1I) => 77.78/10.58 (( 77.78/10.58 (injFuncInInjFuncSet) => 77.78/10.58 (( 77.78/10.58 (injFuncSetFuncIn) => 77.78/10.58 (( 77.78/10.58 (injFuncSetFuncInj) => 77.78/10.58 (( 77.78/10.58 (surjFuncSetFuncIn) => 77.78/10.58 (( 77.78/10.58 (surjFuncSetFuncSurj) => 77.78/10.58 (( 77.78/10.58 (leftInvIsSurj) => 77.78/10.58 (( 77.78/10.58 (surjCantorThm) => 77.78/10.58 (( 77.78/10.58 (foundation2) => 77.78/10.58 (( 77.78/10.58 (notinself) => 77.78/10.58 (( 77.78/10.58 (notinself2) => 77.78/10.58 (( 77.78/10.58 (omegaSp) => 77.78/10.58 (( 77.78/10.58 (omegaSclos) => 77.78/10.58 (( 77.78/10.58 (peano0notS) => 77.78/10.58 (( 77.78/10.58 (peanoSinj) => 77.78/10.58 (( 77.78/10.58 (transitivesetOp1) => 77.78/10.58 (( 77.78/10.58 (binintTransitive) => 77.78/10.58 (( 77.78/10.58 (transitivesetOp2) => 77.78/10.58 (( 77.78/10.58 (setunionTransitive) => 77.78/10.58 (( 77.78/10.58 (ordinalMinLem1) => 77.78/10.58 (( 77.78/10.58 (!!) @ ( 77.78/10.58 ^[Y0 : $i]: 77.78/10.58 (( 77.78/10.58 (ordinal @ 77.78/10.58 Y0) => 77.78/10.58 (( 77.78/10.58 (!!) @ ( 77.78/10.58 ^[Y1 : $i]: 77.78/10.58 (( 77.78/10.58 (!!) @ ( 77.78/10.58 ^[Y2 : $i]: 77.78/10.58 (( 77.78/10.58 (in @ 77.78/10.58 Y2 @ 77.78/10.58 Y0) => 77.78/10.58 (( 77.78/10.58 (in @ 77.78/10.58 Y1 @ 77.78/10.58 Y2) => 77.78/10.58 (in @ 77.78/10.58 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 77.78/10.58 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl297])). 77.78/10.58 thf(zip_derived_cl312, plain, 77.78/10.58 (~ (((setadjoinE) => 77.78/10.58 (((setadjoinOr) => 77.78/10.58 (((setoftrueEq) => 77.78/10.58 (((powersetI) => 77.78/10.58 (((emptyinPowerset) => 77.78/10.58 (((emptyInPowerset) => 77.78/10.58 (((powersetE) => 77.78/10.58 (((setunionI) => 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(powerset__Cong) => 77.78/10.58 (( 77.78/10.58 (setunion__Cong) => 77.78/10.58 (( 77.78/10.58 (exuEu) => 77.78/10.58 (( 77.78/10.58 (descr__Cong) => 77.78/10.58 (( 77.78/10.58 (dsetconstr__Cong) => 77.78/10.58 (( 77.78/10.58 (subsetI1) => 77.78/10.58 (( 77.78/10.58 (eqimpsubset2) => 77.78/10.58 (( 77.78/10.58 (eqimpsubset1) => 77.78/10.58 (( 77.78/10.58 (subsetI2) => 77.78/10.58 (( 77.78/10.58 (emptysetsubset) => 77.78/10.58 (( 77.78/10.58 (subsetE) => 77.78/10.58 (( 77.78/10.58 (subsetE2) => 77.78/10.58 (( 77.78/10.58 (notsubsetI) => 77.78/10.58 (( 77.78/10.58 (notequalI1) => 77.78/10.58 (( 77.78/10.58 (notequalI2) => 77.78/10.58 (( 77.78/10.58 (subsetRefl) => 77.78/10.58 (( 77.78/10.58 (subsetTrans) => 77.78/10.58 (( 77.78/10.58 (setadjoinSub) => 77.78/10.58 (( 77.78/10.58 (setadjoinSub2) => 77.78/10.58 (( 77.78/10.58 (subset2powerset) => 77.78/10.58 (( 77.78/10.58 (setextsub) => 77.78/10.58 (( 77.78/10.58 (subsetemptysetimpeq) => 77.78/10.58 (( 77.78/10.58 (powersetI1) => 77.78/10.58 (( 77.78/10.58 (powersetE1) => 77.78/10.58 (( 77.78/10.58 (inPowerset) => 77.78/10.58 (( 77.78/10.58 (powersetsubset) => 77.78/10.58 (( 77.78/10.58 (sepInPowerset) => 77.78/10.58 (( 77.78/10.58 (sepSubset) => 77.78/10.58 (( 77.78/10.58 (binunionIL) => 77.78/10.58 (( 77.78/10.58 (upairset2IR) => 77.78/10.58 (( 77.78/10.58 (binunionIR) => 77.78/10.58 (( 77.78/10.58 (binunionEcases) => 77.78/10.58 (( 77.78/10.58 (binunionE) => 77.78/10.58 (( 77.78/10.58 (binunionLsub) => 77.78/10.58 (( 77.78/10.58 (binunionRsub) => 77.78/10.58 (( 77.78/10.58 (binintersectI) => 77.78/10.58 (( 77.78/10.58 (binintersectSubset5) => 77.78/10.58 (( 77.78/10.58 (binintersectEL) => 77.78/10.58 (( 77.78/10.58 (binintersectLsub) => 77.78/10.58 (( 77.78/10.58 (binintersectSubset2) => 77.78/10.58 (( 77.78/10.58 (binintersectSubset3) => 77.78/10.58 (( 77.78/10.58 (binintersectER) => 77.78/10.58 (( 77.78/10.58 (disjointsetsI1) => 77.78/10.58 (( 77.78/10.58 (binintersectRsub) => 77.78/10.58 (( 77.78/10.58 (binintersectSubset4) => 77.78/10.58 (( 77.78/10.58 (binintersectSubset1) => 77.78/10.58 (( 77.78/10.58 (bs114d) => 77.78/10.58 (( 77.78/10.58 (setminusI) => 77.78/10.58 (( 77.78/10.58 (setminusEL) => 77.78/10.58 (( 77.78/10.58 (setminusER) => 77.78/10.58 (( 77.78/10.58 (setminusSubset2) => 77.78/10.58 (( 77.78/10.58 (setminusERneg) => 77.78/10.58 (( 77.78/10.58 (setminusELneg) => 77.78/10.58 (( 77.78/10.58 (setminusILneg) => 77.78/10.58 (( 77.78/10.58 (setminusIRneg) => 77.78/10.58 (( 77.78/10.58 (setminusLsub) => 77.78/10.58 (( 77.78/10.58 (setminusSubset1) => 77.78/10.58 (( 77.78/10.58 (symdiffE) => 77.78/10.58 (( 77.78/10.58 (symdiffI1) => 77.78/10.58 (( 77.78/10.58 (symdiffI2) => 77.78/10.58 (( 77.78/10.58 (symdiffIneg1) => 77.78/10.58 (( 77.78/10.58 (symdiffIneg2) => 77.78/10.58 (( 77.78/10.58 (secondinupair) => 77.78/10.58 (( 77.78/10.58 (setukpairIL) => 77.78/10.58 (( 77.78/10.58 (setukpairIR) => 77.78/10.58 (( 77.78/10.58 (kpairiskpair) => 77.78/10.58 (( 77.78/10.58 (kpairp) => 77.78/10.58 (( 77.78/10.58 (singletonsubset) => 77.78/10.58 (( 77.78/10.58 (singletoninpowerset) => 77.78/10.58 (( 77.78/10.58 (singletoninpowunion) => 77.78/10.58 (( 77.78/10.58 (upairset2E) => 77.78/10.58 (( 77.78/10.58 (upairsubunion) => 77.78/10.58 (( 77.78/10.58 (upairinpowunion) => 77.78/10.58 (( 77.78/10.58 (ubforcartprodlem1) => 77.78/10.58 (( 77.78/10.58 (ubforcartprodlem2) => 77.78/10.58 (( 77.78/10.58 (ubforcartprodlem3) => 77.78/10.58 (( 77.78/10.58 (cartprodpairin) => 77.78/10.58 (( 77.78/10.58 (cartprodmempair1) => 77.78/10.58 (( 77.78/10.58 (cartprodmempair) => 77.78/10.58 (( 77.78/10.58 (setunionE2) => 77.78/10.58 (( 77.78/10.58 (setunionsingleton1) => 77.78/10.58 (( 77.78/10.58 (setunionsingleton2) => 77.78/10.58 (( 77.78/10.58 (setunionsingleton) => 77.78/10.58 (( 77.78/10.58 (singletonprop) => 77.78/10.58 (( 77.78/10.58 (ex1E1) => 77.78/10.58 (( 77.78/10.58 (ex1I) => 77.78/10.58 (( 77.78/10.58 (ex1I2) => 77.78/10.58 (( 77.78/10.58 (singletonsuniq) => 77.78/10.58 (( 77.78/10.58 (setukpairinjL1) => 77.78/10.58 (( 77.78/10.58 (kfstsingleton) => 77.78/10.58 (( 77.78/10.58 (theprop) => 77.78/10.58 (( 77.78/10.58 (kfstpairEq) => 77.78/10.58 (( 77.78/10.58 (cartprodfstin) => 77.78/10.58 (( 77.78/10.58 (setukpairinjL2) => 77.78/10.58 (( 77.78/10.58 (setukpairinjL) => 77.78/10.58 (( 77.78/10.58 (setukpairinjR11) => 77.78/10.58 (( 77.78/10.58 (setukpairinjR12) => 77.78/10.58 (( 77.78/10.58 (setukpairinjR1) => 77.78/10.58 (( 77.78/10.58 (upairequniteq) => 77.78/10.58 (( 77.78/10.58 (setukpairinjR2) => 77.78/10.58 (( 77.78/10.58 (setukpairinjR) => 77.78/10.58 (( 77.78/10.58 (ksndsingleton) => 77.78/10.58 (( 77.78/10.58 (ksndpairEq) => 77.78/10.58 (( 77.78/10.58 (kpairsurjEq) => 77.78/10.58 (( 77.78/10.58 (cartprodsndin) => 77.78/10.58 (( 77.78/10.58 (cartprodpairmemEL) => 77.78/10.58 (( 77.78/10.58 (cartprodpairmemER) => 77.78/10.58 (( 77.78/10.58 (cartprodmempaircEq) => 77.78/10.58 (( 77.78/10.58 (cartprodfstpairEq) => 77.78/10.58 (( 77.78/10.58 (cartprodsndpairEq) => 77.78/10.58 (( 77.78/10.58 (cartprodpairsurjEq) => 77.78/10.58 (( 77.78/10.58 (dpsetconstrI) => 77.78/10.58 (( 77.78/10.58 (dpsetconstrSub) => 77.78/10.58 (( 77.78/10.58 (setOfPairsIsBReln) => 77.78/10.58 (( 77.78/10.58 (dpsetconstrERa) => 77.78/10.58 (( 77.78/10.58 (dpsetconstrEL1) => 77.78/10.58 (( 77.78/10.58 (dpsetconstrEL2) => 77.78/10.58 (( 77.78/10.58 (dpsetconstrER) => 77.78/10.58 (( 77.78/10.58 (funcImageSingleton) => 77.78/10.58 (( 77.78/10.58 (apProp) => 77.78/10.58 (( 77.78/10.58 (app) => 77.78/10.58 (( 77.78/10.58 (infuncsetfunc) => 77.78/10.58 (( 77.78/10.58 (ap2p) => 77.78/10.58 (( 77.78/10.58 (funcinfuncset) => 77.78/10.58 (( 77.78/10.58 (lamProp) => 77.78/10.58 (( 77.78/10.58 (lamp) => 77.78/10.58 (( 77.78/10.58 (lam2p) => 77.78/10.58 (( 77.78/10.58 (brelnall1) => 77.78/10.58 (( 77.78/10.58 (brelnall2) => 77.78/10.58 (( 77.78/10.58 (ex1E2) => 77.78/10.58 (( 77.78/10.58 (funcGraphProp1) => 77.78/10.58 (( 77.78/10.58 (funcGraphProp3) => 77.78/10.58 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77.78/10.58 (doubleComplementEq) => 77.78/10.58 (( 77.78/10.58 (complementTnotintersectT) => 77.78/10.58 (( 77.78/10.58 (complementImpComplementIntersect) => 77.78/10.58 (( 77.78/10.58 (complementSubsetComplementIntersect) => 77.78/10.58 (( 77.78/10.58 (complementInPowersetComplementIntersect) => 77.78/10.58 (( 77.78/10.58 (contraSubsetComplement) => 77.78/10.58 (( 77.78/10.58 (complementTcontraSubset) => 77.78/10.58 (( 77.78/10.58 (binunionTILcontra) => 77.78/10.58 (( 77.78/10.58 (binunionTIRcontra) => 77.78/10.58 (( 77.78/10.58 (inIntersectImpInUnion) => 77.78/10.58 (( 77.78/10.58 (inIntersectImpInUnion2) => 77.78/10.58 (( 77.78/10.58 (inIntersectImpInIntersectUnions) => 77.78/10.58 (( 77.78/10.58 (intersectInPowersetIntersectUnions) => 77.78/10.58 (( 77.78/10.58 (inComplementUnionImpNotIn1) => 77.78/10.58 (( 77.78/10.58 (inComplementUnionImpInComplement1) => 77.78/10.58 (( 77.78/10.58 (binunionTE) => 77.78/10.58 (( 77.78/10.58 (binunionTEcontra) => 77.78/10.58 (( 77.78/10.58 (demorgan2a1) => 77.78/10.58 (( 77.78/10.58 (complementUnionInPowersetComplement) => 77.78/10.58 (( 77.78/10.58 (demorgan2a2) => 77.78/10.58 (( 77.78/10.58 (demorgan1a) => 77.78/10.58 (( 77.78/10.58 (demorgan1b) => 77.78/10.58 (( 77.78/10.58 (demorgan1) => 77.78/10.58 (( 77.78/10.58 (demorgan2a) => 77.78/10.58 (( 77.78/10.58 (demorgan2b2) => 77.78/10.58 (( 77.78/10.58 (demorgan2b) => 77.78/10.58 (( 77.78/10.58 (demorgan2) => 77.78/10.58 (( 77.78/10.58 (woz13rule0) => 77.78/10.58 (( 77.78/10.58 (woz13rule1) => 77.78/10.58 (( 77.78/10.58 (woz13rule2) => 77.78/10.58 (( 77.78/10.58 (woz13rule3) => 77.78/10.58 (( 77.78/10.58 (woz13rule4) => 77.78/10.58 (( 77.78/10.58 (woz1_1) => 77.78/10.58 (( 77.78/10.58 (woz1_2) => 77.78/10.58 (( 77.78/10.58 (woz1_3) => 77.78/10.58 (( 77.78/10.58 (woz1_4) => 77.78/10.58 (( 77.78/10.58 (woz1_5) => 77.78/10.58 (( 77.78/10.58 (breln1all2) => 77.78/10.58 (( 77.78/10.58 (breln1SetBreln1) => 77.78/10.58 (( 77.78/10.58 (choice2fnsingleton) => 77.78/10.58 (( 77.78/10.58 (setOfPairsIsBReln1) => 77.78/10.58 (( 77.78/10.58 (breln1all1) => 77.78/10.58 (( 77.78/10.58 (subbreln1) => 77.78/10.58 (( 77.78/10.58 (eqbreln1) => 77.78/10.58 (( 77.78/10.58 (breln1invprop) => 77.78/10.58 (( 77.78/10.58 (breln1invI) => 77.78/10.58 (( 77.78/10.58 (breln1invE) => 77.78/10.58 (( 77.78/10.58 (breln1compprop) => 77.78/10.58 (( 77.78/10.58 (breln1compI) => 77.78/10.58 (( 77.78/10.58 (breln1compE) => 77.78/10.58 (( 77.78/10.58 (breln1compEex) => 77.78/10.58 (( 77.78/10.58 (breln1unionprop) => 77.78/10.58 (( 77.78/10.58 (breln1unionIL) => 77.78/10.58 (( 77.78/10.58 (breln1unionIR) => 77.78/10.58 (( 77.78/10.58 (breln1unionI) => 77.78/10.58 (( 77.78/10.58 (breln1unionE) => 77.78/10.58 (( 77.78/10.58 (breln1unionEcases) => 77.78/10.58 (( 77.78/10.58 (breln1unionCommutes) => 77.78/10.58 (( 77.78/10.58 (woz2Ex) => 77.78/10.58 (( 77.78/10.58 (woz2W) => 77.78/10.58 (( 77.78/10.58 (woz2A) => 77.78/10.58 (( 77.78/10.58 (woz2B) => 77.78/10.58 (( 77.78/10.58 (image1Ex) => 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(setunionTransitive) => 77.78/10.58 (( 77.78/10.58 (ordinalMinLem1) => 77.78/10.58 (( 77.78/10.58 (!!) @ ( 77.78/10.58 ^[Y0 : $i]: 77.78/10.58 (( 77.78/10.58 (ordinal @ 77.78/10.58 Y0) => 77.78/10.58 (( 77.78/10.58 (!!) @ ( 77.78/10.58 ^[Y1 : $i]: 77.78/10.58 (( 77.78/10.58 (!!) @ ( 77.78/10.58 ^[Y2 : $i]: 77.78/10.58 (( 77.78/10.58 (in @ 77.78/10.58 Y2 @ 77.78/10.58 Y0) => 77.78/10.58 (( 77.78/10.58 (in @ 77.78/10.58 Y1 @ 77.78/10.58 Y2) => 77.78/10.58 (in @ 77.78/10.58 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 77.78/10.58 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl305])). 77.78/10.58 thf(zip_derived_cl318, plain, 77.78/10.58 (~ (((setadjoinOr) => 77.78/10.58 (((setoftrueEq) => 77.78/10.58 (((powersetI) => 77.78/10.58 (((emptyinPowerset) => 77.78/10.58 (((emptyInPowerset) => 77.78/10.58 (((powersetE) => 77.78/10.58 (((setunionI) => 77.78/10.58 (((setunionE) => 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(setunion__Cong) => 77.78/10.58 (( 77.78/10.58 (exuEu) => 77.78/10.58 (( 77.78/10.58 (descr__Cong) => 77.78/10.58 (( 77.78/10.58 (dsetconstr__Cong) => 77.78/10.58 (( 77.78/10.58 (subsetI1) => 77.78/10.58 (( 77.78/10.58 (eqimpsubset2) => 77.78/10.58 (( 77.78/10.58 (eqimpsubset1) => 77.78/10.58 (( 77.78/10.58 (subsetI2) => 77.78/10.58 (( 77.78/10.58 (emptysetsubset) => 77.78/10.58 (( 77.78/10.58 (subsetE) => 77.78/10.58 (( 77.78/10.58 (subsetE2) => 77.78/10.58 (( 77.78/10.58 (notsubsetI) => 77.78/10.58 (( 77.78/10.58 (notequalI1) => 77.78/10.58 (( 77.78/10.58 (notequalI2) => 77.78/10.58 (( 77.78/10.58 (subsetRefl) => 77.78/10.58 (( 77.78/10.58 (subsetTrans) => 77.78/10.58 (( 77.78/10.58 (setadjoinSub) => 77.78/10.58 (( 77.78/10.58 (setadjoinSub2) => 77.78/10.58 (( 77.78/10.58 (subset2powerset) => 77.78/10.58 (( 77.78/10.58 (setextsub) => 77.78/10.58 (( 77.78/10.58 (subsetemptysetimpeq) => 77.78/10.58 (( 77.78/10.58 (powersetI1) => 77.78/10.58 (( 77.78/10.58 (powersetE1) => 77.78/10.58 (( 77.78/10.58 (inPowerset) => 77.78/10.58 (( 77.78/10.58 (powersetsubset) => 77.78/10.58 (( 77.78/10.58 (sepInPowerset) => 77.78/10.58 (( 77.78/10.58 (sepSubset) => 77.78/10.58 (( 77.78/10.58 (binunionIL) => 77.78/10.58 (( 77.78/10.58 (upairset2IR) => 77.78/10.58 (( 77.78/10.58 (binunionIR) => 77.78/10.58 (( 77.78/10.58 (binunionEcases) => 77.78/10.58 (( 77.78/10.58 (binunionE) => 77.78/10.58 (( 77.78/10.58 (binunionLsub) => 77.78/10.58 (( 77.78/10.58 (binunionRsub) => 77.78/10.58 (( 77.78/10.58 (binintersectI) => 77.78/10.58 (( 77.78/10.58 (binintersectSubset5) => 77.78/10.58 (( 77.78/10.58 (binintersectEL) => 77.78/10.58 (( 77.78/10.58 (binintersectLsub) => 77.78/10.58 (( 77.78/10.58 (binintersectSubset2) => 77.78/10.58 (( 77.78/10.58 (binintersectSubset3) => 77.78/10.58 (( 77.78/10.58 (binintersectER) => 77.78/10.58 (( 77.78/10.58 (disjointsetsI1) => 77.78/10.58 (( 77.78/10.58 (binintersectRsub) => 77.78/10.58 (( 77.78/10.58 (binintersectSubset4) => 77.78/10.58 (( 77.78/10.58 (binintersectSubset1) => 77.78/10.58 (( 77.78/10.58 (bs114d) => 77.78/10.58 (( 77.78/10.58 (setminusI) => 77.78/10.58 (( 77.78/10.58 (setminusEL) => 77.78/10.58 (( 77.78/10.58 (setminusER) => 77.78/10.58 (( 77.78/10.58 (setminusSubset2) => 77.78/10.58 (( 77.78/10.58 (setminusERneg) => 77.78/10.58 (( 77.78/10.58 (setminusELneg) => 77.78/10.58 (( 77.78/10.58 (setminusILneg) => 77.78/10.58 (( 77.78/10.58 (setminusIRneg) => 77.78/10.58 (( 77.78/10.58 (setminusLsub) => 77.78/10.58 (( 77.78/10.58 (setminusSubset1) => 77.78/10.58 (( 77.78/10.58 (symdiffE) => 77.78/10.58 (( 77.78/10.58 (symdiffI1) => 77.78/10.58 (( 77.78/10.58 (symdiffI2) => 77.78/10.58 (( 77.78/10.59 (symdiffIneg1) => 77.78/10.59 (( 77.78/10.59 (symdiffIneg2) => 77.78/10.59 (( 77.78/10.59 (secondinupair) => 77.78/10.59 (( 77.78/10.59 (setukpairIL) => 77.78/10.59 (( 77.78/10.59 (setukpairIR) => 77.78/10.59 (( 77.78/10.59 (kpairiskpair) => 77.78/10.59 (( 77.78/10.59 (kpairp) => 77.78/10.59 (( 77.78/10.59 (singletonsubset) => 77.78/10.59 (( 77.78/10.59 (singletoninpowerset) => 77.78/10.59 (( 77.78/10.59 (singletoninpowunion) => 77.78/10.59 (( 77.78/10.59 (upairset2E) => 77.78/10.59 (( 77.78/10.59 (upairsubunion) => 77.78/10.59 (( 77.78/10.59 (upairinpowunion) => 77.78/10.59 (( 77.78/10.59 (ubforcartprodlem1) => 77.78/10.59 (( 77.78/10.59 (ubforcartprodlem2) => 77.78/10.59 (( 77.78/10.59 (ubforcartprodlem3) => 77.78/10.59 (( 77.78/10.59 (cartprodpairin) => 77.78/10.59 (( 77.78/10.59 (cartprodmempair1) => 77.78/10.59 (( 77.78/10.59 (cartprodmempair) => 77.78/10.59 (( 77.78/10.59 (setunionE2) => 77.78/10.59 (( 77.78/10.59 (setunionsingleton1) => 77.78/10.59 (( 77.78/10.59 (setunionsingleton2) => 77.78/10.59 (( 77.78/10.59 (setunionsingleton) => 77.78/10.59 (( 77.78/10.59 (singletonprop) => 77.78/10.59 (( 77.78/10.59 (ex1E1) => 77.78/10.59 (( 77.78/10.59 (ex1I) => 77.78/10.59 (( 77.78/10.59 (ex1I2) => 77.78/10.59 (( 77.78/10.59 (singletonsuniq) => 77.78/10.59 (( 77.78/10.59 (setukpairinjL1) => 77.78/10.59 (( 77.78/10.59 (kfstsingleton) => 77.78/10.59 (( 77.78/10.59 (theprop) => 77.78/10.59 (( 77.78/10.59 (kfstpairEq) => 77.78/10.59 (( 77.78/10.59 (cartprodfstin) => 77.78/10.59 (( 77.78/10.59 (setukpairinjL2) => 77.78/10.59 (( 77.78/10.59 (setukpairinjL) => 77.78/10.59 (( 77.78/10.59 (setukpairinjR11) => 77.78/10.59 (( 77.78/10.59 (setukpairinjR12) => 77.78/10.59 (( 77.78/10.59 (setukpairinjR1) => 77.78/10.59 (( 77.78/10.59 (upairequniteq) => 77.78/10.59 (( 77.78/10.59 (setukpairinjR2) => 77.78/10.59 (( 77.78/10.59 (setukpairinjR) => 77.78/10.59 (( 77.78/10.59 (ksndsingleton) => 77.78/10.59 (( 77.78/10.59 (ksndpairEq) => 77.78/10.59 (( 77.78/10.59 (kpairsurjEq) => 77.78/10.59 (( 77.78/10.59 (cartprodsndin) => 77.78/10.59 (( 77.78/10.59 (cartprodpairmemEL) => 77.78/10.59 (( 77.78/10.59 (cartprodpairmemER) => 77.78/10.59 (( 77.78/10.59 (cartprodmempaircEq) => 77.78/10.59 (( 77.78/10.59 (cartprodfstpairEq) => 77.78/10.59 (( 77.78/10.59 (cartprodsndpairEq) => 77.78/10.59 (( 77.78/10.59 (cartprodpairsurjEq) => 77.78/10.59 (( 77.78/10.59 (dpsetconstrI) => 77.78/10.59 (( 77.78/10.59 (dpsetconstrSub) => 77.78/10.59 (( 77.78/10.59 (setOfPairsIsBReln) => 77.78/10.59 (( 77.78/10.59 (dpsetconstrERa) => 77.78/10.59 (( 77.78/10.59 (dpsetconstrEL1) => 77.78/10.59 (( 77.78/10.59 (dpsetconstrEL2) => 77.78/10.59 (( 77.78/10.59 (dpsetconstrER) => 77.78/10.59 (( 77.78/10.59 (funcImageSingleton) => 77.78/10.59 (( 77.78/10.59 (apProp) => 77.78/10.59 (( 77.78/10.59 (app) => 77.78/10.59 (( 77.78/10.59 (infuncsetfunc) => 77.78/10.59 (( 77.78/10.59 (ap2p) => 77.78/10.59 (( 77.78/10.59 (funcinfuncset) => 77.78/10.59 (( 77.78/10.59 (lamProp) => 77.78/10.59 (( 77.78/10.59 (lamp) => 77.78/10.59 (( 77.78/10.59 (lam2p) => 77.78/10.59 (( 77.78/10.59 (brelnall1) => 77.78/10.59 (( 77.78/10.59 (brelnall2) => 77.78/10.59 (( 77.78/10.59 (ex1E2) => 77.78/10.59 (( 77.78/10.59 (funcGraphProp1) => 77.78/10.59 (( 77.78/10.59 (funcGraphProp3) => 77.78/10.59 (( 77.78/10.59 (funcGraphProp2) => 77.78/10.59 (( 77.78/10.59 (funcextLem) => 77.78/10.59 (( 77.78/10.59 (funcGraphProp4) => 77.78/10.59 (( 77.78/10.59 (subbreln) => 77.78/10.59 (( 77.78/10.59 (eqbreln) => 77.78/10.59 (( 77.78/10.59 (funcext) => 77.78/10.59 (( 77.78/10.59 (funcext2) => 77.78/10.59 (( 77.78/10.59 (ap2apEq1) => 77.78/10.59 (( 77.78/10.59 (ap2apEq2) => 77.78/10.59 (( 77.78/10.59 (beta1) => 77.78/10.59 (( 77.78/10.59 (eta1) => 77.78/10.59 (( 77.78/10.59 (lam2lamEq) => 77.78/10.59 (( 77.78/10.59 (beta2) => 77.78/10.59 (( 77.78/10.59 (eta2) => 77.78/10.59 (( 77.78/10.59 (iffalseProp1) => 77.78/10.59 (( 77.78/10.59 (iffalseProp2) => 77.78/10.59 (( 77.78/10.59 (iftrueProp1) => 77.78/10.59 (( 77.78/10.59 (iftrueProp2) => 77.78/10.59 (( 77.78/10.59 (ifSingleton) => 77.78/10.59 (( 77.78/10.59 (ifp) => 77.78/10.59 (( 77.78/10.59 (theeq) => 77.78/10.59 (( 77.78/10.59 (iftrue) => 77.78/10.59 (( 77.78/10.59 (iffalse) => 77.78/10.59 (( 77.78/10.59 (iftrueorfalse) => 77.78/10.59 (( 77.78/10.59 (binintersectT_lem) => 77.78/10.59 (( 77.78/10.59 (binunionT_lem) => 77.78/10.59 (( 77.78/10.59 (powersetT_lem) => 77.78/10.59 (( 77.78/10.59 (setminusT_lem) => 77.78/10.59 (( 77.78/10.59 (complementT_lem) => 77.78/10.59 (( 77.78/10.59 (setextT) => 77.78/10.59 (( 77.78/10.59 (subsetTI) => 77.78/10.59 (( 77.78/10.59 (powersetTI1) => 77.78/10.59 (( 77.78/10.59 (powersetTE1) => 77.78/10.59 (( 77.78/10.59 (complementTI1) => 77.78/10.59 (( 77.78/10.59 (complementTE1) => 77.78/10.59 (( 77.78/10.59 (binintersectTELcontra) => 77.78/10.59 (( 77.78/10.59 (binintersectTERcontra) => 77.78/10.59 (( 77.78/10.59 (contrasubsetT) => 77.78/10.59 (( 77.78/10.59 (contrasubsetT1) => 77.78/10.59 (( 77.78/10.59 (contrasubsetT2) => 77.78/10.59 (( 77.78/10.59 (contrasubsetT3) => 77.78/10.59 (( 77.78/10.59 (doubleComplementI1) => 77.78/10.59 (( 77.78/10.59 (doubleComplementE1) => 77.78/10.59 (( 77.78/10.59 (doubleComplementSub1) => 77.78/10.59 (( 77.78/10.59 (doubleComplementSub2) => 77.78/10.59 (( 77.78/10.59 (doubleComplementEq) => 77.78/10.59 (( 77.78/10.59 (complementTnotintersectT) => 77.78/10.59 (( 77.78/10.59 (complementImpComplementIntersect) => 77.78/10.59 (( 77.78/10.59 (complementSubsetComplementIntersect) => 77.78/10.59 (( 77.78/10.59 (complementInPowersetComplementIntersect) => 77.78/10.59 (( 77.78/10.59 (contraSubsetComplement) => 77.78/10.59 (( 77.78/10.59 (complementTcontraSubset) => 77.78/10.59 (( 77.78/10.59 (binunionTILcontra) => 77.78/10.59 (( 77.78/10.59 (binunionTIRcontra) => 77.78/10.59 (( 77.78/10.59 (inIntersectImpInUnion) => 77.78/10.59 (( 77.78/10.59 (inIntersectImpInUnion2) => 77.78/10.59 (( 77.78/10.59 (inIntersectImpInIntersectUnions) => 77.78/10.59 (( 77.78/10.59 (intersectInPowersetIntersectUnions) => 77.78/10.59 (( 77.78/10.59 (inComplementUnionImpNotIn1) => 77.78/10.59 (( 77.78/10.59 (inComplementUnionImpInComplement1) => 77.78/10.59 (( 77.78/10.59 (binunionTE) => 77.78/10.59 (( 77.78/10.59 (binunionTEcontra) => 77.78/10.59 (( 77.78/10.59 (demorgan2a1) => 77.78/10.59 (( 77.78/10.59 (complementUnionInPowersetComplement) => 77.78/10.59 (( 77.78/10.59 (demorgan2a2) => 77.78/10.59 (( 77.78/10.59 (demorgan1a) => 77.78/10.59 (( 77.78/10.59 (demorgan1b) => 77.78/10.59 (( 77.78/10.59 (demorgan1) => 77.78/10.59 (( 77.78/10.59 (demorgan2a) => 77.78/10.59 (( 77.78/10.59 (demorgan2b2) => 77.78/10.59 (( 77.78/10.59 (demorgan2b) => 77.78/10.59 (( 77.78/10.59 (demorgan2) => 77.78/10.59 (( 77.78/10.59 (woz13rule0) => 77.78/10.59 (( 77.78/10.59 (woz13rule1) => 77.78/10.59 (( 77.78/10.59 (woz13rule2) => 77.78/10.59 (( 77.78/10.59 (woz13rule3) => 77.78/10.59 (( 77.78/10.59 (woz13rule4) => 77.78/10.59 (( 77.78/10.59 (woz1_1) => 77.78/10.59 (( 77.78/10.59 (woz1_2) => 77.78/10.59 (( 77.78/10.59 (woz1_3) => 77.78/10.59 (( 77.78/10.59 (woz1_4) => 77.78/10.59 (( 77.78/10.59 (woz1_5) => 77.78/10.59 (( 77.78/10.59 (breln1all2) => 77.78/10.59 (( 77.78/10.59 (breln1SetBreln1) => 77.78/10.59 (( 77.78/10.59 (choice2fnsingleton) => 77.78/10.59 (( 77.78/10.59 (setOfPairsIsBReln1) => 77.78/10.59 (( 77.78/10.59 (breln1all1) => 77.78/10.59 (( 77.78/10.59 (subbreln1) => 77.78/10.59 (( 77.78/10.59 (eqbreln1) => 77.78/10.59 (( 77.78/10.59 (breln1invprop) => 77.78/10.59 (( 77.78/10.59 (breln1invI) => 77.78/10.59 (( 77.78/10.59 (breln1invE) => 77.78/10.59 (( 77.78/10.59 (breln1compprop) => 77.78/10.59 (( 77.78/10.59 (breln1compI) => 77.78/10.59 (( 77.78/10.59 (breln1compE) => 77.78/10.59 (( 77.78/10.59 (breln1compEex) => 77.78/10.59 (( 77.78/10.59 (breln1unionprop) => 77.78/10.59 (( 77.78/10.59 (breln1unionIL) => 77.78/10.59 (( 77.78/10.59 (breln1unionIR) => 77.78/10.59 (( 77.78/10.59 (breln1unionI) => 77.78/10.59 (( 77.78/10.59 (breln1unionE) => 77.78/10.59 (( 77.78/10.59 (breln1unionEcases) => 77.78/10.59 (( 77.78/10.59 (breln1unionCommutes) => 77.78/10.59 (( 77.78/10.59 (woz2Ex) => 77.78/10.59 (( 77.78/10.59 (woz2W) => 77.78/10.59 (( 77.78/10.59 (woz2A) => 77.78/10.59 (( 77.78/10.59 (woz2B) => 77.78/10.59 (( 77.78/10.59 (image1Ex) => 77.78/10.59 (( 77.78/10.59 (image1Ex1) => 77.78/10.59 (( 77.78/10.59 (image1Equiv) => 77.78/10.59 (( 77.78/10.59 (image1E) => 77.78/10.59 (( 77.78/10.59 (image1I) => 77.78/10.59 (( 77.78/10.59 (injFuncInInjFuncSet) => 77.78/10.59 (( 77.78/10.59 (injFuncSetFuncIn) => 77.78/10.59 (( 77.78/10.59 (injFuncSetFuncInj) => 77.78/10.59 (( 77.78/10.59 (surjFuncSetFuncIn) => 77.78/10.59 (( 77.78/10.59 (surjFuncSetFuncSurj) => 77.78/10.59 (( 77.78/10.59 (leftInvIsSurj) => 77.78/10.59 (( 77.78/10.59 (surjCantorThm) => 77.78/10.59 (( 77.78/10.59 (foundation2) => 77.78/10.59 (( 77.78/10.59 (notinself) => 77.78/10.59 (( 77.78/10.59 (notinself2) => 77.78/10.59 (( 77.78/10.59 (omegaSp) => 77.78/10.59 (( 77.78/10.59 (omegaSclos) => 77.78/10.59 (( 77.78/10.59 (peano0notS) => 77.78/10.59 (( 77.78/10.59 (peanoSinj) => 77.78/10.59 (( 77.78/10.59 (transitivesetOp1) => 77.78/10.59 (( 77.78/10.59 (binintTransitive) => 77.78/10.59 (( 77.78/10.59 (transitivesetOp2) => 77.78/10.59 (( 77.78/10.59 (setunionTransitive) => 77.78/10.59 (( 77.78/10.59 (ordinalMinLem1) => 77.78/10.59 (( 77.78/10.59 (!!) @ ( 77.78/10.59 ^[Y0 : $i]: 77.78/10.59 (( 77.78/10.59 (ordinal @ 77.78/10.59 Y0) => 77.78/10.59 (( 77.78/10.59 (!!) @ ( 77.78/10.59 ^[Y1 : $i]: 77.78/10.59 (( 77.78/10.59 (!!) @ ( 77.78/10.59 ^[Y2 : $i]: 77.78/10.59 (( 77.78/10.59 (in @ 77.78/10.59 Y2 @ 77.78/10.59 Y0) => 77.78/10.59 (( 77.78/10.59 (in @ 77.78/10.59 Y1 @ 77.78/10.59 Y2) => 77.78/10.59 (in @ 77.78/10.59 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 77.78/10.59 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl312])). 77.78/10.59 thf(zip_derived_cl325, plain, 77.78/10.59 (~ (((setoftrueEq) => 77.78/10.59 (((powersetI) => 77.78/10.59 (((emptyinPowerset) => 77.78/10.59 (((emptyInPowerset) => 77.78/10.59 (((powersetE) => 77.78/10.59 (((setunionI) => 77.78/10.59 (((setunionE) => 77.78/10.59 (((subPowSU) => 77.78/10.59 (((exuE2) => 77.78/10.59 (((nonemptyImpWitness) => 77.78/10.59 (((uniqinunit) => 77.78/10.59 (((notinsingleton) => 77.78/10.59 (((eqinunit) => 77.78/10.59 (((singletonsswitch) => 77.78/10.59 (((upairsetE) => 77.78/10.59 (((upairsetIL) => 77.78/10.59 (((upairsetIR) => 77.78/10.59 (((emptyE1) => 77.78/10.59 (((vacuousDall) => 77.78/10.59 (((quantDeMorgan1) => 77.78/10.59 (((quantDeMorgan2) => 77.78/10.59 (((quantDeMorgan3) => 77.78/10.59 (((quantDeMorgan4) => 77.78/10.59 (((prop2setI) => 77.78/10.59 (((prop2set2propI) => 77.78/10.59 (((notdexE) => 77.78/10.59 (((notdallE) => 77.78/10.59 (((exuI1) => 77.78/10.59 (((exuI3) => 77.78/10.59 (((exuI2) => 77.78/10.59 (( 77.78/10.59 (inCongP) => 77.78/10.59 (( 77.78/10.59 (in__Cong) => 77.78/10.59 (( 77.78/10.59 (exuE3u) => 77.78/10.59 (( 77.78/10.59 (exu__Cong) => 77.78/10.59 (( 77.78/10.59 (setadjoin__Cong) => 77.78/10.59 (( 77.78/10.59 (powerset__Cong) => 77.78/10.59 (( 77.78/10.59 (setunion__Cong) => 77.78/10.59 (( 77.78/10.59 (exuEu) => 77.78/10.59 (( 77.78/10.59 (descr__Cong) => 77.78/10.59 (( 77.78/10.59 (dsetconstr__Cong) => 77.78/10.59 (( 77.78/10.59 (subsetI1) => 77.78/10.59 (( 77.78/10.59 (eqimpsubset2) => 77.78/10.59 (( 77.78/10.59 (eqimpsubset1) => 77.78/10.59 (( 77.78/10.59 (subsetI2) => 77.78/10.59 (( 77.78/10.59 (emptysetsubset) => 77.78/10.59 (( 77.78/10.59 (subsetE) => 77.78/10.59 (( 77.78/10.59 (subsetE2) => 77.78/10.59 (( 77.78/10.59 (notsubsetI) => 77.78/10.59 (( 77.78/10.59 (notequalI1) => 77.78/10.59 (( 77.78/10.59 (notequalI2) => 77.78/10.59 (( 77.78/10.59 (subsetRefl) => 77.78/10.59 (( 77.78/10.59 (subsetTrans) => 77.78/10.59 (( 77.78/10.59 (setadjoinSub) => 77.78/10.59 (( 77.78/10.59 (setadjoinSub2) => 77.78/10.59 (( 77.78/10.59 (subset2powerset) => 77.78/10.59 (( 77.78/10.59 (setextsub) => 77.78/10.59 (( 77.78/10.59 (subsetemptysetimpeq) => 77.78/10.59 (( 77.78/10.59 (powersetI1) => 77.78/10.59 (( 77.78/10.59 (powersetE1) => 77.78/10.59 (( 77.78/10.59 (inPowerset) => 77.78/10.59 (( 77.78/10.59 (powersetsubset) => 77.78/10.59 (( 77.78/10.59 (sepInPowerset) => 77.78/10.59 (( 77.78/10.59 (sepSubset) => 77.78/10.59 (( 77.78/10.59 (binunionIL) => 77.78/10.59 (( 77.78/10.59 (upairset2IR) => 77.78/10.59 (( 77.78/10.59 (binunionIR) => 77.78/10.59 (( 77.78/10.59 (binunionEcases) => 77.78/10.59 (( 77.78/10.59 (binunionE) => 77.78/10.59 (( 77.78/10.59 (binunionLsub) => 77.78/10.59 (( 77.78/10.59 (binunionRsub) => 77.78/10.59 (( 77.78/10.59 (binintersectI) => 77.78/10.59 (( 77.78/10.59 (binintersectSubset5) => 77.78/10.59 (( 77.78/10.59 (binintersectEL) => 77.78/10.59 (( 77.78/10.59 (binintersectLsub) => 77.78/10.59 (( 77.78/10.59 (binintersectSubset2) => 77.78/10.59 (( 77.78/10.59 (binintersectSubset3) => 77.78/10.59 (( 77.78/10.59 (binintersectER) => 77.78/10.59 (( 77.78/10.59 (disjointsetsI1) => 77.78/10.59 (( 77.78/10.59 (binintersectRsub) => 77.78/10.59 (( 77.78/10.59 (binintersectSubset4) => 77.78/10.59 (( 77.78/10.59 (binintersectSubset1) => 77.78/10.59 (( 77.78/10.59 (bs114d) => 77.78/10.59 (( 77.78/10.59 (setminusI) => 77.78/10.59 (( 77.78/10.59 (setminusEL) => 77.78/10.59 (( 77.78/10.59 (setminusER) => 77.78/10.59 (( 77.78/10.59 (setminusSubset2) => 77.78/10.59 (( 77.78/10.59 (setminusERneg) => 77.78/10.59 (( 77.78/10.59 (setminusELneg) => 77.78/10.59 (( 77.78/10.59 (setminusILneg) => 77.78/10.59 (( 77.78/10.59 (setminusIRneg) => 77.78/10.59 (( 77.78/10.59 (setminusLsub) => 77.78/10.59 (( 77.78/10.59 (setminusSubset1) => 77.78/10.59 (( 77.78/10.59 (symdiffE) => 77.78/10.59 (( 77.78/10.59 (symdiffI1) => 77.78/10.59 (( 77.78/10.59 (symdiffI2) => 77.78/10.59 (( 77.78/10.59 (symdiffIneg1) => 77.78/10.59 (( 77.78/10.59 (symdiffIneg2) => 77.78/10.59 (( 77.78/10.59 (secondinupair) => 77.78/10.59 (( 77.78/10.59 (setukpairIL) => 77.78/10.59 (( 77.78/10.59 (setukpairIR) => 77.78/10.59 (( 77.78/10.59 (kpairiskpair) => 77.78/10.59 (( 77.78/10.59 (kpairp) => 77.78/10.59 (( 77.78/10.59 (singletonsubset) => 77.78/10.59 (( 77.78/10.59 (singletoninpowerset) => 77.78/10.59 (( 77.78/10.59 (singletoninpowunion) => 77.78/10.59 (( 77.78/10.59 (upairset2E) => 77.78/10.59 (( 77.78/10.59 (upairsubunion) => 77.78/10.59 (( 77.78/10.59 (upairinpowunion) => 77.78/10.59 (( 77.78/10.59 (ubforcartprodlem1) => 77.78/10.59 (( 77.78/10.59 (ubforcartprodlem2) => 77.78/10.59 (( 77.78/10.59 (ubforcartprodlem3) => 77.78/10.59 (( 77.78/10.59 (cartprodpairin) => 77.78/10.59 (( 77.78/10.59 (cartprodmempair1) => 77.78/10.59 (( 77.78/10.59 (cartprodmempair) => 77.78/10.59 (( 77.78/10.59 (setunionE2) => 77.78/10.59 (( 77.78/10.59 (setunionsingleton1) => 77.78/10.59 (( 77.78/10.59 (setunionsingleton2) => 77.78/10.59 (( 77.78/10.59 (setunionsingleton) => 77.78/10.59 (( 77.78/10.59 (singletonprop) => 77.78/10.59 (( 77.78/10.59 (ex1E1) => 77.78/10.59 (( 77.78/10.59 (ex1I) => 77.78/10.59 (( 77.78/10.59 (ex1I2) => 77.78/10.59 (( 77.78/10.59 (singletonsuniq) => 77.78/10.59 (( 77.78/10.59 (setukpairinjL1) => 77.78/10.59 (( 77.78/10.59 (kfstsingleton) => 77.78/10.59 (( 77.78/10.59 (theprop) => 77.78/10.59 (( 77.78/10.59 (kfstpairEq) => 77.78/10.59 (( 77.78/10.59 (cartprodfstin) => 77.78/10.59 (( 77.78/10.59 (setukpairinjL2) => 77.78/10.59 (( 77.78/10.59 (setukpairinjL) => 77.78/10.59 (( 77.78/10.59 (setukpairinjR11) => 77.78/10.59 (( 77.78/10.59 (setukpairinjR12) => 77.78/10.59 (( 77.78/10.59 (setukpairinjR1) => 77.78/10.59 (( 77.78/10.59 (upairequniteq) => 77.78/10.59 (( 77.78/10.59 (setukpairinjR2) => 77.78/10.59 (( 77.78/10.59 (setukpairinjR) => 77.78/10.59 (( 77.78/10.59 (ksndsingleton) => 77.78/10.59 (( 77.78/10.59 (ksndpairEq) => 77.78/10.59 (( 77.78/10.59 (kpairsurjEq) => 77.78/10.59 (( 77.78/10.59 (cartprodsndin) => 77.78/10.59 (( 77.78/10.59 (cartprodpairmemEL) => 77.78/10.59 (( 77.78/10.59 (cartprodpairmemER) => 77.78/10.59 (( 77.78/10.59 (cartprodmempaircEq) => 77.78/10.59 (( 77.78/10.59 (cartprodfstpairEq) => 77.78/10.59 (( 77.78/10.59 (cartprodsndpairEq) => 77.78/10.59 (( 77.78/10.59 (cartprodpairsurjEq) => 77.78/10.59 (( 77.78/10.59 (dpsetconstrI) => 77.78/10.59 (( 77.78/10.59 (dpsetconstrSub) => 77.78/10.59 (( 77.78/10.59 (setOfPairsIsBReln) => 77.78/10.59 (( 77.78/10.59 (dpsetconstrERa) => 77.78/10.59 (( 77.78/10.59 (dpsetconstrEL1) => 77.78/10.59 (( 77.78/10.59 (dpsetconstrEL2) => 77.78/10.59 (( 77.78/10.59 (dpsetconstrER) => 77.78/10.59 (( 77.78/10.59 (funcImageSingleton) => 77.78/10.59 (( 77.78/10.59 (apProp) => 77.78/10.59 (( 77.78/10.59 (app) => 77.78/10.59 (( 77.78/10.59 (infuncsetfunc) => 77.78/10.59 (( 77.78/10.59 (ap2p) => 77.78/10.59 (( 77.78/10.59 (funcinfuncset) => 77.78/10.59 (( 77.78/10.59 (lamProp) => 77.78/10.59 (( 77.78/10.59 (lamp) => 77.78/10.59 (( 77.78/10.59 (lam2p) => 77.78/10.59 (( 77.78/10.59 (brelnall1) => 77.78/10.59 (( 77.78/10.59 (brelnall2) => 77.78/10.59 (( 77.78/10.59 (ex1E2) => 77.78/10.59 (( 77.78/10.59 (funcGraphProp1) => 77.78/10.59 (( 77.78/10.59 (funcGraphProp3) => 77.78/10.59 (( 77.78/10.59 (funcGraphProp2) => 77.78/10.59 (( 77.78/10.59 (funcextLem) => 77.78/10.59 (( 77.78/10.59 (funcGraphProp4) => 77.78/10.59 (( 77.78/10.59 (subbreln) => 77.78/10.59 (( 77.78/10.59 (eqbreln) => 77.78/10.59 (( 77.78/10.59 (funcext) => 77.78/10.59 (( 77.78/10.59 (funcext2) => 77.78/10.59 (( 77.78/10.59 (ap2apEq1) => 77.78/10.59 (( 77.78/10.59 (ap2apEq2) => 77.78/10.59 (( 77.78/10.59 (beta1) => 77.78/10.59 (( 77.78/10.59 (eta1) => 77.78/10.59 (( 77.78/10.59 (lam2lamEq) => 77.78/10.59 (( 77.78/10.59 (beta2) => 77.78/10.59 (( 77.78/10.59 (eta2) => 77.78/10.59 (( 77.78/10.59 (iffalseProp1) => 77.78/10.59 (( 77.78/10.59 (iffalseProp2) => 77.78/10.59 (( 77.78/10.59 (iftrueProp1) => 77.78/10.59 (( 77.78/10.59 (iftrueProp2) => 77.78/10.59 (( 77.78/10.59 (ifSingleton) => 77.78/10.59 (( 77.78/10.59 (ifp) => 77.78/10.59 (( 77.78/10.59 (theeq) => 77.78/10.59 (( 77.78/10.59 (iftrue) => 77.78/10.59 (( 77.78/10.59 (iffalse) => 77.78/10.59 (( 77.78/10.59 (iftrueorfalse) => 77.78/10.59 (( 77.78/10.59 (binintersectT_lem) => 77.78/10.59 (( 77.78/10.59 (binunionT_lem) => 77.78/10.59 (( 77.78/10.59 (powersetT_lem) => 77.78/10.59 (( 77.78/10.59 (setminusT_lem) => 77.78/10.59 (( 77.78/10.59 (complementT_lem) => 77.78/10.59 (( 77.78/10.59 (setextT) => 77.78/10.59 (( 77.78/10.59 (subsetTI) => 77.78/10.59 (( 77.78/10.59 (powersetTI1) => 77.78/10.59 (( 77.78/10.59 (powersetTE1) => 77.78/10.59 (( 77.78/10.59 (complementTI1) => 77.78/10.59 (( 77.78/10.59 (complementTE1) => 77.78/10.59 (( 77.78/10.59 (binintersectTELcontra) => 77.78/10.59 (( 77.78/10.59 (binintersectTERcontra) => 77.78/10.59 (( 77.78/10.59 (contrasubsetT) => 77.78/10.59 (( 77.78/10.59 (contrasubsetT1) => 77.78/10.59 (( 77.78/10.59 (contrasubsetT2) => 77.78/10.59 (( 77.78/10.59 (contrasubsetT3) => 77.78/10.59 (( 77.78/10.59 (doubleComplementI1) => 77.78/10.59 (( 77.78/10.59 (doubleComplementE1) => 77.78/10.59 (( 77.78/10.59 (doubleComplementSub1) => 77.78/10.59 (( 77.78/10.59 (doubleComplementSub2) => 77.78/10.59 (( 77.78/10.59 (doubleComplementEq) => 77.78/10.59 (( 77.78/10.59 (complementTnotintersectT) => 77.78/10.59 (( 77.78/10.59 (complementImpComplementIntersect) => 77.78/10.59 (( 77.78/10.59 (complementSubsetComplementIntersect) => 77.78/10.59 (( 77.78/10.59 (complementInPowersetComplementIntersect) => 77.78/10.59 (( 77.78/10.59 (contraSubsetComplement) => 77.78/10.59 (( 77.78/10.59 (complementTcontraSubset) => 77.78/10.59 (( 77.78/10.59 (binunionTILcontra) => 77.78/10.59 (( 77.78/10.59 (binunionTIRcontra) => 77.78/10.59 (( 77.78/10.59 (inIntersectImpInUnion) => 77.78/10.59 (( 77.78/10.59 (inIntersectImpInUnion2) => 77.78/10.59 (( 77.78/10.59 (inIntersectImpInIntersectUnions) => 77.78/10.59 (( 77.78/10.59 (intersectInPowersetIntersectUnions) => 77.78/10.59 (( 77.78/10.59 (inComplementUnionImpNotIn1) => 77.78/10.59 (( 77.78/10.59 (inComplementUnionImpInComplement1) => 77.78/10.59 (( 77.78/10.59 (binunionTE) => 77.78/10.59 (( 77.78/10.59 (binunionTEcontra) => 77.78/10.59 (( 77.78/10.59 (demorgan2a1) => 77.78/10.59 (( 77.78/10.59 (complementUnionInPowersetComplement) => 77.78/10.59 (( 77.78/10.59 (demorgan2a2) => 77.78/10.59 (( 77.78/10.59 (demorgan1a) => 77.78/10.59 (( 77.78/10.59 (demorgan1b) => 77.78/10.59 (( 77.78/10.59 (demorgan1) => 77.78/10.59 (( 77.78/10.59 (demorgan2a) => 77.78/10.59 (( 77.78/10.59 (demorgan2b2) => 77.78/10.59 (( 77.78/10.59 (demorgan2b) => 77.78/10.59 (( 77.78/10.59 (demorgan2) => 77.78/10.59 (( 77.78/10.59 (woz13rule0) => 77.78/10.59 (( 77.78/10.59 (woz13rule1) => 77.78/10.59 (( 77.78/10.59 (woz13rule2) => 77.78/10.59 (( 77.78/10.59 (woz13rule3) => 77.78/10.59 (( 77.78/10.59 (woz13rule4) => 77.78/10.59 (( 77.78/10.59 (woz1_1) => 77.78/10.59 (( 77.78/10.59 (woz1_2) => 77.78/10.59 (( 77.78/10.59 (woz1_3) => 77.78/10.59 (( 77.78/10.59 (woz1_4) => 77.78/10.59 (( 77.78/10.59 (woz1_5) => 77.78/10.59 (( 77.78/10.59 (breln1all2) => 77.78/10.59 (( 77.78/10.59 (breln1SetBreln1) => 77.78/10.59 (( 77.78/10.59 (choice2fnsingleton) => 77.78/10.59 (( 77.78/10.59 (setOfPairsIsBReln1) => 77.78/10.59 (( 77.78/10.59 (breln1all1) => 77.78/10.59 (( 77.78/10.59 (subbreln1) => 77.78/10.59 (( 77.78/10.59 (eqbreln1) => 77.78/10.59 (( 77.78/10.59 (breln1invprop) => 77.78/10.59 (( 77.78/10.59 (breln1invI) => 77.78/10.59 (( 77.78/10.59 (breln1invE) => 77.78/10.59 (( 77.78/10.59 (breln1compprop) => 77.78/10.59 (( 77.78/10.59 (breln1compI) => 77.78/10.59 (( 77.78/10.59 (breln1compE) => 77.78/10.59 (( 77.78/10.59 (breln1compEex) => 77.78/10.59 (( 77.78/10.59 (breln1unionprop) => 77.78/10.59 (( 77.78/10.59 (breln1unionIL) => 77.78/10.59 (( 77.78/10.59 (breln1unionIR) => 77.78/10.59 (( 77.78/10.59 (breln1unionI) => 77.78/10.59 (( 77.78/10.59 (breln1unionE) => 77.78/10.59 (( 77.78/10.59 (breln1unionEcases) => 77.78/10.59 (( 77.78/10.59 (breln1unionCommutes) => 77.78/10.59 (( 77.78/10.59 (woz2Ex) => 77.78/10.59 (( 77.78/10.59 (woz2W) => 77.78/10.59 (( 77.78/10.59 (woz2A) => 77.78/10.59 (( 77.78/10.59 (woz2B) => 77.78/10.59 (( 77.78/10.59 (image1Ex) => 77.78/10.59 (( 77.78/10.59 (image1Ex1) => 77.78/10.59 (( 77.78/10.59 (image1Equiv) => 77.78/10.59 (( 77.78/10.59 (image1E) => 77.78/10.59 (( 77.78/10.59 (image1I) => 77.78/10.59 (( 77.78/10.59 (injFuncInInjFuncSet) => 77.78/10.59 (( 77.78/10.59 (injFuncSetFuncIn) => 77.78/10.59 (( 77.78/10.59 (injFuncSetFuncInj) => 77.78/10.59 (( 77.78/10.59 (surjFuncSetFuncIn) => 77.78/10.59 (( 77.78/10.59 (surjFuncSetFuncSurj) => 77.78/10.59 (( 77.78/10.59 (leftInvIsSurj) => 77.78/10.59 (( 77.78/10.59 (surjCantorThm) => 77.78/10.59 (( 77.78/10.59 (foundation2) => 77.78/10.59 (( 77.78/10.59 (notinself) => 77.78/10.59 (( 77.78/10.59 (notinself2) => 77.78/10.59 (( 77.78/10.59 (omegaSp) => 77.78/10.59 (( 77.78/10.59 (omegaSclos) => 77.78/10.59 (( 77.78/10.59 (peano0notS) => 77.78/10.59 (( 77.78/10.59 (peanoSinj) => 77.78/10.59 (( 77.78/10.59 (transitivesetOp1) => 77.78/10.59 (( 77.78/10.59 (binintTransitive) => 77.78/10.59 (( 77.78/10.59 (transitivesetOp2) => 77.78/10.59 (( 77.78/10.59 (setunionTransitive) => 77.78/10.59 (( 77.78/10.59 (ordinalMinLem1) => 77.78/10.59 (( 77.78/10.59 (!!) @ ( 77.78/10.59 ^[Y0 : $i]: 77.78/10.59 (( 77.78/10.59 (ordinal @ 77.78/10.59 Y0) => 77.78/10.59 (( 77.78/10.59 (!!) @ ( 77.78/10.59 ^[Y1 : $i]: 77.78/10.59 (( 77.78/10.59 (!!) @ ( 77.78/10.59 ^[Y2 : $i]: 77.78/10.59 (( 77.78/10.59 (in @ 77.78/10.59 Y2 @ 77.78/10.59 Y0) => 77.78/10.59 (( 77.78/10.59 (in @ 77.78/10.59 Y1 @ 77.78/10.59 Y2) => 77.78/10.59 (in @ 77.78/10.59 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 77.78/10.59 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl318])). 77.78/10.59 thf(zip_derived_cl331, plain, 77.78/10.59 (~ (((powersetI) => 77.78/10.59 (((emptyinPowerset) => 77.78/10.59 (((emptyInPowerset) => 77.78/10.59 (((powersetE) => 77.78/10.59 (((setunionI) => 77.78/10.59 (((setunionE) => 77.78/10.59 (((subPowSU) => 77.78/10.59 (((exuE2) => 77.78/10.59 (((nonemptyImpWitness) => 77.78/10.59 (((uniqinunit) => 77.78/10.59 (((notinsingleton) => 77.78/10.59 (((eqinunit) => 77.78/10.59 (((singletonsswitch) => 77.78/10.59 (((upairsetE) => 77.78/10.59 (((upairsetIL) => 77.78/10.59 (((upairsetIR) => 77.78/10.59 (((emptyE1) => 77.78/10.59 (((vacuousDall) => 77.78/10.59 (((quantDeMorgan1) => 77.78/10.59 (((quantDeMorgan2) => 77.78/10.59 (((quantDeMorgan3) => 77.78/10.59 (((quantDeMorgan4) => 77.78/10.59 (((prop2setI) => 77.78/10.59 (((prop2set2propI) => 77.78/10.59 (((notdexE) => 77.78/10.59 (((notdallE) => 77.78/10.59 (((exuI1) => 77.78/10.59 (((exuI3) => 77.78/10.59 (((exuI2) => 77.78/10.59 (((inCongP) => 77.78/10.59 (( 77.78/10.59 (in__Cong) => 77.78/10.59 (( 77.78/10.59 (exuE3u) => 77.78/10.59 (( 77.78/10.59 (exu__Cong) => 77.78/10.59 (( 77.78/10.59 (setadjoin__Cong) => 77.78/10.59 (( 77.78/10.59 (powerset__Cong) => 77.78/10.59 (( 77.78/10.59 (setunion__Cong) => 77.78/10.59 (( 77.78/10.59 (exuEu) => 77.78/10.59 (( 77.78/10.59 (descr__Cong) => 77.78/10.59 (( 77.78/10.59 (dsetconstr__Cong) => 77.78/10.59 (( 77.78/10.59 (subsetI1) => 77.78/10.59 (( 77.78/10.59 (eqimpsubset2) => 77.78/10.59 (( 77.78/10.59 (eqimpsubset1) => 77.78/10.59 (( 77.78/10.59 (subsetI2) => 77.78/10.59 (( 77.78/10.59 (emptysetsubset) => 77.78/10.59 (( 77.78/10.59 (subsetE) => 77.78/10.59 (( 77.78/10.59 (subsetE2) => 77.78/10.59 (( 77.78/10.59 (notsubsetI) => 77.78/10.59 (( 77.78/10.59 (notequalI1) => 77.78/10.59 (( 77.78/10.59 (notequalI2) => 77.78/10.59 (( 77.78/10.59 (subsetRefl) => 77.78/10.59 (( 77.78/10.59 (subsetTrans) => 77.78/10.59 (( 77.78/10.59 (setadjoinSub) => 77.78/10.59 (( 77.78/10.59 (setadjoinSub2) => 77.78/10.59 (( 77.78/10.59 (subset2powerset) => 77.78/10.59 (( 77.78/10.59 (setextsub) => 77.78/10.59 (( 77.78/10.59 (subsetemptysetimpeq) => 77.78/10.59 (( 77.78/10.59 (powersetI1) => 77.78/10.59 (( 77.78/10.59 (powersetE1) => 77.78/10.59 (( 77.78/10.59 (inPowerset) => 77.78/10.59 (( 77.78/10.59 (powersetsubset) => 77.78/10.59 (( 77.78/10.59 (sepInPowerset) => 77.78/10.59 (( 77.78/10.59 (sepSubset) => 77.78/10.59 (( 77.78/10.59 (binunionIL) => 77.78/10.59 (( 77.78/10.59 (upairset2IR) => 77.78/10.59 (( 77.78/10.59 (binunionIR) => 77.78/10.59 (( 77.78/10.59 (binunionEcases) => 77.78/10.59 (( 77.78/10.59 (binunionE) => 77.78/10.59 (( 77.78/10.59 (binunionLsub) => 77.78/10.59 (( 77.78/10.59 (binunionRsub) => 77.78/10.59 (( 77.78/10.59 (binintersectI) => 77.78/10.59 (( 77.78/10.59 (binintersectSubset5) => 77.78/10.59 (( 77.78/10.59 (binintersectEL) => 77.78/10.59 (( 77.78/10.59 (binintersectLsub) => 77.78/10.59 (( 77.78/10.59 (binintersectSubset2) => 77.78/10.59 (( 77.78/10.59 (binintersectSubset3) => 77.78/10.59 (( 77.78/10.59 (binintersectER) => 77.78/10.59 (( 77.78/10.59 (disjointsetsI1) => 77.78/10.59 (( 77.78/10.59 (binintersectRsub) => 77.78/10.59 (( 77.78/10.59 (binintersectSubset4) => 77.78/10.59 (( 77.78/10.59 (binintersectSubset1) => 77.78/10.59 (( 77.78/10.59 (bs114d) => 77.78/10.59 (( 77.78/10.59 (setminusI) => 77.78/10.59 (( 77.78/10.59 (setminusEL) => 77.78/10.59 (( 77.78/10.59 (setminusER) => 77.78/10.59 (( 77.78/10.59 (setminusSubset2) => 77.78/10.59 (( 77.78/10.59 (setminusERneg) => 77.78/10.59 (( 77.78/10.59 (setminusELneg) => 77.78/10.59 (( 77.78/10.59 (setminusILneg) => 77.78/10.59 (( 77.78/10.59 (setminusIRneg) => 77.78/10.59 (( 77.78/10.59 (setminusLsub) => 77.78/10.59 (( 77.78/10.59 (setminusSubset1) => 77.78/10.59 (( 77.78/10.59 (symdiffE) => 77.78/10.59 (( 77.78/10.59 (symdiffI1) => 77.78/10.59 (( 77.78/10.59 (symdiffI2) => 77.78/10.59 (( 77.78/10.59 (symdiffIneg1) => 77.78/10.59 (( 77.78/10.59 (symdiffIneg2) => 77.78/10.59 (( 77.78/10.59 (secondinupair) => 77.78/10.59 (( 77.78/10.59 (setukpairIL) => 77.78/10.59 (( 77.78/10.59 (setukpairIR) => 77.78/10.59 (( 77.78/10.59 (kpairiskpair) => 77.78/10.59 (( 77.78/10.59 (kpairp) => 77.78/10.59 (( 77.78/10.59 (singletonsubset) => 77.78/10.59 (( 77.78/10.59 (singletoninpowerset) => 77.78/10.59 (( 77.78/10.59 (singletoninpowunion) => 77.78/10.59 (( 77.78/10.59 (upairset2E) => 77.78/10.59 (( 77.78/10.59 (upairsubunion) => 77.78/10.59 (( 77.78/10.59 (upairinpowunion) => 77.78/10.59 (( 77.78/10.59 (ubforcartprodlem1) => 77.78/10.59 (( 77.78/10.59 (ubforcartprodlem2) => 77.78/10.59 (( 77.78/10.59 (ubforcartprodlem3) => 77.78/10.59 (( 77.78/10.59 (cartprodpairin) => 77.78/10.59 (( 77.78/10.59 (cartprodmempair1) => 77.78/10.59 (( 77.78/10.59 (cartprodmempair) => 77.78/10.59 (( 77.78/10.59 (setunionE2) => 77.78/10.59 (( 77.78/10.59 (setunionsingleton1) => 77.78/10.59 (( 77.78/10.59 (setunionsingleton2) => 77.78/10.59 (( 77.78/10.59 (setunionsingleton) => 77.78/10.59 (( 77.78/10.59 (singletonprop) => 77.78/10.59 (( 77.78/10.59 (ex1E1) => 77.78/10.59 (( 77.78/10.59 (ex1I) => 77.78/10.59 (( 77.78/10.59 (ex1I2) => 77.78/10.59 (( 77.78/10.59 (singletonsuniq) => 77.78/10.59 (( 77.78/10.59 (setukpairinjL1) => 77.78/10.59 (( 77.78/10.59 (kfstsingleton) => 77.78/10.59 (( 77.78/10.59 (theprop) => 77.78/10.59 (( 77.78/10.59 (kfstpairEq) => 77.78/10.59 (( 77.78/10.59 (cartprodfstin) => 77.78/10.59 (( 77.78/10.59 (setukpairinjL2) => 77.78/10.59 (( 77.78/10.59 (setukpairinjL) => 77.78/10.59 (( 77.78/10.59 (setukpairinjR11) => 77.78/10.59 (( 77.78/10.59 (setukpairinjR12) => 77.78/10.59 (( 77.78/10.59 (setukpairinjR1) => 77.78/10.59 (( 77.78/10.59 (upairequniteq) => 77.78/10.59 (( 77.78/10.59 (setukpairinjR2) => 77.78/10.59 (( 77.78/10.59 (setukpairinjR) => 77.78/10.59 (( 77.78/10.59 (ksndsingleton) => 77.78/10.59 (( 77.78/10.59 (ksndpairEq) => 77.78/10.59 (( 77.78/10.59 (kpairsurjEq) => 77.78/10.59 (( 77.78/10.59 (cartprodsndin) => 77.78/10.59 (( 77.78/10.59 (cartprodpairmemEL) => 77.78/10.59 (( 77.78/10.59 (cartprodpairmemER) => 77.78/10.59 (( 77.78/10.59 (cartprodmempaircEq) => 77.78/10.59 (( 77.78/10.59 (cartprodfstpairEq) => 77.78/10.59 (( 77.78/10.59 (cartprodsndpairEq) => 77.78/10.59 (( 77.78/10.59 (cartprodpairsurjEq) => 77.78/10.59 (( 77.78/10.59 (dpsetconstrI) => 77.78/10.59 (( 77.78/10.59 (dpsetconstrSub) => 77.78/10.59 (( 77.78/10.59 (setOfPairsIsBReln) => 77.78/10.59 (( 77.78/10.59 (dpsetconstrERa) => 77.78/10.59 (( 77.78/10.59 (dpsetconstrEL1) => 77.78/10.59 (( 77.78/10.59 (dpsetconstrEL2) => 77.78/10.59 (( 77.78/10.59 (dpsetconstrER) => 77.78/10.59 (( 77.78/10.59 (funcImageSingleton) => 77.78/10.59 (( 77.78/10.59 (apProp) => 77.78/10.59 (( 77.78/10.59 (app) => 77.78/10.59 (( 77.78/10.59 (infuncsetfunc) => 77.78/10.59 (( 77.78/10.59 (ap2p) => 77.78/10.59 (( 77.78/10.59 (funcinfuncset) => 77.78/10.59 (( 77.78/10.59 (lamProp) => 77.78/10.59 (( 77.78/10.59 (lamp) => 77.78/10.59 (( 77.78/10.59 (lam2p) => 77.78/10.59 (( 77.78/10.59 (brelnall1) => 77.78/10.59 (( 77.78/10.59 (brelnall2) => 77.78/10.59 (( 77.78/10.59 (ex1E2) => 77.78/10.59 (( 77.78/10.59 (funcGraphProp1) => 77.78/10.59 (( 77.78/10.59 (funcGraphProp3) => 77.78/10.59 (( 77.78/10.59 (funcGraphProp2) => 77.78/10.59 (( 77.78/10.59 (funcextLem) => 77.78/10.59 (( 77.78/10.59 (funcGraphProp4) => 77.78/10.59 (( 77.78/10.59 (subbreln) => 77.78/10.59 (( 77.78/10.59 (eqbreln) => 77.78/10.59 (( 77.78/10.59 (funcext) => 77.78/10.59 (( 77.78/10.59 (funcext2) => 77.78/10.59 (( 77.78/10.59 (ap2apEq1) => 77.78/10.59 (( 77.78/10.59 (ap2apEq2) => 77.78/10.59 (( 77.78/10.59 (beta1) => 77.78/10.59 (( 77.78/10.59 (eta1) => 77.78/10.59 (( 77.78/10.59 (lam2lamEq) => 77.78/10.59 (( 77.78/10.59 (beta2) => 77.78/10.59 (( 77.78/10.59 (eta2) => 77.78/10.59 (( 77.78/10.59 (iffalseProp1) => 77.78/10.59 (( 77.78/10.59 (iffalseProp2) => 77.78/10.59 (( 77.78/10.59 (iftrueProp1) => 77.78/10.59 (( 77.78/10.59 (iftrueProp2) => 77.78/10.59 (( 77.78/10.59 (ifSingleton) => 77.78/10.59 (( 77.78/10.59 (ifp) => 77.78/10.59 (( 77.78/10.59 (theeq) => 77.78/10.59 (( 77.78/10.59 (iftrue) => 77.78/10.59 (( 77.78/10.59 (iffalse) => 77.78/10.59 (( 77.78/10.59 (iftrueorfalse) => 77.78/10.59 (( 77.78/10.59 (binintersectT_lem) => 77.78/10.59 (( 77.78/10.59 (binunionT_lem) => 77.78/10.59 (( 77.78/10.59 (powersetT_lem) => 77.78/10.59 (( 77.78/10.59 (setminusT_lem) => 77.78/10.59 (( 77.78/10.59 (complementT_lem) => 77.78/10.59 (( 77.78/10.59 (setextT) => 77.78/10.59 (( 77.78/10.59 (subsetTI) => 77.78/10.59 (( 77.78/10.59 (powersetTI1) => 77.78/10.59 (( 77.78/10.59 (powersetTE1) => 77.78/10.59 (( 77.78/10.59 (complementTI1) => 77.78/10.59 (( 77.78/10.59 (complementTE1) => 77.78/10.59 (( 77.78/10.59 (binintersectTELcontra) => 77.78/10.59 (( 77.78/10.59 (binintersectTERcontra) => 77.78/10.59 (( 77.78/10.59 (contrasubsetT) => 77.78/10.59 (( 77.78/10.59 (contrasubsetT1) => 77.78/10.59 (( 77.78/10.59 (contrasubsetT2) => 77.78/10.59 (( 77.78/10.59 (contrasubsetT3) => 77.78/10.59 (( 77.78/10.59 (doubleComplementI1) => 77.78/10.59 (( 77.78/10.59 (doubleComplementE1) => 77.78/10.59 (( 77.78/10.59 (doubleComplementSub1) => 77.78/10.59 (( 77.78/10.59 (doubleComplementSub2) => 77.78/10.59 (( 77.78/10.59 (doubleComplementEq) => 77.78/10.59 (( 77.78/10.59 (complementTnotintersectT) => 77.78/10.59 (( 77.78/10.59 (complementImpComplementIntersect) => 77.78/10.59 (( 77.78/10.59 (complementSubsetComplementIntersect) => 77.78/10.59 (( 77.78/10.59 (complementInPowersetComplementIntersect) => 77.78/10.59 (( 77.78/10.59 (contraSubsetComplement) => 77.78/10.59 (( 77.78/10.59 (complementTcontraSubset) => 77.78/10.59 (( 77.78/10.59 (binunionTILcontra) => 77.78/10.59 (( 77.78/10.59 (binunionTIRcontra) => 77.78/10.59 (( 77.78/10.59 (inIntersectImpInUnion) => 77.78/10.59 (( 77.78/10.59 (inIntersectImpInUnion2) => 77.78/10.59 (( 77.78/10.59 (inIntersectImpInIntersectUnions) => 77.78/10.59 (( 77.78/10.59 (intersectInPowersetIntersectUnions) => 77.78/10.59 (( 77.78/10.59 (inComplementUnionImpNotIn1) => 77.78/10.59 (( 77.78/10.59 (inComplementUnionImpInComplement1) => 77.78/10.59 (( 77.78/10.59 (binunionTE) => 77.78/10.59 (( 77.78/10.59 (binunionTEcontra) => 77.78/10.59 (( 77.78/10.59 (demorgan2a1) => 77.78/10.59 (( 77.78/10.59 (complementUnionInPowersetComplement) => 77.78/10.59 (( 77.78/10.59 (demorgan2a2) => 77.78/10.59 (( 77.78/10.59 (demorgan1a) => 77.78/10.59 (( 77.78/10.59 (demorgan1b) => 77.78/10.59 (( 77.78/10.59 (demorgan1) => 77.78/10.59 (( 77.78/10.59 (demorgan2a) => 77.78/10.59 (( 77.78/10.59 (demorgan2b2) => 77.78/10.59 (( 77.78/10.59 (demorgan2b) => 77.78/10.59 (( 77.78/10.59 (demorgan2) => 77.78/10.59 (( 77.78/10.59 (woz13rule0) => 77.78/10.59 (( 77.78/10.59 (woz13rule1) => 77.78/10.59 (( 77.78/10.59 (woz13rule2) => 77.78/10.59 (( 77.78/10.59 (woz13rule3) => 77.78/10.59 (( 77.78/10.59 (woz13rule4) => 77.78/10.59 (( 77.78/10.59 (woz1_1) => 77.78/10.59 (( 77.78/10.59 (woz1_2) => 77.78/10.59 (( 77.78/10.59 (woz1_3) => 77.78/10.59 (( 77.78/10.59 (woz1_4) => 77.78/10.59 (( 77.78/10.59 (woz1_5) => 77.78/10.59 (( 77.78/10.59 (breln1all2) => 77.78/10.59 (( 77.78/10.59 (breln1SetBreln1) => 77.78/10.59 (( 77.78/10.59 (choice2fnsingleton) => 77.78/10.59 (( 77.78/10.59 (setOfPairsIsBReln1) => 77.78/10.59 (( 77.78/10.59 (breln1all1) => 77.78/10.59 (( 77.78/10.59 (subbreln1) => 77.78/10.59 (( 77.78/10.59 (eqbreln1) => 77.78/10.59 (( 77.78/10.59 (breln1invprop) => 77.78/10.59 (( 77.78/10.59 (breln1invI) => 77.78/10.59 (( 77.78/10.59 (breln1invE) => 77.78/10.59 (( 77.78/10.59 (breln1compprop) => 77.78/10.59 (( 77.78/10.59 (breln1compI) => 77.78/10.59 (( 77.78/10.59 (breln1compE) => 77.78/10.59 (( 77.78/10.59 (breln1compEex) => 77.78/10.59 (( 77.78/10.59 (breln1unionprop) => 77.78/10.59 (( 77.78/10.59 (breln1unionIL) => 77.78/10.59 (( 77.78/10.59 (breln1unionIR) => 77.78/10.59 (( 77.78/10.59 (breln1unionI) => 77.78/10.59 (( 77.78/10.59 (breln1unionE) => 77.78/10.59 (( 77.78/10.59 (breln1unionEcases) => 77.78/10.59 (( 77.78/10.59 (breln1unionCommutes) => 77.78/10.59 (( 77.78/10.59 (woz2Ex) => 77.78/10.59 (( 77.78/10.59 (woz2W) => 77.78/10.59 (( 77.78/10.59 (woz2A) => 77.78/10.59 (( 77.78/10.59 (woz2B) => 77.78/10.59 (( 77.78/10.59 (image1Ex) => 77.78/10.59 (( 77.78/10.59 (image1Ex1) => 77.78/10.59 (( 77.78/10.59 (image1Equiv) => 77.78/10.59 (( 77.78/10.59 (image1E) => 77.78/10.59 (( 77.78/10.59 (image1I) => 77.78/10.59 (( 77.78/10.59 (injFuncInInjFuncSet) => 77.78/10.59 (( 77.78/10.59 (injFuncSetFuncIn) => 77.78/10.59 (( 77.78/10.59 (injFuncSetFuncInj) => 77.78/10.59 (( 77.78/10.59 (surjFuncSetFuncIn) => 77.78/10.59 (( 77.78/10.59 (surjFuncSetFuncSurj) => 77.78/10.59 (( 77.78/10.59 (leftInvIsSurj) => 77.78/10.59 (( 77.78/10.59 (surjCantorThm) => 77.78/10.59 (( 77.78/10.59 (foundation2) => 77.78/10.59 (( 77.78/10.59 (notinself) => 77.78/10.59 (( 77.78/10.59 (notinself2) => 77.78/10.59 (( 77.78/10.59 (omegaSp) => 77.78/10.59 (( 77.78/10.59 (omegaSclos) => 77.78/10.59 (( 77.78/10.59 (peano0notS) => 77.78/10.59 (( 77.78/10.59 (peanoSinj) => 77.78/10.59 (( 77.78/10.59 (transitivesetOp1) => 77.78/10.59 (( 77.78/10.59 (binintTransitive) => 77.78/10.59 (( 77.78/10.59 (transitivesetOp2) => 77.78/10.59 (( 77.78/10.59 (setunionTransitive) => 77.78/10.59 (( 77.78/10.59 (ordinalMinLem1) => 77.78/10.59 (( 77.78/10.59 (!!) @ ( 77.78/10.59 ^[Y0 : $i]: 77.78/10.59 (( 77.78/10.59 (ordinal @ 77.78/10.59 Y0) => 77.78/10.59 (( 77.78/10.59 (!!) @ ( 77.78/10.59 ^[Y1 : $i]: 77.78/10.59 (( 77.78/10.59 (!!) @ ( 77.78/10.59 ^[Y2 : $i]: 77.78/10.59 (( 77.78/10.59 (in @ 77.78/10.59 Y2 @ 77.78/10.59 Y0) => 77.78/10.59 (( 77.78/10.59 (in @ 77.78/10.59 Y1 @ 77.78/10.59 Y2) => 77.78/10.59 (in @ 77.78/10.59 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 77.78/10.59 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl325])). 77.78/10.59 thf(zip_derived_cl337, plain, 77.78/10.59 (~ (((emptyinPowerset) => 77.78/10.59 (((emptyInPowerset) => 77.78/10.59 (((powersetE) => 77.78/10.59 (((setunionI) => 77.78/10.59 (((setunionE) => 77.78/10.59 (((subPowSU) => 77.78/10.59 (((exuE2) => 77.78/10.59 (((nonemptyImpWitness) => 77.78/10.59 (((uniqinunit) => 77.78/10.59 (((notinsingleton) => 77.78/10.59 (((eqinunit) => 77.78/10.59 (((singletonsswitch) => 77.78/10.59 (((upairsetE) => 77.78/10.59 (((upairsetIL) => 77.78/10.59 (((upairsetIR) => 77.78/10.59 (((emptyE1) => 77.78/10.59 (((vacuousDall) => 77.78/10.59 (((quantDeMorgan1) => 77.78/10.59 (((quantDeMorgan2) => 77.78/10.59 (((quantDeMorgan3) => 77.78/10.59 (((quantDeMorgan4) => 77.78/10.59 (((prop2setI) => 77.78/10.59 (((prop2set2propI) => 77.78/10.59 (((notdexE) => 77.78/10.59 (((notdallE) => 77.78/10.59 (((exuI1) => 77.78/10.59 (((exuI3) => 77.78/10.59 (((exuI2) => 77.78/10.59 (((inCongP) => 77.78/10.59 (((in__Cong) => 77.78/10.59 (( 77.78/10.59 (exuE3u) => 77.78/10.59 (( 77.78/10.59 (exu__Cong) => 77.78/10.59 (( 77.78/10.59 (setadjoin__Cong) => 77.78/10.59 (( 77.78/10.59 (powerset__Cong) => 77.78/10.59 (( 77.78/10.59 (setunion__Cong) => 77.78/10.59 (( 77.78/10.59 (exuEu) => 77.78/10.59 (( 77.78/10.59 (descr__Cong) => 77.78/10.59 (( 77.78/10.59 (dsetconstr__Cong) => 77.78/10.59 (( 77.78/10.59 (subsetI1) => 77.78/10.59 (( 77.78/10.59 (eqimpsubset2) => 77.78/10.59 (( 77.78/10.59 (eqimpsubset1) => 77.78/10.59 (( 77.78/10.59 (subsetI2) => 77.78/10.59 (( 77.78/10.59 (emptysetsubset) => 77.78/10.59 (( 77.78/10.59 (subsetE) => 77.78/10.59 (( 77.78/10.59 (subsetE2) => 77.78/10.59 (( 77.78/10.59 (notsubsetI) => 77.78/10.59 (( 77.78/10.59 (notequalI1) => 77.78/10.59 (( 77.78/10.59 (notequalI2) => 77.78/10.59 (( 77.78/10.59 (subsetRefl) => 77.78/10.59 (( 77.78/10.59 (subsetTrans) => 77.78/10.59 (( 77.78/10.59 (setadjoinSub) => 77.78/10.59 (( 77.78/10.59 (setadjoinSub2) => 77.78/10.59 (( 77.78/10.59 (subset2powerset) => 77.78/10.59 (( 77.78/10.59 (setextsub) => 77.78/10.59 (( 77.78/10.59 (subsetemptysetimpeq) => 77.78/10.59 (( 77.78/10.59 (powersetI1) => 77.78/10.59 (( 77.78/10.59 (powersetE1) => 77.78/10.59 (( 77.78/10.59 (inPowerset) => 77.78/10.59 (( 77.78/10.59 (powersetsubset) => 77.78/10.59 (( 77.78/10.59 (sepInPowerset) => 77.78/10.59 (( 77.78/10.59 (sepSubset) => 77.78/10.59 (( 77.78/10.59 (binunionIL) => 77.78/10.59 (( 77.78/10.59 (upairset2IR) => 77.78/10.59 (( 77.78/10.59 (binunionIR) => 77.78/10.59 (( 77.78/10.59 (binunionEcases) => 77.78/10.59 (( 77.78/10.59 (binunionE) => 77.78/10.59 (( 77.78/10.59 (binunionLsub) => 77.78/10.59 (( 77.78/10.59 (binunionRsub) => 77.78/10.59 (( 77.78/10.59 (binintersectI) => 77.78/10.59 (( 77.78/10.59 (binintersectSubset5) => 77.78/10.59 (( 77.78/10.59 (binintersectEL) => 77.78/10.59 (( 77.78/10.59 (binintersectLsub) => 77.78/10.59 (( 77.78/10.59 (binintersectSubset2) => 77.78/10.59 (( 77.78/10.59 (binintersectSubset3) => 77.78/10.59 (( 77.78/10.59 (binintersectER) => 77.78/10.59 (( 77.78/10.59 (disjointsetsI1) => 77.78/10.59 (( 77.78/10.59 (binintersectRsub) => 77.78/10.59 (( 77.78/10.59 (binintersectSubset4) => 77.78/10.59 (( 77.78/10.59 (binintersectSubset1) => 77.78/10.59 (( 77.78/10.59 (bs114d) => 77.78/10.59 (( 77.78/10.59 (setminusI) => 77.78/10.59 (( 77.78/10.59 (setminusEL) => 77.78/10.59 (( 77.78/10.59 (setminusER) => 77.78/10.59 (( 77.78/10.59 (setminusSubset2) => 77.78/10.59 (( 77.78/10.59 (setminusERneg) => 77.78/10.59 (( 77.78/10.59 (setminusELneg) => 77.78/10.59 (( 77.78/10.59 (setminusILneg) => 77.78/10.59 (( 77.78/10.59 (setminusIRneg) => 77.78/10.59 (( 77.78/10.59 (setminusLsub) => 77.78/10.59 (( 77.78/10.59 (setminusSubset1) => 77.78/10.59 (( 77.78/10.59 (symdiffE) => 77.78/10.59 (( 77.78/10.59 (symdiffI1) => 77.78/10.59 (( 77.78/10.59 (symdiffI2) => 77.78/10.59 (( 77.78/10.59 (symdiffIneg1) => 77.78/10.59 (( 77.78/10.59 (symdiffIneg2) => 77.78/10.59 (( 77.78/10.59 (secondinupair) => 77.78/10.59 (( 77.78/10.59 (setukpairIL) => 77.78/10.59 (( 77.78/10.59 (setukpairIR) => 77.78/10.59 (( 77.78/10.59 (kpairiskpair) => 77.78/10.59 (( 77.78/10.59 (kpairp) => 77.78/10.59 (( 77.78/10.59 (singletonsubset) => 77.78/10.59 (( 77.78/10.59 (singletoninpowerset) => 77.78/10.59 (( 77.78/10.59 (singletoninpowunion) => 77.78/10.59 (( 77.78/10.59 (upairset2E) => 77.78/10.59 (( 77.78/10.59 (upairsubunion) => 77.78/10.59 (( 77.78/10.59 (upairinpowunion) => 77.78/10.59 (( 77.78/10.59 (ubforcartprodlem1) => 77.78/10.59 (( 77.78/10.59 (ubforcartprodlem2) => 77.78/10.59 (( 77.78/10.59 (ubforcartprodlem3) => 77.78/10.59 (( 77.78/10.59 (cartprodpairin) => 77.78/10.59 (( 77.78/10.59 (cartprodmempair1) => 77.78/10.59 (( 77.78/10.59 (cartprodmempair) => 77.78/10.59 (( 77.78/10.59 (setunionE2) => 77.78/10.59 (( 77.78/10.59 (setunionsingleton1) => 77.78/10.59 (( 77.78/10.59 (setunionsingleton2) => 77.78/10.59 (( 77.78/10.59 (setunionsingleton) => 77.78/10.59 (( 77.78/10.59 (singletonprop) => 77.78/10.59 (( 77.78/10.59 (ex1E1) => 77.78/10.59 (( 77.78/10.59 (ex1I) => 77.78/10.59 (( 77.78/10.59 (ex1I2) => 77.78/10.59 (( 77.78/10.59 (singletonsuniq) => 77.78/10.59 (( 77.78/10.59 (setukpairinjL1) => 77.78/10.59 (( 77.78/10.59 (kfstsingleton) => 77.78/10.59 (( 77.78/10.59 (theprop) => 77.78/10.59 (( 77.78/10.59 (kfstpairEq) => 77.78/10.59 (( 77.78/10.59 (cartprodfstin) => 77.78/10.59 (( 77.78/10.59 (setukpairinjL2) => 77.78/10.59 (( 77.78/10.59 (setukpairinjL) => 77.78/10.59 (( 77.78/10.59 (setukpairinjR11) => 77.78/10.59 (( 77.78/10.59 (setukpairinjR12) => 77.78/10.59 (( 77.78/10.59 (setukpairinjR1) => 77.78/10.59 (( 77.78/10.59 (upairequniteq) => 77.78/10.59 (( 77.78/10.59 (setukpairinjR2) => 77.78/10.59 (( 77.78/10.59 (setukpairinjR) => 77.78/10.59 (( 77.78/10.59 (ksndsingleton) => 77.78/10.59 (( 77.78/10.59 (ksndpairEq) => 77.78/10.59 (( 77.78/10.59 (kpairsurjEq) => 77.78/10.59 (( 77.78/10.59 (cartprodsndin) => 77.78/10.59 (( 77.78/10.59 (cartprodpairmemEL) => 77.78/10.59 (( 77.78/10.59 (cartprodpairmemER) => 77.78/10.59 (( 77.78/10.59 (cartprodmempaircEq) => 77.78/10.59 (( 77.78/10.59 (cartprodfstpairEq) => 77.78/10.59 (( 77.78/10.59 (cartprodsndpairEq) => 77.78/10.59 (( 77.78/10.59 (cartprodpairsurjEq) => 77.78/10.59 (( 77.78/10.59 (dpsetconstrI) => 77.78/10.59 (( 77.78/10.59 (dpsetconstrSub) => 77.78/10.59 (( 77.78/10.59 (setOfPairsIsBReln) => 77.78/10.59 (( 77.78/10.59 (dpsetconstrERa) => 77.78/10.59 (( 77.78/10.59 (dpsetconstrEL1) => 77.78/10.59 (( 77.78/10.59 (dpsetconstrEL2) => 77.78/10.59 (( 77.78/10.59 (dpsetconstrER) => 77.78/10.59 (( 77.78/10.59 (funcImageSingleton) => 77.78/10.59 (( 77.78/10.59 (apProp) => 77.78/10.59 (( 77.78/10.59 (app) => 77.78/10.59 (( 77.78/10.59 (infuncsetfunc) => 77.78/10.59 (( 77.78/10.59 (ap2p) => 77.78/10.59 (( 77.78/10.59 (funcinfuncset) => 77.78/10.59 (( 77.78/10.59 (lamProp) => 77.78/10.59 (( 77.78/10.59 (lamp) => 77.78/10.59 (( 77.78/10.59 (lam2p) => 77.78/10.59 (( 77.78/10.59 (brelnall1) => 77.78/10.59 (( 77.78/10.59 (brelnall2) => 77.78/10.59 (( 77.78/10.59 (ex1E2) => 77.78/10.59 (( 77.78/10.59 (funcGraphProp1) => 77.78/10.59 (( 77.78/10.59 (funcGraphProp3) => 77.78/10.59 (( 77.78/10.59 (funcGraphProp2) => 77.78/10.59 (( 77.78/10.59 (funcextLem) => 77.78/10.59 (( 77.78/10.59 (funcGraphProp4) => 77.78/10.59 (( 77.78/10.59 (subbreln) => 77.78/10.59 (( 77.78/10.59 (eqbreln) => 77.78/10.59 (( 77.78/10.59 (funcext) => 77.78/10.59 (( 77.78/10.59 (funcext2) => 77.78/10.59 (( 77.78/10.59 (ap2apEq1) => 77.78/10.59 (( 77.78/10.59 (ap2apEq2) => 77.78/10.59 (( 77.78/10.59 (beta1) => 77.78/10.59 (( 77.78/10.59 (eta1) => 77.78/10.59 (( 77.78/10.59 (lam2lamEq) => 77.78/10.59 (( 77.78/10.59 (beta2) => 77.78/10.59 (( 77.78/10.59 (eta2) => 77.78/10.59 (( 77.78/10.59 (iffalseProp1) => 77.78/10.59 (( 77.78/10.59 (iffalseProp2) => 77.78/10.59 (( 77.78/10.59 (iftrueProp1) => 77.78/10.59 (( 77.78/10.59 (iftrueProp2) => 77.78/10.59 (( 77.78/10.59 (ifSingleton) => 77.78/10.59 (( 77.78/10.59 (ifp) => 77.78/10.59 (( 77.78/10.59 (theeq) => 77.78/10.59 (( 77.78/10.59 (iftrue) => 77.78/10.59 (( 77.78/10.59 (iffalse) => 77.78/10.59 (( 77.78/10.59 (iftrueorfalse) => 77.78/10.59 (( 77.78/10.59 (binintersectT_lem) => 77.78/10.59 (( 77.78/10.59 (binunionT_lem) => 77.78/10.59 (( 77.78/10.59 (powersetT_lem) => 77.78/10.59 (( 77.78/10.59 (setminusT_lem) => 77.78/10.59 (( 77.78/10.59 (complementT_lem) => 77.78/10.59 (( 77.78/10.59 (setextT) => 77.78/10.59 (( 77.78/10.59 (subsetTI) => 77.78/10.59 (( 77.78/10.59 (powersetTI1) => 77.78/10.59 (( 77.78/10.59 (powersetTE1) => 77.78/10.59 (( 77.78/10.59 (complementTI1) => 77.78/10.59 (( 77.78/10.59 (complementTE1) => 77.78/10.59 (( 77.78/10.59 (binintersectTELcontra) => 77.78/10.59 (( 77.78/10.59 (binintersectTERcontra) => 77.78/10.59 (( 77.78/10.59 (contrasubsetT) => 77.78/10.59 (( 77.78/10.59 (contrasubsetT1) => 77.78/10.59 (( 77.78/10.59 (contrasubsetT2) => 77.78/10.59 (( 77.78/10.59 (contrasubsetT3) => 77.78/10.59 (( 77.78/10.59 (doubleComplementI1) => 77.78/10.59 (( 77.78/10.59 (doubleComplementE1) => 77.78/10.59 (( 77.78/10.59 (doubleComplementSub1) => 77.78/10.59 (( 77.78/10.59 (doubleComplementSub2) => 77.78/10.59 (( 77.78/10.59 (doubleComplementEq) => 77.78/10.59 (( 77.78/10.59 (complementTnotintersectT) => 77.78/10.59 (( 77.78/10.59 (complementImpComplementIntersect) => 77.78/10.59 (( 77.78/10.59 (complementSubsetComplementIntersect) => 77.78/10.59 (( 77.78/10.59 (complementInPowersetComplementIntersect) => 77.78/10.59 (( 77.78/10.59 (contraSubsetComplement) => 77.78/10.59 (( 77.78/10.59 (complementTcontraSubset) => 77.78/10.59 (( 77.78/10.59 (binunionTILcontra) => 77.78/10.59 (( 77.78/10.59 (binunionTIRcontra) => 77.78/10.59 (( 77.78/10.59 (inIntersectImpInUnion) => 77.78/10.59 (( 77.78/10.59 (inIntersectImpInUnion2) => 77.78/10.59 (( 77.78/10.59 (inIntersectImpInIntersectUnions) => 77.78/10.59 (( 77.78/10.59 (intersectInPowersetIntersectUnions) => 77.78/10.59 (( 77.78/10.59 (inComplementUnionImpNotIn1) => 77.78/10.59 (( 77.78/10.59 (inComplementUnionImpInComplement1) => 77.78/10.59 (( 77.78/10.59 (binunionTE) => 77.78/10.59 (( 77.78/10.59 (binunionTEcontra) => 77.78/10.59 (( 77.78/10.59 (demorgan2a1) => 77.78/10.59 (( 77.78/10.59 (complementUnionInPowersetComplement) => 77.78/10.59 (( 77.78/10.59 (demorgan2a2) => 77.78/10.59 (( 77.78/10.59 (demorgan1a) => 77.78/10.59 (( 77.78/10.59 (demorgan1b) => 77.78/10.59 (( 77.78/10.59 (demorgan1) => 77.78/10.59 (( 77.78/10.59 (demorgan2a) => 77.78/10.59 (( 77.78/10.59 (demorgan2b2) => 77.78/10.59 (( 77.78/10.59 (demorgan2b) => 77.78/10.59 (( 77.78/10.59 (demorgan2) => 77.78/10.59 (( 77.78/10.59 (woz13rule0) => 77.78/10.59 (( 77.78/10.59 (woz13rule1) => 77.78/10.59 (( 77.78/10.59 (woz13rule2) => 77.78/10.59 (( 77.78/10.59 (woz13rule3) => 77.78/10.59 (( 77.78/10.59 (woz13rule4) => 77.78/10.59 (( 77.78/10.59 (woz1_1) => 77.78/10.59 (( 77.78/10.59 (woz1_2) => 77.78/10.59 (( 77.78/10.59 (woz1_3) => 77.78/10.59 (( 77.78/10.59 (woz1_4) => 77.78/10.59 (( 77.78/10.59 (woz1_5) => 77.78/10.59 (( 77.78/10.59 (breln1all2) => 77.78/10.59 (( 77.78/10.59 (breln1SetBreln1) => 77.78/10.59 (( 77.78/10.59 (choice2fnsingleton) => 77.78/10.59 (( 77.78/10.59 (setOfPairsIsBReln1) => 77.78/10.59 (( 77.78/10.59 (breln1all1) => 77.78/10.59 (( 77.78/10.59 (subbreln1) => 77.78/10.59 (( 77.78/10.59 (eqbreln1) => 77.78/10.59 (( 77.78/10.59 (breln1invprop) => 77.78/10.59 (( 77.78/10.59 (breln1invI) => 77.78/10.59 (( 77.78/10.59 (breln1invE) => 77.78/10.59 (( 77.78/10.59 (breln1compprop) => 77.78/10.59 (( 77.78/10.59 (breln1compI) => 77.78/10.59 (( 77.78/10.59 (breln1compE) => 77.78/10.59 (( 77.78/10.59 (breln1compEex) => 77.78/10.59 (( 77.78/10.59 (breln1unionprop) => 77.78/10.59 (( 77.78/10.59 (breln1unionIL) => 77.78/10.59 (( 77.78/10.59 (breln1unionIR) => 77.78/10.59 (( 77.78/10.59 (breln1unionI) => 77.78/10.59 (( 77.78/10.59 (breln1unionE) => 77.78/10.59 (( 77.78/10.59 (breln1unionEcases) => 77.78/10.59 (( 77.78/10.59 (breln1unionCommutes) => 77.78/10.59 (( 77.78/10.59 (woz2Ex) => 77.78/10.59 (( 77.78/10.59 (woz2W) => 77.78/10.59 (( 77.78/10.59 (woz2A) => 77.78/10.59 (( 77.78/10.59 (woz2B) => 77.78/10.59 (( 77.78/10.59 (image1Ex) => 77.78/10.59 (( 77.78/10.59 (image1Ex1) => 77.78/10.59 (( 77.78/10.59 (image1Equiv) => 77.78/10.59 (( 77.78/10.59 (image1E) => 77.78/10.59 (( 77.78/10.59 (image1I) => 77.78/10.59 (( 77.78/10.59 (injFuncInInjFuncSet) => 77.78/10.59 (( 77.78/10.59 (injFuncSetFuncIn) => 77.78/10.59 (( 77.78/10.59 (injFuncSetFuncInj) => 77.78/10.59 (( 77.78/10.59 (surjFuncSetFuncIn) => 77.78/10.59 (( 77.78/10.59 (surjFuncSetFuncSurj) => 77.78/10.59 (( 77.78/10.59 (leftInvIsSurj) => 77.78/10.59 (( 77.78/10.59 (surjCantorThm) => 77.78/10.59 (( 77.78/10.59 (foundation2) => 77.78/10.59 (( 77.78/10.59 (notinself) => 77.78/10.59 (( 77.78/10.59 (notinself2) => 77.78/10.59 (( 77.78/10.59 (omegaSp) => 77.78/10.59 (( 77.78/10.59 (omegaSclos) => 77.78/10.59 (( 77.78/10.59 (peano0notS) => 77.78/10.59 (( 77.78/10.59 (peanoSinj) => 77.78/10.59 (( 77.78/10.59 (transitivesetOp1) => 77.78/10.59 (( 77.78/10.59 (binintTransitive) => 77.78/10.59 (( 77.78/10.59 (transitivesetOp2) => 77.78/10.59 (( 77.78/10.59 (setunionTransitive) => 77.78/10.59 (( 77.78/10.59 (ordinalMinLem1) => 77.78/10.59 (( 77.78/10.59 (!!) @ ( 77.78/10.59 ^[Y0 : $i]: 77.78/10.59 (( 77.78/10.59 (ordinal @ 77.78/10.59 Y0) => 77.78/10.59 (( 77.78/10.59 (!!) @ ( 77.78/10.59 ^[Y1 : $i]: 77.78/10.59 (( 77.78/10.59 (!!) @ ( 77.78/10.59 ^[Y2 : $i]: 77.78/10.59 (( 77.78/10.59 (in @ 77.78/10.59 Y2 @ 77.78/10.59 Y0) => 77.78/10.59 (( 77.78/10.59 (in @ 77.78/10.59 Y1 @ 77.78/10.59 Y2) => 77.78/10.59 (in @ 77.78/10.59 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 77.78/10.59 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl331])). 77.78/10.59 thf(zip_derived_cl343, plain, 77.78/10.59 (~ (((emptyInPowerset) => 77.78/10.59 (((powersetE) => 77.78/10.59 (((setunionI) => 77.78/10.59 (((setunionE) => 77.78/10.59 (((subPowSU) => 77.78/10.59 (((exuE2) => 77.78/10.59 (((nonemptyImpWitness) => 77.78/10.59 (((uniqinunit) => 77.78/10.59 (((notinsingleton) => 77.78/10.59 (((eqinunit) => 77.78/10.59 (((singletonsswitch) => 77.78/10.59 (((upairsetE) => 77.78/10.59 (((upairsetIL) => 77.78/10.59 (((upairsetIR) => 77.78/10.59 (((emptyE1) => 77.78/10.59 (((vacuousDall) => 77.78/10.59 (((quantDeMorgan1) => 77.78/10.59 (((quantDeMorgan2) => 77.78/10.59 (((quantDeMorgan3) => 77.78/10.59 (((quantDeMorgan4) => 77.78/10.59 (((prop2setI) => 77.78/10.59 (((prop2set2propI) => 77.78/10.59 (((notdexE) => 77.78/10.59 (((notdallE) => 77.78/10.59 (((exuI1) => 77.78/10.59 (((exuI3) => 77.78/10.59 (((exuI2) => 77.78/10.59 (((inCongP) => 77.78/10.59 (((in__Cong) => 77.78/10.59 (((exuE3u) => 77.78/10.59 (( 77.78/10.59 (exu__Cong) => 77.78/10.59 (( 77.78/10.59 (setadjoin__Cong) => 77.78/10.59 (( 77.78/10.59 (powerset__Cong) => 77.78/10.59 (( 77.78/10.59 (setunion__Cong) => 77.78/10.59 (( 77.78/10.59 (exuEu) => 77.78/10.59 (( 77.78/10.59 (descr__Cong) => 77.78/10.59 (( 77.78/10.59 (dsetconstr__Cong) => 77.78/10.59 (( 77.78/10.59 (subsetI1) => 77.78/10.59 (( 77.78/10.59 (eqimpsubset2) => 77.78/10.59 (( 77.78/10.59 (eqimpsubset1) => 77.78/10.59 (( 77.78/10.59 (subsetI2) => 77.78/10.59 (( 77.78/10.59 (emptysetsubset) => 77.78/10.59 (( 77.78/10.59 (subsetE) => 77.78/10.59 (( 77.78/10.59 (subsetE2) => 77.78/10.59 (( 77.78/10.59 (notsubsetI) => 77.78/10.59 (( 77.78/10.59 (notequalI1) => 77.78/10.59 (( 77.78/10.59 (notequalI2) => 77.78/10.59 (( 77.78/10.59 (subsetRefl) => 77.78/10.59 (( 77.78/10.59 (subsetTrans) => 77.78/10.59 (( 77.78/10.59 (setadjoinSub) => 77.78/10.59 (( 77.78/10.59 (setadjoinSub2) => 77.78/10.59 (( 77.78/10.59 (subset2powerset) => 77.78/10.59 (( 77.78/10.59 (setextsub) => 77.78/10.59 (( 77.78/10.59 (subsetemptysetimpeq) => 77.78/10.59 (( 77.78/10.59 (powersetI1) => 77.78/10.59 (( 77.78/10.59 (powersetE1) => 77.78/10.59 (( 77.78/10.59 (inPowerset) => 77.78/10.59 (( 77.78/10.59 (powersetsubset) => 77.78/10.59 (( 77.78/10.59 (sepInPowerset) => 77.78/10.59 (( 77.78/10.59 (sepSubset) => 77.78/10.59 (( 77.78/10.59 (binunionIL) => 77.78/10.59 (( 77.78/10.59 (upairset2IR) => 77.78/10.59 (( 77.78/10.59 (binunionIR) => 77.78/10.59 (( 77.78/10.59 (binunionEcases) => 77.78/10.59 (( 77.78/10.59 (binunionE) => 77.78/10.59 (( 77.78/10.59 (binunionLsub) => 77.78/10.59 (( 77.78/10.59 (binunionRsub) => 77.78/10.59 (( 77.78/10.59 (binintersectI) => 77.78/10.59 (( 77.78/10.59 (binintersectSubset5) => 77.78/10.59 (( 77.78/10.59 (binintersectEL) => 77.78/10.59 (( 77.78/10.59 (binintersectLsub) => 77.78/10.59 (( 77.78/10.59 (binintersectSubset2) => 77.78/10.59 (( 77.78/10.59 (binintersectSubset3) => 77.78/10.59 (( 77.78/10.59 (binintersectER) => 77.78/10.59 (( 77.78/10.59 (disjointsetsI1) => 77.78/10.59 (( 77.78/10.59 (binintersectRsub) => 77.78/10.59 (( 77.78/10.59 (binintersectSubset4) => 77.78/10.59 (( 77.78/10.59 (binintersectSubset1) => 77.78/10.59 (( 77.78/10.59 (bs114d) => 77.78/10.59 (( 77.78/10.59 (setminusI) => 77.78/10.59 (( 77.78/10.59 (setminusEL) => 77.78/10.59 (( 77.78/10.59 (setminusER) => 77.78/10.59 (( 77.78/10.59 (setminusSubset2) => 77.78/10.59 (( 77.78/10.59 (setminusERneg) => 77.78/10.59 (( 77.78/10.59 (setminusELneg) => 77.78/10.59 (( 77.78/10.59 (setminusILneg) => 77.78/10.59 (( 77.78/10.59 (setminusIRneg) => 77.78/10.59 (( 77.78/10.59 (setminusLsub) => 77.78/10.59 (( 77.78/10.59 (setminusSubset1) => 77.78/10.59 (( 77.78/10.59 (symdiffE) => 77.78/10.59 (( 77.78/10.59 (symdiffI1) => 77.78/10.59 (( 77.78/10.59 (symdiffI2) => 77.78/10.59 (( 77.78/10.59 (symdiffIneg1) => 77.78/10.59 (( 77.78/10.59 (symdiffIneg2) => 77.78/10.59 (( 77.78/10.59 (secondinupair) => 77.78/10.59 (( 77.78/10.59 (setukpairIL) => 77.78/10.59 (( 77.78/10.59 (setukpairIR) => 77.78/10.59 (( 77.78/10.59 (kpairiskpair) => 77.78/10.59 (( 77.78/10.59 (kpairp) => 77.78/10.59 (( 77.78/10.59 (singletonsubset) => 77.78/10.59 (( 77.78/10.59 (singletoninpowerset) => 77.78/10.59 (( 77.78/10.59 (singletoninpowunion) => 77.78/10.59 (( 77.78/10.59 (upairset2E) => 77.78/10.59 (( 77.78/10.59 (upairsubunion) => 77.78/10.59 (( 77.78/10.59 (upairinpowunion) => 77.78/10.59 (( 77.78/10.59 (ubforcartprodlem1) => 77.78/10.59 (( 77.78/10.59 (ubforcartprodlem2) => 77.78/10.59 (( 77.78/10.59 (ubforcartprodlem3) => 77.78/10.59 (( 77.78/10.59 (cartprodpairin) => 77.78/10.59 (( 77.78/10.59 (cartprodmempair1) => 77.78/10.59 (( 77.78/10.59 (cartprodmempair) => 77.78/10.59 (( 77.78/10.59 (setunionE2) => 77.78/10.59 (( 77.78/10.59 (setunionsingleton1) => 77.78/10.59 (( 77.78/10.59 (setunionsingleton2) => 77.78/10.59 (( 77.78/10.59 (setunionsingleton) => 77.78/10.59 (( 77.78/10.59 (singletonprop) => 77.78/10.59 (( 77.78/10.59 (ex1E1) => 77.78/10.59 (( 77.78/10.59 (ex1I) => 77.78/10.59 (( 77.78/10.59 (ex1I2) => 77.78/10.59 (( 77.78/10.59 (singletonsuniq) => 77.78/10.59 (( 77.78/10.59 (setukpairinjL1) => 77.78/10.59 (( 77.78/10.59 (kfstsingleton) => 77.78/10.59 (( 77.78/10.59 (theprop) => 77.78/10.59 (( 77.78/10.59 (kfstpairEq) => 77.78/10.59 (( 77.78/10.59 (cartprodfstin) => 77.78/10.59 (( 77.78/10.59 (setukpairinjL2) => 77.78/10.59 (( 77.78/10.59 (setukpairinjL) => 77.78/10.59 (( 77.78/10.59 (setukpairinjR11) => 77.78/10.59 (( 77.78/10.59 (setukpairinjR12) => 77.78/10.59 (( 77.78/10.59 (setukpairinjR1) => 77.78/10.59 (( 77.78/10.59 (upairequniteq) => 77.78/10.59 (( 77.78/10.59 (setukpairinjR2) => 77.78/10.59 (( 77.78/10.59 (setukpairinjR) => 77.78/10.59 (( 77.78/10.59 (ksndsingleton) => 77.78/10.59 (( 77.78/10.59 (ksndpairEq) => 77.78/10.59 (( 77.78/10.59 (kpairsurjEq) => 77.78/10.59 (( 77.78/10.59 (cartprodsndin) => 77.78/10.59 (( 77.78/10.59 (cartprodpairmemEL) => 77.78/10.59 (( 77.78/10.59 (cartprodpairmemER) => 77.78/10.59 (( 77.78/10.59 (cartprodmempaircEq) => 77.78/10.59 (( 77.78/10.59 (cartprodfstpairEq) => 77.78/10.59 (( 77.78/10.59 (cartprodsndpairEq) => 77.78/10.59 (( 77.78/10.59 (cartprodpairsurjEq) => 77.78/10.59 (( 77.78/10.59 (dpsetconstrI) => 77.78/10.59 (( 77.78/10.59 (dpsetconstrSub) => 77.78/10.59 (( 77.78/10.59 (setOfPairsIsBReln) => 77.78/10.59 (( 77.78/10.59 (dpsetconstrERa) => 77.78/10.59 (( 77.78/10.59 (dpsetconstrEL1) => 77.78/10.59 (( 77.78/10.59 (dpsetconstrEL2) => 77.78/10.59 (( 77.78/10.59 (dpsetconstrER) => 77.78/10.59 (( 77.78/10.59 (funcImageSingleton) => 77.78/10.59 (( 77.78/10.59 (apProp) => 77.78/10.59 (( 77.78/10.59 (app) => 77.78/10.59 (( 77.78/10.59 (infuncsetfunc) => 77.78/10.59 (( 77.78/10.59 (ap2p) => 77.78/10.59 (( 77.78/10.59 (funcinfuncset) => 77.78/10.59 (( 77.78/10.59 (lamProp) => 77.78/10.59 (( 77.78/10.59 (lamp) => 77.78/10.59 (( 77.78/10.59 (lam2p) => 77.78/10.59 (( 77.78/10.59 (brelnall1) => 77.78/10.59 (( 77.78/10.59 (brelnall2) => 77.78/10.59 (( 77.78/10.59 (ex1E2) => 77.78/10.59 (( 77.78/10.59 (funcGraphProp1) => 77.78/10.59 (( 77.78/10.59 (funcGraphProp3) => 77.78/10.59 (( 77.78/10.59 (funcGraphProp2) => 77.78/10.59 (( 77.78/10.59 (funcextLem) => 77.78/10.59 (( 77.78/10.59 (funcGraphProp4) => 77.78/10.59 (( 77.78/10.59 (subbreln) => 77.78/10.59 (( 77.78/10.59 (eqbreln) => 77.78/10.59 (( 77.78/10.59 (funcext) => 77.78/10.59 (( 77.78/10.59 (funcext2) => 77.78/10.59 (( 77.78/10.59 (ap2apEq1) => 77.78/10.59 (( 77.78/10.59 (ap2apEq2) => 77.78/10.59 (( 77.78/10.59 (beta1) => 77.78/10.59 (( 77.78/10.59 (eta1) => 77.78/10.59 (( 77.78/10.59 (lam2lamEq) => 77.78/10.59 (( 77.78/10.59 (beta2) => 77.78/10.59 (( 77.78/10.59 (eta2) => 77.78/10.59 (( 77.78/10.59 (iffalseProp1) => 77.78/10.59 (( 77.78/10.59 (iffalseProp2) => 77.78/10.59 (( 77.78/10.59 (iftrueProp1) => 77.78/10.59 (( 77.78/10.59 (iftrueProp2) => 77.78/10.59 (( 77.78/10.59 (ifSingleton) => 77.78/10.59 (( 77.78/10.59 (ifp) => 77.78/10.59 (( 77.78/10.59 (theeq) => 77.78/10.59 (( 77.78/10.59 (iftrue) => 77.78/10.59 (( 77.78/10.59 (iffalse) => 77.78/10.59 (( 77.78/10.59 (iftrueorfalse) => 77.78/10.59 (( 77.78/10.59 (binintersectT_lem) => 77.78/10.59 (( 77.78/10.59 (binunionT_lem) => 77.78/10.59 (( 77.78/10.59 (powersetT_lem) => 77.78/10.59 (( 77.78/10.59 (setminusT_lem) => 77.78/10.59 (( 77.78/10.59 (complementT_lem) => 77.78/10.59 (( 77.78/10.59 (setextT) => 77.78/10.59 (( 77.78/10.59 (subsetTI) => 77.78/10.59 (( 77.78/10.59 (powersetTI1) => 77.78/10.59 (( 77.78/10.59 (powersetTE1) => 77.78/10.59 (( 77.78/10.59 (complementTI1) => 77.78/10.59 (( 77.78/10.59 (complementTE1) => 77.78/10.59 (( 77.78/10.59 (binintersectTELcontra) => 77.78/10.59 (( 77.78/10.59 (binintersectTERcontra) => 77.78/10.59 (( 77.78/10.59 (contrasubsetT) => 77.78/10.59 (( 77.78/10.59 (contrasubsetT1) => 77.78/10.59 (( 77.78/10.59 (contrasubsetT2) => 77.78/10.59 (( 77.78/10.59 (contrasubsetT3) => 77.78/10.59 (( 77.78/10.59 (doubleComplementI1) => 77.78/10.59 (( 77.78/10.59 (doubleComplementE1) => 77.78/10.59 (( 77.78/10.59 (doubleComplementSub1) => 77.78/10.59 (( 77.78/10.59 (doubleComplementSub2) => 77.78/10.59 (( 77.78/10.59 (doubleComplementEq) => 77.78/10.59 (( 77.78/10.59 (complementTnotintersectT) => 77.78/10.59 (( 77.78/10.59 (complementImpComplementIntersect) => 77.78/10.59 (( 77.78/10.59 (complementSubsetComplementIntersect) => 77.78/10.59 (( 77.78/10.59 (complementInPowersetComplementIntersect) => 77.78/10.59 (( 77.78/10.59 (contraSubsetComplement) => 77.78/10.59 (( 77.78/10.59 (complementTcontraSubset) => 77.78/10.59 (( 77.78/10.59 (binunionTILcontra) => 77.78/10.59 (( 77.78/10.59 (binunionTIRcontra) => 77.78/10.59 (( 77.78/10.59 (inIntersectImpInUnion) => 77.78/10.59 (( 77.78/10.59 (inIntersectImpInUnion2) => 77.78/10.59 (( 77.78/10.59 (inIntersectImpInIntersectUnions) => 77.78/10.59 (( 77.78/10.59 (intersectInPowersetIntersectUnions) => 77.78/10.59 (( 77.78/10.59 (inComplementUnionImpNotIn1) => 77.78/10.59 (( 77.78/10.59 (inComplementUnionImpInComplement1) => 77.78/10.59 (( 77.78/10.59 (binunionTE) => 77.78/10.59 (( 77.78/10.59 (binunionTEcontra) => 77.78/10.59 (( 77.78/10.59 (demorgan2a1) => 77.78/10.59 (( 77.78/10.59 (complementUnionInPowersetComplement) => 77.78/10.59 (( 77.78/10.59 (demorgan2a2) => 77.78/10.59 (( 77.78/10.59 (demorgan1a) => 77.78/10.59 (( 77.78/10.59 (demorgan1b) => 77.78/10.59 (( 77.78/10.59 (demorgan1) => 77.78/10.59 (( 77.78/10.59 (demorgan2a) => 77.78/10.59 (( 77.78/10.59 (demorgan2b2) => 77.78/10.59 (( 77.78/10.59 (demorgan2b) => 77.78/10.59 (( 77.78/10.59 (demorgan2) => 77.78/10.59 (( 77.78/10.59 (woz13rule0) => 77.78/10.59 (( 77.78/10.59 (woz13rule1) => 77.78/10.59 (( 77.78/10.59 (woz13rule2) => 77.78/10.59 (( 77.78/10.59 (woz13rule3) => 77.78/10.59 (( 77.78/10.59 (woz13rule4) => 77.78/10.59 (( 77.78/10.59 (woz1_1) => 77.78/10.59 (( 77.78/10.59 (woz1_2) => 77.78/10.59 (( 77.78/10.59 (woz1_3) => 77.78/10.59 (( 77.78/10.59 (woz1_4) => 77.78/10.59 (( 77.78/10.59 (woz1_5) => 77.78/10.59 (( 77.78/10.59 (breln1all2) => 77.78/10.59 (( 77.78/10.59 (breln1SetBreln1) => 77.78/10.59 (( 77.78/10.59 (choice2fnsingleton) => 77.78/10.59 (( 77.78/10.59 (setOfPairsIsBReln1) => 77.78/10.59 (( 77.78/10.59 (breln1all1) => 77.78/10.59 (( 77.78/10.59 (subbreln1) => 77.78/10.59 (( 77.78/10.59 (eqbreln1) => 77.78/10.59 (( 77.78/10.59 (breln1invprop) => 77.78/10.59 (( 77.78/10.59 (breln1invI) => 77.78/10.59 (( 77.78/10.59 (breln1invE) => 77.78/10.59 (( 77.78/10.59 (breln1compprop) => 77.78/10.59 (( 77.78/10.59 (breln1compI) => 77.78/10.59 (( 77.78/10.59 (breln1compE) => 77.78/10.59 (( 77.78/10.59 (breln1compEex) => 77.78/10.59 (( 77.78/10.59 (breln1unionprop) => 77.78/10.59 (( 77.78/10.59 (breln1unionIL) => 77.78/10.59 (( 77.78/10.59 (breln1unionIR) => 77.78/10.59 (( 77.78/10.59 (breln1unionI) => 77.78/10.59 (( 77.78/10.59 (breln1unionE) => 77.78/10.59 (( 77.78/10.59 (breln1unionEcases) => 77.78/10.59 (( 77.78/10.59 (breln1unionCommutes) => 77.78/10.59 (( 77.78/10.59 (woz2Ex) => 77.78/10.59 (( 77.78/10.59 (woz2W) => 77.78/10.59 (( 77.78/10.59 (woz2A) => 77.78/10.59 (( 77.78/10.59 (woz2B) => 77.78/10.59 (( 77.78/10.59 (image1Ex) => 77.78/10.59 (( 77.78/10.59 (image1Ex1) => 77.78/10.59 (( 77.78/10.59 (image1Equiv) => 77.78/10.59 (( 77.78/10.59 (image1E) => 77.78/10.59 (( 77.78/10.59 (image1I) => 77.78/10.59 (( 77.78/10.59 (injFuncInInjFuncSet) => 77.78/10.59 (( 77.78/10.59 (injFuncSetFuncIn) => 77.78/10.59 (( 77.78/10.59 (injFuncSetFuncInj) => 77.78/10.59 (( 77.78/10.59 (surjFuncSetFuncIn) => 77.78/10.59 (( 77.78/10.59 (surjFuncSetFuncSurj) => 77.78/10.59 (( 77.78/10.59 (leftInvIsSurj) => 77.78/10.59 (( 77.78/10.59 (surjCantorThm) => 77.78/10.59 (( 77.78/10.59 (foundation2) => 77.78/10.59 (( 77.78/10.59 (notinself) => 77.78/10.59 (( 77.78/10.59 (notinself2) => 77.78/10.59 (( 77.78/10.59 (omegaSp) => 77.78/10.59 (( 77.78/10.59 (omegaSclos) => 77.78/10.59 (( 77.78/10.59 (peano0notS) => 77.78/10.59 (( 77.78/10.59 (peanoSinj) => 77.78/10.59 (( 77.78/10.59 (transitivesetOp1) => 77.78/10.59 (( 77.78/10.59 (binintTransitive) => 77.78/10.59 (( 77.78/10.59 (transitivesetOp2) => 77.78/10.59 (( 77.78/10.59 (setunionTransitive) => 77.78/10.59 (( 77.78/10.59 (ordinalMinLem1) => 77.78/10.59 (( 77.78/10.59 (!!) @ ( 77.78/10.59 ^[Y0 : $i]: 77.78/10.59 (( 77.78/10.59 (ordinal @ 77.78/10.59 Y0) => 77.78/10.59 (( 77.78/10.59 (!!) @ ( 77.78/10.59 ^[Y1 : $i]: 77.78/10.59 (( 77.78/10.59 (!!) @ ( 77.78/10.59 ^[Y2 : $i]: 77.78/10.59 (( 77.78/10.59 (in @ 77.78/10.59 Y2 @ 77.78/10.59 Y0) => 77.78/10.59 (( 77.78/10.59 (in @ 77.78/10.59 Y1 @ 77.78/10.59 Y2) => 77.78/10.59 (in @ 77.78/10.59 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 77.78/10.59 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl337])). 77.78/10.59 thf(zip_derived_cl350, plain, 77.78/10.59 (~ (((powersetE) => 77.78/10.59 (((setunionI) => 77.78/10.59 (((setunionE) => 77.78/10.59 (((subPowSU) => 77.78/10.59 (((exuE2) => 77.78/10.59 (((nonemptyImpWitness) => 77.78/10.59 (((uniqinunit) => 77.78/10.59 (((notinsingleton) => 77.78/10.59 (((eqinunit) => 77.78/10.59 (((singletonsswitch) => 77.78/10.59 (((upairsetE) => 77.78/10.59 (((upairsetIL) => 77.78/10.59 (((upairsetIR) => 77.78/10.59 (((emptyE1) => 77.78/10.59 (((vacuousDall) => 77.78/10.59 (((quantDeMorgan1) => 77.78/10.59 (((quantDeMorgan2) => 77.78/10.59 (((quantDeMorgan3) => 77.78/10.59 (((quantDeMorgan4) => 77.78/10.59 (((prop2setI) => 77.78/10.59 (((prop2set2propI) => 77.78/10.59 (((notdexE) => 77.78/10.59 (((notdallE) => 77.78/10.59 (((exuI1) => 77.78/10.59 (((exuI3) => 77.78/10.59 (((exuI2) => 77.78/10.59 (((inCongP) => 77.78/10.59 (((in__Cong) => 77.78/10.59 (((exuE3u) => 77.78/10.59 (((exu__Cong) => 77.78/10.59 (( 77.78/10.59 (setadjoin__Cong) => 77.78/10.59 (( 77.78/10.59 (powerset__Cong) => 77.78/10.59 (( 77.78/10.59 (setunion__Cong) => 77.78/10.59 (( 77.78/10.59 (exuEu) => 77.78/10.59 (( 77.78/10.59 (descr__Cong) => 77.78/10.59 (( 77.78/10.59 (dsetconstr__Cong) => 77.78/10.59 (( 77.78/10.59 (subsetI1) => 77.78/10.59 (( 77.78/10.59 (eqimpsubset2) => 77.78/10.59 (( 77.78/10.59 (eqimpsubset1) => 77.78/10.59 (( 77.78/10.59 (subsetI2) => 77.78/10.59 (( 77.78/10.59 (emptysetsubset) => 77.78/10.59 (( 77.78/10.59 (subsetE) => 77.78/10.59 (( 77.78/10.59 (subsetE2) => 77.78/10.59 (( 77.78/10.59 (notsubsetI) => 77.78/10.59 (( 77.78/10.59 (notequalI1) => 77.78/10.59 (( 77.78/10.59 (notequalI2) => 77.78/10.59 (( 77.78/10.59 (subsetRefl) => 77.78/10.59 (( 77.78/10.59 (subsetTrans) => 77.78/10.59 (( 77.78/10.59 (setadjoinSub) => 77.78/10.59 (( 77.78/10.59 (setadjoinSub2) => 77.78/10.59 (( 77.78/10.59 (subset2powerset) => 77.78/10.59 (( 77.78/10.59 (setextsub) => 77.78/10.59 (( 77.78/10.59 (subsetemptysetimpeq) => 77.78/10.59 (( 77.78/10.59 (powersetI1) => 77.78/10.59 (( 77.78/10.59 (powersetE1) => 77.78/10.59 (( 77.78/10.59 (inPowerset) => 77.78/10.59 (( 77.78/10.59 (powersetsubset) => 77.78/10.59 (( 77.78/10.59 (sepInPowerset) => 77.78/10.59 (( 77.78/10.59 (sepSubset) => 77.78/10.59 (( 77.78/10.59 (binunionIL) => 77.78/10.59 (( 77.78/10.59 (upairset2IR) => 77.78/10.59 (( 77.78/10.59 (binunionIR) => 77.78/10.59 (( 77.78/10.59 (binunionEcases) => 77.78/10.59 (( 77.78/10.59 (binunionE) => 77.78/10.59 (( 77.78/10.59 (binunionLsub) => 77.78/10.59 (( 77.78/10.59 (binunionRsub) => 77.78/10.59 (( 77.78/10.59 (binintersectI) => 77.78/10.59 (( 77.78/10.59 (binintersectSubset5) => 77.78/10.59 (( 77.78/10.59 (binintersectEL) => 77.78/10.59 (( 77.78/10.59 (binintersectLsub) => 77.78/10.59 (( 77.78/10.59 (binintersectSubset2) => 77.78/10.59 (( 77.78/10.59 (binintersectSubset3) => 77.78/10.59 (( 77.78/10.59 (binintersectER) => 77.78/10.59 (( 77.78/10.59 (disjointsetsI1) => 77.78/10.59 (( 77.78/10.59 (binintersectRsub) => 77.78/10.59 (( 77.78/10.59 (binintersectSubset4) => 77.78/10.59 (( 77.78/10.59 (binintersectSubset1) => 77.78/10.59 (( 77.78/10.59 (bs114d) => 77.78/10.59 (( 77.78/10.59 (setminusI) => 77.78/10.59 (( 77.78/10.59 (setminusEL) => 77.78/10.59 (( 77.78/10.59 (setminusER) => 77.78/10.59 (( 77.78/10.59 (setminusSubset2) => 77.78/10.59 (( 77.78/10.59 (setminusERneg) => 77.78/10.59 (( 77.78/10.59 (setminusELneg) => 77.78/10.59 (( 77.78/10.59 (setminusILneg) => 77.78/10.59 (( 77.78/10.59 (setminusIRneg) => 77.78/10.59 (( 77.78/10.59 (setminusLsub) => 77.78/10.59 (( 77.78/10.59 (setminusSubset1) => 77.78/10.59 (( 77.78/10.59 (symdiffE) => 77.78/10.59 (( 77.78/10.59 (symdiffI1) => 77.78/10.59 (( 77.78/10.59 (symdiffI2) => 77.78/10.59 (( 77.78/10.59 (symdiffIneg1) => 77.78/10.59 (( 77.78/10.59 (symdiffIneg2) => 77.78/10.59 (( 77.78/10.59 (secondinupair) => 77.78/10.59 (( 77.78/10.59 (setukpairIL) => 77.78/10.59 (( 77.78/10.59 (setukpairIR) => 77.78/10.59 (( 77.78/10.59 (kpairiskpair) => 77.78/10.59 (( 77.78/10.59 (kpairp) => 77.78/10.59 (( 77.78/10.59 (singletonsubset) => 77.78/10.59 (( 77.78/10.59 (singletoninpowerset) => 77.78/10.59 (( 77.78/10.59 (singletoninpowunion) => 77.78/10.59 (( 77.78/10.59 (upairset2E) => 77.78/10.59 (( 77.78/10.59 (upairsubunion) => 77.78/10.59 (( 77.78/10.59 (upairinpowunion) => 77.78/10.59 (( 77.78/10.59 (ubforcartprodlem1) => 77.78/10.59 (( 77.78/10.59 (ubforcartprodlem2) => 77.78/10.59 (( 77.78/10.59 (ubforcartprodlem3) => 77.78/10.59 (( 77.78/10.59 (cartprodpairin) => 77.78/10.59 (( 77.78/10.59 (cartprodmempair1) => 77.78/10.59 (( 77.78/10.59 (cartprodmempair) => 77.78/10.59 (( 77.78/10.59 (setunionE2) => 77.78/10.59 (( 77.78/10.59 (setunionsingleton1) => 77.78/10.59 (( 77.78/10.59 (setunionsingleton2) => 77.78/10.59 (( 77.78/10.59 (setunionsingleton) => 77.78/10.59 (( 77.78/10.59 (singletonprop) => 77.78/10.59 (( 77.78/10.59 (ex1E1) => 77.78/10.59 (( 77.78/10.59 (ex1I) => 77.78/10.59 (( 77.78/10.59 (ex1I2) => 77.78/10.59 (( 77.78/10.59 (singletonsuniq) => 77.78/10.59 (( 77.78/10.59 (setukpairinjL1) => 77.78/10.59 (( 77.78/10.59 (kfstsingleton) => 77.78/10.59 (( 77.78/10.59 (theprop) => 77.78/10.59 (( 77.78/10.59 (kfstpairEq) => 77.78/10.59 (( 77.78/10.59 (cartprodfstin) => 77.78/10.59 (( 77.78/10.59 (setukpairinjL2) => 77.78/10.59 (( 77.78/10.59 (setukpairinjL) => 77.78/10.59 (( 77.78/10.59 (setukpairinjR11) => 77.78/10.59 (( 77.78/10.59 (setukpairinjR12) => 77.78/10.59 (( 77.78/10.59 (setukpairinjR1) => 77.78/10.59 (( 77.78/10.59 (upairequniteq) => 77.78/10.59 (( 77.78/10.59 (setukpairinjR2) => 77.78/10.59 (( 77.78/10.59 (setukpairinjR) => 77.78/10.59 (( 77.78/10.59 (ksndsingleton) => 77.78/10.59 (( 77.78/10.59 (ksndpairEq) => 77.78/10.59 (( 77.78/10.59 (kpairsurjEq) => 77.78/10.59 (( 77.78/10.59 (cartprodsndin) => 77.78/10.59 (( 77.78/10.59 (cartprodpairmemEL) => 77.78/10.59 (( 77.78/10.59 (cartprodpairmemER) => 77.78/10.59 (( 77.78/10.59 (cartprodmempaircEq) => 77.78/10.59 (( 77.78/10.59 (cartprodfstpairEq) => 77.78/10.59 (( 77.78/10.59 (cartprodsndpairEq) => 77.78/10.59 (( 77.78/10.59 (cartprodpairsurjEq) => 77.78/10.59 (( 77.78/10.59 (dpsetconstrI) => 77.78/10.59 (( 77.78/10.59 (dpsetconstrSub) => 77.78/10.59 (( 77.78/10.59 (setOfPairsIsBReln) => 77.78/10.59 (( 77.78/10.59 (dpsetconstrERa) => 77.78/10.59 (( 77.78/10.59 (dpsetconstrEL1) => 77.78/10.59 (( 77.78/10.59 (dpsetconstrEL2) => 77.78/10.59 (( 77.78/10.59 (dpsetconstrER) => 77.78/10.59 (( 77.78/10.59 (funcImageSingleton) => 77.78/10.59 (( 77.78/10.59 (apProp) => 77.78/10.59 (( 77.78/10.59 (app) => 77.78/10.59 (( 77.78/10.59 (infuncsetfunc) => 77.78/10.59 (( 77.78/10.59 (ap2p) => 77.78/10.59 (( 77.78/10.59 (funcinfuncset) => 77.78/10.59 (( 77.78/10.59 (lamProp) => 77.78/10.59 (( 77.78/10.59 (lamp) => 77.78/10.59 (( 77.78/10.59 (lam2p) => 77.78/10.59 (( 77.78/10.59 (brelnall1) => 77.78/10.59 (( 77.78/10.59 (brelnall2) => 77.78/10.59 (( 77.78/10.59 (ex1E2) => 77.78/10.59 (( 77.78/10.59 (funcGraphProp1) => 77.78/10.59 (( 77.78/10.59 (funcGraphProp3) => 77.78/10.59 (( 77.78/10.59 (funcGraphProp2) => 77.78/10.59 (( 77.78/10.59 (funcextLem) => 77.78/10.59 (( 77.78/10.59 (funcGraphProp4) => 77.78/10.59 (( 77.78/10.59 (subbreln) => 77.78/10.59 (( 77.78/10.59 (eqbreln) => 77.78/10.59 (( 77.78/10.59 (funcext) => 77.78/10.59 (( 77.78/10.59 (funcext2) => 77.78/10.59 (( 77.78/10.59 (ap2apEq1) => 77.78/10.59 (( 77.78/10.59 (ap2apEq2) => 77.78/10.59 (( 77.78/10.59 (beta1) => 77.78/10.59 (( 77.78/10.59 (eta1) => 77.78/10.59 (( 77.78/10.59 (lam2lamEq) => 77.78/10.59 (( 77.78/10.59 (beta2) => 77.78/10.59 (( 77.78/10.59 (eta2) => 77.78/10.59 (( 77.78/10.59 (iffalseProp1) => 77.78/10.59 (( 77.78/10.59 (iffalseProp2) => 77.78/10.59 (( 77.78/10.59 (iftrueProp1) => 77.78/10.59 (( 77.78/10.59 (iftrueProp2) => 77.78/10.59 (( 77.78/10.59 (ifSingleton) => 77.78/10.59 (( 77.78/10.59 (ifp) => 77.78/10.59 (( 77.78/10.59 (theeq) => 77.78/10.59 (( 77.78/10.59 (iftrue) => 77.78/10.59 (( 77.78/10.59 (iffalse) => 77.78/10.59 (( 77.78/10.59 (iftrueorfalse) => 77.78/10.59 (( 77.78/10.59 (binintersectT_lem) => 77.78/10.59 (( 77.78/10.59 (binunionT_lem) => 77.78/10.59 (( 77.78/10.59 (powersetT_lem) => 77.78/10.59 (( 77.78/10.59 (setminusT_lem) => 77.78/10.59 (( 77.78/10.59 (complementT_lem) => 77.78/10.59 (( 77.78/10.59 (setextT) => 77.78/10.59 (( 77.78/10.59 (subsetTI) => 77.78/10.59 (( 77.78/10.59 (powersetTI1) => 77.78/10.59 (( 77.78/10.59 (powersetTE1) => 77.78/10.59 (( 77.78/10.59 (complementTI1) => 77.78/10.59 (( 77.78/10.59 (complementTE1) => 77.78/10.59 (( 77.78/10.59 (binintersectTELcontra) => 77.78/10.59 (( 77.78/10.59 (binintersectTERcontra) => 77.78/10.59 (( 77.78/10.59 (contrasubsetT) => 77.78/10.59 (( 77.78/10.59 (contrasubsetT1) => 77.78/10.59 (( 77.78/10.59 (contrasubsetT2) => 77.78/10.59 (( 77.78/10.59 (contrasubsetT3) => 77.78/10.59 (( 77.78/10.59 (doubleComplementI1) => 77.78/10.59 (( 77.78/10.59 (doubleComplementE1) => 77.78/10.59 (( 77.78/10.59 (doubleComplementSub1) => 77.78/10.59 (( 77.78/10.59 (doubleComplementSub2) => 77.78/10.59 (( 77.78/10.59 (doubleComplementEq) => 77.78/10.59 (( 77.78/10.59 (complementTnotintersectT) => 77.78/10.59 (( 77.78/10.59 (complementImpComplementIntersect) => 77.78/10.59 (( 77.78/10.59 (complementSubsetComplementIntersect) => 77.78/10.59 (( 77.78/10.59 (complementInPowersetComplementIntersect) => 77.78/10.59 (( 77.78/10.59 (contraSubsetComplement) => 77.78/10.59 (( 77.78/10.59 (complementTcontraSubset) => 77.78/10.59 (( 77.78/10.59 (binunionTILcontra) => 77.78/10.59 (( 77.78/10.59 (binunionTIRcontra) => 77.78/10.59 (( 77.78/10.59 (inIntersectImpInUnion) => 77.78/10.59 (( 77.78/10.59 (inIntersectImpInUnion2) => 77.78/10.59 (( 77.78/10.59 (inIntersectImpInIntersectUnions) => 77.78/10.59 (( 77.78/10.59 (intersectInPowersetIntersectUnions) => 77.78/10.59 (( 77.78/10.59 (inComplementUnionImpNotIn1) => 77.78/10.59 (( 77.78/10.59 (inComplementUnionImpInComplement1) => 77.78/10.59 (( 77.78/10.59 (binunionTE) => 77.78/10.59 (( 77.78/10.59 (binunionTEcontra) => 77.78/10.59 (( 77.78/10.59 (demorgan2a1) => 77.78/10.59 (( 77.78/10.59 (complementUnionInPowersetComplement) => 77.78/10.59 (( 77.78/10.59 (demorgan2a2) => 77.78/10.59 (( 77.78/10.59 (demorgan1a) => 77.78/10.59 (( 77.78/10.59 (demorgan1b) => 77.78/10.59 (( 77.78/10.59 (demorgan1) => 77.78/10.59 (( 77.78/10.59 (demorgan2a) => 77.78/10.59 (( 77.78/10.59 (demorgan2b2) => 77.78/10.59 (( 77.78/10.59 (demorgan2b) => 77.78/10.59 (( 77.78/10.59 (demorgan2) => 77.78/10.59 (( 77.78/10.59 (woz13rule0) => 77.78/10.59 (( 77.78/10.59 (woz13rule1) => 77.78/10.59 (( 77.78/10.59 (woz13rule2) => 77.78/10.59 (( 77.78/10.59 (woz13rule3) => 77.78/10.59 (( 77.78/10.59 (woz13rule4) => 77.78/10.59 (( 77.78/10.59 (woz1_1) => 77.78/10.59 (( 77.78/10.59 (woz1_2) => 77.78/10.59 (( 77.78/10.59 (woz1_3) => 77.78/10.59 (( 77.78/10.59 (woz1_4) => 77.78/10.59 (( 77.78/10.59 (woz1_5) => 77.78/10.59 (( 77.78/10.59 (breln1all2) => 77.78/10.59 (( 77.78/10.59 (breln1SetBreln1) => 77.78/10.59 (( 77.78/10.59 (choice2fnsingleton) => 77.78/10.59 (( 77.78/10.59 (setOfPairsIsBReln1) => 77.78/10.59 (( 77.78/10.59 (breln1all1) => 77.78/10.59 (( 77.78/10.59 (subbreln1) => 77.78/10.59 (( 77.78/10.59 (eqbreln1) => 77.78/10.59 (( 77.78/10.59 (breln1invprop) => 77.78/10.59 (( 77.78/10.59 (breln1invI) => 77.78/10.59 (( 77.78/10.59 (breln1invE) => 77.78/10.59 (( 77.78/10.59 (breln1compprop) => 77.78/10.59 (( 77.78/10.59 (breln1compI) => 77.78/10.59 (( 77.78/10.59 (breln1compE) => 77.78/10.59 (( 77.78/10.59 (breln1compEex) => 77.78/10.59 (( 77.78/10.59 (breln1unionprop) => 77.78/10.59 (( 77.78/10.59 (breln1unionIL) => 77.78/10.59 (( 77.78/10.59 (breln1unionIR) => 77.78/10.59 (( 77.78/10.59 (breln1unionI) => 77.78/10.59 (( 77.78/10.59 (breln1unionE) => 77.78/10.59 (( 77.78/10.59 (breln1unionEcases) => 77.78/10.59 (( 77.78/10.59 (breln1unionCommutes) => 77.78/10.59 (( 77.78/10.59 (woz2Ex) => 77.78/10.59 (( 77.78/10.59 (woz2W) => 77.78/10.59 (( 77.78/10.59 (woz2A) => 77.78/10.59 (( 77.78/10.59 (woz2B) => 77.78/10.59 (( 77.78/10.59 (image1Ex) => 77.78/10.59 (( 77.78/10.59 (image1Ex1) => 77.78/10.59 (( 77.78/10.59 (image1Equiv) => 77.78/10.59 (( 77.78/10.59 (image1E) => 77.78/10.59 (( 77.78/10.59 (image1I) => 77.78/10.59 (( 77.78/10.59 (injFuncInInjFuncSet) => 77.78/10.59 (( 77.78/10.59 (injFuncSetFuncIn) => 77.78/10.59 (( 77.78/10.59 (injFuncSetFuncInj) => 77.78/10.59 (( 77.78/10.59 (surjFuncSetFuncIn) => 77.78/10.59 (( 77.78/10.59 (surjFuncSetFuncSurj) => 77.78/10.59 (( 77.78/10.59 (leftInvIsSurj) => 77.78/10.59 (( 77.78/10.59 (surjCantorThm) => 77.78/10.59 (( 77.78/10.59 (foundation2) => 77.78/10.59 (( 77.78/10.59 (notinself) => 77.78/10.59 (( 77.78/10.59 (notinself2) => 77.78/10.59 (( 77.78/10.59 (omegaSp) => 77.78/10.59 (( 77.78/10.59 (omegaSclos) => 77.78/10.59 (( 77.78/10.59 (peano0notS) => 77.78/10.59 (( 77.78/10.59 (peanoSinj) => 77.78/10.59 (( 77.78/10.59 (transitivesetOp1) => 77.78/10.59 (( 77.78/10.59 (binintTransitive) => 77.78/10.59 (( 77.78/10.59 (transitivesetOp2) => 77.78/10.59 (( 77.78/10.59 (setunionTransitive) => 77.78/10.59 (( 77.78/10.59 (ordinalMinLem1) => 77.78/10.59 (( 77.78/10.59 (!!) @ ( 77.78/10.59 ^[Y0 : $i]: 77.78/10.59 (( 77.78/10.59 (ordinal @ 77.78/10.59 Y0) => 77.78/10.59 (( 77.78/10.59 (!!) @ ( 77.78/10.59 ^[Y1 : $i]: 77.78/10.59 (( 77.78/10.59 (!!) @ ( 77.78/10.59 ^[Y2 : $i]: 77.78/10.59 (( 77.78/10.59 (in @ 77.78/10.59 Y2 @ 77.78/10.59 Y0) => 77.78/10.59 (( 77.78/10.59 (in @ 77.78/10.59 Y1 @ 77.78/10.59 Y2) => 77.78/10.59 (in @ 77.78/10.59 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 77.78/10.59 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl343])). 77.78/10.59 thf(zip_derived_cl357, plain, 77.78/10.59 (~ (((setunionI) => 77.78/10.59 (((setunionE) => 77.78/10.59 (((subPowSU) => 77.78/10.59 (((exuE2) => 77.78/10.59 (((nonemptyImpWitness) => 77.78/10.59 (((uniqinunit) => 77.78/10.59 (((notinsingleton) => 77.78/10.59 (((eqinunit) => 77.78/10.59 (((singletonsswitch) => 77.78/10.59 (((upairsetE) => 77.78/10.59 (((upairsetIL) => 77.78/10.59 (((upairsetIR) => 77.78/10.59 (((emptyE1) => 77.78/10.59 (((vacuousDall) => 77.78/10.59 (((quantDeMorgan1) => 77.78/10.59 (((quantDeMorgan2) => 77.78/10.59 (((quantDeMorgan3) => 77.78/10.59 (((quantDeMorgan4) => 77.78/10.59 (((prop2setI) => 77.78/10.59 (((prop2set2propI) => 77.78/10.59 (((notdexE) => 77.78/10.59 (((notdallE) => 77.78/10.59 (((exuI1) => 77.78/10.59 (((exuI3) => 77.78/10.59 (((exuI2) => 77.78/10.59 (((inCongP) => 77.78/10.59 (((in__Cong) => 77.78/10.59 (((exuE3u) => 77.78/10.59 (((exu__Cong) => 77.78/10.59 (((setadjoin__Cong) => 77.78/10.59 (( 77.78/10.59 (powerset__Cong) => 77.78/10.59 (( 77.78/10.59 (setunion__Cong) => 77.78/10.59 (( 77.78/10.59 (exuEu) => 77.78/10.59 (( 77.78/10.59 (descr__Cong) => 77.78/10.59 (( 77.78/10.59 (dsetconstr__Cong) => 77.78/10.59 (( 77.78/10.59 (subsetI1) => 77.78/10.59 (( 77.78/10.59 (eqimpsubset2) => 77.78/10.59 (( 77.78/10.59 (eqimpsubset1) => 77.78/10.59 (( 77.78/10.59 (subsetI2) => 77.78/10.59 (( 77.78/10.59 (emptysetsubset) => 77.78/10.59 (( 77.78/10.59 (subsetE) => 77.78/10.59 (( 77.78/10.59 (subsetE2) => 77.78/10.59 (( 77.78/10.59 (notsubsetI) => 77.78/10.59 (( 77.78/10.59 (notequalI1) => 77.78/10.59 (( 77.78/10.59 (notequalI2) => 77.78/10.59 (( 77.78/10.59 (subsetRefl) => 77.78/10.59 (( 77.78/10.59 (subsetTrans) => 77.78/10.59 (( 77.78/10.59 (setadjoinSub) => 77.78/10.59 (( 77.78/10.59 (setadjoinSub2) => 77.78/10.59 (( 77.78/10.59 (subset2powerset) => 77.78/10.59 (( 77.78/10.59 (setextsub) => 77.78/10.59 (( 77.78/10.59 (subsetemptysetimpeq) => 77.78/10.59 (( 77.78/10.59 (powersetI1) => 77.78/10.59 (( 77.78/10.59 (powersetE1) => 77.78/10.59 (( 77.78/10.59 (inPowerset) => 77.78/10.59 (( 77.78/10.59 (powersetsubset) => 77.78/10.59 (( 77.78/10.59 (sepInPowerset) => 77.78/10.59 (( 77.78/10.59 (sepSubset) => 77.78/10.59 (( 77.78/10.59 (binunionIL) => 77.78/10.59 (( 77.78/10.59 (upairset2IR) => 77.78/10.59 (( 77.78/10.59 (binunionIR) => 77.78/10.59 (( 77.78/10.59 (binunionEcases) => 77.78/10.59 (( 77.78/10.59 (binunionE) => 77.78/10.59 (( 77.78/10.59 (binunionLsub) => 77.78/10.59 (( 77.78/10.59 (binunionRsub) => 77.78/10.59 (( 77.78/10.59 (binintersectI) => 77.78/10.59 (( 77.78/10.59 (binintersectSubset5) => 77.78/10.59 (( 77.78/10.59 (binintersectEL) => 77.78/10.59 (( 77.78/10.59 (binintersectLsub) => 77.78/10.59 (( 77.78/10.59 (binintersectSubset2) => 77.78/10.59 (( 77.78/10.59 (binintersectSubset3) => 77.78/10.59 (( 77.78/10.59 (binintersectER) => 77.78/10.59 (( 77.78/10.59 (disjointsetsI1) => 77.78/10.59 (( 77.78/10.59 (binintersectRsub) => 77.78/10.59 (( 77.78/10.59 (binintersectSubset4) => 77.78/10.59 (( 77.78/10.59 (binintersectSubset1) => 77.78/10.59 (( 77.78/10.59 (bs114d) => 77.78/10.59 (( 77.78/10.59 (setminusI) => 77.78/10.59 (( 77.78/10.59 (setminusEL) => 77.78/10.59 (( 77.78/10.59 (setminusER) => 77.78/10.59 (( 77.78/10.59 (setminusSubset2) => 77.78/10.59 (( 77.78/10.59 (setminusERneg) => 77.78/10.59 (( 77.78/10.59 (setminusELneg) => 77.78/10.59 (( 77.78/10.59 (setminusILneg) => 77.78/10.59 (( 77.78/10.59 (setminusIRneg) => 77.78/10.59 (( 77.78/10.59 (setminusLsub) => 77.78/10.59 (( 77.78/10.59 (setminusSubset1) => 77.78/10.59 (( 77.78/10.59 (symdiffE) => 77.78/10.59 (( 77.78/10.59 (symdiffI1) => 77.78/10.59 (( 77.78/10.59 (symdiffI2) => 77.78/10.59 (( 77.78/10.59 (symdiffIneg1) => 77.78/10.59 (( 77.78/10.59 (symdiffIneg2) => 77.78/10.59 (( 77.78/10.59 (secondinupair) => 77.78/10.59 (( 77.78/10.59 (setukpairIL) => 77.78/10.59 (( 77.78/10.59 (setukpairIR) => 77.78/10.59 (( 77.78/10.59 (kpairiskpair) => 77.78/10.59 (( 77.78/10.59 (kpairp) => 77.78/10.59 (( 77.78/10.59 (singletonsubset) => 77.78/10.59 (( 77.78/10.59 (singletoninpowerset) => 77.78/10.59 (( 77.78/10.59 (singletoninpowunion) => 77.78/10.59 (( 77.78/10.59 (upairset2E) => 77.78/10.59 (( 77.78/10.59 (upairsubunion) => 77.78/10.59 (( 77.78/10.59 (upairinpowunion) => 77.78/10.59 (( 77.78/10.59 (ubforcartprodlem1) => 77.78/10.59 (( 77.78/10.59 (ubforcartprodlem2) => 77.78/10.59 (( 77.78/10.59 (ubforcartprodlem3) => 77.78/10.59 (( 77.78/10.59 (cartprodpairin) => 77.78/10.59 (( 77.78/10.59 (cartprodmempair1) => 77.78/10.59 (( 77.78/10.59 (cartprodmempair) => 77.78/10.59 (( 77.78/10.59 (setunionE2) => 77.78/10.59 (( 77.78/10.59 (setunionsingleton1) => 77.78/10.59 (( 77.78/10.59 (setunionsingleton2) => 77.78/10.59 (( 77.78/10.59 (setunionsingleton) => 77.78/10.59 (( 77.78/10.59 (singletonprop) => 77.78/10.59 (( 77.78/10.59 (ex1E1) => 77.78/10.59 (( 77.78/10.59 (ex1I) => 77.78/10.59 (( 77.78/10.59 (ex1I2) => 77.78/10.59 (( 77.78/10.59 (singletonsuniq) => 77.78/10.59 (( 77.78/10.59 (setukpairinjL1) => 77.78/10.59 (( 77.78/10.59 (kfstsingleton) => 77.78/10.59 (( 77.78/10.59 (theprop) => 77.78/10.59 (( 77.78/10.59 (kfstpairEq) => 77.78/10.59 (( 77.78/10.59 (cartprodfstin) => 77.78/10.59 (( 77.78/10.59 (setukpairinjL2) => 77.78/10.59 (( 77.78/10.59 (setukpairinjL) => 77.78/10.59 (( 77.78/10.59 (setukpairinjR11) => 77.78/10.59 (( 77.78/10.59 (setukpairinjR12) => 77.78/10.59 (( 77.78/10.59 (setukpairinjR1) => 77.78/10.59 (( 77.78/10.59 (upairequniteq) => 77.78/10.59 (( 77.78/10.59 (setukpairinjR2) => 77.78/10.59 (( 77.78/10.59 (setukpairinjR) => 77.78/10.59 (( 77.78/10.59 (ksndsingleton) => 77.78/10.59 (( 77.78/10.59 (ksndpairEq) => 77.78/10.59 (( 77.78/10.59 (kpairsurjEq) => 77.78/10.59 (( 77.78/10.59 (cartprodsndin) => 77.78/10.59 (( 77.78/10.59 (cartprodpairmemEL) => 77.78/10.59 (( 77.78/10.59 (cartprodpairmemER) => 77.78/10.59 (( 77.78/10.59 (cartprodmempaircEq) => 77.78/10.59 (( 77.78/10.59 (cartprodfstpairEq) => 77.78/10.59 (( 77.78/10.59 (cartprodsndpairEq) => 77.78/10.59 (( 77.78/10.59 (cartprodpairsurjEq) => 77.78/10.59 (( 77.78/10.59 (dpsetconstrI) => 77.78/10.59 (( 77.78/10.59 (dpsetconstrSub) => 77.78/10.59 (( 77.78/10.59 (setOfPairsIsBReln) => 77.78/10.59 (( 77.78/10.59 (dpsetconstrERa) => 77.78/10.59 (( 77.78/10.59 (dpsetconstrEL1) => 77.78/10.59 (( 77.78/10.59 (dpsetconstrEL2) => 77.78/10.59 (( 77.78/10.59 (dpsetconstrER) => 77.78/10.59 (( 77.78/10.59 (funcImageSingleton) => 77.78/10.59 (( 77.78/10.59 (apProp) => 77.78/10.59 (( 77.78/10.59 (app) => 77.78/10.59 (( 77.78/10.59 (infuncsetfunc) => 77.78/10.59 (( 77.78/10.59 (ap2p) => 77.78/10.59 (( 77.78/10.59 (funcinfuncset) => 77.78/10.59 (( 77.78/10.59 (lamProp) => 77.78/10.59 (( 77.78/10.59 (lamp) => 77.78/10.59 (( 77.78/10.59 (lam2p) => 77.78/10.59 (( 77.78/10.59 (brelnall1) => 77.78/10.59 (( 77.78/10.59 (brelnall2) => 77.78/10.59 (( 77.78/10.59 (ex1E2) => 77.78/10.59 (( 77.78/10.59 (funcGraphProp1) => 77.78/10.59 (( 77.78/10.59 (funcGraphProp3) => 77.78/10.59 (( 77.78/10.59 (funcGraphProp2) => 77.78/10.59 (( 77.78/10.59 (funcextLem) => 77.78/10.59 (( 77.78/10.59 (funcGraphProp4) => 77.78/10.59 (( 77.78/10.59 (subbreln) => 77.78/10.59 (( 77.78/10.59 (eqbreln) => 77.78/10.59 (( 77.78/10.59 (funcext) => 77.78/10.59 (( 77.78/10.59 (funcext2) => 77.78/10.59 (( 77.78/10.59 (ap2apEq1) => 77.78/10.59 (( 77.78/10.59 (ap2apEq2) => 77.78/10.59 (( 77.78/10.59 (beta1) => 77.78/10.59 (( 77.78/10.59 (eta1) => 77.78/10.59 (( 77.78/10.59 (lam2lamEq) => 77.78/10.59 (( 77.78/10.59 (beta2) => 77.78/10.59 (( 77.78/10.59 (eta2) => 77.78/10.59 (( 77.78/10.59 (iffalseProp1) => 77.78/10.59 (( 77.78/10.59 (iffalseProp2) => 77.78/10.59 (( 77.78/10.59 (iftrueProp1) => 77.78/10.59 (( 77.78/10.59 (iftrueProp2) => 77.78/10.59 (( 77.78/10.59 (ifSingleton) => 77.78/10.59 (( 77.78/10.59 (ifp) => 77.78/10.59 (( 77.78/10.59 (theeq) => 77.78/10.59 (( 77.78/10.59 (iftrue) => 77.78/10.59 (( 77.78/10.59 (iffalse) => 77.78/10.59 (( 77.78/10.59 (iftrueorfalse) => 77.78/10.59 (( 77.78/10.59 (binintersectT_lem) => 77.78/10.59 (( 77.78/10.59 (binunionT_lem) => 77.78/10.59 (( 77.78/10.59 (powersetT_lem) => 77.78/10.59 (( 77.78/10.59 (setminusT_lem) => 77.78/10.59 (( 77.78/10.59 (complementT_lem) => 77.78/10.59 (( 77.78/10.59 (setextT) => 77.78/10.59 (( 77.78/10.59 (subsetTI) => 77.78/10.59 (( 77.78/10.59 (powersetTI1) => 77.78/10.59 (( 77.78/10.59 (powersetTE1) => 77.78/10.59 (( 77.78/10.59 (complementTI1) => 77.78/10.59 (( 77.78/10.59 (complementTE1) => 77.78/10.59 (( 77.78/10.59 (binintersectTELcontra) => 77.78/10.59 (( 77.78/10.59 (binintersectTERcontra) => 77.78/10.59 (( 77.78/10.59 (contrasubsetT) => 77.78/10.59 (( 77.78/10.59 (contrasubsetT1) => 77.78/10.59 (( 77.78/10.59 (contrasubsetT2) => 77.78/10.59 (( 77.78/10.59 (contrasubsetT3) => 77.78/10.59 (( 77.78/10.59 (doubleComplementI1) => 77.78/10.59 (( 77.78/10.59 (doubleComplementE1) => 77.78/10.59 (( 77.78/10.59 (doubleComplementSub1) => 77.78/10.59 (( 77.78/10.59 (doubleComplementSub2) => 77.78/10.59 (( 77.78/10.59 (doubleComplementEq) => 77.78/10.59 (( 77.78/10.59 (complementTnotintersectT) => 77.78/10.59 (( 77.78/10.59 (complementImpComplementIntersect) => 77.78/10.59 (( 77.78/10.59 (complementSubsetComplementIntersect) => 77.78/10.59 (( 77.78/10.59 (complementInPowersetComplementIntersect) => 77.78/10.59 (( 77.78/10.59 (contraSubsetComplement) => 77.78/10.59 (( 77.78/10.59 (complementTcontraSubset) => 77.78/10.59 (( 77.78/10.59 (binunionTILcontra) => 77.78/10.59 (( 77.78/10.59 (binunionTIRcontra) => 77.78/10.59 (( 77.78/10.59 (inIntersectImpInUnion) => 77.78/10.59 (( 77.78/10.59 (inIntersectImpInUnion2) => 77.78/10.59 (( 77.78/10.59 (inIntersectImpInIntersectUnions) => 77.78/10.59 (( 77.78/10.59 (intersectInPowersetIntersectUnions) => 77.78/10.59 (( 77.78/10.59 (inComplementUnionImpNotIn1) => 77.78/10.59 (( 77.78/10.59 (inComplementUnionImpInComplement1) => 77.78/10.59 (( 77.78/10.59 (binunionTE) => 77.78/10.59 (( 77.78/10.59 (binunionTEcontra) => 77.78/10.59 (( 77.78/10.59 (demorgan2a1) => 77.78/10.59 (( 77.78/10.59 (complementUnionInPowersetComplement) => 77.78/10.59 (( 77.78/10.59 (demorgan2a2) => 77.78/10.59 (( 77.78/10.59 (demorgan1a) => 77.78/10.59 (( 77.78/10.59 (demorgan1b) => 77.78/10.59 (( 77.78/10.59 (demorgan1) => 77.78/10.59 (( 77.78/10.59 (demorgan2a) => 77.78/10.59 (( 77.78/10.59 (demorgan2b2) => 77.78/10.59 (( 77.78/10.59 (demorgan2b) => 77.78/10.59 (( 77.78/10.59 (demorgan2) => 77.78/10.59 (( 77.78/10.59 (woz13rule0) => 77.78/10.59 (( 77.78/10.59 (woz13rule1) => 77.78/10.59 (( 77.78/10.59 (woz13rule2) => 77.78/10.59 (( 77.78/10.59 (woz13rule3) => 77.78/10.59 (( 77.78/10.59 (woz13rule4) => 77.78/10.59 (( 77.78/10.59 (woz1_1) => 77.78/10.59 (( 77.78/10.59 (woz1_2) => 77.78/10.59 (( 77.78/10.59 (woz1_3) => 77.78/10.59 (( 77.78/10.59 (woz1_4) => 77.78/10.59 (( 77.78/10.59 (woz1_5) => 77.78/10.59 (( 77.78/10.59 (breln1all2) => 77.78/10.59 (( 77.78/10.59 (breln1SetBreln1) => 77.78/10.59 (( 77.78/10.59 (choice2fnsingleton) => 77.78/10.59 (( 77.78/10.59 (setOfPairsIsBReln1) => 77.78/10.59 (( 77.78/10.59 (breln1all1) => 77.78/10.59 (( 77.78/10.59 (subbreln1) => 77.78/10.59 (( 77.78/10.59 (eqbreln1) => 77.78/10.59 (( 77.78/10.59 (breln1invprop) => 77.78/10.59 (( 77.78/10.59 (breln1invI) => 77.78/10.59 (( 77.78/10.59 (breln1invE) => 77.78/10.59 (( 77.78/10.59 (breln1compprop) => 77.78/10.59 (( 77.78/10.59 (breln1compI) => 77.78/10.59 (( 77.78/10.59 (breln1compE) => 77.78/10.59 (( 77.78/10.59 (breln1compEex) => 77.78/10.59 (( 77.78/10.59 (breln1unionprop) => 77.78/10.59 (( 77.78/10.59 (breln1unionIL) => 77.78/10.59 (( 77.78/10.59 (breln1unionIR) => 77.78/10.59 (( 77.78/10.59 (breln1unionI) => 77.78/10.59 (( 77.78/10.59 (breln1unionE) => 77.78/10.59 (( 77.78/10.59 (breln1unionEcases) => 77.78/10.59 (( 77.78/10.59 (breln1unionCommutes) => 77.78/10.59 (( 77.78/10.59 (woz2Ex) => 77.78/10.59 (( 77.78/10.59 (woz2W) => 77.78/10.59 (( 77.78/10.59 (woz2A) => 77.78/10.59 (( 77.78/10.59 (woz2B) => 77.78/10.59 (( 77.78/10.59 (image1Ex) => 77.78/10.59 (( 77.78/10.59 (image1Ex1) => 77.78/10.59 (( 77.78/10.59 (image1Equiv) => 77.78/10.59 (( 77.78/10.59 (image1E) => 77.78/10.59 (( 77.78/10.59 (image1I) => 77.78/10.59 (( 77.78/10.59 (injFuncInInjFuncSet) => 77.78/10.59 (( 77.78/10.59 (injFuncSetFuncIn) => 77.78/10.59 (( 77.78/10.59 (injFuncSetFuncInj) => 77.78/10.59 (( 77.78/10.59 (surjFuncSetFuncIn) => 77.78/10.59 (( 77.78/10.59 (surjFuncSetFuncSurj) => 77.78/10.59 (( 77.78/10.59 (leftInvIsSurj) => 77.78/10.59 (( 77.78/10.59 (surjCantorThm) => 77.78/10.59 (( 77.78/10.59 (foundation2) => 77.78/10.59 (( 77.78/10.59 (notinself) => 77.78/10.59 (( 77.78/10.59 (notinself2) => 77.78/10.59 (( 77.78/10.59 (omegaSp) => 77.78/10.59 (( 77.78/10.59 (omegaSclos) => 77.78/10.59 (( 77.78/10.59 (peano0notS) => 77.78/10.59 (( 77.78/10.59 (peanoSinj) => 77.78/10.59 (( 77.78/10.59 (transitivesetOp1) => 77.78/10.59 (( 77.78/10.59 (binintTransitive) => 77.78/10.59 (( 77.78/10.59 (transitivesetOp2) => 77.78/10.59 (( 77.78/10.59 (setunionTransitive) => 77.78/10.59 (( 77.78/10.59 (ordinalMinLem1) => 77.78/10.59 (( 77.78/10.59 (!!) @ ( 77.78/10.59 ^[Y0 : $i]: 77.78/10.59 (( 77.78/10.59 (ordinal @ 77.78/10.59 Y0) => 77.78/10.59 (( 77.78/10.59 (!!) @ ( 77.78/10.59 ^[Y1 : $i]: 77.78/10.59 (( 77.78/10.59 (!!) @ ( 77.78/10.59 ^[Y2 : $i]: 77.78/10.59 (( 77.78/10.59 (in @ 77.78/10.59 Y2 @ 77.78/10.59 Y0) => 77.78/10.59 (( 77.78/10.59 (in @ 77.78/10.59 Y1 @ 77.78/10.59 Y2) => 77.78/10.59 (in @ 77.78/10.59 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 77.78/10.59 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl350])). 77.78/10.59 thf(zip_derived_cl364, plain, 77.78/10.59 (~ (((setunionE) => 77.78/10.59 (((subPowSU) => 77.78/10.59 (((exuE2) => 77.78/10.59 (((nonemptyImpWitness) => 77.78/10.59 (((uniqinunit) => 77.78/10.59 (((notinsingleton) => 77.78/10.59 (((eqinunit) => 77.78/10.59 (((singletonsswitch) => 77.78/10.59 (((upairsetE) => 77.78/10.59 (((upairsetIL) => 77.78/10.59 (((upairsetIR) => 77.78/10.59 (((emptyE1) => 77.78/10.59 (((vacuousDall) => 77.78/10.59 (((quantDeMorgan1) => 77.78/10.59 (((quantDeMorgan2) => 77.78/10.59 (((quantDeMorgan3) => 77.78/10.59 (((quantDeMorgan4) => 77.78/10.59 (((prop2setI) => 77.78/10.59 (((prop2set2propI) => 77.78/10.59 (((notdexE) => 77.78/10.59 (((notdallE) => 77.78/10.59 (((exuI1) => 77.78/10.59 (((exuI3) => 77.78/10.59 (((exuI2) => 77.78/10.59 (((inCongP) => 77.78/10.59 (((in__Cong) => 77.78/10.59 (((exuE3u) => 77.78/10.59 (((exu__Cong) => 77.78/10.59 (((setadjoin__Cong) => 77.78/10.59 (((powerset__Cong) => 77.78/10.59 (( 77.78/10.59 (setunion__Cong) => 77.78/10.59 (( 77.78/10.59 (exuEu) => 77.78/10.59 (( 77.78/10.59 (descr__Cong) => 77.78/10.59 (( 77.78/10.59 (dsetconstr__Cong) => 77.78/10.59 (( 77.78/10.59 (subsetI1) => 77.78/10.59 (( 77.78/10.59 (eqimpsubset2) => 77.78/10.59 (( 77.78/10.59 (eqimpsubset1) => 77.78/10.59 (( 77.78/10.59 (subsetI2) => 77.78/10.59 (( 77.78/10.59 (emptysetsubset) => 77.78/10.59 (( 77.78/10.59 (subsetE) => 77.78/10.59 (( 77.78/10.59 (subsetE2) => 77.78/10.59 (( 77.78/10.59 (notsubsetI) => 77.78/10.59 (( 77.78/10.59 (notequalI1) => 77.78/10.59 (( 77.78/10.59 (notequalI2) => 77.78/10.59 (( 77.78/10.59 (subsetRefl) => 77.78/10.59 (( 77.78/10.59 (subsetTrans) => 77.78/10.59 (( 77.78/10.59 (setadjoinSub) => 77.78/10.59 (( 77.78/10.59 (setadjoinSub2) => 77.78/10.59 (( 77.78/10.59 (subset2powerset) => 77.78/10.59 (( 77.78/10.59 (setextsub) => 77.78/10.59 (( 77.78/10.59 (subsetemptysetimpeq) => 77.78/10.59 (( 77.78/10.59 (powersetI1) => 77.78/10.59 (( 77.78/10.59 (powersetE1) => 77.78/10.59 (( 77.78/10.59 (inPowerset) => 77.78/10.59 (( 77.78/10.59 (powersetsubset) => 77.78/10.59 (( 77.78/10.59 (sepInPowerset) => 77.78/10.59 (( 77.78/10.59 (sepSubset) => 77.78/10.59 (( 77.78/10.59 (binunionIL) => 77.78/10.59 (( 77.78/10.59 (upairset2IR) => 77.78/10.59 (( 77.78/10.59 (binunionIR) => 77.78/10.59 (( 77.78/10.59 (binunionEcases) => 77.78/10.59 (( 77.78/10.59 (binunionE) => 77.78/10.59 (( 77.78/10.59 (binunionLsub) => 77.78/10.59 (( 77.78/10.59 (binunionRsub) => 77.78/10.59 (( 77.78/10.59 (binintersectI) => 77.78/10.59 (( 77.78/10.59 (binintersectSubset5) => 77.78/10.59 (( 77.78/10.59 (binintersectEL) => 77.78/10.59 (( 77.78/10.59 (binintersectLsub) => 77.78/10.59 (( 77.78/10.59 (binintersectSubset2) => 77.78/10.59 (( 77.78/10.59 (binintersectSubset3) => 77.78/10.59 (( 77.78/10.59 (binintersectER) => 77.78/10.59 (( 77.78/10.59 (disjointsetsI1) => 77.78/10.59 (( 77.78/10.59 (binintersectRsub) => 77.78/10.59 (( 77.78/10.59 (binintersectSubset4) => 77.78/10.59 (( 77.78/10.59 (binintersectSubset1) => 77.78/10.59 (( 77.78/10.59 (bs114d) => 77.78/10.59 (( 77.78/10.59 (setminusI) => 77.78/10.59 (( 77.78/10.59 (setminusEL) => 77.78/10.59 (( 77.78/10.59 (setminusER) => 77.78/10.59 (( 77.78/10.59 (setminusSubset2) => 77.78/10.59 (( 77.78/10.59 (setminusERneg) => 77.78/10.59 (( 77.78/10.59 (setminusELneg) => 77.78/10.59 (( 77.78/10.59 (setminusILneg) => 77.78/10.59 (( 77.78/10.59 (setminusIRneg) => 77.78/10.59 (( 77.78/10.59 (setminusLsub) => 77.78/10.59 (( 77.78/10.59 (setminusSubset1) => 77.78/10.59 (( 77.78/10.59 (symdiffE) => 77.78/10.59 (( 77.78/10.59 (symdiffI1) => 77.78/10.59 (( 77.78/10.59 (symdiffI2) => 77.78/10.59 (( 77.78/10.59 (symdiffIneg1) => 77.78/10.59 (( 77.78/10.59 (symdiffIneg2) => 77.78/10.59 (( 77.78/10.59 (secondinupair) => 77.78/10.59 (( 77.78/10.59 (setukpairIL) => 77.78/10.59 (( 77.78/10.59 (setukpairIR) => 77.78/10.59 (( 77.78/10.59 (kpairiskpair) => 77.78/10.59 (( 77.78/10.59 (kpairp) => 77.78/10.59 (( 77.78/10.59 (singletonsubset) => 77.78/10.59 (( 77.78/10.59 (singletoninpowerset) => 77.78/10.59 (( 77.78/10.59 (singletoninpowunion) => 77.78/10.59 (( 77.78/10.59 (upairset2E) => 77.78/10.59 (( 77.78/10.59 (upairsubunion) => 77.78/10.59 (( 77.78/10.59 (upairinpowunion) => 77.78/10.59 (( 77.78/10.59 (ubforcartprodlem1) => 77.78/10.59 (( 77.78/10.59 (ubforcartprodlem2) => 77.78/10.59 (( 77.78/10.59 (ubforcartprodlem3) => 77.78/10.59 (( 77.78/10.59 (cartprodpairin) => 77.78/10.59 (( 77.78/10.59 (cartprodmempair1) => 77.78/10.59 (( 77.78/10.59 (cartprodmempair) => 77.78/10.59 (( 77.78/10.59 (setunionE2) => 77.78/10.59 (( 77.78/10.59 (setunionsingleton1) => 77.78/10.59 (( 77.78/10.59 (setunionsingleton2) => 77.78/10.59 (( 77.78/10.59 (setunionsingleton) => 77.78/10.59 (( 77.78/10.59 (singletonprop) => 77.78/10.59 (( 77.78/10.59 (ex1E1) => 77.78/10.59 (( 77.78/10.59 (ex1I) => 77.78/10.59 (( 77.78/10.59 (ex1I2) => 77.78/10.59 (( 77.78/10.59 (singletonsuniq) => 77.78/10.59 (( 77.78/10.59 (setukpairinjL1) => 77.78/10.59 (( 77.78/10.59 (kfstsingleton) => 77.78/10.59 (( 77.78/10.59 (theprop) => 77.78/10.59 (( 77.78/10.59 (kfstpairEq) => 77.78/10.59 (( 77.78/10.59 (cartprodfstin) => 77.78/10.59 (( 77.78/10.59 (setukpairinjL2) => 77.78/10.59 (( 77.78/10.59 (setukpairinjL) => 77.78/10.59 (( 77.78/10.59 (setukpairinjR11) => 77.78/10.59 (( 77.78/10.59 (setukpairinjR12) => 77.78/10.59 (( 77.78/10.59 (setukpairinjR1) => 77.78/10.59 (( 77.78/10.59 (upairequniteq) => 77.78/10.59 (( 77.78/10.59 (setukpairinjR2) => 77.78/10.59 (( 77.78/10.59 (setukpairinjR) => 77.78/10.59 (( 77.78/10.59 (ksndsingleton) => 77.78/10.59 (( 77.78/10.59 (ksndpairEq) => 77.78/10.59 (( 77.78/10.59 (kpairsurjEq) => 77.78/10.59 (( 77.78/10.59 (cartprodsndin) => 77.78/10.59 (( 77.78/10.59 (cartprodpairmemEL) => 77.78/10.59 (( 77.78/10.59 (cartprodpairmemER) => 77.78/10.59 (( 77.78/10.59 (cartprodmempaircEq) => 77.78/10.59 (( 77.78/10.59 (cartprodfstpairEq) => 77.78/10.59 (( 77.78/10.59 (cartprodsndpairEq) => 77.78/10.59 (( 77.78/10.59 (cartprodpairsurjEq) => 77.78/10.59 (( 77.78/10.59 (dpsetconstrI) => 77.78/10.59 (( 77.78/10.59 (dpsetconstrSub) => 77.78/10.59 (( 77.78/10.59 (setOfPairsIsBReln) => 77.78/10.59 (( 77.78/10.59 (dpsetconstrERa) => 77.78/10.59 (( 77.78/10.59 (dpsetconstrEL1) => 77.78/10.59 (( 77.78/10.59 (dpsetconstrEL2) => 77.78/10.59 (( 77.78/10.59 (dpsetconstrER) => 77.78/10.59 (( 77.78/10.59 (funcImageSingleton) => 77.78/10.59 (( 77.78/10.59 (apProp) => 77.78/10.59 (( 77.78/10.59 (app) => 77.78/10.59 (( 77.78/10.59 (infuncsetfunc) => 77.78/10.59 (( 77.78/10.59 (ap2p) => 77.78/10.59 (( 77.78/10.59 (funcinfuncset) => 77.78/10.59 (( 77.78/10.59 (lamProp) => 77.78/10.59 (( 77.78/10.59 (lamp) => 77.78/10.59 (( 77.78/10.59 (lam2p) => 77.78/10.59 (( 77.78/10.59 (brelnall1) => 77.78/10.59 (( 77.78/10.59 (brelnall2) => 77.78/10.59 (( 77.78/10.59 (ex1E2) => 77.78/10.59 (( 77.78/10.59 (funcGraphProp1) => 77.78/10.59 (( 77.78/10.59 (funcGraphProp3) => 77.78/10.59 (( 77.78/10.59 (funcGraphProp2) => 77.78/10.59 (( 77.78/10.59 (funcextLem) => 77.78/10.59 (( 77.78/10.59 (funcGraphProp4) => 77.78/10.59 (( 77.78/10.59 (subbreln) => 77.78/10.59 (( 77.78/10.59 (eqbreln) => 77.78/10.59 (( 77.78/10.59 (funcext) => 77.78/10.59 (( 77.78/10.59 (funcext2) => 77.78/10.59 (( 77.78/10.59 (ap2apEq1) => 77.78/10.59 (( 77.78/10.59 (ap2apEq2) => 77.78/10.59 (( 77.78/10.59 (beta1) => 77.78/10.59 (( 77.78/10.59 (eta1) => 77.78/10.59 (( 77.78/10.59 (lam2lamEq) => 77.78/10.59 (( 77.78/10.59 (beta2) => 77.78/10.59 (( 77.78/10.59 (eta2) => 77.78/10.59 (( 77.78/10.59 (iffalseProp1) => 77.78/10.59 (( 77.78/10.59 (iffalseProp2) => 77.78/10.59 (( 77.78/10.59 (iftrueProp1) => 77.78/10.59 (( 77.78/10.59 (iftrueProp2) => 77.78/10.59 (( 77.78/10.59 (ifSingleton) => 77.78/10.59 (( 77.78/10.59 (ifp) => 77.78/10.59 (( 77.78/10.59 (theeq) => 77.78/10.59 (( 77.78/10.59 (iftrue) => 77.78/10.59 (( 77.78/10.59 (iffalse) => 77.78/10.59 (( 77.78/10.59 (iftrueorfalse) => 77.78/10.59 (( 77.78/10.59 (binintersectT_lem) => 77.78/10.59 (( 77.78/10.59 (binunionT_lem) => 77.78/10.59 (( 77.78/10.59 (powersetT_lem) => 77.78/10.59 (( 77.78/10.59 (setminusT_lem) => 77.78/10.59 (( 77.78/10.59 (complementT_lem) => 77.78/10.59 (( 77.78/10.59 (setextT) => 77.78/10.59 (( 77.78/10.59 (subsetTI) => 77.78/10.59 (( 77.78/10.59 (powersetTI1) => 77.78/10.59 (( 77.78/10.59 (powersetTE1) => 77.78/10.59 (( 77.78/10.59 (complementTI1) => 77.78/10.59 (( 77.78/10.59 (complementTE1) => 77.78/10.59 (( 77.78/10.59 (binintersectTELcontra) => 77.78/10.59 (( 77.78/10.59 (binintersectTERcontra) => 77.78/10.59 (( 77.78/10.59 (contrasubsetT) => 77.78/10.59 (( 77.78/10.59 (contrasubsetT1) => 77.78/10.59 (( 77.78/10.59 (contrasubsetT2) => 77.78/10.59 (( 77.78/10.59 (contrasubsetT3) => 77.78/10.59 (( 77.78/10.59 (doubleComplementI1) => 77.78/10.59 (( 77.78/10.59 (doubleComplementE1) => 77.78/10.59 (( 77.78/10.59 (doubleComplementSub1) => 77.78/10.59 (( 77.78/10.59 (doubleComplementSub2) => 77.78/10.59 (( 77.78/10.59 (doubleComplementEq) => 77.78/10.59 (( 77.78/10.59 (complementTnotintersectT) => 77.78/10.59 (( 77.78/10.59 (complementImpComplementIntersect) => 77.78/10.59 (( 77.78/10.59 (complementSubsetComplementIntersect) => 77.78/10.59 (( 77.78/10.59 (complementInPowersetComplementIntersect) => 77.78/10.59 (( 77.78/10.59 (contraSubsetComplement) => 77.78/10.59 (( 77.78/10.59 (complementTcontraSubset) => 77.78/10.59 (( 77.78/10.59 (binunionTILcontra) => 77.78/10.59 (( 77.78/10.59 (binunionTIRcontra) => 77.78/10.59 (( 77.78/10.59 (inIntersectImpInUnion) => 77.78/10.59 (( 77.78/10.59 (inIntersectImpInUnion2) => 77.78/10.59 (( 77.78/10.59 (inIntersectImpInIntersectUnions) => 77.78/10.59 (( 77.78/10.59 (intersectInPowersetIntersectUnions) => 77.78/10.59 (( 77.78/10.59 (inComplementUnionImpNotIn1) => 77.78/10.59 (( 77.78/10.59 (inComplementUnionImpInComplement1) => 77.78/10.59 (( 77.78/10.59 (binunionTE) => 77.78/10.59 (( 77.78/10.59 (binunionTEcontra) => 77.78/10.59 (( 77.78/10.59 (demorgan2a1) => 77.78/10.59 (( 77.78/10.59 (complementUnionInPowersetComplement) => 77.78/10.59 (( 77.78/10.59 (demorgan2a2) => 77.78/10.59 (( 77.78/10.59 (demorgan1a) => 77.78/10.59 (( 77.78/10.59 (demorgan1b) => 77.78/10.59 (( 77.78/10.59 (demorgan1) => 77.78/10.59 (( 77.78/10.59 (demorgan2a) => 77.78/10.59 (( 77.78/10.59 (demorgan2b2) => 77.78/10.59 (( 77.78/10.59 (demorgan2b) => 77.78/10.59 (( 77.78/10.59 (demorgan2) => 77.78/10.59 (( 77.78/10.59 (woz13rule0) => 77.78/10.59 (( 77.78/10.59 (woz13rule1) => 77.78/10.59 (( 77.78/10.59 (woz13rule2) => 77.78/10.59 (( 77.78/10.59 (woz13rule3) => 77.78/10.59 (( 77.78/10.59 (woz13rule4) => 77.78/10.59 (( 77.78/10.59 (woz1_1) => 77.78/10.59 (( 77.78/10.59 (woz1_2) => 77.78/10.59 (( 77.78/10.59 (woz1_3) => 77.78/10.59 (( 77.78/10.59 (woz1_4) => 77.78/10.59 (( 77.78/10.59 (woz1_5) => 77.78/10.59 (( 77.78/10.59 (breln1all2) => 77.78/10.59 (( 77.78/10.59 (breln1SetBreln1) => 77.78/10.59 (( 77.78/10.59 (choice2fnsingleton) => 77.78/10.59 (( 77.78/10.59 (setOfPairsIsBReln1) => 77.78/10.59 (( 77.78/10.59 (breln1all1) => 77.78/10.59 (( 77.78/10.59 (subbreln1) => 77.78/10.59 (( 77.78/10.59 (eqbreln1) => 77.78/10.59 (( 77.78/10.59 (breln1invprop) => 77.78/10.59 (( 77.78/10.59 (breln1invI) => 77.78/10.59 (( 77.78/10.59 (breln1invE) => 77.78/10.59 (( 77.78/10.59 (breln1compprop) => 77.78/10.59 (( 77.78/10.59 (breln1compI) => 77.78/10.59 (( 77.78/10.59 (breln1compE) => 77.78/10.59 (( 77.78/10.59 (breln1compEex) => 77.78/10.59 (( 77.78/10.59 (breln1unionprop) => 77.78/10.59 (( 77.78/10.59 (breln1unionIL) => 77.78/10.59 (( 77.78/10.59 (breln1unionIR) => 77.78/10.59 (( 77.78/10.59 (breln1unionI) => 77.78/10.59 (( 77.78/10.59 (breln1unionE) => 77.78/10.59 (( 77.78/10.59 (breln1unionEcases) => 77.78/10.59 (( 77.78/10.59 (breln1unionCommutes) => 77.78/10.59 (( 77.78/10.59 (woz2Ex) => 77.78/10.59 (( 77.78/10.59 (woz2W) => 77.78/10.59 (( 77.78/10.59 (woz2A) => 77.78/10.59 (( 77.78/10.59 (woz2B) => 77.78/10.59 (( 77.78/10.59 (image1Ex) => 77.78/10.59 (( 77.78/10.59 (image1Ex1) => 77.78/10.59 (( 77.78/10.59 (image1Equiv) => 77.78/10.59 (( 77.78/10.59 (image1E) => 77.78/10.59 (( 77.78/10.59 (image1I) => 77.78/10.59 (( 77.78/10.59 (injFuncInInjFuncSet) => 77.78/10.59 (( 77.78/10.59 (injFuncSetFuncIn) => 77.78/10.59 (( 77.78/10.59 (injFuncSetFuncInj) => 77.78/10.59 (( 77.78/10.59 (surjFuncSetFuncIn) => 77.78/10.59 (( 77.78/10.59 (surjFuncSetFuncSurj) => 77.78/10.59 (( 77.78/10.59 (leftInvIsSurj) => 77.78/10.59 (( 77.78/10.59 (surjCantorThm) => 77.78/10.59 (( 77.78/10.59 (foundation2) => 77.78/10.59 (( 77.78/10.59 (notinself) => 77.78/10.59 (( 77.78/10.59 (notinself2) => 77.78/10.59 (( 77.78/10.59 (omegaSp) => 77.78/10.59 (( 77.78/10.59 (omegaSclos) => 77.78/10.59 (( 77.78/10.59 (peano0notS) => 77.78/10.59 (( 77.78/10.59 (peanoSinj) => 77.78/10.59 (( 77.78/10.59 (transitivesetOp1) => 77.78/10.59 (( 77.78/10.59 (binintTransitive) => 77.78/10.59 (( 77.78/10.59 (transitivesetOp2) => 77.78/10.59 (( 77.78/10.59 (setunionTransitive) => 77.78/10.59 (( 77.78/10.59 (ordinalMinLem1) => 77.78/10.59 (( 77.78/10.59 (!!) @ ( 77.78/10.59 ^[Y0 : $i]: 77.78/10.59 (( 77.78/10.59 (ordinal @ 77.78/10.59 Y0) => 77.78/10.59 (( 77.78/10.59 (!!) @ ( 77.78/10.59 ^[Y1 : $i]: 77.78/10.59 (( 77.78/10.59 (!!) @ ( 77.78/10.59 ^[Y2 : $i]: 77.78/10.59 (( 77.78/10.59 (in @ 77.78/10.59 Y2 @ 77.78/10.59 Y0) => 77.78/10.59 (( 77.78/10.59 (in @ 77.78/10.59 Y1 @ 77.78/10.59 Y2) => 77.78/10.59 (in @ 77.78/10.59 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 77.78/10.59 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl357])). 77.78/10.59 thf(zip_derived_cl372, plain, 77.78/10.59 (~ (((subPowSU) => 77.78/10.59 (((exuE2) => 77.78/10.59 (((nonemptyImpWitness) => 77.78/10.59 (((uniqinunit) => 77.78/10.59 (((notinsingleton) => 77.78/10.59 (((eqinunit) => 77.78/10.59 (((singletonsswitch) => 77.78/10.59 (((upairsetE) => 77.78/10.59 (((upairsetIL) => 77.78/10.59 (((upairsetIR) => 77.78/10.59 (((emptyE1) => 77.78/10.59 (((vacuousDall) => 77.78/10.59 (((quantDeMorgan1) => 77.78/10.59 (((quantDeMorgan2) => 77.78/10.59 (((quantDeMorgan3) => 77.78/10.59 (((quantDeMorgan4) => 77.78/10.59 (((prop2setI) => 77.78/10.59 (((prop2set2propI) => 77.78/10.59 (((notdexE) => 77.78/10.59 (((notdallE) => 77.78/10.59 (((exuI1) => 77.78/10.59 (((exuI3) => 77.78/10.59 (((exuI2) => 77.78/10.59 (((inCongP) => 77.78/10.59 (((in__Cong) => 77.78/10.59 (((exuE3u) => 77.78/10.59 (((exu__Cong) => 77.78/10.59 (((setadjoin__Cong) => 77.78/10.59 (((powerset__Cong) => 77.78/10.59 (((setunion__Cong) => 77.78/10.59 (( 77.78/10.59 (exuEu) => 77.78/10.59 (( 77.78/10.59 (descr__Cong) => 77.78/10.59 (( 77.78/10.59 (dsetconstr__Cong) => 77.78/10.59 (( 77.78/10.59 (subsetI1) => 77.78/10.59 (( 77.78/10.59 (eqimpsubset2) => 77.78/10.59 (( 77.78/10.59 (eqimpsubset1) => 77.78/10.59 (( 77.78/10.59 (subsetI2) => 77.78/10.59 (( 77.78/10.59 (emptysetsubset) => 77.78/10.59 (( 77.78/10.59 (subsetE) => 77.78/10.59 (( 77.78/10.59 (subsetE2) => 77.78/10.59 (( 77.78/10.59 (notsubsetI) => 77.78/10.59 (( 77.78/10.59 (notequalI1) => 77.78/10.59 (( 77.78/10.59 (notequalI2) => 77.78/10.59 (( 77.78/10.59 (subsetRefl) => 77.78/10.59 (( 77.78/10.59 (subsetTrans) => 77.78/10.59 (( 77.78/10.59 (setadjoinSub) => 77.78/10.59 (( 77.78/10.59 (setadjoinSub2) => 77.78/10.59 (( 77.78/10.59 (subset2powerset) => 77.78/10.59 (( 77.78/10.59 (setextsub) => 77.78/10.59 (( 77.78/10.59 (subsetemptysetimpeq) => 77.78/10.59 (( 77.78/10.59 (powersetI1) => 77.78/10.59 (( 77.78/10.59 (powersetE1) => 77.78/10.59 (( 77.78/10.59 (inPowerset) => 77.78/10.59 (( 77.78/10.59 (powersetsubset) => 77.78/10.59 (( 77.78/10.59 (sepInPowerset) => 77.78/10.59 (( 77.78/10.59 (sepSubset) => 77.78/10.59 (( 77.78/10.59 (binunionIL) => 77.78/10.59 (( 77.78/10.59 (upairset2IR) => 77.78/10.59 (( 77.78/10.59 (binunionIR) => 77.78/10.59 (( 77.78/10.59 (binunionEcases) => 77.78/10.59 (( 77.78/10.59 (binunionE) => 77.78/10.59 (( 77.78/10.59 (binunionLsub) => 77.78/10.59 (( 77.78/10.59 (binunionRsub) => 77.78/10.59 (( 77.78/10.59 (binintersectI) => 77.78/10.59 (( 77.78/10.59 (binintersectSubset5) => 77.78/10.59 (( 77.78/10.59 (binintersectEL) => 77.78/10.59 (( 77.78/10.59 (binintersectLsub) => 77.78/10.59 (( 77.78/10.59 (binintersectSubset2) => 77.78/10.59 (( 77.78/10.59 (binintersectSubset3) => 77.78/10.59 (( 77.78/10.59 (binintersectER) => 77.78/10.59 (( 77.78/10.59 (disjointsetsI1) => 77.78/10.59 (( 77.78/10.59 (binintersectRsub) => 77.78/10.59 (( 77.78/10.59 (binintersectSubset4) => 77.78/10.59 (( 77.78/10.59 (binintersectSubset1) => 77.78/10.59 (( 77.78/10.59 (bs114d) => 77.78/10.59 (( 77.78/10.59 (setminusI) => 77.78/10.59 (( 77.78/10.59 (setminusEL) => 77.78/10.59 (( 77.78/10.59 (setminusER) => 77.78/10.59 (( 77.78/10.59 (setminusSubset2) => 77.78/10.59 (( 77.78/10.59 (setminusERneg) => 77.78/10.59 (( 77.78/10.59 (setminusELneg) => 77.78/10.59 (( 77.78/10.59 (setminusILneg) => 77.78/10.59 (( 77.78/10.59 (setminusIRneg) => 77.78/10.59 (( 77.78/10.59 (setminusLsub) => 77.78/10.59 (( 77.78/10.59 (setminusSubset1) => 77.78/10.59 (( 77.78/10.59 (symdiffE) => 77.78/10.59 (( 77.78/10.59 (symdiffI1) => 77.78/10.59 (( 77.78/10.59 (symdiffI2) => 77.78/10.59 (( 77.78/10.59 (symdiffIneg1) => 77.78/10.59 (( 77.78/10.59 (symdiffIneg2) => 77.78/10.59 (( 77.78/10.59 (secondinupair) => 77.78/10.59 (( 77.78/10.59 (setukpairIL) => 77.78/10.59 (( 77.78/10.59 (setukpairIR) => 77.78/10.59 (( 77.78/10.59 (kpairiskpair) => 77.78/10.59 (( 77.78/10.59 (kpairp) => 77.78/10.59 (( 77.78/10.59 (singletonsubset) => 77.78/10.59 (( 77.78/10.59 (singletoninpowerset) => 77.78/10.59 (( 77.78/10.59 (singletoninpowunion) => 77.78/10.59 (( 77.78/10.59 (upairset2E) => 77.78/10.59 (( 77.78/10.59 (upairsubunion) => 77.78/10.59 (( 77.78/10.59 (upairinpowunion) => 77.78/10.59 (( 77.78/10.59 (ubforcartprodlem1) => 77.78/10.59 (( 77.78/10.59 (ubforcartprodlem2) => 77.78/10.59 (( 77.78/10.59 (ubforcartprodlem3) => 77.78/10.59 (( 77.78/10.59 (cartprodpairin) => 77.78/10.59 (( 77.78/10.59 (cartprodmempair1) => 77.78/10.59 (( 77.78/10.59 (cartprodmempair) => 77.78/10.59 (( 77.78/10.59 (setunionE2) => 77.78/10.59 (( 77.78/10.59 (setunionsingleton1) => 77.78/10.59 (( 77.78/10.59 (setunionsingleton2) => 77.78/10.59 (( 77.78/10.59 (setunionsingleton) => 77.78/10.59 (( 77.78/10.59 (singletonprop) => 77.78/10.59 (( 77.78/10.59 (ex1E1) => 77.78/10.59 (( 77.78/10.59 (ex1I) => 77.78/10.59 (( 77.78/10.59 (ex1I2) => 77.78/10.59 (( 77.78/10.59 (singletonsuniq) => 77.78/10.59 (( 77.78/10.59 (setukpairinjL1) => 77.78/10.59 (( 77.78/10.59 (kfstsingleton) => 77.78/10.59 (( 77.78/10.59 (theprop) => 77.78/10.59 (( 77.78/10.59 (kfstpairEq) => 77.78/10.59 (( 77.78/10.59 (cartprodfstin) => 77.78/10.59 (( 77.78/10.59 (setukpairinjL2) => 77.78/10.59 (( 77.78/10.59 (setukpairinjL) => 77.78/10.59 (( 77.78/10.59 (setukpairinjR11) => 77.78/10.59 (( 77.78/10.59 (setukpairinjR12) => 77.78/10.59 (( 77.78/10.59 (setukpairinjR1) => 77.78/10.59 (( 77.78/10.59 (upairequniteq) => 77.78/10.59 (( 77.78/10.59 (setukpairinjR2) => 77.78/10.59 (( 77.78/10.59 (setukpairinjR) => 77.78/10.59 (( 77.78/10.59 (ksndsingleton) => 77.78/10.59 (( 77.78/10.59 (ksndpairEq) => 77.78/10.59 (( 77.78/10.59 (kpairsurjEq) => 77.78/10.59 (( 77.78/10.59 (cartprodsndin) => 77.78/10.59 (( 77.78/10.59 (cartprodpairmemEL) => 77.78/10.59 (( 77.78/10.59 (cartprodpairmemER) => 77.78/10.59 (( 77.78/10.59 (cartprodmempaircEq) => 77.78/10.59 (( 77.78/10.59 (cartprodfstpairEq) => 77.78/10.59 (( 77.78/10.59 (cartprodsndpairEq) => 77.78/10.59 (( 77.78/10.59 (cartprodpairsurjEq) => 77.78/10.59 (( 77.78/10.59 (dpsetconstrI) => 77.78/10.59 (( 77.78/10.59 (dpsetconstrSub) => 77.78/10.59 (( 77.78/10.59 (setOfPairsIsBReln) => 77.78/10.59 (( 77.78/10.59 (dpsetconstrERa) => 77.78/10.59 (( 77.78/10.59 (dpsetconstrEL1) => 77.78/10.59 (( 77.78/10.59 (dpsetconstrEL2) => 77.78/10.59 (( 77.78/10.59 (dpsetconstrER) => 77.78/10.59 (( 77.78/10.59 (funcImageSingleton) => 77.78/10.59 (( 77.78/10.59 (apProp) => 77.78/10.59 (( 77.78/10.59 (app) => 77.78/10.59 (( 77.78/10.59 (infuncsetfunc) => 77.78/10.59 (( 77.78/10.59 (ap2p) => 77.78/10.59 (( 77.78/10.59 (funcinfuncset) => 77.78/10.59 (( 77.78/10.59 (lamProp) => 77.78/10.59 (( 77.78/10.59 (lamp) => 77.78/10.59 (( 77.78/10.59 (lam2p) => 77.78/10.59 (( 77.78/10.59 (brelnall1) => 77.78/10.59 (( 77.78/10.59 (brelnall2) => 77.78/10.59 (( 77.78/10.59 (ex1E2) => 77.78/10.59 (( 77.78/10.59 (funcGraphProp1) => 77.78/10.59 (( 77.78/10.59 (funcGraphProp3) => 77.78/10.59 (( 77.78/10.59 (funcGraphProp2) => 77.78/10.59 (( 77.78/10.59 (funcextLem) => 77.78/10.59 (( 77.78/10.59 (funcGraphProp4) => 77.78/10.59 (( 77.78/10.59 (subbreln) => 77.78/10.59 (( 77.78/10.59 (eqbreln) => 77.78/10.59 (( 77.78/10.59 (funcext) => 77.78/10.59 (( 77.78/10.59 (funcext2) => 77.78/10.59 (( 77.78/10.59 (ap2apEq1) => 77.78/10.59 (( 77.78/10.59 (ap2apEq2) => 77.78/10.59 (( 77.78/10.59 (beta1) => 77.78/10.59 (( 77.78/10.59 (eta1) => 77.78/10.59 (( 77.78/10.59 (lam2lamEq) => 77.78/10.59 (( 77.78/10.59 (beta2) => 77.78/10.59 (( 77.78/10.59 (eta2) => 77.78/10.59 (( 77.78/10.59 (iffalseProp1) => 77.78/10.59 (( 77.78/10.59 (iffalseProp2) => 77.78/10.59 (( 77.78/10.59 (iftrueProp1) => 77.78/10.59 (( 77.78/10.59 (iftrueProp2) => 77.78/10.59 (( 77.78/10.59 (ifSingleton) => 77.78/10.59 (( 77.78/10.59 (ifp) => 77.78/10.59 (( 77.78/10.59 (theeq) => 77.78/10.59 (( 77.78/10.59 (iftrue) => 77.78/10.59 (( 77.78/10.59 (iffalse) => 77.78/10.59 (( 77.78/10.59 (iftrueorfalse) => 77.78/10.59 (( 77.78/10.59 (binintersectT_lem) => 77.78/10.59 (( 77.78/10.59 (binunionT_lem) => 77.78/10.59 (( 77.78/10.59 (powersetT_lem) => 77.78/10.59 (( 77.78/10.59 (setminusT_lem) => 77.78/10.59 (( 77.78/10.59 (complementT_lem) => 77.78/10.59 (( 77.78/10.59 (setextT) => 77.78/10.59 (( 77.78/10.59 (subsetTI) => 77.78/10.59 (( 77.78/10.59 (powersetTI1) => 77.78/10.59 (( 77.78/10.59 (powersetTE1) => 77.78/10.59 (( 77.78/10.59 (complementTI1) => 77.78/10.59 (( 77.78/10.59 (complementTE1) => 77.78/10.59 (( 77.78/10.59 (binintersectTELcontra) => 77.78/10.59 (( 77.78/10.59 (binintersectTERcontra) => 77.78/10.59 (( 77.78/10.59 (contrasubsetT) => 77.78/10.59 (( 77.78/10.59 (contrasubsetT1) => 77.78/10.59 (( 77.78/10.59 (contrasubsetT2) => 77.78/10.59 (( 77.78/10.59 (contrasubsetT3) => 77.78/10.59 (( 77.78/10.59 (doubleComplementI1) => 77.78/10.59 (( 77.78/10.59 (doubleComplementE1) => 77.78/10.59 (( 77.78/10.59 (doubleComplementSub1) => 77.78/10.59 (( 77.78/10.59 (doubleComplementSub2) => 77.78/10.59 (( 77.78/10.59 (doubleComplementEq) => 77.78/10.59 (( 77.78/10.59 (complementTnotintersectT) => 77.78/10.59 (( 77.78/10.59 (complementImpComplementIntersect) => 77.78/10.59 (( 77.78/10.59 (complementSubsetComplementIntersect) => 77.78/10.59 (( 77.78/10.59 (complementInPowersetComplementIntersect) => 77.78/10.59 (( 77.78/10.59 (contraSubsetComplement) => 77.78/10.59 (( 77.78/10.59 (complementTcontraSubset) => 77.78/10.59 (( 77.78/10.59 (binunionTILcontra) => 77.78/10.59 (( 77.78/10.59 (binunionTIRcontra) => 77.78/10.59 (( 77.78/10.59 (inIntersectImpInUnion) => 77.78/10.59 (( 77.78/10.59 (inIntersectImpInUnion2) => 77.78/10.59 (( 77.78/10.59 (inIntersectImpInIntersectUnions) => 77.78/10.59 (( 77.78/10.59 (intersectInPowersetIntersectUnions) => 77.78/10.59 (( 77.78/10.59 (inComplementUnionImpNotIn1) => 77.78/10.59 (( 77.78/10.59 (inComplementUnionImpInComplement1) => 77.78/10.59 (( 77.78/10.59 (binunionTE) => 77.78/10.59 (( 77.78/10.59 (binunionTEcontra) => 77.78/10.59 (( 77.78/10.59 (demorgan2a1) => 77.78/10.59 (( 77.78/10.59 (complementUnionInPowersetComplement) => 77.78/10.59 (( 77.78/10.59 (demorgan2a2) => 77.78/10.59 (( 77.78/10.59 (demorgan1a) => 77.78/10.59 (( 77.78/10.59 (demorgan1b) => 77.78/10.59 (( 77.78/10.59 (demorgan1) => 77.78/10.59 (( 77.78/10.59 (demorgan2a) => 77.78/10.59 (( 77.78/10.59 (demorgan2b2) => 77.78/10.59 (( 77.78/10.59 (demorgan2b) => 77.78/10.59 (( 77.78/10.59 (demorgan2) => 77.78/10.59 (( 77.78/10.59 (woz13rule0) => 77.78/10.59 (( 77.78/10.59 (woz13rule1) => 77.78/10.59 (( 77.78/10.59 (woz13rule2) => 77.78/10.59 (( 77.78/10.59 (woz13rule3) => 77.78/10.59 (( 77.78/10.59 (woz13rule4) => 77.78/10.59 (( 77.78/10.59 (woz1_1) => 77.78/10.59 (( 77.78/10.59 (woz1_2) => 77.78/10.59 (( 77.78/10.59 (woz1_3) => 77.78/10.59 (( 77.78/10.59 (woz1_4) => 77.78/10.59 (( 77.78/10.59 (woz1_5) => 77.78/10.59 (( 77.78/10.59 (breln1all2) => 77.78/10.59 (( 77.78/10.59 (breln1SetBreln1) => 77.78/10.59 (( 77.78/10.59 (choice2fnsingleton) => 77.78/10.59 (( 77.78/10.59 (setOfPairsIsBReln1) => 77.78/10.59 (( 77.78/10.59 (breln1all1) => 77.78/10.59 (( 77.78/10.59 (subbreln1) => 77.78/10.59 (( 77.78/10.59 (eqbreln1) => 77.78/10.59 (( 77.78/10.59 (breln1invprop) => 77.78/10.59 (( 77.78/10.59 (breln1invI) => 77.78/10.59 (( 77.78/10.59 (breln1invE) => 77.78/10.59 (( 77.78/10.59 (breln1compprop) => 77.78/10.59 (( 77.78/10.59 (breln1compI) => 77.78/10.59 (( 77.78/10.59 (breln1compE) => 77.78/10.59 (( 77.78/10.59 (breln1compEex) => 77.78/10.59 (( 77.78/10.59 (breln1unionprop) => 77.78/10.59 (( 77.78/10.59 (breln1unionIL) => 77.78/10.59 (( 77.78/10.59 (breln1unionIR) => 77.78/10.59 (( 77.78/10.59 (breln1unionI) => 77.78/10.59 (( 77.78/10.59 (breln1unionE) => 77.78/10.59 (( 77.78/10.59 (breln1unionEcases) => 77.78/10.59 (( 77.78/10.59 (breln1unionCommutes) => 77.78/10.59 (( 77.78/10.59 (woz2Ex) => 77.78/10.59 (( 77.78/10.59 (woz2W) => 77.78/10.59 (( 77.78/10.59 (woz2A) => 77.78/10.59 (( 77.78/10.59 (woz2B) => 77.78/10.59 (( 77.78/10.59 (image1Ex) => 77.78/10.59 (( 77.78/10.59 (image1Ex1) => 77.78/10.59 (( 77.78/10.59 (image1Equiv) => 77.78/10.59 (( 77.78/10.59 (image1E) => 77.78/10.59 (( 77.78/10.59 (image1I) => 77.78/10.59 (( 77.78/10.59 (injFuncInInjFuncSet) => 77.78/10.59 (( 77.78/10.59 (injFuncSetFuncIn) => 77.78/10.59 (( 77.78/10.59 (injFuncSetFuncInj) => 77.78/10.59 (( 77.78/10.59 (surjFuncSetFuncIn) => 77.78/10.59 (( 77.78/10.59 (surjFuncSetFuncSurj) => 77.78/10.59 (( 77.78/10.59 (leftInvIsSurj) => 77.78/10.59 (( 77.78/10.59 (surjCantorThm) => 77.78/10.59 (( 77.78/10.59 (foundation2) => 77.78/10.59 (( 77.78/10.59 (notinself) => 77.78/10.59 (( 77.78/10.59 (notinself2) => 77.78/10.59 (( 77.78/10.59 (omegaSp) => 77.78/10.59 (( 77.78/10.59 (omegaSclos) => 77.78/10.59 (( 77.78/10.59 (peano0notS) => 77.78/10.59 (( 77.78/10.59 (peanoSinj) => 77.78/10.59 (( 77.78/10.59 (transitivesetOp1) => 77.78/10.59 (( 77.78/10.59 (binintTransitive) => 77.78/10.59 (( 77.78/10.59 (transitivesetOp2) => 77.78/10.59 (( 77.78/10.59 (setunionTransitive) => 77.78/10.59 (( 77.78/10.59 (ordinalMinLem1) => 77.78/10.59 (( 77.78/10.59 (!!) @ ( 77.78/10.59 ^[Y0 : $i]: 77.78/10.59 (( 77.78/10.59 (ordinal @ 77.78/10.59 Y0) => 77.78/10.59 (( 77.78/10.59 (!!) @ ( 77.78/10.59 ^[Y1 : $i]: 77.78/10.59 (( 77.78/10.59 (!!) @ ( 77.78/10.59 ^[Y2 : $i]: 77.78/10.59 (( 77.78/10.59 (in @ 77.78/10.59 Y2 @ 77.78/10.59 Y0) => 77.78/10.59 (( 77.78/10.59 (in @ 77.78/10.59 Y1 @ 77.78/10.59 Y2) => 77.78/10.59 (in @ 77.78/10.59 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 77.78/10.59 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl364])). 77.78/10.59 thf(zip_derived_cl382, plain, 77.78/10.59 (~ (((exuE2) => 77.78/10.59 (((nonemptyImpWitness) => 77.78/10.59 (((uniqinunit) => 77.78/10.59 (((notinsingleton) => 77.78/10.59 (((eqinunit) => 77.78/10.59 (((singletonsswitch) => 77.78/10.59 (((upairsetE) => 77.78/10.59 (((upairsetIL) => 77.78/10.59 (((upairsetIR) => 77.78/10.59 (((emptyE1) => 77.78/10.59 (((vacuousDall) => 77.78/10.59 (((quantDeMorgan1) => 77.78/10.59 (((quantDeMorgan2) => 77.78/10.59 (((quantDeMorgan3) => 77.78/10.59 (((quantDeMorgan4) => 77.78/10.59 (((prop2setI) => 77.78/10.59 (((prop2set2propI) => 77.78/10.59 (((notdexE) => 77.78/10.59 (((notdallE) => 77.78/10.59 (((exuI1) => 77.78/10.59 (((exuI3) => 77.78/10.59 (((exuI2) => 77.78/10.59 (((inCongP) => 77.78/10.59 (((in__Cong) => 77.78/10.59 (((exuE3u) => 77.78/10.59 (((exu__Cong) => 77.78/10.59 (((setadjoin__Cong) => 77.78/10.59 (((powerset__Cong) => 77.78/10.59 (((setunion__Cong) => 77.78/10.59 (((exuEu) => 77.78/10.59 (( 77.78/10.59 (descr__Cong) => 77.78/10.59 (( 77.78/10.59 (dsetconstr__Cong) => 77.78/10.59 (( 77.78/10.59 (subsetI1) => 77.78/10.59 (( 77.78/10.59 (eqimpsubset2) => 77.78/10.59 (( 77.78/10.59 (eqimpsubset1) => 77.78/10.59 (( 77.78/10.59 (subsetI2) => 77.78/10.59 (( 77.78/10.59 (emptysetsubset) => 77.78/10.59 (( 77.78/10.59 (subsetE) => 77.78/10.59 (( 77.78/10.59 (subsetE2) => 77.78/10.59 (( 77.78/10.59 (notsubsetI) => 77.78/10.59 (( 77.78/10.59 (notequalI1) => 77.78/10.59 (( 77.78/10.59 (notequalI2) => 77.78/10.59 (( 77.78/10.59 (subsetRefl) => 77.78/10.59 (( 77.78/10.59 (subsetTrans) => 77.78/10.59 (( 77.78/10.59 (setadjoinSub) => 77.78/10.59 (( 77.78/10.59 (setadjoinSub2) => 77.78/10.59 (( 77.78/10.59 (subset2powerset) => 77.78/10.59 (( 77.78/10.59 (setextsub) => 77.78/10.59 (( 77.78/10.59 (subsetemptysetimpeq) => 77.78/10.59 (( 77.78/10.59 (powersetI1) => 77.78/10.59 (( 77.78/10.59 (powersetE1) => 77.78/10.59 (( 77.78/10.59 (inPowerset) => 77.78/10.59 (( 77.78/10.59 (powersetsubset) => 77.78/10.59 (( 77.78/10.59 (sepInPowerset) => 77.78/10.59 (( 77.78/10.59 (sepSubset) => 77.78/10.59 (( 77.78/10.59 (binunionIL) => 77.78/10.59 (( 77.78/10.59 (upairset2IR) => 77.78/10.59 (( 77.78/10.59 (binunionIR) => 77.78/10.59 (( 77.78/10.59 (binunionEcases) => 77.78/10.59 (( 77.78/10.59 (binunionE) => 77.78/10.59 (( 77.78/10.59 (binunionLsub) => 77.78/10.59 (( 77.78/10.59 (binunionRsub) => 77.78/10.59 (( 77.78/10.59 (binintersectI) => 77.78/10.59 (( 77.78/10.59 (binintersectSubset5) => 77.78/10.59 (( 77.78/10.59 (binintersectEL) => 77.78/10.59 (( 77.78/10.59 (binintersectLsub) => 77.78/10.59 (( 77.78/10.59 (binintersectSubset2) => 77.78/10.59 (( 77.78/10.59 (binintersectSubset3) => 77.78/10.59 (( 77.78/10.59 (binintersectER) => 77.78/10.59 (( 77.78/10.59 (disjointsetsI1) => 77.78/10.59 (( 77.78/10.59 (binintersectRsub) => 77.78/10.59 (( 77.78/10.59 (binintersectSubset4) => 77.78/10.59 (( 77.78/10.59 (binintersectSubset1) => 77.78/10.59 (( 77.78/10.59 (bs114d) => 77.78/10.59 (( 77.78/10.59 (setminusI) => 77.78/10.59 (( 77.78/10.59 (setminusEL) => 77.78/10.59 (( 77.78/10.59 (setminusER) => 77.78/10.59 (( 77.78/10.59 (setminusSubset2) => 77.78/10.59 (( 77.78/10.59 (setminusERneg) => 77.78/10.59 (( 77.78/10.59 (setminusELneg) => 77.78/10.59 (( 77.78/10.59 (setminusILneg) => 77.78/10.59 (( 77.78/10.59 (setminusIRneg) => 77.78/10.59 (( 77.78/10.59 (setminusLsub) => 77.78/10.59 (( 77.78/10.59 (setminusSubset1) => 77.78/10.59 (( 77.78/10.59 (symdiffE) => 77.78/10.59 (( 77.78/10.59 (symdiffI1) => 77.78/10.59 (( 77.78/10.59 (symdiffI2) => 77.78/10.59 (( 77.78/10.59 (symdiffIneg1) => 77.78/10.59 (( 77.78/10.59 (symdiffIneg2) => 77.78/10.59 (( 77.78/10.59 (secondinupair) => 77.78/10.59 (( 77.78/10.59 (setukpairIL) => 77.78/10.59 (( 77.78/10.59 (setukpairIR) => 77.78/10.59 (( 77.78/10.59 (kpairiskpair) => 77.78/10.59 (( 77.78/10.59 (kpairp) => 77.78/10.59 (( 77.78/10.59 (singletonsubset) => 77.78/10.59 (( 77.78/10.59 (singletoninpowerset) => 77.78/10.59 (( 77.78/10.59 (singletoninpowunion) => 77.78/10.59 (( 77.78/10.60 (upairset2E) => 77.78/10.60 (( 77.78/10.60 (upairsubunion) => 77.78/10.60 (( 77.78/10.60 (upairinpowunion) => 77.78/10.60 (( 77.78/10.60 (ubforcartprodlem1) => 77.78/10.60 (( 77.78/10.60 (ubforcartprodlem2) => 77.78/10.60 (( 77.78/10.60 (ubforcartprodlem3) => 77.78/10.60 (( 77.78/10.60 (cartprodpairin) => 77.78/10.60 (( 77.78/10.60 (cartprodmempair1) => 77.78/10.60 (( 77.78/10.60 (cartprodmempair) => 77.78/10.60 (( 77.78/10.60 (setunionE2) => 77.78/10.60 (( 77.78/10.60 (setunionsingleton1) => 77.78/10.60 (( 77.78/10.60 (setunionsingleton2) => 77.78/10.60 (( 77.78/10.60 (setunionsingleton) => 77.78/10.60 (( 77.78/10.60 (singletonprop) => 77.78/10.60 (( 77.78/10.60 (ex1E1) => 77.78/10.60 (( 77.78/10.60 (ex1I) => 77.78/10.60 (( 77.78/10.60 (ex1I2) => 77.78/10.60 (( 77.78/10.60 (singletonsuniq) => 77.78/10.60 (( 77.78/10.60 (setukpairinjL1) => 77.78/10.60 (( 77.78/10.60 (kfstsingleton) => 77.78/10.60 (( 77.78/10.60 (theprop) => 77.78/10.60 (( 77.78/10.60 (kfstpairEq) => 77.78/10.60 (( 77.78/10.60 (cartprodfstin) => 77.78/10.60 (( 77.78/10.60 (setukpairinjL2) => 77.78/10.60 (( 77.78/10.60 (setukpairinjL) => 77.78/10.60 (( 77.78/10.60 (setukpairinjR11) => 77.78/10.60 (( 77.78/10.60 (setukpairinjR12) => 77.78/10.60 (( 77.78/10.60 (setukpairinjR1) => 77.78/10.60 (( 77.78/10.60 (upairequniteq) => 77.78/10.60 (( 77.78/10.60 (setukpairinjR2) => 77.78/10.60 (( 77.78/10.60 (setukpairinjR) => 77.78/10.60 (( 77.78/10.60 (ksndsingleton) => 77.78/10.60 (( 77.78/10.60 (ksndpairEq) => 77.78/10.60 (( 77.78/10.60 (kpairsurjEq) => 77.78/10.60 (( 77.78/10.60 (cartprodsndin) => 77.78/10.60 (( 77.78/10.60 (cartprodpairmemEL) => 77.78/10.60 (( 77.78/10.60 (cartprodpairmemER) => 77.78/10.60 (( 77.78/10.60 (cartprodmempaircEq) => 77.78/10.60 (( 77.78/10.60 (cartprodfstpairEq) => 77.78/10.60 (( 77.78/10.60 (cartprodsndpairEq) => 77.78/10.60 (( 77.78/10.60 (cartprodpairsurjEq) => 77.78/10.60 (( 77.78/10.60 (dpsetconstrI) => 77.78/10.60 (( 77.78/10.60 (dpsetconstrSub) => 77.78/10.60 (( 77.78/10.60 (setOfPairsIsBReln) => 77.78/10.60 (( 77.78/10.60 (dpsetconstrERa) => 77.78/10.60 (( 77.78/10.60 (dpsetconstrEL1) => 77.78/10.60 (( 77.78/10.60 (dpsetconstrEL2) => 77.78/10.60 (( 77.78/10.60 (dpsetconstrER) => 77.78/10.60 (( 77.78/10.60 (funcImageSingleton) => 77.78/10.60 (( 77.78/10.60 (apProp) => 77.78/10.60 (( 77.78/10.60 (app) => 77.78/10.60 (( 77.78/10.60 (infuncsetfunc) => 77.78/10.60 (( 77.78/10.60 (ap2p) => 77.78/10.60 (( 77.78/10.60 (funcinfuncset) => 77.78/10.60 (( 77.78/10.60 (lamProp) => 77.78/10.60 (( 77.78/10.60 (lamp) => 77.78/10.60 (( 77.78/10.60 (lam2p) => 77.78/10.60 (( 77.78/10.60 (brelnall1) => 77.78/10.60 (( 77.78/10.60 (brelnall2) => 77.78/10.60 (( 77.78/10.60 (ex1E2) => 77.78/10.60 (( 77.78/10.60 (funcGraphProp1) => 77.78/10.60 (( 77.78/10.60 (funcGraphProp3) => 77.78/10.60 (( 77.78/10.60 (funcGraphProp2) => 77.78/10.60 (( 77.78/10.60 (funcextLem) => 77.78/10.60 (( 77.78/10.60 (funcGraphProp4) => 77.78/10.60 (( 77.78/10.60 (subbreln) => 77.78/10.60 (( 77.78/10.60 (eqbreln) => 77.78/10.60 (( 77.78/10.60 (funcext) => 77.78/10.60 (( 77.78/10.60 (funcext2) => 77.78/10.60 (( 77.78/10.60 (ap2apEq1) => 77.78/10.60 (( 77.78/10.60 (ap2apEq2) => 77.78/10.60 (( 77.78/10.60 (beta1) => 77.78/10.60 (( 77.78/10.60 (eta1) => 77.78/10.60 (( 77.78/10.60 (lam2lamEq) => 77.78/10.60 (( 77.78/10.60 (beta2) => 77.78/10.60 (( 77.78/10.60 (eta2) => 77.78/10.60 (( 77.78/10.60 (iffalseProp1) => 77.78/10.60 (( 77.78/10.60 (iffalseProp2) => 77.78/10.60 (( 77.78/10.60 (iftrueProp1) => 77.78/10.60 (( 77.78/10.60 (iftrueProp2) => 77.78/10.60 (( 77.78/10.60 (ifSingleton) => 77.78/10.60 (( 77.78/10.60 (ifp) => 77.78/10.60 (( 77.78/10.60 (theeq) => 77.78/10.60 (( 77.78/10.60 (iftrue) => 77.78/10.60 (( 77.78/10.60 (iffalse) => 77.78/10.60 (( 77.78/10.60 (iftrueorfalse) => 77.78/10.60 (( 77.78/10.60 (binintersectT_lem) => 77.78/10.60 (( 77.78/10.60 (binunionT_lem) => 77.78/10.60 (( 77.78/10.60 (powersetT_lem) => 77.78/10.60 (( 77.78/10.60 (setminusT_lem) => 77.78/10.60 (( 77.78/10.60 (complementT_lem) => 77.78/10.60 (( 77.78/10.60 (setextT) => 77.78/10.60 (( 77.78/10.60 (subsetTI) => 77.78/10.60 (( 77.78/10.60 (powersetTI1) => 77.78/10.60 (( 77.78/10.60 (powersetTE1) => 77.78/10.60 (( 77.78/10.60 (complementTI1) => 77.78/10.60 (( 77.78/10.60 (complementTE1) => 77.78/10.60 (( 77.78/10.60 (binintersectTELcontra) => 77.78/10.60 (( 77.78/10.60 (binintersectTERcontra) => 77.78/10.60 (( 77.78/10.60 (contrasubsetT) => 77.78/10.60 (( 77.78/10.60 (contrasubsetT1) => 77.78/10.60 (( 77.78/10.60 (contrasubsetT2) => 77.78/10.60 (( 77.78/10.60 (contrasubsetT3) => 77.78/10.60 (( 77.78/10.60 (doubleComplementI1) => 77.78/10.60 (( 77.78/10.60 (doubleComplementE1) => 77.78/10.60 (( 77.78/10.60 (doubleComplementSub1) => 77.78/10.60 (( 77.78/10.60 (doubleComplementSub2) => 77.78/10.60 (( 77.78/10.60 (doubleComplementEq) => 77.78/10.60 (( 77.78/10.60 (complementTnotintersectT) => 77.78/10.60 (( 77.78/10.60 (complementImpComplementIntersect) => 77.78/10.60 (( 77.78/10.60 (complementSubsetComplementIntersect) => 77.78/10.60 (( 77.78/10.60 (complementInPowersetComplementIntersect) => 77.78/10.60 (( 77.78/10.60 (contraSubsetComplement) => 77.78/10.60 (( 77.78/10.60 (complementTcontraSubset) => 77.78/10.60 (( 77.78/10.60 (binunionTILcontra) => 77.78/10.60 (( 77.78/10.60 (binunionTIRcontra) => 77.78/10.60 (( 77.78/10.60 (inIntersectImpInUnion) => 77.78/10.60 (( 77.78/10.60 (inIntersectImpInUnion2) => 77.78/10.60 (( 77.78/10.60 (inIntersectImpInIntersectUnions) => 77.78/10.60 (( 77.78/10.60 (intersectInPowersetIntersectUnions) => 77.78/10.60 (( 77.78/10.60 (inComplementUnionImpNotIn1) => 77.78/10.60 (( 77.78/10.60 (inComplementUnionImpInComplement1) => 77.78/10.60 (( 77.78/10.60 (binunionTE) => 77.78/10.60 (( 77.78/10.60 (binunionTEcontra) => 77.78/10.60 (( 77.78/10.60 (demorgan2a1) => 77.78/10.60 (( 77.78/10.60 (complementUnionInPowersetComplement) => 77.78/10.60 (( 77.78/10.60 (demorgan2a2) => 77.78/10.60 (( 77.78/10.60 (demorgan1a) => 77.78/10.60 (( 77.78/10.60 (demorgan1b) => 77.78/10.60 (( 77.78/10.60 (demorgan1) => 77.78/10.60 (( 77.78/10.60 (demorgan2a) => 77.78/10.60 (( 77.78/10.60 (demorgan2b2) => 77.78/10.60 (( 77.78/10.60 (demorgan2b) => 77.78/10.60 (( 77.78/10.60 (demorgan2) => 77.78/10.60 (( 77.78/10.60 (woz13rule0) => 77.78/10.60 (( 77.78/10.60 (woz13rule1) => 77.78/10.60 (( 77.78/10.60 (woz13rule2) => 77.78/10.60 (( 77.78/10.60 (woz13rule3) => 77.78/10.60 (( 77.78/10.60 (woz13rule4) => 77.78/10.60 (( 77.78/10.60 (woz1_1) => 77.78/10.60 (( 77.78/10.60 (woz1_2) => 77.78/10.60 (( 77.78/10.60 (woz1_3) => 77.78/10.60 (( 77.78/10.60 (woz1_4) => 77.78/10.60 (( 77.78/10.60 (woz1_5) => 77.78/10.60 (( 77.78/10.60 (breln1all2) => 77.78/10.60 (( 77.78/10.60 (breln1SetBreln1) => 77.78/10.60 (( 77.78/10.60 (choice2fnsingleton) => 77.78/10.60 (( 77.78/10.60 (setOfPairsIsBReln1) => 77.78/10.60 (( 77.78/10.60 (breln1all1) => 77.78/10.60 (( 77.78/10.60 (subbreln1) => 77.78/10.60 (( 77.78/10.60 (eqbreln1) => 77.78/10.60 (( 77.78/10.60 (breln1invprop) => 77.78/10.60 (( 77.78/10.60 (breln1invI) => 77.78/10.60 (( 77.78/10.60 (breln1invE) => 77.78/10.60 (( 77.78/10.60 (breln1compprop) => 77.78/10.60 (( 77.78/10.60 (breln1compI) => 77.78/10.60 (( 77.78/10.60 (breln1compE) => 77.78/10.60 (( 77.78/10.60 (breln1compEex) => 77.78/10.60 (( 77.78/10.60 (breln1unionprop) => 77.78/10.60 (( 77.78/10.60 (breln1unionIL) => 77.78/10.60 (( 77.78/10.60 (breln1unionIR) => 77.78/10.60 (( 77.78/10.60 (breln1unionI) => 77.78/10.60 (( 77.78/10.60 (breln1unionE) => 77.78/10.60 (( 77.78/10.60 (breln1unionEcases) => 77.78/10.60 (( 77.78/10.60 (breln1unionCommutes) => 77.78/10.60 (( 77.78/10.60 (woz2Ex) => 77.78/10.60 (( 77.78/10.60 (woz2W) => 77.78/10.60 (( 77.78/10.60 (woz2A) => 77.78/10.60 (( 77.78/10.60 (woz2B) => 77.78/10.60 (( 77.78/10.60 (image1Ex) => 77.78/10.60 (( 77.78/10.60 (image1Ex1) => 77.78/10.60 (( 77.78/10.60 (image1Equiv) => 77.78/10.60 (( 77.78/10.60 (image1E) => 77.78/10.60 (( 77.78/10.60 (image1I) => 77.78/10.60 (( 77.78/10.60 (injFuncInInjFuncSet) => 77.78/10.60 (( 77.78/10.60 (injFuncSetFuncIn) => 77.78/10.60 (( 77.78/10.60 (injFuncSetFuncInj) => 77.78/10.60 (( 77.78/10.60 (surjFuncSetFuncIn) => 77.78/10.60 (( 77.78/10.60 (surjFuncSetFuncSurj) => 77.78/10.60 (( 77.78/10.60 (leftInvIsSurj) => 77.78/10.60 (( 77.78/10.60 (surjCantorThm) => 77.78/10.60 (( 77.78/10.60 (foundation2) => 77.78/10.60 (( 77.78/10.60 (notinself) => 77.78/10.60 (( 77.78/10.60 (notinself2) => 77.78/10.60 (( 77.78/10.60 (omegaSp) => 77.78/10.60 (( 77.78/10.60 (omegaSclos) => 77.78/10.60 (( 77.78/10.60 (peano0notS) => 77.78/10.60 (( 77.78/10.60 (peanoSinj) => 77.78/10.60 (( 77.78/10.60 (transitivesetOp1) => 77.78/10.60 (( 77.78/10.60 (binintTransitive) => 77.78/10.60 (( 77.78/10.60 (transitivesetOp2) => 77.78/10.60 (( 77.78/10.60 (setunionTransitive) => 77.78/10.60 (( 77.78/10.60 (ordinalMinLem1) => 77.78/10.60 (( 77.78/10.60 (!!) @ ( 77.78/10.60 ^[Y0 : $i]: 77.78/10.60 (( 77.78/10.60 (ordinal @ 77.78/10.60 Y0) => 77.78/10.60 (( 77.78/10.60 (!!) @ ( 77.78/10.60 ^[Y1 : $i]: 77.78/10.60 (( 77.78/10.60 (!!) @ ( 77.78/10.60 ^[Y2 : $i]: 77.78/10.60 (( 77.78/10.60 (in @ 77.78/10.60 Y2 @ 77.78/10.60 Y0) => 77.78/10.60 (( 77.78/10.60 (in @ 77.78/10.60 Y1 @ 77.78/10.60 Y2) => 77.78/10.60 (in @ 77.78/10.60 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 77.78/10.60 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl372])). 77.78/10.60 thf(zip_derived_cl390, plain, 77.78/10.60 (~ (((nonemptyImpWitness) => 77.78/10.60 (((uniqinunit) => 77.78/10.60 (((notinsingleton) => 77.78/10.60 (((eqinunit) => 77.78/10.60 (((singletonsswitch) => 77.78/10.60 (((upairsetE) => 77.78/10.60 (((upairsetIL) => 77.78/10.60 (((upairsetIR) => 77.78/10.60 (((emptyE1) => 77.78/10.60 (((vacuousDall) => 77.78/10.60 (((quantDeMorgan1) => 77.78/10.60 (((quantDeMorgan2) => 77.78/10.60 (((quantDeMorgan3) => 77.78/10.60 (((quantDeMorgan4) => 77.78/10.60 (((prop2setI) => 77.78/10.60 (((prop2set2propI) => 77.78/10.60 (((notdexE) => 77.78/10.60 (((notdallE) => 77.78/10.60 (((exuI1) => 77.78/10.60 (((exuI3) => 77.78/10.60 (((exuI2) => 77.78/10.60 (((inCongP) => 77.78/10.60 (((in__Cong) => 77.78/10.60 (((exuE3u) => 77.78/10.60 (((exu__Cong) => 77.78/10.60 (((setadjoin__Cong) => 77.78/10.60 (((powerset__Cong) => 77.78/10.60 (((setunion__Cong) => 77.78/10.60 (((exuEu) => 77.78/10.60 (((descr__Cong) => 77.78/10.60 (( 77.78/10.60 (dsetconstr__Cong) => 77.78/10.60 (( 77.78/10.60 (subsetI1) => 77.78/10.60 (( 77.78/10.60 (eqimpsubset2) => 77.78/10.60 (( 77.78/10.60 (eqimpsubset1) => 77.78/10.60 (( 77.78/10.60 (subsetI2) => 77.78/10.60 (( 77.78/10.60 (emptysetsubset) => 77.78/10.60 (( 77.78/10.60 (subsetE) => 77.78/10.60 (( 77.78/10.60 (subsetE2) => 77.78/10.60 (( 77.78/10.60 (notsubsetI) => 77.78/10.60 (( 77.78/10.60 (notequalI1) => 77.78/10.60 (( 77.78/10.60 (notequalI2) => 77.78/10.60 (( 77.78/10.60 (subsetRefl) => 77.78/10.60 (( 77.78/10.60 (subsetTrans) => 77.78/10.60 (( 77.78/10.60 (setadjoinSub) => 77.78/10.60 (( 77.78/10.60 (setadjoinSub2) => 77.78/10.60 (( 77.78/10.60 (subset2powerset) => 77.78/10.60 (( 77.78/10.60 (setextsub) => 77.78/10.60 (( 77.78/10.60 (subsetemptysetimpeq) => 77.78/10.60 (( 77.78/10.60 (powersetI1) => 77.78/10.60 (( 77.78/10.60 (powersetE1) => 77.78/10.60 (( 77.78/10.60 (inPowerset) => 77.78/10.60 (( 77.78/10.60 (powersetsubset) => 77.78/10.60 (( 77.78/10.60 (sepInPowerset) => 77.78/10.60 (( 77.78/10.60 (sepSubset) => 77.78/10.60 (( 77.78/10.60 (binunionIL) => 77.78/10.60 (( 77.78/10.60 (upairset2IR) => 77.78/10.60 (( 77.78/10.60 (binunionIR) => 77.78/10.60 (( 77.78/10.60 (binunionEcases) => 77.78/10.60 (( 77.78/10.60 (binunionE) => 77.78/10.60 (( 77.78/10.60 (binunionLsub) => 77.78/10.60 (( 77.78/10.60 (binunionRsub) => 77.78/10.60 (( 77.78/10.60 (binintersectI) => 77.78/10.60 (( 77.78/10.60 (binintersectSubset5) => 77.78/10.60 (( 77.78/10.60 (binintersectEL) => 77.78/10.60 (( 77.78/10.60 (binintersectLsub) => 77.78/10.60 (( 77.78/10.60 (binintersectSubset2) => 77.78/10.60 (( 77.78/10.60 (binintersectSubset3) => 77.78/10.60 (( 77.78/10.60 (binintersectER) => 77.78/10.60 (( 77.78/10.60 (disjointsetsI1) => 77.78/10.60 (( 77.78/10.60 (binintersectRsub) => 77.78/10.60 (( 77.78/10.60 (binintersectSubset4) => 77.78/10.60 (( 77.78/10.60 (binintersectSubset1) => 77.78/10.60 (( 77.78/10.60 (bs114d) => 77.78/10.60 (( 77.78/10.60 (setminusI) => 77.78/10.60 (( 77.78/10.60 (setminusEL) => 77.78/10.60 (( 77.78/10.60 (setminusER) => 77.78/10.60 (( 77.78/10.60 (setminusSubset2) => 77.78/10.60 (( 77.78/10.60 (setminusERneg) => 77.78/10.60 (( 77.78/10.60 (setminusELneg) => 77.78/10.60 (( 77.78/10.60 (setminusILneg) => 77.78/10.60 (( 77.78/10.60 (setminusIRneg) => 77.78/10.60 (( 77.78/10.60 (setminusLsub) => 77.78/10.60 (( 77.78/10.60 (setminusSubset1) => 77.78/10.60 (( 77.78/10.60 (symdiffE) => 77.78/10.60 (( 77.78/10.60 (symdiffI1) => 77.78/10.60 (( 77.78/10.60 (symdiffI2) => 77.78/10.60 (( 77.78/10.60 (symdiffIneg1) => 77.78/10.60 (( 77.78/10.60 (symdiffIneg2) => 77.78/10.60 (( 77.78/10.60 (secondinupair) => 77.78/10.60 (( 77.78/10.60 (setukpairIL) => 77.78/10.60 (( 77.78/10.60 (setukpairIR) => 77.78/10.60 (( 77.78/10.60 (kpairiskpair) => 77.78/10.60 (( 77.78/10.60 (kpairp) => 77.78/10.60 (( 77.78/10.60 (singletonsubset) => 77.78/10.60 (( 77.78/10.60 (singletoninpowerset) => 77.78/10.60 (( 77.78/10.60 (singletoninpowunion) => 77.78/10.60 (( 77.78/10.60 (upairset2E) => 77.78/10.60 (( 77.78/10.60 (upairsubunion) => 77.78/10.60 (( 77.78/10.60 (upairinpowunion) => 77.78/10.60 (( 77.78/10.60 (ubforcartprodlem1) => 77.78/10.60 (( 77.78/10.60 (ubforcartprodlem2) => 77.78/10.60 (( 77.78/10.60 (ubforcartprodlem3) => 77.78/10.60 (( 77.78/10.60 (cartprodpairin) => 77.78/10.60 (( 77.78/10.60 (cartprodmempair1) => 77.78/10.60 (( 77.78/10.60 (cartprodmempair) => 77.78/10.60 (( 77.78/10.60 (setunionE2) => 77.78/10.60 (( 77.78/10.60 (setunionsingleton1) => 77.78/10.60 (( 77.78/10.60 (setunionsingleton2) => 77.78/10.60 (( 77.78/10.60 (setunionsingleton) => 77.78/10.60 (( 77.78/10.60 (singletonprop) => 77.78/10.60 (( 77.78/10.60 (ex1E1) => 77.78/10.60 (( 77.78/10.60 (ex1I) => 77.78/10.60 (( 77.78/10.60 (ex1I2) => 77.78/10.60 (( 77.78/10.60 (singletonsuniq) => 77.78/10.60 (( 77.78/10.60 (setukpairinjL1) => 77.78/10.60 (( 77.78/10.60 (kfstsingleton) => 77.78/10.60 (( 77.78/10.60 (theprop) => 77.78/10.60 (( 77.78/10.60 (kfstpairEq) => 77.78/10.60 (( 77.78/10.60 (cartprodfstin) => 77.78/10.60 (( 77.78/10.60 (setukpairinjL2) => 77.78/10.60 (( 77.78/10.60 (setukpairinjL) => 77.78/10.60 (( 77.78/10.60 (setukpairinjR11) => 77.78/10.60 (( 77.78/10.60 (setukpairinjR12) => 77.78/10.60 (( 77.78/10.60 (setukpairinjR1) => 77.78/10.60 (( 77.78/10.60 (upairequniteq) => 77.78/10.60 (( 77.78/10.60 (setukpairinjR2) => 77.78/10.60 (( 77.78/10.60 (setukpairinjR) => 77.78/10.60 (( 77.78/10.60 (ksndsingleton) => 77.78/10.60 (( 77.78/10.60 (ksndpairEq) => 77.78/10.60 (( 77.78/10.60 (kpairsurjEq) => 77.78/10.60 (( 77.78/10.60 (cartprodsndin) => 77.78/10.60 (( 77.78/10.60 (cartprodpairmemEL) => 77.78/10.60 (( 77.78/10.60 (cartprodpairmemER) => 77.78/10.60 (( 77.78/10.60 (cartprodmempaircEq) => 77.78/10.60 (( 77.78/10.60 (cartprodfstpairEq) => 77.78/10.60 (( 77.78/10.60 (cartprodsndpairEq) => 77.78/10.60 (( 77.78/10.60 (cartprodpairsurjEq) => 77.78/10.60 (( 77.78/10.60 (dpsetconstrI) => 77.78/10.60 (( 77.78/10.60 (dpsetconstrSub) => 77.78/10.60 (( 77.78/10.60 (setOfPairsIsBReln) => 77.78/10.60 (( 77.78/10.60 (dpsetconstrERa) => 77.78/10.60 (( 77.78/10.60 (dpsetconstrEL1) => 77.78/10.60 (( 77.78/10.60 (dpsetconstrEL2) => 77.78/10.60 (( 77.78/10.60 (dpsetconstrER) => 77.78/10.60 (( 77.78/10.60 (funcImageSingleton) => 77.78/10.60 (( 77.78/10.60 (apProp) => 77.78/10.60 (( 77.78/10.60 (app) => 77.78/10.60 (( 77.78/10.60 (infuncsetfunc) => 77.78/10.60 (( 77.78/10.60 (ap2p) => 77.78/10.60 (( 77.78/10.60 (funcinfuncset) => 77.78/10.60 (( 77.78/10.60 (lamProp) => 77.78/10.60 (( 77.78/10.60 (lamp) => 77.78/10.60 (( 77.78/10.60 (lam2p) => 77.78/10.60 (( 77.78/10.60 (brelnall1) => 77.78/10.60 (( 77.78/10.60 (brelnall2) => 77.78/10.60 (( 77.78/10.60 (ex1E2) => 77.78/10.60 (( 77.78/10.60 (funcGraphProp1) => 77.78/10.60 (( 77.78/10.60 (funcGraphProp3) => 77.78/10.60 (( 77.78/10.60 (funcGraphProp2) => 77.78/10.60 (( 77.78/10.60 (funcextLem) => 77.78/10.60 (( 77.78/10.60 (funcGraphProp4) => 77.78/10.60 (( 77.78/10.60 (subbreln) => 77.78/10.60 (( 77.78/10.60 (eqbreln) => 77.78/10.60 (( 77.78/10.60 (funcext) => 77.78/10.60 (( 77.78/10.60 (funcext2) => 77.78/10.60 (( 77.78/10.60 (ap2apEq1) => 77.78/10.60 (( 77.78/10.60 (ap2apEq2) => 77.78/10.60 (( 77.78/10.60 (beta1) => 77.78/10.60 (( 77.78/10.60 (eta1) => 77.78/10.60 (( 77.78/10.60 (lam2lamEq) => 77.78/10.60 (( 77.78/10.60 (beta2) => 77.78/10.60 (( 77.78/10.60 (eta2) => 77.78/10.60 (( 77.78/10.60 (iffalseProp1) => 77.78/10.60 (( 77.78/10.60 (iffalseProp2) => 77.78/10.60 (( 77.78/10.60 (iftrueProp1) => 77.78/10.60 (( 77.78/10.60 (iftrueProp2) => 77.78/10.60 (( 77.78/10.60 (ifSingleton) => 77.78/10.60 (( 77.78/10.60 (ifp) => 77.78/10.60 (( 77.78/10.60 (theeq) => 77.78/10.60 (( 77.78/10.60 (iftrue) => 77.78/10.60 (( 77.78/10.60 (iffalse) => 77.78/10.60 (( 77.78/10.60 (iftrueorfalse) => 77.78/10.60 (( 77.78/10.60 (binintersectT_lem) => 77.78/10.60 (( 77.78/10.60 (binunionT_lem) => 77.78/10.60 (( 77.78/10.60 (powersetT_lem) => 77.78/10.60 (( 77.78/10.60 (setminusT_lem) => 77.78/10.60 (( 77.78/10.60 (complementT_lem) => 77.78/10.60 (( 77.78/10.60 (setextT) => 77.78/10.60 (( 77.78/10.60 (subsetTI) => 77.78/10.60 (( 77.78/10.60 (powersetTI1) => 77.78/10.60 (( 77.78/10.60 (powersetTE1) => 77.78/10.60 (( 77.78/10.60 (complementTI1) => 77.78/10.60 (( 77.78/10.60 (complementTE1) => 77.78/10.60 (( 77.78/10.60 (binintersectTELcontra) => 77.78/10.60 (( 77.78/10.60 (binintersectTERcontra) => 77.78/10.60 (( 77.78/10.60 (contrasubsetT) => 77.78/10.60 (( 77.78/10.60 (contrasubsetT1) => 77.78/10.60 (( 77.78/10.60 (contrasubsetT2) => 77.78/10.60 (( 77.78/10.60 (contrasubsetT3) => 77.78/10.60 (( 77.78/10.60 (doubleComplementI1) => 77.78/10.60 (( 77.78/10.60 (doubleComplementE1) => 77.78/10.60 (( 77.78/10.60 (doubleComplementSub1) => 77.78/10.60 (( 77.78/10.60 (doubleComplementSub2) => 77.78/10.60 (( 77.78/10.60 (doubleComplementEq) => 77.78/10.60 (( 77.78/10.60 (complementTnotintersectT) => 77.78/10.60 (( 77.78/10.60 (complementImpComplementIntersect) => 77.78/10.60 (( 77.78/10.60 (complementSubsetComplementIntersect) => 77.78/10.60 (( 77.78/10.60 (complementInPowersetComplementIntersect) => 77.78/10.60 (( 77.78/10.60 (contraSubsetComplement) => 77.78/10.60 (( 77.78/10.60 (complementTcontraSubset) => 77.78/10.60 (( 77.78/10.60 (binunionTILcontra) => 77.78/10.60 (( 77.78/10.60 (binunionTIRcontra) => 77.78/10.60 (( 77.78/10.60 (inIntersectImpInUnion) => 77.78/10.60 (( 77.78/10.60 (inIntersectImpInUnion2) => 77.78/10.60 (( 77.78/10.60 (inIntersectImpInIntersectUnions) => 77.78/10.60 (( 77.78/10.60 (intersectInPowersetIntersectUnions) => 77.78/10.60 (( 77.78/10.60 (inComplementUnionImpNotIn1) => 77.78/10.60 (( 77.78/10.60 (inComplementUnionImpInComplement1) => 77.78/10.60 (( 77.78/10.60 (binunionTE) => 77.78/10.60 (( 77.78/10.60 (binunionTEcontra) => 77.78/10.60 (( 77.78/10.60 (demorgan2a1) => 77.78/10.60 (( 77.78/10.60 (complementUnionInPowersetComplement) => 77.78/10.60 (( 77.78/10.60 (demorgan2a2) => 77.78/10.60 (( 77.78/10.60 (demorgan1a) => 77.78/10.60 (( 77.78/10.60 (demorgan1b) => 77.78/10.60 (( 77.78/10.60 (demorgan1) => 77.78/10.60 (( 77.78/10.60 (demorgan2a) => 77.78/10.60 (( 77.78/10.60 (demorgan2b2) => 77.78/10.60 (( 77.78/10.60 (demorgan2b) => 77.78/10.60 (( 77.78/10.60 (demorgan2) => 77.78/10.60 (( 77.78/10.60 (woz13rule0) => 77.78/10.60 (( 77.78/10.60 (woz13rule1) => 77.78/10.60 (( 77.78/10.60 (woz13rule2) => 77.78/10.60 (( 77.78/10.60 (woz13rule3) => 77.78/10.60 (( 77.78/10.60 (woz13rule4) => 77.78/10.60 (( 77.78/10.60 (woz1_1) => 77.78/10.60 (( 77.78/10.60 (woz1_2) => 77.78/10.60 (( 77.78/10.60 (woz1_3) => 77.78/10.60 (( 77.78/10.60 (woz1_4) => 77.78/10.60 (( 77.78/10.60 (woz1_5) => 77.78/10.60 (( 77.78/10.60 (breln1all2) => 77.78/10.60 (( 77.78/10.60 (breln1SetBreln1) => 77.78/10.60 (( 77.78/10.60 (choice2fnsingleton) => 77.78/10.60 (( 77.78/10.60 (setOfPairsIsBReln1) => 77.78/10.60 (( 77.78/10.60 (breln1all1) => 77.78/10.60 (( 77.78/10.60 (subbreln1) => 77.78/10.60 (( 77.78/10.60 (eqbreln1) => 77.78/10.60 (( 77.78/10.60 (breln1invprop) => 77.78/10.60 (( 77.78/10.60 (breln1invI) => 77.78/10.60 (( 77.78/10.60 (breln1invE) => 77.78/10.60 (( 77.78/10.60 (breln1compprop) => 77.78/10.60 (( 77.78/10.60 (breln1compI) => 77.78/10.60 (( 77.78/10.60 (breln1compE) => 77.78/10.60 (( 77.78/10.60 (breln1compEex) => 77.78/10.60 (( 77.78/10.60 (breln1unionprop) => 77.78/10.60 (( 77.78/10.60 (breln1unionIL) => 77.78/10.60 (( 77.78/10.60 (breln1unionIR) => 77.78/10.60 (( 77.78/10.60 (breln1unionI) => 77.78/10.60 (( 77.78/10.60 (breln1unionE) => 77.78/10.60 (( 77.78/10.60 (breln1unionEcases) => 77.78/10.60 (( 77.78/10.60 (breln1unionCommutes) => 77.78/10.60 (( 77.78/10.60 (woz2Ex) => 77.78/10.60 (( 77.78/10.60 (woz2W) => 77.78/10.60 (( 77.78/10.60 (woz2A) => 77.78/10.60 (( 77.78/10.60 (woz2B) => 77.78/10.60 (( 77.78/10.60 (image1Ex) => 77.78/10.60 (( 77.78/10.60 (image1Ex1) => 77.78/10.60 (( 77.78/10.60 (image1Equiv) => 77.78/10.60 (( 77.78/10.60 (image1E) => 77.78/10.60 (( 77.78/10.60 (image1I) => 77.78/10.60 (( 77.78/10.60 (injFuncInInjFuncSet) => 77.78/10.60 (( 77.78/10.60 (injFuncSetFuncIn) => 77.78/10.60 (( 77.78/10.60 (injFuncSetFuncInj) => 77.78/10.60 (( 77.78/10.60 (surjFuncSetFuncIn) => 77.78/10.60 (( 77.78/10.60 (surjFuncSetFuncSurj) => 77.78/10.60 (( 77.78/10.60 (leftInvIsSurj) => 77.78/10.60 (( 77.78/10.60 (surjCantorThm) => 77.78/10.60 (( 77.78/10.60 (foundation2) => 77.78/10.60 (( 77.78/10.60 (notinself) => 77.78/10.60 (( 77.78/10.60 (notinself2) => 77.78/10.60 (( 77.78/10.60 (omegaSp) => 77.78/10.60 (( 77.78/10.60 (omegaSclos) => 77.78/10.60 (( 77.78/10.60 (peano0notS) => 77.78/10.60 (( 77.78/10.60 (peanoSinj) => 77.78/10.60 (( 77.78/10.60 (transitivesetOp1) => 77.78/10.60 (( 77.78/10.60 (binintTransitive) => 77.78/10.60 (( 77.78/10.60 (transitivesetOp2) => 77.78/10.60 (( 77.78/10.60 (setunionTransitive) => 77.78/10.60 (( 77.78/10.60 (ordinalMinLem1) => 77.78/10.60 (( 77.78/10.60 (!!) @ ( 77.78/10.60 ^[Y0 : $i]: 77.78/10.60 (( 77.78/10.60 (ordinal @ 77.78/10.60 Y0) => 77.78/10.60 (( 77.78/10.60 (!!) @ ( 77.78/10.60 ^[Y1 : $i]: 77.78/10.60 (( 77.78/10.60 (!!) @ ( 77.78/10.60 ^[Y2 : $i]: 77.78/10.60 (( 77.78/10.60 (in @ 77.78/10.60 Y2 @ 77.78/10.60 Y0) => 77.78/10.60 (( 77.78/10.60 (in @ 77.78/10.60 Y1 @ 77.78/10.60 Y2) => 77.78/10.60 (in @ 77.78/10.60 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 77.78/10.60 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl382])). 77.78/10.60 thf(zip_derived_cl397, plain, 77.78/10.60 (~ (((uniqinunit) => 77.78/10.60 (((notinsingleton) => 77.78/10.60 (((eqinunit) => 77.78/10.60 (((singletonsswitch) => 77.78/10.60 (((upairsetE) => 77.78/10.60 (((upairsetIL) => 77.78/10.60 (((upairsetIR) => 77.78/10.60 (((emptyE1) => 77.78/10.60 (((vacuousDall) => 77.78/10.60 (((quantDeMorgan1) => 77.78/10.60 (((quantDeMorgan2) => 77.78/10.60 (((quantDeMorgan3) => 77.78/10.60 (((quantDeMorgan4) => 77.78/10.60 (((prop2setI) => 77.78/10.60 (((prop2set2propI) => 77.78/10.60 (((notdexE) => 77.78/10.60 (((notdallE) => 77.78/10.60 (((exuI1) => 77.78/10.60 (((exuI3) => 77.78/10.60 (((exuI2) => 77.78/10.60 (((inCongP) => 77.78/10.60 (((in__Cong) => 77.78/10.60 (((exuE3u) => 77.78/10.60 (((exu__Cong) => 77.78/10.60 (((setadjoin__Cong) => 77.78/10.60 (((powerset__Cong) => 77.78/10.60 (((setunion__Cong) => 77.78/10.60 (((exuEu) => 77.78/10.60 (((descr__Cong) => 77.78/10.60 (((dsetconstr__Cong) => 77.78/10.60 (( 77.78/10.60 (subsetI1) => 77.78/10.60 (( 77.78/10.60 (eqimpsubset2) => 77.78/10.60 (( 77.78/10.60 (eqimpsubset1) => 77.78/10.60 (( 77.78/10.60 (subsetI2) => 77.78/10.60 (( 77.78/10.60 (emptysetsubset) => 77.78/10.60 (( 77.78/10.60 (subsetE) => 77.78/10.60 (( 77.78/10.60 (subsetE2) => 77.78/10.60 (( 77.78/10.60 (notsubsetI) => 77.78/10.60 (( 77.78/10.60 (notequalI1) => 77.78/10.60 (( 77.78/10.60 (notequalI2) => 77.78/10.60 (( 77.78/10.60 (subsetRefl) => 77.78/10.60 (( 77.78/10.60 (subsetTrans) => 77.78/10.60 (( 77.78/10.60 (setadjoinSub) => 77.78/10.60 (( 77.78/10.60 (setadjoinSub2) => 77.78/10.60 (( 77.78/10.60 (subset2powerset) => 77.78/10.60 (( 77.78/10.60 (setextsub) => 77.78/10.60 (( 77.78/10.60 (subsetemptysetimpeq) => 77.78/10.60 (( 77.78/10.60 (powersetI1) => 77.78/10.60 (( 77.78/10.60 (powersetE1) => 77.78/10.60 (( 77.78/10.60 (inPowerset) => 77.78/10.60 (( 77.78/10.60 (powersetsubset) => 77.78/10.60 (( 77.78/10.60 (sepInPowerset) => 77.78/10.60 (( 77.78/10.60 (sepSubset) => 77.78/10.60 (( 77.78/10.60 (binunionIL) => 77.78/10.60 (( 77.78/10.60 (upairset2IR) => 77.78/10.60 (( 77.78/10.60 (binunionIR) => 77.78/10.60 (( 77.78/10.60 (binunionEcases) => 77.78/10.60 (( 77.78/10.60 (binunionE) => 77.78/10.60 (( 77.78/10.60 (binunionLsub) => 77.78/10.60 (( 77.78/10.60 (binunionRsub) => 77.78/10.60 (( 77.78/10.60 (binintersectI) => 77.78/10.60 (( 77.78/10.60 (binintersectSubset5) => 77.78/10.60 (( 77.78/10.60 (binintersectEL) => 77.78/10.60 (( 77.78/10.60 (binintersectLsub) => 77.78/10.60 (( 77.78/10.60 (binintersectSubset2) => 77.78/10.60 (( 77.78/10.60 (binintersectSubset3) => 77.78/10.60 (( 77.78/10.60 (binintersectER) => 77.78/10.60 (( 77.78/10.60 (disjointsetsI1) => 77.78/10.60 (( 77.78/10.60 (binintersectRsub) => 77.78/10.60 (( 77.78/10.60 (binintersectSubset4) => 77.78/10.60 (( 77.78/10.60 (binintersectSubset1) => 77.78/10.60 (( 77.78/10.60 (bs114d) => 77.78/10.60 (( 77.78/10.60 (setminusI) => 77.78/10.60 (( 77.78/10.60 (setminusEL) => 77.78/10.60 (( 77.78/10.60 (setminusER) => 77.78/10.60 (( 77.78/10.60 (setminusSubset2) => 77.78/10.60 (( 77.78/10.60 (setminusERneg) => 77.78/10.60 (( 77.78/10.60 (setminusELneg) => 77.78/10.60 (( 77.78/10.60 (setminusILneg) => 77.78/10.60 (( 77.78/10.60 (setminusIRneg) => 77.78/10.60 (( 77.78/10.60 (setminusLsub) => 77.78/10.60 (( 77.78/10.60 (setminusSubset1) => 77.78/10.60 (( 77.78/10.60 (symdiffE) => 77.78/10.60 (( 77.78/10.60 (symdiffI1) => 77.78/10.60 (( 77.78/10.60 (symdiffI2) => 77.78/10.60 (( 77.78/10.60 (symdiffIneg1) => 77.78/10.60 (( 77.78/10.60 (symdiffIneg2) => 77.78/10.60 (( 77.78/10.60 (secondinupair) => 77.78/10.60 (( 77.78/10.60 (setukpairIL) => 77.78/10.60 (( 77.78/10.60 (setukpairIR) => 77.78/10.60 (( 77.78/10.60 (kpairiskpair) => 77.78/10.60 (( 77.78/10.60 (kpairp) => 77.78/10.60 (( 77.78/10.60 (singletonsubset) => 77.78/10.60 (( 77.78/10.60 (singletoninpowerset) => 77.78/10.60 (( 77.78/10.60 (singletoninpowunion) => 77.78/10.60 (( 77.78/10.60 (upairset2E) => 77.78/10.60 (( 77.78/10.60 (upairsubunion) => 77.78/10.60 (( 77.78/10.60 (upairinpowunion) => 77.78/10.60 (( 77.78/10.60 (ubforcartprodlem1) => 77.78/10.60 (( 77.78/10.60 (ubforcartprodlem2) => 77.78/10.60 (( 77.78/10.60 (ubforcartprodlem3) => 77.78/10.60 (( 77.78/10.60 (cartprodpairin) => 77.78/10.60 (( 77.78/10.60 (cartprodmempair1) => 77.78/10.60 (( 77.78/10.60 (cartprodmempair) => 77.78/10.60 (( 77.78/10.60 (setunionE2) => 77.78/10.60 (( 77.78/10.60 (setunionsingleton1) => 77.78/10.60 (( 77.78/10.60 (setunionsingleton2) => 77.78/10.60 (( 77.78/10.60 (setunionsingleton) => 77.78/10.60 (( 77.78/10.60 (singletonprop) => 77.78/10.60 (( 77.78/10.60 (ex1E1) => 77.78/10.60 (( 77.78/10.60 (ex1I) => 77.78/10.60 (( 77.78/10.60 (ex1I2) => 77.78/10.60 (( 77.78/10.60 (singletonsuniq) => 77.78/10.60 (( 77.78/10.60 (setukpairinjL1) => 77.78/10.60 (( 77.78/10.60 (kfstsingleton) => 77.78/10.60 (( 77.78/10.60 (theprop) => 77.78/10.60 (( 77.78/10.60 (kfstpairEq) => 77.78/10.60 (( 77.78/10.60 (cartprodfstin) => 77.78/10.60 (( 77.78/10.60 (setukpairinjL2) => 77.78/10.60 (( 77.78/10.60 (setukpairinjL) => 77.78/10.60 (( 77.78/10.60 (setukpairinjR11) => 77.78/10.60 (( 77.78/10.60 (setukpairinjR12) => 77.78/10.60 (( 77.78/10.60 (setukpairinjR1) => 77.78/10.60 (( 77.78/10.60 (upairequniteq) => 77.78/10.60 (( 77.78/10.60 (setukpairinjR2) => 77.78/10.60 (( 77.78/10.60 (setukpairinjR) => 77.78/10.60 (( 77.78/10.60 (ksndsingleton) => 77.78/10.60 (( 77.78/10.60 (ksndpairEq) => 77.78/10.60 (( 77.78/10.60 (kpairsurjEq) => 77.78/10.60 (( 77.78/10.60 (cartprodsndin) => 77.78/10.60 (( 77.78/10.60 (cartprodpairmemEL) => 77.78/10.60 (( 77.78/10.60 (cartprodpairmemER) => 77.78/10.60 (( 77.78/10.60 (cartprodmempaircEq) => 77.78/10.60 (( 77.78/10.60 (cartprodfstpairEq) => 77.78/10.60 (( 77.78/10.60 (cartprodsndpairEq) => 77.78/10.60 (( 77.78/10.60 (cartprodpairsurjEq) => 77.78/10.60 (( 77.78/10.60 (dpsetconstrI) => 77.78/10.60 (( 77.78/10.60 (dpsetconstrSub) => 77.78/10.60 (( 77.78/10.60 (setOfPairsIsBReln) => 77.78/10.60 (( 77.78/10.60 (dpsetconstrERa) => 77.78/10.60 (( 77.78/10.60 (dpsetconstrEL1) => 77.78/10.60 (( 77.78/10.60 (dpsetconstrEL2) => 77.78/10.60 (( 77.78/10.60 (dpsetconstrER) => 77.78/10.60 (( 77.78/10.60 (funcImageSingleton) => 77.78/10.60 (( 77.78/10.60 (apProp) => 77.78/10.60 (( 77.78/10.60 (app) => 77.78/10.60 (( 77.78/10.60 (infuncsetfunc) => 77.78/10.60 (( 77.78/10.60 (ap2p) => 77.78/10.60 (( 77.78/10.60 (funcinfuncset) => 77.78/10.60 (( 77.78/10.60 (lamProp) => 77.78/10.60 (( 77.78/10.60 (lamp) => 77.78/10.60 (( 77.78/10.60 (lam2p) => 77.78/10.60 (( 77.78/10.60 (brelnall1) => 77.78/10.60 (( 77.78/10.60 (brelnall2) => 77.78/10.60 (( 77.78/10.60 (ex1E2) => 77.78/10.60 (( 77.78/10.60 (funcGraphProp1) => 77.78/10.60 (( 77.78/10.60 (funcGraphProp3) => 77.78/10.60 (( 77.78/10.60 (funcGraphProp2) => 77.78/10.60 (( 77.78/10.60 (funcextLem) => 77.78/10.60 (( 77.78/10.60 (funcGraphProp4) => 77.78/10.60 (( 77.78/10.60 (subbreln) => 77.78/10.60 (( 77.78/10.60 (eqbreln) => 77.78/10.60 (( 77.78/10.60 (funcext) => 77.78/10.60 (( 77.78/10.60 (funcext2) => 77.78/10.60 (( 77.78/10.60 (ap2apEq1) => 77.78/10.60 (( 77.78/10.60 (ap2apEq2) => 77.78/10.60 (( 77.78/10.60 (beta1) => 77.78/10.60 (( 77.78/10.60 (eta1) => 77.78/10.60 (( 77.78/10.60 (lam2lamEq) => 77.78/10.60 (( 77.78/10.60 (beta2) => 77.78/10.60 (( 77.78/10.60 (eta2) => 77.78/10.60 (( 77.78/10.60 (iffalseProp1) => 77.78/10.60 (( 77.78/10.60 (iffalseProp2) => 77.78/10.60 (( 77.78/10.60 (iftrueProp1) => 77.78/10.60 (( 77.78/10.60 (iftrueProp2) => 77.78/10.60 (( 77.78/10.60 (ifSingleton) => 77.78/10.60 (( 77.78/10.60 (ifp) => 77.78/10.60 (( 77.78/10.60 (theeq) => 77.78/10.60 (( 77.78/10.60 (iftrue) => 77.78/10.60 (( 77.78/10.60 (iffalse) => 77.78/10.60 (( 77.78/10.60 (iftrueorfalse) => 77.78/10.60 (( 77.78/10.60 (binintersectT_lem) => 77.78/10.60 (( 77.78/10.60 (binunionT_lem) => 77.78/10.60 (( 77.78/10.60 (powersetT_lem) => 77.78/10.60 (( 77.78/10.60 (setminusT_lem) => 77.78/10.60 (( 77.78/10.60 (complementT_lem) => 77.78/10.60 (( 77.78/10.60 (setextT) => 77.78/10.60 (( 77.78/10.60 (subsetTI) => 77.78/10.60 (( 77.78/10.60 (powersetTI1) => 77.78/10.60 (( 77.78/10.60 (powersetTE1) => 77.78/10.60 (( 77.78/10.60 (complementTI1) => 77.78/10.60 (( 77.78/10.60 (complementTE1) => 77.78/10.60 (( 77.78/10.60 (binintersectTELcontra) => 77.78/10.60 (( 77.78/10.60 (binintersectTERcontra) => 77.78/10.60 (( 77.78/10.60 (contrasubsetT) => 77.78/10.60 (( 77.78/10.60 (contrasubsetT1) => 77.78/10.60 (( 77.78/10.60 (contrasubsetT2) => 77.78/10.60 (( 77.78/10.60 (contrasubsetT3) => 77.78/10.60 (( 77.78/10.60 (doubleComplementI1) => 77.78/10.60 (( 77.78/10.60 (doubleComplementE1) => 77.78/10.60 (( 77.78/10.60 (doubleComplementSub1) => 77.78/10.60 (( 77.78/10.60 (doubleComplementSub2) => 77.78/10.60 (( 77.78/10.60 (doubleComplementEq) => 77.78/10.60 (( 77.78/10.60 (complementTnotintersectT) => 77.78/10.60 (( 77.78/10.60 (complementImpComplementIntersect) => 77.78/10.60 (( 77.78/10.60 (complementSubsetComplementIntersect) => 77.78/10.60 (( 77.78/10.60 (complementInPowersetComplementIntersect) => 77.78/10.60 (( 77.78/10.60 (contraSubsetComplement) => 77.78/10.60 (( 77.78/10.60 (complementTcontraSubset) => 77.78/10.60 (( 77.78/10.60 (binunionTILcontra) => 77.78/10.60 (( 77.78/10.60 (binunionTIRcontra) => 77.78/10.60 (( 77.78/10.60 (inIntersectImpInUnion) => 77.78/10.60 (( 77.78/10.60 (inIntersectImpInUnion2) => 77.78/10.60 (( 77.78/10.60 (inIntersectImpInIntersectUnions) => 77.78/10.60 (( 77.78/10.60 (intersectInPowersetIntersectUnions) => 77.78/10.60 (( 77.78/10.60 (inComplementUnionImpNotIn1) => 77.78/10.60 (( 77.78/10.60 (inComplementUnionImpInComplement1) => 77.78/10.60 (( 77.78/10.60 (binunionTE) => 77.78/10.60 (( 77.78/10.60 (binunionTEcontra) => 77.78/10.60 (( 77.78/10.60 (demorgan2a1) => 77.78/10.60 (( 77.78/10.60 (complementUnionInPowersetComplement) => 77.78/10.60 (( 77.78/10.60 (demorgan2a2) => 77.78/10.60 (( 77.78/10.60 (demorgan1a) => 77.78/10.60 (( 77.78/10.60 (demorgan1b) => 77.78/10.60 (( 77.78/10.60 (demorgan1) => 77.78/10.60 (( 77.78/10.60 (demorgan2a) => 77.78/10.60 (( 77.78/10.60 (demorgan2b2) => 77.78/10.60 (( 77.78/10.60 (demorgan2b) => 77.78/10.60 (( 77.78/10.60 (demorgan2) => 77.78/10.60 (( 77.78/10.60 (woz13rule0) => 77.78/10.60 (( 77.78/10.60 (woz13rule1) => 77.78/10.60 (( 77.78/10.60 (woz13rule2) => 77.78/10.60 (( 77.78/10.60 (woz13rule3) => 77.78/10.60 (( 77.78/10.60 (woz13rule4) => 77.78/10.60 (( 77.78/10.60 (woz1_1) => 77.78/10.60 (( 77.78/10.60 (woz1_2) => 77.78/10.60 (( 77.78/10.60 (woz1_3) => 77.78/10.60 (( 77.78/10.60 (woz1_4) => 77.78/10.60 (( 77.78/10.60 (woz1_5) => 77.78/10.60 (( 77.78/10.60 (breln1all2) => 77.78/10.60 (( 77.78/10.60 (breln1SetBreln1) => 77.78/10.60 (( 77.78/10.60 (choice2fnsingleton) => 77.78/10.60 (( 77.78/10.60 (setOfPairsIsBReln1) => 77.78/10.60 (( 77.78/10.60 (breln1all1) => 77.78/10.60 (( 77.78/10.60 (subbreln1) => 77.78/10.60 (( 77.78/10.60 (eqbreln1) => 77.78/10.60 (( 77.78/10.60 (breln1invprop) => 77.78/10.60 (( 77.78/10.60 (breln1invI) => 77.78/10.60 (( 77.78/10.60 (breln1invE) => 77.78/10.60 (( 77.78/10.60 (breln1compprop) => 77.78/10.60 (( 77.78/10.60 (breln1compI) => 77.78/10.60 (( 77.78/10.60 (breln1compE) => 77.78/10.60 (( 77.78/10.60 (breln1compEex) => 77.78/10.60 (( 77.78/10.60 (breln1unionprop) => 77.78/10.60 (( 77.78/10.60 (breln1unionIL) => 77.78/10.60 (( 77.78/10.60 (breln1unionIR) => 77.78/10.60 (( 77.78/10.60 (breln1unionI) => 77.78/10.60 (( 77.78/10.60 (breln1unionE) => 77.78/10.60 (( 77.78/10.60 (breln1unionEcases) => 77.78/10.60 (( 77.78/10.60 (breln1unionCommutes) => 77.78/10.60 (( 77.78/10.60 (woz2Ex) => 77.78/10.60 (( 77.78/10.60 (woz2W) => 77.78/10.60 (( 77.78/10.60 (woz2A) => 77.78/10.60 (( 77.78/10.60 (woz2B) => 77.78/10.60 (( 77.78/10.60 (image1Ex) => 77.78/10.60 (( 77.78/10.60 (image1Ex1) => 77.78/10.60 (( 77.78/10.60 (image1Equiv) => 77.78/10.60 (( 77.78/10.60 (image1E) => 77.78/10.60 (( 77.78/10.60 (image1I) => 77.78/10.60 (( 77.78/10.60 (injFuncInInjFuncSet) => 77.78/10.60 (( 77.78/10.60 (injFuncSetFuncIn) => 77.78/10.60 (( 77.78/10.60 (injFuncSetFuncInj) => 77.78/10.60 (( 77.78/10.60 (surjFuncSetFuncIn) => 77.78/10.60 (( 77.78/10.60 (surjFuncSetFuncSurj) => 77.78/10.60 (( 77.78/10.60 (leftInvIsSurj) => 77.78/10.60 (( 77.78/10.60 (surjCantorThm) => 77.78/10.60 (( 77.78/10.60 (foundation2) => 77.78/10.60 (( 77.78/10.60 (notinself) => 77.78/10.60 (( 77.78/10.60 (notinself2) => 77.78/10.60 (( 77.78/10.60 (omegaSp) => 77.78/10.60 (( 77.78/10.60 (omegaSclos) => 77.78/10.60 (( 77.78/10.60 (peano0notS) => 77.78/10.60 (( 77.78/10.60 (peanoSinj) => 77.78/10.60 (( 77.78/10.60 (transitivesetOp1) => 77.78/10.60 (( 77.78/10.60 (binintTransitive) => 77.78/10.60 (( 77.78/10.60 (transitivesetOp2) => 77.78/10.60 (( 77.78/10.60 (setunionTransitive) => 77.78/10.60 (( 77.78/10.60 (ordinalMinLem1) => 77.78/10.60 (( 77.78/10.60 (!!) @ ( 77.78/10.60 ^[Y0 : $i]: 77.78/10.60 (( 77.78/10.60 (ordinal @ 77.78/10.60 Y0) => 77.78/10.60 (( 77.78/10.60 (!!) @ ( 77.78/10.60 ^[Y1 : $i]: 77.78/10.60 (( 77.78/10.60 (!!) @ ( 77.78/10.60 ^[Y2 : $i]: 77.78/10.60 (( 77.78/10.60 (in @ 77.78/10.60 Y2 @ 77.78/10.60 Y0) => 77.78/10.60 (( 77.78/10.60 (in @ 77.78/10.60 Y1 @ 77.78/10.60 Y2) => 77.78/10.60 (in @ 77.78/10.60 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 77.78/10.60 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl390])). 77.78/10.60 thf(zip_derived_cl406, plain, 77.78/10.60 (~ (((notinsingleton) => 77.78/10.60 (((eqinunit) => 77.78/10.60 (((singletonsswitch) => 77.78/10.60 (((upairsetE) => 77.78/10.60 (((upairsetIL) => 77.78/10.60 (((upairsetIR) => 77.78/10.60 (((emptyE1) => 77.78/10.60 (((vacuousDall) => 77.78/10.60 (((quantDeMorgan1) => 77.78/10.60 (((quantDeMorgan2) => 77.78/10.60 (((quantDeMorgan3) => 77.78/10.60 (((quantDeMorgan4) => 77.78/10.60 (((prop2setI) => 77.78/10.60 (((prop2set2propI) => 77.78/10.60 (((notdexE) => 77.78/10.60 (((notdallE) => 77.78/10.60 (((exuI1) => 77.78/10.60 (((exuI3) => 77.78/10.60 (((exuI2) => 77.78/10.60 (((inCongP) => 77.78/10.60 (((in__Cong) => 77.78/10.60 (((exuE3u) => 77.78/10.60 (((exu__Cong) => 77.78/10.60 (((setadjoin__Cong) => 77.78/10.60 (((powerset__Cong) => 77.78/10.60 (((setunion__Cong) => 77.78/10.60 (((exuEu) => 77.78/10.60 (((descr__Cong) => 77.78/10.60 (((dsetconstr__Cong) => 77.78/10.60 (((subsetI1) => 77.78/10.60 (( 77.78/10.60 (eqimpsubset2) => 77.78/10.60 (( 77.78/10.60 (eqimpsubset1) => 77.78/10.60 (( 77.78/10.60 (subsetI2) => 77.78/10.60 (( 77.78/10.60 (emptysetsubset) => 77.78/10.60 (( 77.78/10.60 (subsetE) => 77.78/10.60 (( 77.78/10.60 (subsetE2) => 77.78/10.60 (( 77.78/10.60 (notsubsetI) => 77.78/10.60 (( 77.78/10.60 (notequalI1) => 77.78/10.60 (( 77.78/10.60 (notequalI2) => 77.78/10.60 (( 77.78/10.60 (subsetRefl) => 77.78/10.60 (( 77.78/10.60 (subsetTrans) => 77.78/10.60 (( 77.78/10.60 (setadjoinSub) => 77.78/10.60 (( 77.78/10.60 (setadjoinSub2) => 77.78/10.60 (( 77.78/10.60 (subset2powerset) => 77.78/10.60 (( 77.78/10.60 (setextsub) => 77.78/10.60 (( 77.78/10.60 (subsetemptysetimpeq) => 77.78/10.60 (( 77.78/10.60 (powersetI1) => 77.78/10.60 (( 77.78/10.60 (powersetE1) => 77.78/10.60 (( 77.78/10.60 (inPowerset) => 77.78/10.60 (( 77.78/10.60 (powersetsubset) => 77.78/10.60 (( 77.78/10.60 (sepInPowerset) => 77.78/10.60 (( 77.78/10.60 (sepSubset) => 77.78/10.60 (( 77.78/10.60 (binunionIL) => 77.78/10.60 (( 77.78/10.60 (upairset2IR) => 77.78/10.60 (( 77.78/10.60 (binunionIR) => 77.78/10.60 (( 77.78/10.60 (binunionEcases) => 77.78/10.60 (( 77.78/10.60 (binunionE) => 77.78/10.60 (( 77.78/10.60 (binunionLsub) => 77.78/10.60 (( 77.78/10.60 (binunionRsub) => 77.78/10.60 (( 77.78/10.60 (binintersectI) => 77.78/10.60 (( 77.78/10.60 (binintersectSubset5) => 77.78/10.60 (( 77.78/10.60 (binintersectEL) => 77.78/10.60 (( 77.78/10.60 (binintersectLsub) => 77.78/10.60 (( 77.78/10.60 (binintersectSubset2) => 77.78/10.60 (( 77.78/10.60 (binintersectSubset3) => 77.78/10.60 (( 77.78/10.60 (binintersectER) => 77.78/10.60 (( 77.78/10.60 (disjointsetsI1) => 77.78/10.60 (( 77.78/10.60 (binintersectRsub) => 77.78/10.60 (( 77.78/10.60 (binintersectSubset4) => 77.78/10.60 (( 77.78/10.60 (binintersectSubset1) => 77.78/10.60 (( 77.78/10.60 (bs114d) => 77.78/10.60 (( 77.78/10.60 (setminusI) => 77.78/10.60 (( 77.78/10.60 (setminusEL) => 77.78/10.60 (( 77.78/10.60 (setminusER) => 77.78/10.60 (( 77.78/10.60 (setminusSubset2) => 77.78/10.60 (( 77.78/10.60 (setminusERneg) => 77.78/10.60 (( 77.78/10.60 (setminusELneg) => 77.78/10.60 (( 77.78/10.60 (setminusILneg) => 77.78/10.60 (( 77.78/10.60 (setminusIRneg) => 77.78/10.60 (( 77.78/10.60 (setminusLsub) => 77.78/10.60 (( 77.78/10.60 (setminusSubset1) => 77.78/10.60 (( 77.78/10.60 (symdiffE) => 77.78/10.60 (( 77.78/10.60 (symdiffI1) => 77.78/10.60 (( 77.78/10.60 (symdiffI2) => 77.78/10.60 (( 77.78/10.60 (symdiffIneg1) => 77.78/10.60 (( 77.78/10.60 (symdiffIneg2) => 77.78/10.60 (( 77.78/10.60 (secondinupair) => 77.78/10.60 (( 77.78/10.60 (setukpairIL) => 77.78/10.60 (( 77.78/10.60 (setukpairIR) => 77.78/10.60 (( 77.78/10.60 (kpairiskpair) => 77.78/10.60 (( 77.78/10.60 (kpairp) => 77.78/10.60 (( 77.78/10.60 (singletonsubset) => 77.78/10.60 (( 77.78/10.60 (singletoninpowerset) => 77.78/10.60 (( 77.78/10.60 (singletoninpowunion) => 77.78/10.60 (( 77.78/10.60 (upairset2E) => 77.78/10.60 (( 77.78/10.60 (upairsubunion) => 77.78/10.60 (( 77.78/10.60 (upairinpowunion) => 77.78/10.60 (( 77.78/10.60 (ubforcartprodlem1) => 77.78/10.60 (( 77.78/10.60 (ubforcartprodlem2) => 77.78/10.60 (( 77.78/10.60 (ubforcartprodlem3) => 77.78/10.60 (( 77.78/10.60 (cartprodpairin) => 77.78/10.60 (( 77.78/10.60 (cartprodmempair1) => 77.78/10.60 (( 77.78/10.60 (cartprodmempair) => 77.78/10.60 (( 77.78/10.60 (setunionE2) => 77.78/10.60 (( 77.78/10.60 (setunionsingleton1) => 77.78/10.60 (( 77.78/10.60 (setunionsingleton2) => 77.78/10.60 (( 77.78/10.60 (setunionsingleton) => 77.78/10.60 (( 77.78/10.60 (singletonprop) => 77.78/10.60 (( 77.78/10.60 (ex1E1) => 77.78/10.60 (( 77.78/10.60 (ex1I) => 77.78/10.60 (( 77.78/10.60 (ex1I2) => 77.78/10.60 (( 77.78/10.60 (singletonsuniq) => 77.78/10.60 (( 77.78/10.60 (setukpairinjL1) => 77.78/10.60 (( 77.78/10.60 (kfstsingleton) => 77.78/10.60 (( 77.78/10.60 (theprop) => 77.78/10.60 (( 77.78/10.60 (kfstpairEq) => 77.78/10.60 (( 77.78/10.60 (cartprodfstin) => 77.78/10.60 (( 77.78/10.60 (setukpairinjL2) => 77.78/10.60 (( 77.78/10.60 (setukpairinjL) => 77.78/10.60 (( 77.78/10.60 (setukpairinjR11) => 77.78/10.60 (( 77.78/10.60 (setukpairinjR12) => 77.78/10.60 (( 77.78/10.60 (setukpairinjR1) => 77.78/10.60 (( 77.78/10.60 (upairequniteq) => 77.78/10.60 (( 77.78/10.60 (setukpairinjR2) => 77.78/10.60 (( 77.78/10.60 (setukpairinjR) => 77.78/10.60 (( 77.78/10.60 (ksndsingleton) => 77.78/10.60 (( 77.78/10.60 (ksndpairEq) => 77.78/10.60 (( 77.78/10.60 (kpairsurjEq) => 77.78/10.60 (( 77.78/10.60 (cartprodsndin) => 77.78/10.60 (( 77.78/10.60 (cartprodpairmemEL) => 77.78/10.60 (( 77.78/10.60 (cartprodpairmemER) => 77.78/10.60 (( 77.78/10.60 (cartprodmempaircEq) => 77.78/10.60 (( 77.78/10.60 (cartprodfstpairEq) => 77.78/10.60 (( 77.78/10.60 (cartprodsndpairEq) => 77.78/10.60 (( 77.78/10.60 (cartprodpairsurjEq) => 77.78/10.60 (( 77.78/10.60 (dpsetconstrI) => 77.78/10.60 (( 77.78/10.60 (dpsetconstrSub) => 77.78/10.60 (( 77.78/10.60 (setOfPairsIsBReln) => 77.78/10.60 (( 77.78/10.60 (dpsetconstrERa) => 77.78/10.60 (( 77.78/10.60 (dpsetconstrEL1) => 77.78/10.60 (( 77.78/10.60 (dpsetconstrEL2) => 77.78/10.60 (( 77.78/10.60 (dpsetconstrER) => 77.78/10.60 (( 77.78/10.60 (funcImageSingleton) => 77.78/10.60 (( 77.78/10.60 (apProp) => 77.78/10.60 (( 77.78/10.60 (app) => 77.78/10.60 (( 77.78/10.60 (infuncsetfunc) => 77.78/10.60 (( 77.78/10.60 (ap2p) => 77.78/10.60 (( 77.78/10.60 (funcinfuncset) => 77.78/10.60 (( 77.78/10.60 (lamProp) => 77.78/10.60 (( 77.78/10.60 (lamp) => 77.78/10.60 (( 77.78/10.60 (lam2p) => 77.78/10.60 (( 77.78/10.60 (brelnall1) => 77.78/10.60 (( 77.78/10.60 (brelnall2) => 77.78/10.60 (( 77.78/10.60 (ex1E2) => 77.78/10.60 (( 77.78/10.60 (funcGraphProp1) => 77.78/10.60 (( 77.78/10.60 (funcGraphProp3) => 77.78/10.60 (( 77.78/10.60 (funcGraphProp2) => 77.78/10.60 (( 77.78/10.60 (funcextLem) => 77.78/10.60 (( 77.78/10.60 (funcGraphProp4) => 77.78/10.60 (( 77.78/10.60 (subbreln) => 77.78/10.60 (( 77.78/10.60 (eqbreln) => 77.78/10.60 (( 77.78/10.60 (funcext) => 77.78/10.60 (( 77.78/10.60 (funcext2) => 77.78/10.60 (( 77.78/10.60 (ap2apEq1) => 77.78/10.60 (( 77.78/10.60 (ap2apEq2) => 77.78/10.60 (( 77.78/10.60 (beta1) => 77.78/10.60 (( 77.78/10.60 (eta1) => 77.78/10.60 (( 77.78/10.60 (lam2lamEq) => 77.78/10.60 (( 77.78/10.60 (beta2) => 77.78/10.60 (( 77.78/10.60 (eta2) => 77.78/10.60 (( 77.78/10.60 (iffalseProp1) => 77.78/10.60 (( 77.78/10.60 (iffalseProp2) => 77.78/10.60 (( 77.78/10.60 (iftrueProp1) => 77.78/10.60 (( 77.78/10.60 (iftrueProp2) => 77.78/10.60 (( 77.78/10.60 (ifSingleton) => 77.78/10.60 (( 77.78/10.60 (ifp) => 77.78/10.60 (( 77.78/10.60 (theeq) => 77.78/10.60 (( 77.78/10.60 (iftrue) => 77.78/10.60 (( 77.78/10.60 (iffalse) => 77.78/10.60 (( 77.78/10.60 (iftrueorfalse) => 77.78/10.60 (( 77.78/10.60 (binintersectT_lem) => 77.78/10.60 (( 77.78/10.60 (binunionT_lem) => 77.78/10.60 (( 77.78/10.60 (powersetT_lem) => 77.78/10.60 (( 77.78/10.60 (setminusT_lem) => 77.78/10.60 (( 77.78/10.60 (complementT_lem) => 77.78/10.60 (( 77.78/10.60 (setextT) => 77.78/10.60 (( 77.78/10.60 (subsetTI) => 77.78/10.60 (( 77.78/10.60 (powersetTI1) => 77.78/10.60 (( 77.78/10.60 (powersetTE1) => 77.78/10.60 (( 77.78/10.60 (complementTI1) => 77.78/10.60 (( 77.78/10.60 (complementTE1) => 77.78/10.60 (( 77.78/10.60 (binintersectTELcontra) => 77.78/10.60 (( 77.78/10.60 (binintersectTERcontra) => 77.78/10.60 (( 77.78/10.60 (contrasubsetT) => 77.78/10.60 (( 77.78/10.60 (contrasubsetT1) => 77.78/10.60 (( 77.78/10.60 (contrasubsetT2) => 77.78/10.60 (( 77.78/10.60 (contrasubsetT3) => 77.78/10.60 (( 77.78/10.60 (doubleComplementI1) => 77.78/10.60 (( 77.78/10.60 (doubleComplementE1) => 77.78/10.60 (( 77.78/10.60 (doubleComplementSub1) => 77.78/10.60 (( 77.78/10.60 (doubleComplementSub2) => 77.78/10.60 (( 77.78/10.60 (doubleComplementEq) => 77.78/10.60 (( 77.78/10.60 (complementTnotintersectT) => 77.78/10.60 (( 77.78/10.60 (complementImpComplementIntersect) => 77.78/10.60 (( 77.78/10.60 (complementSubsetComplementIntersect) => 77.78/10.60 (( 77.78/10.60 (complementInPowersetComplementIntersect) => 77.78/10.60 (( 77.78/10.60 (contraSubsetComplement) => 77.78/10.60 (( 77.78/10.60 (complementTcontraSubset) => 77.78/10.60 (( 77.78/10.60 (binunionTILcontra) => 77.78/10.60 (( 77.78/10.60 (binunionTIRcontra) => 77.78/10.60 (( 77.78/10.60 (inIntersectImpInUnion) => 77.78/10.60 (( 77.78/10.60 (inIntersectImpInUnion2) => 77.78/10.60 (( 77.78/10.60 (inIntersectImpInIntersectUnions) => 77.78/10.60 (( 77.78/10.60 (intersectInPowersetIntersectUnions) => 77.78/10.60 (( 77.78/10.60 (inComplementUnionImpNotIn1) => 77.78/10.60 (( 77.78/10.60 (inComplementUnionImpInComplement1) => 77.78/10.60 (( 77.78/10.60 (binunionTE) => 77.78/10.60 (( 77.78/10.60 (binunionTEcontra) => 77.78/10.60 (( 77.78/10.60 (demorgan2a1) => 77.78/10.60 (( 77.78/10.60 (complementUnionInPowersetComplement) => 77.78/10.60 (( 77.78/10.60 (demorgan2a2) => 77.78/10.60 (( 77.78/10.60 (demorgan1a) => 77.78/10.60 (( 77.78/10.60 (demorgan1b) => 77.78/10.60 (( 77.78/10.60 (demorgan1) => 77.78/10.60 (( 77.78/10.60 (demorgan2a) => 77.78/10.60 (( 77.78/10.60 (demorgan2b2) => 77.78/10.60 (( 77.78/10.60 (demorgan2b) => 77.78/10.60 (( 77.78/10.60 (demorgan2) => 77.78/10.60 (( 77.78/10.60 (woz13rule0) => 77.78/10.60 (( 77.78/10.60 (woz13rule1) => 77.78/10.60 (( 77.78/10.60 (woz13rule2) => 77.78/10.60 (( 77.78/10.60 (woz13rule3) => 77.78/10.60 (( 77.78/10.60 (woz13rule4) => 77.78/10.60 (( 77.78/10.60 (woz1_1) => 77.78/10.60 (( 77.78/10.60 (woz1_2) => 77.78/10.60 (( 77.78/10.60 (woz1_3) => 77.78/10.60 (( 77.78/10.60 (woz1_4) => 77.78/10.60 (( 77.78/10.60 (woz1_5) => 77.78/10.60 (( 77.78/10.60 (breln1all2) => 77.78/10.60 (( 77.78/10.60 (breln1SetBreln1) => 77.78/10.60 (( 77.78/10.60 (choice2fnsingleton) => 77.78/10.60 (( 77.78/10.60 (setOfPairsIsBReln1) => 77.78/10.60 (( 77.78/10.60 (breln1all1) => 77.78/10.60 (( 77.78/10.60 (subbreln1) => 77.78/10.60 (( 77.78/10.60 (eqbreln1) => 77.78/10.60 (( 77.78/10.60 (breln1invprop) => 77.78/10.60 (( 77.78/10.60 (breln1invI) => 77.78/10.60 (( 77.78/10.60 (breln1invE) => 77.78/10.60 (( 77.78/10.60 (breln1compprop) => 77.78/10.60 (( 77.78/10.60 (breln1compI) => 77.78/10.60 (( 77.78/10.60 (breln1compE) => 77.78/10.60 (( 77.78/10.60 (breln1compEex) => 77.78/10.60 (( 77.78/10.60 (breln1unionprop) => 77.78/10.60 (( 77.78/10.60 (breln1unionIL) => 77.78/10.60 (( 77.78/10.60 (breln1unionIR) => 77.78/10.60 (( 77.78/10.60 (breln1unionI) => 77.78/10.60 (( 77.78/10.60 (breln1unionE) => 77.78/10.60 (( 77.78/10.60 (breln1unionEcases) => 77.78/10.60 (( 77.78/10.60 (breln1unionCommutes) => 77.78/10.60 (( 77.78/10.60 (woz2Ex) => 77.78/10.60 (( 77.78/10.60 (woz2W) => 77.78/10.60 (( 77.78/10.60 (woz2A) => 77.78/10.60 (( 77.78/10.60 (woz2B) => 77.78/10.60 (( 77.78/10.60 (image1Ex) => 77.78/10.60 (( 77.78/10.60 (image1Ex1) => 77.78/10.60 (( 77.78/10.60 (image1Equiv) => 77.78/10.60 (( 77.78/10.60 (image1E) => 77.78/10.60 (( 77.78/10.60 (image1I) => 77.78/10.60 (( 77.78/10.60 (injFuncInInjFuncSet) => 77.78/10.60 (( 77.78/10.60 (injFuncSetFuncIn) => 77.78/10.60 (( 77.78/10.60 (injFuncSetFuncInj) => 77.78/10.60 (( 77.78/10.60 (surjFuncSetFuncIn) => 77.78/10.60 (( 77.78/10.60 (surjFuncSetFuncSurj) => 77.78/10.60 (( 77.78/10.60 (leftInvIsSurj) => 77.78/10.60 (( 77.78/10.60 (surjCantorThm) => 77.78/10.60 (( 77.78/10.60 (foundation2) => 77.78/10.60 (( 77.78/10.60 (notinself) => 77.78/10.60 (( 77.78/10.60 (notinself2) => 77.78/10.60 (( 77.78/10.60 (omegaSp) => 77.78/10.60 (( 77.78/10.60 (omegaSclos) => 77.78/10.60 (( 77.78/10.60 (peano0notS) => 77.78/10.60 (( 77.78/10.60 (peanoSinj) => 77.78/10.60 (( 77.78/10.60 (transitivesetOp1) => 77.78/10.60 (( 77.78/10.60 (binintTransitive) => 77.78/10.60 (( 77.78/10.60 (transitivesetOp2) => 77.78/10.60 (( 77.78/10.60 (setunionTransitive) => 77.78/10.60 (( 77.78/10.60 (ordinalMinLem1) => 77.78/10.60 (( 77.78/10.60 (!!) @ ( 77.78/10.60 ^[Y0 : $i]: 77.78/10.60 (( 77.78/10.60 (ordinal @ 77.78/10.60 Y0) => 77.78/10.60 (( 77.78/10.60 (!!) @ ( 77.78/10.60 ^[Y1 : $i]: 77.78/10.60 (( 77.78/10.60 (!!) @ ( 77.78/10.60 ^[Y2 : $i]: 77.78/10.60 (( 77.78/10.60 (in @ 77.78/10.60 Y2 @ 77.78/10.60 Y0) => 77.78/10.60 (( 77.78/10.60 (in @ 77.78/10.60 Y1 @ 77.78/10.60 Y2) => 77.78/10.60 (in @ 77.78/10.60 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 77.78/10.60 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl397])). 77.78/10.60 thf(zip_derived_cl413, plain, 77.78/10.60 (~ (((eqinunit) => 77.78/10.60 (((singletonsswitch) => 77.78/10.60 (((upairsetE) => 77.78/10.60 (((upairsetIL) => 77.78/10.60 (((upairsetIR) => 77.78/10.60 (((emptyE1) => 77.78/10.60 (((vacuousDall) => 77.78/10.60 (((quantDeMorgan1) => 77.78/10.60 (((quantDeMorgan2) => 77.78/10.60 (((quantDeMorgan3) => 77.78/10.60 (((quantDeMorgan4) => 77.78/10.60 (((prop2setI) => 77.78/10.60 (((prop2set2propI) => 77.78/10.60 (((notdexE) => 77.78/10.60 (((notdallE) => 77.78/10.60 (((exuI1) => 77.78/10.60 (((exuI3) => 77.78/10.60 (((exuI2) => 77.78/10.60 (((inCongP) => 77.78/10.60 (((in__Cong) => 77.78/10.60 (((exuE3u) => 77.78/10.60 (((exu__Cong) => 77.78/10.60 (((setadjoin__Cong) => 77.78/10.60 (((powerset__Cong) => 77.78/10.60 (((setunion__Cong) => 77.78/10.60 (((exuEu) => 77.78/10.60 (((descr__Cong) => 77.78/10.60 (((dsetconstr__Cong) => 77.78/10.60 (((subsetI1) => 77.78/10.60 (((eqimpsubset2) => 77.78/10.60 (( 77.78/10.60 (eqimpsubset1) => 77.78/10.60 (( 77.78/10.60 (subsetI2) => 77.78/10.60 (( 77.78/10.60 (emptysetsubset) => 77.78/10.60 (( 77.78/10.60 (subsetE) => 77.78/10.60 (( 77.78/10.60 (subsetE2) => 77.78/10.60 (( 77.78/10.60 (notsubsetI) => 77.78/10.60 (( 77.78/10.60 (notequalI1) => 77.78/10.60 (( 77.78/10.60 (notequalI2) => 77.78/10.60 (( 77.78/10.60 (subsetRefl) => 77.78/10.60 (( 77.78/10.60 (subsetTrans) => 77.78/10.60 (( 77.78/10.60 (setadjoinSub) => 77.78/10.60 (( 77.78/10.60 (setadjoinSub2) => 77.78/10.60 (( 77.78/10.60 (subset2powerset) => 77.78/10.60 (( 77.78/10.60 (setextsub) => 77.78/10.60 (( 77.78/10.60 (subsetemptysetimpeq) => 77.78/10.60 (( 77.78/10.60 (powersetI1) => 77.78/10.60 (( 77.78/10.60 (powersetE1) => 77.78/10.60 (( 77.78/10.60 (inPowerset) => 77.78/10.60 (( 77.78/10.60 (powersetsubset) => 77.78/10.60 (( 77.78/10.60 (sepInPowerset) => 77.78/10.60 (( 77.78/10.60 (sepSubset) => 77.78/10.60 (( 77.78/10.60 (binunionIL) => 77.78/10.60 (( 77.78/10.60 (upairset2IR) => 77.78/10.60 (( 77.78/10.60 (binunionIR) => 77.78/10.60 (( 77.78/10.60 (binunionEcases) => 77.78/10.60 (( 77.78/10.60 (binunionE) => 77.78/10.60 (( 77.78/10.60 (binunionLsub) => 77.78/10.60 (( 77.78/10.60 (binunionRsub) => 77.78/10.60 (( 77.78/10.60 (binintersectI) => 77.78/10.60 (( 77.78/10.60 (binintersectSubset5) => 77.78/10.60 (( 77.78/10.60 (binintersectEL) => 77.78/10.60 (( 77.78/10.60 (binintersectLsub) => 77.78/10.60 (( 77.78/10.60 (binintersectSubset2) => 77.78/10.60 (( 77.78/10.60 (binintersectSubset3) => 77.78/10.60 (( 77.78/10.60 (binintersectER) => 77.78/10.60 (( 77.78/10.60 (disjointsetsI1) => 77.78/10.60 (( 77.78/10.60 (binintersectRsub) => 77.78/10.60 (( 77.78/10.60 (binintersectSubset4) => 77.78/10.60 (( 77.78/10.60 (binintersectSubset1) => 77.78/10.60 (( 77.78/10.60 (bs114d) => 77.78/10.60 (( 77.78/10.60 (setminusI) => 77.78/10.60 (( 77.78/10.60 (setminusEL) => 77.78/10.60 (( 77.78/10.60 (setminusER) => 77.78/10.60 (( 77.78/10.60 (setminusSubset2) => 77.78/10.60 (( 77.78/10.60 (setminusERneg) => 77.78/10.60 (( 77.78/10.60 (setminusELneg) => 77.78/10.60 (( 77.78/10.60 (setminusILneg) => 77.78/10.60 (( 77.78/10.60 (setminusIRneg) => 77.78/10.60 (( 77.78/10.60 (setminusLsub) => 77.78/10.60 (( 77.78/10.60 (setminusSubset1) => 77.78/10.60 (( 77.78/10.60 (symdiffE) => 77.78/10.60 (( 77.78/10.60 (symdiffI1) => 77.78/10.60 (( 77.78/10.60 (symdiffI2) => 77.78/10.60 (( 77.78/10.60 (symdiffIneg1) => 77.78/10.60 (( 77.78/10.60 (symdiffIneg2) => 77.78/10.60 (( 77.78/10.60 (secondinupair) => 77.78/10.60 (( 77.78/10.60 (setukpairIL) => 77.78/10.60 (( 77.78/10.60 (setukpairIR) => 77.78/10.60 (( 77.78/10.60 (kpairiskpair) => 77.78/10.60 (( 77.78/10.60 (kpairp) => 77.78/10.60 (( 77.78/10.60 (singletonsubset) => 77.78/10.60 (( 77.78/10.60 (singletoninpowerset) => 77.78/10.60 (( 77.78/10.60 (singletoninpowunion) => 77.78/10.60 (( 77.78/10.60 (upairset2E) => 77.78/10.60 (( 77.78/10.60 (upairsubunion) => 77.78/10.60 (( 77.78/10.60 (upairinpowunion) => 77.78/10.60 (( 77.78/10.60 (ubforcartprodlem1) => 77.78/10.60 (( 77.78/10.60 (ubforcartprodlem2) => 77.78/10.60 (( 77.78/10.60 (ubforcartprodlem3) => 77.78/10.60 (( 77.78/10.60 (cartprodpairin) => 77.78/10.60 (( 77.78/10.60 (cartprodmempair1) => 77.78/10.60 (( 77.78/10.60 (cartprodmempair) => 77.78/10.60 (( 77.78/10.60 (setunionE2) => 77.78/10.60 (( 77.78/10.60 (setunionsingleton1) => 77.78/10.60 (( 77.78/10.60 (setunionsingleton2) => 77.78/10.60 (( 77.78/10.60 (setunionsingleton) => 77.78/10.60 (( 77.78/10.60 (singletonprop) => 77.78/10.60 (( 77.78/10.60 (ex1E1) => 77.78/10.60 (( 77.78/10.60 (ex1I) => 77.78/10.60 (( 77.78/10.60 (ex1I2) => 77.78/10.60 (( 77.78/10.60 (singletonsuniq) => 77.78/10.60 (( 77.78/10.60 (setukpairinjL1) => 77.78/10.60 (( 77.78/10.60 (kfstsingleton) => 77.78/10.60 (( 77.78/10.60 (theprop) => 77.78/10.60 (( 77.78/10.60 (kfstpairEq) => 77.78/10.60 (( 77.78/10.60 (cartprodfstin) => 77.78/10.60 (( 77.78/10.60 (setukpairinjL2) => 77.78/10.60 (( 77.78/10.60 (setukpairinjL) => 77.78/10.60 (( 77.78/10.60 (setukpairinjR11) => 77.78/10.60 (( 77.78/10.60 (setukpairinjR12) => 77.78/10.60 (( 77.78/10.60 (setukpairinjR1) => 77.78/10.60 (( 77.78/10.60 (upairequniteq) => 77.78/10.60 (( 77.78/10.60 (setukpairinjR2) => 77.78/10.60 (( 77.78/10.60 (setukpairinjR) => 77.78/10.60 (( 77.78/10.60 (ksndsingleton) => 77.78/10.60 (( 77.78/10.60 (ksndpairEq) => 77.78/10.60 (( 77.78/10.60 (kpairsurjEq) => 77.78/10.60 (( 77.78/10.60 (cartprodsndin) => 77.78/10.60 (( 77.78/10.60 (cartprodpairmemEL) => 77.78/10.60 (( 77.78/10.60 (cartprodpairmemER) => 77.78/10.60 (( 77.78/10.60 (cartprodmempaircEq) => 77.78/10.60 (( 77.78/10.60 (cartprodfstpairEq) => 77.78/10.60 (( 77.78/10.60 (cartprodsndpairEq) => 77.78/10.60 (( 77.78/10.60 (cartprodpairsurjEq) => 77.78/10.60 (( 77.78/10.60 (dpsetconstrI) => 77.78/10.60 (( 77.78/10.60 (dpsetconstrSub) => 77.78/10.60 (( 77.78/10.60 (setOfPairsIsBReln) => 77.78/10.60 (( 77.78/10.60 (dpsetconstrERa) => 77.78/10.60 (( 77.78/10.60 (dpsetconstrEL1) => 77.78/10.60 (( 77.78/10.60 (dpsetconstrEL2) => 77.78/10.60 (( 77.78/10.60 (dpsetconstrER) => 77.78/10.60 (( 77.78/10.60 (funcImageSingleton) => 77.78/10.60 (( 77.78/10.60 (apProp) => 77.78/10.60 (( 77.78/10.60 (app) => 77.78/10.60 (( 77.78/10.60 (infuncsetfunc) => 77.78/10.60 (( 77.78/10.60 (ap2p) => 77.78/10.60 (( 77.78/10.60 (funcinfuncset) => 77.78/10.60 (( 77.78/10.60 (lamProp) => 77.78/10.60 (( 77.78/10.60 (lamp) => 77.78/10.60 (( 77.78/10.60 (lam2p) => 77.78/10.60 (( 77.78/10.60 (brelnall1) => 77.78/10.60 (( 77.78/10.60 (brelnall2) => 77.78/10.60 (( 77.78/10.60 (ex1E2) => 77.78/10.60 (( 77.78/10.60 (funcGraphProp1) => 77.78/10.60 (( 77.78/10.60 (funcGraphProp3) => 77.78/10.60 (( 77.78/10.60 (funcGraphProp2) => 77.78/10.60 (( 77.78/10.60 (funcextLem) => 77.78/10.60 (( 77.78/10.60 (funcGraphProp4) => 77.78/10.60 (( 77.78/10.60 (subbreln) => 77.78/10.60 (( 77.78/10.60 (eqbreln) => 77.78/10.60 (( 77.78/10.60 (funcext) => 77.78/10.60 (( 77.78/10.60 (funcext2) => 77.78/10.60 (( 77.78/10.60 (ap2apEq1) => 77.78/10.60 (( 77.78/10.60 (ap2apEq2) => 77.78/10.60 (( 77.78/10.60 (beta1) => 77.78/10.60 (( 77.78/10.60 (eta1) => 77.78/10.60 (( 77.78/10.60 (lam2lamEq) => 77.78/10.60 (( 77.78/10.60 (beta2) => 77.78/10.60 (( 77.78/10.60 (eta2) => 77.78/10.60 (( 77.78/10.60 (iffalseProp1) => 77.78/10.60 (( 77.78/10.60 (iffalseProp2) => 77.78/10.60 (( 77.78/10.60 (iftrueProp1) => 77.78/10.60 (( 77.78/10.60 (iftrueProp2) => 77.78/10.60 (( 77.78/10.60 (ifSingleton) => 77.78/10.60 (( 77.78/10.60 (ifp) => 77.78/10.60 (( 77.78/10.60 (theeq) => 77.78/10.60 (( 77.78/10.60 (iftrue) => 77.78/10.60 (( 77.78/10.60 (iffalse) => 77.78/10.60 (( 77.78/10.60 (iftrueorfalse) => 77.78/10.60 (( 77.78/10.60 (binintersectT_lem) => 77.78/10.60 (( 77.78/10.60 (binunionT_lem) => 77.78/10.60 (( 77.78/10.60 (powersetT_lem) => 77.78/10.60 (( 77.78/10.60 (setminusT_lem) => 77.78/10.60 (( 77.78/10.60 (complementT_lem) => 77.78/10.60 (( 77.78/10.60 (setextT) => 77.78/10.60 (( 77.78/10.60 (subsetTI) => 77.78/10.60 (( 77.78/10.60 (powersetTI1) => 77.78/10.60 (( 77.78/10.60 (powersetTE1) => 77.78/10.60 (( 77.78/10.60 (complementTI1) => 77.78/10.60 (( 77.78/10.60 (complementTE1) => 77.78/10.60 (( 77.78/10.60 (binintersectTELcontra) => 77.78/10.60 (( 77.78/10.60 (binintersectTERcontra) => 77.78/10.60 (( 77.78/10.60 (contrasubsetT) => 77.78/10.60 (( 77.78/10.60 (contrasubsetT1) => 77.78/10.60 (( 77.78/10.60 (contrasubsetT2) => 77.78/10.60 (( 77.78/10.60 (contrasubsetT3) => 77.78/10.60 (( 77.78/10.60 (doubleComplementI1) => 77.78/10.60 (( 77.78/10.60 (doubleComplementE1) => 77.78/10.60 (( 77.78/10.60 (doubleComplementSub1) => 77.78/10.60 (( 77.78/10.60 (doubleComplementSub2) => 77.78/10.60 (( 77.78/10.60 (doubleComplementEq) => 77.78/10.60 (( 77.78/10.60 (complementTnotintersectT) => 77.78/10.60 (( 77.78/10.60 (complementImpComplementIntersect) => 77.78/10.60 (( 77.78/10.60 (complementSubsetComplementIntersect) => 77.78/10.60 (( 77.78/10.60 (complementInPowersetComplementIntersect) => 77.78/10.60 (( 77.78/10.60 (contraSubsetComplement) => 77.78/10.60 (( 77.78/10.60 (complementTcontraSubset) => 77.78/10.60 (( 77.78/10.60 (binunionTILcontra) => 77.78/10.60 (( 77.78/10.60 (binunionTIRcontra) => 77.78/10.60 (( 77.78/10.60 (inIntersectImpInUnion) => 77.78/10.60 (( 77.78/10.60 (inIntersectImpInUnion2) => 77.78/10.60 (( 77.78/10.60 (inIntersectImpInIntersectUnions) => 77.78/10.60 (( 77.78/10.60 (intersectInPowersetIntersectUnions) => 77.78/10.60 (( 77.78/10.60 (inComplementUnionImpNotIn1) => 77.78/10.60 (( 77.78/10.60 (inComplementUnionImpInComplement1) => 77.78/10.60 (( 77.78/10.60 (binunionTE) => 77.78/10.60 (( 77.78/10.60 (binunionTEcontra) => 77.78/10.60 (( 77.78/10.60 (demorgan2a1) => 77.78/10.60 (( 77.78/10.60 (complementUnionInPowersetComplement) => 77.78/10.60 (( 77.78/10.60 (demorgan2a2) => 77.78/10.60 (( 77.78/10.60 (demorgan1a) => 77.78/10.60 (( 77.78/10.60 (demorgan1b) => 77.78/10.60 (( 77.78/10.60 (demorgan1) => 77.78/10.60 (( 77.78/10.60 (demorgan2a) => 77.78/10.60 (( 77.78/10.60 (demorgan2b2) => 77.78/10.60 (( 77.78/10.60 (demorgan2b) => 77.78/10.60 (( 77.78/10.60 (demorgan2) => 77.78/10.60 (( 77.78/10.60 (woz13rule0) => 77.78/10.60 (( 77.78/10.60 (woz13rule1) => 77.78/10.60 (( 77.78/10.60 (woz13rule2) => 77.78/10.60 (( 77.78/10.60 (woz13rule3) => 77.78/10.60 (( 77.78/10.60 (woz13rule4) => 77.78/10.60 (( 77.78/10.60 (woz1_1) => 77.78/10.60 (( 77.78/10.60 (woz1_2) => 77.78/10.60 (( 77.78/10.60 (woz1_3) => 77.78/10.60 (( 77.78/10.60 (woz1_4) => 77.78/10.60 (( 77.78/10.60 (woz1_5) => 77.78/10.60 (( 77.78/10.60 (breln1all2) => 77.78/10.60 (( 77.78/10.60 (breln1SetBreln1) => 77.78/10.60 (( 77.78/10.60 (choice2fnsingleton) => 77.78/10.60 (( 77.78/10.60 (setOfPairsIsBReln1) => 77.78/10.60 (( 77.78/10.60 (breln1all1) => 77.78/10.60 (( 77.78/10.60 (subbreln1) => 77.78/10.60 (( 77.78/10.60 (eqbreln1) => 77.78/10.60 (( 77.78/10.60 (breln1invprop) => 77.78/10.60 (( 77.78/10.60 (breln1invI) => 77.78/10.60 (( 77.78/10.60 (breln1invE) => 77.78/10.60 (( 77.78/10.60 (breln1compprop) => 77.78/10.60 (( 77.78/10.60 (breln1compI) => 77.78/10.60 (( 77.78/10.60 (breln1compE) => 77.78/10.60 (( 77.78/10.60 (breln1compEex) => 77.78/10.60 (( 77.78/10.60 (breln1unionprop) => 77.78/10.60 (( 77.78/10.60 (breln1unionIL) => 77.78/10.60 (( 77.78/10.60 (breln1unionIR) => 77.78/10.60 (( 77.78/10.60 (breln1unionI) => 77.78/10.60 (( 77.78/10.60 (breln1unionE) => 77.78/10.60 (( 77.78/10.60 (breln1unionEcases) => 77.78/10.60 (( 77.78/10.60 (breln1unionCommutes) => 77.78/10.60 (( 77.78/10.60 (woz2Ex) => 77.78/10.60 (( 77.78/10.60 (woz2W) => 77.78/10.60 (( 77.78/10.60 (woz2A) => 77.78/10.60 (( 77.78/10.60 (woz2B) => 77.78/10.60 (( 77.78/10.60 (image1Ex) => 77.78/10.60 (( 77.78/10.60 (image1Ex1) => 77.78/10.60 (( 77.78/10.60 (image1Equiv) => 77.78/10.60 (( 77.78/10.60 (image1E) => 77.78/10.60 (( 77.78/10.60 (image1I) => 77.78/10.60 (( 77.78/10.60 (injFuncInInjFuncSet) => 77.78/10.60 (( 77.78/10.60 (injFuncSetFuncIn) => 77.78/10.60 (( 77.78/10.60 (injFuncSetFuncInj) => 77.78/10.60 (( 77.78/10.60 (surjFuncSetFuncIn) => 77.78/10.60 (( 77.78/10.60 (surjFuncSetFuncSurj) => 77.78/10.60 (( 77.78/10.60 (leftInvIsSurj) => 77.78/10.60 (( 77.78/10.60 (surjCantorThm) => 77.78/10.60 (( 77.78/10.60 (foundation2) => 77.78/10.60 (( 77.78/10.60 (notinself) => 77.78/10.60 (( 77.78/10.60 (notinself2) => 77.78/10.60 (( 77.78/10.60 (omegaSp) => 77.78/10.60 (( 77.78/10.60 (omegaSclos) => 77.78/10.60 (( 77.78/10.60 (peano0notS) => 77.78/10.60 (( 77.78/10.60 (peanoSinj) => 77.78/10.60 (( 77.78/10.60 (transitivesetOp1) => 77.78/10.60 (( 77.78/10.60 (binintTransitive) => 77.78/10.60 (( 77.78/10.60 (transitivesetOp2) => 77.78/10.60 (( 77.78/10.60 (setunionTransitive) => 77.78/10.60 (( 77.78/10.60 (ordinalMinLem1) => 77.78/10.60 (( 77.78/10.60 (!!) @ ( 77.78/10.60 ^[Y0 : $i]: 77.78/10.60 (( 77.78/10.60 (ordinal @ 77.78/10.60 Y0) => 77.78/10.60 (( 77.78/10.60 (!!) @ ( 77.78/10.60 ^[Y1 : $i]: 77.78/10.60 (( 77.78/10.60 (!!) @ ( 77.78/10.60 ^[Y2 : $i]: 77.78/10.60 (( 77.78/10.60 (in @ 77.78/10.60 Y2 @ 77.78/10.60 Y0) => 77.78/10.60 (( 77.78/10.60 (in @ 77.78/10.60 Y1 @ 77.78/10.60 Y2) => 77.78/10.60 (in @ 77.78/10.60 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 77.78/10.60 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl406])). 77.78/10.60 thf(zip_derived_cl420, plain, 77.78/10.60 (~ (((singletonsswitch) => 77.78/10.60 (((upairsetE) => 77.78/10.60 (((upairsetIL) => 77.78/10.60 (((upairsetIR) => 77.78/10.60 (((emptyE1) => 77.78/10.60 (((vacuousDall) => 77.78/10.60 (((quantDeMorgan1) => 77.78/10.60 (((quantDeMorgan2) => 77.78/10.60 (((quantDeMorgan3) => 77.78/10.60 (((quantDeMorgan4) => 77.78/10.60 (((prop2setI) => 77.78/10.60 (((prop2set2propI) => 77.78/10.60 (((notdexE) => 77.78/10.60 (((notdallE) => 77.78/10.60 (((exuI1) => 77.78/10.60 (((exuI3) => 77.78/10.60 (((exuI2) => 77.78/10.60 (((inCongP) => 77.78/10.60 (((in__Cong) => 77.78/10.60 (((exuE3u) => 77.78/10.60 (((exu__Cong) => 77.78/10.60 (((setadjoin__Cong) => 77.78/10.60 (((powerset__Cong) => 77.78/10.60 (((setunion__Cong) => 77.78/10.60 (((exuEu) => 77.78/10.60 (((descr__Cong) => 77.78/10.60 (((dsetconstr__Cong) => 77.78/10.60 (((subsetI1) => 77.78/10.60 (((eqimpsubset2) => 77.78/10.60 (((eqimpsubset1) => 77.78/10.60 (( 77.78/10.60 (subsetI2) => 77.78/10.60 (( 77.78/10.60 (emptysetsubset) => 77.78/10.60 (( 77.78/10.60 (subsetE) => 77.78/10.60 (( 77.78/10.60 (subsetE2) => 77.78/10.60 (( 77.78/10.60 (notsubsetI) => 77.78/10.60 (( 77.78/10.60 (notequalI1) => 77.78/10.60 (( 77.78/10.60 (notequalI2) => 77.78/10.60 (( 77.78/10.60 (subsetRefl) => 77.78/10.60 (( 77.78/10.60 (subsetTrans) => 77.78/10.60 (( 77.78/10.60 (setadjoinSub) => 77.78/10.60 (( 77.78/10.60 (setadjoinSub2) => 77.78/10.60 (( 77.78/10.60 (subset2powerset) => 77.78/10.60 (( 77.78/10.60 (setextsub) => 77.78/10.60 (( 77.78/10.60 (subsetemptysetimpeq) => 77.78/10.60 (( 77.78/10.60 (powersetI1) => 77.78/10.60 (( 77.78/10.60 (powersetE1) => 77.78/10.60 (( 77.78/10.60 (inPowerset) => 77.78/10.60 (( 77.78/10.60 (powersetsubset) => 77.78/10.60 (( 77.78/10.60 (sepInPowerset) => 77.78/10.60 (( 77.78/10.60 (sepSubset) => 77.78/10.60 (( 77.78/10.60 (binunionIL) => 77.78/10.60 (( 77.78/10.60 (upairset2IR) => 77.78/10.60 (( 77.78/10.60 (binunionIR) => 77.78/10.60 (( 77.78/10.60 (binunionEcases) => 77.78/10.60 (( 77.78/10.60 (binunionE) => 77.78/10.60 (( 77.78/10.60 (binunionLsub) => 77.78/10.60 (( 77.78/10.60 (binunionRsub) => 77.78/10.60 (( 77.78/10.60 (binintersectI) => 77.78/10.60 (( 77.78/10.60 (binintersectSubset5) => 77.78/10.60 (( 77.78/10.60 (binintersectEL) => 77.78/10.60 (( 77.78/10.60 (binintersectLsub) => 77.78/10.60 (( 77.78/10.60 (binintersectSubset2) => 77.78/10.60 (( 77.78/10.60 (binintersectSubset3) => 77.78/10.60 (( 77.78/10.60 (binintersectER) => 77.78/10.60 (( 77.78/10.60 (disjointsetsI1) => 77.78/10.60 (( 77.78/10.60 (binintersectRsub) => 77.78/10.60 (( 77.78/10.60 (binintersectSubset4) => 77.78/10.60 (( 77.78/10.60 (binintersectSubset1) => 77.78/10.60 (( 77.78/10.60 (bs114d) => 77.78/10.60 (( 77.78/10.60 (setminusI) => 77.78/10.60 (( 77.78/10.60 (setminusEL) => 77.78/10.60 (( 77.78/10.60 (setminusER) => 77.78/10.60 (( 77.78/10.60 (setminusSubset2) => 77.78/10.60 (( 77.78/10.60 (setminusERneg) => 77.78/10.60 (( 77.78/10.60 (setminusELneg) => 77.78/10.60 (( 77.78/10.60 (setminusILneg) => 77.78/10.60 (( 77.78/10.60 (setminusIRneg) => 77.78/10.60 (( 77.78/10.60 (setminusLsub) => 77.78/10.60 (( 77.78/10.60 (setminusSubset1) => 77.78/10.60 (( 77.78/10.60 (symdiffE) => 77.78/10.60 (( 77.78/10.60 (symdiffI1) => 77.78/10.60 (( 77.78/10.60 (symdiffI2) => 77.78/10.60 (( 77.78/10.60 (symdiffIneg1) => 77.78/10.60 (( 77.78/10.60 (symdiffIneg2) => 77.78/10.60 (( 77.78/10.60 (secondinupair) => 77.78/10.60 (( 77.78/10.60 (setukpairIL) => 77.78/10.60 (( 77.78/10.60 (setukpairIR) => 77.78/10.60 (( 77.78/10.60 (kpairiskpair) => 77.78/10.60 (( 77.78/10.60 (kpairp) => 77.78/10.60 (( 77.78/10.60 (singletonsubset) => 77.78/10.60 (( 77.78/10.60 (singletoninpowerset) => 77.78/10.60 (( 77.78/10.60 (singletoninpowunion) => 77.78/10.60 (( 77.78/10.60 (upairset2E) => 77.78/10.60 (( 77.78/10.60 (upairsubunion) => 77.78/10.60 (( 77.78/10.60 (upairinpowunion) => 77.78/10.60 (( 77.78/10.60 (ubforcartprodlem1) => 77.78/10.60 (( 77.78/10.60 (ubforcartprodlem2) => 77.78/10.60 (( 77.78/10.60 (ubforcartprodlem3) => 77.78/10.60 (( 77.78/10.60 (cartprodpairin) => 77.78/10.60 (( 77.78/10.60 (cartprodmempair1) => 77.78/10.60 (( 77.78/10.60 (cartprodmempair) => 77.78/10.60 (( 77.78/10.60 (setunionE2) => 77.78/10.60 (( 77.78/10.60 (setunionsingleton1) => 77.78/10.60 (( 77.78/10.60 (setunionsingleton2) => 77.78/10.60 (( 77.78/10.60 (setunionsingleton) => 77.78/10.60 (( 77.78/10.60 (singletonprop) => 77.78/10.60 (( 77.78/10.60 (ex1E1) => 77.78/10.60 (( 77.78/10.60 (ex1I) => 77.78/10.60 (( 77.78/10.60 (ex1I2) => 77.78/10.60 (( 77.78/10.60 (singletonsuniq) => 77.78/10.60 (( 77.78/10.60 (setukpairinjL1) => 77.78/10.60 (( 77.78/10.60 (kfstsingleton) => 77.78/10.60 (( 77.78/10.60 (theprop) => 77.78/10.60 (( 77.78/10.60 (kfstpairEq) => 77.78/10.60 (( 77.78/10.60 (cartprodfstin) => 77.78/10.60 (( 77.78/10.60 (setukpairinjL2) => 77.78/10.60 (( 77.78/10.60 (setukpairinjL) => 77.78/10.60 (( 77.78/10.60 (setukpairinjR11) => 77.78/10.60 (( 77.78/10.60 (setukpairinjR12) => 77.78/10.60 (( 77.78/10.60 (setukpairinjR1) => 77.78/10.60 (( 77.78/10.60 (upairequniteq) => 77.78/10.60 (( 77.78/10.60 (setukpairinjR2) => 77.78/10.60 (( 77.78/10.60 (setukpairinjR) => 77.78/10.60 (( 77.78/10.60 (ksndsingleton) => 77.78/10.60 (( 77.78/10.60 (ksndpairEq) => 77.78/10.60 (( 77.78/10.60 (kpairsurjEq) => 77.78/10.60 (( 77.78/10.60 (cartprodsndin) => 77.78/10.60 (( 77.78/10.60 (cartprodpairmemEL) => 77.78/10.60 (( 77.78/10.60 (cartprodpairmemER) => 77.78/10.60 (( 77.78/10.60 (cartprodmempaircEq) => 77.78/10.60 (( 77.78/10.60 (cartprodfstpairEq) => 77.78/10.60 (( 77.78/10.60 (cartprodsndpairEq) => 77.78/10.60 (( 77.78/10.60 (cartprodpairsurjEq) => 77.78/10.60 (( 77.78/10.60 (dpsetconstrI) => 77.78/10.60 (( 77.78/10.60 (dpsetconstrSub) => 77.78/10.60 (( 77.78/10.60 (setOfPairsIsBReln) => 77.78/10.60 (( 77.78/10.60 (dpsetconstrERa) => 77.78/10.60 (( 77.78/10.60 (dpsetconstrEL1) => 77.78/10.60 (( 77.78/10.60 (dpsetconstrEL2) => 77.78/10.60 (( 77.78/10.60 (dpsetconstrER) => 77.78/10.60 (( 77.78/10.60 (funcImageSingleton) => 77.78/10.60 (( 77.78/10.60 (apProp) => 77.78/10.60 (( 77.78/10.60 (app) => 77.78/10.60 (( 77.78/10.60 (infuncsetfunc) => 77.78/10.60 (( 77.78/10.60 (ap2p) => 77.78/10.60 (( 77.78/10.60 (funcinfuncset) => 77.78/10.60 (( 77.78/10.60 (lamProp) => 77.78/10.60 (( 77.78/10.60 (lamp) => 77.78/10.60 (( 77.78/10.60 (lam2p) => 77.78/10.60 (( 77.78/10.60 (brelnall1) => 77.78/10.60 (( 77.78/10.60 (brelnall2) => 77.78/10.60 (( 77.78/10.60 (ex1E2) => 77.78/10.60 (( 77.78/10.60 (funcGraphProp1) => 77.78/10.60 (( 77.78/10.60 (funcGraphProp3) => 77.78/10.60 (( 77.78/10.60 (funcGraphProp2) => 77.78/10.60 (( 77.78/10.60 (funcextLem) => 77.78/10.60 (( 77.78/10.60 (funcGraphProp4) => 77.78/10.60 (( 77.78/10.60 (subbreln) => 77.78/10.60 (( 77.78/10.60 (eqbreln) => 77.78/10.60 (( 77.78/10.60 (funcext) => 77.78/10.60 (( 77.78/10.60 (funcext2) => 77.78/10.60 (( 77.78/10.60 (ap2apEq1) => 77.78/10.60 (( 77.78/10.60 (ap2apEq2) => 77.78/10.60 (( 77.78/10.60 (beta1) => 77.78/10.60 (( 77.78/10.60 (eta1) => 77.78/10.60 (( 77.78/10.60 (lam2lamEq) => 77.78/10.60 (( 77.78/10.60 (beta2) => 77.78/10.60 (( 77.78/10.60 (eta2) => 77.78/10.60 (( 77.78/10.60 (iffalseProp1) => 77.78/10.60 (( 77.78/10.60 (iffalseProp2) => 77.78/10.60 (( 77.78/10.60 (iftrueProp1) => 77.78/10.60 (( 77.78/10.60 (iftrueProp2) => 77.78/10.60 (( 77.78/10.60 (ifSingleton) => 77.78/10.60 (( 77.78/10.60 (ifp) => 77.78/10.60 (( 77.78/10.60 (theeq) => 77.78/10.60 (( 77.78/10.60 (iftrue) => 77.78/10.60 (( 77.78/10.60 (iffalse) => 77.78/10.60 (( 77.78/10.60 (iftrueorfalse) => 77.78/10.60 (( 77.78/10.60 (binintersectT_lem) => 77.78/10.60 (( 77.78/10.60 (binunionT_lem) => 77.78/10.60 (( 77.78/10.60 (powersetT_lem) => 77.78/10.60 (( 77.78/10.60 (setminusT_lem) => 77.78/10.60 (( 77.78/10.60 (complementT_lem) => 77.78/10.60 (( 77.78/10.60 (setextT) => 77.78/10.60 (( 77.78/10.60 (subsetTI) => 77.78/10.60 (( 77.78/10.60 (powersetTI1) => 77.78/10.60 (( 77.78/10.60 (powersetTE1) => 77.78/10.60 (( 77.78/10.60 (complementTI1) => 77.78/10.60 (( 77.78/10.60 (complementTE1) => 77.78/10.60 (( 77.78/10.60 (binintersectTELcontra) => 77.78/10.60 (( 77.78/10.60 (binintersectTERcontra) => 77.78/10.60 (( 77.78/10.60 (contrasubsetT) => 77.78/10.60 (( 77.78/10.60 (contrasubsetT1) => 77.78/10.60 (( 77.78/10.60 (contrasubsetT2) => 77.78/10.60 (( 77.78/10.60 (contrasubsetT3) => 77.78/10.60 (( 77.78/10.60 (doubleComplementI1) => 77.78/10.60 (( 77.78/10.60 (doubleComplementE1) => 77.78/10.60 (( 77.78/10.60 (doubleComplementSub1) => 77.78/10.60 (( 77.78/10.60 (doubleComplementSub2) => 77.78/10.60 (( 77.78/10.60 (doubleComplementEq) => 77.78/10.60 (( 77.78/10.60 (complementTnotintersectT) => 77.78/10.60 (( 77.78/10.60 (complementImpComplementIntersect) => 77.78/10.60 (( 77.78/10.60 (complementSubsetComplementIntersect) => 77.78/10.60 (( 77.78/10.60 (complementInPowersetComplementIntersect) => 77.78/10.60 (( 77.78/10.60 (contraSubsetComplement) => 77.78/10.60 (( 77.78/10.60 (complementTcontraSubset) => 77.78/10.60 (( 77.78/10.60 (binunionTILcontra) => 77.78/10.60 (( 77.78/10.60 (binunionTIRcontra) => 77.78/10.60 (( 77.78/10.60 (inIntersectImpInUnion) => 77.78/10.60 (( 77.78/10.60 (inIntersectImpInUnion2) => 77.78/10.60 (( 77.78/10.60 (inIntersectImpInIntersectUnions) => 77.78/10.60 (( 77.78/10.60 (intersectInPowersetIntersectUnions) => 77.78/10.60 (( 77.78/10.60 (inComplementUnionImpNotIn1) => 77.78/10.60 (( 77.78/10.60 (inComplementUnionImpInComplement1) => 77.78/10.60 (( 77.78/10.60 (binunionTE) => 77.78/10.60 (( 77.78/10.60 (binunionTEcontra) => 77.78/10.60 (( 77.78/10.60 (demorgan2a1) => 77.78/10.60 (( 77.78/10.60 (complementUnionInPowersetComplement) => 77.78/10.60 (( 77.78/10.60 (demorgan2a2) => 77.78/10.60 (( 77.78/10.60 (demorgan1a) => 77.78/10.60 (( 77.78/10.60 (demorgan1b) => 77.78/10.60 (( 77.78/10.60 (demorgan1) => 77.78/10.60 (( 77.78/10.60 (demorgan2a) => 77.78/10.60 (( 77.78/10.60 (demorgan2b2) => 77.78/10.60 (( 77.78/10.60 (demorgan2b) => 77.78/10.60 (( 77.78/10.60 (demorgan2) => 77.78/10.60 (( 77.78/10.60 (woz13rule0) => 77.78/10.60 (( 77.78/10.60 (woz13rule1) => 77.78/10.60 (( 77.78/10.60 (woz13rule2) => 77.78/10.60 (( 77.78/10.60 (woz13rule3) => 77.78/10.60 (( 77.78/10.60 (woz13rule4) => 77.78/10.60 (( 77.78/10.60 (woz1_1) => 77.78/10.60 (( 77.78/10.60 (woz1_2) => 77.78/10.60 (( 77.78/10.60 (woz1_3) => 77.78/10.60 (( 77.78/10.60 (woz1_4) => 77.78/10.60 (( 77.78/10.60 (woz1_5) => 77.78/10.60 (( 77.78/10.60 (breln1all2) => 77.78/10.60 (( 77.78/10.60 (breln1SetBreln1) => 77.78/10.60 (( 77.78/10.60 (choice2fnsingleton) => 77.78/10.60 (( 77.78/10.60 (setOfPairsIsBReln1) => 77.78/10.60 (( 77.78/10.60 (breln1all1) => 77.78/10.60 (( 77.78/10.60 (subbreln1) => 77.78/10.60 (( 77.78/10.60 (eqbreln1) => 77.78/10.60 (( 77.78/10.60 (breln1invprop) => 77.78/10.60 (( 77.78/10.60 (breln1invI) => 77.78/10.60 (( 77.78/10.60 (breln1invE) => 77.78/10.60 (( 77.78/10.60 (breln1compprop) => 77.78/10.60 (( 77.78/10.60 (breln1compI) => 77.78/10.60 (( 77.78/10.60 (breln1compE) => 77.78/10.60 (( 77.78/10.60 (breln1compEex) => 77.78/10.60 (( 77.78/10.60 (breln1unionprop) => 77.78/10.60 (( 77.78/10.60 (breln1unionIL) => 77.78/10.60 (( 77.78/10.60 (breln1unionIR) => 77.78/10.60 (( 77.78/10.60 (breln1unionI) => 77.78/10.60 (( 77.78/10.60 (breln1unionE) => 77.78/10.60 (( 77.78/10.60 (breln1unionEcases) => 77.78/10.60 (( 77.78/10.60 (breln1unionCommutes) => 77.78/10.60 (( 77.78/10.60 (woz2Ex) => 77.78/10.60 (( 77.78/10.60 (woz2W) => 77.78/10.60 (( 77.78/10.60 (woz2A) => 77.78/10.60 (( 77.78/10.60 (woz2B) => 77.78/10.60 (( 77.78/10.60 (image1Ex) => 77.78/10.60 (( 77.78/10.60 (image1Ex1) => 77.78/10.60 (( 77.78/10.60 (image1Equiv) => 77.78/10.60 (( 77.78/10.60 (image1E) => 77.78/10.60 (( 77.78/10.60 (image1I) => 77.78/10.60 (( 77.78/10.60 (injFuncInInjFuncSet) => 77.78/10.60 (( 77.78/10.60 (injFuncSetFuncIn) => 77.78/10.60 (( 77.78/10.60 (injFuncSetFuncInj) => 77.78/10.60 (( 77.78/10.60 (surjFuncSetFuncIn) => 77.78/10.60 (( 77.78/10.60 (surjFuncSetFuncSurj) => 77.78/10.60 (( 77.78/10.60 (leftInvIsSurj) => 77.78/10.60 (( 77.78/10.60 (surjCantorThm) => 77.78/10.60 (( 77.78/10.60 (foundation2) => 77.78/10.60 (( 77.78/10.60 (notinself) => 77.78/10.60 (( 77.78/10.60 (notinself2) => 77.78/10.60 (( 77.78/10.60 (omegaSp) => 77.78/10.60 (( 77.78/10.60 (omegaSclos) => 77.78/10.60 (( 77.78/10.60 (peano0notS) => 77.78/10.60 (( 77.78/10.60 (peanoSinj) => 77.78/10.60 (( 77.78/10.60 (transitivesetOp1) => 77.78/10.60 (( 77.78/10.60 (binintTransitive) => 77.78/10.60 (( 77.78/10.60 (transitivesetOp2) => 77.78/10.60 (( 77.78/10.60 (setunionTransitive) => 77.78/10.60 (( 77.78/10.60 (ordinalMinLem1) => 77.78/10.60 (( 77.78/10.60 (!!) @ ( 77.78/10.60 ^[Y0 : $i]: 77.78/10.60 (( 77.78/10.60 (ordinal @ 77.78/10.60 Y0) => 77.78/10.60 (( 77.78/10.60 (!!) @ ( 77.78/10.60 ^[Y1 : $i]: 77.78/10.60 (( 77.78/10.60 (!!) @ ( 77.78/10.60 ^[Y2 : $i]: 77.78/10.60 (( 77.78/10.60 (in @ 77.78/10.60 Y2 @ 77.78/10.60 Y0) => 77.78/10.60 (( 77.78/10.60 (in @ 77.78/10.60 Y1 @ 77.78/10.60 Y2) => 77.78/10.60 (in @ 77.78/10.60 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 77.78/10.60 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl413])). 77.78/10.60 thf(zip_derived_cl428, plain, 77.78/10.60 (~ (((upairsetE) => 77.78/10.60 (((upairsetIL) => 77.78/10.60 (((upairsetIR) => 77.78/10.60 (((emptyE1) => 77.78/10.60 (((vacuousDall) => 77.78/10.60 (((quantDeMorgan1) => 77.78/10.60 (((quantDeMorgan2) => 77.78/10.60 (((quantDeMorgan3) => 77.78/10.60 (((quantDeMorgan4) => 77.78/10.60 (((prop2setI) => 77.78/10.60 (((prop2set2propI) => 77.78/10.60 (((notdexE) => 77.78/10.60 (((notdallE) => 77.78/10.60 (((exuI1) => 77.78/10.60 (((exuI3) => 77.78/10.60 (((exuI2) => 77.78/10.60 (((inCongP) => 77.78/10.60 (((in__Cong) => 77.78/10.60 (((exuE3u) => 77.78/10.60 (((exu__Cong) => 77.78/10.60 (((setadjoin__Cong) => 77.78/10.60 (((powerset__Cong) => 77.78/10.60 (((setunion__Cong) => 77.78/10.60 (((exuEu) => 77.78/10.60 (((descr__Cong) => 77.78/10.60 (((dsetconstr__Cong) => 77.78/10.60 (((subsetI1) => 77.78/10.60 (((eqimpsubset2) => 77.78/10.60 (((eqimpsubset1) => 77.78/10.60 (((subsetI2) => 77.78/10.60 (( 77.78/10.60 (emptysetsubset) => 77.78/10.60 (( 77.78/10.60 (subsetE) => 77.78/10.60 (( 77.78/10.60 (subsetE2) => 77.78/10.60 (( 77.78/10.60 (notsubsetI) => 77.78/10.60 (( 77.78/10.60 (notequalI1) => 77.78/10.60 (( 77.78/10.60 (notequalI2) => 77.78/10.60 (( 77.78/10.60 (subsetRefl) => 77.78/10.60 (( 77.78/10.60 (subsetTrans) => 77.78/10.60 (( 77.78/10.60 (setadjoinSub) => 77.78/10.60 (( 77.78/10.60 (setadjoinSub2) => 77.78/10.60 (( 77.78/10.60 (subset2powerset) => 77.78/10.60 (( 77.78/10.60 (setextsub) => 77.78/10.60 (( 77.78/10.60 (subsetemptysetimpeq) => 77.78/10.60 (( 77.78/10.60 (powersetI1) => 77.78/10.60 (( 77.78/10.60 (powersetE1) => 77.78/10.60 (( 77.78/10.60 (inPowerset) => 77.78/10.60 (( 77.78/10.60 (powersetsubset) => 77.78/10.60 (( 77.78/10.60 (sepInPowerset) => 77.78/10.60 (( 77.78/10.60 (sepSubset) => 77.78/10.60 (( 77.78/10.60 (binunionIL) => 77.78/10.60 (( 77.78/10.60 (upairset2IR) => 77.78/10.60 (( 77.78/10.60 (binunionIR) => 77.78/10.60 (( 77.78/10.60 (binunionEcases) => 77.78/10.60 (( 77.78/10.60 (binunionE) => 77.78/10.60 (( 77.78/10.60 (binunionLsub) => 77.78/10.60 (( 77.78/10.60 (binunionRsub) => 77.78/10.60 (( 77.78/10.60 (binintersectI) => 77.78/10.60 (( 77.78/10.60 (binintersectSubset5) => 77.78/10.60 (( 77.78/10.60 (binintersectEL) => 77.78/10.60 (( 77.78/10.60 (binintersectLsub) => 77.78/10.60 (( 77.78/10.60 (binintersectSubset2) => 77.78/10.60 (( 77.78/10.60 (binintersectSubset3) => 77.78/10.60 (( 77.78/10.60 (binintersectER) => 77.78/10.60 (( 77.78/10.60 (disjointsetsI1) => 77.78/10.60 (( 77.78/10.60 (binintersectRsub) => 77.78/10.60 (( 77.78/10.60 (binintersectSubset4) => 77.78/10.60 (( 77.78/10.60 (binintersectSubset1) => 77.78/10.60 (( 77.78/10.60 (bs114d) => 77.78/10.60 (( 77.78/10.60 (setminusI) => 77.78/10.60 (( 77.78/10.60 (setminusEL) => 77.78/10.60 (( 77.78/10.60 (setminusER) => 77.78/10.60 (( 77.78/10.60 (setminusSubset2) => 77.78/10.60 (( 77.78/10.60 (setminusERneg) => 77.78/10.60 (( 77.78/10.60 (setminusELneg) => 77.78/10.60 (( 77.78/10.60 (setminusILneg) => 77.78/10.60 (( 77.78/10.60 (setminusIRneg) => 77.78/10.60 (( 77.78/10.60 (setminusLsub) => 77.78/10.60 (( 77.78/10.60 (setminusSubset1) => 77.78/10.60 (( 77.78/10.60 (symdiffE) => 77.78/10.60 (( 77.78/10.60 (symdiffI1) => 77.78/10.60 (( 77.78/10.60 (symdiffI2) => 77.78/10.60 (( 77.78/10.60 (symdiffIneg1) => 77.78/10.60 (( 77.78/10.60 (symdiffIneg2) => 77.78/10.60 (( 77.78/10.60 (secondinupair) => 77.78/10.60 (( 77.78/10.60 (setukpairIL) => 77.78/10.60 (( 77.78/10.60 (setukpairIR) => 77.78/10.60 (( 77.78/10.60 (kpairiskpair) => 77.78/10.60 (( 77.78/10.60 (kpairp) => 77.78/10.60 (( 77.78/10.60 (singletonsubset) => 77.78/10.60 (( 77.78/10.60 (singletoninpowerset) => 77.78/10.60 (( 77.78/10.60 (singletoninpowunion) => 77.78/10.60 (( 77.78/10.60 (upairset2E) => 77.78/10.60 (( 77.78/10.60 (upairsubunion) => 77.78/10.60 (( 77.78/10.60 (upairinpowunion) => 77.78/10.60 (( 77.78/10.60 (ubforcartprodlem1) => 77.78/10.60 (( 77.78/10.60 (ubforcartprodlem2) => 77.78/10.60 (( 77.78/10.60 (ubforcartprodlem3) => 77.78/10.60 (( 77.78/10.60 (cartprodpairin) => 77.78/10.60 (( 77.78/10.60 (cartprodmempair1) => 77.78/10.60 (( 77.78/10.60 (cartprodmempair) => 77.78/10.60 (( 77.78/10.60 (setunionE2) => 77.78/10.60 (( 77.78/10.60 (setunionsingleton1) => 77.78/10.60 (( 77.78/10.60 (setunionsingleton2) => 77.78/10.60 (( 77.78/10.60 (setunionsingleton) => 77.78/10.60 (( 77.78/10.60 (singletonprop) => 77.78/10.60 (( 77.78/10.60 (ex1E1) => 77.78/10.60 (( 77.78/10.60 (ex1I) => 77.78/10.60 (( 77.78/10.60 (ex1I2) => 77.78/10.60 (( 77.78/10.60 (singletonsuniq) => 77.78/10.60 (( 77.78/10.60 (setukpairinjL1) => 77.78/10.60 (( 77.78/10.60 (kfstsingleton) => 77.78/10.60 (( 77.78/10.60 (theprop) => 77.78/10.60 (( 77.78/10.60 (kfstpairEq) => 77.78/10.60 (( 77.78/10.60 (cartprodfstin) => 77.78/10.60 (( 77.78/10.60 (setukpairinjL2) => 77.78/10.60 (( 77.78/10.60 (setukpairinjL) => 77.78/10.60 (( 77.78/10.60 (setukpairinjR11) => 77.78/10.60 (( 77.78/10.60 (setukpairinjR12) => 77.78/10.60 (( 77.78/10.60 (setukpairinjR1) => 77.78/10.60 (( 77.78/10.60 (upairequniteq) => 77.78/10.60 (( 77.78/10.60 (setukpairinjR2) => 77.78/10.60 (( 77.78/10.60 (setukpairinjR) => 77.78/10.60 (( 77.78/10.60 (ksndsingleton) => 77.78/10.60 (( 77.78/10.60 (ksndpairEq) => 77.78/10.60 (( 77.78/10.60 (kpairsurjEq) => 77.78/10.60 (( 77.78/10.60 (cartprodsndin) => 77.78/10.60 (( 77.78/10.60 (cartprodpairmemEL) => 77.78/10.60 (( 77.78/10.60 (cartprodpairmemER) => 77.78/10.60 (( 77.78/10.60 (cartprodmempaircEq) => 77.78/10.60 (( 77.78/10.60 (cartprodfstpairEq) => 77.78/10.60 (( 77.78/10.60 (cartprodsndpairEq) => 77.78/10.60 (( 77.78/10.60 (cartprodpairsurjEq) => 77.78/10.60 (( 77.78/10.60 (dpsetconstrI) => 77.78/10.60 (( 77.78/10.60 (dpsetconstrSub) => 77.78/10.60 (( 77.78/10.60 (setOfPairsIsBReln) => 77.78/10.60 (( 77.78/10.60 (dpsetconstrERa) => 77.78/10.60 (( 77.78/10.60 (dpsetconstrEL1) => 77.78/10.60 (( 77.78/10.60 (dpsetconstrEL2) => 77.78/10.60 (( 77.78/10.60 (dpsetconstrER) => 77.78/10.60 (( 77.78/10.60 (funcImageSingleton) => 77.78/10.60 (( 77.78/10.60 (apProp) => 77.78/10.60 (( 77.78/10.60 (app) => 77.78/10.60 (( 77.78/10.60 (infuncsetfunc) => 77.78/10.60 (( 77.78/10.60 (ap2p) => 77.78/10.60 (( 77.78/10.60 (funcinfuncset) => 77.78/10.60 (( 77.78/10.60 (lamProp) => 77.78/10.60 (( 77.78/10.60 (lamp) => 77.78/10.60 (( 77.78/10.60 (lam2p) => 77.78/10.60 (( 77.78/10.60 (brelnall1) => 77.78/10.60 (( 77.78/10.60 (brelnall2) => 77.78/10.60 (( 77.78/10.60 (ex1E2) => 77.78/10.60 (( 77.78/10.60 (funcGraphProp1) => 77.78/10.60 (( 77.78/10.60 (funcGraphProp3) => 77.78/10.60 (( 77.78/10.60 (funcGraphProp2) => 77.78/10.60 (( 77.78/10.60 (funcextLem) => 77.78/10.60 (( 77.78/10.60 (funcGraphProp4) => 77.78/10.60 (( 77.78/10.60 (subbreln) => 77.78/10.60 (( 77.78/10.60 (eqbreln) => 77.78/10.60 (( 77.78/10.60 (funcext) => 77.78/10.60 (( 77.78/10.60 (funcext2) => 77.78/10.60 (( 77.78/10.60 (ap2apEq1) => 77.78/10.60 (( 77.78/10.60 (ap2apEq2) => 77.78/10.60 (( 77.78/10.60 (beta1) => 77.78/10.60 (( 77.78/10.60 (eta1) => 77.78/10.60 (( 77.78/10.60 (lam2lamEq) => 77.78/10.60 (( 77.78/10.60 (beta2) => 77.78/10.60 (( 77.78/10.60 (eta2) => 77.78/10.60 (( 77.78/10.60 (iffalseProp1) => 77.78/10.60 (( 77.78/10.60 (iffalseProp2) => 77.78/10.60 (( 77.78/10.60 (iftrueProp1) => 77.78/10.60 (( 77.78/10.60 (iftrueProp2) => 77.78/10.60 (( 77.78/10.60 (ifSingleton) => 77.78/10.60 (( 77.78/10.60 (ifp) => 77.78/10.60 (( 77.78/10.60 (theeq) => 77.78/10.60 (( 77.78/10.60 (iftrue) => 77.78/10.60 (( 77.78/10.60 (iffalse) => 77.78/10.60 (( 77.78/10.60 (iftrueorfalse) => 77.78/10.60 (( 77.78/10.60 (binintersectT_lem) => 77.78/10.60 (( 77.78/10.60 (binunionT_lem) => 77.78/10.60 (( 77.78/10.60 (powersetT_lem) => 77.78/10.60 (( 77.78/10.60 (setminusT_lem) => 77.78/10.60 (( 77.78/10.60 (complementT_lem) => 77.78/10.60 (( 77.78/10.60 (setextT) => 77.78/10.60 (( 77.78/10.60 (subsetTI) => 77.78/10.60 (( 77.78/10.60 (powersetTI1) => 77.78/10.60 (( 77.78/10.60 (powersetTE1) => 77.78/10.60 (( 77.78/10.60 (complementTI1) => 77.78/10.60 (( 77.78/10.60 (complementTE1) => 77.78/10.60 (( 77.78/10.60 (binintersectTELcontra) => 77.78/10.60 (( 77.78/10.60 (binintersectTERcontra) => 77.78/10.60 (( 77.78/10.60 (contrasubsetT) => 77.78/10.60 (( 77.78/10.60 (contrasubsetT1) => 77.78/10.60 (( 77.78/10.60 (contrasubsetT2) => 77.78/10.60 (( 77.78/10.60 (contrasubsetT3) => 77.78/10.60 (( 77.78/10.60 (doubleComplementI1) => 77.78/10.60 (( 77.78/10.60 (doubleComplementE1) => 77.78/10.60 (( 77.78/10.60 (doubleComplementSub1) => 77.78/10.60 (( 77.78/10.60 (doubleComplementSub2) => 77.78/10.60 (( 77.78/10.60 (doubleComplementEq) => 77.78/10.60 (( 77.78/10.60 (complementTnotintersectT) => 77.78/10.60 (( 77.78/10.60 (complementImpComplementIntersect) => 77.78/10.60 (( 77.78/10.60 (complementSubsetComplementIntersect) => 77.78/10.60 (( 77.78/10.60 (complementInPowersetComplementIntersect) => 77.78/10.60 (( 77.78/10.60 (contraSubsetComplement) => 77.78/10.60 (( 77.78/10.60 (complementTcontraSubset) => 77.78/10.60 (( 77.78/10.60 (binunionTILcontra) => 77.78/10.60 (( 77.78/10.60 (binunionTIRcontra) => 77.78/10.60 (( 77.78/10.60 (inIntersectImpInUnion) => 77.78/10.60 (( 77.78/10.60 (inIntersectImpInUnion2) => 77.78/10.60 (( 77.78/10.60 (inIntersectImpInIntersectUnions) => 77.78/10.60 (( 77.78/10.60 (intersectInPowersetIntersectUnions) => 77.78/10.60 (( 77.78/10.60 (inComplementUnionImpNotIn1) => 77.78/10.60 (( 77.78/10.60 (inComplementUnionImpInComplement1) => 77.78/10.60 (( 77.78/10.60 (binunionTE) => 77.78/10.60 (( 77.78/10.60 (binunionTEcontra) => 77.78/10.60 (( 77.78/10.60 (demorgan2a1) => 77.78/10.60 (( 77.78/10.60 (complementUnionInPowersetComplement) => 77.78/10.60 (( 77.78/10.60 (demorgan2a2) => 77.78/10.60 (( 77.78/10.60 (demorgan1a) => 77.78/10.60 (( 77.78/10.60 (demorgan1b) => 77.78/10.60 (( 77.78/10.60 (demorgan1) => 77.78/10.60 (( 77.78/10.60 (demorgan2a) => 77.78/10.60 (( 77.78/10.60 (demorgan2b2) => 77.78/10.60 (( 77.78/10.60 (demorgan2b) => 77.78/10.60 (( 77.78/10.60 (demorgan2) => 77.78/10.60 (( 77.78/10.60 (woz13rule0) => 77.78/10.60 (( 77.78/10.60 (woz13rule1) => 77.78/10.60 (( 77.78/10.60 (woz13rule2) => 77.78/10.60 (( 77.78/10.60 (woz13rule3) => 77.78/10.60 (( 77.78/10.60 (woz13rule4) => 77.78/10.60 (( 77.78/10.60 (woz1_1) => 77.78/10.60 (( 77.78/10.60 (woz1_2) => 77.78/10.60 (( 77.78/10.60 (woz1_3) => 77.78/10.60 (( 77.78/10.60 (woz1_4) => 77.78/10.60 (( 77.78/10.60 (woz1_5) => 77.78/10.60 (( 77.78/10.60 (breln1all2) => 77.78/10.60 (( 77.78/10.60 (breln1SetBreln1) => 77.78/10.60 (( 77.78/10.60 (choice2fnsingleton) => 77.78/10.60 (( 77.78/10.60 (setOfPairsIsBReln1) => 77.78/10.60 (( 77.78/10.60 (breln1all1) => 77.78/10.60 (( 77.78/10.60 (subbreln1) => 77.78/10.60 (( 77.78/10.60 (eqbreln1) => 77.78/10.60 (( 77.78/10.60 (breln1invprop) => 77.78/10.60 (( 77.78/10.60 (breln1invI) => 77.78/10.60 (( 77.78/10.60 (breln1invE) => 77.78/10.60 (( 77.78/10.60 (breln1compprop) => 77.78/10.60 (( 77.78/10.60 (breln1compI) => 77.78/10.60 (( 77.78/10.60 (breln1compE) => 77.78/10.60 (( 77.78/10.60 (breln1compEex) => 77.78/10.60 (( 77.78/10.60 (breln1unionprop) => 77.78/10.60 (( 77.78/10.60 (breln1unionIL) => 77.78/10.60 (( 77.78/10.60 (breln1unionIR) => 77.78/10.60 (( 77.78/10.60 (breln1unionI) => 77.78/10.60 (( 77.78/10.60 (breln1unionE) => 77.78/10.60 (( 77.78/10.60 (breln1unionEcases) => 77.78/10.60 (( 77.78/10.60 (breln1unionCommutes) => 77.78/10.60 (( 77.78/10.60 (woz2Ex) => 77.78/10.60 (( 77.78/10.60 (woz2W) => 77.78/10.60 (( 77.78/10.60 (woz2A) => 77.78/10.60 (( 77.78/10.60 (woz2B) => 77.78/10.60 (( 77.78/10.60 (image1Ex) => 77.78/10.60 (( 77.78/10.60 (image1Ex1) => 77.78/10.60 (( 77.78/10.60 (image1Equiv) => 77.78/10.60 (( 77.78/10.60 (image1E) => 77.78/10.60 (( 77.78/10.60 (image1I) => 77.78/10.60 (( 77.78/10.60 (injFuncInInjFuncSet) => 77.78/10.60 (( 77.78/10.60 (injFuncSetFuncIn) => 77.78/10.60 (( 77.78/10.60 (injFuncSetFuncInj) => 77.78/10.60 (( 77.78/10.60 (surjFuncSetFuncIn) => 77.78/10.60 (( 77.78/10.60 (surjFuncSetFuncSurj) => 77.78/10.60 (( 77.78/10.60 (leftInvIsSurj) => 77.78/10.60 (( 77.78/10.60 (surjCantorThm) => 77.78/10.60 (( 77.78/10.60 (foundation2) => 77.78/10.60 (( 77.78/10.60 (notinself) => 77.78/10.60 (( 77.78/10.60 (notinself2) => 77.78/10.60 (( 77.78/10.60 (omegaSp) => 77.78/10.60 (( 77.78/10.60 (omegaSclos) => 77.78/10.60 (( 77.78/10.60 (peano0notS) => 77.78/10.60 (( 77.78/10.60 (peanoSinj) => 77.78/10.60 (( 77.78/10.60 (transitivesetOp1) => 77.78/10.60 (( 77.78/10.60 (binintTransitive) => 77.78/10.60 (( 77.78/10.60 (transitivesetOp2) => 77.78/10.60 (( 77.78/10.60 (setunionTransitive) => 77.78/10.60 (( 77.78/10.60 (ordinalMinLem1) => 77.78/10.60 (( 77.78/10.60 (!!) @ ( 77.78/10.60 ^[Y0 : $i]: 77.78/10.60 (( 77.78/10.60 (ordinal @ 77.78/10.60 Y0) => 77.78/10.60 (( 77.78/10.60 (!!) @ ( 77.78/10.60 ^[Y1 : $i]: 77.78/10.60 (( 77.78/10.60 (!!) @ ( 77.78/10.60 ^[Y2 : $i]: 77.78/10.60 (( 77.78/10.60 (in @ 77.78/10.60 Y2 @ 77.78/10.60 Y0) => 77.78/10.60 (( 77.78/10.60 (in @ 77.78/10.60 Y1 @ 77.78/10.60 Y2) => 77.78/10.60 (in @ 77.78/10.60 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 77.78/10.60 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl420])). 77.78/10.60 thf(zip_derived_cl439, plain, 77.78/10.60 (~ (((upairsetIL) => 77.78/10.60 (((upairsetIR) => 77.78/10.60 (((emptyE1) => 77.78/10.60 (((vacuousDall) => 77.78/10.60 (((quantDeMorgan1) => 77.78/10.60 (((quantDeMorgan2) => 77.78/10.60 (((quantDeMorgan3) => 77.78/10.60 (((quantDeMorgan4) => 77.78/10.60 (((prop2setI) => 77.78/10.60 (((prop2set2propI) => 77.78/10.60 (((notdexE) => 77.78/10.60 (((notdallE) => 77.78/10.60 (((exuI1) => 77.78/10.60 (((exuI3) => 77.78/10.60 (((exuI2) => 77.78/10.60 (((inCongP) => 77.78/10.60 (((in__Cong) => 77.78/10.60 (((exuE3u) => 77.78/10.60 (((exu__Cong) => 77.78/10.60 (((setadjoin__Cong) => 77.78/10.60 (((powerset__Cong) => 77.78/10.60 (((setunion__Cong) => 77.78/10.60 (((exuEu) => 77.78/10.60 (((descr__Cong) => 77.78/10.60 (((dsetconstr__Cong) => 77.78/10.60 (((subsetI1) => 77.78/10.60 (((eqimpsubset2) => 77.78/10.60 (((eqimpsubset1) => 77.78/10.60 (((subsetI2) => 77.78/10.60 (((emptysetsubset) => 77.78/10.60 (( 77.78/10.60 (subsetE) => 77.78/10.60 (( 77.78/10.60 (subsetE2) => 77.78/10.60 (( 77.78/10.60 (notsubsetI) => 77.78/10.60 (( 77.78/10.60 (notequalI1) => 77.78/10.60 (( 77.78/10.60 (notequalI2) => 77.78/10.60 (( 77.78/10.60 (subsetRefl) => 77.78/10.60 (( 77.78/10.60 (subsetTrans) => 77.78/10.60 (( 77.78/10.60 (setadjoinSub) => 77.78/10.60 (( 77.78/10.60 (setadjoinSub2) => 77.78/10.60 (( 77.78/10.60 (subset2powerset) => 77.78/10.60 (( 77.78/10.60 (setextsub) => 77.78/10.60 (( 77.78/10.60 (subsetemptysetimpeq) => 77.78/10.60 (( 77.78/10.60 (powersetI1) => 77.78/10.60 (( 77.78/10.60 (powersetE1) => 77.78/10.60 (( 77.78/10.60 (inPowerset) => 77.78/10.60 (( 77.78/10.60 (powersetsubset) => 77.78/10.60 (( 77.78/10.60 (sepInPowerset) => 77.78/10.60 (( 77.78/10.60 (sepSubset) => 77.78/10.60 (( 77.78/10.60 (binunionIL) => 77.78/10.60 (( 77.78/10.60 (upairset2IR) => 77.78/10.60 (( 77.78/10.60 (binunionIR) => 77.78/10.60 (( 77.78/10.60 (binunionEcases) => 77.78/10.60 (( 77.78/10.60 (binunionE) => 77.78/10.60 (( 77.78/10.60 (binunionLsub) => 77.78/10.60 (( 77.78/10.60 (binunionRsub) => 77.78/10.60 (( 77.78/10.60 (binintersectI) => 77.78/10.60 (( 77.78/10.60 (binintersectSubset5) => 77.78/10.60 (( 77.78/10.60 (binintersectEL) => 77.78/10.60 (( 77.78/10.60 (binintersectLsub) => 77.78/10.60 (( 77.78/10.60 (binintersectSubset2) => 77.78/10.60 (( 77.78/10.60 (binintersectSubset3) => 77.78/10.60 (( 77.78/10.60 (binintersectER) => 77.78/10.60 (( 77.78/10.60 (disjointsetsI1) => 77.78/10.60 (( 77.78/10.60 (binintersectRsub) => 77.78/10.60 (( 77.78/10.60 (binintersectSubset4) => 77.78/10.60 (( 77.78/10.60 (binintersectSubset1) => 77.78/10.60 (( 77.78/10.60 (bs114d) => 77.78/10.60 (( 77.78/10.60 (setminusI) => 77.78/10.60 (( 77.78/10.60 (setminusEL) => 77.78/10.60 (( 77.78/10.60 (setminusER) => 77.78/10.60 (( 77.78/10.60 (setminusSubset2) => 77.78/10.60 (( 77.78/10.60 (setminusERneg) => 77.78/10.60 (( 77.78/10.60 (setminusELneg) => 77.78/10.60 (( 77.78/10.60 (setminusILneg) => 77.78/10.60 (( 77.78/10.60 (setminusIRneg) => 77.78/10.60 (( 77.78/10.60 (setminusLsub) => 77.78/10.60 (( 77.78/10.60 (setminusSubset1) => 77.78/10.60 (( 77.78/10.60 (symdiffE) => 77.78/10.60 (( 77.78/10.60 (symdiffI1) => 77.78/10.60 (( 77.78/10.60 (symdiffI2) => 77.78/10.60 (( 77.78/10.60 (symdiffIneg1) => 77.78/10.60 (( 77.78/10.60 (symdiffIneg2) => 77.78/10.60 (( 77.78/10.60 (secondinupair) => 77.78/10.60 (( 77.78/10.60 (setukpairIL) => 77.78/10.60 (( 77.78/10.60 (setukpairIR) => 77.78/10.60 (( 77.78/10.60 (kpairiskpair) => 77.78/10.60 (( 77.78/10.60 (kpairp) => 77.78/10.60 (( 77.78/10.60 (singletonsubset) => 77.78/10.60 (( 77.78/10.60 (singletoninpowerset) => 77.78/10.60 (( 77.78/10.60 (singletoninpowunion) => 77.78/10.60 (( 77.78/10.60 (upairset2E) => 77.78/10.60 (( 77.78/10.60 (upairsubunion) => 77.78/10.60 (( 77.78/10.60 (upairinpowunion) => 77.78/10.60 (( 77.78/10.60 (ubforcartprodlem1) => 77.78/10.60 (( 77.78/10.60 (ubforcartprodlem2) => 77.78/10.60 (( 77.78/10.60 (ubforcartprodlem3) => 77.78/10.60 (( 77.78/10.60 (cartprodpairin) => 77.78/10.60 (( 77.78/10.60 (cartprodmempair1) => 77.78/10.60 (( 77.78/10.60 (cartprodmempair) => 77.78/10.60 (( 77.78/10.60 (setunionE2) => 77.78/10.60 (( 77.78/10.60 (setunionsingleton1) => 77.78/10.60 (( 77.78/10.60 (setunionsingleton2) => 77.78/10.60 (( 77.78/10.60 (setunionsingleton) => 77.78/10.60 (( 77.78/10.60 (singletonprop) => 77.78/10.60 (( 77.78/10.60 (ex1E1) => 77.78/10.60 (( 77.78/10.60 (ex1I) => 77.78/10.60 (( 77.78/10.60 (ex1I2) => 77.78/10.60 (( 77.78/10.60 (singletonsuniq) => 77.78/10.60 (( 77.78/10.60 (setukpairinjL1) => 77.78/10.60 (( 77.78/10.60 (kfstsingleton) => 77.78/10.60 (( 77.78/10.60 (theprop) => 77.78/10.60 (( 77.78/10.60 (kfstpairEq) => 77.78/10.60 (( 77.78/10.60 (cartprodfstin) => 77.78/10.60 (( 77.78/10.60 (setukpairinjL2) => 77.78/10.60 (( 77.78/10.60 (setukpairinjL) => 77.78/10.60 (( 77.78/10.60 (setukpairinjR11) => 77.78/10.60 (( 77.78/10.60 (setukpairinjR12) => 77.78/10.60 (( 77.78/10.60 (setukpairinjR1) => 77.78/10.60 (( 77.78/10.60 (upairequniteq) => 77.78/10.60 (( 77.78/10.60 (setukpairinjR2) => 77.78/10.60 (( 77.78/10.60 (setukpairinjR) => 77.78/10.60 (( 77.78/10.60 (ksndsingleton) => 77.78/10.60 (( 77.78/10.60 (ksndpairEq) => 77.78/10.60 (( 77.78/10.60 (kpairsurjEq) => 77.78/10.60 (( 77.78/10.60 (cartprodsndin) => 77.78/10.60 (( 77.78/10.60 (cartprodpairmemEL) => 77.78/10.60 (( 77.78/10.60 (cartprodpairmemER) => 77.78/10.60 (( 77.78/10.60 (cartprodmempaircEq) => 77.78/10.60 (( 77.78/10.60 (cartprodfstpairEq) => 77.78/10.60 (( 77.78/10.60 (cartprodsndpairEq) => 77.78/10.60 (( 77.78/10.60 (cartprodpairsurjEq) => 77.78/10.60 (( 77.78/10.60 (dpsetconstrI) => 77.78/10.60 (( 77.78/10.60 (dpsetconstrSub) => 77.78/10.60 (( 77.78/10.60 (setOfPairsIsBReln) => 77.78/10.60 (( 77.78/10.60 (dpsetconstrERa) => 77.78/10.60 (( 77.78/10.60 (dpsetconstrEL1) => 77.78/10.60 (( 77.78/10.60 (dpsetconstrEL2) => 77.78/10.60 (( 77.78/10.60 (dpsetconstrER) => 77.78/10.60 (( 77.78/10.60 (funcImageSingleton) => 77.78/10.60 (( 77.78/10.60 (apProp) => 77.78/10.60 (( 77.78/10.60 (app) => 77.78/10.60 (( 77.78/10.60 (infuncsetfunc) => 77.78/10.60 (( 77.78/10.60 (ap2p) => 77.78/10.60 (( 77.78/10.60 (funcinfuncset) => 77.78/10.60 (( 77.78/10.60 (lamProp) => 77.78/10.60 (( 77.78/10.60 (lamp) => 77.78/10.60 (( 77.78/10.60 (lam2p) => 77.78/10.60 (( 77.78/10.60 (brelnall1) => 77.78/10.60 (( 77.78/10.60 (brelnall2) => 77.78/10.60 (( 77.78/10.60 (ex1E2) => 77.78/10.60 (( 77.78/10.60 (funcGraphProp1) => 77.78/10.60 (( 77.78/10.60 (funcGraphProp3) => 77.78/10.60 (( 77.78/10.60 (funcGraphProp2) => 77.78/10.60 (( 77.78/10.60 (funcextLem) => 77.78/10.60 (( 77.78/10.60 (funcGraphProp4) => 77.78/10.60 (( 77.78/10.60 (subbreln) => 77.78/10.60 (( 77.78/10.60 (eqbreln) => 77.78/10.60 (( 77.78/10.60 (funcext) => 77.78/10.60 (( 77.78/10.60 (funcext2) => 77.78/10.60 (( 77.78/10.60 (ap2apEq1) => 77.78/10.60 (( 77.78/10.60 (ap2apEq2) => 77.78/10.60 (( 77.78/10.60 (beta1) => 77.78/10.60 (( 77.78/10.60 (eta1) => 77.78/10.60 (( 77.78/10.60 (lam2lamEq) => 77.78/10.60 (( 77.78/10.60 (beta2) => 77.78/10.60 (( 77.78/10.60 (eta2) => 77.78/10.60 (( 77.78/10.60 (iffalseProp1) => 77.78/10.60 (( 77.78/10.60 (iffalseProp2) => 77.78/10.60 (( 77.78/10.60 (iftrueProp1) => 77.78/10.60 (( 77.78/10.60 (iftrueProp2) => 77.78/10.60 (( 77.78/10.60 (ifSingleton) => 77.78/10.60 (( 77.78/10.60 (ifp) => 77.78/10.60 (( 77.78/10.60 (theeq) => 77.78/10.60 (( 77.78/10.60 (iftrue) => 77.78/10.60 (( 77.78/10.60 (iffalse) => 77.78/10.60 (( 77.78/10.60 (iftrueorfalse) => 77.78/10.60 (( 77.78/10.60 (binintersectT_lem) => 77.78/10.60 (( 77.78/10.60 (binunionT_lem) => 77.78/10.60 (( 77.78/10.60 (powersetT_lem) => 77.78/10.60 (( 77.78/10.60 (setminusT_lem) => 77.78/10.60 (( 77.78/10.60 (complementT_lem) => 77.78/10.60 (( 77.78/10.60 (setextT) => 77.78/10.60 (( 77.78/10.60 (subsetTI) => 77.78/10.60 (( 77.78/10.60 (powersetTI1) => 77.78/10.60 (( 77.78/10.60 (powersetTE1) => 77.78/10.60 (( 77.78/10.60 (complementTI1) => 77.78/10.60 (( 77.78/10.60 (complementTE1) => 77.78/10.60 (( 77.78/10.60 (binintersectTELcontra) => 77.78/10.60 (( 77.78/10.60 (binintersectTERcontra) => 77.78/10.60 (( 77.78/10.60 (contrasubsetT) => 77.78/10.60 (( 77.78/10.60 (contrasubsetT1) => 77.78/10.60 (( 77.78/10.60 (contrasubsetT2) => 77.78/10.60 (( 77.78/10.60 (contrasubsetT3) => 77.78/10.60 (( 77.78/10.60 (doubleComplementI1) => 77.78/10.60 (( 77.78/10.60 (doubleComplementE1) => 77.78/10.60 (( 77.78/10.60 (doubleComplementSub1) => 77.78/10.60 (( 77.78/10.60 (doubleComplementSub2) => 77.78/10.60 (( 77.78/10.60 (doubleComplementEq) => 77.78/10.60 (( 77.78/10.60 (complementTnotintersectT) => 77.78/10.60 (( 77.78/10.60 (complementImpComplementIntersect) => 77.78/10.60 (( 77.78/10.60 (complementSubsetComplementIntersect) => 77.78/10.60 (( 77.78/10.60 (complementInPowersetComplementIntersect) => 77.78/10.60 (( 77.78/10.60 (contraSubsetComplement) => 77.78/10.60 (( 77.78/10.60 (complementTcontraSubset) => 77.78/10.60 (( 77.78/10.60 (binunionTILcontra) => 77.78/10.60 (( 77.78/10.60 (binunionTIRcontra) => 77.78/10.60 (( 77.78/10.60 (inIntersectImpInUnion) => 77.78/10.60 (( 77.78/10.60 (inIntersectImpInUnion2) => 77.78/10.60 (( 77.78/10.60 (inIntersectImpInIntersectUnions) => 77.78/10.60 (( 77.78/10.60 (intersectInPowersetIntersectUnions) => 77.78/10.60 (( 77.78/10.60 (inComplementUnionImpNotIn1) => 77.78/10.60 (( 77.78/10.60 (inComplementUnionImpInComplement1) => 77.78/10.60 (( 77.78/10.60 (binunionTE) => 77.78/10.60 (( 77.78/10.60 (binunionTEcontra) => 77.78/10.60 (( 77.78/10.60 (demorgan2a1) => 77.78/10.60 (( 77.78/10.60 (complementUnionInPowersetComplement) => 77.78/10.60 (( 77.78/10.60 (demorgan2a2) => 77.78/10.60 (( 77.78/10.60 (demorgan1a) => 77.78/10.60 (( 77.78/10.60 (demorgan1b) => 77.78/10.60 (( 77.78/10.60 (demorgan1) => 77.78/10.60 (( 77.78/10.60 (demorgan2a) => 77.78/10.60 (( 77.78/10.60 (demorgan2b2) => 77.78/10.60 (( 77.78/10.60 (demorgan2b) => 77.78/10.60 (( 77.78/10.60 (demorgan2) => 77.78/10.60 (( 77.78/10.60 (woz13rule0) => 77.78/10.60 (( 77.78/10.60 (woz13rule1) => 77.78/10.60 (( 77.78/10.60 (woz13rule2) => 77.78/10.60 (( 77.78/10.60 (woz13rule3) => 77.78/10.60 (( 77.78/10.60 (woz13rule4) => 77.78/10.60 (( 77.78/10.60 (woz1_1) => 77.78/10.60 (( 77.78/10.60 (woz1_2) => 77.78/10.60 (( 77.78/10.60 (woz1_3) => 77.78/10.60 (( 77.78/10.60 (woz1_4) => 77.78/10.60 (( 77.78/10.60 (woz1_5) => 77.78/10.60 (( 77.78/10.60 (breln1all2) => 77.78/10.60 (( 77.78/10.60 (breln1SetBreln1) => 77.78/10.60 (( 77.78/10.60 (choice2fnsingleton) => 77.78/10.60 (( 77.78/10.60 (setOfPairsIsBReln1) => 77.78/10.60 (( 77.78/10.60 (breln1all1) => 77.78/10.60 (( 77.78/10.60 (subbreln1) => 77.78/10.60 (( 77.78/10.60 (eqbreln1) => 77.78/10.60 (( 77.78/10.60 (breln1invprop) => 77.78/10.60 (( 77.78/10.60 (breln1invI) => 77.78/10.60 (( 77.78/10.60 (breln1invE) => 77.78/10.60 (( 77.78/10.60 (breln1compprop) => 77.78/10.60 (( 77.78/10.60 (breln1compI) => 77.78/10.60 (( 77.78/10.60 (breln1compE) => 77.78/10.60 (( 77.78/10.60 (breln1compEex) => 77.78/10.60 (( 77.78/10.60 (breln1unionprop) => 77.78/10.60 (( 77.78/10.60 (breln1unionIL) => 77.78/10.60 (( 77.78/10.60 (breln1unionIR) => 77.78/10.60 (( 77.78/10.60 (breln1unionI) => 77.78/10.60 (( 77.78/10.60 (breln1unionE) => 77.78/10.60 (( 77.78/10.60 (breln1unionEcases) => 77.78/10.60 (( 77.78/10.60 (breln1unionCommutes) => 77.78/10.60 (( 77.78/10.60 (woz2Ex) => 77.78/10.60 (( 77.78/10.60 (woz2W) => 77.78/10.60 (( 77.78/10.60 (woz2A) => 77.78/10.60 (( 77.78/10.60 (woz2B) => 77.78/10.60 (( 77.78/10.60 (image1Ex) => 77.78/10.60 (( 77.78/10.60 (image1Ex1) => 77.78/10.60 (( 77.78/10.60 (image1Equiv) => 77.78/10.60 (( 77.78/10.60 (image1E) => 77.78/10.60 (( 77.78/10.60 (image1I) => 77.78/10.60 (( 77.78/10.60 (injFuncInInjFuncSet) => 77.78/10.60 (( 77.78/10.60 (injFuncSetFuncIn) => 77.78/10.60 (( 77.78/10.60 (injFuncSetFuncInj) => 77.78/10.60 (( 77.78/10.60 (surjFuncSetFuncIn) => 77.78/10.60 (( 77.78/10.60 (surjFuncSetFuncSurj) => 77.78/10.60 (( 77.78/10.60 (leftInvIsSurj) => 77.78/10.60 (( 77.78/10.60 (surjCantorThm) => 77.78/10.60 (( 77.78/10.60 (foundation2) => 77.78/10.60 (( 77.78/10.60 (notinself) => 77.78/10.60 (( 77.78/10.60 (notinself2) => 77.78/10.60 (( 77.78/10.60 (omegaSp) => 77.78/10.60 (( 77.78/10.60 (omegaSclos) => 77.78/10.60 (( 77.78/10.60 (peano0notS) => 77.78/10.60 (( 77.78/10.60 (peanoSinj) => 77.78/10.60 (( 77.78/10.60 (transitivesetOp1) => 77.78/10.60 (( 77.78/10.60 (binintTransitive) => 77.78/10.60 (( 77.78/10.60 (transitivesetOp2) => 77.78/10.60 (( 77.78/10.60 (setunionTransitive) => 77.78/10.60 (( 77.78/10.60 (ordinalMinLem1) => 77.78/10.60 (( 77.78/10.60 (!!) @ ( 77.78/10.60 ^[Y0 : $i]: 77.78/10.60 (( 77.78/10.60 (ordinal @ 77.78/10.60 Y0) => 77.78/10.60 (( 77.78/10.60 (!!) @ ( 77.78/10.60 ^[Y1 : $i]: 77.78/10.60 (( 77.78/10.60 (!!) @ ( 77.78/10.60 ^[Y2 : $i]: 77.78/10.60 (( 77.78/10.60 (in @ 77.78/10.60 Y2 @ 77.78/10.60 Y0) => 77.78/10.60 (( 77.78/10.60 (in @ 77.78/10.60 Y1 @ 77.78/10.60 Y2) => 77.78/10.60 (in @ 77.78/10.60 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 77.78/10.60 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl428])). 77.78/10.60 thf(zip_derived_cl449, plain, 77.78/10.60 (~ (((upairsetIR) => 77.78/10.60 (((emptyE1) => 77.78/10.60 (((vacuousDall) => 77.78/10.60 (((quantDeMorgan1) => 77.78/10.60 (((quantDeMorgan2) => 77.78/10.60 (((quantDeMorgan3) => 77.78/10.60 (((quantDeMorgan4) => 77.78/10.60 (((prop2setI) => 77.78/10.60 (((prop2set2propI) => 77.78/10.60 (((notdexE) => 77.78/10.60 (((notdallE) => 77.78/10.60 (((exuI1) => 77.78/10.60 (((exuI3) => 77.78/10.60 (((exuI2) => 77.78/10.60 (((inCongP) => 77.78/10.60 (((in__Cong) => 77.78/10.60 (((exuE3u) => 77.78/10.60 (((exu__Cong) => 77.78/10.60 (((setadjoin__Cong) => 77.78/10.60 (((powerset__Cong) => 77.78/10.60 (((setunion__Cong) => 77.78/10.60 (((exuEu) => 77.78/10.60 (((descr__Cong) => 77.78/10.60 (((dsetconstr__Cong) => 77.78/10.60 (((subsetI1) => 77.78/10.60 (((eqimpsubset2) => 77.78/10.60 (((eqimpsubset1) => 77.78/10.60 (((subsetI2) => 77.78/10.60 (((emptysetsubset) => 77.78/10.60 (((subsetE) => 77.78/10.60 (( 77.78/10.60 (subsetE2) => 77.78/10.60 (( 77.78/10.60 (notsubsetI) => 77.78/10.60 (( 77.78/10.60 (notequalI1) => 77.78/10.60 (( 77.78/10.60 (notequalI2) => 77.78/10.60 (( 77.78/10.60 (subsetRefl) => 77.78/10.60 (( 77.78/10.60 (subsetTrans) => 77.78/10.60 (( 77.78/10.60 (setadjoinSub) => 77.78/10.60 (( 77.78/10.60 (setadjoinSub2) => 77.78/10.60 (( 77.78/10.60 (subset2powerset) => 77.78/10.60 (( 77.78/10.60 (setextsub) => 77.78/10.60 (( 77.78/10.60 (subsetemptysetimpeq) => 77.78/10.60 (( 77.78/10.60 (powersetI1) => 77.78/10.60 (( 77.78/10.60 (powersetE1) => 77.78/10.60 (( 77.78/10.60 (inPowerset) => 77.78/10.60 (( 77.78/10.60 (powersetsubset) => 77.78/10.60 (( 77.78/10.60 (sepInPowerset) => 77.78/10.60 (( 77.78/10.60 (sepSubset) => 77.78/10.60 (( 77.78/10.60 (binunionIL) => 77.78/10.60 (( 77.78/10.60 (upairset2IR) => 77.78/10.60 (( 77.78/10.60 (binunionIR) => 77.78/10.60 (( 77.78/10.60 (binunionEcases) => 77.78/10.60 (( 77.78/10.60 (binunionE) => 77.78/10.60 (( 77.78/10.60 (binunionLsub) => 77.78/10.60 (( 77.78/10.60 (binunionRsub) => 77.78/10.60 (( 77.78/10.60 (binintersectI) => 77.78/10.60 (( 77.78/10.60 (binintersectSubset5) => 77.78/10.60 (( 77.78/10.60 (binintersectEL) => 77.78/10.60 (( 77.78/10.60 (binintersectLsub) => 77.78/10.60 (( 77.78/10.60 (binintersectSubset2) => 77.78/10.60 (( 77.78/10.60 (binintersectSubset3) => 77.78/10.60 (( 77.78/10.60 (binintersectER) => 77.78/10.60 (( 77.78/10.60 (disjointsetsI1) => 77.78/10.60 (( 77.78/10.60 (binintersectRsub) => 77.78/10.60 (( 77.78/10.60 (binintersectSubset4) => 77.78/10.60 (( 77.78/10.60 (binintersectSubset1) => 77.78/10.60 (( 77.78/10.60 (bs114d) => 77.78/10.60 (( 77.78/10.60 (setminusI) => 77.78/10.60 (( 77.78/10.60 (setminusEL) => 77.78/10.60 (( 77.78/10.60 (setminusER) => 77.78/10.60 (( 77.78/10.60 (setminusSubset2) => 77.78/10.60 (( 77.78/10.60 (setminusERneg) => 77.78/10.60 (( 77.78/10.60 (setminusELneg) => 77.78/10.60 (( 77.78/10.60 (setminusILneg) => 77.78/10.60 (( 77.78/10.60 (setminusIRneg) => 77.78/10.60 (( 77.78/10.60 (setminusLsub) => 77.78/10.60 (( 77.78/10.60 (setminusSubset1) => 77.78/10.60 (( 77.78/10.60 (symdiffE) => 77.78/10.60 (( 77.78/10.60 (symdiffI1) => 77.78/10.60 (( 77.78/10.60 (symdiffI2) => 77.78/10.60 (( 77.78/10.60 (symdiffIneg1) => 77.78/10.60 (( 77.78/10.60 (symdiffIneg2) => 77.78/10.60 (( 77.78/10.60 (secondinupair) => 77.78/10.60 (( 77.78/10.60 (setukpairIL) => 77.78/10.60 (( 77.78/10.60 (setukpairIR) => 77.78/10.60 (( 77.78/10.60 (kpairiskpair) => 77.78/10.60 (( 77.78/10.60 (kpairp) => 77.78/10.60 (( 77.78/10.60 (singletonsubset) => 77.78/10.60 (( 77.78/10.60 (singletoninpowerset) => 77.78/10.60 (( 77.78/10.60 (singletoninpowunion) => 77.78/10.60 (( 77.78/10.60 (upairset2E) => 77.78/10.60 (( 77.78/10.60 (upairsubunion) => 77.78/10.60 (( 77.78/10.60 (upairinpowunion) => 77.78/10.60 (( 77.78/10.60 (ubforcartprodlem1) => 77.78/10.60 (( 77.78/10.60 (ubforcartprodlem2) => 77.78/10.60 (( 77.78/10.60 (ubforcartprodlem3) => 77.78/10.60 (( 77.78/10.60 (cartprodpairin) => 77.78/10.60 (( 77.78/10.60 (cartprodmempair1) => 77.78/10.60 (( 77.78/10.60 (cartprodmempair) => 77.78/10.60 (( 77.78/10.60 (setunionE2) => 77.78/10.60 (( 77.78/10.60 (setunionsingleton1) => 77.78/10.60 (( 77.78/10.60 (setunionsingleton2) => 77.78/10.60 (( 77.78/10.60 (setunionsingleton) => 77.78/10.60 (( 77.78/10.60 (singletonprop) => 77.78/10.60 (( 77.78/10.60 (ex1E1) => 77.78/10.60 (( 77.78/10.60 (ex1I) => 77.78/10.60 (( 77.78/10.60 (ex1I2) => 77.78/10.60 (( 77.78/10.60 (singletonsuniq) => 77.78/10.60 (( 77.78/10.60 (setukpairinjL1) => 77.78/10.60 (( 77.78/10.60 (kfstsingleton) => 77.78/10.60 (( 77.78/10.60 (theprop) => 77.78/10.60 (( 77.78/10.60 (kfstpairEq) => 77.78/10.60 (( 77.78/10.60 (cartprodfstin) => 77.78/10.60 (( 77.78/10.60 (setukpairinjL2) => 77.78/10.60 (( 77.78/10.60 (setukpairinjL) => 77.78/10.60 (( 77.78/10.60 (setukpairinjR11) => 77.78/10.60 (( 77.78/10.60 (setukpairinjR12) => 77.78/10.60 (( 77.78/10.60 (setukpairinjR1) => 77.78/10.60 (( 77.78/10.60 (upairequniteq) => 77.78/10.60 (( 77.78/10.60 (setukpairinjR2) => 77.78/10.60 (( 77.78/10.60 (setukpairinjR) => 77.78/10.60 (( 77.78/10.60 (ksndsingleton) => 77.78/10.60 (( 77.78/10.60 (ksndpairEq) => 77.78/10.60 (( 77.78/10.60 (kpairsurjEq) => 77.78/10.60 (( 77.78/10.60 (cartprodsndin) => 77.78/10.60 (( 77.78/10.60 (cartprodpairmemEL) => 77.78/10.60 (( 77.78/10.60 (cartprodpairmemER) => 77.78/10.60 (( 77.78/10.60 (cartprodmempaircEq) => 77.78/10.60 (( 77.78/10.60 (cartprodfstpairEq) => 77.78/10.60 (( 77.78/10.60 (cartprodsndpairEq) => 77.78/10.60 (( 77.78/10.60 (cartprodpairsurjEq) => 77.78/10.60 (( 77.78/10.60 (dpsetconstrI) => 77.78/10.60 (( 77.78/10.60 (dpsetconstrSub) => 77.78/10.60 (( 77.78/10.60 (setOfPairsIsBReln) => 77.78/10.60 (( 77.78/10.60 (dpsetconstrERa) => 77.78/10.60 (( 77.78/10.60 (dpsetconstrEL1) => 77.78/10.60 (( 77.78/10.60 (dpsetconstrEL2) => 77.78/10.60 (( 77.78/10.60 (dpsetconstrER) => 77.78/10.60 (( 77.78/10.60 (funcImageSingleton) => 77.78/10.60 (( 77.78/10.60 (apProp) => 77.78/10.60 (( 77.78/10.60 (app) => 77.78/10.60 (( 77.78/10.60 (infuncsetfunc) => 77.78/10.60 (( 77.78/10.60 (ap2p) => 77.78/10.60 (( 77.78/10.60 (funcinfuncset) => 77.78/10.60 (( 77.78/10.60 (lamProp) => 77.78/10.60 (( 77.78/10.60 (lamp) => 77.78/10.60 (( 77.78/10.60 (lam2p) => 77.78/10.60 (( 77.78/10.60 (brelnall1) => 77.78/10.60 (( 77.78/10.60 (brelnall2) => 77.78/10.60 (( 77.78/10.60 (ex1E2) => 77.78/10.60 (( 77.78/10.60 (funcGraphProp1) => 77.78/10.60 (( 77.78/10.60 (funcGraphProp3) => 77.78/10.60 (( 77.78/10.60 (funcGraphProp2) => 77.78/10.60 (( 77.78/10.60 (funcextLem) => 77.78/10.60 (( 77.78/10.60 (funcGraphProp4) => 77.78/10.60 (( 77.78/10.60 (subbreln) => 77.78/10.60 (( 77.78/10.60 (eqbreln) => 77.78/10.60 (( 77.78/10.60 (funcext) => 77.78/10.60 (( 77.78/10.60 (funcext2) => 77.78/10.60 (( 77.78/10.60 (ap2apEq1) => 77.78/10.60 (( 77.78/10.60 (ap2apEq2) => 77.78/10.60 (( 77.78/10.60 (beta1) => 77.78/10.60 (( 77.78/10.60 (eta1) => 77.78/10.60 (( 77.78/10.60 (lam2lamEq) => 77.78/10.60 (( 77.78/10.60 (beta2) => 77.78/10.60 (( 77.78/10.60 (eta2) => 77.78/10.60 (( 77.78/10.60 (iffalseProp1) => 77.78/10.60 (( 77.78/10.60 (iffalseProp2) => 77.78/10.60 (( 77.78/10.60 (iftrueProp1) => 77.78/10.60 (( 77.78/10.60 (iftrueProp2) => 77.78/10.60 (( 77.78/10.60 (ifSingleton) => 77.78/10.60 (( 77.78/10.60 (ifp) => 77.78/10.60 (( 77.78/10.60 (theeq) => 77.78/10.60 (( 77.78/10.60 (iftrue) => 77.78/10.60 (( 77.78/10.60 (iffalse) => 77.78/10.60 (( 77.78/10.60 (iftrueorfalse) => 77.78/10.60 (( 77.78/10.60 (binintersectT_lem) => 77.78/10.60 (( 77.78/10.60 (binunionT_lem) => 77.78/10.60 (( 77.78/10.60 (powersetT_lem) => 77.78/10.60 (( 77.78/10.60 (setminusT_lem) => 77.78/10.60 (( 77.78/10.60 (complementT_lem) => 77.78/10.60 (( 77.78/10.60 (setextT) => 77.78/10.60 (( 77.78/10.60 (subsetTI) => 77.78/10.60 (( 77.78/10.60 (powersetTI1) => 77.78/10.60 (( 77.78/10.60 (powersetTE1) => 77.78/10.60 (( 77.78/10.60 (complementTI1) => 77.78/10.60 (( 77.78/10.60 (complementTE1) => 77.78/10.60 (( 77.78/10.60 (binintersectTELcontra) => 77.78/10.60 (( 77.78/10.60 (binintersectTERcontra) => 77.78/10.60 (( 77.78/10.60 (contrasubsetT) => 77.78/10.60 (( 77.78/10.60 (contrasubsetT1) => 77.78/10.60 (( 77.78/10.60 (contrasubsetT2) => 77.78/10.60 (( 77.78/10.60 (contrasubsetT3) => 77.78/10.60 (( 77.78/10.60 (doubleComplementI1) => 77.78/10.60 (( 77.78/10.60 (doubleComplementE1) => 77.78/10.60 (( 77.78/10.60 (doubleComplementSub1) => 77.78/10.60 (( 77.78/10.60 (doubleComplementSub2) => 77.78/10.60 (( 77.78/10.60 (doubleComplementEq) => 77.78/10.60 (( 77.78/10.60 (complementTnotintersectT) => 77.78/10.60 (( 77.78/10.60 (complementImpComplementIntersect) => 77.78/10.60 (( 77.78/10.60 (complementSubsetComplementIntersect) => 77.78/10.60 (( 77.78/10.60 (complementInPowersetComplementIntersect) => 77.78/10.60 (( 77.78/10.60 (contraSubsetComplement) => 77.78/10.60 (( 77.78/10.60 (complementTcontraSubset) => 77.78/10.60 (( 77.78/10.60 (binunionTILcontra) => 77.78/10.60 (( 77.78/10.60 (binunionTIRcontra) => 77.78/10.60 (( 77.78/10.60 (inIntersectImpInUnion) => 77.78/10.60 (( 77.78/10.60 (inIntersectImpInUnion2) => 77.78/10.60 (( 77.78/10.60 (inIntersectImpInIntersectUnions) => 77.78/10.60 (( 77.78/10.60 (intersectInPowersetIntersectUnions) => 77.78/10.60 (( 77.78/10.60 (inComplementUnionImpNotIn1) => 77.78/10.60 (( 77.78/10.60 (inComplementUnionImpInComplement1) => 77.78/10.60 (( 77.78/10.60 (binunionTE) => 77.78/10.60 (( 77.78/10.60 (binunionTEcontra) => 77.78/10.60 (( 77.78/10.60 (demorgan2a1) => 77.78/10.60 (( 77.78/10.60 (complementUnionInPowersetComplement) => 77.78/10.60 (( 77.78/10.60 (demorgan2a2) => 77.78/10.60 (( 77.78/10.60 (demorgan1a) => 77.78/10.60 (( 77.78/10.60 (demorgan1b) => 77.78/10.60 (( 77.78/10.60 (demorgan1) => 77.78/10.60 (( 77.78/10.60 (demorgan2a) => 77.78/10.60 (( 77.78/10.60 (demorgan2b2) => 77.78/10.60 (( 77.78/10.60 (demorgan2b) => 77.78/10.60 (( 77.78/10.60 (demorgan2) => 77.78/10.60 (( 77.78/10.60 (woz13rule0) => 77.78/10.60 (( 77.78/10.60 (woz13rule1) => 77.78/10.60 (( 77.78/10.60 (woz13rule2) => 77.78/10.60 (( 77.78/10.60 (woz13rule3) => 77.78/10.60 (( 77.78/10.60 (woz13rule4) => 77.78/10.60 (( 77.78/10.60 (woz1_1) => 77.78/10.60 (( 77.78/10.60 (woz1_2) => 77.78/10.60 (( 77.78/10.60 (woz1_3) => 77.78/10.60 (( 77.78/10.60 (woz1_4) => 77.78/10.60 (( 77.78/10.60 (woz1_5) => 77.78/10.60 (( 77.78/10.60 (breln1all2) => 77.78/10.60 (( 77.78/10.60 (breln1SetBreln1) => 77.78/10.60 (( 77.78/10.60 (choice2fnsingleton) => 77.78/10.60 (( 77.78/10.60 (setOfPairsIsBReln1) => 77.78/10.60 (( 77.78/10.60 (breln1all1) => 77.78/10.60 (( 77.78/10.60 (subbreln1) => 77.78/10.60 (( 77.78/10.60 (eqbreln1) => 77.78/10.60 (( 77.78/10.60 (breln1invprop) => 77.78/10.60 (( 77.78/10.60 (breln1invI) => 77.78/10.60 (( 77.78/10.60 (breln1invE) => 77.78/10.60 (( 77.78/10.60 (breln1compprop) => 77.78/10.60 (( 77.78/10.60 (breln1compI) => 77.78/10.60 (( 77.78/10.60 (breln1compE) => 77.78/10.60 (( 77.78/10.60 (breln1compEex) => 77.78/10.60 (( 77.78/10.60 (breln1unionprop) => 77.78/10.60 (( 77.78/10.60 (breln1unionIL) => 77.78/10.60 (( 77.78/10.60 (breln1unionIR) => 77.78/10.60 (( 77.78/10.60 (breln1unionI) => 77.78/10.60 (( 77.78/10.60 (breln1unionE) => 77.78/10.60 (( 77.78/10.60 (breln1unionEcases) => 77.78/10.60 (( 77.78/10.60 (breln1unionCommutes) => 77.78/10.60 (( 77.78/10.60 (woz2Ex) => 77.78/10.60 (( 77.78/10.60 (woz2W) => 77.78/10.60 (( 77.78/10.60 (woz2A) => 77.78/10.60 (( 77.78/10.60 (woz2B) => 77.78/10.60 (( 77.78/10.60 (image1Ex) => 77.78/10.60 (( 77.78/10.60 (image1Ex1) => 77.78/10.60 (( 77.78/10.60 (image1Equiv) => 77.78/10.60 (( 77.78/10.60 (image1E) => 77.78/10.60 (( 77.78/10.60 (image1I) => 77.78/10.60 (( 77.78/10.60 (injFuncInInjFuncSet) => 77.78/10.60 (( 77.78/10.60 (injFuncSetFuncIn) => 77.78/10.60 (( 77.78/10.60 (injFuncSetFuncInj) => 77.78/10.60 (( 77.78/10.60 (surjFuncSetFuncIn) => 77.78/10.60 (( 77.78/10.60 (surjFuncSetFuncSurj) => 77.78/10.60 (( 77.78/10.60 (leftInvIsSurj) => 77.78/10.60 (( 77.78/10.60 (surjCantorThm) => 77.78/10.60 (( 77.78/10.60 (foundation2) => 77.78/10.60 (( 77.78/10.60 (notinself) => 77.78/10.60 (( 77.78/10.60 (notinself2) => 77.78/10.60 (( 77.78/10.60 (omegaSp) => 77.78/10.60 (( 77.78/10.60 (omegaSclos) => 77.78/10.60 (( 77.78/10.60 (peano0notS) => 77.78/10.60 (( 77.78/10.60 (peanoSinj) => 77.78/10.60 (( 77.78/10.60 (transitivesetOp1) => 77.78/10.60 (( 77.78/10.60 (binintTransitive) => 77.78/10.60 (( 77.78/10.60 (transitivesetOp2) => 77.78/10.60 (( 77.78/10.60 (setunionTransitive) => 77.78/10.60 (( 77.78/10.60 (ordinalMinLem1) => 77.78/10.60 (( 77.78/10.60 (!!) @ ( 77.78/10.60 ^[Y0 : $i]: 77.78/10.60 (( 77.78/10.60 (ordinal @ 77.78/10.60 Y0) => 77.78/10.60 (( 77.78/10.60 (!!) @ ( 77.78/10.60 ^[Y1 : $i]: 77.78/10.60 (( 77.78/10.60 (!!) @ ( 77.78/10.60 ^[Y2 : $i]: 77.78/10.60 (( 77.78/10.60 (in @ 77.78/10.60 Y2 @ 77.78/10.60 Y0) => 77.78/10.60 (( 77.78/10.60 (in @ 77.78/10.60 Y1 @ 77.78/10.60 Y2) => 77.78/10.60 (in @ 77.78/10.60 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 77.78/10.60 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl439])). 77.78/10.60 thf(zip_derived_cl457, plain, 77.78/10.60 (~ (((emptyE1) => 77.78/10.60 (((vacuousDall) => 77.78/10.60 (((quantDeMorgan1) => 77.78/10.60 (((quantDeMorgan2) => 77.78/10.60 (((quantDeMorgan3) => 77.78/10.60 (((quantDeMorgan4) => 77.78/10.60 (((prop2setI) => 77.78/10.60 (((prop2set2propI) => 77.78/10.60 (((notdexE) => 77.78/10.60 (((notdallE) => 77.78/10.60 (((exuI1) => 77.78/10.60 (((exuI3) => 77.78/10.60 (((exuI2) => 77.78/10.60 (((inCongP) => 77.78/10.60 (((in__Cong) => 77.78/10.60 (((exuE3u) => 77.78/10.60 (((exu__Cong) => 77.78/10.60 (((setadjoin__Cong) => 77.78/10.60 (((powerset__Cong) => 77.78/10.60 (((setunion__Cong) => 77.78/10.60 (((exuEu) => 77.78/10.60 (((descr__Cong) => 77.78/10.60 (((dsetconstr__Cong) => 77.78/10.60 (((subsetI1) => 77.78/10.60 (((eqimpsubset2) => 77.78/10.60 (((eqimpsubset1) => 77.78/10.60 (((subsetI2) => 77.78/10.60 (((emptysetsubset) => 77.78/10.60 (((subsetE) => 77.78/10.60 (((subsetE2) => 77.78/10.60 (( 77.78/10.60 (notsubsetI) => 77.78/10.60 (( 77.78/10.60 (notequalI1) => 77.78/10.60 (( 77.78/10.60 (notequalI2) => 77.78/10.60 (( 77.78/10.60 (subsetRefl) => 77.78/10.60 (( 77.78/10.60 (subsetTrans) => 77.78/10.60 (( 77.78/10.60 (setadjoinSub) => 77.78/10.60 (( 77.78/10.60 (setadjoinSub2) => 77.78/10.60 (( 77.78/10.60 (subset2powerset) => 77.78/10.60 (( 77.78/10.60 (setextsub) => 77.78/10.60 (( 77.78/10.60 (subsetemptysetimpeq) => 77.78/10.60 (( 77.78/10.60 (powersetI1) => 77.78/10.60 (( 77.78/10.60 (powersetE1) => 77.78/10.60 (( 77.78/10.60 (inPowerset) => 77.78/10.60 (( 77.78/10.60 (powersetsubset) => 77.78/10.60 (( 77.78/10.60 (sepInPowerset) => 77.78/10.60 (( 77.78/10.60 (sepSubset) => 77.78/10.60 (( 77.78/10.60 (binunionIL) => 77.78/10.60 (( 77.78/10.60 (upairset2IR) => 77.78/10.60 (( 77.78/10.60 (binunionIR) => 77.78/10.60 (( 77.78/10.60 (binunionEcases) => 77.78/10.60 (( 77.78/10.60 (binunionE) => 77.78/10.60 (( 77.78/10.60 (binunionLsub) => 77.78/10.60 (( 77.78/10.60 (binunionRsub) => 77.78/10.60 (( 77.78/10.60 (binintersectI) => 77.78/10.60 (( 77.78/10.60 (binintersectSubset5) => 77.78/10.60 (( 77.78/10.60 (binintersectEL) => 77.78/10.60 (( 77.78/10.60 (binintersectLsub) => 77.78/10.60 (( 77.78/10.60 (binintersectSubset2) => 77.78/10.60 (( 77.78/10.60 (binintersectSubset3) => 77.78/10.60 (( 77.78/10.60 (binintersectER) => 77.78/10.60 (( 77.78/10.60 (disjointsetsI1) => 77.78/10.60 (( 77.78/10.60 (binintersectRsub) => 77.78/10.60 (( 77.78/10.60 (binintersectSubset4) => 77.78/10.60 (( 77.78/10.60 (binintersectSubset1) => 77.78/10.60 (( 77.78/10.60 (bs114d) => 77.78/10.60 (( 77.78/10.60 (setminusI) => 77.78/10.60 (( 77.78/10.60 (setminusEL) => 77.78/10.60 (( 77.78/10.60 (setminusER) => 77.78/10.60 (( 77.78/10.60 (setminusSubset2) => 77.78/10.60 (( 77.78/10.60 (setminusERneg) => 77.78/10.60 (( 77.78/10.60 (setminusELneg) => 77.78/10.60 (( 77.78/10.60 (setminusILneg) => 77.78/10.60 (( 77.78/10.60 (setminusIRneg) => 77.78/10.60 (( 77.78/10.60 (setminusLsub) => 77.78/10.60 (( 77.78/10.60 (setminusSubset1) => 77.78/10.60 (( 77.78/10.60 (symdiffE) => 77.78/10.60 (( 77.78/10.60 (symdiffI1) => 77.78/10.60 (( 77.78/10.60 (symdiffI2) => 77.78/10.60 (( 77.78/10.60 (symdiffIneg1) => 77.78/10.60 (( 77.78/10.60 (symdiffIneg2) => 77.78/10.60 (( 77.78/10.60 (secondinupair) => 77.78/10.60 (( 77.78/10.60 (setukpairIL) => 77.78/10.60 (( 77.78/10.60 (setukpairIR) => 77.78/10.60 (( 77.78/10.60 (kpairiskpair) => 77.78/10.60 (( 77.78/10.60 (kpairp) => 77.78/10.60 (( 77.78/10.60 (singletonsubset) => 77.78/10.60 (( 77.78/10.60 (singletoninpowerset) => 77.78/10.60 (( 77.78/10.60 (singletoninpowunion) => 77.78/10.60 (( 77.78/10.60 (upairset2E) => 77.78/10.60 (( 77.78/10.60 (upairsubunion) => 77.78/10.60 (( 77.78/10.60 (upairinpowunion) => 77.78/10.60 (( 77.78/10.60 (ubforcartprodlem1) => 77.78/10.60 (( 77.78/10.60 (ubforcartprodlem2) => 77.78/10.60 (( 77.78/10.60 (ubforcartprodlem3) => 77.78/10.60 (( 77.78/10.60 (cartprodpairin) => 77.78/10.60 (( 77.78/10.60 (cartprodmempair1) => 77.78/10.60 (( 77.78/10.60 (cartprodmempair) => 77.78/10.60 (( 77.78/10.60 (setunionE2) => 77.78/10.60 (( 77.78/10.60 (setunionsingleton1) => 77.78/10.60 (( 77.78/10.60 (setunionsingleton2) => 77.78/10.60 (( 77.78/10.60 (setunionsingleton) => 77.78/10.60 (( 77.78/10.60 (singletonprop) => 77.78/10.60 (( 77.78/10.60 (ex1E1) => 77.78/10.60 (( 77.78/10.60 (ex1I) => 77.78/10.60 (( 77.78/10.60 (ex1I2) => 77.78/10.60 (( 77.78/10.60 (singletonsuniq) => 77.78/10.60 (( 77.78/10.60 (setukpairinjL1) => 77.78/10.60 (( 77.78/10.60 (kfstsingleton) => 77.78/10.60 (( 77.78/10.60 (theprop) => 77.78/10.60 (( 77.78/10.60 (kfstpairEq) => 77.78/10.60 (( 77.78/10.60 (cartprodfstin) => 77.78/10.60 (( 77.78/10.60 (setukpairinjL2) => 77.78/10.60 (( 77.78/10.60 (setukpairinjL) => 77.78/10.60 (( 77.78/10.60 (setukpairinjR11) => 77.78/10.60 (( 77.78/10.60 (setukpairinjR12) => 77.78/10.60 (( 77.78/10.60 (setukpairinjR1) => 77.78/10.60 (( 77.78/10.60 (upairequniteq) => 77.78/10.60 (( 77.78/10.60 (setukpairinjR2) => 77.78/10.60 (( 77.78/10.60 (setukpairinjR) => 77.78/10.60 (( 77.78/10.60 (ksndsingleton) => 77.78/10.60 (( 77.78/10.60 (ksndpairEq) => 77.78/10.60 (( 77.78/10.60 (kpairsurjEq) => 77.78/10.60 (( 77.78/10.60 (cartprodsndin) => 77.78/10.60 (( 77.78/10.60 (cartprodpairmemEL) => 77.78/10.60 (( 77.78/10.60 (cartprodpairmemER) => 77.78/10.60 (( 77.78/10.60 (cartprodmempaircEq) => 77.78/10.60 (( 77.78/10.60 (cartprodfstpairEq) => 77.78/10.60 (( 77.78/10.60 (cartprodsndpairEq) => 77.78/10.60 (( 77.78/10.60 (cartprodpairsurjEq) => 77.78/10.60 (( 77.78/10.60 (dpsetconstrI) => 77.78/10.60 (( 77.78/10.60 (dpsetconstrSub) => 77.78/10.60 (( 77.78/10.60 (setOfPairsIsBReln) => 77.78/10.60 (( 77.78/10.60 (dpsetconstrERa) => 77.78/10.60 (( 77.78/10.60 (dpsetconstrEL1) => 77.78/10.60 (( 77.78/10.60 (dpsetconstrEL2) => 77.78/10.60 (( 77.78/10.60 (dpsetconstrER) => 77.78/10.60 (( 77.78/10.60 (funcImageSingleton) => 77.78/10.60 (( 77.78/10.60 (apProp) => 77.78/10.60 (( 77.78/10.60 (app) => 77.78/10.60 (( 77.78/10.60 (infuncsetfunc) => 77.78/10.60 (( 77.78/10.60 (ap2p) => 77.78/10.60 (( 77.78/10.60 (funcinfuncset) => 77.78/10.60 (( 77.78/10.60 (lamProp) => 77.78/10.60 (( 77.78/10.60 (lamp) => 77.78/10.60 (( 77.78/10.60 (lam2p) => 77.78/10.60 (( 77.78/10.60 (brelnall1) => 77.78/10.60 (( 77.78/10.60 (brelnall2) => 77.78/10.60 (( 77.78/10.60 (ex1E2) => 77.78/10.60 (( 77.78/10.60 (funcGraphProp1) => 77.78/10.60 (( 77.78/10.60 (funcGraphProp3) => 77.78/10.60 (( 77.78/10.60 (funcGraphProp2) => 77.78/10.60 (( 77.78/10.60 (funcextLem) => 77.78/10.60 (( 77.78/10.60 (funcGraphProp4) => 77.78/10.60 (( 77.78/10.60 (subbreln) => 77.78/10.60 (( 77.78/10.60 (eqbreln) => 77.78/10.60 (( 77.78/10.60 (funcext) => 77.78/10.60 (( 77.78/10.60 (funcext2) => 77.78/10.60 (( 77.78/10.60 (ap2apEq1) => 77.78/10.60 (( 77.78/10.60 (ap2apEq2) => 77.78/10.60 (( 77.78/10.60 (beta1) => 77.78/10.60 (( 77.78/10.60 (eta1) => 77.78/10.60 (( 77.78/10.60 (lam2lamEq) => 77.78/10.60 (( 77.78/10.60 (beta2) => 77.78/10.60 (( 77.78/10.60 (eta2) => 77.78/10.60 (( 77.78/10.60 (iffalseProp1) => 77.78/10.60 (( 77.78/10.60 (iffalseProp2) => 77.78/10.60 (( 77.78/10.60 (iftrueProp1) => 77.78/10.60 (( 77.78/10.60 (iftrueProp2) => 77.78/10.60 (( 77.78/10.60 (ifSingleton) => 77.78/10.60 (( 77.78/10.60 (ifp) => 77.78/10.60 (( 77.78/10.60 (theeq) => 77.78/10.60 (( 77.78/10.60 (iftrue) => 77.78/10.60 (( 77.78/10.60 (iffalse) => 77.78/10.60 (( 77.78/10.60 (iftrueorfalse) => 77.78/10.60 (( 77.78/10.60 (binintersectT_lem) => 77.78/10.60 (( 77.78/10.60 (binunionT_lem) => 77.78/10.60 (( 77.78/10.60 (powersetT_lem) => 77.78/10.60 (( 77.78/10.60 (setminusT_lem) => 77.78/10.60 (( 77.78/10.60 (complementT_lem) => 77.78/10.60 (( 77.78/10.60 (setextT) => 77.78/10.60 (( 77.78/10.61 (subsetTI) => 77.78/10.61 (( 77.78/10.61 (powersetTI1) => 77.78/10.61 (( 77.78/10.61 (powersetTE1) => 77.78/10.61 (( 77.78/10.61 (complementTI1) => 77.78/10.61 (( 77.78/10.61 (complementTE1) => 77.78/10.61 (( 77.78/10.61 (binintersectTELcontra) => 77.78/10.61 (( 77.78/10.61 (binintersectTERcontra) => 77.78/10.61 (( 77.78/10.61 (contrasubsetT) => 77.78/10.61 (( 77.78/10.61 (contrasubsetT1) => 77.78/10.61 (( 77.78/10.61 (contrasubsetT2) => 77.78/10.61 (( 77.78/10.61 (contrasubsetT3) => 77.78/10.61 (( 77.78/10.61 (doubleComplementI1) => 77.78/10.61 (( 77.78/10.61 (doubleComplementE1) => 77.78/10.61 (( 77.78/10.61 (doubleComplementSub1) => 77.78/10.61 (( 77.78/10.61 (doubleComplementSub2) => 77.78/10.61 (( 77.78/10.61 (doubleComplementEq) => 77.78/10.61 (( 77.78/10.61 (complementTnotintersectT) => 77.78/10.61 (( 77.78/10.61 (complementImpComplementIntersect) => 77.78/10.61 (( 77.78/10.61 (complementSubsetComplementIntersect) => 77.78/10.61 (( 77.78/10.61 (complementInPowersetComplementIntersect) => 77.78/10.61 (( 77.78/10.61 (contraSubsetComplement) => 77.78/10.61 (( 77.78/10.61 (complementTcontraSubset) => 77.78/10.61 (( 77.78/10.61 (binunionTILcontra) => 77.78/10.61 (( 77.78/10.61 (binunionTIRcontra) => 77.78/10.61 (( 77.78/10.61 (inIntersectImpInUnion) => 77.78/10.61 (( 77.78/10.61 (inIntersectImpInUnion2) => 77.78/10.61 (( 77.78/10.61 (inIntersectImpInIntersectUnions) => 77.78/10.61 (( 77.78/10.61 (intersectInPowersetIntersectUnions) => 77.78/10.61 (( 77.78/10.61 (inComplementUnionImpNotIn1) => 77.78/10.61 (( 77.78/10.61 (inComplementUnionImpInComplement1) => 77.78/10.61 (( 77.78/10.61 (binunionTE) => 77.78/10.61 (( 77.78/10.61 (binunionTEcontra) => 77.78/10.61 (( 77.78/10.61 (demorgan2a1) => 77.78/10.61 (( 77.78/10.61 (complementUnionInPowersetComplement) => 77.78/10.61 (( 77.78/10.61 (demorgan2a2) => 77.78/10.61 (( 77.78/10.61 (demorgan1a) => 77.78/10.61 (( 77.78/10.61 (demorgan1b) => 77.78/10.61 (( 77.78/10.61 (demorgan1) => 77.78/10.61 (( 77.78/10.61 (demorgan2a) => 77.78/10.61 (( 77.78/10.61 (demorgan2b2) => 77.78/10.61 (( 77.78/10.61 (demorgan2b) => 77.78/10.61 (( 77.78/10.61 (demorgan2) => 77.78/10.61 (( 77.78/10.61 (woz13rule0) => 77.78/10.61 (( 77.78/10.61 (woz13rule1) => 77.78/10.61 (( 77.78/10.61 (woz13rule2) => 77.78/10.61 (( 77.78/10.61 (woz13rule3) => 77.78/10.61 (( 77.78/10.61 (woz13rule4) => 77.78/10.61 (( 77.78/10.61 (woz1_1) => 77.78/10.61 (( 77.78/10.61 (woz1_2) => 77.78/10.61 (( 77.78/10.61 (woz1_3) => 77.78/10.61 (( 77.78/10.61 (woz1_4) => 77.78/10.61 (( 77.78/10.61 (woz1_5) => 77.78/10.61 (( 77.78/10.61 (breln1all2) => 77.78/10.61 (( 77.78/10.61 (breln1SetBreln1) => 77.78/10.61 (( 77.78/10.61 (choice2fnsingleton) => 77.78/10.61 (( 77.78/10.61 (setOfPairsIsBReln1) => 77.78/10.61 (( 77.78/10.61 (breln1all1) => 77.78/10.61 (( 77.78/10.61 (subbreln1) => 77.78/10.61 (( 77.78/10.61 (eqbreln1) => 77.78/10.61 (( 77.78/10.61 (breln1invprop) => 77.78/10.61 (( 77.78/10.61 (breln1invI) => 77.78/10.61 (( 77.78/10.61 (breln1invE) => 77.78/10.61 (( 77.78/10.61 (breln1compprop) => 77.78/10.61 (( 77.78/10.61 (breln1compI) => 77.78/10.61 (( 77.78/10.61 (breln1compE) => 77.78/10.61 (( 77.78/10.61 (breln1compEex) => 77.78/10.61 (( 77.78/10.61 (breln1unionprop) => 77.78/10.61 (( 77.78/10.61 (breln1unionIL) => 77.78/10.61 (( 77.78/10.61 (breln1unionIR) => 77.78/10.61 (( 77.78/10.61 (breln1unionI) => 77.78/10.61 (( 77.78/10.61 (breln1unionE) => 77.78/10.61 (( 77.78/10.61 (breln1unionEcases) => 77.78/10.61 (( 77.78/10.61 (breln1unionCommutes) => 77.78/10.61 (( 77.78/10.61 (woz2Ex) => 77.78/10.61 (( 77.78/10.61 (woz2W) => 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(binintTransitive) => 77.78/10.61 (( 77.78/10.61 (transitivesetOp2) => 77.78/10.61 (( 77.78/10.61 (setunionTransitive) => 77.78/10.61 (( 77.78/10.61 (ordinalMinLem1) => 77.78/10.61 (( 77.78/10.61 (!!) @ ( 77.78/10.61 ^[Y0 : $i]: 77.78/10.61 (( 77.78/10.61 (ordinal @ 77.78/10.61 Y0) => 77.78/10.61 (( 77.78/10.61 (!!) @ ( 77.78/10.61 ^[Y1 : $i]: 77.78/10.61 (( 77.78/10.61 (!!) @ ( 77.78/10.61 ^[Y2 : $i]: 77.78/10.61 (( 77.78/10.61 (in @ 77.78/10.61 Y2 @ 77.78/10.61 Y0) => 77.78/10.61 (( 77.78/10.61 (in @ 77.78/10.61 Y1 @ 77.78/10.61 Y2) => 77.78/10.61 (in @ 77.78/10.61 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 77.78/10.61 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl449])). 77.78/10.61 thf(zip_derived_cl465, plain, 77.78/10.61 (~ (((vacuousDall) => 77.78/10.61 (((quantDeMorgan1) => 77.78/10.61 (((quantDeMorgan2) => 77.78/10.61 (((quantDeMorgan3) => 77.78/10.61 (((quantDeMorgan4) => 77.78/10.61 (((prop2setI) => 77.78/10.61 (((prop2set2propI) => 77.78/10.61 (((notdexE) => 77.78/10.61 (((notdallE) => 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(subsetemptysetimpeq) => 77.78/10.61 (( 77.78/10.61 (powersetI1) => 77.78/10.61 (( 77.78/10.61 (powersetE1) => 77.78/10.61 (( 77.78/10.61 (inPowerset) => 77.78/10.61 (( 77.78/10.61 (powersetsubset) => 77.78/10.61 (( 77.78/10.61 (sepInPowerset) => 77.78/10.61 (( 77.78/10.61 (sepSubset) => 77.78/10.61 (( 77.78/10.61 (binunionIL) => 77.78/10.61 (( 77.78/10.61 (upairset2IR) => 77.78/10.61 (( 77.78/10.61 (binunionIR) => 77.78/10.61 (( 77.78/10.61 (binunionEcases) => 77.78/10.61 (( 77.78/10.61 (binunionE) => 77.78/10.61 (( 77.78/10.61 (binunionLsub) => 77.78/10.61 (( 77.78/10.61 (binunionRsub) => 77.78/10.61 (( 77.78/10.61 (binintersectI) => 77.78/10.61 (( 77.78/10.61 (binintersectSubset5) => 77.78/10.61 (( 77.78/10.61 (binintersectEL) => 77.78/10.61 (( 77.78/10.61 (binintersectLsub) => 77.78/10.61 (( 77.78/10.61 (binintersectSubset2) => 77.78/10.61 (( 77.78/10.61 (binintersectSubset3) => 77.78/10.61 (( 77.78/10.61 (binintersectER) => 77.78/10.61 (( 77.78/10.61 (disjointsetsI1) => 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77.78/10.61 (( 77.78/10.61 (kpairiskpair) => 77.78/10.61 (( 77.78/10.61 (kpairp) => 77.78/10.61 (( 77.78/10.61 (singletonsubset) => 77.78/10.61 (( 77.78/10.61 (singletoninpowerset) => 77.78/10.61 (( 77.78/10.61 (singletoninpowunion) => 77.78/10.61 (( 77.78/10.61 (upairset2E) => 77.78/10.61 (( 77.78/10.61 (upairsubunion) => 77.78/10.61 (( 77.78/10.61 (upairinpowunion) => 77.78/10.61 (( 77.78/10.61 (ubforcartprodlem1) => 77.78/10.61 (( 77.78/10.61 (ubforcartprodlem2) => 77.78/10.61 (( 77.78/10.61 (ubforcartprodlem3) => 77.78/10.61 (( 77.78/10.61 (cartprodpairin) => 77.78/10.61 (( 77.78/10.61 (cartprodmempair1) => 77.78/10.61 (( 77.78/10.61 (cartprodmempair) => 77.78/10.61 (( 77.78/10.61 (setunionE2) => 77.78/10.61 (( 77.78/10.61 (setunionsingleton1) => 77.78/10.61 (( 77.78/10.61 (setunionsingleton2) => 77.78/10.61 (( 77.78/10.61 (setunionsingleton) => 77.78/10.61 (( 77.78/10.61 (singletonprop) => 77.78/10.61 (( 77.78/10.61 (ex1E1) => 77.78/10.61 (( 77.78/10.61 (ex1I) => 77.78/10.61 (( 77.78/10.61 (ex1I2) => 77.78/10.61 (( 77.78/10.61 (singletonsuniq) => 77.78/10.61 (( 77.78/10.61 (setukpairinjL1) => 77.78/10.61 (( 77.78/10.61 (kfstsingleton) => 77.78/10.61 (( 77.78/10.61 (theprop) => 77.78/10.61 (( 77.78/10.61 (kfstpairEq) => 77.78/10.61 (( 77.78/10.61 (cartprodfstin) => 77.78/10.61 (( 77.78/10.61 (setukpairinjL2) => 77.78/10.61 (( 77.78/10.61 (setukpairinjL) => 77.78/10.61 (( 77.78/10.61 (setukpairinjR11) => 77.78/10.61 (( 77.78/10.61 (setukpairinjR12) => 77.78/10.61 (( 77.78/10.61 (setukpairinjR1) => 77.78/10.61 (( 77.78/10.61 (upairequniteq) => 77.78/10.61 (( 77.78/10.61 (setukpairinjR2) => 77.78/10.61 (( 77.78/10.61 (setukpairinjR) => 77.78/10.61 (( 77.78/10.61 (ksndsingleton) => 77.78/10.61 (( 77.78/10.61 (ksndpairEq) => 77.78/10.61 (( 77.78/10.61 (kpairsurjEq) => 77.78/10.61 (( 77.78/10.61 (cartprodsndin) => 77.78/10.61 (( 77.78/10.61 (cartprodpairmemEL) => 77.78/10.61 (( 77.78/10.61 (cartprodpairmemER) => 77.78/10.61 (( 77.78/10.61 (cartprodmempaircEq) => 77.78/10.61 (( 77.78/10.61 (cartprodfstpairEq) => 77.78/10.61 (( 77.78/10.61 (cartprodsndpairEq) => 77.78/10.61 (( 77.78/10.61 (cartprodpairsurjEq) => 77.78/10.61 (( 77.78/10.61 (dpsetconstrI) => 77.78/10.61 (( 77.78/10.61 (dpsetconstrSub) => 77.78/10.61 (( 77.78/10.61 (setOfPairsIsBReln) => 77.78/10.61 (( 77.78/10.61 (dpsetconstrERa) => 77.78/10.61 (( 77.78/10.61 (dpsetconstrEL1) => 77.78/10.61 (( 77.78/10.61 (dpsetconstrEL2) => 77.78/10.61 (( 77.78/10.61 (dpsetconstrER) => 77.78/10.61 (( 77.78/10.61 (funcImageSingleton) => 77.78/10.61 (( 77.78/10.61 (apProp) => 77.78/10.61 (( 77.78/10.61 (app) => 77.78/10.61 (( 77.78/10.61 (infuncsetfunc) => 77.78/10.61 (( 77.78/10.61 (ap2p) => 77.78/10.61 (( 77.78/10.61 (funcinfuncset) => 77.78/10.61 (( 77.78/10.61 (lamProp) => 77.78/10.61 (( 77.78/10.61 (lamp) => 77.78/10.61 (( 77.78/10.61 (lam2p) => 77.78/10.61 (( 77.78/10.61 (brelnall1) => 77.78/10.61 (( 77.78/10.61 (brelnall2) => 77.78/10.61 (( 77.78/10.61 (ex1E2) => 77.78/10.61 (( 77.78/10.61 (funcGraphProp1) => 77.78/10.61 (( 77.78/10.61 (funcGraphProp3) => 77.78/10.61 (( 77.78/10.61 (funcGraphProp2) => 77.78/10.61 (( 77.78/10.61 (funcextLem) => 77.78/10.61 (( 77.78/10.61 (funcGraphProp4) => 77.78/10.61 (( 77.78/10.61 (subbreln) => 77.78/10.61 (( 77.78/10.61 (eqbreln) => 77.78/10.61 (( 77.78/10.61 (funcext) => 77.78/10.61 (( 77.78/10.61 (funcext2) => 77.78/10.61 (( 77.78/10.61 (ap2apEq1) => 77.78/10.61 (( 77.78/10.61 (ap2apEq2) => 77.78/10.61 (( 77.78/10.61 (beta1) => 77.78/10.61 (( 77.78/10.61 (eta1) => 77.78/10.61 (( 77.78/10.61 (lam2lamEq) => 77.78/10.61 (( 77.78/10.61 (beta2) => 77.78/10.61 (( 77.78/10.61 (eta2) => 77.78/10.61 (( 77.78/10.61 (iffalseProp1) => 77.78/10.61 (( 77.78/10.61 (iffalseProp2) => 77.78/10.61 (( 77.78/10.61 (iftrueProp1) => 77.78/10.61 (( 77.78/10.61 (iftrueProp2) => 77.78/10.61 (( 77.78/10.61 (ifSingleton) => 77.78/10.61 (( 77.78/10.61 (ifp) => 77.78/10.61 (( 77.78/10.61 (theeq) => 77.78/10.61 (( 77.78/10.61 (iftrue) => 77.78/10.61 (( 77.78/10.61 (iffalse) => 77.78/10.61 (( 77.78/10.61 (iftrueorfalse) => 77.78/10.61 (( 77.78/10.61 (binintersectT_lem) => 77.78/10.61 (( 77.78/10.61 (binunionT_lem) => 77.78/10.61 (( 77.78/10.61 (powersetT_lem) => 77.78/10.61 (( 77.78/10.61 (setminusT_lem) => 77.78/10.61 (( 77.78/10.61 (complementT_lem) => 77.78/10.61 (( 77.78/10.61 (setextT) => 77.78/10.61 (( 77.78/10.61 (subsetTI) => 77.78/10.61 (( 77.78/10.61 (powersetTI1) => 77.78/10.61 (( 77.78/10.61 (powersetTE1) => 77.78/10.61 (( 77.78/10.61 (complementTI1) => 77.78/10.61 (( 77.78/10.61 (complementTE1) => 77.78/10.61 (( 77.78/10.61 (binintersectTELcontra) => 77.78/10.61 (( 77.78/10.61 (binintersectTERcontra) => 77.78/10.61 (( 77.78/10.61 (contrasubsetT) => 77.78/10.61 (( 77.78/10.61 (contrasubsetT1) => 77.78/10.61 (( 77.78/10.61 (contrasubsetT2) => 77.78/10.61 (( 77.78/10.61 (contrasubsetT3) => 77.78/10.61 (( 77.78/10.61 (doubleComplementI1) => 77.78/10.61 (( 77.78/10.61 (doubleComplementE1) => 77.78/10.61 (( 77.78/10.61 (doubleComplementSub1) => 77.78/10.61 (( 77.78/10.61 (doubleComplementSub2) => 77.78/10.61 (( 77.78/10.61 (doubleComplementEq) => 77.78/10.61 (( 77.78/10.61 (complementTnotintersectT) => 77.78/10.61 (( 77.78/10.61 (complementImpComplementIntersect) => 77.78/10.61 (( 77.78/10.61 (complementSubsetComplementIntersect) => 77.78/10.61 (( 77.78/10.61 (complementInPowersetComplementIntersect) => 77.78/10.61 (( 77.78/10.61 (contraSubsetComplement) => 77.78/10.61 (( 77.78/10.61 (complementTcontraSubset) => 77.78/10.61 (( 77.78/10.61 (binunionTILcontra) => 77.78/10.61 (( 77.78/10.61 (binunionTIRcontra) => 77.78/10.61 (( 77.78/10.61 (inIntersectImpInUnion) => 77.78/10.61 (( 77.78/10.61 (inIntersectImpInUnion2) => 77.78/10.61 (( 77.78/10.61 (inIntersectImpInIntersectUnions) => 77.78/10.61 (( 77.78/10.61 (intersectInPowersetIntersectUnions) => 77.78/10.61 (( 77.78/10.61 (inComplementUnionImpNotIn1) => 77.78/10.61 (( 77.78/10.61 (inComplementUnionImpInComplement1) => 77.78/10.61 (( 77.78/10.61 (binunionTE) => 77.78/10.61 (( 77.78/10.61 (binunionTEcontra) => 77.78/10.61 (( 77.78/10.61 (demorgan2a1) => 77.78/10.61 (( 77.78/10.61 (complementUnionInPowersetComplement) => 77.78/10.61 (( 77.78/10.61 (demorgan2a2) => 77.78/10.61 (( 77.78/10.61 (demorgan1a) => 77.78/10.61 (( 77.78/10.61 (demorgan1b) => 77.78/10.61 (( 77.78/10.61 (demorgan1) => 77.78/10.61 (( 77.78/10.61 (demorgan2a) => 77.78/10.61 (( 77.78/10.61 (demorgan2b2) => 77.78/10.61 (( 77.78/10.61 (demorgan2b) => 77.78/10.61 (( 77.78/10.61 (demorgan2) => 77.78/10.61 (( 77.78/10.61 (woz13rule0) => 77.78/10.61 (( 77.78/10.61 (woz13rule1) => 77.78/10.61 (( 77.78/10.61 (woz13rule2) => 77.78/10.61 (( 77.78/10.61 (woz13rule3) => 77.78/10.61 (( 77.78/10.61 (woz13rule4) => 77.78/10.61 (( 77.78/10.61 (woz1_1) => 77.78/10.61 (( 77.78/10.61 (woz1_2) => 77.78/10.61 (( 77.78/10.61 (woz1_3) => 77.78/10.61 (( 77.78/10.61 (woz1_4) => 77.78/10.61 (( 77.78/10.61 (woz1_5) => 77.78/10.61 (( 77.78/10.61 (breln1all2) => 77.78/10.61 (( 77.78/10.61 (breln1SetBreln1) => 77.78/10.61 (( 77.78/10.61 (choice2fnsingleton) => 77.78/10.61 (( 77.78/10.61 (setOfPairsIsBReln1) => 77.78/10.61 (( 77.78/10.61 (breln1all1) => 77.78/10.61 (( 77.78/10.61 (subbreln1) => 77.78/10.61 (( 77.78/10.61 (eqbreln1) => 77.78/10.61 (( 77.78/10.61 (breln1invprop) => 77.78/10.61 (( 77.78/10.61 (breln1invI) => 77.78/10.61 (( 77.78/10.61 (breln1invE) => 77.78/10.61 (( 77.78/10.61 (breln1compprop) => 77.78/10.61 (( 77.78/10.61 (breln1compI) => 77.78/10.61 (( 77.78/10.61 (breln1compE) => 77.78/10.61 (( 77.78/10.61 (breln1compEex) => 77.78/10.61 (( 77.78/10.61 (breln1unionprop) => 77.78/10.61 (( 77.78/10.61 (breln1unionIL) => 77.78/10.61 (( 77.78/10.61 (breln1unionIR) => 77.78/10.61 (( 77.78/10.61 (breln1unionI) => 77.78/10.61 (( 77.78/10.61 (breln1unionE) => 77.78/10.61 (( 77.78/10.61 (breln1unionEcases) => 77.78/10.61 (( 77.78/10.61 (breln1unionCommutes) => 77.78/10.61 (( 77.78/10.61 (woz2Ex) => 77.78/10.61 (( 77.78/10.61 (woz2W) => 77.78/10.61 (( 77.78/10.61 (woz2A) => 77.78/10.61 (( 77.78/10.61 (woz2B) => 77.78/10.61 (( 77.78/10.61 (image1Ex) => 77.78/10.61 (( 77.78/10.61 (image1Ex1) => 77.78/10.61 (( 77.78/10.61 (image1Equiv) => 77.78/10.61 (( 77.78/10.61 (image1E) => 77.78/10.61 (( 77.78/10.61 (image1I) => 77.78/10.61 (( 77.78/10.61 (injFuncInInjFuncSet) => 77.78/10.61 (( 77.78/10.61 (injFuncSetFuncIn) => 77.78/10.61 (( 77.78/10.61 (injFuncSetFuncInj) => 77.78/10.61 (( 77.78/10.61 (surjFuncSetFuncIn) => 77.78/10.61 (( 77.78/10.61 (surjFuncSetFuncSurj) => 77.78/10.61 (( 77.78/10.61 (leftInvIsSurj) => 77.78/10.61 (( 77.78/10.61 (surjCantorThm) => 77.78/10.61 (( 77.78/10.61 (foundation2) => 77.78/10.61 (( 77.78/10.61 (notinself) => 77.78/10.61 (( 77.78/10.61 (notinself2) => 77.78/10.61 (( 77.78/10.61 (omegaSp) => 77.78/10.61 (( 77.78/10.61 (omegaSclos) => 77.78/10.61 (( 77.78/10.61 (peano0notS) => 77.78/10.61 (( 77.78/10.61 (peanoSinj) => 77.78/10.61 (( 77.78/10.61 (transitivesetOp1) => 77.78/10.61 (( 77.78/10.61 (binintTransitive) => 77.78/10.61 (( 77.78/10.61 (transitivesetOp2) => 77.78/10.61 (( 77.78/10.61 (setunionTransitive) => 77.78/10.61 (( 77.78/10.61 (ordinalMinLem1) => 77.78/10.61 (( 77.78/10.61 (!!) @ ( 77.78/10.61 ^[Y0 : $i]: 77.78/10.61 (( 77.78/10.61 (ordinal @ 77.78/10.61 Y0) => 77.78/10.61 (( 77.78/10.61 (!!) @ ( 77.78/10.61 ^[Y1 : $i]: 77.78/10.61 (( 77.78/10.61 (!!) @ ( 77.78/10.61 ^[Y2 : $i]: 77.78/10.61 (( 77.78/10.61 (in @ 77.78/10.61 Y2 @ 77.78/10.61 Y0) => 77.78/10.61 (( 77.78/10.61 (in @ 77.78/10.61 Y1 @ 77.78/10.61 Y2) => 77.78/10.61 (in @ 77.78/10.61 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 77.78/10.61 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl457])). 77.78/10.61 thf(zip_derived_cl471, plain, 77.78/10.61 (~ (((quantDeMorgan1) => 77.78/10.61 (((quantDeMorgan2) => 77.78/10.61 (((quantDeMorgan3) => 77.78/10.61 (((quantDeMorgan4) => 77.78/10.61 (((prop2setI) => 77.78/10.61 (((prop2set2propI) => 77.78/10.61 (((notdexE) => 77.78/10.61 (((notdallE) => 77.78/10.61 (((exuI1) => 77.78/10.61 (((exuI3) => 77.78/10.61 (((exuI2) => 77.78/10.61 (((inCongP) => 77.78/10.61 (((in__Cong) => 77.78/10.61 (((exuE3u) => 77.78/10.61 (((exu__Cong) => 77.78/10.61 (((setadjoin__Cong) => 77.78/10.61 (((powerset__Cong) => 77.78/10.61 (((setunion__Cong) => 77.78/10.61 (((exuEu) => 77.78/10.61 (((descr__Cong) => 77.78/10.61 (((dsetconstr__Cong) => 77.78/10.61 (((subsetI1) => 77.78/10.61 (((eqimpsubset2) => 77.78/10.61 (((eqimpsubset1) => 77.78/10.61 (((subsetI2) => 77.78/10.61 (((emptysetsubset) => 77.78/10.61 (((subsetE) => 77.78/10.61 (((subsetE2) => 77.78/10.61 (((notsubsetI) => 77.78/10.61 (((notequalI1) => 77.78/10.61 (( 77.78/10.61 (notequalI2) => 77.78/10.61 (( 77.78/10.61 (subsetRefl) => 77.78/10.61 (( 77.78/10.61 (subsetTrans) => 77.78/10.61 (( 77.78/10.61 (setadjoinSub) => 77.78/10.61 (( 77.78/10.61 (setadjoinSub2) => 77.78/10.61 (( 77.78/10.61 (subset2powerset) => 77.78/10.61 (( 77.78/10.61 (setextsub) => 77.78/10.61 (( 77.78/10.61 (subsetemptysetimpeq) => 77.78/10.61 (( 77.78/10.61 (powersetI1) => 77.78/10.61 (( 77.78/10.61 (powersetE1) => 77.78/10.61 (( 77.78/10.61 (inPowerset) => 77.78/10.61 (( 77.78/10.61 (powersetsubset) => 77.78/10.61 (( 77.78/10.61 (sepInPowerset) => 77.78/10.61 (( 77.78/10.61 (sepSubset) => 77.78/10.61 (( 77.78/10.61 (binunionIL) => 77.78/10.61 (( 77.78/10.61 (upairset2IR) => 77.78/10.61 (( 77.78/10.61 (binunionIR) => 77.78/10.61 (( 77.78/10.61 (binunionEcases) => 77.78/10.61 (( 77.78/10.61 (binunionE) => 77.78/10.61 (( 77.78/10.61 (binunionLsub) => 77.78/10.61 (( 77.78/10.61 (binunionRsub) => 77.78/10.61 (( 77.78/10.61 (binintersectI) => 77.78/10.61 (( 77.78/10.61 (binintersectSubset5) => 77.78/10.61 (( 77.78/10.61 (binintersectEL) => 77.78/10.61 (( 77.78/10.61 (binintersectLsub) => 77.78/10.61 (( 77.78/10.61 (binintersectSubset2) => 77.78/10.61 (( 77.78/10.61 (binintersectSubset3) => 77.78/10.61 (( 77.78/10.61 (binintersectER) => 77.78/10.61 (( 77.78/10.61 (disjointsetsI1) => 77.78/10.61 (( 77.78/10.61 (binintersectRsub) => 77.78/10.61 (( 77.78/10.61 (binintersectSubset4) => 77.78/10.61 (( 77.78/10.61 (binintersectSubset1) => 77.78/10.61 (( 77.78/10.61 (bs114d) => 77.78/10.61 (( 77.78/10.61 (setminusI) => 77.78/10.61 (( 77.78/10.61 (setminusEL) => 77.78/10.61 (( 77.78/10.61 (setminusER) => 77.78/10.61 (( 77.78/10.61 (setminusSubset2) => 77.78/10.61 (( 77.78/10.61 (setminusERneg) => 77.78/10.61 (( 77.78/10.61 (setminusELneg) => 77.78/10.61 (( 77.78/10.61 (setminusILneg) => 77.78/10.61 (( 77.78/10.61 (setminusIRneg) => 77.78/10.61 (( 77.78/10.61 (setminusLsub) => 77.78/10.61 (( 77.78/10.61 (setminusSubset1) => 77.78/10.61 (( 77.78/10.61 (symdiffE) => 77.78/10.61 (( 77.78/10.61 (symdiffI1) => 77.78/10.61 (( 77.78/10.61 (symdiffI2) => 77.78/10.61 (( 77.78/10.61 (symdiffIneg1) => 77.78/10.61 (( 77.78/10.61 (symdiffIneg2) => 77.78/10.61 (( 77.78/10.61 (secondinupair) => 77.78/10.61 (( 77.78/10.61 (setukpairIL) => 77.78/10.61 (( 77.78/10.61 (setukpairIR) => 77.78/10.61 (( 77.78/10.61 (kpairiskpair) => 77.78/10.61 (( 77.78/10.61 (kpairp) => 77.78/10.61 (( 77.78/10.61 (singletonsubset) => 77.78/10.61 (( 77.78/10.61 (singletoninpowerset) => 77.78/10.61 (( 77.78/10.61 (singletoninpowunion) => 77.78/10.61 (( 77.78/10.61 (upairset2E) => 77.78/10.61 (( 77.78/10.61 (upairsubunion) => 77.78/10.61 (( 77.78/10.61 (upairinpowunion) => 77.78/10.61 (( 77.78/10.61 (ubforcartprodlem1) => 77.78/10.61 (( 77.78/10.61 (ubforcartprodlem2) => 77.78/10.61 (( 77.78/10.61 (ubforcartprodlem3) => 77.78/10.61 (( 77.78/10.61 (cartprodpairin) => 77.78/10.61 (( 77.78/10.61 (cartprodmempair1) => 77.78/10.61 (( 77.78/10.61 (cartprodmempair) => 77.78/10.61 (( 77.78/10.61 (setunionE2) => 77.78/10.61 (( 77.78/10.61 (setunionsingleton1) => 77.78/10.61 (( 77.78/10.61 (setunionsingleton2) => 77.78/10.61 (( 77.78/10.61 (setunionsingleton) => 77.78/10.61 (( 77.78/10.61 (singletonprop) => 77.78/10.61 (( 77.78/10.61 (ex1E1) => 77.78/10.61 (( 77.78/10.61 (ex1I) => 77.78/10.61 (( 77.78/10.61 (ex1I2) => 77.78/10.61 (( 77.78/10.61 (singletonsuniq) => 77.78/10.61 (( 77.78/10.61 (setukpairinjL1) => 77.78/10.61 (( 77.78/10.61 (kfstsingleton) => 77.78/10.61 (( 77.78/10.61 (theprop) => 77.78/10.61 (( 77.78/10.61 (kfstpairEq) => 77.78/10.61 (( 77.78/10.61 (cartprodfstin) => 77.78/10.61 (( 77.78/10.61 (setukpairinjL2) => 77.78/10.61 (( 77.78/10.61 (setukpairinjL) => 77.78/10.61 (( 77.78/10.61 (setukpairinjR11) => 77.78/10.61 (( 77.78/10.61 (setukpairinjR12) => 77.78/10.61 (( 77.78/10.61 (setukpairinjR1) => 77.78/10.61 (( 77.78/10.61 (upairequniteq) => 77.78/10.61 (( 77.78/10.61 (setukpairinjR2) => 77.78/10.61 (( 77.78/10.61 (setukpairinjR) => 77.78/10.61 (( 77.78/10.61 (ksndsingleton) => 77.78/10.61 (( 77.78/10.61 (ksndpairEq) => 77.78/10.61 (( 77.78/10.61 (kpairsurjEq) => 77.78/10.61 (( 77.78/10.61 (cartprodsndin) => 77.78/10.61 (( 77.78/10.61 (cartprodpairmemEL) => 77.78/10.61 (( 77.78/10.61 (cartprodpairmemER) => 77.78/10.61 (( 77.78/10.61 (cartprodmempaircEq) => 77.78/10.61 (( 77.78/10.61 (cartprodfstpairEq) => 77.78/10.61 (( 77.78/10.61 (cartprodsndpairEq) => 77.78/10.61 (( 77.78/10.61 (cartprodpairsurjEq) => 77.78/10.61 (( 77.78/10.61 (dpsetconstrI) => 77.78/10.61 (( 77.78/10.61 (dpsetconstrSub) => 77.78/10.61 (( 77.78/10.61 (setOfPairsIsBReln) => 77.78/10.61 (( 77.78/10.61 (dpsetconstrERa) => 77.78/10.61 (( 77.78/10.61 (dpsetconstrEL1) => 77.78/10.61 (( 77.78/10.61 (dpsetconstrEL2) => 77.78/10.61 (( 77.78/10.61 (dpsetconstrER) => 77.78/10.61 (( 77.78/10.61 (funcImageSingleton) => 77.78/10.61 (( 77.78/10.61 (apProp) => 77.78/10.61 (( 77.78/10.61 (app) => 77.78/10.61 (( 77.78/10.61 (infuncsetfunc) => 77.78/10.61 (( 77.78/10.61 (ap2p) => 77.78/10.61 (( 77.78/10.61 (funcinfuncset) => 77.78/10.61 (( 77.78/10.61 (lamProp) => 77.78/10.61 (( 77.78/10.61 (lamp) => 77.78/10.61 (( 77.78/10.61 (lam2p) => 77.78/10.61 (( 77.78/10.61 (brelnall1) => 77.78/10.61 (( 77.78/10.61 (brelnall2) => 77.78/10.61 (( 77.78/10.61 (ex1E2) => 77.78/10.61 (( 77.78/10.61 (funcGraphProp1) => 77.78/10.61 (( 77.78/10.61 (funcGraphProp3) => 77.78/10.61 (( 77.78/10.61 (funcGraphProp2) => 77.78/10.61 (( 77.78/10.61 (funcextLem) => 77.78/10.61 (( 77.78/10.61 (funcGraphProp4) => 77.78/10.61 (( 77.78/10.61 (subbreln) => 77.78/10.61 (( 77.78/10.61 (eqbreln) => 77.78/10.61 (( 77.78/10.61 (funcext) => 77.78/10.61 (( 77.78/10.61 (funcext2) => 77.78/10.61 (( 77.78/10.61 (ap2apEq1) => 77.78/10.61 (( 77.78/10.61 (ap2apEq2) => 77.78/10.61 (( 77.78/10.61 (beta1) => 77.78/10.61 (( 77.78/10.61 (eta1) => 77.78/10.61 (( 77.78/10.61 (lam2lamEq) => 77.78/10.61 (( 77.78/10.61 (beta2) => 77.78/10.61 (( 77.78/10.61 (eta2) => 77.78/10.61 (( 77.78/10.61 (iffalseProp1) => 77.78/10.61 (( 77.78/10.61 (iffalseProp2) => 77.78/10.61 (( 77.78/10.61 (iftrueProp1) => 77.78/10.61 (( 77.78/10.61 (iftrueProp2) => 77.78/10.61 (( 77.78/10.61 (ifSingleton) => 77.78/10.61 (( 77.78/10.61 (ifp) => 77.78/10.61 (( 77.78/10.61 (theeq) => 77.78/10.61 (( 77.78/10.61 (iftrue) => 77.78/10.61 (( 77.78/10.61 (iffalse) => 77.78/10.61 (( 77.78/10.61 (iftrueorfalse) => 77.78/10.61 (( 77.78/10.61 (binintersectT_lem) => 77.78/10.61 (( 77.78/10.61 (binunionT_lem) => 77.78/10.61 (( 77.78/10.61 (powersetT_lem) => 77.78/10.61 (( 77.78/10.61 (setminusT_lem) => 77.78/10.61 (( 77.78/10.61 (complementT_lem) => 77.78/10.61 (( 77.78/10.61 (setextT) => 77.78/10.61 (( 77.78/10.61 (subsetTI) => 77.78/10.61 (( 77.78/10.61 (powersetTI1) => 77.78/10.61 (( 77.78/10.61 (powersetTE1) => 77.78/10.61 (( 77.78/10.61 (complementTI1) => 77.78/10.61 (( 77.78/10.61 (complementTE1) => 77.78/10.61 (( 77.78/10.61 (binintersectTELcontra) => 77.78/10.61 (( 77.78/10.61 (binintersectTERcontra) => 77.78/10.61 (( 77.78/10.61 (contrasubsetT) => 77.78/10.61 (( 77.78/10.61 (contrasubsetT1) => 77.78/10.61 (( 77.78/10.61 (contrasubsetT2) => 77.78/10.61 (( 77.78/10.61 (contrasubsetT3) => 77.78/10.61 (( 77.78/10.61 (doubleComplementI1) => 77.78/10.61 (( 77.78/10.61 (doubleComplementE1) => 77.78/10.61 (( 77.78/10.61 (doubleComplementSub1) => 77.78/10.61 (( 77.78/10.61 (doubleComplementSub2) => 77.78/10.61 (( 77.78/10.61 (doubleComplementEq) => 77.78/10.61 (( 77.78/10.61 (complementTnotintersectT) => 77.78/10.61 (( 77.78/10.61 (complementImpComplementIntersect) => 77.78/10.61 (( 77.78/10.61 (complementSubsetComplementIntersect) => 77.78/10.61 (( 77.78/10.61 (complementInPowersetComplementIntersect) => 77.78/10.61 (( 77.78/10.61 (contraSubsetComplement) => 77.78/10.61 (( 77.78/10.61 (complementTcontraSubset) => 77.78/10.61 (( 77.78/10.61 (binunionTILcontra) => 77.78/10.61 (( 77.78/10.61 (binunionTIRcontra) => 77.78/10.61 (( 77.78/10.61 (inIntersectImpInUnion) => 77.78/10.61 (( 77.78/10.61 (inIntersectImpInUnion2) => 77.78/10.61 (( 77.78/10.61 (inIntersectImpInIntersectUnions) => 77.78/10.61 (( 77.78/10.61 (intersectInPowersetIntersectUnions) => 77.78/10.61 (( 77.78/10.61 (inComplementUnionImpNotIn1) => 77.78/10.61 (( 77.78/10.61 (inComplementUnionImpInComplement1) => 77.78/10.61 (( 77.78/10.61 (binunionTE) => 77.78/10.61 (( 77.78/10.61 (binunionTEcontra) => 77.78/10.61 (( 77.78/10.61 (demorgan2a1) => 77.78/10.61 (( 77.78/10.61 (complementUnionInPowersetComplement) => 77.78/10.61 (( 77.78/10.61 (demorgan2a2) => 77.78/10.61 (( 77.78/10.61 (demorgan1a) => 77.78/10.61 (( 77.78/10.61 (demorgan1b) => 77.78/10.61 (( 77.78/10.61 (demorgan1) => 77.78/10.61 (( 77.78/10.61 (demorgan2a) => 77.78/10.61 (( 77.78/10.61 (demorgan2b2) => 77.78/10.61 (( 77.78/10.61 (demorgan2b) => 77.78/10.61 (( 77.78/10.61 (demorgan2) => 77.78/10.61 (( 77.78/10.61 (woz13rule0) => 77.78/10.61 (( 77.78/10.61 (woz13rule1) => 77.78/10.61 (( 77.78/10.61 (woz13rule2) => 77.78/10.61 (( 77.78/10.61 (woz13rule3) => 77.78/10.61 (( 77.78/10.61 (woz13rule4) => 77.78/10.61 (( 77.78/10.61 (woz1_1) => 77.78/10.61 (( 77.78/10.61 (woz1_2) => 77.78/10.61 (( 77.78/10.61 (woz1_3) => 77.78/10.61 (( 77.78/10.61 (woz1_4) => 77.78/10.61 (( 77.78/10.61 (woz1_5) => 77.78/10.61 (( 77.78/10.61 (breln1all2) => 77.78/10.61 (( 77.78/10.61 (breln1SetBreln1) => 77.78/10.61 (( 77.78/10.61 (choice2fnsingleton) => 77.78/10.61 (( 77.78/10.61 (setOfPairsIsBReln1) => 77.78/10.61 (( 77.78/10.61 (breln1all1) => 77.78/10.61 (( 77.78/10.61 (subbreln1) => 77.78/10.61 (( 77.78/10.61 (eqbreln1) => 77.78/10.61 (( 77.78/10.61 (breln1invprop) => 77.78/10.61 (( 77.78/10.61 (breln1invI) => 77.78/10.61 (( 77.78/10.61 (breln1invE) => 77.78/10.61 (( 77.78/10.61 (breln1compprop) => 77.78/10.61 (( 77.78/10.61 (breln1compI) => 77.78/10.61 (( 77.78/10.61 (breln1compE) => 77.78/10.61 (( 77.78/10.61 (breln1compEex) => 77.78/10.61 (( 77.78/10.61 (breln1unionprop) => 77.78/10.61 (( 77.78/10.61 (breln1unionIL) => 77.78/10.61 (( 77.78/10.61 (breln1unionIR) => 77.78/10.61 (( 77.78/10.61 (breln1unionI) => 77.78/10.61 (( 77.78/10.61 (breln1unionE) => 77.78/10.61 (( 77.78/10.61 (breln1unionEcases) => 77.78/10.61 (( 77.78/10.61 (breln1unionCommutes) => 77.78/10.61 (( 77.78/10.61 (woz2Ex) => 77.78/10.61 (( 77.78/10.61 (woz2W) => 77.78/10.61 (( 77.78/10.61 (woz2A) => 77.78/10.61 (( 77.78/10.61 (woz2B) => 77.78/10.61 (( 77.78/10.61 (image1Ex) => 77.78/10.61 (( 77.78/10.61 (image1Ex1) => 77.78/10.61 (( 77.78/10.61 (image1Equiv) => 77.78/10.61 (( 77.78/10.61 (image1E) => 77.78/10.61 (( 77.78/10.61 (image1I) => 77.78/10.61 (( 77.78/10.61 (injFuncInInjFuncSet) => 77.78/10.61 (( 77.78/10.61 (injFuncSetFuncIn) => 77.78/10.61 (( 77.78/10.61 (injFuncSetFuncInj) => 77.78/10.61 (( 77.78/10.61 (surjFuncSetFuncIn) => 77.78/10.61 (( 77.78/10.61 (surjFuncSetFuncSurj) => 77.78/10.61 (( 77.78/10.61 (leftInvIsSurj) => 77.78/10.61 (( 77.78/10.61 (surjCantorThm) => 77.78/10.61 (( 77.78/10.61 (foundation2) => 77.78/10.61 (( 77.78/10.61 (notinself) => 77.78/10.61 (( 77.78/10.61 (notinself2) => 77.78/10.61 (( 77.78/10.61 (omegaSp) => 77.78/10.61 (( 77.78/10.61 (omegaSclos) => 77.78/10.61 (( 77.78/10.61 (peano0notS) => 77.78/10.61 (( 77.78/10.61 (peanoSinj) => 77.78/10.61 (( 77.78/10.61 (transitivesetOp1) => 77.78/10.61 (( 77.78/10.61 (binintTransitive) => 77.78/10.61 (( 77.78/10.61 (transitivesetOp2) => 77.78/10.61 (( 77.78/10.61 (setunionTransitive) => 77.78/10.61 (( 77.78/10.61 (ordinalMinLem1) => 77.78/10.61 (( 77.78/10.61 (!!) @ ( 77.78/10.61 ^[Y0 : $i]: 77.78/10.61 (( 77.78/10.61 (ordinal @ 77.78/10.61 Y0) => 77.78/10.61 (( 77.78/10.61 (!!) @ ( 77.78/10.61 ^[Y1 : $i]: 77.78/10.61 (( 77.78/10.61 (!!) @ ( 77.78/10.61 ^[Y2 : $i]: 77.78/10.61 (( 77.78/10.61 (in @ 77.78/10.61 Y2 @ 77.78/10.61 Y0) => 77.78/10.61 (( 77.78/10.61 (in @ 77.78/10.61 Y1 @ 77.78/10.61 Y2) => 77.78/10.61 (in @ 77.78/10.61 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 77.78/10.61 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl465])). 77.78/10.61 thf(zip_derived_cl478, plain, 77.78/10.61 (~ (((quantDeMorgan2) => 77.78/10.61 (((quantDeMorgan3) => 77.78/10.61 (((quantDeMorgan4) => 77.78/10.61 (((prop2setI) => 77.78/10.61 (((prop2set2propI) => 77.78/10.61 (((notdexE) => 77.78/10.61 (((notdallE) => 77.78/10.61 (((exuI1) => 77.78/10.61 (((exuI3) => 77.78/10.61 (((exuI2) => 77.78/10.61 (((inCongP) => 77.78/10.61 (((in__Cong) => 77.78/10.61 (((exuE3u) => 77.78/10.61 (((exu__Cong) => 77.78/10.61 (((setadjoin__Cong) => 77.78/10.61 (((powerset__Cong) => 77.78/10.61 (((setunion__Cong) => 77.78/10.61 (((exuEu) => 77.78/10.61 (((descr__Cong) => 77.78/10.61 (((dsetconstr__Cong) => 77.78/10.61 (((subsetI1) => 77.78/10.61 (((eqimpsubset2) => 77.78/10.61 (((eqimpsubset1) => 77.78/10.61 (((subsetI2) => 77.78/10.61 (((emptysetsubset) => 77.78/10.61 (((subsetE) => 77.78/10.61 (((subsetE2) => 77.78/10.61 (((notsubsetI) => 77.78/10.61 (((notequalI1) => 77.78/10.61 (((notequalI2) => 77.78/10.61 (( 77.78/10.61 (subsetRefl) => 77.78/10.61 (( 77.78/10.61 (subsetTrans) => 77.78/10.61 (( 77.78/10.61 (setadjoinSub) => 77.78/10.61 (( 77.78/10.61 (setadjoinSub2) => 77.78/10.61 (( 77.78/10.61 (subset2powerset) => 77.78/10.61 (( 77.78/10.61 (setextsub) => 77.78/10.61 (( 77.78/10.61 (subsetemptysetimpeq) => 77.78/10.61 (( 77.78/10.61 (powersetI1) => 77.78/10.61 (( 77.78/10.61 (powersetE1) => 77.78/10.61 (( 77.78/10.61 (inPowerset) => 77.78/10.61 (( 77.78/10.61 (powersetsubset) => 77.78/10.61 (( 77.78/10.61 (sepInPowerset) => 77.78/10.61 (( 77.78/10.61 (sepSubset) => 77.78/10.61 (( 77.78/10.61 (binunionIL) => 77.78/10.61 (( 77.78/10.61 (upairset2IR) => 77.78/10.61 (( 77.78/10.61 (binunionIR) => 77.78/10.61 (( 77.78/10.61 (binunionEcases) => 77.78/10.61 (( 77.78/10.61 (binunionE) => 77.78/10.61 (( 77.78/10.61 (binunionLsub) => 77.78/10.61 (( 77.78/10.61 (binunionRsub) => 77.78/10.61 (( 77.78/10.61 (binintersectI) => 77.78/10.61 (( 77.78/10.61 (binintersectSubset5) => 77.78/10.61 (( 77.78/10.61 (binintersectEL) => 77.78/10.61 (( 77.78/10.61 (binintersectLsub) => 77.78/10.61 (( 77.78/10.61 (binintersectSubset2) => 77.78/10.61 (( 77.78/10.61 (binintersectSubset3) => 77.78/10.61 (( 77.78/10.61 (binintersectER) => 77.78/10.61 (( 77.78/10.61 (disjointsetsI1) => 77.78/10.61 (( 77.78/10.61 (binintersectRsub) => 77.78/10.61 (( 77.78/10.61 (binintersectSubset4) => 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77.78/10.61 (singletonsubset) => 77.78/10.61 (( 77.78/10.61 (singletoninpowerset) => 77.78/10.61 (( 77.78/10.61 (singletoninpowunion) => 77.78/10.61 (( 77.78/10.61 (upairset2E) => 77.78/10.61 (( 77.78/10.61 (upairsubunion) => 77.78/10.61 (( 77.78/10.61 (upairinpowunion) => 77.78/10.61 (( 77.78/10.61 (ubforcartprodlem1) => 77.78/10.61 (( 77.78/10.61 (ubforcartprodlem2) => 77.78/10.61 (( 77.78/10.61 (ubforcartprodlem3) => 77.78/10.61 (( 77.78/10.61 (cartprodpairin) => 77.78/10.61 (( 77.78/10.61 (cartprodmempair1) => 77.78/10.61 (( 77.78/10.61 (cartprodmempair) => 77.78/10.61 (( 77.78/10.61 (setunionE2) => 77.78/10.61 (( 77.78/10.61 (setunionsingleton1) => 77.78/10.61 (( 77.78/10.61 (setunionsingleton2) => 77.78/10.61 (( 77.78/10.61 (setunionsingleton) => 77.78/10.61 (( 77.78/10.61 (singletonprop) => 77.78/10.61 (( 77.78/10.61 (ex1E1) => 77.78/10.61 (( 77.78/10.61 (ex1I) => 77.78/10.61 (( 77.78/10.61 (ex1I2) => 77.78/10.61 (( 77.78/10.61 (singletonsuniq) => 77.78/10.61 (( 77.78/10.61 (setukpairinjL1) => 77.78/10.61 (( 77.78/10.61 (kfstsingleton) => 77.78/10.61 (( 77.78/10.61 (theprop) => 77.78/10.61 (( 77.78/10.61 (kfstpairEq) => 77.78/10.61 (( 77.78/10.61 (cartprodfstin) => 77.78/10.61 (( 77.78/10.61 (setukpairinjL2) => 77.78/10.61 (( 77.78/10.61 (setukpairinjL) => 77.78/10.61 (( 77.78/10.61 (setukpairinjR11) => 77.78/10.61 (( 77.78/10.61 (setukpairinjR12) => 77.78/10.61 (( 77.78/10.61 (setukpairinjR1) => 77.78/10.61 (( 77.78/10.61 (upairequniteq) => 77.78/10.61 (( 77.78/10.61 (setukpairinjR2) => 77.78/10.61 (( 77.78/10.61 (setukpairinjR) => 77.78/10.61 (( 77.78/10.61 (ksndsingleton) => 77.78/10.61 (( 77.78/10.61 (ksndpairEq) => 77.78/10.61 (( 77.78/10.61 (kpairsurjEq) => 77.78/10.61 (( 77.78/10.61 (cartprodsndin) => 77.78/10.61 (( 77.78/10.61 (cartprodpairmemEL) => 77.78/10.61 (( 77.78/10.61 (cartprodpairmemER) => 77.78/10.61 (( 77.78/10.61 (cartprodmempaircEq) => 77.78/10.61 (( 77.78/10.61 (cartprodfstpairEq) => 77.78/10.61 (( 77.78/10.61 (cartprodsndpairEq) => 77.78/10.61 (( 77.78/10.61 (cartprodpairsurjEq) => 77.78/10.61 (( 77.78/10.61 (dpsetconstrI) => 77.78/10.61 (( 77.78/10.61 (dpsetconstrSub) => 77.78/10.61 (( 77.78/10.61 (setOfPairsIsBReln) => 77.78/10.61 (( 77.78/10.61 (dpsetconstrERa) => 77.78/10.61 (( 77.78/10.61 (dpsetconstrEL1) => 77.78/10.61 (( 77.78/10.61 (dpsetconstrEL2) => 77.78/10.61 (( 77.78/10.61 (dpsetconstrER) => 77.78/10.61 (( 77.78/10.61 (funcImageSingleton) => 77.78/10.61 (( 77.78/10.61 (apProp) => 77.78/10.61 (( 77.78/10.61 (app) => 77.78/10.61 (( 77.78/10.61 (infuncsetfunc) => 77.78/10.61 (( 77.78/10.61 (ap2p) => 77.78/10.61 (( 77.78/10.61 (funcinfuncset) => 77.78/10.61 (( 77.78/10.61 (lamProp) => 77.78/10.61 (( 77.78/10.61 (lamp) => 77.78/10.61 (( 77.78/10.61 (lam2p) => 77.78/10.61 (( 77.78/10.61 (brelnall1) => 77.78/10.61 (( 77.78/10.61 (brelnall2) => 77.78/10.61 (( 77.78/10.61 (ex1E2) => 77.78/10.61 (( 77.78/10.61 (funcGraphProp1) => 77.78/10.61 (( 77.78/10.61 (funcGraphProp3) => 77.78/10.61 (( 77.78/10.61 (funcGraphProp2) => 77.78/10.61 (( 77.78/10.61 (funcextLem) => 77.78/10.61 (( 77.78/10.61 (funcGraphProp4) => 77.78/10.61 (( 77.78/10.61 (subbreln) => 77.78/10.61 (( 77.78/10.61 (eqbreln) => 77.78/10.61 (( 77.78/10.61 (funcext) => 77.78/10.61 (( 77.78/10.61 (funcext2) => 77.78/10.61 (( 77.78/10.61 (ap2apEq1) => 77.78/10.61 (( 77.78/10.61 (ap2apEq2) => 77.78/10.61 (( 77.78/10.61 (beta1) => 77.78/10.61 (( 77.78/10.61 (eta1) => 77.78/10.61 (( 77.78/10.61 (lam2lamEq) => 77.78/10.61 (( 77.78/10.61 (beta2) => 77.78/10.61 (( 77.78/10.61 (eta2) => 77.78/10.61 (( 77.78/10.61 (iffalseProp1) => 77.78/10.61 (( 77.78/10.61 (iffalseProp2) => 77.78/10.61 (( 77.78/10.61 (iftrueProp1) => 77.78/10.61 (( 77.78/10.61 (iftrueProp2) => 77.78/10.61 (( 77.78/10.61 (ifSingleton) => 77.78/10.61 (( 77.78/10.61 (ifp) => 77.78/10.61 (( 77.78/10.61 (theeq) => 77.78/10.61 (( 77.78/10.61 (iftrue) => 77.78/10.61 (( 77.78/10.61 (iffalse) => 77.78/10.61 (( 77.78/10.61 (iftrueorfalse) => 77.78/10.61 (( 77.78/10.61 (binintersectT_lem) => 77.78/10.61 (( 77.78/10.61 (binunionT_lem) => 77.78/10.61 (( 77.78/10.61 (powersetT_lem) => 77.78/10.61 (( 77.78/10.61 (setminusT_lem) => 77.78/10.61 (( 77.78/10.61 (complementT_lem) => 77.78/10.61 (( 77.78/10.61 (setextT) => 77.78/10.61 (( 77.78/10.61 (subsetTI) => 77.78/10.61 (( 77.78/10.61 (powersetTI1) => 77.78/10.61 (( 77.78/10.61 (powersetTE1) => 77.78/10.61 (( 77.78/10.61 (complementTI1) => 77.78/10.61 (( 77.78/10.61 (complementTE1) => 77.78/10.61 (( 77.78/10.61 (binintersectTELcontra) => 77.78/10.61 (( 77.78/10.61 (binintersectTERcontra) => 77.78/10.61 (( 77.78/10.61 (contrasubsetT) => 77.78/10.61 (( 77.78/10.61 (contrasubsetT1) => 77.78/10.61 (( 77.78/10.61 (contrasubsetT2) => 77.78/10.61 (( 77.78/10.61 (contrasubsetT3) => 77.78/10.61 (( 77.78/10.61 (doubleComplementI1) => 77.78/10.61 (( 77.78/10.61 (doubleComplementE1) => 77.78/10.61 (( 77.78/10.61 (doubleComplementSub1) => 77.78/10.61 (( 77.78/10.61 (doubleComplementSub2) => 77.78/10.61 (( 77.78/10.61 (doubleComplementEq) => 77.78/10.61 (( 77.78/10.61 (complementTnotintersectT) => 77.78/10.61 (( 77.78/10.61 (complementImpComplementIntersect) => 77.78/10.61 (( 77.78/10.61 (complementSubsetComplementIntersect) => 77.78/10.61 (( 77.78/10.61 (complementInPowersetComplementIntersect) => 77.78/10.61 (( 77.78/10.61 (contraSubsetComplement) => 77.78/10.61 (( 77.78/10.61 (complementTcontraSubset) => 77.78/10.61 (( 77.78/10.61 (binunionTILcontra) => 77.78/10.61 (( 77.78/10.61 (binunionTIRcontra) => 77.78/10.61 (( 77.78/10.61 (inIntersectImpInUnion) => 77.78/10.61 (( 77.78/10.61 (inIntersectImpInUnion2) => 77.78/10.61 (( 77.78/10.61 (inIntersectImpInIntersectUnions) => 77.78/10.61 (( 77.78/10.61 (intersectInPowersetIntersectUnions) => 77.78/10.61 (( 77.78/10.61 (inComplementUnionImpNotIn1) => 77.78/10.61 (( 77.78/10.61 (inComplementUnionImpInComplement1) => 77.78/10.61 (( 77.78/10.61 (binunionTE) => 77.78/10.61 (( 77.78/10.61 (binunionTEcontra) => 77.78/10.61 (( 77.78/10.61 (demorgan2a1) => 77.78/10.61 (( 77.78/10.61 (complementUnionInPowersetComplement) => 77.78/10.61 (( 77.78/10.61 (demorgan2a2) => 77.78/10.61 (( 77.78/10.61 (demorgan1a) => 77.78/10.61 (( 77.78/10.61 (demorgan1b) => 77.78/10.61 (( 77.78/10.61 (demorgan1) => 77.78/10.61 (( 77.78/10.61 (demorgan2a) => 77.78/10.61 (( 77.78/10.61 (demorgan2b2) => 77.78/10.61 (( 77.78/10.61 (demorgan2b) => 77.78/10.61 (( 77.78/10.61 (demorgan2) => 77.78/10.61 (( 77.78/10.61 (woz13rule0) => 77.78/10.61 (( 77.78/10.61 (woz13rule1) => 77.78/10.61 (( 77.78/10.61 (woz13rule2) => 77.78/10.61 (( 77.78/10.61 (woz13rule3) => 77.78/10.61 (( 77.78/10.61 (woz13rule4) => 77.78/10.61 (( 77.78/10.61 (woz1_1) => 77.78/10.61 (( 77.78/10.61 (woz1_2) => 77.78/10.61 (( 77.78/10.61 (woz1_3) => 77.78/10.61 (( 77.78/10.61 (woz1_4) => 77.78/10.61 (( 77.78/10.61 (woz1_5) => 77.78/10.61 (( 77.78/10.61 (breln1all2) => 77.78/10.61 (( 77.78/10.61 (breln1SetBreln1) => 77.78/10.61 (( 77.78/10.61 (choice2fnsingleton) => 77.78/10.61 (( 77.78/10.61 (setOfPairsIsBReln1) => 77.78/10.61 (( 77.78/10.61 (breln1all1) => 77.78/10.61 (( 77.78/10.61 (subbreln1) => 77.78/10.61 (( 77.78/10.61 (eqbreln1) => 77.78/10.61 (( 77.78/10.61 (breln1invprop) => 77.78/10.61 (( 77.78/10.61 (breln1invI) => 77.78/10.61 (( 77.78/10.61 (breln1invE) => 77.78/10.61 (( 77.78/10.61 (breln1compprop) => 77.78/10.61 (( 77.78/10.61 (breln1compI) => 77.78/10.61 (( 77.78/10.61 (breln1compE) => 77.78/10.61 (( 77.78/10.61 (breln1compEex) => 77.78/10.61 (( 77.78/10.61 (breln1unionprop) => 77.78/10.61 (( 77.78/10.61 (breln1unionIL) => 77.78/10.61 (( 77.78/10.61 (breln1unionIR) => 77.78/10.61 (( 77.78/10.61 (breln1unionI) => 77.78/10.61 (( 77.78/10.61 (breln1unionE) => 77.78/10.61 (( 77.78/10.61 (breln1unionEcases) => 77.78/10.61 (( 77.78/10.61 (breln1unionCommutes) => 77.78/10.61 (( 77.78/10.61 (woz2Ex) => 77.78/10.61 (( 77.78/10.61 (woz2W) => 77.78/10.61 (( 77.78/10.61 (woz2A) => 77.78/10.61 (( 77.78/10.61 (woz2B) => 77.78/10.61 (( 77.78/10.61 (image1Ex) => 77.78/10.61 (( 77.78/10.61 (image1Ex1) => 77.78/10.61 (( 77.78/10.61 (image1Equiv) => 77.78/10.61 (( 77.78/10.61 (image1E) => 77.78/10.61 (( 77.78/10.61 (image1I) => 77.78/10.61 (( 77.78/10.61 (injFuncInInjFuncSet) => 77.78/10.61 (( 77.78/10.61 (injFuncSetFuncIn) => 77.78/10.61 (( 77.78/10.61 (injFuncSetFuncInj) => 77.78/10.61 (( 77.78/10.61 (surjFuncSetFuncIn) => 77.78/10.61 (( 77.78/10.61 (surjFuncSetFuncSurj) => 77.78/10.61 (( 77.78/10.61 (leftInvIsSurj) => 77.78/10.61 (( 77.78/10.61 (surjCantorThm) => 77.78/10.61 (( 77.78/10.61 (foundation2) => 77.78/10.61 (( 77.78/10.61 (notinself) => 77.78/10.61 (( 77.78/10.61 (notinself2) => 77.78/10.61 (( 77.78/10.61 (omegaSp) => 77.78/10.61 (( 77.78/10.61 (omegaSclos) => 77.78/10.61 (( 77.78/10.61 (peano0notS) => 77.78/10.61 (( 77.78/10.61 (peanoSinj) => 77.78/10.61 (( 77.78/10.61 (transitivesetOp1) => 77.78/10.61 (( 77.78/10.61 (binintTransitive) => 77.78/10.61 (( 77.78/10.61 (transitivesetOp2) => 77.78/10.61 (( 77.78/10.61 (setunionTransitive) => 77.78/10.61 (( 77.78/10.61 (ordinalMinLem1) => 77.78/10.61 (( 77.78/10.61 (!!) @ ( 77.78/10.61 ^[Y0 : $i]: 77.78/10.61 (( 77.78/10.61 (ordinal @ 77.78/10.61 Y0) => 77.78/10.61 (( 77.78/10.61 (!!) @ ( 77.78/10.61 ^[Y1 : $i]: 77.78/10.61 (( 77.78/10.61 (!!) @ ( 77.78/10.61 ^[Y2 : $i]: 77.78/10.61 (( 77.78/10.61 (in @ 77.78/10.61 Y2 @ 77.78/10.61 Y0) => 77.78/10.61 (( 77.78/10.61 (in @ 77.78/10.61 Y1 @ 77.78/10.61 Y2) => 77.78/10.61 (in @ 77.78/10.61 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 77.78/10.61 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl471])). 77.78/10.61 thf(zip_derived_cl484, plain, 77.78/10.61 (~ (((quantDeMorgan3) => 77.78/10.61 (((quantDeMorgan4) => 77.78/10.61 (((prop2setI) => 77.78/10.61 (((prop2set2propI) => 77.78/10.61 (((notdexE) => 77.78/10.61 (((notdallE) => 77.78/10.61 (((exuI1) => 77.78/10.61 (((exuI3) => 77.78/10.61 (((exuI2) => 77.78/10.61 (((inCongP) => 77.78/10.61 (((in__Cong) => 77.78/10.61 (((exuE3u) => 77.78/10.61 (((exu__Cong) => 77.78/10.61 (((setadjoin__Cong) => 77.78/10.61 (((powerset__Cong) => 77.78/10.61 (((setunion__Cong) => 77.78/10.61 (((exuEu) => 77.78/10.61 (((descr__Cong) => 77.78/10.61 (((dsetconstr__Cong) => 77.78/10.61 (((subsetI1) => 77.78/10.61 (((eqimpsubset2) => 77.78/10.61 (((eqimpsubset1) => 77.78/10.61 (((subsetI2) => 77.78/10.61 (((emptysetsubset) => 77.78/10.61 (((subsetE) => 77.78/10.61 (((subsetE2) => 77.78/10.61 (((notsubsetI) => 77.78/10.61 (((notequalI1) => 77.78/10.61 (((notequalI2) => 77.78/10.61 (((subsetRefl) => 77.78/10.61 (( 77.78/10.61 (subsetTrans) => 77.78/10.61 (( 77.78/10.61 (setadjoinSub) => 77.78/10.61 (( 77.78/10.61 (setadjoinSub2) => 77.78/10.61 (( 77.78/10.61 (subset2powerset) => 77.78/10.61 (( 77.78/10.61 (setextsub) => 77.78/10.61 (( 77.78/10.61 (subsetemptysetimpeq) => 77.78/10.61 (( 77.78/10.61 (powersetI1) => 77.78/10.61 (( 77.78/10.61 (powersetE1) => 77.78/10.61 (( 77.78/10.61 (inPowerset) => 77.78/10.61 (( 77.78/10.61 (powersetsubset) => 77.78/10.61 (( 77.78/10.61 (sepInPowerset) => 77.78/10.61 (( 77.78/10.61 (sepSubset) => 77.78/10.61 (( 77.78/10.61 (binunionIL) => 77.78/10.61 (( 77.78/10.61 (upairset2IR) => 77.78/10.61 (( 77.78/10.61 (binunionIR) => 77.78/10.61 (( 77.78/10.61 (binunionEcases) => 77.78/10.61 (( 77.78/10.61 (binunionE) => 77.78/10.61 (( 77.78/10.61 (binunionLsub) => 77.78/10.61 (( 77.78/10.61 (binunionRsub) => 77.78/10.61 (( 77.78/10.61 (binintersectI) => 77.78/10.61 (( 77.78/10.61 (binintersectSubset5) => 77.78/10.61 (( 77.78/10.61 (binintersectEL) => 77.78/10.61 (( 77.78/10.61 (binintersectLsub) => 77.78/10.61 (( 77.78/10.61 (binintersectSubset2) => 77.78/10.61 (( 77.78/10.61 (binintersectSubset3) => 77.78/10.61 (( 77.78/10.61 (binintersectER) => 77.78/10.61 (( 77.78/10.61 (disjointsetsI1) => 77.78/10.61 (( 77.78/10.61 (binintersectRsub) => 77.78/10.61 (( 77.78/10.61 (binintersectSubset4) => 77.78/10.61 (( 77.78/10.61 (binintersectSubset1) => 77.78/10.61 (( 77.78/10.61 (bs114d) => 77.78/10.61 (( 77.78/10.61 (setminusI) => 77.78/10.61 (( 77.78/10.61 (setminusEL) => 77.78/10.61 (( 77.78/10.61 (setminusER) => 77.78/10.61 (( 77.78/10.61 (setminusSubset2) => 77.78/10.61 (( 77.78/10.61 (setminusERneg) => 77.78/10.61 (( 77.78/10.61 (setminusELneg) => 77.78/10.61 (( 77.78/10.61 (setminusILneg) => 77.78/10.61 (( 77.78/10.61 (setminusIRneg) => 77.78/10.61 (( 77.78/10.61 (setminusLsub) => 77.78/10.61 (( 77.78/10.61 (setminusSubset1) => 77.78/10.61 (( 77.78/10.61 (symdiffE) => 77.78/10.61 (( 77.78/10.61 (symdiffI1) => 77.78/10.61 (( 77.78/10.61 (symdiffI2) => 77.78/10.61 (( 77.78/10.61 (symdiffIneg1) => 77.78/10.61 (( 77.78/10.61 (symdiffIneg2) => 77.78/10.61 (( 77.78/10.61 (secondinupair) => 77.78/10.61 (( 77.78/10.61 (setukpairIL) => 77.78/10.61 (( 77.78/10.61 (setukpairIR) => 77.78/10.61 (( 77.78/10.61 (kpairiskpair) => 77.78/10.61 (( 77.78/10.61 (kpairp) => 77.78/10.61 (( 77.78/10.61 (singletonsubset) => 77.78/10.61 (( 77.78/10.61 (singletoninpowerset) => 77.78/10.61 (( 77.78/10.61 (singletoninpowunion) => 77.78/10.61 (( 77.78/10.61 (upairset2E) => 77.78/10.61 (( 77.78/10.61 (upairsubunion) => 77.78/10.61 (( 77.78/10.61 (upairinpowunion) => 77.78/10.61 (( 77.78/10.61 (ubforcartprodlem1) => 77.78/10.61 (( 77.78/10.61 (ubforcartprodlem2) => 77.78/10.61 (( 77.78/10.61 (ubforcartprodlem3) => 77.78/10.61 (( 77.78/10.61 (cartprodpairin) => 77.78/10.61 (( 77.78/10.61 (cartprodmempair1) => 77.78/10.61 (( 77.78/10.61 (cartprodmempair) => 77.78/10.61 (( 77.78/10.61 (setunionE2) => 77.78/10.61 (( 77.78/10.61 (setunionsingleton1) => 77.78/10.61 (( 77.78/10.61 (setunionsingleton2) => 77.78/10.61 (( 77.78/10.61 (setunionsingleton) => 77.78/10.61 (( 77.78/10.61 (singletonprop) => 77.78/10.61 (( 77.78/10.61 (ex1E1) => 77.78/10.61 (( 77.78/10.61 (ex1I) => 77.78/10.61 (( 77.78/10.61 (ex1I2) => 77.78/10.61 (( 77.78/10.61 (singletonsuniq) => 77.78/10.61 (( 77.78/10.61 (setukpairinjL1) => 77.78/10.61 (( 77.78/10.61 (kfstsingleton) => 77.78/10.61 (( 77.78/10.61 (theprop) => 77.78/10.61 (( 77.78/10.61 (kfstpairEq) => 77.78/10.61 (( 77.78/10.61 (cartprodfstin) => 77.78/10.61 (( 77.78/10.61 (setukpairinjL2) => 77.78/10.61 (( 77.78/10.61 (setukpairinjL) => 77.78/10.61 (( 77.78/10.61 (setukpairinjR11) => 77.78/10.61 (( 77.78/10.61 (setukpairinjR12) => 77.78/10.61 (( 77.78/10.61 (setukpairinjR1) => 77.78/10.61 (( 77.78/10.61 (upairequniteq) => 77.78/10.61 (( 77.78/10.61 (setukpairinjR2) => 77.78/10.61 (( 77.78/10.61 (setukpairinjR) => 77.78/10.61 (( 77.78/10.61 (ksndsingleton) => 77.78/10.61 (( 77.78/10.61 (ksndpairEq) => 77.78/10.61 (( 77.78/10.61 (kpairsurjEq) => 77.78/10.61 (( 77.78/10.61 (cartprodsndin) => 77.78/10.61 (( 77.78/10.61 (cartprodpairmemEL) => 77.78/10.61 (( 77.78/10.61 (cartprodpairmemER) => 77.78/10.61 (( 77.78/10.61 (cartprodmempaircEq) => 77.78/10.61 (( 77.78/10.61 (cartprodfstpairEq) => 77.78/10.61 (( 77.78/10.61 (cartprodsndpairEq) => 77.78/10.61 (( 77.78/10.61 (cartprodpairsurjEq) => 77.78/10.61 (( 77.78/10.61 (dpsetconstrI) => 77.78/10.61 (( 77.78/10.61 (dpsetconstrSub) => 77.78/10.61 (( 77.78/10.61 (setOfPairsIsBReln) => 77.78/10.61 (( 77.78/10.61 (dpsetconstrERa) => 77.78/10.61 (( 77.78/10.61 (dpsetconstrEL1) => 77.78/10.61 (( 77.78/10.61 (dpsetconstrEL2) => 77.78/10.61 (( 77.78/10.61 (dpsetconstrER) => 77.78/10.61 (( 77.78/10.61 (funcImageSingleton) => 77.78/10.61 (( 77.78/10.61 (apProp) => 77.78/10.61 (( 77.78/10.61 (app) => 77.78/10.61 (( 77.78/10.61 (infuncsetfunc) => 77.78/10.61 (( 77.78/10.61 (ap2p) => 77.78/10.61 (( 77.78/10.61 (funcinfuncset) => 77.78/10.61 (( 77.78/10.61 (lamProp) => 77.78/10.61 (( 77.78/10.61 (lamp) => 77.78/10.61 (( 77.78/10.61 (lam2p) => 77.78/10.61 (( 77.78/10.61 (brelnall1) => 77.78/10.61 (( 77.78/10.61 (brelnall2) => 77.78/10.61 (( 77.78/10.61 (ex1E2) => 77.78/10.61 (( 77.78/10.61 (funcGraphProp1) => 77.78/10.61 (( 77.78/10.61 (funcGraphProp3) => 77.78/10.61 (( 77.78/10.61 (funcGraphProp2) => 77.78/10.61 (( 77.78/10.61 (funcextLem) => 77.78/10.61 (( 77.78/10.61 (funcGraphProp4) => 77.78/10.61 (( 77.78/10.61 (subbreln) => 77.78/10.61 (( 77.78/10.61 (eqbreln) => 77.78/10.61 (( 77.78/10.61 (funcext) => 77.78/10.61 (( 77.78/10.61 (funcext2) => 77.78/10.61 (( 77.78/10.61 (ap2apEq1) => 77.78/10.61 (( 77.78/10.61 (ap2apEq2) => 77.78/10.61 (( 77.78/10.61 (beta1) => 77.78/10.61 (( 77.78/10.61 (eta1) => 77.78/10.61 (( 77.78/10.61 (lam2lamEq) => 77.78/10.61 (( 77.78/10.61 (beta2) => 77.78/10.61 (( 77.78/10.61 (eta2) => 77.78/10.61 (( 77.78/10.61 (iffalseProp1) => 77.78/10.61 (( 77.78/10.61 (iffalseProp2) => 77.78/10.61 (( 77.78/10.61 (iftrueProp1) => 77.78/10.61 (( 77.78/10.61 (iftrueProp2) => 77.78/10.61 (( 77.78/10.61 (ifSingleton) => 77.78/10.61 (( 77.78/10.61 (ifp) => 77.78/10.61 (( 77.78/10.61 (theeq) => 77.78/10.61 (( 77.78/10.61 (iftrue) => 77.78/10.61 (( 77.78/10.61 (iffalse) => 77.78/10.61 (( 77.78/10.61 (iftrueorfalse) => 77.78/10.61 (( 77.78/10.61 (binintersectT_lem) => 77.78/10.61 (( 77.78/10.61 (binunionT_lem) => 77.78/10.61 (( 77.78/10.61 (powersetT_lem) => 77.78/10.61 (( 77.78/10.61 (setminusT_lem) => 77.78/10.61 (( 77.78/10.61 (complementT_lem) => 77.78/10.61 (( 77.78/10.61 (setextT) => 77.78/10.61 (( 77.78/10.61 (subsetTI) => 77.78/10.61 (( 77.78/10.61 (powersetTI1) => 77.78/10.61 (( 77.78/10.61 (powersetTE1) => 77.78/10.61 (( 77.78/10.61 (complementTI1) => 77.78/10.61 (( 77.78/10.61 (complementTE1) => 77.78/10.61 (( 77.78/10.61 (binintersectTELcontra) => 77.78/10.61 (( 77.78/10.61 (binintersectTERcontra) => 77.78/10.61 (( 77.78/10.61 (contrasubsetT) => 77.78/10.61 (( 77.78/10.61 (contrasubsetT1) => 77.78/10.61 (( 77.78/10.61 (contrasubsetT2) => 77.78/10.61 (( 77.78/10.61 (contrasubsetT3) => 77.78/10.61 (( 77.78/10.61 (doubleComplementI1) => 77.78/10.61 (( 77.78/10.61 (doubleComplementE1) => 77.78/10.61 (( 77.78/10.61 (doubleComplementSub1) => 77.78/10.61 (( 77.78/10.61 (doubleComplementSub2) => 77.78/10.61 (( 77.78/10.61 (doubleComplementEq) => 77.78/10.61 (( 77.78/10.61 (complementTnotintersectT) => 77.78/10.61 (( 77.78/10.61 (complementImpComplementIntersect) => 77.78/10.61 (( 77.78/10.61 (complementSubsetComplementIntersect) => 77.78/10.61 (( 77.78/10.61 (complementInPowersetComplementIntersect) => 77.78/10.61 (( 77.78/10.61 (contraSubsetComplement) => 77.78/10.61 (( 77.78/10.61 (complementTcontraSubset) => 77.78/10.61 (( 77.78/10.61 (binunionTILcontra) => 77.78/10.61 (( 77.78/10.61 (binunionTIRcontra) => 77.78/10.61 (( 77.78/10.61 (inIntersectImpInUnion) => 77.78/10.61 (( 77.78/10.61 (inIntersectImpInUnion2) => 77.78/10.61 (( 77.78/10.61 (inIntersectImpInIntersectUnions) => 77.78/10.61 (( 77.78/10.61 (intersectInPowersetIntersectUnions) => 77.78/10.61 (( 77.78/10.61 (inComplementUnionImpNotIn1) => 77.78/10.61 (( 77.78/10.61 (inComplementUnionImpInComplement1) => 77.78/10.61 (( 77.78/10.61 (binunionTE) => 77.78/10.61 (( 77.78/10.61 (binunionTEcontra) => 77.78/10.61 (( 77.78/10.61 (demorgan2a1) => 77.78/10.61 (( 77.78/10.61 (complementUnionInPowersetComplement) => 77.78/10.61 (( 77.78/10.61 (demorgan2a2) => 77.78/10.61 (( 77.78/10.61 (demorgan1a) => 77.78/10.61 (( 77.78/10.61 (demorgan1b) => 77.78/10.61 (( 77.78/10.61 (demorgan1) => 77.78/10.61 (( 77.78/10.61 (demorgan2a) => 77.78/10.61 (( 77.78/10.61 (demorgan2b2) => 77.78/10.61 (( 77.78/10.61 (demorgan2b) => 77.78/10.61 (( 77.78/10.61 (demorgan2) => 77.78/10.61 (( 77.78/10.61 (woz13rule0) => 77.78/10.61 (( 77.78/10.61 (woz13rule1) => 77.78/10.61 (( 77.78/10.61 (woz13rule2) => 77.78/10.61 (( 77.78/10.61 (woz13rule3) => 77.78/10.61 (( 77.78/10.61 (woz13rule4) => 77.78/10.61 (( 77.78/10.61 (woz1_1) => 77.78/10.61 (( 77.78/10.61 (woz1_2) => 77.78/10.61 (( 77.78/10.61 (woz1_3) => 77.78/10.61 (( 77.78/10.61 (woz1_4) => 77.78/10.61 (( 77.78/10.61 (woz1_5) => 77.78/10.61 (( 77.78/10.61 (breln1all2) => 77.78/10.61 (( 77.78/10.61 (breln1SetBreln1) => 77.78/10.61 (( 77.78/10.61 (choice2fnsingleton) => 77.78/10.61 (( 77.78/10.61 (setOfPairsIsBReln1) => 77.78/10.61 (( 77.78/10.61 (breln1all1) => 77.78/10.61 (( 77.78/10.61 (subbreln1) => 77.78/10.61 (( 77.78/10.61 (eqbreln1) => 77.78/10.61 (( 77.78/10.61 (breln1invprop) => 77.78/10.61 (( 77.78/10.61 (breln1invI) => 77.78/10.61 (( 77.78/10.61 (breln1invE) => 77.78/10.61 (( 77.78/10.61 (breln1compprop) => 77.78/10.61 (( 77.78/10.61 (breln1compI) => 77.78/10.61 (( 77.78/10.61 (breln1compE) => 77.78/10.61 (( 77.78/10.61 (breln1compEex) => 77.78/10.61 (( 77.78/10.61 (breln1unionprop) => 77.78/10.61 (( 77.78/10.61 (breln1unionIL) => 77.78/10.61 (( 77.78/10.61 (breln1unionIR) => 77.78/10.61 (( 77.78/10.61 (breln1unionI) => 77.78/10.61 (( 77.78/10.61 (breln1unionE) => 77.78/10.61 (( 77.78/10.61 (breln1unionEcases) => 77.78/10.61 (( 77.78/10.61 (breln1unionCommutes) => 77.78/10.61 (( 77.78/10.61 (woz2Ex) => 77.78/10.61 (( 77.78/10.61 (woz2W) => 77.78/10.61 (( 77.78/10.61 (woz2A) => 77.78/10.61 (( 77.78/10.61 (woz2B) => 77.78/10.61 (( 77.78/10.61 (image1Ex) => 77.78/10.61 (( 77.78/10.61 (image1Ex1) => 77.78/10.61 (( 77.78/10.61 (image1Equiv) => 77.78/10.61 (( 77.78/10.61 (image1E) => 77.78/10.61 (( 77.78/10.61 (image1I) => 77.78/10.61 (( 77.78/10.61 (injFuncInInjFuncSet) => 77.78/10.61 (( 77.78/10.61 (injFuncSetFuncIn) => 77.78/10.61 (( 77.78/10.61 (injFuncSetFuncInj) => 77.78/10.61 (( 77.78/10.61 (surjFuncSetFuncIn) => 77.78/10.61 (( 77.78/10.61 (surjFuncSetFuncSurj) => 77.78/10.61 (( 77.78/10.61 (leftInvIsSurj) => 77.78/10.61 (( 77.78/10.61 (surjCantorThm) => 77.78/10.61 (( 77.78/10.61 (foundation2) => 77.78/10.61 (( 77.78/10.61 (notinself) => 77.78/10.61 (( 77.78/10.61 (notinself2) => 77.78/10.61 (( 77.78/10.61 (omegaSp) => 77.78/10.61 (( 77.78/10.61 (omegaSclos) => 77.78/10.61 (( 77.78/10.61 (peano0notS) => 77.78/10.61 (( 77.78/10.61 (peanoSinj) => 77.78/10.61 (( 77.78/10.61 (transitivesetOp1) => 77.78/10.61 (( 77.78/10.61 (binintTransitive) => 77.78/10.61 (( 77.78/10.61 (transitivesetOp2) => 77.78/10.61 (( 77.78/10.61 (setunionTransitive) => 77.78/10.61 (( 77.78/10.61 (ordinalMinLem1) => 77.78/10.61 (( 77.78/10.61 (!!) @ ( 77.78/10.61 ^[Y0 : $i]: 77.78/10.61 (( 77.78/10.61 (ordinal @ 77.78/10.61 Y0) => 77.78/10.61 (( 77.78/10.61 (!!) @ ( 77.78/10.61 ^[Y1 : $i]: 77.78/10.61 (( 77.78/10.61 (!!) @ ( 77.78/10.61 ^[Y2 : $i]: 77.78/10.61 (( 77.78/10.61 (in @ 77.78/10.61 Y2 @ 77.78/10.61 Y0) => 77.78/10.61 (( 77.78/10.61 (in @ 77.78/10.61 Y1 @ 77.78/10.61 Y2) => 77.78/10.61 (in @ 77.78/10.61 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 77.78/10.61 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl478])). 77.78/10.61 thf(zip_derived_cl491, plain, 77.78/10.61 (~ (((quantDeMorgan4) => 77.78/10.61 (((prop2setI) => 77.78/10.61 (((prop2set2propI) => 77.78/10.61 (((notdexE) => 77.78/10.61 (((notdallE) => 77.78/10.61 (((exuI1) => 77.78/10.61 (((exuI3) => 77.78/10.61 (((exuI2) => 77.78/10.61 (((inCongP) => 77.78/10.61 (((in__Cong) => 77.78/10.61 (((exuE3u) => 77.78/10.61 (((exu__Cong) => 77.78/10.61 (((setadjoin__Cong) => 77.78/10.61 (((powerset__Cong) => 77.78/10.61 (((setunion__Cong) => 77.78/10.61 (((exuEu) => 77.78/10.61 (((descr__Cong) => 77.78/10.61 (((dsetconstr__Cong) => 77.78/10.61 (((subsetI1) => 77.78/10.61 (((eqimpsubset2) => 77.78/10.61 (((eqimpsubset1) => 77.78/10.61 (((subsetI2) => 77.78/10.61 (((emptysetsubset) => 77.78/10.61 (((subsetE) => 77.78/10.61 (((subsetE2) => 77.78/10.61 (((notsubsetI) => 77.78/10.61 (((notequalI1) => 77.78/10.61 (((notequalI2) => 77.78/10.61 (((subsetRefl) => 77.78/10.61 (((subsetTrans) => 77.78/10.61 (( 77.78/10.61 (setadjoinSub) => 77.78/10.61 (( 77.78/10.61 (setadjoinSub2) => 77.78/10.61 (( 77.78/10.61 (subset2powerset) => 77.78/10.61 (( 77.78/10.61 (setextsub) => 77.78/10.61 (( 77.78/10.61 (subsetemptysetimpeq) => 77.78/10.61 (( 77.78/10.61 (powersetI1) => 77.78/10.61 (( 77.78/10.61 (powersetE1) => 77.78/10.61 (( 77.78/10.61 (inPowerset) => 77.78/10.61 (( 77.78/10.61 (powersetsubset) => 77.78/10.61 (( 77.78/10.61 (sepInPowerset) => 77.78/10.61 (( 77.78/10.61 (sepSubset) => 77.78/10.61 (( 77.78/10.61 (binunionIL) => 77.78/10.61 (( 77.78/10.61 (upairset2IR) => 77.78/10.61 (( 77.78/10.61 (binunionIR) => 77.78/10.61 (( 77.78/10.61 (binunionEcases) => 77.78/10.61 (( 77.78/10.61 (binunionE) => 77.78/10.61 (( 77.78/10.61 (binunionLsub) => 77.78/10.61 (( 77.78/10.61 (binunionRsub) => 77.78/10.61 (( 77.78/10.61 (binintersectI) => 77.78/10.61 (( 77.78/10.61 (binintersectSubset5) => 77.78/10.61 (( 77.78/10.61 (binintersectEL) => 77.78/10.61 (( 77.78/10.61 (binintersectLsub) => 77.78/10.61 (( 77.78/10.61 (binintersectSubset2) => 77.78/10.61 (( 77.78/10.61 (binintersectSubset3) => 77.78/10.61 (( 77.78/10.61 (binintersectER) => 77.78/10.61 (( 77.78/10.61 (disjointsetsI1) => 77.78/10.61 (( 77.78/10.61 (binintersectRsub) => 77.78/10.61 (( 77.78/10.61 (binintersectSubset4) => 77.78/10.61 (( 77.78/10.61 (binintersectSubset1) => 77.78/10.61 (( 77.78/10.61 (bs114d) => 77.78/10.61 (( 77.78/10.61 (setminusI) => 77.78/10.61 (( 77.78/10.61 (setminusEL) => 77.78/10.61 (( 77.78/10.61 (setminusER) => 77.78/10.61 (( 77.78/10.61 (setminusSubset2) => 77.78/10.61 (( 77.78/10.61 (setminusERneg) => 77.78/10.61 (( 77.78/10.61 (setminusELneg) => 77.78/10.61 (( 77.78/10.61 (setminusILneg) => 77.78/10.61 (( 77.78/10.61 (setminusIRneg) => 77.78/10.61 (( 77.78/10.61 (setminusLsub) => 77.78/10.61 (( 77.78/10.61 (setminusSubset1) => 77.78/10.61 (( 77.78/10.61 (symdiffE) => 77.78/10.61 (( 77.78/10.61 (symdiffI1) => 77.78/10.61 (( 77.78/10.61 (symdiffI2) => 77.78/10.61 (( 77.78/10.61 (symdiffIneg1) => 77.78/10.61 (( 77.78/10.61 (symdiffIneg2) => 77.78/10.61 (( 77.78/10.61 (secondinupair) => 77.78/10.61 (( 77.78/10.61 (setukpairIL) => 77.78/10.61 (( 77.78/10.61 (setukpairIR) => 77.78/10.61 (( 77.78/10.61 (kpairiskpair) => 77.78/10.61 (( 77.78/10.61 (kpairp) => 77.78/10.61 (( 77.78/10.61 (singletonsubset) => 77.78/10.61 (( 77.78/10.61 (singletoninpowerset) => 77.78/10.61 (( 77.78/10.61 (singletoninpowunion) => 77.78/10.61 (( 77.78/10.61 (upairset2E) => 77.78/10.61 (( 77.78/10.61 (upairsubunion) => 77.78/10.61 (( 77.78/10.61 (upairinpowunion) => 77.78/10.61 (( 77.78/10.61 (ubforcartprodlem1) => 77.78/10.61 (( 77.78/10.61 (ubforcartprodlem2) => 77.78/10.61 (( 77.78/10.61 (ubforcartprodlem3) => 77.78/10.61 (( 77.78/10.61 (cartprodpairin) => 77.78/10.61 (( 77.78/10.61 (cartprodmempair1) => 77.78/10.61 (( 77.78/10.61 (cartprodmempair) => 77.78/10.61 (( 77.78/10.61 (setunionE2) => 77.78/10.61 (( 77.78/10.61 (setunionsingleton1) => 77.78/10.61 (( 77.78/10.61 (setunionsingleton2) => 77.78/10.61 (( 77.78/10.61 (setunionsingleton) => 77.78/10.61 (( 77.78/10.61 (singletonprop) => 77.78/10.61 (( 77.78/10.61 (ex1E1) => 77.78/10.61 (( 77.78/10.61 (ex1I) => 77.78/10.61 (( 77.78/10.61 (ex1I2) => 77.78/10.61 (( 77.78/10.61 (singletonsuniq) => 77.78/10.61 (( 77.78/10.61 (setukpairinjL1) => 77.78/10.61 (( 77.78/10.61 (kfstsingleton) => 77.78/10.61 (( 77.78/10.61 (theprop) => 77.78/10.61 (( 77.78/10.61 (kfstpairEq) => 77.78/10.61 (( 77.78/10.61 (cartprodfstin) => 77.78/10.61 (( 77.78/10.61 (setukpairinjL2) => 77.78/10.61 (( 77.78/10.61 (setukpairinjL) => 77.78/10.61 (( 77.78/10.61 (setukpairinjR11) => 77.78/10.61 (( 77.78/10.61 (setukpairinjR12) => 77.78/10.61 (( 77.78/10.61 (setukpairinjR1) => 77.78/10.61 (( 77.78/10.61 (upairequniteq) => 77.78/10.61 (( 77.78/10.61 (setukpairinjR2) => 77.78/10.61 (( 77.78/10.61 (setukpairinjR) => 77.78/10.61 (( 77.78/10.61 (ksndsingleton) => 77.78/10.61 (( 77.78/10.61 (ksndpairEq) => 77.78/10.61 (( 77.78/10.61 (kpairsurjEq) => 77.78/10.61 (( 77.78/10.61 (cartprodsndin) => 77.78/10.61 (( 77.78/10.61 (cartprodpairmemEL) => 77.78/10.61 (( 77.78/10.61 (cartprodpairmemER) => 77.78/10.61 (( 77.78/10.61 (cartprodmempaircEq) => 77.78/10.61 (( 77.78/10.61 (cartprodfstpairEq) => 77.78/10.61 (( 77.78/10.61 (cartprodsndpairEq) => 77.78/10.61 (( 77.78/10.61 (cartprodpairsurjEq) => 77.78/10.61 (( 77.78/10.61 (dpsetconstrI) => 77.78/10.61 (( 77.78/10.61 (dpsetconstrSub) => 77.78/10.61 (( 77.78/10.61 (setOfPairsIsBReln) => 77.78/10.61 (( 77.78/10.61 (dpsetconstrERa) => 77.78/10.61 (( 77.78/10.61 (dpsetconstrEL1) => 77.78/10.61 (( 77.78/10.61 (dpsetconstrEL2) => 77.78/10.61 (( 77.78/10.61 (dpsetconstrER) => 77.78/10.61 (( 77.78/10.61 (funcImageSingleton) => 77.78/10.61 (( 77.78/10.61 (apProp) => 77.78/10.61 (( 77.78/10.61 (app) => 77.78/10.61 (( 77.78/10.61 (infuncsetfunc) => 77.78/10.61 (( 77.78/10.61 (ap2p) => 77.78/10.61 (( 77.78/10.61 (funcinfuncset) => 77.78/10.61 (( 77.78/10.61 (lamProp) => 77.78/10.61 (( 77.78/10.61 (lamp) => 77.78/10.61 (( 77.78/10.61 (lam2p) => 77.78/10.61 (( 77.78/10.61 (brelnall1) => 77.78/10.61 (( 77.78/10.61 (brelnall2) => 77.78/10.61 (( 77.78/10.61 (ex1E2) => 77.78/10.61 (( 77.78/10.61 (funcGraphProp1) => 77.78/10.61 (( 77.78/10.61 (funcGraphProp3) => 77.78/10.61 (( 77.78/10.61 (funcGraphProp2) => 77.78/10.61 (( 77.78/10.61 (funcextLem) => 77.78/10.61 (( 77.78/10.61 (funcGraphProp4) => 77.78/10.61 (( 77.78/10.61 (subbreln) => 77.78/10.61 (( 77.78/10.61 (eqbreln) => 77.78/10.61 (( 77.78/10.61 (funcext) => 77.78/10.61 (( 77.78/10.61 (funcext2) => 77.78/10.61 (( 77.78/10.61 (ap2apEq1) => 77.78/10.61 (( 77.78/10.61 (ap2apEq2) => 77.78/10.61 (( 77.78/10.61 (beta1) => 77.78/10.61 (( 77.78/10.61 (eta1) => 77.78/10.61 (( 77.78/10.61 (lam2lamEq) => 77.78/10.61 (( 77.78/10.61 (beta2) => 77.78/10.61 (( 77.78/10.61 (eta2) => 77.78/10.61 (( 77.78/10.61 (iffalseProp1) => 77.78/10.61 (( 77.78/10.61 (iffalseProp2) => 77.78/10.61 (( 77.78/10.61 (iftrueProp1) => 77.78/10.61 (( 77.78/10.61 (iftrueProp2) => 77.78/10.61 (( 77.78/10.61 (ifSingleton) => 77.78/10.61 (( 77.78/10.61 (ifp) => 77.78/10.61 (( 77.78/10.61 (theeq) => 77.78/10.61 (( 77.78/10.61 (iftrue) => 77.78/10.61 (( 77.78/10.61 (iffalse) => 77.78/10.61 (( 77.78/10.61 (iftrueorfalse) => 77.78/10.61 (( 77.78/10.61 (binintersectT_lem) => 77.78/10.61 (( 77.78/10.61 (binunionT_lem) => 77.78/10.61 (( 77.78/10.61 (powersetT_lem) => 77.78/10.61 (( 77.78/10.61 (setminusT_lem) => 77.78/10.61 (( 77.78/10.61 (complementT_lem) => 77.78/10.61 (( 77.78/10.61 (setextT) => 77.78/10.61 (( 77.78/10.61 (subsetTI) => 77.78/10.61 (( 77.78/10.61 (powersetTI1) => 77.78/10.61 (( 77.78/10.61 (powersetTE1) => 77.78/10.61 (( 77.78/10.61 (complementTI1) => 77.78/10.61 (( 77.78/10.61 (complementTE1) => 77.78/10.61 (( 77.78/10.61 (binintersectTELcontra) => 77.78/10.61 (( 77.78/10.61 (binintersectTERcontra) => 77.78/10.61 (( 77.78/10.61 (contrasubsetT) => 77.78/10.61 (( 77.78/10.61 (contrasubsetT1) => 77.78/10.61 (( 77.78/10.61 (contrasubsetT2) => 77.78/10.61 (( 77.78/10.61 (contrasubsetT3) => 77.78/10.61 (( 77.78/10.61 (doubleComplementI1) => 77.78/10.61 (( 77.78/10.61 (doubleComplementE1) => 77.78/10.61 (( 77.78/10.61 (doubleComplementSub1) => 77.78/10.61 (( 77.78/10.61 (doubleComplementSub2) => 77.78/10.61 (( 77.78/10.61 (doubleComplementEq) => 77.78/10.61 (( 77.78/10.61 (complementTnotintersectT) => 77.78/10.61 (( 77.78/10.61 (complementImpComplementIntersect) => 77.78/10.61 (( 77.78/10.61 (complementSubsetComplementIntersect) => 77.78/10.61 (( 77.78/10.61 (complementInPowersetComplementIntersect) => 77.78/10.61 (( 77.78/10.61 (contraSubsetComplement) => 77.78/10.61 (( 77.78/10.61 (complementTcontraSubset) => 77.78/10.61 (( 77.78/10.61 (binunionTILcontra) => 77.78/10.61 (( 77.78/10.61 (binunionTIRcontra) => 77.78/10.61 (( 77.78/10.61 (inIntersectImpInUnion) => 77.78/10.61 (( 77.78/10.61 (inIntersectImpInUnion2) => 77.78/10.61 (( 77.78/10.61 (inIntersectImpInIntersectUnions) => 77.78/10.61 (( 77.78/10.61 (intersectInPowersetIntersectUnions) => 77.78/10.61 (( 77.78/10.61 (inComplementUnionImpNotIn1) => 77.78/10.61 (( 77.78/10.61 (inComplementUnionImpInComplement1) => 77.78/10.61 (( 77.78/10.61 (binunionTE) => 77.78/10.61 (( 77.78/10.61 (binunionTEcontra) => 77.78/10.61 (( 77.78/10.61 (demorgan2a1) => 77.78/10.61 (( 77.78/10.61 (complementUnionInPowersetComplement) => 77.78/10.61 (( 77.78/10.61 (demorgan2a2) => 77.78/10.61 (( 77.78/10.61 (demorgan1a) => 77.78/10.61 (( 77.78/10.61 (demorgan1b) => 77.78/10.61 (( 77.78/10.61 (demorgan1) => 77.78/10.61 (( 77.78/10.61 (demorgan2a) => 77.78/10.61 (( 77.78/10.61 (demorgan2b2) => 77.78/10.61 (( 77.78/10.61 (demorgan2b) => 77.78/10.61 (( 77.78/10.61 (demorgan2) => 77.78/10.61 (( 77.78/10.61 (woz13rule0) => 77.78/10.61 (( 77.78/10.61 (woz13rule1) => 77.78/10.61 (( 77.78/10.61 (woz13rule2) => 77.78/10.61 (( 77.78/10.61 (woz13rule3) => 77.78/10.61 (( 77.78/10.61 (woz13rule4) => 77.78/10.61 (( 77.78/10.61 (woz1_1) => 77.78/10.61 (( 77.78/10.61 (woz1_2) => 77.78/10.61 (( 77.78/10.61 (woz1_3) => 77.78/10.61 (( 77.78/10.61 (woz1_4) => 77.78/10.61 (( 77.78/10.61 (woz1_5) => 77.78/10.61 (( 77.78/10.61 (breln1all2) => 77.78/10.61 (( 77.78/10.61 (breln1SetBreln1) => 77.78/10.61 (( 77.78/10.61 (choice2fnsingleton) => 77.78/10.61 (( 77.78/10.61 (setOfPairsIsBReln1) => 77.78/10.61 (( 77.78/10.61 (breln1all1) => 77.78/10.61 (( 77.78/10.61 (subbreln1) => 77.78/10.61 (( 77.78/10.61 (eqbreln1) => 77.78/10.61 (( 77.78/10.61 (breln1invprop) => 77.78/10.61 (( 77.78/10.61 (breln1invI) => 77.78/10.61 (( 77.78/10.61 (breln1invE) => 77.78/10.61 (( 77.78/10.61 (breln1compprop) => 77.78/10.61 (( 77.78/10.61 (breln1compI) => 77.78/10.61 (( 77.78/10.61 (breln1compE) => 77.78/10.61 (( 77.78/10.61 (breln1compEex) => 77.78/10.61 (( 77.78/10.61 (breln1unionprop) => 77.78/10.61 (( 77.78/10.61 (breln1unionIL) => 77.78/10.61 (( 77.78/10.61 (breln1unionIR) => 77.78/10.61 (( 77.78/10.61 (breln1unionI) => 77.78/10.61 (( 77.78/10.61 (breln1unionE) => 77.78/10.61 (( 77.78/10.61 (breln1unionEcases) => 77.78/10.61 (( 77.78/10.61 (breln1unionCommutes) => 77.78/10.61 (( 77.78/10.61 (woz2Ex) => 77.78/10.61 (( 77.78/10.61 (woz2W) => 77.78/10.61 (( 77.78/10.61 (woz2A) => 77.78/10.61 (( 77.78/10.61 (woz2B) => 77.78/10.61 (( 77.78/10.61 (image1Ex) => 77.78/10.61 (( 77.78/10.61 (image1Ex1) => 77.78/10.61 (( 77.78/10.61 (image1Equiv) => 77.78/10.61 (( 77.78/10.61 (image1E) => 77.78/10.61 (( 77.78/10.61 (image1I) => 77.78/10.61 (( 77.78/10.61 (injFuncInInjFuncSet) => 77.78/10.61 (( 77.78/10.61 (injFuncSetFuncIn) => 77.78/10.61 (( 77.78/10.61 (injFuncSetFuncInj) => 77.78/10.61 (( 77.78/10.61 (surjFuncSetFuncIn) => 77.78/10.61 (( 77.78/10.61 (surjFuncSetFuncSurj) => 77.78/10.61 (( 77.78/10.61 (leftInvIsSurj) => 77.78/10.61 (( 77.78/10.61 (surjCantorThm) => 77.78/10.61 (( 77.78/10.61 (foundation2) => 77.78/10.61 (( 77.78/10.61 (notinself) => 77.78/10.61 (( 77.78/10.61 (notinself2) => 77.78/10.61 (( 77.78/10.61 (omegaSp) => 77.78/10.61 (( 77.78/10.61 (omegaSclos) => 77.78/10.61 (( 77.78/10.61 (peano0notS) => 77.78/10.61 (( 77.78/10.61 (peanoSinj) => 77.78/10.61 (( 77.78/10.61 (transitivesetOp1) => 77.78/10.61 (( 77.78/10.61 (binintTransitive) => 77.78/10.61 (( 77.78/10.61 (transitivesetOp2) => 77.78/10.61 (( 77.78/10.61 (setunionTransitive) => 77.78/10.61 (( 77.78/10.61 (ordinalMinLem1) => 77.78/10.61 (( 77.78/10.61 (!!) @ ( 77.78/10.61 ^[Y0 : $i]: 77.78/10.61 (( 77.78/10.61 (ordinal @ 77.78/10.61 Y0) => 77.78/10.61 (( 77.78/10.61 (!!) @ ( 77.78/10.61 ^[Y1 : $i]: 77.78/10.61 (( 77.78/10.61 (!!) @ ( 77.78/10.61 ^[Y2 : $i]: 77.78/10.61 (( 77.78/10.61 (in @ 77.78/10.61 Y2 @ 77.78/10.61 Y0) => 77.78/10.61 (( 77.78/10.61 (in @ 77.78/10.61 Y1 @ 77.78/10.61 Y2) => 77.78/10.61 (in @ 77.78/10.61 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 77.78/10.61 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl484])). 77.78/10.61 thf(zip_derived_cl501, plain, 77.78/10.61 (~ (((prop2setI) => 77.78/10.61 (((prop2set2propI) => 77.78/10.61 (((notdexE) => 77.78/10.61 (((notdallE) => 77.78/10.61 (((exuI1) => 77.78/10.61 (((exuI3) => 77.78/10.61 (((exuI2) => 77.78/10.61 (((inCongP) => 77.78/10.61 (((in__Cong) => 77.78/10.61 (((exuE3u) => 77.78/10.61 (((exu__Cong) => 77.78/10.61 (((setadjoin__Cong) => 77.78/10.61 (((powerset__Cong) => 77.78/10.61 (((setunion__Cong) => 77.78/10.61 (((exuEu) => 77.78/10.61 (((descr__Cong) => 77.78/10.61 (((dsetconstr__Cong) => 77.78/10.61 (((subsetI1) => 77.78/10.61 (((eqimpsubset2) => 77.78/10.61 (((eqimpsubset1) => 77.78/10.61 (((subsetI2) => 77.78/10.61 (((emptysetsubset) => 77.78/10.61 (((subsetE) => 77.78/10.61 (((subsetE2) => 77.78/10.61 (((notsubsetI) => 77.78/10.61 (((notequalI1) => 77.78/10.61 (((notequalI2) => 77.78/10.61 (((subsetRefl) => 77.78/10.61 (((subsetTrans) => 77.78/10.61 (((setadjoinSub) => 77.78/10.61 (( 77.78/10.61 (setadjoinSub2) => 77.78/10.61 (( 77.78/10.61 (subset2powerset) => 77.78/10.61 (( 77.78/10.61 (setextsub) => 77.78/10.61 (( 77.78/10.61 (subsetemptysetimpeq) => 77.78/10.61 (( 77.78/10.61 (powersetI1) => 77.78/10.61 (( 77.78/10.61 (powersetE1) => 77.78/10.61 (( 77.78/10.61 (inPowerset) => 77.78/10.61 (( 77.78/10.61 (powersetsubset) => 77.78/10.61 (( 77.78/10.61 (sepInPowerset) => 77.78/10.61 (( 77.78/10.61 (sepSubset) => 77.78/10.61 (( 77.78/10.61 (binunionIL) => 77.78/10.61 (( 77.78/10.61 (upairset2IR) => 77.78/10.61 (( 77.78/10.61 (binunionIR) => 77.78/10.61 (( 77.78/10.61 (binunionEcases) => 77.78/10.61 (( 77.78/10.61 (binunionE) => 77.78/10.61 (( 77.78/10.61 (binunionLsub) => 77.78/10.61 (( 77.78/10.61 (binunionRsub) => 77.78/10.61 (( 77.78/10.61 (binintersectI) => 77.78/10.61 (( 77.78/10.61 (binintersectSubset5) => 77.78/10.61 (( 77.78/10.61 (binintersectEL) => 77.78/10.61 (( 77.78/10.61 (binintersectLsub) => 77.78/10.61 (( 77.78/10.61 (binintersectSubset2) => 77.78/10.61 (( 77.78/10.61 (binintersectSubset3) => 77.78/10.61 (( 77.78/10.61 (binintersectER) => 77.78/10.61 (( 77.78/10.61 (disjointsetsI1) => 77.78/10.61 (( 77.78/10.61 (binintersectRsub) => 77.78/10.61 (( 77.78/10.61 (binintersectSubset4) => 77.78/10.61 (( 77.78/10.61 (binintersectSubset1) => 77.78/10.61 (( 77.78/10.61 (bs114d) => 77.78/10.61 (( 77.78/10.61 (setminusI) => 77.78/10.61 (( 77.78/10.61 (setminusEL) => 77.78/10.61 (( 77.78/10.61 (setminusER) => 77.78/10.61 (( 77.78/10.61 (setminusSubset2) => 77.78/10.61 (( 77.78/10.61 (setminusERneg) => 77.78/10.61 (( 77.78/10.61 (setminusELneg) => 77.78/10.61 (( 77.78/10.61 (setminusILneg) => 77.78/10.61 (( 77.78/10.61 (setminusIRneg) => 77.78/10.61 (( 77.78/10.61 (setminusLsub) => 77.78/10.61 (( 77.78/10.61 (setminusSubset1) => 77.78/10.61 (( 77.78/10.61 (symdiffE) => 77.78/10.61 (( 77.78/10.61 (symdiffI1) => 77.78/10.61 (( 77.78/10.61 (symdiffI2) => 77.78/10.61 (( 77.78/10.61 (symdiffIneg1) => 77.78/10.61 (( 77.78/10.61 (symdiffIneg2) => 77.78/10.61 (( 77.78/10.61 (secondinupair) => 77.78/10.61 (( 77.78/10.61 (setukpairIL) => 77.78/10.61 (( 77.78/10.61 (setukpairIR) => 77.78/10.61 (( 77.78/10.61 (kpairiskpair) => 77.78/10.61 (( 77.78/10.61 (kpairp) => 77.78/10.61 (( 77.78/10.61 (singletonsubset) => 77.78/10.61 (( 77.78/10.61 (singletoninpowerset) => 77.78/10.61 (( 77.78/10.61 (singletoninpowunion) => 77.78/10.61 (( 77.78/10.61 (upairset2E) => 77.78/10.61 (( 77.78/10.61 (upairsubunion) => 77.78/10.61 (( 77.78/10.61 (upairinpowunion) => 77.78/10.61 (( 77.78/10.61 (ubforcartprodlem1) => 77.78/10.61 (( 77.78/10.61 (ubforcartprodlem2) => 77.78/10.61 (( 77.78/10.61 (ubforcartprodlem3) => 77.78/10.61 (( 77.78/10.61 (cartprodpairin) => 77.78/10.61 (( 77.78/10.61 (cartprodmempair1) => 77.78/10.61 (( 77.78/10.61 (cartprodmempair) => 77.78/10.61 (( 77.78/10.61 (setunionE2) => 77.78/10.61 (( 77.78/10.61 (setunionsingleton1) => 77.78/10.61 (( 77.78/10.61 (setunionsingleton2) => 77.78/10.61 (( 77.78/10.61 (setunionsingleton) => 77.78/10.61 (( 77.78/10.61 (singletonprop) => 77.78/10.61 (( 77.78/10.61 (ex1E1) => 77.78/10.61 (( 77.78/10.61 (ex1I) => 77.78/10.61 (( 77.78/10.61 (ex1I2) => 77.78/10.61 (( 77.78/10.61 (singletonsuniq) => 77.78/10.61 (( 77.78/10.61 (setukpairinjL1) => 77.78/10.61 (( 77.78/10.61 (kfstsingleton) => 77.78/10.61 (( 77.78/10.61 (theprop) => 77.78/10.61 (( 77.78/10.61 (kfstpairEq) => 77.78/10.61 (( 77.78/10.61 (cartprodfstin) => 77.78/10.61 (( 77.78/10.61 (setukpairinjL2) => 77.78/10.61 (( 77.78/10.61 (setukpairinjL) => 77.78/10.61 (( 77.78/10.61 (setukpairinjR11) => 77.78/10.61 (( 77.78/10.61 (setukpairinjR12) => 77.78/10.61 (( 77.78/10.61 (setukpairinjR1) => 77.78/10.61 (( 77.78/10.61 (upairequniteq) => 77.78/10.61 (( 77.78/10.61 (setukpairinjR2) => 77.78/10.61 (( 77.78/10.61 (setukpairinjR) => 77.78/10.61 (( 77.78/10.61 (ksndsingleton) => 77.78/10.61 (( 77.78/10.61 (ksndpairEq) => 77.78/10.61 (( 77.78/10.61 (kpairsurjEq) => 77.78/10.61 (( 77.78/10.61 (cartprodsndin) => 77.78/10.61 (( 77.78/10.61 (cartprodpairmemEL) => 77.78/10.61 (( 77.78/10.61 (cartprodpairmemER) => 77.78/10.61 (( 77.78/10.61 (cartprodmempaircEq) => 77.78/10.61 (( 77.78/10.61 (cartprodfstpairEq) => 77.78/10.61 (( 77.78/10.61 (cartprodsndpairEq) => 77.78/10.61 (( 77.78/10.61 (cartprodpairsurjEq) => 77.78/10.61 (( 77.78/10.61 (dpsetconstrI) => 77.78/10.61 (( 77.78/10.61 (dpsetconstrSub) => 77.78/10.61 (( 77.78/10.61 (setOfPairsIsBReln) => 77.78/10.61 (( 77.78/10.61 (dpsetconstrERa) => 77.78/10.61 (( 77.78/10.61 (dpsetconstrEL1) => 77.78/10.61 (( 77.78/10.61 (dpsetconstrEL2) => 77.78/10.61 (( 77.78/10.61 (dpsetconstrER) => 77.78/10.61 (( 77.78/10.61 (funcImageSingleton) => 77.78/10.61 (( 77.78/10.61 (apProp) => 77.78/10.61 (( 77.78/10.61 (app) => 77.78/10.61 (( 77.78/10.61 (infuncsetfunc) => 77.78/10.61 (( 77.78/10.61 (ap2p) => 77.78/10.61 (( 77.78/10.61 (funcinfuncset) => 77.78/10.61 (( 77.78/10.61 (lamProp) => 77.78/10.61 (( 77.78/10.61 (lamp) => 77.78/10.61 (( 77.78/10.61 (lam2p) => 77.78/10.61 (( 77.78/10.61 (brelnall1) => 77.78/10.61 (( 77.78/10.61 (brelnall2) => 77.78/10.61 (( 77.78/10.61 (ex1E2) => 77.78/10.61 (( 77.78/10.61 (funcGraphProp1) => 77.78/10.61 (( 77.78/10.61 (funcGraphProp3) => 77.78/10.61 (( 77.78/10.61 (funcGraphProp2) => 77.78/10.61 (( 77.78/10.61 (funcextLem) => 77.78/10.61 (( 77.78/10.61 (funcGraphProp4) => 77.78/10.61 (( 77.78/10.61 (subbreln) => 77.78/10.61 (( 77.78/10.61 (eqbreln) => 77.78/10.61 (( 77.78/10.61 (funcext) => 77.78/10.61 (( 77.78/10.61 (funcext2) => 77.78/10.61 (( 77.78/10.61 (ap2apEq1) => 77.78/10.61 (( 77.78/10.61 (ap2apEq2) => 77.78/10.61 (( 77.78/10.61 (beta1) => 77.78/10.61 (( 77.78/10.61 (eta1) => 77.78/10.61 (( 77.78/10.61 (lam2lamEq) => 77.78/10.61 (( 77.78/10.61 (beta2) => 77.78/10.61 (( 77.78/10.61 (eta2) => 77.78/10.61 (( 77.78/10.61 (iffalseProp1) => 77.78/10.61 (( 77.78/10.61 (iffalseProp2) => 77.78/10.61 (( 77.78/10.61 (iftrueProp1) => 77.78/10.61 (( 77.78/10.61 (iftrueProp2) => 77.78/10.61 (( 77.78/10.61 (ifSingleton) => 77.78/10.61 (( 77.78/10.61 (ifp) => 77.78/10.61 (( 77.78/10.61 (theeq) => 77.78/10.61 (( 77.78/10.61 (iftrue) => 77.78/10.61 (( 77.78/10.61 (iffalse) => 77.78/10.61 (( 77.78/10.61 (iftrueorfalse) => 77.78/10.61 (( 77.78/10.61 (binintersectT_lem) => 77.78/10.61 (( 77.78/10.61 (binunionT_lem) => 77.78/10.61 (( 77.78/10.61 (powersetT_lem) => 77.78/10.61 (( 77.78/10.61 (setminusT_lem) => 77.78/10.61 (( 77.78/10.61 (complementT_lem) => 77.78/10.61 (( 77.78/10.61 (setextT) => 77.78/10.61 (( 77.78/10.61 (subsetTI) => 77.78/10.61 (( 77.78/10.61 (powersetTI1) => 77.78/10.61 (( 77.78/10.61 (powersetTE1) => 77.78/10.61 (( 77.78/10.61 (complementTI1) => 77.78/10.61 (( 77.78/10.61 (complementTE1) => 77.78/10.61 (( 77.78/10.61 (binintersectTELcontra) => 77.78/10.61 (( 77.78/10.61 (binintersectTERcontra) => 77.78/10.61 (( 77.78/10.61 (contrasubsetT) => 77.78/10.61 (( 77.78/10.61 (contrasubsetT1) => 77.78/10.61 (( 77.78/10.61 (contrasubsetT2) => 77.78/10.61 (( 77.78/10.61 (contrasubsetT3) => 77.78/10.61 (( 77.78/10.61 (doubleComplementI1) => 77.78/10.61 (( 77.78/10.61 (doubleComplementE1) => 77.78/10.61 (( 77.78/10.61 (doubleComplementSub1) => 77.78/10.61 (( 77.78/10.61 (doubleComplementSub2) => 77.78/10.61 (( 77.78/10.61 (doubleComplementEq) => 77.78/10.61 (( 77.78/10.61 (complementTnotintersectT) => 77.78/10.61 (( 77.78/10.61 (complementImpComplementIntersect) => 77.78/10.61 (( 77.78/10.61 (complementSubsetComplementIntersect) => 77.78/10.61 (( 77.78/10.61 (complementInPowersetComplementIntersect) => 77.78/10.61 (( 77.78/10.61 (contraSubsetComplement) => 77.78/10.61 (( 77.78/10.61 (complementTcontraSubset) => 77.78/10.61 (( 77.78/10.61 (binunionTILcontra) => 77.78/10.61 (( 77.78/10.61 (binunionTIRcontra) => 77.78/10.61 (( 77.78/10.61 (inIntersectImpInUnion) => 77.78/10.61 (( 77.78/10.61 (inIntersectImpInUnion2) => 77.78/10.61 (( 77.78/10.61 (inIntersectImpInIntersectUnions) => 77.78/10.61 (( 77.78/10.61 (intersectInPowersetIntersectUnions) => 77.78/10.61 (( 77.78/10.61 (inComplementUnionImpNotIn1) => 77.78/10.61 (( 77.78/10.61 (inComplementUnionImpInComplement1) => 77.78/10.61 (( 77.78/10.61 (binunionTE) => 77.78/10.61 (( 77.78/10.61 (binunionTEcontra) => 77.78/10.61 (( 77.78/10.61 (demorgan2a1) => 77.78/10.61 (( 77.78/10.61 (complementUnionInPowersetComplement) => 77.78/10.61 (( 77.78/10.61 (demorgan2a2) => 77.78/10.61 (( 77.78/10.61 (demorgan1a) => 77.78/10.61 (( 77.78/10.61 (demorgan1b) => 77.78/10.61 (( 77.78/10.61 (demorgan1) => 77.78/10.61 (( 77.78/10.61 (demorgan2a) => 77.78/10.61 (( 77.78/10.61 (demorgan2b2) => 77.78/10.61 (( 77.78/10.61 (demorgan2b) => 77.78/10.61 (( 77.78/10.61 (demorgan2) => 77.78/10.61 (( 77.78/10.61 (woz13rule0) => 77.78/10.61 (( 77.78/10.61 (woz13rule1) => 77.78/10.61 (( 77.78/10.61 (woz13rule2) => 77.78/10.61 (( 77.78/10.61 (woz13rule3) => 77.78/10.61 (( 77.78/10.61 (woz13rule4) => 77.78/10.61 (( 77.78/10.61 (woz1_1) => 77.78/10.61 (( 77.78/10.61 (woz1_2) => 77.78/10.61 (( 77.78/10.61 (woz1_3) => 77.78/10.61 (( 77.78/10.61 (woz1_4) => 77.78/10.61 (( 77.78/10.61 (woz1_5) => 77.78/10.61 (( 77.78/10.61 (breln1all2) => 77.78/10.61 (( 77.78/10.61 (breln1SetBreln1) => 77.78/10.61 (( 77.78/10.61 (choice2fnsingleton) => 77.78/10.61 (( 77.78/10.61 (setOfPairsIsBReln1) => 77.78/10.61 (( 77.78/10.61 (breln1all1) => 77.78/10.61 (( 77.78/10.61 (subbreln1) => 77.78/10.61 (( 77.78/10.61 (eqbreln1) => 77.78/10.61 (( 77.78/10.61 (breln1invprop) => 77.78/10.61 (( 77.78/10.61 (breln1invI) => 77.78/10.61 (( 77.78/10.61 (breln1invE) => 77.78/10.61 (( 77.78/10.61 (breln1compprop) => 77.78/10.61 (( 77.78/10.61 (breln1compI) => 77.78/10.61 (( 77.78/10.61 (breln1compE) => 77.78/10.61 (( 77.78/10.61 (breln1compEex) => 77.78/10.61 (( 77.78/10.61 (breln1unionprop) => 77.78/10.61 (( 77.78/10.61 (breln1unionIL) => 77.78/10.61 (( 77.78/10.61 (breln1unionIR) => 77.78/10.61 (( 77.78/10.61 (breln1unionI) => 77.78/10.61 (( 77.78/10.61 (breln1unionE) => 77.78/10.61 (( 77.78/10.61 (breln1unionEcases) => 77.78/10.61 (( 77.78/10.61 (breln1unionCommutes) => 77.78/10.61 (( 77.78/10.61 (woz2Ex) => 77.78/10.61 (( 77.78/10.61 (woz2W) => 77.78/10.61 (( 77.78/10.61 (woz2A) => 77.78/10.61 (( 77.78/10.61 (woz2B) => 77.78/10.61 (( 77.78/10.61 (image1Ex) => 77.78/10.61 (( 77.78/10.61 (image1Ex1) => 77.78/10.61 (( 77.78/10.61 (image1Equiv) => 77.78/10.61 (( 77.78/10.61 (image1E) => 77.78/10.61 (( 77.78/10.61 (image1I) => 77.78/10.61 (( 77.78/10.61 (injFuncInInjFuncSet) => 77.78/10.61 (( 77.78/10.61 (injFuncSetFuncIn) => 77.78/10.61 (( 77.78/10.61 (injFuncSetFuncInj) => 77.78/10.61 (( 77.78/10.61 (surjFuncSetFuncIn) => 77.78/10.61 (( 77.78/10.61 (surjFuncSetFuncSurj) => 77.78/10.61 (( 77.78/10.61 (leftInvIsSurj) => 77.78/10.61 (( 77.78/10.61 (surjCantorThm) => 77.78/10.61 (( 77.78/10.61 (foundation2) => 77.78/10.61 (( 77.78/10.61 (notinself) => 77.78/10.61 (( 77.78/10.61 (notinself2) => 77.78/10.61 (( 77.78/10.61 (omegaSp) => 77.78/10.61 (( 77.78/10.61 (omegaSclos) => 77.78/10.61 (( 77.78/10.61 (peano0notS) => 77.78/10.61 (( 77.78/10.61 (peanoSinj) => 77.78/10.61 (( 77.78/10.61 (transitivesetOp1) => 77.78/10.61 (( 77.78/10.61 (binintTransitive) => 77.78/10.61 (( 77.78/10.61 (transitivesetOp2) => 77.78/10.61 (( 77.78/10.61 (setunionTransitive) => 77.78/10.61 (( 77.78/10.61 (ordinalMinLem1) => 77.78/10.61 (( 77.78/10.61 (!!) @ ( 77.78/10.61 ^[Y0 : $i]: 77.78/10.61 (( 77.78/10.61 (ordinal @ 77.78/10.61 Y0) => 77.78/10.61 (( 77.78/10.61 (!!) @ ( 77.78/10.61 ^[Y1 : $i]: 77.78/10.61 (( 77.78/10.61 (!!) @ ( 77.78/10.61 ^[Y2 : $i]: 77.78/10.61 (( 77.78/10.61 (in @ 77.78/10.61 Y2 @ 77.78/10.61 Y0) => 77.78/10.61 (( 77.78/10.61 (in @ 77.78/10.61 Y1 @ 77.78/10.61 Y2) => 77.78/10.61 (in @ 77.78/10.61 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 77.78/10.61 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl491])). 77.78/10.61 thf(zip_derived_cl508, plain, 77.78/10.61 (~ (((prop2set2propI) => 77.78/10.61 (((notdexE) => 77.78/10.61 (((notdallE) => 77.78/10.61 (((exuI1) => 77.78/10.61 (((exuI3) => 77.78/10.61 (((exuI2) => 77.78/10.61 (((inCongP) => 77.78/10.61 (((in__Cong) => 77.78/10.61 (((exuE3u) => 77.78/10.61 (((exu__Cong) => 77.78/10.61 (((setadjoin__Cong) => 77.78/10.61 (((powerset__Cong) => 77.78/10.61 (((setunion__Cong) => 77.78/10.61 (((exuEu) => 77.78/10.61 (((descr__Cong) => 77.78/10.61 (((dsetconstr__Cong) => 77.78/10.61 (((subsetI1) => 77.78/10.61 (((eqimpsubset2) => 77.78/10.61 (((eqimpsubset1) => 77.78/10.61 (((subsetI2) => 77.78/10.61 (((emptysetsubset) => 77.78/10.61 (((subsetE) => 77.78/10.61 (((subsetE2) => 77.78/10.61 (((notsubsetI) => 77.78/10.61 (((notequalI1) => 77.78/10.61 (((notequalI2) => 77.78/10.61 (((subsetRefl) => 77.78/10.61 (((subsetTrans) => 77.78/10.61 (((setadjoinSub) => 77.78/10.61 (((setadjoinSub2) => 77.78/10.61 (( 77.78/10.61 (subset2powerset) => 77.78/10.61 (( 77.78/10.61 (setextsub) => 77.78/10.61 (( 77.78/10.61 (subsetemptysetimpeq) => 77.78/10.61 (( 77.78/10.61 (powersetI1) => 77.78/10.61 (( 77.78/10.61 (powersetE1) => 77.78/10.61 (( 77.78/10.61 (inPowerset) => 77.78/10.61 (( 77.78/10.61 (powersetsubset) => 77.78/10.61 (( 77.78/10.61 (sepInPowerset) => 77.78/10.61 (( 77.78/10.61 (sepSubset) => 77.78/10.61 (( 77.78/10.61 (binunionIL) => 77.78/10.61 (( 77.78/10.61 (upairset2IR) => 77.78/10.61 (( 77.78/10.61 (binunionIR) => 77.78/10.61 (( 77.78/10.61 (binunionEcases) => 77.78/10.61 (( 77.78/10.61 (binunionE) => 77.78/10.61 (( 77.78/10.61 (binunionLsub) => 77.78/10.61 (( 77.78/10.61 (binunionRsub) => 77.78/10.61 (( 77.78/10.61 (binintersectI) => 77.78/10.61 (( 77.78/10.61 (binintersectSubset5) => 77.78/10.61 (( 77.78/10.61 (binintersectEL) => 77.78/10.61 (( 77.78/10.61 (binintersectLsub) => 77.78/10.61 (( 77.78/10.61 (binintersectSubset2) => 77.78/10.61 (( 77.78/10.61 (binintersectSubset3) => 77.78/10.61 (( 77.78/10.61 (binintersectER) => 77.78/10.61 (( 77.78/10.61 (disjointsetsI1) => 77.78/10.61 (( 77.78/10.61 (binintersectRsub) => 77.78/10.61 (( 77.78/10.61 (binintersectSubset4) => 77.78/10.61 (( 77.78/10.61 (binintersectSubset1) => 77.78/10.61 (( 77.78/10.61 (bs114d) => 77.78/10.61 (( 77.78/10.61 (setminusI) => 77.78/10.61 (( 77.78/10.61 (setminusEL) => 77.78/10.61 (( 77.78/10.61 (setminusER) => 77.78/10.61 (( 77.78/10.61 (setminusSubset2) => 77.78/10.61 (( 77.78/10.61 (setminusERneg) => 77.78/10.61 (( 77.78/10.61 (setminusELneg) => 77.78/10.61 (( 77.78/10.61 (setminusILneg) => 77.78/10.61 (( 77.78/10.61 (setminusIRneg) => 77.78/10.61 (( 77.78/10.61 (setminusLsub) => 77.78/10.61 (( 77.78/10.61 (setminusSubset1) => 77.78/10.61 (( 77.78/10.61 (symdiffE) => 77.78/10.61 (( 77.78/10.61 (symdiffI1) => 77.78/10.61 (( 77.78/10.61 (symdiffI2) => 77.78/10.61 (( 77.78/10.61 (symdiffIneg1) => 77.78/10.61 (( 77.78/10.61 (symdiffIneg2) => 77.78/10.61 (( 77.78/10.61 (secondinupair) => 77.78/10.61 (( 77.78/10.61 (setukpairIL) => 77.78/10.61 (( 77.78/10.61 (setukpairIR) => 77.78/10.61 (( 77.78/10.61 (kpairiskpair) => 77.78/10.61 (( 77.78/10.61 (kpairp) => 77.78/10.61 (( 77.78/10.61 (singletonsubset) => 77.78/10.61 (( 77.78/10.61 (singletoninpowerset) => 77.78/10.61 (( 77.78/10.61 (singletoninpowunion) => 77.78/10.61 (( 77.78/10.61 (upairset2E) => 77.78/10.61 (( 77.78/10.61 (upairsubunion) => 77.78/10.61 (( 77.78/10.61 (upairinpowunion) => 77.78/10.61 (( 77.78/10.61 (ubforcartprodlem1) => 77.78/10.61 (( 77.78/10.61 (ubforcartprodlem2) => 77.78/10.61 (( 77.78/10.61 (ubforcartprodlem3) => 77.78/10.61 (( 77.78/10.61 (cartprodpairin) => 77.78/10.61 (( 77.78/10.61 (cartprodmempair1) => 77.78/10.61 (( 77.78/10.61 (cartprodmempair) => 77.78/10.61 (( 77.78/10.61 (setunionE2) => 77.78/10.61 (( 77.78/10.61 (setunionsingleton1) => 77.78/10.61 (( 77.78/10.61 (setunionsingleton2) => 77.78/10.61 (( 77.78/10.61 (setunionsingleton) => 77.78/10.61 (( 77.78/10.61 (singletonprop) => 77.78/10.61 (( 77.78/10.61 (ex1E1) => 77.78/10.61 (( 77.78/10.61 (ex1I) => 77.78/10.61 (( 77.78/10.61 (ex1I2) => 77.78/10.61 (( 77.78/10.61 (singletonsuniq) => 77.78/10.61 (( 77.78/10.61 (setukpairinjL1) => 77.78/10.61 (( 77.78/10.61 (kfstsingleton) => 77.78/10.61 (( 77.78/10.61 (theprop) => 77.78/10.61 (( 77.78/10.61 (kfstpairEq) => 77.78/10.61 (( 77.78/10.61 (cartprodfstin) => 77.78/10.61 (( 77.78/10.61 (setukpairinjL2) => 77.78/10.61 (( 77.78/10.61 (setukpairinjL) => 77.78/10.61 (( 77.78/10.61 (setukpairinjR11) => 77.78/10.61 (( 77.78/10.61 (setukpairinjR12) => 77.78/10.61 (( 77.78/10.61 (setukpairinjR1) => 77.78/10.61 (( 77.78/10.61 (upairequniteq) => 77.78/10.61 (( 77.78/10.61 (setukpairinjR2) => 77.78/10.61 (( 77.78/10.61 (setukpairinjR) => 77.78/10.61 (( 77.78/10.61 (ksndsingleton) => 77.78/10.61 (( 77.78/10.61 (ksndpairEq) => 77.78/10.61 (( 77.78/10.61 (kpairsurjEq) => 77.78/10.61 (( 77.78/10.61 (cartprodsndin) => 77.78/10.61 (( 77.78/10.61 (cartprodpairmemEL) => 77.78/10.61 (( 77.78/10.61 (cartprodpairmemER) => 77.78/10.61 (( 77.78/10.61 (cartprodmempaircEq) => 77.78/10.61 (( 77.78/10.61 (cartprodfstpairEq) => 77.78/10.61 (( 77.78/10.61 (cartprodsndpairEq) => 77.78/10.61 (( 77.78/10.61 (cartprodpairsurjEq) => 77.78/10.61 (( 77.78/10.61 (dpsetconstrI) => 77.78/10.61 (( 77.78/10.61 (dpsetconstrSub) => 77.78/10.61 (( 77.78/10.61 (setOfPairsIsBReln) => 77.78/10.61 (( 77.78/10.61 (dpsetconstrERa) => 77.78/10.61 (( 77.78/10.61 (dpsetconstrEL1) => 77.78/10.61 (( 77.78/10.61 (dpsetconstrEL2) => 77.78/10.61 (( 77.78/10.61 (dpsetconstrER) => 77.78/10.61 (( 77.78/10.61 (funcImageSingleton) => 77.78/10.61 (( 77.78/10.61 (apProp) => 77.78/10.61 (( 77.78/10.61 (app) => 77.78/10.61 (( 77.78/10.61 (infuncsetfunc) => 77.78/10.61 (( 77.78/10.61 (ap2p) => 77.78/10.61 (( 77.78/10.61 (funcinfuncset) => 77.78/10.61 (( 77.78/10.61 (lamProp) => 77.78/10.61 (( 77.78/10.61 (lamp) => 77.78/10.61 (( 77.78/10.61 (lam2p) => 77.78/10.61 (( 77.78/10.61 (brelnall1) => 77.78/10.61 (( 77.78/10.61 (brelnall2) => 77.78/10.61 (( 77.78/10.61 (ex1E2) => 77.78/10.61 (( 77.78/10.61 (funcGraphProp1) => 77.78/10.61 (( 77.78/10.61 (funcGraphProp3) => 77.78/10.61 (( 77.78/10.61 (funcGraphProp2) => 77.78/10.61 (( 77.78/10.61 (funcextLem) => 77.78/10.61 (( 77.78/10.61 (funcGraphProp4) => 77.78/10.61 (( 77.78/10.61 (subbreln) => 77.78/10.61 (( 77.78/10.61 (eqbreln) => 77.78/10.61 (( 77.78/10.61 (funcext) => 77.78/10.61 (( 77.78/10.61 (funcext2) => 77.78/10.61 (( 77.78/10.61 (ap2apEq1) => 77.78/10.61 (( 77.78/10.61 (ap2apEq2) => 77.78/10.61 (( 77.78/10.61 (beta1) => 77.78/10.61 (( 77.78/10.61 (eta1) => 77.78/10.61 (( 77.78/10.61 (lam2lamEq) => 77.78/10.61 (( 77.78/10.61 (beta2) => 77.78/10.61 (( 77.78/10.61 (eta2) => 77.78/10.61 (( 77.78/10.61 (iffalseProp1) => 77.78/10.61 (( 77.78/10.61 (iffalseProp2) => 77.78/10.61 (( 77.78/10.61 (iftrueProp1) => 77.78/10.61 (( 77.78/10.61 (iftrueProp2) => 77.78/10.61 (( 77.78/10.61 (ifSingleton) => 77.78/10.61 (( 77.78/10.61 (ifp) => 77.78/10.61 (( 77.78/10.61 (theeq) => 77.78/10.61 (( 77.78/10.61 (iftrue) => 77.78/10.61 (( 77.78/10.61 (iffalse) => 77.78/10.61 (( 77.78/10.61 (iftrueorfalse) => 77.78/10.61 (( 77.78/10.61 (binintersectT_lem) => 77.78/10.61 (( 77.78/10.61 (binunionT_lem) => 77.78/10.61 (( 77.78/10.61 (powersetT_lem) => 77.78/10.61 (( 77.78/10.61 (setminusT_lem) => 77.78/10.61 (( 77.78/10.61 (complementT_lem) => 77.78/10.61 (( 77.78/10.61 (setextT) => 77.78/10.61 (( 77.78/10.61 (subsetTI) => 77.78/10.61 (( 77.78/10.61 (powersetTI1) => 77.78/10.61 (( 77.78/10.61 (powersetTE1) => 77.78/10.61 (( 77.78/10.61 (complementTI1) => 77.78/10.61 (( 77.78/10.61 (complementTE1) => 77.78/10.61 (( 77.78/10.61 (binintersectTELcontra) => 77.78/10.61 (( 77.78/10.61 (binintersectTERcontra) => 77.78/10.61 (( 77.78/10.61 (contrasubsetT) => 77.78/10.61 (( 77.78/10.61 (contrasubsetT1) => 77.78/10.61 (( 77.78/10.61 (contrasubsetT2) => 77.78/10.61 (( 77.78/10.61 (contrasubsetT3) => 77.78/10.61 (( 77.78/10.61 (doubleComplementI1) => 77.78/10.61 (( 77.78/10.61 (doubleComplementE1) => 77.78/10.61 (( 77.78/10.61 (doubleComplementSub1) => 77.78/10.61 (( 77.78/10.61 (doubleComplementSub2) => 77.78/10.61 (( 77.78/10.61 (doubleComplementEq) => 77.78/10.61 (( 77.78/10.61 (complementTnotintersectT) => 77.78/10.61 (( 77.78/10.61 (complementImpComplementIntersect) => 77.78/10.61 (( 77.78/10.61 (complementSubsetComplementIntersect) => 77.78/10.61 (( 77.78/10.61 (complementInPowersetComplementIntersect) => 77.78/10.61 (( 77.78/10.61 (contraSubsetComplement) => 77.78/10.61 (( 77.78/10.61 (complementTcontraSubset) => 77.78/10.61 (( 77.78/10.61 (binunionTILcontra) => 77.78/10.61 (( 77.78/10.61 (binunionTIRcontra) => 77.78/10.61 (( 77.78/10.61 (inIntersectImpInUnion) => 77.78/10.61 (( 77.78/10.61 (inIntersectImpInUnion2) => 77.78/10.61 (( 77.78/10.61 (inIntersectImpInIntersectUnions) => 77.78/10.61 (( 77.78/10.61 (intersectInPowersetIntersectUnions) => 77.78/10.61 (( 77.78/10.61 (inComplementUnionImpNotIn1) => 77.78/10.61 (( 77.78/10.61 (inComplementUnionImpInComplement1) => 77.78/10.61 (( 77.78/10.61 (binunionTE) => 77.78/10.61 (( 77.78/10.61 (binunionTEcontra) => 77.78/10.61 (( 77.78/10.61 (demorgan2a1) => 77.78/10.61 (( 77.78/10.61 (complementUnionInPowersetComplement) => 77.78/10.61 (( 77.78/10.61 (demorgan2a2) => 77.78/10.61 (( 77.78/10.61 (demorgan1a) => 77.78/10.61 (( 77.78/10.61 (demorgan1b) => 77.78/10.61 (( 77.78/10.61 (demorgan1) => 77.78/10.61 (( 77.78/10.61 (demorgan2a) => 77.78/10.61 (( 77.78/10.61 (demorgan2b2) => 77.78/10.61 (( 77.78/10.61 (demorgan2b) => 77.78/10.61 (( 77.78/10.61 (demorgan2) => 77.78/10.61 (( 77.78/10.61 (woz13rule0) => 77.78/10.61 (( 77.78/10.61 (woz13rule1) => 77.78/10.61 (( 77.78/10.61 (woz13rule2) => 77.78/10.61 (( 77.78/10.61 (woz13rule3) => 77.78/10.61 (( 77.78/10.61 (woz13rule4) => 77.78/10.61 (( 77.78/10.61 (woz1_1) => 77.78/10.61 (( 77.78/10.61 (woz1_2) => 77.78/10.61 (( 77.78/10.61 (woz1_3) => 77.78/10.61 (( 77.78/10.61 (woz1_4) => 77.78/10.61 (( 77.78/10.61 (woz1_5) => 77.78/10.61 (( 77.78/10.61 (breln1all2) => 77.78/10.61 (( 77.78/10.61 (breln1SetBreln1) => 77.78/10.61 (( 77.78/10.61 (choice2fnsingleton) => 77.78/10.61 (( 77.78/10.61 (setOfPairsIsBReln1) => 77.78/10.61 (( 77.78/10.61 (breln1all1) => 77.78/10.61 (( 77.78/10.61 (subbreln1) => 77.78/10.61 (( 77.78/10.61 (eqbreln1) => 77.78/10.61 (( 77.78/10.61 (breln1invprop) => 77.78/10.61 (( 77.78/10.61 (breln1invI) => 77.78/10.61 (( 77.78/10.61 (breln1invE) => 77.78/10.61 (( 77.78/10.61 (breln1compprop) => 77.78/10.61 (( 77.78/10.61 (breln1compI) => 77.78/10.61 (( 77.78/10.61 (breln1compE) => 77.78/10.61 (( 77.78/10.61 (breln1compEex) => 77.78/10.61 (( 77.78/10.61 (breln1unionprop) => 77.78/10.61 (( 77.78/10.61 (breln1unionIL) => 77.78/10.61 (( 77.78/10.61 (breln1unionIR) => 77.78/10.61 (( 77.78/10.61 (breln1unionI) => 77.78/10.61 (( 77.78/10.61 (breln1unionE) => 77.78/10.61 (( 77.78/10.61 (breln1unionEcases) => 77.78/10.61 (( 77.78/10.61 (breln1unionCommutes) => 77.78/10.61 (( 77.78/10.61 (woz2Ex) => 77.78/10.61 (( 77.78/10.61 (woz2W) => 77.78/10.61 (( 77.78/10.61 (woz2A) => 77.78/10.61 (( 77.78/10.61 (woz2B) => 77.78/10.61 (( 77.78/10.61 (image1Ex) => 77.78/10.61 (( 77.78/10.61 (image1Ex1) => 77.78/10.61 (( 77.78/10.61 (image1Equiv) => 77.78/10.61 (( 77.78/10.61 (image1E) => 77.78/10.61 (( 77.78/10.61 (image1I) => 77.78/10.61 (( 77.78/10.61 (injFuncInInjFuncSet) => 77.78/10.61 (( 77.78/10.61 (injFuncSetFuncIn) => 77.78/10.61 (( 77.78/10.61 (injFuncSetFuncInj) => 77.78/10.61 (( 77.78/10.61 (surjFuncSetFuncIn) => 77.78/10.61 (( 77.78/10.61 (surjFuncSetFuncSurj) => 77.78/10.61 (( 77.78/10.61 (leftInvIsSurj) => 77.78/10.61 (( 77.78/10.61 (surjCantorThm) => 77.78/10.61 (( 77.78/10.61 (foundation2) => 77.78/10.61 (( 77.78/10.61 (notinself) => 77.78/10.61 (( 77.78/10.61 (notinself2) => 77.78/10.61 (( 77.78/10.61 (omegaSp) => 77.78/10.61 (( 77.78/10.61 (omegaSclos) => 77.78/10.61 (( 77.78/10.61 (peano0notS) => 77.78/10.61 (( 77.78/10.61 (peanoSinj) => 77.78/10.61 (( 77.78/10.61 (transitivesetOp1) => 77.78/10.61 (( 77.78/10.61 (binintTransitive) => 77.78/10.61 (( 77.78/10.61 (transitivesetOp2) => 77.78/10.61 (( 77.78/10.61 (setunionTransitive) => 77.78/10.61 (( 77.78/10.61 (ordinalMinLem1) => 77.78/10.61 (( 77.78/10.61 (!!) @ ( 77.78/10.61 ^[Y0 : $i]: 77.78/10.61 (( 77.78/10.61 (ordinal @ 77.78/10.61 Y0) => 77.78/10.61 (( 77.78/10.61 (!!) @ ( 77.78/10.61 ^[Y1 : $i]: 77.78/10.61 (( 77.78/10.61 (!!) @ ( 77.78/10.61 ^[Y2 : $i]: 77.78/10.61 (( 77.78/10.61 (in @ 77.78/10.61 Y2 @ 77.78/10.61 Y0) => 77.78/10.61 (( 77.78/10.61 (in @ 77.78/10.61 Y1 @ 77.78/10.61 Y2) => 77.78/10.61 (in @ 77.78/10.61 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 77.78/10.61 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl501])). 77.78/10.61 thf(zip_derived_cl515, plain, 77.78/10.61 (~ (((notdexE) => 77.78/10.61 (((notdallE) => 77.78/10.61 (((exuI1) => 77.78/10.61 (((exuI3) => 77.78/10.61 (((exuI2) => 77.78/10.61 (((inCongP) => 77.78/10.61 (((in__Cong) => 77.78/10.61 (((exuE3u) => 77.78/10.61 (((exu__Cong) => 77.78/10.61 (((setadjoin__Cong) => 77.78/10.61 (((powerset__Cong) => 77.78/10.61 (((setunion__Cong) => 77.78/10.61 (((exuEu) => 77.78/10.61 (((descr__Cong) => 77.78/10.61 (((dsetconstr__Cong) => 77.78/10.61 (((subsetI1) => 77.78/10.61 (((eqimpsubset2) => 77.78/10.61 (((eqimpsubset1) => 77.78/10.61 (((subsetI2) => 77.78/10.61 (((emptysetsubset) => 77.78/10.61 (((subsetE) => 77.78/10.61 (((subsetE2) => 77.78/10.61 (((notsubsetI) => 77.78/10.61 (((notequalI1) => 77.78/10.61 (((notequalI2) => 77.78/10.61 (((subsetRefl) => 77.78/10.61 (((subsetTrans) => 77.78/10.61 (((setadjoinSub) => 77.78/10.61 (((setadjoinSub2) => 77.78/10.61 (((subset2powerset) => 77.78/10.61 (( 77.78/10.61 (setextsub) => 77.78/10.61 (( 77.78/10.61 (subsetemptysetimpeq) => 77.78/10.61 (( 77.78/10.61 (powersetI1) => 77.78/10.61 (( 77.78/10.61 (powersetE1) => 77.78/10.61 (( 77.78/10.61 (inPowerset) => 77.78/10.61 (( 77.78/10.61 (powersetsubset) => 77.78/10.61 (( 77.78/10.61 (sepInPowerset) => 77.78/10.61 (( 77.78/10.61 (sepSubset) => 77.78/10.61 (( 77.78/10.61 (binunionIL) => 77.78/10.61 (( 77.78/10.61 (upairset2IR) => 77.78/10.61 (( 77.78/10.61 (binunionIR) => 77.78/10.61 (( 77.78/10.61 (binunionEcases) => 77.78/10.61 (( 77.78/10.61 (binunionE) => 77.78/10.61 (( 77.78/10.61 (binunionLsub) => 77.78/10.61 (( 77.78/10.61 (binunionRsub) => 77.78/10.61 (( 77.78/10.61 (binintersectI) => 77.78/10.61 (( 77.78/10.61 (binintersectSubset5) => 77.78/10.61 (( 77.78/10.61 (binintersectEL) => 77.78/10.61 (( 77.78/10.61 (binintersectLsub) => 77.78/10.61 (( 77.78/10.61 (binintersectSubset2) => 77.78/10.61 (( 77.78/10.61 (binintersectSubset3) => 77.78/10.61 (( 77.78/10.61 (binintersectER) => 77.78/10.61 (( 77.78/10.61 (disjointsetsI1) => 77.78/10.61 (( 77.78/10.61 (binintersectRsub) => 77.78/10.61 (( 77.78/10.61 (binintersectSubset4) => 77.78/10.61 (( 77.78/10.61 (binintersectSubset1) => 77.78/10.61 (( 77.78/10.61 (bs114d) => 77.78/10.61 (( 77.78/10.61 (setminusI) => 77.78/10.61 (( 77.78/10.61 (setminusEL) => 77.78/10.61 (( 77.78/10.61 (setminusER) => 77.78/10.61 (( 77.78/10.61 (setminusSubset2) => 77.78/10.61 (( 77.78/10.61 (setminusERneg) => 77.78/10.61 (( 77.78/10.61 (setminusELneg) => 77.78/10.61 (( 77.78/10.61 (setminusILneg) => 77.78/10.61 (( 77.78/10.61 (setminusIRneg) => 77.78/10.61 (( 77.78/10.61 (setminusLsub) => 77.78/10.61 (( 77.78/10.61 (setminusSubset1) => 77.78/10.61 (( 77.78/10.61 (symdiffE) => 77.78/10.61 (( 77.78/10.61 (symdiffI1) => 77.78/10.61 (( 77.78/10.61 (symdiffI2) => 77.78/10.61 (( 77.78/10.61 (symdiffIneg1) => 77.78/10.61 (( 77.78/10.61 (symdiffIneg2) => 77.78/10.61 (( 77.78/10.61 (secondinupair) => 77.78/10.61 (( 77.78/10.61 (setukpairIL) => 77.78/10.61 (( 77.78/10.61 (setukpairIR) => 77.78/10.61 (( 77.78/10.61 (kpairiskpair) => 77.78/10.61 (( 77.78/10.61 (kpairp) => 77.78/10.61 (( 77.78/10.61 (singletonsubset) => 77.78/10.61 (( 77.78/10.61 (singletoninpowerset) => 77.78/10.61 (( 77.78/10.61 (singletoninpowunion) => 77.78/10.61 (( 77.78/10.61 (upairset2E) => 77.78/10.61 (( 77.78/10.61 (upairsubunion) => 77.78/10.61 (( 77.78/10.61 (upairinpowunion) => 77.78/10.61 (( 77.78/10.61 (ubforcartprodlem1) => 77.78/10.61 (( 77.78/10.61 (ubforcartprodlem2) => 77.78/10.61 (( 77.78/10.61 (ubforcartprodlem3) => 77.78/10.61 (( 77.78/10.61 (cartprodpairin) => 77.78/10.61 (( 77.78/10.61 (cartprodmempair1) => 77.78/10.61 (( 77.78/10.61 (cartprodmempair) => 77.78/10.61 (( 77.78/10.61 (setunionE2) => 77.78/10.61 (( 77.78/10.61 (setunionsingleton1) => 77.78/10.61 (( 77.78/10.61 (setunionsingleton2) => 77.78/10.61 (( 77.78/10.61 (setunionsingleton) => 77.78/10.61 (( 77.78/10.61 (singletonprop) => 77.78/10.61 (( 77.78/10.61 (ex1E1) => 77.78/10.61 (( 77.78/10.61 (ex1I) => 77.78/10.61 (( 77.78/10.61 (ex1I2) => 77.78/10.61 (( 77.78/10.61 (singletonsuniq) => 77.78/10.61 (( 77.78/10.61 (setukpairinjL1) => 77.78/10.61 (( 77.78/10.61 (kfstsingleton) => 77.78/10.61 (( 77.78/10.61 (theprop) => 77.78/10.61 (( 77.78/10.61 (kfstpairEq) => 77.78/10.61 (( 77.78/10.61 (cartprodfstin) => 77.78/10.61 (( 77.78/10.61 (setukpairinjL2) => 77.78/10.61 (( 77.78/10.61 (setukpairinjL) => 77.78/10.61 (( 77.78/10.61 (setukpairinjR11) => 77.78/10.61 (( 77.78/10.61 (setukpairinjR12) => 77.78/10.61 (( 77.78/10.61 (setukpairinjR1) => 77.78/10.61 (( 77.78/10.61 (upairequniteq) => 77.78/10.61 (( 77.78/10.61 (setukpairinjR2) => 77.78/10.61 (( 77.78/10.61 (setukpairinjR) => 77.78/10.61 (( 77.78/10.61 (ksndsingleton) => 77.78/10.61 (( 77.78/10.61 (ksndpairEq) => 77.78/10.61 (( 77.78/10.61 (kpairsurjEq) => 77.78/10.61 (( 77.78/10.61 (cartprodsndin) => 77.78/10.61 (( 77.78/10.61 (cartprodpairmemEL) => 77.78/10.61 (( 77.78/10.61 (cartprodpairmemER) => 77.78/10.61 (( 77.78/10.61 (cartprodmempaircEq) => 77.78/10.61 (( 77.78/10.61 (cartprodfstpairEq) => 77.78/10.61 (( 77.78/10.61 (cartprodsndpairEq) => 77.78/10.61 (( 77.78/10.61 (cartprodpairsurjEq) => 77.78/10.61 (( 77.78/10.61 (dpsetconstrI) => 77.78/10.61 (( 77.78/10.61 (dpsetconstrSub) => 77.78/10.61 (( 77.78/10.61 (setOfPairsIsBReln) => 77.78/10.61 (( 77.78/10.61 (dpsetconstrERa) => 77.78/10.61 (( 77.78/10.61 (dpsetconstrEL1) => 77.78/10.61 (( 77.78/10.61 (dpsetconstrEL2) => 77.78/10.61 (( 77.78/10.61 (dpsetconstrER) => 77.78/10.61 (( 77.78/10.61 (funcImageSingleton) => 77.78/10.61 (( 77.78/10.61 (apProp) => 77.78/10.61 (( 77.78/10.61 (app) => 77.78/10.61 (( 77.78/10.61 (infuncsetfunc) => 77.78/10.61 (( 77.78/10.61 (ap2p) => 77.78/10.61 (( 77.78/10.61 (funcinfuncset) => 77.78/10.61 (( 77.78/10.61 (lamProp) => 77.78/10.61 (( 77.78/10.61 (lamp) => 77.78/10.61 (( 77.78/10.61 (lam2p) => 77.78/10.61 (( 77.78/10.61 (brelnall1) => 77.78/10.61 (( 77.78/10.61 (brelnall2) => 77.78/10.61 (( 77.78/10.61 (ex1E2) => 77.78/10.61 (( 77.78/10.61 (funcGraphProp1) => 77.78/10.61 (( 77.78/10.61 (funcGraphProp3) => 77.78/10.61 (( 77.78/10.61 (funcGraphProp2) => 77.78/10.61 (( 77.78/10.61 (funcextLem) => 77.78/10.61 (( 77.78/10.61 (funcGraphProp4) => 77.78/10.61 (( 77.78/10.61 (subbreln) => 77.78/10.61 (( 77.78/10.61 (eqbreln) => 77.78/10.61 (( 77.78/10.61 (funcext) => 77.78/10.61 (( 77.78/10.61 (funcext2) => 77.78/10.61 (( 77.78/10.61 (ap2apEq1) => 77.78/10.61 (( 77.78/10.61 (ap2apEq2) => 77.78/10.61 (( 77.78/10.61 (beta1) => 77.78/10.61 (( 77.78/10.61 (eta1) => 77.78/10.61 (( 77.78/10.61 (lam2lamEq) => 77.78/10.61 (( 77.78/10.61 (beta2) => 77.78/10.61 (( 77.78/10.61 (eta2) => 77.78/10.61 (( 77.78/10.61 (iffalseProp1) => 77.78/10.61 (( 77.78/10.61 (iffalseProp2) => 77.78/10.61 (( 77.78/10.61 (iftrueProp1) => 77.78/10.61 (( 77.78/10.61 (iftrueProp2) => 77.78/10.61 (( 77.78/10.61 (ifSingleton) => 77.78/10.61 (( 77.78/10.61 (ifp) => 77.78/10.61 (( 77.78/10.61 (theeq) => 77.78/10.61 (( 77.78/10.61 (iftrue) => 77.78/10.61 (( 77.78/10.61 (iffalse) => 77.78/10.61 (( 77.78/10.61 (iftrueorfalse) => 77.78/10.61 (( 77.78/10.61 (binintersectT_lem) => 77.78/10.61 (( 77.78/10.61 (binunionT_lem) => 77.78/10.61 (( 77.78/10.61 (powersetT_lem) => 77.78/10.61 (( 77.78/10.61 (setminusT_lem) => 77.78/10.61 (( 77.78/10.61 (complementT_lem) => 77.78/10.61 (( 77.78/10.61 (setextT) => 77.78/10.61 (( 77.78/10.61 (subsetTI) => 77.78/10.61 (( 77.78/10.61 (powersetTI1) => 77.78/10.61 (( 77.78/10.61 (powersetTE1) => 77.78/10.61 (( 77.78/10.61 (complementTI1) => 77.78/10.61 (( 77.78/10.61 (complementTE1) => 77.78/10.61 (( 77.78/10.61 (binintersectTELcontra) => 77.78/10.61 (( 77.78/10.61 (binintersectTERcontra) => 77.78/10.61 (( 77.78/10.61 (contrasubsetT) => 77.78/10.61 (( 77.78/10.61 (contrasubsetT1) => 77.78/10.61 (( 77.78/10.61 (contrasubsetT2) => 77.78/10.61 (( 77.78/10.61 (contrasubsetT3) => 77.78/10.61 (( 77.78/10.61 (doubleComplementI1) => 77.78/10.61 (( 77.78/10.61 (doubleComplementE1) => 77.78/10.61 (( 77.78/10.61 (doubleComplementSub1) => 77.78/10.61 (( 77.78/10.61 (doubleComplementSub2) => 77.78/10.61 (( 77.78/10.61 (doubleComplementEq) => 77.78/10.61 (( 77.78/10.61 (complementTnotintersectT) => 77.78/10.61 (( 77.78/10.61 (complementImpComplementIntersect) => 77.78/10.61 (( 77.78/10.61 (complementSubsetComplementIntersect) => 77.78/10.61 (( 77.78/10.61 (complementInPowersetComplementIntersect) => 77.78/10.61 (( 77.78/10.61 (contraSubsetComplement) => 77.78/10.61 (( 77.78/10.61 (complementTcontraSubset) => 77.78/10.61 (( 77.78/10.61 (binunionTILcontra) => 77.78/10.61 (( 77.78/10.61 (binunionTIRcontra) => 77.78/10.61 (( 77.78/10.61 (inIntersectImpInUnion) => 77.78/10.61 (( 77.78/10.61 (inIntersectImpInUnion2) => 77.78/10.61 (( 77.78/10.61 (inIntersectImpInIntersectUnions) => 77.78/10.61 (( 77.78/10.61 (intersectInPowersetIntersectUnions) => 77.78/10.61 (( 77.78/10.61 (inComplementUnionImpNotIn1) => 77.78/10.61 (( 77.78/10.61 (inComplementUnionImpInComplement1) => 77.78/10.61 (( 77.78/10.61 (binunionTE) => 77.78/10.61 (( 77.78/10.61 (binunionTEcontra) => 77.78/10.61 (( 77.78/10.61 (demorgan2a1) => 77.78/10.61 (( 77.78/10.61 (complementUnionInPowersetComplement) => 77.78/10.61 (( 77.78/10.61 (demorgan2a2) => 77.78/10.61 (( 77.78/10.61 (demorgan1a) => 77.78/10.61 (( 77.78/10.61 (demorgan1b) => 77.78/10.61 (( 77.78/10.61 (demorgan1) => 77.78/10.61 (( 77.78/10.61 (demorgan2a) => 77.78/10.61 (( 77.78/10.61 (demorgan2b2) => 77.78/10.61 (( 77.78/10.61 (demorgan2b) => 77.78/10.61 (( 77.78/10.61 (demorgan2) => 77.78/10.61 (( 77.78/10.61 (woz13rule0) => 77.78/10.61 (( 77.78/10.61 (woz13rule1) => 77.78/10.61 (( 77.78/10.61 (woz13rule2) => 77.78/10.61 (( 77.78/10.61 (woz13rule3) => 77.78/10.61 (( 77.78/10.61 (woz13rule4) => 77.78/10.61 (( 77.78/10.61 (woz1_1) => 77.78/10.61 (( 77.78/10.61 (woz1_2) => 77.78/10.61 (( 77.78/10.61 (woz1_3) => 77.78/10.61 (( 77.78/10.61 (woz1_4) => 77.78/10.61 (( 77.78/10.61 (woz1_5) => 77.78/10.61 (( 77.78/10.61 (breln1all2) => 77.78/10.61 (( 77.78/10.61 (breln1SetBreln1) => 77.78/10.61 (( 77.78/10.61 (choice2fnsingleton) => 77.78/10.61 (( 77.78/10.61 (setOfPairsIsBReln1) => 77.78/10.61 (( 77.78/10.61 (breln1all1) => 77.78/10.61 (( 77.78/10.61 (subbreln1) => 77.78/10.61 (( 77.78/10.61 (eqbreln1) => 77.78/10.61 (( 77.78/10.61 (breln1invprop) => 77.78/10.61 (( 77.78/10.61 (breln1invI) => 77.78/10.61 (( 77.78/10.61 (breln1invE) => 77.78/10.61 (( 77.78/10.61 (breln1compprop) => 77.78/10.61 (( 77.78/10.61 (breln1compI) => 77.78/10.61 (( 77.78/10.61 (breln1compE) => 77.78/10.61 (( 77.78/10.61 (breln1compEex) => 77.78/10.61 (( 77.78/10.61 (breln1unionprop) => 77.78/10.61 (( 77.78/10.61 (breln1unionIL) => 77.78/10.61 (( 77.78/10.61 (breln1unionIR) => 77.78/10.61 (( 77.78/10.61 (breln1unionI) => 77.78/10.61 (( 77.78/10.61 (breln1unionE) => 77.78/10.61 (( 77.78/10.61 (breln1unionEcases) => 77.78/10.61 (( 77.78/10.61 (breln1unionCommutes) => 77.78/10.61 (( 77.78/10.61 (woz2Ex) => 77.78/10.61 (( 77.78/10.61 (woz2W) => 77.78/10.61 (( 77.78/10.61 (woz2A) => 77.78/10.61 (( 77.78/10.61 (woz2B) => 77.78/10.61 (( 77.78/10.61 (image1Ex) => 77.78/10.61 (( 77.78/10.61 (image1Ex1) => 77.78/10.61 (( 77.78/10.61 (image1Equiv) => 77.78/10.61 (( 77.78/10.61 (image1E) => 77.78/10.61 (( 77.78/10.61 (image1I) => 77.78/10.61 (( 77.78/10.61 (injFuncInInjFuncSet) => 77.78/10.61 (( 77.78/10.61 (injFuncSetFuncIn) => 77.78/10.61 (( 77.78/10.61 (injFuncSetFuncInj) => 77.78/10.61 (( 77.78/10.61 (surjFuncSetFuncIn) => 77.78/10.61 (( 77.78/10.61 (surjFuncSetFuncSurj) => 77.78/10.61 (( 77.78/10.61 (leftInvIsSurj) => 77.78/10.61 (( 77.78/10.61 (surjCantorThm) => 77.78/10.61 (( 77.78/10.61 (foundation2) => 77.78/10.61 (( 77.78/10.61 (notinself) => 77.78/10.61 (( 77.78/10.61 (notinself2) => 77.78/10.61 (( 77.78/10.61 (omegaSp) => 77.78/10.61 (( 77.78/10.61 (omegaSclos) => 77.78/10.61 (( 77.78/10.61 (peano0notS) => 77.78/10.61 (( 77.78/10.61 (peanoSinj) => 77.78/10.61 (( 77.78/10.61 (transitivesetOp1) => 77.78/10.61 (( 77.78/10.61 (binintTransitive) => 77.78/10.61 (( 77.78/10.61 (transitivesetOp2) => 77.78/10.61 (( 77.78/10.61 (setunionTransitive) => 77.78/10.61 (( 77.78/10.61 (ordinalMinLem1) => 77.78/10.61 (( 77.78/10.61 (!!) @ ( 77.78/10.61 ^[Y0 : $i]: 77.78/10.61 (( 77.78/10.61 (ordinal @ 77.78/10.61 Y0) => 77.78/10.61 (( 77.78/10.61 (!!) @ ( 77.78/10.61 ^[Y1 : $i]: 77.78/10.61 (( 77.78/10.61 (!!) @ ( 77.78/10.61 ^[Y2 : $i]: 77.78/10.61 (( 77.78/10.61 (in @ 77.78/10.61 Y2 @ 77.78/10.61 Y0) => 77.78/10.61 (( 77.78/10.61 (in @ 77.78/10.61 Y1 @ 77.78/10.61 Y2) => 77.78/10.61 (in @ 77.78/10.61 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 77.78/10.61 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl508])). 77.78/10.61 thf(zip_derived_cl523, plain, 77.78/10.61 (~ (((notdallE) => 77.78/10.61 (((exuI1) => 77.78/10.61 (((exuI3) => 77.78/10.61 (((exuI2) => 77.78/10.61 (((inCongP) => 77.78/10.61 (((in__Cong) => 77.78/10.61 (((exuE3u) => 77.78/10.61 (((exu__Cong) => 77.78/10.61 (((setadjoin__Cong) => 77.78/10.61 (((powerset__Cong) => 77.78/10.61 (((setunion__Cong) => 77.78/10.61 (((exuEu) => 77.78/10.61 (((descr__Cong) => 77.78/10.61 (((dsetconstr__Cong) => 77.78/10.61 (((subsetI1) => 77.78/10.61 (((eqimpsubset2) => 77.78/10.61 (((eqimpsubset1) => 77.78/10.61 (((subsetI2) => 77.78/10.61 (((emptysetsubset) => 77.78/10.61 (((subsetE) => 77.78/10.61 (((subsetE2) => 77.78/10.61 (((notsubsetI) => 77.78/10.61 (((notequalI1) => 77.78/10.61 (((notequalI2) => 77.78/10.61 (((subsetRefl) => 77.78/10.61 (((subsetTrans) => 77.78/10.61 (((setadjoinSub) => 77.78/10.61 (((setadjoinSub2) => 77.78/10.61 (((subset2powerset) => 77.78/10.61 (((setextsub) => 77.78/10.61 (( 77.78/10.61 (subsetemptysetimpeq) => 77.78/10.61 (( 77.78/10.61 (powersetI1) => 77.78/10.61 (( 77.78/10.61 (powersetE1) => 77.78/10.61 (( 77.78/10.61 (inPowerset) => 77.78/10.61 (( 77.78/10.61 (powersetsubset) => 77.78/10.61 (( 77.78/10.61 (sepInPowerset) => 77.78/10.61 (( 77.78/10.61 (sepSubset) => 77.78/10.61 (( 77.78/10.61 (binunionIL) => 77.78/10.61 (( 77.78/10.61 (upairset2IR) => 77.78/10.61 (( 77.78/10.61 (binunionIR) => 77.78/10.61 (( 77.78/10.61 (binunionEcases) => 77.78/10.61 (( 77.78/10.61 (binunionE) => 77.78/10.61 (( 77.78/10.61 (binunionLsub) => 77.78/10.61 (( 77.78/10.61 (binunionRsub) => 77.78/10.61 (( 77.78/10.61 (binintersectI) => 77.78/10.61 (( 77.78/10.61 (binintersectSubset5) => 77.78/10.61 (( 77.78/10.61 (binintersectEL) => 77.78/10.61 (( 77.78/10.61 (binintersectLsub) => 77.78/10.61 (( 77.78/10.61 (binintersectSubset2) => 77.78/10.61 (( 77.78/10.61 (binintersectSubset3) => 77.78/10.61 (( 77.78/10.61 (binintersectER) => 77.78/10.61 (( 77.78/10.61 (disjointsetsI1) => 77.78/10.61 (( 77.78/10.61 (binintersectRsub) => 77.78/10.61 (( 77.78/10.61 (binintersectSubset4) => 77.78/10.61 (( 77.78/10.61 (binintersectSubset1) => 77.78/10.61 (( 77.78/10.61 (bs114d) => 77.78/10.61 (( 77.78/10.61 (setminusI) => 77.78/10.61 (( 77.78/10.61 (setminusEL) => 77.78/10.61 (( 77.78/10.61 (setminusER) => 77.78/10.61 (( 77.78/10.61 (setminusSubset2) => 77.78/10.61 (( 77.78/10.61 (setminusERneg) => 77.78/10.61 (( 77.78/10.61 (setminusELneg) => 77.78/10.61 (( 77.78/10.61 (setminusILneg) => 77.78/10.61 (( 77.78/10.61 (setminusIRneg) => 77.78/10.61 (( 77.78/10.61 (setminusLsub) => 77.78/10.61 (( 77.78/10.61 (setminusSubset1) => 77.78/10.61 (( 77.78/10.61 (symdiffE) => 77.78/10.61 (( 77.78/10.61 (symdiffI1) => 77.78/10.61 (( 77.78/10.61 (symdiffI2) => 77.78/10.61 (( 77.78/10.61 (symdiffIneg1) => 77.78/10.61 (( 77.78/10.61 (symdiffIneg2) => 77.78/10.61 (( 77.78/10.61 (secondinupair) => 77.78/10.61 (( 77.78/10.61 (setukpairIL) => 77.78/10.61 (( 77.78/10.61 (setukpairIR) => 77.78/10.61 (( 77.78/10.61 (kpairiskpair) => 77.78/10.61 (( 77.78/10.61 (kpairp) => 77.78/10.61 (( 77.78/10.61 (singletonsubset) => 77.78/10.61 (( 77.78/10.61 (singletoninpowerset) => 77.78/10.61 (( 77.78/10.61 (singletoninpowunion) => 77.78/10.61 (( 77.78/10.61 (upairset2E) => 77.78/10.61 (( 77.78/10.61 (upairsubunion) => 77.78/10.61 (( 77.78/10.61 (upairinpowunion) => 77.78/10.61 (( 77.78/10.61 (ubforcartprodlem1) => 77.78/10.61 (( 77.78/10.61 (ubforcartprodlem2) => 77.78/10.61 (( 77.78/10.61 (ubforcartprodlem3) => 77.78/10.61 (( 77.78/10.61 (cartprodpairin) => 77.78/10.61 (( 77.78/10.61 (cartprodmempair1) => 77.78/10.61 (( 77.78/10.61 (cartprodmempair) => 77.78/10.61 (( 77.78/10.61 (setunionE2) => 77.78/10.61 (( 77.78/10.61 (setunionsingleton1) => 77.78/10.61 (( 77.78/10.61 (setunionsingleton2) => 77.78/10.61 (( 77.78/10.61 (setunionsingleton) => 77.78/10.61 (( 77.78/10.61 (singletonprop) => 77.78/10.61 (( 77.78/10.61 (ex1E1) => 77.78/10.61 (( 77.78/10.61 (ex1I) => 77.78/10.61 (( 77.78/10.61 (ex1I2) => 77.78/10.61 (( 77.78/10.61 (singletonsuniq) => 77.78/10.61 (( 77.78/10.61 (setukpairinjL1) => 77.78/10.61 (( 77.78/10.61 (kfstsingleton) => 77.78/10.61 (( 77.78/10.61 (theprop) => 77.78/10.61 (( 77.78/10.61 (kfstpairEq) => 77.78/10.61 (( 77.78/10.61 (cartprodfstin) => 77.78/10.61 (( 77.78/10.61 (setukpairinjL2) => 77.78/10.61 (( 77.78/10.61 (setukpairinjL) => 77.78/10.61 (( 77.78/10.61 (setukpairinjR11) => 77.78/10.61 (( 77.78/10.61 (setukpairinjR12) => 77.78/10.61 (( 77.78/10.61 (setukpairinjR1) => 77.78/10.61 (( 77.78/10.61 (upairequniteq) => 77.78/10.61 (( 77.78/10.61 (setukpairinjR2) => 77.78/10.61 (( 77.78/10.61 (setukpairinjR) => 77.78/10.61 (( 77.78/10.61 (ksndsingleton) => 77.78/10.61 (( 77.78/10.61 (ksndpairEq) => 77.78/10.61 (( 77.78/10.61 (kpairsurjEq) => 77.78/10.61 (( 77.78/10.61 (cartprodsndin) => 77.78/10.61 (( 77.78/10.61 (cartprodpairmemEL) => 77.78/10.61 (( 77.78/10.61 (cartprodpairmemER) => 77.78/10.61 (( 77.78/10.61 (cartprodmempaircEq) => 77.78/10.61 (( 77.78/10.61 (cartprodfstpairEq) => 77.78/10.61 (( 77.78/10.61 (cartprodsndpairEq) => 77.78/10.61 (( 77.78/10.61 (cartprodpairsurjEq) => 77.78/10.61 (( 77.78/10.61 (dpsetconstrI) => 77.78/10.61 (( 77.78/10.61 (dpsetconstrSub) => 77.78/10.61 (( 77.78/10.61 (setOfPairsIsBReln) => 77.78/10.61 (( 77.78/10.61 (dpsetconstrERa) => 77.78/10.61 (( 77.78/10.61 (dpsetconstrEL1) => 77.78/10.61 (( 77.78/10.61 (dpsetconstrEL2) => 77.78/10.61 (( 77.78/10.61 (dpsetconstrER) => 77.78/10.61 (( 77.78/10.61 (funcImageSingleton) => 77.78/10.61 (( 77.78/10.61 (apProp) => 77.78/10.61 (( 77.78/10.61 (app) => 77.78/10.61 (( 77.78/10.61 (infuncsetfunc) => 77.78/10.61 (( 77.78/10.61 (ap2p) => 77.78/10.61 (( 77.78/10.61 (funcinfuncset) => 77.78/10.61 (( 77.78/10.61 (lamProp) => 77.78/10.61 (( 77.78/10.61 (lamp) => 77.78/10.61 (( 77.78/10.61 (lam2p) => 77.78/10.61 (( 77.78/10.61 (brelnall1) => 77.78/10.61 (( 77.78/10.61 (brelnall2) => 77.78/10.61 (( 77.78/10.61 (ex1E2) => 77.78/10.61 (( 77.78/10.61 (funcGraphProp1) => 77.78/10.61 (( 77.78/10.61 (funcGraphProp3) => 77.78/10.61 (( 77.78/10.61 (funcGraphProp2) => 77.78/10.61 (( 77.78/10.61 (funcextLem) => 77.78/10.61 (( 77.78/10.61 (funcGraphProp4) => 77.78/10.61 (( 77.78/10.61 (subbreln) => 77.78/10.61 (( 77.78/10.61 (eqbreln) => 77.78/10.61 (( 77.78/10.61 (funcext) => 77.78/10.61 (( 77.78/10.61 (funcext2) => 77.78/10.61 (( 77.78/10.61 (ap2apEq1) => 77.78/10.61 (( 77.78/10.61 (ap2apEq2) => 77.78/10.61 (( 77.78/10.61 (beta1) => 77.78/10.61 (( 77.78/10.61 (eta1) => 77.78/10.61 (( 77.78/10.61 (lam2lamEq) => 77.78/10.61 (( 77.78/10.61 (beta2) => 77.78/10.61 (( 77.78/10.61 (eta2) => 77.78/10.61 (( 77.78/10.61 (iffalseProp1) => 77.78/10.61 (( 77.78/10.61 (iffalseProp2) => 77.78/10.61 (( 77.78/10.61 (iftrueProp1) => 77.78/10.61 (( 77.78/10.61 (iftrueProp2) => 77.78/10.61 (( 77.78/10.61 (ifSingleton) => 77.78/10.61 (( 77.78/10.61 (ifp) => 77.78/10.61 (( 77.78/10.61 (theeq) => 77.78/10.61 (( 77.78/10.61 (iftrue) => 77.78/10.61 (( 77.78/10.61 (iffalse) => 77.78/10.61 (( 77.78/10.61 (iftrueorfalse) => 77.78/10.61 (( 77.78/10.61 (binintersectT_lem) => 77.78/10.61 (( 77.78/10.61 (binunionT_lem) => 77.78/10.61 (( 77.78/10.61 (powersetT_lem) => 77.78/10.61 (( 77.78/10.61 (setminusT_lem) => 77.78/10.61 (( 77.78/10.61 (complementT_lem) => 77.78/10.61 (( 77.78/10.61 (setextT) => 77.78/10.61 (( 77.78/10.61 (subsetTI) => 77.78/10.61 (( 77.78/10.61 (powersetTI1) => 77.78/10.61 (( 77.78/10.61 (powersetTE1) => 77.78/10.61 (( 77.78/10.61 (complementTI1) => 77.78/10.61 (( 77.78/10.61 (complementTE1) => 77.78/10.61 (( 77.78/10.61 (binintersectTELcontra) => 77.78/10.61 (( 77.78/10.61 (binintersectTERcontra) => 77.78/10.61 (( 77.78/10.61 (contrasubsetT) => 77.78/10.61 (( 77.78/10.61 (contrasubsetT1) => 77.78/10.61 (( 77.78/10.61 (contrasubsetT2) => 77.78/10.61 (( 77.78/10.61 (contrasubsetT3) => 77.78/10.61 (( 77.78/10.61 (doubleComplementI1) => 77.78/10.61 (( 77.78/10.61 (doubleComplementE1) => 77.78/10.61 (( 77.78/10.61 (doubleComplementSub1) => 77.78/10.61 (( 77.78/10.61 (doubleComplementSub2) => 77.78/10.61 (( 77.78/10.61 (doubleComplementEq) => 77.78/10.61 (( 77.78/10.61 (complementTnotintersectT) => 77.78/10.61 (( 77.78/10.61 (complementImpComplementIntersect) => 77.78/10.61 (( 77.78/10.61 (complementSubsetComplementIntersect) => 77.78/10.61 (( 77.78/10.61 (complementInPowersetComplementIntersect) => 77.78/10.61 (( 77.78/10.61 (contraSubsetComplement) => 77.78/10.61 (( 77.78/10.61 (complementTcontraSubset) => 77.78/10.61 (( 77.78/10.61 (binunionTILcontra) => 77.78/10.61 (( 77.78/10.61 (binunionTIRcontra) => 77.78/10.61 (( 77.78/10.61 (inIntersectImpInUnion) => 77.78/10.61 (( 77.78/10.61 (inIntersectImpInUnion2) => 77.78/10.61 (( 77.78/10.61 (inIntersectImpInIntersectUnions) => 77.78/10.61 (( 77.78/10.61 (intersectInPowersetIntersectUnions) => 77.78/10.61 (( 77.78/10.61 (inComplementUnionImpNotIn1) => 77.78/10.61 (( 77.78/10.61 (inComplementUnionImpInComplement1) => 77.78/10.61 (( 77.78/10.61 (binunionTE) => 77.78/10.61 (( 77.78/10.61 (binunionTEcontra) => 77.78/10.61 (( 77.78/10.61 (demorgan2a1) => 77.78/10.61 (( 77.78/10.61 (complementUnionInPowersetComplement) => 77.78/10.61 (( 77.78/10.61 (demorgan2a2) => 77.78/10.61 (( 77.78/10.61 (demorgan1a) => 77.78/10.61 (( 77.78/10.61 (demorgan1b) => 77.78/10.61 (( 77.78/10.61 (demorgan1) => 77.78/10.61 (( 77.78/10.61 (demorgan2a) => 77.78/10.61 (( 77.78/10.61 (demorgan2b2) => 77.78/10.61 (( 77.78/10.61 (demorgan2b) => 77.78/10.61 (( 77.78/10.61 (demorgan2) => 77.78/10.61 (( 77.78/10.61 (woz13rule0) => 77.78/10.61 (( 77.78/10.61 (woz13rule1) => 77.78/10.61 (( 77.78/10.61 (woz13rule2) => 77.78/10.61 (( 77.78/10.61 (woz13rule3) => 77.78/10.61 (( 77.78/10.61 (woz13rule4) => 77.78/10.61 (( 77.78/10.61 (woz1_1) => 77.78/10.61 (( 77.78/10.61 (woz1_2) => 77.78/10.61 (( 77.78/10.61 (woz1_3) => 77.78/10.61 (( 77.78/10.61 (woz1_4) => 77.78/10.61 (( 77.78/10.61 (woz1_5) => 77.78/10.61 (( 77.78/10.61 (breln1all2) => 77.78/10.61 (( 77.78/10.61 (breln1SetBreln1) => 77.78/10.61 (( 77.78/10.61 (choice2fnsingleton) => 77.78/10.61 (( 77.78/10.61 (setOfPairsIsBReln1) => 77.78/10.61 (( 77.78/10.61 (breln1all1) => 77.78/10.61 (( 77.78/10.61 (subbreln1) => 77.78/10.61 (( 77.78/10.61 (eqbreln1) => 77.78/10.61 (( 77.78/10.61 (breln1invprop) => 77.78/10.61 (( 77.78/10.61 (breln1invI) => 77.78/10.61 (( 77.78/10.61 (breln1invE) => 77.78/10.61 (( 77.78/10.61 (breln1compprop) => 77.78/10.61 (( 77.78/10.61 (breln1compI) => 77.78/10.61 (( 77.78/10.61 (breln1compE) => 77.78/10.61 (( 77.78/10.61 (breln1compEex) => 77.78/10.61 (( 77.78/10.61 (breln1unionprop) => 77.78/10.61 (( 77.78/10.61 (breln1unionIL) => 77.78/10.61 (( 77.78/10.61 (breln1unionIR) => 77.78/10.61 (( 77.78/10.61 (breln1unionI) => 77.78/10.61 (( 77.78/10.61 (breln1unionE) => 77.78/10.61 (( 77.78/10.61 (breln1unionEcases) => 77.78/10.61 (( 77.78/10.61 (breln1unionCommutes) => 77.78/10.61 (( 77.78/10.61 (woz2Ex) => 77.78/10.61 (( 77.78/10.61 (woz2W) => 77.78/10.61 (( 77.78/10.61 (woz2A) => 77.78/10.61 (( 77.78/10.61 (woz2B) => 77.78/10.61 (( 77.78/10.61 (image1Ex) => 77.78/10.61 (( 77.78/10.61 (image1Ex1) => 77.78/10.61 (( 77.78/10.61 (image1Equiv) => 77.78/10.61 (( 77.78/10.61 (image1E) => 77.78/10.61 (( 77.78/10.61 (image1I) => 77.78/10.61 (( 77.78/10.61 (injFuncInInjFuncSet) => 77.78/10.61 (( 77.78/10.61 (injFuncSetFuncIn) => 77.78/10.61 (( 77.78/10.61 (injFuncSetFuncInj) => 77.78/10.61 (( 77.78/10.61 (surjFuncSetFuncIn) => 77.78/10.61 (( 77.78/10.61 (surjFuncSetFuncSurj) => 77.78/10.61 (( 77.78/10.61 (leftInvIsSurj) => 77.78/10.61 (( 77.78/10.61 (surjCantorThm) => 77.78/10.61 (( 77.78/10.61 (foundation2) => 77.78/10.61 (( 77.78/10.61 (notinself) => 77.78/10.61 (( 77.78/10.61 (notinself2) => 77.78/10.61 (( 77.78/10.61 (omegaSp) => 77.78/10.61 (( 77.78/10.61 (omegaSclos) => 77.78/10.61 (( 77.78/10.61 (peano0notS) => 77.78/10.61 (( 77.78/10.61 (peanoSinj) => 77.78/10.61 (( 77.78/10.61 (transitivesetOp1) => 77.78/10.61 (( 77.78/10.61 (binintTransitive) => 77.78/10.61 (( 77.78/10.61 (transitivesetOp2) => 77.78/10.61 (( 77.78/10.61 (setunionTransitive) => 77.78/10.61 (( 77.78/10.61 (ordinalMinLem1) => 77.78/10.61 (( 77.78/10.61 (!!) @ ( 77.78/10.61 ^[Y0 : $i]: 77.78/10.61 (( 77.78/10.61 (ordinal @ 77.78/10.61 Y0) => 77.78/10.61 (( 77.78/10.61 (!!) @ ( 77.78/10.61 ^[Y1 : $i]: 77.78/10.61 (( 77.78/10.61 (!!) @ ( 77.78/10.61 ^[Y2 : $i]: 77.78/10.61 (( 77.78/10.61 (in @ 77.78/10.61 Y2 @ 77.78/10.61 Y0) => 77.78/10.61 (( 77.78/10.61 (in @ 77.78/10.61 Y1 @ 77.78/10.61 Y2) => 77.78/10.61 (in @ 77.78/10.61 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 77.78/10.61 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl515])). 77.78/10.61 thf(zip_derived_cl535, plain, 77.78/10.61 (~ (((exuI1) => 77.78/10.61 (((exuI3) => 77.78/10.61 (((exuI2) => 77.78/10.61 (((inCongP) => 77.78/10.61 (((in__Cong) => 77.78/10.61 (((exuE3u) => 77.78/10.61 (((exu__Cong) => 77.78/10.61 (((setadjoin__Cong) => 77.78/10.61 (((powerset__Cong) => 77.78/10.61 (((setunion__Cong) => 77.78/10.61 (((exuEu) => 77.78/10.61 (((descr__Cong) => 77.78/10.61 (((dsetconstr__Cong) => 77.78/10.61 (((subsetI1) => 77.78/10.61 (((eqimpsubset2) => 77.78/10.61 (((eqimpsubset1) => 77.78/10.61 (((subsetI2) => 77.78/10.61 (((emptysetsubset) => 77.78/10.61 (((subsetE) => 77.78/10.61 (((subsetE2) => 77.78/10.61 (((notsubsetI) => 77.78/10.61 (((notequalI1) => 77.78/10.61 (((notequalI2) => 77.78/10.61 (((subsetRefl) => 77.78/10.61 (((subsetTrans) => 77.78/10.61 (((setadjoinSub) => 77.78/10.61 (((setadjoinSub2) => 77.78/10.61 (((subset2powerset) => 77.78/10.61 (((setextsub) => 77.78/10.61 (((subsetemptysetimpeq) => 77.78/10.61 (( 77.78/10.61 (powersetI1) => 77.78/10.61 (( 77.78/10.61 (powersetE1) => 77.78/10.61 (( 77.78/10.61 (inPowerset) => 77.78/10.61 (( 77.78/10.61 (powersetsubset) => 77.78/10.61 (( 77.78/10.61 (sepInPowerset) => 77.78/10.61 (( 77.78/10.61 (sepSubset) => 77.78/10.61 (( 77.78/10.61 (binunionIL) => 77.78/10.61 (( 77.78/10.61 (upairset2IR) => 77.78/10.61 (( 77.78/10.61 (binunionIR) => 77.78/10.61 (( 77.78/10.61 (binunionEcases) => 77.78/10.61 (( 77.78/10.61 (binunionE) => 77.78/10.61 (( 77.78/10.61 (binunionLsub) => 77.78/10.61 (( 77.78/10.61 (binunionRsub) => 77.78/10.61 (( 77.78/10.61 (binintersectI) => 77.78/10.61 (( 77.78/10.61 (binintersectSubset5) => 77.78/10.61 (( 77.78/10.61 (binintersectEL) => 77.78/10.61 (( 77.78/10.61 (binintersectLsub) => 77.78/10.61 (( 77.78/10.61 (binintersectSubset2) => 77.78/10.61 (( 77.78/10.61 (binintersectSubset3) => 77.78/10.61 (( 77.78/10.61 (binintersectER) => 77.78/10.61 (( 77.78/10.61 (disjointsetsI1) => 77.78/10.61 (( 77.78/10.61 (binintersectRsub) => 77.78/10.61 (( 77.78/10.61 (binintersectSubset4) => 77.78/10.61 (( 77.78/10.61 (binintersectSubset1) => 77.78/10.61 (( 77.78/10.61 (bs114d) => 77.78/10.61 (( 77.78/10.61 (setminusI) => 77.78/10.61 (( 77.78/10.61 (setminusEL) => 77.78/10.61 (( 77.78/10.61 (setminusER) => 77.78/10.61 (( 77.78/10.61 (setminusSubset2) => 77.78/10.61 (( 77.78/10.61 (setminusERneg) => 77.78/10.61 (( 77.78/10.61 (setminusELneg) => 77.78/10.61 (( 77.78/10.61 (setminusILneg) => 77.78/10.61 (( 77.78/10.61 (setminusIRneg) => 77.78/10.61 (( 77.78/10.61 (setminusLsub) => 77.78/10.61 (( 77.78/10.61 (setminusSubset1) => 77.78/10.61 (( 77.78/10.61 (symdiffE) => 77.78/10.61 (( 77.78/10.61 (symdiffI1) => 77.78/10.61 (( 77.78/10.61 (symdiffI2) => 77.78/10.61 (( 77.78/10.61 (symdiffIneg1) => 77.78/10.61 (( 77.78/10.61 (symdiffIneg2) => 77.78/10.61 (( 77.78/10.61 (secondinupair) => 77.78/10.61 (( 77.78/10.61 (setukpairIL) => 77.78/10.61 (( 77.78/10.61 (setukpairIR) => 77.78/10.61 (( 77.78/10.61 (kpairiskpair) => 77.78/10.61 (( 77.78/10.61 (kpairp) => 77.78/10.61 (( 77.78/10.61 (singletonsubset) => 77.78/10.61 (( 77.78/10.61 (singletoninpowerset) => 77.78/10.61 (( 77.78/10.61 (singletoninpowunion) => 77.78/10.61 (( 77.78/10.61 (upairset2E) => 77.78/10.61 (( 77.78/10.61 (upairsubunion) => 77.78/10.61 (( 77.78/10.61 (upairinpowunion) => 77.78/10.61 (( 77.78/10.61 (ubforcartprodlem1) => 77.78/10.62 (( 77.78/10.62 (ubforcartprodlem2) => 77.78/10.62 (( 77.78/10.62 (ubforcartprodlem3) => 77.78/10.62 (( 77.78/10.62 (cartprodpairin) => 77.78/10.62 (( 77.78/10.62 (cartprodmempair1) => 77.78/10.62 (( 77.78/10.62 (cartprodmempair) => 77.78/10.62 (( 77.78/10.62 (setunionE2) => 77.78/10.62 (( 77.78/10.62 (setunionsingleton1) => 77.78/10.62 (( 77.78/10.62 (setunionsingleton2) => 77.78/10.62 (( 77.78/10.62 (setunionsingleton) => 77.78/10.62 (( 77.78/10.62 (singletonprop) => 77.78/10.62 (( 77.78/10.62 (ex1E1) => 77.78/10.62 (( 77.78/10.62 (ex1I) => 77.78/10.62 (( 77.78/10.62 (ex1I2) => 77.78/10.62 (( 77.78/10.62 (singletonsuniq) => 77.78/10.62 (( 77.78/10.62 (setukpairinjL1) => 77.78/10.62 (( 77.78/10.62 (kfstsingleton) => 77.78/10.62 (( 77.78/10.62 (theprop) => 77.78/10.62 (( 77.78/10.62 (kfstpairEq) => 77.78/10.62 (( 77.78/10.62 (cartprodfstin) => 77.78/10.62 (( 77.78/10.62 (setukpairinjL2) => 77.78/10.62 (( 77.78/10.62 (setukpairinjL) => 77.78/10.62 (( 77.78/10.62 (setukpairinjR11) => 77.78/10.62 (( 77.78/10.62 (setukpairinjR12) => 77.78/10.62 (( 77.78/10.62 (setukpairinjR1) => 77.78/10.62 (( 77.78/10.62 (upairequniteq) => 77.78/10.62 (( 77.78/10.62 (setukpairinjR2) => 77.78/10.62 (( 77.78/10.62 (setukpairinjR) => 77.78/10.62 (( 77.78/10.62 (ksndsingleton) => 77.78/10.62 (( 77.78/10.62 (ksndpairEq) => 77.78/10.62 (( 77.78/10.62 (kpairsurjEq) => 77.78/10.62 (( 77.78/10.62 (cartprodsndin) => 77.78/10.62 (( 77.78/10.62 (cartprodpairmemEL) => 77.78/10.62 (( 77.78/10.62 (cartprodpairmemER) => 77.78/10.62 (( 77.78/10.62 (cartprodmempaircEq) => 77.78/10.62 (( 77.78/10.62 (cartprodfstpairEq) => 77.78/10.62 (( 77.78/10.62 (cartprodsndpairEq) => 77.78/10.62 (( 77.78/10.62 (cartprodpairsurjEq) => 77.78/10.62 (( 77.78/10.62 (dpsetconstrI) => 77.78/10.62 (( 77.78/10.62 (dpsetconstrSub) => 77.78/10.62 (( 77.78/10.62 (setOfPairsIsBReln) => 77.78/10.62 (( 77.78/10.62 (dpsetconstrERa) => 77.78/10.62 (( 77.78/10.62 (dpsetconstrEL1) => 77.78/10.62 (( 77.78/10.62 (dpsetconstrEL2) => 77.78/10.62 (( 77.78/10.62 (dpsetconstrER) => 77.78/10.62 (( 77.78/10.62 (funcImageSingleton) => 77.78/10.62 (( 77.78/10.62 (apProp) => 77.78/10.62 (( 77.78/10.62 (app) => 77.78/10.62 (( 77.78/10.62 (infuncsetfunc) => 77.78/10.62 (( 77.78/10.62 (ap2p) => 77.78/10.62 (( 77.78/10.62 (funcinfuncset) => 77.78/10.62 (( 77.78/10.62 (lamProp) => 77.78/10.62 (( 77.78/10.62 (lamp) => 77.78/10.62 (( 77.78/10.62 (lam2p) => 77.78/10.62 (( 77.78/10.62 (brelnall1) => 77.78/10.62 (( 77.78/10.62 (brelnall2) => 77.78/10.62 (( 77.78/10.62 (ex1E2) => 77.78/10.62 (( 77.78/10.62 (funcGraphProp1) => 77.78/10.62 (( 77.78/10.62 (funcGraphProp3) => 77.78/10.62 (( 77.78/10.62 (funcGraphProp2) => 77.78/10.62 (( 77.78/10.62 (funcextLem) => 77.78/10.62 (( 77.78/10.62 (funcGraphProp4) => 77.78/10.62 (( 77.78/10.62 (subbreln) => 77.78/10.62 (( 77.78/10.62 (eqbreln) => 77.78/10.62 (( 77.78/10.62 (funcext) => 77.78/10.62 (( 77.78/10.62 (funcext2) => 77.78/10.62 (( 77.78/10.62 (ap2apEq1) => 77.78/10.62 (( 77.78/10.62 (ap2apEq2) => 77.78/10.62 (( 77.78/10.62 (beta1) => 77.78/10.62 (( 77.78/10.62 (eta1) => 77.78/10.62 (( 77.78/10.62 (lam2lamEq) => 77.78/10.62 (( 77.78/10.62 (beta2) => 77.78/10.62 (( 77.78/10.62 (eta2) => 77.78/10.62 (( 77.78/10.62 (iffalseProp1) => 77.78/10.62 (( 77.78/10.62 (iffalseProp2) => 77.78/10.62 (( 77.78/10.62 (iftrueProp1) => 77.78/10.62 (( 77.78/10.62 (iftrueProp2) => 77.78/10.62 (( 77.78/10.62 (ifSingleton) => 77.78/10.62 (( 77.78/10.62 (ifp) => 77.78/10.62 (( 77.78/10.62 (theeq) => 77.78/10.62 (( 77.78/10.62 (iftrue) => 77.78/10.62 (( 77.78/10.62 (iffalse) => 77.78/10.62 (( 77.78/10.62 (iftrueorfalse) => 77.78/10.62 (( 77.78/10.62 (binintersectT_lem) => 77.78/10.62 (( 77.78/10.62 (binunionT_lem) => 77.78/10.62 (( 77.78/10.62 (powersetT_lem) => 77.78/10.62 (( 77.78/10.62 (setminusT_lem) => 77.78/10.62 (( 77.78/10.62 (complementT_lem) => 77.78/10.62 (( 77.78/10.62 (setextT) => 77.78/10.62 (( 77.78/10.62 (subsetTI) => 77.78/10.62 (( 77.78/10.62 (powersetTI1) => 77.78/10.62 (( 77.78/10.62 (powersetTE1) => 77.78/10.62 (( 77.78/10.62 (complementTI1) => 77.78/10.62 (( 77.78/10.62 (complementTE1) => 77.78/10.62 (( 77.78/10.62 (binintersectTELcontra) => 77.78/10.62 (( 77.78/10.62 (binintersectTERcontra) => 77.78/10.62 (( 77.78/10.62 (contrasubsetT) => 77.78/10.62 (( 77.78/10.62 (contrasubsetT1) => 77.78/10.62 (( 77.78/10.62 (contrasubsetT2) => 77.78/10.62 (( 77.78/10.62 (contrasubsetT3) => 77.78/10.62 (( 77.78/10.62 (doubleComplementI1) => 77.78/10.62 (( 77.78/10.62 (doubleComplementE1) => 77.78/10.62 (( 77.78/10.62 (doubleComplementSub1) => 77.78/10.62 (( 77.78/10.62 (doubleComplementSub2) => 77.78/10.62 (( 77.78/10.62 (doubleComplementEq) => 77.78/10.62 (( 77.78/10.62 (complementTnotintersectT) => 77.78/10.62 (( 77.78/10.62 (complementImpComplementIntersect) => 77.78/10.62 (( 77.78/10.62 (complementSubsetComplementIntersect) => 77.78/10.62 (( 77.78/10.62 (complementInPowersetComplementIntersect) => 77.78/10.62 (( 77.78/10.62 (contraSubsetComplement) => 77.78/10.62 (( 77.78/10.62 (complementTcontraSubset) => 77.78/10.62 (( 77.78/10.62 (binunionTILcontra) => 77.78/10.62 (( 77.78/10.62 (binunionTIRcontra) => 77.78/10.62 (( 77.78/10.62 (inIntersectImpInUnion) => 77.78/10.62 (( 77.78/10.62 (inIntersectImpInUnion2) => 77.78/10.62 (( 77.78/10.62 (inIntersectImpInIntersectUnions) => 77.78/10.62 (( 77.78/10.62 (intersectInPowersetIntersectUnions) => 77.78/10.62 (( 77.78/10.62 (inComplementUnionImpNotIn1) => 77.78/10.62 (( 77.78/10.62 (inComplementUnionImpInComplement1) => 77.78/10.62 (( 77.78/10.62 (binunionTE) => 77.78/10.62 (( 77.78/10.62 (binunionTEcontra) => 77.78/10.62 (( 77.78/10.62 (demorgan2a1) => 77.78/10.62 (( 77.78/10.62 (complementUnionInPowersetComplement) => 77.78/10.62 (( 77.78/10.62 (demorgan2a2) => 77.78/10.62 (( 77.78/10.62 (demorgan1a) => 77.78/10.62 (( 77.78/10.62 (demorgan1b) => 77.78/10.62 (( 77.78/10.62 (demorgan1) => 77.78/10.62 (( 77.78/10.62 (demorgan2a) => 77.78/10.62 (( 77.78/10.62 (demorgan2b2) => 77.78/10.62 (( 77.78/10.62 (demorgan2b) => 77.78/10.62 (( 77.78/10.62 (demorgan2) => 77.78/10.62 (( 77.78/10.62 (woz13rule0) => 77.78/10.62 (( 77.78/10.62 (woz13rule1) => 77.78/10.62 (( 77.78/10.62 (woz13rule2) => 77.78/10.62 (( 77.78/10.62 (woz13rule3) => 77.78/10.62 (( 77.78/10.62 (woz13rule4) => 77.78/10.62 (( 77.78/10.62 (woz1_1) => 77.78/10.62 (( 77.78/10.62 (woz1_2) => 77.78/10.62 (( 77.78/10.62 (woz1_3) => 77.78/10.62 (( 77.78/10.62 (woz1_4) => 77.78/10.62 (( 77.78/10.62 (woz1_5) => 77.78/10.62 (( 77.78/10.62 (breln1all2) => 77.78/10.62 (( 77.78/10.62 (breln1SetBreln1) => 77.78/10.62 (( 77.78/10.62 (choice2fnsingleton) => 77.78/10.62 (( 77.78/10.62 (setOfPairsIsBReln1) => 77.78/10.62 (( 77.78/10.62 (breln1all1) => 77.78/10.62 (( 77.78/10.62 (subbreln1) => 77.78/10.62 (( 77.78/10.62 (eqbreln1) => 77.78/10.62 (( 77.78/10.62 (breln1invprop) => 77.78/10.62 (( 77.78/10.62 (breln1invI) => 77.78/10.62 (( 77.78/10.62 (breln1invE) => 77.78/10.62 (( 77.78/10.62 (breln1compprop) => 77.78/10.62 (( 77.78/10.62 (breln1compI) => 77.78/10.62 (( 77.78/10.62 (breln1compE) => 77.78/10.62 (( 77.78/10.62 (breln1compEex) => 77.78/10.62 (( 77.78/10.62 (breln1unionprop) => 77.78/10.62 (( 77.78/10.62 (breln1unionIL) => 77.78/10.62 (( 77.78/10.62 (breln1unionIR) => 77.78/10.62 (( 77.78/10.62 (breln1unionI) => 77.78/10.62 (( 77.78/10.62 (breln1unionE) => 77.78/10.62 (( 77.78/10.62 (breln1unionEcases) => 77.78/10.62 (( 77.78/10.62 (breln1unionCommutes) => 77.78/10.62 (( 77.78/10.62 (woz2Ex) => 77.78/10.62 (( 77.78/10.62 (woz2W) => 77.78/10.62 (( 77.78/10.62 (woz2A) => 77.78/10.62 (( 77.78/10.62 (woz2B) => 77.78/10.62 (( 77.78/10.62 (image1Ex) => 77.78/10.62 (( 77.78/10.62 (image1Ex1) => 77.78/10.62 (( 77.78/10.62 (image1Equiv) => 77.78/10.62 (( 77.78/10.62 (image1E) => 77.78/10.62 (( 77.78/10.62 (image1I) => 77.78/10.62 (( 77.78/10.62 (injFuncInInjFuncSet) => 77.78/10.62 (( 77.78/10.62 (injFuncSetFuncIn) => 77.78/10.62 (( 77.78/10.62 (injFuncSetFuncInj) => 77.78/10.62 (( 77.78/10.62 (surjFuncSetFuncIn) => 77.78/10.62 (( 77.78/10.62 (surjFuncSetFuncSurj) => 77.78/10.62 (( 77.78/10.62 (leftInvIsSurj) => 77.78/10.62 (( 77.78/10.62 (surjCantorThm) => 77.78/10.62 (( 77.78/10.62 (foundation2) => 77.78/10.62 (( 77.78/10.62 (notinself) => 77.78/10.62 (( 77.78/10.62 (notinself2) => 77.78/10.62 (( 77.78/10.62 (omegaSp) => 77.78/10.62 (( 77.78/10.62 (omegaSclos) => 77.78/10.62 (( 77.78/10.62 (peano0notS) => 77.78/10.62 (( 77.78/10.62 (peanoSinj) => 77.78/10.62 (( 77.78/10.62 (transitivesetOp1) => 77.78/10.62 (( 77.78/10.62 (binintTransitive) => 77.78/10.62 (( 77.78/10.62 (transitivesetOp2) => 77.78/10.62 (( 77.78/10.62 (setunionTransitive) => 77.78/10.62 (( 77.78/10.62 (ordinalMinLem1) => 77.78/10.62 (( 77.78/10.62 (!!) @ ( 77.78/10.62 ^[Y0 : $i]: 77.78/10.62 (( 77.78/10.62 (ordinal @ 77.78/10.62 Y0) => 77.78/10.62 (( 77.78/10.62 (!!) @ ( 77.78/10.62 ^[Y1 : $i]: 77.78/10.62 (( 77.78/10.62 (!!) @ ( 77.78/10.62 ^[Y2 : $i]: 77.78/10.62 (( 77.78/10.62 (in @ 77.78/10.62 Y2 @ 77.78/10.62 Y0) => 77.78/10.62 (( 77.78/10.62 (in @ 77.78/10.62 Y1 @ 77.78/10.62 Y2) => 77.78/10.62 (in @ 77.78/10.62 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 77.78/10.62 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl523])). 77.78/10.62 thf(zip_derived_cl550, plain, 77.78/10.62 (~ (((exuI3) => 77.78/10.62 (((exuI2) => 77.78/10.62 (((inCongP) => 77.78/10.62 (((in__Cong) => 77.78/10.62 (((exuE3u) => 77.78/10.62 (((exu__Cong) => 77.78/10.62 (((setadjoin__Cong) => 77.78/10.62 (((powerset__Cong) => 77.78/10.62 (((setunion__Cong) => 77.78/10.62 (((exuEu) => 77.78/10.62 (((descr__Cong) => 77.78/10.62 (((dsetconstr__Cong) => 77.78/10.62 (((subsetI1) => 77.78/10.62 (((eqimpsubset2) => 77.78/10.62 (((eqimpsubset1) => 77.78/10.62 (((subsetI2) => 77.78/10.62 (((emptysetsubset) => 77.78/10.62 (((subsetE) => 77.78/10.62 (((subsetE2) => 77.78/10.62 (((notsubsetI) => 77.78/10.62 (((notequalI1) => 77.78/10.62 (((notequalI2) => 77.78/10.62 (((subsetRefl) => 77.78/10.62 (((subsetTrans) => 77.78/10.62 (((setadjoinSub) => 77.78/10.62 (((setadjoinSub2) => 77.78/10.62 (((subset2powerset) => 77.78/10.62 (((setextsub) => 77.78/10.62 (((subsetemptysetimpeq) => 77.78/10.62 (((powersetI1) => 77.78/10.62 (( 77.78/10.62 (powersetE1) => 77.78/10.62 (( 77.78/10.62 (inPowerset) => 77.78/10.62 (( 77.78/10.62 (powersetsubset) => 77.78/10.62 (( 77.78/10.62 (sepInPowerset) => 77.78/10.62 (( 77.78/10.62 (sepSubset) => 77.78/10.62 (( 77.78/10.62 (binunionIL) => 77.78/10.62 (( 77.78/10.62 (upairset2IR) => 77.78/10.62 (( 77.78/10.62 (binunionIR) => 77.78/10.62 (( 77.78/10.62 (binunionEcases) => 77.78/10.62 (( 77.78/10.62 (binunionE) => 77.78/10.62 (( 77.78/10.62 (binunionLsub) => 77.78/10.62 (( 77.78/10.62 (binunionRsub) => 77.78/10.62 (( 77.78/10.62 (binintersectI) => 77.78/10.62 (( 77.78/10.62 (binintersectSubset5) => 77.78/10.62 (( 77.78/10.62 (binintersectEL) => 77.78/10.62 (( 77.78/10.62 (binintersectLsub) => 77.78/10.62 (( 77.78/10.62 (binintersectSubset2) => 77.78/10.62 (( 77.78/10.62 (binintersectSubset3) => 77.78/10.62 (( 77.78/10.62 (binintersectER) => 77.78/10.62 (( 77.78/10.62 (disjointsetsI1) => 77.78/10.62 (( 77.78/10.62 (binintersectRsub) => 77.78/10.62 (( 77.78/10.62 (binintersectSubset4) => 77.78/10.62 (( 77.78/10.62 (binintersectSubset1) => 77.78/10.62 (( 77.78/10.62 (bs114d) => 77.78/10.62 (( 77.78/10.62 (setminusI) => 77.78/10.62 (( 77.78/10.62 (setminusEL) => 77.78/10.62 (( 77.78/10.62 (setminusER) => 77.78/10.62 (( 77.78/10.62 (setminusSubset2) => 77.78/10.62 (( 77.78/10.62 (setminusERneg) => 77.78/10.62 (( 77.78/10.62 (setminusELneg) => 77.78/10.62 (( 77.78/10.62 (setminusILneg) => 77.78/10.62 (( 77.78/10.62 (setminusIRneg) => 77.78/10.62 (( 77.78/10.62 (setminusLsub) => 77.78/10.62 (( 77.78/10.62 (setminusSubset1) => 77.78/10.62 (( 77.78/10.62 (symdiffE) => 77.78/10.62 (( 77.78/10.62 (symdiffI1) => 77.78/10.62 (( 77.78/10.62 (symdiffI2) => 77.78/10.62 (( 77.78/10.62 (symdiffIneg1) => 77.78/10.62 (( 77.78/10.62 (symdiffIneg2) => 77.78/10.62 (( 77.78/10.62 (secondinupair) => 77.78/10.62 (( 77.78/10.62 (setukpairIL) => 77.78/10.62 (( 77.78/10.62 (setukpairIR) => 77.78/10.62 (( 77.78/10.62 (kpairiskpair) => 77.78/10.62 (( 77.78/10.62 (kpairp) => 77.78/10.62 (( 77.78/10.62 (singletonsubset) => 77.78/10.62 (( 77.78/10.62 (singletoninpowerset) => 77.78/10.62 (( 77.78/10.62 (singletoninpowunion) => 77.78/10.62 (( 77.78/10.62 (upairset2E) => 77.78/10.62 (( 77.78/10.62 (upairsubunion) => 77.78/10.62 (( 77.78/10.62 (upairinpowunion) => 77.78/10.62 (( 77.78/10.62 (ubforcartprodlem1) => 77.78/10.62 (( 77.78/10.62 (ubforcartprodlem2) => 77.78/10.62 (( 77.78/10.62 (ubforcartprodlem3) => 77.78/10.62 (( 77.78/10.62 (cartprodpairin) => 77.78/10.62 (( 77.78/10.62 (cartprodmempair1) => 77.78/10.62 (( 77.78/10.62 (cartprodmempair) => 77.78/10.62 (( 77.78/10.62 (setunionE2) => 77.78/10.62 (( 77.78/10.62 (setunionsingleton1) => 77.78/10.62 (( 77.78/10.62 (setunionsingleton2) => 77.78/10.62 (( 77.78/10.62 (setunionsingleton) => 77.78/10.62 (( 77.78/10.62 (singletonprop) => 77.78/10.62 (( 77.78/10.62 (ex1E1) => 77.78/10.62 (( 77.78/10.62 (ex1I) => 77.78/10.62 (( 77.78/10.62 (ex1I2) => 77.78/10.62 (( 77.78/10.62 (singletonsuniq) => 77.78/10.62 (( 77.78/10.62 (setukpairinjL1) => 77.78/10.62 (( 77.78/10.62 (kfstsingleton) => 77.78/10.62 (( 77.78/10.62 (theprop) => 77.78/10.62 (( 77.78/10.62 (kfstpairEq) => 77.78/10.62 (( 77.78/10.62 (cartprodfstin) => 77.78/10.62 (( 77.78/10.62 (setukpairinjL2) => 77.78/10.62 (( 77.78/10.62 (setukpairinjL) => 77.78/10.62 (( 77.78/10.62 (setukpairinjR11) => 77.78/10.62 (( 77.78/10.62 (setukpairinjR12) => 77.78/10.62 (( 77.78/10.62 (setukpairinjR1) => 77.78/10.62 (( 77.78/10.62 (upairequniteq) => 77.78/10.62 (( 77.78/10.62 (setukpairinjR2) => 77.78/10.62 (( 77.78/10.62 (setukpairinjR) => 77.78/10.62 (( 77.78/10.62 (ksndsingleton) => 77.78/10.62 (( 77.78/10.62 (ksndpairEq) => 77.78/10.62 (( 77.78/10.62 (kpairsurjEq) => 77.78/10.62 (( 77.78/10.62 (cartprodsndin) => 77.78/10.62 (( 77.78/10.62 (cartprodpairmemEL) => 77.78/10.62 (( 77.78/10.62 (cartprodpairmemER) => 77.78/10.62 (( 77.78/10.62 (cartprodmempaircEq) => 77.78/10.62 (( 77.78/10.62 (cartprodfstpairEq) => 77.78/10.62 (( 77.78/10.62 (cartprodsndpairEq) => 77.78/10.62 (( 77.78/10.62 (cartprodpairsurjEq) => 77.78/10.62 (( 77.78/10.62 (dpsetconstrI) => 77.78/10.62 (( 77.78/10.62 (dpsetconstrSub) => 77.78/10.62 (( 77.78/10.62 (setOfPairsIsBReln) => 77.78/10.62 (( 77.78/10.62 (dpsetconstrERa) => 77.78/10.62 (( 77.78/10.62 (dpsetconstrEL1) => 77.78/10.62 (( 77.78/10.62 (dpsetconstrEL2) => 77.78/10.62 (( 77.78/10.62 (dpsetconstrER) => 77.78/10.62 (( 77.78/10.62 (funcImageSingleton) => 77.78/10.62 (( 77.78/10.62 (apProp) => 77.78/10.62 (( 77.78/10.62 (app) => 77.78/10.62 (( 77.78/10.62 (infuncsetfunc) => 77.78/10.62 (( 77.78/10.62 (ap2p) => 77.78/10.62 (( 77.78/10.62 (funcinfuncset) => 77.78/10.62 (( 77.78/10.62 (lamProp) => 77.78/10.62 (( 77.78/10.62 (lamp) => 77.78/10.62 (( 77.78/10.62 (lam2p) => 77.78/10.62 (( 77.78/10.62 (brelnall1) => 77.78/10.62 (( 77.78/10.62 (brelnall2) => 77.78/10.62 (( 77.78/10.62 (ex1E2) => 77.78/10.62 (( 77.78/10.62 (funcGraphProp1) => 77.78/10.62 (( 77.78/10.62 (funcGraphProp3) => 77.78/10.62 (( 77.78/10.62 (funcGraphProp2) => 77.78/10.62 (( 77.78/10.62 (funcextLem) => 77.78/10.62 (( 77.78/10.62 (funcGraphProp4) => 77.78/10.62 (( 77.78/10.62 (subbreln) => 77.78/10.62 (( 77.78/10.62 (eqbreln) => 77.78/10.62 (( 77.78/10.62 (funcext) => 77.78/10.62 (( 77.78/10.62 (funcext2) => 77.78/10.62 (( 77.78/10.62 (ap2apEq1) => 77.78/10.62 (( 77.78/10.62 (ap2apEq2) => 77.78/10.62 (( 77.78/10.62 (beta1) => 77.78/10.62 (( 77.78/10.62 (eta1) => 77.78/10.62 (( 77.78/10.62 (lam2lamEq) => 77.78/10.62 (( 77.78/10.62 (beta2) => 77.78/10.62 (( 77.78/10.62 (eta2) => 77.78/10.62 (( 77.78/10.62 (iffalseProp1) => 77.78/10.62 (( 77.78/10.62 (iffalseProp2) => 77.78/10.62 (( 77.78/10.62 (iftrueProp1) => 77.78/10.62 (( 77.78/10.62 (iftrueProp2) => 77.78/10.62 (( 77.78/10.62 (ifSingleton) => 77.78/10.62 (( 77.78/10.62 (ifp) => 77.78/10.62 (( 77.78/10.62 (theeq) => 77.78/10.62 (( 77.78/10.62 (iftrue) => 77.78/10.62 (( 77.78/10.62 (iffalse) => 77.78/10.62 (( 77.78/10.62 (iftrueorfalse) => 77.78/10.62 (( 77.78/10.62 (binintersectT_lem) => 77.78/10.62 (( 77.78/10.62 (binunionT_lem) => 77.78/10.62 (( 77.78/10.62 (powersetT_lem) => 77.78/10.62 (( 77.78/10.62 (setminusT_lem) => 77.78/10.62 (( 77.78/10.62 (complementT_lem) => 77.78/10.62 (( 77.78/10.62 (setextT) => 77.78/10.62 (( 77.78/10.62 (subsetTI) => 77.78/10.62 (( 77.78/10.62 (powersetTI1) => 77.78/10.62 (( 77.78/10.62 (powersetTE1) => 77.78/10.62 (( 77.78/10.62 (complementTI1) => 77.78/10.62 (( 77.78/10.62 (complementTE1) => 77.78/10.62 (( 77.78/10.62 (binintersectTELcontra) => 77.78/10.62 (( 77.78/10.62 (binintersectTERcontra) => 77.78/10.62 (( 77.78/10.62 (contrasubsetT) => 77.78/10.62 (( 77.78/10.62 (contrasubsetT1) => 77.78/10.62 (( 77.78/10.62 (contrasubsetT2) => 77.78/10.62 (( 77.78/10.62 (contrasubsetT3) => 77.78/10.62 (( 77.78/10.62 (doubleComplementI1) => 77.78/10.62 (( 77.78/10.62 (doubleComplementE1) => 77.78/10.62 (( 77.78/10.62 (doubleComplementSub1) => 77.78/10.62 (( 77.78/10.62 (doubleComplementSub2) => 77.78/10.62 (( 77.78/10.62 (doubleComplementEq) => 77.78/10.62 (( 77.78/10.62 (complementTnotintersectT) => 77.78/10.62 (( 77.78/10.62 (complementImpComplementIntersect) => 77.78/10.62 (( 77.78/10.62 (complementSubsetComplementIntersect) => 77.78/10.62 (( 77.78/10.62 (complementInPowersetComplementIntersect) => 77.78/10.62 (( 77.78/10.62 (contraSubsetComplement) => 77.78/10.62 (( 77.78/10.62 (complementTcontraSubset) => 77.78/10.62 (( 77.78/10.62 (binunionTILcontra) => 77.78/10.62 (( 77.78/10.62 (binunionTIRcontra) => 77.78/10.62 (( 77.78/10.62 (inIntersectImpInUnion) => 77.78/10.62 (( 77.78/10.62 (inIntersectImpInUnion2) => 77.78/10.62 (( 77.78/10.62 (inIntersectImpInIntersectUnions) => 77.78/10.62 (( 77.78/10.62 (intersectInPowersetIntersectUnions) => 77.78/10.62 (( 77.78/10.62 (inComplementUnionImpNotIn1) => 77.78/10.62 (( 77.78/10.62 (inComplementUnionImpInComplement1) => 77.78/10.62 (( 77.78/10.62 (binunionTE) => 77.78/10.62 (( 77.78/10.62 (binunionTEcontra) => 77.78/10.62 (( 77.78/10.62 (demorgan2a1) => 77.78/10.62 (( 77.78/10.62 (complementUnionInPowersetComplement) => 77.78/10.62 (( 77.78/10.62 (demorgan2a2) => 77.78/10.62 (( 77.78/10.62 (demorgan1a) => 77.78/10.62 (( 77.78/10.62 (demorgan1b) => 77.78/10.62 (( 77.78/10.62 (demorgan1) => 77.78/10.62 (( 77.78/10.62 (demorgan2a) => 77.78/10.62 (( 77.78/10.62 (demorgan2b2) => 77.78/10.62 (( 77.78/10.62 (demorgan2b) => 77.78/10.62 (( 77.78/10.62 (demorgan2) => 77.78/10.62 (( 77.78/10.62 (woz13rule0) => 77.78/10.62 (( 77.78/10.62 (woz13rule1) => 77.78/10.62 (( 77.78/10.62 (woz13rule2) => 77.78/10.62 (( 77.78/10.62 (woz13rule3) => 77.78/10.62 (( 77.78/10.62 (woz13rule4) => 77.78/10.62 (( 77.78/10.62 (woz1_1) => 77.78/10.62 (( 77.78/10.62 (woz1_2) => 77.78/10.62 (( 77.78/10.62 (woz1_3) => 77.78/10.62 (( 77.78/10.62 (woz1_4) => 77.78/10.62 (( 77.78/10.62 (woz1_5) => 77.78/10.62 (( 77.78/10.62 (breln1all2) => 77.78/10.62 (( 77.78/10.62 (breln1SetBreln1) => 77.78/10.62 (( 77.78/10.62 (choice2fnsingleton) => 77.78/10.62 (( 77.78/10.62 (setOfPairsIsBReln1) => 77.78/10.62 (( 77.78/10.62 (breln1all1) => 77.78/10.62 (( 77.78/10.62 (subbreln1) => 77.78/10.62 (( 77.78/10.62 (eqbreln1) => 77.78/10.62 (( 77.78/10.62 (breln1invprop) => 77.78/10.62 (( 77.78/10.62 (breln1invI) => 77.78/10.62 (( 77.78/10.62 (breln1invE) => 77.78/10.62 (( 77.78/10.62 (breln1compprop) => 77.78/10.62 (( 77.78/10.62 (breln1compI) => 77.78/10.62 (( 77.78/10.62 (breln1compE) => 77.78/10.62 (( 77.78/10.62 (breln1compEex) => 77.78/10.62 (( 77.78/10.62 (breln1unionprop) => 77.78/10.62 (( 77.78/10.62 (breln1unionIL) => 77.78/10.62 (( 77.78/10.62 (breln1unionIR) => 77.78/10.62 (( 77.78/10.62 (breln1unionI) => 77.78/10.62 (( 77.78/10.62 (breln1unionE) => 77.78/10.62 (( 77.78/10.62 (breln1unionEcases) => 77.78/10.62 (( 77.78/10.62 (breln1unionCommutes) => 77.78/10.62 (( 77.78/10.62 (woz2Ex) => 77.78/10.62 (( 77.78/10.62 (woz2W) => 77.78/10.62 (( 77.78/10.62 (woz2A) => 77.78/10.62 (( 77.78/10.62 (woz2B) => 77.78/10.62 (( 77.78/10.62 (image1Ex) => 77.78/10.62 (( 77.78/10.62 (image1Ex1) => 77.78/10.62 (( 77.78/10.62 (image1Equiv) => 77.78/10.62 (( 77.78/10.62 (image1E) => 77.78/10.62 (( 77.78/10.62 (image1I) => 77.78/10.62 (( 77.78/10.62 (injFuncInInjFuncSet) => 77.78/10.62 (( 77.78/10.62 (injFuncSetFuncIn) => 77.78/10.62 (( 77.78/10.62 (injFuncSetFuncInj) => 77.78/10.62 (( 77.78/10.62 (surjFuncSetFuncIn) => 77.78/10.62 (( 77.78/10.62 (surjFuncSetFuncSurj) => 77.78/10.62 (( 77.78/10.62 (leftInvIsSurj) => 77.78/10.62 (( 77.78/10.62 (surjCantorThm) => 77.78/10.62 (( 77.78/10.62 (foundation2) => 77.78/10.62 (( 77.78/10.62 (notinself) => 77.78/10.62 (( 77.78/10.62 (notinself2) => 77.78/10.62 (( 77.78/10.62 (omegaSp) => 77.78/10.62 (( 77.78/10.62 (omegaSclos) => 77.78/10.62 (( 77.78/10.62 (peano0notS) => 77.78/10.62 (( 77.78/10.62 (peanoSinj) => 77.78/10.62 (( 77.78/10.62 (transitivesetOp1) => 77.78/10.62 (( 77.78/10.62 (binintTransitive) => 77.78/10.62 (( 77.78/10.62 (transitivesetOp2) => 77.78/10.62 (( 77.78/10.62 (setunionTransitive) => 77.78/10.62 (( 77.78/10.62 (ordinalMinLem1) => 77.78/10.62 (( 77.78/10.62 (!!) @ ( 77.78/10.62 ^[Y0 : $i]: 77.78/10.62 (( 77.78/10.62 (ordinal @ 77.78/10.62 Y0) => 77.78/10.62 (( 77.78/10.62 (!!) @ ( 77.78/10.62 ^[Y1 : $i]: 77.78/10.62 (( 77.78/10.62 (!!) @ ( 77.78/10.62 ^[Y2 : $i]: 77.78/10.62 (( 77.78/10.62 (in @ 77.78/10.62 Y2 @ 77.78/10.62 Y0) => 77.78/10.62 (( 77.78/10.62 (in @ 77.78/10.62 Y1 @ 77.78/10.62 Y2) => 77.78/10.62 (in @ 77.78/10.62 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 77.78/10.62 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl535])). 77.78/10.62 thf(zip_derived_cl560, plain, 77.78/10.62 (~ (((exuI2) => 77.78/10.62 (((inCongP) => 77.78/10.62 (((in__Cong) => 77.78/10.62 (((exuE3u) => 77.78/10.62 (((exu__Cong) => 77.78/10.62 (((setadjoin__Cong) => 77.78/10.62 (((powerset__Cong) => 77.78/10.62 (((setunion__Cong) => 77.78/10.62 (((exuEu) => 77.78/10.62 (((descr__Cong) => 77.78/10.62 (((dsetconstr__Cong) => 77.78/10.62 (((subsetI1) => 77.78/10.62 (((eqimpsubset2) => 77.78/10.62 (((eqimpsubset1) => 77.78/10.62 (((subsetI2) => 77.78/10.62 (((emptysetsubset) => 77.78/10.62 (((subsetE) => 77.78/10.62 (((subsetE2) => 77.78/10.62 (((notsubsetI) => 77.78/10.62 (((notequalI1) => 77.78/10.62 (((notequalI2) => 77.78/10.62 (((subsetRefl) => 77.78/10.62 (((subsetTrans) => 77.78/10.62 (((setadjoinSub) => 77.78/10.62 (((setadjoinSub2) => 77.78/10.62 (((subset2powerset) => 77.78/10.62 (((setextsub) => 77.78/10.62 (((subsetemptysetimpeq) => 77.78/10.62 (((powersetI1) => 77.78/10.62 (((powersetE1) => 77.78/10.62 (( 77.78/10.62 (inPowerset) => 77.78/10.62 (( 77.78/10.62 (powersetsubset) => 77.78/10.62 (( 77.78/10.62 (sepInPowerset) => 77.78/10.62 (( 77.78/10.62 (sepSubset) => 77.78/10.62 (( 77.78/10.62 (binunionIL) => 77.78/10.62 (( 77.78/10.62 (upairset2IR) => 77.78/10.62 (( 77.78/10.62 (binunionIR) => 77.78/10.62 (( 77.78/10.62 (binunionEcases) => 77.78/10.62 (( 77.78/10.62 (binunionE) => 77.78/10.62 (( 77.78/10.62 (binunionLsub) => 77.78/10.62 (( 77.78/10.62 (binunionRsub) => 77.78/10.62 (( 77.78/10.62 (binintersectI) => 77.78/10.62 (( 77.78/10.62 (binintersectSubset5) => 77.78/10.62 (( 77.78/10.62 (binintersectEL) => 77.78/10.62 (( 77.78/10.62 (binintersectLsub) => 77.78/10.62 (( 77.78/10.62 (binintersectSubset2) => 77.78/10.62 (( 77.78/10.62 (binintersectSubset3) => 77.78/10.62 (( 77.78/10.62 (binintersectER) => 77.78/10.62 (( 77.78/10.62 (disjointsetsI1) => 77.78/10.62 (( 77.78/10.62 (binintersectRsub) => 77.78/10.62 (( 77.78/10.62 (binintersectSubset4) => 77.78/10.62 (( 77.78/10.62 (binintersectSubset1) => 77.78/10.62 (( 77.78/10.62 (bs114d) => 77.78/10.62 (( 77.78/10.62 (setminusI) => 77.78/10.62 (( 77.78/10.62 (setminusEL) => 77.78/10.62 (( 77.78/10.62 (setminusER) => 77.78/10.62 (( 77.78/10.62 (setminusSubset2) => 77.78/10.62 (( 77.78/10.62 (setminusERneg) => 77.78/10.62 (( 77.78/10.62 (setminusELneg) => 77.78/10.62 (( 77.78/10.62 (setminusILneg) => 77.78/10.62 (( 77.78/10.62 (setminusIRneg) => 77.78/10.62 (( 77.78/10.62 (setminusLsub) => 77.78/10.62 (( 77.78/10.62 (setminusSubset1) => 77.78/10.62 (( 77.78/10.62 (symdiffE) => 77.78/10.62 (( 77.78/10.62 (symdiffI1) => 77.78/10.62 (( 77.78/10.62 (symdiffI2) => 77.78/10.62 (( 77.78/10.62 (symdiffIneg1) => 77.78/10.62 (( 77.78/10.62 (symdiffIneg2) => 77.78/10.62 (( 77.78/10.62 (secondinupair) => 77.78/10.62 (( 77.78/10.62 (setukpairIL) => 77.78/10.62 (( 77.78/10.62 (setukpairIR) => 77.78/10.62 (( 77.78/10.62 (kpairiskpair) => 77.78/10.62 (( 77.78/10.62 (kpairp) => 77.78/10.62 (( 77.78/10.62 (singletonsubset) => 77.78/10.62 (( 77.78/10.62 (singletoninpowerset) => 77.78/10.62 (( 77.78/10.62 (singletoninpowunion) => 77.78/10.62 (( 77.78/10.62 (upairset2E) => 77.78/10.62 (( 77.78/10.62 (upairsubunion) => 77.78/10.62 (( 77.78/10.62 (upairinpowunion) => 77.78/10.62 (( 77.78/10.62 (ubforcartprodlem1) => 77.78/10.62 (( 77.78/10.62 (ubforcartprodlem2) => 77.78/10.62 (( 77.78/10.62 (ubforcartprodlem3) => 77.78/10.62 (( 77.78/10.62 (cartprodpairin) => 77.78/10.62 (( 77.78/10.62 (cartprodmempair1) => 77.78/10.62 (( 77.78/10.62 (cartprodmempair) => 77.78/10.62 (( 77.78/10.62 (setunionE2) => 77.78/10.62 (( 77.78/10.62 (setunionsingleton1) => 77.78/10.62 (( 77.78/10.62 (setunionsingleton2) => 77.78/10.62 (( 77.78/10.62 (setunionsingleton) => 77.78/10.62 (( 77.78/10.62 (singletonprop) => 77.78/10.62 (( 77.78/10.62 (ex1E1) => 77.78/10.62 (( 77.78/10.62 (ex1I) => 77.78/10.62 (( 77.78/10.62 (ex1I2) => 77.78/10.62 (( 77.78/10.62 (singletonsuniq) => 77.78/10.62 (( 77.78/10.62 (setukpairinjL1) => 77.78/10.62 (( 77.78/10.62 (kfstsingleton) => 77.78/10.62 (( 77.78/10.62 (theprop) => 77.78/10.62 (( 77.78/10.62 (kfstpairEq) => 77.78/10.62 (( 77.78/10.62 (cartprodfstin) => 77.78/10.62 (( 77.78/10.62 (setukpairinjL2) => 77.78/10.62 (( 77.78/10.62 (setukpairinjL) => 77.78/10.62 (( 77.78/10.62 (setukpairinjR11) => 77.78/10.62 (( 77.78/10.62 (setukpairinjR12) => 77.78/10.62 (( 77.78/10.62 (setukpairinjR1) => 77.78/10.62 (( 77.78/10.62 (upairequniteq) => 77.78/10.62 (( 77.78/10.62 (setukpairinjR2) => 77.78/10.62 (( 77.78/10.62 (setukpairinjR) => 77.78/10.62 (( 77.78/10.62 (ksndsingleton) => 77.78/10.62 (( 77.78/10.62 (ksndpairEq) => 77.78/10.62 (( 77.78/10.62 (kpairsurjEq) => 77.78/10.62 (( 77.78/10.62 (cartprodsndin) => 77.78/10.62 (( 77.78/10.62 (cartprodpairmemEL) => 77.78/10.62 (( 77.78/10.62 (cartprodpairmemER) => 77.78/10.62 (( 77.78/10.62 (cartprodmempaircEq) => 77.78/10.62 (( 77.78/10.62 (cartprodfstpairEq) => 77.78/10.62 (( 77.78/10.62 (cartprodsndpairEq) => 77.78/10.62 (( 77.78/10.62 (cartprodpairsurjEq) => 77.78/10.62 (( 77.78/10.62 (dpsetconstrI) => 77.78/10.62 (( 77.78/10.62 (dpsetconstrSub) => 77.78/10.62 (( 77.78/10.62 (setOfPairsIsBReln) => 77.78/10.62 (( 77.78/10.62 (dpsetconstrERa) => 77.78/10.62 (( 77.78/10.62 (dpsetconstrEL1) => 77.78/10.62 (( 77.78/10.62 (dpsetconstrEL2) => 77.78/10.62 (( 77.78/10.62 (dpsetconstrER) => 77.78/10.62 (( 77.78/10.62 (funcImageSingleton) => 77.78/10.62 (( 77.78/10.62 (apProp) => 77.78/10.62 (( 77.78/10.62 (app) => 77.78/10.62 (( 77.78/10.62 (infuncsetfunc) => 77.78/10.62 (( 77.78/10.62 (ap2p) => 77.78/10.62 (( 77.78/10.62 (funcinfuncset) => 77.78/10.62 (( 77.78/10.62 (lamProp) => 77.78/10.62 (( 77.78/10.62 (lamp) => 77.78/10.62 (( 77.78/10.62 (lam2p) => 77.78/10.62 (( 77.78/10.62 (brelnall1) => 77.78/10.62 (( 77.78/10.62 (brelnall2) => 77.78/10.62 (( 77.78/10.62 (ex1E2) => 77.78/10.62 (( 77.78/10.62 (funcGraphProp1) => 77.78/10.62 (( 77.78/10.62 (funcGraphProp3) => 77.78/10.62 (( 77.78/10.62 (funcGraphProp2) => 77.78/10.62 (( 77.78/10.62 (funcextLem) => 77.78/10.62 (( 77.78/10.62 (funcGraphProp4) => 77.78/10.62 (( 77.78/10.62 (subbreln) => 77.78/10.62 (( 77.78/10.62 (eqbreln) => 77.78/10.62 (( 77.78/10.62 (funcext) => 77.78/10.62 (( 77.78/10.62 (funcext2) => 77.78/10.62 (( 77.78/10.62 (ap2apEq1) => 77.78/10.62 (( 77.78/10.62 (ap2apEq2) => 77.78/10.62 (( 77.78/10.62 (beta1) => 77.78/10.62 (( 77.78/10.62 (eta1) => 77.78/10.62 (( 77.78/10.62 (lam2lamEq) => 77.78/10.62 (( 77.78/10.62 (beta2) => 77.78/10.62 (( 77.78/10.62 (eta2) => 77.78/10.62 (( 77.78/10.62 (iffalseProp1) => 77.78/10.62 (( 77.78/10.62 (iffalseProp2) => 77.78/10.62 (( 77.78/10.62 (iftrueProp1) => 77.78/10.62 (( 77.78/10.62 (iftrueProp2) => 77.78/10.62 (( 77.78/10.62 (ifSingleton) => 77.78/10.62 (( 77.78/10.62 (ifp) => 77.78/10.62 (( 77.78/10.62 (theeq) => 77.78/10.62 (( 77.78/10.62 (iftrue) => 77.78/10.62 (( 77.78/10.62 (iffalse) => 77.78/10.62 (( 77.78/10.62 (iftrueorfalse) => 77.78/10.62 (( 77.78/10.62 (binintersectT_lem) => 77.78/10.62 (( 77.78/10.62 (binunionT_lem) => 77.78/10.62 (( 77.78/10.62 (powersetT_lem) => 77.78/10.62 (( 77.78/10.62 (setminusT_lem) => 77.78/10.62 (( 77.78/10.62 (complementT_lem) => 77.78/10.62 (( 77.78/10.62 (setextT) => 77.78/10.62 (( 77.78/10.62 (subsetTI) => 77.78/10.62 (( 77.78/10.62 (powersetTI1) => 77.78/10.62 (( 77.78/10.62 (powersetTE1) => 77.78/10.62 (( 77.78/10.62 (complementTI1) => 77.78/10.62 (( 77.78/10.62 (complementTE1) => 77.78/10.62 (( 77.78/10.62 (binintersectTELcontra) => 77.78/10.62 (( 77.78/10.62 (binintersectTERcontra) => 77.78/10.62 (( 77.78/10.62 (contrasubsetT) => 77.78/10.62 (( 77.78/10.62 (contrasubsetT1) => 77.78/10.62 (( 77.78/10.62 (contrasubsetT2) => 77.78/10.62 (( 77.78/10.62 (contrasubsetT3) => 77.78/10.62 (( 77.78/10.62 (doubleComplementI1) => 77.78/10.62 (( 77.78/10.62 (doubleComplementE1) => 77.78/10.62 (( 77.78/10.62 (doubleComplementSub1) => 77.78/10.62 (( 77.78/10.62 (doubleComplementSub2) => 77.78/10.62 (( 77.78/10.62 (doubleComplementEq) => 77.78/10.62 (( 77.78/10.62 (complementTnotintersectT) => 77.78/10.62 (( 77.78/10.62 (complementImpComplementIntersect) => 77.78/10.62 (( 77.78/10.62 (complementSubsetComplementIntersect) => 77.78/10.62 (( 77.78/10.62 (complementInPowersetComplementIntersect) => 77.78/10.62 (( 77.78/10.62 (contraSubsetComplement) => 77.78/10.62 (( 77.78/10.62 (complementTcontraSubset) => 77.78/10.62 (( 77.78/10.62 (binunionTILcontra) => 77.78/10.62 (( 77.78/10.62 (binunionTIRcontra) => 77.78/10.62 (( 77.78/10.62 (inIntersectImpInUnion) => 77.78/10.62 (( 77.78/10.62 (inIntersectImpInUnion2) => 77.78/10.62 (( 77.78/10.62 (inIntersectImpInIntersectUnions) => 77.78/10.62 (( 77.78/10.62 (intersectInPowersetIntersectUnions) => 77.78/10.62 (( 77.78/10.62 (inComplementUnionImpNotIn1) => 77.78/10.62 (( 77.78/10.62 (inComplementUnionImpInComplement1) => 77.78/10.62 (( 77.78/10.62 (binunionTE) => 77.78/10.62 (( 77.78/10.62 (binunionTEcontra) => 77.78/10.62 (( 77.78/10.62 (demorgan2a1) => 77.78/10.62 (( 77.78/10.62 (complementUnionInPowersetComplement) => 77.78/10.62 (( 77.78/10.62 (demorgan2a2) => 77.78/10.62 (( 77.78/10.62 (demorgan1a) => 77.78/10.62 (( 77.78/10.62 (demorgan1b) => 77.78/10.62 (( 77.78/10.62 (demorgan1) => 77.78/10.62 (( 77.78/10.62 (demorgan2a) => 77.78/10.62 (( 77.78/10.62 (demorgan2b2) => 77.78/10.62 (( 77.78/10.62 (demorgan2b) => 77.78/10.62 (( 77.78/10.62 (demorgan2) => 77.78/10.62 (( 77.78/10.62 (woz13rule0) => 77.78/10.62 (( 77.78/10.62 (woz13rule1) => 77.78/10.62 (( 77.78/10.62 (woz13rule2) => 77.78/10.62 (( 77.78/10.62 (woz13rule3) => 77.78/10.62 (( 77.78/10.62 (woz13rule4) => 77.78/10.62 (( 77.78/10.62 (woz1_1) => 77.78/10.62 (( 77.78/10.62 (woz1_2) => 77.78/10.62 (( 77.78/10.62 (woz1_3) => 77.78/10.62 (( 77.78/10.62 (woz1_4) => 77.78/10.62 (( 77.78/10.62 (woz1_5) => 77.78/10.62 (( 77.78/10.62 (breln1all2) => 77.78/10.62 (( 77.78/10.62 (breln1SetBreln1) => 77.78/10.62 (( 77.78/10.62 (choice2fnsingleton) => 77.78/10.62 (( 77.78/10.62 (setOfPairsIsBReln1) => 77.78/10.62 (( 77.78/10.62 (breln1all1) => 77.78/10.62 (( 77.78/10.62 (subbreln1) => 77.78/10.62 (( 77.78/10.62 (eqbreln1) => 77.78/10.62 (( 77.78/10.62 (breln1invprop) => 77.78/10.62 (( 77.78/10.62 (breln1invI) => 77.78/10.62 (( 77.78/10.62 (breln1invE) => 77.78/10.62 (( 77.78/10.62 (breln1compprop) => 77.78/10.62 (( 77.78/10.62 (breln1compI) => 77.78/10.62 (( 77.78/10.62 (breln1compE) => 77.78/10.62 (( 77.78/10.62 (breln1compEex) => 77.78/10.62 (( 77.78/10.62 (breln1unionprop) => 77.78/10.62 (( 77.78/10.62 (breln1unionIL) => 77.78/10.62 (( 77.78/10.62 (breln1unionIR) => 77.78/10.62 (( 77.78/10.62 (breln1unionI) => 77.78/10.62 (( 77.78/10.62 (breln1unionE) => 77.78/10.62 (( 77.78/10.62 (breln1unionEcases) => 77.78/10.62 (( 77.78/10.62 (breln1unionCommutes) => 77.78/10.62 (( 77.78/10.62 (woz2Ex) => 77.78/10.62 (( 77.78/10.62 (woz2W) => 77.78/10.62 (( 77.78/10.62 (woz2A) => 77.78/10.62 (( 77.78/10.62 (woz2B) => 77.78/10.62 (( 77.78/10.62 (image1Ex) => 77.78/10.62 (( 77.78/10.62 (image1Ex1) => 77.78/10.62 (( 77.78/10.62 (image1Equiv) => 77.78/10.62 (( 77.78/10.62 (image1E) => 77.78/10.62 (( 77.78/10.62 (image1I) => 77.78/10.62 (( 77.78/10.62 (injFuncInInjFuncSet) => 77.78/10.62 (( 77.78/10.62 (injFuncSetFuncIn) => 77.78/10.62 (( 77.78/10.62 (injFuncSetFuncInj) => 77.78/10.62 (( 77.78/10.62 (surjFuncSetFuncIn) => 77.78/10.62 (( 77.78/10.62 (surjFuncSetFuncSurj) => 77.78/10.62 (( 77.78/10.62 (leftInvIsSurj) => 77.78/10.62 (( 77.78/10.62 (surjCantorThm) => 77.78/10.62 (( 77.78/10.62 (foundation2) => 77.78/10.62 (( 77.78/10.62 (notinself) => 77.78/10.62 (( 77.78/10.62 (notinself2) => 77.78/10.62 (( 77.78/10.62 (omegaSp) => 77.78/10.62 (( 77.78/10.62 (omegaSclos) => 77.78/10.62 (( 77.78/10.62 (peano0notS) => 77.78/10.62 (( 77.78/10.62 (peanoSinj) => 77.78/10.62 (( 77.78/10.62 (transitivesetOp1) => 77.78/10.62 (( 77.78/10.62 (binintTransitive) => 77.78/10.62 (( 77.78/10.62 (transitivesetOp2) => 77.78/10.62 (( 77.78/10.62 (setunionTransitive) => 77.78/10.62 (( 77.78/10.62 (ordinalMinLem1) => 77.78/10.62 (( 77.78/10.62 (!!) @ ( 77.78/10.62 ^[Y0 : $i]: 77.78/10.62 (( 77.78/10.62 (ordinal @ 77.78/10.62 Y0) => 77.78/10.62 (( 77.78/10.62 (!!) @ ( 77.78/10.62 ^[Y1 : $i]: 77.78/10.62 (( 77.78/10.62 (!!) @ ( 77.78/10.62 ^[Y2 : $i]: 77.78/10.62 (( 77.78/10.62 (in @ 77.78/10.62 Y2 @ 77.78/10.62 Y0) => 77.78/10.62 (( 77.78/10.62 (in @ 77.78/10.62 Y1 @ 77.78/10.62 Y2) => 77.78/10.62 (in @ 77.78/10.62 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 77.78/10.62 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl550])). 77.78/10.62 thf(zip_derived_cl568, plain, 77.78/10.62 (~ (((inCongP) => 77.78/10.62 (((in__Cong) => 77.78/10.62 (((exuE3u) => 77.78/10.62 (((exu__Cong) => 77.78/10.62 (((setadjoin__Cong) => 77.78/10.62 (((powerset__Cong) => 77.78/10.62 (((setunion__Cong) => 77.78/10.62 (((exuEu) => 77.78/10.62 (((descr__Cong) => 77.78/10.62 (((dsetconstr__Cong) => 77.78/10.62 (((subsetI1) => 77.78/10.62 (((eqimpsubset2) => 77.78/10.62 (((eqimpsubset1) => 77.78/10.62 (((subsetI2) => 77.78/10.62 (((emptysetsubset) => 77.78/10.62 (((subsetE) => 77.78/10.62 (((subsetE2) => 77.78/10.62 (((notsubsetI) => 77.78/10.62 (((notequalI1) => 77.78/10.62 (((notequalI2) => 77.78/10.62 (((subsetRefl) => 77.78/10.62 (((subsetTrans) => 77.78/10.62 (((setadjoinSub) => 77.78/10.62 (((setadjoinSub2) => 77.78/10.62 (((subset2powerset) => 77.78/10.62 (((setextsub) => 77.78/10.62 (((subsetemptysetimpeq) => 77.78/10.62 (((powersetI1) => 77.78/10.62 (((powersetE1) => 77.78/10.62 (((inPowerset) => 77.78/10.62 (( 77.78/10.62 (powersetsubset) => 77.78/10.62 (( 77.78/10.62 (sepInPowerset) => 77.78/10.62 (( 77.78/10.62 (sepSubset) => 77.78/10.62 (( 77.78/10.62 (binunionIL) => 77.78/10.62 (( 77.78/10.62 (upairset2IR) => 77.78/10.62 (( 77.78/10.62 (binunionIR) => 77.78/10.62 (( 77.78/10.62 (binunionEcases) => 77.78/10.62 (( 77.78/10.62 (binunionE) => 77.78/10.62 (( 77.78/10.62 (binunionLsub) => 77.78/10.62 (( 77.78/10.62 (binunionRsub) => 77.78/10.62 (( 77.78/10.62 (binintersectI) => 77.78/10.62 (( 77.78/10.62 (binintersectSubset5) => 77.78/10.62 (( 77.78/10.62 (binintersectEL) => 77.78/10.62 (( 77.78/10.62 (binintersectLsub) => 77.78/10.62 (( 77.78/10.62 (binintersectSubset2) => 77.78/10.62 (( 77.78/10.62 (binintersectSubset3) => 77.78/10.62 (( 77.78/10.62 (binintersectER) => 77.78/10.62 (( 77.78/10.62 (disjointsetsI1) => 77.78/10.62 (( 77.78/10.62 (binintersectRsub) => 77.78/10.62 (( 77.78/10.62 (binintersectSubset4) => 77.78/10.62 (( 77.78/10.62 (binintersectSubset1) => 77.78/10.62 (( 77.78/10.62 (bs114d) => 77.78/10.62 (( 77.78/10.62 (setminusI) => 77.78/10.62 (( 77.78/10.62 (setminusEL) => 77.78/10.62 (( 77.78/10.62 (setminusER) => 77.78/10.62 (( 77.78/10.62 (setminusSubset2) => 77.78/10.62 (( 77.78/10.62 (setminusERneg) => 77.78/10.62 (( 77.78/10.62 (setminusELneg) => 77.78/10.62 (( 77.78/10.62 (setminusILneg) => 77.78/10.62 (( 77.78/10.62 (setminusIRneg) => 77.78/10.62 (( 77.78/10.62 (setminusLsub) => 77.78/10.62 (( 77.78/10.62 (setminusSubset1) => 77.78/10.62 (( 77.78/10.62 (symdiffE) => 77.78/10.62 (( 77.78/10.62 (symdiffI1) => 77.78/10.62 (( 77.78/10.62 (symdiffI2) => 77.78/10.62 (( 77.78/10.62 (symdiffIneg1) => 77.78/10.62 (( 77.78/10.62 (symdiffIneg2) => 77.78/10.62 (( 77.78/10.62 (secondinupair) => 77.78/10.62 (( 77.78/10.62 (setukpairIL) => 77.78/10.62 (( 77.78/10.62 (setukpairIR) => 77.78/10.62 (( 77.78/10.62 (kpairiskpair) => 77.78/10.62 (( 77.78/10.62 (kpairp) => 77.78/10.62 (( 77.78/10.62 (singletonsubset) => 77.78/10.62 (( 77.78/10.62 (singletoninpowerset) => 77.78/10.62 (( 77.78/10.62 (singletoninpowunion) => 77.78/10.62 (( 77.78/10.62 (upairset2E) => 77.78/10.62 (( 77.78/10.62 (upairsubunion) => 77.78/10.62 (( 77.78/10.62 (upairinpowunion) => 77.78/10.62 (( 77.78/10.62 (ubforcartprodlem1) => 77.78/10.62 (( 77.78/10.62 (ubforcartprodlem2) => 77.78/10.62 (( 77.78/10.62 (ubforcartprodlem3) => 77.78/10.62 (( 77.78/10.62 (cartprodpairin) => 77.78/10.62 (( 77.78/10.62 (cartprodmempair1) => 77.78/10.62 (( 77.78/10.62 (cartprodmempair) => 77.78/10.62 (( 77.78/10.62 (setunionE2) => 77.78/10.62 (( 77.78/10.62 (setunionsingleton1) => 77.78/10.62 (( 77.78/10.62 (setunionsingleton2) => 77.78/10.62 (( 77.78/10.62 (setunionsingleton) => 77.78/10.62 (( 77.78/10.62 (singletonprop) => 77.78/10.62 (( 77.78/10.62 (ex1E1) => 77.78/10.62 (( 77.78/10.62 (ex1I) => 77.78/10.62 (( 77.78/10.62 (ex1I2) => 77.78/10.62 (( 77.78/10.62 (singletonsuniq) => 77.78/10.62 (( 77.78/10.62 (setukpairinjL1) => 77.78/10.62 (( 77.78/10.62 (kfstsingleton) => 77.78/10.62 (( 77.78/10.62 (theprop) => 77.78/10.62 (( 77.78/10.62 (kfstpairEq) => 77.78/10.62 (( 77.78/10.62 (cartprodfstin) => 77.78/10.62 (( 77.78/10.62 (setukpairinjL2) => 77.78/10.62 (( 77.78/10.62 (setukpairinjL) => 77.78/10.62 (( 77.78/10.62 (setukpairinjR11) => 77.78/10.62 (( 77.78/10.62 (setukpairinjR12) => 77.78/10.62 (( 77.78/10.62 (setukpairinjR1) => 77.78/10.62 (( 77.78/10.62 (upairequniteq) => 77.78/10.62 (( 77.78/10.62 (setukpairinjR2) => 77.78/10.62 (( 77.78/10.62 (setukpairinjR) => 77.78/10.62 (( 77.78/10.62 (ksndsingleton) => 77.78/10.62 (( 77.78/10.62 (ksndpairEq) => 77.78/10.62 (( 77.78/10.62 (kpairsurjEq) => 77.78/10.62 (( 77.78/10.62 (cartprodsndin) => 77.78/10.62 (( 77.78/10.62 (cartprodpairmemEL) => 77.78/10.62 (( 77.78/10.62 (cartprodpairmemER) => 77.78/10.62 (( 77.78/10.62 (cartprodmempaircEq) => 77.78/10.62 (( 77.78/10.62 (cartprodfstpairEq) => 77.78/10.62 (( 77.78/10.62 (cartprodsndpairEq) => 77.78/10.62 (( 77.78/10.62 (cartprodpairsurjEq) => 77.78/10.62 (( 77.78/10.62 (dpsetconstrI) => 77.78/10.62 (( 77.78/10.62 (dpsetconstrSub) => 77.78/10.62 (( 77.78/10.62 (setOfPairsIsBReln) => 77.78/10.62 (( 77.78/10.62 (dpsetconstrERa) => 77.78/10.62 (( 77.78/10.62 (dpsetconstrEL1) => 77.78/10.62 (( 77.78/10.62 (dpsetconstrEL2) => 77.78/10.62 (( 77.78/10.62 (dpsetconstrER) => 77.78/10.62 (( 77.78/10.62 (funcImageSingleton) => 77.78/10.62 (( 77.78/10.62 (apProp) => 77.78/10.62 (( 77.78/10.62 (app) => 77.78/10.62 (( 77.78/10.62 (infuncsetfunc) => 77.78/10.62 (( 77.78/10.62 (ap2p) => 77.78/10.62 (( 77.78/10.62 (funcinfuncset) => 77.78/10.62 (( 77.78/10.62 (lamProp) => 77.78/10.62 (( 77.78/10.62 (lamp) => 77.78/10.62 (( 77.78/10.62 (lam2p) => 77.78/10.62 (( 77.78/10.62 (brelnall1) => 77.78/10.62 (( 77.78/10.62 (brelnall2) => 77.78/10.62 (( 77.78/10.62 (ex1E2) => 77.78/10.62 (( 77.78/10.62 (funcGraphProp1) => 77.78/10.62 (( 77.78/10.62 (funcGraphProp3) => 77.78/10.62 (( 77.78/10.62 (funcGraphProp2) => 77.78/10.62 (( 77.78/10.62 (funcextLem) => 77.78/10.62 (( 77.78/10.62 (funcGraphProp4) => 77.78/10.62 (( 77.78/10.62 (subbreln) => 77.78/10.62 (( 77.78/10.62 (eqbreln) => 77.78/10.62 (( 77.78/10.62 (funcext) => 77.78/10.62 (( 77.78/10.62 (funcext2) => 77.78/10.62 (( 77.78/10.62 (ap2apEq1) => 77.78/10.62 (( 77.78/10.62 (ap2apEq2) => 77.78/10.62 (( 77.78/10.62 (beta1) => 77.78/10.62 (( 77.78/10.62 (eta1) => 77.78/10.62 (( 77.78/10.62 (lam2lamEq) => 77.78/10.62 (( 77.78/10.62 (beta2) => 77.78/10.62 (( 77.78/10.62 (eta2) => 77.78/10.62 (( 77.78/10.62 (iffalseProp1) => 77.78/10.62 (( 77.78/10.62 (iffalseProp2) => 77.78/10.62 (( 77.78/10.62 (iftrueProp1) => 77.78/10.62 (( 77.78/10.62 (iftrueProp2) => 77.78/10.62 (( 77.78/10.62 (ifSingleton) => 77.78/10.62 (( 77.78/10.62 (ifp) => 77.78/10.62 (( 77.78/10.62 (theeq) => 77.78/10.62 (( 77.78/10.62 (iftrue) => 77.78/10.62 (( 77.78/10.62 (iffalse) => 77.78/10.62 (( 77.78/10.62 (iftrueorfalse) => 77.78/10.62 (( 77.78/10.62 (binintersectT_lem) => 77.78/10.62 (( 77.78/10.62 (binunionT_lem) => 77.78/10.62 (( 77.78/10.62 (powersetT_lem) => 77.78/10.62 (( 77.78/10.62 (setminusT_lem) => 77.78/10.62 (( 77.78/10.62 (complementT_lem) => 77.78/10.62 (( 77.78/10.62 (setextT) => 77.78/10.62 (( 77.78/10.62 (subsetTI) => 77.78/10.62 (( 77.78/10.62 (powersetTI1) => 77.78/10.62 (( 77.78/10.62 (powersetTE1) => 77.78/10.62 (( 77.78/10.62 (complementTI1) => 77.78/10.62 (( 77.78/10.62 (complementTE1) => 77.78/10.62 (( 77.78/10.62 (binintersectTELcontra) => 77.78/10.62 (( 77.78/10.62 (binintersectTERcontra) => 77.78/10.62 (( 77.78/10.62 (contrasubsetT) => 77.78/10.62 (( 77.78/10.62 (contrasubsetT1) => 77.78/10.62 (( 77.78/10.62 (contrasubsetT2) => 77.78/10.62 (( 77.78/10.62 (contrasubsetT3) => 77.78/10.62 (( 77.78/10.62 (doubleComplementI1) => 77.78/10.62 (( 77.78/10.62 (doubleComplementE1) => 77.78/10.62 (( 77.78/10.62 (doubleComplementSub1) => 77.78/10.62 (( 77.78/10.62 (doubleComplementSub2) => 77.78/10.62 (( 77.78/10.62 (doubleComplementEq) => 77.78/10.62 (( 77.78/10.62 (complementTnotintersectT) => 77.78/10.62 (( 77.78/10.62 (complementImpComplementIntersect) => 77.78/10.62 (( 77.78/10.62 (complementSubsetComplementIntersect) => 77.78/10.62 (( 77.78/10.62 (complementInPowersetComplementIntersect) => 77.78/10.62 (( 77.78/10.62 (contraSubsetComplement) => 77.78/10.62 (( 77.78/10.62 (complementTcontraSubset) => 77.78/10.62 (( 77.78/10.62 (binunionTILcontra) => 77.78/10.62 (( 77.78/10.62 (binunionTIRcontra) => 77.78/10.62 (( 77.78/10.62 (inIntersectImpInUnion) => 77.78/10.62 (( 77.78/10.62 (inIntersectImpInUnion2) => 77.78/10.62 (( 77.78/10.62 (inIntersectImpInIntersectUnions) => 77.78/10.62 (( 77.78/10.62 (intersectInPowersetIntersectUnions) => 77.78/10.62 (( 77.78/10.62 (inComplementUnionImpNotIn1) => 77.78/10.62 (( 77.78/10.62 (inComplementUnionImpInComplement1) => 77.78/10.62 (( 77.78/10.62 (binunionTE) => 77.78/10.62 (( 77.78/10.62 (binunionTEcontra) => 77.78/10.62 (( 77.78/10.62 (demorgan2a1) => 77.78/10.62 (( 77.78/10.62 (complementUnionInPowersetComplement) => 77.78/10.62 (( 77.78/10.62 (demorgan2a2) => 77.78/10.62 (( 77.78/10.62 (demorgan1a) => 77.78/10.62 (( 77.78/10.62 (demorgan1b) => 77.78/10.62 (( 77.78/10.62 (demorgan1) => 77.78/10.62 (( 77.78/10.62 (demorgan2a) => 77.78/10.62 (( 77.78/10.62 (demorgan2b2) => 77.78/10.62 (( 77.78/10.62 (demorgan2b) => 77.78/10.62 (( 77.78/10.62 (demorgan2) => 77.78/10.62 (( 77.78/10.62 (woz13rule0) => 77.78/10.62 (( 77.78/10.62 (woz13rule1) => 77.78/10.62 (( 77.78/10.62 (woz13rule2) => 77.78/10.62 (( 77.78/10.62 (woz13rule3) => 77.78/10.62 (( 77.78/10.62 (woz13rule4) => 77.78/10.62 (( 77.78/10.62 (woz1_1) => 77.78/10.62 (( 77.78/10.62 (woz1_2) => 77.78/10.62 (( 77.78/10.62 (woz1_3) => 77.78/10.62 (( 77.78/10.62 (woz1_4) => 77.78/10.62 (( 77.78/10.62 (woz1_5) => 77.78/10.62 (( 77.78/10.62 (breln1all2) => 77.78/10.62 (( 77.78/10.62 (breln1SetBreln1) => 77.78/10.62 (( 77.78/10.62 (choice2fnsingleton) => 77.78/10.62 (( 77.78/10.62 (setOfPairsIsBReln1) => 77.78/10.62 (( 77.78/10.62 (breln1all1) => 77.78/10.62 (( 77.78/10.62 (subbreln1) => 77.78/10.62 (( 77.78/10.62 (eqbreln1) => 77.78/10.62 (( 77.78/10.62 (breln1invprop) => 77.78/10.62 (( 77.78/10.62 (breln1invI) => 77.78/10.62 (( 77.78/10.62 (breln1invE) => 77.78/10.62 (( 77.78/10.62 (breln1compprop) => 77.78/10.62 (( 77.78/10.62 (breln1compI) => 77.78/10.62 (( 77.78/10.62 (breln1compE) => 77.78/10.62 (( 77.78/10.62 (breln1compEex) => 77.78/10.62 (( 77.78/10.62 (breln1unionprop) => 77.78/10.62 (( 77.78/10.62 (breln1unionIL) => 77.78/10.62 (( 77.78/10.62 (breln1unionIR) => 77.78/10.62 (( 77.78/10.62 (breln1unionI) => 77.78/10.62 (( 77.78/10.62 (breln1unionE) => 77.78/10.62 (( 77.78/10.62 (breln1unionEcases) => 77.78/10.62 (( 77.78/10.62 (breln1unionCommutes) => 77.78/10.62 (( 77.78/10.62 (woz2Ex) => 77.78/10.62 (( 77.78/10.62 (woz2W) => 77.78/10.62 (( 77.78/10.62 (woz2A) => 77.78/10.62 (( 77.78/10.62 (woz2B) => 77.78/10.62 (( 77.78/10.62 (image1Ex) => 77.78/10.62 (( 77.78/10.62 (image1Ex1) => 77.78/10.62 (( 77.78/10.62 (image1Equiv) => 77.78/10.62 (( 77.78/10.62 (image1E) => 77.78/10.62 (( 77.78/10.62 (image1I) => 77.78/10.62 (( 77.78/10.62 (injFuncInInjFuncSet) => 77.78/10.62 (( 77.78/10.62 (injFuncSetFuncIn) => 77.78/10.62 (( 77.78/10.62 (injFuncSetFuncInj) => 77.78/10.62 (( 77.78/10.62 (surjFuncSetFuncIn) => 77.78/10.62 (( 77.78/10.62 (surjFuncSetFuncSurj) => 77.78/10.62 (( 77.78/10.62 (leftInvIsSurj) => 77.78/10.62 (( 77.78/10.62 (surjCantorThm) => 77.78/10.62 (( 77.78/10.62 (foundation2) => 77.78/10.62 (( 77.78/10.62 (notinself) => 77.78/10.62 (( 77.78/10.62 (notinself2) => 77.78/10.62 (( 77.78/10.62 (omegaSp) => 77.78/10.62 (( 77.78/10.62 (omegaSclos) => 77.78/10.62 (( 77.78/10.62 (peano0notS) => 77.78/10.62 (( 77.78/10.62 (peanoSinj) => 77.78/10.62 (( 77.78/10.62 (transitivesetOp1) => 77.78/10.62 (( 77.78/10.62 (binintTransitive) => 77.78/10.62 (( 77.78/10.62 (transitivesetOp2) => 77.78/10.62 (( 77.78/10.62 (setunionTransitive) => 77.78/10.62 (( 77.78/10.62 (ordinalMinLem1) => 77.78/10.62 (( 77.78/10.62 (!!) @ ( 77.78/10.62 ^[Y0 : $i]: 77.78/10.62 (( 77.78/10.62 (ordinal @ 77.78/10.62 Y0) => 77.78/10.62 (( 77.78/10.62 (!!) @ ( 77.78/10.62 ^[Y1 : $i]: 77.78/10.62 (( 77.78/10.62 (!!) @ ( 77.78/10.62 ^[Y2 : $i]: 77.78/10.62 (( 77.78/10.62 (in @ 77.78/10.62 Y2 @ 77.78/10.62 Y0) => 77.78/10.62 (( 77.78/10.62 (in @ 77.78/10.62 Y1 @ 77.78/10.62 Y2) => 77.78/10.62 (in @ 77.78/10.62 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 77.78/10.62 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl560])). 77.78/10.62 thf(zip_derived_cl578, plain, 77.78/10.62 (~ (((in__Cong) => 77.78/10.62 (((exuE3u) => 77.78/10.62 (((exu__Cong) => 77.78/10.62 (((setadjoin__Cong) => 77.78/10.62 (((powerset__Cong) => 77.78/10.62 (((setunion__Cong) => 77.78/10.62 (((exuEu) => 77.78/10.62 (((descr__Cong) => 77.78/10.62 (((dsetconstr__Cong) => 77.78/10.62 (((subsetI1) => 77.78/10.62 (((eqimpsubset2) => 77.78/10.62 (((eqimpsubset1) => 77.78/10.62 (((subsetI2) => 77.78/10.62 (((emptysetsubset) => 77.78/10.62 (((subsetE) => 77.78/10.62 (((subsetE2) => 77.78/10.62 (((notsubsetI) => 77.78/10.62 (((notequalI1) => 77.78/10.62 (((notequalI2) => 77.78/10.62 (((subsetRefl) => 77.78/10.62 (((subsetTrans) => 77.78/10.62 (((setadjoinSub) => 77.78/10.62 (((setadjoinSub2) => 77.78/10.62 (((subset2powerset) => 77.78/10.62 (((setextsub) => 77.78/10.62 (((subsetemptysetimpeq) => 77.78/10.62 (((powersetI1) => 77.78/10.62 (((powersetE1) => 77.78/10.62 (((inPowerset) => 77.78/10.62 (((powersetsubset) => 77.78/10.62 (( 77.78/10.62 (sepInPowerset) => 77.78/10.62 (( 77.78/10.62 (sepSubset) => 77.78/10.62 (( 77.78/10.62 (binunionIL) => 77.78/10.62 (( 77.78/10.62 (upairset2IR) => 77.78/10.62 (( 77.78/10.62 (binunionIR) => 77.78/10.62 (( 77.78/10.62 (binunionEcases) => 77.78/10.62 (( 77.78/10.62 (binunionE) => 77.78/10.62 (( 77.78/10.62 (binunionLsub) => 77.78/10.62 (( 77.78/10.62 (binunionRsub) => 77.78/10.62 (( 77.78/10.62 (binintersectI) => 77.78/10.62 (( 77.78/10.62 (binintersectSubset5) => 77.78/10.62 (( 77.78/10.62 (binintersectEL) => 77.78/10.62 (( 77.78/10.62 (binintersectLsub) => 77.78/10.62 (( 77.78/10.62 (binintersectSubset2) => 77.78/10.62 (( 77.78/10.62 (binintersectSubset3) => 77.78/10.62 (( 77.78/10.62 (binintersectER) => 77.78/10.62 (( 77.78/10.62 (disjointsetsI1) => 77.78/10.62 (( 77.78/10.62 (binintersectRsub) => 77.78/10.62 (( 77.78/10.62 (binintersectSubset4) => 77.78/10.62 (( 77.78/10.62 (binintersectSubset1) => 77.78/10.62 (( 77.78/10.62 (bs114d) => 77.78/10.62 (( 77.78/10.62 (setminusI) => 77.78/10.62 (( 77.78/10.62 (setminusEL) => 77.78/10.62 (( 77.78/10.62 (setminusER) => 77.78/10.62 (( 77.78/10.62 (setminusSubset2) => 77.78/10.62 (( 77.78/10.62 (setminusERneg) => 77.78/10.62 (( 77.78/10.62 (setminusELneg) => 77.78/10.62 (( 77.78/10.62 (setminusILneg) => 77.78/10.62 (( 77.78/10.62 (setminusIRneg) => 77.78/10.62 (( 77.78/10.62 (setminusLsub) => 77.78/10.62 (( 77.78/10.62 (setminusSubset1) => 77.78/10.62 (( 77.78/10.62 (symdiffE) => 77.78/10.62 (( 77.78/10.62 (symdiffI1) => 77.78/10.62 (( 77.78/10.62 (symdiffI2) => 77.78/10.62 (( 77.78/10.62 (symdiffIneg1) => 77.78/10.62 (( 77.78/10.62 (symdiffIneg2) => 77.78/10.62 (( 77.78/10.62 (secondinupair) => 77.78/10.62 (( 77.78/10.62 (setukpairIL) => 77.78/10.62 (( 77.78/10.62 (setukpairIR) => 77.78/10.62 (( 77.78/10.62 (kpairiskpair) => 77.78/10.62 (( 77.78/10.62 (kpairp) => 77.78/10.62 (( 77.78/10.62 (singletonsubset) => 77.78/10.62 (( 77.78/10.62 (singletoninpowerset) => 77.78/10.62 (( 77.78/10.62 (singletoninpowunion) => 77.78/10.62 (( 77.78/10.62 (upairset2E) => 77.78/10.62 (( 77.78/10.62 (upairsubunion) => 77.78/10.62 (( 77.78/10.62 (upairinpowunion) => 77.78/10.62 (( 77.78/10.62 (ubforcartprodlem1) => 77.78/10.62 (( 77.78/10.62 (ubforcartprodlem2) => 77.78/10.62 (( 77.78/10.62 (ubforcartprodlem3) => 77.78/10.62 (( 77.78/10.62 (cartprodpairin) => 77.78/10.62 (( 77.78/10.62 (cartprodmempair1) => 77.78/10.62 (( 77.78/10.62 (cartprodmempair) => 77.78/10.62 (( 77.78/10.62 (setunionE2) => 77.78/10.62 (( 77.78/10.62 (setunionsingleton1) => 77.78/10.62 (( 77.78/10.62 (setunionsingleton2) => 77.78/10.62 (( 77.78/10.62 (setunionsingleton) => 77.78/10.62 (( 77.78/10.62 (singletonprop) => 77.78/10.62 (( 77.78/10.62 (ex1E1) => 77.78/10.62 (( 77.78/10.62 (ex1I) => 77.78/10.62 (( 77.78/10.62 (ex1I2) => 77.78/10.62 (( 77.78/10.62 (singletonsuniq) => 77.78/10.62 (( 77.78/10.62 (setukpairinjL1) => 77.78/10.62 (( 77.78/10.62 (kfstsingleton) => 77.78/10.62 (( 77.78/10.62 (theprop) => 77.78/10.62 (( 77.78/10.62 (kfstpairEq) => 77.78/10.62 (( 77.78/10.62 (cartprodfstin) => 77.78/10.62 (( 77.78/10.62 (setukpairinjL2) => 77.78/10.62 (( 77.78/10.62 (setukpairinjL) => 77.78/10.62 (( 77.78/10.62 (setukpairinjR11) => 77.78/10.62 (( 77.78/10.62 (setukpairinjR12) => 77.78/10.62 (( 77.78/10.62 (setukpairinjR1) => 77.78/10.62 (( 77.78/10.62 (upairequniteq) => 77.78/10.62 (( 77.78/10.62 (setukpairinjR2) => 77.78/10.62 (( 77.78/10.62 (setukpairinjR) => 77.78/10.62 (( 77.78/10.62 (ksndsingleton) => 77.78/10.62 (( 77.78/10.62 (ksndpairEq) => 77.78/10.62 (( 77.78/10.62 (kpairsurjEq) => 77.78/10.62 (( 77.78/10.62 (cartprodsndin) => 77.78/10.62 (( 77.78/10.62 (cartprodpairmemEL) => 77.78/10.62 (( 77.78/10.62 (cartprodpairmemER) => 77.78/10.62 (( 77.78/10.62 (cartprodmempaircEq) => 77.78/10.62 (( 77.78/10.62 (cartprodfstpairEq) => 77.78/10.62 (( 77.78/10.62 (cartprodsndpairEq) => 77.78/10.62 (( 77.78/10.62 (cartprodpairsurjEq) => 77.78/10.62 (( 77.78/10.62 (dpsetconstrI) => 77.78/10.62 (( 77.78/10.62 (dpsetconstrSub) => 77.78/10.62 (( 77.78/10.62 (setOfPairsIsBReln) => 77.78/10.62 (( 77.78/10.62 (dpsetconstrERa) => 77.78/10.62 (( 77.78/10.62 (dpsetconstrEL1) => 77.78/10.62 (( 77.78/10.62 (dpsetconstrEL2) => 77.78/10.62 (( 77.78/10.62 (dpsetconstrER) => 77.78/10.62 (( 77.78/10.62 (funcImageSingleton) => 77.78/10.62 (( 77.78/10.62 (apProp) => 77.78/10.62 (( 77.78/10.62 (app) => 77.78/10.62 (( 77.78/10.62 (infuncsetfunc) => 77.78/10.62 (( 77.78/10.62 (ap2p) => 77.78/10.62 (( 77.78/10.62 (funcinfuncset) => 77.78/10.62 (( 77.78/10.62 (lamProp) => 77.78/10.62 (( 77.78/10.62 (lamp) => 77.78/10.62 (( 77.78/10.62 (lam2p) => 77.78/10.62 (( 77.78/10.62 (brelnall1) => 77.78/10.62 (( 77.78/10.62 (brelnall2) => 77.78/10.62 (( 77.78/10.62 (ex1E2) => 77.78/10.62 (( 77.78/10.62 (funcGraphProp1) => 77.78/10.62 (( 77.78/10.62 (funcGraphProp3) => 77.78/10.62 (( 77.78/10.62 (funcGraphProp2) => 77.78/10.62 (( 77.78/10.62 (funcextLem) => 77.78/10.62 (( 77.78/10.62 (funcGraphProp4) => 77.78/10.62 (( 77.78/10.62 (subbreln) => 77.78/10.62 (( 77.78/10.62 (eqbreln) => 77.78/10.62 (( 77.78/10.62 (funcext) => 77.78/10.62 (( 77.78/10.62 (funcext2) => 77.78/10.62 (( 77.78/10.62 (ap2apEq1) => 77.78/10.62 (( 77.78/10.62 (ap2apEq2) => 77.78/10.62 (( 77.78/10.62 (beta1) => 77.78/10.62 (( 77.78/10.62 (eta1) => 77.78/10.62 (( 77.78/10.62 (lam2lamEq) => 77.78/10.62 (( 77.78/10.62 (beta2) => 77.78/10.62 (( 77.78/10.62 (eta2) => 77.78/10.62 (( 77.78/10.62 (iffalseProp1) => 77.78/10.62 (( 77.78/10.62 (iffalseProp2) => 77.78/10.62 (( 77.78/10.62 (iftrueProp1) => 77.78/10.62 (( 77.78/10.62 (iftrueProp2) => 77.78/10.62 (( 77.78/10.62 (ifSingleton) => 77.78/10.62 (( 77.78/10.62 (ifp) => 77.78/10.62 (( 77.78/10.62 (theeq) => 77.78/10.62 (( 77.78/10.62 (iftrue) => 77.78/10.62 (( 77.78/10.62 (iffalse) => 77.78/10.62 (( 77.78/10.62 (iftrueorfalse) => 77.78/10.62 (( 77.78/10.62 (binintersectT_lem) => 77.78/10.62 (( 77.78/10.62 (binunionT_lem) => 77.78/10.62 (( 77.78/10.62 (powersetT_lem) => 77.78/10.62 (( 77.78/10.62 (setminusT_lem) => 77.78/10.62 (( 77.78/10.62 (complementT_lem) => 77.78/10.62 (( 77.78/10.62 (setextT) => 77.78/10.62 (( 77.78/10.62 (subsetTI) => 77.78/10.62 (( 77.78/10.62 (powersetTI1) => 77.78/10.62 (( 77.78/10.62 (powersetTE1) => 77.78/10.62 (( 77.78/10.62 (complementTI1) => 77.78/10.62 (( 77.78/10.62 (complementTE1) => 77.78/10.62 (( 77.78/10.62 (binintersectTELcontra) => 77.78/10.62 (( 77.78/10.62 (binintersectTERcontra) => 77.78/10.62 (( 77.78/10.62 (contrasubsetT) => 77.78/10.62 (( 77.78/10.62 (contrasubsetT1) => 77.78/10.62 (( 77.78/10.62 (contrasubsetT2) => 77.78/10.62 (( 77.78/10.62 (contrasubsetT3) => 77.78/10.62 (( 77.78/10.62 (doubleComplementI1) => 77.78/10.62 (( 77.78/10.62 (doubleComplementE1) => 77.78/10.62 (( 77.78/10.62 (doubleComplementSub1) => 77.78/10.62 (( 77.78/10.62 (doubleComplementSub2) => 77.78/10.62 (( 77.78/10.62 (doubleComplementEq) => 77.78/10.62 (( 77.78/10.62 (complementTnotintersectT) => 77.78/10.62 (( 77.78/10.62 (complementImpComplementIntersect) => 77.78/10.62 (( 77.78/10.62 (complementSubsetComplementIntersect) => 77.78/10.62 (( 77.78/10.62 (complementInPowersetComplementIntersect) => 77.78/10.62 (( 77.78/10.62 (contraSubsetComplement) => 77.78/10.62 (( 77.78/10.62 (complementTcontraSubset) => 77.78/10.62 (( 77.78/10.62 (binunionTILcontra) => 77.78/10.62 (( 77.78/10.62 (binunionTIRcontra) => 77.78/10.62 (( 77.78/10.62 (inIntersectImpInUnion) => 77.78/10.62 (( 77.78/10.62 (inIntersectImpInUnion2) => 77.78/10.62 (( 77.78/10.62 (inIntersectImpInIntersectUnions) => 77.78/10.62 (( 77.78/10.62 (intersectInPowersetIntersectUnions) => 77.78/10.62 (( 77.78/10.62 (inComplementUnionImpNotIn1) => 77.78/10.62 (( 77.78/10.62 (inComplementUnionImpInComplement1) => 77.78/10.62 (( 77.78/10.62 (binunionTE) => 77.78/10.62 (( 77.78/10.62 (binunionTEcontra) => 77.78/10.62 (( 77.78/10.62 (demorgan2a1) => 77.78/10.62 (( 77.78/10.62 (complementUnionInPowersetComplement) => 77.78/10.62 (( 77.78/10.62 (demorgan2a2) => 77.78/10.62 (( 77.78/10.62 (demorgan1a) => 77.78/10.62 (( 77.78/10.62 (demorgan1b) => 77.78/10.62 (( 77.78/10.62 (demorgan1) => 77.78/10.62 (( 77.78/10.62 (demorgan2a) => 77.78/10.62 (( 77.78/10.62 (demorgan2b2) => 77.78/10.62 (( 77.78/10.62 (demorgan2b) => 77.78/10.62 (( 77.78/10.62 (demorgan2) => 77.78/10.62 (( 77.78/10.62 (woz13rule0) => 77.78/10.62 (( 77.78/10.62 (woz13rule1) => 77.78/10.62 (( 77.78/10.62 (woz13rule2) => 77.78/10.62 (( 77.78/10.62 (woz13rule3) => 77.78/10.62 (( 77.78/10.62 (woz13rule4) => 77.78/10.62 (( 77.78/10.62 (woz1_1) => 77.78/10.62 (( 77.78/10.62 (woz1_2) => 77.78/10.62 (( 77.78/10.62 (woz1_3) => 77.78/10.62 (( 77.78/10.62 (woz1_4) => 77.78/10.62 (( 77.78/10.62 (woz1_5) => 77.78/10.62 (( 77.78/10.62 (breln1all2) => 77.78/10.62 (( 77.78/10.62 (breln1SetBreln1) => 77.78/10.62 (( 77.78/10.62 (choice2fnsingleton) => 77.78/10.62 (( 77.78/10.62 (setOfPairsIsBReln1) => 77.78/10.62 (( 77.78/10.62 (breln1all1) => 77.78/10.62 (( 77.78/10.62 (subbreln1) => 77.78/10.62 (( 77.78/10.62 (eqbreln1) => 77.78/10.62 (( 77.78/10.62 (breln1invprop) => 77.78/10.62 (( 77.78/10.62 (breln1invI) => 77.78/10.62 (( 77.78/10.62 (breln1invE) => 77.78/10.62 (( 77.78/10.62 (breln1compprop) => 77.78/10.62 (( 77.78/10.62 (breln1compI) => 77.78/10.62 (( 77.78/10.62 (breln1compE) => 77.78/10.62 (( 77.78/10.62 (breln1compEex) => 77.78/10.62 (( 77.78/10.62 (breln1unionprop) => 77.78/10.62 (( 77.78/10.62 (breln1unionIL) => 77.78/10.62 (( 77.78/10.62 (breln1unionIR) => 77.78/10.62 (( 77.78/10.62 (breln1unionI) => 77.78/10.62 (( 77.78/10.62 (breln1unionE) => 77.78/10.62 (( 77.78/10.62 (breln1unionEcases) => 77.78/10.62 (( 77.78/10.62 (breln1unionCommutes) => 77.78/10.62 (( 77.78/10.62 (woz2Ex) => 77.78/10.62 (( 77.78/10.62 (woz2W) => 77.78/10.62 (( 77.78/10.62 (woz2A) => 77.78/10.62 (( 77.78/10.62 (woz2B) => 77.78/10.62 (( 77.78/10.62 (image1Ex) => 77.78/10.62 (( 77.78/10.62 (image1Ex1) => 77.78/10.62 (( 77.78/10.62 (image1Equiv) => 77.78/10.62 (( 77.78/10.62 (image1E) => 77.78/10.62 (( 77.78/10.62 (image1I) => 77.78/10.62 (( 77.78/10.62 (injFuncInInjFuncSet) => 77.78/10.62 (( 77.78/10.62 (injFuncSetFuncIn) => 77.78/10.62 (( 77.78/10.62 (injFuncSetFuncInj) => 77.78/10.62 (( 77.78/10.62 (surjFuncSetFuncIn) => 77.78/10.62 (( 77.78/10.62 (surjFuncSetFuncSurj) => 77.78/10.62 (( 77.78/10.62 (leftInvIsSurj) => 77.78/10.62 (( 77.78/10.62 (surjCantorThm) => 77.78/10.62 (( 77.78/10.62 (foundation2) => 77.78/10.62 (( 77.78/10.62 (notinself) => 77.78/10.62 (( 77.78/10.62 (notinself2) => 77.78/10.62 (( 77.78/10.62 (omegaSp) => 77.78/10.62 (( 77.78/10.62 (omegaSclos) => 77.78/10.62 (( 77.78/10.62 (peano0notS) => 77.78/10.62 (( 77.78/10.62 (peanoSinj) => 77.78/10.62 (( 77.78/10.62 (transitivesetOp1) => 77.78/10.62 (( 77.78/10.62 (binintTransitive) => 77.78/10.62 (( 77.78/10.62 (transitivesetOp2) => 77.78/10.62 (( 77.78/10.62 (setunionTransitive) => 77.78/10.62 (( 77.78/10.62 (ordinalMinLem1) => 77.78/10.62 (( 77.78/10.62 (!!) @ ( 77.78/10.62 ^[Y0 : $i]: 77.78/10.62 (( 77.78/10.62 (ordinal @ 77.78/10.62 Y0) => 77.78/10.62 (( 77.78/10.62 (!!) @ ( 77.78/10.62 ^[Y1 : $i]: 77.78/10.62 (( 77.78/10.62 (!!) @ ( 77.78/10.62 ^[Y2 : $i]: 77.78/10.62 (( 77.78/10.62 (in @ 77.78/10.62 Y2 @ 77.78/10.62 Y0) => 77.78/10.62 (( 77.78/10.62 (in @ 77.78/10.62 Y1 @ 77.78/10.62 Y2) => 77.78/10.62 (in @ 77.78/10.62 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 77.78/10.62 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl568])). 77.78/10.62 thf(zip_derived_cl588, plain, 77.78/10.62 (~ (((exuE3u) => 77.78/10.62 (((exu__Cong) => 77.78/10.62 (((setadjoin__Cong) => 77.78/10.62 (((powerset__Cong) => 77.78/10.62 (((setunion__Cong) => 77.78/10.62 (((exuEu) => 77.78/10.62 (((descr__Cong) => 77.78/10.62 (((dsetconstr__Cong) => 77.78/10.62 (((subsetI1) => 77.78/10.62 (((eqimpsubset2) => 77.78/10.62 (((eqimpsubset1) => 77.78/10.62 (((subsetI2) => 77.78/10.62 (((emptysetsubset) => 77.78/10.62 (((subsetE) => 77.78/10.62 (((subsetE2) => 77.78/10.62 (((notsubsetI) => 77.78/10.62 (((notequalI1) => 77.78/10.62 (((notequalI2) => 77.78/10.62 (((subsetRefl) => 77.78/10.62 (((subsetTrans) => 77.78/10.62 (((setadjoinSub) => 77.78/10.62 (((setadjoinSub2) => 77.78/10.62 (((subset2powerset) => 77.78/10.62 (((setextsub) => 77.78/10.62 (((subsetemptysetimpeq) => 77.78/10.62 (((powersetI1) => 77.78/10.62 (((powersetE1) => 77.78/10.62 (((inPowerset) => 77.78/10.62 (((powersetsubset) => 77.78/10.62 (((sepInPowerset) => 77.78/10.62 (( 77.78/10.62 (sepSubset) => 77.78/10.62 (( 77.78/10.62 (binunionIL) => 77.78/10.62 (( 77.78/10.62 (upairset2IR) => 77.78/10.62 (( 77.78/10.62 (binunionIR) => 77.78/10.62 (( 77.78/10.62 (binunionEcases) => 77.78/10.62 (( 77.78/10.62 (binunionE) => 77.78/10.62 (( 77.78/10.62 (binunionLsub) => 77.78/10.62 (( 77.78/10.62 (binunionRsub) => 77.78/10.62 (( 77.78/10.62 (binintersectI) => 77.78/10.62 (( 77.78/10.62 (binintersectSubset5) => 77.78/10.62 (( 77.78/10.62 (binintersectEL) => 77.78/10.62 (( 77.78/10.62 (binintersectLsub) => 77.78/10.62 (( 77.78/10.62 (binintersectSubset2) => 77.78/10.62 (( 77.78/10.62 (binintersectSubset3) => 77.78/10.62 (( 77.78/10.62 (binintersectER) => 77.78/10.62 (( 77.78/10.62 (disjointsetsI1) => 77.78/10.62 (( 77.78/10.62 (binintersectRsub) => 77.78/10.62 (( 77.78/10.62 (binintersectSubset4) => 77.78/10.62 (( 77.78/10.62 (binintersectSubset1) => 77.78/10.62 (( 77.78/10.62 (bs114d) => 77.78/10.62 (( 77.78/10.62 (setminusI) => 77.78/10.62 (( 77.78/10.62 (setminusEL) => 77.78/10.62 (( 77.78/10.62 (setminusER) => 77.78/10.62 (( 77.78/10.62 (setminusSubset2) => 77.78/10.62 (( 77.78/10.62 (setminusERneg) => 77.78/10.62 (( 77.78/10.62 (setminusELneg) => 77.78/10.62 (( 77.78/10.62 (setminusILneg) => 77.78/10.62 (( 77.78/10.62 (setminusIRneg) => 77.78/10.62 (( 77.78/10.62 (setminusLsub) => 77.78/10.62 (( 77.78/10.62 (setminusSubset1) => 77.78/10.62 (( 77.78/10.62 (symdiffE) => 77.78/10.62 (( 77.78/10.62 (symdiffI1) => 77.78/10.62 (( 77.78/10.62 (symdiffI2) => 77.78/10.62 (( 77.78/10.62 (symdiffIneg1) => 77.78/10.62 (( 77.78/10.62 (symdiffIneg2) => 77.78/10.62 (( 77.78/10.62 (secondinupair) => 77.78/10.62 (( 77.78/10.62 (setukpairIL) => 77.78/10.62 (( 77.78/10.62 (setukpairIR) => 77.78/10.62 (( 77.78/10.62 (kpairiskpair) => 77.78/10.62 (( 77.78/10.62 (kpairp) => 77.78/10.62 (( 77.78/10.62 (singletonsubset) => 77.78/10.62 (( 77.78/10.62 (singletoninpowerset) => 77.78/10.62 (( 77.78/10.62 (singletoninpowunion) => 77.78/10.62 (( 77.78/10.62 (upairset2E) => 77.78/10.62 (( 77.78/10.62 (upairsubunion) => 77.78/10.62 (( 77.78/10.62 (upairinpowunion) => 77.78/10.62 (( 77.78/10.62 (ubforcartprodlem1) => 77.78/10.62 (( 77.78/10.62 (ubforcartprodlem2) => 77.78/10.62 (( 77.78/10.62 (ubforcartprodlem3) => 77.78/10.62 (( 77.78/10.62 (cartprodpairin) => 77.78/10.62 (( 77.78/10.62 (cartprodmempair1) => 77.78/10.62 (( 77.78/10.62 (cartprodmempair) => 77.78/10.62 (( 77.78/10.62 (setunionE2) => 77.78/10.62 (( 77.78/10.62 (setunionsingleton1) => 77.78/10.62 (( 77.78/10.62 (setunionsingleton2) => 77.78/10.62 (( 77.78/10.62 (setunionsingleton) => 77.78/10.62 (( 77.78/10.62 (singletonprop) => 77.78/10.62 (( 77.78/10.62 (ex1E1) => 77.78/10.62 (( 77.78/10.62 (ex1I) => 77.78/10.62 (( 77.78/10.62 (ex1I2) => 77.78/10.62 (( 77.78/10.62 (singletonsuniq) => 77.78/10.62 (( 77.78/10.62 (setukpairinjL1) => 77.78/10.62 (( 77.78/10.62 (kfstsingleton) => 77.78/10.62 (( 77.78/10.62 (theprop) => 77.78/10.62 (( 77.78/10.62 (kfstpairEq) => 77.78/10.62 (( 77.78/10.62 (cartprodfstin) => 77.78/10.62 (( 77.78/10.62 (setukpairinjL2) => 77.78/10.62 (( 77.78/10.62 (setukpairinjL) => 77.78/10.62 (( 77.78/10.62 (setukpairinjR11) => 77.78/10.62 (( 77.78/10.62 (setukpairinjR12) => 77.78/10.62 (( 77.78/10.62 (setukpairinjR1) => 77.78/10.62 (( 77.78/10.62 (upairequniteq) => 77.78/10.62 (( 77.78/10.62 (setukpairinjR2) => 77.78/10.62 (( 77.78/10.62 (setukpairinjR) => 77.78/10.62 (( 77.78/10.62 (ksndsingleton) => 77.78/10.62 (( 77.78/10.62 (ksndpairEq) => 77.78/10.62 (( 77.78/10.62 (kpairsurjEq) => 77.78/10.62 (( 77.78/10.62 (cartprodsndin) => 77.78/10.62 (( 77.78/10.62 (cartprodpairmemEL) => 77.78/10.62 (( 77.78/10.62 (cartprodpairmemER) => 77.78/10.62 (( 77.78/10.62 (cartprodmempaircEq) => 77.78/10.62 (( 77.78/10.62 (cartprodfstpairEq) => 77.78/10.62 (( 77.78/10.62 (cartprodsndpairEq) => 77.78/10.62 (( 77.78/10.62 (cartprodpairsurjEq) => 77.78/10.62 (( 77.78/10.62 (dpsetconstrI) => 77.78/10.62 (( 77.78/10.62 (dpsetconstrSub) => 77.78/10.62 (( 77.78/10.62 (setOfPairsIsBReln) => 77.78/10.62 (( 77.78/10.62 (dpsetconstrERa) => 77.78/10.62 (( 77.78/10.62 (dpsetconstrEL1) => 77.78/10.62 (( 77.78/10.62 (dpsetconstrEL2) => 77.78/10.62 (( 77.78/10.62 (dpsetconstrER) => 77.78/10.62 (( 77.78/10.62 (funcImageSingleton) => 77.78/10.62 (( 77.78/10.62 (apProp) => 77.78/10.62 (( 77.78/10.62 (app) => 77.78/10.62 (( 77.78/10.62 (infuncsetfunc) => 77.78/10.62 (( 77.78/10.62 (ap2p) => 77.78/10.62 (( 77.78/10.62 (funcinfuncset) => 77.78/10.62 (( 77.78/10.62 (lamProp) => 77.78/10.62 (( 77.78/10.62 (lamp) => 77.78/10.62 (( 77.78/10.62 (lam2p) => 77.78/10.62 (( 77.78/10.62 (brelnall1) => 77.78/10.62 (( 77.78/10.62 (brelnall2) => 77.78/10.62 (( 77.78/10.62 (ex1E2) => 77.78/10.62 (( 77.78/10.62 (funcGraphProp1) => 77.78/10.62 (( 77.78/10.62 (funcGraphProp3) => 77.78/10.62 (( 77.78/10.62 (funcGraphProp2) => 77.78/10.62 (( 77.78/10.62 (funcextLem) => 77.78/10.62 (( 77.78/10.62 (funcGraphProp4) => 77.78/10.62 (( 77.78/10.62 (subbreln) => 77.78/10.62 (( 77.78/10.62 (eqbreln) => 77.78/10.62 (( 77.78/10.62 (funcext) => 77.78/10.62 (( 77.78/10.62 (funcext2) => 77.78/10.62 (( 77.78/10.62 (ap2apEq1) => 77.78/10.62 (( 77.78/10.62 (ap2apEq2) => 77.78/10.62 (( 77.78/10.62 (beta1) => 77.78/10.62 (( 77.78/10.62 (eta1) => 77.78/10.62 (( 77.78/10.62 (lam2lamEq) => 77.78/10.62 (( 77.78/10.62 (beta2) => 77.78/10.62 (( 77.78/10.62 (eta2) => 77.78/10.62 (( 77.78/10.62 (iffalseProp1) => 77.78/10.62 (( 77.78/10.62 (iffalseProp2) => 77.78/10.62 (( 77.78/10.62 (iftrueProp1) => 77.78/10.62 (( 77.78/10.62 (iftrueProp2) => 77.78/10.62 (( 77.78/10.62 (ifSingleton) => 77.78/10.62 (( 77.78/10.62 (ifp) => 77.78/10.62 (( 77.78/10.62 (theeq) => 77.78/10.62 (( 77.78/10.62 (iftrue) => 77.78/10.62 (( 77.78/10.62 (iffalse) => 77.78/10.62 (( 77.78/10.62 (iftrueorfalse) => 77.78/10.62 (( 77.78/10.62 (binintersectT_lem) => 77.78/10.62 (( 77.78/10.62 (binunionT_lem) => 77.78/10.62 (( 77.78/10.62 (powersetT_lem) => 77.78/10.62 (( 77.78/10.62 (setminusT_lem) => 77.78/10.62 (( 77.78/10.62 (complementT_lem) => 77.78/10.62 (( 77.78/10.62 (setextT) => 77.78/10.62 (( 77.78/10.62 (subsetTI) => 77.78/10.62 (( 77.78/10.62 (powersetTI1) => 77.78/10.62 (( 77.78/10.62 (powersetTE1) => 77.78/10.62 (( 77.78/10.62 (complementTI1) => 77.78/10.62 (( 77.78/10.62 (complementTE1) => 77.78/10.62 (( 77.78/10.62 (binintersectTELcontra) => 77.78/10.62 (( 77.78/10.62 (binintersectTERcontra) => 77.78/10.62 (( 77.78/10.62 (contrasubsetT) => 77.78/10.62 (( 77.78/10.62 (contrasubsetT1) => 77.78/10.62 (( 77.78/10.62 (contrasubsetT2) => 77.78/10.62 (( 77.78/10.62 (contrasubsetT3) => 77.78/10.62 (( 77.78/10.62 (doubleComplementI1) => 77.78/10.62 (( 77.78/10.62 (doubleComplementE1) => 77.78/10.62 (( 77.78/10.62 (doubleComplementSub1) => 77.78/10.62 (( 77.78/10.62 (doubleComplementSub2) => 77.78/10.62 (( 77.78/10.62 (doubleComplementEq) => 77.78/10.62 (( 77.78/10.62 (complementTnotintersectT) => 77.78/10.62 (( 77.78/10.62 (complementImpComplementIntersect) => 77.78/10.62 (( 77.78/10.62 (complementSubsetComplementIntersect) => 77.78/10.62 (( 77.78/10.62 (complementInPowersetComplementIntersect) => 77.78/10.62 (( 77.78/10.62 (contraSubsetComplement) => 77.78/10.62 (( 77.78/10.62 (complementTcontraSubset) => 77.78/10.62 (( 77.78/10.62 (binunionTILcontra) => 77.78/10.62 (( 77.78/10.62 (binunionTIRcontra) => 77.78/10.62 (( 77.78/10.62 (inIntersectImpInUnion) => 77.78/10.62 (( 77.78/10.62 (inIntersectImpInUnion2) => 77.78/10.62 (( 77.78/10.62 (inIntersectImpInIntersectUnions) => 77.78/10.62 (( 77.78/10.62 (intersectInPowersetIntersectUnions) => 77.78/10.62 (( 77.78/10.62 (inComplementUnionImpNotIn1) => 77.78/10.62 (( 77.78/10.62 (inComplementUnionImpInComplement1) => 77.78/10.62 (( 77.78/10.62 (binunionTE) => 77.78/10.62 (( 77.78/10.62 (binunionTEcontra) => 77.78/10.62 (( 77.78/10.62 (demorgan2a1) => 77.78/10.62 (( 77.78/10.62 (complementUnionInPowersetComplement) => 77.78/10.62 (( 77.78/10.62 (demorgan2a2) => 77.78/10.62 (( 77.78/10.62 (demorgan1a) => 77.78/10.62 (( 77.78/10.62 (demorgan1b) => 77.78/10.62 (( 77.78/10.62 (demorgan1) => 77.78/10.62 (( 77.78/10.62 (demorgan2a) => 77.78/10.62 (( 77.78/10.62 (demorgan2b2) => 77.78/10.62 (( 77.78/10.62 (demorgan2b) => 77.78/10.62 (( 77.78/10.62 (demorgan2) => 77.78/10.62 (( 77.78/10.62 (woz13rule0) => 77.78/10.62 (( 77.78/10.62 (woz13rule1) => 77.78/10.62 (( 77.78/10.62 (woz13rule2) => 77.78/10.62 (( 77.78/10.62 (woz13rule3) => 77.78/10.62 (( 77.78/10.62 (woz13rule4) => 77.78/10.62 (( 77.78/10.62 (woz1_1) => 77.78/10.62 (( 77.78/10.62 (woz1_2) => 77.78/10.62 (( 77.78/10.62 (woz1_3) => 77.78/10.62 (( 77.78/10.62 (woz1_4) => 77.78/10.62 (( 77.78/10.62 (woz1_5) => 77.78/10.62 (( 77.78/10.62 (breln1all2) => 77.78/10.62 (( 77.78/10.62 (breln1SetBreln1) => 77.78/10.62 (( 77.78/10.62 (choice2fnsingleton) => 77.78/10.62 (( 77.78/10.62 (setOfPairsIsBReln1) => 77.78/10.62 (( 77.78/10.62 (breln1all1) => 77.78/10.62 (( 77.78/10.62 (subbreln1) => 77.78/10.62 (( 77.78/10.62 (eqbreln1) => 77.78/10.62 (( 77.78/10.62 (breln1invprop) => 77.78/10.62 (( 77.78/10.62 (breln1invI) => 77.78/10.62 (( 77.78/10.62 (breln1invE) => 77.78/10.62 (( 77.78/10.62 (breln1compprop) => 77.78/10.62 (( 77.78/10.62 (breln1compI) => 77.78/10.62 (( 77.78/10.62 (breln1compE) => 77.78/10.62 (( 77.78/10.62 (breln1compEex) => 77.78/10.62 (( 77.78/10.62 (breln1unionprop) => 77.78/10.62 (( 77.78/10.62 (breln1unionIL) => 77.78/10.62 (( 77.78/10.62 (breln1unionIR) => 77.78/10.62 (( 77.78/10.62 (breln1unionI) => 77.78/10.62 (( 77.78/10.62 (breln1unionE) => 77.78/10.62 (( 77.78/10.62 (breln1unionEcases) => 77.78/10.62 (( 77.78/10.62 (breln1unionCommutes) => 77.78/10.62 (( 77.78/10.62 (woz2Ex) => 77.78/10.62 (( 77.78/10.62 (woz2W) => 77.78/10.62 (( 77.78/10.62 (woz2A) => 77.78/10.62 (( 77.78/10.62 (woz2B) => 77.78/10.62 (( 77.78/10.62 (image1Ex) => 77.78/10.62 (( 77.78/10.62 (image1Ex1) => 77.78/10.62 (( 77.78/10.62 (image1Equiv) => 77.78/10.62 (( 77.78/10.62 (image1E) => 77.78/10.62 (( 77.78/10.62 (image1I) => 77.78/10.62 (( 77.78/10.62 (injFuncInInjFuncSet) => 77.78/10.62 (( 77.78/10.62 (injFuncSetFuncIn) => 77.78/10.62 (( 77.78/10.62 (injFuncSetFuncInj) => 77.78/10.62 (( 77.78/10.62 (surjFuncSetFuncIn) => 77.78/10.62 (( 77.78/10.62 (surjFuncSetFuncSurj) => 77.78/10.62 (( 77.78/10.62 (leftInvIsSurj) => 77.78/10.62 (( 77.78/10.62 (surjCantorThm) => 77.78/10.62 (( 77.78/10.62 (foundation2) => 77.78/10.62 (( 77.78/10.62 (notinself) => 77.78/10.62 (( 77.78/10.62 (notinself2) => 77.78/10.62 (( 77.78/10.62 (omegaSp) => 77.78/10.62 (( 77.78/10.62 (omegaSclos) => 77.78/10.62 (( 77.78/10.62 (peano0notS) => 77.78/10.62 (( 77.78/10.62 (peanoSinj) => 77.78/10.62 (( 77.78/10.62 (transitivesetOp1) => 77.78/10.62 (( 77.78/10.62 (binintTransitive) => 77.78/10.62 (( 77.78/10.62 (transitivesetOp2) => 77.78/10.62 (( 77.78/10.62 (setunionTransitive) => 77.78/10.62 (( 77.78/10.62 (ordinalMinLem1) => 77.78/10.62 (( 77.78/10.62 (!!) @ ( 77.78/10.62 ^[Y0 : $i]: 77.78/10.62 (( 77.78/10.62 (ordinal @ 77.78/10.62 Y0) => 77.78/10.62 (( 77.78/10.62 (!!) @ ( 77.78/10.62 ^[Y1 : $i]: 77.78/10.62 (( 77.78/10.62 (!!) @ ( 77.78/10.62 ^[Y2 : $i]: 77.78/10.62 (( 77.78/10.62 (in @ 77.78/10.62 Y2 @ 77.78/10.62 Y0) => 77.78/10.62 (( 77.78/10.62 (in @ 77.78/10.62 Y1 @ 77.78/10.62 Y2) => 77.78/10.62 (in @ 77.78/10.62 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 77.78/10.62 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl578])). 77.78/10.62 thf(zip_derived_cl598, plain, 77.78/10.62 (~ (((exu__Cong) => 77.78/10.62 (((setadjoin__Cong) => 77.78/10.62 (((powerset__Cong) => 77.78/10.62 (((setunion__Cong) => 77.78/10.62 (((exuEu) => 77.78/10.62 (((descr__Cong) => 77.78/10.62 (((dsetconstr__Cong) => 77.78/10.62 (((subsetI1) => 77.78/10.62 (((eqimpsubset2) => 77.78/10.62 (((eqimpsubset1) => 77.78/10.62 (((subsetI2) => 77.78/10.62 (((emptysetsubset) => 77.78/10.62 (((subsetE) => 77.78/10.62 (((subsetE2) => 77.78/10.62 (((notsubsetI) => 77.78/10.62 (((notequalI1) => 77.78/10.62 (((notequalI2) => 77.78/10.62 (((subsetRefl) => 77.78/10.62 (((subsetTrans) => 77.78/10.62 (((setadjoinSub) => 77.78/10.62 (((setadjoinSub2) => 77.78/10.62 (((subset2powerset) => 77.78/10.62 (((setextsub) => 77.78/10.62 (((subsetemptysetimpeq) => 77.78/10.62 (((powersetI1) => 77.78/10.62 (((powersetE1) => 77.78/10.62 (((inPowerset) => 77.78/10.62 (((powersetsubset) => 77.78/10.62 (((sepInPowerset) => 77.78/10.62 (((sepSubset) => 77.78/10.62 (( 77.78/10.62 (binunionIL) => 77.78/10.62 (( 77.78/10.62 (upairset2IR) => 77.78/10.62 (( 77.78/10.62 (binunionIR) => 77.78/10.62 (( 77.78/10.62 (binunionEcases) => 77.78/10.62 (( 77.78/10.62 (binunionE) => 77.78/10.62 (( 77.78/10.62 (binunionLsub) => 77.78/10.62 (( 77.78/10.62 (binunionRsub) => 77.78/10.62 (( 77.78/10.62 (binintersectI) => 77.78/10.62 (( 77.78/10.62 (binintersectSubset5) => 77.78/10.62 (( 77.78/10.62 (binintersectEL) => 77.78/10.62 (( 77.78/10.62 (binintersectLsub) => 77.78/10.62 (( 77.78/10.62 (binintersectSubset2) => 77.78/10.62 (( 77.78/10.62 (binintersectSubset3) => 77.78/10.62 (( 77.78/10.62 (binintersectER) => 77.78/10.62 (( 77.78/10.62 (disjointsetsI1) => 77.78/10.62 (( 77.78/10.62 (binintersectRsub) => 77.78/10.62 (( 77.78/10.62 (binintersectSubset4) => 77.78/10.62 (( 77.78/10.62 (binintersectSubset1) => 77.78/10.62 (( 77.78/10.62 (bs114d) => 77.78/10.62 (( 77.78/10.62 (setminusI) => 77.78/10.62 (( 77.78/10.62 (setminusEL) => 77.78/10.62 (( 77.78/10.62 (setminusER) => 77.78/10.62 (( 77.78/10.62 (setminusSubset2) => 77.78/10.62 (( 77.78/10.62 (setminusERneg) => 77.78/10.62 (( 77.78/10.62 (setminusELneg) => 77.78/10.62 (( 77.78/10.62 (setminusILneg) => 77.78/10.62 (( 77.78/10.62 (setminusIRneg) => 77.78/10.62 (( 77.78/10.62 (setminusLsub) => 77.78/10.62 (( 77.78/10.62 (setminusSubset1) => 77.78/10.62 (( 77.78/10.62 (symdiffE) => 77.78/10.62 (( 77.78/10.62 (symdiffI1) => 77.78/10.62 (( 77.78/10.62 (symdiffI2) => 77.78/10.62 (( 77.78/10.62 (symdiffIneg1) => 77.78/10.62 (( 77.78/10.62 (symdiffIneg2) => 77.78/10.62 (( 77.78/10.62 (secondinupair) => 77.78/10.62 (( 77.78/10.62 (setukpairIL) => 77.78/10.62 (( 77.78/10.62 (setukpairIR) => 77.78/10.62 (( 77.78/10.62 (kpairiskpair) => 77.78/10.62 (( 77.78/10.62 (kpairp) => 77.78/10.62 (( 77.78/10.62 (singletonsubset) => 77.78/10.62 (( 77.78/10.62 (singletoninpowerset) => 77.78/10.62 (( 77.78/10.62 (singletoninpowunion) => 77.78/10.62 (( 77.78/10.62 (upairset2E) => 77.78/10.62 (( 77.78/10.62 (upairsubunion) => 77.78/10.62 (( 77.78/10.62 (upairinpowunion) => 77.78/10.62 (( 77.78/10.62 (ubforcartprodlem1) => 77.78/10.62 (( 77.78/10.62 (ubforcartprodlem2) => 77.78/10.62 (( 77.78/10.62 (ubforcartprodlem3) => 77.78/10.62 (( 77.78/10.62 (cartprodpairin) => 77.78/10.62 (( 77.78/10.62 (cartprodmempair1) => 77.78/10.62 (( 77.78/10.62 (cartprodmempair) => 77.78/10.62 (( 77.78/10.62 (setunionE2) => 77.78/10.62 (( 77.78/10.62 (setunionsingleton1) => 77.78/10.62 (( 77.78/10.62 (setunionsingleton2) => 77.78/10.62 (( 77.78/10.62 (setunionsingleton) => 77.78/10.62 (( 77.78/10.62 (singletonprop) => 77.78/10.62 (( 77.78/10.62 (ex1E1) => 77.78/10.62 (( 77.78/10.62 (ex1I) => 77.78/10.62 (( 77.78/10.62 (ex1I2) => 77.78/10.62 (( 77.78/10.62 (singletonsuniq) => 77.78/10.62 (( 77.78/10.62 (setukpairinjL1) => 77.78/10.62 (( 77.78/10.62 (kfstsingleton) => 77.78/10.62 (( 77.78/10.62 (theprop) => 77.78/10.62 (( 77.78/10.62 (kfstpairEq) => 77.78/10.62 (( 77.78/10.62 (cartprodfstin) => 77.78/10.62 (( 77.78/10.62 (setukpairinjL2) => 77.78/10.62 (( 77.78/10.62 (setukpairinjL) => 77.78/10.62 (( 77.78/10.62 (setukpairinjR11) => 77.78/10.62 (( 77.78/10.62 (setukpairinjR12) => 77.78/10.62 (( 77.78/10.62 (setukpairinjR1) => 77.78/10.62 (( 77.78/10.62 (upairequniteq) => 77.78/10.62 (( 77.78/10.62 (setukpairinjR2) => 77.78/10.62 (( 77.78/10.62 (setukpairinjR) => 77.78/10.62 (( 77.78/10.62 (ksndsingleton) => 77.78/10.62 (( 77.78/10.62 (ksndpairEq) => 77.78/10.62 (( 77.78/10.62 (kpairsurjEq) => 77.78/10.62 (( 77.78/10.62 (cartprodsndin) => 77.78/10.62 (( 77.78/10.62 (cartprodpairmemEL) => 77.78/10.62 (( 77.78/10.62 (cartprodpairmemER) => 77.78/10.62 (( 77.78/10.62 (cartprodmempaircEq) => 77.78/10.62 (( 77.78/10.62 (cartprodfstpairEq) => 77.78/10.62 (( 77.78/10.62 (cartprodsndpairEq) => 77.78/10.62 (( 77.78/10.62 (cartprodpairsurjEq) => 77.78/10.62 (( 77.78/10.62 (dpsetconstrI) => 77.78/10.62 (( 77.78/10.62 (dpsetconstrSub) => 77.78/10.62 (( 77.78/10.62 (setOfPairsIsBReln) => 77.78/10.62 (( 77.78/10.62 (dpsetconstrERa) => 77.78/10.62 (( 77.78/10.62 (dpsetconstrEL1) => 77.78/10.62 (( 77.78/10.62 (dpsetconstrEL2) => 77.78/10.62 (( 77.78/10.62 (dpsetconstrER) => 77.78/10.62 (( 77.78/10.62 (funcImageSingleton) => 77.78/10.62 (( 77.78/10.62 (apProp) => 77.78/10.62 (( 77.78/10.62 (app) => 77.78/10.62 (( 77.78/10.62 (infuncsetfunc) => 77.78/10.62 (( 77.78/10.62 (ap2p) => 77.78/10.62 (( 77.78/10.62 (funcinfuncset) => 77.78/10.62 (( 77.78/10.62 (lamProp) => 77.78/10.62 (( 77.78/10.62 (lamp) => 77.78/10.62 (( 77.78/10.62 (lam2p) => 77.78/10.62 (( 77.78/10.62 (brelnall1) => 77.78/10.62 (( 77.78/10.62 (brelnall2) => 77.78/10.62 (( 77.78/10.62 (ex1E2) => 77.78/10.62 (( 77.78/10.62 (funcGraphProp1) => 77.78/10.62 (( 77.78/10.62 (funcGraphProp3) => 77.78/10.62 (( 77.78/10.62 (funcGraphProp2) => 77.78/10.62 (( 77.78/10.62 (funcextLem) => 77.78/10.62 (( 77.78/10.62 (funcGraphProp4) => 77.78/10.62 (( 77.78/10.62 (subbreln) => 77.78/10.62 (( 77.78/10.62 (eqbreln) => 77.78/10.62 (( 77.78/10.62 (funcext) => 77.78/10.62 (( 77.78/10.62 (funcext2) => 77.78/10.62 (( 77.78/10.62 (ap2apEq1) => 77.78/10.62 (( 77.78/10.62 (ap2apEq2) => 77.78/10.62 (( 77.78/10.62 (beta1) => 77.78/10.62 (( 77.78/10.62 (eta1) => 77.78/10.62 (( 77.78/10.62 (lam2lamEq) => 77.78/10.62 (( 77.78/10.62 (beta2) => 77.78/10.62 (( 77.78/10.62 (eta2) => 77.78/10.62 (( 77.78/10.62 (iffalseProp1) => 77.78/10.62 (( 77.78/10.62 (iffalseProp2) => 77.78/10.62 (( 77.78/10.62 (iftrueProp1) => 77.78/10.62 (( 77.78/10.62 (iftrueProp2) => 77.78/10.62 (( 77.78/10.62 (ifSingleton) => 77.78/10.62 (( 77.78/10.62 (ifp) => 77.78/10.62 (( 77.78/10.62 (theeq) => 77.78/10.62 (( 77.78/10.62 (iftrue) => 77.78/10.62 (( 77.78/10.62 (iffalse) => 77.78/10.62 (( 77.78/10.62 (iftrueorfalse) => 77.78/10.62 (( 77.78/10.62 (binintersectT_lem) => 77.78/10.62 (( 77.78/10.62 (binunionT_lem) => 77.78/10.62 (( 77.78/10.62 (powersetT_lem) => 77.78/10.62 (( 77.78/10.62 (setminusT_lem) => 77.78/10.62 (( 77.78/10.62 (complementT_lem) => 77.78/10.62 (( 77.78/10.62 (setextT) => 77.78/10.62 (( 77.78/10.62 (subsetTI) => 77.78/10.62 (( 77.78/10.62 (powersetTI1) => 77.78/10.62 (( 77.78/10.62 (powersetTE1) => 77.78/10.62 (( 77.78/10.62 (complementTI1) => 77.78/10.62 (( 77.78/10.62 (complementTE1) => 77.78/10.62 (( 77.78/10.62 (binintersectTELcontra) => 77.78/10.62 (( 77.78/10.62 (binintersectTERcontra) => 77.78/10.62 (( 77.78/10.62 (contrasubsetT) => 77.78/10.62 (( 77.78/10.62 (contrasubsetT1) => 77.78/10.62 (( 77.78/10.62 (contrasubsetT2) => 77.78/10.62 (( 77.78/10.62 (contrasubsetT3) => 77.78/10.62 (( 77.78/10.62 (doubleComplementI1) => 77.78/10.62 (( 77.78/10.62 (doubleComplementE1) => 77.78/10.62 (( 77.78/10.62 (doubleComplementSub1) => 77.78/10.62 (( 77.78/10.62 (doubleComplementSub2) => 77.78/10.62 (( 77.78/10.62 (doubleComplementEq) => 77.78/10.62 (( 77.78/10.62 (complementTnotintersectT) => 77.78/10.62 (( 77.78/10.62 (complementImpComplementIntersect) => 77.78/10.62 (( 77.78/10.62 (complementSubsetComplementIntersect) => 77.78/10.62 (( 77.78/10.62 (complementInPowersetComplementIntersect) => 77.78/10.62 (( 77.78/10.62 (contraSubsetComplement) => 77.78/10.62 (( 77.78/10.62 (complementTcontraSubset) => 77.78/10.62 (( 77.78/10.62 (binunionTILcontra) => 77.78/10.62 (( 77.78/10.62 (binunionTIRcontra) => 77.78/10.62 (( 77.78/10.62 (inIntersectImpInUnion) => 77.78/10.62 (( 77.78/10.62 (inIntersectImpInUnion2) => 77.78/10.62 (( 77.78/10.62 (inIntersectImpInIntersectUnions) => 77.78/10.62 (( 77.78/10.62 (intersectInPowersetIntersectUnions) => 77.78/10.62 (( 77.78/10.62 (inComplementUnionImpNotIn1) => 77.78/10.62 (( 77.78/10.62 (inComplementUnionImpInComplement1) => 77.78/10.62 (( 77.78/10.62 (binunionTE) => 77.78/10.62 (( 77.78/10.62 (binunionTEcontra) => 77.78/10.62 (( 77.78/10.62 (demorgan2a1) => 77.78/10.62 (( 77.78/10.62 (complementUnionInPowersetComplement) => 77.78/10.62 (( 77.78/10.62 (demorgan2a2) => 77.78/10.62 (( 77.78/10.62 (demorgan1a) => 77.78/10.62 (( 77.78/10.62 (demorgan1b) => 77.78/10.62 (( 77.78/10.62 (demorgan1) => 77.78/10.62 (( 77.78/10.62 (demorgan2a) => 77.78/10.62 (( 77.78/10.62 (demorgan2b2) => 77.78/10.62 (( 77.78/10.62 (demorgan2b) => 77.78/10.62 (( 77.78/10.62 (demorgan2) => 77.78/10.62 (( 77.78/10.62 (woz13rule0) => 77.78/10.62 (( 77.78/10.62 (woz13rule1) => 77.78/10.62 (( 77.78/10.62 (woz13rule2) => 77.78/10.62 (( 77.78/10.62 (woz13rule3) => 77.78/10.62 (( 77.78/10.62 (woz13rule4) => 77.78/10.62 (( 77.78/10.62 (woz1_1) => 77.78/10.62 (( 77.78/10.62 (woz1_2) => 77.78/10.62 (( 77.78/10.62 (woz1_3) => 77.78/10.62 (( 77.78/10.62 (woz1_4) => 77.78/10.62 (( 77.78/10.62 (woz1_5) => 77.78/10.62 (( 77.78/10.62 (breln1all2) => 77.78/10.62 (( 77.78/10.62 (breln1SetBreln1) => 77.78/10.62 (( 77.78/10.62 (choice2fnsingleton) => 77.78/10.62 (( 77.78/10.62 (setOfPairsIsBReln1) => 77.78/10.62 (( 77.78/10.62 (breln1all1) => 77.78/10.62 (( 77.78/10.62 (subbreln1) => 77.78/10.62 (( 77.78/10.62 (eqbreln1) => 77.78/10.62 (( 77.78/10.62 (breln1invprop) => 77.78/10.62 (( 77.78/10.62 (breln1invI) => 77.78/10.62 (( 77.78/10.62 (breln1invE) => 77.78/10.62 (( 77.78/10.62 (breln1compprop) => 77.78/10.62 (( 77.78/10.62 (breln1compI) => 77.78/10.62 (( 77.78/10.62 (breln1compE) => 77.78/10.62 (( 77.78/10.62 (breln1compEex) => 77.78/10.62 (( 77.78/10.62 (breln1unionprop) => 77.78/10.62 (( 77.78/10.62 (breln1unionIL) => 77.78/10.62 (( 77.78/10.62 (breln1unionIR) => 77.78/10.62 (( 77.78/10.62 (breln1unionI) => 77.78/10.62 (( 77.78/10.62 (breln1unionE) => 77.78/10.62 (( 77.78/10.62 (breln1unionEcases) => 77.78/10.62 (( 77.78/10.62 (breln1unionCommutes) => 77.78/10.62 (( 77.78/10.62 (woz2Ex) => 77.78/10.62 (( 77.78/10.62 (woz2W) => 77.78/10.62 (( 77.78/10.62 (woz2A) => 77.78/10.62 (( 77.78/10.62 (woz2B) => 77.78/10.62 (( 77.78/10.62 (image1Ex) => 77.78/10.62 (( 77.78/10.62 (image1Ex1) => 77.78/10.62 (( 77.78/10.62 (image1Equiv) => 77.78/10.62 (( 77.78/10.62 (image1E) => 77.78/10.62 (( 77.78/10.62 (image1I) => 77.78/10.62 (( 77.78/10.62 (injFuncInInjFuncSet) => 77.78/10.62 (( 77.78/10.62 (injFuncSetFuncIn) => 77.78/10.62 (( 77.78/10.62 (injFuncSetFuncInj) => 77.78/10.62 (( 77.78/10.62 (surjFuncSetFuncIn) => 77.78/10.62 (( 77.78/10.62 (surjFuncSetFuncSurj) => 77.78/10.62 (( 77.78/10.62 (leftInvIsSurj) => 77.78/10.62 (( 77.78/10.62 (surjCantorThm) => 77.78/10.62 (( 77.78/10.62 (foundation2) => 77.78/10.62 (( 77.78/10.62 (notinself) => 77.78/10.62 (( 77.78/10.62 (notinself2) => 77.78/10.62 (( 77.78/10.62 (omegaSp) => 77.78/10.62 (( 77.78/10.62 (omegaSclos) => 77.78/10.62 (( 77.78/10.62 (peano0notS) => 77.78/10.62 (( 77.78/10.62 (peanoSinj) => 77.78/10.62 (( 77.78/10.62 (transitivesetOp1) => 77.78/10.62 (( 77.78/10.62 (binintTransitive) => 77.78/10.62 (( 77.78/10.62 (transitivesetOp2) => 77.78/10.62 (( 77.78/10.62 (setunionTransitive) => 77.78/10.62 (( 77.78/10.62 (ordinalMinLem1) => 77.78/10.62 (( 77.78/10.62 (!!) @ ( 77.78/10.62 ^[Y0 : $i]: 77.78/10.62 (( 77.78/10.62 (ordinal @ 77.78/10.62 Y0) => 77.78/10.62 (( 77.78/10.62 (!!) @ ( 77.78/10.62 ^[Y1 : $i]: 77.78/10.62 (( 77.78/10.62 (!!) @ ( 77.78/10.62 ^[Y2 : $i]: 77.78/10.62 (( 77.78/10.62 (in @ 77.78/10.62 Y2 @ 77.78/10.62 Y0) => 77.78/10.62 (( 77.78/10.62 (in @ 77.78/10.62 Y1 @ 77.78/10.62 Y2) => 77.78/10.62 (in @ 77.78/10.62 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 77.78/10.62 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl588])). 77.78/10.62 thf(zip_derived_cl609, plain, 77.78/10.62 (~ (((setadjoin__Cong) => 77.78/10.62 (((powerset__Cong) => 77.78/10.62 (((setunion__Cong) => 77.78/10.62 (((exuEu) => 77.78/10.62 (((descr__Cong) => 77.78/10.62 (((dsetconstr__Cong) => 77.78/10.62 (((subsetI1) => 77.78/10.62 (((eqimpsubset2) => 77.78/10.62 (((eqimpsubset1) => 77.78/10.62 (((subsetI2) => 77.78/10.62 (((emptysetsubset) => 77.78/10.62 (((subsetE) => 77.78/10.62 (((subsetE2) => 77.78/10.62 (((notsubsetI) => 77.78/10.62 (((notequalI1) => 77.78/10.62 (((notequalI2) => 77.78/10.62 (((subsetRefl) => 77.78/10.62 (((subsetTrans) => 77.78/10.62 (((setadjoinSub) => 77.78/10.62 (((setadjoinSub2) => 77.78/10.62 (((subset2powerset) => 77.78/10.62 (((setextsub) => 77.78/10.62 (((subsetemptysetimpeq) => 77.78/10.62 (((powersetI1) => 77.78/10.62 (((powersetE1) => 77.78/10.62 (((inPowerset) => 77.78/10.62 (((powersetsubset) => 77.78/10.62 (((sepInPowerset) => 77.78/10.62 (((sepSubset) => 77.78/10.62 (((binunionIL) => 77.78/10.62 (( 77.78/10.62 (upairset2IR) => 77.78/10.62 (( 77.78/10.62 (binunionIR) => 77.78/10.62 (( 77.78/10.62 (binunionEcases) => 77.78/10.62 (( 77.78/10.62 (binunionE) => 77.78/10.62 (( 77.78/10.62 (binunionLsub) => 77.78/10.62 (( 77.78/10.62 (binunionRsub) => 77.78/10.62 (( 77.78/10.62 (binintersectI) => 77.78/10.62 (( 77.78/10.62 (binintersectSubset5) => 77.78/10.62 (( 77.78/10.62 (binintersectEL) => 77.78/10.62 (( 77.78/10.62 (binintersectLsub) => 77.78/10.62 (( 77.78/10.62 (binintersectSubset2) => 77.78/10.62 (( 77.78/10.62 (binintersectSubset3) => 77.78/10.62 (( 77.78/10.62 (binintersectER) => 77.78/10.62 (( 77.78/10.62 (disjointsetsI1) => 77.78/10.62 (( 77.78/10.62 (binintersectRsub) => 77.78/10.62 (( 77.78/10.62 (binintersectSubset4) => 77.78/10.62 (( 77.78/10.62 (binintersectSubset1) => 77.78/10.62 (( 77.78/10.62 (bs114d) => 77.78/10.62 (( 77.78/10.62 (setminusI) => 77.78/10.62 (( 77.78/10.62 (setminusEL) => 77.78/10.62 (( 77.78/10.62 (setminusER) => 77.78/10.62 (( 77.78/10.62 (setminusSubset2) => 77.78/10.62 (( 77.78/10.62 (setminusERneg) => 77.78/10.62 (( 77.78/10.62 (setminusELneg) => 77.78/10.62 (( 77.78/10.62 (setminusILneg) => 77.78/10.62 (( 77.78/10.62 (setminusIRneg) => 77.78/10.62 (( 77.78/10.62 (setminusLsub) => 77.78/10.62 (( 77.78/10.62 (setminusSubset1) => 77.78/10.62 (( 77.78/10.62 (symdiffE) => 77.78/10.62 (( 77.78/10.62 (symdiffI1) => 77.78/10.62 (( 77.78/10.62 (symdiffI2) => 77.78/10.62 (( 77.78/10.62 (symdiffIneg1) => 77.78/10.62 (( 77.78/10.62 (symdiffIneg2) => 77.78/10.62 (( 77.78/10.62 (secondinupair) => 77.78/10.62 (( 77.78/10.62 (setukpairIL) => 77.78/10.62 (( 77.78/10.62 (setukpairIR) => 77.78/10.62 (( 77.78/10.62 (kpairiskpair) => 77.78/10.62 (( 77.78/10.62 (kpairp) => 77.78/10.62 (( 77.78/10.62 (singletonsubset) => 77.78/10.62 (( 77.78/10.62 (singletoninpowerset) => 77.78/10.62 (( 77.78/10.62 (singletoninpowunion) => 77.78/10.62 (( 77.78/10.62 (upairset2E) => 77.78/10.62 (( 77.78/10.62 (upairsubunion) => 77.78/10.62 (( 77.78/10.62 (upairinpowunion) => 77.78/10.62 (( 77.78/10.62 (ubforcartprodlem1) => 77.78/10.62 (( 77.78/10.62 (ubforcartprodlem2) => 77.78/10.62 (( 77.78/10.62 (ubforcartprodlem3) => 77.78/10.62 (( 77.78/10.62 (cartprodpairin) => 77.78/10.62 (( 77.78/10.62 (cartprodmempair1) => 77.78/10.62 (( 77.78/10.62 (cartprodmempair) => 77.78/10.62 (( 77.78/10.62 (setunionE2) => 77.78/10.62 (( 77.78/10.62 (setunionsingleton1) => 77.78/10.62 (( 77.78/10.62 (setunionsingleton2) => 77.78/10.62 (( 77.78/10.62 (setunionsingleton) => 77.78/10.62 (( 77.78/10.62 (singletonprop) => 77.78/10.62 (( 77.78/10.62 (ex1E1) => 77.78/10.62 (( 77.78/10.62 (ex1I) => 77.78/10.62 (( 77.78/10.62 (ex1I2) => 77.78/10.62 (( 77.78/10.62 (singletonsuniq) => 77.78/10.62 (( 77.78/10.62 (setukpairinjL1) => 77.78/10.62 (( 77.78/10.62 (kfstsingleton) => 77.78/10.62 (( 77.78/10.62 (theprop) => 77.78/10.62 (( 77.78/10.62 (kfstpairEq) => 77.78/10.62 (( 77.78/10.62 (cartprodfstin) => 77.78/10.62 (( 77.78/10.62 (setukpairinjL2) => 77.78/10.62 (( 77.78/10.62 (setukpairinjL) => 77.78/10.62 (( 77.78/10.62 (setukpairinjR11) => 77.78/10.62 (( 77.78/10.62 (setukpairinjR12) => 77.78/10.62 (( 77.78/10.62 (setukpairinjR1) => 77.78/10.62 (( 77.78/10.62 (upairequniteq) => 77.78/10.62 (( 77.78/10.62 (setukpairinjR2) => 77.78/10.62 (( 77.78/10.62 (setukpairinjR) => 77.78/10.62 (( 77.78/10.62 (ksndsingleton) => 77.78/10.62 (( 77.78/10.62 (ksndpairEq) => 77.78/10.62 (( 77.78/10.62 (kpairsurjEq) => 77.78/10.62 (( 77.78/10.62 (cartprodsndin) => 77.78/10.62 (( 77.78/10.62 (cartprodpairmemEL) => 77.78/10.62 (( 77.78/10.62 (cartprodpairmemER) => 77.78/10.62 (( 77.78/10.62 (cartprodmempaircEq) => 77.78/10.62 (( 77.78/10.62 (cartprodfstpairEq) => 77.78/10.62 (( 77.78/10.62 (cartprodsndpairEq) => 77.78/10.62 (( 77.78/10.62 (cartprodpairsurjEq) => 77.78/10.62 (( 77.78/10.62 (dpsetconstrI) => 77.78/10.62 (( 77.78/10.62 (dpsetconstrSub) => 77.78/10.62 (( 77.78/10.62 (setOfPairsIsBReln) => 77.78/10.62 (( 77.78/10.62 (dpsetconstrERa) => 77.78/10.62 (( 77.78/10.62 (dpsetconstrEL1) => 77.78/10.62 (( 77.78/10.62 (dpsetconstrEL2) => 77.78/10.62 (( 77.78/10.62 (dpsetconstrER) => 77.78/10.62 (( 77.78/10.62 (funcImageSingleton) => 77.78/10.62 (( 77.78/10.62 (apProp) => 77.78/10.62 (( 77.78/10.62 (app) => 77.78/10.62 (( 77.78/10.62 (infuncsetfunc) => 77.78/10.62 (( 77.78/10.62 (ap2p) => 77.78/10.62 (( 77.78/10.62 (funcinfuncset) => 77.78/10.62 (( 77.78/10.62 (lamProp) => 77.78/10.62 (( 77.78/10.62 (lamp) => 77.78/10.62 (( 77.78/10.62 (lam2p) => 77.78/10.62 (( 77.78/10.62 (brelnall1) => 77.78/10.62 (( 77.78/10.62 (brelnall2) => 77.78/10.62 (( 77.78/10.62 (ex1E2) => 77.78/10.62 (( 77.78/10.62 (funcGraphProp1) => 77.78/10.62 (( 77.78/10.62 (funcGraphProp3) => 77.78/10.62 (( 77.78/10.62 (funcGraphProp2) => 77.78/10.62 (( 77.78/10.62 (funcextLem) => 77.78/10.62 (( 77.78/10.62 (funcGraphProp4) => 77.78/10.62 (( 77.78/10.62 (subbreln) => 77.78/10.62 (( 77.78/10.62 (eqbreln) => 77.78/10.62 (( 77.78/10.62 (funcext) => 77.78/10.62 (( 77.78/10.62 (funcext2) => 77.78/10.62 (( 77.78/10.62 (ap2apEq1) => 77.78/10.62 (( 77.78/10.62 (ap2apEq2) => 77.78/10.62 (( 77.78/10.62 (beta1) => 77.78/10.62 (( 77.78/10.62 (eta1) => 77.78/10.62 (( 77.78/10.62 (lam2lamEq) => 77.78/10.62 (( 77.78/10.62 (beta2) => 77.78/10.62 (( 77.78/10.62 (eta2) => 77.78/10.62 (( 77.78/10.62 (iffalseProp1) => 77.78/10.62 (( 77.78/10.62 (iffalseProp2) => 77.78/10.62 (( 77.78/10.62 (iftrueProp1) => 77.78/10.62 (( 77.78/10.62 (iftrueProp2) => 77.78/10.62 (( 77.78/10.62 (ifSingleton) => 77.78/10.62 (( 77.78/10.62 (ifp) => 77.78/10.62 (( 77.78/10.62 (theeq) => 77.78/10.62 (( 77.78/10.62 (iftrue) => 77.78/10.62 (( 77.78/10.62 (iffalse) => 77.78/10.62 (( 77.78/10.62 (iftrueorfalse) => 77.78/10.62 (( 77.78/10.62 (binintersectT_lem) => 77.78/10.62 (( 77.78/10.62 (binunionT_lem) => 77.78/10.62 (( 77.78/10.62 (powersetT_lem) => 77.78/10.62 (( 77.78/10.62 (setminusT_lem) => 77.78/10.62 (( 77.78/10.62 (complementT_lem) => 77.78/10.62 (( 77.78/10.62 (setextT) => 77.78/10.62 (( 77.78/10.62 (subsetTI) => 77.78/10.62 (( 77.78/10.62 (powersetTI1) => 77.78/10.62 (( 77.78/10.62 (powersetTE1) => 77.78/10.62 (( 77.78/10.62 (complementTI1) => 77.78/10.62 (( 77.78/10.62 (complementTE1) => 77.78/10.62 (( 77.78/10.62 (binintersectTELcontra) => 77.78/10.62 (( 77.78/10.62 (binintersectTERcontra) => 77.78/10.62 (( 77.78/10.62 (contrasubsetT) => 77.78/10.62 (( 77.78/10.62 (contrasubsetT1) => 77.78/10.62 (( 77.78/10.62 (contrasubsetT2) => 77.78/10.62 (( 77.78/10.62 (contrasubsetT3) => 77.78/10.62 (( 77.78/10.62 (doubleComplementI1) => 77.78/10.62 (( 77.78/10.62 (doubleComplementE1) => 77.78/10.62 (( 77.78/10.62 (doubleComplementSub1) => 77.78/10.62 (( 77.78/10.62 (doubleComplementSub2) => 77.78/10.62 (( 77.78/10.62 (doubleComplementEq) => 77.78/10.62 (( 77.78/10.62 (complementTnotintersectT) => 77.78/10.62 (( 77.78/10.62 (complementImpComplementIntersect) => 77.78/10.62 (( 77.78/10.62 (complementSubsetComplementIntersect) => 77.78/10.62 (( 77.78/10.62 (complementInPowersetComplementIntersect) => 77.78/10.62 (( 77.78/10.62 (contraSubsetComplement) => 77.78/10.62 (( 77.78/10.62 (complementTcontraSubset) => 77.78/10.62 (( 77.78/10.62 (binunionTILcontra) => 77.78/10.62 (( 77.78/10.62 (binunionTIRcontra) => 77.78/10.62 (( 77.78/10.62 (inIntersectImpInUnion) => 77.78/10.62 (( 77.78/10.62 (inIntersectImpInUnion2) => 77.78/10.62 (( 77.78/10.62 (inIntersectImpInIntersectUnions) => 77.78/10.62 (( 77.78/10.62 (intersectInPowersetIntersectUnions) => 77.78/10.62 (( 77.78/10.62 (inComplementUnionImpNotIn1) => 77.78/10.62 (( 77.78/10.62 (inComplementUnionImpInComplement1) => 77.78/10.62 (( 77.78/10.62 (binunionTE) => 77.78/10.62 (( 77.78/10.62 (binunionTEcontra) => 77.78/10.62 (( 77.78/10.62 (demorgan2a1) => 77.78/10.62 (( 77.78/10.62 (complementUnionInPowersetComplement) => 77.78/10.62 (( 77.78/10.62 (demorgan2a2) => 77.78/10.62 (( 77.78/10.62 (demorgan1a) => 77.78/10.62 (( 77.78/10.62 (demorgan1b) => 77.78/10.62 (( 77.78/10.62 (demorgan1) => 77.78/10.62 (( 77.78/10.62 (demorgan2a) => 77.78/10.62 (( 77.78/10.62 (demorgan2b2) => 77.78/10.62 (( 77.78/10.62 (demorgan2b) => 77.78/10.62 (( 77.78/10.62 (demorgan2) => 77.78/10.62 (( 77.78/10.62 (woz13rule0) => 77.78/10.62 (( 77.78/10.62 (woz13rule1) => 77.78/10.62 (( 77.78/10.62 (woz13rule2) => 77.78/10.62 (( 77.78/10.62 (woz13rule3) => 77.78/10.62 (( 77.78/10.62 (woz13rule4) => 77.78/10.62 (( 77.78/10.62 (woz1_1) => 77.78/10.62 (( 77.78/10.62 (woz1_2) => 77.78/10.62 (( 77.78/10.62 (woz1_3) => 77.78/10.62 (( 77.78/10.62 (woz1_4) => 77.78/10.62 (( 77.78/10.62 (woz1_5) => 77.78/10.62 (( 77.78/10.62 (breln1all2) => 77.78/10.62 (( 77.78/10.62 (breln1SetBreln1) => 77.78/10.62 (( 77.78/10.62 (choice2fnsingleton) => 77.78/10.62 (( 77.78/10.62 (setOfPairsIsBReln1) => 77.78/10.62 (( 77.78/10.62 (breln1all1) => 77.78/10.62 (( 77.78/10.62 (subbreln1) => 77.78/10.62 (( 77.78/10.62 (eqbreln1) => 77.78/10.62 (( 77.78/10.62 (breln1invprop) => 77.78/10.62 (( 77.78/10.62 (breln1invI) => 77.78/10.62 (( 77.78/10.62 (breln1invE) => 77.78/10.62 (( 77.78/10.62 (breln1compprop) => 77.78/10.62 (( 77.78/10.62 (breln1compI) => 77.78/10.62 (( 77.78/10.62 (breln1compE) => 77.78/10.62 (( 77.78/10.62 (breln1compEex) => 77.78/10.62 (( 77.78/10.62 (breln1unionprop) => 77.78/10.62 (( 77.78/10.62 (breln1unionIL) => 77.78/10.62 (( 77.78/10.62 (breln1unionIR) => 77.78/10.62 (( 77.78/10.62 (breln1unionI) => 77.78/10.62 (( 77.78/10.62 (breln1unionE) => 77.78/10.62 (( 77.78/10.62 (breln1unionEcases) => 77.78/10.62 (( 77.78/10.62 (breln1unionCommutes) => 77.78/10.62 (( 77.78/10.62 (woz2Ex) => 77.78/10.62 (( 77.78/10.62 (woz2W) => 77.78/10.62 (( 77.78/10.62 (woz2A) => 77.78/10.62 (( 77.78/10.62 (woz2B) => 77.78/10.62 (( 77.78/10.62 (image1Ex) => 77.78/10.62 (( 77.78/10.62 (image1Ex1) => 77.78/10.62 (( 77.78/10.62 (image1Equiv) => 77.78/10.62 (( 77.78/10.62 (image1E) => 77.78/10.62 (( 77.78/10.62 (image1I) => 77.78/10.62 (( 77.78/10.62 (injFuncInInjFuncSet) => 77.78/10.62 (( 77.78/10.62 (injFuncSetFuncIn) => 77.78/10.62 (( 77.78/10.62 (injFuncSetFuncInj) => 77.78/10.62 (( 77.78/10.62 (surjFuncSetFuncIn) => 77.78/10.62 (( 77.78/10.62 (surjFuncSetFuncSurj) => 77.78/10.62 (( 77.78/10.62 (leftInvIsSurj) => 77.78/10.62 (( 77.78/10.62 (surjCantorThm) => 77.78/10.62 (( 77.78/10.62 (foundation2) => 77.78/10.62 (( 77.78/10.62 (notinself) => 77.78/10.62 (( 77.78/10.62 (notinself2) => 77.78/10.62 (( 77.78/10.62 (omegaSp) => 77.78/10.62 (( 77.78/10.62 (omegaSclos) => 77.78/10.62 (( 77.78/10.62 (peano0notS) => 77.78/10.62 (( 77.78/10.62 (peanoSinj) => 77.78/10.62 (( 77.78/10.62 (transitivesetOp1) => 77.78/10.62 (( 77.78/10.62 (binintTransitive) => 77.78/10.62 (( 77.78/10.62 (transitivesetOp2) => 77.78/10.62 (( 77.78/10.62 (setunionTransitive) => 77.78/10.62 (( 77.78/10.62 (ordinalMinLem1) => 77.78/10.62 (( 77.78/10.62 (!!) @ ( 77.78/10.62 ^[Y0 : $i]: 77.78/10.62 (( 77.78/10.62 (ordinal @ 77.78/10.62 Y0) => 77.78/10.62 (( 77.78/10.62 (!!) @ ( 77.78/10.62 ^[Y1 : $i]: 77.78/10.62 (( 77.78/10.62 (!!) @ ( 77.78/10.62 ^[Y2 : $i]: 77.78/10.62 (( 77.78/10.62 (in @ 77.78/10.62 Y2 @ 77.78/10.62 Y0) => 77.78/10.62 (( 77.78/10.62 (in @ 77.78/10.62 Y1 @ 77.78/10.62 Y2) => 77.78/10.62 (in @ 77.78/10.62 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 77.78/10.62 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl598])). 77.78/10.62 thf(zip_derived_cl623, plain, 77.78/10.62 (~ (((powerset__Cong) => 77.78/10.62 (((setunion__Cong) => 77.78/10.62 (((exuEu) => 77.78/10.62 (((descr__Cong) => 77.78/10.62 (((dsetconstr__Cong) => 77.78/10.62 (((subsetI1) => 77.78/10.62 (((eqimpsubset2) => 77.78/10.62 (((eqimpsubset1) => 77.78/10.62 (((subsetI2) => 77.78/10.62 (((emptysetsubset) => 77.78/10.62 (((subsetE) => 77.78/10.62 (((subsetE2) => 77.78/10.62 (((notsubsetI) => 77.78/10.62 (((notequalI1) => 77.78/10.62 (((notequalI2) => 77.78/10.62 (((subsetRefl) => 77.78/10.62 (((subsetTrans) => 77.78/10.62 (((setadjoinSub) => 77.78/10.62 (((setadjoinSub2) => 77.78/10.62 (((subset2powerset) => 77.78/10.62 (((setextsub) => 77.78/10.62 (((subsetemptysetimpeq) => 77.78/10.62 (((powersetI1) => 77.78/10.62 (((powersetE1) => 77.78/10.62 (((inPowerset) => 77.78/10.62 (((powersetsubset) => 77.78/10.62 (((sepInPowerset) => 77.78/10.62 (((sepSubset) => 77.78/10.62 (((binunionIL) => 77.78/10.62 (((upairset2IR) => 77.78/10.62 (( 77.78/10.62 (binunionIR) => 77.78/10.62 (( 77.78/10.62 (binunionEcases) => 77.78/10.62 (( 77.78/10.62 (binunionE) => 77.78/10.62 (( 77.78/10.62 (binunionLsub) => 77.78/10.62 (( 77.78/10.62 (binunionRsub) => 77.78/10.62 (( 77.78/10.62 (binintersectI) => 77.78/10.62 (( 77.78/10.62 (binintersectSubset5) => 77.78/10.62 (( 77.78/10.62 (binintersectEL) => 77.78/10.62 (( 77.78/10.62 (binintersectLsub) => 77.78/10.62 (( 77.78/10.62 (binintersectSubset2) => 77.78/10.62 (( 77.78/10.62 (binintersectSubset3) => 77.78/10.62 (( 77.78/10.62 (binintersectER) => 77.78/10.62 (( 77.78/10.62 (disjointsetsI1) => 77.78/10.62 (( 77.78/10.62 (binintersectRsub) => 77.78/10.62 (( 77.78/10.62 (binintersectSubset4) => 77.78/10.62 (( 77.78/10.62 (binintersectSubset1) => 77.78/10.62 (( 77.78/10.62 (bs114d) => 77.78/10.62 (( 77.78/10.62 (setminusI) => 77.78/10.62 (( 77.78/10.62 (setminusEL) => 77.78/10.62 (( 77.78/10.62 (setminusER) => 77.78/10.62 (( 77.78/10.62 (setminusSubset2) => 77.78/10.62 (( 77.78/10.62 (setminusERneg) => 77.78/10.62 (( 77.78/10.62 (setminusELneg) => 77.78/10.62 (( 77.78/10.62 (setminusILneg) => 77.78/10.62 (( 77.78/10.62 (setminusIRneg) => 77.78/10.62 (( 77.78/10.62 (setminusLsub) => 77.78/10.62 (( 77.78/10.62 (setminusSubset1) => 77.78/10.62 (( 77.78/10.62 (symdiffE) => 77.78/10.62 (( 77.78/10.62 (symdiffI1) => 77.78/10.62 (( 77.78/10.62 (symdiffI2) => 77.78/10.62 (( 77.78/10.62 (symdiffIneg1) => 77.78/10.62 (( 77.78/10.62 (symdiffIneg2) => 77.78/10.62 (( 77.78/10.62 (secondinupair) => 77.78/10.62 (( 77.78/10.62 (setukpairIL) => 77.78/10.62 (( 77.78/10.62 (setukpairIR) => 77.78/10.62 (( 77.78/10.62 (kpairiskpair) => 77.78/10.62 (( 77.78/10.62 (kpairp) => 77.78/10.62 (( 77.78/10.62 (singletonsubset) => 77.78/10.62 (( 77.78/10.62 (singletoninpowerset) => 77.78/10.62 (( 77.78/10.62 (singletoninpowunion) => 77.78/10.62 (( 77.78/10.62 (upairset2E) => 77.78/10.62 (( 77.78/10.62 (upairsubunion) => 77.78/10.62 (( 77.78/10.62 (upairinpowunion) => 77.78/10.62 (( 77.78/10.62 (ubforcartprodlem1) => 77.78/10.62 (( 77.78/10.62 (ubforcartprodlem2) => 77.78/10.62 (( 77.78/10.62 (ubforcartprodlem3) => 77.78/10.62 (( 77.78/10.62 (cartprodpairin) => 77.78/10.62 (( 77.78/10.62 (cartprodmempair1) => 77.78/10.62 (( 77.78/10.62 (cartprodmempair) => 77.78/10.62 (( 77.78/10.62 (setunionE2) => 77.78/10.62 (( 77.78/10.62 (setunionsingleton1) => 77.78/10.62 (( 77.78/10.62 (setunionsingleton2) => 77.78/10.62 (( 77.78/10.62 (setunionsingleton) => 77.78/10.62 (( 77.78/10.62 (singletonprop) => 77.78/10.62 (( 77.78/10.62 (ex1E1) => 77.78/10.62 (( 77.78/10.62 (ex1I) => 77.78/10.62 (( 77.78/10.62 (ex1I2) => 77.78/10.62 (( 77.78/10.62 (singletonsuniq) => 77.78/10.62 (( 77.78/10.62 (setukpairinjL1) => 77.78/10.62 (( 77.78/10.62 (kfstsingleton) => 77.78/10.62 (( 77.78/10.62 (theprop) => 77.78/10.62 (( 77.78/10.62 (kfstpairEq) => 77.78/10.62 (( 77.78/10.62 (cartprodfstin) => 77.78/10.62 (( 77.78/10.62 (setukpairinjL2) => 77.78/10.62 (( 77.78/10.62 (setukpairinjL) => 77.78/10.62 (( 77.78/10.62 (setukpairinjR11) => 77.78/10.62 (( 77.78/10.62 (setukpairinjR12) => 77.78/10.62 (( 77.78/10.62 (setukpairinjR1) => 77.78/10.62 (( 77.78/10.62 (upairequniteq) => 77.78/10.62 (( 77.78/10.62 (setukpairinjR2) => 77.78/10.62 (( 77.78/10.62 (setukpairinjR) => 77.78/10.62 (( 77.78/10.62 (ksndsingleton) => 77.78/10.62 (( 77.78/10.62 (ksndpairEq) => 77.78/10.62 (( 77.78/10.62 (kpairsurjEq) => 77.78/10.62 (( 77.78/10.62 (cartprodsndin) => 77.78/10.62 (( 77.78/10.62 (cartprodpairmemEL) => 77.78/10.62 (( 77.78/10.62 (cartprodpairmemER) => 77.78/10.62 (( 77.78/10.62 (cartprodmempaircEq) => 77.78/10.62 (( 77.78/10.62 (cartprodfstpairEq) => 77.78/10.62 (( 77.78/10.62 (cartprodsndpairEq) => 77.78/10.62 (( 77.78/10.62 (cartprodpairsurjEq) => 77.78/10.62 (( 77.78/10.62 (dpsetconstrI) => 77.78/10.62 (( 77.78/10.62 (dpsetconstrSub) => 77.78/10.62 (( 77.78/10.62 (setOfPairsIsBReln) => 77.78/10.62 (( 77.78/10.62 (dpsetconstrERa) => 77.78/10.62 (( 77.78/10.62 (dpsetconstrEL1) => 77.78/10.62 (( 77.78/10.62 (dpsetconstrEL2) => 77.78/10.62 (( 77.78/10.62 (dpsetconstrER) => 77.78/10.62 (( 77.78/10.62 (funcImageSingleton) => 77.78/10.62 (( 77.78/10.62 (apProp) => 77.78/10.62 (( 77.78/10.62 (app) => 77.78/10.62 (( 77.78/10.62 (infuncsetfunc) => 77.78/10.62 (( 77.78/10.62 (ap2p) => 77.78/10.62 (( 77.78/10.62 (funcinfuncset) => 77.78/10.62 (( 77.78/10.62 (lamProp) => 77.78/10.62 (( 77.78/10.62 (lamp) => 77.78/10.62 (( 77.78/10.62 (lam2p) => 77.78/10.62 (( 77.78/10.62 (brelnall1) => 77.78/10.62 (( 77.78/10.62 (brelnall2) => 77.78/10.62 (( 77.78/10.62 (ex1E2) => 77.78/10.62 (( 77.78/10.62 (funcGraphProp1) => 77.78/10.62 (( 77.78/10.62 (funcGraphProp3) => 77.78/10.62 (( 77.78/10.62 (funcGraphProp2) => 77.78/10.62 (( 77.78/10.62 (funcextLem) => 77.78/10.62 (( 77.78/10.62 (funcGraphProp4) => 77.78/10.62 (( 77.78/10.62 (subbreln) => 77.78/10.62 (( 77.78/10.62 (eqbreln) => 77.78/10.62 (( 77.78/10.62 (funcext) => 77.78/10.62 (( 77.78/10.62 (funcext2) => 77.78/10.62 (( 77.78/10.62 (ap2apEq1) => 77.78/10.62 (( 77.78/10.62 (ap2apEq2) => 77.78/10.62 (( 77.78/10.62 (beta1) => 77.78/10.62 (( 77.78/10.62 (eta1) => 77.78/10.62 (( 77.78/10.62 (lam2lamEq) => 77.78/10.62 (( 77.78/10.62 (beta2) => 77.78/10.62 (( 77.78/10.62 (eta2) => 77.78/10.62 (( 77.78/10.62 (iffalseProp1) => 77.78/10.62 (( 77.78/10.62 (iffalseProp2) => 77.78/10.62 (( 77.78/10.62 (iftrueProp1) => 77.78/10.62 (( 77.78/10.62 (iftrueProp2) => 77.78/10.62 (( 77.78/10.62 (ifSingleton) => 77.78/10.62 (( 77.78/10.62 (ifp) => 77.78/10.62 (( 77.78/10.62 (theeq) => 77.78/10.62 (( 77.78/10.62 (iftrue) => 77.78/10.62 (( 77.78/10.62 (iffalse) => 77.78/10.62 (( 77.78/10.62 (iftrueorfalse) => 77.78/10.62 (( 77.78/10.62 (binintersectT_lem) => 77.78/10.62 (( 77.78/10.62 (binunionT_lem) => 77.78/10.62 (( 77.78/10.62 (powersetT_lem) => 77.78/10.62 (( 77.78/10.62 (setminusT_lem) => 77.78/10.62 (( 77.78/10.62 (complementT_lem) => 77.78/10.62 (( 77.78/10.62 (setextT) => 77.78/10.62 (( 77.78/10.62 (subsetTI) => 77.78/10.62 (( 77.78/10.62 (powersetTI1) => 77.78/10.62 (( 77.78/10.62 (powersetTE1) => 77.78/10.62 (( 77.78/10.62 (complementTI1) => 77.78/10.62 (( 77.78/10.62 (complementTE1) => 77.78/10.62 (( 77.78/10.62 (binintersectTELcontra) => 77.78/10.62 (( 77.78/10.62 (binintersectTERcontra) => 77.78/10.62 (( 77.78/10.62 (contrasubsetT) => 77.78/10.62 (( 77.78/10.62 (contrasubsetT1) => 77.78/10.62 (( 77.78/10.62 (contrasubsetT2) => 77.78/10.62 (( 77.78/10.62 (contrasubsetT3) => 77.78/10.62 (( 77.78/10.62 (doubleComplementI1) => 77.78/10.62 (( 77.78/10.62 (doubleComplementE1) => 77.78/10.62 (( 77.78/10.62 (doubleComplementSub1) => 77.78/10.62 (( 77.78/10.62 (doubleComplementSub2) => 77.78/10.62 (( 77.78/10.62 (doubleComplementEq) => 77.78/10.62 (( 77.78/10.62 (complementTnotintersectT) => 77.78/10.62 (( 77.78/10.62 (complementImpComplementIntersect) => 77.78/10.62 (( 77.78/10.62 (complementSubsetComplementIntersect) => 77.78/10.62 (( 77.78/10.62 (complementInPowersetComplementIntersect) => 77.78/10.62 (( 77.78/10.62 (contraSubsetComplement) => 77.78/10.62 (( 77.78/10.62 (complementTcontraSubset) => 77.78/10.62 (( 77.78/10.62 (binunionTILcontra) => 77.78/10.62 (( 77.78/10.62 (binunionTIRcontra) => 77.78/10.62 (( 77.78/10.62 (inIntersectImpInUnion) => 77.78/10.62 (( 77.78/10.62 (inIntersectImpInUnion2) => 77.78/10.62 (( 77.78/10.62 (inIntersectImpInIntersectUnions) => 77.78/10.62 (( 77.78/10.62 (intersectInPowersetIntersectUnions) => 77.78/10.62 (( 77.78/10.62 (inComplementUnionImpNotIn1) => 77.78/10.62 (( 77.78/10.62 (inComplementUnionImpInComplement1) => 77.78/10.62 (( 77.78/10.62 (binunionTE) => 77.78/10.62 (( 77.78/10.62 (binunionTEcontra) => 77.78/10.62 (( 77.78/10.62 (demorgan2a1) => 77.78/10.62 (( 77.78/10.62 (complementUnionInPowersetComplement) => 77.78/10.62 (( 77.78/10.62 (demorgan2a2) => 77.78/10.62 (( 77.78/10.62 (demorgan1a) => 77.78/10.62 (( 77.78/10.62 (demorgan1b) => 77.78/10.62 (( 77.78/10.62 (demorgan1) => 77.78/10.62 (( 77.78/10.62 (demorgan2a) => 77.78/10.62 (( 77.78/10.62 (demorgan2b2) => 77.78/10.62 (( 77.78/10.62 (demorgan2b) => 77.78/10.62 (( 77.78/10.62 (demorgan2) => 77.78/10.62 (( 77.78/10.62 (woz13rule0) => 77.78/10.62 (( 77.78/10.62 (woz13rule1) => 77.78/10.62 (( 77.78/10.62 (woz13rule2) => 77.78/10.62 (( 77.78/10.62 (woz13rule3) => 77.78/10.62 (( 77.78/10.62 (woz13rule4) => 77.78/10.62 (( 77.78/10.62 (woz1_1) => 77.78/10.62 (( 77.78/10.62 (woz1_2) => 77.78/10.62 (( 77.78/10.62 (woz1_3) => 77.78/10.62 (( 77.78/10.62 (woz1_4) => 77.78/10.62 (( 77.78/10.62 (woz1_5) => 77.78/10.62 (( 77.78/10.62 (breln1all2) => 77.78/10.62 (( 77.78/10.62 (breln1SetBreln1) => 77.78/10.62 (( 77.78/10.62 (choice2fnsingleton) => 77.78/10.62 (( 77.78/10.62 (setOfPairsIsBReln1) => 77.78/10.62 (( 77.78/10.62 (breln1all1) => 77.78/10.62 (( 77.78/10.62 (subbreln1) => 77.78/10.62 (( 77.78/10.62 (eqbreln1) => 77.78/10.62 (( 77.78/10.62 (breln1invprop) => 77.78/10.62 (( 77.78/10.62 (breln1invI) => 77.78/10.62 (( 77.78/10.62 (breln1invE) => 77.78/10.62 (( 77.78/10.62 (breln1compprop) => 77.78/10.62 (( 77.78/10.62 (breln1compI) => 77.78/10.62 (( 77.78/10.62 (breln1compE) => 77.78/10.62 (( 77.78/10.62 (breln1compEex) => 77.78/10.62 (( 77.78/10.62 (breln1unionprop) => 77.78/10.62 (( 77.78/10.62 (breln1unionIL) => 77.78/10.62 (( 77.78/10.62 (breln1unionIR) => 77.78/10.62 (( 77.78/10.62 (breln1unionI) => 77.78/10.62 (( 77.78/10.62 (breln1unionE) => 77.78/10.62 (( 77.78/10.62 (breln1unionEcases) => 77.78/10.62 (( 77.78/10.62 (breln1unionCommutes) => 77.78/10.62 (( 77.78/10.62 (woz2Ex) => 77.78/10.62 (( 77.78/10.62 (woz2W) => 77.78/10.62 (( 77.78/10.62 (woz2A) => 77.78/10.62 (( 77.78/10.62 (woz2B) => 77.78/10.62 (( 77.78/10.62 (image1Ex) => 77.78/10.62 (( 77.78/10.62 (image1Ex1) => 77.78/10.62 (( 77.78/10.62 (image1Equiv) => 77.78/10.62 (( 77.78/10.62 (image1E) => 77.78/10.62 (( 77.78/10.62 (image1I) => 77.78/10.62 (( 77.78/10.62 (injFuncInInjFuncSet) => 77.78/10.62 (( 77.78/10.62 (injFuncSetFuncIn) => 77.78/10.62 (( 77.78/10.62 (injFuncSetFuncInj) => 77.78/10.62 (( 77.78/10.62 (surjFuncSetFuncIn) => 77.78/10.62 (( 77.78/10.62 (surjFuncSetFuncSurj) => 77.78/10.62 (( 77.78/10.62 (leftInvIsSurj) => 77.78/10.62 (( 77.78/10.62 (surjCantorThm) => 77.78/10.62 (( 77.78/10.62 (foundation2) => 77.78/10.62 (( 77.78/10.62 (notinself) => 77.78/10.62 (( 77.78/10.62 (notinself2) => 77.78/10.62 (( 77.78/10.62 (omegaSp) => 77.78/10.62 (( 77.78/10.62 (omegaSclos) => 77.78/10.62 (( 77.78/10.62 (peano0notS) => 77.78/10.62 (( 77.78/10.62 (peanoSinj) => 77.78/10.62 (( 77.78/10.62 (transitivesetOp1) => 77.78/10.62 (( 77.78/10.62 (binintTransitive) => 77.78/10.62 (( 77.78/10.62 (transitivesetOp2) => 77.78/10.62 (( 77.78/10.62 (setunionTransitive) => 77.78/10.62 (( 77.78/10.62 (ordinalMinLem1) => 77.78/10.62 (( 77.78/10.62 (!!) @ ( 77.78/10.62 ^[Y0 : $i]: 77.78/10.62 (( 77.78/10.62 (ordinal @ 77.78/10.62 Y0) => 77.78/10.62 (( 77.78/10.62 (!!) @ ( 77.78/10.62 ^[Y1 : $i]: 77.78/10.62 (( 77.78/10.62 (!!) @ ( 77.78/10.62 ^[Y2 : $i]: 77.78/10.62 (( 77.78/10.62 (in @ 77.78/10.62 Y2 @ 77.78/10.62 Y0) => 77.78/10.62 (( 77.78/10.62 (in @ 77.78/10.62 Y1 @ 77.78/10.62 Y2) => 77.78/10.62 (in @ 77.78/10.62 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 77.78/10.62 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl609])). 77.78/10.62 thf(zip_derived_cl637, plain, 77.78/10.62 (~ (((setunion__Cong) => 77.78/10.62 (((exuEu) => 77.78/10.62 (((descr__Cong) => 77.78/10.62 (((dsetconstr__Cong) => 77.78/10.62 (((subsetI1) => 77.78/10.62 (((eqimpsubset2) => 77.78/10.62 (((eqimpsubset1) => 77.78/10.62 (((subsetI2) => 77.78/10.62 (((emptysetsubset) => 77.78/10.62 (((subsetE) => 77.78/10.62 (((subsetE2) => 77.78/10.62 (((notsubsetI) => 77.78/10.62 (((notequalI1) => 77.78/10.62 (((notequalI2) => 77.78/10.62 (((subsetRefl) => 77.78/10.62 (((subsetTrans) => 77.78/10.62 (((setadjoinSub) => 77.78/10.62 (((setadjoinSub2) => 77.78/10.62 (((subset2powerset) => 77.78/10.62 (((setextsub) => 77.78/10.62 (((subsetemptysetimpeq) => 77.78/10.62 (((powersetI1) => 77.78/10.62 (((powersetE1) => 77.78/10.62 (((inPowerset) => 77.78/10.62 (((powersetsubset) => 77.78/10.62 (((sepInPowerset) => 77.78/10.62 (((sepSubset) => 77.78/10.62 (((binunionIL) => 77.78/10.62 (((upairset2IR) => 77.78/10.62 (((binunionIR) => 77.78/10.62 (( 77.78/10.62 (binunionEcases) => 77.78/10.62 (( 77.78/10.62 (binunionE) => 77.78/10.62 (( 77.78/10.62 (binunionLsub) => 77.78/10.62 (( 77.78/10.62 (binunionRsub) => 77.78/10.62 (( 77.78/10.62 (binintersectI) => 77.78/10.62 (( 77.78/10.62 (binintersectSubset5) => 77.78/10.62 (( 77.78/10.62 (binintersectEL) => 77.78/10.62 (( 77.78/10.62 (binintersectLsub) => 77.78/10.62 (( 77.78/10.62 (binintersectSubset2) => 77.78/10.62 (( 77.78/10.62 (binintersectSubset3) => 77.78/10.62 (( 77.78/10.62 (binintersectER) => 77.78/10.62 (( 77.78/10.62 (disjointsetsI1) => 77.78/10.62 (( 77.78/10.62 (binintersectRsub) => 77.78/10.62 (( 77.78/10.62 (binintersectSubset4) => 77.78/10.62 (( 77.78/10.62 (binintersectSubset1) => 77.78/10.62 (( 77.78/10.62 (bs114d) => 77.78/10.62 (( 77.78/10.62 (setminusI) => 77.78/10.62 (( 77.78/10.62 (setminusEL) => 77.78/10.62 (( 77.78/10.62 (setminusER) => 77.78/10.62 (( 77.78/10.62 (setminusSubset2) => 77.78/10.62 (( 77.78/10.62 (setminusERneg) => 77.78/10.62 (( 77.78/10.62 (setminusELneg) => 77.78/10.62 (( 77.78/10.62 (setminusILneg) => 77.78/10.62 (( 77.78/10.62 (setminusIRneg) => 77.78/10.62 (( 77.78/10.62 (setminusLsub) => 77.78/10.62 (( 77.78/10.62 (setminusSubset1) => 77.78/10.62 (( 77.78/10.62 (symdiffE) => 77.78/10.62 (( 77.78/10.62 (symdiffI1) => 77.78/10.62 (( 77.78/10.62 (symdiffI2) => 77.78/10.62 (( 77.78/10.62 (symdiffIneg1) => 77.78/10.62 (( 77.78/10.62 (symdiffIneg2) => 77.78/10.62 (( 77.78/10.62 (secondinupair) => 77.78/10.62 (( 77.78/10.62 (setukpairIL) => 77.78/10.62 (( 77.78/10.62 (setukpairIR) => 77.78/10.62 (( 77.78/10.62 (kpairiskpair) => 77.78/10.62 (( 77.78/10.62 (kpairp) => 77.78/10.62 (( 77.78/10.62 (singletonsubset) => 77.78/10.62 (( 77.78/10.62 (singletoninpowerset) => 77.78/10.62 (( 77.78/10.62 (singletoninpowunion) => 77.78/10.62 (( 77.78/10.62 (upairset2E) => 77.78/10.62 (( 77.78/10.62 (upairsubunion) => 77.78/10.62 (( 77.78/10.62 (upairinpowunion) => 77.78/10.62 (( 77.78/10.62 (ubforcartprodlem1) => 77.78/10.62 (( 77.78/10.62 (ubforcartprodlem2) => 77.78/10.62 (( 77.78/10.62 (ubforcartprodlem3) => 77.78/10.62 (( 77.78/10.62 (cartprodpairin) => 77.78/10.62 (( 77.78/10.62 (cartprodmempair1) => 77.78/10.62 (( 77.78/10.62 (cartprodmempair) => 77.78/10.62 (( 77.78/10.62 (setunionE2) => 77.78/10.62 (( 77.78/10.62 (setunionsingleton1) => 77.78/10.62 (( 77.78/10.62 (setunionsingleton2) => 77.78/10.62 (( 77.78/10.62 (setunionsingleton) => 77.78/10.62 (( 77.78/10.62 (singletonprop) => 77.78/10.62 (( 77.78/10.62 (ex1E1) => 77.78/10.62 (( 77.78/10.62 (ex1I) => 77.78/10.62 (( 77.78/10.62 (ex1I2) => 77.78/10.62 (( 77.78/10.62 (singletonsuniq) => 77.78/10.62 (( 77.78/10.62 (setukpairinjL1) => 77.78/10.62 (( 77.78/10.62 (kfstsingleton) => 77.78/10.62 (( 77.78/10.62 (theprop) => 77.78/10.62 (( 77.78/10.62 (kfstpairEq) => 77.78/10.62 (( 77.78/10.62 (cartprodfstin) => 77.78/10.62 (( 77.78/10.62 (setukpairinjL2) => 77.78/10.62 (( 77.78/10.62 (setukpairinjL) => 77.78/10.62 (( 77.78/10.62 (setukpairinjR11) => 77.78/10.62 (( 77.78/10.62 (setukpairinjR12) => 77.78/10.62 (( 77.78/10.62 (setukpairinjR1) => 77.78/10.62 (( 77.78/10.62 (upairequniteq) => 77.78/10.62 (( 77.78/10.62 (setukpairinjR2) => 77.78/10.62 (( 77.78/10.62 (setukpairinjR) => 77.78/10.62 (( 77.78/10.62 (ksndsingleton) => 77.78/10.62 (( 77.78/10.62 (ksndpairEq) => 77.78/10.62 (( 77.78/10.62 (kpairsurjEq) => 77.78/10.62 (( 77.78/10.62 (cartprodsndin) => 77.78/10.62 (( 77.78/10.62 (cartprodpairmemEL) => 77.78/10.62 (( 77.78/10.62 (cartprodpairmemER) => 77.78/10.62 (( 77.78/10.62 (cartprodmempaircEq) => 77.78/10.62 (( 77.78/10.62 (cartprodfstpairEq) => 77.78/10.62 (( 77.78/10.62 (cartprodsndpairEq) => 77.78/10.62 (( 77.78/10.62 (cartprodpairsurjEq) => 77.78/10.62 (( 77.78/10.62 (dpsetconstrI) => 77.78/10.62 (( 77.78/10.62 (dpsetconstrSub) => 77.78/10.62 (( 77.78/10.62 (setOfPairsIsBReln) => 77.78/10.62 (( 77.78/10.62 (dpsetconstrERa) => 77.78/10.62 (( 77.78/10.62 (dpsetconstrEL1) => 77.78/10.62 (( 77.78/10.62 (dpsetconstrEL2) => 77.78/10.62 (( 77.78/10.62 (dpsetconstrER) => 77.78/10.62 (( 77.78/10.62 (funcImageSingleton) => 77.78/10.62 (( 77.78/10.62 (apProp) => 77.78/10.62 (( 77.78/10.62 (app) => 77.78/10.62 (( 77.78/10.62 (infuncsetfunc) => 77.78/10.62 (( 77.78/10.62 (ap2p) => 77.78/10.62 (( 77.78/10.62 (funcinfuncset) => 77.78/10.62 (( 77.78/10.62 (lamProp) => 77.78/10.62 (( 77.78/10.62 (lamp) => 77.78/10.62 (( 77.78/10.62 (lam2p) => 77.78/10.62 (( 77.78/10.62 (brelnall1) => 77.78/10.62 (( 77.78/10.62 (brelnall2) => 77.78/10.62 (( 77.78/10.62 (ex1E2) => 77.78/10.62 (( 77.78/10.62 (funcGraphProp1) => 77.78/10.62 (( 77.78/10.62 (funcGraphProp3) => 77.78/10.62 (( 77.78/10.62 (funcGraphProp2) => 77.78/10.62 (( 77.78/10.62 (funcextLem) => 77.78/10.62 (( 77.78/10.62 (funcGraphProp4) => 77.78/10.62 (( 77.78/10.62 (subbreln) => 77.78/10.62 (( 77.78/10.62 (eqbreln) => 77.78/10.62 (( 77.78/10.62 (funcext) => 77.78/10.62 (( 77.78/10.62 (funcext2) => 77.78/10.62 (( 77.78/10.62 (ap2apEq1) => 77.78/10.62 (( 77.78/10.62 (ap2apEq2) => 77.78/10.62 (( 77.78/10.62 (beta1) => 77.78/10.62 (( 77.78/10.62 (eta1) => 77.78/10.62 (( 77.78/10.62 (lam2lamEq) => 77.78/10.62 (( 77.78/10.62 (beta2) => 77.78/10.62 (( 77.78/10.62 (eta2) => 77.78/10.62 (( 77.78/10.62 (iffalseProp1) => 77.78/10.62 (( 77.78/10.62 (iffalseProp2) => 77.78/10.62 (( 77.78/10.62 (iftrueProp1) => 77.78/10.62 (( 77.78/10.62 (iftrueProp2) => 77.78/10.62 (( 77.78/10.62 (ifSingleton) => 77.78/10.62 (( 77.78/10.62 (ifp) => 77.78/10.62 (( 77.78/10.62 (theeq) => 77.78/10.62 (( 77.78/10.62 (iftrue) => 77.78/10.62 (( 77.78/10.62 (iffalse) => 77.78/10.62 (( 77.78/10.62 (iftrueorfalse) => 77.78/10.62 (( 77.78/10.62 (binintersectT_lem) => 77.78/10.62 (( 77.78/10.62 (binunionT_lem) => 77.78/10.62 (( 77.78/10.62 (powersetT_lem) => 77.78/10.62 (( 77.78/10.62 (setminusT_lem) => 77.78/10.62 (( 77.78/10.62 (complementT_lem) => 77.78/10.62 (( 77.78/10.62 (setextT) => 77.78/10.62 (( 77.78/10.62 (subsetTI) => 77.78/10.62 (( 77.78/10.62 (powersetTI1) => 77.78/10.62 (( 77.78/10.62 (powersetTE1) => 77.78/10.62 (( 77.78/10.62 (complementTI1) => 77.78/10.62 (( 77.78/10.62 (complementTE1) => 77.78/10.62 (( 77.78/10.62 (binintersectTELcontra) => 77.78/10.62 (( 77.78/10.62 (binintersectTERcontra) => 77.78/10.62 (( 77.78/10.62 (contrasubsetT) => 77.78/10.62 (( 77.78/10.62 (contrasubsetT1) => 77.78/10.62 (( 77.78/10.62 (contrasubsetT2) => 77.78/10.62 (( 77.78/10.62 (contrasubsetT3) => 77.78/10.62 (( 77.78/10.62 (doubleComplementI1) => 77.78/10.62 (( 77.78/10.62 (doubleComplementE1) => 77.78/10.62 (( 77.78/10.62 (doubleComplementSub1) => 77.78/10.62 (( 77.78/10.62 (doubleComplementSub2) => 77.78/10.62 (( 77.78/10.62 (doubleComplementEq) => 77.78/10.62 (( 77.78/10.62 (complementTnotintersectT) => 77.78/10.62 (( 77.78/10.62 (complementImpComplementIntersect) => 77.78/10.62 (( 77.78/10.62 (complementSubsetComplementIntersect) => 77.78/10.62 (( 77.78/10.62 (complementInPowersetComplementIntersect) => 77.78/10.62 (( 77.78/10.62 (contraSubsetComplement) => 77.78/10.62 (( 77.78/10.62 (complementTcontraSubset) => 77.78/10.62 (( 77.78/10.62 (binunionTILcontra) => 77.78/10.62 (( 77.78/10.62 (binunionTIRcontra) => 77.78/10.62 (( 77.78/10.62 (inIntersectImpInUnion) => 77.78/10.62 (( 77.78/10.62 (inIntersectImpInUnion2) => 77.78/10.62 (( 77.78/10.62 (inIntersectImpInIntersectUnions) => 77.78/10.62 (( 77.78/10.62 (intersectInPowersetIntersectUnions) => 77.78/10.62 (( 77.78/10.62 (inComplementUnionImpNotIn1) => 77.78/10.62 (( 77.78/10.62 (inComplementUnionImpInComplement1) => 77.78/10.62 (( 77.78/10.62 (binunionTE) => 77.78/10.62 (( 77.78/10.62 (binunionTEcontra) => 77.78/10.62 (( 77.78/10.62 (demorgan2a1) => 77.78/10.62 (( 77.78/10.62 (complementUnionInPowersetComplement) => 77.78/10.62 (( 77.78/10.62 (demorgan2a2) => 77.78/10.62 (( 77.78/10.62 (demorgan1a) => 77.78/10.62 (( 77.78/10.62 (demorgan1b) => 77.78/10.62 (( 77.78/10.62 (demorgan1) => 77.78/10.62 (( 77.78/10.62 (demorgan2a) => 77.78/10.62 (( 77.78/10.62 (demorgan2b2) => 77.78/10.62 (( 77.78/10.62 (demorgan2b) => 77.78/10.62 (( 77.78/10.62 (demorgan2) => 77.78/10.62 (( 77.78/10.62 (woz13rule0) => 77.78/10.62 (( 77.78/10.62 (woz13rule1) => 77.78/10.62 (( 77.78/10.62 (woz13rule2) => 77.78/10.62 (( 77.78/10.62 (woz13rule3) => 77.78/10.62 (( 77.78/10.62 (woz13rule4) => 77.78/10.62 (( 77.78/10.62 (woz1_1) => 77.78/10.62 (( 77.78/10.62 (woz1_2) => 77.78/10.62 (( 77.78/10.62 (woz1_3) => 77.78/10.62 (( 77.78/10.62 (woz1_4) => 77.78/10.62 (( 77.78/10.62 (woz1_5) => 77.78/10.62 (( 77.78/10.62 (breln1all2) => 77.78/10.62 (( 77.78/10.62 (breln1SetBreln1) => 77.78/10.62 (( 77.78/10.62 (choice2fnsingleton) => 77.78/10.62 (( 77.78/10.62 (setOfPairsIsBReln1) => 77.78/10.62 (( 77.78/10.62 (breln1all1) => 77.78/10.62 (( 77.78/10.62 (subbreln1) => 77.78/10.62 (( 77.78/10.62 (eqbreln1) => 77.78/10.62 (( 77.78/10.62 (breln1invprop) => 77.78/10.62 (( 77.78/10.62 (breln1invI) => 77.78/10.62 (( 77.78/10.62 (breln1invE) => 77.78/10.62 (( 77.78/10.62 (breln1compprop) => 77.78/10.62 (( 77.78/10.62 (breln1compI) => 77.78/10.62 (( 77.78/10.62 (breln1compE) => 77.78/10.62 (( 77.78/10.62 (breln1compEex) => 77.78/10.62 (( 77.78/10.62 (breln1unionprop) => 77.78/10.62 (( 77.78/10.62 (breln1unionIL) => 77.78/10.62 (( 77.78/10.62 (breln1unionIR) => 77.78/10.62 (( 77.78/10.62 (breln1unionI) => 77.78/10.62 (( 77.78/10.62 (breln1unionE) => 77.78/10.62 (( 77.78/10.62 (breln1unionEcases) => 77.78/10.62 (( 77.78/10.62 (breln1unionCommutes) => 77.78/10.62 (( 77.78/10.62 (woz2Ex) => 77.78/10.62 (( 77.78/10.62 (woz2W) => 77.78/10.62 (( 77.78/10.62 (woz2A) => 77.78/10.62 (( 77.78/10.62 (woz2B) => 77.78/10.62 (( 77.78/10.62 (image1Ex) => 77.78/10.62 (( 77.78/10.62 (image1Ex1) => 77.78/10.62 (( 77.78/10.62 (image1Equiv) => 77.78/10.62 (( 77.78/10.62 (image1E) => 77.78/10.62 (( 77.78/10.62 (image1I) => 77.78/10.62 (( 77.78/10.62 (injFuncInInjFuncSet) => 77.78/10.62 (( 77.78/10.62 (injFuncSetFuncIn) => 77.78/10.62 (( 77.78/10.62 (injFuncSetFuncInj) => 77.78/10.62 (( 77.78/10.62 (surjFuncSetFuncIn) => 77.78/10.62 (( 77.78/10.62 (surjFuncSetFuncSurj) => 77.78/10.62 (( 77.78/10.62 (leftInvIsSurj) => 77.78/10.62 (( 77.78/10.62 (surjCantorThm) => 77.78/10.62 (( 77.78/10.62 (foundation2) => 77.78/10.62 (( 77.78/10.62 (notinself) => 77.78/10.62 (( 77.78/10.62 (notinself2) => 77.78/10.62 (( 77.78/10.62 (omegaSp) => 77.78/10.62 (( 77.78/10.62 (omegaSclos) => 77.78/10.62 (( 77.78/10.62 (peano0notS) => 77.78/10.62 (( 77.78/10.62 (peanoSinj) => 77.78/10.62 (( 77.78/10.62 (transitivesetOp1) => 77.78/10.62 (( 77.78/10.62 (binintTransitive) => 77.78/10.62 (( 77.78/10.62 (transitivesetOp2) => 77.78/10.62 (( 77.78/10.62 (setunionTransitive) => 77.78/10.62 (( 77.78/10.62 (ordinalMinLem1) => 77.78/10.62 (( 77.78/10.62 (!!) @ ( 77.78/10.62 ^[Y0 : $i]: 77.78/10.62 (( 77.78/10.62 (ordinal @ 77.78/10.62 Y0) => 77.78/10.62 (( 77.78/10.62 (!!) @ ( 77.78/10.62 ^[Y1 : $i]: 77.78/10.62 (( 77.78/10.62 (!!) @ ( 77.78/10.62 ^[Y2 : $i]: 77.78/10.62 (( 77.78/10.62 (in @ 77.78/10.62 Y2 @ 77.78/10.62 Y0) => 77.78/10.62 (( 77.78/10.62 (in @ 77.78/10.62 Y1 @ 77.78/10.62 Y2) => 77.78/10.62 (in @ 77.78/10.62 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 77.78/10.62 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl623])). 77.78/10.62 thf(zip_derived_cl652, plain, 77.78/10.62 (~ (((exuEu) => 77.78/10.62 (((descr__Cong) => 77.78/10.62 (((dsetconstr__Cong) => 77.78/10.62 (((subsetI1) => 77.78/10.62 (((eqimpsubset2) => 77.78/10.62 (((eqimpsubset1) => 77.78/10.62 (((subsetI2) => 77.78/10.62 (((emptysetsubset) => 77.78/10.62 (((subsetE) => 77.78/10.62 (((subsetE2) => 77.78/10.62 (((notsubsetI) => 77.78/10.62 (((notequalI1) => 77.78/10.62 (((notequalI2) => 77.78/10.62 (((subsetRefl) => 77.78/10.62 (((subsetTrans) => 77.78/10.62 (((setadjoinSub) => 77.78/10.62 (((setadjoinSub2) => 77.78/10.62 (((subset2powerset) => 77.78/10.62 (((setextsub) => 77.78/10.62 (((subsetemptysetimpeq) => 77.78/10.62 (((powersetI1) => 77.78/10.62 (((powersetE1) => 77.78/10.62 (((inPowerset) => 77.78/10.62 (((powersetsubset) => 77.78/10.62 (((sepInPowerset) => 77.78/10.62 (((sepSubset) => 77.78/10.62 (((binunionIL) => 77.78/10.62 (((upairset2IR) => 77.78/10.62 (((binunionIR) => 77.78/10.62 (((binunionEcases) => 77.78/10.62 (( 77.78/10.62 (binunionE) => 77.78/10.62 (( 77.78/10.62 (binunionLsub) => 77.78/10.62 (( 77.78/10.62 (binunionRsub) => 77.78/10.62 (( 77.78/10.62 (binintersectI) => 77.78/10.62 (( 77.78/10.62 (binintersectSubset5) => 77.78/10.62 (( 77.78/10.62 (binintersectEL) => 77.78/10.62 (( 77.78/10.62 (binintersectLsub) => 77.78/10.62 (( 77.78/10.62 (binintersectSubset2) => 77.78/10.62 (( 77.78/10.62 (binintersectSubset3) => 77.78/10.62 (( 77.78/10.62 (binintersectER) => 77.78/10.62 (( 77.78/10.62 (disjointsetsI1) => 77.78/10.62 (( 77.78/10.62 (binintersectRsub) => 77.78/10.62 (( 77.78/10.62 (binintersectSubset4) => 77.78/10.62 (( 77.78/10.62 (binintersectSubset1) => 77.78/10.62 (( 77.78/10.62 (bs114d) => 77.78/10.62 (( 77.78/10.62 (setminusI) => 77.78/10.62 (( 77.78/10.62 (setminusEL) => 77.78/10.62 (( 77.78/10.62 (setminusER) => 77.78/10.62 (( 77.78/10.62 (setminusSubset2) => 77.78/10.62 (( 77.78/10.62 (setminusERneg) => 77.78/10.62 (( 77.78/10.62 (setminusELneg) => 77.78/10.62 (( 77.78/10.62 (setminusILneg) => 77.78/10.62 (( 77.78/10.62 (setminusIRneg) => 77.78/10.62 (( 77.78/10.62 (setminusLsub) => 77.78/10.62 (( 77.78/10.62 (setminusSubset1) => 77.78/10.62 (( 77.78/10.62 (symdiffE) => 77.78/10.62 (( 77.78/10.62 (symdiffI1) => 77.78/10.62 (( 77.78/10.62 (symdiffI2) => 77.78/10.62 (( 77.78/10.62 (symdiffIneg1) => 77.78/10.62 (( 77.78/10.62 (symdiffIneg2) => 77.78/10.62 (( 77.78/10.62 (secondinupair) => 77.78/10.62 (( 77.78/10.62 (setukpairIL) => 77.78/10.62 (( 77.78/10.62 (setukpairIR) => 77.78/10.62 (( 77.78/10.62 (kpairiskpair) => 77.78/10.62 (( 77.78/10.62 (kpairp) => 77.78/10.62 (( 77.78/10.62 (singletonsubset) => 77.78/10.62 (( 77.78/10.62 (singletoninpowerset) => 77.78/10.62 (( 77.78/10.62 (singletoninpowunion) => 77.78/10.62 (( 77.78/10.62 (upairset2E) => 77.78/10.62 (( 77.78/10.62 (upairsubunion) => 77.78/10.62 (( 77.78/10.62 (upairinpowunion) => 77.78/10.62 (( 77.78/10.62 (ubforcartprodlem1) => 77.78/10.62 (( 77.78/10.62 (ubforcartprodlem2) => 77.78/10.62 (( 77.78/10.62 (ubforcartprodlem3) => 77.78/10.62 (( 77.78/10.62 (cartprodpairin) => 77.78/10.62 (( 77.78/10.62 (cartprodmempair1) => 77.78/10.62 (( 77.78/10.62 (cartprodmempair) => 77.78/10.62 (( 77.78/10.62 (setunionE2) => 77.78/10.62 (( 77.78/10.62 (setunionsingleton1) => 77.78/10.62 (( 77.78/10.62 (setunionsingleton2) => 77.78/10.62 (( 77.78/10.62 (setunionsingleton) => 77.78/10.62 (( 77.78/10.62 (singletonprop) => 77.78/10.62 (( 77.78/10.62 (ex1E1) => 77.78/10.63 (( 77.78/10.63 (ex1I) => 77.78/10.63 (( 77.78/10.63 (ex1I2) => 77.78/10.63 (( 77.78/10.63 (singletonsuniq) => 77.78/10.63 (( 77.78/10.63 (setukpairinjL1) => 77.78/10.63 (( 77.78/10.63 (kfstsingleton) => 77.78/10.63 (( 77.78/10.63 (theprop) => 77.78/10.63 (( 77.78/10.63 (kfstpairEq) => 77.78/10.63 (( 77.78/10.63 (cartprodfstin) => 77.78/10.63 (( 77.78/10.63 (setukpairinjL2) => 77.78/10.63 (( 77.78/10.63 (setukpairinjL) => 77.78/10.63 (( 77.78/10.63 (setukpairinjR11) => 77.78/10.63 (( 77.78/10.63 (setukpairinjR12) => 77.78/10.63 (( 77.78/10.63 (setukpairinjR1) => 77.78/10.63 (( 77.78/10.63 (upairequniteq) => 77.78/10.63 (( 77.78/10.63 (setukpairinjR2) => 77.78/10.63 (( 77.78/10.63 (setukpairinjR) => 77.78/10.63 (( 77.78/10.63 (ksndsingleton) => 77.78/10.63 (( 77.78/10.63 (ksndpairEq) => 77.78/10.63 (( 77.78/10.63 (kpairsurjEq) => 77.78/10.63 (( 77.78/10.63 (cartprodsndin) => 77.78/10.63 (( 77.78/10.63 (cartprodpairmemEL) => 77.78/10.63 (( 77.78/10.63 (cartprodpairmemER) => 77.78/10.63 (( 77.78/10.63 (cartprodmempaircEq) => 77.78/10.63 (( 77.78/10.63 (cartprodfstpairEq) => 77.78/10.63 (( 77.78/10.63 (cartprodsndpairEq) => 77.78/10.63 (( 77.78/10.63 (cartprodpairsurjEq) => 77.78/10.63 (( 77.78/10.63 (dpsetconstrI) => 77.78/10.63 (( 77.78/10.63 (dpsetconstrSub) => 77.78/10.63 (( 77.78/10.63 (setOfPairsIsBReln) => 77.78/10.63 (( 77.78/10.63 (dpsetconstrERa) => 77.78/10.63 (( 77.78/10.63 (dpsetconstrEL1) => 77.78/10.63 (( 77.78/10.63 (dpsetconstrEL2) => 77.78/10.63 (( 77.78/10.63 (dpsetconstrER) => 77.78/10.63 (( 77.78/10.63 (funcImageSingleton) => 77.78/10.63 (( 77.78/10.63 (apProp) => 77.78/10.63 (( 77.78/10.63 (app) => 77.78/10.63 (( 77.78/10.63 (infuncsetfunc) => 77.78/10.63 (( 77.78/10.63 (ap2p) => 77.78/10.63 (( 77.78/10.63 (funcinfuncset) => 77.78/10.63 (( 77.78/10.63 (lamProp) => 77.78/10.63 (( 77.78/10.63 (lamp) => 77.78/10.63 (( 77.78/10.63 (lam2p) => 77.78/10.63 (( 77.78/10.63 (brelnall1) => 77.78/10.63 (( 77.78/10.63 (brelnall2) => 77.78/10.63 (( 77.78/10.63 (ex1E2) => 77.78/10.63 (( 77.78/10.63 (funcGraphProp1) => 77.78/10.63 (( 77.78/10.63 (funcGraphProp3) => 77.78/10.63 (( 77.78/10.63 (funcGraphProp2) => 77.78/10.63 (( 77.78/10.63 (funcextLem) => 77.78/10.63 (( 77.78/10.63 (funcGraphProp4) => 77.78/10.63 (( 77.78/10.63 (subbreln) => 77.78/10.63 (( 77.78/10.63 (eqbreln) => 77.78/10.63 (( 77.78/10.63 (funcext) => 77.78/10.63 (( 77.78/10.63 (funcext2) => 77.78/10.63 (( 77.78/10.63 (ap2apEq1) => 77.78/10.63 (( 77.78/10.63 (ap2apEq2) => 77.78/10.63 (( 77.78/10.63 (beta1) => 77.78/10.63 (( 77.78/10.63 (eta1) => 77.78/10.63 (( 77.78/10.63 (lam2lamEq) => 77.78/10.63 (( 77.78/10.63 (beta2) => 77.78/10.63 (( 77.78/10.63 (eta2) => 77.78/10.63 (( 77.78/10.63 (iffalseProp1) => 77.78/10.63 (( 77.78/10.63 (iffalseProp2) => 77.78/10.63 (( 77.78/10.63 (iftrueProp1) => 77.78/10.63 (( 77.78/10.63 (iftrueProp2) => 77.78/10.63 (( 77.78/10.63 (ifSingleton) => 77.78/10.63 (( 77.78/10.63 (ifp) => 77.78/10.63 (( 77.78/10.63 (theeq) => 77.78/10.63 (( 77.78/10.63 (iftrue) => 77.78/10.63 (( 77.78/10.63 (iffalse) => 77.78/10.63 (( 77.78/10.63 (iftrueorfalse) => 77.78/10.63 (( 77.78/10.63 (binintersectT_lem) => 77.78/10.63 (( 77.78/10.63 (binunionT_lem) => 77.78/10.63 (( 77.78/10.63 (powersetT_lem) => 77.78/10.63 (( 77.78/10.63 (setminusT_lem) => 77.78/10.63 (( 77.78/10.63 (complementT_lem) => 77.78/10.63 (( 77.78/10.63 (setextT) => 77.78/10.63 (( 77.78/10.63 (subsetTI) => 77.78/10.63 (( 77.78/10.63 (powersetTI1) => 77.78/10.63 (( 77.78/10.63 (powersetTE1) => 77.78/10.63 (( 77.78/10.63 (complementTI1) => 77.78/10.63 (( 77.78/10.63 (complementTE1) => 77.78/10.63 (( 77.78/10.63 (binintersectTELcontra) => 77.78/10.63 (( 77.78/10.63 (binintersectTERcontra) => 77.78/10.63 (( 77.78/10.63 (contrasubsetT) => 77.78/10.63 (( 77.78/10.63 (contrasubsetT1) => 77.78/10.63 (( 77.78/10.63 (contrasubsetT2) => 77.78/10.63 (( 77.78/10.63 (contrasubsetT3) => 77.78/10.63 (( 77.78/10.63 (doubleComplementI1) => 77.78/10.63 (( 77.78/10.63 (doubleComplementE1) => 77.78/10.63 (( 77.78/10.63 (doubleComplementSub1) => 77.78/10.63 (( 77.78/10.63 (doubleComplementSub2) => 77.78/10.63 (( 77.78/10.63 (doubleComplementEq) => 77.78/10.63 (( 77.78/10.63 (complementTnotintersectT) => 77.78/10.63 (( 77.78/10.63 (complementImpComplementIntersect) => 77.78/10.63 (( 77.78/10.63 (complementSubsetComplementIntersect) => 77.78/10.63 (( 77.78/10.63 (complementInPowersetComplementIntersect) => 77.78/10.63 (( 77.78/10.63 (contraSubsetComplement) => 77.78/10.63 (( 77.78/10.63 (complementTcontraSubset) => 77.78/10.63 (( 77.78/10.63 (binunionTILcontra) => 77.78/10.63 (( 77.78/10.63 (binunionTIRcontra) => 77.78/10.63 (( 77.78/10.63 (inIntersectImpInUnion) => 77.78/10.63 (( 77.78/10.63 (inIntersectImpInUnion2) => 77.78/10.63 (( 77.78/10.63 (inIntersectImpInIntersectUnions) => 77.78/10.63 (( 77.78/10.63 (intersectInPowersetIntersectUnions) => 77.78/10.63 (( 77.78/10.63 (inComplementUnionImpNotIn1) => 77.78/10.63 (( 77.78/10.63 (inComplementUnionImpInComplement1) => 77.78/10.63 (( 77.78/10.63 (binunionTE) => 77.78/10.63 (( 77.78/10.63 (binunionTEcontra) => 77.78/10.63 (( 77.78/10.63 (demorgan2a1) => 77.78/10.63 (( 77.78/10.63 (complementUnionInPowersetComplement) => 77.78/10.63 (( 77.78/10.63 (demorgan2a2) => 77.78/10.63 (( 77.78/10.63 (demorgan1a) => 77.78/10.63 (( 77.78/10.63 (demorgan1b) => 77.78/10.63 (( 77.78/10.63 (demorgan1) => 77.78/10.63 (( 77.78/10.63 (demorgan2a) => 77.78/10.63 (( 77.78/10.63 (demorgan2b2) => 77.78/10.63 (( 77.78/10.63 (demorgan2b) => 77.78/10.63 (( 77.78/10.63 (demorgan2) => 77.78/10.63 (( 77.78/10.63 (woz13rule0) => 77.78/10.63 (( 77.78/10.63 (woz13rule1) => 77.78/10.63 (( 77.78/10.63 (woz13rule2) => 77.78/10.63 (( 77.78/10.63 (woz13rule3) => 77.78/10.63 (( 77.78/10.63 (woz13rule4) => 77.78/10.63 (( 77.78/10.63 (woz1_1) => 77.78/10.63 (( 77.78/10.63 (woz1_2) => 77.78/10.63 (( 77.78/10.63 (woz1_3) => 77.78/10.63 (( 77.78/10.63 (woz1_4) => 77.78/10.63 (( 77.78/10.63 (woz1_5) => 77.78/10.63 (( 77.78/10.63 (breln1all2) => 77.78/10.63 (( 77.78/10.63 (breln1SetBreln1) => 77.78/10.63 (( 77.78/10.63 (choice2fnsingleton) => 77.78/10.63 (( 77.78/10.63 (setOfPairsIsBReln1) => 77.78/10.63 (( 77.78/10.63 (breln1all1) => 77.78/10.63 (( 77.78/10.63 (subbreln1) => 77.78/10.63 (( 77.78/10.63 (eqbreln1) => 77.78/10.63 (( 77.78/10.63 (breln1invprop) => 77.78/10.63 (( 77.78/10.63 (breln1invI) => 77.78/10.63 (( 77.78/10.63 (breln1invE) => 77.78/10.63 (( 77.78/10.63 (breln1compprop) => 77.78/10.63 (( 77.78/10.63 (breln1compI) => 77.78/10.63 (( 77.78/10.63 (breln1compE) => 77.78/10.63 (( 77.78/10.63 (breln1compEex) => 77.78/10.63 (( 77.78/10.63 (breln1unionprop) => 77.78/10.63 (( 77.78/10.63 (breln1unionIL) => 77.78/10.63 (( 77.78/10.63 (breln1unionIR) => 77.78/10.63 (( 77.78/10.63 (breln1unionI) => 77.78/10.63 (( 77.78/10.63 (breln1unionE) => 77.78/10.63 (( 77.78/10.63 (breln1unionEcases) => 77.78/10.63 (( 77.78/10.63 (breln1unionCommutes) => 77.78/10.63 (( 77.78/10.63 (woz2Ex) => 77.78/10.63 (( 77.78/10.63 (woz2W) => 77.78/10.63 (( 77.78/10.63 (woz2A) => 77.78/10.63 (( 77.78/10.63 (woz2B) => 77.78/10.63 (( 77.78/10.63 (image1Ex) => 77.78/10.63 (( 77.78/10.63 (image1Ex1) => 77.78/10.63 (( 77.78/10.63 (image1Equiv) => 77.78/10.63 (( 77.78/10.63 (image1E) => 77.78/10.63 (( 77.78/10.63 (image1I) => 77.78/10.63 (( 77.78/10.63 (injFuncInInjFuncSet) => 77.78/10.63 (( 77.78/10.63 (injFuncSetFuncIn) => 77.78/10.63 (( 77.78/10.63 (injFuncSetFuncInj) => 77.78/10.63 (( 77.78/10.63 (surjFuncSetFuncIn) => 77.78/10.63 (( 77.78/10.63 (surjFuncSetFuncSurj) => 77.78/10.63 (( 77.78/10.63 (leftInvIsSurj) => 77.78/10.63 (( 77.78/10.63 (surjCantorThm) => 77.78/10.63 (( 77.78/10.63 (foundation2) => 77.78/10.63 (( 77.78/10.63 (notinself) => 77.78/10.63 (( 77.78/10.63 (notinself2) => 77.78/10.63 (( 77.78/10.63 (omegaSp) => 77.78/10.63 (( 77.78/10.63 (omegaSclos) => 77.78/10.63 (( 77.78/10.63 (peano0notS) => 77.78/10.63 (( 77.78/10.63 (peanoSinj) => 77.78/10.63 (( 77.78/10.63 (transitivesetOp1) => 77.78/10.63 (( 77.78/10.63 (binintTransitive) => 77.78/10.63 (( 77.78/10.63 (transitivesetOp2) => 77.78/10.63 (( 77.78/10.63 (setunionTransitive) => 77.78/10.63 (( 77.78/10.63 (ordinalMinLem1) => 77.78/10.63 (( 77.78/10.63 (!!) @ ( 77.78/10.63 ^[Y0 : $i]: 77.78/10.63 (( 77.78/10.63 (ordinal @ 77.78/10.63 Y0) => 77.78/10.63 (( 77.78/10.63 (!!) @ ( 77.78/10.63 ^[Y1 : $i]: 77.78/10.63 (( 77.78/10.63 (!!) @ ( 77.78/10.63 ^[Y2 : $i]: 77.78/10.63 (( 77.78/10.63 (in @ 77.78/10.63 Y2 @ 77.78/10.63 Y0) => 77.78/10.63 (( 77.78/10.63 (in @ 77.78/10.63 Y1 @ 77.78/10.63 Y2) => 77.78/10.63 (in @ 77.78/10.63 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 77.78/10.63 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl637])). 77.78/10.63 thf(zip_derived_cl664, plain, 77.78/10.63 (~ (((descr__Cong) => 77.78/10.63 (((dsetconstr__Cong) => 77.78/10.63 (((subsetI1) => 77.78/10.63 (((eqimpsubset2) => 77.78/10.63 (((eqimpsubset1) => 77.78/10.63 (((subsetI2) => 77.78/10.63 (((emptysetsubset) => 77.78/10.63 (((subsetE) => 77.78/10.63 (((subsetE2) => 77.78/10.63 (((notsubsetI) => 77.78/10.63 (((notequalI1) => 77.78/10.63 (((notequalI2) => 77.78/10.63 (((subsetRefl) => 77.78/10.63 (((subsetTrans) => 77.78/10.63 (((setadjoinSub) => 77.78/10.63 (((setadjoinSub2) => 77.78/10.63 (((subset2powerset) => 77.78/10.63 (((setextsub) => 77.78/10.63 (((subsetemptysetimpeq) => 77.78/10.63 (((powersetI1) => 77.78/10.63 (((powersetE1) => 77.78/10.63 (((inPowerset) => 77.78/10.63 (((powersetsubset) => 77.78/10.63 (((sepInPowerset) => 77.78/10.63 (((sepSubset) => 77.78/10.63 (((binunionIL) => 77.78/10.63 (((upairset2IR) => 77.78/10.63 (((binunionIR) => 77.78/10.63 (((binunionEcases) => 77.78/10.63 (((binunionE) => 77.78/10.63 (( 77.78/10.63 (binunionLsub) => 77.78/10.63 (( 77.78/10.63 (binunionRsub) => 77.78/10.63 (( 77.78/10.63 (binintersectI) => 77.78/10.63 (( 77.78/10.63 (binintersectSubset5) => 77.78/10.63 (( 77.78/10.63 (binintersectEL) => 77.78/10.63 (( 77.78/10.63 (binintersectLsub) => 77.78/10.63 (( 77.78/10.63 (binintersectSubset2) => 77.78/10.63 (( 77.78/10.63 (binintersectSubset3) => 77.78/10.63 (( 77.78/10.63 (binintersectER) => 77.78/10.63 (( 77.78/10.63 (disjointsetsI1) => 77.78/10.63 (( 77.78/10.63 (binintersectRsub) => 77.78/10.63 (( 77.78/10.63 (binintersectSubset4) => 77.78/10.63 (( 77.78/10.63 (binintersectSubset1) => 77.78/10.63 (( 77.78/10.63 (bs114d) => 77.78/10.63 (( 77.78/10.63 (setminusI) => 77.78/10.63 (( 77.78/10.63 (setminusEL) => 77.78/10.63 (( 77.78/10.63 (setminusER) => 77.78/10.63 (( 77.78/10.63 (setminusSubset2) => 77.78/10.63 (( 77.78/10.63 (setminusERneg) => 77.78/10.63 (( 77.78/10.63 (setminusELneg) => 77.78/10.63 (( 77.78/10.63 (setminusILneg) => 77.78/10.63 (( 77.78/10.63 (setminusIRneg) => 77.78/10.63 (( 77.78/10.63 (setminusLsub) => 77.78/10.63 (( 77.78/10.63 (setminusSubset1) => 77.78/10.63 (( 77.78/10.63 (symdiffE) => 77.78/10.63 (( 77.78/10.63 (symdiffI1) => 77.78/10.63 (( 77.78/10.63 (symdiffI2) => 77.78/10.63 (( 77.78/10.63 (symdiffIneg1) => 77.78/10.63 (( 77.78/10.63 (symdiffIneg2) => 77.78/10.63 (( 77.78/10.63 (secondinupair) => 77.78/10.63 (( 77.78/10.63 (setukpairIL) => 77.78/10.63 (( 77.78/10.63 (setukpairIR) => 77.78/10.63 (( 77.78/10.63 (kpairiskpair) => 77.78/10.63 (( 77.78/10.63 (kpairp) => 77.78/10.63 (( 77.78/10.63 (singletonsubset) => 77.78/10.63 (( 77.78/10.63 (singletoninpowerset) => 77.78/10.63 (( 77.78/10.63 (singletoninpowunion) => 77.78/10.63 (( 77.78/10.63 (upairset2E) => 77.78/10.63 (( 77.78/10.63 (upairsubunion) => 77.78/10.63 (( 77.78/10.63 (upairinpowunion) => 77.78/10.63 (( 77.78/10.63 (ubforcartprodlem1) => 77.78/10.63 (( 77.78/10.63 (ubforcartprodlem2) => 77.78/10.63 (( 77.78/10.63 (ubforcartprodlem3) => 77.78/10.63 (( 77.78/10.63 (cartprodpairin) => 77.78/10.63 (( 77.78/10.63 (cartprodmempair1) => 77.78/10.63 (( 77.78/10.63 (cartprodmempair) => 77.78/10.63 (( 77.78/10.63 (setunionE2) => 77.78/10.63 (( 77.78/10.63 (setunionsingleton1) => 77.78/10.63 (( 77.78/10.63 (setunionsingleton2) => 77.78/10.63 (( 77.78/10.63 (setunionsingleton) => 77.78/10.63 (( 77.78/10.63 (singletonprop) => 77.78/10.63 (( 77.78/10.63 (ex1E1) => 77.78/10.63 (( 77.78/10.63 (ex1I) => 77.78/10.63 (( 77.78/10.63 (ex1I2) => 77.78/10.63 (( 77.78/10.63 (singletonsuniq) => 77.78/10.63 (( 77.78/10.63 (setukpairinjL1) => 77.78/10.63 (( 77.78/10.63 (kfstsingleton) => 77.78/10.63 (( 77.78/10.63 (theprop) => 77.78/10.63 (( 77.78/10.63 (kfstpairEq) => 77.78/10.63 (( 77.78/10.63 (cartprodfstin) => 77.78/10.63 (( 77.78/10.63 (setukpairinjL2) => 77.78/10.63 (( 77.78/10.63 (setukpairinjL) => 77.78/10.63 (( 77.78/10.63 (setukpairinjR11) => 77.78/10.63 (( 77.78/10.63 (setukpairinjR12) => 77.78/10.63 (( 77.78/10.63 (setukpairinjR1) => 77.78/10.63 (( 77.78/10.63 (upairequniteq) => 77.78/10.63 (( 77.78/10.63 (setukpairinjR2) => 77.78/10.63 (( 77.78/10.63 (setukpairinjR) => 77.78/10.63 (( 77.78/10.63 (ksndsingleton) => 77.78/10.63 (( 77.78/10.63 (ksndpairEq) => 77.78/10.63 (( 77.78/10.63 (kpairsurjEq) => 77.78/10.63 (( 77.78/10.63 (cartprodsndin) => 77.78/10.63 (( 77.78/10.63 (cartprodpairmemEL) => 77.78/10.63 (( 77.78/10.63 (cartprodpairmemER) => 77.78/10.63 (( 77.78/10.63 (cartprodmempaircEq) => 77.78/10.63 (( 77.78/10.63 (cartprodfstpairEq) => 77.78/10.63 (( 77.78/10.63 (cartprodsndpairEq) => 77.78/10.63 (( 77.78/10.63 (cartprodpairsurjEq) => 77.78/10.63 (( 77.78/10.63 (dpsetconstrI) => 77.78/10.63 (( 77.78/10.63 (dpsetconstrSub) => 77.78/10.63 (( 77.78/10.63 (setOfPairsIsBReln) => 77.78/10.63 (( 77.78/10.63 (dpsetconstrERa) => 77.78/10.63 (( 77.78/10.63 (dpsetconstrEL1) => 77.78/10.63 (( 77.78/10.63 (dpsetconstrEL2) => 77.78/10.63 (( 77.78/10.63 (dpsetconstrER) => 77.78/10.63 (( 77.78/10.63 (funcImageSingleton) => 77.78/10.63 (( 77.78/10.63 (apProp) => 77.78/10.63 (( 77.78/10.63 (app) => 77.78/10.63 (( 77.78/10.63 (infuncsetfunc) => 77.78/10.63 (( 77.78/10.63 (ap2p) => 77.78/10.63 (( 77.78/10.63 (funcinfuncset) => 77.78/10.63 (( 77.78/10.63 (lamProp) => 77.78/10.63 (( 77.78/10.63 (lamp) => 77.78/10.63 (( 77.78/10.63 (lam2p) => 77.78/10.63 (( 77.78/10.63 (brelnall1) => 77.78/10.63 (( 77.78/10.63 (brelnall2) => 77.78/10.63 (( 77.78/10.63 (ex1E2) => 77.78/10.63 (( 77.78/10.63 (funcGraphProp1) => 77.78/10.63 (( 77.78/10.63 (funcGraphProp3) => 77.78/10.63 (( 77.78/10.63 (funcGraphProp2) => 77.78/10.63 (( 77.78/10.63 (funcextLem) => 77.78/10.63 (( 77.78/10.63 (funcGraphProp4) => 77.78/10.63 (( 77.78/10.63 (subbreln) => 77.78/10.63 (( 77.78/10.63 (eqbreln) => 77.78/10.63 (( 77.78/10.63 (funcext) => 77.78/10.63 (( 77.78/10.63 (funcext2) => 77.78/10.63 (( 77.78/10.63 (ap2apEq1) => 77.78/10.63 (( 77.78/10.63 (ap2apEq2) => 77.78/10.63 (( 77.78/10.63 (beta1) => 77.78/10.63 (( 77.78/10.63 (eta1) => 77.78/10.63 (( 77.78/10.63 (lam2lamEq) => 77.78/10.63 (( 77.78/10.63 (beta2) => 77.78/10.63 (( 77.78/10.63 (eta2) => 77.78/10.63 (( 77.78/10.63 (iffalseProp1) => 77.78/10.63 (( 77.78/10.63 (iffalseProp2) => 77.78/10.63 (( 77.78/10.63 (iftrueProp1) => 77.78/10.63 (( 77.78/10.63 (iftrueProp2) => 77.78/10.63 (( 77.78/10.63 (ifSingleton) => 77.78/10.63 (( 77.78/10.63 (ifp) => 77.78/10.63 (( 77.78/10.63 (theeq) => 77.78/10.63 (( 77.78/10.63 (iftrue) => 77.78/10.63 (( 77.78/10.63 (iffalse) => 77.78/10.63 (( 77.78/10.63 (iftrueorfalse) => 77.78/10.63 (( 77.78/10.63 (binintersectT_lem) => 77.78/10.63 (( 77.78/10.63 (binunionT_lem) => 77.78/10.63 (( 77.78/10.63 (powersetT_lem) => 77.78/10.63 (( 77.78/10.63 (setminusT_lem) => 77.78/10.63 (( 77.78/10.63 (complementT_lem) => 77.78/10.63 (( 77.78/10.63 (setextT) => 77.78/10.63 (( 77.78/10.63 (subsetTI) => 77.78/10.63 (( 77.78/10.63 (powersetTI1) => 77.78/10.63 (( 77.78/10.63 (powersetTE1) => 77.78/10.63 (( 77.78/10.63 (complementTI1) => 77.78/10.63 (( 77.78/10.63 (complementTE1) => 77.78/10.63 (( 77.78/10.63 (binintersectTELcontra) => 77.78/10.63 (( 77.78/10.63 (binintersectTERcontra) => 77.78/10.63 (( 77.78/10.63 (contrasubsetT) => 77.78/10.63 (( 77.78/10.63 (contrasubsetT1) => 77.78/10.63 (( 77.78/10.63 (contrasubsetT2) => 77.78/10.63 (( 77.78/10.63 (contrasubsetT3) => 77.78/10.63 (( 77.78/10.63 (doubleComplementI1) => 77.78/10.63 (( 77.78/10.63 (doubleComplementE1) => 77.78/10.63 (( 77.78/10.63 (doubleComplementSub1) => 77.78/10.63 (( 77.78/10.63 (doubleComplementSub2) => 77.78/10.63 (( 77.78/10.63 (doubleComplementEq) => 77.78/10.63 (( 77.78/10.63 (complementTnotintersectT) => 77.78/10.63 (( 77.78/10.63 (complementImpComplementIntersect) => 77.78/10.63 (( 77.78/10.63 (complementSubsetComplementIntersect) => 77.78/10.63 (( 77.78/10.63 (complementInPowersetComplementIntersect) => 77.78/10.63 (( 77.78/10.63 (contraSubsetComplement) => 77.78/10.63 (( 77.78/10.63 (complementTcontraSubset) => 77.78/10.63 (( 77.78/10.63 (binunionTILcontra) => 77.78/10.63 (( 77.78/10.63 (binunionTIRcontra) => 77.78/10.63 (( 77.78/10.63 (inIntersectImpInUnion) => 77.78/10.63 (( 77.78/10.63 (inIntersectImpInUnion2) => 77.78/10.63 (( 77.78/10.63 (inIntersectImpInIntersectUnions) => 77.78/10.63 (( 77.78/10.63 (intersectInPowersetIntersectUnions) => 77.78/10.63 (( 77.78/10.63 (inComplementUnionImpNotIn1) => 77.78/10.63 (( 77.78/10.63 (inComplementUnionImpInComplement1) => 77.78/10.63 (( 77.78/10.63 (binunionTE) => 77.78/10.63 (( 77.78/10.63 (binunionTEcontra) => 77.78/10.63 (( 77.78/10.63 (demorgan2a1) => 77.78/10.63 (( 77.78/10.63 (complementUnionInPowersetComplement) => 77.78/10.63 (( 77.78/10.63 (demorgan2a2) => 77.78/10.63 (( 77.78/10.63 (demorgan1a) => 77.78/10.63 (( 77.78/10.63 (demorgan1b) => 77.78/10.63 (( 77.78/10.63 (demorgan1) => 77.78/10.63 (( 77.78/10.63 (demorgan2a) => 77.78/10.63 (( 77.78/10.63 (demorgan2b2) => 77.78/10.63 (( 77.78/10.63 (demorgan2b) => 77.78/10.63 (( 77.78/10.63 (demorgan2) => 77.78/10.63 (( 77.78/10.63 (woz13rule0) => 77.78/10.63 (( 77.78/10.63 (woz13rule1) => 77.78/10.63 (( 77.78/10.63 (woz13rule2) => 77.78/10.63 (( 77.78/10.63 (woz13rule3) => 77.78/10.63 (( 77.78/10.63 (woz13rule4) => 77.78/10.63 (( 77.78/10.63 (woz1_1) => 77.78/10.63 (( 77.78/10.63 (woz1_2) => 77.78/10.63 (( 77.78/10.63 (woz1_3) => 77.78/10.63 (( 77.78/10.63 (woz1_4) => 77.78/10.63 (( 77.78/10.63 (woz1_5) => 77.78/10.63 (( 77.78/10.63 (breln1all2) => 77.78/10.63 (( 77.78/10.63 (breln1SetBreln1) => 77.78/10.63 (( 77.78/10.63 (choice2fnsingleton) => 77.78/10.63 (( 77.78/10.63 (setOfPairsIsBReln1) => 77.78/10.63 (( 77.78/10.63 (breln1all1) => 77.78/10.63 (( 77.78/10.63 (subbreln1) => 77.78/10.63 (( 77.78/10.63 (eqbreln1) => 77.78/10.63 (( 77.78/10.63 (breln1invprop) => 77.78/10.63 (( 77.78/10.63 (breln1invI) => 77.78/10.63 (( 77.78/10.63 (breln1invE) => 77.78/10.63 (( 77.78/10.63 (breln1compprop) => 77.78/10.63 (( 77.78/10.63 (breln1compI) => 77.78/10.63 (( 77.78/10.63 (breln1compE) => 77.78/10.63 (( 77.78/10.63 (breln1compEex) => 77.78/10.63 (( 77.78/10.63 (breln1unionprop) => 77.78/10.63 (( 77.78/10.63 (breln1unionIL) => 77.78/10.63 (( 77.78/10.63 (breln1unionIR) => 77.78/10.63 (( 77.78/10.63 (breln1unionI) => 77.78/10.63 (( 77.78/10.63 (breln1unionE) => 77.78/10.63 (( 77.78/10.63 (breln1unionEcases) => 77.78/10.63 (( 77.78/10.63 (breln1unionCommutes) => 77.78/10.63 (( 77.78/10.63 (woz2Ex) => 77.78/10.63 (( 77.78/10.63 (woz2W) => 77.78/10.63 (( 77.78/10.63 (woz2A) => 77.78/10.63 (( 77.78/10.63 (woz2B) => 77.78/10.63 (( 77.78/10.63 (image1Ex) => 77.78/10.63 (( 77.78/10.63 (image1Ex1) => 77.78/10.63 (( 77.78/10.63 (image1Equiv) => 77.78/10.63 (( 77.78/10.63 (image1E) => 77.78/10.63 (( 77.78/10.63 (image1I) => 77.78/10.63 (( 77.78/10.63 (injFuncInInjFuncSet) => 77.78/10.63 (( 77.78/10.63 (injFuncSetFuncIn) => 77.78/10.63 (( 77.78/10.63 (injFuncSetFuncInj) => 77.78/10.63 (( 77.78/10.63 (surjFuncSetFuncIn) => 77.78/10.63 (( 77.78/10.63 (surjFuncSetFuncSurj) => 77.78/10.63 (( 77.78/10.63 (leftInvIsSurj) => 77.78/10.63 (( 77.78/10.63 (surjCantorThm) => 77.78/10.63 (( 77.78/10.63 (foundation2) => 77.78/10.63 (( 77.78/10.63 (notinself) => 77.78/10.63 (( 77.78/10.63 (notinself2) => 77.78/10.63 (( 77.78/10.63 (omegaSp) => 77.78/10.63 (( 77.78/10.63 (omegaSclos) => 77.78/10.63 (( 77.78/10.63 (peano0notS) => 77.78/10.63 (( 77.78/10.63 (peanoSinj) => 77.78/10.63 (( 77.78/10.63 (transitivesetOp1) => 77.78/10.63 (( 77.78/10.63 (binintTransitive) => 77.78/10.63 (( 77.78/10.63 (transitivesetOp2) => 77.78/10.63 (( 77.78/10.63 (setunionTransitive) => 77.78/10.63 (( 77.78/10.63 (ordinalMinLem1) => 77.78/10.63 (( 77.78/10.63 (!!) @ ( 77.78/10.63 ^[Y0 : $i]: 77.78/10.63 (( 77.78/10.63 (ordinal @ 77.78/10.63 Y0) => 77.78/10.63 (( 77.78/10.63 (!!) @ ( 77.78/10.63 ^[Y1 : $i]: 77.78/10.63 (( 77.78/10.63 (!!) @ ( 77.78/10.63 ^[Y2 : $i]: 77.78/10.63 (( 77.78/10.63 (in @ 77.78/10.63 Y2 @ 77.78/10.63 Y0) => 77.78/10.63 (( 77.78/10.63 (in @ 77.78/10.63 Y1 @ 77.78/10.63 Y2) => 77.78/10.63 (in @ 77.78/10.63 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 77.78/10.63 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl652])). 77.78/10.63 thf(zip_derived_cl681, plain, 77.78/10.63 (~ (((dsetconstr__Cong) => 77.78/10.63 (((subsetI1) => 77.78/10.63 (((eqimpsubset2) => 77.78/10.63 (((eqimpsubset1) => 77.78/10.63 (((subsetI2) => 77.78/10.63 (((emptysetsubset) => 77.78/10.63 (((subsetE) => 77.78/10.63 (((subsetE2) => 77.78/10.63 (((notsubsetI) => 77.78/10.63 (((notequalI1) => 77.78/10.63 (((notequalI2) => 77.78/10.63 (((subsetRefl) => 77.78/10.63 (((subsetTrans) => 77.78/10.63 (((setadjoinSub) => 77.78/10.63 (((setadjoinSub2) => 77.78/10.63 (((subset2powerset) => 77.78/10.63 (((setextsub) => 77.78/10.63 (((subsetemptysetimpeq) => 77.78/10.63 (((powersetI1) => 77.78/10.63 (((powersetE1) => 77.78/10.63 (((inPowerset) => 77.78/10.63 (((powersetsubset) => 77.78/10.63 (((sepInPowerset) => 77.78/10.63 (((sepSubset) => 77.78/10.63 (((binunionIL) => 77.78/10.63 (((upairset2IR) => 77.78/10.63 (((binunionIR) => 77.78/10.63 (((binunionEcases) => 77.78/10.63 (((binunionE) => 77.78/10.63 (((binunionLsub) => 77.78/10.63 (( 77.78/10.63 (binunionRsub) => 77.78/10.63 (( 77.78/10.63 (binintersectI) => 77.78/10.63 (( 77.78/10.63 (binintersectSubset5) => 77.78/10.63 (( 77.78/10.63 (binintersectEL) => 77.78/10.63 (( 77.78/10.63 (binintersectLsub) => 77.78/10.63 (( 77.78/10.63 (binintersectSubset2) => 77.78/10.63 (( 77.78/10.63 (binintersectSubset3) => 77.78/10.63 (( 77.78/10.63 (binintersectER) => 77.78/10.63 (( 77.78/10.63 (disjointsetsI1) => 77.78/10.63 (( 77.78/10.63 (binintersectRsub) => 77.78/10.63 (( 77.78/10.63 (binintersectSubset4) => 77.78/10.63 (( 77.78/10.63 (binintersectSubset1) => 77.78/10.63 (( 77.78/10.63 (bs114d) => 77.78/10.63 (( 77.78/10.63 (setminusI) => 77.78/10.63 (( 77.78/10.63 (setminusEL) => 77.78/10.63 (( 77.78/10.63 (setminusER) => 77.78/10.63 (( 77.78/10.63 (setminusSubset2) => 77.78/10.63 (( 77.78/10.63 (setminusERneg) => 77.78/10.63 (( 77.78/10.63 (setminusELneg) => 77.78/10.63 (( 77.78/10.63 (setminusILneg) => 77.78/10.63 (( 77.78/10.63 (setminusIRneg) => 77.78/10.63 (( 77.78/10.63 (setminusLsub) => 77.78/10.63 (( 77.78/10.63 (setminusSubset1) => 77.78/10.63 (( 77.78/10.63 (symdiffE) => 77.78/10.63 (( 77.78/10.63 (symdiffI1) => 77.78/10.63 (( 77.78/10.63 (symdiffI2) => 77.78/10.63 (( 77.78/10.63 (symdiffIneg1) => 77.78/10.63 (( 77.78/10.63 (symdiffIneg2) => 77.78/10.63 (( 77.78/10.63 (secondinupair) => 77.78/10.63 (( 77.78/10.63 (setukpairIL) => 77.78/10.63 (( 77.78/10.63 (setukpairIR) => 77.78/10.63 (( 77.78/10.63 (kpairiskpair) => 77.78/10.63 (( 77.78/10.63 (kpairp) => 77.78/10.63 (( 77.78/10.63 (singletonsubset) => 77.78/10.63 (( 77.78/10.63 (singletoninpowerset) => 77.78/10.63 (( 77.78/10.63 (singletoninpowunion) => 77.78/10.63 (( 77.78/10.63 (upairset2E) => 77.78/10.63 (( 77.78/10.63 (upairsubunion) => 77.78/10.63 (( 77.78/10.63 (upairinpowunion) => 77.78/10.63 (( 77.78/10.63 (ubforcartprodlem1) => 77.78/10.63 (( 77.78/10.63 (ubforcartprodlem2) => 77.78/10.63 (( 77.78/10.63 (ubforcartprodlem3) => 77.78/10.63 (( 77.78/10.63 (cartprodpairin) => 77.78/10.63 (( 77.78/10.63 (cartprodmempair1) => 77.78/10.63 (( 77.78/10.63 (cartprodmempair) => 77.78/10.63 (( 77.78/10.63 (setunionE2) => 77.78/10.63 (( 77.78/10.63 (setunionsingleton1) => 77.78/10.63 (( 77.78/10.63 (setunionsingleton2) => 77.78/10.63 (( 77.78/10.63 (setunionsingleton) => 77.78/10.63 (( 77.78/10.63 (singletonprop) => 77.78/10.63 (( 77.78/10.63 (ex1E1) => 77.78/10.63 (( 77.78/10.63 (ex1I) => 77.78/10.63 (( 77.78/10.63 (ex1I2) => 77.78/10.63 (( 77.78/10.63 (singletonsuniq) => 77.78/10.63 (( 77.78/10.63 (setukpairinjL1) => 77.78/10.63 (( 77.78/10.63 (kfstsingleton) => 77.78/10.63 (( 77.78/10.63 (theprop) => 77.78/10.63 (( 77.78/10.63 (kfstpairEq) => 77.78/10.63 (( 77.78/10.63 (cartprodfstin) => 77.78/10.63 (( 77.78/10.63 (setukpairinjL2) => 77.78/10.63 (( 77.78/10.63 (setukpairinjL) => 77.78/10.63 (( 77.78/10.63 (setukpairinjR11) => 77.78/10.63 (( 77.78/10.63 (setukpairinjR12) => 77.78/10.63 (( 77.78/10.63 (setukpairinjR1) => 77.78/10.63 (( 77.78/10.63 (upairequniteq) => 77.78/10.63 (( 77.78/10.63 (setukpairinjR2) => 77.78/10.63 (( 77.78/10.63 (setukpairinjR) => 77.78/10.63 (( 77.78/10.63 (ksndsingleton) => 77.78/10.63 (( 77.78/10.63 (ksndpairEq) => 77.78/10.63 (( 77.78/10.63 (kpairsurjEq) => 77.78/10.63 (( 77.78/10.63 (cartprodsndin) => 77.78/10.63 (( 77.78/10.63 (cartprodpairmemEL) => 77.78/10.63 (( 77.78/10.63 (cartprodpairmemER) => 77.78/10.63 (( 77.78/10.63 (cartprodmempaircEq) => 77.78/10.63 (( 77.78/10.63 (cartprodfstpairEq) => 77.78/10.63 (( 77.78/10.63 (cartprodsndpairEq) => 77.78/10.63 (( 77.78/10.63 (cartprodpairsurjEq) => 77.78/10.63 (( 77.78/10.63 (dpsetconstrI) => 77.78/10.63 (( 77.78/10.63 (dpsetconstrSub) => 77.78/10.63 (( 77.78/10.63 (setOfPairsIsBReln) => 77.78/10.63 (( 77.78/10.63 (dpsetconstrERa) => 77.78/10.63 (( 77.78/10.63 (dpsetconstrEL1) => 77.78/10.63 (( 77.78/10.63 (dpsetconstrEL2) => 77.78/10.63 (( 77.78/10.63 (dpsetconstrER) => 77.78/10.63 (( 77.78/10.63 (funcImageSingleton) => 77.78/10.63 (( 77.78/10.63 (apProp) => 77.78/10.63 (( 77.78/10.63 (app) => 77.78/10.63 (( 77.78/10.63 (infuncsetfunc) => 77.78/10.63 (( 77.78/10.63 (ap2p) => 77.78/10.63 (( 77.78/10.63 (funcinfuncset) => 77.78/10.63 (( 77.78/10.63 (lamProp) => 77.78/10.63 (( 77.78/10.63 (lamp) => 77.78/10.63 (( 77.78/10.63 (lam2p) => 77.78/10.63 (( 77.78/10.63 (brelnall1) => 77.78/10.63 (( 77.78/10.63 (brelnall2) => 77.78/10.63 (( 77.78/10.63 (ex1E2) => 77.78/10.63 (( 77.78/10.63 (funcGraphProp1) => 77.78/10.63 (( 77.78/10.63 (funcGraphProp3) => 77.78/10.63 (( 77.78/10.63 (funcGraphProp2) => 77.78/10.63 (( 77.78/10.63 (funcextLem) => 77.78/10.63 (( 77.78/10.63 (funcGraphProp4) => 77.78/10.63 (( 77.78/10.63 (subbreln) => 77.78/10.63 (( 77.78/10.63 (eqbreln) => 77.78/10.63 (( 77.78/10.63 (funcext) => 77.78/10.63 (( 77.78/10.63 (funcext2) => 77.78/10.63 (( 77.78/10.63 (ap2apEq1) => 77.78/10.63 (( 77.78/10.63 (ap2apEq2) => 77.78/10.63 (( 77.78/10.63 (beta1) => 77.78/10.63 (( 77.78/10.63 (eta1) => 77.78/10.63 (( 77.78/10.63 (lam2lamEq) => 77.78/10.63 (( 77.78/10.63 (beta2) => 77.78/10.63 (( 77.78/10.63 (eta2) => 77.78/10.63 (( 77.78/10.63 (iffalseProp1) => 77.78/10.63 (( 77.78/10.63 (iffalseProp2) => 77.78/10.63 (( 77.78/10.63 (iftrueProp1) => 77.78/10.63 (( 77.78/10.63 (iftrueProp2) => 77.78/10.63 (( 77.78/10.63 (ifSingleton) => 77.78/10.63 (( 77.78/10.63 (ifp) => 77.78/10.63 (( 77.78/10.63 (theeq) => 77.78/10.63 (( 77.78/10.63 (iftrue) => 77.78/10.63 (( 77.78/10.63 (iffalse) => 77.78/10.63 (( 77.78/10.63 (iftrueorfalse) => 77.78/10.63 (( 77.78/10.63 (binintersectT_lem) => 77.78/10.63 (( 77.78/10.63 (binunionT_lem) => 77.78/10.63 (( 77.78/10.63 (powersetT_lem) => 77.78/10.63 (( 77.78/10.63 (setminusT_lem) => 77.78/10.63 (( 77.78/10.63 (complementT_lem) => 77.78/10.63 (( 77.78/10.63 (setextT) => 77.78/10.63 (( 77.78/10.63 (subsetTI) => 77.78/10.63 (( 77.78/10.63 (powersetTI1) => 77.78/10.63 (( 77.78/10.63 (powersetTE1) => 77.78/10.63 (( 77.78/10.63 (complementTI1) => 77.78/10.63 (( 77.78/10.63 (complementTE1) => 77.78/10.63 (( 77.78/10.63 (binintersectTELcontra) => 77.78/10.63 (( 77.78/10.63 (binintersectTERcontra) => 77.78/10.63 (( 77.78/10.63 (contrasubsetT) => 77.78/10.63 (( 77.78/10.63 (contrasubsetT1) => 77.78/10.63 (( 77.78/10.63 (contrasubsetT2) => 77.78/10.63 (( 77.78/10.63 (contrasubsetT3) => 77.78/10.63 (( 77.78/10.63 (doubleComplementI1) => 77.78/10.63 (( 77.78/10.63 (doubleComplementE1) => 77.78/10.63 (( 77.78/10.63 (doubleComplementSub1) => 77.78/10.63 (( 77.78/10.63 (doubleComplementSub2) => 77.78/10.63 (( 77.78/10.63 (doubleComplementEq) => 77.78/10.63 (( 77.78/10.63 (complementTnotintersectT) => 77.78/10.63 (( 77.78/10.63 (complementImpComplementIntersect) => 77.78/10.63 (( 77.78/10.63 (complementSubsetComplementIntersect) => 77.78/10.63 (( 77.78/10.63 (complementInPowersetComplementIntersect) => 77.78/10.63 (( 77.78/10.63 (contraSubsetComplement) => 77.78/10.63 (( 77.78/10.63 (complementTcontraSubset) => 77.78/10.63 (( 77.78/10.63 (binunionTILcontra) => 77.78/10.63 (( 77.78/10.63 (binunionTIRcontra) => 77.78/10.63 (( 77.78/10.63 (inIntersectImpInUnion) => 77.78/10.63 (( 77.78/10.63 (inIntersectImpInUnion2) => 77.78/10.63 (( 77.78/10.63 (inIntersectImpInIntersectUnions) => 77.78/10.63 (( 77.78/10.63 (intersectInPowersetIntersectUnions) => 77.78/10.63 (( 77.78/10.63 (inComplementUnionImpNotIn1) => 77.78/10.63 (( 77.78/10.63 (inComplementUnionImpInComplement1) => 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(binintTransitive) => 77.78/10.63 (( 77.78/10.63 (transitivesetOp2) => 77.78/10.63 (( 77.78/10.63 (setunionTransitive) => 77.78/10.63 (( 77.78/10.63 (ordinalMinLem1) => 77.78/10.63 (( 77.78/10.63 (!!) @ ( 77.78/10.63 ^[Y0 : $i]: 77.78/10.63 (( 77.78/10.63 (ordinal @ 77.78/10.63 Y0) => 77.78/10.63 (( 77.78/10.63 (!!) @ ( 77.78/10.63 ^[Y1 : $i]: 77.78/10.63 (( 77.78/10.63 (!!) @ ( 77.78/10.63 ^[Y2 : $i]: 77.78/10.63 (( 77.78/10.63 (in @ 77.78/10.63 Y2 @ 77.78/10.63 Y0) => 77.78/10.63 (( 77.78/10.63 (in @ 77.78/10.63 Y1 @ 77.78/10.63 Y2) => 77.78/10.63 (in @ 77.78/10.63 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 77.78/10.63 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl664])). 77.78/10.63 thf(zip_derived_cl698, plain, 77.78/10.63 (~ (((subsetI1) => 77.78/10.63 (((eqimpsubset2) => 77.78/10.63 (((eqimpsubset1) => 77.78/10.63 (((subsetI2) => 77.78/10.63 (((emptysetsubset) => 77.78/10.63 (((subsetE) => 77.78/10.63 (((subsetE2) => 77.78/10.63 (((notsubsetI) => 77.78/10.63 (((notequalI1) => 77.78/10.63 (((notequalI2) => 77.78/10.63 (((subsetRefl) => 77.78/10.63 (((subsetTrans) => 77.78/10.63 (((setadjoinSub) => 77.78/10.63 (((setadjoinSub2) => 77.78/10.63 (((subset2powerset) => 77.78/10.63 (((setextsub) => 77.78/10.63 (((subsetemptysetimpeq) => 77.78/10.63 (((powersetI1) => 77.78/10.63 (((powersetE1) => 77.78/10.63 (((inPowerset) => 77.78/10.63 (((powersetsubset) => 77.78/10.63 (((sepInPowerset) => 77.78/10.63 (((sepSubset) => 77.78/10.63 (((binunionIL) => 77.78/10.63 (((upairset2IR) => 77.78/10.63 (((binunionIR) => 77.78/10.63 (((binunionEcases) => 77.78/10.63 (((binunionE) => 77.78/10.63 (((binunionLsub) => 77.78/10.63 (((binunionRsub) => 77.78/10.63 (( 77.78/10.63 (binintersectI) => 77.78/10.63 (( 77.78/10.63 (binintersectSubset5) => 77.78/10.63 (( 77.78/10.63 (binintersectEL) => 77.78/10.63 (( 77.78/10.63 (binintersectLsub) => 77.78/10.63 (( 77.78/10.63 (binintersectSubset2) => 77.78/10.63 (( 77.78/10.63 (binintersectSubset3) => 77.78/10.63 (( 77.78/10.63 (binintersectER) => 77.78/10.63 (( 77.78/10.63 (disjointsetsI1) => 77.78/10.63 (( 77.78/10.63 (binintersectRsub) => 77.78/10.63 (( 77.78/10.63 (binintersectSubset4) => 77.78/10.63 (( 77.78/10.63 (binintersectSubset1) => 77.78/10.63 (( 77.78/10.63 (bs114d) => 77.78/10.63 (( 77.78/10.63 (setminusI) => 77.78/10.63 (( 77.78/10.63 (setminusEL) => 77.78/10.63 (( 77.78/10.63 (setminusER) => 77.78/10.63 (( 77.78/10.63 (setminusSubset2) => 77.78/10.63 (( 77.78/10.63 (setminusERneg) => 77.78/10.63 (( 77.78/10.63 (setminusELneg) => 77.78/10.63 (( 77.78/10.63 (setminusILneg) => 77.78/10.63 (( 77.78/10.63 (setminusIRneg) => 77.78/10.63 (( 77.78/10.63 (setminusLsub) => 77.78/10.63 (( 77.78/10.63 (setminusSubset1) => 77.78/10.63 (( 77.78/10.63 (symdiffE) => 77.78/10.63 (( 77.78/10.63 (symdiffI1) => 77.78/10.63 (( 77.78/10.63 (symdiffI2) => 77.78/10.63 (( 77.78/10.63 (symdiffIneg1) => 77.78/10.63 (( 77.78/10.63 (symdiffIneg2) => 77.78/10.63 (( 77.78/10.63 (secondinupair) => 77.78/10.63 (( 77.78/10.63 (setukpairIL) => 77.78/10.63 (( 77.78/10.63 (setukpairIR) => 77.78/10.63 (( 77.78/10.63 (kpairiskpair) => 77.78/10.63 (( 77.78/10.63 (kpairp) => 77.78/10.63 (( 77.78/10.63 (singletonsubset) => 77.78/10.63 (( 77.78/10.63 (singletoninpowerset) => 77.78/10.63 (( 77.78/10.63 (singletoninpowunion) => 77.78/10.63 (( 77.78/10.63 (upairset2E) => 77.78/10.63 (( 77.78/10.63 (upairsubunion) => 77.78/10.63 (( 77.78/10.63 (upairinpowunion) => 77.78/10.63 (( 77.78/10.63 (ubforcartprodlem1) => 77.78/10.63 (( 77.78/10.63 (ubforcartprodlem2) => 77.78/10.63 (( 77.78/10.63 (ubforcartprodlem3) => 77.78/10.63 (( 77.78/10.63 (cartprodpairin) => 77.78/10.63 (( 77.78/10.63 (cartprodmempair1) => 77.78/10.63 (( 77.78/10.63 (cartprodmempair) => 77.78/10.63 (( 77.78/10.63 (setunionE2) => 77.78/10.63 (( 77.78/10.63 (setunionsingleton1) => 77.78/10.63 (( 77.78/10.63 (setunionsingleton2) => 77.78/10.63 (( 77.78/10.63 (setunionsingleton) => 77.78/10.63 (( 77.78/10.63 (singletonprop) => 77.78/10.63 (( 77.78/10.63 (ex1E1) => 77.78/10.63 (( 77.78/10.63 (ex1I) => 77.78/10.63 (( 77.78/10.63 (ex1I2) => 77.78/10.63 (( 77.78/10.63 (singletonsuniq) => 77.78/10.63 (( 77.78/10.63 (setukpairinjL1) => 77.78/10.63 (( 77.78/10.63 (kfstsingleton) => 77.78/10.63 (( 77.78/10.63 (theprop) => 77.78/10.63 (( 77.78/10.63 (kfstpairEq) => 77.78/10.63 (( 77.78/10.63 (cartprodfstin) => 77.78/10.63 (( 77.78/10.63 (setukpairinjL2) => 77.78/10.63 (( 77.78/10.63 (setukpairinjL) => 77.78/10.63 (( 77.78/10.63 (setukpairinjR11) => 77.78/10.63 (( 77.78/10.63 (setukpairinjR12) => 77.78/10.63 (( 77.78/10.63 (setukpairinjR1) => 77.78/10.63 (( 77.78/10.63 (upairequniteq) => 77.78/10.63 (( 77.78/10.63 (setukpairinjR2) => 77.78/10.63 (( 77.78/10.63 (setukpairinjR) => 77.78/10.63 (( 77.78/10.63 (ksndsingleton) => 77.78/10.63 (( 77.78/10.63 (ksndpairEq) => 77.78/10.63 (( 77.78/10.63 (kpairsurjEq) => 77.78/10.63 (( 77.78/10.63 (cartprodsndin) => 77.78/10.63 (( 77.78/10.63 (cartprodpairmemEL) => 77.78/10.63 (( 77.78/10.63 (cartprodpairmemER) => 77.78/10.63 (( 77.78/10.63 (cartprodmempaircEq) => 77.78/10.63 (( 77.78/10.63 (cartprodfstpairEq) => 77.78/10.63 (( 77.78/10.63 (cartprodsndpairEq) => 77.78/10.63 (( 77.78/10.63 (cartprodpairsurjEq) => 77.78/10.63 (( 77.78/10.63 (dpsetconstrI) => 77.78/10.63 (( 77.78/10.63 (dpsetconstrSub) => 77.78/10.63 (( 77.78/10.63 (setOfPairsIsBReln) => 77.78/10.63 (( 77.78/10.63 (dpsetconstrERa) => 77.78/10.63 (( 77.78/10.63 (dpsetconstrEL1) => 77.78/10.63 (( 77.78/10.63 (dpsetconstrEL2) => 77.78/10.63 (( 77.78/10.63 (dpsetconstrER) => 77.78/10.63 (( 77.78/10.63 (funcImageSingleton) => 77.78/10.63 (( 77.78/10.63 (apProp) => 77.78/10.63 (( 77.78/10.63 (app) => 77.78/10.63 (( 77.78/10.63 (infuncsetfunc) => 77.78/10.63 (( 77.78/10.63 (ap2p) => 77.78/10.63 (( 77.78/10.63 (funcinfuncset) => 77.78/10.63 (( 77.78/10.63 (lamProp) => 77.78/10.63 (( 77.78/10.63 (lamp) => 77.78/10.63 (( 77.78/10.63 (lam2p) => 77.78/10.63 (( 77.78/10.63 (brelnall1) => 77.78/10.63 (( 77.78/10.63 (brelnall2) => 77.78/10.63 (( 77.78/10.63 (ex1E2) => 77.78/10.63 (( 77.78/10.63 (funcGraphProp1) => 77.78/10.63 (( 77.78/10.63 (funcGraphProp3) => 77.78/10.63 (( 77.78/10.63 (funcGraphProp2) => 77.78/10.63 (( 77.78/10.63 (funcextLem) => 77.78/10.63 (( 77.78/10.63 (funcGraphProp4) => 77.78/10.63 (( 77.78/10.63 (subbreln) => 77.78/10.63 (( 77.78/10.63 (eqbreln) => 77.78/10.63 (( 77.78/10.63 (funcext) => 77.78/10.63 (( 77.78/10.63 (funcext2) => 77.78/10.63 (( 77.78/10.63 (ap2apEq1) => 77.78/10.63 (( 77.78/10.63 (ap2apEq2) => 77.78/10.63 (( 77.78/10.63 (beta1) => 77.78/10.63 (( 77.78/10.63 (eta1) => 77.78/10.63 (( 77.78/10.63 (lam2lamEq) => 77.78/10.63 (( 77.78/10.63 (beta2) => 77.78/10.63 (( 77.78/10.63 (eta2) => 77.78/10.63 (( 77.78/10.63 (iffalseProp1) => 77.78/10.63 (( 77.78/10.63 (iffalseProp2) => 77.78/10.63 (( 77.78/10.63 (iftrueProp1) => 77.78/10.63 (( 77.78/10.63 (iftrueProp2) => 77.78/10.63 (( 77.78/10.63 (ifSingleton) => 77.78/10.63 (( 77.78/10.63 (ifp) => 77.78/10.63 (( 77.78/10.63 (theeq) => 77.78/10.63 (( 77.78/10.63 (iftrue) => 77.78/10.63 (( 77.78/10.63 (iffalse) => 77.78/10.63 (( 77.78/10.63 (iftrueorfalse) => 77.78/10.63 (( 77.78/10.63 (binintersectT_lem) => 77.78/10.63 (( 77.78/10.63 (binunionT_lem) => 77.78/10.63 (( 77.78/10.63 (powersetT_lem) => 77.78/10.63 (( 77.78/10.63 (setminusT_lem) => 77.78/10.63 (( 77.78/10.63 (complementT_lem) => 77.78/10.63 (( 77.78/10.63 (setextT) => 77.78/10.63 (( 77.78/10.63 (subsetTI) => 77.78/10.63 (( 77.78/10.63 (powersetTI1) => 77.78/10.63 (( 77.78/10.63 (powersetTE1) => 77.78/10.63 (( 77.78/10.63 (complementTI1) => 77.78/10.63 (( 77.78/10.63 (complementTE1) => 77.78/10.63 (( 77.78/10.63 (binintersectTELcontra) => 77.78/10.63 (( 77.78/10.63 (binintersectTERcontra) => 77.78/10.63 (( 77.78/10.63 (contrasubsetT) => 77.78/10.63 (( 77.78/10.63 (contrasubsetT1) => 77.78/10.63 (( 77.78/10.63 (contrasubsetT2) => 77.78/10.63 (( 77.78/10.63 (contrasubsetT3) => 77.78/10.63 (( 77.78/10.63 (doubleComplementI1) => 77.78/10.63 (( 77.78/10.63 (doubleComplementE1) => 77.78/10.63 (( 77.78/10.63 (doubleComplementSub1) => 77.78/10.63 (( 77.78/10.63 (doubleComplementSub2) => 77.78/10.63 (( 77.78/10.63 (doubleComplementEq) => 77.78/10.63 (( 77.78/10.63 (complementTnotintersectT) => 77.78/10.63 (( 77.78/10.63 (complementImpComplementIntersect) => 77.78/10.63 (( 77.78/10.63 (complementSubsetComplementIntersect) => 77.78/10.63 (( 77.78/10.63 (complementInPowersetComplementIntersect) => 77.78/10.63 (( 77.78/10.63 (contraSubsetComplement) => 77.78/10.63 (( 77.78/10.63 (complementTcontraSubset) => 77.78/10.63 (( 77.78/10.63 (binunionTILcontra) => 77.78/10.63 (( 77.78/10.63 (binunionTIRcontra) => 77.78/10.63 (( 77.78/10.63 (inIntersectImpInUnion) => 77.78/10.63 (( 77.78/10.63 (inIntersectImpInUnion2) => 77.78/10.63 (( 77.78/10.63 (inIntersectImpInIntersectUnions) => 77.78/10.63 (( 77.78/10.63 (intersectInPowersetIntersectUnions) => 77.78/10.63 (( 77.78/10.63 (inComplementUnionImpNotIn1) => 77.78/10.63 (( 77.78/10.63 (inComplementUnionImpInComplement1) => 77.78/10.63 (( 77.78/10.63 (binunionTE) => 77.78/10.63 (( 77.78/10.63 (binunionTEcontra) => 77.78/10.63 (( 77.78/10.63 (demorgan2a1) => 77.78/10.63 (( 77.78/10.63 (complementUnionInPowersetComplement) => 77.78/10.63 (( 77.78/10.63 (demorgan2a2) => 77.78/10.63 (( 77.78/10.63 (demorgan1a) => 77.78/10.63 (( 77.78/10.63 (demorgan1b) => 77.78/10.63 (( 77.78/10.63 (demorgan1) => 77.78/10.63 (( 77.78/10.63 (demorgan2a) => 77.78/10.63 (( 77.78/10.63 (demorgan2b2) => 77.78/10.63 (( 77.78/10.63 (demorgan2b) => 77.78/10.63 (( 77.78/10.63 (demorgan2) => 77.78/10.63 (( 77.78/10.63 (woz13rule0) => 77.78/10.63 (( 77.78/10.63 (woz13rule1) => 77.78/10.63 (( 77.78/10.63 (woz13rule2) => 77.78/10.63 (( 77.78/10.63 (woz13rule3) => 77.78/10.63 (( 77.78/10.63 (woz13rule4) => 77.78/10.63 (( 77.78/10.63 (woz1_1) => 77.78/10.63 (( 77.78/10.63 (woz1_2) => 77.78/10.63 (( 77.78/10.63 (woz1_3) => 77.78/10.63 (( 77.78/10.63 (woz1_4) => 77.78/10.63 (( 77.78/10.63 (woz1_5) => 77.78/10.63 (( 77.78/10.63 (breln1all2) => 77.78/10.63 (( 77.78/10.63 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Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 77.78/10.63 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl681])). 77.78/10.63 thf(zip_derived_cl712, plain, 77.78/10.63 (~ (((eqimpsubset2) => 77.78/10.63 (((eqimpsubset1) => 77.78/10.63 (((subsetI2) => 77.78/10.63 (((emptysetsubset) => 77.78/10.63 (((subsetE) => 77.78/10.63 (((subsetE2) => 77.78/10.63 (((notsubsetI) => 77.78/10.63 (((notequalI1) => 77.78/10.63 (((notequalI2) => 77.78/10.63 (((subsetRefl) => 77.78/10.63 (((subsetTrans) => 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(cartprodfstpairEq) => 77.78/10.63 (( 77.78/10.63 (cartprodsndpairEq) => 77.78/10.63 (( 77.78/10.63 (cartprodpairsurjEq) => 77.78/10.63 (( 77.78/10.63 (dpsetconstrI) => 77.78/10.63 (( 77.78/10.63 (dpsetconstrSub) => 77.78/10.63 (( 77.78/10.63 (setOfPairsIsBReln) => 77.78/10.63 (( 77.78/10.63 (dpsetconstrERa) => 77.78/10.63 (( 77.78/10.63 (dpsetconstrEL1) => 77.78/10.63 (( 77.78/10.63 (dpsetconstrEL2) => 77.78/10.63 (( 77.78/10.63 (dpsetconstrER) => 77.78/10.63 (( 77.78/10.63 (funcImageSingleton) => 77.78/10.63 (( 77.78/10.63 (apProp) => 77.78/10.63 (( 77.78/10.63 (app) => 77.78/10.63 (( 77.78/10.63 (infuncsetfunc) => 77.78/10.63 (( 77.78/10.63 (ap2p) => 77.78/10.63 (( 77.78/10.63 (funcinfuncset) => 77.78/10.63 (( 77.78/10.63 (lamProp) => 77.78/10.63 (( 77.78/10.63 (lamp) => 77.78/10.63 (( 77.78/10.63 (lam2p) => 77.78/10.63 (( 77.78/10.63 (brelnall1) => 77.78/10.63 (( 77.78/10.63 (brelnall2) => 77.78/10.63 (( 77.78/10.63 (ex1E2) => 77.78/10.63 (( 77.78/10.63 (funcGraphProp1) => 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(setunionTransitive) => 77.78/10.63 (( 77.78/10.63 (ordinalMinLem1) => 77.78/10.63 (( 77.78/10.63 (!!) @ ( 77.78/10.63 ^[Y0 : $i]: 77.78/10.63 (( 77.78/10.63 (ordinal @ 77.78/10.63 Y0) => 77.78/10.63 (( 77.78/10.63 (!!) @ ( 77.78/10.63 ^[Y1 : $i]: 77.78/10.63 (( 77.78/10.63 (!!) @ ( 77.78/10.63 ^[Y2 : $i]: 77.78/10.63 (( 77.78/10.63 (in @ 77.78/10.63 Y2 @ 77.78/10.63 Y0) => 77.78/10.63 (( 77.78/10.63 (in @ 77.78/10.63 Y1 @ 77.78/10.63 Y2) => 77.78/10.63 (in @ 77.78/10.63 Y1 @ 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(((subset2powerset) => 77.78/10.63 (((setextsub) => 77.78/10.63 (((subsetemptysetimpeq) => 77.78/10.63 (((powersetI1) => 77.78/10.63 (((powersetE1) => 77.78/10.63 (((inPowerset) => 77.78/10.63 (((powersetsubset) => 77.78/10.63 (((sepInPowerset) => 77.78/10.63 (((sepSubset) => 77.78/10.63 (((binunionIL) => 77.78/10.63 (((upairset2IR) => 77.78/10.63 (((binunionIR) => 77.78/10.63 (((binunionEcases) => 77.78/10.63 (((binunionE) => 77.78/10.63 (((binunionLsub) => 77.78/10.63 (((binunionRsub) => 77.78/10.63 (((binintersectI) => 77.78/10.63 (((binintersectSubset5) => 77.78/10.63 (((binintersectEL) => 77.78/10.63 (( 77.78/10.63 (binintersectLsub) => 77.78/10.63 (( 77.78/10.63 (binintersectSubset2) => 77.78/10.63 (( 77.78/10.63 (binintersectSubset3) => 77.78/10.63 (( 77.78/10.63 (binintersectER) => 77.78/10.63 (( 77.78/10.63 (disjointsetsI1) => 77.78/10.63 (( 77.78/10.63 (binintersectRsub) => 77.78/10.63 (( 77.78/10.63 (binintersectSubset4) => 77.78/10.63 (( 77.78/10.63 (binintersectSubset1) => 77.78/10.63 (( 77.78/10.63 (bs114d) => 77.78/10.63 (( 77.78/10.63 (setminusI) => 77.78/10.63 (( 77.78/10.63 (setminusEL) => 77.78/10.63 (( 77.78/10.63 (setminusER) => 77.78/10.63 (( 77.78/10.63 (setminusSubset2) => 77.78/10.63 (( 77.78/10.63 (setminusERneg) => 77.78/10.63 (( 77.78/10.63 (setminusELneg) => 77.78/10.63 (( 77.78/10.63 (setminusILneg) => 77.78/10.63 (( 77.78/10.63 (setminusIRneg) => 77.78/10.63 (( 77.78/10.63 (setminusLsub) => 77.78/10.63 (( 77.78/10.63 (setminusSubset1) => 77.78/10.63 (( 77.78/10.63 (symdiffE) => 77.78/10.63 (( 77.78/10.63 (symdiffI1) => 77.78/10.63 (( 77.78/10.63 (symdiffI2) => 77.78/10.63 (( 77.78/10.63 (symdiffIneg1) => 77.78/10.63 (( 77.78/10.63 (symdiffIneg2) => 77.78/10.63 (( 77.78/10.63 (secondinupair) => 77.78/10.63 (( 77.78/10.63 (setukpairIL) => 77.78/10.63 (( 77.78/10.63 (setukpairIR) => 77.78/10.63 (( 77.78/10.63 (kpairiskpair) => 77.78/10.63 (( 77.78/10.63 (kpairp) => 77.78/10.63 (( 77.78/10.63 (singletonsubset) => 77.78/10.63 (( 77.78/10.63 (singletoninpowerset) => 77.78/10.63 (( 77.78/10.63 (singletoninpowunion) => 77.78/10.63 (( 77.78/10.63 (upairset2E) => 77.78/10.63 (( 77.78/10.63 (upairsubunion) => 77.78/10.63 (( 77.78/10.63 (upairinpowunion) => 77.78/10.63 (( 77.78/10.63 (ubforcartprodlem1) => 77.78/10.63 (( 77.78/10.63 (ubforcartprodlem2) => 77.78/10.63 (( 77.78/10.63 (ubforcartprodlem3) => 77.78/10.63 (( 77.78/10.63 (cartprodpairin) => 77.78/10.63 (( 77.78/10.63 (cartprodmempair1) => 77.78/10.63 (( 77.78/10.63 (cartprodmempair) => 77.78/10.63 (( 77.78/10.63 (setunionE2) => 77.78/10.63 (( 77.78/10.63 (setunionsingleton1) => 77.78/10.63 (( 77.78/10.63 (setunionsingleton2) => 77.78/10.63 (( 77.78/10.63 (setunionsingleton) => 77.78/10.63 (( 77.78/10.63 (singletonprop) => 77.78/10.63 (( 77.78/10.63 (ex1E1) => 77.78/10.63 (( 77.78/10.63 (ex1I) => 77.78/10.63 (( 77.78/10.63 (ex1I2) => 77.78/10.63 (( 77.78/10.63 (singletonsuniq) => 77.78/10.63 (( 77.78/10.63 (setukpairinjL1) => 77.78/10.63 (( 77.78/10.63 (kfstsingleton) => 77.78/10.63 (( 77.78/10.63 (theprop) => 77.78/10.63 (( 77.78/10.63 (kfstpairEq) => 77.78/10.63 (( 77.78/10.63 (cartprodfstin) => 77.78/10.63 (( 77.78/10.63 (setukpairinjL2) => 77.78/10.63 (( 77.78/10.63 (setukpairinjL) => 77.78/10.63 (( 77.78/10.63 (setukpairinjR11) => 77.78/10.63 (( 77.78/10.63 (setukpairinjR12) => 77.78/10.63 (( 77.78/10.63 (setukpairinjR1) => 77.78/10.63 (( 77.78/10.63 (upairequniteq) => 77.78/10.63 (( 77.78/10.63 (setukpairinjR2) => 77.78/10.63 (( 77.78/10.63 (setukpairinjR) => 77.78/10.63 (( 77.78/10.63 (ksndsingleton) => 77.78/10.63 (( 77.78/10.63 (ksndpairEq) => 77.78/10.63 (( 77.78/10.63 (kpairsurjEq) => 77.78/10.63 (( 77.78/10.63 (cartprodsndin) => 77.78/10.63 (( 77.78/10.63 (cartprodpairmemEL) => 77.78/10.63 (( 77.78/10.63 (cartprodpairmemER) => 77.78/10.63 (( 77.78/10.63 (cartprodmempaircEq) => 77.78/10.63 (( 77.78/10.63 (cartprodfstpairEq) => 77.78/10.63 (( 77.78/10.63 (cartprodsndpairEq) => 77.78/10.63 (( 77.78/10.63 (cartprodpairsurjEq) => 77.78/10.63 (( 77.78/10.63 (dpsetconstrI) => 77.78/10.63 (( 77.78/10.63 (dpsetconstrSub) => 77.78/10.63 (( 77.78/10.63 (setOfPairsIsBReln) => 77.78/10.63 (( 77.78/10.63 (dpsetconstrERa) => 77.78/10.63 (( 77.78/10.63 (dpsetconstrEL1) => 77.78/10.63 (( 77.78/10.63 (dpsetconstrEL2) => 77.78/10.63 (( 77.78/10.63 (dpsetconstrER) => 77.78/10.63 (( 77.78/10.63 (funcImageSingleton) => 77.78/10.63 (( 77.78/10.63 (apProp) => 77.78/10.63 (( 77.78/10.63 (app) => 77.78/10.63 (( 77.78/10.63 (infuncsetfunc) => 77.78/10.63 (( 77.78/10.63 (ap2p) => 77.78/10.63 (( 77.78/10.63 (funcinfuncset) => 77.78/10.63 (( 77.78/10.63 (lamProp) => 77.78/10.63 (( 77.78/10.63 (lamp) => 77.78/10.63 (( 77.78/10.63 (lam2p) => 77.78/10.63 (( 77.78/10.63 (brelnall1) => 77.78/10.63 (( 77.78/10.63 (brelnall2) => 77.78/10.63 (( 77.78/10.63 (ex1E2) => 77.78/10.63 (( 77.78/10.63 (funcGraphProp1) => 77.78/10.63 (( 77.78/10.63 (funcGraphProp3) => 77.78/10.63 (( 77.78/10.63 (funcGraphProp2) => 77.78/10.63 (( 77.78/10.63 (funcextLem) => 77.78/10.63 (( 77.78/10.63 (funcGraphProp4) => 77.78/10.63 (( 77.78/10.63 (subbreln) => 77.78/10.63 (( 77.78/10.63 (eqbreln) => 77.78/10.63 (( 77.78/10.63 (funcext) => 77.78/10.63 (( 77.78/10.63 (funcext2) => 77.78/10.63 (( 77.78/10.63 (ap2apEq1) => 77.78/10.63 (( 77.78/10.63 (ap2apEq2) => 77.78/10.63 (( 77.78/10.63 (beta1) => 77.78/10.63 (( 77.78/10.63 (eta1) => 77.78/10.63 (( 77.78/10.63 (lam2lamEq) => 77.78/10.63 (( 77.78/10.63 (beta2) => 77.78/10.63 (( 77.78/10.63 (eta2) => 77.78/10.63 (( 77.78/10.63 (iffalseProp1) => 77.78/10.63 (( 77.78/10.63 (iffalseProp2) => 77.78/10.63 (( 77.78/10.63 (iftrueProp1) => 77.78/10.63 (( 77.78/10.63 (iftrueProp2) => 77.78/10.63 (( 77.78/10.63 (ifSingleton) => 77.78/10.63 (( 77.78/10.63 (ifp) => 77.78/10.63 (( 77.78/10.63 (theeq) => 77.78/10.63 (( 77.78/10.63 (iftrue) => 77.78/10.63 (( 77.78/10.63 (iffalse) => 77.78/10.63 (( 77.78/10.63 (iftrueorfalse) => 77.78/10.63 (( 77.78/10.63 (binintersectT_lem) => 77.78/10.63 (( 77.78/10.63 (binunionT_lem) => 77.78/10.63 (( 77.78/10.63 (powersetT_lem) => 77.78/10.63 (( 77.78/10.63 (setminusT_lem) => 77.78/10.63 (( 77.78/10.63 (complementT_lem) => 77.78/10.63 (( 77.78/10.63 (setextT) => 77.78/10.63 (( 77.78/10.63 (subsetTI) => 77.78/10.63 (( 77.78/10.63 (powersetTI1) => 77.78/10.63 (( 77.78/10.63 (powersetTE1) => 77.78/10.63 (( 77.78/10.63 (complementTI1) => 77.78/10.63 (( 77.78/10.63 (complementTE1) => 77.78/10.63 (( 77.78/10.63 (binintersectTELcontra) => 77.78/10.63 (( 77.78/10.63 (binintersectTERcontra) => 77.78/10.63 (( 77.78/10.63 (contrasubsetT) => 77.78/10.63 (( 77.78/10.63 (contrasubsetT1) => 77.78/10.63 (( 77.78/10.63 (contrasubsetT2) => 77.78/10.63 (( 77.78/10.63 (contrasubsetT3) => 77.78/10.63 (( 77.78/10.63 (doubleComplementI1) => 77.78/10.63 (( 77.78/10.63 (doubleComplementE1) => 77.78/10.63 (( 77.78/10.63 (doubleComplementSub1) => 77.78/10.63 (( 77.78/10.63 (doubleComplementSub2) => 77.78/10.63 (( 77.78/10.63 (doubleComplementEq) => 77.78/10.63 (( 77.78/10.63 (complementTnotintersectT) => 77.78/10.63 (( 77.78/10.63 (complementImpComplementIntersect) => 77.78/10.63 (( 77.78/10.63 (complementSubsetComplementIntersect) => 77.78/10.63 (( 77.78/10.63 (complementInPowersetComplementIntersect) => 77.78/10.63 (( 77.78/10.63 (contraSubsetComplement) => 77.78/10.63 (( 77.78/10.63 (complementTcontraSubset) => 77.78/10.63 (( 77.78/10.63 (binunionTILcontra) => 77.78/10.63 (( 77.78/10.63 (binunionTIRcontra) => 77.78/10.63 (( 77.78/10.63 (inIntersectImpInUnion) => 77.78/10.63 (( 77.78/10.63 (inIntersectImpInUnion2) => 77.78/10.63 (( 77.78/10.63 (inIntersectImpInIntersectUnions) => 77.78/10.63 (( 77.78/10.63 (intersectInPowersetIntersectUnions) => 77.78/10.63 (( 77.78/10.63 (inComplementUnionImpNotIn1) => 77.78/10.63 (( 77.78/10.63 (inComplementUnionImpInComplement1) => 77.78/10.63 (( 77.78/10.63 (binunionTE) => 77.78/10.63 (( 77.78/10.63 (binunionTEcontra) => 77.78/10.63 (( 77.78/10.63 (demorgan2a1) => 77.78/10.63 (( 77.78/10.63 (complementUnionInPowersetComplement) => 77.78/10.63 (( 77.78/10.63 (demorgan2a2) => 77.78/10.63 (( 77.78/10.63 (demorgan1a) => 77.78/10.63 (( 77.78/10.63 (demorgan1b) => 77.78/10.63 (( 77.78/10.63 (demorgan1) => 77.78/10.63 (( 77.78/10.63 (demorgan2a) => 77.78/10.63 (( 77.78/10.63 (demorgan2b2) => 77.78/10.63 (( 77.78/10.63 (demorgan2b) => 77.78/10.63 (( 77.78/10.63 (demorgan2) => 77.78/10.63 (( 77.78/10.63 (woz13rule0) => 77.78/10.63 (( 77.78/10.63 (woz13rule1) => 77.78/10.63 (( 77.78/10.63 (woz13rule2) => 77.78/10.63 (( 77.78/10.63 (woz13rule3) => 77.78/10.63 (( 77.78/10.63 (woz13rule4) => 77.78/10.63 (( 77.78/10.63 (woz1_1) => 77.78/10.63 (( 77.78/10.63 (woz1_2) => 77.78/10.63 (( 77.78/10.63 (woz1_3) => 77.78/10.63 (( 77.78/10.63 (woz1_4) => 77.78/10.63 (( 77.78/10.63 (woz1_5) => 77.78/10.63 (( 77.78/10.63 (breln1all2) => 77.78/10.63 (( 77.78/10.63 (breln1SetBreln1) => 77.78/10.63 (( 77.78/10.63 (choice2fnsingleton) => 77.78/10.63 (( 77.78/10.63 (setOfPairsIsBReln1) => 77.78/10.63 (( 77.78/10.63 (breln1all1) => 77.78/10.63 (( 77.78/10.63 (subbreln1) => 77.78/10.63 (( 77.78/10.63 (eqbreln1) => 77.78/10.63 (( 77.78/10.63 (breln1invprop) => 77.78/10.63 (( 77.78/10.63 (breln1invI) => 77.78/10.63 (( 77.78/10.63 (breln1invE) => 77.78/10.63 (( 77.78/10.63 (breln1compprop) => 77.78/10.63 (( 77.78/10.63 (breln1compI) => 77.78/10.63 (( 77.78/10.63 (breln1compE) => 77.78/10.63 (( 77.78/10.63 (breln1compEex) => 77.78/10.63 (( 77.78/10.63 (breln1unionprop) => 77.78/10.63 (( 77.78/10.63 (breln1unionIL) => 77.78/10.63 (( 77.78/10.63 (breln1unionIR) => 77.78/10.63 (( 77.78/10.63 (breln1unionI) => 77.78/10.63 (( 77.78/10.63 (breln1unionE) => 77.78/10.63 (( 77.78/10.63 (breln1unionEcases) => 77.78/10.63 (( 77.78/10.63 (breln1unionCommutes) => 77.78/10.63 (( 77.78/10.63 (woz2Ex) => 77.78/10.63 (( 77.78/10.63 (woz2W) => 77.78/10.63 (( 77.78/10.63 (woz2A) => 77.78/10.63 (( 77.78/10.63 (woz2B) => 77.78/10.63 (( 77.78/10.63 (image1Ex) => 77.78/10.63 (( 77.78/10.63 (image1Ex1) => 77.78/10.63 (( 77.78/10.63 (image1Equiv) => 77.78/10.63 (( 77.78/10.63 (image1E) => 77.78/10.63 (( 77.78/10.63 (image1I) => 77.78/10.63 (( 77.78/10.63 (injFuncInInjFuncSet) => 77.78/10.63 (( 77.78/10.63 (injFuncSetFuncIn) => 77.78/10.63 (( 77.78/10.63 (injFuncSetFuncInj) => 77.78/10.63 (( 77.78/10.63 (surjFuncSetFuncIn) => 77.78/10.63 (( 77.78/10.63 (surjFuncSetFuncSurj) => 77.78/10.63 (( 77.78/10.63 (leftInvIsSurj) => 77.78/10.63 (( 77.78/10.63 (surjCantorThm) => 77.78/10.63 (( 77.78/10.63 (foundation2) => 77.78/10.63 (( 77.78/10.63 (notinself) => 77.78/10.63 (( 77.78/10.63 (notinself2) => 77.78/10.63 (( 77.78/10.63 (omegaSp) => 77.78/10.63 (( 77.78/10.63 (omegaSclos) => 77.78/10.63 (( 77.78/10.63 (peano0notS) => 77.78/10.63 (( 77.78/10.63 (peanoSinj) => 77.78/10.63 (( 77.78/10.63 (transitivesetOp1) => 77.78/10.63 (( 77.78/10.63 (binintTransitive) => 77.78/10.63 (( 77.78/10.63 (transitivesetOp2) => 77.78/10.63 (( 77.78/10.63 (setunionTransitive) => 77.78/10.63 (( 77.78/10.63 (ordinalMinLem1) => 77.78/10.63 (( 77.78/10.63 (!!) @ ( 77.78/10.63 ^[Y0 : $i]: 77.78/10.63 (( 77.78/10.63 (ordinal @ 77.78/10.63 Y0) => 77.78/10.63 (( 77.78/10.63 (!!) @ ( 77.78/10.63 ^[Y1 : $i]: 77.78/10.63 (( 77.78/10.63 (!!) @ ( 77.78/10.63 ^[Y2 : $i]: 77.78/10.63 (( 77.78/10.63 (in @ 77.78/10.63 Y2 @ 77.78/10.63 Y0) => 77.78/10.63 (( 77.78/10.63 (in @ 77.78/10.63 Y1 @ 77.78/10.63 Y2) => 77.78/10.63 (in @ 77.78/10.63 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 77.78/10.63 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl725])). 77.78/10.63 thf(zip_derived_cl746, plain, 77.78/10.63 (~ (((emptysetsubset) => 77.78/10.63 (((subsetE) => 77.78/10.63 (((subsetE2) => 77.78/10.63 (((notsubsetI) => 77.78/10.63 (((notequalI1) => 77.78/10.63 (((notequalI2) => 77.78/10.63 (((subsetRefl) => 77.78/10.63 (((subsetTrans) => 77.78/10.63 (((setadjoinSub) => 77.78/10.63 (((setadjoinSub2) => 77.78/10.63 (((subset2powerset) => 77.78/10.63 (((setextsub) => 77.78/10.63 (((subsetemptysetimpeq) => 77.78/10.63 (((powersetI1) => 77.78/10.63 (((powersetE1) => 77.78/10.63 (((inPowerset) => 77.78/10.63 (((powersetsubset) => 77.78/10.63 (((sepInPowerset) => 77.78/10.63 (((sepSubset) => 77.78/10.63 (((binunionIL) => 77.78/10.63 (((upairset2IR) => 77.78/10.63 (((binunionIR) => 77.78/10.63 (((binunionEcases) => 77.78/10.63 (((binunionE) => 77.78/10.63 (((binunionLsub) => 77.78/10.63 (((binunionRsub) => 77.78/10.63 (((binintersectI) => 77.78/10.63 (((binintersectSubset5) => 77.78/10.63 (((binintersectEL) => 77.78/10.63 (((binintersectLsub) => 77.78/10.63 (( 77.78/10.63 (binintersectSubset2) => 77.78/10.63 (( 77.78/10.63 (binintersectSubset3) => 77.78/10.63 (( 77.78/10.63 (binintersectER) => 77.78/10.63 (( 77.78/10.63 (disjointsetsI1) => 77.78/10.63 (( 77.78/10.63 (binintersectRsub) => 77.78/10.63 (( 77.78/10.63 (binintersectSubset4) => 77.78/10.63 (( 77.78/10.63 (binintersectSubset1) => 77.78/10.63 (( 77.78/10.63 (bs114d) => 77.78/10.63 (( 77.78/10.63 (setminusI) => 77.78/10.63 (( 77.78/10.63 (setminusEL) => 77.78/10.63 (( 77.78/10.63 (setminusER) => 77.78/10.63 (( 77.78/10.63 (setminusSubset2) => 77.78/10.63 (( 77.78/10.63 (setminusERneg) => 77.78/10.63 (( 77.78/10.63 (setminusELneg) => 77.78/10.63 (( 77.78/10.63 (setminusILneg) => 77.78/10.63 (( 77.78/10.63 (setminusIRneg) => 77.78/10.63 (( 77.78/10.63 (setminusLsub) => 77.78/10.63 (( 77.78/10.63 (setminusSubset1) => 77.78/10.63 (( 77.78/10.63 (symdiffE) => 77.78/10.63 (( 77.78/10.63 (symdiffI1) => 77.78/10.63 (( 77.78/10.63 (symdiffI2) => 77.78/10.63 (( 77.78/10.63 (symdiffIneg1) => 77.78/10.63 (( 77.78/10.63 (symdiffIneg2) => 77.78/10.63 (( 77.78/10.63 (secondinupair) => 77.78/10.63 (( 77.78/10.63 (setukpairIL) => 77.78/10.63 (( 77.78/10.63 (setukpairIR) => 77.78/10.63 (( 77.78/10.63 (kpairiskpair) => 77.78/10.63 (( 77.78/10.63 (kpairp) => 77.78/10.63 (( 77.78/10.63 (singletonsubset) => 77.78/10.63 (( 77.78/10.63 (singletoninpowerset) => 77.78/10.63 (( 77.78/10.63 (singletoninpowunion) => 77.78/10.63 (( 77.78/10.63 (upairset2E) => 77.78/10.63 (( 77.78/10.63 (upairsubunion) => 77.78/10.63 (( 77.78/10.63 (upairinpowunion) => 77.78/10.63 (( 77.78/10.63 (ubforcartprodlem1) => 77.78/10.63 (( 77.78/10.63 (ubforcartprodlem2) => 77.78/10.63 (( 77.78/10.63 (ubforcartprodlem3) => 77.78/10.63 (( 77.78/10.63 (cartprodpairin) => 77.78/10.63 (( 77.78/10.63 (cartprodmempair1) => 77.78/10.63 (( 77.78/10.63 (cartprodmempair) => 77.78/10.63 (( 77.78/10.63 (setunionE2) => 77.78/10.63 (( 77.78/10.63 (setunionsingleton1) => 77.78/10.63 (( 77.78/10.63 (setunionsingleton2) => 77.78/10.63 (( 77.78/10.63 (setunionsingleton) => 77.78/10.63 (( 77.78/10.63 (singletonprop) => 77.78/10.63 (( 77.78/10.63 (ex1E1) => 77.78/10.63 (( 77.78/10.63 (ex1I) => 77.78/10.63 (( 77.78/10.63 (ex1I2) => 77.78/10.63 (( 77.78/10.63 (singletonsuniq) => 77.78/10.63 (( 77.78/10.63 (setukpairinjL1) => 77.78/10.63 (( 77.78/10.63 (kfstsingleton) => 77.78/10.63 (( 77.78/10.63 (theprop) => 77.78/10.63 (( 77.78/10.63 (kfstpairEq) => 77.78/10.63 (( 77.78/10.63 (cartprodfstin) => 77.78/10.63 (( 77.78/10.63 (setukpairinjL2) => 77.78/10.63 (( 77.78/10.63 (setukpairinjL) => 77.78/10.63 (( 77.78/10.63 (setukpairinjR11) => 77.78/10.63 (( 77.78/10.63 (setukpairinjR12) => 77.78/10.63 (( 77.78/10.63 (setukpairinjR1) => 77.78/10.63 (( 77.78/10.63 (upairequniteq) => 77.78/10.63 (( 77.78/10.63 (setukpairinjR2) => 77.78/10.63 (( 77.78/10.63 (setukpairinjR) => 77.78/10.63 (( 77.78/10.63 (ksndsingleton) => 77.78/10.63 (( 77.78/10.63 (ksndpairEq) => 77.78/10.63 (( 77.78/10.63 (kpairsurjEq) => 77.78/10.63 (( 77.78/10.63 (cartprodsndin) => 77.78/10.63 (( 77.78/10.63 (cartprodpairmemEL) => 77.78/10.63 (( 77.78/10.63 (cartprodpairmemER) => 77.78/10.63 (( 77.78/10.63 (cartprodmempaircEq) => 77.78/10.63 (( 77.78/10.63 (cartprodfstpairEq) => 77.78/10.63 (( 77.78/10.63 (cartprodsndpairEq) => 77.78/10.63 (( 77.78/10.63 (cartprodpairsurjEq) => 77.78/10.63 (( 77.78/10.63 (dpsetconstrI) => 77.78/10.63 (( 77.78/10.63 (dpsetconstrSub) => 77.78/10.63 (( 77.78/10.63 (setOfPairsIsBReln) => 77.78/10.63 (( 77.78/10.63 (dpsetconstrERa) => 77.78/10.63 (( 77.78/10.63 (dpsetconstrEL1) => 77.78/10.63 (( 77.78/10.63 (dpsetconstrEL2) => 77.78/10.63 (( 77.78/10.63 (dpsetconstrER) => 77.78/10.63 (( 77.78/10.63 (funcImageSingleton) => 77.78/10.63 (( 77.78/10.63 (apProp) => 77.78/10.63 (( 77.78/10.63 (app) => 77.78/10.63 (( 77.78/10.63 (infuncsetfunc) => 77.78/10.63 (( 77.78/10.63 (ap2p) => 77.78/10.63 (( 77.78/10.63 (funcinfuncset) => 77.78/10.63 (( 77.78/10.63 (lamProp) => 77.78/10.63 (( 77.78/10.63 (lamp) => 77.78/10.63 (( 77.78/10.63 (lam2p) => 77.78/10.63 (( 77.78/10.63 (brelnall1) => 77.78/10.63 (( 77.78/10.63 (brelnall2) => 77.78/10.63 (( 77.78/10.63 (ex1E2) => 77.78/10.63 (( 77.78/10.63 (funcGraphProp1) => 77.78/10.63 (( 77.78/10.63 (funcGraphProp3) => 77.78/10.63 (( 77.78/10.63 (funcGraphProp2) => 77.78/10.63 (( 77.78/10.63 (funcextLem) => 77.78/10.63 (( 77.78/10.63 (funcGraphProp4) => 77.78/10.63 (( 77.78/10.63 (subbreln) => 77.78/10.63 (( 77.78/10.63 (eqbreln) => 77.78/10.63 (( 77.78/10.63 (funcext) => 77.78/10.63 (( 77.78/10.63 (funcext2) => 77.78/10.63 (( 77.78/10.63 (ap2apEq1) => 77.78/10.63 (( 77.78/10.63 (ap2apEq2) => 77.78/10.63 (( 77.78/10.63 (beta1) => 77.78/10.63 (( 77.78/10.63 (eta1) => 77.78/10.63 (( 77.78/10.63 (lam2lamEq) => 77.78/10.63 (( 77.78/10.63 (beta2) => 77.78/10.63 (( 77.78/10.63 (eta2) => 77.78/10.63 (( 77.78/10.63 (iffalseProp1) => 77.78/10.63 (( 77.78/10.63 (iffalseProp2) => 77.78/10.63 (( 77.78/10.63 (iftrueProp1) => 77.78/10.63 (( 77.78/10.63 (iftrueProp2) => 77.78/10.63 (( 77.78/10.63 (ifSingleton) => 77.78/10.63 (( 77.78/10.63 (ifp) => 77.78/10.63 (( 77.78/10.63 (theeq) => 77.78/10.63 (( 77.78/10.63 (iftrue) => 77.78/10.63 (( 77.78/10.63 (iffalse) => 77.78/10.63 (( 77.78/10.63 (iftrueorfalse) => 77.78/10.63 (( 77.78/10.63 (binintersectT_lem) => 77.78/10.63 (( 77.78/10.63 (binunionT_lem) => 77.78/10.63 (( 77.78/10.63 (powersetT_lem) => 77.78/10.63 (( 77.78/10.63 (setminusT_lem) => 77.78/10.63 (( 77.78/10.63 (complementT_lem) => 77.78/10.63 (( 77.78/10.63 (setextT) => 77.78/10.63 (( 77.78/10.63 (subsetTI) => 77.78/10.63 (( 77.78/10.63 (powersetTI1) => 77.78/10.63 (( 77.78/10.63 (powersetTE1) => 77.78/10.63 (( 77.78/10.63 (complementTI1) => 77.78/10.63 (( 77.78/10.63 (complementTE1) => 77.78/10.63 (( 77.78/10.63 (binintersectTELcontra) => 77.78/10.63 (( 77.78/10.63 (binintersectTERcontra) => 77.78/10.63 (( 77.78/10.63 (contrasubsetT) => 77.78/10.63 (( 77.78/10.63 (contrasubsetT1) => 77.78/10.63 (( 77.78/10.63 (contrasubsetT2) => 77.78/10.63 (( 77.78/10.63 (contrasubsetT3) => 77.78/10.63 (( 77.78/10.63 (doubleComplementI1) => 77.78/10.63 (( 77.78/10.63 (doubleComplementE1) => 77.78/10.63 (( 77.78/10.63 (doubleComplementSub1) => 77.78/10.63 (( 77.78/10.63 (doubleComplementSub2) => 77.78/10.63 (( 77.78/10.63 (doubleComplementEq) => 77.78/10.63 (( 77.78/10.63 (complementTnotintersectT) => 77.78/10.63 (( 77.78/10.63 (complementImpComplementIntersect) => 77.78/10.63 (( 77.78/10.63 (complementSubsetComplementIntersect) => 77.78/10.63 (( 77.78/10.63 (complementInPowersetComplementIntersect) => 77.78/10.63 (( 77.78/10.63 (contraSubsetComplement) => 77.78/10.63 (( 77.78/10.63 (complementTcontraSubset) => 77.78/10.63 (( 77.78/10.63 (binunionTILcontra) => 77.78/10.63 (( 77.78/10.63 (binunionTIRcontra) => 77.78/10.63 (( 77.78/10.63 (inIntersectImpInUnion) => 77.78/10.63 (( 77.78/10.63 (inIntersectImpInUnion2) => 77.78/10.63 (( 77.78/10.63 (inIntersectImpInIntersectUnions) => 77.78/10.63 (( 77.78/10.63 (intersectInPowersetIntersectUnions) => 77.78/10.63 (( 77.78/10.63 (inComplementUnionImpNotIn1) => 77.78/10.63 (( 77.78/10.63 (inComplementUnionImpInComplement1) => 77.78/10.63 (( 77.78/10.63 (binunionTE) => 77.78/10.63 (( 77.78/10.63 (binunionTEcontra) => 77.78/10.63 (( 77.78/10.63 (demorgan2a1) => 77.78/10.63 (( 77.78/10.63 (complementUnionInPowersetComplement) => 77.78/10.63 (( 77.78/10.63 (demorgan2a2) => 77.78/10.63 (( 77.78/10.63 (demorgan1a) => 77.78/10.63 (( 77.78/10.63 (demorgan1b) => 77.78/10.63 (( 77.78/10.63 (demorgan1) => 77.78/10.63 (( 77.78/10.63 (demorgan2a) => 77.78/10.63 (( 77.78/10.63 (demorgan2b2) => 77.78/10.63 (( 77.78/10.63 (demorgan2b) => 77.78/10.63 (( 77.78/10.63 (demorgan2) => 77.78/10.63 (( 77.78/10.63 (woz13rule0) => 77.78/10.63 (( 77.78/10.63 (woz13rule1) => 77.78/10.63 (( 77.78/10.63 (woz13rule2) => 77.78/10.63 (( 77.78/10.63 (woz13rule3) => 77.78/10.63 (( 77.78/10.63 (woz13rule4) => 77.78/10.63 (( 77.78/10.63 (woz1_1) => 77.78/10.63 (( 77.78/10.63 (woz1_2) => 77.78/10.63 (( 77.78/10.63 (woz1_3) => 77.78/10.63 (( 77.78/10.63 (woz1_4) => 77.78/10.63 (( 77.78/10.63 (woz1_5) => 77.78/10.63 (( 77.78/10.63 (breln1all2) => 77.78/10.63 (( 77.78/10.63 (breln1SetBreln1) => 77.78/10.63 (( 77.78/10.63 (choice2fnsingleton) => 77.78/10.63 (( 77.78/10.63 (setOfPairsIsBReln1) => 77.78/10.63 (( 77.78/10.63 (breln1all1) => 77.78/10.63 (( 77.78/10.63 (subbreln1) => 77.78/10.63 (( 77.78/10.63 (eqbreln1) => 77.78/10.63 (( 77.78/10.63 (breln1invprop) => 77.78/10.63 (( 77.78/10.63 (breln1invI) => 77.78/10.63 (( 77.78/10.63 (breln1invE) => 77.78/10.63 (( 77.78/10.63 (breln1compprop) => 77.78/10.63 (( 77.78/10.63 (breln1compI) => 77.78/10.63 (( 77.78/10.63 (breln1compE) => 77.78/10.63 (( 77.78/10.63 (breln1compEex) => 77.78/10.63 (( 77.78/10.63 (breln1unionprop) => 77.78/10.63 (( 77.78/10.63 (breln1unionIL) => 77.78/10.63 (( 77.78/10.63 (breln1unionIR) => 77.78/10.63 (( 77.78/10.63 (breln1unionI) => 77.78/10.63 (( 77.78/10.63 (breln1unionE) => 77.78/10.63 (( 77.78/10.63 (breln1unionEcases) => 77.78/10.63 (( 77.78/10.63 (breln1unionCommutes) => 77.78/10.63 (( 77.78/10.63 (woz2Ex) => 77.78/10.63 (( 77.78/10.63 (woz2W) => 77.78/10.63 (( 77.78/10.63 (woz2A) => 77.78/10.63 (( 77.78/10.63 (woz2B) => 77.78/10.63 (( 77.78/10.63 (image1Ex) => 77.78/10.63 (( 77.78/10.63 (image1Ex1) => 77.78/10.63 (( 77.78/10.63 (image1Equiv) => 77.78/10.63 (( 77.78/10.63 (image1E) => 77.78/10.63 (( 77.78/10.63 (image1I) => 77.78/10.63 (( 77.78/10.63 (injFuncInInjFuncSet) => 77.78/10.63 (( 77.78/10.63 (injFuncSetFuncIn) => 77.78/10.63 (( 77.78/10.63 (injFuncSetFuncInj) => 77.78/10.63 (( 77.78/10.63 (surjFuncSetFuncIn) => 77.78/10.63 (( 77.78/10.63 (surjFuncSetFuncSurj) => 77.78/10.63 (( 77.78/10.63 (leftInvIsSurj) => 77.78/10.63 (( 77.78/10.63 (surjCantorThm) => 77.78/10.63 (( 77.78/10.63 (foundation2) => 77.78/10.63 (( 77.78/10.63 (notinself) => 77.78/10.63 (( 77.78/10.63 (notinself2) => 77.78/10.63 (( 77.78/10.63 (omegaSp) => 77.78/10.63 (( 77.78/10.63 (omegaSclos) => 77.78/10.63 (( 77.78/10.63 (peano0notS) => 77.78/10.63 (( 77.78/10.63 (peanoSinj) => 77.78/10.63 (( 77.78/10.63 (transitivesetOp1) => 77.78/10.63 (( 77.78/10.63 (binintTransitive) => 77.78/10.63 (( 77.78/10.63 (transitivesetOp2) => 77.78/10.63 (( 77.78/10.63 (setunionTransitive) => 77.78/10.63 (( 77.78/10.63 (ordinalMinLem1) => 77.78/10.63 (( 77.78/10.63 (!!) @ ( 77.78/10.63 ^[Y0 : $i]: 77.78/10.63 (( 77.78/10.63 (ordinal @ 77.78/10.63 Y0) => 77.78/10.63 (( 77.78/10.63 (!!) @ ( 77.78/10.63 ^[Y1 : $i]: 77.78/10.63 (( 77.78/10.63 (!!) @ ( 77.78/10.63 ^[Y2 : $i]: 77.78/10.63 (( 77.78/10.63 (in @ 77.78/10.63 Y2 @ 77.78/10.63 Y0) => 77.78/10.63 (( 77.78/10.63 (in @ 77.78/10.63 Y1 @ 77.78/10.63 Y2) => 77.78/10.63 (in @ 77.78/10.63 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 77.78/10.63 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl735])). 77.78/10.63 thf(zip_derived_cl758, plain, 77.78/10.63 (~ (((subsetE) => 77.78/10.63 (((subsetE2) => 77.78/10.63 (((notsubsetI) => 77.78/10.63 (((notequalI1) => 77.78/10.63 (((notequalI2) => 77.78/10.63 (((subsetRefl) => 77.78/10.63 (((subsetTrans) => 77.78/10.63 (((setadjoinSub) => 77.78/10.63 (((setadjoinSub2) => 77.78/10.63 (((subset2powerset) => 77.78/10.63 (((setextsub) => 77.78/10.63 (((subsetemptysetimpeq) => 77.78/10.63 (((powersetI1) => 77.78/10.63 (((powersetE1) => 77.78/10.63 (((inPowerset) => 77.78/10.63 (((powersetsubset) => 77.78/10.63 (((sepInPowerset) => 77.78/10.63 (((sepSubset) => 77.78/10.63 (((binunionIL) => 77.78/10.63 (((upairset2IR) => 77.78/10.63 (((binunionIR) => 77.78/10.63 (((binunionEcases) => 77.78/10.63 (((binunionE) => 77.78/10.63 (((binunionLsub) => 77.78/10.63 (((binunionRsub) => 77.78/10.63 (((binintersectI) => 77.78/10.63 (((binintersectSubset5) => 77.78/10.63 (((binintersectEL) => 77.78/10.63 (((binintersectLsub) => 77.78/10.63 (((binintersectSubset2) => 77.78/10.63 (( 77.78/10.63 (binintersectSubset3) => 77.78/10.63 (( 77.78/10.63 (binintersectER) => 77.78/10.63 (( 77.78/10.63 (disjointsetsI1) => 77.78/10.63 (( 77.78/10.63 (binintersectRsub) => 77.78/10.63 (( 77.78/10.63 (binintersectSubset4) => 77.78/10.63 (( 77.78/10.63 (binintersectSubset1) => 77.78/10.63 (( 77.78/10.63 (bs114d) => 77.78/10.63 (( 77.78/10.63 (setminusI) => 77.78/10.63 (( 77.78/10.63 (setminusEL) => 77.78/10.63 (( 77.78/10.63 (setminusER) => 77.78/10.63 (( 77.78/10.63 (setminusSubset2) => 77.78/10.63 (( 77.78/10.63 (setminusERneg) => 77.78/10.63 (( 77.78/10.63 (setminusELneg) => 77.78/10.63 (( 77.78/10.63 (setminusILneg) => 77.78/10.63 (( 77.78/10.63 (setminusIRneg) => 77.78/10.63 (( 77.78/10.63 (setminusLsub) => 77.78/10.63 (( 77.78/10.63 (setminusSubset1) => 77.78/10.63 (( 77.78/10.63 (symdiffE) => 77.78/10.63 (( 77.78/10.63 (symdiffI1) => 77.78/10.63 (( 77.78/10.63 (symdiffI2) => 77.78/10.63 (( 77.78/10.63 (symdiffIneg1) => 77.78/10.63 (( 77.78/10.63 (symdiffIneg2) => 77.78/10.63 (( 77.78/10.63 (secondinupair) => 77.78/10.63 (( 77.78/10.63 (setukpairIL) => 77.78/10.63 (( 77.78/10.63 (setukpairIR) => 77.78/10.63 (( 77.78/10.63 (kpairiskpair) => 77.78/10.63 (( 77.78/10.63 (kpairp) => 77.78/10.63 (( 77.78/10.63 (singletonsubset) => 77.78/10.63 (( 77.78/10.63 (singletoninpowerset) => 77.78/10.63 (( 77.78/10.63 (singletoninpowunion) => 77.78/10.63 (( 77.78/10.63 (upairset2E) => 77.78/10.63 (( 77.78/10.63 (upairsubunion) => 77.78/10.63 (( 77.78/10.63 (upairinpowunion) => 77.78/10.63 (( 77.78/10.63 (ubforcartprodlem1) => 77.78/10.63 (( 77.78/10.63 (ubforcartprodlem2) => 77.78/10.63 (( 77.78/10.63 (ubforcartprodlem3) => 77.78/10.63 (( 77.78/10.63 (cartprodpairin) => 77.78/10.63 (( 77.78/10.63 (cartprodmempair1) => 77.78/10.63 (( 77.78/10.63 (cartprodmempair) => 77.78/10.63 (( 77.78/10.63 (setunionE2) => 77.78/10.63 (( 77.78/10.63 (setunionsingleton1) => 77.78/10.63 (( 77.78/10.63 (setunionsingleton2) => 77.78/10.63 (( 77.78/10.63 (setunionsingleton) => 77.78/10.63 (( 77.78/10.63 (singletonprop) => 77.78/10.63 (( 77.78/10.63 (ex1E1) => 77.78/10.63 (( 77.78/10.63 (ex1I) => 77.78/10.63 (( 77.78/10.63 (ex1I2) => 77.78/10.63 (( 77.78/10.63 (singletonsuniq) => 77.78/10.63 (( 77.78/10.63 (setukpairinjL1) => 77.78/10.63 (( 77.78/10.63 (kfstsingleton) => 77.78/10.63 (( 77.78/10.63 (theprop) => 77.78/10.63 (( 77.78/10.63 (kfstpairEq) => 77.78/10.63 (( 77.78/10.63 (cartprodfstin) => 77.78/10.63 (( 77.78/10.63 (setukpairinjL2) => 77.78/10.63 (( 77.78/10.63 (setukpairinjL) => 77.78/10.63 (( 77.78/10.63 (setukpairinjR11) => 77.78/10.63 (( 77.78/10.63 (setukpairinjR12) => 77.78/10.63 (( 77.78/10.63 (setukpairinjR1) => 77.78/10.63 (( 77.78/10.63 (upairequniteq) => 77.78/10.63 (( 77.78/10.63 (setukpairinjR2) => 77.78/10.63 (( 77.78/10.63 (setukpairinjR) => 77.78/10.63 (( 77.78/10.63 (ksndsingleton) => 77.78/10.63 (( 77.78/10.63 (ksndpairEq) => 77.78/10.63 (( 77.78/10.63 (kpairsurjEq) => 77.78/10.63 (( 77.78/10.63 (cartprodsndin) => 77.78/10.63 (( 77.78/10.63 (cartprodpairmemEL) => 77.78/10.63 (( 77.78/10.63 (cartprodpairmemER) => 77.78/10.63 (( 77.78/10.63 (cartprodmempaircEq) => 77.78/10.63 (( 77.78/10.63 (cartprodfstpairEq) => 77.78/10.63 (( 77.78/10.63 (cartprodsndpairEq) => 77.78/10.63 (( 77.78/10.63 (cartprodpairsurjEq) => 77.78/10.63 (( 77.78/10.63 (dpsetconstrI) => 77.78/10.63 (( 77.78/10.63 (dpsetconstrSub) => 77.78/10.63 (( 77.78/10.63 (setOfPairsIsBReln) => 77.78/10.63 (( 77.78/10.63 (dpsetconstrERa) => 77.78/10.63 (( 77.78/10.63 (dpsetconstrEL1) => 77.78/10.63 (( 77.78/10.63 (dpsetconstrEL2) => 77.78/10.63 (( 77.78/10.63 (dpsetconstrER) => 77.78/10.63 (( 77.78/10.63 (funcImageSingleton) => 77.78/10.63 (( 77.78/10.63 (apProp) => 77.78/10.63 (( 77.78/10.63 (app) => 77.78/10.63 (( 77.78/10.63 (infuncsetfunc) => 77.78/10.63 (( 77.78/10.63 (ap2p) => 77.78/10.63 (( 77.78/10.63 (funcinfuncset) => 77.78/10.63 (( 77.78/10.63 (lamProp) => 77.78/10.63 (( 77.78/10.63 (lamp) => 77.78/10.63 (( 77.78/10.63 (lam2p) => 77.78/10.63 (( 77.78/10.63 (brelnall1) => 77.78/10.63 (( 77.78/10.63 (brelnall2) => 77.78/10.63 (( 77.78/10.63 (ex1E2) => 77.78/10.63 (( 77.78/10.63 (funcGraphProp1) => 77.78/10.63 (( 77.78/10.63 (funcGraphProp3) => 77.78/10.63 (( 77.78/10.63 (funcGraphProp2) => 77.78/10.63 (( 77.78/10.63 (funcextLem) => 77.78/10.63 (( 77.78/10.63 (funcGraphProp4) => 77.78/10.63 (( 77.78/10.63 (subbreln) => 77.78/10.63 (( 77.78/10.63 (eqbreln) => 77.78/10.63 (( 77.78/10.63 (funcext) => 77.78/10.63 (( 77.78/10.63 (funcext2) => 77.78/10.63 (( 77.78/10.63 (ap2apEq1) => 77.78/10.63 (( 77.78/10.63 (ap2apEq2) => 77.78/10.63 (( 77.78/10.63 (beta1) => 77.78/10.63 (( 77.78/10.63 (eta1) => 77.78/10.63 (( 77.78/10.63 (lam2lamEq) => 77.78/10.63 (( 77.78/10.63 (beta2) => 77.78/10.63 (( 77.78/10.63 (eta2) => 77.78/10.63 (( 77.78/10.63 (iffalseProp1) => 77.78/10.63 (( 77.78/10.63 (iffalseProp2) => 77.78/10.63 (( 77.78/10.63 (iftrueProp1) => 77.78/10.63 (( 77.78/10.63 (iftrueProp2) => 77.78/10.63 (( 77.78/10.63 (ifSingleton) => 77.78/10.63 (( 77.78/10.63 (ifp) => 77.78/10.63 (( 77.78/10.63 (theeq) => 77.78/10.63 (( 77.78/10.63 (iftrue) => 77.78/10.63 (( 77.78/10.63 (iffalse) => 77.78/10.63 (( 77.78/10.63 (iftrueorfalse) => 77.78/10.63 (( 77.78/10.63 (binintersectT_lem) => 77.78/10.63 (( 77.78/10.63 (binunionT_lem) => 77.78/10.63 (( 77.78/10.63 (powersetT_lem) => 77.78/10.63 (( 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=> 77.78/10.63 (( 77.78/10.63 (demorgan1a) => 77.78/10.63 (( 77.78/10.63 (demorgan1b) => 77.78/10.63 (( 77.78/10.63 (demorgan1) => 77.78/10.63 (( 77.78/10.63 (demorgan2a) => 77.78/10.63 (( 77.78/10.63 (demorgan2b2) => 77.78/10.63 (( 77.78/10.63 (demorgan2b) => 77.78/10.63 (( 77.78/10.63 (demorgan2) => 77.78/10.63 (( 77.78/10.63 (woz13rule0) => 77.78/10.63 (( 77.78/10.63 (woz13rule1) => 77.78/10.63 (( 77.78/10.63 (woz13rule2) => 77.78/10.63 (( 77.78/10.63 (woz13rule3) => 77.78/10.63 (( 77.78/10.63 (woz13rule4) => 77.78/10.63 (( 77.78/10.63 (woz1_1) => 77.78/10.63 (( 77.78/10.63 (woz1_2) => 77.78/10.63 (( 77.78/10.63 (woz1_3) => 77.78/10.63 (( 77.78/10.63 (woz1_4) => 77.78/10.63 (( 77.78/10.63 (woz1_5) => 77.78/10.63 (( 77.78/10.63 (breln1all2) => 77.78/10.63 (( 77.78/10.63 (breln1SetBreln1) => 77.78/10.63 (( 77.78/10.63 (choice2fnsingleton) => 77.78/10.63 (( 77.78/10.63 (setOfPairsIsBReln1) => 77.78/10.63 (( 77.78/10.63 (breln1all1) => 77.78/10.63 (( 77.78/10.63 (subbreln1) => 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(image1E) => 77.78/10.63 (( 77.78/10.63 (image1I) => 77.78/10.63 (( 77.78/10.63 (injFuncInInjFuncSet) => 77.78/10.63 (( 77.78/10.63 (injFuncSetFuncIn) => 77.78/10.63 (( 77.78/10.63 (injFuncSetFuncInj) => 77.78/10.63 (( 77.78/10.63 (surjFuncSetFuncIn) => 77.78/10.63 (( 77.78/10.63 (surjFuncSetFuncSurj) => 77.78/10.63 (( 77.78/10.63 (leftInvIsSurj) => 77.78/10.63 (( 77.78/10.63 (surjCantorThm) => 77.78/10.63 (( 77.78/10.63 (foundation2) => 77.78/10.63 (( 77.78/10.63 (notinself) => 77.78/10.63 (( 77.78/10.63 (notinself2) => 77.78/10.63 (( 77.78/10.63 (omegaSp) => 77.78/10.63 (( 77.78/10.63 (omegaSclos) => 77.78/10.63 (( 77.78/10.63 (peano0notS) => 77.78/10.63 (( 77.78/10.63 (peanoSinj) => 77.78/10.63 (( 77.78/10.63 (transitivesetOp1) => 77.78/10.63 (( 77.78/10.63 (binintTransitive) => 77.78/10.63 (( 77.78/10.63 (transitivesetOp2) => 77.78/10.63 (( 77.78/10.63 (setunionTransitive) => 77.78/10.63 (( 77.78/10.63 (ordinalMinLem1) => 77.78/10.63 (( 77.78/10.63 (!!) @ ( 77.78/10.63 ^[Y0 : $i]: 77.78/10.63 (( 77.78/10.63 (ordinal @ 77.78/10.63 Y0) => 77.78/10.63 (( 77.78/10.63 (!!) @ ( 77.78/10.63 ^[Y1 : $i]: 77.78/10.63 (( 77.78/10.63 (!!) @ ( 77.78/10.63 ^[Y2 : $i]: 77.78/10.63 (( 77.78/10.63 (in @ 77.78/10.63 Y2 @ 77.78/10.63 Y0) => 77.78/10.63 (( 77.78/10.63 (in @ 77.78/10.63 Y1 @ 77.78/10.63 Y2) => 77.78/10.63 (in @ 77.78/10.63 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 77.78/10.63 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl746])). 77.78/10.63 thf(zip_derived_cl770, plain, 77.78/10.63 (~ (((subsetE2) => 77.78/10.63 (((notsubsetI) => 77.78/10.63 (((notequalI1) => 77.78/10.63 (((notequalI2) => 77.78/10.63 (((subsetRefl) => 77.78/10.63 (((subsetTrans) => 77.78/10.63 (((setadjoinSub) => 77.78/10.63 (((setadjoinSub2) => 77.78/10.63 (((subset2powerset) => 77.78/10.63 (((setextsub) => 77.78/10.63 (((subsetemptysetimpeq) => 77.78/10.63 (((powersetI1) => 77.78/10.63 (((powersetE1) => 77.78/10.63 (((inPowerset) => 77.78/10.63 (((powersetsubset) => 77.78/10.63 (((sepInPowerset) => 77.78/10.63 (((sepSubset) => 77.78/10.63 (((binunionIL) => 77.78/10.63 (((upairset2IR) => 77.78/10.63 (((binunionIR) => 77.78/10.63 (((binunionEcases) => 77.78/10.63 (((binunionE) => 77.78/10.63 (((binunionLsub) => 77.78/10.63 (((binunionRsub) => 77.78/10.63 (((binintersectI) => 77.78/10.63 (((binintersectSubset5) => 77.78/10.63 (((binintersectEL) => 77.78/10.63 (((binintersectLsub) => 77.78/10.63 (((binintersectSubset2) => 77.78/10.63 (((binintersectSubset3) => 77.78/10.63 (( 77.78/10.63 (binintersectER) => 77.78/10.63 (( 77.78/10.63 (disjointsetsI1) => 77.78/10.63 (( 77.78/10.63 (binintersectRsub) => 77.78/10.63 (( 77.78/10.63 (binintersectSubset4) => 77.78/10.63 (( 77.78/10.63 (binintersectSubset1) => 77.78/10.63 (( 77.78/10.63 (bs114d) => 77.78/10.63 (( 77.78/10.63 (setminusI) => 77.78/10.63 (( 77.78/10.63 (setminusEL) => 77.78/10.63 (( 77.78/10.63 (setminusER) => 77.78/10.63 (( 77.78/10.63 (setminusSubset2) => 77.78/10.63 (( 77.78/10.63 (setminusERneg) => 77.78/10.63 (( 77.78/10.63 (setminusELneg) => 77.78/10.63 (( 77.78/10.63 (setminusILneg) => 77.78/10.63 (( 77.78/10.63 (setminusIRneg) => 77.78/10.63 (( 77.78/10.63 (setminusLsub) => 77.78/10.63 (( 77.78/10.63 (setminusSubset1) => 77.78/10.63 (( 77.78/10.63 (symdiffE) => 77.78/10.63 (( 77.78/10.63 (symdiffI1) => 77.78/10.63 (( 77.78/10.63 (symdiffI2) => 77.78/10.63 (( 77.78/10.63 (symdiffIneg1) => 77.78/10.63 (( 77.78/10.63 (symdiffIneg2) => 77.78/10.63 (( 77.78/10.63 (secondinupair) => 77.78/10.63 (( 77.78/10.63 (setukpairIL) => 77.78/10.63 (( 77.78/10.63 (setukpairIR) => 77.78/10.63 (( 77.78/10.63 (kpairiskpair) => 77.78/10.63 (( 77.78/10.63 (kpairp) => 77.78/10.63 (( 77.78/10.63 (singletonsubset) => 77.78/10.63 (( 77.78/10.63 (singletoninpowerset) => 77.78/10.63 (( 77.78/10.63 (singletoninpowunion) => 77.78/10.63 (( 77.78/10.63 (upairset2E) => 77.78/10.63 (( 77.78/10.63 (upairsubunion) => 77.78/10.63 (( 77.78/10.63 (upairinpowunion) => 77.78/10.63 (( 77.78/10.63 (ubforcartprodlem1) => 77.78/10.63 (( 77.78/10.63 (ubforcartprodlem2) => 77.78/10.63 (( 77.78/10.63 (ubforcartprodlem3) => 77.78/10.63 (( 77.78/10.63 (cartprodpairin) => 77.78/10.63 (( 77.78/10.63 (cartprodmempair1) => 77.78/10.63 (( 77.78/10.63 (cartprodmempair) => 77.78/10.63 (( 77.78/10.63 (setunionE2) => 77.78/10.63 (( 77.78/10.63 (setunionsingleton1) => 77.78/10.63 (( 77.78/10.63 (setunionsingleton2) => 77.78/10.63 (( 77.78/10.63 (setunionsingleton) => 77.78/10.63 (( 77.78/10.63 (singletonprop) => 77.78/10.63 (( 77.78/10.63 (ex1E1) => 77.78/10.63 (( 77.78/10.63 (ex1I) => 77.78/10.63 (( 77.78/10.63 (ex1I2) => 77.78/10.63 (( 77.78/10.63 (singletonsuniq) => 77.78/10.63 (( 77.78/10.63 (setukpairinjL1) => 77.78/10.63 (( 77.78/10.63 (kfstsingleton) => 77.78/10.63 (( 77.78/10.63 (theprop) => 77.78/10.63 (( 77.78/10.63 (kfstpairEq) => 77.78/10.63 (( 77.78/10.63 (cartprodfstin) => 77.78/10.63 (( 77.78/10.63 (setukpairinjL2) => 77.78/10.63 (( 77.78/10.63 (setukpairinjL) => 77.78/10.63 (( 77.78/10.63 (setukpairinjR11) => 77.78/10.63 (( 77.78/10.63 (setukpairinjR12) => 77.78/10.63 (( 77.78/10.63 (setukpairinjR1) => 77.78/10.63 (( 77.78/10.63 (upairequniteq) => 77.78/10.63 (( 77.78/10.63 (setukpairinjR2) => 77.78/10.63 (( 77.78/10.63 (setukpairinjR) => 77.78/10.63 (( 77.78/10.63 (ksndsingleton) => 77.78/10.63 (( 77.78/10.63 (ksndpairEq) => 77.78/10.63 (( 77.78/10.63 (kpairsurjEq) => 77.78/10.63 (( 77.78/10.63 (cartprodsndin) => 77.78/10.63 (( 77.78/10.63 (cartprodpairmemEL) => 77.78/10.63 (( 77.78/10.63 (cartprodpairmemER) => 77.78/10.63 (( 77.78/10.63 (cartprodmempaircEq) => 77.78/10.63 (( 77.78/10.63 (cartprodfstpairEq) => 77.78/10.63 (( 77.78/10.63 (cartprodsndpairEq) => 77.78/10.63 (( 77.78/10.63 (cartprodpairsurjEq) => 77.78/10.63 (( 77.78/10.63 (dpsetconstrI) => 77.78/10.63 (( 77.78/10.63 (dpsetconstrSub) => 77.78/10.63 (( 77.78/10.63 (setOfPairsIsBReln) => 77.78/10.63 (( 77.78/10.63 (dpsetconstrERa) => 77.78/10.63 (( 77.78/10.63 (dpsetconstrEL1) => 77.78/10.63 (( 77.78/10.63 (dpsetconstrEL2) => 77.78/10.63 (( 77.78/10.63 (dpsetconstrER) => 77.78/10.63 (( 77.78/10.63 (funcImageSingleton) => 77.78/10.63 (( 77.78/10.63 (apProp) => 77.78/10.63 (( 77.78/10.63 (app) => 77.78/10.63 (( 77.78/10.63 (infuncsetfunc) => 77.78/10.63 (( 77.78/10.63 (ap2p) => 77.78/10.63 (( 77.78/10.63 (funcinfuncset) => 77.78/10.63 (( 77.78/10.63 (lamProp) => 77.78/10.63 (( 77.78/10.63 (lamp) => 77.78/10.63 (( 77.78/10.63 (lam2p) => 77.78/10.63 (( 77.78/10.63 (brelnall1) => 77.78/10.63 (( 77.78/10.63 (brelnall2) => 77.78/10.63 (( 77.78/10.63 (ex1E2) => 77.78/10.63 (( 77.78/10.63 (funcGraphProp1) => 77.78/10.63 (( 77.78/10.63 (funcGraphProp3) => 77.78/10.63 (( 77.78/10.63 (funcGraphProp2) => 77.78/10.63 (( 77.78/10.63 (funcextLem) => 77.78/10.63 (( 77.78/10.63 (funcGraphProp4) => 77.78/10.63 (( 77.78/10.63 (subbreln) => 77.78/10.63 (( 77.78/10.63 (eqbreln) => 77.78/10.63 (( 77.78/10.63 (funcext) => 77.78/10.63 (( 77.78/10.63 (funcext2) => 77.78/10.63 (( 77.78/10.63 (ap2apEq1) => 77.78/10.63 (( 77.78/10.63 (ap2apEq2) => 77.78/10.63 (( 77.78/10.63 (beta1) => 77.78/10.63 (( 77.78/10.63 (eta1) => 77.78/10.63 (( 77.78/10.63 (lam2lamEq) => 77.78/10.63 (( 77.78/10.63 (beta2) => 77.78/10.63 (( 77.78/10.63 (eta2) => 77.78/10.63 (( 77.78/10.63 (iffalseProp1) => 77.78/10.63 (( 77.78/10.63 (iffalseProp2) => 77.78/10.63 (( 77.78/10.63 (iftrueProp1) => 77.78/10.63 (( 77.78/10.63 (iftrueProp2) => 77.78/10.63 (( 77.78/10.63 (ifSingleton) => 77.78/10.63 (( 77.78/10.63 (ifp) => 77.78/10.63 (( 77.78/10.63 (theeq) => 77.78/10.63 (( 77.78/10.63 (iftrue) => 77.78/10.63 (( 77.78/10.63 (iffalse) => 77.78/10.63 (( 77.78/10.63 (iftrueorfalse) => 77.78/10.63 (( 77.78/10.63 (binintersectT_lem) => 77.78/10.63 (( 77.78/10.63 (binunionT_lem) => 77.78/10.63 (( 77.78/10.63 (powersetT_lem) => 77.78/10.63 (( 77.78/10.63 (setminusT_lem) => 77.78/10.63 (( 77.78/10.63 (complementT_lem) => 77.78/10.63 (( 77.78/10.63 (setextT) => 77.78/10.63 (( 77.78/10.63 (subsetTI) => 77.78/10.63 (( 77.78/10.63 (powersetTI1) => 77.78/10.63 (( 77.78/10.63 (powersetTE1) => 77.78/10.63 (( 77.78/10.63 (complementTI1) => 77.78/10.63 (( 77.78/10.63 (complementTE1) => 77.78/10.63 (( 77.78/10.63 (binintersectTELcontra) => 77.78/10.63 (( 77.78/10.63 (binintersectTERcontra) => 77.78/10.63 (( 77.78/10.63 (contrasubsetT) => 77.78/10.63 (( 77.78/10.63 (contrasubsetT1) => 77.78/10.63 (( 77.78/10.63 (contrasubsetT2) => 77.78/10.63 (( 77.78/10.63 (contrasubsetT3) => 77.78/10.63 (( 77.78/10.63 (doubleComplementI1) => 77.78/10.63 (( 77.78/10.63 (doubleComplementE1) => 77.78/10.63 (( 77.78/10.63 (doubleComplementSub1) => 77.78/10.63 (( 77.78/10.63 (doubleComplementSub2) => 77.78/10.63 (( 77.78/10.63 (doubleComplementEq) => 77.78/10.63 (( 77.78/10.63 (complementTnotintersectT) => 77.78/10.63 (( 77.78/10.63 (complementImpComplementIntersect) => 77.78/10.63 (( 77.78/10.63 (complementSubsetComplementIntersect) => 77.78/10.63 (( 77.78/10.63 (complementInPowersetComplementIntersect) => 77.78/10.63 (( 77.78/10.63 (contraSubsetComplement) => 77.78/10.63 (( 77.78/10.63 (complementTcontraSubset) => 77.78/10.63 (( 77.78/10.63 (binunionTILcontra) => 77.78/10.63 (( 77.78/10.63 (binunionTIRcontra) => 77.78/10.63 (( 77.78/10.63 (inIntersectImpInUnion) => 77.78/10.63 (( 77.78/10.63 (inIntersectImpInUnion2) => 77.78/10.63 (( 77.78/10.63 (inIntersectImpInIntersectUnions) => 77.78/10.63 (( 77.78/10.63 (intersectInPowersetIntersectUnions) => 77.78/10.63 (( 77.78/10.63 (inComplementUnionImpNotIn1) => 77.78/10.63 (( 77.78/10.63 (inComplementUnionImpInComplement1) => 77.78/10.63 (( 77.78/10.63 (binunionTE) => 77.78/10.63 (( 77.78/10.63 (binunionTEcontra) => 77.78/10.63 (( 77.78/10.63 (demorgan2a1) => 77.78/10.63 (( 77.78/10.63 (complementUnionInPowersetComplement) => 77.78/10.63 (( 77.78/10.63 (demorgan2a2) => 77.78/10.63 (( 77.78/10.63 (demorgan1a) => 77.78/10.63 (( 77.78/10.63 (demorgan1b) => 77.78/10.63 (( 77.78/10.63 (demorgan1) => 77.78/10.63 (( 77.78/10.63 (demorgan2a) => 77.78/10.63 (( 77.78/10.63 (demorgan2b2) => 77.78/10.63 (( 77.78/10.63 (demorgan2b) => 77.78/10.63 (( 77.78/10.63 (demorgan2) => 77.78/10.63 (( 77.78/10.63 (woz13rule0) => 77.78/10.63 (( 77.78/10.63 (woz13rule1) => 77.78/10.63 (( 77.78/10.63 (woz13rule2) => 77.78/10.63 (( 77.78/10.63 (woz13rule3) => 77.78/10.63 (( 77.78/10.63 (woz13rule4) => 77.78/10.63 (( 77.78/10.63 (woz1_1) => 77.78/10.63 (( 77.78/10.63 (woz1_2) => 77.78/10.63 (( 77.78/10.63 (woz1_3) => 77.78/10.63 (( 77.78/10.63 (woz1_4) => 77.78/10.63 (( 77.78/10.63 (woz1_5) => 77.78/10.63 (( 77.78/10.63 (breln1all2) => 77.78/10.63 (( 77.78/10.63 (breln1SetBreln1) => 77.78/10.63 (( 77.78/10.63 (choice2fnsingleton) => 77.78/10.63 (( 77.78/10.63 (setOfPairsIsBReln1) => 77.78/10.63 (( 77.78/10.63 (breln1all1) => 77.78/10.63 (( 77.78/10.63 (subbreln1) => 77.78/10.63 (( 77.78/10.63 (eqbreln1) => 77.78/10.63 (( 77.78/10.63 (breln1invprop) => 77.78/10.63 (( 77.78/10.63 (breln1invI) => 77.78/10.63 (( 77.78/10.63 (breln1invE) => 77.78/10.63 (( 77.78/10.63 (breln1compprop) => 77.78/10.63 (( 77.78/10.63 (breln1compI) => 77.78/10.63 (( 77.78/10.63 (breln1compE) => 77.78/10.63 (( 77.78/10.63 (breln1compEex) => 77.78/10.63 (( 77.78/10.63 (breln1unionprop) => 77.78/10.63 (( 77.78/10.63 (breln1unionIL) => 77.78/10.63 (( 77.78/10.63 (breln1unionIR) => 77.78/10.63 (( 77.78/10.63 (breln1unionI) => 77.78/10.63 (( 77.78/10.63 (breln1unionE) => 77.78/10.63 (( 77.78/10.63 (breln1unionEcases) => 77.78/10.63 (( 77.78/10.63 (breln1unionCommutes) => 77.78/10.63 (( 77.78/10.63 (woz2Ex) => 77.78/10.63 (( 77.78/10.63 (woz2W) => 77.78/10.63 (( 77.78/10.63 (woz2A) => 77.78/10.63 (( 77.78/10.63 (woz2B) => 77.78/10.63 (( 77.78/10.63 (image1Ex) => 77.78/10.63 (( 77.78/10.63 (image1Ex1) => 77.78/10.63 (( 77.78/10.63 (image1Equiv) => 77.78/10.63 (( 77.78/10.63 (image1E) => 77.78/10.63 (( 77.78/10.63 (image1I) => 77.78/10.63 (( 77.78/10.63 (injFuncInInjFuncSet) => 77.78/10.63 (( 77.78/10.63 (injFuncSetFuncIn) => 77.78/10.63 (( 77.78/10.63 (injFuncSetFuncInj) => 77.78/10.63 (( 77.78/10.63 (surjFuncSetFuncIn) => 77.78/10.63 (( 77.78/10.63 (surjFuncSetFuncSurj) => 77.78/10.63 (( 77.78/10.63 (leftInvIsSurj) => 77.78/10.63 (( 77.78/10.63 (surjCantorThm) => 77.78/10.63 (( 77.78/10.63 (foundation2) => 77.78/10.63 (( 77.78/10.63 (notinself) => 77.78/10.63 (( 77.78/10.63 (notinself2) => 77.78/10.63 (( 77.78/10.63 (omegaSp) => 77.78/10.63 (( 77.78/10.63 (omegaSclos) => 77.78/10.63 (( 77.78/10.63 (peano0notS) => 77.78/10.63 (( 77.78/10.63 (peanoSinj) => 77.78/10.63 (( 77.78/10.63 (transitivesetOp1) => 77.78/10.63 (( 77.78/10.63 (binintTransitive) => 77.78/10.63 (( 77.78/10.63 (transitivesetOp2) => 77.78/10.63 (( 77.78/10.63 (setunionTransitive) => 77.78/10.63 (( 77.78/10.63 (ordinalMinLem1) => 77.78/10.63 (( 77.78/10.63 (!!) @ ( 77.78/10.63 ^[Y0 : $i]: 77.78/10.63 (( 77.78/10.63 (ordinal @ 77.78/10.63 Y0) => 77.78/10.63 (( 77.78/10.63 (!!) @ ( 77.78/10.63 ^[Y1 : $i]: 77.78/10.63 (( 77.78/10.63 (!!) @ ( 77.78/10.63 ^[Y2 : $i]: 77.78/10.63 (( 77.78/10.63 (in @ 77.78/10.63 Y2 @ 77.78/10.63 Y0) => 77.78/10.63 (( 77.78/10.63 (in @ 77.78/10.63 Y1 @ 77.78/10.63 Y2) => 77.78/10.63 (in @ 77.78/10.63 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 77.78/10.63 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl758])). 77.78/10.63 thf(zip_derived_cl783, plain, 77.78/10.63 (~ (((notsubsetI) => 77.78/10.63 (((notequalI1) => 77.78/10.63 (((notequalI2) => 77.78/10.63 (((subsetRefl) => 77.78/10.63 (((subsetTrans) => 77.78/10.63 (((setadjoinSub) => 77.78/10.63 (((setadjoinSub2) => 77.78/10.63 (((subset2powerset) => 77.78/10.63 (((setextsub) => 77.78/10.63 (((subsetemptysetimpeq) => 77.78/10.63 (((powersetI1) => 77.78/10.63 (((powersetE1) => 77.78/10.63 (((inPowerset) => 77.78/10.63 (((powersetsubset) => 77.78/10.63 (((sepInPowerset) => 77.78/10.63 (((sepSubset) => 77.78/10.63 (((binunionIL) => 77.78/10.63 (((upairset2IR) => 77.78/10.63 (((binunionIR) => 77.78/10.63 (((binunionEcases) => 77.78/10.63 (((binunionE) => 77.78/10.63 (((binunionLsub) => 77.78/10.63 (((binunionRsub) => 77.78/10.63 (((binintersectI) => 77.78/10.63 (((binintersectSubset5) => 77.78/10.63 (((binintersectEL) => 77.78/10.63 (((binintersectLsub) => 77.78/10.63 (((binintersectSubset2) => 77.78/10.63 (((binintersectSubset3) => 77.78/10.63 (((binintersectER) => 77.78/10.63 (( 77.78/10.63 (disjointsetsI1) => 77.78/10.63 (( 77.78/10.63 (binintersectRsub) => 77.78/10.63 (( 77.78/10.63 (binintersectSubset4) => 77.78/10.63 (( 77.78/10.63 (binintersectSubset1) => 77.78/10.63 (( 77.78/10.63 (bs114d) => 77.78/10.63 (( 77.78/10.63 (setminusI) => 77.78/10.63 (( 77.78/10.63 (setminusEL) => 77.78/10.63 (( 77.78/10.63 (setminusER) => 77.78/10.63 (( 77.78/10.63 (setminusSubset2) => 77.78/10.63 (( 77.78/10.63 (setminusERneg) => 77.78/10.63 (( 77.78/10.63 (setminusELneg) => 77.78/10.63 (( 77.78/10.63 (setminusILneg) => 77.78/10.63 (( 77.78/10.63 (setminusIRneg) => 77.78/10.63 (( 77.78/10.63 (setminusLsub) => 77.78/10.63 (( 77.78/10.63 (setminusSubset1) => 77.78/10.63 (( 77.78/10.63 (symdiffE) => 77.78/10.63 (( 77.78/10.63 (symdiffI1) => 77.78/10.63 (( 77.78/10.63 (symdiffI2) => 77.78/10.63 (( 77.78/10.63 (symdiffIneg1) => 77.78/10.63 (( 77.78/10.63 (symdiffIneg2) => 77.78/10.63 (( 77.78/10.63 (secondinupair) => 77.78/10.63 (( 77.78/10.63 (setukpairIL) => 77.78/10.63 (( 77.78/10.63 (setukpairIR) => 77.78/10.63 (( 77.78/10.63 (kpairiskpair) => 77.78/10.63 (( 77.78/10.63 (kpairp) => 77.78/10.63 (( 77.78/10.63 (singletonsubset) => 77.78/10.63 (( 77.78/10.63 (singletoninpowerset) => 77.78/10.63 (( 77.78/10.63 (singletoninpowunion) => 77.78/10.63 (( 77.78/10.63 (upairset2E) => 77.78/10.63 (( 77.78/10.63 (upairsubunion) => 77.78/10.63 (( 77.78/10.63 (upairinpowunion) => 77.78/10.63 (( 77.78/10.63 (ubforcartprodlem1) => 77.78/10.63 (( 77.78/10.63 (ubforcartprodlem2) => 77.78/10.63 (( 77.78/10.63 (ubforcartprodlem3) => 77.78/10.63 (( 77.78/10.63 (cartprodpairin) => 77.78/10.63 (( 77.78/10.63 (cartprodmempair1) => 77.78/10.63 (( 77.78/10.63 (cartprodmempair) => 77.78/10.63 (( 77.78/10.63 (setunionE2) => 77.78/10.63 (( 77.78/10.63 (setunionsingleton1) => 77.78/10.63 (( 77.78/10.63 (setunionsingleton2) => 77.78/10.63 (( 77.78/10.63 (setunionsingleton) => 77.78/10.63 (( 77.78/10.63 (singletonprop) => 77.78/10.63 (( 77.78/10.63 (ex1E1) => 77.78/10.63 (( 77.78/10.63 (ex1I) => 77.78/10.63 (( 77.78/10.63 (ex1I2) => 77.78/10.63 (( 77.78/10.63 (singletonsuniq) => 77.78/10.63 (( 77.78/10.63 (setukpairinjL1) => 77.78/10.63 (( 77.78/10.63 (kfstsingleton) => 77.78/10.63 (( 77.78/10.63 (theprop) => 77.78/10.63 (( 77.78/10.63 (kfstpairEq) => 77.78/10.63 (( 77.78/10.63 (cartprodfstin) => 77.78/10.63 (( 77.78/10.63 (setukpairinjL2) => 77.78/10.63 (( 77.78/10.63 (setukpairinjL) => 77.78/10.63 (( 77.78/10.63 (setukpairinjR11) => 77.78/10.63 (( 77.78/10.63 (setukpairinjR12) => 77.78/10.63 (( 77.78/10.63 (setukpairinjR1) => 77.78/10.63 (( 77.78/10.63 (upairequniteq) => 77.78/10.63 (( 77.78/10.63 (setukpairinjR2) => 77.78/10.63 (( 77.78/10.63 (setukpairinjR) => 77.78/10.63 (( 77.78/10.63 (ksndsingleton) => 77.78/10.63 (( 77.78/10.63 (ksndpairEq) => 77.78/10.63 (( 77.78/10.63 (kpairsurjEq) => 77.78/10.63 (( 77.78/10.63 (cartprodsndin) => 77.78/10.63 (( 77.78/10.63 (cartprodpairmemEL) => 77.78/10.63 (( 77.78/10.63 (cartprodpairmemER) => 77.78/10.63 (( 77.78/10.63 (cartprodmempaircEq) => 77.78/10.63 (( 77.78/10.63 (cartprodfstpairEq) => 77.78/10.63 (( 77.78/10.63 (cartprodsndpairEq) => 77.78/10.63 (( 77.78/10.63 (cartprodpairsurjEq) => 77.78/10.63 (( 77.78/10.63 (dpsetconstrI) => 77.78/10.63 (( 77.78/10.63 (dpsetconstrSub) => 77.78/10.63 (( 77.78/10.63 (setOfPairsIsBReln) => 77.78/10.63 (( 77.78/10.63 (dpsetconstrERa) => 77.78/10.63 (( 77.78/10.63 (dpsetconstrEL1) => 77.78/10.63 (( 77.78/10.63 (dpsetconstrEL2) => 77.78/10.63 (( 77.78/10.63 (dpsetconstrER) => 77.78/10.63 (( 77.78/10.63 (funcImageSingleton) => 77.78/10.63 (( 77.78/10.63 (apProp) => 77.78/10.63 (( 77.78/10.63 (app) => 77.78/10.63 (( 77.78/10.63 (infuncsetfunc) => 77.78/10.63 (( 77.78/10.63 (ap2p) => 77.78/10.63 (( 77.78/10.63 (funcinfuncset) => 77.78/10.63 (( 77.78/10.63 (lamProp) => 77.78/10.63 (( 77.78/10.63 (lamp) => 77.78/10.63 (( 77.78/10.63 (lam2p) => 77.78/10.63 (( 77.78/10.63 (brelnall1) => 77.78/10.63 (( 77.78/10.63 (brelnall2) => 77.78/10.63 (( 77.78/10.63 (ex1E2) => 77.78/10.63 (( 77.78/10.63 (funcGraphProp1) => 77.78/10.63 (( 77.78/10.63 (funcGraphProp3) => 77.78/10.63 (( 77.78/10.63 (funcGraphProp2) => 77.78/10.63 (( 77.78/10.63 (funcextLem) => 77.78/10.63 (( 77.78/10.63 (funcGraphProp4) => 77.78/10.63 (( 77.78/10.63 (subbreln) => 77.78/10.63 (( 77.78/10.63 (eqbreln) => 77.78/10.63 (( 77.78/10.63 (funcext) => 77.78/10.63 (( 77.78/10.63 (funcext2) => 77.78/10.63 (( 77.78/10.63 (ap2apEq1) => 77.78/10.63 (( 77.78/10.63 (ap2apEq2) => 77.78/10.63 (( 77.78/10.63 (beta1) => 77.78/10.63 (( 77.78/10.63 (eta1) => 77.78/10.63 (( 77.78/10.63 (lam2lamEq) => 77.78/10.63 (( 77.78/10.63 (beta2) => 77.78/10.63 (( 77.78/10.63 (eta2) => 77.78/10.63 (( 77.78/10.63 (iffalseProp1) => 77.78/10.63 (( 77.78/10.63 (iffalseProp2) => 77.78/10.63 (( 77.78/10.63 (iftrueProp1) => 77.78/10.63 (( 77.78/10.63 (iftrueProp2) => 77.78/10.63 (( 77.78/10.63 (ifSingleton) => 77.78/10.63 (( 77.78/10.63 (ifp) => 77.78/10.63 (( 77.78/10.63 (theeq) => 77.78/10.63 (( 77.78/10.63 (iftrue) => 77.78/10.63 (( 77.78/10.63 (iffalse) => 77.78/10.63 (( 77.78/10.63 (iftrueorfalse) => 77.78/10.63 (( 77.78/10.63 (binintersectT_lem) => 77.78/10.63 (( 77.78/10.63 (binunionT_lem) => 77.78/10.63 (( 77.78/10.63 (powersetT_lem) => 77.78/10.63 (( 77.78/10.63 (setminusT_lem) => 77.78/10.63 (( 77.78/10.63 (complementT_lem) => 77.78/10.63 (( 77.78/10.63 (setextT) => 77.78/10.63 (( 77.78/10.63 (subsetTI) => 77.78/10.63 (( 77.78/10.63 (powersetTI1) => 77.78/10.63 (( 77.78/10.63 (powersetTE1) => 77.78/10.63 (( 77.78/10.63 (complementTI1) => 77.78/10.63 (( 77.78/10.63 (complementTE1) => 77.78/10.63 (( 77.78/10.63 (binintersectTELcontra) => 77.78/10.63 (( 77.78/10.63 (binintersectTERcontra) => 77.78/10.63 (( 77.78/10.63 (contrasubsetT) => 77.78/10.63 (( 77.78/10.63 (contrasubsetT1) => 77.78/10.63 (( 77.78/10.63 (contrasubsetT2) => 77.78/10.63 (( 77.78/10.63 (contrasubsetT3) => 77.78/10.63 (( 77.78/10.63 (doubleComplementI1) => 77.78/10.63 (( 77.78/10.63 (doubleComplementE1) => 77.78/10.63 (( 77.78/10.63 (doubleComplementSub1) => 77.78/10.63 (( 77.78/10.63 (doubleComplementSub2) => 77.78/10.63 (( 77.78/10.63 (doubleComplementEq) => 77.78/10.63 (( 77.78/10.63 (complementTnotintersectT) => 77.78/10.63 (( 77.78/10.63 (complementImpComplementIntersect) => 77.78/10.63 (( 77.78/10.63 (complementSubsetComplementIntersect) => 77.78/10.63 (( 77.78/10.63 (complementInPowersetComplementIntersect) => 77.78/10.63 (( 77.78/10.63 (contraSubsetComplement) => 77.78/10.63 (( 77.78/10.63 (complementTcontraSubset) => 77.78/10.63 (( 77.78/10.63 (binunionTILcontra) => 77.78/10.63 (( 77.78/10.63 (binunionTIRcontra) => 77.78/10.63 (( 77.78/10.63 (inIntersectImpInUnion) => 77.78/10.63 (( 77.78/10.63 (inIntersectImpInUnion2) => 77.78/10.63 (( 77.78/10.63 (inIntersectImpInIntersectUnions) => 77.78/10.64 (( 77.78/10.64 (intersectInPowersetIntersectUnions) => 77.78/10.64 (( 77.78/10.64 (inComplementUnionImpNotIn1) => 77.78/10.64 (( 77.78/10.64 (inComplementUnionImpInComplement1) => 77.78/10.64 (( 77.78/10.64 (binunionTE) => 77.78/10.64 (( 77.78/10.64 (binunionTEcontra) => 77.78/10.64 (( 77.78/10.64 (demorgan2a1) => 77.78/10.64 (( 77.78/10.64 (complementUnionInPowersetComplement) => 77.78/10.64 (( 77.78/10.64 (demorgan2a2) => 77.78/10.64 (( 77.78/10.64 (demorgan1a) => 77.78/10.64 (( 77.78/10.64 (demorgan1b) => 77.78/10.64 (( 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=> 77.78/10.64 (( 77.78/10.64 (setminusILneg) => 77.78/10.64 (( 77.78/10.64 (setminusIRneg) => 77.78/10.64 (( 77.78/10.64 (setminusLsub) => 77.78/10.64 (( 77.78/10.64 (setminusSubset1) => 77.78/10.64 (( 77.78/10.64 (symdiffE) => 77.78/10.64 (( 77.78/10.64 (symdiffI1) => 77.78/10.64 (( 77.78/10.64 (symdiffI2) => 77.78/10.64 (( 77.78/10.64 (symdiffIneg1) => 77.78/10.64 (( 77.78/10.64 (symdiffIneg2) => 77.78/10.64 (( 77.78/10.64 (secondinupair) => 77.78/10.64 (( 77.78/10.64 (setukpairIL) => 77.78/10.64 (( 77.78/10.64 (setukpairIR) => 77.78/10.64 (( 77.78/10.64 (kpairiskpair) => 77.78/10.64 (( 77.78/10.64 (kpairp) => 77.78/10.64 (( 77.78/10.64 (singletonsubset) => 77.78/10.64 (( 77.78/10.64 (singletoninpowerset) => 77.78/10.64 (( 77.78/10.64 (singletoninpowunion) => 77.78/10.64 (( 77.78/10.64 (upairset2E) => 77.78/10.64 (( 77.78/10.64 (upairsubunion) => 77.78/10.64 (( 77.78/10.64 (upairinpowunion) => 77.78/10.64 (( 77.78/10.64 (ubforcartprodlem1) => 77.78/10.64 (( 77.78/10.64 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77.78/10.64 (setukpairinjR12) => 77.78/10.64 (( 77.78/10.64 (setukpairinjR1) => 77.78/10.64 (( 77.78/10.64 (upairequniteq) => 77.78/10.64 (( 77.78/10.64 (setukpairinjR2) => 77.78/10.64 (( 77.78/10.64 (setukpairinjR) => 77.78/10.64 (( 77.78/10.64 (ksndsingleton) => 77.78/10.64 (( 77.78/10.64 (ksndpairEq) => 77.78/10.64 (( 77.78/10.64 (kpairsurjEq) => 77.78/10.64 (( 77.78/10.64 (cartprodsndin) => 77.78/10.64 (( 77.78/10.64 (cartprodpairmemEL) => 77.78/10.64 (( 77.78/10.64 (cartprodpairmemER) => 77.78/10.64 (( 77.78/10.64 (cartprodmempaircEq) => 77.78/10.64 (( 77.78/10.64 (cartprodfstpairEq) => 77.78/10.64 (( 77.78/10.64 (cartprodsndpairEq) => 77.78/10.64 (( 77.78/10.64 (cartprodpairsurjEq) => 77.78/10.64 (( 77.78/10.64 (dpsetconstrI) => 77.78/10.64 (( 77.78/10.64 (dpsetconstrSub) => 77.78/10.64 (( 77.78/10.64 (setOfPairsIsBReln) => 77.78/10.64 (( 77.78/10.64 (dpsetconstrERa) => 77.78/10.64 (( 77.78/10.64 (dpsetconstrEL1) => 77.78/10.64 (( 77.78/10.64 (dpsetconstrEL2) => 77.78/10.64 (( 77.78/10.64 (dpsetconstrER) => 77.78/10.64 (( 77.78/10.64 (funcImageSingleton) => 77.78/10.64 (( 77.78/10.64 (apProp) => 77.78/10.64 (( 77.78/10.64 (app) => 77.78/10.64 (( 77.78/10.64 (infuncsetfunc) => 77.78/10.64 (( 77.78/10.64 (ap2p) => 77.78/10.64 (( 77.78/10.64 (funcinfuncset) => 77.78/10.64 (( 77.78/10.64 (lamProp) => 77.78/10.64 (( 77.78/10.64 (lamp) => 77.78/10.64 (( 77.78/10.64 (lam2p) => 77.78/10.64 (( 77.78/10.64 (brelnall1) => 77.78/10.64 (( 77.78/10.64 (brelnall2) => 77.78/10.64 (( 77.78/10.64 (ex1E2) => 77.78/10.64 (( 77.78/10.64 (funcGraphProp1) => 77.78/10.64 (( 77.78/10.64 (funcGraphProp3) => 77.78/10.64 (( 77.78/10.64 (funcGraphProp2) => 77.78/10.64 (( 77.78/10.64 (funcextLem) => 77.78/10.64 (( 77.78/10.64 (funcGraphProp4) => 77.78/10.64 (( 77.78/10.64 (subbreln) => 77.78/10.64 (( 77.78/10.64 (eqbreln) => 77.78/10.64 (( 77.78/10.64 (funcext) => 77.78/10.64 (( 77.78/10.64 (funcext2) => 77.78/10.64 (( 77.78/10.64 (ap2apEq1) => 77.78/10.64 (( 77.78/10.64 (ap2apEq2) => 77.78/10.64 (( 77.78/10.64 (beta1) => 77.78/10.64 (( 77.78/10.64 (eta1) => 77.78/10.64 (( 77.78/10.64 (lam2lamEq) => 77.78/10.64 (( 77.78/10.64 (beta2) => 77.78/10.64 (( 77.78/10.64 (eta2) => 77.78/10.64 (( 77.78/10.64 (iffalseProp1) => 77.78/10.64 (( 77.78/10.64 (iffalseProp2) => 77.78/10.64 (( 77.78/10.64 (iftrueProp1) => 77.78/10.64 (( 77.78/10.64 (iftrueProp2) => 77.78/10.64 (( 77.78/10.64 (ifSingleton) => 77.78/10.64 (( 77.78/10.64 (ifp) => 77.78/10.64 (( 77.78/10.64 (theeq) => 77.78/10.64 (( 77.78/10.64 (iftrue) => 77.78/10.64 (( 77.78/10.64 (iffalse) => 77.78/10.64 (( 77.78/10.64 (iftrueorfalse) => 77.78/10.64 (( 77.78/10.64 (binintersectT_lem) => 77.78/10.64 (( 77.78/10.64 (binunionT_lem) => 77.78/10.64 (( 77.78/10.64 (powersetT_lem) => 77.78/10.64 (( 77.78/10.64 (setminusT_lem) => 77.78/10.64 (( 77.78/10.64 (complementT_lem) => 77.78/10.64 (( 77.78/10.64 (setextT) => 77.78/10.64 (( 77.78/10.64 (subsetTI) => 77.78/10.64 (( 77.78/10.64 (powersetTI1) => 77.78/10.64 (( 77.78/10.64 (powersetTE1) => 77.78/10.64 (( 77.78/10.64 (complementTI1) => 77.78/10.64 (( 77.78/10.64 (complementTE1) => 77.78/10.64 (( 77.78/10.64 (binintersectTELcontra) => 77.78/10.64 (( 77.78/10.64 (binintersectTERcontra) => 77.78/10.64 (( 77.78/10.64 (contrasubsetT) => 77.78/10.64 (( 77.78/10.64 (contrasubsetT1) => 77.78/10.64 (( 77.78/10.64 (contrasubsetT2) => 77.78/10.64 (( 77.78/10.64 (contrasubsetT3) => 77.78/10.64 (( 77.78/10.64 (doubleComplementI1) => 77.78/10.64 (( 77.78/10.64 (doubleComplementE1) => 77.78/10.64 (( 77.78/10.64 (doubleComplementSub1) => 77.78/10.64 (( 77.78/10.64 (doubleComplementSub2) => 77.78/10.64 (( 77.78/10.64 (doubleComplementEq) => 77.78/10.64 (( 77.78/10.64 (complementTnotintersectT) => 77.78/10.64 (( 77.78/10.64 (complementImpComplementIntersect) => 77.78/10.64 (( 77.78/10.64 (complementSubsetComplementIntersect) => 77.78/10.64 (( 77.78/10.64 (complementInPowersetComplementIntersect) => 77.78/10.64 (( 77.78/10.64 (contraSubsetComplement) => 77.78/10.64 (( 77.78/10.64 (complementTcontraSubset) => 77.78/10.64 (( 77.78/10.64 (binunionTILcontra) => 77.78/10.64 (( 77.78/10.64 (binunionTIRcontra) => 77.78/10.64 (( 77.78/10.64 (inIntersectImpInUnion) => 77.78/10.64 (( 77.78/10.64 (inIntersectImpInUnion2) => 77.78/10.64 (( 77.78/10.64 (inIntersectImpInIntersectUnions) => 77.78/10.64 (( 77.78/10.64 (intersectInPowersetIntersectUnions) => 77.78/10.64 (( 77.78/10.64 (inComplementUnionImpNotIn1) => 77.78/10.64 (( 77.78/10.64 (inComplementUnionImpInComplement1) => 77.78/10.64 (( 77.78/10.64 (binunionTE) => 77.78/10.64 (( 77.78/10.64 (binunionTEcontra) => 77.78/10.64 (( 77.78/10.64 (demorgan2a1) => 77.78/10.64 (( 77.78/10.64 (complementUnionInPowersetComplement) => 77.78/10.64 (( 77.78/10.64 (demorgan2a2) => 77.78/10.64 (( 77.78/10.64 (demorgan1a) => 77.78/10.64 (( 77.78/10.64 (demorgan1b) => 77.78/10.64 (( 77.78/10.64 (demorgan1) => 77.78/10.64 (( 77.78/10.64 (demorgan2a) => 77.78/10.64 (( 77.78/10.64 (demorgan2b2) => 77.78/10.64 (( 77.78/10.64 (demorgan2b) => 77.78/10.64 (( 77.78/10.64 (demorgan2) => 77.78/10.64 (( 77.78/10.64 (woz13rule0) => 77.78/10.64 (( 77.78/10.64 (woz13rule1) => 77.78/10.64 (( 77.78/10.64 (woz13rule2) => 77.78/10.64 (( 77.78/10.64 (woz13rule3) => 77.78/10.64 (( 77.78/10.64 (woz13rule4) => 77.78/10.64 (( 77.78/10.64 (woz1_1) => 77.78/10.64 (( 77.78/10.64 (woz1_2) => 77.78/10.64 (( 77.78/10.64 (woz1_3) => 77.78/10.64 (( 77.78/10.64 (woz1_4) => 77.78/10.64 (( 77.78/10.64 (woz1_5) => 77.78/10.64 (( 77.78/10.64 (breln1all2) => 77.78/10.64 (( 77.78/10.64 (breln1SetBreln1) => 77.78/10.64 (( 77.78/10.64 (choice2fnsingleton) => 77.78/10.64 (( 77.78/10.64 (setOfPairsIsBReln1) => 77.78/10.64 (( 77.78/10.64 (breln1all1) => 77.78/10.64 (( 77.78/10.64 (subbreln1) => 77.78/10.64 (( 77.78/10.64 (eqbreln1) => 77.78/10.64 (( 77.78/10.64 (breln1invprop) => 77.78/10.64 (( 77.78/10.64 (breln1invI) => 77.78/10.64 (( 77.78/10.64 (breln1invE) => 77.78/10.64 (( 77.78/10.64 (breln1compprop) => 77.78/10.64 (( 77.78/10.64 (breln1compI) => 77.78/10.64 (( 77.78/10.64 (breln1compE) => 77.78/10.64 (( 77.78/10.64 (breln1compEex) => 77.78/10.64 (( 77.78/10.64 (breln1unionprop) => 77.78/10.64 (( 77.78/10.64 (breln1unionIL) => 77.78/10.64 (( 77.78/10.64 (breln1unionIR) => 77.78/10.64 (( 77.78/10.64 (breln1unionI) => 77.78/10.64 (( 77.78/10.64 (breln1unionE) => 77.78/10.64 (( 77.78/10.64 (breln1unionEcases) => 77.78/10.64 (( 77.78/10.64 (breln1unionCommutes) => 77.78/10.64 (( 77.78/10.64 (woz2Ex) => 77.78/10.64 (( 77.78/10.64 (woz2W) => 77.78/10.64 (( 77.78/10.64 (woz2A) => 77.78/10.64 (( 77.78/10.64 (woz2B) => 77.78/10.64 (( 77.78/10.64 (image1Ex) => 77.78/10.64 (( 77.78/10.64 (image1Ex1) => 77.78/10.64 (( 77.78/10.64 (image1Equiv) => 77.78/10.64 (( 77.78/10.64 (image1E) => 77.78/10.64 (( 77.78/10.64 (image1I) => 77.78/10.64 (( 77.78/10.64 (injFuncInInjFuncSet) => 77.78/10.64 (( 77.78/10.64 (injFuncSetFuncIn) => 77.78/10.64 (( 77.78/10.64 (injFuncSetFuncInj) => 77.78/10.64 (( 77.78/10.64 (surjFuncSetFuncIn) => 77.78/10.64 (( 77.78/10.64 (surjFuncSetFuncSurj) => 77.78/10.64 (( 77.78/10.64 (leftInvIsSurj) => 77.78/10.64 (( 77.78/10.64 (surjCantorThm) => 77.78/10.64 (( 77.78/10.64 (foundation2) => 77.78/10.64 (( 77.78/10.64 (notinself) => 77.78/10.64 (( 77.78/10.64 (notinself2) => 77.78/10.64 (( 77.78/10.64 (omegaSp) => 77.78/10.64 (( 77.78/10.64 (omegaSclos) => 77.78/10.64 (( 77.78/10.64 (peano0notS) => 77.78/10.64 (( 77.78/10.64 (peanoSinj) => 77.78/10.64 (( 77.78/10.64 (transitivesetOp1) => 77.78/10.64 (( 77.78/10.64 (binintTransitive) => 77.78/10.64 (( 77.78/10.64 (transitivesetOp2) => 77.78/10.64 (( 77.78/10.64 (setunionTransitive) => 77.78/10.64 (( 77.78/10.64 (ordinalMinLem1) => 77.78/10.64 (( 77.78/10.64 (!!) @ ( 77.78/10.64 ^[Y0 : $i]: 77.78/10.64 (( 77.78/10.64 (ordinal @ 77.78/10.64 Y0) => 77.78/10.64 (( 77.78/10.64 (!!) @ ( 77.78/10.64 ^[Y1 : $i]: 77.78/10.64 (( 77.78/10.64 (!!) @ ( 77.78/10.64 ^[Y2 : $i]: 77.78/10.64 (( 77.78/10.64 (in @ 77.78/10.64 Y2 @ 77.78/10.64 Y0) => 77.78/10.64 (( 77.78/10.64 (in @ 77.78/10.64 Y1 @ 77.78/10.64 Y2) => 77.78/10.64 (in @ 77.78/10.64 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 77.78/10.64 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl805])). 77.78/10.64 thf(zip_derived_cl823, plain, 77.78/10.64 (~ (((subsetTrans) => 77.78/10.64 (((setadjoinSub) => 77.78/10.64 (((setadjoinSub2) => 77.78/10.64 (((subset2powerset) => 77.78/10.64 (((setextsub) => 77.78/10.64 (((subsetemptysetimpeq) => 77.78/10.64 (((powersetI1) => 77.78/10.64 (((powersetE1) => 77.78/10.64 (((inPowerset) => 77.78/10.64 (((powersetsubset) => 77.78/10.64 (((sepInPowerset) => 77.78/10.64 (((sepSubset) => 77.78/10.64 (((binunionIL) => 77.78/10.64 (((upairset2IR) => 77.78/10.64 (((binunionIR) => 77.78/10.64 (((binunionEcases) => 77.78/10.64 (((binunionE) => 77.78/10.64 (((binunionLsub) => 77.78/10.64 (((binunionRsub) => 77.78/10.64 (((binintersectI) => 77.78/10.64 (((binintersectSubset5) => 77.78/10.64 (((binintersectEL) => 77.78/10.64 (((binintersectLsub) => 77.78/10.64 (((binintersectSubset2) => 77.78/10.64 (((binintersectSubset3) => 77.78/10.64 (((binintersectER) => 77.78/10.64 (((disjointsetsI1) => 77.78/10.64 (((binintersectRsub) => 77.78/10.64 (((binintersectSubset4) => 77.78/10.64 (((binintersectSubset1) => 77.78/10.64 (( 77.78/10.64 (bs114d) => 77.78/10.64 (( 77.78/10.64 (setminusI) => 77.78/10.64 (( 77.78/10.64 (setminusEL) => 77.78/10.64 (( 77.78/10.64 (setminusER) => 77.78/10.64 (( 77.78/10.64 (setminusSubset2) => 77.78/10.64 (( 77.78/10.64 (setminusERneg) => 77.78/10.64 (( 77.78/10.64 (setminusELneg) => 77.78/10.64 (( 77.78/10.64 (setminusILneg) => 77.78/10.64 (( 77.78/10.64 (setminusIRneg) => 77.78/10.64 (( 77.78/10.64 (setminusLsub) => 77.78/10.64 (( 77.78/10.64 (setminusSubset1) => 77.78/10.64 (( 77.78/10.64 (symdiffE) => 77.78/10.64 (( 77.78/10.64 (symdiffI1) => 77.78/10.64 (( 77.78/10.64 (symdiffI2) => 77.78/10.64 (( 77.78/10.64 (symdiffIneg1) => 77.78/10.64 (( 77.78/10.64 (symdiffIneg2) => 77.78/10.64 (( 77.78/10.64 (secondinupair) => 77.78/10.64 (( 77.78/10.64 (setukpairIL) => 77.78/10.64 (( 77.78/10.64 (setukpairIR) => 77.78/10.64 (( 77.78/10.64 (kpairiskpair) => 77.78/10.64 (( 77.78/10.64 (kpairp) => 77.78/10.64 (( 77.78/10.64 (singletonsubset) => 77.78/10.64 (( 77.78/10.64 (singletoninpowerset) => 77.78/10.64 (( 77.78/10.64 (singletoninpowunion) => 77.78/10.64 (( 77.78/10.64 (upairset2E) => 77.78/10.64 (( 77.78/10.64 (upairsubunion) => 77.78/10.64 (( 77.78/10.64 (upairinpowunion) => 77.78/10.64 (( 77.78/10.64 (ubforcartprodlem1) => 77.78/10.64 (( 77.78/10.64 (ubforcartprodlem2) => 77.78/10.64 (( 77.78/10.64 (ubforcartprodlem3) => 77.78/10.64 (( 77.78/10.64 (cartprodpairin) => 77.78/10.64 (( 77.78/10.64 (cartprodmempair1) => 77.78/10.64 (( 77.78/10.64 (cartprodmempair) => 77.78/10.64 (( 77.78/10.64 (setunionE2) => 77.78/10.64 (( 77.78/10.64 (setunionsingleton1) => 77.78/10.64 (( 77.78/10.64 (setunionsingleton2) => 77.78/10.64 (( 77.78/10.64 (setunionsingleton) => 77.78/10.64 (( 77.78/10.64 (singletonprop) => 77.78/10.64 (( 77.78/10.64 (ex1E1) => 77.78/10.64 (( 77.78/10.64 (ex1I) => 77.78/10.64 (( 77.78/10.64 (ex1I2) => 77.78/10.64 (( 77.78/10.64 (singletonsuniq) => 77.78/10.64 (( 77.78/10.64 (setukpairinjL1) => 77.78/10.64 (( 77.78/10.64 (kfstsingleton) => 77.78/10.64 (( 77.78/10.64 (theprop) => 77.78/10.64 (( 77.78/10.64 (kfstpairEq) => 77.78/10.64 (( 77.78/10.64 (cartprodfstin) => 77.78/10.64 (( 77.78/10.64 (setukpairinjL2) => 77.78/10.64 (( 77.78/10.64 (setukpairinjL) => 77.78/10.64 (( 77.78/10.64 (setukpairinjR11) => 77.78/10.64 (( 77.78/10.64 (setukpairinjR12) => 77.78/10.64 (( 77.78/10.64 (setukpairinjR1) => 77.78/10.64 (( 77.78/10.64 (upairequniteq) => 77.78/10.64 (( 77.78/10.64 (setukpairinjR2) => 77.78/10.64 (( 77.78/10.64 (setukpairinjR) => 77.78/10.64 (( 77.78/10.64 (ksndsingleton) => 77.78/10.64 (( 77.78/10.64 (ksndpairEq) => 77.78/10.64 (( 77.78/10.64 (kpairsurjEq) => 77.78/10.64 (( 77.78/10.64 (cartprodsndin) => 77.78/10.64 (( 77.78/10.64 (cartprodpairmemEL) => 77.78/10.64 (( 77.78/10.64 (cartprodpairmemER) => 77.78/10.64 (( 77.78/10.64 (cartprodmempaircEq) => 77.78/10.64 (( 77.78/10.64 (cartprodfstpairEq) => 77.78/10.64 (( 77.78/10.64 (cartprodsndpairEq) => 77.78/10.64 (( 77.78/10.64 (cartprodpairsurjEq) => 77.78/10.64 (( 77.78/10.64 (dpsetconstrI) => 77.78/10.64 (( 77.78/10.64 (dpsetconstrSub) => 77.78/10.64 (( 77.78/10.64 (setOfPairsIsBReln) => 77.78/10.64 (( 77.78/10.64 (dpsetconstrERa) => 77.78/10.64 (( 77.78/10.64 (dpsetconstrEL1) => 77.78/10.64 (( 77.78/10.64 (dpsetconstrEL2) => 77.78/10.64 (( 77.78/10.64 (dpsetconstrER) => 77.78/10.64 (( 77.78/10.64 (funcImageSingleton) => 77.78/10.64 (( 77.78/10.64 (apProp) => 77.78/10.64 (( 77.78/10.64 (app) => 77.78/10.64 (( 77.78/10.64 (infuncsetfunc) => 77.78/10.64 (( 77.78/10.64 (ap2p) => 77.78/10.64 (( 77.78/10.64 (funcinfuncset) => 77.78/10.64 (( 77.78/10.64 (lamProp) => 77.78/10.64 (( 77.78/10.64 (lamp) => 77.78/10.64 (( 77.78/10.64 (lam2p) => 77.78/10.64 (( 77.78/10.64 (brelnall1) => 77.78/10.64 (( 77.78/10.64 (brelnall2) => 77.78/10.64 (( 77.78/10.64 (ex1E2) => 77.78/10.64 (( 77.78/10.64 (funcGraphProp1) => 77.78/10.64 (( 77.78/10.64 (funcGraphProp3) => 77.78/10.64 (( 77.78/10.64 (funcGraphProp2) => 77.78/10.64 (( 77.78/10.64 (funcextLem) => 77.78/10.64 (( 77.78/10.64 (funcGraphProp4) => 77.78/10.64 (( 77.78/10.64 (subbreln) => 77.78/10.64 (( 77.78/10.64 (eqbreln) => 77.78/10.64 (( 77.78/10.64 (funcext) => 77.78/10.64 (( 77.78/10.64 (funcext2) => 77.78/10.64 (( 77.78/10.64 (ap2apEq1) 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=> 78.24/10.64 (( 78.24/10.64 (woz13rule4) => 78.24/10.64 (( 78.24/10.64 (woz1_1) => 78.24/10.64 (( 78.24/10.64 (woz1_2) => 78.24/10.64 (( 78.24/10.64 (woz1_3) => 78.24/10.64 (( 78.24/10.64 (woz1_4) => 78.24/10.64 (( 78.24/10.64 (woz1_5) => 78.24/10.64 (( 78.24/10.64 (breln1all2) => 78.24/10.64 (( 78.24/10.64 (breln1SetBreln1) => 78.24/10.64 (( 78.24/10.64 (choice2fnsingleton) => 78.24/10.64 (( 78.24/10.64 (setOfPairsIsBReln1) => 78.24/10.64 (( 78.24/10.64 (breln1all1) => 78.24/10.64 (( 78.24/10.64 (subbreln1) => 78.24/10.64 (( 78.24/10.64 (eqbreln1) => 78.24/10.64 (( 78.24/10.64 (breln1invprop) => 78.24/10.64 (( 78.24/10.64 (breln1invI) => 78.24/10.64 (( 78.24/10.64 (breln1invE) => 78.24/10.64 (( 78.24/10.64 (breln1compprop) => 78.24/10.64 (( 78.24/10.64 (breln1compI) => 78.24/10.64 (( 78.24/10.64 (breln1compE) => 78.24/10.64 (( 78.24/10.64 (breln1compEex) => 78.24/10.64 (( 78.24/10.64 (breln1unionprop) => 78.24/10.64 (( 78.24/10.64 (breln1unionIL) => 78.24/10.64 (( 78.24/10.64 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=> 78.24/10.64 (( 78.24/10.64 (notinself2) => 78.24/10.64 (( 78.24/10.64 (omegaSp) => 78.24/10.64 (( 78.24/10.64 (omegaSclos) => 78.24/10.64 (( 78.24/10.64 (peano0notS) => 78.24/10.64 (( 78.24/10.64 (peanoSinj) => 78.24/10.64 (( 78.24/10.64 (transitivesetOp1) => 78.24/10.64 (( 78.24/10.64 (binintTransitive) => 78.24/10.64 (( 78.24/10.64 (transitivesetOp2) => 78.24/10.64 (( 78.24/10.64 (setunionTransitive) => 78.24/10.64 (( 78.24/10.64 (ordinalMinLem1) => 78.24/10.64 (( 78.24/10.64 (!!) @ ( 78.24/10.64 ^[Y0 : $i]: 78.24/10.64 (( 78.24/10.64 (ordinal @ 78.24/10.64 Y0) => 78.24/10.64 (( 78.24/10.64 (!!) @ ( 78.24/10.64 ^[Y1 : $i]: 78.24/10.64 (( 78.24/10.64 (!!) @ ( 78.24/10.64 ^[Y2 : $i]: 78.24/10.64 (( 78.24/10.64 (in @ 78.24/10.64 Y2 @ 78.24/10.64 Y0) => 78.24/10.64 (( 78.24/10.64 (in @ 78.24/10.64 Y1 @ 78.24/10.64 Y2) => 78.24/10.64 (in @ 78.24/10.64 Y1 @ 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78.24/10.65 (cartprodpairmemER) => 78.24/10.65 (( 78.24/10.65 (cartprodmempaircEq) => 78.24/10.65 (( 78.24/10.65 (cartprodfstpairEq) => 78.24/10.65 (( 78.24/10.65 (cartprodsndpairEq) => 78.24/10.65 (( 78.24/10.65 (cartprodpairsurjEq) => 78.24/10.65 (( 78.24/10.65 (dpsetconstrI) => 78.24/10.65 (( 78.24/10.65 (dpsetconstrSub) => 78.24/10.65 (( 78.24/10.65 (setOfPairsIsBReln) => 78.24/10.65 (( 78.24/10.65 (dpsetconstrERa) => 78.24/10.65 (( 78.24/10.65 (dpsetconstrEL1) => 78.24/10.65 (( 78.24/10.65 (dpsetconstrEL2) => 78.24/10.65 (( 78.24/10.65 (dpsetconstrER) => 78.24/10.65 (( 78.24/10.65 (funcImageSingleton) => 78.24/10.65 (( 78.24/10.65 (apProp) => 78.24/10.65 (( 78.24/10.65 (app) => 78.24/10.65 (( 78.24/10.65 (infuncsetfunc) => 78.24/10.65 (( 78.24/10.65 (ap2p) => 78.24/10.65 (( 78.24/10.65 (funcinfuncset) => 78.24/10.65 (( 78.24/10.65 (lamProp) => 78.24/10.65 (( 78.24/10.65 (lamp) => 78.24/10.65 (( 78.24/10.65 (lam2p) => 78.24/10.65 (( 78.24/10.65 (brelnall1) => 78.24/10.65 (( 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=> 78.24/10.65 (( 78.24/10.65 (inComplementUnionImpInComplement1) => 78.24/10.65 (( 78.24/10.65 (binunionTE) => 78.24/10.65 (( 78.24/10.65 (binunionTEcontra) => 78.24/10.65 (( 78.24/10.65 (demorgan2a1) => 78.24/10.65 (( 78.24/10.65 (complementUnionInPowersetComplement) => 78.24/10.65 (( 78.24/10.65 (demorgan2a2) => 78.24/10.65 (( 78.24/10.65 (demorgan1a) => 78.24/10.65 (( 78.24/10.65 (demorgan1b) => 78.24/10.65 (( 78.24/10.65 (demorgan1) => 78.24/10.65 (( 78.24/10.65 (demorgan2a) => 78.24/10.65 (( 78.24/10.65 (demorgan2b2) => 78.24/10.65 (( 78.24/10.65 (demorgan2b) => 78.24/10.65 (( 78.24/10.65 (demorgan2) => 78.24/10.65 (( 78.24/10.65 (woz13rule0) => 78.24/10.65 (( 78.24/10.65 (woz13rule1) => 78.24/10.65 (( 78.24/10.65 (woz13rule2) => 78.24/10.65 (( 78.24/10.65 (woz13rule3) => 78.24/10.65 (( 78.24/10.65 (woz13rule4) => 78.24/10.65 (( 78.24/10.65 (woz1_1) => 78.24/10.65 (( 78.24/10.65 (woz1_2) => 78.24/10.65 (( 78.24/10.65 (woz1_3) => 78.24/10.65 (( 78.24/10.65 (woz1_4) => 78.24/10.65 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=> 78.24/10.65 (( 78.24/10.65 (transitivesetOp1) => 78.24/10.65 (( 78.24/10.65 (binintTransitive) => 78.24/10.65 (( 78.24/10.65 (transitivesetOp2) => 78.24/10.65 (( 78.24/10.65 (setunionTransitive) => 78.24/10.65 (( 78.24/10.65 (ordinalMinLem1) => 78.24/10.65 (( 78.24/10.65 (!!) @ ( 78.24/10.65 ^[Y0 : $i]: 78.24/10.65 (( 78.24/10.65 (ordinal @ 78.24/10.65 Y0) => 78.24/10.65 (( 78.24/10.65 (!!) @ ( 78.24/10.65 ^[Y1 : $i]: 78.24/10.65 (( 78.24/10.65 (!!) @ ( 78.24/10.65 ^[Y2 : $i]: 78.24/10.65 (( 78.24/10.65 (in @ 78.24/10.65 Y2 @ 78.24/10.65 Y0) => 78.24/10.65 (( 78.24/10.65 (in @ 78.24/10.65 Y1 @ 78.24/10.65 Y2) => 78.24/10.65 (in @ 78.24/10.65 Y1 @ 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(((binintersectEL) => 78.24/10.65 (((binintersectLsub) => 78.24/10.65 (((binintersectSubset2) => 78.24/10.65 (((binintersectSubset3) => 78.24/10.65 (((binintersectER) => 78.24/10.65 (((disjointsetsI1) => 78.24/10.65 (((binintersectRsub) => 78.24/10.65 (((binintersectSubset4) => 78.24/10.65 (((binintersectSubset1) => 78.24/10.65 (((bs114d) => 78.24/10.65 (((setminusI) => 78.24/10.65 (((setminusEL) => 78.24/10.65 (((setminusER) => 78.24/10.65 (((setminusSubset2) => 78.24/10.65 (((setminusERneg) => 78.24/10.65 (((setminusELneg) => 78.24/10.65 (((setminusILneg) => 78.24/10.65 (((setminusIRneg) => 78.24/10.65 (((setminusLsub) => 78.24/10.65 (( 78.24/10.65 (setminusSubset1) => 78.24/10.65 (( 78.24/10.65 (symdiffE) => 78.24/10.65 (( 78.24/10.65 (symdiffI1) => 78.24/10.65 (( 78.24/10.65 (symdiffI2) => 78.24/10.65 (( 78.24/10.65 (symdiffIneg1) => 78.24/10.65 (( 78.24/10.65 (symdiffIneg2) => 78.24/10.65 (( 78.24/10.65 (secondinupair) => 78.24/10.65 (( 78.24/10.65 (setukpairIL) => 78.24/10.65 (( 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78.24/10.65 (ex1I) => 78.24/10.65 (( 78.24/10.65 (ex1I2) => 78.24/10.65 (( 78.24/10.65 (singletonsuniq) => 78.24/10.65 (( 78.24/10.65 (setukpairinjL1) => 78.24/10.65 (( 78.24/10.65 (kfstsingleton) => 78.24/10.65 (( 78.24/10.65 (theprop) => 78.24/10.65 (( 78.24/10.65 (kfstpairEq) => 78.24/10.65 (( 78.24/10.65 (cartprodfstin) => 78.24/10.65 (( 78.24/10.65 (setukpairinjL2) => 78.24/10.65 (( 78.24/10.65 (setukpairinjL) => 78.24/10.65 (( 78.24/10.65 (setukpairinjR11) => 78.24/10.65 (( 78.24/10.65 (setukpairinjR12) => 78.24/10.65 (( 78.24/10.65 (setukpairinjR1) => 78.24/10.65 (( 78.24/10.65 (upairequniteq) => 78.24/10.65 (( 78.24/10.65 (setukpairinjR2) => 78.24/10.65 (( 78.24/10.65 (setukpairinjR) => 78.24/10.65 (( 78.24/10.65 (ksndsingleton) => 78.24/10.65 (( 78.24/10.65 (ksndpairEq) => 78.24/10.65 (( 78.24/10.65 (kpairsurjEq) => 78.24/10.65 (( 78.24/10.65 (cartprodsndin) => 78.24/10.65 (( 78.24/10.65 (cartprodpairmemEL) => 78.24/10.65 (( 78.24/10.65 (cartprodpairmemER) => 78.24/10.65 (( 78.24/10.65 (cartprodmempaircEq) => 78.24/10.65 (( 78.24/10.65 (cartprodfstpairEq) => 78.24/10.65 (( 78.24/10.65 (cartprodsndpairEq) => 78.24/10.65 (( 78.24/10.65 (cartprodpairsurjEq) => 78.24/10.65 (( 78.24/10.65 (dpsetconstrI) => 78.24/10.65 (( 78.24/10.65 (dpsetconstrSub) => 78.24/10.65 (( 78.24/10.65 (setOfPairsIsBReln) => 78.24/10.65 (( 78.24/10.65 (dpsetconstrERa) => 78.24/10.65 (( 78.24/10.65 (dpsetconstrEL1) => 78.24/10.65 (( 78.24/10.65 (dpsetconstrEL2) => 78.24/10.65 (( 78.24/10.65 (dpsetconstrER) => 78.24/10.65 (( 78.24/10.65 (funcImageSingleton) => 78.24/10.65 (( 78.24/10.65 (apProp) => 78.24/10.65 (( 78.24/10.65 (app) => 78.24/10.65 (( 78.24/10.65 (infuncsetfunc) => 78.24/10.65 (( 78.24/10.65 (ap2p) => 78.24/10.65 (( 78.24/10.65 (funcinfuncset) => 78.24/10.65 (( 78.24/10.65 (lamProp) => 78.24/10.65 (( 78.24/10.65 (lamp) => 78.24/10.65 (( 78.24/10.65 (lam2p) => 78.24/10.65 (( 78.24/10.65 (brelnall1) => 78.24/10.65 (( 78.24/10.65 (brelnall2) => 78.24/10.65 (( 78.24/10.65 (ex1E2) => 78.24/10.65 (( 78.24/10.65 (funcGraphProp1) => 78.24/10.65 (( 78.24/10.65 (funcGraphProp3) => 78.24/10.65 (( 78.24/10.65 (funcGraphProp2) => 78.24/10.65 (( 78.24/10.65 (funcextLem) => 78.24/10.65 (( 78.24/10.65 (funcGraphProp4) => 78.24/10.65 (( 78.24/10.65 (subbreln) => 78.24/10.65 (( 78.24/10.65 (eqbreln) => 78.24/10.65 (( 78.24/10.65 (funcext) => 78.24/10.65 (( 78.24/10.65 (funcext2) => 78.24/10.65 (( 78.24/10.65 (ap2apEq1) => 78.24/10.65 (( 78.24/10.65 (ap2apEq2) => 78.24/10.65 (( 78.24/10.65 (beta1) => 78.24/10.65 (( 78.24/10.65 (eta1) => 78.24/10.65 (( 78.24/10.65 (lam2lamEq) => 78.24/10.65 (( 78.24/10.65 (beta2) => 78.24/10.65 (( 78.24/10.65 (eta2) => 78.24/10.65 (( 78.24/10.65 (iffalseProp1) => 78.24/10.65 (( 78.24/10.65 (iffalseProp2) => 78.24/10.65 (( 78.24/10.65 (iftrueProp1) => 78.24/10.65 (( 78.24/10.65 (iftrueProp2) => 78.24/10.65 (( 78.24/10.65 (ifSingleton) => 78.24/10.65 (( 78.24/10.65 (ifp) => 78.24/10.65 (( 78.24/10.65 (theeq) => 78.24/10.65 (( 78.24/10.65 (iftrue) => 78.24/10.65 (( 78.24/10.65 (iffalse) => 78.24/10.65 (( 78.24/10.65 (iftrueorfalse) => 78.24/10.65 (( 78.24/10.65 (binintersectT_lem) => 78.24/10.65 (( 78.24/10.65 (binunionT_lem) => 78.24/10.65 (( 78.24/10.65 (powersetT_lem) => 78.24/10.65 (( 78.24/10.65 (setminusT_lem) => 78.24/10.65 (( 78.24/10.65 (complementT_lem) => 78.24/10.65 (( 78.24/10.65 (setextT) => 78.24/10.65 (( 78.24/10.65 (subsetTI) => 78.24/10.65 (( 78.24/10.65 (powersetTI1) => 78.24/10.65 (( 78.24/10.65 (powersetTE1) => 78.24/10.65 (( 78.24/10.65 (complementTI1) => 78.24/10.65 (( 78.24/10.65 (complementTE1) => 78.24/10.65 (( 78.24/10.65 (binintersectTELcontra) => 78.24/10.65 (( 78.24/10.65 (binintersectTERcontra) => 78.24/10.65 (( 78.24/10.65 (contrasubsetT) => 78.24/10.65 (( 78.24/10.65 (contrasubsetT1) => 78.24/10.65 (( 78.24/10.65 (contrasubsetT2) => 78.24/10.65 (( 78.24/10.65 (contrasubsetT3) => 78.24/10.65 (( 78.24/10.65 (doubleComplementI1) => 78.24/10.65 (( 78.24/10.65 (doubleComplementE1) => 78.24/10.65 (( 78.24/10.65 (doubleComplementSub1) => 78.24/10.65 (( 78.24/10.65 (doubleComplementSub2) => 78.24/10.65 (( 78.24/10.65 (doubleComplementEq) => 78.24/10.65 (( 78.24/10.65 (complementTnotintersectT) => 78.24/10.65 (( 78.24/10.65 (complementImpComplementIntersect) => 78.24/10.65 (( 78.24/10.65 (complementSubsetComplementIntersect) => 78.24/10.65 (( 78.24/10.65 (complementInPowersetComplementIntersect) => 78.24/10.65 (( 78.24/10.65 (contraSubsetComplement) => 78.24/10.65 (( 78.24/10.65 (complementTcontraSubset) => 78.24/10.65 (( 78.24/10.65 (binunionTILcontra) => 78.24/10.65 (( 78.24/10.65 (binunionTIRcontra) => 78.24/10.65 (( 78.24/10.65 (inIntersectImpInUnion) => 78.24/10.65 (( 78.24/10.65 (inIntersectImpInUnion2) => 78.24/10.65 (( 78.24/10.65 (inIntersectImpInIntersectUnions) => 78.24/10.65 (( 78.24/10.65 (intersectInPowersetIntersectUnions) => 78.24/10.65 (( 78.24/10.65 (inComplementUnionImpNotIn1) => 78.24/10.65 (( 78.24/10.65 (inComplementUnionImpInComplement1) => 78.24/10.65 (( 78.24/10.65 (binunionTE) => 78.24/10.65 (( 78.24/10.65 (binunionTEcontra) => 78.24/10.65 (( 78.24/10.65 (demorgan2a1) => 78.24/10.65 (( 78.24/10.65 (complementUnionInPowersetComplement) => 78.24/10.65 (( 78.24/10.65 (demorgan2a2) => 78.24/10.65 (( 78.24/10.65 (demorgan1a) => 78.24/10.65 (( 78.24/10.65 (demorgan1b) => 78.24/10.65 (( 78.24/10.65 (demorgan1) => 78.24/10.65 (( 78.24/10.65 (demorgan2a) => 78.24/10.65 (( 78.24/10.65 (demorgan2b2) => 78.24/10.65 (( 78.24/10.65 (demorgan2b) => 78.24/10.65 (( 78.24/10.65 (demorgan2) => 78.24/10.65 (( 78.24/10.65 (woz13rule0) => 78.24/10.65 (( 78.24/10.65 (woz13rule1) => 78.24/10.65 (( 78.24/10.65 (woz13rule2) => 78.24/10.65 (( 78.24/10.65 (woz13rule3) => 78.24/10.65 (( 78.24/10.65 (woz13rule4) => 78.24/10.65 (( 78.24/10.65 (woz1_1) => 78.24/10.65 (( 78.24/10.65 (woz1_2) => 78.24/10.65 (( 78.24/10.65 (woz1_3) => 78.24/10.65 (( 78.24/10.65 (woz1_4) => 78.24/10.65 (( 78.24/10.65 (woz1_5) => 78.24/10.65 (( 78.24/10.65 (breln1all2) => 78.24/10.65 (( 78.24/10.65 (breln1SetBreln1) => 78.24/10.65 (( 78.24/10.65 (choice2fnsingleton) => 78.24/10.65 (( 78.24/10.65 (setOfPairsIsBReln1) => 78.24/10.65 (( 78.24/10.65 (breln1all1) => 78.24/10.65 (( 78.24/10.65 (subbreln1) => 78.24/10.65 (( 78.24/10.65 (eqbreln1) => 78.24/10.65 (( 78.24/10.65 (breln1invprop) => 78.24/10.65 (( 78.24/10.65 (breln1invI) => 78.24/10.65 (( 78.24/10.65 (breln1invE) => 78.24/10.65 (( 78.24/10.65 (breln1compprop) => 78.24/10.65 (( 78.24/10.65 (breln1compI) => 78.24/10.65 (( 78.24/10.65 (breln1compE) => 78.24/10.65 (( 78.24/10.65 (breln1compEex) => 78.24/10.65 (( 78.24/10.65 (breln1unionprop) => 78.24/10.65 (( 78.24/10.65 (breln1unionIL) => 78.24/10.65 (( 78.24/10.65 (breln1unionIR) => 78.24/10.65 (( 78.24/10.65 (breln1unionI) => 78.24/10.65 (( 78.24/10.65 (breln1unionE) => 78.24/10.65 (( 78.24/10.65 (breln1unionEcases) => 78.24/10.65 (( 78.24/10.65 (breln1unionCommutes) => 78.24/10.65 (( 78.24/10.65 (woz2Ex) => 78.24/10.65 (( 78.24/10.65 (woz2W) => 78.24/10.65 (( 78.24/10.65 (woz2A) => 78.24/10.65 (( 78.24/10.65 (woz2B) => 78.24/10.65 (( 78.24/10.65 (image1Ex) => 78.24/10.65 (( 78.24/10.65 (image1Ex1) => 78.24/10.65 (( 78.24/10.65 (image1Equiv) => 78.24/10.65 (( 78.24/10.65 (image1E) => 78.24/10.65 (( 78.24/10.65 (image1I) => 78.24/10.65 (( 78.24/10.65 (injFuncInInjFuncSet) => 78.24/10.65 (( 78.24/10.65 (injFuncSetFuncIn) => 78.24/10.65 (( 78.24/10.65 (injFuncSetFuncInj) => 78.24/10.65 (( 78.24/10.65 (surjFuncSetFuncIn) => 78.24/10.65 (( 78.24/10.65 (surjFuncSetFuncSurj) => 78.24/10.65 (( 78.24/10.65 (leftInvIsSurj) => 78.24/10.65 (( 78.24/10.65 (surjCantorThm) => 78.24/10.65 (( 78.24/10.65 (foundation2) => 78.24/10.65 (( 78.24/10.65 (notinself) => 78.24/10.65 (( 78.24/10.65 (notinself2) => 78.24/10.65 (( 78.24/10.65 (omegaSp) => 78.24/10.65 (( 78.24/10.65 (omegaSclos) => 78.24/10.65 (( 78.24/10.65 (peano0notS) => 78.24/10.65 (( 78.24/10.65 (peanoSinj) => 78.24/10.65 (( 78.24/10.65 (transitivesetOp1) => 78.24/10.65 (( 78.24/10.65 (binintTransitive) => 78.24/10.65 (( 78.24/10.65 (transitivesetOp2) => 78.24/10.65 (( 78.24/10.65 (setunionTransitive) => 78.24/10.65 (( 78.24/10.65 (ordinalMinLem1) => 78.24/10.65 (( 78.24/10.65 (!!) @ ( 78.24/10.65 ^[Y0 : $i]: 78.24/10.65 (( 78.24/10.65 (ordinal @ 78.24/10.65 Y0) => 78.24/10.65 (( 78.24/10.65 (!!) @ ( 78.24/10.65 ^[Y1 : $i]: 78.24/10.65 (( 78.24/10.65 (!!) @ ( 78.24/10.65 ^[Y2 : $i]: 78.24/10.65 (( 78.24/10.65 (in @ 78.24/10.65 Y2 @ 78.24/10.65 Y0) => 78.24/10.65 (( 78.24/10.65 (in @ 78.24/10.65 Y1 @ 78.24/10.65 Y2) => 78.24/10.65 (in @ 78.24/10.65 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 78.24/10.65 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl892])). 78.24/10.65 thf(zip_derived_cl906, plain, 78.24/10.65 (~ (((sepSubset) => 78.24/10.65 (((binunionIL) => 78.24/10.65 (((upairset2IR) => 78.24/10.65 (((binunionIR) => 78.24/10.65 (((binunionEcases) => 78.24/10.65 (((binunionE) => 78.24/10.65 (((binunionLsub) => 78.24/10.65 (((binunionRsub) => 78.24/10.65 (((binintersectI) => 78.24/10.65 (((binintersectSubset5) => 78.24/10.65 (((binintersectEL) => 78.24/10.65 (((binintersectLsub) => 78.24/10.65 (((binintersectSubset2) => 78.24/10.65 (((binintersectSubset3) => 78.24/10.65 (((binintersectER) => 78.24/10.65 (((disjointsetsI1) => 78.24/10.65 (((binintersectRsub) => 78.24/10.65 (((binintersectSubset4) => 78.24/10.65 (((binintersectSubset1) => 78.24/10.65 (((bs114d) => 78.24/10.65 (((setminusI) => 78.24/10.65 (((setminusEL) => 78.24/10.65 (((setminusER) => 78.24/10.65 (((setminusSubset2) => 78.24/10.65 (((setminusERneg) => 78.24/10.65 (((setminusELneg) => 78.24/10.65 (((setminusILneg) => 78.24/10.65 (((setminusIRneg) => 78.24/10.65 (((setminusLsub) => 78.24/10.65 (((setminusSubset1) => 78.24/10.65 (( 78.24/10.65 (symdiffE) => 78.24/10.65 (( 78.24/10.65 (symdiffI1) => 78.24/10.65 (( 78.24/10.65 (symdiffI2) => 78.24/10.65 (( 78.24/10.65 (symdiffIneg1) => 78.24/10.65 (( 78.24/10.65 (symdiffIneg2) => 78.24/10.65 (( 78.24/10.65 (secondinupair) => 78.24/10.65 (( 78.24/10.65 (setukpairIL) => 78.24/10.65 (( 78.24/10.65 (setukpairIR) => 78.24/10.65 (( 78.24/10.65 (kpairiskpair) => 78.24/10.65 (( 78.24/10.65 (kpairp) => 78.24/10.65 (( 78.24/10.65 (singletonsubset) => 78.24/10.65 (( 78.24/10.65 (singletoninpowerset) => 78.24/10.65 (( 78.24/10.65 (singletoninpowunion) => 78.24/10.65 (( 78.24/10.65 (upairset2E) => 78.24/10.65 (( 78.24/10.65 (upairsubunion) => 78.24/10.65 (( 78.24/10.65 (upairinpowunion) => 78.24/10.65 (( 78.24/10.65 (ubforcartprodlem1) => 78.24/10.65 (( 78.24/10.65 (ubforcartprodlem2) => 78.24/10.65 (( 78.24/10.65 (ubforcartprodlem3) => 78.24/10.65 (( 78.24/10.65 (cartprodpairin) => 78.24/10.65 (( 78.24/10.65 (cartprodmempair1) => 78.24/10.65 (( 78.24/10.65 (cartprodmempair) => 78.24/10.65 (( 78.24/10.65 (setunionE2) => 78.24/10.65 (( 78.24/10.65 (setunionsingleton1) => 78.24/10.65 (( 78.24/10.65 (setunionsingleton2) => 78.24/10.65 (( 78.24/10.65 (setunionsingleton) => 78.24/10.65 (( 78.24/10.65 (singletonprop) => 78.24/10.65 (( 78.24/10.65 (ex1E1) => 78.24/10.65 (( 78.24/10.65 (ex1I) => 78.24/10.65 (( 78.24/10.65 (ex1I2) => 78.24/10.65 (( 78.24/10.65 (singletonsuniq) => 78.24/10.65 (( 78.24/10.65 (setukpairinjL1) => 78.24/10.65 (( 78.24/10.65 (kfstsingleton) => 78.24/10.65 (( 78.24/10.65 (theprop) => 78.24/10.65 (( 78.24/10.65 (kfstpairEq) => 78.24/10.65 (( 78.24/10.65 (cartprodfstin) => 78.24/10.65 (( 78.24/10.65 (setukpairinjL2) => 78.24/10.65 (( 78.24/10.65 (setukpairinjL) => 78.24/10.65 (( 78.24/10.65 (setukpairinjR11) => 78.24/10.65 (( 78.24/10.65 (setukpairinjR12) => 78.24/10.65 (( 78.24/10.65 (setukpairinjR1) => 78.24/10.65 (( 78.24/10.65 (upairequniteq) => 78.24/10.65 (( 78.24/10.65 (setukpairinjR2) => 78.24/10.65 (( 78.24/10.65 (setukpairinjR) => 78.24/10.65 (( 78.24/10.65 (ksndsingleton) => 78.24/10.65 (( 78.24/10.65 (ksndpairEq) => 78.24/10.65 (( 78.24/10.65 (kpairsurjEq) => 78.24/10.65 (( 78.24/10.65 (cartprodsndin) => 78.24/10.65 (( 78.24/10.65 (cartprodpairmemEL) => 78.24/10.65 (( 78.24/10.65 (cartprodpairmemER) => 78.24/10.65 (( 78.24/10.65 (cartprodmempaircEq) => 78.24/10.65 (( 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(woz2B) => 78.24/10.65 (( 78.24/10.65 (image1Ex) => 78.24/10.65 (( 78.24/10.65 (image1Ex1) => 78.24/10.65 (( 78.24/10.65 (image1Equiv) => 78.24/10.65 (( 78.24/10.65 (image1E) => 78.24/10.65 (( 78.24/10.65 (image1I) => 78.24/10.65 (( 78.24/10.65 (injFuncInInjFuncSet) => 78.24/10.65 (( 78.24/10.65 (injFuncSetFuncIn) => 78.24/10.65 (( 78.24/10.65 (injFuncSetFuncInj) => 78.24/10.65 (( 78.24/10.65 (surjFuncSetFuncIn) => 78.24/10.65 (( 78.24/10.65 (surjFuncSetFuncSurj) => 78.24/10.65 (( 78.24/10.65 (leftInvIsSurj) => 78.24/10.65 (( 78.24/10.65 (surjCantorThm) => 78.24/10.65 (( 78.24/10.65 (foundation2) => 78.24/10.65 (( 78.24/10.65 (notinself) => 78.24/10.65 (( 78.24/10.65 (notinself2) => 78.24/10.65 (( 78.24/10.65 (omegaSp) => 78.24/10.65 (( 78.24/10.65 (omegaSclos) => 78.24/10.65 (( 78.24/10.65 (peano0notS) => 78.24/10.65 (( 78.24/10.65 (peanoSinj) => 78.24/10.65 (( 78.24/10.65 (transitivesetOp1) => 78.24/10.65 (( 78.24/10.65 (binintTransitive) => 78.24/10.65 (( 78.24/10.65 (transitivesetOp2) => 78.24/10.65 (( 78.24/10.65 (setunionTransitive) => 78.24/10.65 (( 78.24/10.65 (ordinalMinLem1) => 78.24/10.65 (( 78.24/10.65 (!!) @ ( 78.24/10.65 ^[Y0 : $i]: 78.24/10.65 (( 78.24/10.65 (ordinal @ 78.24/10.65 Y0) => 78.24/10.65 (( 78.24/10.65 (!!) @ ( 78.24/10.65 ^[Y1 : $i]: 78.24/10.65 (( 78.24/10.65 (!!) @ ( 78.24/10.65 ^[Y2 : $i]: 78.24/10.65 (( 78.24/10.65 (in @ 78.24/10.65 Y2 @ 78.24/10.65 Y0) => 78.24/10.65 (( 78.24/10.65 (in @ 78.24/10.65 Y1 @ 78.24/10.65 Y2) => 78.24/10.65 (in @ 78.24/10.65 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 78.24/10.65 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl906])). 78.24/10.65 thf(zip_derived_cl917, plain, 78.24/10.65 (~ (((upairset2IR) => 78.24/10.65 (((binunionIR) => 78.24/10.65 (((binunionEcases) => 78.24/10.65 (((binunionE) => 78.24/10.65 (((binunionLsub) => 78.24/10.65 (((binunionRsub) => 78.24/10.65 (((binintersectI) => 78.24/10.65 (((binintersectSubset5) => 78.24/10.65 (((binintersectEL) => 78.24/10.65 (((binintersectLsub) => 78.24/10.65 (((binintersectSubset2) => 78.24/10.65 (((binintersectSubset3) => 78.24/10.65 (((binintersectER) => 78.24/10.65 (((disjointsetsI1) => 78.24/10.65 (((binintersectRsub) => 78.24/10.65 (((binintersectSubset4) => 78.24/10.65 (((binintersectSubset1) => 78.24/10.65 (((bs114d) => 78.24/10.65 (((setminusI) => 78.24/10.65 (((setminusEL) => 78.24/10.65 (((setminusER) => 78.24/10.65 (((setminusSubset2) => 78.24/10.65 (((setminusERneg) => 78.24/10.65 (((setminusELneg) => 78.24/10.65 (((setminusILneg) => 78.24/10.65 (((setminusIRneg) => 78.24/10.65 (((setminusLsub) => 78.24/10.65 (((setminusSubset1) => 78.24/10.65 (((symdiffE) => 78.24/10.65 (((symdiffI1) => 78.24/10.65 (( 78.24/10.65 (symdiffI2) => 78.24/10.65 (( 78.24/10.65 (symdiffIneg1) => 78.24/10.65 (( 78.24/10.65 (symdiffIneg2) => 78.24/10.65 (( 78.24/10.65 (secondinupair) => 78.24/10.65 (( 78.24/10.65 (setukpairIL) => 78.24/10.65 (( 78.24/10.65 (setukpairIR) => 78.24/10.65 (( 78.24/10.65 (kpairiskpair) => 78.24/10.65 (( 78.24/10.65 (kpairp) => 78.24/10.65 (( 78.24/10.65 (singletonsubset) => 78.24/10.65 (( 78.24/10.65 (singletoninpowerset) => 78.24/10.65 (( 78.24/10.65 (singletoninpowunion) => 78.24/10.65 (( 78.24/10.65 (upairset2E) => 78.24/10.65 (( 78.24/10.65 (upairsubunion) => 78.24/10.65 (( 78.24/10.65 (upairinpowunion) => 78.24/10.65 (( 78.24/10.65 (ubforcartprodlem1) => 78.24/10.65 (( 78.24/10.65 (ubforcartprodlem2) => 78.24/10.65 (( 78.24/10.65 (ubforcartprodlem3) => 78.24/10.65 (( 78.24/10.65 (cartprodpairin) => 78.24/10.65 (( 78.24/10.65 (cartprodmempair1) => 78.24/10.65 (( 78.24/10.65 (cartprodmempair) => 78.24/10.65 (( 78.24/10.65 (setunionE2) => 78.24/10.65 (( 78.24/10.65 (setunionsingleton1) => 78.24/10.65 (( 78.24/10.65 (setunionsingleton2) => 78.24/10.65 (( 78.24/10.65 (setunionsingleton) => 78.24/10.65 (( 78.24/10.65 (singletonprop) => 78.24/10.65 (( 78.24/10.65 (ex1E1) => 78.24/10.65 (( 78.24/10.65 (ex1I) => 78.24/10.65 (( 78.24/10.65 (ex1I2) => 78.24/10.65 (( 78.24/10.65 (singletonsuniq) => 78.24/10.65 (( 78.24/10.65 (setukpairinjL1) => 78.24/10.65 (( 78.24/10.65 (kfstsingleton) => 78.24/10.65 (( 78.24/10.65 (theprop) => 78.24/10.65 (( 78.24/10.65 (kfstpairEq) => 78.24/10.65 (( 78.24/10.65 (cartprodfstin) => 78.24/10.65 (( 78.24/10.65 (setukpairinjL2) => 78.24/10.65 (( 78.24/10.65 (setukpairinjL) => 78.24/10.65 (( 78.24/10.65 (setukpairinjR11) => 78.24/10.65 (( 78.24/10.65 (setukpairinjR12) => 78.24/10.65 (( 78.24/10.65 (setukpairinjR1) => 78.24/10.65 (( 78.24/10.65 (upairequniteq) => 78.24/10.65 (( 78.24/10.65 (setukpairinjR2) => 78.24/10.65 (( 78.24/10.65 (setukpairinjR) => 78.24/10.65 (( 78.24/10.65 (ksndsingleton) => 78.24/10.65 (( 78.24/10.65 (ksndpairEq) => 78.24/10.65 (( 78.24/10.65 (kpairsurjEq) => 78.24/10.65 (( 78.24/10.65 (cartprodsndin) => 78.24/10.65 (( 78.24/10.65 (cartprodpairmemEL) => 78.24/10.65 (( 78.24/10.65 (cartprodpairmemER) => 78.24/10.65 (( 78.24/10.65 (cartprodmempaircEq) => 78.24/10.65 (( 78.24/10.65 (cartprodfstpairEq) => 78.24/10.65 (( 78.24/10.65 (cartprodsndpairEq) => 78.24/10.65 (( 78.24/10.65 (cartprodpairsurjEq) => 78.24/10.65 (( 78.24/10.65 (dpsetconstrI) => 78.24/10.65 (( 78.24/10.65 (dpsetconstrSub) => 78.24/10.65 (( 78.24/10.65 (setOfPairsIsBReln) => 78.24/10.65 (( 78.24/10.65 (dpsetconstrERa) => 78.24/10.65 (( 78.24/10.65 (dpsetconstrEL1) => 78.24/10.65 (( 78.24/10.65 (dpsetconstrEL2) => 78.24/10.65 (( 78.24/10.65 (dpsetconstrER) => 78.24/10.65 (( 78.24/10.65 (funcImageSingleton) => 78.24/10.65 (( 78.24/10.65 (apProp) => 78.24/10.65 (( 78.24/10.65 (app) => 78.24/10.65 (( 78.24/10.65 (infuncsetfunc) => 78.24/10.65 (( 78.24/10.65 (ap2p) => 78.24/10.65 (( 78.24/10.65 (funcinfuncset) => 78.24/10.65 (( 78.24/10.65 (lamProp) => 78.24/10.65 (( 78.24/10.65 (lamp) => 78.24/10.65 (( 78.24/10.65 (lam2p) => 78.24/10.65 (( 78.24/10.65 (brelnall1) => 78.24/10.65 (( 78.24/10.65 (brelnall2) => 78.24/10.65 (( 78.24/10.65 (ex1E2) => 78.24/10.65 (( 78.24/10.65 (funcGraphProp1) => 78.24/10.65 (( 78.24/10.65 (funcGraphProp3) => 78.24/10.65 (( 78.24/10.65 (funcGraphProp2) => 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78.24/10.65 (( 78.24/10.65 (binunionT_lem) => 78.24/10.65 (( 78.24/10.65 (powersetT_lem) => 78.24/10.65 (( 78.24/10.65 (setminusT_lem) => 78.24/10.65 (( 78.24/10.65 (complementT_lem) => 78.24/10.65 (( 78.24/10.65 (setextT) => 78.24/10.65 (( 78.24/10.65 (subsetTI) => 78.24/10.65 (( 78.24/10.65 (powersetTI1) => 78.24/10.65 (( 78.24/10.65 (powersetTE1) => 78.24/10.65 (( 78.24/10.65 (complementTI1) => 78.24/10.65 (( 78.24/10.65 (complementTE1) => 78.24/10.65 (( 78.24/10.65 (binintersectTELcontra) => 78.24/10.65 (( 78.24/10.65 (binintersectTERcontra) => 78.24/10.65 (( 78.24/10.65 (contrasubsetT) => 78.24/10.65 (( 78.24/10.65 (contrasubsetT1) => 78.24/10.65 (( 78.24/10.65 (contrasubsetT2) => 78.24/10.65 (( 78.24/10.65 (contrasubsetT3) => 78.24/10.65 (( 78.24/10.65 (doubleComplementI1) => 78.24/10.65 (( 78.24/10.65 (doubleComplementE1) => 78.24/10.65 (( 78.24/10.65 (doubleComplementSub1) => 78.24/10.65 (( 78.24/10.65 (doubleComplementSub2) => 78.24/10.65 (( 78.24/10.65 (doubleComplementEq) => 78.24/10.65 (( 78.24/10.65 (complementTnotintersectT) => 78.24/10.65 (( 78.24/10.65 (complementImpComplementIntersect) => 78.24/10.65 (( 78.24/10.65 (complementSubsetComplementIntersect) => 78.24/10.65 (( 78.24/10.65 (complementInPowersetComplementIntersect) => 78.24/10.65 (( 78.24/10.65 (contraSubsetComplement) => 78.24/10.65 (( 78.24/10.65 (complementTcontraSubset) => 78.24/10.65 (( 78.24/10.65 (binunionTILcontra) => 78.24/10.65 (( 78.24/10.65 (binunionTIRcontra) => 78.24/10.65 (( 78.24/10.65 (inIntersectImpInUnion) => 78.24/10.65 (( 78.24/10.65 (inIntersectImpInUnion2) => 78.24/10.65 (( 78.24/10.65 (inIntersectImpInIntersectUnions) => 78.24/10.65 (( 78.24/10.65 (intersectInPowersetIntersectUnions) => 78.24/10.65 (( 78.24/10.65 (inComplementUnionImpNotIn1) => 78.24/10.65 (( 78.24/10.65 (inComplementUnionImpInComplement1) => 78.24/10.65 (( 78.24/10.65 (binunionTE) => 78.24/10.65 (( 78.24/10.65 (binunionTEcontra) => 78.24/10.65 (( 78.24/10.65 (demorgan2a1) => 78.24/10.65 (( 78.24/10.65 (complementUnionInPowersetComplement) => 78.24/10.65 (( 78.24/10.65 (demorgan2a2) => 78.24/10.65 (( 78.24/10.65 (demorgan1a) => 78.24/10.65 (( 78.24/10.65 (demorgan1b) => 78.24/10.65 (( 78.24/10.65 (demorgan1) => 78.24/10.65 (( 78.24/10.65 (demorgan2a) => 78.24/10.65 (( 78.24/10.65 (demorgan2b2) => 78.24/10.65 (( 78.24/10.65 (demorgan2b) => 78.24/10.65 (( 78.24/10.65 (demorgan2) => 78.24/10.65 (( 78.24/10.65 (woz13rule0) => 78.24/10.65 (( 78.24/10.65 (woz13rule1) => 78.24/10.65 (( 78.24/10.65 (woz13rule2) => 78.24/10.65 (( 78.24/10.65 (woz13rule3) => 78.24/10.65 (( 78.24/10.65 (woz13rule4) => 78.24/10.65 (( 78.24/10.65 (woz1_1) => 78.24/10.65 (( 78.24/10.65 (woz1_2) => 78.24/10.65 (( 78.24/10.65 (woz1_3) => 78.24/10.65 (( 78.24/10.65 (woz1_4) => 78.24/10.65 (( 78.24/10.65 (woz1_5) => 78.24/10.65 (( 78.24/10.65 (breln1all2) => 78.24/10.65 (( 78.24/10.65 (breln1SetBreln1) => 78.24/10.65 (( 78.24/10.65 (choice2fnsingleton) => 78.24/10.65 (( 78.24/10.65 (setOfPairsIsBReln1) => 78.24/10.65 (( 78.24/10.65 (breln1all1) => 78.24/10.65 (( 78.24/10.65 (subbreln1) => 78.24/10.65 (( 78.24/10.65 (eqbreln1) => 78.24/10.65 (( 78.24/10.65 (breln1invprop) => 78.24/10.65 (( 78.24/10.65 (breln1invI) => 78.24/10.65 (( 78.24/10.65 (breln1invE) => 78.24/10.65 (( 78.24/10.65 (breln1compprop) => 78.24/10.65 (( 78.24/10.65 (breln1compI) => 78.24/10.65 (( 78.24/10.65 (breln1compE) => 78.24/10.65 (( 78.24/10.65 (breln1compEex) => 78.24/10.65 (( 78.24/10.65 (breln1unionprop) => 78.24/10.65 (( 78.24/10.65 (breln1unionIL) => 78.24/10.65 (( 78.24/10.65 (breln1unionIR) => 78.24/10.65 (( 78.24/10.65 (breln1unionI) => 78.24/10.65 (( 78.24/10.65 (breln1unionE) => 78.24/10.65 (( 78.24/10.65 (breln1unionEcases) => 78.24/10.65 (( 78.24/10.65 (breln1unionCommutes) => 78.24/10.65 (( 78.24/10.65 (woz2Ex) => 78.24/10.65 (( 78.24/10.65 (woz2W) => 78.24/10.65 (( 78.24/10.65 (woz2A) => 78.24/10.65 (( 78.24/10.65 (woz2B) => 78.24/10.65 (( 78.24/10.65 (image1Ex) => 78.24/10.65 (( 78.24/10.65 (image1Ex1) => 78.24/10.65 (( 78.24/10.65 (image1Equiv) => 78.24/10.65 (( 78.24/10.65 (image1E) => 78.24/10.65 (( 78.24/10.65 (image1I) => 78.24/10.65 (( 78.24/10.65 (injFuncInInjFuncSet) => 78.24/10.65 (( 78.24/10.65 (injFuncSetFuncIn) => 78.24/10.65 (( 78.24/10.65 (injFuncSetFuncInj) => 78.24/10.65 (( 78.24/10.65 (surjFuncSetFuncIn) => 78.24/10.65 (( 78.24/10.65 (surjFuncSetFuncSurj) => 78.24/10.65 (( 78.24/10.65 (leftInvIsSurj) => 78.24/10.65 (( 78.24/10.65 (surjCantorThm) => 78.24/10.65 (( 78.24/10.65 (foundation2) => 78.24/10.65 (( 78.24/10.65 (notinself) => 78.24/10.65 (( 78.24/10.65 (notinself2) => 78.24/10.65 (( 78.24/10.65 (omegaSp) => 78.24/10.65 (( 78.24/10.65 (omegaSclos) => 78.24/10.65 (( 78.24/10.65 (peano0notS) => 78.24/10.65 (( 78.24/10.65 (peanoSinj) => 78.24/10.65 (( 78.24/10.65 (transitivesetOp1) => 78.24/10.65 (( 78.24/10.65 (binintTransitive) => 78.24/10.65 (( 78.24/10.65 (transitivesetOp2) => 78.24/10.65 (( 78.24/10.65 (setunionTransitive) => 78.24/10.65 (( 78.24/10.65 (ordinalMinLem1) => 78.24/10.65 (( 78.24/10.65 (!!) @ ( 78.24/10.65 ^[Y0 : $i]: 78.24/10.65 (( 78.24/10.65 (ordinal @ 78.24/10.65 Y0) => 78.24/10.65 (( 78.24/10.65 (!!) @ ( 78.24/10.65 ^[Y1 : $i]: 78.24/10.65 (( 78.24/10.65 (!!) @ ( 78.24/10.65 ^[Y2 : $i]: 78.24/10.65 (( 78.24/10.65 (in @ 78.24/10.65 Y2 @ 78.24/10.65 Y0) => 78.24/10.65 (( 78.24/10.65 (in @ 78.24/10.65 Y1 @ 78.24/10.65 Y2) => 78.24/10.65 (in @ 78.24/10.65 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 78.24/10.65 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl911])). 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(((symdiffI1) => 78.24/10.65 (((symdiffI2) => 78.24/10.65 (( 78.24/10.65 (symdiffIneg1) => 78.24/10.65 (( 78.24/10.65 (symdiffIneg2) => 78.24/10.65 (( 78.24/10.65 (secondinupair) => 78.24/10.65 (( 78.24/10.65 (setukpairIL) => 78.24/10.65 (( 78.24/10.65 (setukpairIR) => 78.24/10.65 (( 78.24/10.65 (kpairiskpair) => 78.24/10.65 (( 78.24/10.65 (kpairp) => 78.24/10.65 (( 78.24/10.65 (singletonsubset) => 78.24/10.65 (( 78.24/10.65 (singletoninpowerset) => 78.24/10.65 (( 78.24/10.65 (singletoninpowunion) => 78.24/10.65 (( 78.24/10.65 (upairset2E) => 78.24/10.65 (( 78.24/10.65 (upairsubunion) => 78.24/10.65 (( 78.24/10.65 (upairinpowunion) => 78.24/10.65 (( 78.24/10.65 (ubforcartprodlem1) => 78.24/10.65 (( 78.24/10.65 (ubforcartprodlem2) => 78.24/10.65 (( 78.24/10.65 (ubforcartprodlem3) => 78.24/10.65 (( 78.24/10.65 (cartprodpairin) => 78.24/10.65 (( 78.24/10.65 (cartprodmempair1) => 78.24/10.65 (( 78.24/10.65 (cartprodmempair) => 78.24/10.65 (( 78.24/10.65 (setunionE2) => 78.24/10.65 (( 78.24/10.65 (setunionsingleton1) => 78.24/10.65 (( 78.24/10.65 (setunionsingleton2) => 78.24/10.65 (( 78.24/10.65 (setunionsingleton) => 78.24/10.65 (( 78.24/10.65 (singletonprop) => 78.24/10.65 (( 78.24/10.65 (ex1E1) => 78.24/10.65 (( 78.24/10.65 (ex1I) => 78.24/10.65 (( 78.24/10.65 (ex1I2) => 78.24/10.65 (( 78.24/10.65 (singletonsuniq) => 78.24/10.65 (( 78.24/10.65 (setukpairinjL1) => 78.24/10.65 (( 78.24/10.65 (kfstsingleton) => 78.24/10.65 (( 78.24/10.65 (theprop) => 78.24/10.65 (( 78.24/10.65 (kfstpairEq) => 78.24/10.65 (( 78.24/10.65 (cartprodfstin) => 78.24/10.65 (( 78.24/10.65 (setukpairinjL2) => 78.24/10.65 (( 78.24/10.65 (setukpairinjL) => 78.24/10.65 (( 78.24/10.65 (setukpairinjR11) => 78.24/10.65 (( 78.24/10.65 (setukpairinjR12) => 78.24/10.65 (( 78.24/10.65 (setukpairinjR1) => 78.24/10.65 (( 78.24/10.65 (upairequniteq) => 78.24/10.65 (( 78.24/10.65 (setukpairinjR2) => 78.24/10.65 (( 78.24/10.65 (setukpairinjR) => 78.24/10.65 (( 78.24/10.65 (ksndsingleton) => 78.24/10.65 (( 78.24/10.65 (ksndpairEq) => 78.24/10.65 (( 78.24/10.65 (kpairsurjEq) => 78.24/10.65 (( 78.24/10.65 (cartprodsndin) => 78.24/10.65 (( 78.24/10.65 (cartprodpairmemEL) => 78.24/10.65 (( 78.24/10.65 (cartprodpairmemER) => 78.24/10.65 (( 78.24/10.65 (cartprodmempaircEq) => 78.24/10.65 (( 78.24/10.65 (cartprodfstpairEq) => 78.24/10.65 (( 78.24/10.65 (cartprodsndpairEq) => 78.24/10.65 (( 78.24/10.65 (cartprodpairsurjEq) => 78.24/10.65 (( 78.24/10.65 (dpsetconstrI) => 78.24/10.65 (( 78.24/10.65 (dpsetconstrSub) => 78.24/10.65 (( 78.24/10.65 (setOfPairsIsBReln) => 78.24/10.65 (( 78.24/10.65 (dpsetconstrERa) => 78.24/10.65 (( 78.24/10.65 (dpsetconstrEL1) => 78.24/10.65 (( 78.24/10.65 (dpsetconstrEL2) => 78.24/10.65 (( 78.24/10.65 (dpsetconstrER) => 78.24/10.65 (( 78.24/10.65 (funcImageSingleton) => 78.24/10.65 (( 78.24/10.65 (apProp) => 78.24/10.65 (( 78.24/10.65 (app) => 78.24/10.65 (( 78.24/10.65 (infuncsetfunc) => 78.24/10.65 (( 78.24/10.65 (ap2p) => 78.24/10.65 (( 78.24/10.65 (funcinfuncset) => 78.24/10.65 (( 78.24/10.65 (lamProp) => 78.24/10.65 (( 78.24/10.65 (lamp) => 78.24/10.65 (( 78.24/10.65 (lam2p) => 78.24/10.65 (( 78.24/10.65 (brelnall1) => 78.24/10.65 (( 78.24/10.65 (brelnall2) => 78.24/10.65 (( 78.24/10.65 (ex1E2) => 78.24/10.65 (( 78.24/10.65 (funcGraphProp1) => 78.24/10.65 (( 78.24/10.65 (funcGraphProp3) => 78.24/10.65 (( 78.24/10.65 (funcGraphProp2) => 78.24/10.65 (( 78.24/10.65 (funcextLem) => 78.24/10.65 (( 78.24/10.65 (funcGraphProp4) => 78.24/10.65 (( 78.24/10.65 (subbreln) => 78.24/10.65 (( 78.24/10.65 (eqbreln) => 78.24/10.65 (( 78.24/10.65 (funcext) => 78.24/10.65 (( 78.24/10.65 (funcext2) => 78.24/10.65 (( 78.24/10.65 (ap2apEq1) => 78.24/10.65 (( 78.24/10.65 (ap2apEq2) => 78.24/10.65 (( 78.24/10.65 (beta1) => 78.24/10.65 (( 78.24/10.65 (eta1) => 78.24/10.65 (( 78.24/10.65 (lam2lamEq) => 78.24/10.65 (( 78.24/10.65 (beta2) => 78.24/10.65 (( 78.24/10.65 (eta2) => 78.24/10.65 (( 78.24/10.65 (iffalseProp1) => 78.24/10.65 (( 78.24/10.65 (iffalseProp2) => 78.24/10.65 (( 78.24/10.65 (iftrueProp1) => 78.24/10.65 (( 78.24/10.65 (iftrueProp2) => 78.24/10.65 (( 78.24/10.65 (ifSingleton) => 78.24/10.65 (( 78.24/10.65 (ifp) => 78.24/10.65 (( 78.24/10.65 (theeq) => 78.24/10.65 (( 78.24/10.65 (iftrue) => 78.24/10.65 (( 78.24/10.65 (iffalse) => 78.24/10.65 (( 78.24/10.65 (iftrueorfalse) => 78.24/10.65 (( 78.24/10.65 (binintersectT_lem) => 78.24/10.65 (( 78.24/10.65 (binunionT_lem) => 78.24/10.65 (( 78.24/10.65 (powersetT_lem) => 78.24/10.65 (( 78.24/10.65 (setminusT_lem) => 78.24/10.65 (( 78.24/10.65 (complementT_lem) => 78.24/10.65 (( 78.24/10.65 (setextT) => 78.24/10.65 (( 78.24/10.65 (subsetTI) => 78.24/10.65 (( 78.24/10.65 (powersetTI1) => 78.24/10.65 (( 78.24/10.65 (powersetTE1) => 78.24/10.65 (( 78.24/10.65 (complementTI1) => 78.24/10.65 (( 78.24/10.65 (complementTE1) => 78.24/10.65 (( 78.24/10.65 (binintersectTELcontra) => 78.24/10.65 (( 78.24/10.65 (binintersectTERcontra) => 78.24/10.65 (( 78.24/10.65 (contrasubsetT) => 78.24/10.65 (( 78.24/10.65 (contrasubsetT1) => 78.24/10.65 (( 78.24/10.65 (contrasubsetT2) => 78.24/10.65 (( 78.24/10.65 (contrasubsetT3) => 78.24/10.65 (( 78.24/10.65 (doubleComplementI1) => 78.24/10.65 (( 78.24/10.65 (doubleComplementE1) => 78.24/10.65 (( 78.24/10.65 (doubleComplementSub1) => 78.24/10.65 (( 78.24/10.65 (doubleComplementSub2) => 78.24/10.65 (( 78.24/10.65 (doubleComplementEq) => 78.24/10.65 (( 78.24/10.65 (complementTnotintersectT) => 78.24/10.65 (( 78.24/10.65 (complementImpComplementIntersect) => 78.24/10.65 (( 78.24/10.65 (complementSubsetComplementIntersect) => 78.24/10.65 (( 78.24/10.65 (complementInPowersetComplementIntersect) => 78.24/10.65 (( 78.24/10.65 (contraSubsetComplement) => 78.24/10.65 (( 78.24/10.65 (complementTcontraSubset) => 78.24/10.65 (( 78.24/10.65 (binunionTILcontra) => 78.24/10.65 (( 78.24/10.65 (binunionTIRcontra) => 78.24/10.65 (( 78.24/10.65 (inIntersectImpInUnion) => 78.24/10.65 (( 78.24/10.65 (inIntersectImpInUnion2) => 78.24/10.65 (( 78.24/10.65 (inIntersectImpInIntersectUnions) => 78.24/10.65 (( 78.24/10.65 (intersectInPowersetIntersectUnions) => 78.24/10.65 (( 78.24/10.65 (inComplementUnionImpNotIn1) => 78.24/10.65 (( 78.24/10.65 (inComplementUnionImpInComplement1) => 78.24/10.65 (( 78.24/10.65 (binunionTE) => 78.24/10.65 (( 78.24/10.65 (binunionTEcontra) => 78.24/10.65 (( 78.24/10.65 (demorgan2a1) => 78.24/10.65 (( 78.24/10.65 (complementUnionInPowersetComplement) => 78.24/10.65 (( 78.24/10.65 (demorgan2a2) => 78.24/10.65 (( 78.24/10.65 (demorgan1a) => 78.24/10.65 (( 78.24/10.65 (demorgan1b) => 78.24/10.65 (( 78.24/10.65 (demorgan1) => 78.24/10.65 (( 78.24/10.65 (demorgan2a) => 78.24/10.65 (( 78.24/10.65 (demorgan2b2) => 78.24/10.65 (( 78.24/10.65 (demorgan2b) => 78.24/10.65 (( 78.24/10.65 (demorgan2) => 78.24/10.65 (( 78.24/10.65 (woz13rule0) => 78.24/10.65 (( 78.24/10.65 (woz13rule1) => 78.24/10.65 (( 78.24/10.65 (woz13rule2) => 78.24/10.65 (( 78.24/10.65 (woz13rule3) => 78.24/10.65 (( 78.24/10.65 (woz13rule4) => 78.24/10.65 (( 78.24/10.65 (woz1_1) => 78.24/10.65 (( 78.24/10.65 (woz1_2) => 78.24/10.65 (( 78.24/10.65 (woz1_3) => 78.24/10.65 (( 78.24/10.65 (woz1_4) => 78.24/10.65 (( 78.24/10.65 (woz1_5) => 78.24/10.65 (( 78.24/10.65 (breln1all2) => 78.24/10.65 (( 78.24/10.65 (breln1SetBreln1) => 78.24/10.65 (( 78.24/10.65 (choice2fnsingleton) => 78.24/10.65 (( 78.24/10.65 (setOfPairsIsBReln1) => 78.24/10.65 (( 78.24/10.65 (breln1all1) => 78.24/10.65 (( 78.24/10.65 (subbreln1) => 78.24/10.65 (( 78.24/10.65 (eqbreln1) => 78.24/10.65 (( 78.24/10.65 (breln1invprop) => 78.24/10.65 (( 78.24/10.65 (breln1invI) => 78.24/10.65 (( 78.24/10.65 (breln1invE) => 78.24/10.65 (( 78.24/10.65 (breln1compprop) => 78.24/10.65 (( 78.24/10.65 (breln1compI) => 78.24/10.65 (( 78.24/10.65 (breln1compE) => 78.24/10.65 (( 78.24/10.65 (breln1compEex) => 78.24/10.65 (( 78.24/10.65 (breln1unionprop) => 78.24/10.65 (( 78.24/10.65 (breln1unionIL) => 78.24/10.65 (( 78.24/10.65 (breln1unionIR) => 78.24/10.65 (( 78.24/10.65 (breln1unionI) => 78.24/10.65 (( 78.24/10.65 (breln1unionE) => 78.24/10.65 (( 78.24/10.65 (breln1unionEcases) => 78.24/10.65 (( 78.24/10.65 (breln1unionCommutes) => 78.24/10.65 (( 78.24/10.65 (woz2Ex) => 78.24/10.65 (( 78.24/10.65 (woz2W) => 78.24/10.65 (( 78.24/10.65 (woz2A) => 78.24/10.65 (( 78.24/10.65 (woz2B) => 78.24/10.65 (( 78.24/10.65 (image1Ex) => 78.24/10.65 (( 78.24/10.65 (image1Ex1) => 78.24/10.65 (( 78.24/10.65 (image1Equiv) => 78.24/10.65 (( 78.24/10.65 (image1E) => 78.24/10.65 (( 78.24/10.65 (image1I) => 78.24/10.65 (( 78.24/10.65 (injFuncInInjFuncSet) => 78.24/10.65 (( 78.24/10.65 (injFuncSetFuncIn) => 78.24/10.65 (( 78.24/10.65 (injFuncSetFuncInj) => 78.24/10.65 (( 78.24/10.65 (surjFuncSetFuncIn) => 78.24/10.65 (( 78.24/10.65 (surjFuncSetFuncSurj) => 78.24/10.65 (( 78.24/10.65 (leftInvIsSurj) => 78.24/10.65 (( 78.24/10.65 (surjCantorThm) => 78.24/10.65 (( 78.24/10.65 (foundation2) => 78.24/10.65 (( 78.24/10.65 (notinself) => 78.24/10.65 (( 78.24/10.65 (notinself2) => 78.24/10.65 (( 78.24/10.65 (omegaSp) => 78.24/10.65 (( 78.24/10.65 (omegaSclos) => 78.24/10.65 (( 78.24/10.65 (peano0notS) => 78.24/10.65 (( 78.24/10.65 (peanoSinj) => 78.24/10.65 (( 78.24/10.65 (transitivesetOp1) => 78.24/10.65 (( 78.24/10.65 (binintTransitive) => 78.24/10.65 (( 78.24/10.65 (transitivesetOp2) => 78.24/10.65 (( 78.24/10.65 (setunionTransitive) => 78.24/10.65 (( 78.24/10.65 (ordinalMinLem1) => 78.24/10.65 (( 78.24/10.65 (!!) @ ( 78.24/10.65 ^[Y0 : $i]: 78.24/10.65 (( 78.24/10.65 (ordinal @ 78.24/10.65 Y0) => 78.24/10.65 (( 78.24/10.65 (!!) @ ( 78.24/10.65 ^[Y1 : $i]: 78.24/10.65 (( 78.24/10.65 (!!) @ ( 78.24/10.65 ^[Y2 : $i]: 78.24/10.65 (( 78.24/10.65 (in @ 78.24/10.65 Y2 @ 78.24/10.65 Y0) => 78.24/10.65 (( 78.24/10.65 (in @ 78.24/10.65 Y1 @ 78.24/10.65 Y2) => 78.24/10.65 (in @ 78.24/10.65 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 78.24/10.65 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl917])). 78.24/10.65 thf(zip_derived_cl929, plain, 78.24/10.65 (~ (((binunionEcases) => 78.24/10.65 (((binunionE) => 78.24/10.65 (((binunionLsub) => 78.24/10.65 (((binunionRsub) => 78.24/10.65 (((binintersectI) => 78.24/10.65 (((binintersectSubset5) => 78.24/10.65 (((binintersectEL) => 78.24/10.65 (((binintersectLsub) => 78.24/10.65 (((binintersectSubset2) => 78.24/10.65 (((binintersectSubset3) => 78.24/10.65 (((binintersectER) => 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78.24/10.65 (demorgan1b) => 78.24/10.65 (( 78.24/10.65 (demorgan1) => 78.24/10.65 (( 78.24/10.65 (demorgan2a) => 78.24/10.65 (( 78.24/10.65 (demorgan2b2) => 78.24/10.65 (( 78.24/10.65 (demorgan2b) => 78.24/10.65 (( 78.24/10.65 (demorgan2) => 78.24/10.65 (( 78.24/10.65 (woz13rule0) => 78.24/10.65 (( 78.24/10.65 (woz13rule1) => 78.24/10.65 (( 78.24/10.65 (woz13rule2) => 78.24/10.65 (( 78.24/10.65 (woz13rule3) => 78.24/10.65 (( 78.24/10.65 (woz13rule4) => 78.24/10.65 (( 78.24/10.65 (woz1_1) => 78.24/10.65 (( 78.24/10.65 (woz1_2) => 78.24/10.65 (( 78.24/10.65 (woz1_3) => 78.24/10.65 (( 78.24/10.65 (woz1_4) => 78.24/10.65 (( 78.24/10.65 (woz1_5) => 78.24/10.65 (( 78.24/10.65 (breln1all2) => 78.24/10.65 (( 78.24/10.65 (breln1SetBreln1) => 78.24/10.65 (( 78.24/10.65 (choice2fnsingleton) => 78.24/10.65 (( 78.24/10.65 (setOfPairsIsBReln1) => 78.24/10.65 (( 78.24/10.65 (breln1all1) => 78.24/10.65 (( 78.24/10.65 (subbreln1) => 78.24/10.65 (( 78.24/10.65 (eqbreln1) => 78.24/10.65 (( 78.24/10.65 (breln1invprop) => 78.24/10.65 (( 78.24/10.65 (breln1invI) => 78.24/10.65 (( 78.24/10.65 (breln1invE) => 78.24/10.65 (( 78.24/10.65 (breln1compprop) => 78.24/10.65 (( 78.24/10.65 (breln1compI) => 78.24/10.65 (( 78.24/10.65 (breln1compE) => 78.24/10.65 (( 78.24/10.65 (breln1compEex) => 78.24/10.65 (( 78.24/10.65 (breln1unionprop) => 78.24/10.65 (( 78.24/10.65 (breln1unionIL) => 78.24/10.65 (( 78.24/10.65 (breln1unionIR) => 78.24/10.65 (( 78.24/10.65 (breln1unionI) => 78.24/10.65 (( 78.24/10.65 (breln1unionE) => 78.24/10.65 (( 78.24/10.65 (breln1unionEcases) => 78.24/10.65 (( 78.24/10.65 (breln1unionCommutes) => 78.24/10.65 (( 78.24/10.65 (woz2Ex) => 78.24/10.65 (( 78.24/10.65 (woz2W) => 78.24/10.65 (( 78.24/10.65 (woz2A) => 78.24/10.65 (( 78.24/10.65 (woz2B) => 78.24/10.65 (( 78.24/10.65 (image1Ex) => 78.24/10.65 (( 78.24/10.65 (image1Ex1) => 78.24/10.65 (( 78.24/10.65 (image1Equiv) => 78.24/10.65 (( 78.24/10.65 (image1E) => 78.24/10.65 (( 78.24/10.65 (image1I) => 78.24/10.65 (( 78.24/10.65 (injFuncInInjFuncSet) => 78.24/10.65 (( 78.24/10.65 (injFuncSetFuncIn) => 78.24/10.65 (( 78.24/10.65 (injFuncSetFuncInj) => 78.24/10.65 (( 78.24/10.65 (surjFuncSetFuncIn) => 78.24/10.65 (( 78.24/10.65 (surjFuncSetFuncSurj) => 78.24/10.65 (( 78.24/10.65 (leftInvIsSurj) => 78.24/10.65 (( 78.24/10.65 (surjCantorThm) => 78.24/10.65 (( 78.24/10.65 (foundation2) => 78.24/10.65 (( 78.24/10.65 (notinself) => 78.24/10.65 (( 78.24/10.65 (notinself2) => 78.24/10.65 (( 78.24/10.65 (omegaSp) => 78.24/10.65 (( 78.24/10.65 (omegaSclos) => 78.24/10.65 (( 78.24/10.65 (peano0notS) => 78.24/10.65 (( 78.24/10.65 (peanoSinj) => 78.24/10.65 (( 78.24/10.65 (transitivesetOp1) => 78.24/10.65 (( 78.24/10.65 (binintTransitive) => 78.24/10.65 (( 78.24/10.65 (transitivesetOp2) => 78.24/10.65 (( 78.24/10.65 (setunionTransitive) => 78.24/10.65 (( 78.24/10.65 (ordinalMinLem1) => 78.24/10.65 (( 78.24/10.65 (!!) @ ( 78.24/10.65 ^[Y0 : $i]: 78.24/10.65 (( 78.24/10.65 (ordinal @ 78.24/10.65 Y0) => 78.24/10.65 (( 78.24/10.65 (!!) @ ( 78.24/10.65 ^[Y1 : $i]: 78.24/10.65 (( 78.24/10.65 (!!) @ ( 78.24/10.65 ^[Y2 : $i]: 78.24/10.65 (( 78.24/10.65 (in @ 78.24/10.65 Y2 @ 78.24/10.65 Y0) => 78.24/10.65 (( 78.24/10.65 (in @ 78.24/10.65 Y1 @ 78.24/10.65 Y2) => 78.24/10.65 (in @ 78.24/10.65 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 78.24/10.65 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl934])). 78.24/10.65 thf(zip_derived_cl945, plain, 78.24/10.65 (~ (((binunionRsub) => 78.24/10.65 (((binintersectI) => 78.24/10.65 (((binintersectSubset5) => 78.24/10.65 (((binintersectEL) => 78.24/10.65 (((binintersectLsub) => 78.24/10.65 (((binintersectSubset2) => 78.24/10.65 (((binintersectSubset3) => 78.24/10.65 (((binintersectER) => 78.24/10.65 (((disjointsetsI1) => 78.24/10.65 (((binintersectRsub) => 78.24/10.65 (((binintersectSubset4) => 78.24/10.65 (((binintersectSubset1) => 78.24/10.65 (((bs114d) => 78.24/10.65 (((setminusI) => 78.24/10.65 (((setminusEL) => 78.24/10.65 (((setminusER) => 78.24/10.65 (((setminusSubset2) => 78.24/10.65 (((setminusERneg) => 78.24/10.65 (((setminusELneg) => 78.24/10.65 (((setminusILneg) => 78.24/10.65 (((setminusIRneg) => 78.24/10.65 (((setminusLsub) => 78.24/10.65 (((setminusSubset1) => 78.24/10.65 (((symdiffE) => 78.24/10.65 (((symdiffI1) => 78.24/10.65 (((symdiffI2) => 78.24/10.65 (((symdiffIneg1) => 78.24/10.65 (((symdiffIneg2) => 78.24/10.65 (((secondinupair) => 78.24/10.65 (((setukpairIL) => 78.24/10.65 (( 78.24/10.65 (setukpairIR) => 78.24/10.65 (( 78.24/10.65 (kpairiskpair) => 78.24/10.65 (( 78.24/10.65 (kpairp) => 78.24/10.65 (( 78.24/10.65 (singletonsubset) => 78.24/10.65 (( 78.24/10.65 (singletoninpowerset) => 78.24/10.65 (( 78.24/10.65 (singletoninpowunion) => 78.24/10.65 (( 78.24/10.65 (upairset2E) => 78.24/10.65 (( 78.24/10.65 (upairsubunion) => 78.24/10.65 (( 78.24/10.65 (upairinpowunion) => 78.24/10.65 (( 78.24/10.65 (ubforcartprodlem1) => 78.24/10.65 (( 78.24/10.65 (ubforcartprodlem2) => 78.24/10.65 (( 78.24/10.65 (ubforcartprodlem3) => 78.24/10.65 (( 78.24/10.65 (cartprodpairin) => 78.24/10.65 (( 78.24/10.65 (cartprodmempair1) => 78.24/10.65 (( 78.24/10.65 (cartprodmempair) => 78.24/10.65 (( 78.24/10.65 (setunionE2) => 78.24/10.65 (( 78.24/10.65 (setunionsingleton1) => 78.24/10.65 (( 78.24/10.65 (setunionsingleton2) => 78.24/10.65 (( 78.24/10.65 (setunionsingleton) => 78.24/10.65 (( 78.24/10.65 (singletonprop) => 78.24/10.65 (( 78.24/10.65 (ex1E1) => 78.24/10.65 (( 78.24/10.65 (ex1I) => 78.24/10.65 (( 78.24/10.65 (ex1I2) => 78.24/10.65 (( 78.24/10.65 (singletonsuniq) => 78.24/10.65 (( 78.24/10.65 (setukpairinjL1) => 78.24/10.65 (( 78.24/10.65 (kfstsingleton) => 78.24/10.65 (( 78.24/10.65 (theprop) => 78.24/10.65 (( 78.24/10.65 (kfstpairEq) => 78.24/10.65 (( 78.24/10.65 (cartprodfstin) => 78.24/10.65 (( 78.24/10.65 (setukpairinjL2) => 78.24/10.65 (( 78.24/10.65 (setukpairinjL) => 78.24/10.65 (( 78.24/10.65 (setukpairinjR11) => 78.24/10.65 (( 78.24/10.65 (setukpairinjR12) => 78.24/10.65 (( 78.24/10.65 (setukpairinjR1) => 78.24/10.65 (( 78.24/10.65 (upairequniteq) => 78.24/10.65 (( 78.24/10.65 (setukpairinjR2) => 78.24/10.65 (( 78.24/10.65 (setukpairinjR) => 78.24/10.65 (( 78.24/10.65 (ksndsingleton) => 78.24/10.65 (( 78.24/10.65 (ksndpairEq) => 78.24/10.65 (( 78.24/10.65 (kpairsurjEq) => 78.24/10.65 (( 78.24/10.65 (cartprodsndin) => 78.24/10.65 (( 78.24/10.65 (cartprodpairmemEL) => 78.24/10.65 (( 78.24/10.65 (cartprodpairmemER) => 78.24/10.65 (( 78.24/10.65 (cartprodmempaircEq) => 78.24/10.65 (( 78.24/10.65 (cartprodfstpairEq) => 78.24/10.65 (( 78.24/10.65 (cartprodsndpairEq) => 78.24/10.65 (( 78.24/10.65 (cartprodpairsurjEq) => 78.24/10.65 (( 78.24/10.65 (dpsetconstrI) => 78.24/10.65 (( 78.24/10.65 (dpsetconstrSub) => 78.24/10.65 (( 78.24/10.65 (setOfPairsIsBReln) => 78.24/10.65 (( 78.24/10.65 (dpsetconstrERa) => 78.24/10.65 (( 78.24/10.65 (dpsetconstrEL1) => 78.24/10.65 (( 78.24/10.65 (dpsetconstrEL2) => 78.24/10.65 (( 78.24/10.65 (dpsetconstrER) => 78.24/10.65 (( 78.24/10.65 (funcImageSingleton) => 78.24/10.65 (( 78.24/10.65 (apProp) => 78.24/10.65 (( 78.24/10.65 (app) => 78.24/10.65 (( 78.24/10.65 (infuncsetfunc) => 78.24/10.65 (( 78.24/10.65 (ap2p) => 78.24/10.65 (( 78.24/10.65 (funcinfuncset) => 78.24/10.65 (( 78.24/10.65 (lamProp) => 78.24/10.65 (( 78.24/10.65 (lamp) => 78.24/10.65 (( 78.24/10.65 (lam2p) => 78.24/10.65 (( 78.24/10.65 (brelnall1) => 78.24/10.65 (( 78.24/10.65 (brelnall2) => 78.24/10.65 (( 78.24/10.65 (ex1E2) => 78.24/10.65 (( 78.24/10.65 (funcGraphProp1) => 78.24/10.65 (( 78.24/10.65 (funcGraphProp3) => 78.24/10.65 (( 78.24/10.65 (funcGraphProp2) => 78.24/10.65 (( 78.24/10.65 (funcextLem) => 78.24/10.65 (( 78.24/10.65 (funcGraphProp4) => 78.24/10.65 (( 78.24/10.65 (subbreln) => 78.24/10.65 (( 78.24/10.65 (eqbreln) => 78.24/10.65 (( 78.24/10.65 (funcext) => 78.24/10.65 (( 78.24/10.65 (funcext2) => 78.24/10.65 (( 78.24/10.65 (ap2apEq1) => 78.24/10.65 (( 78.24/10.65 (ap2apEq2) => 78.24/10.65 (( 78.24/10.65 (beta1) => 78.24/10.65 (( 78.24/10.65 (eta1) => 78.24/10.65 (( 78.24/10.65 (lam2lamEq) => 78.24/10.65 (( 78.24/10.65 (beta2) => 78.24/10.65 (( 78.24/10.65 (eta2) => 78.24/10.65 (( 78.24/10.65 (iffalseProp1) => 78.24/10.65 (( 78.24/10.65 (iffalseProp2) => 78.24/10.65 (( 78.24/10.65 (iftrueProp1) => 78.24/10.65 (( 78.24/10.65 (iftrueProp2) => 78.24/10.65 (( 78.24/10.65 (ifSingleton) => 78.24/10.65 (( 78.24/10.65 (ifp) => 78.24/10.65 (( 78.24/10.65 (theeq) => 78.24/10.65 (( 78.24/10.65 (iftrue) => 78.24/10.65 (( 78.24/10.65 (iffalse) => 78.24/10.65 (( 78.24/10.65 (iftrueorfalse) => 78.24/10.65 (( 78.24/10.65 (binintersectT_lem) => 78.24/10.65 (( 78.24/10.65 (binunionT_lem) => 78.24/10.65 (( 78.24/10.65 (powersetT_lem) => 78.24/10.65 (( 78.24/10.65 (setminusT_lem) => 78.24/10.65 (( 78.24/10.65 (complementT_lem) => 78.24/10.65 (( 78.24/10.65 (setextT) => 78.24/10.65 (( 78.24/10.65 (subsetTI) => 78.24/10.65 (( 78.24/10.65 (powersetTI1) => 78.24/10.65 (( 78.24/10.65 (powersetTE1) => 78.24/10.65 (( 78.24/10.65 (complementTI1) => 78.24/10.65 (( 78.24/10.65 (complementTE1) => 78.24/10.65 (( 78.24/10.65 (binintersectTELcontra) => 78.24/10.65 (( 78.24/10.65 (binintersectTERcontra) => 78.24/10.65 (( 78.24/10.65 (contrasubsetT) => 78.24/10.65 (( 78.24/10.65 (contrasubsetT1) => 78.24/10.65 (( 78.24/10.65 (contrasubsetT2) => 78.24/10.65 (( 78.24/10.65 (contrasubsetT3) => 78.24/10.65 (( 78.24/10.65 (doubleComplementI1) => 78.24/10.65 (( 78.24/10.65 (doubleComplementE1) => 78.24/10.65 (( 78.24/10.65 (doubleComplementSub1) => 78.24/10.65 (( 78.24/10.65 (doubleComplementSub2) => 78.24/10.65 (( 78.24/10.65 (doubleComplementEq) => 78.24/10.65 (( 78.24/10.65 (complementTnotintersectT) => 78.24/10.65 (( 78.24/10.65 (complementImpComplementIntersect) => 78.24/10.65 (( 78.24/10.65 (complementSubsetComplementIntersect) => 78.24/10.65 (( 78.24/10.65 (complementInPowersetComplementIntersect) => 78.24/10.65 (( 78.24/10.65 (contraSubsetComplement) => 78.24/10.65 (( 78.24/10.65 (complementTcontraSubset) => 78.24/10.65 (( 78.24/10.65 (binunionTILcontra) => 78.24/10.65 (( 78.24/10.65 (binunionTIRcontra) => 78.24/10.65 (( 78.24/10.65 (inIntersectImpInUnion) => 78.24/10.65 (( 78.24/10.65 (inIntersectImpInUnion2) => 78.24/10.65 (( 78.24/10.65 (inIntersectImpInIntersectUnions) => 78.24/10.65 (( 78.24/10.65 (intersectInPowersetIntersectUnions) => 78.24/10.65 (( 78.24/10.65 (inComplementUnionImpNotIn1) => 78.24/10.65 (( 78.24/10.65 (inComplementUnionImpInComplement1) => 78.24/10.65 (( 78.24/10.65 (binunionTE) => 78.24/10.65 (( 78.24/10.65 (binunionTEcontra) => 78.24/10.65 (( 78.24/10.65 (demorgan2a1) => 78.24/10.65 (( 78.24/10.65 (complementUnionInPowersetComplement) => 78.24/10.65 (( 78.24/10.65 (demorgan2a2) => 78.24/10.65 (( 78.24/10.65 (demorgan1a) => 78.24/10.65 (( 78.24/10.65 (demorgan1b) => 78.24/10.65 (( 78.24/10.65 (demorgan1) => 78.24/10.65 (( 78.24/10.65 (demorgan2a) => 78.24/10.65 (( 78.24/10.65 (demorgan2b2) => 78.24/10.65 (( 78.24/10.65 (demorgan2b) => 78.24/10.65 (( 78.24/10.65 (demorgan2) => 78.24/10.65 (( 78.24/10.65 (woz13rule0) => 78.24/10.65 (( 78.24/10.65 (woz13rule1) => 78.24/10.65 (( 78.24/10.65 (woz13rule2) => 78.24/10.65 (( 78.24/10.65 (woz13rule3) => 78.24/10.65 (( 78.24/10.65 (woz13rule4) => 78.24/10.65 (( 78.24/10.65 (woz1_1) => 78.24/10.65 (( 78.24/10.65 (woz1_2) => 78.24/10.65 (( 78.24/10.65 (woz1_3) => 78.24/10.65 (( 78.24/10.65 (woz1_4) => 78.24/10.65 (( 78.24/10.65 (woz1_5) => 78.24/10.65 (( 78.24/10.65 (breln1all2) => 78.24/10.65 (( 78.24/10.65 (breln1SetBreln1) => 78.24/10.65 (( 78.24/10.65 (choice2fnsingleton) => 78.24/10.65 (( 78.24/10.65 (setOfPairsIsBReln1) => 78.24/10.65 (( 78.24/10.65 (breln1all1) => 78.24/10.65 (( 78.24/10.65 (subbreln1) => 78.24/10.65 (( 78.24/10.65 (eqbreln1) => 78.24/10.65 (( 78.24/10.65 (breln1invprop) => 78.24/10.65 (( 78.24/10.65 (breln1invI) => 78.24/10.65 (( 78.24/10.65 (breln1invE) => 78.24/10.65 (( 78.24/10.65 (breln1compprop) => 78.24/10.65 (( 78.24/10.65 (breln1compI) => 78.24/10.65 (( 78.24/10.65 (breln1compE) => 78.24/10.65 (( 78.24/10.65 (breln1compEex) => 78.24/10.65 (( 78.24/10.66 (breln1unionprop) => 78.24/10.66 (( 78.24/10.66 (breln1unionIL) => 78.24/10.66 (( 78.24/10.66 (breln1unionIR) => 78.24/10.66 (( 78.24/10.66 (breln1unionI) => 78.24/10.66 (( 78.24/10.66 (breln1unionE) => 78.24/10.66 (( 78.24/10.66 (breln1unionEcases) => 78.24/10.66 (( 78.24/10.66 (breln1unionCommutes) => 78.24/10.66 (( 78.24/10.66 (woz2Ex) => 78.24/10.66 (( 78.24/10.66 (woz2W) => 78.24/10.66 (( 78.24/10.66 (woz2A) => 78.24/10.66 (( 78.24/10.66 (woz2B) => 78.24/10.66 (( 78.24/10.66 (image1Ex) => 78.24/10.66 (( 78.24/10.66 (image1Ex1) => 78.24/10.66 (( 78.24/10.66 (image1Equiv) => 78.24/10.66 (( 78.24/10.66 (image1E) => 78.24/10.66 (( 78.24/10.66 (image1I) => 78.24/10.66 (( 78.24/10.66 (injFuncInInjFuncSet) => 78.24/10.66 (( 78.24/10.66 (injFuncSetFuncIn) => 78.24/10.66 (( 78.24/10.66 (injFuncSetFuncInj) => 78.24/10.66 (( 78.24/10.66 (surjFuncSetFuncIn) => 78.24/10.66 (( 78.24/10.66 (surjFuncSetFuncSurj) => 78.24/10.66 (( 78.24/10.66 (leftInvIsSurj) => 78.24/10.66 (( 78.24/10.66 (surjCantorThm) => 78.24/10.66 (( 78.24/10.66 (foundation2) => 78.24/10.66 (( 78.24/10.66 (notinself) => 78.24/10.66 (( 78.24/10.66 (notinself2) => 78.24/10.66 (( 78.24/10.66 (omegaSp) => 78.24/10.66 (( 78.24/10.66 (omegaSclos) => 78.24/10.66 (( 78.24/10.66 (peano0notS) => 78.24/10.66 (( 78.24/10.66 (peanoSinj) => 78.24/10.66 (( 78.24/10.66 (transitivesetOp1) => 78.24/10.66 (( 78.24/10.66 (binintTransitive) => 78.24/10.66 (( 78.24/10.66 (transitivesetOp2) => 78.24/10.66 (( 78.24/10.66 (setunionTransitive) => 78.24/10.66 (( 78.24/10.66 (ordinalMinLem1) => 78.24/10.66 (( 78.24/10.66 (!!) @ ( 78.24/10.66 ^[Y0 : $i]: 78.24/10.66 (( 78.24/10.66 (ordinal @ 78.24/10.66 Y0) => 78.24/10.66 (( 78.24/10.66 (!!) @ ( 78.24/10.66 ^[Y1 : $i]: 78.24/10.66 (( 78.24/10.66 (!!) @ ( 78.24/10.66 ^[Y2 : $i]: 78.24/10.66 (( 78.24/10.66 (in @ 78.24/10.66 Y2 @ 78.24/10.66 Y0) => 78.24/10.66 (( 78.24/10.66 (in @ 78.24/10.66 Y1 @ 78.24/10.66 Y2) => 78.24/10.66 (in @ 78.24/10.66 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 78.24/10.66 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl940])). 78.24/10.66 thf(zip_derived_cl951, plain, 78.24/10.66 (~ (((binintersectI) => 78.24/10.66 (((binintersectSubset5) => 78.24/10.66 (((binintersectEL) => 78.24/10.66 (((binintersectLsub) => 78.24/10.66 (((binintersectSubset2) => 78.24/10.66 (((binintersectSubset3) => 78.24/10.66 (((binintersectER) => 78.24/10.66 (((disjointsetsI1) => 78.24/10.66 (((binintersectRsub) => 78.24/10.66 (((binintersectSubset4) => 78.24/10.66 (((binintersectSubset1) => 78.24/10.66 (((bs114d) => 78.24/10.66 (((setminusI) => 78.24/10.66 (((setminusEL) => 78.24/10.66 (((setminusER) => 78.24/10.66 (((setminusSubset2) => 78.24/10.66 (((setminusERneg) => 78.24/10.66 (((setminusELneg) => 78.24/10.66 (((setminusILneg) => 78.24/10.66 (((setminusIRneg) => 78.24/10.66 (((setminusLsub) => 78.24/10.66 (((setminusSubset1) => 78.24/10.66 (((symdiffE) => 78.24/10.66 (((symdiffI1) => 78.24/10.66 (((symdiffI2) => 78.24/10.66 (((symdiffIneg1) => 78.24/10.66 (((symdiffIneg2) => 78.24/10.66 (((secondinupair) => 78.24/10.66 (((setukpairIL) => 78.24/10.66 (((setukpairIR) => 78.24/10.66 (( 78.24/10.66 (kpairiskpair) => 78.24/10.66 (( 78.24/10.66 (kpairp) => 78.24/10.66 (( 78.24/10.66 (singletonsubset) => 78.24/10.66 (( 78.24/10.66 (singletoninpowerset) => 78.24/10.66 (( 78.24/10.66 (singletoninpowunion) => 78.24/10.66 (( 78.24/10.66 (upairset2E) => 78.24/10.66 (( 78.24/10.66 (upairsubunion) => 78.24/10.66 (( 78.24/10.66 (upairinpowunion) => 78.24/10.66 (( 78.24/10.66 (ubforcartprodlem1) => 78.24/10.66 (( 78.24/10.66 (ubforcartprodlem2) => 78.24/10.66 (( 78.24/10.66 (ubforcartprodlem3) => 78.24/10.66 (( 78.24/10.66 (cartprodpairin) => 78.24/10.66 (( 78.24/10.66 (cartprodmempair1) => 78.24/10.66 (( 78.24/10.66 (cartprodmempair) => 78.24/10.66 (( 78.24/10.66 (setunionE2) => 78.24/10.66 (( 78.24/10.66 (setunionsingleton1) => 78.24/10.66 (( 78.24/10.66 (setunionsingleton2) => 78.24/10.66 (( 78.24/10.66 (setunionsingleton) => 78.24/10.66 (( 78.24/10.66 (singletonprop) => 78.24/10.66 (( 78.24/10.66 (ex1E1) => 78.24/10.66 (( 78.24/10.66 (ex1I) => 78.24/10.66 (( 78.24/10.66 (ex1I2) => 78.24/10.66 (( 78.24/10.66 (singletonsuniq) => 78.24/10.66 (( 78.24/10.66 (setukpairinjL1) => 78.24/10.66 (( 78.24/10.66 (kfstsingleton) => 78.24/10.66 (( 78.24/10.66 (theprop) => 78.24/10.66 (( 78.24/10.66 (kfstpairEq) => 78.24/10.66 (( 78.24/10.66 (cartprodfstin) => 78.24/10.66 (( 78.24/10.66 (setukpairinjL2) => 78.24/10.66 (( 78.24/10.66 (setukpairinjL) => 78.24/10.66 (( 78.24/10.66 (setukpairinjR11) => 78.24/10.66 (( 78.24/10.66 (setukpairinjR12) => 78.24/10.66 (( 78.24/10.66 (setukpairinjR1) => 78.24/10.66 (( 78.24/10.66 (upairequniteq) => 78.24/10.66 (( 78.24/10.66 (setukpairinjR2) => 78.24/10.66 (( 78.24/10.66 (setukpairinjR) => 78.24/10.66 (( 78.24/10.66 (ksndsingleton) => 78.24/10.66 (( 78.24/10.66 (ksndpairEq) => 78.24/10.66 (( 78.24/10.66 (kpairsurjEq) => 78.24/10.66 (( 78.24/10.66 (cartprodsndin) => 78.24/10.66 (( 78.24/10.66 (cartprodpairmemEL) => 78.24/10.66 (( 78.24/10.66 (cartprodpairmemER) => 78.24/10.66 (( 78.24/10.66 (cartprodmempaircEq) => 78.24/10.66 (( 78.24/10.66 (cartprodfstpairEq) => 78.24/10.66 (( 78.24/10.66 (cartprodsndpairEq) => 78.24/10.66 (( 78.24/10.66 (cartprodpairsurjEq) => 78.24/10.66 (( 78.24/10.66 (dpsetconstrI) => 78.24/10.66 (( 78.24/10.66 (dpsetconstrSub) => 78.24/10.66 (( 78.24/10.66 (setOfPairsIsBReln) => 78.24/10.66 (( 78.24/10.66 (dpsetconstrERa) => 78.24/10.66 (( 78.24/10.66 (dpsetconstrEL1) => 78.24/10.66 (( 78.24/10.66 (dpsetconstrEL2) => 78.24/10.66 (( 78.24/10.66 (dpsetconstrER) => 78.24/10.66 (( 78.24/10.66 (funcImageSingleton) => 78.24/10.66 (( 78.24/10.66 (apProp) => 78.24/10.66 (( 78.24/10.66 (app) => 78.24/10.66 (( 78.24/10.66 (infuncsetfunc) => 78.24/10.66 (( 78.24/10.66 (ap2p) => 78.24/10.66 (( 78.24/10.66 (funcinfuncset) => 78.24/10.66 (( 78.24/10.66 (lamProp) => 78.24/10.66 (( 78.24/10.66 (lamp) => 78.24/10.66 (( 78.24/10.66 (lam2p) => 78.24/10.66 (( 78.24/10.66 (brelnall1) => 78.24/10.66 (( 78.24/10.66 (brelnall2) => 78.24/10.66 (( 78.24/10.66 (ex1E2) => 78.24/10.66 (( 78.24/10.66 (funcGraphProp1) => 78.24/10.66 (( 78.24/10.66 (funcGraphProp3) => 78.24/10.66 (( 78.24/10.66 (funcGraphProp2) => 78.24/10.66 (( 78.24/10.66 (funcextLem) => 78.24/10.66 (( 78.24/10.66 (funcGraphProp4) => 78.24/10.66 (( 78.24/10.66 (subbreln) => 78.24/10.66 (( 78.24/10.66 (eqbreln) => 78.24/10.66 (( 78.24/10.66 (funcext) => 78.24/10.66 (( 78.24/10.66 (funcext2) => 78.24/10.66 (( 78.24/10.66 (ap2apEq1) => 78.24/10.66 (( 78.24/10.66 (ap2apEq2) => 78.24/10.66 (( 78.24/10.66 (beta1) => 78.24/10.66 (( 78.24/10.66 (eta1) => 78.24/10.66 (( 78.24/10.66 (lam2lamEq) => 78.24/10.66 (( 78.24/10.66 (beta2) => 78.24/10.66 (( 78.24/10.66 (eta2) => 78.24/10.66 (( 78.24/10.66 (iffalseProp1) => 78.24/10.66 (( 78.24/10.66 (iffalseProp2) => 78.24/10.66 (( 78.24/10.66 (iftrueProp1) => 78.24/10.66 (( 78.24/10.66 (iftrueProp2) => 78.24/10.66 (( 78.24/10.66 (ifSingleton) => 78.24/10.66 (( 78.24/10.66 (ifp) => 78.24/10.66 (( 78.24/10.66 (theeq) => 78.24/10.66 (( 78.24/10.66 (iftrue) => 78.24/10.66 (( 78.24/10.66 (iffalse) => 78.24/10.66 (( 78.24/10.66 (iftrueorfalse) => 78.24/10.66 (( 78.24/10.66 (binintersectT_lem) => 78.24/10.66 (( 78.24/10.66 (binunionT_lem) => 78.24/10.66 (( 78.24/10.66 (powersetT_lem) => 78.24/10.66 (( 78.24/10.66 (setminusT_lem) => 78.24/10.66 (( 78.24/10.66 (complementT_lem) => 78.24/10.66 (( 78.24/10.66 (setextT) => 78.24/10.66 (( 78.24/10.66 (subsetTI) => 78.24/10.66 (( 78.24/10.66 (powersetTI1) => 78.24/10.66 (( 78.24/10.66 (powersetTE1) => 78.24/10.66 (( 78.24/10.66 (complementTI1) => 78.24/10.66 (( 78.24/10.66 (complementTE1) => 78.24/10.66 (( 78.24/10.66 (binintersectTELcontra) => 78.24/10.66 (( 78.24/10.66 (binintersectTERcontra) => 78.24/10.66 (( 78.24/10.66 (contrasubsetT) => 78.24/10.66 (( 78.24/10.66 (contrasubsetT1) => 78.24/10.66 (( 78.24/10.66 (contrasubsetT2) => 78.24/10.66 (( 78.24/10.66 (contrasubsetT3) => 78.24/10.66 (( 78.24/10.66 (doubleComplementI1) => 78.24/10.66 (( 78.24/10.66 (doubleComplementE1) => 78.24/10.66 (( 78.24/10.66 (doubleComplementSub1) => 78.24/10.66 (( 78.24/10.66 (doubleComplementSub2) => 78.24/10.66 (( 78.24/10.66 (doubleComplementEq) => 78.24/10.66 (( 78.24/10.66 (complementTnotintersectT) => 78.24/10.66 (( 78.24/10.66 (complementImpComplementIntersect) => 78.24/10.66 (( 78.24/10.66 (complementSubsetComplementIntersect) => 78.24/10.66 (( 78.24/10.66 (complementInPowersetComplementIntersect) => 78.24/10.66 (( 78.24/10.66 (contraSubsetComplement) => 78.24/10.66 (( 78.24/10.66 (complementTcontraSubset) => 78.24/10.66 (( 78.24/10.66 (binunionTILcontra) => 78.24/10.66 (( 78.24/10.66 (binunionTIRcontra) => 78.24/10.66 (( 78.24/10.66 (inIntersectImpInUnion) => 78.24/10.66 (( 78.24/10.66 (inIntersectImpInUnion2) => 78.24/10.66 (( 78.24/10.66 (inIntersectImpInIntersectUnions) => 78.24/10.66 (( 78.24/10.66 (intersectInPowersetIntersectUnions) => 78.24/10.66 (( 78.24/10.66 (inComplementUnionImpNotIn1) => 78.24/10.66 (( 78.24/10.66 (inComplementUnionImpInComplement1) => 78.24/10.66 (( 78.24/10.66 (binunionTE) => 78.24/10.66 (( 78.24/10.66 (binunionTEcontra) => 78.24/10.66 (( 78.24/10.66 (demorgan2a1) => 78.24/10.66 (( 78.24/10.66 (complementUnionInPowersetComplement) => 78.24/10.66 (( 78.24/10.66 (demorgan2a2) => 78.24/10.66 (( 78.24/10.66 (demorgan1a) => 78.24/10.66 (( 78.24/10.66 (demorgan1b) => 78.24/10.66 (( 78.24/10.66 (demorgan1) => 78.24/10.66 (( 78.24/10.66 (demorgan2a) => 78.24/10.66 (( 78.24/10.66 (demorgan2b2) => 78.24/10.66 (( 78.24/10.66 (demorgan2b) => 78.24/10.66 (( 78.24/10.66 (demorgan2) => 78.24/10.66 (( 78.24/10.66 (woz13rule0) => 78.24/10.66 (( 78.24/10.66 (woz13rule1) => 78.24/10.66 (( 78.24/10.66 (woz13rule2) => 78.24/10.66 (( 78.24/10.66 (woz13rule3) => 78.24/10.66 (( 78.24/10.66 (woz13rule4) => 78.24/10.66 (( 78.24/10.66 (woz1_1) => 78.24/10.66 (( 78.24/10.66 (woz1_2) => 78.24/10.66 (( 78.24/10.66 (woz1_3) => 78.24/10.66 (( 78.24/10.66 (woz1_4) => 78.24/10.66 (( 78.24/10.66 (woz1_5) => 78.24/10.66 (( 78.24/10.66 (breln1all2) => 78.24/10.66 (( 78.24/10.66 (breln1SetBreln1) => 78.24/10.66 (( 78.24/10.66 (choice2fnsingleton) => 78.24/10.66 (( 78.24/10.66 (setOfPairsIsBReln1) => 78.24/10.66 (( 78.24/10.66 (breln1all1) => 78.24/10.66 (( 78.24/10.66 (subbreln1) => 78.24/10.66 (( 78.24/10.66 (eqbreln1) => 78.24/10.66 (( 78.24/10.66 (breln1invprop) => 78.24/10.66 (( 78.24/10.66 (breln1invI) => 78.24/10.66 (( 78.24/10.66 (breln1invE) => 78.24/10.66 (( 78.24/10.66 (breln1compprop) => 78.24/10.66 (( 78.24/10.66 (breln1compI) => 78.24/10.66 (( 78.24/10.66 (breln1compE) => 78.24/10.66 (( 78.24/10.66 (breln1compEex) => 78.24/10.66 (( 78.24/10.66 (breln1unionprop) => 78.24/10.66 (( 78.24/10.66 (breln1unionIL) => 78.24/10.66 (( 78.24/10.66 (breln1unionIR) => 78.24/10.66 (( 78.24/10.66 (breln1unionI) => 78.24/10.66 (( 78.24/10.66 (breln1unionE) => 78.24/10.66 (( 78.24/10.66 (breln1unionEcases) => 78.24/10.66 (( 78.24/10.66 (breln1unionCommutes) => 78.24/10.66 (( 78.24/10.66 (woz2Ex) => 78.24/10.66 (( 78.24/10.66 (woz2W) => 78.24/10.66 (( 78.24/10.66 (woz2A) => 78.24/10.66 (( 78.24/10.66 (woz2B) => 78.24/10.66 (( 78.24/10.66 (image1Ex) => 78.24/10.66 (( 78.24/10.66 (image1Ex1) => 78.24/10.66 (( 78.24/10.66 (image1Equiv) => 78.24/10.66 (( 78.24/10.66 (image1E) => 78.24/10.66 (( 78.24/10.66 (image1I) => 78.24/10.66 (( 78.24/10.66 (injFuncInInjFuncSet) => 78.24/10.66 (( 78.24/10.66 (injFuncSetFuncIn) => 78.24/10.66 (( 78.24/10.66 (injFuncSetFuncInj) => 78.24/10.66 (( 78.24/10.66 (surjFuncSetFuncIn) => 78.24/10.66 (( 78.24/10.66 (surjFuncSetFuncSurj) => 78.24/10.66 (( 78.24/10.66 (leftInvIsSurj) => 78.24/10.66 (( 78.24/10.66 (surjCantorThm) => 78.24/10.66 (( 78.24/10.66 (foundation2) => 78.24/10.66 (( 78.24/10.66 (notinself) => 78.24/10.66 (( 78.24/10.66 (notinself2) => 78.24/10.66 (( 78.24/10.66 (omegaSp) => 78.24/10.66 (( 78.24/10.66 (omegaSclos) => 78.24/10.66 (( 78.24/10.66 (peano0notS) => 78.24/10.66 (( 78.24/10.66 (peanoSinj) => 78.24/10.66 (( 78.24/10.66 (transitivesetOp1) => 78.24/10.66 (( 78.24/10.66 (binintTransitive) => 78.24/10.66 (( 78.24/10.66 (transitivesetOp2) => 78.24/10.66 (( 78.24/10.66 (setunionTransitive) => 78.24/10.66 (( 78.24/10.66 (ordinalMinLem1) => 78.24/10.66 (( 78.24/10.66 (!!) @ ( 78.24/10.66 ^[Y0 : $i]: 78.24/10.66 (( 78.24/10.66 (ordinal @ 78.24/10.66 Y0) => 78.24/10.66 (( 78.24/10.66 (!!) @ ( 78.24/10.66 ^[Y1 : $i]: 78.24/10.66 (( 78.24/10.66 (!!) @ ( 78.24/10.66 ^[Y2 : $i]: 78.24/10.66 (( 78.24/10.66 (in @ 78.24/10.66 Y2 @ 78.24/10.66 Y0) => 78.24/10.66 (( 78.24/10.66 (in @ 78.24/10.66 Y1 @ 78.24/10.66 Y2) => 78.24/10.66 (in @ 78.24/10.66 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 78.24/10.66 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl945])). 78.24/10.66 thf(zip_derived_cl957, plain, 78.24/10.66 (~ (((binintersectSubset5) => 78.24/10.66 (((binintersectEL) => 78.24/10.66 (((binintersectLsub) => 78.24/10.66 (((binintersectSubset2) => 78.24/10.66 (((binintersectSubset3) => 78.24/10.66 (((binintersectER) => 78.24/10.66 (((disjointsetsI1) => 78.24/10.66 (((binintersectRsub) => 78.24/10.66 (((binintersectSubset4) => 78.24/10.66 (((binintersectSubset1) => 78.24/10.66 (((bs114d) => 78.24/10.66 (((setminusI) => 78.24/10.66 (((setminusEL) => 78.24/10.66 (((setminusER) => 78.24/10.66 (((setminusSubset2) => 78.24/10.66 (((setminusERneg) => 78.24/10.66 (((setminusELneg) => 78.24/10.66 (((setminusILneg) => 78.24/10.66 (((setminusIRneg) => 78.24/10.66 (((setminusLsub) => 78.24/10.66 (((setminusSubset1) => 78.24/10.66 (((symdiffE) => 78.24/10.66 (((symdiffI1) => 78.24/10.66 (((symdiffI2) => 78.24/10.66 (((symdiffIneg1) => 78.24/10.66 (((symdiffIneg2) => 78.24/10.66 (((secondinupair) => 78.24/10.66 (((setukpairIL) => 78.24/10.66 (((setukpairIR) => 78.24/10.66 (((kpairiskpair) => 78.24/10.66 (( 78.24/10.66 (kpairp) => 78.24/10.66 (( 78.24/10.66 (singletonsubset) => 78.24/10.66 (( 78.24/10.66 (singletoninpowerset) => 78.24/10.66 (( 78.24/10.66 (singletoninpowunion) => 78.24/10.66 (( 78.24/10.66 (upairset2E) => 78.24/10.66 (( 78.24/10.66 (upairsubunion) => 78.24/10.66 (( 78.24/10.66 (upairinpowunion) => 78.24/10.66 (( 78.24/10.66 (ubforcartprodlem1) => 78.24/10.66 (( 78.24/10.66 (ubforcartprodlem2) => 78.24/10.66 (( 78.24/10.66 (ubforcartprodlem3) => 78.24/10.66 (( 78.24/10.66 (cartprodpairin) => 78.24/10.66 (( 78.24/10.66 (cartprodmempair1) => 78.24/10.66 (( 78.24/10.66 (cartprodmempair) => 78.24/10.66 (( 78.24/10.66 (setunionE2) => 78.24/10.66 (( 78.24/10.66 (setunionsingleton1) => 78.24/10.66 (( 78.24/10.66 (setunionsingleton2) => 78.24/10.66 (( 78.24/10.66 (setunionsingleton) => 78.24/10.66 (( 78.24/10.66 (singletonprop) => 78.24/10.66 (( 78.24/10.66 (ex1E1) => 78.24/10.66 (( 78.24/10.66 (ex1I) => 78.24/10.66 (( 78.24/10.66 (ex1I2) => 78.24/10.66 (( 78.24/10.66 (singletonsuniq) => 78.24/10.66 (( 78.24/10.66 (setukpairinjL1) => 78.24/10.66 (( 78.24/10.66 (kfstsingleton) => 78.24/10.66 (( 78.24/10.66 (theprop) => 78.24/10.66 (( 78.24/10.66 (kfstpairEq) => 78.24/10.66 (( 78.24/10.66 (cartprodfstin) => 78.24/10.66 (( 78.24/10.66 (setukpairinjL2) => 78.24/10.66 (( 78.24/10.66 (setukpairinjL) => 78.24/10.66 (( 78.24/10.66 (setukpairinjR11) => 78.24/10.66 (( 78.24/10.66 (setukpairinjR12) => 78.24/10.66 (( 78.24/10.66 (setukpairinjR1) => 78.24/10.66 (( 78.24/10.66 (upairequniteq) => 78.24/10.66 (( 78.24/10.66 (setukpairinjR2) => 78.24/10.66 (( 78.24/10.66 (setukpairinjR) => 78.24/10.66 (( 78.24/10.66 (ksndsingleton) => 78.24/10.66 (( 78.24/10.66 (ksndpairEq) => 78.24/10.66 (( 78.24/10.66 (kpairsurjEq) => 78.24/10.66 (( 78.24/10.66 (cartprodsndin) => 78.24/10.66 (( 78.24/10.66 (cartprodpairmemEL) => 78.24/10.66 (( 78.24/10.66 (cartprodpairmemER) => 78.24/10.66 (( 78.24/10.66 (cartprodmempaircEq) => 78.24/10.66 (( 78.24/10.66 (cartprodfstpairEq) => 78.24/10.66 (( 78.24/10.66 (cartprodsndpairEq) => 78.24/10.66 (( 78.24/10.66 (cartprodpairsurjEq) => 78.24/10.66 (( 78.24/10.66 (dpsetconstrI) => 78.24/10.66 (( 78.24/10.66 (dpsetconstrSub) => 78.24/10.66 (( 78.24/10.66 (setOfPairsIsBReln) => 78.24/10.66 (( 78.24/10.66 (dpsetconstrERa) => 78.24/10.66 (( 78.24/10.66 (dpsetconstrEL1) => 78.24/10.66 (( 78.24/10.66 (dpsetconstrEL2) => 78.24/10.66 (( 78.24/10.66 (dpsetconstrER) => 78.24/10.66 (( 78.24/10.66 (funcImageSingleton) => 78.24/10.66 (( 78.24/10.66 (apProp) => 78.24/10.66 (( 78.24/10.66 (app) => 78.24/10.66 (( 78.24/10.66 (infuncsetfunc) => 78.24/10.66 (( 78.24/10.66 (ap2p) => 78.24/10.66 (( 78.24/10.66 (funcinfuncset) => 78.24/10.66 (( 78.24/10.66 (lamProp) => 78.24/10.66 (( 78.24/10.66 (lamp) => 78.24/10.66 (( 78.24/10.66 (lam2p) => 78.24/10.66 (( 78.24/10.66 (brelnall1) => 78.24/10.66 (( 78.24/10.66 (brelnall2) => 78.24/10.66 (( 78.24/10.66 (ex1E2) => 78.24/10.66 (( 78.24/10.66 (funcGraphProp1) => 78.24/10.66 (( 78.24/10.66 (funcGraphProp3) => 78.24/10.66 (( 78.24/10.66 (funcGraphProp2) => 78.24/10.66 (( 78.24/10.66 (funcextLem) => 78.24/10.66 (( 78.24/10.66 (funcGraphProp4) => 78.24/10.66 (( 78.24/10.66 (subbreln) => 78.24/10.66 (( 78.24/10.66 (eqbreln) => 78.24/10.66 (( 78.24/10.66 (funcext) => 78.24/10.66 (( 78.24/10.66 (funcext2) => 78.24/10.66 (( 78.24/10.66 (ap2apEq1) => 78.24/10.66 (( 78.24/10.66 (ap2apEq2) => 78.24/10.66 (( 78.24/10.66 (beta1) => 78.24/10.66 (( 78.24/10.66 (eta1) => 78.24/10.66 (( 78.24/10.66 (lam2lamEq) => 78.24/10.66 (( 78.24/10.66 (beta2) => 78.24/10.66 (( 78.24/10.66 (eta2) => 78.24/10.66 (( 78.24/10.66 (iffalseProp1) => 78.24/10.66 (( 78.24/10.66 (iffalseProp2) => 78.24/10.66 (( 78.24/10.66 (iftrueProp1) => 78.24/10.66 (( 78.24/10.66 (iftrueProp2) => 78.24/10.66 (( 78.24/10.66 (ifSingleton) => 78.24/10.66 (( 78.24/10.66 (ifp) => 78.24/10.66 (( 78.24/10.66 (theeq) => 78.24/10.66 (( 78.24/10.66 (iftrue) => 78.24/10.66 (( 78.24/10.66 (iffalse) => 78.24/10.66 (( 78.24/10.66 (iftrueorfalse) => 78.24/10.66 (( 78.24/10.66 (binintersectT_lem) => 78.24/10.66 (( 78.24/10.66 (binunionT_lem) => 78.24/10.66 (( 78.24/10.66 (powersetT_lem) => 78.24/10.66 (( 78.24/10.66 (setminusT_lem) => 78.24/10.66 (( 78.24/10.66 (complementT_lem) => 78.24/10.66 (( 78.24/10.66 (setextT) => 78.24/10.66 (( 78.24/10.66 (subsetTI) => 78.24/10.66 (( 78.24/10.66 (powersetTI1) => 78.24/10.66 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78.24/10.66 Y0) => 78.24/10.66 (( 78.24/10.66 (in @ 78.24/10.66 Y1 @ 78.24/10.66 Y2) => 78.24/10.66 (in @ 78.24/10.66 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 78.24/10.66 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl951])). 78.24/10.66 thf(zip_derived_cl964, plain, 78.24/10.66 (~ (((binintersectEL) => 78.24/10.66 (((binintersectLsub) => 78.24/10.66 (((binintersectSubset2) => 78.24/10.66 (((binintersectSubset3) => 78.24/10.66 (((binintersectER) => 78.24/10.66 (((disjointsetsI1) => 78.24/10.66 (((binintersectRsub) => 78.24/10.66 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(complementInPowersetComplementIntersect) => 78.24/10.66 (( 78.24/10.66 (contraSubsetComplement) => 78.24/10.66 (( 78.24/10.66 (complementTcontraSubset) => 78.24/10.66 (( 78.24/10.66 (binunionTILcontra) => 78.24/10.66 (( 78.24/10.66 (binunionTIRcontra) => 78.24/10.66 (( 78.24/10.66 (inIntersectImpInUnion) => 78.24/10.66 (( 78.24/10.66 (inIntersectImpInUnion2) => 78.24/10.66 (( 78.24/10.66 (inIntersectImpInIntersectUnions) => 78.24/10.66 (( 78.24/10.66 (intersectInPowersetIntersectUnions) => 78.24/10.66 (( 78.24/10.66 (inComplementUnionImpNotIn1) => 78.24/10.66 (( 78.24/10.66 (inComplementUnionImpInComplement1) => 78.24/10.66 (( 78.24/10.66 (binunionTE) => 78.24/10.66 (( 78.24/10.66 (binunionTEcontra) => 78.24/10.66 (( 78.24/10.66 (demorgan2a1) => 78.24/10.66 (( 78.24/10.66 (complementUnionInPowersetComplement) => 78.24/10.66 (( 78.24/10.66 (demorgan2a2) => 78.24/10.66 (( 78.24/10.66 (demorgan1a) => 78.24/10.66 (( 78.24/10.66 (demorgan1b) => 78.24/10.66 (( 78.24/10.66 (demorgan1) => 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78.24/10.66 (( 78.24/10.66 (breln1invE) => 78.24/10.66 (( 78.24/10.66 (breln1compprop) => 78.24/10.66 (( 78.24/10.66 (breln1compI) => 78.24/10.66 (( 78.24/10.66 (breln1compE) => 78.24/10.66 (( 78.24/10.66 (breln1compEex) => 78.24/10.66 (( 78.24/10.66 (breln1unionprop) => 78.24/10.66 (( 78.24/10.66 (breln1unionIL) => 78.24/10.66 (( 78.24/10.66 (breln1unionIR) => 78.24/10.66 (( 78.24/10.66 (breln1unionI) => 78.24/10.66 (( 78.24/10.66 (breln1unionE) => 78.24/10.66 (( 78.24/10.66 (breln1unionEcases) => 78.24/10.66 (( 78.24/10.66 (breln1unionCommutes) => 78.24/10.66 (( 78.24/10.66 (woz2Ex) => 78.24/10.66 (( 78.24/10.66 (woz2W) => 78.24/10.66 (( 78.24/10.66 (woz2A) => 78.24/10.66 (( 78.24/10.66 (woz2B) => 78.24/10.66 (( 78.24/10.66 (image1Ex) => 78.24/10.66 (( 78.24/10.66 (image1Ex1) => 78.24/10.66 (( 78.24/10.66 (image1Equiv) => 78.24/10.66 (( 78.24/10.66 (image1E) => 78.24/10.66 (( 78.24/10.66 (image1I) => 78.24/10.66 (( 78.24/10.66 (injFuncInInjFuncSet) => 78.24/10.66 (( 78.24/10.66 (injFuncSetFuncIn) => 78.24/10.66 (( 78.24/10.66 (injFuncSetFuncInj) => 78.24/10.66 (( 78.24/10.66 (surjFuncSetFuncIn) => 78.24/10.66 (( 78.24/10.66 (surjFuncSetFuncSurj) => 78.24/10.66 (( 78.24/10.66 (leftInvIsSurj) => 78.24/10.66 (( 78.24/10.66 (surjCantorThm) => 78.24/10.66 (( 78.24/10.66 (foundation2) => 78.24/10.66 (( 78.24/10.66 (notinself) => 78.24/10.66 (( 78.24/10.66 (notinself2) => 78.24/10.66 (( 78.24/10.66 (omegaSp) => 78.24/10.66 (( 78.24/10.66 (omegaSclos) => 78.24/10.66 (( 78.24/10.66 (peano0notS) => 78.24/10.66 (( 78.24/10.66 (peanoSinj) => 78.24/10.66 (( 78.24/10.66 (transitivesetOp1) => 78.24/10.66 (( 78.24/10.66 (binintTransitive) => 78.24/10.66 (( 78.24/10.66 (transitivesetOp2) => 78.24/10.66 (( 78.24/10.66 (setunionTransitive) => 78.24/10.66 (( 78.24/10.66 (ordinalMinLem1) => 78.24/10.66 (( 78.24/10.66 (!!) @ ( 78.24/10.66 ^[Y0 : $i]: 78.24/10.66 (( 78.24/10.66 (ordinal @ 78.24/10.66 Y0) => 78.24/10.66 (( 78.24/10.66 (!!) @ ( 78.24/10.66 ^[Y1 : $i]: 78.24/10.66 (( 78.24/10.66 (!!) @ ( 78.24/10.66 ^[Y2 : $i]: 78.24/10.66 (( 78.24/10.66 (in @ 78.24/10.66 Y2 @ 78.24/10.66 Y0) => 78.24/10.66 (( 78.24/10.66 (in @ 78.24/10.66 Y1 @ 78.24/10.66 Y2) => 78.24/10.66 (in @ 78.24/10.66 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 78.24/10.66 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl957])). 78.24/10.66 thf(zip_derived_cl971, plain, 78.24/10.66 (~ (((binintersectLsub) => 78.24/10.66 (((binintersectSubset2) => 78.24/10.66 (((binintersectSubset3) => 78.24/10.66 (((binintersectER) => 78.24/10.66 (((disjointsetsI1) => 78.24/10.66 (((binintersectRsub) => 78.24/10.66 (((binintersectSubset4) => 78.24/10.66 (((binintersectSubset1) => 78.24/10.66 (((bs114d) => 78.24/10.66 (((setminusI) => 78.24/10.66 (((setminusEL) => 78.24/10.66 (((setminusER) => 78.24/10.66 (((setminusSubset2) => 78.24/10.66 (((setminusERneg) => 78.24/10.66 (((setminusELneg) => 78.24/10.66 (((setminusILneg) => 78.24/10.66 (((setminusIRneg) => 78.24/10.66 (((setminusLsub) => 78.24/10.66 (((setminusSubset1) => 78.24/10.66 (((symdiffE) => 78.24/10.66 (((symdiffI1) => 78.24/10.66 (((symdiffI2) => 78.24/10.66 (((symdiffIneg1) => 78.24/10.66 (((symdiffIneg2) => 78.24/10.66 (((secondinupair) => 78.24/10.66 (((setukpairIL) => 78.24/10.66 (((setukpairIR) => 78.24/10.66 (((kpairiskpair) => 78.24/10.66 (((kpairp) => 78.24/10.66 (((singletonsubset) => 78.24/10.66 (( 78.24/10.66 (singletoninpowerset) => 78.24/10.66 (( 78.24/10.66 (singletoninpowunion) => 78.24/10.66 (( 78.24/10.66 (upairset2E) => 78.24/10.66 (( 78.24/10.66 (upairsubunion) => 78.24/10.66 (( 78.24/10.66 (upairinpowunion) => 78.24/10.66 (( 78.24/10.66 (ubforcartprodlem1) => 78.24/10.66 (( 78.24/10.66 (ubforcartprodlem2) => 78.24/10.66 (( 78.24/10.66 (ubforcartprodlem3) => 78.24/10.66 (( 78.24/10.66 (cartprodpairin) => 78.24/10.66 (( 78.24/10.66 (cartprodmempair1) => 78.24/10.66 (( 78.24/10.66 (cartprodmempair) => 78.24/10.66 (( 78.24/10.66 (setunionE2) => 78.24/10.66 (( 78.24/10.66 (setunionsingleton1) => 78.24/10.66 (( 78.24/10.66 (setunionsingleton2) => 78.24/10.66 (( 78.24/10.66 (setunionsingleton) => 78.24/10.66 (( 78.24/10.66 (singletonprop) => 78.24/10.66 (( 78.24/10.66 (ex1E1) => 78.24/10.66 (( 78.24/10.66 (ex1I) => 78.24/10.66 (( 78.24/10.66 (ex1I2) => 78.24/10.66 (( 78.24/10.66 (singletonsuniq) => 78.24/10.66 (( 78.24/10.66 (setukpairinjL1) => 78.24/10.66 (( 78.24/10.66 (kfstsingleton) => 78.24/10.66 (( 78.24/10.66 (theprop) => 78.24/10.66 (( 78.24/10.66 (kfstpairEq) => 78.24/10.66 (( 78.24/10.66 (cartprodfstin) => 78.24/10.66 (( 78.24/10.66 (setukpairinjL2) => 78.24/10.66 (( 78.24/10.66 (setukpairinjL) => 78.24/10.66 (( 78.24/10.66 (setukpairinjR11) => 78.24/10.66 (( 78.24/10.66 (setukpairinjR12) => 78.24/10.66 (( 78.24/10.66 (setukpairinjR1) => 78.24/10.66 (( 78.24/10.66 (upairequniteq) => 78.24/10.66 (( 78.24/10.66 (setukpairinjR2) => 78.24/10.66 (( 78.24/10.66 (setukpairinjR) => 78.24/10.66 (( 78.24/10.66 (ksndsingleton) => 78.24/10.66 (( 78.24/10.66 (ksndpairEq) => 78.24/10.66 (( 78.24/10.66 (kpairsurjEq) => 78.24/10.66 (( 78.24/10.66 (cartprodsndin) => 78.24/10.66 (( 78.24/10.66 (cartprodpairmemEL) => 78.24/10.66 (( 78.24/10.66 (cartprodpairmemER) => 78.24/10.66 (( 78.24/10.66 (cartprodmempaircEq) => 78.24/10.66 (( 78.24/10.66 (cartprodfstpairEq) => 78.24/10.66 (( 78.24/10.66 (cartprodsndpairEq) => 78.24/10.66 (( 78.24/10.66 (cartprodpairsurjEq) => 78.24/10.66 (( 78.24/10.66 (dpsetconstrI) => 78.24/10.66 (( 78.24/10.66 (dpsetconstrSub) => 78.24/10.66 (( 78.24/10.66 (setOfPairsIsBReln) => 78.24/10.66 (( 78.24/10.66 (dpsetconstrERa) => 78.24/10.66 (( 78.24/10.66 (dpsetconstrEL1) => 78.24/10.66 (( 78.24/10.66 (dpsetconstrEL2) => 78.24/10.66 (( 78.24/10.66 (dpsetconstrER) => 78.24/10.66 (( 78.24/10.66 (funcImageSingleton) => 78.24/10.66 (( 78.24/10.66 (apProp) => 78.24/10.66 (( 78.24/10.66 (app) => 78.24/10.66 (( 78.24/10.66 (infuncsetfunc) => 78.24/10.66 (( 78.24/10.66 (ap2p) => 78.24/10.66 (( 78.24/10.66 (funcinfuncset) => 78.24/10.66 (( 78.24/10.66 (lamProp) => 78.24/10.66 (( 78.24/10.66 (lamp) => 78.24/10.66 (( 78.24/10.66 (lam2p) => 78.24/10.66 (( 78.24/10.66 (brelnall1) => 78.24/10.66 (( 78.24/10.66 (brelnall2) => 78.24/10.66 (( 78.24/10.66 (ex1E2) => 78.24/10.66 (( 78.24/10.66 (funcGraphProp1) => 78.24/10.66 (( 78.24/10.66 (funcGraphProp3) => 78.24/10.66 (( 78.24/10.66 (funcGraphProp2) => 78.24/10.66 (( 78.24/10.66 (funcextLem) => 78.24/10.66 (( 78.24/10.66 (funcGraphProp4) => 78.24/10.66 (( 78.24/10.66 (subbreln) => 78.24/10.66 (( 78.24/10.66 (eqbreln) => 78.24/10.66 (( 78.24/10.66 (funcext) => 78.24/10.66 (( 78.24/10.66 (funcext2) => 78.24/10.66 (( 78.24/10.66 (ap2apEq1) => 78.24/10.66 (( 78.24/10.66 (ap2apEq2) => 78.24/10.66 (( 78.24/10.66 (beta1) => 78.24/10.66 (( 78.24/10.66 (eta1) => 78.24/10.66 (( 78.24/10.66 (lam2lamEq) => 78.24/10.66 (( 78.24/10.66 (beta2) => 78.24/10.66 (( 78.24/10.66 (eta2) => 78.24/10.66 (( 78.24/10.66 (iffalseProp1) => 78.24/10.66 (( 78.24/10.66 (iffalseProp2) => 78.24/10.66 (( 78.24/10.66 (iftrueProp1) => 78.24/10.66 (( 78.24/10.66 (iftrueProp2) => 78.24/10.66 (( 78.24/10.66 (ifSingleton) => 78.24/10.66 (( 78.24/10.66 (ifp) => 78.24/10.66 (( 78.24/10.66 (theeq) => 78.24/10.66 (( 78.24/10.66 (iftrue) => 78.24/10.66 (( 78.24/10.66 (iffalse) => 78.24/10.66 (( 78.24/10.66 (iftrueorfalse) => 78.24/10.66 (( 78.24/10.66 (binintersectT_lem) => 78.24/10.66 (( 78.24/10.66 (binunionT_lem) => 78.24/10.66 (( 78.24/10.66 (powersetT_lem) => 78.24/10.66 (( 78.24/10.66 (setminusT_lem) => 78.24/10.66 (( 78.24/10.66 (complementT_lem) => 78.24/10.66 (( 78.24/10.66 (setextT) => 78.24/10.66 (( 78.24/10.66 (subsetTI) => 78.24/10.66 (( 78.24/10.66 (powersetTI1) => 78.24/10.66 (( 78.24/10.66 (powersetTE1) => 78.24/10.66 (( 78.24/10.66 (complementTI1) => 78.24/10.66 (( 78.24/10.66 (complementTE1) => 78.24/10.66 (( 78.24/10.66 (binintersectTELcontra) => 78.24/10.66 (( 78.24/10.66 (binintersectTERcontra) => 78.24/10.66 (( 78.24/10.66 (contrasubsetT) => 78.24/10.66 (( 78.24/10.66 (contrasubsetT1) => 78.24/10.66 (( 78.24/10.66 (contrasubsetT2) => 78.24/10.66 (( 78.24/10.66 (contrasubsetT3) => 78.24/10.66 (( 78.24/10.66 (doubleComplementI1) => 78.24/10.66 (( 78.24/10.66 (doubleComplementE1) => 78.24/10.66 (( 78.24/10.66 (doubleComplementSub1) => 78.24/10.66 (( 78.24/10.66 (doubleComplementSub2) => 78.24/10.66 (( 78.24/10.66 (doubleComplementEq) => 78.24/10.66 (( 78.24/10.66 (complementTnotintersectT) => 78.24/10.66 (( 78.24/10.66 (complementImpComplementIntersect) => 78.24/10.66 (( 78.24/10.66 (complementSubsetComplementIntersect) => 78.24/10.66 (( 78.24/10.66 (complementInPowersetComplementIntersect) => 78.24/10.66 (( 78.24/10.66 (contraSubsetComplement) => 78.24/10.66 (( 78.24/10.66 (complementTcontraSubset) => 78.24/10.66 (( 78.24/10.66 (binunionTILcontra) => 78.24/10.66 (( 78.24/10.66 (binunionTIRcontra) => 78.24/10.66 (( 78.24/10.66 (inIntersectImpInUnion) => 78.24/10.66 (( 78.24/10.66 (inIntersectImpInUnion2) => 78.24/10.66 (( 78.24/10.66 (inIntersectImpInIntersectUnions) => 78.24/10.66 (( 78.24/10.66 (intersectInPowersetIntersectUnions) => 78.24/10.66 (( 78.24/10.66 (inComplementUnionImpNotIn1) => 78.24/10.66 (( 78.24/10.66 (inComplementUnionImpInComplement1) => 78.24/10.66 (( 78.24/10.66 (binunionTE) => 78.24/10.66 (( 78.24/10.66 (binunionTEcontra) => 78.24/10.66 (( 78.24/10.66 (demorgan2a1) => 78.24/10.66 (( 78.24/10.66 (complementUnionInPowersetComplement) => 78.24/10.66 (( 78.24/10.66 (demorgan2a2) => 78.24/10.66 (( 78.24/10.66 (demorgan1a) => 78.24/10.66 (( 78.24/10.66 (demorgan1b) => 78.24/10.66 (( 78.24/10.66 (demorgan1) => 78.24/10.66 (( 78.24/10.66 (demorgan2a) => 78.24/10.66 (( 78.24/10.66 (demorgan2b2) => 78.24/10.66 (( 78.24/10.66 (demorgan2b) => 78.24/10.66 (( 78.24/10.66 (demorgan2) => 78.24/10.66 (( 78.24/10.66 (woz13rule0) => 78.24/10.66 (( 78.24/10.66 (woz13rule1) => 78.24/10.66 (( 78.24/10.66 (woz13rule2) => 78.24/10.66 (( 78.24/10.66 (woz13rule3) => 78.24/10.66 (( 78.24/10.66 (woz13rule4) => 78.24/10.66 (( 78.24/10.66 (woz1_1) => 78.24/10.66 (( 78.24/10.66 (woz1_2) => 78.24/10.66 (( 78.24/10.66 (woz1_3) => 78.24/10.66 (( 78.24/10.66 (woz1_4) => 78.24/10.66 (( 78.24/10.66 (woz1_5) => 78.24/10.66 (( 78.24/10.66 (breln1all2) => 78.24/10.66 (( 78.24/10.66 (breln1SetBreln1) => 78.24/10.66 (( 78.24/10.66 (choice2fnsingleton) => 78.24/10.66 (( 78.24/10.66 (setOfPairsIsBReln1) => 78.24/10.66 (( 78.24/10.66 (breln1all1) => 78.24/10.66 (( 78.24/10.66 (subbreln1) => 78.24/10.66 (( 78.24/10.66 (eqbreln1) => 78.24/10.66 (( 78.24/10.66 (breln1invprop) => 78.24/10.66 (( 78.24/10.66 (breln1invI) => 78.24/10.66 (( 78.24/10.66 (breln1invE) => 78.24/10.66 (( 78.24/10.66 (breln1compprop) => 78.24/10.66 (( 78.24/10.66 (breln1compI) => 78.24/10.66 (( 78.24/10.66 (breln1compE) => 78.24/10.66 (( 78.24/10.66 (breln1compEex) => 78.24/10.66 (( 78.24/10.66 (breln1unionprop) => 78.24/10.66 (( 78.24/10.66 (breln1unionIL) => 78.24/10.66 (( 78.24/10.66 (breln1unionIR) => 78.24/10.66 (( 78.24/10.66 (breln1unionI) => 78.24/10.66 (( 78.24/10.66 (breln1unionE) => 78.24/10.66 (( 78.24/10.66 (breln1unionEcases) => 78.24/10.66 (( 78.24/10.66 (breln1unionCommutes) => 78.24/10.66 (( 78.24/10.66 (woz2Ex) => 78.24/10.66 (( 78.24/10.66 (woz2W) => 78.24/10.66 (( 78.24/10.66 (woz2A) => 78.24/10.66 (( 78.24/10.66 (woz2B) => 78.24/10.66 (( 78.24/10.66 (image1Ex) => 78.24/10.66 (( 78.24/10.66 (image1Ex1) => 78.24/10.66 (( 78.24/10.66 (image1Equiv) => 78.24/10.66 (( 78.24/10.66 (image1E) => 78.24/10.66 (( 78.24/10.66 (image1I) => 78.24/10.66 (( 78.24/10.66 (injFuncInInjFuncSet) => 78.24/10.66 (( 78.24/10.66 (injFuncSetFuncIn) => 78.24/10.66 (( 78.24/10.66 (injFuncSetFuncInj) => 78.24/10.66 (( 78.24/10.66 (surjFuncSetFuncIn) => 78.24/10.66 (( 78.24/10.66 (surjFuncSetFuncSurj) => 78.24/10.66 (( 78.24/10.66 (leftInvIsSurj) => 78.24/10.66 (( 78.24/10.66 (surjCantorThm) => 78.24/10.66 (( 78.24/10.66 (foundation2) => 78.24/10.66 (( 78.24/10.66 (notinself) => 78.24/10.66 (( 78.24/10.66 (notinself2) => 78.24/10.66 (( 78.24/10.66 (omegaSp) => 78.24/10.66 (( 78.24/10.66 (omegaSclos) => 78.24/10.66 (( 78.24/10.66 (peano0notS) => 78.24/10.66 (( 78.24/10.66 (peanoSinj) => 78.24/10.66 (( 78.24/10.66 (transitivesetOp1) => 78.24/10.66 (( 78.24/10.66 (binintTransitive) => 78.24/10.66 (( 78.24/10.66 (transitivesetOp2) => 78.24/10.66 (( 78.24/10.66 (setunionTransitive) => 78.24/10.66 (( 78.24/10.66 (ordinalMinLem1) => 78.24/10.66 (( 78.24/10.66 (!!) @ ( 78.24/10.66 ^[Y0 : $i]: 78.24/10.66 (( 78.24/10.66 (ordinal @ 78.24/10.66 Y0) => 78.24/10.66 (( 78.24/10.66 (!!) @ ( 78.24/10.66 ^[Y1 : $i]: 78.24/10.66 (( 78.24/10.66 (!!) @ ( 78.24/10.66 ^[Y2 : $i]: 78.24/10.66 (( 78.24/10.66 (in @ 78.24/10.66 Y2 @ 78.24/10.66 Y0) => 78.24/10.66 (( 78.24/10.66 (in @ 78.24/10.66 Y1 @ 78.24/10.66 Y2) => 78.24/10.66 (in @ 78.24/10.66 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 78.24/10.66 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl964])). 78.24/10.66 thf(zip_derived_cl978, plain, 78.24/10.66 (~ (((binintersectSubset2) => 78.24/10.66 (((binintersectSubset3) => 78.24/10.66 (((binintersectER) => 78.24/10.66 (((disjointsetsI1) => 78.24/10.66 (((binintersectRsub) => 78.24/10.66 (((binintersectSubset4) => 78.24/10.66 (((binintersectSubset1) => 78.24/10.66 (((bs114d) => 78.24/10.66 (((setminusI) => 78.24/10.66 (((setminusEL) => 78.24/10.66 (((setminusER) => 78.24/10.66 (((setminusSubset2) => 78.24/10.66 (((setminusERneg) => 78.24/10.66 (((setminusELneg) => 78.24/10.66 (((setminusILneg) => 78.24/10.66 (((setminusIRneg) => 78.24/10.66 (((setminusLsub) => 78.24/10.66 (((setminusSubset1) => 78.24/10.66 (((symdiffE) => 78.24/10.66 (((symdiffI1) => 78.24/10.66 (((symdiffI2) => 78.24/10.66 (((symdiffIneg1) => 78.24/10.66 (((symdiffIneg2) => 78.24/10.66 (((secondinupair) => 78.24/10.66 (((setukpairIL) => 78.24/10.66 (((setukpairIR) => 78.24/10.66 (((kpairiskpair) => 78.24/10.66 (((kpairp) => 78.24/10.66 (((singletonsubset) => 78.24/10.66 (((singletoninpowerset) => 78.24/10.66 (( 78.24/10.66 (singletoninpowunion) => 78.24/10.66 (( 78.24/10.66 (upairset2E) => 78.24/10.66 (( 78.24/10.66 (upairsubunion) => 78.24/10.66 (( 78.24/10.66 (upairinpowunion) => 78.24/10.66 (( 78.24/10.66 (ubforcartprodlem1) => 78.24/10.66 (( 78.24/10.66 (ubforcartprodlem2) => 78.24/10.66 (( 78.24/10.66 (ubforcartprodlem3) => 78.24/10.66 (( 78.24/10.66 (cartprodpairin) => 78.24/10.66 (( 78.24/10.66 (cartprodmempair1) => 78.24/10.66 (( 78.24/10.66 (cartprodmempair) => 78.24/10.66 (( 78.24/10.66 (setunionE2) => 78.24/10.66 (( 78.24/10.66 (setunionsingleton1) => 78.24/10.66 (( 78.24/10.66 (setunionsingleton2) => 78.24/10.66 (( 78.24/10.66 (setunionsingleton) => 78.24/10.66 (( 78.24/10.66 (singletonprop) => 78.24/10.66 (( 78.24/10.66 (ex1E1) => 78.24/10.66 (( 78.24/10.66 (ex1I) => 78.24/10.66 (( 78.24/10.66 (ex1I2) => 78.24/10.66 (( 78.24/10.66 (singletonsuniq) => 78.24/10.66 (( 78.24/10.66 (setukpairinjL1) => 78.24/10.66 (( 78.24/10.66 (kfstsingleton) => 78.24/10.66 (( 78.24/10.66 (theprop) => 78.24/10.66 (( 78.24/10.66 (kfstpairEq) => 78.24/10.66 (( 78.24/10.66 (cartprodfstin) => 78.24/10.66 (( 78.24/10.66 (setukpairinjL2) => 78.24/10.66 (( 78.24/10.66 (setukpairinjL) => 78.24/10.66 (( 78.24/10.66 (setukpairinjR11) => 78.24/10.66 (( 78.24/10.66 (setukpairinjR12) => 78.24/10.66 (( 78.24/10.66 (setukpairinjR1) => 78.24/10.66 (( 78.24/10.66 (upairequniteq) => 78.24/10.66 (( 78.24/10.66 (setukpairinjR2) => 78.24/10.66 (( 78.24/10.66 (setukpairinjR) => 78.24/10.66 (( 78.24/10.66 (ksndsingleton) => 78.24/10.66 (( 78.24/10.66 (ksndpairEq) => 78.24/10.66 (( 78.24/10.66 (kpairsurjEq) => 78.24/10.66 (( 78.24/10.66 (cartprodsndin) => 78.24/10.66 (( 78.24/10.66 (cartprodpairmemEL) => 78.24/10.66 (( 78.24/10.66 (cartprodpairmemER) => 78.24/10.66 (( 78.24/10.66 (cartprodmempaircEq) => 78.24/10.66 (( 78.24/10.66 (cartprodfstpairEq) => 78.24/10.66 (( 78.24/10.66 (cartprodsndpairEq) => 78.24/10.66 (( 78.24/10.66 (cartprodpairsurjEq) => 78.24/10.66 (( 78.24/10.66 (dpsetconstrI) => 78.24/10.66 (( 78.24/10.66 (dpsetconstrSub) => 78.24/10.66 (( 78.24/10.66 (setOfPairsIsBReln) => 78.24/10.66 (( 78.24/10.66 (dpsetconstrERa) => 78.24/10.66 (( 78.24/10.66 (dpsetconstrEL1) => 78.24/10.66 (( 78.24/10.66 (dpsetconstrEL2) => 78.24/10.66 (( 78.24/10.66 (dpsetconstrER) => 78.24/10.66 (( 78.24/10.66 (funcImageSingleton) => 78.24/10.66 (( 78.24/10.66 (apProp) => 78.24/10.66 (( 78.24/10.66 (app) => 78.24/10.66 (( 78.24/10.66 (infuncsetfunc) => 78.24/10.66 (( 78.24/10.66 (ap2p) => 78.24/10.66 (( 78.24/10.66 (funcinfuncset) => 78.24/10.66 (( 78.24/10.66 (lamProp) => 78.24/10.66 (( 78.24/10.66 (lamp) => 78.24/10.66 (( 78.24/10.66 (lam2p) => 78.24/10.66 (( 78.24/10.66 (brelnall1) => 78.24/10.66 (( 78.24/10.66 (brelnall2) => 78.24/10.66 (( 78.24/10.66 (ex1E2) => 78.24/10.66 (( 78.24/10.66 (funcGraphProp1) => 78.24/10.66 (( 78.24/10.66 (funcGraphProp3) => 78.24/10.66 (( 78.24/10.66 (funcGraphProp2) => 78.24/10.66 (( 78.24/10.66 (funcextLem) => 78.24/10.66 (( 78.24/10.66 (funcGraphProp4) => 78.24/10.66 (( 78.24/10.66 (subbreln) => 78.24/10.66 (( 78.24/10.66 (eqbreln) => 78.24/10.66 (( 78.24/10.66 (funcext) => 78.24/10.66 (( 78.24/10.66 (funcext2) => 78.24/10.66 (( 78.24/10.66 (ap2apEq1) => 78.24/10.66 (( 78.24/10.66 (ap2apEq2) => 78.24/10.66 (( 78.24/10.66 (beta1) => 78.24/10.66 (( 78.24/10.66 (eta1) => 78.24/10.66 (( 78.24/10.66 (lam2lamEq) => 78.24/10.66 (( 78.24/10.66 (beta2) => 78.24/10.66 (( 78.24/10.66 (eta2) => 78.24/10.66 (( 78.24/10.66 (iffalseProp1) => 78.24/10.66 (( 78.24/10.66 (iffalseProp2) => 78.24/10.66 (( 78.24/10.66 (iftrueProp1) => 78.24/10.66 (( 78.24/10.66 (iftrueProp2) => 78.24/10.66 (( 78.24/10.66 (ifSingleton) => 78.24/10.66 (( 78.24/10.66 (ifp) => 78.24/10.66 (( 78.24/10.66 (theeq) => 78.24/10.66 (( 78.24/10.66 (iftrue) => 78.24/10.66 (( 78.24/10.66 (iffalse) => 78.24/10.66 (( 78.24/10.66 (iftrueorfalse) => 78.24/10.66 (( 78.24/10.66 (binintersectT_lem) => 78.24/10.66 (( 78.24/10.66 (binunionT_lem) => 78.24/10.66 (( 78.24/10.66 (powersetT_lem) => 78.24/10.66 (( 78.24/10.66 (setminusT_lem) => 78.24/10.66 (( 78.24/10.66 (complementT_lem) => 78.24/10.66 (( 78.24/10.66 (setextT) => 78.24/10.66 (( 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(complementInPowersetComplementIntersect) => 78.24/10.66 (( 78.24/10.66 (contraSubsetComplement) => 78.24/10.66 (( 78.24/10.66 (complementTcontraSubset) => 78.24/10.66 (( 78.24/10.66 (binunionTILcontra) => 78.24/10.66 (( 78.24/10.66 (binunionTIRcontra) => 78.24/10.66 (( 78.24/10.66 (inIntersectImpInUnion) => 78.24/10.66 (( 78.24/10.66 (inIntersectImpInUnion2) => 78.24/10.66 (( 78.24/10.66 (inIntersectImpInIntersectUnions) => 78.24/10.66 (( 78.24/10.66 (intersectInPowersetIntersectUnions) => 78.24/10.66 (( 78.24/10.66 (inComplementUnionImpNotIn1) => 78.24/10.66 (( 78.24/10.66 (inComplementUnionImpInComplement1) => 78.24/10.66 (( 78.24/10.66 (binunionTE) => 78.24/10.66 (( 78.24/10.66 (binunionTEcontra) => 78.24/10.66 (( 78.24/10.66 (demorgan2a1) => 78.24/10.66 (( 78.24/10.66 (complementUnionInPowersetComplement) => 78.24/10.66 (( 78.24/10.66 (demorgan2a2) => 78.24/10.66 (( 78.24/10.66 (demorgan1a) => 78.24/10.66 (( 78.24/10.66 (demorgan1b) => 78.24/10.66 (( 78.24/10.66 (demorgan1) => 78.24/10.66 (( 78.24/10.66 (demorgan2a) => 78.24/10.66 (( 78.24/10.66 (demorgan2b2) => 78.24/10.66 (( 78.24/10.66 (demorgan2b) => 78.24/10.66 (( 78.24/10.66 (demorgan2) => 78.24/10.66 (( 78.24/10.66 (woz13rule0) => 78.24/10.66 (( 78.24/10.66 (woz13rule1) => 78.24/10.66 (( 78.24/10.66 (woz13rule2) => 78.24/10.66 (( 78.24/10.66 (woz13rule3) => 78.24/10.66 (( 78.24/10.66 (woz13rule4) => 78.24/10.66 (( 78.24/10.66 (woz1_1) => 78.24/10.66 (( 78.24/10.66 (woz1_2) => 78.24/10.66 (( 78.24/10.66 (woz1_3) => 78.24/10.66 (( 78.24/10.66 (woz1_4) => 78.24/10.66 (( 78.24/10.66 (woz1_5) => 78.24/10.66 (( 78.24/10.66 (breln1all2) => 78.24/10.66 (( 78.24/10.66 (breln1SetBreln1) => 78.24/10.66 (( 78.24/10.66 (choice2fnsingleton) => 78.24/10.66 (( 78.24/10.66 (setOfPairsIsBReln1) => 78.24/10.66 (( 78.24/10.66 (breln1all1) => 78.24/10.66 (( 78.24/10.66 (subbreln1) => 78.24/10.66 (( 78.24/10.66 (eqbreln1) => 78.24/10.66 (( 78.24/10.66 (breln1invprop) => 78.24/10.66 (( 78.24/10.66 (breln1invI) => 78.24/10.66 (( 78.24/10.66 (breln1invE) => 78.24/10.66 (( 78.24/10.66 (breln1compprop) => 78.24/10.66 (( 78.24/10.66 (breln1compI) => 78.24/10.66 (( 78.24/10.66 (breln1compE) => 78.24/10.66 (( 78.24/10.66 (breln1compEex) => 78.24/10.66 (( 78.24/10.66 (breln1unionprop) => 78.24/10.66 (( 78.24/10.66 (breln1unionIL) => 78.24/10.66 (( 78.24/10.66 (breln1unionIR) => 78.24/10.66 (( 78.24/10.66 (breln1unionI) => 78.24/10.66 (( 78.24/10.66 (breln1unionE) => 78.24/10.66 (( 78.24/10.66 (breln1unionEcases) => 78.24/10.66 (( 78.24/10.66 (breln1unionCommutes) => 78.24/10.66 (( 78.24/10.66 (woz2Ex) => 78.24/10.66 (( 78.24/10.66 (woz2W) => 78.24/10.66 (( 78.24/10.66 (woz2A) => 78.24/10.66 (( 78.24/10.66 (woz2B) => 78.24/10.66 (( 78.24/10.66 (image1Ex) => 78.24/10.66 (( 78.24/10.66 (image1Ex1) => 78.24/10.66 (( 78.24/10.66 (image1Equiv) => 78.24/10.66 (( 78.24/10.66 (image1E) => 78.24/10.66 (( 78.24/10.66 (image1I) => 78.24/10.66 (( 78.24/10.66 (injFuncInInjFuncSet) => 78.24/10.66 (( 78.24/10.66 (injFuncSetFuncIn) => 78.24/10.66 (( 78.24/10.66 (injFuncSetFuncInj) => 78.24/10.66 (( 78.24/10.66 (surjFuncSetFuncIn) => 78.24/10.66 (( 78.24/10.66 (surjFuncSetFuncSurj) => 78.24/10.66 (( 78.24/10.66 (leftInvIsSurj) => 78.24/10.66 (( 78.24/10.66 (surjCantorThm) => 78.24/10.66 (( 78.24/10.66 (foundation2) => 78.24/10.66 (( 78.24/10.66 (notinself) => 78.24/10.66 (( 78.24/10.66 (notinself2) => 78.24/10.66 (( 78.24/10.66 (omegaSp) => 78.24/10.66 (( 78.24/10.66 (omegaSclos) => 78.24/10.66 (( 78.24/10.66 (peano0notS) => 78.24/10.66 (( 78.24/10.66 (peanoSinj) => 78.24/10.66 (( 78.24/10.66 (transitivesetOp1) => 78.24/10.66 (( 78.24/10.66 (binintTransitive) => 78.24/10.66 (( 78.24/10.66 (transitivesetOp2) => 78.24/10.66 (( 78.24/10.66 (setunionTransitive) => 78.24/10.66 (( 78.24/10.66 (ordinalMinLem1) => 78.24/10.66 (( 78.24/10.66 (!!) @ ( 78.24/10.66 ^[Y0 : $i]: 78.24/10.66 (( 78.24/10.66 (ordinal @ 78.24/10.66 Y0) => 78.24/10.66 (( 78.24/10.66 (!!) @ ( 78.24/10.66 ^[Y1 : $i]: 78.24/10.66 (( 78.24/10.66 (!!) @ ( 78.24/10.66 ^[Y2 : $i]: 78.24/10.66 (( 78.24/10.66 (in @ 78.24/10.66 Y2 @ 78.24/10.66 Y0) => 78.24/10.66 (( 78.24/10.66 (in @ 78.24/10.66 Y1 @ 78.24/10.66 Y2) => 78.24/10.66 (in @ 78.24/10.66 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 78.24/10.66 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl971])). 78.24/10.66 thf(zip_derived_cl985, plain, 78.24/10.66 (~ (((binintersectSubset3) => 78.24/10.66 (((binintersectER) => 78.24/10.66 (((disjointsetsI1) => 78.24/10.66 (((binintersectRsub) => 78.24/10.66 (((binintersectSubset4) => 78.24/10.66 (((binintersectSubset1) => 78.24/10.66 (((bs114d) => 78.24/10.66 (((setminusI) => 78.24/10.66 (((setminusEL) => 78.24/10.66 (((setminusER) => 78.24/10.66 (((setminusSubset2) => 78.24/10.66 (((setminusERneg) => 78.24/10.66 (((setminusELneg) => 78.24/10.66 (((setminusILneg) => 78.24/10.66 (((setminusIRneg) => 78.24/10.66 (((setminusLsub) => 78.24/10.66 (((setminusSubset1) => 78.24/10.66 (((symdiffE) => 78.24/10.66 (((symdiffI1) => 78.24/10.66 (((symdiffI2) => 78.24/10.66 (((symdiffIneg1) => 78.24/10.66 (((symdiffIneg2) => 78.24/10.66 (((secondinupair) => 78.24/10.66 (((setukpairIL) => 78.24/10.66 (((setukpairIR) => 78.24/10.66 (((kpairiskpair) => 78.24/10.66 (((kpairp) => 78.24/10.66 (((singletonsubset) => 78.24/10.66 (((singletoninpowerset) => 78.24/10.66 (((singletoninpowunion) => 78.24/10.66 (( 78.24/10.66 (upairset2E) => 78.24/10.66 (( 78.24/10.66 (upairsubunion) => 78.24/10.66 (( 78.24/10.66 (upairinpowunion) => 78.24/10.66 (( 78.24/10.66 (ubforcartprodlem1) => 78.24/10.66 (( 78.24/10.66 (ubforcartprodlem2) => 78.24/10.66 (( 78.24/10.66 (ubforcartprodlem3) => 78.24/10.66 (( 78.24/10.66 (cartprodpairin) => 78.24/10.66 (( 78.24/10.66 (cartprodmempair1) => 78.24/10.66 (( 78.24/10.66 (cartprodmempair) => 78.24/10.66 (( 78.24/10.66 (setunionE2) => 78.24/10.66 (( 78.24/10.66 (setunionsingleton1) => 78.24/10.66 (( 78.24/10.66 (setunionsingleton2) => 78.24/10.66 (( 78.24/10.66 (setunionsingleton) => 78.24/10.66 (( 78.24/10.66 (singletonprop) => 78.24/10.66 (( 78.24/10.66 (ex1E1) => 78.24/10.66 (( 78.24/10.66 (ex1I) => 78.24/10.66 (( 78.24/10.66 (ex1I2) => 78.24/10.66 (( 78.24/10.66 (singletonsuniq) => 78.24/10.66 (( 78.24/10.66 (setukpairinjL1) => 78.24/10.66 (( 78.24/10.66 (kfstsingleton) => 78.24/10.66 (( 78.24/10.66 (theprop) => 78.24/10.66 (( 78.24/10.66 (kfstpairEq) => 78.24/10.66 (( 78.24/10.66 (cartprodfstin) => 78.24/10.66 (( 78.24/10.66 (setukpairinjL2) => 78.24/10.66 (( 78.24/10.66 (setukpairinjL) => 78.24/10.66 (( 78.24/10.66 (setukpairinjR11) => 78.24/10.66 (( 78.24/10.66 (setukpairinjR12) => 78.24/10.66 (( 78.24/10.66 (setukpairinjR1) => 78.24/10.66 (( 78.24/10.66 (upairequniteq) => 78.24/10.66 (( 78.24/10.66 (setukpairinjR2) => 78.24/10.66 (( 78.24/10.66 (setukpairinjR) => 78.24/10.66 (( 78.24/10.66 (ksndsingleton) => 78.24/10.66 (( 78.24/10.66 (ksndpairEq) => 78.24/10.66 (( 78.24/10.66 (kpairsurjEq) => 78.24/10.66 (( 78.24/10.66 (cartprodsndin) => 78.24/10.66 (( 78.24/10.66 (cartprodpairmemEL) => 78.24/10.66 (( 78.24/10.66 (cartprodpairmemER) => 78.24/10.66 (( 78.24/10.66 (cartprodmempaircEq) => 78.24/10.66 (( 78.24/10.66 (cartprodfstpairEq) => 78.24/10.66 (( 78.24/10.66 (cartprodsndpairEq) => 78.24/10.66 (( 78.24/10.66 (cartprodpairsurjEq) => 78.24/10.66 (( 78.24/10.66 (dpsetconstrI) => 78.24/10.66 (( 78.24/10.66 (dpsetconstrSub) => 78.24/10.66 (( 78.24/10.66 (setOfPairsIsBReln) => 78.24/10.66 (( 78.24/10.66 (dpsetconstrERa) => 78.24/10.66 (( 78.24/10.66 (dpsetconstrEL1) => 78.24/10.66 (( 78.24/10.66 (dpsetconstrEL2) => 78.24/10.66 (( 78.24/10.66 (dpsetconstrER) => 78.24/10.66 (( 78.24/10.66 (funcImageSingleton) => 78.24/10.66 (( 78.24/10.66 (apProp) => 78.24/10.66 (( 78.24/10.66 (app) => 78.24/10.66 (( 78.24/10.66 (infuncsetfunc) => 78.24/10.66 (( 78.24/10.66 (ap2p) => 78.24/10.66 (( 78.24/10.66 (funcinfuncset) => 78.24/10.66 (( 78.24/10.66 (lamProp) => 78.24/10.66 (( 78.24/10.66 (lamp) => 78.24/10.66 (( 78.24/10.66 (lam2p) => 78.24/10.66 (( 78.24/10.66 (brelnall1) => 78.24/10.66 (( 78.24/10.66 (brelnall2) => 78.24/10.66 (( 78.24/10.66 (ex1E2) => 78.24/10.66 (( 78.24/10.66 (funcGraphProp1) => 78.24/10.66 (( 78.24/10.66 (funcGraphProp3) => 78.24/10.66 (( 78.24/10.66 (funcGraphProp2) => 78.24/10.66 (( 78.24/10.66 (funcextLem) => 78.24/10.66 (( 78.24/10.66 (funcGraphProp4) => 78.24/10.66 (( 78.24/10.66 (subbreln) => 78.24/10.66 (( 78.24/10.66 (eqbreln) => 78.24/10.66 (( 78.24/10.66 (funcext) => 78.24/10.66 (( 78.24/10.66 (funcext2) => 78.24/10.66 (( 78.24/10.66 (ap2apEq1) => 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(demorgan2b2) => 78.24/10.66 (( 78.24/10.66 (demorgan2b) => 78.24/10.66 (( 78.24/10.66 (demorgan2) => 78.24/10.66 (( 78.24/10.66 (woz13rule0) => 78.24/10.66 (( 78.24/10.66 (woz13rule1) => 78.24/10.66 (( 78.24/10.66 (woz13rule2) => 78.24/10.66 (( 78.24/10.66 (woz13rule3) => 78.24/10.66 (( 78.24/10.66 (woz13rule4) => 78.24/10.66 (( 78.24/10.66 (woz1_1) => 78.24/10.66 (( 78.24/10.66 (woz1_2) => 78.24/10.66 (( 78.24/10.66 (woz1_3) => 78.24/10.66 (( 78.24/10.66 (woz1_4) => 78.24/10.66 (( 78.24/10.66 (woz1_5) => 78.24/10.66 (( 78.24/10.66 (breln1all2) => 78.24/10.66 (( 78.24/10.66 (breln1SetBreln1) => 78.24/10.66 (( 78.24/10.66 (choice2fnsingleton) => 78.24/10.66 (( 78.24/10.66 (setOfPairsIsBReln1) => 78.24/10.66 (( 78.24/10.66 (breln1all1) => 78.24/10.66 (( 78.24/10.66 (subbreln1) => 78.24/10.66 (( 78.24/10.66 (eqbreln1) => 78.24/10.66 (( 78.24/10.66 (breln1invprop) => 78.24/10.66 (( 78.24/10.66 (breln1invI) => 78.24/10.66 (( 78.24/10.66 (breln1invE) => 78.24/10.66 (( 78.24/10.66 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78.24/10.66 (( 78.24/10.66 (surjFuncSetFuncIn) => 78.24/10.66 (( 78.24/10.66 (surjFuncSetFuncSurj) => 78.24/10.66 (( 78.24/10.66 (leftInvIsSurj) => 78.24/10.66 (( 78.24/10.66 (surjCantorThm) => 78.24/10.66 (( 78.24/10.66 (foundation2) => 78.24/10.66 (( 78.24/10.66 (notinself) => 78.24/10.66 (( 78.24/10.66 (notinself2) => 78.24/10.66 (( 78.24/10.66 (omegaSp) => 78.24/10.66 (( 78.24/10.66 (omegaSclos) => 78.24/10.66 (( 78.24/10.66 (peano0notS) => 78.24/10.66 (( 78.24/10.66 (peanoSinj) => 78.24/10.66 (( 78.24/10.66 (transitivesetOp1) => 78.24/10.66 (( 78.24/10.66 (binintTransitive) => 78.24/10.66 (( 78.24/10.66 (transitivesetOp2) => 78.24/10.66 (( 78.24/10.66 (setunionTransitive) => 78.24/10.66 (( 78.24/10.66 (ordinalMinLem1) => 78.24/10.66 (( 78.24/10.66 (!!) @ ( 78.24/10.66 ^[Y0 : $i]: 78.24/10.66 (( 78.24/10.66 (ordinal @ 78.24/10.66 Y0) => 78.24/10.66 (( 78.24/10.66 (!!) @ ( 78.24/10.66 ^[Y1 : $i]: 78.24/10.66 (( 78.24/10.66 (!!) @ ( 78.24/10.66 ^[Y2 : $i]: 78.24/10.66 (( 78.24/10.66 (in @ 78.24/10.66 Y2 @ 78.24/10.66 Y0) => 78.24/10.66 (( 78.24/10.66 (in @ 78.24/10.66 Y1 @ 78.24/10.66 Y2) => 78.24/10.66 (in @ 78.24/10.66 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 78.24/10.66 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl978])). 78.24/10.66 thf(zip_derived_cl994, plain, 78.24/10.66 (~ (((binintersectER) => 78.24/10.66 (((disjointsetsI1) => 78.24/10.66 (((binintersectRsub) => 78.24/10.66 (((binintersectSubset4) => 78.24/10.66 (((binintersectSubset1) => 78.24/10.66 (((bs114d) => 78.24/10.66 (((setminusI) => 78.24/10.66 (((setminusEL) => 78.24/10.66 (((setminusER) => 78.24/10.66 (((setminusSubset2) => 78.24/10.66 (((setminusERneg) => 78.24/10.66 (((setminusELneg) => 78.24/10.66 (((setminusILneg) => 78.24/10.66 (((setminusIRneg) => 78.24/10.66 (((setminusLsub) => 78.24/10.66 (((setminusSubset1) => 78.24/10.66 (((symdiffE) => 78.24/10.66 (((symdiffI1) => 78.24/10.66 (((symdiffI2) => 78.24/10.66 (((symdiffIneg1) => 78.24/10.66 (((symdiffIneg2) => 78.24/10.66 (((secondinupair) => 78.24/10.66 (((setukpairIL) => 78.24/10.66 (((setukpairIR) => 78.24/10.66 (((kpairiskpair) => 78.24/10.66 (((kpairp) => 78.24/10.66 (((singletonsubset) => 78.24/10.66 (((singletoninpowerset) => 78.24/10.66 (((singletoninpowunion) => 78.24/10.66 (((upairset2E) => 78.24/10.66 (( 78.24/10.66 (upairsubunion) => 78.24/10.66 (( 78.24/10.66 (upairinpowunion) => 78.24/10.66 (( 78.24/10.66 (ubforcartprodlem1) => 78.24/10.66 (( 78.24/10.66 (ubforcartprodlem2) => 78.24/10.66 (( 78.24/10.66 (ubforcartprodlem3) => 78.24/10.66 (( 78.24/10.66 (cartprodpairin) => 78.24/10.66 (( 78.24/10.66 (cartprodmempair1) => 78.24/10.66 (( 78.24/10.66 (cartprodmempair) => 78.24/10.66 (( 78.24/10.66 (setunionE2) => 78.24/10.66 (( 78.24/10.66 (setunionsingleton1) => 78.24/10.66 (( 78.24/10.66 (setunionsingleton2) => 78.24/10.66 (( 78.24/10.66 (setunionsingleton) => 78.24/10.66 (( 78.24/10.66 (singletonprop) => 78.24/10.66 (( 78.24/10.66 (ex1E1) => 78.24/10.66 (( 78.24/10.66 (ex1I) => 78.24/10.66 (( 78.24/10.66 (ex1I2) => 78.24/10.66 (( 78.24/10.66 (singletonsuniq) => 78.24/10.66 (( 78.24/10.66 (setukpairinjL1) => 78.24/10.66 (( 78.24/10.66 (kfstsingleton) => 78.24/10.66 (( 78.24/10.66 (theprop) => 78.24/10.66 (( 78.24/10.66 (kfstpairEq) => 78.24/10.66 (( 78.24/10.66 (cartprodfstin) => 78.24/10.66 (( 78.24/10.66 (setukpairinjL2) => 78.24/10.66 (( 78.24/10.66 (setukpairinjL) => 78.24/10.66 (( 78.24/10.66 (setukpairinjR11) => 78.24/10.66 (( 78.24/10.66 (setukpairinjR12) => 78.24/10.66 (( 78.24/10.66 (setukpairinjR1) => 78.24/10.66 (( 78.24/10.66 (upairequniteq) => 78.24/10.66 (( 78.24/10.66 (setukpairinjR2) => 78.24/10.66 (( 78.24/10.66 (setukpairinjR) => 78.24/10.66 (( 78.24/10.66 (ksndsingleton) => 78.24/10.66 (( 78.24/10.66 (ksndpairEq) => 78.24/10.66 (( 78.24/10.66 (kpairsurjEq) => 78.24/10.66 (( 78.24/10.66 (cartprodsndin) => 78.24/10.66 (( 78.24/10.66 (cartprodpairmemEL) => 78.24/10.66 (( 78.24/10.66 (cartprodpairmemER) => 78.24/10.66 (( 78.24/10.66 (cartprodmempaircEq) => 78.24/10.66 (( 78.24/10.66 (cartprodfstpairEq) => 78.24/10.66 (( 78.24/10.66 (cartprodsndpairEq) => 78.24/10.66 (( 78.24/10.66 (cartprodpairsurjEq) => 78.24/10.66 (( 78.24/10.66 (dpsetconstrI) => 78.24/10.66 (( 78.24/10.66 (dpsetconstrSub) => 78.24/10.66 (( 78.24/10.66 (setOfPairsIsBReln) => 78.24/10.66 (( 78.24/10.66 (dpsetconstrERa) => 78.24/10.66 (( 78.24/10.66 (dpsetconstrEL1) => 78.24/10.66 (( 78.24/10.66 (dpsetconstrEL2) => 78.24/10.66 (( 78.24/10.66 (dpsetconstrER) => 78.24/10.66 (( 78.24/10.66 (funcImageSingleton) => 78.24/10.66 (( 78.24/10.66 (apProp) => 78.24/10.66 (( 78.24/10.66 (app) => 78.24/10.66 (( 78.24/10.66 (infuncsetfunc) => 78.24/10.66 (( 78.24/10.66 (ap2p) => 78.24/10.66 (( 78.24/10.66 (funcinfuncset) => 78.24/10.66 (( 78.24/10.66 (lamProp) => 78.24/10.66 (( 78.24/10.66 (lamp) => 78.24/10.66 (( 78.24/10.66 (lam2p) => 78.24/10.66 (( 78.24/10.66 (brelnall1) => 78.24/10.66 (( 78.24/10.66 (brelnall2) => 78.24/10.66 (( 78.24/10.66 (ex1E2) => 78.24/10.66 (( 78.24/10.66 (funcGraphProp1) => 78.24/10.66 (( 78.24/10.66 (funcGraphProp3) => 78.24/10.66 (( 78.24/10.66 (funcGraphProp2) => 78.24/10.66 (( 78.24/10.66 (funcextLem) => 78.24/10.66 (( 78.24/10.66 (funcGraphProp4) => 78.24/10.66 (( 78.24/10.66 (subbreln) => 78.24/10.66 (( 78.24/10.66 (eqbreln) => 78.24/10.66 (( 78.24/10.66 (funcext) => 78.24/10.66 (( 78.24/10.66 (funcext2) => 78.24/10.66 (( 78.24/10.66 (ap2apEq1) => 78.24/10.66 (( 78.24/10.66 (ap2apEq2) => 78.24/10.66 (( 78.24/10.66 (beta1) => 78.24/10.66 (( 78.24/10.66 (eta1) => 78.24/10.66 (( 78.24/10.66 (lam2lamEq) => 78.24/10.66 (( 78.24/10.66 (beta2) => 78.24/10.66 (( 78.24/10.66 (eta2) => 78.24/10.66 (( 78.24/10.66 (iffalseProp1) => 78.24/10.66 (( 78.24/10.66 (iffalseProp2) => 78.24/10.66 (( 78.24/10.66 (iftrueProp1) => 78.24/10.66 (( 78.24/10.66 (iftrueProp2) => 78.24/10.66 (( 78.24/10.66 (ifSingleton) => 78.24/10.66 (( 78.24/10.66 (ifp) => 78.24/10.66 (( 78.24/10.66 (theeq) => 78.24/10.66 (( 78.24/10.66 (iftrue) => 78.24/10.66 (( 78.24/10.66 (iffalse) => 78.24/10.66 (( 78.24/10.66 (iftrueorfalse) => 78.24/10.66 (( 78.24/10.66 (binintersectT_lem) => 78.24/10.66 (( 78.24/10.66 (binunionT_lem) => 78.24/10.66 (( 78.24/10.66 (powersetT_lem) => 78.24/10.66 (( 78.24/10.66 (setminusT_lem) => 78.24/10.66 (( 78.24/10.66 (complementT_lem) => 78.24/10.66 (( 78.24/10.66 (setextT) => 78.24/10.66 (( 78.24/10.66 (subsetTI) => 78.24/10.66 (( 78.24/10.66 (powersetTI1) => 78.24/10.66 (( 78.24/10.66 (powersetTE1) => 78.24/10.66 (( 78.24/10.66 (complementTI1) => 78.24/10.66 (( 78.24/10.66 (complementTE1) => 78.24/10.66 (( 78.24/10.66 (binintersectTELcontra) => 78.24/10.66 (( 78.24/10.66 (binintersectTERcontra) => 78.24/10.66 (( 78.24/10.66 (contrasubsetT) => 78.24/10.66 (( 78.24/10.66 (contrasubsetT1) => 78.24/10.66 (( 78.24/10.66 (contrasubsetT2) => 78.24/10.66 (( 78.24/10.66 (contrasubsetT3) => 78.24/10.66 (( 78.24/10.66 (doubleComplementI1) => 78.24/10.66 (( 78.24/10.66 (doubleComplementE1) => 78.24/10.66 (( 78.24/10.66 (doubleComplementSub1) => 78.24/10.66 (( 78.24/10.66 (doubleComplementSub2) => 78.24/10.66 (( 78.24/10.66 (doubleComplementEq) => 78.24/10.66 (( 78.24/10.66 (complementTnotintersectT) => 78.24/10.66 (( 78.24/10.66 (complementImpComplementIntersect) => 78.24/10.66 (( 78.24/10.66 (complementSubsetComplementIntersect) => 78.24/10.66 (( 78.24/10.66 (complementInPowersetComplementIntersect) => 78.24/10.66 (( 78.24/10.66 (contraSubsetComplement) => 78.24/10.66 (( 78.24/10.66 (complementTcontraSubset) => 78.24/10.66 (( 78.24/10.66 (binunionTILcontra) => 78.24/10.66 (( 78.24/10.66 (binunionTIRcontra) => 78.24/10.66 (( 78.24/10.66 (inIntersectImpInUnion) => 78.24/10.66 (( 78.24/10.66 (inIntersectImpInUnion2) => 78.24/10.66 (( 78.24/10.66 (inIntersectImpInIntersectUnions) => 78.24/10.66 (( 78.24/10.66 (intersectInPowersetIntersectUnions) => 78.24/10.66 (( 78.24/10.66 (inComplementUnionImpNotIn1) => 78.24/10.66 (( 78.24/10.66 (inComplementUnionImpInComplement1) => 78.24/10.66 (( 78.24/10.66 (binunionTE) => 78.24/10.66 (( 78.24/10.66 (binunionTEcontra) => 78.24/10.66 (( 78.24/10.66 (demorgan2a1) => 78.24/10.66 (( 78.24/10.66 (complementUnionInPowersetComplement) => 78.24/10.66 (( 78.24/10.66 (demorgan2a2) => 78.24/10.66 (( 78.24/10.66 (demorgan1a) => 78.24/10.66 (( 78.24/10.66 (demorgan1b) => 78.24/10.66 (( 78.24/10.66 (demorgan1) => 78.24/10.66 (( 78.24/10.66 (demorgan2a) => 78.24/10.66 (( 78.24/10.66 (demorgan2b2) => 78.24/10.66 (( 78.24/10.66 (demorgan2b) => 78.24/10.66 (( 78.24/10.66 (demorgan2) => 78.24/10.66 (( 78.24/10.66 (woz13rule0) => 78.24/10.66 (( 78.24/10.66 (woz13rule1) => 78.24/10.66 (( 78.24/10.66 (woz13rule2) => 78.24/10.66 (( 78.24/10.66 (woz13rule3) => 78.24/10.66 (( 78.24/10.66 (woz13rule4) => 78.24/10.66 (( 78.24/10.66 (woz1_1) => 78.24/10.66 (( 78.24/10.66 (woz1_2) => 78.24/10.66 (( 78.24/10.66 (woz1_3) => 78.24/10.66 (( 78.24/10.66 (woz1_4) => 78.24/10.66 (( 78.24/10.66 (woz1_5) => 78.24/10.66 (( 78.24/10.66 (breln1all2) => 78.24/10.66 (( 78.24/10.66 (breln1SetBreln1) => 78.24/10.66 (( 78.24/10.66 (choice2fnsingleton) => 78.24/10.66 (( 78.24/10.66 (setOfPairsIsBReln1) => 78.24/10.66 (( 78.24/10.66 (breln1all1) => 78.24/10.66 (( 78.24/10.66 (subbreln1) => 78.24/10.66 (( 78.24/10.66 (eqbreln1) => 78.24/10.66 (( 78.24/10.66 (breln1invprop) => 78.24/10.66 (( 78.24/10.66 (breln1invI) => 78.24/10.66 (( 78.24/10.66 (breln1invE) => 78.24/10.66 (( 78.24/10.66 (breln1compprop) => 78.24/10.66 (( 78.24/10.66 (breln1compI) => 78.24/10.66 (( 78.24/10.66 (breln1compE) => 78.24/10.66 (( 78.24/10.66 (breln1compEex) => 78.24/10.66 (( 78.24/10.66 (breln1unionprop) => 78.24/10.66 (( 78.24/10.66 (breln1unionIL) => 78.24/10.66 (( 78.24/10.66 (breln1unionIR) => 78.24/10.66 (( 78.24/10.66 (breln1unionI) => 78.24/10.66 (( 78.24/10.66 (breln1unionE) => 78.24/10.66 (( 78.24/10.66 (breln1unionEcases) => 78.24/10.66 (( 78.24/10.66 (breln1unionCommutes) => 78.24/10.66 (( 78.24/10.66 (woz2Ex) => 78.24/10.66 (( 78.24/10.66 (woz2W) => 78.24/10.66 (( 78.24/10.66 (woz2A) => 78.24/10.66 (( 78.24/10.66 (woz2B) => 78.24/10.66 (( 78.24/10.66 (image1Ex) => 78.24/10.66 (( 78.24/10.66 (image1Ex1) => 78.24/10.66 (( 78.24/10.66 (image1Equiv) => 78.24/10.66 (( 78.24/10.66 (image1E) => 78.24/10.66 (( 78.24/10.66 (image1I) => 78.24/10.66 (( 78.24/10.66 (injFuncInInjFuncSet) => 78.24/10.66 (( 78.24/10.66 (injFuncSetFuncIn) => 78.24/10.66 (( 78.24/10.66 (injFuncSetFuncInj) => 78.24/10.66 (( 78.24/10.66 (surjFuncSetFuncIn) => 78.24/10.66 (( 78.24/10.66 (surjFuncSetFuncSurj) => 78.24/10.66 (( 78.24/10.66 (leftInvIsSurj) => 78.24/10.66 (( 78.24/10.66 (surjCantorThm) => 78.24/10.66 (( 78.24/10.66 (foundation2) => 78.24/10.66 (( 78.24/10.66 (notinself) => 78.24/10.66 (( 78.24/10.66 (notinself2) => 78.24/10.66 (( 78.24/10.66 (omegaSp) => 78.24/10.66 (( 78.24/10.66 (omegaSclos) => 78.24/10.66 (( 78.24/10.66 (peano0notS) => 78.24/10.66 (( 78.24/10.66 (peanoSinj) => 78.24/10.66 (( 78.24/10.66 (transitivesetOp1) => 78.24/10.66 (( 78.24/10.66 (binintTransitive) => 78.24/10.66 (( 78.24/10.66 (transitivesetOp2) => 78.24/10.66 (( 78.24/10.66 (setunionTransitive) => 78.24/10.66 (( 78.24/10.66 (ordinalMinLem1) => 78.24/10.66 (( 78.24/10.66 (!!) @ ( 78.24/10.66 ^[Y0 : $i]: 78.24/10.66 (( 78.24/10.66 (ordinal @ 78.24/10.66 Y0) => 78.24/10.66 (( 78.24/10.66 (!!) @ ( 78.24/10.66 ^[Y1 : $i]: 78.24/10.66 (( 78.24/10.66 (!!) @ ( 78.24/10.66 ^[Y2 : $i]: 78.24/10.66 (( 78.24/10.66 (in @ 78.24/10.66 Y2 @ 78.24/10.66 Y0) => 78.24/10.66 (( 78.24/10.66 (in @ 78.24/10.66 Y1 @ 78.24/10.66 Y2) => 78.24/10.66 (in @ 78.24/10.66 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 78.24/10.66 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl985])). 78.24/10.66 thf(zip_derived_cl1002, plain, 78.24/10.66 (~ (((disjointsetsI1) => 78.24/10.66 (((binintersectRsub) => 78.24/10.66 (((binintersectSubset4) => 78.24/10.66 (((binintersectSubset1) => 78.24/10.66 (((bs114d) => 78.24/10.66 (((setminusI) => 78.24/10.66 (((setminusEL) => 78.24/10.66 (((setminusER) => 78.24/10.66 (((setminusSubset2) => 78.24/10.66 (((setminusERneg) => 78.24/10.66 (((setminusELneg) => 78.24/10.66 (((setminusILneg) => 78.24/10.66 (((setminusIRneg) => 78.24/10.66 (((setminusLsub) => 78.24/10.66 (((setminusSubset1) => 78.24/10.66 (((symdiffE) => 78.24/10.66 (((symdiffI1) => 78.24/10.66 (((symdiffI2) => 78.24/10.66 (((symdiffIneg1) => 78.24/10.66 (((symdiffIneg2) => 78.24/10.66 (((secondinupair) => 78.24/10.66 (((setukpairIL) => 78.24/10.66 (((setukpairIR) => 78.24/10.66 (((kpairiskpair) => 78.24/10.66 (((kpairp) => 78.24/10.66 (((singletonsubset) => 78.24/10.66 (((singletoninpowerset) => 78.24/10.66 (((singletoninpowunion) => 78.24/10.66 (((upairset2E) => 78.24/10.66 (((upairsubunion) => 78.24/10.66 (( 78.24/10.66 (upairinpowunion) => 78.24/10.66 (( 78.24/10.66 (ubforcartprodlem1) => 78.24/10.66 (( 78.24/10.66 (ubforcartprodlem2) => 78.24/10.66 (( 78.24/10.66 (ubforcartprodlem3) => 78.24/10.66 (( 78.24/10.66 (cartprodpairin) => 78.24/10.66 (( 78.24/10.66 (cartprodmempair1) => 78.24/10.66 (( 78.24/10.66 (cartprodmempair) => 78.24/10.66 (( 78.24/10.66 (setunionE2) => 78.24/10.66 (( 78.24/10.66 (setunionsingleton1) => 78.24/10.66 (( 78.24/10.66 (setunionsingleton2) => 78.24/10.66 (( 78.24/10.66 (setunionsingleton) => 78.24/10.66 (( 78.24/10.66 (singletonprop) => 78.24/10.66 (( 78.24/10.66 (ex1E1) => 78.24/10.66 (( 78.24/10.66 (ex1I) => 78.24/10.66 (( 78.24/10.66 (ex1I2) => 78.24/10.66 (( 78.24/10.66 (singletonsuniq) => 78.24/10.66 (( 78.24/10.66 (setukpairinjL1) => 78.24/10.66 (( 78.24/10.66 (kfstsingleton) => 78.24/10.66 (( 78.24/10.66 (theprop) => 78.24/10.66 (( 78.24/10.66 (kfstpairEq) => 78.24/10.66 (( 78.24/10.66 (cartprodfstin) => 78.24/10.66 (( 78.24/10.66 (setukpairinjL2) => 78.24/10.66 (( 78.24/10.66 (setukpairinjL) => 78.24/10.66 (( 78.24/10.66 (setukpairinjR11) => 78.24/10.66 (( 78.24/10.66 (setukpairinjR12) => 78.24/10.66 (( 78.24/10.66 (setukpairinjR1) => 78.24/10.66 (( 78.24/10.66 (upairequniteq) => 78.24/10.66 (( 78.24/10.66 (setukpairinjR2) => 78.24/10.66 (( 78.24/10.66 (setukpairinjR) => 78.24/10.66 (( 78.24/10.66 (ksndsingleton) => 78.24/10.66 (( 78.24/10.66 (ksndpairEq) => 78.24/10.66 (( 78.24/10.66 (kpairsurjEq) => 78.24/10.66 (( 78.24/10.66 (cartprodsndin) => 78.24/10.66 (( 78.24/10.66 (cartprodpairmemEL) => 78.24/10.66 (( 78.24/10.66 (cartprodpairmemER) => 78.24/10.66 (( 78.24/10.66 (cartprodmempaircEq) => 78.24/10.66 (( 78.24/10.66 (cartprodfstpairEq) => 78.24/10.66 (( 78.24/10.66 (cartprodsndpairEq) => 78.24/10.66 (( 78.24/10.66 (cartprodpairsurjEq) => 78.24/10.66 (( 78.24/10.66 (dpsetconstrI) => 78.24/10.66 (( 78.24/10.66 (dpsetconstrSub) => 78.24/10.66 (( 78.24/10.66 (setOfPairsIsBReln) => 78.24/10.66 (( 78.24/10.66 (dpsetconstrERa) => 78.24/10.66 (( 78.24/10.66 (dpsetconstrEL1) => 78.24/10.66 (( 78.24/10.66 (dpsetconstrEL2) => 78.24/10.66 (( 78.24/10.66 (dpsetconstrER) => 78.24/10.66 (( 78.24/10.66 (funcImageSingleton) => 78.24/10.66 (( 78.24/10.66 (apProp) => 78.24/10.66 (( 78.24/10.66 (app) => 78.24/10.66 (( 78.24/10.66 (infuncsetfunc) => 78.24/10.66 (( 78.24/10.66 (ap2p) => 78.24/10.66 (( 78.24/10.66 (funcinfuncset) => 78.24/10.66 (( 78.24/10.66 (lamProp) => 78.24/10.66 (( 78.24/10.66 (lamp) => 78.24/10.66 (( 78.24/10.66 (lam2p) => 78.24/10.66 (( 78.24/10.66 (brelnall1) => 78.24/10.66 (( 78.24/10.66 (brelnall2) => 78.24/10.66 (( 78.24/10.66 (ex1E2) => 78.24/10.66 (( 78.24/10.66 (funcGraphProp1) => 78.24/10.66 (( 78.24/10.66 (funcGraphProp3) => 78.24/10.66 (( 78.24/10.66 (funcGraphProp2) => 78.24/10.66 (( 78.24/10.66 (funcextLem) => 78.24/10.66 (( 78.24/10.66 (funcGraphProp4) => 78.24/10.66 (( 78.24/10.66 (subbreln) => 78.24/10.66 (( 78.24/10.66 (eqbreln) => 78.24/10.66 (( 78.24/10.66 (funcext) => 78.24/10.66 (( 78.24/10.66 (funcext2) => 78.24/10.66 (( 78.24/10.66 (ap2apEq1) => 78.24/10.66 (( 78.24/10.66 (ap2apEq2) => 78.24/10.66 (( 78.24/10.66 (beta1) => 78.24/10.66 (( 78.24/10.66 (eta1) => 78.24/10.66 (( 78.24/10.66 (lam2lamEq) => 78.24/10.66 (( 78.24/10.66 (beta2) => 78.24/10.66 (( 78.24/10.66 (eta2) => 78.24/10.66 (( 78.24/10.66 (iffalseProp1) => 78.24/10.66 (( 78.24/10.66 (iffalseProp2) => 78.24/10.66 (( 78.24/10.66 (iftrueProp1) => 78.24/10.66 (( 78.24/10.66 (iftrueProp2) => 78.24/10.66 (( 78.24/10.66 (ifSingleton) => 78.24/10.66 (( 78.24/10.66 (ifp) => 78.24/10.66 (( 78.24/10.66 (theeq) => 78.24/10.66 (( 78.24/10.66 (iftrue) => 78.24/10.66 (( 78.24/10.66 (iffalse) => 78.24/10.66 (( 78.24/10.66 (iftrueorfalse) => 78.24/10.66 (( 78.24/10.66 (binintersectT_lem) => 78.24/10.66 (( 78.24/10.66 (binunionT_lem) => 78.24/10.66 (( 78.24/10.66 (powersetT_lem) => 78.24/10.66 (( 78.24/10.66 (setminusT_lem) => 78.24/10.66 (( 78.24/10.66 (complementT_lem) => 78.24/10.66 (( 78.24/10.66 (setextT) => 78.24/10.66 (( 78.24/10.66 (subsetTI) => 78.24/10.66 (( 78.24/10.66 (powersetTI1) => 78.24/10.66 (( 78.24/10.66 (powersetTE1) => 78.24/10.66 (( 78.24/10.66 (complementTI1) => 78.24/10.66 (( 78.24/10.66 (complementTE1) => 78.24/10.66 (( 78.24/10.66 (binintersectTELcontra) => 78.24/10.66 (( 78.24/10.66 (binintersectTERcontra) => 78.24/10.66 (( 78.24/10.66 (contrasubsetT) => 78.24/10.66 (( 78.24/10.66 (contrasubsetT1) => 78.24/10.66 (( 78.24/10.66 (contrasubsetT2) => 78.24/10.66 (( 78.24/10.66 (contrasubsetT3) => 78.24/10.66 (( 78.24/10.66 (doubleComplementI1) => 78.24/10.66 (( 78.24/10.66 (doubleComplementE1) => 78.24/10.66 (( 78.24/10.66 (doubleComplementSub1) => 78.24/10.66 (( 78.24/10.66 (doubleComplementSub2) => 78.24/10.66 (( 78.24/10.66 (doubleComplementEq) => 78.24/10.66 (( 78.24/10.66 (complementTnotintersectT) => 78.24/10.66 (( 78.24/10.66 (complementImpComplementIntersect) => 78.24/10.66 (( 78.24/10.66 (complementSubsetComplementIntersect) => 78.24/10.66 (( 78.24/10.66 (complementInPowersetComplementIntersect) => 78.24/10.66 (( 78.24/10.66 (contraSubsetComplement) => 78.24/10.66 (( 78.24/10.66 (complementTcontraSubset) => 78.24/10.66 (( 78.24/10.66 (binunionTILcontra) => 78.24/10.66 (( 78.24/10.66 (binunionTIRcontra) => 78.24/10.66 (( 78.24/10.66 (inIntersectImpInUnion) => 78.24/10.66 (( 78.24/10.66 (inIntersectImpInUnion2) => 78.24/10.66 (( 78.24/10.66 (inIntersectImpInIntersectUnions) => 78.24/10.66 (( 78.24/10.66 (intersectInPowersetIntersectUnions) => 78.24/10.66 (( 78.24/10.66 (inComplementUnionImpNotIn1) => 78.24/10.66 (( 78.24/10.66 (inComplementUnionImpInComplement1) => 78.24/10.66 (( 78.24/10.66 (binunionTE) => 78.24/10.66 (( 78.24/10.66 (binunionTEcontra) => 78.24/10.66 (( 78.24/10.66 (demorgan2a1) => 78.24/10.66 (( 78.24/10.66 (complementUnionInPowersetComplement) => 78.24/10.66 (( 78.24/10.66 (demorgan2a2) => 78.24/10.66 (( 78.24/10.66 (demorgan1a) => 78.24/10.66 (( 78.24/10.66 (demorgan1b) => 78.24/10.66 (( 78.24/10.66 (demorgan1) => 78.24/10.66 (( 78.24/10.66 (demorgan2a) => 78.24/10.66 (( 78.24/10.66 (demorgan2b2) => 78.24/10.66 (( 78.24/10.66 (demorgan2b) => 78.24/10.66 (( 78.24/10.66 (demorgan2) => 78.24/10.66 (( 78.24/10.66 (woz13rule0) => 78.24/10.66 (( 78.24/10.66 (woz13rule1) => 78.24/10.66 (( 78.24/10.66 (woz13rule2) => 78.24/10.66 (( 78.24/10.66 (woz13rule3) => 78.24/10.66 (( 78.24/10.66 (woz13rule4) => 78.24/10.66 (( 78.24/10.66 (woz1_1) => 78.24/10.66 (( 78.24/10.66 (woz1_2) => 78.24/10.66 (( 78.24/10.66 (woz1_3) => 78.24/10.66 (( 78.24/10.66 (woz1_4) => 78.24/10.66 (( 78.24/10.66 (woz1_5) => 78.24/10.66 (( 78.24/10.66 (breln1all2) => 78.24/10.66 (( 78.24/10.66 (breln1SetBreln1) => 78.24/10.66 (( 78.24/10.66 (choice2fnsingleton) => 78.24/10.66 (( 78.24/10.66 (setOfPairsIsBReln1) => 78.24/10.66 (( 78.24/10.66 (breln1all1) => 78.24/10.66 (( 78.24/10.66 (subbreln1) => 78.24/10.66 (( 78.24/10.66 (eqbreln1) => 78.24/10.66 (( 78.24/10.66 (breln1invprop) => 78.24/10.66 (( 78.24/10.66 (breln1invI) => 78.24/10.66 (( 78.24/10.66 (breln1invE) => 78.24/10.66 (( 78.24/10.66 (breln1compprop) => 78.24/10.66 (( 78.24/10.66 (breln1compI) => 78.24/10.66 (( 78.24/10.66 (breln1compE) => 78.24/10.66 (( 78.24/10.66 (breln1compEex) => 78.24/10.66 (( 78.24/10.66 (breln1unionprop) => 78.24/10.66 (( 78.24/10.66 (breln1unionIL) => 78.24/10.66 (( 78.24/10.66 (breln1unionIR) => 78.24/10.66 (( 78.24/10.66 (breln1unionI) => 78.24/10.66 (( 78.24/10.66 (breln1unionE) => 78.24/10.66 (( 78.24/10.66 (breln1unionEcases) => 78.24/10.66 (( 78.24/10.66 (breln1unionCommutes) => 78.24/10.66 (( 78.24/10.66 (woz2Ex) => 78.24/10.66 (( 78.24/10.66 (woz2W) => 78.24/10.66 (( 78.24/10.66 (woz2A) => 78.24/10.66 (( 78.24/10.66 (woz2B) => 78.24/10.66 (( 78.24/10.66 (image1Ex) => 78.24/10.66 (( 78.24/10.66 (image1Ex1) => 78.24/10.66 (( 78.24/10.66 (image1Equiv) => 78.24/10.66 (( 78.24/10.66 (image1E) => 78.24/10.66 (( 78.24/10.66 (image1I) => 78.24/10.66 (( 78.24/10.66 (injFuncInInjFuncSet) => 78.24/10.66 (( 78.24/10.66 (injFuncSetFuncIn) => 78.24/10.66 (( 78.24/10.66 (injFuncSetFuncInj) => 78.24/10.66 (( 78.24/10.66 (surjFuncSetFuncIn) => 78.24/10.66 (( 78.24/10.66 (surjFuncSetFuncSurj) => 78.24/10.66 (( 78.24/10.66 (leftInvIsSurj) => 78.24/10.66 (( 78.24/10.66 (surjCantorThm) => 78.24/10.66 (( 78.24/10.66 (foundation2) => 78.24/10.66 (( 78.24/10.66 (notinself) => 78.24/10.66 (( 78.24/10.66 (notinself2) => 78.24/10.66 (( 78.24/10.66 (omegaSp) => 78.24/10.66 (( 78.24/10.66 (omegaSclos) => 78.24/10.66 (( 78.24/10.66 (peano0notS) => 78.24/10.66 (( 78.24/10.66 (peanoSinj) => 78.24/10.66 (( 78.24/10.66 (transitivesetOp1) => 78.24/10.66 (( 78.24/10.66 (binintTransitive) => 78.24/10.66 (( 78.24/10.66 (transitivesetOp2) => 78.24/10.66 (( 78.24/10.66 (setunionTransitive) => 78.24/10.66 (( 78.24/10.66 (ordinalMinLem1) => 78.24/10.66 (( 78.24/10.66 (!!) @ ( 78.24/10.66 ^[Y0 : $i]: 78.24/10.66 (( 78.24/10.66 (ordinal @ 78.24/10.66 Y0) => 78.24/10.66 (( 78.24/10.66 (!!) @ ( 78.24/10.66 ^[Y1 : $i]: 78.24/10.66 (( 78.24/10.66 (!!) @ ( 78.24/10.66 ^[Y2 : $i]: 78.24/10.66 (( 78.24/10.66 (in @ 78.39/10.66 Y2 @ 78.39/10.66 Y0) => 78.39/10.66 (( 78.39/10.66 (in @ 78.39/10.66 Y1 @ 78.39/10.66 Y2) => 78.39/10.66 (in @ 78.39/10.66 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 78.39/10.66 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl994])). 78.39/10.66 thf(zip_derived_cl1008, plain, 78.39/10.66 (~ (((binintersectRsub) => 78.39/10.66 (((binintersectSubset4) => 78.39/10.66 (((binintersectSubset1) => 78.39/10.66 (((bs114d) => 78.39/10.66 (((setminusI) => 78.39/10.66 (((setminusEL) => 78.39/10.66 (((setminusER) => 78.39/10.66 (((setminusSubset2) => 78.39/10.66 (((setminusERneg) => 78.39/10.66 (((setminusELneg) => 78.39/10.66 (((setminusILneg) => 78.39/10.66 (((setminusIRneg) => 78.39/10.66 (((setminusLsub) => 78.39/10.66 (((setminusSubset1) => 78.39/10.66 (((symdiffE) => 78.39/10.66 (((symdiffI1) => 78.39/10.66 (((symdiffI2) => 78.39/10.66 (((symdiffIneg1) => 78.39/10.66 (((symdiffIneg2) => 78.39/10.66 (((secondinupair) => 78.39/10.66 (((setukpairIL) => 78.39/10.66 (((setukpairIR) => 78.39/10.66 (((kpairiskpair) => 78.39/10.66 (((kpairp) => 78.39/10.66 (((singletonsubset) => 78.39/10.66 (((singletoninpowerset) => 78.39/10.66 (((singletoninpowunion) => 78.39/10.66 (((upairset2E) => 78.39/10.66 (((upairsubunion) => 78.39/10.66 (((upairinpowunion) => 78.39/10.66 (( 78.39/10.66 (ubforcartprodlem1) => 78.39/10.66 (( 78.39/10.66 (ubforcartprodlem2) => 78.39/10.66 (( 78.39/10.66 (ubforcartprodlem3) => 78.39/10.66 (( 78.39/10.66 (cartprodpairin) => 78.39/10.66 (( 78.39/10.66 (cartprodmempair1) => 78.39/10.66 (( 78.39/10.66 (cartprodmempair) => 78.39/10.66 (( 78.39/10.66 (setunionE2) => 78.39/10.66 (( 78.39/10.66 (setunionsingleton1) => 78.39/10.66 (( 78.39/10.66 (setunionsingleton2) => 78.39/10.66 (( 78.39/10.66 (setunionsingleton) => 78.39/10.66 (( 78.39/10.66 (singletonprop) => 78.39/10.66 (( 78.39/10.66 (ex1E1) => 78.39/10.66 (( 78.39/10.66 (ex1I) => 78.39/10.66 (( 78.39/10.66 (ex1I2) => 78.39/10.66 (( 78.39/10.66 (singletonsuniq) => 78.39/10.66 (( 78.39/10.66 (setukpairinjL1) => 78.39/10.66 (( 78.39/10.66 (kfstsingleton) => 78.39/10.66 (( 78.39/10.66 (theprop) => 78.39/10.66 (( 78.39/10.66 (kfstpairEq) => 78.39/10.66 (( 78.39/10.66 (cartprodfstin) => 78.39/10.66 (( 78.39/10.66 (setukpairinjL2) => 78.39/10.66 (( 78.39/10.66 (setukpairinjL) => 78.39/10.66 (( 78.39/10.66 (setukpairinjR11) => 78.39/10.66 (( 78.39/10.66 (setukpairinjR12) => 78.39/10.66 (( 78.39/10.66 (setukpairinjR1) => 78.39/10.66 (( 78.39/10.66 (upairequniteq) => 78.39/10.66 (( 78.39/10.66 (setukpairinjR2) => 78.39/10.66 (( 78.39/10.66 (setukpairinjR) => 78.39/10.66 (( 78.39/10.66 (ksndsingleton) => 78.39/10.66 (( 78.39/10.66 (ksndpairEq) => 78.39/10.66 (( 78.39/10.66 (kpairsurjEq) => 78.39/10.66 (( 78.39/10.66 (cartprodsndin) => 78.39/10.66 (( 78.39/10.66 (cartprodpairmemEL) => 78.39/10.66 (( 78.39/10.66 (cartprodpairmemER) => 78.39/10.66 (( 78.39/10.66 (cartprodmempaircEq) => 78.39/10.66 (( 78.39/10.66 (cartprodfstpairEq) => 78.39/10.66 (( 78.39/10.66 (cartprodsndpairEq) => 78.39/10.66 (( 78.39/10.66 (cartprodpairsurjEq) => 78.39/10.66 (( 78.39/10.66 (dpsetconstrI) => 78.39/10.66 (( 78.39/10.66 (dpsetconstrSub) => 78.39/10.66 (( 78.39/10.66 (setOfPairsIsBReln) => 78.39/10.66 (( 78.39/10.66 (dpsetconstrERa) => 78.39/10.66 (( 78.39/10.66 (dpsetconstrEL1) => 78.39/10.66 (( 78.39/10.66 (dpsetconstrEL2) => 78.39/10.66 (( 78.39/10.66 (dpsetconstrER) => 78.39/10.66 (( 78.39/10.66 (funcImageSingleton) => 78.39/10.66 (( 78.39/10.66 (apProp) => 78.39/10.66 (( 78.39/10.66 (app) => 78.39/10.66 (( 78.39/10.66 (infuncsetfunc) => 78.39/10.66 (( 78.39/10.66 (ap2p) => 78.39/10.66 (( 78.39/10.66 (funcinfuncset) => 78.39/10.66 (( 78.39/10.66 (lamProp) => 78.39/10.66 (( 78.39/10.66 (lamp) => 78.39/10.66 (( 78.39/10.66 (lam2p) => 78.39/10.66 (( 78.39/10.66 (brelnall1) => 78.39/10.66 (( 78.39/10.66 (brelnall2) => 78.39/10.66 (( 78.39/10.66 (ex1E2) => 78.39/10.66 (( 78.39/10.66 (funcGraphProp1) => 78.39/10.66 (( 78.39/10.66 (funcGraphProp3) => 78.39/10.66 (( 78.39/10.66 (funcGraphProp2) => 78.39/10.66 (( 78.39/10.66 (funcextLem) => 78.39/10.66 (( 78.39/10.66 (funcGraphProp4) => 78.39/10.66 (( 78.39/10.66 (subbreln) => 78.39/10.66 (( 78.39/10.66 (eqbreln) => 78.39/10.66 (( 78.39/10.66 (funcext) => 78.39/10.66 (( 78.39/10.66 (funcext2) => 78.39/10.66 (( 78.39/10.66 (ap2apEq1) => 78.39/10.66 (( 78.39/10.66 (ap2apEq2) => 78.39/10.66 (( 78.39/10.66 (beta1) => 78.39/10.66 (( 78.39/10.66 (eta1) => 78.39/10.66 (( 78.39/10.66 (lam2lamEq) => 78.39/10.66 (( 78.39/10.66 (beta2) => 78.39/10.66 (( 78.39/10.66 (eta2) => 78.39/10.66 (( 78.39/10.66 (iffalseProp1) => 78.39/10.66 (( 78.39/10.66 (iffalseProp2) => 78.39/10.66 (( 78.39/10.66 (iftrueProp1) => 78.39/10.66 (( 78.39/10.66 (iftrueProp2) => 78.39/10.66 (( 78.39/10.66 (ifSingleton) => 78.39/10.66 (( 78.39/10.66 (ifp) => 78.39/10.66 (( 78.39/10.66 (theeq) => 78.39/10.66 (( 78.39/10.66 (iftrue) => 78.39/10.66 (( 78.39/10.66 (iffalse) => 78.39/10.66 (( 78.39/10.66 (iftrueorfalse) => 78.39/10.66 (( 78.39/10.66 (binintersectT_lem) => 78.39/10.66 (( 78.39/10.66 (binunionT_lem) => 78.39/10.66 (( 78.39/10.66 (powersetT_lem) => 78.39/10.66 (( 78.39/10.66 (setminusT_lem) => 78.39/10.66 (( 78.39/10.66 (complementT_lem) => 78.39/10.66 (( 78.39/10.66 (setextT) => 78.39/10.66 (( 78.39/10.66 (subsetTI) => 78.39/10.66 (( 78.39/10.66 (powersetTI1) => 78.39/10.66 (( 78.39/10.66 (powersetTE1) => 78.39/10.66 (( 78.39/10.66 (complementTI1) => 78.39/10.66 (( 78.39/10.66 (complementTE1) => 78.39/10.66 (( 78.39/10.66 (binintersectTELcontra) => 78.39/10.66 (( 78.39/10.66 (binintersectTERcontra) => 78.39/10.66 (( 78.39/10.66 (contrasubsetT) => 78.39/10.66 (( 78.39/10.66 (contrasubsetT1) => 78.39/10.66 (( 78.39/10.66 (contrasubsetT2) => 78.39/10.66 (( 78.39/10.66 (contrasubsetT3) => 78.39/10.66 (( 78.39/10.66 (doubleComplementI1) => 78.39/10.66 (( 78.39/10.66 (doubleComplementE1) => 78.39/10.66 (( 78.39/10.66 (doubleComplementSub1) => 78.39/10.66 (( 78.39/10.66 (doubleComplementSub2) => 78.39/10.66 (( 78.39/10.66 (doubleComplementEq) => 78.39/10.66 (( 78.39/10.66 (complementTnotintersectT) => 78.39/10.66 (( 78.39/10.66 (complementImpComplementIntersect) => 78.39/10.66 (( 78.39/10.66 (complementSubsetComplementIntersect) => 78.39/10.66 (( 78.39/10.66 (complementInPowersetComplementIntersect) => 78.39/10.66 (( 78.39/10.66 (contraSubsetComplement) => 78.39/10.66 (( 78.39/10.66 (complementTcontraSubset) => 78.39/10.66 (( 78.39/10.66 (binunionTILcontra) => 78.39/10.66 (( 78.39/10.66 (binunionTIRcontra) => 78.39/10.66 (( 78.39/10.66 (inIntersectImpInUnion) => 78.39/10.66 (( 78.39/10.66 (inIntersectImpInUnion2) => 78.39/10.66 (( 78.39/10.66 (inIntersectImpInIntersectUnions) => 78.39/10.66 (( 78.39/10.66 (intersectInPowersetIntersectUnions) => 78.39/10.66 (( 78.39/10.66 (inComplementUnionImpNotIn1) => 78.39/10.66 (( 78.39/10.66 (inComplementUnionImpInComplement1) => 78.39/10.66 (( 78.39/10.66 (binunionTE) => 78.39/10.66 (( 78.39/10.66 (binunionTEcontra) => 78.39/10.66 (( 78.39/10.66 (demorgan2a1) => 78.39/10.66 (( 78.39/10.66 (complementUnionInPowersetComplement) => 78.39/10.66 (( 78.39/10.66 (demorgan2a2) => 78.39/10.66 (( 78.39/10.66 (demorgan1a) => 78.39/10.66 (( 78.39/10.66 (demorgan1b) => 78.39/10.66 (( 78.39/10.66 (demorgan1) => 78.39/10.66 (( 78.39/10.66 (demorgan2a) => 78.39/10.66 (( 78.39/10.66 (demorgan2b2) => 78.39/10.66 (( 78.39/10.66 (demorgan2b) => 78.39/10.66 (( 78.39/10.66 (demorgan2) => 78.39/10.66 (( 78.39/10.66 (woz13rule0) => 78.39/10.66 (( 78.39/10.66 (woz13rule1) => 78.39/10.66 (( 78.39/10.66 (woz13rule2) => 78.39/10.66 (( 78.39/10.66 (woz13rule3) => 78.39/10.66 (( 78.39/10.66 (woz13rule4) => 78.39/10.66 (( 78.39/10.66 (woz1_1) => 78.39/10.66 (( 78.39/10.66 (woz1_2) => 78.39/10.66 (( 78.39/10.66 (woz1_3) => 78.39/10.66 (( 78.39/10.66 (woz1_4) => 78.39/10.66 (( 78.39/10.66 (woz1_5) => 78.39/10.66 (( 78.39/10.66 (breln1all2) => 78.39/10.66 (( 78.39/10.66 (breln1SetBreln1) => 78.39/10.66 (( 78.39/10.66 (choice2fnsingleton) => 78.39/10.66 (( 78.39/10.66 (setOfPairsIsBReln1) => 78.39/10.66 (( 78.39/10.66 (breln1all1) => 78.39/10.66 (( 78.39/10.66 (subbreln1) => 78.39/10.66 (( 78.39/10.66 (eqbreln1) => 78.39/10.66 (( 78.39/10.66 (breln1invprop) => 78.39/10.66 (( 78.39/10.66 (breln1invI) => 78.39/10.66 (( 78.39/10.66 (breln1invE) => 78.39/10.66 (( 78.39/10.66 (breln1compprop) => 78.39/10.66 (( 78.39/10.66 (breln1compI) => 78.39/10.66 (( 78.39/10.66 (breln1compE) => 78.39/10.66 (( 78.39/10.66 (breln1compEex) => 78.39/10.66 (( 78.39/10.66 (breln1unionprop) => 78.39/10.66 (( 78.39/10.66 (breln1unionIL) => 78.39/10.66 (( 78.39/10.66 (breln1unionIR) => 78.39/10.66 (( 78.39/10.66 (breln1unionI) => 78.39/10.66 (( 78.39/10.66 (breln1unionE) => 78.39/10.66 (( 78.39/10.66 (breln1unionEcases) => 78.39/10.66 (( 78.39/10.66 (breln1unionCommutes) => 78.39/10.66 (( 78.39/10.66 (woz2Ex) => 78.39/10.66 (( 78.39/10.66 (woz2W) => 78.39/10.66 (( 78.39/10.66 (woz2A) => 78.39/10.66 (( 78.39/10.66 (woz2B) => 78.39/10.66 (( 78.39/10.66 (image1Ex) => 78.39/10.66 (( 78.39/10.66 (image1Ex1) => 78.39/10.66 (( 78.39/10.66 (image1Equiv) => 78.39/10.66 (( 78.39/10.66 (image1E) => 78.39/10.66 (( 78.39/10.66 (image1I) => 78.39/10.66 (( 78.39/10.66 (injFuncInInjFuncSet) => 78.39/10.66 (( 78.39/10.66 (injFuncSetFuncIn) => 78.39/10.66 (( 78.39/10.66 (injFuncSetFuncInj) => 78.39/10.66 (( 78.39/10.66 (surjFuncSetFuncIn) => 78.39/10.66 (( 78.39/10.66 (surjFuncSetFuncSurj) => 78.39/10.66 (( 78.39/10.66 (leftInvIsSurj) => 78.39/10.66 (( 78.39/10.66 (surjCantorThm) => 78.39/10.66 (( 78.39/10.66 (foundation2) => 78.39/10.66 (( 78.39/10.66 (notinself) => 78.39/10.66 (( 78.39/10.66 (notinself2) => 78.39/10.66 (( 78.39/10.66 (omegaSp) => 78.39/10.66 (( 78.39/10.66 (omegaSclos) => 78.39/10.66 (( 78.39/10.66 (peano0notS) => 78.39/10.66 (( 78.39/10.66 (peanoSinj) => 78.39/10.66 (( 78.39/10.66 (transitivesetOp1) => 78.39/10.66 (( 78.39/10.66 (binintTransitive) => 78.39/10.66 (( 78.39/10.66 (transitivesetOp2) => 78.39/10.66 (( 78.39/10.66 (setunionTransitive) => 78.39/10.66 (( 78.39/10.66 (ordinalMinLem1) => 78.39/10.66 (( 78.39/10.66 (!!) @ ( 78.39/10.66 ^[Y0 : $i]: 78.39/10.66 (( 78.39/10.66 (ordinal @ 78.39/10.66 Y0) => 78.39/10.66 (( 78.39/10.66 (!!) @ ( 78.39/10.66 ^[Y1 : $i]: 78.39/10.66 (( 78.39/10.66 (!!) @ ( 78.39/10.66 ^[Y2 : $i]: 78.39/10.66 (( 78.39/10.66 (in @ 78.39/10.66 Y2 @ 78.39/10.66 Y0) => 78.39/10.66 (( 78.39/10.66 (in @ 78.39/10.66 Y1 @ 78.39/10.66 Y2) => 78.39/10.66 (in @ 78.39/10.66 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 78.39/10.66 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1002])). 78.39/10.66 thf(zip_derived_cl1014, plain, 78.39/10.66 (~ (((binintersectSubset4) => 78.39/10.66 (((binintersectSubset1) => 78.39/10.66 (((bs114d) => 78.39/10.66 (((setminusI) => 78.39/10.66 (((setminusEL) => 78.39/10.66 (((setminusER) => 78.39/10.66 (((setminusSubset2) => 78.39/10.66 (((setminusERneg) => 78.39/10.66 (((setminusELneg) => 78.39/10.66 (((setminusILneg) => 78.39/10.66 (((setminusIRneg) => 78.39/10.66 (((setminusLsub) => 78.39/10.66 (((setminusSubset1) => 78.39/10.66 (((symdiffE) => 78.39/10.66 (((symdiffI1) => 78.39/10.66 (((symdiffI2) => 78.39/10.66 (((symdiffIneg1) => 78.39/10.66 (((symdiffIneg2) => 78.39/10.66 (((secondinupair) => 78.39/10.66 (((setukpairIL) => 78.39/10.66 (((setukpairIR) => 78.39/10.66 (((kpairiskpair) => 78.39/10.66 (((kpairp) => 78.39/10.66 (((singletonsubset) => 78.39/10.66 (((singletoninpowerset) => 78.39/10.66 (((singletoninpowunion) => 78.39/10.66 (((upairset2E) => 78.39/10.66 (((upairsubunion) => 78.39/10.66 (((upairinpowunion) => 78.39/10.66 (((ubforcartprodlem1) => 78.39/10.66 (( 78.39/10.66 (ubforcartprodlem2) => 78.39/10.66 (( 78.39/10.66 (ubforcartprodlem3) => 78.39/10.66 (( 78.39/10.66 (cartprodpairin) => 78.39/10.66 (( 78.39/10.66 (cartprodmempair1) => 78.39/10.66 (( 78.39/10.66 (cartprodmempair) => 78.39/10.66 (( 78.39/10.66 (setunionE2) => 78.39/10.66 (( 78.39/10.66 (setunionsingleton1) => 78.39/10.66 (( 78.39/10.66 (setunionsingleton2) => 78.39/10.66 (( 78.39/10.66 (setunionsingleton) => 78.39/10.66 (( 78.39/10.66 (singletonprop) => 78.39/10.66 (( 78.39/10.66 (ex1E1) => 78.39/10.66 (( 78.39/10.66 (ex1I) => 78.39/10.66 (( 78.39/10.66 (ex1I2) => 78.39/10.66 (( 78.39/10.66 (singletonsuniq) => 78.39/10.66 (( 78.39/10.66 (setukpairinjL1) => 78.39/10.66 (( 78.39/10.66 (kfstsingleton) => 78.39/10.66 (( 78.39/10.66 (theprop) => 78.39/10.66 (( 78.39/10.66 (kfstpairEq) => 78.39/10.66 (( 78.39/10.66 (cartprodfstin) => 78.39/10.66 (( 78.39/10.66 (setukpairinjL2) => 78.39/10.66 (( 78.39/10.66 (setukpairinjL) => 78.39/10.66 (( 78.39/10.66 (setukpairinjR11) => 78.39/10.66 (( 78.39/10.66 (setukpairinjR12) => 78.39/10.66 (( 78.39/10.66 (setukpairinjR1) => 78.39/10.66 (( 78.39/10.66 (upairequniteq) => 78.39/10.66 (( 78.39/10.66 (setukpairinjR2) => 78.39/10.66 (( 78.39/10.66 (setukpairinjR) => 78.39/10.66 (( 78.39/10.66 (ksndsingleton) => 78.39/10.66 (( 78.39/10.66 (ksndpairEq) => 78.39/10.66 (( 78.39/10.66 (kpairsurjEq) => 78.39/10.66 (( 78.39/10.66 (cartprodsndin) => 78.39/10.66 (( 78.39/10.66 (cartprodpairmemEL) => 78.39/10.66 (( 78.39/10.66 (cartprodpairmemER) => 78.39/10.66 (( 78.39/10.66 (cartprodmempaircEq) => 78.39/10.66 (( 78.39/10.66 (cartprodfstpairEq) => 78.39/10.66 (( 78.39/10.66 (cartprodsndpairEq) => 78.39/10.66 (( 78.39/10.66 (cartprodpairsurjEq) => 78.39/10.66 (( 78.39/10.66 (dpsetconstrI) => 78.39/10.66 (( 78.39/10.66 (dpsetconstrSub) => 78.39/10.66 (( 78.39/10.66 (setOfPairsIsBReln) => 78.39/10.66 (( 78.39/10.66 (dpsetconstrERa) => 78.39/10.66 (( 78.39/10.66 (dpsetconstrEL1) => 78.39/10.66 (( 78.39/10.66 (dpsetconstrEL2) => 78.39/10.66 (( 78.39/10.66 (dpsetconstrER) => 78.39/10.66 (( 78.39/10.66 (funcImageSingleton) => 78.39/10.66 (( 78.39/10.66 (apProp) => 78.39/10.66 (( 78.39/10.66 (app) => 78.39/10.66 (( 78.39/10.66 (infuncsetfunc) => 78.39/10.66 (( 78.39/10.66 (ap2p) => 78.39/10.66 (( 78.39/10.66 (funcinfuncset) => 78.39/10.66 (( 78.39/10.66 (lamProp) => 78.39/10.66 (( 78.39/10.66 (lamp) => 78.39/10.66 (( 78.39/10.66 (lam2p) => 78.39/10.66 (( 78.39/10.66 (brelnall1) => 78.39/10.66 (( 78.39/10.66 (brelnall2) => 78.39/10.66 (( 78.39/10.66 (ex1E2) => 78.39/10.66 (( 78.39/10.66 (funcGraphProp1) => 78.39/10.66 (( 78.39/10.66 (funcGraphProp3) => 78.39/10.66 (( 78.39/10.66 (funcGraphProp2) => 78.39/10.66 (( 78.39/10.66 (funcextLem) => 78.39/10.66 (( 78.39/10.66 (funcGraphProp4) => 78.39/10.66 (( 78.39/10.66 (subbreln) => 78.39/10.66 (( 78.39/10.66 (eqbreln) => 78.39/10.66 (( 78.39/10.66 (funcext) => 78.39/10.66 (( 78.39/10.66 (funcext2) => 78.39/10.66 (( 78.39/10.66 (ap2apEq1) => 78.39/10.66 (( 78.39/10.66 (ap2apEq2) => 78.39/10.66 (( 78.39/10.66 (beta1) => 78.39/10.66 (( 78.39/10.66 (eta1) => 78.39/10.66 (( 78.39/10.66 (lam2lamEq) => 78.39/10.66 (( 78.39/10.66 (beta2) => 78.39/10.66 (( 78.39/10.66 (eta2) => 78.39/10.66 (( 78.39/10.66 (iffalseProp1) => 78.39/10.66 (( 78.39/10.66 (iffalseProp2) => 78.39/10.66 (( 78.39/10.66 (iftrueProp1) => 78.39/10.66 (( 78.39/10.66 (iftrueProp2) => 78.39/10.66 (( 78.39/10.66 (ifSingleton) => 78.39/10.66 (( 78.39/10.66 (ifp) => 78.39/10.66 (( 78.39/10.66 (theeq) => 78.39/10.66 (( 78.39/10.66 (iftrue) => 78.39/10.66 (( 78.39/10.66 (iffalse) => 78.39/10.66 (( 78.39/10.66 (iftrueorfalse) => 78.39/10.66 (( 78.39/10.66 (binintersectT_lem) => 78.39/10.66 (( 78.39/10.66 (binunionT_lem) => 78.39/10.66 (( 78.39/10.66 (powersetT_lem) => 78.39/10.66 (( 78.39/10.66 (setminusT_lem) => 78.39/10.66 (( 78.39/10.66 (complementT_lem) => 78.39/10.66 (( 78.39/10.66 (setextT) => 78.39/10.66 (( 78.39/10.66 (subsetTI) => 78.39/10.66 (( 78.39/10.66 (powersetTI1) => 78.39/10.66 (( 78.39/10.66 (powersetTE1) => 78.39/10.66 (( 78.39/10.66 (complementTI1) => 78.39/10.66 (( 78.39/10.66 (complementTE1) => 78.39/10.66 (( 78.39/10.66 (binintersectTELcontra) => 78.39/10.66 (( 78.39/10.66 (binintersectTERcontra) => 78.39/10.66 (( 78.39/10.66 (contrasubsetT) => 78.39/10.66 (( 78.39/10.66 (contrasubsetT1) => 78.39/10.66 (( 78.39/10.66 (contrasubsetT2) => 78.39/10.66 (( 78.39/10.66 (contrasubsetT3) => 78.39/10.66 (( 78.39/10.66 (doubleComplementI1) => 78.39/10.66 (( 78.39/10.66 (doubleComplementE1) => 78.39/10.66 (( 78.39/10.66 (doubleComplementSub1) => 78.39/10.66 (( 78.39/10.66 (doubleComplementSub2) => 78.39/10.66 (( 78.39/10.66 (doubleComplementEq) => 78.39/10.66 (( 78.39/10.66 (complementTnotintersectT) => 78.39/10.66 (( 78.39/10.66 (complementImpComplementIntersect) => 78.39/10.66 (( 78.39/10.66 (complementSubsetComplementIntersect) => 78.39/10.66 (( 78.39/10.66 (complementInPowersetComplementIntersect) => 78.39/10.66 (( 78.39/10.66 (contraSubsetComplement) => 78.39/10.66 (( 78.39/10.66 (complementTcontraSubset) => 78.39/10.66 (( 78.39/10.66 (binunionTILcontra) => 78.39/10.66 (( 78.39/10.66 (binunionTIRcontra) => 78.39/10.66 (( 78.39/10.66 (inIntersectImpInUnion) => 78.39/10.66 (( 78.39/10.66 (inIntersectImpInUnion2) => 78.39/10.66 (( 78.39/10.66 (inIntersectImpInIntersectUnions) => 78.39/10.66 (( 78.39/10.66 (intersectInPowersetIntersectUnions) => 78.39/10.66 (( 78.39/10.66 (inComplementUnionImpNotIn1) => 78.39/10.66 (( 78.39/10.66 (inComplementUnionImpInComplement1) => 78.39/10.66 (( 78.39/10.66 (binunionTE) => 78.39/10.66 (( 78.39/10.66 (binunionTEcontra) => 78.39/10.66 (( 78.39/10.66 (demorgan2a1) => 78.39/10.66 (( 78.39/10.66 (complementUnionInPowersetComplement) => 78.39/10.66 (( 78.39/10.66 (demorgan2a2) => 78.39/10.66 (( 78.39/10.66 (demorgan1a) => 78.39/10.66 (( 78.39/10.66 (demorgan1b) => 78.39/10.66 (( 78.39/10.66 (demorgan1) => 78.39/10.66 (( 78.39/10.66 (demorgan2a) => 78.39/10.66 (( 78.39/10.66 (demorgan2b2) => 78.39/10.66 (( 78.39/10.66 (demorgan2b) => 78.39/10.66 (( 78.39/10.66 (demorgan2) => 78.39/10.66 (( 78.39/10.66 (woz13rule0) => 78.39/10.66 (( 78.39/10.66 (woz13rule1) => 78.39/10.66 (( 78.39/10.66 (woz13rule2) => 78.39/10.66 (( 78.39/10.66 (woz13rule3) => 78.39/10.66 (( 78.39/10.66 (woz13rule4) => 78.39/10.66 (( 78.39/10.66 (woz1_1) => 78.39/10.66 (( 78.39/10.66 (woz1_2) => 78.39/10.66 (( 78.39/10.66 (woz1_3) => 78.39/10.66 (( 78.39/10.66 (woz1_4) => 78.39/10.66 (( 78.39/10.66 (woz1_5) => 78.39/10.66 (( 78.39/10.66 (breln1all2) => 78.39/10.66 (( 78.39/10.66 (breln1SetBreln1) => 78.39/10.66 (( 78.39/10.66 (choice2fnsingleton) => 78.39/10.66 (( 78.39/10.66 (setOfPairsIsBReln1) => 78.39/10.66 (( 78.39/10.66 (breln1all1) => 78.39/10.66 (( 78.39/10.66 (subbreln1) => 78.39/10.66 (( 78.39/10.66 (eqbreln1) => 78.39/10.66 (( 78.39/10.66 (breln1invprop) => 78.39/10.66 (( 78.39/10.66 (breln1invI) => 78.39/10.66 (( 78.39/10.66 (breln1invE) => 78.39/10.66 (( 78.39/10.66 (breln1compprop) => 78.39/10.66 (( 78.39/10.66 (breln1compI) => 78.39/10.66 (( 78.39/10.66 (breln1compE) => 78.39/10.66 (( 78.39/10.66 (breln1compEex) => 78.39/10.66 (( 78.39/10.66 (breln1unionprop) => 78.39/10.66 (( 78.39/10.66 (breln1unionIL) => 78.39/10.66 (( 78.39/10.66 (breln1unionIR) => 78.39/10.66 (( 78.39/10.66 (breln1unionI) => 78.39/10.66 (( 78.39/10.66 (breln1unionE) => 78.39/10.66 (( 78.39/10.66 (breln1unionEcases) => 78.39/10.66 (( 78.39/10.66 (breln1unionCommutes) => 78.39/10.66 (( 78.39/10.66 (woz2Ex) => 78.39/10.66 (( 78.39/10.66 (woz2W) => 78.39/10.66 (( 78.39/10.66 (woz2A) => 78.39/10.66 (( 78.39/10.66 (woz2B) => 78.39/10.66 (( 78.39/10.66 (image1Ex) => 78.39/10.66 (( 78.39/10.66 (image1Ex1) => 78.39/10.66 (( 78.39/10.66 (image1Equiv) => 78.39/10.66 (( 78.39/10.66 (image1E) => 78.39/10.66 (( 78.39/10.66 (image1I) => 78.39/10.66 (( 78.39/10.66 (injFuncInInjFuncSet) => 78.39/10.66 (( 78.39/10.66 (injFuncSetFuncIn) => 78.39/10.66 (( 78.39/10.66 (injFuncSetFuncInj) => 78.39/10.66 (( 78.39/10.66 (surjFuncSetFuncIn) => 78.39/10.66 (( 78.39/10.66 (surjFuncSetFuncSurj) => 78.39/10.66 (( 78.39/10.66 (leftInvIsSurj) => 78.39/10.66 (( 78.39/10.66 (surjCantorThm) => 78.39/10.66 (( 78.39/10.66 (foundation2) => 78.39/10.66 (( 78.39/10.66 (notinself) => 78.39/10.66 (( 78.39/10.66 (notinself2) => 78.39/10.66 (( 78.39/10.66 (omegaSp) => 78.39/10.66 (( 78.39/10.66 (omegaSclos) => 78.39/10.66 (( 78.39/10.66 (peano0notS) => 78.39/10.66 (( 78.39/10.66 (peanoSinj) => 78.39/10.66 (( 78.39/10.66 (transitivesetOp1) => 78.39/10.66 (( 78.39/10.66 (binintTransitive) => 78.39/10.66 (( 78.39/10.66 (transitivesetOp2) => 78.39/10.66 (( 78.39/10.66 (setunionTransitive) => 78.39/10.66 (( 78.39/10.66 (ordinalMinLem1) => 78.39/10.66 (( 78.39/10.66 (!!) @ ( 78.39/10.66 ^[Y0 : $i]: 78.39/10.66 (( 78.39/10.66 (ordinal @ 78.39/10.66 Y0) => 78.39/10.66 (( 78.39/10.66 (!!) @ ( 78.39/10.66 ^[Y1 : $i]: 78.39/10.66 (( 78.39/10.66 (!!) @ ( 78.39/10.66 ^[Y2 : $i]: 78.39/10.66 (( 78.39/10.66 (in @ 78.39/10.66 Y2 @ 78.39/10.66 Y0) => 78.39/10.66 (( 78.39/10.66 (in @ 78.39/10.66 Y1 @ 78.39/10.66 Y2) => 78.39/10.66 (in @ 78.39/10.66 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 78.39/10.66 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1008])). 78.39/10.66 thf(zip_derived_cl1021, plain, 78.39/10.66 (~ (((binintersectSubset1) => 78.39/10.66 (((bs114d) => 78.39/10.66 (((setminusI) => 78.39/10.66 (((setminusEL) => 78.39/10.66 (((setminusER) => 78.39/10.66 (((setminusSubset2) => 78.39/10.66 (((setminusERneg) => 78.39/10.66 (((setminusELneg) => 78.39/10.66 (((setminusILneg) => 78.39/10.66 (((setminusIRneg) => 78.39/10.66 (((setminusLsub) => 78.39/10.66 (((setminusSubset1) => 78.39/10.66 (((symdiffE) => 78.39/10.66 (((symdiffI1) => 78.39/10.66 (((symdiffI2) => 78.39/10.66 (((symdiffIneg1) => 78.39/10.66 (((symdiffIneg2) => 78.39/10.66 (((secondinupair) => 78.39/10.66 (((setukpairIL) => 78.39/10.66 (((setukpairIR) => 78.39/10.66 (((kpairiskpair) => 78.39/10.66 (((kpairp) => 78.39/10.66 (((singletonsubset) => 78.39/10.66 (((singletoninpowerset) => 78.39/10.66 (((singletoninpowunion) => 78.39/10.66 (((upairset2E) => 78.39/10.66 (((upairsubunion) => 78.39/10.66 (((upairinpowunion) => 78.39/10.66 (((ubforcartprodlem1) => 78.39/10.66 (((ubforcartprodlem2) => 78.39/10.66 (( 78.39/10.66 (ubforcartprodlem3) => 78.39/10.66 (( 78.39/10.66 (cartprodpairin) => 78.39/10.66 (( 78.39/10.66 (cartprodmempair1) => 78.39/10.66 (( 78.39/10.66 (cartprodmempair) => 78.39/10.66 (( 78.39/10.66 (setunionE2) => 78.39/10.66 (( 78.39/10.66 (setunionsingleton1) => 78.39/10.66 (( 78.39/10.66 (setunionsingleton2) => 78.39/10.66 (( 78.39/10.66 (setunionsingleton) => 78.39/10.66 (( 78.39/10.66 (singletonprop) => 78.39/10.66 (( 78.39/10.66 (ex1E1) => 78.39/10.66 (( 78.39/10.66 (ex1I) => 78.39/10.66 (( 78.39/10.66 (ex1I2) => 78.39/10.66 (( 78.39/10.66 (singletonsuniq) => 78.39/10.66 (( 78.39/10.66 (setukpairinjL1) => 78.39/10.66 (( 78.39/10.66 (kfstsingleton) => 78.39/10.66 (( 78.39/10.66 (theprop) => 78.39/10.66 (( 78.39/10.66 (kfstpairEq) => 78.39/10.66 (( 78.39/10.66 (cartprodfstin) => 78.39/10.66 (( 78.39/10.66 (setukpairinjL2) => 78.39/10.66 (( 78.39/10.66 (setukpairinjL) => 78.39/10.66 (( 78.39/10.66 (setukpairinjR11) => 78.39/10.66 (( 78.39/10.66 (setukpairinjR12) => 78.39/10.66 (( 78.39/10.66 (setukpairinjR1) => 78.39/10.66 (( 78.39/10.66 (upairequniteq) => 78.39/10.66 (( 78.39/10.66 (setukpairinjR2) => 78.39/10.66 (( 78.39/10.66 (setukpairinjR) => 78.39/10.66 (( 78.39/10.66 (ksndsingleton) => 78.39/10.66 (( 78.39/10.66 (ksndpairEq) => 78.39/10.66 (( 78.39/10.66 (kpairsurjEq) => 78.39/10.66 (( 78.39/10.66 (cartprodsndin) => 78.39/10.66 (( 78.39/10.66 (cartprodpairmemEL) => 78.39/10.66 (( 78.39/10.66 (cartprodpairmemER) => 78.39/10.66 (( 78.39/10.66 (cartprodmempaircEq) => 78.39/10.66 (( 78.39/10.66 (cartprodfstpairEq) => 78.39/10.66 (( 78.39/10.66 (cartprodsndpairEq) => 78.39/10.66 (( 78.39/10.66 (cartprodpairsurjEq) => 78.39/10.66 (( 78.39/10.66 (dpsetconstrI) => 78.39/10.66 (( 78.39/10.66 (dpsetconstrSub) => 78.39/10.66 (( 78.39/10.66 (setOfPairsIsBReln) => 78.39/10.66 (( 78.39/10.66 (dpsetconstrERa) => 78.39/10.66 (( 78.39/10.66 (dpsetconstrEL1) => 78.39/10.66 (( 78.39/10.66 (dpsetconstrEL2) => 78.39/10.66 (( 78.39/10.66 (dpsetconstrER) => 78.39/10.66 (( 78.39/10.66 (funcImageSingleton) => 78.39/10.66 (( 78.39/10.66 (apProp) => 78.39/10.66 (( 78.39/10.66 (app) => 78.39/10.66 (( 78.39/10.66 (infuncsetfunc) => 78.39/10.66 (( 78.39/10.66 (ap2p) => 78.39/10.66 (( 78.39/10.66 (funcinfuncset) => 78.39/10.66 (( 78.39/10.66 (lamProp) => 78.39/10.66 (( 78.39/10.66 (lamp) => 78.39/10.66 (( 78.39/10.66 (lam2p) => 78.39/10.66 (( 78.39/10.66 (brelnall1) => 78.39/10.66 (( 78.39/10.66 (brelnall2) => 78.39/10.66 (( 78.39/10.66 (ex1E2) => 78.39/10.66 (( 78.39/10.66 (funcGraphProp1) => 78.39/10.66 (( 78.39/10.66 (funcGraphProp3) => 78.39/10.66 (( 78.39/10.66 (funcGraphProp2) => 78.39/10.66 (( 78.39/10.66 (funcextLem) => 78.39/10.66 (( 78.39/10.66 (funcGraphProp4) => 78.39/10.66 (( 78.39/10.66 (subbreln) => 78.39/10.66 (( 78.39/10.66 (eqbreln) => 78.39/10.66 (( 78.39/10.66 (funcext) => 78.39/10.66 (( 78.39/10.66 (funcext2) => 78.39/10.66 (( 78.39/10.66 (ap2apEq1) => 78.39/10.66 (( 78.39/10.66 (ap2apEq2) => 78.39/10.66 (( 78.39/10.66 (beta1) => 78.39/10.66 (( 78.39/10.66 (eta1) => 78.39/10.66 (( 78.39/10.66 (lam2lamEq) => 78.39/10.66 (( 78.39/10.66 (beta2) => 78.39/10.66 (( 78.39/10.66 (eta2) => 78.39/10.66 (( 78.39/10.66 (iffalseProp1) => 78.39/10.66 (( 78.39/10.66 (iffalseProp2) => 78.39/10.66 (( 78.39/10.66 (iftrueProp1) => 78.39/10.66 (( 78.39/10.66 (iftrueProp2) => 78.39/10.66 (( 78.39/10.66 (ifSingleton) => 78.39/10.66 (( 78.39/10.66 (ifp) => 78.39/10.66 (( 78.39/10.66 (theeq) => 78.39/10.66 (( 78.39/10.66 (iftrue) => 78.39/10.66 (( 78.39/10.66 (iffalse) => 78.39/10.66 (( 78.39/10.66 (iftrueorfalse) => 78.39/10.66 (( 78.39/10.66 (binintersectT_lem) => 78.39/10.66 (( 78.39/10.66 (binunionT_lem) => 78.39/10.66 (( 78.39/10.66 (powersetT_lem) => 78.39/10.66 (( 78.39/10.66 (setminusT_lem) => 78.39/10.66 (( 78.39/10.66 (complementT_lem) => 78.39/10.66 (( 78.39/10.66 (setextT) => 78.39/10.66 (( 78.39/10.66 (subsetTI) => 78.39/10.66 (( 78.39/10.66 (powersetTI1) => 78.39/10.66 (( 78.39/10.66 (powersetTE1) => 78.39/10.66 (( 78.39/10.66 (complementTI1) => 78.39/10.66 (( 78.39/10.66 (complementTE1) => 78.39/10.66 (( 78.39/10.66 (binintersectTELcontra) => 78.39/10.66 (( 78.39/10.66 (binintersectTERcontra) => 78.39/10.66 (( 78.39/10.66 (contrasubsetT) => 78.39/10.66 (( 78.39/10.66 (contrasubsetT1) => 78.39/10.66 (( 78.39/10.66 (contrasubsetT2) => 78.39/10.66 (( 78.39/10.66 (contrasubsetT3) => 78.39/10.66 (( 78.39/10.66 (doubleComplementI1) => 78.39/10.66 (( 78.39/10.66 (doubleComplementE1) => 78.39/10.66 (( 78.39/10.66 (doubleComplementSub1) => 78.39/10.66 (( 78.39/10.66 (doubleComplementSub2) => 78.39/10.66 (( 78.39/10.66 (doubleComplementEq) => 78.39/10.66 (( 78.39/10.66 (complementTnotintersectT) => 78.39/10.66 (( 78.39/10.66 (complementImpComplementIntersect) => 78.39/10.66 (( 78.39/10.66 (complementSubsetComplementIntersect) => 78.39/10.66 (( 78.39/10.66 (complementInPowersetComplementIntersect) => 78.39/10.66 (( 78.39/10.66 (contraSubsetComplement) => 78.39/10.66 (( 78.39/10.66 (complementTcontraSubset) => 78.39/10.66 (( 78.39/10.66 (binunionTILcontra) => 78.39/10.66 (( 78.39/10.66 (binunionTIRcontra) => 78.39/10.66 (( 78.39/10.66 (inIntersectImpInUnion) => 78.39/10.66 (( 78.39/10.66 (inIntersectImpInUnion2) => 78.39/10.66 (( 78.39/10.66 (inIntersectImpInIntersectUnions) => 78.39/10.66 (( 78.39/10.66 (intersectInPowersetIntersectUnions) => 78.39/10.66 (( 78.39/10.66 (inComplementUnionImpNotIn1) => 78.39/10.66 (( 78.39/10.66 (inComplementUnionImpInComplement1) => 78.39/10.66 (( 78.39/10.66 (binunionTE) => 78.39/10.66 (( 78.39/10.66 (binunionTEcontra) => 78.39/10.66 (( 78.39/10.66 (demorgan2a1) => 78.39/10.66 (( 78.39/10.66 (complementUnionInPowersetComplement) => 78.39/10.66 (( 78.39/10.66 (demorgan2a2) => 78.39/10.66 (( 78.39/10.66 (demorgan1a) => 78.39/10.66 (( 78.39/10.66 (demorgan1b) => 78.39/10.66 (( 78.39/10.66 (demorgan1) => 78.39/10.66 (( 78.39/10.66 (demorgan2a) => 78.39/10.66 (( 78.39/10.66 (demorgan2b2) => 78.39/10.66 (( 78.39/10.66 (demorgan2b) => 78.39/10.66 (( 78.39/10.66 (demorgan2) => 78.39/10.66 (( 78.39/10.66 (woz13rule0) => 78.39/10.66 (( 78.39/10.66 (woz13rule1) => 78.39/10.66 (( 78.39/10.66 (woz13rule2) => 78.39/10.66 (( 78.39/10.66 (woz13rule3) => 78.39/10.66 (( 78.39/10.66 (woz13rule4) => 78.39/10.66 (( 78.39/10.66 (woz1_1) => 78.39/10.66 (( 78.39/10.66 (woz1_2) => 78.39/10.66 (( 78.39/10.66 (woz1_3) => 78.39/10.66 (( 78.39/10.66 (woz1_4) => 78.39/10.66 (( 78.39/10.66 (woz1_5) => 78.39/10.66 (( 78.39/10.66 (breln1all2) => 78.39/10.66 (( 78.39/10.66 (breln1SetBreln1) => 78.39/10.66 (( 78.39/10.66 (choice2fnsingleton) => 78.39/10.66 (( 78.39/10.66 (setOfPairsIsBReln1) => 78.39/10.66 (( 78.39/10.66 (breln1all1) => 78.39/10.66 (( 78.39/10.66 (subbreln1) => 78.39/10.66 (( 78.39/10.66 (eqbreln1) => 78.39/10.66 (( 78.39/10.66 (breln1invprop) => 78.39/10.66 (( 78.39/10.66 (breln1invI) => 78.39/10.66 (( 78.39/10.66 (breln1invE) => 78.39/10.66 (( 78.39/10.66 (breln1compprop) => 78.39/10.66 (( 78.39/10.66 (breln1compI) => 78.39/10.66 (( 78.39/10.66 (breln1compE) => 78.39/10.66 (( 78.39/10.66 (breln1compEex) => 78.39/10.66 (( 78.39/10.66 (breln1unionprop) => 78.39/10.66 (( 78.39/10.66 (breln1unionIL) => 78.39/10.66 (( 78.39/10.66 (breln1unionIR) => 78.39/10.66 (( 78.39/10.66 (breln1unionI) => 78.39/10.66 (( 78.39/10.66 (breln1unionE) => 78.39/10.66 (( 78.39/10.66 (breln1unionEcases) => 78.39/10.66 (( 78.39/10.66 (breln1unionCommutes) => 78.39/10.66 (( 78.39/10.66 (woz2Ex) => 78.39/10.66 (( 78.39/10.66 (woz2W) => 78.39/10.66 (( 78.39/10.66 (woz2A) => 78.39/10.66 (( 78.39/10.66 (woz2B) => 78.39/10.66 (( 78.39/10.66 (image1Ex) => 78.39/10.66 (( 78.39/10.66 (image1Ex1) => 78.39/10.66 (( 78.39/10.66 (image1Equiv) => 78.39/10.66 (( 78.39/10.66 (image1E) => 78.39/10.66 (( 78.39/10.66 (image1I) => 78.39/10.66 (( 78.39/10.66 (injFuncInInjFuncSet) => 78.39/10.66 (( 78.39/10.66 (injFuncSetFuncIn) => 78.39/10.66 (( 78.39/10.66 (injFuncSetFuncInj) => 78.39/10.66 (( 78.39/10.66 (surjFuncSetFuncIn) => 78.39/10.66 (( 78.39/10.66 (surjFuncSetFuncSurj) => 78.39/10.66 (( 78.39/10.66 (leftInvIsSurj) => 78.39/10.66 (( 78.39/10.66 (surjCantorThm) => 78.39/10.66 (( 78.39/10.66 (foundation2) => 78.39/10.66 (( 78.39/10.66 (notinself) => 78.39/10.66 (( 78.39/10.66 (notinself2) => 78.39/10.66 (( 78.39/10.66 (omegaSp) => 78.39/10.66 (( 78.39/10.66 (omegaSclos) => 78.39/10.66 (( 78.39/10.66 (peano0notS) => 78.39/10.66 (( 78.39/10.66 (peanoSinj) => 78.39/10.66 (( 78.39/10.66 (transitivesetOp1) => 78.39/10.66 (( 78.39/10.66 (binintTransitive) => 78.39/10.66 (( 78.39/10.66 (transitivesetOp2) => 78.39/10.66 (( 78.39/10.66 (setunionTransitive) => 78.39/10.66 (( 78.39/10.66 (ordinalMinLem1) => 78.39/10.66 (( 78.39/10.66 (!!) @ ( 78.39/10.66 ^[Y0 : $i]: 78.39/10.66 (( 78.39/10.66 (ordinal @ 78.39/10.66 Y0) => 78.39/10.66 (( 78.39/10.66 (!!) @ ( 78.39/10.66 ^[Y1 : $i]: 78.39/10.66 (( 78.39/10.66 (!!) @ ( 78.39/10.66 ^[Y2 : $i]: 78.39/10.66 (( 78.39/10.66 (in @ 78.39/10.66 Y2 @ 78.39/10.66 Y0) => 78.39/10.66 (( 78.39/10.66 (in @ 78.39/10.66 Y1 @ 78.39/10.66 Y2) => 78.39/10.66 (in @ 78.39/10.66 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 78.39/10.66 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1014])). 78.39/10.66 thf(zip_derived_cl1028, plain, 78.39/10.66 (~ (((bs114d) => 78.39/10.66 (((setminusI) => 78.39/10.66 (((setminusEL) => 78.39/10.66 (((setminusER) => 78.39/10.66 (((setminusSubset2) => 78.39/10.66 (((setminusERneg) => 78.39/10.66 (((setminusELneg) => 78.39/10.66 (((setminusILneg) => 78.39/10.66 (((setminusIRneg) => 78.39/10.66 (((setminusLsub) => 78.39/10.66 (((setminusSubset1) => 78.39/10.66 (((symdiffE) => 78.39/10.66 (((symdiffI1) => 78.39/10.66 (((symdiffI2) => 78.39/10.66 (((symdiffIneg1) => 78.39/10.66 (((symdiffIneg2) => 78.39/10.66 (((secondinupair) => 78.39/10.66 (((setukpairIL) => 78.39/10.66 (((setukpairIR) => 78.39/10.66 (((kpairiskpair) => 78.39/10.66 (((kpairp) => 78.39/10.66 (((singletonsubset) => 78.39/10.66 (((singletoninpowerset) => 78.39/10.66 (((singletoninpowunion) => 78.39/10.66 (((upairset2E) => 78.39/10.66 (((upairsubunion) => 78.39/10.66 (((upairinpowunion) => 78.39/10.66 (((ubforcartprodlem1) => 78.39/10.66 (((ubforcartprodlem2) => 78.39/10.66 (((ubforcartprodlem3) => 78.39/10.66 (( 78.39/10.66 (cartprodpairin) => 78.39/10.66 (( 78.39/10.66 (cartprodmempair1) => 78.39/10.66 (( 78.39/10.66 (cartprodmempair) => 78.39/10.66 (( 78.39/10.66 (setunionE2) => 78.39/10.66 (( 78.39/10.66 (setunionsingleton1) => 78.39/10.66 (( 78.39/10.66 (setunionsingleton2) => 78.39/10.66 (( 78.39/10.66 (setunionsingleton) => 78.39/10.66 (( 78.39/10.66 (singletonprop) => 78.39/10.66 (( 78.39/10.66 (ex1E1) => 78.39/10.66 (( 78.39/10.66 (ex1I) => 78.39/10.66 (( 78.39/10.66 (ex1I2) => 78.39/10.66 (( 78.39/10.66 (singletonsuniq) => 78.39/10.66 (( 78.39/10.66 (setukpairinjL1) => 78.39/10.66 (( 78.39/10.66 (kfstsingleton) => 78.39/10.66 (( 78.39/10.66 (theprop) => 78.39/10.66 (( 78.39/10.66 (kfstpairEq) => 78.39/10.66 (( 78.39/10.66 (cartprodfstin) => 78.39/10.66 (( 78.39/10.66 (setukpairinjL2) => 78.39/10.66 (( 78.39/10.66 (setukpairinjL) => 78.39/10.66 (( 78.39/10.66 (setukpairinjR11) => 78.39/10.66 (( 78.39/10.66 (setukpairinjR12) => 78.39/10.66 (( 78.39/10.66 (setukpairinjR1) => 78.39/10.66 (( 78.39/10.66 (upairequniteq) => 78.39/10.66 (( 78.39/10.66 (setukpairinjR2) => 78.39/10.66 (( 78.39/10.66 (setukpairinjR) => 78.39/10.66 (( 78.39/10.66 (ksndsingleton) => 78.39/10.66 (( 78.39/10.66 (ksndpairEq) => 78.39/10.66 (( 78.39/10.66 (kpairsurjEq) => 78.39/10.66 (( 78.39/10.66 (cartprodsndin) => 78.39/10.66 (( 78.39/10.66 (cartprodpairmemEL) => 78.39/10.66 (( 78.39/10.66 (cartprodpairmemER) => 78.39/10.66 (( 78.39/10.66 (cartprodmempaircEq) => 78.39/10.66 (( 78.39/10.66 (cartprodfstpairEq) => 78.39/10.66 (( 78.39/10.66 (cartprodsndpairEq) => 78.39/10.66 (( 78.39/10.66 (cartprodpairsurjEq) => 78.39/10.66 (( 78.39/10.66 (dpsetconstrI) => 78.39/10.66 (( 78.39/10.66 (dpsetconstrSub) => 78.39/10.66 (( 78.39/10.66 (setOfPairsIsBReln) => 78.39/10.66 (( 78.39/10.66 (dpsetconstrERa) => 78.39/10.66 (( 78.39/10.66 (dpsetconstrEL1) => 78.39/10.66 (( 78.39/10.66 (dpsetconstrEL2) => 78.39/10.66 (( 78.39/10.66 (dpsetconstrER) => 78.39/10.66 (( 78.39/10.66 (funcImageSingleton) => 78.39/10.66 (( 78.39/10.66 (apProp) => 78.39/10.66 (( 78.39/10.66 (app) => 78.39/10.66 (( 78.39/10.66 (infuncsetfunc) => 78.39/10.66 (( 78.39/10.66 (ap2p) => 78.39/10.66 (( 78.39/10.66 (funcinfuncset) => 78.39/10.66 (( 78.39/10.66 (lamProp) => 78.39/10.66 (( 78.39/10.66 (lamp) => 78.39/10.66 (( 78.39/10.66 (lam2p) => 78.39/10.66 (( 78.39/10.66 (brelnall1) => 78.39/10.66 (( 78.39/10.66 (brelnall2) => 78.39/10.66 (( 78.39/10.66 (ex1E2) => 78.39/10.66 (( 78.39/10.66 (funcGraphProp1) => 78.39/10.66 (( 78.39/10.66 (funcGraphProp3) => 78.39/10.66 (( 78.39/10.66 (funcGraphProp2) => 78.39/10.66 (( 78.39/10.66 (funcextLem) => 78.39/10.66 (( 78.39/10.66 (funcGraphProp4) => 78.39/10.66 (( 78.39/10.66 (subbreln) => 78.39/10.66 (( 78.39/10.66 (eqbreln) => 78.39/10.66 (( 78.39/10.66 (funcext) => 78.39/10.66 (( 78.39/10.66 (funcext2) => 78.39/10.66 (( 78.39/10.66 (ap2apEq1) => 78.39/10.66 (( 78.39/10.66 (ap2apEq2) => 78.39/10.66 (( 78.39/10.66 (beta1) => 78.39/10.66 (( 78.39/10.66 (eta1) => 78.39/10.66 (( 78.39/10.66 (lam2lamEq) => 78.39/10.66 (( 78.39/10.66 (beta2) => 78.39/10.66 (( 78.39/10.66 (eta2) => 78.39/10.66 (( 78.39/10.66 (iffalseProp1) => 78.39/10.66 (( 78.39/10.66 (iffalseProp2) => 78.39/10.66 (( 78.39/10.66 (iftrueProp1) => 78.39/10.66 (( 78.39/10.66 (iftrueProp2) => 78.39/10.66 (( 78.39/10.66 (ifSingleton) => 78.39/10.66 (( 78.39/10.66 (ifp) => 78.39/10.66 (( 78.39/10.66 (theeq) => 78.39/10.66 (( 78.39/10.66 (iftrue) => 78.39/10.66 (( 78.39/10.66 (iffalse) => 78.39/10.66 (( 78.39/10.66 (iftrueorfalse) => 78.39/10.66 (( 78.39/10.66 (binintersectT_lem) => 78.39/10.66 (( 78.39/10.66 (binunionT_lem) => 78.39/10.66 (( 78.39/10.66 (powersetT_lem) => 78.39/10.66 (( 78.39/10.66 (setminusT_lem) => 78.39/10.66 (( 78.39/10.66 (complementT_lem) => 78.39/10.66 (( 78.39/10.66 (setextT) => 78.39/10.66 (( 78.39/10.66 (subsetTI) => 78.39/10.66 (( 78.39/10.66 (powersetTI1) => 78.39/10.66 (( 78.39/10.66 (powersetTE1) => 78.39/10.66 (( 78.39/10.66 (complementTI1) => 78.39/10.66 (( 78.39/10.66 (complementTE1) => 78.39/10.66 (( 78.39/10.66 (binintersectTELcontra) => 78.39/10.66 (( 78.39/10.66 (binintersectTERcontra) => 78.39/10.66 (( 78.39/10.66 (contrasubsetT) => 78.39/10.66 (( 78.39/10.66 (contrasubsetT1) => 78.39/10.66 (( 78.39/10.66 (contrasubsetT2) => 78.39/10.66 (( 78.39/10.66 (contrasubsetT3) => 78.39/10.66 (( 78.39/10.66 (doubleComplementI1) => 78.39/10.66 (( 78.39/10.66 (doubleComplementE1) => 78.39/10.66 (( 78.39/10.66 (doubleComplementSub1) => 78.39/10.66 (( 78.39/10.66 (doubleComplementSub2) => 78.39/10.66 (( 78.39/10.66 (doubleComplementEq) => 78.39/10.66 (( 78.39/10.66 (complementTnotintersectT) => 78.39/10.66 (( 78.39/10.66 (complementImpComplementIntersect) => 78.39/10.66 (( 78.39/10.66 (complementSubsetComplementIntersect) => 78.39/10.66 (( 78.39/10.66 (complementInPowersetComplementIntersect) => 78.39/10.66 (( 78.39/10.66 (contraSubsetComplement) => 78.39/10.66 (( 78.39/10.66 (complementTcontraSubset) => 78.39/10.66 (( 78.39/10.66 (binunionTILcontra) => 78.39/10.66 (( 78.39/10.66 (binunionTIRcontra) => 78.39/10.66 (( 78.39/10.66 (inIntersectImpInUnion) => 78.39/10.66 (( 78.39/10.66 (inIntersectImpInUnion2) => 78.39/10.66 (( 78.39/10.66 (inIntersectImpInIntersectUnions) => 78.39/10.66 (( 78.39/10.66 (intersectInPowersetIntersectUnions) => 78.39/10.66 (( 78.39/10.66 (inComplementUnionImpNotIn1) => 78.39/10.66 (( 78.39/10.66 (inComplementUnionImpInComplement1) => 78.39/10.66 (( 78.39/10.66 (binunionTE) => 78.39/10.66 (( 78.39/10.66 (binunionTEcontra) => 78.39/10.66 (( 78.39/10.66 (demorgan2a1) => 78.39/10.66 (( 78.39/10.66 (complementUnionInPowersetComplement) => 78.39/10.66 (( 78.39/10.66 (demorgan2a2) => 78.39/10.66 (( 78.39/10.66 (demorgan1a) => 78.39/10.66 (( 78.39/10.66 (demorgan1b) => 78.39/10.66 (( 78.39/10.66 (demorgan1) => 78.39/10.66 (( 78.39/10.66 (demorgan2a) => 78.39/10.66 (( 78.39/10.66 (demorgan2b2) => 78.39/10.66 (( 78.39/10.66 (demorgan2b) => 78.39/10.67 (( 78.39/10.67 (demorgan2) => 78.39/10.67 (( 78.39/10.67 (woz13rule0) => 78.39/10.67 (( 78.39/10.67 (woz13rule1) => 78.39/10.67 (( 78.39/10.67 (woz13rule2) => 78.39/10.67 (( 78.39/10.67 (woz13rule3) => 78.39/10.67 (( 78.39/10.67 (woz13rule4) => 78.39/10.67 (( 78.39/10.67 (woz1_1) => 78.39/10.67 (( 78.39/10.67 (woz1_2) => 78.39/10.67 (( 78.39/10.67 (woz1_3) => 78.39/10.67 (( 78.39/10.67 (woz1_4) => 78.39/10.67 (( 78.39/10.67 (woz1_5) => 78.39/10.67 (( 78.39/10.67 (breln1all2) => 78.39/10.67 (( 78.39/10.67 (breln1SetBreln1) => 78.39/10.67 (( 78.39/10.67 (choice2fnsingleton) => 78.39/10.67 (( 78.39/10.67 (setOfPairsIsBReln1) => 78.39/10.67 (( 78.39/10.67 (breln1all1) => 78.39/10.67 (( 78.39/10.67 (subbreln1) => 78.39/10.67 (( 78.39/10.67 (eqbreln1) => 78.39/10.67 (( 78.39/10.67 (breln1invprop) => 78.39/10.67 (( 78.39/10.67 (breln1invI) => 78.39/10.67 (( 78.39/10.67 (breln1invE) => 78.39/10.67 (( 78.39/10.67 (breln1compprop) => 78.39/10.67 (( 78.39/10.67 (breln1compI) => 78.39/10.67 (( 78.39/10.67 (breln1compE) => 78.39/10.67 (( 78.39/10.67 (breln1compEex) => 78.39/10.67 (( 78.39/10.67 (breln1unionprop) => 78.39/10.67 (( 78.39/10.67 (breln1unionIL) => 78.39/10.67 (( 78.39/10.67 (breln1unionIR) => 78.39/10.67 (( 78.39/10.67 (breln1unionI) => 78.39/10.67 (( 78.39/10.67 (breln1unionE) => 78.39/10.67 (( 78.39/10.67 (breln1unionEcases) => 78.39/10.67 (( 78.39/10.67 (breln1unionCommutes) => 78.39/10.67 (( 78.39/10.67 (woz2Ex) => 78.39/10.67 (( 78.39/10.67 (woz2W) => 78.39/10.67 (( 78.39/10.67 (woz2A) => 78.39/10.67 (( 78.39/10.67 (woz2B) => 78.39/10.67 (( 78.39/10.67 (image1Ex) => 78.39/10.67 (( 78.39/10.67 (image1Ex1) => 78.39/10.67 (( 78.39/10.67 (image1Equiv) => 78.39/10.67 (( 78.39/10.67 (image1E) => 78.39/10.67 (( 78.39/10.67 (image1I) => 78.39/10.67 (( 78.39/10.67 (injFuncInInjFuncSet) => 78.39/10.67 (( 78.39/10.67 (injFuncSetFuncIn) => 78.39/10.67 (( 78.39/10.67 (injFuncSetFuncInj) => 78.39/10.67 (( 78.39/10.67 (surjFuncSetFuncIn) => 78.39/10.67 (( 78.39/10.67 (surjFuncSetFuncSurj) => 78.39/10.67 (( 78.39/10.67 (leftInvIsSurj) => 78.39/10.67 (( 78.39/10.67 (surjCantorThm) => 78.39/10.67 (( 78.39/10.67 (foundation2) => 78.39/10.67 (( 78.39/10.67 (notinself) => 78.39/10.67 (( 78.39/10.67 (notinself2) => 78.39/10.67 (( 78.39/10.67 (omegaSp) => 78.39/10.67 (( 78.39/10.67 (omegaSclos) => 78.39/10.67 (( 78.39/10.67 (peano0notS) => 78.39/10.67 (( 78.39/10.67 (peanoSinj) => 78.39/10.67 (( 78.39/10.67 (transitivesetOp1) => 78.39/10.67 (( 78.39/10.67 (binintTransitive) => 78.39/10.67 (( 78.39/10.67 (transitivesetOp2) => 78.39/10.67 (( 78.39/10.67 (setunionTransitive) => 78.39/10.67 (( 78.39/10.67 (ordinalMinLem1) => 78.39/10.67 (( 78.39/10.67 (!!) @ ( 78.39/10.67 ^[Y0 : $i]: 78.39/10.67 (( 78.39/10.67 (ordinal @ 78.39/10.67 Y0) => 78.39/10.67 (( 78.39/10.67 (!!) @ ( 78.39/10.67 ^[Y1 : $i]: 78.39/10.67 (( 78.39/10.67 (!!) @ ( 78.39/10.67 ^[Y2 : $i]: 78.39/10.67 (( 78.39/10.67 (in @ 78.39/10.67 Y2 @ 78.39/10.67 Y0) => 78.39/10.67 (( 78.39/10.67 (in @ 78.39/10.67 Y1 @ 78.39/10.67 Y2) => 78.39/10.67 (in @ 78.39/10.67 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 78.39/10.67 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1021])). 78.39/10.67 thf(zip_derived_cl1034, plain, 78.39/10.67 (~ (((setminusI) => 78.39/10.67 (((setminusEL) => 78.39/10.67 (((setminusER) => 78.39/10.67 (((setminusSubset2) => 78.39/10.67 (((setminusERneg) => 78.39/10.67 (((setminusELneg) => 78.39/10.67 (((setminusILneg) => 78.39/10.67 (((setminusIRneg) => 78.39/10.67 (((setminusLsub) => 78.39/10.67 (((setminusSubset1) => 78.39/10.67 (((symdiffE) => 78.39/10.67 (((symdiffI1) => 78.39/10.67 (((symdiffI2) => 78.39/10.67 (((symdiffIneg1) => 78.39/10.67 (((symdiffIneg2) => 78.39/10.67 (((secondinupair) => 78.39/10.67 (((setukpairIL) => 78.39/10.67 (((setukpairIR) => 78.39/10.67 (((kpairiskpair) => 78.39/10.67 (((kpairp) => 78.39/10.67 (((singletonsubset) => 78.39/10.67 (((singletoninpowerset) => 78.39/10.67 (((singletoninpowunion) => 78.39/10.67 (((upairset2E) => 78.39/10.67 (((upairsubunion) => 78.39/10.67 (((upairinpowunion) => 78.39/10.67 (((ubforcartprodlem1) => 78.39/10.67 (((ubforcartprodlem2) => 78.39/10.67 (((ubforcartprodlem3) => 78.39/10.67 (((cartprodpairin) => 78.39/10.67 (( 78.39/10.67 (cartprodmempair1) => 78.39/10.67 (( 78.39/10.67 (cartprodmempair) => 78.39/10.67 (( 78.39/10.67 (setunionE2) => 78.39/10.67 (( 78.39/10.67 (setunionsingleton1) => 78.39/10.67 (( 78.39/10.67 (setunionsingleton2) => 78.39/10.67 (( 78.39/10.67 (setunionsingleton) => 78.39/10.67 (( 78.39/10.67 (singletonprop) => 78.39/10.67 (( 78.39/10.67 (ex1E1) => 78.39/10.67 (( 78.39/10.67 (ex1I) => 78.39/10.67 (( 78.39/10.67 (ex1I2) => 78.39/10.67 (( 78.39/10.67 (singletonsuniq) => 78.39/10.67 (( 78.39/10.67 (setukpairinjL1) => 78.39/10.67 (( 78.39/10.67 (kfstsingleton) => 78.39/10.67 (( 78.39/10.67 (theprop) => 78.39/10.67 (( 78.39/10.67 (kfstpairEq) => 78.39/10.67 (( 78.39/10.67 (cartprodfstin) => 78.39/10.67 (( 78.39/10.67 (setukpairinjL2) => 78.39/10.67 (( 78.39/10.67 (setukpairinjL) => 78.39/10.67 (( 78.39/10.67 (setukpairinjR11) => 78.39/10.67 (( 78.39/10.67 (setukpairinjR12) => 78.39/10.67 (( 78.39/10.67 (setukpairinjR1) => 78.39/10.67 (( 78.39/10.67 (upairequniteq) => 78.39/10.67 (( 78.39/10.67 (setukpairinjR2) => 78.39/10.67 (( 78.39/10.67 (setukpairinjR) => 78.39/10.67 (( 78.39/10.67 (ksndsingleton) => 78.39/10.67 (( 78.39/10.67 (ksndpairEq) => 78.39/10.67 (( 78.39/10.67 (kpairsurjEq) => 78.39/10.67 (( 78.39/10.67 (cartprodsndin) => 78.39/10.67 (( 78.39/10.67 (cartprodpairmemEL) => 78.39/10.67 (( 78.39/10.67 (cartprodpairmemER) => 78.39/10.67 (( 78.39/10.67 (cartprodmempaircEq) => 78.39/10.67 (( 78.39/10.67 (cartprodfstpairEq) => 78.39/10.67 (( 78.39/10.67 (cartprodsndpairEq) => 78.39/10.67 (( 78.39/10.67 (cartprodpairsurjEq) => 78.39/10.67 (( 78.39/10.67 (dpsetconstrI) => 78.39/10.67 (( 78.39/10.67 (dpsetconstrSub) => 78.39/10.67 (( 78.39/10.67 (setOfPairsIsBReln) => 78.39/10.67 (( 78.39/10.67 (dpsetconstrERa) => 78.39/10.67 (( 78.39/10.67 (dpsetconstrEL1) => 78.39/10.67 (( 78.39/10.67 (dpsetconstrEL2) => 78.39/10.67 (( 78.39/10.67 (dpsetconstrER) => 78.39/10.67 (( 78.39/10.67 (funcImageSingleton) => 78.39/10.67 (( 78.39/10.67 (apProp) => 78.39/10.67 (( 78.39/10.67 (app) => 78.39/10.67 (( 78.39/10.67 (infuncsetfunc) => 78.39/10.67 (( 78.39/10.67 (ap2p) => 78.39/10.67 (( 78.39/10.67 (funcinfuncset) => 78.39/10.67 (( 78.39/10.67 (lamProp) => 78.39/10.67 (( 78.39/10.67 (lamp) => 78.39/10.67 (( 78.39/10.67 (lam2p) => 78.39/10.67 (( 78.39/10.67 (brelnall1) => 78.39/10.67 (( 78.39/10.67 (brelnall2) => 78.39/10.67 (( 78.39/10.67 (ex1E2) => 78.39/10.67 (( 78.39/10.67 (funcGraphProp1) => 78.39/10.67 (( 78.39/10.67 (funcGraphProp3) => 78.39/10.67 (( 78.39/10.67 (funcGraphProp2) => 78.39/10.67 (( 78.39/10.67 (funcextLem) => 78.39/10.67 (( 78.39/10.67 (funcGraphProp4) => 78.39/10.67 (( 78.39/10.67 (subbreln) => 78.39/10.67 (( 78.39/10.67 (eqbreln) => 78.39/10.67 (( 78.39/10.67 (funcext) => 78.39/10.67 (( 78.39/10.67 (funcext2) => 78.39/10.67 (( 78.39/10.67 (ap2apEq1) => 78.39/10.67 (( 78.39/10.67 (ap2apEq2) => 78.39/10.67 (( 78.39/10.67 (beta1) => 78.39/10.67 (( 78.39/10.67 (eta1) => 78.39/10.67 (( 78.39/10.67 (lam2lamEq) => 78.39/10.67 (( 78.39/10.67 (beta2) => 78.39/10.67 (( 78.39/10.67 (eta2) => 78.39/10.67 (( 78.39/10.67 (iffalseProp1) => 78.39/10.67 (( 78.39/10.67 (iffalseProp2) => 78.39/10.67 (( 78.39/10.67 (iftrueProp1) => 78.39/10.67 (( 78.39/10.67 (iftrueProp2) => 78.39/10.67 (( 78.39/10.67 (ifSingleton) => 78.39/10.67 (( 78.39/10.67 (ifp) => 78.39/10.67 (( 78.39/10.67 (theeq) => 78.39/10.67 (( 78.39/10.67 (iftrue) => 78.39/10.67 (( 78.39/10.67 (iffalse) => 78.39/10.67 (( 78.39/10.67 (iftrueorfalse) => 78.39/10.67 (( 78.39/10.67 (binintersectT_lem) => 78.39/10.67 (( 78.39/10.67 (binunionT_lem) => 78.39/10.67 (( 78.39/10.67 (powersetT_lem) => 78.39/10.67 (( 78.39/10.67 (setminusT_lem) => 78.39/10.67 (( 78.39/10.67 (complementT_lem) => 78.39/10.67 (( 78.39/10.67 (setextT) => 78.39/10.67 (( 78.39/10.67 (subsetTI) => 78.39/10.67 (( 78.39/10.67 (powersetTI1) => 78.39/10.67 (( 78.39/10.67 (powersetTE1) => 78.39/10.67 (( 78.39/10.67 (complementTI1) => 78.39/10.67 (( 78.39/10.67 (complementTE1) => 78.39/10.67 (( 78.39/10.67 (binintersectTELcontra) => 78.39/10.67 (( 78.39/10.67 (binintersectTERcontra) => 78.39/10.67 (( 78.39/10.67 (contrasubsetT) => 78.39/10.67 (( 78.39/10.67 (contrasubsetT1) => 78.39/10.67 (( 78.39/10.67 (contrasubsetT2) => 78.39/10.67 (( 78.39/10.67 (contrasubsetT3) => 78.39/10.67 (( 78.39/10.67 (doubleComplementI1) => 78.39/10.67 (( 78.39/10.67 (doubleComplementE1) => 78.39/10.67 (( 78.39/10.67 (doubleComplementSub1) => 78.39/10.67 (( 78.39/10.67 (doubleComplementSub2) => 78.39/10.67 (( 78.39/10.67 (doubleComplementEq) => 78.39/10.67 (( 78.39/10.67 (complementTnotintersectT) => 78.39/10.67 (( 78.39/10.67 (complementImpComplementIntersect) => 78.39/10.67 (( 78.39/10.67 (complementSubsetComplementIntersect) => 78.39/10.67 (( 78.39/10.67 (complementInPowersetComplementIntersect) => 78.39/10.67 (( 78.39/10.67 (contraSubsetComplement) => 78.39/10.67 (( 78.39/10.67 (complementTcontraSubset) => 78.39/10.67 (( 78.39/10.67 (binunionTILcontra) => 78.39/10.67 (( 78.39/10.67 (binunionTIRcontra) => 78.39/10.67 (( 78.39/10.67 (inIntersectImpInUnion) => 78.39/10.67 (( 78.39/10.67 (inIntersectImpInUnion2) => 78.39/10.67 (( 78.39/10.67 (inIntersectImpInIntersectUnions) => 78.39/10.67 (( 78.39/10.67 (intersectInPowersetIntersectUnions) => 78.39/10.67 (( 78.39/10.67 (inComplementUnionImpNotIn1) => 78.39/10.67 (( 78.39/10.67 (inComplementUnionImpInComplement1) => 78.39/10.67 (( 78.39/10.67 (binunionTE) => 78.39/10.67 (( 78.39/10.67 (binunionTEcontra) => 78.39/10.67 (( 78.39/10.67 (demorgan2a1) => 78.39/10.67 (( 78.39/10.67 (complementUnionInPowersetComplement) => 78.39/10.67 (( 78.39/10.67 (demorgan2a2) => 78.39/10.67 (( 78.39/10.67 (demorgan1a) => 78.39/10.67 (( 78.39/10.67 (demorgan1b) => 78.39/10.67 (( 78.39/10.67 (demorgan1) => 78.39/10.67 (( 78.39/10.67 (demorgan2a) => 78.39/10.67 (( 78.39/10.67 (demorgan2b2) => 78.39/10.67 (( 78.39/10.67 (demorgan2b) => 78.39/10.67 (( 78.39/10.67 (demorgan2) => 78.39/10.67 (( 78.39/10.67 (woz13rule0) => 78.39/10.67 (( 78.39/10.67 (woz13rule1) => 78.39/10.67 (( 78.39/10.67 (woz13rule2) => 78.39/10.67 (( 78.39/10.67 (woz13rule3) => 78.39/10.67 (( 78.39/10.67 (woz13rule4) => 78.39/10.67 (( 78.39/10.67 (woz1_1) => 78.39/10.67 (( 78.39/10.67 (woz1_2) => 78.39/10.67 (( 78.39/10.67 (woz1_3) => 78.39/10.67 (( 78.39/10.67 (woz1_4) => 78.39/10.67 (( 78.39/10.67 (woz1_5) => 78.39/10.67 (( 78.39/10.67 (breln1all2) => 78.39/10.67 (( 78.39/10.67 (breln1SetBreln1) => 78.39/10.67 (( 78.39/10.67 (choice2fnsingleton) => 78.39/10.67 (( 78.39/10.67 (setOfPairsIsBReln1) => 78.39/10.67 (( 78.39/10.67 (breln1all1) => 78.39/10.67 (( 78.39/10.67 (subbreln1) => 78.39/10.67 (( 78.39/10.67 (eqbreln1) => 78.39/10.67 (( 78.39/10.67 (breln1invprop) => 78.39/10.67 (( 78.39/10.67 (breln1invI) => 78.39/10.67 (( 78.39/10.67 (breln1invE) => 78.39/10.67 (( 78.39/10.67 (breln1compprop) => 78.39/10.67 (( 78.39/10.67 (breln1compI) => 78.39/10.67 (( 78.39/10.67 (breln1compE) => 78.39/10.67 (( 78.39/10.67 (breln1compEex) => 78.39/10.67 (( 78.39/10.67 (breln1unionprop) => 78.39/10.67 (( 78.39/10.67 (breln1unionIL) => 78.39/10.67 (( 78.39/10.67 (breln1unionIR) => 78.39/10.67 (( 78.39/10.67 (breln1unionI) => 78.39/10.67 (( 78.39/10.67 (breln1unionE) => 78.39/10.67 (( 78.39/10.67 (breln1unionEcases) => 78.39/10.67 (( 78.39/10.67 (breln1unionCommutes) => 78.39/10.67 (( 78.39/10.67 (woz2Ex) => 78.39/10.67 (( 78.39/10.67 (woz2W) => 78.39/10.67 (( 78.39/10.67 (woz2A) => 78.39/10.67 (( 78.39/10.67 (woz2B) => 78.39/10.67 (( 78.39/10.67 (image1Ex) => 78.39/10.67 (( 78.39/10.67 (image1Ex1) => 78.39/10.67 (( 78.39/10.67 (image1Equiv) => 78.39/10.67 (( 78.39/10.67 (image1E) => 78.39/10.67 (( 78.39/10.67 (image1I) => 78.39/10.67 (( 78.39/10.67 (injFuncInInjFuncSet) => 78.39/10.67 (( 78.39/10.67 (injFuncSetFuncIn) => 78.39/10.67 (( 78.39/10.67 (injFuncSetFuncInj) => 78.39/10.67 (( 78.39/10.67 (surjFuncSetFuncIn) => 78.39/10.67 (( 78.39/10.67 (surjFuncSetFuncSurj) => 78.39/10.67 (( 78.39/10.67 (leftInvIsSurj) => 78.39/10.67 (( 78.39/10.67 (surjCantorThm) => 78.39/10.67 (( 78.39/10.67 (foundation2) => 78.39/10.67 (( 78.39/10.67 (notinself) => 78.39/10.67 (( 78.39/10.67 (notinself2) => 78.39/10.67 (( 78.39/10.67 (omegaSp) => 78.39/10.67 (( 78.39/10.67 (omegaSclos) => 78.39/10.67 (( 78.39/10.67 (peano0notS) => 78.39/10.67 (( 78.39/10.67 (peanoSinj) => 78.39/10.67 (( 78.39/10.67 (transitivesetOp1) => 78.39/10.67 (( 78.39/10.67 (binintTransitive) => 78.39/10.67 (( 78.39/10.67 (transitivesetOp2) => 78.39/10.67 (( 78.39/10.67 (setunionTransitive) => 78.39/10.67 (( 78.39/10.67 (ordinalMinLem1) => 78.39/10.67 (( 78.39/10.67 (!!) @ ( 78.39/10.67 ^[Y0 : $i]: 78.39/10.67 (( 78.39/10.67 (ordinal @ 78.39/10.67 Y0) => 78.39/10.67 (( 78.39/10.67 (!!) @ ( 78.39/10.67 ^[Y1 : $i]: 78.39/10.67 (( 78.39/10.67 (!!) @ ( 78.39/10.67 ^[Y2 : $i]: 78.39/10.67 (( 78.39/10.67 (in @ 78.39/10.67 Y2 @ 78.39/10.67 Y0) => 78.39/10.67 (( 78.39/10.67 (in @ 78.39/10.67 Y1 @ 78.39/10.67 Y2) => 78.39/10.67 (in @ 78.39/10.67 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 78.39/10.67 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1028])). 78.39/10.67 thf(zip_derived_cl1041, plain, 78.39/10.67 (~ (((setminusEL) => 78.39/10.67 (((setminusER) => 78.39/10.67 (((setminusSubset2) => 78.39/10.67 (((setminusERneg) => 78.39/10.67 (((setminusELneg) => 78.39/10.67 (((setminusILneg) => 78.39/10.67 (((setminusIRneg) => 78.39/10.67 (((setminusLsub) => 78.39/10.67 (((setminusSubset1) => 78.39/10.67 (((symdiffE) => 78.39/10.67 (((symdiffI1) => 78.39/10.67 (((symdiffI2) => 78.39/10.67 (((symdiffIneg1) => 78.39/10.67 (((symdiffIneg2) => 78.39/10.67 (((secondinupair) => 78.39/10.67 (((setukpairIL) => 78.39/10.67 (((setukpairIR) => 78.39/10.67 (((kpairiskpair) => 78.39/10.67 (((kpairp) => 78.39/10.67 (((singletonsubset) => 78.39/10.67 (((singletoninpowerset) => 78.39/10.67 (((singletoninpowunion) => 78.39/10.67 (((upairset2E) => 78.39/10.67 (((upairsubunion) => 78.39/10.67 (((upairinpowunion) => 78.39/10.67 (((ubforcartprodlem1) => 78.39/10.67 (((ubforcartprodlem2) => 78.39/10.67 (((ubforcartprodlem3) => 78.39/10.67 (((cartprodpairin) => 78.39/10.67 (((cartprodmempair1) => 78.39/10.67 (( 78.39/10.67 (cartprodmempair) => 78.39/10.67 (( 78.39/10.67 (setunionE2) => 78.39/10.67 (( 78.39/10.67 (setunionsingleton1) => 78.39/10.67 (( 78.39/10.67 (setunionsingleton2) => 78.39/10.67 (( 78.39/10.67 (setunionsingleton) => 78.39/10.67 (( 78.39/10.67 (singletonprop) => 78.39/10.67 (( 78.39/10.67 (ex1E1) => 78.39/10.67 (( 78.39/10.67 (ex1I) => 78.39/10.67 (( 78.39/10.67 (ex1I2) => 78.39/10.67 (( 78.39/10.67 (singletonsuniq) => 78.39/10.67 (( 78.39/10.67 (setukpairinjL1) => 78.39/10.67 (( 78.39/10.67 (kfstsingleton) => 78.39/10.67 (( 78.39/10.67 (theprop) => 78.39/10.67 (( 78.39/10.67 (kfstpairEq) => 78.39/10.67 (( 78.39/10.67 (cartprodfstin) => 78.39/10.67 (( 78.39/10.67 (setukpairinjL2) => 78.39/10.67 (( 78.39/10.67 (setukpairinjL) => 78.39/10.67 (( 78.39/10.67 (setukpairinjR11) => 78.39/10.67 (( 78.39/10.67 (setukpairinjR12) => 78.39/10.67 (( 78.39/10.67 (setukpairinjR1) => 78.39/10.67 (( 78.39/10.67 (upairequniteq) => 78.39/10.67 (( 78.39/10.67 (setukpairinjR2) => 78.39/10.67 (( 78.39/10.67 (setukpairinjR) => 78.39/10.67 (( 78.39/10.67 (ksndsingleton) => 78.39/10.67 (( 78.39/10.67 (ksndpairEq) => 78.39/10.67 (( 78.39/10.67 (kpairsurjEq) => 78.39/10.67 (( 78.39/10.67 (cartprodsndin) => 78.39/10.67 (( 78.39/10.67 (cartprodpairmemEL) => 78.39/10.67 (( 78.39/10.67 (cartprodpairmemER) => 78.39/10.67 (( 78.39/10.67 (cartprodmempaircEq) => 78.39/10.67 (( 78.39/10.67 (cartprodfstpairEq) => 78.39/10.67 (( 78.39/10.67 (cartprodsndpairEq) => 78.39/10.67 (( 78.39/10.67 (cartprodpairsurjEq) => 78.39/10.67 (( 78.39/10.67 (dpsetconstrI) => 78.39/10.67 (( 78.39/10.67 (dpsetconstrSub) => 78.39/10.67 (( 78.39/10.67 (setOfPairsIsBReln) => 78.39/10.67 (( 78.39/10.67 (dpsetconstrERa) => 78.39/10.67 (( 78.39/10.67 (dpsetconstrEL1) => 78.39/10.67 (( 78.39/10.67 (dpsetconstrEL2) => 78.39/10.67 (( 78.39/10.67 (dpsetconstrER) => 78.39/10.67 (( 78.39/10.67 (funcImageSingleton) => 78.39/10.67 (( 78.39/10.67 (apProp) => 78.39/10.67 (( 78.39/10.67 (app) => 78.39/10.67 (( 78.39/10.67 (infuncsetfunc) => 78.39/10.67 (( 78.39/10.67 (ap2p) => 78.39/10.67 (( 78.39/10.67 (funcinfuncset) => 78.39/10.67 (( 78.39/10.67 (lamProp) => 78.39/10.67 (( 78.39/10.67 (lamp) => 78.39/10.67 (( 78.39/10.67 (lam2p) => 78.39/10.67 (( 78.39/10.67 (brelnall1) => 78.39/10.67 (( 78.39/10.67 (brelnall2) => 78.39/10.67 (( 78.39/10.67 (ex1E2) => 78.39/10.67 (( 78.39/10.67 (funcGraphProp1) => 78.39/10.67 (( 78.39/10.67 (funcGraphProp3) => 78.39/10.67 (( 78.39/10.67 (funcGraphProp2) => 78.39/10.67 (( 78.39/10.67 (funcextLem) => 78.39/10.67 (( 78.39/10.67 (funcGraphProp4) => 78.39/10.67 (( 78.39/10.67 (subbreln) => 78.39/10.67 (( 78.39/10.67 (eqbreln) => 78.39/10.67 (( 78.39/10.67 (funcext) => 78.39/10.67 (( 78.39/10.67 (funcext2) => 78.39/10.67 (( 78.39/10.67 (ap2apEq1) => 78.39/10.67 (( 78.39/10.67 (ap2apEq2) => 78.39/10.67 (( 78.39/10.67 (beta1) => 78.39/10.67 (( 78.39/10.67 (eta1) => 78.39/10.67 (( 78.39/10.67 (lam2lamEq) => 78.39/10.67 (( 78.39/10.67 (beta2) => 78.39/10.67 (( 78.39/10.67 (eta2) => 78.39/10.67 (( 78.39/10.67 (iffalseProp1) => 78.39/10.67 (( 78.39/10.67 (iffalseProp2) => 78.39/10.67 (( 78.39/10.67 (iftrueProp1) => 78.39/10.67 (( 78.39/10.67 (iftrueProp2) => 78.39/10.67 (( 78.39/10.67 (ifSingleton) => 78.39/10.67 (( 78.39/10.67 (ifp) => 78.39/10.67 (( 78.39/10.67 (theeq) => 78.39/10.67 (( 78.39/10.67 (iftrue) => 78.39/10.67 (( 78.39/10.67 (iffalse) => 78.39/10.67 (( 78.39/10.67 (iftrueorfalse) => 78.39/10.67 (( 78.39/10.67 (binintersectT_lem) => 78.39/10.67 (( 78.39/10.67 (binunionT_lem) => 78.39/10.67 (( 78.39/10.67 (powersetT_lem) => 78.39/10.67 (( 78.39/10.67 (setminusT_lem) => 78.39/10.67 (( 78.39/10.67 (complementT_lem) => 78.39/10.67 (( 78.39/10.67 (setextT) => 78.39/10.67 (( 78.39/10.67 (subsetTI) => 78.39/10.67 (( 78.39/10.67 (powersetTI1) => 78.39/10.67 (( 78.39/10.67 (powersetTE1) => 78.39/10.67 (( 78.39/10.67 (complementTI1) => 78.39/10.67 (( 78.39/10.67 (complementTE1) => 78.39/10.67 (( 78.39/10.67 (binintersectTELcontra) => 78.39/10.67 (( 78.39/10.67 (binintersectTERcontra) => 78.39/10.67 (( 78.39/10.67 (contrasubsetT) => 78.39/10.67 (( 78.39/10.67 (contrasubsetT1) => 78.39/10.67 (( 78.39/10.67 (contrasubsetT2) => 78.39/10.67 (( 78.39/10.67 (contrasubsetT3) => 78.39/10.67 (( 78.39/10.67 (doubleComplementI1) => 78.39/10.67 (( 78.39/10.67 (doubleComplementE1) => 78.39/10.67 (( 78.39/10.67 (doubleComplementSub1) => 78.39/10.67 (( 78.39/10.67 (doubleComplementSub2) => 78.39/10.67 (( 78.39/10.67 (doubleComplementEq) => 78.39/10.67 (( 78.39/10.67 (complementTnotintersectT) => 78.39/10.67 (( 78.39/10.67 (complementImpComplementIntersect) => 78.39/10.67 (( 78.39/10.67 (complementSubsetComplementIntersect) => 78.39/10.67 (( 78.39/10.67 (complementInPowersetComplementIntersect) => 78.39/10.67 (( 78.39/10.67 (contraSubsetComplement) => 78.39/10.67 (( 78.39/10.67 (complementTcontraSubset) => 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(demorgan2) => 78.39/10.67 (( 78.39/10.67 (woz13rule0) => 78.39/10.67 (( 78.39/10.67 (woz13rule1) => 78.39/10.67 (( 78.39/10.67 (woz13rule2) => 78.39/10.67 (( 78.39/10.67 (woz13rule3) => 78.39/10.67 (( 78.39/10.67 (woz13rule4) => 78.39/10.67 (( 78.39/10.67 (woz1_1) => 78.39/10.67 (( 78.39/10.67 (woz1_2) => 78.39/10.67 (( 78.39/10.67 (woz1_3) => 78.39/10.67 (( 78.39/10.67 (woz1_4) => 78.39/10.67 (( 78.39/10.67 (woz1_5) => 78.39/10.67 (( 78.39/10.67 (breln1all2) => 78.39/10.67 (( 78.39/10.67 (breln1SetBreln1) => 78.39/10.67 (( 78.39/10.67 (choice2fnsingleton) => 78.39/10.67 (( 78.39/10.67 (setOfPairsIsBReln1) => 78.39/10.67 (( 78.39/10.67 (breln1all1) => 78.39/10.67 (( 78.39/10.67 (subbreln1) => 78.39/10.67 (( 78.39/10.67 (eqbreln1) => 78.39/10.67 (( 78.39/10.67 (breln1invprop) => 78.39/10.67 (( 78.39/10.67 (breln1invI) => 78.39/10.67 (( 78.39/10.67 (breln1invE) => 78.39/10.67 (( 78.39/10.67 (breln1compprop) => 78.39/10.67 (( 78.39/10.67 (breln1compI) => 78.39/10.67 (( 78.39/10.67 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(surjFuncSetFuncSurj) => 78.39/10.67 (( 78.39/10.67 (leftInvIsSurj) => 78.39/10.67 (( 78.39/10.67 (surjCantorThm) => 78.39/10.67 (( 78.39/10.67 (foundation2) => 78.39/10.67 (( 78.39/10.67 (notinself) => 78.39/10.67 (( 78.39/10.67 (notinself2) => 78.39/10.67 (( 78.39/10.67 (omegaSp) => 78.39/10.67 (( 78.39/10.67 (omegaSclos) => 78.39/10.67 (( 78.39/10.67 (peano0notS) => 78.39/10.67 (( 78.39/10.67 (peanoSinj) => 78.39/10.67 (( 78.39/10.67 (transitivesetOp1) => 78.39/10.67 (( 78.39/10.67 (binintTransitive) => 78.39/10.67 (( 78.39/10.67 (transitivesetOp2) => 78.39/10.67 (( 78.39/10.67 (setunionTransitive) => 78.39/10.67 (( 78.39/10.67 (ordinalMinLem1) => 78.39/10.67 (( 78.39/10.67 (!!) @ ( 78.39/10.67 ^[Y0 : $i]: 78.39/10.67 (( 78.39/10.67 (ordinal @ 78.39/10.67 Y0) => 78.39/10.67 (( 78.39/10.67 (!!) @ ( 78.39/10.67 ^[Y1 : $i]: 78.39/10.67 (( 78.39/10.67 (!!) @ ( 78.39/10.67 ^[Y2 : $i]: 78.39/10.67 (( 78.39/10.67 (in @ 78.39/10.67 Y2 @ 78.39/10.67 Y0) => 78.39/10.67 (( 78.39/10.67 (in @ 78.39/10.67 Y1 @ 78.39/10.67 Y2) => 78.39/10.67 (in @ 78.39/10.67 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 78.39/10.67 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1034])). 78.39/10.67 thf(zip_derived_cl1047, plain, 78.39/10.67 (~ (((setminusER) => 78.39/10.67 (((setminusSubset2) => 78.39/10.67 (((setminusERneg) => 78.39/10.67 (((setminusELneg) => 78.39/10.67 (((setminusILneg) => 78.39/10.67 (((setminusIRneg) => 78.39/10.67 (((setminusLsub) => 78.39/10.67 (((setminusSubset1) => 78.39/10.67 (((symdiffE) => 78.39/10.67 (((symdiffI1) => 78.39/10.67 (((symdiffI2) => 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78.39/10.67 (( 78.39/10.67 (singletonsuniq) => 78.39/10.67 (( 78.39/10.67 (setukpairinjL1) => 78.39/10.67 (( 78.39/10.67 (kfstsingleton) => 78.39/10.67 (( 78.39/10.67 (theprop) => 78.39/10.67 (( 78.39/10.67 (kfstpairEq) => 78.39/10.67 (( 78.39/10.67 (cartprodfstin) => 78.39/10.67 (( 78.39/10.67 (setukpairinjL2) => 78.39/10.67 (( 78.39/10.67 (setukpairinjL) => 78.39/10.67 (( 78.39/10.67 (setukpairinjR11) => 78.39/10.67 (( 78.39/10.67 (setukpairinjR12) => 78.39/10.67 (( 78.39/10.67 (setukpairinjR1) => 78.39/10.67 (( 78.39/10.67 (upairequniteq) => 78.39/10.67 (( 78.39/10.67 (setukpairinjR2) => 78.39/10.67 (( 78.39/10.67 (setukpairinjR) => 78.39/10.67 (( 78.39/10.67 (ksndsingleton) => 78.39/10.67 (( 78.39/10.67 (ksndpairEq) => 78.39/10.67 (( 78.39/10.67 (kpairsurjEq) => 78.39/10.67 (( 78.39/10.67 (cartprodsndin) => 78.39/10.67 (( 78.39/10.67 (cartprodpairmemEL) => 78.39/10.67 (( 78.39/10.67 (cartprodpairmemER) => 78.39/10.67 (( 78.39/10.67 (cartprodmempaircEq) => 78.39/10.67 (( 78.39/10.67 (cartprodfstpairEq) => 78.39/10.67 (( 78.39/10.67 (cartprodsndpairEq) => 78.39/10.67 (( 78.39/10.67 (cartprodpairsurjEq) => 78.39/10.67 (( 78.39/10.67 (dpsetconstrI) => 78.39/10.67 (( 78.39/10.67 (dpsetconstrSub) => 78.39/10.67 (( 78.39/10.67 (setOfPairsIsBReln) => 78.39/10.67 (( 78.39/10.67 (dpsetconstrERa) => 78.39/10.67 (( 78.39/10.67 (dpsetconstrEL1) => 78.39/10.67 (( 78.39/10.67 (dpsetconstrEL2) => 78.39/10.67 (( 78.39/10.67 (dpsetconstrER) => 78.39/10.67 (( 78.39/10.67 (funcImageSingleton) => 78.39/10.67 (( 78.39/10.67 (apProp) => 78.39/10.67 (( 78.39/10.67 (app) => 78.39/10.67 (( 78.39/10.67 (infuncsetfunc) => 78.39/10.67 (( 78.39/10.67 (ap2p) => 78.39/10.67 (( 78.39/10.67 (funcinfuncset) => 78.39/10.67 (( 78.39/10.67 (lamProp) => 78.39/10.67 (( 78.39/10.67 (lamp) => 78.39/10.67 (( 78.39/10.67 (lam2p) => 78.39/10.67 (( 78.39/10.67 (brelnall1) => 78.39/10.67 (( 78.39/10.67 (brelnall2) => 78.39/10.67 (( 78.39/10.67 (ex1E2) => 78.39/10.67 (( 78.39/10.67 (funcGraphProp1) => 78.39/10.67 (( 78.39/10.67 (funcGraphProp3) => 78.39/10.67 (( 78.39/10.67 (funcGraphProp2) => 78.39/10.67 (( 78.39/10.67 (funcextLem) => 78.39/10.67 (( 78.39/10.67 (funcGraphProp4) => 78.39/10.67 (( 78.39/10.67 (subbreln) => 78.39/10.67 (( 78.39/10.67 (eqbreln) => 78.39/10.67 (( 78.39/10.67 (funcext) => 78.39/10.67 (( 78.39/10.67 (funcext2) => 78.39/10.67 (( 78.39/10.67 (ap2apEq1) => 78.39/10.67 (( 78.39/10.67 (ap2apEq2) => 78.39/10.67 (( 78.39/10.67 (beta1) => 78.39/10.67 (( 78.39/10.67 (eta1) => 78.39/10.67 (( 78.39/10.67 (lam2lamEq) => 78.39/10.67 (( 78.39/10.67 (beta2) => 78.39/10.67 (( 78.39/10.67 (eta2) => 78.39/10.67 (( 78.39/10.67 (iffalseProp1) => 78.39/10.67 (( 78.39/10.67 (iffalseProp2) => 78.39/10.67 (( 78.39/10.67 (iftrueProp1) => 78.39/10.67 (( 78.39/10.67 (iftrueProp2) => 78.39/10.67 (( 78.39/10.67 (ifSingleton) => 78.39/10.67 (( 78.39/10.67 (ifp) => 78.39/10.67 (( 78.39/10.67 (theeq) => 78.39/10.67 (( 78.39/10.67 (iftrue) => 78.39/10.67 (( 78.39/10.67 (iffalse) => 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78.39/10.67 (( 78.39/10.67 (doubleComplementSub2) => 78.39/10.67 (( 78.39/10.67 (doubleComplementEq) => 78.39/10.67 (( 78.39/10.67 (complementTnotintersectT) => 78.39/10.67 (( 78.39/10.67 (complementImpComplementIntersect) => 78.39/10.67 (( 78.39/10.67 (complementSubsetComplementIntersect) => 78.39/10.67 (( 78.39/10.67 (complementInPowersetComplementIntersect) => 78.39/10.67 (( 78.39/10.67 (contraSubsetComplement) => 78.39/10.67 (( 78.39/10.67 (complementTcontraSubset) => 78.39/10.67 (( 78.39/10.67 (binunionTILcontra) => 78.39/10.67 (( 78.39/10.67 (binunionTIRcontra) => 78.39/10.67 (( 78.39/10.67 (inIntersectImpInUnion) => 78.39/10.67 (( 78.39/10.67 (inIntersectImpInUnion2) => 78.39/10.67 (( 78.39/10.67 (inIntersectImpInIntersectUnions) => 78.39/10.67 (( 78.39/10.67 (intersectInPowersetIntersectUnions) => 78.39/10.67 (( 78.39/10.67 (inComplementUnionImpNotIn1) => 78.39/10.67 (( 78.39/10.67 (inComplementUnionImpInComplement1) => 78.39/10.67 (( 78.39/10.67 (binunionTE) => 78.39/10.67 (( 78.39/10.67 (binunionTEcontra) => 78.39/10.67 (( 78.39/10.67 (demorgan2a1) => 78.39/10.67 (( 78.39/10.67 (complementUnionInPowersetComplement) => 78.39/10.67 (( 78.39/10.67 (demorgan2a2) => 78.39/10.67 (( 78.39/10.67 (demorgan1a) => 78.39/10.67 (( 78.39/10.67 (demorgan1b) => 78.39/10.67 (( 78.39/10.67 (demorgan1) => 78.39/10.67 (( 78.39/10.67 (demorgan2a) => 78.39/10.67 (( 78.39/10.67 (demorgan2b2) => 78.39/10.67 (( 78.39/10.67 (demorgan2b) => 78.39/10.67 (( 78.39/10.67 (demorgan2) => 78.39/10.67 (( 78.39/10.67 (woz13rule0) => 78.39/10.67 (( 78.39/10.67 (woz13rule1) => 78.39/10.67 (( 78.39/10.67 (woz13rule2) => 78.39/10.67 (( 78.39/10.67 (woz13rule3) => 78.39/10.67 (( 78.39/10.67 (woz13rule4) => 78.39/10.67 (( 78.39/10.67 (woz1_1) => 78.39/10.67 (( 78.39/10.67 (woz1_2) => 78.39/10.67 (( 78.39/10.67 (woz1_3) => 78.39/10.67 (( 78.39/10.67 (woz1_4) => 78.39/10.67 (( 78.39/10.67 (woz1_5) => 78.39/10.67 (( 78.39/10.67 (breln1all2) => 78.39/10.67 (( 78.39/10.67 (breln1SetBreln1) => 78.39/10.67 (( 78.39/10.67 (choice2fnsingleton) => 78.39/10.67 (( 78.39/10.67 (setOfPairsIsBReln1) => 78.39/10.67 (( 78.39/10.67 (breln1all1) => 78.39/10.67 (( 78.39/10.67 (subbreln1) => 78.39/10.67 (( 78.39/10.67 (eqbreln1) => 78.39/10.67 (( 78.39/10.67 (breln1invprop) => 78.39/10.67 (( 78.39/10.67 (breln1invI) => 78.39/10.67 (( 78.39/10.67 (breln1invE) => 78.39/10.67 (( 78.39/10.67 (breln1compprop) => 78.39/10.67 (( 78.39/10.67 (breln1compI) => 78.39/10.67 (( 78.39/10.67 (breln1compE) => 78.39/10.67 (( 78.39/10.67 (breln1compEex) => 78.39/10.67 (( 78.39/10.67 (breln1unionprop) => 78.39/10.67 (( 78.39/10.67 (breln1unionIL) => 78.39/10.67 (( 78.39/10.67 (breln1unionIR) => 78.39/10.67 (( 78.39/10.67 (breln1unionI) => 78.39/10.67 (( 78.39/10.67 (breln1unionE) => 78.39/10.67 (( 78.39/10.67 (breln1unionEcases) => 78.39/10.67 (( 78.39/10.67 (breln1unionCommutes) => 78.39/10.67 (( 78.39/10.67 (woz2Ex) => 78.39/10.67 (( 78.39/10.67 (woz2W) => 78.39/10.67 (( 78.39/10.67 (woz2A) => 78.39/10.67 (( 78.39/10.67 (woz2B) => 78.39/10.67 (( 78.39/10.67 (image1Ex) => 78.39/10.67 (( 78.39/10.67 (image1Ex1) => 78.39/10.67 (( 78.39/10.67 (image1Equiv) => 78.39/10.67 (( 78.39/10.67 (image1E) => 78.39/10.67 (( 78.39/10.67 (image1I) => 78.39/10.67 (( 78.39/10.67 (injFuncInInjFuncSet) => 78.39/10.67 (( 78.39/10.67 (injFuncSetFuncIn) => 78.39/10.67 (( 78.39/10.67 (injFuncSetFuncInj) => 78.39/10.67 (( 78.39/10.67 (surjFuncSetFuncIn) => 78.39/10.67 (( 78.39/10.67 (surjFuncSetFuncSurj) => 78.39/10.67 (( 78.39/10.67 (leftInvIsSurj) => 78.39/10.67 (( 78.39/10.67 (surjCantorThm) => 78.39/10.67 (( 78.39/10.67 (foundation2) => 78.39/10.67 (( 78.39/10.67 (notinself) => 78.39/10.67 (( 78.39/10.67 (notinself2) => 78.39/10.67 (( 78.39/10.67 (omegaSp) => 78.39/10.67 (( 78.39/10.67 (omegaSclos) => 78.39/10.67 (( 78.39/10.67 (peano0notS) => 78.39/10.67 (( 78.39/10.67 (peanoSinj) => 78.39/10.67 (( 78.39/10.67 (transitivesetOp1) => 78.39/10.67 (( 78.39/10.67 (binintTransitive) => 78.39/10.67 (( 78.39/10.67 (transitivesetOp2) => 78.39/10.67 (( 78.39/10.67 (setunionTransitive) => 78.39/10.67 (( 78.39/10.67 (ordinalMinLem1) => 78.39/10.67 (( 78.39/10.67 (!!) @ ( 78.39/10.67 ^[Y0 : $i]: 78.39/10.67 (( 78.39/10.67 (ordinal @ 78.39/10.67 Y0) => 78.39/10.67 (( 78.39/10.67 (!!) @ ( 78.39/10.67 ^[Y1 : $i]: 78.39/10.67 (( 78.39/10.67 (!!) @ ( 78.39/10.67 ^[Y2 : $i]: 78.39/10.67 (( 78.39/10.67 (in @ 78.39/10.67 Y2 @ 78.39/10.67 Y0) => 78.39/10.67 (( 78.39/10.67 (in @ 78.39/10.67 Y1 @ 78.39/10.67 Y2) => 78.39/10.67 (in @ 78.39/10.67 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 78.39/10.67 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1041])). 78.39/10.67 thf(zip_derived_cl1054, plain, 78.39/10.67 (~ (((setminusSubset2) => 78.39/10.67 (((setminusERneg) => 78.39/10.67 (((setminusELneg) => 78.39/10.67 (((setminusILneg) => 78.39/10.67 (((setminusIRneg) => 78.39/10.67 (((setminusLsub) => 78.39/10.67 (((setminusSubset1) => 78.39/10.67 (((symdiffE) => 78.39/10.67 (((symdiffI1) => 78.39/10.67 (((symdiffI2) => 78.39/10.67 (((symdiffIneg1) => 78.39/10.67 (((symdiffIneg2) => 78.39/10.67 (((secondinupair) => 78.39/10.67 (((setukpairIL) => 78.39/10.67 (((setukpairIR) => 78.39/10.67 (((kpairiskpair) => 78.39/10.67 (((kpairp) => 78.39/10.67 (((singletonsubset) => 78.39/10.67 (((singletoninpowerset) => 78.39/10.67 (((singletoninpowunion) => 78.39/10.67 (((upairset2E) => 78.39/10.67 (((upairsubunion) => 78.39/10.67 (((upairinpowunion) => 78.39/10.67 (((ubforcartprodlem1) => 78.39/10.67 (((ubforcartprodlem2) => 78.39/10.67 (((ubforcartprodlem3) => 78.39/10.67 (((cartprodpairin) => 78.39/10.67 (((cartprodmempair1) => 78.39/10.67 (((cartprodmempair) => 78.39/10.67 (((setunionE2) => 78.39/10.67 (( 78.39/10.67 (setunionsingleton1) => 78.39/10.67 (( 78.39/10.67 (setunionsingleton2) => 78.39/10.67 (( 78.39/10.67 (setunionsingleton) => 78.39/10.67 (( 78.39/10.67 (singletonprop) => 78.39/10.67 (( 78.39/10.67 (ex1E1) => 78.39/10.67 (( 78.39/10.67 (ex1I) => 78.39/10.67 (( 78.39/10.67 (ex1I2) => 78.39/10.67 (( 78.39/10.67 (singletonsuniq) => 78.39/10.67 (( 78.39/10.67 (setukpairinjL1) => 78.39/10.67 (( 78.39/10.67 (kfstsingleton) => 78.39/10.67 (( 78.39/10.67 (theprop) => 78.39/10.67 (( 78.39/10.67 (kfstpairEq) => 78.39/10.67 (( 78.39/10.67 (cartprodfstin) => 78.39/10.67 (( 78.39/10.67 (setukpairinjL2) => 78.39/10.67 (( 78.39/10.67 (setukpairinjL) => 78.39/10.67 (( 78.39/10.67 (setukpairinjR11) => 78.39/10.67 (( 78.39/10.67 (setukpairinjR12) => 78.39/10.67 (( 78.39/10.67 (setukpairinjR1) => 78.39/10.67 (( 78.39/10.67 (upairequniteq) => 78.39/10.67 (( 78.39/10.67 (setukpairinjR2) => 78.39/10.67 (( 78.39/10.67 (setukpairinjR) => 78.39/10.67 (( 78.39/10.67 (ksndsingleton) => 78.39/10.67 (( 78.39/10.67 (ksndpairEq) => 78.39/10.67 (( 78.39/10.67 (kpairsurjEq) => 78.39/10.67 (( 78.39/10.67 (cartprodsndin) => 78.39/10.67 (( 78.39/10.67 (cartprodpairmemEL) => 78.39/10.67 (( 78.39/10.67 (cartprodpairmemER) => 78.39/10.67 (( 78.39/10.67 (cartprodmempaircEq) => 78.39/10.67 (( 78.39/10.67 (cartprodfstpairEq) => 78.39/10.67 (( 78.39/10.67 (cartprodsndpairEq) => 78.39/10.67 (( 78.39/10.67 (cartprodpairsurjEq) => 78.39/10.67 (( 78.39/10.67 (dpsetconstrI) => 78.39/10.67 (( 78.39/10.67 (dpsetconstrSub) => 78.39/10.67 (( 78.39/10.67 (setOfPairsIsBReln) => 78.39/10.67 (( 78.39/10.67 (dpsetconstrERa) => 78.39/10.67 (( 78.39/10.67 (dpsetconstrEL1) => 78.39/10.67 (( 78.39/10.67 (dpsetconstrEL2) => 78.39/10.67 (( 78.39/10.67 (dpsetconstrER) => 78.39/10.67 (( 78.39/10.67 (funcImageSingleton) => 78.39/10.67 (( 78.39/10.67 (apProp) => 78.39/10.67 (( 78.39/10.67 (app) => 78.39/10.67 (( 78.39/10.67 (infuncsetfunc) => 78.39/10.67 (( 78.39/10.67 (ap2p) => 78.39/10.67 (( 78.39/10.67 (funcinfuncset) => 78.39/10.67 (( 78.39/10.67 (lamProp) => 78.39/10.67 (( 78.39/10.67 (lamp) => 78.39/10.67 (( 78.39/10.67 (lam2p) => 78.39/10.67 (( 78.39/10.67 (brelnall1) => 78.39/10.67 (( 78.39/10.67 (brelnall2) => 78.39/10.67 (( 78.39/10.67 (ex1E2) => 78.39/10.67 (( 78.39/10.67 (funcGraphProp1) => 78.39/10.67 (( 78.39/10.67 (funcGraphProp3) => 78.39/10.67 (( 78.39/10.67 (funcGraphProp2) => 78.39/10.67 (( 78.39/10.67 (funcextLem) => 78.39/10.67 (( 78.39/10.67 (funcGraphProp4) => 78.39/10.67 (( 78.39/10.67 (subbreln) => 78.39/10.67 (( 78.39/10.67 (eqbreln) => 78.39/10.67 (( 78.39/10.67 (funcext) => 78.39/10.67 (( 78.39/10.67 (funcext2) => 78.39/10.67 (( 78.39/10.67 (ap2apEq1) => 78.39/10.67 (( 78.39/10.67 (ap2apEq2) => 78.39/10.67 (( 78.39/10.67 (beta1) => 78.39/10.67 (( 78.39/10.67 (eta1) => 78.39/10.67 (( 78.39/10.67 (lam2lamEq) => 78.39/10.67 (( 78.39/10.67 (beta2) => 78.39/10.67 (( 78.39/10.67 (eta2) => 78.39/10.67 (( 78.39/10.67 (iffalseProp1) => 78.39/10.67 (( 78.39/10.67 (iffalseProp2) => 78.39/10.67 (( 78.39/10.67 (iftrueProp1) => 78.39/10.67 (( 78.39/10.67 (iftrueProp2) => 78.39/10.67 (( 78.39/10.67 (ifSingleton) => 78.39/10.67 (( 78.39/10.67 (ifp) => 78.39/10.67 (( 78.39/10.67 (theeq) => 78.39/10.67 (( 78.39/10.67 (iftrue) => 78.39/10.67 (( 78.39/10.67 (iffalse) => 78.39/10.67 (( 78.39/10.67 (iftrueorfalse) => 78.39/10.67 (( 78.39/10.67 (binintersectT_lem) => 78.39/10.67 (( 78.39/10.67 (binunionT_lem) => 78.39/10.67 (( 78.39/10.67 (powersetT_lem) => 78.39/10.67 (( 78.39/10.67 (setminusT_lem) => 78.39/10.67 (( 78.39/10.67 (complementT_lem) => 78.39/10.67 (( 78.39/10.67 (setextT) => 78.39/10.67 (( 78.39/10.67 (subsetTI) => 78.39/10.67 (( 78.39/10.67 (powersetTI1) => 78.39/10.67 (( 78.39/10.67 (powersetTE1) => 78.39/10.67 (( 78.39/10.67 (complementTI1) => 78.39/10.67 (( 78.39/10.67 (complementTE1) => 78.39/10.67 (( 78.39/10.67 (binintersectTELcontra) => 78.39/10.67 (( 78.39/10.67 (binintersectTERcontra) => 78.39/10.67 (( 78.39/10.67 (contrasubsetT) => 78.39/10.67 (( 78.39/10.67 (contrasubsetT1) => 78.39/10.67 (( 78.39/10.67 (contrasubsetT2) => 78.39/10.67 (( 78.39/10.67 (contrasubsetT3) => 78.39/10.67 (( 78.39/10.67 (doubleComplementI1) => 78.39/10.67 (( 78.39/10.67 (doubleComplementE1) => 78.39/10.67 (( 78.39/10.67 (doubleComplementSub1) => 78.39/10.67 (( 78.39/10.67 (doubleComplementSub2) => 78.39/10.67 (( 78.39/10.67 (doubleComplementEq) => 78.39/10.67 (( 78.39/10.67 (complementTnotintersectT) => 78.39/10.67 (( 78.39/10.67 (complementImpComplementIntersect) => 78.39/10.67 (( 78.39/10.67 (complementSubsetComplementIntersect) => 78.39/10.67 (( 78.39/10.67 (complementInPowersetComplementIntersect) => 78.39/10.67 (( 78.39/10.67 (contraSubsetComplement) => 78.39/10.67 (( 78.39/10.67 (complementTcontraSubset) => 78.39/10.67 (( 78.39/10.67 (binunionTILcontra) => 78.39/10.67 (( 78.39/10.67 (binunionTIRcontra) => 78.39/10.67 (( 78.39/10.67 (inIntersectImpInUnion) => 78.39/10.67 (( 78.39/10.67 (inIntersectImpInUnion2) => 78.39/10.67 (( 78.39/10.67 (inIntersectImpInIntersectUnions) => 78.39/10.67 (( 78.39/10.67 (intersectInPowersetIntersectUnions) => 78.39/10.67 (( 78.39/10.67 (inComplementUnionImpNotIn1) => 78.39/10.67 (( 78.39/10.67 (inComplementUnionImpInComplement1) => 78.39/10.67 (( 78.39/10.67 (binunionTE) => 78.39/10.67 (( 78.39/10.67 (binunionTEcontra) => 78.39/10.67 (( 78.39/10.67 (demorgan2a1) => 78.39/10.67 (( 78.39/10.67 (complementUnionInPowersetComplement) => 78.39/10.67 (( 78.39/10.67 (demorgan2a2) => 78.39/10.67 (( 78.39/10.67 (demorgan1a) => 78.39/10.67 (( 78.39/10.67 (demorgan1b) => 78.39/10.67 (( 78.39/10.67 (demorgan1) => 78.39/10.67 (( 78.39/10.67 (demorgan2a) => 78.39/10.67 (( 78.39/10.67 (demorgan2b2) => 78.39/10.67 (( 78.39/10.67 (demorgan2b) => 78.39/10.67 (( 78.39/10.67 (demorgan2) => 78.39/10.67 (( 78.39/10.67 (woz13rule0) => 78.39/10.67 (( 78.39/10.67 (woz13rule1) => 78.39/10.67 (( 78.39/10.67 (woz13rule2) => 78.39/10.67 (( 78.39/10.67 (woz13rule3) => 78.39/10.67 (( 78.39/10.67 (woz13rule4) => 78.39/10.67 (( 78.39/10.67 (woz1_1) => 78.39/10.67 (( 78.39/10.67 (woz1_2) => 78.39/10.67 (( 78.39/10.67 (woz1_3) => 78.39/10.67 (( 78.39/10.67 (woz1_4) => 78.39/10.67 (( 78.39/10.67 (woz1_5) => 78.39/10.67 (( 78.39/10.67 (breln1all2) => 78.39/10.67 (( 78.39/10.67 (breln1SetBreln1) => 78.39/10.67 (( 78.39/10.67 (choice2fnsingleton) => 78.39/10.67 (( 78.39/10.67 (setOfPairsIsBReln1) => 78.39/10.67 (( 78.39/10.67 (breln1all1) => 78.39/10.67 (( 78.39/10.67 (subbreln1) => 78.39/10.67 (( 78.39/10.67 (eqbreln1) => 78.39/10.67 (( 78.39/10.67 (breln1invprop) => 78.39/10.67 (( 78.39/10.67 (breln1invI) => 78.39/10.67 (( 78.39/10.67 (breln1invE) => 78.39/10.67 (( 78.39/10.67 (breln1compprop) => 78.39/10.67 (( 78.39/10.67 (breln1compI) => 78.39/10.67 (( 78.39/10.67 (breln1compE) => 78.39/10.67 (( 78.39/10.67 (breln1compEex) => 78.39/10.67 (( 78.39/10.67 (breln1unionprop) => 78.39/10.67 (( 78.39/10.67 (breln1unionIL) => 78.39/10.67 (( 78.39/10.67 (breln1unionIR) => 78.39/10.67 (( 78.39/10.67 (breln1unionI) => 78.39/10.67 (( 78.39/10.67 (breln1unionE) => 78.39/10.67 (( 78.39/10.67 (breln1unionEcases) => 78.39/10.67 (( 78.39/10.67 (breln1unionCommutes) => 78.39/10.67 (( 78.39/10.67 (woz2Ex) => 78.39/10.67 (( 78.39/10.67 (woz2W) => 78.39/10.67 (( 78.39/10.67 (woz2A) => 78.39/10.67 (( 78.39/10.67 (woz2B) => 78.39/10.67 (( 78.39/10.67 (image1Ex) => 78.39/10.67 (( 78.39/10.67 (image1Ex1) => 78.39/10.67 (( 78.39/10.67 (image1Equiv) => 78.39/10.67 (( 78.39/10.67 (image1E) => 78.39/10.67 (( 78.39/10.67 (image1I) => 78.39/10.67 (( 78.39/10.67 (injFuncInInjFuncSet) => 78.39/10.67 (( 78.39/10.67 (injFuncSetFuncIn) => 78.39/10.67 (( 78.39/10.67 (injFuncSetFuncInj) => 78.39/10.67 (( 78.39/10.67 (surjFuncSetFuncIn) => 78.39/10.67 (( 78.39/10.67 (surjFuncSetFuncSurj) => 78.39/10.67 (( 78.39/10.67 (leftInvIsSurj) => 78.39/10.67 (( 78.39/10.67 (surjCantorThm) => 78.39/10.67 (( 78.39/10.67 (foundation2) => 78.39/10.67 (( 78.39/10.67 (notinself) => 78.39/10.67 (( 78.39/10.67 (notinself2) => 78.39/10.67 (( 78.39/10.67 (omegaSp) => 78.39/10.67 (( 78.39/10.67 (omegaSclos) => 78.39/10.67 (( 78.39/10.67 (peano0notS) => 78.39/10.67 (( 78.39/10.67 (peanoSinj) => 78.39/10.67 (( 78.39/10.67 (transitivesetOp1) => 78.39/10.67 (( 78.39/10.67 (binintTransitive) => 78.39/10.67 (( 78.39/10.67 (transitivesetOp2) => 78.39/10.67 (( 78.39/10.67 (setunionTransitive) => 78.39/10.67 (( 78.39/10.67 (ordinalMinLem1) => 78.39/10.67 (( 78.39/10.67 (!!) @ ( 78.39/10.67 ^[Y0 : $i]: 78.39/10.67 (( 78.39/10.67 (ordinal @ 78.39/10.67 Y0) => 78.39/10.67 (( 78.39/10.67 (!!) @ ( 78.39/10.67 ^[Y1 : $i]: 78.39/10.67 (( 78.39/10.67 (!!) @ ( 78.39/10.67 ^[Y2 : $i]: 78.39/10.67 (( 78.39/10.67 (in @ 78.39/10.67 Y2 @ 78.39/10.67 Y0) => 78.39/10.67 (( 78.39/10.67 (in @ 78.39/10.67 Y1 @ 78.39/10.67 Y2) => 78.39/10.67 (in @ 78.39/10.67 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 78.39/10.67 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1047])). 78.39/10.67 thf(zip_derived_cl1061, plain, 78.39/10.67 (~ (((setminusERneg) => 78.39/10.67 (((setminusELneg) => 78.39/10.67 (((setminusILneg) => 78.39/10.67 (((setminusIRneg) => 78.39/10.67 (((setminusLsub) => 78.39/10.67 (((setminusSubset1) => 78.39/10.67 (((symdiffE) => 78.39/10.67 (((symdiffI1) => 78.39/10.67 (((symdiffI2) => 78.39/10.67 (((symdiffIneg1) => 78.39/10.67 (((symdiffIneg2) => 78.39/10.67 (((secondinupair) => 78.39/10.67 (((setukpairIL) => 78.39/10.67 (((setukpairIR) => 78.39/10.67 (((kpairiskpair) => 78.39/10.67 (((kpairp) => 78.39/10.67 (((singletonsubset) => 78.39/10.67 (((singletoninpowerset) => 78.39/10.67 (((singletoninpowunion) => 78.39/10.67 (((upairset2E) => 78.39/10.67 (((upairsubunion) => 78.39/10.67 (((upairinpowunion) => 78.39/10.67 (((ubforcartprodlem1) => 78.39/10.67 (((ubforcartprodlem2) => 78.39/10.67 (((ubforcartprodlem3) => 78.39/10.67 (((cartprodpairin) => 78.39/10.67 (((cartprodmempair1) => 78.39/10.67 (((cartprodmempair) => 78.39/10.67 (((setunionE2) => 78.39/10.67 (((setunionsingleton1) => 78.39/10.67 (( 78.39/10.67 (setunionsingleton2) => 78.39/10.67 (( 78.39/10.67 (setunionsingleton) => 78.39/10.67 (( 78.39/10.67 (singletonprop) => 78.39/10.67 (( 78.39/10.67 (ex1E1) => 78.39/10.67 (( 78.39/10.67 (ex1I) => 78.39/10.67 (( 78.39/10.67 (ex1I2) => 78.39/10.67 (( 78.39/10.67 (singletonsuniq) => 78.39/10.67 (( 78.39/10.67 (setukpairinjL1) => 78.39/10.67 (( 78.39/10.67 (kfstsingleton) => 78.39/10.67 (( 78.39/10.67 (theprop) => 78.39/10.67 (( 78.39/10.67 (kfstpairEq) => 78.39/10.67 (( 78.39/10.67 (cartprodfstin) => 78.39/10.67 (( 78.39/10.67 (setukpairinjL2) => 78.39/10.67 (( 78.39/10.67 (setukpairinjL) => 78.39/10.67 (( 78.39/10.67 (setukpairinjR11) => 78.39/10.67 (( 78.39/10.67 (setukpairinjR12) => 78.39/10.67 (( 78.39/10.67 (setukpairinjR1) => 78.39/10.67 (( 78.39/10.67 (upairequniteq) => 78.39/10.67 (( 78.39/10.67 (setukpairinjR2) => 78.39/10.67 (( 78.39/10.67 (setukpairinjR) => 78.39/10.67 (( 78.39/10.67 (ksndsingleton) => 78.39/10.67 (( 78.39/10.67 (ksndpairEq) => 78.39/10.67 (( 78.39/10.67 (kpairsurjEq) => 78.39/10.67 (( 78.39/10.67 (cartprodsndin) => 78.39/10.67 (( 78.39/10.67 (cartprodpairmemEL) => 78.39/10.67 (( 78.39/10.67 (cartprodpairmemER) => 78.39/10.67 (( 78.39/10.67 (cartprodmempaircEq) => 78.39/10.67 (( 78.39/10.67 (cartprodfstpairEq) => 78.39/10.67 (( 78.39/10.67 (cartprodsndpairEq) => 78.39/10.67 (( 78.39/10.67 (cartprodpairsurjEq) => 78.39/10.67 (( 78.39/10.67 (dpsetconstrI) => 78.39/10.67 (( 78.39/10.67 (dpsetconstrSub) => 78.39/10.67 (( 78.39/10.67 (setOfPairsIsBReln) => 78.39/10.67 (( 78.39/10.67 (dpsetconstrERa) => 78.39/10.67 (( 78.39/10.67 (dpsetconstrEL1) => 78.39/10.67 (( 78.39/10.67 (dpsetconstrEL2) => 78.39/10.67 (( 78.39/10.67 (dpsetconstrER) => 78.39/10.67 (( 78.39/10.67 (funcImageSingleton) => 78.39/10.67 (( 78.39/10.67 (apProp) => 78.39/10.67 (( 78.39/10.67 (app) => 78.39/10.67 (( 78.39/10.67 (infuncsetfunc) => 78.39/10.67 (( 78.39/10.67 (ap2p) => 78.39/10.67 (( 78.39/10.67 (funcinfuncset) => 78.39/10.67 (( 78.39/10.67 (lamProp) => 78.39/10.67 (( 78.39/10.67 (lamp) => 78.39/10.67 (( 78.39/10.67 (lam2p) => 78.39/10.67 (( 78.39/10.67 (brelnall1) => 78.39/10.67 (( 78.39/10.67 (brelnall2) => 78.39/10.67 (( 78.39/10.67 (ex1E2) => 78.39/10.67 (( 78.39/10.67 (funcGraphProp1) => 78.39/10.67 (( 78.39/10.67 (funcGraphProp3) => 78.39/10.67 (( 78.39/10.67 (funcGraphProp2) => 78.39/10.67 (( 78.39/10.67 (funcextLem) => 78.39/10.67 (( 78.39/10.67 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(powersetT_lem) => 78.39/10.67 (( 78.39/10.67 (setminusT_lem) => 78.39/10.67 (( 78.39/10.67 (complementT_lem) => 78.39/10.67 (( 78.39/10.67 (setextT) => 78.39/10.67 (( 78.39/10.67 (subsetTI) => 78.39/10.67 (( 78.39/10.67 (powersetTI1) => 78.39/10.67 (( 78.39/10.67 (powersetTE1) => 78.39/10.67 (( 78.39/10.67 (complementTI1) => 78.39/10.67 (( 78.39/10.67 (complementTE1) => 78.39/10.67 (( 78.39/10.67 (binintersectTELcontra) => 78.39/10.67 (( 78.39/10.67 (binintersectTERcontra) => 78.39/10.67 (( 78.39/10.67 (contrasubsetT) => 78.39/10.67 (( 78.39/10.67 (contrasubsetT1) => 78.39/10.67 (( 78.39/10.67 (contrasubsetT2) => 78.39/10.67 (( 78.39/10.67 (contrasubsetT3) => 78.39/10.67 (( 78.39/10.67 (doubleComplementI1) => 78.39/10.67 (( 78.39/10.67 (doubleComplementE1) => 78.39/10.67 (( 78.39/10.67 (doubleComplementSub1) => 78.39/10.67 (( 78.39/10.67 (doubleComplementSub2) => 78.39/10.67 (( 78.39/10.67 (doubleComplementEq) => 78.39/10.67 (( 78.39/10.67 (complementTnotintersectT) => 78.39/10.67 (( 78.39/10.67 (complementImpComplementIntersect) => 78.39/10.67 (( 78.39/10.67 (complementSubsetComplementIntersect) => 78.39/10.67 (( 78.39/10.67 (complementInPowersetComplementIntersect) => 78.39/10.67 (( 78.39/10.67 (contraSubsetComplement) => 78.39/10.67 (( 78.39/10.67 (complementTcontraSubset) => 78.39/10.67 (( 78.39/10.67 (binunionTILcontra) => 78.39/10.67 (( 78.39/10.67 (binunionTIRcontra) => 78.39/10.67 (( 78.39/10.67 (inIntersectImpInUnion) => 78.39/10.67 (( 78.39/10.67 (inIntersectImpInUnion2) => 78.39/10.67 (( 78.39/10.67 (inIntersectImpInIntersectUnions) => 78.39/10.67 (( 78.39/10.67 (intersectInPowersetIntersectUnions) => 78.39/10.67 (( 78.39/10.67 (inComplementUnionImpNotIn1) => 78.39/10.67 (( 78.39/10.67 (inComplementUnionImpInComplement1) => 78.39/10.67 (( 78.39/10.67 (binunionTE) => 78.39/10.67 (( 78.39/10.67 (binunionTEcontra) => 78.39/10.67 (( 78.39/10.67 (demorgan2a1) => 78.39/10.67 (( 78.39/10.67 (complementUnionInPowersetComplement) => 78.39/10.67 (( 78.39/10.67 (demorgan2a2) => 78.39/10.67 (( 78.39/10.67 (demorgan1a) => 78.39/10.67 (( 78.39/10.67 (demorgan1b) => 78.39/10.67 (( 78.39/10.67 (demorgan1) => 78.39/10.67 (( 78.39/10.67 (demorgan2a) => 78.39/10.67 (( 78.39/10.67 (demorgan2b2) => 78.39/10.67 (( 78.39/10.67 (demorgan2b) => 78.39/10.67 (( 78.39/10.67 (demorgan2) => 78.39/10.67 (( 78.39/10.67 (woz13rule0) => 78.39/10.67 (( 78.39/10.67 (woz13rule1) => 78.39/10.67 (( 78.39/10.67 (woz13rule2) => 78.39/10.67 (( 78.39/10.67 (woz13rule3) => 78.39/10.67 (( 78.39/10.67 (woz13rule4) => 78.39/10.67 (( 78.39/10.67 (woz1_1) => 78.39/10.67 (( 78.39/10.67 (woz1_2) => 78.39/10.67 (( 78.39/10.67 (woz1_3) => 78.39/10.67 (( 78.39/10.67 (woz1_4) => 78.39/10.67 (( 78.39/10.67 (woz1_5) => 78.39/10.67 (( 78.39/10.67 (breln1all2) => 78.39/10.67 (( 78.39/10.67 (breln1SetBreln1) => 78.39/10.67 (( 78.39/10.67 (choice2fnsingleton) => 78.39/10.67 (( 78.39/10.67 (setOfPairsIsBReln1) => 78.39/10.67 (( 78.39/10.67 (breln1all1) => 78.39/10.67 (( 78.39/10.67 (subbreln1) => 78.39/10.67 (( 78.39/10.67 (eqbreln1) => 78.39/10.67 (( 78.39/10.67 (breln1invprop) => 78.39/10.67 (( 78.39/10.67 (breln1invI) => 78.39/10.67 (( 78.39/10.67 (breln1invE) => 78.39/10.67 (( 78.39/10.67 (breln1compprop) => 78.39/10.67 (( 78.39/10.67 (breln1compI) => 78.39/10.67 (( 78.39/10.67 (breln1compE) => 78.39/10.67 (( 78.39/10.67 (breln1compEex) => 78.39/10.67 (( 78.39/10.67 (breln1unionprop) => 78.39/10.67 (( 78.39/10.67 (breln1unionIL) => 78.39/10.67 (( 78.39/10.67 (breln1unionIR) => 78.39/10.67 (( 78.39/10.67 (breln1unionI) => 78.39/10.67 (( 78.39/10.67 (breln1unionE) => 78.39/10.67 (( 78.39/10.67 (breln1unionEcases) => 78.39/10.67 (( 78.39/10.67 (breln1unionCommutes) => 78.39/10.67 (( 78.39/10.67 (woz2Ex) => 78.39/10.67 (( 78.39/10.67 (woz2W) => 78.39/10.67 (( 78.39/10.67 (woz2A) => 78.39/10.67 (( 78.39/10.67 (woz2B) => 78.39/10.67 (( 78.39/10.67 (image1Ex) => 78.39/10.67 (( 78.39/10.67 (image1Ex1) => 78.39/10.67 (( 78.39/10.67 (image1Equiv) => 78.39/10.67 (( 78.39/10.67 (image1E) => 78.39/10.67 (( 78.39/10.67 (image1I) => 78.39/10.67 (( 78.39/10.67 (injFuncInInjFuncSet) => 78.39/10.67 (( 78.39/10.67 (injFuncSetFuncIn) => 78.39/10.67 (( 78.39/10.67 (injFuncSetFuncInj) => 78.39/10.67 (( 78.39/10.67 (surjFuncSetFuncIn) => 78.39/10.67 (( 78.39/10.67 (surjFuncSetFuncSurj) => 78.39/10.67 (( 78.39/10.67 (leftInvIsSurj) => 78.39/10.67 (( 78.39/10.67 (surjCantorThm) => 78.39/10.67 (( 78.39/10.67 (foundation2) => 78.39/10.67 (( 78.39/10.67 (notinself) => 78.39/10.67 (( 78.39/10.67 (notinself2) => 78.39/10.67 (( 78.39/10.67 (omegaSp) => 78.39/10.67 (( 78.39/10.67 (omegaSclos) => 78.39/10.67 (( 78.39/10.67 (peano0notS) => 78.39/10.67 (( 78.39/10.67 (peanoSinj) => 78.39/10.67 (( 78.39/10.67 (transitivesetOp1) => 78.39/10.67 (( 78.39/10.67 (binintTransitive) => 78.39/10.67 (( 78.39/10.67 (transitivesetOp2) => 78.39/10.67 (( 78.39/10.67 (setunionTransitive) => 78.39/10.67 (( 78.39/10.67 (ordinalMinLem1) => 78.39/10.67 (( 78.39/10.67 (!!) @ ( 78.39/10.67 ^[Y0 : $i]: 78.39/10.67 (( 78.39/10.67 (ordinal @ 78.39/10.67 Y0) => 78.39/10.67 (( 78.39/10.67 (!!) @ ( 78.39/10.67 ^[Y1 : $i]: 78.39/10.67 (( 78.39/10.67 (!!) @ ( 78.39/10.67 ^[Y2 : $i]: 78.39/10.67 (( 78.39/10.67 (in @ 78.39/10.67 Y2 @ 78.39/10.67 Y0) => 78.39/10.67 (( 78.39/10.67 (in @ 78.39/10.67 Y1 @ 78.39/10.67 Y2) => 78.39/10.67 (in @ 78.39/10.67 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 78.39/10.67 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1054])). 78.39/10.67 thf(zip_derived_cl1068, plain, 78.39/10.67 (~ (((setminusELneg) => 78.39/10.67 (((setminusILneg) => 78.39/10.67 (((setminusIRneg) => 78.39/10.67 (((setminusLsub) => 78.39/10.67 (((setminusSubset1) => 78.39/10.67 (((symdiffE) => 78.39/10.67 (((symdiffI1) => 78.39/10.67 (((symdiffI2) => 78.39/10.67 (((symdiffIneg1) => 78.39/10.67 (((symdiffIneg2) => 78.39/10.67 (((secondinupair) => 78.39/10.67 (((setukpairIL) => 78.39/10.67 (((setukpairIR) => 78.39/10.67 (((kpairiskpair) => 78.39/10.67 (((kpairp) => 78.39/10.67 (((singletonsubset) => 78.39/10.67 (((singletoninpowerset) => 78.39/10.67 (((singletoninpowunion) => 78.39/10.67 (((upairset2E) => 78.39/10.67 (((upairsubunion) => 78.39/10.67 (((upairinpowunion) => 78.39/10.67 (((ubforcartprodlem1) => 78.39/10.67 (((ubforcartprodlem2) => 78.39/10.67 (((ubforcartprodlem3) => 78.39/10.67 (((cartprodpairin) => 78.39/10.67 (((cartprodmempair1) => 78.39/10.67 (((cartprodmempair) => 78.39/10.67 (((setunionE2) => 78.39/10.67 (((setunionsingleton1) => 78.39/10.67 (((setunionsingleton2) => 78.39/10.67 (( 78.39/10.67 (setunionsingleton) => 78.39/10.67 (( 78.39/10.67 (singletonprop) => 78.39/10.67 (( 78.39/10.67 (ex1E1) => 78.39/10.67 (( 78.39/10.67 (ex1I) => 78.39/10.67 (( 78.39/10.67 (ex1I2) => 78.39/10.67 (( 78.39/10.67 (singletonsuniq) => 78.39/10.67 (( 78.39/10.67 (setukpairinjL1) => 78.39/10.67 (( 78.39/10.67 (kfstsingleton) => 78.39/10.67 (( 78.39/10.67 (theprop) => 78.39/10.67 (( 78.39/10.67 (kfstpairEq) => 78.39/10.67 (( 78.39/10.67 (cartprodfstin) => 78.39/10.67 (( 78.39/10.67 (setukpairinjL2) => 78.39/10.67 (( 78.39/10.67 (setukpairinjL) => 78.39/10.67 (( 78.39/10.67 (setukpairinjR11) => 78.39/10.67 (( 78.39/10.67 (setukpairinjR12) => 78.39/10.67 (( 78.39/10.67 (setukpairinjR1) => 78.39/10.67 (( 78.39/10.67 (upairequniteq) => 78.39/10.67 (( 78.39/10.67 (setukpairinjR2) => 78.39/10.67 (( 78.39/10.67 (setukpairinjR) => 78.39/10.67 (( 78.39/10.67 (ksndsingleton) => 78.39/10.67 (( 78.39/10.67 (ksndpairEq) => 78.39/10.67 (( 78.39/10.67 (kpairsurjEq) => 78.39/10.67 (( 78.39/10.67 (cartprodsndin) => 78.39/10.67 (( 78.39/10.67 (cartprodpairmemEL) => 78.39/10.67 (( 78.39/10.67 (cartprodpairmemER) => 78.39/10.67 (( 78.39/10.67 (cartprodmempaircEq) => 78.39/10.67 (( 78.39/10.67 (cartprodfstpairEq) => 78.39/10.67 (( 78.39/10.67 (cartprodsndpairEq) => 78.39/10.67 (( 78.39/10.67 (cartprodpairsurjEq) => 78.39/10.67 (( 78.39/10.67 (dpsetconstrI) => 78.39/10.67 (( 78.39/10.67 (dpsetconstrSub) => 78.39/10.67 (( 78.39/10.67 (setOfPairsIsBReln) => 78.39/10.67 (( 78.39/10.67 (dpsetconstrERa) => 78.39/10.67 (( 78.39/10.67 (dpsetconstrEL1) => 78.39/10.67 (( 78.39/10.67 (dpsetconstrEL2) => 78.39/10.67 (( 78.39/10.67 (dpsetconstrER) => 78.39/10.67 (( 78.39/10.67 (funcImageSingleton) => 78.39/10.67 (( 78.39/10.67 (apProp) => 78.39/10.67 (( 78.39/10.67 (app) => 78.39/10.67 (( 78.39/10.67 (infuncsetfunc) => 78.39/10.67 (( 78.39/10.67 (ap2p) => 78.39/10.67 (( 78.39/10.67 (funcinfuncset) => 78.39/10.67 (( 78.39/10.67 (lamProp) => 78.39/10.67 (( 78.39/10.67 (lamp) => 78.39/10.67 (( 78.39/10.67 (lam2p) => 78.39/10.67 (( 78.39/10.67 (brelnall1) => 78.39/10.67 (( 78.39/10.67 (brelnall2) => 78.39/10.67 (( 78.39/10.67 (ex1E2) => 78.39/10.67 (( 78.39/10.67 (funcGraphProp1) => 78.39/10.67 (( 78.39/10.67 (funcGraphProp3) => 78.39/10.67 (( 78.39/10.67 (funcGraphProp2) => 78.39/10.67 (( 78.39/10.67 (funcextLem) => 78.39/10.67 (( 78.39/10.67 (funcGraphProp4) => 78.39/10.67 (( 78.39/10.67 (subbreln) => 78.39/10.67 (( 78.39/10.67 (eqbreln) => 78.39/10.67 (( 78.39/10.67 (funcext) => 78.39/10.67 (( 78.39/10.67 (funcext2) => 78.39/10.67 (( 78.39/10.67 (ap2apEq1) => 78.39/10.67 (( 78.39/10.67 (ap2apEq2) => 78.39/10.67 (( 78.39/10.67 (beta1) => 78.39/10.67 (( 78.39/10.67 (eta1) => 78.39/10.67 (( 78.39/10.67 (lam2lamEq) => 78.39/10.67 (( 78.39/10.67 (beta2) => 78.39/10.67 (( 78.39/10.67 (eta2) => 78.39/10.67 (( 78.39/10.67 (iffalseProp1) => 78.39/10.67 (( 78.39/10.67 (iffalseProp2) => 78.39/10.67 (( 78.39/10.67 (iftrueProp1) => 78.39/10.67 (( 78.39/10.67 (iftrueProp2) => 78.39/10.67 (( 78.39/10.67 (ifSingleton) => 78.39/10.67 (( 78.39/10.67 (ifp) => 78.39/10.67 (( 78.39/10.67 (theeq) => 78.39/10.67 (( 78.39/10.67 (iftrue) => 78.39/10.67 (( 78.39/10.67 (iffalse) => 78.39/10.67 (( 78.39/10.67 (iftrueorfalse) => 78.39/10.67 (( 78.39/10.67 (binintersectT_lem) => 78.39/10.67 (( 78.39/10.67 (binunionT_lem) => 78.39/10.67 (( 78.39/10.67 (powersetT_lem) => 78.39/10.67 (( 78.39/10.67 (setminusT_lem) => 78.39/10.67 (( 78.39/10.67 (complementT_lem) => 78.39/10.67 (( 78.39/10.67 (setextT) => 78.39/10.67 (( 78.39/10.67 (subsetTI) => 78.39/10.67 (( 78.39/10.67 (powersetTI1) => 78.39/10.67 (( 78.39/10.67 (powersetTE1) => 78.39/10.67 (( 78.39/10.67 (complementTI1) => 78.39/10.67 (( 78.39/10.67 (complementTE1) => 78.39/10.67 (( 78.39/10.67 (binintersectTELcontra) => 78.39/10.67 (( 78.39/10.67 (binintersectTERcontra) => 78.39/10.67 (( 78.39/10.67 (contrasubsetT) => 78.39/10.67 (( 78.39/10.67 (contrasubsetT1) => 78.39/10.67 (( 78.39/10.67 (contrasubsetT2) => 78.39/10.67 (( 78.39/10.67 (contrasubsetT3) => 78.39/10.67 (( 78.39/10.67 (doubleComplementI1) => 78.39/10.67 (( 78.39/10.67 (doubleComplementE1) => 78.39/10.67 (( 78.39/10.67 (doubleComplementSub1) => 78.39/10.67 (( 78.39/10.67 (doubleComplementSub2) => 78.39/10.67 (( 78.39/10.67 (doubleComplementEq) => 78.39/10.67 (( 78.39/10.67 (complementTnotintersectT) => 78.39/10.67 (( 78.39/10.67 (complementImpComplementIntersect) => 78.39/10.67 (( 78.39/10.67 (complementSubsetComplementIntersect) => 78.39/10.67 (( 78.39/10.67 (complementInPowersetComplementIntersect) => 78.39/10.67 (( 78.39/10.67 (contraSubsetComplement) => 78.39/10.67 (( 78.39/10.67 (complementTcontraSubset) => 78.39/10.67 (( 78.39/10.67 (binunionTILcontra) => 78.39/10.67 (( 78.39/10.67 (binunionTIRcontra) => 78.39/10.67 (( 78.39/10.67 (inIntersectImpInUnion) => 78.39/10.67 (( 78.39/10.67 (inIntersectImpInUnion2) => 78.39/10.67 (( 78.39/10.67 (inIntersectImpInIntersectUnions) => 78.39/10.67 (( 78.39/10.67 (intersectInPowersetIntersectUnions) => 78.39/10.67 (( 78.39/10.67 (inComplementUnionImpNotIn1) => 78.39/10.67 (( 78.39/10.67 (inComplementUnionImpInComplement1) => 78.39/10.67 (( 78.39/10.67 (binunionTE) => 78.39/10.67 (( 78.39/10.67 (binunionTEcontra) => 78.39/10.67 (( 78.39/10.67 (demorgan2a1) => 78.39/10.67 (( 78.39/10.67 (complementUnionInPowersetComplement) => 78.39/10.67 (( 78.39/10.67 (demorgan2a2) => 78.39/10.67 (( 78.39/10.67 (demorgan1a) => 78.39/10.67 (( 78.39/10.67 (demorgan1b) => 78.39/10.67 (( 78.39/10.67 (demorgan1) => 78.39/10.67 (( 78.39/10.67 (demorgan2a) => 78.39/10.67 (( 78.39/10.67 (demorgan2b2) => 78.39/10.67 (( 78.39/10.67 (demorgan2b) => 78.39/10.67 (( 78.39/10.67 (demorgan2) => 78.39/10.67 (( 78.39/10.67 (woz13rule0) => 78.39/10.67 (( 78.39/10.67 (woz13rule1) => 78.39/10.67 (( 78.39/10.67 (woz13rule2) => 78.39/10.67 (( 78.39/10.67 (woz13rule3) => 78.39/10.67 (( 78.39/10.67 (woz13rule4) => 78.39/10.67 (( 78.39/10.67 (woz1_1) => 78.39/10.67 (( 78.39/10.67 (woz1_2) => 78.39/10.67 (( 78.39/10.67 (woz1_3) => 78.39/10.67 (( 78.39/10.67 (woz1_4) => 78.39/10.67 (( 78.39/10.67 (woz1_5) => 78.39/10.67 (( 78.39/10.67 (breln1all2) => 78.39/10.67 (( 78.39/10.67 (breln1SetBreln1) => 78.39/10.67 (( 78.39/10.67 (choice2fnsingleton) => 78.39/10.67 (( 78.39/10.67 (setOfPairsIsBReln1) => 78.39/10.67 (( 78.39/10.67 (breln1all1) => 78.39/10.67 (( 78.39/10.67 (subbreln1) => 78.39/10.67 (( 78.39/10.67 (eqbreln1) => 78.39/10.67 (( 78.39/10.67 (breln1invprop) => 78.39/10.67 (( 78.39/10.67 (breln1invI) => 78.39/10.67 (( 78.39/10.67 (breln1invE) => 78.39/10.67 (( 78.39/10.67 (breln1compprop) => 78.39/10.67 (( 78.39/10.67 (breln1compI) => 78.39/10.67 (( 78.39/10.67 (breln1compE) => 78.39/10.67 (( 78.39/10.67 (breln1compEex) => 78.39/10.67 (( 78.39/10.67 (breln1unionprop) => 78.39/10.67 (( 78.39/10.67 (breln1unionIL) => 78.39/10.67 (( 78.39/10.67 (breln1unionIR) => 78.39/10.67 (( 78.39/10.67 (breln1unionI) => 78.39/10.67 (( 78.39/10.67 (breln1unionE) => 78.39/10.67 (( 78.39/10.67 (breln1unionEcases) => 78.39/10.67 (( 78.39/10.67 (breln1unionCommutes) => 78.39/10.67 (( 78.39/10.67 (woz2Ex) => 78.39/10.67 (( 78.39/10.67 (woz2W) => 78.39/10.67 (( 78.39/10.67 (woz2A) => 78.39/10.67 (( 78.39/10.67 (woz2B) => 78.39/10.67 (( 78.39/10.67 (image1Ex) => 78.39/10.67 (( 78.39/10.67 (image1Ex1) => 78.39/10.67 (( 78.39/10.67 (image1Equiv) => 78.39/10.67 (( 78.39/10.67 (image1E) => 78.39/10.67 (( 78.39/10.67 (image1I) => 78.39/10.67 (( 78.39/10.67 (injFuncInInjFuncSet) => 78.39/10.67 (( 78.39/10.67 (injFuncSetFuncIn) => 78.39/10.67 (( 78.39/10.67 (injFuncSetFuncInj) => 78.39/10.67 (( 78.39/10.67 (surjFuncSetFuncIn) => 78.39/10.67 (( 78.39/10.67 (surjFuncSetFuncSurj) => 78.39/10.67 (( 78.39/10.67 (leftInvIsSurj) => 78.39/10.67 (( 78.39/10.67 (surjCantorThm) => 78.39/10.67 (( 78.39/10.67 (foundation2) => 78.39/10.67 (( 78.39/10.67 (notinself) => 78.39/10.67 (( 78.39/10.67 (notinself2) => 78.39/10.67 (( 78.39/10.67 (omegaSp) => 78.39/10.67 (( 78.39/10.67 (omegaSclos) => 78.39/10.67 (( 78.39/10.67 (peano0notS) => 78.39/10.67 (( 78.39/10.67 (peanoSinj) => 78.39/10.67 (( 78.39/10.67 (transitivesetOp1) => 78.39/10.67 (( 78.39/10.67 (binintTransitive) => 78.39/10.67 (( 78.39/10.67 (transitivesetOp2) => 78.39/10.67 (( 78.39/10.67 (setunionTransitive) => 78.39/10.67 (( 78.39/10.67 (ordinalMinLem1) => 78.39/10.67 (( 78.39/10.67 (!!) @ ( 78.39/10.67 ^[Y0 : $i]: 78.39/10.67 (( 78.39/10.67 (ordinal @ 78.39/10.67 Y0) => 78.39/10.67 (( 78.39/10.67 (!!) @ ( 78.39/10.67 ^[Y1 : $i]: 78.39/10.67 (( 78.39/10.67 (!!) @ ( 78.39/10.67 ^[Y2 : $i]: 78.39/10.67 (( 78.39/10.67 (in @ 78.39/10.67 Y2 @ 78.39/10.67 Y0) => 78.39/10.67 (( 78.39/10.67 (in @ 78.39/10.67 Y1 @ 78.39/10.67 Y2) => 78.39/10.67 (in @ 78.39/10.67 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 78.39/10.67 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1061])). 78.39/10.67 thf(zip_derived_cl1075, plain, 78.39/10.67 (~ (((setminusILneg) => 78.39/10.67 (((setminusIRneg) => 78.39/10.67 (((setminusLsub) => 78.39/10.67 (((setminusSubset1) => 78.39/10.67 (((symdiffE) => 78.39/10.67 (((symdiffI1) => 78.39/10.67 (((symdiffI2) => 78.39/10.67 (((symdiffIneg1) => 78.39/10.67 (((symdiffIneg2) => 78.39/10.67 (((secondinupair) => 78.39/10.67 (((setukpairIL) => 78.39/10.67 (((setukpairIR) => 78.39/10.67 (((kpairiskpair) => 78.39/10.67 (((kpairp) => 78.39/10.67 (((singletonsubset) => 78.39/10.67 (((singletoninpowerset) => 78.39/10.67 (((singletoninpowunion) => 78.39/10.67 (((upairset2E) => 78.39/10.67 (((upairsubunion) => 78.39/10.67 (((upairinpowunion) => 78.39/10.67 (((ubforcartprodlem1) => 78.39/10.67 (((ubforcartprodlem2) => 78.39/10.67 (((ubforcartprodlem3) => 78.39/10.67 (((cartprodpairin) => 78.39/10.67 (((cartprodmempair1) => 78.39/10.67 (((cartprodmempair) => 78.39/10.67 (((setunionE2) => 78.39/10.67 (((setunionsingleton1) => 78.39/10.67 (((setunionsingleton2) => 78.39/10.67 (((setunionsingleton) => 78.39/10.67 (( 78.39/10.67 (singletonprop) => 78.39/10.67 (( 78.39/10.67 (ex1E1) => 78.39/10.67 (( 78.39/10.67 (ex1I) => 78.39/10.67 (( 78.39/10.67 (ex1I2) => 78.39/10.67 (( 78.39/10.67 (singletonsuniq) => 78.39/10.67 (( 78.39/10.67 (setukpairinjL1) => 78.39/10.67 (( 78.39/10.67 (kfstsingleton) => 78.39/10.67 (( 78.39/10.67 (theprop) => 78.39/10.67 (( 78.39/10.67 (kfstpairEq) => 78.39/10.67 (( 78.39/10.67 (cartprodfstin) => 78.39/10.67 (( 78.39/10.67 (setukpairinjL2) => 78.39/10.67 (( 78.39/10.67 (setukpairinjL) => 78.39/10.67 (( 78.39/10.67 (setukpairinjR11) => 78.39/10.67 (( 78.39/10.67 (setukpairinjR12) => 78.39/10.67 (( 78.39/10.67 (setukpairinjR1) => 78.39/10.67 (( 78.39/10.67 (upairequniteq) => 78.39/10.67 (( 78.39/10.67 (setukpairinjR2) => 78.39/10.67 (( 78.39/10.67 (setukpairinjR) => 78.39/10.67 (( 78.39/10.67 (ksndsingleton) => 78.39/10.67 (( 78.39/10.67 (ksndpairEq) => 78.39/10.67 (( 78.39/10.67 (kpairsurjEq) => 78.39/10.67 (( 78.39/10.67 (cartprodsndin) => 78.39/10.67 (( 78.39/10.67 (cartprodpairmemEL) => 78.39/10.67 (( 78.39/10.67 (cartprodpairmemER) => 78.39/10.67 (( 78.39/10.67 (cartprodmempaircEq) => 78.39/10.67 (( 78.39/10.67 (cartprodfstpairEq) => 78.39/10.67 (( 78.39/10.67 (cartprodsndpairEq) => 78.39/10.67 (( 78.39/10.67 (cartprodpairsurjEq) => 78.39/10.67 (( 78.39/10.67 (dpsetconstrI) => 78.39/10.67 (( 78.39/10.67 (dpsetconstrSub) => 78.39/10.67 (( 78.39/10.67 (setOfPairsIsBReln) => 78.39/10.67 (( 78.39/10.67 (dpsetconstrERa) => 78.39/10.67 (( 78.39/10.67 (dpsetconstrEL1) => 78.39/10.67 (( 78.39/10.67 (dpsetconstrEL2) => 78.39/10.67 (( 78.39/10.67 (dpsetconstrER) => 78.39/10.67 (( 78.39/10.67 (funcImageSingleton) => 78.39/10.67 (( 78.39/10.67 (apProp) => 78.39/10.67 (( 78.39/10.67 (app) => 78.39/10.67 (( 78.39/10.67 (infuncsetfunc) => 78.39/10.67 (( 78.39/10.67 (ap2p) => 78.39/10.67 (( 78.39/10.67 (funcinfuncset) => 78.39/10.67 (( 78.39/10.67 (lamProp) => 78.39/10.67 (( 78.39/10.67 (lamp) => 78.39/10.67 (( 78.39/10.67 (lam2p) => 78.39/10.67 (( 78.39/10.67 (brelnall1) => 78.39/10.67 (( 78.39/10.67 (brelnall2) => 78.39/10.67 (( 78.39/10.67 (ex1E2) => 78.39/10.67 (( 78.39/10.67 (funcGraphProp1) => 78.39/10.67 (( 78.39/10.67 (funcGraphProp3) => 78.39/10.67 (( 78.39/10.67 (funcGraphProp2) => 78.39/10.67 (( 78.39/10.67 (funcextLem) => 78.39/10.67 (( 78.39/10.67 (funcGraphProp4) => 78.39/10.67 (( 78.39/10.67 (subbreln) => 78.39/10.67 (( 78.39/10.67 (eqbreln) => 78.39/10.67 (( 78.39/10.67 (funcext) => 78.39/10.67 (( 78.39/10.67 (funcext2) => 78.39/10.67 (( 78.39/10.67 (ap2apEq1) => 78.39/10.67 (( 78.39/10.67 (ap2apEq2) => 78.39/10.67 (( 78.39/10.67 (beta1) => 78.39/10.67 (( 78.39/10.67 (eta1) => 78.39/10.67 (( 78.39/10.67 (lam2lamEq) => 78.39/10.67 (( 78.39/10.67 (beta2) => 78.39/10.67 (( 78.39/10.67 (eta2) => 78.39/10.67 (( 78.39/10.67 (iffalseProp1) => 78.39/10.67 (( 78.39/10.67 (iffalseProp2) => 78.39/10.67 (( 78.39/10.67 (iftrueProp1) => 78.39/10.67 (( 78.39/10.67 (iftrueProp2) => 78.39/10.67 (( 78.39/10.67 (ifSingleton) => 78.39/10.67 (( 78.39/10.67 (ifp) => 78.39/10.67 (( 78.39/10.67 (theeq) => 78.39/10.67 (( 78.39/10.67 (iftrue) => 78.39/10.67 (( 78.39/10.67 (iffalse) => 78.39/10.67 (( 78.39/10.67 (iftrueorfalse) => 78.39/10.67 (( 78.39/10.67 (binintersectT_lem) => 78.39/10.67 (( 78.39/10.67 (binunionT_lem) => 78.39/10.67 (( 78.39/10.67 (powersetT_lem) => 78.39/10.67 (( 78.39/10.67 (setminusT_lem) => 78.39/10.67 (( 78.39/10.67 (complementT_lem) => 78.39/10.67 (( 78.39/10.67 (setextT) => 78.39/10.67 (( 78.39/10.67 (subsetTI) => 78.39/10.67 (( 78.39/10.67 (powersetTI1) => 78.39/10.67 (( 78.39/10.67 (powersetTE1) => 78.39/10.67 (( 78.39/10.67 (complementTI1) => 78.39/10.67 (( 78.39/10.67 (complementTE1) => 78.39/10.67 (( 78.39/10.67 (binintersectTELcontra) => 78.39/10.67 (( 78.39/10.67 (binintersectTERcontra) => 78.39/10.67 (( 78.39/10.67 (contrasubsetT) => 78.39/10.67 (( 78.39/10.67 (contrasubsetT1) => 78.39/10.67 (( 78.39/10.67 (contrasubsetT2) => 78.39/10.67 (( 78.39/10.67 (contrasubsetT3) => 78.39/10.67 (( 78.39/10.67 (doubleComplementI1) => 78.39/10.67 (( 78.39/10.67 (doubleComplementE1) => 78.39/10.67 (( 78.39/10.67 (doubleComplementSub1) => 78.39/10.67 (( 78.39/10.67 (doubleComplementSub2) => 78.39/10.67 (( 78.39/10.67 (doubleComplementEq) => 78.39/10.67 (( 78.39/10.67 (complementTnotintersectT) => 78.39/10.67 (( 78.39/10.67 (complementImpComplementIntersect) => 78.39/10.67 (( 78.39/10.67 (complementSubsetComplementIntersect) => 78.39/10.67 (( 78.39/10.67 (complementInPowersetComplementIntersect) => 78.39/10.67 (( 78.39/10.67 (contraSubsetComplement) => 78.39/10.67 (( 78.39/10.67 (complementTcontraSubset) => 78.39/10.67 (( 78.39/10.67 (binunionTILcontra) => 78.39/10.67 (( 78.39/10.67 (binunionTIRcontra) => 78.39/10.67 (( 78.39/10.67 (inIntersectImpInUnion) => 78.39/10.67 (( 78.39/10.67 (inIntersectImpInUnion2) => 78.39/10.67 (( 78.39/10.67 (inIntersectImpInIntersectUnions) => 78.39/10.67 (( 78.39/10.67 (intersectInPowersetIntersectUnions) => 78.39/10.67 (( 78.39/10.67 (inComplementUnionImpNotIn1) => 78.39/10.67 (( 78.39/10.67 (inComplementUnionImpInComplement1) => 78.39/10.67 (( 78.39/10.67 (binunionTE) => 78.39/10.67 (( 78.39/10.67 (binunionTEcontra) => 78.39/10.67 (( 78.39/10.67 (demorgan2a1) => 78.39/10.67 (( 78.39/10.67 (complementUnionInPowersetComplement) => 78.39/10.67 (( 78.39/10.67 (demorgan2a2) => 78.39/10.67 (( 78.39/10.67 (demorgan1a) => 78.39/10.67 (( 78.39/10.67 (demorgan1b) => 78.39/10.67 (( 78.39/10.67 (demorgan1) => 78.39/10.67 (( 78.39/10.67 (demorgan2a) => 78.39/10.67 (( 78.39/10.67 (demorgan2b2) => 78.39/10.67 (( 78.39/10.67 (demorgan2b) => 78.39/10.67 (( 78.39/10.67 (demorgan2) => 78.39/10.67 (( 78.39/10.67 (woz13rule0) => 78.39/10.67 (( 78.39/10.67 (woz13rule1) => 78.39/10.67 (( 78.39/10.67 (woz13rule2) => 78.39/10.67 (( 78.39/10.67 (woz13rule3) => 78.39/10.67 (( 78.39/10.67 (woz13rule4) => 78.39/10.67 (( 78.39/10.67 (woz1_1) => 78.39/10.67 (( 78.39/10.67 (woz1_2) => 78.39/10.67 (( 78.39/10.67 (woz1_3) => 78.39/10.67 (( 78.39/10.67 (woz1_4) => 78.39/10.67 (( 78.39/10.67 (woz1_5) => 78.39/10.67 (( 78.39/10.67 (breln1all2) => 78.39/10.67 (( 78.39/10.67 (breln1SetBreln1) => 78.39/10.67 (( 78.39/10.67 (choice2fnsingleton) => 78.39/10.67 (( 78.39/10.67 (setOfPairsIsBReln1) => 78.39/10.67 (( 78.39/10.67 (breln1all1) => 78.39/10.67 (( 78.39/10.67 (subbreln1) => 78.39/10.67 (( 78.39/10.67 (eqbreln1) => 78.39/10.67 (( 78.39/10.67 (breln1invprop) => 78.39/10.67 (( 78.39/10.67 (breln1invI) => 78.39/10.67 (( 78.39/10.67 (breln1invE) => 78.39/10.67 (( 78.39/10.67 (breln1compprop) => 78.39/10.67 (( 78.39/10.67 (breln1compI) => 78.39/10.67 (( 78.39/10.67 (breln1compE) => 78.39/10.67 (( 78.39/10.67 (breln1compEex) => 78.39/10.67 (( 78.39/10.67 (breln1unionprop) => 78.39/10.67 (( 78.39/10.67 (breln1unionIL) => 78.39/10.67 (( 78.39/10.67 (breln1unionIR) => 78.39/10.67 (( 78.39/10.67 (breln1unionI) => 78.39/10.67 (( 78.39/10.67 (breln1unionE) => 78.39/10.67 (( 78.39/10.67 (breln1unionEcases) => 78.39/10.67 (( 78.39/10.67 (breln1unionCommutes) => 78.39/10.67 (( 78.39/10.67 (woz2Ex) => 78.39/10.67 (( 78.39/10.67 (woz2W) => 78.39/10.67 (( 78.39/10.67 (woz2A) => 78.39/10.67 (( 78.39/10.67 (woz2B) => 78.39/10.67 (( 78.39/10.67 (image1Ex) => 78.39/10.67 (( 78.39/10.67 (image1Ex1) => 78.39/10.67 (( 78.39/10.67 (image1Equiv) => 78.39/10.67 (( 78.39/10.67 (image1E) => 78.39/10.67 (( 78.39/10.67 (image1I) => 78.39/10.67 (( 78.39/10.67 (injFuncInInjFuncSet) => 78.39/10.67 (( 78.39/10.67 (injFuncSetFuncIn) => 78.39/10.67 (( 78.39/10.67 (injFuncSetFuncInj) => 78.39/10.67 (( 78.39/10.67 (surjFuncSetFuncIn) => 78.39/10.67 (( 78.39/10.67 (surjFuncSetFuncSurj) => 78.39/10.67 (( 78.39/10.67 (leftInvIsSurj) => 78.39/10.67 (( 78.39/10.67 (surjCantorThm) => 78.39/10.67 (( 78.39/10.67 (foundation2) => 78.39/10.67 (( 78.39/10.67 (notinself) => 78.39/10.67 (( 78.39/10.67 (notinself2) => 78.39/10.67 (( 78.39/10.67 (omegaSp) => 78.39/10.67 (( 78.39/10.67 (omegaSclos) => 78.39/10.67 (( 78.39/10.67 (peano0notS) => 78.39/10.67 (( 78.39/10.67 (peanoSinj) => 78.39/10.67 (( 78.39/10.67 (transitivesetOp1) => 78.39/10.67 (( 78.39/10.67 (binintTransitive) => 78.39/10.67 (( 78.39/10.67 (transitivesetOp2) => 78.39/10.67 (( 78.39/10.67 (setunionTransitive) => 78.39/10.67 (( 78.39/10.67 (ordinalMinLem1) => 78.39/10.67 (( 78.39/10.67 (!!) @ ( 78.39/10.67 ^[Y0 : $i]: 78.39/10.67 (( 78.39/10.67 (ordinal @ 78.39/10.67 Y0) => 78.39/10.67 (( 78.39/10.67 (!!) @ ( 78.39/10.67 ^[Y1 : $i]: 78.39/10.67 (( 78.39/10.67 (!!) @ ( 78.39/10.67 ^[Y2 : $i]: 78.39/10.67 (( 78.39/10.67 (in @ 78.39/10.67 Y2 @ 78.39/10.67 Y0) => 78.39/10.67 (( 78.39/10.67 (in @ 78.39/10.67 Y1 @ 78.39/10.67 Y2) => 78.39/10.67 (in @ 78.39/10.67 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 78.39/10.67 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1068])). 78.39/10.67 thf(zip_derived_cl1082, plain, 78.39/10.67 (~ (((setminusIRneg) => 78.39/10.67 (((setminusLsub) => 78.39/10.67 (((setminusSubset1) => 78.39/10.67 (((symdiffE) => 78.39/10.67 (((symdiffI1) => 78.39/10.67 (((symdiffI2) => 78.39/10.67 (((symdiffIneg1) => 78.39/10.67 (((symdiffIneg2) => 78.39/10.67 (((secondinupair) => 78.39/10.67 (((setukpairIL) => 78.39/10.67 (((setukpairIR) => 78.39/10.67 (((kpairiskpair) => 78.39/10.67 (((kpairp) => 78.39/10.67 (((singletonsubset) => 78.39/10.67 (((singletoninpowerset) => 78.39/10.67 (((singletoninpowunion) => 78.39/10.67 (((upairset2E) => 78.39/10.67 (((upairsubunion) => 78.39/10.67 (((upairinpowunion) => 78.39/10.67 (((ubforcartprodlem1) => 78.39/10.67 (((ubforcartprodlem2) => 78.39/10.67 (((ubforcartprodlem3) => 78.39/10.67 (((cartprodpairin) => 78.39/10.67 (((cartprodmempair1) => 78.39/10.67 (((cartprodmempair) => 78.39/10.67 (((setunionE2) => 78.39/10.67 (((setunionsingleton1) => 78.39/10.67 (((setunionsingleton2) => 78.39/10.67 (((setunionsingleton) => 78.39/10.67 (((singletonprop) => 78.39/10.67 (( 78.39/10.67 (ex1E1) => 78.39/10.67 (( 78.39/10.67 (ex1I) => 78.39/10.67 (( 78.39/10.67 (ex1I2) => 78.39/10.67 (( 78.39/10.67 (singletonsuniq) => 78.39/10.67 (( 78.39/10.67 (setukpairinjL1) => 78.39/10.67 (( 78.39/10.67 (kfstsingleton) => 78.39/10.67 (( 78.39/10.67 (theprop) => 78.39/10.67 (( 78.39/10.67 (kfstpairEq) => 78.39/10.67 (( 78.39/10.67 (cartprodfstin) => 78.39/10.67 (( 78.39/10.67 (setukpairinjL2) => 78.39/10.67 (( 78.39/10.67 (setukpairinjL) => 78.39/10.67 (( 78.39/10.67 (setukpairinjR11) => 78.39/10.67 (( 78.39/10.67 (setukpairinjR12) => 78.39/10.67 (( 78.39/10.67 (setukpairinjR1) => 78.39/10.67 (( 78.39/10.67 (upairequniteq) => 78.39/10.67 (( 78.39/10.67 (setukpairinjR2) => 78.39/10.67 (( 78.39/10.67 (setukpairinjR) => 78.39/10.67 (( 78.39/10.67 (ksndsingleton) => 78.39/10.67 (( 78.39/10.67 (ksndpairEq) => 78.39/10.67 (( 78.39/10.67 (kpairsurjEq) => 78.39/10.67 (( 78.39/10.67 (cartprodsndin) => 78.39/10.67 (( 78.39/10.67 (cartprodpairmemEL) => 78.39/10.67 (( 78.39/10.67 (cartprodpairmemER) => 78.39/10.67 (( 78.39/10.67 (cartprodmempaircEq) => 78.39/10.67 (( 78.39/10.67 (cartprodfstpairEq) => 78.39/10.67 (( 78.39/10.67 (cartprodsndpairEq) => 78.39/10.67 (( 78.39/10.67 (cartprodpairsurjEq) => 78.39/10.67 (( 78.39/10.67 (dpsetconstrI) => 78.39/10.67 (( 78.39/10.67 (dpsetconstrSub) => 78.39/10.67 (( 78.39/10.67 (setOfPairsIsBReln) => 78.39/10.67 (( 78.39/10.67 (dpsetconstrERa) => 78.39/10.67 (( 78.39/10.67 (dpsetconstrEL1) => 78.39/10.67 (( 78.39/10.67 (dpsetconstrEL2) => 78.39/10.67 (( 78.39/10.67 (dpsetconstrER) => 78.39/10.67 (( 78.39/10.67 (funcImageSingleton) => 78.39/10.67 (( 78.39/10.67 (apProp) => 78.39/10.67 (( 78.39/10.67 (app) => 78.39/10.67 (( 78.39/10.67 (infuncsetfunc) => 78.39/10.67 (( 78.39/10.67 (ap2p) => 78.39/10.67 (( 78.39/10.67 (funcinfuncset) => 78.39/10.67 (( 78.39/10.67 (lamProp) => 78.39/10.67 (( 78.39/10.67 (lamp) => 78.39/10.67 (( 78.39/10.67 (lam2p) => 78.39/10.67 (( 78.39/10.67 (brelnall1) => 78.39/10.67 (( 78.39/10.67 (brelnall2) => 78.39/10.67 (( 78.39/10.67 (ex1E2) => 78.39/10.67 (( 78.39/10.67 (funcGraphProp1) => 78.39/10.67 (( 78.39/10.67 (funcGraphProp3) => 78.39/10.67 (( 78.39/10.67 (funcGraphProp2) => 78.39/10.67 (( 78.39/10.67 (funcextLem) => 78.39/10.67 (( 78.39/10.67 (funcGraphProp4) => 78.39/10.67 (( 78.39/10.67 (subbreln) => 78.39/10.67 (( 78.39/10.67 (eqbreln) => 78.39/10.67 (( 78.39/10.67 (funcext) => 78.39/10.67 (( 78.39/10.67 (funcext2) => 78.39/10.67 (( 78.39/10.67 (ap2apEq1) => 78.39/10.67 (( 78.39/10.67 (ap2apEq2) => 78.39/10.67 (( 78.39/10.67 (beta1) => 78.39/10.67 (( 78.39/10.67 (eta1) => 78.39/10.67 (( 78.39/10.67 (lam2lamEq) => 78.39/10.67 (( 78.39/10.67 (beta2) => 78.39/10.67 (( 78.39/10.67 (eta2) => 78.39/10.67 (( 78.39/10.67 (iffalseProp1) => 78.39/10.67 (( 78.39/10.67 (iffalseProp2) => 78.39/10.67 (( 78.39/10.67 (iftrueProp1) => 78.39/10.67 (( 78.39/10.67 (iftrueProp2) => 78.39/10.67 (( 78.39/10.67 (ifSingleton) => 78.39/10.67 (( 78.39/10.67 (ifp) => 78.39/10.67 (( 78.39/10.67 (theeq) => 78.39/10.67 (( 78.39/10.67 (iftrue) => 78.39/10.67 (( 78.39/10.67 (iffalse) => 78.39/10.67 (( 78.39/10.67 (iftrueorfalse) => 78.39/10.67 (( 78.39/10.67 (binintersectT_lem) => 78.39/10.67 (( 78.39/10.67 (binunionT_lem) => 78.39/10.67 (( 78.39/10.67 (powersetT_lem) => 78.39/10.67 (( 78.39/10.67 (setminusT_lem) => 78.39/10.67 (( 78.39/10.67 (complementT_lem) => 78.39/10.67 (( 78.39/10.67 (setextT) => 78.39/10.67 (( 78.39/10.67 (subsetTI) => 78.39/10.67 (( 78.39/10.67 (powersetTI1) => 78.39/10.67 (( 78.39/10.67 (powersetTE1) => 78.39/10.67 (( 78.39/10.67 (complementTI1) => 78.39/10.67 (( 78.39/10.67 (complementTE1) => 78.39/10.67 (( 78.39/10.67 (binintersectTELcontra) => 78.39/10.67 (( 78.39/10.67 (binintersectTERcontra) => 78.39/10.67 (( 78.39/10.67 (contrasubsetT) => 78.39/10.67 (( 78.39/10.67 (contrasubsetT1) => 78.39/10.67 (( 78.39/10.67 (contrasubsetT2) => 78.39/10.67 (( 78.39/10.67 (contrasubsetT3) => 78.39/10.67 (( 78.39/10.67 (doubleComplementI1) => 78.39/10.67 (( 78.39/10.67 (doubleComplementE1) => 78.39/10.67 (( 78.39/10.67 (doubleComplementSub1) => 78.39/10.67 (( 78.39/10.67 (doubleComplementSub2) => 78.39/10.67 (( 78.39/10.67 (doubleComplementEq) => 78.39/10.67 (( 78.39/10.67 (complementTnotintersectT) => 78.39/10.67 (( 78.39/10.67 (complementImpComplementIntersect) => 78.39/10.67 (( 78.39/10.67 (complementSubsetComplementIntersect) => 78.39/10.67 (( 78.39/10.67 (complementInPowersetComplementIntersect) => 78.39/10.67 (( 78.39/10.67 (contraSubsetComplement) => 78.39/10.67 (( 78.39/10.67 (complementTcontraSubset) => 78.39/10.67 (( 78.39/10.67 (binunionTILcontra) => 78.39/10.67 (( 78.39/10.67 (binunionTIRcontra) => 78.39/10.67 (( 78.39/10.67 (inIntersectImpInUnion) => 78.39/10.67 (( 78.39/10.67 (inIntersectImpInUnion2) => 78.39/10.67 (( 78.39/10.67 (inIntersectImpInIntersectUnions) => 78.39/10.67 (( 78.39/10.67 (intersectInPowersetIntersectUnions) => 78.39/10.67 (( 78.39/10.67 (inComplementUnionImpNotIn1) => 78.39/10.67 (( 78.39/10.67 (inComplementUnionImpInComplement1) => 78.39/10.67 (( 78.39/10.67 (binunionTE) => 78.39/10.67 (( 78.39/10.67 (binunionTEcontra) => 78.39/10.67 (( 78.39/10.67 (demorgan2a1) => 78.39/10.67 (( 78.39/10.67 (complementUnionInPowersetComplement) => 78.39/10.67 (( 78.39/10.67 (demorgan2a2) => 78.39/10.67 (( 78.39/10.67 (demorgan1a) => 78.39/10.67 (( 78.39/10.67 (demorgan1b) => 78.39/10.67 (( 78.39/10.67 (demorgan1) => 78.39/10.67 (( 78.39/10.67 (demorgan2a) => 78.39/10.67 (( 78.39/10.67 (demorgan2b2) => 78.39/10.67 (( 78.39/10.67 (demorgan2b) => 78.39/10.67 (( 78.39/10.67 (demorgan2) => 78.39/10.67 (( 78.39/10.67 (woz13rule0) => 78.39/10.67 (( 78.39/10.67 (woz13rule1) => 78.39/10.67 (( 78.39/10.67 (woz13rule2) => 78.39/10.67 (( 78.39/10.67 (woz13rule3) => 78.39/10.67 (( 78.39/10.67 (woz13rule4) => 78.39/10.67 (( 78.39/10.67 (woz1_1) => 78.39/10.67 (( 78.39/10.67 (woz1_2) => 78.39/10.67 (( 78.39/10.67 (woz1_3) => 78.39/10.67 (( 78.39/10.67 (woz1_4) => 78.39/10.67 (( 78.39/10.67 (woz1_5) => 78.39/10.67 (( 78.39/10.67 (breln1all2) => 78.39/10.67 (( 78.39/10.67 (breln1SetBreln1) => 78.39/10.67 (( 78.39/10.67 (choice2fnsingleton) => 78.39/10.67 (( 78.39/10.67 (setOfPairsIsBReln1) => 78.39/10.67 (( 78.39/10.67 (breln1all1) => 78.39/10.67 (( 78.39/10.67 (subbreln1) => 78.39/10.67 (( 78.39/10.67 (eqbreln1) => 78.39/10.67 (( 78.39/10.67 (breln1invprop) => 78.39/10.67 (( 78.39/10.67 (breln1invI) => 78.39/10.67 (( 78.39/10.67 (breln1invE) => 78.39/10.67 (( 78.39/10.67 (breln1compprop) => 78.39/10.67 (( 78.39/10.67 (breln1compI) => 78.39/10.67 (( 78.39/10.67 (breln1compE) => 78.39/10.67 (( 78.39/10.67 (breln1compEex) => 78.39/10.67 (( 78.39/10.67 (breln1unionprop) => 78.39/10.67 (( 78.39/10.67 (breln1unionIL) => 78.39/10.67 (( 78.39/10.67 (breln1unionIR) => 78.39/10.67 (( 78.39/10.67 (breln1unionI) => 78.39/10.67 (( 78.39/10.67 (breln1unionE) => 78.39/10.67 (( 78.39/10.67 (breln1unionEcases) => 78.39/10.67 (( 78.39/10.67 (breln1unionCommutes) => 78.39/10.67 (( 78.39/10.67 (woz2Ex) => 78.39/10.67 (( 78.39/10.67 (woz2W) => 78.39/10.67 (( 78.39/10.67 (woz2A) => 78.39/10.67 (( 78.39/10.67 (woz2B) => 78.39/10.67 (( 78.39/10.67 (image1Ex) => 78.39/10.67 (( 78.39/10.67 (image1Ex1) => 78.39/10.67 (( 78.39/10.67 (image1Equiv) => 78.39/10.67 (( 78.39/10.67 (image1E) => 78.39/10.67 (( 78.39/10.67 (image1I) => 78.39/10.67 (( 78.39/10.67 (injFuncInInjFuncSet) => 78.39/10.67 (( 78.39/10.67 (injFuncSetFuncIn) => 78.39/10.67 (( 78.39/10.67 (injFuncSetFuncInj) => 78.39/10.67 (( 78.39/10.67 (surjFuncSetFuncIn) => 78.39/10.67 (( 78.39/10.67 (surjFuncSetFuncSurj) => 78.39/10.67 (( 78.39/10.67 (leftInvIsSurj) => 78.39/10.67 (( 78.39/10.67 (surjCantorThm) => 78.39/10.67 (( 78.39/10.67 (foundation2) => 78.39/10.67 (( 78.39/10.67 (notinself) => 78.39/10.67 (( 78.39/10.67 (notinself2) => 78.39/10.67 (( 78.39/10.67 (omegaSp) => 78.39/10.67 (( 78.39/10.67 (omegaSclos) => 78.39/10.67 (( 78.39/10.67 (peano0notS) => 78.39/10.67 (( 78.39/10.67 (peanoSinj) => 78.39/10.67 (( 78.39/10.67 (transitivesetOp1) => 78.39/10.67 (( 78.39/10.67 (binintTransitive) => 78.39/10.67 (( 78.39/10.67 (transitivesetOp2) => 78.39/10.67 (( 78.39/10.67 (setunionTransitive) => 78.39/10.67 (( 78.39/10.67 (ordinalMinLem1) => 78.39/10.67 (( 78.39/10.67 (!!) @ ( 78.39/10.67 ^[Y0 : $i]: 78.39/10.67 (( 78.39/10.67 (ordinal @ 78.39/10.67 Y0) => 78.39/10.67 (( 78.39/10.67 (!!) @ ( 78.39/10.67 ^[Y1 : $i]: 78.39/10.67 (( 78.39/10.67 (!!) @ ( 78.39/10.67 ^[Y2 : $i]: 78.39/10.67 (( 78.39/10.67 (in @ 78.39/10.67 Y2 @ 78.39/10.67 Y0) => 78.39/10.67 (( 78.39/10.67 (in @ 78.39/10.67 Y1 @ 78.39/10.67 Y2) => 78.39/10.67 (in @ 78.39/10.67 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 78.39/10.67 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1075])). 78.39/10.67 thf(zip_derived_cl1089, plain, 78.39/10.67 (~ (((setminusLsub) => 78.39/10.67 (((setminusSubset1) => 78.39/10.67 (((symdiffE) => 78.39/10.67 (((symdiffI1) => 78.39/10.67 (((symdiffI2) => 78.39/10.67 (((symdiffIneg1) => 78.39/10.67 (((symdiffIneg2) => 78.39/10.67 (((secondinupair) => 78.39/10.67 (((setukpairIL) => 78.39/10.67 (((setukpairIR) => 78.39/10.67 (((kpairiskpair) => 78.39/10.67 (((kpairp) => 78.39/10.67 (((singletonsubset) => 78.39/10.67 (((singletoninpowerset) => 78.39/10.67 (((singletoninpowunion) => 78.39/10.67 (((upairset2E) => 78.39/10.67 (((upairsubunion) => 78.39/10.67 (((upairinpowunion) => 78.39/10.67 (((ubforcartprodlem1) => 78.39/10.67 (((ubforcartprodlem2) => 78.39/10.67 (((ubforcartprodlem3) => 78.39/10.67 (((cartprodpairin) => 78.39/10.67 (((cartprodmempair1) => 78.39/10.67 (((cartprodmempair) => 78.39/10.67 (((setunionE2) => 78.39/10.67 (((setunionsingleton1) => 78.39/10.67 (((setunionsingleton2) => 78.39/10.67 (((setunionsingleton) => 78.39/10.67 (((singletonprop) => 78.39/10.67 (((ex1E1) => 78.39/10.67 (( 78.39/10.67 (ex1I) => 78.39/10.67 (( 78.39/10.67 (ex1I2) => 78.39/10.67 (( 78.39/10.67 (singletonsuniq) => 78.39/10.67 (( 78.39/10.67 (setukpairinjL1) => 78.39/10.67 (( 78.39/10.67 (kfstsingleton) => 78.39/10.67 (( 78.39/10.67 (theprop) => 78.39/10.67 (( 78.39/10.67 (kfstpairEq) => 78.39/10.67 (( 78.39/10.67 (cartprodfstin) => 78.39/10.67 (( 78.39/10.67 (setukpairinjL2) => 78.39/10.67 (( 78.39/10.67 (setukpairinjL) => 78.39/10.67 (( 78.39/10.67 (setukpairinjR11) => 78.39/10.67 (( 78.39/10.67 (setukpairinjR12) => 78.39/10.67 (( 78.39/10.67 (setukpairinjR1) => 78.39/10.67 (( 78.39/10.67 (upairequniteq) => 78.39/10.67 (( 78.39/10.67 (setukpairinjR2) => 78.39/10.67 (( 78.39/10.67 (setukpairinjR) => 78.39/10.67 (( 78.39/10.67 (ksndsingleton) => 78.39/10.67 (( 78.39/10.67 (ksndpairEq) => 78.39/10.67 (( 78.39/10.67 (kpairsurjEq) => 78.39/10.67 (( 78.39/10.67 (cartprodsndin) => 78.39/10.67 (( 78.39/10.67 (cartprodpairmemEL) => 78.39/10.67 (( 78.39/10.67 (cartprodpairmemER) => 78.39/10.67 (( 78.39/10.67 (cartprodmempaircEq) => 78.39/10.67 (( 78.39/10.67 (cartprodfstpairEq) => 78.39/10.67 (( 78.39/10.67 (cartprodsndpairEq) => 78.39/10.67 (( 78.39/10.67 (cartprodpairsurjEq) => 78.39/10.67 (( 78.39/10.67 (dpsetconstrI) => 78.39/10.67 (( 78.39/10.67 (dpsetconstrSub) => 78.39/10.67 (( 78.39/10.67 (setOfPairsIsBReln) => 78.39/10.67 (( 78.39/10.67 (dpsetconstrERa) => 78.39/10.67 (( 78.39/10.67 (dpsetconstrEL1) => 78.39/10.67 (( 78.39/10.67 (dpsetconstrEL2) => 78.39/10.67 (( 78.39/10.67 (dpsetconstrER) => 78.39/10.67 (( 78.39/10.67 (funcImageSingleton) => 78.39/10.67 (( 78.39/10.67 (apProp) => 78.39/10.67 (( 78.39/10.67 (app) => 78.39/10.67 (( 78.39/10.67 (infuncsetfunc) => 78.39/10.67 (( 78.39/10.67 (ap2p) => 78.39/10.67 (( 78.39/10.67 (funcinfuncset) => 78.39/10.67 (( 78.39/10.67 (lamProp) => 78.39/10.67 (( 78.39/10.67 (lamp) => 78.39/10.67 (( 78.39/10.67 (lam2p) => 78.39/10.67 (( 78.39/10.67 (brelnall1) => 78.39/10.67 (( 78.39/10.67 (brelnall2) => 78.39/10.67 (( 78.39/10.67 (ex1E2) => 78.39/10.67 (( 78.39/10.67 (funcGraphProp1) => 78.39/10.67 (( 78.39/10.67 (funcGraphProp3) => 78.39/10.67 (( 78.39/10.67 (funcGraphProp2) => 78.39/10.67 (( 78.39/10.67 (funcextLem) => 78.39/10.67 (( 78.39/10.67 (funcGraphProp4) => 78.39/10.67 (( 78.39/10.67 (subbreln) => 78.39/10.67 (( 78.39/10.67 (eqbreln) => 78.39/10.67 (( 78.39/10.67 (funcext) => 78.39/10.67 (( 78.39/10.67 (funcext2) => 78.39/10.67 (( 78.39/10.67 (ap2apEq1) => 78.39/10.67 (( 78.39/10.67 (ap2apEq2) => 78.39/10.67 (( 78.39/10.67 (beta1) => 78.39/10.67 (( 78.39/10.67 (eta1) => 78.39/10.67 (( 78.39/10.67 (lam2lamEq) => 78.39/10.67 (( 78.39/10.67 (beta2) => 78.39/10.67 (( 78.39/10.67 (eta2) => 78.39/10.67 (( 78.39/10.67 (iffalseProp1) => 78.39/10.67 (( 78.39/10.67 (iffalseProp2) => 78.39/10.67 (( 78.39/10.67 (iftrueProp1) => 78.39/10.67 (( 78.39/10.67 (iftrueProp2) => 78.39/10.67 (( 78.39/10.67 (ifSingleton) => 78.39/10.67 (( 78.39/10.67 (ifp) => 78.39/10.67 (( 78.39/10.67 (theeq) => 78.39/10.67 (( 78.39/10.67 (iftrue) => 78.39/10.67 (( 78.39/10.67 (iffalse) => 78.39/10.67 (( 78.39/10.67 (iftrueorfalse) => 78.39/10.67 (( 78.39/10.67 (binintersectT_lem) => 78.39/10.67 (( 78.39/10.67 (binunionT_lem) => 78.39/10.67 (( 78.39/10.67 (powersetT_lem) => 78.39/10.67 (( 78.39/10.67 (setminusT_lem) => 78.39/10.67 (( 78.39/10.67 (complementT_lem) => 78.39/10.67 (( 78.39/10.67 (setextT) => 78.39/10.67 (( 78.39/10.67 (subsetTI) => 78.39/10.67 (( 78.39/10.67 (powersetTI1) => 78.39/10.67 (( 78.39/10.67 (powersetTE1) => 78.39/10.67 (( 78.39/10.67 (complementTI1) => 78.39/10.67 (( 78.39/10.67 (complementTE1) => 78.39/10.67 (( 78.39/10.67 (binintersectTELcontra) => 78.39/10.67 (( 78.39/10.67 (binintersectTERcontra) => 78.39/10.67 (( 78.39/10.67 (contrasubsetT) => 78.39/10.67 (( 78.39/10.67 (contrasubsetT1) => 78.39/10.67 (( 78.39/10.67 (contrasubsetT2) => 78.39/10.67 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(intersectInPowersetIntersectUnions) => 78.39/10.67 (( 78.39/10.67 (inComplementUnionImpNotIn1) => 78.39/10.67 (( 78.39/10.67 (inComplementUnionImpInComplement1) => 78.39/10.67 (( 78.39/10.67 (binunionTE) => 78.39/10.67 (( 78.39/10.67 (binunionTEcontra) => 78.39/10.67 (( 78.39/10.67 (demorgan2a1) => 78.39/10.67 (( 78.39/10.67 (complementUnionInPowersetComplement) => 78.39/10.67 (( 78.39/10.67 (demorgan2a2) => 78.39/10.67 (( 78.39/10.67 (demorgan1a) => 78.39/10.67 (( 78.39/10.67 (demorgan1b) => 78.39/10.67 (( 78.39/10.67 (demorgan1) => 78.39/10.67 (( 78.39/10.67 (demorgan2a) => 78.39/10.67 (( 78.39/10.67 (demorgan2b2) => 78.39/10.67 (( 78.39/10.67 (demorgan2b) => 78.39/10.67 (( 78.39/10.67 (demorgan2) => 78.39/10.67 (( 78.39/10.67 (woz13rule0) => 78.39/10.67 (( 78.39/10.67 (woz13rule1) => 78.39/10.67 (( 78.39/10.67 (woz13rule2) => 78.39/10.67 (( 78.39/10.67 (woz13rule3) => 78.39/10.67 (( 78.39/10.67 (woz13rule4) => 78.39/10.67 (( 78.39/10.67 (woz1_1) => 78.39/10.67 (( 78.39/10.67 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78.39/10.67 (omegaSclos) => 78.39/10.67 (( 78.39/10.67 (peano0notS) => 78.39/10.67 (( 78.39/10.67 (peanoSinj) => 78.39/10.67 (( 78.39/10.67 (transitivesetOp1) => 78.39/10.67 (( 78.39/10.67 (binintTransitive) => 78.39/10.67 (( 78.39/10.67 (transitivesetOp2) => 78.39/10.67 (( 78.39/10.67 (setunionTransitive) => 78.39/10.67 (( 78.39/10.67 (ordinalMinLem1) => 78.39/10.67 (( 78.39/10.67 (!!) @ ( 78.39/10.67 ^[Y0 : $i]: 78.39/10.67 (( 78.39/10.67 (ordinal @ 78.39/10.67 Y0) => 78.39/10.67 (( 78.39/10.67 (!!) @ ( 78.39/10.67 ^[Y1 : $i]: 78.39/10.67 (( 78.39/10.67 (!!) @ ( 78.39/10.67 ^[Y2 : $i]: 78.39/10.67 (( 78.39/10.67 (in @ 78.39/10.67 Y2 @ 78.39/10.67 Y0) => 78.39/10.67 (( 78.39/10.67 (in @ 78.39/10.67 Y1 @ 78.39/10.67 Y2) => 78.39/10.67 (in @ 78.39/10.67 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 78.39/10.67 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1082])). 78.39/10.67 thf(zip_derived_cl1096, plain, 78.39/10.67 (~ (((setminusSubset1) => 78.39/10.67 (((symdiffE) => 78.39/10.67 (((symdiffI1) => 78.39/10.67 (((symdiffI2) => 78.39/10.67 (((symdiffIneg1) => 78.39/10.67 (((symdiffIneg2) => 78.39/10.67 (((secondinupair) => 78.39/10.67 (((setukpairIL) => 78.39/10.67 (((setukpairIR) => 78.39/10.67 (((kpairiskpair) => 78.39/10.67 (((kpairp) => 78.39/10.67 (((singletonsubset) => 78.39/10.67 (((singletoninpowerset) => 78.39/10.67 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(setukpairinjR11) => 78.39/10.67 (( 78.39/10.67 (setukpairinjR12) => 78.39/10.67 (( 78.39/10.67 (setukpairinjR1) => 78.39/10.67 (( 78.39/10.67 (upairequniteq) => 78.39/10.67 (( 78.39/10.67 (setukpairinjR2) => 78.39/10.67 (( 78.39/10.67 (setukpairinjR) => 78.39/10.67 (( 78.39/10.67 (ksndsingleton) => 78.39/10.67 (( 78.39/10.67 (ksndpairEq) => 78.39/10.67 (( 78.39/10.67 (kpairsurjEq) => 78.39/10.67 (( 78.39/10.67 (cartprodsndin) => 78.39/10.67 (( 78.39/10.67 (cartprodpairmemEL) => 78.39/10.67 (( 78.39/10.67 (cartprodpairmemER) => 78.39/10.67 (( 78.39/10.67 (cartprodmempaircEq) => 78.39/10.67 (( 78.39/10.67 (cartprodfstpairEq) => 78.39/10.67 (( 78.39/10.67 (cartprodsndpairEq) => 78.39/10.67 (( 78.39/10.67 (cartprodpairsurjEq) => 78.39/10.67 (( 78.39/10.67 (dpsetconstrI) => 78.39/10.67 (( 78.39/10.67 (dpsetconstrSub) => 78.39/10.67 (( 78.39/10.67 (setOfPairsIsBReln) => 78.39/10.67 (( 78.39/10.67 (dpsetconstrERa) => 78.39/10.67 (( 78.39/10.67 (dpsetconstrEL1) => 78.39/10.67 (( 78.39/10.67 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(contraSubsetComplement) => 78.39/10.67 (( 78.39/10.67 (complementTcontraSubset) => 78.39/10.67 (( 78.39/10.67 (binunionTILcontra) => 78.39/10.67 (( 78.39/10.67 (binunionTIRcontra) => 78.39/10.67 (( 78.39/10.67 (inIntersectImpInUnion) => 78.39/10.67 (( 78.39/10.67 (inIntersectImpInUnion2) => 78.39/10.67 (( 78.39/10.67 (inIntersectImpInIntersectUnions) => 78.39/10.67 (( 78.39/10.67 (intersectInPowersetIntersectUnions) => 78.39/10.67 (( 78.39/10.67 (inComplementUnionImpNotIn1) => 78.39/10.67 (( 78.39/10.67 (inComplementUnionImpInComplement1) => 78.39/10.67 (( 78.39/10.67 (binunionTE) => 78.39/10.67 (( 78.39/10.67 (binunionTEcontra) => 78.39/10.67 (( 78.39/10.67 (demorgan2a1) => 78.39/10.67 (( 78.39/10.67 (complementUnionInPowersetComplement) => 78.39/10.67 (( 78.39/10.67 (demorgan2a2) => 78.39/10.67 (( 78.39/10.67 (demorgan1a) => 78.39/10.67 (( 78.39/10.67 (demorgan1b) => 78.39/10.67 (( 78.39/10.67 (demorgan1) => 78.39/10.67 (( 78.39/10.67 (demorgan2a) => 78.39/10.67 (( 78.39/10.67 (demorgan2b2) => 78.39/10.67 (( 78.39/10.67 (demorgan2b) => 78.39/10.67 (( 78.39/10.67 (demorgan2) => 78.39/10.67 (( 78.39/10.67 (woz13rule0) => 78.39/10.67 (( 78.39/10.67 (woz13rule1) => 78.39/10.67 (( 78.39/10.67 (woz13rule2) => 78.39/10.67 (( 78.39/10.67 (woz13rule3) => 78.39/10.67 (( 78.39/10.67 (woz13rule4) => 78.39/10.67 (( 78.39/10.67 (woz1_1) => 78.39/10.67 (( 78.39/10.67 (woz1_2) => 78.39/10.67 (( 78.39/10.67 (woz1_3) => 78.39/10.67 (( 78.39/10.67 (woz1_4) => 78.39/10.67 (( 78.39/10.67 (woz1_5) => 78.39/10.67 (( 78.39/10.67 (breln1all2) => 78.39/10.67 (( 78.39/10.67 (breln1SetBreln1) => 78.39/10.67 (( 78.39/10.67 (choice2fnsingleton) => 78.39/10.67 (( 78.39/10.67 (setOfPairsIsBReln1) => 78.39/10.67 (( 78.39/10.67 (breln1all1) => 78.39/10.67 (( 78.39/10.67 (subbreln1) => 78.39/10.67 (( 78.39/10.67 (eqbreln1) => 78.39/10.67 (( 78.39/10.67 (breln1invprop) => 78.39/10.67 (( 78.39/10.67 (breln1invI) => 78.39/10.67 (( 78.39/10.67 (breln1invE) => 78.39/10.67 (( 78.39/10.67 (breln1compprop) => 78.39/10.67 (( 78.39/10.67 (breln1compI) => 78.39/10.67 (( 78.39/10.67 (breln1compE) => 78.39/10.67 (( 78.39/10.67 (breln1compEex) => 78.39/10.67 (( 78.39/10.67 (breln1unionprop) => 78.39/10.67 (( 78.39/10.67 (breln1unionIL) => 78.39/10.67 (( 78.39/10.67 (breln1unionIR) => 78.39/10.67 (( 78.39/10.67 (breln1unionI) => 78.39/10.67 (( 78.39/10.67 (breln1unionE) => 78.39/10.67 (( 78.39/10.67 (breln1unionEcases) => 78.39/10.67 (( 78.39/10.67 (breln1unionCommutes) => 78.39/10.67 (( 78.39/10.67 (woz2Ex) => 78.39/10.67 (( 78.39/10.67 (woz2W) => 78.39/10.67 (( 78.39/10.67 (woz2A) => 78.39/10.67 (( 78.39/10.67 (woz2B) => 78.39/10.67 (( 78.39/10.67 (image1Ex) => 78.39/10.67 (( 78.39/10.67 (image1Ex1) => 78.39/10.67 (( 78.39/10.67 (image1Equiv) => 78.39/10.67 (( 78.39/10.67 (image1E) => 78.39/10.67 (( 78.39/10.67 (image1I) => 78.39/10.67 (( 78.39/10.67 (injFuncInInjFuncSet) => 78.39/10.67 (( 78.39/10.67 (injFuncSetFuncIn) => 78.39/10.67 (( 78.39/10.67 (injFuncSetFuncInj) => 78.39/10.67 (( 78.39/10.67 (surjFuncSetFuncIn) => 78.39/10.67 (( 78.39/10.67 (surjFuncSetFuncSurj) => 78.39/10.67 (( 78.39/10.67 (leftInvIsSurj) => 78.39/10.67 (( 78.39/10.67 (surjCantorThm) => 78.39/10.67 (( 78.39/10.67 (foundation2) => 78.39/10.67 (( 78.39/10.67 (notinself) => 78.39/10.67 (( 78.39/10.67 (notinself2) => 78.39/10.67 (( 78.39/10.67 (omegaSp) => 78.39/10.67 (( 78.39/10.67 (omegaSclos) => 78.39/10.67 (( 78.39/10.67 (peano0notS) => 78.39/10.67 (( 78.39/10.67 (peanoSinj) => 78.39/10.67 (( 78.39/10.67 (transitivesetOp1) => 78.39/10.67 (( 78.39/10.67 (binintTransitive) => 78.39/10.67 (( 78.39/10.67 (transitivesetOp2) => 78.39/10.67 (( 78.39/10.67 (setunionTransitive) => 78.39/10.67 (( 78.39/10.67 (ordinalMinLem1) => 78.39/10.67 (( 78.39/10.67 (!!) @ ( 78.39/10.67 ^[Y0 : $i]: 78.39/10.67 (( 78.39/10.67 (ordinal @ 78.39/10.67 Y0) => 78.39/10.67 (( 78.39/10.67 (!!) @ ( 78.39/10.67 ^[Y1 : $i]: 78.39/10.67 (( 78.39/10.67 (!!) @ ( 78.39/10.67 ^[Y2 : $i]: 78.39/10.67 (( 78.39/10.67 (in @ 78.39/10.67 Y2 @ 78.39/10.67 Y0) => 78.39/10.67 (( 78.39/10.67 (in @ 78.39/10.67 Y1 @ 78.39/10.67 Y2) => 78.39/10.67 (in @ 78.39/10.67 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 78.39/10.67 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1089])). 78.39/10.67 thf(zip_derived_cl1103, plain, 78.39/10.67 (~ (((symdiffE) => 78.39/10.67 (((symdiffI1) => 78.39/10.67 (((symdiffI2) => 78.39/10.67 (((symdiffIneg1) => 78.39/10.67 (((symdiffIneg2) => 78.39/10.67 (((secondinupair) => 78.39/10.67 (((setukpairIL) => 78.39/10.67 (((setukpairIR) => 78.39/10.67 (((kpairiskpair) => 78.39/10.67 (((kpairp) => 78.39/10.67 (((singletonsubset) => 78.39/10.67 (((singletoninpowerset) => 78.39/10.67 (((singletoninpowunion) => 78.39/10.67 (((upairset2E) => 78.39/10.67 (((upairsubunion) => 78.39/10.67 (((upairinpowunion) => 78.39/10.67 (((ubforcartprodlem1) => 78.39/10.67 (((ubforcartprodlem2) => 78.39/10.67 (((ubforcartprodlem3) => 78.39/10.67 (((cartprodpairin) => 78.39/10.67 (((cartprodmempair1) => 78.39/10.67 (((cartprodmempair) => 78.39/10.67 (((setunionE2) => 78.39/10.67 (((setunionsingleton1) => 78.39/10.67 (((setunionsingleton2) => 78.39/10.67 (((setunionsingleton) => 78.39/10.67 (((singletonprop) => 78.39/10.67 (((ex1E1) => 78.39/10.67 (((ex1I) => 78.39/10.67 (((ex1I2) => 78.39/10.67 (( 78.39/10.67 (singletonsuniq) => 78.39/10.67 (( 78.39/10.67 (setukpairinjL1) => 78.39/10.67 (( 78.39/10.67 (kfstsingleton) => 78.39/10.67 (( 78.39/10.67 (theprop) => 78.39/10.67 (( 78.39/10.67 (kfstpairEq) => 78.39/10.67 (( 78.39/10.67 (cartprodfstin) => 78.39/10.67 (( 78.39/10.67 (setukpairinjL2) => 78.39/10.67 (( 78.39/10.67 (setukpairinjL) => 78.39/10.67 (( 78.39/10.67 (setukpairinjR11) => 78.39/10.67 (( 78.39/10.67 (setukpairinjR12) => 78.39/10.67 (( 78.39/10.67 (setukpairinjR1) => 78.39/10.67 (( 78.39/10.67 (upairequniteq) => 78.39/10.67 (( 78.39/10.67 (setukpairinjR2) => 78.39/10.67 (( 78.39/10.67 (setukpairinjR) => 78.39/10.67 (( 78.39/10.67 (ksndsingleton) => 78.39/10.67 (( 78.39/10.67 (ksndpairEq) => 78.39/10.67 (( 78.39/10.67 (kpairsurjEq) => 78.39/10.67 (( 78.39/10.67 (cartprodsndin) => 78.39/10.67 (( 78.39/10.67 (cartprodpairmemEL) => 78.39/10.67 (( 78.39/10.67 (cartprodpairmemER) => 78.39/10.67 (( 78.39/10.67 (cartprodmempaircEq) => 78.39/10.67 (( 78.39/10.67 (cartprodfstpairEq) => 78.39/10.67 (( 78.39/10.67 (cartprodsndpairEq) => 78.39/10.67 (( 78.39/10.67 (cartprodpairsurjEq) => 78.39/10.67 (( 78.39/10.67 (dpsetconstrI) => 78.39/10.67 (( 78.39/10.67 (dpsetconstrSub) => 78.39/10.67 (( 78.39/10.67 (setOfPairsIsBReln) => 78.39/10.67 (( 78.39/10.67 (dpsetconstrERa) => 78.39/10.67 (( 78.39/10.67 (dpsetconstrEL1) => 78.39/10.67 (( 78.39/10.67 (dpsetconstrEL2) => 78.39/10.67 (( 78.39/10.67 (dpsetconstrER) => 78.39/10.67 (( 78.39/10.67 (funcImageSingleton) => 78.39/10.67 (( 78.39/10.67 (apProp) => 78.39/10.67 (( 78.39/10.67 (app) => 78.39/10.67 (( 78.39/10.67 (infuncsetfunc) => 78.39/10.67 (( 78.39/10.67 (ap2p) => 78.39/10.67 (( 78.39/10.67 (funcinfuncset) => 78.39/10.67 (( 78.39/10.67 (lamProp) => 78.39/10.67 (( 78.39/10.67 (lamp) => 78.39/10.67 (( 78.39/10.67 (lam2p) => 78.39/10.67 (( 78.39/10.67 (brelnall1) => 78.39/10.67 (( 78.39/10.67 (brelnall2) => 78.39/10.67 (( 78.39/10.67 (ex1E2) => 78.39/10.67 (( 78.39/10.67 (funcGraphProp1) => 78.39/10.67 (( 78.39/10.67 (funcGraphProp3) => 78.39/10.67 (( 78.39/10.67 (funcGraphProp2) => 78.39/10.67 (( 78.39/10.67 (funcextLem) => 78.39/10.67 (( 78.39/10.67 (funcGraphProp4) => 78.39/10.67 (( 78.39/10.67 (subbreln) => 78.39/10.67 (( 78.39/10.67 (eqbreln) => 78.39/10.67 (( 78.39/10.67 (funcext) => 78.39/10.67 (( 78.39/10.67 (funcext2) => 78.39/10.67 (( 78.39/10.67 (ap2apEq1) => 78.39/10.67 (( 78.39/10.67 (ap2apEq2) => 78.39/10.67 (( 78.39/10.67 (beta1) => 78.39/10.67 (( 78.39/10.67 (eta1) => 78.39/10.67 (( 78.39/10.67 (lam2lamEq) => 78.39/10.67 (( 78.39/10.67 (beta2) => 78.39/10.67 (( 78.39/10.67 (eta2) => 78.39/10.67 (( 78.39/10.67 (iffalseProp1) => 78.39/10.67 (( 78.39/10.67 (iffalseProp2) => 78.39/10.67 (( 78.39/10.67 (iftrueProp1) => 78.39/10.67 (( 78.39/10.67 (iftrueProp2) => 78.39/10.67 (( 78.39/10.67 (ifSingleton) => 78.39/10.67 (( 78.39/10.67 (ifp) => 78.39/10.67 (( 78.39/10.67 (theeq) => 78.39/10.67 (( 78.39/10.67 (iftrue) => 78.39/10.67 (( 78.39/10.67 (iffalse) => 78.39/10.67 (( 78.39/10.67 (iftrueorfalse) => 78.39/10.67 (( 78.39/10.67 (binintersectT_lem) => 78.39/10.67 (( 78.39/10.67 (binunionT_lem) => 78.39/10.67 (( 78.39/10.67 (powersetT_lem) => 78.39/10.67 (( 78.39/10.67 (setminusT_lem) => 78.39/10.67 (( 78.39/10.67 (complementT_lem) => 78.39/10.67 (( 78.39/10.67 (setextT) => 78.39/10.67 (( 78.39/10.67 (subsetTI) => 78.39/10.67 (( 78.39/10.67 (powersetTI1) => 78.39/10.67 (( 78.39/10.67 (powersetTE1) => 78.39/10.67 (( 78.39/10.67 (complementTI1) => 78.39/10.67 (( 78.39/10.67 (complementTE1) => 78.39/10.67 (( 78.39/10.67 (binintersectTELcontra) => 78.39/10.67 (( 78.39/10.67 (binintersectTERcontra) => 78.39/10.67 (( 78.39/10.67 (contrasubsetT) => 78.39/10.67 (( 78.39/10.67 (contrasubsetT1) => 78.39/10.67 (( 78.39/10.67 (contrasubsetT2) => 78.39/10.67 (( 78.39/10.67 (contrasubsetT3) => 78.39/10.67 (( 78.39/10.67 (doubleComplementI1) => 78.39/10.67 (( 78.39/10.67 (doubleComplementE1) => 78.39/10.67 (( 78.39/10.67 (doubleComplementSub1) => 78.39/10.67 (( 78.39/10.67 (doubleComplementSub2) => 78.39/10.67 (( 78.39/10.67 (doubleComplementEq) => 78.39/10.67 (( 78.39/10.67 (complementTnotintersectT) => 78.39/10.67 (( 78.39/10.67 (complementImpComplementIntersect) => 78.39/10.67 (( 78.39/10.67 (complementSubsetComplementIntersect) => 78.39/10.67 (( 78.39/10.67 (complementInPowersetComplementIntersect) => 78.39/10.67 (( 78.39/10.67 (contraSubsetComplement) => 78.39/10.67 (( 78.39/10.67 (complementTcontraSubset) => 78.39/10.67 (( 78.39/10.67 (binunionTILcontra) => 78.39/10.67 (( 78.39/10.67 (binunionTIRcontra) => 78.39/10.67 (( 78.39/10.67 (inIntersectImpInUnion) => 78.39/10.67 (( 78.39/10.67 (inIntersectImpInUnion2) => 78.39/10.67 (( 78.39/10.67 (inIntersectImpInIntersectUnions) => 78.39/10.67 (( 78.39/10.67 (intersectInPowersetIntersectUnions) => 78.39/10.67 (( 78.39/10.67 (inComplementUnionImpNotIn1) => 78.39/10.67 (( 78.39/10.67 (inComplementUnionImpInComplement1) => 78.39/10.67 (( 78.39/10.67 (binunionTE) => 78.39/10.67 (( 78.39/10.67 (binunionTEcontra) => 78.39/10.67 (( 78.39/10.67 (demorgan2a1) => 78.39/10.67 (( 78.39/10.67 (complementUnionInPowersetComplement) => 78.39/10.67 (( 78.39/10.67 (demorgan2a2) => 78.39/10.67 (( 78.39/10.67 (demorgan1a) => 78.39/10.67 (( 78.39/10.67 (demorgan1b) => 78.39/10.67 (( 78.39/10.67 (demorgan1) => 78.39/10.67 (( 78.39/10.67 (demorgan2a) => 78.39/10.67 (( 78.39/10.67 (demorgan2b2) => 78.39/10.67 (( 78.39/10.67 (demorgan2b) => 78.39/10.67 (( 78.39/10.67 (demorgan2) => 78.39/10.67 (( 78.39/10.67 (woz13rule0) => 78.39/10.67 (( 78.39/10.67 (woz13rule1) => 78.39/10.67 (( 78.39/10.67 (woz13rule2) => 78.39/10.67 (( 78.39/10.67 (woz13rule3) => 78.39/10.67 (( 78.39/10.67 (woz13rule4) => 78.39/10.67 (( 78.39/10.67 (woz1_1) => 78.39/10.67 (( 78.39/10.67 (woz1_2) => 78.39/10.67 (( 78.39/10.67 (woz1_3) => 78.39/10.67 (( 78.39/10.67 (woz1_4) => 78.39/10.67 (( 78.39/10.67 (woz1_5) => 78.39/10.67 (( 78.39/10.67 (breln1all2) => 78.39/10.67 (( 78.39/10.67 (breln1SetBreln1) => 78.39/10.67 (( 78.39/10.67 (choice2fnsingleton) => 78.39/10.67 (( 78.39/10.67 (setOfPairsIsBReln1) => 78.39/10.67 (( 78.39/10.67 (breln1all1) => 78.39/10.67 (( 78.39/10.67 (subbreln1) => 78.39/10.67 (( 78.39/10.67 (eqbreln1) => 78.39/10.67 (( 78.39/10.67 (breln1invprop) => 78.39/10.67 (( 78.39/10.67 (breln1invI) => 78.39/10.67 (( 78.39/10.67 (breln1invE) => 78.39/10.67 (( 78.39/10.67 (breln1compprop) => 78.39/10.67 (( 78.39/10.67 (breln1compI) => 78.39/10.67 (( 78.39/10.67 (breln1compE) => 78.39/10.67 (( 78.39/10.67 (breln1compEex) => 78.39/10.67 (( 78.39/10.67 (breln1unionprop) => 78.39/10.67 (( 78.39/10.67 (breln1unionIL) => 78.39/10.67 (( 78.39/10.67 (breln1unionIR) => 78.39/10.67 (( 78.39/10.67 (breln1unionI) => 78.39/10.67 (( 78.39/10.67 (breln1unionE) => 78.39/10.67 (( 78.39/10.67 (breln1unionEcases) => 78.39/10.67 (( 78.39/10.67 (breln1unionCommutes) => 78.39/10.67 (( 78.39/10.67 (woz2Ex) => 78.39/10.67 (( 78.39/10.67 (woz2W) => 78.39/10.67 (( 78.39/10.67 (woz2A) => 78.39/10.67 (( 78.39/10.67 (woz2B) => 78.39/10.67 (( 78.39/10.67 (image1Ex) => 78.39/10.67 (( 78.39/10.67 (image1Ex1) => 78.39/10.67 (( 78.39/10.67 (image1Equiv) => 78.39/10.67 (( 78.39/10.67 (image1E) => 78.39/10.67 (( 78.39/10.67 (image1I) => 78.39/10.67 (( 78.39/10.67 (injFuncInInjFuncSet) => 78.39/10.67 (( 78.39/10.67 (injFuncSetFuncIn) => 78.39/10.67 (( 78.39/10.67 (injFuncSetFuncInj) => 78.39/10.67 (( 78.39/10.67 (surjFuncSetFuncIn) => 78.39/10.67 (( 78.39/10.67 (surjFuncSetFuncSurj) => 78.39/10.67 (( 78.39/10.67 (leftInvIsSurj) => 78.39/10.67 (( 78.39/10.67 (surjCantorThm) => 78.39/10.67 (( 78.39/10.67 (foundation2) => 78.39/10.67 (( 78.39/10.67 (notinself) => 78.39/10.67 (( 78.39/10.67 (notinself2) => 78.39/10.67 (( 78.39/10.67 (omegaSp) => 78.39/10.67 (( 78.39/10.67 (omegaSclos) => 78.39/10.67 (( 78.39/10.67 (peano0notS) => 78.39/10.67 (( 78.39/10.67 (peanoSinj) => 78.39/10.67 (( 78.39/10.67 (transitivesetOp1) => 78.39/10.67 (( 78.39/10.67 (binintTransitive) => 78.39/10.67 (( 78.39/10.67 (transitivesetOp2) => 78.39/10.67 (( 78.39/10.67 (setunionTransitive) => 78.39/10.67 (( 78.39/10.67 (ordinalMinLem1) => 78.39/10.67 (( 78.39/10.67 (!!) @ ( 78.39/10.67 ^[Y0 : $i]: 78.39/10.67 (( 78.39/10.67 (ordinal @ 78.39/10.67 Y0) => 78.39/10.67 (( 78.39/10.67 (!!) @ ( 78.39/10.67 ^[Y1 : $i]: 78.39/10.67 (( 78.39/10.67 (!!) @ ( 78.39/10.67 ^[Y2 : $i]: 78.39/10.67 (( 78.39/10.67 (in @ 78.39/10.67 Y2 @ 78.39/10.67 Y0) => 78.39/10.67 (( 78.39/10.67 (in @ 78.39/10.67 Y1 @ 78.39/10.67 Y2) => 78.39/10.67 (in @ 78.39/10.67 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 78.39/10.67 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1096])). 78.39/10.67 thf(zip_derived_cl1111, plain, 78.39/10.67 (~ (((symdiffI1) => 78.39/10.67 (((symdiffI2) => 78.39/10.67 (((symdiffIneg1) => 78.39/10.67 (((symdiffIneg2) => 78.39/10.67 (((secondinupair) => 78.39/10.67 (((setukpairIL) => 78.39/10.67 (((setukpairIR) => 78.39/10.67 (((kpairiskpair) => 78.39/10.67 (((kpairp) => 78.39/10.67 (((singletonsubset) => 78.39/10.67 (((singletoninpowerset) => 78.39/10.67 (((singletoninpowunion) => 78.39/10.67 (((upairset2E) => 78.39/10.67 (((upairsubunion) => 78.39/10.67 (((upairinpowunion) => 78.39/10.67 (((ubforcartprodlem1) => 78.39/10.67 (((ubforcartprodlem2) => 78.39/10.67 (((ubforcartprodlem3) => 78.39/10.67 (((cartprodpairin) => 78.39/10.67 (((cartprodmempair1) => 78.39/10.67 (((cartprodmempair) => 78.39/10.67 (((setunionE2) => 78.39/10.67 (((setunionsingleton1) => 78.39/10.67 (((setunionsingleton2) => 78.39/10.67 (((setunionsingleton) => 78.39/10.67 (((singletonprop) => 78.39/10.67 (((ex1E1) => 78.39/10.67 (((ex1I) => 78.39/10.67 (((ex1I2) => 78.39/10.67 (((singletonsuniq) => 78.39/10.67 (( 78.39/10.67 (setukpairinjL1) => 78.39/10.67 (( 78.39/10.67 (kfstsingleton) => 78.39/10.67 (( 78.39/10.67 (theprop) => 78.39/10.67 (( 78.39/10.67 (kfstpairEq) => 78.39/10.67 (( 78.39/10.67 (cartprodfstin) => 78.39/10.67 (( 78.39/10.67 (setukpairinjL2) => 78.39/10.67 (( 78.39/10.67 (setukpairinjL) => 78.39/10.67 (( 78.39/10.67 (setukpairinjR11) => 78.39/10.67 (( 78.39/10.67 (setukpairinjR12) => 78.39/10.67 (( 78.39/10.67 (setukpairinjR1) => 78.39/10.67 (( 78.39/10.67 (upairequniteq) => 78.39/10.67 (( 78.39/10.67 (setukpairinjR2) => 78.39/10.67 (( 78.39/10.67 (setukpairinjR) => 78.39/10.67 (( 78.39/10.67 (ksndsingleton) => 78.39/10.67 (( 78.39/10.67 (ksndpairEq) => 78.39/10.67 (( 78.39/10.67 (kpairsurjEq) => 78.39/10.67 (( 78.39/10.67 (cartprodsndin) => 78.39/10.67 (( 78.39/10.67 (cartprodpairmemEL) => 78.39/10.67 (( 78.39/10.67 (cartprodpairmemER) => 78.39/10.67 (( 78.39/10.67 (cartprodmempaircEq) => 78.39/10.67 (( 78.39/10.67 (cartprodfstpairEq) => 78.39/10.67 (( 78.39/10.67 (cartprodsndpairEq) => 78.39/10.67 (( 78.39/10.67 (cartprodpairsurjEq) => 78.39/10.67 (( 78.39/10.67 (dpsetconstrI) => 78.39/10.67 (( 78.39/10.67 (dpsetconstrSub) => 78.39/10.67 (( 78.39/10.67 (setOfPairsIsBReln) => 78.39/10.67 (( 78.39/10.67 (dpsetconstrERa) => 78.39/10.67 (( 78.39/10.67 (dpsetconstrEL1) => 78.39/10.67 (( 78.39/10.67 (dpsetconstrEL2) => 78.39/10.67 (( 78.39/10.67 (dpsetconstrER) => 78.39/10.67 (( 78.39/10.67 (funcImageSingleton) => 78.39/10.67 (( 78.39/10.67 (apProp) => 78.39/10.67 (( 78.39/10.67 (app) => 78.39/10.67 (( 78.39/10.67 (infuncsetfunc) => 78.39/10.67 (( 78.39/10.67 (ap2p) => 78.39/10.67 (( 78.39/10.67 (funcinfuncset) => 78.39/10.67 (( 78.39/10.67 (lamProp) => 78.39/10.67 (( 78.39/10.67 (lamp) => 78.39/10.67 (( 78.39/10.67 (lam2p) => 78.39/10.67 (( 78.39/10.67 (brelnall1) => 78.39/10.67 (( 78.39/10.67 (brelnall2) => 78.39/10.67 (( 78.39/10.67 (ex1E2) => 78.39/10.67 (( 78.39/10.67 (funcGraphProp1) => 78.39/10.67 (( 78.39/10.67 (funcGraphProp3) => 78.39/10.67 (( 78.39/10.67 (funcGraphProp2) => 78.39/10.67 (( 78.39/10.67 (funcextLem) => 78.39/10.67 (( 78.39/10.67 (funcGraphProp4) => 78.39/10.67 (( 78.39/10.67 (subbreln) => 78.39/10.67 (( 78.39/10.67 (eqbreln) => 78.39/10.67 (( 78.39/10.67 (funcext) => 78.39/10.67 (( 78.39/10.67 (funcext2) => 78.39/10.67 (( 78.39/10.67 (ap2apEq1) => 78.39/10.67 (( 78.39/10.67 (ap2apEq2) => 78.39/10.67 (( 78.39/10.67 (beta1) => 78.39/10.67 (( 78.39/10.67 (eta1) => 78.39/10.67 (( 78.39/10.67 (lam2lamEq) => 78.39/10.67 (( 78.39/10.67 (beta2) => 78.39/10.67 (( 78.39/10.67 (eta2) => 78.39/10.67 (( 78.39/10.67 (iffalseProp1) => 78.39/10.67 (( 78.39/10.67 (iffalseProp2) => 78.39/10.67 (( 78.39/10.67 (iftrueProp1) => 78.39/10.67 (( 78.39/10.67 (iftrueProp2) => 78.39/10.67 (( 78.39/10.67 (ifSingleton) => 78.39/10.67 (( 78.39/10.67 (ifp) => 78.39/10.67 (( 78.39/10.67 (theeq) => 78.39/10.67 (( 78.39/10.67 (iftrue) => 78.39/10.67 (( 78.39/10.67 (iffalse) => 78.39/10.67 (( 78.39/10.67 (iftrueorfalse) => 78.39/10.67 (( 78.39/10.67 (binintersectT_lem) => 78.39/10.67 (( 78.39/10.67 (binunionT_lem) => 78.39/10.67 (( 78.39/10.67 (powersetT_lem) => 78.39/10.67 (( 78.39/10.67 (setminusT_lem) => 78.39/10.67 (( 78.39/10.67 (complementT_lem) => 78.39/10.67 (( 78.39/10.67 (setextT) => 78.39/10.67 (( 78.39/10.67 (subsetTI) => 78.39/10.67 (( 78.39/10.67 (powersetTI1) => 78.39/10.67 (( 78.39/10.67 (powersetTE1) => 78.39/10.67 (( 78.39/10.67 (complementTI1) => 78.39/10.67 (( 78.39/10.67 (complementTE1) => 78.39/10.67 (( 78.39/10.67 (binintersectTELcontra) => 78.39/10.67 (( 78.39/10.67 (binintersectTERcontra) => 78.39/10.67 (( 78.39/10.67 (contrasubsetT) => 78.39/10.67 (( 78.39/10.67 (contrasubsetT1) => 78.39/10.67 (( 78.39/10.67 (contrasubsetT2) => 78.39/10.67 (( 78.39/10.67 (contrasubsetT3) => 78.39/10.67 (( 78.39/10.67 (doubleComplementI1) => 78.39/10.67 (( 78.39/10.67 (doubleComplementE1) => 78.39/10.67 (( 78.39/10.67 (doubleComplementSub1) => 78.39/10.67 (( 78.39/10.67 (doubleComplementSub2) => 78.39/10.67 (( 78.39/10.67 (doubleComplementEq) => 78.39/10.67 (( 78.39/10.67 (complementTnotintersectT) => 78.39/10.67 (( 78.39/10.67 (complementImpComplementIntersect) => 78.39/10.67 (( 78.39/10.67 (complementSubsetComplementIntersect) => 78.39/10.67 (( 78.39/10.67 (complementInPowersetComplementIntersect) => 78.39/10.67 (( 78.39/10.67 (contraSubsetComplement) => 78.39/10.67 (( 78.39/10.67 (complementTcontraSubset) => 78.39/10.67 (( 78.39/10.67 (binunionTILcontra) => 78.39/10.67 (( 78.39/10.67 (binunionTIRcontra) => 78.39/10.67 (( 78.39/10.67 (inIntersectImpInUnion) => 78.39/10.67 (( 78.39/10.67 (inIntersectImpInUnion2) => 78.39/10.67 (( 78.39/10.67 (inIntersectImpInIntersectUnions) => 78.39/10.67 (( 78.39/10.67 (intersectInPowersetIntersectUnions) => 78.39/10.67 (( 78.39/10.67 (inComplementUnionImpNotIn1) => 78.39/10.67 (( 78.39/10.67 (inComplementUnionImpInComplement1) => 78.39/10.67 (( 78.39/10.67 (binunionTE) => 78.39/10.67 (( 78.39/10.67 (binunionTEcontra) => 78.39/10.67 (( 78.39/10.67 (demorgan2a1) => 78.39/10.67 (( 78.39/10.67 (complementUnionInPowersetComplement) => 78.39/10.67 (( 78.39/10.67 (demorgan2a2) => 78.39/10.67 (( 78.39/10.67 (demorgan1a) => 78.39/10.67 (( 78.39/10.67 (demorgan1b) => 78.39/10.67 (( 78.39/10.67 (demorgan1) => 78.39/10.67 (( 78.39/10.67 (demorgan2a) => 78.39/10.67 (( 78.39/10.67 (demorgan2b2) => 78.39/10.67 (( 78.39/10.67 (demorgan2b) => 78.39/10.67 (( 78.39/10.67 (demorgan2) => 78.39/10.67 (( 78.39/10.67 (woz13rule0) => 78.39/10.67 (( 78.39/10.67 (woz13rule1) => 78.39/10.67 (( 78.39/10.67 (woz13rule2) => 78.39/10.67 (( 78.39/10.67 (woz13rule3) => 78.39/10.67 (( 78.39/10.67 (woz13rule4) => 78.39/10.67 (( 78.39/10.67 (woz1_1) => 78.39/10.67 (( 78.39/10.67 (woz1_2) => 78.39/10.67 (( 78.39/10.67 (woz1_3) => 78.39/10.67 (( 78.39/10.67 (woz1_4) => 78.39/10.67 (( 78.39/10.67 (woz1_5) => 78.39/10.67 (( 78.39/10.67 (breln1all2) => 78.39/10.67 (( 78.39/10.67 (breln1SetBreln1) => 78.39/10.67 (( 78.39/10.67 (choice2fnsingleton) => 78.39/10.67 (( 78.39/10.67 (setOfPairsIsBReln1) => 78.39/10.67 (( 78.39/10.67 (breln1all1) => 78.39/10.67 (( 78.39/10.67 (subbreln1) => 78.39/10.67 (( 78.39/10.67 (eqbreln1) => 78.39/10.67 (( 78.39/10.67 (breln1invprop) => 78.39/10.67 (( 78.39/10.67 (breln1invI) => 78.39/10.67 (( 78.39/10.67 (breln1invE) => 78.39/10.67 (( 78.39/10.67 (breln1compprop) => 78.39/10.67 (( 78.39/10.67 (breln1compI) => 78.39/10.67 (( 78.39/10.67 (breln1compE) => 78.39/10.67 (( 78.39/10.67 (breln1compEex) => 78.39/10.67 (( 78.39/10.67 (breln1unionprop) => 78.39/10.67 (( 78.39/10.67 (breln1unionIL) => 78.39/10.67 (( 78.39/10.67 (breln1unionIR) => 78.39/10.67 (( 78.39/10.67 (breln1unionI) => 78.39/10.67 (( 78.39/10.67 (breln1unionE) => 78.39/10.67 (( 78.39/10.67 (breln1unionEcases) => 78.39/10.67 (( 78.39/10.67 (breln1unionCommutes) => 78.39/10.67 (( 78.39/10.67 (woz2Ex) => 78.39/10.67 (( 78.39/10.67 (woz2W) => 78.39/10.67 (( 78.39/10.67 (woz2A) => 78.39/10.67 (( 78.39/10.67 (woz2B) => 78.39/10.67 (( 78.39/10.67 (image1Ex) => 78.39/10.67 (( 78.39/10.67 (image1Ex1) => 78.39/10.67 (( 78.39/10.67 (image1Equiv) => 78.39/10.67 (( 78.39/10.67 (image1E) => 78.39/10.67 (( 78.39/10.67 (image1I) => 78.39/10.67 (( 78.39/10.67 (injFuncInInjFuncSet) => 78.39/10.67 (( 78.39/10.67 (injFuncSetFuncIn) => 78.39/10.67 (( 78.39/10.67 (injFuncSetFuncInj) => 78.39/10.67 (( 78.39/10.67 (surjFuncSetFuncIn) => 78.39/10.67 (( 78.39/10.67 (surjFuncSetFuncSurj) => 78.39/10.67 (( 78.39/10.67 (leftInvIsSurj) => 78.39/10.67 (( 78.39/10.67 (surjCantorThm) => 78.39/10.67 (( 78.39/10.67 (foundation2) => 78.39/10.67 (( 78.39/10.67 (notinself) => 78.39/10.67 (( 78.39/10.67 (notinself2) => 78.39/10.67 (( 78.39/10.67 (omegaSp) => 78.39/10.67 (( 78.39/10.67 (omegaSclos) => 78.39/10.67 (( 78.39/10.67 (peano0notS) => 78.39/10.67 (( 78.39/10.67 (peanoSinj) => 78.39/10.67 (( 78.39/10.67 (transitivesetOp1) => 78.39/10.67 (( 78.39/10.67 (binintTransitive) => 78.39/10.67 (( 78.39/10.67 (transitivesetOp2) => 78.39/10.67 (( 78.39/10.67 (setunionTransitive) => 78.39/10.67 (( 78.39/10.67 (ordinalMinLem1) => 78.39/10.67 (( 78.39/10.67 (!!) @ ( 78.39/10.67 ^[Y0 : $i]: 78.39/10.67 (( 78.39/10.67 (ordinal @ 78.39/10.67 Y0) => 78.39/10.67 (( 78.39/10.67 (!!) @ ( 78.39/10.67 ^[Y1 : $i]: 78.39/10.67 (( 78.39/10.67 (!!) @ ( 78.39/10.67 ^[Y2 : $i]: 78.39/10.67 (( 78.39/10.67 (in @ 78.39/10.67 Y2 @ 78.39/10.67 Y0) => 78.39/10.67 (( 78.39/10.67 (in @ 78.39/10.67 Y1 @ 78.39/10.67 Y2) => 78.39/10.67 (in @ 78.39/10.67 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 78.39/10.67 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1103])). 78.39/10.67 thf(zip_derived_cl1119, plain, 78.39/10.67 (~ (((symdiffI2) => 78.39/10.67 (((symdiffIneg1) => 78.39/10.67 (((symdiffIneg2) => 78.39/10.67 (((secondinupair) => 78.39/10.67 (((setukpairIL) => 78.39/10.67 (((setukpairIR) => 78.39/10.67 (((kpairiskpair) => 78.39/10.67 (((kpairp) => 78.39/10.67 (((singletonsubset) => 78.39/10.67 (((singletoninpowerset) => 78.39/10.67 (((singletoninpowunion) => 78.39/10.67 (((upairset2E) => 78.39/10.67 (((upairsubunion) => 78.39/10.67 (((upairinpowunion) => 78.39/10.67 (((ubforcartprodlem1) => 78.39/10.67 (((ubforcartprodlem2) => 78.39/10.67 (((ubforcartprodlem3) => 78.39/10.67 (((cartprodpairin) => 78.39/10.67 (((cartprodmempair1) => 78.39/10.67 (((cartprodmempair) => 78.39/10.67 (((setunionE2) => 78.39/10.67 (((setunionsingleton1) => 78.39/10.67 (((setunionsingleton2) => 78.39/10.67 (((setunionsingleton) => 78.39/10.67 (((singletonprop) => 78.39/10.67 (((ex1E1) => 78.39/10.67 (((ex1I) => 78.39/10.67 (((ex1I2) => 78.39/10.67 (((singletonsuniq) => 78.39/10.67 (((setukpairinjL1) => 78.39/10.67 (( 78.39/10.67 (kfstsingleton) => 78.39/10.67 (( 78.39/10.67 (theprop) => 78.39/10.67 (( 78.39/10.67 (kfstpairEq) => 78.39/10.67 (( 78.39/10.67 (cartprodfstin) => 78.39/10.67 (( 78.39/10.67 (setukpairinjL2) => 78.39/10.67 (( 78.39/10.67 (setukpairinjL) => 78.39/10.67 (( 78.39/10.67 (setukpairinjR11) => 78.39/10.67 (( 78.39/10.67 (setukpairinjR12) => 78.39/10.67 (( 78.39/10.67 (setukpairinjR1) => 78.39/10.67 (( 78.39/10.67 (upairequniteq) => 78.39/10.67 (( 78.39/10.67 (setukpairinjR2) => 78.39/10.67 (( 78.39/10.67 (setukpairinjR) => 78.39/10.67 (( 78.39/10.67 (ksndsingleton) => 78.39/10.67 (( 78.39/10.67 (ksndpairEq) => 78.39/10.67 (( 78.39/10.67 (kpairsurjEq) => 78.39/10.67 (( 78.39/10.67 (cartprodsndin) => 78.39/10.67 (( 78.39/10.67 (cartprodpairmemEL) => 78.39/10.67 (( 78.39/10.67 (cartprodpairmemER) => 78.39/10.67 (( 78.39/10.67 (cartprodmempaircEq) => 78.39/10.67 (( 78.39/10.67 (cartprodfstpairEq) => 78.39/10.67 (( 78.39/10.67 (cartprodsndpairEq) => 78.39/10.67 (( 78.39/10.67 (cartprodpairsurjEq) => 78.39/10.67 (( 78.39/10.67 (dpsetconstrI) => 78.39/10.67 (( 78.39/10.67 (dpsetconstrSub) => 78.39/10.67 (( 78.39/10.67 (setOfPairsIsBReln) => 78.39/10.67 (( 78.39/10.67 (dpsetconstrERa) => 78.39/10.67 (( 78.39/10.67 (dpsetconstrEL1) => 78.39/10.67 (( 78.39/10.67 (dpsetconstrEL2) => 78.39/10.67 (( 78.39/10.67 (dpsetconstrER) => 78.39/10.67 (( 78.39/10.67 (funcImageSingleton) => 78.39/10.67 (( 78.39/10.67 (apProp) => 78.39/10.67 (( 78.39/10.67 (app) => 78.39/10.67 (( 78.39/10.67 (infuncsetfunc) => 78.39/10.67 (( 78.39/10.67 (ap2p) => 78.39/10.67 (( 78.39/10.67 (funcinfuncset) => 78.39/10.67 (( 78.39/10.67 (lamProp) => 78.39/10.67 (( 78.39/10.67 (lamp) => 78.39/10.67 (( 78.39/10.67 (lam2p) => 78.39/10.67 (( 78.39/10.67 (brelnall1) => 78.39/10.67 (( 78.39/10.67 (brelnall2) => 78.39/10.67 (( 78.39/10.67 (ex1E2) => 78.39/10.67 (( 78.39/10.67 (funcGraphProp1) => 78.39/10.67 (( 78.39/10.67 (funcGraphProp3) => 78.39/10.67 (( 78.39/10.67 (funcGraphProp2) => 78.39/10.67 (( 78.39/10.67 (funcextLem) => 78.39/10.67 (( 78.39/10.67 (funcGraphProp4) => 78.39/10.67 (( 78.39/10.67 (subbreln) => 78.39/10.67 (( 78.39/10.67 (eqbreln) => 78.39/10.67 (( 78.39/10.67 (funcext) => 78.39/10.67 (( 78.39/10.67 (funcext2) => 78.39/10.67 (( 78.39/10.68 (ap2apEq1) => 78.39/10.68 (( 78.39/10.68 (ap2apEq2) => 78.39/10.68 (( 78.39/10.68 (beta1) => 78.39/10.68 (( 78.39/10.68 (eta1) => 78.39/10.68 (( 78.39/10.68 (lam2lamEq) => 78.39/10.68 (( 78.39/10.68 (beta2) => 78.39/10.68 (( 78.39/10.68 (eta2) => 78.39/10.68 (( 78.39/10.68 (iffalseProp1) => 78.39/10.68 (( 78.39/10.68 (iffalseProp2) => 78.39/10.68 (( 78.39/10.68 (iftrueProp1) => 78.39/10.68 (( 78.39/10.68 (iftrueProp2) => 78.39/10.68 (( 78.39/10.68 (ifSingleton) => 78.39/10.68 (( 78.39/10.68 (ifp) => 78.39/10.68 (( 78.39/10.68 (theeq) => 78.39/10.68 (( 78.39/10.68 (iftrue) => 78.39/10.68 (( 78.39/10.68 (iffalse) => 78.39/10.68 (( 78.39/10.68 (iftrueorfalse) => 78.39/10.68 (( 78.39/10.68 (binintersectT_lem) => 78.39/10.68 (( 78.39/10.68 (binunionT_lem) => 78.39/10.68 (( 78.39/10.68 (powersetT_lem) => 78.39/10.68 (( 78.39/10.68 (setminusT_lem) => 78.39/10.68 (( 78.39/10.68 (complementT_lem) => 78.39/10.68 (( 78.39/10.68 (setextT) => 78.39/10.68 (( 78.39/10.68 (subsetTI) => 78.39/10.68 (( 78.39/10.68 (powersetTI1) => 78.39/10.68 (( 78.39/10.68 (powersetTE1) => 78.39/10.68 (( 78.39/10.68 (complementTI1) => 78.39/10.68 (( 78.39/10.68 (complementTE1) => 78.39/10.68 (( 78.39/10.68 (binintersectTELcontra) => 78.39/10.68 (( 78.39/10.68 (binintersectTERcontra) => 78.39/10.68 (( 78.39/10.68 (contrasubsetT) => 78.39/10.68 (( 78.39/10.68 (contrasubsetT1) => 78.39/10.68 (( 78.39/10.68 (contrasubsetT2) => 78.39/10.68 (( 78.39/10.68 (contrasubsetT3) => 78.39/10.68 (( 78.39/10.68 (doubleComplementI1) => 78.39/10.68 (( 78.39/10.68 (doubleComplementE1) => 78.39/10.68 (( 78.39/10.68 (doubleComplementSub1) => 78.39/10.68 (( 78.39/10.68 (doubleComplementSub2) => 78.39/10.68 (( 78.39/10.68 (doubleComplementEq) => 78.39/10.68 (( 78.39/10.68 (complementTnotintersectT) => 78.39/10.68 (( 78.39/10.68 (complementImpComplementIntersect) => 78.39/10.68 (( 78.39/10.68 (complementSubsetComplementIntersect) => 78.39/10.68 (( 78.39/10.68 (complementInPowersetComplementIntersect) => 78.39/10.68 (( 78.39/10.68 (contraSubsetComplement) => 78.39/10.68 (( 78.39/10.68 (complementTcontraSubset) => 78.39/10.68 (( 78.39/10.68 (binunionTILcontra) => 78.39/10.68 (( 78.39/10.68 (binunionTIRcontra) => 78.39/10.68 (( 78.39/10.68 (inIntersectImpInUnion) => 78.39/10.68 (( 78.39/10.68 (inIntersectImpInUnion2) => 78.39/10.68 (( 78.39/10.68 (inIntersectImpInIntersectUnions) => 78.39/10.68 (( 78.39/10.68 (intersectInPowersetIntersectUnions) => 78.39/10.68 (( 78.39/10.68 (inComplementUnionImpNotIn1) => 78.39/10.68 (( 78.39/10.68 (inComplementUnionImpInComplement1) => 78.39/10.68 (( 78.39/10.68 (binunionTE) => 78.39/10.68 (( 78.39/10.68 (binunionTEcontra) => 78.39/10.68 (( 78.39/10.68 (demorgan2a1) => 78.39/10.68 (( 78.39/10.68 (complementUnionInPowersetComplement) => 78.39/10.68 (( 78.39/10.68 (demorgan2a2) => 78.39/10.68 (( 78.39/10.68 (demorgan1a) => 78.39/10.68 (( 78.39/10.68 (demorgan1b) => 78.39/10.68 (( 78.39/10.68 (demorgan1) => 78.39/10.68 (( 78.39/10.68 (demorgan2a) => 78.39/10.68 (( 78.39/10.68 (demorgan2b2) => 78.39/10.68 (( 78.39/10.68 (demorgan2b) => 78.39/10.68 (( 78.39/10.68 (demorgan2) => 78.39/10.68 (( 78.39/10.68 (woz13rule0) => 78.39/10.68 (( 78.39/10.68 (woz13rule1) => 78.39/10.68 (( 78.39/10.68 (woz13rule2) => 78.39/10.68 (( 78.39/10.68 (woz13rule3) => 78.39/10.68 (( 78.39/10.68 (woz13rule4) => 78.39/10.68 (( 78.39/10.68 (woz1_1) => 78.39/10.68 (( 78.39/10.68 (woz1_2) => 78.39/10.68 (( 78.39/10.68 (woz1_3) => 78.39/10.68 (( 78.39/10.68 (woz1_4) => 78.39/10.68 (( 78.39/10.68 (woz1_5) => 78.39/10.68 (( 78.39/10.68 (breln1all2) => 78.39/10.68 (( 78.39/10.68 (breln1SetBreln1) => 78.39/10.68 (( 78.39/10.68 (choice2fnsingleton) => 78.39/10.68 (( 78.39/10.68 (setOfPairsIsBReln1) => 78.39/10.68 (( 78.39/10.68 (breln1all1) => 78.39/10.68 (( 78.39/10.68 (subbreln1) => 78.39/10.68 (( 78.39/10.68 (eqbreln1) => 78.39/10.68 (( 78.39/10.68 (breln1invprop) => 78.39/10.68 (( 78.39/10.68 (breln1invI) => 78.39/10.68 (( 78.39/10.68 (breln1invE) => 78.39/10.68 (( 78.39/10.68 (breln1compprop) => 78.39/10.68 (( 78.39/10.68 (breln1compI) => 78.39/10.68 (( 78.39/10.68 (breln1compE) => 78.39/10.68 (( 78.39/10.68 (breln1compEex) => 78.39/10.68 (( 78.39/10.68 (breln1unionprop) => 78.39/10.68 (( 78.39/10.68 (breln1unionIL) => 78.39/10.68 (( 78.39/10.68 (breln1unionIR) => 78.39/10.68 (( 78.39/10.68 (breln1unionI) => 78.39/10.68 (( 78.39/10.68 (breln1unionE) => 78.39/10.68 (( 78.39/10.68 (breln1unionEcases) => 78.39/10.68 (( 78.39/10.68 (breln1unionCommutes) => 78.39/10.68 (( 78.39/10.68 (woz2Ex) => 78.39/10.68 (( 78.39/10.68 (woz2W) => 78.39/10.68 (( 78.39/10.68 (woz2A) => 78.39/10.68 (( 78.39/10.68 (woz2B) => 78.39/10.68 (( 78.39/10.68 (image1Ex) => 78.39/10.68 (( 78.39/10.68 (image1Ex1) => 78.39/10.68 (( 78.39/10.68 (image1Equiv) => 78.39/10.68 (( 78.39/10.68 (image1E) => 78.39/10.68 (( 78.39/10.68 (image1I) => 78.39/10.68 (( 78.39/10.68 (injFuncInInjFuncSet) => 78.39/10.68 (( 78.39/10.68 (injFuncSetFuncIn) => 78.39/10.68 (( 78.39/10.68 (injFuncSetFuncInj) => 78.39/10.68 (( 78.39/10.68 (surjFuncSetFuncIn) => 78.39/10.68 (( 78.39/10.68 (surjFuncSetFuncSurj) => 78.39/10.68 (( 78.39/10.68 (leftInvIsSurj) => 78.39/10.68 (( 78.39/10.68 (surjCantorThm) => 78.39/10.68 (( 78.39/10.68 (foundation2) => 78.39/10.68 (( 78.39/10.68 (notinself) => 78.39/10.68 (( 78.39/10.68 (notinself2) => 78.39/10.68 (( 78.39/10.68 (omegaSp) => 78.39/10.68 (( 78.39/10.68 (omegaSclos) => 78.39/10.68 (( 78.39/10.68 (peano0notS) => 78.39/10.68 (( 78.39/10.68 (peanoSinj) => 78.39/10.68 (( 78.39/10.68 (transitivesetOp1) => 78.39/10.68 (( 78.39/10.68 (binintTransitive) => 78.39/10.68 (( 78.39/10.68 (transitivesetOp2) => 78.39/10.68 (( 78.39/10.68 (setunionTransitive) => 78.39/10.68 (( 78.39/10.68 (ordinalMinLem1) => 78.39/10.68 (( 78.39/10.68 (!!) @ ( 78.39/10.68 ^[Y0 : $i]: 78.39/10.68 (( 78.39/10.68 (ordinal @ 78.39/10.68 Y0) => 78.39/10.68 (( 78.39/10.68 (!!) @ ( 78.39/10.68 ^[Y1 : $i]: 78.39/10.68 (( 78.39/10.68 (!!) @ ( 78.39/10.68 ^[Y2 : $i]: 78.39/10.68 (( 78.39/10.68 (in @ 78.39/10.68 Y2 @ 78.39/10.68 Y0) => 78.39/10.68 (( 78.39/10.68 (in @ 78.39/10.68 Y1 @ 78.39/10.68 Y2) => 78.39/10.68 (in @ 78.39/10.68 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 78.39/10.68 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1111])). 78.39/10.68 thf(zip_derived_cl1125, plain, 78.39/10.68 (~ (((symdiffIneg1) => 78.39/10.68 (((symdiffIneg2) => 78.39/10.68 (((secondinupair) => 78.39/10.68 (((setukpairIL) => 78.39/10.68 (((setukpairIR) => 78.39/10.68 (((kpairiskpair) => 78.39/10.68 (((kpairp) => 78.39/10.68 (((singletonsubset) => 78.39/10.68 (((singletoninpowerset) => 78.39/10.68 (((singletoninpowunion) => 78.39/10.68 (((upairset2E) => 78.39/10.68 (((upairsubunion) => 78.39/10.68 (((upairinpowunion) => 78.39/10.68 (((ubforcartprodlem1) => 78.39/10.68 (((ubforcartprodlem2) => 78.39/10.68 (((ubforcartprodlem3) => 78.39/10.68 (((cartprodpairin) => 78.39/10.68 (((cartprodmempair1) => 78.39/10.68 (((cartprodmempair) => 78.39/10.68 (((setunionE2) => 78.39/10.68 (((setunionsingleton1) => 78.39/10.68 (((setunionsingleton2) => 78.39/10.68 (((setunionsingleton) => 78.39/10.68 (((singletonprop) => 78.39/10.68 (((ex1E1) => 78.39/10.68 (((ex1I) => 78.39/10.68 (((ex1I2) => 78.39/10.68 (((singletonsuniq) => 78.39/10.68 (((setukpairinjL1) => 78.39/10.68 (((kfstsingleton) => 78.39/10.68 (( 78.39/10.68 (theprop) => 78.39/10.68 (( 78.39/10.68 (kfstpairEq) => 78.39/10.68 (( 78.39/10.68 (cartprodfstin) => 78.39/10.68 (( 78.39/10.68 (setukpairinjL2) => 78.39/10.68 (( 78.39/10.68 (setukpairinjL) => 78.39/10.68 (( 78.39/10.68 (setukpairinjR11) => 78.39/10.68 (( 78.39/10.68 (setukpairinjR12) => 78.39/10.68 (( 78.39/10.68 (setukpairinjR1) => 78.39/10.68 (( 78.39/10.68 (upairequniteq) => 78.39/10.68 (( 78.39/10.68 (setukpairinjR2) => 78.39/10.68 (( 78.39/10.68 (setukpairinjR) => 78.39/10.68 (( 78.39/10.68 (ksndsingleton) => 78.39/10.68 (( 78.39/10.68 (ksndpairEq) => 78.39/10.68 (( 78.39/10.68 (kpairsurjEq) => 78.39/10.68 (( 78.39/10.68 (cartprodsndin) => 78.39/10.68 (( 78.39/10.68 (cartprodpairmemEL) => 78.39/10.68 (( 78.39/10.68 (cartprodpairmemER) => 78.39/10.68 (( 78.39/10.68 (cartprodmempaircEq) => 78.39/10.68 (( 78.39/10.68 (cartprodfstpairEq) => 78.39/10.68 (( 78.39/10.68 (cartprodsndpairEq) => 78.39/10.68 (( 78.39/10.68 (cartprodpairsurjEq) => 78.39/10.68 (( 78.39/10.68 (dpsetconstrI) => 78.39/10.68 (( 78.39/10.68 (dpsetconstrSub) => 78.39/10.68 (( 78.39/10.68 (setOfPairsIsBReln) => 78.39/10.68 (( 78.39/10.68 (dpsetconstrERa) => 78.39/10.68 (( 78.39/10.68 (dpsetconstrEL1) => 78.39/10.68 (( 78.39/10.68 (dpsetconstrEL2) => 78.39/10.68 (( 78.39/10.68 (dpsetconstrER) => 78.39/10.68 (( 78.39/10.68 (funcImageSingleton) => 78.39/10.68 (( 78.39/10.68 (apProp) => 78.39/10.68 (( 78.39/10.68 (app) => 78.39/10.68 (( 78.39/10.68 (infuncsetfunc) => 78.39/10.68 (( 78.39/10.68 (ap2p) => 78.39/10.68 (( 78.39/10.68 (funcinfuncset) => 78.39/10.68 (( 78.39/10.68 (lamProp) => 78.39/10.68 (( 78.39/10.68 (lamp) => 78.39/10.68 (( 78.39/10.68 (lam2p) => 78.39/10.68 (( 78.39/10.68 (brelnall1) => 78.39/10.68 (( 78.39/10.68 (brelnall2) => 78.39/10.68 (( 78.39/10.68 (ex1E2) => 78.39/10.68 (( 78.39/10.68 (funcGraphProp1) => 78.39/10.68 (( 78.39/10.68 (funcGraphProp3) => 78.39/10.68 (( 78.39/10.68 (funcGraphProp2) => 78.39/10.68 (( 78.39/10.68 (funcextLem) => 78.39/10.68 (( 78.39/10.68 (funcGraphProp4) => 78.39/10.68 (( 78.39/10.68 (subbreln) => 78.39/10.68 (( 78.39/10.68 (eqbreln) => 78.39/10.68 (( 78.39/10.68 (funcext) => 78.39/10.68 (( 78.39/10.68 (funcext2) => 78.39/10.68 (( 78.39/10.68 (ap2apEq1) => 78.39/10.68 (( 78.39/10.68 (ap2apEq2) => 78.39/10.68 (( 78.39/10.68 (beta1) => 78.39/10.68 (( 78.39/10.68 (eta1) => 78.39/10.68 (( 78.39/10.68 (lam2lamEq) => 78.39/10.68 (( 78.39/10.68 (beta2) => 78.39/10.68 (( 78.39/10.68 (eta2) => 78.39/10.68 (( 78.39/10.68 (iffalseProp1) => 78.39/10.68 (( 78.39/10.68 (iffalseProp2) => 78.39/10.68 (( 78.39/10.68 (iftrueProp1) => 78.39/10.68 (( 78.39/10.68 (iftrueProp2) => 78.39/10.68 (( 78.39/10.68 (ifSingleton) => 78.39/10.68 (( 78.39/10.68 (ifp) => 78.39/10.68 (( 78.39/10.68 (theeq) => 78.39/10.68 (( 78.39/10.68 (iftrue) => 78.39/10.68 (( 78.39/10.68 (iffalse) => 78.39/10.68 (( 78.39/10.68 (iftrueorfalse) => 78.39/10.68 (( 78.39/10.68 (binintersectT_lem) => 78.39/10.68 (( 78.39/10.68 (binunionT_lem) => 78.39/10.68 (( 78.39/10.68 (powersetT_lem) => 78.39/10.68 (( 78.39/10.68 (setminusT_lem) => 78.39/10.68 (( 78.39/10.68 (complementT_lem) => 78.39/10.68 (( 78.39/10.68 (setextT) => 78.39/10.68 (( 78.39/10.68 (subsetTI) => 78.39/10.68 (( 78.39/10.68 (powersetTI1) => 78.39/10.68 (( 78.39/10.68 (powersetTE1) => 78.39/10.68 (( 78.39/10.68 (complementTI1) => 78.39/10.68 (( 78.39/10.68 (complementTE1) => 78.39/10.68 (( 78.39/10.68 (binintersectTELcontra) => 78.39/10.68 (( 78.39/10.68 (binintersectTERcontra) => 78.39/10.68 (( 78.39/10.68 (contrasubsetT) => 78.39/10.68 (( 78.39/10.68 (contrasubsetT1) => 78.39/10.68 (( 78.39/10.68 (contrasubsetT2) => 78.39/10.68 (( 78.39/10.68 (contrasubsetT3) => 78.39/10.68 (( 78.39/10.68 (doubleComplementI1) => 78.39/10.68 (( 78.39/10.68 (doubleComplementE1) => 78.39/10.68 (( 78.39/10.68 (doubleComplementSub1) => 78.39/10.68 (( 78.39/10.68 (doubleComplementSub2) => 78.39/10.68 (( 78.39/10.68 (doubleComplementEq) => 78.39/10.68 (( 78.39/10.68 (complementTnotintersectT) => 78.39/10.68 (( 78.39/10.68 (complementImpComplementIntersect) => 78.39/10.68 (( 78.39/10.68 (complementSubsetComplementIntersect) => 78.39/10.68 (( 78.39/10.68 (complementInPowersetComplementIntersect) => 78.39/10.68 (( 78.39/10.68 (contraSubsetComplement) => 78.39/10.68 (( 78.39/10.68 (complementTcontraSubset) => 78.39/10.68 (( 78.39/10.68 (binunionTILcontra) => 78.39/10.68 (( 78.39/10.68 (binunionTIRcontra) => 78.39/10.68 (( 78.39/10.68 (inIntersectImpInUnion) => 78.39/10.68 (( 78.39/10.68 (inIntersectImpInUnion2) => 78.39/10.68 (( 78.39/10.68 (inIntersectImpInIntersectUnions) => 78.39/10.68 (( 78.39/10.68 (intersectInPowersetIntersectUnions) => 78.39/10.68 (( 78.39/10.68 (inComplementUnionImpNotIn1) => 78.39/10.68 (( 78.39/10.68 (inComplementUnionImpInComplement1) => 78.39/10.68 (( 78.39/10.68 (binunionTE) => 78.39/10.68 (( 78.39/10.68 (binunionTEcontra) => 78.39/10.68 (( 78.39/10.68 (demorgan2a1) => 78.39/10.68 (( 78.39/10.68 (complementUnionInPowersetComplement) => 78.39/10.68 (( 78.39/10.68 (demorgan2a2) => 78.39/10.68 (( 78.39/10.68 (demorgan1a) => 78.39/10.68 (( 78.39/10.68 (demorgan1b) => 78.39/10.68 (( 78.39/10.68 (demorgan1) => 78.39/10.68 (( 78.39/10.68 (demorgan2a) => 78.39/10.68 (( 78.39/10.68 (demorgan2b2) => 78.39/10.68 (( 78.39/10.68 (demorgan2b) => 78.39/10.68 (( 78.39/10.68 (demorgan2) => 78.39/10.68 (( 78.39/10.68 (woz13rule0) => 78.39/10.68 (( 78.39/10.68 (woz13rule1) => 78.39/10.68 (( 78.39/10.68 (woz13rule2) => 78.39/10.68 (( 78.39/10.68 (woz13rule3) => 78.39/10.68 (( 78.39/10.68 (woz13rule4) => 78.39/10.68 (( 78.39/10.68 (woz1_1) => 78.39/10.68 (( 78.39/10.68 (woz1_2) => 78.39/10.68 (( 78.39/10.68 (woz1_3) => 78.39/10.68 (( 78.39/10.68 (woz1_4) => 78.39/10.68 (( 78.39/10.68 (woz1_5) => 78.39/10.68 (( 78.39/10.68 (breln1all2) => 78.39/10.68 (( 78.39/10.68 (breln1SetBreln1) => 78.39/10.68 (( 78.39/10.68 (choice2fnsingleton) => 78.39/10.68 (( 78.39/10.68 (setOfPairsIsBReln1) => 78.39/10.68 (( 78.39/10.68 (breln1all1) => 78.39/10.68 (( 78.39/10.68 (subbreln1) => 78.39/10.68 (( 78.39/10.68 (eqbreln1) => 78.39/10.68 (( 78.39/10.68 (breln1invprop) => 78.39/10.68 (( 78.39/10.68 (breln1invI) => 78.39/10.68 (( 78.39/10.68 (breln1invE) => 78.39/10.68 (( 78.39/10.68 (breln1compprop) => 78.39/10.68 (( 78.39/10.68 (breln1compI) => 78.39/10.68 (( 78.39/10.68 (breln1compE) => 78.39/10.68 (( 78.39/10.68 (breln1compEex) => 78.39/10.68 (( 78.39/10.68 (breln1unionprop) => 78.39/10.68 (( 78.39/10.68 (breln1unionIL) => 78.39/10.68 (( 78.39/10.68 (breln1unionIR) => 78.39/10.68 (( 78.39/10.68 (breln1unionI) => 78.39/10.68 (( 78.39/10.68 (breln1unionE) => 78.39/10.68 (( 78.39/10.68 (breln1unionEcases) => 78.39/10.68 (( 78.39/10.68 (breln1unionCommutes) => 78.39/10.68 (( 78.39/10.68 (woz2Ex) => 78.39/10.68 (( 78.39/10.68 (woz2W) => 78.39/10.68 (( 78.39/10.68 (woz2A) => 78.39/10.68 (( 78.39/10.68 (woz2B) => 78.39/10.68 (( 78.39/10.68 (image1Ex) => 78.39/10.68 (( 78.39/10.68 (image1Ex1) => 78.39/10.68 (( 78.39/10.68 (image1Equiv) => 78.39/10.68 (( 78.39/10.68 (image1E) => 78.39/10.68 (( 78.39/10.68 (image1I) => 78.39/10.68 (( 78.39/10.68 (injFuncInInjFuncSet) => 78.39/10.68 (( 78.39/10.68 (injFuncSetFuncIn) => 78.39/10.68 (( 78.39/10.68 (injFuncSetFuncInj) => 78.39/10.68 (( 78.39/10.68 (surjFuncSetFuncIn) => 78.39/10.68 (( 78.39/10.68 (surjFuncSetFuncSurj) => 78.39/10.68 (( 78.39/10.68 (leftInvIsSurj) => 78.39/10.68 (( 78.39/10.68 (surjCantorThm) => 78.39/10.68 (( 78.39/10.68 (foundation2) => 78.39/10.68 (( 78.39/10.68 (notinself) => 78.39/10.68 (( 78.39/10.68 (notinself2) => 78.39/10.68 (( 78.39/10.68 (omegaSp) => 78.39/10.68 (( 78.39/10.68 (omegaSclos) => 78.39/10.68 (( 78.39/10.68 (peano0notS) => 78.39/10.68 (( 78.39/10.68 (peanoSinj) => 78.39/10.68 (( 78.39/10.68 (transitivesetOp1) => 78.39/10.68 (( 78.39/10.68 (binintTransitive) => 78.39/10.68 (( 78.39/10.68 (transitivesetOp2) => 78.39/10.68 (( 78.39/10.68 (setunionTransitive) => 78.39/10.68 (( 78.39/10.68 (ordinalMinLem1) => 78.39/10.68 (( 78.39/10.68 (!!) @ ( 78.39/10.68 ^[Y0 : $i]: 78.39/10.68 (( 78.39/10.68 (ordinal @ 78.39/10.68 Y0) => 78.39/10.68 (( 78.39/10.68 (!!) @ ( 78.39/10.68 ^[Y1 : $i]: 78.39/10.68 (( 78.39/10.68 (!!) @ ( 78.39/10.68 ^[Y2 : $i]: 78.39/10.68 (( 78.39/10.68 (in @ 78.39/10.68 Y2 @ 78.39/10.68 Y0) => 78.39/10.68 (( 78.39/10.68 (in @ 78.39/10.68 Y1 @ 78.39/10.68 Y2) => 78.39/10.68 (in @ 78.39/10.68 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 78.39/10.68 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1119])). 78.39/10.68 thf(zip_derived_cl1131, plain, 78.39/10.68 (~ (((symdiffIneg2) => 78.39/10.68 (((secondinupair) => 78.39/10.68 (((setukpairIL) => 78.39/10.68 (((setukpairIR) => 78.39/10.68 (((kpairiskpair) => 78.39/10.68 (((kpairp) => 78.39/10.68 (((singletonsubset) => 78.39/10.68 (((singletoninpowerset) => 78.39/10.68 (((singletoninpowunion) => 78.39/10.68 (((upairset2E) => 78.39/10.68 (((upairsubunion) => 78.39/10.68 (((upairinpowunion) => 78.39/10.68 (((ubforcartprodlem1) => 78.39/10.68 (((ubforcartprodlem2) => 78.39/10.68 (((ubforcartprodlem3) => 78.39/10.68 (((cartprodpairin) => 78.39/10.68 (((cartprodmempair1) => 78.39/10.68 (((cartprodmempair) => 78.39/10.68 (((setunionE2) => 78.39/10.68 (((setunionsingleton1) => 78.39/10.68 (((setunionsingleton2) => 78.39/10.68 (((setunionsingleton) => 78.39/10.68 (((singletonprop) => 78.39/10.68 (((ex1E1) => 78.39/10.68 (((ex1I) => 78.39/10.68 (((ex1I2) => 78.39/10.68 (((singletonsuniq) => 78.39/10.68 (((setukpairinjL1) => 78.39/10.68 (((kfstsingleton) => 78.39/10.68 (((theprop) => 78.39/10.68 (( 78.39/10.68 (kfstpairEq) => 78.39/10.68 (( 78.39/10.68 (cartprodfstin) => 78.39/10.68 (( 78.39/10.68 (setukpairinjL2) => 78.39/10.68 (( 78.39/10.68 (setukpairinjL) => 78.39/10.68 (( 78.39/10.68 (setukpairinjR11) => 78.39/10.68 (( 78.39/10.68 (setukpairinjR12) => 78.39/10.68 (( 78.39/10.68 (setukpairinjR1) => 78.39/10.68 (( 78.39/10.68 (upairequniteq) => 78.39/10.68 (( 78.39/10.68 (setukpairinjR2) => 78.39/10.68 (( 78.39/10.68 (setukpairinjR) => 78.39/10.68 (( 78.39/10.68 (ksndsingleton) => 78.39/10.68 (( 78.39/10.68 (ksndpairEq) => 78.39/10.68 (( 78.39/10.68 (kpairsurjEq) => 78.39/10.68 (( 78.39/10.68 (cartprodsndin) => 78.39/10.68 (( 78.39/10.68 (cartprodpairmemEL) => 78.39/10.68 (( 78.39/10.68 (cartprodpairmemER) => 78.39/10.68 (( 78.39/10.68 (cartprodmempaircEq) => 78.39/10.68 (( 78.39/10.68 (cartprodfstpairEq) => 78.39/10.68 (( 78.39/10.68 (cartprodsndpairEq) => 78.39/10.68 (( 78.39/10.68 (cartprodpairsurjEq) => 78.39/10.68 (( 78.39/10.68 (dpsetconstrI) => 78.39/10.68 (( 78.39/10.68 (dpsetconstrSub) => 78.39/10.68 (( 78.39/10.68 (setOfPairsIsBReln) => 78.39/10.68 (( 78.39/10.68 (dpsetconstrERa) => 78.39/10.68 (( 78.39/10.68 (dpsetconstrEL1) => 78.39/10.68 (( 78.39/10.68 (dpsetconstrEL2) => 78.39/10.68 (( 78.39/10.68 (dpsetconstrER) => 78.39/10.68 (( 78.39/10.68 (funcImageSingleton) => 78.39/10.68 (( 78.39/10.68 (apProp) => 78.39/10.68 (( 78.39/10.68 (app) => 78.39/10.68 (( 78.39/10.68 (infuncsetfunc) => 78.39/10.68 (( 78.39/10.68 (ap2p) => 78.39/10.68 (( 78.39/10.68 (funcinfuncset) => 78.39/10.68 (( 78.39/10.68 (lamProp) => 78.39/10.68 (( 78.39/10.68 (lamp) => 78.39/10.68 (( 78.39/10.68 (lam2p) => 78.39/10.68 (( 78.39/10.68 (brelnall1) => 78.39/10.68 (( 78.39/10.68 (brelnall2) => 78.39/10.68 (( 78.39/10.68 (ex1E2) => 78.39/10.68 (( 78.39/10.68 (funcGraphProp1) => 78.39/10.68 (( 78.39/10.68 (funcGraphProp3) => 78.39/10.68 (( 78.39/10.68 (funcGraphProp2) => 78.39/10.68 (( 78.39/10.68 (funcextLem) => 78.39/10.68 (( 78.39/10.68 (funcGraphProp4) => 78.39/10.68 (( 78.39/10.68 (subbreln) => 78.39/10.68 (( 78.39/10.68 (eqbreln) => 78.39/10.68 (( 78.39/10.68 (funcext) => 78.39/10.68 (( 78.39/10.68 (funcext2) => 78.39/10.68 (( 78.39/10.68 (ap2apEq1) => 78.39/10.68 (( 78.39/10.68 (ap2apEq2) => 78.39/10.68 (( 78.39/10.68 (beta1) => 78.39/10.68 (( 78.39/10.68 (eta1) => 78.39/10.68 (( 78.39/10.68 (lam2lamEq) => 78.39/10.68 (( 78.39/10.68 (beta2) => 78.39/10.68 (( 78.39/10.68 (eta2) => 78.39/10.68 (( 78.39/10.68 (iffalseProp1) => 78.39/10.68 (( 78.39/10.68 (iffalseProp2) => 78.39/10.68 (( 78.39/10.68 (iftrueProp1) => 78.39/10.68 (( 78.39/10.68 (iftrueProp2) => 78.39/10.68 (( 78.39/10.68 (ifSingleton) => 78.39/10.68 (( 78.39/10.68 (ifp) => 78.39/10.68 (( 78.39/10.68 (theeq) => 78.39/10.68 (( 78.39/10.68 (iftrue) => 78.39/10.68 (( 78.39/10.68 (iffalse) => 78.39/10.68 (( 78.39/10.68 (iftrueorfalse) => 78.39/10.68 (( 78.39/10.68 (binintersectT_lem) => 78.39/10.68 (( 78.39/10.68 (binunionT_lem) => 78.39/10.68 (( 78.39/10.68 (powersetT_lem) => 78.39/10.68 (( 78.39/10.68 (setminusT_lem) => 78.39/10.68 (( 78.39/10.68 (complementT_lem) => 78.39/10.68 (( 78.39/10.68 (setextT) => 78.39/10.68 (( 78.39/10.68 (subsetTI) => 78.39/10.68 (( 78.39/10.68 (powersetTI1) => 78.39/10.68 (( 78.39/10.68 (powersetTE1) => 78.39/10.68 (( 78.39/10.68 (complementTI1) => 78.39/10.68 (( 78.39/10.68 (complementTE1) => 78.39/10.68 (( 78.39/10.68 (binintersectTELcontra) => 78.39/10.68 (( 78.39/10.68 (binintersectTERcontra) => 78.39/10.68 (( 78.39/10.68 (contrasubsetT) => 78.39/10.68 (( 78.39/10.68 (contrasubsetT1) => 78.39/10.68 (( 78.39/10.68 (contrasubsetT2) => 78.39/10.68 (( 78.39/10.68 (contrasubsetT3) => 78.39/10.68 (( 78.39/10.68 (doubleComplementI1) => 78.39/10.68 (( 78.39/10.68 (doubleComplementE1) => 78.39/10.68 (( 78.39/10.68 (doubleComplementSub1) => 78.39/10.68 (( 78.39/10.68 (doubleComplementSub2) => 78.39/10.68 (( 78.39/10.68 (doubleComplementEq) => 78.39/10.68 (( 78.39/10.68 (complementTnotintersectT) => 78.39/10.68 (( 78.39/10.68 (complementImpComplementIntersect) => 78.39/10.68 (( 78.39/10.68 (complementSubsetComplementIntersect) => 78.39/10.68 (( 78.39/10.68 (complementInPowersetComplementIntersect) => 78.39/10.68 (( 78.39/10.68 (contraSubsetComplement) => 78.39/10.68 (( 78.39/10.68 (complementTcontraSubset) => 78.39/10.68 (( 78.39/10.68 (binunionTILcontra) => 78.39/10.68 (( 78.39/10.68 (binunionTIRcontra) => 78.39/10.68 (( 78.39/10.68 (inIntersectImpInUnion) => 78.39/10.68 (( 78.39/10.68 (inIntersectImpInUnion2) => 78.39/10.68 (( 78.39/10.68 (inIntersectImpInIntersectUnions) => 78.39/10.68 (( 78.39/10.68 (intersectInPowersetIntersectUnions) => 78.39/10.68 (( 78.39/10.68 (inComplementUnionImpNotIn1) => 78.39/10.68 (( 78.39/10.68 (inComplementUnionImpInComplement1) => 78.39/10.68 (( 78.39/10.68 (binunionTE) => 78.39/10.68 (( 78.39/10.68 (binunionTEcontra) => 78.39/10.68 (( 78.39/10.68 (demorgan2a1) => 78.39/10.68 (( 78.39/10.68 (complementUnionInPowersetComplement) => 78.39/10.68 (( 78.39/10.68 (demorgan2a2) => 78.39/10.68 (( 78.39/10.68 (demorgan1a) => 78.39/10.68 (( 78.39/10.68 (demorgan1b) => 78.39/10.68 (( 78.39/10.68 (demorgan1) => 78.39/10.68 (( 78.39/10.68 (demorgan2a) => 78.39/10.68 (( 78.39/10.68 (demorgan2b2) => 78.39/10.68 (( 78.39/10.68 (demorgan2b) => 78.39/10.68 (( 78.39/10.68 (demorgan2) => 78.39/10.68 (( 78.39/10.68 (woz13rule0) => 78.39/10.68 (( 78.39/10.68 (woz13rule1) => 78.39/10.68 (( 78.39/10.68 (woz13rule2) => 78.39/10.68 (( 78.39/10.68 (woz13rule3) => 78.39/10.68 (( 78.39/10.68 (woz13rule4) => 78.39/10.68 (( 78.39/10.68 (woz1_1) => 78.39/10.68 (( 78.39/10.68 (woz1_2) => 78.39/10.68 (( 78.39/10.68 (woz1_3) => 78.39/10.68 (( 78.39/10.68 (woz1_4) => 78.39/10.68 (( 78.39/10.68 (woz1_5) => 78.39/10.68 (( 78.39/10.68 (breln1all2) => 78.39/10.68 (( 78.39/10.68 (breln1SetBreln1) => 78.39/10.68 (( 78.39/10.68 (choice2fnsingleton) => 78.39/10.68 (( 78.39/10.68 (setOfPairsIsBReln1) => 78.39/10.68 (( 78.39/10.68 (breln1all1) => 78.39/10.68 (( 78.39/10.68 (subbreln1) => 78.39/10.68 (( 78.39/10.68 (eqbreln1) => 78.39/10.68 (( 78.39/10.68 (breln1invprop) => 78.39/10.68 (( 78.39/10.68 (breln1invI) => 78.39/10.68 (( 78.39/10.68 (breln1invE) => 78.39/10.68 (( 78.39/10.68 (breln1compprop) => 78.39/10.68 (( 78.39/10.68 (breln1compI) => 78.39/10.68 (( 78.39/10.68 (breln1compE) => 78.39/10.68 (( 78.39/10.68 (breln1compEex) => 78.39/10.68 (( 78.39/10.68 (breln1unionprop) => 78.39/10.68 (( 78.39/10.68 (breln1unionIL) => 78.39/10.68 (( 78.39/10.68 (breln1unionIR) => 78.39/10.68 (( 78.39/10.68 (breln1unionI) => 78.39/10.68 (( 78.39/10.68 (breln1unionE) => 78.39/10.68 (( 78.39/10.68 (breln1unionEcases) => 78.39/10.68 (( 78.39/10.68 (breln1unionCommutes) => 78.39/10.68 (( 78.39/10.68 (woz2Ex) => 78.39/10.68 (( 78.39/10.68 (woz2W) => 78.39/10.68 (( 78.39/10.68 (woz2A) => 78.39/10.68 (( 78.39/10.68 (woz2B) => 78.39/10.68 (( 78.39/10.68 (image1Ex) => 78.39/10.68 (( 78.39/10.68 (image1Ex1) => 78.39/10.68 (( 78.39/10.68 (image1Equiv) => 78.39/10.68 (( 78.39/10.68 (image1E) => 78.39/10.68 (( 78.39/10.68 (image1I) => 78.39/10.68 (( 78.39/10.68 (injFuncInInjFuncSet) => 78.39/10.68 (( 78.39/10.68 (injFuncSetFuncIn) => 78.39/10.68 (( 78.39/10.68 (injFuncSetFuncInj) => 78.39/10.68 (( 78.39/10.68 (surjFuncSetFuncIn) => 78.39/10.68 (( 78.39/10.68 (surjFuncSetFuncSurj) => 78.39/10.68 (( 78.39/10.68 (leftInvIsSurj) => 78.39/10.68 (( 78.39/10.68 (surjCantorThm) => 78.39/10.68 (( 78.39/10.68 (foundation2) => 78.39/10.68 (( 78.39/10.68 (notinself) => 78.39/10.68 (( 78.39/10.68 (notinself2) => 78.39/10.68 (( 78.39/10.68 (omegaSp) => 78.39/10.68 (( 78.39/10.68 (omegaSclos) => 78.39/10.68 (( 78.39/10.68 (peano0notS) => 78.39/10.68 (( 78.39/10.68 (peanoSinj) => 78.39/10.68 (( 78.39/10.68 (transitivesetOp1) => 78.39/10.68 (( 78.39/10.68 (binintTransitive) => 78.39/10.68 (( 78.39/10.68 (transitivesetOp2) => 78.39/10.68 (( 78.39/10.68 (setunionTransitive) => 78.39/10.68 (( 78.39/10.68 (ordinalMinLem1) => 78.39/10.68 (( 78.39/10.68 (!!) @ ( 78.39/10.68 ^[Y0 : $i]: 78.39/10.68 (( 78.39/10.68 (ordinal @ 78.39/10.68 Y0) => 78.39/10.68 (( 78.39/10.68 (!!) @ ( 78.39/10.68 ^[Y1 : $i]: 78.39/10.68 (( 78.39/10.68 (!!) @ ( 78.39/10.68 ^[Y2 : $i]: 78.39/10.68 (( 78.39/10.68 (in @ 78.39/10.68 Y2 @ 78.39/10.68 Y0) => 78.39/10.68 (( 78.39/10.68 (in @ 78.39/10.68 Y1 @ 78.39/10.68 Y2) => 78.39/10.68 (in @ 78.39/10.68 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 78.39/10.68 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1125])). 78.39/10.68 thf(zip_derived_cl1138, plain, 78.39/10.68 (~ (((secondinupair) => 78.39/10.68 (((setukpairIL) => 78.39/10.68 (((setukpairIR) => 78.39/10.68 (((kpairiskpair) => 78.39/10.68 (((kpairp) => 78.39/10.68 (((singletonsubset) => 78.39/10.68 (((singletoninpowerset) => 78.39/10.68 (((singletoninpowunion) => 78.39/10.68 (((upairset2E) => 78.39/10.68 (((upairsubunion) => 78.39/10.68 (((upairinpowunion) => 78.39/10.68 (((ubforcartprodlem1) => 78.39/10.68 (((ubforcartprodlem2) => 78.39/10.68 (((ubforcartprodlem3) => 78.39/10.68 (((cartprodpairin) => 78.39/10.68 (((cartprodmempair1) => 78.39/10.68 (((cartprodmempair) => 78.39/10.68 (((setunionE2) => 78.39/10.68 (((setunionsingleton1) => 78.39/10.68 (((setunionsingleton2) => 78.39/10.68 (((setunionsingleton) => 78.39/10.68 (((singletonprop) => 78.39/10.68 (((ex1E1) => 78.39/10.68 (((ex1I) => 78.39/10.68 (((ex1I2) => 78.39/10.68 (((singletonsuniq) => 78.39/10.68 (((setukpairinjL1) => 78.39/10.68 (((kfstsingleton) => 78.39/10.68 (((theprop) => 78.39/10.68 (((kfstpairEq) => 78.39/10.68 (( 78.39/10.68 (cartprodfstin) => 78.39/10.68 (( 78.39/10.68 (setukpairinjL2) => 78.39/10.68 (( 78.39/10.68 (setukpairinjL) => 78.39/10.68 (( 78.39/10.68 (setukpairinjR11) => 78.39/10.68 (( 78.39/10.68 (setukpairinjR12) => 78.39/10.68 (( 78.39/10.68 (setukpairinjR1) => 78.39/10.68 (( 78.39/10.68 (upairequniteq) => 78.39/10.68 (( 78.39/10.68 (setukpairinjR2) => 78.39/10.68 (( 78.39/10.68 (setukpairinjR) => 78.39/10.68 (( 78.39/10.68 (ksndsingleton) => 78.39/10.68 (( 78.39/10.68 (ksndpairEq) => 78.39/10.68 (( 78.39/10.68 (kpairsurjEq) => 78.39/10.68 (( 78.39/10.68 (cartprodsndin) => 78.39/10.68 (( 78.39/10.68 (cartprodpairmemEL) => 78.39/10.68 (( 78.39/10.68 (cartprodpairmemER) => 78.39/10.68 (( 78.39/10.68 (cartprodmempaircEq) => 78.39/10.68 (( 78.39/10.68 (cartprodfstpairEq) => 78.39/10.68 (( 78.39/10.68 (cartprodsndpairEq) => 78.39/10.68 (( 78.39/10.68 (cartprodpairsurjEq) => 78.39/10.68 (( 78.39/10.68 (dpsetconstrI) => 78.39/10.68 (( 78.39/10.68 (dpsetconstrSub) => 78.39/10.68 (( 78.39/10.68 (setOfPairsIsBReln) => 78.39/10.68 (( 78.39/10.68 (dpsetconstrERa) => 78.39/10.68 (( 78.39/10.68 (dpsetconstrEL1) => 78.39/10.68 (( 78.39/10.68 (dpsetconstrEL2) => 78.39/10.68 (( 78.39/10.68 (dpsetconstrER) => 78.39/10.68 (( 78.39/10.68 (funcImageSingleton) => 78.39/10.68 (( 78.39/10.68 (apProp) => 78.39/10.68 (( 78.39/10.68 (app) => 78.39/10.68 (( 78.39/10.68 (infuncsetfunc) => 78.39/10.68 (( 78.39/10.68 (ap2p) => 78.39/10.68 (( 78.39/10.68 (funcinfuncset) => 78.39/10.68 (( 78.39/10.68 (lamProp) => 78.39/10.68 (( 78.39/10.68 (lamp) => 78.39/10.68 (( 78.39/10.68 (lam2p) => 78.39/10.68 (( 78.39/10.68 (brelnall1) => 78.39/10.68 (( 78.39/10.68 (brelnall2) => 78.39/10.68 (( 78.39/10.68 (ex1E2) => 78.39/10.68 (( 78.39/10.68 (funcGraphProp1) => 78.39/10.68 (( 78.39/10.68 (funcGraphProp3) => 78.39/10.68 (( 78.39/10.68 (funcGraphProp2) => 78.39/10.68 (( 78.39/10.68 (funcextLem) => 78.39/10.68 (( 78.39/10.68 (funcGraphProp4) => 78.39/10.68 (( 78.39/10.68 (subbreln) => 78.39/10.68 (( 78.39/10.68 (eqbreln) => 78.39/10.68 (( 78.39/10.68 (funcext) => 78.39/10.68 (( 78.39/10.68 (funcext2) => 78.39/10.68 (( 78.39/10.68 (ap2apEq1) => 78.39/10.68 (( 78.39/10.68 (ap2apEq2) => 78.39/10.68 (( 78.39/10.68 (beta1) => 78.39/10.68 (( 78.39/10.68 (eta1) => 78.39/10.68 (( 78.39/10.68 (lam2lamEq) => 78.39/10.68 (( 78.39/10.68 (beta2) => 78.39/10.68 (( 78.39/10.68 (eta2) => 78.39/10.68 (( 78.39/10.68 (iffalseProp1) => 78.39/10.68 (( 78.39/10.68 (iffalseProp2) => 78.39/10.68 (( 78.39/10.68 (iftrueProp1) => 78.39/10.68 (( 78.39/10.68 (iftrueProp2) => 78.39/10.68 (( 78.39/10.68 (ifSingleton) => 78.39/10.68 (( 78.39/10.68 (ifp) => 78.39/10.68 (( 78.39/10.68 (theeq) => 78.39/10.68 (( 78.39/10.68 (iftrue) => 78.39/10.68 (( 78.39/10.68 (iffalse) => 78.39/10.68 (( 78.39/10.68 (iftrueorfalse) => 78.39/10.68 (( 78.39/10.68 (binintersectT_lem) => 78.39/10.68 (( 78.39/10.68 (binunionT_lem) => 78.39/10.68 (( 78.39/10.68 (powersetT_lem) => 78.39/10.68 (( 78.39/10.68 (setminusT_lem) => 78.39/10.68 (( 78.39/10.68 (complementT_lem) => 78.39/10.68 (( 78.39/10.68 (setextT) => 78.39/10.68 (( 78.39/10.68 (subsetTI) => 78.39/10.68 (( 78.39/10.68 (powersetTI1) => 78.39/10.68 (( 78.39/10.68 (powersetTE1) => 78.39/10.68 (( 78.39/10.68 (complementTI1) => 78.39/10.68 (( 78.39/10.68 (complementTE1) => 78.39/10.68 (( 78.39/10.68 (binintersectTELcontra) => 78.39/10.68 (( 78.39/10.68 (binintersectTERcontra) => 78.39/10.68 (( 78.39/10.68 (contrasubsetT) => 78.39/10.68 (( 78.39/10.68 (contrasubsetT1) => 78.39/10.68 (( 78.39/10.68 (contrasubsetT2) => 78.39/10.68 (( 78.39/10.68 (contrasubsetT3) => 78.39/10.68 (( 78.39/10.68 (doubleComplementI1) => 78.39/10.68 (( 78.39/10.68 (doubleComplementE1) => 78.39/10.68 (( 78.39/10.68 (doubleComplementSub1) => 78.39/10.68 (( 78.39/10.68 (doubleComplementSub2) => 78.39/10.68 (( 78.39/10.68 (doubleComplementEq) => 78.39/10.68 (( 78.39/10.68 (complementTnotintersectT) => 78.39/10.68 (( 78.39/10.68 (complementImpComplementIntersect) => 78.39/10.68 (( 78.39/10.68 (complementSubsetComplementIntersect) => 78.39/10.68 (( 78.39/10.68 (complementInPowersetComplementIntersect) => 78.39/10.68 (( 78.39/10.68 (contraSubsetComplement) => 78.39/10.68 (( 78.39/10.68 (complementTcontraSubset) => 78.39/10.68 (( 78.39/10.68 (binunionTILcontra) => 78.39/10.68 (( 78.39/10.68 (binunionTIRcontra) => 78.39/10.68 (( 78.39/10.68 (inIntersectImpInUnion) => 78.39/10.68 (( 78.39/10.68 (inIntersectImpInUnion2) => 78.39/10.68 (( 78.39/10.68 (inIntersectImpInIntersectUnions) => 78.39/10.68 (( 78.39/10.68 (intersectInPowersetIntersectUnions) => 78.39/10.68 (( 78.39/10.68 (inComplementUnionImpNotIn1) => 78.39/10.68 (( 78.39/10.68 (inComplementUnionImpInComplement1) => 78.39/10.68 (( 78.39/10.68 (binunionTE) => 78.39/10.68 (( 78.39/10.68 (binunionTEcontra) => 78.39/10.68 (( 78.39/10.68 (demorgan2a1) => 78.39/10.68 (( 78.39/10.68 (complementUnionInPowersetComplement) => 78.39/10.68 (( 78.39/10.68 (demorgan2a2) => 78.39/10.68 (( 78.39/10.68 (demorgan1a) => 78.39/10.68 (( 78.39/10.68 (demorgan1b) => 78.39/10.68 (( 78.39/10.68 (demorgan1) => 78.39/10.68 (( 78.39/10.68 (demorgan2a) => 78.39/10.68 (( 78.39/10.68 (demorgan2b2) => 78.39/10.68 (( 78.39/10.68 (demorgan2b) => 78.39/10.68 (( 78.39/10.68 (demorgan2) => 78.39/10.68 (( 78.39/10.68 (woz13rule0) => 78.39/10.68 (( 78.39/10.68 (woz13rule1) => 78.39/10.68 (( 78.39/10.68 (woz13rule2) => 78.39/10.68 (( 78.39/10.68 (woz13rule3) => 78.39/10.68 (( 78.39/10.68 (woz13rule4) => 78.39/10.68 (( 78.39/10.68 (woz1_1) => 78.39/10.68 (( 78.39/10.68 (woz1_2) => 78.39/10.68 (( 78.39/10.68 (woz1_3) => 78.39/10.68 (( 78.39/10.68 (woz1_4) => 78.39/10.68 (( 78.39/10.68 (woz1_5) => 78.39/10.68 (( 78.39/10.68 (breln1all2) => 78.39/10.68 (( 78.39/10.68 (breln1SetBreln1) => 78.39/10.68 (( 78.39/10.68 (choice2fnsingleton) => 78.39/10.68 (( 78.39/10.68 (setOfPairsIsBReln1) => 78.39/10.68 (( 78.39/10.68 (breln1all1) => 78.39/10.68 (( 78.39/10.68 (subbreln1) => 78.39/10.68 (( 78.39/10.68 (eqbreln1) => 78.39/10.68 (( 78.39/10.68 (breln1invprop) => 78.39/10.68 (( 78.39/10.68 (breln1invI) => 78.39/10.68 (( 78.39/10.68 (breln1invE) => 78.39/10.68 (( 78.39/10.68 (breln1compprop) => 78.39/10.68 (( 78.39/10.68 (breln1compI) => 78.39/10.68 (( 78.39/10.68 (breln1compE) => 78.39/10.68 (( 78.39/10.68 (breln1compEex) => 78.39/10.68 (( 78.39/10.68 (breln1unionprop) => 78.39/10.68 (( 78.39/10.68 (breln1unionIL) => 78.39/10.68 (( 78.39/10.68 (breln1unionIR) => 78.39/10.68 (( 78.39/10.68 (breln1unionI) => 78.39/10.68 (( 78.39/10.68 (breln1unionE) => 78.39/10.68 (( 78.39/10.68 (breln1unionEcases) => 78.39/10.68 (( 78.39/10.68 (breln1unionCommutes) => 78.39/10.68 (( 78.39/10.68 (woz2Ex) => 78.39/10.68 (( 78.39/10.68 (woz2W) => 78.39/10.68 (( 78.39/10.68 (woz2A) => 78.39/10.68 (( 78.39/10.68 (woz2B) => 78.39/10.68 (( 78.39/10.68 (image1Ex) => 78.39/10.68 (( 78.39/10.68 (image1Ex1) => 78.39/10.68 (( 78.39/10.68 (image1Equiv) => 78.39/10.68 (( 78.39/10.68 (image1E) => 78.39/10.68 (( 78.39/10.68 (image1I) => 78.39/10.68 (( 78.39/10.68 (injFuncInInjFuncSet) => 78.39/10.68 (( 78.39/10.68 (injFuncSetFuncIn) => 78.39/10.68 (( 78.39/10.68 (injFuncSetFuncInj) => 78.39/10.68 (( 78.39/10.68 (surjFuncSetFuncIn) => 78.39/10.68 (( 78.39/10.68 (surjFuncSetFuncSurj) => 78.39/10.68 (( 78.39/10.68 (leftInvIsSurj) => 78.39/10.68 (( 78.39/10.68 (surjCantorThm) => 78.39/10.68 (( 78.39/10.68 (foundation2) => 78.39/10.68 (( 78.39/10.68 (notinself) => 78.39/10.68 (( 78.39/10.68 (notinself2) => 78.39/10.68 (( 78.39/10.68 (omegaSp) => 78.39/10.68 (( 78.39/10.68 (omegaSclos) => 78.39/10.68 (( 78.39/10.68 (peano0notS) => 78.39/10.68 (( 78.39/10.68 (peanoSinj) => 78.39/10.68 (( 78.39/10.68 (transitivesetOp1) => 78.39/10.68 (( 78.39/10.68 (binintTransitive) => 78.39/10.68 (( 78.39/10.68 (transitivesetOp2) => 78.39/10.68 (( 78.39/10.68 (setunionTransitive) => 78.39/10.68 (( 78.39/10.68 (ordinalMinLem1) => 78.39/10.68 (( 78.39/10.68 (!!) @ ( 78.39/10.68 ^[Y0 : $i]: 78.39/10.68 (( 78.39/10.68 (ordinal @ 78.39/10.68 Y0) => 78.39/10.68 (( 78.39/10.68 (!!) @ ( 78.39/10.68 ^[Y1 : $i]: 78.39/10.68 (( 78.39/10.68 (!!) @ ( 78.39/10.68 ^[Y2 : $i]: 78.39/10.68 (( 78.39/10.68 (in @ 78.39/10.68 Y2 @ 78.39/10.68 Y0) => 78.39/10.68 (( 78.39/10.68 (in @ 78.39/10.68 Y1 @ 78.39/10.68 Y2) => 78.39/10.68 (in @ 78.39/10.68 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 78.39/10.68 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1131])). 78.39/10.68 thf(zip_derived_cl1145, plain, 78.39/10.68 (~ (((setukpairIL) => 78.39/10.68 (((setukpairIR) => 78.39/10.68 (((kpairiskpair) => 78.39/10.68 (((kpairp) => 78.39/10.68 (((singletonsubset) => 78.39/10.68 (((singletoninpowerset) => 78.39/10.68 (((singletoninpowunion) => 78.39/10.68 (((upairset2E) => 78.39/10.68 (((upairsubunion) => 78.39/10.68 (((upairinpowunion) => 78.39/10.68 (((ubforcartprodlem1) => 78.39/10.68 (((ubforcartprodlem2) => 78.39/10.68 (((ubforcartprodlem3) => 78.39/10.68 (((cartprodpairin) => 78.39/10.68 (((cartprodmempair1) => 78.39/10.68 (((cartprodmempair) => 78.39/10.68 (((setunionE2) => 78.39/10.68 (((setunionsingleton1) => 78.39/10.68 (((setunionsingleton2) => 78.39/10.68 (((setunionsingleton) => 78.39/10.68 (((singletonprop) => 78.39/10.68 (((ex1E1) => 78.39/10.68 (((ex1I) => 78.39/10.68 (((ex1I2) => 78.39/10.68 (((singletonsuniq) => 78.39/10.68 (((setukpairinjL1) => 78.39/10.68 (((kfstsingleton) => 78.39/10.68 (((theprop) => 78.39/10.68 (((kfstpairEq) => 78.39/10.68 (((cartprodfstin) => 78.39/10.68 (( 78.39/10.68 (setukpairinjL2) => 78.39/10.68 (( 78.39/10.68 (setukpairinjL) => 78.39/10.68 (( 78.39/10.68 (setukpairinjR11) => 78.39/10.68 (( 78.39/10.68 (setukpairinjR12) => 78.39/10.68 (( 78.39/10.68 (setukpairinjR1) => 78.39/10.68 (( 78.39/10.68 (upairequniteq) => 78.39/10.68 (( 78.39/10.68 (setukpairinjR2) => 78.39/10.68 (( 78.39/10.68 (setukpairinjR) => 78.39/10.68 (( 78.39/10.68 (ksndsingleton) => 78.39/10.68 (( 78.39/10.68 (ksndpairEq) => 78.39/10.68 (( 78.39/10.68 (kpairsurjEq) => 78.39/10.68 (( 78.39/10.68 (cartprodsndin) => 78.39/10.68 (( 78.39/10.68 (cartprodpairmemEL) => 78.39/10.68 (( 78.39/10.68 (cartprodpairmemER) => 78.39/10.68 (( 78.39/10.68 (cartprodmempaircEq) => 78.39/10.68 (( 78.39/10.68 (cartprodfstpairEq) => 78.39/10.68 (( 78.39/10.68 (cartprodsndpairEq) => 78.39/10.68 (( 78.39/10.68 (cartprodpairsurjEq) => 78.39/10.68 (( 78.39/10.68 (dpsetconstrI) => 78.39/10.68 (( 78.39/10.68 (dpsetconstrSub) => 78.39/10.68 (( 78.39/10.68 (setOfPairsIsBReln) => 78.39/10.68 (( 78.39/10.68 (dpsetconstrERa) => 78.39/10.68 (( 78.39/10.68 (dpsetconstrEL1) => 78.39/10.68 (( 78.39/10.68 (dpsetconstrEL2) => 78.39/10.68 (( 78.39/10.68 (dpsetconstrER) => 78.39/10.68 (( 78.39/10.68 (funcImageSingleton) => 78.39/10.68 (( 78.39/10.68 (apProp) => 78.39/10.68 (( 78.39/10.68 (app) => 78.39/10.68 (( 78.39/10.68 (infuncsetfunc) => 78.39/10.68 (( 78.39/10.68 (ap2p) => 78.39/10.68 (( 78.39/10.68 (funcinfuncset) => 78.39/10.68 (( 78.39/10.68 (lamProp) => 78.39/10.68 (( 78.39/10.68 (lamp) => 78.39/10.68 (( 78.39/10.68 (lam2p) => 78.39/10.68 (( 78.39/10.68 (brelnall1) => 78.39/10.68 (( 78.39/10.68 (brelnall2) => 78.39/10.68 (( 78.39/10.68 (ex1E2) => 78.39/10.68 (( 78.39/10.68 (funcGraphProp1) => 78.39/10.68 (( 78.39/10.68 (funcGraphProp3) => 78.39/10.68 (( 78.39/10.68 (funcGraphProp2) => 78.39/10.68 (( 78.39/10.68 (funcextLem) => 78.39/10.68 (( 78.39/10.68 (funcGraphProp4) => 78.39/10.68 (( 78.39/10.68 (subbreln) => 78.39/10.68 (( 78.39/10.68 (eqbreln) => 78.39/10.68 (( 78.39/10.68 (funcext) => 78.39/10.68 (( 78.39/10.68 (funcext2) => 78.39/10.68 (( 78.39/10.68 (ap2apEq1) => 78.39/10.68 (( 78.39/10.68 (ap2apEq2) => 78.39/10.68 (( 78.39/10.68 (beta1) => 78.39/10.68 (( 78.39/10.68 (eta1) => 78.39/10.68 (( 78.39/10.68 (lam2lamEq) => 78.39/10.68 (( 78.39/10.68 (beta2) => 78.39/10.68 (( 78.39/10.68 (eta2) => 78.39/10.68 (( 78.39/10.68 (iffalseProp1) => 78.39/10.68 (( 78.39/10.68 (iffalseProp2) => 78.39/10.68 (( 78.39/10.68 (iftrueProp1) => 78.39/10.68 (( 78.39/10.68 (iftrueProp2) => 78.39/10.68 (( 78.39/10.68 (ifSingleton) => 78.39/10.68 (( 78.39/10.68 (ifp) => 78.39/10.68 (( 78.39/10.68 (theeq) => 78.39/10.68 (( 78.39/10.68 (iftrue) => 78.39/10.68 (( 78.39/10.68 (iffalse) => 78.39/10.68 (( 78.39/10.68 (iftrueorfalse) => 78.39/10.68 (( 78.39/10.68 (binintersectT_lem) => 78.39/10.68 (( 78.39/10.68 (binunionT_lem) => 78.39/10.68 (( 78.39/10.68 (powersetT_lem) => 78.39/10.68 (( 78.39/10.68 (setminusT_lem) => 78.39/10.68 (( 78.39/10.68 (complementT_lem) => 78.39/10.68 (( 78.39/10.68 (setextT) => 78.39/10.68 (( 78.39/10.68 (subsetTI) => 78.39/10.68 (( 78.39/10.68 (powersetTI1) => 78.39/10.68 (( 78.39/10.68 (powersetTE1) => 78.39/10.68 (( 78.39/10.68 (complementTI1) => 78.39/10.68 (( 78.39/10.68 (complementTE1) => 78.39/10.68 (( 78.39/10.68 (binintersectTELcontra) => 78.39/10.68 (( 78.39/10.68 (binintersectTERcontra) => 78.39/10.68 (( 78.39/10.68 (contrasubsetT) => 78.39/10.68 (( 78.39/10.68 (contrasubsetT1) => 78.39/10.68 (( 78.39/10.68 (contrasubsetT2) => 78.39/10.68 (( 78.39/10.68 (contrasubsetT3) => 78.39/10.68 (( 78.39/10.68 (doubleComplementI1) => 78.39/10.68 (( 78.39/10.68 (doubleComplementE1) => 78.39/10.68 (( 78.39/10.68 (doubleComplementSub1) => 78.39/10.68 (( 78.39/10.68 (doubleComplementSub2) => 78.39/10.68 (( 78.39/10.68 (doubleComplementEq) => 78.39/10.68 (( 78.39/10.68 (complementTnotintersectT) => 78.39/10.68 (( 78.39/10.68 (complementImpComplementIntersect) => 78.39/10.68 (( 78.39/10.68 (complementSubsetComplementIntersect) => 78.39/10.68 (( 78.39/10.68 (complementInPowersetComplementIntersect) => 78.39/10.68 (( 78.39/10.68 (contraSubsetComplement) => 78.39/10.68 (( 78.39/10.68 (complementTcontraSubset) => 78.39/10.68 (( 78.39/10.68 (binunionTILcontra) => 78.39/10.68 (( 78.39/10.68 (binunionTIRcontra) => 78.39/10.68 (( 78.39/10.68 (inIntersectImpInUnion) => 78.39/10.68 (( 78.39/10.68 (inIntersectImpInUnion2) => 78.39/10.68 (( 78.39/10.68 (inIntersectImpInIntersectUnions) => 78.39/10.68 (( 78.39/10.68 (intersectInPowersetIntersectUnions) => 78.39/10.68 (( 78.39/10.68 (inComplementUnionImpNotIn1) => 78.39/10.68 (( 78.39/10.68 (inComplementUnionImpInComplement1) => 78.39/10.68 (( 78.39/10.68 (binunionTE) => 78.39/10.68 (( 78.39/10.68 (binunionTEcontra) => 78.39/10.68 (( 78.39/10.68 (demorgan2a1) => 78.39/10.68 (( 78.39/10.68 (complementUnionInPowersetComplement) => 78.39/10.68 (( 78.39/10.68 (demorgan2a2) => 78.39/10.68 (( 78.39/10.68 (demorgan1a) => 78.39/10.68 (( 78.39/10.68 (demorgan1b) => 78.39/10.68 (( 78.39/10.68 (demorgan1) => 78.39/10.68 (( 78.39/10.68 (demorgan2a) => 78.39/10.68 (( 78.39/10.68 (demorgan2b2) => 78.39/10.68 (( 78.39/10.68 (demorgan2b) => 78.39/10.68 (( 78.39/10.68 (demorgan2) => 78.39/10.68 (( 78.39/10.68 (woz13rule0) => 78.39/10.68 (( 78.39/10.68 (woz13rule1) => 78.39/10.68 (( 78.39/10.68 (woz13rule2) => 78.39/10.68 (( 78.39/10.68 (woz13rule3) => 78.39/10.68 (( 78.39/10.68 (woz13rule4) => 78.39/10.68 (( 78.39/10.68 (woz1_1) => 78.39/10.68 (( 78.39/10.68 (woz1_2) => 78.39/10.68 (( 78.39/10.68 (woz1_3) => 78.39/10.68 (( 78.39/10.68 (woz1_4) => 78.39/10.68 (( 78.39/10.68 (woz1_5) => 78.39/10.68 (( 78.39/10.68 (breln1all2) => 78.39/10.68 (( 78.39/10.68 (breln1SetBreln1) => 78.39/10.68 (( 78.39/10.68 (choice2fnsingleton) => 78.39/10.68 (( 78.39/10.68 (setOfPairsIsBReln1) => 78.39/10.68 (( 78.39/10.68 (breln1all1) => 78.39/10.68 (( 78.39/10.68 (subbreln1) => 78.39/10.68 (( 78.39/10.68 (eqbreln1) => 78.39/10.68 (( 78.39/10.68 (breln1invprop) => 78.39/10.68 (( 78.39/10.68 (breln1invI) => 78.39/10.68 (( 78.39/10.68 (breln1invE) => 78.39/10.68 (( 78.39/10.68 (breln1compprop) => 78.39/10.68 (( 78.39/10.68 (breln1compI) => 78.39/10.68 (( 78.39/10.68 (breln1compE) => 78.39/10.68 (( 78.39/10.68 (breln1compEex) => 78.39/10.68 (( 78.39/10.68 (breln1unionprop) => 78.39/10.68 (( 78.39/10.68 (breln1unionIL) => 78.39/10.68 (( 78.39/10.68 (breln1unionIR) => 78.39/10.68 (( 78.39/10.68 (breln1unionI) => 78.39/10.68 (( 78.39/10.68 (breln1unionE) => 78.39/10.68 (( 78.39/10.68 (breln1unionEcases) => 78.39/10.68 (( 78.39/10.68 (breln1unionCommutes) => 78.39/10.68 (( 78.39/10.68 (woz2Ex) => 78.39/10.68 (( 78.39/10.68 (woz2W) => 78.39/10.68 (( 78.39/10.68 (woz2A) => 78.39/10.68 (( 78.39/10.68 (woz2B) => 78.39/10.68 (( 78.39/10.68 (image1Ex) => 78.39/10.68 (( 78.39/10.68 (image1Ex1) => 78.39/10.68 (( 78.39/10.68 (image1Equiv) => 78.39/10.68 (( 78.39/10.68 (image1E) => 78.39/10.68 (( 78.39/10.68 (image1I) => 78.39/10.68 (( 78.39/10.68 (injFuncInInjFuncSet) => 78.39/10.68 (( 78.39/10.68 (injFuncSetFuncIn) => 78.39/10.68 (( 78.39/10.68 (injFuncSetFuncInj) => 78.39/10.68 (( 78.39/10.68 (surjFuncSetFuncIn) => 78.39/10.68 (( 78.39/10.68 (surjFuncSetFuncSurj) => 78.39/10.68 (( 78.39/10.68 (leftInvIsSurj) => 78.39/10.68 (( 78.39/10.68 (surjCantorThm) => 78.39/10.68 (( 78.39/10.68 (foundation2) => 78.39/10.68 (( 78.39/10.68 (notinself) => 78.39/10.68 (( 78.39/10.68 (notinself2) => 78.39/10.68 (( 78.39/10.68 (omegaSp) => 78.39/10.68 (( 78.39/10.68 (omegaSclos) => 78.39/10.68 (( 78.39/10.68 (peano0notS) => 78.39/10.68 (( 78.39/10.68 (peanoSinj) => 78.39/10.68 (( 78.39/10.68 (transitivesetOp1) => 78.39/10.68 (( 78.39/10.68 (binintTransitive) => 78.39/10.68 (( 78.39/10.68 (transitivesetOp2) => 78.39/10.68 (( 78.39/10.68 (setunionTransitive) => 78.39/10.68 (( 78.39/10.68 (ordinalMinLem1) => 78.39/10.68 (( 78.39/10.68 (!!) @ ( 78.39/10.68 ^[Y0 : $i]: 78.39/10.68 (( 78.39/10.68 (ordinal @ 78.39/10.68 Y0) => 78.39/10.68 (( 78.39/10.68 (!!) @ ( 78.39/10.68 ^[Y1 : $i]: 78.39/10.68 (( 78.39/10.68 (!!) @ ( 78.39/10.68 ^[Y2 : $i]: 78.39/10.68 (( 78.39/10.68 (in @ 78.39/10.68 Y2 @ 78.39/10.68 Y0) => 78.39/10.68 (( 78.39/10.68 (in @ 78.39/10.68 Y1 @ 78.39/10.68 Y2) => 78.39/10.68 (in @ 78.39/10.68 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 78.39/10.68 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1138])). 78.39/10.68 thf(zip_derived_cl1153, plain, 78.39/10.68 (~ (((setukpairIR) => 78.39/10.68 (((kpairiskpair) => 78.39/10.68 (((kpairp) => 78.39/10.68 (((singletonsubset) => 78.39/10.68 (((singletoninpowerset) => 78.39/10.68 (((singletoninpowunion) => 78.39/10.68 (((upairset2E) => 78.39/10.68 (((upairsubunion) => 78.39/10.68 (((upairinpowunion) => 78.39/10.68 (((ubforcartprodlem1) => 78.39/10.68 (((ubforcartprodlem2) => 78.39/10.68 (((ubforcartprodlem3) => 78.39/10.68 (((cartprodpairin) => 78.39/10.68 (((cartprodmempair1) => 78.39/10.68 (((cartprodmempair) => 78.39/10.68 (((setunionE2) => 78.39/10.68 (((setunionsingleton1) => 78.39/10.68 (((setunionsingleton2) => 78.39/10.68 (((setunionsingleton) => 78.39/10.68 (((singletonprop) => 78.39/10.68 (((ex1E1) => 78.39/10.68 (((ex1I) => 78.39/10.68 (((ex1I2) => 78.39/10.68 (((singletonsuniq) => 78.39/10.68 (((setukpairinjL1) => 78.39/10.68 (((kfstsingleton) => 78.39/10.68 (((theprop) => 78.39/10.68 (((kfstpairEq) => 78.39/10.68 (((cartprodfstin) => 78.39/10.68 (((setukpairinjL2) => 78.39/10.68 (( 78.39/10.68 (setukpairinjL) => 78.39/10.68 (( 78.39/10.68 (setukpairinjR11) => 78.39/10.68 (( 78.39/10.68 (setukpairinjR12) => 78.39/10.68 (( 78.39/10.68 (setukpairinjR1) => 78.39/10.68 (( 78.39/10.68 (upairequniteq) => 78.39/10.68 (( 78.39/10.68 (setukpairinjR2) => 78.39/10.68 (( 78.39/10.68 (setukpairinjR) => 78.39/10.68 (( 78.39/10.68 (ksndsingleton) => 78.39/10.68 (( 78.39/10.68 (ksndpairEq) => 78.39/10.68 (( 78.39/10.68 (kpairsurjEq) => 78.39/10.68 (( 78.39/10.68 (cartprodsndin) => 78.39/10.68 (( 78.39/10.68 (cartprodpairmemEL) => 78.39/10.68 (( 78.39/10.68 (cartprodpairmemER) => 78.39/10.68 (( 78.39/10.68 (cartprodmempaircEq) => 78.39/10.68 (( 78.39/10.68 (cartprodfstpairEq) => 78.39/10.68 (( 78.39/10.68 (cartprodsndpairEq) => 78.39/10.68 (( 78.39/10.68 (cartprodpairsurjEq) => 78.39/10.68 (( 78.39/10.68 (dpsetconstrI) => 78.39/10.68 (( 78.39/10.68 (dpsetconstrSub) => 78.39/10.68 (( 78.39/10.68 (setOfPairsIsBReln) => 78.39/10.68 (( 78.39/10.68 (dpsetconstrERa) => 78.39/10.68 (( 78.39/10.68 (dpsetconstrEL1) => 78.39/10.68 (( 78.39/10.68 (dpsetconstrEL2) => 78.39/10.68 (( 78.39/10.68 (dpsetconstrER) => 78.39/10.68 (( 78.39/10.68 (funcImageSingleton) => 78.39/10.68 (( 78.39/10.68 (apProp) => 78.39/10.68 (( 78.39/10.68 (app) => 78.39/10.68 (( 78.39/10.68 (infuncsetfunc) => 78.39/10.68 (( 78.39/10.68 (ap2p) => 78.39/10.68 (( 78.39/10.68 (funcinfuncset) => 78.39/10.68 (( 78.39/10.68 (lamProp) => 78.39/10.68 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78.39/10.68 (iftrueProp2) => 78.39/10.68 (( 78.39/10.68 (ifSingleton) => 78.39/10.68 (( 78.39/10.68 (ifp) => 78.39/10.68 (( 78.39/10.68 (theeq) => 78.39/10.68 (( 78.39/10.68 (iftrue) => 78.39/10.68 (( 78.39/10.68 (iffalse) => 78.39/10.68 (( 78.39/10.68 (iftrueorfalse) => 78.39/10.68 (( 78.39/10.68 (binintersectT_lem) => 78.39/10.68 (( 78.39/10.68 (binunionT_lem) => 78.39/10.68 (( 78.39/10.68 (powersetT_lem) => 78.39/10.68 (( 78.39/10.68 (setminusT_lem) => 78.39/10.68 (( 78.39/10.68 (complementT_lem) => 78.39/10.68 (( 78.39/10.68 (setextT) => 78.39/10.68 (( 78.39/10.68 (subsetTI) => 78.39/10.68 (( 78.39/10.68 (powersetTI1) => 78.39/10.68 (( 78.39/10.68 (powersetTE1) => 78.39/10.68 (( 78.39/10.68 (complementTI1) => 78.39/10.68 (( 78.39/10.68 (complementTE1) => 78.39/10.68 (( 78.39/10.68 (binintersectTELcontra) => 78.39/10.68 (( 78.39/10.68 (binintersectTERcontra) => 78.39/10.68 (( 78.39/10.68 (contrasubsetT) => 78.39/10.68 (( 78.39/10.68 (contrasubsetT1) => 78.39/10.68 (( 78.39/10.68 (contrasubsetT2) => 78.39/10.68 (( 78.39/10.68 (contrasubsetT3) => 78.39/10.68 (( 78.39/10.68 (doubleComplementI1) => 78.39/10.68 (( 78.39/10.68 (doubleComplementE1) => 78.39/10.68 (( 78.39/10.68 (doubleComplementSub1) => 78.39/10.68 (( 78.39/10.68 (doubleComplementSub2) => 78.39/10.68 (( 78.39/10.68 (doubleComplementEq) => 78.39/10.68 (( 78.39/10.68 (complementTnotintersectT) => 78.39/10.68 (( 78.39/10.68 (complementImpComplementIntersect) => 78.39/10.68 (( 78.39/10.68 (complementSubsetComplementIntersect) => 78.39/10.68 (( 78.39/10.68 (complementInPowersetComplementIntersect) => 78.39/10.68 (( 78.39/10.68 (contraSubsetComplement) => 78.39/10.68 (( 78.39/10.68 (complementTcontraSubset) => 78.39/10.68 (( 78.39/10.68 (binunionTILcontra) => 78.39/10.68 (( 78.39/10.68 (binunionTIRcontra) => 78.39/10.68 (( 78.39/10.68 (inIntersectImpInUnion) => 78.39/10.68 (( 78.39/10.68 (inIntersectImpInUnion2) => 78.39/10.68 (( 78.39/10.68 (inIntersectImpInIntersectUnions) => 78.39/10.68 (( 78.39/10.68 (intersectInPowersetIntersectUnions) => 78.39/10.68 (( 78.39/10.68 (inComplementUnionImpNotIn1) => 78.39/10.68 (( 78.39/10.68 (inComplementUnionImpInComplement1) => 78.39/10.68 (( 78.39/10.68 (binunionTE) => 78.39/10.68 (( 78.39/10.68 (binunionTEcontra) => 78.39/10.68 (( 78.39/10.68 (demorgan2a1) => 78.39/10.68 (( 78.39/10.68 (complementUnionInPowersetComplement) => 78.39/10.68 (( 78.39/10.68 (demorgan2a2) => 78.39/10.68 (( 78.39/10.68 (demorgan1a) => 78.39/10.68 (( 78.39/10.68 (demorgan1b) => 78.39/10.68 (( 78.39/10.68 (demorgan1) => 78.39/10.68 (( 78.39/10.68 (demorgan2a) => 78.39/10.68 (( 78.39/10.68 (demorgan2b2) => 78.39/10.68 (( 78.39/10.68 (demorgan2b) => 78.39/10.68 (( 78.39/10.68 (demorgan2) => 78.39/10.68 (( 78.39/10.68 (woz13rule0) => 78.39/10.68 (( 78.39/10.68 (woz13rule1) => 78.39/10.68 (( 78.39/10.68 (woz13rule2) => 78.39/10.68 (( 78.39/10.68 (woz13rule3) => 78.39/10.68 (( 78.39/10.68 (woz13rule4) => 78.39/10.68 (( 78.39/10.68 (woz1_1) => 78.39/10.68 (( 78.39/10.68 (woz1_2) => 78.39/10.68 (( 78.39/10.68 (woz1_3) => 78.39/10.68 (( 78.39/10.68 (woz1_4) => 78.39/10.68 (( 78.39/10.68 (woz1_5) => 78.39/10.68 (( 78.39/10.68 (breln1all2) => 78.39/10.68 (( 78.39/10.68 (breln1SetBreln1) => 78.39/10.68 (( 78.39/10.68 (choice2fnsingleton) => 78.39/10.68 (( 78.39/10.68 (setOfPairsIsBReln1) => 78.39/10.68 (( 78.39/10.68 (breln1all1) => 78.39/10.68 (( 78.39/10.68 (subbreln1) => 78.39/10.68 (( 78.39/10.68 (eqbreln1) => 78.39/10.68 (( 78.39/10.68 (breln1invprop) => 78.39/10.68 (( 78.39/10.68 (breln1invI) => 78.39/10.68 (( 78.39/10.68 (breln1invE) => 78.39/10.68 (( 78.39/10.68 (breln1compprop) => 78.39/10.68 (( 78.39/10.68 (breln1compI) => 78.39/10.68 (( 78.39/10.68 (breln1compE) => 78.39/10.68 (( 78.39/10.68 (breln1compEex) => 78.39/10.68 (( 78.39/10.68 (breln1unionprop) => 78.39/10.68 (( 78.39/10.68 (breln1unionIL) => 78.39/10.68 (( 78.39/10.68 (breln1unionIR) => 78.39/10.68 (( 78.39/10.68 (breln1unionI) => 78.39/10.68 (( 78.39/10.68 (breln1unionE) => 78.39/10.68 (( 78.39/10.68 (breln1unionEcases) => 78.39/10.68 (( 78.39/10.68 (breln1unionCommutes) => 78.39/10.68 (( 78.39/10.68 (woz2Ex) => 78.39/10.68 (( 78.39/10.68 (woz2W) => 78.39/10.68 (( 78.39/10.68 (woz2A) => 78.39/10.68 (( 78.39/10.68 (woz2B) => 78.39/10.68 (( 78.39/10.68 (image1Ex) => 78.39/10.68 (( 78.39/10.68 (image1Ex1) => 78.39/10.68 (( 78.39/10.68 (image1Equiv) => 78.39/10.68 (( 78.39/10.68 (image1E) => 78.39/10.68 (( 78.39/10.68 (image1I) => 78.39/10.68 (( 78.39/10.68 (injFuncInInjFuncSet) => 78.39/10.68 (( 78.39/10.68 (injFuncSetFuncIn) => 78.39/10.68 (( 78.39/10.68 (injFuncSetFuncInj) => 78.39/10.68 (( 78.39/10.68 (surjFuncSetFuncIn) => 78.39/10.68 (( 78.39/10.68 (surjFuncSetFuncSurj) => 78.39/10.68 (( 78.39/10.68 (leftInvIsSurj) => 78.39/10.68 (( 78.39/10.68 (surjCantorThm) => 78.39/10.68 (( 78.39/10.68 (foundation2) => 78.39/10.68 (( 78.39/10.68 (notinself) => 78.39/10.68 (( 78.39/10.68 (notinself2) => 78.39/10.68 (( 78.39/10.68 (omegaSp) => 78.39/10.68 (( 78.39/10.68 (omegaSclos) => 78.39/10.68 (( 78.39/10.68 (peano0notS) => 78.39/10.68 (( 78.39/10.68 (peanoSinj) => 78.39/10.68 (( 78.39/10.68 (transitivesetOp1) => 78.39/10.68 (( 78.39/10.68 (binintTransitive) => 78.39/10.68 (( 78.39/10.68 (transitivesetOp2) => 78.39/10.68 (( 78.39/10.68 (setunionTransitive) => 78.39/10.68 (( 78.39/10.68 (ordinalMinLem1) => 78.39/10.68 (( 78.39/10.68 (!!) @ ( 78.39/10.68 ^[Y0 : $i]: 78.39/10.68 (( 78.39/10.68 (ordinal @ 78.39/10.68 Y0) => 78.39/10.68 (( 78.39/10.68 (!!) @ ( 78.39/10.68 ^[Y1 : $i]: 78.39/10.68 (( 78.39/10.68 (!!) @ ( 78.39/10.68 ^[Y2 : $i]: 78.39/10.68 (( 78.39/10.68 (in @ 78.39/10.68 Y2 @ 78.39/10.68 Y0) => 78.39/10.68 (( 78.39/10.68 (in @ 78.39/10.68 Y1 @ 78.39/10.68 Y2) => 78.39/10.68 (in @ 78.39/10.68 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 78.39/10.68 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1145])). 78.39/10.68 thf(zip_derived_cl1162, plain, 78.39/10.68 (~ (((kpairiskpair) => 78.39/10.68 (((kpairp) => 78.39/10.68 (((singletonsubset) => 78.39/10.68 (((singletoninpowerset) => 78.39/10.68 (((singletoninpowunion) => 78.39/10.68 (((upairset2E) => 78.39/10.68 (((upairsubunion) => 78.39/10.68 (((upairinpowunion) => 78.39/10.68 (((ubforcartprodlem1) => 78.39/10.68 (((ubforcartprodlem2) => 78.39/10.68 (((ubforcartprodlem3) => 78.39/10.68 (((cartprodpairin) => 78.39/10.68 (((cartprodmempair1) => 78.39/10.68 (((cartprodmempair) => 78.39/10.68 (((setunionE2) => 78.39/10.68 (((setunionsingleton1) => 78.39/10.68 (((setunionsingleton2) => 78.39/10.68 (((setunionsingleton) => 78.39/10.68 (((singletonprop) => 78.39/10.68 (((ex1E1) => 78.39/10.68 (((ex1I) => 78.39/10.68 (((ex1I2) => 78.39/10.68 (((singletonsuniq) => 78.39/10.68 (((setukpairinjL1) => 78.39/10.68 (((kfstsingleton) => 78.39/10.68 (((theprop) => 78.39/10.68 (((kfstpairEq) => 78.39/10.68 (((cartprodfstin) => 78.39/10.68 (((setukpairinjL2) => 78.39/10.68 (((setukpairinjL) => 78.39/10.68 (( 78.39/10.68 (setukpairinjR11) => 78.39/10.68 (( 78.39/10.68 (setukpairinjR12) => 78.39/10.68 (( 78.39/10.68 (setukpairinjR1) => 78.39/10.68 (( 78.39/10.68 (upairequniteq) => 78.39/10.68 (( 78.39/10.68 (setukpairinjR2) => 78.39/10.68 (( 78.39/10.68 (setukpairinjR) => 78.39/10.68 (( 78.39/10.68 (ksndsingleton) => 78.39/10.68 (( 78.39/10.68 (ksndpairEq) => 78.39/10.68 (( 78.39/10.68 (kpairsurjEq) => 78.39/10.68 (( 78.39/10.68 (cartprodsndin) => 78.39/10.68 (( 78.39/10.68 (cartprodpairmemEL) => 78.39/10.68 (( 78.39/10.68 (cartprodpairmemER) => 78.39/10.68 (( 78.39/10.68 (cartprodmempaircEq) => 78.39/10.68 (( 78.39/10.68 (cartprodfstpairEq) => 78.39/10.68 (( 78.39/10.68 (cartprodsndpairEq) => 78.39/10.68 (( 78.39/10.68 (cartprodpairsurjEq) => 78.39/10.68 (( 78.39/10.68 (dpsetconstrI) => 78.39/10.68 (( 78.39/10.68 (dpsetconstrSub) => 78.39/10.68 (( 78.39/10.68 (setOfPairsIsBReln) => 78.39/10.68 (( 78.39/10.68 (dpsetconstrERa) => 78.39/10.68 (( 78.39/10.68 (dpsetconstrEL1) => 78.39/10.68 (( 78.39/10.68 (dpsetconstrEL2) => 78.39/10.68 (( 78.39/10.68 (dpsetconstrER) => 78.39/10.68 (( 78.39/10.68 (funcImageSingleton) => 78.39/10.68 (( 78.39/10.68 (apProp) => 78.39/10.68 (( 78.39/10.68 (app) => 78.39/10.68 (( 78.39/10.68 (infuncsetfunc) => 78.39/10.68 (( 78.39/10.68 (ap2p) => 78.39/10.68 (( 78.39/10.68 (funcinfuncset) => 78.39/10.68 (( 78.39/10.68 (lamProp) => 78.39/10.68 (( 78.39/10.68 (lamp) => 78.39/10.68 (( 78.39/10.68 (lam2p) => 78.39/10.68 (( 78.39/10.68 (brelnall1) => 78.39/10.68 (( 78.39/10.68 (brelnall2) => 78.39/10.68 (( 78.39/10.68 (ex1E2) => 78.39/10.68 (( 78.39/10.68 (funcGraphProp1) => 78.39/10.68 (( 78.39/10.68 (funcGraphProp3) => 78.39/10.68 (( 78.39/10.68 (funcGraphProp2) => 78.39/10.68 (( 78.39/10.68 (funcextLem) => 78.39/10.68 (( 78.39/10.68 (funcGraphProp4) => 78.39/10.68 (( 78.39/10.68 (subbreln) => 78.39/10.68 (( 78.39/10.68 (eqbreln) => 78.39/10.68 (( 78.39/10.68 (funcext) => 78.39/10.68 (( 78.39/10.68 (funcext2) => 78.39/10.68 (( 78.39/10.68 (ap2apEq1) => 78.39/10.68 (( 78.39/10.68 (ap2apEq2) => 78.39/10.68 (( 78.39/10.68 (beta1) => 78.39/10.68 (( 78.39/10.68 (eta1) => 78.39/10.68 (( 78.39/10.68 (lam2lamEq) => 78.39/10.68 (( 78.39/10.68 (beta2) => 78.39/10.68 (( 78.39/10.68 (eta2) => 78.39/10.68 (( 78.39/10.68 (iffalseProp1) => 78.39/10.68 (( 78.39/10.68 (iffalseProp2) => 78.39/10.68 (( 78.39/10.68 (iftrueProp1) => 78.39/10.68 (( 78.39/10.68 (iftrueProp2) => 78.39/10.68 (( 78.39/10.68 (ifSingleton) => 78.39/10.68 (( 78.39/10.68 (ifp) => 78.39/10.68 (( 78.39/10.68 (theeq) => 78.39/10.68 (( 78.39/10.68 (iftrue) => 78.39/10.68 (( 78.39/10.68 (iffalse) => 78.39/10.68 (( 78.39/10.68 (iftrueorfalse) => 78.39/10.68 (( 78.39/10.68 (binintersectT_lem) => 78.39/10.68 (( 78.39/10.68 (binunionT_lem) => 78.39/10.68 (( 78.39/10.68 (powersetT_lem) => 78.39/10.68 (( 78.39/10.68 (setminusT_lem) => 78.39/10.68 (( 78.39/10.68 (complementT_lem) => 78.39/10.68 (( 78.39/10.68 (setextT) => 78.39/10.68 (( 78.39/10.68 (subsetTI) => 78.39/10.68 (( 78.39/10.68 (powersetTI1) => 78.39/10.68 (( 78.39/10.68 (powersetTE1) => 78.39/10.68 (( 78.39/10.68 (complementTI1) => 78.39/10.68 (( 78.39/10.68 (complementTE1) => 78.39/10.68 (( 78.39/10.68 (binintersectTELcontra) => 78.39/10.68 (( 78.39/10.68 (binintersectTERcontra) => 78.39/10.68 (( 78.39/10.68 (contrasubsetT) => 78.39/10.68 (( 78.39/10.68 (contrasubsetT1) => 78.39/10.68 (( 78.39/10.68 (contrasubsetT2) => 78.39/10.68 (( 78.39/10.68 (contrasubsetT3) => 78.39/10.68 (( 78.39/10.68 (doubleComplementI1) => 78.39/10.68 (( 78.39/10.68 (doubleComplementE1) => 78.39/10.68 (( 78.39/10.68 (doubleComplementSub1) => 78.39/10.68 (( 78.39/10.68 (doubleComplementSub2) => 78.39/10.68 (( 78.39/10.68 (doubleComplementEq) => 78.39/10.68 (( 78.39/10.68 (complementTnotintersectT) => 78.39/10.68 (( 78.39/10.68 (complementImpComplementIntersect) => 78.39/10.68 (( 78.39/10.68 (complementSubsetComplementIntersect) => 78.39/10.68 (( 78.39/10.68 (complementInPowersetComplementIntersect) => 78.39/10.68 (( 78.39/10.68 (contraSubsetComplement) => 78.39/10.68 (( 78.39/10.68 (complementTcontraSubset) => 78.39/10.68 (( 78.39/10.68 (binunionTILcontra) => 78.39/10.68 (( 78.39/10.68 (binunionTIRcontra) => 78.39/10.68 (( 78.39/10.68 (inIntersectImpInUnion) => 78.39/10.68 (( 78.39/10.68 (inIntersectImpInUnion2) => 78.39/10.68 (( 78.39/10.68 (inIntersectImpInIntersectUnions) => 78.39/10.68 (( 78.39/10.68 (intersectInPowersetIntersectUnions) => 78.39/10.68 (( 78.39/10.68 (inComplementUnionImpNotIn1) => 78.39/10.68 (( 78.39/10.68 (inComplementUnionImpInComplement1) => 78.39/10.68 (( 78.39/10.68 (binunionTE) => 78.39/10.68 (( 78.39/10.68 (binunionTEcontra) => 78.39/10.68 (( 78.39/10.68 (demorgan2a1) => 78.39/10.68 (( 78.39/10.68 (complementUnionInPowersetComplement) => 78.39/10.68 (( 78.39/10.68 (demorgan2a2) => 78.39/10.68 (( 78.39/10.68 (demorgan1a) => 78.39/10.68 (( 78.39/10.68 (demorgan1b) => 78.39/10.68 (( 78.39/10.68 (demorgan1) => 78.39/10.68 (( 78.39/10.68 (demorgan2a) => 78.39/10.68 (( 78.39/10.68 (demorgan2b2) => 78.39/10.68 (( 78.39/10.68 (demorgan2b) => 78.39/10.68 (( 78.39/10.68 (demorgan2) => 78.39/10.68 (( 78.39/10.68 (woz13rule0) => 78.39/10.68 (( 78.39/10.68 (woz13rule1) => 78.39/10.68 (( 78.39/10.68 (woz13rule2) => 78.39/10.68 (( 78.39/10.68 (woz13rule3) => 78.39/10.68 (( 78.39/10.68 (woz13rule4) => 78.39/10.68 (( 78.39/10.68 (woz1_1) => 78.39/10.68 (( 78.39/10.68 (woz1_2) => 78.39/10.68 (( 78.39/10.68 (woz1_3) => 78.39/10.68 (( 78.39/10.68 (woz1_4) => 78.39/10.68 (( 78.39/10.68 (woz1_5) => 78.39/10.68 (( 78.39/10.68 (breln1all2) => 78.39/10.68 (( 78.39/10.68 (breln1SetBreln1) => 78.39/10.68 (( 78.39/10.68 (choice2fnsingleton) => 78.39/10.68 (( 78.39/10.68 (setOfPairsIsBReln1) => 78.39/10.68 (( 78.39/10.68 (breln1all1) => 78.39/10.68 (( 78.39/10.68 (subbreln1) => 78.39/10.68 (( 78.39/10.68 (eqbreln1) => 78.39/10.68 (( 78.39/10.68 (breln1invprop) => 78.39/10.68 (( 78.39/10.68 (breln1invI) => 78.39/10.68 (( 78.39/10.68 (breln1invE) => 78.39/10.68 (( 78.39/10.68 (breln1compprop) => 78.39/10.68 (( 78.39/10.68 (breln1compI) => 78.39/10.68 (( 78.39/10.68 (breln1compE) => 78.39/10.68 (( 78.39/10.68 (breln1compEex) => 78.39/10.68 (( 78.39/10.68 (breln1unionprop) => 78.39/10.68 (( 78.39/10.68 (breln1unionIL) => 78.39/10.68 (( 78.39/10.68 (breln1unionIR) => 78.39/10.68 (( 78.39/10.68 (breln1unionI) => 78.39/10.68 (( 78.39/10.68 (breln1unionE) => 78.39/10.68 (( 78.39/10.68 (breln1unionEcases) => 78.39/10.68 (( 78.39/10.68 (breln1unionCommutes) => 78.39/10.68 (( 78.39/10.68 (woz2Ex) => 78.39/10.68 (( 78.39/10.68 (woz2W) => 78.39/10.68 (( 78.39/10.68 (woz2A) => 78.39/10.68 (( 78.39/10.68 (woz2B) => 78.39/10.68 (( 78.39/10.68 (image1Ex) => 78.39/10.68 (( 78.39/10.68 (image1Ex1) => 78.39/10.68 (( 78.39/10.68 (image1Equiv) => 78.39/10.68 (( 78.39/10.68 (image1E) => 78.39/10.68 (( 78.39/10.68 (image1I) => 78.39/10.68 (( 78.39/10.68 (injFuncInInjFuncSet) => 78.39/10.68 (( 78.39/10.68 (injFuncSetFuncIn) => 78.39/10.68 (( 78.39/10.68 (injFuncSetFuncInj) => 78.39/10.68 (( 78.39/10.68 (surjFuncSetFuncIn) => 78.39/10.68 (( 78.39/10.68 (surjFuncSetFuncSurj) => 78.39/10.68 (( 78.39/10.68 (leftInvIsSurj) => 78.39/10.68 (( 78.39/10.68 (surjCantorThm) => 78.39/10.68 (( 78.39/10.68 (foundation2) => 78.39/10.68 (( 78.39/10.68 (notinself) => 78.39/10.68 (( 78.39/10.68 (notinself2) => 78.39/10.68 (( 78.39/10.68 (omegaSp) => 78.39/10.68 (( 78.39/10.68 (omegaSclos) => 78.39/10.68 (( 78.39/10.68 (peano0notS) => 78.39/10.68 (( 78.39/10.68 (peanoSinj) => 78.39/10.68 (( 78.39/10.68 (transitivesetOp1) => 78.39/10.68 (( 78.39/10.68 (binintTransitive) => 78.39/10.68 (( 78.39/10.68 (transitivesetOp2) => 78.39/10.68 (( 78.39/10.68 (setunionTransitive) => 78.39/10.68 (( 78.39/10.68 (ordinalMinLem1) => 78.39/10.68 (( 78.39/10.68 (!!) @ ( 78.39/10.68 ^[Y0 : $i]: 78.39/10.68 (( 78.39/10.68 (ordinal @ 78.39/10.68 Y0) => 78.39/10.68 (( 78.39/10.68 (!!) @ ( 78.39/10.68 ^[Y1 : $i]: 78.39/10.68 (( 78.39/10.68 (!!) @ ( 78.39/10.68 ^[Y2 : $i]: 78.39/10.68 (( 78.39/10.68 (in @ 78.39/10.68 Y2 @ 78.39/10.68 Y0) => 78.39/10.68 (( 78.39/10.68 (in @ 78.39/10.68 Y1 @ 78.39/10.68 Y2) => 78.39/10.68 (in @ 78.39/10.68 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 78.39/10.68 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1153])). 78.39/10.68 thf(zip_derived_cl1172, plain, 78.39/10.68 (~ (((kpairp) => 78.39/10.68 (((singletonsubset) => 78.39/10.68 (((singletoninpowerset) => 78.39/10.68 (((singletoninpowunion) => 78.39/10.68 (((upairset2E) => 78.39/10.68 (((upairsubunion) => 78.39/10.68 (((upairinpowunion) => 78.39/10.68 (((ubforcartprodlem1) => 78.39/10.68 (((ubforcartprodlem2) => 78.39/10.68 (((ubforcartprodlem3) => 78.39/10.68 (((cartprodpairin) => 78.39/10.68 (((cartprodmempair1) => 78.39/10.68 (((cartprodmempair) => 78.39/10.68 (((setunionE2) => 78.39/10.68 (((setunionsingleton1) => 78.39/10.68 (((setunionsingleton2) => 78.39/10.68 (((setunionsingleton) => 78.39/10.68 (((singletonprop) => 78.39/10.68 (((ex1E1) => 78.39/10.68 (((ex1I) => 78.39/10.68 (((ex1I2) => 78.39/10.68 (((singletonsuniq) => 78.39/10.68 (((setukpairinjL1) => 78.39/10.68 (((kfstsingleton) => 78.39/10.68 (((theprop) => 78.39/10.68 (((kfstpairEq) => 78.39/10.68 (((cartprodfstin) => 78.39/10.68 (((setukpairinjL2) => 78.39/10.68 (((setukpairinjL) => 78.39/10.68 (((setukpairinjR11) => 78.39/10.68 (( 78.39/10.68 (setukpairinjR12) => 78.39/10.68 (( 78.39/10.68 (setukpairinjR1) => 78.39/10.68 (( 78.39/10.68 (upairequniteq) => 78.39/10.68 (( 78.39/10.68 (setukpairinjR2) => 78.39/10.68 (( 78.39/10.68 (setukpairinjR) => 78.39/10.68 (( 78.39/10.68 (ksndsingleton) => 78.39/10.68 (( 78.39/10.68 (ksndpairEq) => 78.39/10.68 (( 78.39/10.68 (kpairsurjEq) => 78.39/10.68 (( 78.39/10.68 (cartprodsndin) => 78.39/10.68 (( 78.39/10.68 (cartprodpairmemEL) => 78.39/10.68 (( 78.39/10.68 (cartprodpairmemER) => 78.39/10.68 (( 78.39/10.68 (cartprodmempaircEq) => 78.39/10.68 (( 78.39/10.68 (cartprodfstpairEq) => 78.39/10.68 (( 78.39/10.68 (cartprodsndpairEq) => 78.39/10.68 (( 78.39/10.68 (cartprodpairsurjEq) => 78.39/10.68 (( 78.39/10.68 (dpsetconstrI) => 78.39/10.68 (( 78.39/10.68 (dpsetconstrSub) => 78.39/10.68 (( 78.39/10.68 (setOfPairsIsBReln) => 78.39/10.68 (( 78.39/10.68 (dpsetconstrERa) => 78.39/10.68 (( 78.39/10.68 (dpsetconstrEL1) => 78.39/10.68 (( 78.39/10.68 (dpsetconstrEL2) => 78.39/10.68 (( 78.39/10.68 (dpsetconstrER) => 78.39/10.68 (( 78.39/10.68 (funcImageSingleton) => 78.39/10.68 (( 78.39/10.68 (apProp) => 78.39/10.68 (( 78.39/10.68 (app) => 78.39/10.68 (( 78.39/10.68 (infuncsetfunc) => 78.39/10.68 (( 78.39/10.68 (ap2p) => 78.39/10.68 (( 78.39/10.68 (funcinfuncset) => 78.39/10.68 (( 78.39/10.68 (lamProp) => 78.39/10.68 (( 78.39/10.68 (lamp) => 78.39/10.68 (( 78.39/10.68 (lam2p) => 78.39/10.68 (( 78.39/10.68 (brelnall1) => 78.39/10.68 (( 78.39/10.68 (brelnall2) => 78.39/10.68 (( 78.39/10.68 (ex1E2) => 78.39/10.68 (( 78.39/10.68 (funcGraphProp1) => 78.39/10.68 (( 78.39/10.68 (funcGraphProp3) => 78.39/10.68 (( 78.39/10.68 (funcGraphProp2) => 78.39/10.68 (( 78.39/10.68 (funcextLem) => 78.39/10.68 (( 78.39/10.68 (funcGraphProp4) => 78.39/10.68 (( 78.39/10.68 (subbreln) => 78.39/10.68 (( 78.39/10.68 (eqbreln) => 78.39/10.68 (( 78.39/10.68 (funcext) => 78.39/10.68 (( 78.39/10.68 (funcext2) => 78.39/10.68 (( 78.39/10.68 (ap2apEq1) => 78.39/10.68 (( 78.39/10.68 (ap2apEq2) => 78.39/10.68 (( 78.39/10.68 (beta1) => 78.39/10.68 (( 78.39/10.68 (eta1) => 78.39/10.68 (( 78.39/10.68 (lam2lamEq) => 78.39/10.68 (( 78.39/10.68 (beta2) => 78.39/10.68 (( 78.39/10.68 (eta2) => 78.39/10.68 (( 78.39/10.68 (iffalseProp1) => 78.39/10.68 (( 78.39/10.68 (iffalseProp2) => 78.39/10.68 (( 78.39/10.68 (iftrueProp1) => 78.39/10.68 (( 78.39/10.68 (iftrueProp2) => 78.39/10.68 (( 78.39/10.68 (ifSingleton) => 78.39/10.68 (( 78.39/10.68 (ifp) => 78.39/10.68 (( 78.39/10.68 (theeq) => 78.39/10.68 (( 78.39/10.68 (iftrue) => 78.39/10.68 (( 78.39/10.68 (iffalse) => 78.39/10.68 (( 78.39/10.68 (iftrueorfalse) => 78.39/10.68 (( 78.39/10.68 (binintersectT_lem) => 78.39/10.68 (( 78.39/10.68 (binunionT_lem) => 78.39/10.68 (( 78.39/10.68 (powersetT_lem) => 78.39/10.68 (( 78.39/10.68 (setminusT_lem) => 78.39/10.68 (( 78.39/10.68 (complementT_lem) => 78.39/10.68 (( 78.39/10.68 (setextT) => 78.39/10.68 (( 78.39/10.68 (subsetTI) => 78.39/10.68 (( 78.39/10.68 (powersetTI1) => 78.39/10.68 (( 78.39/10.68 (powersetTE1) => 78.39/10.68 (( 78.39/10.68 (complementTI1) => 78.39/10.68 (( 78.39/10.68 (complementTE1) => 78.39/10.68 (( 78.39/10.68 (binintersectTELcontra) => 78.39/10.68 (( 78.39/10.68 (binintersectTERcontra) => 78.39/10.68 (( 78.39/10.68 (contrasubsetT) => 78.39/10.68 (( 78.39/10.68 (contrasubsetT1) => 78.39/10.68 (( 78.39/10.68 (contrasubsetT2) => 78.39/10.68 (( 78.39/10.68 (contrasubsetT3) => 78.39/10.68 (( 78.39/10.68 (doubleComplementI1) => 78.39/10.68 (( 78.39/10.68 (doubleComplementE1) => 78.39/10.68 (( 78.39/10.68 (doubleComplementSub1) => 78.39/10.68 (( 78.39/10.68 (doubleComplementSub2) => 78.39/10.68 (( 78.39/10.68 (doubleComplementEq) => 78.39/10.68 (( 78.39/10.68 (complementTnotintersectT) => 78.39/10.68 (( 78.39/10.68 (complementImpComplementIntersect) => 78.39/10.68 (( 78.39/10.68 (complementSubsetComplementIntersect) => 78.39/10.68 (( 78.39/10.68 (complementInPowersetComplementIntersect) => 78.39/10.68 (( 78.39/10.68 (contraSubsetComplement) => 78.39/10.68 (( 78.39/10.68 (complementTcontraSubset) => 78.39/10.68 (( 78.39/10.68 (binunionTILcontra) => 78.39/10.68 (( 78.39/10.68 (binunionTIRcontra) => 78.39/10.68 (( 78.39/10.68 (inIntersectImpInUnion) => 78.39/10.68 (( 78.39/10.68 (inIntersectImpInUnion2) => 78.39/10.68 (( 78.39/10.68 (inIntersectImpInIntersectUnions) => 78.39/10.68 (( 78.39/10.68 (intersectInPowersetIntersectUnions) => 78.39/10.68 (( 78.39/10.68 (inComplementUnionImpNotIn1) => 78.39/10.68 (( 78.39/10.68 (inComplementUnionImpInComplement1) => 78.39/10.68 (( 78.39/10.68 (binunionTE) => 78.39/10.68 (( 78.39/10.68 (binunionTEcontra) => 78.39/10.68 (( 78.39/10.68 (demorgan2a1) => 78.39/10.68 (( 78.39/10.68 (complementUnionInPowersetComplement) => 78.39/10.68 (( 78.39/10.68 (demorgan2a2) => 78.39/10.68 (( 78.39/10.68 (demorgan1a) => 78.39/10.68 (( 78.39/10.68 (demorgan1b) => 78.39/10.68 (( 78.39/10.68 (demorgan1) => 78.39/10.68 (( 78.39/10.68 (demorgan2a) => 78.39/10.68 (( 78.39/10.68 (demorgan2b2) => 78.39/10.68 (( 78.39/10.68 (demorgan2b) => 78.39/10.68 (( 78.39/10.68 (demorgan2) => 78.39/10.68 (( 78.39/10.68 (woz13rule0) => 78.39/10.68 (( 78.39/10.68 (woz13rule1) => 78.39/10.68 (( 78.39/10.68 (woz13rule2) => 78.39/10.68 (( 78.39/10.68 (woz13rule3) => 78.39/10.68 (( 78.39/10.68 (woz13rule4) => 78.39/10.68 (( 78.39/10.68 (woz1_1) => 78.39/10.68 (( 78.39/10.68 (woz1_2) => 78.39/10.68 (( 78.39/10.68 (woz1_3) => 78.39/10.68 (( 78.39/10.68 (woz1_4) => 78.39/10.68 (( 78.39/10.68 (woz1_5) => 78.39/10.68 (( 78.39/10.68 (breln1all2) => 78.39/10.68 (( 78.39/10.68 (breln1SetBreln1) => 78.39/10.68 (( 78.39/10.68 (choice2fnsingleton) => 78.39/10.68 (( 78.39/10.68 (setOfPairsIsBReln1) => 78.39/10.68 (( 78.39/10.68 (breln1all1) => 78.39/10.68 (( 78.39/10.68 (subbreln1) => 78.39/10.68 (( 78.39/10.68 (eqbreln1) => 78.39/10.68 (( 78.39/10.68 (breln1invprop) => 78.39/10.68 (( 78.39/10.68 (breln1invI) => 78.39/10.68 (( 78.39/10.68 (breln1invE) => 78.39/10.68 (( 78.39/10.68 (breln1compprop) => 78.39/10.68 (( 78.39/10.68 (breln1compI) => 78.39/10.68 (( 78.39/10.68 (breln1compE) => 78.39/10.68 (( 78.39/10.68 (breln1compEex) => 78.39/10.68 (( 78.39/10.68 (breln1unionprop) => 78.39/10.68 (( 78.39/10.68 (breln1unionIL) => 78.39/10.68 (( 78.39/10.68 (breln1unionIR) => 78.39/10.68 (( 78.39/10.68 (breln1unionI) => 78.39/10.68 (( 78.39/10.68 (breln1unionE) => 78.39/10.68 (( 78.39/10.68 (breln1unionEcases) => 78.39/10.68 (( 78.39/10.68 (breln1unionCommutes) => 78.39/10.68 (( 78.39/10.68 (woz2Ex) => 78.39/10.68 (( 78.39/10.68 (woz2W) => 78.39/10.68 (( 78.39/10.68 (woz2A) => 78.39/10.68 (( 78.39/10.68 (woz2B) => 78.39/10.68 (( 78.39/10.68 (image1Ex) => 78.39/10.68 (( 78.39/10.68 (image1Ex1) => 78.39/10.68 (( 78.39/10.68 (image1Equiv) => 78.39/10.68 (( 78.39/10.68 (image1E) => 78.39/10.68 (( 78.39/10.68 (image1I) => 78.39/10.68 (( 78.39/10.68 (injFuncInInjFuncSet) => 78.39/10.68 (( 78.39/10.68 (injFuncSetFuncIn) => 78.39/10.68 (( 78.39/10.68 (injFuncSetFuncInj) => 78.39/10.68 (( 78.39/10.68 (surjFuncSetFuncIn) => 78.39/10.68 (( 78.39/10.68 (surjFuncSetFuncSurj) => 78.39/10.68 (( 78.39/10.68 (leftInvIsSurj) => 78.39/10.68 (( 78.39/10.68 (surjCantorThm) => 78.39/10.68 (( 78.39/10.68 (foundation2) => 78.39/10.68 (( 78.39/10.68 (notinself) => 78.39/10.68 (( 78.39/10.68 (notinself2) => 78.39/10.68 (( 78.39/10.68 (omegaSp) => 78.39/10.68 (( 78.39/10.68 (omegaSclos) => 78.39/10.68 (( 78.39/10.68 (peano0notS) => 78.39/10.68 (( 78.39/10.68 (peanoSinj) => 78.39/10.68 (( 78.39/10.68 (transitivesetOp1) => 78.39/10.68 (( 78.39/10.68 (binintTransitive) => 78.39/10.68 (( 78.39/10.68 (transitivesetOp2) => 78.39/10.68 (( 78.39/10.68 (setunionTransitive) => 78.39/10.68 (( 78.39/10.68 (ordinalMinLem1) => 78.39/10.68 (( 78.39/10.68 (!!) @ ( 78.39/10.68 ^[Y0 : $i]: 78.39/10.68 (( 78.39/10.68 (ordinal @ 78.39/10.68 Y0) => 78.39/10.68 (( 78.39/10.68 (!!) @ ( 78.39/10.68 ^[Y1 : $i]: 78.39/10.68 (( 78.39/10.68 (!!) @ ( 78.39/10.68 ^[Y2 : $i]: 78.39/10.68 (( 78.39/10.68 (in @ 78.39/10.68 Y2 @ 78.39/10.68 Y0) => 78.39/10.68 (( 78.39/10.68 (in @ 78.39/10.68 Y1 @ 78.39/10.68 Y2) => 78.39/10.68 (in @ 78.39/10.68 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 78.39/10.68 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1162])). 78.39/10.68 thf(zip_derived_cl1185, plain, 78.39/10.68 (~ (((singletonsubset) => 78.39/10.68 (((singletoninpowerset) => 78.39/10.68 (((singletoninpowunion) => 78.39/10.68 (((upairset2E) => 78.39/10.68 (((upairsubunion) => 78.39/10.68 (((upairinpowunion) => 78.39/10.68 (((ubforcartprodlem1) => 78.39/10.68 (((ubforcartprodlem2) => 78.39/10.68 (((ubforcartprodlem3) => 78.39/10.68 (((cartprodpairin) => 78.39/10.68 (((cartprodmempair1) => 78.39/10.68 (((cartprodmempair) => 78.39/10.68 (((setunionE2) => 78.39/10.68 (((setunionsingleton1) => 78.39/10.68 (((setunionsingleton2) => 78.39/10.68 (((setunionsingleton) => 78.39/10.68 (((singletonprop) => 78.39/10.68 (((ex1E1) => 78.39/10.68 (((ex1I) => 78.39/10.68 (((ex1I2) => 78.39/10.68 (((singletonsuniq) => 78.39/10.68 (((setukpairinjL1) => 78.39/10.68 (((kfstsingleton) => 78.39/10.68 (((theprop) => 78.39/10.68 (((kfstpairEq) => 78.39/10.68 (((cartprodfstin) => 78.39/10.68 (((setukpairinjL2) => 78.39/10.68 (((setukpairinjL) => 78.39/10.68 (((setukpairinjR11) => 78.39/10.68 (((setukpairinjR12) => 78.39/10.68 (( 78.39/10.68 (setukpairinjR1) => 78.39/10.68 (( 78.39/10.68 (upairequniteq) => 78.39/10.68 (( 78.39/10.68 (setukpairinjR2) => 78.39/10.68 (( 78.39/10.68 (setukpairinjR) => 78.39/10.68 (( 78.39/10.68 (ksndsingleton) => 78.39/10.68 (( 78.39/10.68 (ksndpairEq) => 78.39/10.68 (( 78.39/10.68 (kpairsurjEq) => 78.39/10.68 (( 78.39/10.68 (cartprodsndin) => 78.39/10.68 (( 78.39/10.68 (cartprodpairmemEL) => 78.39/10.68 (( 78.39/10.68 (cartprodpairmemER) => 78.39/10.68 (( 78.39/10.68 (cartprodmempaircEq) => 78.39/10.68 (( 78.39/10.68 (cartprodfstpairEq) => 78.39/10.68 (( 78.39/10.68 (cartprodsndpairEq) => 78.39/10.68 (( 78.39/10.68 (cartprodpairsurjEq) => 78.39/10.68 (( 78.39/10.68 (dpsetconstrI) => 78.39/10.68 (( 78.39/10.68 (dpsetconstrSub) => 78.39/10.68 (( 78.39/10.68 (setOfPairsIsBReln) => 78.39/10.68 (( 78.39/10.68 (dpsetconstrERa) => 78.39/10.68 (( 78.39/10.68 (dpsetconstrEL1) => 78.39/10.68 (( 78.39/10.68 (dpsetconstrEL2) => 78.39/10.68 (( 78.39/10.68 (dpsetconstrER) => 78.39/10.68 (( 78.39/10.68 (funcImageSingleton) => 78.39/10.68 (( 78.39/10.68 (apProp) => 78.39/10.68 (( 78.39/10.68 (app) => 78.39/10.68 (( 78.39/10.68 (infuncsetfunc) => 78.39/10.68 (( 78.39/10.68 (ap2p) => 78.39/10.68 (( 78.39/10.68 (funcinfuncset) => 78.39/10.68 (( 78.39/10.68 (lamProp) => 78.39/10.68 (( 78.39/10.68 (lamp) => 78.39/10.68 (( 78.39/10.68 (lam2p) => 78.39/10.68 (( 78.39/10.68 (brelnall1) => 78.39/10.68 (( 78.39/10.68 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78.39/10.68 (theeq) => 78.39/10.68 (( 78.39/10.68 (iftrue) => 78.39/10.68 (( 78.39/10.68 (iffalse) => 78.39/10.68 (( 78.39/10.68 (iftrueorfalse) => 78.39/10.68 (( 78.39/10.68 (binintersectT_lem) => 78.39/10.68 (( 78.39/10.68 (binunionT_lem) => 78.39/10.68 (( 78.39/10.68 (powersetT_lem) => 78.39/10.68 (( 78.39/10.68 (setminusT_lem) => 78.39/10.68 (( 78.39/10.68 (complementT_lem) => 78.39/10.68 (( 78.39/10.68 (setextT) => 78.39/10.68 (( 78.39/10.68 (subsetTI) => 78.39/10.68 (( 78.39/10.68 (powersetTI1) => 78.39/10.68 (( 78.39/10.68 (powersetTE1) => 78.39/10.68 (( 78.39/10.68 (complementTI1) => 78.39/10.68 (( 78.39/10.68 (complementTE1) => 78.39/10.68 (( 78.39/10.68 (binintersectTELcontra) => 78.39/10.68 (( 78.39/10.68 (binintersectTERcontra) => 78.39/10.68 (( 78.39/10.68 (contrasubsetT) => 78.39/10.68 (( 78.39/10.68 (contrasubsetT1) => 78.39/10.68 (( 78.39/10.68 (contrasubsetT2) => 78.39/10.68 (( 78.39/10.68 (contrasubsetT3) => 78.39/10.68 (( 78.39/10.68 (doubleComplementI1) => 78.39/10.68 (( 78.39/10.68 (doubleComplementE1) => 78.39/10.68 (( 78.39/10.68 (doubleComplementSub1) => 78.39/10.68 (( 78.39/10.68 (doubleComplementSub2) => 78.39/10.68 (( 78.39/10.68 (doubleComplementEq) => 78.39/10.68 (( 78.39/10.68 (complementTnotintersectT) => 78.39/10.68 (( 78.39/10.68 (complementImpComplementIntersect) => 78.39/10.68 (( 78.39/10.68 (complementSubsetComplementIntersect) => 78.39/10.68 (( 78.39/10.68 (complementInPowersetComplementIntersect) => 78.39/10.68 (( 78.39/10.68 (contraSubsetComplement) => 78.39/10.68 (( 78.39/10.68 (complementTcontraSubset) => 78.39/10.68 (( 78.39/10.68 (binunionTILcontra) => 78.39/10.68 (( 78.39/10.68 (binunionTIRcontra) => 78.39/10.68 (( 78.39/10.68 (inIntersectImpInUnion) => 78.39/10.68 (( 78.39/10.68 (inIntersectImpInUnion2) => 78.39/10.68 (( 78.39/10.68 (inIntersectImpInIntersectUnions) => 78.39/10.68 (( 78.39/10.68 (intersectInPowersetIntersectUnions) => 78.39/10.68 (( 78.39/10.68 (inComplementUnionImpNotIn1) => 78.39/10.68 (( 78.39/10.68 (inComplementUnionImpInComplement1) => 78.39/10.68 (( 78.39/10.68 (binunionTE) => 78.39/10.68 (( 78.39/10.68 (binunionTEcontra) => 78.39/10.68 (( 78.39/10.68 (demorgan2a1) => 78.39/10.68 (( 78.39/10.68 (complementUnionInPowersetComplement) => 78.39/10.68 (( 78.39/10.68 (demorgan2a2) => 78.39/10.68 (( 78.39/10.68 (demorgan1a) => 78.39/10.68 (( 78.39/10.68 (demorgan1b) => 78.39/10.68 (( 78.39/10.68 (demorgan1) => 78.39/10.68 (( 78.39/10.68 (demorgan2a) => 78.39/10.68 (( 78.39/10.68 (demorgan2b2) => 78.39/10.68 (( 78.39/10.68 (demorgan2b) => 78.39/10.68 (( 78.39/10.68 (demorgan2) => 78.39/10.68 (( 78.39/10.68 (woz13rule0) => 78.39/10.68 (( 78.39/10.68 (woz13rule1) => 78.39/10.68 (( 78.39/10.68 (woz13rule2) => 78.39/10.68 (( 78.39/10.68 (woz13rule3) => 78.39/10.68 (( 78.39/10.68 (woz13rule4) => 78.39/10.68 (( 78.39/10.68 (woz1_1) => 78.39/10.68 (( 78.39/10.68 (woz1_2) => 78.39/10.68 (( 78.39/10.68 (woz1_3) => 78.39/10.68 (( 78.39/10.68 (woz1_4) => 78.39/10.68 (( 78.39/10.68 (woz1_5) => 78.39/10.68 (( 78.39/10.68 (breln1all2) => 78.39/10.68 (( 78.39/10.68 (breln1SetBreln1) => 78.39/10.68 (( 78.39/10.68 (choice2fnsingleton) => 78.39/10.68 (( 78.39/10.68 (setOfPairsIsBReln1) => 78.39/10.68 (( 78.39/10.68 (breln1all1) => 78.39/10.68 (( 78.39/10.68 (subbreln1) => 78.39/10.68 (( 78.39/10.68 (eqbreln1) => 78.39/10.68 (( 78.39/10.68 (breln1invprop) => 78.39/10.68 (( 78.39/10.68 (breln1invI) => 78.39/10.68 (( 78.39/10.68 (breln1invE) => 78.39/10.68 (( 78.39/10.68 (breln1compprop) => 78.39/10.68 (( 78.39/10.68 (breln1compI) => 78.39/10.68 (( 78.39/10.68 (breln1compE) => 78.39/10.68 (( 78.39/10.68 (breln1compEex) => 78.39/10.68 (( 78.39/10.68 (breln1unionprop) => 78.39/10.68 (( 78.39/10.68 (breln1unionIL) => 78.39/10.68 (( 78.39/10.68 (breln1unionIR) => 78.39/10.68 (( 78.39/10.68 (breln1unionI) => 78.39/10.68 (( 78.39/10.68 (breln1unionE) => 78.39/10.68 (( 78.39/10.68 (breln1unionEcases) => 78.39/10.68 (( 78.39/10.68 (breln1unionCommutes) => 78.39/10.68 (( 78.39/10.68 (woz2Ex) => 78.39/10.68 (( 78.39/10.68 (woz2W) => 78.39/10.68 (( 78.39/10.68 (woz2A) => 78.39/10.68 (( 78.39/10.68 (woz2B) => 78.39/10.68 (( 78.39/10.68 (image1Ex) => 78.39/10.68 (( 78.39/10.68 (image1Ex1) => 78.39/10.68 (( 78.39/10.68 (image1Equiv) => 78.39/10.68 (( 78.39/10.68 (image1E) => 78.39/10.68 (( 78.39/10.68 (image1I) => 78.39/10.68 (( 78.39/10.68 (injFuncInInjFuncSet) => 78.39/10.68 (( 78.39/10.68 (injFuncSetFuncIn) => 78.39/10.68 (( 78.39/10.68 (injFuncSetFuncInj) => 78.39/10.68 (( 78.39/10.68 (surjFuncSetFuncIn) => 78.39/10.68 (( 78.39/10.68 (surjFuncSetFuncSurj) => 78.39/10.68 (( 78.39/10.68 (leftInvIsSurj) => 78.39/10.68 (( 78.39/10.68 (surjCantorThm) => 78.39/10.68 (( 78.39/10.68 (foundation2) => 78.39/10.68 (( 78.39/10.68 (notinself) => 78.39/10.68 (( 78.39/10.68 (notinself2) => 78.39/10.68 (( 78.39/10.68 (omegaSp) => 78.39/10.68 (( 78.39/10.68 (omegaSclos) => 78.39/10.68 (( 78.39/10.68 (peano0notS) => 78.39/10.68 (( 78.39/10.68 (peanoSinj) => 78.39/10.68 (( 78.39/10.68 (transitivesetOp1) => 78.39/10.68 (( 78.39/10.68 (binintTransitive) => 78.39/10.68 (( 78.39/10.68 (transitivesetOp2) => 78.39/10.68 (( 78.39/10.68 (setunionTransitive) => 78.39/10.68 (( 78.39/10.68 (ordinalMinLem1) => 78.39/10.68 (( 78.39/10.68 (!!) @ ( 78.39/10.68 ^[Y0 : $i]: 78.39/10.68 (( 78.39/10.68 (ordinal @ 78.39/10.68 Y0) => 78.39/10.68 (( 78.39/10.68 (!!) @ ( 78.39/10.68 ^[Y1 : $i]: 78.39/10.68 (( 78.39/10.68 (!!) @ ( 78.39/10.68 ^[Y2 : $i]: 78.39/10.68 (( 78.39/10.68 (in @ 78.39/10.68 Y2 @ 78.39/10.68 Y0) => 78.39/10.68 (( 78.39/10.68 (in @ 78.39/10.68 Y1 @ 78.39/10.68 Y2) => 78.39/10.68 (in @ 78.39/10.68 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 78.39/10.68 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1172])). 78.39/10.68 thf(zip_derived_cl1195, plain, 78.39/10.68 (~ (((singletoninpowerset) => 78.39/10.68 (((singletoninpowunion) => 78.39/10.68 (((upairset2E) => 78.39/10.68 (((upairsubunion) => 78.39/10.68 (((upairinpowunion) => 78.39/10.68 (((ubforcartprodlem1) => 78.39/10.68 (((ubforcartprodlem2) => 78.39/10.68 (((ubforcartprodlem3) => 78.39/10.68 (((cartprodpairin) => 78.39/10.68 (((cartprodmempair1) => 78.39/10.68 (((cartprodmempair) => 78.39/10.68 (((setunionE2) => 78.39/10.68 (((setunionsingleton1) => 78.39/10.68 (((setunionsingleton2) => 78.39/10.68 (((setunionsingleton) => 78.39/10.68 (((singletonprop) => 78.39/10.68 (((ex1E1) => 78.39/10.68 (((ex1I) => 78.39/10.68 (((ex1I2) => 78.39/10.68 (((singletonsuniq) => 78.39/10.68 (((setukpairinjL1) => 78.39/10.68 (((kfstsingleton) => 78.39/10.68 (((theprop) => 78.39/10.68 (((kfstpairEq) => 78.39/10.68 (((cartprodfstin) => 78.39/10.68 (((setukpairinjL2) => 78.39/10.68 (((setukpairinjL) => 78.39/10.68 (((setukpairinjR11) => 78.39/10.68 (((setukpairinjR12) => 78.39/10.68 (((setukpairinjR1) => 78.39/10.68 (( 78.39/10.68 (upairequniteq) => 78.39/10.68 (( 78.39/10.68 (setukpairinjR2) => 78.39/10.68 (( 78.39/10.68 (setukpairinjR) => 78.39/10.68 (( 78.39/10.68 (ksndsingleton) => 78.39/10.68 (( 78.39/10.68 (ksndpairEq) => 78.39/10.68 (( 78.39/10.68 (kpairsurjEq) => 78.39/10.68 (( 78.39/10.68 (cartprodsndin) => 78.39/10.68 (( 78.39/10.68 (cartprodpairmemEL) => 78.39/10.68 (( 78.39/10.68 (cartprodpairmemER) => 78.39/10.68 (( 78.39/10.68 (cartprodmempaircEq) => 78.39/10.68 (( 78.39/10.68 (cartprodfstpairEq) => 78.39/10.68 (( 78.39/10.68 (cartprodsndpairEq) => 78.39/10.68 (( 78.39/10.68 (cartprodpairsurjEq) => 78.39/10.68 (( 78.39/10.68 (dpsetconstrI) => 78.39/10.68 (( 78.39/10.68 (dpsetconstrSub) => 78.39/10.68 (( 78.39/10.68 (setOfPairsIsBReln) => 78.39/10.68 (( 78.39/10.68 (dpsetconstrERa) => 78.39/10.68 (( 78.39/10.68 (dpsetconstrEL1) => 78.39/10.68 (( 78.39/10.68 (dpsetconstrEL2) => 78.39/10.68 (( 78.39/10.68 (dpsetconstrER) => 78.39/10.68 (( 78.39/10.68 (funcImageSingleton) => 78.39/10.68 (( 78.39/10.68 (apProp) => 78.39/10.68 (( 78.39/10.68 (app) => 78.39/10.68 (( 78.39/10.68 (infuncsetfunc) => 78.39/10.68 (( 78.39/10.68 (ap2p) => 78.39/10.68 (( 78.39/10.68 (funcinfuncset) => 78.39/10.68 (( 78.39/10.68 (lamProp) => 78.39/10.68 (( 78.39/10.68 (lamp) => 78.39/10.68 (( 78.39/10.68 (lam2p) => 78.39/10.68 (( 78.39/10.68 (brelnall1) => 78.39/10.68 (( 78.39/10.68 (brelnall2) => 78.39/10.68 (( 78.39/10.68 (ex1E2) => 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=> 78.39/10.68 (( 78.39/10.68 (iffalse) => 78.39/10.68 (( 78.39/10.68 (iftrueorfalse) => 78.39/10.68 (( 78.39/10.68 (binintersectT_lem) => 78.39/10.68 (( 78.39/10.68 (binunionT_lem) => 78.39/10.68 (( 78.39/10.68 (powersetT_lem) => 78.39/10.68 (( 78.39/10.68 (setminusT_lem) => 78.39/10.68 (( 78.39/10.68 (complementT_lem) => 78.39/10.68 (( 78.39/10.68 (setextT) => 78.39/10.68 (( 78.39/10.68 (subsetTI) => 78.39/10.68 (( 78.39/10.68 (powersetTI1) => 78.39/10.68 (( 78.39/10.68 (powersetTE1) => 78.39/10.68 (( 78.39/10.68 (complementTI1) => 78.39/10.68 (( 78.39/10.68 (complementTE1) => 78.39/10.68 (( 78.39/10.68 (binintersectTELcontra) => 78.39/10.68 (( 78.39/10.68 (binintersectTERcontra) => 78.39/10.68 (( 78.39/10.68 (contrasubsetT) => 78.39/10.68 (( 78.39/10.68 (contrasubsetT1) => 78.39/10.68 (( 78.39/10.68 (contrasubsetT2) => 78.39/10.68 (( 78.39/10.68 (contrasubsetT3) => 78.39/10.68 (( 78.39/10.68 (doubleComplementI1) => 78.39/10.68 (( 78.39/10.68 (doubleComplementE1) => 78.39/10.68 (( 78.39/10.68 (doubleComplementSub1) => 78.39/10.68 (( 78.39/10.68 (doubleComplementSub2) => 78.39/10.68 (( 78.39/10.68 (doubleComplementEq) => 78.39/10.68 (( 78.39/10.68 (complementTnotintersectT) => 78.39/10.68 (( 78.39/10.68 (complementImpComplementIntersect) => 78.39/10.68 (( 78.39/10.68 (complementSubsetComplementIntersect) => 78.39/10.68 (( 78.39/10.68 (complementInPowersetComplementIntersect) => 78.39/10.68 (( 78.39/10.68 (contraSubsetComplement) => 78.39/10.68 (( 78.39/10.68 (complementTcontraSubset) => 78.39/10.68 (( 78.39/10.68 (binunionTILcontra) => 78.39/10.68 (( 78.39/10.68 (binunionTIRcontra) => 78.39/10.68 (( 78.39/10.68 (inIntersectImpInUnion) => 78.39/10.68 (( 78.39/10.68 (inIntersectImpInUnion2) => 78.39/10.68 (( 78.39/10.68 (inIntersectImpInIntersectUnions) => 78.39/10.68 (( 78.39/10.68 (intersectInPowersetIntersectUnions) => 78.39/10.68 (( 78.39/10.68 (inComplementUnionImpNotIn1) => 78.39/10.68 (( 78.39/10.68 (inComplementUnionImpInComplement1) => 78.39/10.68 (( 78.39/10.68 (binunionTE) => 78.39/10.68 (( 78.39/10.68 (binunionTEcontra) => 78.39/10.68 (( 78.39/10.68 (demorgan2a1) => 78.39/10.68 (( 78.39/10.68 (complementUnionInPowersetComplement) => 78.39/10.68 (( 78.39/10.68 (demorgan2a2) => 78.39/10.68 (( 78.39/10.68 (demorgan1a) => 78.39/10.68 (( 78.39/10.68 (demorgan1b) => 78.39/10.68 (( 78.39/10.68 (demorgan1) => 78.39/10.68 (( 78.39/10.68 (demorgan2a) => 78.39/10.68 (( 78.39/10.68 (demorgan2b2) => 78.39/10.68 (( 78.39/10.68 (demorgan2b) => 78.39/10.68 (( 78.39/10.68 (demorgan2) => 78.39/10.68 (( 78.39/10.68 (woz13rule0) => 78.39/10.68 (( 78.39/10.68 (woz13rule1) => 78.39/10.68 (( 78.39/10.68 (woz13rule2) => 78.39/10.68 (( 78.39/10.68 (woz13rule3) => 78.39/10.68 (( 78.39/10.68 (woz13rule4) => 78.39/10.68 (( 78.39/10.68 (woz1_1) => 78.39/10.68 (( 78.39/10.68 (woz1_2) => 78.39/10.68 (( 78.39/10.68 (woz1_3) => 78.39/10.68 (( 78.39/10.68 (woz1_4) => 78.39/10.68 (( 78.39/10.68 (woz1_5) => 78.39/10.68 (( 78.39/10.68 (breln1all2) => 78.39/10.68 (( 78.39/10.68 (breln1SetBreln1) => 78.39/10.68 (( 78.39/10.68 (choice2fnsingleton) => 78.39/10.68 (( 78.39/10.68 (setOfPairsIsBReln1) => 78.39/10.68 (( 78.39/10.68 (breln1all1) => 78.39/10.68 (( 78.39/10.68 (subbreln1) => 78.39/10.68 (( 78.39/10.68 (eqbreln1) => 78.39/10.68 (( 78.39/10.68 (breln1invprop) => 78.39/10.68 (( 78.39/10.68 (breln1invI) => 78.39/10.68 (( 78.39/10.68 (breln1invE) => 78.39/10.68 (( 78.39/10.68 (breln1compprop) => 78.39/10.68 (( 78.39/10.68 (breln1compI) => 78.39/10.68 (( 78.39/10.68 (breln1compE) => 78.39/10.68 (( 78.39/10.68 (breln1compEex) => 78.39/10.68 (( 78.39/10.68 (breln1unionprop) => 78.39/10.68 (( 78.39/10.68 (breln1unionIL) => 78.39/10.68 (( 78.39/10.68 (breln1unionIR) => 78.39/10.68 (( 78.39/10.68 (breln1unionI) => 78.39/10.68 (( 78.39/10.68 (breln1unionE) => 78.39/10.68 (( 78.39/10.68 (breln1unionEcases) => 78.39/10.68 (( 78.39/10.68 (breln1unionCommutes) => 78.39/10.68 (( 78.39/10.68 (woz2Ex) => 78.39/10.68 (( 78.39/10.68 (woz2W) => 78.39/10.68 (( 78.39/10.68 (woz2A) => 78.39/10.68 (( 78.39/10.68 (woz2B) => 78.39/10.68 (( 78.39/10.68 (image1Ex) => 78.39/10.68 (( 78.39/10.68 (image1Ex1) => 78.39/10.68 (( 78.39/10.68 (image1Equiv) => 78.39/10.68 (( 78.39/10.68 (image1E) => 78.39/10.68 (( 78.39/10.68 (image1I) => 78.39/10.68 (( 78.39/10.68 (injFuncInInjFuncSet) => 78.39/10.68 (( 78.39/10.68 (injFuncSetFuncIn) => 78.39/10.68 (( 78.39/10.68 (injFuncSetFuncInj) => 78.39/10.68 (( 78.39/10.68 (surjFuncSetFuncIn) => 78.39/10.68 (( 78.39/10.68 (surjFuncSetFuncSurj) => 78.39/10.68 (( 78.39/10.68 (leftInvIsSurj) => 78.39/10.68 (( 78.39/10.68 (surjCantorThm) => 78.39/10.68 (( 78.39/10.68 (foundation2) => 78.39/10.68 (( 78.39/10.68 (notinself) => 78.39/10.68 (( 78.39/10.68 (notinself2) => 78.39/10.68 (( 78.39/10.68 (omegaSp) => 78.39/10.68 (( 78.39/10.68 (omegaSclos) => 78.39/10.68 (( 78.39/10.68 (peano0notS) => 78.39/10.68 (( 78.39/10.68 (peanoSinj) => 78.39/10.68 (( 78.39/10.68 (transitivesetOp1) => 78.39/10.68 (( 78.39/10.68 (binintTransitive) => 78.39/10.68 (( 78.39/10.68 (transitivesetOp2) => 78.39/10.68 (( 78.39/10.68 (setunionTransitive) => 78.39/10.68 (( 78.39/10.68 (ordinalMinLem1) => 78.39/10.68 (( 78.39/10.68 (!!) @ ( 78.39/10.68 ^[Y0 : $i]: 78.39/10.68 (( 78.39/10.68 (ordinal @ 78.39/10.68 Y0) => 78.39/10.68 (( 78.39/10.68 (!!) @ ( 78.39/10.68 ^[Y1 : $i]: 78.39/10.68 (( 78.39/10.68 (!!) @ ( 78.39/10.68 ^[Y2 : $i]: 78.39/10.68 (( 78.39/10.68 (in @ 78.39/10.68 Y2 @ 78.39/10.68 Y0) => 78.39/10.68 (( 78.39/10.68 (in @ 78.39/10.68 Y1 @ 78.39/10.68 Y2) => 78.39/10.68 (in @ 78.39/10.68 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 78.39/10.68 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1185])). 78.39/10.68 thf(zip_derived_cl1202, plain, 78.39/10.68 (~ (((singletoninpowunion) => 78.39/10.68 (((upairset2E) => 78.39/10.68 (((upairsubunion) => 78.39/10.68 (((upairinpowunion) => 78.39/10.68 (((ubforcartprodlem1) => 78.39/10.68 (((ubforcartprodlem2) => 78.39/10.68 (((ubforcartprodlem3) => 78.39/10.68 (((cartprodpairin) => 78.39/10.68 (((cartprodmempair1) => 78.39/10.68 (((cartprodmempair) => 78.39/10.68 (((setunionE2) => 78.39/10.68 (((setunionsingleton1) => 78.39/10.68 (((setunionsingleton2) => 78.39/10.68 (((setunionsingleton) => 78.39/10.68 (((singletonprop) => 78.39/10.68 (((ex1E1) => 78.39/10.68 (((ex1I) => 78.39/10.68 (((ex1I2) => 78.39/10.68 (((singletonsuniq) => 78.39/10.68 (((setukpairinjL1) => 78.39/10.68 (((kfstsingleton) => 78.39/10.68 (((theprop) => 78.39/10.68 (((kfstpairEq) => 78.39/10.68 (((cartprodfstin) => 78.39/10.68 (((setukpairinjL2) => 78.39/10.68 (((setukpairinjL) => 78.39/10.68 (((setukpairinjR11) => 78.39/10.68 (((setukpairinjR12) => 78.39/10.68 (((setukpairinjR1) => 78.39/10.68 (((upairequniteq) => 78.39/10.68 (( 78.39/10.68 (setukpairinjR2) => 78.39/10.68 (( 78.39/10.68 (setukpairinjR) => 78.39/10.68 (( 78.39/10.68 (ksndsingleton) => 78.39/10.68 (( 78.39/10.68 (ksndpairEq) => 78.39/10.68 (( 78.39/10.68 (kpairsurjEq) => 78.39/10.68 (( 78.39/10.68 (cartprodsndin) => 78.39/10.68 (( 78.39/10.68 (cartprodpairmemEL) => 78.39/10.68 (( 78.39/10.68 (cartprodpairmemER) => 78.39/10.68 (( 78.39/10.68 (cartprodmempaircEq) => 78.39/10.68 (( 78.39/10.68 (cartprodfstpairEq) => 78.39/10.68 (( 78.39/10.68 (cartprodsndpairEq) => 78.39/10.68 (( 78.39/10.68 (cartprodpairsurjEq) => 78.39/10.68 (( 78.39/10.68 (dpsetconstrI) => 78.39/10.68 (( 78.39/10.68 (dpsetconstrSub) => 78.39/10.68 (( 78.39/10.68 (setOfPairsIsBReln) => 78.39/10.68 (( 78.39/10.68 (dpsetconstrERa) => 78.39/10.68 (( 78.39/10.68 (dpsetconstrEL1) => 78.39/10.68 (( 78.39/10.68 (dpsetconstrEL2) => 78.39/10.68 (( 78.39/10.68 (dpsetconstrER) => 78.39/10.68 (( 78.39/10.68 (funcImageSingleton) => 78.39/10.68 (( 78.39/10.68 (apProp) => 78.39/10.68 (( 78.39/10.68 (app) => 78.39/10.68 (( 78.39/10.68 (infuncsetfunc) => 78.39/10.68 (( 78.39/10.68 (ap2p) => 78.39/10.68 (( 78.39/10.68 (funcinfuncset) => 78.39/10.68 (( 78.39/10.68 (lamProp) => 78.39/10.68 (( 78.39/10.68 (lamp) => 78.39/10.68 (( 78.39/10.68 (lam2p) => 78.39/10.68 (( 78.39/10.68 (brelnall1) => 78.39/10.68 (( 78.39/10.68 (brelnall2) => 78.39/10.68 (( 78.39/10.68 (ex1E2) => 78.39/10.68 (( 78.39/10.68 (funcGraphProp1) => 78.39/10.68 (( 78.39/10.68 (funcGraphProp3) => 78.39/10.68 (( 78.39/10.68 (funcGraphProp2) => 78.39/10.68 (( 78.39/10.68 (funcextLem) => 78.39/10.68 (( 78.39/10.68 (funcGraphProp4) => 78.39/10.68 (( 78.39/10.68 (subbreln) => 78.39/10.68 (( 78.39/10.68 (eqbreln) => 78.39/10.68 (( 78.39/10.68 (funcext) => 78.39/10.68 (( 78.39/10.68 (funcext2) => 78.39/10.68 (( 78.39/10.68 (ap2apEq1) => 78.39/10.68 (( 78.39/10.68 (ap2apEq2) => 78.39/10.68 (( 78.39/10.68 (beta1) => 78.39/10.68 (( 78.39/10.68 (eta1) => 78.39/10.68 (( 78.39/10.68 (lam2lamEq) => 78.39/10.68 (( 78.39/10.68 (beta2) => 78.39/10.68 (( 78.39/10.68 (eta2) => 78.39/10.68 (( 78.39/10.68 (iffalseProp1) => 78.39/10.68 (( 78.39/10.68 (iffalseProp2) => 78.39/10.68 (( 78.39/10.68 (iftrueProp1) => 78.39/10.68 (( 78.39/10.68 (iftrueProp2) => 78.39/10.68 (( 78.39/10.68 (ifSingleton) => 78.39/10.68 (( 78.39/10.68 (ifp) => 78.39/10.68 (( 78.39/10.68 (theeq) => 78.39/10.68 (( 78.39/10.68 (iftrue) => 78.39/10.68 (( 78.39/10.68 (iffalse) => 78.39/10.68 (( 78.39/10.68 (iftrueorfalse) => 78.39/10.68 (( 78.39/10.68 (binintersectT_lem) => 78.39/10.68 (( 78.39/10.68 (binunionT_lem) => 78.39/10.68 (( 78.39/10.68 (powersetT_lem) => 78.39/10.68 (( 78.39/10.68 (setminusT_lem) => 78.39/10.68 (( 78.39/10.68 (complementT_lem) => 78.39/10.68 (( 78.39/10.68 (setextT) => 78.39/10.68 (( 78.39/10.68 (subsetTI) => 78.39/10.68 (( 78.39/10.68 (powersetTI1) => 78.39/10.68 (( 78.39/10.68 (powersetTE1) => 78.39/10.68 (( 78.39/10.68 (complementTI1) => 78.39/10.68 (( 78.39/10.68 (complementTE1) => 78.39/10.68 (( 78.39/10.68 (binintersectTELcontra) => 78.39/10.68 (( 78.39/10.68 (binintersectTERcontra) => 78.39/10.68 (( 78.39/10.68 (contrasubsetT) => 78.39/10.68 (( 78.39/10.68 (contrasubsetT1) => 78.39/10.68 (( 78.39/10.68 (contrasubsetT2) => 78.39/10.68 (( 78.39/10.68 (contrasubsetT3) => 78.39/10.68 (( 78.39/10.68 (doubleComplementI1) => 78.39/10.68 (( 78.39/10.68 (doubleComplementE1) => 78.39/10.68 (( 78.39/10.68 (doubleComplementSub1) => 78.39/10.68 (( 78.39/10.68 (doubleComplementSub2) => 78.39/10.68 (( 78.39/10.68 (doubleComplementEq) => 78.39/10.68 (( 78.39/10.68 (complementTnotintersectT) => 78.39/10.68 (( 78.39/10.68 (complementImpComplementIntersect) => 78.39/10.68 (( 78.39/10.68 (complementSubsetComplementIntersect) => 78.39/10.68 (( 78.39/10.68 (complementInPowersetComplementIntersect) => 78.39/10.68 (( 78.39/10.68 (contraSubsetComplement) => 78.39/10.68 (( 78.39/10.68 (complementTcontraSubset) => 78.39/10.68 (( 78.39/10.68 (binunionTILcontra) => 78.39/10.68 (( 78.39/10.68 (binunionTIRcontra) => 78.39/10.68 (( 78.39/10.68 (inIntersectImpInUnion) => 78.39/10.68 (( 78.39/10.68 (inIntersectImpInUnion2) => 78.39/10.68 (( 78.39/10.68 (inIntersectImpInIntersectUnions) => 78.39/10.68 (( 78.39/10.68 (intersectInPowersetIntersectUnions) => 78.39/10.68 (( 78.39/10.68 (inComplementUnionImpNotIn1) => 78.39/10.68 (( 78.39/10.68 (inComplementUnionImpInComplement1) => 78.39/10.68 (( 78.39/10.68 (binunionTE) => 78.39/10.68 (( 78.39/10.68 (binunionTEcontra) => 78.39/10.68 (( 78.39/10.68 (demorgan2a1) => 78.39/10.68 (( 78.39/10.68 (complementUnionInPowersetComplement) => 78.39/10.68 (( 78.39/10.68 (demorgan2a2) => 78.39/10.68 (( 78.39/10.68 (demorgan1a) => 78.39/10.68 (( 78.39/10.68 (demorgan1b) => 78.39/10.68 (( 78.39/10.68 (demorgan1) => 78.39/10.68 (( 78.39/10.68 (demorgan2a) => 78.39/10.68 (( 78.39/10.68 (demorgan2b2) => 78.39/10.68 (( 78.39/10.68 (demorgan2b) => 78.39/10.68 (( 78.39/10.68 (demorgan2) => 78.39/10.68 (( 78.39/10.68 (woz13rule0) => 78.39/10.68 (( 78.39/10.68 (woz13rule1) => 78.39/10.68 (( 78.39/10.68 (woz13rule2) => 78.39/10.68 (( 78.39/10.68 (woz13rule3) => 78.39/10.68 (( 78.39/10.68 (woz13rule4) => 78.39/10.68 (( 78.39/10.68 (woz1_1) => 78.39/10.68 (( 78.39/10.68 (woz1_2) => 78.39/10.68 (( 78.39/10.68 (woz1_3) => 78.39/10.68 (( 78.39/10.68 (woz1_4) => 78.39/10.68 (( 78.39/10.68 (woz1_5) => 78.39/10.68 (( 78.39/10.68 (breln1all2) => 78.39/10.68 (( 78.39/10.68 (breln1SetBreln1) => 78.39/10.68 (( 78.39/10.68 (choice2fnsingleton) => 78.39/10.68 (( 78.39/10.68 (setOfPairsIsBReln1) => 78.39/10.68 (( 78.39/10.68 (breln1all1) => 78.39/10.68 (( 78.39/10.68 (subbreln1) => 78.39/10.68 (( 78.39/10.68 (eqbreln1) => 78.39/10.68 (( 78.39/10.68 (breln1invprop) => 78.39/10.68 (( 78.39/10.68 (breln1invI) => 78.39/10.68 (( 78.39/10.68 (breln1invE) => 78.39/10.68 (( 78.39/10.68 (breln1compprop) => 78.39/10.68 (( 78.39/10.68 (breln1compI) => 78.39/10.68 (( 78.39/10.68 (breln1compE) => 78.39/10.68 (( 78.39/10.68 (breln1compEex) => 78.39/10.68 (( 78.39/10.68 (breln1unionprop) => 78.39/10.68 (( 78.39/10.68 (breln1unionIL) => 78.39/10.68 (( 78.39/10.68 (breln1unionIR) => 78.39/10.68 (( 78.39/10.68 (breln1unionI) => 78.39/10.68 (( 78.39/10.68 (breln1unionE) => 78.39/10.68 (( 78.39/10.68 (breln1unionEcases) => 78.39/10.68 (( 78.39/10.68 (breln1unionCommutes) => 78.39/10.68 (( 78.39/10.68 (woz2Ex) => 78.39/10.68 (( 78.39/10.68 (woz2W) => 78.39/10.68 (( 78.39/10.68 (woz2A) => 78.39/10.68 (( 78.39/10.68 (woz2B) => 78.39/10.68 (( 78.39/10.68 (image1Ex) => 78.39/10.68 (( 78.39/10.68 (image1Ex1) => 78.39/10.68 (( 78.39/10.68 (image1Equiv) => 78.39/10.68 (( 78.39/10.68 (image1E) => 78.39/10.68 (( 78.39/10.68 (image1I) => 78.39/10.68 (( 78.39/10.68 (injFuncInInjFuncSet) => 78.39/10.68 (( 78.39/10.68 (injFuncSetFuncIn) => 78.39/10.68 (( 78.39/10.68 (injFuncSetFuncInj) => 78.39/10.68 (( 78.39/10.68 (surjFuncSetFuncIn) => 78.39/10.68 (( 78.39/10.68 (surjFuncSetFuncSurj) => 78.39/10.68 (( 78.39/10.68 (leftInvIsSurj) => 78.39/10.68 (( 78.39/10.68 (surjCantorThm) => 78.39/10.68 (( 78.39/10.68 (foundation2) => 78.39/10.68 (( 78.39/10.68 (notinself) => 78.39/10.68 (( 78.39/10.68 (notinself2) => 78.39/10.68 (( 78.39/10.68 (omegaSp) => 78.39/10.68 (( 78.39/10.68 (omegaSclos) => 78.39/10.68 (( 78.39/10.68 (peano0notS) => 78.39/10.68 (( 78.39/10.68 (peanoSinj) => 78.39/10.68 (( 78.39/10.68 (transitivesetOp1) => 78.39/10.68 (( 78.39/10.68 (binintTransitive) => 78.39/10.68 (( 78.39/10.68 (transitivesetOp2) => 78.39/10.68 (( 78.39/10.68 (setunionTransitive) => 78.39/10.68 (( 78.39/10.68 (ordinalMinLem1) => 78.39/10.68 (( 78.39/10.68 (!!) @ ( 78.39/10.68 ^[Y0 : $i]: 78.39/10.68 (( 78.39/10.68 (ordinal @ 78.39/10.68 Y0) => 78.39/10.68 (( 78.39/10.68 (!!) @ ( 78.39/10.68 ^[Y1 : $i]: 78.39/10.68 (( 78.39/10.68 (!!) @ ( 78.39/10.68 ^[Y2 : $i]: 78.39/10.68 (( 78.39/10.68 (in @ 78.39/10.68 Y2 @ 78.39/10.68 Y0) => 78.39/10.68 (( 78.39/10.68 (in @ 78.39/10.68 Y1 @ 78.39/10.68 Y2) => 78.39/10.68 (in @ 78.39/10.68 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 78.39/10.68 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1195])). 78.39/10.68 thf(zip_derived_cl1207, plain, 78.39/10.68 (~ (((upairset2E) => 78.39/10.68 (((upairsubunion) => 78.39/10.68 (((upairinpowunion) => 78.39/10.68 (((ubforcartprodlem1) => 78.39/10.68 (((ubforcartprodlem2) => 78.39/10.68 (((ubforcartprodlem3) => 78.39/10.68 (((cartprodpairin) => 78.39/10.68 (((cartprodmempair1) => 78.39/10.68 (((cartprodmempair) => 78.39/10.68 (((setunionE2) => 78.39/10.68 (((setunionsingleton1) => 78.39/10.68 (((setunionsingleton2) => 78.39/10.68 (((setunionsingleton) => 78.39/10.68 (((singletonprop) => 78.39/10.68 (((ex1E1) => 78.39/10.68 (((ex1I) => 78.39/10.68 (((ex1I2) => 78.39/10.68 (((singletonsuniq) => 78.39/10.68 (((setukpairinjL1) => 78.39/10.68 (((kfstsingleton) => 78.39/10.68 (((theprop) => 78.39/10.68 (((kfstpairEq) => 78.39/10.68 (((cartprodfstin) => 78.39/10.68 (((setukpairinjL2) => 78.39/10.68 (((setukpairinjL) => 78.39/10.68 (((setukpairinjR11) => 78.39/10.68 (((setukpairinjR12) => 78.39/10.68 (((setukpairinjR1) => 78.39/10.68 (((upairequniteq) => 78.39/10.68 (((setukpairinjR2) => 78.39/10.68 (( 78.39/10.68 (setukpairinjR) => 78.39/10.68 (( 78.39/10.68 (ksndsingleton) => 78.39/10.68 (( 78.39/10.68 (ksndpairEq) => 78.39/10.68 (( 78.39/10.68 (kpairsurjEq) => 78.39/10.68 (( 78.39/10.68 (cartprodsndin) => 78.39/10.68 (( 78.39/10.68 (cartprodpairmemEL) => 78.39/10.68 (( 78.39/10.68 (cartprodpairmemER) => 78.39/10.68 (( 78.39/10.68 (cartprodmempaircEq) => 78.39/10.68 (( 78.39/10.68 (cartprodfstpairEq) => 78.39/10.68 (( 78.39/10.68 (cartprodsndpairEq) => 78.39/10.68 (( 78.39/10.68 (cartprodpairsurjEq) => 78.39/10.68 (( 78.39/10.68 (dpsetconstrI) => 78.39/10.68 (( 78.39/10.68 (dpsetconstrSub) => 78.39/10.68 (( 78.39/10.68 (setOfPairsIsBReln) => 78.39/10.68 (( 78.39/10.68 (dpsetconstrERa) => 78.39/10.68 (( 78.39/10.68 (dpsetconstrEL1) => 78.39/10.68 (( 78.39/10.68 (dpsetconstrEL2) => 78.39/10.68 (( 78.39/10.68 (dpsetconstrER) => 78.39/10.68 (( 78.39/10.68 (funcImageSingleton) => 78.39/10.68 (( 78.39/10.68 (apProp) => 78.39/10.68 (( 78.39/10.68 (app) => 78.39/10.68 (( 78.39/10.68 (infuncsetfunc) => 78.39/10.68 (( 78.39/10.68 (ap2p) => 78.39/10.68 (( 78.39/10.68 (funcinfuncset) => 78.39/10.68 (( 78.39/10.68 (lamProp) => 78.39/10.68 (( 78.39/10.68 (lamp) => 78.39/10.68 (( 78.39/10.68 (lam2p) => 78.39/10.68 (( 78.39/10.68 (brelnall1) => 78.39/10.68 (( 78.39/10.68 (brelnall2) => 78.39/10.68 (( 78.39/10.68 (ex1E2) => 78.39/10.68 (( 78.39/10.68 (funcGraphProp1) => 78.39/10.68 (( 78.39/10.68 (funcGraphProp3) => 78.39/10.68 (( 78.39/10.68 (funcGraphProp2) => 78.39/10.68 (( 78.39/10.68 (funcextLem) => 78.39/10.68 (( 78.39/10.68 (funcGraphProp4) => 78.39/10.68 (( 78.39/10.68 (subbreln) => 78.39/10.68 (( 78.39/10.68 (eqbreln) => 78.39/10.68 (( 78.39/10.68 (funcext) => 78.39/10.68 (( 78.39/10.68 (funcext2) => 78.39/10.68 (( 78.39/10.68 (ap2apEq1) => 78.39/10.68 (( 78.39/10.68 (ap2apEq2) => 78.39/10.68 (( 78.39/10.68 (beta1) => 78.39/10.68 (( 78.39/10.68 (eta1) => 78.39/10.68 (( 78.39/10.68 (lam2lamEq) => 78.39/10.68 (( 78.39/10.68 (beta2) => 78.39/10.68 (( 78.39/10.68 (eta2) => 78.39/10.68 (( 78.39/10.68 (iffalseProp1) => 78.39/10.68 (( 78.39/10.68 (iffalseProp2) => 78.39/10.68 (( 78.39/10.68 (iftrueProp1) => 78.39/10.68 (( 78.39/10.68 (iftrueProp2) => 78.39/10.68 (( 78.39/10.68 (ifSingleton) => 78.39/10.68 (( 78.39/10.68 (ifp) => 78.39/10.68 (( 78.39/10.68 (theeq) => 78.39/10.68 (( 78.39/10.68 (iftrue) => 78.39/10.68 (( 78.39/10.68 (iffalse) => 78.39/10.68 (( 78.39/10.68 (iftrueorfalse) => 78.39/10.68 (( 78.39/10.68 (binintersectT_lem) => 78.39/10.68 (( 78.39/10.68 (binunionT_lem) => 78.39/10.68 (( 78.39/10.68 (powersetT_lem) => 78.39/10.68 (( 78.39/10.68 (setminusT_lem) => 78.39/10.68 (( 78.39/10.68 (complementT_lem) => 78.39/10.68 (( 78.39/10.68 (setextT) => 78.39/10.68 (( 78.39/10.68 (subsetTI) => 78.39/10.68 (( 78.39/10.68 (powersetTI1) => 78.39/10.68 (( 78.39/10.68 (powersetTE1) => 78.39/10.68 (( 78.39/10.68 (complementTI1) => 78.39/10.68 (( 78.39/10.68 (complementTE1) => 78.39/10.68 (( 78.39/10.68 (binintersectTELcontra) => 78.39/10.68 (( 78.39/10.68 (binintersectTERcontra) => 78.39/10.68 (( 78.39/10.68 (contrasubsetT) => 78.39/10.68 (( 78.39/10.68 (contrasubsetT1) => 78.39/10.68 (( 78.39/10.68 (contrasubsetT2) => 78.39/10.68 (( 78.39/10.68 (contrasubsetT3) => 78.39/10.68 (( 78.39/10.68 (doubleComplementI1) => 78.39/10.68 (( 78.39/10.68 (doubleComplementE1) => 78.39/10.68 (( 78.39/10.68 (doubleComplementSub1) => 78.39/10.68 (( 78.39/10.68 (doubleComplementSub2) => 78.39/10.68 (( 78.39/10.68 (doubleComplementEq) => 78.39/10.68 (( 78.39/10.68 (complementTnotintersectT) => 78.39/10.68 (( 78.39/10.68 (complementImpComplementIntersect) => 78.39/10.68 (( 78.39/10.68 (complementSubsetComplementIntersect) => 78.39/10.68 (( 78.39/10.68 (complementInPowersetComplementIntersect) => 78.39/10.68 (( 78.39/10.68 (contraSubsetComplement) => 78.39/10.68 (( 78.39/10.68 (complementTcontraSubset) => 78.39/10.68 (( 78.39/10.68 (binunionTILcontra) => 78.39/10.68 (( 78.39/10.68 (binunionTIRcontra) => 78.39/10.68 (( 78.39/10.68 (inIntersectImpInUnion) => 78.39/10.68 (( 78.39/10.68 (inIntersectImpInUnion2) => 78.39/10.68 (( 78.39/10.68 (inIntersectImpInIntersectUnions) => 78.39/10.68 (( 78.39/10.68 (intersectInPowersetIntersectUnions) => 78.39/10.68 (( 78.39/10.68 (inComplementUnionImpNotIn1) => 78.39/10.68 (( 78.39/10.68 (inComplementUnionImpInComplement1) => 78.39/10.68 (( 78.39/10.68 (binunionTE) => 78.39/10.68 (( 78.39/10.68 (binunionTEcontra) => 78.39/10.68 (( 78.39/10.68 (demorgan2a1) => 78.39/10.68 (( 78.39/10.68 (complementUnionInPowersetComplement) => 78.39/10.68 (( 78.39/10.68 (demorgan2a2) => 78.39/10.68 (( 78.39/10.68 (demorgan1a) => 78.39/10.68 (( 78.39/10.68 (demorgan1b) => 78.39/10.68 (( 78.39/10.68 (demorgan1) => 78.39/10.68 (( 78.39/10.68 (demorgan2a) => 78.39/10.68 (( 78.39/10.68 (demorgan2b2) => 78.39/10.68 (( 78.39/10.68 (demorgan2b) => 78.39/10.68 (( 78.39/10.68 (demorgan2) => 78.39/10.68 (( 78.39/10.68 (woz13rule0) => 78.39/10.68 (( 78.39/10.68 (woz13rule1) => 78.39/10.68 (( 78.39/10.68 (woz13rule2) => 78.39/10.68 (( 78.39/10.68 (woz13rule3) => 78.39/10.68 (( 78.39/10.68 (woz13rule4) => 78.39/10.68 (( 78.39/10.68 (woz1_1) => 78.39/10.68 (( 78.39/10.68 (woz1_2) => 78.39/10.68 (( 78.39/10.68 (woz1_3) => 78.39/10.68 (( 78.39/10.68 (woz1_4) => 78.39/10.68 (( 78.39/10.68 (woz1_5) => 78.39/10.68 (( 78.39/10.68 (breln1all2) => 78.39/10.68 (( 78.39/10.68 (breln1SetBreln1) => 78.39/10.68 (( 78.39/10.68 (choice2fnsingleton) => 78.39/10.68 (( 78.39/10.68 (setOfPairsIsBReln1) => 78.39/10.68 (( 78.39/10.68 (breln1all1) => 78.39/10.68 (( 78.39/10.68 (subbreln1) => 78.39/10.68 (( 78.39/10.68 (eqbreln1) => 78.39/10.68 (( 78.39/10.68 (breln1invprop) => 78.39/10.68 (( 78.39/10.68 (breln1invI) => 78.39/10.68 (( 78.39/10.68 (breln1invE) => 78.39/10.68 (( 78.39/10.68 (breln1compprop) => 78.39/10.68 (( 78.39/10.68 (breln1compI) => 78.39/10.68 (( 78.39/10.68 (breln1compE) => 78.39/10.68 (( 78.39/10.68 (breln1compEex) => 78.39/10.68 (( 78.39/10.68 (breln1unionprop) => 78.39/10.68 (( 78.39/10.68 (breln1unionIL) => 78.39/10.68 (( 78.39/10.68 (breln1unionIR) => 78.39/10.68 (( 78.39/10.68 (breln1unionI) => 78.39/10.68 (( 78.39/10.68 (breln1unionE) => 78.39/10.68 (( 78.39/10.68 (breln1unionEcases) => 78.39/10.68 (( 78.39/10.68 (breln1unionCommutes) => 78.39/10.68 (( 78.39/10.68 (woz2Ex) => 78.39/10.68 (( 78.39/10.68 (woz2W) => 78.39/10.68 (( 78.39/10.68 (woz2A) => 78.39/10.68 (( 78.39/10.68 (woz2B) => 78.39/10.68 (( 78.39/10.68 (image1Ex) => 78.39/10.68 (( 78.39/10.68 (image1Ex1) => 78.39/10.68 (( 78.39/10.68 (image1Equiv) => 78.39/10.68 (( 78.39/10.68 (image1E) => 78.39/10.68 (( 78.39/10.68 (image1I) => 78.39/10.68 (( 78.39/10.68 (injFuncInInjFuncSet) => 78.39/10.68 (( 78.39/10.68 (injFuncSetFuncIn) => 78.39/10.68 (( 78.39/10.68 (injFuncSetFuncInj) => 78.39/10.68 (( 78.39/10.68 (surjFuncSetFuncIn) => 78.39/10.68 (( 78.39/10.68 (surjFuncSetFuncSurj) => 78.39/10.68 (( 78.39/10.68 (leftInvIsSurj) => 78.39/10.68 (( 78.39/10.68 (surjCantorThm) => 78.39/10.68 (( 78.39/10.68 (foundation2) => 78.39/10.68 (( 78.39/10.68 (notinself) => 78.39/10.68 (( 78.39/10.68 (notinself2) => 78.39/10.68 (( 78.39/10.68 (omegaSp) => 78.39/10.68 (( 78.39/10.68 (omegaSclos) => 78.39/10.68 (( 78.39/10.68 (peano0notS) => 78.39/10.68 (( 78.39/10.68 (peanoSinj) => 78.39/10.68 (( 78.39/10.68 (transitivesetOp1) => 78.39/10.68 (( 78.39/10.68 (binintTransitive) => 78.39/10.68 (( 78.39/10.68 (transitivesetOp2) => 78.39/10.68 (( 78.39/10.68 (setunionTransitive) => 78.39/10.68 (( 78.39/10.68 (ordinalMinLem1) => 78.39/10.68 (( 78.39/10.68 (!!) @ ( 78.39/10.68 ^[Y0 : $i]: 78.39/10.68 (( 78.39/10.68 (ordinal @ 78.39/10.68 Y0) => 78.39/10.68 (( 78.39/10.68 (!!) @ ( 78.39/10.68 ^[Y1 : $i]: 78.39/10.68 (( 78.39/10.68 (!!) @ ( 78.39/10.68 ^[Y2 : $i]: 78.39/10.68 (( 78.39/10.68 (in @ 78.39/10.68 Y2 @ 78.39/10.68 Y0) => 78.39/10.68 (( 78.39/10.68 (in @ 78.39/10.68 Y1 @ 78.39/10.68 Y2) => 78.39/10.68 (in @ 78.39/10.68 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 78.39/10.68 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1202])). 78.39/10.68 thf(zip_derived_cl1212, plain, 78.39/10.68 (~ (((upairsubunion) => 78.39/10.68 (((upairinpowunion) => 78.39/10.68 (((ubforcartprodlem1) => 78.39/10.68 (((ubforcartprodlem2) => 78.39/10.68 (((ubforcartprodlem3) => 78.39/10.68 (((cartprodpairin) => 78.39/10.68 (((cartprodmempair1) => 78.39/10.68 (((cartprodmempair) => 78.39/10.68 (((setunionE2) => 78.39/10.68 (((setunionsingleton1) => 78.39/10.68 (((setunionsingleton2) => 78.39/10.68 (((setunionsingleton) => 78.39/10.68 (((singletonprop) => 78.39/10.68 (((ex1E1) => 78.39/10.68 (((ex1I) => 78.39/10.68 (((ex1I2) => 78.39/10.68 (((singletonsuniq) => 78.39/10.68 (((setukpairinjL1) => 78.39/10.68 (((kfstsingleton) => 78.39/10.68 (((theprop) => 78.39/10.68 (((kfstpairEq) => 78.39/10.68 (((cartprodfstin) => 78.39/10.68 (((setukpairinjL2) => 78.39/10.68 (((setukpairinjL) => 78.39/10.68 (((setukpairinjR11) => 78.39/10.68 (((setukpairinjR12) => 78.39/10.68 (((setukpairinjR1) => 78.39/10.68 (((upairequniteq) => 78.39/10.68 (((setukpairinjR2) => 78.39/10.68 (((setukpairinjR) => 78.39/10.68 (( 78.39/10.68 (ksndsingleton) => 78.39/10.68 (( 78.39/10.68 (ksndpairEq) => 78.39/10.68 (( 78.39/10.68 (kpairsurjEq) => 78.39/10.68 (( 78.39/10.68 (cartprodsndin) => 78.39/10.68 (( 78.39/10.68 (cartprodpairmemEL) => 78.39/10.68 (( 78.39/10.68 (cartprodpairmemER) => 78.39/10.68 (( 78.39/10.68 (cartprodmempaircEq) => 78.39/10.68 (( 78.39/10.68 (cartprodfstpairEq) => 78.39/10.68 (( 78.39/10.68 (cartprodsndpairEq) => 78.39/10.68 (( 78.39/10.68 (cartprodpairsurjEq) => 78.39/10.68 (( 78.39/10.68 (dpsetconstrI) => 78.39/10.68 (( 78.39/10.68 (dpsetconstrSub) => 78.39/10.68 (( 78.39/10.68 (setOfPairsIsBReln) => 78.39/10.68 (( 78.39/10.68 (dpsetconstrERa) => 78.39/10.68 (( 78.39/10.68 (dpsetconstrEL1) => 78.39/10.68 (( 78.39/10.68 (dpsetconstrEL2) => 78.39/10.68 (( 78.39/10.68 (dpsetconstrER) => 78.39/10.68 (( 78.39/10.68 (funcImageSingleton) => 78.39/10.68 (( 78.39/10.68 (apProp) => 78.39/10.68 (( 78.39/10.68 (app) => 78.39/10.68 (( 78.39/10.68 (infuncsetfunc) => 78.39/10.68 (( 78.39/10.68 (ap2p) => 78.39/10.68 (( 78.39/10.68 (funcinfuncset) => 78.39/10.68 (( 78.39/10.68 (lamProp) => 78.39/10.68 (( 78.39/10.68 (lamp) => 78.39/10.68 (( 78.39/10.68 (lam2p) => 78.39/10.68 (( 78.39/10.68 (brelnall1) => 78.39/10.68 (( 78.39/10.68 (brelnall2) => 78.39/10.68 (( 78.39/10.68 (ex1E2) => 78.39/10.68 (( 78.39/10.68 (funcGraphProp1) => 78.39/10.68 (( 78.39/10.68 (funcGraphProp3) => 78.39/10.68 (( 78.39/10.68 (funcGraphProp2) => 78.39/10.68 (( 78.39/10.68 (funcextLem) => 78.39/10.68 (( 78.39/10.68 (funcGraphProp4) => 78.39/10.68 (( 78.39/10.68 (subbreln) => 78.39/10.68 (( 78.39/10.68 (eqbreln) => 78.39/10.68 (( 78.39/10.68 (funcext) => 78.39/10.68 (( 78.39/10.68 (funcext2) => 78.39/10.68 (( 78.39/10.68 (ap2apEq1) => 78.39/10.68 (( 78.39/10.68 (ap2apEq2) => 78.39/10.68 (( 78.39/10.68 (beta1) => 78.39/10.68 (( 78.39/10.68 (eta1) => 78.39/10.68 (( 78.39/10.68 (lam2lamEq) => 78.39/10.68 (( 78.39/10.68 (beta2) => 78.39/10.68 (( 78.39/10.68 (eta2) => 78.39/10.68 (( 78.39/10.68 (iffalseProp1) => 78.39/10.68 (( 78.39/10.68 (iffalseProp2) => 78.39/10.68 (( 78.39/10.68 (iftrueProp1) => 78.39/10.68 (( 78.39/10.68 (iftrueProp2) => 78.39/10.68 (( 78.39/10.68 (ifSingleton) => 78.39/10.68 (( 78.39/10.68 (ifp) => 78.39/10.68 (( 78.39/10.68 (theeq) => 78.39/10.68 (( 78.39/10.68 (iftrue) => 78.39/10.68 (( 78.39/10.68 (iffalse) => 78.39/10.68 (( 78.39/10.68 (iftrueorfalse) => 78.39/10.68 (( 78.39/10.68 (binintersectT_lem) => 78.39/10.68 (( 78.39/10.68 (binunionT_lem) => 78.39/10.68 (( 78.39/10.68 (powersetT_lem) => 78.39/10.68 (( 78.39/10.68 (setminusT_lem) => 78.39/10.68 (( 78.39/10.68 (complementT_lem) => 78.39/10.68 (( 78.39/10.68 (setextT) => 78.39/10.68 (( 78.39/10.68 (subsetTI) => 78.39/10.68 (( 78.39/10.68 (powersetTI1) => 78.39/10.68 (( 78.39/10.68 (powersetTE1) => 78.39/10.68 (( 78.39/10.68 (complementTI1) => 78.39/10.68 (( 78.39/10.68 (complementTE1) => 78.39/10.68 (( 78.39/10.68 (binintersectTELcontra) => 78.39/10.68 (( 78.39/10.68 (binintersectTERcontra) => 78.39/10.68 (( 78.39/10.68 (contrasubsetT) => 78.39/10.68 (( 78.39/10.68 (contrasubsetT1) => 78.39/10.68 (( 78.39/10.68 (contrasubsetT2) => 78.39/10.68 (( 78.39/10.68 (contrasubsetT3) => 78.39/10.68 (( 78.39/10.68 (doubleComplementI1) => 78.39/10.68 (( 78.39/10.68 (doubleComplementE1) => 78.39/10.68 (( 78.39/10.68 (doubleComplementSub1) => 78.39/10.68 (( 78.39/10.68 (doubleComplementSub2) => 78.39/10.68 (( 78.39/10.68 (doubleComplementEq) => 78.39/10.68 (( 78.39/10.68 (complementTnotintersectT) => 78.39/10.68 (( 78.39/10.68 (complementImpComplementIntersect) => 78.39/10.68 (( 78.39/10.68 (complementSubsetComplementIntersect) => 78.39/10.68 (( 78.39/10.68 (complementInPowersetComplementIntersect) => 78.39/10.68 (( 78.39/10.68 (contraSubsetComplement) => 78.39/10.68 (( 78.39/10.68 (complementTcontraSubset) => 78.39/10.68 (( 78.39/10.68 (binunionTILcontra) => 78.39/10.68 (( 78.39/10.68 (binunionTIRcontra) => 78.39/10.68 (( 78.39/10.68 (inIntersectImpInUnion) => 78.39/10.68 (( 78.39/10.68 (inIntersectImpInUnion2) => 78.39/10.68 (( 78.39/10.68 (inIntersectImpInIntersectUnions) => 78.39/10.68 (( 78.39/10.68 (intersectInPowersetIntersectUnions) => 78.39/10.68 (( 78.39/10.68 (inComplementUnionImpNotIn1) => 78.39/10.68 (( 78.39/10.68 (inComplementUnionImpInComplement1) => 78.39/10.68 (( 78.39/10.68 (binunionTE) => 78.39/10.68 (( 78.39/10.68 (binunionTEcontra) => 78.39/10.68 (( 78.39/10.68 (demorgan2a1) => 78.39/10.68 (( 78.39/10.68 (complementUnionInPowersetComplement) => 78.39/10.68 (( 78.39/10.68 (demorgan2a2) => 78.39/10.68 (( 78.39/10.68 (demorgan1a) => 78.39/10.68 (( 78.39/10.68 (demorgan1b) => 78.39/10.68 (( 78.39/10.68 (demorgan1) => 78.39/10.68 (( 78.39/10.68 (demorgan2a) => 78.39/10.68 (( 78.39/10.68 (demorgan2b2) => 78.39/10.68 (( 78.39/10.68 (demorgan2b) => 78.39/10.68 (( 78.39/10.68 (demorgan2) => 78.39/10.68 (( 78.39/10.68 (woz13rule0) => 78.39/10.68 (( 78.39/10.68 (woz13rule1) => 78.39/10.68 (( 78.39/10.68 (woz13rule2) => 78.39/10.68 (( 78.39/10.68 (woz13rule3) => 78.39/10.68 (( 78.39/10.68 (woz13rule4) => 78.39/10.68 (( 78.39/10.68 (woz1_1) => 78.39/10.68 (( 78.39/10.68 (woz1_2) => 78.39/10.68 (( 78.39/10.68 (woz1_3) => 78.39/10.68 (( 78.39/10.68 (woz1_4) => 78.39/10.68 (( 78.39/10.68 (woz1_5) => 78.39/10.68 (( 78.39/10.68 (breln1all2) => 78.39/10.68 (( 78.39/10.68 (breln1SetBreln1) => 78.39/10.68 (( 78.39/10.68 (choice2fnsingleton) => 78.39/10.68 (( 78.39/10.68 (setOfPairsIsBReln1) => 78.39/10.68 (( 78.39/10.68 (breln1all1) => 78.39/10.68 (( 78.39/10.68 (subbreln1) => 78.39/10.68 (( 78.39/10.68 (eqbreln1) => 78.39/10.68 (( 78.39/10.68 (breln1invprop) => 78.39/10.68 (( 78.39/10.68 (breln1invI) => 78.39/10.68 (( 78.39/10.68 (breln1invE) => 78.39/10.68 (( 78.39/10.68 (breln1compprop) => 78.39/10.68 (( 78.39/10.68 (breln1compI) => 78.39/10.68 (( 78.39/10.68 (breln1compE) => 78.39/10.68 (( 78.39/10.68 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78.39/10.69 (injFuncInInjFuncSet) => 78.39/10.69 (( 78.39/10.69 (injFuncSetFuncIn) => 78.39/10.69 (( 78.39/10.69 (injFuncSetFuncInj) => 78.39/10.69 (( 78.39/10.69 (surjFuncSetFuncIn) => 78.39/10.69 (( 78.39/10.69 (surjFuncSetFuncSurj) => 78.39/10.69 (( 78.39/10.69 (leftInvIsSurj) => 78.39/10.69 (( 78.39/10.69 (surjCantorThm) => 78.39/10.69 (( 78.39/10.69 (foundation2) => 78.39/10.69 (( 78.39/10.69 (notinself) => 78.39/10.69 (( 78.39/10.69 (notinself2) => 78.39/10.69 (( 78.39/10.69 (omegaSp) => 78.39/10.69 (( 78.39/10.69 (omegaSclos) => 78.39/10.69 (( 78.39/10.69 (peano0notS) => 78.39/10.69 (( 78.39/10.69 (peanoSinj) => 78.39/10.69 (( 78.39/10.69 (transitivesetOp1) => 78.39/10.69 (( 78.39/10.69 (binintTransitive) => 78.39/10.69 (( 78.39/10.69 (transitivesetOp2) => 78.39/10.69 (( 78.39/10.69 (setunionTransitive) => 78.39/10.69 (( 78.39/10.69 (ordinalMinLem1) => 78.39/10.69 (( 78.39/10.69 (!!) @ ( 78.39/10.69 ^[Y0 : $i]: 78.39/10.69 (( 78.39/10.69 (ordinal @ 78.39/10.69 Y0) => 78.39/10.69 (( 78.39/10.69 (!!) @ ( 78.39/10.69 ^[Y1 : $i]: 78.39/10.69 (( 78.39/10.69 (!!) @ ( 78.39/10.69 ^[Y2 : $i]: 78.39/10.69 (( 78.39/10.69 (in @ 78.39/10.69 Y2 @ 78.39/10.69 Y0) => 78.39/10.69 (( 78.39/10.69 (in @ 78.39/10.69 Y1 @ 78.39/10.69 Y2) => 78.39/10.69 (in @ 78.39/10.69 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 78.39/10.69 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1224])). 78.39/10.69 thf(zip_derived_cl1237, plain, 78.39/10.69 (~ (((ubforcartprodlem3) => 78.39/10.69 (((cartprodpairin) => 78.39/10.69 (((cartprodmempair1) => 78.39/10.69 (((cartprodmempair) => 78.39/10.69 (((setunionE2) => 78.39/10.69 (((setunionsingleton1) => 78.39/10.69 (((setunionsingleton2) => 78.39/10.69 (((setunionsingleton) => 78.39/10.69 (((singletonprop) => 78.39/10.69 (((ex1E1) => 78.39/10.69 (((ex1I) => 78.39/10.69 (((ex1I2) => 78.39/10.69 (((singletonsuniq) => 78.39/10.69 (((setukpairinjL1) => 78.39/10.69 (((kfstsingleton) => 78.39/10.69 (((theprop) => 78.39/10.69 (((kfstpairEq) => 78.39/10.69 (((cartprodfstin) => 78.39/10.69 (((setukpairinjL2) => 78.39/10.69 (((setukpairinjL) => 78.39/10.69 (((setukpairinjR11) => 78.39/10.69 (((setukpairinjR12) => 78.39/10.69 (((setukpairinjR1) => 78.39/10.69 (((upairequniteq) => 78.39/10.69 (((setukpairinjR2) => 78.39/10.69 (((setukpairinjR) => 78.39/10.69 (((ksndsingleton) => 78.39/10.69 (((ksndpairEq) => 78.39/10.69 (((kpairsurjEq) => 78.39/10.69 (((cartprodsndin) => 78.39/10.69 (( 78.39/10.69 (cartprodpairmemEL) => 78.39/10.69 (( 78.39/10.69 (cartprodpairmemER) => 78.39/10.69 (( 78.39/10.69 (cartprodmempaircEq) => 78.39/10.69 (( 78.39/10.69 (cartprodfstpairEq) => 78.39/10.69 (( 78.39/10.69 (cartprodsndpairEq) => 78.39/10.69 (( 78.39/10.69 (cartprodpairsurjEq) => 78.39/10.69 (( 78.39/10.69 (dpsetconstrI) => 78.39/10.69 (( 78.39/10.69 (dpsetconstrSub) => 78.39/10.69 (( 78.39/10.69 (setOfPairsIsBReln) => 78.39/10.69 (( 78.39/10.69 (dpsetconstrERa) => 78.39/10.69 (( 78.39/10.69 (dpsetconstrEL1) => 78.39/10.69 (( 78.39/10.69 (dpsetconstrEL2) => 78.39/10.69 (( 78.39/10.69 (dpsetconstrER) => 78.39/10.69 (( 78.39/10.69 (funcImageSingleton) => 78.39/10.69 (( 78.39/10.69 (apProp) => 78.39/10.69 (( 78.39/10.69 (app) => 78.39/10.69 (( 78.39/10.69 (infuncsetfunc) => 78.39/10.69 (( 78.39/10.69 (ap2p) => 78.39/10.69 (( 78.39/10.69 (funcinfuncset) => 78.39/10.69 (( 78.39/10.69 (lamProp) => 78.39/10.69 (( 78.39/10.69 (lamp) => 78.39/10.69 (( 78.39/10.69 (lam2p) => 78.39/10.69 (( 78.39/10.69 (brelnall1) => 78.39/10.69 (( 78.39/10.69 (brelnall2) => 78.39/10.69 (( 78.39/10.69 (ex1E2) => 78.39/10.69 (( 78.39/10.69 (funcGraphProp1) => 78.39/10.69 (( 78.39/10.69 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(iftrueorfalse) => 78.39/10.69 (( 78.39/10.69 (binintersectT_lem) => 78.39/10.69 (( 78.39/10.69 (binunionT_lem) => 78.39/10.69 (( 78.39/10.69 (powersetT_lem) => 78.39/10.69 (( 78.39/10.69 (setminusT_lem) => 78.39/10.69 (( 78.39/10.69 (complementT_lem) => 78.39/10.69 (( 78.39/10.69 (setextT) => 78.39/10.69 (( 78.39/10.69 (subsetTI) => 78.39/10.69 (( 78.39/10.69 (powersetTI1) => 78.39/10.69 (( 78.39/10.69 (powersetTE1) => 78.39/10.69 (( 78.39/10.69 (complementTI1) => 78.39/10.69 (( 78.39/10.69 (complementTE1) => 78.39/10.69 (( 78.39/10.69 (binintersectTELcontra) => 78.39/10.69 (( 78.39/10.69 (binintersectTERcontra) => 78.39/10.69 (( 78.39/10.69 (contrasubsetT) => 78.39/10.69 (( 78.39/10.69 (contrasubsetT1) => 78.39/10.69 (( 78.39/10.69 (contrasubsetT2) => 78.39/10.69 (( 78.39/10.69 (contrasubsetT3) => 78.39/10.69 (( 78.39/10.69 (doubleComplementI1) => 78.39/10.69 (( 78.39/10.69 (doubleComplementE1) => 78.39/10.69 (( 78.39/10.69 (doubleComplementSub1) => 78.39/10.69 (( 78.39/10.69 (doubleComplementSub2) => 78.39/10.69 (( 78.39/10.69 (doubleComplementEq) => 78.39/10.69 (( 78.39/10.69 (complementTnotintersectT) => 78.39/10.69 (( 78.39/10.69 (complementImpComplementIntersect) => 78.39/10.69 (( 78.39/10.69 (complementSubsetComplementIntersect) => 78.39/10.69 (( 78.39/10.69 (complementInPowersetComplementIntersect) => 78.39/10.69 (( 78.39/10.69 (contraSubsetComplement) => 78.39/10.69 (( 78.39/10.69 (complementTcontraSubset) => 78.39/10.69 (( 78.39/10.69 (binunionTILcontra) => 78.39/10.69 (( 78.39/10.69 (binunionTIRcontra) => 78.39/10.69 (( 78.39/10.69 (inIntersectImpInUnion) => 78.39/10.69 (( 78.39/10.69 (inIntersectImpInUnion2) => 78.39/10.69 (( 78.39/10.69 (inIntersectImpInIntersectUnions) => 78.39/10.69 (( 78.39/10.69 (intersectInPowersetIntersectUnions) => 78.39/10.69 (( 78.39/10.69 (inComplementUnionImpNotIn1) => 78.39/10.69 (( 78.39/10.69 (inComplementUnionImpInComplement1) => 78.39/10.69 (( 78.39/10.69 (binunionTE) => 78.39/10.69 (( 78.39/10.69 (binunionTEcontra) => 78.39/10.69 (( 78.39/10.69 (demorgan2a1) => 78.39/10.69 (( 78.39/10.69 (complementUnionInPowersetComplement) => 78.39/10.69 (( 78.39/10.69 (demorgan2a2) => 78.39/10.69 (( 78.39/10.69 (demorgan1a) => 78.39/10.69 (( 78.39/10.69 (demorgan1b) => 78.39/10.69 (( 78.39/10.69 (demorgan1) => 78.39/10.69 (( 78.39/10.69 (demorgan2a) => 78.39/10.69 (( 78.39/10.69 (demorgan2b2) => 78.39/10.69 (( 78.39/10.69 (demorgan2b) => 78.39/10.69 (( 78.39/10.69 (demorgan2) => 78.39/10.69 (( 78.39/10.69 (woz13rule0) => 78.39/10.69 (( 78.39/10.69 (woz13rule1) => 78.39/10.69 (( 78.39/10.69 (woz13rule2) => 78.39/10.69 (( 78.39/10.69 (woz13rule3) => 78.39/10.69 (( 78.39/10.69 (woz13rule4) => 78.39/10.69 (( 78.39/10.69 (woz1_1) => 78.39/10.69 (( 78.39/10.69 (woz1_2) => 78.39/10.69 (( 78.39/10.69 (woz1_3) => 78.39/10.69 (( 78.39/10.69 (woz1_4) => 78.39/10.69 (( 78.39/10.69 (woz1_5) => 78.39/10.69 (( 78.39/10.69 (breln1all2) => 78.39/10.69 (( 78.39/10.69 (breln1SetBreln1) => 78.39/10.69 (( 78.39/10.69 (choice2fnsingleton) => 78.39/10.69 (( 78.39/10.69 (setOfPairsIsBReln1) => 78.39/10.69 (( 78.39/10.69 (breln1all1) => 78.39/10.69 (( 78.39/10.69 (subbreln1) => 78.39/10.69 (( 78.39/10.69 (eqbreln1) => 78.39/10.69 (( 78.39/10.69 (breln1invprop) => 78.39/10.69 (( 78.39/10.69 (breln1invI) => 78.39/10.69 (( 78.39/10.69 (breln1invE) => 78.39/10.69 (( 78.39/10.69 (breln1compprop) => 78.39/10.69 (( 78.39/10.69 (breln1compI) => 78.39/10.69 (( 78.39/10.69 (breln1compE) => 78.39/10.69 (( 78.39/10.69 (breln1compEex) => 78.39/10.69 (( 78.39/10.69 (breln1unionprop) => 78.39/10.69 (( 78.39/10.69 (breln1unionIL) => 78.39/10.69 (( 78.39/10.69 (breln1unionIR) => 78.39/10.69 (( 78.39/10.69 (breln1unionI) => 78.39/10.69 (( 78.39/10.69 (breln1unionE) => 78.39/10.69 (( 78.39/10.69 (breln1unionEcases) => 78.39/10.69 (( 78.39/10.69 (breln1unionCommutes) => 78.39/10.69 (( 78.39/10.69 (woz2Ex) => 78.39/10.69 (( 78.39/10.69 (woz2W) => 78.39/10.69 (( 78.39/10.69 (woz2A) => 78.39/10.69 (( 78.39/10.69 (woz2B) => 78.39/10.69 (( 78.39/10.69 (image1Ex) => 78.39/10.69 (( 78.39/10.69 (image1Ex1) => 78.39/10.69 (( 78.39/10.69 (image1Equiv) => 78.39/10.69 (( 78.39/10.69 (image1E) => 78.39/10.69 (( 78.39/10.69 (image1I) => 78.39/10.69 (( 78.39/10.69 (injFuncInInjFuncSet) => 78.39/10.69 (( 78.39/10.69 (injFuncSetFuncIn) => 78.39/10.69 (( 78.39/10.69 (injFuncSetFuncInj) => 78.39/10.69 (( 78.39/10.69 (surjFuncSetFuncIn) => 78.39/10.69 (( 78.39/10.69 (surjFuncSetFuncSurj) => 78.39/10.69 (( 78.39/10.69 (leftInvIsSurj) => 78.39/10.69 (( 78.39/10.69 (surjCantorThm) => 78.39/10.69 (( 78.39/10.69 (foundation2) => 78.39/10.69 (( 78.39/10.69 (notinself) => 78.39/10.69 (( 78.39/10.69 (notinself2) => 78.39/10.69 (( 78.39/10.69 (omegaSp) => 78.39/10.69 (( 78.39/10.69 (omegaSclos) => 78.39/10.69 (( 78.39/10.69 (peano0notS) => 78.39/10.69 (( 78.39/10.69 (peanoSinj) => 78.39/10.69 (( 78.39/10.69 (transitivesetOp1) => 78.39/10.69 (( 78.39/10.69 (binintTransitive) => 78.39/10.69 (( 78.39/10.69 (transitivesetOp2) => 78.39/10.69 (( 78.39/10.69 (setunionTransitive) => 78.39/10.69 (( 78.39/10.69 (ordinalMinLem1) => 78.39/10.69 (( 78.39/10.69 (!!) @ ( 78.39/10.69 ^[Y0 : $i]: 78.39/10.69 (( 78.39/10.69 (ordinal @ 78.39/10.69 Y0) => 78.39/10.69 (( 78.39/10.69 (!!) @ ( 78.39/10.69 ^[Y1 : $i]: 78.39/10.69 (( 78.39/10.69 (!!) @ ( 78.39/10.69 ^[Y2 : $i]: 78.39/10.69 (( 78.39/10.69 (in @ 78.39/10.69 Y2 @ 78.39/10.69 Y0) => 78.39/10.69 (( 78.39/10.69 (in @ 78.39/10.69 Y1 @ 78.39/10.69 Y2) => 78.39/10.69 (in @ 78.39/10.69 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 78.39/10.69 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1230])). 78.39/10.69 thf(zip_derived_cl1244, plain, 78.39/10.69 (~ (((cartprodpairin) => 78.39/10.69 (((cartprodmempair1) => 78.39/10.69 (((cartprodmempair) => 78.39/10.69 (((setunionE2) => 78.39/10.69 (((setunionsingleton1) => 78.39/10.69 (((setunionsingleton2) => 78.39/10.69 (((setunionsingleton) => 78.39/10.69 (((singletonprop) => 78.39/10.69 (((ex1E1) => 78.39/10.69 (((ex1I) => 78.39/10.69 (((ex1I2) => 78.39/10.69 (((singletonsuniq) => 78.39/10.69 (((setukpairinjL1) => 78.39/10.69 (((kfstsingleton) => 78.39/10.69 (((theprop) => 78.39/10.69 (((kfstpairEq) => 78.39/10.69 (((cartprodfstin) => 78.39/10.69 (((setukpairinjL2) => 78.39/10.69 (((setukpairinjL) => 78.39/10.69 (((setukpairinjR11) => 78.39/10.69 (((setukpairinjR12) => 78.39/10.69 (((setukpairinjR1) => 78.39/10.69 (((upairequniteq) => 78.39/10.69 (((setukpairinjR2) => 78.39/10.69 (((setukpairinjR) => 78.39/10.69 (((ksndsingleton) => 78.39/10.69 (((ksndpairEq) => 78.39/10.69 (((kpairsurjEq) => 78.39/10.69 (((cartprodsndin) => 78.39/10.69 (((cartprodpairmemEL) => 78.39/10.69 (( 78.39/10.69 (cartprodpairmemER) => 78.39/10.69 (( 78.39/10.69 (cartprodmempaircEq) => 78.39/10.69 (( 78.39/10.69 (cartprodfstpairEq) => 78.39/10.69 (( 78.39/10.69 (cartprodsndpairEq) => 78.39/10.69 (( 78.39/10.69 (cartprodpairsurjEq) => 78.39/10.69 (( 78.39/10.69 (dpsetconstrI) => 78.39/10.69 (( 78.39/10.69 (dpsetconstrSub) => 78.39/10.69 (( 78.39/10.69 (setOfPairsIsBReln) => 78.39/10.69 (( 78.39/10.69 (dpsetconstrERa) => 78.39/10.69 (( 78.39/10.69 (dpsetconstrEL1) => 78.39/10.69 (( 78.39/10.69 (dpsetconstrEL2) => 78.39/10.69 (( 78.39/10.69 (dpsetconstrER) => 78.39/10.69 (( 78.39/10.69 (funcImageSingleton) => 78.39/10.69 (( 78.39/10.69 (apProp) => 78.39/10.69 (( 78.39/10.69 (app) => 78.39/10.69 (( 78.39/10.69 (infuncsetfunc) => 78.39/10.69 (( 78.39/10.69 (ap2p) => 78.39/10.69 (( 78.39/10.69 (funcinfuncset) => 78.39/10.69 (( 78.39/10.69 (lamProp) => 78.39/10.69 (( 78.39/10.69 (lamp) => 78.39/10.69 (( 78.39/10.69 (lam2p) => 78.39/10.69 (( 78.39/10.69 (brelnall1) => 78.39/10.69 (( 78.39/10.69 (brelnall2) => 78.39/10.69 (( 78.39/10.69 (ex1E2) => 78.39/10.69 (( 78.39/10.69 (funcGraphProp1) => 78.39/10.69 (( 78.39/10.69 (funcGraphProp3) => 78.39/10.69 (( 78.39/10.69 (funcGraphProp2) => 78.39/10.69 (( 78.39/10.69 (funcextLem) => 78.39/10.69 (( 78.39/10.69 (funcGraphProp4) => 78.39/10.69 (( 78.39/10.69 (subbreln) => 78.39/10.69 (( 78.39/10.69 (eqbreln) => 78.39/10.69 (( 78.39/10.69 (funcext) => 78.39/10.69 (( 78.39/10.69 (funcext2) => 78.39/10.69 (( 78.39/10.69 (ap2apEq1) => 78.39/10.69 (( 78.39/10.69 (ap2apEq2) => 78.39/10.69 (( 78.39/10.69 (beta1) => 78.39/10.69 (( 78.39/10.69 (eta1) => 78.39/10.69 (( 78.39/10.69 (lam2lamEq) => 78.39/10.69 (( 78.39/10.69 (beta2) => 78.39/10.69 (( 78.39/10.69 (eta2) => 78.39/10.69 (( 78.39/10.69 (iffalseProp1) => 78.39/10.69 (( 78.39/10.69 (iffalseProp2) => 78.39/10.69 (( 78.39/10.69 (iftrueProp1) => 78.39/10.69 (( 78.39/10.69 (iftrueProp2) => 78.39/10.69 (( 78.39/10.69 (ifSingleton) => 78.39/10.69 (( 78.39/10.69 (ifp) => 78.39/10.69 (( 78.39/10.69 (theeq) => 78.39/10.69 (( 78.39/10.69 (iftrue) => 78.39/10.69 (( 78.39/10.69 (iffalse) => 78.39/10.69 (( 78.39/10.69 (iftrueorfalse) => 78.39/10.69 (( 78.39/10.69 (binintersectT_lem) => 78.39/10.69 (( 78.39/10.69 (binunionT_lem) => 78.39/10.69 (( 78.39/10.69 (powersetT_lem) => 78.39/10.69 (( 78.39/10.69 (setminusT_lem) => 78.39/10.69 (( 78.39/10.69 (complementT_lem) => 78.39/10.69 (( 78.39/10.69 (setextT) => 78.39/10.69 (( 78.39/10.69 (subsetTI) => 78.39/10.69 (( 78.39/10.69 (powersetTI1) => 78.39/10.69 (( 78.39/10.69 (powersetTE1) => 78.39/10.69 (( 78.39/10.69 (complementTI1) => 78.39/10.69 (( 78.39/10.69 (complementTE1) => 78.39/10.69 (( 78.39/10.69 (binintersectTELcontra) => 78.39/10.69 (( 78.39/10.69 (binintersectTERcontra) => 78.39/10.69 (( 78.39/10.69 (contrasubsetT) => 78.39/10.69 (( 78.39/10.69 (contrasubsetT1) => 78.39/10.69 (( 78.39/10.69 (contrasubsetT2) => 78.39/10.69 (( 78.39/10.69 (contrasubsetT3) => 78.39/10.69 (( 78.39/10.69 (doubleComplementI1) => 78.39/10.69 (( 78.39/10.69 (doubleComplementE1) => 78.39/10.69 (( 78.39/10.69 (doubleComplementSub1) => 78.39/10.69 (( 78.39/10.69 (doubleComplementSub2) => 78.39/10.69 (( 78.39/10.69 (doubleComplementEq) => 78.39/10.69 (( 78.39/10.69 (complementTnotintersectT) => 78.39/10.69 (( 78.39/10.69 (complementImpComplementIntersect) => 78.39/10.69 (( 78.39/10.69 (complementSubsetComplementIntersect) => 78.39/10.69 (( 78.39/10.69 (complementInPowersetComplementIntersect) => 78.39/10.69 (( 78.39/10.69 (contraSubsetComplement) => 78.39/10.69 (( 78.39/10.69 (complementTcontraSubset) => 78.39/10.69 (( 78.39/10.69 (binunionTILcontra) => 78.39/10.69 (( 78.39/10.69 (binunionTIRcontra) => 78.39/10.69 (( 78.39/10.69 (inIntersectImpInUnion) => 78.39/10.69 (( 78.39/10.69 (inIntersectImpInUnion2) => 78.39/10.69 (( 78.39/10.69 (inIntersectImpInIntersectUnions) => 78.39/10.69 (( 78.39/10.69 (intersectInPowersetIntersectUnions) => 78.39/10.69 (( 78.39/10.69 (inComplementUnionImpNotIn1) => 78.39/10.69 (( 78.39/10.69 (inComplementUnionImpInComplement1) => 78.39/10.69 (( 78.39/10.69 (binunionTE) => 78.39/10.69 (( 78.39/10.69 (binunionTEcontra) => 78.39/10.69 (( 78.39/10.69 (demorgan2a1) => 78.39/10.69 (( 78.39/10.69 (complementUnionInPowersetComplement) => 78.39/10.69 (( 78.39/10.69 (demorgan2a2) => 78.39/10.69 (( 78.39/10.69 (demorgan1a) => 78.39/10.69 (( 78.39/10.69 (demorgan1b) => 78.39/10.69 (( 78.39/10.69 (demorgan1) => 78.39/10.69 (( 78.39/10.69 (demorgan2a) => 78.39/10.69 (( 78.39/10.69 (demorgan2b2) => 78.39/10.69 (( 78.39/10.69 (demorgan2b) => 78.39/10.69 (( 78.39/10.69 (demorgan2) => 78.39/10.69 (( 78.39/10.69 (woz13rule0) => 78.39/10.69 (( 78.39/10.69 (woz13rule1) => 78.39/10.69 (( 78.39/10.69 (woz13rule2) => 78.39/10.69 (( 78.39/10.69 (woz13rule3) => 78.39/10.69 (( 78.39/10.69 (woz13rule4) => 78.39/10.69 (( 78.39/10.69 (woz1_1) => 78.39/10.69 (( 78.39/10.69 (woz1_2) => 78.39/10.69 (( 78.39/10.69 (woz1_3) => 78.39/10.69 (( 78.39/10.69 (woz1_4) => 78.39/10.69 (( 78.39/10.69 (woz1_5) => 78.39/10.69 (( 78.39/10.69 (breln1all2) => 78.39/10.69 (( 78.39/10.69 (breln1SetBreln1) => 78.39/10.69 (( 78.39/10.69 (choice2fnsingleton) => 78.39/10.69 (( 78.39/10.69 (setOfPairsIsBReln1) => 78.39/10.69 (( 78.39/10.69 (breln1all1) => 78.39/10.69 (( 78.39/10.69 (subbreln1) => 78.39/10.69 (( 78.39/10.69 (eqbreln1) => 78.39/10.69 (( 78.39/10.69 (breln1invprop) => 78.39/10.69 (( 78.39/10.69 (breln1invI) => 78.39/10.69 (( 78.39/10.69 (breln1invE) => 78.39/10.69 (( 78.39/10.69 (breln1compprop) => 78.39/10.69 (( 78.39/10.69 (breln1compI) => 78.39/10.69 (( 78.39/10.69 (breln1compE) => 78.39/10.69 (( 78.39/10.69 (breln1compEex) => 78.39/10.69 (( 78.39/10.69 (breln1unionprop) => 78.39/10.69 (( 78.39/10.69 (breln1unionIL) => 78.39/10.69 (( 78.39/10.69 (breln1unionIR) => 78.39/10.69 (( 78.39/10.69 (breln1unionI) => 78.39/10.69 (( 78.39/10.69 (breln1unionE) => 78.39/10.69 (( 78.39/10.69 (breln1unionEcases) => 78.39/10.69 (( 78.39/10.69 (breln1unionCommutes) => 78.39/10.69 (( 78.39/10.69 (woz2Ex) => 78.39/10.69 (( 78.39/10.69 (woz2W) => 78.39/10.69 (( 78.39/10.69 (woz2A) => 78.39/10.69 (( 78.39/10.69 (woz2B) => 78.39/10.69 (( 78.39/10.69 (image1Ex) => 78.39/10.69 (( 78.39/10.69 (image1Ex1) => 78.39/10.69 (( 78.39/10.69 (image1Equiv) => 78.39/10.69 (( 78.39/10.69 (image1E) => 78.39/10.69 (( 78.39/10.69 (image1I) => 78.39/10.69 (( 78.39/10.69 (injFuncInInjFuncSet) => 78.39/10.69 (( 78.39/10.69 (injFuncSetFuncIn) => 78.39/10.69 (( 78.39/10.69 (injFuncSetFuncInj) => 78.39/10.69 (( 78.39/10.69 (surjFuncSetFuncIn) => 78.39/10.69 (( 78.39/10.69 (surjFuncSetFuncSurj) => 78.39/10.69 (( 78.39/10.69 (leftInvIsSurj) => 78.39/10.69 (( 78.39/10.69 (surjCantorThm) => 78.39/10.69 (( 78.39/10.69 (foundation2) => 78.39/10.69 (( 78.39/10.69 (notinself) => 78.39/10.69 (( 78.39/10.69 (notinself2) => 78.39/10.69 (( 78.39/10.69 (omegaSp) => 78.39/10.69 (( 78.39/10.69 (omegaSclos) => 78.39/10.69 (( 78.39/10.69 (peano0notS) => 78.39/10.69 (( 78.39/10.69 (peanoSinj) => 78.39/10.69 (( 78.39/10.69 (transitivesetOp1) => 78.39/10.69 (( 78.39/10.69 (binintTransitive) => 78.39/10.69 (( 78.39/10.69 (transitivesetOp2) => 78.39/10.69 (( 78.39/10.69 (setunionTransitive) => 78.39/10.69 (( 78.39/10.69 (ordinalMinLem1) => 78.39/10.69 (( 78.39/10.69 (!!) @ ( 78.39/10.69 ^[Y0 : $i]: 78.39/10.69 (( 78.39/10.69 (ordinal @ 78.39/10.69 Y0) => 78.39/10.69 (( 78.39/10.69 (!!) @ ( 78.39/10.69 ^[Y1 : $i]: 78.39/10.69 (( 78.39/10.69 (!!) @ ( 78.39/10.69 ^[Y2 : $i]: 78.39/10.69 (( 78.39/10.69 (in @ 78.39/10.69 Y2 @ 78.39/10.69 Y0) => 78.39/10.69 (( 78.39/10.69 (in @ 78.39/10.69 Y1 @ 78.39/10.69 Y2) => 78.39/10.69 (in @ 78.39/10.69 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 78.39/10.69 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1237])). 78.39/10.69 thf(zip_derived_cl1252, plain, 78.39/10.69 (~ (((cartprodmempair1) => 78.39/10.69 (((cartprodmempair) => 78.39/10.69 (((setunionE2) => 78.39/10.69 (((setunionsingleton1) => 78.39/10.69 (((setunionsingleton2) => 78.39/10.69 (((setunionsingleton) => 78.39/10.69 (((singletonprop) => 78.39/10.69 (((ex1E1) => 78.39/10.69 (((ex1I) => 78.39/10.69 (((ex1I2) => 78.39/10.69 (((singletonsuniq) => 78.39/10.69 (((setukpairinjL1) => 78.39/10.69 (((kfstsingleton) => 78.39/10.69 (((theprop) => 78.39/10.69 (((kfstpairEq) => 78.39/10.69 (((cartprodfstin) => 78.39/10.69 (((setukpairinjL2) => 78.39/10.69 (((setukpairinjL) => 78.39/10.69 (((setukpairinjR11) => 78.39/10.69 (((setukpairinjR12) => 78.39/10.69 (((setukpairinjR1) => 78.39/10.69 (((upairequniteq) => 78.39/10.69 (((setukpairinjR2) => 78.39/10.69 (((setukpairinjR) => 78.39/10.69 (((ksndsingleton) => 78.39/10.69 (((ksndpairEq) => 78.39/10.69 (((kpairsurjEq) => 78.39/10.69 (((cartprodsndin) => 78.39/10.69 (((cartprodpairmemEL) => 78.39/10.69 (((cartprodpairmemER) => 78.39/10.69 (( 78.39/10.69 (cartprodmempaircEq) => 78.39/10.69 (( 78.39/10.69 (cartprodfstpairEq) => 78.39/10.69 (( 78.39/10.69 (cartprodsndpairEq) => 78.39/10.69 (( 78.39/10.69 (cartprodpairsurjEq) => 78.39/10.69 (( 78.39/10.69 (dpsetconstrI) => 78.39/10.69 (( 78.39/10.69 (dpsetconstrSub) => 78.39/10.69 (( 78.39/10.69 (setOfPairsIsBReln) => 78.39/10.69 (( 78.39/10.69 (dpsetconstrERa) => 78.39/10.69 (( 78.39/10.69 (dpsetconstrEL1) => 78.39/10.69 (( 78.39/10.69 (dpsetconstrEL2) => 78.39/10.69 (( 78.39/10.69 (dpsetconstrER) => 78.39/10.69 (( 78.39/10.69 (funcImageSingleton) => 78.39/10.69 (( 78.39/10.69 (apProp) => 78.39/10.69 (( 78.39/10.69 (app) => 78.39/10.69 (( 78.39/10.69 (infuncsetfunc) => 78.39/10.69 (( 78.39/10.69 (ap2p) => 78.39/10.69 (( 78.39/10.69 (funcinfuncset) => 78.39/10.69 (( 78.39/10.69 (lamProp) => 78.39/10.69 (( 78.39/10.69 (lamp) => 78.39/10.69 (( 78.39/10.69 (lam2p) => 78.39/10.69 (( 78.39/10.69 (brelnall1) => 78.39/10.69 (( 78.39/10.69 (brelnall2) => 78.39/10.69 (( 78.39/10.69 (ex1E2) => 78.39/10.69 (( 78.39/10.69 (funcGraphProp1) => 78.39/10.69 (( 78.39/10.69 (funcGraphProp3) => 78.39/10.69 (( 78.39/10.69 (funcGraphProp2) => 78.39/10.69 (( 78.39/10.69 (funcextLem) => 78.39/10.69 (( 78.39/10.69 (funcGraphProp4) => 78.39/10.69 (( 78.39/10.69 (subbreln) => 78.39/10.69 (( 78.39/10.69 (eqbreln) => 78.39/10.69 (( 78.39/10.69 (funcext) => 78.39/10.69 (( 78.39/10.69 (funcext2) => 78.39/10.69 (( 78.39/10.69 (ap2apEq1) => 78.39/10.69 (( 78.39/10.69 (ap2apEq2) => 78.39/10.69 (( 78.39/10.69 (beta1) => 78.39/10.69 (( 78.39/10.69 (eta1) => 78.39/10.69 (( 78.39/10.69 (lam2lamEq) => 78.39/10.69 (( 78.39/10.69 (beta2) => 78.39/10.69 (( 78.39/10.69 (eta2) => 78.39/10.69 (( 78.39/10.69 (iffalseProp1) => 78.39/10.69 (( 78.39/10.69 (iffalseProp2) => 78.39/10.69 (( 78.39/10.69 (iftrueProp1) => 78.39/10.69 (( 78.39/10.69 (iftrueProp2) => 78.39/10.69 (( 78.39/10.69 (ifSingleton) => 78.39/10.69 (( 78.39/10.69 (ifp) => 78.39/10.69 (( 78.39/10.69 (theeq) => 78.39/10.69 (( 78.39/10.69 (iftrue) => 78.39/10.69 (( 78.39/10.69 (iffalse) => 78.39/10.69 (( 78.39/10.69 (iftrueorfalse) => 78.39/10.69 (( 78.39/10.69 (binintersectT_lem) => 78.39/10.69 (( 78.39/10.69 (binunionT_lem) => 78.39/10.69 (( 78.39/10.69 (powersetT_lem) => 78.39/10.69 (( 78.39/10.69 (setminusT_lem) => 78.39/10.69 (( 78.39/10.69 (complementT_lem) => 78.39/10.69 (( 78.39/10.69 (setextT) => 78.39/10.69 (( 78.39/10.69 (subsetTI) => 78.39/10.69 (( 78.39/10.69 (powersetTI1) => 78.39/10.69 (( 78.39/10.69 (powersetTE1) => 78.39/10.69 (( 78.39/10.69 (complementTI1) => 78.39/10.69 (( 78.39/10.69 (complementTE1) => 78.39/10.69 (( 78.39/10.69 (binintersectTELcontra) => 78.39/10.69 (( 78.39/10.69 (binintersectTERcontra) => 78.39/10.69 (( 78.39/10.69 (contrasubsetT) => 78.39/10.69 (( 78.39/10.69 (contrasubsetT1) => 78.39/10.69 (( 78.39/10.69 (contrasubsetT2) => 78.39/10.69 (( 78.39/10.69 (contrasubsetT3) => 78.39/10.69 (( 78.39/10.69 (doubleComplementI1) => 78.39/10.69 (( 78.39/10.69 (doubleComplementE1) => 78.39/10.69 (( 78.39/10.69 (doubleComplementSub1) => 78.39/10.69 (( 78.39/10.69 (doubleComplementSub2) => 78.39/10.69 (( 78.39/10.69 (doubleComplementEq) => 78.39/10.69 (( 78.39/10.69 (complementTnotintersectT) => 78.39/10.69 (( 78.39/10.69 (complementImpComplementIntersect) => 78.39/10.69 (( 78.39/10.69 (complementSubsetComplementIntersect) => 78.39/10.69 (( 78.39/10.69 (complementInPowersetComplementIntersect) => 78.39/10.69 (( 78.39/10.69 (contraSubsetComplement) => 78.39/10.69 (( 78.39/10.69 (complementTcontraSubset) => 78.39/10.69 (( 78.39/10.69 (binunionTILcontra) => 78.39/10.69 (( 78.39/10.69 (binunionTIRcontra) => 78.39/10.69 (( 78.39/10.69 (inIntersectImpInUnion) => 78.39/10.69 (( 78.39/10.69 (inIntersectImpInUnion2) => 78.39/10.69 (( 78.39/10.69 (inIntersectImpInIntersectUnions) => 78.39/10.69 (( 78.39/10.69 (intersectInPowersetIntersectUnions) => 78.39/10.69 (( 78.39/10.69 (inComplementUnionImpNotIn1) => 78.39/10.69 (( 78.39/10.69 (inComplementUnionImpInComplement1) => 78.39/10.69 (( 78.39/10.69 (binunionTE) => 78.39/10.69 (( 78.39/10.69 (binunionTEcontra) => 78.39/10.69 (( 78.39/10.69 (demorgan2a1) => 78.39/10.69 (( 78.39/10.69 (complementUnionInPowersetComplement) => 78.39/10.69 (( 78.39/10.69 (demorgan2a2) => 78.39/10.69 (( 78.39/10.69 (demorgan1a) => 78.39/10.69 (( 78.39/10.69 (demorgan1b) => 78.39/10.69 (( 78.39/10.69 (demorgan1) => 78.39/10.69 (( 78.39/10.69 (demorgan2a) => 78.39/10.69 (( 78.39/10.69 (demorgan2b2) => 78.39/10.69 (( 78.39/10.69 (demorgan2b) => 78.39/10.69 (( 78.39/10.69 (demorgan2) => 78.39/10.69 (( 78.39/10.69 (woz13rule0) => 78.39/10.69 (( 78.39/10.69 (woz13rule1) => 78.39/10.69 (( 78.39/10.69 (woz13rule2) => 78.39/10.69 (( 78.39/10.69 (woz13rule3) => 78.39/10.69 (( 78.39/10.69 (woz13rule4) => 78.39/10.69 (( 78.39/10.69 (woz1_1) => 78.39/10.69 (( 78.39/10.69 (woz1_2) => 78.39/10.69 (( 78.39/10.69 (woz1_3) => 78.39/10.69 (( 78.39/10.69 (woz1_4) => 78.39/10.69 (( 78.39/10.69 (woz1_5) => 78.39/10.69 (( 78.39/10.69 (breln1all2) => 78.39/10.69 (( 78.39/10.69 (breln1SetBreln1) => 78.39/10.69 (( 78.39/10.69 (choice2fnsingleton) => 78.39/10.69 (( 78.39/10.69 (setOfPairsIsBReln1) => 78.39/10.69 (( 78.39/10.69 (breln1all1) => 78.39/10.69 (( 78.39/10.69 (subbreln1) => 78.39/10.69 (( 78.39/10.69 (eqbreln1) => 78.39/10.69 (( 78.39/10.69 (breln1invprop) => 78.39/10.69 (( 78.39/10.69 (breln1invI) => 78.39/10.69 (( 78.39/10.69 (breln1invE) => 78.39/10.69 (( 78.39/10.69 (breln1compprop) => 78.39/10.69 (( 78.39/10.69 (breln1compI) => 78.39/10.69 (( 78.39/10.69 (breln1compE) => 78.39/10.69 (( 78.39/10.69 (breln1compEex) => 78.39/10.69 (( 78.39/10.69 (breln1unionprop) => 78.39/10.69 (( 78.39/10.69 (breln1unionIL) => 78.39/10.69 (( 78.39/10.69 (breln1unionIR) => 78.39/10.69 (( 78.39/10.69 (breln1unionI) => 78.39/10.69 (( 78.39/10.69 (breln1unionE) => 78.39/10.69 (( 78.39/10.69 (breln1unionEcases) => 78.39/10.69 (( 78.39/10.69 (breln1unionCommutes) => 78.39/10.69 (( 78.39/10.69 (woz2Ex) => 78.39/10.69 (( 78.39/10.69 (woz2W) => 78.39/10.69 (( 78.39/10.69 (woz2A) => 78.39/10.69 (( 78.39/10.69 (woz2B) => 78.39/10.69 (( 78.39/10.69 (image1Ex) => 78.39/10.69 (( 78.39/10.69 (image1Ex1) => 78.39/10.69 (( 78.39/10.69 (image1Equiv) => 78.39/10.69 (( 78.39/10.69 (image1E) => 78.39/10.69 (( 78.39/10.69 (image1I) => 78.39/10.69 (( 78.39/10.69 (injFuncInInjFuncSet) => 78.39/10.69 (( 78.39/10.69 (injFuncSetFuncIn) => 78.39/10.69 (( 78.39/10.69 (injFuncSetFuncInj) => 78.39/10.69 (( 78.39/10.69 (surjFuncSetFuncIn) => 78.39/10.69 (( 78.39/10.69 (surjFuncSetFuncSurj) => 78.39/10.69 (( 78.39/10.69 (leftInvIsSurj) => 78.39/10.69 (( 78.39/10.69 (surjCantorThm) => 78.39/10.69 (( 78.39/10.69 (foundation2) => 78.39/10.69 (( 78.39/10.69 (notinself) => 78.39/10.69 (( 78.39/10.69 (notinself2) => 78.39/10.69 (( 78.39/10.69 (omegaSp) => 78.39/10.69 (( 78.39/10.69 (omegaSclos) => 78.39/10.69 (( 78.39/10.69 (peano0notS) => 78.39/10.69 (( 78.39/10.69 (peanoSinj) => 78.39/10.69 (( 78.39/10.69 (transitivesetOp1) => 78.39/10.69 (( 78.39/10.69 (binintTransitive) => 78.39/10.69 (( 78.39/10.69 (transitivesetOp2) => 78.39/10.69 (( 78.39/10.69 (setunionTransitive) => 78.39/10.69 (( 78.39/10.69 (ordinalMinLem1) => 78.39/10.69 (( 78.39/10.69 (!!) @ ( 78.39/10.69 ^[Y0 : $i]: 78.39/10.69 (( 78.39/10.69 (ordinal @ 78.39/10.69 Y0) => 78.39/10.69 (( 78.39/10.69 (!!) @ ( 78.39/10.69 ^[Y1 : $i]: 78.39/10.69 (( 78.39/10.69 (!!) @ ( 78.39/10.69 ^[Y2 : $i]: 78.39/10.69 (( 78.39/10.69 (in @ 78.39/10.69 Y2 @ 78.39/10.69 Y0) => 78.39/10.69 (( 78.39/10.69 (in @ 78.39/10.69 Y1 @ 78.39/10.69 Y2) => 78.39/10.69 (in @ 78.39/10.69 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 78.39/10.69 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1244])). 78.39/10.69 thf(zip_derived_cl1261, plain, 78.39/10.69 (~ (((cartprodmempair) => 78.39/10.69 (((setunionE2) => 78.39/10.69 (((setunionsingleton1) => 78.39/10.69 (((setunionsingleton2) => 78.39/10.69 (((setunionsingleton) => 78.39/10.69 (((singletonprop) => 78.39/10.69 (((ex1E1) => 78.39/10.69 (((ex1I) => 78.39/10.69 (((ex1I2) => 78.39/10.69 (((singletonsuniq) => 78.39/10.69 (((setukpairinjL1) => 78.39/10.69 (((kfstsingleton) => 78.39/10.69 (((theprop) => 78.39/10.69 (((kfstpairEq) => 78.39/10.69 (((cartprodfstin) => 78.39/10.69 (((setukpairinjL2) => 78.39/10.69 (((setukpairinjL) => 78.39/10.69 (((setukpairinjR11) => 78.39/10.69 (((setukpairinjR12) => 78.39/10.69 (((setukpairinjR1) => 78.39/10.69 (((upairequniteq) => 78.39/10.69 (((setukpairinjR2) => 78.39/10.69 (((setukpairinjR) => 78.39/10.69 (((ksndsingleton) => 78.39/10.69 (((ksndpairEq) => 78.39/10.69 (((kpairsurjEq) => 78.39/10.69 (((cartprodsndin) => 78.39/10.69 (((cartprodpairmemEL) => 78.39/10.69 (((cartprodpairmemER) => 78.39/10.69 (((cartprodmempaircEq) => 78.39/10.69 (( 78.39/10.69 (cartprodfstpairEq) => 78.39/10.69 (( 78.39/10.69 (cartprodsndpairEq) => 78.39/10.69 (( 78.39/10.69 (cartprodpairsurjEq) => 78.39/10.69 (( 78.39/10.69 (dpsetconstrI) => 78.39/10.69 (( 78.39/10.69 (dpsetconstrSub) => 78.39/10.69 (( 78.39/10.69 (setOfPairsIsBReln) => 78.39/10.69 (( 78.39/10.69 (dpsetconstrERa) => 78.39/10.69 (( 78.39/10.69 (dpsetconstrEL1) => 78.39/10.69 (( 78.39/10.69 (dpsetconstrEL2) => 78.39/10.69 (( 78.39/10.69 (dpsetconstrER) => 78.39/10.69 (( 78.39/10.69 (funcImageSingleton) => 78.39/10.69 (( 78.39/10.69 (apProp) => 78.39/10.69 (( 78.39/10.69 (app) => 78.39/10.69 (( 78.39/10.69 (infuncsetfunc) => 78.39/10.69 (( 78.39/10.69 (ap2p) => 78.39/10.69 (( 78.39/10.69 (funcinfuncset) => 78.39/10.69 (( 78.39/10.69 (lamProp) => 78.39/10.69 (( 78.39/10.69 (lamp) => 78.39/10.69 (( 78.39/10.69 (lam2p) => 78.39/10.69 (( 78.39/10.69 (brelnall1) => 78.39/10.69 (( 78.39/10.69 (brelnall2) => 78.39/10.69 (( 78.39/10.69 (ex1E2) => 78.39/10.69 (( 78.39/10.69 (funcGraphProp1) => 78.39/10.69 (( 78.39/10.69 (funcGraphProp3) => 78.39/10.69 (( 78.39/10.69 (funcGraphProp2) => 78.39/10.69 (( 78.39/10.69 (funcextLem) => 78.39/10.69 (( 78.39/10.69 (funcGraphProp4) => 78.39/10.69 (( 78.39/10.69 (subbreln) => 78.39/10.69 (( 78.39/10.69 (eqbreln) => 78.39/10.69 (( 78.39/10.69 (funcext) => 78.39/10.69 (( 78.39/10.69 (funcext2) => 78.39/10.69 (( 78.39/10.69 (ap2apEq1) => 78.39/10.69 (( 78.39/10.69 (ap2apEq2) => 78.39/10.69 (( 78.39/10.69 (beta1) => 78.39/10.69 (( 78.39/10.69 (eta1) => 78.39/10.69 (( 78.39/10.69 (lam2lamEq) => 78.39/10.69 (( 78.39/10.69 (beta2) => 78.39/10.69 (( 78.39/10.69 (eta2) => 78.39/10.69 (( 78.39/10.69 (iffalseProp1) => 78.39/10.69 (( 78.39/10.69 (iffalseProp2) => 78.39/10.69 (( 78.39/10.69 (iftrueProp1) => 78.39/10.69 (( 78.39/10.69 (iftrueProp2) => 78.39/10.69 (( 78.39/10.69 (ifSingleton) => 78.39/10.69 (( 78.39/10.69 (ifp) => 78.39/10.69 (( 78.39/10.69 (theeq) => 78.39/10.69 (( 78.39/10.69 (iftrue) => 78.39/10.69 (( 78.39/10.69 (iffalse) => 78.39/10.69 (( 78.39/10.69 (iftrueorfalse) => 78.39/10.69 (( 78.39/10.69 (binintersectT_lem) => 78.39/10.69 (( 78.39/10.69 (binunionT_lem) => 78.39/10.69 (( 78.39/10.69 (powersetT_lem) => 78.39/10.69 (( 78.39/10.69 (setminusT_lem) => 78.39/10.69 (( 78.39/10.69 (complementT_lem) => 78.39/10.69 (( 78.39/10.69 (setextT) => 78.39/10.69 (( 78.39/10.69 (subsetTI) => 78.39/10.69 (( 78.39/10.69 (powersetTI1) => 78.39/10.69 (( 78.39/10.69 (powersetTE1) => 78.39/10.69 (( 78.39/10.69 (complementTI1) => 78.39/10.69 (( 78.39/10.69 (complementTE1) => 78.39/10.69 (( 78.39/10.69 (binintersectTELcontra) => 78.39/10.69 (( 78.39/10.69 (binintersectTERcontra) => 78.39/10.69 (( 78.39/10.69 (contrasubsetT) => 78.39/10.69 (( 78.39/10.69 (contrasubsetT1) => 78.39/10.69 (( 78.39/10.69 (contrasubsetT2) => 78.39/10.69 (( 78.39/10.69 (contrasubsetT3) => 78.39/10.69 (( 78.39/10.69 (doubleComplementI1) => 78.39/10.69 (( 78.39/10.69 (doubleComplementE1) => 78.39/10.69 (( 78.39/10.69 (doubleComplementSub1) => 78.39/10.69 (( 78.39/10.69 (doubleComplementSub2) => 78.39/10.69 (( 78.39/10.69 (doubleComplementEq) => 78.39/10.69 (( 78.39/10.69 (complementTnotintersectT) => 78.39/10.69 (( 78.39/10.69 (complementImpComplementIntersect) => 78.39/10.69 (( 78.39/10.69 (complementSubsetComplementIntersect) => 78.39/10.69 (( 78.39/10.69 (complementInPowersetComplementIntersect) => 78.39/10.69 (( 78.39/10.69 (contraSubsetComplement) => 78.39/10.69 (( 78.39/10.69 (complementTcontraSubset) => 78.39/10.69 (( 78.39/10.69 (binunionTILcontra) => 78.39/10.69 (( 78.39/10.69 (binunionTIRcontra) => 78.39/10.69 (( 78.39/10.69 (inIntersectImpInUnion) => 78.39/10.69 (( 78.39/10.69 (inIntersectImpInUnion2) => 78.39/10.69 (( 78.39/10.69 (inIntersectImpInIntersectUnions) => 78.39/10.69 (( 78.39/10.69 (intersectInPowersetIntersectUnions) => 78.39/10.69 (( 78.39/10.69 (inComplementUnionImpNotIn1) => 78.39/10.69 (( 78.39/10.69 (inComplementUnionImpInComplement1) => 78.39/10.69 (( 78.39/10.69 (binunionTE) => 78.39/10.69 (( 78.39/10.69 (binunionTEcontra) => 78.39/10.69 (( 78.39/10.69 (demorgan2a1) => 78.39/10.69 (( 78.39/10.69 (complementUnionInPowersetComplement) => 78.39/10.69 (( 78.39/10.69 (demorgan2a2) => 78.39/10.69 (( 78.39/10.69 (demorgan1a) => 78.39/10.69 (( 78.39/10.69 (demorgan1b) => 78.39/10.69 (( 78.39/10.69 (demorgan1) => 78.39/10.69 (( 78.39/10.69 (demorgan2a) => 78.39/10.69 (( 78.39/10.69 (demorgan2b2) => 78.39/10.69 (( 78.39/10.69 (demorgan2b) => 78.39/10.69 (( 78.39/10.69 (demorgan2) => 78.39/10.69 (( 78.39/10.69 (woz13rule0) => 78.39/10.69 (( 78.39/10.69 (woz13rule1) => 78.39/10.69 (( 78.39/10.69 (woz13rule2) => 78.39/10.69 (( 78.39/10.69 (woz13rule3) => 78.39/10.69 (( 78.39/10.69 (woz13rule4) => 78.39/10.69 (( 78.39/10.69 (woz1_1) => 78.39/10.69 (( 78.39/10.69 (woz1_2) => 78.39/10.69 (( 78.39/10.69 (woz1_3) => 78.39/10.69 (( 78.39/10.69 (woz1_4) => 78.39/10.69 (( 78.39/10.69 (woz1_5) => 78.39/10.69 (( 78.39/10.69 (breln1all2) => 78.39/10.69 (( 78.39/10.69 (breln1SetBreln1) => 78.39/10.69 (( 78.39/10.69 (choice2fnsingleton) => 78.39/10.69 (( 78.39/10.69 (setOfPairsIsBReln1) => 78.39/10.69 (( 78.39/10.69 (breln1all1) => 78.39/10.69 (( 78.39/10.69 (subbreln1) => 78.39/10.69 (( 78.39/10.69 (eqbreln1) => 78.39/10.69 (( 78.39/10.69 (breln1invprop) => 78.39/10.69 (( 78.39/10.69 (breln1invI) => 78.39/10.69 (( 78.39/10.69 (breln1invE) => 78.39/10.69 (( 78.39/10.69 (breln1compprop) => 78.39/10.69 (( 78.39/10.69 (breln1compI) => 78.39/10.69 (( 78.39/10.69 (breln1compE) => 78.39/10.69 (( 78.39/10.69 (breln1compEex) => 78.39/10.69 (( 78.39/10.69 (breln1unionprop) => 78.39/10.69 (( 78.39/10.69 (breln1unionIL) => 78.39/10.69 (( 78.39/10.69 (breln1unionIR) => 78.39/10.69 (( 78.39/10.69 (breln1unionI) => 78.39/10.69 (( 78.39/10.69 (breln1unionE) => 78.39/10.69 (( 78.39/10.69 (breln1unionEcases) => 78.39/10.69 (( 78.39/10.69 (breln1unionCommutes) => 78.39/10.69 (( 78.39/10.69 (woz2Ex) => 78.39/10.69 (( 78.39/10.69 (woz2W) => 78.39/10.69 (( 78.39/10.69 (woz2A) => 78.39/10.69 (( 78.39/10.69 (woz2B) => 78.39/10.69 (( 78.39/10.69 (image1Ex) => 78.39/10.69 (( 78.39/10.69 (image1Ex1) => 78.39/10.69 (( 78.39/10.69 (image1Equiv) => 78.39/10.69 (( 78.39/10.69 (image1E) => 78.39/10.69 (( 78.39/10.69 (image1I) => 78.39/10.69 (( 78.39/10.69 (injFuncInInjFuncSet) => 78.39/10.69 (( 78.39/10.69 (injFuncSetFuncIn) => 78.39/10.69 (( 78.39/10.69 (injFuncSetFuncInj) => 78.39/10.69 (( 78.39/10.69 (surjFuncSetFuncIn) => 78.39/10.69 (( 78.39/10.69 (surjFuncSetFuncSurj) => 78.39/10.69 (( 78.39/10.69 (leftInvIsSurj) => 78.39/10.69 (( 78.39/10.69 (surjCantorThm) => 78.39/10.69 (( 78.39/10.69 (foundation2) => 78.39/10.69 (( 78.39/10.69 (notinself) => 78.39/10.69 (( 78.39/10.69 (notinself2) => 78.39/10.69 (( 78.39/10.69 (omegaSp) => 78.39/10.69 (( 78.39/10.69 (omegaSclos) => 78.39/10.69 (( 78.39/10.69 (peano0notS) => 78.39/10.69 (( 78.39/10.69 (peanoSinj) => 78.39/10.69 (( 78.39/10.69 (transitivesetOp1) => 78.39/10.69 (( 78.39/10.69 (binintTransitive) => 78.39/10.69 (( 78.39/10.69 (transitivesetOp2) => 78.39/10.69 (( 78.39/10.69 (setunionTransitive) => 78.39/10.69 (( 78.39/10.69 (ordinalMinLem1) => 78.39/10.69 (( 78.39/10.69 (!!) @ ( 78.39/10.69 ^[Y0 : $i]: 78.39/10.69 (( 78.39/10.69 (ordinal @ 78.39/10.69 Y0) => 78.39/10.69 (( 78.39/10.69 (!!) @ ( 78.39/10.69 ^[Y1 : $i]: 78.39/10.69 (( 78.39/10.69 (!!) @ ( 78.39/10.69 ^[Y2 : $i]: 78.39/10.69 (( 78.39/10.69 (in @ 78.39/10.69 Y2 @ 78.39/10.69 Y0) => 78.39/10.69 (( 78.39/10.69 (in @ 78.39/10.69 Y1 @ 78.39/10.69 Y2) => 78.39/10.69 (in @ 78.39/10.69 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 78.39/10.69 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1252])). 78.39/10.69 thf(zip_derived_cl1270, plain, 78.39/10.69 (~ (((setunionE2) => 78.39/10.69 (((setunionsingleton1) => 78.39/10.69 (((setunionsingleton2) => 78.39/10.69 (((setunionsingleton) => 78.39/10.69 (((singletonprop) => 78.39/10.69 (((ex1E1) => 78.39/10.69 (((ex1I) => 78.39/10.69 (((ex1I2) => 78.39/10.69 (((singletonsuniq) => 78.39/10.69 (((setukpairinjL1) => 78.39/10.69 (((kfstsingleton) => 78.39/10.69 (((theprop) => 78.39/10.69 (((kfstpairEq) => 78.39/10.69 (((cartprodfstin) => 78.39/10.69 (((setukpairinjL2) => 78.39/10.69 (((setukpairinjL) => 78.39/10.69 (((setukpairinjR11) => 78.39/10.69 (((setukpairinjR12) => 78.39/10.69 (((setukpairinjR1) => 78.39/10.69 (((upairequniteq) => 78.39/10.69 (((setukpairinjR2) => 78.39/10.69 (((setukpairinjR) => 78.39/10.69 (((ksndsingleton) => 78.39/10.69 (((ksndpairEq) => 78.39/10.69 (((kpairsurjEq) => 78.39/10.69 (((cartprodsndin) => 78.39/10.69 (((cartprodpairmemEL) => 78.39/10.69 (((cartprodpairmemER) => 78.39/10.69 (((cartprodmempaircEq) => 78.39/10.69 (((cartprodfstpairEq) => 78.39/10.69 (( 78.39/10.69 (cartprodsndpairEq) => 78.39/10.69 (( 78.39/10.69 (cartprodpairsurjEq) => 78.39/10.69 (( 78.39/10.69 (dpsetconstrI) => 78.39/10.69 (( 78.39/10.69 (dpsetconstrSub) => 78.39/10.69 (( 78.39/10.69 (setOfPairsIsBReln) => 78.39/10.69 (( 78.39/10.69 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=> 78.39/10.69 (( 78.39/10.69 (funcext2) => 78.39/10.69 (( 78.39/10.69 (ap2apEq1) => 78.39/10.69 (( 78.39/10.69 (ap2apEq2) => 78.39/10.69 (( 78.39/10.69 (beta1) => 78.39/10.69 (( 78.39/10.69 (eta1) => 78.39/10.69 (( 78.39/10.69 (lam2lamEq) => 78.39/10.69 (( 78.39/10.69 (beta2) => 78.39/10.69 (( 78.39/10.69 (eta2) => 78.39/10.69 (( 78.39/10.69 (iffalseProp1) => 78.39/10.69 (( 78.39/10.69 (iffalseProp2) => 78.39/10.69 (( 78.39/10.69 (iftrueProp1) => 78.39/10.69 (( 78.39/10.69 (iftrueProp2) => 78.39/10.69 (( 78.39/10.69 (ifSingleton) => 78.39/10.69 (( 78.39/10.69 (ifp) => 78.39/10.69 (( 78.39/10.69 (theeq) => 78.39/10.69 (( 78.39/10.69 (iftrue) => 78.39/10.69 (( 78.39/10.69 (iffalse) => 78.39/10.69 (( 78.39/10.69 (iftrueorfalse) => 78.39/10.69 (( 78.39/10.69 (binintersectT_lem) => 78.39/10.69 (( 78.39/10.69 (binunionT_lem) => 78.39/10.69 (( 78.39/10.69 (powersetT_lem) => 78.39/10.69 (( 78.39/10.69 (setminusT_lem) => 78.39/10.69 (( 78.39/10.69 (complementT_lem) => 78.39/10.69 (( 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(woz13rule0) => 78.39/10.69 (( 78.39/10.69 (woz13rule1) => 78.39/10.69 (( 78.39/10.69 (woz13rule2) => 78.39/10.69 (( 78.39/10.69 (woz13rule3) => 78.39/10.69 (( 78.39/10.69 (woz13rule4) => 78.39/10.69 (( 78.39/10.69 (woz1_1) => 78.39/10.69 (( 78.39/10.69 (woz1_2) => 78.39/10.69 (( 78.39/10.69 (woz1_3) => 78.39/10.69 (( 78.39/10.69 (woz1_4) => 78.39/10.69 (( 78.39/10.69 (woz1_5) => 78.39/10.69 (( 78.39/10.69 (breln1all2) => 78.39/10.69 (( 78.39/10.69 (breln1SetBreln1) => 78.39/10.69 (( 78.39/10.69 (choice2fnsingleton) => 78.39/10.69 (( 78.39/10.69 (setOfPairsIsBReln1) => 78.39/10.69 (( 78.39/10.69 (breln1all1) => 78.39/10.69 (( 78.39/10.69 (subbreln1) => 78.39/10.69 (( 78.39/10.69 (eqbreln1) => 78.39/10.69 (( 78.39/10.69 (breln1invprop) => 78.39/10.69 (( 78.39/10.69 (breln1invI) => 78.39/10.69 (( 78.39/10.69 (breln1invE) => 78.39/10.69 (( 78.39/10.69 (breln1compprop) => 78.39/10.69 (( 78.39/10.69 (breln1compI) => 78.39/10.69 (( 78.39/10.69 (breln1compE) => 78.39/10.69 (( 78.39/10.69 (breln1compEex) => 78.39/10.69 (( 78.39/10.69 (breln1unionprop) => 78.39/10.69 (( 78.39/10.69 (breln1unionIL) => 78.39/10.69 (( 78.39/10.69 (breln1unionIR) => 78.39/10.69 (( 78.39/10.69 (breln1unionI) => 78.39/10.69 (( 78.39/10.69 (breln1unionE) => 78.39/10.69 (( 78.39/10.69 (breln1unionEcases) => 78.39/10.69 (( 78.39/10.69 (breln1unionCommutes) => 78.39/10.69 (( 78.39/10.69 (woz2Ex) => 78.39/10.69 (( 78.39/10.69 (woz2W) => 78.39/10.69 (( 78.39/10.69 (woz2A) => 78.39/10.69 (( 78.39/10.69 (woz2B) => 78.39/10.69 (( 78.39/10.69 (image1Ex) => 78.39/10.69 (( 78.39/10.69 (image1Ex1) => 78.39/10.69 (( 78.39/10.69 (image1Equiv) => 78.39/10.69 (( 78.39/10.69 (image1E) => 78.39/10.69 (( 78.39/10.69 (image1I) => 78.39/10.69 (( 78.39/10.69 (injFuncInInjFuncSet) => 78.39/10.69 (( 78.39/10.69 (injFuncSetFuncIn) => 78.39/10.69 (( 78.39/10.69 (injFuncSetFuncInj) => 78.39/10.69 (( 78.39/10.69 (surjFuncSetFuncIn) => 78.39/10.69 (( 78.39/10.69 (surjFuncSetFuncSurj) => 78.39/10.69 (( 78.39/10.69 (leftInvIsSurj) => 78.39/10.69 (( 78.39/10.69 (surjCantorThm) => 78.39/10.69 (( 78.39/10.69 (foundation2) => 78.39/10.69 (( 78.39/10.69 (notinself) => 78.39/10.69 (( 78.39/10.69 (notinself2) => 78.39/10.69 (( 78.39/10.69 (omegaSp) => 78.39/10.69 (( 78.39/10.69 (omegaSclos) => 78.39/10.69 (( 78.39/10.69 (peano0notS) => 78.39/10.69 (( 78.39/10.69 (peanoSinj) => 78.39/10.69 (( 78.39/10.69 (transitivesetOp1) => 78.39/10.69 (( 78.39/10.69 (binintTransitive) => 78.39/10.69 (( 78.39/10.69 (transitivesetOp2) => 78.39/10.69 (( 78.39/10.69 (setunionTransitive) => 78.39/10.69 (( 78.39/10.69 (ordinalMinLem1) => 78.39/10.69 (( 78.39/10.69 (!!) @ ( 78.39/10.69 ^[Y0 : $i]: 78.39/10.69 (( 78.39/10.69 (ordinal @ 78.39/10.69 Y0) => 78.39/10.69 (( 78.39/10.69 (!!) @ ( 78.39/10.69 ^[Y1 : $i]: 78.39/10.69 (( 78.39/10.69 (!!) @ ( 78.39/10.69 ^[Y2 : $i]: 78.39/10.69 (( 78.39/10.69 (in @ 78.39/10.69 Y2 @ 78.39/10.69 Y0) => 78.39/10.69 (( 78.39/10.69 (in @ 78.39/10.69 Y1 @ 78.39/10.69 Y2) => 78.39/10.69 (in @ 78.39/10.69 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 78.39/10.69 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1288])). 78.39/10.69 thf(zip_derived_cl1306, plain, 78.39/10.69 (~ (((singletonprop) => 78.39/10.69 (((ex1E1) => 78.39/10.69 (((ex1I) => 78.39/10.69 (((ex1I2) => 78.39/10.69 (((singletonsuniq) => 78.39/10.69 (((setukpairinjL1) => 78.39/10.69 (((kfstsingleton) => 78.39/10.69 (((theprop) => 78.39/10.69 (((kfstpairEq) => 78.39/10.69 (((cartprodfstin) => 78.39/10.69 (((setukpairinjL2) => 78.39/10.69 (((setukpairinjL) => 78.39/10.69 (((setukpairinjR11) => 78.39/10.69 (((setukpairinjR12) => 78.39/10.69 (((setukpairinjR1) => 78.39/10.69 (((upairequniteq) => 78.39/10.69 (((setukpairinjR2) => 78.39/10.69 (((setukpairinjR) => 78.39/10.69 (((ksndsingleton) => 78.39/10.69 (((ksndpairEq) => 78.39/10.69 (((kpairsurjEq) => 78.39/10.69 (((cartprodsndin) => 78.39/10.69 (((cartprodpairmemEL) => 78.39/10.69 (((cartprodpairmemER) => 78.39/10.69 (((cartprodmempaircEq) => 78.39/10.69 (((cartprodfstpairEq) => 78.39/10.69 (((cartprodsndpairEq) => 78.39/10.69 (((cartprodpairsurjEq) => 78.39/10.69 (((dpsetconstrI) => 78.39/10.69 (((dpsetconstrSub) => 78.39/10.69 (( 78.39/10.69 (setOfPairsIsBReln) => 78.39/10.69 (( 78.39/10.69 (dpsetconstrERa) => 78.39/10.69 (( 78.39/10.69 (dpsetconstrEL1) => 78.39/10.69 (( 78.39/10.69 (dpsetconstrEL2) => 78.39/10.69 (( 78.39/10.69 (dpsetconstrER) => 78.39/10.69 (( 78.39/10.69 (funcImageSingleton) => 78.39/10.69 (( 78.39/10.69 (apProp) => 78.39/10.69 (( 78.39/10.69 (app) => 78.39/10.69 (( 78.39/10.69 (infuncsetfunc) => 78.39/10.69 (( 78.39/10.69 (ap2p) => 78.39/10.69 (( 78.39/10.69 (funcinfuncset) => 78.39/10.69 (( 78.39/10.69 (lamProp) => 78.39/10.69 (( 78.39/10.69 (lamp) => 78.39/10.69 (( 78.39/10.69 (lam2p) => 78.39/10.69 (( 78.39/10.69 (brelnall1) => 78.39/10.69 (( 78.39/10.69 (brelnall2) => 78.39/10.69 (( 78.39/10.69 (ex1E2) => 78.39/10.69 (( 78.39/10.69 (funcGraphProp1) => 78.39/10.69 (( 78.39/10.69 (funcGraphProp3) => 78.39/10.69 (( 78.39/10.69 (funcGraphProp2) => 78.39/10.69 (( 78.39/10.69 (funcextLem) => 78.39/10.69 (( 78.39/10.69 (funcGraphProp4) => 78.39/10.69 (( 78.39/10.69 (subbreln) => 78.39/10.69 (( 78.39/10.69 (eqbreln) => 78.39/10.69 (( 78.39/10.69 (funcext) => 78.39/10.69 (( 78.39/10.69 (funcext2) => 78.39/10.69 (( 78.39/10.69 (ap2apEq1) => 78.39/10.69 (( 78.39/10.69 (ap2apEq2) => 78.39/10.69 (( 78.39/10.69 (beta1) => 78.39/10.69 (( 78.39/10.69 (eta1) => 78.39/10.69 (( 78.39/10.69 (lam2lamEq) => 78.39/10.69 (( 78.39/10.69 (beta2) => 78.39/10.69 (( 78.39/10.69 (eta2) => 78.39/10.69 (( 78.39/10.69 (iffalseProp1) => 78.39/10.69 (( 78.39/10.69 (iffalseProp2) => 78.39/10.69 (( 78.39/10.69 (iftrueProp1) => 78.39/10.69 (( 78.39/10.69 (iftrueProp2) => 78.39/10.69 (( 78.39/10.69 (ifSingleton) => 78.39/10.69 (( 78.39/10.69 (ifp) => 78.39/10.69 (( 78.39/10.69 (theeq) => 78.39/10.69 (( 78.39/10.69 (iftrue) => 78.39/10.69 (( 78.39/10.69 (iffalse) => 78.39/10.69 (( 78.39/10.69 (iftrueorfalse) => 78.39/10.69 (( 78.39/10.69 (binintersectT_lem) => 78.39/10.69 (( 78.39/10.69 (binunionT_lem) => 78.39/10.69 (( 78.39/10.69 (powersetT_lem) => 78.39/10.69 (( 78.39/10.69 (setminusT_lem) => 78.39/10.69 (( 78.39/10.69 (complementT_lem) => 78.39/10.69 (( 78.39/10.69 (setextT) => 78.39/10.69 (( 78.39/10.69 (subsetTI) => 78.39/10.69 (( 78.39/10.69 (powersetTI1) => 78.39/10.69 (( 78.39/10.69 (powersetTE1) => 78.39/10.69 (( 78.39/10.69 (complementTI1) => 78.39/10.69 (( 78.39/10.69 (complementTE1) => 78.39/10.69 (( 78.39/10.69 (binintersectTELcontra) => 78.39/10.69 (( 78.39/10.69 (binintersectTERcontra) => 78.39/10.69 (( 78.39/10.69 (contrasubsetT) => 78.39/10.69 (( 78.39/10.69 (contrasubsetT1) => 78.39/10.69 (( 78.39/10.69 (contrasubsetT2) => 78.39/10.69 (( 78.39/10.69 (contrasubsetT3) => 78.39/10.69 (( 78.39/10.69 (doubleComplementI1) => 78.39/10.69 (( 78.39/10.69 (doubleComplementE1) => 78.39/10.69 (( 78.39/10.69 (doubleComplementSub1) => 78.39/10.69 (( 78.39/10.69 (doubleComplementSub2) => 78.39/10.69 (( 78.39/10.69 (doubleComplementEq) => 78.39/10.69 (( 78.39/10.69 (complementTnotintersectT) => 78.39/10.69 (( 78.39/10.69 (complementImpComplementIntersect) => 78.39/10.69 (( 78.39/10.69 (complementSubsetComplementIntersect) => 78.39/10.69 (( 78.39/10.69 (complementInPowersetComplementIntersect) => 78.39/10.69 (( 78.39/10.69 (contraSubsetComplement) => 78.39/10.69 (( 78.39/10.69 (complementTcontraSubset) => 78.39/10.69 (( 78.39/10.69 (binunionTILcontra) => 78.39/10.69 (( 78.39/10.69 (binunionTIRcontra) => 78.39/10.69 (( 78.39/10.69 (inIntersectImpInUnion) => 78.39/10.69 (( 78.39/10.69 (inIntersectImpInUnion2) => 78.39/10.69 (( 78.39/10.69 (inIntersectImpInIntersectUnions) => 78.39/10.69 (( 78.39/10.69 (intersectInPowersetIntersectUnions) => 78.39/10.69 (( 78.39/10.69 (inComplementUnionImpNotIn1) => 78.39/10.69 (( 78.39/10.69 (inComplementUnionImpInComplement1) => 78.39/10.69 (( 78.39/10.69 (binunionTE) => 78.39/10.69 (( 78.39/10.69 (binunionTEcontra) => 78.39/10.69 (( 78.39/10.69 (demorgan2a1) => 78.39/10.69 (( 78.39/10.69 (complementUnionInPowersetComplement) => 78.39/10.69 (( 78.39/10.69 (demorgan2a2) => 78.39/10.69 (( 78.39/10.69 (demorgan1a) => 78.39/10.69 (( 78.39/10.69 (demorgan1b) => 78.39/10.69 (( 78.39/10.69 (demorgan1) => 78.39/10.69 (( 78.39/10.69 (demorgan2a) => 78.39/10.69 (( 78.39/10.69 (demorgan2b2) => 78.39/10.69 (( 78.39/10.69 (demorgan2b) => 78.39/10.69 (( 78.39/10.69 (demorgan2) => 78.39/10.69 (( 78.39/10.69 (woz13rule0) => 78.39/10.69 (( 78.39/10.69 (woz13rule1) => 78.39/10.69 (( 78.39/10.69 (woz13rule2) => 78.39/10.69 (( 78.39/10.69 (woz13rule3) => 78.39/10.69 (( 78.39/10.69 (woz13rule4) => 78.39/10.69 (( 78.39/10.69 (woz1_1) => 78.39/10.69 (( 78.39/10.69 (woz1_2) => 78.39/10.69 (( 78.39/10.69 (woz1_3) => 78.39/10.69 (( 78.39/10.69 (woz1_4) => 78.39/10.69 (( 78.39/10.69 (woz1_5) => 78.39/10.69 (( 78.39/10.69 (breln1all2) => 78.39/10.69 (( 78.39/10.69 (breln1SetBreln1) => 78.39/10.69 (( 78.39/10.69 (choice2fnsingleton) => 78.39/10.69 (( 78.39/10.69 (setOfPairsIsBReln1) => 78.39/10.69 (( 78.39/10.69 (breln1all1) => 78.39/10.69 (( 78.39/10.69 (subbreln1) => 78.39/10.69 (( 78.39/10.69 (eqbreln1) => 78.39/10.69 (( 78.39/10.69 (breln1invprop) => 78.39/10.69 (( 78.39/10.69 (breln1invI) => 78.39/10.69 (( 78.39/10.69 (breln1invE) => 78.39/10.69 (( 78.39/10.69 (breln1compprop) => 78.39/10.69 (( 78.39/10.69 (breln1compI) => 78.39/10.69 (( 78.39/10.69 (breln1compE) => 78.39/10.69 (( 78.39/10.69 (breln1compEex) => 78.39/10.69 (( 78.39/10.69 (breln1unionprop) => 78.39/10.69 (( 78.39/10.69 (breln1unionIL) => 78.39/10.69 (( 78.39/10.69 (breln1unionIR) => 78.39/10.69 (( 78.39/10.69 (breln1unionI) => 78.39/10.69 (( 78.39/10.69 (breln1unionE) => 78.39/10.69 (( 78.39/10.69 (breln1unionEcases) => 78.39/10.69 (( 78.39/10.69 (breln1unionCommutes) => 78.39/10.69 (( 78.39/10.69 (woz2Ex) => 78.39/10.69 (( 78.39/10.69 (woz2W) => 78.39/10.69 (( 78.39/10.69 (woz2A) => 78.39/10.69 (( 78.39/10.69 (woz2B) => 78.39/10.69 (( 78.39/10.69 (image1Ex) => 78.39/10.69 (( 78.39/10.69 (image1Ex1) => 78.39/10.69 (( 78.39/10.69 (image1Equiv) => 78.39/10.69 (( 78.39/10.69 (image1E) => 78.39/10.69 (( 78.39/10.69 (image1I) => 78.39/10.69 (( 78.39/10.69 (injFuncInInjFuncSet) => 78.39/10.69 (( 78.39/10.69 (injFuncSetFuncIn) => 78.39/10.69 (( 78.39/10.69 (injFuncSetFuncInj) => 78.39/10.69 (( 78.39/10.69 (surjFuncSetFuncIn) => 78.39/10.69 (( 78.39/10.69 (surjFuncSetFuncSurj) => 78.39/10.69 (( 78.39/10.69 (leftInvIsSurj) => 78.39/10.69 (( 78.39/10.69 (surjCantorThm) => 78.39/10.69 (( 78.39/10.69 (foundation2) => 78.39/10.69 (( 78.39/10.69 (notinself) => 78.39/10.69 (( 78.39/10.69 (notinself2) => 78.39/10.69 (( 78.39/10.69 (omegaSp) => 78.39/10.69 (( 78.39/10.69 (omegaSclos) => 78.39/10.69 (( 78.39/10.69 (peano0notS) => 78.39/10.69 (( 78.39/10.69 (peanoSinj) => 78.39/10.69 (( 78.39/10.69 (transitivesetOp1) => 78.39/10.69 (( 78.39/10.69 (binintTransitive) => 78.39/10.69 (( 78.39/10.69 (transitivesetOp2) => 78.39/10.69 (( 78.39/10.69 (setunionTransitive) => 78.39/10.69 (( 78.39/10.69 (ordinalMinLem1) => 78.39/10.69 (( 78.39/10.69 (!!) @ ( 78.39/10.69 ^[Y0 : $i]: 78.39/10.69 (( 78.39/10.69 (ordinal @ 78.39/10.69 Y0) => 78.39/10.69 (( 78.39/10.69 (!!) @ ( 78.39/10.69 ^[Y1 : $i]: 78.39/10.69 (( 78.39/10.69 (!!) @ ( 78.39/10.69 ^[Y2 : $i]: 78.39/10.69 (( 78.39/10.69 (in @ 78.39/10.69 Y2 @ 78.39/10.69 Y0) => 78.39/10.69 (( 78.39/10.69 (in @ 78.39/10.69 Y1 @ 78.39/10.69 Y2) => 78.39/10.69 (in @ 78.39/10.69 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 78.39/10.69 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1297])). 78.39/10.69 thf(zip_derived_cl1314, plain, 78.39/10.69 (~ (((ex1E1) => 78.39/10.69 (((ex1I) => 78.39/10.69 (((ex1I2) => 78.39/10.69 (((singletonsuniq) => 78.39/10.69 (((setukpairinjL1) => 78.39/10.69 (((kfstsingleton) => 78.39/10.69 (((theprop) => 78.39/10.69 (((kfstpairEq) => 78.39/10.69 (((cartprodfstin) => 78.39/10.69 (((setukpairinjL2) => 78.39/10.69 (((setukpairinjL) => 78.39/10.69 (((setukpairinjR11) => 78.39/10.69 (((setukpairinjR12) => 78.39/10.69 (((setukpairinjR1) => 78.39/10.69 (((upairequniteq) => 78.39/10.69 (((setukpairinjR2) => 78.39/10.69 (((setukpairinjR) => 78.39/10.69 (((ksndsingleton) => 78.39/10.69 (((ksndpairEq) => 78.39/10.69 (((kpairsurjEq) => 78.39/10.69 (((cartprodsndin) => 78.39/10.69 (((cartprodpairmemEL) => 78.39/10.69 (((cartprodpairmemER) => 78.39/10.69 (((cartprodmempaircEq) => 78.39/10.69 (((cartprodfstpairEq) => 78.39/10.69 (((cartprodsndpairEq) => 78.39/10.69 (((cartprodpairsurjEq) => 78.39/10.69 (((dpsetconstrI) => 78.39/10.69 (((dpsetconstrSub) => 78.39/10.69 (((setOfPairsIsBReln) => 78.39/10.69 (( 78.39/10.69 (dpsetconstrERa) => 78.39/10.69 (( 78.39/10.69 (dpsetconstrEL1) => 78.39/10.69 (( 78.39/10.69 (dpsetconstrEL2) => 78.39/10.69 (( 78.39/10.69 (dpsetconstrER) => 78.39/10.69 (( 78.39/10.69 (funcImageSingleton) => 78.39/10.69 (( 78.39/10.69 (apProp) => 78.39/10.69 (( 78.39/10.69 (app) => 78.39/10.69 (( 78.39/10.69 (infuncsetfunc) => 78.39/10.69 (( 78.39/10.69 (ap2p) => 78.39/10.69 (( 78.39/10.69 (funcinfuncset) => 78.39/10.69 (( 78.39/10.69 (lamProp) => 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78.39/10.69 (contrasubsetT2) => 78.39/10.69 (( 78.39/10.69 (contrasubsetT3) => 78.39/10.69 (( 78.39/10.69 (doubleComplementI1) => 78.39/10.69 (( 78.39/10.69 (doubleComplementE1) => 78.39/10.69 (( 78.39/10.69 (doubleComplementSub1) => 78.39/10.69 (( 78.39/10.69 (doubleComplementSub2) => 78.39/10.69 (( 78.39/10.69 (doubleComplementEq) => 78.39/10.69 (( 78.39/10.69 (complementTnotintersectT) => 78.39/10.69 (( 78.39/10.69 (complementImpComplementIntersect) => 78.39/10.69 (( 78.39/10.69 (complementSubsetComplementIntersect) => 78.39/10.69 (( 78.39/10.69 (complementInPowersetComplementIntersect) => 78.39/10.69 (( 78.39/10.69 (contraSubsetComplement) => 78.39/10.69 (( 78.39/10.69 (complementTcontraSubset) => 78.39/10.69 (( 78.39/10.69 (binunionTILcontra) => 78.39/10.69 (( 78.39/10.69 (binunionTIRcontra) => 78.39/10.69 (( 78.39/10.69 (inIntersectImpInUnion) => 78.39/10.69 (( 78.39/10.69 (inIntersectImpInUnion2) => 78.39/10.69 (( 78.39/10.69 (inIntersectImpInIntersectUnions) => 78.39/10.69 (( 78.39/10.69 (intersectInPowersetIntersectUnions) => 78.39/10.69 (( 78.39/10.69 (inComplementUnionImpNotIn1) => 78.39/10.69 (( 78.39/10.69 (inComplementUnionImpInComplement1) => 78.39/10.69 (( 78.39/10.69 (binunionTE) => 78.39/10.69 (( 78.39/10.69 (binunionTEcontra) => 78.39/10.69 (( 78.39/10.69 (demorgan2a1) => 78.39/10.69 (( 78.39/10.69 (complementUnionInPowersetComplement) => 78.39/10.69 (( 78.39/10.69 (demorgan2a2) => 78.39/10.69 (( 78.39/10.69 (demorgan1a) => 78.39/10.69 (( 78.39/10.69 (demorgan1b) => 78.39/10.69 (( 78.39/10.69 (demorgan1) => 78.39/10.69 (( 78.39/10.69 (demorgan2a) => 78.39/10.69 (( 78.39/10.69 (demorgan2b2) => 78.39/10.69 (( 78.39/10.69 (demorgan2b) => 78.39/10.69 (( 78.39/10.69 (demorgan2) => 78.39/10.69 (( 78.39/10.69 (woz13rule0) => 78.39/10.69 (( 78.39/10.69 (woz13rule1) => 78.39/10.69 (( 78.39/10.69 (woz13rule2) => 78.39/10.69 (( 78.39/10.69 (woz13rule3) => 78.39/10.69 (( 78.39/10.69 (woz13rule4) => 78.39/10.69 (( 78.39/10.69 (woz1_1) => 78.39/10.69 (( 78.39/10.69 (woz1_2) => 78.39/10.69 (( 78.39/10.69 (woz1_3) => 78.39/10.69 (( 78.39/10.69 (woz1_4) => 78.39/10.69 (( 78.39/10.69 (woz1_5) => 78.39/10.69 (( 78.39/10.69 (breln1all2) => 78.39/10.69 (( 78.39/10.69 (breln1SetBreln1) => 78.39/10.69 (( 78.39/10.69 (choice2fnsingleton) => 78.39/10.69 (( 78.39/10.69 (setOfPairsIsBReln1) => 78.39/10.69 (( 78.39/10.69 (breln1all1) => 78.39/10.69 (( 78.39/10.69 (subbreln1) => 78.39/10.69 (( 78.39/10.69 (eqbreln1) => 78.39/10.69 (( 78.39/10.69 (breln1invprop) => 78.39/10.69 (( 78.39/10.69 (breln1invI) => 78.39/10.69 (( 78.39/10.69 (breln1invE) => 78.39/10.69 (( 78.39/10.69 (breln1compprop) => 78.39/10.69 (( 78.39/10.69 (breln1compI) => 78.39/10.69 (( 78.39/10.69 (breln1compE) => 78.39/10.69 (( 78.39/10.69 (breln1compEex) => 78.39/10.69 (( 78.39/10.69 (breln1unionprop) => 78.39/10.69 (( 78.39/10.69 (breln1unionIL) => 78.39/10.69 (( 78.39/10.69 (breln1unionIR) => 78.39/10.69 (( 78.39/10.69 (breln1unionI) => 78.39/10.69 (( 78.39/10.69 (breln1unionE) => 78.39/10.69 (( 78.39/10.69 (breln1unionEcases) => 78.39/10.69 (( 78.39/10.69 (breln1unionCommutes) => 78.39/10.69 (( 78.39/10.69 (woz2Ex) => 78.39/10.69 (( 78.39/10.69 (woz2W) => 78.39/10.69 (( 78.39/10.69 (woz2A) => 78.39/10.69 (( 78.39/10.69 (woz2B) => 78.39/10.69 (( 78.39/10.69 (image1Ex) => 78.39/10.69 (( 78.39/10.69 (image1Ex1) => 78.39/10.69 (( 78.39/10.69 (image1Equiv) => 78.39/10.69 (( 78.39/10.69 (image1E) => 78.39/10.69 (( 78.39/10.69 (image1I) => 78.39/10.69 (( 78.39/10.69 (injFuncInInjFuncSet) => 78.39/10.69 (( 78.39/10.69 (injFuncSetFuncIn) => 78.39/10.69 (( 78.39/10.69 (injFuncSetFuncInj) => 78.39/10.69 (( 78.39/10.69 (surjFuncSetFuncIn) => 78.39/10.69 (( 78.39/10.69 (surjFuncSetFuncSurj) => 78.39/10.69 (( 78.39/10.69 (leftInvIsSurj) => 78.39/10.69 (( 78.39/10.69 (surjCantorThm) => 78.39/10.69 (( 78.39/10.69 (foundation2) => 78.39/10.69 (( 78.39/10.69 (notinself) => 78.39/10.69 (( 78.39/10.69 (notinself2) => 78.39/10.69 (( 78.39/10.69 (omegaSp) => 78.39/10.69 (( 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Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 78.39/10.69 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1306])). 78.39/10.69 thf(zip_derived_cl1321, plain, 78.39/10.69 (~ (((ex1I) => 78.39/10.69 (((ex1I2) => 78.39/10.69 (((singletonsuniq) => 78.39/10.69 (((setukpairinjL1) => 78.39/10.69 (((kfstsingleton) => 78.39/10.69 (((theprop) => 78.39/10.69 (((kfstpairEq) => 78.39/10.69 (((cartprodfstin) => 78.39/10.69 (((setukpairinjL2) => 78.39/10.69 (((setukpairinjL) => 78.39/10.69 (((setukpairinjR11) => 78.39/10.69 (((setukpairinjR12) => 78.39/10.69 (((setukpairinjR1) => 78.39/10.69 (((upairequniteq) => 78.39/10.69 (((setukpairinjR2) => 78.39/10.69 (((setukpairinjR) => 78.39/10.69 (((ksndsingleton) => 78.39/10.69 (((ksndpairEq) => 78.39/10.69 (((kpairsurjEq) => 78.39/10.69 (((cartprodsndin) => 78.39/10.69 (((cartprodpairmemEL) => 78.39/10.69 (((cartprodpairmemER) => 78.39/10.69 (((cartprodmempaircEq) => 78.39/10.69 (((cartprodfstpairEq) => 78.39/10.69 (((cartprodsndpairEq) => 78.39/10.69 (((cartprodpairsurjEq) => 78.39/10.69 (((dpsetconstrI) => 78.39/10.69 (((dpsetconstrSub) => 78.39/10.69 (((setOfPairsIsBReln) => 78.39/10.69 (((dpsetconstrERa) => 78.39/10.69 (( 78.39/10.69 (dpsetconstrEL1) => 78.39/10.69 (( 78.39/10.69 (dpsetconstrEL2) => 78.39/10.69 (( 78.39/10.69 (dpsetconstrER) => 78.39/10.69 (( 78.39/10.69 (funcImageSingleton) => 78.39/10.69 (( 78.39/10.69 (apProp) => 78.39/10.69 (( 78.39/10.69 (app) => 78.39/10.69 (( 78.39/10.69 (infuncsetfunc) => 78.39/10.69 (( 78.39/10.69 (ap2p) => 78.39/10.69 (( 78.39/10.69 (funcinfuncset) => 78.39/10.69 (( 78.39/10.69 (lamProp) => 78.39/10.69 (( 78.39/10.69 (lamp) => 78.39/10.69 (( 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(( 78.39/10.69 (contrasubsetT3) => 78.39/10.69 (( 78.39/10.69 (doubleComplementI1) => 78.39/10.69 (( 78.39/10.69 (doubleComplementE1) => 78.39/10.69 (( 78.39/10.69 (doubleComplementSub1) => 78.39/10.69 (( 78.39/10.69 (doubleComplementSub2) => 78.39/10.69 (( 78.39/10.69 (doubleComplementEq) => 78.39/10.69 (( 78.39/10.69 (complementTnotintersectT) => 78.39/10.69 (( 78.39/10.69 (complementImpComplementIntersect) => 78.39/10.69 (( 78.39/10.69 (complementSubsetComplementIntersect) => 78.39/10.69 (( 78.39/10.69 (complementInPowersetComplementIntersect) => 78.39/10.69 (( 78.39/10.69 (contraSubsetComplement) => 78.39/10.69 (( 78.39/10.69 (complementTcontraSubset) => 78.39/10.69 (( 78.39/10.69 (binunionTILcontra) => 78.39/10.69 (( 78.39/10.69 (binunionTIRcontra) => 78.39/10.69 (( 78.39/10.69 (inIntersectImpInUnion) => 78.39/10.69 (( 78.39/10.69 (inIntersectImpInUnion2) => 78.39/10.69 (( 78.39/10.69 (inIntersectImpInIntersectUnions) => 78.39/10.69 (( 78.39/10.69 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=> 78.39/10.70 (( 78.39/10.70 (inComplementUnionImpInComplement1) => 78.39/10.70 (( 78.39/10.70 (binunionTE) => 78.39/10.70 (( 78.39/10.70 (binunionTEcontra) => 78.39/10.70 (( 78.39/10.70 (demorgan2a1) => 78.39/10.70 (( 78.39/10.70 (complementUnionInPowersetComplement) => 78.39/10.70 (( 78.39/10.70 (demorgan2a2) => 78.39/10.70 (( 78.39/10.70 (demorgan1a) => 78.39/10.70 (( 78.39/10.70 (demorgan1b) => 78.39/10.70 (( 78.39/10.70 (demorgan1) => 78.39/10.70 (( 78.39/10.70 (demorgan2a) => 78.39/10.70 (( 78.39/10.70 (demorgan2b2) => 78.39/10.70 (( 78.39/10.70 (demorgan2b) => 78.39/10.70 (( 78.39/10.70 (demorgan2) => 78.39/10.70 (( 78.39/10.70 (woz13rule0) => 78.39/10.70 (( 78.39/10.70 (woz13rule1) => 78.39/10.70 (( 78.39/10.70 (woz13rule2) => 78.39/10.70 (( 78.39/10.70 (woz13rule3) => 78.39/10.70 (( 78.39/10.70 (woz13rule4) => 78.39/10.70 (( 78.39/10.70 (woz1_1) => 78.39/10.70 (( 78.39/10.70 (woz1_2) => 78.39/10.70 (( 78.39/10.70 (woz1_3) => 78.39/10.70 (( 78.39/10.70 (woz1_4) => 78.39/10.70 (( 78.39/10.70 (woz1_5) => 78.39/10.70 (( 78.39/10.70 (breln1all2) => 78.39/10.70 (( 78.39/10.70 (breln1SetBreln1) => 78.39/10.70 (( 78.39/10.70 (choice2fnsingleton) => 78.39/10.70 (( 78.39/10.70 (setOfPairsIsBReln1) => 78.39/10.70 (( 78.39/10.70 (breln1all1) => 78.39/10.70 (( 78.39/10.70 (subbreln1) => 78.39/10.70 (( 78.39/10.70 (eqbreln1) => 78.39/10.70 (( 78.39/10.70 (breln1invprop) => 78.39/10.70 (( 78.39/10.70 (breln1invI) => 78.39/10.70 (( 78.39/10.70 (breln1invE) => 78.39/10.70 (( 78.39/10.70 (breln1compprop) => 78.39/10.70 (( 78.39/10.70 (breln1compI) => 78.39/10.70 (( 78.39/10.70 (breln1compE) => 78.39/10.70 (( 78.39/10.70 (breln1compEex) => 78.39/10.70 (( 78.39/10.70 (breln1unionprop) => 78.39/10.70 (( 78.39/10.70 (breln1unionIL) => 78.39/10.70 (( 78.39/10.70 (breln1unionIR) => 78.39/10.70 (( 78.39/10.70 (breln1unionI) => 78.39/10.70 (( 78.39/10.70 (breln1unionE) => 78.39/10.70 (( 78.39/10.70 (breln1unionEcases) => 78.39/10.70 (( 78.39/10.70 (breln1unionCommutes) => 78.39/10.70 (( 78.39/10.70 (woz2Ex) => 78.39/10.70 (( 78.39/10.70 (woz2W) => 78.39/10.70 (( 78.39/10.70 (woz2A) => 78.39/10.70 (( 78.39/10.70 (woz2B) => 78.39/10.70 (( 78.39/10.70 (image1Ex) => 78.39/10.70 (( 78.39/10.70 (image1Ex1) => 78.39/10.70 (( 78.39/10.70 (image1Equiv) => 78.39/10.70 (( 78.39/10.70 (image1E) => 78.39/10.70 (( 78.39/10.70 (image1I) => 78.39/10.70 (( 78.39/10.70 (injFuncInInjFuncSet) => 78.39/10.70 (( 78.39/10.70 (injFuncSetFuncIn) => 78.39/10.70 (( 78.39/10.70 (injFuncSetFuncInj) => 78.39/10.70 (( 78.39/10.70 (surjFuncSetFuncIn) => 78.39/10.70 (( 78.39/10.70 (surjFuncSetFuncSurj) => 78.39/10.70 (( 78.39/10.70 (leftInvIsSurj) => 78.39/10.70 (( 78.39/10.70 (surjCantorThm) => 78.39/10.70 (( 78.39/10.70 (foundation2) => 78.39/10.70 (( 78.39/10.70 (notinself) => 78.39/10.70 (( 78.39/10.70 (notinself2) => 78.39/10.70 (( 78.39/10.70 (omegaSp) => 78.39/10.70 (( 78.39/10.70 (omegaSclos) => 78.39/10.70 (( 78.39/10.70 (peano0notS) => 78.39/10.70 (( 78.39/10.70 (peanoSinj) => 78.39/10.70 (( 78.39/10.70 (transitivesetOp1) => 78.39/10.70 (( 78.39/10.70 (binintTransitive) => 78.39/10.70 (( 78.39/10.70 (transitivesetOp2) => 78.39/10.70 (( 78.39/10.70 (setunionTransitive) => 78.39/10.70 (( 78.39/10.70 (ordinalMinLem1) => 78.39/10.70 (( 78.39/10.70 (!!) @ ( 78.39/10.70 ^[Y0 : $i]: 78.39/10.70 (( 78.39/10.70 (ordinal @ 78.39/10.70 Y0) => 78.39/10.70 (( 78.39/10.70 (!!) @ ( 78.39/10.70 ^[Y1 : $i]: 78.39/10.70 (( 78.39/10.70 (!!) @ ( 78.39/10.70 ^[Y2 : $i]: 78.39/10.70 (( 78.39/10.70 (in @ 78.39/10.70 Y2 @ 78.39/10.70 Y0) => 78.39/10.70 (( 78.39/10.70 (in @ 78.39/10.70 Y1 @ 78.39/10.70 Y2) => 78.39/10.70 (in @ 78.39/10.70 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 78.39/10.70 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1328])). 78.39/10.70 thf(zip_derived_cl1344, plain, 78.39/10.70 (~ (((setukpairinjL1) => 78.39/10.70 (((kfstsingleton) => 78.39/10.70 (((theprop) => 78.39/10.70 (((kfstpairEq) => 78.39/10.70 (((cartprodfstin) => 78.39/10.70 (((setukpairinjL2) => 78.39/10.70 (((setukpairinjL) => 78.39/10.70 (((setukpairinjR11) => 78.39/10.70 (((setukpairinjR12) => 78.39/10.70 (((setukpairinjR1) => 78.39/10.70 (((upairequniteq) => 78.39/10.70 (((setukpairinjR2) => 78.39/10.70 (((setukpairinjR) => 78.39/10.70 (((ksndsingleton) => 78.39/10.70 (((ksndpairEq) => 78.39/10.70 (((kpairsurjEq) => 78.39/10.70 (((cartprodsndin) => 78.39/10.70 (((cartprodpairmemEL) => 78.39/10.70 (((cartprodpairmemER) => 78.39/10.70 (((cartprodmempaircEq) => 78.39/10.70 (((cartprodfstpairEq) => 78.39/10.70 (((cartprodsndpairEq) => 78.39/10.70 (((cartprodpairsurjEq) => 78.39/10.70 (((dpsetconstrI) => 78.39/10.70 (((dpsetconstrSub) => 78.39/10.70 (((setOfPairsIsBReln) => 78.39/10.70 (((dpsetconstrERa) => 78.39/10.70 (((dpsetconstrEL1) => 78.39/10.70 (((dpsetconstrEL2) => 78.39/10.70 (((dpsetconstrER) => 78.39/10.70 (( 78.39/10.70 (funcImageSingleton) => 78.39/10.70 (( 78.39/10.70 (apProp) => 78.39/10.70 (( 78.39/10.70 (app) => 78.39/10.70 (( 78.39/10.70 (infuncsetfunc) => 78.39/10.70 (( 78.39/10.70 (ap2p) => 78.39/10.70 (( 78.39/10.70 (funcinfuncset) => 78.39/10.70 (( 78.39/10.70 (lamProp) => 78.39/10.70 (( 78.39/10.70 (lamp) => 78.39/10.70 (( 78.39/10.70 (lam2p) => 78.39/10.70 (( 78.39/10.70 (brelnall1) => 78.39/10.70 (( 78.39/10.70 (brelnall2) => 78.39/10.70 (( 78.39/10.70 (ex1E2) => 78.39/10.70 (( 78.39/10.70 (funcGraphProp1) => 78.39/10.70 (( 78.39/10.70 (funcGraphProp3) => 78.39/10.70 (( 78.39/10.70 (funcGraphProp2) => 78.39/10.70 (( 78.39/10.70 (funcextLem) => 78.39/10.70 (( 78.39/10.70 (funcGraphProp4) => 78.39/10.70 (( 78.39/10.70 (subbreln) => 78.39/10.70 (( 78.39/10.70 (eqbreln) => 78.39/10.70 (( 78.39/10.70 (funcext) => 78.39/10.70 (( 78.39/10.70 (funcext2) => 78.39/10.70 (( 78.39/10.70 (ap2apEq1) => 78.39/10.70 (( 78.39/10.70 (ap2apEq2) => 78.39/10.70 (( 78.39/10.70 (beta1) => 78.39/10.70 (( 78.39/10.70 (eta1) => 78.39/10.70 (( 78.39/10.70 (lam2lamEq) => 78.39/10.70 (( 78.39/10.70 (beta2) => 78.39/10.70 (( 78.39/10.70 (eta2) => 78.39/10.70 (( 78.39/10.70 (iffalseProp1) => 78.39/10.70 (( 78.39/10.70 (iffalseProp2) => 78.39/10.70 (( 78.39/10.70 (iftrueProp1) => 78.39/10.70 (( 78.39/10.70 (iftrueProp2) => 78.39/10.70 (( 78.39/10.70 (ifSingleton) => 78.39/10.70 (( 78.39/10.70 (ifp) => 78.39/10.70 (( 78.39/10.70 (theeq) => 78.39/10.70 (( 78.39/10.70 (iftrue) => 78.39/10.70 (( 78.39/10.70 (iffalse) => 78.39/10.70 (( 78.39/10.70 (iftrueorfalse) => 78.39/10.70 (( 78.39/10.70 (binintersectT_lem) => 78.39/10.70 (( 78.39/10.70 (binunionT_lem) => 78.39/10.70 (( 78.39/10.70 (powersetT_lem) => 78.39/10.70 (( 78.39/10.70 (setminusT_lem) => 78.39/10.70 (( 78.39/10.70 (complementT_lem) => 78.39/10.70 (( 78.39/10.70 (setextT) => 78.39/10.70 (( 78.39/10.70 (subsetTI) => 78.39/10.70 (( 78.39/10.70 (powersetTI1) => 78.39/10.70 (( 78.39/10.70 (powersetTE1) => 78.39/10.70 (( 78.39/10.70 (complementTI1) => 78.39/10.70 (( 78.39/10.70 (complementTE1) => 78.39/10.70 (( 78.39/10.70 (binintersectTELcontra) => 78.39/10.70 (( 78.39/10.70 (binintersectTERcontra) => 78.39/10.70 (( 78.39/10.70 (contrasubsetT) => 78.39/10.70 (( 78.39/10.70 (contrasubsetT1) => 78.39/10.70 (( 78.39/10.70 (contrasubsetT2) => 78.39/10.70 (( 78.39/10.70 (contrasubsetT3) => 78.39/10.70 (( 78.39/10.70 (doubleComplementI1) => 78.39/10.70 (( 78.39/10.70 (doubleComplementE1) => 78.39/10.70 (( 78.39/10.70 (doubleComplementSub1) => 78.39/10.70 (( 78.39/10.70 (doubleComplementSub2) => 78.39/10.70 (( 78.39/10.70 (doubleComplementEq) => 78.39/10.70 (( 78.39/10.70 (complementTnotintersectT) => 78.39/10.70 (( 78.39/10.70 (complementImpComplementIntersect) => 78.39/10.70 (( 78.39/10.70 (complementSubsetComplementIntersect) => 78.39/10.70 (( 78.39/10.70 (complementInPowersetComplementIntersect) => 78.39/10.70 (( 78.39/10.70 (contraSubsetComplement) => 78.39/10.70 (( 78.39/10.70 (complementTcontraSubset) => 78.39/10.70 (( 78.39/10.70 (binunionTILcontra) => 78.39/10.70 (( 78.39/10.70 (binunionTIRcontra) => 78.39/10.70 (( 78.39/10.70 (inIntersectImpInUnion) => 78.39/10.70 (( 78.39/10.70 (inIntersectImpInUnion2) => 78.39/10.70 (( 78.39/10.70 (inIntersectImpInIntersectUnions) => 78.39/10.70 (( 78.39/10.70 (intersectInPowersetIntersectUnions) => 78.39/10.70 (( 78.39/10.70 (inComplementUnionImpNotIn1) => 78.39/10.70 (( 78.39/10.70 (inComplementUnionImpInComplement1) => 78.39/10.70 (( 78.39/10.70 (binunionTE) => 78.39/10.70 (( 78.39/10.70 (binunionTEcontra) => 78.39/10.70 (( 78.39/10.70 (demorgan2a1) => 78.39/10.70 (( 78.39/10.70 (complementUnionInPowersetComplement) => 78.39/10.70 (( 78.39/10.70 (demorgan2a2) => 78.39/10.70 (( 78.39/10.70 (demorgan1a) => 78.39/10.70 (( 78.39/10.70 (demorgan1b) => 78.39/10.70 (( 78.39/10.70 (demorgan1) => 78.39/10.70 (( 78.39/10.70 (demorgan2a) => 78.39/10.70 (( 78.39/10.70 (demorgan2b2) => 78.39/10.70 (( 78.39/10.70 (demorgan2b) => 78.39/10.70 (( 78.39/10.70 (demorgan2) => 78.39/10.70 (( 78.39/10.70 (woz13rule0) => 78.39/10.70 (( 78.39/10.70 (woz13rule1) => 78.39/10.70 (( 78.39/10.70 (woz13rule2) => 78.39/10.70 (( 78.39/10.70 (woz13rule3) => 78.39/10.70 (( 78.39/10.70 (woz13rule4) => 78.39/10.70 (( 78.39/10.70 (woz1_1) => 78.39/10.70 (( 78.39/10.70 (woz1_2) => 78.39/10.70 (( 78.39/10.70 (woz1_3) => 78.39/10.70 (( 78.39/10.70 (woz1_4) => 78.39/10.70 (( 78.39/10.70 (woz1_5) => 78.39/10.70 (( 78.39/10.70 (breln1all2) => 78.39/10.70 (( 78.39/10.70 (breln1SetBreln1) => 78.39/10.70 (( 78.39/10.70 (choice2fnsingleton) => 78.39/10.70 (( 78.39/10.70 (setOfPairsIsBReln1) => 78.39/10.70 (( 78.39/10.70 (breln1all1) => 78.39/10.70 (( 78.39/10.70 (subbreln1) => 78.39/10.70 (( 78.39/10.70 (eqbreln1) => 78.39/10.70 (( 78.39/10.70 (breln1invprop) => 78.39/10.70 (( 78.39/10.70 (breln1invI) => 78.39/10.70 (( 78.39/10.70 (breln1invE) => 78.39/10.70 (( 78.39/10.70 (breln1compprop) => 78.39/10.70 (( 78.39/10.70 (breln1compI) => 78.39/10.70 (( 78.39/10.70 (breln1compE) => 78.39/10.70 (( 78.39/10.70 (breln1compEex) => 78.39/10.70 (( 78.39/10.70 (breln1unionprop) => 78.39/10.70 (( 78.39/10.70 (breln1unionIL) => 78.39/10.70 (( 78.39/10.70 (breln1unionIR) => 78.39/10.70 (( 78.39/10.70 (breln1unionI) => 78.39/10.70 (( 78.39/10.70 (breln1unionE) => 78.39/10.70 (( 78.39/10.70 (breln1unionEcases) => 78.39/10.70 (( 78.39/10.70 (breln1unionCommutes) => 78.39/10.70 (( 78.39/10.70 (woz2Ex) => 78.39/10.70 (( 78.39/10.70 (woz2W) => 78.39/10.70 (( 78.39/10.70 (woz2A) => 78.39/10.70 (( 78.39/10.70 (woz2B) => 78.39/10.70 (( 78.39/10.70 (image1Ex) => 78.39/10.70 (( 78.39/10.70 (image1Ex1) => 78.39/10.70 (( 78.39/10.70 (image1Equiv) => 78.39/10.70 (( 78.39/10.70 (image1E) => 78.39/10.70 (( 78.39/10.70 (image1I) => 78.39/10.70 (( 78.39/10.70 (injFuncInInjFuncSet) => 78.39/10.70 (( 78.39/10.70 (injFuncSetFuncIn) => 78.39/10.70 (( 78.39/10.70 (injFuncSetFuncInj) => 78.39/10.70 (( 78.39/10.70 (surjFuncSetFuncIn) => 78.39/10.70 (( 78.39/10.70 (surjFuncSetFuncSurj) => 78.39/10.70 (( 78.39/10.70 (leftInvIsSurj) => 78.39/10.70 (( 78.39/10.70 (surjCantorThm) => 78.39/10.70 (( 78.39/10.70 (foundation2) => 78.39/10.70 (( 78.39/10.70 (notinself) => 78.39/10.70 (( 78.39/10.70 (notinself2) => 78.39/10.70 (( 78.39/10.70 (omegaSp) => 78.39/10.70 (( 78.39/10.70 (omegaSclos) => 78.39/10.70 (( 78.39/10.70 (peano0notS) => 78.39/10.70 (( 78.39/10.70 (peanoSinj) => 78.39/10.70 (( 78.39/10.70 (transitivesetOp1) => 78.39/10.70 (( 78.39/10.70 (binintTransitive) => 78.39/10.70 (( 78.39/10.70 (transitivesetOp2) => 78.39/10.70 (( 78.39/10.70 (setunionTransitive) => 78.39/10.70 (( 78.39/10.70 (ordinalMinLem1) => 78.39/10.70 (( 78.39/10.70 (!!) @ ( 78.39/10.70 ^[Y0 : $i]: 78.39/10.70 (( 78.39/10.70 (ordinal @ 78.39/10.70 Y0) => 78.39/10.70 (( 78.39/10.70 (!!) @ ( 78.39/10.70 ^[Y1 : $i]: 78.39/10.70 (( 78.39/10.70 (!!) @ ( 78.39/10.70 ^[Y2 : $i]: 78.39/10.70 (( 78.39/10.70 (in @ 78.39/10.70 Y2 @ 78.39/10.70 Y0) => 78.39/10.70 (( 78.39/10.70 (in @ 78.39/10.70 Y1 @ 78.39/10.70 Y2) => 78.39/10.70 (in @ 78.39/10.70 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 78.39/10.70 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1336])). 78.39/10.70 thf(zip_derived_cl1352, plain, 78.39/10.70 (~ (((kfstsingleton) => 78.39/10.70 (((theprop) => 78.39/10.70 (((kfstpairEq) => 78.39/10.70 (((cartprodfstin) => 78.39/10.70 (((setukpairinjL2) => 78.39/10.70 (((setukpairinjL) => 78.39/10.70 (((setukpairinjR11) => 78.39/10.70 (((setukpairinjR12) => 78.39/10.70 (((setukpairinjR1) => 78.39/10.70 (((upairequniteq) => 78.39/10.70 (((setukpairinjR2) => 78.39/10.70 (((setukpairinjR) => 78.39/10.70 (((ksndsingleton) => 78.39/10.70 (((ksndpairEq) => 78.39/10.70 (((kpairsurjEq) => 78.39/10.70 (((cartprodsndin) => 78.39/10.70 (((cartprodpairmemEL) => 78.39/10.70 (((cartprodpairmemER) => 78.39/10.70 (((cartprodmempaircEq) => 78.39/10.70 (((cartprodfstpairEq) => 78.39/10.70 (((cartprodsndpairEq) => 78.39/10.70 (((cartprodpairsurjEq) => 78.39/10.70 (((dpsetconstrI) => 78.39/10.70 (((dpsetconstrSub) => 78.39/10.70 (((setOfPairsIsBReln) => 78.39/10.70 (((dpsetconstrERa) => 78.39/10.70 (((dpsetconstrEL1) => 78.39/10.70 (((dpsetconstrEL2) => 78.39/10.70 (((dpsetconstrER) => 78.39/10.70 (((funcImageSingleton) => 78.39/10.70 (( 78.39/10.70 (apProp) => 78.39/10.70 (( 78.39/10.70 (app) => 78.39/10.70 (( 78.39/10.70 (infuncsetfunc) => 78.39/10.70 (( 78.39/10.70 (ap2p) => 78.39/10.70 (( 78.39/10.70 (funcinfuncset) => 78.39/10.70 (( 78.39/10.70 (lamProp) => 78.39/10.70 (( 78.39/10.70 (lamp) => 78.39/10.70 (( 78.39/10.70 (lam2p) => 78.39/10.70 (( 78.39/10.70 (brelnall1) => 78.39/10.70 (( 78.39/10.70 (brelnall2) => 78.39/10.70 (( 78.39/10.70 (ex1E2) => 78.39/10.70 (( 78.39/10.70 (funcGraphProp1) => 78.39/10.70 (( 78.39/10.70 (funcGraphProp3) => 78.39/10.70 (( 78.39/10.70 (funcGraphProp2) => 78.39/10.70 (( 78.39/10.70 (funcextLem) => 78.39/10.70 (( 78.39/10.70 (funcGraphProp4) => 78.39/10.70 (( 78.39/10.70 (subbreln) => 78.39/10.70 (( 78.39/10.70 (eqbreln) => 78.39/10.70 (( 78.39/10.70 (funcext) => 78.39/10.70 (( 78.39/10.70 (funcext2) => 78.39/10.70 (( 78.39/10.70 (ap2apEq1) => 78.39/10.70 (( 78.39/10.70 (ap2apEq2) => 78.39/10.70 (( 78.39/10.70 (beta1) => 78.39/10.70 (( 78.39/10.70 (eta1) => 78.39/10.70 (( 78.39/10.70 (lam2lamEq) => 78.39/10.70 (( 78.39/10.70 (beta2) => 78.39/10.70 (( 78.39/10.70 (eta2) => 78.39/10.70 (( 78.39/10.70 (iffalseProp1) => 78.39/10.70 (( 78.39/10.70 (iffalseProp2) => 78.39/10.70 (( 78.39/10.70 (iftrueProp1) => 78.39/10.70 (( 78.39/10.70 (iftrueProp2) => 78.39/10.70 (( 78.39/10.70 (ifSingleton) => 78.39/10.70 (( 78.39/10.70 (ifp) => 78.39/10.70 (( 78.39/10.70 (theeq) => 78.39/10.70 (( 78.39/10.70 (iftrue) => 78.39/10.70 (( 78.39/10.70 (iffalse) => 78.39/10.70 (( 78.39/10.70 (iftrueorfalse) => 78.39/10.70 (( 78.39/10.70 (binintersectT_lem) => 78.39/10.70 (( 78.39/10.70 (binunionT_lem) => 78.39/10.70 (( 78.39/10.70 (powersetT_lem) => 78.39/10.70 (( 78.39/10.70 (setminusT_lem) => 78.39/10.70 (( 78.39/10.70 (complementT_lem) => 78.39/10.70 (( 78.39/10.70 (setextT) => 78.39/10.70 (( 78.39/10.70 (subsetTI) => 78.39/10.70 (( 78.39/10.70 (powersetTI1) => 78.39/10.70 (( 78.39/10.70 (powersetTE1) => 78.39/10.70 (( 78.39/10.70 (complementTI1) => 78.39/10.70 (( 78.39/10.70 (complementTE1) => 78.39/10.70 (( 78.39/10.70 (binintersectTELcontra) => 78.39/10.70 (( 78.39/10.70 (binintersectTERcontra) => 78.39/10.70 (( 78.39/10.70 (contrasubsetT) => 78.39/10.70 (( 78.39/10.70 (contrasubsetT1) => 78.39/10.70 (( 78.39/10.70 (contrasubsetT2) => 78.39/10.70 (( 78.39/10.70 (contrasubsetT3) => 78.39/10.70 (( 78.39/10.70 (doubleComplementI1) => 78.39/10.70 (( 78.39/10.70 (doubleComplementE1) => 78.39/10.70 (( 78.39/10.70 (doubleComplementSub1) => 78.39/10.70 (( 78.39/10.70 (doubleComplementSub2) => 78.39/10.70 (( 78.39/10.70 (doubleComplementEq) => 78.39/10.70 (( 78.39/10.70 (complementTnotintersectT) => 78.39/10.70 (( 78.39/10.70 (complementImpComplementIntersect) => 78.39/10.70 (( 78.39/10.70 (complementSubsetComplementIntersect) => 78.39/10.70 (( 78.39/10.70 (complementInPowersetComplementIntersect) => 78.39/10.70 (( 78.39/10.70 (contraSubsetComplement) => 78.39/10.70 (( 78.39/10.70 (complementTcontraSubset) => 78.39/10.70 (( 78.39/10.70 (binunionTILcontra) => 78.39/10.70 (( 78.39/10.70 (binunionTIRcontra) => 78.39/10.70 (( 78.39/10.70 (inIntersectImpInUnion) => 78.39/10.70 (( 78.39/10.70 (inIntersectImpInUnion2) => 78.39/10.70 (( 78.39/10.70 (inIntersectImpInIntersectUnions) => 78.39/10.70 (( 78.39/10.70 (intersectInPowersetIntersectUnions) => 78.39/10.70 (( 78.39/10.70 (inComplementUnionImpNotIn1) => 78.39/10.70 (( 78.39/10.70 (inComplementUnionImpInComplement1) => 78.39/10.70 (( 78.39/10.70 (binunionTE) => 78.39/10.70 (( 78.39/10.70 (binunionTEcontra) => 78.39/10.70 (( 78.39/10.70 (demorgan2a1) => 78.39/10.70 (( 78.39/10.70 (complementUnionInPowersetComplement) => 78.39/10.70 (( 78.39/10.70 (demorgan2a2) => 78.39/10.70 (( 78.39/10.70 (demorgan1a) => 78.39/10.70 (( 78.39/10.70 (demorgan1b) => 78.39/10.70 (( 78.39/10.70 (demorgan1) => 78.39/10.70 (( 78.39/10.70 (demorgan2a) => 78.39/10.70 (( 78.39/10.70 (demorgan2b2) => 78.39/10.70 (( 78.39/10.70 (demorgan2b) => 78.39/10.70 (( 78.39/10.70 (demorgan2) => 78.39/10.70 (( 78.39/10.70 (woz13rule0) => 78.39/10.70 (( 78.39/10.70 (woz13rule1) => 78.39/10.70 (( 78.39/10.70 (woz13rule2) => 78.39/10.70 (( 78.39/10.70 (woz13rule3) => 78.39/10.70 (( 78.39/10.70 (woz13rule4) => 78.39/10.70 (( 78.39/10.70 (woz1_1) => 78.39/10.70 (( 78.39/10.70 (woz1_2) => 78.39/10.70 (( 78.39/10.70 (woz1_3) => 78.39/10.70 (( 78.39/10.70 (woz1_4) => 78.39/10.70 (( 78.39/10.70 (woz1_5) => 78.39/10.70 (( 78.39/10.70 (breln1all2) => 78.39/10.70 (( 78.39/10.70 (breln1SetBreln1) => 78.39/10.70 (( 78.39/10.70 (choice2fnsingleton) => 78.39/10.70 (( 78.39/10.70 (setOfPairsIsBReln1) => 78.39/10.70 (( 78.39/10.70 (breln1all1) => 78.39/10.70 (( 78.39/10.70 (subbreln1) => 78.39/10.70 (( 78.39/10.70 (eqbreln1) => 78.39/10.70 (( 78.39/10.70 (breln1invprop) => 78.39/10.70 (( 78.39/10.70 (breln1invI) => 78.39/10.70 (( 78.39/10.70 (breln1invE) => 78.39/10.70 (( 78.39/10.70 (breln1compprop) => 78.39/10.70 (( 78.39/10.70 (breln1compI) => 78.39/10.70 (( 78.39/10.70 (breln1compE) => 78.39/10.70 (( 78.39/10.70 (breln1compEex) => 78.39/10.70 (( 78.39/10.70 (breln1unionprop) => 78.39/10.70 (( 78.39/10.70 (breln1unionIL) => 78.39/10.70 (( 78.39/10.70 (breln1unionIR) => 78.39/10.70 (( 78.39/10.70 (breln1unionI) => 78.39/10.70 (( 78.39/10.70 (breln1unionE) => 78.39/10.70 (( 78.39/10.70 (breln1unionEcases) => 78.39/10.70 (( 78.39/10.70 (breln1unionCommutes) => 78.39/10.70 (( 78.39/10.70 (woz2Ex) => 78.39/10.70 (( 78.39/10.70 (woz2W) => 78.39/10.70 (( 78.39/10.70 (woz2A) => 78.39/10.70 (( 78.39/10.70 (woz2B) => 78.39/10.70 (( 78.39/10.70 (image1Ex) => 78.39/10.70 (( 78.39/10.70 (image1Ex1) => 78.39/10.70 (( 78.39/10.70 (image1Equiv) => 78.39/10.70 (( 78.39/10.70 (image1E) => 78.39/10.70 (( 78.39/10.70 (image1I) => 78.39/10.70 (( 78.39/10.70 (injFuncInInjFuncSet) => 78.39/10.70 (( 78.39/10.70 (injFuncSetFuncIn) => 78.39/10.70 (( 78.39/10.70 (injFuncSetFuncInj) => 78.39/10.70 (( 78.39/10.70 (surjFuncSetFuncIn) => 78.39/10.70 (( 78.39/10.70 (surjFuncSetFuncSurj) => 78.39/10.70 (( 78.39/10.70 (leftInvIsSurj) => 78.39/10.70 (( 78.39/10.70 (surjCantorThm) => 78.39/10.70 (( 78.39/10.70 (foundation2) => 78.39/10.70 (( 78.39/10.70 (notinself) => 78.39/10.70 (( 78.39/10.70 (notinself2) => 78.39/10.70 (( 78.39/10.70 (omegaSp) => 78.39/10.70 (( 78.39/10.70 (omegaSclos) => 78.39/10.70 (( 78.39/10.70 (peano0notS) => 78.39/10.70 (( 78.39/10.70 (peanoSinj) => 78.39/10.70 (( 78.39/10.70 (transitivesetOp1) => 78.39/10.70 (( 78.39/10.70 (binintTransitive) => 78.39/10.70 (( 78.39/10.70 (transitivesetOp2) => 78.39/10.70 (( 78.39/10.70 (setunionTransitive) => 78.39/10.70 (( 78.39/10.70 (ordinalMinLem1) => 78.39/10.70 (( 78.39/10.70 (!!) @ ( 78.39/10.70 ^[Y0 : $i]: 78.39/10.70 (( 78.39/10.70 (ordinal @ 78.39/10.70 Y0) => 78.39/10.70 (( 78.39/10.70 (!!) @ ( 78.39/10.70 ^[Y1 : $i]: 78.39/10.70 (( 78.39/10.70 (!!) @ ( 78.39/10.70 ^[Y2 : $i]: 78.39/10.70 (( 78.39/10.70 (in @ 78.39/10.70 Y2 @ 78.39/10.70 Y0) => 78.39/10.70 (( 78.39/10.70 (in @ 78.39/10.70 Y1 @ 78.39/10.70 Y2) => 78.39/10.70 (in @ 78.39/10.70 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 78.39/10.70 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1344])). 78.39/10.70 thf(zip_derived_cl1361, plain, 78.39/10.70 (~ (((theprop) => 78.39/10.70 (((kfstpairEq) => 78.39/10.70 (((cartprodfstin) => 78.39/10.70 (((setukpairinjL2) => 78.39/10.70 (((setukpairinjL) => 78.39/10.70 (((setukpairinjR11) => 78.39/10.70 (((setukpairinjR12) => 78.39/10.70 (((setukpairinjR1) => 78.39/10.70 (((upairequniteq) => 78.39/10.70 (((setukpairinjR2) => 78.39/10.70 (((setukpairinjR) => 78.39/10.70 (((ksndsingleton) => 78.39/10.70 (((ksndpairEq) => 78.39/10.70 (((kpairsurjEq) => 78.39/10.70 (((cartprodsndin) => 78.39/10.70 (((cartprodpairmemEL) => 78.39/10.70 (((cartprodpairmemER) => 78.39/10.70 (((cartprodmempaircEq) => 78.39/10.70 (((cartprodfstpairEq) => 78.39/10.70 (((cartprodsndpairEq) => 78.39/10.70 (((cartprodpairsurjEq) => 78.39/10.70 (((dpsetconstrI) => 78.39/10.70 (((dpsetconstrSub) => 78.39/10.70 (((setOfPairsIsBReln) => 78.39/10.70 (((dpsetconstrERa) => 78.39/10.70 (((dpsetconstrEL1) => 78.39/10.70 (((dpsetconstrEL2) => 78.39/10.70 (((dpsetconstrER) => 78.39/10.70 (((funcImageSingleton) => 78.39/10.70 (((apProp) => 78.39/10.70 (( 78.39/10.70 (app) => 78.39/10.70 (( 78.39/10.70 (infuncsetfunc) => 78.39/10.70 (( 78.39/10.70 (ap2p) => 78.39/10.70 (( 78.39/10.70 (funcinfuncset) => 78.39/10.70 (( 78.39/10.70 (lamProp) => 78.39/10.70 (( 78.39/10.70 (lamp) => 78.39/10.70 (( 78.39/10.70 (lam2p) => 78.39/10.70 (( 78.39/10.70 (brelnall1) => 78.39/10.70 (( 78.39/10.70 (brelnall2) => 78.39/10.70 (( 78.39/10.70 (ex1E2) => 78.39/10.70 (( 78.39/10.70 (funcGraphProp1) => 78.39/10.70 (( 78.39/10.70 (funcGraphProp3) => 78.39/10.70 (( 78.39/10.70 (funcGraphProp2) => 78.39/10.70 (( 78.39/10.70 (funcextLem) => 78.39/10.70 (( 78.39/10.70 (funcGraphProp4) => 78.39/10.70 (( 78.39/10.70 (subbreln) => 78.39/10.70 (( 78.39/10.70 (eqbreln) => 78.39/10.70 (( 78.39/10.70 (funcext) => 78.39/10.70 (( 78.39/10.70 (funcext2) => 78.39/10.70 (( 78.39/10.70 (ap2apEq1) => 78.39/10.70 (( 78.39/10.70 (ap2apEq2) => 78.39/10.70 (( 78.39/10.70 (beta1) => 78.39/10.70 (( 78.39/10.70 (eta1) => 78.39/10.70 (( 78.39/10.70 (lam2lamEq) => 78.39/10.70 (( 78.39/10.70 (beta2) => 78.39/10.70 (( 78.39/10.70 (eta2) => 78.39/10.70 (( 78.39/10.70 (iffalseProp1) => 78.39/10.70 (( 78.39/10.70 (iffalseProp2) => 78.39/10.70 (( 78.39/10.70 (iftrueProp1) => 78.39/10.70 (( 78.39/10.70 (iftrueProp2) => 78.39/10.70 (( 78.39/10.70 (ifSingleton) => 78.39/10.70 (( 78.39/10.70 (ifp) => 78.39/10.70 (( 78.39/10.70 (theeq) => 78.39/10.70 (( 78.39/10.70 (iftrue) => 78.39/10.70 (( 78.39/10.70 (iffalse) => 78.39/10.70 (( 78.39/10.70 (iftrueorfalse) => 78.39/10.70 (( 78.39/10.70 (binintersectT_lem) => 78.39/10.70 (( 78.39/10.70 (binunionT_lem) => 78.39/10.70 (( 78.39/10.70 (powersetT_lem) => 78.39/10.70 (( 78.39/10.70 (setminusT_lem) => 78.39/10.70 (( 78.39/10.70 (complementT_lem) => 78.39/10.70 (( 78.39/10.70 (setextT) => 78.39/10.70 (( 78.39/10.70 (subsetTI) => 78.39/10.70 (( 78.39/10.70 (powersetTI1) => 78.39/10.70 (( 78.39/10.70 (powersetTE1) => 78.39/10.70 (( 78.39/10.70 (complementTI1) => 78.39/10.70 (( 78.39/10.70 (complementTE1) => 78.39/10.70 (( 78.39/10.70 (binintersectTELcontra) => 78.39/10.70 (( 78.39/10.70 (binintersectTERcontra) => 78.39/10.70 (( 78.39/10.70 (contrasubsetT) => 78.39/10.70 (( 78.39/10.70 (contrasubsetT1) => 78.39/10.70 (( 78.39/10.70 (contrasubsetT2) => 78.39/10.70 (( 78.39/10.70 (contrasubsetT3) => 78.39/10.70 (( 78.39/10.70 (doubleComplementI1) => 78.39/10.70 (( 78.39/10.70 (doubleComplementE1) => 78.39/10.70 (( 78.39/10.70 (doubleComplementSub1) => 78.39/10.70 (( 78.39/10.70 (doubleComplementSub2) => 78.39/10.70 (( 78.39/10.70 (doubleComplementEq) => 78.39/10.70 (( 78.39/10.70 (complementTnotintersectT) => 78.39/10.70 (( 78.39/10.70 (complementImpComplementIntersect) => 78.39/10.70 (( 78.39/10.70 (complementSubsetComplementIntersect) => 78.39/10.70 (( 78.39/10.70 (complementInPowersetComplementIntersect) => 78.39/10.70 (( 78.39/10.70 (contraSubsetComplement) => 78.39/10.70 (( 78.39/10.70 (complementTcontraSubset) => 78.39/10.70 (( 78.39/10.70 (binunionTILcontra) => 78.39/10.70 (( 78.39/10.70 (binunionTIRcontra) => 78.39/10.70 (( 78.39/10.70 (inIntersectImpInUnion) => 78.39/10.70 (( 78.39/10.70 (inIntersectImpInUnion2) => 78.39/10.70 (( 78.39/10.70 (inIntersectImpInIntersectUnions) => 78.39/10.70 (( 78.39/10.70 (intersectInPowersetIntersectUnions) => 78.39/10.70 (( 78.39/10.70 (inComplementUnionImpNotIn1) => 78.39/10.70 (( 78.39/10.70 (inComplementUnionImpInComplement1) => 78.39/10.70 (( 78.39/10.70 (binunionTE) => 78.39/10.70 (( 78.39/10.70 (binunionTEcontra) => 78.39/10.70 (( 78.39/10.70 (demorgan2a1) => 78.39/10.70 (( 78.39/10.70 (complementUnionInPowersetComplement) => 78.39/10.70 (( 78.39/10.70 (demorgan2a2) => 78.39/10.70 (( 78.39/10.70 (demorgan1a) => 78.39/10.70 (( 78.39/10.70 (demorgan1b) => 78.39/10.70 (( 78.39/10.70 (demorgan1) => 78.39/10.70 (( 78.39/10.70 (demorgan2a) => 78.39/10.70 (( 78.39/10.70 (demorgan2b2) => 78.39/10.70 (( 78.39/10.70 (demorgan2b) => 78.39/10.70 (( 78.39/10.70 (demorgan2) => 78.39/10.70 (( 78.39/10.70 (woz13rule0) => 78.39/10.70 (( 78.39/10.70 (woz13rule1) => 78.39/10.70 (( 78.39/10.70 (woz13rule2) => 78.39/10.70 (( 78.39/10.70 (woz13rule3) => 78.39/10.70 (( 78.39/10.70 (woz13rule4) => 78.39/10.70 (( 78.39/10.70 (woz1_1) => 78.39/10.70 (( 78.39/10.70 (woz1_2) => 78.39/10.70 (( 78.39/10.70 (woz1_3) => 78.39/10.70 (( 78.39/10.70 (woz1_4) => 78.39/10.70 (( 78.39/10.70 (woz1_5) => 78.39/10.70 (( 78.39/10.70 (breln1all2) => 78.39/10.70 (( 78.39/10.70 (breln1SetBreln1) => 78.39/10.70 (( 78.39/10.70 (choice2fnsingleton) => 78.39/10.70 (( 78.39/10.70 (setOfPairsIsBReln1) => 78.39/10.70 (( 78.39/10.70 (breln1all1) => 78.39/10.70 (( 78.39/10.70 (subbreln1) => 78.39/10.70 (( 78.39/10.70 (eqbreln1) => 78.39/10.70 (( 78.39/10.70 (breln1invprop) => 78.39/10.70 (( 78.39/10.70 (breln1invI) => 78.39/10.70 (( 78.39/10.70 (breln1invE) => 78.39/10.70 (( 78.39/10.70 (breln1compprop) => 78.39/10.70 (( 78.39/10.70 (breln1compI) => 78.39/10.70 (( 78.39/10.70 (breln1compE) => 78.39/10.70 (( 78.39/10.70 (breln1compEex) => 78.39/10.70 (( 78.39/10.70 (breln1unionprop) => 78.39/10.70 (( 78.39/10.70 (breln1unionIL) => 78.39/10.70 (( 78.39/10.70 (breln1unionIR) => 78.39/10.70 (( 78.39/10.70 (breln1unionI) => 78.39/10.70 (( 78.39/10.70 (breln1unionE) => 78.39/10.70 (( 78.39/10.70 (breln1unionEcases) => 78.39/10.70 (( 78.39/10.70 (breln1unionCommutes) => 78.39/10.70 (( 78.39/10.70 (woz2Ex) => 78.39/10.70 (( 78.39/10.70 (woz2W) => 78.39/10.70 (( 78.39/10.70 (woz2A) => 78.39/10.70 (( 78.39/10.70 (woz2B) => 78.39/10.70 (( 78.39/10.70 (image1Ex) => 78.39/10.70 (( 78.39/10.70 (image1Ex1) => 78.39/10.70 (( 78.39/10.70 (image1Equiv) => 78.39/10.70 (( 78.39/10.70 (image1E) => 78.39/10.70 (( 78.39/10.70 (image1I) => 78.39/10.70 (( 78.39/10.70 (injFuncInInjFuncSet) => 78.39/10.70 (( 78.39/10.70 (injFuncSetFuncIn) => 78.39/10.70 (( 78.39/10.70 (injFuncSetFuncInj) => 78.39/10.70 (( 78.39/10.70 (surjFuncSetFuncIn) => 78.39/10.70 (( 78.39/10.70 (surjFuncSetFuncSurj) => 78.39/10.70 (( 78.39/10.70 (leftInvIsSurj) => 78.39/10.70 (( 78.39/10.70 (surjCantorThm) => 78.39/10.70 (( 78.39/10.70 (foundation2) => 78.39/10.70 (( 78.39/10.70 (notinself) => 78.39/10.70 (( 78.39/10.70 (notinself2) => 78.39/10.70 (( 78.39/10.70 (omegaSp) => 78.39/10.70 (( 78.39/10.70 (omegaSclos) => 78.39/10.70 (( 78.39/10.70 (peano0notS) => 78.39/10.70 (( 78.39/10.70 (peanoSinj) => 78.39/10.70 (( 78.39/10.70 (transitivesetOp1) => 78.39/10.70 (( 78.39/10.70 (binintTransitive) => 78.39/10.70 (( 78.39/10.70 (transitivesetOp2) => 78.39/10.70 (( 78.39/10.70 (setunionTransitive) => 78.39/10.70 (( 78.39/10.70 (ordinalMinLem1) => 78.39/10.70 (( 78.39/10.70 (!!) @ ( 78.39/10.70 ^[Y0 : $i]: 78.39/10.70 (( 78.39/10.70 (ordinal @ 78.39/10.70 Y0) => 78.39/10.70 (( 78.39/10.70 (!!) @ ( 78.39/10.70 ^[Y1 : $i]: 78.39/10.70 (( 78.39/10.70 (!!) @ ( 78.39/10.70 ^[Y2 : $i]: 78.39/10.70 (( 78.39/10.70 (in @ 78.39/10.70 Y2 @ 78.39/10.70 Y0) => 78.39/10.70 (( 78.39/10.70 (in @ 78.39/10.70 Y1 @ 78.39/10.70 Y2) => 78.39/10.70 (in @ 78.39/10.70 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 78.39/10.70 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1352])). 78.39/10.70 thf(zip_derived_cl1371, plain, 78.39/10.70 (~ (((kfstpairEq) => 78.39/10.70 (((cartprodfstin) => 78.39/10.70 (((setukpairinjL2) => 78.39/10.70 (((setukpairinjL) => 78.39/10.70 (((setukpairinjR11) => 78.39/10.70 (((setukpairinjR12) => 78.39/10.70 (((setukpairinjR1) => 78.39/10.70 (((upairequniteq) => 78.39/10.70 (((setukpairinjR2) => 78.39/10.70 (((setukpairinjR) => 78.39/10.70 (((ksndsingleton) => 78.39/10.70 (((ksndpairEq) => 78.39/10.70 (((kpairsurjEq) => 78.39/10.70 (((cartprodsndin) => 78.39/10.70 (((cartprodpairmemEL) => 78.39/10.70 (((cartprodpairmemER) => 78.39/10.70 (((cartprodmempaircEq) => 78.39/10.70 (((cartprodfstpairEq) => 78.39/10.70 (((cartprodsndpairEq) => 78.39/10.70 (((cartprodpairsurjEq) => 78.39/10.70 (((dpsetconstrI) => 78.39/10.70 (((dpsetconstrSub) => 78.39/10.70 (((setOfPairsIsBReln) => 78.39/10.70 (((dpsetconstrERa) => 78.39/10.70 (((dpsetconstrEL1) => 78.39/10.70 (((dpsetconstrEL2) => 78.39/10.70 (((dpsetconstrER) => 78.39/10.70 (((funcImageSingleton) => 78.39/10.70 (((apProp) => 78.39/10.70 (((app) => 78.39/10.70 (( 78.39/10.70 (infuncsetfunc) => 78.39/10.70 (( 78.39/10.70 (ap2p) => 78.39/10.70 (( 78.39/10.70 (funcinfuncset) => 78.39/10.70 (( 78.39/10.70 (lamProp) => 78.39/10.70 (( 78.39/10.70 (lamp) => 78.39/10.70 (( 78.39/10.70 (lam2p) => 78.39/10.70 (( 78.39/10.70 (brelnall1) => 78.39/10.70 (( 78.39/10.70 (brelnall2) => 78.39/10.70 (( 78.39/10.70 (ex1E2) => 78.39/10.70 (( 78.39/10.70 (funcGraphProp1) => 78.39/10.70 (( 78.39/10.70 (funcGraphProp3) => 78.39/10.70 (( 78.39/10.70 (funcGraphProp2) => 78.39/10.70 (( 78.39/10.70 (funcextLem) => 78.39/10.70 (( 78.39/10.70 (funcGraphProp4) => 78.39/10.70 (( 78.39/10.70 (subbreln) => 78.39/10.70 (( 78.39/10.70 (eqbreln) => 78.39/10.70 (( 78.39/10.70 (funcext) => 78.39/10.70 (( 78.39/10.70 (funcext2) => 78.39/10.70 (( 78.39/10.70 (ap2apEq1) => 78.39/10.70 (( 78.39/10.70 (ap2apEq2) => 78.39/10.70 (( 78.39/10.70 (beta1) => 78.39/10.70 (( 78.39/10.70 (eta1) => 78.39/10.70 (( 78.39/10.70 (lam2lamEq) => 78.39/10.70 (( 78.39/10.70 (beta2) => 78.39/10.70 (( 78.39/10.70 (eta2) => 78.39/10.70 (( 78.39/10.70 (iffalseProp1) => 78.39/10.70 (( 78.39/10.70 (iffalseProp2) => 78.39/10.70 (( 78.39/10.70 (iftrueProp1) => 78.39/10.70 (( 78.39/10.70 (iftrueProp2) => 78.39/10.70 (( 78.39/10.70 (ifSingleton) => 78.39/10.70 (( 78.39/10.70 (ifp) => 78.39/10.70 (( 78.39/10.70 (theeq) => 78.39/10.70 (( 78.39/10.70 (iftrue) => 78.39/10.70 (( 78.39/10.70 (iffalse) => 78.39/10.70 (( 78.39/10.70 (iftrueorfalse) => 78.39/10.70 (( 78.39/10.70 (binintersectT_lem) => 78.39/10.70 (( 78.39/10.70 (binunionT_lem) => 78.39/10.70 (( 78.39/10.70 (powersetT_lem) => 78.39/10.70 (( 78.39/10.70 (setminusT_lem) => 78.39/10.70 (( 78.39/10.70 (complementT_lem) => 78.39/10.70 (( 78.39/10.70 (setextT) => 78.39/10.70 (( 78.39/10.70 (subsetTI) => 78.39/10.70 (( 78.39/10.70 (powersetTI1) => 78.39/10.70 (( 78.39/10.70 (powersetTE1) => 78.39/10.70 (( 78.39/10.70 (complementTI1) => 78.39/10.70 (( 78.39/10.70 (complementTE1) => 78.39/10.70 (( 78.39/10.70 (binintersectTELcontra) => 78.39/10.70 (( 78.39/10.70 (binintersectTERcontra) => 78.39/10.70 (( 78.39/10.70 (contrasubsetT) => 78.39/10.70 (( 78.39/10.70 (contrasubsetT1) => 78.39/10.70 (( 78.39/10.70 (contrasubsetT2) => 78.39/10.70 (( 78.39/10.70 (contrasubsetT3) => 78.39/10.70 (( 78.39/10.70 (doubleComplementI1) => 78.39/10.70 (( 78.39/10.70 (doubleComplementE1) => 78.39/10.70 (( 78.39/10.70 (doubleComplementSub1) => 78.39/10.70 (( 78.39/10.70 (doubleComplementSub2) => 78.39/10.70 (( 78.39/10.70 (doubleComplementEq) => 78.39/10.70 (( 78.39/10.70 (complementTnotintersectT) => 78.39/10.70 (( 78.39/10.70 (complementImpComplementIntersect) => 78.39/10.70 (( 78.39/10.70 (complementSubsetComplementIntersect) => 78.39/10.70 (( 78.39/10.70 (complementInPowersetComplementIntersect) => 78.39/10.70 (( 78.39/10.70 (contraSubsetComplement) => 78.39/10.70 (( 78.39/10.70 (complementTcontraSubset) => 78.39/10.70 (( 78.39/10.70 (binunionTILcontra) => 78.39/10.70 (( 78.39/10.70 (binunionTIRcontra) => 78.39/10.70 (( 78.39/10.70 (inIntersectImpInUnion) => 78.39/10.70 (( 78.39/10.70 (inIntersectImpInUnion2) => 78.39/10.70 (( 78.39/10.70 (inIntersectImpInIntersectUnions) => 78.39/10.70 (( 78.39/10.70 (intersectInPowersetIntersectUnions) => 78.39/10.70 (( 78.39/10.70 (inComplementUnionImpNotIn1) => 78.39/10.70 (( 78.39/10.70 (inComplementUnionImpInComplement1) => 78.39/10.70 (( 78.39/10.70 (binunionTE) => 78.39/10.70 (( 78.39/10.70 (binunionTEcontra) => 78.39/10.70 (( 78.39/10.70 (demorgan2a1) => 78.39/10.70 (( 78.39/10.70 (complementUnionInPowersetComplement) => 78.39/10.70 (( 78.39/10.70 (demorgan2a2) => 78.39/10.70 (( 78.39/10.70 (demorgan1a) => 78.39/10.70 (( 78.39/10.70 (demorgan1b) => 78.39/10.70 (( 78.39/10.70 (demorgan1) => 78.39/10.70 (( 78.39/10.70 (demorgan2a) => 78.39/10.70 (( 78.39/10.70 (demorgan2b2) => 78.39/10.70 (( 78.39/10.70 (demorgan2b) => 78.39/10.70 (( 78.39/10.70 (demorgan2) => 78.39/10.70 (( 78.39/10.70 (woz13rule0) => 78.39/10.70 (( 78.39/10.70 (woz13rule1) => 78.39/10.70 (( 78.39/10.70 (woz13rule2) => 78.39/10.70 (( 78.39/10.70 (woz13rule3) => 78.39/10.70 (( 78.39/10.70 (woz13rule4) => 78.39/10.70 (( 78.39/10.70 (woz1_1) => 78.39/10.70 (( 78.39/10.70 (woz1_2) => 78.39/10.70 (( 78.39/10.70 (woz1_3) => 78.39/10.70 (( 78.39/10.70 (woz1_4) => 78.39/10.70 (( 78.39/10.70 (woz1_5) => 78.39/10.70 (( 78.39/10.70 (breln1all2) => 78.39/10.70 (( 78.39/10.70 (breln1SetBreln1) => 78.39/10.70 (( 78.39/10.70 (choice2fnsingleton) => 78.39/10.70 (( 78.39/10.70 (setOfPairsIsBReln1) => 78.39/10.70 (( 78.39/10.70 (breln1all1) => 78.39/10.70 (( 78.39/10.70 (subbreln1) => 78.39/10.70 (( 78.39/10.70 (eqbreln1) => 78.39/10.70 (( 78.39/10.70 (breln1invprop) => 78.39/10.70 (( 78.39/10.70 (breln1invI) => 78.39/10.70 (( 78.39/10.70 (breln1invE) => 78.39/10.70 (( 78.39/10.70 (breln1compprop) => 78.39/10.70 (( 78.39/10.70 (breln1compI) => 78.39/10.70 (( 78.39/10.70 (breln1compE) => 78.39/10.70 (( 78.39/10.70 (breln1compEex) => 78.39/10.70 (( 78.39/10.70 (breln1unionprop) => 78.39/10.70 (( 78.39/10.70 (breln1unionIL) => 78.39/10.70 (( 78.39/10.70 (breln1unionIR) => 78.39/10.70 (( 78.39/10.70 (breln1unionI) => 78.39/10.70 (( 78.39/10.70 (breln1unionE) => 78.39/10.70 (( 78.39/10.70 (breln1unionEcases) => 78.39/10.70 (( 78.39/10.70 (breln1unionCommutes) => 78.39/10.70 (( 78.39/10.70 (woz2Ex) => 78.39/10.70 (( 78.39/10.70 (woz2W) => 78.39/10.70 (( 78.39/10.70 (woz2A) => 78.39/10.70 (( 78.39/10.70 (woz2B) => 78.39/10.70 (( 78.39/10.70 (image1Ex) => 78.39/10.70 (( 78.39/10.70 (image1Ex1) => 78.39/10.70 (( 78.39/10.70 (image1Equiv) => 78.39/10.70 (( 78.39/10.70 (image1E) => 78.39/10.70 (( 78.39/10.70 (image1I) => 78.39/10.70 (( 78.39/10.70 (injFuncInInjFuncSet) => 78.39/10.70 (( 78.39/10.70 (injFuncSetFuncIn) => 78.39/10.70 (( 78.39/10.70 (injFuncSetFuncInj) => 78.39/10.70 (( 78.39/10.70 (surjFuncSetFuncIn) => 78.39/10.70 (( 78.39/10.70 (surjFuncSetFuncSurj) => 78.39/10.70 (( 78.39/10.70 (leftInvIsSurj) => 78.39/10.70 (( 78.39/10.70 (surjCantorThm) => 78.39/10.70 (( 78.39/10.70 (foundation2) => 78.39/10.70 (( 78.39/10.70 (notinself) => 78.39/10.70 (( 78.39/10.70 (notinself2) => 78.39/10.70 (( 78.39/10.70 (omegaSp) => 78.39/10.70 (( 78.39/10.70 (omegaSclos) => 78.39/10.70 (( 78.39/10.70 (peano0notS) => 78.39/10.70 (( 78.39/10.70 (peanoSinj) => 78.39/10.70 (( 78.39/10.70 (transitivesetOp1) => 78.39/10.70 (( 78.39/10.70 (binintTransitive) => 78.39/10.70 (( 78.39/10.70 (transitivesetOp2) => 78.39/10.70 (( 78.39/10.70 (setunionTransitive) => 78.39/10.70 (( 78.39/10.70 (ordinalMinLem1) => 78.39/10.70 (( 78.39/10.70 (!!) @ ( 78.39/10.70 ^[Y0 : $i]: 78.39/10.70 (( 78.39/10.70 (ordinal @ 78.39/10.70 Y0) => 78.39/10.70 (( 78.39/10.70 (!!) @ ( 78.39/10.70 ^[Y1 : $i]: 78.39/10.70 (( 78.39/10.70 (!!) @ ( 78.39/10.70 ^[Y2 : $i]: 78.39/10.70 (( 78.39/10.70 (in @ 78.39/10.70 Y2 @ 78.39/10.70 Y0) => 78.39/10.70 (( 78.39/10.70 (in @ 78.39/10.70 Y1 @ 78.39/10.70 Y2) => 78.39/10.70 (in @ 78.39/10.70 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 78.39/10.70 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1361])). 78.39/10.70 thf(zip_derived_cl1382, plain, 78.39/10.70 (~ (((cartprodfstin) => 78.39/10.70 (((setukpairinjL2) => 78.39/10.70 (((setukpairinjL) => 78.39/10.70 (((setukpairinjR11) => 78.39/10.70 (((setukpairinjR12) => 78.39/10.70 (((setukpairinjR1) => 78.39/10.70 (((upairequniteq) => 78.39/10.70 (((setukpairinjR2) => 78.39/10.70 (((setukpairinjR) => 78.39/10.70 (((ksndsingleton) => 78.39/10.70 (((ksndpairEq) => 78.39/10.70 (((kpairsurjEq) => 78.39/10.70 (((cartprodsndin) => 78.39/10.70 (((cartprodpairmemEL) => 78.39/10.70 (((cartprodpairmemER) => 78.39/10.70 (((cartprodmempaircEq) => 78.39/10.70 (((cartprodfstpairEq) => 78.39/10.70 (((cartprodsndpairEq) => 78.39/10.70 (((cartprodpairsurjEq) => 78.39/10.70 (((dpsetconstrI) => 78.39/10.70 (((dpsetconstrSub) => 78.39/10.70 (((setOfPairsIsBReln) => 78.39/10.70 (((dpsetconstrERa) => 78.39/10.70 (((dpsetconstrEL1) => 78.39/10.70 (((dpsetconstrEL2) => 78.39/10.70 (((dpsetconstrER) => 78.39/10.70 (((funcImageSingleton) => 78.39/10.70 (((apProp) => 78.39/10.70 (((app) => 78.39/10.70 (((infuncsetfunc) => 78.39/10.70 (( 78.39/10.70 (ap2p) => 78.39/10.70 (( 78.39/10.70 (funcinfuncset) => 78.39/10.70 (( 78.39/10.70 (lamProp) => 78.39/10.70 (( 78.39/10.70 (lamp) => 78.39/10.70 (( 78.39/10.70 (lam2p) => 78.39/10.70 (( 78.39/10.70 (brelnall1) => 78.39/10.70 (( 78.39/10.70 (brelnall2) => 78.39/10.70 (( 78.39/10.70 (ex1E2) => 78.39/10.70 (( 78.39/10.70 (funcGraphProp1) => 78.39/10.70 (( 78.39/10.70 (funcGraphProp3) => 78.39/10.70 (( 78.39/10.70 (funcGraphProp2) => 78.39/10.70 (( 78.39/10.70 (funcextLem) => 78.39/10.70 (( 78.39/10.70 (funcGraphProp4) => 78.39/10.70 (( 78.39/10.70 (subbreln) => 78.39/10.70 (( 78.39/10.70 (eqbreln) => 78.39/10.70 (( 78.39/10.70 (funcext) => 78.39/10.70 (( 78.39/10.70 (funcext2) => 78.39/10.70 (( 78.39/10.70 (ap2apEq1) => 78.39/10.70 (( 78.39/10.70 (ap2apEq2) => 78.39/10.70 (( 78.39/10.70 (beta1) => 78.39/10.70 (( 78.39/10.70 (eta1) => 78.39/10.70 (( 78.39/10.70 (lam2lamEq) => 78.39/10.70 (( 78.39/10.70 (beta2) => 78.39/10.70 (( 78.39/10.70 (eta2) => 78.39/10.70 (( 78.39/10.70 (iffalseProp1) => 78.39/10.70 (( 78.39/10.70 (iffalseProp2) => 78.39/10.70 (( 78.39/10.70 (iftrueProp1) => 78.39/10.70 (( 78.39/10.70 (iftrueProp2) => 78.39/10.70 (( 78.39/10.70 (ifSingleton) => 78.39/10.70 (( 78.39/10.70 (ifp) => 78.39/10.70 (( 78.39/10.70 (theeq) => 78.39/10.70 (( 78.39/10.70 (iftrue) => 78.39/10.70 (( 78.39/10.70 (iffalse) => 78.39/10.70 (( 78.39/10.70 (iftrueorfalse) => 78.39/10.70 (( 78.39/10.70 (binintersectT_lem) => 78.39/10.70 (( 78.39/10.70 (binunionT_lem) => 78.39/10.70 (( 78.39/10.70 (powersetT_lem) => 78.39/10.70 (( 78.39/10.70 (setminusT_lem) => 78.39/10.70 (( 78.39/10.70 (complementT_lem) => 78.39/10.70 (( 78.39/10.70 (setextT) => 78.39/10.70 (( 78.39/10.70 (subsetTI) => 78.39/10.70 (( 78.39/10.70 (powersetTI1) => 78.39/10.70 (( 78.39/10.70 (powersetTE1) => 78.39/10.70 (( 78.39/10.70 (complementTI1) => 78.39/10.70 (( 78.39/10.70 (complementTE1) => 78.39/10.70 (( 78.39/10.70 (binintersectTELcontra) => 78.39/10.70 (( 78.39/10.70 (binintersectTERcontra) => 78.39/10.70 (( 78.39/10.70 (contrasubsetT) => 78.39/10.70 (( 78.39/10.70 (contrasubsetT1) => 78.39/10.70 (( 78.39/10.70 (contrasubsetT2) => 78.39/10.70 (( 78.39/10.70 (contrasubsetT3) => 78.39/10.70 (( 78.39/10.70 (doubleComplementI1) => 78.39/10.70 (( 78.39/10.70 (doubleComplementE1) => 78.39/10.70 (( 78.39/10.70 (doubleComplementSub1) => 78.39/10.70 (( 78.39/10.70 (doubleComplementSub2) => 78.39/10.70 (( 78.39/10.70 (doubleComplementEq) => 78.39/10.70 (( 78.39/10.70 (complementTnotintersectT) => 78.39/10.70 (( 78.39/10.70 (complementImpComplementIntersect) => 78.39/10.70 (( 78.39/10.70 (complementSubsetComplementIntersect) => 78.39/10.70 (( 78.39/10.70 (complementInPowersetComplementIntersect) => 78.39/10.70 (( 78.39/10.70 (contraSubsetComplement) => 78.39/10.70 (( 78.39/10.70 (complementTcontraSubset) => 78.39/10.70 (( 78.39/10.70 (binunionTILcontra) => 78.39/10.70 (( 78.39/10.70 (binunionTIRcontra) => 78.39/10.70 (( 78.39/10.70 (inIntersectImpInUnion) => 78.39/10.70 (( 78.39/10.70 (inIntersectImpInUnion2) => 78.39/10.70 (( 78.39/10.70 (inIntersectImpInIntersectUnions) => 78.39/10.70 (( 78.39/10.70 (intersectInPowersetIntersectUnions) => 78.39/10.70 (( 78.39/10.70 (inComplementUnionImpNotIn1) => 78.39/10.70 (( 78.39/10.70 (inComplementUnionImpInComplement1) => 78.39/10.70 (( 78.39/10.70 (binunionTE) => 78.39/10.70 (( 78.39/10.70 (binunionTEcontra) => 78.39/10.70 (( 78.39/10.70 (demorgan2a1) => 78.39/10.70 (( 78.39/10.70 (complementUnionInPowersetComplement) => 78.39/10.70 (( 78.39/10.70 (demorgan2a2) => 78.39/10.70 (( 78.39/10.70 (demorgan1a) => 78.39/10.70 (( 78.39/10.70 (demorgan1b) => 78.39/10.70 (( 78.39/10.70 (demorgan1) => 78.39/10.70 (( 78.39/10.70 (demorgan2a) => 78.39/10.70 (( 78.39/10.70 (demorgan2b2) => 78.39/10.70 (( 78.39/10.70 (demorgan2b) => 78.39/10.70 (( 78.39/10.70 (demorgan2) => 78.39/10.70 (( 78.39/10.70 (woz13rule0) => 78.39/10.70 (( 78.39/10.70 (woz13rule1) => 78.39/10.70 (( 78.39/10.70 (woz13rule2) => 78.39/10.70 (( 78.39/10.70 (woz13rule3) => 78.39/10.70 (( 78.39/10.70 (woz13rule4) => 78.39/10.70 (( 78.39/10.70 (woz1_1) => 78.39/10.70 (( 78.39/10.70 (woz1_2) => 78.39/10.70 (( 78.39/10.70 (woz1_3) => 78.39/10.70 (( 78.39/10.70 (woz1_4) => 78.39/10.70 (( 78.39/10.70 (woz1_5) => 78.39/10.70 (( 78.39/10.70 (breln1all2) => 78.39/10.70 (( 78.39/10.70 (breln1SetBreln1) => 78.39/10.70 (( 78.39/10.70 (choice2fnsingleton) => 78.39/10.70 (( 78.39/10.70 (setOfPairsIsBReln1) => 78.39/10.70 (( 78.39/10.70 (breln1all1) => 78.39/10.70 (( 78.39/10.70 (subbreln1) => 78.39/10.70 (( 78.39/10.70 (eqbreln1) => 78.39/10.70 (( 78.39/10.70 (breln1invprop) => 78.39/10.70 (( 78.39/10.70 (breln1invI) => 78.39/10.70 (( 78.39/10.70 (breln1invE) => 78.39/10.70 (( 78.39/10.70 (breln1compprop) => 78.39/10.70 (( 78.39/10.70 (breln1compI) => 78.39/10.70 (( 78.39/10.70 (breln1compE) => 78.39/10.70 (( 78.39/10.70 (breln1compEex) => 78.39/10.70 (( 78.39/10.70 (breln1unionprop) => 78.39/10.70 (( 78.39/10.70 (breln1unionIL) => 78.39/10.70 (( 78.39/10.70 (breln1unionIR) => 78.39/10.70 (( 78.39/10.70 (breln1unionI) => 78.39/10.70 (( 78.39/10.70 (breln1unionE) => 78.39/10.70 (( 78.39/10.70 (breln1unionEcases) => 78.39/10.70 (( 78.39/10.70 (breln1unionCommutes) => 78.39/10.70 (( 78.39/10.70 (woz2Ex) => 78.39/10.70 (( 78.39/10.70 (woz2W) => 78.39/10.70 (( 78.39/10.70 (woz2A) => 78.39/10.70 (( 78.39/10.70 (woz2B) => 78.39/10.70 (( 78.39/10.70 (image1Ex) => 78.39/10.70 (( 78.39/10.70 (image1Ex1) => 78.39/10.70 (( 78.39/10.70 (image1Equiv) => 78.39/10.70 (( 78.39/10.70 (image1E) => 78.39/10.70 (( 78.39/10.70 (image1I) => 78.39/10.70 (( 78.39/10.70 (injFuncInInjFuncSet) => 78.39/10.70 (( 78.39/10.70 (injFuncSetFuncIn) => 78.39/10.70 (( 78.39/10.70 (injFuncSetFuncInj) => 78.39/10.70 (( 78.39/10.70 (surjFuncSetFuncIn) => 78.39/10.70 (( 78.39/10.70 (surjFuncSetFuncSurj) => 78.39/10.70 (( 78.39/10.70 (leftInvIsSurj) => 78.39/10.70 (( 78.39/10.70 (surjCantorThm) => 78.39/10.70 (( 78.39/10.70 (foundation2) => 78.39/10.70 (( 78.39/10.70 (notinself) => 78.39/10.70 (( 78.39/10.70 (notinself2) => 78.39/10.70 (( 78.39/10.70 (omegaSp) => 78.39/10.70 (( 78.39/10.70 (omegaSclos) => 78.39/10.70 (( 78.39/10.70 (peano0notS) => 78.39/10.70 (( 78.39/10.70 (peanoSinj) => 78.39/10.70 (( 78.39/10.70 (transitivesetOp1) => 78.39/10.70 (( 78.39/10.70 (binintTransitive) => 78.39/10.70 (( 78.39/10.70 (transitivesetOp2) => 78.39/10.70 (( 78.39/10.70 (setunionTransitive) => 78.39/10.70 (( 78.39/10.70 (ordinalMinLem1) => 78.39/10.70 (( 78.39/10.70 (!!) @ ( 78.39/10.70 ^[Y0 : $i]: 78.39/10.70 (( 78.39/10.70 (ordinal @ 78.39/10.70 Y0) => 78.39/10.70 (( 78.39/10.70 (!!) @ ( 78.39/10.70 ^[Y1 : $i]: 78.39/10.70 (( 78.39/10.70 (!!) @ ( 78.39/10.70 ^[Y2 : $i]: 78.39/10.70 (( 78.39/10.70 (in @ 78.39/10.70 Y2 @ 78.39/10.70 Y0) => 78.39/10.70 (( 78.39/10.70 (in @ 78.39/10.70 Y1 @ 78.39/10.70 Y2) => 78.39/10.70 (in @ 78.39/10.70 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 78.39/10.70 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1371])). 78.39/10.70 thf(zip_derived_cl1396, plain, 78.39/10.70 (~ (((setukpairinjL2) => 78.39/10.70 (((setukpairinjL) => 78.39/10.70 (((setukpairinjR11) => 78.39/10.70 (((setukpairinjR12) => 78.39/10.70 (((setukpairinjR1) => 78.39/10.70 (((upairequniteq) => 78.39/10.70 (((setukpairinjR2) => 78.39/10.70 (((setukpairinjR) => 78.39/10.70 (((ksndsingleton) => 78.39/10.70 (((ksndpairEq) => 78.39/10.70 (((kpairsurjEq) => 78.39/10.70 (((cartprodsndin) => 78.39/10.70 (((cartprodpairmemEL) => 78.39/10.70 (((cartprodpairmemER) => 78.39/10.70 (((cartprodmempaircEq) => 78.39/10.70 (((cartprodfstpairEq) => 78.39/10.70 (((cartprodsndpairEq) => 78.39/10.70 (((cartprodpairsurjEq) => 78.39/10.70 (((dpsetconstrI) => 78.39/10.70 (((dpsetconstrSub) => 78.39/10.70 (((setOfPairsIsBReln) => 78.39/10.70 (((dpsetconstrERa) => 78.39/10.70 (((dpsetconstrEL1) => 78.39/10.70 (((dpsetconstrEL2) => 78.39/10.70 (((dpsetconstrER) => 78.39/10.70 (((funcImageSingleton) => 78.39/10.70 (((apProp) => 78.39/10.70 (((app) => 78.39/10.70 (((infuncsetfunc) => 78.39/10.70 (((ap2p) => 78.39/10.70 (( 78.39/10.70 (funcinfuncset) => 78.39/10.70 (( 78.39/10.70 (lamProp) => 78.39/10.70 (( 78.39/10.70 (lamp) => 78.39/10.70 (( 78.39/10.70 (lam2p) => 78.39/10.70 (( 78.39/10.70 (brelnall1) => 78.39/10.70 (( 78.39/10.70 (brelnall2) => 78.39/10.70 (( 78.39/10.70 (ex1E2) => 78.39/10.70 (( 78.39/10.70 (funcGraphProp1) => 78.39/10.70 (( 78.39/10.70 (funcGraphProp3) => 78.39/10.70 (( 78.39/10.70 (funcGraphProp2) => 78.39/10.70 (( 78.39/10.70 (funcextLem) => 78.39/10.70 (( 78.39/10.70 (funcGraphProp4) => 78.39/10.70 (( 78.39/10.70 (subbreln) => 78.39/10.70 (( 78.39/10.70 (eqbreln) => 78.39/10.70 (( 78.39/10.70 (funcext) => 78.39/10.70 (( 78.39/10.70 (funcext2) => 78.39/10.70 (( 78.39/10.70 (ap2apEq1) => 78.39/10.70 (( 78.39/10.70 (ap2apEq2) => 78.39/10.70 (( 78.39/10.70 (beta1) => 78.39/10.70 (( 78.39/10.70 (eta1) => 78.39/10.70 (( 78.39/10.70 (lam2lamEq) => 78.39/10.70 (( 78.39/10.70 (beta2) => 78.39/10.70 (( 78.39/10.70 (eta2) => 78.39/10.70 (( 78.39/10.70 (iffalseProp1) => 78.39/10.70 (( 78.39/10.70 (iffalseProp2) => 78.39/10.70 (( 78.39/10.70 (iftrueProp1) => 78.39/10.70 (( 78.39/10.70 (iftrueProp2) => 78.39/10.70 (( 78.39/10.70 (ifSingleton) => 78.39/10.70 (( 78.39/10.70 (ifp) => 78.39/10.70 (( 78.39/10.70 (theeq) => 78.39/10.70 (( 78.39/10.70 (iftrue) => 78.39/10.70 (( 78.39/10.70 (iffalse) => 78.39/10.70 (( 78.39/10.70 (iftrueorfalse) => 78.39/10.70 (( 78.39/10.70 (binintersectT_lem) => 78.39/10.70 (( 78.39/10.70 (binunionT_lem) => 78.39/10.70 (( 78.39/10.70 (powersetT_lem) => 78.39/10.70 (( 78.39/10.70 (setminusT_lem) => 78.39/10.70 (( 78.39/10.70 (complementT_lem) => 78.39/10.70 (( 78.39/10.70 (setextT) => 78.39/10.70 (( 78.39/10.70 (subsetTI) => 78.39/10.70 (( 78.39/10.70 (powersetTI1) => 78.39/10.70 (( 78.39/10.70 (powersetTE1) => 78.39/10.70 (( 78.39/10.70 (complementTI1) => 78.39/10.70 (( 78.39/10.70 (complementTE1) => 78.39/10.70 (( 78.39/10.70 (binintersectTELcontra) => 78.39/10.70 (( 78.39/10.70 (binintersectTERcontra) => 78.39/10.70 (( 78.39/10.70 (contrasubsetT) => 78.39/10.70 (( 78.39/10.70 (contrasubsetT1) => 78.39/10.70 (( 78.39/10.70 (contrasubsetT2) => 78.39/10.70 (( 78.39/10.70 (contrasubsetT3) => 78.39/10.70 (( 78.39/10.70 (doubleComplementI1) => 78.39/10.70 (( 78.39/10.70 (doubleComplementE1) => 78.39/10.70 (( 78.39/10.70 (doubleComplementSub1) => 78.39/10.70 (( 78.39/10.70 (doubleComplementSub2) => 78.39/10.70 (( 78.39/10.70 (doubleComplementEq) => 78.39/10.70 (( 78.39/10.70 (complementTnotintersectT) => 78.39/10.70 (( 78.39/10.70 (complementImpComplementIntersect) => 78.39/10.70 (( 78.39/10.70 (complementSubsetComplementIntersect) => 78.39/10.70 (( 78.39/10.70 (complementInPowersetComplementIntersect) => 78.39/10.70 (( 78.39/10.70 (contraSubsetComplement) => 78.39/10.70 (( 78.39/10.70 (complementTcontraSubset) => 78.39/10.70 (( 78.39/10.70 (binunionTILcontra) => 78.39/10.70 (( 78.39/10.70 (binunionTIRcontra) => 78.39/10.70 (( 78.39/10.70 (inIntersectImpInUnion) => 78.39/10.70 (( 78.39/10.70 (inIntersectImpInUnion2) => 78.39/10.70 (( 78.39/10.70 (inIntersectImpInIntersectUnions) => 78.39/10.70 (( 78.39/10.70 (intersectInPowersetIntersectUnions) => 78.39/10.70 (( 78.39/10.70 (inComplementUnionImpNotIn1) => 78.39/10.70 (( 78.39/10.70 (inComplementUnionImpInComplement1) => 78.39/10.70 (( 78.39/10.70 (binunionTE) => 78.39/10.70 (( 78.39/10.70 (binunionTEcontra) => 78.39/10.70 (( 78.39/10.70 (demorgan2a1) => 78.39/10.70 (( 78.39/10.70 (complementUnionInPowersetComplement) => 78.39/10.70 (( 78.39/10.70 (demorgan2a2) => 78.39/10.70 (( 78.39/10.70 (demorgan1a) => 78.39/10.70 (( 78.39/10.70 (demorgan1b) => 78.39/10.70 (( 78.39/10.70 (demorgan1) => 78.39/10.70 (( 78.39/10.70 (demorgan2a) => 78.39/10.70 (( 78.39/10.70 (demorgan2b2) => 78.39/10.70 (( 78.39/10.70 (demorgan2b) => 78.39/10.70 (( 78.39/10.70 (demorgan2) => 78.39/10.70 (( 78.39/10.70 (woz13rule0) => 78.39/10.70 (( 78.39/10.70 (woz13rule1) => 78.39/10.70 (( 78.39/10.70 (woz13rule2) => 78.39/10.70 (( 78.39/10.70 (woz13rule3) => 78.39/10.70 (( 78.39/10.70 (woz13rule4) => 78.39/10.70 (( 78.39/10.70 (woz1_1) => 78.39/10.70 (( 78.39/10.70 (woz1_2) => 78.39/10.70 (( 78.39/10.70 (woz1_3) => 78.39/10.70 (( 78.39/10.70 (woz1_4) => 78.39/10.70 (( 78.39/10.70 (woz1_5) => 78.39/10.70 (( 78.39/10.70 (breln1all2) => 78.39/10.70 (( 78.39/10.70 (breln1SetBreln1) => 78.39/10.70 (( 78.39/10.70 (choice2fnsingleton) => 78.39/10.70 (( 78.39/10.70 (setOfPairsIsBReln1) => 78.39/10.70 (( 78.39/10.70 (breln1all1) => 78.39/10.70 (( 78.39/10.70 (subbreln1) => 78.39/10.70 (( 78.39/10.70 (eqbreln1) => 78.39/10.70 (( 78.39/10.70 (breln1invprop) => 78.39/10.70 (( 78.39/10.70 (breln1invI) => 78.39/10.70 (( 78.39/10.70 (breln1invE) => 78.39/10.70 (( 78.39/10.70 (breln1compprop) => 78.39/10.70 (( 78.39/10.70 (breln1compI) => 78.39/10.70 (( 78.39/10.70 (breln1compE) => 78.39/10.70 (( 78.39/10.70 (breln1compEex) => 78.39/10.70 (( 78.39/10.70 (breln1unionprop) => 78.39/10.70 (( 78.39/10.70 (breln1unionIL) => 78.39/10.70 (( 78.39/10.70 (breln1unionIR) => 78.39/10.70 (( 78.39/10.70 (breln1unionI) => 78.39/10.70 (( 78.39/10.70 (breln1unionE) => 78.39/10.70 (( 78.39/10.70 (breln1unionEcases) => 78.39/10.70 (( 78.39/10.70 (breln1unionCommutes) => 78.39/10.70 (( 78.39/10.70 (woz2Ex) => 78.39/10.70 (( 78.39/10.70 (woz2W) => 78.39/10.70 (( 78.39/10.70 (woz2A) => 78.39/10.70 (( 78.39/10.70 (woz2B) => 78.39/10.70 (( 78.39/10.70 (image1Ex) => 78.39/10.70 (( 78.39/10.70 (image1Ex1) => 78.39/10.70 (( 78.39/10.70 (image1Equiv) => 78.39/10.70 (( 78.39/10.70 (image1E) => 78.39/10.70 (( 78.39/10.70 (image1I) => 78.39/10.70 (( 78.39/10.70 (injFuncInInjFuncSet) => 78.39/10.70 (( 78.39/10.70 (injFuncSetFuncIn) => 78.39/10.70 (( 78.39/10.70 (injFuncSetFuncInj) => 78.39/10.70 (( 78.39/10.70 (surjFuncSetFuncIn) => 78.39/10.70 (( 78.39/10.70 (surjFuncSetFuncSurj) => 78.39/10.70 (( 78.39/10.70 (leftInvIsSurj) => 78.39/10.70 (( 78.39/10.70 (surjCantorThm) => 78.39/10.70 (( 78.39/10.70 (foundation2) => 78.39/10.70 (( 78.39/10.70 (notinself) => 78.39/10.70 (( 78.39/10.70 (notinself2) => 78.39/10.70 (( 78.39/10.70 (omegaSp) => 78.39/10.70 (( 78.39/10.70 (omegaSclos) => 78.39/10.70 (( 78.39/10.70 (peano0notS) => 78.39/10.70 (( 78.39/10.70 (peanoSinj) => 78.39/10.70 (( 78.39/10.70 (transitivesetOp1) => 78.39/10.70 (( 78.39/10.70 (binintTransitive) => 78.39/10.70 (( 78.39/10.70 (transitivesetOp2) => 78.39/10.70 (( 78.39/10.70 (setunionTransitive) => 78.39/10.70 (( 78.39/10.70 (ordinalMinLem1) => 78.39/10.70 (( 78.39/10.70 (!!) @ ( 78.39/10.70 ^[Y0 : $i]: 78.39/10.70 (( 78.39/10.70 (ordinal @ 78.39/10.70 Y0) => 78.39/10.70 (( 78.39/10.70 (!!) @ ( 78.39/10.70 ^[Y1 : $i]: 78.39/10.70 (( 78.39/10.70 (!!) @ ( 78.39/10.70 ^[Y2 : $i]: 78.39/10.70 (( 78.39/10.70 (in @ 78.39/10.70 Y2 @ 78.39/10.70 Y0) => 78.39/10.70 (( 78.39/10.70 (in @ 78.39/10.70 Y1 @ 78.39/10.70 Y2) => 78.39/10.70 (in @ 78.39/10.70 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 78.39/10.70 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1382])). 78.39/10.70 thf(zip_derived_cl1409, plain, 78.39/10.70 (~ (((setukpairinjL) => 78.39/10.70 (((setukpairinjR11) => 78.39/10.70 (((setukpairinjR12) => 78.39/10.70 (((setukpairinjR1) => 78.39/10.70 (((upairequniteq) => 78.39/10.70 (((setukpairinjR2) => 78.39/10.70 (((setukpairinjR) => 78.39/10.70 (((ksndsingleton) => 78.39/10.70 (((ksndpairEq) => 78.39/10.70 (((kpairsurjEq) => 78.39/10.70 (((cartprodsndin) => 78.39/10.70 (((cartprodpairmemEL) => 78.39/10.70 (((cartprodpairmemER) => 78.39/10.70 (((cartprodmempaircEq) => 78.39/10.70 (((cartprodfstpairEq) => 78.39/10.70 (((cartprodsndpairEq) => 78.39/10.70 (((cartprodpairsurjEq) => 78.39/10.70 (((dpsetconstrI) => 78.39/10.70 (((dpsetconstrSub) => 78.39/10.70 (((setOfPairsIsBReln) => 78.39/10.70 (((dpsetconstrERa) => 78.39/10.70 (((dpsetconstrEL1) => 78.39/10.70 (((dpsetconstrEL2) => 78.39/10.70 (((dpsetconstrER) => 78.39/10.70 (((funcImageSingleton) => 78.39/10.70 (((apProp) => 78.39/10.70 (((app) => 78.39/10.70 (((infuncsetfunc) => 78.39/10.70 (((ap2p) => 78.39/10.70 (((funcinfuncset) => 78.39/10.70 (( 78.39/10.70 (lamProp) => 78.39/10.70 (( 78.39/10.70 (lamp) => 78.39/10.70 (( 78.39/10.70 (lam2p) => 78.39/10.70 (( 78.39/10.70 (brelnall1) => 78.39/10.70 (( 78.39/10.70 (brelnall2) => 78.39/10.70 (( 78.39/10.70 (ex1E2) => 78.39/10.70 (( 78.39/10.70 (funcGraphProp1) => 78.39/10.70 (( 78.39/10.70 (funcGraphProp3) => 78.39/10.70 (( 78.39/10.70 (funcGraphProp2) => 78.39/10.70 (( 78.39/10.70 (funcextLem) => 78.39/10.70 (( 78.39/10.70 (funcGraphProp4) => 78.39/10.70 (( 78.39/10.70 (subbreln) => 78.39/10.70 (( 78.39/10.70 (eqbreln) => 78.39/10.70 (( 78.39/10.70 (funcext) => 78.39/10.70 (( 78.39/10.70 (funcext2) => 78.39/10.70 (( 78.39/10.70 (ap2apEq1) => 78.39/10.70 (( 78.39/10.70 (ap2apEq2) => 78.39/10.70 (( 78.39/10.70 (beta1) => 78.39/10.70 (( 78.39/10.70 (eta1) => 78.39/10.70 (( 78.39/10.70 (lam2lamEq) => 78.39/10.70 (( 78.39/10.70 (beta2) => 78.39/10.70 (( 78.39/10.70 (eta2) => 78.39/10.70 (( 78.39/10.70 (iffalseProp1) => 78.39/10.70 (( 78.39/10.70 (iffalseProp2) => 78.39/10.70 (( 78.39/10.70 (iftrueProp1) => 78.39/10.70 (( 78.39/10.70 (iftrueProp2) => 78.39/10.70 (( 78.39/10.70 (ifSingleton) => 78.39/10.70 (( 78.39/10.70 (ifp) => 78.39/10.70 (( 78.39/10.70 (theeq) => 78.39/10.70 (( 78.39/10.70 (iftrue) => 78.39/10.70 (( 78.39/10.70 (iffalse) => 78.39/10.70 (( 78.39/10.70 (iftrueorfalse) => 78.39/10.70 (( 78.39/10.70 (binintersectT_lem) => 78.39/10.70 (( 78.39/10.70 (binunionT_lem) => 78.39/10.70 (( 78.39/10.70 (powersetT_lem) => 78.39/10.70 (( 78.39/10.70 (setminusT_lem) => 78.39/10.70 (( 78.39/10.70 (complementT_lem) => 78.39/10.70 (( 78.39/10.70 (setextT) => 78.39/10.70 (( 78.39/10.70 (subsetTI) => 78.39/10.70 (( 78.39/10.70 (powersetTI1) => 78.39/10.70 (( 78.39/10.70 (powersetTE1) => 78.39/10.70 (( 78.39/10.70 (complementTI1) => 78.39/10.70 (( 78.39/10.70 (complementTE1) => 78.39/10.70 (( 78.39/10.70 (binintersectTELcontra) => 78.39/10.70 (( 78.39/10.70 (binintersectTERcontra) => 78.39/10.70 (( 78.39/10.70 (contrasubsetT) => 78.39/10.70 (( 78.39/10.70 (contrasubsetT1) => 78.39/10.70 (( 78.39/10.70 (contrasubsetT2) => 78.39/10.70 (( 78.39/10.70 (contrasubsetT3) => 78.39/10.70 (( 78.39/10.70 (doubleComplementI1) => 78.39/10.70 (( 78.39/10.70 (doubleComplementE1) => 78.39/10.70 (( 78.39/10.70 (doubleComplementSub1) => 78.39/10.70 (( 78.39/10.70 (doubleComplementSub2) => 78.39/10.70 (( 78.39/10.70 (doubleComplementEq) => 78.39/10.70 (( 78.39/10.70 (complementTnotintersectT) => 78.39/10.70 (( 78.39/10.70 (complementImpComplementIntersect) => 78.39/10.70 (( 78.39/10.70 (complementSubsetComplementIntersect) => 78.39/10.70 (( 78.39/10.70 (complementInPowersetComplementIntersect) => 78.39/10.70 (( 78.39/10.70 (contraSubsetComplement) => 78.39/10.70 (( 78.39/10.70 (complementTcontraSubset) => 78.39/10.70 (( 78.39/10.70 (binunionTILcontra) => 78.39/10.70 (( 78.39/10.70 (binunionTIRcontra) => 78.39/10.70 (( 78.39/10.70 (inIntersectImpInUnion) => 78.39/10.70 (( 78.39/10.70 (inIntersectImpInUnion2) => 78.39/10.70 (( 78.39/10.70 (inIntersectImpInIntersectUnions) => 78.39/10.70 (( 78.39/10.70 (intersectInPowersetIntersectUnions) => 78.39/10.70 (( 78.39/10.70 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(breln1invprop) => 78.39/10.70 (( 78.39/10.70 (breln1invI) => 78.39/10.70 (( 78.39/10.70 (breln1invE) => 78.39/10.70 (( 78.39/10.70 (breln1compprop) => 78.39/10.70 (( 78.39/10.70 (breln1compI) => 78.39/10.70 (( 78.39/10.70 (breln1compE) => 78.39/10.70 (( 78.39/10.70 (breln1compEex) => 78.39/10.70 (( 78.39/10.70 (breln1unionprop) => 78.39/10.70 (( 78.39/10.70 (breln1unionIL) => 78.39/10.70 (( 78.39/10.70 (breln1unionIR) => 78.39/10.70 (( 78.39/10.70 (breln1unionI) => 78.39/10.70 (( 78.39/10.70 (breln1unionE) => 78.39/10.70 (( 78.39/10.70 (breln1unionEcases) => 78.39/10.70 (( 78.39/10.70 (breln1unionCommutes) => 78.39/10.70 (( 78.39/10.70 (woz2Ex) => 78.39/10.70 (( 78.39/10.70 (woz2W) => 78.39/10.70 (( 78.39/10.70 (woz2A) => 78.39/10.70 (( 78.39/10.70 (woz2B) => 78.39/10.70 (( 78.39/10.70 (image1Ex) => 78.39/10.70 (( 78.39/10.70 (image1Ex1) => 78.39/10.70 (( 78.39/10.70 (image1Equiv) => 78.39/10.70 (( 78.39/10.70 (image1E) => 78.39/10.70 (( 78.39/10.70 (image1I) => 78.39/10.70 (( 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(( 78.39/10.70 (!!) @ ( 78.39/10.70 ^[Y1 : $i]: 78.39/10.70 (( 78.39/10.70 (!!) @ ( 78.39/10.70 ^[Y2 : $i]: 78.39/10.70 (( 78.39/10.70 (in @ 78.39/10.70 Y2 @ 78.39/10.70 Y0) => 78.39/10.70 (( 78.39/10.70 (in @ 78.39/10.70 Y1 @ 78.39/10.70 Y2) => 78.39/10.70 (in @ 78.39/10.70 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 78.39/10.70 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1409])). 78.39/10.70 thf(zip_derived_cl1440, plain, 78.39/10.70 (~ (((setukpairinjR12) => 78.39/10.70 (((setukpairinjR1) => 78.39/10.70 (((upairequniteq) => 78.39/10.70 (((setukpairinjR2) => 78.39/10.70 (((setukpairinjR) => 78.39/10.70 (((ksndsingleton) => 78.39/10.70 (((ksndpairEq) => 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(surjFuncSetFuncIn) => 78.39/10.70 (( 78.39/10.70 (surjFuncSetFuncSurj) => 78.39/10.70 (( 78.39/10.70 (leftInvIsSurj) => 78.39/10.70 (( 78.39/10.70 (surjCantorThm) => 78.39/10.70 (( 78.39/10.70 (foundation2) => 78.39/10.70 (( 78.39/10.70 (notinself) => 78.39/10.70 (( 78.39/10.70 (notinself2) => 78.39/10.70 (( 78.39/10.70 (omegaSp) => 78.39/10.70 (( 78.39/10.70 (omegaSclos) => 78.39/10.70 (( 78.39/10.70 (peano0notS) => 78.39/10.70 (( 78.39/10.70 (peanoSinj) => 78.39/10.70 (( 78.39/10.70 (transitivesetOp1) => 78.39/10.70 (( 78.39/10.70 (binintTransitive) => 78.39/10.70 (( 78.39/10.70 (transitivesetOp2) => 78.39/10.70 (( 78.39/10.70 (setunionTransitive) => 78.39/10.70 (( 78.39/10.70 (ordinalMinLem1) => 78.39/10.70 (( 78.39/10.70 (!!) @ ( 78.39/10.70 ^[Y0 : $i]: 78.39/10.70 (( 78.39/10.70 (ordinal @ 78.39/10.70 Y0) => 78.39/10.70 (( 78.39/10.70 (!!) @ ( 78.39/10.70 ^[Y1 : $i]: 78.39/10.70 (( 78.39/10.70 (!!) @ ( 78.39/10.70 ^[Y2 : $i]: 78.39/10.70 (( 78.39/10.70 (in @ 78.39/10.70 Y2 @ 78.39/10.70 Y0) => 78.39/10.70 (( 78.39/10.70 (in @ 78.39/10.70 Y1 @ 78.39/10.70 Y2) => 78.39/10.70 (in @ 78.39/10.70 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 78.39/10.70 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1453])). 78.39/10.70 thf(zip_derived_cl1475, plain, 78.39/10.70 (~ (((setukpairinjR2) => 78.39/10.70 (((setukpairinjR) => 78.39/10.70 (((ksndsingleton) => 78.39/10.70 (((ksndpairEq) => 78.39/10.70 (((kpairsurjEq) => 78.39/10.70 (((cartprodsndin) => 78.39/10.70 (((cartprodpairmemEL) => 78.39/10.70 (((cartprodpairmemER) => 78.39/10.70 (((cartprodmempaircEq) => 78.39/10.70 (((cartprodfstpairEq) => 78.39/10.70 (((cartprodsndpairEq) => 78.39/10.70 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78.39/10.70 (!!) @ ( 78.39/10.70 ^[Y2 : $i]: 78.39/10.70 (( 78.39/10.70 (in @ 78.39/10.70 Y2 @ 78.39/10.70 Y0) => 78.39/10.70 (( 78.39/10.70 (in @ 78.39/10.70 Y1 @ 78.39/10.70 Y2) => 78.39/10.70 (in @ 78.39/10.70 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 78.39/10.70 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1485])). 78.39/10.70 thf(zip_derived_cl1504, plain, 78.39/10.70 (~ (((ksndpairEq) => 78.39/10.70 (((kpairsurjEq) => 78.39/10.70 (((cartprodsndin) => 78.39/10.70 (((cartprodpairmemEL) => 78.39/10.70 (((cartprodpairmemER) => 78.39/10.70 (((cartprodmempaircEq) => 78.39/10.70 (((cartprodfstpairEq) => 78.39/10.70 (((cartprodsndpairEq) => 78.39/10.70 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78.39/10.70 (demorgan2b2) => 78.39/10.70 (( 78.39/10.70 (demorgan2b) => 78.39/10.70 (( 78.39/10.70 (demorgan2) => 78.39/10.70 (( 78.39/10.70 (woz13rule0) => 78.39/10.70 (( 78.39/10.70 (woz13rule1) => 78.39/10.70 (( 78.39/10.70 (woz13rule2) => 78.39/10.70 (( 78.39/10.70 (woz13rule3) => 78.39/10.70 (( 78.39/10.70 (woz13rule4) => 78.39/10.70 (( 78.39/10.70 (woz1_1) => 78.39/10.70 (( 78.39/10.70 (woz1_2) => 78.39/10.70 (( 78.39/10.70 (woz1_3) => 78.39/10.70 (( 78.39/10.70 (woz1_4) => 78.39/10.70 (( 78.39/10.70 (woz1_5) => 78.39/10.70 (( 78.39/10.70 (breln1all2) => 78.39/10.70 (( 78.39/10.70 (breln1SetBreln1) => 78.39/10.70 (( 78.39/10.70 (choice2fnsingleton) => 78.39/10.70 (( 78.39/10.70 (setOfPairsIsBReln1) => 78.39/10.70 (( 78.39/10.70 (breln1all1) => 78.39/10.70 (( 78.39/10.70 (subbreln1) => 78.39/10.70 (( 78.39/10.70 (eqbreln1) => 78.39/10.70 (( 78.39/10.70 (breln1invprop) => 78.39/10.70 (( 78.39/10.70 (breln1invI) => 78.39/10.70 (( 78.39/10.70 (breln1invE) => 78.39/10.70 (( 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(injFuncSetFuncInj) => 78.39/10.70 (( 78.39/10.70 (surjFuncSetFuncIn) => 78.39/10.70 (( 78.39/10.70 (surjFuncSetFuncSurj) => 78.39/10.70 (( 78.39/10.70 (leftInvIsSurj) => 78.39/10.70 (( 78.39/10.70 (surjCantorThm) => 78.39/10.70 (( 78.39/10.70 (foundation2) => 78.39/10.70 (( 78.39/10.70 (notinself) => 78.39/10.70 (( 78.39/10.70 (notinself2) => 78.39/10.70 (( 78.39/10.70 (omegaSp) => 78.39/10.70 (( 78.39/10.70 (omegaSclos) => 78.39/10.70 (( 78.39/10.70 (peano0notS) => 78.39/10.70 (( 78.39/10.70 (peanoSinj) => 78.39/10.70 (( 78.39/10.70 (transitivesetOp1) => 78.39/10.70 (( 78.39/10.70 (binintTransitive) => 78.39/10.70 (( 78.39/10.70 (transitivesetOp2) => 78.39/10.70 (( 78.39/10.70 (setunionTransitive) => 78.39/10.70 (( 78.39/10.70 (ordinalMinLem1) => 78.39/10.70 (( 78.39/10.70 (!!) @ ( 78.39/10.70 ^[Y0 : $i]: 78.39/10.70 (( 78.39/10.70 (ordinal @ 78.39/10.70 Y0) => 78.39/10.70 (( 78.39/10.70 (!!) @ ( 78.39/10.70 ^[Y1 : $i]: 78.39/10.70 (( 78.39/10.70 (!!) @ ( 78.39/10.70 ^[Y2 : $i]: 78.39/10.70 (( 78.39/10.70 (in @ 78.39/10.70 Y2 @ 78.39/10.70 Y0) => 78.39/10.70 (( 78.39/10.70 (in @ 78.39/10.70 Y1 @ 78.39/10.70 Y2) => 78.39/10.70 (in @ 78.39/10.70 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 78.39/10.70 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1495])). 78.39/10.70 thf(zip_derived_cl1511, plain, 78.39/10.70 (~ (((kpairsurjEq) => 78.39/10.70 (((cartprodsndin) => 78.39/10.70 (((cartprodpairmemEL) => 78.39/10.70 (((cartprodpairmemER) => 78.39/10.70 (((cartprodmempaircEq) => 78.39/10.70 (((cartprodfstpairEq) => 78.39/10.70 (((cartprodsndpairEq) => 78.39/10.70 (((cartprodpairsurjEq) => 78.39/10.70 (((dpsetconstrI) => 78.39/10.70 (((dpsetconstrSub) => 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(( 78.39/10.71 (woz13rule3) => 78.39/10.71 (( 78.39/10.71 (woz13rule4) => 78.39/10.71 (( 78.39/10.71 (woz1_1) => 78.39/10.71 (( 78.39/10.71 (woz1_2) => 78.39/10.71 (( 78.39/10.71 (woz1_3) => 78.39/10.71 (( 78.39/10.71 (woz1_4) => 78.39/10.71 (( 78.39/10.71 (woz1_5) => 78.39/10.71 (( 78.39/10.71 (breln1all2) => 78.39/10.71 (( 78.39/10.71 (breln1SetBreln1) => 78.39/10.71 (( 78.39/10.71 (choice2fnsingleton) => 78.39/10.71 (( 78.39/10.71 (setOfPairsIsBReln1) => 78.39/10.71 (( 78.39/10.71 (breln1all1) => 78.39/10.71 (( 78.39/10.71 (subbreln1) => 78.39/10.71 (( 78.39/10.71 (eqbreln1) => 78.39/10.71 (( 78.39/10.71 (breln1invprop) => 78.39/10.71 (( 78.39/10.71 (breln1invI) => 78.39/10.71 (( 78.39/10.71 (breln1invE) => 78.39/10.71 (( 78.39/10.71 (breln1compprop) => 78.39/10.71 (( 78.39/10.71 (breln1compI) => 78.39/10.71 (( 78.39/10.71 (breln1compE) => 78.39/10.71 (( 78.39/10.71 (breln1compEex) => 78.39/10.71 (( 78.39/10.71 (breln1unionprop) => 78.39/10.71 (( 78.39/10.71 (breln1unionIL) => 78.39/10.71 (( 78.39/10.71 (breln1unionIR) => 78.39/10.71 (( 78.39/10.71 (breln1unionI) => 78.39/10.71 (( 78.39/10.71 (breln1unionE) => 78.39/10.71 (( 78.39/10.71 (breln1unionEcases) => 78.39/10.71 (( 78.39/10.71 (breln1unionCommutes) => 78.39/10.71 (( 78.39/10.71 (woz2Ex) => 78.39/10.71 (( 78.39/10.71 (woz2W) => 78.39/10.71 (( 78.39/10.71 (woz2A) => 78.39/10.71 (( 78.39/10.71 (woz2B) => 78.39/10.71 (( 78.39/10.71 (image1Ex) => 78.39/10.71 (( 78.39/10.71 (image1Ex1) => 78.39/10.71 (( 78.39/10.71 (image1Equiv) => 78.39/10.71 (( 78.39/10.71 (image1E) => 78.39/10.71 (( 78.39/10.71 (image1I) => 78.39/10.71 (( 78.39/10.71 (injFuncInInjFuncSet) => 78.39/10.71 (( 78.39/10.71 (injFuncSetFuncIn) => 78.39/10.71 (( 78.39/10.71 (injFuncSetFuncInj) => 78.39/10.71 (( 78.39/10.71 (surjFuncSetFuncIn) => 78.39/10.71 (( 78.39/10.71 (surjFuncSetFuncSurj) => 78.39/10.71 (( 78.39/10.71 (leftInvIsSurj) => 78.39/10.71 (( 78.39/10.71 (surjCantorThm) => 78.39/10.71 (( 78.39/10.71 (foundation2) => 78.39/10.71 (( 78.39/10.71 (notinself) => 78.39/10.71 (( 78.39/10.71 (notinself2) => 78.39/10.71 (( 78.39/10.71 (omegaSp) => 78.39/10.71 (( 78.39/10.71 (omegaSclos) => 78.39/10.71 (( 78.39/10.71 (peano0notS) => 78.39/10.71 (( 78.39/10.71 (peanoSinj) => 78.39/10.71 (( 78.39/10.71 (transitivesetOp1) => 78.39/10.71 (( 78.39/10.71 (binintTransitive) => 78.39/10.71 (( 78.39/10.71 (transitivesetOp2) => 78.39/10.71 (( 78.39/10.71 (setunionTransitive) => 78.39/10.71 (( 78.39/10.71 (ordinalMinLem1) => 78.39/10.71 (( 78.39/10.71 (!!) @ ( 78.39/10.71 ^[Y0 : $i]: 78.39/10.71 (( 78.39/10.71 (ordinal @ 78.39/10.71 Y0) => 78.39/10.71 (( 78.39/10.71 (!!) @ ( 78.39/10.71 ^[Y1 : $i]: 78.39/10.71 (( 78.39/10.71 (!!) @ ( 78.39/10.71 ^[Y2 : $i]: 78.39/10.71 (( 78.39/10.71 (in @ 78.39/10.71 Y2 @ 78.39/10.71 Y0) => 78.39/10.71 (( 78.39/10.71 (in @ 78.39/10.71 Y1 @ 78.39/10.71 Y2) => 78.39/10.71 (in @ 78.39/10.71 Y1 @ 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78.39/10.71 (omegaSclos) => 78.39/10.71 (( 78.39/10.71 (peano0notS) => 78.39/10.71 (( 78.39/10.71 (peanoSinj) => 78.39/10.71 (( 78.39/10.71 (transitivesetOp1) => 78.39/10.71 (( 78.39/10.71 (binintTransitive) => 78.39/10.71 (( 78.39/10.71 (transitivesetOp2) => 78.39/10.71 (( 78.39/10.71 (setunionTransitive) => 78.39/10.71 (( 78.39/10.71 (ordinalMinLem1) => 78.39/10.71 (( 78.39/10.71 (!!) @ ( 78.39/10.71 ^[Y0 : $i]: 78.39/10.71 (( 78.39/10.71 (ordinal @ 78.39/10.71 Y0) => 78.39/10.71 (( 78.39/10.71 (!!) @ ( 78.39/10.71 ^[Y1 : $i]: 78.39/10.71 (( 78.39/10.71 (!!) @ ( 78.39/10.71 ^[Y2 : $i]: 78.39/10.71 (( 78.39/10.71 (in @ 78.39/10.71 Y2 @ 78.39/10.71 Y0) => 78.39/10.71 (( 78.39/10.71 (in @ 78.39/10.71 Y1 @ 78.39/10.71 Y2) => 78.39/10.71 (in @ 78.39/10.71 Y1 @ 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78.39/10.71 (( 78.39/10.71 (ifp) => 78.39/10.71 (( 78.39/10.71 (theeq) => 78.39/10.71 (( 78.39/10.71 (iftrue) => 78.39/10.71 (( 78.39/10.71 (iffalse) => 78.39/10.71 (( 78.39/10.71 (iftrueorfalse) => 78.39/10.71 (( 78.39/10.71 (binintersectT_lem) => 78.39/10.71 (( 78.39/10.71 (binunionT_lem) => 78.39/10.71 (( 78.39/10.71 (powersetT_lem) => 78.39/10.71 (( 78.39/10.71 (setminusT_lem) => 78.39/10.71 (( 78.39/10.71 (complementT_lem) => 78.39/10.71 (( 78.39/10.71 (setextT) => 78.39/10.71 (( 78.39/10.71 (subsetTI) => 78.39/10.71 (( 78.39/10.71 (powersetTI1) => 78.39/10.71 (( 78.39/10.71 (powersetTE1) => 78.39/10.71 (( 78.39/10.71 (complementTI1) => 78.39/10.71 (( 78.39/10.71 (complementTE1) => 78.39/10.71 (( 78.39/10.71 (binintersectTELcontra) => 78.39/10.71 (( 78.39/10.71 (binintersectTERcontra) => 78.39/10.71 (( 78.39/10.71 (contrasubsetT) => 78.39/10.71 (( 78.39/10.71 (contrasubsetT1) => 78.39/10.71 (( 78.39/10.71 (contrasubsetT2) => 78.39/10.71 (( 78.39/10.71 (contrasubsetT3) => 78.39/10.71 (( 78.39/10.71 (doubleComplementI1) => 78.39/10.71 (( 78.39/10.71 (doubleComplementE1) => 78.39/10.71 (( 78.39/10.71 (doubleComplementSub1) => 78.39/10.71 (( 78.39/10.71 (doubleComplementSub2) => 78.39/10.71 (( 78.39/10.71 (doubleComplementEq) => 78.39/10.71 (( 78.39/10.71 (complementTnotintersectT) => 78.39/10.71 (( 78.39/10.71 (complementImpComplementIntersect) => 78.39/10.71 (( 78.39/10.71 (complementSubsetComplementIntersect) => 78.39/10.71 (( 78.39/10.71 (complementInPowersetComplementIntersect) => 78.39/10.71 (( 78.39/10.71 (contraSubsetComplement) => 78.39/10.71 (( 78.39/10.71 (complementTcontraSubset) => 78.39/10.71 (( 78.39/10.71 (binunionTILcontra) => 78.39/10.71 (( 78.39/10.71 (binunionTIRcontra) => 78.39/10.71 (( 78.39/10.71 (inIntersectImpInUnion) => 78.39/10.71 (( 78.39/10.71 (inIntersectImpInUnion2) => 78.39/10.71 (( 78.39/10.71 (inIntersectImpInIntersectUnions) => 78.39/10.71 (( 78.39/10.71 (intersectInPowersetIntersectUnions) => 78.39/10.71 (( 78.39/10.71 (inComplementUnionImpNotIn1) => 78.39/10.71 (( 78.39/10.71 (inComplementUnionImpInComplement1) => 78.39/10.71 (( 78.39/10.71 (binunionTE) => 78.39/10.71 (( 78.39/10.71 (binunionTEcontra) => 78.39/10.71 (( 78.39/10.71 (demorgan2a1) => 78.39/10.71 (( 78.39/10.71 (complementUnionInPowersetComplement) => 78.39/10.71 (( 78.39/10.71 (demorgan2a2) => 78.39/10.71 (( 78.39/10.71 (demorgan1a) => 78.39/10.71 (( 78.39/10.71 (demorgan1b) => 78.39/10.71 (( 78.39/10.71 (demorgan1) => 78.39/10.71 (( 78.39/10.71 (demorgan2a) => 78.39/10.71 (( 78.39/10.71 (demorgan2b2) => 78.39/10.71 (( 78.39/10.71 (demorgan2b) => 78.39/10.71 (( 78.39/10.71 (demorgan2) => 78.39/10.71 (( 78.39/10.71 (woz13rule0) => 78.39/10.71 (( 78.39/10.71 (woz13rule1) => 78.39/10.71 (( 78.39/10.71 (woz13rule2) => 78.39/10.71 (( 78.39/10.71 (woz13rule3) => 78.39/10.71 (( 78.39/10.71 (woz13rule4) => 78.39/10.71 (( 78.39/10.71 (woz1_1) => 78.39/10.71 (( 78.39/10.71 (woz1_2) => 78.39/10.71 (( 78.39/10.71 (woz1_3) => 78.39/10.71 (( 78.39/10.71 (woz1_4) => 78.39/10.71 (( 78.39/10.71 (woz1_5) => 78.39/10.71 (( 78.39/10.71 (breln1all2) => 78.39/10.71 (( 78.39/10.71 (breln1SetBreln1) => 78.39/10.71 (( 78.39/10.71 (choice2fnsingleton) => 78.39/10.71 (( 78.39/10.71 (setOfPairsIsBReln1) => 78.39/10.71 (( 78.39/10.71 (breln1all1) => 78.39/10.71 (( 78.39/10.71 (subbreln1) => 78.39/10.71 (( 78.39/10.71 (eqbreln1) => 78.39/10.71 (( 78.39/10.71 (breln1invprop) => 78.39/10.71 (( 78.39/10.71 (breln1invI) => 78.39/10.71 (( 78.39/10.71 (breln1invE) => 78.39/10.71 (( 78.39/10.71 (breln1compprop) => 78.39/10.71 (( 78.39/10.71 (breln1compI) => 78.39/10.71 (( 78.39/10.71 (breln1compE) => 78.39/10.71 (( 78.39/10.71 (breln1compEex) => 78.39/10.71 (( 78.39/10.71 (breln1unionprop) => 78.39/10.71 (( 78.39/10.71 (breln1unionIL) => 78.39/10.71 (( 78.39/10.71 (breln1unionIR) => 78.39/10.71 (( 78.39/10.71 (breln1unionI) => 78.39/10.71 (( 78.39/10.71 (breln1unionE) => 78.39/10.71 (( 78.39/10.71 (breln1unionEcases) => 78.39/10.71 (( 78.39/10.71 (breln1unionCommutes) => 78.39/10.71 (( 78.39/10.71 (woz2Ex) => 78.39/10.71 (( 78.39/10.71 (woz2W) => 78.39/10.71 (( 78.39/10.71 (woz2A) => 78.39/10.71 (( 78.39/10.71 (woz2B) => 78.39/10.71 (( 78.39/10.71 (image1Ex) => 78.39/10.71 (( 78.39/10.71 (image1Ex1) => 78.39/10.71 (( 78.39/10.71 (image1Equiv) => 78.39/10.71 (( 78.39/10.71 (image1E) => 78.39/10.71 (( 78.39/10.71 (image1I) => 78.39/10.71 (( 78.39/10.71 (injFuncInInjFuncSet) => 78.39/10.71 (( 78.39/10.71 (injFuncSetFuncIn) => 78.39/10.71 (( 78.39/10.71 (injFuncSetFuncInj) => 78.39/10.71 (( 78.39/10.71 (surjFuncSetFuncIn) => 78.39/10.71 (( 78.39/10.71 (surjFuncSetFuncSurj) => 78.39/10.71 (( 78.39/10.71 (leftInvIsSurj) => 78.39/10.71 (( 78.39/10.71 (surjCantorThm) => 78.39/10.71 (( 78.39/10.71 (foundation2) => 78.39/10.71 (( 78.39/10.71 (notinself) => 78.39/10.71 (( 78.39/10.71 (notinself2) => 78.39/10.71 (( 78.39/10.71 (omegaSp) => 78.39/10.71 (( 78.39/10.71 (omegaSclos) => 78.39/10.71 (( 78.39/10.71 (peano0notS) => 78.39/10.71 (( 78.39/10.71 (peanoSinj) => 78.39/10.71 (( 78.39/10.71 (transitivesetOp1) => 78.39/10.71 (( 78.39/10.71 (binintTransitive) => 78.39/10.71 (( 78.39/10.71 (transitivesetOp2) => 78.39/10.71 (( 78.39/10.71 (setunionTransitive) => 78.39/10.71 (( 78.39/10.71 (ordinalMinLem1) => 78.39/10.71 (( 78.39/10.71 (!!) @ ( 78.39/10.71 ^[Y0 : $i]: 78.39/10.71 (( 78.39/10.71 (ordinal @ 78.39/10.71 Y0) => 78.39/10.71 (( 78.39/10.71 (!!) @ ( 78.39/10.71 ^[Y1 : $i]: 78.39/10.71 (( 78.39/10.71 (!!) @ ( 78.39/10.71 ^[Y2 : $i]: 78.39/10.71 (( 78.39/10.71 (in @ 78.39/10.71 Y2 @ 78.39/10.71 Y0) => 78.39/10.71 (( 78.39/10.71 (in @ 78.39/10.71 Y1 @ 78.39/10.71 Y2) => 78.39/10.71 (in @ 78.39/10.71 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 78.39/10.71 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1538])). 78.39/10.71 thf(zip_derived_cl1553, plain, 78.39/10.71 (~ (((cartprodfstpairEq) => 78.39/10.71 (((cartprodsndpairEq) => 78.39/10.71 (((cartprodpairsurjEq) => 78.39/10.71 (((dpsetconstrI) => 78.39/10.71 (((dpsetconstrSub) => 78.39/10.71 (((setOfPairsIsBReln) => 78.39/10.71 (((dpsetconstrERa) => 78.39/10.71 (((dpsetconstrEL1) => 78.39/10.71 (((dpsetconstrEL2) => 78.39/10.71 (((dpsetconstrER) => 78.39/10.71 (((funcImageSingleton) => 78.39/10.71 (((apProp) => 78.39/10.71 (((app) => 78.39/10.71 (((infuncsetfunc) => 78.39/10.71 (((ap2p) => 78.39/10.71 (((funcinfuncset) => 78.39/10.71 (((lamProp) => 78.39/10.71 (((lamp) => 78.39/10.71 (((lam2p) => 78.39/10.71 (((brelnall1) => 78.39/10.71 (((brelnall2) => 78.39/10.71 (((ex1E2) => 78.39/10.71 (((funcGraphProp1) => 78.39/10.71 (((funcGraphProp3) => 78.39/10.71 (((funcGraphProp2) => 78.39/10.71 (((funcextLem) => 78.39/10.71 (((funcGraphProp4) => 78.39/10.71 (((subbreln) => 78.39/10.71 (((eqbreln) => 78.39/10.71 (((funcext) => 78.39/10.71 (( 78.39/10.71 (funcext2) => 78.39/10.71 (( 78.39/10.71 (ap2apEq1) => 78.39/10.71 (( 78.39/10.71 (ap2apEq2) => 78.39/10.71 (( 78.39/10.71 (beta1) => 78.39/10.71 (( 78.39/10.71 (eta1) => 78.39/10.71 (( 78.39/10.71 (lam2lamEq) => 78.39/10.71 (( 78.39/10.71 (beta2) => 78.39/10.71 (( 78.39/10.71 (eta2) => 78.39/10.71 (( 78.39/10.71 (iffalseProp1) => 78.39/10.71 (( 78.39/10.71 (iffalseProp2) => 78.39/10.71 (( 78.39/10.71 (iftrueProp1) => 78.39/10.71 (( 78.39/10.71 (iftrueProp2) => 78.39/10.71 (( 78.39/10.71 (ifSingleton) => 78.39/10.71 (( 78.39/10.71 (ifp) => 78.39/10.71 (( 78.39/10.71 (theeq) => 78.39/10.71 (( 78.39/10.71 (iftrue) => 78.39/10.71 (( 78.39/10.71 (iffalse) => 78.39/10.71 (( 78.39/10.71 (iftrueorfalse) => 78.39/10.71 (( 78.39/10.71 (binintersectT_lem) => 78.39/10.71 (( 78.39/10.71 (binunionT_lem) => 78.39/10.71 (( 78.39/10.71 (powersetT_lem) => 78.39/10.71 (( 78.39/10.71 (setminusT_lem) => 78.39/10.71 (( 78.39/10.71 (complementT_lem) => 78.39/10.71 (( 78.39/10.71 (setextT) => 78.39/10.71 (( 78.39/10.71 (subsetTI) => 78.39/10.71 (( 78.39/10.71 (powersetTI1) => 78.39/10.71 (( 78.39/10.71 (powersetTE1) => 78.39/10.71 (( 78.39/10.71 (complementTI1) => 78.39/10.71 (( 78.39/10.71 (complementTE1) => 78.39/10.71 (( 78.39/10.71 (binintersectTELcontra) => 78.39/10.71 (( 78.39/10.71 (binintersectTERcontra) => 78.39/10.71 (( 78.39/10.71 (contrasubsetT) => 78.39/10.71 (( 78.39/10.71 (contrasubsetT1) => 78.39/10.71 (( 78.39/10.71 (contrasubsetT2) => 78.39/10.71 (( 78.39/10.71 (contrasubsetT3) => 78.39/10.71 (( 78.39/10.71 (doubleComplementI1) => 78.39/10.71 (( 78.39/10.71 (doubleComplementE1) => 78.39/10.71 (( 78.39/10.71 (doubleComplementSub1) => 78.39/10.71 (( 78.39/10.71 (doubleComplementSub2) => 78.39/10.71 (( 78.39/10.71 (doubleComplementEq) => 78.39/10.71 (( 78.39/10.71 (complementTnotintersectT) => 78.39/10.71 (( 78.39/10.71 (complementImpComplementIntersect) => 78.39/10.71 (( 78.39/10.71 (complementSubsetComplementIntersect) => 78.39/10.71 (( 78.39/10.71 (complementInPowersetComplementIntersect) => 78.39/10.71 (( 78.39/10.71 (contraSubsetComplement) => 78.39/10.71 (( 78.39/10.71 (complementTcontraSubset) => 78.39/10.71 (( 78.39/10.71 (binunionTILcontra) => 78.39/10.71 (( 78.39/10.71 (binunionTIRcontra) => 78.39/10.71 (( 78.39/10.71 (inIntersectImpInUnion) => 78.39/10.71 (( 78.39/10.71 (inIntersectImpInUnion2) => 78.39/10.71 (( 78.39/10.71 (inIntersectImpInIntersectUnions) => 78.39/10.71 (( 78.39/10.71 (intersectInPowersetIntersectUnions) => 78.39/10.71 (( 78.39/10.71 (inComplementUnionImpNotIn1) => 78.39/10.71 (( 78.39/10.71 (inComplementUnionImpInComplement1) => 78.39/10.71 (( 78.39/10.71 (binunionTE) => 78.39/10.71 (( 78.39/10.71 (binunionTEcontra) => 78.39/10.71 (( 78.39/10.71 (demorgan2a1) => 78.39/10.71 (( 78.39/10.71 (complementUnionInPowersetComplement) => 78.39/10.71 (( 78.39/10.71 (demorgan2a2) => 78.39/10.71 (( 78.39/10.71 (demorgan1a) => 78.39/10.71 (( 78.39/10.71 (demorgan1b) => 78.39/10.71 (( 78.39/10.71 (demorgan1) => 78.39/10.71 (( 78.39/10.71 (demorgan2a) => 78.39/10.71 (( 78.39/10.71 (demorgan2b2) => 78.39/10.71 (( 78.39/10.71 (demorgan2b) => 78.39/10.71 (( 78.39/10.71 (demorgan2) => 78.39/10.71 (( 78.39/10.71 (woz13rule0) => 78.39/10.71 (( 78.39/10.71 (woz13rule1) => 78.39/10.71 (( 78.39/10.71 (woz13rule2) => 78.39/10.71 (( 78.39/10.71 (woz13rule3) => 78.39/10.71 (( 78.39/10.71 (woz13rule4) => 78.39/10.71 (( 78.39/10.71 (woz1_1) => 78.39/10.71 (( 78.39/10.71 (woz1_2) => 78.39/10.71 (( 78.39/10.71 (woz1_3) => 78.39/10.71 (( 78.39/10.71 (woz1_4) => 78.39/10.71 (( 78.39/10.71 (woz1_5) => 78.39/10.71 (( 78.39/10.71 (breln1all2) => 78.39/10.71 (( 78.39/10.71 (breln1SetBreln1) => 78.39/10.71 (( 78.39/10.71 (choice2fnsingleton) => 78.39/10.71 (( 78.39/10.71 (setOfPairsIsBReln1) => 78.39/10.71 (( 78.39/10.71 (breln1all1) => 78.39/10.71 (( 78.39/10.71 (subbreln1) => 78.39/10.71 (( 78.39/10.71 (eqbreln1) => 78.39/10.71 (( 78.39/10.71 (breln1invprop) => 78.39/10.71 (( 78.39/10.71 (breln1invI) => 78.39/10.71 (( 78.39/10.71 (breln1invE) => 78.39/10.71 (( 78.39/10.71 (breln1compprop) => 78.39/10.71 (( 78.39/10.71 (breln1compI) => 78.39/10.71 (( 78.39/10.71 (breln1compE) => 78.39/10.71 (( 78.39/10.71 (breln1compEex) => 78.39/10.71 (( 78.39/10.71 (breln1unionprop) => 78.39/10.71 (( 78.39/10.71 (breln1unionIL) => 78.39/10.71 (( 78.39/10.71 (breln1unionIR) => 78.39/10.71 (( 78.39/10.71 (breln1unionI) => 78.39/10.71 (( 78.39/10.71 (breln1unionE) => 78.39/10.71 (( 78.39/10.71 (breln1unionEcases) => 78.39/10.71 (( 78.39/10.71 (breln1unionCommutes) => 78.39/10.71 (( 78.39/10.71 (woz2Ex) => 78.39/10.71 (( 78.39/10.71 (woz2W) => 78.39/10.71 (( 78.39/10.71 (woz2A) => 78.39/10.71 (( 78.39/10.71 (woz2B) => 78.39/10.71 (( 78.39/10.71 (image1Ex) => 78.39/10.71 (( 78.39/10.71 (image1Ex1) => 78.39/10.71 (( 78.39/10.71 (image1Equiv) => 78.39/10.71 (( 78.39/10.71 (image1E) => 78.39/10.71 (( 78.39/10.71 (image1I) => 78.39/10.71 (( 78.39/10.71 (injFuncInInjFuncSet) => 78.39/10.71 (( 78.39/10.71 (injFuncSetFuncIn) => 78.39/10.71 (( 78.39/10.71 (injFuncSetFuncInj) => 78.39/10.71 (( 78.39/10.71 (surjFuncSetFuncIn) => 78.39/10.71 (( 78.39/10.71 (surjFuncSetFuncSurj) => 78.39/10.71 (( 78.39/10.71 (leftInvIsSurj) => 78.39/10.71 (( 78.39/10.71 (surjCantorThm) => 78.39/10.71 (( 78.39/10.71 (foundation2) => 78.39/10.71 (( 78.39/10.71 (notinself) => 78.39/10.71 (( 78.39/10.71 (notinself2) => 78.39/10.71 (( 78.39/10.71 (omegaSp) => 78.39/10.71 (( 78.39/10.71 (omegaSclos) => 78.39/10.71 (( 78.39/10.71 (peano0notS) => 78.39/10.71 (( 78.39/10.71 (peanoSinj) => 78.39/10.71 (( 78.39/10.71 (transitivesetOp1) => 78.39/10.71 (( 78.39/10.71 (binintTransitive) => 78.39/10.71 (( 78.39/10.71 (transitivesetOp2) => 78.39/10.71 (( 78.39/10.71 (setunionTransitive) => 78.39/10.71 (( 78.39/10.71 (ordinalMinLem1) => 78.39/10.71 (( 78.39/10.71 (!!) @ ( 78.39/10.71 ^[Y0 : $i]: 78.39/10.71 (( 78.39/10.71 (ordinal @ 78.39/10.71 Y0) => 78.39/10.71 (( 78.39/10.71 (!!) @ ( 78.39/10.71 ^[Y1 : $i]: 78.39/10.71 (( 78.39/10.71 (!!) @ ( 78.39/10.71 ^[Y2 : $i]: 78.39/10.71 (( 78.39/10.71 (in @ 78.39/10.71 Y2 @ 78.39/10.71 Y0) => 78.39/10.71 (( 78.39/10.71 (in @ 78.39/10.71 Y1 @ 78.39/10.71 Y2) => 78.39/10.71 (in @ 78.39/10.71 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 78.39/10.71 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1546])). 78.39/10.71 thf(zip_derived_cl1559, plain, 78.39/10.71 (~ (((cartprodsndpairEq) => 78.39/10.71 (((cartprodpairsurjEq) => 78.39/10.71 (((dpsetconstrI) => 78.39/10.71 (((dpsetconstrSub) => 78.39/10.71 (((setOfPairsIsBReln) => 78.39/10.71 (((dpsetconstrERa) => 78.39/10.71 (((dpsetconstrEL1) => 78.39/10.71 (((dpsetconstrEL2) => 78.39/10.71 (((dpsetconstrER) => 78.39/10.71 (((funcImageSingleton) => 78.39/10.71 (((apProp) => 78.39/10.71 (((app) => 78.39/10.71 (((infuncsetfunc) => 78.39/10.71 (((ap2p) => 78.39/10.71 (((funcinfuncset) => 78.39/10.71 (((lamProp) => 78.39/10.71 (((lamp) => 78.39/10.71 (((lam2p) => 78.39/10.71 (((brelnall1) => 78.39/10.71 (((brelnall2) => 78.39/10.71 (((ex1E2) => 78.39/10.71 (((funcGraphProp1) => 78.39/10.71 (((funcGraphProp3) => 78.39/10.71 (((funcGraphProp2) => 78.39/10.71 (((funcextLem) => 78.39/10.71 (((funcGraphProp4) => 78.39/10.71 (((subbreln) => 78.39/10.71 (((eqbreln) => 78.39/10.71 (((funcext) => 78.39/10.71 (((funcext2) => 78.39/10.71 (( 78.39/10.71 (ap2apEq1) => 78.39/10.71 (( 78.39/10.71 (ap2apEq2) => 78.39/10.71 (( 78.39/10.71 (beta1) => 78.39/10.71 (( 78.39/10.71 (eta1) => 78.39/10.71 (( 78.39/10.71 (lam2lamEq) => 78.39/10.71 (( 78.39/10.71 (beta2) => 78.39/10.71 (( 78.39/10.71 (eta2) => 78.39/10.71 (( 78.39/10.71 (iffalseProp1) => 78.39/10.71 (( 78.39/10.71 (iffalseProp2) => 78.39/10.71 (( 78.39/10.71 (iftrueProp1) => 78.39/10.71 (( 78.39/10.71 (iftrueProp2) => 78.39/10.71 (( 78.39/10.71 (ifSingleton) => 78.39/10.71 (( 78.39/10.71 (ifp) => 78.39/10.71 (( 78.39/10.71 (theeq) => 78.39/10.71 (( 78.39/10.71 (iftrue) => 78.39/10.71 (( 78.39/10.71 (iffalse) => 78.39/10.71 (( 78.39/10.71 (iftrueorfalse) => 78.39/10.71 (( 78.39/10.71 (binintersectT_lem) => 78.39/10.71 (( 78.39/10.71 (binunionT_lem) => 78.39/10.71 (( 78.39/10.71 (powersetT_lem) => 78.39/10.71 (( 78.39/10.71 (setminusT_lem) => 78.39/10.71 (( 78.39/10.71 (complementT_lem) => 78.39/10.71 (( 78.39/10.71 (setextT) => 78.39/10.71 (( 78.39/10.71 (subsetTI) => 78.39/10.71 (( 78.39/10.71 (powersetTI1) => 78.39/10.71 (( 78.39/10.71 (powersetTE1) => 78.39/10.71 (( 78.39/10.71 (complementTI1) => 78.39/10.71 (( 78.39/10.71 (complementTE1) => 78.39/10.71 (( 78.39/10.71 (binintersectTELcontra) => 78.39/10.71 (( 78.39/10.71 (binintersectTERcontra) => 78.39/10.71 (( 78.39/10.71 (contrasubsetT) => 78.39/10.71 (( 78.39/10.71 (contrasubsetT1) => 78.39/10.71 (( 78.39/10.71 (contrasubsetT2) => 78.39/10.71 (( 78.39/10.71 (contrasubsetT3) => 78.39/10.71 (( 78.39/10.71 (doubleComplementI1) => 78.39/10.71 (( 78.39/10.71 (doubleComplementE1) => 78.39/10.71 (( 78.39/10.71 (doubleComplementSub1) => 78.39/10.71 (( 78.39/10.71 (doubleComplementSub2) => 78.39/10.71 (( 78.39/10.71 (doubleComplementEq) => 78.39/10.71 (( 78.39/10.71 (complementTnotintersectT) => 78.39/10.71 (( 78.39/10.71 (complementImpComplementIntersect) => 78.39/10.71 (( 78.39/10.71 (complementSubsetComplementIntersect) => 78.39/10.71 (( 78.39/10.71 (complementInPowersetComplementIntersect) => 78.39/10.71 (( 78.39/10.71 (contraSubsetComplement) => 78.39/10.71 (( 78.39/10.71 (complementTcontraSubset) => 78.39/10.71 (( 78.39/10.71 (binunionTILcontra) => 78.39/10.71 (( 78.39/10.71 (binunionTIRcontra) => 78.39/10.71 (( 78.39/10.71 (inIntersectImpInUnion) => 78.39/10.71 (( 78.39/10.71 (inIntersectImpInUnion2) => 78.39/10.71 (( 78.39/10.71 (inIntersectImpInIntersectUnions) => 78.39/10.71 (( 78.39/10.71 (intersectInPowersetIntersectUnions) => 78.39/10.71 (( 78.39/10.71 (inComplementUnionImpNotIn1) => 78.39/10.71 (( 78.39/10.71 (inComplementUnionImpInComplement1) => 78.39/10.71 (( 78.39/10.71 (binunionTE) => 78.39/10.71 (( 78.39/10.71 (binunionTEcontra) => 78.39/10.71 (( 78.39/10.71 (demorgan2a1) => 78.39/10.71 (( 78.39/10.71 (complementUnionInPowersetComplement) => 78.39/10.71 (( 78.39/10.71 (demorgan2a2) => 78.39/10.71 (( 78.39/10.71 (demorgan1a) => 78.39/10.71 (( 78.39/10.71 (demorgan1b) => 78.39/10.71 (( 78.39/10.71 (demorgan1) => 78.39/10.71 (( 78.39/10.71 (demorgan2a) => 78.39/10.71 (( 78.39/10.71 (demorgan2b2) => 78.39/10.71 (( 78.39/10.71 (demorgan2b) => 78.39/10.71 (( 78.39/10.71 (demorgan2) => 78.39/10.71 (( 78.39/10.71 (woz13rule0) => 78.39/10.71 (( 78.39/10.71 (woz13rule1) => 78.39/10.71 (( 78.39/10.71 (woz13rule2) => 78.39/10.71 (( 78.39/10.71 (woz13rule3) => 78.39/10.71 (( 78.39/10.71 (woz13rule4) => 78.39/10.71 (( 78.39/10.71 (woz1_1) => 78.39/10.71 (( 78.39/10.71 (woz1_2) => 78.39/10.71 (( 78.39/10.71 (woz1_3) => 78.39/10.71 (( 78.39/10.71 (woz1_4) => 78.39/10.71 (( 78.39/10.71 (woz1_5) => 78.39/10.71 (( 78.39/10.71 (breln1all2) => 78.39/10.71 (( 78.39/10.71 (breln1SetBreln1) => 78.39/10.71 (( 78.39/10.71 (choice2fnsingleton) => 78.39/10.71 (( 78.39/10.71 (setOfPairsIsBReln1) => 78.39/10.71 (( 78.39/10.71 (breln1all1) => 78.39/10.71 (( 78.39/10.71 (subbreln1) => 78.39/10.71 (( 78.39/10.71 (eqbreln1) => 78.39/10.71 (( 78.39/10.71 (breln1invprop) => 78.39/10.71 (( 78.39/10.71 (breln1invI) => 78.39/10.71 (( 78.39/10.71 (breln1invE) => 78.39/10.71 (( 78.39/10.71 (breln1compprop) => 78.39/10.71 (( 78.39/10.71 (breln1compI) => 78.39/10.71 (( 78.39/10.71 (breln1compE) => 78.39/10.71 (( 78.39/10.71 (breln1compEex) => 78.39/10.71 (( 78.39/10.71 (breln1unionprop) => 78.39/10.71 (( 78.39/10.71 (breln1unionIL) => 78.39/10.71 (( 78.39/10.71 (breln1unionIR) => 78.39/10.71 (( 78.39/10.71 (breln1unionI) => 78.39/10.71 (( 78.39/10.71 (breln1unionE) => 78.39/10.71 (( 78.39/10.71 (breln1unionEcases) => 78.39/10.71 (( 78.39/10.71 (breln1unionCommutes) => 78.39/10.71 (( 78.39/10.71 (woz2Ex) => 78.39/10.71 (( 78.39/10.71 (woz2W) => 78.39/10.71 (( 78.39/10.71 (woz2A) => 78.39/10.71 (( 78.39/10.71 (woz2B) => 78.39/10.71 (( 78.39/10.71 (image1Ex) => 78.39/10.71 (( 78.39/10.71 (image1Ex1) => 78.39/10.71 (( 78.39/10.71 (image1Equiv) => 78.39/10.71 (( 78.39/10.71 (image1E) => 78.39/10.71 (( 78.39/10.71 (image1I) => 78.39/10.71 (( 78.39/10.71 (injFuncInInjFuncSet) => 78.39/10.71 (( 78.39/10.71 (injFuncSetFuncIn) => 78.39/10.71 (( 78.39/10.71 (injFuncSetFuncInj) => 78.39/10.71 (( 78.39/10.71 (surjFuncSetFuncIn) => 78.39/10.71 (( 78.39/10.71 (surjFuncSetFuncSurj) => 78.39/10.71 (( 78.39/10.71 (leftInvIsSurj) => 78.39/10.71 (( 78.39/10.71 (surjCantorThm) => 78.39/10.71 (( 78.39/10.71 (foundation2) => 78.39/10.71 (( 78.39/10.71 (notinself) => 78.39/10.71 (( 78.39/10.71 (notinself2) => 78.39/10.71 (( 78.39/10.71 (omegaSp) => 78.39/10.71 (( 78.39/10.71 (omegaSclos) => 78.39/10.71 (( 78.39/10.71 (peano0notS) => 78.39/10.71 (( 78.39/10.71 (peanoSinj) => 78.39/10.71 (( 78.39/10.71 (transitivesetOp1) => 78.39/10.71 (( 78.39/10.71 (binintTransitive) => 78.39/10.71 (( 78.39/10.71 (transitivesetOp2) => 78.39/10.71 (( 78.39/10.71 (setunionTransitive) => 78.39/10.71 (( 78.39/10.71 (ordinalMinLem1) => 78.39/10.71 (( 78.39/10.71 (!!) @ ( 78.39/10.71 ^[Y0 : $i]: 78.39/10.71 (( 78.39/10.71 (ordinal @ 78.39/10.71 Y0) => 78.39/10.71 (( 78.39/10.71 (!!) @ ( 78.39/10.71 ^[Y1 : $i]: 78.39/10.71 (( 78.39/10.71 (!!) @ ( 78.39/10.71 ^[Y2 : $i]: 78.39/10.71 (( 78.39/10.71 (in @ 78.39/10.71 Y2 @ 78.39/10.71 Y0) => 78.39/10.71 (( 78.39/10.71 (in @ 78.39/10.71 Y1 @ 78.39/10.71 Y2) => 78.39/10.71 (in @ 78.39/10.71 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 78.39/10.71 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1553])). 78.39/10.71 thf(zip_derived_cl1566, plain, 78.39/10.71 (~ (((cartprodpairsurjEq) => 78.39/10.71 (((dpsetconstrI) => 78.39/10.71 (((dpsetconstrSub) => 78.39/10.71 (((setOfPairsIsBReln) => 78.39/10.71 (((dpsetconstrERa) => 78.39/10.71 (((dpsetconstrEL1) => 78.39/10.71 (((dpsetconstrEL2) => 78.39/10.71 (((dpsetconstrER) => 78.39/10.71 (((funcImageSingleton) => 78.39/10.71 (((apProp) => 78.39/10.71 (((app) => 78.39/10.71 (((infuncsetfunc) => 78.39/10.71 (((ap2p) => 78.39/10.71 (((funcinfuncset) => 78.39/10.71 (((lamProp) => 78.39/10.71 (((lamp) => 78.39/10.71 (((lam2p) => 78.39/10.71 (((brelnall1) => 78.39/10.71 (((brelnall2) => 78.39/10.71 (((ex1E2) => 78.39/10.71 (((funcGraphProp1) => 78.39/10.71 (((funcGraphProp3) => 78.39/10.71 (((funcGraphProp2) => 78.39/10.71 (((funcextLem) => 78.39/10.71 (((funcGraphProp4) => 78.39/10.71 (((subbreln) => 78.39/10.71 (((eqbreln) => 78.39/10.71 (((funcext) => 78.39/10.71 (((funcext2) => 78.39/10.71 (((ap2apEq1) => 78.39/10.71 (( 78.39/10.71 (ap2apEq2) => 78.39/10.71 (( 78.39/10.71 (beta1) => 78.39/10.71 (( 78.39/10.71 (eta1) => 78.39/10.71 (( 78.39/10.71 (lam2lamEq) => 78.39/10.71 (( 78.39/10.71 (beta2) => 78.39/10.71 (( 78.39/10.71 (eta2) => 78.39/10.71 (( 78.39/10.71 (iffalseProp1) => 78.39/10.71 (( 78.39/10.71 (iffalseProp2) => 78.39/10.71 (( 78.39/10.71 (iftrueProp1) => 78.39/10.71 (( 78.39/10.71 (iftrueProp2) => 78.39/10.71 (( 78.39/10.71 (ifSingleton) => 78.39/10.71 (( 78.39/10.71 (ifp) => 78.39/10.71 (( 78.39/10.71 (theeq) => 78.39/10.71 (( 78.39/10.71 (iftrue) => 78.39/10.71 (( 78.39/10.71 (iffalse) => 78.39/10.71 (( 78.39/10.71 (iftrueorfalse) => 78.39/10.71 (( 78.39/10.71 (binintersectT_lem) => 78.39/10.71 (( 78.39/10.71 (binunionT_lem) => 78.39/10.71 (( 78.39/10.71 (powersetT_lem) => 78.39/10.71 (( 78.39/10.71 (setminusT_lem) => 78.39/10.71 (( 78.39/10.71 (complementT_lem) => 78.39/10.71 (( 78.39/10.71 (setextT) => 78.39/10.71 (( 78.39/10.71 (subsetTI) => 78.39/10.71 (( 78.39/10.71 (powersetTI1) => 78.39/10.71 (( 78.39/10.71 (powersetTE1) => 78.39/10.71 (( 78.39/10.71 (complementTI1) => 78.39/10.71 (( 78.39/10.71 (complementTE1) => 78.39/10.71 (( 78.39/10.71 (binintersectTELcontra) => 78.39/10.71 (( 78.39/10.71 (binintersectTERcontra) => 78.39/10.71 (( 78.39/10.71 (contrasubsetT) => 78.39/10.71 (( 78.39/10.71 (contrasubsetT1) => 78.39/10.71 (( 78.39/10.71 (contrasubsetT2) => 78.39/10.71 (( 78.39/10.71 (contrasubsetT3) => 78.39/10.71 (( 78.39/10.71 (doubleComplementI1) => 78.39/10.71 (( 78.39/10.71 (doubleComplementE1) => 78.39/10.71 (( 78.39/10.71 (doubleComplementSub1) => 78.39/10.71 (( 78.39/10.71 (doubleComplementSub2) => 78.39/10.71 (( 78.39/10.71 (doubleComplementEq) => 78.39/10.71 (( 78.39/10.71 (complementTnotintersectT) => 78.39/10.71 (( 78.39/10.71 (complementImpComplementIntersect) => 78.39/10.71 (( 78.39/10.71 (complementSubsetComplementIntersect) => 78.39/10.71 (( 78.39/10.71 (complementInPowersetComplementIntersect) => 78.39/10.71 (( 78.39/10.71 (contraSubsetComplement) => 78.39/10.71 (( 78.39/10.71 (complementTcontraSubset) => 78.39/10.71 (( 78.39/10.71 (binunionTILcontra) => 78.39/10.71 (( 78.39/10.71 (binunionTIRcontra) => 78.39/10.71 (( 78.39/10.71 (inIntersectImpInUnion) => 78.39/10.71 (( 78.39/10.71 (inIntersectImpInUnion2) => 78.39/10.71 (( 78.39/10.71 (inIntersectImpInIntersectUnions) => 78.39/10.71 (( 78.39/10.71 (intersectInPowersetIntersectUnions) => 78.39/10.71 (( 78.39/10.71 (inComplementUnionImpNotIn1) => 78.39/10.71 (( 78.39/10.71 (inComplementUnionImpInComplement1) => 78.39/10.71 (( 78.39/10.71 (binunionTE) => 78.39/10.71 (( 78.39/10.71 (binunionTEcontra) => 78.39/10.71 (( 78.39/10.71 (demorgan2a1) => 78.39/10.71 (( 78.39/10.71 (complementUnionInPowersetComplement) => 78.39/10.71 (( 78.39/10.71 (demorgan2a2) => 78.39/10.71 (( 78.39/10.71 (demorgan1a) => 78.39/10.71 (( 78.39/10.71 (demorgan1b) => 78.39/10.71 (( 78.39/10.71 (demorgan1) => 78.39/10.71 (( 78.39/10.71 (demorgan2a) => 78.39/10.71 (( 78.39/10.71 (demorgan2b2) => 78.39/10.71 (( 78.39/10.71 (demorgan2b) => 78.39/10.71 (( 78.39/10.71 (demorgan2) => 78.39/10.71 (( 78.39/10.71 (woz13rule0) => 78.39/10.71 (( 78.39/10.71 (woz13rule1) => 78.39/10.71 (( 78.39/10.71 (woz13rule2) => 78.39/10.71 (( 78.39/10.71 (woz13rule3) => 78.39/10.71 (( 78.39/10.71 (woz13rule4) => 78.39/10.71 (( 78.39/10.71 (woz1_1) => 78.39/10.71 (( 78.39/10.71 (woz1_2) => 78.39/10.71 (( 78.39/10.71 (woz1_3) => 78.39/10.71 (( 78.39/10.71 (woz1_4) => 78.39/10.71 (( 78.39/10.71 (woz1_5) => 78.39/10.71 (( 78.39/10.71 (breln1all2) => 78.39/10.71 (( 78.39/10.71 (breln1SetBreln1) => 78.39/10.71 (( 78.39/10.71 (choice2fnsingleton) => 78.39/10.71 (( 78.39/10.71 (setOfPairsIsBReln1) => 78.39/10.71 (( 78.39/10.71 (breln1all1) => 78.39/10.71 (( 78.39/10.71 (subbreln1) => 78.39/10.71 (( 78.39/10.71 (eqbreln1) => 78.39/10.71 (( 78.39/10.71 (breln1invprop) => 78.39/10.71 (( 78.39/10.71 (breln1invI) => 78.39/10.71 (( 78.39/10.71 (breln1invE) => 78.39/10.71 (( 78.39/10.71 (breln1compprop) => 78.39/10.71 (( 78.39/10.71 (breln1compI) => 78.39/10.71 (( 78.39/10.71 (breln1compE) => 78.39/10.71 (( 78.39/10.71 (breln1compEex) => 78.39/10.71 (( 78.39/10.71 (breln1unionprop) => 78.39/10.71 (( 78.39/10.71 (breln1unionIL) => 78.39/10.71 (( 78.39/10.71 (breln1unionIR) => 78.39/10.71 (( 78.39/10.71 (breln1unionI) => 78.39/10.71 (( 78.39/10.71 (breln1unionE) => 78.39/10.71 (( 78.39/10.71 (breln1unionEcases) => 78.39/10.71 (( 78.39/10.71 (breln1unionCommutes) => 78.39/10.71 (( 78.39/10.71 (woz2Ex) => 78.39/10.71 (( 78.39/10.71 (woz2W) => 78.39/10.71 (( 78.39/10.71 (woz2A) => 78.39/10.71 (( 78.39/10.71 (woz2B) => 78.39/10.71 (( 78.39/10.71 (image1Ex) => 78.39/10.71 (( 78.39/10.71 (image1Ex1) => 78.39/10.71 (( 78.39/10.71 (image1Equiv) => 78.39/10.71 (( 78.39/10.71 (image1E) => 78.39/10.71 (( 78.39/10.71 (image1I) => 78.39/10.71 (( 78.39/10.71 (injFuncInInjFuncSet) => 78.39/10.71 (( 78.39/10.71 (injFuncSetFuncIn) => 78.39/10.71 (( 78.39/10.71 (injFuncSetFuncInj) => 78.39/10.71 (( 78.39/10.71 (surjFuncSetFuncIn) => 78.39/10.71 (( 78.39/10.71 (surjFuncSetFuncSurj) => 78.39/10.71 (( 78.39/10.71 (leftInvIsSurj) => 78.39/10.71 (( 78.39/10.71 (surjCantorThm) => 78.39/10.71 (( 78.39/10.71 (foundation2) => 78.39/10.71 (( 78.39/10.71 (notinself) => 78.39/10.71 (( 78.39/10.71 (notinself2) => 78.39/10.71 (( 78.39/10.71 (omegaSp) => 78.39/10.71 (( 78.39/10.71 (omegaSclos) => 78.39/10.71 (( 78.39/10.71 (peano0notS) => 78.39/10.71 (( 78.39/10.71 (peanoSinj) => 78.39/10.71 (( 78.39/10.71 (transitivesetOp1) => 78.39/10.71 (( 78.39/10.71 (binintTransitive) => 78.39/10.71 (( 78.39/10.71 (transitivesetOp2) => 78.39/10.71 (( 78.39/10.71 (setunionTransitive) => 78.39/10.71 (( 78.39/10.71 (ordinalMinLem1) => 78.39/10.71 (( 78.39/10.71 (!!) @ ( 78.39/10.71 ^[Y0 : $i]: 78.39/10.71 (( 78.39/10.71 (ordinal @ 78.39/10.71 Y0) => 78.39/10.71 (( 78.39/10.71 (!!) @ ( 78.39/10.71 ^[Y1 : $i]: 78.39/10.71 (( 78.39/10.71 (!!) @ ( 78.39/10.71 ^[Y2 : $i]: 78.39/10.71 (( 78.39/10.71 (in @ 78.39/10.71 Y2 @ 78.39/10.71 Y0) => 78.39/10.71 (( 78.39/10.71 (in @ 78.39/10.71 Y1 @ 78.39/10.71 Y2) => 78.39/10.71 (in @ 78.39/10.71 Y1 @ 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=> 78.39/10.71 (( 78.39/10.71 (woz13rule4) => 78.39/10.71 (( 78.39/10.71 (woz1_1) => 78.39/10.71 (( 78.39/10.71 (woz1_2) => 78.39/10.71 (( 78.39/10.71 (woz1_3) => 78.39/10.71 (( 78.39/10.71 (woz1_4) => 78.39/10.71 (( 78.39/10.71 (woz1_5) => 78.39/10.71 (( 78.39/10.71 (breln1all2) => 78.39/10.71 (( 78.39/10.71 (breln1SetBreln1) => 78.39/10.71 (( 78.39/10.71 (choice2fnsingleton) => 78.39/10.71 (( 78.39/10.71 (setOfPairsIsBReln1) => 78.39/10.71 (( 78.39/10.71 (breln1all1) => 78.39/10.71 (( 78.39/10.71 (subbreln1) => 78.39/10.71 (( 78.39/10.71 (eqbreln1) => 78.39/10.71 (( 78.39/10.71 (breln1invprop) => 78.39/10.71 (( 78.39/10.71 (breln1invI) => 78.39/10.71 (( 78.39/10.71 (breln1invE) => 78.39/10.71 (( 78.39/10.71 (breln1compprop) => 78.39/10.71 (( 78.39/10.71 (breln1compI) => 78.39/10.71 (( 78.39/10.71 (breln1compE) => 78.39/10.71 (( 78.39/10.71 (breln1compEex) => 78.39/10.71 (( 78.39/10.71 (breln1unionprop) => 78.39/10.71 (( 78.39/10.71 (breln1unionIL) => 78.39/10.71 (( 78.39/10.71 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=> 78.39/10.71 (( 78.39/10.71 (notinself2) => 78.39/10.71 (( 78.39/10.71 (omegaSp) => 78.39/10.71 (( 78.39/10.71 (omegaSclos) => 78.39/10.71 (( 78.39/10.71 (peano0notS) => 78.39/10.71 (( 78.39/10.71 (peanoSinj) => 78.39/10.71 (( 78.39/10.71 (transitivesetOp1) => 78.39/10.71 (( 78.39/10.71 (binintTransitive) => 78.39/10.71 (( 78.39/10.71 (transitivesetOp2) => 78.39/10.71 (( 78.39/10.71 (setunionTransitive) => 78.39/10.71 (( 78.39/10.71 (ordinalMinLem1) => 78.39/10.71 (( 78.39/10.71 (!!) @ ( 78.39/10.71 ^[Y0 : $i]: 78.39/10.71 (( 78.39/10.71 (ordinal @ 78.39/10.71 Y0) => 78.39/10.71 (( 78.39/10.71 (!!) @ ( 78.39/10.71 ^[Y1 : $i]: 78.39/10.71 (( 78.39/10.71 (!!) @ ( 78.39/10.71 ^[Y2 : $i]: 78.39/10.71 (( 78.39/10.71 (in @ 78.39/10.71 Y2 @ 78.39/10.71 Y0) => 78.39/10.71 (( 78.39/10.71 (in @ 78.39/10.71 Y1 @ 78.39/10.71 Y2) => 78.39/10.71 (in @ 78.39/10.71 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 78.39/10.71 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1572])). 78.39/10.71 thf(zip_derived_cl1586, plain, 78.39/10.71 (~ (((setOfPairsIsBReln) => 78.39/10.71 (((dpsetconstrERa) => 78.39/10.71 (((dpsetconstrEL1) => 78.39/10.71 (((dpsetconstrEL2) => 78.39/10.71 (((dpsetconstrER) => 78.39/10.71 (((funcImageSingleton) => 78.39/10.71 (((apProp) => 78.39/10.71 (((app) => 78.39/10.71 (((infuncsetfunc) => 78.39/10.71 (((ap2p) => 78.39/10.71 (((funcinfuncset) => 78.39/10.71 (((lamProp) => 78.39/10.71 (((lamp) => 78.39/10.71 (((lam2p) => 78.39/10.71 (((brelnall1) => 78.39/10.71 (((brelnall2) => 78.39/10.71 (((ex1E2) => 78.39/10.71 (((funcGraphProp1) => 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( 78.39/10.71 ^[Y0 : $i]: 78.39/10.71 (( 78.39/10.71 (ordinal @ 78.39/10.71 Y0) => 78.39/10.71 (( 78.39/10.71 (!!) @ ( 78.39/10.71 ^[Y1 : $i]: 78.39/10.71 (( 78.39/10.71 (!!) @ ( 78.39/10.71 ^[Y2 : $i]: 78.39/10.71 (( 78.39/10.71 (in @ 78.39/10.71 Y2 @ 78.39/10.71 Y0) => 78.39/10.71 (( 78.39/10.71 (in @ 78.39/10.71 Y1 @ 78.39/10.71 Y2) => 78.39/10.71 (in @ 78.39/10.71 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 78.39/10.71 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1579])). 78.39/10.71 thf(zip_derived_cl1594, plain, 78.39/10.71 (~ (((dpsetconstrERa) => 78.39/10.71 (((dpsetconstrEL1) => 78.39/10.71 (((dpsetconstrEL2) => 78.39/10.71 (((dpsetconstrER) => 78.39/10.71 (((funcImageSingleton) => 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(ifSingleton) => 78.39/10.71 (( 78.39/10.71 (ifp) => 78.39/10.71 (( 78.39/10.71 (theeq) => 78.39/10.71 (( 78.39/10.71 (iftrue) => 78.39/10.71 (( 78.39/10.71 (iffalse) => 78.39/10.71 (( 78.39/10.71 (iftrueorfalse) => 78.39/10.71 (( 78.39/10.71 (binintersectT_lem) => 78.39/10.71 (( 78.39/10.71 (binunionT_lem) => 78.39/10.71 (( 78.39/10.71 (powersetT_lem) => 78.39/10.71 (( 78.39/10.71 (setminusT_lem) => 78.39/10.71 (( 78.39/10.71 (complementT_lem) => 78.39/10.71 (( 78.39/10.71 (setextT) => 78.39/10.71 (( 78.39/10.71 (subsetTI) => 78.39/10.71 (( 78.39/10.71 (powersetTI1) => 78.39/10.71 (( 78.39/10.71 (powersetTE1) => 78.39/10.71 (( 78.39/10.71 (complementTI1) => 78.39/10.71 (( 78.39/10.71 (complementTE1) => 78.39/10.71 (( 78.39/10.71 (binintersectTELcontra) => 78.39/10.71 (( 78.39/10.71 (binintersectTERcontra) => 78.39/10.71 (( 78.39/10.71 (contrasubsetT) => 78.39/10.71 (( 78.39/10.71 (contrasubsetT1) => 78.39/10.71 (( 78.39/10.71 (contrasubsetT2) => 78.39/10.71 (( 78.39/10.71 (contrasubsetT3) => 78.39/10.71 (( 78.39/10.71 (doubleComplementI1) => 78.39/10.71 (( 78.39/10.71 (doubleComplementE1) => 78.39/10.71 (( 78.39/10.71 (doubleComplementSub1) => 78.39/10.71 (( 78.39/10.71 (doubleComplementSub2) => 78.39/10.71 (( 78.39/10.71 (doubleComplementEq) => 78.39/10.71 (( 78.39/10.71 (complementTnotintersectT) => 78.39/10.71 (( 78.39/10.71 (complementImpComplementIntersect) => 78.39/10.71 (( 78.39/10.71 (complementSubsetComplementIntersect) => 78.39/10.71 (( 78.39/10.71 (complementInPowersetComplementIntersect) => 78.39/10.71 (( 78.39/10.71 (contraSubsetComplement) => 78.39/10.71 (( 78.39/10.71 (complementTcontraSubset) => 78.39/10.71 (( 78.39/10.71 (binunionTILcontra) => 78.39/10.71 (( 78.39/10.71 (binunionTIRcontra) => 78.39/10.71 (( 78.39/10.71 (inIntersectImpInUnion) => 78.39/10.71 (( 78.39/10.71 (inIntersectImpInUnion2) => 78.39/10.71 (( 78.39/10.71 (inIntersectImpInIntersectUnions) => 78.39/10.71 (( 78.39/10.71 (intersectInPowersetIntersectUnions) => 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78.39/10.71 (injFuncInInjFuncSet) => 78.39/10.71 (( 78.39/10.71 (injFuncSetFuncIn) => 78.39/10.71 (( 78.39/10.71 (injFuncSetFuncInj) => 78.39/10.71 (( 78.39/10.71 (surjFuncSetFuncIn) => 78.39/10.71 (( 78.39/10.71 (surjFuncSetFuncSurj) => 78.39/10.71 (( 78.39/10.71 (leftInvIsSurj) => 78.39/10.71 (( 78.39/10.71 (surjCantorThm) => 78.39/10.71 (( 78.39/10.71 (foundation2) => 78.39/10.71 (( 78.39/10.71 (notinself) => 78.39/10.71 (( 78.39/10.71 (notinself2) => 78.39/10.71 (( 78.39/10.71 (omegaSp) => 78.39/10.71 (( 78.39/10.71 (omegaSclos) => 78.39/10.71 (( 78.39/10.71 (peano0notS) => 78.39/10.71 (( 78.39/10.71 (peanoSinj) => 78.39/10.71 (( 78.39/10.71 (transitivesetOp1) => 78.39/10.71 (( 78.39/10.71 (binintTransitive) => 78.39/10.71 (( 78.39/10.71 (transitivesetOp2) => 78.39/10.71 (( 78.39/10.71 (setunionTransitive) => 78.39/10.71 (( 78.39/10.71 (ordinalMinLem1) => 78.39/10.71 (( 78.39/10.71 (!!) @ ( 78.39/10.71 ^[Y0 : $i]: 78.39/10.71 (( 78.39/10.71 (ordinal @ 78.39/10.71 Y0) => 78.39/10.71 (( 78.39/10.71 (!!) @ ( 78.39/10.71 ^[Y1 : $i]: 78.39/10.71 (( 78.39/10.71 (!!) @ ( 78.39/10.71 ^[Y2 : $i]: 78.39/10.71 (( 78.39/10.71 (in @ 78.39/10.71 Y2 @ 78.39/10.71 Y0) => 78.39/10.71 (( 78.39/10.71 (in @ 78.39/10.71 Y1 @ 78.39/10.71 Y2) => 78.39/10.71 (in @ 78.39/10.71 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 78.39/10.71 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1594])). 78.39/10.71 thf(zip_derived_cl1613, plain, 78.39/10.71 (~ (((dpsetconstrEL2) => 78.39/10.71 (((dpsetconstrER) => 78.39/10.71 (((funcImageSingleton) => 78.39/10.71 (((apProp) => 78.39/10.71 (((app) => 78.39/10.71 (((infuncsetfunc) => 78.39/10.71 (((ap2p) => 78.39/10.71 (((funcinfuncset) => 78.39/10.71 (((lamProp) => 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78.39/10.72 (( 78.39/10.72 (surjFuncSetFuncIn) => 78.39/10.72 (( 78.39/10.72 (surjFuncSetFuncSurj) => 78.39/10.72 (( 78.39/10.72 (leftInvIsSurj) => 78.39/10.72 (( 78.39/10.72 (surjCantorThm) => 78.39/10.72 (( 78.39/10.72 (foundation2) => 78.39/10.72 (( 78.39/10.72 (notinself) => 78.39/10.72 (( 78.39/10.72 (notinself2) => 78.39/10.72 (( 78.39/10.72 (omegaSp) => 78.39/10.72 (( 78.39/10.72 (omegaSclos) => 78.39/10.72 (( 78.39/10.72 (peano0notS) => 78.39/10.72 (( 78.39/10.72 (peanoSinj) => 78.39/10.72 (( 78.39/10.72 (transitivesetOp1) => 78.39/10.72 (( 78.39/10.72 (binintTransitive) => 78.39/10.72 (( 78.39/10.72 (transitivesetOp2) => 78.39/10.72 (( 78.39/10.72 (setunionTransitive) => 78.39/10.72 (( 78.39/10.72 (ordinalMinLem1) => 78.39/10.72 (( 78.39/10.72 (!!) @ ( 78.39/10.72 ^[Y0 : $i]: 78.39/10.72 (( 78.39/10.72 (ordinal @ 78.39/10.72 Y0) => 78.39/10.72 (( 78.39/10.72 (!!) @ ( 78.39/10.72 ^[Y1 : $i]: 78.39/10.72 (( 78.39/10.72 (!!) @ ( 78.39/10.72 ^[Y2 : $i]: 78.39/10.72 (( 78.39/10.72 (in @ 78.39/10.72 Y2 @ 78.39/10.72 Y0) => 78.39/10.72 (( 78.39/10.72 (in @ 78.39/10.72 Y1 @ 78.39/10.72 Y2) => 78.39/10.72 (in @ 78.39/10.72 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 78.39/10.72 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1668])). 78.39/10.72 thf(zip_derived_cl1688, plain, 78.39/10.72 (~ (((lamProp) => 78.39/10.72 (((lamp) => 78.39/10.72 (((lam2p) => 78.39/10.72 (((brelnall1) => 78.39/10.72 (((brelnall2) => 78.39/10.72 (((ex1E2) => 78.39/10.72 (((funcGraphProp1) => 78.39/10.72 (((funcGraphProp3) => 78.39/10.72 (((funcGraphProp2) => 78.39/10.72 (((funcextLem) => 78.39/10.72 (((funcGraphProp4) => 78.39/10.72 (((subbreln) => 78.39/10.72 (((eqbreln) => 78.39/10.72 (((funcext) => 78.39/10.72 (((funcext2) => 78.39/10.72 (((ap2apEq1) => 78.39/10.72 (((ap2apEq2) => 78.39/10.72 (((beta1) => 78.39/10.72 (((eta1) => 78.39/10.72 (((lam2lamEq) => 78.39/10.72 (((beta2) => 78.39/10.72 (((eta2) => 78.39/10.72 (((iffalseProp1) => 78.39/10.72 (((iffalseProp2) => 78.39/10.72 (((iftrueProp1) => 78.39/10.72 (((iftrueProp2) => 78.39/10.72 (((ifSingleton) => 78.39/10.72 (((ifp) => 78.39/10.72 (((theeq) => 78.39/10.72 (((iftrue) => 78.39/10.72 (( 78.39/10.72 (iffalse) => 78.39/10.72 (( 78.39/10.72 (iftrueorfalse) => 78.39/10.72 (( 78.39/10.72 (binintersectT_lem) => 78.39/10.72 (( 78.39/10.72 (binunionT_lem) => 78.39/10.72 (( 78.39/10.72 (powersetT_lem) => 78.39/10.72 (( 78.39/10.72 (setminusT_lem) => 78.39/10.72 (( 78.39/10.72 (complementT_lem) => 78.39/10.72 (( 78.39/10.72 (setextT) => 78.39/10.72 (( 78.39/10.72 (subsetTI) => 78.39/10.72 (( 78.39/10.72 (powersetTI1) => 78.39/10.72 (( 78.39/10.72 (powersetTE1) => 78.39/10.72 (( 78.39/10.72 (complementTI1) => 78.39/10.72 (( 78.39/10.72 (complementTE1) => 78.39/10.72 (( 78.39/10.72 (binintersectTELcontra) => 78.39/10.72 (( 78.39/10.72 (binintersectTERcontra) => 78.39/10.72 (( 78.39/10.72 (contrasubsetT) => 78.39/10.72 (( 78.39/10.72 (contrasubsetT1) => 78.39/10.72 (( 78.39/10.72 (contrasubsetT2) => 78.39/10.72 (( 78.39/10.72 (contrasubsetT3) => 78.39/10.72 (( 78.39/10.72 (doubleComplementI1) => 78.39/10.72 (( 78.39/10.72 (doubleComplementE1) => 78.39/10.72 (( 78.39/10.72 (doubleComplementSub1) => 78.39/10.72 (( 78.39/10.72 (doubleComplementSub2) => 78.39/10.72 (( 78.39/10.72 (doubleComplementEq) => 78.39/10.72 (( 78.39/10.72 (complementTnotintersectT) => 78.39/10.72 (( 78.39/10.72 (complementImpComplementIntersect) => 78.39/10.72 (( 78.39/10.72 (complementSubsetComplementIntersect) => 78.39/10.72 (( 78.39/10.72 (complementInPowersetComplementIntersect) => 78.39/10.72 (( 78.39/10.72 (contraSubsetComplement) => 78.39/10.72 (( 78.39/10.72 (complementTcontraSubset) => 78.39/10.72 (( 78.39/10.72 (binunionTILcontra) => 78.39/10.72 (( 78.39/10.72 (binunionTIRcontra) => 78.39/10.72 (( 78.39/10.72 (inIntersectImpInUnion) => 78.39/10.72 (( 78.39/10.72 (inIntersectImpInUnion2) => 78.39/10.72 (( 78.39/10.72 (inIntersectImpInIntersectUnions) => 78.39/10.72 (( 78.39/10.72 (intersectInPowersetIntersectUnions) => 78.39/10.72 (( 78.39/10.72 (inComplementUnionImpNotIn1) => 78.39/10.72 (( 78.39/10.72 (inComplementUnionImpInComplement1) => 78.39/10.72 (( 78.39/10.72 (binunionTE) => 78.39/10.72 (( 78.39/10.72 (binunionTEcontra) => 78.39/10.72 (( 78.39/10.72 (demorgan2a1) => 78.39/10.72 (( 78.39/10.72 (complementUnionInPowersetComplement) => 78.39/10.72 (( 78.39/10.72 (demorgan2a2) => 78.39/10.72 (( 78.39/10.72 (demorgan1a) => 78.39/10.72 (( 78.39/10.72 (demorgan1b) => 78.39/10.72 (( 78.39/10.72 (demorgan1) => 78.39/10.72 (( 78.39/10.72 (demorgan2a) => 78.39/10.72 (( 78.39/10.72 (demorgan2b2) => 78.39/10.72 (( 78.39/10.72 (demorgan2b) => 78.39/10.72 (( 78.39/10.72 (demorgan2) => 78.39/10.72 (( 78.39/10.72 (woz13rule0) => 78.39/10.72 (( 78.39/10.72 (woz13rule1) => 78.39/10.72 (( 78.39/10.72 (woz13rule2) => 78.39/10.72 (( 78.39/10.72 (woz13rule3) => 78.39/10.72 (( 78.39/10.72 (woz13rule4) => 78.39/10.72 (( 78.39/10.72 (woz1_1) => 78.39/10.72 (( 78.39/10.72 (woz1_2) => 78.39/10.72 (( 78.39/10.72 (woz1_3) => 78.39/10.72 (( 78.39/10.72 (woz1_4) => 78.39/10.72 (( 78.39/10.72 (woz1_5) => 78.39/10.72 (( 78.39/10.72 (breln1all2) => 78.39/10.72 (( 78.39/10.72 (breln1SetBreln1) => 78.39/10.72 (( 78.39/10.72 (choice2fnsingleton) => 78.39/10.72 (( 78.39/10.72 (setOfPairsIsBReln1) => 78.39/10.72 (( 78.39/10.72 (breln1all1) => 78.39/10.72 (( 78.39/10.72 (subbreln1) => 78.39/10.72 (( 78.39/10.72 (eqbreln1) => 78.39/10.72 (( 78.39/10.72 (breln1invprop) => 78.39/10.72 (( 78.39/10.72 (breln1invI) => 78.39/10.72 (( 78.39/10.72 (breln1invE) => 78.39/10.72 (( 78.39/10.72 (breln1compprop) => 78.39/10.72 (( 78.39/10.72 (breln1compI) => 78.39/10.72 (( 78.39/10.72 (breln1compE) => 78.39/10.72 (( 78.39/10.72 (breln1compEex) => 78.39/10.72 (( 78.39/10.72 (breln1unionprop) => 78.39/10.72 (( 78.39/10.72 (breln1unionIL) => 78.39/10.72 (( 78.39/10.72 (breln1unionIR) => 78.39/10.72 (( 78.39/10.72 (breln1unionI) => 78.39/10.72 (( 78.39/10.72 (breln1unionE) => 78.39/10.72 (( 78.39/10.72 (breln1unionEcases) => 78.39/10.72 (( 78.39/10.72 (breln1unionCommutes) => 78.39/10.72 (( 78.39/10.72 (woz2Ex) => 78.39/10.72 (( 78.39/10.72 (woz2W) => 78.39/10.72 (( 78.39/10.72 (woz2A) => 78.39/10.72 (( 78.39/10.72 (woz2B) => 78.39/10.72 (( 78.39/10.72 (image1Ex) => 78.39/10.72 (( 78.39/10.72 (image1Ex1) => 78.39/10.72 (( 78.39/10.72 (image1Equiv) => 78.39/10.72 (( 78.39/10.72 (image1E) => 78.39/10.72 (( 78.39/10.72 (image1I) => 78.39/10.72 (( 78.39/10.72 (injFuncInInjFuncSet) => 78.39/10.72 (( 78.39/10.72 (injFuncSetFuncIn) => 78.39/10.72 (( 78.39/10.72 (injFuncSetFuncInj) => 78.39/10.72 (( 78.39/10.72 (surjFuncSetFuncIn) => 78.39/10.72 (( 78.39/10.72 (surjFuncSetFuncSurj) => 78.39/10.72 (( 78.39/10.72 (leftInvIsSurj) => 78.39/10.72 (( 78.39/10.72 (surjCantorThm) => 78.39/10.72 (( 78.39/10.72 (foundation2) => 78.39/10.72 (( 78.39/10.72 (notinself) => 78.39/10.72 (( 78.39/10.72 (notinself2) => 78.39/10.72 (( 78.39/10.72 (omegaSp) => 78.39/10.72 (( 78.39/10.72 (omegaSclos) => 78.39/10.72 (( 78.39/10.72 (peano0notS) => 78.39/10.72 (( 78.39/10.72 (peanoSinj) => 78.39/10.72 (( 78.39/10.72 (transitivesetOp1) => 78.39/10.72 (( 78.39/10.72 (binintTransitive) => 78.39/10.72 (( 78.39/10.72 (transitivesetOp2) => 78.39/10.72 (( 78.39/10.72 (setunionTransitive) => 78.39/10.72 (( 78.39/10.72 (ordinalMinLem1) => 78.39/10.72 (( 78.39/10.72 (!!) @ ( 78.39/10.72 ^[Y0 : $i]: 78.39/10.72 (( 78.39/10.72 (ordinal @ 78.39/10.72 Y0) => 78.39/10.72 (( 78.39/10.72 (!!) @ ( 78.39/10.72 ^[Y1 : $i]: 78.39/10.72 (( 78.39/10.72 (!!) @ ( 78.39/10.72 ^[Y2 : $i]: 78.39/10.72 (( 78.39/10.72 (in @ 78.39/10.72 Y2 @ 78.39/10.72 Y0) => 78.39/10.72 (( 78.39/10.72 (in @ 78.39/10.72 Y1 @ 78.39/10.72 Y2) => 78.39/10.72 (in @ 78.39/10.72 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 78.39/10.72 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1678])). 78.39/10.72 thf(zip_derived_cl1697, plain, 78.39/10.72 (~ (((lamp) => 78.39/10.72 (((lam2p) => 78.39/10.72 (((brelnall1) => 78.39/10.72 (((brelnall2) => 78.39/10.72 (((ex1E2) => 78.39/10.72 (((funcGraphProp1) => 78.39/10.72 (((funcGraphProp3) => 78.39/10.72 (((funcGraphProp2) => 78.39/10.72 (((funcextLem) => 78.39/10.72 (((funcGraphProp4) => 78.39/10.72 (((subbreln) => 78.39/10.72 (((eqbreln) => 78.39/10.72 (((funcext) => 78.39/10.72 (((funcext2) => 78.39/10.72 (((ap2apEq1) => 78.39/10.72 (((ap2apEq2) => 78.39/10.72 (((beta1) => 78.39/10.72 (((eta1) => 78.39/10.72 (((lam2lamEq) => 78.39/10.72 (((beta2) => 78.39/10.72 (((eta2) => 78.39/10.72 (((iffalseProp1) => 78.39/10.72 (((iffalseProp2) => 78.39/10.72 (((iftrueProp1) => 78.39/10.72 (((iftrueProp2) => 78.39/10.72 (((ifSingleton) => 78.39/10.72 (((ifp) => 78.39/10.72 (((theeq) => 78.39/10.72 (((iftrue) => 78.39/10.72 (((iffalse) => 78.39/10.72 (( 78.39/10.72 (iftrueorfalse) => 78.39/10.72 (( 78.39/10.72 (binintersectT_lem) => 78.39/10.72 (( 78.39/10.72 (binunionT_lem) => 78.39/10.72 (( 78.39/10.72 (powersetT_lem) => 78.39/10.72 (( 78.39/10.72 (setminusT_lem) => 78.39/10.72 (( 78.39/10.72 (complementT_lem) => 78.39/10.72 (( 78.39/10.72 (setextT) => 78.39/10.72 (( 78.39/10.72 (subsetTI) => 78.39/10.72 (( 78.39/10.72 (powersetTI1) => 78.39/10.72 (( 78.39/10.72 (powersetTE1) => 78.39/10.72 (( 78.39/10.72 (complementTI1) => 78.39/10.72 (( 78.39/10.72 (complementTE1) => 78.39/10.72 (( 78.39/10.72 (binintersectTELcontra) => 78.39/10.72 (( 78.39/10.72 (binintersectTERcontra) => 78.39/10.72 (( 78.39/10.72 (contrasubsetT) => 78.39/10.72 (( 78.39/10.72 (contrasubsetT1) => 78.39/10.72 (( 78.39/10.72 (contrasubsetT2) => 78.39/10.72 (( 78.39/10.72 (contrasubsetT3) => 78.39/10.72 (( 78.39/10.72 (doubleComplementI1) => 78.39/10.72 (( 78.39/10.72 (doubleComplementE1) => 78.39/10.72 (( 78.39/10.72 (doubleComplementSub1) => 78.39/10.72 (( 78.39/10.72 (doubleComplementSub2) => 78.39/10.72 (( 78.39/10.72 (doubleComplementEq) => 78.39/10.72 (( 78.39/10.72 (complementTnotintersectT) => 78.39/10.72 (( 78.39/10.72 (complementImpComplementIntersect) => 78.39/10.72 (( 78.39/10.72 (complementSubsetComplementIntersect) => 78.39/10.72 (( 78.39/10.72 (complementInPowersetComplementIntersect) => 78.39/10.72 (( 78.39/10.72 (contraSubsetComplement) => 78.39/10.72 (( 78.39/10.72 (complementTcontraSubset) => 78.39/10.72 (( 78.39/10.72 (binunionTILcontra) => 78.39/10.72 (( 78.39/10.72 (binunionTIRcontra) => 78.39/10.72 (( 78.39/10.72 (inIntersectImpInUnion) => 78.39/10.72 (( 78.39/10.72 (inIntersectImpInUnion2) => 78.39/10.72 (( 78.39/10.72 (inIntersectImpInIntersectUnions) => 78.39/10.72 (( 78.39/10.72 (intersectInPowersetIntersectUnions) => 78.39/10.72 (( 78.39/10.72 (inComplementUnionImpNotIn1) => 78.39/10.72 (( 78.39/10.72 (inComplementUnionImpInComplement1) => 78.39/10.72 (( 78.39/10.72 (binunionTE) => 78.39/10.72 (( 78.39/10.72 (binunionTEcontra) => 78.39/10.72 (( 78.39/10.72 (demorgan2a1) => 78.39/10.72 (( 78.39/10.72 (complementUnionInPowersetComplement) => 78.39/10.72 (( 78.39/10.72 (demorgan2a2) => 78.39/10.72 (( 78.39/10.72 (demorgan1a) => 78.39/10.72 (( 78.39/10.72 (demorgan1b) => 78.39/10.72 (( 78.39/10.72 (demorgan1) => 78.39/10.72 (( 78.39/10.72 (demorgan2a) => 78.39/10.72 (( 78.39/10.72 (demorgan2b2) => 78.39/10.72 (( 78.39/10.72 (demorgan2b) => 78.39/10.72 (( 78.39/10.72 (demorgan2) => 78.39/10.72 (( 78.39/10.72 (woz13rule0) => 78.39/10.72 (( 78.39/10.72 (woz13rule1) => 78.39/10.72 (( 78.39/10.72 (woz13rule2) => 78.39/10.72 (( 78.39/10.72 (woz13rule3) => 78.39/10.72 (( 78.39/10.72 (woz13rule4) => 78.39/10.72 (( 78.39/10.72 (woz1_1) => 78.39/10.72 (( 78.39/10.72 (woz1_2) => 78.39/10.72 (( 78.39/10.72 (woz1_3) => 78.39/10.72 (( 78.39/10.72 (woz1_4) => 78.39/10.72 (( 78.39/10.72 (woz1_5) => 78.39/10.72 (( 78.39/10.72 (breln1all2) => 78.39/10.72 (( 78.39/10.72 (breln1SetBreln1) => 78.39/10.72 (( 78.39/10.72 (choice2fnsingleton) => 78.39/10.72 (( 78.39/10.72 (setOfPairsIsBReln1) => 78.39/10.72 (( 78.39/10.72 (breln1all1) => 78.39/10.72 (( 78.39/10.72 (subbreln1) => 78.39/10.72 (( 78.39/10.72 (eqbreln1) => 78.39/10.72 (( 78.39/10.72 (breln1invprop) => 78.39/10.72 (( 78.39/10.72 (breln1invI) => 78.39/10.72 (( 78.39/10.72 (breln1invE) => 78.39/10.72 (( 78.39/10.72 (breln1compprop) => 78.39/10.72 (( 78.39/10.72 (breln1compI) => 78.39/10.72 (( 78.39/10.72 (breln1compE) => 78.39/10.72 (( 78.39/10.72 (breln1compEex) => 78.39/10.72 (( 78.39/10.72 (breln1unionprop) => 78.39/10.72 (( 78.39/10.72 (breln1unionIL) => 78.39/10.72 (( 78.39/10.72 (breln1unionIR) => 78.39/10.72 (( 78.39/10.72 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78.39/10.72 (( 78.39/10.72 (omegaSp) => 78.39/10.72 (( 78.39/10.72 (omegaSclos) => 78.39/10.72 (( 78.39/10.72 (peano0notS) => 78.39/10.72 (( 78.39/10.72 (peanoSinj) => 78.39/10.72 (( 78.39/10.72 (transitivesetOp1) => 78.39/10.72 (( 78.39/10.72 (binintTransitive) => 78.39/10.72 (( 78.39/10.72 (transitivesetOp2) => 78.39/10.72 (( 78.39/10.72 (setunionTransitive) => 78.39/10.72 (( 78.39/10.72 (ordinalMinLem1) => 78.39/10.72 (( 78.39/10.72 (!!) @ ( 78.39/10.72 ^[Y0 : $i]: 78.39/10.72 (( 78.39/10.72 (ordinal @ 78.39/10.72 Y0) => 78.39/10.72 (( 78.39/10.72 (!!) @ ( 78.39/10.72 ^[Y1 : $i]: 78.39/10.72 (( 78.39/10.72 (!!) @ ( 78.39/10.72 ^[Y2 : $i]: 78.39/10.72 (( 78.39/10.72 (in @ 78.39/10.72 Y2 @ 78.39/10.72 Y0) => 78.39/10.72 (( 78.39/10.72 (in @ 78.39/10.72 Y1 @ 78.39/10.72 Y2) => 78.39/10.72 (in @ 78.39/10.72 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 78.39/10.72 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1688])). 78.39/10.72 thf(zip_derived_cl1706, plain, 78.39/10.72 (~ (((lam2p) => 78.39/10.72 (((brelnall1) => 78.39/10.72 (((brelnall2) => 78.39/10.72 (((ex1E2) => 78.39/10.72 (((funcGraphProp1) => 78.39/10.72 (((funcGraphProp3) => 78.39/10.72 (((funcGraphProp2) => 78.39/10.72 (((funcextLem) => 78.39/10.72 (((funcGraphProp4) => 78.39/10.72 (((subbreln) => 78.39/10.72 (((eqbreln) => 78.39/10.72 (((funcext) => 78.39/10.72 (((funcext2) => 78.39/10.72 (((ap2apEq1) => 78.39/10.72 (((ap2apEq2) => 78.39/10.72 (((beta1) => 78.39/10.72 (((eta1) => 78.39/10.72 (((lam2lamEq) => 78.39/10.72 (((beta2) => 78.39/10.72 (((eta2) => 78.39/10.72 (((iffalseProp1) => 78.39/10.72 (((iffalseProp2) => 78.39/10.72 (((iftrueProp1) => 78.39/10.72 (((iftrueProp2) => 78.39/10.72 (((ifSingleton) => 78.39/10.72 (((ifp) => 78.39/10.72 (((theeq) => 78.39/10.72 (((iftrue) => 78.39/10.72 (((iffalse) => 78.39/10.72 (((iftrueorfalse) => 78.39/10.72 (( 78.39/10.72 (binintersectT_lem) => 78.39/10.72 (( 78.39/10.72 (binunionT_lem) => 78.39/10.72 (( 78.39/10.72 (powersetT_lem) => 78.39/10.72 (( 78.39/10.72 (setminusT_lem) => 78.39/10.72 (( 78.39/10.72 (complementT_lem) => 78.39/10.72 (( 78.39/10.72 (setextT) => 78.39/10.72 (( 78.39/10.72 (subsetTI) => 78.39/10.72 (( 78.39/10.72 (powersetTI1) => 78.39/10.72 (( 78.39/10.72 (powersetTE1) => 78.39/10.72 (( 78.39/10.72 (complementTI1) => 78.39/10.72 (( 78.39/10.72 (complementTE1) => 78.39/10.72 (( 78.39/10.72 (binintersectTELcontra) => 78.39/10.72 (( 78.39/10.72 (binintersectTERcontra) => 78.39/10.72 (( 78.39/10.72 (contrasubsetT) => 78.39/10.72 (( 78.39/10.72 (contrasubsetT1) => 78.39/10.72 (( 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78.39/10.72 (intersectInPowersetIntersectUnions) => 78.39/10.72 (( 78.39/10.72 (inComplementUnionImpNotIn1) => 78.39/10.72 (( 78.39/10.72 (inComplementUnionImpInComplement1) => 78.39/10.72 (( 78.39/10.72 (binunionTE) => 78.39/10.72 (( 78.39/10.72 (binunionTEcontra) => 78.39/10.72 (( 78.39/10.72 (demorgan2a1) => 78.39/10.72 (( 78.39/10.72 (complementUnionInPowersetComplement) => 78.39/10.72 (( 78.39/10.72 (demorgan2a2) => 78.39/10.72 (( 78.39/10.72 (demorgan1a) => 78.39/10.72 (( 78.39/10.72 (demorgan1b) => 78.39/10.72 (( 78.39/10.72 (demorgan1) => 78.39/10.72 (( 78.39/10.72 (demorgan2a) => 78.39/10.72 (( 78.39/10.72 (demorgan2b2) => 78.39/10.72 (( 78.39/10.72 (demorgan2b) => 78.39/10.72 (( 78.39/10.72 (demorgan2) => 78.39/10.72 (( 78.39/10.72 (woz13rule0) => 78.39/10.72 (( 78.39/10.72 (woz13rule1) => 78.39/10.72 (( 78.39/10.72 (woz13rule2) => 78.39/10.72 (( 78.39/10.72 (woz13rule3) => 78.39/10.72 (( 78.39/10.72 (woz13rule4) => 78.39/10.72 (( 78.39/10.72 (woz1_1) => 78.39/10.72 (( 78.39/10.72 (woz1_2) => 78.39/10.72 (( 78.39/10.72 (woz1_3) => 78.39/10.72 (( 78.39/10.72 (woz1_4) => 78.39/10.72 (( 78.39/10.72 (woz1_5) => 78.39/10.72 (( 78.39/10.72 (breln1all2) => 78.39/10.72 (( 78.39/10.72 (breln1SetBreln1) => 78.39/10.72 (( 78.39/10.72 (choice2fnsingleton) => 78.39/10.72 (( 78.39/10.72 (setOfPairsIsBReln1) => 78.39/10.72 (( 78.39/10.72 (breln1all1) => 78.39/10.72 (( 78.39/10.72 (subbreln1) => 78.39/10.72 (( 78.39/10.72 (eqbreln1) => 78.39/10.72 (( 78.39/10.72 (breln1invprop) => 78.39/10.72 (( 78.39/10.72 (breln1invI) => 78.39/10.72 (( 78.39/10.72 (breln1invE) => 78.39/10.72 (( 78.39/10.72 (breln1compprop) => 78.39/10.72 (( 78.39/10.72 (breln1compI) => 78.39/10.72 (( 78.39/10.72 (breln1compE) => 78.39/10.72 (( 78.39/10.72 (breln1compEex) => 78.39/10.72 (( 78.39/10.72 (breln1unionprop) => 78.39/10.72 (( 78.39/10.72 (breln1unionIL) => 78.39/10.72 (( 78.39/10.72 (breln1unionIR) => 78.39/10.72 (( 78.39/10.72 (breln1unionI) => 78.39/10.72 (( 78.39/10.72 (breln1unionE) => 78.39/10.72 (( 78.39/10.72 (breln1unionEcases) => 78.39/10.72 (( 78.39/10.72 (breln1unionCommutes) => 78.39/10.72 (( 78.39/10.72 (woz2Ex) => 78.39/10.72 (( 78.39/10.72 (woz2W) => 78.39/10.72 (( 78.39/10.72 (woz2A) => 78.39/10.72 (( 78.39/10.72 (woz2B) => 78.39/10.72 (( 78.39/10.72 (image1Ex) => 78.39/10.72 (( 78.39/10.72 (image1Ex1) => 78.39/10.72 (( 78.39/10.72 (image1Equiv) => 78.39/10.72 (( 78.39/10.72 (image1E) => 78.39/10.72 (( 78.39/10.72 (image1I) => 78.39/10.72 (( 78.39/10.72 (injFuncInInjFuncSet) => 78.39/10.72 (( 78.39/10.72 (injFuncSetFuncIn) => 78.39/10.72 (( 78.39/10.72 (injFuncSetFuncInj) => 78.39/10.72 (( 78.39/10.72 (surjFuncSetFuncIn) => 78.39/10.72 (( 78.39/10.72 (surjFuncSetFuncSurj) => 78.39/10.72 (( 78.39/10.72 (leftInvIsSurj) => 78.39/10.72 (( 78.39/10.72 (surjCantorThm) => 78.39/10.72 (( 78.39/10.72 (foundation2) => 78.39/10.72 (( 78.39/10.72 (notinself) => 78.39/10.72 (( 78.39/10.72 (notinself2) => 78.39/10.72 (( 78.39/10.72 (omegaSp) => 78.39/10.72 (( 78.39/10.72 (omegaSclos) => 78.39/10.72 (( 78.39/10.72 (peano0notS) => 78.39/10.72 (( 78.39/10.72 (peanoSinj) => 78.39/10.72 (( 78.39/10.72 (transitivesetOp1) => 78.39/10.72 (( 78.39/10.72 (binintTransitive) => 78.39/10.72 (( 78.39/10.72 (transitivesetOp2) => 78.39/10.72 (( 78.39/10.72 (setunionTransitive) => 78.39/10.72 (( 78.39/10.72 (ordinalMinLem1) => 78.39/10.72 (( 78.39/10.72 (!!) @ ( 78.39/10.72 ^[Y0 : $i]: 78.39/10.72 (( 78.39/10.72 (ordinal @ 78.39/10.72 Y0) => 78.39/10.72 (( 78.39/10.72 (!!) @ ( 78.39/10.72 ^[Y1 : $i]: 78.39/10.72 (( 78.39/10.72 (!!) @ ( 78.39/10.72 ^[Y2 : $i]: 78.39/10.72 (( 78.39/10.72 (in @ 78.39/10.72 Y2 @ 78.39/10.72 Y0) => 78.39/10.72 (( 78.39/10.72 (in @ 78.39/10.72 Y1 @ 78.39/10.72 Y2) => 78.39/10.72 (in @ 78.39/10.72 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 78.39/10.72 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1697])). 78.39/10.72 thf(zip_derived_cl1716, plain, 78.39/10.72 (~ (((brelnall1) => 78.39/10.72 (((brelnall2) => 78.39/10.72 (((ex1E2) => 78.39/10.72 (((funcGraphProp1) => 78.39/10.72 (((funcGraphProp3) => 78.39/10.72 (((funcGraphProp2) => 78.39/10.72 (((funcextLem) => 78.39/10.72 (((funcGraphProp4) => 78.39/10.72 (((subbreln) => 78.39/10.72 (((eqbreln) => 78.39/10.72 (((funcext) => 78.39/10.72 (((funcext2) => 78.39/10.72 (((ap2apEq1) => 78.39/10.72 (((ap2apEq2) => 78.39/10.72 (((beta1) => 78.39/10.72 (((eta1) => 78.39/10.72 (((lam2lamEq) => 78.39/10.72 (((beta2) => 78.39/10.72 (((eta2) => 78.39/10.72 (((iffalseProp1) => 78.39/10.72 (((iffalseProp2) => 78.39/10.72 (((iftrueProp1) => 78.39/10.72 (((iftrueProp2) => 78.39/10.72 (((ifSingleton) => 78.39/10.72 (((ifp) => 78.39/10.72 (((theeq) => 78.39/10.72 (((iftrue) => 78.39/10.72 (((iffalse) => 78.39/10.72 (((iftrueorfalse) => 78.39/10.72 (((binintersectT_lem) => 78.39/10.72 (( 78.39/10.72 (binunionT_lem) => 78.39/10.72 (( 78.39/10.72 (powersetT_lem) => 78.39/10.72 (( 78.39/10.72 (setminusT_lem) => 78.39/10.72 (( 78.39/10.72 (complementT_lem) => 78.39/10.72 (( 78.39/10.72 (setextT) => 78.39/10.72 (( 78.39/10.72 (subsetTI) => 78.39/10.72 (( 78.39/10.72 (powersetTI1) => 78.39/10.72 (( 78.39/10.72 (powersetTE1) => 78.39/10.72 (( 78.39/10.72 (complementTI1) => 78.39/10.72 (( 78.39/10.72 (complementTE1) => 78.39/10.72 (( 78.39/10.72 (binintersectTELcontra) => 78.39/10.72 (( 78.39/10.72 (binintersectTERcontra) => 78.39/10.72 (( 78.39/10.72 (contrasubsetT) => 78.39/10.72 (( 78.39/10.72 (contrasubsetT1) => 78.39/10.72 (( 78.39/10.72 (contrasubsetT2) => 78.39/10.72 (( 78.39/10.72 (contrasubsetT3) => 78.39/10.72 (( 78.39/10.72 (doubleComplementI1) => 78.39/10.72 (( 78.39/10.72 (doubleComplementE1) => 78.39/10.72 (( 78.39/10.72 (doubleComplementSub1) => 78.39/10.72 (( 78.39/10.72 (doubleComplementSub2) => 78.39/10.72 (( 78.39/10.72 (doubleComplementEq) => 78.39/10.72 (( 78.39/10.72 (complementTnotintersectT) => 78.39/10.72 (( 78.39/10.72 (complementImpComplementIntersect) => 78.39/10.72 (( 78.39/10.72 (complementSubsetComplementIntersect) => 78.39/10.72 (( 78.39/10.72 (complementInPowersetComplementIntersect) => 78.39/10.72 (( 78.39/10.72 (contraSubsetComplement) => 78.39/10.72 (( 78.39/10.72 (complementTcontraSubset) => 78.39/10.72 (( 78.39/10.72 (binunionTILcontra) => 78.39/10.72 (( 78.39/10.72 (binunionTIRcontra) => 78.39/10.72 (( 78.39/10.72 (inIntersectImpInUnion) => 78.39/10.72 (( 78.39/10.72 (inIntersectImpInUnion2) => 78.39/10.72 (( 78.39/10.72 (inIntersectImpInIntersectUnions) => 78.39/10.72 (( 78.39/10.72 (intersectInPowersetIntersectUnions) => 78.39/10.72 (( 78.39/10.72 (inComplementUnionImpNotIn1) => 78.39/10.72 (( 78.39/10.72 (inComplementUnionImpInComplement1) => 78.39/10.72 (( 78.39/10.72 (binunionTE) => 78.39/10.72 (( 78.39/10.72 (binunionTEcontra) => 78.39/10.72 (( 78.39/10.72 (demorgan2a1) => 78.39/10.72 (( 78.39/10.72 (complementUnionInPowersetComplement) => 78.39/10.72 (( 78.39/10.72 (demorgan2a2) => 78.39/10.72 (( 78.39/10.72 (demorgan1a) => 78.39/10.72 (( 78.39/10.72 (demorgan1b) => 78.39/10.72 (( 78.39/10.72 (demorgan1) => 78.39/10.72 (( 78.39/10.72 (demorgan2a) => 78.39/10.72 (( 78.39/10.72 (demorgan2b2) => 78.39/10.72 (( 78.39/10.72 (demorgan2b) => 78.39/10.72 (( 78.39/10.72 (demorgan2) => 78.39/10.72 (( 78.39/10.72 (woz13rule0) => 78.39/10.72 (( 78.39/10.72 (woz13rule1) => 78.39/10.72 (( 78.39/10.72 (woz13rule2) => 78.39/10.72 (( 78.39/10.72 (woz13rule3) => 78.39/10.72 (( 78.39/10.72 (woz13rule4) => 78.39/10.72 (( 78.39/10.72 (woz1_1) => 78.39/10.72 (( 78.39/10.72 (woz1_2) => 78.39/10.72 (( 78.39/10.72 (woz1_3) => 78.39/10.72 (( 78.39/10.72 (woz1_4) => 78.39/10.72 (( 78.39/10.72 (woz1_5) => 78.39/10.72 (( 78.39/10.72 (breln1all2) => 78.39/10.72 (( 78.39/10.72 (breln1SetBreln1) => 78.39/10.72 (( 78.39/10.72 (choice2fnsingleton) => 78.39/10.72 (( 78.39/10.72 (setOfPairsIsBReln1) => 78.39/10.72 (( 78.39/10.72 (breln1all1) => 78.39/10.72 (( 78.39/10.72 (subbreln1) => 78.39/10.72 (( 78.39/10.72 (eqbreln1) => 78.39/10.72 (( 78.39/10.72 (breln1invprop) => 78.39/10.72 (( 78.39/10.72 (breln1invI) => 78.39/10.72 (( 78.39/10.72 (breln1invE) => 78.39/10.72 (( 78.39/10.72 (breln1compprop) => 78.39/10.72 (( 78.39/10.72 (breln1compI) => 78.39/10.72 (( 78.39/10.72 (breln1compE) => 78.39/10.72 (( 78.39/10.72 (breln1compEex) => 78.39/10.72 (( 78.39/10.72 (breln1unionprop) => 78.39/10.72 (( 78.39/10.72 (breln1unionIL) => 78.39/10.72 (( 78.39/10.72 (breln1unionIR) => 78.39/10.72 (( 78.39/10.72 (breln1unionI) => 78.39/10.72 (( 78.39/10.72 (breln1unionE) => 78.39/10.72 (( 78.39/10.72 (breln1unionEcases) => 78.39/10.72 (( 78.39/10.72 (breln1unionCommutes) => 78.39/10.72 (( 78.39/10.72 (woz2Ex) => 78.39/10.72 (( 78.39/10.72 (woz2W) => 78.39/10.72 (( 78.39/10.72 (woz2A) => 78.39/10.72 (( 78.39/10.72 (woz2B) => 78.39/10.72 (( 78.39/10.72 (image1Ex) => 78.39/10.72 (( 78.39/10.72 (image1Ex1) => 78.39/10.72 (( 78.39/10.72 (image1Equiv) => 78.39/10.72 (( 78.39/10.72 (image1E) => 78.39/10.72 (( 78.39/10.72 (image1I) => 78.39/10.72 (( 78.39/10.72 (injFuncInInjFuncSet) => 78.39/10.72 (( 78.39/10.72 (injFuncSetFuncIn) => 78.39/10.72 (( 78.39/10.72 (injFuncSetFuncInj) => 78.39/10.72 (( 78.39/10.72 (surjFuncSetFuncIn) => 78.39/10.72 (( 78.39/10.72 (surjFuncSetFuncSurj) => 78.39/10.72 (( 78.39/10.72 (leftInvIsSurj) => 78.39/10.72 (( 78.39/10.72 (surjCantorThm) => 78.39/10.72 (( 78.39/10.72 (foundation2) => 78.39/10.72 (( 78.39/10.72 (notinself) => 78.39/10.72 (( 78.39/10.72 (notinself2) => 78.39/10.72 (( 78.39/10.72 (omegaSp) => 78.39/10.72 (( 78.39/10.72 (omegaSclos) => 78.39/10.72 (( 78.39/10.72 (peano0notS) => 78.39/10.72 (( 78.39/10.72 (peanoSinj) => 78.39/10.72 (( 78.39/10.72 (transitivesetOp1) => 78.39/10.72 (( 78.39/10.72 (binintTransitive) => 78.39/10.72 (( 78.39/10.72 (transitivesetOp2) => 78.39/10.72 (( 78.39/10.72 (setunionTransitive) => 78.39/10.72 (( 78.39/10.72 (ordinalMinLem1) => 78.39/10.72 (( 78.39/10.72 (!!) @ ( 78.39/10.72 ^[Y0 : $i]: 78.39/10.72 (( 78.39/10.72 (ordinal @ 78.39/10.72 Y0) => 78.39/10.72 (( 78.39/10.72 (!!) @ ( 78.39/10.72 ^[Y1 : $i]: 78.39/10.72 (( 78.39/10.72 (!!) @ ( 78.39/10.72 ^[Y2 : $i]: 78.39/10.72 (( 78.39/10.72 (in @ 78.39/10.72 Y2 @ 78.39/10.72 Y0) => 78.39/10.72 (( 78.39/10.72 (in @ 78.39/10.72 Y1 @ 78.39/10.72 Y2) => 78.39/10.72 (in @ 78.39/10.72 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 78.39/10.72 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1706])). 78.39/10.72 thf(zip_derived_cl1725, plain, 78.39/10.72 (~ (((brelnall2) => 78.39/10.72 (((ex1E2) => 78.39/10.72 (((funcGraphProp1) => 78.39/10.72 (((funcGraphProp3) => 78.39/10.72 (((funcGraphProp2) => 78.39/10.72 (((funcextLem) => 78.39/10.72 (((funcGraphProp4) => 78.39/10.72 (((subbreln) => 78.39/10.72 (((eqbreln) => 78.39/10.72 (((funcext) => 78.39/10.72 (((funcext2) => 78.39/10.72 (((ap2apEq1) => 78.39/10.72 (((ap2apEq2) => 78.39/10.72 (((beta1) => 78.39/10.72 (((eta1) => 78.39/10.72 (((lam2lamEq) => 78.39/10.72 (((beta2) => 78.39/10.72 (((eta2) => 78.39/10.72 (((iffalseProp1) => 78.39/10.72 (((iffalseProp2) => 78.39/10.72 (((iftrueProp1) => 78.39/10.72 (((iftrueProp2) => 78.39/10.72 (((ifSingleton) => 78.39/10.72 (((ifp) => 78.39/10.72 (((theeq) => 78.39/10.72 (((iftrue) => 78.39/10.72 (((iffalse) => 78.39/10.72 (((iftrueorfalse) => 78.39/10.72 (((binintersectT_lem) => 78.39/10.72 (((binunionT_lem) => 78.39/10.72 (( 78.39/10.72 (powersetT_lem) => 78.39/10.72 (( 78.39/10.72 (setminusT_lem) => 78.39/10.72 (( 78.39/10.72 (complementT_lem) => 78.39/10.72 (( 78.39/10.72 (setextT) => 78.39/10.72 (( 78.39/10.72 (subsetTI) => 78.39/10.72 (( 78.39/10.72 (powersetTI1) => 78.39/10.72 (( 78.39/10.72 (powersetTE1) => 78.39/10.72 (( 78.39/10.72 (complementTI1) => 78.39/10.72 (( 78.39/10.72 (complementTE1) => 78.39/10.72 (( 78.39/10.72 (binintersectTELcontra) => 78.39/10.72 (( 78.39/10.72 (binintersectTERcontra) => 78.39/10.72 (( 78.39/10.72 (contrasubsetT) => 78.39/10.72 (( 78.39/10.72 (contrasubsetT1) => 78.39/10.72 (( 78.39/10.72 (contrasubsetT2) => 78.39/10.72 (( 78.39/10.72 (contrasubsetT3) => 78.39/10.72 (( 78.39/10.72 (doubleComplementI1) => 78.39/10.72 (( 78.39/10.72 (doubleComplementE1) => 78.39/10.72 (( 78.39/10.72 (doubleComplementSub1) => 78.39/10.72 (( 78.39/10.72 (doubleComplementSub2) => 78.39/10.72 (( 78.39/10.72 (doubleComplementEq) => 78.39/10.72 (( 78.39/10.72 (complementTnotintersectT) => 78.39/10.72 (( 78.39/10.72 (complementImpComplementIntersect) => 78.39/10.72 (( 78.39/10.72 (complementSubsetComplementIntersect) => 78.39/10.72 (( 78.39/10.72 (complementInPowersetComplementIntersect) => 78.39/10.72 (( 78.39/10.72 (contraSubsetComplement) => 78.39/10.72 (( 78.39/10.72 (complementTcontraSubset) => 78.39/10.72 (( 78.39/10.72 (binunionTILcontra) => 78.39/10.72 (( 78.39/10.72 (binunionTIRcontra) => 78.39/10.72 (( 78.39/10.72 (inIntersectImpInUnion) => 78.39/10.72 (( 78.39/10.72 (inIntersectImpInUnion2) => 78.39/10.72 (( 78.39/10.72 (inIntersectImpInIntersectUnions) => 78.39/10.72 (( 78.39/10.72 (intersectInPowersetIntersectUnions) => 78.39/10.72 (( 78.39/10.72 (inComplementUnionImpNotIn1) => 78.39/10.72 (( 78.39/10.72 (inComplementUnionImpInComplement1) => 78.39/10.72 (( 78.39/10.72 (binunionTE) => 78.39/10.72 (( 78.39/10.72 (binunionTEcontra) => 78.39/10.72 (( 78.39/10.72 (demorgan2a1) => 78.39/10.72 (( 78.39/10.72 (complementUnionInPowersetComplement) => 78.39/10.72 (( 78.39/10.72 (demorgan2a2) => 78.39/10.72 (( 78.39/10.72 (demorgan1a) => 78.39/10.72 (( 78.39/10.72 (demorgan1b) => 78.39/10.72 (( 78.39/10.72 (demorgan1) => 78.39/10.72 (( 78.39/10.72 (demorgan2a) => 78.39/10.72 (( 78.39/10.72 (demorgan2b2) => 78.39/10.72 (( 78.39/10.72 (demorgan2b) => 78.39/10.72 (( 78.39/10.72 (demorgan2) => 78.39/10.72 (( 78.39/10.72 (woz13rule0) => 78.39/10.72 (( 78.39/10.72 (woz13rule1) => 78.39/10.72 (( 78.39/10.72 (woz13rule2) => 78.39/10.72 (( 78.39/10.72 (woz13rule3) => 78.39/10.72 (( 78.39/10.72 (woz13rule4) => 78.39/10.72 (( 78.39/10.72 (woz1_1) => 78.39/10.72 (( 78.39/10.72 (woz1_2) => 78.39/10.72 (( 78.39/10.72 (woz1_3) => 78.39/10.72 (( 78.39/10.72 (woz1_4) => 78.39/10.72 (( 78.39/10.72 (woz1_5) => 78.39/10.72 (( 78.39/10.72 (breln1all2) => 78.39/10.72 (( 78.39/10.72 (breln1SetBreln1) => 78.39/10.72 (( 78.39/10.72 (choice2fnsingleton) => 78.39/10.72 (( 78.39/10.72 (setOfPairsIsBReln1) => 78.39/10.72 (( 78.39/10.72 (breln1all1) => 78.39/10.72 (( 78.39/10.72 (subbreln1) => 78.39/10.72 (( 78.39/10.72 (eqbreln1) => 78.39/10.72 (( 78.39/10.72 (breln1invprop) => 78.39/10.72 (( 78.39/10.72 (breln1invI) => 78.39/10.72 (( 78.39/10.72 (breln1invE) => 78.39/10.72 (( 78.39/10.72 (breln1compprop) => 78.39/10.72 (( 78.39/10.72 (breln1compI) => 78.39/10.72 (( 78.39/10.72 (breln1compE) => 78.39/10.72 (( 78.39/10.72 (breln1compEex) => 78.39/10.72 (( 78.39/10.72 (breln1unionprop) => 78.39/10.72 (( 78.39/10.72 (breln1unionIL) => 78.39/10.72 (( 78.39/10.72 (breln1unionIR) => 78.39/10.72 (( 78.39/10.72 (breln1unionI) => 78.39/10.72 (( 78.39/10.72 (breln1unionE) => 78.39/10.72 (( 78.39/10.72 (breln1unionEcases) => 78.39/10.72 (( 78.39/10.72 (breln1unionCommutes) => 78.39/10.72 (( 78.39/10.72 (woz2Ex) => 78.39/10.72 (( 78.39/10.72 (woz2W) => 78.39/10.72 (( 78.39/10.72 (woz2A) => 78.39/10.72 (( 78.39/10.72 (woz2B) => 78.39/10.72 (( 78.39/10.72 (image1Ex) => 78.39/10.72 (( 78.39/10.72 (image1Ex1) => 78.39/10.72 (( 78.39/10.72 (image1Equiv) => 78.39/10.72 (( 78.39/10.72 (image1E) => 78.39/10.72 (( 78.39/10.72 (image1I) => 78.39/10.72 (( 78.39/10.72 (injFuncInInjFuncSet) => 78.39/10.72 (( 78.39/10.72 (injFuncSetFuncIn) => 78.39/10.72 (( 78.39/10.72 (injFuncSetFuncInj) => 78.39/10.72 (( 78.39/10.72 (surjFuncSetFuncIn) => 78.39/10.72 (( 78.39/10.72 (surjFuncSetFuncSurj) => 78.39/10.72 (( 78.39/10.72 (leftInvIsSurj) => 78.39/10.72 (( 78.39/10.72 (surjCantorThm) => 78.39/10.72 (( 78.39/10.72 (foundation2) => 78.39/10.72 (( 78.39/10.72 (notinself) => 78.39/10.72 (( 78.39/10.72 (notinself2) => 78.39/10.72 (( 78.39/10.72 (omegaSp) => 78.39/10.72 (( 78.39/10.72 (omegaSclos) => 78.39/10.72 (( 78.39/10.72 (peano0notS) => 78.39/10.72 (( 78.39/10.72 (peanoSinj) => 78.39/10.72 (( 78.39/10.72 (transitivesetOp1) => 78.39/10.72 (( 78.39/10.72 (binintTransitive) => 78.39/10.72 (( 78.39/10.72 (transitivesetOp2) => 78.39/10.72 (( 78.39/10.72 (setunionTransitive) => 78.39/10.72 (( 78.39/10.72 (ordinalMinLem1) => 78.39/10.72 (( 78.39/10.72 (!!) @ ( 78.39/10.72 ^[Y0 : $i]: 78.39/10.72 (( 78.39/10.72 (ordinal @ 78.39/10.72 Y0) => 78.39/10.72 (( 78.39/10.72 (!!) @ ( 78.39/10.72 ^[Y1 : $i]: 78.39/10.72 (( 78.39/10.72 (!!) @ ( 78.39/10.72 ^[Y2 : $i]: 78.39/10.72 (( 78.39/10.72 (in @ 78.39/10.72 Y2 @ 78.39/10.72 Y0) => 78.39/10.72 (( 78.39/10.72 (in @ 78.39/10.72 Y1 @ 78.39/10.72 Y2) => 78.39/10.72 (in @ 78.39/10.72 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 78.39/10.72 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1716])). 78.39/10.72 thf(zip_derived_cl1734, plain, 78.39/10.72 (~ (((ex1E2) => 78.39/10.72 (((funcGraphProp1) => 78.39/10.72 (((funcGraphProp3) => 78.39/10.72 (((funcGraphProp2) => 78.39/10.72 (((funcextLem) => 78.39/10.72 (((funcGraphProp4) => 78.39/10.72 (((subbreln) => 78.39/10.72 (((eqbreln) => 78.39/10.72 (((funcext) => 78.39/10.72 (((funcext2) => 78.39/10.72 (((ap2apEq1) => 78.39/10.72 (((ap2apEq2) => 78.39/10.72 (((beta1) => 78.39/10.72 (((eta1) => 78.39/10.72 (((lam2lamEq) => 78.39/10.72 (((beta2) => 78.39/10.72 (((eta2) => 78.39/10.72 (((iffalseProp1) => 78.39/10.72 (((iffalseProp2) => 78.39/10.72 (((iftrueProp1) => 78.39/10.72 (((iftrueProp2) => 78.39/10.72 (((ifSingleton) => 78.39/10.72 (((ifp) => 78.39/10.72 (((theeq) => 78.39/10.72 (((iftrue) => 78.39/10.72 (((iffalse) => 78.39/10.72 (((iftrueorfalse) => 78.39/10.72 (((binintersectT_lem) => 78.39/10.72 (((binunionT_lem) => 78.39/10.72 (((powersetT_lem) => 78.39/10.72 (( 78.39/10.72 (setminusT_lem) => 78.39/10.72 (( 78.39/10.72 (complementT_lem) => 78.39/10.72 (( 78.39/10.72 (setextT) => 78.39/10.72 (( 78.39/10.72 (subsetTI) => 78.39/10.72 (( 78.39/10.72 (powersetTI1) => 78.39/10.72 (( 78.39/10.72 (powersetTE1) => 78.39/10.72 (( 78.39/10.72 (complementTI1) => 78.39/10.72 (( 78.39/10.72 (complementTE1) => 78.39/10.72 (( 78.39/10.72 (binintersectTELcontra) => 78.39/10.72 (( 78.39/10.72 (binintersectTERcontra) => 78.39/10.72 (( 78.39/10.72 (contrasubsetT) => 78.39/10.72 (( 78.39/10.72 (contrasubsetT1) => 78.39/10.72 (( 78.39/10.72 (contrasubsetT2) => 78.39/10.72 (( 78.39/10.72 (contrasubsetT3) => 78.39/10.72 (( 78.39/10.72 (doubleComplementI1) => 78.39/10.72 (( 78.39/10.72 (doubleComplementE1) => 78.39/10.72 (( 78.39/10.72 (doubleComplementSub1) => 78.39/10.72 (( 78.39/10.72 (doubleComplementSub2) => 78.39/10.72 (( 78.39/10.72 (doubleComplementEq) => 78.39/10.72 (( 78.39/10.72 (complementTnotintersectT) => 78.39/10.72 (( 78.39/10.72 (complementImpComplementIntersect) => 78.39/10.72 (( 78.39/10.72 (complementSubsetComplementIntersect) => 78.39/10.72 (( 78.39/10.72 (complementInPowersetComplementIntersect) => 78.39/10.72 (( 78.39/10.72 (contraSubsetComplement) => 78.39/10.72 (( 78.39/10.72 (complementTcontraSubset) => 78.39/10.72 (( 78.39/10.72 (binunionTILcontra) => 78.39/10.72 (( 78.39/10.72 (binunionTIRcontra) => 78.39/10.72 (( 78.39/10.72 (inIntersectImpInUnion) => 78.39/10.72 (( 78.39/10.72 (inIntersectImpInUnion2) => 78.39/10.72 (( 78.39/10.72 (inIntersectImpInIntersectUnions) => 78.39/10.72 (( 78.39/10.72 (intersectInPowersetIntersectUnions) => 78.39/10.72 (( 78.39/10.72 (inComplementUnionImpNotIn1) => 78.39/10.72 (( 78.39/10.72 (inComplementUnionImpInComplement1) => 78.39/10.72 (( 78.39/10.72 (binunionTE) => 78.39/10.72 (( 78.39/10.72 (binunionTEcontra) => 78.39/10.72 (( 78.39/10.72 (demorgan2a1) => 78.39/10.72 (( 78.39/10.72 (complementUnionInPowersetComplement) => 78.39/10.72 (( 78.39/10.72 (demorgan2a2) => 78.39/10.72 (( 78.39/10.72 (demorgan1a) => 78.39/10.72 (( 78.39/10.72 (demorgan1b) => 78.39/10.72 (( 78.39/10.72 (demorgan1) => 78.39/10.72 (( 78.39/10.72 (demorgan2a) => 78.39/10.72 (( 78.39/10.72 (demorgan2b2) => 78.39/10.72 (( 78.39/10.72 (demorgan2b) => 78.39/10.72 (( 78.39/10.72 (demorgan2) => 78.39/10.72 (( 78.39/10.72 (woz13rule0) => 78.39/10.72 (( 78.39/10.72 (woz13rule1) => 78.39/10.72 (( 78.39/10.72 (woz13rule2) => 78.39/10.72 (( 78.39/10.72 (woz13rule3) => 78.39/10.72 (( 78.39/10.72 (woz13rule4) => 78.39/10.72 (( 78.39/10.72 (woz1_1) => 78.39/10.72 (( 78.39/10.72 (woz1_2) => 78.39/10.72 (( 78.39/10.72 (woz1_3) => 78.39/10.72 (( 78.39/10.72 (woz1_4) => 78.39/10.72 (( 78.39/10.72 (woz1_5) => 78.39/10.72 (( 78.39/10.72 (breln1all2) => 78.39/10.72 (( 78.39/10.72 (breln1SetBreln1) => 78.39/10.72 (( 78.39/10.72 (choice2fnsingleton) => 78.39/10.72 (( 78.39/10.72 (setOfPairsIsBReln1) => 78.39/10.72 (( 78.39/10.72 (breln1all1) => 78.39/10.72 (( 78.39/10.72 (subbreln1) => 78.39/10.72 (( 78.39/10.72 (eqbreln1) => 78.39/10.72 (( 78.39/10.72 (breln1invprop) => 78.39/10.72 (( 78.39/10.72 (breln1invI) => 78.39/10.72 (( 78.39/10.72 (breln1invE) => 78.39/10.72 (( 78.39/10.72 (breln1compprop) => 78.39/10.72 (( 78.39/10.72 (breln1compI) => 78.39/10.72 (( 78.39/10.72 (breln1compE) => 78.39/10.72 (( 78.39/10.72 (breln1compEex) => 78.39/10.72 (( 78.39/10.72 (breln1unionprop) => 78.39/10.72 (( 78.39/10.72 (breln1unionIL) => 78.39/10.72 (( 78.39/10.72 (breln1unionIR) => 78.39/10.72 (( 78.39/10.72 (breln1unionI) => 78.39/10.72 (( 78.39/10.72 (breln1unionE) => 78.39/10.72 (( 78.39/10.72 (breln1unionEcases) => 78.39/10.72 (( 78.39/10.72 (breln1unionCommutes) => 78.39/10.72 (( 78.39/10.72 (woz2Ex) => 78.39/10.72 (( 78.39/10.72 (woz2W) => 78.39/10.72 (( 78.39/10.72 (woz2A) => 78.39/10.72 (( 78.39/10.72 (woz2B) => 78.39/10.72 (( 78.39/10.72 (image1Ex) => 78.39/10.72 (( 78.39/10.72 (image1Ex1) => 78.39/10.72 (( 78.39/10.72 (image1Equiv) => 78.39/10.72 (( 78.39/10.72 (image1E) => 78.39/10.72 (( 78.39/10.72 (image1I) => 78.39/10.72 (( 78.39/10.72 (injFuncInInjFuncSet) => 78.39/10.72 (( 78.39/10.72 (injFuncSetFuncIn) => 78.39/10.72 (( 78.39/10.72 (injFuncSetFuncInj) => 78.39/10.72 (( 78.39/10.72 (surjFuncSetFuncIn) => 78.39/10.72 (( 78.39/10.72 (surjFuncSetFuncSurj) => 78.39/10.72 (( 78.39/10.72 (leftInvIsSurj) => 78.39/10.72 (( 78.39/10.72 (surjCantorThm) => 78.39/10.72 (( 78.39/10.72 (foundation2) => 78.39/10.72 (( 78.39/10.72 (notinself) => 78.39/10.72 (( 78.39/10.72 (notinself2) => 78.39/10.72 (( 78.39/10.72 (omegaSp) => 78.39/10.72 (( 78.39/10.72 (omegaSclos) => 78.39/10.72 (( 78.39/10.72 (peano0notS) => 78.39/10.72 (( 78.39/10.72 (peanoSinj) => 78.39/10.72 (( 78.39/10.72 (transitivesetOp1) => 78.39/10.72 (( 78.39/10.72 (binintTransitive) => 78.39/10.72 (( 78.39/10.72 (transitivesetOp2) => 78.39/10.72 (( 78.80/10.72 (setunionTransitive) => 78.80/10.72 (( 78.80/10.72 (ordinalMinLem1) => 78.80/10.72 (( 78.80/10.72 (!!) @ ( 78.80/10.72 ^[Y0 : $i]: 78.80/10.72 (( 78.80/10.72 (ordinal @ 78.80/10.72 Y0) => 78.80/10.72 (( 78.80/10.72 (!!) @ ( 78.80/10.72 ^[Y1 : $i]: 78.80/10.72 (( 78.80/10.72 (!!) @ ( 78.80/10.72 ^[Y2 : $i]: 78.80/10.72 (( 78.80/10.72 (in @ 78.80/10.72 Y2 @ 78.80/10.72 Y0) => 78.80/10.72 (( 78.80/10.72 (in @ 78.80/10.72 Y1 @ 78.80/10.72 Y2) => 78.80/10.72 (in @ 78.80/10.72 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 78.80/10.72 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1725])). 78.80/10.72 thf(zip_derived_cl1742, plain, 78.80/10.72 (~ (((funcGraphProp1) => 78.80/10.72 (((funcGraphProp3) => 78.80/10.72 (((funcGraphProp2) => 78.80/10.72 (((funcextLem) => 78.80/10.72 (((funcGraphProp4) => 78.80/10.72 (((subbreln) => 78.80/10.72 (((eqbreln) => 78.80/10.72 (((funcext) => 78.80/10.72 (((funcext2) => 78.80/10.72 (((ap2apEq1) => 78.80/10.72 (((ap2apEq2) => 78.80/10.72 (((beta1) => 78.80/10.72 (((eta1) => 78.80/10.72 (((lam2lamEq) => 78.80/10.72 (((beta2) => 78.80/10.72 (((eta2) => 78.80/10.72 (((iffalseProp1) => 78.80/10.72 (((iffalseProp2) => 78.80/10.72 (((iftrueProp1) => 78.80/10.72 (((iftrueProp2) => 78.80/10.72 (((ifSingleton) => 78.80/10.72 (((ifp) => 78.80/10.72 (((theeq) => 78.80/10.72 (((iftrue) => 78.80/10.72 (((iffalse) => 78.80/10.72 (((iftrueorfalse) => 78.80/10.72 (((binintersectT_lem) => 78.80/10.72 (((binunionT_lem) => 78.80/10.72 (((powersetT_lem) => 78.80/10.72 (((setminusT_lem) => 78.80/10.72 (( 78.80/10.72 (complementT_lem) => 78.80/10.72 (( 78.80/10.72 (setextT) => 78.80/10.72 (( 78.80/10.72 (subsetTI) => 78.80/10.72 (( 78.80/10.72 (powersetTI1) => 78.80/10.72 (( 78.80/10.72 (powersetTE1) => 78.80/10.72 (( 78.80/10.72 (complementTI1) => 78.80/10.72 (( 78.80/10.72 (complementTE1) => 78.80/10.72 (( 78.80/10.72 (binintersectTELcontra) => 78.80/10.72 (( 78.80/10.72 (binintersectTERcontra) => 78.80/10.72 (( 78.80/10.72 (contrasubsetT) => 78.80/10.72 (( 78.80/10.72 (contrasubsetT1) => 78.80/10.72 (( 78.80/10.72 (contrasubsetT2) => 78.80/10.72 (( 78.80/10.72 (contrasubsetT3) => 78.80/10.72 (( 78.80/10.72 (doubleComplementI1) => 78.80/10.72 (( 78.80/10.72 (doubleComplementE1) => 78.80/10.72 (( 78.80/10.72 (doubleComplementSub1) => 78.80/10.72 (( 78.80/10.72 (doubleComplementSub2) => 78.80/10.72 (( 78.80/10.72 (doubleComplementEq) => 78.80/10.72 (( 78.80/10.72 (complementTnotintersectT) => 78.80/10.72 (( 78.80/10.72 (complementImpComplementIntersect) => 78.80/10.72 (( 78.80/10.72 (complementSubsetComplementIntersect) => 78.80/10.72 (( 78.80/10.72 (complementInPowersetComplementIntersect) => 78.80/10.72 (( 78.80/10.72 (contraSubsetComplement) => 78.80/10.72 (( 78.80/10.72 (complementTcontraSubset) => 78.80/10.72 (( 78.80/10.72 (binunionTILcontra) => 78.80/10.72 (( 78.80/10.72 (binunionTIRcontra) => 78.80/10.72 (( 78.80/10.72 (inIntersectImpInUnion) => 78.80/10.72 (( 78.80/10.72 (inIntersectImpInUnion2) => 78.80/10.72 (( 78.80/10.72 (inIntersectImpInIntersectUnions) => 78.80/10.72 (( 78.80/10.72 (intersectInPowersetIntersectUnions) => 78.80/10.72 (( 78.80/10.72 (inComplementUnionImpNotIn1) => 78.80/10.72 (( 78.80/10.72 (inComplementUnionImpInComplement1) => 78.80/10.72 (( 78.80/10.72 (binunionTE) => 78.80/10.72 (( 78.80/10.72 (binunionTEcontra) => 78.80/10.72 (( 78.80/10.72 (demorgan2a1) => 78.80/10.72 (( 78.80/10.72 (complementUnionInPowersetComplement) => 78.80/10.72 (( 78.80/10.72 (demorgan2a2) => 78.80/10.72 (( 78.80/10.72 (demorgan1a) => 78.80/10.72 (( 78.80/10.72 (demorgan1b) => 78.80/10.72 (( 78.80/10.72 (demorgan1) => 78.80/10.72 (( 78.80/10.72 (demorgan2a) => 78.80/10.72 (( 78.80/10.72 (demorgan2b2) => 78.80/10.72 (( 78.80/10.72 (demorgan2b) => 78.80/10.72 (( 78.80/10.72 (demorgan2) => 78.80/10.72 (( 78.80/10.72 (woz13rule0) => 78.80/10.72 (( 78.80/10.72 (woz13rule1) => 78.80/10.72 (( 78.80/10.72 (woz13rule2) => 78.80/10.72 (( 78.80/10.72 (woz13rule3) => 78.80/10.72 (( 78.80/10.72 (woz13rule4) => 78.80/10.72 (( 78.80/10.72 (woz1_1) => 78.80/10.72 (( 78.80/10.72 (woz1_2) => 78.80/10.72 (( 78.80/10.72 (woz1_3) => 78.80/10.72 (( 78.80/10.72 (woz1_4) => 78.80/10.72 (( 78.80/10.72 (woz1_5) => 78.80/10.72 (( 78.80/10.72 (breln1all2) => 78.80/10.72 (( 78.80/10.72 (breln1SetBreln1) => 78.80/10.72 (( 78.80/10.72 (choice2fnsingleton) => 78.80/10.72 (( 78.80/10.72 (setOfPairsIsBReln1) => 78.80/10.72 (( 78.80/10.72 (breln1all1) => 78.80/10.72 (( 78.80/10.72 (subbreln1) => 78.80/10.72 (( 78.80/10.72 (eqbreln1) => 78.80/10.72 (( 78.80/10.72 (breln1invprop) => 78.80/10.72 (( 78.80/10.72 (breln1invI) => 78.80/10.72 (( 78.80/10.72 (breln1invE) => 78.80/10.72 (( 78.80/10.72 (breln1compprop) => 78.80/10.72 (( 78.80/10.72 (breln1compI) => 78.80/10.72 (( 78.80/10.72 (breln1compE) => 78.80/10.72 (( 78.80/10.72 (breln1compEex) => 78.80/10.72 (( 78.80/10.72 (breln1unionprop) => 78.80/10.72 (( 78.80/10.72 (breln1unionIL) => 78.80/10.72 (( 78.80/10.72 (breln1unionIR) => 78.80/10.72 (( 78.80/10.72 (breln1unionI) => 78.80/10.72 (( 78.80/10.72 (breln1unionE) => 78.80/10.72 (( 78.80/10.72 (breln1unionEcases) => 78.80/10.72 (( 78.80/10.72 (breln1unionCommutes) => 78.80/10.72 (( 78.80/10.72 (woz2Ex) => 78.80/10.72 (( 78.80/10.72 (woz2W) => 78.80/10.72 (( 78.80/10.72 (woz2A) => 78.80/10.72 (( 78.80/10.72 (woz2B) => 78.80/10.72 (( 78.80/10.72 (image1Ex) => 78.80/10.72 (( 78.80/10.72 (image1Ex1) => 78.80/10.72 (( 78.80/10.72 (image1Equiv) => 78.80/10.72 (( 78.80/10.72 (image1E) => 78.80/10.72 (( 78.80/10.72 (image1I) => 78.80/10.72 (( 78.80/10.72 (injFuncInInjFuncSet) => 78.80/10.72 (( 78.80/10.72 (injFuncSetFuncIn) => 78.80/10.72 (( 78.80/10.72 (injFuncSetFuncInj) => 78.80/10.72 (( 78.80/10.72 (surjFuncSetFuncIn) => 78.80/10.72 (( 78.80/10.72 (surjFuncSetFuncSurj) => 78.80/10.72 (( 78.80/10.72 (leftInvIsSurj) => 78.80/10.72 (( 78.80/10.72 (surjCantorThm) => 78.80/10.72 (( 78.80/10.72 (foundation2) => 78.80/10.72 (( 78.80/10.72 (notinself) => 78.80/10.72 (( 78.80/10.72 (notinself2) => 78.80/10.72 (( 78.80/10.72 (omegaSp) => 78.80/10.72 (( 78.80/10.72 (omegaSclos) => 78.80/10.72 (( 78.80/10.72 (peano0notS) => 78.80/10.72 (( 78.80/10.72 (peanoSinj) => 78.80/10.72 (( 78.80/10.72 (transitivesetOp1) => 78.80/10.72 (( 78.80/10.72 (binintTransitive) => 78.80/10.72 (( 78.80/10.72 (transitivesetOp2) => 78.80/10.72 (( 78.80/10.72 (setunionTransitive) => 78.80/10.72 (( 78.80/10.72 (ordinalMinLem1) => 78.80/10.72 (( 78.80/10.72 (!!) @ ( 78.80/10.72 ^[Y0 : $i]: 78.80/10.72 (( 78.80/10.72 (ordinal @ 78.80/10.72 Y0) => 78.80/10.72 (( 78.80/10.72 (!!) @ ( 78.80/10.72 ^[Y1 : $i]: 78.80/10.72 (( 78.80/10.72 (!!) @ ( 78.80/10.72 ^[Y2 : $i]: 78.80/10.72 (( 78.80/10.72 (in @ 78.80/10.72 Y2 @ 78.80/10.72 Y0) => 78.80/10.72 (( 78.80/10.72 (in @ 78.80/10.72 Y1 @ 78.80/10.72 Y2) => 78.80/10.72 (in @ 78.80/10.72 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 78.80/10.72 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1734])). 78.80/10.72 thf(zip_derived_cl1750, plain, 78.80/10.72 (~ (((funcGraphProp3) => 78.80/10.72 (((funcGraphProp2) => 78.80/10.72 (((funcextLem) => 78.80/10.72 (((funcGraphProp4) => 78.80/10.72 (((subbreln) => 78.80/10.72 (((eqbreln) => 78.80/10.72 (((funcext) => 78.80/10.72 (((funcext2) => 78.80/10.72 (((ap2apEq1) => 78.80/10.72 (((ap2apEq2) => 78.80/10.72 (((beta1) => 78.80/10.72 (((eta1) => 78.80/10.72 (((lam2lamEq) => 78.80/10.72 (((beta2) => 78.80/10.72 (((eta2) => 78.80/10.72 (((iffalseProp1) => 78.80/10.72 (((iffalseProp2) => 78.80/10.72 (((iftrueProp1) => 78.80/10.72 (((iftrueProp2) => 78.80/10.72 (((ifSingleton) => 78.80/10.72 (((ifp) => 78.80/10.72 (((theeq) => 78.80/10.72 (((iftrue) => 78.80/10.72 (((iffalse) => 78.80/10.72 (((iftrueorfalse) => 78.80/10.72 (((binintersectT_lem) => 78.80/10.72 (((binunionT_lem) => 78.80/10.72 (((powersetT_lem) => 78.80/10.72 (((setminusT_lem) => 78.80/10.72 (((complementT_lem) => 78.80/10.72 (( 78.80/10.72 (setextT) => 78.80/10.72 (( 78.80/10.72 (subsetTI) => 78.80/10.72 (( 78.80/10.72 (powersetTI1) => 78.80/10.72 (( 78.80/10.72 (powersetTE1) => 78.80/10.72 (( 78.80/10.72 (complementTI1) => 78.80/10.72 (( 78.80/10.72 (complementTE1) => 78.80/10.72 (( 78.80/10.72 (binintersectTELcontra) => 78.80/10.72 (( 78.80/10.72 (binintersectTERcontra) => 78.80/10.72 (( 78.80/10.72 (contrasubsetT) => 78.80/10.72 (( 78.80/10.72 (contrasubsetT1) => 78.80/10.72 (( 78.80/10.72 (contrasubsetT2) => 78.80/10.72 (( 78.80/10.72 (contrasubsetT3) => 78.80/10.72 (( 78.80/10.72 (doubleComplementI1) => 78.80/10.72 (( 78.80/10.72 (doubleComplementE1) => 78.80/10.72 (( 78.80/10.72 (doubleComplementSub1) => 78.80/10.72 (( 78.80/10.72 (doubleComplementSub2) => 78.80/10.72 (( 78.80/10.72 (doubleComplementEq) => 78.80/10.72 (( 78.80/10.72 (complementTnotintersectT) => 78.80/10.72 (( 78.80/10.72 (complementImpComplementIntersect) => 78.80/10.72 (( 78.80/10.72 (complementSubsetComplementIntersect) => 78.80/10.72 (( 78.80/10.72 (complementInPowersetComplementIntersect) => 78.80/10.72 (( 78.80/10.72 (contraSubsetComplement) => 78.80/10.72 (( 78.80/10.72 (complementTcontraSubset) => 78.80/10.72 (( 78.80/10.72 (binunionTILcontra) => 78.80/10.72 (( 78.80/10.72 (binunionTIRcontra) => 78.80/10.72 (( 78.80/10.72 (inIntersectImpInUnion) => 78.80/10.72 (( 78.80/10.72 (inIntersectImpInUnion2) => 78.80/10.72 (( 78.80/10.72 (inIntersectImpInIntersectUnions) => 78.80/10.72 (( 78.80/10.72 (intersectInPowersetIntersectUnions) => 78.80/10.72 (( 78.80/10.72 (inComplementUnionImpNotIn1) => 78.80/10.72 (( 78.80/10.72 (inComplementUnionImpInComplement1) => 78.80/10.72 (( 78.80/10.72 (binunionTE) => 78.80/10.72 (( 78.80/10.72 (binunionTEcontra) => 78.80/10.72 (( 78.80/10.72 (demorgan2a1) => 78.80/10.72 (( 78.80/10.72 (complementUnionInPowersetComplement) => 78.80/10.72 (( 78.80/10.72 (demorgan2a2) => 78.80/10.72 (( 78.80/10.72 (demorgan1a) => 78.80/10.72 (( 78.80/10.72 (demorgan1b) => 78.80/10.72 (( 78.80/10.72 (demorgan1) => 78.80/10.72 (( 78.80/10.72 (demorgan2a) => 78.80/10.72 (( 78.80/10.72 (demorgan2b2) => 78.80/10.72 (( 78.80/10.72 (demorgan2b) => 78.80/10.72 (( 78.80/10.72 (demorgan2) => 78.80/10.72 (( 78.80/10.72 (woz13rule0) => 78.80/10.72 (( 78.80/10.72 (woz13rule1) => 78.80/10.72 (( 78.80/10.72 (woz13rule2) => 78.80/10.72 (( 78.80/10.72 (woz13rule3) => 78.80/10.72 (( 78.80/10.72 (woz13rule4) => 78.80/10.72 (( 78.80/10.72 (woz1_1) => 78.80/10.72 (( 78.80/10.72 (woz1_2) => 78.80/10.72 (( 78.80/10.72 (woz1_3) => 78.80/10.72 (( 78.80/10.72 (woz1_4) => 78.80/10.72 (( 78.80/10.72 (woz1_5) => 78.80/10.72 (( 78.80/10.72 (breln1all2) => 78.80/10.72 (( 78.80/10.72 (breln1SetBreln1) => 78.80/10.72 (( 78.80/10.72 (choice2fnsingleton) => 78.80/10.72 (( 78.80/10.72 (setOfPairsIsBReln1) => 78.80/10.72 (( 78.80/10.72 (breln1all1) => 78.80/10.72 (( 78.80/10.72 (subbreln1) => 78.80/10.72 (( 78.80/10.72 (eqbreln1) => 78.80/10.72 (( 78.80/10.72 (breln1invprop) => 78.80/10.72 (( 78.80/10.72 (breln1invI) => 78.80/10.72 (( 78.80/10.72 (breln1invE) => 78.80/10.72 (( 78.80/10.72 (breln1compprop) => 78.80/10.72 (( 78.80/10.72 (breln1compI) => 78.80/10.72 (( 78.80/10.72 (breln1compE) => 78.80/10.72 (( 78.80/10.72 (breln1compEex) => 78.80/10.72 (( 78.80/10.72 (breln1unionprop) => 78.80/10.72 (( 78.80/10.72 (breln1unionIL) => 78.80/10.72 (( 78.80/10.72 (breln1unionIR) => 78.80/10.72 (( 78.80/10.72 (breln1unionI) => 78.80/10.72 (( 78.80/10.72 (breln1unionE) => 78.80/10.72 (( 78.80/10.72 (breln1unionEcases) => 78.80/10.72 (( 78.80/10.72 (breln1unionCommutes) => 78.80/10.72 (( 78.80/10.72 (woz2Ex) => 78.80/10.72 (( 78.80/10.72 (woz2W) => 78.80/10.72 (( 78.80/10.72 (woz2A) => 78.80/10.72 (( 78.80/10.72 (woz2B) => 78.80/10.72 (( 78.80/10.72 (image1Ex) => 78.80/10.72 (( 78.80/10.72 (image1Ex1) => 78.80/10.72 (( 78.80/10.72 (image1Equiv) => 78.80/10.72 (( 78.80/10.72 (image1E) => 78.80/10.72 (( 78.80/10.72 (image1I) => 78.80/10.72 (( 78.80/10.72 (injFuncInInjFuncSet) => 78.80/10.72 (( 78.80/10.72 (injFuncSetFuncIn) => 78.80/10.72 (( 78.80/10.72 (injFuncSetFuncInj) => 78.80/10.72 (( 78.80/10.72 (surjFuncSetFuncIn) => 78.80/10.72 (( 78.80/10.72 (surjFuncSetFuncSurj) => 78.80/10.72 (( 78.80/10.72 (leftInvIsSurj) => 78.80/10.72 (( 78.80/10.72 (surjCantorThm) => 78.80/10.72 (( 78.80/10.72 (foundation2) => 78.80/10.72 (( 78.80/10.72 (notinself) => 78.80/10.72 (( 78.80/10.72 (notinself2) => 78.80/10.72 (( 78.80/10.72 (omegaSp) => 78.80/10.72 (( 78.80/10.72 (omegaSclos) => 78.80/10.72 (( 78.80/10.72 (peano0notS) => 78.80/10.72 (( 78.80/10.72 (peanoSinj) => 78.80/10.72 (( 78.80/10.72 (transitivesetOp1) => 78.80/10.72 (( 78.80/10.72 (binintTransitive) => 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(((beta2) => 78.80/10.72 (((eta2) => 78.80/10.72 (((iffalseProp1) => 78.80/10.72 (((iffalseProp2) => 78.80/10.72 (((iftrueProp1) => 78.80/10.72 (((iftrueProp2) => 78.80/10.72 (((ifSingleton) => 78.80/10.72 (((ifp) => 78.80/10.72 (((theeq) => 78.80/10.72 (((iftrue) => 78.80/10.72 (((iffalse) => 78.80/10.72 (((iftrueorfalse) => 78.80/10.72 (((binintersectT_lem) => 78.80/10.72 (((binunionT_lem) => 78.80/10.72 (((powersetT_lem) => 78.80/10.72 (((setminusT_lem) => 78.80/10.72 (((complementT_lem) => 78.80/10.72 (((setextT) => 78.80/10.72 (((subsetTI) => 78.80/10.72 (((powersetTI1) => 78.80/10.72 (((powersetTE1) => 78.80/10.72 (((complementTI1) => 78.80/10.72 (( 78.80/10.72 (complementTE1) => 78.80/10.72 (( 78.80/10.72 (binintersectTELcontra) => 78.80/10.72 (( 78.80/10.72 (binintersectTERcontra) => 78.80/10.72 (( 78.80/10.72 (contrasubsetT) => 78.80/10.72 (( 78.80/10.72 (contrasubsetT1) => 78.80/10.72 (( 78.80/10.72 (contrasubsetT2) => 78.80/10.72 (( 78.80/10.72 (contrasubsetT3) => 78.80/10.72 (( 78.80/10.72 (doubleComplementI1) => 78.80/10.72 (( 78.80/10.72 (doubleComplementE1) => 78.80/10.72 (( 78.80/10.72 (doubleComplementSub1) => 78.80/10.72 (( 78.80/10.72 (doubleComplementSub2) => 78.80/10.72 (( 78.80/10.72 (doubleComplementEq) => 78.80/10.72 (( 78.80/10.72 (complementTnotintersectT) => 78.80/10.72 (( 78.80/10.72 (complementImpComplementIntersect) => 78.80/10.72 (( 78.80/10.72 (complementSubsetComplementIntersect) => 78.80/10.72 (( 78.80/10.72 (complementInPowersetComplementIntersect) => 78.80/10.72 (( 78.80/10.72 (contraSubsetComplement) => 78.80/10.72 (( 78.80/10.72 (complementTcontraSubset) => 78.80/10.72 (( 78.80/10.72 (binunionTILcontra) => 78.80/10.72 (( 78.80/10.72 (binunionTIRcontra) => 78.80/10.72 (( 78.80/10.72 (inIntersectImpInUnion) => 78.80/10.72 (( 78.80/10.72 (inIntersectImpInUnion2) => 78.80/10.72 (( 78.80/10.72 (inIntersectImpInIntersectUnions) => 78.80/10.72 (( 78.80/10.72 (intersectInPowersetIntersectUnions) => 78.80/10.72 (( 78.80/10.72 (inComplementUnionImpNotIn1) => 78.80/10.72 (( 78.80/10.72 (inComplementUnionImpInComplement1) => 78.80/10.72 (( 78.80/10.72 (binunionTE) => 78.80/10.72 (( 78.80/10.72 (binunionTEcontra) => 78.80/10.72 (( 78.80/10.72 (demorgan2a1) => 78.80/10.72 (( 78.80/10.72 (complementUnionInPowersetComplement) => 78.80/10.72 (( 78.80/10.72 (demorgan2a2) => 78.80/10.72 (( 78.80/10.72 (demorgan1a) => 78.80/10.72 (( 78.80/10.72 (demorgan1b) => 78.80/10.72 (( 78.80/10.72 (demorgan1) => 78.80/10.72 (( 78.80/10.72 (demorgan2a) => 78.80/10.72 (( 78.80/10.72 (demorgan2b2) => 78.80/10.72 (( 78.80/10.72 (demorgan2b) => 78.80/10.72 (( 78.80/10.72 (demorgan2) => 78.80/10.72 (( 78.80/10.72 (woz13rule0) => 78.80/10.72 (( 78.80/10.72 (woz13rule1) => 78.80/10.72 (( 78.80/10.72 (woz13rule2) => 78.80/10.72 (( 78.80/10.72 (woz13rule3) => 78.80/10.72 (( 78.80/10.72 (woz13rule4) => 78.80/10.72 (( 78.80/10.72 (woz1_1) => 78.80/10.72 (( 78.80/10.72 (woz1_2) => 78.80/10.72 (( 78.80/10.72 (woz1_3) => 78.80/10.72 (( 78.80/10.72 (woz1_4) => 78.80/10.72 (( 78.80/10.72 (woz1_5) => 78.80/10.72 (( 78.80/10.72 (breln1all2) => 78.80/10.72 (( 78.80/10.72 (breln1SetBreln1) => 78.80/10.72 (( 78.80/10.72 (choice2fnsingleton) => 78.80/10.72 (( 78.80/10.72 (setOfPairsIsBReln1) => 78.80/10.72 (( 78.80/10.72 (breln1all1) => 78.80/10.72 (( 78.80/10.72 (subbreln1) => 78.80/10.72 (( 78.80/10.72 (eqbreln1) => 78.80/10.72 (( 78.80/10.72 (breln1invprop) => 78.80/10.72 (( 78.80/10.72 (breln1invI) => 78.80/10.72 (( 78.80/10.72 (breln1invE) => 78.80/10.72 (( 78.80/10.72 (breln1compprop) => 78.80/10.72 (( 78.80/10.72 (breln1compI) => 78.80/10.72 (( 78.80/10.72 (breln1compE) => 78.80/10.72 (( 78.80/10.72 (breln1compEex) => 78.80/10.72 (( 78.80/10.72 (breln1unionprop) => 78.80/10.72 (( 78.80/10.72 (breln1unionIL) => 78.80/10.72 (( 78.80/10.72 (breln1unionIR) => 78.80/10.72 (( 78.80/10.72 (breln1unionI) => 78.80/10.72 (( 78.80/10.72 (breln1unionE) => 78.80/10.72 (( 78.80/10.72 (breln1unionEcases) => 78.80/10.72 (( 78.80/10.72 (breln1unionCommutes) => 78.80/10.72 (( 78.80/10.72 (woz2Ex) => 78.80/10.72 (( 78.80/10.72 (woz2W) => 78.80/10.72 (( 78.80/10.72 (woz2A) => 78.80/10.72 (( 78.80/10.72 (woz2B) => 78.80/10.72 (( 78.80/10.72 (image1Ex) => 78.80/10.72 (( 78.80/10.72 (image1Ex1) => 78.80/10.72 (( 78.80/10.72 (image1Equiv) => 78.80/10.72 (( 78.80/10.72 (image1E) => 78.80/10.72 (( 78.80/10.72 (image1I) => 78.80/10.72 (( 78.80/10.72 (injFuncInInjFuncSet) => 78.80/10.72 (( 78.80/10.72 (injFuncSetFuncIn) => 78.80/10.72 (( 78.80/10.72 (injFuncSetFuncInj) => 78.80/10.72 (( 78.80/10.72 (surjFuncSetFuncIn) => 78.80/10.72 (( 78.80/10.72 (surjFuncSetFuncSurj) => 78.80/10.72 (( 78.80/10.72 (leftInvIsSurj) => 78.80/10.72 (( 78.80/10.72 (surjCantorThm) => 78.80/10.72 (( 78.80/10.72 (foundation2) => 78.80/10.72 (( 78.80/10.72 (notinself) => 78.80/10.72 (( 78.80/10.72 (notinself2) => 78.80/10.72 (( 78.80/10.72 (omegaSp) => 78.80/10.72 (( 78.80/10.72 (omegaSclos) => 78.80/10.72 (( 78.80/10.72 (peano0notS) => 78.80/10.72 (( 78.80/10.72 (peanoSinj) => 78.80/10.72 (( 78.80/10.72 (transitivesetOp1) => 78.80/10.72 (( 78.80/10.72 (binintTransitive) => 78.80/10.72 (( 78.80/10.72 (transitivesetOp2) => 78.80/10.72 (( 78.80/10.72 (setunionTransitive) => 78.80/10.72 (( 78.80/10.72 (ordinalMinLem1) => 78.80/10.72 (( 78.80/10.72 (!!) @ ( 78.80/10.72 ^[Y0 : $i]: 78.80/10.72 (( 78.80/10.72 (ordinal @ 78.80/10.72 Y0) => 78.80/10.72 (( 78.80/10.72 (!!) @ ( 78.80/10.72 ^[Y1 : $i]: 78.80/10.72 (( 78.80/10.72 (!!) @ ( 78.80/10.72 ^[Y2 : $i]: 78.80/10.72 (( 78.80/10.72 (in @ 78.80/10.72 Y2 @ 78.80/10.72 Y0) => 78.80/10.72 (( 78.80/10.72 (in @ 78.80/10.72 Y1 @ 78.80/10.72 Y2) => 78.80/10.72 (in @ 78.80/10.72 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 78.80/10.72 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1790])). 78.80/10.72 thf(zip_derived_cl1812, plain, 78.80/10.72 (~ (((funcext) => 78.80/10.72 (((funcext2) => 78.80/10.72 (((ap2apEq1) => 78.80/10.72 (((ap2apEq2) => 78.80/10.72 (((beta1) => 78.80/10.72 (((eta1) => 78.80/10.72 (((lam2lamEq) => 78.80/10.72 (((beta2) => 78.80/10.72 (((eta2) => 78.80/10.72 (((iffalseProp1) => 78.80/10.72 (((iffalseProp2) => 78.80/10.72 (((iftrueProp1) => 78.80/10.72 (((iftrueProp2) => 78.80/10.72 (((ifSingleton) => 78.80/10.72 (((ifp) => 78.80/10.72 (((theeq) => 78.80/10.72 (((iftrue) => 78.80/10.72 (((iffalse) => 78.80/10.72 (((iftrueorfalse) => 78.80/10.72 (((binintersectT_lem) => 78.80/10.72 (((binunionT_lem) => 78.80/10.72 (((powersetT_lem) => 78.80/10.72 (((setminusT_lem) => 78.80/10.72 (((complementT_lem) => 78.80/10.72 (((setextT) => 78.80/10.72 (((subsetTI) => 78.80/10.72 (((powersetTI1) => 78.80/10.72 (((powersetTE1) => 78.80/10.72 (((complementTI1) => 78.80/10.72 (((complementTE1) => 78.80/10.72 (( 78.80/10.72 (binintersectTELcontra) => 78.80/10.72 (( 78.80/10.72 (binintersectTERcontra) => 78.80/10.72 (( 78.80/10.72 (contrasubsetT) => 78.80/10.72 (( 78.80/10.72 (contrasubsetT1) => 78.80/10.72 (( 78.80/10.72 (contrasubsetT2) => 78.80/10.72 (( 78.80/10.72 (contrasubsetT3) => 78.80/10.72 (( 78.80/10.72 (doubleComplementI1) => 78.80/10.72 (( 78.80/10.72 (doubleComplementE1) => 78.80/10.72 (( 78.80/10.72 (doubleComplementSub1) => 78.80/10.72 (( 78.80/10.72 (doubleComplementSub2) => 78.80/10.72 (( 78.80/10.72 (doubleComplementEq) => 78.80/10.72 (( 78.80/10.72 (complementTnotintersectT) => 78.80/10.72 (( 78.80/10.72 (complementImpComplementIntersect) => 78.80/10.72 (( 78.80/10.72 (complementSubsetComplementIntersect) => 78.80/10.72 (( 78.80/10.72 (complementInPowersetComplementIntersect) => 78.80/10.72 (( 78.80/10.72 (contraSubsetComplement) => 78.80/10.72 (( 78.80/10.72 (complementTcontraSubset) => 78.80/10.72 (( 78.80/10.72 (binunionTILcontra) => 78.80/10.72 (( 78.80/10.72 (binunionTIRcontra) => 78.80/10.72 (( 78.80/10.72 (inIntersectImpInUnion) => 78.80/10.72 (( 78.80/10.72 (inIntersectImpInUnion2) => 78.80/10.72 (( 78.80/10.72 (inIntersectImpInIntersectUnions) => 78.80/10.72 (( 78.80/10.72 (intersectInPowersetIntersectUnions) => 78.80/10.72 (( 78.80/10.72 (inComplementUnionImpNotIn1) => 78.80/10.72 (( 78.80/10.72 (inComplementUnionImpInComplement1) => 78.80/10.72 (( 78.80/10.72 (binunionTE) => 78.80/10.72 (( 78.80/10.72 (binunionTEcontra) => 78.80/10.72 (( 78.80/10.72 (demorgan2a1) => 78.80/10.72 (( 78.80/10.72 (complementUnionInPowersetComplement) => 78.80/10.72 (( 78.80/10.72 (demorgan2a2) => 78.80/10.72 (( 78.80/10.72 (demorgan1a) => 78.80/10.72 (( 78.80/10.72 (demorgan1b) => 78.80/10.72 (( 78.80/10.72 (demorgan1) => 78.80/10.72 (( 78.80/10.72 (demorgan2a) => 78.80/10.72 (( 78.80/10.72 (demorgan2b2) => 78.80/10.72 (( 78.80/10.72 (demorgan2b) => 78.80/10.72 (( 78.80/10.72 (demorgan2) => 78.80/10.72 (( 78.80/10.72 (woz13rule0) => 78.80/10.72 (( 78.80/10.72 (woz13rule1) => 78.80/10.72 (( 78.80/10.72 (woz13rule2) => 78.80/10.72 (( 78.80/10.72 (woz13rule3) => 78.80/10.72 (( 78.80/10.72 (woz13rule4) => 78.80/10.72 (( 78.80/10.72 (woz1_1) => 78.80/10.72 (( 78.80/10.72 (woz1_2) => 78.80/10.72 (( 78.80/10.72 (woz1_3) => 78.80/10.72 (( 78.80/10.72 (woz1_4) => 78.80/10.72 (( 78.80/10.72 (woz1_5) => 78.80/10.72 (( 78.80/10.72 (breln1all2) => 78.80/10.72 (( 78.80/10.72 (breln1SetBreln1) => 78.80/10.72 (( 78.80/10.72 (choice2fnsingleton) => 78.80/10.72 (( 78.80/10.72 (setOfPairsIsBReln1) => 78.80/10.72 (( 78.80/10.72 (breln1all1) => 78.80/10.72 (( 78.80/10.72 (subbreln1) => 78.80/10.72 (( 78.80/10.72 (eqbreln1) => 78.80/10.72 (( 78.80/10.72 (breln1invprop) => 78.80/10.72 (( 78.80/10.72 (breln1invI) => 78.80/10.72 (( 78.80/10.72 (breln1invE) => 78.80/10.72 (( 78.80/10.72 (breln1compprop) => 78.80/10.72 (( 78.80/10.72 (breln1compI) => 78.80/10.72 (( 78.80/10.72 (breln1compE) => 78.80/10.72 (( 78.80/10.72 (breln1compEex) => 78.80/10.72 (( 78.80/10.72 (breln1unionprop) => 78.80/10.72 (( 78.80/10.72 (breln1unionIL) => 78.80/10.72 (( 78.80/10.72 (breln1unionIR) => 78.80/10.72 (( 78.80/10.72 (breln1unionI) => 78.80/10.72 (( 78.80/10.72 (breln1unionE) => 78.80/10.72 (( 78.80/10.72 (breln1unionEcases) => 78.80/10.72 (( 78.80/10.72 (breln1unionCommutes) => 78.80/10.72 (( 78.80/10.72 (woz2Ex) => 78.80/10.72 (( 78.80/10.72 (woz2W) => 78.80/10.72 (( 78.80/10.72 (woz2A) => 78.80/10.72 (( 78.80/10.72 (woz2B) => 78.80/10.72 (( 78.80/10.72 (image1Ex) => 78.80/10.72 (( 78.80/10.72 (image1Ex1) => 78.80/10.72 (( 78.80/10.72 (image1Equiv) => 78.80/10.72 (( 78.80/10.72 (image1E) => 78.80/10.72 (( 78.80/10.72 (image1I) => 78.80/10.72 (( 78.80/10.72 (injFuncInInjFuncSet) => 78.80/10.72 (( 78.80/10.72 (injFuncSetFuncIn) => 78.80/10.72 (( 78.80/10.72 (injFuncSetFuncInj) => 78.80/10.72 (( 78.80/10.72 (surjFuncSetFuncIn) => 78.80/10.72 (( 78.80/10.72 (surjFuncSetFuncSurj) => 78.80/10.72 (( 78.80/10.72 (leftInvIsSurj) => 78.80/10.72 (( 78.80/10.72 (surjCantorThm) => 78.80/10.72 (( 78.80/10.72 (foundation2) => 78.80/10.72 (( 78.80/10.72 (notinself) => 78.80/10.72 (( 78.80/10.72 (notinself2) => 78.80/10.72 (( 78.80/10.72 (omegaSp) => 78.80/10.72 (( 78.80/10.72 (omegaSclos) => 78.80/10.72 (( 78.80/10.72 (peano0notS) => 78.80/10.72 (( 78.80/10.72 (peanoSinj) => 78.80/10.72 (( 78.80/10.72 (transitivesetOp1) => 78.80/10.72 (( 78.80/10.72 (binintTransitive) => 78.80/10.72 (( 78.80/10.72 (transitivesetOp2) => 78.80/10.72 (( 78.80/10.72 (setunionTransitive) => 78.80/10.72 (( 78.80/10.72 (ordinalMinLem1) => 78.80/10.72 (( 78.80/10.72 (!!) @ ( 78.80/10.72 ^[Y0 : $i]: 78.80/10.72 (( 78.80/10.72 (ordinal @ 78.80/10.72 Y0) => 78.80/10.72 (( 78.80/10.72 (!!) @ ( 78.80/10.72 ^[Y1 : $i]: 78.80/10.72 (( 78.80/10.72 (!!) @ ( 78.80/10.72 ^[Y2 : $i]: 78.80/10.72 (( 78.80/10.72 (in @ 78.80/10.72 Y2 @ 78.80/10.72 Y0) => 78.80/10.72 (( 78.80/10.72 (in @ 78.80/10.72 Y1 @ 78.80/10.72 Y2) => 78.80/10.72 (in @ 78.80/10.72 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 78.80/10.72 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1800])). 78.80/10.72 thf(zip_derived_cl1826, plain, 78.80/10.72 (~ (((funcext2) => 78.80/10.72 (((ap2apEq1) => 78.80/10.72 (((ap2apEq2) => 78.80/10.72 (((beta1) => 78.80/10.72 (((eta1) => 78.80/10.72 (((lam2lamEq) => 78.80/10.72 (((beta2) => 78.80/10.72 (((eta2) => 78.80/10.72 (((iffalseProp1) => 78.80/10.72 (((iffalseProp2) => 78.80/10.72 (((iftrueProp1) => 78.80/10.72 (((iftrueProp2) => 78.80/10.72 (((ifSingleton) => 78.80/10.72 (((ifp) => 78.80/10.72 (((theeq) => 78.80/10.72 (((iftrue) => 78.80/10.72 (((iffalse) => 78.80/10.72 (((iftrueorfalse) => 78.80/10.72 (((binintersectT_lem) => 78.80/10.72 (((binunionT_lem) => 78.80/10.72 (((powersetT_lem) => 78.80/10.72 (((setminusT_lem) => 78.80/10.72 (((complementT_lem) => 78.80/10.72 (((setextT) => 78.80/10.72 (((subsetTI) => 78.80/10.72 (((powersetTI1) => 78.80/10.72 (((powersetTE1) => 78.80/10.72 (((complementTI1) => 78.80/10.72 (((complementTE1) => 78.80/10.72 (((binintersectTELcontra) => 78.80/10.72 (( 78.80/10.72 (binintersectTERcontra) => 78.80/10.72 (( 78.80/10.72 (contrasubsetT) => 78.80/10.72 (( 78.80/10.72 (contrasubsetT1) => 78.80/10.72 (( 78.80/10.72 (contrasubsetT2) => 78.80/10.72 (( 78.80/10.72 (contrasubsetT3) => 78.80/10.72 (( 78.80/10.72 (doubleComplementI1) => 78.80/10.72 (( 78.80/10.72 (doubleComplementE1) => 78.80/10.72 (( 78.80/10.72 (doubleComplementSub1) => 78.80/10.72 (( 78.80/10.72 (doubleComplementSub2) => 78.80/10.72 (( 78.80/10.72 (doubleComplementEq) => 78.80/10.72 (( 78.80/10.72 (complementTnotintersectT) => 78.80/10.72 (( 78.80/10.72 (complementImpComplementIntersect) => 78.80/10.72 (( 78.80/10.72 (complementSubsetComplementIntersect) => 78.80/10.72 (( 78.80/10.72 (complementInPowersetComplementIntersect) => 78.80/10.72 (( 78.80/10.72 (contraSubsetComplement) => 78.80/10.72 (( 78.80/10.72 (complementTcontraSubset) => 78.80/10.72 (( 78.80/10.72 (binunionTILcontra) => 78.80/10.72 (( 78.80/10.72 (binunionTIRcontra) => 78.80/10.72 (( 78.80/10.72 (inIntersectImpInUnion) => 78.80/10.72 (( 78.80/10.72 (inIntersectImpInUnion2) => 78.80/10.72 (( 78.80/10.72 (inIntersectImpInIntersectUnions) => 78.80/10.72 (( 78.80/10.72 (intersectInPowersetIntersectUnions) => 78.80/10.72 (( 78.80/10.72 (inComplementUnionImpNotIn1) => 78.80/10.72 (( 78.80/10.72 (inComplementUnionImpInComplement1) => 78.80/10.72 (( 78.80/10.72 (binunionTE) => 78.80/10.72 (( 78.80/10.72 (binunionTEcontra) => 78.80/10.72 (( 78.80/10.72 (demorgan2a1) => 78.80/10.72 (( 78.80/10.72 (complementUnionInPowersetComplement) => 78.80/10.72 (( 78.80/10.72 (demorgan2a2) => 78.80/10.72 (( 78.80/10.72 (demorgan1a) => 78.80/10.72 (( 78.80/10.72 (demorgan1b) => 78.80/10.72 (( 78.80/10.72 (demorgan1) => 78.80/10.72 (( 78.80/10.72 (demorgan2a) => 78.80/10.72 (( 78.80/10.72 (demorgan2b2) => 78.80/10.72 (( 78.80/10.72 (demorgan2b) => 78.80/10.72 (( 78.80/10.72 (demorgan2) => 78.80/10.72 (( 78.80/10.72 (woz13rule0) => 78.80/10.72 (( 78.80/10.72 (woz13rule1) => 78.80/10.72 (( 78.80/10.72 (woz13rule2) => 78.80/10.72 (( 78.80/10.72 (woz13rule3) => 78.80/10.72 (( 78.80/10.72 (woz13rule4) => 78.80/10.72 (( 78.80/10.72 (woz1_1) => 78.80/10.72 (( 78.80/10.72 (woz1_2) => 78.80/10.72 (( 78.80/10.72 (woz1_3) => 78.80/10.72 (( 78.80/10.72 (woz1_4) => 78.80/10.72 (( 78.80/10.72 (woz1_5) => 78.80/10.72 (( 78.80/10.72 (breln1all2) => 78.80/10.72 (( 78.80/10.72 (breln1SetBreln1) => 78.80/10.72 (( 78.80/10.72 (choice2fnsingleton) => 78.80/10.72 (( 78.80/10.72 (setOfPairsIsBReln1) => 78.80/10.72 (( 78.80/10.72 (breln1all1) => 78.80/10.72 (( 78.80/10.72 (subbreln1) => 78.80/10.72 (( 78.80/10.72 (eqbreln1) => 78.80/10.72 (( 78.80/10.72 (breln1invprop) => 78.80/10.72 (( 78.80/10.72 (breln1invI) => 78.80/10.72 (( 78.80/10.72 (breln1invE) => 78.80/10.72 (( 78.80/10.72 (breln1compprop) => 78.80/10.72 (( 78.80/10.72 (breln1compI) => 78.80/10.72 (( 78.80/10.72 (breln1compE) => 78.80/10.72 (( 78.80/10.72 (breln1compEex) => 78.80/10.72 (( 78.80/10.72 (breln1unionprop) => 78.80/10.72 (( 78.80/10.72 (breln1unionIL) => 78.80/10.72 (( 78.80/10.72 (breln1unionIR) => 78.80/10.72 (( 78.80/10.72 (breln1unionI) => 78.80/10.72 (( 78.80/10.72 (breln1unionE) => 78.80/10.72 (( 78.80/10.72 (breln1unionEcases) => 78.80/10.72 (( 78.80/10.72 (breln1unionCommutes) => 78.80/10.72 (( 78.80/10.72 (woz2Ex) => 78.80/10.72 (( 78.80/10.72 (woz2W) => 78.80/10.72 (( 78.80/10.72 (woz2A) => 78.80/10.72 (( 78.80/10.72 (woz2B) => 78.80/10.72 (( 78.80/10.72 (image1Ex) => 78.80/10.72 (( 78.80/10.72 (image1Ex1) => 78.80/10.72 (( 78.80/10.72 (image1Equiv) => 78.80/10.72 (( 78.80/10.72 (image1E) => 78.80/10.72 (( 78.80/10.72 (image1I) => 78.80/10.72 (( 78.80/10.72 (injFuncInInjFuncSet) => 78.80/10.72 (( 78.80/10.72 (injFuncSetFuncIn) => 78.80/10.72 (( 78.80/10.72 (injFuncSetFuncInj) => 78.80/10.72 (( 78.80/10.72 (surjFuncSetFuncIn) => 78.80/10.72 (( 78.80/10.72 (surjFuncSetFuncSurj) => 78.80/10.72 (( 78.80/10.72 (leftInvIsSurj) => 78.80/10.72 (( 78.80/10.72 (surjCantorThm) => 78.80/10.72 (( 78.80/10.72 (foundation2) => 78.80/10.72 (( 78.80/10.72 (notinself) => 78.80/10.72 (( 78.80/10.72 (notinself2) => 78.80/10.72 (( 78.80/10.72 (omegaSp) => 78.80/10.72 (( 78.80/10.72 (omegaSclos) => 78.80/10.72 (( 78.80/10.72 (peano0notS) => 78.80/10.72 (( 78.80/10.72 (peanoSinj) => 78.80/10.72 (( 78.80/10.72 (transitivesetOp1) => 78.80/10.72 (( 78.80/10.72 (binintTransitive) => 78.80/10.72 (( 78.80/10.72 (transitivesetOp2) => 78.80/10.72 (( 78.80/10.72 (setunionTransitive) => 78.80/10.72 (( 78.80/10.72 (ordinalMinLem1) => 78.80/10.72 (( 78.80/10.72 (!!) @ ( 78.80/10.72 ^[Y0 : $i]: 78.80/10.72 (( 78.80/10.72 (ordinal @ 78.80/10.72 Y0) => 78.80/10.72 (( 78.80/10.72 (!!) @ ( 78.80/10.72 ^[Y1 : $i]: 78.80/10.72 (( 78.80/10.72 (!!) @ ( 78.80/10.72 ^[Y2 : $i]: 78.80/10.72 (( 78.80/10.72 (in @ 78.80/10.72 Y2 @ 78.80/10.72 Y0) => 78.80/10.72 (( 78.80/10.72 (in @ 78.80/10.72 Y1 @ 78.80/10.72 Y2) => 78.80/10.72 (in @ 78.80/10.72 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 78.80/10.72 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1812])). 78.80/10.72 thf(zip_derived_cl1841, plain, 78.80/10.72 (~ (((ap2apEq1) => 78.80/10.72 (((ap2apEq2) => 78.80/10.72 (((beta1) => 78.80/10.72 (((eta1) => 78.80/10.72 (((lam2lamEq) => 78.80/10.72 (((beta2) => 78.80/10.72 (((eta2) => 78.80/10.72 (((iffalseProp1) => 78.80/10.72 (((iffalseProp2) => 78.80/10.72 (((iftrueProp1) => 78.80/10.72 (((iftrueProp2) => 78.80/10.72 (((ifSingleton) => 78.80/10.72 (((ifp) => 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78.80/10.72 (( 78.80/10.72 (complementTnotintersectT) => 78.80/10.72 (( 78.80/10.72 (complementImpComplementIntersect) => 78.80/10.72 (( 78.80/10.72 (complementSubsetComplementIntersect) => 78.80/10.72 (( 78.80/10.72 (complementInPowersetComplementIntersect) => 78.80/10.72 (( 78.80/10.72 (contraSubsetComplement) => 78.80/10.72 (( 78.80/10.72 (complementTcontraSubset) => 78.80/10.72 (( 78.80/10.72 (binunionTILcontra) => 78.80/10.72 (( 78.80/10.72 (binunionTIRcontra) => 78.80/10.72 (( 78.80/10.72 (inIntersectImpInUnion) => 78.80/10.72 (( 78.80/10.72 (inIntersectImpInUnion2) => 78.80/10.72 (( 78.80/10.72 (inIntersectImpInIntersectUnions) => 78.80/10.72 (( 78.80/10.72 (intersectInPowersetIntersectUnions) => 78.80/10.72 (( 78.80/10.72 (inComplementUnionImpNotIn1) => 78.80/10.72 (( 78.80/10.72 (inComplementUnionImpInComplement1) => 78.80/10.72 (( 78.80/10.72 (binunionTE) => 78.80/10.72 (( 78.80/10.72 (binunionTEcontra) => 78.80/10.72 (( 78.80/10.72 (demorgan2a1) => 78.80/10.72 (( 78.80/10.72 (complementUnionInPowersetComplement) => 78.80/10.72 (( 78.80/10.72 (demorgan2a2) => 78.80/10.72 (( 78.80/10.72 (demorgan1a) => 78.80/10.72 (( 78.80/10.72 (demorgan1b) => 78.80/10.72 (( 78.80/10.72 (demorgan1) => 78.80/10.72 (( 78.80/10.72 (demorgan2a) => 78.80/10.72 (( 78.80/10.72 (demorgan2b2) => 78.80/10.72 (( 78.80/10.72 (demorgan2b) => 78.80/10.72 (( 78.80/10.72 (demorgan2) => 78.80/10.72 (( 78.80/10.72 (woz13rule0) => 78.80/10.72 (( 78.80/10.72 (woz13rule1) => 78.80/10.72 (( 78.80/10.72 (woz13rule2) => 78.80/10.72 (( 78.80/10.72 (woz13rule3) => 78.80/10.72 (( 78.80/10.72 (woz13rule4) => 78.80/10.72 (( 78.80/10.72 (woz1_1) => 78.80/10.72 (( 78.80/10.72 (woz1_2) => 78.80/10.72 (( 78.80/10.72 (woz1_3) => 78.80/10.72 (( 78.80/10.72 (woz1_4) => 78.80/10.72 (( 78.80/10.72 (woz1_5) => 78.80/10.72 (( 78.80/10.72 (breln1all2) => 78.80/10.72 (( 78.80/10.72 (breln1SetBreln1) => 78.80/10.72 (( 78.80/10.72 (choice2fnsingleton) => 78.80/10.72 (( 78.80/10.72 (setOfPairsIsBReln1) => 78.80/10.72 (( 78.80/10.72 (breln1all1) => 78.80/10.72 (( 78.80/10.72 (subbreln1) => 78.80/10.72 (( 78.80/10.72 (eqbreln1) => 78.80/10.72 (( 78.80/10.72 (breln1invprop) => 78.80/10.72 (( 78.80/10.72 (breln1invI) => 78.80/10.72 (( 78.80/10.72 (breln1invE) => 78.80/10.72 (( 78.80/10.72 (breln1compprop) => 78.80/10.72 (( 78.80/10.72 (breln1compI) => 78.80/10.72 (( 78.80/10.72 (breln1compE) => 78.80/10.72 (( 78.80/10.72 (breln1compEex) => 78.80/10.72 (( 78.80/10.72 (breln1unionprop) => 78.80/10.72 (( 78.80/10.72 (breln1unionIL) => 78.80/10.72 (( 78.80/10.72 (breln1unionIR) => 78.80/10.72 (( 78.80/10.72 (breln1unionI) => 78.80/10.72 (( 78.80/10.72 (breln1unionE) => 78.80/10.72 (( 78.80/10.72 (breln1unionEcases) => 78.80/10.72 (( 78.80/10.72 (breln1unionCommutes) => 78.80/10.72 (( 78.80/10.72 (woz2Ex) => 78.80/10.72 (( 78.80/10.72 (woz2W) => 78.80/10.72 (( 78.80/10.72 (woz2A) => 78.80/10.72 (( 78.80/10.72 (woz2B) => 78.80/10.72 (( 78.80/10.72 (image1Ex) => 78.80/10.72 (( 78.80/10.72 (image1Ex1) => 78.80/10.72 (( 78.80/10.72 (image1Equiv) => 78.80/10.72 (( 78.80/10.72 (image1E) => 78.80/10.72 (( 78.80/10.72 (image1I) => 78.80/10.72 (( 78.80/10.72 (injFuncInInjFuncSet) => 78.80/10.72 (( 78.80/10.72 (injFuncSetFuncIn) => 78.80/10.72 (( 78.80/10.72 (injFuncSetFuncInj) => 78.80/10.72 (( 78.80/10.72 (surjFuncSetFuncIn) => 78.80/10.72 (( 78.80/10.72 (surjFuncSetFuncSurj) => 78.80/10.72 (( 78.80/10.72 (leftInvIsSurj) => 78.80/10.72 (( 78.80/10.72 (surjCantorThm) => 78.80/10.72 (( 78.80/10.72 (foundation2) => 78.80/10.72 (( 78.80/10.72 (notinself) => 78.80/10.72 (( 78.80/10.72 (notinself2) => 78.80/10.72 (( 78.80/10.72 (omegaSp) => 78.80/10.72 (( 78.80/10.72 (omegaSclos) => 78.80/10.72 (( 78.80/10.72 (peano0notS) => 78.80/10.72 (( 78.80/10.72 (peanoSinj) => 78.80/10.72 (( 78.80/10.72 (transitivesetOp1) => 78.80/10.72 (( 78.80/10.72 (binintTransitive) => 78.80/10.72 (( 78.80/10.72 (transitivesetOp2) => 78.80/10.72 (( 78.80/10.72 (setunionTransitive) => 78.80/10.72 (( 78.80/10.72 (ordinalMinLem1) => 78.80/10.72 (( 78.80/10.72 (!!) @ ( 78.80/10.72 ^[Y0 : $i]: 78.80/10.72 (( 78.80/10.72 (ordinal @ 78.80/10.72 Y0) => 78.80/10.72 (( 78.80/10.72 (!!) @ ( 78.80/10.72 ^[Y1 : $i]: 78.80/10.72 (( 78.80/10.72 (!!) @ ( 78.80/10.72 ^[Y2 : $i]: 78.80/10.72 (( 78.80/10.72 (in @ 78.80/10.72 Y2 @ 78.80/10.72 Y0) => 78.80/10.72 (( 78.80/10.72 (in @ 78.80/10.72 Y1 @ 78.80/10.72 Y2) => 78.80/10.72 (in @ 78.80/10.72 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 78.80/10.72 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1826])). 78.80/10.72 thf(zip_derived_cl1857, plain, 78.80/10.72 (~ (((ap2apEq2) => 78.80/10.72 (((beta1) => 78.80/10.72 (((eta1) => 78.80/10.72 (((lam2lamEq) => 78.80/10.72 (((beta2) => 78.80/10.72 (((eta2) => 78.80/10.72 (((iffalseProp1) => 78.80/10.72 (((iffalseProp2) => 78.80/10.72 (((iftrueProp1) => 78.80/10.72 (((iftrueProp2) => 78.80/10.72 (((ifSingleton) => 78.80/10.72 (((ifp) => 78.80/10.72 (((theeq) => 78.80/10.72 (((iftrue) => 78.80/10.72 (((iffalse) => 78.80/10.72 (((iftrueorfalse) => 78.80/10.72 (((binintersectT_lem) => 78.80/10.72 (((binunionT_lem) => 78.80/10.72 (((powersetT_lem) => 78.80/10.72 (((setminusT_lem) => 78.80/10.72 (((complementT_lem) => 78.80/10.72 (((setextT) => 78.80/10.72 (((subsetTI) => 78.80/10.72 (((powersetTI1) => 78.80/10.72 (((powersetTE1) => 78.80/10.72 (((complementTI1) => 78.80/10.72 (((complementTE1) => 78.80/10.72 (((binintersectTELcontra) => 78.80/10.72 (((binintersectTERcontra) => 78.80/10.72 (((contrasubsetT) => 78.80/10.72 (( 78.80/10.72 (contrasubsetT1) => 78.80/10.72 (( 78.80/10.72 (contrasubsetT2) => 78.80/10.72 (( 78.80/10.72 (contrasubsetT3) => 78.80/10.72 (( 78.80/10.72 (doubleComplementI1) => 78.80/10.72 (( 78.80/10.72 (doubleComplementE1) => 78.80/10.72 (( 78.80/10.72 (doubleComplementSub1) => 78.80/10.72 (( 78.80/10.72 (doubleComplementSub2) => 78.80/10.72 (( 78.80/10.72 (doubleComplementEq) => 78.80/10.72 (( 78.80/10.72 (complementTnotintersectT) => 78.80/10.72 (( 78.80/10.72 (complementImpComplementIntersect) => 78.80/10.72 (( 78.80/10.72 (complementSubsetComplementIntersect) => 78.80/10.72 (( 78.80/10.72 (complementInPowersetComplementIntersect) => 78.80/10.72 (( 78.80/10.72 (contraSubsetComplement) => 78.80/10.72 (( 78.80/10.72 (complementTcontraSubset) => 78.80/10.72 (( 78.80/10.72 (binunionTILcontra) => 78.80/10.72 (( 78.80/10.72 (binunionTIRcontra) => 78.80/10.72 (( 78.80/10.72 (inIntersectImpInUnion) => 78.80/10.72 (( 78.80/10.72 (inIntersectImpInUnion2) => 78.80/10.72 (( 78.80/10.72 (inIntersectImpInIntersectUnions) => 78.80/10.72 (( 78.80/10.72 (intersectInPowersetIntersectUnions) => 78.80/10.72 (( 78.80/10.72 (inComplementUnionImpNotIn1) => 78.80/10.72 (( 78.80/10.72 (inComplementUnionImpInComplement1) => 78.80/10.72 (( 78.80/10.72 (binunionTE) => 78.80/10.72 (( 78.80/10.72 (binunionTEcontra) => 78.80/10.72 (( 78.80/10.72 (demorgan2a1) => 78.80/10.72 (( 78.80/10.72 (complementUnionInPowersetComplement) => 78.80/10.72 (( 78.80/10.72 (demorgan2a2) => 78.80/10.72 (( 78.80/10.72 (demorgan1a) => 78.80/10.72 (( 78.80/10.72 (demorgan1b) => 78.80/10.72 (( 78.80/10.72 (demorgan1) => 78.80/10.72 (( 78.80/10.72 (demorgan2a) => 78.80/10.72 (( 78.80/10.72 (demorgan2b2) => 78.80/10.72 (( 78.80/10.72 (demorgan2b) => 78.80/10.72 (( 78.80/10.72 (demorgan2) => 78.80/10.72 (( 78.80/10.72 (woz13rule0) => 78.80/10.72 (( 78.80/10.72 (woz13rule1) => 78.80/10.72 (( 78.80/10.72 (woz13rule2) => 78.80/10.72 (( 78.80/10.72 (woz13rule3) => 78.80/10.72 (( 78.80/10.72 (woz13rule4) => 78.80/10.72 (( 78.80/10.72 (woz1_1) => 78.80/10.72 (( 78.80/10.72 (woz1_2) => 78.80/10.72 (( 78.80/10.72 (woz1_3) => 78.80/10.72 (( 78.80/10.72 (woz1_4) => 78.80/10.72 (( 78.80/10.72 (woz1_5) => 78.80/10.72 (( 78.80/10.72 (breln1all2) => 78.80/10.72 (( 78.80/10.72 (breln1SetBreln1) => 78.80/10.72 (( 78.80/10.72 (choice2fnsingleton) => 78.80/10.72 (( 78.80/10.72 (setOfPairsIsBReln1) => 78.80/10.72 (( 78.80/10.72 (breln1all1) => 78.80/10.72 (( 78.80/10.72 (subbreln1) => 78.80/10.72 (( 78.80/10.72 (eqbreln1) => 78.80/10.72 (( 78.80/10.72 (breln1invprop) => 78.80/10.72 (( 78.80/10.72 (breln1invI) => 78.80/10.72 (( 78.80/10.72 (breln1invE) => 78.80/10.72 (( 78.80/10.72 (breln1compprop) => 78.80/10.72 (( 78.80/10.72 (breln1compI) => 78.80/10.72 (( 78.80/10.72 (breln1compE) => 78.80/10.72 (( 78.80/10.72 (breln1compEex) => 78.80/10.72 (( 78.80/10.72 (breln1unionprop) => 78.80/10.72 (( 78.80/10.72 (breln1unionIL) => 78.80/10.72 (( 78.80/10.72 (breln1unionIR) => 78.80/10.72 (( 78.80/10.72 (breln1unionI) => 78.80/10.72 (( 78.80/10.72 (breln1unionE) => 78.80/10.72 (( 78.80/10.72 (breln1unionEcases) => 78.80/10.72 (( 78.80/10.72 (breln1unionCommutes) => 78.80/10.72 (( 78.80/10.72 (woz2Ex) => 78.80/10.72 (( 78.80/10.72 (woz2W) => 78.80/10.72 (( 78.80/10.72 (woz2A) => 78.80/10.72 (( 78.80/10.72 (woz2B) => 78.80/10.72 (( 78.80/10.72 (image1Ex) => 78.80/10.72 (( 78.80/10.72 (image1Ex1) => 78.80/10.72 (( 78.80/10.72 (image1Equiv) => 78.80/10.72 (( 78.80/10.72 (image1E) => 78.80/10.72 (( 78.80/10.72 (image1I) => 78.80/10.72 (( 78.80/10.72 (injFuncInInjFuncSet) => 78.80/10.72 (( 78.80/10.72 (injFuncSetFuncIn) => 78.80/10.72 (( 78.80/10.72 (injFuncSetFuncInj) => 78.80/10.72 (( 78.80/10.72 (surjFuncSetFuncIn) => 78.80/10.72 (( 78.80/10.72 (surjFuncSetFuncSurj) => 78.80/10.72 (( 78.80/10.72 (leftInvIsSurj) => 78.80/10.72 (( 78.80/10.72 (surjCantorThm) => 78.80/10.72 (( 78.80/10.72 (foundation2) => 78.80/10.72 (( 78.80/10.72 (notinself) => 78.80/10.72 (( 78.80/10.72 (notinself2) => 78.80/10.72 (( 78.80/10.72 (omegaSp) => 78.80/10.72 (( 78.80/10.72 (omegaSclos) => 78.80/10.72 (( 78.80/10.72 (peano0notS) => 78.80/10.72 (( 78.80/10.72 (peanoSinj) => 78.80/10.72 (( 78.80/10.72 (transitivesetOp1) => 78.80/10.72 (( 78.80/10.72 (binintTransitive) => 78.80/10.72 (( 78.80/10.72 (transitivesetOp2) => 78.80/10.72 (( 78.80/10.72 (setunionTransitive) => 78.80/10.72 (( 78.80/10.72 (ordinalMinLem1) => 78.80/10.72 (( 78.80/10.72 (!!) @ ( 78.80/10.72 ^[Y0 : $i]: 78.80/10.72 (( 78.80/10.72 (ordinal @ 78.80/10.72 Y0) => 78.80/10.72 (( 78.80/10.72 (!!) @ ( 78.80/10.72 ^[Y1 : $i]: 78.80/10.72 (( 78.80/10.72 (!!) @ ( 78.80/10.72 ^[Y2 : $i]: 78.80/10.72 (( 78.80/10.72 (in @ 78.80/10.72 Y2 @ 78.80/10.72 Y0) => 78.80/10.72 (( 78.80/10.72 (in @ 78.80/10.72 Y1 @ 78.80/10.72 Y2) => 78.80/10.72 (in @ 78.80/10.72 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 78.80/10.72 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1841])). 78.80/10.72 thf(zip_derived_cl1874, plain, 78.80/10.72 (~ (((beta1) => 78.80/10.72 (((eta1) => 78.80/10.72 (((lam2lamEq) => 78.80/10.72 (((beta2) => 78.80/10.72 (((eta2) => 78.80/10.72 (((iffalseProp1) => 78.80/10.72 (((iffalseProp2) => 78.80/10.72 (((iftrueProp1) => 78.80/10.72 (((iftrueProp2) => 78.80/10.72 (((ifSingleton) => 78.80/10.72 (((ifp) => 78.80/10.72 (((theeq) => 78.80/10.72 (((iftrue) => 78.80/10.72 (((iffalse) => 78.80/10.72 (((iftrueorfalse) => 78.80/10.72 (((binintersectT_lem) => 78.80/10.72 (((binunionT_lem) => 78.80/10.72 (((powersetT_lem) => 78.80/10.72 (((setminusT_lem) => 78.80/10.72 (((complementT_lem) => 78.80/10.72 (((setextT) => 78.80/10.72 (((subsetTI) => 78.80/10.72 (((powersetTI1) => 78.80/10.72 (((powersetTE1) => 78.80/10.72 (((complementTI1) => 78.80/10.72 (((complementTE1) => 78.80/10.72 (((binintersectTELcontra) => 78.80/10.72 (((binintersectTERcontra) => 78.80/10.72 (((contrasubsetT) => 78.80/10.72 (((contrasubsetT1) => 78.80/10.72 (( 78.80/10.72 (contrasubsetT2) => 78.80/10.72 (( 78.80/10.72 (contrasubsetT3) => 78.80/10.72 (( 78.80/10.72 (doubleComplementI1) => 78.80/10.72 (( 78.80/10.72 (doubleComplementE1) => 78.80/10.72 (( 78.80/10.72 (doubleComplementSub1) => 78.80/10.72 (( 78.80/10.72 (doubleComplementSub2) => 78.80/10.72 (( 78.80/10.72 (doubleComplementEq) => 78.80/10.72 (( 78.80/10.72 (complementTnotintersectT) => 78.80/10.72 (( 78.80/10.72 (complementImpComplementIntersect) => 78.80/10.72 (( 78.80/10.72 (complementSubsetComplementIntersect) => 78.80/10.72 (( 78.80/10.72 (complementInPowersetComplementIntersect) => 78.80/10.72 (( 78.80/10.72 (contraSubsetComplement) => 78.80/10.72 (( 78.80/10.72 (complementTcontraSubset) => 78.80/10.72 (( 78.80/10.72 (binunionTILcontra) => 78.80/10.72 (( 78.80/10.72 (binunionTIRcontra) => 78.80/10.72 (( 78.80/10.72 (inIntersectImpInUnion) => 78.80/10.72 (( 78.80/10.72 (inIntersectImpInUnion2) => 78.80/10.72 (( 78.80/10.72 (inIntersectImpInIntersectUnions) => 78.80/10.72 (( 78.80/10.72 (intersectInPowersetIntersectUnions) => 78.80/10.72 (( 78.80/10.72 (inComplementUnionImpNotIn1) => 78.80/10.72 (( 78.80/10.72 (inComplementUnionImpInComplement1) => 78.80/10.72 (( 78.80/10.72 (binunionTE) => 78.80/10.72 (( 78.80/10.72 (binunionTEcontra) => 78.80/10.72 (( 78.80/10.72 (demorgan2a1) => 78.80/10.72 (( 78.80/10.72 (complementUnionInPowersetComplement) => 78.80/10.72 (( 78.80/10.72 (demorgan2a2) => 78.80/10.72 (( 78.80/10.72 (demorgan1a) => 78.80/10.72 (( 78.80/10.72 (demorgan1b) => 78.80/10.72 (( 78.80/10.72 (demorgan1) => 78.80/10.72 (( 78.80/10.72 (demorgan2a) => 78.80/10.72 (( 78.80/10.72 (demorgan2b2) => 78.80/10.72 (( 78.80/10.72 (demorgan2b) => 78.80/10.72 (( 78.80/10.72 (demorgan2) => 78.80/10.72 (( 78.80/10.72 (woz13rule0) => 78.80/10.72 (( 78.80/10.72 (woz13rule1) => 78.80/10.72 (( 78.80/10.72 (woz13rule2) => 78.80/10.72 (( 78.80/10.72 (woz13rule3) => 78.80/10.72 (( 78.80/10.72 (woz13rule4) => 78.80/10.72 (( 78.80/10.72 (woz1_1) => 78.80/10.72 (( 78.80/10.72 (woz1_2) => 78.80/10.72 (( 78.80/10.72 (woz1_3) => 78.80/10.72 (( 78.80/10.73 (woz1_4) => 78.80/10.73 (( 78.80/10.73 (woz1_5) => 78.80/10.73 (( 78.80/10.73 (breln1all2) => 78.80/10.73 (( 78.80/10.73 (breln1SetBreln1) => 78.80/10.73 (( 78.80/10.73 (choice2fnsingleton) => 78.80/10.73 (( 78.80/10.73 (setOfPairsIsBReln1) => 78.80/10.73 (( 78.80/10.73 (breln1all1) => 78.80/10.73 (( 78.80/10.73 (subbreln1) => 78.80/10.73 (( 78.80/10.73 (eqbreln1) => 78.80/10.73 (( 78.80/10.73 (breln1invprop) => 78.80/10.73 (( 78.80/10.73 (breln1invI) => 78.80/10.73 (( 78.80/10.73 (breln1invE) => 78.80/10.73 (( 78.80/10.73 (breln1compprop) => 78.80/10.73 (( 78.80/10.73 (breln1compI) => 78.80/10.73 (( 78.80/10.73 (breln1compE) => 78.80/10.73 (( 78.80/10.73 (breln1compEex) => 78.80/10.73 (( 78.80/10.73 (breln1unionprop) => 78.80/10.73 (( 78.80/10.73 (breln1unionIL) => 78.80/10.73 (( 78.80/10.73 (breln1unionIR) => 78.80/10.73 (( 78.80/10.73 (breln1unionI) => 78.80/10.73 (( 78.80/10.73 (breln1unionE) => 78.80/10.73 (( 78.80/10.73 (breln1unionEcases) => 78.80/10.73 (( 78.80/10.73 (breln1unionCommutes) => 78.80/10.73 (( 78.80/10.73 (woz2Ex) => 78.80/10.73 (( 78.80/10.73 (woz2W) => 78.80/10.73 (( 78.80/10.73 (woz2A) => 78.80/10.73 (( 78.80/10.73 (woz2B) => 78.80/10.73 (( 78.80/10.73 (image1Ex) => 78.80/10.73 (( 78.80/10.73 (image1Ex1) => 78.80/10.73 (( 78.80/10.73 (image1Equiv) => 78.80/10.73 (( 78.80/10.73 (image1E) => 78.80/10.73 (( 78.80/10.73 (image1I) => 78.80/10.73 (( 78.80/10.73 (injFuncInInjFuncSet) => 78.80/10.73 (( 78.80/10.73 (injFuncSetFuncIn) => 78.80/10.73 (( 78.80/10.73 (injFuncSetFuncInj) => 78.80/10.73 (( 78.80/10.73 (surjFuncSetFuncIn) => 78.80/10.73 (( 78.80/10.73 (surjFuncSetFuncSurj) => 78.80/10.73 (( 78.80/10.73 (leftInvIsSurj) => 78.80/10.73 (( 78.80/10.73 (surjCantorThm) => 78.80/10.73 (( 78.80/10.73 (foundation2) => 78.80/10.73 (( 78.80/10.73 (notinself) => 78.80/10.73 (( 78.80/10.73 (notinself2) => 78.80/10.73 (( 78.80/10.73 (omegaSp) => 78.80/10.73 (( 78.80/10.73 (omegaSclos) => 78.80/10.73 (( 78.80/10.73 (peano0notS) => 78.80/10.73 (( 78.80/10.73 (peanoSinj) => 78.80/10.73 (( 78.80/10.73 (transitivesetOp1) => 78.80/10.73 (( 78.80/10.73 (binintTransitive) => 78.80/10.73 (( 78.80/10.73 (transitivesetOp2) => 78.80/10.73 (( 78.80/10.73 (setunionTransitive) => 78.80/10.73 (( 78.80/10.73 (ordinalMinLem1) => 78.80/10.73 (( 78.80/10.73 (!!) @ ( 78.80/10.73 ^[Y0 : $i]: 78.80/10.73 (( 78.80/10.73 (ordinal @ 78.80/10.73 Y0) => 78.80/10.73 (( 78.80/10.73 (!!) @ ( 78.80/10.73 ^[Y1 : $i]: 78.80/10.73 (( 78.80/10.73 (!!) @ ( 78.80/10.73 ^[Y2 : $i]: 78.80/10.73 (( 78.80/10.73 (in @ 78.80/10.73 Y2 @ 78.80/10.73 Y0) => 78.80/10.73 (( 78.80/10.73 (in @ 78.80/10.73 Y1 @ 78.80/10.73 Y2) => 78.80/10.73 (in @ 78.80/10.73 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 78.80/10.73 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1857])). 78.80/10.73 thf(zip_derived_cl1890, plain, 78.80/10.73 (~ (((eta1) => 78.80/10.73 (((lam2lamEq) => 78.80/10.73 (((beta2) => 78.80/10.73 (((eta2) => 78.80/10.73 (((iffalseProp1) => 78.80/10.73 (((iffalseProp2) => 78.80/10.73 (((iftrueProp1) => 78.80/10.73 (((iftrueProp2) => 78.80/10.73 (((ifSingleton) => 78.80/10.73 (((ifp) => 78.80/10.73 (((theeq) => 78.80/10.73 (((iftrue) => 78.80/10.73 (((iffalse) => 78.80/10.73 (((iftrueorfalse) => 78.80/10.73 (((binintersectT_lem) => 78.80/10.73 (((binunionT_lem) => 78.80/10.73 (((powersetT_lem) => 78.80/10.73 (((setminusT_lem) => 78.80/10.73 (((complementT_lem) => 78.80/10.73 (((setextT) => 78.80/10.73 (((subsetTI) => 78.80/10.73 (((powersetTI1) => 78.80/10.73 (((powersetTE1) => 78.80/10.73 (((complementTI1) => 78.80/10.73 (((complementTE1) => 78.80/10.73 (((binintersectTELcontra) => 78.80/10.73 (((binintersectTERcontra) => 78.80/10.73 (((contrasubsetT) => 78.80/10.73 (((contrasubsetT1) => 78.80/10.73 (((contrasubsetT2) => 78.80/10.73 (( 78.80/10.73 (contrasubsetT3) => 78.80/10.73 (( 78.80/10.73 (doubleComplementI1) => 78.80/10.73 (( 78.80/10.73 (doubleComplementE1) => 78.80/10.73 (( 78.80/10.73 (doubleComplementSub1) => 78.80/10.73 (( 78.80/10.73 (doubleComplementSub2) => 78.80/10.73 (( 78.80/10.73 (doubleComplementEq) => 78.80/10.73 (( 78.80/10.73 (complementTnotintersectT) => 78.80/10.73 (( 78.80/10.73 (complementImpComplementIntersect) => 78.80/10.73 (( 78.80/10.73 (complementSubsetComplementIntersect) => 78.80/10.73 (( 78.80/10.73 (complementInPowersetComplementIntersect) => 78.80/10.73 (( 78.80/10.73 (contraSubsetComplement) => 78.80/10.73 (( 78.80/10.73 (complementTcontraSubset) => 78.80/10.73 (( 78.80/10.73 (binunionTILcontra) => 78.80/10.73 (( 78.80/10.73 (binunionTIRcontra) => 78.80/10.73 (( 78.80/10.73 (inIntersectImpInUnion) => 78.80/10.73 (( 78.80/10.73 (inIntersectImpInUnion2) => 78.80/10.73 (( 78.80/10.73 (inIntersectImpInIntersectUnions) => 78.80/10.73 (( 78.80/10.73 (intersectInPowersetIntersectUnions) => 78.80/10.73 (( 78.80/10.73 (inComplementUnionImpNotIn1) => 78.80/10.73 (( 78.80/10.73 (inComplementUnionImpInComplement1) => 78.80/10.73 (( 78.80/10.73 (binunionTE) => 78.80/10.73 (( 78.80/10.73 (binunionTEcontra) => 78.80/10.73 (( 78.80/10.73 (demorgan2a1) => 78.80/10.73 (( 78.80/10.73 (complementUnionInPowersetComplement) => 78.80/10.73 (( 78.80/10.73 (demorgan2a2) => 78.80/10.73 (( 78.80/10.73 (demorgan1a) => 78.80/10.73 (( 78.80/10.73 (demorgan1b) => 78.80/10.73 (( 78.80/10.73 (demorgan1) => 78.80/10.73 (( 78.80/10.73 (demorgan2a) => 78.80/10.73 (( 78.80/10.73 (demorgan2b2) => 78.80/10.73 (( 78.80/10.73 (demorgan2b) => 78.80/10.73 (( 78.80/10.73 (demorgan2) => 78.80/10.73 (( 78.80/10.73 (woz13rule0) => 78.80/10.73 (( 78.80/10.73 (woz13rule1) => 78.80/10.73 (( 78.80/10.73 (woz13rule2) => 78.80/10.73 (( 78.80/10.73 (woz13rule3) => 78.80/10.73 (( 78.80/10.73 (woz13rule4) => 78.80/10.73 (( 78.80/10.73 (woz1_1) => 78.80/10.73 (( 78.80/10.73 (woz1_2) => 78.80/10.73 (( 78.80/10.73 (woz1_3) => 78.80/10.73 (( 78.80/10.73 (woz1_4) => 78.80/10.73 (( 78.80/10.73 (woz1_5) => 78.80/10.73 (( 78.80/10.73 (breln1all2) => 78.80/10.73 (( 78.80/10.73 (breln1SetBreln1) => 78.80/10.73 (( 78.80/10.73 (choice2fnsingleton) => 78.80/10.73 (( 78.80/10.73 (setOfPairsIsBReln1) => 78.80/10.73 (( 78.80/10.73 (breln1all1) => 78.80/10.73 (( 78.80/10.73 (subbreln1) => 78.80/10.73 (( 78.80/10.73 (eqbreln1) => 78.80/10.73 (( 78.80/10.73 (breln1invprop) => 78.80/10.73 (( 78.80/10.73 (breln1invI) => 78.80/10.73 (( 78.80/10.73 (breln1invE) => 78.80/10.73 (( 78.80/10.73 (breln1compprop) => 78.80/10.73 (( 78.80/10.73 (breln1compI) => 78.80/10.73 (( 78.80/10.73 (breln1compE) => 78.80/10.73 (( 78.80/10.73 (breln1compEex) => 78.80/10.73 (( 78.80/10.73 (breln1unionprop) => 78.80/10.73 (( 78.80/10.73 (breln1unionIL) => 78.80/10.73 (( 78.80/10.73 (breln1unionIR) => 78.80/10.73 (( 78.80/10.73 (breln1unionI) => 78.80/10.73 (( 78.80/10.73 (breln1unionE) => 78.80/10.73 (( 78.80/10.73 (breln1unionEcases) => 78.80/10.73 (( 78.80/10.73 (breln1unionCommutes) => 78.80/10.73 (( 78.80/10.73 (woz2Ex) => 78.80/10.73 (( 78.80/10.73 (woz2W) => 78.80/10.73 (( 78.80/10.73 (woz2A) => 78.80/10.73 (( 78.80/10.73 (woz2B) => 78.80/10.73 (( 78.80/10.73 (image1Ex) => 78.80/10.73 (( 78.80/10.73 (image1Ex1) => 78.80/10.73 (( 78.80/10.73 (image1Equiv) => 78.80/10.73 (( 78.80/10.73 (image1E) => 78.80/10.73 (( 78.80/10.73 (image1I) => 78.80/10.73 (( 78.80/10.73 (injFuncInInjFuncSet) => 78.80/10.73 (( 78.80/10.73 (injFuncSetFuncIn) => 78.80/10.73 (( 78.80/10.73 (injFuncSetFuncInj) => 78.80/10.73 (( 78.80/10.73 (surjFuncSetFuncIn) => 78.80/10.73 (( 78.80/10.73 (surjFuncSetFuncSurj) => 78.80/10.73 (( 78.80/10.73 (leftInvIsSurj) => 78.80/10.73 (( 78.80/10.73 (surjCantorThm) => 78.80/10.73 (( 78.80/10.73 (foundation2) => 78.80/10.73 (( 78.80/10.73 (notinself) => 78.80/10.73 (( 78.80/10.73 (notinself2) => 78.80/10.73 (( 78.80/10.73 (omegaSp) => 78.80/10.73 (( 78.80/10.73 (omegaSclos) => 78.80/10.73 (( 78.80/10.73 (peano0notS) => 78.80/10.73 (( 78.80/10.73 (peanoSinj) => 78.80/10.73 (( 78.80/10.73 (transitivesetOp1) => 78.80/10.73 (( 78.80/10.73 (binintTransitive) => 78.80/10.73 (( 78.80/10.73 (transitivesetOp2) => 78.80/10.73 (( 78.80/10.73 (setunionTransitive) => 78.80/10.73 (( 78.80/10.73 (ordinalMinLem1) => 78.80/10.73 (( 78.80/10.73 (!!) @ ( 78.80/10.73 ^[Y0 : $i]: 78.80/10.73 (( 78.80/10.73 (ordinal @ 78.80/10.73 Y0) => 78.80/10.73 (( 78.80/10.73 (!!) @ ( 78.80/10.73 ^[Y1 : $i]: 78.80/10.73 (( 78.80/10.73 (!!) @ ( 78.80/10.73 ^[Y2 : $i]: 78.80/10.73 (( 78.80/10.73 (in @ 78.80/10.73 Y2 @ 78.80/10.73 Y0) => 78.80/10.73 (( 78.80/10.73 (in @ 78.80/10.73 Y1 @ 78.80/10.73 Y2) => 78.80/10.73 (in @ 78.80/10.73 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 78.80/10.73 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1874])). 78.80/10.73 thf(zip_derived_cl1903, plain, 78.80/10.73 (~ (((lam2lamEq) => 78.80/10.73 (((beta2) => 78.80/10.73 (((eta2) => 78.80/10.73 (((iffalseProp1) => 78.80/10.73 (((iffalseProp2) => 78.80/10.73 (((iftrueProp1) => 78.80/10.73 (((iftrueProp2) => 78.80/10.73 (((ifSingleton) => 78.80/10.73 (((ifp) => 78.80/10.73 (((theeq) => 78.80/10.73 (((iftrue) => 78.80/10.73 (((iffalse) => 78.80/10.73 (((iftrueorfalse) => 78.80/10.73 (((binintersectT_lem) => 78.80/10.73 (((binunionT_lem) => 78.80/10.73 (((powersetT_lem) => 78.80/10.73 (((setminusT_lem) => 78.80/10.73 (((complementT_lem) => 78.80/10.73 (((setextT) => 78.80/10.73 (((subsetTI) => 78.80/10.73 (((powersetTI1) => 78.80/10.73 (((powersetTE1) => 78.80/10.73 (((complementTI1) => 78.80/10.73 (((complementTE1) => 78.80/10.73 (((binintersectTELcontra) => 78.80/10.73 (((binintersectTERcontra) => 78.80/10.73 (((contrasubsetT) => 78.80/10.73 (((contrasubsetT1) => 78.80/10.73 (((contrasubsetT2) => 78.80/10.73 (((contrasubsetT3) => 78.80/10.73 (( 78.80/10.73 (doubleComplementI1) => 78.80/10.73 (( 78.80/10.73 (doubleComplementE1) => 78.80/10.73 (( 78.80/10.73 (doubleComplementSub1) => 78.80/10.73 (( 78.80/10.73 (doubleComplementSub2) => 78.80/10.73 (( 78.80/10.73 (doubleComplementEq) => 78.80/10.73 (( 78.80/10.73 (complementTnotintersectT) => 78.80/10.73 (( 78.80/10.73 (complementImpComplementIntersect) => 78.80/10.73 (( 78.80/10.73 (complementSubsetComplementIntersect) => 78.80/10.73 (( 78.80/10.73 (complementInPowersetComplementIntersect) => 78.80/10.73 (( 78.80/10.73 (contraSubsetComplement) => 78.80/10.73 (( 78.80/10.73 (complementTcontraSubset) => 78.80/10.73 (( 78.80/10.73 (binunionTILcontra) => 78.80/10.73 (( 78.80/10.73 (binunionTIRcontra) => 78.80/10.73 (( 78.80/10.73 (inIntersectImpInUnion) => 78.80/10.73 (( 78.80/10.73 (inIntersectImpInUnion2) => 78.80/10.73 (( 78.80/10.73 (inIntersectImpInIntersectUnions) => 78.80/10.73 (( 78.80/10.73 (intersectInPowersetIntersectUnions) => 78.80/10.73 (( 78.80/10.73 (inComplementUnionImpNotIn1) => 78.80/10.73 (( 78.80/10.73 (inComplementUnionImpInComplement1) => 78.80/10.73 (( 78.80/10.73 (binunionTE) => 78.80/10.73 (( 78.80/10.73 (binunionTEcontra) => 78.80/10.73 (( 78.80/10.73 (demorgan2a1) => 78.80/10.73 (( 78.80/10.73 (complementUnionInPowersetComplement) => 78.80/10.73 (( 78.80/10.73 (demorgan2a2) => 78.80/10.73 (( 78.80/10.73 (demorgan1a) => 78.80/10.73 (( 78.80/10.73 (demorgan1b) => 78.80/10.73 (( 78.80/10.73 (demorgan1) => 78.80/10.73 (( 78.80/10.73 (demorgan2a) => 78.80/10.73 (( 78.80/10.73 (demorgan2b2) => 78.80/10.73 (( 78.80/10.73 (demorgan2b) => 78.80/10.73 (( 78.80/10.73 (demorgan2) => 78.80/10.73 (( 78.80/10.73 (woz13rule0) => 78.80/10.73 (( 78.80/10.73 (woz13rule1) => 78.80/10.73 (( 78.80/10.73 (woz13rule2) => 78.80/10.73 (( 78.80/10.73 (woz13rule3) => 78.80/10.73 (( 78.80/10.73 (woz13rule4) => 78.80/10.73 (( 78.80/10.73 (woz1_1) => 78.80/10.73 (( 78.80/10.73 (woz1_2) => 78.80/10.73 (( 78.80/10.73 (woz1_3) => 78.80/10.73 (( 78.80/10.73 (woz1_4) => 78.80/10.73 (( 78.80/10.73 (woz1_5) => 78.80/10.73 (( 78.80/10.73 (breln1all2) => 78.80/10.73 (( 78.80/10.73 (breln1SetBreln1) => 78.80/10.73 (( 78.80/10.73 (choice2fnsingleton) => 78.80/10.73 (( 78.80/10.73 (setOfPairsIsBReln1) => 78.80/10.73 (( 78.80/10.73 (breln1all1) => 78.80/10.73 (( 78.80/10.73 (subbreln1) => 78.80/10.73 (( 78.80/10.73 (eqbreln1) => 78.80/10.73 (( 78.80/10.73 (breln1invprop) => 78.80/10.73 (( 78.80/10.73 (breln1invI) => 78.80/10.73 (( 78.80/10.73 (breln1invE) => 78.80/10.73 (( 78.80/10.73 (breln1compprop) => 78.80/10.73 (( 78.80/10.73 (breln1compI) => 78.80/10.73 (( 78.80/10.73 (breln1compE) => 78.80/10.73 (( 78.80/10.73 (breln1compEex) => 78.80/10.73 (( 78.80/10.73 (breln1unionprop) => 78.80/10.73 (( 78.80/10.73 (breln1unionIL) => 78.80/10.73 (( 78.80/10.73 (breln1unionIR) => 78.80/10.73 (( 78.80/10.73 (breln1unionI) => 78.80/10.73 (( 78.80/10.73 (breln1unionE) => 78.80/10.73 (( 78.80/10.73 (breln1unionEcases) => 78.80/10.73 (( 78.80/10.73 (breln1unionCommutes) => 78.80/10.73 (( 78.80/10.73 (woz2Ex) => 78.80/10.73 (( 78.80/10.73 (woz2W) => 78.80/10.73 (( 78.80/10.73 (woz2A) => 78.80/10.73 (( 78.80/10.73 (woz2B) => 78.80/10.73 (( 78.80/10.73 (image1Ex) => 78.80/10.73 (( 78.80/10.73 (image1Ex1) => 78.80/10.73 (( 78.80/10.73 (image1Equiv) => 78.80/10.73 (( 78.80/10.73 (image1E) => 78.80/10.73 (( 78.80/10.73 (image1I) => 78.80/10.73 (( 78.80/10.73 (injFuncInInjFuncSet) => 78.80/10.73 (( 78.80/10.73 (injFuncSetFuncIn) => 78.80/10.73 (( 78.80/10.73 (injFuncSetFuncInj) => 78.80/10.73 (( 78.80/10.73 (surjFuncSetFuncIn) => 78.80/10.73 (( 78.80/10.73 (surjFuncSetFuncSurj) => 78.80/10.73 (( 78.80/10.73 (leftInvIsSurj) => 78.80/10.73 (( 78.80/10.73 (surjCantorThm) => 78.80/10.73 (( 78.80/10.73 (foundation2) => 78.80/10.73 (( 78.80/10.73 (notinself) => 78.80/10.73 (( 78.80/10.73 (notinself2) => 78.80/10.73 (( 78.80/10.73 (omegaSp) => 78.80/10.73 (( 78.80/10.73 (omegaSclos) => 78.80/10.73 (( 78.80/10.73 (peano0notS) => 78.80/10.73 (( 78.80/10.73 (peanoSinj) => 78.80/10.73 (( 78.80/10.73 (transitivesetOp1) => 78.80/10.73 (( 78.80/10.73 (binintTransitive) => 78.80/10.73 (( 78.80/10.73 (transitivesetOp2) => 78.80/10.73 (( 78.80/10.73 (setunionTransitive) => 78.80/10.73 (( 78.80/10.73 (ordinalMinLem1) => 78.80/10.73 (( 78.80/10.73 (!!) @ ( 78.80/10.73 ^[Y0 : $i]: 78.80/10.73 (( 78.80/10.73 (ordinal @ 78.80/10.73 Y0) => 78.80/10.73 (( 78.80/10.73 (!!) @ ( 78.80/10.73 ^[Y1 : $i]: 78.80/10.73 (( 78.80/10.73 (!!) @ ( 78.80/10.73 ^[Y2 : $i]: 78.80/10.73 (( 78.80/10.73 (in @ 78.80/10.73 Y2 @ 78.80/10.73 Y0) => 78.80/10.73 (( 78.80/10.73 (in @ 78.80/10.73 Y1 @ 78.80/10.73 Y2) => 78.80/10.73 (in @ 78.80/10.73 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 78.80/10.73 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1890])). 78.80/10.73 thf(zip_derived_cl1916, plain, 78.80/10.73 (~ (((beta2) => 78.80/10.73 (((eta2) => 78.80/10.73 (((iffalseProp1) => 78.80/10.73 (((iffalseProp2) => 78.80/10.73 (((iftrueProp1) => 78.80/10.73 (((iftrueProp2) => 78.80/10.73 (((ifSingleton) => 78.80/10.73 (((ifp) => 78.80/10.73 (((theeq) => 78.80/10.73 (((iftrue) => 78.80/10.73 (((iffalse) => 78.80/10.73 (((iftrueorfalse) => 78.80/10.73 (((binintersectT_lem) => 78.80/10.73 (((binunionT_lem) => 78.80/10.73 (((powersetT_lem) => 78.80/10.73 (((setminusT_lem) => 78.80/10.73 (((complementT_lem) => 78.80/10.73 (((setextT) => 78.80/10.73 (((subsetTI) => 78.80/10.73 (((powersetTI1) => 78.80/10.73 (((powersetTE1) => 78.80/10.73 (((complementTI1) => 78.80/10.73 (((complementTE1) => 78.80/10.73 (((binintersectTELcontra) => 78.80/10.73 (((binintersectTERcontra) => 78.80/10.73 (((contrasubsetT) => 78.80/10.73 (((contrasubsetT1) => 78.80/10.73 (((contrasubsetT2) => 78.80/10.73 (((contrasubsetT3) => 78.80/10.73 (((doubleComplementI1) => 78.80/10.73 (( 78.80/10.73 (doubleComplementE1) => 78.80/10.73 (( 78.80/10.73 (doubleComplementSub1) => 78.80/10.73 (( 78.80/10.73 (doubleComplementSub2) => 78.80/10.73 (( 78.80/10.73 (doubleComplementEq) => 78.80/10.73 (( 78.80/10.73 (complementTnotintersectT) => 78.80/10.73 (( 78.80/10.73 (complementImpComplementIntersect) => 78.80/10.73 (( 78.80/10.73 (complementSubsetComplementIntersect) => 78.80/10.73 (( 78.80/10.73 (complementInPowersetComplementIntersect) => 78.80/10.73 (( 78.80/10.73 (contraSubsetComplement) => 78.80/10.73 (( 78.80/10.73 (complementTcontraSubset) => 78.80/10.73 (( 78.80/10.73 (binunionTILcontra) => 78.80/10.73 (( 78.80/10.73 (binunionTIRcontra) => 78.80/10.73 (( 78.80/10.73 (inIntersectImpInUnion) => 78.80/10.73 (( 78.80/10.73 (inIntersectImpInUnion2) => 78.80/10.73 (( 78.80/10.73 (inIntersectImpInIntersectUnions) => 78.80/10.73 (( 78.80/10.73 (intersectInPowersetIntersectUnions) => 78.80/10.73 (( 78.80/10.73 (inComplementUnionImpNotIn1) => 78.80/10.73 (( 78.80/10.73 (inComplementUnionImpInComplement1) => 78.80/10.73 (( 78.80/10.73 (binunionTE) => 78.80/10.73 (( 78.80/10.73 (binunionTEcontra) => 78.80/10.73 (( 78.80/10.73 (demorgan2a1) => 78.80/10.73 (( 78.80/10.73 (complementUnionInPowersetComplement) => 78.80/10.73 (( 78.80/10.73 (demorgan2a2) => 78.80/10.73 (( 78.80/10.73 (demorgan1a) => 78.80/10.73 (( 78.80/10.73 (demorgan1b) => 78.80/10.73 (( 78.80/10.73 (demorgan1) => 78.80/10.73 (( 78.80/10.73 (demorgan2a) => 78.80/10.73 (( 78.80/10.73 (demorgan2b2) => 78.80/10.73 (( 78.80/10.73 (demorgan2b) => 78.80/10.73 (( 78.80/10.73 (demorgan2) => 78.80/10.73 (( 78.80/10.73 (woz13rule0) => 78.80/10.73 (( 78.80/10.73 (woz13rule1) => 78.80/10.73 (( 78.80/10.73 (woz13rule2) => 78.80/10.73 (( 78.80/10.73 (woz13rule3) => 78.80/10.73 (( 78.80/10.73 (woz13rule4) => 78.80/10.73 (( 78.80/10.73 (woz1_1) => 78.80/10.73 (( 78.80/10.73 (woz1_2) => 78.80/10.73 (( 78.80/10.73 (woz1_3) => 78.80/10.73 (( 78.80/10.73 (woz1_4) => 78.80/10.73 (( 78.80/10.73 (woz1_5) => 78.80/10.73 (( 78.80/10.73 (breln1all2) => 78.80/10.73 (( 78.80/10.73 (breln1SetBreln1) => 78.80/10.73 (( 78.80/10.73 (choice2fnsingleton) => 78.80/10.73 (( 78.80/10.73 (setOfPairsIsBReln1) => 78.80/10.73 (( 78.80/10.73 (breln1all1) => 78.80/10.73 (( 78.80/10.73 (subbreln1) => 78.80/10.73 (( 78.80/10.73 (eqbreln1) => 78.80/10.73 (( 78.80/10.73 (breln1invprop) => 78.80/10.73 (( 78.80/10.73 (breln1invI) => 78.80/10.73 (( 78.80/10.73 (breln1invE) => 78.80/10.73 (( 78.80/10.73 (breln1compprop) => 78.80/10.73 (( 78.80/10.73 (breln1compI) => 78.80/10.73 (( 78.80/10.73 (breln1compE) => 78.80/10.73 (( 78.80/10.73 (breln1compEex) => 78.80/10.73 (( 78.80/10.73 (breln1unionprop) => 78.80/10.73 (( 78.80/10.73 (breln1unionIL) => 78.80/10.73 (( 78.80/10.73 (breln1unionIR) => 78.80/10.73 (( 78.80/10.73 (breln1unionI) => 78.80/10.73 (( 78.80/10.73 (breln1unionE) => 78.80/10.73 (( 78.80/10.73 (breln1unionEcases) => 78.80/10.73 (( 78.80/10.73 (breln1unionCommutes) => 78.80/10.73 (( 78.80/10.73 (woz2Ex) => 78.80/10.73 (( 78.80/10.73 (woz2W) => 78.80/10.73 (( 78.80/10.73 (woz2A) => 78.80/10.73 (( 78.80/10.73 (woz2B) => 78.80/10.73 (( 78.80/10.73 (image1Ex) => 78.80/10.73 (( 78.80/10.73 (image1Ex1) => 78.80/10.73 (( 78.80/10.73 (image1Equiv) => 78.80/10.73 (( 78.80/10.73 (image1E) => 78.80/10.73 (( 78.80/10.73 (image1I) => 78.80/10.73 (( 78.80/10.73 (injFuncInInjFuncSet) => 78.80/10.73 (( 78.80/10.73 (injFuncSetFuncIn) => 78.80/10.73 (( 78.80/10.73 (injFuncSetFuncInj) => 78.80/10.73 (( 78.80/10.73 (surjFuncSetFuncIn) => 78.80/10.73 (( 78.80/10.73 (surjFuncSetFuncSurj) => 78.80/10.73 (( 78.80/10.73 (leftInvIsSurj) => 78.80/10.73 (( 78.80/10.73 (surjCantorThm) => 78.80/10.73 (( 78.80/10.73 (foundation2) => 78.80/10.73 (( 78.80/10.73 (notinself) => 78.80/10.73 (( 78.80/10.73 (notinself2) => 78.80/10.73 (( 78.80/10.73 (omegaSp) => 78.80/10.73 (( 78.80/10.73 (omegaSclos) => 78.80/10.73 (( 78.80/10.73 (peano0notS) => 78.80/10.73 (( 78.80/10.73 (peanoSinj) => 78.80/10.73 (( 78.80/10.73 (transitivesetOp1) => 78.80/10.73 (( 78.80/10.73 (binintTransitive) => 78.80/10.73 (( 78.80/10.73 (transitivesetOp2) => 78.80/10.73 (( 78.80/10.73 (setunionTransitive) => 78.80/10.73 (( 78.80/10.73 (ordinalMinLem1) => 78.80/10.73 (( 78.80/10.73 (!!) @ ( 78.80/10.73 ^[Y0 : $i]: 78.80/10.73 (( 78.80/10.73 (ordinal @ 78.80/10.73 Y0) => 78.80/10.73 (( 78.80/10.73 (!!) @ ( 78.80/10.73 ^[Y1 : $i]: 78.80/10.73 (( 78.80/10.73 (!!) @ ( 78.80/10.73 ^[Y2 : $i]: 78.80/10.73 (( 78.80/10.73 (in @ 78.80/10.73 Y2 @ 78.80/10.73 Y0) => 78.80/10.73 (( 78.80/10.73 (in @ 78.80/10.73 Y1 @ 78.80/10.73 Y2) => 78.80/10.73 (in @ 78.80/10.73 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 78.80/10.73 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1903])). 78.80/10.73 thf(zip_derived_cl1930, plain, 78.80/10.73 (~ (((eta2) => 78.80/10.73 (((iffalseProp1) => 78.80/10.73 (((iffalseProp2) => 78.80/10.73 (((iftrueProp1) => 78.80/10.73 (((iftrueProp2) => 78.80/10.73 (((ifSingleton) => 78.80/10.73 (((ifp) => 78.80/10.73 (((theeq) => 78.80/10.73 (((iftrue) => 78.80/10.73 (((iffalse) => 78.80/10.73 (((iftrueorfalse) => 78.80/10.73 (((binintersectT_lem) => 78.80/10.73 (((binunionT_lem) => 78.80/10.73 (((powersetT_lem) => 78.80/10.73 (((setminusT_lem) => 78.80/10.73 (((complementT_lem) => 78.80/10.73 (((setextT) => 78.80/10.73 (((subsetTI) => 78.80/10.73 (((powersetTI1) => 78.80/10.73 (((powersetTE1) => 78.80/10.73 (((complementTI1) => 78.80/10.73 (((complementTE1) => 78.80/10.73 (((binintersectTELcontra) => 78.80/10.73 (((binintersectTERcontra) => 78.80/10.73 (((contrasubsetT) => 78.80/10.73 (((contrasubsetT1) => 78.80/10.73 (((contrasubsetT2) => 78.80/10.73 (((contrasubsetT3) => 78.80/10.73 (((doubleComplementI1) => 78.80/10.73 (((doubleComplementE1) => 78.80/10.73 (( 78.80/10.73 (doubleComplementSub1) => 78.80/10.73 (( 78.80/10.73 (doubleComplementSub2) => 78.80/10.73 (( 78.80/10.73 (doubleComplementEq) => 78.80/10.73 (( 78.80/10.73 (complementTnotintersectT) => 78.80/10.73 (( 78.80/10.73 (complementImpComplementIntersect) => 78.80/10.73 (( 78.80/10.73 (complementSubsetComplementIntersect) => 78.80/10.73 (( 78.80/10.73 (complementInPowersetComplementIntersect) => 78.80/10.73 (( 78.80/10.73 (contraSubsetComplement) => 78.80/10.73 (( 78.80/10.73 (complementTcontraSubset) => 78.80/10.73 (( 78.80/10.73 (binunionTILcontra) => 78.80/10.73 (( 78.80/10.73 (binunionTIRcontra) => 78.80/10.73 (( 78.80/10.73 (inIntersectImpInUnion) => 78.80/10.73 (( 78.80/10.73 (inIntersectImpInUnion2) => 78.80/10.73 (( 78.80/10.73 (inIntersectImpInIntersectUnions) => 78.80/10.73 (( 78.80/10.73 (intersectInPowersetIntersectUnions) => 78.80/10.73 (( 78.80/10.73 (inComplementUnionImpNotIn1) => 78.80/10.73 (( 78.80/10.73 (inComplementUnionImpInComplement1) => 78.80/10.73 (( 78.80/10.73 (binunionTE) => 78.80/10.73 (( 78.80/10.73 (binunionTEcontra) => 78.80/10.73 (( 78.80/10.73 (demorgan2a1) => 78.80/10.73 (( 78.80/10.73 (complementUnionInPowersetComplement) => 78.80/10.73 (( 78.80/10.73 (demorgan2a2) => 78.80/10.73 (( 78.80/10.73 (demorgan1a) => 78.80/10.73 (( 78.80/10.73 (demorgan1b) => 78.80/10.73 (( 78.80/10.73 (demorgan1) => 78.80/10.73 (( 78.80/10.73 (demorgan2a) => 78.80/10.73 (( 78.80/10.73 (demorgan2b2) => 78.80/10.73 (( 78.80/10.73 (demorgan2b) => 78.80/10.73 (( 78.80/10.73 (demorgan2) => 78.80/10.73 (( 78.80/10.73 (woz13rule0) => 78.80/10.73 (( 78.80/10.73 (woz13rule1) => 78.80/10.73 (( 78.80/10.73 (woz13rule2) => 78.80/10.73 (( 78.80/10.73 (woz13rule3) => 78.80/10.73 (( 78.80/10.73 (woz13rule4) => 78.80/10.73 (( 78.80/10.73 (woz1_1) => 78.80/10.73 (( 78.80/10.73 (woz1_2) => 78.80/10.73 (( 78.80/10.73 (woz1_3) => 78.80/10.73 (( 78.80/10.73 (woz1_4) => 78.80/10.73 (( 78.80/10.73 (woz1_5) => 78.80/10.73 (( 78.80/10.73 (breln1all2) => 78.80/10.73 (( 78.80/10.73 (breln1SetBreln1) => 78.80/10.73 (( 78.80/10.73 (choice2fnsingleton) => 78.80/10.73 (( 78.80/10.73 (setOfPairsIsBReln1) => 78.80/10.73 (( 78.80/10.73 (breln1all1) => 78.80/10.73 (( 78.80/10.73 (subbreln1) => 78.80/10.73 (( 78.80/10.73 (eqbreln1) => 78.80/10.73 (( 78.80/10.73 (breln1invprop) => 78.80/10.73 (( 78.80/10.73 (breln1invI) => 78.80/10.73 (( 78.80/10.73 (breln1invE) => 78.80/10.73 (( 78.80/10.73 (breln1compprop) => 78.80/10.73 (( 78.80/10.73 (breln1compI) => 78.80/10.73 (( 78.80/10.73 (breln1compE) => 78.80/10.73 (( 78.80/10.73 (breln1compEex) => 78.80/10.73 (( 78.80/10.73 (breln1unionprop) => 78.80/10.73 (( 78.80/10.73 (breln1unionIL) => 78.80/10.73 (( 78.80/10.73 (breln1unionIR) => 78.80/10.73 (( 78.80/10.73 (breln1unionI) => 78.80/10.73 (( 78.80/10.73 (breln1unionE) => 78.80/10.73 (( 78.80/10.73 (breln1unionEcases) => 78.80/10.73 (( 78.80/10.73 (breln1unionCommutes) => 78.80/10.73 (( 78.80/10.73 (woz2Ex) => 78.80/10.73 (( 78.80/10.73 (woz2W) => 78.80/10.73 (( 78.80/10.73 (woz2A) => 78.80/10.73 (( 78.80/10.73 (woz2B) => 78.80/10.73 (( 78.80/10.73 (image1Ex) => 78.80/10.73 (( 78.80/10.73 (image1Ex1) => 78.80/10.73 (( 78.80/10.73 (image1Equiv) => 78.80/10.73 (( 78.80/10.73 (image1E) => 78.80/10.73 (( 78.80/10.73 (image1I) => 78.80/10.73 (( 78.80/10.73 (injFuncInInjFuncSet) => 78.80/10.73 (( 78.80/10.73 (injFuncSetFuncIn) => 78.80/10.73 (( 78.80/10.73 (injFuncSetFuncInj) => 78.80/10.73 (( 78.80/10.73 (surjFuncSetFuncIn) => 78.80/10.73 (( 78.80/10.73 (surjFuncSetFuncSurj) => 78.80/10.73 (( 78.80/10.73 (leftInvIsSurj) => 78.80/10.73 (( 78.80/10.73 (surjCantorThm) => 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=> 78.80/10.73 (( 78.80/10.73 (woz13rule4) => 78.80/10.73 (( 78.80/10.73 (woz1_1) => 78.80/10.73 (( 78.80/10.73 (woz1_2) => 78.80/10.73 (( 78.80/10.73 (woz1_3) => 78.80/10.73 (( 78.80/10.73 (woz1_4) => 78.80/10.73 (( 78.80/10.73 (woz1_5) => 78.80/10.73 (( 78.80/10.73 (breln1all2) => 78.80/10.73 (( 78.80/10.73 (breln1SetBreln1) => 78.80/10.73 (( 78.80/10.73 (choice2fnsingleton) => 78.80/10.73 (( 78.80/10.73 (setOfPairsIsBReln1) => 78.80/10.73 (( 78.80/10.73 (breln1all1) => 78.80/10.73 (( 78.80/10.73 (subbreln1) => 78.80/10.73 (( 78.80/10.73 (eqbreln1) => 78.80/10.73 (( 78.80/10.73 (breln1invprop) => 78.80/10.73 (( 78.80/10.73 (breln1invI) => 78.80/10.73 (( 78.80/10.73 (breln1invE) => 78.80/10.73 (( 78.80/10.73 (breln1compprop) => 78.80/10.73 (( 78.80/10.73 (breln1compI) => 78.80/10.73 (( 78.80/10.73 (breln1compE) => 78.80/10.73 (( 78.80/10.73 (breln1compEex) => 78.80/10.73 (( 78.80/10.73 (breln1unionprop) => 78.80/10.73 (( 78.80/10.73 (breln1unionIL) => 78.80/10.73 (( 78.80/10.73 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Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 78.80/10.73 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1960])). 78.80/10.73 thf(zip_derived_cl2001, plain, 78.80/10.73 (~ (((iftrueProp2) => 78.80/10.73 (((ifSingleton) => 78.80/10.73 (((ifp) => 78.80/10.73 (((theeq) => 78.80/10.73 (((iftrue) => 78.80/10.73 (((iffalse) => 78.80/10.73 (((iftrueorfalse) => 78.80/10.73 (((binintersectT_lem) => 78.80/10.73 (((binunionT_lem) => 78.80/10.73 (((powersetT_lem) => 78.80/10.73 (((setminusT_lem) => 78.80/10.73 (((complementT_lem) => 78.80/10.73 (((setextT) => 78.80/10.73 (((subsetTI) => 78.80/10.73 (((powersetTI1) => 78.80/10.73 (((powersetTE1) => 78.80/10.73 (((complementTI1) => 78.80/10.73 (((complementTE1) => 78.80/10.73 (((binintersectTELcontra) => 78.80/10.73 (((binintersectTERcontra) => 78.80/10.73 (((contrasubsetT) => 78.80/10.73 (((contrasubsetT1) => 78.80/10.73 (((contrasubsetT2) => 78.80/10.73 (((contrasubsetT3) => 78.80/10.73 (((doubleComplementI1) => 78.80/10.73 (((doubleComplementE1) => 78.80/10.73 (((doubleComplementSub1) => 78.80/10.73 (((doubleComplementSub2) => 78.80/10.73 (((doubleComplementEq) => 78.80/10.73 (((complementTnotintersectT) => 78.80/10.73 (( 78.80/10.73 (complementImpComplementIntersect) => 78.80/10.73 (( 78.80/10.73 (complementSubsetComplementIntersect) => 78.80/10.73 (( 78.80/10.73 (complementInPowersetComplementIntersect) => 78.80/10.73 (( 78.80/10.73 (contraSubsetComplement) => 78.80/10.73 (( 78.80/10.73 (complementTcontraSubset) => 78.80/10.73 (( 78.80/10.73 (binunionTILcontra) => 78.80/10.73 (( 78.80/10.73 (binunionTIRcontra) => 78.80/10.73 (( 78.80/10.73 (inIntersectImpInUnion) => 78.80/10.73 (( 78.80/10.73 (inIntersectImpInUnion2) => 78.80/10.73 (( 78.80/10.73 (inIntersectImpInIntersectUnions) => 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(breln1unionE) => 78.80/10.73 (( 78.80/10.73 (breln1unionEcases) => 78.80/10.73 (( 78.80/10.73 (breln1unionCommutes) => 78.80/10.73 (( 78.80/10.73 (woz2Ex) => 78.80/10.73 (( 78.80/10.73 (woz2W) => 78.80/10.73 (( 78.80/10.73 (woz2A) => 78.80/10.73 (( 78.80/10.73 (woz2B) => 78.80/10.73 (( 78.80/10.73 (image1Ex) => 78.80/10.73 (( 78.80/10.73 (image1Ex1) => 78.80/10.73 (( 78.80/10.73 (image1Equiv) => 78.80/10.73 (( 78.80/10.73 (image1E) => 78.80/10.73 (( 78.80/10.73 (image1I) => 78.80/10.73 (( 78.80/10.73 (injFuncInInjFuncSet) => 78.80/10.73 (( 78.80/10.73 (injFuncSetFuncIn) => 78.80/10.73 (( 78.80/10.73 (injFuncSetFuncInj) => 78.80/10.73 (( 78.80/10.73 (surjFuncSetFuncIn) => 78.80/10.73 (( 78.80/10.73 (surjFuncSetFuncSurj) => 78.80/10.73 (( 78.80/10.73 (leftInvIsSurj) => 78.80/10.73 (( 78.80/10.73 (surjCantorThm) => 78.80/10.73 (( 78.80/10.73 (foundation2) => 78.80/10.73 (( 78.80/10.73 (notinself) => 78.80/10.73 (( 78.80/10.73 (notinself2) => 78.80/10.73 (( 78.80/10.73 (omegaSp) => 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Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 78.80/10.73 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1982])). 78.80/10.73 thf(zip_derived_cl2017, plain, 78.80/10.73 (~ (((ifSingleton) => 78.80/10.73 (((ifp) => 78.80/10.73 (((theeq) => 78.80/10.73 (((iftrue) => 78.80/10.73 (((iffalse) => 78.80/10.73 (((iftrueorfalse) => 78.80/10.73 (((binintersectT_lem) => 78.80/10.73 (((binunionT_lem) => 78.80/10.73 (((powersetT_lem) => 78.80/10.73 (((setminusT_lem) => 78.80/10.73 (((complementT_lem) => 78.80/10.73 (((setextT) => 78.80/10.73 (((subsetTI) => 78.80/10.73 (((powersetTI1) => 78.80/10.73 (((powersetTE1) => 78.80/10.73 (((complementTI1) => 78.80/10.73 (((complementTE1) => 78.80/10.73 (((binintersectTELcontra) => 78.80/10.73 (((binintersectTERcontra) => 78.80/10.73 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(woz1_3) => 78.80/10.73 (( 78.80/10.73 (woz1_4) => 78.80/10.73 (( 78.80/10.73 (woz1_5) => 78.80/10.73 (( 78.80/10.73 (breln1all2) => 78.80/10.73 (( 78.80/10.73 (breln1SetBreln1) => 78.80/10.73 (( 78.80/10.73 (choice2fnsingleton) => 78.80/10.73 (( 78.80/10.73 (setOfPairsIsBReln1) => 78.80/10.73 (( 78.80/10.73 (breln1all1) => 78.80/10.73 (( 78.80/10.73 (subbreln1) => 78.80/10.73 (( 78.80/10.73 (eqbreln1) => 78.80/10.73 (( 78.80/10.73 (breln1invprop) => 78.80/10.73 (( 78.80/10.73 (breln1invI) => 78.80/10.73 (( 78.80/10.73 (breln1invE) => 78.80/10.73 (( 78.80/10.73 (breln1compprop) => 78.80/10.73 (( 78.80/10.73 (breln1compI) => 78.80/10.73 (( 78.80/10.73 (breln1compE) => 78.80/10.73 (( 78.80/10.73 (breln1compEex) => 78.80/10.73 (( 78.80/10.73 (breln1unionprop) => 78.80/10.73 (( 78.80/10.73 (breln1unionIL) => 78.80/10.73 (( 78.80/10.73 (breln1unionIR) => 78.80/10.73 (( 78.80/10.73 (breln1unionI) => 78.80/10.73 (( 78.80/10.73 (breln1unionE) => 78.80/10.73 (( 78.80/10.73 (breln1unionEcases) => 78.80/10.73 (( 78.80/10.73 (breln1unionCommutes) => 78.80/10.73 (( 78.80/10.73 (woz2Ex) => 78.80/10.73 (( 78.80/10.73 (woz2W) => 78.80/10.73 (( 78.80/10.73 (woz2A) => 78.80/10.73 (( 78.80/10.73 (woz2B) => 78.80/10.73 (( 78.80/10.73 (image1Ex) => 78.80/10.73 (( 78.80/10.73 (image1Ex1) => 78.80/10.73 (( 78.80/10.73 (image1Equiv) => 78.80/10.73 (( 78.80/10.73 (image1E) => 78.80/10.73 (( 78.80/10.73 (image1I) => 78.80/10.73 (( 78.80/10.73 (injFuncInInjFuncSet) => 78.80/10.73 (( 78.80/10.73 (injFuncSetFuncIn) => 78.80/10.73 (( 78.80/10.73 (injFuncSetFuncInj) => 78.80/10.73 (( 78.80/10.73 (surjFuncSetFuncIn) => 78.80/10.73 (( 78.80/10.73 (surjFuncSetFuncSurj) => 78.80/10.73 (( 78.80/10.73 (leftInvIsSurj) => 78.80/10.73 (( 78.80/10.73 (surjCantorThm) => 78.80/10.73 (( 78.80/10.73 (foundation2) => 78.80/10.73 (( 78.80/10.73 (notinself) => 78.80/10.73 (( 78.80/10.73 (notinself2) => 78.80/10.73 (( 78.80/10.73 (omegaSp) => 78.80/10.73 (( 78.80/10.73 (omegaSclos) => 78.80/10.73 (( 78.80/10.73 (peano0notS) => 78.80/10.73 (( 78.80/10.73 (peanoSinj) => 78.80/10.73 (( 78.80/10.73 (transitivesetOp1) => 78.80/10.73 (( 78.80/10.73 (binintTransitive) => 78.80/10.73 (( 78.80/10.73 (transitivesetOp2) => 78.80/10.73 (( 78.80/10.73 (setunionTransitive) => 78.80/10.73 (( 78.80/10.73 (ordinalMinLem1) => 78.80/10.73 (( 78.80/10.73 (!!) @ ( 78.80/10.73 ^[Y0 : $i]: 78.80/10.73 (( 78.80/10.73 (ordinal @ 78.80/10.73 Y0) => 78.80/10.73 (( 78.80/10.73 (!!) @ ( 78.80/10.73 ^[Y1 : $i]: 78.80/10.73 (( 78.80/10.73 (!!) @ ( 78.80/10.73 ^[Y2 : $i]: 78.80/10.73 (( 78.80/10.73 (in @ 78.80/10.73 Y2 @ 78.80/10.73 Y0) => 78.80/10.73 (( 78.80/10.73 (in @ 78.80/10.73 Y1 @ 78.80/10.73 Y2) => 78.80/10.73 (in @ 78.80/10.73 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 78.80/10.73 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2001])). 78.80/10.73 thf(zip_derived_cl2029, plain, 78.80/10.73 (~ (((ifp) => 78.80/10.73 (((theeq) => 78.80/10.73 (((iftrue) => 78.80/10.73 (((iffalse) => 78.80/10.73 (((iftrueorfalse) => 78.80/10.73 (((binintersectT_lem) => 78.80/10.73 (((binunionT_lem) => 78.80/10.73 (((powersetT_lem) => 78.80/10.73 (((setminusT_lem) => 78.80/10.73 (((complementT_lem) => 78.80/10.73 (((setextT) => 78.80/10.73 (((subsetTI) => 78.80/10.73 (((powersetTI1) => 78.80/10.73 (((powersetTE1) => 78.80/10.73 (((complementTI1) => 78.80/10.73 (((complementTE1) => 78.80/10.73 (((binintersectTELcontra) => 78.80/10.73 (((binintersectTERcontra) => 78.80/10.73 (((contrasubsetT) => 78.80/10.73 (((contrasubsetT1) => 78.80/10.73 (((contrasubsetT2) => 78.80/10.73 (((contrasubsetT3) => 78.80/10.73 (((doubleComplementI1) => 78.80/10.73 (((doubleComplementE1) => 78.80/10.73 (((doubleComplementSub1) => 78.80/10.73 (((doubleComplementSub2) => 78.80/10.73 (((doubleComplementEq) => 78.80/10.73 (((complementTnotintersectT) => 78.80/10.73 (((complementImpComplementIntersect) => 78.80/10.73 (((complementSubsetComplementIntersect) => 78.80/10.73 (( 78.80/10.73 (complementInPowersetComplementIntersect) => 78.80/10.73 (( 78.80/10.73 (contraSubsetComplement) => 78.80/10.73 (( 78.80/10.73 (complementTcontraSubset) => 78.80/10.73 (( 78.80/10.73 (binunionTILcontra) => 78.80/10.73 (( 78.80/10.73 (binunionTIRcontra) => 78.80/10.73 (( 78.80/10.73 (inIntersectImpInUnion) => 78.80/10.73 (( 78.80/10.73 (inIntersectImpInUnion2) => 78.80/10.73 (( 78.80/10.73 (inIntersectImpInIntersectUnions) => 78.80/10.73 (( 78.80/10.73 (intersectInPowersetIntersectUnions) => 78.80/10.73 (( 78.80/10.73 (inComplementUnionImpNotIn1) => 78.80/10.73 (( 78.80/10.73 (inComplementUnionImpInComplement1) => 78.80/10.73 (( 78.80/10.73 (binunionTE) => 78.80/10.73 (( 78.80/10.73 (binunionTEcontra) => 78.80/10.73 (( 78.80/10.73 (demorgan2a1) => 78.80/10.73 (( 78.80/10.73 (complementUnionInPowersetComplement) => 78.80/10.73 (( 78.80/10.73 (demorgan2a2) => 78.80/10.73 (( 78.80/10.73 (demorgan1a) => 78.80/10.73 (( 78.80/10.73 (demorgan1b) => 78.80/10.73 (( 78.80/10.73 (demorgan1) => 78.80/10.73 (( 78.80/10.73 (demorgan2a) => 78.80/10.73 (( 78.80/10.73 (demorgan2b2) => 78.80/10.73 (( 78.80/10.73 (demorgan2b) => 78.80/10.73 (( 78.80/10.73 (demorgan2) => 78.80/10.73 (( 78.80/10.73 (woz13rule0) => 78.80/10.73 (( 78.80/10.73 (woz13rule1) => 78.80/10.73 (( 78.80/10.73 (woz13rule2) => 78.80/10.73 (( 78.80/10.73 (woz13rule3) => 78.80/10.73 (( 78.80/10.73 (woz13rule4) => 78.80/10.73 (( 78.80/10.73 (woz1_1) => 78.80/10.73 (( 78.80/10.73 (woz1_2) => 78.80/10.73 (( 78.80/10.73 (woz1_3) => 78.80/10.73 (( 78.80/10.73 (woz1_4) => 78.80/10.73 (( 78.80/10.73 (woz1_5) => 78.80/10.73 (( 78.80/10.73 (breln1all2) => 78.80/10.73 (( 78.80/10.73 (breln1SetBreln1) => 78.80/10.73 (( 78.80/10.73 (choice2fnsingleton) => 78.80/10.73 (( 78.80/10.73 (setOfPairsIsBReln1) => 78.80/10.73 (( 78.80/10.73 (breln1all1) => 78.80/10.73 (( 78.80/10.73 (subbreln1) => 78.80/10.73 (( 78.80/10.73 (eqbreln1) => 78.80/10.73 (( 78.80/10.73 (breln1invprop) => 78.80/10.73 (( 78.80/10.73 (breln1invI) => 78.80/10.73 (( 78.80/10.73 (breln1invE) => 78.80/10.73 (( 78.80/10.73 (breln1compprop) => 78.80/10.73 (( 78.80/10.73 (breln1compI) => 78.80/10.73 (( 78.80/10.73 (breln1compE) => 78.80/10.73 (( 78.80/10.73 (breln1compEex) => 78.80/10.73 (( 78.80/10.73 (breln1unionprop) => 78.80/10.73 (( 78.80/10.73 (breln1unionIL) => 78.80/10.73 (( 78.80/10.73 (breln1unionIR) => 78.80/10.73 (( 78.80/10.73 (breln1unionI) => 78.80/10.73 (( 78.80/10.73 (breln1unionE) => 78.80/10.73 (( 78.80/10.73 (breln1unionEcases) => 78.80/10.73 (( 78.80/10.73 (breln1unionCommutes) => 78.80/10.73 (( 78.80/10.73 (woz2Ex) => 78.80/10.73 (( 78.80/10.73 (woz2W) => 78.80/10.73 (( 78.80/10.73 (woz2A) => 78.80/10.73 (( 78.80/10.73 (woz2B) => 78.80/10.73 (( 78.80/10.73 (image1Ex) => 78.80/10.73 (( 78.80/10.73 (image1Ex1) => 78.80/10.73 (( 78.80/10.73 (image1Equiv) => 78.80/10.73 (( 78.80/10.73 (image1E) => 78.80/10.73 (( 78.80/10.73 (image1I) => 78.80/10.73 (( 78.80/10.73 (injFuncInInjFuncSet) => 78.80/10.73 (( 78.80/10.73 (injFuncSetFuncIn) => 78.80/10.73 (( 78.80/10.73 (injFuncSetFuncInj) => 78.80/10.73 (( 78.80/10.73 (surjFuncSetFuncIn) => 78.80/10.73 (( 78.80/10.73 (surjFuncSetFuncSurj) => 78.80/10.73 (( 78.80/10.73 (leftInvIsSurj) => 78.80/10.73 (( 78.80/10.73 (surjCantorThm) => 78.80/10.73 (( 78.80/10.73 (foundation2) => 78.80/10.73 (( 78.80/10.73 (notinself) => 78.80/10.73 (( 78.80/10.73 (notinself2) => 78.80/10.73 (( 78.80/10.73 (omegaSp) => 78.80/10.73 (( 78.80/10.73 (omegaSclos) => 78.80/10.73 (( 78.80/10.73 (peano0notS) => 78.80/10.73 (( 78.80/10.73 (peanoSinj) => 78.80/10.73 (( 78.80/10.73 (transitivesetOp1) => 78.80/10.73 (( 78.80/10.73 (binintTransitive) => 78.80/10.73 (( 78.80/10.73 (transitivesetOp2) => 78.80/10.73 (( 78.80/10.73 (setunionTransitive) => 78.80/10.73 (( 78.80/10.73 (ordinalMinLem1) => 78.80/10.73 (( 78.80/10.73 (!!) @ ( 78.80/10.73 ^[Y0 : $i]: 78.80/10.73 (( 78.80/10.73 (ordinal @ 78.80/10.73 Y0) => 78.80/10.73 (( 78.80/10.73 (!!) @ ( 78.80/10.73 ^[Y1 : $i]: 78.80/10.73 (( 78.80/10.73 (!!) @ ( 78.80/10.73 ^[Y2 : $i]: 78.80/10.73 (( 78.80/10.73 (in @ 78.80/10.73 Y2 @ 78.80/10.73 Y0) => 78.80/10.73 (( 78.80/10.73 (in @ 78.80/10.73 Y1 @ 78.80/10.73 Y2) => 78.80/10.73 (in @ 78.80/10.73 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 78.80/10.73 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2017])). 78.80/10.73 thf(zip_derived_cl2041, plain, 78.80/10.73 (~ (((theeq) => 78.80/10.73 (((iftrue) => 78.80/10.73 (((iffalse) => 78.80/10.73 (((iftrueorfalse) => 78.80/10.73 (((binintersectT_lem) => 78.80/10.73 (((binunionT_lem) => 78.80/10.73 (((powersetT_lem) => 78.80/10.73 (((setminusT_lem) => 78.80/10.73 (((complementT_lem) => 78.80/10.73 (((setextT) => 78.80/10.73 (((subsetTI) => 78.80/10.73 (((powersetTI1) => 78.80/10.73 (((powersetTE1) => 78.80/10.73 (((complementTI1) => 78.80/10.73 (((complementTE1) => 78.80/10.73 (((binintersectTELcontra) => 78.80/10.73 (((binintersectTERcontra) => 78.80/10.73 (((contrasubsetT) => 78.80/10.73 (((contrasubsetT1) => 78.80/10.73 (((contrasubsetT2) => 78.80/10.73 (((contrasubsetT3) => 78.80/10.73 (((doubleComplementI1) => 78.80/10.73 (((doubleComplementE1) => 78.80/10.73 (((doubleComplementSub1) => 78.80/10.73 (((doubleComplementSub2) => 78.80/10.73 (((doubleComplementEq) => 78.80/10.73 (((complementTnotintersectT) => 78.80/10.73 (((complementImpComplementIntersect) => 78.80/10.73 (((complementSubsetComplementIntersect) => 78.80/10.73 (((complementInPowersetComplementIntersect) => 78.80/10.73 (( 78.80/10.73 (contraSubsetComplement) => 78.80/10.73 (( 78.80/10.73 (complementTcontraSubset) => 78.80/10.73 (( 78.80/10.73 (binunionTILcontra) => 78.80/10.73 (( 78.80/10.73 (binunionTIRcontra) => 78.80/10.73 (( 78.80/10.73 (inIntersectImpInUnion) => 78.80/10.73 (( 78.80/10.73 (inIntersectImpInUnion2) => 78.80/10.73 (( 78.80/10.73 (inIntersectImpInIntersectUnions) => 78.80/10.73 (( 78.80/10.73 (intersectInPowersetIntersectUnions) => 78.80/10.73 (( 78.80/10.73 (inComplementUnionImpNotIn1) => 78.80/10.73 (( 78.80/10.73 (inComplementUnionImpInComplement1) => 78.80/10.73 (( 78.80/10.73 (binunionTE) => 78.80/10.73 (( 78.80/10.73 (binunionTEcontra) => 78.80/10.73 (( 78.80/10.73 (demorgan2a1) => 78.80/10.73 (( 78.80/10.73 (complementUnionInPowersetComplement) => 78.80/10.73 (( 78.80/10.73 (demorgan2a2) => 78.80/10.73 (( 78.80/10.73 (demorgan1a) => 78.80/10.73 (( 78.80/10.73 (demorgan1b) => 78.80/10.73 (( 78.80/10.73 (demorgan1) => 78.80/10.73 (( 78.80/10.73 (demorgan2a) => 78.80/10.73 (( 78.80/10.73 (demorgan2b2) => 78.80/10.73 (( 78.80/10.73 (demorgan2b) => 78.80/10.73 (( 78.80/10.73 (demorgan2) => 78.80/10.73 (( 78.80/10.73 (woz13rule0) => 78.80/10.73 (( 78.80/10.73 (woz13rule1) => 78.80/10.73 (( 78.80/10.73 (woz13rule2) => 78.80/10.73 (( 78.80/10.73 (woz13rule3) => 78.80/10.73 (( 78.80/10.73 (woz13rule4) => 78.80/10.73 (( 78.80/10.73 (woz1_1) => 78.80/10.73 (( 78.80/10.73 (woz1_2) => 78.80/10.73 (( 78.80/10.73 (woz1_3) => 78.80/10.73 (( 78.80/10.73 (woz1_4) => 78.80/10.73 (( 78.80/10.73 (woz1_5) => 78.80/10.73 (( 78.80/10.73 (breln1all2) => 78.80/10.73 (( 78.80/10.73 (breln1SetBreln1) => 78.80/10.73 (( 78.80/10.73 (choice2fnsingleton) => 78.80/10.73 (( 78.80/10.73 (setOfPairsIsBReln1) => 78.80/10.73 (( 78.80/10.73 (breln1all1) => 78.80/10.73 (( 78.80/10.73 (subbreln1) => 78.80/10.73 (( 78.80/10.73 (eqbreln1) => 78.80/10.73 (( 78.80/10.73 (breln1invprop) => 78.80/10.73 (( 78.80/10.73 (breln1invI) => 78.80/10.73 (( 78.80/10.73 (breln1invE) => 78.80/10.73 (( 78.80/10.73 (breln1compprop) => 78.80/10.73 (( 78.80/10.73 (breln1compI) => 78.80/10.73 (( 78.80/10.73 (breln1compE) => 78.80/10.73 (( 78.80/10.73 (breln1compEex) => 78.80/10.73 (( 78.80/10.73 (breln1unionprop) => 78.80/10.73 (( 78.80/10.73 (breln1unionIL) => 78.80/10.73 (( 78.80/10.73 (breln1unionIR) => 78.80/10.73 (( 78.80/10.73 (breln1unionI) => 78.80/10.73 (( 78.80/10.73 (breln1unionE) => 78.80/10.73 (( 78.80/10.73 (breln1unionEcases) => 78.80/10.73 (( 78.80/10.73 (breln1unionCommutes) => 78.80/10.73 (( 78.80/10.73 (woz2Ex) => 78.80/10.73 (( 78.80/10.73 (woz2W) => 78.80/10.73 (( 78.80/10.73 (woz2A) => 78.80/10.73 (( 78.80/10.73 (woz2B) => 78.80/10.73 (( 78.80/10.73 (image1Ex) => 78.80/10.73 (( 78.80/10.73 (image1Ex1) => 78.80/10.73 (( 78.80/10.73 (image1Equiv) => 78.80/10.73 (( 78.80/10.73 (image1E) => 78.80/10.73 (( 78.80/10.73 (image1I) => 78.80/10.73 (( 78.80/10.73 (injFuncInInjFuncSet) => 78.80/10.73 (( 78.80/10.73 (injFuncSetFuncIn) => 78.80/10.73 (( 78.80/10.73 (injFuncSetFuncInj) => 78.80/10.73 (( 78.80/10.73 (surjFuncSetFuncIn) => 78.80/10.73 (( 78.80/10.73 (surjFuncSetFuncSurj) => 78.80/10.73 (( 78.80/10.73 (leftInvIsSurj) => 78.80/10.73 (( 78.80/10.73 (surjCantorThm) => 78.80/10.73 (( 78.80/10.73 (foundation2) => 78.80/10.73 (( 78.80/10.73 (notinself) => 78.80/10.73 (( 78.80/10.73 (notinself2) => 78.80/10.73 (( 78.80/10.73 (omegaSp) => 78.80/10.73 (( 78.80/10.73 (omegaSclos) => 78.80/10.73 (( 78.80/10.73 (peano0notS) => 78.80/10.73 (( 78.80/10.73 (peanoSinj) => 78.80/10.73 (( 78.80/10.73 (transitivesetOp1) => 78.80/10.73 (( 78.80/10.73 (binintTransitive) => 78.80/10.73 (( 78.80/10.73 (transitivesetOp2) => 78.80/10.73 (( 78.80/10.73 (setunionTransitive) => 78.80/10.73 (( 78.80/10.73 (ordinalMinLem1) => 78.80/10.73 (( 78.80/10.73 (!!) @ ( 78.80/10.73 ^[Y0 : $i]: 78.80/10.73 (( 78.80/10.73 (ordinal @ 78.80/10.73 Y0) => 78.80/10.73 (( 78.80/10.73 (!!) @ ( 78.80/10.73 ^[Y1 : $i]: 78.80/10.73 (( 78.80/10.73 (!!) @ ( 78.80/10.73 ^[Y2 : $i]: 78.80/10.73 (( 78.80/10.73 (in @ 78.80/10.73 Y2 @ 78.80/10.73 Y0) => 78.80/10.73 (( 78.80/10.73 (in @ 78.80/10.73 Y1 @ 78.80/10.73 Y2) => 78.80/10.73 (in @ 78.80/10.73 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 78.80/10.73 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2029])). 78.80/10.73 thf(zip_derived_cl2053, plain, 78.80/10.73 (~ (((iftrue) => 78.80/10.73 (((iffalse) => 78.80/10.73 (((iftrueorfalse) => 78.80/10.73 (((binintersectT_lem) => 78.80/10.73 (((binunionT_lem) => 78.80/10.73 (((powersetT_lem) => 78.80/10.73 (((setminusT_lem) => 78.80/10.73 (((complementT_lem) => 78.80/10.73 (((setextT) => 78.80/10.73 (((subsetTI) => 78.80/10.73 (((powersetTI1) => 78.80/10.73 (((powersetTE1) => 78.80/10.73 (((complementTI1) => 78.80/10.73 (((complementTE1) => 78.80/10.73 (((binintersectTELcontra) => 78.80/10.73 (((binintersectTERcontra) => 78.80/10.73 (((contrasubsetT) => 78.80/10.73 (((contrasubsetT1) => 78.80/10.73 (((contrasubsetT2) => 78.80/10.73 (((contrasubsetT3) => 78.80/10.73 (((doubleComplementI1) => 78.80/10.73 (((doubleComplementE1) => 78.80/10.73 (((doubleComplementSub1) => 78.80/10.73 (((doubleComplementSub2) => 78.80/10.73 (((doubleComplementEq) => 78.80/10.73 (((complementTnotintersectT) => 78.80/10.73 (((complementImpComplementIntersect) => 78.80/10.73 (((complementSubsetComplementIntersect) => 78.80/10.73 (((complementInPowersetComplementIntersect) => 78.80/10.73 (((contraSubsetComplement) => 78.80/10.73 (( 78.80/10.73 (complementTcontraSubset) => 78.80/10.73 (( 78.80/10.73 (binunionTILcontra) => 78.80/10.73 (( 78.80/10.73 (binunionTIRcontra) => 78.80/10.73 (( 78.80/10.73 (inIntersectImpInUnion) => 78.80/10.73 (( 78.80/10.73 (inIntersectImpInUnion2) => 78.80/10.73 (( 78.80/10.73 (inIntersectImpInIntersectUnions) => 78.80/10.73 (( 78.80/10.73 (intersectInPowersetIntersectUnions) => 78.80/10.73 (( 78.80/10.73 (inComplementUnionImpNotIn1) => 78.80/10.73 (( 78.80/10.73 (inComplementUnionImpInComplement1) => 78.80/10.73 (( 78.80/10.73 (binunionTE) => 78.80/10.73 (( 78.80/10.73 (binunionTEcontra) => 78.80/10.73 (( 78.80/10.73 (demorgan2a1) => 78.80/10.73 (( 78.80/10.73 (complementUnionInPowersetComplement) => 78.80/10.73 (( 78.80/10.73 (demorgan2a2) => 78.80/10.73 (( 78.80/10.73 (demorgan1a) => 78.80/10.73 (( 78.80/10.73 (demorgan1b) => 78.80/10.73 (( 78.80/10.73 (demorgan1) => 78.80/10.73 (( 78.80/10.73 (demorgan2a) => 78.80/10.73 (( 78.80/10.73 (demorgan2b2) => 78.80/10.73 (( 78.80/10.73 (demorgan2b) => 78.80/10.73 (( 78.80/10.73 (demorgan2) => 78.80/10.73 (( 78.80/10.73 (woz13rule0) => 78.80/10.73 (( 78.80/10.73 (woz13rule1) => 78.80/10.73 (( 78.80/10.73 (woz13rule2) => 78.80/10.73 (( 78.80/10.73 (woz13rule3) => 78.80/10.73 (( 78.80/10.73 (woz13rule4) => 78.80/10.73 (( 78.80/10.73 (woz1_1) => 78.80/10.73 (( 78.80/10.73 (woz1_2) => 78.80/10.73 (( 78.80/10.73 (woz1_3) => 78.80/10.73 (( 78.80/10.73 (woz1_4) => 78.80/10.73 (( 78.80/10.73 (woz1_5) => 78.80/10.73 (( 78.80/10.73 (breln1all2) => 78.80/10.73 (( 78.80/10.73 (breln1SetBreln1) => 78.80/10.73 (( 78.80/10.73 (choice2fnsingleton) => 78.80/10.73 (( 78.80/10.73 (setOfPairsIsBReln1) => 78.80/10.73 (( 78.80/10.73 (breln1all1) => 78.80/10.73 (( 78.80/10.73 (subbreln1) => 78.80/10.73 (( 78.80/10.73 (eqbreln1) => 78.80/10.73 (( 78.80/10.73 (breln1invprop) => 78.80/10.73 (( 78.80/10.73 (breln1invI) => 78.80/10.73 (( 78.80/10.73 (breln1invE) => 78.80/10.73 (( 78.80/10.73 (breln1compprop) => 78.80/10.73 (( 78.80/10.73 (breln1compI) => 78.80/10.73 (( 78.80/10.73 (breln1compE) => 78.80/10.73 (( 78.80/10.73 (breln1compEex) => 78.80/10.73 (( 78.80/10.73 (breln1unionprop) => 78.80/10.73 (( 78.80/10.73 (breln1unionIL) => 78.80/10.73 (( 78.80/10.73 (breln1unionIR) => 78.80/10.73 (( 78.80/10.73 (breln1unionI) => 78.80/10.73 (( 78.80/10.73 (breln1unionE) => 78.80/10.73 (( 78.80/10.73 (breln1unionEcases) => 78.80/10.73 (( 78.80/10.73 (breln1unionCommutes) => 78.80/10.73 (( 78.80/10.73 (woz2Ex) => 78.80/10.73 (( 78.80/10.73 (woz2W) => 78.80/10.73 (( 78.80/10.73 (woz2A) => 78.80/10.73 (( 78.80/10.73 (woz2B) => 78.80/10.73 (( 78.80/10.73 (image1Ex) => 78.80/10.73 (( 78.80/10.73 (image1Ex1) => 78.80/10.73 (( 78.80/10.73 (image1Equiv) => 78.80/10.73 (( 78.80/10.73 (image1E) => 78.80/10.73 (( 78.80/10.73 (image1I) => 78.80/10.73 (( 78.80/10.73 (injFuncInInjFuncSet) => 78.80/10.73 (( 78.80/10.73 (injFuncSetFuncIn) => 78.80/10.73 (( 78.80/10.73 (injFuncSetFuncInj) => 78.80/10.73 (( 78.80/10.73 (surjFuncSetFuncIn) => 78.80/10.73 (( 78.80/10.73 (surjFuncSetFuncSurj) => 78.80/10.73 (( 78.80/10.73 (leftInvIsSurj) => 78.80/10.73 (( 78.80/10.73 (surjCantorThm) => 78.80/10.73 (( 78.80/10.73 (foundation2) => 78.80/10.73 (( 78.80/10.73 (notinself) => 78.80/10.73 (( 78.80/10.73 (notinself2) => 78.80/10.73 (( 78.80/10.73 (omegaSp) => 78.80/10.73 (( 78.80/10.73 (omegaSclos) => 78.80/10.73 (( 78.80/10.73 (peano0notS) => 78.80/10.73 (( 78.80/10.73 (peanoSinj) => 78.80/10.73 (( 78.80/10.73 (transitivesetOp1) => 78.80/10.73 (( 78.80/10.73 (binintTransitive) => 78.80/10.73 (( 78.80/10.73 (transitivesetOp2) => 78.80/10.73 (( 78.80/10.73 (setunionTransitive) => 78.80/10.73 (( 78.80/10.73 (ordinalMinLem1) => 78.80/10.73 (( 78.80/10.73 (!!) @ ( 78.80/10.73 ^[Y0 : $i]: 78.80/10.73 (( 78.80/10.73 (ordinal @ 78.80/10.73 Y0) => 78.80/10.73 (( 78.80/10.73 (!!) @ ( 78.80/10.73 ^[Y1 : $i]: 78.80/10.73 (( 78.80/10.73 (!!) @ ( 78.80/10.73 ^[Y2 : $i]: 78.80/10.73 (( 78.80/10.73 (in @ 78.80/10.73 Y2 @ 78.80/10.73 Y0) => 78.80/10.73 (( 78.80/10.73 (in @ 78.80/10.73 Y1 @ 78.80/10.73 Y2) => 78.80/10.73 (in @ 78.80/10.73 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 78.80/10.73 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2041])). 78.80/10.73 thf(zip_derived_cl2062, plain, 78.80/10.73 (~ (((iffalse) => 78.80/10.73 (((iftrueorfalse) => 78.80/10.73 (((binintersectT_lem) => 78.80/10.73 (((binunionT_lem) => 78.80/10.73 (((powersetT_lem) => 78.80/10.73 (((setminusT_lem) => 78.80/10.73 (((complementT_lem) => 78.80/10.73 (((setextT) => 78.80/10.73 (((subsetTI) => 78.80/10.73 (((powersetTI1) => 78.80/10.73 (((powersetTE1) => 78.80/10.73 (((complementTI1) => 78.80/10.73 (((complementTE1) => 78.80/10.73 (((binintersectTELcontra) => 78.80/10.73 (((binintersectTERcontra) => 78.80/10.73 (((contrasubsetT) => 78.80/10.73 (((contrasubsetT1) => 78.80/10.73 (((contrasubsetT2) => 78.80/10.73 (((contrasubsetT3) => 78.80/10.73 (((doubleComplementI1) => 78.80/10.73 (((doubleComplementE1) => 78.80/10.73 (((doubleComplementSub1) => 78.80/10.73 (((doubleComplementSub2) => 78.80/10.73 (((doubleComplementEq) => 78.80/10.73 (((complementTnotintersectT) => 78.80/10.73 (((complementImpComplementIntersect) => 78.80/10.73 (((complementSubsetComplementIntersect) => 78.80/10.73 (((complementInPowersetComplementIntersect) => 78.80/10.73 (((contraSubsetComplement) => 78.80/10.73 (((complementTcontraSubset) => 78.80/10.73 (( 78.80/10.73 (binunionTILcontra) => 78.80/10.73 (( 78.80/10.73 (binunionTIRcontra) => 78.80/10.73 (( 78.80/10.73 (inIntersectImpInUnion) => 78.80/10.73 (( 78.80/10.73 (inIntersectImpInUnion2) => 78.80/10.73 (( 78.80/10.73 (inIntersectImpInIntersectUnions) => 78.80/10.73 (( 78.80/10.73 (intersectInPowersetIntersectUnions) => 78.80/10.73 (( 78.80/10.73 (inComplementUnionImpNotIn1) => 78.80/10.73 (( 78.80/10.73 (inComplementUnionImpInComplement1) => 78.80/10.73 (( 78.80/10.73 (binunionTE) => 78.80/10.73 (( 78.80/10.73 (binunionTEcontra) => 78.80/10.73 (( 78.80/10.73 (demorgan2a1) => 78.80/10.73 (( 78.80/10.73 (complementUnionInPowersetComplement) => 78.80/10.73 (( 78.80/10.73 (demorgan2a2) => 78.80/10.73 (( 78.80/10.73 (demorgan1a) => 78.80/10.73 (( 78.80/10.73 (demorgan1b) => 78.80/10.73 (( 78.80/10.73 (demorgan1) => 78.80/10.73 (( 78.80/10.73 (demorgan2a) => 78.80/10.73 (( 78.80/10.73 (demorgan2b2) => 78.80/10.73 (( 78.80/10.73 (demorgan2b) => 78.80/10.73 (( 78.80/10.73 (demorgan2) => 78.80/10.73 (( 78.80/10.73 (woz13rule0) => 78.80/10.73 (( 78.80/10.73 (woz13rule1) => 78.80/10.73 (( 78.80/10.73 (woz13rule2) => 78.80/10.73 (( 78.80/10.73 (woz13rule3) => 78.80/10.73 (( 78.80/10.73 (woz13rule4) => 78.80/10.73 (( 78.80/10.73 (woz1_1) => 78.80/10.73 (( 78.80/10.73 (woz1_2) => 78.80/10.73 (( 78.80/10.73 (woz1_3) => 78.80/10.73 (( 78.80/10.73 (woz1_4) => 78.80/10.73 (( 78.80/10.73 (woz1_5) => 78.80/10.73 (( 78.80/10.73 (breln1all2) => 78.80/10.73 (( 78.80/10.73 (breln1SetBreln1) => 78.80/10.73 (( 78.80/10.73 (choice2fnsingleton) => 78.80/10.73 (( 78.80/10.73 (setOfPairsIsBReln1) => 78.80/10.73 (( 78.80/10.73 (breln1all1) => 78.80/10.73 (( 78.80/10.73 (subbreln1) => 78.80/10.73 (( 78.80/10.73 (eqbreln1) => 78.80/10.73 (( 78.80/10.73 (breln1invprop) => 78.80/10.73 (( 78.80/10.73 (breln1invI) => 78.80/10.73 (( 78.80/10.73 (breln1invE) => 78.80/10.73 (( 78.80/10.73 (breln1compprop) => 78.80/10.73 (( 78.80/10.73 (breln1compI) => 78.80/10.73 (( 78.80/10.73 (breln1compE) => 78.80/10.73 (( 78.80/10.73 (breln1compEex) => 78.80/10.73 (( 78.80/10.73 (breln1unionprop) => 78.80/10.73 (( 78.80/10.73 (breln1unionIL) => 78.80/10.73 (( 78.80/10.73 (breln1unionIR) => 78.80/10.73 (( 78.80/10.73 (breln1unionI) => 78.80/10.73 (( 78.80/10.73 (breln1unionE) => 78.80/10.73 (( 78.80/10.73 (breln1unionEcases) => 78.80/10.73 (( 78.80/10.73 (breln1unionCommutes) => 78.80/10.73 (( 78.80/10.73 (woz2Ex) => 78.80/10.73 (( 78.80/10.73 (woz2W) => 78.80/10.73 (( 78.80/10.73 (woz2A) => 78.80/10.73 (( 78.80/10.73 (woz2B) => 78.80/10.73 (( 78.80/10.73 (image1Ex) => 78.80/10.73 (( 78.80/10.73 (image1Ex1) => 78.80/10.73 (( 78.80/10.73 (image1Equiv) => 78.80/10.73 (( 78.80/10.73 (image1E) => 78.80/10.73 (( 78.80/10.73 (image1I) => 78.80/10.73 (( 78.80/10.73 (injFuncInInjFuncSet) => 78.80/10.73 (( 78.80/10.73 (injFuncSetFuncIn) => 78.80/10.73 (( 78.80/10.73 (injFuncSetFuncInj) => 78.80/10.73 (( 78.80/10.73 (surjFuncSetFuncIn) => 78.80/10.73 (( 78.80/10.73 (surjFuncSetFuncSurj) => 78.80/10.73 (( 78.80/10.73 (leftInvIsSurj) => 78.80/10.73 (( 78.80/10.73 (surjCantorThm) => 78.80/10.73 (( 78.80/10.73 (foundation2) => 78.80/10.73 (( 78.80/10.73 (notinself) => 78.80/10.73 (( 78.80/10.73 (notinself2) => 78.80/10.73 (( 78.80/10.73 (omegaSp) => 78.80/10.73 (( 78.80/10.73 (omegaSclos) => 78.80/10.73 (( 78.80/10.73 (peano0notS) => 78.80/10.73 (( 78.80/10.73 (peanoSinj) => 78.80/10.73 (( 78.80/10.73 (transitivesetOp1) => 78.80/10.73 (( 78.80/10.73 (binintTransitive) => 78.80/10.73 (( 78.80/10.73 (transitivesetOp2) => 78.80/10.73 (( 78.80/10.73 (setunionTransitive) => 78.80/10.73 (( 78.80/10.73 (ordinalMinLem1) => 78.80/10.73 (( 78.80/10.73 (!!) @ ( 78.80/10.73 ^[Y0 : $i]: 78.80/10.73 (( 78.80/10.73 (ordinal @ 78.80/10.73 Y0) => 78.80/10.73 (( 78.80/10.73 (!!) @ ( 78.80/10.73 ^[Y1 : $i]: 78.80/10.73 (( 78.80/10.73 (!!) @ ( 78.80/10.73 ^[Y2 : $i]: 78.80/10.73 (( 78.80/10.73 (in @ 78.80/10.73 Y2 @ 78.80/10.73 Y0) => 78.80/10.73 (( 78.80/10.73 (in @ 78.80/10.73 Y1 @ 78.80/10.73 Y2) => 78.80/10.73 (in @ 78.80/10.73 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 78.80/10.73 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2053])). 78.80/10.73 thf(zip_derived_cl2072, plain, 78.80/10.73 (~ (((iftrueorfalse) => 78.80/10.73 (((binintersectT_lem) => 78.80/10.73 (((binunionT_lem) => 78.80/10.73 (((powersetT_lem) => 78.80/10.73 (((setminusT_lem) => 78.80/10.73 (((complementT_lem) => 78.80/10.73 (((setextT) => 78.80/10.73 (((subsetTI) => 78.80/10.73 (((powersetTI1) => 78.80/10.73 (((powersetTE1) => 78.80/10.73 (((complementTI1) => 78.80/10.73 (((complementTE1) => 78.80/10.73 (((binintersectTELcontra) => 78.80/10.73 (((binintersectTERcontra) => 78.80/10.73 (((contrasubsetT) => 78.80/10.73 (((contrasubsetT1) => 78.80/10.73 (((contrasubsetT2) => 78.80/10.73 (((contrasubsetT3) => 78.80/10.73 (((doubleComplementI1) => 78.80/10.73 (((doubleComplementE1) => 78.80/10.73 (((doubleComplementSub1) => 78.80/10.73 (((doubleComplementSub2) => 78.80/10.73 (((doubleComplementEq) => 78.80/10.73 (((complementTnotintersectT) => 78.80/10.73 (((complementImpComplementIntersect) => 78.80/10.73 (((complementSubsetComplementIntersect) => 78.80/10.73 (((complementInPowersetComplementIntersect) => 78.80/10.73 (((contraSubsetComplement) => 78.80/10.73 (((complementTcontraSubset) => 78.80/10.73 (((binunionTILcontra) => 78.80/10.73 (( 78.80/10.73 (binunionTIRcontra) => 78.80/10.73 (( 78.80/10.73 (inIntersectImpInUnion) => 78.80/10.73 (( 78.80/10.73 (inIntersectImpInUnion2) => 78.80/10.73 (( 78.80/10.73 (inIntersectImpInIntersectUnions) => 78.80/10.73 (( 78.80/10.73 (intersectInPowersetIntersectUnions) => 78.80/10.73 (( 78.80/10.73 (inComplementUnionImpNotIn1) => 78.80/10.73 (( 78.80/10.73 (inComplementUnionImpInComplement1) => 78.80/10.73 (( 78.80/10.73 (binunionTE) => 78.80/10.73 (( 78.80/10.73 (binunionTEcontra) => 78.80/10.73 (( 78.80/10.73 (demorgan2a1) => 78.80/10.73 (( 78.80/10.73 (complementUnionInPowersetComplement) => 78.80/10.73 (( 78.80/10.73 (demorgan2a2) => 78.80/10.73 (( 78.80/10.73 (demorgan1a) => 78.80/10.73 (( 78.80/10.73 (demorgan1b) => 78.80/10.73 (( 78.80/10.73 (demorgan1) => 78.80/10.73 (( 78.80/10.73 (demorgan2a) => 78.80/10.73 (( 78.80/10.73 (demorgan2b2) => 78.80/10.73 (( 78.80/10.73 (demorgan2b) => 78.80/10.73 (( 78.80/10.73 (demorgan2) => 78.80/10.73 (( 78.80/10.73 (woz13rule0) => 78.80/10.73 (( 78.80/10.73 (woz13rule1) => 78.80/10.73 (( 78.80/10.73 (woz13rule2) => 78.80/10.73 (( 78.80/10.73 (woz13rule3) => 78.80/10.73 (( 78.80/10.73 (woz13rule4) => 78.80/10.73 (( 78.80/10.73 (woz1_1) => 78.80/10.73 (( 78.80/10.73 (woz1_2) => 78.80/10.73 (( 78.80/10.73 (woz1_3) => 78.80/10.73 (( 78.80/10.73 (woz1_4) => 78.80/10.73 (( 78.80/10.73 (woz1_5) => 78.80/10.73 (( 78.80/10.73 (breln1all2) => 78.80/10.73 (( 78.80/10.73 (breln1SetBreln1) => 78.80/10.73 (( 78.80/10.73 (choice2fnsingleton) => 78.80/10.73 (( 78.80/10.73 (setOfPairsIsBReln1) => 78.80/10.73 (( 78.80/10.73 (breln1all1) => 78.80/10.73 (( 78.80/10.73 (subbreln1) => 78.80/10.73 (( 78.80/10.73 (eqbreln1) => 78.80/10.73 (( 78.80/10.73 (breln1invprop) => 78.80/10.73 (( 78.80/10.73 (breln1invI) => 78.80/10.73 (( 78.80/10.73 (breln1invE) => 78.80/10.73 (( 78.80/10.73 (breln1compprop) => 78.80/10.73 (( 78.80/10.73 (breln1compI) => 78.80/10.73 (( 78.80/10.73 (breln1compE) => 78.80/10.73 (( 78.80/10.73 (breln1compEex) => 78.80/10.73 (( 78.80/10.73 (breln1unionprop) => 78.80/10.73 (( 78.80/10.73 (breln1unionIL) => 78.80/10.73 (( 78.80/10.73 (breln1unionIR) => 78.80/10.73 (( 78.80/10.73 (breln1unionI) => 78.80/10.73 (( 78.80/10.73 (breln1unionE) => 78.80/10.73 (( 78.80/10.73 (breln1unionEcases) => 78.80/10.73 (( 78.80/10.73 (breln1unionCommutes) => 78.80/10.73 (( 78.80/10.73 (woz2Ex) => 78.80/10.73 (( 78.80/10.73 (woz2W) => 78.80/10.73 (( 78.80/10.73 (woz2A) => 78.80/10.73 (( 78.80/10.73 (woz2B) => 78.80/10.73 (( 78.80/10.73 (image1Ex) => 78.80/10.73 (( 78.80/10.73 (image1Ex1) => 78.80/10.73 (( 78.80/10.73 (image1Equiv) => 78.80/10.73 (( 78.80/10.73 (image1E) => 78.80/10.73 (( 78.80/10.73 (image1I) => 78.80/10.73 (( 78.80/10.73 (injFuncInInjFuncSet) => 78.80/10.73 (( 78.80/10.73 (injFuncSetFuncIn) => 78.80/10.73 (( 78.80/10.73 (injFuncSetFuncInj) => 78.80/10.73 (( 78.80/10.73 (surjFuncSetFuncIn) => 78.80/10.73 (( 78.80/10.73 (surjFuncSetFuncSurj) => 78.80/10.73 (( 78.80/10.73 (leftInvIsSurj) => 78.80/10.73 (( 78.80/10.73 (surjCantorThm) => 78.80/10.73 (( 78.80/10.73 (foundation2) => 78.80/10.73 (( 78.80/10.73 (notinself) => 78.80/10.73 (( 78.80/10.73 (notinself2) => 78.80/10.73 (( 78.80/10.73 (omegaSp) => 78.80/10.73 (( 78.80/10.73 (omegaSclos) => 78.80/10.73 (( 78.80/10.73 (peano0notS) => 78.80/10.73 (( 78.80/10.73 (peanoSinj) => 78.80/10.73 (( 78.80/10.73 (transitivesetOp1) => 78.80/10.73 (( 78.80/10.73 (binintTransitive) => 78.80/10.73 (( 78.80/10.73 (transitivesetOp2) => 78.80/10.73 (( 78.80/10.73 (setunionTransitive) => 78.80/10.73 (( 78.80/10.73 (ordinalMinLem1) => 78.80/10.73 (( 78.80/10.73 (!!) @ ( 78.80/10.73 ^[Y0 : $i]: 78.80/10.73 (( 78.80/10.73 (ordinal @ 78.80/10.73 Y0) => 78.80/10.73 (( 78.80/10.73 (!!) @ ( 78.80/10.73 ^[Y1 : $i]: 78.80/10.73 (( 78.80/10.73 (!!) @ ( 78.80/10.73 ^[Y2 : $i]: 78.80/10.73 (( 78.80/10.73 (in @ 78.80/10.73 Y2 @ 78.80/10.73 Y0) => 78.80/10.73 (( 78.80/10.73 (in @ 78.80/10.73 Y1 @ 78.80/10.73 Y2) => 78.80/10.73 (in @ 78.80/10.73 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 78.80/10.73 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2062])). 78.80/10.73 thf(zip_derived_cl2082, plain, 78.80/10.73 (~ (((binintersectT_lem) => 78.80/10.73 (((binunionT_lem) => 78.80/10.73 (((powersetT_lem) => 78.80/10.73 (((setminusT_lem) => 78.80/10.73 (((complementT_lem) => 78.80/10.73 (((setextT) => 78.80/10.73 (((subsetTI) => 78.80/10.73 (((powersetTI1) => 78.80/10.73 (((powersetTE1) => 78.80/10.73 (((complementTI1) => 78.80/10.73 (((complementTE1) => 78.80/10.73 (((binintersectTELcontra) => 78.80/10.73 (((binintersectTERcontra) => 78.80/10.73 (((contrasubsetT) => 78.80/10.73 (((contrasubsetT1) => 78.80/10.73 (((contrasubsetT2) => 78.80/10.73 (((contrasubsetT3) => 78.80/10.73 (((doubleComplementI1) => 78.80/10.73 (((doubleComplementE1) => 78.80/10.73 (((doubleComplementSub1) => 78.80/10.73 (((doubleComplementSub2) => 78.80/10.73 (((doubleComplementEq) => 78.80/10.73 (((complementTnotintersectT) => 78.80/10.73 (((complementImpComplementIntersect) => 78.80/10.73 (((complementSubsetComplementIntersect) => 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=> 78.80/10.73 (( 78.80/10.73 (demorgan2b2) => 78.80/10.73 (( 78.80/10.73 (demorgan2b) => 78.80/10.73 (( 78.80/10.73 (demorgan2) => 78.80/10.73 (( 78.80/10.73 (woz13rule0) => 78.80/10.73 (( 78.80/10.73 (woz13rule1) => 78.80/10.73 (( 78.80/10.73 (woz13rule2) => 78.80/10.73 (( 78.80/10.73 (woz13rule3) => 78.80/10.73 (( 78.80/10.73 (woz13rule4) => 78.80/10.73 (( 78.80/10.73 (woz1_1) => 78.80/10.73 (( 78.80/10.73 (woz1_2) => 78.80/10.73 (( 78.80/10.73 (woz1_3) => 78.80/10.73 (( 78.80/10.73 (woz1_4) => 78.80/10.73 (( 78.80/10.73 (woz1_5) => 78.80/10.73 (( 78.80/10.73 (breln1all2) => 78.80/10.73 (( 78.80/10.73 (breln1SetBreln1) => 78.80/10.73 (( 78.80/10.73 (choice2fnsingleton) => 78.80/10.73 (( 78.80/10.73 (setOfPairsIsBReln1) => 78.80/10.73 (( 78.80/10.73 (breln1all1) => 78.80/10.73 (( 78.80/10.73 (subbreln1) => 78.80/10.73 (( 78.80/10.73 (eqbreln1) => 78.80/10.73 (( 78.80/10.73 (breln1invprop) => 78.80/10.73 (( 78.80/10.73 (breln1invI) => 78.80/10.73 (( 78.80/10.73 (breln1invE) => 78.80/10.73 (( 78.80/10.73 (breln1compprop) => 78.80/10.73 (( 78.80/10.73 (breln1compI) => 78.80/10.73 (( 78.80/10.73 (breln1compE) => 78.80/10.73 (( 78.80/10.73 (breln1compEex) => 78.80/10.73 (( 78.80/10.73 (breln1unionprop) => 78.80/10.73 (( 78.80/10.73 (breln1unionIL) => 78.80/10.73 (( 78.80/10.73 (breln1unionIR) => 78.80/10.73 (( 78.80/10.73 (breln1unionI) => 78.80/10.73 (( 78.80/10.73 (breln1unionE) => 78.80/10.73 (( 78.80/10.73 (breln1unionEcases) => 78.80/10.73 (( 78.80/10.73 (breln1unionCommutes) => 78.80/10.73 (( 78.80/10.73 (woz2Ex) => 78.80/10.73 (( 78.80/10.73 (woz2W) => 78.80/10.73 (( 78.80/10.73 (woz2A) => 78.80/10.73 (( 78.80/10.73 (woz2B) => 78.80/10.73 (( 78.80/10.73 (image1Ex) => 78.80/10.73 (( 78.80/10.73 (image1Ex1) => 78.80/10.73 (( 78.80/10.73 (image1Equiv) => 78.80/10.73 (( 78.80/10.73 (image1E) => 78.80/10.73 (( 78.80/10.73 (image1I) => 78.80/10.73 (( 78.80/10.73 (injFuncInInjFuncSet) => 78.80/10.73 (( 78.80/10.73 (injFuncSetFuncIn) => 78.80/10.73 (( 78.80/10.73 (injFuncSetFuncInj) => 78.80/10.73 (( 78.80/10.73 (surjFuncSetFuncIn) => 78.80/10.73 (( 78.80/10.73 (surjFuncSetFuncSurj) => 78.80/10.73 (( 78.80/10.73 (leftInvIsSurj) => 78.80/10.73 (( 78.80/10.73 (surjCantorThm) => 78.80/10.73 (( 78.80/10.73 (foundation2) => 78.80/10.73 (( 78.80/10.73 (notinself) => 78.80/10.73 (( 78.80/10.73 (notinself2) => 78.80/10.73 (( 78.80/10.73 (omegaSp) => 78.80/10.73 (( 78.80/10.73 (omegaSclos) => 78.80/10.73 (( 78.80/10.73 (peano0notS) => 78.80/10.73 (( 78.80/10.73 (peanoSinj) => 78.80/10.73 (( 78.80/10.73 (transitivesetOp1) => 78.80/10.73 (( 78.80/10.73 (binintTransitive) => 78.80/10.73 (( 78.80/10.73 (transitivesetOp2) => 78.80/10.73 (( 78.80/10.73 (setunionTransitive) => 78.80/10.73 (( 78.80/10.73 (ordinalMinLem1) => 78.80/10.73 (( 78.80/10.73 (!!) @ ( 78.80/10.73 ^[Y0 : $i]: 78.80/10.73 (( 78.80/10.73 (ordinal @ 78.80/10.73 Y0) => 78.80/10.73 (( 78.80/10.73 (!!) @ ( 78.80/10.73 ^[Y1 : $i]: 78.80/10.73 (( 78.80/10.73 (!!) @ ( 78.80/10.73 ^[Y2 : $i]: 78.80/10.73 (( 78.80/10.73 (in @ 78.80/10.73 Y2 @ 78.80/10.73 Y0) => 78.80/10.73 (( 78.80/10.73 (in @ 78.80/10.73 Y1 @ 78.80/10.73 Y2) => 78.80/10.73 (in @ 78.80/10.73 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 78.80/10.73 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2072])). 78.80/10.73 thf(zip_derived_cl2093, plain, 78.80/10.73 (~ (((binunionT_lem) => 78.80/10.73 (((powersetT_lem) => 78.80/10.73 (((setminusT_lem) => 78.80/10.73 (((complementT_lem) => 78.80/10.73 (((setextT) => 78.80/10.73 (((subsetTI) => 78.80/10.73 (((powersetTI1) => 78.80/10.73 (((powersetTE1) => 78.80/10.73 (((complementTI1) => 78.80/10.73 (((complementTE1) => 78.80/10.73 (((binintersectTELcontra) => 78.80/10.73 (((binintersectTERcontra) => 78.80/10.73 (((contrasubsetT) => 78.80/10.73 (((contrasubsetT1) => 78.80/10.73 (((contrasubsetT2) => 78.80/10.73 (((contrasubsetT3) => 78.80/10.73 (((doubleComplementI1) => 78.80/10.73 (((doubleComplementE1) => 78.80/10.73 (((doubleComplementSub1) => 78.80/10.73 (((doubleComplementSub2) => 78.80/10.73 (((doubleComplementEq) => 78.80/10.73 (((complementTnotintersectT) => 78.80/10.73 (((complementImpComplementIntersect) => 78.80/10.73 (((complementSubsetComplementIntersect) => 78.80/10.73 (((complementInPowersetComplementIntersect) => 78.80/10.73 (((contraSubsetComplement) => 78.80/10.73 (((complementTcontraSubset) => 78.80/10.73 (((binunionTILcontra) => 78.80/10.73 (((binunionTIRcontra) => 78.80/10.73 (((inIntersectImpInUnion) => 78.80/10.73 (( 78.80/10.73 (inIntersectImpInUnion2) => 78.80/10.73 (( 78.80/10.73 (inIntersectImpInIntersectUnions) => 78.80/10.73 (( 78.80/10.73 (intersectInPowersetIntersectUnions) => 78.80/10.73 (( 78.80/10.73 (inComplementUnionImpNotIn1) => 78.80/10.73 (( 78.80/10.73 (inComplementUnionImpInComplement1) => 78.80/10.73 (( 78.80/10.73 (binunionTE) => 78.80/10.73 (( 78.80/10.73 (binunionTEcontra) => 78.80/10.73 (( 78.80/10.73 (demorgan2a1) => 78.80/10.73 (( 78.80/10.73 (complementUnionInPowersetComplement) => 78.80/10.73 (( 78.80/10.73 (demorgan2a2) => 78.80/10.73 (( 78.80/10.73 (demorgan1a) => 78.80/10.73 (( 78.80/10.73 (demorgan1b) => 78.80/10.73 (( 78.80/10.73 (demorgan1) => 78.80/10.73 (( 78.80/10.73 (demorgan2a) => 78.80/10.73 (( 78.80/10.73 (demorgan2b2) => 78.80/10.73 (( 78.80/10.73 (demorgan2b) => 78.80/10.73 (( 78.80/10.73 (demorgan2) => 78.80/10.73 (( 78.80/10.73 (woz13rule0) => 78.80/10.73 (( 78.80/10.73 (woz13rule1) => 78.80/10.73 (( 78.80/10.73 (woz13rule2) => 78.80/10.73 (( 78.80/10.73 (woz13rule3) => 78.80/10.73 (( 78.80/10.73 (woz13rule4) => 78.80/10.73 (( 78.80/10.73 (woz1_1) => 78.80/10.73 (( 78.80/10.73 (woz1_2) => 78.80/10.73 (( 78.80/10.73 (woz1_3) => 78.80/10.73 (( 78.80/10.73 (woz1_4) => 78.80/10.73 (( 78.80/10.73 (woz1_5) => 78.80/10.73 (( 78.80/10.73 (breln1all2) => 78.80/10.73 (( 78.80/10.73 (breln1SetBreln1) => 78.80/10.73 (( 78.80/10.73 (choice2fnsingleton) => 78.80/10.73 (( 78.80/10.73 (setOfPairsIsBReln1) => 78.80/10.73 (( 78.80/10.73 (breln1all1) => 78.80/10.73 (( 78.80/10.73 (subbreln1) => 78.80/10.73 (( 78.80/10.73 (eqbreln1) => 78.80/10.73 (( 78.80/10.73 (breln1invprop) => 78.80/10.73 (( 78.80/10.73 (breln1invI) => 78.80/10.73 (( 78.80/10.73 (breln1invE) => 78.80/10.73 (( 78.80/10.73 (breln1compprop) => 78.80/10.73 (( 78.80/10.73 (breln1compI) => 78.80/10.73 (( 78.80/10.73 (breln1compE) => 78.80/10.73 (( 78.80/10.73 (breln1compEex) => 78.80/10.73 (( 78.80/10.73 (breln1unionprop) => 78.80/10.73 (( 78.80/10.73 (breln1unionIL) => 78.80/10.73 (( 78.80/10.73 (breln1unionIR) => 78.80/10.73 (( 78.80/10.73 (breln1unionI) => 78.80/10.73 (( 78.80/10.73 (breln1unionE) => 78.80/10.73 (( 78.80/10.73 (breln1unionEcases) => 78.80/10.73 (( 78.80/10.73 (breln1unionCommutes) => 78.80/10.73 (( 78.80/10.73 (woz2Ex) => 78.80/10.73 (( 78.80/10.73 (woz2W) => 78.80/10.73 (( 78.80/10.73 (woz2A) => 78.80/10.73 (( 78.80/10.73 (woz2B) => 78.80/10.73 (( 78.80/10.73 (image1Ex) => 78.80/10.73 (( 78.80/10.73 (image1Ex1) => 78.80/10.73 (( 78.80/10.73 (image1Equiv) => 78.80/10.73 (( 78.80/10.73 (image1E) => 78.80/10.73 (( 78.80/10.73 (image1I) => 78.80/10.73 (( 78.80/10.73 (injFuncInInjFuncSet) => 78.80/10.73 (( 78.80/10.73 (injFuncSetFuncIn) => 78.80/10.73 (( 78.80/10.73 (injFuncSetFuncInj) => 78.80/10.73 (( 78.80/10.73 (surjFuncSetFuncIn) => 78.80/10.73 (( 78.80/10.73 (surjFuncSetFuncSurj) => 78.80/10.73 (( 78.80/10.73 (leftInvIsSurj) => 78.80/10.73 (( 78.80/10.73 (surjCantorThm) => 78.80/10.73 (( 78.80/10.73 (foundation2) => 78.80/10.73 (( 78.80/10.73 (notinself) => 78.80/10.73 (( 78.80/10.73 (notinself2) => 78.80/10.73 (( 78.80/10.73 (omegaSp) => 78.80/10.73 (( 78.80/10.73 (omegaSclos) => 78.80/10.73 (( 78.80/10.73 (peano0notS) => 78.80/10.73 (( 78.80/10.73 (peanoSinj) => 78.80/10.73 (( 78.80/10.73 (transitivesetOp1) => 78.80/10.73 (( 78.80/10.73 (binintTransitive) => 78.80/10.73 (( 78.80/10.73 (transitivesetOp2) => 78.80/10.73 (( 78.80/10.73 (setunionTransitive) => 78.80/10.73 (( 78.80/10.73 (ordinalMinLem1) => 78.80/10.73 (( 78.80/10.73 (!!) @ ( 78.80/10.73 ^[Y0 : $i]: 78.80/10.73 (( 78.80/10.73 (ordinal @ 78.80/10.73 Y0) => 78.80/10.73 (( 78.80/10.73 (!!) @ ( 78.80/10.73 ^[Y1 : $i]: 78.80/10.73 (( 78.80/10.73 (!!) @ ( 78.80/10.73 ^[Y2 : $i]: 78.80/10.73 (( 78.80/10.73 (in @ 78.80/10.73 Y2 @ 78.80/10.73 Y0) => 78.80/10.73 (( 78.80/10.73 (in @ 78.80/10.73 Y1 @ 78.80/10.73 Y2) => 78.80/10.73 (in @ 78.80/10.73 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 78.80/10.73 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2082])). 78.80/10.73 thf(zip_derived_cl2103, plain, 78.80/10.73 (~ (((powersetT_lem) => 78.80/10.73 (((setminusT_lem) => 78.80/10.73 (((complementT_lem) => 78.80/10.73 (((setextT) => 78.80/10.73 (((subsetTI) => 78.80/10.73 (((powersetTI1) => 78.80/10.73 (((powersetTE1) => 78.80/10.73 (((complementTI1) => 78.80/10.73 (((complementTE1) => 78.80/10.73 (((binintersectTELcontra) => 78.80/10.73 (((binintersectTERcontra) => 78.80/10.73 (((contrasubsetT) => 78.80/10.73 (((contrasubsetT1) => 78.80/10.73 (((contrasubsetT2) => 78.80/10.73 (((contrasubsetT3) => 78.80/10.73 (((doubleComplementI1) => 78.80/10.73 (((doubleComplementE1) => 78.80/10.73 (((doubleComplementSub1) => 78.80/10.73 (((doubleComplementSub2) => 78.80/10.73 (((doubleComplementEq) => 78.80/10.73 (((complementTnotintersectT) => 78.80/10.73 (((complementImpComplementIntersect) => 78.80/10.73 (((complementSubsetComplementIntersect) => 78.80/10.73 (((complementInPowersetComplementIntersect) => 78.80/10.73 (((contraSubsetComplement) => 78.80/10.73 (((complementTcontraSubset) => 78.80/10.73 (((binunionTILcontra) => 78.80/10.73 (((binunionTIRcontra) => 78.80/10.73 (((inIntersectImpInUnion) => 78.80/10.73 (((inIntersectImpInUnion2) => 78.80/10.73 (( 78.80/10.73 (inIntersectImpInIntersectUnions) => 78.80/10.73 (( 78.80/10.73 (intersectInPowersetIntersectUnions) => 78.80/10.73 (( 78.80/10.73 (inComplementUnionImpNotIn1) => 78.80/10.73 (( 78.80/10.73 (inComplementUnionImpInComplement1) => 78.80/10.73 (( 78.80/10.73 (binunionTE) => 78.80/10.73 (( 78.80/10.73 (binunionTEcontra) => 78.80/10.73 (( 78.80/10.73 (demorgan2a1) => 78.80/10.73 (( 78.80/10.73 (complementUnionInPowersetComplement) => 78.80/10.73 (( 78.80/10.73 (demorgan2a2) => 78.80/10.73 (( 78.80/10.73 (demorgan1a) => 78.80/10.73 (( 78.80/10.73 (demorgan1b) => 78.80/10.73 (( 78.80/10.73 (demorgan1) => 78.80/10.73 (( 78.80/10.73 (demorgan2a) => 78.80/10.73 (( 78.80/10.73 (demorgan2b2) => 78.80/10.73 (( 78.80/10.73 (demorgan2b) => 78.80/10.73 (( 78.80/10.73 (demorgan2) => 78.80/10.73 (( 78.80/10.73 (woz13rule0) => 78.80/10.73 (( 78.80/10.73 (woz13rule1) => 78.80/10.73 (( 78.80/10.73 (woz13rule2) => 78.80/10.73 (( 78.80/10.73 (woz13rule3) => 78.80/10.73 (( 78.80/10.73 (woz13rule4) => 78.80/10.73 (( 78.80/10.73 (woz1_1) => 78.80/10.73 (( 78.80/10.73 (woz1_2) => 78.80/10.73 (( 78.80/10.73 (woz1_3) => 78.80/10.73 (( 78.80/10.73 (woz1_4) => 78.80/10.73 (( 78.80/10.73 (woz1_5) => 78.80/10.73 (( 78.80/10.73 (breln1all2) => 78.80/10.73 (( 78.80/10.73 (breln1SetBreln1) => 78.80/10.73 (( 78.80/10.73 (choice2fnsingleton) => 78.80/10.73 (( 78.80/10.73 (setOfPairsIsBReln1) => 78.80/10.73 (( 78.80/10.73 (breln1all1) => 78.80/10.73 (( 78.80/10.73 (subbreln1) => 78.80/10.73 (( 78.80/10.73 (eqbreln1) => 78.80/10.73 (( 78.80/10.73 (breln1invprop) => 78.80/10.73 (( 78.80/10.73 (breln1invI) => 78.80/10.73 (( 78.80/10.73 (breln1invE) => 78.80/10.73 (( 78.80/10.73 (breln1compprop) => 78.80/10.73 (( 78.80/10.73 (breln1compI) => 78.80/10.73 (( 78.80/10.73 (breln1compE) => 78.80/10.73 (( 78.80/10.73 (breln1compEex) => 78.80/10.73 (( 78.80/10.73 (breln1unionprop) => 78.80/10.73 (( 78.80/10.73 (breln1unionIL) => 78.80/10.73 (( 78.80/10.73 (breln1unionIR) => 78.80/10.73 (( 78.80/10.73 (breln1unionI) => 78.80/10.73 (( 78.80/10.73 (breln1unionE) => 78.80/10.73 (( 78.80/10.73 (breln1unionEcases) => 78.80/10.73 (( 78.80/10.73 (breln1unionCommutes) => 78.80/10.73 (( 78.80/10.73 (woz2Ex) => 78.80/10.73 (( 78.80/10.73 (woz2W) => 78.80/10.73 (( 78.80/10.73 (woz2A) => 78.80/10.73 (( 78.80/10.73 (woz2B) => 78.80/10.73 (( 78.80/10.73 (image1Ex) => 78.80/10.73 (( 78.80/10.73 (image1Ex1) => 78.80/10.73 (( 78.80/10.73 (image1Equiv) => 78.80/10.73 (( 78.80/10.73 (image1E) => 78.80/10.73 (( 78.80/10.73 (image1I) => 78.80/10.73 (( 78.80/10.73 (injFuncInInjFuncSet) => 78.80/10.73 (( 78.80/10.73 (injFuncSetFuncIn) => 78.80/10.73 (( 78.80/10.73 (injFuncSetFuncInj) => 78.80/10.73 (( 78.80/10.73 (surjFuncSetFuncIn) => 78.80/10.73 (( 78.80/10.73 (surjFuncSetFuncSurj) => 78.80/10.73 (( 78.80/10.73 (leftInvIsSurj) => 78.80/10.73 (( 78.80/10.73 (surjCantorThm) => 78.80/10.73 (( 78.80/10.73 (foundation2) => 78.80/10.73 (( 78.80/10.73 (notinself) => 78.80/10.73 (( 78.80/10.73 (notinself2) => 78.80/10.73 (( 78.80/10.73 (omegaSp) => 78.80/10.73 (( 78.80/10.73 (omegaSclos) => 78.80/10.73 (( 78.80/10.73 (peano0notS) => 78.80/10.73 (( 78.80/10.73 (peanoSinj) => 78.80/10.73 (( 78.80/10.73 (transitivesetOp1) => 78.80/10.73 (( 78.80/10.73 (binintTransitive) => 78.80/10.73 (( 78.80/10.73 (transitivesetOp2) => 78.80/10.73 (( 78.80/10.73 (setunionTransitive) => 78.80/10.73 (( 78.80/10.73 (ordinalMinLem1) => 78.80/10.73 (( 78.80/10.73 (!!) @ ( 78.80/10.73 ^[Y0 : $i]: 78.80/10.73 (( 78.80/10.73 (ordinal @ 78.80/10.73 Y0) => 78.80/10.73 (( 78.80/10.73 (!!) @ ( 78.80/10.73 ^[Y1 : $i]: 78.80/10.73 (( 78.80/10.73 (!!) @ ( 78.80/10.73 ^[Y2 : $i]: 78.80/10.73 (( 78.80/10.73 (in @ 78.80/10.73 Y2 @ 78.80/10.73 Y0) => 78.80/10.73 (( 78.80/10.73 (in @ 78.80/10.73 Y1 @ 78.80/10.73 Y2) => 78.80/10.73 (in @ 78.80/10.73 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 78.80/10.73 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2093])). 78.80/10.73 thf(zip_derived_cl2113, plain, 78.80/10.73 (~ (((setminusT_lem) => 78.80/10.73 (((complementT_lem) => 78.80/10.73 (((setextT) => 78.80/10.73 (((subsetTI) => 78.80/10.73 (((powersetTI1) => 78.80/10.73 (((powersetTE1) => 78.80/10.73 (((complementTI1) => 78.80/10.73 (((complementTE1) => 78.80/10.73 (((binintersectTELcontra) => 78.80/10.73 (((binintersectTERcontra) => 78.80/10.73 (((contrasubsetT) => 78.80/10.73 (((contrasubsetT1) => 78.80/10.73 (((contrasubsetT2) => 78.80/10.73 (((contrasubsetT3) => 78.80/10.73 (((doubleComplementI1) => 78.80/10.73 (((doubleComplementE1) => 78.80/10.73 (((doubleComplementSub1) => 78.80/10.73 (((doubleComplementSub2) => 78.80/10.73 (((doubleComplementEq) => 78.80/10.73 (((complementTnotintersectT) => 78.80/10.73 (((complementImpComplementIntersect) => 78.80/10.73 (((complementSubsetComplementIntersect) => 78.80/10.73 (((complementInPowersetComplementIntersect) => 78.80/10.73 (((contraSubsetComplement) => 78.80/10.73 (((complementTcontraSubset) => 78.80/10.73 (((binunionTILcontra) => 78.80/10.73 (((binunionTIRcontra) => 78.80/10.73 (((inIntersectImpInUnion) => 78.80/10.73 (((inIntersectImpInUnion2) => 78.80/10.73 (((inIntersectImpInIntersectUnions) => 78.80/10.73 (( 78.80/10.73 (intersectInPowersetIntersectUnions) => 78.80/10.73 (( 78.80/10.73 (inComplementUnionImpNotIn1) => 78.80/10.73 (( 78.80/10.73 (inComplementUnionImpInComplement1) => 78.80/10.73 (( 78.80/10.73 (binunionTE) => 78.80/10.73 (( 78.80/10.73 (binunionTEcontra) => 78.80/10.73 (( 78.80/10.73 (demorgan2a1) => 78.80/10.73 (( 78.80/10.73 (complementUnionInPowersetComplement) => 78.80/10.73 (( 78.80/10.73 (demorgan2a2) => 78.80/10.73 (( 78.80/10.73 (demorgan1a) => 78.80/10.73 (( 78.80/10.73 (demorgan1b) => 78.80/10.73 (( 78.80/10.73 (demorgan1) => 78.80/10.73 (( 78.80/10.73 (demorgan2a) => 78.80/10.73 (( 78.80/10.73 (demorgan2b2) => 78.80/10.73 (( 78.80/10.73 (demorgan2b) => 78.80/10.73 (( 78.80/10.73 (demorgan2) => 78.80/10.73 (( 78.80/10.73 (woz13rule0) => 78.80/10.73 (( 78.80/10.73 (woz13rule1) => 78.80/10.73 (( 78.80/10.73 (woz13rule2) => 78.80/10.73 (( 78.80/10.73 (woz13rule3) => 78.80/10.73 (( 78.80/10.73 (woz13rule4) => 78.80/10.73 (( 78.80/10.73 (woz1_1) => 78.80/10.73 (( 78.80/10.73 (woz1_2) => 78.80/10.73 (( 78.80/10.73 (woz1_3) => 78.80/10.73 (( 78.80/10.73 (woz1_4) => 78.80/10.73 (( 78.80/10.73 (woz1_5) => 78.80/10.73 (( 78.80/10.73 (breln1all2) => 78.80/10.73 (( 78.80/10.73 (breln1SetBreln1) => 78.80/10.73 (( 78.80/10.73 (choice2fnsingleton) => 78.80/10.73 (( 78.80/10.73 (setOfPairsIsBReln1) => 78.80/10.73 (( 78.80/10.73 (breln1all1) => 78.80/10.73 (( 78.80/10.73 (subbreln1) => 78.80/10.73 (( 78.80/10.73 (eqbreln1) => 78.80/10.73 (( 78.80/10.73 (breln1invprop) => 78.80/10.73 (( 78.80/10.73 (breln1invI) => 78.80/10.73 (( 78.80/10.73 (breln1invE) => 78.80/10.73 (( 78.80/10.73 (breln1compprop) => 78.80/10.73 (( 78.80/10.73 (breln1compI) => 78.80/10.73 (( 78.80/10.73 (breln1compE) => 78.80/10.73 (( 78.80/10.73 (breln1compEex) => 78.80/10.73 (( 78.80/10.73 (breln1unionprop) => 78.80/10.73 (( 78.80/10.73 (breln1unionIL) => 78.80/10.73 (( 78.80/10.73 (breln1unionIR) => 78.80/10.73 (( 78.80/10.73 (breln1unionI) => 78.80/10.73 (( 78.80/10.73 (breln1unionE) => 78.80/10.73 (( 78.80/10.73 (breln1unionEcases) => 78.80/10.73 (( 78.80/10.73 (breln1unionCommutes) => 78.80/10.73 (( 78.80/10.73 (woz2Ex) => 78.80/10.73 (( 78.80/10.73 (woz2W) => 78.80/10.73 (( 78.80/10.73 (woz2A) => 78.80/10.73 (( 78.80/10.73 (woz2B) => 78.80/10.73 (( 78.80/10.73 (image1Ex) => 78.80/10.73 (( 78.80/10.73 (image1Ex1) => 78.80/10.73 (( 78.80/10.73 (image1Equiv) => 78.80/10.73 (( 78.80/10.73 (image1E) => 78.80/10.73 (( 78.80/10.73 (image1I) => 78.80/10.73 (( 78.80/10.73 (injFuncInInjFuncSet) => 78.80/10.73 (( 78.80/10.73 (injFuncSetFuncIn) => 78.80/10.73 (( 78.80/10.73 (injFuncSetFuncInj) => 78.80/10.73 (( 78.80/10.73 (surjFuncSetFuncIn) => 78.80/10.73 (( 78.80/10.73 (surjFuncSetFuncSurj) => 78.80/10.73 (( 78.80/10.73 (leftInvIsSurj) => 78.80/10.73 (( 78.80/10.73 (surjCantorThm) => 78.80/10.73 (( 78.80/10.73 (foundation2) => 78.80/10.73 (( 78.80/10.73 (notinself) => 78.80/10.73 (( 78.80/10.73 (notinself2) => 78.80/10.73 (( 78.80/10.73 (omegaSp) => 78.80/10.73 (( 78.80/10.73 (omegaSclos) => 78.80/10.73 (( 78.80/10.73 (peano0notS) => 78.80/10.73 (( 78.80/10.73 (peanoSinj) => 78.80/10.73 (( 78.80/10.73 (transitivesetOp1) => 78.80/10.73 (( 78.80/10.73 (binintTransitive) => 78.80/10.73 (( 78.80/10.73 (transitivesetOp2) => 78.80/10.73 (( 78.80/10.73 (setunionTransitive) => 78.80/10.73 (( 78.80/10.73 (ordinalMinLem1) => 78.80/10.73 (( 78.80/10.73 (!!) @ ( 78.80/10.73 ^[Y0 : $i]: 78.80/10.73 (( 78.80/10.73 (ordinal @ 78.80/10.73 Y0) => 78.80/10.73 (( 78.80/10.73 (!!) @ ( 78.80/10.73 ^[Y1 : $i]: 78.80/10.73 (( 78.80/10.73 (!!) @ ( 78.80/10.73 ^[Y2 : $i]: 78.80/10.73 (( 78.80/10.73 (in @ 78.80/10.73 Y2 @ 78.80/10.73 Y0) => 78.80/10.73 (( 78.80/10.73 (in @ 78.80/10.73 Y1 @ 78.80/10.73 Y2) => 78.80/10.73 (in @ 78.80/10.73 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 78.80/10.73 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2103])). 78.80/10.73 thf(zip_derived_cl2121, plain, 78.80/10.73 (~ (((complementT_lem) => 78.80/10.73 (((setextT) => 78.80/10.73 (((subsetTI) => 78.80/10.73 (((powersetTI1) => 78.80/10.73 (((powersetTE1) => 78.80/10.73 (((complementTI1) => 78.80/10.73 (((complementTE1) => 78.80/10.73 (((binintersectTELcontra) => 78.80/10.73 (((binintersectTERcontra) => 78.80/10.73 (((contrasubsetT) => 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78.80/10.73 (binunionTE) => 78.80/10.73 (( 78.80/10.73 (binunionTEcontra) => 78.80/10.73 (( 78.80/10.73 (demorgan2a1) => 78.80/10.73 (( 78.80/10.73 (complementUnionInPowersetComplement) => 78.80/10.73 (( 78.80/10.73 (demorgan2a2) => 78.80/10.73 (( 78.80/10.73 (demorgan1a) => 78.80/10.73 (( 78.80/10.73 (demorgan1b) => 78.80/10.73 (( 78.80/10.73 (demorgan1) => 78.80/10.73 (( 78.80/10.73 (demorgan2a) => 78.80/10.73 (( 78.80/10.73 (demorgan2b2) => 78.80/10.73 (( 78.80/10.73 (demorgan2b) => 78.80/10.73 (( 78.80/10.73 (demorgan2) => 78.80/10.73 (( 78.80/10.73 (woz13rule0) => 78.80/10.73 (( 78.80/10.73 (woz13rule1) => 78.80/10.73 (( 78.80/10.73 (woz13rule2) => 78.80/10.73 (( 78.80/10.73 (woz13rule3) => 78.80/10.73 (( 78.80/10.73 (woz13rule4) => 78.80/10.73 (( 78.80/10.73 (woz1_1) => 78.80/10.73 (( 78.80/10.73 (woz1_2) => 78.80/10.73 (( 78.80/10.73 (woz1_3) => 78.80/10.73 (( 78.80/10.73 (woz1_4) => 78.80/10.73 (( 78.80/10.73 (woz1_5) => 78.80/10.73 (( 78.80/10.73 (breln1all2) => 78.80/10.73 (( 78.80/10.73 (breln1SetBreln1) => 78.80/10.73 (( 78.80/10.73 (choice2fnsingleton) => 78.80/10.73 (( 78.80/10.73 (setOfPairsIsBReln1) => 78.80/10.73 (( 78.80/10.73 (breln1all1) => 78.80/10.73 (( 78.80/10.73 (subbreln1) => 78.80/10.73 (( 78.80/10.73 (eqbreln1) => 78.80/10.73 (( 78.80/10.73 (breln1invprop) => 78.80/10.73 (( 78.80/10.73 (breln1invI) => 78.80/10.73 (( 78.80/10.73 (breln1invE) => 78.80/10.73 (( 78.80/10.73 (breln1compprop) => 78.80/10.73 (( 78.80/10.73 (breln1compI) => 78.80/10.73 (( 78.80/10.73 (breln1compE) => 78.80/10.73 (( 78.80/10.73 (breln1compEex) => 78.80/10.73 (( 78.80/10.73 (breln1unionprop) => 78.80/10.73 (( 78.80/10.73 (breln1unionIL) => 78.80/10.73 (( 78.80/10.73 (breln1unionIR) => 78.80/10.73 (( 78.80/10.73 (breln1unionI) => 78.80/10.73 (( 78.80/10.73 (breln1unionE) => 78.80/10.73 (( 78.80/10.73 (breln1unionEcases) => 78.80/10.73 (( 78.80/10.73 (breln1unionCommutes) => 78.80/10.73 (( 78.80/10.73 (woz2Ex) => 78.80/10.73 (( 78.80/10.73 (woz2W) => 78.80/10.73 (( 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(binintTransitive) => 78.80/10.73 (( 78.80/10.73 (transitivesetOp2) => 78.80/10.73 (( 78.80/10.73 (setunionTransitive) => 78.80/10.73 (( 78.80/10.73 (ordinalMinLem1) => 78.80/10.73 (( 78.80/10.73 (!!) @ ( 78.80/10.73 ^[Y0 : $i]: 78.80/10.73 (( 78.80/10.73 (ordinal @ 78.80/10.73 Y0) => 78.80/10.73 (( 78.80/10.73 (!!) @ ( 78.80/10.73 ^[Y1 : $i]: 78.80/10.73 (( 78.80/10.73 (!!) @ ( 78.80/10.73 ^[Y2 : $i]: 78.80/10.73 (( 78.80/10.73 (in @ 78.80/10.73 Y2 @ 78.80/10.73 Y0) => 78.80/10.73 (( 78.80/10.73 (in @ 78.80/10.73 Y1 @ 78.80/10.73 Y2) => 78.80/10.73 (in @ 78.80/10.73 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 78.80/10.73 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2113])). 78.80/10.73 thf(zip_derived_cl2130, plain, 78.80/10.73 (~ (((setextT) => 78.80/10.73 (((subsetTI) => 78.80/10.73 (((powersetTI1) => 78.80/10.73 (((powersetTE1) => 78.80/10.73 (((complementTI1) => 78.80/10.73 (((complementTE1) => 78.80/10.73 (((binintersectTELcontra) => 78.80/10.73 (((binintersectTERcontra) => 78.80/10.73 (((contrasubsetT) => 78.80/10.73 (((contrasubsetT1) => 78.80/10.73 (((contrasubsetT2) => 78.80/10.73 (((contrasubsetT3) => 78.80/10.73 (((doubleComplementI1) => 78.80/10.73 (((doubleComplementE1) => 78.80/10.73 (((doubleComplementSub1) => 78.80/10.73 (((doubleComplementSub2) => 78.80/10.73 (((doubleComplementEq) => 78.80/10.73 (((complementTnotintersectT) => 78.80/10.73 (((complementImpComplementIntersect) => 78.80/10.73 (((complementSubsetComplementIntersect) => 78.80/10.73 (((complementInPowersetComplementIntersect) => 78.80/10.73 (((contraSubsetComplement) => 78.80/10.73 (((complementTcontraSubset) => 78.80/10.73 (((binunionTILcontra) => 78.80/10.73 (((binunionTIRcontra) => 78.80/10.73 (((inIntersectImpInUnion) => 78.80/10.73 (((inIntersectImpInUnion2) => 78.80/10.73 (((inIntersectImpInIntersectUnions) => 78.80/10.73 (((intersectInPowersetIntersectUnions) => 78.80/10.73 (((inComplementUnionImpNotIn1) => 78.80/10.73 (( 78.80/10.73 (inComplementUnionImpInComplement1) => 78.80/10.73 (( 78.80/10.73 (binunionTE) => 78.80/10.73 (( 78.80/10.73 (binunionTEcontra) => 78.80/10.73 (( 78.80/10.73 (demorgan2a1) => 78.80/10.73 (( 78.80/10.73 (complementUnionInPowersetComplement) => 78.80/10.73 (( 78.80/10.73 (demorgan2a2) => 78.80/10.73 (( 78.80/10.73 (demorgan1a) => 78.80/10.73 (( 78.80/10.73 (demorgan1b) => 78.80/10.73 (( 78.80/10.73 (demorgan1) => 78.80/10.73 (( 78.80/10.73 (demorgan2a) => 78.80/10.73 (( 78.80/10.73 (demorgan2b2) => 78.80/10.73 (( 78.80/10.73 (demorgan2b) => 78.80/10.73 (( 78.80/10.73 (demorgan2) => 78.80/10.73 (( 78.80/10.73 (woz13rule0) => 78.80/10.73 (( 78.80/10.73 (woz13rule1) => 78.80/10.73 (( 78.80/10.73 (woz13rule2) => 78.80/10.73 (( 78.80/10.73 (woz13rule3) => 78.80/10.73 (( 78.80/10.73 (woz13rule4) => 78.80/10.73 (( 78.80/10.73 (woz1_1) => 78.80/10.73 (( 78.80/10.73 (woz1_2) => 78.80/10.73 (( 78.80/10.73 (woz1_3) => 78.80/10.73 (( 78.80/10.73 (woz1_4) => 78.80/10.73 (( 78.80/10.73 (woz1_5) => 78.80/10.73 (( 78.80/10.73 (breln1all2) => 78.80/10.73 (( 78.80/10.73 (breln1SetBreln1) => 78.80/10.73 (( 78.80/10.73 (choice2fnsingleton) => 78.80/10.73 (( 78.80/10.73 (setOfPairsIsBReln1) => 78.80/10.73 (( 78.80/10.73 (breln1all1) => 78.80/10.73 (( 78.80/10.73 (subbreln1) => 78.80/10.73 (( 78.80/10.73 (eqbreln1) => 78.80/10.73 (( 78.80/10.73 (breln1invprop) => 78.80/10.73 (( 78.80/10.73 (breln1invI) => 78.80/10.73 (( 78.80/10.73 (breln1invE) => 78.80/10.73 (( 78.80/10.73 (breln1compprop) => 78.80/10.73 (( 78.80/10.73 (breln1compI) => 78.80/10.73 (( 78.80/10.73 (breln1compE) => 78.80/10.73 (( 78.80/10.73 (breln1compEex) => 78.80/10.73 (( 78.80/10.73 (breln1unionprop) => 78.80/10.73 (( 78.80/10.73 (breln1unionIL) => 78.80/10.73 (( 78.80/10.73 (breln1unionIR) => 78.80/10.73 (( 78.80/10.73 (breln1unionI) => 78.80/10.73 (( 78.80/10.73 (breln1unionE) => 78.80/10.73 (( 78.80/10.73 (breln1unionEcases) => 78.80/10.73 (( 78.80/10.73 (breln1unionCommutes) => 78.80/10.73 (( 78.80/10.73 (woz2Ex) => 78.80/10.73 (( 78.80/10.73 (woz2W) => 78.80/10.73 (( 78.80/10.73 (woz2A) => 78.80/10.73 (( 78.80/10.73 (woz2B) => 78.80/10.73 (( 78.80/10.73 (image1Ex) => 78.80/10.73 (( 78.80/10.73 (image1Ex1) => 78.80/10.73 (( 78.80/10.73 (image1Equiv) => 78.80/10.73 (( 78.80/10.73 (image1E) => 78.80/10.73 (( 78.80/10.73 (image1I) => 78.80/10.73 (( 78.80/10.73 (injFuncInInjFuncSet) => 78.80/10.73 (( 78.80/10.73 (injFuncSetFuncIn) => 78.80/10.73 (( 78.80/10.73 (injFuncSetFuncInj) => 78.80/10.73 (( 78.80/10.73 (surjFuncSetFuncIn) => 78.80/10.73 (( 78.80/10.73 (surjFuncSetFuncSurj) => 78.80/10.73 (( 78.80/10.73 (leftInvIsSurj) => 78.80/10.73 (( 78.80/10.73 (surjCantorThm) => 78.80/10.73 (( 78.80/10.73 (foundation2) => 78.80/10.73 (( 78.80/10.73 (notinself) => 78.80/10.73 (( 78.80/10.73 (notinself2) => 78.80/10.73 (( 78.80/10.73 (omegaSp) => 78.80/10.73 (( 78.80/10.73 (omegaSclos) => 78.80/10.73 (( 78.80/10.73 (peano0notS) => 78.80/10.73 (( 78.80/10.73 (peanoSinj) => 78.80/10.73 (( 78.80/10.73 (transitivesetOp1) => 78.80/10.73 (( 78.80/10.73 (binintTransitive) => 78.80/10.73 (( 78.80/10.73 (transitivesetOp2) => 78.80/10.73 (( 78.80/10.73 (setunionTransitive) => 78.80/10.73 (( 78.80/10.73 (ordinalMinLem1) => 78.80/10.73 (( 78.80/10.73 (!!) @ ( 78.80/10.73 ^[Y0 : $i]: 78.80/10.73 (( 78.80/10.73 (ordinal @ 78.80/10.73 Y0) => 78.80/10.73 (( 78.80/10.73 (!!) @ ( 78.80/10.73 ^[Y1 : $i]: 78.80/10.73 (( 78.80/10.73 (!!) @ ( 78.80/10.73 ^[Y2 : $i]: 78.80/10.73 (( 78.80/10.73 (in @ 78.80/10.73 Y2 @ 78.80/10.73 Y0) => 78.80/10.73 (( 78.80/10.73 (in @ 78.80/10.73 Y1 @ 78.80/10.73 Y2) => 78.80/10.73 (in @ 78.80/10.73 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 78.80/10.73 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2121])). 78.80/10.73 thf(zip_derived_cl2140, plain, 78.80/10.73 (~ (((subsetTI) => 78.80/10.73 (((powersetTI1) => 78.80/10.73 (((powersetTE1) => 78.80/10.73 (((complementTI1) => 78.80/10.73 (((complementTE1) => 78.80/10.73 (((binintersectTELcontra) => 78.80/10.73 (((binintersectTERcontra) => 78.80/10.73 (((contrasubsetT) => 78.80/10.73 (((contrasubsetT1) => 78.80/10.73 (((contrasubsetT2) => 78.80/10.73 (((contrasubsetT3) => 78.80/10.73 (((doubleComplementI1) => 78.80/10.73 (((doubleComplementE1) => 78.80/10.73 (((doubleComplementSub1) => 78.80/10.73 (((doubleComplementSub2) => 78.80/10.73 (((doubleComplementEq) => 78.80/10.73 (((complementTnotintersectT) => 78.80/10.73 (((complementImpComplementIntersect) => 78.80/10.73 (((complementSubsetComplementIntersect) => 78.80/10.73 (((complementInPowersetComplementIntersect) => 78.80/10.73 (((contraSubsetComplement) => 78.80/10.73 (((complementTcontraSubset) => 78.80/10.73 (((binunionTILcontra) => 78.80/10.73 (((binunionTIRcontra) => 78.80/10.73 (((inIntersectImpInUnion) => 78.80/10.73 (((inIntersectImpInUnion2) => 78.80/10.73 (((inIntersectImpInIntersectUnions) => 78.80/10.73 (((intersectInPowersetIntersectUnions) => 78.80/10.73 (((inComplementUnionImpNotIn1) => 78.80/10.73 (((inComplementUnionImpInComplement1) => 78.80/10.73 (( 78.80/10.73 (binunionTE) => 78.80/10.73 (( 78.80/10.73 (binunionTEcontra) => 78.80/10.73 (( 78.80/10.73 (demorgan2a1) => 78.80/10.73 (( 78.80/10.73 (complementUnionInPowersetComplement) => 78.80/10.73 (( 78.80/10.73 (demorgan2a2) => 78.80/10.73 (( 78.80/10.73 (demorgan1a) => 78.80/10.73 (( 78.80/10.73 (demorgan1b) => 78.80/10.73 (( 78.80/10.73 (demorgan1) => 78.80/10.73 (( 78.80/10.73 (demorgan2a) => 78.80/10.73 (( 78.80/10.73 (demorgan2b2) => 78.80/10.73 (( 78.80/10.73 (demorgan2b) => 78.80/10.73 (( 78.80/10.73 (demorgan2) => 78.80/10.73 (( 78.80/10.73 (woz13rule0) => 78.80/10.73 (( 78.80/10.73 (woz13rule1) => 78.80/10.73 (( 78.80/10.73 (woz13rule2) => 78.80/10.73 (( 78.80/10.73 (woz13rule3) => 78.80/10.73 (( 78.80/10.73 (woz13rule4) => 78.80/10.73 (( 78.80/10.73 (woz1_1) => 78.80/10.73 (( 78.80/10.73 (woz1_2) => 78.80/10.73 (( 78.80/10.73 (woz1_3) => 78.80/10.73 (( 78.80/10.73 (woz1_4) => 78.80/10.73 (( 78.80/10.73 (woz1_5) => 78.80/10.73 (( 78.80/10.73 (breln1all2) => 78.80/10.73 (( 78.80/10.73 (breln1SetBreln1) => 78.80/10.73 (( 78.80/10.73 (choice2fnsingleton) => 78.80/10.73 (( 78.80/10.73 (setOfPairsIsBReln1) => 78.80/10.73 (( 78.80/10.73 (breln1all1) => 78.80/10.73 (( 78.80/10.73 (subbreln1) => 78.80/10.73 (( 78.80/10.73 (eqbreln1) => 78.80/10.73 (( 78.80/10.73 (breln1invprop) => 78.80/10.73 (( 78.80/10.73 (breln1invI) => 78.80/10.73 (( 78.80/10.73 (breln1invE) => 78.80/10.73 (( 78.80/10.73 (breln1compprop) => 78.80/10.73 (( 78.80/10.73 (breln1compI) => 78.80/10.73 (( 78.80/10.73 (breln1compE) => 78.80/10.73 (( 78.80/10.73 (breln1compEex) => 78.80/10.73 (( 78.80/10.73 (breln1unionprop) => 78.80/10.73 (( 78.80/10.73 (breln1unionIL) => 78.80/10.73 (( 78.80/10.73 (breln1unionIR) => 78.80/10.73 (( 78.80/10.73 (breln1unionI) => 78.80/10.73 (( 78.80/10.73 (breln1unionE) => 78.80/10.73 (( 78.80/10.73 (breln1unionEcases) => 78.80/10.73 (( 78.80/10.73 (breln1unionCommutes) => 78.80/10.73 (( 78.80/10.73 (woz2Ex) => 78.80/10.73 (( 78.80/10.73 (woz2W) => 78.80/10.73 (( 78.80/10.73 (woz2A) => 78.80/10.73 (( 78.80/10.73 (woz2B) => 78.80/10.73 (( 78.80/10.73 (image1Ex) => 78.80/10.73 (( 78.80/10.73 (image1Ex1) => 78.80/10.73 (( 78.80/10.73 (image1Equiv) => 78.80/10.73 (( 78.80/10.73 (image1E) => 78.80/10.73 (( 78.80/10.73 (image1I) => 78.80/10.73 (( 78.80/10.73 (injFuncInInjFuncSet) => 78.80/10.73 (( 78.80/10.73 (injFuncSetFuncIn) => 78.80/10.73 (( 78.80/10.73 (injFuncSetFuncInj) => 78.80/10.73 (( 78.80/10.73 (surjFuncSetFuncIn) => 78.80/10.73 (( 78.80/10.73 (surjFuncSetFuncSurj) => 78.80/10.73 (( 78.80/10.73 (leftInvIsSurj) => 78.80/10.73 (( 78.80/10.73 (surjCantorThm) => 78.80/10.73 (( 78.80/10.73 (foundation2) => 78.80/10.73 (( 78.80/10.73 (notinself) => 78.80/10.73 (( 78.80/10.73 (notinself2) => 78.80/10.73 (( 78.80/10.73 (omegaSp) => 78.80/10.73 (( 78.80/10.73 (omegaSclos) => 78.80/10.73 (( 78.80/10.73 (peano0notS) => 78.80/10.73 (( 78.80/10.73 (peanoSinj) => 78.80/10.73 (( 78.80/10.73 (transitivesetOp1) => 78.80/10.73 (( 78.80/10.73 (binintTransitive) => 78.80/10.73 (( 78.80/10.73 (transitivesetOp2) => 78.80/10.73 (( 78.80/10.73 (setunionTransitive) => 78.80/10.73 (( 78.80/10.73 (ordinalMinLem1) => 78.80/10.73 (( 78.80/10.73 (!!) @ ( 78.80/10.73 ^[Y0 : $i]: 78.80/10.73 (( 78.80/10.73 (ordinal @ 78.80/10.73 Y0) => 78.80/10.73 (( 78.80/10.73 (!!) @ ( 78.80/10.73 ^[Y1 : $i]: 78.80/10.73 (( 78.80/10.73 (!!) @ ( 78.80/10.73 ^[Y2 : $i]: 78.80/10.73 (( 78.80/10.73 (in @ 78.80/10.73 Y2 @ 78.80/10.73 Y0) => 78.80/10.73 (( 78.80/10.73 (in @ 78.80/10.73 Y1 @ 78.80/10.73 Y2) => 78.80/10.73 (in @ 78.80/10.73 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 78.80/10.73 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2130])). 78.80/10.73 thf(zip_derived_cl2151, plain, 78.80/10.73 (~ (((powersetTI1) => 78.80/10.73 (((powersetTE1) => 78.80/10.73 (((complementTI1) => 78.80/10.73 (((complementTE1) => 78.80/10.73 (((binintersectTELcontra) => 78.80/10.73 (((binintersectTERcontra) => 78.80/10.73 (((contrasubsetT) => 78.80/10.73 (((contrasubsetT1) => 78.80/10.73 (((contrasubsetT2) => 78.80/10.73 (((contrasubsetT3) => 78.80/10.73 (((doubleComplementI1) => 78.80/10.73 (((doubleComplementE1) => 78.80/10.73 (((doubleComplementSub1) => 78.80/10.73 (((doubleComplementSub2) => 78.80/10.73 (((doubleComplementEq) => 78.80/10.73 (((complementTnotintersectT) => 78.80/10.73 (((complementImpComplementIntersect) => 78.80/10.73 (((complementSubsetComplementIntersect) => 78.80/10.73 (((complementInPowersetComplementIntersect) => 78.80/10.73 (((contraSubsetComplement) => 78.80/10.73 (((complementTcontraSubset) => 78.80/10.73 (((binunionTILcontra) => 78.80/10.73 (((binunionTIRcontra) => 78.80/10.73 (((inIntersectImpInUnion) => 78.80/10.73 (((inIntersectImpInUnion2) => 78.80/10.73 (((inIntersectImpInIntersectUnions) => 78.80/10.73 (((intersectInPowersetIntersectUnions) => 78.80/10.73 (((inComplementUnionImpNotIn1) => 78.80/10.73 (((inComplementUnionImpInComplement1) => 78.80/10.73 (((binunionTE) => 78.80/10.73 (( 78.80/10.73 (binunionTEcontra) => 78.80/10.73 (( 78.80/10.73 (demorgan2a1) => 78.80/10.73 (( 78.80/10.73 (complementUnionInPowersetComplement) => 78.80/10.73 (( 78.80/10.73 (demorgan2a2) => 78.80/10.73 (( 78.80/10.73 (demorgan1a) => 78.80/10.73 (( 78.80/10.73 (demorgan1b) => 78.80/10.73 (( 78.80/10.73 (demorgan1) => 78.80/10.73 (( 78.80/10.73 (demorgan2a) => 78.80/10.73 (( 78.80/10.73 (demorgan2b2) => 78.80/10.73 (( 78.80/10.73 (demorgan2b) => 78.80/10.73 (( 78.80/10.73 (demorgan2) => 78.80/10.73 (( 78.80/10.73 (woz13rule0) => 78.80/10.73 (( 78.80/10.73 (woz13rule1) => 78.80/10.73 (( 78.80/10.73 (woz13rule2) => 78.80/10.73 (( 78.80/10.73 (woz13rule3) => 78.80/10.73 (( 78.80/10.73 (woz13rule4) => 78.80/10.73 (( 78.80/10.73 (woz1_1) => 78.80/10.73 (( 78.80/10.73 (woz1_2) => 78.80/10.73 (( 78.80/10.73 (woz1_3) => 78.80/10.73 (( 78.80/10.73 (woz1_4) => 78.80/10.73 (( 78.80/10.73 (woz1_5) => 78.80/10.73 (( 78.80/10.73 (breln1all2) => 78.80/10.73 (( 78.80/10.73 (breln1SetBreln1) => 78.80/10.73 (( 78.80/10.73 (choice2fnsingleton) => 78.80/10.73 (( 78.80/10.73 (setOfPairsIsBReln1) => 78.80/10.73 (( 78.80/10.73 (breln1all1) => 78.80/10.73 (( 78.80/10.73 (subbreln1) => 78.80/10.73 (( 78.80/10.73 (eqbreln1) => 78.80/10.73 (( 78.80/10.73 (breln1invprop) => 78.80/10.73 (( 78.80/10.73 (breln1invI) => 78.80/10.73 (( 78.80/10.73 (breln1invE) => 78.80/10.73 (( 78.80/10.73 (breln1compprop) => 78.80/10.73 (( 78.80/10.73 (breln1compI) => 78.80/10.73 (( 78.80/10.73 (breln1compE) => 78.80/10.73 (( 78.80/10.73 (breln1compEex) => 78.80/10.73 (( 78.80/10.73 (breln1unionprop) => 78.80/10.73 (( 78.80/10.73 (breln1unionIL) => 78.80/10.73 (( 78.80/10.73 (breln1unionIR) => 78.80/10.73 (( 78.80/10.73 (breln1unionI) => 78.80/10.73 (( 78.80/10.73 (breln1unionE) => 78.80/10.73 (( 78.80/10.73 (breln1unionEcases) => 78.80/10.73 (( 78.80/10.73 (breln1unionCommutes) => 78.80/10.73 (( 78.80/10.73 (woz2Ex) => 78.80/10.73 (( 78.80/10.73 (woz2W) => 78.80/10.73 (( 78.80/10.73 (woz2A) => 78.80/10.73 (( 78.80/10.73 (woz2B) => 78.80/10.73 (( 78.80/10.73 (image1Ex) => 78.80/10.73 (( 78.80/10.73 (image1Ex1) => 78.80/10.73 (( 78.80/10.73 (image1Equiv) => 78.80/10.73 (( 78.80/10.73 (image1E) => 78.80/10.73 (( 78.80/10.73 (image1I) => 78.80/10.73 (( 78.80/10.73 (injFuncInInjFuncSet) => 78.80/10.73 (( 78.80/10.73 (injFuncSetFuncIn) => 78.80/10.73 (( 78.80/10.73 (injFuncSetFuncInj) => 78.80/10.73 (( 78.80/10.73 (surjFuncSetFuncIn) => 78.80/10.73 (( 78.80/10.73 (surjFuncSetFuncSurj) => 78.80/10.73 (( 78.80/10.73 (leftInvIsSurj) => 78.80/10.73 (( 78.80/10.73 (surjCantorThm) => 78.80/10.73 (( 78.80/10.73 (foundation2) => 78.80/10.73 (( 78.80/10.73 (notinself) => 78.80/10.73 (( 78.80/10.73 (notinself2) => 78.80/10.73 (( 78.80/10.73 (omegaSp) => 78.80/10.73 (( 78.80/10.73 (omegaSclos) => 78.80/10.73 (( 78.80/10.73 (peano0notS) => 78.80/10.73 (( 78.80/10.73 (peanoSinj) => 78.80/10.73 (( 78.80/10.73 (transitivesetOp1) => 78.80/10.73 (( 78.80/10.73 (binintTransitive) => 78.80/10.73 (( 78.80/10.73 (transitivesetOp2) => 78.80/10.73 (( 78.80/10.73 (setunionTransitive) => 78.80/10.73 (( 78.80/10.73 (ordinalMinLem1) => 78.80/10.73 (( 78.80/10.73 (!!) @ ( 78.80/10.73 ^[Y0 : $i]: 78.80/10.73 (( 78.80/10.73 (ordinal @ 78.80/10.73 Y0) => 78.80/10.73 (( 78.80/10.73 (!!) @ ( 78.80/10.73 ^[Y1 : $i]: 78.80/10.73 (( 78.80/10.73 (!!) @ ( 78.80/10.73 ^[Y2 : $i]: 78.80/10.73 (( 78.80/10.73 (in @ 78.80/10.73 Y2 @ 78.80/10.73 Y0) => 78.80/10.73 (( 78.80/10.73 (in @ 78.80/10.73 Y1 @ 78.80/10.73 Y2) => 78.80/10.73 (in @ 78.80/10.73 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 78.80/10.73 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2140])). 78.80/10.73 thf(zip_derived_cl2159, plain, 78.80/10.73 (~ (((powersetTE1) => 78.80/10.73 (((complementTI1) => 78.80/10.73 (((complementTE1) => 78.80/10.73 (((binintersectTELcontra) => 78.80/10.73 (((binintersectTERcontra) => 78.80/10.73 (((contrasubsetT) => 78.80/10.73 (((contrasubsetT1) => 78.80/10.73 (((contrasubsetT2) => 78.80/10.73 (((contrasubsetT3) => 78.80/10.73 (((doubleComplementI1) => 78.80/10.73 (((doubleComplementE1) => 78.80/10.73 (((doubleComplementSub1) => 78.80/10.73 (((doubleComplementSub2) => 78.80/10.73 (((doubleComplementEq) => 78.80/10.73 (((complementTnotintersectT) => 78.80/10.73 (((complementImpComplementIntersect) => 78.80/10.73 (((complementSubsetComplementIntersect) => 78.80/10.73 (((complementInPowersetComplementIntersect) => 78.80/10.73 (((contraSubsetComplement) => 78.80/10.73 (((complementTcontraSubset) => 78.80/10.73 (((binunionTILcontra) => 78.80/10.73 (((binunionTIRcontra) => 78.80/10.73 (((inIntersectImpInUnion) => 78.80/10.73 (((inIntersectImpInUnion2) => 78.80/10.73 (((inIntersectImpInIntersectUnions) => 78.80/10.73 (((intersectInPowersetIntersectUnions) => 78.80/10.73 (((inComplementUnionImpNotIn1) => 78.80/10.73 (((inComplementUnionImpInComplement1) => 78.80/10.73 (((binunionTE) => 78.80/10.73 (((binunionTEcontra) => 78.80/10.73 (( 78.80/10.73 (demorgan2a1) => 78.80/10.73 (( 78.80/10.73 (complementUnionInPowersetComplement) => 78.80/10.73 (( 78.80/10.73 (demorgan2a2) => 78.80/10.73 (( 78.80/10.73 (demorgan1a) => 78.80/10.73 (( 78.80/10.73 (demorgan1b) => 78.80/10.73 (( 78.80/10.73 (demorgan1) => 78.80/10.73 (( 78.80/10.73 (demorgan2a) => 78.80/10.73 (( 78.80/10.73 (demorgan2b2) => 78.80/10.73 (( 78.80/10.73 (demorgan2b) => 78.80/10.73 (( 78.80/10.73 (demorgan2) => 78.80/10.73 (( 78.80/10.73 (woz13rule0) => 78.80/10.73 (( 78.80/10.73 (woz13rule1) => 78.80/10.73 (( 78.80/10.73 (woz13rule2) => 78.80/10.73 (( 78.80/10.73 (woz13rule3) => 78.80/10.73 (( 78.80/10.73 (woz13rule4) => 78.80/10.73 (( 78.80/10.73 (woz1_1) => 78.80/10.73 (( 78.80/10.73 (woz1_2) => 78.80/10.73 (( 78.80/10.73 (woz1_3) => 78.80/10.73 (( 78.80/10.73 (woz1_4) => 78.80/10.73 (( 78.80/10.73 (woz1_5) => 78.80/10.73 (( 78.80/10.73 (breln1all2) => 78.80/10.73 (( 78.80/10.73 (breln1SetBreln1) => 78.80/10.73 (( 78.80/10.73 (choice2fnsingleton) => 78.80/10.73 (( 78.80/10.73 (setOfPairsIsBReln1) => 78.80/10.73 (( 78.80/10.73 (breln1all1) => 78.80/10.73 (( 78.80/10.73 (subbreln1) => 78.80/10.73 (( 78.80/10.73 (eqbreln1) => 78.80/10.73 (( 78.80/10.73 (breln1invprop) => 78.80/10.73 (( 78.80/10.73 (breln1invI) => 78.80/10.73 (( 78.80/10.73 (breln1invE) => 78.80/10.73 (( 78.80/10.73 (breln1compprop) => 78.80/10.73 (( 78.80/10.73 (breln1compI) => 78.80/10.73 (( 78.80/10.73 (breln1compE) => 78.80/10.73 (( 78.80/10.73 (breln1compEex) => 78.80/10.73 (( 78.80/10.73 (breln1unionprop) => 78.80/10.73 (( 78.80/10.73 (breln1unionIL) => 78.80/10.73 (( 78.80/10.73 (breln1unionIR) => 78.80/10.73 (( 78.80/10.73 (breln1unionI) => 78.80/10.73 (( 78.80/10.73 (breln1unionE) => 78.80/10.73 (( 78.80/10.73 (breln1unionEcases) => 78.80/10.73 (( 78.80/10.73 (breln1unionCommutes) => 78.80/10.73 (( 78.80/10.73 (woz2Ex) => 78.80/10.73 (( 78.80/10.73 (woz2W) => 78.80/10.73 (( 78.80/10.73 (woz2A) => 78.80/10.73 (( 78.80/10.73 (woz2B) => 78.80/10.73 (( 78.80/10.73 (image1Ex) => 78.80/10.73 (( 78.80/10.73 (image1Ex1) => 78.80/10.73 (( 78.80/10.73 (image1Equiv) => 78.80/10.73 (( 78.80/10.73 (image1E) => 78.80/10.73 (( 78.80/10.73 (image1I) => 78.80/10.73 (( 78.80/10.73 (injFuncInInjFuncSet) => 78.80/10.73 (( 78.80/10.73 (injFuncSetFuncIn) => 78.80/10.73 (( 78.80/10.73 (injFuncSetFuncInj) => 78.80/10.73 (( 78.80/10.73 (surjFuncSetFuncIn) => 78.80/10.73 (( 78.80/10.73 (surjFuncSetFuncSurj) => 78.80/10.73 (( 78.80/10.73 (leftInvIsSurj) => 78.80/10.73 (( 78.80/10.73 (surjCantorThm) => 78.80/10.73 (( 78.80/10.73 (foundation2) => 78.80/10.73 (( 78.80/10.73 (notinself) => 78.80/10.73 (( 78.80/10.73 (notinself2) => 78.80/10.73 (( 78.80/10.73 (omegaSp) => 78.80/10.73 (( 78.80/10.73 (omegaSclos) => 78.80/10.73 (( 78.80/10.73 (peano0notS) => 78.80/10.73 (( 78.80/10.73 (peanoSinj) => 78.80/10.73 (( 78.80/10.73 (transitivesetOp1) => 78.80/10.73 (( 78.80/10.73 (binintTransitive) => 78.80/10.73 (( 78.80/10.73 (transitivesetOp2) => 78.80/10.73 (( 78.80/10.73 (setunionTransitive) => 78.80/10.73 (( 78.80/10.73 (ordinalMinLem1) => 78.80/10.73 (( 78.80/10.73 (!!) @ ( 78.80/10.73 ^[Y0 : $i]: 78.80/10.73 (( 78.80/10.73 (ordinal @ 78.80/10.73 Y0) => 78.80/10.73 (( 78.80/10.73 (!!) @ ( 78.80/10.73 ^[Y1 : $i]: 78.80/10.73 (( 78.80/10.73 (!!) @ ( 78.80/10.73 ^[Y2 : $i]: 78.80/10.73 (( 78.80/10.73 (in @ 78.80/10.73 Y2 @ 78.80/10.73 Y0) => 78.80/10.73 (( 78.80/10.73 (in @ 78.80/10.73 Y1 @ 78.80/10.73 Y2) => 78.80/10.73 (in @ 78.80/10.73 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 78.80/10.73 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2151])). 78.80/10.73 thf(zip_derived_cl2166, plain, 78.80/10.73 (~ (((complementTI1) => 78.80/10.73 (((complementTE1) => 78.80/10.73 (((binintersectTELcontra) => 78.80/10.73 (((binintersectTERcontra) => 78.80/10.73 (((contrasubsetT) => 78.80/10.73 (((contrasubsetT1) => 78.80/10.73 (((contrasubsetT2) => 78.80/10.73 (((contrasubsetT3) => 78.80/10.73 (((doubleComplementI1) => 78.80/10.73 (((doubleComplementE1) => 78.80/10.73 (((doubleComplementSub1) => 78.80/10.73 (((doubleComplementSub2) => 78.80/10.73 (((doubleComplementEq) => 78.80/10.73 (((complementTnotintersectT) => 78.80/10.73 (((complementImpComplementIntersect) => 78.80/10.73 (((complementSubsetComplementIntersect) => 78.80/10.73 (((complementInPowersetComplementIntersect) => 78.80/10.73 (((contraSubsetComplement) => 78.80/10.73 (((complementTcontraSubset) => 78.80/10.73 (((binunionTILcontra) => 78.80/10.73 (((binunionTIRcontra) => 78.80/10.73 (((inIntersectImpInUnion) => 78.80/10.73 (((inIntersectImpInUnion2) => 78.80/10.73 (((inIntersectImpInIntersectUnions) => 78.80/10.73 (((intersectInPowersetIntersectUnions) => 78.80/10.73 (((inComplementUnionImpNotIn1) => 78.80/10.73 (((inComplementUnionImpInComplement1) => 78.80/10.73 (((binunionTE) => 78.80/10.73 (((binunionTEcontra) => 78.80/10.73 (((demorgan2a1) => 78.80/10.73 (( 78.80/10.73 (complementUnionInPowersetComplement) => 78.80/10.73 (( 78.80/10.73 (demorgan2a2) => 78.80/10.73 (( 78.80/10.73 (demorgan1a) => 78.80/10.73 (( 78.80/10.73 (demorgan1b) => 78.80/10.73 (( 78.80/10.73 (demorgan1) => 78.80/10.73 (( 78.80/10.73 (demorgan2a) => 78.80/10.73 (( 78.80/10.73 (demorgan2b2) => 78.80/10.73 (( 78.80/10.73 (demorgan2b) => 78.80/10.73 (( 78.80/10.73 (demorgan2) => 78.80/10.73 (( 78.80/10.73 (woz13rule0) => 78.80/10.73 (( 78.80/10.73 (woz13rule1) => 78.80/10.73 (( 78.80/10.73 (woz13rule2) => 78.80/10.73 (( 78.80/10.73 (woz13rule3) => 78.80/10.73 (( 78.80/10.73 (woz13rule4) => 78.80/10.73 (( 78.80/10.73 (woz1_1) => 78.80/10.73 (( 78.80/10.73 (woz1_2) => 78.80/10.73 (( 78.80/10.73 (woz1_3) => 78.80/10.73 (( 78.80/10.73 (woz1_4) => 78.80/10.73 (( 78.80/10.73 (woz1_5) => 78.80/10.73 (( 78.80/10.73 (breln1all2) => 78.80/10.73 (( 78.80/10.73 (breln1SetBreln1) => 78.80/10.73 (( 78.80/10.73 (choice2fnsingleton) => 78.80/10.73 (( 78.80/10.73 (setOfPairsIsBReln1) => 78.80/10.73 (( 78.80/10.73 (breln1all1) => 78.80/10.73 (( 78.80/10.73 (subbreln1) => 78.80/10.73 (( 78.80/10.73 (eqbreln1) => 78.80/10.73 (( 78.80/10.73 (breln1invprop) => 78.80/10.73 (( 78.80/10.73 (breln1invI) => 78.80/10.73 (( 78.80/10.73 (breln1invE) => 78.80/10.73 (( 78.80/10.73 (breln1compprop) => 78.80/10.73 (( 78.80/10.73 (breln1compI) => 78.80/10.73 (( 78.80/10.73 (breln1compE) => 78.80/10.73 (( 78.80/10.73 (breln1compEex) => 78.80/10.73 (( 78.80/10.73 (breln1unionprop) => 78.80/10.73 (( 78.80/10.73 (breln1unionIL) => 78.80/10.73 (( 78.80/10.73 (breln1unionIR) => 78.80/10.73 (( 78.80/10.73 (breln1unionI) => 78.80/10.73 (( 78.80/10.73 (breln1unionE) => 78.80/10.73 (( 78.80/10.73 (breln1unionEcases) => 78.80/10.73 (( 78.80/10.73 (breln1unionCommutes) => 78.80/10.73 (( 78.80/10.73 (woz2Ex) => 78.80/10.73 (( 78.80/10.73 (woz2W) => 78.80/10.73 (( 78.80/10.73 (woz2A) => 78.80/10.73 (( 78.80/10.73 (woz2B) => 78.80/10.73 (( 78.80/10.73 (image1Ex) => 78.80/10.73 (( 78.80/10.73 (image1Ex1) => 78.80/10.73 (( 78.80/10.73 (image1Equiv) => 78.80/10.73 (( 78.80/10.73 (image1E) => 78.80/10.73 (( 78.80/10.73 (image1I) => 78.80/10.73 (( 78.80/10.73 (injFuncInInjFuncSet) => 78.80/10.73 (( 78.80/10.73 (injFuncSetFuncIn) => 78.80/10.73 (( 78.80/10.73 (injFuncSetFuncInj) => 78.80/10.73 (( 78.80/10.73 (surjFuncSetFuncIn) => 78.80/10.73 (( 78.80/10.73 (surjFuncSetFuncSurj) => 78.80/10.73 (( 78.80/10.73 (leftInvIsSurj) => 78.80/10.73 (( 78.80/10.73 (surjCantorThm) => 78.80/10.73 (( 78.80/10.73 (foundation2) => 78.80/10.73 (( 78.80/10.73 (notinself) => 78.80/10.73 (( 78.80/10.73 (notinself2) => 78.80/10.73 (( 78.80/10.73 (omegaSp) => 78.80/10.73 (( 78.80/10.73 (omegaSclos) => 78.80/10.73 (( 78.80/10.73 (peano0notS) => 78.80/10.73 (( 78.80/10.73 (peanoSinj) => 78.80/10.73 (( 78.80/10.73 (transitivesetOp1) => 78.80/10.73 (( 78.80/10.73 (binintTransitive) => 78.80/10.73 (( 78.80/10.73 (transitivesetOp2) => 78.80/10.73 (( 78.80/10.73 (setunionTransitive) => 78.80/10.73 (( 78.80/10.73 (ordinalMinLem1) => 78.80/10.73 (( 78.80/10.73 (!!) @ ( 78.80/10.73 ^[Y0 : $i]: 78.80/10.73 (( 78.80/10.73 (ordinal @ 78.80/10.73 Y0) => 78.80/10.73 (( 78.80/10.73 (!!) @ ( 78.80/10.73 ^[Y1 : $i]: 78.80/10.73 (( 78.80/10.73 (!!) @ ( 78.80/10.73 ^[Y2 : $i]: 78.80/10.73 (( 78.80/10.73 (in @ 78.80/10.73 Y2 @ 78.80/10.73 Y0) => 78.80/10.73 (( 78.80/10.73 (in @ 78.80/10.73 Y1 @ 78.80/10.73 Y2) => 78.80/10.73 (in @ 78.80/10.73 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 78.80/10.73 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2159])). 78.80/10.73 thf(zip_derived_cl2173, plain, 78.80/10.73 (~ (((complementTE1) => 78.80/10.73 (((binintersectTELcontra) => 78.80/10.73 (((binintersectTERcontra) => 78.80/10.73 (((contrasubsetT) => 78.80/10.73 (((contrasubsetT1) => 78.80/10.73 (((contrasubsetT2) => 78.80/10.73 (((contrasubsetT3) => 78.80/10.73 (((doubleComplementI1) => 78.80/10.73 (((doubleComplementE1) => 78.80/10.73 (((doubleComplementSub1) => 78.80/10.73 (((doubleComplementSub2) => 78.80/10.73 (((doubleComplementEq) => 78.80/10.73 (((complementTnotintersectT) => 78.80/10.73 (((complementImpComplementIntersect) => 78.80/10.73 (((complementSubsetComplementIntersect) => 78.80/10.73 (((complementInPowersetComplementIntersect) => 78.80/10.73 (((contraSubsetComplement) => 78.80/10.73 (((complementTcontraSubset) => 78.80/10.73 (((binunionTILcontra) => 78.80/10.73 (((binunionTIRcontra) => 78.80/10.73 (((inIntersectImpInUnion) => 78.80/10.73 (((inIntersectImpInUnion2) => 78.80/10.73 (((inIntersectImpInIntersectUnions) => 78.80/10.73 (((intersectInPowersetIntersectUnions) => 78.80/10.73 (((inComplementUnionImpNotIn1) => 78.80/10.73 (((inComplementUnionImpInComplement1) => 78.80/10.73 (((binunionTE) => 78.80/10.73 (((binunionTEcontra) => 78.80/10.73 (((demorgan2a1) => 78.80/10.73 (((complementUnionInPowersetComplement) => 78.80/10.73 (( 78.80/10.73 (demorgan2a2) => 78.80/10.73 (( 78.80/10.73 (demorgan1a) => 78.80/10.73 (( 78.80/10.73 (demorgan1b) => 78.80/10.74 (( 78.80/10.74 (demorgan1) => 78.80/10.74 (( 78.80/10.74 (demorgan2a) => 78.80/10.74 (( 78.80/10.74 (demorgan2b2) => 78.80/10.74 (( 78.80/10.74 (demorgan2b) => 78.80/10.74 (( 78.80/10.74 (demorgan2) => 78.80/10.74 (( 78.80/10.74 (woz13rule0) => 78.80/10.74 (( 78.80/10.74 (woz13rule1) => 78.80/10.74 (( 78.80/10.74 (woz13rule2) => 78.80/10.74 (( 78.80/10.74 (woz13rule3) => 78.80/10.74 (( 78.80/10.74 (woz13rule4) => 78.80/10.74 (( 78.80/10.74 (woz1_1) => 78.80/10.74 (( 78.80/10.74 (woz1_2) => 78.80/10.74 (( 78.80/10.74 (woz1_3) => 78.80/10.74 (( 78.80/10.74 (woz1_4) => 78.80/10.74 (( 78.80/10.74 (woz1_5) => 78.80/10.74 (( 78.80/10.74 (breln1all2) => 78.80/10.74 (( 78.80/10.74 (breln1SetBreln1) => 78.80/10.74 (( 78.80/10.74 (choice2fnsingleton) => 78.80/10.74 (( 78.80/10.74 (setOfPairsIsBReln1) => 78.80/10.74 (( 78.80/10.74 (breln1all1) => 78.80/10.74 (( 78.80/10.74 (subbreln1) => 78.80/10.74 (( 78.80/10.74 (eqbreln1) => 78.80/10.74 (( 78.80/10.74 (breln1invprop) => 78.80/10.74 (( 78.80/10.74 (breln1invI) => 78.80/10.74 (( 78.80/10.74 (breln1invE) => 78.80/10.74 (( 78.80/10.74 (breln1compprop) => 78.80/10.74 (( 78.80/10.74 (breln1compI) => 78.80/10.74 (( 78.80/10.74 (breln1compE) => 78.80/10.74 (( 78.80/10.74 (breln1compEex) => 78.80/10.74 (( 78.80/10.74 (breln1unionprop) => 78.80/10.74 (( 78.80/10.74 (breln1unionIL) => 78.80/10.74 (( 78.80/10.74 (breln1unionIR) => 78.80/10.74 (( 78.80/10.74 (breln1unionI) => 78.80/10.74 (( 78.80/10.74 (breln1unionE) => 78.80/10.74 (( 78.80/10.74 (breln1unionEcases) => 78.80/10.74 (( 78.80/10.74 (breln1unionCommutes) => 78.80/10.74 (( 78.80/10.74 (woz2Ex) => 78.80/10.74 (( 78.80/10.74 (woz2W) => 78.80/10.74 (( 78.80/10.74 (woz2A) => 78.80/10.74 (( 78.80/10.74 (woz2B) => 78.80/10.74 (( 78.80/10.74 (image1Ex) => 78.80/10.74 (( 78.80/10.74 (image1Ex1) => 78.80/10.74 (( 78.80/10.74 (image1Equiv) => 78.80/10.74 (( 78.80/10.74 (image1E) => 78.80/10.74 (( 78.80/10.74 (image1I) => 78.80/10.74 (( 78.80/10.74 (injFuncInInjFuncSet) => 78.80/10.74 (( 78.80/10.74 (injFuncSetFuncIn) => 78.80/10.74 (( 78.80/10.74 (injFuncSetFuncInj) => 78.80/10.74 (( 78.80/10.74 (surjFuncSetFuncIn) => 78.80/10.74 (( 78.80/10.74 (surjFuncSetFuncSurj) => 78.80/10.74 (( 78.80/10.74 (leftInvIsSurj) => 78.80/10.74 (( 78.80/10.74 (surjCantorThm) => 78.80/10.74 (( 78.80/10.74 (foundation2) => 78.80/10.74 (( 78.80/10.74 (notinself) => 78.80/10.74 (( 78.80/10.74 (notinself2) => 78.80/10.74 (( 78.80/10.74 (omegaSp) => 78.80/10.74 (( 78.80/10.74 (omegaSclos) => 78.80/10.74 (( 78.80/10.74 (peano0notS) => 78.80/10.74 (( 78.80/10.74 (peanoSinj) => 78.80/10.74 (( 78.80/10.74 (transitivesetOp1) => 78.80/10.74 (( 78.80/10.74 (binintTransitive) => 78.80/10.74 (( 78.80/10.74 (transitivesetOp2) => 78.80/10.74 (( 78.80/10.74 (setunionTransitive) => 78.80/10.74 (( 78.80/10.74 (ordinalMinLem1) => 78.80/10.74 (( 78.80/10.74 (!!) @ ( 78.80/10.74 ^[Y0 : $i]: 78.80/10.74 (( 78.80/10.74 (ordinal @ 78.80/10.74 Y0) => 78.80/10.74 (( 78.80/10.74 (!!) @ ( 78.80/10.74 ^[Y1 : $i]: 78.80/10.74 (( 78.80/10.74 (!!) @ ( 78.80/10.74 ^[Y2 : $i]: 78.80/10.74 (( 78.80/10.74 (in @ 78.80/10.74 Y2 @ 78.80/10.74 Y0) => 78.80/10.74 (( 78.80/10.74 (in @ 78.80/10.74 Y1 @ 78.80/10.74 Y2) => 78.80/10.74 (in @ 78.80/10.74 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 78.80/10.74 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2166])). 78.80/10.74 thf(zip_derived_cl2180, plain, 78.80/10.74 (~ (((binintersectTELcontra) => 78.80/10.74 (((binintersectTERcontra) => 78.80/10.74 (((contrasubsetT) => 78.80/10.74 (((contrasubsetT1) => 78.80/10.74 (((contrasubsetT2) => 78.80/10.74 (((contrasubsetT3) => 78.80/10.74 (((doubleComplementI1) => 78.80/10.74 (((doubleComplementE1) => 78.80/10.74 (((doubleComplementSub1) => 78.80/10.74 (((doubleComplementSub2) => 78.80/10.74 (((doubleComplementEq) => 78.80/10.74 (((complementTnotintersectT) => 78.80/10.74 (((complementImpComplementIntersect) => 78.80/10.74 (((complementSubsetComplementIntersect) => 78.80/10.74 (((complementInPowersetComplementIntersect) => 78.80/10.74 (((contraSubsetComplement) => 78.80/10.74 (((complementTcontraSubset) => 78.80/10.74 (((binunionTILcontra) => 78.80/10.74 (((binunionTIRcontra) => 78.80/10.74 (((inIntersectImpInUnion) => 78.80/10.74 (((inIntersectImpInUnion2) => 78.80/10.74 (((inIntersectImpInIntersectUnions) => 78.80/10.74 (((intersectInPowersetIntersectUnions) => 78.80/10.74 (((inComplementUnionImpNotIn1) => 78.80/10.74 (((inComplementUnionImpInComplement1) => 78.80/10.74 (((binunionTE) => 78.80/10.74 (((binunionTEcontra) => 78.80/10.74 (((demorgan2a1) => 78.80/10.74 (((complementUnionInPowersetComplement) => 78.80/10.74 (((demorgan2a2) => 78.80/10.74 (( 78.80/10.74 (demorgan1a) => 78.80/10.74 (( 78.80/10.74 (demorgan1b) => 78.80/10.74 (( 78.80/10.74 (demorgan1) => 78.80/10.74 (( 78.80/10.74 (demorgan2a) => 78.80/10.74 (( 78.80/10.74 (demorgan2b2) => 78.80/10.74 (( 78.80/10.74 (demorgan2b) => 78.80/10.74 (( 78.80/10.74 (demorgan2) => 78.80/10.74 (( 78.80/10.74 (woz13rule0) => 78.80/10.74 (( 78.80/10.74 (woz13rule1) => 78.80/10.74 (( 78.80/10.74 (woz13rule2) => 78.80/10.74 (( 78.80/10.74 (woz13rule3) => 78.80/10.74 (( 78.80/10.74 (woz13rule4) => 78.80/10.74 (( 78.80/10.74 (woz1_1) => 78.80/10.74 (( 78.80/10.74 (woz1_2) => 78.80/10.74 (( 78.80/10.74 (woz1_3) => 78.80/10.74 (( 78.80/10.74 (woz1_4) => 78.80/10.74 (( 78.80/10.74 (woz1_5) => 78.80/10.74 (( 78.80/10.74 (breln1all2) => 78.80/10.74 (( 78.80/10.74 (breln1SetBreln1) => 78.80/10.74 (( 78.80/10.74 (choice2fnsingleton) => 78.80/10.74 (( 78.80/10.74 (setOfPairsIsBReln1) => 78.80/10.74 (( 78.80/10.74 (breln1all1) => 78.80/10.74 (( 78.80/10.74 (subbreln1) => 78.80/10.74 (( 78.80/10.74 (eqbreln1) => 78.80/10.74 (( 78.80/10.74 (breln1invprop) => 78.80/10.74 (( 78.80/10.74 (breln1invI) => 78.80/10.74 (( 78.80/10.74 (breln1invE) => 78.80/10.74 (( 78.80/10.74 (breln1compprop) => 78.80/10.74 (( 78.80/10.74 (breln1compI) => 78.80/10.74 (( 78.80/10.74 (breln1compE) => 78.80/10.74 (( 78.80/10.74 (breln1compEex) => 78.80/10.74 (( 78.80/10.74 (breln1unionprop) => 78.80/10.74 (( 78.80/10.74 (breln1unionIL) => 78.80/10.74 (( 78.80/10.74 (breln1unionIR) => 78.80/10.74 (( 78.80/10.74 (breln1unionI) => 78.80/10.74 (( 78.80/10.74 (breln1unionE) => 78.80/10.74 (( 78.80/10.74 (breln1unionEcases) => 78.80/10.74 (( 78.80/10.74 (breln1unionCommutes) => 78.80/10.74 (( 78.80/10.74 (woz2Ex) => 78.80/10.74 (( 78.80/10.74 (woz2W) => 78.80/10.74 (( 78.80/10.74 (woz2A) => 78.80/10.74 (( 78.80/10.74 (woz2B) => 78.80/10.74 (( 78.80/10.74 (image1Ex) => 78.80/10.74 (( 78.80/10.74 (image1Ex1) => 78.80/10.74 (( 78.80/10.74 (image1Equiv) => 78.80/10.74 (( 78.80/10.74 (image1E) => 78.80/10.74 (( 78.80/10.74 (image1I) => 78.80/10.74 (( 78.80/10.74 (injFuncInInjFuncSet) => 78.80/10.74 (( 78.80/10.74 (injFuncSetFuncIn) => 78.80/10.74 (( 78.80/10.74 (injFuncSetFuncInj) => 78.80/10.74 (( 78.80/10.74 (surjFuncSetFuncIn) => 78.80/10.74 (( 78.80/10.74 (surjFuncSetFuncSurj) => 78.80/10.74 (( 78.80/10.74 (leftInvIsSurj) => 78.80/10.74 (( 78.80/10.74 (surjCantorThm) => 78.80/10.74 (( 78.80/10.74 (foundation2) => 78.80/10.74 (( 78.80/10.74 (notinself) => 78.80/10.74 (( 78.80/10.74 (notinself2) => 78.80/10.74 (( 78.80/10.74 (omegaSp) => 78.80/10.74 (( 78.80/10.74 (omegaSclos) => 78.80/10.74 (( 78.80/10.74 (peano0notS) => 78.80/10.74 (( 78.80/10.74 (peanoSinj) => 78.80/10.74 (( 78.80/10.74 (transitivesetOp1) => 78.80/10.74 (( 78.80/10.74 (binintTransitive) => 78.80/10.74 (( 78.80/10.74 (transitivesetOp2) => 78.80/10.74 (( 78.80/10.74 (setunionTransitive) => 78.80/10.74 (( 78.80/10.74 (ordinalMinLem1) => 78.80/10.74 (( 78.80/10.74 (!!) @ ( 78.80/10.74 ^[Y0 : $i]: 78.80/10.74 (( 78.80/10.74 (ordinal @ 78.80/10.74 Y0) => 78.80/10.74 (( 78.80/10.74 (!!) @ ( 78.80/10.74 ^[Y1 : $i]: 78.80/10.74 (( 78.80/10.74 (!!) @ ( 78.80/10.74 ^[Y2 : $i]: 78.80/10.74 (( 78.80/10.74 (in @ 78.80/10.74 Y2 @ 78.80/10.74 Y0) => 78.80/10.74 (( 78.80/10.74 (in @ 78.80/10.74 Y1 @ 78.80/10.74 Y2) => 78.80/10.74 (in @ 78.80/10.74 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 78.80/10.74 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2173])). 78.80/10.74 thf(zip_derived_cl2188, plain, 78.80/10.74 (~ (((binintersectTERcontra) => 78.80/10.74 (((contrasubsetT) => 78.80/10.74 (((contrasubsetT1) => 78.80/10.74 (((contrasubsetT2) => 78.80/10.74 (((contrasubsetT3) => 78.80/10.74 (((doubleComplementI1) => 78.80/10.74 (((doubleComplementE1) => 78.80/10.74 (((doubleComplementSub1) => 78.80/10.74 (((doubleComplementSub2) => 78.80/10.74 (((doubleComplementEq) => 78.80/10.74 (((complementTnotintersectT) => 78.80/10.74 (((complementImpComplementIntersect) => 78.80/10.74 (((complementSubsetComplementIntersect) => 78.80/10.74 (((complementInPowersetComplementIntersect) => 78.80/10.74 (((contraSubsetComplement) => 78.80/10.74 (((complementTcontraSubset) => 78.80/10.74 (((binunionTILcontra) => 78.80/10.74 (((binunionTIRcontra) => 78.80/10.74 (((inIntersectImpInUnion) => 78.80/10.74 (((inIntersectImpInUnion2) => 78.80/10.74 (((inIntersectImpInIntersectUnions) => 78.80/10.74 (((intersectInPowersetIntersectUnions) => 78.80/10.74 (((inComplementUnionImpNotIn1) => 78.80/10.74 (((inComplementUnionImpInComplement1) => 78.80/10.74 (((binunionTE) => 78.80/10.74 (((binunionTEcontra) => 78.80/10.74 (((demorgan2a1) => 78.80/10.74 (((complementUnionInPowersetComplement) => 78.80/10.74 (((demorgan2a2) => 78.80/10.74 (((demorgan1a) => 78.80/10.74 (( 78.80/10.74 (demorgan1b) => 78.80/10.74 (( 78.80/10.74 (demorgan1) => 78.80/10.74 (( 78.80/10.74 (demorgan2a) => 78.80/10.74 (( 78.80/10.74 (demorgan2b2) => 78.80/10.74 (( 78.80/10.74 (demorgan2b) => 78.80/10.74 (( 78.80/10.74 (demorgan2) => 78.80/10.74 (( 78.80/10.74 (woz13rule0) => 78.80/10.74 (( 78.80/10.74 (woz13rule1) => 78.80/10.74 (( 78.80/10.74 (woz13rule2) => 78.80/10.74 (( 78.80/10.74 (woz13rule3) => 78.80/10.74 (( 78.80/10.74 (woz13rule4) => 78.80/10.74 (( 78.80/10.74 (woz1_1) => 78.80/10.74 (( 78.80/10.74 (woz1_2) => 78.80/10.74 (( 78.80/10.74 (woz1_3) => 78.80/10.74 (( 78.80/10.74 (woz1_4) => 78.80/10.74 (( 78.80/10.74 (woz1_5) => 78.80/10.74 (( 78.80/10.74 (breln1all2) => 78.80/10.74 (( 78.80/10.74 (breln1SetBreln1) => 78.80/10.74 (( 78.80/10.74 (choice2fnsingleton) => 78.80/10.74 (( 78.80/10.74 (setOfPairsIsBReln1) => 78.80/10.74 (( 78.80/10.74 (breln1all1) => 78.80/10.74 (( 78.80/10.74 (subbreln1) => 78.80/10.74 (( 78.80/10.74 (eqbreln1) => 78.80/10.74 (( 78.80/10.74 (breln1invprop) => 78.80/10.74 (( 78.80/10.74 (breln1invI) => 78.80/10.74 (( 78.80/10.74 (breln1invE) => 78.80/10.74 (( 78.80/10.74 (breln1compprop) => 78.80/10.74 (( 78.80/10.74 (breln1compI) => 78.80/10.74 (( 78.80/10.74 (breln1compE) => 78.80/10.74 (( 78.80/10.74 (breln1compEex) => 78.80/10.74 (( 78.80/10.74 (breln1unionprop) => 78.80/10.74 (( 78.80/10.74 (breln1unionIL) => 78.80/10.74 (( 78.80/10.74 (breln1unionIR) => 78.80/10.74 (( 78.80/10.74 (breln1unionI) => 78.80/10.74 (( 78.80/10.74 (breln1unionE) => 78.80/10.74 (( 78.80/10.74 (breln1unionEcases) => 78.80/10.74 (( 78.80/10.74 (breln1unionCommutes) => 78.80/10.74 (( 78.80/10.74 (woz2Ex) => 78.80/10.74 (( 78.80/10.74 (woz2W) => 78.80/10.74 (( 78.80/10.74 (woz2A) => 78.80/10.74 (( 78.80/10.74 (woz2B) => 78.80/10.74 (( 78.80/10.74 (image1Ex) => 78.80/10.74 (( 78.80/10.74 (image1Ex1) => 78.80/10.74 (( 78.80/10.74 (image1Equiv) => 78.80/10.74 (( 78.80/10.74 (image1E) => 78.80/10.74 (( 78.80/10.74 (image1I) => 78.80/10.74 (( 78.80/10.74 (injFuncInInjFuncSet) => 78.80/10.74 (( 78.80/10.74 (injFuncSetFuncIn) => 78.80/10.74 (( 78.80/10.74 (injFuncSetFuncInj) => 78.80/10.74 (( 78.80/10.74 (surjFuncSetFuncIn) => 78.80/10.74 (( 78.80/10.74 (surjFuncSetFuncSurj) => 78.80/10.74 (( 78.80/10.74 (leftInvIsSurj) => 78.80/10.74 (( 78.80/10.74 (surjCantorThm) => 78.80/10.74 (( 78.80/10.74 (foundation2) => 78.80/10.74 (( 78.80/10.74 (notinself) => 78.80/10.74 (( 78.80/10.74 (notinself2) => 78.80/10.74 (( 78.80/10.74 (omegaSp) => 78.80/10.74 (( 78.80/10.74 (omegaSclos) => 78.80/10.74 (( 78.80/10.74 (peano0notS) => 78.80/10.74 (( 78.80/10.74 (peanoSinj) => 78.80/10.74 (( 78.80/10.74 (transitivesetOp1) => 78.80/10.74 (( 78.80/10.74 (binintTransitive) => 78.80/10.74 (( 78.80/10.74 (transitivesetOp2) => 78.80/10.74 (( 78.80/10.74 (setunionTransitive) => 78.80/10.74 (( 78.80/10.74 (ordinalMinLem1) => 78.80/10.74 (( 78.80/10.74 (!!) @ ( 78.80/10.74 ^[Y0 : $i]: 78.80/10.74 (( 78.80/10.74 (ordinal @ 78.80/10.74 Y0) => 78.80/10.74 (( 78.80/10.74 (!!) @ ( 78.80/10.74 ^[Y1 : $i]: 78.80/10.74 (( 78.80/10.74 (!!) @ ( 78.80/10.74 ^[Y2 : $i]: 78.80/10.74 (( 78.80/10.74 (in @ 78.80/10.74 Y2 @ 78.80/10.74 Y0) => 78.80/10.74 (( 78.80/10.74 (in @ 78.80/10.74 Y1 @ 78.80/10.74 Y2) => 78.80/10.74 (in @ 78.80/10.74 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 78.80/10.74 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2180])). 78.80/10.74 thf(zip_derived_cl2197, plain, 78.80/10.74 (~ (((contrasubsetT) => 78.80/10.74 (((contrasubsetT1) => 78.80/10.74 (((contrasubsetT2) => 78.80/10.74 (((contrasubsetT3) => 78.80/10.74 (((doubleComplementI1) => 78.80/10.74 (((doubleComplementE1) => 78.80/10.74 (((doubleComplementSub1) => 78.80/10.74 (((doubleComplementSub2) => 78.80/10.74 (((doubleComplementEq) => 78.80/10.74 (((complementTnotintersectT) => 78.80/10.74 (((complementImpComplementIntersect) => 78.80/10.74 (((complementSubsetComplementIntersect) => 78.80/10.74 (((complementInPowersetComplementIntersect) => 78.80/10.74 (((contraSubsetComplement) => 78.80/10.74 (((complementTcontraSubset) => 78.80/10.74 (((binunionTILcontra) => 78.80/10.74 (((binunionTIRcontra) => 78.80/10.74 (((inIntersectImpInUnion) => 78.80/10.74 (((inIntersectImpInUnion2) => 78.80/10.74 (((inIntersectImpInIntersectUnions) => 78.80/10.74 (((intersectInPowersetIntersectUnions) => 78.80/10.74 (((inComplementUnionImpNotIn1) => 78.80/10.74 (((inComplementUnionImpInComplement1) => 78.80/10.74 (((binunionTE) => 78.80/10.74 (((binunionTEcontra) => 78.80/10.74 (((demorgan2a1) => 78.80/10.74 (((complementUnionInPowersetComplement) => 78.80/10.74 (((demorgan2a2) => 78.80/10.74 (((demorgan1a) => 78.80/10.74 (((demorgan1b) => 78.80/10.74 (( 78.80/10.74 (demorgan1) => 78.80/10.74 (( 78.80/10.74 (demorgan2a) => 78.80/10.74 (( 78.80/10.74 (demorgan2b2) => 78.80/10.74 (( 78.80/10.74 (demorgan2b) => 78.80/10.74 (( 78.80/10.74 (demorgan2) => 78.80/10.74 (( 78.80/10.74 (woz13rule0) => 78.80/10.74 (( 78.80/10.74 (woz13rule1) => 78.80/10.74 (( 78.80/10.74 (woz13rule2) => 78.80/10.74 (( 78.80/10.74 (woz13rule3) => 78.80/10.74 (( 78.80/10.74 (woz13rule4) => 78.80/10.74 (( 78.80/10.74 (woz1_1) => 78.80/10.74 (( 78.80/10.74 (woz1_2) => 78.80/10.74 (( 78.80/10.74 (woz1_3) => 78.80/10.74 (( 78.80/10.74 (woz1_4) => 78.80/10.74 (( 78.80/10.74 (woz1_5) => 78.80/10.74 (( 78.80/10.74 (breln1all2) => 78.80/10.74 (( 78.80/10.74 (breln1SetBreln1) => 78.80/10.74 (( 78.80/10.74 (choice2fnsingleton) => 78.80/10.74 (( 78.80/10.74 (setOfPairsIsBReln1) => 78.80/10.74 (( 78.80/10.74 (breln1all1) => 78.80/10.74 (( 78.80/10.74 (subbreln1) => 78.80/10.74 (( 78.80/10.74 (eqbreln1) => 78.80/10.74 (( 78.80/10.74 (breln1invprop) => 78.80/10.74 (( 78.80/10.74 (breln1invI) => 78.80/10.74 (( 78.80/10.74 (breln1invE) => 78.80/10.74 (( 78.80/10.74 (breln1compprop) => 78.80/10.74 (( 78.80/10.74 (breln1compI) => 78.80/10.74 (( 78.80/10.74 (breln1compE) => 78.80/10.74 (( 78.80/10.74 (breln1compEex) => 78.80/10.74 (( 78.80/10.74 (breln1unionprop) => 78.80/10.74 (( 78.80/10.74 (breln1unionIL) => 78.80/10.74 (( 78.80/10.74 (breln1unionIR) => 78.80/10.74 (( 78.80/10.74 (breln1unionI) => 78.80/10.74 (( 78.80/10.74 (breln1unionE) => 78.80/10.74 (( 78.80/10.74 (breln1unionEcases) => 78.80/10.74 (( 78.80/10.74 (breln1unionCommutes) => 78.80/10.74 (( 78.80/10.74 (woz2Ex) => 78.80/10.74 (( 78.80/10.74 (woz2W) => 78.80/10.74 (( 78.80/10.74 (woz2A) => 78.80/10.74 (( 78.80/10.74 (woz2B) => 78.80/10.74 (( 78.80/10.74 (image1Ex) => 78.80/10.74 (( 78.80/10.74 (image1Ex1) => 78.80/10.74 (( 78.80/10.74 (image1Equiv) => 78.80/10.74 (( 78.80/10.74 (image1E) => 78.80/10.74 (( 78.80/10.74 (image1I) => 78.80/10.74 (( 78.80/10.74 (injFuncInInjFuncSet) => 78.80/10.74 (( 78.80/10.74 (injFuncSetFuncIn) => 78.80/10.74 (( 78.80/10.74 (injFuncSetFuncInj) => 78.80/10.74 (( 78.80/10.74 (surjFuncSetFuncIn) => 78.80/10.74 (( 78.80/10.74 (surjFuncSetFuncSurj) => 78.80/10.74 (( 78.80/10.74 (leftInvIsSurj) => 78.80/10.74 (( 78.80/10.74 (surjCantorThm) => 78.80/10.74 (( 78.80/10.74 (foundation2) => 78.80/10.74 (( 78.80/10.74 (notinself) => 78.80/10.74 (( 78.80/10.74 (notinself2) => 78.80/10.74 (( 78.80/10.74 (omegaSp) => 78.80/10.74 (( 78.80/10.74 (omegaSclos) => 78.80/10.74 (( 78.80/10.74 (peano0notS) => 78.80/10.74 (( 78.80/10.74 (peanoSinj) => 78.80/10.74 (( 78.80/10.74 (transitivesetOp1) => 78.80/10.74 (( 78.80/10.74 (binintTransitive) => 78.80/10.74 (( 78.80/10.74 (transitivesetOp2) => 78.80/10.74 (( 78.80/10.74 (setunionTransitive) => 78.80/10.74 (( 78.80/10.74 (ordinalMinLem1) => 78.80/10.74 (( 78.80/10.74 (!!) @ ( 78.80/10.74 ^[Y0 : $i]: 78.80/10.74 (( 78.80/10.74 (ordinal @ 78.80/10.74 Y0) => 78.80/10.74 (( 78.80/10.74 (!!) @ ( 78.80/10.74 ^[Y1 : $i]: 78.80/10.74 (( 78.80/10.74 (!!) @ ( 78.80/10.74 ^[Y2 : $i]: 78.80/10.74 (( 78.80/10.74 (in @ 78.80/10.74 Y2 @ 78.80/10.74 Y0) => 78.80/10.74 (( 78.80/10.74 (in @ 78.80/10.74 Y1 @ 78.80/10.74 Y2) => 78.80/10.74 (in @ 78.80/10.74 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 78.80/10.74 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2188])). 78.80/10.74 thf(zip_derived_cl2207, plain, 78.80/10.74 (~ (((contrasubsetT1) => 78.80/10.74 (((contrasubsetT2) => 78.80/10.74 (((contrasubsetT3) => 78.80/10.74 (((doubleComplementI1) => 78.80/10.74 (((doubleComplementE1) => 78.80/10.74 (((doubleComplementSub1) => 78.80/10.74 (((doubleComplementSub2) => 78.80/10.74 (((doubleComplementEq) => 78.80/10.74 (((complementTnotintersectT) => 78.80/10.74 (((complementImpComplementIntersect) => 78.80/10.74 (((complementSubsetComplementIntersect) => 78.80/10.74 (((complementInPowersetComplementIntersect) => 78.80/10.74 (((contraSubsetComplement) => 78.80/10.74 (((complementTcontraSubset) => 78.80/10.74 (((binunionTILcontra) => 78.80/10.74 (((binunionTIRcontra) => 78.80/10.74 (((inIntersectImpInUnion) => 78.80/10.74 (((inIntersectImpInUnion2) => 78.80/10.74 (((inIntersectImpInIntersectUnions) => 78.80/10.74 (((intersectInPowersetIntersectUnions) => 78.80/10.74 (((inComplementUnionImpNotIn1) => 78.80/10.74 (((inComplementUnionImpInComplement1) => 78.80/10.74 (((binunionTE) => 78.80/10.74 (((binunionTEcontra) => 78.80/10.74 (((demorgan2a1) => 78.80/10.74 (((complementUnionInPowersetComplement) => 78.80/10.74 (((demorgan2a2) => 78.80/10.74 (((demorgan1a) => 78.80/10.74 (((demorgan1b) => 78.80/10.74 (((demorgan1) => 78.80/10.74 (( 78.80/10.74 (demorgan2a) => 78.80/10.74 (( 78.80/10.74 (demorgan2b2) => 78.80/10.74 (( 78.80/10.74 (demorgan2b) => 78.80/10.74 (( 78.80/10.74 (demorgan2) => 78.80/10.74 (( 78.80/10.74 (woz13rule0) => 78.80/10.74 (( 78.80/10.74 (woz13rule1) => 78.80/10.74 (( 78.80/10.74 (woz13rule2) => 78.80/10.74 (( 78.80/10.74 (woz13rule3) => 78.80/10.74 (( 78.80/10.74 (woz13rule4) => 78.80/10.74 (( 78.80/10.74 (woz1_1) => 78.80/10.74 (( 78.80/10.74 (woz1_2) => 78.80/10.74 (( 78.80/10.74 (woz1_3) => 78.80/10.74 (( 78.80/10.74 (woz1_4) => 78.80/10.74 (( 78.80/10.74 (woz1_5) => 78.80/10.74 (( 78.80/10.74 (breln1all2) => 78.80/10.74 (( 78.80/10.74 (breln1SetBreln1) => 78.80/10.74 (( 78.80/10.74 (choice2fnsingleton) => 78.80/10.74 (( 78.80/10.74 (setOfPairsIsBReln1) => 78.80/10.74 (( 78.80/10.74 (breln1all1) => 78.80/10.74 (( 78.80/10.74 (subbreln1) => 78.80/10.74 (( 78.80/10.74 (eqbreln1) => 78.80/10.74 (( 78.80/10.74 (breln1invprop) => 78.80/10.74 (( 78.80/10.74 (breln1invI) => 78.80/10.74 (( 78.80/10.74 (breln1invE) => 78.80/10.74 (( 78.80/10.74 (breln1compprop) => 78.80/10.74 (( 78.80/10.74 (breln1compI) => 78.80/10.74 (( 78.80/10.74 (breln1compE) => 78.80/10.74 (( 78.80/10.74 (breln1compEex) => 78.80/10.74 (( 78.80/10.74 (breln1unionprop) => 78.80/10.74 (( 78.80/10.74 (breln1unionIL) => 78.80/10.74 (( 78.80/10.74 (breln1unionIR) => 78.80/10.74 (( 78.80/10.74 (breln1unionI) => 78.80/10.74 (( 78.80/10.74 (breln1unionE) => 78.80/10.74 (( 78.80/10.74 (breln1unionEcases) => 78.80/10.74 (( 78.80/10.74 (breln1unionCommutes) => 78.80/10.74 (( 78.80/10.74 (woz2Ex) => 78.80/10.74 (( 78.80/10.74 (woz2W) => 78.80/10.74 (( 78.80/10.74 (woz2A) => 78.80/10.74 (( 78.80/10.74 (woz2B) => 78.80/10.74 (( 78.80/10.74 (image1Ex) => 78.80/10.74 (( 78.80/10.74 (image1Ex1) => 78.80/10.74 (( 78.80/10.74 (image1Equiv) => 78.80/10.74 (( 78.80/10.74 (image1E) => 78.80/10.74 (( 78.80/10.74 (image1I) => 78.80/10.74 (( 78.80/10.74 (injFuncInInjFuncSet) => 78.80/10.74 (( 78.80/10.74 (injFuncSetFuncIn) => 78.80/10.74 (( 78.80/10.74 (injFuncSetFuncInj) => 78.80/10.74 (( 78.80/10.74 (surjFuncSetFuncIn) => 78.80/10.74 (( 78.80/10.74 (surjFuncSetFuncSurj) => 78.80/10.74 (( 78.80/10.74 (leftInvIsSurj) => 78.80/10.74 (( 78.80/10.74 (surjCantorThm) => 78.80/10.74 (( 78.80/10.74 (foundation2) => 78.80/10.74 (( 78.80/10.74 (notinself) => 78.80/10.74 (( 78.80/10.74 (notinself2) => 78.80/10.74 (( 78.80/10.74 (omegaSp) => 78.80/10.74 (( 78.80/10.74 (omegaSclos) => 78.80/10.74 (( 78.80/10.74 (peano0notS) => 78.80/10.74 (( 78.80/10.74 (peanoSinj) => 78.80/10.74 (( 78.80/10.74 (transitivesetOp1) => 78.80/10.74 (( 78.80/10.74 (binintTransitive) => 78.80/10.74 (( 78.80/10.74 (transitivesetOp2) => 78.80/10.74 (( 78.80/10.74 (setunionTransitive) => 78.80/10.74 (( 78.80/10.74 (ordinalMinLem1) => 78.80/10.74 (( 78.80/10.74 (!!) @ ( 78.80/10.74 ^[Y0 : $i]: 78.80/10.74 (( 78.80/10.74 (ordinal @ 78.80/10.74 Y0) => 78.80/10.74 (( 78.80/10.74 (!!) @ ( 78.80/10.74 ^[Y1 : $i]: 78.80/10.74 (( 78.80/10.74 (!!) @ ( 78.80/10.74 ^[Y2 : $i]: 78.80/10.74 (( 78.80/10.74 (in @ 78.80/10.74 Y2 @ 78.80/10.74 Y0) => 78.80/10.74 (( 78.80/10.74 (in @ 78.80/10.74 Y1 @ 78.80/10.74 Y2) => 78.80/10.74 (in @ 78.80/10.74 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 78.80/10.74 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2197])). 78.80/10.74 thf(zip_derived_cl2219, plain, 78.80/10.74 (~ (((contrasubsetT2) => 78.80/10.74 (((contrasubsetT3) => 78.80/10.74 (((doubleComplementI1) => 78.80/10.74 (((doubleComplementE1) => 78.80/10.74 (((doubleComplementSub1) => 78.80/10.74 (((doubleComplementSub2) => 78.80/10.74 (((doubleComplementEq) => 78.80/10.74 (((complementTnotintersectT) => 78.80/10.74 (((complementImpComplementIntersect) => 78.80/10.74 (((complementSubsetComplementIntersect) => 78.80/10.74 (((complementInPowersetComplementIntersect) => 78.80/10.74 (((contraSubsetComplement) => 78.80/10.74 (((complementTcontraSubset) => 78.80/10.74 (((binunionTILcontra) => 78.80/10.74 (((binunionTIRcontra) => 78.80/10.74 (((inIntersectImpInUnion) => 78.80/10.74 (((inIntersectImpInUnion2) => 78.80/10.74 (((inIntersectImpInIntersectUnions) => 78.80/10.74 (((intersectInPowersetIntersectUnions) => 78.80/10.74 (((inComplementUnionImpNotIn1) => 78.80/10.74 (((inComplementUnionImpInComplement1) => 78.80/10.74 (((binunionTE) => 78.80/10.74 (((binunionTEcontra) => 78.80/10.74 (((demorgan2a1) => 78.80/10.74 (((complementUnionInPowersetComplement) => 78.80/10.74 (((demorgan2a2) => 78.80/10.74 (((demorgan1a) => 78.80/10.74 (((demorgan1b) => 78.80/10.74 (((demorgan1) => 78.80/10.74 (((demorgan2a) => 78.80/10.74 (( 78.80/10.74 (demorgan2b2) => 78.80/10.74 (( 78.80/10.74 (demorgan2b) => 78.80/10.74 (( 78.80/10.74 (demorgan2) => 78.80/10.74 (( 78.80/10.74 (woz13rule0) => 78.80/10.74 (( 78.80/10.74 (woz13rule1) => 78.80/10.74 (( 78.80/10.74 (woz13rule2) => 78.80/10.74 (( 78.80/10.74 (woz13rule3) => 78.80/10.74 (( 78.80/10.74 (woz13rule4) => 78.80/10.74 (( 78.80/10.74 (woz1_1) => 78.80/10.74 (( 78.80/10.74 (woz1_2) => 78.80/10.74 (( 78.80/10.74 (woz1_3) => 78.80/10.74 (( 78.80/10.74 (woz1_4) => 78.80/10.74 (( 78.80/10.74 (woz1_5) => 78.80/10.74 (( 78.80/10.74 (breln1all2) => 78.80/10.74 (( 78.80/10.74 (breln1SetBreln1) => 78.80/10.74 (( 78.80/10.74 (choice2fnsingleton) => 78.80/10.74 (( 78.80/10.74 (setOfPairsIsBReln1) => 78.80/10.74 (( 78.80/10.74 (breln1all1) => 78.80/10.74 (( 78.80/10.74 (subbreln1) => 78.80/10.74 (( 78.80/10.74 (eqbreln1) => 78.80/10.74 (( 78.80/10.74 (breln1invprop) => 78.80/10.74 (( 78.80/10.74 (breln1invI) => 78.80/10.74 (( 78.80/10.74 (breln1invE) => 78.80/10.74 (( 78.80/10.74 (breln1compprop) => 78.80/10.74 (( 78.80/10.74 (breln1compI) => 78.80/10.74 (( 78.80/10.74 (breln1compE) => 78.80/10.74 (( 78.80/10.74 (breln1compEex) => 78.80/10.74 (( 78.80/10.74 (breln1unionprop) => 78.80/10.74 (( 78.80/10.74 (breln1unionIL) => 78.80/10.74 (( 78.80/10.74 (breln1unionIR) => 78.80/10.74 (( 78.80/10.74 (breln1unionI) => 78.80/10.74 (( 78.80/10.74 (breln1unionE) => 78.80/10.74 (( 78.80/10.74 (breln1unionEcases) => 78.80/10.74 (( 78.80/10.74 (breln1unionCommutes) => 78.80/10.74 (( 78.80/10.74 (woz2Ex) => 78.80/10.74 (( 78.80/10.74 (woz2W) => 78.80/10.74 (( 78.80/10.74 (woz2A) => 78.80/10.74 (( 78.80/10.74 (woz2B) => 78.80/10.74 (( 78.80/10.74 (image1Ex) => 78.80/10.74 (( 78.80/10.74 (image1Ex1) => 78.80/10.74 (( 78.80/10.74 (image1Equiv) => 78.80/10.74 (( 78.80/10.74 (image1E) => 78.80/10.74 (( 78.80/10.74 (image1I) => 78.80/10.74 (( 78.80/10.74 (injFuncInInjFuncSet) => 78.80/10.74 (( 78.80/10.74 (injFuncSetFuncIn) => 78.80/10.74 (( 78.80/10.74 (injFuncSetFuncInj) => 78.80/10.74 (( 78.80/10.74 (surjFuncSetFuncIn) => 78.80/10.74 (( 78.80/10.74 (surjFuncSetFuncSurj) => 78.80/10.74 (( 78.80/10.74 (leftInvIsSurj) => 78.80/10.74 (( 78.80/10.74 (surjCantorThm) => 78.80/10.74 (( 78.80/10.74 (foundation2) => 78.80/10.74 (( 78.80/10.74 (notinself) => 78.80/10.74 (( 78.80/10.74 (notinself2) => 78.80/10.74 (( 78.80/10.74 (omegaSp) => 78.80/10.74 (( 78.80/10.74 (omegaSclos) => 78.80/10.74 (( 78.80/10.74 (peano0notS) => 78.80/10.74 (( 78.80/10.74 (peanoSinj) => 78.80/10.74 (( 78.80/10.74 (transitivesetOp1) => 78.80/10.74 (( 78.80/10.74 (binintTransitive) => 78.80/10.74 (( 78.80/10.74 (transitivesetOp2) => 78.80/10.74 (( 78.80/10.74 (setunionTransitive) => 78.80/10.74 (( 78.80/10.74 (ordinalMinLem1) => 78.80/10.74 (( 78.80/10.74 (!!) @ ( 78.80/10.74 ^[Y0 : $i]: 78.80/10.74 (( 78.80/10.74 (ordinal @ 78.80/10.74 Y0) => 78.80/10.74 (( 78.80/10.74 (!!) @ ( 78.80/10.74 ^[Y1 : $i]: 78.80/10.74 (( 78.80/10.74 (!!) @ ( 78.80/10.74 ^[Y2 : $i]: 78.80/10.74 (( 78.80/10.74 (in @ 78.80/10.74 Y2 @ 78.80/10.74 Y0) => 78.80/10.74 (( 78.80/10.74 (in @ 78.80/10.74 Y1 @ 78.80/10.74 Y2) => 78.80/10.74 (in @ 78.80/10.74 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 78.80/10.74 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2207])). 78.80/10.74 thf(zip_derived_cl2235, plain, 78.80/10.74 (~ (((contrasubsetT3) => 78.80/10.74 (((doubleComplementI1) => 78.80/10.74 (((doubleComplementE1) => 78.80/10.74 (((doubleComplementSub1) => 78.80/10.74 (((doubleComplementSub2) => 78.80/10.74 (((doubleComplementEq) => 78.80/10.74 (((complementTnotintersectT) => 78.80/10.74 (((complementImpComplementIntersect) => 78.80/10.74 (((complementSubsetComplementIntersect) => 78.80/10.74 (((complementInPowersetComplementIntersect) => 78.80/10.74 (((contraSubsetComplement) => 78.80/10.74 (((complementTcontraSubset) => 78.80/10.74 (((binunionTILcontra) => 78.80/10.74 (((binunionTIRcontra) => 78.80/10.74 (((inIntersectImpInUnion) => 78.80/10.74 (((inIntersectImpInUnion2) => 78.80/10.74 (((inIntersectImpInIntersectUnions) => 78.80/10.74 (((intersectInPowersetIntersectUnions) => 78.80/10.74 (((inComplementUnionImpNotIn1) => 78.80/10.74 (((inComplementUnionImpInComplement1) => 78.80/10.74 (((binunionTE) => 78.80/10.74 (((binunionTEcontra) => 78.80/10.74 (((demorgan2a1) => 78.80/10.74 (((complementUnionInPowersetComplement) => 78.80/10.74 (((demorgan2a2) => 78.80/10.74 (((demorgan1a) => 78.80/10.74 (((demorgan1b) => 78.80/10.74 (((demorgan1) => 78.80/10.74 (((demorgan2a) => 78.80/10.74 (((demorgan2b2) => 78.80/10.74 (( 78.80/10.74 (demorgan2b) => 78.80/10.74 (( 78.80/10.74 (demorgan2) => 78.80/10.74 (( 78.80/10.74 (woz13rule0) => 78.80/10.74 (( 78.80/10.74 (woz13rule1) => 78.80/10.74 (( 78.80/10.74 (woz13rule2) => 78.80/10.74 (( 78.80/10.74 (woz13rule3) => 78.80/10.74 (( 78.80/10.74 (woz13rule4) => 78.80/10.74 (( 78.80/10.74 (woz1_1) => 78.80/10.74 (( 78.80/10.74 (woz1_2) => 78.80/10.74 (( 78.80/10.74 (woz1_3) => 78.80/10.74 (( 78.80/10.74 (woz1_4) => 78.80/10.74 (( 78.80/10.74 (woz1_5) => 78.80/10.74 (( 78.80/10.74 (breln1all2) => 78.80/10.74 (( 78.80/10.74 (breln1SetBreln1) => 78.80/10.74 (( 78.80/10.74 (choice2fnsingleton) => 78.80/10.74 (( 78.80/10.74 (setOfPairsIsBReln1) => 78.80/10.74 (( 78.80/10.74 (breln1all1) => 78.80/10.74 (( 78.80/10.74 (subbreln1) => 78.80/10.74 (( 78.80/10.74 (eqbreln1) => 78.80/10.74 (( 78.80/10.74 (breln1invprop) => 78.80/10.74 (( 78.80/10.74 (breln1invI) => 78.80/10.74 (( 78.80/10.74 (breln1invE) => 78.80/10.74 (( 78.80/10.74 (breln1compprop) => 78.80/10.74 (( 78.80/10.74 (breln1compI) => 78.80/10.74 (( 78.80/10.74 (breln1compE) => 78.80/10.74 (( 78.80/10.74 (breln1compEex) => 78.80/10.74 (( 78.80/10.74 (breln1unionprop) => 78.80/10.74 (( 78.80/10.74 (breln1unionIL) => 78.80/10.74 (( 78.80/10.74 (breln1unionIR) => 78.80/10.74 (( 78.80/10.74 (breln1unionI) => 78.80/10.74 (( 78.80/10.74 (breln1unionE) => 78.80/10.74 (( 78.80/10.74 (breln1unionEcases) => 78.80/10.74 (( 78.80/10.74 (breln1unionCommutes) => 78.80/10.74 (( 78.80/10.74 (woz2Ex) => 78.80/10.74 (( 78.80/10.74 (woz2W) => 78.80/10.74 (( 78.80/10.74 (woz2A) => 78.80/10.74 (( 78.80/10.74 (woz2B) => 78.80/10.74 (( 78.80/10.74 (image1Ex) => 78.80/10.74 (( 78.80/10.74 (image1Ex1) => 78.80/10.74 (( 78.80/10.74 (image1Equiv) => 78.80/10.74 (( 78.80/10.74 (image1E) => 78.80/10.74 (( 78.80/10.74 (image1I) => 78.80/10.74 (( 78.80/10.74 (injFuncInInjFuncSet) => 78.80/10.74 (( 78.80/10.74 (injFuncSetFuncIn) => 78.80/10.74 (( 78.80/10.74 (injFuncSetFuncInj) => 78.80/10.74 (( 78.80/10.74 (surjFuncSetFuncIn) => 78.80/10.74 (( 78.80/10.74 (surjFuncSetFuncSurj) => 78.80/10.74 (( 78.80/10.74 (leftInvIsSurj) => 78.80/10.74 (( 78.80/10.74 (surjCantorThm) => 78.80/10.74 (( 78.80/10.74 (foundation2) => 78.80/10.74 (( 78.80/10.74 (notinself) => 78.80/10.74 (( 78.80/10.74 (notinself2) => 78.80/10.74 (( 78.80/10.74 (omegaSp) => 78.80/10.74 (( 78.80/10.74 (omegaSclos) => 78.80/10.74 (( 78.80/10.74 (peano0notS) => 78.80/10.74 (( 78.80/10.74 (peanoSinj) => 78.80/10.74 (( 78.80/10.74 (transitivesetOp1) => 78.80/10.74 (( 78.80/10.74 (binintTransitive) => 78.80/10.74 (( 78.80/10.74 (transitivesetOp2) => 78.80/10.74 (( 78.80/10.74 (setunionTransitive) => 78.80/10.74 (( 78.80/10.74 (ordinalMinLem1) => 78.80/10.74 (( 78.80/10.74 (!!) @ ( 78.80/10.74 ^[Y0 : $i]: 78.80/10.74 (( 78.80/10.74 (ordinal @ 78.80/10.74 Y0) => 78.80/10.74 (( 78.80/10.74 (!!) @ ( 78.80/10.74 ^[Y1 : $i]: 78.80/10.74 (( 78.80/10.74 (!!) @ ( 78.80/10.74 ^[Y2 : $i]: 78.80/10.74 (( 78.80/10.74 (in @ 78.80/10.74 Y2 @ 78.80/10.74 Y0) => 78.80/10.74 (( 78.80/10.74 (in @ 78.80/10.74 Y1 @ 78.80/10.74 Y2) => 78.80/10.74 (in @ 78.80/10.74 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 78.80/10.74 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2219])). 78.80/10.74 thf(zip_derived_cl2254, plain, 78.80/10.74 (~ (((doubleComplementI1) => 78.80/10.74 (((doubleComplementE1) => 78.80/10.74 (((doubleComplementSub1) => 78.80/10.74 (((doubleComplementSub2) => 78.80/10.74 (((doubleComplementEq) => 78.80/10.74 (((complementTnotintersectT) => 78.80/10.74 (((complementImpComplementIntersect) => 78.80/10.74 (((complementSubsetComplementIntersect) => 78.80/10.74 (((complementInPowersetComplementIntersect) => 78.80/10.74 (((contraSubsetComplement) => 78.80/10.74 (((complementTcontraSubset) => 78.80/10.74 (((binunionTILcontra) => 78.80/10.74 (((binunionTIRcontra) => 78.80/10.74 (((inIntersectImpInUnion) => 78.80/10.74 (((inIntersectImpInUnion2) => 78.80/10.74 (((inIntersectImpInIntersectUnions) => 78.80/10.74 (((intersectInPowersetIntersectUnions) => 78.80/10.74 (((inComplementUnionImpNotIn1) => 78.80/10.74 (((inComplementUnionImpInComplement1) => 78.80/10.74 (((binunionTE) => 78.80/10.74 (((binunionTEcontra) => 78.80/10.74 (((demorgan2a1) => 78.80/10.74 (((complementUnionInPowersetComplement) => 78.80/10.74 (((demorgan2a2) => 78.80/10.74 (((demorgan1a) => 78.80/10.74 (((demorgan1b) => 78.80/10.74 (((demorgan1) => 78.80/10.74 (((demorgan2a) => 78.80/10.74 (((demorgan2b2) => 78.80/10.74 (((demorgan2b) => 78.80/10.74 (( 78.80/10.74 (demorgan2) => 78.80/10.74 (( 78.80/10.74 (woz13rule0) => 78.80/10.74 (( 78.80/10.74 (woz13rule1) => 78.80/10.74 (( 78.80/10.74 (woz13rule2) => 78.80/10.74 (( 78.80/10.74 (woz13rule3) => 78.80/10.74 (( 78.80/10.74 (woz13rule4) => 78.80/10.74 (( 78.80/10.74 (woz1_1) => 78.80/10.74 (( 78.80/10.74 (woz1_2) => 78.80/10.74 (( 78.80/10.74 (woz1_3) => 78.80/10.74 (( 78.80/10.74 (woz1_4) => 78.80/10.74 (( 78.80/10.74 (woz1_5) => 78.80/10.74 (( 78.80/10.74 (breln1all2) => 78.80/10.74 (( 78.80/10.74 (breln1SetBreln1) => 78.80/10.74 (( 78.80/10.74 (choice2fnsingleton) => 78.80/10.74 (( 78.80/10.74 (setOfPairsIsBReln1) => 78.80/10.74 (( 78.80/10.74 (breln1all1) => 78.80/10.74 (( 78.80/10.74 (subbreln1) => 78.80/10.74 (( 78.80/10.74 (eqbreln1) => 78.80/10.74 (( 78.80/10.74 (breln1invprop) => 78.80/10.74 (( 78.80/10.74 (breln1invI) => 78.80/10.74 (( 78.80/10.74 (breln1invE) => 78.80/10.74 (( 78.80/10.74 (breln1compprop) => 78.80/10.74 (( 78.80/10.74 (breln1compI) => 78.80/10.74 (( 78.80/10.74 (breln1compE) => 78.80/10.74 (( 78.80/10.74 (breln1compEex) => 78.80/10.74 (( 78.80/10.74 (breln1unionprop) => 78.80/10.74 (( 78.80/10.74 (breln1unionIL) => 78.80/10.74 (( 78.80/10.74 (breln1unionIR) => 78.80/10.74 (( 78.80/10.74 (breln1unionI) => 78.80/10.74 (( 78.80/10.74 (breln1unionE) => 78.80/10.74 (( 78.80/10.74 (breln1unionEcases) => 78.80/10.74 (( 78.80/10.74 (breln1unionCommutes) => 78.80/10.74 (( 78.80/10.74 (woz2Ex) => 78.80/10.74 (( 78.80/10.74 (woz2W) => 78.80/10.74 (( 78.80/10.74 (woz2A) => 78.80/10.74 (( 78.80/10.74 (woz2B) => 78.80/10.74 (( 78.80/10.74 (image1Ex) => 78.80/10.74 (( 78.80/10.74 (image1Ex1) => 78.80/10.74 (( 78.80/10.74 (image1Equiv) => 78.80/10.74 (( 78.80/10.74 (image1E) => 78.80/10.74 (( 78.80/10.74 (image1I) => 78.80/10.74 (( 78.80/10.74 (injFuncInInjFuncSet) => 78.80/10.74 (( 78.80/10.74 (injFuncSetFuncIn) => 78.80/10.74 (( 78.80/10.74 (injFuncSetFuncInj) => 78.80/10.74 (( 78.80/10.74 (surjFuncSetFuncIn) => 78.80/10.74 (( 78.80/10.74 (surjFuncSetFuncSurj) => 78.80/10.74 (( 78.80/10.74 (leftInvIsSurj) => 78.80/10.74 (( 78.80/10.74 (surjCantorThm) => 78.80/10.74 (( 78.80/10.74 (foundation2) => 78.80/10.74 (( 78.80/10.74 (notinself) => 78.80/10.74 (( 78.80/10.74 (notinself2) => 78.80/10.74 (( 78.80/10.74 (omegaSp) => 78.80/10.74 (( 78.80/10.74 (omegaSclos) => 78.80/10.74 (( 78.80/10.74 (peano0notS) => 78.80/10.74 (( 78.80/10.74 (peanoSinj) => 78.80/10.74 (( 78.80/10.74 (transitivesetOp1) => 78.80/10.74 (( 78.80/10.74 (binintTransitive) => 78.80/10.74 (( 78.80/10.74 (transitivesetOp2) => 78.80/10.74 (( 78.80/10.74 (setunionTransitive) => 78.80/10.74 (( 78.80/10.74 (ordinalMinLem1) => 78.80/10.74 (( 78.80/10.74 (!!) @ ( 78.80/10.74 ^[Y0 : $i]: 78.80/10.74 (( 78.80/10.74 (ordinal @ 78.80/10.74 Y0) => 78.80/10.74 (( 78.80/10.74 (!!) @ ( 78.80/10.74 ^[Y1 : $i]: 78.80/10.74 (( 78.80/10.74 (!!) @ ( 78.80/10.74 ^[Y2 : $i]: 78.80/10.74 (( 78.80/10.74 (in @ 78.80/10.74 Y2 @ 78.80/10.74 Y0) => 78.80/10.74 (( 78.80/10.74 (in @ 78.80/10.74 Y1 @ 78.80/10.74 Y2) => 78.80/10.74 (in @ 78.80/10.74 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 78.80/10.74 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2235])). 78.80/10.74 thf(zip_derived_cl2267, plain, 78.80/10.74 (~ (((doubleComplementE1) => 78.80/10.74 (((doubleComplementSub1) => 78.80/10.74 (((doubleComplementSub2) => 78.80/10.74 (((doubleComplementEq) => 78.80/10.74 (((complementTnotintersectT) => 78.80/10.74 (((complementImpComplementIntersect) => 78.80/10.74 (((complementSubsetComplementIntersect) => 78.80/10.74 (((complementInPowersetComplementIntersect) => 78.80/10.74 (((contraSubsetComplement) => 78.80/10.74 (((complementTcontraSubset) => 78.80/10.74 (((binunionTILcontra) => 78.80/10.74 (((binunionTIRcontra) => 78.80/10.74 (((inIntersectImpInUnion) => 78.80/10.74 (((inIntersectImpInUnion2) => 78.80/10.74 (((inIntersectImpInIntersectUnions) => 78.80/10.74 (((intersectInPowersetIntersectUnions) => 78.80/10.74 (((inComplementUnionImpNotIn1) => 78.80/10.74 (((inComplementUnionImpInComplement1) => 78.80/10.74 (((binunionTE) => 78.80/10.74 (((binunionTEcontra) => 78.80/10.74 (((demorgan2a1) => 78.80/10.74 (((complementUnionInPowersetComplement) => 78.80/10.74 (((demorgan2a2) => 78.80/10.74 (((demorgan1a) => 78.80/10.74 (((demorgan1b) => 78.80/10.74 (((demorgan1) => 78.80/10.74 (((demorgan2a) => 78.80/10.74 (((demorgan2b2) => 78.80/10.74 (((demorgan2b) => 78.80/10.74 (((demorgan2) => 78.80/10.74 (( 78.80/10.74 (woz13rule0) => 78.80/10.74 (( 78.80/10.74 (woz13rule1) => 78.80/10.74 (( 78.80/10.74 (woz13rule2) => 78.80/10.74 (( 78.80/10.74 (woz13rule3) => 78.80/10.74 (( 78.80/10.74 (woz13rule4) => 78.80/10.74 (( 78.80/10.74 (woz1_1) => 78.80/10.74 (( 78.80/10.74 (woz1_2) => 78.80/10.74 (( 78.80/10.74 (woz1_3) => 78.80/10.74 (( 78.80/10.74 (woz1_4) => 78.80/10.74 (( 78.80/10.74 (woz1_5) => 78.80/10.74 (( 78.80/10.74 (breln1all2) => 78.80/10.74 (( 78.80/10.74 (breln1SetBreln1) => 78.80/10.74 (( 78.80/10.74 (choice2fnsingleton) => 78.80/10.74 (( 78.80/10.74 (setOfPairsIsBReln1) => 78.80/10.74 (( 78.80/10.74 (breln1all1) => 78.80/10.74 (( 78.80/10.74 (subbreln1) => 78.80/10.74 (( 78.80/10.74 (eqbreln1) => 78.80/10.74 (( 78.80/10.74 (breln1invprop) => 78.80/10.74 (( 78.80/10.74 (breln1invI) => 78.80/10.74 (( 78.80/10.74 (breln1invE) => 78.80/10.74 (( 78.80/10.74 (breln1compprop) => 78.80/10.74 (( 78.80/10.74 (breln1compI) => 78.80/10.74 (( 78.80/10.74 (breln1compE) => 78.80/10.74 (( 78.80/10.74 (breln1compEex) => 78.80/10.74 (( 78.80/10.74 (breln1unionprop) => 78.80/10.74 (( 78.80/10.74 (breln1unionIL) => 78.80/10.74 (( 78.80/10.74 (breln1unionIR) => 78.80/10.74 (( 78.80/10.74 (breln1unionI) => 78.80/10.74 (( 78.80/10.74 (breln1unionE) => 78.80/10.74 (( 78.80/10.74 (breln1unionEcases) => 78.80/10.74 (( 78.80/10.74 (breln1unionCommutes) => 78.80/10.74 (( 78.80/10.74 (woz2Ex) => 78.80/10.74 (( 78.80/10.74 (woz2W) => 78.80/10.74 (( 78.80/10.74 (woz2A) => 78.80/10.74 (( 78.80/10.74 (woz2B) => 78.80/10.74 (( 78.80/10.74 (image1Ex) => 78.80/10.74 (( 78.80/10.74 (image1Ex1) => 78.80/10.74 (( 78.80/10.74 (image1Equiv) => 78.80/10.74 (( 78.80/10.74 (image1E) => 78.80/10.74 (( 78.80/10.74 (image1I) => 78.80/10.74 (( 78.80/10.74 (injFuncInInjFuncSet) => 78.80/10.74 (( 78.80/10.74 (injFuncSetFuncIn) => 78.80/10.74 (( 78.80/10.74 (injFuncSetFuncInj) => 78.80/10.74 (( 78.80/10.74 (surjFuncSetFuncIn) => 78.80/10.74 (( 78.80/10.74 (surjFuncSetFuncSurj) => 78.80/10.74 (( 78.80/10.74 (leftInvIsSurj) => 78.80/10.74 (( 78.80/10.74 (surjCantorThm) => 78.80/10.74 (( 78.80/10.74 (foundation2) => 78.80/10.74 (( 78.80/10.74 (notinself) => 78.80/10.74 (( 78.80/10.74 (notinself2) => 78.80/10.74 (( 78.80/10.74 (omegaSp) => 78.80/10.74 (( 78.80/10.74 (omegaSclos) => 78.80/10.74 (( 78.80/10.74 (peano0notS) => 78.80/10.74 (( 78.80/10.74 (peanoSinj) => 78.80/10.74 (( 78.80/10.74 (transitivesetOp1) => 78.80/10.74 (( 78.80/10.74 (binintTransitive) => 78.80/10.74 (( 78.80/10.74 (transitivesetOp2) => 78.80/10.74 (( 78.80/10.74 (setunionTransitive) => 78.80/10.74 (( 78.80/10.74 (ordinalMinLem1) => 78.80/10.74 (( 78.80/10.74 (!!) @ ( 78.80/10.74 ^[Y0 : $i]: 78.80/10.74 (( 78.80/10.74 (ordinal @ 78.80/10.74 Y0) => 78.80/10.74 (( 78.80/10.74 (!!) @ ( 78.80/10.74 ^[Y1 : $i]: 78.80/10.74 (( 78.80/10.74 (!!) @ ( 78.80/10.74 ^[Y2 : $i]: 78.80/10.74 (( 78.80/10.74 (in @ 78.80/10.74 Y2 @ 78.80/10.74 Y0) => 78.80/10.74 (( 78.80/10.74 (in @ 78.80/10.74 Y1 @ 78.80/10.74 Y2) => 78.80/10.74 (in @ 78.80/10.74 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 78.80/10.74 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2254])). 78.80/10.74 thf(zip_derived_cl2278, plain, 78.80/10.74 (~ (((doubleComplementSub1) => 78.80/10.74 (((doubleComplementSub2) => 78.80/10.74 (((doubleComplementEq) => 78.80/10.74 (((complementTnotintersectT) => 78.80/10.74 (((complementImpComplementIntersect) => 78.80/10.74 (((complementSubsetComplementIntersect) => 78.80/10.74 (((complementInPowersetComplementIntersect) => 78.80/10.74 (((contraSubsetComplement) => 78.80/10.74 (((complementTcontraSubset) => 78.80/10.74 (((binunionTILcontra) => 78.80/10.74 (((binunionTIRcontra) => 78.80/10.74 (((inIntersectImpInUnion) => 78.80/10.74 (((inIntersectImpInUnion2) => 78.80/10.74 (((inIntersectImpInIntersectUnions) => 78.80/10.74 (((intersectInPowersetIntersectUnions) => 78.80/10.74 (((inComplementUnionImpNotIn1) => 78.80/10.74 (((inComplementUnionImpInComplement1) => 78.80/10.74 (((binunionTE) => 78.80/10.74 (((binunionTEcontra) => 78.80/10.74 (((demorgan2a1) => 78.80/10.74 (((complementUnionInPowersetComplement) => 78.80/10.74 (((demorgan2a2) => 78.80/10.74 (((demorgan1a) => 78.80/10.74 (((demorgan1b) => 78.80/10.74 (((demorgan1) => 78.80/10.74 (((demorgan2a) => 78.80/10.74 (((demorgan2b2) => 78.80/10.74 (((demorgan2b) => 78.80/10.74 (((demorgan2) => 78.80/10.74 (((woz13rule0) => 78.80/10.74 (( 78.80/10.74 (woz13rule1) => 78.80/10.74 (( 78.80/10.74 (woz13rule2) => 78.80/10.74 (( 78.80/10.74 (woz13rule3) => 78.80/10.74 (( 78.80/10.74 (woz13rule4) => 78.80/10.74 (( 78.80/10.74 (woz1_1) => 78.80/10.74 (( 78.80/10.74 (woz1_2) => 78.80/10.74 (( 78.80/10.74 (woz1_3) => 78.80/10.74 (( 78.80/10.74 (woz1_4) => 78.80/10.74 (( 78.80/10.74 (woz1_5) => 78.80/10.74 (( 78.80/10.74 (breln1all2) => 78.80/10.74 (( 78.80/10.74 (breln1SetBreln1) => 78.80/10.74 (( 78.80/10.74 (choice2fnsingleton) => 78.80/10.74 (( 78.80/10.74 (setOfPairsIsBReln1) => 78.80/10.74 (( 78.80/10.74 (breln1all1) => 78.80/10.74 (( 78.80/10.74 (subbreln1) => 78.80/10.74 (( 78.80/10.74 (eqbreln1) => 78.80/10.74 (( 78.80/10.74 (breln1invprop) => 78.80/10.74 (( 78.80/10.74 (breln1invI) => 78.80/10.74 (( 78.80/10.74 (breln1invE) => 78.80/10.74 (( 78.80/10.74 (breln1compprop) => 78.80/10.74 (( 78.80/10.74 (breln1compI) => 78.80/10.74 (( 78.80/10.74 (breln1compE) => 78.80/10.74 (( 78.80/10.74 (breln1compEex) => 78.80/10.74 (( 78.80/10.74 (breln1unionprop) => 78.80/10.74 (( 78.80/10.74 (breln1unionIL) => 78.80/10.74 (( 78.80/10.74 (breln1unionIR) => 78.80/10.74 (( 78.80/10.74 (breln1unionI) => 78.80/10.74 (( 78.80/10.74 (breln1unionE) => 78.80/10.74 (( 78.80/10.74 (breln1unionEcases) => 78.80/10.74 (( 78.80/10.74 (breln1unionCommutes) => 78.80/10.74 (( 78.80/10.74 (woz2Ex) => 78.80/10.74 (( 78.80/10.74 (woz2W) => 78.80/10.74 (( 78.80/10.74 (woz2A) => 78.80/10.74 (( 78.80/10.74 (woz2B) => 78.80/10.74 (( 78.80/10.74 (image1Ex) => 78.80/10.74 (( 78.80/10.74 (image1Ex1) => 78.80/10.74 (( 78.80/10.74 (image1Equiv) => 78.80/10.74 (( 78.80/10.74 (image1E) => 78.80/10.74 (( 78.80/10.74 (image1I) => 78.80/10.74 (( 78.80/10.74 (injFuncInInjFuncSet) => 78.80/10.74 (( 78.80/10.74 (injFuncSetFuncIn) => 78.80/10.74 (( 78.80/10.74 (injFuncSetFuncInj) => 78.80/10.74 (( 78.80/10.74 (surjFuncSetFuncIn) => 78.80/10.74 (( 78.80/10.74 (surjFuncSetFuncSurj) => 78.80/10.74 (( 78.80/10.74 (leftInvIsSurj) => 78.80/10.74 (( 78.80/10.74 (surjCantorThm) => 78.80/10.74 (( 78.80/10.74 (foundation2) => 78.80/10.74 (( 78.80/10.74 (notinself) => 78.80/10.74 (( 78.80/10.74 (notinself2) => 78.80/10.74 (( 78.80/10.74 (omegaSp) => 78.80/10.74 (( 78.80/10.74 (omegaSclos) => 78.80/10.74 (( 78.80/10.74 (peano0notS) => 78.80/10.74 (( 78.80/10.74 (peanoSinj) => 78.80/10.74 (( 78.80/10.74 (transitivesetOp1) => 78.80/10.74 (( 78.80/10.74 (binintTransitive) => 78.80/10.74 (( 78.80/10.74 (transitivesetOp2) => 78.80/10.74 (( 78.80/10.74 (setunionTransitive) => 78.80/10.74 (( 78.80/10.74 (ordinalMinLem1) => 78.80/10.74 (( 78.80/10.74 (!!) @ ( 78.80/10.74 ^[Y0 : $i]: 78.80/10.74 (( 78.80/10.74 (ordinal @ 78.80/10.74 Y0) => 78.80/10.74 (( 78.80/10.74 (!!) @ ( 78.80/10.74 ^[Y1 : $i]: 78.80/10.74 (( 78.80/10.74 (!!) @ ( 78.80/10.74 ^[Y2 : $i]: 78.80/10.74 (( 78.80/10.74 (in @ 78.80/10.74 Y2 @ 78.80/10.74 Y0) => 78.80/10.74 (( 78.80/10.74 (in @ 78.80/10.74 Y1 @ 78.80/10.74 Y2) => 78.80/10.74 (in @ 78.80/10.74 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 78.80/10.74 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2267])). 78.80/10.74 thf(zip_derived_cl2288, plain, 78.80/10.74 (~ (((doubleComplementSub2) => 78.80/10.74 (((doubleComplementEq) => 78.80/10.74 (((complementTnotintersectT) => 78.80/10.74 (((complementImpComplementIntersect) => 78.80/10.74 (((complementSubsetComplementIntersect) => 78.80/10.74 (((complementInPowersetComplementIntersect) => 78.80/10.74 (((contraSubsetComplement) => 78.80/10.74 (((complementTcontraSubset) => 78.80/10.74 (((binunionTILcontra) => 78.80/10.74 (((binunionTIRcontra) => 78.80/10.74 (((inIntersectImpInUnion) => 78.80/10.74 (((inIntersectImpInUnion2) => 78.80/10.74 (((inIntersectImpInIntersectUnions) => 78.80/10.74 (((intersectInPowersetIntersectUnions) => 78.80/10.74 (((inComplementUnionImpNotIn1) => 78.80/10.74 (((inComplementUnionImpInComplement1) => 78.80/10.74 (((binunionTE) => 78.80/10.74 (((binunionTEcontra) => 78.80/10.74 (((demorgan2a1) => 78.80/10.74 (((complementUnionInPowersetComplement) => 78.80/10.74 (((demorgan2a2) => 78.80/10.74 (((demorgan1a) => 78.80/10.74 (((demorgan1b) => 78.80/10.74 (((demorgan1) => 78.80/10.74 (((demorgan2a) => 78.80/10.74 (((demorgan2b2) => 78.80/10.74 (((demorgan2b) => 78.80/10.74 (((demorgan2) => 78.80/10.74 (((woz13rule0) => 78.80/10.74 (((woz13rule1) => 78.80/10.74 (( 78.80/10.74 (woz13rule2) => 78.80/10.74 (( 78.80/10.74 (woz13rule3) => 78.80/10.74 (( 78.80/10.74 (woz13rule4) => 78.80/10.74 (( 78.80/10.74 (woz1_1) => 78.80/10.74 (( 78.80/10.74 (woz1_2) => 78.80/10.74 (( 78.80/10.74 (woz1_3) => 78.80/10.74 (( 78.80/10.74 (woz1_4) => 78.80/10.74 (( 78.80/10.74 (woz1_5) => 78.80/10.74 (( 78.80/10.74 (breln1all2) => 78.80/10.74 (( 78.80/10.74 (breln1SetBreln1) => 78.80/10.74 (( 78.80/10.74 (choice2fnsingleton) => 78.80/10.74 (( 78.80/10.74 (setOfPairsIsBReln1) => 78.80/10.74 (( 78.80/10.74 (breln1all1) => 78.80/10.74 (( 78.80/10.74 (subbreln1) => 78.80/10.74 (( 78.80/10.74 (eqbreln1) => 78.80/10.74 (( 78.80/10.74 (breln1invprop) => 78.80/10.74 (( 78.80/10.74 (breln1invI) => 78.80/10.74 (( 78.80/10.74 (breln1invE) => 78.80/10.74 (( 78.80/10.74 (breln1compprop) => 78.80/10.74 (( 78.80/10.74 (breln1compI) => 78.80/10.74 (( 78.80/10.74 (breln1compE) => 78.80/10.74 (( 78.80/10.74 (breln1compEex) => 78.80/10.74 (( 78.80/10.74 (breln1unionprop) => 78.80/10.74 (( 78.80/10.74 (breln1unionIL) => 78.80/10.74 (( 78.80/10.74 (breln1unionIR) => 78.80/10.74 (( 78.80/10.74 (breln1unionI) => 78.80/10.74 (( 78.80/10.74 (breln1unionE) => 78.80/10.74 (( 78.80/10.74 (breln1unionEcases) => 78.80/10.74 (( 78.80/10.74 (breln1unionCommutes) => 78.80/10.74 (( 78.80/10.74 (woz2Ex) => 78.80/10.74 (( 78.80/10.74 (woz2W) => 78.80/10.74 (( 78.80/10.74 (woz2A) => 78.80/10.74 (( 78.80/10.74 (woz2B) => 78.80/10.74 (( 78.80/10.74 (image1Ex) => 78.80/10.74 (( 78.80/10.74 (image1Ex1) => 78.80/10.74 (( 78.80/10.74 (image1Equiv) => 78.80/10.74 (( 78.80/10.74 (image1E) => 78.80/10.74 (( 78.80/10.74 (image1I) => 78.80/10.74 (( 78.80/10.74 (injFuncInInjFuncSet) => 78.80/10.74 (( 78.80/10.74 (injFuncSetFuncIn) => 78.80/10.74 (( 78.80/10.74 (injFuncSetFuncInj) => 78.80/10.74 (( 78.80/10.74 (surjFuncSetFuncIn) => 78.80/10.74 (( 78.80/10.74 (surjFuncSetFuncSurj) => 78.80/10.74 (( 78.80/10.74 (leftInvIsSurj) => 78.80/10.74 (( 78.80/10.74 (surjCantorThm) => 78.80/10.74 (( 78.80/10.74 (foundation2) => 78.80/10.74 (( 78.80/10.74 (notinself) => 78.80/10.74 (( 78.80/10.74 (notinself2) => 78.80/10.74 (( 78.80/10.74 (omegaSp) => 78.80/10.74 (( 78.80/10.74 (omegaSclos) => 78.80/10.74 (( 78.80/10.74 (peano0notS) => 78.80/10.74 (( 78.80/10.74 (peanoSinj) => 78.80/10.74 (( 78.80/10.74 (transitivesetOp1) => 78.80/10.74 (( 78.80/10.74 (binintTransitive) => 78.80/10.74 (( 78.80/10.74 (transitivesetOp2) => 78.80/10.74 (( 78.80/10.74 (setunionTransitive) => 78.80/10.74 (( 78.80/10.74 (ordinalMinLem1) => 78.80/10.74 (( 78.80/10.74 (!!) @ ( 78.80/10.74 ^[Y0 : $i]: 78.80/10.74 (( 78.80/10.74 (ordinal @ 78.80/10.74 Y0) => 78.80/10.74 (( 78.80/10.74 (!!) @ ( 78.80/10.74 ^[Y1 : $i]: 78.80/10.74 (( 78.80/10.74 (!!) @ ( 78.80/10.74 ^[Y2 : $i]: 78.80/10.74 (( 78.80/10.74 (in @ 78.80/10.74 Y2 @ 78.80/10.74 Y0) => 78.80/10.74 (( 78.80/10.74 (in @ 78.80/10.74 Y1 @ 78.80/10.74 Y2) => 78.80/10.74 (in @ 78.80/10.74 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 78.80/10.74 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2278])). 78.80/10.74 thf(zip_derived_cl2299, plain, 78.80/10.74 (~ (((doubleComplementEq) => 78.80/10.74 (((complementTnotintersectT) => 78.80/10.74 (((complementImpComplementIntersect) => 78.80/10.74 (((complementSubsetComplementIntersect) => 78.80/10.74 (((complementInPowersetComplementIntersect) => 78.80/10.74 (((contraSubsetComplement) => 78.80/10.74 (((complementTcontraSubset) => 78.80/10.74 (((binunionTILcontra) => 78.80/10.74 (((binunionTIRcontra) => 78.80/10.74 (((inIntersectImpInUnion) => 78.80/10.74 (((inIntersectImpInUnion2) => 78.80/10.74 (((inIntersectImpInIntersectUnions) => 78.80/10.74 (((intersectInPowersetIntersectUnions) => 78.80/10.74 (((inComplementUnionImpNotIn1) => 78.80/10.74 (((inComplementUnionImpInComplement1) => 78.80/10.74 (((binunionTE) => 78.80/10.74 (((binunionTEcontra) => 78.80/10.74 (((demorgan2a1) => 78.80/10.74 (((complementUnionInPowersetComplement) => 78.80/10.74 (((demorgan2a2) => 78.80/10.74 (((demorgan1a) => 78.80/10.74 (((demorgan1b) => 78.80/10.74 (((demorgan1) => 78.80/10.74 (((demorgan2a) => 78.80/10.74 (((demorgan2b2) => 78.80/10.74 (((demorgan2b) => 78.80/10.74 (((demorgan2) => 78.80/10.74 (((woz13rule0) => 78.80/10.74 (((woz13rule1) => 78.80/10.74 (((woz13rule2) => 78.80/10.74 (( 78.80/10.74 (woz13rule3) => 78.80/10.74 (( 78.80/10.74 (woz13rule4) => 78.80/10.74 (( 78.80/10.74 (woz1_1) => 78.80/10.74 (( 78.80/10.74 (woz1_2) => 78.80/10.74 (( 78.80/10.74 (woz1_3) => 78.80/10.74 (( 78.80/10.74 (woz1_4) => 78.80/10.74 (( 78.80/10.74 (woz1_5) => 78.80/10.74 (( 78.80/10.74 (breln1all2) => 78.80/10.74 (( 78.80/10.74 (breln1SetBreln1) => 78.80/10.74 (( 78.80/10.74 (choice2fnsingleton) => 78.80/10.74 (( 78.80/10.74 (setOfPairsIsBReln1) => 78.80/10.74 (( 78.80/10.74 (breln1all1) => 78.80/10.74 (( 78.80/10.74 (subbreln1) => 78.80/10.74 (( 78.80/10.74 (eqbreln1) => 78.80/10.74 (( 78.80/10.74 (breln1invprop) => 78.80/10.74 (( 78.80/10.74 (breln1invI) => 78.80/10.74 (( 78.80/10.74 (breln1invE) => 78.80/10.74 (( 78.80/10.74 (breln1compprop) => 78.80/10.74 (( 78.80/10.74 (breln1compI) => 78.80/10.74 (( 78.80/10.74 (breln1compE) => 78.80/10.74 (( 78.80/10.74 (breln1compEex) => 78.80/10.74 (( 78.80/10.74 (breln1unionprop) => 78.80/10.74 (( 78.80/10.74 (breln1unionIL) => 78.80/10.74 (( 78.80/10.74 (breln1unionIR) => 78.80/10.74 (( 78.80/10.74 (breln1unionI) => 78.80/10.74 (( 78.80/10.74 (breln1unionE) => 78.80/10.74 (( 78.80/10.74 (breln1unionEcases) => 78.80/10.74 (( 78.80/10.74 (breln1unionCommutes) => 78.80/10.74 (( 78.80/10.74 (woz2Ex) => 78.80/10.74 (( 78.80/10.74 (woz2W) => 78.80/10.74 (( 78.80/10.74 (woz2A) => 78.80/10.74 (( 78.80/10.74 (woz2B) => 78.80/10.74 (( 78.80/10.74 (image1Ex) => 78.80/10.74 (( 78.80/10.74 (image1Ex1) => 78.80/10.74 (( 78.80/10.74 (image1Equiv) => 78.80/10.74 (( 78.80/10.74 (image1E) => 78.80/10.74 (( 78.80/10.74 (image1I) => 78.80/10.74 (( 78.80/10.74 (injFuncInInjFuncSet) => 78.80/10.74 (( 78.80/10.74 (injFuncSetFuncIn) => 78.80/10.74 (( 78.80/10.74 (injFuncSetFuncInj) => 78.80/10.74 (( 78.80/10.74 (surjFuncSetFuncIn) => 78.80/10.74 (( 78.80/10.74 (surjFuncSetFuncSurj) => 78.80/10.74 (( 78.80/10.74 (leftInvIsSurj) => 78.80/10.74 (( 78.80/10.74 (surjCantorThm) => 78.80/10.74 (( 78.80/10.74 (foundation2) => 78.80/10.74 (( 78.80/10.74 (notinself) => 78.80/10.74 (( 78.80/10.74 (notinself2) => 78.80/10.74 (( 78.80/10.74 (omegaSp) => 78.80/10.74 (( 78.80/10.74 (omegaSclos) => 78.80/10.74 (( 78.80/10.74 (peano0notS) => 78.80/10.74 (( 78.80/10.74 (peanoSinj) => 78.80/10.74 (( 78.80/10.74 (transitivesetOp1) => 78.80/10.74 (( 78.80/10.74 (binintTransitive) => 78.80/10.74 (( 78.80/10.74 (transitivesetOp2) => 78.80/10.74 (( 78.80/10.74 (setunionTransitive) => 78.80/10.74 (( 78.80/10.74 (ordinalMinLem1) => 78.80/10.74 (( 78.80/10.74 (!!) @ ( 78.80/10.74 ^[Y0 : $i]: 78.80/10.74 (( 78.80/10.74 (ordinal @ 78.80/10.74 Y0) => 78.80/10.74 (( 78.80/10.74 (!!) @ ( 78.80/10.74 ^[Y1 : $i]: 78.80/10.74 (( 78.80/10.74 (!!) @ ( 78.80/10.74 ^[Y2 : $i]: 78.80/10.74 (( 78.80/10.74 (in @ 78.80/10.74 Y2 @ 78.80/10.74 Y0) => 78.80/10.74 (( 78.80/10.74 (in @ 78.80/10.74 Y1 @ 78.80/10.74 Y2) => 78.80/10.74 (in @ 78.80/10.74 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 78.80/10.74 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2288])). 78.80/10.74 thf(zip_derived_cl2310, plain, 78.80/10.74 (~ (((complementTnotintersectT) => 78.80/10.74 (((complementImpComplementIntersect) => 78.80/10.74 (((complementSubsetComplementIntersect) => 78.80/10.74 (((complementInPowersetComplementIntersect) => 78.80/10.74 (((contraSubsetComplement) => 78.80/10.74 (((complementTcontraSubset) => 78.80/10.74 (((binunionTILcontra) => 78.80/10.74 (((binunionTIRcontra) => 78.80/10.74 (((inIntersectImpInUnion) => 78.80/10.74 (((inIntersectImpInUnion2) => 78.80/10.74 (((inIntersectImpInIntersectUnions) => 78.80/10.74 (((intersectInPowersetIntersectUnions) => 78.80/10.74 (((inComplementUnionImpNotIn1) => 78.80/10.74 (((inComplementUnionImpInComplement1) => 78.80/10.74 (((binunionTE) => 78.80/10.74 (((binunionTEcontra) => 78.80/10.74 (((demorgan2a1) => 78.80/10.74 (((complementUnionInPowersetComplement) => 78.80/10.74 (((demorgan2a2) => 78.80/10.74 (((demorgan1a) => 78.80/10.74 (((demorgan1b) => 78.80/10.74 (((demorgan1) => 78.80/10.74 (((demorgan2a) => 78.80/10.74 (((demorgan2b2) => 78.80/10.74 (((demorgan2b) => 78.80/10.74 (((demorgan2) => 78.80/10.74 (((woz13rule0) => 78.80/10.74 (((woz13rule1) => 78.80/10.74 (((woz13rule2) => 78.80/10.74 (((woz13rule3) => 78.80/10.74 (( 78.80/10.74 (woz13rule4) => 78.80/10.74 (( 78.80/10.74 (woz1_1) => 78.80/10.74 (( 78.80/10.74 (woz1_2) => 78.80/10.74 (( 78.80/10.74 (woz1_3) => 78.80/10.74 (( 78.80/10.74 (woz1_4) => 78.80/10.74 (( 78.80/10.74 (woz1_5) => 78.80/10.74 (( 78.80/10.74 (breln1all2) => 78.80/10.74 (( 78.80/10.74 (breln1SetBreln1) => 78.80/10.74 (( 78.80/10.74 (choice2fnsingleton) => 78.80/10.74 (( 78.80/10.74 (setOfPairsIsBReln1) => 78.80/10.74 (( 78.80/10.74 (breln1all1) => 78.80/10.74 (( 78.80/10.74 (subbreln1) => 78.80/10.74 (( 78.80/10.74 (eqbreln1) => 78.80/10.74 (( 78.80/10.74 (breln1invprop) => 78.80/10.74 (( 78.80/10.74 (breln1invI) => 78.80/10.74 (( 78.80/10.74 (breln1invE) => 78.80/10.74 (( 78.80/10.74 (breln1compprop) => 78.80/10.74 (( 78.80/10.74 (breln1compI) => 78.80/10.74 (( 78.80/10.74 (breln1compE) => 78.80/10.74 (( 78.80/10.74 (breln1compEex) => 78.80/10.74 (( 78.80/10.74 (breln1unionprop) => 78.80/10.74 (( 78.80/10.74 (breln1unionIL) => 78.80/10.74 (( 78.80/10.74 (breln1unionIR) => 78.80/10.74 (( 78.80/10.74 (breln1unionI) => 78.80/10.74 (( 78.80/10.74 (breln1unionE) => 78.80/10.74 (( 78.80/10.74 (breln1unionEcases) => 78.80/10.74 (( 78.80/10.74 (breln1unionCommutes) => 78.80/10.74 (( 78.80/10.74 (woz2Ex) => 78.80/10.74 (( 78.80/10.74 (woz2W) => 78.80/10.74 (( 78.80/10.74 (woz2A) => 78.80/10.74 (( 78.80/10.74 (woz2B) => 78.80/10.74 (( 78.80/10.74 (image1Ex) => 78.80/10.74 (( 78.80/10.74 (image1Ex1) => 78.80/10.74 (( 78.80/10.74 (image1Equiv) => 78.80/10.74 (( 78.80/10.74 (image1E) => 78.80/10.74 (( 78.80/10.74 (image1I) => 78.80/10.74 (( 78.80/10.74 (injFuncInInjFuncSet) => 78.80/10.74 (( 78.80/10.74 (injFuncSetFuncIn) => 78.80/10.74 (( 78.80/10.74 (injFuncSetFuncInj) => 78.80/10.74 (( 78.80/10.74 (surjFuncSetFuncIn) => 78.80/10.74 (( 78.80/10.74 (surjFuncSetFuncSurj) => 78.80/10.74 (( 78.80/10.74 (leftInvIsSurj) => 78.80/10.74 (( 78.80/10.74 (surjCantorThm) => 78.80/10.74 (( 78.80/10.74 (foundation2) => 78.80/10.74 (( 78.80/10.74 (notinself) => 78.80/10.74 (( 78.80/10.74 (notinself2) => 78.80/10.74 (( 78.80/10.74 (omegaSp) => 78.80/10.74 (( 78.80/10.74 (omegaSclos) => 78.80/10.74 (( 78.80/10.74 (peano0notS) => 78.80/10.74 (( 78.80/10.74 (peanoSinj) => 78.80/10.74 (( 78.80/10.74 (transitivesetOp1) => 78.80/10.74 (( 78.80/10.74 (binintTransitive) => 78.80/10.74 (( 78.80/10.74 (transitivesetOp2) => 78.80/10.74 (( 78.80/10.74 (setunionTransitive) => 78.80/10.74 (( 78.80/10.74 (ordinalMinLem1) => 78.80/10.74 (( 78.80/10.74 (!!) @ ( 78.80/10.74 ^[Y0 : $i]: 78.80/10.74 (( 78.80/10.74 (ordinal @ 78.80/10.74 Y0) => 78.80/10.74 (( 78.80/10.74 (!!) @ ( 78.80/10.74 ^[Y1 : $i]: 78.80/10.74 (( 78.80/10.74 (!!) @ ( 78.80/10.74 ^[Y2 : $i]: 78.80/10.74 (( 78.80/10.74 (in @ 78.80/10.74 Y2 @ 78.80/10.74 Y0) => 78.80/10.74 (( 78.80/10.74 (in @ 78.80/10.74 Y1 @ 78.80/10.74 Y2) => 78.80/10.74 (in @ 78.80/10.74 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 78.80/10.74 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2299])). 78.80/10.74 thf(zip_derived_cl2321, plain, 78.80/10.74 (~ (((complementImpComplementIntersect) => 78.80/10.74 (((complementSubsetComplementIntersect) => 78.80/10.74 (((complementInPowersetComplementIntersect) => 78.80/10.74 (((contraSubsetComplement) => 78.80/10.74 (((complementTcontraSubset) => 78.80/10.74 (((binunionTILcontra) => 78.80/10.74 (((binunionTIRcontra) => 78.80/10.74 (((inIntersectImpInUnion) => 78.80/10.74 (((inIntersectImpInUnion2) => 78.80/10.74 (((inIntersectImpInIntersectUnions) => 78.80/10.74 (((intersectInPowersetIntersectUnions) => 78.80/10.74 (((inComplementUnionImpNotIn1) => 78.80/10.74 (((inComplementUnionImpInComplement1) => 78.80/10.74 (((binunionTE) => 78.80/10.74 (((binunionTEcontra) => 78.80/10.74 (((demorgan2a1) => 78.80/10.74 (((complementUnionInPowersetComplement) => 78.80/10.74 (((demorgan2a2) => 78.80/10.74 (((demorgan1a) => 78.80/10.74 (((demorgan1b) => 78.80/10.74 (((demorgan1) => 78.80/10.74 (((demorgan2a) => 78.80/10.74 (((demorgan2b2) => 78.80/10.74 (((demorgan2b) => 78.80/10.74 (((demorgan2) => 78.80/10.74 (((woz13rule0) => 78.80/10.74 (((woz13rule1) => 78.80/10.74 (((woz13rule2) => 78.80/10.74 (((woz13rule3) => 78.80/10.74 (((woz13rule4) => 78.80/10.74 (( 78.80/10.74 (woz1_1) => 78.80/10.74 (( 78.80/10.74 (woz1_2) => 78.80/10.74 (( 78.80/10.74 (woz1_3) => 78.80/10.74 (( 78.80/10.74 (woz1_4) => 78.80/10.74 (( 78.80/10.74 (woz1_5) => 78.80/10.74 (( 78.80/10.74 (breln1all2) => 78.80/10.74 (( 78.80/10.74 (breln1SetBreln1) => 78.80/10.74 (( 78.80/10.74 (choice2fnsingleton) => 78.80/10.74 (( 78.80/10.74 (setOfPairsIsBReln1) => 78.80/10.74 (( 78.80/10.74 (breln1all1) => 78.80/10.74 (( 78.80/10.74 (subbreln1) => 78.80/10.74 (( 78.80/10.74 (eqbreln1) => 78.80/10.74 (( 78.80/10.74 (breln1invprop) => 78.80/10.74 (( 78.80/10.74 (breln1invI) => 78.80/10.74 (( 78.80/10.74 (breln1invE) => 78.80/10.74 (( 78.80/10.74 (breln1compprop) => 78.80/10.74 (( 78.80/10.74 (breln1compI) => 78.80/10.74 (( 78.80/10.74 (breln1compE) => 78.80/10.74 (( 78.80/10.74 (breln1compEex) => 78.80/10.74 (( 78.80/10.74 (breln1unionprop) => 78.80/10.74 (( 78.80/10.74 (breln1unionIL) => 78.80/10.74 (( 78.80/10.74 (breln1unionIR) => 78.80/10.74 (( 78.80/10.74 (breln1unionI) => 78.80/10.74 (( 78.80/10.74 (breln1unionE) => 78.80/10.74 (( 78.80/10.74 (breln1unionEcases) => 78.80/10.74 (( 78.80/10.74 (breln1unionCommutes) => 78.80/10.74 (( 78.80/10.74 (woz2Ex) => 78.80/10.74 (( 78.80/10.74 (woz2W) => 78.80/10.74 (( 78.80/10.74 (woz2A) => 78.80/10.74 (( 78.80/10.74 (woz2B) => 78.80/10.74 (( 78.80/10.74 (image1Ex) => 78.80/10.74 (( 78.80/10.74 (image1Ex1) => 78.80/10.74 (( 78.80/10.74 (image1Equiv) => 78.80/10.74 (( 78.80/10.74 (image1E) => 78.80/10.74 (( 78.80/10.74 (image1I) => 78.80/10.74 (( 78.80/10.74 (injFuncInInjFuncSet) => 78.80/10.74 (( 78.80/10.74 (injFuncSetFuncIn) => 78.80/10.74 (( 78.80/10.74 (injFuncSetFuncInj) => 78.80/10.74 (( 78.80/10.74 (surjFuncSetFuncIn) => 78.80/10.74 (( 78.80/10.74 (surjFuncSetFuncSurj) => 78.80/10.74 (( 78.80/10.74 (leftInvIsSurj) => 78.80/10.74 (( 78.80/10.74 (surjCantorThm) => 78.80/10.74 (( 78.80/10.74 (foundation2) => 78.80/10.74 (( 78.80/10.74 (notinself) => 78.80/10.74 (( 78.80/10.74 (notinself2) => 78.80/10.74 (( 78.80/10.74 (omegaSp) => 78.80/10.74 (( 78.80/10.74 (omegaSclos) => 78.80/10.74 (( 78.80/10.74 (peano0notS) => 78.80/10.74 (( 78.80/10.74 (peanoSinj) => 78.80/10.74 (( 78.80/10.74 (transitivesetOp1) => 78.80/10.74 (( 78.80/10.74 (binintTransitive) => 78.80/10.74 (( 78.80/10.74 (transitivesetOp2) => 78.80/10.74 (( 78.80/10.74 (setunionTransitive) => 78.80/10.74 (( 78.80/10.74 (ordinalMinLem1) => 78.80/10.74 (( 78.80/10.74 (!!) @ ( 78.80/10.74 ^[Y0 : $i]: 78.80/10.74 (( 78.80/10.74 (ordinal @ 78.80/10.74 Y0) => 78.80/10.74 (( 78.80/10.74 (!!) @ ( 78.80/10.74 ^[Y1 : $i]: 78.80/10.74 (( 78.80/10.74 (!!) @ ( 78.80/10.74 ^[Y2 : $i]: 78.80/10.74 (( 78.80/10.74 (in @ 78.80/10.74 Y2 @ 78.80/10.74 Y0) => 78.80/10.74 (( 78.80/10.74 (in @ 78.80/10.74 Y1 @ 78.80/10.74 Y2) => 78.80/10.74 (in @ 78.80/10.74 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 78.80/10.74 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2310])). 78.80/10.74 thf(zip_derived_cl2332, plain, 78.80/10.74 (~ (((complementSubsetComplementIntersect) => 78.80/10.74 (((complementInPowersetComplementIntersect) => 78.80/10.74 (((contraSubsetComplement) => 78.80/10.74 (((complementTcontraSubset) => 78.80/10.74 (((binunionTILcontra) => 78.80/10.74 (((binunionTIRcontra) => 78.80/10.74 (((inIntersectImpInUnion) => 78.80/10.74 (((inIntersectImpInUnion2) => 78.80/10.74 (((inIntersectImpInIntersectUnions) => 78.80/10.74 (((intersectInPowersetIntersectUnions) => 78.80/10.74 (((inComplementUnionImpNotIn1) => 78.80/10.74 (((inComplementUnionImpInComplement1) => 78.80/10.74 (((binunionTE) => 78.80/10.74 (((binunionTEcontra) => 78.80/10.74 (((demorgan2a1) => 78.80/10.74 (((complementUnionInPowersetComplement) => 78.80/10.74 (((demorgan2a2) => 78.80/10.74 (((demorgan1a) => 78.80/10.74 (((demorgan1b) => 78.80/10.74 (((demorgan1) => 78.80/10.74 (((demorgan2a) => 78.80/10.74 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78.80/10.74 (( 78.80/10.74 (breln1compEex) => 78.80/10.74 (( 78.80/10.74 (breln1unionprop) => 78.80/10.74 (( 78.80/10.74 (breln1unionIL) => 78.80/10.74 (( 78.80/10.74 (breln1unionIR) => 78.80/10.74 (( 78.80/10.74 (breln1unionI) => 78.80/10.74 (( 78.80/10.74 (breln1unionE) => 78.80/10.74 (( 78.80/10.74 (breln1unionEcases) => 78.80/10.74 (( 78.80/10.74 (breln1unionCommutes) => 78.80/10.74 (( 78.80/10.74 (woz2Ex) => 78.80/10.74 (( 78.80/10.74 (woz2W) => 78.80/10.74 (( 78.80/10.74 (woz2A) => 78.80/10.74 (( 78.80/10.74 (woz2B) => 78.80/10.74 (( 78.80/10.74 (image1Ex) => 78.80/10.74 (( 78.80/10.74 (image1Ex1) => 78.80/10.74 (( 78.80/10.74 (image1Equiv) => 78.80/10.74 (( 78.80/10.74 (image1E) => 78.80/10.74 (( 78.80/10.74 (image1I) => 78.80/10.74 (( 78.80/10.74 (injFuncInInjFuncSet) => 78.80/10.74 (( 78.80/10.74 (injFuncSetFuncIn) => 78.80/10.74 (( 78.80/10.74 (injFuncSetFuncInj) => 78.80/10.74 (( 78.80/10.74 (surjFuncSetFuncIn) => 78.80/10.74 (( 78.80/10.74 (surjFuncSetFuncSurj) => 78.80/10.74 (( 78.80/10.74 (leftInvIsSurj) => 78.80/10.74 (( 78.80/10.74 (surjCantorThm) => 78.80/10.74 (( 78.80/10.74 (foundation2) => 78.80/10.74 (( 78.80/10.74 (notinself) => 78.80/10.74 (( 78.80/10.74 (notinself2) => 78.80/10.74 (( 78.80/10.74 (omegaSp) => 78.80/10.74 (( 78.80/10.74 (omegaSclos) => 78.80/10.74 (( 78.80/10.74 (peano0notS) => 78.80/10.74 (( 78.80/10.74 (peanoSinj) => 78.80/10.74 (( 78.80/10.74 (transitivesetOp1) => 78.80/10.74 (( 78.80/10.74 (binintTransitive) => 78.80/10.74 (( 78.80/10.74 (transitivesetOp2) => 78.80/10.74 (( 78.80/10.74 (setunionTransitive) => 78.80/10.74 (( 78.80/10.74 (ordinalMinLem1) => 78.80/10.74 (( 78.80/10.74 (!!) @ ( 78.80/10.74 ^[Y0 : $i]: 78.80/10.74 (( 78.80/10.74 (ordinal @ 78.80/10.74 Y0) => 78.80/10.74 (( 78.80/10.74 (!!) @ ( 78.80/10.74 ^[Y1 : $i]: 78.80/10.74 (( 78.80/10.74 (!!) @ ( 78.80/10.74 ^[Y2 : $i]: 78.80/10.74 (( 78.80/10.74 (in @ 78.80/10.74 Y2 @ 78.80/10.74 Y0) => 78.80/10.74 (( 78.80/10.74 (in @ 78.80/10.74 Y1 @ 78.80/10.74 Y2) => 78.80/10.74 (in @ 78.80/10.74 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 78.80/10.74 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2321])). 78.80/10.74 thf(zip_derived_cl2341, plain, 78.80/10.74 (~ (((complementInPowersetComplementIntersect) => 78.80/10.74 (((contraSubsetComplement) => 78.80/10.74 (((complementTcontraSubset) => 78.80/10.74 (((binunionTILcontra) => 78.80/10.74 (((binunionTIRcontra) => 78.80/10.74 (((inIntersectImpInUnion) => 78.80/10.74 (((inIntersectImpInUnion2) => 78.80/10.74 (((inIntersectImpInIntersectUnions) => 78.80/10.74 (((intersectInPowersetIntersectUnions) => 78.80/10.74 (((inComplementUnionImpNotIn1) => 78.80/10.74 (((inComplementUnionImpInComplement1) => 78.80/10.74 (((binunionTE) => 78.80/10.74 (((binunionTEcontra) => 78.80/10.74 (((demorgan2a1) => 78.80/10.74 (((complementUnionInPowersetComplement) => 78.80/10.74 (((demorgan2a2) => 78.80/10.74 (((demorgan1a) => 78.80/10.74 (((demorgan1b) => 78.80/10.74 (((demorgan1) => 78.80/10.74 (((demorgan2a) => 78.80/10.74 (((demorgan2b2) => 78.80/10.74 (((demorgan2b) => 78.80/10.74 (((demorgan2) => 78.80/10.74 (((woz13rule0) => 78.80/10.74 (((woz13rule1) => 78.80/10.74 (((woz13rule2) => 78.80/10.74 (((woz13rule3) => 78.80/10.74 (((woz13rule4) => 78.80/10.74 (((woz1_1) => 78.80/10.74 (((woz1_2) => 78.80/10.74 (( 78.80/10.74 (woz1_3) => 78.80/10.74 (( 78.80/10.74 (woz1_4) => 78.80/10.74 (( 78.80/10.74 (woz1_5) => 78.80/10.74 (( 78.80/10.74 (breln1all2) => 78.80/10.74 (( 78.80/10.74 (breln1SetBreln1) => 78.80/10.74 (( 78.80/10.74 (choice2fnsingleton) => 78.80/10.74 (( 78.80/10.74 (setOfPairsIsBReln1) => 78.80/10.74 (( 78.80/10.74 (breln1all1) => 78.80/10.74 (( 78.80/10.74 (subbreln1) => 78.80/10.74 (( 78.80/10.74 (eqbreln1) => 78.80/10.74 (( 78.80/10.74 (breln1invprop) => 78.80/10.74 (( 78.80/10.74 (breln1invI) => 78.80/10.74 (( 78.80/10.74 (breln1invE) => 78.80/10.74 (( 78.80/10.74 (breln1compprop) => 78.80/10.74 (( 78.80/10.74 (breln1compI) => 78.80/10.74 (( 78.80/10.74 (breln1compE) => 78.80/10.74 (( 78.80/10.74 (breln1compEex) => 78.80/10.74 (( 78.80/10.74 (breln1unionprop) => 78.80/10.74 (( 78.80/10.74 (breln1unionIL) => 78.80/10.74 (( 78.80/10.74 (breln1unionIR) => 78.80/10.74 (( 78.80/10.74 (breln1unionI) => 78.80/10.74 (( 78.80/10.74 (breln1unionE) => 78.80/10.74 (( 78.80/10.74 (breln1unionEcases) => 78.80/10.74 (( 78.80/10.74 (breln1unionCommutes) => 78.80/10.74 (( 78.80/10.74 (woz2Ex) => 78.80/10.74 (( 78.80/10.74 (woz2W) => 78.80/10.74 (( 78.80/10.74 (woz2A) => 78.80/10.74 (( 78.80/10.74 (woz2B) => 78.80/10.74 (( 78.80/10.74 (image1Ex) => 78.80/10.74 (( 78.80/10.74 (image1Ex1) => 78.80/10.74 (( 78.80/10.74 (image1Equiv) => 78.80/10.74 (( 78.80/10.74 (image1E) => 78.80/10.74 (( 78.80/10.74 (image1I) => 78.80/10.74 (( 78.80/10.74 (injFuncInInjFuncSet) => 78.80/10.74 (( 78.80/10.74 (injFuncSetFuncIn) => 78.80/10.74 (( 78.80/10.74 (injFuncSetFuncInj) => 78.80/10.74 (( 78.80/10.74 (surjFuncSetFuncIn) => 78.80/10.74 (( 78.80/10.74 (surjFuncSetFuncSurj) => 78.80/10.74 (( 78.80/10.74 (leftInvIsSurj) => 78.80/10.74 (( 78.80/10.74 (surjCantorThm) => 78.80/10.74 (( 78.80/10.74 (foundation2) => 78.80/10.74 (( 78.80/10.74 (notinself) => 78.80/10.74 (( 78.80/10.74 (notinself2) => 78.80/10.74 (( 78.80/10.74 (omegaSp) => 78.80/10.74 (( 78.80/10.74 (omegaSclos) => 78.80/10.74 (( 78.80/10.74 (peano0notS) => 78.80/10.74 (( 78.80/10.74 (peanoSinj) => 78.80/10.74 (( 78.80/10.74 (transitivesetOp1) => 78.80/10.74 (( 78.80/10.74 (binintTransitive) => 78.80/10.74 (( 78.80/10.74 (transitivesetOp2) => 78.80/10.74 (( 78.80/10.74 (setunionTransitive) => 78.80/10.74 (( 78.80/10.74 (ordinalMinLem1) => 78.80/10.74 (( 78.80/10.74 (!!) @ ( 78.80/10.74 ^[Y0 : $i]: 78.80/10.74 (( 78.80/10.74 (ordinal @ 78.80/10.74 Y0) => 78.80/10.74 (( 78.80/10.74 (!!) @ ( 78.80/10.74 ^[Y1 : $i]: 78.80/10.74 (( 78.80/10.74 (!!) @ ( 78.80/10.74 ^[Y2 : $i]: 78.80/10.74 (( 78.80/10.74 (in @ 78.80/10.74 Y2 @ 78.80/10.74 Y0) => 78.80/10.74 (( 78.80/10.74 (in @ 78.80/10.74 Y1 @ 78.80/10.74 Y2) => 78.80/10.74 (in @ 78.80/10.74 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 78.80/10.74 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2332])). 78.80/10.74 thf(zip_derived_cl2348, plain, 78.80/10.74 (~ (((contraSubsetComplement) => 78.80/10.74 (((complementTcontraSubset) => 78.80/10.74 (((binunionTILcontra) => 78.80/10.74 (((binunionTIRcontra) => 78.80/10.74 (((inIntersectImpInUnion) => 78.80/10.74 (((inIntersectImpInUnion2) => 78.80/10.74 (((inIntersectImpInIntersectUnions) => 78.80/10.74 (((intersectInPowersetIntersectUnions) => 78.80/10.74 (((inComplementUnionImpNotIn1) => 78.80/10.74 (((inComplementUnionImpInComplement1) => 78.80/10.74 (((binunionTE) => 78.80/10.74 (((binunionTEcontra) => 78.80/10.74 (((demorgan2a1) => 78.80/10.74 (((complementUnionInPowersetComplement) => 78.80/10.74 (((demorgan2a2) => 78.80/10.74 (((demorgan1a) => 78.80/10.74 (((demorgan1b) => 78.80/10.74 (((demorgan1) => 78.80/10.74 (((demorgan2a) => 78.80/10.74 (((demorgan2b2) => 78.80/10.74 (((demorgan2b) => 78.80/10.74 (((demorgan2) => 78.80/10.74 (((woz13rule0) => 78.80/10.74 (((woz13rule1) => 78.80/10.74 (((woz13rule2) => 78.80/10.74 (((woz13rule3) => 78.80/10.74 (((woz13rule4) => 78.80/10.74 (((woz1_1) => 78.80/10.74 (((woz1_2) => 78.80/10.74 (((woz1_3) => 78.80/10.74 (( 78.80/10.74 (woz1_4) => 78.80/10.74 (( 78.80/10.74 (woz1_5) => 78.80/10.74 (( 78.80/10.74 (breln1all2) => 78.80/10.74 (( 78.80/10.74 (breln1SetBreln1) => 78.80/10.74 (( 78.80/10.74 (choice2fnsingleton) => 78.80/10.74 (( 78.80/10.74 (setOfPairsIsBReln1) => 78.80/10.74 (( 78.80/10.74 (breln1all1) => 78.80/10.74 (( 78.80/10.74 (subbreln1) => 78.80/10.74 (( 78.80/10.74 (eqbreln1) => 78.80/10.74 (( 78.80/10.74 (breln1invprop) => 78.80/10.74 (( 78.80/10.74 (breln1invI) => 78.80/10.74 (( 78.80/10.74 (breln1invE) => 78.80/10.74 (( 78.80/10.74 (breln1compprop) => 78.80/10.74 (( 78.80/10.74 (breln1compI) => 78.80/10.74 (( 78.80/10.74 (breln1compE) => 78.80/10.74 (( 78.80/10.74 (breln1compEex) => 78.80/10.74 (( 78.80/10.74 (breln1unionprop) => 78.80/10.74 (( 78.80/10.74 (breln1unionIL) => 78.80/10.74 (( 78.80/10.74 (breln1unionIR) => 78.80/10.74 (( 78.80/10.74 (breln1unionI) => 78.80/10.74 (( 78.80/10.74 (breln1unionE) => 78.80/10.74 (( 78.80/10.74 (breln1unionEcases) => 78.80/10.74 (( 78.80/10.74 (breln1unionCommutes) => 78.80/10.74 (( 78.80/10.74 (woz2Ex) => 78.80/10.74 (( 78.80/10.74 (woz2W) => 78.80/10.74 (( 78.80/10.74 (woz2A) => 78.80/10.74 (( 78.80/10.74 (woz2B) => 78.80/10.74 (( 78.80/10.74 (image1Ex) => 78.80/10.74 (( 78.80/10.74 (image1Ex1) => 78.80/10.74 (( 78.80/10.74 (image1Equiv) => 78.80/10.74 (( 78.80/10.74 (image1E) => 78.80/10.74 (( 78.80/10.74 (image1I) => 78.80/10.74 (( 78.80/10.74 (injFuncInInjFuncSet) => 78.80/10.74 (( 78.80/10.74 (injFuncSetFuncIn) => 78.80/10.74 (( 78.80/10.74 (injFuncSetFuncInj) => 78.80/10.74 (( 78.80/10.74 (surjFuncSetFuncIn) => 78.80/10.74 (( 78.80/10.74 (surjFuncSetFuncSurj) => 78.80/10.74 (( 78.80/10.74 (leftInvIsSurj) => 78.80/10.74 (( 78.80/10.74 (surjCantorThm) => 78.80/10.74 (( 78.80/10.74 (foundation2) => 78.80/10.74 (( 78.80/10.74 (notinself) => 78.80/10.74 (( 78.80/10.74 (notinself2) => 78.80/10.74 (( 78.80/10.74 (omegaSp) => 78.80/10.74 (( 78.80/10.74 (omegaSclos) => 78.80/10.74 (( 78.80/10.74 (peano0notS) => 78.80/10.74 (( 78.80/10.74 (peanoSinj) => 78.80/10.74 (( 78.80/10.74 (transitivesetOp1) => 78.80/10.74 (( 78.80/10.74 (binintTransitive) => 78.80/10.74 (( 78.80/10.74 (transitivesetOp2) => 78.80/10.74 (( 78.80/10.74 (setunionTransitive) => 78.80/10.74 (( 78.80/10.74 (ordinalMinLem1) => 78.80/10.74 (( 78.80/10.74 (!!) @ ( 78.80/10.74 ^[Y0 : $i]: 78.80/10.74 (( 78.80/10.74 (ordinal @ 78.80/10.74 Y0) => 78.80/10.74 (( 78.80/10.74 (!!) @ ( 78.80/10.74 ^[Y1 : $i]: 78.80/10.74 (( 78.80/10.74 (!!) @ ( 78.80/10.74 ^[Y2 : $i]: 78.80/10.74 (( 78.80/10.74 (in @ 78.80/10.74 Y2 @ 78.80/10.74 Y0) => 78.80/10.74 (( 78.80/10.74 (in @ 78.80/10.74 Y1 @ 78.80/10.74 Y2) => 78.80/10.74 (in @ 78.80/10.74 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 78.80/10.74 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2341])). 78.80/10.74 thf(zip_derived_cl2355, plain, 78.80/10.74 (~ (((complementTcontraSubset) => 78.80/10.74 (((binunionTILcontra) => 78.80/10.74 (((binunionTIRcontra) => 78.80/10.74 (((inIntersectImpInUnion) => 78.80/10.74 (((inIntersectImpInUnion2) => 78.80/10.74 (((inIntersectImpInIntersectUnions) => 78.80/10.74 (((intersectInPowersetIntersectUnions) => 78.80/10.74 (((inComplementUnionImpNotIn1) => 78.80/10.74 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(surjFuncSetFuncIn) => 78.80/10.74 (( 78.80/10.74 (surjFuncSetFuncSurj) => 78.80/10.74 (( 78.80/10.74 (leftInvIsSurj) => 78.80/10.74 (( 78.80/10.74 (surjCantorThm) => 78.80/10.74 (( 78.80/10.74 (foundation2) => 78.80/10.74 (( 78.80/10.74 (notinself) => 78.80/10.74 (( 78.80/10.74 (notinself2) => 78.80/10.74 (( 78.80/10.74 (omegaSp) => 78.80/10.74 (( 78.80/10.74 (omegaSclos) => 78.80/10.74 (( 78.80/10.74 (peano0notS) => 78.80/10.74 (( 78.80/10.74 (peanoSinj) => 78.80/10.74 (( 78.80/10.74 (transitivesetOp1) => 78.80/10.74 (( 78.80/10.74 (binintTransitive) => 78.80/10.74 (( 78.80/10.74 (transitivesetOp2) => 78.80/10.74 (( 78.80/10.74 (setunionTransitive) => 78.80/10.74 (( 78.80/10.74 (ordinalMinLem1) => 78.80/10.74 (( 78.80/10.74 (!!) @ ( 78.80/10.74 ^[Y0 : $i]: 78.80/10.74 (( 78.80/10.74 (ordinal @ 78.80/10.74 Y0) => 78.80/10.74 (( 78.80/10.74 (!!) @ ( 78.80/10.74 ^[Y1 : $i]: 78.80/10.74 (( 78.80/10.74 (!!) @ ( 78.80/10.74 ^[Y2 : $i]: 78.80/10.74 (( 78.80/10.74 (in @ 78.80/10.74 Y2 @ 78.80/10.74 Y0) => 78.80/10.74 (( 78.80/10.74 (in @ 78.80/10.74 Y1 @ 78.80/10.74 Y2) => 78.80/10.74 (in @ 78.80/10.74 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 78.80/10.74 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2408])). 78.80/10.74 thf(zip_derived_cl2427, plain, 78.80/10.74 (~ (((inComplementUnionImpInComplement1) => 78.80/10.74 (((binunionTE) => 78.80/10.74 (((binunionTEcontra) => 78.80/10.74 (((demorgan2a1) => 78.80/10.74 (((complementUnionInPowersetComplement) => 78.80/10.74 (((demorgan2a2) => 78.80/10.74 (((demorgan1a) => 78.80/10.74 (((demorgan1b) => 78.80/10.74 (((demorgan1) => 78.80/10.74 (((demorgan2a) => 78.80/10.74 (((demorgan2b2) => 78.80/10.74 (((demorgan2b) => 78.80/10.74 (((demorgan2) => 78.80/10.74 (((woz13rule0) => 78.80/10.74 (((woz13rule1) => 78.80/10.74 (((woz13rule2) => 78.80/10.74 (((woz13rule3) => 78.80/10.74 (((woz13rule4) => 78.80/10.74 (((woz1_1) => 78.80/10.74 (((woz1_2) => 78.80/10.74 (((woz1_3) => 78.80/10.74 (((woz1_4) => 78.80/10.74 (((woz1_5) => 78.80/10.74 (((breln1all2) => 78.80/10.74 (((breln1SetBreln1) => 78.80/10.74 (((choice2fnsingleton) => 78.80/10.74 (((setOfPairsIsBReln1) => 78.80/10.74 (((breln1all1) => 78.80/10.74 (((subbreln1) => 78.80/10.74 (((eqbreln1) => 78.80/10.74 (( 78.80/10.74 (breln1invprop) => 78.80/10.74 (( 78.80/10.74 (breln1invI) => 78.80/10.74 (( 78.80/10.74 (breln1invE) => 78.80/10.74 (( 78.80/10.74 (breln1compprop) => 78.80/10.74 (( 78.80/10.74 (breln1compI) => 78.80/10.74 (( 78.80/10.74 (breln1compE) => 78.80/10.74 (( 78.80/10.74 (breln1compEex) => 78.80/10.74 (( 78.80/10.74 (breln1unionprop) => 78.80/10.74 (( 78.80/10.74 (breln1unionIL) => 78.80/10.74 (( 78.80/10.74 (breln1unionIR) => 78.80/10.74 (( 78.80/10.74 (breln1unionI) => 78.80/10.74 (( 78.80/10.74 (breln1unionE) => 78.80/10.74 (( 78.80/10.74 (breln1unionEcases) => 78.80/10.74 (( 78.80/10.74 (breln1unionCommutes) => 78.80/10.74 (( 78.80/10.74 (woz2Ex) => 78.80/10.74 (( 78.80/10.74 (woz2W) => 78.80/10.74 (( 78.80/10.74 (woz2A) => 78.80/10.74 (( 78.80/10.74 (woz2B) => 78.80/10.74 (( 78.80/10.74 (image1Ex) => 78.80/10.74 (( 78.80/10.74 (image1Ex1) => 78.80/10.74 (( 78.80/10.74 (image1Equiv) => 78.80/10.74 (( 78.80/10.74 (image1E) => 78.80/10.74 (( 78.80/10.74 (image1I) => 78.80/10.74 (( 78.80/10.74 (injFuncInInjFuncSet) => 78.80/10.74 (( 78.80/10.74 (injFuncSetFuncIn) => 78.80/10.74 (( 78.80/10.74 (injFuncSetFuncInj) => 78.80/10.74 (( 78.80/10.74 (surjFuncSetFuncIn) => 78.80/10.74 (( 78.80/10.74 (surjFuncSetFuncSurj) => 78.80/10.74 (( 78.80/10.74 (leftInvIsSurj) => 78.80/10.74 (( 78.80/10.74 (surjCantorThm) => 78.80/10.74 (( 78.80/10.74 (foundation2) => 78.80/10.74 (( 78.80/10.74 (notinself) => 78.80/10.74 (( 78.80/10.74 (notinself2) => 78.80/10.74 (( 78.80/10.74 (omegaSp) => 78.80/10.74 (( 78.80/10.74 (omegaSclos) => 78.80/10.74 (( 78.80/10.74 (peano0notS) => 78.80/10.74 (( 78.80/10.74 (peanoSinj) => 78.80/10.74 (( 78.80/10.74 (transitivesetOp1) => 78.80/10.74 (( 78.80/10.74 (binintTransitive) => 78.80/10.74 (( 78.80/10.74 (transitivesetOp2) => 78.80/10.74 (( 78.80/10.74 (setunionTransitive) => 78.80/10.74 (( 78.80/10.74 (ordinalMinLem1) => 78.80/10.74 (( 78.80/10.74 (!!) @ ( 78.80/10.74 ^[Y0 : $i]: 78.80/10.74 (( 78.80/10.74 (ordinal @ 78.80/10.74 Y0) => 78.80/10.74 (( 78.80/10.74 (!!) @ ( 78.80/10.74 ^[Y1 : $i]: 78.80/10.74 (( 78.80/10.74 (!!) @ ( 78.80/10.74 ^[Y2 : $i]: 78.80/10.74 (( 78.80/10.74 (in @ 78.80/10.74 Y2 @ 78.80/10.74 Y0) => 78.80/10.74 (( 78.80/10.74 (in @ 78.80/10.74 Y1 @ 78.80/10.74 Y2) => 78.80/10.74 (in @ 78.80/10.74 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 78.80/10.74 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2417])). 78.80/10.74 thf(zip_derived_cl2437, plain, 78.80/10.74 (~ (((binunionTE) => 78.80/10.74 (((binunionTEcontra) => 78.80/10.74 (((demorgan2a1) => 78.80/10.74 (((complementUnionInPowersetComplement) => 78.80/10.74 (((demorgan2a2) => 78.80/10.74 (((demorgan1a) => 78.80/10.74 (((demorgan1b) => 78.80/10.74 (((demorgan1) => 78.80/10.74 (((demorgan2a) => 78.80/10.74 (((demorgan2b2) => 78.80/10.74 (((demorgan2b) => 78.80/10.74 (((demorgan2) => 78.80/10.74 (((woz13rule0) => 78.80/10.74 (((woz13rule1) => 78.80/10.74 (((woz13rule2) => 78.80/10.74 (((woz13rule3) => 78.80/10.74 (((woz13rule4) => 78.80/10.74 (((woz1_1) => 78.80/10.74 (((woz1_2) => 78.80/10.74 (((woz1_3) => 78.80/10.74 (((woz1_4) => 78.80/10.74 (((woz1_5) => 78.80/10.74 (((breln1all2) => 78.80/10.74 (((breln1SetBreln1) => 78.80/10.74 (((choice2fnsingleton) => 78.80/10.74 (((setOfPairsIsBReln1) => 78.80/10.74 (((breln1all1) => 78.80/10.74 (((subbreln1) => 78.80/10.74 (((eqbreln1) => 78.80/10.74 (((breln1invprop) => 78.80/10.74 (( 78.80/10.74 (breln1invI) => 78.80/10.74 (( 78.80/10.74 (breln1invE) => 78.80/10.74 (( 78.80/10.74 (breln1compprop) => 78.80/10.74 (( 78.80/10.74 (breln1compI) => 78.80/10.74 (( 78.80/10.74 (breln1compE) => 78.80/10.74 (( 78.80/10.74 (breln1compEex) => 78.80/10.74 (( 78.80/10.74 (breln1unionprop) => 78.80/10.74 (( 78.80/10.74 (breln1unionIL) => 78.80/10.74 (( 78.80/10.74 (breln1unionIR) => 78.80/10.74 (( 78.80/10.74 (breln1unionI) => 78.80/10.74 (( 78.80/10.74 (breln1unionE) => 78.80/10.74 (( 78.80/10.74 (breln1unionEcases) => 78.80/10.74 (( 78.80/10.74 (breln1unionCommutes) => 78.80/10.74 (( 78.80/10.74 (woz2Ex) => 78.80/10.74 (( 78.80/10.74 (woz2W) => 78.80/10.74 (( 78.80/10.74 (woz2A) => 78.80/10.74 (( 78.80/10.74 (woz2B) => 78.80/10.74 (( 78.80/10.74 (image1Ex) => 78.80/10.74 (( 78.80/10.74 (image1Ex1) => 78.80/10.74 (( 78.80/10.74 (image1Equiv) => 78.80/10.74 (( 78.80/10.74 (image1E) => 78.80/10.74 (( 78.80/10.74 (image1I) => 78.80/10.74 (( 78.80/10.74 (injFuncInInjFuncSet) => 78.80/10.74 (( 78.80/10.74 (injFuncSetFuncIn) => 78.80/10.74 (( 78.80/10.74 (injFuncSetFuncInj) => 78.80/10.74 (( 78.80/10.74 (surjFuncSetFuncIn) => 78.80/10.74 (( 78.80/10.74 (surjFuncSetFuncSurj) => 78.80/10.74 (( 78.80/10.74 (leftInvIsSurj) => 78.80/10.74 (( 78.80/10.74 (surjCantorThm) => 78.80/10.74 (( 78.80/10.74 (foundation2) => 78.80/10.74 (( 78.80/10.74 (notinself) => 78.80/10.74 (( 78.80/10.74 (notinself2) => 78.80/10.74 (( 78.80/10.74 (omegaSp) => 78.80/10.74 (( 78.80/10.74 (omegaSclos) => 78.80/10.74 (( 78.80/10.74 (peano0notS) => 78.80/10.74 (( 78.80/10.74 (peanoSinj) => 78.80/10.74 (( 78.80/10.74 (transitivesetOp1) => 78.80/10.74 (( 78.80/10.74 (binintTransitive) => 78.80/10.74 (( 78.80/10.74 (transitivesetOp2) => 78.80/10.74 (( 78.80/10.74 (setunionTransitive) => 78.80/10.74 (( 78.80/10.74 (ordinalMinLem1) => 78.80/10.74 (( 78.80/10.74 (!!) @ ( 78.80/10.74 ^[Y0 : $i]: 78.80/10.74 (( 78.80/10.74 (ordinal @ 78.80/10.74 Y0) => 78.80/10.74 (( 78.80/10.74 (!!) @ ( 78.80/10.74 ^[Y1 : $i]: 78.80/10.74 (( 78.80/10.74 (!!) @ ( 78.80/10.74 ^[Y2 : $i]: 78.80/10.74 (( 78.80/10.74 (in @ 78.80/10.74 Y2 @ 78.80/10.74 Y0) => 78.80/10.74 (( 78.80/10.74 (in @ 78.80/10.74 Y1 @ 78.80/10.74 Y2) => 78.80/10.74 (in @ 78.80/10.74 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 78.80/10.74 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2427])). 78.80/10.74 thf(zip_derived_cl2448, plain, 78.80/10.74 (~ (((binunionTEcontra) => 78.80/10.74 (((demorgan2a1) => 78.80/10.74 (((complementUnionInPowersetComplement) => 78.80/10.74 (((demorgan2a2) => 78.80/10.74 (((demorgan1a) => 78.80/10.74 (((demorgan1b) => 78.80/10.74 (((demorgan1) => 78.80/10.74 (((demorgan2a) => 78.80/10.74 (((demorgan2b2) => 78.80/10.74 (((demorgan2b) => 78.80/10.74 (((demorgan2) => 78.80/10.74 (((woz13rule0) => 78.80/10.74 (((woz13rule1) => 78.80/10.74 (((woz13rule2) => 78.80/10.74 (((woz13rule3) => 78.80/10.74 (((woz13rule4) => 78.80/10.74 (((woz1_1) => 78.80/10.74 (((woz1_2) => 78.80/10.74 (((woz1_3) => 78.80/10.74 (((woz1_4) => 78.80/10.74 (((woz1_5) => 78.80/10.74 (((breln1all2) => 78.80/10.74 (((breln1SetBreln1) => 78.80/10.74 (((choice2fnsingleton) => 78.80/10.74 (((setOfPairsIsBReln1) => 78.80/10.74 (((breln1all1) => 78.80/10.74 (((subbreln1) => 78.80/10.74 (((eqbreln1) => 78.80/10.74 (((breln1invprop) => 78.80/10.74 (((breln1invI) => 78.80/10.74 (( 78.80/10.74 (breln1invE) => 78.80/10.74 (( 78.80/10.74 (breln1compprop) => 78.80/10.74 (( 78.80/10.74 (breln1compI) => 78.80/10.74 (( 78.80/10.74 (breln1compE) => 78.80/10.74 (( 78.80/10.74 (breln1compEex) => 78.80/10.74 (( 78.80/10.74 (breln1unionprop) => 78.80/10.74 (( 78.80/10.74 (breln1unionIL) => 78.80/10.74 (( 78.80/10.74 (breln1unionIR) => 78.80/10.74 (( 78.80/10.74 (breln1unionI) => 78.80/10.74 (( 78.80/10.74 (breln1unionE) => 78.80/10.74 (( 78.80/10.74 (breln1unionEcases) => 78.80/10.74 (( 78.80/10.74 (breln1unionCommutes) => 78.80/10.74 (( 78.80/10.74 (woz2Ex) => 78.80/10.74 (( 78.80/10.74 (woz2W) => 78.80/10.74 (( 78.80/10.74 (woz2A) => 78.80/10.74 (( 78.80/10.74 (woz2B) => 78.80/10.74 (( 78.80/10.74 (image1Ex) => 78.80/10.74 (( 78.80/10.74 (image1Ex1) => 78.80/10.74 (( 78.80/10.74 (image1Equiv) => 78.80/10.74 (( 78.80/10.74 (image1E) => 78.80/10.74 (( 78.80/10.74 (image1I) => 78.80/10.74 (( 78.80/10.74 (injFuncInInjFuncSet) => 78.80/10.74 (( 78.80/10.74 (injFuncSetFuncIn) => 78.80/10.74 (( 78.80/10.74 (injFuncSetFuncInj) => 78.80/10.74 (( 78.80/10.74 (surjFuncSetFuncIn) => 78.80/10.74 (( 78.80/10.74 (surjFuncSetFuncSurj) => 78.80/10.74 (( 78.80/10.74 (leftInvIsSurj) => 78.80/10.74 (( 78.80/10.74 (surjCantorThm) => 78.80/10.74 (( 78.80/10.74 (foundation2) => 78.80/10.74 (( 78.80/10.74 (notinself) => 78.80/10.74 (( 78.80/10.74 (notinself2) => 78.80/10.74 (( 78.80/10.74 (omegaSp) => 78.80/10.74 (( 78.80/10.74 (omegaSclos) => 78.80/10.74 (( 78.80/10.74 (peano0notS) => 78.80/10.74 (( 78.80/10.74 (peanoSinj) => 78.80/10.74 (( 78.80/10.74 (transitivesetOp1) => 78.80/10.74 (( 78.80/10.74 (binintTransitive) => 78.80/10.74 (( 78.80/10.74 (transitivesetOp2) => 78.80/10.74 (( 78.80/10.74 (setunionTransitive) => 78.80/10.74 (( 78.80/10.74 (ordinalMinLem1) => 78.80/10.74 (( 78.80/10.74 (!!) @ ( 78.80/10.74 ^[Y0 : $i]: 78.80/10.74 (( 78.80/10.74 (ordinal @ 78.80/10.74 Y0) => 78.80/10.74 (( 78.80/10.74 (!!) @ ( 78.80/10.74 ^[Y1 : $i]: 78.80/10.74 (( 78.80/10.74 (!!) @ ( 78.80/10.74 ^[Y2 : $i]: 78.80/10.74 (( 78.80/10.74 (in @ 78.80/10.74 Y2 @ 78.80/10.74 Y0) => 78.80/10.74 (( 78.80/10.74 (in @ 78.80/10.74 Y1 @ 78.80/10.74 Y2) => 78.80/10.74 (in @ 78.80/10.74 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 78.80/10.74 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2437])). 78.80/10.74 thf(zip_derived_cl2459, plain, 78.80/10.74 (~ (((demorgan2a1) => 78.80/10.74 (((complementUnionInPowersetComplement) => 78.80/10.74 (((demorgan2a2) => 78.80/10.74 (((demorgan1a) => 78.80/10.74 (((demorgan1b) => 78.80/10.74 (((demorgan1) => 78.80/10.74 (((demorgan2a) => 78.80/10.74 (((demorgan2b2) => 78.80/10.74 (((demorgan2b) => 78.80/10.74 (((demorgan2) => 78.80/10.74 (((woz13rule0) => 78.80/10.74 (((woz13rule1) => 78.80/10.74 (((woz13rule2) => 78.80/10.74 (((woz13rule3) => 78.80/10.74 (((woz13rule4) => 78.80/10.74 (((woz1_1) => 78.80/10.74 (((woz1_2) => 78.80/10.74 (((woz1_3) => 78.80/10.74 (((woz1_4) => 78.80/10.74 (((woz1_5) => 78.80/10.74 (((breln1all2) => 78.80/10.74 (((breln1SetBreln1) => 78.80/10.74 (((choice2fnsingleton) => 78.80/10.74 (((setOfPairsIsBReln1) => 78.80/10.74 (((breln1all1) => 78.80/10.74 (((subbreln1) => 78.80/10.74 (((eqbreln1) => 78.80/10.74 (((breln1invprop) => 78.80/10.74 (((breln1invI) => 78.80/10.74 (((breln1invE) => 78.80/10.74 (( 78.80/10.74 (breln1compprop) => 78.80/10.74 (( 78.80/10.74 (breln1compI) => 78.80/10.74 (( 78.80/10.74 (breln1compE) => 78.80/10.74 (( 78.80/10.74 (breln1compEex) => 78.80/10.74 (( 78.80/10.74 (breln1unionprop) => 78.80/10.74 (( 78.80/10.74 (breln1unionIL) => 78.80/10.74 (( 78.80/10.74 (breln1unionIR) => 78.80/10.74 (( 78.80/10.74 (breln1unionI) => 78.80/10.74 (( 78.80/10.74 (breln1unionE) => 78.80/10.74 (( 78.80/10.74 (breln1unionEcases) => 78.80/10.74 (( 78.80/10.74 (breln1unionCommutes) => 78.80/10.74 (( 78.80/10.74 (woz2Ex) => 78.80/10.74 (( 78.80/10.74 (woz2W) => 78.80/10.74 (( 78.80/10.74 (woz2A) => 78.80/10.74 (( 78.80/10.74 (woz2B) => 78.80/10.74 (( 78.80/10.74 (image1Ex) => 78.80/10.74 (( 78.80/10.74 (image1Ex1) => 78.80/10.74 (( 78.80/10.74 (image1Equiv) => 78.80/10.74 (( 78.80/10.74 (image1E) => 78.80/10.74 (( 78.80/10.74 (image1I) => 78.80/10.74 (( 78.80/10.74 (injFuncInInjFuncSet) => 78.80/10.74 (( 78.80/10.74 (injFuncSetFuncIn) => 78.80/10.74 (( 78.80/10.74 (injFuncSetFuncInj) => 78.80/10.74 (( 78.80/10.74 (surjFuncSetFuncIn) => 78.80/10.74 (( 78.80/10.74 (surjFuncSetFuncSurj) => 78.80/10.74 (( 78.80/10.74 (leftInvIsSurj) => 78.80/10.74 (( 78.80/10.74 (surjCantorThm) => 78.80/10.74 (( 78.80/10.74 (foundation2) => 78.80/10.74 (( 78.80/10.74 (notinself) => 78.80/10.74 (( 78.80/10.74 (notinself2) => 78.80/10.74 (( 78.80/10.74 (omegaSp) => 78.80/10.74 (( 78.80/10.74 (omegaSclos) => 78.80/10.74 (( 78.80/10.74 (peano0notS) => 78.80/10.74 (( 78.80/10.74 (peanoSinj) => 78.80/10.74 (( 78.80/10.74 (transitivesetOp1) => 78.80/10.74 (( 78.80/10.74 (binintTransitive) => 78.80/10.74 (( 78.80/10.74 (transitivesetOp2) => 78.80/10.74 (( 78.80/10.74 (setunionTransitive) => 78.80/10.74 (( 78.80/10.74 (ordinalMinLem1) => 78.80/10.74 (( 78.80/10.74 (!!) @ ( 78.80/10.74 ^[Y0 : $i]: 78.80/10.74 (( 78.80/10.74 (ordinal @ 78.80/10.74 Y0) => 78.80/10.74 (( 78.80/10.74 (!!) @ ( 78.80/10.74 ^[Y1 : $i]: 78.80/10.74 (( 78.80/10.74 (!!) @ ( 78.80/10.74 ^[Y2 : $i]: 78.80/10.74 (( 78.80/10.74 (in @ 78.80/10.74 Y2 @ 78.80/10.74 Y0) => 78.80/10.74 (( 78.80/10.74 (in @ 78.80/10.74 Y1 @ 78.80/10.74 Y2) => 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( 78.80/10.74 ^[Y0 : $i]: 78.80/10.74 (( 78.80/10.74 (ordinal @ 78.80/10.74 Y0) => 78.80/10.74 (( 78.80/10.74 (!!) @ ( 78.80/10.74 ^[Y1 : $i]: 78.80/10.74 (( 78.80/10.74 (!!) @ ( 78.80/10.74 ^[Y2 : $i]: 78.80/10.74 (( 78.80/10.74 (in @ 78.80/10.74 Y2 @ 78.80/10.74 Y0) => 78.80/10.74 (( 78.80/10.74 (in @ 78.80/10.74 Y1 @ 78.80/10.74 Y2) => 78.80/10.74 (in @ 78.80/10.74 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 78.80/10.74 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2459])). 78.80/10.74 thf(zip_derived_cl2481, plain, 78.80/10.74 (~ (((demorgan2a2) => 78.80/10.74 (((demorgan1a) => 78.80/10.74 (((demorgan1b) => 78.80/10.74 (((demorgan1) => 78.80/10.74 (((demorgan2a) => 78.80/10.74 (((demorgan2b2) => 78.80/10.74 (((demorgan2b) => 78.80/10.74 (((demorgan2) => 78.80/10.74 (((woz13rule0) => 78.80/10.74 (((woz13rule1) => 78.80/10.74 (((woz13rule2) => 78.80/10.74 (((woz13rule3) => 78.80/10.74 (((woz13rule4) => 78.80/10.74 (((woz1_1) => 78.80/10.74 (((woz1_2) => 78.80/10.74 (((woz1_3) => 78.80/10.74 (((woz1_4) => 78.80/10.74 (((woz1_5) => 78.80/10.74 (((breln1all2) => 78.80/10.74 (((breln1SetBreln1) => 78.80/10.74 (((choice2fnsingleton) => 78.80/10.74 (((setOfPairsIsBReln1) => 78.80/10.74 (((breln1all1) => 78.80/10.74 (((subbreln1) => 78.80/10.74 (((eqbreln1) => 78.80/10.74 (((breln1invprop) => 78.80/10.74 (((breln1invI) => 78.80/10.74 (((breln1invE) => 78.80/10.74 (((breln1compprop) => 78.80/10.74 (((breln1compI) => 78.80/10.74 (( 78.80/10.74 (breln1compE) => 78.80/10.74 (( 78.80/10.74 (breln1compEex) => 78.80/10.74 (( 78.80/10.74 (breln1unionprop) => 78.80/10.74 (( 78.80/10.74 (breln1unionIL) => 78.80/10.74 (( 78.80/10.74 (breln1unionIR) => 78.80/10.74 (( 78.80/10.74 (breln1unionI) => 78.80/10.74 (( 78.80/10.74 (breln1unionE) => 78.80/10.74 (( 78.80/10.74 (breln1unionEcases) => 78.80/10.74 (( 78.80/10.74 (breln1unionCommutes) => 78.80/10.74 (( 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(( 78.80/10.74 (transitivesetOp1) => 78.80/10.74 (( 78.80/10.74 (binintTransitive) => 78.80/10.74 (( 78.80/10.74 (transitivesetOp2) => 78.80/10.74 (( 78.80/10.74 (setunionTransitive) => 78.80/10.74 (( 78.80/10.74 (ordinalMinLem1) => 78.80/10.74 (( 78.80/10.74 (!!) @ ( 78.80/10.74 ^[Y0 : $i]: 78.80/10.74 (( 78.80/10.74 (ordinal @ 78.80/10.74 Y0) => 78.80/10.74 (( 78.80/10.74 (!!) @ ( 78.80/10.74 ^[Y1 : $i]: 78.80/10.74 (( 78.80/10.74 (!!) @ ( 78.80/10.74 ^[Y2 : $i]: 78.80/10.74 (( 78.80/10.74 (in @ 78.80/10.74 Y2 @ 78.80/10.74 Y0) => 78.80/10.74 (( 78.80/10.74 (in @ 78.80/10.74 Y1 @ 78.80/10.74 Y2) => 78.80/10.74 (in @ 78.80/10.74 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 78.80/10.74 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2470])). 78.80/10.74 thf(zip_derived_cl2493, plain, 78.80/10.74 (~ (((demorgan1a) => 78.80/10.74 (((demorgan1b) => 78.80/10.74 (((demorgan1) => 78.80/10.74 (((demorgan2a) => 78.80/10.74 (((demorgan2b2) => 78.80/10.74 (((demorgan2b) => 78.80/10.74 (((demorgan2) => 78.80/10.74 (((woz13rule0) => 78.80/10.74 (((woz13rule1) => 78.80/10.74 (((woz13rule2) => 78.80/10.74 (((woz13rule3) => 78.80/10.74 (((woz13rule4) => 78.80/10.74 (((woz1_1) => 78.80/10.74 (((woz1_2) => 78.80/10.74 (((woz1_3) => 78.80/10.74 (((woz1_4) => 78.80/10.74 (((woz1_5) => 78.80/10.74 (((breln1all2) => 78.80/10.74 (((breln1SetBreln1) => 78.80/10.74 (((choice2fnsingleton) => 78.80/10.74 (((setOfPairsIsBReln1) => 78.80/10.74 (((breln1all1) => 78.80/10.74 (((subbreln1) => 78.80/10.74 (((eqbreln1) => 78.80/10.74 (((breln1invprop) => 78.80/10.74 (((breln1invI) => 78.80/10.74 (((breln1invE) => 78.80/10.74 (((breln1compprop) => 78.80/10.74 (((breln1compI) => 78.80/10.74 (((breln1compE) => 78.80/10.74 (( 78.80/10.74 (breln1compEex) => 78.80/10.74 (( 78.80/10.74 (breln1unionprop) => 78.80/10.74 (( 78.80/10.74 (breln1unionIL) => 78.80/10.74 (( 78.80/10.74 (breln1unionIR) => 78.80/10.74 (( 78.80/10.74 (breln1unionI) => 78.80/10.74 (( 78.80/10.74 (breln1unionE) => 78.80/10.74 (( 78.80/10.74 (breln1unionEcases) => 78.80/10.74 (( 78.80/10.74 (breln1unionCommutes) => 78.80/10.74 (( 78.80/10.74 (woz2Ex) => 78.80/10.74 (( 78.80/10.74 (woz2W) => 78.80/10.74 (( 78.80/10.74 (woz2A) => 78.80/10.74 (( 78.80/10.74 (woz2B) => 78.80/10.74 (( 78.80/10.74 (image1Ex) => 78.80/10.74 (( 78.80/10.74 (image1Ex1) => 78.80/10.74 (( 78.80/10.74 (image1Equiv) => 78.80/10.74 (( 78.80/10.74 (image1E) => 78.80/10.74 (( 78.80/10.74 (image1I) => 78.80/10.74 (( 78.80/10.74 (injFuncInInjFuncSet) => 78.80/10.74 (( 78.80/10.74 (injFuncSetFuncIn) => 78.80/10.74 (( 78.80/10.74 (injFuncSetFuncInj) => 78.80/10.74 (( 78.80/10.74 (surjFuncSetFuncIn) => 78.80/10.74 (( 78.80/10.74 (surjFuncSetFuncSurj) => 78.80/10.74 (( 78.80/10.74 (leftInvIsSurj) => 78.80/10.74 (( 78.80/10.74 (surjCantorThm) => 78.80/10.74 (( 78.80/10.74 (foundation2) => 78.80/10.74 (( 78.80/10.74 (notinself) => 78.80/10.74 (( 78.80/10.74 (notinself2) => 78.80/10.74 (( 78.80/10.74 (omegaSp) => 78.80/10.74 (( 78.80/10.74 (omegaSclos) => 78.80/10.74 (( 78.80/10.74 (peano0notS) => 78.80/10.74 (( 78.80/10.74 (peanoSinj) => 78.80/10.74 (( 78.80/10.74 (transitivesetOp1) => 78.80/10.74 (( 78.80/10.74 (binintTransitive) => 78.80/10.74 (( 78.80/10.74 (transitivesetOp2) => 78.80/10.74 (( 78.80/10.74 (setunionTransitive) => 78.80/10.74 (( 78.80/10.74 (ordinalMinLem1) => 78.80/10.74 (( 78.80/10.74 (!!) @ ( 78.80/10.74 ^[Y0 : $i]: 78.80/10.74 (( 78.80/10.74 (ordinal @ 78.80/10.74 Y0) => 78.80/10.74 (( 78.80/10.74 (!!) @ ( 78.80/10.74 ^[Y1 : $i]: 78.80/10.74 (( 78.80/10.74 (!!) @ ( 78.80/10.74 ^[Y2 : $i]: 78.80/10.74 (( 78.80/10.74 (in @ 78.80/10.74 Y2 @ 78.80/10.74 Y0) => 78.80/10.74 (( 78.80/10.74 (in @ 78.80/10.74 Y1 @ 78.80/10.74 Y2) => 78.80/10.74 (in @ 78.80/10.74 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 78.80/10.74 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2481])). 78.80/10.74 thf(zip_derived_cl2506, plain, 78.80/10.74 (~ (((demorgan1b) => 78.80/10.74 (((demorgan1) => 78.80/10.74 (((demorgan2a) => 78.80/10.74 (((demorgan2b2) => 78.80/10.74 (((demorgan2b) => 78.80/10.74 (((demorgan2) => 78.80/10.74 (((woz13rule0) => 78.80/10.74 (((woz13rule1) => 78.80/10.74 (((woz13rule2) => 78.80/10.74 (((woz13rule3) => 78.80/10.74 (((woz13rule4) => 78.80/10.74 (((woz1_1) => 78.80/10.74 (((woz1_2) => 78.80/10.74 (((woz1_3) => 78.80/10.74 (((woz1_4) => 78.80/10.74 (((woz1_5) => 78.80/10.74 (((breln1all2) => 78.80/10.74 (((breln1SetBreln1) => 78.80/10.74 (((choice2fnsingleton) => 78.80/10.74 (((setOfPairsIsBReln1) => 78.80/10.74 (((breln1all1) => 78.80/10.74 (((subbreln1) => 78.80/10.74 (((eqbreln1) => 78.80/10.74 (((breln1invprop) => 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78.80/10.75 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2599])). 78.80/10.75 thf(zip_derived_cl2620, plain, 78.80/10.75 (~ (((woz13rule4) => 78.80/10.75 (((woz1_1) => 78.80/10.75 (((woz1_2) => 78.80/10.75 (((woz1_3) => 78.80/10.75 (((woz1_4) => 78.80/10.75 (((woz1_5) => 78.80/10.75 (((breln1all2) => 78.80/10.75 (((breln1SetBreln1) => 78.80/10.75 (((choice2fnsingleton) => 78.80/10.75 (((setOfPairsIsBReln1) => 78.80/10.75 (((breln1all1) => 78.80/10.75 (((subbreln1) => 78.80/10.75 (((eqbreln1) => 78.80/10.75 (((breln1invprop) => 78.80/10.75 (((breln1invI) => 78.80/10.75 (((breln1invE) => 78.80/10.75 (((breln1compprop) => 78.80/10.75 (((breln1compI) => 78.80/10.75 (((breln1compE) => 78.80/10.75 (((breln1compEex) => 78.80/10.75 (((breln1unionprop) => 78.80/10.75 (((breln1unionIL) => 78.80/10.75 (((breln1unionIR) => 78.80/10.75 (((breln1unionI) => 78.80/10.75 (((breln1unionE) => 78.80/10.75 (((breln1unionEcases) => 78.80/10.75 (((breln1unionCommutes) => 78.80/10.75 (((woz2Ex) 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(( 78.80/10.75 (binintTransitive) => 78.80/10.75 (( 78.80/10.75 (transitivesetOp2) => 78.80/10.75 (( 78.80/10.75 (setunionTransitive) => 78.80/10.75 (( 78.80/10.75 (ordinalMinLem1) => 78.80/10.75 (( 78.80/10.75 (!!) @ ( 78.80/10.75 ^[Y0 : $i]: 78.80/10.75 (( 78.80/10.75 (ordinal @ 78.80/10.75 Y0) => 78.80/10.75 (( 78.80/10.75 (!!) @ ( 78.80/10.75 ^[Y1 : $i]: 78.80/10.75 (( 78.80/10.75 (!!) @ ( 78.80/10.75 ^[Y2 : $i]: 78.80/10.75 (( 78.80/10.75 (in @ 78.80/10.75 Y2 @ 78.80/10.75 Y0) => 78.80/10.75 (( 78.80/10.75 (in @ 78.80/10.75 Y1 @ 78.80/10.75 Y2) => 78.80/10.75 (in @ 78.80/10.75 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 78.80/10.75 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2610])). 78.80/10.75 thf(zip_derived_cl2630, plain, 78.80/10.75 (~ (((woz1_1) => 78.80/10.75 (((woz1_2) => 78.80/10.75 (((woz1_3) => 78.80/10.75 (((woz1_4) => 78.80/10.75 (((woz1_5) => 78.80/10.75 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(( 78.80/10.75 (injFuncInInjFuncSet) => 78.80/10.75 (( 78.80/10.75 (injFuncSetFuncIn) => 78.80/10.75 (( 78.80/10.75 (injFuncSetFuncInj) => 78.80/10.75 (( 78.80/10.75 (surjFuncSetFuncIn) => 78.80/10.75 (( 78.80/10.75 (surjFuncSetFuncSurj) => 78.80/10.75 (( 78.80/10.75 (leftInvIsSurj) => 78.80/10.75 (( 78.80/10.75 (surjCantorThm) => 78.80/10.75 (( 78.80/10.75 (foundation2) => 78.80/10.75 (( 78.80/10.75 (notinself) => 78.80/10.75 (( 78.80/10.75 (notinself2) => 78.80/10.75 (( 78.80/10.75 (omegaSp) => 78.80/10.75 (( 78.80/10.75 (omegaSclos) => 78.80/10.75 (( 78.80/10.75 (peano0notS) => 78.80/10.75 (( 78.80/10.75 (peanoSinj) => 78.80/10.75 (( 78.80/10.75 (transitivesetOp1) => 78.80/10.75 (( 78.80/10.75 (binintTransitive) => 78.80/10.75 (( 78.80/10.75 (transitivesetOp2) => 78.80/10.75 (( 78.80/10.75 (setunionTransitive) => 78.80/10.75 (( 78.80/10.75 (ordinalMinLem1) => 78.80/10.75 (( 78.80/10.75 (!!) @ ( 78.80/10.75 ^[Y0 : $i]: 78.80/10.75 (( 78.80/10.75 (ordinal @ 78.80/10.75 Y0) => 78.80/10.75 (( 78.80/10.75 (!!) @ ( 78.80/10.75 ^[Y1 : $i]: 78.80/10.75 (( 78.80/10.75 (!!) @ ( 78.80/10.75 ^[Y2 : $i]: 78.80/10.75 (( 78.80/10.75 (in @ 78.80/10.75 Y2 @ 78.80/10.75 Y0) => 78.80/10.75 (( 78.80/10.75 (in @ 78.80/10.75 Y1 @ 78.80/10.75 Y2) => 78.80/10.75 (in @ 78.80/10.75 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 78.80/10.75 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2620])). 78.80/10.75 thf(zip_derived_cl2641, plain, 78.80/10.75 (~ (((woz1_2) => 78.80/10.75 (((woz1_3) => 78.80/10.75 (((woz1_4) => 78.80/10.75 (((woz1_5) => 78.80/10.75 (((breln1all2) => 78.80/10.75 (((breln1SetBreln1) => 78.80/10.75 (((choice2fnsingleton) => 78.80/10.75 (((setOfPairsIsBReln1) => 78.80/10.75 (((breln1all1) => 78.80/10.75 (((subbreln1) => 78.80/10.75 (((eqbreln1) => 78.80/10.75 (((breln1invprop) => 78.80/10.75 (((breln1invI) => 78.80/10.75 (((breln1invE) => 78.80/10.75 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Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 78.80/10.75 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2630])). 78.80/10.75 thf(zip_derived_cl2652, plain, 78.80/10.75 (~ (((woz1_3) => 78.80/10.75 (((woz1_4) => 78.80/10.75 (((woz1_5) => 78.80/10.75 (((breln1all2) => 78.80/10.75 (((breln1SetBreln1) => 78.80/10.75 (((choice2fnsingleton) => 78.80/10.75 (((setOfPairsIsBReln1) => 78.80/10.75 (((breln1all1) => 78.80/10.75 (((subbreln1) => 78.80/10.75 (((eqbreln1) => 78.80/10.75 (((breln1invprop) => 78.80/10.75 (((breln1invI) => 78.80/10.75 (((breln1invE) => 78.80/10.75 (((breln1compprop) => 78.80/10.75 (((breln1compI) => 78.80/10.75 (((breln1compE) => 78.80/10.75 (((breln1compEex) => 78.80/10.75 (((breln1unionprop) => 78.80/10.75 (((breln1unionIL) => 78.80/10.75 (((breln1unionIR) => 78.80/10.75 (((breln1unionI) => 78.80/10.75 (((breln1unionE) => 78.80/10.75 (((breln1unionEcases) => 78.80/10.75 (((breln1unionCommutes) => 78.80/10.75 (((woz2Ex) => 78.80/10.75 (((woz2W) => 78.80/10.75 (((woz2A) => 78.80/10.75 (((woz2B) => 78.80/10.75 (((image1Ex) => 78.80/10.75 (((image1Ex1) => 78.80/10.75 (( 78.80/10.75 (image1Equiv) => 78.80/10.75 (( 78.80/10.75 (image1E) => 78.80/10.75 (( 78.80/10.75 (image1I) => 78.80/10.75 (( 78.80/10.75 (injFuncInInjFuncSet) => 78.80/10.75 (( 78.80/10.75 (injFuncSetFuncIn) => 78.80/10.75 (( 78.80/10.75 (injFuncSetFuncInj) => 78.80/10.75 (( 78.80/10.75 (surjFuncSetFuncIn) => 78.80/10.75 (( 78.80/10.75 (surjFuncSetFuncSurj) => 78.80/10.75 (( 78.80/10.75 (leftInvIsSurj) => 78.80/10.75 (( 78.80/10.75 (surjCantorThm) => 78.80/10.75 (( 78.80/10.75 (foundation2) => 78.80/10.75 (( 78.80/10.75 (notinself) => 78.80/10.75 (( 78.80/10.75 (notinself2) => 78.80/10.75 (( 78.80/10.75 (omegaSp) => 78.80/10.75 (( 78.80/10.75 (omegaSclos) => 78.80/10.75 (( 78.80/10.75 (peano0notS) => 78.80/10.75 (( 78.80/10.75 (peanoSinj) => 78.80/10.75 (( 78.80/10.75 (transitivesetOp1) => 78.80/10.75 (( 78.80/10.75 (binintTransitive) => 78.80/10.75 (( 78.80/10.75 (transitivesetOp2) => 78.80/10.75 (( 78.80/10.75 (setunionTransitive) => 78.80/10.75 (( 78.80/10.75 (ordinalMinLem1) => 78.80/10.75 (( 78.80/10.75 (!!) @ ( 78.80/10.75 ^[Y0 : $i]: 78.80/10.75 (( 78.80/10.75 (ordinal @ 78.80/10.75 Y0) => 78.80/10.75 (( 78.80/10.75 (!!) @ ( 78.80/10.75 ^[Y1 : $i]: 78.80/10.75 (( 78.80/10.75 (!!) @ ( 78.80/10.75 ^[Y2 : $i]: 78.80/10.75 (( 78.80/10.75 (in @ 78.80/10.75 Y2 @ 78.80/10.75 Y0) => 78.80/10.75 (( 78.80/10.75 (in @ 78.80/10.75 Y1 @ 78.80/10.75 Y2) => 78.80/10.75 (in @ 78.80/10.75 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 78.80/10.75 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2641])). 78.80/10.75 thf(zip_derived_cl2663, plain, 78.80/10.75 (~ (((woz1_4) => 78.80/10.75 (((woz1_5) => 78.80/10.75 (((breln1all2) => 78.80/10.75 (((breln1SetBreln1) => 78.80/10.75 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78.80/10.75 (injFuncSetFuncInj) => 78.80/10.75 (( 78.80/10.75 (surjFuncSetFuncIn) => 78.80/10.75 (( 78.80/10.75 (surjFuncSetFuncSurj) => 78.80/10.75 (( 78.80/10.75 (leftInvIsSurj) => 78.80/10.75 (( 78.80/10.75 (surjCantorThm) => 78.80/10.75 (( 78.80/10.75 (foundation2) => 78.80/10.75 (( 78.80/10.75 (notinself) => 78.80/10.75 (( 78.80/10.75 (notinself2) => 78.80/10.75 (( 78.80/10.75 (omegaSp) => 78.80/10.75 (( 78.80/10.75 (omegaSclos) => 78.80/10.75 (( 78.80/10.75 (peano0notS) => 78.80/10.75 (( 78.80/10.75 (peanoSinj) => 78.80/10.75 (( 78.80/10.75 (transitivesetOp1) => 78.80/10.75 (( 78.80/10.75 (binintTransitive) => 78.80/10.75 (( 78.80/10.75 (transitivesetOp2) => 78.80/10.75 (( 78.80/10.75 (setunionTransitive) => 78.80/10.75 (( 78.80/10.75 (ordinalMinLem1) => 78.80/10.75 (( 78.80/10.75 (!!) @ ( 78.80/10.75 ^[Y0 : $i]: 78.80/10.75 (( 78.80/10.75 (ordinal @ 78.80/10.75 Y0) => 78.80/10.75 (( 78.80/10.75 (!!) @ ( 78.80/10.75 ^[Y1 : $i]: 78.80/10.75 (( 78.80/10.75 (!!) @ ( 78.80/10.75 ^[Y2 : $i]: 78.80/10.75 (( 78.80/10.75 (in @ 78.80/10.75 Y2 @ 78.80/10.75 Y0) => 78.80/10.75 (( 78.80/10.75 (in @ 78.80/10.75 Y1 @ 78.80/10.75 Y2) => 78.80/10.75 (in @ 78.80/10.75 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 78.80/10.75 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2652])). 78.80/10.75 thf(zip_derived_cl2672, plain, 78.80/10.75 (~ (((woz1_5) => 78.80/10.75 (((breln1all2) => 78.80/10.75 (((breln1SetBreln1) => 78.80/10.75 (((choice2fnsingleton) => 78.80/10.75 (((setOfPairsIsBReln1) => 78.80/10.75 (((breln1all1) => 78.80/10.75 (((subbreln1) => 78.80/10.75 (((eqbreln1) => 78.80/10.75 (((breln1invprop) => 78.80/10.75 (((breln1invI) => 78.80/10.75 (((breln1invE) => 78.80/10.75 (((breln1compprop) => 78.80/10.75 (((breln1compI) => 78.80/10.75 (((breln1compE) => 78.80/10.75 (((breln1compEex) => 78.80/10.75 (((breln1unionprop) => 78.80/10.75 (((breln1unionIL) => 78.80/10.75 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78.80/10.75 (in @ 78.80/10.75 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 78.80/10.75 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2693])). 78.80/10.75 thf(zip_derived_cl2714, plain, 78.80/10.75 (~ (((setOfPairsIsBReln1) => 78.80/10.75 (((breln1all1) => 78.80/10.75 (((subbreln1) => 78.80/10.75 (((eqbreln1) => 78.80/10.75 (((breln1invprop) => 78.80/10.75 (((breln1invI) => 78.80/10.75 (((breln1invE) => 78.80/10.75 (((breln1compprop) => 78.80/10.75 (((breln1compI) => 78.80/10.75 (((breln1compE) => 78.80/10.75 (((breln1compEex) => 78.80/10.75 (((breln1unionprop) => 78.80/10.75 (((breln1unionIL) => 78.80/10.75 (((breln1unionIR) => 78.80/10.75 (((breln1unionI) => 78.80/10.75 (((breln1unionE) => 78.80/10.75 (((breln1unionEcases) => 78.80/10.75 (((breln1unionCommutes) => 78.80/10.75 (((woz2Ex) => 78.80/10.75 (((woz2W) => 78.80/10.75 (((woz2A) => 78.80/10.75 (((woz2B) => 78.80/10.75 (((image1Ex) => 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(((breln1invI) => 78.80/10.75 (((breln1invE) => 78.80/10.75 (((breln1compprop) => 78.80/10.75 (((breln1compI) => 78.80/10.75 (((breln1compE) => 78.80/10.75 (((breln1compEex) => 78.80/10.75 (((breln1unionprop) => 78.80/10.75 (((breln1unionIL) => 78.80/10.75 (((breln1unionIR) => 78.80/10.75 (((breln1unionI) => 78.80/10.75 (((breln1unionE) => 78.80/10.75 (((breln1unionEcases) => 78.80/10.75 (((breln1unionCommutes) => 78.80/10.75 (((woz2Ex) => 78.80/10.75 (((woz2W) => 78.80/10.75 (((woz2A) => 78.80/10.75 (((woz2B) => 78.80/10.75 (((image1Ex) => 78.80/10.75 (((image1Ex1) => 78.80/10.75 (((image1Equiv) => 78.80/10.75 (((image1E) => 78.80/10.75 (((image1I) => 78.80/10.75 (((injFuncInInjFuncSet) => 78.80/10.75 (((injFuncSetFuncIn) => 78.80/10.75 (((injFuncSetFuncInj) => 78.80/10.75 (((surjFuncSetFuncIn) => 78.80/10.75 (((surjFuncSetFuncSurj) => 78.80/10.75 (( 78.80/10.75 (leftInvIsSurj) => 78.80/10.75 (( 78.80/10.75 (surjCantorThm) => 78.80/10.75 (( 78.80/10.75 (foundation2) => 78.80/10.75 (( 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Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 78.80/10.75 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2725])). 78.80/10.75 thf(zip_derived_cl2749, plain, 78.80/10.75 (~ (((eqbreln1) => 78.80/10.75 (((breln1invprop) => 78.80/10.75 (((breln1invI) => 78.80/10.75 (((breln1invE) => 78.80/10.75 (((breln1compprop) => 78.80/10.75 (((breln1compI) => 78.80/10.75 (((breln1compE) => 78.80/10.75 (((breln1compEex) => 78.80/10.75 (((breln1unionprop) => 78.80/10.75 (((breln1unionIL) => 78.80/10.75 (((breln1unionIR) => 78.80/10.75 (((breln1unionI) => 78.80/10.75 (((breln1unionE) => 78.80/10.75 (((breln1unionEcases) => 78.80/10.75 (((breln1unionCommutes) => 78.80/10.75 (((woz2Ex) => 78.80/10.75 (((woz2W) => 78.80/10.75 (((woz2A) => 78.80/10.75 (((woz2B) => 78.80/10.75 (((image1Ex) => 78.80/10.75 (((image1Ex1) => 78.80/10.75 (((image1Equiv) => 78.80/10.75 (((image1E) => 78.80/10.75 (((image1I) => 78.80/10.75 (((injFuncInInjFuncSet) => 78.80/10.75 (((injFuncSetFuncIn) => 78.80/10.75 (((injFuncSetFuncInj) => 78.80/10.75 (((surjFuncSetFuncIn) => 78.80/10.75 (((surjFuncSetFuncSurj) => 78.80/10.75 (((leftInvIsSurj) => 78.80/10.75 (( 78.80/10.75 (surjCantorThm) => 78.80/10.75 (( 78.80/10.75 (foundation2) => 78.80/10.75 (( 78.80/10.75 (notinself) => 78.80/10.75 (( 78.80/10.75 (notinself2) => 78.80/10.75 (( 78.80/10.75 (omegaSp) => 78.80/10.75 (( 78.80/10.75 (omegaSclos) => 78.80/10.75 (( 78.80/10.75 (peano0notS) => 78.80/10.75 (( 78.80/10.75 (peanoSinj) => 78.80/10.75 (( 78.80/10.75 (transitivesetOp1) => 78.80/10.75 (( 78.80/10.75 (binintTransitive) => 78.80/10.75 (( 78.80/10.75 (transitivesetOp2) => 78.80/10.75 (( 78.80/10.75 (setunionTransitive) => 78.80/10.75 (( 78.80/10.75 (ordinalMinLem1) => 78.80/10.75 (( 78.80/10.75 (!!) @ ( 78.80/10.75 ^[Y0 : $i]: 78.80/10.75 (( 78.80/10.75 (ordinal @ 78.80/10.75 Y0) => 78.80/10.75 (( 78.80/10.75 (!!) @ ( 78.80/10.75 ^[Y1 : $i]: 78.80/10.75 (( 78.80/10.75 (!!) @ ( 78.80/10.75 ^[Y2 : $i]: 78.80/10.75 (( 78.80/10.75 (in @ 78.80/10.75 Y2 @ 78.80/10.75 Y0) => 78.80/10.75 (( 78.80/10.75 (in @ 78.80/10.75 Y1 @ 78.80/10.75 Y2) => 78.80/10.75 (in @ 78.80/10.75 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 78.80/10.75 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2736])). 78.80/10.75 thf(zip_derived_cl2758, plain, 78.80/10.75 (~ (((breln1invprop) => 78.80/10.75 (((breln1invI) => 78.80/10.75 (((breln1invE) => 78.80/10.75 (((breln1compprop) => 78.80/10.75 (((breln1compI) => 78.80/10.75 (((breln1compE) => 78.80/10.75 (((breln1compEex) => 78.80/10.75 (((breln1unionprop) => 78.80/10.75 (((breln1unionIL) => 78.80/10.75 (((breln1unionIR) => 78.80/10.75 (((breln1unionI) => 78.80/10.75 (((breln1unionE) => 78.80/10.75 (((breln1unionEcases) => 78.80/10.75 (((breln1unionCommutes) => 78.80/10.75 (((woz2Ex) => 78.80/10.75 (((woz2W) => 78.80/10.75 (((woz2A) => 78.80/10.75 (((woz2B) => 78.80/10.75 (((image1Ex) => 78.80/10.75 (((image1Ex1) => 78.80/10.75 (((image1Equiv) => 78.80/10.75 (((image1E) => 78.80/10.75 (((image1I) => 78.80/10.75 (((injFuncInInjFuncSet) => 78.80/10.75 (((injFuncSetFuncIn) => 78.80/10.75 (((injFuncSetFuncInj) => 78.80/10.75 (((surjFuncSetFuncIn) => 78.80/10.75 (((surjFuncSetFuncSurj) => 78.80/10.75 (((leftInvIsSurj) => 78.80/10.75 (((surjCantorThm) => 78.80/10.75 (( 78.80/10.75 (foundation2) => 78.80/10.75 (( 78.80/10.75 (notinself) => 78.80/10.75 (( 78.80/10.75 (notinself2) => 78.80/10.75 (( 78.80/10.75 (omegaSp) => 78.80/10.75 (( 78.80/10.75 (omegaSclos) => 78.80/10.75 (( 78.80/10.75 (peano0notS) => 78.80/10.75 (( 78.80/10.75 (peanoSinj) => 78.80/10.75 (( 78.80/10.75 (transitivesetOp1) => 78.80/10.75 (( 78.80/10.75 (binintTransitive) => 78.80/10.75 (( 78.80/10.75 (transitivesetOp2) => 78.80/10.75 (( 78.80/10.75 (setunionTransitive) => 78.80/10.75 (( 78.80/10.75 (ordinalMinLem1) => 78.80/10.75 (( 78.80/10.75 (!!) @ ( 78.80/10.75 ^[Y0 : $i]: 78.80/10.75 (( 78.80/10.75 (ordinal @ 78.80/10.75 Y0) => 78.80/10.75 (( 78.80/10.75 (!!) @ ( 78.80/10.75 ^[Y1 : $i]: 78.80/10.75 (( 78.80/10.75 (!!) @ ( 78.80/10.75 ^[Y2 : $i]: 78.80/10.75 (( 78.80/10.75 (in @ 78.80/10.75 Y2 @ 78.80/10.75 Y0) => 78.80/10.75 (( 78.80/10.75 (in @ 78.80/10.75 Y1 @ 78.80/10.75 Y2) => 78.80/10.75 (in @ 78.80/10.75 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 78.80/10.75 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2749])). 78.80/10.75 thf(zip_derived_cl2766, plain, 78.80/10.75 (~ (((breln1invI) => 78.80/10.75 (((breln1invE) => 78.80/10.75 (((breln1compprop) => 78.80/10.75 (((breln1compI) => 78.80/10.75 (((breln1compE) => 78.80/10.75 (((breln1compEex) => 78.80/10.75 (((breln1unionprop) => 78.80/10.75 (((breln1unionIL) => 78.80/10.75 (((breln1unionIR) => 78.80/10.75 (((breln1unionI) => 78.80/10.75 (((breln1unionE) => 78.80/10.75 (((breln1unionEcases) => 78.80/10.75 (((breln1unionCommutes) => 78.80/10.75 (((woz2Ex) => 78.80/10.75 (((woz2W) => 78.80/10.75 (((woz2A) => 78.80/10.75 (((woz2B) => 78.80/10.75 (((image1Ex) => 78.80/10.75 (((image1Ex1) => 78.80/10.75 (((image1Equiv) => 78.80/10.75 (((image1E) => 78.80/10.75 (((image1I) => 78.80/10.75 (((injFuncInInjFuncSet) => 78.80/10.75 (((injFuncSetFuncIn) => 78.80/10.75 (((injFuncSetFuncInj) => 78.80/10.75 (((surjFuncSetFuncIn) => 78.80/10.75 (((surjFuncSetFuncSurj) => 78.80/10.75 (((leftInvIsSurj) => 78.80/10.75 (((surjCantorThm) => 78.80/10.75 (((foundation2) => 78.80/10.75 (( 78.80/10.75 (notinself) => 78.80/10.75 (( 78.80/10.75 (notinself2) => 78.80/10.75 (( 78.80/10.75 (omegaSp) => 78.80/10.75 (( 78.80/10.75 (omegaSclos) => 78.80/10.75 (( 78.80/10.75 (peano0notS) => 78.80/10.75 (( 78.80/10.75 (peanoSinj) => 78.80/10.75 (( 78.80/10.75 (transitivesetOp1) => 78.80/10.75 (( 78.80/10.75 (binintTransitive) => 78.80/10.75 (( 78.80/10.75 (transitivesetOp2) => 78.80/10.75 (( 78.80/10.75 (setunionTransitive) => 78.80/10.75 (( 78.80/10.75 (ordinalMinLem1) => 78.80/10.75 (( 78.80/10.75 (!!) @ ( 78.80/10.75 ^[Y0 : $i]: 78.80/10.75 (( 78.80/10.75 (ordinal @ 78.80/10.75 Y0) => 78.80/10.75 (( 78.80/10.75 (!!) @ ( 78.80/10.75 ^[Y1 : $i]: 78.80/10.75 (( 78.80/10.75 (!!) @ ( 78.80/10.75 ^[Y2 : $i]: 78.80/10.75 (( 78.80/10.75 (in @ 78.80/10.75 Y2 @ 78.80/10.75 Y0) => 78.80/10.75 (( 78.80/10.75 (in @ 78.80/10.75 Y1 @ 78.80/10.75 Y2) => 78.80/10.75 (in @ 78.80/10.75 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 78.80/10.75 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2758])). 78.80/10.75 thf(zip_derived_cl2775, plain, 78.80/10.75 (~ (((breln1invE) => 78.80/10.75 (((breln1compprop) => 78.80/10.75 (((breln1compI) => 78.80/10.75 (((breln1compE) => 78.80/10.75 (((breln1compEex) => 78.80/10.75 (((breln1unionprop) => 78.80/10.75 (((breln1unionIL) => 78.80/10.75 (((breln1unionIR) => 78.80/10.75 (((breln1unionI) => 78.80/10.75 (((breln1unionE) => 78.80/10.75 (((breln1unionEcases) => 78.80/10.75 (((breln1unionCommutes) => 78.80/10.75 (((woz2Ex) => 78.80/10.75 (((woz2W) => 78.80/10.75 (((woz2A) => 78.80/10.75 (((woz2B) => 78.80/10.75 (((image1Ex) => 78.80/10.75 (((image1Ex1) => 78.80/10.75 (((image1Equiv) => 78.80/10.75 (((image1E) => 78.80/10.75 (((image1I) => 78.80/10.75 (((injFuncInInjFuncSet) => 78.80/10.75 (((injFuncSetFuncIn) => 78.80/10.75 (((injFuncSetFuncInj) => 78.80/10.75 (((surjFuncSetFuncIn) => 78.80/10.75 (((surjFuncSetFuncSurj) => 78.80/10.75 (((leftInvIsSurj) => 78.80/10.75 (((surjCantorThm) => 78.80/10.75 (((foundation2) => 78.80/10.75 (((notinself) => 78.80/10.75 (( 78.80/10.75 (notinself2) => 78.80/10.75 (( 78.80/10.75 (omegaSp) => 78.80/10.75 (( 78.80/10.75 (omegaSclos) => 78.80/10.75 (( 78.80/10.75 (peano0notS) => 78.80/10.75 (( 78.80/10.75 (peanoSinj) => 78.80/10.75 (( 78.80/10.75 (transitivesetOp1) => 78.80/10.75 (( 78.80/10.75 (binintTransitive) => 78.80/10.75 (( 78.80/10.75 (transitivesetOp2) => 78.80/10.75 (( 78.80/10.75 (setunionTransitive) => 78.80/10.75 (( 78.80/10.75 (ordinalMinLem1) => 78.80/10.75 (( 78.80/10.75 (!!) @ ( 78.80/10.75 ^[Y0 : $i]: 78.80/10.75 (( 78.80/10.75 (ordinal @ 78.80/10.75 Y0) => 78.80/10.75 (( 78.80/10.75 (!!) @ ( 78.80/10.75 ^[Y1 : $i]: 78.80/10.75 (( 78.80/10.75 (!!) @ ( 78.80/10.75 ^[Y2 : $i]: 78.80/10.75 (( 78.80/10.75 (in @ 78.80/10.75 Y2 @ 78.80/10.75 Y0) => 78.80/10.75 (( 78.80/10.75 (in @ 78.80/10.75 Y1 @ 78.80/10.75 Y2) => 78.80/10.75 (in @ 78.80/10.75 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 78.80/10.75 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2766])). 78.80/10.75 thf(zip_derived_cl2786, plain, 78.80/10.75 (~ (((breln1compprop) => 78.80/10.75 (((breln1compI) => 78.80/10.75 (((breln1compE) => 78.80/10.75 (((breln1compEex) => 78.80/10.75 (((breln1unionprop) => 78.80/10.75 (((breln1unionIL) => 78.80/10.75 (((breln1unionIR) => 78.80/10.75 (((breln1unionI) => 78.80/10.75 (((breln1unionE) => 78.80/10.75 (((breln1unionEcases) => 78.80/10.75 (((breln1unionCommutes) => 78.80/10.75 (((woz2Ex) => 78.80/10.75 (((woz2W) => 78.80/10.75 (((woz2A) => 78.80/10.75 (((woz2B) => 78.80/10.75 (((image1Ex) => 78.80/10.75 (((image1Ex1) => 78.80/10.75 (((image1Equiv) => 78.80/10.75 (((image1E) => 78.80/10.75 (((image1I) => 78.80/10.75 (((injFuncInInjFuncSet) => 78.80/10.75 (((injFuncSetFuncIn) => 78.80/10.75 (((injFuncSetFuncInj) => 78.80/10.75 (((surjFuncSetFuncIn) => 78.80/10.75 (((surjFuncSetFuncSurj) => 78.80/10.75 (((leftInvIsSurj) => 78.80/10.75 (((surjCantorThm) => 78.80/10.75 (((foundation2) => 78.80/10.75 (((notinself) => 78.80/10.75 (((notinself2) => 78.80/10.75 (( 78.80/10.75 (omegaSp) => 78.80/10.75 (( 78.80/10.75 (omegaSclos) => 78.80/10.75 (( 78.80/10.75 (peano0notS) => 78.80/10.75 (( 78.80/10.75 (peanoSinj) => 78.80/10.75 (( 78.80/10.75 (transitivesetOp1) => 78.80/10.75 (( 78.80/10.75 (binintTransitive) => 78.80/10.75 (( 78.80/10.75 (transitivesetOp2) => 78.80/10.75 (( 78.80/10.75 (setunionTransitive) => 78.80/10.75 (( 78.80/10.75 (ordinalMinLem1) => 78.80/10.75 (( 78.80/10.75 (!!) @ ( 78.80/10.75 ^[Y0 : $i]: 78.80/10.75 (( 78.80/10.75 (ordinal @ 78.80/10.75 Y0) => 78.80/10.75 (( 78.80/10.75 (!!) @ ( 78.80/10.75 ^[Y1 : $i]: 78.80/10.75 (( 78.80/10.75 (!!) @ ( 78.80/10.75 ^[Y2 : $i]: 78.80/10.75 (( 78.80/10.75 (in @ 78.80/10.75 Y2 @ 78.80/10.75 Y0) => 78.80/10.75 (( 78.80/10.75 (in @ 78.80/10.75 Y1 @ 78.80/10.75 Y2) => 78.80/10.75 (in @ 78.80/10.75 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 78.80/10.75 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2775])). 78.80/10.75 thf(zip_derived_cl2799, plain, 78.80/10.75 (~ (((breln1compI) => 78.80/10.75 (((breln1compE) => 78.80/10.75 (((breln1compEex) => 78.80/10.75 (((breln1unionprop) => 78.80/10.75 (((breln1unionIL) => 78.80/10.75 (((breln1unionIR) => 78.80/10.75 (((breln1unionI) => 78.80/10.75 (((breln1unionE) => 78.80/10.75 (((breln1unionEcases) => 78.80/10.75 (((breln1unionCommutes) => 78.80/10.75 (((woz2Ex) => 78.80/10.75 (((woz2W) => 78.80/10.75 (((woz2A) => 78.80/10.75 (((woz2B) => 78.80/10.75 (((image1Ex) => 78.80/10.75 (((image1Ex1) => 78.80/10.75 (((image1Equiv) => 78.80/10.75 (((image1E) => 78.80/10.75 (((image1I) => 78.80/10.75 (((injFuncInInjFuncSet) => 78.80/10.75 (((injFuncSetFuncIn) => 78.80/10.75 (((injFuncSetFuncInj) => 78.80/10.75 (((surjFuncSetFuncIn) => 78.80/10.75 (((surjFuncSetFuncSurj) => 78.80/10.75 (((leftInvIsSurj) => 78.80/10.75 (((surjCantorThm) => 78.80/10.75 (((foundation2) => 78.80/10.75 (((notinself) => 78.80/10.75 (((notinself2) => 78.80/10.75 (((omegaSp) => 78.80/10.75 (( 78.80/10.75 (omegaSclos) => 78.80/10.75 (( 78.80/10.75 (peano0notS) => 78.80/10.75 (( 78.80/10.75 (peanoSinj) => 78.80/10.75 (( 78.80/10.75 (transitivesetOp1) => 78.80/10.75 (( 78.80/10.75 (binintTransitive) => 78.80/10.75 (( 78.80/10.75 (transitivesetOp2) => 78.80/10.75 (( 78.80/10.75 (setunionTransitive) => 78.80/10.75 (( 78.80/10.75 (ordinalMinLem1) => 78.80/10.75 (( 78.80/10.75 (!!) @ ( 78.80/10.75 ^[Y0 : $i]: 78.80/10.75 (( 78.80/10.75 (ordinal @ 78.80/10.75 Y0) => 78.80/10.75 (( 78.80/10.75 (!!) @ ( 78.80/10.75 ^[Y1 : $i]: 78.80/10.75 (( 78.80/10.75 (!!) @ ( 78.80/10.75 ^[Y2 : $i]: 78.80/10.75 (( 78.80/10.75 (in @ 78.80/10.75 Y2 @ 78.80/10.75 Y0) => 78.80/10.75 (( 78.80/10.75 (in @ 78.80/10.75 Y1 @ 78.80/10.75 Y2) => 78.80/10.75 (in @ 78.80/10.75 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 78.80/10.75 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2786])). 78.80/10.75 thf(zip_derived_cl2813, plain, 78.80/10.75 (~ (((breln1compE) => 78.80/10.75 (((breln1compEex) => 78.80/10.75 (((breln1unionprop) => 78.80/10.75 (((breln1unionIL) => 78.80/10.75 (((breln1unionIR) => 78.80/10.75 (((breln1unionI) => 78.80/10.75 (((breln1unionE) => 78.80/10.75 (((breln1unionEcases) => 78.80/10.75 (((breln1unionCommutes) => 78.80/10.75 (((woz2Ex) => 78.80/10.75 (((woz2W) => 78.80/10.75 (((woz2A) => 78.80/10.75 (((woz2B) => 78.80/10.75 (((image1Ex) => 78.80/10.75 (((image1Ex1) => 78.80/10.75 (((image1Equiv) => 78.80/10.75 (((image1E) => 78.80/10.75 (((image1I) => 78.80/10.75 (((injFuncInInjFuncSet) => 78.80/10.75 (((injFuncSetFuncIn) => 78.80/10.75 (((injFuncSetFuncInj) => 78.80/10.75 (((surjFuncSetFuncIn) => 78.80/10.75 (((surjFuncSetFuncSurj) => 78.80/10.75 (((leftInvIsSurj) => 78.80/10.75 (((surjCantorThm) => 78.80/10.75 (((foundation2) => 78.80/10.75 (((notinself) => 78.80/10.75 (((notinself2) => 78.80/10.75 (((omegaSp) => 78.80/10.75 (((omegaSclos) => 78.80/10.75 (( 78.80/10.75 (peano0notS) => 78.80/10.75 (( 78.80/10.75 (peanoSinj) => 78.80/10.75 (( 78.80/10.75 (transitivesetOp1) => 78.80/10.75 (( 78.80/10.75 (binintTransitive) => 78.80/10.75 (( 78.80/10.75 (transitivesetOp2) => 78.80/10.75 (( 78.80/10.75 (setunionTransitive) => 78.80/10.75 (( 78.80/10.75 (ordinalMinLem1) => 78.80/10.75 (( 78.80/10.75 (!!) @ ( 78.80/10.75 ^[Y0 : $i]: 78.80/10.75 (( 78.80/10.75 (ordinal @ 78.80/10.75 Y0) => 78.80/10.75 (( 78.80/10.75 (!!) @ ( 78.80/10.75 ^[Y1 : $i]: 78.80/10.75 (( 78.80/10.75 (!!) @ ( 78.80/10.75 ^[Y2 : $i]: 78.80/10.75 (( 78.80/10.75 (in @ 78.80/10.75 Y2 @ 78.80/10.75 Y0) => 78.80/10.75 (( 78.80/10.75 (in @ 78.80/10.75 Y1 @ 78.80/10.75 Y2) => 78.80/10.75 (in @ 78.80/10.75 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 78.80/10.75 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2799])). 78.80/10.75 thf(zip_derived_cl2828, plain, 78.80/10.75 (~ (((breln1compEex) => 78.80/10.75 (((breln1unionprop) => 78.80/10.75 (((breln1unionIL) => 78.80/10.75 (((breln1unionIR) => 78.80/10.75 (((breln1unionI) => 78.80/10.75 (((breln1unionE) => 78.80/10.75 (((breln1unionEcases) => 78.80/10.75 (((breln1unionCommutes) => 78.80/10.75 (((woz2Ex) => 78.80/10.75 (((woz2W) => 78.80/10.75 (((woz2A) => 78.80/10.75 (((woz2B) => 78.80/10.75 (((image1Ex) => 78.80/10.75 (((image1Ex1) => 78.80/10.75 (((image1Equiv) => 78.80/10.75 (((image1E) => 78.80/10.75 (((image1I) => 78.80/10.75 (((injFuncInInjFuncSet) => 78.80/10.75 (((injFuncSetFuncIn) => 78.80/10.75 (((injFuncSetFuncInj) => 78.80/10.75 (((surjFuncSetFuncIn) => 78.80/10.75 (((surjFuncSetFuncSurj) => 78.80/10.75 (((leftInvIsSurj) => 78.80/10.75 (((surjCantorThm) => 78.80/10.75 (((foundation2) => 78.80/10.75 (((notinself) => 78.80/10.75 (((notinself2) => 78.80/10.75 (((omegaSp) => 78.80/10.75 (((omegaSclos) => 78.80/10.75 (((peano0notS) => 78.80/10.75 (( 78.80/10.75 (peanoSinj) => 78.80/10.75 (( 78.80/10.75 (transitivesetOp1) => 78.80/10.75 (( 78.80/10.75 (binintTransitive) => 78.80/10.75 (( 78.80/10.75 (transitivesetOp2) => 78.80/10.75 (( 78.80/10.75 (setunionTransitive) => 78.80/10.75 (( 78.80/10.75 (ordinalMinLem1) => 78.80/10.75 (( 78.80/10.75 (!!) @ ( 78.80/10.75 ^[Y0 : $i]: 78.80/10.75 (( 78.80/10.75 (ordinal @ 78.80/10.75 Y0) => 78.80/10.75 (( 78.80/10.75 (!!) @ ( 78.80/10.75 ^[Y1 : $i]: 78.80/10.75 (( 78.80/10.75 (!!) @ ( 78.80/10.75 ^[Y2 : $i]: 78.80/10.75 (( 78.80/10.75 (in @ 78.80/10.75 Y2 @ 78.80/10.75 Y0) => 78.80/10.75 (( 78.80/10.75 (in @ 78.80/10.75 Y1 @ 78.80/10.75 Y2) => 78.80/10.75 (in @ 78.80/10.75 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 78.80/10.75 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2813])). 78.80/10.75 thf(zip_derived_cl2843, plain, 78.80/10.75 (~ (((breln1unionprop) => 78.80/10.75 (((breln1unionIL) => 78.80/10.75 (((breln1unionIR) => 78.80/10.75 (((breln1unionI) => 78.80/10.75 (((breln1unionE) => 78.80/10.75 (((breln1unionEcases) => 78.80/10.75 (((breln1unionCommutes) => 78.80/10.75 (((woz2Ex) => 78.80/10.75 (((woz2W) => 78.80/10.75 (((woz2A) => 78.80/10.75 (((woz2B) => 78.80/10.75 (((image1Ex) => 78.80/10.75 (((image1Ex1) => 78.80/10.75 (((image1Equiv) => 78.80/10.75 (((image1E) => 78.80/10.75 (((image1I) => 78.80/10.75 (((injFuncInInjFuncSet) => 78.80/10.75 (((injFuncSetFuncIn) => 78.80/10.75 (((injFuncSetFuncInj) => 78.80/10.75 (((surjFuncSetFuncIn) => 78.80/10.75 (((surjFuncSetFuncSurj) => 78.80/10.75 (((leftInvIsSurj) => 78.80/10.75 (((surjCantorThm) => 78.80/10.75 (((foundation2) => 78.80/10.75 (((notinself) => 78.80/10.75 (((notinself2) => 78.80/10.75 (((omegaSp) => 78.80/10.75 (((omegaSclos) => 78.80/10.75 (((peano0notS) => 78.80/10.75 (((peanoSinj) => 78.80/10.75 (( 78.80/10.75 (transitivesetOp1) => 78.80/10.75 (( 78.80/10.75 (binintTransitive) => 78.80/10.75 (( 78.80/10.75 (transitivesetOp2) => 78.80/10.75 (( 78.80/10.75 (setunionTransitive) => 78.80/10.75 (( 78.80/10.75 (ordinalMinLem1) => 78.80/10.75 (( 78.80/10.75 (!!) @ ( 78.80/10.75 ^[Y0 : $i]: 78.80/10.75 (( 78.80/10.75 (ordinal @ 78.80/10.75 Y0) => 78.80/10.75 (( 78.80/10.75 (!!) @ ( 78.80/10.75 ^[Y1 : $i]: 78.80/10.75 (( 78.80/10.75 (!!) @ ( 78.80/10.75 ^[Y2 : $i]: 78.80/10.75 (( 78.80/10.75 (in @ 78.80/10.75 Y2 @ 78.80/10.75 Y0) => 78.80/10.75 (( 78.80/10.75 (in @ 78.80/10.75 Y1 @ 78.80/10.75 Y2) => 78.80/10.75 (in @ 78.80/10.75 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 78.80/10.75 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2828])). 78.80/10.75 thf(zip_derived_cl2859, plain, 78.80/10.75 (~ (((breln1unionIL) => 78.80/10.75 (((breln1unionIR) => 78.80/10.75 (((breln1unionI) => 78.80/10.75 (((breln1unionE) => 78.80/10.75 (((breln1unionEcases) => 78.80/10.75 (((breln1unionCommutes) => 78.80/10.75 (((woz2Ex) => 78.80/10.75 (((woz2W) => 78.80/10.75 (((woz2A) => 78.80/10.75 (((woz2B) => 78.80/10.75 (((image1Ex) => 78.80/10.75 (((image1Ex1) => 78.80/10.75 (((image1Equiv) => 78.80/10.75 (((image1E) => 78.80/10.75 (((image1I) => 78.80/10.75 (((injFuncInInjFuncSet) => 78.80/10.75 (((injFuncSetFuncIn) => 78.80/10.75 (((injFuncSetFuncInj) => 78.80/10.75 (((surjFuncSetFuncIn) => 78.80/10.75 (((surjFuncSetFuncSurj) => 78.80/10.75 (((leftInvIsSurj) => 78.80/10.75 (((surjCantorThm) => 78.80/10.75 (((foundation2) => 78.80/10.75 (((notinself) => 78.80/10.75 (((notinself2) => 78.80/10.75 (((omegaSp) => 78.80/10.75 (((omegaSclos) => 78.80/10.75 (((peano0notS) => 78.80/10.75 (((peanoSinj) => 78.80/10.75 (((transitivesetOp1) => 78.80/10.75 (( 78.80/10.75 (binintTransitive) => 78.80/10.75 (( 78.80/10.75 (transitivesetOp2) => 78.80/10.75 (( 78.80/10.75 (setunionTransitive) => 78.80/10.75 (( 78.80/10.75 (ordinalMinLem1) => 78.80/10.75 (( 78.80/10.75 (!!) @ ( 78.80/10.75 ^[Y0 : $i]: 78.80/10.75 (( 78.80/10.75 (ordinal @ 78.80/10.75 Y0) => 78.80/10.75 (( 78.80/10.75 (!!) @ ( 78.80/10.75 ^[Y1 : $i]: 78.80/10.75 (( 78.80/10.75 (!!) @ ( 78.80/10.75 ^[Y2 : $i]: 78.80/10.75 (( 78.80/10.75 (in @ 78.80/10.75 Y2 @ 78.80/10.75 Y0) => 78.80/10.75 (( 78.80/10.75 (in @ 78.80/10.75 Y1 @ 78.80/10.75 Y2) => 78.80/10.75 (in @ 78.80/10.75 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 78.80/10.75 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2843])). 78.80/10.75 thf(zip_derived_cl2874, plain, 78.80/10.75 (~ (((breln1unionIR) => 78.80/10.75 (((breln1unionI) => 78.80/10.75 (((breln1unionE) => 78.80/10.75 (((breln1unionEcases) => 78.80/10.75 (((breln1unionCommutes) => 78.80/10.75 (((woz2Ex) => 78.80/10.75 (((woz2W) => 78.80/10.75 (((woz2A) => 78.80/10.75 (((woz2B) => 78.80/10.75 (((image1Ex) => 78.80/10.75 (((image1Ex1) => 78.80/10.75 (((image1Equiv) => 78.80/10.75 (((image1E) => 78.80/10.75 (((image1I) => 78.80/10.75 (((injFuncInInjFuncSet) => 78.80/10.75 (((injFuncSetFuncIn) => 78.80/10.75 (((injFuncSetFuncInj) => 78.80/10.75 (((surjFuncSetFuncIn) => 78.80/10.75 (((surjFuncSetFuncSurj) => 78.80/10.75 (((leftInvIsSurj) => 78.80/10.75 (((surjCantorThm) => 78.80/10.75 (((foundation2) => 78.80/10.75 (((notinself) => 78.80/10.75 (((notinself2) => 78.80/10.75 (((omegaSp) => 78.80/10.75 (((omegaSclos) => 78.80/10.75 (((peano0notS) => 78.80/10.75 (((peanoSinj) => 78.80/10.75 (((transitivesetOp1) => 78.80/10.75 (((binintTransitive) => 78.80/10.75 (( 78.80/10.75 (transitivesetOp2) => 78.80/10.75 (( 78.80/10.75 (setunionTransitive) => 78.80/10.75 (( 78.80/10.75 (ordinalMinLem1) => 78.80/10.75 (( 78.80/10.75 (!!) @ ( 78.80/10.75 ^[Y0 : $i]: 78.80/10.75 (( 78.80/10.75 (ordinal @ 78.80/10.75 Y0) => 78.80/10.75 (( 78.80/10.75 (!!) @ ( 78.80/10.75 ^[Y1 : $i]: 78.80/10.75 (( 78.80/10.75 (!!) @ ( 78.80/10.75 ^[Y2 : $i]: 78.80/10.75 (( 78.80/10.75 (in @ 78.80/10.75 Y2 @ 78.80/10.75 Y0) => 78.80/10.75 (( 78.80/10.75 (in @ 78.80/10.75 Y1 @ 78.80/10.75 Y2) => 78.80/10.75 (in @ 78.80/10.75 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 78.80/10.75 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2859])). 78.80/10.75 thf(zip_derived_cl2891, plain, 78.80/10.75 (~ (((breln1unionI) => 78.80/10.75 (((breln1unionE) => 78.80/10.75 (((breln1unionEcases) => 78.80/10.75 (((breln1unionCommutes) => 78.80/10.75 (((woz2Ex) => 78.80/10.75 (((woz2W) => 78.80/10.75 (((woz2A) => 78.80/10.75 (((woz2B) => 78.80/10.75 (((image1Ex) => 78.80/10.75 (((image1Ex1) => 78.80/10.75 (((image1Equiv) => 78.80/10.75 (((image1E) => 78.80/10.75 (((image1I) => 78.80/10.75 (((injFuncInInjFuncSet) => 78.80/10.75 (((injFuncSetFuncIn) => 78.80/10.75 (((injFuncSetFuncInj) => 78.80/10.75 (((surjFuncSetFuncIn) => 78.80/10.75 (((surjFuncSetFuncSurj) => 78.80/10.75 (((leftInvIsSurj) => 78.80/10.75 (((surjCantorThm) => 78.80/10.75 (((foundation2) => 78.80/10.75 (((notinself) => 78.80/10.75 (((notinself2) => 78.80/10.75 (((omegaSp) => 78.80/10.75 (((omegaSclos) => 78.80/10.75 (((peano0notS) => 78.80/10.75 (((peanoSinj) => 78.80/10.75 (((transitivesetOp1) => 78.80/10.75 (((binintTransitive) => 78.80/10.75 (((transitivesetOp2) => 78.80/10.75 (( 78.80/10.75 (setunionTransitive) => 78.80/10.75 (( 78.80/10.75 (ordinalMinLem1) => 78.80/10.75 (( 78.80/10.75 (!!) @ ( 78.80/10.75 ^[Y0 : $i]: 78.80/10.75 (( 78.80/10.75 (ordinal @ 78.80/10.75 Y0) => 78.80/10.75 (( 78.80/10.75 (!!) @ ( 78.80/10.75 ^[Y1 : $i]: 78.80/10.75 (( 78.80/10.75 (!!) @ ( 78.80/10.75 ^[Y2 : $i]: 78.80/10.75 (( 78.80/10.75 (in @ 78.80/10.75 Y2 @ 78.80/10.75 Y0) => 78.80/10.75 (( 78.80/10.75 (in @ 78.80/10.75 Y1 @ 78.80/10.75 Y2) => 78.80/10.75 (in @ 78.80/10.75 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 78.80/10.75 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2874])). 78.80/10.75 thf(zip_derived_cl2906, plain, 78.80/10.75 (~ (((breln1unionE) => 78.80/10.75 (((breln1unionEcases) => 78.80/10.75 (((breln1unionCommutes) => 78.80/10.75 (((woz2Ex) => 78.80/10.75 (((woz2W) => 78.80/10.75 (((woz2A) => 78.80/10.75 (((woz2B) => 78.80/10.75 (((image1Ex) => 78.80/10.75 (((image1Ex1) => 78.80/10.75 (((image1Equiv) => 78.80/10.75 (((image1E) => 78.80/10.75 (((image1I) => 78.80/10.75 (((injFuncInInjFuncSet) => 78.80/10.75 (((injFuncSetFuncIn) => 78.80/10.75 (((injFuncSetFuncInj) => 78.80/10.75 (((surjFuncSetFuncIn) => 78.80/10.75 (((surjFuncSetFuncSurj) => 78.80/10.75 (((leftInvIsSurj) => 78.80/10.75 (((surjCantorThm) => 78.80/10.75 (((foundation2) => 78.80/10.75 (((notinself) => 78.80/10.75 (((notinself2) => 78.80/10.75 (((omegaSp) => 78.80/10.75 (((omegaSclos) => 78.80/10.75 (((peano0notS) => 78.80/10.75 (((peanoSinj) => 78.80/10.75 (((transitivesetOp1) => 78.80/10.75 (((binintTransitive) => 78.80/10.75 (((transitivesetOp2) => 78.80/10.75 (((setunionTransitive) => 78.80/10.75 (( 78.80/10.75 (ordinalMinLem1) => 78.80/10.75 (( 78.80/10.75 (!!) @ ( 78.80/10.75 ^[Y0 : $i]: 78.80/10.75 (( 78.80/10.75 (ordinal @ 78.80/10.75 Y0) => 78.80/10.75 (( 78.80/10.75 (!!) @ ( 78.80/10.75 ^[Y1 : $i]: 78.80/10.75 (( 78.80/10.75 (!!) @ ( 78.80/10.75 ^[Y2 : $i]: 78.80/10.75 (( 78.80/10.75 (in @ 78.80/10.75 Y2 @ 78.80/10.75 Y0) => 78.80/10.75 (( 78.80/10.75 (in @ 78.80/10.75 Y1 @ 78.80/10.75 Y2) => 78.80/10.75 (in @ 78.80/10.75 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 78.80/10.75 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2891])). 78.80/10.75 thf(zip_derived_cl2918, plain, 78.80/10.75 (~ (((breln1unionEcases) => 78.80/10.75 (((breln1unionCommutes) => 78.80/10.75 (((woz2Ex) => 78.80/10.75 (((woz2W) => 78.80/10.75 (((woz2A) => 78.80/10.75 (((woz2B) => 78.80/10.75 (((image1Ex) => 78.80/10.75 (((image1Ex1) => 78.80/10.75 (((image1Equiv) => 78.80/10.75 (((image1E) => 78.80/10.75 (((image1I) => 78.80/10.75 (((injFuncInInjFuncSet) => 78.80/10.75 (((injFuncSetFuncIn) => 78.80/10.75 (((injFuncSetFuncInj) => 78.80/10.75 (((surjFuncSetFuncIn) => 78.80/10.75 (((surjFuncSetFuncSurj) => 78.80/10.75 (((leftInvIsSurj) => 78.80/10.75 (((surjCantorThm) => 78.80/10.75 (((foundation2) => 78.80/10.75 (((notinself) => 78.80/10.75 (((notinself2) => 78.80/10.75 (((omegaSp) => 78.80/10.75 (((omegaSclos) => 78.80/10.75 (((peano0notS) => 78.80/10.75 (((peanoSinj) => 78.80/10.75 (((transitivesetOp1) => 78.80/10.75 (((binintTransitive) => 78.80/10.75 (((transitivesetOp2) => 78.80/10.75 (((setunionTransitive) => 78.80/10.75 (((ordinalMinLem1) => 78.80/10.75 (( 78.80/10.75 (!!) @ ( 78.80/10.75 ^[Y0 : $i]: 78.80/10.75 (( 78.80/10.75 (ordinal @ 78.80/10.75 Y0) => 78.80/10.75 (( 78.80/10.75 (!!) @ ( 78.80/10.75 ^[Y1 : $i]: 78.80/10.75 (( 78.80/10.75 (!!) @ ( 78.80/10.75 ^[Y2 : $i]: 78.80/10.75 (( 78.80/10.75 (in @ 78.80/10.75 Y2 @ 78.80/10.75 Y0) => 78.80/10.75 (( 78.80/10.75 (in @ 78.80/10.75 Y1 @ 78.80/10.75 Y2) => 78.80/10.75 (in @ 78.80/10.75 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 78.80/10.75 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2906])). 78.80/10.75 thf(zip_derived_cl2930, plain, 78.80/10.75 (~ (((breln1unionCommutes) => 78.80/10.75 (((woz2Ex) => 78.80/10.75 (((woz2W) => 78.80/10.75 (((woz2A) => 78.80/10.75 (((woz2B) => 78.80/10.75 (((image1Ex) => 78.80/10.75 (((image1Ex1) => 78.80/10.75 (((image1Equiv) => 78.80/10.75 (((image1E) => 78.80/10.75 (((image1I) => 78.80/10.75 (((injFuncInInjFuncSet) => 78.80/10.75 (((injFuncSetFuncIn) => 78.80/10.75 (((injFuncSetFuncInj) => 78.80/10.75 (((surjFuncSetFuncIn) => 78.80/10.75 (((surjFuncSetFuncSurj) => 78.80/10.75 (((leftInvIsSurj) => 78.80/10.75 (((surjCantorThm) => 78.80/10.75 (((foundation2) => 78.80/10.75 (((notinself) => 78.80/10.75 (((notinself2) => 78.80/10.75 (((omegaSp) => 78.80/10.75 (((omegaSclos) => 78.80/10.75 (((peano0notS) => 78.80/10.75 (((peanoSinj) => 78.80/10.75 (((transitivesetOp1) => 78.80/10.75 (((binintTransitive) => 78.80/10.75 (((transitivesetOp2) => 78.80/10.75 (((setunionTransitive) => 78.80/10.75 (((ordinalMinLem1) => 78.80/10.75 (((!!) @ ( 78.80/10.75 ^[Y0 : $i]: 78.80/10.75 (( 78.80/10.75 (ordinal @ 78.80/10.75 Y0) => 78.80/10.75 (( 78.80/10.75 (!!) @ ( 78.80/10.75 ^[Y1 : $i]: 78.80/10.75 (( 78.80/10.75 (!!) @ ( 78.80/10.75 ^[Y2 : $i]: 78.80/10.75 (( 78.80/10.75 (in @ 78.80/10.75 Y2 @ 78.80/10.75 Y0) => 78.80/10.75 (( 78.80/10.75 (in @ 78.80/10.75 Y1 @ 78.80/10.75 Y2) => 78.80/10.75 (in @ 78.80/10.75 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 78.80/10.75 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2918])). 78.80/10.75 thf(zip_derived_cl2941, plain, 78.80/10.75 (~ (((woz2Ex) => 78.80/10.75 (((woz2W) => 78.80/10.75 (((woz2A) => 78.80/10.75 (((woz2B) => 78.80/10.75 (((image1Ex) => 78.80/10.75 (((image1Ex1) => 78.80/10.75 (((image1Equiv) => 78.80/10.75 (((image1E) => 78.80/10.75 (((image1I) => 78.80/10.75 (((injFuncInInjFuncSet) => 78.80/10.75 (((injFuncSetFuncIn) => 78.80/10.75 (((injFuncSetFuncInj) => 78.80/10.75 (((surjFuncSetFuncIn) => 78.80/10.75 (((surjFuncSetFuncSurj) => 78.80/10.75 (((leftInvIsSurj) => 78.80/10.75 (((surjCantorThm) => 78.80/10.75 (((foundation2) => 78.80/10.75 (((notinself) => 78.80/10.75 (((notinself2) => 78.80/10.75 (((omegaSp) => 78.80/10.75 (((omegaSclos) => 78.80/10.75 (((peano0notS) => 78.80/10.75 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=> 78.80/10.75 (in @ 78.80/10.75 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 78.80/10.75 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2941])). 78.80/10.75 thf(zip_derived_cl2964, plain, 78.80/10.75 (~ (((woz2A) => 78.80/10.75 (((woz2B) => 78.80/10.75 (((image1Ex) => 78.80/10.75 (((image1Ex1) => 78.80/10.75 (((image1Equiv) => 78.80/10.75 (((image1E) => 78.80/10.75 (((image1I) => 78.80/10.75 (((injFuncInInjFuncSet) => 78.80/10.75 (((injFuncSetFuncIn) => 78.80/10.75 (((injFuncSetFuncInj) => 78.80/10.75 (((surjFuncSetFuncIn) => 78.80/10.75 (((surjFuncSetFuncSurj) => 78.80/10.75 (((leftInvIsSurj) => 78.80/10.75 (((surjCantorThm) => 78.80/10.75 (((foundation2) => 78.80/10.75 (((notinself) => 78.80/10.75 (((notinself2) => 78.80/10.75 (((omegaSp) => 78.80/10.75 (((omegaSclos) => 78.80/10.75 (((peano0notS) => 78.80/10.75 (((peanoSinj) => 78.80/10.75 (((transitivesetOp1) => 78.80/10.75 (((binintTransitive) => 78.80/10.75 (((transitivesetOp2) => 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thf(zip_derived_cl2991, plain, 78.80/10.75 (~ (((image1Ex) => 78.80/10.75 (((image1Ex1) => 78.80/10.75 (((image1Equiv) => 78.80/10.75 (((image1E) => 78.80/10.75 (((image1I) => 78.80/10.75 (((injFuncInInjFuncSet) => 78.80/10.75 (((injFuncSetFuncIn) => 78.80/10.75 (((injFuncSetFuncInj) => 78.80/10.75 (((surjFuncSetFuncIn) => 78.80/10.75 (((surjFuncSetFuncSurj) => 78.80/10.75 (((leftInvIsSurj) => 78.80/10.75 (((surjCantorThm) => 78.80/10.75 (((foundation2) => 78.80/10.75 (((notinself) => 78.80/10.75 (((notinself2) => 78.80/10.75 (((omegaSp) => 78.80/10.75 (((omegaSclos) => 78.80/10.75 (((peano0notS) => 78.80/10.75 (((peanoSinj) => 78.80/10.75 (((transitivesetOp1) => 78.80/10.75 (((binintTransitive) => 78.80/10.75 (((transitivesetOp2) => 78.80/10.75 (((setunionTransitive) => 78.80/10.75 (((ordinalMinLem1) => 78.80/10.75 (((!!) @ (^[Y0 : $i]: 78.80/10.75 (( 78.80/10.75 (ordinal @ 78.80/10.75 Y0) => 78.80/10.75 (( 78.80/10.75 (!!) @ ( 78.80/10.75 ^[Y1 : $i]: 78.80/10.75 (( 78.80/10.75 (!!) @ ( 78.80/10.75 ^[Y2 : $i]: 78.80/10.75 (( 78.80/10.75 (in @ 78.80/10.75 Y2 @ 78.80/10.75 Y0) => 78.80/10.75 (( 78.80/10.75 (in @ 78.80/10.75 Y1 @ 78.80/10.75 Y2) => 78.80/10.75 (in @ 78.80/10.75 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 78.80/10.75 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2977])). 78.80/10.75 thf(zip_derived_cl3008, plain, 78.80/10.75 (~ (((image1Ex1) => 78.80/10.75 (((image1Equiv) => 78.80/10.75 (((image1E) => 78.80/10.75 (((image1I) => 78.80/10.75 (((injFuncInInjFuncSet) => 78.80/10.75 (((injFuncSetFuncIn) => 78.80/10.75 (((injFuncSetFuncInj) => 78.80/10.75 (((surjFuncSetFuncIn) => 78.80/10.75 (((surjFuncSetFuncSurj) => 78.80/10.75 (((leftInvIsSurj) => 78.80/10.75 (((surjCantorThm) => 78.80/10.75 (((foundation2) => 78.80/10.75 (((notinself) => 78.80/10.75 (((notinself2) => 78.80/10.75 (((omegaSp) => 78.80/10.75 (((omegaSclos) => 78.80/10.75 (((peano0notS) => 78.80/10.75 (((peanoSinj) => 78.80/10.75 (((transitivesetOp1) 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(((peanoSinj) => 78.80/10.75 (((transitivesetOp1) => 78.80/10.75 (((binintTransitive) => 78.80/10.75 (((transitivesetOp2) => 78.80/10.75 (((setunionTransitive) => 78.80/10.75 (((ordinalMinLem1) => 78.80/10.75 (((!!) @ (^[Y0 : $i]: 78.80/10.75 (((ordinal @ Y0) => 78.80/10.75 (((!!) @ (^[Y1 : $i]: 78.80/10.75 (( 78.80/10.75 (!!) @ ( 78.80/10.75 ^[Y2 : $i]: 78.80/10.75 (( 78.80/10.75 (in @ 78.80/10.75 Y2 @ 78.80/10.75 Y0) => 78.80/10.75 (( 78.80/10.75 (in @ 78.80/10.75 Y1 @ 78.80/10.75 Y2) => 78.80/10.75 (in @ 78.80/10.75 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))), 78.80/10.75 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3064])). 78.80/10.75 thf(zip_derived_cl3091, plain, 78.80/10.75 (~ (((injFuncSetFuncInj) => 78.80/10.75 (((surjFuncSetFuncIn) => 78.80/10.75 (((surjFuncSetFuncSurj) => 78.80/10.75 (((leftInvIsSurj) => 78.80/10.75 (((surjCantorThm) => 78.80/10.75 (((foundation2) => 78.80/10.75 (((notinself) => 78.80/10.75 (((notinself2) => 78.80/10.75 (((omegaSp) => 78.80/10.75 (((omegaSclos) => 78.80/10.75 (((peano0notS) => 78.80/10.75 (((peanoSinj) => 78.80/10.75 (((transitivesetOp1) => 78.80/10.75 (((binintTransitive) => 78.80/10.75 (((transitivesetOp2) => 78.80/10.75 (((setunionTransitive) => 78.80/10.75 (((ordinalMinLem1) => 78.80/10.75 (((!!) @ (^[Y0 : $i]: 78.80/10.75 (((ordinal @ Y0) => 78.80/10.75 (((!!) @ (^[Y1 : $i]: 78.80/10.75 (( 78.80/10.75 (!!) @ ( 78.80/10.75 ^[Y2 : $i]: 78.80/10.75 (( 78.80/10.75 (in @ 78.80/10.75 Y2 @ 78.80/10.75 Y0) => 78.80/10.75 (( 78.80/10.75 (in @ 78.80/10.75 Y1 @ 78.80/10.75 Y2) => 78.80/10.75 (in @ 78.80/10.75 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))), 78.80/10.75 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3078])). 78.80/10.75 thf(zip_derived_cl3103, plain, 78.80/10.75 (~ (((surjFuncSetFuncIn) => 78.80/10.75 (((surjFuncSetFuncSurj) => 78.80/10.75 (((leftInvIsSurj) => 78.80/10.75 (((surjCantorThm) => 78.80/10.75 (((foundation2) => 78.80/10.75 (((notinself) => 78.80/10.75 (((notinself2) => 78.80/10.75 (((omegaSp) => 78.80/10.75 (((omegaSclos) => 78.80/10.75 (((peano0notS) => 78.80/10.75 (((peanoSinj) => 78.80/10.75 (((transitivesetOp1) => 78.80/10.75 (((binintTransitive) => 78.80/10.75 (((transitivesetOp2) => 78.80/10.75 (((setunionTransitive) => 78.80/10.75 (((ordinalMinLem1) => 78.80/10.75 (((!!) @ (^[Y0 : $i]: 78.80/10.75 (((ordinal @ Y0) => 78.80/10.75 (((!!) @ (^[Y1 : $i]: 78.80/10.75 (((!!) @ ( 78.80/10.75 ^[Y2 : $i]: 78.80/10.75 (( 78.80/10.75 (in @ 78.80/10.75 Y2 @ 78.80/10.75 Y0) => 78.80/10.75 (( 78.80/10.75 (in @ 78.80/10.75 Y1 @ 78.80/10.75 Y2) => 78.80/10.75 (in @ 78.80/10.75 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))), 78.80/10.75 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3091])). 78.80/10.75 thf(zip_derived_cl3114, plain, 78.80/10.75 (~ (((surjFuncSetFuncSurj) => 78.80/10.75 (((leftInvIsSurj) => 78.80/10.75 (((surjCantorThm) => 78.80/10.75 (((foundation2) => 78.80/10.75 (((notinself) => 78.80/10.75 (((notinself2) => 78.80/10.75 (((omegaSp) => 78.80/10.75 (((omegaSclos) => 78.80/10.75 (((peano0notS) => 78.80/10.75 (((peanoSinj) => 78.80/10.75 (((transitivesetOp1) => 78.80/10.75 (((binintTransitive) => 78.80/10.75 (((transitivesetOp2) => 78.80/10.75 (((setunionTransitive) => 78.80/10.75 (((ordinalMinLem1) => 78.80/10.75 (((!!) @ (^[Y0 : $i]: 78.80/10.75 (((ordinal @ Y0) => 78.80/10.75 (((!!) @ (^[Y1 : $i]: 78.80/10.75 (((!!) @ ( 78.80/10.75 ^[Y2 : $i]: 78.80/10.75 (( 78.80/10.75 (in @ 78.80/10.75 Y2 @ 78.80/10.75 Y0) => 78.80/10.75 (( 78.80/10.75 (in @ 78.80/10.75 Y1 @ 78.80/10.75 Y2) => 78.80/10.75 (in @ 78.80/10.75 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))), 78.80/10.75 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3103])). 78.80/10.75 thf(zip_derived_cl3126, plain, 78.80/10.75 (~ (((leftInvIsSurj) => 78.80/10.75 (((surjCantorThm) => 78.80/10.75 (((foundation2) => 78.80/10.75 (((notinself) => 78.80/10.75 (((notinself2) => 78.80/10.75 (((omegaSp) => 78.80/10.75 (((omegaSclos) => 78.80/10.75 (((peano0notS) => 78.80/10.75 (((peanoSinj) => 78.80/10.75 (((transitivesetOp1) => 78.80/10.75 (((binintTransitive) => 78.80/10.75 (((transitivesetOp2) => 78.80/10.75 (((setunionTransitive) => 78.80/10.75 (((ordinalMinLem1) => 78.80/10.75 (((!!) @ (^[Y0 : $i]: 78.80/10.75 (((ordinal @ Y0) => 78.80/10.75 (((!!) @ (^[Y1 : $i]: 78.80/10.75 (((!!) @ ( 78.80/10.75 ^[Y2 : $i]: 78.80/10.75 (((in @ 78.80/10.75 Y2 @ 78.80/10.75 Y0) => 78.80/10.75 (( 78.80/10.75 (in @ 78.80/10.75 Y1 @ 78.80/10.75 Y2) => 78.80/10.75 (in @ 78.80/10.75 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))), 78.80/10.75 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3114])). 78.80/10.75 thf(zip_derived_cl3138, plain, 78.80/10.75 (~ (((surjCantorThm) => 78.80/10.75 (((foundation2) => 78.80/10.75 (((notinself) => 78.80/10.75 (((notinself2) => 78.80/10.75 (((omegaSp) => 78.80/10.75 (((omegaSclos) => 78.80/10.75 (((peano0notS) => 78.80/10.75 (((peanoSinj) => 78.80/10.75 (((transitivesetOp1) => 78.80/10.75 (((binintTransitive) => 78.80/10.75 (((transitivesetOp2) => 78.80/10.75 (((setunionTransitive) => 78.80/10.75 (((ordinalMinLem1) => 78.80/10.75 (((!!) @ (^[Y0 : $i]: 78.80/10.75 (((ordinal @ Y0) => 78.80/10.75 (((!!) @ (^[Y1 : $i]: 78.80/10.75 (((!!) @ ( 78.80/10.75 ^[Y2 : $i]: 78.80/10.75 (((in @ Y2 @ 78.80/10.75 Y0) => 78.80/10.75 (((in @ 78.80/10.75 Y1 @ 78.80/10.75 Y2) => 78.80/10.75 (in @ 78.80/10.75 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))), 78.80/10.75 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3126])). 78.80/10.75 thf(zip_derived_cl3148, plain, 78.80/10.75 (~ (((foundation2) => 78.80/10.75 (((notinself) => 78.80/10.75 (((notinself2) => 78.80/10.75 (((omegaSp) => 78.80/10.75 (((omegaSclos) => 78.80/10.75 (((peano0notS) => 78.80/10.75 (((peanoSinj) => 78.80/10.75 (((transitivesetOp1) => 78.80/10.75 (((binintTransitive) => 78.80/10.75 (((transitivesetOp2) => 78.80/10.75 (((setunionTransitive) => 78.80/10.75 (((ordinalMinLem1) => 78.80/10.75 (((!!) @ (^[Y0 : $i]: 78.80/10.75 (((ordinal @ Y0) => 78.80/10.75 (((!!) @ (^[Y1 : $i]: 78.80/10.75 (((!!) @ (^[Y2 : $i]: 78.80/10.75 (( 78.80/10.75 (in @ 78.80/10.75 Y2 @ 78.80/10.75 Y0) => 78.80/10.75 (( 78.80/10.75 (in @ 78.80/10.75 Y1 @ 78.80/10.75 Y2) => 78.80/10.75 (in @ 78.80/10.75 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))), 78.80/10.75 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3138])). 78.80/10.75 thf(zip_derived_cl3157, plain, 78.80/10.75 (~ (((notinself) => 78.80/10.75 (((notinself2) => 78.80/10.75 (((omegaSp) => 78.80/10.75 (((omegaSclos) => 78.80/10.75 (((peano0notS) => 78.80/10.75 (((peanoSinj) => 78.80/10.75 (((transitivesetOp1) => 78.80/10.75 (((binintTransitive) => 78.80/10.75 (((transitivesetOp2) => 78.80/10.75 (((setunionTransitive) => 78.80/10.75 (((ordinalMinLem1) => 78.80/10.75 (((!!) @ (^[Y0 : $i]: 78.80/10.75 (((ordinal @ Y0) => 78.80/10.75 (((!!) @ (^[Y1 : $i]: 78.80/10.75 (((!!) @ (^[Y2 : $i]: 78.80/10.75 (( 78.80/10.75 (in @ 78.80/10.75 Y2 @ 78.80/10.75 Y0) => 78.80/10.75 (( 78.80/10.75 (in @ 78.80/10.75 Y1 @ 78.80/10.75 Y2) => 78.80/10.75 (in @ 78.80/10.75 Y1 @ Y0))))))))))))))))))))))))))))))))))))))), 78.80/10.75 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3148])). 78.80/10.75 thf(zip_derived_cl3163, plain, 78.80/10.75 (~ (((notinself2) => 78.80/10.75 (((omegaSp) => 78.80/10.75 (((omegaSclos) => 78.80/10.75 (((peano0notS) => 78.80/10.75 (((peanoSinj) => 78.80/10.75 (((transitivesetOp1) => 78.80/10.75 (((binintTransitive) => 78.80/10.75 (((transitivesetOp2) => 78.80/10.75 (((setunionTransitive) => 78.80/10.75 (((ordinalMinLem1) => 78.80/10.75 (((!!) @ (^[Y0 : $i]: 78.80/10.75 (((ordinal @ Y0) => 78.80/10.75 (((!!) @ (^[Y1 : $i]: 78.80/10.75 (((!!) @ (^[Y2 : $i]: 78.80/10.75 (((in @ 78.80/10.75 Y2 @ 78.80/10.75 Y0) => 78.80/10.75 (( 78.80/10.75 (in @ 78.80/10.75 Y1 @ 78.80/10.75 Y2) => 78.80/10.75 (in @ 78.80/10.75 Y1 @ Y0))))))))))))))))))))))))))))))))))))), 78.80/10.75 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3157])). 78.80/10.75 thf(zip_derived_cl3170, plain, 78.80/10.75 (~ (((omegaSp) => 78.80/10.75 (((omegaSclos) => 78.80/10.75 (((peano0notS) => 78.80/10.75 (((peanoSinj) => 78.80/10.75 (((transitivesetOp1) => 78.80/10.75 (((binintTransitive) => 78.80/10.75 (((transitivesetOp2) => 78.80/10.75 (((setunionTransitive) => 78.80/10.75 (((ordinalMinLem1) => 78.80/10.75 (((!!) @ (^[Y0 : $i]: 78.80/10.75 (((ordinal @ Y0) => 78.80/10.75 (((!!) @ (^[Y1 : $i]: 78.80/10.75 (((!!) @ (^[Y2 : $i]: 78.80/10.75 (((in @ Y2 @ 78.80/10.75 Y0) => 78.80/10.75 (((in @ 78.80/10.75 Y1 @ 78.80/10.75 Y2) => 78.80/10.75 (in @ 78.80/10.75 Y1 @ Y0))))))))))))))))))))))))))))))))))), 78.80/10.75 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3163])). 78.80/10.75 thf(zip_derived_cl3177, plain, 78.80/10.75 (~ (((omegaSclos) => 78.80/10.75 (((peano0notS) => 78.80/10.75 (((peanoSinj) => 78.80/10.75 (((transitivesetOp1) => 78.80/10.75 (((binintTransitive) => 78.80/10.75 (((transitivesetOp2) => 78.80/10.75 (((setunionTransitive) => 78.80/10.75 (((ordinalMinLem1) => 78.80/10.75 (((!!) @ (^[Y0 : $i]: 78.80/10.75 (((ordinal @ Y0) => 78.80/10.75 (((!!) @ (^[Y1 : $i]: 78.80/10.75 (((!!) @ (^[Y2 : $i]: 78.80/10.75 (((in @ Y2 @ 78.80/10.75 Y0) => 78.80/10.75 (((in @ Y1 @ 78.80/10.75 Y2) => 78.80/10.75 (in @ Y1 @ 78.80/10.75 Y0))))))))))))))))))))))))))))))))), 78.80/10.75 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3170])). 78.80/10.75 thf(zip_derived_cl3185, plain, 78.80/10.75 (~ (((peano0notS) => 78.80/10.75 (((peanoSinj) => 78.80/10.75 (((transitivesetOp1) => 78.80/10.75 (((binintTransitive) => 78.80/10.75 (((transitivesetOp2) => 78.80/10.75 (((setunionTransitive) => 78.80/10.75 (((ordinalMinLem1) => 78.80/10.75 (((!!) @ (^[Y0 : $i]: 78.80/10.75 (((ordinal @ Y0) => 78.80/10.75 (((!!) @ (^[Y1 : $i]: 78.80/10.75 (((!!) @ (^[Y2 : $i]: 78.80/10.75 (((in @ Y2 @ 78.80/10.75 Y0) => 78.80/10.75 (((in @ Y1 @ 78.80/10.75 Y2) => (in @ 78.80/10.75 Y1 @ Y0))))))))))))))))))))))))))))))), 78.80/10.75 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3177])). 78.80/10.75 thf(zip_derived_cl3196, plain, 78.80/10.75 (~ (((peanoSinj) => 78.80/10.75 (((transitivesetOp1) => 78.80/10.75 (((binintTransitive) => 78.80/10.75 (((transitivesetOp2) => 78.80/10.75 (((setunionTransitive) => 78.80/10.75 (((ordinalMinLem1) => 78.80/10.75 (((!!) @ (^[Y0 : $i]: 78.80/10.75 (((ordinal @ Y0) => 78.80/10.75 (((!!) @ (^[Y1 : $i]: 78.80/10.75 (((!!) @ (^[Y2 : $i]: 78.80/10.75 (((in @ Y2 @ Y0) => 78.80/10.75 (((in @ Y1 @ 78.80/10.75 Y2) => (in @ 78.80/10.75 Y1 @ Y0))))))))))))))))))))))))))))), 78.80/10.75 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3185])). 78.80/10.75 thf(zip_derived_cl3205, plain, 78.80/10.75 (~ (((transitivesetOp1) => 78.80/10.75 (((binintTransitive) => 78.80/10.75 (((transitivesetOp2) => 78.80/10.75 (((setunionTransitive) => 78.80/10.75 (((ordinalMinLem1) => 78.80/10.75 (((!!) @ (^[Y0 : $i]: 78.80/10.75 (((ordinal @ Y0) => 78.80/10.75 (((!!) @ (^[Y1 : $i]: 78.80/10.75 (((!!) @ (^[Y2 : $i]: 78.80/10.75 (((in @ Y2 @ Y0) => 78.80/10.75 (((in @ Y1 @ Y2) => 78.80/10.75 (in @ Y1 @ Y0))))))))))))))))))))))))))), 78.80/10.75 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3196])). 78.80/10.75 thf(zip_derived_cl3211, plain, 78.80/10.75 (~ (((binintTransitive) => 78.80/10.75 (((transitivesetOp2) => 78.80/10.75 (((setunionTransitive) => 78.80/10.75 (((ordinalMinLem1) => 78.80/10.75 (((!!) @ (^[Y0 : $i]: 78.80/10.75 (((ordinal @ Y0) => 78.80/10.75 (((!!) @ (^[Y1 : $i]: 78.80/10.75 (((!!) @ (^[Y2 : $i]: 78.80/10.75 (((in @ Y2 @ Y0) => 78.80/10.75 (((in @ Y1 @ Y2) => 78.80/10.75 (in @ Y1 @ Y0))))))))))))))))))))))))), 78.80/10.75 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3205])). 78.80/10.75 thf(zip_derived_cl3217, plain, 78.80/10.75 (~ (((transitivesetOp2) => 78.80/10.75 (((setunionTransitive) => 78.80/10.75 (((ordinalMinLem1) => 78.80/10.75 (((!!) @ (^[Y0 : $i]: 78.80/10.75 (((ordinal @ Y0) => 78.80/10.75 (((!!) @ (^[Y1 : $i]: 78.80/10.75 (((!!) @ (^[Y2 : $i]: 78.80/10.75 (((in @ Y2 @ Y0) => 78.80/10.75 (((in @ Y1 @ Y2) => 78.80/10.75 (in @ Y1 @ Y0))))))))))))))))))))))), 78.80/10.75 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3211])). 78.80/10.75 thf(zip_derived_cl3225, plain, 78.80/10.75 (~ (((setunionTransitive) => 78.80/10.75 (((ordinalMinLem1) => 78.80/10.75 (((!!) @ (^[Y0 : $i]: 78.80/10.75 (((ordinal @ Y0) => 78.80/10.75 (((!!) @ (^[Y1 : $i]: 78.80/10.75 (((!!) @ (^[Y2 : $i]: 78.80/10.75 (((in @ Y2 @ Y0) => 78.80/10.75 (((in @ Y1 @ Y2) => (in @ 78.80/10.75 Y1 @ Y0))))))))))))))))))))), 78.80/10.75 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3217])). 78.80/10.75 thf(zip_derived_cl3232, plain, 78.80/10.75 (~ (((ordinalMinLem1) => 78.80/10.75 (((!!) @ (^[Y0 : $i]: 78.80/10.75 (((ordinal @ Y0) => 78.80/10.75 (((!!) @ (^[Y1 : $i]: 78.80/10.75 (((!!) @ (^[Y2 : $i]: 78.80/10.75 (((in @ Y2 @ Y0) => 78.80/10.75 (((in @ Y1 @ Y2) => (in @ 78.80/10.75 Y1 @ Y0))))))))))))))))))), 78.80/10.75 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3225])). 78.80/10.75 thf(zip_derived_cl3239, plain, 78.80/10.75 (~ (((!!) @ (^[Y0 : $i]: 78.80/10.75 (((ordinal @ Y0) => 78.80/10.75 (((!!) @ (^[Y1 : $i]: 78.80/10.75 (((!!) @ (^[Y2 : $i]: 78.80/10.75 (((in @ Y2 @ Y0) => 78.80/10.75 (((in @ Y1 @ Y2) => (in @ 78.80/10.75 Y1 @ Y0))))))))))))))))), 78.80/10.75 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3232])). 78.80/10.75 thf(zip_derived_cl3246, plain, 78.80/10.75 (~ (((ordinal @ '#sk1597') => 78.80/10.75 (((!!) @ (^[Y0 : $i]: 78.80/10.75 (((!!) @ (^[Y1 : $i]: 78.80/10.75 (((in @ Y1 @ '#sk1597') => 78.80/10.75 (((in @ Y0 @ Y1) => (in @ Y0 @ '#sk1597')))))))))))))), 78.80/10.75 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl3239])). 78.80/10.75 thf(zip_derived_cl3257, plain, 78.80/10.75 (~ (((!!) @ (^[Y0 : $i]: 78.80/10.75 (((!!) @ (^[Y1 : $i]: 78.80/10.75 (((in @ Y1 @ '#sk1597') => 78.80/10.75 (((in @ Y0 @ Y1) => (in @ Y0 @ '#sk1597')))))))))))), 78.80/10.75 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3246])). 78.80/10.75 thf(zip_derived_cl3269, plain, 78.80/10.75 (~ (((!!) @ (^[Y0 : $i]: 78.80/10.75 (((in @ Y0 @ '#sk1597') => 78.80/10.75 (((in @ '#sk1599' @ Y0) => (in @ '#sk1599' @ '#sk1597'))))))))), 78.80/10.75 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl3257])). 78.80/10.75 thf(zip_derived_cl3277, plain, 78.80/10.75 (~ (((in @ '#sk1600' @ '#sk1597') => 78.80/10.75 (((in @ '#sk1599' @ '#sk1600') => (in @ '#sk1599' @ '#sk1597')))))), 78.80/10.75 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl3269])). 78.80/10.75 thf(zip_derived_cl3285, plain, 78.80/10.75 (~ (((in @ '#sk1599' @ '#sk1600') => (in @ '#sk1599' @ '#sk1597')))), 78.80/10.75 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3277])). 78.80/10.75 thf(zip_derived_cl3294, plain, ( (in @ '#sk1599' @ '#sk1600')), 78.80/10.75 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3285])). 78.80/10.75 thf(zip_derived_cl3295, plain, (~ (in @ '#sk1599' @ '#sk1597')), 78.80/10.75 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3285])). 78.80/10.75 thf(zip_derived_cl3256, plain, ( (ordinal @ '#sk1597')), 78.80/10.75 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3246])). 78.80/10.75 thf(ordinal, axiom, (ordinal @ X0) => 78.80/10.75 ((((wellorderedByIn @ X0) & (transitiveset @ X0))) = ($true))). 78.80/10.75 thf('4', plain, 78.80/10.75 (![X0:$i]: 78.80/10.75 ( ( ordinal @ X0 ) <=> 78.80/10.75 ( ( transitiveset @ X0 ) & ( wellorderedByIn @ X0 ) ) )), 78.80/10.75 inference('rw.lit', [status(esa)], [ordinal])). 78.80/10.75 thf(zip_derived_cl3268, plain, 78.80/10.75 ( (((wellorderedByIn @ '#sk1597') & (transitiveset @ '#sk1597')))), 78.80/10.75 inference('rw_clause', [status(thm)], [zip_derived_cl3256, '4'])). 78.80/10.75 thf(zip_derived_cl3276, plain, ( (transitiveset @ '#sk1597')), 78.80/10.75 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl3268])). 78.80/10.75 thf(transitiveset, axiom, (transitiveset @ X0) => 78.80/10.75 ((((!!) @ (^[Y0 : $i]: (((in @ Y0 @ X0) => (subset @ Y0 @ X0)))))) = 78.80/10.75 ($true))). 78.80/10.75 thf('5', plain, 78.80/10.75 (![X0:$i]: 78.80/10.75 ( ( transitiveset @ X0 ) <=> 78.80/10.75 ( ![X5:$i]: ( ( in @ X5 @ X0 ) => ( subset @ X5 @ X0 ) ) ) )), 78.80/10.75 inference('rw.lit', [status(esa)], [transitiveset])). 78.80/10.75 thf(zip_derived_cl3283, plain, 78.80/10.75 ( (((!!) @ (^[Y0 : $i]: 78.80/10.75 (((in @ Y0 @ '#sk1597') => (subset @ Y0 @ '#sk1597'))))))), 78.80/10.75 inference('rw_clause', [status(thm)], [zip_derived_cl3276, '5'])). 78.80/10.75 thf(zip_derived_cl3210, plain, ( (transitivesetOp1)), 78.80/10.75 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3205])). 78.80/10.75 thf(transitivesetOp1, axiom, (transitivesetOp1) => 78.80/10.75 ((((!!) @ (^[Y0 : $i]: 78.80/10.75 (((transitiveset @ Y0) => 78.80/10.75 (((!!) @ (^[Y1 : $i]: 78.80/10.75 (((in @ Y1 @ Y0) => (subset @ Y1 @ Y0))))))))))) 78.80/10.75 = ($true))). 78.80/10.75 thf('6', plain, 78.80/10.75 (( transitivesetOp1 ) <=> 78.80/10.75 ( ![X5:$i]: 78.80/10.75 ( ( transitiveset @ X5 ) => 78.80/10.75 ( ![X7:$i]: ( ( in @ X7 @ X5 ) => ( subset @ X7 @ X5 ) ) ) ) )), 78.80/10.75 inference('rw.lit', [status(esa)], [transitivesetOp1])). 78.80/10.75 thf(zip_derived_cl3215, plain, 78.80/10.75 ( (((!!) @ (^[Y0 : $i]: 78.80/10.75 (((transitiveset @ Y0) => 78.80/10.75 (((!!) @ (^[Y1 : $i]: 78.80/10.75 (((in @ Y1 @ Y0) => (subset @ Y1 @ Y0)))))))))))), 78.80/10.75 inference('rw_clause', [status(thm)], [zip_derived_cl3210, '6'])). 78.80/10.75 thf(zip_derived_cl3222, plain, 78.80/10.75 (![X2 : $i]: 78.80/10.75 (((transitiveset @ X2) => 78.80/10.75 (((!!) @ (^[Y0 : $i]: (((in @ Y0 @ X2) => (subset @ Y0 @ X2))))))))), 78.80/10.75 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl3215])). 78.80/10.75 thf(zip_derived_cl3228, plain, 78.80/10.75 (![X2 : $i]: 78.80/10.75 (~ (transitiveset @ X2) 78.80/10.75 | (((!!) @ (^[Y0 : $i]: (((in @ Y0 @ X2) => (subset @ Y0 @ X2)))))))), 78.80/10.75 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3222])). 78.80/10.75 thf(transitiveset, axiom, ~ (transitiveset @ X0) => 78.80/10.75 ((((!!) @ (^[Y0 : $i]: (((in @ Y0 @ X0) => (subset @ Y0 @ X0)))))) != 78.80/10.75 ($true))). 78.80/10.75 thf('7', plain, 78.80/10.75 (![X0:$i]: 78.80/10.75 ( ( ~( transitiveset @ X0 ) ) <=> 78.80/10.75 ( ~( ![X5:$i]: ( ( in @ X5 @ X0 ) => ( subset @ X5 @ X0 ) ) ) ) )), 78.80/10.75 inference('rw.lit', [status(esa)], [transitiveset])). 78.80/10.75 thf(zip_derived_cl3234, plain, 78.80/10.75 (![X0 : $i]: 78.80/10.75 (~ (((!!) @ (^[Y0 : $i]: (((in @ Y0 @ X0) => (subset @ Y0 @ X0)))))) 78.80/10.75 | (((!!) @ (^[Y0 : $i]: (((in @ Y0 @ X0) => (subset @ Y0 @ X0)))))))), 78.80/10.75 inference('rw_clause', [status(thm)], [zip_derived_cl3228, '7'])). 78.80/10.75 thf(zip_derived_cl3241, plain, 78.80/10.75 (![X0 : $i]: 78.80/10.75 (~ (((in @ ('#sk337' @ X0 @ (^[Y0 : $i]: (subset @ Y0 @ X0))) @ X0) => 78.80/10.75 (subset @ ('#sk337' @ X0 @ (^[Y0 : $i]: (subset @ Y0 @ X0))) @ 78.80/10.75 X0))) 78.80/10.75 | (((!!) @ (^[Y0 : $i]: (((in @ Y0 @ X0) => (subset @ Y0 @ X0)))))))), 78.80/10.75 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl3234])). 78.80/10.75 thf(zip_derived_cl3248, plain, 78.80/10.75 (![X0 : $i]: 78.80/10.75 ( (in @ ('#sk337' @ X0 @ (^[Y0 : $i]: (subset @ Y0 @ X0))) @ X0) 78.80/10.75 | (((!!) @ (^[Y0 : $i]: (((in @ Y0 @ X0) => (subset @ Y0 @ X0)))))))), 78.80/10.75 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3241])). 78.80/10.75 thf(zip_derived_cl3258, plain, 78.80/10.75 (![X0 : $i]: 78.80/10.75 (~ ('#form1598' @ X0) 78.80/10.75 | (((!!) @ (^[Y0 : $i]: (((in @ Y0 @ X0) => (subset @ Y0 @ X0)))))))), 78.80/10.75 define([status(thm)])). 78.80/10.75 thf(zip_derived_cl3216, plain, ( (binintTransitive)), 78.80/10.75 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3211])). 78.80/10.75 thf(binintTransitive, axiom, (binintTransitive) => 78.80/10.75 ((((!!) @ (^[Y0 : $i]: 78.80/10.75 (((transitiveset @ Y0) => 78.80/10.75 (((!!) @ (^[Y1 : $i]: 78.80/10.75 (((transitiveset @ Y1) => (transitiveset @ 78.80/10.75 (binintersect @ Y0 @ Y1)))))))))))) 78.80/10.75 = ($true))). 78.80/10.75 thf('8', plain, 78.80/10.75 (( binintTransitive ) <=> 78.80/10.75 ( ![X5:$i]: 78.80/10.75 ( ( transitiveset @ X5 ) => 78.80/10.75 ( ![X7:$i]: 78.80/10.75 ( ( transitiveset @ X7 ) => 78.80/10.75 ( transitiveset @ ( binintersect @ X5 @ X7 ) ) ) ) ) )), 78.80/10.75 inference('rw.lit', [status(esa)], [binintTransitive])). 78.80/10.75 thf(zip_derived_cl3223, plain, 78.80/10.75 ( (((!!) @ (^[Y0 : $i]: 78.80/10.75 (((transitiveset @ Y0) => 78.80/10.75 (((!!) @ (^[Y1 : $i]: 78.80/10.75 (((transitiveset @ Y1) => (transitiveset @ 78.80/10.75 (binintersect @ Y0 @ Y1))))))))))))), 78.80/10.75 inference('rw_clause', [status(thm)], [zip_derived_cl3216, '8'])). 78.80/10.75 thf(zip_derived_cl3229, plain, 78.80/10.75 (![X2 : $i]: 78.80/10.75 (((transitiveset @ X2) => 78.80/10.75 (((!!) @ (^[Y0 : $i]: 78.80/10.75 (((transitiveset @ Y0) => (transitiveset @ 78.80/10.75 (binintersect @ X2 @ Y0)))))))))), 78.80/10.75 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl3223])). 78.80/10.75 thf(zip_derived_cl3235, plain, 78.80/10.75 (![X2 : $i]: 78.80/10.75 (~ (transitiveset @ X2) 78.80/10.75 | (((!!) @ (^[Y0 : $i]: 78.80/10.75 (((transitiveset @ Y0) => (transitiveset @ 78.80/10.75 (binintersect @ X2 @ Y0))))))))), 78.80/10.75 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3229])). 78.80/10.75 thf(zip_derived_cl3242, plain, 78.80/10.75 (![X0 : $i]: 78.80/10.75 (~ (((!!) @ (^[Y0 : $i]: (((in @ Y0 @ X0) => (subset @ Y0 @ X0)))))) 78.80/10.75 | (((!!) @ (^[Y0 : $i]: 78.80/10.75 (((transitiveset @ Y0) => (transitiveset @ 78.80/10.75 (binintersect @ X0 @ Y0))))))))), 78.80/10.75 inference('rw_clause', [status(thm)], [zip_derived_cl3235, '7'])). 78.80/10.75 thf(zip_derived_cl3250, plain, 78.80/10.75 (![X0 : $i]: 78.80/10.75 ( ('#form1598' @ X0) 78.80/10.75 | ~ (((!!) @ (^[Y0 : $i]: (((in @ Y0 @ X0) => (subset @ Y0 @ X0)))))))), 78.80/10.75 define([status(thm)])). 78.80/10.75 thf(zip_derived_cl3293, plain, ( ('#form1598' @ '#sk1597')), 78.80/10.75 inference('renaming', [status(thm)], 78.80/10.75 [zip_derived_cl3283, zip_derived_cl3258, zip_derived_cl3250])). 78.80/10.75 thf(zip_derived_cl3284, plain, ( (in @ '#sk1600' @ '#sk1597')), 78.80/10.75 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3277])). 78.80/10.75 thf(zip_derived_cl3224, plain, ( (transitivesetOp2)), 78.80/10.75 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3217])). 78.80/10.75 thf(transitivesetOp2, axiom, (transitivesetOp2) => 78.80/10.75 ((((!!) @ (^[Y0 : $i]: 78.80/10.75 (((transitiveset @ Y0) => 78.80/10.75 (((!!) @ (^[Y1 : $i]: 78.80/10.75 (((!!) @ (^[Y2 : $i]: 78.80/10.75 (((in @ Y1 @ Y0) => 78.80/10.75 (((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))))))))))))))) 78.80/10.75 = ($true))). 78.80/10.75 thf('9', plain, 78.80/10.75 (( transitivesetOp2 ) <=> 78.80/10.75 ( ![X5:$i]: 78.80/10.75 ( ( transitiveset @ X5 ) => 78.80/10.75 ( ![X7:$i,X9:$i]: 78.80/10.75 ( ( in @ X7 @ X5 ) => ( ( in @ X9 @ X7 ) => ( in @ X9 @ X5 ) ) ) ) ) )), 78.80/10.75 inference('rw.lit', [status(esa)], [transitivesetOp2])). 78.80/10.75 thf(zip_derived_cl3230, plain, 78.80/10.75 ( (((!!) @ (^[Y0 : $i]: 78.80/10.75 (((transitiveset @ Y0) => 78.80/10.75 (((!!) @ (^[Y1 : $i]: 78.80/10.75 (((!!) @ (^[Y2 : $i]: 78.80/10.75 (((in @ Y1 @ Y0) => 78.80/10.75 (((in @ Y2 @ Y1) => (in @ Y2 @ 78.80/10.75 Y0))))))))))))))))), 78.80/10.75 inference('rw_clause', [status(thm)], [zip_derived_cl3224, '9'])). 78.80/10.75 thf(zip_derived_cl3236, plain, 78.80/10.75 (![X2 : $i]: 78.80/10.75 (((transitiveset @ X2) => 78.80/10.75 (((!!) @ (^[Y0 : $i]: 78.80/10.75 (((!!) @ (^[Y1 : $i]: 78.80/10.75 (((in @ Y0 @ X2) => 78.80/10.75 (((in @ Y1 @ Y0) => (in @ Y1 @ X2)))))))))))))), 78.80/10.75 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl3230])). 78.80/10.75 thf(zip_derived_cl3243, plain, 78.80/10.75 (![X2 : $i]: 78.80/10.75 (~ (transitiveset @ X2) 78.80/10.75 | (((!!) @ (^[Y0 : $i]: 78.80/10.75 (((!!) @ (^[Y1 : $i]: 78.80/10.75 (((in @ Y0 @ X2) => 78.80/10.75 (((in @ Y1 @ Y0) => (in @ Y1 @ X2))))))))))))), 78.80/10.75 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3236])). 78.80/10.75 thf(zip_derived_cl3253, plain, 78.80/10.75 (![X0 : $i]: 78.80/10.75 (~ (((!!) @ (^[Y0 : $i]: (((in @ Y0 @ X0) => (subset @ Y0 @ X0)))))) 78.80/10.75 | (((!!) @ (^[Y0 : $i]: 78.80/10.75 (((!!) @ (^[Y1 : $i]: 78.80/10.75 (((in @ Y0 @ X0) => 78.80/10.75 (((in @ Y1 @ Y0) => (in @ Y1 @ X0))))))))))))), 78.80/10.75 inference('rw_clause', [status(thm)], [zip_derived_cl3243, '7'])). 78.80/10.75 thf(zip_derived_cl3258, plain, 78.80/10.75 (![X0 : $i]: 78.80/10.75 (~ ('#form1598' @ X0) 78.80/10.75 | (((!!) @ (^[Y0 : $i]: (((in @ Y0 @ X0) => (subset @ Y0 @ X0)))))))), 78.80/10.75 define([status(thm)])). 78.80/10.75 thf(zip_derived_cl3250, plain, 78.80/10.75 (![X0 : $i]: 78.80/10.75 ( ('#form1598' @ X0) 78.80/10.75 | ~ (((!!) @ (^[Y0 : $i]: (((in @ Y0 @ X0) => (subset @ Y0 @ X0)))))))), 78.80/10.75 define([status(thm)])). 78.80/10.75 thf(zip_derived_cl3265, plain, 78.80/10.75 (![X0 : $i]: 78.80/10.75 (~ ('#form1598' @ X0) 78.80/10.75 | (((!!) @ (^[Y0 : $i]: 78.80/10.75 (((!!) @ (^[Y1 : $i]: 78.80/10.75 (((in @ Y0 @ X0) => 78.80/10.75 (((in @ Y1 @ Y0) => (in @ Y1 @ X0))))))))))))), 78.80/10.75 inference('renaming', [status(thm)], 78.80/10.75 [zip_derived_cl3253, zip_derived_cl3258, zip_derived_cl3250])). 78.80/10.75 thf(zip_derived_cl3272, plain, 78.80/10.75 (![X0 : $i, X2 : $i]: 78.80/10.75 ( (((!!) @ (^[Y0 : $i]: 78.80/10.75 (((in @ X2 @ X0) => (((in @ Y0 @ X2) => (in @ Y0 @ X0)))))))) 78.80/10.75 | ~ ('#form1598' @ X0))), 78.80/10.75 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl3265])). 78.80/10.75 thf(zip_derived_cl3279, plain, 78.80/10.75 (![X0 : $i, X2 : $i, X4 : $i]: 78.80/10.75 ( (((in @ X2 @ X0) => (((in @ X4 @ X2) => (in @ X4 @ X0))))) 78.80/10.75 | ~ ('#form1598' @ X0))), 78.80/10.75 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl3272])). 78.80/10.75 thf(zip_derived_cl3287, plain, 78.80/10.75 (![X0 : $i, X2 : $i, X4 : $i]: 78.80/10.75 (~ (in @ X2 @ X0) 78.80/10.75 | (((in @ X4 @ X2) => (in @ X4 @ X0))) 78.80/10.75 | ~ ('#form1598' @ X0))), 78.80/10.75 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3279])). 78.80/10.75 thf(zip_derived_cl3297, plain, 78.80/10.75 (![X0 : $i, X2 : $i, X4 : $i]: 78.80/10.75 (~ (in @ X4 @ X2) 78.80/10.75 | (in @ X4 @ X0) 78.80/10.75 | ~ ('#form1598' @ X0) 78.80/10.75 | ~ (in @ X2 @ X0))), 78.80/10.75 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3287])). 78.80/10.75 thf(zip_derived_cl10795, plain, ($false), 78.80/10.75 inference('eprover', [status(thm)], 78.80/10.75 [zip_derived_cl3294, zip_derived_cl3295, zip_derived_cl3293, 78.80/10.75 zip_derived_cl3284, zip_derived_cl3297])). 78.80/10.75 78.80/10.75 % SZS output end Refutation 78.80/10.75 78.80/10.75 78.80/10.75 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif.sh running for 33s 78.80/10.75 % Terminating... 79.58/10.92 % Runner terminated. 79.58/10.93 % Zipperpin 1.5 exiting 79.58/10.95 EOF