%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SEU745^1 : TPTP v9.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.Ur5dqrBkGW true
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Oct 2 04:56:05 PM UTC 2025
% Result : Theorem 1.03s 1.14s
% Output : Refutation 1.03s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SEU745^1 : TPTP v9.2.0. Released v3.7.0.
% 0.07/0.14 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.Ur5dqrBkGW true
% 0.12/0.33 % Computer : n013.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Wed Oct 1 16:09:53 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.12/0.34 % Running portfolio for 300 s
% 0.12/0.34 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.34 % Number of cores: 8
% 0.12/0.34 % Python version: Python 3.6.8
% 0.12/0.34 % Running in HO mode
% 0.54/0.60 % Total configuration time : 828
% 0.54/0.60 % Estimated wc time : 1656
% 0.54/0.60 % Estimated cpu time (8 cpus) : 207.0
% 0.73/0.69 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
% 0.73/0.69 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
% 0.73/0.69 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.73/0.70 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
% 0.73/0.70 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s
% 0.73/0.70 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.73/0.70 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s
% 0.73/0.72 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s
% 1.03/1.14 % Solved by lams/40_c_ic.sh.
% 1.03/1.14 % done 361 iterations in 0.313s
% 1.03/1.14 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 1.03/1.14 % SZS output start Refutation
% 1.03/1.14 thf(setadjoinAx_type, type, setadjoinAx: $o).
% 1.03/1.14 thf(notdexE_type, type, notdexE: $o).
% 1.03/1.14 thf(setukpairinjL2_type, type, setukpairinjL2: $o).
% 1.03/1.14 thf(doubleComplementI1_type, type, doubleComplementI1: $o).
% 1.03/1.14 thf(setunionAx_type, type, setunionAx: $o).
% 1.03/1.14 thf(setminusELneg_type, type, setminusELneg: $o).
% 1.03/1.14 thf(cartprodsndin_type, type, cartprodsndin: $o).
% 1.03/1.14 thf(ex1E1_type, type, ex1E1: $o).
% 1.03/1.14 thf(powersetE_type, type, powersetE: $o).
% 1.03/1.14 thf(sk__181_type, type, sk__181: $i).
% 1.03/1.14 thf(omegaSAx_type, type, omegaSAx: $o).
% 1.03/1.14 thf(exuI1_type, type, exuI1: $o).
% 1.03/1.14 thf(exuI2_type, type, exuI2: $o).
% 1.03/1.14 thf(notequalI2_type, type, notequalI2: $o).
% 1.03/1.14 thf(setukpairinjL_type, type, setukpairinjL: $o).
% 1.03/1.14 thf(kpairiskpair_type, type, kpairiskpair: $o).
% 1.03/1.14 thf(upairsubunion_type, type, upairsubunion: $o).
% 1.03/1.14 thf(funcGraphProp3_type, type, funcGraphProp3: $o).
% 1.03/1.14 thf(cartprodmempaircEq_type, type, cartprodmempaircEq: $o).
% 1.03/1.14 thf(binintersectTERcontra_type, type, binintersectTERcontra: $o).
% 1.03/1.14 thf(powerset__Cong_type, type, powerset__Cong: $o).
% 1.03/1.14 thf(setminusILneg_type, type, setminusILneg: $o).
% 1.03/1.14 thf(wellorderingAx_type, type, wellorderingAx: $o).
% 1.03/1.14 thf(ksndpairEq_type, type, ksndpairEq: $o).
% 1.03/1.14 thf(funcGraphProp2_type, type, funcGraphProp2: $o).
% 1.03/1.14 thf(setadjoinSub2_type, type, setadjoinSub2: $o).
% 1.03/1.14 thf(binintersectSubset5_type, type, binintersectSubset5: $o).
% 1.03/1.14 thf(iftrue_type, type, iftrue: $o).
% 1.03/1.14 thf(upairinpowunion_type, type, upairinpowunion: $o).
% 1.03/1.14 thf(ifSingleton_type, type, ifSingleton: $o).
% 1.03/1.14 thf(doubleComplementSub2_type, type, doubleComplementSub2: $o).
% 1.03/1.14 thf(setoftrueEq_type, type, setoftrueEq: $o).
% 1.03/1.14 thf(funcImageSingleton_type, type, funcImageSingleton: $o).
% 1.03/1.14 thf(inIntersectImpInUnion2_type, type, inIntersectImpInUnion2: $o).
% 1.03/1.14 thf(dpsetconstrERa_type, type, dpsetconstrERa: $o).
% 1.03/1.14 thf(lamProp_type, type, lamProp: $o).
% 1.03/1.14 thf(cartprodpairmemEL_type, type, cartprodpairmemEL: $o).
% 1.03/1.14 thf(emptyset__Cong_type, type, emptyset__Cong: $o).
% 1.03/1.14 thf(sk__180_type, type, sk__180: $i).
% 1.03/1.14 thf(dpsetconstrER_type, type, dpsetconstrER: $o).
% 1.03/1.14 thf(sepInPowerset_type, type, sepInPowerset: $o).
% 1.03/1.14 thf(setukpairIR_type, type, setukpairIR: $o).
% 1.03/1.14 thf(setukpairinjR1_type, type, setukpairinjR1: $o).
% 1.03/1.14 thf(lam2p_type, type, lam2p: $o).
% 1.03/1.14 thf(kpair_type, type, kpair: $i > $i > $i).
% 1.03/1.14 thf(binunionE_type, type, binunionE: $o).
% 1.03/1.14 thf(setext_type, type, setext: $o).
% 1.03/1.14 thf(emptyinPowerset_type, type, emptyinPowerset: $o).
% 1.03/1.14 thf(ubforcartprodlem1_type, type, ubforcartprodlem1: $o).
% 1.03/1.14 thf(descr__Cong_type, type, descr__Cong: $o).
% 1.03/1.14 thf(kfstsingleton_type, type, kfstsingleton: $o).
% 1.03/1.14 thf(binintersectTELcontra_type, type, binintersectTELcontra: $o).
% 1.03/1.14 thf(doubleComplementEq_type, type, doubleComplementEq: $o).
% 1.03/1.14 thf(eqbreln_type, type, eqbreln: $o).
% 1.03/1.14 thf(binintersectSubset1_type, type, binintersectSubset1: $o).
% 1.03/1.14 thf(complementImpComplementIntersect_type, type, complementImpComplementIntersect:
% 1.03/1.14 $o).
% 1.03/1.14 thf(in_type, type, in: $i > $i > $o).
% 1.03/1.14 thf(binunionT_lem_type, type, binunionT_lem: $o).
% 1.03/1.14 thf(quantDeMorgan1_type, type, quantDeMorgan1: $o).
% 1.03/1.14 thf(complementT_lem_type, type, complementT_lem: $o).
% 1.03/1.14 thf(binunion_type, type, binunion: $i > $i > $i).
% 1.03/1.14 thf(kpairsurjEq_type, type, kpairsurjEq: $o).
% 1.03/1.14 thf(setadjoinIR_type, type, setadjoinIR: $o).
% 1.03/1.14 thf(doubleComplementE1_type, type, doubleComplementE1: $o).
% 1.03/1.14 thf(beta1_type, type, beta1: $o).
% 1.03/1.14 thf(setadjoin__Cong_type, type, setadjoin__Cong: $o).
% 1.03/1.14 thf(powersetTE1_type, type, powersetTE1: $o).
% 1.03/1.14 thf(symdiffI2_type, type, symdiffI2: $o).
% 1.03/1.14 thf(iftrueProp2_type, type, iftrueProp2: $o).
% 1.03/1.14 thf(upairset2IR_type, type, upairset2IR: $o).
% 1.03/1.14 thf(iffalseProp2_type, type, iffalseProp2: $o).
% 1.03/1.14 thf(subsetE_type, type, subsetE: $o).
% 1.03/1.14 thf(prop2set2propI_type, type, prop2set2propI: $o).
% 1.03/1.14 thf(dsetconstrEL_type, type, dsetconstrEL: $o).
% 1.03/1.14 thf(setbeta_type, type, setbeta: $o).
% 1.03/1.14 thf(eqinunit_type, type, eqinunit: $o).
% 1.03/1.14 thf(upairsetIL_type, type, upairsetIL: $o).
% 1.03/1.14 thf(powersetI1_type, type, powersetI1: $o).
% 1.03/1.14 thf(kfstpairEq_type, type, kfstpairEq: $o).
% 1.03/1.14 thf(binintersectSubset3_type, type, binintersectSubset3: $o).
% 1.03/1.14 thf(inComplementUnionImpNotIn1_type, type, inComplementUnionImpNotIn1: $o).
% 1.03/1.14 thf(setminusIRneg_type, type, setminusIRneg: $o).
% 1.03/1.14 thf(ap2apEq1_type, type, ap2apEq1: $o).
% 1.03/1.14 thf(powersetAx_type, type, powersetAx: $o).
% 1.03/1.14 thf(binintersectSubset4_type, type, binintersectSubset4: $o).
% 1.03/1.14 thf(singletoninpowunion_type, type, singletoninpowunion: $o).
% 1.03/1.14 thf(binunionTIRcontra_type, type, binunionTIRcontra: $o).
% 1.03/1.14 thf(powersetI_type, type, powersetI: $o).
% 1.03/1.14 thf(cartprodmempair_type, type, cartprodmempair: $o).
% 1.03/1.14 thf(upairsetIR_type, type, upairsetIR: $o).
% 1.03/1.14 thf(lamp_type, type, lamp: $o).
% 1.03/1.14 thf(dpsetconstrEL1_type, type, dpsetconstrEL1: $o).
% 1.03/1.14 thf(inCongP_type, type, inCongP: $o).
% 1.03/1.14 thf(setadjoinSub_type, type, setadjoinSub: $o).
% 1.03/1.14 thf(exuE3e_type, type, exuE3e: $o).
% 1.03/1.14 thf(emptysetE_type, type, emptysetE: $o).
% 1.03/1.14 thf(binintersectSubset2_type, type, binintersectSubset2: $o).
% 1.03/1.14 thf(setunionI_type, type, setunionI: $o).
% 1.03/1.14 thf(setunion__Cong_type, type, setunion__Cong: $o).
% 1.03/1.14 thf(prop2setI_type, type, prop2setI: $o).
% 1.03/1.14 thf(singletonsuniq_type, type, singletonsuniq: $o).
% 1.03/1.14 thf(nonemptyImpWitness_type, type, nonemptyImpWitness: $o).
% 1.03/1.14 thf(setminusER_type, type, setminusER: $o).
% 1.03/1.14 thf(exuE2_type, type, exuE2: $o).
% 1.03/1.14 thf(emptyset_type, type, emptyset: $i).
% 1.03/1.14 thf(setukpairinjR11_type, type, setukpairinjR11: $o).
% 1.03/1.14 thf(ex1I_type, type, ex1I: $o).
% 1.03/1.14 thf(ex1E2_type, type, ex1E2: $o).
% 1.03/1.14 thf(setminus_type, type, setminus: $i > $i > $i).
% 1.03/1.14 thf(setukpairinjL1_type, type, setukpairinjL1: $o).
% 1.03/1.14 thf(powersetsubset_type, type, powersetsubset: $o).
% 1.03/1.14 thf(binunionTILcontra_type, type, binunionTILcontra: $o).
% 1.03/1.14 thf(subPowSU_type, type, subPowSU: $o).
% 1.03/1.14 thf(notequalI1_type, type, notequalI1: $o).
% 1.03/1.14 thf(contrasubsetT_type, type, contrasubsetT: $o).
% 1.03/1.14 thf(notinemptyset_type, type, notinemptyset: $o).
% 1.03/1.14 thf(lam2lamEq_type, type, lam2lamEq: $o).
% 1.03/1.14 thf(nonemptyI1_type, type, nonemptyI1: $o).
% 1.03/1.14 thf(subsetTrans_type, type, subsetTrans: $o).
% 1.03/1.14 thf(kpairp_type, type, kpairp: $o).
% 1.03/1.14 thf(setukpairinjR12_type, type, setukpairinjR12: $o).
% 1.03/1.14 thf(setminusI_type, type, setminusI: $o).
% 1.03/1.14 thf(binunionIL_type, type, binunionIL: $o).
% 1.03/1.14 thf(dpsetconstrSub_type, type, dpsetconstrSub: $o).
% 1.03/1.14 thf(setunionsingleton_type, type, setunionsingleton: $o).
% 1.03/1.14 thf(subsetE2_type, type, subsetE2: $o).
% 1.03/1.14 thf(singletonsswitch_type, type, singletonsswitch: $o).
% 1.03/1.14 thf(ubforcartprodlem3_type, type, ubforcartprodlem3: $o).
% 1.03/1.14 thf(beta2_type, type, beta2: $o).
% 1.03/1.14 thf(dpsetconstrI_type, type, dpsetconstrI: $o).
% 1.03/1.14 thf(setextsub_type, type, setextsub: $o).
% 1.03/1.14 thf(binunionLsub_type, type, binunionLsub: $o).
% 1.03/1.14 thf(setunionsingleton1_type, type, setunionsingleton1: $o).
% 1.03/1.14 thf(binintersect_type, type, binintersect: $i > $i > $i).
% 1.03/1.14 thf(sk__178_type, type, sk__178: $i).
% 1.03/1.14 thf(iftrueorfalse_type, type, iftrueorfalse: $o).
% 1.03/1.14 thf(emptysetsubset_type, type, emptysetsubset: $o).
% 1.03/1.14 thf(quantDeMorgan3_type, type, quantDeMorgan3: $o).
% 1.03/1.14 thf(cartprodpairsurjEq_type, type, cartprodpairsurjEq: $o).
% 1.03/1.14 thf(setOfPairsIsBReln_type, type, setOfPairsIsBReln: $o).
% 1.03/1.14 thf(setunionE_type, type, setunionE: $o).
% 1.03/1.14 thf(ksndsingleton_type, type, ksndsingleton: $o).
% 1.03/1.14 thf(setminusSubset1_type, type, setminusSubset1: $o).
% 1.03/1.14 thf(powersetT_lem_type, type, powersetT_lem: $o).
% 1.03/1.14 thf(emptyinunitempty_type, type, emptyinunitempty: $o).
% 1.03/1.14 thf(binunionIR_type, type, binunionIR: $o).
% 1.03/1.14 thf(theeq_type, type, theeq: $o).
% 1.03/1.14 thf(setadjoinE_type, type, setadjoinE: $o).
% 1.03/1.14 thf(doubleComplementSub1_type, type, doubleComplementSub1: $o).
% 1.03/1.14 thf(infuncsetfunc_type, type, infuncsetfunc: $o).
% 1.03/1.14 thf(ap2apEq2_type, type, ap2apEq2: $o).
% 1.03/1.14 thf(ap2p_type, type, ap2p: $o).
% 1.03/1.14 thf(setadjoinIL_type, type, setadjoinIL: $o).
% 1.03/1.14 thf(cartprodsndpairEq_type, type, cartprodsndpairEq: $o).
% 1.03/1.14 thf(exuE1_type, type, exuE1: $o).
% 1.03/1.14 thf(ubforcartprodlem2_type, type, ubforcartprodlem2: $o).
% 1.03/1.14 thf(binintersectRsub_type, type, binintersectRsub: $o).
% 1.03/1.14 thf(setminusLsub_type, type, setminusLsub: $o).
% 1.03/1.14 thf(funcextLem_type, type, funcextLem: $o).
% 1.03/1.14 thf(setukpairinjR_type, type, setukpairinjR: $o).
% 1.03/1.14 thf(notinsingleton_type, type, notinsingleton: $o).
% 1.03/1.14 thf(inIntersectImpInIntersectUnions_type, type, inIntersectImpInIntersectUnions:
% 1.03/1.14 $o).
% 1.03/1.14 thf(eqimpsubset2_type, type, eqimpsubset2: $o).
% 1.03/1.14 thf(exuEu_type, type, exuEu: $o).
% 1.03/1.14 thf(emptysetimpfalse_type, type, emptysetimpfalse: $o).
% 1.03/1.14 thf(upairsetE_type, type, upairsetE: $o).
% 1.03/1.14 thf(omega0Ax_type, type, omega0Ax: $o).
% 1.03/1.14 thf(subsetTI_type, type, subsetTI: $o).
% 1.03/1.14 thf(notsubsetI_type, type, notsubsetI: $o).
% 1.03/1.14 thf(contraSubsetComplement_type, type, contraSubsetComplement: $o).
% 1.03/1.14 thf(sk__179_type, type, sk__179: $i).
% 1.03/1.14 thf(iffalseProp1_type, type, iffalseProp1: $o).
% 1.03/1.14 thf(quantDeMorgan4_type, type, quantDeMorgan4: $o).
% 1.03/1.14 thf(setextAx_type, type, setextAx: $o).
% 1.03/1.14 thf(cartprodpairmemER_type, type, cartprodpairmemER: $o).
% 1.03/1.14 thf(powersetE1_type, type, powersetE1: $o).
% 1.03/1.14 thf(bs114d_type, type, bs114d: $o).
% 1.03/1.14 thf(contrasubsetT3_type, type, contrasubsetT3: $o).
% 1.03/1.14 thf(noeltsimpempty_type, type, noeltsimpempty: $o).
% 1.03/1.14 thf(complementTcontraSubset_type, type, complementTcontraSubset: $o).
% 1.03/1.14 thf(ifp_type, type, ifp: $o).
% 1.03/1.14 thf(inIntersectImpInUnion_type, type, inIntersectImpInUnion: $o).
% 1.03/1.14 thf(powersetTI1_type, type, powersetTI1: $o).
% 1.03/1.14 thf(binintersectLsub_type, type, binintersectLsub: $o).
% 1.03/1.14 thf(subsetI1_type, type, subsetI1: $o).
% 1.03/1.14 thf(symdiffE_type, type, symdiffE: $o).
% 1.03/1.14 thf(descrp_type, type, descrp: $o).
% 1.03/1.14 thf(dsetconstr__Cong_type, type, dsetconstr__Cong: $o).
% 1.03/1.14 thf(foundationAx_type, type, foundationAx: $o).
% 1.03/1.14 thf(emptysetAx_type, type, emptysetAx: $o).
% 1.03/1.14 thf(emptyI_type, type, emptyI: $o).
% 1.03/1.14 thf(setadjoinOr_type, type, setadjoinOr: $o).
% 1.03/1.14 thf(eta2_type, type, eta2: $o).
% 1.03/1.14 thf(binintersectEL_type, type, binintersectEL: $o).
% 1.03/1.14 thf(emptyE1_type, type, emptyE1: $o).
% 1.03/1.14 thf(emptyInPowerset_type, type, emptyInPowerset: $o).
% 1.03/1.14 thf(complementTI1_type, type, complementTI1: $o).
% 1.03/1.14 thf(vacuousDall_type, type, vacuousDall: $o).
% 1.03/1.14 thf(dsetconstrER_type, type, dsetconstrER: $o).
% 1.03/1.14 thf(binintersectI_type, type, binintersectI: $o).
% 1.03/1.14 thf(funcext_type, type, funcext: $o).
% 1.03/1.14 thf(funcGraphProp4_type, type, funcGraphProp4: $o).
% 1.03/1.14 thf(cartprodpairin_type, type, cartprodpairin: $o).
% 1.03/1.14 thf(cartprodmempair1_type, type, cartprodmempair1: $o).
% 1.03/1.14 thf(zip_tseitin_0_type, type, zip_tseitin_0: $i > $i > $i > $o).
% 1.03/1.14 thf(brelnall2_type, type, brelnall2: $o).
% 1.03/1.14 thf(setextT_type, type, setextT: $o).
% 1.03/1.14 thf(ex1I2_type, type, ex1I2: $o).
% 1.03/1.14 thf(symdiffI1_type, type, symdiffI1: $o).
% 1.03/1.14 thf(setukpairinjR2_type, type, setukpairinjR2: $o).
% 1.03/1.14 thf(dpsetconstrEL2_type, type, dpsetconstrEL2: $o).
% 1.03/1.14 thf(theprop_type, type, theprop: $o).
% 1.03/1.14 thf(subsetI2_type, type, subsetI2: $o).
% 1.03/1.14 thf(complementInPowersetComplementIntersect_type, type, complementInPowersetComplementIntersect:
% 1.03/1.14 $o).
% 1.03/1.14 thf(setminusT_lem_type, type, setminusT_lem: $o).
% 1.03/1.14 thf(symdiffIneg1_type, type, symdiffIneg1: $o).
% 1.03/1.14 thf(setminusERneg_type, type, setminusERneg: $o).
% 1.03/1.14 thf(symdiffIneg2_type, type, symdiffIneg2: $o).
% 1.03/1.14 thf(omega__Cong_type, type, omega__Cong: $o).
% 1.03/1.14 thf(subsetRefl_type, type, subsetRefl: $o).
% 1.03/1.14 thf(uniqinunit_type, type, uniqinunit: $o).
% 1.03/1.14 thf(complementSubsetComplementIntersect_type, type, complementSubsetComplementIntersect:
% 1.03/1.14 $o).
% 1.03/1.14 thf(setminusSubset2_type, type, setminusSubset2: $o).
% 1.03/1.14 thf(prop2setE_type, type, prop2setE: $o).
% 1.03/1.14 thf(binunionEcases_type, type, binunionEcases: $o).
% 1.03/1.14 thf(funcinfuncset_type, type, funcinfuncset: $o).
% 1.03/1.14 thf(complementTE1_type, type, complementTE1: $o).
% 1.03/1.14 thf(nonemptyI_type, type, nonemptyI: $o).
% 1.03/1.14 thf(app_type, type, app: $o).
% 1.03/1.14 thf(disjointsetsI1_type, type, disjointsetsI1: $o).
% 1.03/1.14 thf(exuE3u_type, type, exuE3u: $o).
% 1.03/1.14 thf(eta1_type, type, eta1: $o).
% 1.03/1.14 thf(setminusEL_type, type, setminusEL: $o).
% 1.03/1.14 thf(cartprodfstin_type, type, cartprodfstin: $o).
% 1.03/1.14 thf(setunionsingleton2_type, type, setunionsingleton2: $o).
% 1.03/1.14 thf(sepSubset_type, type, sepSubset: $o).
% 1.03/1.14 thf(complementTnotintersectT_type, type, complementTnotintersectT: $o).
% 1.03/1.14 thf(upairset2E_type, type, upairset2E: $o).
% 1.03/1.14 thf(eqimpsubset1_type, type, eqimpsubset1: $o).
% 1.03/1.14 thf(exuI3_type, type, exuI3: $o).
% 1.03/1.14 thf(cartprodfstpairEq_type, type, cartprodfstpairEq: $o).
% 1.03/1.14 thf(apProp_type, type, apProp: $o).
% 1.03/1.14 thf(notdallE_type, type, notdallE: $o).
% 1.03/1.14 thf(iftrueProp1_type, type, iftrueProp1: $o).
% 1.03/1.14 thf(binintersectER_type, type, binintersectER: $o).
% 1.03/1.14 thf(brelnall1_type, type, brelnall1: $o).
% 1.03/1.14 thf(powerset_type, type, powerset: $i > $i).
% 1.03/1.14 thf(dsetconstrI_type, type, dsetconstrI: $o).
% 1.03/1.14 thf(funcGraphProp1_type, type, funcGraphProp1: $o).
% 1.03/1.14 thf(binintersectT_lem_type, type, binintersectT_lem: $o).
% 1.03/1.14 thf(setadjoin_type, type, setadjoin: $i > $i > $i).
% 1.03/1.14 thf(exu__Cong_type, type, exu__Cong: $o).
% 1.03/1.14 thf(intersectInPowersetIntersectUnions_type, type, intersectInPowersetIntersectUnions:
% 1.03/1.14 $o).
% 1.03/1.14 thf(quantDeMorgan2_type, type, quantDeMorgan2: $o).
% 1.03/1.14 thf(contrasubsetT2_type, type, contrasubsetT2: $o).
% 1.03/1.14 thf(secondinupair_type, type, secondinupair: $o).
% 1.03/1.14 thf(singletonprop_type, type, singletonprop: $o).
% 1.03/1.14 thf(singletonsubset_type, type, singletonsubset: $o).
% 1.03/1.14 thf(contrasubsetT1_type, type, contrasubsetT1: $o).
% 1.03/1.14 thf(singletoninpowerset_type, type, singletoninpowerset: $o).
% 1.03/1.14 thf(subsetemptysetimpeq_type, type, subsetemptysetimpeq: $o).
% 1.03/1.14 thf(replAx_type, type, replAx: $o).
% 1.03/1.14 thf(upairequniteq_type, type, upairequniteq: $o).
% 1.03/1.14 thf(nonemptyE1_type, type, nonemptyE1: $o).
% 1.03/1.14 thf(omegaIndAx_type, type, omegaIndAx: $o).
% 1.03/1.14 thf(setukpairIL_type, type, setukpairIL: $o).
% 1.03/1.14 thf(setunionE2_type, type, setunionE2: $o).
% 1.03/1.14 thf(inPowerset_type, type, inPowerset: $o).
% 1.03/1.14 thf(iffalse_type, type, iffalse: $o).
% 1.03/1.14 thf(funcext2_type, type, funcext2: $o).
% 1.03/1.14 thf(subset_type, type, subset: $i > $i > $o).
% 1.03/1.14 thf(subbreln_type, type, subbreln: $o).
% 1.03/1.14 thf(in__Cong_type, type, in__Cong: $o).
% 1.03/1.14 thf(binunionRsub_type, type, binunionRsub: $o).
% 1.03/1.14 thf(subset2powerset_type, type, subset2powerset: $o).
% 1.03/1.14 thf(inComplementUnionImpNotIn1, axiom, inComplementUnionImpNotIn1 =
% 1.03/1.14 (![A:$i,X:$i]:
% 1.03/1.14 ( ( in @ X @ ( powerset @ A ) ) =>
% 1.03/1.14 ( ![Y:$i]:
% 1.03/1.14 ( ( in @ Y @ ( powerset @ A ) ) =>
% 1.03/1.14 ( ![Xx:$i]:
% 1.03/1.14 ( ( in @ Xx @ A ) =>
% 1.03/1.14 ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) ) =>
% 1.03/1.14 ( ~( in @ Xx @ X ) ) ) ) ) ) ) ))).
% 1.03/1.14 thf('0', plain,
% 1.03/1.14 (( inComplementUnionImpNotIn1 ) =
% 1.03/1.14 ( ![X4:$i,X6:$i]:
% 1.03/1.14 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 1.03/1.14 ( ![X8:$i]:
% 1.03/1.14 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 1.03/1.14 ( ![X10:$i]:
% 1.03/1.14 ( ( in @ X10 @ X4 ) =>
% 1.03/1.14 ( ( in @ X10 @ ( setminus @ X4 @ ( binunion @ X6 @ X8 ) ) ) =>
% 1.03/1.14 ( ~( in @ X10 @ X6 ) ) ) ) ) ) ) ) )),
% 1.03/1.14 define([status(thm)])).
% 1.03/1.14 thf(intersectInPowersetIntersectUnions, axiom,
% 1.03/1.14 intersectInPowersetIntersectUnions =
% 1.03/1.14 (![A:$i,X:$i]:
% 1.03/1.14 ( ( in @ X @ ( powerset @ A ) ) =>
% 1.03/1.14 ( ![Y:$i]:
% 1.03/1.14 ( ( in @ Y @ ( powerset @ A ) ) =>
% 1.03/1.14 ( ![Z:$i]:
% 1.03/1.14 ( ( in @ Z @ ( powerset @ A ) ) =>
% 1.03/1.14 ( in @
% 1.03/1.14 ( binintersect @ X @ Y ) @
% 1.03/1.14 ( powerset @
% 1.03/1.14 ( binintersect @ ( binunion @ X @ Z ) @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ))).
% 1.03/1.14 thf('1', plain,
% 1.03/1.14 (( intersectInPowersetIntersectUnions ) =
% 1.03/1.14 ( ![X4:$i,X6:$i]:
% 1.03/1.14 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 1.03/1.14 ( ![X8:$i]:
% 1.03/1.14 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 1.03/1.14 ( ![X10:$i]:
% 1.03/1.14 ( ( in @ X10 @ ( powerset @ X4 ) ) =>
% 1.03/1.14 ( in @
% 1.03/1.14 ( binintersect @ X6 @ X8 ) @
% 1.03/1.14 ( powerset @
% 1.03/1.14 ( binintersect @
% 1.03/1.14 ( binunion @ X6 @ X10 ) @ ( binunion @ X8 @ X10 ) ) ) ) ) ) ) ) ) )),
% 1.03/1.14 define([status(thm)])).
% 1.03/1.14 thf(inIntersectImpInIntersectUnions, axiom, inIntersectImpInIntersectUnions =
% 1.03/1.14 (![A:$i,X:$i]:
% 1.03/1.14 ( ( in @ X @ ( powerset @ A ) ) =>
% 1.03/1.14 ( ![Y:$i]:
% 1.03/1.14 ( ( in @ Y @ ( powerset @ A ) ) =>
% 1.03/1.14 ( ![Z:$i]:
% 1.03/1.14 ( ( in @ Z @ ( powerset @ A ) ) =>
% 1.03/1.14 ( ![Xx:$i]:
% 1.03/1.14 ( ( in @ Xx @ A ) =>
% 1.03/1.14 ( ( in @ Xx @ ( binintersect @ X @ Y ) ) =>
% 1.03/1.14 ( in @
% 1.03/1.14 Xx @
% 1.03/1.14 ( binintersect @
% 1.03/1.14 ( binunion @ X @ Z ) @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ) ))).
% 1.03/1.14 thf('2', plain,
% 1.03/1.14 (( inIntersectImpInIntersectUnions ) =
% 1.03/1.14 ( ![X4:$i,X6:$i]:
% 1.03/1.14 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 1.03/1.14 ( ![X8:$i]:
% 1.03/1.14 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 1.03/1.14 ( ![X10:$i]:
% 1.03/1.14 ( ( in @ X10 @ ( powerset @ X4 ) ) =>
% 1.03/1.14 ( ![X12:$i]:
% 1.03/1.14 ( ( in @ X12 @ X4 ) =>
% 1.03/1.14 ( ( in @ X12 @ ( binintersect @ X6 @ X8 ) ) =>
% 1.03/1.14 ( in @
% 1.03/1.14 X12 @
% 1.03/1.14 ( binintersect @
% 1.03/1.14 ( binunion @ X6 @ X10 ) @ ( binunion @ X8 @ X10 ) ) ) ) ) ) ) ) ) ) ) )),
% 1.03/1.14 define([status(thm)])).
% 1.03/1.14 thf(inIntersectImpInUnion2, axiom, inIntersectImpInUnion2 =
% 1.03/1.14 (![A:$i,X:$i]:
% 1.03/1.14 ( ( in @ X @ ( powerset @ A ) ) =>
% 1.03/1.14 ( ![Y:$i]:
% 1.03/1.14 ( ( in @ Y @ ( powerset @ A ) ) =>
% 1.03/1.14 ( ![Z:$i]:
% 1.03/1.14 ( ( in @ Z @ ( powerset @ A ) ) =>
% 1.03/1.14 ( ![Xx:$i]:
% 1.03/1.14 ( ( in @ Xx @ A ) =>
% 1.03/1.14 ( ( in @ Xx @ ( binintersect @ X @ Y ) ) =>
% 1.03/1.14 ( in @ Xx @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ))).
% 1.03/1.14 thf('3', plain,
% 1.03/1.14 (( inIntersectImpInUnion2 ) =
% 1.03/1.14 ( ![X4:$i,X6:$i]:
% 1.03/1.14 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 1.03/1.14 ( ![X8:$i]:
% 1.03/1.14 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 1.03/1.14 ( ![X10:$i]:
% 1.03/1.14 ( ( in @ X10 @ ( powerset @ X4 ) ) =>
% 1.03/1.14 ( ![X12:$i]:
% 1.03/1.14 ( ( in @ X12 @ X4 ) =>
% 1.03/1.14 ( ( in @ X12 @ ( binintersect @ X6 @ X8 ) ) =>
% 1.03/1.14 ( in @ X12 @ ( binunion @ X8 @ X10 ) ) ) ) ) ) ) ) ) ) )),
% 1.03/1.14 define([status(thm)])).
% 1.03/1.14 thf(inIntersectImpInUnion, axiom, inIntersectImpInUnion =
% 1.03/1.14 (![A:$i,X:$i]:
% 1.03/1.14 ( ( in @ X @ ( powerset @ A ) ) =>
% 1.03/1.14 ( ![Y:$i]:
% 1.03/1.14 ( ( in @ Y @ ( powerset @ A ) ) =>
% 1.03/1.14 ( ![Z:$i]:
% 1.03/1.14 ( ( in @ Z @ ( powerset @ A ) ) =>
% 1.03/1.14 ( ![Xx:$i]:
% 1.03/1.14 ( ( in @ Xx @ A ) =>
% 1.03/1.14 ( ( in @ Xx @ ( binintersect @ X @ Y ) ) =>
% 1.03/1.14 ( in @ Xx @ ( binunion @ X @ Z ) ) ) ) ) ) ) ) ) ))).
% 1.03/1.14 thf('4', plain,
% 1.03/1.14 (( inIntersectImpInUnion ) =
% 1.03/1.14 ( ![X4:$i,X6:$i]:
% 1.03/1.14 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 1.03/1.14 ( ![X8:$i]:
% 1.03/1.14 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 1.03/1.14 ( ![X10:$i]:
% 1.03/1.14 ( ( in @ X10 @ ( powerset @ X4 ) ) =>
% 1.03/1.14 ( ![X12:$i]:
% 1.03/1.14 ( ( in @ X12 @ X4 ) =>
% 1.03/1.14 ( ( in @ X12 @ ( binintersect @ X6 @ X8 ) ) =>
% 1.03/1.14 ( in @ X12 @ ( binunion @ X6 @ X10 ) ) ) ) ) ) ) ) ) ) )),
% 1.03/1.14 define([status(thm)])).
% 1.03/1.14 thf(binunionTIRcontra, axiom, binunionTIRcontra =
% 1.03/1.14 (![A:$i,X:$i]:
% 1.03/1.14 ( ( in @ X @ ( powerset @ A ) ) =>
% 1.03/1.14 ( ![Y:$i]:
% 1.03/1.14 ( ( in @ Y @ ( powerset @ A ) ) =>
% 1.03/1.14 ( ![Xx:$i]:
% 1.03/1.14 ( ( in @ Xx @ A ) =>
% 1.03/1.14 ( ( ~( in @ Xx @ ( binunion @ X @ Y ) ) ) =>
% 1.03/1.14 ( ~( in @ Xx @ Y ) ) ) ) ) ) ) ))).
% 1.03/1.14 thf('5', plain,
% 1.03/1.14 (( binunionTIRcontra ) =
% 1.03/1.14 ( ![X4:$i,X6:$i]:
% 1.03/1.14 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 1.03/1.14 ( ![X8:$i]:
% 1.03/1.14 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 1.03/1.14 ( ![X10:$i]:
% 1.03/1.14 ( ( in @ X10 @ X4 ) =>
% 1.03/1.14 ( ( ~( in @ X10 @ ( binunion @ X6 @ X8 ) ) ) =>
% 1.03/1.14 ( ~( in @ X10 @ X8 ) ) ) ) ) ) ) ) )),
% 1.03/1.14 define([status(thm)])).
% 1.03/1.14 thf(binunionTILcontra, axiom, binunionTILcontra =
% 1.03/1.14 (![A:$i,X:$i]:
% 1.03/1.14 ( ( in @ X @ ( powerset @ A ) ) =>
% 1.03/1.14 ( ![Y:$i]:
% 1.03/1.14 ( ( in @ Y @ ( powerset @ A ) ) =>
% 1.03/1.14 ( ![Xx:$i]:
% 1.03/1.14 ( ( in @ Xx @ A ) =>
% 1.03/1.14 ( ( ~( in @ Xx @ ( binunion @ X @ Y ) ) ) =>
% 1.03/1.14 ( ~( in @ Xx @ X ) ) ) ) ) ) ) ))).
% 1.03/1.14 thf('6', plain,
% 1.03/1.14 (( binunionTILcontra ) =
% 1.03/1.14 ( ![X4:$i,X6:$i]:
% 1.03/1.14 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 1.03/1.14 ( ![X8:$i]:
% 1.03/1.14 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 1.03/1.14 ( ![X10:$i]:
% 1.03/1.14 ( ( in @ X10 @ X4 ) =>
% 1.03/1.14 ( ( ~( in @ X10 @ ( binunion @ X6 @ X8 ) ) ) =>
% 1.03/1.14 ( ~( in @ X10 @ X6 ) ) ) ) ) ) ) ) )),
% 1.03/1.14 define([status(thm)])).
% 1.03/1.14 thf(complementTcontraSubset, axiom, complementTcontraSubset =
% 1.03/1.14 (![A:$i,X:$i]:
% 1.03/1.14 ( ( in @ X @ ( powerset @ A ) ) =>
% 1.03/1.14 ( ![Y:$i]:
% 1.03/1.14 ( ( in @ Y @ ( powerset @ A ) ) =>
% 1.03/1.14 ( ( subset @ X @ ( setminus @ A @ Y ) ) =>
% 1.03/1.14 ( subset @ Y @ ( setminus @ A @ X ) ) ) ) ) ))).
% 1.03/1.14 thf('7', plain,
% 1.03/1.14 (( complementTcontraSubset ) =
% 1.03/1.14 ( ![X4:$i,X6:$i]:
% 1.03/1.14 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 1.03/1.14 ( ![X8:$i]:
% 1.03/1.14 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 1.03/1.14 ( ( subset @ X6 @ ( setminus @ X4 @ X8 ) ) =>
% 1.03/1.14 ( subset @ X8 @ ( setminus @ X4 @ X6 ) ) ) ) ) ) )),
% 1.03/1.14 define([status(thm)])).
% 1.03/1.14 thf(contraSubsetComplement, axiom, contraSubsetComplement =
% 1.03/1.14 (![A:$i,X:$i]:
% 1.03/1.14 ( ( in @ X @ ( powerset @ A ) ) =>
% 1.03/1.14 ( ![Y:$i]:
% 1.03/1.14 ( ( in @ Y @ ( powerset @ A ) ) =>
% 1.03/1.14 ( ( subset @ X @ ( setminus @ A @ Y ) ) =>
% 1.03/1.14 ( ![Xx:$i]:
% 1.03/1.14 ( ( in @ Xx @ A ) =>
% 1.03/1.14 ( ( in @ Xx @ Y ) => ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ))).
% 1.03/1.14 thf('8', plain,
% 1.03/1.14 (( contraSubsetComplement ) =
% 1.03/1.14 ( ![X4:$i,X6:$i]:
% 1.03/1.14 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 1.03/1.14 ( ![X8:$i]:
% 1.03/1.14 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 1.03/1.14 ( ( subset @ X6 @ ( setminus @ X4 @ X8 ) ) =>
% 1.03/1.14 ( ![X10:$i]:
% 1.03/1.14 ( ( in @ X10 @ X4 ) =>
% 1.03/1.14 ( ( in @ X10 @ X8 ) =>
% 1.03/1.14 ( in @ X10 @ ( setminus @ X4 @ X6 ) ) ) ) ) ) ) ) ) )),
% 1.03/1.14 define([status(thm)])).
% 1.03/1.14 thf(doubleComplementEq, axiom, doubleComplementEq =
% 1.03/1.14 (![A:$i,X:$i]:
% 1.03/1.14 ( ( in @ X @ ( powerset @ A ) ) =>
% 1.03/1.14 ( ( X ) = ( setminus @ A @ ( setminus @ A @ X ) ) ) ))).
% 1.03/1.14 thf('9', plain,
% 1.03/1.14 (( doubleComplementEq ) =
% 1.03/1.14 ( ![X4:$i,X6:$i]:
% 1.03/1.14 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 1.03/1.14 ( ( X6 ) = ( setminus @ X4 @ ( setminus @ X4 @ X6 ) ) ) ) )),
% 1.03/1.14 define([status(thm)])).
% 1.03/1.14 thf(doubleComplementSub2, axiom, doubleComplementSub2 =
% 1.03/1.14 (![A:$i,X:$i]:
% 1.03/1.14 ( ( in @ X @ ( powerset @ A ) ) =>
% 1.03/1.14 ( subset @ ( setminus @ A @ ( setminus @ A @ X ) ) @ X ) ))).
% 1.03/1.14 thf('10', plain,
% 1.03/1.14 (( doubleComplementSub2 ) =
% 1.03/1.14 ( ![X4:$i,X6:$i]:
% 1.03/1.14 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 1.03/1.14 ( subset @ ( setminus @ X4 @ ( setminus @ X4 @ X6 ) ) @ X6 ) ) )),
% 1.03/1.14 define([status(thm)])).
% 1.03/1.14 thf(doubleComplementSub1, axiom, doubleComplementSub1 =
% 1.03/1.14 (![A:$i,X:$i]:
% 1.03/1.14 ( ( in @ X @ ( powerset @ A ) ) =>
% 1.03/1.14 ( subset @ X @ ( setminus @ A @ ( setminus @ A @ X ) ) ) ))).
% 1.03/1.14 thf('11', plain,
% 1.03/1.14 (( doubleComplementSub1 ) =
% 1.03/1.14 ( ![X4:$i,X6:$i]:
% 1.03/1.14 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 1.03/1.14 ( subset @ X6 @ ( setminus @ X4 @ ( setminus @ X4 @ X6 ) ) ) ) )),
% 1.03/1.14 define([status(thm)])).
% 1.03/1.14 thf(doubleComplementE1, axiom, doubleComplementE1 =
% 1.03/1.14 (![A:$i,X:$i]:
% 1.03/1.14 ( ( in @ X @ ( powerset @ A ) ) =>
% 1.03/1.14 ( ![Xx:$i]:
% 1.03/1.14 ( ( in @ Xx @ A ) =>
% 1.03/1.14 ( ( in @ Xx @ ( setminus @ A @ ( setminus @ A @ X ) ) ) =>
% 1.03/1.14 ( in @ Xx @ X ) ) ) ) ))).
% 1.03/1.14 thf('12', plain,
% 1.03/1.14 (( doubleComplementE1 ) =
% 1.03/1.14 ( ![X4:$i,X6:$i]:
% 1.03/1.14 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 1.03/1.14 ( ![X8:$i]:
% 1.03/1.14 ( ( in @ X8 @ X4 ) =>
% 1.03/1.14 ( ( in @ X8 @ ( setminus @ X4 @ ( setminus @ X4 @ X6 ) ) ) =>
% 1.03/1.14 ( in @ X8 @ X6 ) ) ) ) ) )),
% 1.03/1.14 define([status(thm)])).
% 1.03/1.14 thf(doubleComplementI1, axiom, doubleComplementI1 =
% 1.03/1.14 (![A:$i,X:$i]:
% 1.03/1.14 ( ( in @ X @ ( powerset @ A ) ) =>
% 1.03/1.14 ( ![Xx:$i]:
% 1.03/1.14 ( ( in @ Xx @ A ) =>
% 1.03/1.14 ( ( in @ Xx @ X ) =>
% 1.03/1.14 ( in @ Xx @ ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) ))).
% 1.03/1.14 thf('13', plain,
% 1.03/1.14 (( doubleComplementI1 ) =
% 1.03/1.14 ( ![X4:$i,X6:$i]:
% 1.03/1.14 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 1.03/1.14 ( ![X8:$i]:
% 1.03/1.14 ( ( in @ X8 @ X4 ) =>
% 1.03/1.14 ( ( in @ X8 @ X6 ) =>
% 1.03/1.14 ( in @ X8 @ ( setminus @ X4 @ ( setminus @ X4 @ X6 ) ) ) ) ) ) ) )),
% 1.03/1.14 define([status(thm)])).
% 1.03/1.14 thf(contrasubsetT3, axiom, contrasubsetT3 =
% 1.03/1.14 (![A:$i,X:$i]:
% 1.03/1.14 ( ( in @ X @ ( powerset @ A ) ) =>
% 1.03/1.14 ( ![Y:$i]:
% 1.03/1.14 ( ( in @ Y @ ( powerset @ A ) ) =>
% 1.03/1.14 ( ( subset @ ( setminus @ A @ Y ) @ ( setminus @ A @ X ) ) =>
% 1.03/1.14 ( subset @ X @ Y ) ) ) ) ))).
% 1.03/1.14 thf('14', plain,
% 1.03/1.14 (( contrasubsetT3 ) =
% 1.03/1.14 ( ![X4:$i,X6:$i]:
% 1.03/1.14 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 1.03/1.14 ( ![X8:$i]:
% 1.03/1.14 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 1.03/1.14 ( ( subset @ ( setminus @ X4 @ X8 ) @ ( setminus @ X4 @ X6 ) ) =>
% 1.03/1.14 ( subset @ X6 @ X8 ) ) ) ) ) )),
% 1.03/1.14 define([status(thm)])).
% 1.03/1.14 thf(contrasubsetT2, axiom, contrasubsetT2 =
% 1.03/1.14 (![A:$i,X:$i]:
% 1.03/1.14 ( ( in @ X @ ( powerset @ A ) ) =>
% 1.03/1.14 ( ![Y:$i]:
% 1.03/1.14 ( ( in @ Y @ ( powerset @ A ) ) =>
% 1.03/1.14 ( ( subset @ X @ Y ) =>
% 1.03/1.14 ( subset @ ( setminus @ A @ Y ) @ ( setminus @ A @ X ) ) ) ) ) ))).
% 1.03/1.14 thf('15', plain,
% 1.03/1.14 (( contrasubsetT2 ) =
% 1.03/1.14 ( ![X4:$i,X6:$i]:
% 1.03/1.14 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 1.03/1.14 ( ![X8:$i]:
% 1.03/1.14 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 1.03/1.14 ( ( subset @ X6 @ X8 ) =>
% 1.03/1.14 ( subset @ ( setminus @ X4 @ X8 ) @ ( setminus @ X4 @ X6 ) ) ) ) ) ) )),
% 1.03/1.14 define([status(thm)])).
% 1.03/1.14 thf(contrasubsetT, axiom, contrasubsetT =
% 1.03/1.14 (![A:$i,X:$i]:
% 1.03/1.14 ( ( in @ X @ ( powerset @ A ) ) =>
% 1.03/1.14 ( ![Y:$i]:
% 1.03/1.14 ( ( in @ Y @ ( powerset @ A ) ) =>
% 1.03/1.14 ( ![Xx:$i]:
% 1.03/1.14 ( ( in @ Xx @ A ) =>
% 1.03/1.14 ( ( subset @ X @ ( setminus @ A @ Y ) ) =>
% 1.03/1.14 ( ( in @ Xx @ Y ) => ( ~( in @ Xx @ X ) ) ) ) ) ) ) ) ))).
% 1.03/1.14 thf('16', plain,
% 1.03/1.14 (( contrasubsetT ) =
% 1.03/1.14 ( ![X4:$i,X6:$i]:
% 1.03/1.14 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 1.03/1.14 ( ![X8:$i]:
% 1.03/1.14 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 1.03/1.14 ( ![X10:$i]:
% 1.03/1.14 ( ( in @ X10 @ X4 ) =>
% 1.03/1.14 ( ( subset @ X6 @ ( setminus @ X4 @ X8 ) ) =>
% 1.03/1.14 ( ( in @ X10 @ X8 ) => ( ~( in @ X10 @ X6 ) ) ) ) ) ) ) ) ) )),
% 1.03/1.14 define([status(thm)])).
% 1.03/1.14 thf(complementTE1, axiom, complementTE1 =
% 1.03/1.14 (![A:$i,X:$i]:
% 1.03/1.14 ( ( in @ X @ ( powerset @ A ) ) =>
% 1.03/1.14 ( ![Xx:$i]:
% 1.03/1.14 ( ( in @ Xx @ A ) =>
% 1.03/1.14 ( ( ~( in @ Xx @ ( setminus @ A @ X ) ) ) => ( in @ Xx @ X ) ) ) ) ))).
% 1.03/1.14 thf('17', plain,
% 1.03/1.14 (( complementTE1 ) =
% 1.03/1.14 ( ![X4:$i,X6:$i]:
% 1.03/1.14 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 1.03/1.14 ( ![X8:$i]:
% 1.03/1.14 ( ( in @ X8 @ X4 ) =>
% 1.03/1.14 ( ( ~( in @ X8 @ ( setminus @ X4 @ X6 ) ) ) => ( in @ X8 @ X6 ) ) ) ) ) )),
% 1.03/1.14 define([status(thm)])).
% 1.03/1.14 thf(complementTI1, axiom, complementTI1 =
% 1.03/1.14 (![A:$i,X:$i]:
% 1.03/1.14 ( ( in @ X @ ( powerset @ A ) ) =>
% 1.03/1.14 ( ![Xx:$i]:
% 1.03/1.14 ( ( in @ Xx @ A ) =>
% 1.03/1.14 ( ( in @ Xx @ X ) => ( ~( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ))).
% 1.03/1.14 thf('18', plain,
% 1.03/1.14 (( complementTI1 ) =
% 1.03/1.14 ( ![X4:$i,X6:$i]:
% 1.03/1.14 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 1.03/1.14 ( ![X8:$i]:
% 1.03/1.14 ( ( in @ X8 @ X4 ) =>
% 1.03/1.14 ( ( in @ X8 @ X6 ) => ( ~( in @ X8 @ ( setminus @ X4 @ X6 ) ) ) ) ) ) ) )),
% 1.03/1.14 define([status(thm)])).
% 1.03/1.14 thf(powersetTE1, axiom, powersetTE1 =
% 1.03/1.14 (![A:$i,X:$i]:
% 1.03/1.14 ( ( in @ X @ ( powerset @ A ) ) =>
% 1.03/1.14 ( ![Y:$i]:
% 1.03/1.14 ( ( in @ Y @ ( powerset @ A ) ) =>
% 1.03/1.14 ( ![Xx:$i]:
% 1.03/1.14 ( ( in @ Xx @ A ) =>
% 1.03/1.14 ( ( in @ X @ ( powerset @ Y ) ) =>
% 1.03/1.14 ( ( in @ Xx @ X ) => ( in @ Xx @ Y ) ) ) ) ) ) ) ))).
% 1.03/1.14 thf('19', plain,
% 1.03/1.14 (( powersetTE1 ) =
% 1.03/1.14 ( ![X4:$i,X6:$i]:
% 1.03/1.14 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 1.03/1.14 ( ![X8:$i]:
% 1.03/1.14 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 1.03/1.14 ( ![X10:$i]:
% 1.03/1.14 ( ( in @ X10 @ X4 ) =>
% 1.03/1.14 ( ( in @ X6 @ ( powerset @ X8 ) ) =>
% 1.03/1.14 ( ( in @ X10 @ X6 ) => ( in @ X10 @ X8 ) ) ) ) ) ) ) ) )),
% 1.03/1.14 define([status(thm)])).
% 1.03/1.14 thf(powersetTI1, axiom, powersetTI1 =
% 1.03/1.14 (![A:$i,X:$i]:
% 1.03/1.14 ( ( in @ X @ ( powerset @ A ) ) =>
% 1.03/1.14 ( ![Y:$i]:
% 1.03/1.14 ( ( in @ Y @ ( powerset @ A ) ) =>
% 1.03/1.14 ( ( ![Xx:$i]:
% 1.03/1.14 ( ( in @ Xx @ A ) => ( ( in @ Xx @ X ) => ( in @ Xx @ Y ) ) ) ) =>
% 1.03/1.14 ( in @ X @ ( powerset @ Y ) ) ) ) ) ))).
% 1.03/1.14 thf('20', plain,
% 1.03/1.14 (( powersetTI1 ) =
% 1.03/1.14 ( ![X4:$i,X6:$i]:
% 1.03/1.14 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 1.03/1.14 ( ![X8:$i]:
% 1.03/1.14 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 1.03/1.14 ( ( ![X10:$i]:
% 1.03/1.14 ( ( in @ X10 @ X4 ) =>
% 1.03/1.14 ( ( in @ X10 @ X6 ) => ( in @ X10 @ X8 ) ) ) ) =>
% 1.03/1.14 ( in @ X6 @ ( powerset @ X8 ) ) ) ) ) ) )),
% 1.03/1.14 define([status(thm)])).
% 1.03/1.14 thf(setextT, axiom, setextT =
% 1.03/1.14 (![A:$i,X:$i]:
% 1.03/1.14 ( ( in @ X @ ( powerset @ A ) ) =>
% 1.03/1.14 ( ![Y:$i]:
% 1.03/1.14 ( ( in @ Y @ ( powerset @ A ) ) =>
% 1.03/1.14 ( ( ![Xx:$i]:
% 1.03/1.14 ( ( in @ Xx @ A ) => ( ( in @ Xx @ X ) => ( in @ Xx @ Y ) ) ) ) =>
% 1.03/1.14 ( ( ![Xx:$i]:
% 1.03/1.14 ( ( in @ Xx @ A ) => ( ( in @ Xx @ Y ) => ( in @ Xx @ X ) ) ) ) =>
% 1.03/1.14 ( ( X ) = ( Y ) ) ) ) ) ) ))).
% 1.03/1.14 thf('21', plain,
% 1.03/1.14 (( setextT ) =
% 1.03/1.14 ( ![X4:$i,X6:$i]:
% 1.03/1.14 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 1.03/1.14 ( ![X8:$i]:
% 1.03/1.14 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 1.03/1.14 ( ( ![X10:$i]:
% 1.03/1.14 ( ( in @ X10 @ X4 ) =>
% 1.03/1.14 ( ( in @ X10 @ X6 ) => ( in @ X10 @ X8 ) ) ) ) =>
% 1.03/1.14 ( ( ![X12:$i]:
% 1.03/1.14 ( ( in @ X12 @ X4 ) =>
% 1.03/1.14 ( ( in @ X12 @ X8 ) => ( in @ X12 @ X6 ) ) ) ) =>
% 1.03/1.14 ( ( X6 ) = ( X8 ) ) ) ) ) ) ) )),
% 1.03/1.14 define([status(thm)])).
% 1.03/1.14 thf(complementT_lem, axiom, complementT_lem =
% 1.03/1.14 (![A:$i,X:$i]:
% 1.03/1.14 ( ( in @ X @ ( powerset @ A ) ) =>
% 1.03/1.14 ( in @ ( setminus @ A @ X ) @ ( powerset @ A ) ) ))).
% 1.03/1.14 thf('22', plain,
% 1.03/1.14 (( complementT_lem ) =
% 1.03/1.14 ( ![X4:$i,X6:$i]:
% 1.03/1.14 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 1.03/1.14 ( in @ ( setminus @ X4 @ X6 ) @ ( powerset @ X4 ) ) ) )),
% 1.03/1.14 define([status(thm)])).
% 1.03/1.14 thf(setminusT_lem, axiom, setminusT_lem =
% 1.03/1.14 (![A:$i,X:$i]:
% 1.03/1.14 ( ( in @ X @ ( powerset @ A ) ) =>
% 1.03/1.14 ( ![Y:$i]:
% 1.03/1.14 ( ( in @ Y @ ( powerset @ A ) ) =>
% 1.03/1.14 ( in @ ( setminus @ X @ Y ) @ ( powerset @ A ) ) ) ) ))).
% 1.03/1.14 thf('23', plain,
% 1.03/1.14 (( setminusT_lem ) =
% 1.03/1.14 ( ![X4:$i,X6:$i]:
% 1.03/1.14 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 1.03/1.14 ( ![X8:$i]:
% 1.03/1.14 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 1.03/1.14 ( in @ ( setminus @ X6 @ X8 ) @ ( powerset @ X4 ) ) ) ) ) )),
% 1.03/1.14 define([status(thm)])).
% 1.03/1.14 thf(powersetT_lem, axiom, powersetT_lem =
% 1.03/1.14 (![A:$i,X:$i]:
% 1.03/1.14 ( ( in @ X @ ( powerset @ A ) ) =>
% 1.03/1.14 ( in @ ( powerset @ X ) @ ( powerset @ ( powerset @ A ) ) ) ))).
% 1.03/1.14 thf('24', plain,
% 1.03/1.14 (( powersetT_lem ) =
% 1.03/1.14 ( ![X4:$i,X6:$i]:
% 1.03/1.14 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 1.03/1.14 ( in @ ( powerset @ X6 ) @ ( powerset @ ( powerset @ X4 ) ) ) ) )),
% 1.03/1.14 define([status(thm)])).
% 1.03/1.14 thf(binunionT_lem, axiom, binunionT_lem =
% 1.03/1.14 (![A:$i,X:$i]:
% 1.03/1.14 ( ( in @ X @ ( powerset @ A ) ) =>
% 1.03/1.14 ( ![Y:$i]:
% 1.03/1.14 ( ( in @ Y @ ( powerset @ A ) ) =>
% 1.03/1.14 ( in @ ( binunion @ X @ Y ) @ ( powerset @ A ) ) ) ) ))).
% 1.03/1.14 thf('25', plain,
% 1.03/1.14 (( binunionT_lem ) =
% 1.03/1.14 ( ![X4:$i,X6:$i]:
% 1.03/1.14 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 1.03/1.14 ( ![X8:$i]:
% 1.03/1.14 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 1.03/1.14 ( in @ ( binunion @ X6 @ X8 ) @ ( powerset @ X4 ) ) ) ) ) )),
% 1.03/1.14 define([status(thm)])).
% 1.03/1.14 thf(ubforcartprodlem3, axiom, ubforcartprodlem3 =
% 1.03/1.14 (![A:$i,B:$i,Xx:$i]:
% 1.03/1.14 ( ( in @ Xx @ A ) =>
% 1.03/1.14 ( ![Xy:$i]:
% 1.03/1.14 ( ( in @ Xy @ B ) =>
% 1.03/1.14 ( in @
% 1.03/1.14 ( kpair @ Xx @ Xy ) @
% 1.03/1.14 ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ))).
% 1.03/1.14 thf('26', plain,
% 1.03/1.14 (( ubforcartprodlem3 ) =
% 1.03/1.14 ( ![X4:$i,X6:$i,X8:$i]:
% 1.03/1.14 ( ( in @ X8 @ X4 ) =>
% 1.03/1.14 ( ![X10:$i]:
% 1.03/1.14 ( ( in @ X10 @ X6 ) =>
% 1.03/1.14 ( in @
% 1.03/1.14 ( kpair @ X8 @ X10 ) @
% 1.03/1.14 ( powerset @ ( powerset @ ( binunion @ X4 @ X6 ) ) ) ) ) ) ) )),
% 1.03/1.14 define([status(thm)])).
% 1.03/1.14 thf(ubforcartprodlem2, axiom, ubforcartprodlem2 =
% 1.03/1.14 (![A:$i,B:$i,Xx:$i]:
% 1.03/1.14 ( ( in @ Xx @ A ) =>
% 1.03/1.14 ( ![Xy:$i]:
% 1.03/1.14 ( ( in @ Xy @ B ) =>
% 1.03/1.14 ( in @
% 1.03/1.14 ( setadjoin @
% 1.03/1.14 ( setadjoin @ Xx @ emptyset ) @
% 1.03/1.14 ( setadjoin @
% 1.03/1.14 ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @
% 1.03/1.14 ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ))).
% 1.03/1.14 thf('27', plain,
% 1.03/1.14 (( ubforcartprodlem2 ) =
% 1.03/1.14 ( ![X4:$i,X6:$i,X8:$i]:
% 1.03/1.14 ( ( in @ X8 @ X4 ) =>
% 1.03/1.14 ( ![X10:$i]:
% 1.03/1.14 ( ( in @ X10 @ X6 ) =>
% 1.03/1.14 ( in @
% 1.03/1.14 ( setadjoin @
% 1.03/1.14 ( setadjoin @ X8 @ emptyset ) @
% 1.03/1.14 ( setadjoin @
% 1.03/1.14 ( setadjoin @ X8 @ ( setadjoin @ X10 @ emptyset ) ) @
% 1.03/1.14 emptyset ) ) @
% 1.03/1.14 ( powerset @ ( powerset @ ( binunion @ X4 @ X6 ) ) ) ) ) ) ) )),
% 1.03/1.14 define([status(thm)])).
% 1.03/1.14 thf(ubforcartprodlem1, axiom, ubforcartprodlem1 =
% 1.03/1.14 (![A:$i,B:$i,Xx:$i]:
% 1.03/1.14 ( ( in @ Xx @ A ) =>
% 1.03/1.14 ( ![Xy:$i]:
% 1.03/1.14 ( ( in @ Xy @ B ) =>
% 1.03/1.14 ( subset @
% 1.03/1.14 ( setadjoin @
% 1.03/1.14 ( setadjoin @ Xx @ emptyset ) @
% 1.03/1.14 ( setadjoin @
% 1.03/1.14 ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @
% 1.03/1.14 ( powerset @ ( binunion @ A @ B ) ) ) ) ) ))).
% 1.03/1.14 thf('28', plain,
% 1.03/1.14 (( ubforcartprodlem1 ) =
% 1.03/1.14 ( ![X4:$i,X6:$i,X8:$i]:
% 1.03/1.14 ( ( in @ X8 @ X4 ) =>
% 1.03/1.14 ( ![X10:$i]:
% 1.03/1.14 ( ( in @ X10 @ X6 ) =>
% 1.03/1.14 ( subset @
% 1.03/1.14 ( setadjoin @
% 1.03/1.14 ( setadjoin @ X8 @ emptyset ) @
% 1.03/1.14 ( setadjoin @
% 1.03/1.14 ( setadjoin @ X8 @ ( setadjoin @ X10 @ emptyset ) ) @
% 1.03/1.14 emptyset ) ) @
% 1.03/1.14 ( powerset @ ( binunion @ X4 @ X6 ) ) ) ) ) ) )),
% 1.03/1.14 define([status(thm)])).
% 1.03/1.14 thf(upairinpowunion, axiom, upairinpowunion =
% 1.03/1.14 (![A:$i,B:$i,Xx:$i]:
% 1.03/1.14 ( ( in @ Xx @ A ) =>
% 1.03/1.14 ( ![Xy:$i]:
% 1.03/1.14 ( ( in @ Xy @ B ) =>
% 1.03/1.14 ( in @
% 1.03/1.14 ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @
% 1.03/1.14 ( powerset @ ( binunion @ A @ B ) ) ) ) ) ))).
% 1.03/1.14 thf('29', plain,
% 1.03/1.14 (( upairinpowunion ) =
% 1.03/1.14 ( ![X4:$i,X6:$i,X8:$i]:
% 1.03/1.14 ( ( in @ X8 @ X4 ) =>
% 1.03/1.14 ( ![X10:$i]:
% 1.03/1.14 ( ( in @ X10 @ X6 ) =>
% 1.03/1.14 ( in @
% 1.03/1.14 ( setadjoin @ X8 @ ( setadjoin @ X10 @ emptyset ) ) @
% 1.03/1.14 ( powerset @ ( binunion @ X4 @ X6 ) ) ) ) ) ) )),
% 1.03/1.14 define([status(thm)])).
% 1.03/1.14 thf(upairsubunion, axiom, upairsubunion =
% 1.03/1.14 (![A:$i,B:$i,Xx:$i]:
% 1.03/1.14 ( ( in @ Xx @ A ) =>
% 1.03/1.14 ( ![Xy:$i]:
% 1.03/1.14 ( ( in @ Xy @ B ) =>
% 1.03/1.14 ( subset @
% 1.03/1.14 ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @
% 1.03/1.14 ( binunion @ A @ B ) ) ) ) ))).
% 1.03/1.14 thf('30', plain,
% 1.03/1.14 (( upairsubunion ) =
% 1.03/1.14 ( ![X4:$i,X6:$i,X8:$i]:
% 1.03/1.14 ( ( in @ X8 @ X4 ) =>
% 1.03/1.14 ( ![X10:$i]:
% 1.03/1.14 ( ( in @ X10 @ X6 ) =>
% 1.03/1.14 ( subset @
% 1.03/1.14 ( setadjoin @ X8 @ ( setadjoin @ X10 @ emptyset ) ) @
% 1.03/1.14 ( binunion @ X4 @ X6 ) ) ) ) ) )),
% 1.03/1.14 define([status(thm)])).
% 1.03/1.14 thf(singletoninpowunion, axiom, singletoninpowunion =
% 1.03/1.14 (![A:$i,B:$i,Xx:$i]:
% 1.03/1.14 ( ( in @ Xx @ A ) =>
% 1.03/1.14 ( in @
% 1.03/1.14 ( setadjoin @ Xx @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) ))).
% 1.03/1.14 thf('31', plain,
% 1.03/1.14 (( singletoninpowunion ) =
% 1.03/1.14 ( ![X4:$i,X6:$i,X8:$i]:
% 1.03/1.14 ( ( in @ X8 @ X4 ) =>
% 1.03/1.14 ( in @
% 1.03/1.14 ( setadjoin @ X8 @ emptyset ) @
% 1.03/1.14 ( powerset @ ( binunion @ X4 @ X6 ) ) ) ) )),
% 1.03/1.14 define([status(thm)])).
% 1.03/1.14 thf(setminusSubset1, axiom, setminusSubset1 =
% 1.03/1.14 (![A:$i,B:$i]:
% 1.03/1.14 ( ( ( setminus @ A @ B ) = ( emptyset ) ) => ( subset @ A @ B ) ))).
% 1.03/1.14 thf('32', plain,
% 1.03/1.14 (( setminusSubset1 ) =
% 1.03/1.14 ( ![X4:$i,X6:$i]:
% 1.03/1.14 ( ( ( setminus @ X4 @ X6 ) = ( emptyset ) ) => ( subset @ X4 @ X6 ) ) )),
% 1.03/1.14 define([status(thm)])).
% 1.03/1.14 thf(setminusLsub, axiom, setminusLsub =
% 1.03/1.14 (![A:$i,B:$i]: ( subset @ ( setminus @ A @ B ) @ A ))).
% 1.03/1.14 thf('33', plain,
% 1.03/1.14 (( setminusLsub ) =
% 1.03/1.14 ( ![X4:$i,X6:$i]: ( subset @ ( setminus @ X4 @ X6 ) @ X4 ) )),
% 1.03/1.14 define([status(thm)])).
% 1.03/1.14 thf(setminusIRneg, axiom, setminusIRneg =
% 1.03/1.14 (![A:$i,B:$i,Xx:$i]:
% 1.03/1.14 ( ( in @ Xx @ B ) => ( ~( in @ Xx @ ( setminus @ A @ B ) ) ) ))).
% 1.03/1.14 thf('34', plain,
% 1.03/1.14 (( setminusIRneg ) =
% 1.03/1.14 ( ![X4:$i,X6:$i,X8:$i]:
% 1.03/1.14 ( ( in @ X8 @ X6 ) => ( ~( in @ X8 @ ( setminus @ X4 @ X6 ) ) ) ) )),
% 1.03/1.14 define([status(thm)])).
% 1.03/1.14 thf(setminusILneg, axiom, setminusILneg =
% 1.03/1.14 (![A:$i,B:$i,Xx:$i]:
% 1.03/1.14 ( ( ~( in @ Xx @ A ) ) => ( ~( in @ Xx @ ( setminus @ A @ B ) ) ) ))).
% 1.03/1.14 thf('35', plain,
% 1.03/1.14 (( setminusILneg ) =
% 1.03/1.14 ( ![X4:$i,X6:$i,X8:$i]:
% 1.03/1.14 ( ( ~( in @ X8 @ X4 ) ) => ( ~( in @ X8 @ ( setminus @ X4 @ X6 ) ) ) ) )),
% 1.03/1.14 define([status(thm)])).
% 1.03/1.14 thf(setminusELneg, axiom, setminusELneg =
% 1.03/1.14 (![A:$i,B:$i,Xx:$i]:
% 1.03/1.14 ( ( ~( in @ Xx @ ( setminus @ A @ B ) ) ) =>
% 1.03/1.14 ( ( ~( in @ Xx @ B ) ) => ( ~( in @ Xx @ A ) ) ) ))).
% 1.03/1.14 thf('36', plain,
% 1.03/1.14 (( setminusELneg ) =
% 1.03/1.14 ( ![X4:$i,X6:$i,X8:$i]:
% 1.03/1.14 ( ( ~( in @ X8 @ ( setminus @ X4 @ X6 ) ) ) =>
% 1.03/1.14 ( ( ~( in @ X8 @ X6 ) ) => ( ~( in @ X8 @ X4 ) ) ) ) )),
% 1.03/1.14 define([status(thm)])).
% 1.03/1.14 thf(setminusERneg, axiom, setminusERneg =
% 1.03/1.14 (![A:$i,B:$i,Xx:$i]:
% 1.03/1.14 ( ( ~( in @ Xx @ ( setminus @ A @ B ) ) ) =>
% 1.03/1.14 ( ( in @ Xx @ A ) => ( in @ Xx @ B ) ) ))).
% 1.03/1.14 thf('37', plain,
% 1.03/1.14 (( setminusERneg ) =
% 1.03/1.14 ( ![X4:$i,X6:$i,X8:$i]:
% 1.03/1.14 ( ( ~( in @ X8 @ ( setminus @ X4 @ X6 ) ) ) =>
% 1.03/1.14 ( ( in @ X8 @ X4 ) => ( in @ X8 @ X6 ) ) ) )),
% 1.03/1.14 define([status(thm)])).
% 1.03/1.14 thf(setminusSubset2, axiom, setminusSubset2 =
% 1.03/1.14 (![A:$i,B:$i]:
% 1.03/1.14 ( ( subset @ A @ B ) => ( ( setminus @ A @ B ) = ( emptyset ) ) ))).
% 1.03/1.14 thf('38', plain,
% 1.03/1.14 (( setminusSubset2 ) =
% 1.03/1.14 ( ![X4:$i,X6:$i]:
% 1.03/1.14 ( ( subset @ X4 @ X6 ) => ( ( setminus @ X4 @ X6 ) = ( emptyset ) ) ) )),
% 1.03/1.14 define([status(thm)])).
% 1.03/1.14 thf(setminusER, axiom, setminusER =
% 1.03/1.14 (![A:$i,B:$i,Xx:$i]:
% 1.03/1.14 ( ( in @ Xx @ ( setminus @ A @ B ) ) => ( ~( in @ Xx @ B ) ) ))).
% 1.03/1.14 thf('39', plain,
% 1.03/1.14 (( setminusER ) =
% 1.03/1.14 ( ![X4:$i,X6:$i,X8:$i]:
% 1.03/1.14 ( ( in @ X8 @ ( setminus @ X4 @ X6 ) ) => ( ~( in @ X8 @ X6 ) ) ) )),
% 1.03/1.14 define([status(thm)])).
% 1.03/1.14 thf(setminusEL, axiom, setminusEL =
% 1.03/1.14 (![A:$i,B:$i,Xx:$i]:
% 1.03/1.14 ( ( in @ Xx @ ( setminus @ A @ B ) ) => ( in @ Xx @ A ) ))).
% 1.03/1.14 thf('40', plain,
% 1.03/1.14 (( setminusEL ) =
% 1.03/1.14 ( ![X4:$i,X6:$i,X8:$i]:
% 1.03/1.14 ( ( in @ X8 @ ( setminus @ X4 @ X6 ) ) => ( in @ X8 @ X4 ) ) )),
% 1.03/1.14 define([status(thm)])).
% 1.03/1.14 thf(setminusI, axiom, setminusI =
% 1.03/1.14 (![A:$i,B:$i,Xx:$i]:
% 1.03/1.14 ( ( in @ Xx @ A ) =>
% 1.03/1.14 ( ( ~( in @ Xx @ B ) ) => ( in @ Xx @ ( setminus @ A @ B ) ) ) ))).
% 1.03/1.14 thf('41', plain,
% 1.03/1.14 (( setminusI ) =
% 1.03/1.14 ( ![X4:$i,X6:$i,X8:$i]:
% 1.03/1.14 ( ( in @ X8 @ X4 ) =>
% 1.03/1.14 ( ( ~( in @ X8 @ X6 ) ) => ( in @ X8 @ ( setminus @ X4 @ X6 ) ) ) ) )),
% 1.03/1.14 define([status(thm)])).
% 1.03/1.14 thf(bs114d, axiom, bs114d =
% 1.03/1.14 (![A:$i,B:$i,C:$i]:
% 1.03/1.14 ( ( binintersect @ A @ ( binunion @ B @ C ) ) =
% 1.03/1.14 ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) ))).
% 1.03/1.14 thf('42', plain,
% 1.03/1.14 (( bs114d ) =
% 1.03/1.14 ( ![X4:$i,X6:$i,X8:$i]:
% 1.03/1.14 ( ( binintersect @ X4 @ ( binunion @ X6 @ X8 ) ) =
% 1.03/1.14 ( binunion @ ( binintersect @ X4 @ X6 ) @ ( binintersect @ X4 @ X8 ) ) ) )),
% 1.03/1.14 define([status(thm)])).
% 1.03/1.14 thf(binunionRsub, axiom, binunionRsub =
% 1.03/1.14 (![A:$i,B:$i]: ( subset @ B @ ( binunion @ A @ B ) ))).
% 1.03/1.14 thf('43', plain,
% 1.03/1.14 (( binunionRsub ) =
% 1.03/1.14 ( ![X4:$i,X6:$i]: ( subset @ X6 @ ( binunion @ X4 @ X6 ) ) )),
% 1.03/1.14 define([status(thm)])).
% 1.03/1.14 thf(binunionLsub, axiom, binunionLsub =
% 1.03/1.14 (![A:$i,B:$i]: ( subset @ A @ ( binunion @ A @ B ) ))).
% 1.03/1.14 thf('44', plain,
% 1.03/1.14 (( binunionLsub ) =
% 1.03/1.14 ( ![X4:$i,X6:$i]: ( subset @ X4 @ ( binunion @ X4 @ X6 ) ) )),
% 1.03/1.14 define([status(thm)])).
% 1.03/1.14 thf(binunionE, axiom, binunionE =
% 1.03/1.14 (![A:$i,B:$i,Xx:$i]:
% 1.03/1.14 ( ( in @ Xx @ ( binunion @ A @ B ) ) =>
% 1.03/1.14 ( ( in @ Xx @ A ) | ( in @ Xx @ B ) ) ))).
% 1.03/1.14 thf('45', plain,
% 1.03/1.14 (( binunionE ) =
% 1.03/1.14 ( ![X4:$i,X6:$i,X8:$i]:
% 1.03/1.14 ( ( in @ X8 @ ( binunion @ X4 @ X6 ) ) =>
% 1.03/1.14 ( ( in @ X8 @ X4 ) | ( in @ X8 @ X6 ) ) ) )),
% 1.03/1.14 define([status(thm)])).
% 1.03/1.14 thf(binunionEcases, axiom, binunionEcases =
% 1.03/1.14 (![A:$i,B:$i,Xx:$i,Xphi:$o]:
% 1.03/1.14 ( ( in @ Xx @ ( binunion @ A @ B ) ) =>
% 1.03/1.14 ( ( ( in @ Xx @ A ) => ( Xphi ) ) =>
% 1.03/1.14 ( ( ( in @ Xx @ B ) => ( Xphi ) ) => ( Xphi ) ) ) ))).
% 1.03/1.14 thf('46', plain,
% 1.03/1.14 (( binunionEcases ) =
% 1.03/1.14 ( ![X4:$i,X6:$i,X8:$i,X10:$o]:
% 1.03/1.14 ( ( in @ X8 @ ( binunion @ X4 @ X6 ) ) =>
% 1.03/1.14 ( ( ( in @ X8 @ X4 ) => ( X10 ) ) =>
% 1.03/1.14 ( ( ( in @ X8 @ X6 ) => ( X10 ) ) => ( X10 ) ) ) ) )),
% 1.03/1.14 define([status(thm)])).
% 1.03/1.14 thf(binunionIR, axiom, binunionIR =
% 1.03/1.14 (![A:$i,B:$i,Xx:$i]:
% 1.03/1.14 ( ( in @ Xx @ B ) => ( in @ Xx @ ( binunion @ A @ B ) ) ))).
% 1.03/1.14 thf('47', plain,
% 1.03/1.14 (( binunionIR ) =
% 1.03/1.14 ( ![X4:$i,X6:$i,X8:$i]:
% 1.03/1.14 ( ( in @ X8 @ X6 ) => ( in @ X8 @ ( binunion @ X4 @ X6 ) ) ) )),
% 1.03/1.14 define([status(thm)])).
% 1.03/1.14 thf(binunionIL, axiom, binunionIL =
% 1.03/1.14 (![A:$i,B:$i,Xx:$i]:
% 1.03/1.14 ( ( in @ Xx @ A ) => ( in @ Xx @ ( binunion @ A @ B ) ) ))).
% 1.03/1.14 thf('48', plain,
% 1.03/1.14 (( binunionIL ) =
% 1.03/1.14 ( ![X4:$i,X6:$i,X8:$i]:
% 1.03/1.14 ( ( in @ X8 @ X4 ) => ( in @ X8 @ ( binunion @ X4 @ X6 ) ) ) )),
% 1.03/1.14 define([status(thm)])).
% 1.03/1.14 thf(inPowerset, axiom, inPowerset = (![A:$i]: ( in @ A @ ( powerset @ A ) ))).
% 1.03/1.14 thf('49', plain,
% 1.03/1.14 (( inPowerset ) = ( ![X4:$i]: ( in @ X4 @ ( powerset @ X4 ) ) )),
% 1.03/1.14 define([status(thm)])).
% 1.03/1.14 thf(powerset__Cong, axiom, powerset__Cong =
% 1.03/1.14 (![A:$i,B:$i]:
% 1.03/1.14 ( ( ( A ) = ( B ) ) => ( ( powerset @ A ) = ( powerset @ B ) ) ))).
% 1.03/1.14 thf('50', plain,
% 1.03/1.14 (( powerset__Cong ) =
% 1.03/1.14 ( ![X4:$i,X6:$i]:
% 1.03/1.14 ( ( ( X4 ) = ( X6 ) ) => ( ( powerset @ X4 ) = ( powerset @ X6 ) ) ) )),
% 1.03/1.14 define([status(thm)])).
% 1.03/1.14 thf(powersetE, axiom, powersetE =
% 1.03/1.14 (![A:$i,B:$i,Xx:$i]:
% 1.03/1.14 ( ( in @ B @ ( powerset @ A ) ) => ( ( in @ Xx @ B ) => ( in @ Xx @ A ) ) ))).
% 1.03/1.14 thf('51', plain,
% 1.03/1.14 (( powersetE ) =
% 1.03/1.14 ( ![X4:$i,X6:$i,X8:$i]:
% 1.03/1.14 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 1.03/1.14 ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ) )),
% 1.03/1.14 define([status(thm)])).
% 1.03/1.14 thf(emptyInPowerset, axiom, emptyInPowerset =
% 1.03/1.14 (![A:$i]: ( in @ emptyset @ ( powerset @ A ) ))).
% 1.03/1.14 thf('52', plain,
% 1.03/1.14 (( emptyInPowerset ) =
% 1.03/1.14 ( ![X4:$i]: ( in @ emptyset @ ( powerset @ X4 ) ) )),
% 1.03/1.14 define([status(thm)])).
% 1.03/1.14 thf(emptyinPowerset, axiom, emptyinPowerset =
% 1.03/1.14 (![A:$i]: ( in @ emptyset @ ( powerset @ A ) ))).
% 1.03/1.14 thf('53', plain,
% 1.03/1.14 (( emptyinPowerset ) =
% 1.03/1.14 ( ![X4:$i]: ( in @ emptyset @ ( powerset @ X4 ) ) )),
% 1.03/1.14 define([status(thm)])).
% 1.03/1.14 thf(powersetI, axiom, powersetI =
% 1.03/1.14 (![A:$i,B:$i]:
% 1.03/1.14 ( ( ![Xx:$i]: ( ( in @ Xx @ B ) => ( in @ Xx @ A ) ) ) =>
% 1.03/1.14 ( in @ B @ ( powerset @ A ) ) ))).
% 1.03/1.14 thf('54', plain,
% 1.03/1.14 (( powersetI ) =
% 1.03/1.14 ( ![X4:$i,X6:$i]:
% 1.03/1.14 ( ( ![X8:$i]: ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ) =>
% 1.03/1.14 ( in @ X6 @ ( powerset @ X4 ) ) ) )),
% 1.03/1.14 define([status(thm)])).
% 1.03/1.14 thf(powersetAx, axiom, powersetAx =
% 1.03/1.14 (![A:$i,B:$i]:
% 1.03/1.14 ( ( in @ B @ ( powerset @ A ) ) <=>
% 1.03/1.14 ( ![Xx:$i]: ( ( in @ Xx @ B ) => ( in @ Xx @ A ) ) ) ))).
% 1.03/1.14 thf('55', plain,
% 1.03/1.14 (( powersetAx ) =
% 1.03/1.14 ( ![X4:$i,X6:$i]:
% 1.03/1.14 ( ( in @ X6 @ ( powerset @ X4 ) ) <=>
% 1.03/1.14 ( ![X8:$i]: ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ) ) )),
% 1.03/1.14 define([status(thm)])).
% 1.03/1.14 thf(inComplementUnionImpInComplement1, conjecture,
% 1.03/1.14 (( setextAx ) =>
% 1.03/1.14 ( ( emptysetAx ) =>
% 1.03/1.14 ( ( setadjoinAx ) =>
% 1.03/1.14 ( ( powersetAx ) =>
% 1.03/1.14 ( ( setunionAx ) =>
% 1.03/1.14 ( ( omega0Ax ) =>
% 1.03/1.14 ( ( omegaSAx ) =>
% 1.03/1.14 ( ( omegaIndAx ) =>
% 1.03/1.14 ( ( replAx ) =>
% 1.03/1.14 ( ( foundationAx ) =>
% 1.03/1.14 ( ( wellorderingAx ) =>
% 1.03/1.14 ( ( descrp ) =>
% 1.03/1.14 ( ( dsetconstrI ) =>
% 1.03/1.14 ( ( dsetconstrEL ) =>
% 1.03/1.14 ( ( dsetconstrER ) =>
% 1.03/1.14 ( ( exuE1 ) =>
% 1.03/1.14 ( ( prop2setE ) =>
% 1.03/1.14 ( ( emptysetE ) =>
% 1.03/1.14 ( ( emptysetimpfalse ) =>
% 1.03/1.14 ( ( notinemptyset ) =>
% 1.03/1.14 ( ( exuE3e ) =>
% 1.03/1.14 ( ( setext ) =>
% 1.03/1.14 ( ( emptyI ) =>
% 1.03/1.14 ( ( noeltsimpempty ) =>
% 1.03/1.14 ( ( setbeta ) =>
% 1.03/1.14 ( ( nonemptyE1 ) =>
% 1.03/1.14 ( ( nonemptyI ) =>
% 1.03/1.14 ( ( nonemptyI1 ) =>
% 1.03/1.14 ( ( setadjoinIL ) =>
% 1.03/1.14 ( ( emptyinunitempty ) =>
% 1.03/1.14 ( ( setadjoinIR ) =>
% 1.03/1.14 ( ( setadjoinE ) =>
% 1.03/1.14 ( (
% 1.03/1.14 setadjoinOr ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 setoftrueEq ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 powersetI ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 emptyinPowerset ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 emptyInPowerset ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 powersetE ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 setunionI ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 setunionE ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 subPowSU ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 exuE2 ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 nonemptyImpWitness ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 uniqinunit ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 notinsingleton ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 eqinunit ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 singletonsswitch ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 upairsetE ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 upairsetIL ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 upairsetIR ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 emptyE1 ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 vacuousDall ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 quantDeMorgan1 ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 quantDeMorgan2 ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 quantDeMorgan3 ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 quantDeMorgan4 ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 prop2setI ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 prop2set2propI ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 notdexE ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 notdallE ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 exuI1 ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 exuI3 ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 exuI2 ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 inCongP ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 in__Cong ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 exuE3u ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 exu__Cong ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 emptyset__Cong ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 setadjoin__Cong ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 powerset__Cong ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 setunion__Cong ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 omega__Cong ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 exuEu ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 descr__Cong ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 dsetconstr__Cong ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 subsetI1 ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 eqimpsubset2 ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 eqimpsubset1 ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 subsetI2 ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 emptysetsubset ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 subsetE ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 subsetE2 ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 notsubsetI ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 notequalI1 ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 notequalI2 ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 subsetRefl ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 subsetTrans ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 setadjoinSub ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 setadjoinSub2 ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 subset2powerset ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 setextsub ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 subsetemptysetimpeq ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 powersetI1 ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 powersetE1 ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 inPowerset ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 powersetsubset ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 sepInPowerset ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 sepSubset ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 binunionIL ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 upairset2IR ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 binunionIR ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 binunionEcases ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 binunionE ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 binunionLsub ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 binunionRsub ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 binintersectI ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 binintersectSubset5 ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 binintersectEL ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 binintersectLsub ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 binintersectSubset2 ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 binintersectSubset3 ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 binintersectER ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 disjointsetsI1 ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 binintersectRsub ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 binintersectSubset4 ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 binintersectSubset1 ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 bs114d ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 setminusI ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 setminusEL ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 setminusER ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 setminusSubset2 ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 setminusERneg ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 setminusELneg ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 setminusILneg ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 setminusIRneg ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 setminusLsub ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 setminusSubset1 ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 symdiffE ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 symdiffI1 ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 symdiffI2 ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 symdiffIneg1 ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 symdiffIneg2 ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 secondinupair ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 setukpairIL ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 setukpairIR ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 kpairiskpair ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 kpairp ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 singletonsubset ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 singletoninpowerset ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 singletoninpowunion ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 upairset2E ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 upairsubunion ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 upairinpowunion ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 ubforcartprodlem1 ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 ubforcartprodlem2 ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 ubforcartprodlem3 ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 cartprodpairin ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 cartprodmempair1 ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 cartprodmempair ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 setunionE2 ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 setunionsingleton1 ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 setunionsingleton2 ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 setunionsingleton ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 singletonprop ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 ex1E1 ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 ex1I ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 ex1I2 ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 singletonsuniq ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 setukpairinjL1 ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 kfstsingleton ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 theprop ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 kfstpairEq ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 cartprodfstin ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 setukpairinjL2 ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 setukpairinjL ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 setukpairinjR11 ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 setukpairinjR12 ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 setukpairinjR1 ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 upairequniteq ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 setukpairinjR2 ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 setukpairinjR ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 ksndsingleton ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 ksndpairEq ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 kpairsurjEq ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 cartprodsndin ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 cartprodpairmemEL ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 cartprodpairmemER ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 cartprodmempaircEq ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 cartprodfstpairEq ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 cartprodsndpairEq ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 cartprodpairsurjEq ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 dpsetconstrI ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 dpsetconstrSub ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 setOfPairsIsBReln ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 dpsetconstrERa ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 dpsetconstrEL1 ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 dpsetconstrEL2 ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 dpsetconstrER ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 funcImageSingleton ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 apProp ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 app ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 infuncsetfunc ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 ap2p ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 funcinfuncset ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 lamProp ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 lamp ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 lam2p ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 brelnall1 ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 brelnall2 ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 ex1E2 ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 funcGraphProp1 ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 funcGraphProp3 ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 funcGraphProp2 ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 funcextLem ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 funcGraphProp4 ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 subbreln ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 eqbreln ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 funcext ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 funcext2 ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 ap2apEq1 ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 ap2apEq2 ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 beta1 ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 eta1 ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 lam2lamEq ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 beta2 ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 eta2 ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 iffalseProp1 ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 iffalseProp2 ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 iftrueProp1 ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 iftrueProp2 ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 ifSingleton ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 ifp ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 theeq ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 iftrue ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 iffalse ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 iftrueorfalse ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 binintersectT_lem ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 binunionT_lem ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 powersetT_lem ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 setminusT_lem ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 complementT_lem ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 setextT ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 subsetTI ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 powersetTI1 ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 powersetTE1 ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 complementTI1 ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 complementTE1 ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 binintersectTELcontra ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 binintersectTERcontra ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 contrasubsetT ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 contrasubsetT1 ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 contrasubsetT2 ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 contrasubsetT3 ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 doubleComplementI1 ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 doubleComplementE1 ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 doubleComplementSub1 ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 doubleComplementSub2 ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 doubleComplementEq ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 complementTnotintersectT ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 complementImpComplementIntersect ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 complementSubsetComplementIntersect ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 complementInPowersetComplementIntersect ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 contraSubsetComplement ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 complementTcontraSubset ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 binunionTILcontra ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 binunionTIRcontra ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 inIntersectImpInUnion ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 inIntersectImpInUnion2 ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 inIntersectImpInIntersectUnions ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 intersectInPowersetIntersectUnions ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 inComplementUnionImpNotIn1 ) =>
% 1.03/1.14 (
% 1.03/1.14 ![
% 1.03/1.14 A:$i,X:$i]:
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 in @
% 1.03/1.14 X @
% 1.03/1.14 (
% 1.03/1.14 powerset @
% 1.03/1.14 A ) ) =>
% 1.03/1.14 (
% 1.03/1.14 ![
% 1.03/1.14 Y:$i]:
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 in @
% 1.03/1.14 Y @
% 1.03/1.14 (
% 1.03/1.14 powerset @
% 1.03/1.14 A ) ) =>
% 1.03/1.14 (
% 1.03/1.14 ![
% 1.03/1.14 Xx:$i]:
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 in @
% 1.03/1.14 Xx @ A ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 in @
% 1.03/1.14 Xx @
% 1.03/1.14 (
% 1.03/1.14 setminus @
% 1.03/1.14 A @
% 1.03/1.14 (
% 1.03/1.14 binunion @
% 1.03/1.14 X @ Y ) ) ) =>
% 1.03/1.14 (
% 1.03/1.14 in @
% 1.03/1.14 Xx @
% 1.03/1.14 (
% 1.03/1.14 setminus @
% 1.03/1.14 A @ X ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 1.03/1.14 thf(zf_stmt_0, conjecture,
% 1.03/1.14 (( setextAx ) =>
% 1.03/1.14 ( ( emptysetAx ) =>
% 1.03/1.14 ( ( setadjoinAx ) =>
% 1.03/1.14 ( ( ![X4:$i,X6:$i]:
% 1.03/1.14 ( ( in @ X6 @ ( powerset @ X4 ) ) <=>
% 1.03/1.14 ( ![X8:$i]: ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ) ) ) =>
% 1.03/1.14 ( ( setunionAx ) =>
% 1.03/1.14 ( ( omega0Ax ) =>
% 1.03/1.14 ( ( omegaSAx ) =>
% 1.03/1.14 ( ( omegaIndAx ) =>
% 1.03/1.14 ( ( replAx ) =>
% 1.03/1.14 ( ( foundationAx ) =>
% 1.03/1.14 ( ( wellorderingAx ) =>
% 1.03/1.14 ( ( descrp ) =>
% 1.03/1.14 ( ( dsetconstrI ) =>
% 1.03/1.14 ( ( dsetconstrEL ) =>
% 1.03/1.14 ( ( dsetconstrER ) =>
% 1.03/1.14 ( ( exuE1 ) =>
% 1.03/1.14 ( ( prop2setE ) =>
% 1.03/1.14 ( ( emptysetE ) =>
% 1.03/1.14 ( ( emptysetimpfalse ) =>
% 1.03/1.14 ( ( notinemptyset ) =>
% 1.03/1.14 ( ( exuE3e ) =>
% 1.03/1.14 ( ( setext ) =>
% 1.03/1.14 ( ( emptyI ) =>
% 1.03/1.14 ( ( noeltsimpempty ) =>
% 1.03/1.14 ( ( setbeta ) =>
% 1.03/1.14 ( ( nonemptyE1 ) =>
% 1.03/1.14 ( ( nonemptyI ) =>
% 1.03/1.14 ( ( nonemptyI1 ) =>
% 1.03/1.14 ( ( setadjoinIL ) =>
% 1.03/1.14 ( ( emptyinunitempty ) =>
% 1.03/1.14 ( ( setadjoinIR ) =>
% 1.03/1.14 ( ( setadjoinE ) =>
% 1.03/1.14 ( (
% 1.03/1.14 setadjoinOr ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 setoftrueEq ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 ![
% 1.03/1.14 X10:$i,
% 1.03/1.14 X12:$i]:
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 ![
% 1.03/1.14 X14:$i]:
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 in @
% 1.03/1.14 X14 @ X12 ) =>
% 1.03/1.14 (
% 1.03/1.14 in @
% 1.03/1.14 X14 @ X10 ) ) ) =>
% 1.03/1.14 (
% 1.03/1.14 in @
% 1.03/1.14 X12 @
% 1.03/1.14 (
% 1.03/1.14 powerset @
% 1.03/1.14 X10 ) ) ) ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 ![
% 1.03/1.14 X16:$i]:
% 1.03/1.14 (
% 1.03/1.14 in @
% 1.03/1.14 emptyset @
% 1.03/1.14 (
% 1.03/1.14 powerset @
% 1.03/1.14 X16 ) ) ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 ![
% 1.03/1.14 X18:$i]:
% 1.03/1.14 (
% 1.03/1.14 in @
% 1.03/1.14 emptyset @
% 1.03/1.14 (
% 1.03/1.14 powerset @
% 1.03/1.14 X18 ) ) ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 ![
% 1.03/1.14 X20:$i,
% 1.03/1.14 X22:$i,
% 1.03/1.14 X24:$i]:
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 in @
% 1.03/1.14 X22 @
% 1.03/1.14 (
% 1.03/1.14 powerset @
% 1.03/1.14 X20 ) ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 in @
% 1.03/1.14 X24 @ X22 ) =>
% 1.03/1.14 (
% 1.03/1.14 in @
% 1.03/1.14 X24 @ X20 ) ) ) ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 setunionI ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 setunionE ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 subPowSU ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 exuE2 ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 nonemptyImpWitness ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 uniqinunit ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 notinsingleton ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 eqinunit ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 singletonsswitch ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 upairsetE ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 upairsetIL ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 upairsetIR ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 emptyE1 ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 vacuousDall ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 quantDeMorgan1 ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 quantDeMorgan2 ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 quantDeMorgan3 ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 quantDeMorgan4 ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 prop2setI ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 prop2set2propI ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 notdexE ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 notdallE ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 exuI1 ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 exuI3 ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 exuI2 ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 inCongP ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 in__Cong ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 exuE3u ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 exu__Cong ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 emptyset__Cong ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 setadjoin__Cong ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 ![
% 1.03/1.14 X26:$i,
% 1.03/1.14 X28:$i]:
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 X26 ) =
% 1.03/1.14 (
% 1.03/1.14 X28 ) ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 powerset @
% 1.03/1.14 X26 ) =
% 1.03/1.14 (
% 1.03/1.14 powerset @
% 1.03/1.14 X28 ) ) ) ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 setunion__Cong ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 omega__Cong ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 exuEu ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 descr__Cong ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 dsetconstr__Cong ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 subsetI1 ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 eqimpsubset2 ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 eqimpsubset1 ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 subsetI2 ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 emptysetsubset ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 subsetE ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 subsetE2 ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 notsubsetI ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 notequalI1 ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 notequalI2 ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 subsetRefl ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 subsetTrans ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 setadjoinSub ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 setadjoinSub2 ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 subset2powerset ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 setextsub ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 subsetemptysetimpeq ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 powersetI1 ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 powersetE1 ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 ![
% 1.03/1.14 X30:$i]:
% 1.03/1.14 (
% 1.03/1.14 in @
% 1.03/1.14 X30 @
% 1.03/1.14 (
% 1.03/1.14 powerset @
% 1.03/1.14 X30 ) ) ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 powersetsubset ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 sepInPowerset ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 sepSubset ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 ![
% 1.03/1.14 X32:$i,
% 1.03/1.14 X34:$i,
% 1.03/1.14 X36:$i]:
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 in @
% 1.03/1.14 X36 @ X32 ) =>
% 1.03/1.14 (
% 1.03/1.14 in @
% 1.03/1.14 X36 @
% 1.03/1.14 (
% 1.03/1.14 binunion @
% 1.03/1.14 X32 @ X34 ) ) ) ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 upairset2IR ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 ![
% 1.03/1.14 X38:$i,
% 1.03/1.14 X40:$i,
% 1.03/1.14 X42:$i]:
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 in @
% 1.03/1.14 X42 @ X40 ) =>
% 1.03/1.14 (
% 1.03/1.14 in @
% 1.03/1.14 X42 @
% 1.03/1.14 (
% 1.03/1.14 binunion @
% 1.03/1.14 X38 @ X40 ) ) ) ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 ![
% 1.03/1.14 X44:$i,
% 1.03/1.14 X46:$i,
% 1.03/1.14 X48:$i,
% 1.03/1.14 X50:$o]:
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 in @
% 1.03/1.14 X48 @
% 1.03/1.14 (
% 1.03/1.14 binunion @
% 1.03/1.14 X44 @ X46 ) ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 in @
% 1.03/1.14 X48 @ X44 ) =>
% 1.03/1.14 (
% 1.03/1.14 X50 ) ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 in @
% 1.03/1.14 X48 @ X46 ) =>
% 1.03/1.14 (
% 1.03/1.14 X50 ) ) =>
% 1.03/1.14 (
% 1.03/1.14 X50 ) ) ) ) ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 ![
% 1.03/1.14 X52:$i,
% 1.03/1.14 X54:$i,
% 1.03/1.14 X56:$i]:
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 in @
% 1.03/1.14 X56 @
% 1.03/1.14 (
% 1.03/1.14 binunion @
% 1.03/1.14 X52 @ X54 ) ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 in @
% 1.03/1.14 X56 @ X54 ) |
% 1.03/1.14 (
% 1.03/1.14 in @
% 1.03/1.14 X56 @ X52 ) ) ) ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 ![
% 1.03/1.14 X58:$i,
% 1.03/1.14 X60:$i]:
% 1.03/1.14 (
% 1.03/1.14 subset @
% 1.03/1.14 X58 @
% 1.03/1.14 (
% 1.03/1.14 binunion @
% 1.03/1.14 X58 @ X60 ) ) ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 ![
% 1.03/1.14 X62:$i,
% 1.03/1.14 X64:$i]:
% 1.03/1.14 (
% 1.03/1.14 subset @
% 1.03/1.14 X64 @
% 1.03/1.14 (
% 1.03/1.14 binunion @
% 1.03/1.14 X62 @ X64 ) ) ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 binintersectI ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 binintersectSubset5 ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 binintersectEL ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 binintersectLsub ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 binintersectSubset2 ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 binintersectSubset3 ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 binintersectER ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 disjointsetsI1 ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 binintersectRsub ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 binintersectSubset4 ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 binintersectSubset1 ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 ![
% 1.03/1.14 X66:$i,
% 1.03/1.14 X68:$i,
% 1.03/1.14 X70:$i]:
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 binintersect
% 1.03/1.14 @
% 1.03/1.14 X66 @
% 1.03/1.14 (
% 1.03/1.14 binunion @
% 1.03/1.14 X68 @ X70 ) ) =
% 1.03/1.14 (
% 1.03/1.14 binunion @
% 1.03/1.14 (
% 1.03/1.14 binintersect
% 1.03/1.14 @
% 1.03/1.14 X66 @ X68 ) @
% 1.03/1.14 (
% 1.03/1.14 binintersect
% 1.03/1.14 @
% 1.03/1.14 X66 @ X70 ) ) ) ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 ![
% 1.03/1.14 X72:$i,
% 1.03/1.14 X74:$i,
% 1.03/1.14 X76:$i]:
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 in @
% 1.03/1.14 X76 @ X72 ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 ~(
% 1.03/1.14 in @
% 1.03/1.14 X76 @ X74 ) ) =>
% 1.03/1.14 (
% 1.03/1.14 in @
% 1.03/1.14 X76 @
% 1.03/1.14 (
% 1.03/1.14 setminus @
% 1.03/1.14 X72 @ X74 ) ) ) ) ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 ![
% 1.03/1.14 X78:$i,
% 1.03/1.14 X80:$i,
% 1.03/1.14 X82:$i]:
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 in @
% 1.03/1.14 X82 @
% 1.03/1.14 (
% 1.03/1.14 setminus @
% 1.03/1.14 X78 @ X80 ) ) =>
% 1.03/1.14 (
% 1.03/1.14 in @
% 1.03/1.14 X82 @ X78 ) ) ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 ![
% 1.03/1.14 X84:$i,
% 1.03/1.14 X86:$i,
% 1.03/1.14 X88:$i]:
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 in @
% 1.03/1.14 X88 @
% 1.03/1.14 (
% 1.03/1.14 setminus @
% 1.03/1.14 X84 @ X86 ) ) =>
% 1.03/1.14 (
% 1.03/1.14 ~(
% 1.03/1.14 in @
% 1.03/1.14 X88 @ X86 ) ) ) ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 ![
% 1.03/1.14 X90:$i,
% 1.03/1.14 X92:$i]:
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 subset @
% 1.03/1.14 X90 @ X92 ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 setminus @
% 1.03/1.14 X90 @ X92 ) =
% 1.03/1.14 (
% 1.03/1.14 emptyset ) ) ) ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 ![
% 1.03/1.14 X94:$i,
% 1.03/1.14 X96:$i,
% 1.03/1.14 X98:$i]:
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 ~(
% 1.03/1.14 in @
% 1.03/1.14 X98 @
% 1.03/1.14 (
% 1.03/1.14 setminus
% 1.03/1.14 @
% 1.03/1.14 X94 @ X96 ) ) ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 in @
% 1.03/1.14 X98 @ X94 ) =>
% 1.03/1.14 (
% 1.03/1.14 in @
% 1.03/1.14 X98 @ X96 ) ) ) ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 ![
% 1.03/1.14 X100:$i,
% 1.03/1.14 X102:$i,
% 1.03/1.14 X104:$i]:
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 ~(
% 1.03/1.14 in @
% 1.03/1.14 X104 @
% 1.03/1.14 (
% 1.03/1.14 setminus
% 1.03/1.14 @
% 1.03/1.14 X100 @
% 1.03/1.14 X102 ) ) ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 ~(
% 1.03/1.14 in @
% 1.03/1.14 X104 @
% 1.03/1.14 X102 ) ) =>
% 1.03/1.14 (
% 1.03/1.14 ~(
% 1.03/1.14 in @
% 1.03/1.14 X104 @
% 1.03/1.14 X100 ) ) ) ) ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 ![
% 1.03/1.14 X106:$i,
% 1.03/1.14 X108:$i,
% 1.03/1.14 X110:$i]:
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 ~(
% 1.03/1.14 in @
% 1.03/1.14 X110 @
% 1.03/1.14 X106 ) ) =>
% 1.03/1.14 (
% 1.03/1.14 ~(
% 1.03/1.14 in @
% 1.03/1.14 X110 @
% 1.03/1.14 (
% 1.03/1.14 setminus
% 1.03/1.14 @
% 1.03/1.14 X106 @
% 1.03/1.14 X108 ) ) ) ) ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 ![
% 1.03/1.14 X112:$i,
% 1.03/1.14 X114:$i,
% 1.03/1.14 X116:$i]:
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 in @
% 1.03/1.14 X116 @
% 1.03/1.14 X114 ) =>
% 1.03/1.14 (
% 1.03/1.14 ~(
% 1.03/1.14 in @
% 1.03/1.14 X116 @
% 1.03/1.14 (
% 1.03/1.14 setminus
% 1.03/1.14 @
% 1.03/1.14 X112 @
% 1.03/1.14 X114 ) ) ) ) ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 ![
% 1.03/1.14 X118:$i,
% 1.03/1.14 X120:$i]:
% 1.03/1.14 (
% 1.03/1.14 subset @
% 1.03/1.14 (
% 1.03/1.14 setminus @
% 1.03/1.14 X118 @
% 1.03/1.14 X120 ) @
% 1.03/1.14 X118 ) ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 ![
% 1.03/1.14 X122:$i,
% 1.03/1.14 X124:$i]:
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 setminus @
% 1.03/1.14 X122 @
% 1.03/1.14 X124 ) =
% 1.03/1.14 (
% 1.03/1.14 emptyset ) ) =>
% 1.03/1.14 (
% 1.03/1.14 subset @
% 1.03/1.14 X122 @
% 1.03/1.14 X124 ) ) ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 symdiffE ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 symdiffI1 ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 symdiffI2 ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 symdiffIneg1 ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 symdiffIneg2 ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 secondinupair ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 setukpairIL ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 setukpairIR ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 kpairiskpair ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 kpairp ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 singletonsubset ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 singletoninpowerset ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 ![
% 1.03/1.14 X126:$i,
% 1.03/1.14 X128:$i,
% 1.03/1.14 X130:$i]:
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 in @
% 1.03/1.14 X130 @
% 1.03/1.14 X126 ) =>
% 1.03/1.14 (
% 1.03/1.14 in @
% 1.03/1.14 (
% 1.03/1.14 setadjoin
% 1.03/1.14 @
% 1.03/1.14 X130 @
% 1.03/1.14 emptyset ) @
% 1.03/1.14 (
% 1.03/1.14 powerset @
% 1.03/1.14 (
% 1.03/1.14 binunion @
% 1.03/1.14 X126 @
% 1.03/1.14 X128 ) ) ) ) ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 upairset2E ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 ![
% 1.03/1.14 X132:$i,
% 1.03/1.14 X134:$i,
% 1.03/1.14 X136:$i]:
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 in @
% 1.03/1.14 X136 @
% 1.03/1.14 X132 ) =>
% 1.03/1.14 (
% 1.03/1.14 ![
% 1.03/1.14 X138:$i]:
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 in @
% 1.03/1.14 X138 @
% 1.03/1.14 X134 ) =>
% 1.03/1.14 (
% 1.03/1.14 subset @
% 1.03/1.14 (
% 1.03/1.14 setadjoin
% 1.03/1.14 @
% 1.03/1.14 X136 @
% 1.03/1.14 (
% 1.03/1.14 setadjoin
% 1.03/1.14 @
% 1.03/1.14 X138 @
% 1.03/1.14 emptyset ) ) @
% 1.03/1.14 (
% 1.03/1.14 binunion @
% 1.03/1.14 X132 @
% 1.03/1.14 X134 ) ) ) ) ) ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 ![
% 1.03/1.14 X140:$i,
% 1.03/1.14 X142:$i,
% 1.03/1.14 X144:$i]:
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 in @
% 1.03/1.14 X144 @
% 1.03/1.14 X140 ) =>
% 1.03/1.14 (
% 1.03/1.14 ![
% 1.03/1.14 X146:$i]:
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 in @
% 1.03/1.14 X146 @
% 1.03/1.14 X142 ) =>
% 1.03/1.14 (
% 1.03/1.14 in @
% 1.03/1.14 (
% 1.03/1.14 setadjoin
% 1.03/1.14 @
% 1.03/1.14 X144 @
% 1.03/1.14 (
% 1.03/1.14 setadjoin
% 1.03/1.14 @
% 1.03/1.14 X146 @
% 1.03/1.14 emptyset ) ) @
% 1.03/1.14 (
% 1.03/1.14 powerset @
% 1.03/1.14 (
% 1.03/1.14 binunion @
% 1.03/1.14 X140 @
% 1.03/1.14 X142 ) ) ) ) ) ) ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 ![
% 1.03/1.14 X148:$i,
% 1.03/1.14 X150:$i,
% 1.03/1.14 X152:$i]:
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 in @
% 1.03/1.14 X152 @
% 1.03/1.14 X148 ) =>
% 1.03/1.14 (
% 1.03/1.14 ![
% 1.03/1.14 X154:$i]:
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 in @
% 1.03/1.14 X154 @
% 1.03/1.14 X150 ) =>
% 1.03/1.14 (
% 1.03/1.14 subset @
% 1.03/1.14 (
% 1.03/1.14 setadjoin
% 1.03/1.14 @
% 1.03/1.14 (
% 1.03/1.14 setadjoin
% 1.03/1.14 @
% 1.03/1.14 X152 @
% 1.03/1.14 emptyset ) @
% 1.03/1.14 (
% 1.03/1.14 setadjoin
% 1.03/1.14 @
% 1.03/1.14 (
% 1.03/1.14 setadjoin
% 1.03/1.14 @
% 1.03/1.14 X152 @
% 1.03/1.14 (
% 1.03/1.14 setadjoin
% 1.03/1.14 @
% 1.03/1.14 X154 @
% 1.03/1.14 emptyset ) ) @
% 1.03/1.14 emptyset ) ) @
% 1.03/1.14 (
% 1.03/1.14 powerset @
% 1.03/1.14 (
% 1.03/1.14 binunion @
% 1.03/1.14 X148 @
% 1.03/1.14 X150 ) ) ) ) ) ) ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 ![
% 1.03/1.14 X156:$i,
% 1.03/1.14 X158:$i,
% 1.03/1.14 X160:$i]:
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 in @
% 1.03/1.14 X160 @
% 1.03/1.14 X156 ) =>
% 1.03/1.14 (
% 1.03/1.14 ![
% 1.03/1.14 X162:$i]:
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 in @
% 1.03/1.14 X162 @
% 1.03/1.14 X158 ) =>
% 1.03/1.14 (
% 1.03/1.14 in @
% 1.03/1.14 (
% 1.03/1.14 setadjoin
% 1.03/1.14 @
% 1.03/1.14 (
% 1.03/1.14 setadjoin
% 1.03/1.14 @
% 1.03/1.14 X160 @
% 1.03/1.14 emptyset ) @
% 1.03/1.14 (
% 1.03/1.14 setadjoin
% 1.03/1.14 @
% 1.03/1.14 (
% 1.03/1.14 setadjoin
% 1.03/1.14 @
% 1.03/1.14 X160 @
% 1.03/1.14 (
% 1.03/1.14 setadjoin
% 1.03/1.14 @
% 1.03/1.14 X162 @
% 1.03/1.14 emptyset ) ) @
% 1.03/1.14 emptyset ) ) @
% 1.03/1.14 (
% 1.03/1.14 powerset @
% 1.03/1.14 (
% 1.03/1.14 powerset @
% 1.03/1.14 (
% 1.03/1.14 binunion @
% 1.03/1.14 X156 @
% 1.03/1.14 X158 ) ) ) ) ) ) ) ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 ![
% 1.03/1.14 X164:$i,
% 1.03/1.14 X166:$i,
% 1.03/1.14 X168:$i]:
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 in @
% 1.03/1.14 X168 @
% 1.03/1.14 X164 ) =>
% 1.03/1.14 (
% 1.03/1.14 ![
% 1.03/1.14 X170:$i]:
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 in @
% 1.03/1.14 X170 @
% 1.03/1.14 X166 ) =>
% 1.03/1.14 (
% 1.03/1.14 in @
% 1.03/1.14 (
% 1.03/1.14 kpair @
% 1.03/1.14 X168 @
% 1.03/1.14 X170 ) @
% 1.03/1.14 (
% 1.03/1.14 powerset @
% 1.03/1.14 (
% 1.03/1.14 powerset @
% 1.03/1.14 (
% 1.03/1.14 binunion @
% 1.03/1.14 X164 @
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% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 cartprodpairin ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 cartprodmempair1 ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 cartprodmempair ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 setunionE2 ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 setunionsingleton1 ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 setunionsingleton2 ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 setunionsingleton ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 singletonprop ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 ex1E1 ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 ex1I ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 ex1I2 ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 singletonsuniq ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 setukpairinjL1 ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 kfstsingleton ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 theprop ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 kfstpairEq ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 cartprodfstin ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 setukpairinjL2 ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 setukpairinjL ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 setukpairinjR11 ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 setukpairinjR12 ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 setukpairinjR1 ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 upairequniteq ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 setukpairinjR2 ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 setukpairinjR ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 ksndsingleton ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 ksndpairEq ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 kpairsurjEq ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 cartprodsndin ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 cartprodpairmemEL ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 cartprodpairmemER ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 cartprodmempaircEq ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 cartprodfstpairEq ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 cartprodsndpairEq ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 cartprodpairsurjEq ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 dpsetconstrI ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 dpsetconstrSub ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 setOfPairsIsBReln ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 dpsetconstrERa ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 dpsetconstrEL1 ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 dpsetconstrEL2 ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 dpsetconstrER ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 funcImageSingleton ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 apProp ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 app ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 infuncsetfunc ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 ap2p ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 funcinfuncset ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 lamProp ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 lamp ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 lam2p ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 brelnall1 ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 brelnall2 ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 ex1E2 ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 funcGraphProp1 ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 funcGraphProp3 ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 funcGraphProp2 ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 funcextLem ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 funcGraphProp4 ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 subbreln ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 eqbreln ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 funcext ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 funcext2 ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 ap2apEq1 ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 ap2apEq2 ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 beta1 ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 eta1 ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 lam2lamEq ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 beta2 ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 eta2 ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 iffalseProp1 ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 iffalseProp2 ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 iftrueProp1 ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 iftrueProp2 ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 ifSingleton ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 ifp ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 theeq ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 iftrue ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 iffalse ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 iftrueorfalse ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 binintersectT_lem ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 ![
% 1.03/1.14 X172:$i,
% 1.03/1.14 X174:$i]:
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 in @
% 1.03/1.14 X174 @
% 1.03/1.14 (
% 1.03/1.14 powerset @
% 1.03/1.14 X172 ) ) =>
% 1.03/1.14 (
% 1.03/1.14 ![
% 1.03/1.14 X176:$i]:
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 in @
% 1.03/1.14 X176 @
% 1.03/1.14 (
% 1.03/1.14 powerset @
% 1.03/1.14 X172 ) ) =>
% 1.03/1.14 (
% 1.03/1.14 in @
% 1.03/1.14 (
% 1.03/1.14 binunion @
% 1.03/1.14 X174 @
% 1.03/1.14 X176 ) @
% 1.03/1.14 (
% 1.03/1.14 powerset @
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% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 ![
% 1.03/1.14 X178:$i,
% 1.03/1.14 X180:$i]:
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 in @
% 1.03/1.14 X180 @
% 1.03/1.14 (
% 1.03/1.14 powerset @
% 1.03/1.14 X178 ) ) =>
% 1.03/1.14 (
% 1.03/1.14 in @
% 1.03/1.14 (
% 1.03/1.14 powerset @
% 1.03/1.14 X180 ) @
% 1.03/1.14 (
% 1.03/1.14 powerset @
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% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 ![
% 1.03/1.14 X182:$i,
% 1.03/1.14 X184:$i]:
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 in @
% 1.03/1.14 X184 @
% 1.03/1.14 (
% 1.03/1.14 powerset @
% 1.03/1.14 X182 ) ) =>
% 1.03/1.14 (
% 1.03/1.14 ![
% 1.03/1.14 X186:$i]:
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 in @
% 1.03/1.14 X186 @
% 1.03/1.14 (
% 1.03/1.14 powerset @
% 1.03/1.14 X182 ) ) =>
% 1.03/1.14 (
% 1.03/1.14 in @
% 1.03/1.14 (
% 1.03/1.14 setminus @
% 1.03/1.14 X184 @
% 1.03/1.14 X186 ) @
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% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 ![
% 1.03/1.14 X188:$i,
% 1.03/1.14 X190:$i]:
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 in @
% 1.03/1.14 X190 @
% 1.03/1.14 (
% 1.03/1.14 powerset @
% 1.03/1.14 X188 ) ) =>
% 1.03/1.14 (
% 1.03/1.14 in @
% 1.03/1.14 (
% 1.03/1.14 setminus @
% 1.03/1.14 X188 @
% 1.03/1.14 X190 ) @
% 1.03/1.14 (
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% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 ![
% 1.03/1.14 X192:$i,
% 1.03/1.14 X194:$i]:
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 in @
% 1.03/1.14 X194 @
% 1.03/1.14 (
% 1.03/1.14 powerset @
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% 1.03/1.14 (
% 1.03/1.14 ![
% 1.03/1.14 X196:$i]:
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 in @
% 1.03/1.14 X196 @
% 1.03/1.14 (
% 1.03/1.14 powerset @
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% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 ![
% 1.03/1.14 X198:$i]:
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 in @
% 1.03/1.14 X198 @
% 1.03/1.14 X192 ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 in @
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% 1.03/1.14 (
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% 1.03/1.14 (
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% 1.03/1.14 X200 @
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% 1.03/1.14 (
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% 1.03/1.14 X200 @
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% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 subsetTI ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 ![
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% 1.03/1.14 X204:$i]:
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 in @
% 1.03/1.14 X204 @
% 1.03/1.14 (
% 1.03/1.14 powerset @
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% 1.03/1.14 ![
% 1.03/1.14 X206:$i]:
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 in @
% 1.03/1.14 X206 @
% 1.03/1.14 (
% 1.03/1.14 powerset @
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% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 ![
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% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 in @
% 1.03/1.14 X208 @
% 1.03/1.14 X202 ) =>
% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 in @
% 1.03/1.14 X208 @
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% 1.03/1.14 (
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% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 ![
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% 1.03/1.14 X212:$i]:
% 1.03/1.14 (
% 1.03/1.14 (
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% 1.03/1.14 X212 @
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% 1.03/1.14 X214 @
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% 1.03/1.14 (
% 1.03/1.14 (
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% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 in @
% 1.03/1.14 X212 @
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% 1.03/1.14 powerset @
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% 1.03/1.14 (
% 1.03/1.14 (
% 1.03/1.14 in @
% 1.03/1.14 X216 @
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% 1.03/1.14 (
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% 1.03/1.14 (
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% 1.03/1.14 (
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% 1.03/1.14 (
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% 1.03/1.14 (
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% 1.03/1.15 (
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% 1.03/1.15 (
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% 1.03/1.15 (
% 1.03/1.15 in @
% 1.03/1.15 X338 @
% 1.03/1.15 (
% 1.03/1.15 powerset @
% 1.03/1.15 X334 ) ) =>
% 1.03/1.15 (
% 1.03/1.15 ![
% 1.03/1.15 X340:$i]:
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 in @
% 1.03/1.15 X340 @
% 1.03/1.15 (
% 1.03/1.15 powerset @
% 1.03/1.15 X334 ) ) =>
% 1.03/1.15 (
% 1.03/1.15 in @
% 1.03/1.15 (
% 1.03/1.15 binintersect
% 1.03/1.15 @
% 1.03/1.15 X336 @
% 1.03/1.15 X338 ) @
% 1.03/1.15 (
% 1.03/1.15 powerset @
% 1.03/1.15 (
% 1.03/1.15 binintersect
% 1.03/1.15 @
% 1.03/1.15 (
% 1.03/1.15 binunion @
% 1.03/1.15 X336 @
% 1.03/1.15 X340 ) @
% 1.03/1.15 (
% 1.03/1.15 binunion @
% 1.03/1.15 X338 @
% 1.03/1.15 X340 ) ) ) ) ) ) ) ) ) ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 ![
% 1.03/1.15 X342:$i,
% 1.03/1.15 X344:$i]:
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 in @
% 1.03/1.15 X344 @
% 1.03/1.15 (
% 1.03/1.15 powerset @
% 1.03/1.15 X342 ) ) =>
% 1.03/1.15 (
% 1.03/1.15 ![
% 1.03/1.15 X346:$i]:
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 in @
% 1.03/1.15 X346 @
% 1.03/1.15 (
% 1.03/1.15 powerset @
% 1.03/1.15 X342 ) ) =>
% 1.03/1.15 (
% 1.03/1.15 ![
% 1.03/1.15 X348:$i]:
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 in @
% 1.03/1.15 X348 @
% 1.03/1.15 X342 ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 in @
% 1.03/1.15 X348 @
% 1.03/1.15 (
% 1.03/1.15 setminus @
% 1.03/1.15 X342 @
% 1.03/1.15 (
% 1.03/1.15 binunion @
% 1.03/1.15 X344 @
% 1.03/1.15 X346 ) ) ) =>
% 1.03/1.15 (
% 1.03/1.15 ~(
% 1.03/1.15 in @
% 1.03/1.15 X348 @
% 1.03/1.15 X344 ) ) ) ) ) ) ) ) ) =>
% 1.03/1.15 (
% 1.03/1.15 ![
% 1.03/1.15 X350:$i,
% 1.03/1.15 X352:$i]:
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 in @
% 1.03/1.15 X352 @
% 1.03/1.15 (
% 1.03/1.15 powerset @
% 1.03/1.15 X350 ) ) =>
% 1.03/1.15 (
% 1.03/1.15 ![
% 1.03/1.15 X354:$i]:
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 in @
% 1.03/1.15 X354 @
% 1.03/1.15 (
% 1.03/1.15 powerset @
% 1.03/1.15 X350 ) ) =>
% 1.03/1.15 (
% 1.03/1.15 ![
% 1.03/1.15 X356:$i]:
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 in @
% 1.03/1.15 X356 @
% 1.03/1.15 X350 ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 in @
% 1.03/1.15 X356 @
% 1.03/1.15 (
% 1.03/1.15 setminus @
% 1.03/1.15 X350 @
% 1.03/1.15 (
% 1.03/1.15 binunion @
% 1.03/1.15 X352 @
% 1.03/1.15 X354 ) ) ) =>
% 1.03/1.15 (
% 1.03/1.15 in @
% 1.03/1.15 X356 @
% 1.03/1.15 (
% 1.03/1.15 setminus @
% 1.03/1.15 X350 @
% 1.03/1.15 X352 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 1.03/1.15 thf(zf_stmt_1, type, zip_tseitin_0 : $i > $i > $i > $o).
% 1.03/1.15 thf(zf_stmt_2, axiom,
% 1.03/1.15 (![X8:$i,X6:$i,X4:$i]:
% 1.03/1.15 ( ( zip_tseitin_0 @ X8 @ X6 @ X4 ) <=>
% 1.03/1.15 ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ))).
% 1.03/1.15 thf(zf_stmt_3, conjecture,
% 1.03/1.15 (( setextAx ) =>
% 1.03/1.15 ( ( emptysetAx ) =>
% 1.03/1.15 ( ( setadjoinAx ) =>
% 1.03/1.15 ( ( ![X4:$i,X6:$i]:
% 1.03/1.15 ( ( in @ X6 @ ( powerset @ X4 ) ) <=>
% 1.03/1.15 ( ![X8:$i]: ( zip_tseitin_0 @ X8 @ X6 @ X4 ) ) ) ) =>
% 1.03/1.15 ( ( setunionAx ) =>
% 1.03/1.15 ( ( omega0Ax ) =>
% 1.03/1.15 ( ( omegaSAx ) =>
% 1.03/1.15 ( ( omegaIndAx ) =>
% 1.03/1.15 ( ( replAx ) =>
% 1.03/1.15 ( ( foundationAx ) =>
% 1.03/1.15 ( ( wellorderingAx ) =>
% 1.03/1.15 ( ( descrp ) =>
% 1.03/1.15 ( ( dsetconstrI ) =>
% 1.03/1.15 ( ( dsetconstrEL ) =>
% 1.03/1.15 ( ( dsetconstrER ) =>
% 1.03/1.15 ( ( exuE1 ) =>
% 1.03/1.15 ( ( prop2setE ) =>
% 1.03/1.15 ( ( emptysetE ) =>
% 1.03/1.15 ( ( emptysetimpfalse ) =>
% 1.03/1.15 ( ( notinemptyset ) =>
% 1.03/1.15 ( ( exuE3e ) =>
% 1.03/1.15 ( ( setext ) =>
% 1.03/1.15 ( ( emptyI ) =>
% 1.03/1.15 ( ( noeltsimpempty ) =>
% 1.03/1.15 ( ( setbeta ) =>
% 1.03/1.15 ( ( nonemptyE1 ) =>
% 1.03/1.15 ( ( nonemptyI ) =>
% 1.03/1.15 ( ( nonemptyI1 ) =>
% 1.03/1.15 ( ( setadjoinIL ) =>
% 1.03/1.15 ( ( emptyinunitempty ) =>
% 1.03/1.15 ( ( setadjoinIR ) =>
% 1.03/1.15 ( ( setadjoinE ) =>
% 1.03/1.15 ( (
% 1.03/1.15 setadjoinOr ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 setoftrueEq ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 ![
% 1.03/1.15 X10:$i,
% 1.03/1.15 X12:$i]:
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 ![
% 1.03/1.15 X14:$i]:
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 in @
% 1.03/1.15 X14 @ X12 ) =>
% 1.03/1.15 (
% 1.03/1.15 in @
% 1.03/1.15 X14 @ X10 ) ) ) =>
% 1.03/1.15 (
% 1.03/1.15 in @
% 1.03/1.15 X12 @
% 1.03/1.15 (
% 1.03/1.15 powerset @
% 1.03/1.15 X10 ) ) ) ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 ![
% 1.03/1.15 X16:$i]:
% 1.03/1.15 (
% 1.03/1.15 in @
% 1.03/1.15 emptyset @
% 1.03/1.15 (
% 1.03/1.15 powerset @
% 1.03/1.15 X16 ) ) ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 ![
% 1.03/1.15 X18:$i]:
% 1.03/1.15 (
% 1.03/1.15 in @
% 1.03/1.15 emptyset @
% 1.03/1.15 (
% 1.03/1.15 powerset @
% 1.03/1.15 X18 ) ) ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 ![
% 1.03/1.15 X20:$i,
% 1.03/1.15 X22:$i,
% 1.03/1.15 X24:$i]:
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 in @
% 1.03/1.15 X22 @
% 1.03/1.15 (
% 1.03/1.15 powerset @
% 1.03/1.15 X20 ) ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 in @
% 1.03/1.15 X24 @ X22 ) =>
% 1.03/1.15 (
% 1.03/1.15 in @
% 1.03/1.15 X24 @ X20 ) ) ) ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 setunionI ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 setunionE ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 subPowSU ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 exuE2 ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 nonemptyImpWitness ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 uniqinunit ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 notinsingleton ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 eqinunit ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 singletonsswitch ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 upairsetE ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 upairsetIL ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 upairsetIR ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 emptyE1 ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 vacuousDall ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 quantDeMorgan1 ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 quantDeMorgan2 ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 quantDeMorgan3 ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 quantDeMorgan4 ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 prop2setI ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 prop2set2propI ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 notdexE ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 notdallE ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 exuI1 ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 exuI3 ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 exuI2 ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 inCongP ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 in__Cong ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 exuE3u ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 exu__Cong ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 emptyset__Cong ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 setadjoin__Cong ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 ![
% 1.03/1.15 X26:$i,
% 1.03/1.15 X28:$i]:
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 X26 ) =
% 1.03/1.15 (
% 1.03/1.15 X28 ) ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 powerset @
% 1.03/1.15 X26 ) =
% 1.03/1.15 (
% 1.03/1.15 powerset @
% 1.03/1.15 X28 ) ) ) ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 setunion__Cong ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 omega__Cong ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 exuEu ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 descr__Cong ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 dsetconstr__Cong ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 subsetI1 ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 eqimpsubset2 ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 eqimpsubset1 ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 subsetI2 ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 emptysetsubset ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 subsetE ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 subsetE2 ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 notsubsetI ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 notequalI1 ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 notequalI2 ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 subsetRefl ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 subsetTrans ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 setadjoinSub ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 setadjoinSub2 ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 subset2powerset ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 setextsub ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 subsetemptysetimpeq ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 powersetI1 ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 powersetE1 ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 ![
% 1.03/1.15 X30:$i]:
% 1.03/1.15 (
% 1.03/1.15 in @
% 1.03/1.15 X30 @
% 1.03/1.15 (
% 1.03/1.15 powerset @
% 1.03/1.15 X30 ) ) ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 powersetsubset ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 sepInPowerset ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 sepSubset ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 ![
% 1.03/1.15 X32:$i,
% 1.03/1.15 X34:$i,
% 1.03/1.15 X36:$i]:
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 in @
% 1.03/1.15 X36 @ X32 ) =>
% 1.03/1.15 (
% 1.03/1.15 in @
% 1.03/1.15 X36 @
% 1.03/1.15 (
% 1.03/1.15 binunion @
% 1.03/1.15 X32 @ X34 ) ) ) ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 upairset2IR ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 ![
% 1.03/1.15 X38:$i,
% 1.03/1.15 X40:$i,
% 1.03/1.15 X42:$i]:
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 in @
% 1.03/1.15 X42 @ X40 ) =>
% 1.03/1.15 (
% 1.03/1.15 in @
% 1.03/1.15 X42 @
% 1.03/1.15 (
% 1.03/1.15 binunion @
% 1.03/1.15 X38 @ X40 ) ) ) ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 ![
% 1.03/1.15 X44:$i,
% 1.03/1.15 X46:$i,
% 1.03/1.15 X48:$i,
% 1.03/1.15 X50:$o]:
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 in @
% 1.03/1.15 X48 @
% 1.03/1.15 (
% 1.03/1.15 binunion @
% 1.03/1.15 X44 @ X46 ) ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 in @
% 1.03/1.15 X48 @ X44 ) =>
% 1.03/1.15 (
% 1.03/1.15 X50 ) ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 in @
% 1.03/1.15 X48 @ X46 ) =>
% 1.03/1.15 (
% 1.03/1.15 X50 ) ) =>
% 1.03/1.15 (
% 1.03/1.15 X50 ) ) ) ) ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 ![
% 1.03/1.15 X52:$i,
% 1.03/1.15 X54:$i,
% 1.03/1.15 X56:$i]:
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 in @
% 1.03/1.15 X56 @
% 1.03/1.15 (
% 1.03/1.15 binunion @
% 1.03/1.15 X52 @ X54 ) ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 in @
% 1.03/1.15 X56 @ X52 ) |
% 1.03/1.15 (
% 1.03/1.15 in @
% 1.03/1.15 X56 @ X54 ) ) ) ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 ![
% 1.03/1.15 X58:$i,
% 1.03/1.15 X60:$i]:
% 1.03/1.15 (
% 1.03/1.15 subset @
% 1.03/1.15 X58 @
% 1.03/1.15 (
% 1.03/1.15 binunion @
% 1.03/1.15 X58 @ X60 ) ) ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 ![
% 1.03/1.15 X62:$i,
% 1.03/1.15 X64:$i]:
% 1.03/1.15 (
% 1.03/1.15 subset @
% 1.03/1.15 X64 @
% 1.03/1.15 (
% 1.03/1.15 binunion @
% 1.03/1.15 X62 @ X64 ) ) ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 binintersectI ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 binintersectSubset5 ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 binintersectEL ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 binintersectLsub ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 binintersectSubset2 ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 binintersectSubset3 ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 binintersectER ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 disjointsetsI1 ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 binintersectRsub ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 binintersectSubset4 ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 binintersectSubset1 ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 ![
% 1.03/1.15 X66:$i,
% 1.03/1.15 X68:$i,
% 1.03/1.15 X70:$i]:
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 binintersect
% 1.03/1.15 @
% 1.03/1.15 X66 @
% 1.03/1.15 (
% 1.03/1.15 binunion @
% 1.03/1.15 X68 @ X70 ) ) =
% 1.03/1.15 (
% 1.03/1.15 binunion @
% 1.03/1.15 (
% 1.03/1.15 binintersect
% 1.03/1.15 @
% 1.03/1.15 X66 @ X68 ) @
% 1.03/1.15 (
% 1.03/1.15 binintersect
% 1.03/1.15 @
% 1.03/1.15 X66 @ X70 ) ) ) ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 ![
% 1.03/1.15 X72:$i,
% 1.03/1.15 X74:$i,
% 1.03/1.15 X76:$i]:
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 in @
% 1.03/1.15 X76 @ X72 ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 ~(
% 1.03/1.15 in @
% 1.03/1.15 X76 @ X74 ) ) =>
% 1.03/1.15 (
% 1.03/1.15 in @
% 1.03/1.15 X76 @
% 1.03/1.15 (
% 1.03/1.15 setminus @
% 1.03/1.15 X72 @ X74 ) ) ) ) ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 ![
% 1.03/1.15 X78:$i,
% 1.03/1.15 X80:$i,
% 1.03/1.15 X82:$i]:
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 in @
% 1.03/1.15 X82 @
% 1.03/1.15 (
% 1.03/1.15 setminus @
% 1.03/1.15 X78 @ X80 ) ) =>
% 1.03/1.15 (
% 1.03/1.15 in @
% 1.03/1.15 X82 @ X78 ) ) ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 ![
% 1.03/1.15 X84:$i,
% 1.03/1.15 X86:$i,
% 1.03/1.15 X88:$i]:
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 in @
% 1.03/1.15 X88 @
% 1.03/1.15 (
% 1.03/1.15 setminus @
% 1.03/1.15 X84 @ X86 ) ) =>
% 1.03/1.15 (
% 1.03/1.15 ~(
% 1.03/1.15 in @
% 1.03/1.15 X88 @ X86 ) ) ) ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 ![
% 1.03/1.15 X90:$i,
% 1.03/1.15 X92:$i]:
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 subset @
% 1.03/1.15 X90 @ X92 ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 setminus @
% 1.03/1.15 X90 @ X92 ) =
% 1.03/1.15 (
% 1.03/1.15 emptyset ) ) ) ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 ![
% 1.03/1.15 X94:$i,
% 1.03/1.15 X96:$i,
% 1.03/1.15 X98:$i]:
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 ~(
% 1.03/1.15 in @
% 1.03/1.15 X98 @
% 1.03/1.15 (
% 1.03/1.15 setminus
% 1.03/1.15 @
% 1.03/1.15 X94 @ X96 ) ) ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 in @
% 1.03/1.15 X98 @ X94 ) =>
% 1.03/1.15 (
% 1.03/1.15 in @
% 1.03/1.15 X98 @ X96 ) ) ) ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 ![
% 1.03/1.15 X100:$i,
% 1.03/1.15 X102:$i,
% 1.03/1.15 X104:$i]:
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 ~(
% 1.03/1.15 in @
% 1.03/1.15 X104 @
% 1.03/1.15 (
% 1.03/1.15 setminus
% 1.03/1.15 @
% 1.03/1.15 X100 @
% 1.03/1.15 X102 ) ) ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 ~(
% 1.03/1.15 in @
% 1.03/1.15 X104 @
% 1.03/1.15 X102 ) ) =>
% 1.03/1.15 (
% 1.03/1.15 ~(
% 1.03/1.15 in @
% 1.03/1.15 X104 @
% 1.03/1.15 X100 ) ) ) ) ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 ![
% 1.03/1.15 X106:$i,
% 1.03/1.15 X108:$i,
% 1.03/1.15 X110:$i]:
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 ~(
% 1.03/1.15 in @
% 1.03/1.15 X110 @
% 1.03/1.15 X106 ) ) =>
% 1.03/1.15 (
% 1.03/1.15 ~(
% 1.03/1.15 in @
% 1.03/1.15 X110 @
% 1.03/1.15 (
% 1.03/1.15 setminus
% 1.03/1.15 @
% 1.03/1.15 X106 @
% 1.03/1.15 X108 ) ) ) ) ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 ![
% 1.03/1.15 X112:$i,
% 1.03/1.15 X114:$i,
% 1.03/1.15 X116:$i]:
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 in @
% 1.03/1.15 X116 @
% 1.03/1.15 X114 ) =>
% 1.03/1.15 (
% 1.03/1.15 ~(
% 1.03/1.15 in @
% 1.03/1.15 X116 @
% 1.03/1.15 (
% 1.03/1.15 setminus
% 1.03/1.15 @
% 1.03/1.15 X112 @
% 1.03/1.15 X114 ) ) ) ) ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 ![
% 1.03/1.15 X118:$i,
% 1.03/1.15 X120:$i]:
% 1.03/1.15 (
% 1.03/1.15 subset @
% 1.03/1.15 (
% 1.03/1.15 setminus @
% 1.03/1.15 X118 @
% 1.03/1.15 X120 ) @
% 1.03/1.15 X118 ) ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 ![
% 1.03/1.15 X122:$i,
% 1.03/1.15 X124:$i]:
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 setminus @
% 1.03/1.15 X122 @
% 1.03/1.15 X124 ) =
% 1.03/1.15 (
% 1.03/1.15 emptyset ) ) =>
% 1.03/1.15 (
% 1.03/1.15 subset @
% 1.03/1.15 X122 @
% 1.03/1.15 X124 ) ) ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 symdiffE ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 symdiffI1 ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 symdiffI2 ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 symdiffIneg1 ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 symdiffIneg2 ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 secondinupair ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 setukpairIL ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 setukpairIR ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 kpairiskpair ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 kpairp ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 singletonsubset ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 singletoninpowerset ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 ![
% 1.03/1.15 X126:$i,
% 1.03/1.15 X128:$i,
% 1.03/1.15 X130:$i]:
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 in @
% 1.03/1.15 X130 @
% 1.03/1.15 X126 ) =>
% 1.03/1.15 (
% 1.03/1.15 in @
% 1.03/1.15 (
% 1.03/1.15 setadjoin
% 1.03/1.15 @
% 1.03/1.15 X130 @
% 1.03/1.15 emptyset ) @
% 1.03/1.15 (
% 1.03/1.15 powerset @
% 1.03/1.15 (
% 1.03/1.15 binunion @
% 1.03/1.15 X126 @
% 1.03/1.15 X128 ) ) ) ) ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 upairset2E ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 ![
% 1.03/1.15 X132:$i,
% 1.03/1.15 X134:$i,
% 1.03/1.15 X136:$i]:
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 in @
% 1.03/1.15 X136 @
% 1.03/1.15 X132 ) =>
% 1.03/1.15 (
% 1.03/1.15 ![
% 1.03/1.15 X138:$i]:
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 in @
% 1.03/1.15 X138 @
% 1.03/1.15 X134 ) =>
% 1.03/1.15 (
% 1.03/1.15 subset @
% 1.03/1.15 (
% 1.03/1.15 setadjoin
% 1.03/1.15 @
% 1.03/1.15 X136 @
% 1.03/1.15 (
% 1.03/1.15 setadjoin
% 1.03/1.15 @
% 1.03/1.15 X138 @
% 1.03/1.15 emptyset ) ) @
% 1.03/1.15 (
% 1.03/1.15 binunion @
% 1.03/1.15 X132 @
% 1.03/1.15 X134 ) ) ) ) ) ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 ![
% 1.03/1.15 X140:$i,
% 1.03/1.15 X142:$i,
% 1.03/1.15 X144:$i]:
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 in @
% 1.03/1.15 X144 @
% 1.03/1.15 X140 ) =>
% 1.03/1.15 (
% 1.03/1.15 ![
% 1.03/1.15 X146:$i]:
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 in @
% 1.03/1.15 X146 @
% 1.03/1.15 X142 ) =>
% 1.03/1.15 (
% 1.03/1.15 in @
% 1.03/1.15 (
% 1.03/1.15 setadjoin
% 1.03/1.15 @
% 1.03/1.15 X144 @
% 1.03/1.15 (
% 1.03/1.15 setadjoin
% 1.03/1.15 @
% 1.03/1.15 X146 @
% 1.03/1.15 emptyset ) ) @
% 1.03/1.15 (
% 1.03/1.15 powerset @
% 1.03/1.15 (
% 1.03/1.15 binunion @
% 1.03/1.15 X140 @
% 1.03/1.15 X142 ) ) ) ) ) ) ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 ![
% 1.03/1.15 X148:$i,
% 1.03/1.15 X150:$i,
% 1.03/1.15 X152:$i]:
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 in @
% 1.03/1.15 X152 @
% 1.03/1.15 X148 ) =>
% 1.03/1.15 (
% 1.03/1.15 ![
% 1.03/1.15 X154:$i]:
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 in @
% 1.03/1.15 X154 @
% 1.03/1.15 X150 ) =>
% 1.03/1.15 (
% 1.03/1.15 subset @
% 1.03/1.15 (
% 1.03/1.15 setadjoin
% 1.03/1.15 @
% 1.03/1.15 (
% 1.03/1.15 setadjoin
% 1.03/1.15 @
% 1.03/1.15 X152 @
% 1.03/1.15 emptyset ) @
% 1.03/1.15 (
% 1.03/1.15 setadjoin
% 1.03/1.15 @
% 1.03/1.15 (
% 1.03/1.15 setadjoin
% 1.03/1.15 @
% 1.03/1.15 X152 @
% 1.03/1.15 (
% 1.03/1.15 setadjoin
% 1.03/1.15 @
% 1.03/1.15 X154 @
% 1.03/1.15 emptyset ) ) @
% 1.03/1.15 emptyset ) ) @
% 1.03/1.15 (
% 1.03/1.15 powerset @
% 1.03/1.15 (
% 1.03/1.15 binunion @
% 1.03/1.15 X148 @
% 1.03/1.15 X150 ) ) ) ) ) ) ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 ![
% 1.03/1.15 X156:$i,
% 1.03/1.15 X158:$i,
% 1.03/1.15 X160:$i]:
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 in @
% 1.03/1.15 X160 @
% 1.03/1.15 X156 ) =>
% 1.03/1.15 (
% 1.03/1.15 ![
% 1.03/1.15 X162:$i]:
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 in @
% 1.03/1.15 X162 @
% 1.03/1.15 X158 ) =>
% 1.03/1.15 (
% 1.03/1.15 in @
% 1.03/1.15 (
% 1.03/1.15 setadjoin
% 1.03/1.15 @
% 1.03/1.15 (
% 1.03/1.15 setadjoin
% 1.03/1.15 @
% 1.03/1.15 X160 @
% 1.03/1.15 emptyset ) @
% 1.03/1.15 (
% 1.03/1.15 setadjoin
% 1.03/1.15 @
% 1.03/1.15 (
% 1.03/1.15 setadjoin
% 1.03/1.15 @
% 1.03/1.15 X160 @
% 1.03/1.15 (
% 1.03/1.15 setadjoin
% 1.03/1.15 @
% 1.03/1.15 X162 @
% 1.03/1.15 emptyset ) ) @
% 1.03/1.15 emptyset ) ) @
% 1.03/1.15 (
% 1.03/1.15 powerset @
% 1.03/1.15 (
% 1.03/1.15 powerset @
% 1.03/1.15 (
% 1.03/1.15 binunion @
% 1.03/1.15 X156 @
% 1.03/1.15 X158 ) ) ) ) ) ) ) ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 ![
% 1.03/1.15 X164:$i,
% 1.03/1.15 X166:$i,
% 1.03/1.15 X168:$i]:
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 in @
% 1.03/1.15 X168 @
% 1.03/1.15 X164 ) =>
% 1.03/1.15 (
% 1.03/1.15 ![
% 1.03/1.15 X170:$i]:
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 in @
% 1.03/1.15 X170 @
% 1.03/1.15 X166 ) =>
% 1.03/1.15 (
% 1.03/1.15 in @
% 1.03/1.15 (
% 1.03/1.15 kpair @
% 1.03/1.15 X168 @
% 1.03/1.15 X170 ) @
% 1.03/1.15 (
% 1.03/1.15 powerset @
% 1.03/1.15 (
% 1.03/1.15 powerset @
% 1.03/1.15 (
% 1.03/1.15 binunion @
% 1.03/1.15 X164 @
% 1.03/1.15 X166 ) ) ) ) ) ) ) ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 cartprodpairin ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 cartprodmempair1 ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 cartprodmempair ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 setunionE2 ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 setunionsingleton1 ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 setunionsingleton2 ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 setunionsingleton ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 singletonprop ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 ex1E1 ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 ex1I ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 ex1I2 ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 singletonsuniq ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 setukpairinjL1 ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 kfstsingleton ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 theprop ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 kfstpairEq ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 cartprodfstin ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 setukpairinjL2 ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 setukpairinjL ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 setukpairinjR11 ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 setukpairinjR12 ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 setukpairinjR1 ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 upairequniteq ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 setukpairinjR2 ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 setukpairinjR ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 ksndsingleton ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 ksndpairEq ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 kpairsurjEq ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 cartprodsndin ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 cartprodpairmemEL ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 cartprodpairmemER ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 cartprodmempaircEq ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 cartprodfstpairEq ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 cartprodsndpairEq ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 cartprodpairsurjEq ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 dpsetconstrI ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 dpsetconstrSub ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 setOfPairsIsBReln ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 dpsetconstrERa ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 dpsetconstrEL1 ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 dpsetconstrEL2 ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 dpsetconstrER ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 funcImageSingleton ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 apProp ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 app ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 infuncsetfunc ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 ap2p ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 funcinfuncset ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 lamProp ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 lamp ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 lam2p ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 brelnall1 ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 brelnall2 ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 ex1E2 ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 funcGraphProp1 ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 funcGraphProp3 ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 funcGraphProp2 ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 funcextLem ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 funcGraphProp4 ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 subbreln ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 eqbreln ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 funcext ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 funcext2 ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 ap2apEq1 ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 ap2apEq2 ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 beta1 ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 eta1 ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 lam2lamEq ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 beta2 ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 eta2 ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 iffalseProp1 ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 iffalseProp2 ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 iftrueProp1 ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 iftrueProp2 ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 ifSingleton ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 ifp ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 theeq ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 iftrue ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 iffalse ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 iftrueorfalse ) =>
% 1.03/1.15 (
% 1.03/1.15 (
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% 1.03/1.15 (
% 1.03/1.15 in @
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% 1.03/1.15 subsetTI ) =>
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% 1.03/1.15 (
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% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 binintersectTELcontra ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 binintersectTERcontra ) =>
% 1.03/1.15 (
% 1.03/1.15 (
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% 1.03/1.15 X232:$i]:
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% 1.03/1.15 (
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% 1.03/1.15 contrasubsetT1 ) =>
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% 1.03/1.15 X270 @
% 1.03/1.15 (
% 1.03/1.15 setminus @
% 1.03/1.15 X270 @
% 1.03/1.15 X272 ) ) ) ) ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 complementTnotintersectT ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 complementImpComplementIntersect ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 complementSubsetComplementIntersect ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 complementInPowersetComplementIntersect ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 ![
% 1.03/1.15 X274:$i,
% 1.03/1.15 X276:$i]:
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 in @
% 1.03/1.15 X276 @
% 1.03/1.15 (
% 1.03/1.15 powerset @
% 1.03/1.15 X274 ) ) =>
% 1.03/1.15 (
% 1.03/1.15 ![
% 1.03/1.15 X278:$i]:
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 in @
% 1.03/1.15 X278 @
% 1.03/1.15 (
% 1.03/1.15 powerset @
% 1.03/1.15 X274 ) ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 subset @
% 1.03/1.15 X276 @
% 1.03/1.15 (
% 1.03/1.15 setminus @
% 1.03/1.15 X274 @
% 1.03/1.15 X278 ) ) =>
% 1.03/1.15 (
% 1.03/1.15 ![
% 1.03/1.15 X280:$i]:
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 in @
% 1.03/1.15 X280 @
% 1.03/1.15 X274 ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 in @
% 1.03/1.15 X280 @
% 1.03/1.15 X278 ) =>
% 1.03/1.15 (
% 1.03/1.15 in @
% 1.03/1.15 X280 @
% 1.03/1.15 (
% 1.03/1.15 setminus @
% 1.03/1.15 X274 @
% 1.03/1.15 X276 ) ) ) ) ) ) ) ) ) ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 ![
% 1.03/1.15 X282:$i,
% 1.03/1.15 X284:$i]:
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 in @
% 1.03/1.15 X284 @
% 1.03/1.15 (
% 1.03/1.15 powerset @
% 1.03/1.15 X282 ) ) =>
% 1.03/1.15 (
% 1.03/1.15 ![
% 1.03/1.15 X286:$i]:
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 in @
% 1.03/1.15 X286 @
% 1.03/1.15 (
% 1.03/1.15 powerset @
% 1.03/1.15 X282 ) ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 subset @
% 1.03/1.15 X284 @
% 1.03/1.15 (
% 1.03/1.15 setminus @
% 1.03/1.15 X282 @
% 1.03/1.15 X286 ) ) =>
% 1.03/1.15 (
% 1.03/1.15 subset @
% 1.03/1.15 X286 @
% 1.03/1.15 (
% 1.03/1.15 setminus @
% 1.03/1.15 X282 @
% 1.03/1.15 X284 ) ) ) ) ) ) ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 ![
% 1.03/1.15 X288:$i,
% 1.03/1.15 X290:$i]:
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 in @
% 1.03/1.15 X290 @
% 1.03/1.15 (
% 1.03/1.15 powerset @
% 1.03/1.15 X288 ) ) =>
% 1.03/1.15 (
% 1.03/1.15 ![
% 1.03/1.15 X292:$i]:
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 in @
% 1.03/1.15 X292 @
% 1.03/1.15 (
% 1.03/1.15 powerset @
% 1.03/1.15 X288 ) ) =>
% 1.03/1.15 (
% 1.03/1.15 ![
% 1.03/1.15 X294:$i]:
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 in @
% 1.03/1.15 X294 @
% 1.03/1.15 X288 ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 ~(
% 1.03/1.15 in @
% 1.03/1.15 X294 @
% 1.03/1.15 (
% 1.03/1.15 binunion
% 1.03/1.15 @
% 1.03/1.15 X290 @
% 1.03/1.15 X292 ) ) ) =>
% 1.03/1.15 (
% 1.03/1.15 ~(
% 1.03/1.15 in @
% 1.03/1.15 X294 @
% 1.03/1.15 X290 ) ) ) ) ) ) ) ) ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 ![
% 1.03/1.15 X296:$i,
% 1.03/1.15 X298:$i]:
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 in @
% 1.03/1.15 X298 @
% 1.03/1.15 (
% 1.03/1.15 powerset @
% 1.03/1.15 X296 ) ) =>
% 1.03/1.15 (
% 1.03/1.15 ![
% 1.03/1.15 X300:$i]:
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 in @
% 1.03/1.15 X300 @
% 1.03/1.15 (
% 1.03/1.15 powerset @
% 1.03/1.15 X296 ) ) =>
% 1.03/1.15 (
% 1.03/1.15 ![
% 1.03/1.15 X302:$i]:
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 in @
% 1.03/1.15 X302 @
% 1.03/1.15 X296 ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 ~(
% 1.03/1.15 in @
% 1.03/1.15 X302 @
% 1.03/1.15 (
% 1.03/1.15 binunion
% 1.03/1.15 @
% 1.03/1.15 X298 @
% 1.03/1.15 X300 ) ) ) =>
% 1.03/1.15 (
% 1.03/1.15 ~(
% 1.03/1.15 in @
% 1.03/1.15 X302 @
% 1.03/1.15 X300 ) ) ) ) ) ) ) ) ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 ![
% 1.03/1.15 X304:$i,
% 1.03/1.15 X306:$i]:
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 in @
% 1.03/1.15 X306 @
% 1.03/1.15 (
% 1.03/1.15 powerset @
% 1.03/1.15 X304 ) ) =>
% 1.03/1.15 (
% 1.03/1.15 ![
% 1.03/1.15 X308:$i]:
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 in @
% 1.03/1.15 X308 @
% 1.03/1.15 (
% 1.03/1.15 powerset @
% 1.03/1.15 X304 ) ) =>
% 1.03/1.15 (
% 1.03/1.15 ![
% 1.03/1.15 X310:$i]:
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 in @
% 1.03/1.15 X310 @
% 1.03/1.15 (
% 1.03/1.15 powerset @
% 1.03/1.15 X304 ) ) =>
% 1.03/1.15 (
% 1.03/1.15 ![
% 1.03/1.15 X312:$i]:
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 in @
% 1.03/1.15 X312 @
% 1.03/1.15 X304 ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 in @
% 1.03/1.15 X312 @
% 1.03/1.15 (
% 1.03/1.15 binintersect
% 1.03/1.15 @
% 1.03/1.15 X306 @
% 1.03/1.15 X308 ) ) =>
% 1.03/1.15 (
% 1.03/1.15 in @
% 1.03/1.15 X312 @
% 1.03/1.15 (
% 1.03/1.15 binunion @
% 1.03/1.15 X306 @
% 1.03/1.15 X310 ) ) ) ) ) ) ) ) ) ) ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 ![
% 1.03/1.15 X314:$i,
% 1.03/1.15 X316:$i]:
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 in @
% 1.03/1.15 X316 @
% 1.03/1.15 (
% 1.03/1.15 powerset @
% 1.03/1.15 X314 ) ) =>
% 1.03/1.15 (
% 1.03/1.15 ![
% 1.03/1.15 X318:$i]:
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 in @
% 1.03/1.15 X318 @
% 1.03/1.15 (
% 1.03/1.15 powerset @
% 1.03/1.15 X314 ) ) =>
% 1.03/1.15 (
% 1.03/1.15 ![
% 1.03/1.15 X320:$i]:
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 in @
% 1.03/1.15 X320 @
% 1.03/1.15 (
% 1.03/1.15 powerset @
% 1.03/1.15 X314 ) ) =>
% 1.03/1.15 (
% 1.03/1.15 ![
% 1.03/1.15 X322:$i]:
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 in @
% 1.03/1.15 X322 @
% 1.03/1.15 X314 ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 in @
% 1.03/1.15 X322 @
% 1.03/1.15 (
% 1.03/1.15 binintersect
% 1.03/1.15 @
% 1.03/1.15 X316 @
% 1.03/1.15 X318 ) ) =>
% 1.03/1.15 (
% 1.03/1.15 in @
% 1.03/1.15 X322 @
% 1.03/1.15 (
% 1.03/1.15 binunion @
% 1.03/1.15 X318 @
% 1.03/1.15 X320 ) ) ) ) ) ) ) ) ) ) ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 ![
% 1.03/1.15 X324:$i,
% 1.03/1.15 X326:$i]:
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 in @
% 1.03/1.15 X326 @
% 1.03/1.15 (
% 1.03/1.15 powerset @
% 1.03/1.15 X324 ) ) =>
% 1.03/1.15 (
% 1.03/1.15 ![
% 1.03/1.15 X328:$i]:
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 in @
% 1.03/1.15 X328 @
% 1.03/1.15 (
% 1.03/1.15 powerset @
% 1.03/1.15 X324 ) ) =>
% 1.03/1.15 (
% 1.03/1.15 ![
% 1.03/1.15 X330:$i]:
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 in @
% 1.03/1.15 X330 @
% 1.03/1.15 (
% 1.03/1.15 powerset @
% 1.03/1.15 X324 ) ) =>
% 1.03/1.15 (
% 1.03/1.15 ![
% 1.03/1.15 X332:$i]:
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 in @
% 1.03/1.15 X332 @
% 1.03/1.15 X324 ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 in @
% 1.03/1.15 X332 @
% 1.03/1.15 (
% 1.03/1.15 binintersect
% 1.03/1.15 @
% 1.03/1.15 X326 @
% 1.03/1.15 X328 ) ) =>
% 1.03/1.15 (
% 1.03/1.15 in @
% 1.03/1.15 X332 @
% 1.03/1.15 (
% 1.03/1.15 binintersect
% 1.03/1.15 @
% 1.03/1.15 (
% 1.03/1.15 binunion @
% 1.03/1.15 X326 @
% 1.03/1.15 X330 ) @
% 1.03/1.15 (
% 1.03/1.15 binunion @
% 1.03/1.15 X328 @
% 1.03/1.15 X330 ) ) ) ) ) ) ) ) ) ) ) ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 ![
% 1.03/1.15 X334:$i,
% 1.03/1.15 X336:$i]:
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 in @
% 1.03/1.15 X336 @
% 1.03/1.15 (
% 1.03/1.15 powerset @
% 1.03/1.15 X334 ) ) =>
% 1.03/1.15 (
% 1.03/1.15 ![
% 1.03/1.15 X338:$i]:
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 in @
% 1.03/1.15 X338 @
% 1.03/1.15 (
% 1.03/1.15 powerset @
% 1.03/1.15 X334 ) ) =>
% 1.03/1.15 (
% 1.03/1.15 ![
% 1.03/1.15 X340:$i]:
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 in @
% 1.03/1.15 X340 @
% 1.03/1.15 (
% 1.03/1.15 powerset @
% 1.03/1.15 X334 ) ) =>
% 1.03/1.15 (
% 1.03/1.15 in @
% 1.03/1.15 (
% 1.03/1.15 binintersect
% 1.03/1.15 @
% 1.03/1.15 X336 @
% 1.03/1.15 X338 ) @
% 1.03/1.15 (
% 1.03/1.15 powerset @
% 1.03/1.15 (
% 1.03/1.15 binintersect
% 1.03/1.15 @
% 1.03/1.15 (
% 1.03/1.15 binunion @
% 1.03/1.15 X336 @
% 1.03/1.15 X340 ) @
% 1.03/1.15 (
% 1.03/1.15 binunion @
% 1.03/1.15 X338 @
% 1.03/1.15 X340 ) ) ) ) ) ) ) ) ) ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 ![
% 1.03/1.15 X342:$i,
% 1.03/1.15 X344:$i]:
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 in @
% 1.03/1.15 X344 @
% 1.03/1.15 (
% 1.03/1.15 powerset @
% 1.03/1.15 X342 ) ) =>
% 1.03/1.15 (
% 1.03/1.15 ![
% 1.03/1.15 X346:$i]:
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 in @
% 1.03/1.15 X346 @
% 1.03/1.15 (
% 1.03/1.15 powerset @
% 1.03/1.15 X342 ) ) =>
% 1.03/1.15 (
% 1.03/1.15 ![
% 1.03/1.15 X348:$i]:
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 in @
% 1.03/1.15 X348 @
% 1.03/1.15 X342 ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 in @
% 1.03/1.15 X348 @
% 1.03/1.15 (
% 1.03/1.15 setminus @
% 1.03/1.15 X342 @
% 1.03/1.15 (
% 1.03/1.15 binunion @
% 1.03/1.15 X344 @
% 1.03/1.15 X346 ) ) ) =>
% 1.03/1.15 (
% 1.03/1.15 ~(
% 1.03/1.15 in @
% 1.03/1.15 X348 @
% 1.03/1.15 X344 ) ) ) ) ) ) ) ) ) =>
% 1.03/1.15 (
% 1.03/1.15 ![
% 1.03/1.15 X350:$i,
% 1.03/1.15 X352:$i]:
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 in @
% 1.03/1.15 X352 @
% 1.03/1.15 (
% 1.03/1.15 powerset @
% 1.03/1.15 X350 ) ) =>
% 1.03/1.15 (
% 1.03/1.15 ![
% 1.03/1.15 X354:$i]:
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 in @
% 1.03/1.15 X354 @
% 1.03/1.15 (
% 1.03/1.15 powerset @
% 1.03/1.15 X350 ) ) =>
% 1.03/1.15 (
% 1.03/1.15 ![
% 1.03/1.15 X356:$i]:
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 in @
% 1.03/1.15 X356 @
% 1.03/1.15 X350 ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 in @
% 1.03/1.15 X356 @
% 1.03/1.15 (
% 1.03/1.15 setminus @
% 1.03/1.15 X350 @
% 1.03/1.15 (
% 1.03/1.15 binunion @
% 1.03/1.15 X352 @
% 1.03/1.15 X354 ) ) ) =>
% 1.03/1.15 (
% 1.03/1.15 in @
% 1.03/1.15 X356 @
% 1.03/1.15 (
% 1.03/1.15 setminus @
% 1.03/1.15 X350 @
% 1.03/1.15 X352 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 1.03/1.15 thf(zf_stmt_4, negated_conjecture,
% 1.03/1.15 (~( ( setextAx ) =>
% 1.03/1.15 ( ( emptysetAx ) =>
% 1.03/1.15 ( ( setadjoinAx ) =>
% 1.03/1.15 ( ( ![X4:$i,X6:$i]:
% 1.03/1.15 ( ( in @ X6 @ ( powerset @ X4 ) ) <=>
% 1.03/1.15 ( ![X8:$i]: ( zip_tseitin_0 @ X8 @ X6 @ X4 ) ) ) ) =>
% 1.03/1.15 ( ( setunionAx ) =>
% 1.03/1.15 ( ( omega0Ax ) =>
% 1.03/1.15 ( ( omegaSAx ) =>
% 1.03/1.15 ( ( omegaIndAx ) =>
% 1.03/1.15 ( ( replAx ) =>
% 1.03/1.15 ( ( foundationAx ) =>
% 1.03/1.15 ( ( wellorderingAx ) =>
% 1.03/1.15 ( ( descrp ) =>
% 1.03/1.15 ( ( dsetconstrI ) =>
% 1.03/1.15 ( ( dsetconstrEL ) =>
% 1.03/1.15 ( ( dsetconstrER ) =>
% 1.03/1.15 ( ( exuE1 ) =>
% 1.03/1.15 ( ( prop2setE ) =>
% 1.03/1.15 ( ( emptysetE ) =>
% 1.03/1.15 ( ( emptysetimpfalse ) =>
% 1.03/1.15 ( ( notinemptyset ) =>
% 1.03/1.15 ( ( exuE3e ) =>
% 1.03/1.15 ( ( setext ) =>
% 1.03/1.15 ( ( emptyI ) =>
% 1.03/1.15 ( ( noeltsimpempty ) =>
% 1.03/1.15 ( ( setbeta ) =>
% 1.03/1.15 ( ( nonemptyE1 ) =>
% 1.03/1.15 ( ( nonemptyI ) =>
% 1.03/1.15 ( ( nonemptyI1 ) =>
% 1.03/1.15 ( ( setadjoinIL ) =>
% 1.03/1.15 ( ( emptyinunitempty ) =>
% 1.03/1.15 ( ( setadjoinIR ) =>
% 1.03/1.15 ( (
% 1.03/1.15 setadjoinE ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 setadjoinOr ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 setoftrueEq ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 ![
% 1.03/1.15 X10:$i,
% 1.03/1.15 X12:$i]:
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 ![
% 1.03/1.15 X14:$i]:
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 in @
% 1.03/1.15 X14 @ X12 ) =>
% 1.03/1.15 (
% 1.03/1.15 in @
% 1.03/1.15 X14 @ X10 ) ) ) =>
% 1.03/1.15 (
% 1.03/1.15 in @
% 1.03/1.15 X12 @
% 1.03/1.15 (
% 1.03/1.15 powerset
% 1.03/1.15 @
% 1.03/1.15 X10 ) ) ) ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 ![
% 1.03/1.15 X16:$i]:
% 1.03/1.15 (
% 1.03/1.15 in @
% 1.03/1.15 emptyset @
% 1.03/1.15 (
% 1.03/1.15 powerset
% 1.03/1.15 @
% 1.03/1.15 X16 ) ) ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 ![
% 1.03/1.15 X18:$i]:
% 1.03/1.15 (
% 1.03/1.15 in @
% 1.03/1.15 emptyset @
% 1.03/1.15 (
% 1.03/1.15 powerset
% 1.03/1.15 @
% 1.03/1.15 X18 ) ) ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 ![
% 1.03/1.15 X20:$i,
% 1.03/1.15 X22:$i,
% 1.03/1.15 X24:$i]:
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 in @
% 1.03/1.15 X22 @
% 1.03/1.15 (
% 1.03/1.15 powerset
% 1.03/1.15 @
% 1.03/1.15 X20 ) ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 in @
% 1.03/1.15 X24 @ X22 ) =>
% 1.03/1.15 (
% 1.03/1.15 in @
% 1.03/1.15 X24 @ X20 ) ) ) ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 setunionI ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 setunionE ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 subPowSU ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 exuE2 ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 nonemptyImpWitness ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 uniqinunit ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 notinsingleton ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 eqinunit ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 singletonsswitch ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 upairsetE ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 upairsetIL ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 upairsetIR ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 emptyE1 ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 vacuousDall ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 quantDeMorgan1 ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 quantDeMorgan2 ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 quantDeMorgan3 ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 quantDeMorgan4 ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 prop2setI ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 prop2set2propI ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 notdexE ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 notdallE ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 exuI1 ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 exuI3 ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 exuI2 ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 inCongP ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 in__Cong ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 exuE3u ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 exu__Cong ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 emptyset__Cong ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 setadjoin__Cong ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 ![
% 1.03/1.15 X26:$i,
% 1.03/1.15 X28:$i]:
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 X26 ) =
% 1.03/1.15 (
% 1.03/1.15 X28 ) ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 powerset
% 1.03/1.15 @
% 1.03/1.15 X26 ) =
% 1.03/1.15 (
% 1.03/1.15 powerset
% 1.03/1.15 @
% 1.03/1.15 X28 ) ) ) ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 setunion__Cong ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 omega__Cong ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 exuEu ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 descr__Cong ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 dsetconstr__Cong ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 subsetI1 ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 eqimpsubset2 ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 eqimpsubset1 ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 subsetI2 ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 emptysetsubset ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 subsetE ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 subsetE2 ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 notsubsetI ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 notequalI1 ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 notequalI2 ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 subsetRefl ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 subsetTrans ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 setadjoinSub ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 setadjoinSub2 ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 subset2powerset ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 setextsub ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 subsetemptysetimpeq ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 powersetI1 ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 powersetE1 ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 ![
% 1.03/1.15 X30:$i]:
% 1.03/1.15 (
% 1.03/1.15 in @
% 1.03/1.15 X30 @
% 1.03/1.15 (
% 1.03/1.15 powerset
% 1.03/1.15 @
% 1.03/1.15 X30 ) ) ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 powersetsubset ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 sepInPowerset ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 sepSubset ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 ![
% 1.03/1.15 X32:$i,
% 1.03/1.15 X34:$i,
% 1.03/1.15 X36:$i]:
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 in @
% 1.03/1.15 X36 @ X32 ) =>
% 1.03/1.15 (
% 1.03/1.15 in @
% 1.03/1.15 X36 @
% 1.03/1.15 (
% 1.03/1.15 binunion
% 1.03/1.15 @
% 1.03/1.15 X32 @ X34 ) ) ) ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 upairset2IR ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 ![
% 1.03/1.15 X38:$i,
% 1.03/1.15 X40:$i,
% 1.03/1.15 X42:$i]:
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 in @
% 1.03/1.15 X42 @ X40 ) =>
% 1.03/1.15 (
% 1.03/1.15 in @
% 1.03/1.15 X42 @
% 1.03/1.15 (
% 1.03/1.15 binunion
% 1.03/1.15 @
% 1.03/1.15 X38 @ X40 ) ) ) ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 ![
% 1.03/1.15 X44:$i,
% 1.03/1.15 X46:$i,
% 1.03/1.15 X48:$i,
% 1.03/1.15 X50:$o]:
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 in @
% 1.03/1.15 X48 @
% 1.03/1.15 (
% 1.03/1.15 binunion
% 1.03/1.15 @
% 1.03/1.15 X44 @ X46 ) ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 in @
% 1.03/1.15 X48 @ X44 ) =>
% 1.03/1.15 (
% 1.03/1.15 X50 ) ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 in @
% 1.03/1.15 X48 @ X46 ) =>
% 1.03/1.15 (
% 1.03/1.15 X50 ) ) =>
% 1.03/1.15 (
% 1.03/1.15 X50 ) ) ) ) ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 ![
% 1.03/1.15 X52:$i,
% 1.03/1.15 X54:$i,
% 1.03/1.15 X56:$i]:
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 in @
% 1.03/1.15 X56 @
% 1.03/1.15 (
% 1.03/1.15 binunion
% 1.03/1.15 @
% 1.03/1.15 X52 @ X54 ) ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 in @
% 1.03/1.15 X56 @ X52 ) |
% 1.03/1.15 (
% 1.03/1.15 in @
% 1.03/1.15 X56 @ X54 ) ) ) ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 ![
% 1.03/1.15 X58:$i,
% 1.03/1.15 X60:$i]:
% 1.03/1.15 (
% 1.03/1.15 subset @
% 1.03/1.15 X58 @
% 1.03/1.15 (
% 1.03/1.15 binunion
% 1.03/1.15 @
% 1.03/1.15 X58 @ X60 ) ) ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 ![
% 1.03/1.15 X62:$i,
% 1.03/1.15 X64:$i]:
% 1.03/1.15 (
% 1.03/1.15 subset @
% 1.03/1.15 X64 @
% 1.03/1.15 (
% 1.03/1.15 binunion
% 1.03/1.15 @
% 1.03/1.15 X62 @ X64 ) ) ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 binintersectI ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 binintersectSubset5 ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 binintersectEL ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 binintersectLsub ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 binintersectSubset2 ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 binintersectSubset3 ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 binintersectER ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 disjointsetsI1 ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 binintersectRsub ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 binintersectSubset4 ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 binintersectSubset1 ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 ![
% 1.03/1.15 X66:$i,
% 1.03/1.15 X68:$i,
% 1.03/1.15 X70:$i]:
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 binintersect
% 1.03/1.15 @
% 1.03/1.15 X66 @
% 1.03/1.15 (
% 1.03/1.15 binunion
% 1.03/1.15 @
% 1.03/1.15 X68 @ X70 ) ) =
% 1.03/1.15 (
% 1.03/1.15 binunion
% 1.03/1.15 @
% 1.03/1.15 (
% 1.03/1.15 binintersect
% 1.03/1.15 @
% 1.03/1.15 X66 @ X68 ) @
% 1.03/1.15 (
% 1.03/1.15 binintersect
% 1.03/1.15 @
% 1.03/1.15 X66 @ X70 ) ) ) ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 ![
% 1.03/1.15 X72:$i,
% 1.03/1.15 X74:$i,
% 1.03/1.15 X76:$i]:
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 in @
% 1.03/1.15 X76 @ X72 ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 ~
% 1.03/1.15 (
% 1.03/1.15 in @
% 1.03/1.15 X76 @ X74 ) ) =>
% 1.03/1.15 (
% 1.03/1.15 in @
% 1.03/1.15 X76 @
% 1.03/1.15 (
% 1.03/1.15 setminus
% 1.03/1.15 @
% 1.03/1.15 X72 @ X74 ) ) ) ) ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 ![
% 1.03/1.15 X78:$i,
% 1.03/1.15 X80:$i,
% 1.03/1.15 X82:$i]:
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 in @
% 1.03/1.15 X82 @
% 1.03/1.15 (
% 1.03/1.15 setminus
% 1.03/1.15 @
% 1.03/1.15 X78 @ X80 ) ) =>
% 1.03/1.15 (
% 1.03/1.15 in @
% 1.03/1.15 X82 @ X78 ) ) ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 ![
% 1.03/1.15 X84:$i,
% 1.03/1.15 X86:$i,
% 1.03/1.15 X88:$i]:
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 in @
% 1.03/1.15 X88 @
% 1.03/1.15 (
% 1.03/1.15 setminus
% 1.03/1.15 @
% 1.03/1.15 X84 @ X86 ) ) =>
% 1.03/1.15 (
% 1.03/1.15 ~
% 1.03/1.15 (
% 1.03/1.15 in @
% 1.03/1.15 X88 @ X86 ) ) ) ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 ![
% 1.03/1.15 X90:$i,
% 1.03/1.15 X92:$i]:
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 subset @
% 1.03/1.15 X90 @ X92 ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 setminus
% 1.03/1.15 @
% 1.03/1.15 X90 @ X92 ) =
% 1.03/1.15 (
% 1.03/1.15 emptyset ) ) ) ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 ![
% 1.03/1.15 X94:$i,
% 1.03/1.15 X96:$i,
% 1.03/1.15 X98:$i]:
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 ~
% 1.03/1.15 (
% 1.03/1.15 in @
% 1.03/1.15 X98 @
% 1.03/1.15 (
% 1.03/1.15 setminus
% 1.03/1.15 @
% 1.03/1.15 X94 @ X96 ) ) ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 in @
% 1.03/1.15 X98 @ X94 ) =>
% 1.03/1.15 (
% 1.03/1.15 in @
% 1.03/1.15 X98 @ X96 ) ) ) ) =>
% 1.03/1.15 (
% 1.03/1.15 (
% 1.03/1.15 ![
% 1.03/1.15 X100:$i,
% 1.03/1.15 X102:$i,
% 1.03/1.15 X104:$i]:
% 1.03/1.16 (
% 1.03/1.16 (
% 1.03/1.16 ~
% 1.03/1.16 (
% 1.03/1.16 in @
% 1.03/1.16 X104 @
% 1.03/1.16 (
% 1.03/1.16 setminus
% 1.03/1.16 @
% 1.03/1.16 X100 @
% 1.03/1.16 X102 ) ) ) =>
% 1.03/1.16 (
% 1.03/1.16 (
% 1.03/1.16 ~
% 1.03/1.16 (
% 1.03/1.16 in @
% 1.03/1.16 X104 @
% 1.03/1.16 X102 ) ) =>
% 1.03/1.16 (
% 1.03/1.16 ~
% 1.03/1.16 (
% 1.03/1.16 in @
% 1.03/1.16 X104 @
% 1.03/1.16 X100 ) ) ) ) ) =>
% 1.03/1.16 (
% 1.03/1.16 (
% 1.03/1.16 ![
% 1.03/1.16 X106:$i,
% 1.03/1.16 X108:$i,
% 1.03/1.16 X110:$i]:
% 1.03/1.16 (
% 1.03/1.16 (
% 1.03/1.16 ~
% 1.03/1.16 (
% 1.03/1.16 in @
% 1.03/1.16 X110 @
% 1.03/1.16 X106 ) ) =>
% 1.03/1.16 (
% 1.03/1.16 ~
% 1.03/1.16 (
% 1.03/1.16 in @
% 1.03/1.16 X110 @
% 1.03/1.16 (
% 1.03/1.16 setminus
% 1.03/1.16 @
% 1.03/1.16 X106 @
% 1.03/1.16 X108 ) ) ) ) ) =>
% 1.03/1.16 (
% 1.03/1.16 (
% 1.03/1.16 ![
% 1.03/1.16 X112:$i,
% 1.03/1.16 X114:$i,
% 1.03/1.16 X116:$i]:
% 1.03/1.16 (
% 1.03/1.16 (
% 1.03/1.16 in @
% 1.03/1.16 X116 @
% 1.03/1.16 X114 ) =>
% 1.03/1.16 (
% 1.03/1.16 ~
% 1.03/1.16 (
% 1.03/1.16 in @
% 1.03/1.16 X116 @
% 1.03/1.16 (
% 1.03/1.16 setminus
% 1.03/1.16 @
% 1.03/1.16 X112 @
% 1.03/1.16 X114 ) ) ) ) ) =>
% 1.03/1.16 (
% 1.03/1.16 (
% 1.03/1.16 ![
% 1.03/1.16 X118:$i,
% 1.03/1.16 X120:$i]:
% 1.03/1.16 (
% 1.03/1.16 subset @
% 1.03/1.16 (
% 1.03/1.16 setminus
% 1.03/1.16 @
% 1.03/1.16 X118 @
% 1.03/1.16 X120 ) @
% 1.03/1.16 X118 ) ) =>
% 1.03/1.16 (
% 1.03/1.16 (
% 1.03/1.16 ![
% 1.03/1.16 X122:$i,
% 1.03/1.16 X124:$i]:
% 1.03/1.16 (
% 1.03/1.16 (
% 1.03/1.16 (
% 1.03/1.16 setminus
% 1.03/1.16 @
% 1.03/1.16 X122 @
% 1.03/1.16 X124 ) =
% 1.03/1.16 (
% 1.03/1.16 emptyset ) ) =>
% 1.03/1.16 (
% 1.03/1.16 subset @
% 1.03/1.16 X122 @
% 1.03/1.16 X124 ) ) ) =>
% 1.03/1.16 (
% 1.03/1.16 (
% 1.03/1.16 symdiffE ) =>
% 1.03/1.16 (
% 1.03/1.16 (
% 1.03/1.16 symdiffI1 ) =>
% 1.03/1.16 (
% 1.03/1.16 (
% 1.03/1.16 symdiffI2 ) =>
% 1.03/1.16 (
% 1.03/1.16 (
% 1.03/1.16 symdiffIneg1 ) =>
% 1.03/1.16 (
% 1.03/1.16 (
% 1.03/1.16 symdiffIneg2 ) =>
% 1.03/1.16 (
% 1.03/1.16 (
% 1.03/1.16 secondinupair ) =>
% 1.03/1.16 (
% 1.03/1.16 (
% 1.03/1.16 setukpairIL ) =>
% 1.03/1.16 (
% 1.03/1.16 (
% 1.03/1.16 setukpairIR ) =>
% 1.03/1.16 (
% 1.03/1.16 (
% 1.03/1.16 kpairiskpair ) =>
% 1.03/1.16 (
% 1.03/1.16 (
% 1.03/1.16 kpairp ) =>
% 1.03/1.16 (
% 1.03/1.16 (
% 1.03/1.16 singletonsubset ) =>
% 1.03/1.16 (
% 1.03/1.16 (
% 1.03/1.16 singletoninpowerset ) =>
% 1.03/1.16 (
% 1.03/1.16 (
% 1.03/1.16 ![
% 1.03/1.16 X126:$i,
% 1.03/1.16 X128:$i,
% 1.03/1.16 X130:$i]:
% 1.03/1.16 (
% 1.03/1.16 (
% 1.03/1.16 in @
% 1.03/1.16 X130 @
% 1.03/1.16 X126 ) =>
% 1.03/1.16 (
% 1.03/1.16 in @
% 1.03/1.16 (
% 1.03/1.16 setadjoin
% 1.03/1.16 @
% 1.03/1.16 X130 @
% 1.03/1.16 emptyset ) @
% 1.03/1.16 (
% 1.03/1.16 powerset
% 1.03/1.16 @
% 1.03/1.16 (
% 1.03/1.16 binunion
% 1.03/1.16 @
% 1.03/1.16 X126 @
% 1.03/1.16 X128 ) ) ) ) ) =>
% 1.03/1.16 (
% 1.03/1.16 (
% 1.03/1.16 upairset2E ) =>
% 1.03/1.16 (
% 1.03/1.16 (
% 1.03/1.16 ![
% 1.03/1.16 X132:$i,
% 1.03/1.16 X134:$i,
% 1.03/1.16 X136:$i]:
% 1.03/1.16 (
% 1.03/1.16 (
% 1.03/1.16 in @
% 1.03/1.16 X136 @
% 1.03/1.16 X132 ) =>
% 1.03/1.16 (
% 1.03/1.16 ![
% 1.03/1.16 X138:$i]:
% 1.03/1.16 (
% 1.03/1.16 (
% 1.03/1.16 in @
% 1.03/1.16 X138 @
% 1.03/1.16 X134 ) =>
% 1.03/1.16 (
% 1.03/1.16 subset @
% 1.03/1.16 (
% 1.03/1.16 setadjoin
% 1.03/1.16 @
% 1.03/1.16 X136 @
% 1.03/1.16 (
% 1.03/1.16 setadjoin
% 1.03/1.16 @
% 1.03/1.16 X138 @
% 1.03/1.16 emptyset ) ) @
% 1.03/1.16 (
% 1.03/1.16 binunion
% 1.03/1.16 @
% 1.03/1.16 X132 @
% 1.03/1.16 X134 ) ) ) ) ) ) =>
% 1.03/1.16 (
% 1.03/1.16 (
% 1.03/1.16 ![
% 1.03/1.16 X140:$i,
% 1.03/1.16 X142:$i,
% 1.03/1.16 X144:$i]:
% 1.03/1.16 (
% 1.03/1.16 (
% 1.03/1.16 in @
% 1.03/1.16 X144 @
% 1.03/1.16 X140 ) =>
% 1.03/1.16 (
% 1.03/1.16 ![
% 1.03/1.16 X146:$i]:
% 1.03/1.16 (
% 1.03/1.16 (
% 1.03/1.16 in @
% 1.03/1.16 X146 @
% 1.03/1.16 X142 ) =>
% 1.03/1.16 (
% 1.03/1.16 in @
% 1.03/1.16 (
% 1.03/1.16 setadjoin
% 1.03/1.16 @
% 1.03/1.16 X144 @
% 1.03/1.16 (
% 1.03/1.16 setadjoin
% 1.03/1.16 @
% 1.03/1.16 X146 @
% 1.03/1.16 emptyset ) ) @
% 1.03/1.16 (
% 1.03/1.16 powerset
% 1.03/1.16 @
% 1.03/1.16 (
% 1.03/1.16 binunion
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% 1.03/1.16 X140 @
% 1.03/1.16 X142 ) ) ) ) ) ) ) =>
% 1.03/1.16 (
% 1.03/1.16 (
% 1.03/1.16 ![
% 1.03/1.16 X148:$i,
% 1.03/1.16 X150:$i,
% 1.03/1.16 X152:$i]:
% 1.03/1.16 (
% 1.03/1.16 (
% 1.03/1.16 in @
% 1.03/1.16 X152 @
% 1.03/1.16 X148 ) =>
% 1.03/1.16 (
% 1.03/1.16 ![
% 1.03/1.16 X154:$i]:
% 1.03/1.16 (
% 1.03/1.16 (
% 1.03/1.16 in @
% 1.03/1.16 X154 @
% 1.03/1.16 X150 ) =>
% 1.03/1.16 (
% 1.03/1.16 subset @
% 1.03/1.16 (
% 1.03/1.16 setadjoin
% 1.03/1.16 @
% 1.03/1.16 (
% 1.03/1.16 setadjoin
% 1.03/1.16 @
% 1.03/1.16 X152 @
% 1.03/1.16 emptyset ) @
% 1.03/1.16 (
% 1.03/1.16 setadjoin
% 1.03/1.16 @
% 1.03/1.16 (
% 1.03/1.16 setadjoin
% 1.03/1.16 @
% 1.03/1.16 X152 @
% 1.03/1.16 (
% 1.03/1.16 setadjoin
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% 1.03/1.16 X154 @
% 1.03/1.16 emptyset ) ) @
% 1.03/1.16 emptyset ) ) @
% 1.03/1.16 (
% 1.03/1.16 powerset
% 1.03/1.16 @
% 1.03/1.16 (
% 1.03/1.16 binunion
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% 1.03/1.16 (
% 1.03/1.16 (
% 1.03/1.16 ![
% 1.03/1.16 X156:$i,
% 1.03/1.16 X158:$i,
% 1.03/1.16 X160:$i]:
% 1.03/1.16 (
% 1.03/1.16 (
% 1.03/1.16 in @
% 1.03/1.16 X160 @
% 1.03/1.16 X156 ) =>
% 1.03/1.16 (
% 1.03/1.16 ![
% 1.03/1.16 X162:$i]:
% 1.03/1.16 (
% 1.03/1.16 (
% 1.03/1.16 in @
% 1.03/1.16 X162 @
% 1.03/1.16 X158 ) =>
% 1.03/1.16 (
% 1.03/1.16 in @
% 1.03/1.16 (
% 1.03/1.16 setadjoin
% 1.03/1.16 @
% 1.03/1.16 (
% 1.03/1.16 setadjoin
% 1.03/1.16 @
% 1.03/1.16 X160 @
% 1.03/1.16 emptyset ) @
% 1.03/1.16 (
% 1.03/1.16 setadjoin
% 1.03/1.16 @
% 1.03/1.16 (
% 1.03/1.16 setadjoin
% 1.03/1.16 @
% 1.03/1.16 X160 @
% 1.03/1.16 (
% 1.03/1.16 setadjoin
% 1.03/1.16 @
% 1.03/1.16 X162 @
% 1.03/1.16 emptyset ) ) @
% 1.03/1.16 emptyset ) ) @
% 1.03/1.16 (
% 1.03/1.16 powerset
% 1.03/1.16 @
% 1.03/1.16 (
% 1.03/1.16 powerset
% 1.03/1.16 @
% 1.03/1.16 (
% 1.03/1.16 binunion
% 1.03/1.16 @
% 1.03/1.16 X156 @
% 1.03/1.16 X158 ) ) ) ) ) ) ) ) =>
% 1.03/1.16 (
% 1.03/1.16 (
% 1.03/1.16 ![
% 1.03/1.16 X164:$i,
% 1.03/1.16 X166:$i,
% 1.03/1.16 X168:$i]:
% 1.03/1.16 (
% 1.03/1.16 (
% 1.03/1.16 in @
% 1.03/1.16 X168 @
% 1.03/1.16 X164 ) =>
% 1.03/1.16 (
% 1.03/1.16 ![
% 1.03/1.16 X170:$i]:
% 1.03/1.16 (
% 1.03/1.16 (
% 1.03/1.16 in @
% 1.03/1.16 X170 @
% 1.03/1.16 X166 ) =>
% 1.03/1.16 (
% 1.03/1.16 in @
% 1.03/1.16 (
% 1.03/1.16 kpair @
% 1.03/1.16 X168 @
% 1.03/1.16 X170 ) @
% 1.03/1.16 (
% 1.03/1.16 powerset
% 1.03/1.16 @
% 1.03/1.16 (
% 1.03/1.16 powerset
% 1.03/1.16 @
% 1.03/1.16 (
% 1.03/1.16 binunion
% 1.03/1.16 @
% 1.03/1.16 X164 @
% 1.03/1.16 X166 ) ) ) ) ) ) ) ) =>
% 1.03/1.16 (
% 1.03/1.16 (
% 1.03/1.16 cartprodpairin ) =>
% 1.03/1.16 (
% 1.03/1.16 (
% 1.03/1.16 cartprodmempair1 ) =>
% 1.03/1.16 (
% 1.03/1.16 (
% 1.03/1.16 cartprodmempair ) =>
% 1.03/1.16 (
% 1.03/1.16 (
% 1.03/1.16 setunionE2 ) =>
% 1.03/1.16 (
% 1.03/1.16 (
% 1.03/1.16 setunionsingleton1 ) =>
% 1.03/1.16 (
% 1.03/1.16 (
% 1.03/1.16 setunionsingleton2 ) =>
% 1.03/1.16 (
% 1.03/1.16 (
% 1.03/1.16 setunionsingleton ) =>
% 1.03/1.16 (
% 1.03/1.16 (
% 1.03/1.16 singletonprop ) =>
% 1.03/1.16 (
% 1.03/1.16 (
% 1.03/1.16 ex1E1 ) =>
% 1.03/1.16 (
% 1.03/1.16 (
% 1.03/1.16 ex1I ) =>
% 1.03/1.16 (
% 1.03/1.16 (
% 1.03/1.16 ex1I2 ) =>
% 1.03/1.16 (
% 1.03/1.16 (
% 1.03/1.16 singletonsuniq ) =>
% 1.03/1.16 (
% 1.03/1.16 (
% 1.03/1.16 setukpairinjL1 ) =>
% 1.03/1.16 (
% 1.03/1.16 (
% 1.03/1.16 kfstsingleton ) =>
% 1.03/1.16 (
% 1.03/1.16 (
% 1.03/1.16 theprop ) =>
% 1.03/1.16 (
% 1.03/1.16 (
% 1.03/1.16 kfstpairEq ) =>
% 1.03/1.16 (
% 1.03/1.16 (
% 1.03/1.16 cartprodfstin ) =>
% 1.03/1.16 (
% 1.03/1.16 (
% 1.03/1.16 setukpairinjL2 ) =>
% 1.03/1.16 (
% 1.03/1.16 (
% 1.03/1.16 setukpairinjL ) =>
% 1.03/1.16 (
% 1.03/1.16 (
% 1.03/1.16 setukpairinjR11 ) =>
% 1.03/1.16 (
% 1.03/1.16 (
% 1.03/1.16 setukpairinjR12 ) =>
% 1.03/1.16 (
% 1.03/1.16 (
% 1.03/1.16 setukpairinjR1 ) =>
% 1.03/1.16 (
% 1.03/1.16 (
% 1.03/1.16 upairequniteq ) =>
% 1.03/1.16 (
% 1.03/1.16 (
% 1.03/1.16 setukpairinjR2 ) =>
% 1.03/1.16 (
% 1.03/1.16 (
% 1.03/1.16 setukpairinjR ) =>
% 1.03/1.16 (
% 1.03/1.16 (
% 1.03/1.16 ksndsingleton ) =>
% 1.03/1.16 (
% 1.03/1.16 (
% 1.03/1.16 ksndpairEq ) =>
% 1.03/1.16 (
% 1.03/1.16 (
% 1.03/1.16 kpairsurjEq ) =>
% 1.03/1.16 (
% 1.03/1.16 (
% 1.03/1.16 cartprodsndin ) =>
% 1.03/1.16 (
% 1.03/1.16 (
% 1.03/1.16 cartprodpairmemEL ) =>
% 1.03/1.16 (
% 1.03/1.16 (
% 1.03/1.16 cartprodpairmemER ) =>
% 1.03/1.16 (
% 1.03/1.16 (
% 1.03/1.16 cartprodmempaircEq ) =>
% 1.03/1.16 (
% 1.03/1.16 (
% 1.03/1.16 cartprodfstpairEq ) =>
% 1.03/1.16 (
% 1.03/1.16 (
% 1.03/1.16 cartprodsndpairEq ) =>
% 1.03/1.16 (
% 1.03/1.16 (
% 1.03/1.16 cartprodpairsurjEq ) =>
% 1.03/1.16 (
% 1.03/1.16 (
% 1.03/1.16 dpsetconstrI ) =>
% 1.03/1.16 (
% 1.03/1.16 (
% 1.03/1.16 dpsetconstrSub ) =>
% 1.03/1.16 (
% 1.03/1.16 (
% 1.03/1.16 setOfPairsIsBReln ) =>
% 1.03/1.16 (
% 1.03/1.16 (
% 1.03/1.16 dpsetconstrERa ) =>
% 1.03/1.16 (
% 1.03/1.16 (
% 1.03/1.16 dpsetconstrEL1 ) =>
% 1.03/1.16 (
% 1.03/1.16 (
% 1.03/1.16 dpsetconstrEL2 ) =>
% 1.03/1.16 (
% 1.03/1.16 (
% 1.03/1.16 dpsetconstrER ) =>
% 1.03/1.16 (
% 1.03/1.16 (
% 1.03/1.16 funcImageSingleton ) =>
% 1.03/1.16 (
% 1.03/1.16 (
% 1.03/1.16 apProp ) =>
% 1.03/1.16 (
% 1.03/1.16 (
% 1.03/1.16 app ) =>
% 1.03/1.16 (
% 1.03/1.16 (
% 1.03/1.16 infuncsetfunc ) =>
% 1.03/1.16 (
% 1.03/1.16 (
% 1.03/1.16 ap2p ) =>
% 1.03/1.16 (
% 1.03/1.16 (
% 1.03/1.16 funcinfuncset ) =>
% 1.03/1.16 (
% 1.03/1.16 (
% 1.03/1.16 lamProp ) =>
% 1.03/1.16 (
% 1.03/1.16 (
% 1.03/1.16 lamp ) =>
% 1.03/1.16 (
% 1.03/1.16 (
% 1.03/1.16 lam2p ) =>
% 1.03/1.16 (
% 1.03/1.16 (
% 1.03/1.16 brelnall1 ) =>
% 1.03/1.16 (
% 1.03/1.16 (
% 1.03/1.16 brelnall2 ) =>
% 1.03/1.16 (
% 1.03/1.16 (
% 1.03/1.16 ex1E2 ) =>
% 1.03/1.16 (
% 1.03/1.16 (
% 1.03/1.16 funcGraphProp1 ) =>
% 1.03/1.16 (
% 1.03/1.16 (
% 1.03/1.16 funcGraphProp3 ) =>
% 1.03/1.16 (
% 1.03/1.16 (
% 1.03/1.16 funcGraphProp2 ) =>
% 1.03/1.16 (
% 1.03/1.16 (
% 1.03/1.16 funcextLem ) =>
% 1.03/1.16 (
% 1.03/1.16 (
% 1.03/1.16 funcGraphProp4 ) =>
% 1.03/1.16 (
% 1.03/1.16 (
% 1.03/1.16 subbreln ) =>
% 1.03/1.16 (
% 1.03/1.16 (
% 1.03/1.16 eqbreln ) =>
% 1.03/1.16 (
% 1.03/1.16 (
% 1.03/1.16 funcext ) =>
% 1.03/1.16 (
% 1.03/1.16 (
% 1.03/1.16 funcext2 ) =>
% 1.03/1.16 (
% 1.03/1.16 (
% 1.03/1.16 ap2apEq1 ) =>
% 1.03/1.16 (
% 1.03/1.16 (
% 1.03/1.16 ap2apEq2 ) =>
% 1.03/1.16 (
% 1.03/1.16 (
% 1.03/1.16 beta1 ) =>
% 1.03/1.16 (
% 1.03/1.16 (
% 1.03/1.16 eta1 ) =>
% 1.03/1.16 (
% 1.03/1.16 (
% 1.03/1.16 lam2lamEq ) =>
% 1.03/1.16 (
% 1.03/1.16 (
% 1.03/1.16 beta2 ) =>
% 1.03/1.16 (
% 1.03/1.16 (
% 1.03/1.16 eta2 ) =>
% 1.03/1.16 (
% 1.03/1.16 (
% 1.03/1.16 iffalseProp1 ) =>
% 1.03/1.16 (
% 1.03/1.16 (
% 1.03/1.16 iffalseProp2 ) =>
% 1.03/1.16 (
% 1.03/1.16 (
% 1.03/1.16 iftrueProp1 ) =>
% 1.03/1.16 (
% 1.03/1.16 (
% 1.03/1.16 iftrueProp2 ) =>
% 1.03/1.16 (
% 1.03/1.16 (
% 1.03/1.16 ifSingleton ) =>
% 1.03/1.16 (
% 1.03/1.16 (
% 1.03/1.16 ifp ) =>
% 1.03/1.16 (
% 1.03/1.16 (
% 1.03/1.16 theeq ) =>
% 1.03/1.16 (
% 1.03/1.16 (
% 1.03/1.16 iftrue ) =>
% 1.03/1.16 (
% 1.03/1.16 (
% 1.03/1.16 iffalse ) =>
% 1.03/1.16 (
% 1.03/1.16 (
% 1.03/1.16 iftrueorfalse ) =>
% 1.03/1.16 (
% 1.03/1.16 (
% 1.03/1.16 binintersectT_lem ) =>
% 1.03/1.16 (
% 1.03/1.16 (
% 1.03/1.16 ![
% 1.03/1.16 X172:$i,
% 1.03/1.16 X174:$i]:
% 1.03/1.16 (
% 1.03/1.16 (
% 1.03/1.16 in @
% 1.03/1.16 X174 @
% 1.03/1.16 (
% 1.03/1.16 powerset
% 1.03/1.16 @
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% 1.03/1.16 (
% 1.03/1.16 ![
% 1.03/1.16 X176:$i]:
% 1.03/1.16 (
% 1.03/1.16 (
% 1.03/1.16 in @
% 1.03/1.16 X176 @
% 1.03/1.16 (
% 1.03/1.16 powerset
% 1.03/1.16 @
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% 1.03/1.16 (
% 1.03/1.16 in @
% 1.03/1.16 (
% 1.03/1.16 binunion
% 1.03/1.16 @
% 1.03/1.16 X174 @
% 1.03/1.16 X176 ) @
% 1.03/1.16 (
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% 1.03/1.16 (
% 1.03/1.16 (
% 1.03/1.16 ![
% 1.03/1.16 X178:$i,
% 1.03/1.16 X180:$i]:
% 1.03/1.16 (
% 1.03/1.16 (
% 1.03/1.16 in @
% 1.03/1.16 X180 @
% 1.03/1.16 (
% 1.03/1.16 powerset
% 1.03/1.16 @
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% 1.03/1.16 (
% 1.03/1.16 in @
% 1.03/1.16 (
% 1.03/1.16 powerset
% 1.03/1.16 @
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% 1.03/1.16 (
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% 1.03/1.16 (
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% 1.03/1.16 X184:$i]:
% 1.03/1.16 (
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% 1.03/1.16 in @
% 1.03/1.16 X184 @
% 1.03/1.16 (
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% 1.03/1.16 (
% 1.03/1.16 ![
% 1.03/1.16 X186:$i]:
% 1.03/1.16 (
% 1.03/1.16 (
% 1.03/1.16 in @
% 1.03/1.16 X186 @
% 1.03/1.16 (
% 1.03/1.16 powerset
% 1.03/1.16 @
% 1.03/1.16 X182 ) ) =>
% 1.03/1.16 (
% 1.03/1.16 in @
% 1.03/1.16 (
% 1.03/1.16 setminus
% 1.03/1.16 @
% 1.03/1.16 X184 @
% 1.03/1.16 X186 ) @
% 1.03/1.16 (
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% 1.03/1.16 ![
% 1.03/1.16 X188:$i,
% 1.03/1.16 X190:$i]:
% 1.03/1.16 (
% 1.03/1.16 (
% 1.03/1.16 in @
% 1.03/1.16 X190 @
% 1.03/1.16 (
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% 1.03/1.16 @
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% 1.03/1.16 (
% 1.03/1.16 in @
% 1.03/1.16 (
% 1.03/1.16 setminus
% 1.03/1.16 @
% 1.03/1.16 X188 @
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% 1.03/1.16 (
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% 1.03/1.16 X192:$i,
% 1.03/1.16 X194:$i]:
% 1.03/1.16 (
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% 1.03/1.16 (
% 1.03/1.16 (
% 1.03/1.16 subsetTI ) =>
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% 1.03/1.16 X298 @
% 1.03/1.16 X300 ) ) ) =>
% 1.03/1.16 (
% 1.03/1.16 ~
% 1.03/1.16 (
% 1.03/1.16 in @
% 1.03/1.16 X302 @
% 1.03/1.16 X300 ) ) ) ) ) ) ) ) ) =>
% 1.03/1.16 (
% 1.03/1.16 (
% 1.03/1.16 ![
% 1.03/1.16 X304:$i,
% 1.03/1.16 X306:$i]:
% 1.03/1.16 (
% 1.03/1.16 (
% 1.03/1.16 in @
% 1.03/1.16 X306 @
% 1.03/1.16 (
% 1.03/1.16 powerset
% 1.03/1.16 @
% 1.03/1.16 X304 ) ) =>
% 1.03/1.16 (
% 1.03/1.16 ![
% 1.03/1.16 X308:$i]:
% 1.03/1.16 (
% 1.03/1.16 (
% 1.03/1.16 in @
% 1.03/1.16 X308 @
% 1.03/1.16 (
% 1.03/1.16 powerset
% 1.03/1.16 @
% 1.03/1.16 X304 ) ) =>
% 1.03/1.16 (
% 1.03/1.16 ![
% 1.03/1.16 X310:$i]:
% 1.03/1.16 (
% 1.03/1.16 (
% 1.03/1.16 in @
% 1.03/1.16 X310 @
% 1.03/1.16 (
% 1.03/1.16 powerset
% 1.03/1.16 @
% 1.03/1.16 X304 ) ) =>
% 1.03/1.16 (
% 1.03/1.16 ![
% 1.03/1.16 X312:$i]:
% 1.03/1.16 (
% 1.03/1.16 (
% 1.03/1.16 in @
% 1.03/1.16 X312 @
% 1.03/1.16 X304 ) =>
% 1.03/1.16 (
% 1.03/1.16 (
% 1.03/1.16 in @
% 1.03/1.16 X312 @
% 1.03/1.16 (
% 1.03/1.16 binintersect
% 1.03/1.16 @
% 1.03/1.16 X306 @
% 1.03/1.16 X308 ) ) =>
% 1.03/1.16 (
% 1.03/1.16 in @
% 1.03/1.16 X312 @
% 1.03/1.16 (
% 1.03/1.16 binunion
% 1.03/1.16 @
% 1.03/1.16 X306 @
% 1.03/1.16 X310 ) ) ) ) ) ) ) ) ) ) ) =>
% 1.03/1.16 (
% 1.03/1.16 (
% 1.03/1.16 ![
% 1.03/1.16 X314:$i,
% 1.03/1.16 X316:$i]:
% 1.03/1.16 (
% 1.03/1.16 (
% 1.03/1.16 in @
% 1.03/1.16 X316 @
% 1.03/1.16 (
% 1.03/1.16 powerset
% 1.03/1.16 @
% 1.03/1.16 X314 ) ) =>
% 1.03/1.16 (
% 1.03/1.16 ![
% 1.03/1.16 X318:$i]:
% 1.03/1.16 (
% 1.03/1.16 (
% 1.03/1.16 in @
% 1.03/1.16 X318 @
% 1.03/1.16 (
% 1.03/1.16 powerset
% 1.03/1.16 @
% 1.03/1.16 X314 ) ) =>
% 1.03/1.16 (
% 1.03/1.16 ![
% 1.03/1.16 X320:$i]:
% 1.03/1.16 (
% 1.03/1.16 (
% 1.03/1.16 in @
% 1.03/1.16 X320 @
% 1.03/1.16 (
% 1.03/1.16 powerset
% 1.03/1.16 @
% 1.03/1.16 X314 ) ) =>
% 1.03/1.16 (
% 1.03/1.16 ![
% 1.03/1.16 X322:$i]:
% 1.03/1.16 (
% 1.03/1.16 (
% 1.03/1.16 in @
% 1.03/1.16 X322 @
% 1.03/1.16 X314 ) =>
% 1.03/1.16 (
% 1.03/1.16 (
% 1.03/1.16 in @
% 1.03/1.16 X322 @
% 1.03/1.16 (
% 1.03/1.16 binintersect
% 1.03/1.16 @
% 1.03/1.16 X316 @
% 1.03/1.16 X318 ) ) =>
% 1.03/1.16 (
% 1.03/1.16 in @
% 1.03/1.16 X322 @
% 1.03/1.16 (
% 1.03/1.16 binunion
% 1.03/1.16 @
% 1.03/1.16 X318 @
% 1.03/1.16 X320 ) ) ) ) ) ) ) ) ) ) ) =>
% 1.03/1.16 (
% 1.03/1.16 (
% 1.03/1.16 ![
% 1.03/1.16 X324:$i,
% 1.03/1.16 X326:$i]:
% 1.03/1.16 (
% 1.03/1.16 (
% 1.03/1.16 in @
% 1.03/1.16 X326 @
% 1.03/1.16 (
% 1.03/1.16 powerset
% 1.03/1.16 @
% 1.03/1.16 X324 ) ) =>
% 1.03/1.16 (
% 1.03/1.16 ![
% 1.03/1.16 X328:$i]:
% 1.03/1.16 (
% 1.03/1.16 (
% 1.03/1.16 in @
% 1.03/1.16 X328 @
% 1.03/1.16 (
% 1.03/1.16 powerset
% 1.03/1.16 @
% 1.03/1.16 X324 ) ) =>
% 1.03/1.16 (
% 1.03/1.16 ![
% 1.03/1.16 X330:$i]:
% 1.03/1.16 (
% 1.03/1.16 (
% 1.03/1.16 in @
% 1.03/1.16 X330 @
% 1.03/1.16 (
% 1.03/1.16 powerset
% 1.03/1.16 @
% 1.03/1.16 X324 ) ) =>
% 1.03/1.16 (
% 1.03/1.16 ![
% 1.03/1.16 X332:$i]:
% 1.03/1.16 (
% 1.03/1.16 (
% 1.03/1.16 in @
% 1.03/1.16 X332 @
% 1.03/1.16 X324 ) =>
% 1.03/1.16 (
% 1.03/1.16 (
% 1.03/1.16 in @
% 1.03/1.16 X332 @
% 1.03/1.16 (
% 1.03/1.16 binintersect
% 1.03/1.16 @
% 1.03/1.16 X326 @
% 1.03/1.16 X328 ) ) =>
% 1.03/1.16 (
% 1.03/1.16 in @
% 1.03/1.16 X332 @
% 1.03/1.16 (
% 1.03/1.16 binintersect
% 1.03/1.16 @
% 1.03/1.16 (
% 1.03/1.16 binunion
% 1.03/1.16 @
% 1.03/1.16 X326 @
% 1.03/1.16 X330 ) @
% 1.03/1.16 (
% 1.03/1.16 binunion
% 1.03/1.16 @
% 1.03/1.16 X328 @
% 1.03/1.16 X330 ) ) ) ) ) ) ) ) ) ) ) ) =>
% 1.03/1.16 (
% 1.03/1.16 (
% 1.03/1.16 ![
% 1.03/1.16 X334:$i,
% 1.03/1.16 X336:$i]:
% 1.03/1.16 (
% 1.03/1.16 (
% 1.03/1.16 in @
% 1.03/1.16 X336 @
% 1.03/1.16 (
% 1.03/1.16 powerset
% 1.03/1.16 @
% 1.03/1.16 X334 ) ) =>
% 1.03/1.16 (
% 1.03/1.16 ![
% 1.03/1.16 X338:$i]:
% 1.03/1.16 (
% 1.03/1.16 (
% 1.03/1.16 in @
% 1.03/1.16 X338 @
% 1.03/1.16 (
% 1.03/1.16 powerset
% 1.03/1.16 @
% 1.03/1.16 X334 ) ) =>
% 1.03/1.16 (
% 1.03/1.16 ![
% 1.03/1.16 X340:$i]:
% 1.03/1.16 (
% 1.03/1.16 (
% 1.03/1.16 in @
% 1.03/1.16 X340 @
% 1.03/1.16 (
% 1.03/1.16 powerset
% 1.03/1.16 @
% 1.03/1.16 X334 ) ) =>
% 1.03/1.16 (
% 1.03/1.16 in @
% 1.03/1.16 (
% 1.03/1.16 binintersect
% 1.03/1.16 @
% 1.03/1.16 X336 @
% 1.03/1.16 X338 ) @
% 1.03/1.16 (
% 1.03/1.16 powerset
% 1.03/1.16 @
% 1.03/1.16 (
% 1.03/1.16 binintersect
% 1.03/1.16 @
% 1.03/1.16 (
% 1.03/1.16 binunion
% 1.03/1.16 @
% 1.03/1.16 X336 @
% 1.03/1.16 X340 ) @
% 1.03/1.16 (
% 1.03/1.16 binunion
% 1.03/1.16 @
% 1.03/1.16 X338 @
% 1.03/1.16 X340 ) ) ) ) ) ) ) ) ) ) =>
% 1.03/1.16 (
% 1.03/1.16 (
% 1.03/1.16 ![
% 1.03/1.16 X342:$i,
% 1.03/1.16 X344:$i]:
% 1.03/1.16 (
% 1.03/1.16 (
% 1.03/1.16 in @
% 1.03/1.16 X344 @
% 1.03/1.16 (
% 1.03/1.16 powerset
% 1.03/1.16 @
% 1.03/1.16 X342 ) ) =>
% 1.03/1.16 (
% 1.03/1.16 ![
% 1.03/1.16 X346:$i]:
% 1.03/1.16 (
% 1.03/1.16 (
% 1.03/1.16 in @
% 1.03/1.16 X346 @
% 1.03/1.16 (
% 1.03/1.16 powerset
% 1.03/1.16 @
% 1.03/1.16 X342 ) ) =>
% 1.03/1.16 (
% 1.03/1.16 ![
% 1.03/1.16 X348:$i]:
% 1.03/1.16 (
% 1.03/1.16 (
% 1.03/1.16 in @
% 1.03/1.16 X348 @
% 1.03/1.16 X342 ) =>
% 1.03/1.16 (
% 1.03/1.16 (
% 1.03/1.16 in @
% 1.03/1.16 X348 @
% 1.03/1.16 (
% 1.03/1.16 setminus
% 1.03/1.16 @
% 1.03/1.16 X342 @
% 1.03/1.16 (
% 1.03/1.16 binunion
% 1.03/1.16 @
% 1.03/1.16 X344 @
% 1.03/1.16 X346 ) ) ) =>
% 1.03/1.16 (
% 1.03/1.16 ~
% 1.03/1.16 (
% 1.03/1.16 in @
% 1.03/1.16 X348 @
% 1.03/1.16 X344 ) ) ) ) ) ) ) ) ) =>
% 1.03/1.16 (
% 1.03/1.16 ![
% 1.03/1.16 X350:$i,
% 1.03/1.16 X352:$i]:
% 1.03/1.16 (
% 1.03/1.16 (
% 1.03/1.16 in @
% 1.03/1.16 X352 @
% 1.03/1.16 (
% 1.03/1.16 powerset
% 1.03/1.16 @
% 1.03/1.16 X350 ) ) =>
% 1.03/1.16 (
% 1.03/1.16 ![
% 1.03/1.16 X354:$i]:
% 1.03/1.16 (
% 1.03/1.16 (
% 1.03/1.16 in @
% 1.03/1.16 X354 @
% 1.03/1.16 (
% 1.03/1.16 powerset
% 1.03/1.16 @
% 1.03/1.16 X350 ) ) =>
% 1.03/1.16 (
% 1.03/1.16 ![
% 1.03/1.16 X356:$i]:
% 1.03/1.16 (
% 1.03/1.16 (
% 1.03/1.16 in @
% 1.03/1.16 X356 @
% 1.03/1.16 X350 ) =>
% 1.03/1.16 (
% 1.03/1.16 (
% 1.03/1.16 in @
% 1.03/1.16 X356 @
% 1.03/1.16 (
% 1.03/1.16 setminus
% 1.03/1.16 @
% 1.03/1.16 X350 @
% 1.03/1.16 (
% 1.03/1.16 binunion
% 1.03/1.16 @
% 1.03/1.16 X352 @
% 1.03/1.16 X354 ) ) ) =>
% 1.03/1.16 (
% 1.03/1.16 in @
% 1.03/1.16 X356 @
% 1.03/1.16 (
% 1.03/1.16 setminus
% 1.03/1.16 @
% 1.03/1.16 X350 @
% 1.03/1.16 X352 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )),
% 1.03/1.16 inference('cnf.neg', [status(esa)], [zf_stmt_3])).
% 1.03/1.16 thf(zip_derived_cl53, plain,
% 1.03/1.16 (![X4 : $i, X5 : $i, X6 : $i]:
% 1.03/1.16 ( (in @ X4 @ (binunion @ X5 @ X6)) | ~ (in @ X4 @ X5))),
% 1.03/1.16 inference('cnf', [status(esa)], [zf_stmt_4])).
% 1.03/1.16 thf(zip_derived_cl136, plain,
% 1.03/1.16 ( (in @ sk__181 @ (setminus @ sk__178 @ (binunion @ sk__179 @ sk__180)))),
% 1.03/1.16 inference('cnf', [status(esa)], [zf_stmt_4])).
% 1.03/1.16 thf(zip_derived_cl66, plain,
% 1.03/1.16 (![X26 : $i, X27 : $i, X28 : $i]:
% 1.03/1.16 (~ (in @ X26 @ (setminus @ X27 @ X28)) | ~ (in @ X26 @ X28))),
% 1.03/1.16 inference('cnf', [status(esa)], [zf_stmt_4])).
% 1.03/1.16 thf(zip_derived_cl342, plain,
% 1.03/1.16 (~ (in @ sk__181 @ (binunion @ sk__179 @ sk__180))),
% 1.03/1.16 inference('sup-', [status(thm)], [zip_derived_cl136, zip_derived_cl66])).
% 1.03/1.16 thf(zip_derived_cl355, plain, (~ (in @ sk__181 @ sk__179)),
% 1.03/1.16 inference('sup-', [status(thm)], [zip_derived_cl53, zip_derived_cl342])).
% 1.03/1.16 thf(zip_derived_cl138, plain, ( (in @ sk__181 @ sk__178)),
% 1.03/1.16 inference('cnf', [status(esa)], [zf_stmt_4])).
% 1.03/1.16 thf(zip_derived_cl65, plain,
% 1.03/1.16 (![X23 : $i, X24 : $i, X25 : $i]:
% 1.03/1.16 ( (in @ X23 @ X24)
% 1.03/1.16 | ~ (in @ X23 @ X25)
% 1.03/1.16 | (in @ X23 @ (setminus @ X25 @ X24)))),
% 1.03/1.16 inference('cnf', [status(esa)], [zf_stmt_4])).
% 1.03/1.16 thf(zip_derived_cl412, plain,
% 1.03/1.16 (![X0 : $i]:
% 1.03/1.16 ( (in @ sk__181 @ (setminus @ sk__178 @ X0)) | (in @ sk__181 @ X0))),
% 1.03/1.16 inference('sup-', [status(thm)], [zip_derived_cl138, zip_derived_cl65])).
% 1.03/1.16 thf(zip_derived_cl137, plain,
% 1.03/1.16 (~ (in @ sk__181 @ (setminus @ sk__178 @ sk__179))),
% 1.03/1.16 inference('cnf', [status(esa)], [zf_stmt_4])).
% 1.03/1.16 thf(zip_derived_cl581, plain, ( (in @ sk__181 @ sk__179)),
% 1.03/1.16 inference('sup-', [status(thm)], [zip_derived_cl412, zip_derived_cl137])).
% 1.03/1.16 thf(zip_derived_cl597, plain, ($false),
% 1.03/1.16 inference('demod', [status(thm)], [zip_derived_cl355, zip_derived_cl581])).
% 1.03/1.16
% 1.03/1.16 % SZS output end Refutation
% 1.03/1.16
% 1.03/1.16
% 1.03/1.16 % Terminating...
% 4.91/1.28 % Runner terminated.
% 4.91/1.29 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------