%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SEU746^1 : 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.PDAPfW2Nj5 true
% Computer : n027.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 3.74s 1.49s
% Output : Refutation 3.99s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SEU746^1 : TPTP v9.2.0. Released v3.7.0.
% 0.08/0.13 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.PDAPfW2Nj5 true
% 0.09/0.33 % Computer : n027.cluster.edu
% 0.09/0.33 % Model : x86_64 x86_64
% 0.09/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.33 % Memory : 8042.1875MB
% 0.09/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.34 % CPULimit : 300
% 0.09/0.34 % WCLimit : 300
% 0.09/0.34 % DateTime : Wed Oct 1 16:10:53 EDT 2025
% 0.09/0.34 % CPUTime :
% 0.09/0.34 % Running portfolio for 300 s
% 0.09/0.34 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Number of cores: 8
% 0.09/0.35 % Python version: Python 3.6.8
% 0.09/0.35 % Running in HO mode
% 0.42/0.68 % Total configuration time : 828
% 0.42/0.68 % Estimated wc time : 1656
% 0.42/0.68 % Estimated cpu time (8 cpus) : 207.0
% 0.44/0.81 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
% 0.44/0.88 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.45/0.90 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
% 0.45/0.92 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
% 0.45/0.93 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s
% 0.45/0.93 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.45/0.94 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s
% 0.45/0.95 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s
% 3.74/1.49 % Solved by lams/40_c_ic.sh.
% 3.74/1.49 % done 255 iterations in 0.400s
% 3.74/1.49 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 3.74/1.49 % SZS output start Refutation
% 3.74/1.49 thf(setadjoinAx_type, type, setadjoinAx: $o).
% 3.74/1.49 thf(notdexE_type, type, notdexE: $o).
% 3.74/1.49 thf(sk__116_type, type, sk__116: $i).
% 3.74/1.49 thf(setukpairinjL2_type, type, setukpairinjL2: $o).
% 3.74/1.49 thf(doubleComplementI1_type, type, doubleComplementI1: $o).
% 3.74/1.49 thf(setunionAx_type, type, setunionAx: $o).
% 3.74/1.49 thf(setminusELneg_type, type, setminusELneg: $o).
% 3.74/1.49 thf(sk__117_type, type, sk__117: $i).
% 3.74/1.49 thf(cartprodsndin_type, type, cartprodsndin: $o).
% 3.74/1.49 thf(ex1E1_type, type, ex1E1: $o).
% 3.74/1.49 thf(powersetE_type, type, powersetE: $o).
% 3.74/1.49 thf(omegaSAx_type, type, omegaSAx: $o).
% 3.74/1.49 thf(exuI1_type, type, exuI1: $o).
% 3.74/1.49 thf(exuI2_type, type, exuI2: $o).
% 3.74/1.49 thf(notequalI2_type, type, notequalI2: $o).
% 3.74/1.49 thf(setukpairinjL_type, type, setukpairinjL: $o).
% 3.74/1.49 thf(kpairiskpair_type, type, kpairiskpair: $o).
% 3.74/1.49 thf(upairsubunion_type, type, upairsubunion: $o).
% 3.74/1.49 thf(funcGraphProp3_type, type, funcGraphProp3: $o).
% 3.74/1.49 thf(cartprodmempaircEq_type, type, cartprodmempaircEq: $o).
% 3.74/1.49 thf(binintersectTERcontra_type, type, binintersectTERcontra: $o).
% 3.74/1.49 thf(powerset__Cong_type, type, powerset__Cong: $o).
% 3.74/1.49 thf(setminusILneg_type, type, setminusILneg: $o).
% 3.74/1.49 thf(wellorderingAx_type, type, wellorderingAx: $o).
% 3.74/1.49 thf(ksndpairEq_type, type, ksndpairEq: $o).
% 3.74/1.49 thf(funcGraphProp2_type, type, funcGraphProp2: $o).
% 3.74/1.49 thf(setadjoinSub2_type, type, setadjoinSub2: $o).
% 3.74/1.49 thf(binintersectSubset5_type, type, binintersectSubset5: $o).
% 3.74/1.49 thf(iftrue_type, type, iftrue: $o).
% 3.74/1.49 thf(upairinpowunion_type, type, upairinpowunion: $o).
% 3.74/1.49 thf(ifSingleton_type, type, ifSingleton: $o).
% 3.74/1.49 thf(doubleComplementSub2_type, type, doubleComplementSub2: $o).
% 3.74/1.49 thf(setoftrueEq_type, type, setoftrueEq: $o).
% 3.74/1.49 thf(funcImageSingleton_type, type, funcImageSingleton: $o).
% 3.74/1.49 thf(inIntersectImpInUnion2_type, type, inIntersectImpInUnion2: $o).
% 3.74/1.49 thf(dpsetconstrERa_type, type, dpsetconstrERa: $o).
% 3.74/1.49 thf(lamProp_type, type, lamProp: $o).
% 3.74/1.49 thf(cartprodpairmemEL_type, type, cartprodpairmemEL: $o).
% 3.74/1.49 thf(emptyset__Cong_type, type, emptyset__Cong: $o).
% 3.74/1.49 thf(dpsetconstrER_type, type, dpsetconstrER: $o).
% 3.74/1.49 thf(sepInPowerset_type, type, sepInPowerset: $o).
% 3.74/1.49 thf(setukpairIR_type, type, setukpairIR: $o).
% 3.74/1.49 thf(setukpairinjR1_type, type, setukpairinjR1: $o).
% 3.74/1.49 thf(lam2p_type, type, lam2p: $o).
% 3.74/1.49 thf(kpair_type, type, kpair: $i > $i > $i).
% 3.74/1.49 thf(binunionE_type, type, binunionE: $o).
% 3.74/1.49 thf(setext_type, type, setext: $o).
% 3.74/1.49 thf(emptyinPowerset_type, type, emptyinPowerset: $o).
% 3.74/1.49 thf(ubforcartprodlem1_type, type, ubforcartprodlem1: $o).
% 3.74/1.49 thf(descr__Cong_type, type, descr__Cong: $o).
% 3.74/1.49 thf(kfstsingleton_type, type, kfstsingleton: $o).
% 3.74/1.49 thf(binintersectTELcontra_type, type, binintersectTELcontra: $o).
% 3.74/1.49 thf(doubleComplementEq_type, type, doubleComplementEq: $o).
% 3.74/1.49 thf(eqbreln_type, type, eqbreln: $o).
% 3.74/1.49 thf(binintersectSubset1_type, type, binintersectSubset1: $o).
% 3.74/1.49 thf(inComplementUnionImpInComplement1_type, type, inComplementUnionImpInComplement1:
% 3.74/1.49 $o).
% 3.74/1.49 thf(complementImpComplementIntersect_type, type, complementImpComplementIntersect:
% 3.74/1.49 $o).
% 3.74/1.49 thf(in_type, type, in: $i > $i > $o).
% 3.74/1.49 thf(binunionT_lem_type, type, binunionT_lem: $o).
% 3.74/1.49 thf(quantDeMorgan1_type, type, quantDeMorgan1: $o).
% 3.74/1.49 thf(complementT_lem_type, type, complementT_lem: $o).
% 3.74/1.49 thf(binunion_type, type, binunion: $i > $i > $i).
% 3.74/1.49 thf(kpairsurjEq_type, type, kpairsurjEq: $o).
% 3.74/1.49 thf(setadjoinIR_type, type, setadjoinIR: $o).
% 3.74/1.49 thf(doubleComplementE1_type, type, doubleComplementE1: $o).
% 3.74/1.49 thf(beta1_type, type, beta1: $o).
% 3.74/1.49 thf(setadjoin__Cong_type, type, setadjoin__Cong: $o).
% 3.74/1.49 thf(powersetTE1_type, type, powersetTE1: $o).
% 3.74/1.49 thf(symdiffI2_type, type, symdiffI2: $o).
% 3.74/1.49 thf(iftrueProp2_type, type, iftrueProp2: $o).
% 3.74/1.49 thf(upairset2IR_type, type, upairset2IR: $o).
% 3.74/1.49 thf(iffalseProp2_type, type, iffalseProp2: $o).
% 3.74/1.49 thf(subsetE_type, type, subsetE: $o).
% 3.74/1.49 thf(prop2set2propI_type, type, prop2set2propI: $o).
% 3.74/1.49 thf(dsetconstrEL_type, type, dsetconstrEL: $o).
% 3.74/1.49 thf(setbeta_type, type, setbeta: $o).
% 3.74/1.49 thf(eqinunit_type, type, eqinunit: $o).
% 3.74/1.49 thf(upairsetIL_type, type, upairsetIL: $o).
% 3.74/1.49 thf(powersetI1_type, type, powersetI1: $o).
% 3.74/1.49 thf(kfstpairEq_type, type, kfstpairEq: $o).
% 3.74/1.49 thf(binintersectSubset3_type, type, binintersectSubset3: $o).
% 3.74/1.49 thf(inComplementUnionImpNotIn1_type, type, inComplementUnionImpNotIn1: $o).
% 3.74/1.49 thf(setminusIRneg_type, type, setminusIRneg: $o).
% 3.74/1.49 thf(ap2apEq1_type, type, ap2apEq1: $o).
% 3.74/1.49 thf(powersetAx_type, type, powersetAx: $o).
% 3.74/1.49 thf(binintersectSubset4_type, type, binintersectSubset4: $o).
% 3.74/1.49 thf(singletoninpowunion_type, type, singletoninpowunion: $o).
% 3.74/1.49 thf(binunionTIRcontra_type, type, binunionTIRcontra: $o).
% 3.74/1.49 thf(powersetI_type, type, powersetI: $o).
% 3.74/1.49 thf(cartprodmempair_type, type, cartprodmempair: $o).
% 3.74/1.49 thf(upairsetIR_type, type, upairsetIR: $o).
% 3.74/1.49 thf(lamp_type, type, lamp: $o).
% 3.74/1.49 thf(dpsetconstrEL1_type, type, dpsetconstrEL1: $o).
% 3.74/1.49 thf(inCongP_type, type, inCongP: $o).
% 3.74/1.49 thf(setadjoinSub_type, type, setadjoinSub: $o).
% 3.74/1.49 thf(exuE3e_type, type, exuE3e: $o).
% 3.74/1.49 thf(emptysetE_type, type, emptysetE: $o).
% 3.74/1.49 thf(binintersectSubset2_type, type, binintersectSubset2: $o).
% 3.74/1.49 thf(setunionI_type, type, setunionI: $o).
% 3.74/1.49 thf(setunion__Cong_type, type, setunion__Cong: $o).
% 3.74/1.49 thf(prop2setI_type, type, prop2setI: $o).
% 3.74/1.49 thf(singletonsuniq_type, type, singletonsuniq: $o).
% 3.74/1.49 thf(nonemptyImpWitness_type, type, nonemptyImpWitness: $o).
% 3.74/1.49 thf(setminusER_type, type, setminusER: $o).
% 3.74/1.49 thf(exuE2_type, type, exuE2: $o).
% 3.74/1.49 thf(emptyset_type, type, emptyset: $i).
% 3.74/1.49 thf(setukpairinjR11_type, type, setukpairinjR11: $o).
% 3.74/1.49 thf(ex1I_type, type, ex1I: $o).
% 3.74/1.49 thf(ex1E2_type, type, ex1E2: $o).
% 3.74/1.49 thf(setminus_type, type, setminus: $i > $i > $i).
% 3.74/1.49 thf(setukpairinjL1_type, type, setukpairinjL1: $o).
% 3.74/1.49 thf(powersetsubset_type, type, powersetsubset: $o).
% 3.74/1.49 thf(binunionTILcontra_type, type, binunionTILcontra: $o).
% 3.74/1.49 thf(subPowSU_type, type, subPowSU: $o).
% 3.74/1.49 thf(notequalI1_type, type, notequalI1: $o).
% 3.74/1.49 thf(contrasubsetT_type, type, contrasubsetT: $o).
% 3.74/1.49 thf(notinemptyset_type, type, notinemptyset: $o).
% 3.74/1.49 thf(lam2lamEq_type, type, lam2lamEq: $o).
% 3.74/1.49 thf(nonemptyI1_type, type, nonemptyI1: $o).
% 3.74/1.49 thf(sk__118_type, type, sk__118: $o).
% 3.74/1.49 thf(subsetTrans_type, type, subsetTrans: $o).
% 3.74/1.49 thf(kpairp_type, type, kpairp: $o).
% 3.74/1.49 thf(setukpairinjR12_type, type, setukpairinjR12: $o).
% 3.74/1.49 thf(setminusI_type, type, setminusI: $o).
% 3.74/1.49 thf(binunionIL_type, type, binunionIL: $o).
% 3.74/1.49 thf(dpsetconstrSub_type, type, dpsetconstrSub: $o).
% 3.74/1.49 thf(setunionsingleton_type, type, setunionsingleton: $o).
% 3.74/1.49 thf(subsetE2_type, type, subsetE2: $o).
% 3.74/1.49 thf(singletonsswitch_type, type, singletonsswitch: $o).
% 3.74/1.49 thf(ubforcartprodlem3_type, type, ubforcartprodlem3: $o).
% 3.74/1.49 thf(beta2_type, type, beta2: $o).
% 3.74/1.49 thf(dpsetconstrI_type, type, dpsetconstrI: $o).
% 3.74/1.49 thf(setextsub_type, type, setextsub: $o).
% 3.74/1.49 thf(binunionLsub_type, type, binunionLsub: $o).
% 3.74/1.49 thf(setunionsingleton1_type, type, setunionsingleton1: $o).
% 3.74/1.49 thf(binintersect_type, type, binintersect: $i > $i > $i).
% 3.74/1.49 thf(iftrueorfalse_type, type, iftrueorfalse: $o).
% 3.74/1.49 thf(emptysetsubset_type, type, emptysetsubset: $o).
% 3.74/1.49 thf(quantDeMorgan3_type, type, quantDeMorgan3: $o).
% 3.74/1.49 thf(cartprodpairsurjEq_type, type, cartprodpairsurjEq: $o).
% 3.74/1.49 thf(setOfPairsIsBReln_type, type, setOfPairsIsBReln: $o).
% 3.74/1.49 thf(setunionE_type, type, setunionE: $o).
% 3.74/1.49 thf(ksndsingleton_type, type, ksndsingleton: $o).
% 3.74/1.49 thf(setminusSubset1_type, type, setminusSubset1: $o).
% 3.74/1.49 thf(powersetT_lem_type, type, powersetT_lem: $o).
% 3.74/1.49 thf(emptyinunitempty_type, type, emptyinunitempty: $o).
% 3.74/1.49 thf(binunionIR_type, type, binunionIR: $o).
% 3.74/1.49 thf(theeq_type, type, theeq: $o).
% 3.74/1.49 thf(setadjoinE_type, type, setadjoinE: $o).
% 3.74/1.49 thf(doubleComplementSub1_type, type, doubleComplementSub1: $o).
% 3.74/1.49 thf(infuncsetfunc_type, type, infuncsetfunc: $o).
% 3.74/1.49 thf(ap2apEq2_type, type, ap2apEq2: $o).
% 3.74/1.49 thf(ap2p_type, type, ap2p: $o).
% 3.74/1.49 thf(setadjoinIL_type, type, setadjoinIL: $o).
% 3.74/1.49 thf(cartprodsndpairEq_type, type, cartprodsndpairEq: $o).
% 3.74/1.49 thf(exuE1_type, type, exuE1: $o).
% 3.74/1.49 thf(ubforcartprodlem2_type, type, ubforcartprodlem2: $o).
% 3.74/1.49 thf(binintersectRsub_type, type, binintersectRsub: $o).
% 3.74/1.49 thf(setminusLsub_type, type, setminusLsub: $o).
% 3.74/1.49 thf(funcextLem_type, type, funcextLem: $o).
% 3.74/1.49 thf(setukpairinjR_type, type, setukpairinjR: $o).
% 3.74/1.49 thf(notinsingleton_type, type, notinsingleton: $o).
% 3.74/1.49 thf(inIntersectImpInIntersectUnions_type, type, inIntersectImpInIntersectUnions:
% 3.74/1.49 $o).
% 3.74/1.49 thf(eqimpsubset2_type, type, eqimpsubset2: $o).
% 3.74/1.49 thf(exuEu_type, type, exuEu: $o).
% 3.74/1.49 thf(emptysetimpfalse_type, type, emptysetimpfalse: $o).
% 3.74/1.49 thf(upairsetE_type, type, upairsetE: $o).
% 3.74/1.49 thf(omega0Ax_type, type, omega0Ax: $o).
% 3.74/1.49 thf(subsetTI_type, type, subsetTI: $o).
% 3.74/1.49 thf(notsubsetI_type, type, notsubsetI: $o).
% 3.74/1.49 thf(contraSubsetComplement_type, type, contraSubsetComplement: $o).
% 3.74/1.49 thf(iffalseProp1_type, type, iffalseProp1: $o).
% 3.74/1.49 thf(quantDeMorgan4_type, type, quantDeMorgan4: $o).
% 3.74/1.49 thf(setextAx_type, type, setextAx: $o).
% 3.74/1.49 thf(cartprodpairmemER_type, type, cartprodpairmemER: $o).
% 3.74/1.49 thf(powersetE1_type, type, powersetE1: $o).
% 3.74/1.49 thf(bs114d_type, type, bs114d: $o).
% 3.74/1.49 thf(contrasubsetT3_type, type, contrasubsetT3: $o).
% 3.74/1.49 thf(noeltsimpempty_type, type, noeltsimpempty: $o).
% 3.74/1.49 thf(complementTcontraSubset_type, type, complementTcontraSubset: $o).
% 3.74/1.49 thf(ifp_type, type, ifp: $o).
% 3.74/1.49 thf(inIntersectImpInUnion_type, type, inIntersectImpInUnion: $o).
% 3.74/1.49 thf(powersetTI1_type, type, powersetTI1: $o).
% 3.74/1.49 thf(binintersectLsub_type, type, binintersectLsub: $o).
% 3.74/1.49 thf(subsetI1_type, type, subsetI1: $o).
% 3.74/1.49 thf(symdiffE_type, type, symdiffE: $o).
% 3.74/1.49 thf(descrp_type, type, descrp: $o).
% 3.74/1.49 thf(dsetconstr__Cong_type, type, dsetconstr__Cong: $o).
% 3.74/1.49 thf(foundationAx_type, type, foundationAx: $o).
% 3.74/1.49 thf(emptysetAx_type, type, emptysetAx: $o).
% 3.74/1.49 thf(emptyI_type, type, emptyI: $o).
% 3.74/1.49 thf(setadjoinOr_type, type, setadjoinOr: $o).
% 3.74/1.49 thf(eta2_type, type, eta2: $o).
% 3.74/1.49 thf(binintersectEL_type, type, binintersectEL: $o).
% 3.74/1.49 thf(emptyE1_type, type, emptyE1: $o).
% 3.74/1.49 thf(emptyInPowerset_type, type, emptyInPowerset: $o).
% 3.74/1.49 thf(complementTI1_type, type, complementTI1: $o).
% 3.74/1.49 thf(vacuousDall_type, type, vacuousDall: $o).
% 3.74/1.49 thf(dsetconstrER_type, type, dsetconstrER: $o).
% 3.74/1.49 thf(binintersectI_type, type, binintersectI: $o).
% 3.74/1.49 thf(funcext_type, type, funcext: $o).
% 3.74/1.49 thf(funcGraphProp4_type, type, funcGraphProp4: $o).
% 3.74/1.49 thf(zip_tseitin_0_type, type, zip_tseitin_0: $i > $i > $i > $o).
% 3.74/1.49 thf(cartprodpairin_type, type, cartprodpairin: $o).
% 3.74/1.49 thf(cartprodmempair1_type, type, cartprodmempair1: $o).
% 3.74/1.49 thf(brelnall2_type, type, brelnall2: $o).
% 3.74/1.49 thf(setextT_type, type, setextT: $o).
% 3.74/1.49 thf(ex1I2_type, type, ex1I2: $o).
% 3.74/1.49 thf(symdiffI1_type, type, symdiffI1: $o).
% 3.74/1.49 thf(setukpairinjR2_type, type, setukpairinjR2: $o).
% 3.74/1.49 thf(dpsetconstrEL2_type, type, dpsetconstrEL2: $o).
% 3.74/1.49 thf(theprop_type, type, theprop: $o).
% 3.74/1.49 thf(subsetI2_type, type, subsetI2: $o).
% 3.74/1.49 thf(complementInPowersetComplementIntersect_type, type, complementInPowersetComplementIntersect:
% 3.74/1.49 $o).
% 3.74/1.49 thf(setminusT_lem_type, type, setminusT_lem: $o).
% 3.74/1.49 thf(symdiffIneg1_type, type, symdiffIneg1: $o).
% 3.74/1.49 thf(setminusERneg_type, type, setminusERneg: $o).
% 3.74/1.49 thf(symdiffIneg2_type, type, symdiffIneg2: $o).
% 3.74/1.49 thf(omega__Cong_type, type, omega__Cong: $o).
% 3.74/1.49 thf(subsetRefl_type, type, subsetRefl: $o).
% 3.74/1.49 thf(uniqinunit_type, type, uniqinunit: $o).
% 3.74/1.49 thf(complementSubsetComplementIntersect_type, type, complementSubsetComplementIntersect:
% 3.74/1.49 $o).
% 3.74/1.49 thf(setminusSubset2_type, type, setminusSubset2: $o).
% 3.74/1.49 thf(prop2setE_type, type, prop2setE: $o).
% 3.74/1.49 thf(binunionEcases_type, type, binunionEcases: $o).
% 3.74/1.49 thf(funcinfuncset_type, type, funcinfuncset: $o).
% 3.74/1.49 thf(complementTE1_type, type, complementTE1: $o).
% 3.74/1.49 thf(nonemptyI_type, type, nonemptyI: $o).
% 3.74/1.49 thf(app_type, type, app: $o).
% 3.74/1.49 thf(disjointsetsI1_type, type, disjointsetsI1: $o).
% 3.74/1.49 thf(exuE3u_type, type, exuE3u: $o).
% 3.74/1.49 thf(eta1_type, type, eta1: $o).
% 3.74/1.49 thf(setminusEL_type, type, setminusEL: $o).
% 3.74/1.49 thf(cartprodfstin_type, type, cartprodfstin: $o).
% 3.74/1.49 thf(setunionsingleton2_type, type, setunionsingleton2: $o).
% 3.74/1.49 thf(sepSubset_type, type, sepSubset: $o).
% 3.74/1.49 thf(complementTnotintersectT_type, type, complementTnotintersectT: $o).
% 3.74/1.49 thf(upairset2E_type, type, upairset2E: $o).
% 3.74/1.49 thf(eqimpsubset1_type, type, eqimpsubset1: $o).
% 3.74/1.49 thf(exuI3_type, type, exuI3: $o).
% 3.74/1.49 thf(cartprodfstpairEq_type, type, cartprodfstpairEq: $o).
% 3.74/1.49 thf(apProp_type, type, apProp: $o).
% 3.74/1.49 thf(notdallE_type, type, notdallE: $o).
% 3.74/1.49 thf(iftrueProp1_type, type, iftrueProp1: $o).
% 3.74/1.49 thf(binintersectER_type, type, binintersectER: $o).
% 3.74/1.49 thf(brelnall1_type, type, brelnall1: $o).
% 3.74/1.49 thf(powerset_type, type, powerset: $i > $i).
% 3.74/1.49 thf(dsetconstrI_type, type, dsetconstrI: $o).
% 3.74/1.49 thf(funcGraphProp1_type, type, funcGraphProp1: $o).
% 3.74/1.49 thf(binintersectT_lem_type, type, binintersectT_lem: $o).
% 3.74/1.49 thf(setadjoin_type, type, setadjoin: $i > $i > $i).
% 3.74/1.49 thf(exu__Cong_type, type, exu__Cong: $o).
% 3.74/1.49 thf(intersectInPowersetIntersectUnions_type, type, intersectInPowersetIntersectUnions:
% 3.74/1.49 $o).
% 3.74/1.49 thf(quantDeMorgan2_type, type, quantDeMorgan2: $o).
% 3.74/1.49 thf(contrasubsetT2_type, type, contrasubsetT2: $o).
% 3.74/1.49 thf(secondinupair_type, type, secondinupair: $o).
% 3.74/1.49 thf(singletonprop_type, type, singletonprop: $o).
% 3.74/1.49 thf(singletonsubset_type, type, singletonsubset: $o).
% 3.74/1.49 thf(contrasubsetT1_type, type, contrasubsetT1: $o).
% 3.74/1.49 thf(singletoninpowerset_type, type, singletoninpowerset: $o).
% 3.74/1.49 thf(subsetemptysetimpeq_type, type, subsetemptysetimpeq: $o).
% 3.74/1.49 thf(replAx_type, type, replAx: $o).
% 3.74/1.49 thf(upairequniteq_type, type, upairequniteq: $o).
% 3.74/1.49 thf(nonemptyE1_type, type, nonemptyE1: $o).
% 3.74/1.49 thf(omegaIndAx_type, type, omegaIndAx: $o).
% 3.74/1.49 thf(setukpairIL_type, type, setukpairIL: $o).
% 3.74/1.49 thf(setunionE2_type, type, setunionE2: $o).
% 3.74/1.49 thf(inPowerset_type, type, inPowerset: $o).
% 3.74/1.49 thf(iffalse_type, type, iffalse: $o).
% 3.74/1.49 thf(funcext2_type, type, funcext2: $o).
% 3.74/1.49 thf(subset_type, type, subset: $i > $i > $o).
% 3.74/1.49 thf(subbreln_type, type, subbreln: $o).
% 3.74/1.49 thf(in__Cong_type, type, in__Cong: $o).
% 3.74/1.49 thf(binunionRsub_type, type, binunionRsub: $o).
% 3.74/1.49 thf(sk__119_type, type, sk__119: $i).
% 3.74/1.49 thf(subset2powerset_type, type, subset2powerset: $o).
% 3.74/1.49 thf(inComplementUnionImpInComplement1, axiom,
% 3.74/1.49 inComplementUnionImpInComplement1 =
% 3.74/1.49 (![A:$i,X:$i]:
% 3.74/1.49 ( ( in @ X @ ( powerset @ A ) ) =>
% 3.74/1.49 ( ![Y:$i]:
% 3.74/1.49 ( ( in @ Y @ ( powerset @ A ) ) =>
% 3.74/1.49 ( ![Xx:$i]:
% 3.74/1.49 ( ( in @ Xx @ A ) =>
% 3.74/1.49 ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) ) =>
% 3.74/1.49 ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ))).
% 3.74/1.49 thf('0', plain,
% 3.74/1.49 (( inComplementUnionImpInComplement1 ) =
% 3.74/1.49 ( ![X4:$i,X6:$i]:
% 3.74/1.49 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 3.74/1.49 ( ![X8:$i]:
% 3.74/1.49 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 3.74/1.49 ( ![X10:$i]:
% 3.74/1.49 ( ( in @ X10 @ X4 ) =>
% 3.74/1.49 ( ( in @ X10 @ ( setminus @ X4 @ ( binunion @ X6 @ X8 ) ) ) =>
% 3.74/1.49 ( in @ X10 @ ( setminus @ X4 @ X6 ) ) ) ) ) ) ) ) )),
% 3.74/1.49 define([status(thm)])).
% 3.74/1.49 thf(inComplementUnionImpNotIn1, axiom, inComplementUnionImpNotIn1 =
% 3.74/1.49 (![A:$i,X:$i]:
% 3.74/1.49 ( ( in @ X @ ( powerset @ A ) ) =>
% 3.74/1.49 ( ![Y:$i]:
% 3.74/1.49 ( ( in @ Y @ ( powerset @ A ) ) =>
% 3.74/1.49 ( ![Xx:$i]:
% 3.74/1.49 ( ( in @ Xx @ A ) =>
% 3.74/1.49 ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) ) =>
% 3.74/1.49 ( ~( in @ Xx @ X ) ) ) ) ) ) ) ))).
% 3.74/1.49 thf('1', plain,
% 3.74/1.49 (( inComplementUnionImpNotIn1 ) =
% 3.74/1.49 ( ![X4:$i,X6:$i]:
% 3.74/1.49 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 3.74/1.49 ( ![X8:$i]:
% 3.74/1.49 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 3.74/1.49 ( ![X10:$i]:
% 3.74/1.49 ( ( in @ X10 @ X4 ) =>
% 3.74/1.49 ( ( in @ X10 @ ( setminus @ X4 @ ( binunion @ X6 @ X8 ) ) ) =>
% 3.74/1.49 ( ~( in @ X10 @ X6 ) ) ) ) ) ) ) ) )),
% 3.74/1.49 define([status(thm)])).
% 3.74/1.49 thf(intersectInPowersetIntersectUnions, axiom,
% 3.74/1.49 intersectInPowersetIntersectUnions =
% 3.74/1.49 (![A:$i,X:$i]:
% 3.74/1.49 ( ( in @ X @ ( powerset @ A ) ) =>
% 3.74/1.49 ( ![Y:$i]:
% 3.74/1.49 ( ( in @ Y @ ( powerset @ A ) ) =>
% 3.74/1.49 ( ![Z:$i]:
% 3.74/1.49 ( ( in @ Z @ ( powerset @ A ) ) =>
% 3.74/1.49 ( in @
% 3.74/1.49 ( binintersect @ X @ Y ) @
% 3.74/1.49 ( powerset @
% 3.74/1.49 ( binintersect @ ( binunion @ X @ Z ) @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ))).
% 3.74/1.49 thf('2', plain,
% 3.74/1.49 (( intersectInPowersetIntersectUnions ) =
% 3.74/1.49 ( ![X4:$i,X6:$i]:
% 3.74/1.49 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 3.74/1.49 ( ![X8:$i]:
% 3.74/1.49 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 3.74/1.49 ( ![X10:$i]:
% 3.74/1.49 ( ( in @ X10 @ ( powerset @ X4 ) ) =>
% 3.74/1.49 ( in @
% 3.74/1.49 ( binintersect @ X6 @ X8 ) @
% 3.74/1.49 ( powerset @
% 3.74/1.49 ( binintersect @
% 3.74/1.49 ( binunion @ X6 @ X10 ) @ ( binunion @ X8 @ X10 ) ) ) ) ) ) ) ) ) )),
% 3.74/1.49 define([status(thm)])).
% 3.74/1.49 thf(inIntersectImpInIntersectUnions, axiom, inIntersectImpInIntersectUnions =
% 3.74/1.49 (![A:$i,X:$i]:
% 3.74/1.49 ( ( in @ X @ ( powerset @ A ) ) =>
% 3.74/1.49 ( ![Y:$i]:
% 3.74/1.49 ( ( in @ Y @ ( powerset @ A ) ) =>
% 3.74/1.49 ( ![Z:$i]:
% 3.74/1.49 ( ( in @ Z @ ( powerset @ A ) ) =>
% 3.74/1.49 ( ![Xx:$i]:
% 3.74/1.49 ( ( in @ Xx @ A ) =>
% 3.74/1.49 ( ( in @ Xx @ ( binintersect @ X @ Y ) ) =>
% 3.74/1.49 ( in @
% 3.74/1.49 Xx @
% 3.74/1.49 ( binintersect @
% 3.74/1.49 ( binunion @ X @ Z ) @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ) ))).
% 3.74/1.49 thf('3', plain,
% 3.74/1.49 (( inIntersectImpInIntersectUnions ) =
% 3.74/1.49 ( ![X4:$i,X6:$i]:
% 3.74/1.49 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 3.74/1.49 ( ![X8:$i]:
% 3.74/1.49 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 3.74/1.49 ( ![X10:$i]:
% 3.74/1.49 ( ( in @ X10 @ ( powerset @ X4 ) ) =>
% 3.74/1.49 ( ![X12:$i]:
% 3.74/1.49 ( ( in @ X12 @ X4 ) =>
% 3.74/1.49 ( ( in @ X12 @ ( binintersect @ X6 @ X8 ) ) =>
% 3.74/1.49 ( in @
% 3.74/1.49 X12 @
% 3.74/1.49 ( binintersect @
% 3.74/1.49 ( binunion @ X6 @ X10 ) @ ( binunion @ X8 @ X10 ) ) ) ) ) ) ) ) ) ) ) )),
% 3.74/1.49 define([status(thm)])).
% 3.74/1.49 thf(inIntersectImpInUnion2, axiom, inIntersectImpInUnion2 =
% 3.74/1.49 (![A:$i,X:$i]:
% 3.74/1.49 ( ( in @ X @ ( powerset @ A ) ) =>
% 3.74/1.49 ( ![Y:$i]:
% 3.74/1.49 ( ( in @ Y @ ( powerset @ A ) ) =>
% 3.74/1.49 ( ![Z:$i]:
% 3.74/1.49 ( ( in @ Z @ ( powerset @ A ) ) =>
% 3.74/1.49 ( ![Xx:$i]:
% 3.74/1.49 ( ( in @ Xx @ A ) =>
% 3.74/1.49 ( ( in @ Xx @ ( binintersect @ X @ Y ) ) =>
% 3.74/1.49 ( in @ Xx @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ))).
% 3.74/1.49 thf('4', plain,
% 3.74/1.49 (( inIntersectImpInUnion2 ) =
% 3.74/1.49 ( ![X4:$i,X6:$i]:
% 3.74/1.49 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 3.74/1.49 ( ![X8:$i]:
% 3.74/1.49 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 3.74/1.49 ( ![X10:$i]:
% 3.74/1.49 ( ( in @ X10 @ ( powerset @ X4 ) ) =>
% 3.74/1.49 ( ![X12:$i]:
% 3.74/1.49 ( ( in @ X12 @ X4 ) =>
% 3.74/1.49 ( ( in @ X12 @ ( binintersect @ X6 @ X8 ) ) =>
% 3.74/1.49 ( in @ X12 @ ( binunion @ X8 @ X10 ) ) ) ) ) ) ) ) ) ) )),
% 3.74/1.49 define([status(thm)])).
% 3.74/1.49 thf(inIntersectImpInUnion, axiom, inIntersectImpInUnion =
% 3.74/1.49 (![A:$i,X:$i]:
% 3.74/1.49 ( ( in @ X @ ( powerset @ A ) ) =>
% 3.74/1.49 ( ![Y:$i]:
% 3.74/1.49 ( ( in @ Y @ ( powerset @ A ) ) =>
% 3.74/1.49 ( ![Z:$i]:
% 3.74/1.49 ( ( in @ Z @ ( powerset @ A ) ) =>
% 3.74/1.49 ( ![Xx:$i]:
% 3.74/1.49 ( ( in @ Xx @ A ) =>
% 3.74/1.49 ( ( in @ Xx @ ( binintersect @ X @ Y ) ) =>
% 3.74/1.49 ( in @ Xx @ ( binunion @ X @ Z ) ) ) ) ) ) ) ) ) ))).
% 3.74/1.49 thf('5', plain,
% 3.74/1.49 (( inIntersectImpInUnion ) =
% 3.74/1.49 ( ![X4:$i,X6:$i]:
% 3.74/1.49 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 3.74/1.49 ( ![X8:$i]:
% 3.74/1.49 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 3.74/1.49 ( ![X10:$i]:
% 3.74/1.49 ( ( in @ X10 @ ( powerset @ X4 ) ) =>
% 3.74/1.49 ( ![X12:$i]:
% 3.74/1.49 ( ( in @ X12 @ X4 ) =>
% 3.74/1.49 ( ( in @ X12 @ ( binintersect @ X6 @ X8 ) ) =>
% 3.74/1.49 ( in @ X12 @ ( binunion @ X6 @ X10 ) ) ) ) ) ) ) ) ) ) )),
% 3.74/1.49 define([status(thm)])).
% 3.74/1.49 thf(binunionTIRcontra, axiom, binunionTIRcontra =
% 3.74/1.49 (![A:$i,X:$i]:
% 3.74/1.49 ( ( in @ X @ ( powerset @ A ) ) =>
% 3.74/1.49 ( ![Y:$i]:
% 3.74/1.49 ( ( in @ Y @ ( powerset @ A ) ) =>
% 3.74/1.49 ( ![Xx:$i]:
% 3.74/1.49 ( ( in @ Xx @ A ) =>
% 3.74/1.49 ( ( ~( in @ Xx @ ( binunion @ X @ Y ) ) ) =>
% 3.74/1.49 ( ~( in @ Xx @ Y ) ) ) ) ) ) ) ))).
% 3.74/1.49 thf('6', plain,
% 3.74/1.49 (( binunionTIRcontra ) =
% 3.74/1.49 ( ![X4:$i,X6:$i]:
% 3.74/1.49 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 3.74/1.49 ( ![X8:$i]:
% 3.74/1.49 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 3.74/1.49 ( ![X10:$i]:
% 3.74/1.49 ( ( in @ X10 @ X4 ) =>
% 3.74/1.49 ( ( ~( in @ X10 @ ( binunion @ X6 @ X8 ) ) ) =>
% 3.74/1.49 ( ~( in @ X10 @ X8 ) ) ) ) ) ) ) ) )),
% 3.74/1.49 define([status(thm)])).
% 3.74/1.49 thf(binunionTILcontra, axiom, binunionTILcontra =
% 3.74/1.49 (![A:$i,X:$i]:
% 3.74/1.49 ( ( in @ X @ ( powerset @ A ) ) =>
% 3.74/1.49 ( ![Y:$i]:
% 3.74/1.49 ( ( in @ Y @ ( powerset @ A ) ) =>
% 3.74/1.49 ( ![Xx:$i]:
% 3.74/1.49 ( ( in @ Xx @ A ) =>
% 3.74/1.49 ( ( ~( in @ Xx @ ( binunion @ X @ Y ) ) ) =>
% 3.74/1.49 ( ~( in @ Xx @ X ) ) ) ) ) ) ) ))).
% 3.74/1.49 thf('7', plain,
% 3.74/1.49 (( binunionTILcontra ) =
% 3.74/1.49 ( ![X4:$i,X6:$i]:
% 3.74/1.49 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 3.74/1.49 ( ![X8:$i]:
% 3.74/1.49 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 3.74/1.49 ( ![X10:$i]:
% 3.74/1.49 ( ( in @ X10 @ X4 ) =>
% 3.74/1.49 ( ( ~( in @ X10 @ ( binunion @ X6 @ X8 ) ) ) =>
% 3.74/1.49 ( ~( in @ X10 @ X6 ) ) ) ) ) ) ) ) )),
% 3.74/1.49 define([status(thm)])).
% 3.74/1.49 thf(powersetTE1, axiom, powersetTE1 =
% 3.74/1.49 (![A:$i,X:$i]:
% 3.74/1.49 ( ( in @ X @ ( powerset @ A ) ) =>
% 3.74/1.49 ( ![Y:$i]:
% 3.74/1.49 ( ( in @ Y @ ( powerset @ A ) ) =>
% 3.74/1.49 ( ![Xx:$i]:
% 3.74/1.49 ( ( in @ Xx @ A ) =>
% 3.74/1.49 ( ( in @ X @ ( powerset @ Y ) ) =>
% 3.74/1.49 ( ( in @ Xx @ X ) => ( in @ Xx @ Y ) ) ) ) ) ) ) ))).
% 3.74/1.49 thf('8', plain,
% 3.74/1.49 (( powersetTE1 ) =
% 3.74/1.49 ( ![X4:$i,X6:$i]:
% 3.74/1.49 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 3.74/1.49 ( ![X8:$i]:
% 3.74/1.49 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 3.74/1.49 ( ![X10:$i]:
% 3.74/1.49 ( ( in @ X10 @ X4 ) =>
% 3.74/1.49 ( ( in @ X6 @ ( powerset @ X8 ) ) =>
% 3.74/1.49 ( ( in @ X10 @ X6 ) => ( in @ X10 @ X8 ) ) ) ) ) ) ) ) )),
% 3.74/1.49 define([status(thm)])).
% 3.74/1.49 thf(powersetTI1, axiom, powersetTI1 =
% 3.74/1.49 (![A:$i,X:$i]:
% 3.74/1.49 ( ( in @ X @ ( powerset @ A ) ) =>
% 3.74/1.49 ( ![Y:$i]:
% 3.74/1.49 ( ( in @ Y @ ( powerset @ A ) ) =>
% 3.74/1.49 ( ( ![Xx:$i]:
% 3.74/1.49 ( ( in @ Xx @ A ) => ( ( in @ Xx @ X ) => ( in @ Xx @ Y ) ) ) ) =>
% 3.74/1.49 ( in @ X @ ( powerset @ Y ) ) ) ) ) ))).
% 3.74/1.49 thf('9', plain,
% 3.74/1.49 (( powersetTI1 ) =
% 3.74/1.49 ( ![X4:$i,X6:$i]:
% 3.74/1.49 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 3.74/1.49 ( ![X8:$i]:
% 3.74/1.49 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 3.74/1.49 ( ( ![X10:$i]:
% 3.74/1.49 ( ( in @ X10 @ X4 ) =>
% 3.74/1.49 ( ( in @ X10 @ X6 ) => ( in @ X10 @ X8 ) ) ) ) =>
% 3.74/1.49 ( in @ X6 @ ( powerset @ X8 ) ) ) ) ) ) )),
% 3.74/1.49 define([status(thm)])).
% 3.74/1.49 thf(setextT, axiom, setextT =
% 3.74/1.49 (![A:$i,X:$i]:
% 3.74/1.49 ( ( in @ X @ ( powerset @ A ) ) =>
% 3.74/1.49 ( ![Y:$i]:
% 3.74/1.49 ( ( in @ Y @ ( powerset @ A ) ) =>
% 3.74/1.49 ( ( ![Xx:$i]:
% 3.74/1.49 ( ( in @ Xx @ A ) => ( ( in @ Xx @ X ) => ( in @ Xx @ Y ) ) ) ) =>
% 3.74/1.49 ( ( ![Xx:$i]:
% 3.74/1.49 ( ( in @ Xx @ A ) => ( ( in @ Xx @ Y ) => ( in @ Xx @ X ) ) ) ) =>
% 3.74/1.49 ( ( X ) = ( Y ) ) ) ) ) ) ))).
% 3.74/1.49 thf('10', plain,
% 3.74/1.49 (( setextT ) =
% 3.74/1.49 ( ![X4:$i,X6:$i]:
% 3.74/1.49 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 3.74/1.49 ( ![X8:$i]:
% 3.74/1.49 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 3.74/1.49 ( ( ![X10:$i]:
% 3.74/1.49 ( ( in @ X10 @ X4 ) =>
% 3.74/1.49 ( ( in @ X10 @ X6 ) => ( in @ X10 @ X8 ) ) ) ) =>
% 3.74/1.49 ( ( ![X12:$i]:
% 3.74/1.49 ( ( in @ X12 @ X4 ) =>
% 3.74/1.49 ( ( in @ X12 @ X8 ) => ( in @ X12 @ X6 ) ) ) ) =>
% 3.74/1.49 ( ( X6 ) = ( X8 ) ) ) ) ) ) ) )),
% 3.74/1.49 define([status(thm)])).
% 3.74/1.49 thf(powersetT_lem, axiom, powersetT_lem =
% 3.74/1.49 (![A:$i,X:$i]:
% 3.74/1.49 ( ( in @ X @ ( powerset @ A ) ) =>
% 3.74/1.49 ( in @ ( powerset @ X ) @ ( powerset @ ( powerset @ A ) ) ) ))).
% 3.74/1.49 thf('11', plain,
% 3.74/1.49 (( powersetT_lem ) =
% 3.74/1.49 ( ![X4:$i,X6:$i]:
% 3.74/1.49 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 3.74/1.49 ( in @ ( powerset @ X6 ) @ ( powerset @ ( powerset @ X4 ) ) ) ) )),
% 3.74/1.49 define([status(thm)])).
% 3.74/1.49 thf(binunionT_lem, axiom, binunionT_lem =
% 3.74/1.49 (![A:$i,X:$i]:
% 3.74/1.49 ( ( in @ X @ ( powerset @ A ) ) =>
% 3.74/1.49 ( ![Y:$i]:
% 3.74/1.49 ( ( in @ Y @ ( powerset @ A ) ) =>
% 3.74/1.49 ( in @ ( binunion @ X @ Y ) @ ( powerset @ A ) ) ) ) ))).
% 3.74/1.49 thf('12', plain,
% 3.74/1.49 (( binunionT_lem ) =
% 3.74/1.49 ( ![X4:$i,X6:$i]:
% 3.74/1.49 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 3.74/1.49 ( ![X8:$i]:
% 3.74/1.49 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 3.74/1.49 ( in @ ( binunion @ X6 @ X8 ) @ ( powerset @ X4 ) ) ) ) ) )),
% 3.74/1.49 define([status(thm)])).
% 3.74/1.49 thf(ubforcartprodlem3, axiom, ubforcartprodlem3 =
% 3.74/1.49 (![A:$i,B:$i,Xx:$i]:
% 3.74/1.49 ( ( in @ Xx @ A ) =>
% 3.74/1.49 ( ![Xy:$i]:
% 3.74/1.49 ( ( in @ Xy @ B ) =>
% 3.74/1.49 ( in @
% 3.74/1.49 ( kpair @ Xx @ Xy ) @
% 3.74/1.49 ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ))).
% 3.74/1.49 thf('13', plain,
% 3.74/1.49 (( ubforcartprodlem3 ) =
% 3.74/1.49 ( ![X4:$i,X6:$i,X8:$i]:
% 3.74/1.49 ( ( in @ X8 @ X4 ) =>
% 3.74/1.49 ( ![X10:$i]:
% 3.74/1.49 ( ( in @ X10 @ X6 ) =>
% 3.74/1.49 ( in @
% 3.74/1.49 ( kpair @ X8 @ X10 ) @
% 3.74/1.49 ( powerset @ ( powerset @ ( binunion @ X4 @ X6 ) ) ) ) ) ) ) )),
% 3.74/1.49 define([status(thm)])).
% 3.74/1.49 thf(ubforcartprodlem2, axiom, ubforcartprodlem2 =
% 3.74/1.49 (![A:$i,B:$i,Xx:$i]:
% 3.74/1.49 ( ( in @ Xx @ A ) =>
% 3.74/1.49 ( ![Xy:$i]:
% 3.74/1.49 ( ( in @ Xy @ B ) =>
% 3.74/1.49 ( in @
% 3.74/1.49 ( setadjoin @
% 3.74/1.49 ( setadjoin @ Xx @ emptyset ) @
% 3.74/1.49 ( setadjoin @
% 3.74/1.49 ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @
% 3.74/1.49 ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ))).
% 3.74/1.49 thf('14', plain,
% 3.74/1.49 (( ubforcartprodlem2 ) =
% 3.74/1.49 ( ![X4:$i,X6:$i,X8:$i]:
% 3.74/1.49 ( ( in @ X8 @ X4 ) =>
% 3.74/1.49 ( ![X10:$i]:
% 3.74/1.49 ( ( in @ X10 @ X6 ) =>
% 3.74/1.49 ( in @
% 3.74/1.49 ( setadjoin @
% 3.74/1.49 ( setadjoin @ X8 @ emptyset ) @
% 3.74/1.49 ( setadjoin @
% 3.74/1.49 ( setadjoin @ X8 @ ( setadjoin @ X10 @ emptyset ) ) @
% 3.74/1.49 emptyset ) ) @
% 3.74/1.49 ( powerset @ ( powerset @ ( binunion @ X4 @ X6 ) ) ) ) ) ) ) )),
% 3.74/1.49 define([status(thm)])).
% 3.74/1.49 thf(ubforcartprodlem1, axiom, ubforcartprodlem1 =
% 3.74/1.49 (![A:$i,B:$i,Xx:$i]:
% 3.74/1.49 ( ( in @ Xx @ A ) =>
% 3.74/1.49 ( ![Xy:$i]:
% 3.74/1.49 ( ( in @ Xy @ B ) =>
% 3.74/1.49 ( subset @
% 3.74/1.49 ( setadjoin @
% 3.74/1.49 ( setadjoin @ Xx @ emptyset ) @
% 3.74/1.49 ( setadjoin @
% 3.74/1.49 ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @
% 3.74/1.49 ( powerset @ ( binunion @ A @ B ) ) ) ) ) ))).
% 3.74/1.49 thf('15', plain,
% 3.74/1.49 (( ubforcartprodlem1 ) =
% 3.74/1.49 ( ![X4:$i,X6:$i,X8:$i]:
% 3.74/1.49 ( ( in @ X8 @ X4 ) =>
% 3.74/1.49 ( ![X10:$i]:
% 3.74/1.49 ( ( in @ X10 @ X6 ) =>
% 3.74/1.49 ( subset @
% 3.74/1.49 ( setadjoin @
% 3.74/1.49 ( setadjoin @ X8 @ emptyset ) @
% 3.74/1.49 ( setadjoin @
% 3.74/1.49 ( setadjoin @ X8 @ ( setadjoin @ X10 @ emptyset ) ) @
% 3.74/1.49 emptyset ) ) @
% 3.74/1.49 ( powerset @ ( binunion @ X4 @ X6 ) ) ) ) ) ) )),
% 3.74/1.49 define([status(thm)])).
% 3.74/1.49 thf(upairinpowunion, axiom, upairinpowunion =
% 3.74/1.49 (![A:$i,B:$i,Xx:$i]:
% 3.74/1.49 ( ( in @ Xx @ A ) =>
% 3.74/1.49 ( ![Xy:$i]:
% 3.74/1.49 ( ( in @ Xy @ B ) =>
% 3.74/1.49 ( in @
% 3.74/1.49 ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @
% 3.74/1.49 ( powerset @ ( binunion @ A @ B ) ) ) ) ) ))).
% 3.74/1.49 thf('16', plain,
% 3.74/1.49 (( upairinpowunion ) =
% 3.74/1.49 ( ![X4:$i,X6:$i,X8:$i]:
% 3.74/1.49 ( ( in @ X8 @ X4 ) =>
% 3.74/1.49 ( ![X10:$i]:
% 3.74/1.49 ( ( in @ X10 @ X6 ) =>
% 3.74/1.49 ( in @
% 3.74/1.49 ( setadjoin @ X8 @ ( setadjoin @ X10 @ emptyset ) ) @
% 3.74/1.49 ( powerset @ ( binunion @ X4 @ X6 ) ) ) ) ) ) )),
% 3.74/1.49 define([status(thm)])).
% 3.74/1.49 thf(upairsubunion, axiom, upairsubunion =
% 3.74/1.49 (![A:$i,B:$i,Xx:$i]:
% 3.74/1.49 ( ( in @ Xx @ A ) =>
% 3.74/1.49 ( ![Xy:$i]:
% 3.74/1.49 ( ( in @ Xy @ B ) =>
% 3.74/1.49 ( subset @
% 3.74/1.49 ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @
% 3.74/1.49 ( binunion @ A @ B ) ) ) ) ))).
% 3.74/1.49 thf('17', plain,
% 3.74/1.49 (( upairsubunion ) =
% 3.74/1.49 ( ![X4:$i,X6:$i,X8:$i]:
% 3.74/1.49 ( ( in @ X8 @ X4 ) =>
% 3.74/1.49 ( ![X10:$i]:
% 3.74/1.49 ( ( in @ X10 @ X6 ) =>
% 3.74/1.49 ( subset @
% 3.74/1.49 ( setadjoin @ X8 @ ( setadjoin @ X10 @ emptyset ) ) @
% 3.74/1.49 ( binunion @ X4 @ X6 ) ) ) ) ) )),
% 3.74/1.49 define([status(thm)])).
% 3.74/1.49 thf(singletoninpowunion, axiom, singletoninpowunion =
% 3.74/1.49 (![A:$i,B:$i,Xx:$i]:
% 3.74/1.49 ( ( in @ Xx @ A ) =>
% 3.74/1.49 ( in @
% 3.74/1.49 ( setadjoin @ Xx @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) ))).
% 3.74/1.49 thf('18', plain,
% 3.74/1.49 (( singletoninpowunion ) =
% 3.74/1.49 ( ![X4:$i,X6:$i,X8:$i]:
% 3.74/1.49 ( ( in @ X8 @ X4 ) =>
% 3.74/1.49 ( in @
% 3.74/1.49 ( setadjoin @ X8 @ emptyset ) @
% 3.74/1.49 ( powerset @ ( binunion @ X4 @ X6 ) ) ) ) )),
% 3.74/1.49 define([status(thm)])).
% 3.74/1.49 thf(bs114d, axiom, bs114d =
% 3.74/1.49 (![A:$i,B:$i,C:$i]:
% 3.74/1.49 ( ( binintersect @ A @ ( binunion @ B @ C ) ) =
% 3.74/1.49 ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) ))).
% 3.74/1.49 thf('19', plain,
% 3.74/1.49 (( bs114d ) =
% 3.74/1.49 ( ![X4:$i,X6:$i,X8:$i]:
% 3.74/1.49 ( ( binintersect @ X4 @ ( binunion @ X6 @ X8 ) ) =
% 3.74/1.49 ( binunion @ ( binintersect @ X4 @ X6 ) @ ( binintersect @ X4 @ X8 ) ) ) )),
% 3.74/1.49 define([status(thm)])).
% 3.74/1.49 thf(binunionRsub, axiom, binunionRsub =
% 3.74/1.49 (![A:$i,B:$i]: ( subset @ B @ ( binunion @ A @ B ) ))).
% 3.74/1.49 thf('20', plain,
% 3.74/1.49 (( binunionRsub ) =
% 3.74/1.49 ( ![X4:$i,X6:$i]: ( subset @ X6 @ ( binunion @ X4 @ X6 ) ) )),
% 3.74/1.49 define([status(thm)])).
% 3.74/1.49 thf(binunionLsub, axiom, binunionLsub =
% 3.74/1.49 (![A:$i,B:$i]: ( subset @ A @ ( binunion @ A @ B ) ))).
% 3.74/1.49 thf('21', plain,
% 3.74/1.49 (( binunionLsub ) =
% 3.74/1.49 ( ![X4:$i,X6:$i]: ( subset @ X4 @ ( binunion @ X4 @ X6 ) ) )),
% 3.74/1.49 define([status(thm)])).
% 3.74/1.49 thf(binunionE, axiom, binunionE =
% 3.74/1.49 (![A:$i,B:$i,Xx:$i]:
% 3.74/1.49 ( ( in @ Xx @ ( binunion @ A @ B ) ) =>
% 3.74/1.49 ( ( in @ Xx @ A ) | ( in @ Xx @ B ) ) ))).
% 3.74/1.49 thf('22', plain,
% 3.74/1.49 (( binunionE ) =
% 3.74/1.49 ( ![X4:$i,X6:$i,X8:$i]:
% 3.74/1.49 ( ( in @ X8 @ ( binunion @ X4 @ X6 ) ) =>
% 3.74/1.49 ( ( in @ X8 @ X4 ) | ( in @ X8 @ X6 ) ) ) )),
% 3.74/1.49 define([status(thm)])).
% 3.74/1.49 thf(binunionEcases, axiom, binunionEcases =
% 3.74/1.49 (![A:$i,B:$i,Xx:$i,Xphi:$o]:
% 3.74/1.49 ( ( in @ Xx @ ( binunion @ A @ B ) ) =>
% 3.74/1.49 ( ( ( in @ Xx @ A ) => ( Xphi ) ) =>
% 3.74/1.49 ( ( ( in @ Xx @ B ) => ( Xphi ) ) => ( Xphi ) ) ) ))).
% 3.74/1.49 thf('23', plain,
% 3.74/1.49 (( binunionEcases ) =
% 3.74/1.49 ( ![X4:$i,X6:$i,X8:$i,X10:$o]:
% 3.74/1.49 ( ( in @ X8 @ ( binunion @ X4 @ X6 ) ) =>
% 3.74/1.49 ( ( ( in @ X8 @ X4 ) => ( X10 ) ) =>
% 3.74/1.49 ( ( ( in @ X8 @ X6 ) => ( X10 ) ) => ( X10 ) ) ) ) )),
% 3.74/1.49 define([status(thm)])).
% 3.74/1.49 thf(binunionIR, axiom, binunionIR =
% 3.74/1.49 (![A:$i,B:$i,Xx:$i]:
% 3.74/1.49 ( ( in @ Xx @ B ) => ( in @ Xx @ ( binunion @ A @ B ) ) ))).
% 3.74/1.49 thf('24', plain,
% 3.74/1.49 (( binunionIR ) =
% 3.74/1.49 ( ![X4:$i,X6:$i,X8:$i]:
% 3.74/1.49 ( ( in @ X8 @ X6 ) => ( in @ X8 @ ( binunion @ X4 @ X6 ) ) ) )),
% 3.74/1.49 define([status(thm)])).
% 3.74/1.49 thf(binunionIL, axiom, binunionIL =
% 3.74/1.49 (![A:$i,B:$i,Xx:$i]:
% 3.74/1.49 ( ( in @ Xx @ A ) => ( in @ Xx @ ( binunion @ A @ B ) ) ))).
% 3.74/1.49 thf('25', plain,
% 3.74/1.49 (( binunionIL ) =
% 3.74/1.49 ( ![X4:$i,X6:$i,X8:$i]:
% 3.74/1.49 ( ( in @ X8 @ X4 ) => ( in @ X8 @ ( binunion @ X4 @ X6 ) ) ) )),
% 3.74/1.49 define([status(thm)])).
% 3.74/1.49 thf(inPowerset, axiom, inPowerset = (![A:$i]: ( in @ A @ ( powerset @ A ) ))).
% 3.74/1.49 thf('26', plain,
% 3.74/1.49 (( inPowerset ) = ( ![X4:$i]: ( in @ X4 @ ( powerset @ X4 ) ) )),
% 3.74/1.49 define([status(thm)])).
% 3.74/1.49 thf(powerset__Cong, axiom, powerset__Cong =
% 3.74/1.49 (![A:$i,B:$i]:
% 3.74/1.49 ( ( ( A ) = ( B ) ) => ( ( powerset @ A ) = ( powerset @ B ) ) ))).
% 3.74/1.49 thf('27', plain,
% 3.74/1.49 (( powerset__Cong ) =
% 3.74/1.49 ( ![X4:$i,X6:$i]:
% 3.74/1.49 ( ( ( X4 ) = ( X6 ) ) => ( ( powerset @ X4 ) = ( powerset @ X6 ) ) ) )),
% 3.74/1.49 define([status(thm)])).
% 3.74/1.49 thf(powersetE, axiom, powersetE =
% 3.74/1.49 (![A:$i,B:$i,Xx:$i]:
% 3.74/1.49 ( ( in @ B @ ( powerset @ A ) ) => ( ( in @ Xx @ B ) => ( in @ Xx @ A ) ) ))).
% 3.74/1.49 thf('28', plain,
% 3.74/1.49 (( powersetE ) =
% 3.74/1.49 ( ![X4:$i,X6:$i,X8:$i]:
% 3.74/1.49 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 3.74/1.49 ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ) )),
% 3.74/1.49 define([status(thm)])).
% 3.74/1.49 thf(emptyInPowerset, axiom, emptyInPowerset =
% 3.74/1.49 (![A:$i]: ( in @ emptyset @ ( powerset @ A ) ))).
% 3.74/1.49 thf('29', plain,
% 3.74/1.49 (( emptyInPowerset ) =
% 3.74/1.49 ( ![X4:$i]: ( in @ emptyset @ ( powerset @ X4 ) ) )),
% 3.74/1.49 define([status(thm)])).
% 3.74/1.49 thf(emptyinPowerset, axiom, emptyinPowerset =
% 3.74/1.49 (![A:$i]: ( in @ emptyset @ ( powerset @ A ) ))).
% 3.74/1.49 thf('30', plain,
% 3.74/1.49 (( emptyinPowerset ) =
% 3.74/1.49 ( ![X4:$i]: ( in @ emptyset @ ( powerset @ X4 ) ) )),
% 3.74/1.49 define([status(thm)])).
% 3.74/1.49 thf(powersetI, axiom, powersetI =
% 3.74/1.49 (![A:$i,B:$i]:
% 3.74/1.49 ( ( ![Xx:$i]: ( ( in @ Xx @ B ) => ( in @ Xx @ A ) ) ) =>
% 3.74/1.49 ( in @ B @ ( powerset @ A ) ) ))).
% 3.74/1.49 thf('31', plain,
% 3.74/1.49 (( powersetI ) =
% 3.74/1.49 ( ![X4:$i,X6:$i]:
% 3.74/1.49 ( ( ![X8:$i]: ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ) =>
% 3.74/1.49 ( in @ X6 @ ( powerset @ X4 ) ) ) )),
% 3.74/1.49 define([status(thm)])).
% 3.74/1.49 thf(powersetAx, axiom, powersetAx =
% 3.74/1.49 (![A:$i,B:$i]:
% 3.74/1.49 ( ( in @ B @ ( powerset @ A ) ) <=>
% 3.74/1.49 ( ![Xx:$i]: ( ( in @ Xx @ B ) => ( in @ Xx @ A ) ) ) ))).
% 3.74/1.49 thf('32', plain,
% 3.74/1.49 (( powersetAx ) =
% 3.74/1.49 ( ![X4:$i,X6:$i]:
% 3.74/1.49 ( ( in @ X6 @ ( powerset @ X4 ) ) <=>
% 3.74/1.49 ( ![X8:$i]: ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ) ) )),
% 3.74/1.49 define([status(thm)])).
% 3.74/1.49 thf(binunionTE, conjecture,
% 3.74/1.49 (( setextAx ) =>
% 3.74/1.49 ( ( emptysetAx ) =>
% 3.74/1.49 ( ( setadjoinAx ) =>
% 3.74/1.49 ( ( powersetAx ) =>
% 3.74/1.49 ( ( setunionAx ) =>
% 3.74/1.49 ( ( omega0Ax ) =>
% 3.74/1.49 ( ( omegaSAx ) =>
% 3.74/1.49 ( ( omegaIndAx ) =>
% 3.74/1.49 ( ( replAx ) =>
% 3.74/1.49 ( ( foundationAx ) =>
% 3.74/1.49 ( ( wellorderingAx ) =>
% 3.74/1.49 ( ( descrp ) =>
% 3.74/1.49 ( ( dsetconstrI ) =>
% 3.74/1.49 ( ( dsetconstrEL ) =>
% 3.74/1.49 ( ( dsetconstrER ) =>
% 3.74/1.49 ( ( exuE1 ) =>
% 3.74/1.49 ( ( prop2setE ) =>
% 3.74/1.49 ( ( emptysetE ) =>
% 3.74/1.49 ( ( emptysetimpfalse ) =>
% 3.74/1.49 ( ( notinemptyset ) =>
% 3.74/1.49 ( ( exuE3e ) =>
% 3.74/1.49 ( ( setext ) =>
% 3.74/1.49 ( ( emptyI ) =>
% 3.74/1.49 ( ( noeltsimpempty ) =>
% 3.74/1.49 ( ( setbeta ) =>
% 3.74/1.49 ( ( nonemptyE1 ) =>
% 3.74/1.49 ( ( nonemptyI ) =>
% 3.74/1.49 ( ( nonemptyI1 ) =>
% 3.74/1.49 ( ( setadjoinIL ) =>
% 3.74/1.49 ( ( emptyinunitempty ) =>
% 3.74/1.49 ( ( setadjoinIR ) =>
% 3.74/1.49 ( ( setadjoinE ) =>
% 3.74/1.49 ( (
% 3.74/1.49 setadjoinOr ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 setoftrueEq ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 powersetI ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 emptyinPowerset ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 emptyInPowerset ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 powersetE ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 setunionI ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 setunionE ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 subPowSU ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 exuE2 ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 nonemptyImpWitness ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 uniqinunit ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 notinsingleton ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 eqinunit ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 singletonsswitch ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 upairsetE ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 upairsetIL ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 upairsetIR ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 emptyE1 ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 vacuousDall ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 quantDeMorgan1 ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 quantDeMorgan2 ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 quantDeMorgan3 ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 quantDeMorgan4 ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 prop2setI ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 prop2set2propI ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 notdexE ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 notdallE ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 exuI1 ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 exuI3 ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 exuI2 ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 inCongP ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 in__Cong ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 exuE3u ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 exu__Cong ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 emptyset__Cong ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 setadjoin__Cong ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 powerset__Cong ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 setunion__Cong ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 omega__Cong ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 exuEu ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 descr__Cong ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 dsetconstr__Cong ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 subsetI1 ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 eqimpsubset2 ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 eqimpsubset1 ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 subsetI2 ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 emptysetsubset ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 subsetE ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 subsetE2 ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 notsubsetI ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 notequalI1 ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 notequalI2 ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 subsetRefl ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 subsetTrans ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 setadjoinSub ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 setadjoinSub2 ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 subset2powerset ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 setextsub ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 subsetemptysetimpeq ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 powersetI1 ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 powersetE1 ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 inPowerset ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 powersetsubset ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 sepInPowerset ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 sepSubset ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 binunionIL ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 upairset2IR ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 binunionIR ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 binunionEcases ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 binunionE ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 binunionLsub ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 binunionRsub ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 binintersectI ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 binintersectSubset5 ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 binintersectEL ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 binintersectLsub ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 binintersectSubset2 ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 binintersectSubset3 ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 binintersectER ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 disjointsetsI1 ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 binintersectRsub ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 binintersectSubset4 ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 binintersectSubset1 ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 bs114d ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 setminusI ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 setminusEL ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 setminusER ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 setminusSubset2 ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 setminusERneg ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 setminusELneg ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 setminusILneg ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 setminusIRneg ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 setminusLsub ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 setminusSubset1 ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 symdiffE ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 symdiffI1 ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 symdiffI2 ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 symdiffIneg1 ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 symdiffIneg2 ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 secondinupair ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 setukpairIL ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 setukpairIR ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 kpairiskpair ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 kpairp ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 singletonsubset ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 singletoninpowerset ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 singletoninpowunion ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 upairset2E ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 upairsubunion ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 upairinpowunion ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 ubforcartprodlem1 ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 ubforcartprodlem2 ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 ubforcartprodlem3 ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 cartprodpairin ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 cartprodmempair1 ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 cartprodmempair ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 setunionE2 ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 setunionsingleton1 ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 setunionsingleton2 ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 setunionsingleton ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 singletonprop ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 ex1E1 ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 ex1I ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 ex1I2 ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 singletonsuniq ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 setukpairinjL1 ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 kfstsingleton ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 theprop ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 kfstpairEq ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 cartprodfstin ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 setukpairinjL2 ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 setukpairinjL ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 setukpairinjR11 ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 setukpairinjR12 ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 setukpairinjR1 ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 upairequniteq ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 setukpairinjR2 ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 setukpairinjR ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 ksndsingleton ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 ksndpairEq ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 kpairsurjEq ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 cartprodsndin ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 cartprodpairmemEL ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 cartprodpairmemER ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 cartprodmempaircEq ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 cartprodfstpairEq ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 cartprodsndpairEq ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 cartprodpairsurjEq ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 dpsetconstrI ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 dpsetconstrSub ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 setOfPairsIsBReln ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 dpsetconstrERa ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 dpsetconstrEL1 ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 dpsetconstrEL2 ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 dpsetconstrER ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 funcImageSingleton ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 apProp ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 app ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 infuncsetfunc ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 ap2p ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 funcinfuncset ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 lamProp ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 lamp ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 lam2p ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 brelnall1 ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 brelnall2 ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 ex1E2 ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 funcGraphProp1 ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 funcGraphProp3 ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 funcGraphProp2 ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 funcextLem ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 funcGraphProp4 ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 subbreln ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 eqbreln ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 funcext ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 funcext2 ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 ap2apEq1 ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 ap2apEq2 ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 beta1 ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 eta1 ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 lam2lamEq ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 beta2 ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 eta2 ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 iffalseProp1 ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 iffalseProp2 ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 iftrueProp1 ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 iftrueProp2 ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 ifSingleton ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 ifp ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 theeq ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 iftrue ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 iffalse ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 iftrueorfalse ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 binintersectT_lem ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 binunionT_lem ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 powersetT_lem ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 setminusT_lem ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 complementT_lem ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 setextT ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 subsetTI ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 powersetTI1 ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 powersetTE1 ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 complementTI1 ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 complementTE1 ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 binintersectTELcontra ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 binintersectTERcontra ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 contrasubsetT ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 contrasubsetT1 ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 contrasubsetT2 ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 contrasubsetT3 ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 doubleComplementI1 ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 doubleComplementE1 ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 doubleComplementSub1 ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 doubleComplementSub2 ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 doubleComplementEq ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 complementTnotintersectT ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 complementImpComplementIntersect ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 complementSubsetComplementIntersect ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 complementInPowersetComplementIntersect ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 contraSubsetComplement ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 complementTcontraSubset ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 binunionTILcontra ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 binunionTIRcontra ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 inIntersectImpInUnion ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 inIntersectImpInUnion2 ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 inIntersectImpInIntersectUnions ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 intersectInPowersetIntersectUnions ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 inComplementUnionImpNotIn1 ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 inComplementUnionImpInComplement1 ) =>
% 3.74/1.49 (
% 3.74/1.49 ![
% 3.74/1.49 A:$i,X:$i]:
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 in @
% 3.74/1.49 X @
% 3.74/1.49 (
% 3.74/1.49 powerset @
% 3.74/1.49 A ) ) =>
% 3.74/1.49 (
% 3.74/1.49 ![
% 3.74/1.49 Y:$i]:
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 in @
% 3.74/1.49 Y @
% 3.74/1.49 (
% 3.74/1.49 powerset @
% 3.74/1.49 A ) ) =>
% 3.74/1.49 (
% 3.74/1.49 ![
% 3.74/1.49 Xphi:$o,
% 3.74/1.49 Xx:$i]:
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 in @
% 3.74/1.49 Xx @ A ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 in @
% 3.74/1.49 Xx @
% 3.74/1.49 (
% 3.74/1.49 binunion @
% 3.74/1.49 X @ Y ) ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 in @
% 3.74/1.49 Xx @ X ) =>
% 3.74/1.49 (
% 3.74/1.49 Xphi ) ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 in @
% 3.74/1.49 Xx @ Y ) =>
% 3.74/1.49 (
% 3.74/1.49 Xphi ) ) =>
% 3.74/1.49 (
% 3.74/1.49 Xphi ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 3.74/1.49 thf(zf_stmt_0, conjecture,
% 3.74/1.49 (( setextAx ) =>
% 3.74/1.49 ( ( emptysetAx ) =>
% 3.74/1.49 ( ( setadjoinAx ) =>
% 3.74/1.49 ( ( ![X4:$i,X6:$i]:
% 3.74/1.49 ( ( in @ X6 @ ( powerset @ X4 ) ) <=>
% 3.74/1.49 ( ![X8:$i]: ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ) ) ) =>
% 3.74/1.49 ( ( setunionAx ) =>
% 3.74/1.49 ( ( omega0Ax ) =>
% 3.74/1.49 ( ( omegaSAx ) =>
% 3.74/1.49 ( ( omegaIndAx ) =>
% 3.74/1.49 ( ( replAx ) =>
% 3.74/1.49 ( ( foundationAx ) =>
% 3.74/1.49 ( ( wellorderingAx ) =>
% 3.74/1.49 ( ( descrp ) =>
% 3.74/1.49 ( ( dsetconstrI ) =>
% 3.74/1.49 ( ( dsetconstrEL ) =>
% 3.74/1.49 ( ( dsetconstrER ) =>
% 3.74/1.49 ( ( exuE1 ) =>
% 3.74/1.49 ( ( prop2setE ) =>
% 3.74/1.49 ( ( emptysetE ) =>
% 3.74/1.49 ( ( emptysetimpfalse ) =>
% 3.74/1.49 ( ( notinemptyset ) =>
% 3.74/1.49 ( ( exuE3e ) =>
% 3.74/1.49 ( ( setext ) =>
% 3.74/1.49 ( ( emptyI ) =>
% 3.74/1.49 ( ( noeltsimpempty ) =>
% 3.74/1.49 ( ( setbeta ) =>
% 3.74/1.49 ( ( nonemptyE1 ) =>
% 3.74/1.49 ( ( nonemptyI ) =>
% 3.74/1.49 ( ( nonemptyI1 ) =>
% 3.74/1.49 ( ( setadjoinIL ) =>
% 3.74/1.49 ( ( emptyinunitempty ) =>
% 3.74/1.49 ( ( setadjoinIR ) =>
% 3.74/1.49 ( ( setadjoinE ) =>
% 3.74/1.49 ( (
% 3.74/1.49 setadjoinOr ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 setoftrueEq ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 ![
% 3.74/1.49 X10:$i,
% 3.74/1.49 X12:$i]:
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 ![
% 3.74/1.49 X14:$i]:
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 in @
% 3.74/1.49 X14 @ X12 ) =>
% 3.74/1.49 (
% 3.74/1.49 in @
% 3.74/1.49 X14 @ X10 ) ) ) =>
% 3.74/1.49 (
% 3.74/1.49 in @
% 3.74/1.49 X12 @
% 3.74/1.49 (
% 3.74/1.49 powerset @
% 3.74/1.49 X10 ) ) ) ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 ![
% 3.74/1.49 X16:$i]:
% 3.74/1.49 (
% 3.74/1.49 in @
% 3.74/1.49 emptyset @
% 3.74/1.49 (
% 3.74/1.49 powerset @
% 3.74/1.49 X16 ) ) ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 ![
% 3.74/1.49 X18:$i]:
% 3.74/1.49 (
% 3.74/1.49 in @
% 3.74/1.49 emptyset @
% 3.74/1.49 (
% 3.74/1.49 powerset @
% 3.74/1.49 X18 ) ) ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 ![
% 3.74/1.49 X20:$i,
% 3.74/1.49 X22:$i,
% 3.74/1.49 X24:$i]:
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 in @
% 3.74/1.49 X22 @
% 3.74/1.49 (
% 3.74/1.49 powerset @
% 3.74/1.49 X20 ) ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 in @
% 3.74/1.49 X24 @ X22 ) =>
% 3.74/1.49 (
% 3.74/1.49 in @
% 3.74/1.49 X24 @ X20 ) ) ) ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 setunionI ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 setunionE ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 subPowSU ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 exuE2 ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 nonemptyImpWitness ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 uniqinunit ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 notinsingleton ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 eqinunit ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 singletonsswitch ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 upairsetE ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 upairsetIL ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 upairsetIR ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 emptyE1 ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 vacuousDall ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 quantDeMorgan1 ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 quantDeMorgan2 ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 quantDeMorgan3 ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 quantDeMorgan4 ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 prop2setI ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 prop2set2propI ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 notdexE ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 notdallE ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 exuI1 ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 exuI3 ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 exuI2 ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 inCongP ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 in__Cong ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 exuE3u ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 exu__Cong ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 emptyset__Cong ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 setadjoin__Cong ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 ![
% 3.74/1.49 X26:$i,
% 3.74/1.49 X28:$i]:
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 X26 ) =
% 3.74/1.49 (
% 3.74/1.49 X28 ) ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 powerset @
% 3.74/1.49 X26 ) =
% 3.74/1.49 (
% 3.74/1.49 powerset @
% 3.74/1.49 X28 ) ) ) ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 setunion__Cong ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 omega__Cong ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 exuEu ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 descr__Cong ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 dsetconstr__Cong ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 subsetI1 ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 eqimpsubset2 ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 eqimpsubset1 ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 subsetI2 ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 emptysetsubset ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 subsetE ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 subsetE2 ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 notsubsetI ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 notequalI1 ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 notequalI2 ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 subsetRefl ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 subsetTrans ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 setadjoinSub ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 setadjoinSub2 ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 subset2powerset ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 setextsub ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 subsetemptysetimpeq ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 powersetI1 ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 powersetE1 ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 ![
% 3.74/1.49 X30:$i]:
% 3.74/1.49 (
% 3.74/1.49 in @
% 3.74/1.49 X30 @
% 3.74/1.49 (
% 3.74/1.49 powerset @
% 3.74/1.49 X30 ) ) ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 powersetsubset ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 sepInPowerset ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 sepSubset ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 ![
% 3.74/1.49 X32:$i,
% 3.74/1.49 X34:$i,
% 3.74/1.49 X36:$i]:
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 in @
% 3.74/1.49 X36 @ X32 ) =>
% 3.74/1.49 (
% 3.74/1.49 in @
% 3.74/1.49 X36 @
% 3.74/1.49 (
% 3.74/1.49 binunion @
% 3.74/1.49 X32 @ X34 ) ) ) ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 upairset2IR ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 ![
% 3.74/1.49 X38:$i,
% 3.74/1.49 X40:$i,
% 3.74/1.49 X42:$i]:
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 in @
% 3.74/1.49 X42 @ X40 ) =>
% 3.74/1.49 (
% 3.74/1.49 in @
% 3.74/1.49 X42 @
% 3.74/1.49 (
% 3.74/1.49 binunion @
% 3.74/1.49 X38 @ X40 ) ) ) ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 ![
% 3.74/1.49 X44:$i,
% 3.74/1.49 X46:$i,
% 3.74/1.49 X48:$i,
% 3.74/1.49 X50:$o]:
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 in @
% 3.74/1.49 X48 @
% 3.74/1.49 (
% 3.74/1.49 binunion @
% 3.74/1.49 X44 @ X46 ) ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 in @
% 3.74/1.49 X48 @ X44 ) =>
% 3.74/1.49 (
% 3.74/1.49 X50 ) ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 in @
% 3.74/1.49 X48 @ X46 ) =>
% 3.74/1.49 (
% 3.74/1.49 X50 ) ) =>
% 3.74/1.49 (
% 3.74/1.49 X50 ) ) ) ) ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 ![
% 3.74/1.49 X52:$i,
% 3.74/1.49 X54:$i,
% 3.74/1.49 X56:$i]:
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 in @
% 3.74/1.49 X56 @
% 3.74/1.49 (
% 3.74/1.49 binunion @
% 3.74/1.49 X52 @ X54 ) ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 in @
% 3.74/1.49 X56 @ X54 ) |
% 3.74/1.49 (
% 3.74/1.49 in @
% 3.74/1.49 X56 @ X52 ) ) ) ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 ![
% 3.74/1.49 X58:$i,
% 3.74/1.49 X60:$i]:
% 3.74/1.49 (
% 3.74/1.49 subset @
% 3.74/1.49 X58 @
% 3.74/1.49 (
% 3.74/1.49 binunion @
% 3.74/1.49 X58 @ X60 ) ) ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 ![
% 3.74/1.49 X62:$i,
% 3.74/1.49 X64:$i]:
% 3.74/1.49 (
% 3.74/1.49 subset @
% 3.74/1.49 X64 @
% 3.74/1.49 (
% 3.74/1.49 binunion @
% 3.74/1.49 X62 @ X64 ) ) ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 binintersectI ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 binintersectSubset5 ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 binintersectEL ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 binintersectLsub ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 binintersectSubset2 ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 binintersectSubset3 ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 binintersectER ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 disjointsetsI1 ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 binintersectRsub ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 binintersectSubset4 ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 binintersectSubset1 ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 ![
% 3.74/1.49 X66:$i,
% 3.74/1.49 X68:$i,
% 3.74/1.49 X70:$i]:
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 binintersect
% 3.74/1.49 @
% 3.74/1.49 X66 @
% 3.74/1.49 (
% 3.74/1.49 binunion @
% 3.74/1.49 X68 @ X70 ) ) =
% 3.74/1.49 (
% 3.74/1.49 binunion @
% 3.74/1.49 (
% 3.74/1.49 binintersect
% 3.74/1.49 @
% 3.74/1.49 X66 @ X68 ) @
% 3.74/1.49 (
% 3.74/1.49 binintersect
% 3.74/1.49 @
% 3.74/1.49 X66 @ X70 ) ) ) ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 setminusI ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 setminusEL ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 setminusER ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 setminusSubset2 ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 setminusERneg ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 setminusELneg ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 setminusILneg ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 setminusIRneg ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 setminusLsub ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 setminusSubset1 ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 symdiffE ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 symdiffI1 ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 symdiffI2 ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 symdiffIneg1 ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 symdiffIneg2 ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 secondinupair ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 setukpairIL ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 setukpairIR ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 kpairiskpair ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 kpairp ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 singletonsubset ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 singletoninpowerset ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 ![
% 3.74/1.49 X72:$i,
% 3.74/1.49 X74:$i,
% 3.74/1.49 X76:$i]:
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 in @
% 3.74/1.49 X76 @ X72 ) =>
% 3.74/1.49 (
% 3.74/1.49 in @
% 3.74/1.49 (
% 3.74/1.49 setadjoin
% 3.74/1.49 @
% 3.74/1.49 X76 @
% 3.74/1.49 emptyset ) @
% 3.74/1.49 (
% 3.74/1.49 powerset @
% 3.74/1.49 (
% 3.74/1.49 binunion @
% 3.74/1.49 X72 @ X74 ) ) ) ) ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 upairset2E ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 ![
% 3.74/1.49 X78:$i,
% 3.74/1.49 X80:$i,
% 3.74/1.49 X82:$i]:
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 in @
% 3.74/1.49 X82 @ X78 ) =>
% 3.74/1.49 (
% 3.74/1.49 ![
% 3.74/1.49 X84:$i]:
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 in @
% 3.74/1.49 X84 @ X80 ) =>
% 3.74/1.49 (
% 3.74/1.49 subset @
% 3.74/1.49 (
% 3.74/1.49 setadjoin
% 3.74/1.49 @
% 3.74/1.49 X82 @
% 3.74/1.49 (
% 3.74/1.49 setadjoin
% 3.74/1.49 @
% 3.74/1.49 X84 @
% 3.74/1.49 emptyset ) ) @
% 3.74/1.49 (
% 3.74/1.49 binunion @
% 3.74/1.49 X78 @ X80 ) ) ) ) ) ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 ![
% 3.74/1.49 X86:$i,
% 3.74/1.49 X88:$i,
% 3.74/1.49 X90:$i]:
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 in @
% 3.74/1.49 X90 @ X86 ) =>
% 3.74/1.49 (
% 3.74/1.49 ![
% 3.74/1.49 X92:$i]:
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 in @
% 3.74/1.49 X92 @ X88 ) =>
% 3.74/1.49 (
% 3.74/1.49 in @
% 3.74/1.49 (
% 3.74/1.49 setadjoin
% 3.74/1.49 @
% 3.74/1.49 X90 @
% 3.74/1.49 (
% 3.74/1.49 setadjoin
% 3.74/1.49 @
% 3.74/1.49 X92 @
% 3.74/1.49 emptyset ) ) @
% 3.74/1.49 (
% 3.74/1.49 powerset @
% 3.74/1.49 (
% 3.74/1.49 binunion @
% 3.74/1.49 X86 @ X88 ) ) ) ) ) ) ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 ![
% 3.74/1.49 X94:$i,
% 3.74/1.49 X96:$i,
% 3.74/1.49 X98:$i]:
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 in @
% 3.74/1.49 X98 @ X94 ) =>
% 3.74/1.49 (
% 3.74/1.49 ![
% 3.74/1.49 X100:$i]:
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 in @
% 3.74/1.49 X100 @ X96 ) =>
% 3.74/1.49 (
% 3.74/1.49 subset @
% 3.74/1.49 (
% 3.74/1.49 setadjoin
% 3.74/1.49 @
% 3.74/1.49 (
% 3.74/1.49 setadjoin
% 3.74/1.49 @
% 3.74/1.49 X98 @
% 3.74/1.49 emptyset ) @
% 3.74/1.49 (
% 3.74/1.49 setadjoin
% 3.74/1.49 @
% 3.74/1.49 (
% 3.74/1.49 setadjoin
% 3.74/1.49 @
% 3.74/1.49 X98 @
% 3.74/1.49 (
% 3.74/1.49 setadjoin
% 3.74/1.49 @
% 3.74/1.49 X100 @
% 3.74/1.49 emptyset ) ) @
% 3.74/1.49 emptyset ) ) @
% 3.74/1.49 (
% 3.74/1.49 powerset @
% 3.74/1.49 (
% 3.74/1.49 binunion @
% 3.74/1.49 X94 @ X96 ) ) ) ) ) ) ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 ![
% 3.74/1.49 X102:$i,
% 3.74/1.49 X104:$i,
% 3.74/1.49 X106:$i]:
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 in @
% 3.74/1.49 X106 @
% 3.74/1.49 X102 ) =>
% 3.74/1.49 (
% 3.74/1.49 ![
% 3.74/1.49 X108:$i]:
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 in @
% 3.74/1.49 X108 @
% 3.74/1.49 X104 ) =>
% 3.74/1.49 (
% 3.74/1.49 in @
% 3.74/1.49 (
% 3.74/1.49 setadjoin
% 3.74/1.49 @
% 3.74/1.49 (
% 3.74/1.49 setadjoin
% 3.74/1.49 @
% 3.74/1.49 X106 @
% 3.74/1.49 emptyset ) @
% 3.74/1.49 (
% 3.74/1.49 setadjoin
% 3.74/1.49 @
% 3.74/1.49 (
% 3.74/1.49 setadjoin
% 3.74/1.49 @
% 3.74/1.49 X106 @
% 3.74/1.49 (
% 3.74/1.49 setadjoin
% 3.74/1.49 @
% 3.74/1.49 X108 @
% 3.74/1.49 emptyset ) ) @
% 3.74/1.49 emptyset ) ) @
% 3.74/1.49 (
% 3.74/1.49 powerset @
% 3.74/1.49 (
% 3.74/1.49 powerset @
% 3.74/1.49 (
% 3.74/1.49 binunion @
% 3.74/1.49 X102 @
% 3.74/1.49 X104 ) ) ) ) ) ) ) ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 ![
% 3.74/1.49 X110:$i,
% 3.74/1.49 X112:$i,
% 3.74/1.49 X114:$i]:
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 in @
% 3.74/1.49 X114 @
% 3.74/1.49 X110 ) =>
% 3.74/1.49 (
% 3.74/1.49 ![
% 3.74/1.49 X116:$i]:
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 in @
% 3.74/1.49 X116 @
% 3.74/1.49 X112 ) =>
% 3.74/1.49 (
% 3.74/1.49 in @
% 3.74/1.49 (
% 3.74/1.49 kpair @
% 3.74/1.49 X114 @
% 3.74/1.49 X116 ) @
% 3.74/1.49 (
% 3.74/1.49 powerset @
% 3.74/1.49 (
% 3.74/1.49 powerset @
% 3.74/1.49 (
% 3.74/1.49 binunion @
% 3.74/1.49 X110 @
% 3.74/1.49 X112 ) ) ) ) ) ) ) ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 cartprodpairin ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 cartprodmempair1 ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 cartprodmempair ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 setunionE2 ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 setunionsingleton1 ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 setunionsingleton2 ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 setunionsingleton ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 singletonprop ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 ex1E1 ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 ex1I ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 ex1I2 ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 singletonsuniq ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 setukpairinjL1 ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 kfstsingleton ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 theprop ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 kfstpairEq ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 cartprodfstin ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 setukpairinjL2 ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 setukpairinjL ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 setukpairinjR11 ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 setukpairinjR12 ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 setukpairinjR1 ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 upairequniteq ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 setukpairinjR2 ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 setukpairinjR ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 ksndsingleton ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 ksndpairEq ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 kpairsurjEq ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 cartprodsndin ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 cartprodpairmemEL ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 cartprodpairmemER ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 cartprodmempaircEq ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 cartprodfstpairEq ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 cartprodsndpairEq ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 cartprodpairsurjEq ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 dpsetconstrI ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 dpsetconstrSub ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 setOfPairsIsBReln ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 dpsetconstrERa ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 dpsetconstrEL1 ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 dpsetconstrEL2 ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 dpsetconstrER ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 funcImageSingleton ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 apProp ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 app ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 infuncsetfunc ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 ap2p ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 funcinfuncset ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 lamProp ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 lamp ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 lam2p ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 brelnall1 ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 brelnall2 ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 ex1E2 ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 funcGraphProp1 ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 funcGraphProp3 ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 funcGraphProp2 ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 funcextLem ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 funcGraphProp4 ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 subbreln ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 eqbreln ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 funcext ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 funcext2 ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 ap2apEq1 ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 ap2apEq2 ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 beta1 ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 eta1 ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 lam2lamEq ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 beta2 ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 eta2 ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 iffalseProp1 ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 iffalseProp2 ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 iftrueProp1 ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 iftrueProp2 ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 ifSingleton ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 ifp ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 theeq ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 iftrue ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 iffalse ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 iftrueorfalse ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 binintersectT_lem ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 ![
% 3.74/1.49 X118:$i,
% 3.74/1.49 X120:$i]:
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 in @
% 3.74/1.49 X120 @
% 3.74/1.49 (
% 3.74/1.49 powerset @
% 3.74/1.49 X118 ) ) =>
% 3.74/1.49 (
% 3.74/1.49 ![
% 3.74/1.49 X122:$i]:
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 in @
% 3.74/1.49 X122 @
% 3.74/1.49 (
% 3.74/1.49 powerset @
% 3.74/1.49 X118 ) ) =>
% 3.74/1.49 (
% 3.74/1.49 in @
% 3.74/1.49 (
% 3.74/1.49 binunion @
% 3.74/1.49 X120 @
% 3.74/1.49 X122 ) @
% 3.74/1.49 (
% 3.74/1.49 powerset @
% 3.74/1.49 X118 ) ) ) ) ) ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 ![
% 3.74/1.49 X124:$i,
% 3.74/1.49 X126:$i]:
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 in @
% 3.74/1.49 X126 @
% 3.74/1.49 (
% 3.74/1.49 powerset @
% 3.74/1.49 X124 ) ) =>
% 3.74/1.49 (
% 3.74/1.49 in @
% 3.74/1.49 (
% 3.74/1.49 powerset @
% 3.74/1.49 X126 ) @
% 3.74/1.49 (
% 3.74/1.49 powerset @
% 3.74/1.49 (
% 3.74/1.49 powerset @
% 3.74/1.49 X124 ) ) ) ) ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 setminusT_lem ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 complementT_lem ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 ![
% 3.74/1.49 X128:$i,
% 3.74/1.49 X130:$i]:
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 in @
% 3.74/1.49 X130 @
% 3.74/1.49 (
% 3.74/1.49 powerset @
% 3.74/1.49 X128 ) ) =>
% 3.74/1.49 (
% 3.74/1.49 ![
% 3.74/1.49 X132:$i]:
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 in @
% 3.74/1.49 X132 @
% 3.74/1.49 (
% 3.74/1.49 powerset @
% 3.74/1.49 X128 ) ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 ![
% 3.74/1.49 X134:$i]:
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 in @
% 3.74/1.49 X134 @
% 3.74/1.49 X128 ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 in @
% 3.74/1.49 X134 @
% 3.74/1.49 X130 ) =>
% 3.74/1.49 (
% 3.74/1.49 in @
% 3.74/1.49 X134 @
% 3.74/1.49 X132 ) ) ) ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 ![
% 3.74/1.49 X136:$i]:
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 in @
% 3.74/1.49 X136 @
% 3.74/1.49 X128 ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 in @
% 3.74/1.49 X136 @
% 3.74/1.49 X132 ) =>
% 3.74/1.49 (
% 3.74/1.49 in @
% 3.74/1.49 X136 @
% 3.74/1.49 X130 ) ) ) ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 X130 ) =
% 3.74/1.49 (
% 3.74/1.49 X132 ) ) ) ) ) ) ) ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 subsetTI ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 ![
% 3.74/1.49 X138:$i,
% 3.74/1.49 X140:$i]:
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 in @
% 3.74/1.49 X140 @
% 3.74/1.49 (
% 3.74/1.49 powerset @
% 3.74/1.49 X138 ) ) =>
% 3.74/1.49 (
% 3.74/1.49 ![
% 3.74/1.49 X142:$i]:
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 in @
% 3.74/1.49 X142 @
% 3.74/1.49 (
% 3.74/1.49 powerset @
% 3.74/1.49 X138 ) ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 ![
% 3.74/1.49 X144:$i]:
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 in @
% 3.74/1.49 X144 @
% 3.74/1.49 X138 ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 in @
% 3.74/1.49 X144 @
% 3.74/1.49 X140 ) =>
% 3.74/1.49 (
% 3.74/1.49 in @
% 3.74/1.49 X144 @
% 3.74/1.49 X142 ) ) ) ) =>
% 3.74/1.49 (
% 3.74/1.49 in @
% 3.74/1.49 X140 @
% 3.74/1.49 (
% 3.74/1.49 powerset @
% 3.74/1.49 X142 ) ) ) ) ) ) ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 ![
% 3.74/1.49 X146:$i,
% 3.74/1.49 X148:$i]:
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 in @
% 3.74/1.49 X148 @
% 3.74/1.49 (
% 3.74/1.49 powerset @
% 3.74/1.49 X146 ) ) =>
% 3.74/1.49 (
% 3.74/1.49 ![
% 3.74/1.49 X150:$i]:
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 in @
% 3.74/1.49 X150 @
% 3.74/1.49 (
% 3.74/1.49 powerset @
% 3.74/1.49 X146 ) ) =>
% 3.74/1.49 (
% 3.74/1.49 ![
% 3.74/1.49 X152:$i]:
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 in @
% 3.74/1.49 X152 @
% 3.74/1.49 X146 ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 in @
% 3.74/1.49 X148 @
% 3.74/1.49 (
% 3.74/1.49 powerset @
% 3.74/1.49 X150 ) ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 in @
% 3.74/1.49 X152 @
% 3.74/1.49 X148 ) =>
% 3.74/1.49 (
% 3.74/1.49 in @
% 3.74/1.49 X152 @
% 3.74/1.49 X150 ) ) ) ) ) ) ) ) ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 complementTI1 ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 complementTE1 ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 binintersectTELcontra ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 binintersectTERcontra ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 contrasubsetT ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 contrasubsetT1 ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 contrasubsetT2 ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 contrasubsetT3 ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 doubleComplementI1 ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 doubleComplementE1 ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 doubleComplementSub1 ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 doubleComplementSub2 ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 doubleComplementEq ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 complementTnotintersectT ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 complementImpComplementIntersect ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 complementSubsetComplementIntersect ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 complementInPowersetComplementIntersect ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 contraSubsetComplement ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 complementTcontraSubset ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 ![
% 3.74/1.49 X154:$i,
% 3.74/1.49 X156:$i]:
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 in @
% 3.74/1.49 X156 @
% 3.74/1.49 (
% 3.74/1.49 powerset @
% 3.74/1.49 X154 ) ) =>
% 3.74/1.49 (
% 3.74/1.49 ![
% 3.74/1.49 X158:$i]:
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 in @
% 3.74/1.49 X158 @
% 3.74/1.49 (
% 3.74/1.49 powerset @
% 3.74/1.49 X154 ) ) =>
% 3.74/1.49 (
% 3.74/1.49 ![
% 3.74/1.49 X160:$i]:
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 in @
% 3.74/1.49 X160 @
% 3.74/1.49 X154 ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 ~(
% 3.74/1.49 in @
% 3.74/1.49 X160 @
% 3.74/1.49 (
% 3.74/1.49 binunion
% 3.74/1.49 @
% 3.74/1.49 X156 @
% 3.74/1.49 X158 ) ) ) =>
% 3.74/1.49 (
% 3.74/1.49 ~(
% 3.74/1.49 in @
% 3.74/1.49 X160 @
% 3.74/1.49 X156 ) ) ) ) ) ) ) ) ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 ![
% 3.74/1.49 X162:$i,
% 3.74/1.49 X164:$i]:
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 in @
% 3.74/1.49 X164 @
% 3.74/1.49 (
% 3.74/1.49 powerset @
% 3.74/1.49 X162 ) ) =>
% 3.74/1.49 (
% 3.74/1.49 ![
% 3.74/1.49 X166:$i]:
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 in @
% 3.74/1.49 X166 @
% 3.74/1.49 (
% 3.74/1.49 powerset @
% 3.74/1.49 X162 ) ) =>
% 3.74/1.49 (
% 3.74/1.49 ![
% 3.74/1.49 X168:$i]:
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 in @
% 3.74/1.49 X168 @
% 3.74/1.49 X162 ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 ~(
% 3.74/1.49 in @
% 3.74/1.49 X168 @
% 3.74/1.49 (
% 3.74/1.49 binunion
% 3.74/1.49 @
% 3.74/1.49 X164 @
% 3.74/1.49 X166 ) ) ) =>
% 3.74/1.49 (
% 3.74/1.49 ~(
% 3.74/1.49 in @
% 3.74/1.49 X168 @
% 3.74/1.49 X166 ) ) ) ) ) ) ) ) ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 ![
% 3.74/1.49 X170:$i,
% 3.74/1.49 X172:$i]:
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 in @
% 3.74/1.49 X172 @
% 3.74/1.49 (
% 3.74/1.49 powerset @
% 3.74/1.49 X170 ) ) =>
% 3.74/1.49 (
% 3.74/1.49 ![
% 3.74/1.49 X174:$i]:
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 in @
% 3.74/1.49 X174 @
% 3.74/1.49 (
% 3.74/1.49 powerset @
% 3.74/1.49 X170 ) ) =>
% 3.74/1.49 (
% 3.74/1.49 ![
% 3.74/1.49 X176:$i]:
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 in @
% 3.74/1.49 X176 @
% 3.74/1.49 (
% 3.74/1.49 powerset @
% 3.74/1.49 X170 ) ) =>
% 3.74/1.49 (
% 3.74/1.49 ![
% 3.74/1.49 X178:$i]:
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 in @
% 3.74/1.49 X178 @
% 3.74/1.49 X170 ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 in @
% 3.74/1.49 X178 @
% 3.74/1.49 (
% 3.74/1.49 binintersect
% 3.74/1.49 @
% 3.74/1.49 X172 @
% 3.74/1.49 X174 ) ) =>
% 3.74/1.49 (
% 3.74/1.49 in @
% 3.74/1.49 X178 @
% 3.74/1.49 (
% 3.74/1.49 binunion @
% 3.74/1.49 X172 @
% 3.74/1.49 X176 ) ) ) ) ) ) ) ) ) ) ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 ![
% 3.74/1.49 X180:$i,
% 3.74/1.49 X182:$i]:
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 in @
% 3.74/1.49 X182 @
% 3.74/1.49 (
% 3.74/1.49 powerset @
% 3.74/1.49 X180 ) ) =>
% 3.74/1.49 (
% 3.74/1.49 ![
% 3.74/1.49 X184:$i]:
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 in @
% 3.74/1.49 X184 @
% 3.74/1.49 (
% 3.74/1.49 powerset @
% 3.74/1.49 X180 ) ) =>
% 3.74/1.49 (
% 3.74/1.49 ![
% 3.74/1.49 X186:$i]:
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 in @
% 3.74/1.49 X186 @
% 3.74/1.49 (
% 3.74/1.49 powerset @
% 3.74/1.49 X180 ) ) =>
% 3.74/1.49 (
% 3.74/1.49 ![
% 3.74/1.49 X188:$i]:
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 in @
% 3.74/1.49 X188 @
% 3.74/1.49 X180 ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 in @
% 3.74/1.49 X188 @
% 3.74/1.49 (
% 3.74/1.49 binintersect
% 3.74/1.49 @
% 3.74/1.49 X182 @
% 3.74/1.49 X184 ) ) =>
% 3.74/1.49 (
% 3.74/1.49 in @
% 3.74/1.49 X188 @
% 3.74/1.49 (
% 3.74/1.49 binunion @
% 3.74/1.49 X184 @
% 3.74/1.49 X186 ) ) ) ) ) ) ) ) ) ) ) =>
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 ![
% 3.74/1.49 X190:$i,
% 3.74/1.49 X192:$i]:
% 3.74/1.49 (
% 3.74/1.49 (
% 3.74/1.49 in @
% 3.74/1.49 X192 @
% 3.74/1.49 (
% 3.74/1.49 powerset @
% 3.74/1.49 X190 ) ) =>
% 3.74/1.49 (
% 3.74/1.49 ![
% 3.74/1.49 X194:$i]:
% 3.74/1.49 (
% 3.74/1.50 (
% 3.74/1.50 in @
% 3.74/1.50 X194 @
% 3.74/1.50 (
% 3.74/1.50 powerset @
% 3.74/1.50 X190 ) ) =>
% 3.74/1.50 (
% 3.74/1.50 ![
% 3.74/1.50 X196:$i]:
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 in @
% 3.74/1.50 X196 @
% 3.74/1.50 (
% 3.74/1.50 powerset @
% 3.74/1.50 X190 ) ) =>
% 3.74/1.50 (
% 3.74/1.50 ![
% 3.74/1.50 X198:$i]:
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 in @
% 3.74/1.50 X198 @
% 3.74/1.50 X190 ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 in @
% 3.74/1.50 X198 @
% 3.74/1.50 (
% 3.74/1.50 binintersect
% 3.74/1.50 @
% 3.74/1.50 X192 @
% 3.74/1.50 X194 ) ) =>
% 3.74/1.50 (
% 3.74/1.50 in @
% 3.74/1.50 X198 @
% 3.74/1.50 (
% 3.74/1.50 binintersect
% 3.74/1.50 @
% 3.74/1.50 (
% 3.74/1.50 binunion @
% 3.74/1.50 X192 @
% 3.74/1.50 X196 ) @
% 3.74/1.50 (
% 3.74/1.50 binunion @
% 3.74/1.50 X194 @
% 3.74/1.50 X196 ) ) ) ) ) ) ) ) ) ) ) ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 ![
% 3.74/1.50 X200:$i,
% 3.74/1.50 X202:$i]:
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 in @
% 3.74/1.50 X202 @
% 3.74/1.50 (
% 3.74/1.50 powerset @
% 3.74/1.50 X200 ) ) =>
% 3.74/1.50 (
% 3.74/1.50 ![
% 3.74/1.50 X204:$i]:
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 in @
% 3.74/1.50 X204 @
% 3.74/1.50 (
% 3.74/1.50 powerset @
% 3.74/1.50 X200 ) ) =>
% 3.74/1.50 (
% 3.74/1.50 ![
% 3.74/1.50 X206:$i]:
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 in @
% 3.74/1.50 X206 @
% 3.74/1.50 (
% 3.74/1.50 powerset @
% 3.74/1.50 X200 ) ) =>
% 3.74/1.50 (
% 3.74/1.50 in @
% 3.74/1.50 (
% 3.74/1.50 binintersect
% 3.74/1.50 @
% 3.74/1.50 X202 @
% 3.74/1.50 X204 ) @
% 3.74/1.50 (
% 3.74/1.50 powerset @
% 3.74/1.50 (
% 3.74/1.50 binintersect
% 3.74/1.50 @
% 3.74/1.50 (
% 3.74/1.50 binunion @
% 3.74/1.50 X202 @
% 3.74/1.50 X206 ) @
% 3.74/1.50 (
% 3.74/1.50 binunion @
% 3.74/1.50 X204 @
% 3.74/1.50 X206 ) ) ) ) ) ) ) ) ) ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 ![
% 3.74/1.50 X208:$i,
% 3.74/1.50 X210:$i]:
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 in @
% 3.74/1.50 X210 @
% 3.74/1.50 (
% 3.74/1.50 powerset @
% 3.74/1.50 X208 ) ) =>
% 3.74/1.50 (
% 3.74/1.50 ![
% 3.74/1.50 X212:$i]:
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 in @
% 3.74/1.50 X212 @
% 3.74/1.50 (
% 3.74/1.50 powerset @
% 3.74/1.50 X208 ) ) =>
% 3.74/1.50 (
% 3.74/1.50 ![
% 3.74/1.50 X214:$i]:
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 in @
% 3.74/1.50 X214 @
% 3.74/1.50 X208 ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 in @
% 3.74/1.50 X214 @
% 3.74/1.50 (
% 3.74/1.50 setminus @
% 3.74/1.50 X208 @
% 3.74/1.50 (
% 3.74/1.50 binunion @
% 3.74/1.50 X210 @
% 3.74/1.50 X212 ) ) ) =>
% 3.74/1.50 (
% 3.74/1.50 ~(
% 3.74/1.50 in @
% 3.74/1.50 X214 @
% 3.74/1.50 X210 ) ) ) ) ) ) ) ) ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 ![
% 3.74/1.50 X216:$i,
% 3.74/1.50 X218:$i]:
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 in @
% 3.74/1.50 X218 @
% 3.74/1.50 (
% 3.74/1.50 powerset @
% 3.74/1.50 X216 ) ) =>
% 3.74/1.50 (
% 3.74/1.50 ![
% 3.74/1.50 X220:$i]:
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 in @
% 3.74/1.50 X220 @
% 3.74/1.50 (
% 3.74/1.50 powerset @
% 3.74/1.50 X216 ) ) =>
% 3.74/1.50 (
% 3.74/1.50 ![
% 3.74/1.50 X222:$i]:
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 in @
% 3.74/1.50 X222 @
% 3.74/1.50 X216 ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 in @
% 3.74/1.50 X222 @
% 3.74/1.50 (
% 3.74/1.50 setminus @
% 3.74/1.50 X216 @
% 3.74/1.50 (
% 3.74/1.50 binunion @
% 3.74/1.50 X218 @
% 3.74/1.50 X220 ) ) ) =>
% 3.74/1.50 (
% 3.74/1.50 in @
% 3.74/1.50 X222 @
% 3.74/1.50 (
% 3.74/1.50 setminus @
% 3.74/1.50 X216 @
% 3.74/1.50 X218 ) ) ) ) ) ) ) ) ) =>
% 3.74/1.50 (
% 3.74/1.50 ![
% 3.74/1.50 X224:$i,
% 3.74/1.50 X226:$i]:
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 in @
% 3.74/1.50 X226 @
% 3.74/1.50 (
% 3.74/1.50 powerset @
% 3.74/1.50 X224 ) ) =>
% 3.74/1.50 (
% 3.74/1.50 ![
% 3.74/1.50 X228:$i]:
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 in @
% 3.74/1.50 X228 @
% 3.74/1.50 (
% 3.74/1.50 powerset @
% 3.74/1.50 X224 ) ) =>
% 3.74/1.50 (
% 3.74/1.50 ![
% 3.74/1.50 X230:$o,
% 3.74/1.50 X232:$i]:
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 in @
% 3.74/1.50 X232 @
% 3.74/1.50 X224 ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 in @
% 3.74/1.50 X232 @
% 3.74/1.50 (
% 3.74/1.50 binunion @
% 3.74/1.50 X226 @
% 3.74/1.50 X228 ) ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 in @
% 3.74/1.50 X232 @
% 3.74/1.50 X226 ) =>
% 3.74/1.50 (
% 3.74/1.50 X230 ) ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 in @
% 3.74/1.50 X232 @
% 3.74/1.50 X228 ) =>
% 3.74/1.50 (
% 3.74/1.50 X230 ) ) =>
% 3.74/1.50 (
% 3.74/1.50 X230 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 3.74/1.50 thf(zf_stmt_1, type, zip_tseitin_0 : $i > $i > $i > $o).
% 3.74/1.50 thf(zf_stmt_2, axiom,
% 3.74/1.50 (![X8:$i,X6:$i,X4:$i]:
% 3.74/1.50 ( ( zip_tseitin_0 @ X8 @ X6 @ X4 ) <=>
% 3.74/1.50 ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ))).
% 3.74/1.50 thf(zf_stmt_3, conjecture,
% 3.74/1.50 (( setextAx ) =>
% 3.74/1.50 ( ( emptysetAx ) =>
% 3.74/1.50 ( ( setadjoinAx ) =>
% 3.74/1.50 ( ( ![X4:$i,X6:$i]:
% 3.74/1.50 ( ( in @ X6 @ ( powerset @ X4 ) ) <=>
% 3.74/1.50 ( ![X8:$i]: ( zip_tseitin_0 @ X8 @ X6 @ X4 ) ) ) ) =>
% 3.74/1.50 ( ( setunionAx ) =>
% 3.74/1.50 ( ( omega0Ax ) =>
% 3.74/1.50 ( ( omegaSAx ) =>
% 3.74/1.50 ( ( omegaIndAx ) =>
% 3.74/1.50 ( ( replAx ) =>
% 3.74/1.50 ( ( foundationAx ) =>
% 3.74/1.50 ( ( wellorderingAx ) =>
% 3.74/1.50 ( ( descrp ) =>
% 3.74/1.50 ( ( dsetconstrI ) =>
% 3.74/1.50 ( ( dsetconstrEL ) =>
% 3.74/1.50 ( ( dsetconstrER ) =>
% 3.74/1.50 ( ( exuE1 ) =>
% 3.74/1.50 ( ( prop2setE ) =>
% 3.74/1.50 ( ( emptysetE ) =>
% 3.74/1.50 ( ( emptysetimpfalse ) =>
% 3.74/1.50 ( ( notinemptyset ) =>
% 3.74/1.50 ( ( exuE3e ) =>
% 3.74/1.50 ( ( setext ) =>
% 3.74/1.50 ( ( emptyI ) =>
% 3.74/1.50 ( ( noeltsimpempty ) =>
% 3.74/1.50 ( ( setbeta ) =>
% 3.74/1.50 ( ( nonemptyE1 ) =>
% 3.74/1.50 ( ( nonemptyI ) =>
% 3.74/1.50 ( ( nonemptyI1 ) =>
% 3.74/1.50 ( ( setadjoinIL ) =>
% 3.74/1.50 ( ( emptyinunitempty ) =>
% 3.74/1.50 ( ( setadjoinIR ) =>
% 3.74/1.50 ( ( setadjoinE ) =>
% 3.74/1.50 ( (
% 3.74/1.50 setadjoinOr ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 setoftrueEq ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 ![
% 3.74/1.50 X10:$i,
% 3.74/1.50 X12:$i]:
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 ![
% 3.74/1.50 X14:$i]:
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 in @
% 3.74/1.50 X14 @ X12 ) =>
% 3.74/1.50 (
% 3.74/1.50 in @
% 3.74/1.50 X14 @ X10 ) ) ) =>
% 3.74/1.50 (
% 3.74/1.50 in @
% 3.74/1.50 X12 @
% 3.74/1.50 (
% 3.74/1.50 powerset @
% 3.74/1.50 X10 ) ) ) ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 ![
% 3.74/1.50 X16:$i]:
% 3.74/1.50 (
% 3.74/1.50 in @
% 3.74/1.50 emptyset @
% 3.74/1.50 (
% 3.74/1.50 powerset @
% 3.74/1.50 X16 ) ) ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 ![
% 3.74/1.50 X18:$i]:
% 3.74/1.50 (
% 3.74/1.50 in @
% 3.74/1.50 emptyset @
% 3.74/1.50 (
% 3.74/1.50 powerset @
% 3.74/1.50 X18 ) ) ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 ![
% 3.74/1.50 X20:$i,
% 3.74/1.50 X22:$i,
% 3.74/1.50 X24:$i]:
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 in @
% 3.74/1.50 X22 @
% 3.74/1.50 (
% 3.74/1.50 powerset @
% 3.74/1.50 X20 ) ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 in @
% 3.74/1.50 X24 @ X22 ) =>
% 3.74/1.50 (
% 3.74/1.50 in @
% 3.74/1.50 X24 @ X20 ) ) ) ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 setunionI ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 setunionE ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 subPowSU ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 exuE2 ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 nonemptyImpWitness ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 uniqinunit ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 notinsingleton ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 eqinunit ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 singletonsswitch ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 upairsetE ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 upairsetIL ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 upairsetIR ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 emptyE1 ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 vacuousDall ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 quantDeMorgan1 ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 quantDeMorgan2 ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 quantDeMorgan3 ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 quantDeMorgan4 ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 prop2setI ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 prop2set2propI ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 notdexE ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 notdallE ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 exuI1 ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 exuI3 ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 exuI2 ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 inCongP ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 in__Cong ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 exuE3u ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 exu__Cong ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 emptyset__Cong ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 setadjoin__Cong ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 ![
% 3.74/1.50 X26:$i,
% 3.74/1.50 X28:$i]:
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 X26 ) =
% 3.74/1.50 (
% 3.74/1.50 X28 ) ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 powerset @
% 3.74/1.50 X26 ) =
% 3.74/1.50 (
% 3.74/1.50 powerset @
% 3.74/1.50 X28 ) ) ) ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 setunion__Cong ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 omega__Cong ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 exuEu ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 descr__Cong ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 dsetconstr__Cong ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 subsetI1 ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 eqimpsubset2 ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 eqimpsubset1 ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 subsetI2 ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 emptysetsubset ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 subsetE ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 subsetE2 ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 notsubsetI ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 notequalI1 ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 notequalI2 ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 subsetRefl ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 subsetTrans ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 setadjoinSub ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 setadjoinSub2 ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 subset2powerset ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 setextsub ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 subsetemptysetimpeq ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 powersetI1 ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 powersetE1 ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 ![
% 3.74/1.50 X30:$i]:
% 3.74/1.50 (
% 3.74/1.50 in @
% 3.74/1.50 X30 @
% 3.74/1.50 (
% 3.74/1.50 powerset @
% 3.74/1.50 X30 ) ) ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 powersetsubset ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 sepInPowerset ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 sepSubset ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 ![
% 3.74/1.50 X32:$i,
% 3.74/1.50 X34:$i,
% 3.74/1.50 X36:$i]:
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 in @
% 3.74/1.50 X36 @ X32 ) =>
% 3.74/1.50 (
% 3.74/1.50 in @
% 3.74/1.50 X36 @
% 3.74/1.50 (
% 3.74/1.50 binunion @
% 3.74/1.50 X32 @ X34 ) ) ) ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 upairset2IR ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 ![
% 3.74/1.50 X38:$i,
% 3.74/1.50 X40:$i,
% 3.74/1.50 X42:$i]:
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 in @
% 3.74/1.50 X42 @ X40 ) =>
% 3.74/1.50 (
% 3.74/1.50 in @
% 3.74/1.50 X42 @
% 3.74/1.50 (
% 3.74/1.50 binunion @
% 3.74/1.50 X38 @ X40 ) ) ) ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 ![
% 3.74/1.50 X44:$i,
% 3.74/1.50 X46:$i,
% 3.74/1.50 X48:$i,
% 3.74/1.50 X50:$o]:
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 in @
% 3.74/1.50 X48 @
% 3.74/1.50 (
% 3.74/1.50 binunion @
% 3.74/1.50 X44 @ X46 ) ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 in @
% 3.74/1.50 X48 @ X44 ) =>
% 3.74/1.50 (
% 3.74/1.50 X50 ) ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 in @
% 3.74/1.50 X48 @ X46 ) =>
% 3.74/1.50 (
% 3.74/1.50 X50 ) ) =>
% 3.74/1.50 (
% 3.74/1.50 X50 ) ) ) ) ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 ![
% 3.74/1.50 X52:$i,
% 3.74/1.50 X54:$i,
% 3.74/1.50 X56:$i]:
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 in @
% 3.74/1.50 X56 @
% 3.74/1.50 (
% 3.74/1.50 binunion @
% 3.74/1.50 X52 @ X54 ) ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 in @
% 3.74/1.50 X56 @ X52 ) |
% 3.74/1.50 (
% 3.74/1.50 in @
% 3.74/1.50 X56 @ X54 ) ) ) ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 ![
% 3.74/1.50 X58:$i,
% 3.74/1.50 X60:$i]:
% 3.74/1.50 (
% 3.74/1.50 subset @
% 3.74/1.50 X58 @
% 3.74/1.50 (
% 3.74/1.50 binunion @
% 3.74/1.50 X58 @ X60 ) ) ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 ![
% 3.74/1.50 X62:$i,
% 3.74/1.50 X64:$i]:
% 3.74/1.50 (
% 3.74/1.50 subset @
% 3.74/1.50 X64 @
% 3.74/1.50 (
% 3.74/1.50 binunion @
% 3.74/1.50 X62 @ X64 ) ) ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 binintersectI ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 binintersectSubset5 ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 binintersectEL ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 binintersectLsub ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 binintersectSubset2 ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 binintersectSubset3 ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 binintersectER ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 disjointsetsI1 ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 binintersectRsub ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 binintersectSubset4 ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 binintersectSubset1 ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 ![
% 3.74/1.50 X66:$i,
% 3.74/1.50 X68:$i,
% 3.74/1.50 X70:$i]:
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 binintersect
% 3.74/1.50 @
% 3.74/1.50 X66 @
% 3.74/1.50 (
% 3.74/1.50 binunion @
% 3.74/1.50 X68 @ X70 ) ) =
% 3.74/1.50 (
% 3.74/1.50 binunion @
% 3.74/1.50 (
% 3.74/1.50 binintersect
% 3.74/1.50 @
% 3.74/1.50 X66 @ X68 ) @
% 3.74/1.50 (
% 3.74/1.50 binintersect
% 3.74/1.50 @
% 3.74/1.50 X66 @ X70 ) ) ) ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 setminusI ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 setminusEL ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 setminusER ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 setminusSubset2 ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 setminusERneg ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 setminusELneg ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 setminusILneg ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 setminusIRneg ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 setminusLsub ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 setminusSubset1 ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 symdiffE ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 symdiffI1 ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 symdiffI2 ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 symdiffIneg1 ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 symdiffIneg2 ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 secondinupair ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 setukpairIL ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 setukpairIR ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 kpairiskpair ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 kpairp ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 singletonsubset ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 singletoninpowerset ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 ![
% 3.74/1.50 X72:$i,
% 3.74/1.50 X74:$i,
% 3.74/1.50 X76:$i]:
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 in @
% 3.74/1.50 X76 @ X72 ) =>
% 3.74/1.50 (
% 3.74/1.50 in @
% 3.74/1.50 (
% 3.74/1.50 setadjoin
% 3.74/1.50 @
% 3.74/1.50 X76 @
% 3.74/1.50 emptyset ) @
% 3.74/1.50 (
% 3.74/1.50 powerset @
% 3.74/1.50 (
% 3.74/1.50 binunion @
% 3.74/1.50 X72 @ X74 ) ) ) ) ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 upairset2E ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 ![
% 3.74/1.50 X78:$i,
% 3.74/1.50 X80:$i,
% 3.74/1.50 X82:$i]:
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 in @
% 3.74/1.50 X82 @ X78 ) =>
% 3.74/1.50 (
% 3.74/1.50 ![
% 3.74/1.50 X84:$i]:
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 in @
% 3.74/1.50 X84 @ X80 ) =>
% 3.74/1.50 (
% 3.74/1.50 subset @
% 3.74/1.50 (
% 3.74/1.50 setadjoin
% 3.74/1.50 @
% 3.74/1.50 X82 @
% 3.74/1.50 (
% 3.74/1.50 setadjoin
% 3.74/1.50 @
% 3.74/1.50 X84 @
% 3.74/1.50 emptyset ) ) @
% 3.74/1.50 (
% 3.74/1.50 binunion @
% 3.74/1.50 X78 @ X80 ) ) ) ) ) ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 ![
% 3.74/1.50 X86:$i,
% 3.74/1.50 X88:$i,
% 3.74/1.50 X90:$i]:
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 in @
% 3.74/1.50 X90 @ X86 ) =>
% 3.74/1.50 (
% 3.74/1.50 ![
% 3.74/1.50 X92:$i]:
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 in @
% 3.74/1.50 X92 @ X88 ) =>
% 3.74/1.50 (
% 3.74/1.50 in @
% 3.74/1.50 (
% 3.74/1.50 setadjoin
% 3.74/1.50 @
% 3.74/1.50 X90 @
% 3.74/1.50 (
% 3.74/1.50 setadjoin
% 3.74/1.50 @
% 3.74/1.50 X92 @
% 3.74/1.50 emptyset ) ) @
% 3.74/1.50 (
% 3.74/1.50 powerset @
% 3.74/1.50 (
% 3.74/1.50 binunion @
% 3.74/1.50 X86 @ X88 ) ) ) ) ) ) ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 ![
% 3.74/1.50 X94:$i,
% 3.74/1.50 X96:$i,
% 3.74/1.50 X98:$i]:
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 in @
% 3.74/1.50 X98 @ X94 ) =>
% 3.74/1.50 (
% 3.74/1.50 ![
% 3.74/1.50 X100:$i]:
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 in @
% 3.74/1.50 X100 @ X96 ) =>
% 3.74/1.50 (
% 3.74/1.50 subset @
% 3.74/1.50 (
% 3.74/1.50 setadjoin
% 3.74/1.50 @
% 3.74/1.50 (
% 3.74/1.50 setadjoin
% 3.74/1.50 @
% 3.74/1.50 X98 @
% 3.74/1.50 emptyset ) @
% 3.74/1.50 (
% 3.74/1.50 setadjoin
% 3.74/1.50 @
% 3.74/1.50 (
% 3.74/1.50 setadjoin
% 3.74/1.50 @
% 3.74/1.50 X98 @
% 3.74/1.50 (
% 3.74/1.50 setadjoin
% 3.74/1.50 @
% 3.74/1.50 X100 @
% 3.74/1.50 emptyset ) ) @
% 3.74/1.50 emptyset ) ) @
% 3.74/1.50 (
% 3.74/1.50 powerset @
% 3.74/1.50 (
% 3.74/1.50 binunion @
% 3.74/1.50 X94 @ X96 ) ) ) ) ) ) ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 ![
% 3.74/1.50 X102:$i,
% 3.74/1.50 X104:$i,
% 3.74/1.50 X106:$i]:
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 in @
% 3.74/1.50 X106 @
% 3.74/1.50 X102 ) =>
% 3.74/1.50 (
% 3.74/1.50 ![
% 3.74/1.50 X108:$i]:
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 in @
% 3.74/1.50 X108 @
% 3.74/1.50 X104 ) =>
% 3.74/1.50 (
% 3.74/1.50 in @
% 3.74/1.50 (
% 3.74/1.50 setadjoin
% 3.74/1.50 @
% 3.74/1.50 (
% 3.74/1.50 setadjoin
% 3.74/1.50 @
% 3.74/1.50 X106 @
% 3.74/1.50 emptyset ) @
% 3.74/1.50 (
% 3.74/1.50 setadjoin
% 3.74/1.50 @
% 3.74/1.50 (
% 3.74/1.50 setadjoin
% 3.74/1.50 @
% 3.74/1.50 X106 @
% 3.74/1.50 (
% 3.74/1.50 setadjoin
% 3.74/1.50 @
% 3.74/1.50 X108 @
% 3.74/1.50 emptyset ) ) @
% 3.74/1.50 emptyset ) ) @
% 3.74/1.50 (
% 3.74/1.50 powerset @
% 3.74/1.50 (
% 3.74/1.50 powerset @
% 3.74/1.50 (
% 3.74/1.50 binunion @
% 3.74/1.50 X102 @
% 3.74/1.50 X104 ) ) ) ) ) ) ) ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 ![
% 3.74/1.50 X110:$i,
% 3.74/1.50 X112:$i,
% 3.74/1.50 X114:$i]:
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 in @
% 3.74/1.50 X114 @
% 3.74/1.50 X110 ) =>
% 3.74/1.50 (
% 3.74/1.50 ![
% 3.74/1.50 X116:$i]:
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 in @
% 3.74/1.50 X116 @
% 3.74/1.50 X112 ) =>
% 3.74/1.50 (
% 3.74/1.50 in @
% 3.74/1.50 (
% 3.74/1.50 kpair @
% 3.74/1.50 X114 @
% 3.74/1.50 X116 ) @
% 3.74/1.50 (
% 3.74/1.50 powerset @
% 3.74/1.50 (
% 3.74/1.50 powerset @
% 3.74/1.50 (
% 3.74/1.50 binunion @
% 3.74/1.50 X110 @
% 3.74/1.50 X112 ) ) ) ) ) ) ) ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 cartprodpairin ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 cartprodmempair1 ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 cartprodmempair ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 setunionE2 ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 setunionsingleton1 ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 setunionsingleton2 ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 setunionsingleton ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 singletonprop ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 ex1E1 ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 ex1I ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 ex1I2 ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 singletonsuniq ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 setukpairinjL1 ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 kfstsingleton ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 theprop ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 kfstpairEq ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 cartprodfstin ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 setukpairinjL2 ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 setukpairinjL ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 setukpairinjR11 ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 setukpairinjR12 ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 setukpairinjR1 ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 upairequniteq ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 setukpairinjR2 ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 setukpairinjR ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 ksndsingleton ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 ksndpairEq ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 kpairsurjEq ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 cartprodsndin ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 cartprodpairmemEL ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 cartprodpairmemER ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 cartprodmempaircEq ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 cartprodfstpairEq ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 cartprodsndpairEq ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 cartprodpairsurjEq ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 dpsetconstrI ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 dpsetconstrSub ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 setOfPairsIsBReln ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 dpsetconstrERa ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 dpsetconstrEL1 ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 dpsetconstrEL2 ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 dpsetconstrER ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 funcImageSingleton ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 apProp ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 app ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 infuncsetfunc ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 ap2p ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 funcinfuncset ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 lamProp ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 lamp ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 lam2p ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 brelnall1 ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 brelnall2 ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 ex1E2 ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 funcGraphProp1 ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 funcGraphProp3 ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 funcGraphProp2 ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 funcextLem ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 funcGraphProp4 ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 subbreln ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 eqbreln ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 funcext ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 funcext2 ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 ap2apEq1 ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 ap2apEq2 ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 beta1 ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 eta1 ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 lam2lamEq ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 beta2 ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 eta2 ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 iffalseProp1 ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 iffalseProp2 ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 iftrueProp1 ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 iftrueProp2 ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 ifSingleton ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 ifp ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 theeq ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 iftrue ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 iffalse ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 iftrueorfalse ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 binintersectT_lem ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 ![
% 3.74/1.50 X118:$i,
% 3.74/1.50 X120:$i]:
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 in @
% 3.74/1.50 X120 @
% 3.74/1.50 (
% 3.74/1.50 powerset @
% 3.74/1.50 X118 ) ) =>
% 3.74/1.50 (
% 3.74/1.50 ![
% 3.74/1.50 X122:$i]:
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 in @
% 3.74/1.50 X122 @
% 3.74/1.50 (
% 3.74/1.50 powerset @
% 3.74/1.50 X118 ) ) =>
% 3.74/1.50 (
% 3.74/1.50 in @
% 3.74/1.50 (
% 3.74/1.50 binunion @
% 3.74/1.50 X120 @
% 3.74/1.50 X122 ) @
% 3.74/1.50 (
% 3.74/1.50 powerset @
% 3.74/1.50 X118 ) ) ) ) ) ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 ![
% 3.74/1.50 X124:$i,
% 3.74/1.50 X126:$i]:
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 in @
% 3.74/1.50 X126 @
% 3.74/1.50 (
% 3.74/1.50 powerset @
% 3.74/1.50 X124 ) ) =>
% 3.74/1.50 (
% 3.74/1.50 in @
% 3.74/1.50 (
% 3.74/1.50 powerset @
% 3.74/1.50 X126 ) @
% 3.74/1.50 (
% 3.74/1.50 powerset @
% 3.74/1.50 (
% 3.74/1.50 powerset @
% 3.74/1.50 X124 ) ) ) ) ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 setminusT_lem ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 complementT_lem ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 ![
% 3.74/1.50 X128:$i,
% 3.74/1.50 X130:$i]:
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 in @
% 3.74/1.50 X130 @
% 3.74/1.50 (
% 3.74/1.50 powerset @
% 3.74/1.50 X128 ) ) =>
% 3.74/1.50 (
% 3.74/1.50 ![
% 3.74/1.50 X132:$i]:
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 in @
% 3.74/1.50 X132 @
% 3.74/1.50 (
% 3.74/1.50 powerset @
% 3.74/1.50 X128 ) ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 ![
% 3.74/1.50 X134:$i]:
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 in @
% 3.74/1.50 X134 @
% 3.74/1.50 X128 ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 in @
% 3.74/1.50 X134 @
% 3.74/1.50 X130 ) =>
% 3.74/1.50 (
% 3.74/1.50 in @
% 3.74/1.50 X134 @
% 3.74/1.50 X132 ) ) ) ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 ![
% 3.74/1.50 X136:$i]:
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 in @
% 3.74/1.50 X136 @
% 3.74/1.50 X128 ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 in @
% 3.74/1.50 X136 @
% 3.74/1.50 X132 ) =>
% 3.74/1.50 (
% 3.74/1.50 in @
% 3.74/1.50 X136 @
% 3.74/1.50 X130 ) ) ) ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 X130 ) =
% 3.74/1.50 (
% 3.74/1.50 X132 ) ) ) ) ) ) ) ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 subsetTI ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 ![
% 3.74/1.50 X138:$i,
% 3.74/1.50 X140:$i]:
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 in @
% 3.74/1.50 X140 @
% 3.74/1.50 (
% 3.74/1.50 powerset @
% 3.74/1.50 X138 ) ) =>
% 3.74/1.50 (
% 3.74/1.50 ![
% 3.74/1.50 X142:$i]:
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 in @
% 3.74/1.50 X142 @
% 3.74/1.50 (
% 3.74/1.50 powerset @
% 3.74/1.50 X138 ) ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 ![
% 3.74/1.50 X144:$i]:
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 in @
% 3.74/1.50 X144 @
% 3.74/1.50 X138 ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 in @
% 3.74/1.50 X144 @
% 3.74/1.50 X140 ) =>
% 3.74/1.50 (
% 3.74/1.50 in @
% 3.74/1.50 X144 @
% 3.74/1.50 X142 ) ) ) ) =>
% 3.74/1.50 (
% 3.74/1.50 in @
% 3.74/1.50 X140 @
% 3.74/1.50 (
% 3.74/1.50 powerset @
% 3.74/1.50 X142 ) ) ) ) ) ) ) =>
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 ![
% 3.74/1.50 X146:$i,
% 3.74/1.50 X148:$i]:
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 in @
% 3.74/1.50 X148 @
% 3.74/1.50 (
% 3.74/1.50 powerset @
% 3.74/1.50 X146 ) ) =>
% 3.74/1.50 (
% 3.74/1.50 ![
% 3.74/1.50 X150:$i]:
% 3.74/1.50 (
% 3.74/1.50 (
% 3.74/1.50 in @
% 3.74/1.50 X150 @
% 3.74/1.50 (
% 3.74/1.50 powerset @
% 3.74/1.50 X146 ) ) =>
% 3.74/1.50 (
% 3.74/1.50 ![
% 3.74/1.51 X152:$i]:
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 in @
% 3.74/1.51 X152 @
% 3.74/1.51 X146 ) =>
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 in @
% 3.74/1.51 X148 @
% 3.74/1.51 (
% 3.74/1.51 powerset @
% 3.74/1.51 X150 ) ) =>
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 in @
% 3.74/1.51 X152 @
% 3.74/1.51 X148 ) =>
% 3.74/1.51 (
% 3.74/1.51 in @
% 3.74/1.51 X152 @
% 3.74/1.51 X150 ) ) ) ) ) ) ) ) ) =>
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 complementTI1 ) =>
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 complementTE1 ) =>
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 binintersectTELcontra ) =>
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 binintersectTERcontra ) =>
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 contrasubsetT ) =>
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 contrasubsetT1 ) =>
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 contrasubsetT2 ) =>
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 contrasubsetT3 ) =>
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 doubleComplementI1 ) =>
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 doubleComplementE1 ) =>
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 doubleComplementSub1 ) =>
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 doubleComplementSub2 ) =>
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 doubleComplementEq ) =>
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 complementTnotintersectT ) =>
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 complementImpComplementIntersect ) =>
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 complementSubsetComplementIntersect ) =>
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 complementInPowersetComplementIntersect ) =>
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 contraSubsetComplement ) =>
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 complementTcontraSubset ) =>
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 ![
% 3.74/1.51 X154:$i,
% 3.74/1.51 X156:$i]:
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 in @
% 3.74/1.51 X156 @
% 3.74/1.51 (
% 3.74/1.51 powerset @
% 3.74/1.51 X154 ) ) =>
% 3.74/1.51 (
% 3.74/1.51 ![
% 3.74/1.51 X158:$i]:
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 in @
% 3.74/1.51 X158 @
% 3.74/1.51 (
% 3.74/1.51 powerset @
% 3.74/1.51 X154 ) ) =>
% 3.74/1.51 (
% 3.74/1.51 ![
% 3.74/1.51 X160:$i]:
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 in @
% 3.74/1.51 X160 @
% 3.74/1.51 X154 ) =>
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 ~(
% 3.74/1.51 in @
% 3.74/1.51 X160 @
% 3.74/1.51 (
% 3.74/1.51 binunion
% 3.74/1.51 @
% 3.74/1.51 X156 @
% 3.74/1.51 X158 ) ) ) =>
% 3.74/1.51 (
% 3.74/1.51 ~(
% 3.74/1.51 in @
% 3.74/1.51 X160 @
% 3.74/1.51 X156 ) ) ) ) ) ) ) ) ) =>
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 ![
% 3.74/1.51 X162:$i,
% 3.74/1.51 X164:$i]:
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 in @
% 3.74/1.51 X164 @
% 3.74/1.51 (
% 3.74/1.51 powerset @
% 3.74/1.51 X162 ) ) =>
% 3.74/1.51 (
% 3.74/1.51 ![
% 3.74/1.51 X166:$i]:
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 in @
% 3.74/1.51 X166 @
% 3.74/1.51 (
% 3.74/1.51 powerset @
% 3.74/1.51 X162 ) ) =>
% 3.74/1.51 (
% 3.74/1.51 ![
% 3.74/1.51 X168:$i]:
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 in @
% 3.74/1.51 X168 @
% 3.74/1.51 X162 ) =>
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 ~(
% 3.74/1.51 in @
% 3.74/1.51 X168 @
% 3.74/1.51 (
% 3.74/1.51 binunion
% 3.74/1.51 @
% 3.74/1.51 X164 @
% 3.74/1.51 X166 ) ) ) =>
% 3.74/1.51 (
% 3.74/1.51 ~(
% 3.74/1.51 in @
% 3.74/1.51 X168 @
% 3.74/1.51 X166 ) ) ) ) ) ) ) ) ) =>
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 ![
% 3.74/1.51 X170:$i,
% 3.74/1.51 X172:$i]:
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 in @
% 3.74/1.51 X172 @
% 3.74/1.51 (
% 3.74/1.51 powerset @
% 3.74/1.51 X170 ) ) =>
% 3.74/1.51 (
% 3.74/1.51 ![
% 3.74/1.51 X174:$i]:
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 in @
% 3.74/1.51 X174 @
% 3.74/1.51 (
% 3.74/1.51 powerset @
% 3.74/1.51 X170 ) ) =>
% 3.74/1.51 (
% 3.74/1.51 ![
% 3.74/1.51 X176:$i]:
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 in @
% 3.74/1.51 X176 @
% 3.74/1.51 (
% 3.74/1.51 powerset @
% 3.74/1.51 X170 ) ) =>
% 3.74/1.51 (
% 3.74/1.51 ![
% 3.74/1.51 X178:$i]:
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 in @
% 3.74/1.51 X178 @
% 3.74/1.51 X170 ) =>
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 in @
% 3.74/1.51 X178 @
% 3.74/1.51 (
% 3.74/1.51 binintersect
% 3.74/1.51 @
% 3.74/1.51 X172 @
% 3.74/1.51 X174 ) ) =>
% 3.74/1.51 (
% 3.74/1.51 in @
% 3.74/1.51 X178 @
% 3.74/1.51 (
% 3.74/1.51 binunion @
% 3.74/1.51 X172 @
% 3.74/1.51 X176 ) ) ) ) ) ) ) ) ) ) ) =>
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 ![
% 3.74/1.51 X180:$i,
% 3.74/1.51 X182:$i]:
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 in @
% 3.74/1.51 X182 @
% 3.74/1.51 (
% 3.74/1.51 powerset @
% 3.74/1.51 X180 ) ) =>
% 3.74/1.51 (
% 3.74/1.51 ![
% 3.74/1.51 X184:$i]:
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 in @
% 3.74/1.51 X184 @
% 3.74/1.51 (
% 3.74/1.51 powerset @
% 3.74/1.51 X180 ) ) =>
% 3.74/1.51 (
% 3.74/1.51 ![
% 3.74/1.51 X186:$i]:
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 in @
% 3.74/1.51 X186 @
% 3.74/1.51 (
% 3.74/1.51 powerset @
% 3.74/1.51 X180 ) ) =>
% 3.74/1.51 (
% 3.74/1.51 ![
% 3.74/1.51 X188:$i]:
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 in @
% 3.74/1.51 X188 @
% 3.74/1.51 X180 ) =>
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 in @
% 3.74/1.51 X188 @
% 3.74/1.51 (
% 3.74/1.51 binintersect
% 3.74/1.51 @
% 3.74/1.51 X182 @
% 3.74/1.51 X184 ) ) =>
% 3.74/1.51 (
% 3.74/1.51 in @
% 3.74/1.51 X188 @
% 3.74/1.51 (
% 3.74/1.51 binunion @
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% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 ![
% 3.74/1.51 X190:$i,
% 3.74/1.51 X192:$i]:
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 in @
% 3.74/1.51 X192 @
% 3.74/1.51 (
% 3.74/1.51 powerset @
% 3.74/1.51 X190 ) ) =>
% 3.74/1.51 (
% 3.74/1.51 ![
% 3.74/1.51 X194:$i]:
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 in @
% 3.74/1.51 X194 @
% 3.74/1.51 (
% 3.74/1.51 powerset @
% 3.74/1.51 X190 ) ) =>
% 3.74/1.51 (
% 3.74/1.51 ![
% 3.74/1.51 X196:$i]:
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 in @
% 3.74/1.51 X196 @
% 3.74/1.51 (
% 3.74/1.51 powerset @
% 3.74/1.51 X190 ) ) =>
% 3.74/1.51 (
% 3.74/1.51 ![
% 3.74/1.51 X198:$i]:
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 in @
% 3.74/1.51 X198 @
% 3.74/1.51 X190 ) =>
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 in @
% 3.74/1.51 X198 @
% 3.74/1.51 (
% 3.74/1.51 binintersect
% 3.74/1.51 @
% 3.74/1.51 X192 @
% 3.74/1.51 X194 ) ) =>
% 3.74/1.51 (
% 3.74/1.51 in @
% 3.74/1.51 X198 @
% 3.74/1.51 (
% 3.74/1.51 binintersect
% 3.74/1.51 @
% 3.74/1.51 (
% 3.74/1.51 binunion @
% 3.74/1.51 X192 @
% 3.74/1.51 X196 ) @
% 3.74/1.51 (
% 3.74/1.51 binunion @
% 3.74/1.51 X194 @
% 3.74/1.51 X196 ) ) ) ) ) ) ) ) ) ) ) ) =>
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 ![
% 3.74/1.51 X200:$i,
% 3.74/1.51 X202:$i]:
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 in @
% 3.74/1.51 X202 @
% 3.74/1.51 (
% 3.74/1.51 powerset @
% 3.74/1.51 X200 ) ) =>
% 3.74/1.51 (
% 3.74/1.51 ![
% 3.74/1.51 X204:$i]:
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 in @
% 3.74/1.51 X204 @
% 3.74/1.51 (
% 3.74/1.51 powerset @
% 3.74/1.51 X200 ) ) =>
% 3.74/1.51 (
% 3.74/1.51 ![
% 3.74/1.51 X206:$i]:
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 in @
% 3.74/1.51 X206 @
% 3.74/1.51 (
% 3.74/1.51 powerset @
% 3.74/1.51 X200 ) ) =>
% 3.74/1.51 (
% 3.74/1.51 in @
% 3.74/1.51 (
% 3.74/1.51 binintersect
% 3.74/1.51 @
% 3.74/1.51 X202 @
% 3.74/1.51 X204 ) @
% 3.74/1.51 (
% 3.74/1.51 powerset @
% 3.74/1.51 (
% 3.74/1.51 binintersect
% 3.74/1.51 @
% 3.74/1.51 (
% 3.74/1.51 binunion @
% 3.74/1.51 X202 @
% 3.74/1.51 X206 ) @
% 3.74/1.51 (
% 3.74/1.51 binunion @
% 3.74/1.51 X204 @
% 3.74/1.51 X206 ) ) ) ) ) ) ) ) ) ) =>
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 ![
% 3.74/1.51 X208:$i,
% 3.74/1.51 X210:$i]:
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 in @
% 3.74/1.51 X210 @
% 3.74/1.51 (
% 3.74/1.51 powerset @
% 3.74/1.51 X208 ) ) =>
% 3.74/1.51 (
% 3.74/1.51 ![
% 3.74/1.51 X212:$i]:
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 in @
% 3.74/1.51 X212 @
% 3.74/1.51 (
% 3.74/1.51 powerset @
% 3.74/1.51 X208 ) ) =>
% 3.74/1.51 (
% 3.74/1.51 ![
% 3.74/1.51 X214:$i]:
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 in @
% 3.74/1.51 X214 @
% 3.74/1.51 X208 ) =>
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 in @
% 3.74/1.51 X214 @
% 3.74/1.51 (
% 3.74/1.51 setminus @
% 3.74/1.51 X208 @
% 3.74/1.51 (
% 3.74/1.51 binunion @
% 3.74/1.51 X210 @
% 3.74/1.51 X212 ) ) ) =>
% 3.74/1.51 (
% 3.74/1.51 ~(
% 3.74/1.51 in @
% 3.74/1.51 X214 @
% 3.74/1.51 X210 ) ) ) ) ) ) ) ) ) =>
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 ![
% 3.74/1.51 X216:$i,
% 3.74/1.51 X218:$i]:
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 in @
% 3.74/1.51 X218 @
% 3.74/1.51 (
% 3.74/1.51 powerset @
% 3.74/1.51 X216 ) ) =>
% 3.74/1.51 (
% 3.74/1.51 ![
% 3.74/1.51 X220:$i]:
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 in @
% 3.74/1.51 X220 @
% 3.74/1.51 (
% 3.74/1.51 powerset @
% 3.74/1.51 X216 ) ) =>
% 3.74/1.51 (
% 3.74/1.51 ![
% 3.74/1.51 X222:$i]:
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 in @
% 3.74/1.51 X222 @
% 3.74/1.51 X216 ) =>
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 in @
% 3.74/1.51 X222 @
% 3.74/1.51 (
% 3.74/1.51 setminus @
% 3.74/1.51 X216 @
% 3.74/1.51 (
% 3.74/1.51 binunion @
% 3.74/1.51 X218 @
% 3.74/1.51 X220 ) ) ) =>
% 3.74/1.51 (
% 3.74/1.51 in @
% 3.74/1.51 X222 @
% 3.74/1.51 (
% 3.74/1.51 setminus @
% 3.74/1.51 X216 @
% 3.74/1.51 X218 ) ) ) ) ) ) ) ) ) =>
% 3.74/1.51 (
% 3.74/1.51 ![
% 3.74/1.51 X224:$i,
% 3.74/1.51 X226:$i]:
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 in @
% 3.74/1.51 X226 @
% 3.74/1.51 (
% 3.74/1.51 powerset @
% 3.74/1.51 X224 ) ) =>
% 3.74/1.51 (
% 3.74/1.51 ![
% 3.74/1.51 X228:$i]:
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 in @
% 3.74/1.51 X228 @
% 3.74/1.51 (
% 3.74/1.51 powerset @
% 3.74/1.51 X224 ) ) =>
% 3.74/1.51 (
% 3.74/1.51 ![
% 3.74/1.51 X230:$o,
% 3.74/1.51 X232:$i]:
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 in @
% 3.74/1.51 X232 @
% 3.74/1.51 X224 ) =>
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 in @
% 3.74/1.51 X232 @
% 3.74/1.51 (
% 3.74/1.51 binunion @
% 3.74/1.51 X226 @
% 3.74/1.51 X228 ) ) =>
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 in @
% 3.74/1.51 X232 @
% 3.74/1.51 X226 ) =>
% 3.74/1.51 (
% 3.74/1.51 X230 ) ) =>
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 in @
% 3.74/1.51 X232 @
% 3.74/1.51 X228 ) =>
% 3.74/1.51 (
% 3.74/1.51 X230 ) ) =>
% 3.74/1.51 (
% 3.74/1.51 X230 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 3.74/1.51 thf(zf_stmt_4, negated_conjecture,
% 3.74/1.51 (~( ( setextAx ) =>
% 3.74/1.51 ( ( emptysetAx ) =>
% 3.74/1.51 ( ( setadjoinAx ) =>
% 3.74/1.51 ( ( ![X4:$i,X6:$i]:
% 3.74/1.51 ( ( in @ X6 @ ( powerset @ X4 ) ) <=>
% 3.74/1.51 ( ![X8:$i]: ( zip_tseitin_0 @ X8 @ X6 @ X4 ) ) ) ) =>
% 3.74/1.51 ( ( setunionAx ) =>
% 3.74/1.51 ( ( omega0Ax ) =>
% 3.74/1.51 ( ( omegaSAx ) =>
% 3.74/1.51 ( ( omegaIndAx ) =>
% 3.74/1.51 ( ( replAx ) =>
% 3.74/1.51 ( ( foundationAx ) =>
% 3.74/1.51 ( ( wellorderingAx ) =>
% 3.74/1.51 ( ( descrp ) =>
% 3.74/1.51 ( ( dsetconstrI ) =>
% 3.74/1.51 ( ( dsetconstrEL ) =>
% 3.74/1.51 ( ( dsetconstrER ) =>
% 3.74/1.51 ( ( exuE1 ) =>
% 3.74/1.51 ( ( prop2setE ) =>
% 3.74/1.51 ( ( emptysetE ) =>
% 3.74/1.51 ( ( emptysetimpfalse ) =>
% 3.74/1.51 ( ( notinemptyset ) =>
% 3.74/1.51 ( ( exuE3e ) =>
% 3.74/1.51 ( ( setext ) =>
% 3.74/1.51 ( ( emptyI ) =>
% 3.74/1.51 ( ( noeltsimpempty ) =>
% 3.74/1.51 ( ( setbeta ) =>
% 3.74/1.51 ( ( nonemptyE1 ) =>
% 3.74/1.51 ( ( nonemptyI ) =>
% 3.74/1.51 ( ( nonemptyI1 ) =>
% 3.74/1.51 ( ( setadjoinIL ) =>
% 3.74/1.51 ( ( emptyinunitempty ) =>
% 3.74/1.51 ( ( setadjoinIR ) =>
% 3.74/1.51 ( (
% 3.74/1.51 setadjoinE ) =>
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 setadjoinOr ) =>
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 setoftrueEq ) =>
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 ![
% 3.74/1.51 X10:$i,
% 3.74/1.51 X12:$i]:
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 ![
% 3.74/1.51 X14:$i]:
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 in @
% 3.74/1.51 X14 @ X12 ) =>
% 3.74/1.51 (
% 3.74/1.51 in @
% 3.74/1.51 X14 @ X10 ) ) ) =>
% 3.74/1.51 (
% 3.74/1.51 in @
% 3.74/1.51 X12 @
% 3.74/1.51 (
% 3.74/1.51 powerset
% 3.74/1.51 @
% 3.74/1.51 X10 ) ) ) ) =>
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 ![
% 3.74/1.51 X16:$i]:
% 3.74/1.51 (
% 3.74/1.51 in @
% 3.74/1.51 emptyset @
% 3.74/1.51 (
% 3.74/1.51 powerset
% 3.74/1.51 @
% 3.74/1.51 X16 ) ) ) =>
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 ![
% 3.74/1.51 X18:$i]:
% 3.74/1.51 (
% 3.74/1.51 in @
% 3.74/1.51 emptyset @
% 3.74/1.51 (
% 3.74/1.51 powerset
% 3.74/1.51 @
% 3.74/1.51 X18 ) ) ) =>
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 ![
% 3.74/1.51 X20:$i,
% 3.74/1.51 X22:$i,
% 3.74/1.51 X24:$i]:
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 in @
% 3.74/1.51 X22 @
% 3.74/1.51 (
% 3.74/1.51 powerset
% 3.74/1.51 @
% 3.74/1.51 X20 ) ) =>
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 in @
% 3.74/1.51 X24 @ X22 ) =>
% 3.74/1.51 (
% 3.74/1.51 in @
% 3.74/1.51 X24 @ X20 ) ) ) ) =>
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 setunionI ) =>
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 setunionE ) =>
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 subPowSU ) =>
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 exuE2 ) =>
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 nonemptyImpWitness ) =>
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 uniqinunit ) =>
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 notinsingleton ) =>
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 eqinunit ) =>
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 singletonsswitch ) =>
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 upairsetE ) =>
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 upairsetIL ) =>
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 upairsetIR ) =>
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 emptyE1 ) =>
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 vacuousDall ) =>
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 quantDeMorgan1 ) =>
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 quantDeMorgan2 ) =>
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 quantDeMorgan3 ) =>
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 quantDeMorgan4 ) =>
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 prop2setI ) =>
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 prop2set2propI ) =>
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 notdexE ) =>
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 notdallE ) =>
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 exuI1 ) =>
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 exuI3 ) =>
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 exuI2 ) =>
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 inCongP ) =>
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 in__Cong ) =>
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 exuE3u ) =>
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 exu__Cong ) =>
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 emptyset__Cong ) =>
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 setadjoin__Cong ) =>
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 ![
% 3.74/1.51 X26:$i,
% 3.74/1.51 X28:$i]:
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 X26 ) =
% 3.74/1.51 (
% 3.74/1.51 X28 ) ) =>
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 powerset
% 3.74/1.51 @
% 3.74/1.51 X26 ) =
% 3.74/1.51 (
% 3.74/1.51 powerset
% 3.74/1.51 @
% 3.74/1.51 X28 ) ) ) ) =>
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 setunion__Cong ) =>
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 omega__Cong ) =>
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 exuEu ) =>
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 descr__Cong ) =>
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 dsetconstr__Cong ) =>
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 subsetI1 ) =>
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 eqimpsubset2 ) =>
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 eqimpsubset1 ) =>
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 subsetI2 ) =>
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 emptysetsubset ) =>
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 subsetE ) =>
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 subsetE2 ) =>
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 notsubsetI ) =>
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 notequalI1 ) =>
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 notequalI2 ) =>
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 subsetRefl ) =>
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 subsetTrans ) =>
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 setadjoinSub ) =>
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 setadjoinSub2 ) =>
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 subset2powerset ) =>
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 setextsub ) =>
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 subsetemptysetimpeq ) =>
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 powersetI1 ) =>
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 powersetE1 ) =>
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 ![
% 3.74/1.51 X30:$i]:
% 3.74/1.51 (
% 3.74/1.51 in @
% 3.74/1.51 X30 @
% 3.74/1.51 (
% 3.74/1.51 powerset
% 3.74/1.51 @
% 3.74/1.51 X30 ) ) ) =>
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 powersetsubset ) =>
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 sepInPowerset ) =>
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 sepSubset ) =>
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 ![
% 3.74/1.51 X32:$i,
% 3.74/1.51 X34:$i,
% 3.74/1.51 X36:$i]:
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 in @
% 3.74/1.51 X36 @ X32 ) =>
% 3.74/1.51 (
% 3.74/1.51 in @
% 3.74/1.51 X36 @
% 3.74/1.51 (
% 3.74/1.51 binunion
% 3.74/1.51 @
% 3.74/1.51 X32 @ X34 ) ) ) ) =>
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 upairset2IR ) =>
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 ![
% 3.74/1.51 X38:$i,
% 3.74/1.51 X40:$i,
% 3.74/1.51 X42:$i]:
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 in @
% 3.74/1.51 X42 @ X40 ) =>
% 3.74/1.51 (
% 3.74/1.51 in @
% 3.74/1.51 X42 @
% 3.74/1.51 (
% 3.74/1.51 binunion
% 3.74/1.51 @
% 3.74/1.51 X38 @ X40 ) ) ) ) =>
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 ![
% 3.74/1.51 X44:$i,
% 3.74/1.51 X46:$i,
% 3.74/1.51 X48:$i,
% 3.74/1.51 X50:$o]:
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 in @
% 3.74/1.51 X48 @
% 3.74/1.51 (
% 3.74/1.51 binunion
% 3.74/1.51 @
% 3.74/1.51 X44 @ X46 ) ) =>
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 in @
% 3.74/1.51 X48 @ X44 ) =>
% 3.74/1.51 (
% 3.74/1.51 X50 ) ) =>
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 in @
% 3.74/1.51 X48 @ X46 ) =>
% 3.74/1.51 (
% 3.74/1.51 X50 ) ) =>
% 3.74/1.51 (
% 3.74/1.51 X50 ) ) ) ) ) =>
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 ![
% 3.74/1.51 X52:$i,
% 3.74/1.51 X54:$i,
% 3.74/1.51 X56:$i]:
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 in @
% 3.74/1.51 X56 @
% 3.74/1.51 (
% 3.74/1.51 binunion
% 3.74/1.51 @
% 3.74/1.51 X52 @ X54 ) ) =>
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 in @
% 3.74/1.51 X56 @ X52 ) |
% 3.74/1.51 (
% 3.74/1.51 in @
% 3.74/1.51 X56 @ X54 ) ) ) ) =>
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 ![
% 3.74/1.51 X58:$i,
% 3.74/1.51 X60:$i]:
% 3.74/1.51 (
% 3.74/1.51 subset @
% 3.74/1.51 X58 @
% 3.74/1.51 (
% 3.74/1.51 binunion
% 3.74/1.51 @
% 3.74/1.51 X58 @ X60 ) ) ) =>
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 ![
% 3.74/1.51 X62:$i,
% 3.74/1.51 X64:$i]:
% 3.74/1.51 (
% 3.74/1.51 subset @
% 3.74/1.51 X64 @
% 3.74/1.51 (
% 3.74/1.51 binunion
% 3.74/1.51 @
% 3.74/1.51 X62 @ X64 ) ) ) =>
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 binintersectI ) =>
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 binintersectSubset5 ) =>
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 binintersectEL ) =>
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 binintersectLsub ) =>
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 binintersectSubset2 ) =>
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 binintersectSubset3 ) =>
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 binintersectER ) =>
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 disjointsetsI1 ) =>
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 binintersectRsub ) =>
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 binintersectSubset4 ) =>
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 binintersectSubset1 ) =>
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 ![
% 3.74/1.51 X66:$i,
% 3.74/1.51 X68:$i,
% 3.74/1.51 X70:$i]:
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 binintersect
% 3.74/1.51 @
% 3.74/1.51 X66 @
% 3.74/1.51 (
% 3.74/1.51 binunion
% 3.74/1.51 @
% 3.74/1.51 X68 @ X70 ) ) =
% 3.74/1.51 (
% 3.74/1.51 binunion
% 3.74/1.51 @
% 3.74/1.51 (
% 3.74/1.51 binintersect
% 3.74/1.51 @
% 3.74/1.51 X66 @ X68 ) @
% 3.74/1.51 (
% 3.74/1.51 binintersect
% 3.74/1.51 @
% 3.74/1.51 X66 @ X70 ) ) ) ) =>
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 setminusI ) =>
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 setminusEL ) =>
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 setminusER ) =>
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 setminusSubset2 ) =>
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 setminusERneg ) =>
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 setminusELneg ) =>
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 setminusILneg ) =>
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 setminusIRneg ) =>
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 setminusLsub ) =>
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 setminusSubset1 ) =>
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 symdiffE ) =>
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 symdiffI1 ) =>
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 symdiffI2 ) =>
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 symdiffIneg1 ) =>
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 symdiffIneg2 ) =>
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 secondinupair ) =>
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 setukpairIL ) =>
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 setukpairIR ) =>
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 kpairiskpair ) =>
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 kpairp ) =>
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 singletonsubset ) =>
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 singletoninpowerset ) =>
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 ![
% 3.74/1.51 X72:$i,
% 3.74/1.51 X74:$i,
% 3.74/1.51 X76:$i]:
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 in @
% 3.74/1.51 X76 @ X72 ) =>
% 3.74/1.51 (
% 3.74/1.51 in @
% 3.74/1.51 (
% 3.74/1.51 setadjoin
% 3.74/1.51 @
% 3.74/1.51 X76 @
% 3.74/1.51 emptyset ) @
% 3.74/1.51 (
% 3.74/1.51 powerset
% 3.74/1.51 @
% 3.74/1.51 (
% 3.74/1.51 binunion
% 3.74/1.51 @
% 3.74/1.51 X72 @ X74 ) ) ) ) ) =>
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 upairset2E ) =>
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 ![
% 3.74/1.51 X78:$i,
% 3.74/1.51 X80:$i,
% 3.74/1.51 X82:$i]:
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 in @
% 3.74/1.51 X82 @ X78 ) =>
% 3.74/1.51 (
% 3.74/1.51 ![
% 3.74/1.51 X84:$i]:
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 in @
% 3.74/1.51 X84 @ X80 ) =>
% 3.74/1.51 (
% 3.74/1.51 subset @
% 3.74/1.51 (
% 3.74/1.51 setadjoin
% 3.74/1.51 @
% 3.74/1.51 X82 @
% 3.74/1.51 (
% 3.74/1.51 setadjoin
% 3.74/1.51 @
% 3.74/1.51 X84 @
% 3.74/1.51 emptyset ) ) @
% 3.74/1.51 (
% 3.74/1.51 binunion
% 3.74/1.51 @
% 3.74/1.51 X78 @ X80 ) ) ) ) ) ) =>
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 ![
% 3.74/1.51 X86:$i,
% 3.74/1.51 X88:$i,
% 3.74/1.51 X90:$i]:
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 in @
% 3.74/1.51 X90 @ X86 ) =>
% 3.74/1.51 (
% 3.74/1.51 ![
% 3.74/1.51 X92:$i]:
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 in @
% 3.74/1.51 X92 @ X88 ) =>
% 3.74/1.51 (
% 3.74/1.51 in @
% 3.74/1.51 (
% 3.74/1.51 setadjoin
% 3.74/1.51 @
% 3.74/1.51 X90 @
% 3.74/1.51 (
% 3.74/1.51 setadjoin
% 3.74/1.51 @
% 3.74/1.51 X92 @
% 3.74/1.51 emptyset ) ) @
% 3.74/1.51 (
% 3.74/1.51 powerset
% 3.74/1.51 @
% 3.74/1.51 (
% 3.74/1.51 binunion
% 3.74/1.51 @
% 3.74/1.51 X86 @ X88 ) ) ) ) ) ) ) =>
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 ![
% 3.74/1.51 X94:$i,
% 3.74/1.51 X96:$i,
% 3.74/1.51 X98:$i]:
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 in @
% 3.74/1.51 X98 @ X94 ) =>
% 3.74/1.51 (
% 3.74/1.51 ![
% 3.74/1.51 X100:$i]:
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 in @
% 3.74/1.51 X100 @
% 3.74/1.51 X96 ) =>
% 3.74/1.51 (
% 3.74/1.51 subset @
% 3.74/1.51 (
% 3.74/1.51 setadjoin
% 3.74/1.51 @
% 3.74/1.51 (
% 3.74/1.51 setadjoin
% 3.74/1.51 @
% 3.74/1.51 X98 @
% 3.74/1.51 emptyset ) @
% 3.74/1.51 (
% 3.74/1.51 setadjoin
% 3.74/1.51 @
% 3.74/1.51 (
% 3.74/1.51 setadjoin
% 3.74/1.51 @
% 3.74/1.51 X98 @
% 3.74/1.51 (
% 3.74/1.51 setadjoin
% 3.74/1.51 @
% 3.74/1.51 X100 @
% 3.74/1.51 emptyset ) ) @
% 3.74/1.51 emptyset ) ) @
% 3.74/1.51 (
% 3.74/1.51 powerset
% 3.74/1.51 @
% 3.74/1.51 (
% 3.74/1.51 binunion
% 3.74/1.51 @
% 3.74/1.51 X94 @ X96 ) ) ) ) ) ) ) =>
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 ![
% 3.74/1.51 X102:$i,
% 3.74/1.51 X104:$i,
% 3.74/1.51 X106:$i]:
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 in @
% 3.74/1.51 X106 @
% 3.74/1.51 X102 ) =>
% 3.74/1.51 (
% 3.74/1.51 ![
% 3.74/1.51 X108:$i]:
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.51 in @
% 3.74/1.51 X108 @
% 3.74/1.51 X104 ) =>
% 3.74/1.51 (
% 3.74/1.51 in @
% 3.74/1.51 (
% 3.74/1.51 setadjoin
% 3.74/1.51 @
% 3.74/1.51 (
% 3.74/1.51 setadjoin
% 3.74/1.51 @
% 3.74/1.51 X106 @
% 3.74/1.51 emptyset ) @
% 3.74/1.51 (
% 3.74/1.51 setadjoin
% 3.74/1.51 @
% 3.74/1.51 (
% 3.74/1.51 setadjoin
% 3.74/1.51 @
% 3.74/1.51 X106 @
% 3.74/1.51 (
% 3.74/1.51 setadjoin
% 3.74/1.51 @
% 3.74/1.51 X108 @
% 3.74/1.51 emptyset ) ) @
% 3.74/1.51 emptyset ) ) @
% 3.74/1.51 (
% 3.74/1.51 powerset
% 3.74/1.51 @
% 3.74/1.51 (
% 3.74/1.51 powerset
% 3.74/1.51 @
% 3.74/1.51 (
% 3.74/1.51 binunion
% 3.74/1.51 @
% 3.74/1.51 X102 @
% 3.74/1.51 X104 ) ) ) ) ) ) ) ) =>
% 3.74/1.51 (
% 3.74/1.51 (
% 3.74/1.52 ![
% 3.74/1.52 X110:$i,
% 3.74/1.52 X112:$i,
% 3.74/1.52 X114:$i]:
% 3.74/1.52 (
% 3.74/1.52 (
% 3.74/1.52 in @
% 3.74/1.52 X114 @
% 3.74/1.52 X110 ) =>
% 3.74/1.52 (
% 3.74/1.52 ![
% 3.74/1.52 X116:$i]:
% 3.74/1.52 (
% 3.74/1.52 (
% 3.74/1.52 in @
% 3.74/1.52 X116 @
% 3.74/1.52 X112 ) =>
% 3.74/1.52 (
% 3.74/1.52 in @
% 3.74/1.52 (
% 3.74/1.52 kpair @
% 3.74/1.52 X114 @
% 3.74/1.52 X116 ) @
% 3.74/1.52 (
% 3.74/1.52 powerset
% 3.74/1.52 @
% 3.74/1.52 (
% 3.74/1.52 powerset
% 3.74/1.52 @
% 3.74/1.52 (
% 3.74/1.52 binunion
% 3.74/1.52 @
% 3.74/1.52 X110 @
% 3.74/1.52 X112 ) ) ) ) ) ) ) ) =>
% 3.74/1.52 (
% 3.74/1.52 (
% 3.74/1.52 cartprodpairin ) =>
% 3.74/1.52 (
% 3.74/1.52 (
% 3.74/1.52 cartprodmempair1 ) =>
% 3.74/1.52 (
% 3.74/1.52 (
% 3.74/1.52 cartprodmempair ) =>
% 3.74/1.52 (
% 3.74/1.52 (
% 3.74/1.52 setunionE2 ) =>
% 3.74/1.52 (
% 3.74/1.52 (
% 3.74/1.52 setunionsingleton1 ) =>
% 3.74/1.52 (
% 3.74/1.52 (
% 3.74/1.52 setunionsingleton2 ) =>
% 3.74/1.52 (
% 3.74/1.52 (
% 3.74/1.52 setunionsingleton ) =>
% 3.74/1.52 (
% 3.74/1.52 (
% 3.74/1.52 singletonprop ) =>
% 3.74/1.52 (
% 3.74/1.52 (
% 3.74/1.52 ex1E1 ) =>
% 3.74/1.52 (
% 3.74/1.52 (
% 3.74/1.52 ex1I ) =>
% 3.74/1.52 (
% 3.74/1.52 (
% 3.74/1.52 ex1I2 ) =>
% 3.74/1.52 (
% 3.74/1.52 (
% 3.74/1.52 singletonsuniq ) =>
% 3.74/1.52 (
% 3.74/1.52 (
% 3.74/1.52 setukpairinjL1 ) =>
% 3.74/1.52 (
% 3.74/1.52 (
% 3.74/1.52 kfstsingleton ) =>
% 3.74/1.52 (
% 3.74/1.52 (
% 3.74/1.52 theprop ) =>
% 3.74/1.52 (
% 3.74/1.52 (
% 3.74/1.52 kfstpairEq ) =>
% 3.74/1.52 (
% 3.74/1.52 (
% 3.74/1.52 cartprodfstin ) =>
% 3.74/1.52 (
% 3.74/1.52 (
% 3.74/1.52 setukpairinjL2 ) =>
% 3.74/1.52 (
% 3.74/1.52 (
% 3.74/1.52 setukpairinjL ) =>
% 3.74/1.52 (
% 3.74/1.52 (
% 3.74/1.52 setukpairinjR11 ) =>
% 3.74/1.52 (
% 3.74/1.52 (
% 3.74/1.52 setukpairinjR12 ) =>
% 3.74/1.52 (
% 3.74/1.52 (
% 3.74/1.52 setukpairinjR1 ) =>
% 3.74/1.52 (
% 3.74/1.52 (
% 3.74/1.52 upairequniteq ) =>
% 3.74/1.52 (
% 3.74/1.52 (
% 3.74/1.52 setukpairinjR2 ) =>
% 3.74/1.52 (
% 3.74/1.52 (
% 3.74/1.52 setukpairinjR ) =>
% 3.74/1.52 (
% 3.74/1.52 (
% 3.74/1.52 ksndsingleton ) =>
% 3.74/1.52 (
% 3.74/1.52 (
% 3.74/1.52 ksndpairEq ) =>
% 3.74/1.52 (
% 3.74/1.52 (
% 3.74/1.52 kpairsurjEq ) =>
% 3.74/1.52 (
% 3.74/1.52 (
% 3.74/1.52 cartprodsndin ) =>
% 3.74/1.52 (
% 3.74/1.52 (
% 3.74/1.52 cartprodpairmemEL ) =>
% 3.74/1.52 (
% 3.74/1.52 (
% 3.74/1.52 cartprodpairmemER ) =>
% 3.74/1.52 (
% 3.74/1.52 (
% 3.74/1.52 cartprodmempaircEq ) =>
% 3.74/1.52 (
% 3.74/1.52 (
% 3.74/1.52 cartprodfstpairEq ) =>
% 3.74/1.52 (
% 3.74/1.52 (
% 3.74/1.52 cartprodsndpairEq ) =>
% 3.74/1.52 (
% 3.74/1.52 (
% 3.74/1.52 cartprodpairsurjEq ) =>
% 3.74/1.52 (
% 3.74/1.52 (
% 3.74/1.52 dpsetconstrI ) =>
% 3.74/1.52 (
% 3.74/1.52 (
% 3.74/1.52 dpsetconstrSub ) =>
% 3.74/1.52 (
% 3.74/1.52 (
% 3.74/1.52 setOfPairsIsBReln ) =>
% 3.74/1.52 (
% 3.74/1.52 (
% 3.74/1.52 dpsetconstrERa ) =>
% 3.74/1.52 (
% 3.74/1.52 (
% 3.74/1.52 dpsetconstrEL1 ) =>
% 3.74/1.52 (
% 3.74/1.52 (
% 3.74/1.52 dpsetconstrEL2 ) =>
% 3.74/1.52 (
% 3.74/1.52 (
% 3.74/1.52 dpsetconstrER ) =>
% 3.74/1.52 (
% 3.74/1.52 (
% 3.74/1.52 funcImageSingleton ) =>
% 3.74/1.52 (
% 3.74/1.52 (
% 3.74/1.52 apProp ) =>
% 3.74/1.52 (
% 3.74/1.52 (
% 3.74/1.52 app ) =>
% 3.74/1.52 (
% 3.74/1.52 (
% 3.74/1.52 infuncsetfunc ) =>
% 3.74/1.52 (
% 3.74/1.52 (
% 3.74/1.52 ap2p ) =>
% 3.74/1.52 (
% 3.74/1.52 (
% 3.74/1.52 funcinfuncset ) =>
% 3.74/1.52 (
% 3.74/1.52 (
% 3.74/1.52 lamProp ) =>
% 3.74/1.52 (
% 3.74/1.52 (
% 3.74/1.52 lamp ) =>
% 3.74/1.52 (
% 3.74/1.52 (
% 3.74/1.52 lam2p ) =>
% 3.74/1.52 (
% 3.74/1.52 (
% 3.74/1.52 brelnall1 ) =>
% 3.74/1.52 (
% 3.74/1.52 (
% 3.74/1.52 brelnall2 ) =>
% 3.74/1.52 (
% 3.74/1.52 (
% 3.74/1.52 ex1E2 ) =>
% 3.74/1.52 (
% 3.74/1.52 (
% 3.74/1.52 funcGraphProp1 ) =>
% 3.74/1.52 (
% 3.74/1.52 (
% 3.74/1.52 funcGraphProp3 ) =>
% 3.74/1.52 (
% 3.74/1.52 (
% 3.74/1.52 funcGraphProp2 ) =>
% 3.74/1.52 (
% 3.74/1.52 (
% 3.74/1.52 funcextLem ) =>
% 3.74/1.52 (
% 3.74/1.52 (
% 3.74/1.52 funcGraphProp4 ) =>
% 3.74/1.52 (
% 3.74/1.52 (
% 3.74/1.52 subbreln ) =>
% 3.74/1.52 (
% 3.74/1.52 (
% 3.74/1.52 eqbreln ) =>
% 3.74/1.52 (
% 3.74/1.52 (
% 3.74/1.52 funcext ) =>
% 3.74/1.52 (
% 3.74/1.52 (
% 3.74/1.52 funcext2 ) =>
% 3.74/1.52 (
% 3.74/1.52 (
% 3.74/1.52 ap2apEq1 ) =>
% 3.74/1.52 (
% 3.74/1.52 (
% 3.74/1.52 ap2apEq2 ) =>
% 3.74/1.52 (
% 3.74/1.52 (
% 3.74/1.52 beta1 ) =>
% 3.74/1.52 (
% 3.74/1.52 (
% 3.74/1.52 eta1 ) =>
% 3.74/1.52 (
% 3.74/1.52 (
% 3.74/1.52 lam2lamEq ) =>
% 3.74/1.52 (
% 3.74/1.52 (
% 3.74/1.52 beta2 ) =>
% 3.74/1.52 (
% 3.74/1.52 (
% 3.74/1.52 eta2 ) =>
% 3.74/1.52 (
% 3.74/1.52 (
% 3.74/1.52 iffalseProp1 ) =>
% 3.74/1.52 (
% 3.74/1.52 (
% 3.74/1.52 iffalseProp2 ) =>
% 3.74/1.52 (
% 3.74/1.52 (
% 3.74/1.52 iftrueProp1 ) =>
% 3.74/1.52 (
% 3.74/1.52 (
% 3.74/1.52 iftrueProp2 ) =>
% 3.74/1.52 (
% 3.74/1.52 (
% 3.74/1.52 ifSingleton ) =>
% 3.74/1.52 (
% 3.74/1.52 (
% 3.74/1.52 ifp ) =>
% 3.74/1.52 (
% 3.74/1.52 (
% 3.74/1.52 theeq ) =>
% 3.74/1.52 (
% 3.74/1.52 (
% 3.74/1.52 iftrue ) =>
% 3.74/1.52 (
% 3.74/1.52 (
% 3.74/1.52 iffalse ) =>
% 3.74/1.52 (
% 3.74/1.52 (
% 3.74/1.52 iftrueorfalse ) =>
% 3.74/1.52 (
% 3.74/1.52 (
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% 3.74/1.52 (
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% 3.74/1.52 X118:$i,
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% 3.74/1.52 (
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% 3.74/1.52 (
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% 3.74/1.52 (
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% 3.74/1.52 (
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% 3.74/1.52 (
% 3.74/1.52 (
% 3.74/1.52 setminusT_lem ) =>
% 3.74/1.52 (
% 3.74/1.52 (
% 3.74/1.52 complementT_lem ) =>
% 3.74/1.52 (
% 3.74/1.52 (
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% 3.74/1.52 (
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% 3.74/1.52 X138:$i,
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% 3.74/1.52 (
% 3.74/1.52 (
% 3.74/1.52 complementTI1 ) =>
% 3.74/1.52 (
% 3.74/1.52 (
% 3.74/1.52 complementTE1 ) =>
% 3.74/1.52 (
% 3.74/1.52 (
% 3.74/1.52 binintersectTELcontra ) =>
% 3.74/1.52 (
% 3.74/1.52 (
% 3.74/1.52 binintersectTERcontra ) =>
% 3.74/1.52 (
% 3.74/1.52 (
% 3.74/1.52 contrasubsetT ) =>
% 3.74/1.52 (
% 3.74/1.52 (
% 3.74/1.52 contrasubsetT1 ) =>
% 3.74/1.52 (
% 3.74/1.52 (
% 3.74/1.52 contrasubsetT2 ) =>
% 3.74/1.52 (
% 3.99/1.52 (
% 3.99/1.52 contrasubsetT3 ) =>
% 3.99/1.52 (
% 3.99/1.52 (
% 3.99/1.52 doubleComplementI1 ) =>
% 3.99/1.52 (
% 3.99/1.52 (
% 3.99/1.52 doubleComplementE1 ) =>
% 3.99/1.52 (
% 3.99/1.52 (
% 3.99/1.52 doubleComplementSub1 ) =>
% 3.99/1.52 (
% 3.99/1.52 (
% 3.99/1.52 doubleComplementSub2 ) =>
% 3.99/1.52 (
% 3.99/1.52 (
% 3.99/1.52 doubleComplementEq ) =>
% 3.99/1.52 (
% 3.99/1.52 (
% 3.99/1.52 complementTnotintersectT ) =>
% 3.99/1.52 (
% 3.99/1.52 (
% 3.99/1.52 complementImpComplementIntersect ) =>
% 3.99/1.52 (
% 3.99/1.52 (
% 3.99/1.52 complementSubsetComplementIntersect ) =>
% 3.99/1.52 (
% 3.99/1.52 (
% 3.99/1.52 complementInPowersetComplementIntersect ) =>
% 3.99/1.52 (
% 3.99/1.52 (
% 3.99/1.52 contraSubsetComplement ) =>
% 3.99/1.52 (
% 3.99/1.52 (
% 3.99/1.52 complementTcontraSubset ) =>
% 3.99/1.52 (
% 3.99/1.52 (
% 3.99/1.52 ![
% 3.99/1.52 X154:$i,
% 3.99/1.52 X156:$i]:
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% 3.99/1.52 (
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% 3.99/1.52 X210 @
% 3.99/1.52 (
% 3.99/1.52 powerset
% 3.99/1.52 @
% 3.99/1.52 X208 ) ) =>
% 3.99/1.52 (
% 3.99/1.52 ![
% 3.99/1.52 X212:$i]:
% 3.99/1.52 (
% 3.99/1.52 (
% 3.99/1.52 in @
% 3.99/1.52 X212 @
% 3.99/1.52 (
% 3.99/1.52 powerset
% 3.99/1.52 @
% 3.99/1.52 X208 ) ) =>
% 3.99/1.52 (
% 3.99/1.52 ![
% 3.99/1.52 X214:$i]:
% 3.99/1.52 (
% 3.99/1.52 (
% 3.99/1.52 in @
% 3.99/1.52 X214 @
% 3.99/1.52 X208 ) =>
% 3.99/1.52 (
% 3.99/1.52 (
% 3.99/1.52 in @
% 3.99/1.52 X214 @
% 3.99/1.52 (
% 3.99/1.52 setminus
% 3.99/1.52 @
% 3.99/1.52 X208 @
% 3.99/1.52 (
% 3.99/1.52 binunion
% 3.99/1.52 @
% 3.99/1.52 X210 @
% 3.99/1.52 X212 ) ) ) =>
% 3.99/1.52 (
% 3.99/1.52 ~
% 3.99/1.52 (
% 3.99/1.52 in @
% 3.99/1.52 X214 @
% 3.99/1.52 X210 ) ) ) ) ) ) ) ) ) =>
% 3.99/1.52 (
% 3.99/1.52 (
% 3.99/1.52 ![
% 3.99/1.52 X216:$i,
% 3.99/1.52 X218:$i]:
% 3.99/1.52 (
% 3.99/1.52 (
% 3.99/1.52 in @
% 3.99/1.52 X218 @
% 3.99/1.52 (
% 3.99/1.52 powerset
% 3.99/1.52 @
% 3.99/1.52 X216 ) ) =>
% 3.99/1.52 (
% 3.99/1.52 ![
% 3.99/1.52 X220:$i]:
% 3.99/1.52 (
% 3.99/1.52 (
% 3.99/1.52 in @
% 3.99/1.52 X220 @
% 3.99/1.52 (
% 3.99/1.52 powerset
% 3.99/1.52 @
% 3.99/1.52 X216 ) ) =>
% 3.99/1.52 (
% 3.99/1.52 ![
% 3.99/1.52 X222:$i]:
% 3.99/1.52 (
% 3.99/1.52 (
% 3.99/1.52 in @
% 3.99/1.52 X222 @
% 3.99/1.52 X216 ) =>
% 3.99/1.52 (
% 3.99/1.52 (
% 3.99/1.52 in @
% 3.99/1.52 X222 @
% 3.99/1.52 (
% 3.99/1.52 setminus
% 3.99/1.52 @
% 3.99/1.52 X216 @
% 3.99/1.52 (
% 3.99/1.52 binunion
% 3.99/1.52 @
% 3.99/1.52 X218 @
% 3.99/1.52 X220 ) ) ) =>
% 3.99/1.52 (
% 3.99/1.52 in @
% 3.99/1.52 X222 @
% 3.99/1.52 (
% 3.99/1.52 setminus
% 3.99/1.52 @
% 3.99/1.52 X216 @
% 3.99/1.52 X218 ) ) ) ) ) ) ) ) ) =>
% 3.99/1.52 (
% 3.99/1.52 ![
% 3.99/1.52 X224:$i,
% 3.99/1.52 X226:$i]:
% 3.99/1.52 (
% 3.99/1.52 (
% 3.99/1.52 in @
% 3.99/1.52 X226 @
% 3.99/1.52 (
% 3.99/1.52 powerset
% 3.99/1.52 @
% 3.99/1.52 X224 ) ) =>
% 3.99/1.52 (
% 3.99/1.52 ![
% 3.99/1.52 X228:$i]:
% 3.99/1.52 (
% 3.99/1.52 (
% 3.99/1.52 in @
% 3.99/1.52 X228 @
% 3.99/1.52 (
% 3.99/1.52 powerset
% 3.99/1.52 @
% 3.99/1.52 X224 ) ) =>
% 3.99/1.52 (
% 3.99/1.52 ![
% 3.99/1.52 X230:$o,
% 3.99/1.52 X232:$i]:
% 3.99/1.52 (
% 3.99/1.52 (
% 3.99/1.52 in @
% 3.99/1.52 X232 @
% 3.99/1.52 X224 ) =>
% 3.99/1.52 (
% 3.99/1.52 (
% 3.99/1.52 in @
% 3.99/1.52 X232 @
% 3.99/1.52 (
% 3.99/1.52 binunion
% 3.99/1.52 @
% 3.99/1.52 X226 @
% 3.99/1.52 X228 ) ) =>
% 3.99/1.52 (
% 3.99/1.52 (
% 3.99/1.52 (
% 3.99/1.52 in @
% 3.99/1.52 X232 @
% 3.99/1.52 X226 ) =>
% 3.99/1.52 (
% 3.99/1.52 X230 ) ) =>
% 3.99/1.52 (
% 3.99/1.52 (
% 3.99/1.52 (
% 3.99/1.52 in @
% 3.99/1.52 X232 @
% 3.99/1.52 X228 ) =>
% 3.99/1.52 (
% 3.99/1.52 X230 ) ) =>
% 3.99/1.52 (
% 3.99/1.52 X230 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )),
% 3.99/1.52 inference('cnf.neg', [status(esa)], [zf_stmt_3])).
% 3.99/1.52 thf(zip_derived_cl139, plain, (( (sk__118) | ~ (in @ sk__119 @ sk__117))),
% 3.99/1.52 inference('cnf', [status(esa)], [zf_stmt_4])).
% 3.99/1.52 thf(zip_derived_cl136, plain, (~ (sk__118)),
% 3.99/1.52 inference('cnf', [status(esa)], [zf_stmt_4])).
% 3.99/1.52 thf(zip_derived_cl324, plain, (~ (in @ sk__119 @ sk__117)),
% 3.99/1.52 inference('demod', [status(thm)], [zip_derived_cl139, zip_derived_cl136])).
% 3.99/1.52 thf(zip_derived_cl140, plain,
% 3.99/1.52 ( (in @ sk__119 @ (binunion @ sk__116 @ sk__117))),
% 3.99/1.52 inference('cnf', [status(esa)], [zf_stmt_4])).
% 3.99/1.52 thf(zip_derived_cl55, plain,
% 3.99/1.52 (![X10 : $i, X11 : $i, X12 : $i]:
% 3.99/1.52 ( (in @ X10 @ X11)
% 3.99/1.52 | (in @ X10 @ X12)
% 3.99/1.52 | ~ (in @ X10 @ (binunion @ X12 @ X11)))),
% 3.99/1.52 inference('cnf', [status(esa)], [zf_stmt_4])).
% 3.99/1.52 thf(zip_derived_cl327, plain,
% 3.99/1.52 (( (in @ sk__119 @ sk__116) | (in @ sk__119 @ sk__117))),
% 3.99/1.52 inference('sup-', [status(thm)], [zip_derived_cl140, zip_derived_cl55])).
% 3.99/1.52 thf(zip_derived_cl138, plain, (( (sk__118) | ~ (in @ sk__119 @ sk__116))),
% 3.99/1.52 inference('cnf', [status(esa)], [zf_stmt_4])).
% 3.99/1.52 thf(zip_derived_cl136, plain, (~ (sk__118)),
% 3.99/1.52 inference('cnf', [status(esa)], [zf_stmt_4])).
% 3.99/1.52 thf(zip_derived_cl323, plain, (~ (in @ sk__119 @ sk__116)),
% 3.99/1.52 inference('demod', [status(thm)], [zip_derived_cl138, zip_derived_cl136])).
% 3.99/1.52 thf(zip_derived_cl329, plain, ( (in @ sk__119 @ sk__117)),
% 3.99/1.52 inference('demod', [status(thm)], [zip_derived_cl327, zip_derived_cl323])).
% 3.99/1.52 thf(zip_derived_cl331, plain, ($false),
% 3.99/1.52 inference('demod', [status(thm)], [zip_derived_cl324, zip_derived_cl329])).
% 3.99/1.52
% 3.99/1.52 % SZS output end Refutation
% 3.99/1.52
% 3.99/1.52
% 3.99/1.52 % Terminating...
% 4.18/1.69 % Runner terminated.
% 4.18/1.70 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------