%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SEU739^1 : 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.Znwb5TDtFu true
% Computer : n019.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 04:56:03 PM UTC 2025
% Result : Theorem 2.45s 1.16s
% Output : Refutation 2.45s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.14 % Problem : SEU739^1 : TPTP v9.2.0. Released v3.7.0.
% 0.02/0.15 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.Znwb5TDtFu true
% 0.11/0.36 % Computer : n019.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8042.1875MB
% 0.11/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Wed Oct 1 16:02:23 EDT 2025
% 0.11/0.36 % CPUTime :
% 0.11/0.36 % Running portfolio for 300 s
% 0.11/0.36 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.37 % Number of cores: 8
% 0.11/0.37 % Python version: Python 3.6.8
% 0.11/0.37 % Running in HO mode
% 0.51/0.69 % Total configuration time : 828
% 0.51/0.69 % Estimated wc time : 1656
% 0.51/0.69 % Estimated cpu time (8 cpus) : 207.0
% 0.51/0.80 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
% 0.51/0.84 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.51/0.84 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
% 0.52/0.85 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
% 0.52/0.89 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s
% 0.52/0.89 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s
% 0.52/0.97 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.53/0.99 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s
% 2.45/1.16 % Solved by lams/40_c_ic.sh.
% 2.45/1.16 % done 240 iterations in 0.176s
% 2.45/1.16 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 2.45/1.16 % SZS output start Refutation
% 2.45/1.16 thf(setadjoinAx_type, type, setadjoinAx: $o).
% 2.45/1.16 thf(notdexE_type, type, notdexE: $o).
% 2.45/1.16 thf(setukpairinjL2_type, type, setukpairinjL2: $o).
% 2.45/1.16 thf(doubleComplementI1_type, type, doubleComplementI1: $o).
% 2.45/1.16 thf(setunionAx_type, type, setunionAx: $o).
% 2.45/1.16 thf(setminusELneg_type, type, setminusELneg: $o).
% 2.45/1.16 thf(cartprodsndin_type, type, cartprodsndin: $o).
% 2.45/1.16 thf(ex1E1_type, type, ex1E1: $o).
% 2.45/1.16 thf(sk__103_type, type, sk__103: $i).
% 2.45/1.16 thf(powersetE_type, type, powersetE: $o).
% 2.45/1.16 thf(omegaSAx_type, type, omegaSAx: $o).
% 2.45/1.16 thf(sk__101_type, type, sk__101: $i).
% 2.45/1.16 thf(exuI1_type, type, exuI1: $o).
% 2.45/1.16 thf(exuI2_type, type, exuI2: $o).
% 2.45/1.16 thf(notequalI2_type, type, notequalI2: $o).
% 2.45/1.16 thf(sk__102_type, type, sk__102: $i).
% 2.45/1.16 thf(setukpairinjL_type, type, setukpairinjL: $o).
% 2.45/1.16 thf(kpairiskpair_type, type, kpairiskpair: $o).
% 2.45/1.16 thf(upairsubunion_type, type, upairsubunion: $o).
% 2.45/1.16 thf(funcGraphProp3_type, type, funcGraphProp3: $o).
% 2.45/1.16 thf(cartprodmempaircEq_type, type, cartprodmempaircEq: $o).
% 2.45/1.16 thf(binintersectTERcontra_type, type, binintersectTERcontra: $o).
% 2.45/1.16 thf(powerset__Cong_type, type, powerset__Cong: $o).
% 2.45/1.16 thf(setminusILneg_type, type, setminusILneg: $o).
% 2.45/1.16 thf(wellorderingAx_type, type, wellorderingAx: $o).
% 2.45/1.16 thf(ksndpairEq_type, type, ksndpairEq: $o).
% 2.45/1.16 thf(funcGraphProp2_type, type, funcGraphProp2: $o).
% 2.45/1.16 thf(setadjoinSub2_type, type, setadjoinSub2: $o).
% 2.45/1.16 thf(binintersectSubset5_type, type, binintersectSubset5: $o).
% 2.45/1.16 thf(iftrue_type, type, iftrue: $o).
% 2.45/1.16 thf(upairinpowunion_type, type, upairinpowunion: $o).
% 2.45/1.16 thf(ifSingleton_type, type, ifSingleton: $o).
% 2.45/1.16 thf(doubleComplementSub2_type, type, doubleComplementSub2: $o).
% 2.45/1.16 thf(setoftrueEq_type, type, setoftrueEq: $o).
% 2.45/1.16 thf(funcImageSingleton_type, type, funcImageSingleton: $o).
% 2.45/1.16 thf(dpsetconstrERa_type, type, dpsetconstrERa: $o).
% 2.45/1.16 thf(lamProp_type, type, lamProp: $o).
% 2.45/1.16 thf(cartprodpairmemEL_type, type, cartprodpairmemEL: $o).
% 2.45/1.16 thf(emptyset__Cong_type, type, emptyset__Cong: $o).
% 2.45/1.16 thf(dpsetconstrER_type, type, dpsetconstrER: $o).
% 2.45/1.16 thf(sepInPowerset_type, type, sepInPowerset: $o).
% 2.45/1.16 thf(setukpairIR_type, type, setukpairIR: $o).
% 2.45/1.16 thf(setukpairinjR1_type, type, setukpairinjR1: $o).
% 2.45/1.16 thf(lam2p_type, type, lam2p: $o).
% 2.45/1.16 thf(kpair_type, type, kpair: $i > $i > $i).
% 2.45/1.16 thf(binunionE_type, type, binunionE: $o).
% 2.45/1.16 thf(setext_type, type, setext: $o).
% 2.45/1.16 thf(emptyinPowerset_type, type, emptyinPowerset: $o).
% 2.45/1.16 thf(ubforcartprodlem1_type, type, ubforcartprodlem1: $o).
% 2.45/1.16 thf(descr__Cong_type, type, descr__Cong: $o).
% 2.45/1.16 thf(kfstsingleton_type, type, kfstsingleton: $o).
% 2.45/1.16 thf(binintersectTELcontra_type, type, binintersectTELcontra: $o).
% 2.45/1.16 thf(doubleComplementEq_type, type, doubleComplementEq: $o).
% 2.45/1.16 thf(eqbreln_type, type, eqbreln: $o).
% 2.45/1.16 thf(binintersectSubset1_type, type, binintersectSubset1: $o).
% 2.45/1.16 thf(complementImpComplementIntersect_type, type, complementImpComplementIntersect:
% 2.45/1.16 $o).
% 2.45/1.16 thf(in_type, type, in: $i > $i > $o).
% 2.45/1.16 thf(binunionT_lem_type, type, binunionT_lem: $o).
% 2.45/1.16 thf(quantDeMorgan1_type, type, quantDeMorgan1: $o).
% 2.45/1.16 thf(complementT_lem_type, type, complementT_lem: $o).
% 2.45/1.16 thf(binunion_type, type, binunion: $i > $i > $i).
% 2.45/1.16 thf(kpairsurjEq_type, type, kpairsurjEq: $o).
% 2.45/1.16 thf(setadjoinIR_type, type, setadjoinIR: $o).
% 2.45/1.16 thf(doubleComplementE1_type, type, doubleComplementE1: $o).
% 2.45/1.16 thf(beta1_type, type, beta1: $o).
% 2.45/1.16 thf(setadjoin__Cong_type, type, setadjoin__Cong: $o).
% 2.45/1.16 thf(powersetTE1_type, type, powersetTE1: $o).
% 2.45/1.16 thf(symdiffI2_type, type, symdiffI2: $o).
% 2.45/1.16 thf(iftrueProp2_type, type, iftrueProp2: $o).
% 2.45/1.16 thf(upairset2IR_type, type, upairset2IR: $o).
% 2.45/1.16 thf(iffalseProp2_type, type, iffalseProp2: $o).
% 2.45/1.16 thf(subsetE_type, type, subsetE: $o).
% 2.45/1.16 thf(prop2set2propI_type, type, prop2set2propI: $o).
% 2.45/1.16 thf(dsetconstrEL_type, type, dsetconstrEL: $o).
% 2.45/1.16 thf(setbeta_type, type, setbeta: $o).
% 2.45/1.16 thf(eqinunit_type, type, eqinunit: $o).
% 2.45/1.16 thf(upairsetIL_type, type, upairsetIL: $o).
% 2.45/1.16 thf(powersetI1_type, type, powersetI1: $o).
% 2.45/1.16 thf(kfstpairEq_type, type, kfstpairEq: $o).
% 2.45/1.16 thf(binintersectSubset3_type, type, binintersectSubset3: $o).
% 2.45/1.16 thf(setminusIRneg_type, type, setminusIRneg: $o).
% 2.45/1.16 thf(ap2apEq1_type, type, ap2apEq1: $o).
% 2.45/1.16 thf(powersetAx_type, type, powersetAx: $o).
% 2.45/1.16 thf(binintersectSubset4_type, type, binintersectSubset4: $o).
% 2.45/1.16 thf(singletoninpowunion_type, type, singletoninpowunion: $o).
% 2.45/1.16 thf(powersetI_type, type, powersetI: $o).
% 2.45/1.16 thf(cartprodmempair_type, type, cartprodmempair: $o).
% 2.45/1.16 thf(upairsetIR_type, type, upairsetIR: $o).
% 2.45/1.16 thf(lamp_type, type, lamp: $o).
% 2.45/1.16 thf(dpsetconstrEL1_type, type, dpsetconstrEL1: $o).
% 2.45/1.16 thf(inCongP_type, type, inCongP: $o).
% 2.45/1.16 thf(setadjoinSub_type, type, setadjoinSub: $o).
% 2.45/1.16 thf(exuE3e_type, type, exuE3e: $o).
% 2.45/1.16 thf(emptysetE_type, type, emptysetE: $o).
% 2.45/1.16 thf(binintersectSubset2_type, type, binintersectSubset2: $o).
% 2.45/1.16 thf(setunionI_type, type, setunionI: $o).
% 2.45/1.16 thf(setunion__Cong_type, type, setunion__Cong: $o).
% 2.45/1.16 thf(prop2setI_type, type, prop2setI: $o).
% 2.45/1.16 thf(singletonsuniq_type, type, singletonsuniq: $o).
% 2.45/1.16 thf(nonemptyImpWitness_type, type, nonemptyImpWitness: $o).
% 2.45/1.16 thf(setminusER_type, type, setminusER: $o).
% 2.45/1.16 thf(exuE2_type, type, exuE2: $o).
% 2.45/1.16 thf(emptyset_type, type, emptyset: $i).
% 2.45/1.16 thf(setukpairinjR11_type, type, setukpairinjR11: $o).
% 2.45/1.16 thf(ex1I_type, type, ex1I: $o).
% 2.45/1.16 thf(ex1E2_type, type, ex1E2: $o).
% 2.45/1.16 thf(setukpairinjL1_type, type, setukpairinjL1: $o).
% 2.45/1.16 thf(powersetsubset_type, type, powersetsubset: $o).
% 2.45/1.16 thf(binunionTILcontra_type, type, binunionTILcontra: $o).
% 2.45/1.16 thf(subPowSU_type, type, subPowSU: $o).
% 2.45/1.16 thf(notequalI1_type, type, notequalI1: $o).
% 2.45/1.16 thf(contrasubsetT_type, type, contrasubsetT: $o).
% 2.45/1.16 thf(notinemptyset_type, type, notinemptyset: $o).
% 2.45/1.16 thf(lam2lamEq_type, type, lam2lamEq: $o).
% 2.45/1.16 thf(nonemptyI1_type, type, nonemptyI1: $o).
% 2.45/1.16 thf(subsetTrans_type, type, subsetTrans: $o).
% 2.45/1.16 thf(kpairp_type, type, kpairp: $o).
% 2.45/1.16 thf(setukpairinjR12_type, type, setukpairinjR12: $o).
% 2.45/1.16 thf(setminusI_type, type, setminusI: $o).
% 2.45/1.16 thf(binunionIL_type, type, binunionIL: $o).
% 2.45/1.16 thf(dpsetconstrSub_type, type, dpsetconstrSub: $o).
% 2.45/1.16 thf(setunionsingleton_type, type, setunionsingleton: $o).
% 2.45/1.16 thf(subsetE2_type, type, subsetE2: $o).
% 2.45/1.16 thf(singletonsswitch_type, type, singletonsswitch: $o).
% 2.45/1.16 thf(ubforcartprodlem3_type, type, ubforcartprodlem3: $o).
% 2.45/1.16 thf(beta2_type, type, beta2: $o).
% 2.45/1.16 thf(dpsetconstrI_type, type, dpsetconstrI: $o).
% 2.45/1.16 thf(setextsub_type, type, setextsub: $o).
% 2.45/1.16 thf(binunionLsub_type, type, binunionLsub: $o).
% 2.45/1.16 thf(setunionsingleton1_type, type, setunionsingleton1: $o).
% 2.45/1.16 thf(binintersect_type, type, binintersect: $i > $i > $i).
% 2.45/1.16 thf(iftrueorfalse_type, type, iftrueorfalse: $o).
% 2.45/1.16 thf(emptysetsubset_type, type, emptysetsubset: $o).
% 2.45/1.16 thf(quantDeMorgan3_type, type, quantDeMorgan3: $o).
% 2.45/1.16 thf(cartprodpairsurjEq_type, type, cartprodpairsurjEq: $o).
% 2.45/1.16 thf(setOfPairsIsBReln_type, type, setOfPairsIsBReln: $o).
% 2.45/1.16 thf(setunionE_type, type, setunionE: $o).
% 2.45/1.16 thf(ksndsingleton_type, type, ksndsingleton: $o).
% 2.45/1.16 thf(setminusSubset1_type, type, setminusSubset1: $o).
% 2.45/1.16 thf(powersetT_lem_type, type, powersetT_lem: $o).
% 2.45/1.16 thf(emptyinunitempty_type, type, emptyinunitempty: $o).
% 2.45/1.16 thf(binunionIR_type, type, binunionIR: $o).
% 2.45/1.16 thf(theeq_type, type, theeq: $o).
% 2.45/1.16 thf(setadjoinE_type, type, setadjoinE: $o).
% 2.45/1.16 thf(doubleComplementSub1_type, type, doubleComplementSub1: $o).
% 2.45/1.16 thf(infuncsetfunc_type, type, infuncsetfunc: $o).
% 2.45/1.16 thf(ap2apEq2_type, type, ap2apEq2: $o).
% 2.45/1.16 thf(ap2p_type, type, ap2p: $o).
% 2.45/1.16 thf(setadjoinIL_type, type, setadjoinIL: $o).
% 2.45/1.16 thf(cartprodsndpairEq_type, type, cartprodsndpairEq: $o).
% 2.45/1.16 thf(exuE1_type, type, exuE1: $o).
% 2.45/1.16 thf(ubforcartprodlem2_type, type, ubforcartprodlem2: $o).
% 2.45/1.16 thf(binintersectRsub_type, type, binintersectRsub: $o).
% 2.45/1.16 thf(setminusLsub_type, type, setminusLsub: $o).
% 2.45/1.16 thf(funcextLem_type, type, funcextLem: $o).
% 2.45/1.16 thf(setukpairinjR_type, type, setukpairinjR: $o).
% 2.45/1.16 thf(notinsingleton_type, type, notinsingleton: $o).
% 2.45/1.16 thf(eqimpsubset2_type, type, eqimpsubset2: $o).
% 2.45/1.16 thf(exuEu_type, type, exuEu: $o).
% 2.45/1.16 thf(emptysetimpfalse_type, type, emptysetimpfalse: $o).
% 2.45/1.16 thf(upairsetE_type, type, upairsetE: $o).
% 2.45/1.16 thf(omega0Ax_type, type, omega0Ax: $o).
% 2.45/1.16 thf(subsetTI_type, type, subsetTI: $o).
% 2.45/1.16 thf(notsubsetI_type, type, notsubsetI: $o).
% 2.45/1.16 thf(contraSubsetComplement_type, type, contraSubsetComplement: $o).
% 2.45/1.16 thf(iffalseProp1_type, type, iffalseProp1: $o).
% 2.45/1.16 thf(quantDeMorgan4_type, type, quantDeMorgan4: $o).
% 2.45/1.16 thf(setextAx_type, type, setextAx: $o).
% 2.45/1.16 thf(cartprodpairmemER_type, type, cartprodpairmemER: $o).
% 2.45/1.16 thf(powersetE1_type, type, powersetE1: $o).
% 2.45/1.16 thf(bs114d_type, type, bs114d: $o).
% 2.45/1.16 thf(contrasubsetT3_type, type, contrasubsetT3: $o).
% 2.45/1.16 thf(noeltsimpempty_type, type, noeltsimpempty: $o).
% 2.45/1.16 thf(complementTcontraSubset_type, type, complementTcontraSubset: $o).
% 2.45/1.16 thf(ifp_type, type, ifp: $o).
% 2.45/1.16 thf(powersetTI1_type, type, powersetTI1: $o).
% 2.45/1.16 thf(binintersectLsub_type, type, binintersectLsub: $o).
% 2.45/1.16 thf(subsetI1_type, type, subsetI1: $o).
% 2.45/1.16 thf(symdiffE_type, type, symdiffE: $o).
% 2.45/1.16 thf(descrp_type, type, descrp: $o).
% 2.45/1.16 thf(dsetconstr__Cong_type, type, dsetconstr__Cong: $o).
% 2.45/1.16 thf(foundationAx_type, type, foundationAx: $o).
% 2.45/1.16 thf(emptysetAx_type, type, emptysetAx: $o).
% 2.45/1.16 thf(emptyI_type, type, emptyI: $o).
% 2.45/1.16 thf(setadjoinOr_type, type, setadjoinOr: $o).
% 2.45/1.16 thf(eta2_type, type, eta2: $o).
% 2.45/1.16 thf(binintersectEL_type, type, binintersectEL: $o).
% 2.45/1.16 thf(emptyE1_type, type, emptyE1: $o).
% 2.45/1.16 thf(emptyInPowerset_type, type, emptyInPowerset: $o).
% 2.45/1.16 thf(complementTI1_type, type, complementTI1: $o).
% 2.45/1.16 thf(vacuousDall_type, type, vacuousDall: $o).
% 2.45/1.16 thf(dsetconstrER_type, type, dsetconstrER: $o).
% 2.45/1.16 thf(binintersectI_type, type, binintersectI: $o).
% 2.45/1.16 thf(funcext_type, type, funcext: $o).
% 2.45/1.16 thf(funcGraphProp4_type, type, funcGraphProp4: $o).
% 2.45/1.16 thf(zip_tseitin_0_type, type, zip_tseitin_0: $i > $i > $i > $o).
% 2.45/1.16 thf(cartprodpairin_type, type, cartprodpairin: $o).
% 2.45/1.16 thf(cartprodmempair1_type, type, cartprodmempair1: $o).
% 2.45/1.16 thf(brelnall2_type, type, brelnall2: $o).
% 2.45/1.16 thf(setextT_type, type, setextT: $o).
% 2.45/1.16 thf(ex1I2_type, type, ex1I2: $o).
% 2.45/1.16 thf(symdiffI1_type, type, symdiffI1: $o).
% 2.45/1.16 thf(setukpairinjR2_type, type, setukpairinjR2: $o).
% 2.45/1.16 thf(dpsetconstrEL2_type, type, dpsetconstrEL2: $o).
% 2.45/1.16 thf(theprop_type, type, theprop: $o).
% 2.45/1.16 thf(subsetI2_type, type, subsetI2: $o).
% 2.45/1.16 thf(complementInPowersetComplementIntersect_type, type, complementInPowersetComplementIntersect:
% 2.45/1.16 $o).
% 2.45/1.16 thf(setminusT_lem_type, type, setminusT_lem: $o).
% 2.45/1.16 thf(symdiffIneg1_type, type, symdiffIneg1: $o).
% 2.45/1.16 thf(setminusERneg_type, type, setminusERneg: $o).
% 2.45/1.16 thf(symdiffIneg2_type, type, symdiffIneg2: $o).
% 2.45/1.16 thf(omega__Cong_type, type, omega__Cong: $o).
% 2.45/1.16 thf(subsetRefl_type, type, subsetRefl: $o).
% 2.45/1.16 thf(uniqinunit_type, type, uniqinunit: $o).
% 2.45/1.16 thf(complementSubsetComplementIntersect_type, type, complementSubsetComplementIntersect:
% 2.45/1.16 $o).
% 2.45/1.16 thf(setminusSubset2_type, type, setminusSubset2: $o).
% 2.45/1.16 thf(prop2setE_type, type, prop2setE: $o).
% 2.45/1.16 thf(binunionEcases_type, type, binunionEcases: $o).
% 2.45/1.16 thf(funcinfuncset_type, type, funcinfuncset: $o).
% 2.45/1.16 thf(complementTE1_type, type, complementTE1: $o).
% 2.45/1.16 thf(nonemptyI_type, type, nonemptyI: $o).
% 2.45/1.16 thf(app_type, type, app: $o).
% 2.45/1.16 thf(disjointsetsI1_type, type, disjointsetsI1: $o).
% 2.45/1.16 thf(exuE3u_type, type, exuE3u: $o).
% 2.45/1.16 thf(eta1_type, type, eta1: $o).
% 2.45/1.16 thf(setminusEL_type, type, setminusEL: $o).
% 2.45/1.16 thf(cartprodfstin_type, type, cartprodfstin: $o).
% 2.45/1.16 thf(setunionsingleton2_type, type, setunionsingleton2: $o).
% 2.45/1.16 thf(sepSubset_type, type, sepSubset: $o).
% 2.45/1.16 thf(complementTnotintersectT_type, type, complementTnotintersectT: $o).
% 2.45/1.16 thf(upairset2E_type, type, upairset2E: $o).
% 2.45/1.16 thf(eqimpsubset1_type, type, eqimpsubset1: $o).
% 2.45/1.16 thf(exuI3_type, type, exuI3: $o).
% 2.45/1.16 thf(cartprodfstpairEq_type, type, cartprodfstpairEq: $o).
% 2.45/1.16 thf(apProp_type, type, apProp: $o).
% 2.45/1.16 thf(notdallE_type, type, notdallE: $o).
% 2.45/1.16 thf(iftrueProp1_type, type, iftrueProp1: $o).
% 2.45/1.16 thf(binintersectER_type, type, binintersectER: $o).
% 2.45/1.16 thf(brelnall1_type, type, brelnall1: $o).
% 2.45/1.16 thf(powerset_type, type, powerset: $i > $i).
% 2.45/1.16 thf(dsetconstrI_type, type, dsetconstrI: $o).
% 2.45/1.16 thf(funcGraphProp1_type, type, funcGraphProp1: $o).
% 2.45/1.16 thf(binintersectT_lem_type, type, binintersectT_lem: $o).
% 2.45/1.16 thf(setadjoin_type, type, setadjoin: $i > $i > $i).
% 2.45/1.16 thf(exu__Cong_type, type, exu__Cong: $o).
% 2.45/1.16 thf(quantDeMorgan2_type, type, quantDeMorgan2: $o).
% 2.45/1.16 thf(contrasubsetT2_type, type, contrasubsetT2: $o).
% 2.45/1.16 thf(secondinupair_type, type, secondinupair: $o).
% 2.45/1.16 thf(singletonprop_type, type, singletonprop: $o).
% 2.45/1.16 thf(singletonsubset_type, type, singletonsubset: $o).
% 2.45/1.16 thf(contrasubsetT1_type, type, contrasubsetT1: $o).
% 2.45/1.16 thf(singletoninpowerset_type, type, singletoninpowerset: $o).
% 2.45/1.16 thf(subsetemptysetimpeq_type, type, subsetemptysetimpeq: $o).
% 2.45/1.16 thf(replAx_type, type, replAx: $o).
% 2.45/1.16 thf(upairequniteq_type, type, upairequniteq: $o).
% 2.45/1.16 thf(nonemptyE1_type, type, nonemptyE1: $o).
% 2.45/1.16 thf(omegaIndAx_type, type, omegaIndAx: $o).
% 2.45/1.16 thf(setukpairIL_type, type, setukpairIL: $o).
% 2.45/1.16 thf(setunionE2_type, type, setunionE2: $o).
% 2.45/1.16 thf(inPowerset_type, type, inPowerset: $o).
% 2.45/1.16 thf(iffalse_type, type, iffalse: $o).
% 2.45/1.16 thf(funcext2_type, type, funcext2: $o).
% 2.45/1.16 thf(subset_type, type, subset: $i > $i > $o).
% 2.45/1.16 thf(subbreln_type, type, subbreln: $o).
% 2.45/1.16 thf(in__Cong_type, type, in__Cong: $o).
% 2.45/1.16 thf(binunionRsub_type, type, binunionRsub: $o).
% 2.45/1.16 thf(subset2powerset_type, type, subset2powerset: $o).
% 2.45/1.16 thf(binunionTILcontra, axiom, binunionTILcontra =
% 2.45/1.16 (![A:$i,X:$i]:
% 2.45/1.16 ( ( in @ X @ ( powerset @ A ) ) =>
% 2.45/1.16 ( ![Y:$i]:
% 2.45/1.16 ( ( in @ Y @ ( powerset @ A ) ) =>
% 2.45/1.16 ( ![Xx:$i]:
% 2.45/1.16 ( ( in @ Xx @ A ) =>
% 2.45/1.16 ( ( ~( in @ Xx @ ( binunion @ X @ Y ) ) ) =>
% 2.45/1.16 ( ~( in @ Xx @ X ) ) ) ) ) ) ) ))).
% 2.45/1.16 thf('0', plain,
% 2.45/1.16 (( binunionTILcontra ) =
% 2.45/1.16 ( ![X4:$i,X6:$i]:
% 2.45/1.16 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 2.45/1.16 ( ![X8:$i]:
% 2.45/1.16 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 2.45/1.16 ( ![X10:$i]:
% 2.45/1.16 ( ( in @ X10 @ X4 ) =>
% 2.45/1.16 ( ( ~( in @ X10 @ ( binunion @ X6 @ X8 ) ) ) =>
% 2.45/1.16 ( ~( in @ X10 @ X6 ) ) ) ) ) ) ) ) )),
% 2.45/1.16 define([status(thm)])).
% 2.45/1.16 thf(contrasubsetT1, axiom, contrasubsetT1 =
% 2.45/1.16 (![A:$i,X:$i]:
% 2.45/1.16 ( ( in @ X @ ( powerset @ A ) ) =>
% 2.45/1.16 ( ![Y:$i]:
% 2.45/1.16 ( ( in @ Y @ ( powerset @ A ) ) =>
% 2.45/1.16 ( ![Xx:$i]:
% 2.45/1.16 ( ( in @ Xx @ A ) =>
% 2.45/1.16 ( ( subset @ X @ Y ) =>
% 2.45/1.16 ( ( ~( in @ Xx @ Y ) ) => ( ~( in @ Xx @ X ) ) ) ) ) ) ) ) ))).
% 2.45/1.16 thf('1', plain,
% 2.45/1.16 (( contrasubsetT1 ) =
% 2.45/1.16 ( ![X4:$i,X6:$i]:
% 2.45/1.16 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 2.45/1.16 ( ![X8:$i]:
% 2.45/1.16 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 2.45/1.16 ( ![X10:$i]:
% 2.45/1.16 ( ( in @ X10 @ X4 ) =>
% 2.45/1.16 ( ( subset @ X6 @ X8 ) =>
% 2.45/1.16 ( ( ~( in @ X10 @ X8 ) ) => ( ~( in @ X10 @ X6 ) ) ) ) ) ) ) ) ) )),
% 2.45/1.16 define([status(thm)])).
% 2.45/1.16 thf(powersetTE1, axiom, powersetTE1 =
% 2.45/1.16 (![A:$i,X:$i]:
% 2.45/1.16 ( ( in @ X @ ( powerset @ A ) ) =>
% 2.45/1.16 ( ![Y:$i]:
% 2.45/1.16 ( ( in @ Y @ ( powerset @ A ) ) =>
% 2.45/1.16 ( ![Xx:$i]:
% 2.45/1.16 ( ( in @ Xx @ A ) =>
% 2.45/1.16 ( ( in @ X @ ( powerset @ Y ) ) =>
% 2.45/1.16 ( ( in @ Xx @ X ) => ( in @ Xx @ Y ) ) ) ) ) ) ) ))).
% 2.45/1.16 thf('2', plain,
% 2.45/1.16 (( powersetTE1 ) =
% 2.45/1.16 ( ![X4:$i,X6:$i]:
% 2.45/1.16 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 2.45/1.16 ( ![X8:$i]:
% 2.45/1.16 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 2.45/1.16 ( ![X10:$i]:
% 2.45/1.16 ( ( in @ X10 @ X4 ) =>
% 2.45/1.16 ( ( in @ X6 @ ( powerset @ X8 ) ) =>
% 2.45/1.16 ( ( in @ X10 @ X6 ) => ( in @ X10 @ X8 ) ) ) ) ) ) ) ) )),
% 2.45/1.16 define([status(thm)])).
% 2.45/1.16 thf(powersetTI1, axiom, powersetTI1 =
% 2.45/1.16 (![A:$i,X:$i]:
% 2.45/1.16 ( ( in @ X @ ( powerset @ A ) ) =>
% 2.45/1.16 ( ![Y:$i]:
% 2.45/1.16 ( ( in @ Y @ ( powerset @ A ) ) =>
% 2.45/1.16 ( ( ![Xx:$i]:
% 2.45/1.16 ( ( in @ Xx @ A ) => ( ( in @ Xx @ X ) => ( in @ Xx @ Y ) ) ) ) =>
% 2.45/1.16 ( in @ X @ ( powerset @ Y ) ) ) ) ) ))).
% 2.45/1.16 thf('3', plain,
% 2.45/1.16 (( powersetTI1 ) =
% 2.45/1.16 ( ![X4:$i,X6:$i]:
% 2.45/1.16 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 2.45/1.16 ( ![X8:$i]:
% 2.45/1.16 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 2.45/1.16 ( ( ![X10:$i]:
% 2.45/1.16 ( ( in @ X10 @ X4 ) =>
% 2.45/1.16 ( ( in @ X10 @ X6 ) => ( in @ X10 @ X8 ) ) ) ) =>
% 2.45/1.16 ( in @ X6 @ ( powerset @ X8 ) ) ) ) ) ) )),
% 2.45/1.16 define([status(thm)])).
% 2.45/1.16 thf(subsetTI, axiom, subsetTI =
% 2.45/1.16 (![A:$i,X:$i]:
% 2.45/1.16 ( ( in @ X @ ( powerset @ A ) ) =>
% 2.45/1.16 ( ![Y:$i]:
% 2.45/1.16 ( ( in @ Y @ ( powerset @ A ) ) =>
% 2.45/1.16 ( ( ![Xx:$i]:
% 2.45/1.16 ( ( in @ Xx @ A ) => ( ( in @ Xx @ X ) => ( in @ Xx @ Y ) ) ) ) =>
% 2.45/1.16 ( subset @ X @ Y ) ) ) ) ))).
% 2.45/1.16 thf('4', plain,
% 2.45/1.16 (( subsetTI ) =
% 2.45/1.16 ( ![X4:$i,X6:$i]:
% 2.45/1.16 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 2.45/1.16 ( ![X8:$i]:
% 2.45/1.16 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 2.45/1.16 ( ( ![X10:$i]:
% 2.45/1.16 ( ( in @ X10 @ X4 ) =>
% 2.45/1.16 ( ( in @ X10 @ X6 ) => ( in @ X10 @ X8 ) ) ) ) =>
% 2.45/1.16 ( subset @ X6 @ X8 ) ) ) ) ) )),
% 2.45/1.16 define([status(thm)])).
% 2.45/1.16 thf(setextT, axiom, setextT =
% 2.45/1.16 (![A:$i,X:$i]:
% 2.45/1.16 ( ( in @ X @ ( powerset @ A ) ) =>
% 2.45/1.16 ( ![Y:$i]:
% 2.45/1.16 ( ( in @ Y @ ( powerset @ A ) ) =>
% 2.45/1.16 ( ( ![Xx:$i]:
% 2.45/1.16 ( ( in @ Xx @ A ) => ( ( in @ Xx @ X ) => ( in @ Xx @ Y ) ) ) ) =>
% 2.45/1.16 ( ( ![Xx:$i]:
% 2.45/1.16 ( ( in @ Xx @ A ) => ( ( in @ Xx @ Y ) => ( in @ Xx @ X ) ) ) ) =>
% 2.45/1.16 ( ( X ) = ( Y ) ) ) ) ) ) ))).
% 2.45/1.16 thf('5', plain,
% 2.45/1.16 (( setextT ) =
% 2.45/1.16 ( ![X4:$i,X6:$i]:
% 2.45/1.16 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 2.45/1.16 ( ![X8:$i]:
% 2.45/1.16 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 2.45/1.16 ( ( ![X10:$i]:
% 2.45/1.16 ( ( in @ X10 @ X4 ) =>
% 2.45/1.16 ( ( in @ X10 @ X6 ) => ( in @ X10 @ X8 ) ) ) ) =>
% 2.45/1.16 ( ( ![X12:$i]:
% 2.45/1.16 ( ( in @ X12 @ X4 ) =>
% 2.45/1.16 ( ( in @ X12 @ X8 ) => ( in @ X12 @ X6 ) ) ) ) =>
% 2.45/1.16 ( ( X6 ) = ( X8 ) ) ) ) ) ) ) )),
% 2.45/1.16 define([status(thm)])).
% 2.45/1.16 thf(powersetT_lem, axiom, powersetT_lem =
% 2.45/1.16 (![A:$i,X:$i]:
% 2.45/1.16 ( ( in @ X @ ( powerset @ A ) ) =>
% 2.45/1.16 ( in @ ( powerset @ X ) @ ( powerset @ ( powerset @ A ) ) ) ))).
% 2.45/1.16 thf('6', plain,
% 2.45/1.16 (( powersetT_lem ) =
% 2.45/1.16 ( ![X4:$i,X6:$i]:
% 2.45/1.16 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 2.45/1.16 ( in @ ( powerset @ X6 ) @ ( powerset @ ( powerset @ X4 ) ) ) ) )),
% 2.45/1.16 define([status(thm)])).
% 2.45/1.16 thf(binunionT_lem, axiom, binunionT_lem =
% 2.45/1.16 (![A:$i,X:$i]:
% 2.45/1.16 ( ( in @ X @ ( powerset @ A ) ) =>
% 2.45/1.16 ( ![Y:$i]:
% 2.45/1.16 ( ( in @ Y @ ( powerset @ A ) ) =>
% 2.45/1.16 ( in @ ( binunion @ X @ Y ) @ ( powerset @ A ) ) ) ) ))).
% 2.45/1.16 thf('7', plain,
% 2.45/1.16 (( binunionT_lem ) =
% 2.45/1.16 ( ![X4:$i,X6:$i]:
% 2.45/1.16 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 2.45/1.16 ( ![X8:$i]:
% 2.45/1.16 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 2.45/1.16 ( in @ ( binunion @ X6 @ X8 ) @ ( powerset @ X4 ) ) ) ) ) )),
% 2.45/1.16 define([status(thm)])).
% 2.45/1.16 thf(ubforcartprodlem3, axiom, ubforcartprodlem3 =
% 2.45/1.16 (![A:$i,B:$i,Xx:$i]:
% 2.45/1.16 ( ( in @ Xx @ A ) =>
% 2.45/1.16 ( ![Xy:$i]:
% 2.45/1.16 ( ( in @ Xy @ B ) =>
% 2.45/1.16 ( in @
% 2.45/1.16 ( kpair @ Xx @ Xy ) @
% 2.45/1.16 ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ))).
% 2.45/1.16 thf('8', plain,
% 2.45/1.16 (( ubforcartprodlem3 ) =
% 2.45/1.16 ( ![X4:$i,X6:$i,X8:$i]:
% 2.45/1.16 ( ( in @ X8 @ X4 ) =>
% 2.45/1.16 ( ![X10:$i]:
% 2.45/1.16 ( ( in @ X10 @ X6 ) =>
% 2.45/1.16 ( in @
% 2.45/1.16 ( kpair @ X8 @ X10 ) @
% 2.45/1.16 ( powerset @ ( powerset @ ( binunion @ X4 @ X6 ) ) ) ) ) ) ) )),
% 2.45/1.16 define([status(thm)])).
% 2.45/1.16 thf(ubforcartprodlem2, axiom, ubforcartprodlem2 =
% 2.45/1.16 (![A:$i,B:$i,Xx:$i]:
% 2.45/1.16 ( ( in @ Xx @ A ) =>
% 2.45/1.16 ( ![Xy:$i]:
% 2.45/1.16 ( ( in @ Xy @ B ) =>
% 2.45/1.16 ( in @
% 2.45/1.16 ( setadjoin @
% 2.45/1.16 ( setadjoin @ Xx @ emptyset ) @
% 2.45/1.16 ( setadjoin @
% 2.45/1.16 ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @
% 2.45/1.16 ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ))).
% 2.45/1.16 thf('9', plain,
% 2.45/1.16 (( ubforcartprodlem2 ) =
% 2.45/1.16 ( ![X4:$i,X6:$i,X8:$i]:
% 2.45/1.16 ( ( in @ X8 @ X4 ) =>
% 2.45/1.16 ( ![X10:$i]:
% 2.45/1.16 ( ( in @ X10 @ X6 ) =>
% 2.45/1.16 ( in @
% 2.45/1.16 ( setadjoin @
% 2.45/1.16 ( setadjoin @ X8 @ emptyset ) @
% 2.45/1.16 ( setadjoin @
% 2.45/1.16 ( setadjoin @ X8 @ ( setadjoin @ X10 @ emptyset ) ) @
% 2.45/1.16 emptyset ) ) @
% 2.45/1.16 ( powerset @ ( powerset @ ( binunion @ X4 @ X6 ) ) ) ) ) ) ) )),
% 2.45/1.16 define([status(thm)])).
% 2.45/1.16 thf(ubforcartprodlem1, axiom, ubforcartprodlem1 =
% 2.45/1.16 (![A:$i,B:$i,Xx:$i]:
% 2.45/1.16 ( ( in @ Xx @ A ) =>
% 2.45/1.16 ( ![Xy:$i]:
% 2.45/1.16 ( ( in @ Xy @ B ) =>
% 2.45/1.16 ( subset @
% 2.45/1.16 ( setadjoin @
% 2.45/1.16 ( setadjoin @ Xx @ emptyset ) @
% 2.45/1.16 ( setadjoin @
% 2.45/1.16 ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @
% 2.45/1.16 ( powerset @ ( binunion @ A @ B ) ) ) ) ) ))).
% 2.45/1.16 thf('10', plain,
% 2.45/1.16 (( ubforcartprodlem1 ) =
% 2.45/1.16 ( ![X4:$i,X6:$i,X8:$i]:
% 2.45/1.16 ( ( in @ X8 @ X4 ) =>
% 2.45/1.16 ( ![X10:$i]:
% 2.45/1.16 ( ( in @ X10 @ X6 ) =>
% 2.45/1.16 ( subset @
% 2.45/1.16 ( setadjoin @
% 2.45/1.16 ( setadjoin @ X8 @ emptyset ) @
% 2.45/1.16 ( setadjoin @
% 2.45/1.16 ( setadjoin @ X8 @ ( setadjoin @ X10 @ emptyset ) ) @
% 2.45/1.16 emptyset ) ) @
% 2.45/1.16 ( powerset @ ( binunion @ X4 @ X6 ) ) ) ) ) ) )),
% 2.45/1.16 define([status(thm)])).
% 2.45/1.16 thf(upairinpowunion, axiom, upairinpowunion =
% 2.45/1.16 (![A:$i,B:$i,Xx:$i]:
% 2.45/1.16 ( ( in @ Xx @ A ) =>
% 2.45/1.16 ( ![Xy:$i]:
% 2.45/1.16 ( ( in @ Xy @ B ) =>
% 2.45/1.16 ( in @
% 2.45/1.16 ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @
% 2.45/1.16 ( powerset @ ( binunion @ A @ B ) ) ) ) ) ))).
% 2.45/1.16 thf('11', plain,
% 2.45/1.16 (( upairinpowunion ) =
% 2.45/1.16 ( ![X4:$i,X6:$i,X8:$i]:
% 2.45/1.16 ( ( in @ X8 @ X4 ) =>
% 2.45/1.16 ( ![X10:$i]:
% 2.45/1.16 ( ( in @ X10 @ X6 ) =>
% 2.45/1.16 ( in @
% 2.45/1.16 ( setadjoin @ X8 @ ( setadjoin @ X10 @ emptyset ) ) @
% 2.45/1.16 ( powerset @ ( binunion @ X4 @ X6 ) ) ) ) ) ) )),
% 2.45/1.16 define([status(thm)])).
% 2.45/1.16 thf(upairsubunion, axiom, upairsubunion =
% 2.45/1.16 (![A:$i,B:$i,Xx:$i]:
% 2.45/1.16 ( ( in @ Xx @ A ) =>
% 2.45/1.16 ( ![Xy:$i]:
% 2.45/1.16 ( ( in @ Xy @ B ) =>
% 2.45/1.16 ( subset @
% 2.45/1.16 ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @
% 2.45/1.16 ( binunion @ A @ B ) ) ) ) ))).
% 2.45/1.16 thf('12', plain,
% 2.45/1.16 (( upairsubunion ) =
% 2.45/1.16 ( ![X4:$i,X6:$i,X8:$i]:
% 2.45/1.16 ( ( in @ X8 @ X4 ) =>
% 2.45/1.16 ( ![X10:$i]:
% 2.45/1.16 ( ( in @ X10 @ X6 ) =>
% 2.45/1.16 ( subset @
% 2.45/1.16 ( setadjoin @ X8 @ ( setadjoin @ X10 @ emptyset ) ) @
% 2.45/1.16 ( binunion @ X4 @ X6 ) ) ) ) ) )),
% 2.45/1.16 define([status(thm)])).
% 2.45/1.16 thf(singletoninpowunion, axiom, singletoninpowunion =
% 2.45/1.16 (![A:$i,B:$i,Xx:$i]:
% 2.45/1.16 ( ( in @ Xx @ A ) =>
% 2.45/1.16 ( in @
% 2.45/1.16 ( setadjoin @ Xx @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) ))).
% 2.45/1.16 thf('13', plain,
% 2.45/1.16 (( singletoninpowunion ) =
% 2.45/1.16 ( ![X4:$i,X6:$i,X8:$i]:
% 2.45/1.16 ( ( in @ X8 @ X4 ) =>
% 2.45/1.16 ( in @
% 2.45/1.16 ( setadjoin @ X8 @ emptyset ) @
% 2.45/1.16 ( powerset @ ( binunion @ X4 @ X6 ) ) ) ) )),
% 2.45/1.16 define([status(thm)])).
% 2.45/1.16 thf(bs114d, axiom, bs114d =
% 2.45/1.16 (![A:$i,B:$i,C:$i]:
% 2.45/1.16 ( ( binintersect @ A @ ( binunion @ B @ C ) ) =
% 2.45/1.16 ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) ))).
% 2.45/1.16 thf('14', plain,
% 2.45/1.16 (( bs114d ) =
% 2.45/1.16 ( ![X4:$i,X6:$i,X8:$i]:
% 2.45/1.16 ( ( binintersect @ X4 @ ( binunion @ X6 @ X8 ) ) =
% 2.45/1.16 ( binunion @ ( binintersect @ X4 @ X6 ) @ ( binintersect @ X4 @ X8 ) ) ) )),
% 2.45/1.16 define([status(thm)])).
% 2.45/1.16 thf(binunionRsub, axiom, binunionRsub =
% 2.45/1.16 (![A:$i,B:$i]: ( subset @ B @ ( binunion @ A @ B ) ))).
% 2.45/1.16 thf('15', plain,
% 2.45/1.16 (( binunionRsub ) =
% 2.45/1.16 ( ![X4:$i,X6:$i]: ( subset @ X6 @ ( binunion @ X4 @ X6 ) ) )),
% 2.45/1.16 define([status(thm)])).
% 2.45/1.16 thf(binunionLsub, axiom, binunionLsub =
% 2.45/1.16 (![A:$i,B:$i]: ( subset @ A @ ( binunion @ A @ B ) ))).
% 2.45/1.16 thf('16', plain,
% 2.45/1.16 (( binunionLsub ) =
% 2.45/1.16 ( ![X4:$i,X6:$i]: ( subset @ X4 @ ( binunion @ X4 @ X6 ) ) )),
% 2.45/1.16 define([status(thm)])).
% 2.45/1.16 thf(binunionE, axiom, binunionE =
% 2.45/1.16 (![A:$i,B:$i,Xx:$i]:
% 2.45/1.16 ( ( in @ Xx @ ( binunion @ A @ B ) ) =>
% 2.45/1.16 ( ( in @ Xx @ A ) | ( in @ Xx @ B ) ) ))).
% 2.45/1.16 thf('17', plain,
% 2.45/1.16 (( binunionE ) =
% 2.45/1.16 ( ![X4:$i,X6:$i,X8:$i]:
% 2.45/1.16 ( ( in @ X8 @ ( binunion @ X4 @ X6 ) ) =>
% 2.45/1.16 ( ( in @ X8 @ X4 ) | ( in @ X8 @ X6 ) ) ) )),
% 2.45/1.16 define([status(thm)])).
% 2.45/1.16 thf(binunionEcases, axiom, binunionEcases =
% 2.45/1.16 (![A:$i,B:$i,Xx:$i,Xphi:$o]:
% 2.45/1.16 ( ( in @ Xx @ ( binunion @ A @ B ) ) =>
% 2.45/1.16 ( ( ( in @ Xx @ A ) => ( Xphi ) ) =>
% 2.45/1.16 ( ( ( in @ Xx @ B ) => ( Xphi ) ) => ( Xphi ) ) ) ))).
% 2.45/1.16 thf('18', plain,
% 2.45/1.16 (( binunionEcases ) =
% 2.45/1.16 ( ![X4:$i,X6:$i,X8:$i,X10:$o]:
% 2.45/1.16 ( ( in @ X8 @ ( binunion @ X4 @ X6 ) ) =>
% 2.45/1.16 ( ( ( in @ X8 @ X4 ) => ( X10 ) ) =>
% 2.45/1.16 ( ( ( in @ X8 @ X6 ) => ( X10 ) ) => ( X10 ) ) ) ) )),
% 2.45/1.16 define([status(thm)])).
% 2.45/1.16 thf(binunionIR, axiom, binunionIR =
% 2.45/1.16 (![A:$i,B:$i,Xx:$i]:
% 2.45/1.16 ( ( in @ Xx @ B ) => ( in @ Xx @ ( binunion @ A @ B ) ) ))).
% 2.45/1.16 thf('19', plain,
% 2.45/1.16 (( binunionIR ) =
% 2.45/1.16 ( ![X4:$i,X6:$i,X8:$i]:
% 2.45/1.16 ( ( in @ X8 @ X6 ) => ( in @ X8 @ ( binunion @ X4 @ X6 ) ) ) )),
% 2.45/1.16 define([status(thm)])).
% 2.45/1.16 thf(binunionIL, axiom, binunionIL =
% 2.45/1.16 (![A:$i,B:$i,Xx:$i]:
% 2.45/1.16 ( ( in @ Xx @ A ) => ( in @ Xx @ ( binunion @ A @ B ) ) ))).
% 2.45/1.16 thf('20', plain,
% 2.45/1.16 (( binunionIL ) =
% 2.45/1.16 ( ![X4:$i,X6:$i,X8:$i]:
% 2.45/1.16 ( ( in @ X8 @ X4 ) => ( in @ X8 @ ( binunion @ X4 @ X6 ) ) ) )),
% 2.45/1.16 define([status(thm)])).
% 2.45/1.16 thf(powersetsubset, axiom, powersetsubset =
% 2.45/1.16 (![A:$i,B:$i]:
% 2.45/1.16 ( ( subset @ A @ B ) => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ))).
% 2.45/1.16 thf('21', plain,
% 2.45/1.16 (( powersetsubset ) =
% 2.45/1.16 ( ![X4:$i,X6:$i]:
% 2.45/1.16 ( ( subset @ X4 @ X6 ) =>
% 2.45/1.16 ( subset @ ( powerset @ X4 ) @ ( powerset @ X6 ) ) ) )),
% 2.45/1.16 define([status(thm)])).
% 2.45/1.16 thf(inPowerset, axiom, inPowerset = (![A:$i]: ( in @ A @ ( powerset @ A ) ))).
% 2.45/1.16 thf('22', plain,
% 2.45/1.16 (( inPowerset ) = ( ![X4:$i]: ( in @ X4 @ ( powerset @ X4 ) ) )),
% 2.45/1.16 define([status(thm)])).
% 2.45/1.16 thf(powersetE1, axiom, powersetE1 =
% 2.45/1.16 (![A:$i,B:$i]: ( ( in @ B @ ( powerset @ A ) ) => ( subset @ B @ A ) ))).
% 2.45/1.16 thf('23', plain,
% 2.45/1.16 (( powersetE1 ) =
% 2.45/1.16 ( ![X4:$i,X6:$i]:
% 2.45/1.16 ( ( in @ X6 @ ( powerset @ X4 ) ) => ( subset @ X6 @ X4 ) ) )),
% 2.45/1.16 define([status(thm)])).
% 2.45/1.16 thf(powersetI1, axiom, powersetI1 =
% 2.45/1.16 (![A:$i,B:$i]: ( ( subset @ B @ A ) => ( in @ B @ ( powerset @ A ) ) ))).
% 2.45/1.16 thf('24', plain,
% 2.45/1.16 (( powersetI1 ) =
% 2.45/1.16 ( ![X4:$i,X6:$i]:
% 2.45/1.16 ( ( subset @ X6 @ X4 ) => ( in @ X6 @ ( powerset @ X4 ) ) ) )),
% 2.45/1.16 define([status(thm)])).
% 2.45/1.16 thf(subset2powerset, axiom, subset2powerset =
% 2.45/1.16 (![A:$i,B:$i]: ( ( subset @ A @ B ) => ( in @ A @ ( powerset @ B ) ) ))).
% 2.45/1.16 thf('25', plain,
% 2.45/1.16 (( subset2powerset ) =
% 2.45/1.16 ( ![X4:$i,X6:$i]:
% 2.45/1.16 ( ( subset @ X4 @ X6 ) => ( in @ X4 @ ( powerset @ X6 ) ) ) )),
% 2.45/1.16 define([status(thm)])).
% 2.45/1.16 thf(powerset__Cong, axiom, powerset__Cong =
% 2.45/1.16 (![A:$i,B:$i]:
% 2.45/1.16 ( ( ( A ) = ( B ) ) => ( ( powerset @ A ) = ( powerset @ B ) ) ))).
% 2.45/1.16 thf('26', plain,
% 2.45/1.16 (( powerset__Cong ) =
% 2.45/1.16 ( ![X4:$i,X6:$i]:
% 2.45/1.16 ( ( ( X4 ) = ( X6 ) ) => ( ( powerset @ X4 ) = ( powerset @ X6 ) ) ) )),
% 2.45/1.16 define([status(thm)])).
% 2.45/1.16 thf(powersetE, axiom, powersetE =
% 2.45/1.16 (![A:$i,B:$i,Xx:$i]:
% 2.45/1.16 ( ( in @ B @ ( powerset @ A ) ) => ( ( in @ Xx @ B ) => ( in @ Xx @ A ) ) ))).
% 2.45/1.16 thf('27', plain,
% 2.45/1.16 (( powersetE ) =
% 2.45/1.16 ( ![X4:$i,X6:$i,X8:$i]:
% 2.45/1.16 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 2.45/1.16 ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ) )),
% 2.45/1.16 define([status(thm)])).
% 2.45/1.16 thf(emptyInPowerset, axiom, emptyInPowerset =
% 2.45/1.16 (![A:$i]: ( in @ emptyset @ ( powerset @ A ) ))).
% 2.45/1.16 thf('28', plain,
% 2.45/1.16 (( emptyInPowerset ) =
% 2.45/1.16 ( ![X4:$i]: ( in @ emptyset @ ( powerset @ X4 ) ) )),
% 2.45/1.16 define([status(thm)])).
% 2.45/1.16 thf(emptyinPowerset, axiom, emptyinPowerset =
% 2.45/1.16 (![A:$i]: ( in @ emptyset @ ( powerset @ A ) ))).
% 2.45/1.16 thf('29', plain,
% 2.45/1.16 (( emptyinPowerset ) =
% 2.45/1.16 ( ![X4:$i]: ( in @ emptyset @ ( powerset @ X4 ) ) )),
% 2.45/1.16 define([status(thm)])).
% 2.45/1.16 thf(powersetI, axiom, powersetI =
% 2.45/1.16 (![A:$i,B:$i]:
% 2.45/1.16 ( ( ![Xx:$i]: ( ( in @ Xx @ B ) => ( in @ Xx @ A ) ) ) =>
% 2.45/1.16 ( in @ B @ ( powerset @ A ) ) ))).
% 2.45/1.16 thf('30', plain,
% 2.45/1.16 (( powersetI ) =
% 2.45/1.16 ( ![X4:$i,X6:$i]:
% 2.45/1.16 ( ( ![X8:$i]: ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ) =>
% 2.45/1.16 ( in @ X6 @ ( powerset @ X4 ) ) ) )),
% 2.45/1.16 define([status(thm)])).
% 2.45/1.16 thf(powersetAx, axiom, powersetAx =
% 2.45/1.16 (![A:$i,B:$i]:
% 2.45/1.16 ( ( in @ B @ ( powerset @ A ) ) <=>
% 2.45/1.16 ( ![Xx:$i]: ( ( in @ Xx @ B ) => ( in @ Xx @ A ) ) ) ))).
% 2.45/1.16 thf('31', plain,
% 2.45/1.16 (( powersetAx ) =
% 2.45/1.16 ( ![X4:$i,X6:$i]:
% 2.45/1.16 ( ( in @ X6 @ ( powerset @ X4 ) ) <=>
% 2.45/1.16 ( ![X8:$i]: ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ) ) )),
% 2.45/1.16 define([status(thm)])).
% 2.45/1.16 thf(binunionTIRcontra, conjecture,
% 2.45/1.16 (( setextAx ) =>
% 2.45/1.16 ( ( emptysetAx ) =>
% 2.45/1.16 ( ( setadjoinAx ) =>
% 2.45/1.16 ( ( powersetAx ) =>
% 2.45/1.16 ( ( setunionAx ) =>
% 2.45/1.16 ( ( omega0Ax ) =>
% 2.45/1.16 ( ( omegaSAx ) =>
% 2.45/1.16 ( ( omegaIndAx ) =>
% 2.45/1.16 ( ( replAx ) =>
% 2.45/1.16 ( ( foundationAx ) =>
% 2.45/1.16 ( ( wellorderingAx ) =>
% 2.45/1.16 ( ( descrp ) =>
% 2.45/1.16 ( ( dsetconstrI ) =>
% 2.45/1.16 ( ( dsetconstrEL ) =>
% 2.45/1.16 ( ( dsetconstrER ) =>
% 2.45/1.16 ( ( exuE1 ) =>
% 2.45/1.16 ( ( prop2setE ) =>
% 2.45/1.16 ( ( emptysetE ) =>
% 2.45/1.16 ( ( emptysetimpfalse ) =>
% 2.45/1.16 ( ( notinemptyset ) =>
% 2.45/1.16 ( ( exuE3e ) =>
% 2.45/1.16 ( ( setext ) =>
% 2.45/1.16 ( ( emptyI ) =>
% 2.45/1.16 ( ( noeltsimpempty ) =>
% 2.45/1.16 ( ( setbeta ) =>
% 2.45/1.16 ( ( nonemptyE1 ) =>
% 2.45/1.16 ( ( nonemptyI ) =>
% 2.45/1.16 ( ( nonemptyI1 ) =>
% 2.45/1.16 ( ( setadjoinIL ) =>
% 2.45/1.16 ( ( emptyinunitempty ) =>
% 2.45/1.16 ( ( setadjoinIR ) =>
% 2.45/1.16 ( ( setadjoinE ) =>
% 2.45/1.16 ( (
% 2.45/1.16 setadjoinOr ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 setoftrueEq ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 powersetI ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 emptyinPowerset ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 emptyInPowerset ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 powersetE ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 setunionI ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 setunionE ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 subPowSU ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 exuE2 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 nonemptyImpWitness ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 uniqinunit ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 notinsingleton ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 eqinunit ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 singletonsswitch ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 upairsetE ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 upairsetIL ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 upairsetIR ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 emptyE1 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 vacuousDall ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 quantDeMorgan1 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 quantDeMorgan2 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 quantDeMorgan3 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 quantDeMorgan4 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 prop2setI ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 prop2set2propI ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 notdexE ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 notdallE ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 exuI1 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 exuI3 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 exuI2 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 inCongP ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 in__Cong ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 exuE3u ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 exu__Cong ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 emptyset__Cong ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 setadjoin__Cong ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 powerset__Cong ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 setunion__Cong ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 omega__Cong ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 exuEu ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 descr__Cong ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 dsetconstr__Cong ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 subsetI1 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 eqimpsubset2 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 eqimpsubset1 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 subsetI2 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 emptysetsubset ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 subsetE ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 subsetE2 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 notsubsetI ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 notequalI1 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 notequalI2 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 subsetRefl ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 subsetTrans ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 setadjoinSub ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 setadjoinSub2 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 subset2powerset ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 setextsub ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 subsetemptysetimpeq ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 powersetI1 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 powersetE1 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 inPowerset ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 powersetsubset ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 sepInPowerset ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 sepSubset ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 binunionIL ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 upairset2IR ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 binunionIR ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 binunionEcases ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 binunionE ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 binunionLsub ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 binunionRsub ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 binintersectI ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 binintersectSubset5 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 binintersectEL ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 binintersectLsub ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 binintersectSubset2 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 binintersectSubset3 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 binintersectER ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 disjointsetsI1 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 binintersectRsub ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 binintersectSubset4 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 binintersectSubset1 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 bs114d ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 setminusI ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 setminusEL ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 setminusER ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 setminusSubset2 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 setminusERneg ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 setminusELneg ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 setminusILneg ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 setminusIRneg ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 setminusLsub ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 setminusSubset1 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 symdiffE ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 symdiffI1 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 symdiffI2 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 symdiffIneg1 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 symdiffIneg2 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 secondinupair ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 setukpairIL ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 setukpairIR ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 kpairiskpair ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 kpairp ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 singletonsubset ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 singletoninpowerset ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 singletoninpowunion ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 upairset2E ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 upairsubunion ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 upairinpowunion ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 ubforcartprodlem1 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 ubforcartprodlem2 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 ubforcartprodlem3 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 cartprodpairin ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 cartprodmempair1 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 cartprodmempair ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 setunionE2 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 setunionsingleton1 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 setunionsingleton2 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 setunionsingleton ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 singletonprop ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 ex1E1 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 ex1I ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 ex1I2 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 singletonsuniq ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 setukpairinjL1 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 kfstsingleton ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 theprop ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 kfstpairEq ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 cartprodfstin ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 setukpairinjL2 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 setukpairinjL ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 setukpairinjR11 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 setukpairinjR12 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 setukpairinjR1 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 upairequniteq ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 setukpairinjR2 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 setukpairinjR ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 ksndsingleton ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 ksndpairEq ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 kpairsurjEq ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 cartprodsndin ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 cartprodpairmemEL ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 cartprodpairmemER ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 cartprodmempaircEq ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 cartprodfstpairEq ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 cartprodsndpairEq ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 cartprodpairsurjEq ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 dpsetconstrI ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 dpsetconstrSub ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 setOfPairsIsBReln ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 dpsetconstrERa ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 dpsetconstrEL1 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 dpsetconstrEL2 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 dpsetconstrER ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 funcImageSingleton ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 apProp ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 app ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 infuncsetfunc ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 ap2p ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 funcinfuncset ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 lamProp ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 lamp ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 lam2p ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 brelnall1 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 brelnall2 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 ex1E2 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 funcGraphProp1 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 funcGraphProp3 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 funcGraphProp2 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 funcextLem ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 funcGraphProp4 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 subbreln ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 eqbreln ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 funcext ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 funcext2 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 ap2apEq1 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 ap2apEq2 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 beta1 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 eta1 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 lam2lamEq ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 beta2 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 eta2 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 iffalseProp1 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 iffalseProp2 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 iftrueProp1 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 iftrueProp2 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 ifSingleton ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 ifp ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 theeq ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 iftrue ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 iffalse ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 iftrueorfalse ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 binintersectT_lem ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 binunionT_lem ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 powersetT_lem ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 setminusT_lem ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 complementT_lem ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 setextT ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 subsetTI ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 powersetTI1 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 powersetTE1 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 complementTI1 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 complementTE1 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 binintersectTELcontra ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 binintersectTERcontra ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 contrasubsetT ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 contrasubsetT1 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 contrasubsetT2 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 contrasubsetT3 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 doubleComplementI1 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 doubleComplementE1 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 doubleComplementSub1 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 doubleComplementSub2 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 doubleComplementEq ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 complementTnotintersectT ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 complementImpComplementIntersect ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 complementSubsetComplementIntersect ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 complementInPowersetComplementIntersect ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 contraSubsetComplement ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 complementTcontraSubset ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 binunionTILcontra ) =>
% 2.45/1.16 (
% 2.45/1.16 ![
% 2.45/1.16 A:$i,X:$i]:
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 in @
% 2.45/1.16 X @
% 2.45/1.16 (
% 2.45/1.16 powerset @
% 2.45/1.16 A ) ) =>
% 2.45/1.16 (
% 2.45/1.16 ![
% 2.45/1.16 Y:$i]:
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 in @
% 2.45/1.16 Y @
% 2.45/1.16 (
% 2.45/1.16 powerset @
% 2.45/1.16 A ) ) =>
% 2.45/1.16 (
% 2.45/1.16 ![
% 2.45/1.16 Xx:$i]:
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 in @
% 2.45/1.16 Xx @ A ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 ~(
% 2.45/1.16 in @
% 2.45/1.16 Xx @
% 2.45/1.16 (
% 2.45/1.16 binunion
% 2.45/1.16 @
% 2.45/1.16 X @ Y ) ) ) =>
% 2.45/1.16 (
% 2.45/1.16 ~(
% 2.45/1.16 in @
% 2.45/1.16 Xx @ Y ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 2.45/1.16 thf(zf_stmt_0, conjecture,
% 2.45/1.16 (( setextAx ) =>
% 2.45/1.16 ( ( emptysetAx ) =>
% 2.45/1.16 ( ( setadjoinAx ) =>
% 2.45/1.16 ( ( ![X4:$i,X6:$i]:
% 2.45/1.16 ( ( in @ X6 @ ( powerset @ X4 ) ) <=>
% 2.45/1.16 ( ![X8:$i]: ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ) ) ) =>
% 2.45/1.16 ( ( setunionAx ) =>
% 2.45/1.16 ( ( omega0Ax ) =>
% 2.45/1.16 ( ( omegaSAx ) =>
% 2.45/1.16 ( ( omegaIndAx ) =>
% 2.45/1.16 ( ( replAx ) =>
% 2.45/1.16 ( ( foundationAx ) =>
% 2.45/1.16 ( ( wellorderingAx ) =>
% 2.45/1.16 ( ( descrp ) =>
% 2.45/1.16 ( ( dsetconstrI ) =>
% 2.45/1.16 ( ( dsetconstrEL ) =>
% 2.45/1.16 ( ( dsetconstrER ) =>
% 2.45/1.16 ( ( exuE1 ) =>
% 2.45/1.16 ( ( prop2setE ) =>
% 2.45/1.16 ( ( emptysetE ) =>
% 2.45/1.16 ( ( emptysetimpfalse ) =>
% 2.45/1.16 ( ( notinemptyset ) =>
% 2.45/1.16 ( ( exuE3e ) =>
% 2.45/1.16 ( ( setext ) =>
% 2.45/1.16 ( ( emptyI ) =>
% 2.45/1.16 ( ( noeltsimpempty ) =>
% 2.45/1.16 ( ( setbeta ) =>
% 2.45/1.16 ( ( nonemptyE1 ) =>
% 2.45/1.16 ( ( nonemptyI ) =>
% 2.45/1.16 ( ( nonemptyI1 ) =>
% 2.45/1.16 ( ( setadjoinIL ) =>
% 2.45/1.16 ( ( emptyinunitempty ) =>
% 2.45/1.16 ( ( setadjoinIR ) =>
% 2.45/1.16 ( ( setadjoinE ) =>
% 2.45/1.16 ( (
% 2.45/1.16 setadjoinOr ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 setoftrueEq ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 ![
% 2.45/1.16 X10:$i,
% 2.45/1.16 X12:$i]:
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 ![
% 2.45/1.16 X14:$i]:
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 in @
% 2.45/1.16 X14 @ X12 ) =>
% 2.45/1.16 (
% 2.45/1.16 in @
% 2.45/1.16 X14 @ X10 ) ) ) =>
% 2.45/1.16 (
% 2.45/1.16 in @
% 2.45/1.16 X12 @
% 2.45/1.16 (
% 2.45/1.16 powerset @
% 2.45/1.16 X10 ) ) ) ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 ![
% 2.45/1.16 X16:$i]:
% 2.45/1.16 (
% 2.45/1.16 in @
% 2.45/1.16 emptyset @
% 2.45/1.16 (
% 2.45/1.16 powerset @
% 2.45/1.16 X16 ) ) ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 ![
% 2.45/1.16 X18:$i]:
% 2.45/1.16 (
% 2.45/1.16 in @
% 2.45/1.16 emptyset @
% 2.45/1.16 (
% 2.45/1.16 powerset @
% 2.45/1.16 X18 ) ) ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 ![
% 2.45/1.16 X20:$i,
% 2.45/1.16 X22:$i,
% 2.45/1.16 X24:$i]:
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 in @
% 2.45/1.16 X22 @
% 2.45/1.16 (
% 2.45/1.16 powerset @
% 2.45/1.16 X20 ) ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 in @
% 2.45/1.16 X24 @ X22 ) =>
% 2.45/1.16 (
% 2.45/1.16 in @
% 2.45/1.16 X24 @ X20 ) ) ) ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 setunionI ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 setunionE ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 subPowSU ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 exuE2 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 nonemptyImpWitness ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 uniqinunit ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 notinsingleton ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 eqinunit ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 singletonsswitch ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 upairsetE ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 upairsetIL ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 upairsetIR ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 emptyE1 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 vacuousDall ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 quantDeMorgan1 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 quantDeMorgan2 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 quantDeMorgan3 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 quantDeMorgan4 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 prop2setI ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 prop2set2propI ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 notdexE ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 notdallE ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 exuI1 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 exuI3 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 exuI2 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 inCongP ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 in__Cong ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 exuE3u ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 exu__Cong ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 emptyset__Cong ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 setadjoin__Cong ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 ![
% 2.45/1.16 X26:$i,
% 2.45/1.16 X28:$i]:
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 X26 ) =
% 2.45/1.16 (
% 2.45/1.16 X28 ) ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 powerset @
% 2.45/1.16 X26 ) =
% 2.45/1.16 (
% 2.45/1.16 powerset @
% 2.45/1.16 X28 ) ) ) ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 setunion__Cong ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 omega__Cong ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 exuEu ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 descr__Cong ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 dsetconstr__Cong ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 subsetI1 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 eqimpsubset2 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 eqimpsubset1 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 subsetI2 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 emptysetsubset ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 subsetE ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 subsetE2 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 notsubsetI ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 notequalI1 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 notequalI2 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 subsetRefl ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 subsetTrans ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 setadjoinSub ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 setadjoinSub2 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 ![
% 2.45/1.16 X30:$i,
% 2.45/1.16 X32:$i]:
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 subset @
% 2.45/1.16 X30 @ X32 ) =>
% 2.45/1.16 (
% 2.45/1.16 in @
% 2.45/1.16 X30 @
% 2.45/1.16 (
% 2.45/1.16 powerset @
% 2.45/1.16 X32 ) ) ) ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 setextsub ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 subsetemptysetimpeq ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 ![
% 2.45/1.16 X34:$i,
% 2.45/1.16 X36:$i]:
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 subset @
% 2.45/1.16 X36 @ X34 ) =>
% 2.45/1.16 (
% 2.45/1.16 in @
% 2.45/1.16 X36 @
% 2.45/1.16 (
% 2.45/1.16 powerset @
% 2.45/1.16 X34 ) ) ) ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 ![
% 2.45/1.16 X38:$i,
% 2.45/1.16 X40:$i]:
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 in @
% 2.45/1.16 X40 @
% 2.45/1.16 (
% 2.45/1.16 powerset @
% 2.45/1.16 X38 ) ) =>
% 2.45/1.16 (
% 2.45/1.16 subset @
% 2.45/1.16 X40 @ X38 ) ) ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 ![
% 2.45/1.16 X42:$i]:
% 2.45/1.16 (
% 2.45/1.16 in @
% 2.45/1.16 X42 @
% 2.45/1.16 (
% 2.45/1.16 powerset @
% 2.45/1.16 X42 ) ) ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 ![
% 2.45/1.16 X44:$i,
% 2.45/1.16 X46:$i]:
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 subset @
% 2.45/1.16 X44 @ X46 ) =>
% 2.45/1.16 (
% 2.45/1.16 subset @
% 2.45/1.16 (
% 2.45/1.16 powerset @
% 2.45/1.16 X44 ) @
% 2.45/1.16 (
% 2.45/1.16 powerset @
% 2.45/1.16 X46 ) ) ) ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 sepInPowerset ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 sepSubset ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 ![
% 2.45/1.16 X48:$i,
% 2.45/1.16 X50:$i,
% 2.45/1.16 X52:$i]:
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 in @
% 2.45/1.16 X52 @ X48 ) =>
% 2.45/1.16 (
% 2.45/1.16 in @
% 2.45/1.16 X52 @
% 2.45/1.16 (
% 2.45/1.16 binunion @
% 2.45/1.16 X48 @ X50 ) ) ) ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 upairset2IR ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 ![
% 2.45/1.16 X54:$i,
% 2.45/1.16 X56:$i,
% 2.45/1.16 X58:$i]:
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 in @
% 2.45/1.16 X58 @ X56 ) =>
% 2.45/1.16 (
% 2.45/1.16 in @
% 2.45/1.16 X58 @
% 2.45/1.16 (
% 2.45/1.16 binunion @
% 2.45/1.16 X54 @ X56 ) ) ) ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 ![
% 2.45/1.16 X60:$i,
% 2.45/1.16 X62:$i,
% 2.45/1.16 X64:$i,
% 2.45/1.16 X66:$o]:
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 in @
% 2.45/1.16 X64 @
% 2.45/1.16 (
% 2.45/1.16 binunion @
% 2.45/1.16 X60 @ X62 ) ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 in @
% 2.45/1.16 X64 @ X60 ) =>
% 2.45/1.16 (
% 2.45/1.16 X66 ) ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 in @
% 2.45/1.16 X64 @ X62 ) =>
% 2.45/1.16 (
% 2.45/1.16 X66 ) ) =>
% 2.45/1.16 (
% 2.45/1.16 X66 ) ) ) ) ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 ![
% 2.45/1.16 X68:$i,
% 2.45/1.16 X70:$i,
% 2.45/1.16 X72:$i]:
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 in @
% 2.45/1.16 X72 @
% 2.45/1.16 (
% 2.45/1.16 binunion @
% 2.45/1.16 X68 @ X70 ) ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 in @
% 2.45/1.16 X72 @ X70 ) |
% 2.45/1.16 (
% 2.45/1.16 in @
% 2.45/1.16 X72 @ X68 ) ) ) ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 ![
% 2.45/1.16 X74:$i,
% 2.45/1.16 X76:$i]:
% 2.45/1.16 (
% 2.45/1.16 subset @
% 2.45/1.16 X74 @
% 2.45/1.16 (
% 2.45/1.16 binunion @
% 2.45/1.16 X74 @ X76 ) ) ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 ![
% 2.45/1.16 X78:$i,
% 2.45/1.16 X80:$i]:
% 2.45/1.16 (
% 2.45/1.16 subset @
% 2.45/1.16 X80 @
% 2.45/1.16 (
% 2.45/1.16 binunion @
% 2.45/1.16 X78 @ X80 ) ) ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 binintersectI ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 binintersectSubset5 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 binintersectEL ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 binintersectLsub ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 binintersectSubset2 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 binintersectSubset3 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 binintersectER ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 disjointsetsI1 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 binintersectRsub ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 binintersectSubset4 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 binintersectSubset1 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 ![
% 2.45/1.16 X82:$i,
% 2.45/1.16 X84:$i,
% 2.45/1.16 X86:$i]:
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 binintersect
% 2.45/1.16 @
% 2.45/1.16 X82 @
% 2.45/1.16 (
% 2.45/1.16 binunion @
% 2.45/1.16 X84 @ X86 ) ) =
% 2.45/1.16 (
% 2.45/1.16 binunion @
% 2.45/1.16 (
% 2.45/1.16 binintersect
% 2.45/1.16 @
% 2.45/1.16 X82 @ X84 ) @
% 2.45/1.16 (
% 2.45/1.16 binintersect
% 2.45/1.16 @
% 2.45/1.16 X82 @ X86 ) ) ) ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 setminusI ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 setminusEL ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 setminusER ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 setminusSubset2 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 setminusERneg ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 setminusELneg ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 setminusILneg ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 setminusIRneg ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 setminusLsub ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 setminusSubset1 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 symdiffE ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 symdiffI1 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 symdiffI2 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 symdiffIneg1 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 symdiffIneg2 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 secondinupair ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 setukpairIL ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 setukpairIR ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 kpairiskpair ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 kpairp ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 singletonsubset ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 singletoninpowerset ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 ![
% 2.45/1.16 X88:$i,
% 2.45/1.16 X90:$i,
% 2.45/1.16 X92:$i]:
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 in @
% 2.45/1.16 X92 @ X88 ) =>
% 2.45/1.16 (
% 2.45/1.16 in @
% 2.45/1.16 (
% 2.45/1.16 setadjoin
% 2.45/1.16 @
% 2.45/1.16 X92 @
% 2.45/1.16 emptyset ) @
% 2.45/1.16 (
% 2.45/1.16 powerset @
% 2.45/1.16 (
% 2.45/1.16 binunion @
% 2.45/1.16 X88 @ X90 ) ) ) ) ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 upairset2E ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 ![
% 2.45/1.16 X94:$i,
% 2.45/1.16 X96:$i,
% 2.45/1.16 X98:$i]:
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 in @
% 2.45/1.16 X98 @ X94 ) =>
% 2.45/1.16 (
% 2.45/1.16 ![
% 2.45/1.16 X100:$i]:
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 in @
% 2.45/1.16 X100 @ X96 ) =>
% 2.45/1.16 (
% 2.45/1.16 subset @
% 2.45/1.16 (
% 2.45/1.16 setadjoin
% 2.45/1.16 @
% 2.45/1.16 X98 @
% 2.45/1.16 (
% 2.45/1.16 setadjoin
% 2.45/1.16 @
% 2.45/1.16 X100 @
% 2.45/1.16 emptyset ) ) @
% 2.45/1.16 (
% 2.45/1.16 binunion @
% 2.45/1.16 X94 @ X96 ) ) ) ) ) ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 ![
% 2.45/1.16 X102:$i,
% 2.45/1.16 X104:$i,
% 2.45/1.16 X106:$i]:
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 in @
% 2.45/1.16 X106 @
% 2.45/1.16 X102 ) =>
% 2.45/1.16 (
% 2.45/1.16 ![
% 2.45/1.16 X108:$i]:
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 in @
% 2.45/1.16 X108 @
% 2.45/1.16 X104 ) =>
% 2.45/1.16 (
% 2.45/1.16 in @
% 2.45/1.16 (
% 2.45/1.16 setadjoin
% 2.45/1.16 @
% 2.45/1.16 X106 @
% 2.45/1.16 (
% 2.45/1.16 setadjoin
% 2.45/1.16 @
% 2.45/1.16 X108 @
% 2.45/1.16 emptyset ) ) @
% 2.45/1.16 (
% 2.45/1.16 powerset @
% 2.45/1.16 (
% 2.45/1.16 binunion @
% 2.45/1.16 X102 @
% 2.45/1.16 X104 ) ) ) ) ) ) ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 ![
% 2.45/1.16 X110:$i,
% 2.45/1.16 X112:$i,
% 2.45/1.16 X114:$i]:
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 in @
% 2.45/1.16 X114 @
% 2.45/1.16 X110 ) =>
% 2.45/1.16 (
% 2.45/1.16 ![
% 2.45/1.16 X116:$i]:
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 in @
% 2.45/1.16 X116 @
% 2.45/1.16 X112 ) =>
% 2.45/1.16 (
% 2.45/1.16 subset @
% 2.45/1.16 (
% 2.45/1.16 setadjoin
% 2.45/1.16 @
% 2.45/1.16 (
% 2.45/1.16 setadjoin
% 2.45/1.16 @
% 2.45/1.16 X114 @
% 2.45/1.16 emptyset ) @
% 2.45/1.16 (
% 2.45/1.16 setadjoin
% 2.45/1.16 @
% 2.45/1.16 (
% 2.45/1.16 setadjoin
% 2.45/1.16 @
% 2.45/1.16 X114 @
% 2.45/1.16 (
% 2.45/1.16 setadjoin
% 2.45/1.16 @
% 2.45/1.16 X116 @
% 2.45/1.16 emptyset ) ) @
% 2.45/1.16 emptyset ) ) @
% 2.45/1.16 (
% 2.45/1.16 powerset @
% 2.45/1.16 (
% 2.45/1.16 binunion @
% 2.45/1.16 X110 @
% 2.45/1.16 X112 ) ) ) ) ) ) ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 ![
% 2.45/1.16 X118:$i,
% 2.45/1.16 X120:$i,
% 2.45/1.16 X122:$i]:
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 in @
% 2.45/1.16 X122 @
% 2.45/1.16 X118 ) =>
% 2.45/1.16 (
% 2.45/1.16 ![
% 2.45/1.16 X124:$i]:
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 in @
% 2.45/1.16 X124 @
% 2.45/1.16 X120 ) =>
% 2.45/1.16 (
% 2.45/1.16 in @
% 2.45/1.16 (
% 2.45/1.16 setadjoin
% 2.45/1.16 @
% 2.45/1.16 (
% 2.45/1.16 setadjoin
% 2.45/1.16 @
% 2.45/1.16 X122 @
% 2.45/1.16 emptyset ) @
% 2.45/1.16 (
% 2.45/1.16 setadjoin
% 2.45/1.16 @
% 2.45/1.16 (
% 2.45/1.16 setadjoin
% 2.45/1.16 @
% 2.45/1.16 X122 @
% 2.45/1.16 (
% 2.45/1.16 setadjoin
% 2.45/1.16 @
% 2.45/1.16 X124 @
% 2.45/1.16 emptyset ) ) @
% 2.45/1.16 emptyset ) ) @
% 2.45/1.16 (
% 2.45/1.16 powerset @
% 2.45/1.16 (
% 2.45/1.16 powerset @
% 2.45/1.16 (
% 2.45/1.16 binunion @
% 2.45/1.16 X118 @
% 2.45/1.16 X120 ) ) ) ) ) ) ) ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 ![
% 2.45/1.16 X126:$i,
% 2.45/1.16 X128:$i,
% 2.45/1.16 X130:$i]:
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 in @
% 2.45/1.16 X130 @
% 2.45/1.16 X126 ) =>
% 2.45/1.16 (
% 2.45/1.16 ![
% 2.45/1.16 X132:$i]:
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 in @
% 2.45/1.16 X132 @
% 2.45/1.16 X128 ) =>
% 2.45/1.16 (
% 2.45/1.16 in @
% 2.45/1.16 (
% 2.45/1.16 kpair @
% 2.45/1.16 X130 @
% 2.45/1.16 X132 ) @
% 2.45/1.16 (
% 2.45/1.16 powerset @
% 2.45/1.16 (
% 2.45/1.16 powerset @
% 2.45/1.16 (
% 2.45/1.16 binunion @
% 2.45/1.16 X126 @
% 2.45/1.16 X128 ) ) ) ) ) ) ) ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 cartprodpairin ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 cartprodmempair1 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 cartprodmempair ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 setunionE2 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 setunionsingleton1 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 setunionsingleton2 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 setunionsingleton ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 singletonprop ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 ex1E1 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 ex1I ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 ex1I2 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 singletonsuniq ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 setukpairinjL1 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 kfstsingleton ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 theprop ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 kfstpairEq ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 cartprodfstin ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 setukpairinjL2 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 setukpairinjL ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 setukpairinjR11 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 setukpairinjR12 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 setukpairinjR1 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 upairequniteq ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 setukpairinjR2 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 setukpairinjR ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 ksndsingleton ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 ksndpairEq ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 kpairsurjEq ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 cartprodsndin ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 cartprodpairmemEL ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 cartprodpairmemER ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 cartprodmempaircEq ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 cartprodfstpairEq ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 cartprodsndpairEq ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 cartprodpairsurjEq ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 dpsetconstrI ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 dpsetconstrSub ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 setOfPairsIsBReln ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 dpsetconstrERa ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 dpsetconstrEL1 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 dpsetconstrEL2 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 dpsetconstrER ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 funcImageSingleton ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 apProp ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 app ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 infuncsetfunc ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 ap2p ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 funcinfuncset ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 lamProp ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 lamp ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 lam2p ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 brelnall1 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 brelnall2 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 ex1E2 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 funcGraphProp1 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 funcGraphProp3 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 funcGraphProp2 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 funcextLem ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 funcGraphProp4 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 subbreln ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 eqbreln ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 funcext ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 funcext2 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 ap2apEq1 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 ap2apEq2 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 beta1 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 eta1 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 lam2lamEq ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 beta2 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 eta2 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 iffalseProp1 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 iffalseProp2 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 iftrueProp1 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 iftrueProp2 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 ifSingleton ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 ifp ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 theeq ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 iftrue ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 iffalse ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 iftrueorfalse ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 binintersectT_lem ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 ![
% 2.45/1.16 X134:$i,
% 2.45/1.16 X136:$i]:
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 in @
% 2.45/1.16 X136 @
% 2.45/1.16 (
% 2.45/1.16 powerset @
% 2.45/1.16 X134 ) ) =>
% 2.45/1.16 (
% 2.45/1.16 ![
% 2.45/1.16 X138:$i]:
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 in @
% 2.45/1.16 X138 @
% 2.45/1.16 (
% 2.45/1.16 powerset @
% 2.45/1.16 X134 ) ) =>
% 2.45/1.16 (
% 2.45/1.16 in @
% 2.45/1.16 (
% 2.45/1.16 binunion @
% 2.45/1.16 X136 @
% 2.45/1.16 X138 ) @
% 2.45/1.16 (
% 2.45/1.16 powerset @
% 2.45/1.16 X134 ) ) ) ) ) ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 ![
% 2.45/1.16 X140:$i,
% 2.45/1.16 X142:$i]:
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 in @
% 2.45/1.16 X142 @
% 2.45/1.16 (
% 2.45/1.16 powerset @
% 2.45/1.16 X140 ) ) =>
% 2.45/1.16 (
% 2.45/1.16 in @
% 2.45/1.16 (
% 2.45/1.16 powerset @
% 2.45/1.16 X142 ) @
% 2.45/1.16 (
% 2.45/1.16 powerset @
% 2.45/1.16 (
% 2.45/1.16 powerset @
% 2.45/1.16 X140 ) ) ) ) ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 setminusT_lem ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 complementT_lem ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 ![
% 2.45/1.16 X144:$i,
% 2.45/1.16 X146:$i]:
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 in @
% 2.45/1.16 X146 @
% 2.45/1.16 (
% 2.45/1.16 powerset @
% 2.45/1.16 X144 ) ) =>
% 2.45/1.16 (
% 2.45/1.16 ![
% 2.45/1.16 X148:$i]:
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 in @
% 2.45/1.16 X148 @
% 2.45/1.16 (
% 2.45/1.16 powerset @
% 2.45/1.16 X144 ) ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 ![
% 2.45/1.16 X150:$i]:
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 in @
% 2.45/1.16 X150 @
% 2.45/1.16 X144 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 in @
% 2.45/1.16 X150 @
% 2.45/1.16 X146 ) =>
% 2.45/1.16 (
% 2.45/1.16 in @
% 2.45/1.16 X150 @
% 2.45/1.16 X148 ) ) ) ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 ![
% 2.45/1.16 X152:$i]:
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 in @
% 2.45/1.16 X152 @
% 2.45/1.16 X144 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 in @
% 2.45/1.16 X152 @
% 2.45/1.16 X148 ) =>
% 2.45/1.16 (
% 2.45/1.16 in @
% 2.45/1.16 X152 @
% 2.45/1.16 X146 ) ) ) ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 X146 ) =
% 2.45/1.16 (
% 2.45/1.16 X148 ) ) ) ) ) ) ) ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 ![
% 2.45/1.16 X154:$i,
% 2.45/1.16 X156:$i]:
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 in @
% 2.45/1.16 X156 @
% 2.45/1.16 (
% 2.45/1.16 powerset @
% 2.45/1.16 X154 ) ) =>
% 2.45/1.16 (
% 2.45/1.16 ![
% 2.45/1.16 X158:$i]:
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 in @
% 2.45/1.16 X158 @
% 2.45/1.16 (
% 2.45/1.16 powerset @
% 2.45/1.16 X154 ) ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 ![
% 2.45/1.16 X160:$i]:
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 in @
% 2.45/1.16 X160 @
% 2.45/1.16 X154 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 in @
% 2.45/1.16 X160 @
% 2.45/1.16 X156 ) =>
% 2.45/1.16 (
% 2.45/1.16 in @
% 2.45/1.16 X160 @
% 2.45/1.16 X158 ) ) ) ) =>
% 2.45/1.16 (
% 2.45/1.16 subset @
% 2.45/1.16 X156 @
% 2.45/1.16 X158 ) ) ) ) ) ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 ![
% 2.45/1.16 X162:$i,
% 2.45/1.16 X164:$i]:
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 in @
% 2.45/1.16 X164 @
% 2.45/1.16 (
% 2.45/1.16 powerset @
% 2.45/1.16 X162 ) ) =>
% 2.45/1.16 (
% 2.45/1.16 ![
% 2.45/1.16 X166:$i]:
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 in @
% 2.45/1.16 X166 @
% 2.45/1.16 (
% 2.45/1.16 powerset @
% 2.45/1.16 X162 ) ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 ![
% 2.45/1.16 X168:$i]:
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 in @
% 2.45/1.16 X168 @
% 2.45/1.16 X162 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 in @
% 2.45/1.16 X168 @
% 2.45/1.16 X164 ) =>
% 2.45/1.16 (
% 2.45/1.16 in @
% 2.45/1.16 X168 @
% 2.45/1.16 X166 ) ) ) ) =>
% 2.45/1.16 (
% 2.45/1.16 in @
% 2.45/1.16 X164 @
% 2.45/1.16 (
% 2.45/1.16 powerset @
% 2.45/1.16 X166 ) ) ) ) ) ) ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 ![
% 2.45/1.16 X170:$i,
% 2.45/1.16 X172:$i]:
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 in @
% 2.45/1.16 X172 @
% 2.45/1.16 (
% 2.45/1.16 powerset @
% 2.45/1.16 X170 ) ) =>
% 2.45/1.16 (
% 2.45/1.16 ![
% 2.45/1.16 X174:$i]:
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 in @
% 2.45/1.16 X174 @
% 2.45/1.16 (
% 2.45/1.16 powerset @
% 2.45/1.16 X170 ) ) =>
% 2.45/1.16 (
% 2.45/1.16 ![
% 2.45/1.16 X176:$i]:
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 in @
% 2.45/1.16 X176 @
% 2.45/1.16 X170 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 in @
% 2.45/1.16 X172 @
% 2.45/1.16 (
% 2.45/1.16 powerset @
% 2.45/1.16 X174 ) ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 in @
% 2.45/1.16 X176 @
% 2.45/1.16 X172 ) =>
% 2.45/1.16 (
% 2.45/1.16 in @
% 2.45/1.16 X176 @
% 2.45/1.16 X174 ) ) ) ) ) ) ) ) ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 complementTI1 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 complementTE1 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 binintersectTELcontra ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 binintersectTERcontra ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 contrasubsetT ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 ![
% 2.45/1.16 X178:$i,
% 2.45/1.16 X180:$i]:
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 in @
% 2.45/1.16 X180 @
% 2.45/1.16 (
% 2.45/1.16 powerset @
% 2.45/1.16 X178 ) ) =>
% 2.45/1.16 (
% 2.45/1.16 ![
% 2.45/1.16 X182:$i]:
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 in @
% 2.45/1.16 X182 @
% 2.45/1.16 (
% 2.45/1.16 powerset @
% 2.45/1.16 X178 ) ) =>
% 2.45/1.16 (
% 2.45/1.16 ![
% 2.45/1.16 X184:$i]:
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 in @
% 2.45/1.16 X184 @
% 2.45/1.16 X178 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 subset @
% 2.45/1.16 X180 @
% 2.45/1.16 X182 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 ~(
% 2.45/1.16 in @
% 2.45/1.16 X184 @
% 2.45/1.16 X182 ) ) =>
% 2.45/1.16 (
% 2.45/1.16 ~(
% 2.45/1.16 in @
% 2.45/1.16 X184 @
% 2.45/1.16 X180 ) ) ) ) ) ) ) ) ) ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 contrasubsetT2 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 contrasubsetT3 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 doubleComplementI1 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 doubleComplementE1 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 doubleComplementSub1 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 doubleComplementSub2 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 doubleComplementEq ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 complementTnotintersectT ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 complementImpComplementIntersect ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 complementSubsetComplementIntersect ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 complementInPowersetComplementIntersect ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 contraSubsetComplement ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 complementTcontraSubset ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 ![
% 2.45/1.16 X186:$i,
% 2.45/1.16 X188:$i]:
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 in @
% 2.45/1.16 X188 @
% 2.45/1.16 (
% 2.45/1.16 powerset @
% 2.45/1.16 X186 ) ) =>
% 2.45/1.16 (
% 2.45/1.16 ![
% 2.45/1.16 X190:$i]:
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 in @
% 2.45/1.16 X190 @
% 2.45/1.16 (
% 2.45/1.16 powerset @
% 2.45/1.16 X186 ) ) =>
% 2.45/1.16 (
% 2.45/1.16 ![
% 2.45/1.16 X192:$i]:
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 in @
% 2.45/1.16 X192 @
% 2.45/1.16 X186 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 ~(
% 2.45/1.16 in @
% 2.45/1.16 X192 @
% 2.45/1.16 (
% 2.45/1.16 binunion
% 2.45/1.16 @
% 2.45/1.16 X188 @
% 2.45/1.16 X190 ) ) ) =>
% 2.45/1.16 (
% 2.45/1.16 ~(
% 2.45/1.16 in @
% 2.45/1.16 X192 @
% 2.45/1.16 X188 ) ) ) ) ) ) ) ) ) =>
% 2.45/1.16 (
% 2.45/1.16 ![
% 2.45/1.16 X194:$i,
% 2.45/1.16 X196:$i]:
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 in @
% 2.45/1.16 X196 @
% 2.45/1.16 (
% 2.45/1.16 powerset @
% 2.45/1.16 X194 ) ) =>
% 2.45/1.16 (
% 2.45/1.16 ![
% 2.45/1.16 X198:$i]:
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 in @
% 2.45/1.16 X198 @
% 2.45/1.16 (
% 2.45/1.16 powerset @
% 2.45/1.16 X194 ) ) =>
% 2.45/1.16 (
% 2.45/1.16 ![
% 2.45/1.16 X200:$i]:
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 in @
% 2.45/1.16 X200 @
% 2.45/1.16 X194 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 ~(
% 2.45/1.16 in @
% 2.45/1.16 X200 @
% 2.45/1.16 (
% 2.45/1.16 binunion
% 2.45/1.16 @
% 2.45/1.16 X196 @
% 2.45/1.16 X198 ) ) ) =>
% 2.45/1.16 (
% 2.45/1.16 ~(
% 2.45/1.16 in @
% 2.45/1.16 X200 @
% 2.45/1.16 X198 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 2.45/1.16 thf(zf_stmt_1, type, zip_tseitin_0 : $i > $i > $i > $o).
% 2.45/1.16 thf(zf_stmt_2, axiom,
% 2.45/1.16 (![X8:$i,X6:$i,X4:$i]:
% 2.45/1.16 ( ( zip_tseitin_0 @ X8 @ X6 @ X4 ) <=>
% 2.45/1.16 ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ))).
% 2.45/1.16 thf(zf_stmt_3, conjecture,
% 2.45/1.16 (( setextAx ) =>
% 2.45/1.16 ( ( emptysetAx ) =>
% 2.45/1.16 ( ( setadjoinAx ) =>
% 2.45/1.16 ( ( ![X4:$i,X6:$i]:
% 2.45/1.16 ( ( in @ X6 @ ( powerset @ X4 ) ) <=>
% 2.45/1.16 ( ![X8:$i]: ( zip_tseitin_0 @ X8 @ X6 @ X4 ) ) ) ) =>
% 2.45/1.16 ( ( setunionAx ) =>
% 2.45/1.16 ( ( omega0Ax ) =>
% 2.45/1.16 ( ( omegaSAx ) =>
% 2.45/1.16 ( ( omegaIndAx ) =>
% 2.45/1.16 ( ( replAx ) =>
% 2.45/1.16 ( ( foundationAx ) =>
% 2.45/1.16 ( ( wellorderingAx ) =>
% 2.45/1.16 ( ( descrp ) =>
% 2.45/1.16 ( ( dsetconstrI ) =>
% 2.45/1.16 ( ( dsetconstrEL ) =>
% 2.45/1.16 ( ( dsetconstrER ) =>
% 2.45/1.16 ( ( exuE1 ) =>
% 2.45/1.16 ( ( prop2setE ) =>
% 2.45/1.16 ( ( emptysetE ) =>
% 2.45/1.16 ( ( emptysetimpfalse ) =>
% 2.45/1.16 ( ( notinemptyset ) =>
% 2.45/1.16 ( ( exuE3e ) =>
% 2.45/1.16 ( ( setext ) =>
% 2.45/1.16 ( ( emptyI ) =>
% 2.45/1.16 ( ( noeltsimpempty ) =>
% 2.45/1.16 ( ( setbeta ) =>
% 2.45/1.16 ( ( nonemptyE1 ) =>
% 2.45/1.16 ( ( nonemptyI ) =>
% 2.45/1.16 ( ( nonemptyI1 ) =>
% 2.45/1.16 ( ( setadjoinIL ) =>
% 2.45/1.16 ( ( emptyinunitempty ) =>
% 2.45/1.16 ( ( setadjoinIR ) =>
% 2.45/1.16 ( ( setadjoinE ) =>
% 2.45/1.16 ( (
% 2.45/1.16 setadjoinOr ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 setoftrueEq ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 ![
% 2.45/1.16 X10:$i,
% 2.45/1.16 X12:$i]:
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 ![
% 2.45/1.16 X14:$i]:
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 in @
% 2.45/1.16 X14 @ X12 ) =>
% 2.45/1.16 (
% 2.45/1.16 in @
% 2.45/1.16 X14 @ X10 ) ) ) =>
% 2.45/1.16 (
% 2.45/1.16 in @
% 2.45/1.16 X12 @
% 2.45/1.16 (
% 2.45/1.16 powerset @
% 2.45/1.16 X10 ) ) ) ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 ![
% 2.45/1.16 X16:$i]:
% 2.45/1.16 (
% 2.45/1.16 in @
% 2.45/1.16 emptyset @
% 2.45/1.16 (
% 2.45/1.16 powerset @
% 2.45/1.16 X16 ) ) ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 ![
% 2.45/1.16 X18:$i]:
% 2.45/1.16 (
% 2.45/1.16 in @
% 2.45/1.16 emptyset @
% 2.45/1.16 (
% 2.45/1.16 powerset @
% 2.45/1.16 X18 ) ) ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 ![
% 2.45/1.16 X20:$i,
% 2.45/1.16 X22:$i,
% 2.45/1.16 X24:$i]:
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 in @
% 2.45/1.16 X22 @
% 2.45/1.16 (
% 2.45/1.16 powerset @
% 2.45/1.16 X20 ) ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 in @
% 2.45/1.16 X24 @ X22 ) =>
% 2.45/1.16 (
% 2.45/1.16 in @
% 2.45/1.16 X24 @ X20 ) ) ) ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 setunionI ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 setunionE ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 subPowSU ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 exuE2 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 nonemptyImpWitness ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 uniqinunit ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 notinsingleton ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 eqinunit ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 singletonsswitch ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 upairsetE ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 upairsetIL ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 upairsetIR ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 emptyE1 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 vacuousDall ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 quantDeMorgan1 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 quantDeMorgan2 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 quantDeMorgan3 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 quantDeMorgan4 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 prop2setI ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 prop2set2propI ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 notdexE ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 notdallE ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 exuI1 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 exuI3 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 exuI2 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 inCongP ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 in__Cong ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 exuE3u ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 exu__Cong ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 emptyset__Cong ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 setadjoin__Cong ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 ![
% 2.45/1.16 X26:$i,
% 2.45/1.16 X28:$i]:
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 X26 ) =
% 2.45/1.16 (
% 2.45/1.16 X28 ) ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 powerset @
% 2.45/1.16 X26 ) =
% 2.45/1.16 (
% 2.45/1.16 powerset @
% 2.45/1.16 X28 ) ) ) ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 setunion__Cong ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 omega__Cong ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 exuEu ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 descr__Cong ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 dsetconstr__Cong ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 subsetI1 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 eqimpsubset2 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 eqimpsubset1 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 subsetI2 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 emptysetsubset ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 subsetE ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 subsetE2 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 notsubsetI ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 notequalI1 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 notequalI2 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 subsetRefl ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 subsetTrans ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 setadjoinSub ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 setadjoinSub2 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 ![
% 2.45/1.16 X30:$i,
% 2.45/1.16 X32:$i]:
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 subset @
% 2.45/1.16 X30 @ X32 ) =>
% 2.45/1.16 (
% 2.45/1.16 in @
% 2.45/1.16 X30 @
% 2.45/1.16 (
% 2.45/1.16 powerset @
% 2.45/1.16 X32 ) ) ) ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 setextsub ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 subsetemptysetimpeq ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 ![
% 2.45/1.16 X34:$i,
% 2.45/1.16 X36:$i]:
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 subset @
% 2.45/1.16 X36 @ X34 ) =>
% 2.45/1.16 (
% 2.45/1.16 in @
% 2.45/1.16 X36 @
% 2.45/1.16 (
% 2.45/1.16 powerset @
% 2.45/1.16 X34 ) ) ) ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 ![
% 2.45/1.16 X38:$i,
% 2.45/1.16 X40:$i]:
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 in @
% 2.45/1.16 X40 @
% 2.45/1.16 (
% 2.45/1.16 powerset @
% 2.45/1.16 X38 ) ) =>
% 2.45/1.16 (
% 2.45/1.16 subset @
% 2.45/1.16 X40 @ X38 ) ) ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 ![
% 2.45/1.16 X42:$i]:
% 2.45/1.16 (
% 2.45/1.16 in @
% 2.45/1.16 X42 @
% 2.45/1.16 (
% 2.45/1.16 powerset @
% 2.45/1.16 X42 ) ) ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 ![
% 2.45/1.16 X44:$i,
% 2.45/1.16 X46:$i]:
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 subset @
% 2.45/1.16 X44 @ X46 ) =>
% 2.45/1.16 (
% 2.45/1.16 subset @
% 2.45/1.16 (
% 2.45/1.16 powerset @
% 2.45/1.16 X44 ) @
% 2.45/1.16 (
% 2.45/1.16 powerset @
% 2.45/1.16 X46 ) ) ) ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 sepInPowerset ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 sepSubset ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 ![
% 2.45/1.16 X48:$i,
% 2.45/1.16 X50:$i,
% 2.45/1.16 X52:$i]:
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 in @
% 2.45/1.16 X52 @ X48 ) =>
% 2.45/1.16 (
% 2.45/1.16 in @
% 2.45/1.16 X52 @
% 2.45/1.16 (
% 2.45/1.16 binunion @
% 2.45/1.16 X48 @ X50 ) ) ) ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 upairset2IR ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 ![
% 2.45/1.16 X54:$i,
% 2.45/1.16 X56:$i,
% 2.45/1.16 X58:$i]:
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 in @
% 2.45/1.16 X58 @ X56 ) =>
% 2.45/1.16 (
% 2.45/1.16 in @
% 2.45/1.16 X58 @
% 2.45/1.16 (
% 2.45/1.16 binunion @
% 2.45/1.16 X54 @ X56 ) ) ) ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 ![
% 2.45/1.16 X60:$i,
% 2.45/1.16 X62:$i,
% 2.45/1.16 X64:$i,
% 2.45/1.16 X66:$o]:
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 in @
% 2.45/1.16 X64 @
% 2.45/1.16 (
% 2.45/1.16 binunion @
% 2.45/1.16 X60 @ X62 ) ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 in @
% 2.45/1.16 X64 @ X60 ) =>
% 2.45/1.16 (
% 2.45/1.16 X66 ) ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 in @
% 2.45/1.16 X64 @ X62 ) =>
% 2.45/1.16 (
% 2.45/1.16 X66 ) ) =>
% 2.45/1.16 (
% 2.45/1.16 X66 ) ) ) ) ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 ![
% 2.45/1.16 X68:$i,
% 2.45/1.16 X70:$i,
% 2.45/1.16 X72:$i]:
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 in @
% 2.45/1.16 X72 @
% 2.45/1.16 (
% 2.45/1.16 binunion @
% 2.45/1.16 X68 @ X70 ) ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 in @
% 2.45/1.16 X72 @ X68 ) |
% 2.45/1.16 (
% 2.45/1.16 in @
% 2.45/1.16 X72 @ X70 ) ) ) ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 ![
% 2.45/1.16 X74:$i,
% 2.45/1.16 X76:$i]:
% 2.45/1.16 (
% 2.45/1.16 subset @
% 2.45/1.16 X74 @
% 2.45/1.16 (
% 2.45/1.16 binunion @
% 2.45/1.16 X74 @ X76 ) ) ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 ![
% 2.45/1.16 X78:$i,
% 2.45/1.16 X80:$i]:
% 2.45/1.16 (
% 2.45/1.16 subset @
% 2.45/1.16 X80 @
% 2.45/1.16 (
% 2.45/1.16 binunion @
% 2.45/1.16 X78 @ X80 ) ) ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 binintersectI ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 binintersectSubset5 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 binintersectEL ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 binintersectLsub ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 binintersectSubset2 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 binintersectSubset3 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 binintersectER ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 disjointsetsI1 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 binintersectRsub ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 binintersectSubset4 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 binintersectSubset1 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 ![
% 2.45/1.16 X82:$i,
% 2.45/1.16 X84:$i,
% 2.45/1.16 X86:$i]:
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 binintersect
% 2.45/1.16 @
% 2.45/1.16 X82 @
% 2.45/1.16 (
% 2.45/1.16 binunion @
% 2.45/1.16 X84 @ X86 ) ) =
% 2.45/1.16 (
% 2.45/1.16 binunion @
% 2.45/1.16 (
% 2.45/1.16 binintersect
% 2.45/1.16 @
% 2.45/1.16 X82 @ X84 ) @
% 2.45/1.16 (
% 2.45/1.16 binintersect
% 2.45/1.16 @
% 2.45/1.16 X82 @ X86 ) ) ) ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 setminusI ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 setminusEL ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 setminusER ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 setminusSubset2 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 setminusERneg ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 setminusELneg ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 setminusILneg ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 setminusIRneg ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 setminusLsub ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 setminusSubset1 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 symdiffE ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 symdiffI1 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 symdiffI2 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 symdiffIneg1 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 symdiffIneg2 ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 secondinupair ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 setukpairIL ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 setukpairIR ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 kpairiskpair ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 kpairp ) =>
% 2.45/1.16 (
% 2.45/1.16 (
% 2.45/1.16 singletonsubset ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 singletoninpowerset ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 ![
% 2.45/1.17 X88:$i,
% 2.45/1.17 X90:$i,
% 2.45/1.17 X92:$i]:
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 in @
% 2.45/1.17 X92 @ X88 ) =>
% 2.45/1.17 (
% 2.45/1.17 in @
% 2.45/1.17 (
% 2.45/1.17 setadjoin
% 2.45/1.17 @
% 2.45/1.17 X92 @
% 2.45/1.17 emptyset ) @
% 2.45/1.17 (
% 2.45/1.17 powerset @
% 2.45/1.17 (
% 2.45/1.17 binunion @
% 2.45/1.17 X88 @ X90 ) ) ) ) ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 upairset2E ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 ![
% 2.45/1.17 X94:$i,
% 2.45/1.17 X96:$i,
% 2.45/1.17 X98:$i]:
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 in @
% 2.45/1.17 X98 @ X94 ) =>
% 2.45/1.17 (
% 2.45/1.17 ![
% 2.45/1.17 X100:$i]:
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 in @
% 2.45/1.17 X100 @ X96 ) =>
% 2.45/1.17 (
% 2.45/1.17 subset @
% 2.45/1.17 (
% 2.45/1.17 setadjoin
% 2.45/1.17 @
% 2.45/1.17 X98 @
% 2.45/1.17 (
% 2.45/1.17 setadjoin
% 2.45/1.17 @
% 2.45/1.17 X100 @
% 2.45/1.17 emptyset ) ) @
% 2.45/1.17 (
% 2.45/1.17 binunion @
% 2.45/1.17 X94 @ X96 ) ) ) ) ) ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 ![
% 2.45/1.17 X102:$i,
% 2.45/1.17 X104:$i,
% 2.45/1.17 X106:$i]:
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 in @
% 2.45/1.17 X106 @
% 2.45/1.17 X102 ) =>
% 2.45/1.17 (
% 2.45/1.17 ![
% 2.45/1.17 X108:$i]:
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 in @
% 2.45/1.17 X108 @
% 2.45/1.17 X104 ) =>
% 2.45/1.17 (
% 2.45/1.17 in @
% 2.45/1.17 (
% 2.45/1.17 setadjoin
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% 2.45/1.17 X106 @
% 2.45/1.17 (
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% 2.45/1.17 (
% 2.45/1.17 subset @
% 2.45/1.17 (
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% 2.45/1.17 (
% 2.45/1.17 setadjoin
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% 2.45/1.17 X114 @
% 2.45/1.17 emptyset ) @
% 2.45/1.17 (
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% 2.45/1.17 (
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% 2.45/1.17 (
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% 2.45/1.17 (
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% 2.45/1.17 X122 @
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% 2.45/1.17 (
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% 2.45/1.17 (
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% 2.45/1.17 (
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% 2.45/1.17 (
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% 2.45/1.17 X128 ) =>
% 2.45/1.17 (
% 2.45/1.17 in @
% 2.45/1.17 (
% 2.45/1.17 kpair @
% 2.45/1.17 X130 @
% 2.45/1.17 X132 ) @
% 2.45/1.17 (
% 2.45/1.17 powerset @
% 2.45/1.17 (
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% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 cartprodpairin ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 cartprodmempair1 ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 cartprodmempair ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 setunionE2 ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 setunionsingleton1 ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 setunionsingleton2 ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 setunionsingleton ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 singletonprop ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 ex1E1 ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 ex1I ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 ex1I2 ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 singletonsuniq ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 setukpairinjL1 ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 kfstsingleton ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 theprop ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 kfstpairEq ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 cartprodfstin ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 setukpairinjL2 ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 setukpairinjL ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 setukpairinjR11 ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 setukpairinjR12 ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 setukpairinjR1 ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 upairequniteq ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 setukpairinjR2 ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 setukpairinjR ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 ksndsingleton ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 ksndpairEq ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 kpairsurjEq ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 cartprodsndin ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 cartprodpairmemEL ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 cartprodpairmemER ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 cartprodmempaircEq ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 cartprodfstpairEq ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 cartprodsndpairEq ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 cartprodpairsurjEq ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 dpsetconstrI ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 dpsetconstrSub ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 setOfPairsIsBReln ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 dpsetconstrERa ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 dpsetconstrEL1 ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 dpsetconstrEL2 ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 dpsetconstrER ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 funcImageSingleton ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 apProp ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 app ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 infuncsetfunc ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 ap2p ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 funcinfuncset ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 lamProp ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 lamp ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 lam2p ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 brelnall1 ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 brelnall2 ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 ex1E2 ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 funcGraphProp1 ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 funcGraphProp3 ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 funcGraphProp2 ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 funcextLem ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 funcGraphProp4 ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 subbreln ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 eqbreln ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 funcext ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 funcext2 ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 ap2apEq1 ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 ap2apEq2 ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 beta1 ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 eta1 ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 lam2lamEq ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 beta2 ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 eta2 ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 iffalseProp1 ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 iffalseProp2 ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 iftrueProp1 ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 iftrueProp2 ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 ifSingleton ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 ifp ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 theeq ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 iftrue ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 iffalse ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 iftrueorfalse ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 binintersectT_lem ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 ![
% 2.45/1.17 X134:$i,
% 2.45/1.17 X136:$i]:
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% 2.45/1.17 (
% 2.45/1.17 ![
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% 2.45/1.17 (
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% 2.45/1.17 (
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% 2.45/1.17 X142 @
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% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 setminusT_lem ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 complementT_lem ) =>
% 2.45/1.17 (
% 2.45/1.17 (
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% 2.45/1.17 X144:$i,
% 2.45/1.17 X146:$i]:
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% 2.45/1.17 X174 ) ) ) ) ) ) ) ) ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 complementTI1 ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 complementTE1 ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 binintersectTELcontra ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 binintersectTERcontra ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 contrasubsetT ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 ![
% 2.45/1.17 X178:$i,
% 2.45/1.17 X180:$i]:
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 in @
% 2.45/1.17 X180 @
% 2.45/1.17 (
% 2.45/1.17 powerset @
% 2.45/1.17 X178 ) ) =>
% 2.45/1.17 (
% 2.45/1.17 ![
% 2.45/1.17 X182:$i]:
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 in @
% 2.45/1.17 X182 @
% 2.45/1.17 (
% 2.45/1.17 powerset @
% 2.45/1.17 X178 ) ) =>
% 2.45/1.17 (
% 2.45/1.17 ![
% 2.45/1.17 X184:$i]:
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 in @
% 2.45/1.17 X184 @
% 2.45/1.17 X178 ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 subset @
% 2.45/1.17 X180 @
% 2.45/1.17 X182 ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 ~(
% 2.45/1.17 in @
% 2.45/1.17 X184 @
% 2.45/1.17 X182 ) ) =>
% 2.45/1.17 (
% 2.45/1.17 ~(
% 2.45/1.17 in @
% 2.45/1.17 X184 @
% 2.45/1.17 X180 ) ) ) ) ) ) ) ) ) ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 contrasubsetT2 ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 contrasubsetT3 ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 doubleComplementI1 ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 doubleComplementE1 ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 doubleComplementSub1 ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 doubleComplementSub2 ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 doubleComplementEq ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 complementTnotintersectT ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 complementImpComplementIntersect ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 complementSubsetComplementIntersect ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 complementInPowersetComplementIntersect ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 contraSubsetComplement ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 complementTcontraSubset ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 ![
% 2.45/1.17 X186:$i,
% 2.45/1.17 X188:$i]:
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 in @
% 2.45/1.17 X188 @
% 2.45/1.17 (
% 2.45/1.17 powerset @
% 2.45/1.17 X186 ) ) =>
% 2.45/1.17 (
% 2.45/1.17 ![
% 2.45/1.17 X190:$i]:
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 in @
% 2.45/1.17 X190 @
% 2.45/1.17 (
% 2.45/1.17 powerset @
% 2.45/1.17 X186 ) ) =>
% 2.45/1.17 (
% 2.45/1.17 ![
% 2.45/1.17 X192:$i]:
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 in @
% 2.45/1.17 X192 @
% 2.45/1.17 X186 ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 ~(
% 2.45/1.17 in @
% 2.45/1.17 X192 @
% 2.45/1.17 (
% 2.45/1.17 binunion
% 2.45/1.17 @
% 2.45/1.17 X188 @
% 2.45/1.17 X190 ) ) ) =>
% 2.45/1.17 (
% 2.45/1.17 ~(
% 2.45/1.17 in @
% 2.45/1.17 X192 @
% 2.45/1.17 X188 ) ) ) ) ) ) ) ) ) =>
% 2.45/1.17 (
% 2.45/1.17 ![
% 2.45/1.17 X194:$i,
% 2.45/1.17 X196:$i]:
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 in @
% 2.45/1.17 X196 @
% 2.45/1.17 (
% 2.45/1.17 powerset @
% 2.45/1.17 X194 ) ) =>
% 2.45/1.17 (
% 2.45/1.17 ![
% 2.45/1.17 X198:$i]:
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 in @
% 2.45/1.17 X198 @
% 2.45/1.17 (
% 2.45/1.17 powerset @
% 2.45/1.17 X194 ) ) =>
% 2.45/1.17 (
% 2.45/1.17 ![
% 2.45/1.17 X200:$i]:
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 in @
% 2.45/1.17 X200 @
% 2.45/1.17 X194 ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 ~(
% 2.45/1.17 in @
% 2.45/1.17 X200 @
% 2.45/1.17 (
% 2.45/1.17 binunion
% 2.45/1.17 @
% 2.45/1.17 X196 @
% 2.45/1.17 X198 ) ) ) =>
% 2.45/1.17 (
% 2.45/1.17 ~(
% 2.45/1.17 in @
% 2.45/1.17 X200 @
% 2.45/1.17 X198 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 2.45/1.17 thf(zf_stmt_4, negated_conjecture,
% 2.45/1.17 (~( ( setextAx ) =>
% 2.45/1.17 ( ( emptysetAx ) =>
% 2.45/1.17 ( ( setadjoinAx ) =>
% 2.45/1.17 ( ( ![X4:$i,X6:$i]:
% 2.45/1.17 ( ( in @ X6 @ ( powerset @ X4 ) ) <=>
% 2.45/1.17 ( ![X8:$i]: ( zip_tseitin_0 @ X8 @ X6 @ X4 ) ) ) ) =>
% 2.45/1.17 ( ( setunionAx ) =>
% 2.45/1.17 ( ( omega0Ax ) =>
% 2.45/1.17 ( ( omegaSAx ) =>
% 2.45/1.17 ( ( omegaIndAx ) =>
% 2.45/1.17 ( ( replAx ) =>
% 2.45/1.17 ( ( foundationAx ) =>
% 2.45/1.17 ( ( wellorderingAx ) =>
% 2.45/1.17 ( ( descrp ) =>
% 2.45/1.17 ( ( dsetconstrI ) =>
% 2.45/1.17 ( ( dsetconstrEL ) =>
% 2.45/1.17 ( ( dsetconstrER ) =>
% 2.45/1.17 ( ( exuE1 ) =>
% 2.45/1.17 ( ( prop2setE ) =>
% 2.45/1.17 ( ( emptysetE ) =>
% 2.45/1.17 ( ( emptysetimpfalse ) =>
% 2.45/1.17 ( ( notinemptyset ) =>
% 2.45/1.17 ( ( exuE3e ) =>
% 2.45/1.17 ( ( setext ) =>
% 2.45/1.17 ( ( emptyI ) =>
% 2.45/1.17 ( ( noeltsimpempty ) =>
% 2.45/1.17 ( ( setbeta ) =>
% 2.45/1.17 ( ( nonemptyE1 ) =>
% 2.45/1.17 ( ( nonemptyI ) =>
% 2.45/1.17 ( ( nonemptyI1 ) =>
% 2.45/1.17 ( ( setadjoinIL ) =>
% 2.45/1.17 ( ( emptyinunitempty ) =>
% 2.45/1.17 ( ( setadjoinIR ) =>
% 2.45/1.17 ( (
% 2.45/1.17 setadjoinE ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 setadjoinOr ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 setoftrueEq ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 ![
% 2.45/1.17 X10:$i,
% 2.45/1.17 X12:$i]:
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 ![
% 2.45/1.17 X14:$i]:
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 in @
% 2.45/1.17 X14 @ X12 ) =>
% 2.45/1.17 (
% 2.45/1.17 in @
% 2.45/1.17 X14 @ X10 ) ) ) =>
% 2.45/1.17 (
% 2.45/1.17 in @
% 2.45/1.17 X12 @
% 2.45/1.17 (
% 2.45/1.17 powerset
% 2.45/1.17 @
% 2.45/1.17 X10 ) ) ) ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 ![
% 2.45/1.17 X16:$i]:
% 2.45/1.17 (
% 2.45/1.17 in @
% 2.45/1.17 emptyset @
% 2.45/1.17 (
% 2.45/1.17 powerset
% 2.45/1.17 @
% 2.45/1.17 X16 ) ) ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 ![
% 2.45/1.17 X18:$i]:
% 2.45/1.17 (
% 2.45/1.17 in @
% 2.45/1.17 emptyset @
% 2.45/1.17 (
% 2.45/1.17 powerset
% 2.45/1.17 @
% 2.45/1.17 X18 ) ) ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 ![
% 2.45/1.17 X20:$i,
% 2.45/1.17 X22:$i,
% 2.45/1.17 X24:$i]:
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 in @
% 2.45/1.17 X22 @
% 2.45/1.17 (
% 2.45/1.17 powerset
% 2.45/1.17 @
% 2.45/1.17 X20 ) ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 in @
% 2.45/1.17 X24 @ X22 ) =>
% 2.45/1.17 (
% 2.45/1.17 in @
% 2.45/1.17 X24 @ X20 ) ) ) ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 setunionI ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 setunionE ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 subPowSU ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 exuE2 ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 nonemptyImpWitness ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 uniqinunit ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 notinsingleton ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 eqinunit ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 singletonsswitch ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 upairsetE ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 upairsetIL ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 upairsetIR ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 emptyE1 ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 vacuousDall ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 quantDeMorgan1 ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 quantDeMorgan2 ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 quantDeMorgan3 ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 quantDeMorgan4 ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 prop2setI ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 prop2set2propI ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 notdexE ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 notdallE ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 exuI1 ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 exuI3 ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 exuI2 ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 inCongP ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 in__Cong ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 exuE3u ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 exu__Cong ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 emptyset__Cong ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 setadjoin__Cong ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 ![
% 2.45/1.17 X26:$i,
% 2.45/1.17 X28:$i]:
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 X26 ) =
% 2.45/1.17 (
% 2.45/1.17 X28 ) ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 powerset
% 2.45/1.17 @
% 2.45/1.17 X26 ) =
% 2.45/1.17 (
% 2.45/1.17 powerset
% 2.45/1.17 @
% 2.45/1.17 X28 ) ) ) ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 setunion__Cong ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 omega__Cong ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 exuEu ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 descr__Cong ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 dsetconstr__Cong ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 subsetI1 ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 eqimpsubset2 ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 eqimpsubset1 ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 subsetI2 ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 emptysetsubset ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 subsetE ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 subsetE2 ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 notsubsetI ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 notequalI1 ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 notequalI2 ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 subsetRefl ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 subsetTrans ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 setadjoinSub ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 setadjoinSub2 ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 ![
% 2.45/1.17 X30:$i,
% 2.45/1.17 X32:$i]:
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 subset @
% 2.45/1.17 X30 @ X32 ) =>
% 2.45/1.17 (
% 2.45/1.17 in @
% 2.45/1.17 X30 @
% 2.45/1.17 (
% 2.45/1.17 powerset
% 2.45/1.17 @
% 2.45/1.17 X32 ) ) ) ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 setextsub ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 subsetemptysetimpeq ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 ![
% 2.45/1.17 X34:$i,
% 2.45/1.17 X36:$i]:
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 subset @
% 2.45/1.17 X36 @ X34 ) =>
% 2.45/1.17 (
% 2.45/1.17 in @
% 2.45/1.17 X36 @
% 2.45/1.17 (
% 2.45/1.17 powerset
% 2.45/1.17 @
% 2.45/1.17 X34 ) ) ) ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 ![
% 2.45/1.17 X38:$i,
% 2.45/1.17 X40:$i]:
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 in @
% 2.45/1.17 X40 @
% 2.45/1.17 (
% 2.45/1.17 powerset
% 2.45/1.17 @
% 2.45/1.17 X38 ) ) =>
% 2.45/1.17 (
% 2.45/1.17 subset @
% 2.45/1.17 X40 @ X38 ) ) ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 ![
% 2.45/1.17 X42:$i]:
% 2.45/1.17 (
% 2.45/1.17 in @
% 2.45/1.17 X42 @
% 2.45/1.17 (
% 2.45/1.17 powerset
% 2.45/1.17 @
% 2.45/1.17 X42 ) ) ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 ![
% 2.45/1.17 X44:$i,
% 2.45/1.17 X46:$i]:
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 subset @
% 2.45/1.17 X44 @ X46 ) =>
% 2.45/1.17 (
% 2.45/1.17 subset @
% 2.45/1.17 (
% 2.45/1.17 powerset
% 2.45/1.17 @
% 2.45/1.17 X44 ) @
% 2.45/1.17 (
% 2.45/1.17 powerset
% 2.45/1.17 @
% 2.45/1.17 X46 ) ) ) ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 sepInPowerset ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 sepSubset ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 ![
% 2.45/1.17 X48:$i,
% 2.45/1.17 X50:$i,
% 2.45/1.17 X52:$i]:
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 in @
% 2.45/1.17 X52 @ X48 ) =>
% 2.45/1.17 (
% 2.45/1.17 in @
% 2.45/1.17 X52 @
% 2.45/1.17 (
% 2.45/1.17 binunion
% 2.45/1.17 @
% 2.45/1.17 X48 @ X50 ) ) ) ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 upairset2IR ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 ![
% 2.45/1.17 X54:$i,
% 2.45/1.17 X56:$i,
% 2.45/1.17 X58:$i]:
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 in @
% 2.45/1.17 X58 @ X56 ) =>
% 2.45/1.17 (
% 2.45/1.17 in @
% 2.45/1.17 X58 @
% 2.45/1.17 (
% 2.45/1.17 binunion
% 2.45/1.17 @
% 2.45/1.17 X54 @ X56 ) ) ) ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 ![
% 2.45/1.17 X60:$i,
% 2.45/1.17 X62:$i,
% 2.45/1.17 X64:$i,
% 2.45/1.17 X66:$o]:
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 in @
% 2.45/1.17 X64 @
% 2.45/1.17 (
% 2.45/1.17 binunion
% 2.45/1.17 @
% 2.45/1.17 X60 @ X62 ) ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 in @
% 2.45/1.17 X64 @ X60 ) =>
% 2.45/1.17 (
% 2.45/1.17 X66 ) ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 in @
% 2.45/1.17 X64 @ X62 ) =>
% 2.45/1.17 (
% 2.45/1.17 X66 ) ) =>
% 2.45/1.17 (
% 2.45/1.17 X66 ) ) ) ) ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 ![
% 2.45/1.17 X68:$i,
% 2.45/1.17 X70:$i,
% 2.45/1.17 X72:$i]:
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 in @
% 2.45/1.17 X72 @
% 2.45/1.17 (
% 2.45/1.17 binunion
% 2.45/1.17 @
% 2.45/1.17 X68 @ X70 ) ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 in @
% 2.45/1.17 X72 @ X68 ) |
% 2.45/1.17 (
% 2.45/1.17 in @
% 2.45/1.17 X72 @ X70 ) ) ) ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 ![
% 2.45/1.17 X74:$i,
% 2.45/1.17 X76:$i]:
% 2.45/1.17 (
% 2.45/1.17 subset @
% 2.45/1.17 X74 @
% 2.45/1.17 (
% 2.45/1.17 binunion
% 2.45/1.17 @
% 2.45/1.17 X74 @ X76 ) ) ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 ![
% 2.45/1.17 X78:$i,
% 2.45/1.17 X80:$i]:
% 2.45/1.17 (
% 2.45/1.17 subset @
% 2.45/1.17 X80 @
% 2.45/1.17 (
% 2.45/1.17 binunion
% 2.45/1.17 @
% 2.45/1.17 X78 @ X80 ) ) ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 binintersectI ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 binintersectSubset5 ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 binintersectEL ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 binintersectLsub ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 binintersectSubset2 ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 binintersectSubset3 ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 binintersectER ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 disjointsetsI1 ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 binintersectRsub ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 binintersectSubset4 ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 binintersectSubset1 ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 ![
% 2.45/1.17 X82:$i,
% 2.45/1.17 X84:$i,
% 2.45/1.17 X86:$i]:
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 binintersect
% 2.45/1.17 @
% 2.45/1.17 X82 @
% 2.45/1.17 (
% 2.45/1.17 binunion
% 2.45/1.17 @
% 2.45/1.17 X84 @ X86 ) ) =
% 2.45/1.17 (
% 2.45/1.17 binunion
% 2.45/1.17 @
% 2.45/1.17 (
% 2.45/1.17 binintersect
% 2.45/1.17 @
% 2.45/1.17 X82 @ X84 ) @
% 2.45/1.17 (
% 2.45/1.17 binintersect
% 2.45/1.17 @
% 2.45/1.17 X82 @ X86 ) ) ) ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 setminusI ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 setminusEL ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 setminusER ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 setminusSubset2 ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 setminusERneg ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 setminusELneg ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 setminusILneg ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 setminusIRneg ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 setminusLsub ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 setminusSubset1 ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 symdiffE ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 symdiffI1 ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 symdiffI2 ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 symdiffIneg1 ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 symdiffIneg2 ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 secondinupair ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 setukpairIL ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 setukpairIR ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 kpairiskpair ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 kpairp ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 singletonsubset ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 singletoninpowerset ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 ![
% 2.45/1.17 X88:$i,
% 2.45/1.17 X90:$i,
% 2.45/1.17 X92:$i]:
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 in @
% 2.45/1.17 X92 @ X88 ) =>
% 2.45/1.17 (
% 2.45/1.17 in @
% 2.45/1.17 (
% 2.45/1.17 setadjoin
% 2.45/1.17 @
% 2.45/1.17 X92 @
% 2.45/1.17 emptyset ) @
% 2.45/1.17 (
% 2.45/1.17 powerset
% 2.45/1.17 @
% 2.45/1.17 (
% 2.45/1.17 binunion
% 2.45/1.17 @
% 2.45/1.17 X88 @ X90 ) ) ) ) ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 upairset2E ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 ![
% 2.45/1.17 X94:$i,
% 2.45/1.17 X96:$i,
% 2.45/1.17 X98:$i]:
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 in @
% 2.45/1.17 X98 @ X94 ) =>
% 2.45/1.17 (
% 2.45/1.17 ![
% 2.45/1.17 X100:$i]:
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 in @
% 2.45/1.17 X100 @
% 2.45/1.17 X96 ) =>
% 2.45/1.17 (
% 2.45/1.17 subset @
% 2.45/1.17 (
% 2.45/1.17 setadjoin
% 2.45/1.17 @
% 2.45/1.17 X98 @
% 2.45/1.17 (
% 2.45/1.17 setadjoin
% 2.45/1.17 @
% 2.45/1.17 X100 @
% 2.45/1.17 emptyset ) ) @
% 2.45/1.17 (
% 2.45/1.17 binunion
% 2.45/1.17 @
% 2.45/1.17 X94 @ X96 ) ) ) ) ) ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 ![
% 2.45/1.17 X102:$i,
% 2.45/1.17 X104:$i,
% 2.45/1.17 X106:$i]:
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 in @
% 2.45/1.17 X106 @
% 2.45/1.17 X102 ) =>
% 2.45/1.17 (
% 2.45/1.17 ![
% 2.45/1.17 X108:$i]:
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 in @
% 2.45/1.17 X108 @
% 2.45/1.17 X104 ) =>
% 2.45/1.17 (
% 2.45/1.17 in @
% 2.45/1.17 (
% 2.45/1.17 setadjoin
% 2.45/1.17 @
% 2.45/1.17 X106 @
% 2.45/1.17 (
% 2.45/1.17 setadjoin
% 2.45/1.17 @
% 2.45/1.17 X108 @
% 2.45/1.17 emptyset ) ) @
% 2.45/1.17 (
% 2.45/1.17 powerset
% 2.45/1.17 @
% 2.45/1.17 (
% 2.45/1.17 binunion
% 2.45/1.17 @
% 2.45/1.17 X102 @
% 2.45/1.17 X104 ) ) ) ) ) ) ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 ![
% 2.45/1.17 X110:$i,
% 2.45/1.17 X112:$i,
% 2.45/1.17 X114:$i]:
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 in @
% 2.45/1.17 X114 @
% 2.45/1.17 X110 ) =>
% 2.45/1.17 (
% 2.45/1.17 ![
% 2.45/1.17 X116:$i]:
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 in @
% 2.45/1.17 X116 @
% 2.45/1.17 X112 ) =>
% 2.45/1.17 (
% 2.45/1.17 subset @
% 2.45/1.17 (
% 2.45/1.17 setadjoin
% 2.45/1.17 @
% 2.45/1.17 (
% 2.45/1.17 setadjoin
% 2.45/1.17 @
% 2.45/1.17 X114 @
% 2.45/1.17 emptyset ) @
% 2.45/1.17 (
% 2.45/1.17 setadjoin
% 2.45/1.17 @
% 2.45/1.17 (
% 2.45/1.17 setadjoin
% 2.45/1.17 @
% 2.45/1.17 X114 @
% 2.45/1.17 (
% 2.45/1.17 setadjoin
% 2.45/1.17 @
% 2.45/1.17 X116 @
% 2.45/1.17 emptyset ) ) @
% 2.45/1.17 emptyset ) ) @
% 2.45/1.17 (
% 2.45/1.17 powerset
% 2.45/1.17 @
% 2.45/1.17 (
% 2.45/1.17 binunion
% 2.45/1.17 @
% 2.45/1.17 X110 @
% 2.45/1.17 X112 ) ) ) ) ) ) ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 ![
% 2.45/1.17 X118:$i,
% 2.45/1.17 X120:$i,
% 2.45/1.17 X122:$i]:
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 in @
% 2.45/1.17 X122 @
% 2.45/1.17 X118 ) =>
% 2.45/1.17 (
% 2.45/1.17 ![
% 2.45/1.17 X124:$i]:
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 in @
% 2.45/1.17 X124 @
% 2.45/1.17 X120 ) =>
% 2.45/1.17 (
% 2.45/1.17 in @
% 2.45/1.17 (
% 2.45/1.17 setadjoin
% 2.45/1.17 @
% 2.45/1.17 (
% 2.45/1.17 setadjoin
% 2.45/1.17 @
% 2.45/1.17 X122 @
% 2.45/1.17 emptyset ) @
% 2.45/1.17 (
% 2.45/1.17 setadjoin
% 2.45/1.17 @
% 2.45/1.17 (
% 2.45/1.17 setadjoin
% 2.45/1.17 @
% 2.45/1.17 X122 @
% 2.45/1.17 (
% 2.45/1.17 setadjoin
% 2.45/1.17 @
% 2.45/1.17 X124 @
% 2.45/1.17 emptyset ) ) @
% 2.45/1.17 emptyset ) ) @
% 2.45/1.17 (
% 2.45/1.17 powerset
% 2.45/1.17 @
% 2.45/1.17 (
% 2.45/1.17 powerset
% 2.45/1.17 @
% 2.45/1.17 (
% 2.45/1.17 binunion
% 2.45/1.17 @
% 2.45/1.17 X118 @
% 2.45/1.17 X120 ) ) ) ) ) ) ) ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 ![
% 2.45/1.17 X126:$i,
% 2.45/1.17 X128:$i,
% 2.45/1.17 X130:$i]:
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 in @
% 2.45/1.17 X130 @
% 2.45/1.17 X126 ) =>
% 2.45/1.17 (
% 2.45/1.17 ![
% 2.45/1.17 X132:$i]:
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 in @
% 2.45/1.17 X132 @
% 2.45/1.17 X128 ) =>
% 2.45/1.17 (
% 2.45/1.17 in @
% 2.45/1.17 (
% 2.45/1.17 kpair @
% 2.45/1.17 X130 @
% 2.45/1.17 X132 ) @
% 2.45/1.17 (
% 2.45/1.17 powerset
% 2.45/1.17 @
% 2.45/1.17 (
% 2.45/1.17 powerset
% 2.45/1.17 @
% 2.45/1.17 (
% 2.45/1.17 binunion
% 2.45/1.17 @
% 2.45/1.17 X126 @
% 2.45/1.17 X128 ) ) ) ) ) ) ) ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 cartprodpairin ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 cartprodmempair1 ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 cartprodmempair ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 setunionE2 ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 setunionsingleton1 ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 setunionsingleton2 ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 setunionsingleton ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 singletonprop ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 ex1E1 ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 ex1I ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 ex1I2 ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 singletonsuniq ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 setukpairinjL1 ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 kfstsingleton ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 theprop ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 kfstpairEq ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 cartprodfstin ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 setukpairinjL2 ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 setukpairinjL ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 setukpairinjR11 ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 setukpairinjR12 ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 setukpairinjR1 ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 upairequniteq ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 setukpairinjR2 ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 setukpairinjR ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 ksndsingleton ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 ksndpairEq ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 kpairsurjEq ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 cartprodsndin ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 cartprodpairmemEL ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 cartprodpairmemER ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 cartprodmempaircEq ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 cartprodfstpairEq ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 cartprodsndpairEq ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 cartprodpairsurjEq ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 dpsetconstrI ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 dpsetconstrSub ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 setOfPairsIsBReln ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 dpsetconstrERa ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 dpsetconstrEL1 ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 dpsetconstrEL2 ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 dpsetconstrER ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 funcImageSingleton ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 apProp ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 app ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 infuncsetfunc ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 ap2p ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 funcinfuncset ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 lamProp ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 lamp ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 lam2p ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 brelnall1 ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 brelnall2 ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 ex1E2 ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 funcGraphProp1 ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 funcGraphProp3 ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 funcGraphProp2 ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 funcextLem ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 funcGraphProp4 ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 subbreln ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 eqbreln ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 funcext ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 funcext2 ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 ap2apEq1 ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 ap2apEq2 ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 beta1 ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 eta1 ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 lam2lamEq ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 beta2 ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 eta2 ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 iffalseProp1 ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 iffalseProp2 ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 iftrueProp1 ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 iftrueProp2 ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 ifSingleton ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 ifp ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 theeq ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 iftrue ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 iffalse ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 iftrueorfalse ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 binintersectT_lem ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 ![
% 2.45/1.17 X134:$i,
% 2.45/1.17 X136:$i]:
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 in @
% 2.45/1.17 X136 @
% 2.45/1.17 (
% 2.45/1.17 powerset
% 2.45/1.17 @
% 2.45/1.17 X134 ) ) =>
% 2.45/1.17 (
% 2.45/1.17 ![
% 2.45/1.17 X138:$i]:
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 in @
% 2.45/1.17 X138 @
% 2.45/1.17 (
% 2.45/1.17 powerset
% 2.45/1.17 @
% 2.45/1.17 X134 ) ) =>
% 2.45/1.17 (
% 2.45/1.17 in @
% 2.45/1.17 (
% 2.45/1.17 binunion
% 2.45/1.17 @
% 2.45/1.17 X136 @
% 2.45/1.17 X138 ) @
% 2.45/1.17 (
% 2.45/1.17 powerset
% 2.45/1.17 @
% 2.45/1.17 X134 ) ) ) ) ) ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 ![
% 2.45/1.17 X140:$i,
% 2.45/1.17 X142:$i]:
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 in @
% 2.45/1.17 X142 @
% 2.45/1.17 (
% 2.45/1.17 powerset
% 2.45/1.17 @
% 2.45/1.17 X140 ) ) =>
% 2.45/1.17 (
% 2.45/1.17 in @
% 2.45/1.17 (
% 2.45/1.17 powerset
% 2.45/1.17 @
% 2.45/1.17 X142 ) @
% 2.45/1.17 (
% 2.45/1.17 powerset
% 2.45/1.17 @
% 2.45/1.17 (
% 2.45/1.17 powerset
% 2.45/1.17 @
% 2.45/1.17 X140 ) ) ) ) ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 setminusT_lem ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 complementT_lem ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 ![
% 2.45/1.17 X144:$i,
% 2.45/1.17 X146:$i]:
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 in @
% 2.45/1.17 X146 @
% 2.45/1.17 (
% 2.45/1.17 powerset
% 2.45/1.17 @
% 2.45/1.17 X144 ) ) =>
% 2.45/1.17 (
% 2.45/1.17 ![
% 2.45/1.17 X148:$i]:
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 in @
% 2.45/1.17 X148 @
% 2.45/1.17 (
% 2.45/1.17 powerset
% 2.45/1.17 @
% 2.45/1.17 X144 ) ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 ![
% 2.45/1.17 X150:$i]:
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 in @
% 2.45/1.17 X150 @
% 2.45/1.17 X144 ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 in @
% 2.45/1.17 X150 @
% 2.45/1.17 X146 ) =>
% 2.45/1.17 (
% 2.45/1.17 in @
% 2.45/1.17 X150 @
% 2.45/1.17 X148 ) ) ) ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 ![
% 2.45/1.17 X152:$i]:
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 in @
% 2.45/1.17 X152 @
% 2.45/1.17 X144 ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 in @
% 2.45/1.17 X152 @
% 2.45/1.17 X148 ) =>
% 2.45/1.17 (
% 2.45/1.17 in @
% 2.45/1.17 X152 @
% 2.45/1.17 X146 ) ) ) ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 X146 ) =
% 2.45/1.17 (
% 2.45/1.17 X148 ) ) ) ) ) ) ) ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 ![
% 2.45/1.17 X154:$i,
% 2.45/1.17 X156:$i]:
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 in @
% 2.45/1.17 X156 @
% 2.45/1.17 (
% 2.45/1.17 powerset
% 2.45/1.17 @
% 2.45/1.17 X154 ) ) =>
% 2.45/1.17 (
% 2.45/1.17 ![
% 2.45/1.17 X158:$i]:
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 in @
% 2.45/1.17 X158 @
% 2.45/1.17 (
% 2.45/1.17 powerset
% 2.45/1.17 @
% 2.45/1.17 X154 ) ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 ![
% 2.45/1.17 X160:$i]:
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 in @
% 2.45/1.17 X160 @
% 2.45/1.17 X154 ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 in @
% 2.45/1.17 X160 @
% 2.45/1.17 X156 ) =>
% 2.45/1.17 (
% 2.45/1.17 in @
% 2.45/1.17 X160 @
% 2.45/1.17 X158 ) ) ) ) =>
% 2.45/1.17 (
% 2.45/1.17 subset @
% 2.45/1.17 X156 @
% 2.45/1.17 X158 ) ) ) ) ) ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 ![
% 2.45/1.17 X162:$i,
% 2.45/1.17 X164:$i]:
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 in @
% 2.45/1.17 X164 @
% 2.45/1.17 (
% 2.45/1.17 powerset
% 2.45/1.17 @
% 2.45/1.17 X162 ) ) =>
% 2.45/1.17 (
% 2.45/1.17 ![
% 2.45/1.17 X166:$i]:
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 in @
% 2.45/1.17 X166 @
% 2.45/1.17 (
% 2.45/1.17 powerset
% 2.45/1.17 @
% 2.45/1.17 X162 ) ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 ![
% 2.45/1.17 X168:$i]:
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 in @
% 2.45/1.17 X168 @
% 2.45/1.17 X162 ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 in @
% 2.45/1.17 X168 @
% 2.45/1.17 X164 ) =>
% 2.45/1.17 (
% 2.45/1.17 in @
% 2.45/1.17 X168 @
% 2.45/1.17 X166 ) ) ) ) =>
% 2.45/1.17 (
% 2.45/1.17 in @
% 2.45/1.17 X164 @
% 2.45/1.17 (
% 2.45/1.17 powerset
% 2.45/1.17 @
% 2.45/1.17 X166 ) ) ) ) ) ) ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 ![
% 2.45/1.17 X170:$i,
% 2.45/1.17 X172:$i]:
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 in @
% 2.45/1.17 X172 @
% 2.45/1.17 (
% 2.45/1.17 powerset
% 2.45/1.17 @
% 2.45/1.17 X170 ) ) =>
% 2.45/1.17 (
% 2.45/1.17 ![
% 2.45/1.17 X174:$i]:
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 in @
% 2.45/1.17 X174 @
% 2.45/1.17 (
% 2.45/1.17 powerset
% 2.45/1.17 @
% 2.45/1.17 X170 ) ) =>
% 2.45/1.17 (
% 2.45/1.17 ![
% 2.45/1.17 X176:$i]:
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 in @
% 2.45/1.17 X176 @
% 2.45/1.17 X170 ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 in @
% 2.45/1.17 X172 @
% 2.45/1.17 (
% 2.45/1.17 powerset
% 2.45/1.17 @
% 2.45/1.17 X174 ) ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 in @
% 2.45/1.17 X176 @
% 2.45/1.17 X172 ) =>
% 2.45/1.17 (
% 2.45/1.17 in @
% 2.45/1.17 X176 @
% 2.45/1.17 X174 ) ) ) ) ) ) ) ) ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 complementTI1 ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 complementTE1 ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 binintersectTELcontra ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 binintersectTERcontra ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 contrasubsetT ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 ![
% 2.45/1.17 X178:$i,
% 2.45/1.17 X180:$i]:
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 in @
% 2.45/1.17 X180 @
% 2.45/1.17 (
% 2.45/1.17 powerset
% 2.45/1.17 @
% 2.45/1.17 X178 ) ) =>
% 2.45/1.17 (
% 2.45/1.17 ![
% 2.45/1.17 X182:$i]:
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 in @
% 2.45/1.17 X182 @
% 2.45/1.17 (
% 2.45/1.17 powerset
% 2.45/1.17 @
% 2.45/1.17 X178 ) ) =>
% 2.45/1.17 (
% 2.45/1.17 ![
% 2.45/1.17 X184:$i]:
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 in @
% 2.45/1.17 X184 @
% 2.45/1.17 X178 ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 subset @
% 2.45/1.17 X180 @
% 2.45/1.17 X182 ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 ~
% 2.45/1.17 (
% 2.45/1.17 in @
% 2.45/1.17 X184 @
% 2.45/1.17 X182 ) ) =>
% 2.45/1.17 (
% 2.45/1.17 ~
% 2.45/1.17 (
% 2.45/1.17 in @
% 2.45/1.17 X184 @
% 2.45/1.17 X180 ) ) ) ) ) ) ) ) ) ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 contrasubsetT2 ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 contrasubsetT3 ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 doubleComplementI1 ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 doubleComplementE1 ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 doubleComplementSub1 ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 doubleComplementSub2 ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 doubleComplementEq ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 complementTnotintersectT ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 complementImpComplementIntersect ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 complementSubsetComplementIntersect ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 complementInPowersetComplementIntersect ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 contraSubsetComplement ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 complementTcontraSubset ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 ![
% 2.45/1.17 X186:$i,
% 2.45/1.17 X188:$i]:
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 in @
% 2.45/1.17 X188 @
% 2.45/1.17 (
% 2.45/1.17 powerset
% 2.45/1.17 @
% 2.45/1.17 X186 ) ) =>
% 2.45/1.17 (
% 2.45/1.17 ![
% 2.45/1.17 X190:$i]:
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 in @
% 2.45/1.17 X190 @
% 2.45/1.17 (
% 2.45/1.17 powerset
% 2.45/1.17 @
% 2.45/1.17 X186 ) ) =>
% 2.45/1.17 (
% 2.45/1.17 ![
% 2.45/1.17 X192:$i]:
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 in @
% 2.45/1.17 X192 @
% 2.45/1.17 X186 ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 ~
% 2.45/1.17 (
% 2.45/1.17 in @
% 2.45/1.17 X192 @
% 2.45/1.17 (
% 2.45/1.17 binunion
% 2.45/1.17 @
% 2.45/1.17 X188 @
% 2.45/1.17 X190 ) ) ) =>
% 2.45/1.17 (
% 2.45/1.17 ~
% 2.45/1.17 (
% 2.45/1.17 in @
% 2.45/1.17 X192 @
% 2.45/1.17 X188 ) ) ) ) ) ) ) ) ) =>
% 2.45/1.17 (
% 2.45/1.17 ![
% 2.45/1.17 X194:$i,
% 2.45/1.17 X196:$i]:
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 in @
% 2.45/1.17 X196 @
% 2.45/1.17 (
% 2.45/1.17 powerset
% 2.45/1.17 @
% 2.45/1.17 X194 ) ) =>
% 2.45/1.17 (
% 2.45/1.17 ![
% 2.45/1.17 X198:$i]:
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 in @
% 2.45/1.17 X198 @
% 2.45/1.17 (
% 2.45/1.17 powerset
% 2.45/1.17 @
% 2.45/1.17 X194 ) ) =>
% 2.45/1.17 (
% 2.45/1.17 ![
% 2.45/1.17 X200:$i]:
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 in @
% 2.45/1.17 X200 @
% 2.45/1.17 X194 ) =>
% 2.45/1.17 (
% 2.45/1.17 (
% 2.45/1.17 ~
% 2.45/1.17 (
% 2.45/1.17 in @
% 2.45/1.17 X200 @
% 2.45/1.17 (
% 2.45/1.17 binunion
% 2.45/1.17 @
% 2.45/1.17 X196 @
% 2.45/1.17 X198 ) ) ) =>
% 2.45/1.17 (
% 2.45/1.17 ~
% 2.45/1.17 (
% 2.45/1.17 in @
% 2.45/1.17 X200 @
% 2.45/1.17 X198 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )),
% 2.45/1.17 inference('cnf.neg', [status(esa)], [zf_stmt_3])).
% 2.45/1.17 thf(zip_derived_cl54, plain,
% 2.45/1.17 (![X9 : $i, X10 : $i, X11 : $i]:
% 2.45/1.17 ( (in @ X9 @ (binunion @ X10 @ X11)) | ~ (in @ X9 @ X11))),
% 2.45/1.17 inference('cnf', [status(esa)], [zf_stmt_4])).
% 2.45/1.17 thf(zip_derived_cl135, plain,
% 2.45/1.17 (~ (in @ sk__103 @ (binunion @ sk__101 @ sk__102))),
% 2.45/1.17 inference('cnf', [status(esa)], [zf_stmt_4])).
% 2.45/1.17 thf(zip_derived_cl318, plain, (~ (in @ sk__103 @ sk__102)),
% 2.45/1.17 inference('sup-', [status(thm)], [zip_derived_cl54, zip_derived_cl135])).
% 2.45/1.17 thf(zip_derived_cl136, plain, ( (in @ sk__103 @ sk__102)),
% 2.45/1.17 inference('cnf', [status(esa)], [zf_stmt_4])).
% 2.45/1.17 thf(zip_derived_cl322, plain, ($false),
% 2.45/1.17 inference('demod', [status(thm)], [zip_derived_cl318, zip_derived_cl136])).
% 2.45/1.17
% 2.45/1.17 % SZS output end Refutation
% 2.45/1.17
% 2.45/1.17
% 2.45/1.17 % Terminating...
% 3.19/1.41 % Runner terminated.
% 3.23/1.44 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------