%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SEU734^1 : 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.fYxH7GZ9dU true
% Computer : n025.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 04:56:02 PM UTC 2025
% Result : Theorem 4.45s 1.41s
% Output : Refutation 4.78s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU734^1 : TPTP v9.2.0. Released v3.7.0.
% 0.07/0.14 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.fYxH7GZ9dU true
% 0.14/0.35 % Computer : n025.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Wed Oct 1 16:05:08 EDT 2025
% 0.14/0.35 % CPUTime :
% 0.14/0.35 % Running portfolio for 300 s
% 0.14/0.35 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.35 % Number of cores: 8
% 0.14/0.35 % Python version: Python 3.6.8
% 0.14/0.36 % Running in HO mode
% 0.59/0.69 % Total configuration time : 828
% 0.59/0.69 % Estimated wc time : 1656
% 0.59/0.69 % Estimated cpu time (8 cpus) : 207.0
% 0.59/0.77 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
% 0.59/0.78 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
% 0.59/0.78 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.59/0.79 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s
% 0.59/0.79 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
% 0.59/0.79 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.59/0.79 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s
% 0.60/0.87 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s
% 4.45/1.41 % Solved by lams/40_c_ic.sh.
% 4.45/1.41 % done 728 iterations in 0.555s
% 4.45/1.41 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 4.45/1.41 % SZS output start Refutation
% 4.45/1.41 thf(setadjoinAx_type, type, setadjoinAx: $o).
% 4.45/1.41 thf(notdexE_type, type, notdexE: $o).
% 4.45/1.41 thf(setukpairinjL2_type, type, setukpairinjL2: $o).
% 4.45/1.41 thf(doubleComplementI1_type, type, doubleComplementI1: $o).
% 4.45/1.41 thf(setunionAx_type, type, setunionAx: $o).
% 4.45/1.41 thf(setminusELneg_type, type, setminusELneg: $o).
% 4.45/1.41 thf(cartprodsndin_type, type, cartprodsndin: $o).
% 4.45/1.41 thf(ex1E1_type, type, ex1E1: $o).
% 4.45/1.41 thf(powersetE_type, type, powersetE: $o).
% 4.45/1.41 thf(omegaSAx_type, type, omegaSAx: $o).
% 4.45/1.41 thf(exuI1_type, type, exuI1: $o).
% 4.45/1.41 thf(exuI2_type, type, exuI2: $o).
% 4.45/1.41 thf(notequalI2_type, type, notequalI2: $o).
% 4.45/1.41 thf(setukpairinjL_type, type, setukpairinjL: $o).
% 4.45/1.41 thf(kpairiskpair_type, type, kpairiskpair: $o).
% 4.45/1.41 thf(upairsubunion_type, type, upairsubunion: $o).
% 4.45/1.41 thf(funcGraphProp3_type, type, funcGraphProp3: $o).
% 4.45/1.41 thf(cartprodmempaircEq_type, type, cartprodmempaircEq: $o).
% 4.45/1.41 thf(binintersectTERcontra_type, type, binintersectTERcontra: $o).
% 4.45/1.41 thf(powerset__Cong_type, type, powerset__Cong: $o).
% 4.45/1.41 thf(setminusILneg_type, type, setminusILneg: $o).
% 4.45/1.41 thf(wellorderingAx_type, type, wellorderingAx: $o).
% 4.45/1.41 thf(ksndpairEq_type, type, ksndpairEq: $o).
% 4.45/1.41 thf(funcGraphProp2_type, type, funcGraphProp2: $o).
% 4.45/1.41 thf(setadjoinSub2_type, type, setadjoinSub2: $o).
% 4.45/1.41 thf(binintersectSubset5_type, type, binintersectSubset5: $o).
% 4.45/1.41 thf(iftrue_type, type, iftrue: $o).
% 4.45/1.41 thf(upairinpowunion_type, type, upairinpowunion: $o).
% 4.45/1.41 thf(ifSingleton_type, type, ifSingleton: $o).
% 4.45/1.41 thf(doubleComplementSub2_type, type, doubleComplementSub2: $o).
% 4.45/1.41 thf(setoftrueEq_type, type, setoftrueEq: $o).
% 4.45/1.41 thf(funcImageSingleton_type, type, funcImageSingleton: $o).
% 4.45/1.41 thf(dpsetconstrERa_type, type, dpsetconstrERa: $o).
% 4.45/1.41 thf(lamProp_type, type, lamProp: $o).
% 4.45/1.41 thf(cartprodpairmemEL_type, type, cartprodpairmemEL: $o).
% 4.45/1.41 thf(emptyset__Cong_type, type, emptyset__Cong: $o).
% 4.45/1.41 thf(dpsetconstrER_type, type, dpsetconstrER: $o).
% 4.45/1.41 thf(sepInPowerset_type, type, sepInPowerset: $o).
% 4.45/1.41 thf(setukpairIR_type, type, setukpairIR: $o).
% 4.45/1.41 thf(setukpairinjR1_type, type, setukpairinjR1: $o).
% 4.45/1.41 thf(lam2p_type, type, lam2p: $o).
% 4.45/1.41 thf(binunionE_type, type, binunionE: $o).
% 4.45/1.41 thf(setext_type, type, setext: $o).
% 4.45/1.41 thf(emptyinPowerset_type, type, emptyinPowerset: $o).
% 4.45/1.41 thf(ubforcartprodlem1_type, type, ubforcartprodlem1: $o).
% 4.45/1.41 thf(descr__Cong_type, type, descr__Cong: $o).
% 4.45/1.41 thf(kfstsingleton_type, type, kfstsingleton: $o).
% 4.45/1.41 thf(binintersectTELcontra_type, type, binintersectTELcontra: $o).
% 4.45/1.41 thf(doubleComplementEq_type, type, doubleComplementEq: $o).
% 4.45/1.41 thf(eqbreln_type, type, eqbreln: $o).
% 4.45/1.41 thf(binintersectSubset1_type, type, binintersectSubset1: $o).
% 4.45/1.41 thf(complementImpComplementIntersect_type, type, complementImpComplementIntersect:
% 4.45/1.41 $o).
% 4.45/1.41 thf(in_type, type, in: $i > $i > $o).
% 4.45/1.41 thf(binunionT_lem_type, type, binunionT_lem: $o).
% 4.45/1.41 thf(quantDeMorgan1_type, type, quantDeMorgan1: $o).
% 4.45/1.41 thf(complementT_lem_type, type, complementT_lem: $o).
% 4.45/1.41 thf(kpairsurjEq_type, type, kpairsurjEq: $o).
% 4.45/1.41 thf(setadjoinIR_type, type, setadjoinIR: $o).
% 4.45/1.41 thf(doubleComplementE1_type, type, doubleComplementE1: $o).
% 4.45/1.41 thf(beta1_type, type, beta1: $o).
% 4.45/1.41 thf(setadjoin__Cong_type, type, setadjoin__Cong: $o).
% 4.45/1.41 thf(powersetTE1_type, type, powersetTE1: $o).
% 4.45/1.41 thf(symdiffI2_type, type, symdiffI2: $o).
% 4.45/1.41 thf(iftrueProp2_type, type, iftrueProp2: $o).
% 4.45/1.41 thf(upairset2IR_type, type, upairset2IR: $o).
% 4.45/1.41 thf(iffalseProp2_type, type, iffalseProp2: $o).
% 4.45/1.41 thf(subsetE_type, type, subsetE: $o).
% 4.45/1.41 thf(prop2set2propI_type, type, prop2set2propI: $o).
% 4.45/1.41 thf(dsetconstrEL_type, type, dsetconstrEL: $o).
% 4.45/1.41 thf(setbeta_type, type, setbeta: $o).
% 4.45/1.41 thf(eqinunit_type, type, eqinunit: $o).
% 4.45/1.41 thf(upairsetIL_type, type, upairsetIL: $o).
% 4.45/1.41 thf(powersetI1_type, type, powersetI1: $o).
% 4.45/1.41 thf(kfstpairEq_type, type, kfstpairEq: $o).
% 4.45/1.41 thf(binintersectSubset3_type, type, binintersectSubset3: $o).
% 4.45/1.41 thf(setminusIRneg_type, type, setminusIRneg: $o).
% 4.45/1.41 thf(ap2apEq1_type, type, ap2apEq1: $o).
% 4.45/1.41 thf(powersetAx_type, type, powersetAx: $o).
% 4.45/1.41 thf(sk__189_type, type, sk__189: $i).
% 4.45/1.41 thf(binintersectSubset4_type, type, binintersectSubset4: $o).
% 4.45/1.41 thf(singletoninpowunion_type, type, singletoninpowunion: $o).
% 4.45/1.42 thf(powersetI_type, type, powersetI: $o).
% 4.45/1.42 thf(cartprodmempair_type, type, cartprodmempair: $o).
% 4.45/1.42 thf(upairsetIR_type, type, upairsetIR: $o).
% 4.45/1.42 thf(lamp_type, type, lamp: $o).
% 4.45/1.42 thf(dpsetconstrEL1_type, type, dpsetconstrEL1: $o).
% 4.45/1.42 thf(inCongP_type, type, inCongP: $o).
% 4.45/1.42 thf(setadjoinSub_type, type, setadjoinSub: $o).
% 4.45/1.42 thf(exuE3e_type, type, exuE3e: $o).
% 4.45/1.42 thf(emptysetE_type, type, emptysetE: $o).
% 4.45/1.42 thf(binintersectSubset2_type, type, binintersectSubset2: $o).
% 4.45/1.42 thf(setunionI_type, type, setunionI: $o).
% 4.45/1.42 thf(setunion__Cong_type, type, setunion__Cong: $o).
% 4.45/1.42 thf(prop2setI_type, type, prop2setI: $o).
% 4.45/1.42 thf(singletonsuniq_type, type, singletonsuniq: $o).
% 4.45/1.42 thf(nonemptyImpWitness_type, type, nonemptyImpWitness: $o).
% 4.45/1.42 thf(setminusER_type, type, setminusER: $o).
% 4.45/1.42 thf(exuE2_type, type, exuE2: $o).
% 4.45/1.42 thf(emptyset_type, type, emptyset: $i).
% 4.45/1.42 thf(setukpairinjR11_type, type, setukpairinjR11: $o).
% 4.45/1.42 thf(ex1I_type, type, ex1I: $o).
% 4.45/1.42 thf(ex1E2_type, type, ex1E2: $o).
% 4.45/1.42 thf(setminus_type, type, setminus: $i > $i > $i).
% 4.45/1.42 thf(setukpairinjL1_type, type, setukpairinjL1: $o).
% 4.45/1.42 thf(powersetsubset_type, type, powersetsubset: $o).
% 4.45/1.42 thf(subPowSU_type, type, subPowSU: $o).
% 4.45/1.42 thf(notequalI1_type, type, notequalI1: $o).
% 4.45/1.42 thf(contrasubsetT_type, type, contrasubsetT: $o).
% 4.45/1.42 thf(notinemptyset_type, type, notinemptyset: $o).
% 4.45/1.42 thf(lam2lamEq_type, type, lam2lamEq: $o).
% 4.45/1.42 thf(nonemptyI1_type, type, nonemptyI1: $o).
% 4.45/1.42 thf(subsetTrans_type, type, subsetTrans: $o).
% 4.45/1.42 thf(kpairp_type, type, kpairp: $o).
% 4.45/1.42 thf(setukpairinjR12_type, type, setukpairinjR12: $o).
% 4.45/1.42 thf(setminusI_type, type, setminusI: $o).
% 4.45/1.42 thf(binunionIL_type, type, binunionIL: $o).
% 4.45/1.42 thf(dpsetconstrSub_type, type, dpsetconstrSub: $o).
% 4.45/1.42 thf(setunionsingleton_type, type, setunionsingleton: $o).
% 4.45/1.42 thf(subsetE2_type, type, subsetE2: $o).
% 4.45/1.42 thf(singletonsswitch_type, type, singletonsswitch: $o).
% 4.45/1.42 thf(ubforcartprodlem3_type, type, ubforcartprodlem3: $o).
% 4.45/1.42 thf(beta2_type, type, beta2: $o).
% 4.45/1.42 thf(dpsetconstrI_type, type, dpsetconstrI: $o).
% 4.45/1.42 thf(setextsub_type, type, setextsub: $o).
% 4.45/1.42 thf(binunionLsub_type, type, binunionLsub: $o).
% 4.45/1.42 thf(setunionsingleton1_type, type, setunionsingleton1: $o).
% 4.45/1.42 thf(binintersect_type, type, binintersect: $i > $i > $i).
% 4.45/1.42 thf(iftrueorfalse_type, type, iftrueorfalse: $o).
% 4.45/1.42 thf(emptysetsubset_type, type, emptysetsubset: $o).
% 4.45/1.42 thf(quantDeMorgan3_type, type, quantDeMorgan3: $o).
% 4.45/1.42 thf(cartprodpairsurjEq_type, type, cartprodpairsurjEq: $o).
% 4.45/1.42 thf(setOfPairsIsBReln_type, type, setOfPairsIsBReln: $o).
% 4.45/1.42 thf(setunionE_type, type, setunionE: $o).
% 4.45/1.42 thf(ksndsingleton_type, type, ksndsingleton: $o).
% 4.45/1.42 thf(setminusSubset1_type, type, setminusSubset1: $o).
% 4.45/1.42 thf(powersetT_lem_type, type, powersetT_lem: $o).
% 4.45/1.42 thf(emptyinunitempty_type, type, emptyinunitempty: $o).
% 4.45/1.42 thf(binunionIR_type, type, binunionIR: $o).
% 4.45/1.42 thf(theeq_type, type, theeq: $o).
% 4.45/1.42 thf(setadjoinE_type, type, setadjoinE: $o).
% 4.45/1.42 thf(doubleComplementSub1_type, type, doubleComplementSub1: $o).
% 4.45/1.42 thf(infuncsetfunc_type, type, infuncsetfunc: $o).
% 4.45/1.42 thf(ap2apEq2_type, type, ap2apEq2: $o).
% 4.45/1.42 thf(ap2p_type, type, ap2p: $o).
% 4.45/1.42 thf(setadjoinIL_type, type, setadjoinIL: $o).
% 4.45/1.42 thf(cartprodsndpairEq_type, type, cartprodsndpairEq: $o).
% 4.45/1.42 thf(exuE1_type, type, exuE1: $o).
% 4.45/1.42 thf(ubforcartprodlem2_type, type, ubforcartprodlem2: $o).
% 4.45/1.42 thf(binintersectRsub_type, type, binintersectRsub: $o).
% 4.45/1.42 thf(setminusLsub_type, type, setminusLsub: $o).
% 4.45/1.42 thf(funcextLem_type, type, funcextLem: $o).
% 4.45/1.42 thf(setukpairinjR_type, type, setukpairinjR: $o).
% 4.45/1.42 thf(notinsingleton_type, type, notinsingleton: $o).
% 4.45/1.42 thf(eqimpsubset2_type, type, eqimpsubset2: $o).
% 4.45/1.42 thf(exuEu_type, type, exuEu: $o).
% 4.45/1.42 thf(emptysetimpfalse_type, type, emptysetimpfalse: $o).
% 4.45/1.42 thf(upairsetE_type, type, upairsetE: $o).
% 4.45/1.42 thf(omega0Ax_type, type, omega0Ax: $o).
% 4.45/1.42 thf(subsetTI_type, type, subsetTI: $o).
% 4.45/1.42 thf(notsubsetI_type, type, notsubsetI: $o).
% 4.45/1.42 thf(iffalseProp1_type, type, iffalseProp1: $o).
% 4.45/1.42 thf(quantDeMorgan4_type, type, quantDeMorgan4: $o).
% 4.45/1.42 thf(setextAx_type, type, setextAx: $o).
% 4.45/1.42 thf(cartprodpairmemER_type, type, cartprodpairmemER: $o).
% 4.45/1.42 thf(powersetE1_type, type, powersetE1: $o).
% 4.45/1.42 thf(bs114d_type, type, bs114d: $o).
% 4.45/1.42 thf(contrasubsetT3_type, type, contrasubsetT3: $o).
% 4.45/1.42 thf(noeltsimpempty_type, type, noeltsimpempty: $o).
% 4.45/1.42 thf(ifp_type, type, ifp: $o).
% 4.45/1.42 thf(powersetTI1_type, type, powersetTI1: $o).
% 4.45/1.42 thf(binintersectLsub_type, type, binintersectLsub: $o).
% 4.45/1.42 thf(subsetI1_type, type, subsetI1: $o).
% 4.45/1.42 thf(symdiffE_type, type, symdiffE: $o).
% 4.45/1.42 thf(sk__190_type, type, sk__190: $i).
% 4.45/1.42 thf(descrp_type, type, descrp: $o).
% 4.45/1.42 thf(dsetconstr__Cong_type, type, dsetconstr__Cong: $o).
% 4.45/1.42 thf(foundationAx_type, type, foundationAx: $o).
% 4.45/1.42 thf(emptysetAx_type, type, emptysetAx: $o).
% 4.45/1.42 thf(emptyI_type, type, emptyI: $o).
% 4.45/1.42 thf(setadjoinOr_type, type, setadjoinOr: $o).
% 4.45/1.42 thf(eta2_type, type, eta2: $o).
% 4.45/1.42 thf(binintersectEL_type, type, binintersectEL: $o).
% 4.45/1.42 thf(emptyE1_type, type, emptyE1: $o).
% 4.45/1.42 thf(emptyInPowerset_type, type, emptyInPowerset: $o).
% 4.45/1.42 thf(complementTI1_type, type, complementTI1: $o).
% 4.45/1.42 thf(vacuousDall_type, type, vacuousDall: $o).
% 4.45/1.42 thf(dsetconstrER_type, type, dsetconstrER: $o).
% 4.45/1.42 thf(zip_tseitin_0_type, type, zip_tseitin_0: $i > $i > $i > $o).
% 4.45/1.42 thf(binintersectI_type, type, binintersectI: $o).
% 4.45/1.42 thf(funcext_type, type, funcext: $o).
% 4.45/1.42 thf(funcGraphProp4_type, type, funcGraphProp4: $o).
% 4.45/1.42 thf(cartprodpairin_type, type, cartprodpairin: $o).
% 4.45/1.42 thf(cartprodmempair1_type, type, cartprodmempair1: $o).
% 4.45/1.42 thf(brelnall2_type, type, brelnall2: $o).
% 4.45/1.42 thf(setextT_type, type, setextT: $o).
% 4.45/1.42 thf(ex1I2_type, type, ex1I2: $o).
% 4.45/1.42 thf(symdiffI1_type, type, symdiffI1: $o).
% 4.45/1.42 thf(setukpairinjR2_type, type, setukpairinjR2: $o).
% 4.45/1.42 thf(dpsetconstrEL2_type, type, dpsetconstrEL2: $o).
% 4.45/1.42 thf(theprop_type, type, theprop: $o).
% 4.45/1.42 thf(subsetI2_type, type, subsetI2: $o).
% 4.45/1.42 thf(setminusT_lem_type, type, setminusT_lem: $o).
% 4.45/1.42 thf(symdiffIneg1_type, type, symdiffIneg1: $o).
% 4.45/1.42 thf(setminusERneg_type, type, setminusERneg: $o).
% 4.45/1.42 thf(symdiffIneg2_type, type, symdiffIneg2: $o).
% 4.45/1.42 thf(omega__Cong_type, type, omega__Cong: $o).
% 4.45/1.42 thf(subsetRefl_type, type, subsetRefl: $o).
% 4.45/1.42 thf(uniqinunit_type, type, uniqinunit: $o).
% 4.45/1.42 thf(setminusSubset2_type, type, setminusSubset2: $o).
% 4.45/1.42 thf(prop2setE_type, type, prop2setE: $o).
% 4.45/1.42 thf(binunionEcases_type, type, binunionEcases: $o).
% 4.45/1.42 thf(funcinfuncset_type, type, funcinfuncset: $o).
% 4.45/1.42 thf(complementTE1_type, type, complementTE1: $o).
% 4.45/1.42 thf(nonemptyI_type, type, nonemptyI: $o).
% 4.45/1.42 thf(app_type, type, app: $o).
% 4.45/1.42 thf(disjointsetsI1_type, type, disjointsetsI1: $o).
% 4.45/1.42 thf(exuE3u_type, type, exuE3u: $o).
% 4.45/1.42 thf(eta1_type, type, eta1: $o).
% 4.45/1.42 thf(setminusEL_type, type, setminusEL: $o).
% 4.45/1.42 thf(cartprodfstin_type, type, cartprodfstin: $o).
% 4.45/1.42 thf(setunionsingleton2_type, type, setunionsingleton2: $o).
% 4.45/1.42 thf(sepSubset_type, type, sepSubset: $o).
% 4.45/1.42 thf(complementTnotintersectT_type, type, complementTnotintersectT: $o).
% 4.45/1.42 thf(upairset2E_type, type, upairset2E: $o).
% 4.45/1.42 thf(eqimpsubset1_type, type, eqimpsubset1: $o).
% 4.45/1.42 thf(exuI3_type, type, exuI3: $o).
% 4.45/1.42 thf(cartprodfstpairEq_type, type, cartprodfstpairEq: $o).
% 4.45/1.42 thf(apProp_type, type, apProp: $o).
% 4.45/1.42 thf(notdallE_type, type, notdallE: $o).
% 4.45/1.42 thf(iftrueProp1_type, type, iftrueProp1: $o).
% 4.45/1.42 thf(binintersectER_type, type, binintersectER: $o).
% 4.45/1.42 thf(brelnall1_type, type, brelnall1: $o).
% 4.45/1.42 thf(powerset_type, type, powerset: $i > $i).
% 4.45/1.42 thf(dsetconstrI_type, type, dsetconstrI: $o).
% 4.45/1.42 thf(funcGraphProp1_type, type, funcGraphProp1: $o).
% 4.45/1.42 thf(binintersectT_lem_type, type, binintersectT_lem: $o).
% 4.45/1.42 thf(setadjoin_type, type, setadjoin: $i > $i > $i).
% 4.45/1.42 thf(sk__188_type, type, sk__188: $i).
% 4.45/1.42 thf(exu__Cong_type, type, exu__Cong: $o).
% 4.45/1.42 thf(quantDeMorgan2_type, type, quantDeMorgan2: $o).
% 4.45/1.42 thf(contrasubsetT2_type, type, contrasubsetT2: $o).
% 4.45/1.42 thf(secondinupair_type, type, secondinupair: $o).
% 4.45/1.42 thf(singletonprop_type, type, singletonprop: $o).
% 4.45/1.42 thf(singletonsubset_type, type, singletonsubset: $o).
% 4.45/1.42 thf(contrasubsetT1_type, type, contrasubsetT1: $o).
% 4.45/1.42 thf(singletoninpowerset_type, type, singletoninpowerset: $o).
% 4.45/1.42 thf(subsetemptysetimpeq_type, type, subsetemptysetimpeq: $o).
% 4.45/1.42 thf(replAx_type, type, replAx: $o).
% 4.45/1.42 thf(upairequniteq_type, type, upairequniteq: $o).
% 4.45/1.42 thf(nonemptyE1_type, type, nonemptyE1: $o).
% 4.45/1.42 thf(omegaIndAx_type, type, omegaIndAx: $o).
% 4.45/1.42 thf(setukpairIL_type, type, setukpairIL: $o).
% 4.45/1.42 thf(setunionE2_type, type, setunionE2: $o).
% 4.45/1.42 thf(inPowerset_type, type, inPowerset: $o).
% 4.45/1.42 thf(iffalse_type, type, iffalse: $o).
% 4.45/1.42 thf(funcext2_type, type, funcext2: $o).
% 4.45/1.42 thf(subset_type, type, subset: $i > $i > $o).
% 4.45/1.42 thf(subbreln_type, type, subbreln: $o).
% 4.45/1.42 thf(in__Cong_type, type, in__Cong: $o).
% 4.45/1.42 thf(binunionRsub_type, type, binunionRsub: $o).
% 4.45/1.42 thf(subset2powerset_type, type, subset2powerset: $o).
% 4.45/1.42 thf(complementImpComplementIntersect, axiom,
% 4.45/1.42 complementImpComplementIntersect =
% 4.45/1.42 (![A:$i,X:$i]:
% 4.45/1.42 ( ( in @ X @ ( powerset @ A ) ) =>
% 4.45/1.42 ( ![Y:$i]:
% 4.45/1.42 ( ( in @ Y @ ( powerset @ A ) ) =>
% 4.45/1.42 ( ![Xx:$i]:
% 4.45/1.42 ( ( in @ Xx @ A ) =>
% 4.45/1.42 ( ( in @ Xx @ ( setminus @ A @ X ) ) =>
% 4.45/1.42 ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ))).
% 4.45/1.42 thf('0', plain,
% 4.45/1.42 (( complementImpComplementIntersect ) =
% 4.45/1.42 ( ![X4:$i,X6:$i]:
% 4.45/1.42 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 4.45/1.42 ( ![X8:$i]:
% 4.45/1.42 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 4.45/1.42 ( ![X10:$i]:
% 4.45/1.42 ( ( in @ X10 @ X4 ) =>
% 4.45/1.42 ( ( in @ X10 @ ( setminus @ X4 @ X6 ) ) =>
% 4.45/1.42 ( in @
% 4.45/1.42 X10 @ ( setminus @ X4 @ ( binintersect @ X6 @ X8 ) ) ) ) ) ) ) ) ) )),
% 4.45/1.42 define([status(thm)])).
% 4.45/1.42 thf(complementTnotintersectT, axiom, complementTnotintersectT =
% 4.45/1.42 (![A:$i,X:$i]:
% 4.45/1.42 ( ( in @ X @ ( powerset @ A ) ) =>
% 4.45/1.42 ( ![Y:$i]:
% 4.45/1.42 ( ( in @ Y @ ( powerset @ A ) ) =>
% 4.45/1.42 ( ![Xx:$i]:
% 4.45/1.42 ( ( in @ Xx @ A ) =>
% 4.45/1.42 ( ( in @ Xx @ ( setminus @ A @ X ) ) =>
% 4.45/1.42 ( ~( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ))).
% 4.45/1.42 thf('1', plain,
% 4.45/1.42 (( complementTnotintersectT ) =
% 4.45/1.42 ( ![X4:$i,X6:$i]:
% 4.45/1.42 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 4.45/1.42 ( ![X8:$i]:
% 4.45/1.42 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 4.45/1.42 ( ![X10:$i]:
% 4.45/1.42 ( ( in @ X10 @ X4 ) =>
% 4.45/1.42 ( ( in @ X10 @ ( setminus @ X4 @ X6 ) ) =>
% 4.45/1.42 ( ~( in @ X10 @ ( binintersect @ X6 @ X8 ) ) ) ) ) ) ) ) ) )),
% 4.45/1.42 define([status(thm)])).
% 4.45/1.42 thf(doubleComplementEq, axiom, doubleComplementEq =
% 4.45/1.42 (![A:$i,X:$i]:
% 4.45/1.42 ( ( in @ X @ ( powerset @ A ) ) =>
% 4.45/1.42 ( ( X ) = ( setminus @ A @ ( setminus @ A @ X ) ) ) ))).
% 4.45/1.42 thf('2', plain,
% 4.45/1.42 (( doubleComplementEq ) =
% 4.45/1.42 ( ![X4:$i,X6:$i]:
% 4.45/1.42 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 4.45/1.42 ( ( X6 ) = ( setminus @ X4 @ ( setminus @ X4 @ X6 ) ) ) ) )),
% 4.45/1.42 define([status(thm)])).
% 4.45/1.42 thf(doubleComplementSub2, axiom, doubleComplementSub2 =
% 4.45/1.42 (![A:$i,X:$i]:
% 4.45/1.42 ( ( in @ X @ ( powerset @ A ) ) =>
% 4.45/1.42 ( subset @ ( setminus @ A @ ( setminus @ A @ X ) ) @ X ) ))).
% 4.45/1.42 thf('3', plain,
% 4.45/1.42 (( doubleComplementSub2 ) =
% 4.45/1.42 ( ![X4:$i,X6:$i]:
% 4.45/1.42 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 4.45/1.42 ( subset @ ( setminus @ X4 @ ( setminus @ X4 @ X6 ) ) @ X6 ) ) )),
% 4.45/1.42 define([status(thm)])).
% 4.45/1.42 thf(doubleComplementSub1, axiom, doubleComplementSub1 =
% 4.45/1.42 (![A:$i,X:$i]:
% 4.45/1.42 ( ( in @ X @ ( powerset @ A ) ) =>
% 4.45/1.42 ( subset @ X @ ( setminus @ A @ ( setminus @ A @ X ) ) ) ))).
% 4.45/1.42 thf('4', plain,
% 4.45/1.42 (( doubleComplementSub1 ) =
% 4.45/1.42 ( ![X4:$i,X6:$i]:
% 4.45/1.42 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 4.45/1.42 ( subset @ X6 @ ( setminus @ X4 @ ( setminus @ X4 @ X6 ) ) ) ) )),
% 4.45/1.42 define([status(thm)])).
% 4.45/1.42 thf(doubleComplementE1, axiom, doubleComplementE1 =
% 4.45/1.42 (![A:$i,X:$i]:
% 4.45/1.42 ( ( in @ X @ ( powerset @ A ) ) =>
% 4.45/1.42 ( ![Xx:$i]:
% 4.45/1.42 ( ( in @ Xx @ A ) =>
% 4.45/1.42 ( ( in @ Xx @ ( setminus @ A @ ( setminus @ A @ X ) ) ) =>
% 4.45/1.42 ( in @ Xx @ X ) ) ) ) ))).
% 4.45/1.42 thf('5', plain,
% 4.45/1.42 (( doubleComplementE1 ) =
% 4.45/1.42 ( ![X4:$i,X6:$i]:
% 4.45/1.42 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 4.45/1.42 ( ![X8:$i]:
% 4.45/1.42 ( ( in @ X8 @ X4 ) =>
% 4.45/1.42 ( ( in @ X8 @ ( setminus @ X4 @ ( setminus @ X4 @ X6 ) ) ) =>
% 4.45/1.42 ( in @ X8 @ X6 ) ) ) ) ) )),
% 4.45/1.42 define([status(thm)])).
% 4.45/1.42 thf(doubleComplementI1, axiom, doubleComplementI1 =
% 4.45/1.42 (![A:$i,X:$i]:
% 4.45/1.42 ( ( in @ X @ ( powerset @ A ) ) =>
% 4.45/1.42 ( ![Xx:$i]:
% 4.45/1.42 ( ( in @ Xx @ A ) =>
% 4.45/1.42 ( ( in @ Xx @ X ) =>
% 4.45/1.42 ( in @ Xx @ ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) ))).
% 4.45/1.42 thf('6', plain,
% 4.45/1.42 (( doubleComplementI1 ) =
% 4.45/1.42 ( ![X4:$i,X6:$i]:
% 4.45/1.42 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 4.45/1.42 ( ![X8:$i]:
% 4.45/1.42 ( ( in @ X8 @ X4 ) =>
% 4.45/1.42 ( ( in @ X8 @ X6 ) =>
% 4.45/1.42 ( in @ X8 @ ( setminus @ X4 @ ( setminus @ X4 @ X6 ) ) ) ) ) ) ) )),
% 4.45/1.42 define([status(thm)])).
% 4.45/1.42 thf(contrasubsetT3, axiom, contrasubsetT3 =
% 4.45/1.42 (![A:$i,X:$i]:
% 4.45/1.42 ( ( in @ X @ ( powerset @ A ) ) =>
% 4.45/1.42 ( ![Y:$i]:
% 4.45/1.42 ( ( in @ Y @ ( powerset @ A ) ) =>
% 4.45/1.42 ( ( subset @ ( setminus @ A @ Y ) @ ( setminus @ A @ X ) ) =>
% 4.45/1.42 ( subset @ X @ Y ) ) ) ) ))).
% 4.45/1.42 thf('7', plain,
% 4.45/1.42 (( contrasubsetT3 ) =
% 4.45/1.42 ( ![X4:$i,X6:$i]:
% 4.45/1.42 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 4.45/1.42 ( ![X8:$i]:
% 4.45/1.42 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 4.45/1.42 ( ( subset @ ( setminus @ X4 @ X8 ) @ ( setminus @ X4 @ X6 ) ) =>
% 4.45/1.42 ( subset @ X6 @ X8 ) ) ) ) ) )),
% 4.45/1.42 define([status(thm)])).
% 4.45/1.42 thf(contrasubsetT2, axiom, contrasubsetT2 =
% 4.45/1.42 (![A:$i,X:$i]:
% 4.45/1.42 ( ( in @ X @ ( powerset @ A ) ) =>
% 4.45/1.42 ( ![Y:$i]:
% 4.45/1.42 ( ( in @ Y @ ( powerset @ A ) ) =>
% 4.45/1.42 ( ( subset @ X @ Y ) =>
% 4.45/1.42 ( subset @ ( setminus @ A @ Y ) @ ( setminus @ A @ X ) ) ) ) ) ))).
% 4.45/1.42 thf('8', plain,
% 4.45/1.42 (( contrasubsetT2 ) =
% 4.45/1.42 ( ![X4:$i,X6:$i]:
% 4.45/1.42 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 4.45/1.42 ( ![X8:$i]:
% 4.45/1.42 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 4.45/1.42 ( ( subset @ X6 @ X8 ) =>
% 4.45/1.42 ( subset @ ( setminus @ X4 @ X8 ) @ ( setminus @ X4 @ X6 ) ) ) ) ) ) )),
% 4.45/1.42 define([status(thm)])).
% 4.45/1.42 thf(contrasubsetT1, axiom, contrasubsetT1 =
% 4.45/1.42 (![A:$i,X:$i]:
% 4.45/1.42 ( ( in @ X @ ( powerset @ A ) ) =>
% 4.45/1.42 ( ![Y:$i]:
% 4.45/1.42 ( ( in @ Y @ ( powerset @ A ) ) =>
% 4.45/1.42 ( ![Xx:$i]:
% 4.45/1.42 ( ( in @ Xx @ A ) =>
% 4.45/1.42 ( ( subset @ X @ Y ) =>
% 4.45/1.42 ( ( ~( in @ Xx @ Y ) ) => ( ~( in @ Xx @ X ) ) ) ) ) ) ) ) ))).
% 4.45/1.42 thf('9', plain,
% 4.45/1.42 (( contrasubsetT1 ) =
% 4.45/1.42 ( ![X4:$i,X6:$i]:
% 4.45/1.42 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 4.45/1.42 ( ![X8:$i]:
% 4.45/1.42 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 4.45/1.42 ( ![X10:$i]:
% 4.45/1.42 ( ( in @ X10 @ X4 ) =>
% 4.45/1.42 ( ( subset @ X6 @ X8 ) =>
% 4.45/1.42 ( ( ~( in @ X10 @ X8 ) ) => ( ~( in @ X10 @ X6 ) ) ) ) ) ) ) ) ) )),
% 4.45/1.42 define([status(thm)])).
% 4.45/1.42 thf(contrasubsetT, axiom, contrasubsetT =
% 4.45/1.42 (![A:$i,X:$i]:
% 4.45/1.42 ( ( in @ X @ ( powerset @ A ) ) =>
% 4.45/1.42 ( ![Y:$i]:
% 4.45/1.42 ( ( in @ Y @ ( powerset @ A ) ) =>
% 4.45/1.42 ( ![Xx:$i]:
% 4.45/1.42 ( ( in @ Xx @ A ) =>
% 4.45/1.42 ( ( subset @ X @ ( setminus @ A @ Y ) ) =>
% 4.45/1.42 ( ( in @ Xx @ Y ) => ( ~( in @ Xx @ X ) ) ) ) ) ) ) ) ))).
% 4.45/1.42 thf('10', plain,
% 4.45/1.42 (( contrasubsetT ) =
% 4.45/1.42 ( ![X4:$i,X6:$i]:
% 4.45/1.42 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 4.45/1.42 ( ![X8:$i]:
% 4.45/1.42 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 4.45/1.42 ( ![X10:$i]:
% 4.45/1.42 ( ( in @ X10 @ X4 ) =>
% 4.45/1.42 ( ( subset @ X6 @ ( setminus @ X4 @ X8 ) ) =>
% 4.45/1.42 ( ( in @ X10 @ X8 ) => ( ~( in @ X10 @ X6 ) ) ) ) ) ) ) ) ) )),
% 4.45/1.42 define([status(thm)])).
% 4.45/1.42 thf(binintersectTERcontra, axiom, binintersectTERcontra =
% 4.45/1.42 (![A:$i,X:$i]:
% 4.45/1.42 ( ( in @ X @ ( powerset @ A ) ) =>
% 4.45/1.42 ( ![Y:$i]:
% 4.45/1.42 ( ( in @ Y @ ( powerset @ A ) ) =>
% 4.45/1.42 ( ![Xx:$i]:
% 4.45/1.42 ( ( in @ Xx @ A ) =>
% 4.45/1.42 ( ( ~( in @ Xx @ Y ) ) =>
% 4.45/1.42 ( ~( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ))).
% 4.45/1.42 thf('11', plain,
% 4.45/1.42 (( binintersectTERcontra ) =
% 4.45/1.42 ( ![X4:$i,X6:$i]:
% 4.45/1.42 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 4.45/1.42 ( ![X8:$i]:
% 4.45/1.42 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 4.45/1.42 ( ![X10:$i]:
% 4.45/1.42 ( ( in @ X10 @ X4 ) =>
% 4.45/1.42 ( ( ~( in @ X10 @ X8 ) ) =>
% 4.45/1.42 ( ~( in @ X10 @ ( binintersect @ X6 @ X8 ) ) ) ) ) ) ) ) ) )),
% 4.45/1.42 define([status(thm)])).
% 4.45/1.42 thf(binintersectTELcontra, axiom, binintersectTELcontra =
% 4.45/1.42 (![A:$i,X:$i]:
% 4.45/1.42 ( ( in @ X @ ( powerset @ A ) ) =>
% 4.45/1.42 ( ![Y:$i]:
% 4.45/1.42 ( ( in @ Y @ ( powerset @ A ) ) =>
% 4.45/1.42 ( ![Xx:$i]:
% 4.45/1.42 ( ( in @ Xx @ A ) =>
% 4.45/1.42 ( ( ~( in @ Xx @ X ) ) =>
% 4.45/1.42 ( ~( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ))).
% 4.45/1.42 thf('12', plain,
% 4.45/1.42 (( binintersectTELcontra ) =
% 4.45/1.42 ( ![X4:$i,X6:$i]:
% 4.45/1.42 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 4.45/1.42 ( ![X8:$i]:
% 4.45/1.42 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 4.45/1.42 ( ![X10:$i]:
% 4.45/1.42 ( ( in @ X10 @ X4 ) =>
% 4.45/1.42 ( ( ~( in @ X10 @ X6 ) ) =>
% 4.45/1.42 ( ~( in @ X10 @ ( binintersect @ X6 @ X8 ) ) ) ) ) ) ) ) ) )),
% 4.45/1.42 define([status(thm)])).
% 4.45/1.42 thf(complementTE1, axiom, complementTE1 =
% 4.45/1.42 (![A:$i,X:$i]:
% 4.45/1.42 ( ( in @ X @ ( powerset @ A ) ) =>
% 4.45/1.42 ( ![Xx:$i]:
% 4.45/1.42 ( ( in @ Xx @ A ) =>
% 4.45/1.42 ( ( ~( in @ Xx @ ( setminus @ A @ X ) ) ) => ( in @ Xx @ X ) ) ) ) ))).
% 4.45/1.42 thf('13', plain,
% 4.45/1.42 (( complementTE1 ) =
% 4.45/1.42 ( ![X4:$i,X6:$i]:
% 4.45/1.42 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 4.45/1.42 ( ![X8:$i]:
% 4.45/1.42 ( ( in @ X8 @ X4 ) =>
% 4.45/1.42 ( ( ~( in @ X8 @ ( setminus @ X4 @ X6 ) ) ) => ( in @ X8 @ X6 ) ) ) ) ) )),
% 4.45/1.42 define([status(thm)])).
% 4.45/1.42 thf(complementTI1, axiom, complementTI1 =
% 4.45/1.42 (![A:$i,X:$i]:
% 4.45/1.42 ( ( in @ X @ ( powerset @ A ) ) =>
% 4.45/1.42 ( ![Xx:$i]:
% 4.45/1.42 ( ( in @ Xx @ A ) =>
% 4.45/1.42 ( ( in @ Xx @ X ) => ( ~( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ))).
% 4.45/1.42 thf('14', plain,
% 4.45/1.42 (( complementTI1 ) =
% 4.45/1.42 ( ![X4:$i,X6:$i]:
% 4.45/1.42 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 4.45/1.42 ( ![X8:$i]:
% 4.45/1.42 ( ( in @ X8 @ X4 ) =>
% 4.45/1.42 ( ( in @ X8 @ X6 ) => ( ~( in @ X8 @ ( setminus @ X4 @ X6 ) ) ) ) ) ) ) )),
% 4.45/1.42 define([status(thm)])).
% 4.45/1.42 thf(powersetTE1, axiom, powersetTE1 =
% 4.45/1.42 (![A:$i,X:$i]:
% 4.45/1.42 ( ( in @ X @ ( powerset @ A ) ) =>
% 4.45/1.42 ( ![Y:$i]:
% 4.45/1.42 ( ( in @ Y @ ( powerset @ A ) ) =>
% 4.45/1.42 ( ![Xx:$i]:
% 4.45/1.42 ( ( in @ Xx @ A ) =>
% 4.45/1.42 ( ( in @ X @ ( powerset @ Y ) ) =>
% 4.45/1.42 ( ( in @ Xx @ X ) => ( in @ Xx @ Y ) ) ) ) ) ) ) ))).
% 4.45/1.42 thf('15', plain,
% 4.45/1.42 (( powersetTE1 ) =
% 4.45/1.42 ( ![X4:$i,X6:$i]:
% 4.45/1.42 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 4.45/1.42 ( ![X8:$i]:
% 4.45/1.42 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 4.45/1.42 ( ![X10:$i]:
% 4.45/1.42 ( ( in @ X10 @ X4 ) =>
% 4.45/1.42 ( ( in @ X6 @ ( powerset @ X8 ) ) =>
% 4.45/1.42 ( ( in @ X10 @ X6 ) => ( in @ X10 @ X8 ) ) ) ) ) ) ) ) )),
% 4.45/1.42 define([status(thm)])).
% 4.45/1.42 thf(powersetTI1, axiom, powersetTI1 =
% 4.45/1.42 (![A:$i,X:$i]:
% 4.45/1.42 ( ( in @ X @ ( powerset @ A ) ) =>
% 4.45/1.42 ( ![Y:$i]:
% 4.45/1.42 ( ( in @ Y @ ( powerset @ A ) ) =>
% 4.45/1.42 ( ( ![Xx:$i]:
% 4.45/1.42 ( ( in @ Xx @ A ) => ( ( in @ Xx @ X ) => ( in @ Xx @ Y ) ) ) ) =>
% 4.45/1.42 ( in @ X @ ( powerset @ Y ) ) ) ) ) ))).
% 4.45/1.42 thf('16', plain,
% 4.45/1.42 (( powersetTI1 ) =
% 4.45/1.42 ( ![X4:$i,X6:$i]:
% 4.45/1.42 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 4.45/1.42 ( ![X8:$i]:
% 4.45/1.42 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 4.45/1.42 ( ( ![X10:$i]:
% 4.45/1.42 ( ( in @ X10 @ X4 ) =>
% 4.45/1.42 ( ( in @ X10 @ X6 ) => ( in @ X10 @ X8 ) ) ) ) =>
% 4.45/1.42 ( in @ X6 @ ( powerset @ X8 ) ) ) ) ) ) )),
% 4.45/1.42 define([status(thm)])).
% 4.45/1.42 thf(subsetTI, axiom, subsetTI =
% 4.45/1.42 (![A:$i,X:$i]:
% 4.45/1.42 ( ( in @ X @ ( powerset @ A ) ) =>
% 4.45/1.42 ( ![Y:$i]:
% 4.45/1.42 ( ( in @ Y @ ( powerset @ A ) ) =>
% 4.45/1.42 ( ( ![Xx:$i]:
% 4.45/1.42 ( ( in @ Xx @ A ) => ( ( in @ Xx @ X ) => ( in @ Xx @ Y ) ) ) ) =>
% 4.45/1.42 ( subset @ X @ Y ) ) ) ) ))).
% 4.45/1.42 thf('17', plain,
% 4.45/1.42 (( subsetTI ) =
% 4.45/1.42 ( ![X4:$i,X6:$i]:
% 4.45/1.42 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 4.45/1.42 ( ![X8:$i]:
% 4.45/1.42 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 4.45/1.42 ( ( ![X10:$i]:
% 4.45/1.42 ( ( in @ X10 @ X4 ) =>
% 4.45/1.42 ( ( in @ X10 @ X6 ) => ( in @ X10 @ X8 ) ) ) ) =>
% 4.45/1.42 ( subset @ X6 @ X8 ) ) ) ) ) )),
% 4.45/1.42 define([status(thm)])).
% 4.45/1.42 thf(setextT, axiom, setextT =
% 4.45/1.42 (![A:$i,X:$i]:
% 4.45/1.42 ( ( in @ X @ ( powerset @ A ) ) =>
% 4.45/1.42 ( ![Y:$i]:
% 4.45/1.42 ( ( in @ Y @ ( powerset @ A ) ) =>
% 4.45/1.42 ( ( ![Xx:$i]:
% 4.45/1.42 ( ( in @ Xx @ A ) => ( ( in @ Xx @ X ) => ( in @ Xx @ Y ) ) ) ) =>
% 4.45/1.42 ( ( ![Xx:$i]:
% 4.45/1.42 ( ( in @ Xx @ A ) => ( ( in @ Xx @ Y ) => ( in @ Xx @ X ) ) ) ) =>
% 4.45/1.42 ( ( X ) = ( Y ) ) ) ) ) ) ))).
% 4.45/1.42 thf('18', plain,
% 4.45/1.42 (( setextT ) =
% 4.45/1.42 ( ![X4:$i,X6:$i]:
% 4.45/1.42 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 4.45/1.42 ( ![X8:$i]:
% 4.45/1.42 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 4.45/1.42 ( ( ![X10:$i]:
% 4.45/1.42 ( ( in @ X10 @ X4 ) =>
% 4.45/1.42 ( ( in @ X10 @ X6 ) => ( in @ X10 @ X8 ) ) ) ) =>
% 4.45/1.42 ( ( ![X12:$i]:
% 4.45/1.42 ( ( in @ X12 @ X4 ) =>
% 4.45/1.42 ( ( in @ X12 @ X8 ) => ( in @ X12 @ X6 ) ) ) ) =>
% 4.45/1.42 ( ( X6 ) = ( X8 ) ) ) ) ) ) ) )),
% 4.45/1.42 define([status(thm)])).
% 4.45/1.42 thf(complementT_lem, axiom, complementT_lem =
% 4.45/1.42 (![A:$i,X:$i]:
% 4.45/1.42 ( ( in @ X @ ( powerset @ A ) ) =>
% 4.45/1.42 ( in @ ( setminus @ A @ X ) @ ( powerset @ A ) ) ))).
% 4.45/1.42 thf('19', plain,
% 4.45/1.42 (( complementT_lem ) =
% 4.45/1.42 ( ![X4:$i,X6:$i]:
% 4.45/1.42 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 4.45/1.42 ( in @ ( setminus @ X4 @ X6 ) @ ( powerset @ X4 ) ) ) )),
% 4.45/1.42 define([status(thm)])).
% 4.45/1.42 thf(setminusT_lem, axiom, setminusT_lem =
% 4.45/1.42 (![A:$i,X:$i]:
% 4.45/1.42 ( ( in @ X @ ( powerset @ A ) ) =>
% 4.45/1.42 ( ![Y:$i]:
% 4.45/1.42 ( ( in @ Y @ ( powerset @ A ) ) =>
% 4.45/1.42 ( in @ ( setminus @ X @ Y ) @ ( powerset @ A ) ) ) ) ))).
% 4.45/1.42 thf('20', plain,
% 4.45/1.42 (( setminusT_lem ) =
% 4.45/1.42 ( ![X4:$i,X6:$i]:
% 4.45/1.42 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 4.45/1.42 ( ![X8:$i]:
% 4.45/1.42 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 4.45/1.42 ( in @ ( setminus @ X6 @ X8 ) @ ( powerset @ X4 ) ) ) ) ) )),
% 4.45/1.42 define([status(thm)])).
% 4.45/1.42 thf(powersetT_lem, axiom, powersetT_lem =
% 4.45/1.42 (![A:$i,X:$i]:
% 4.45/1.42 ( ( in @ X @ ( powerset @ A ) ) =>
% 4.45/1.42 ( in @ ( powerset @ X ) @ ( powerset @ ( powerset @ A ) ) ) ))).
% 4.45/1.42 thf('21', plain,
% 4.45/1.42 (( powersetT_lem ) =
% 4.45/1.42 ( ![X4:$i,X6:$i]:
% 4.45/1.42 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 4.45/1.42 ( in @ ( powerset @ X6 ) @ ( powerset @ ( powerset @ X4 ) ) ) ) )),
% 4.45/1.42 define([status(thm)])).
% 4.45/1.42 thf(binintersectT_lem, axiom, binintersectT_lem =
% 4.45/1.42 (![A:$i,X:$i]:
% 4.45/1.42 ( ( in @ X @ ( powerset @ A ) ) =>
% 4.45/1.42 ( ![Y:$i]:
% 4.45/1.42 ( ( in @ Y @ ( powerset @ A ) ) =>
% 4.45/1.42 ( in @ ( binintersect @ X @ Y ) @ ( powerset @ A ) ) ) ) ))).
% 4.45/1.42 thf('22', plain,
% 4.45/1.42 (( binintersectT_lem ) =
% 4.45/1.42 ( ![X4:$i,X6:$i]:
% 4.45/1.42 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 4.45/1.42 ( ![X8:$i]:
% 4.45/1.42 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 4.45/1.42 ( in @ ( binintersect @ X6 @ X8 ) @ ( powerset @ X4 ) ) ) ) ) )),
% 4.45/1.42 define([status(thm)])).
% 4.45/1.42 thf(singletoninpowerset, axiom, singletoninpowerset =
% 4.45/1.42 (![A:$i,Xx:$i]:
% 4.45/1.42 ( ( in @ Xx @ A ) =>
% 4.45/1.42 ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) ))).
% 4.78/1.42 thf('23', plain,
% 4.78/1.42 (( singletoninpowerset ) =
% 4.78/1.42 ( ![X4:$i,X6:$i]:
% 4.78/1.42 ( ( in @ X6 @ X4 ) =>
% 4.78/1.42 ( in @ ( setadjoin @ X6 @ emptyset ) @ ( powerset @ X4 ) ) ) )),
% 4.78/1.42 define([status(thm)])).
% 4.78/1.42 thf(setminusSubset1, axiom, setminusSubset1 =
% 4.78/1.42 (![A:$i,B:$i]:
% 4.78/1.42 ( ( ( setminus @ A @ B ) = ( emptyset ) ) => ( subset @ A @ B ) ))).
% 4.78/1.42 thf('24', plain,
% 4.78/1.42 (( setminusSubset1 ) =
% 4.78/1.42 ( ![X4:$i,X6:$i]:
% 4.78/1.42 ( ( ( setminus @ X4 @ X6 ) = ( emptyset ) ) => ( subset @ X4 @ X6 ) ) )),
% 4.78/1.42 define([status(thm)])).
% 4.78/1.42 thf(setminusLsub, axiom, setminusLsub =
% 4.78/1.42 (![A:$i,B:$i]: ( subset @ ( setminus @ A @ B ) @ A ))).
% 4.78/1.42 thf('25', plain,
% 4.78/1.42 (( setminusLsub ) =
% 4.78/1.42 ( ![X4:$i,X6:$i]: ( subset @ ( setminus @ X4 @ X6 ) @ X4 ) )),
% 4.78/1.42 define([status(thm)])).
% 4.78/1.42 thf(setminusIRneg, axiom, setminusIRneg =
% 4.78/1.42 (![A:$i,B:$i,Xx:$i]:
% 4.78/1.42 ( ( in @ Xx @ B ) => ( ~( in @ Xx @ ( setminus @ A @ B ) ) ) ))).
% 4.78/1.42 thf('26', plain,
% 4.78/1.42 (( setminusIRneg ) =
% 4.78/1.42 ( ![X4:$i,X6:$i,X8:$i]:
% 4.78/1.42 ( ( in @ X8 @ X6 ) => ( ~( in @ X8 @ ( setminus @ X4 @ X6 ) ) ) ) )),
% 4.78/1.42 define([status(thm)])).
% 4.78/1.42 thf(setminusILneg, axiom, setminusILneg =
% 4.78/1.42 (![A:$i,B:$i,Xx:$i]:
% 4.78/1.42 ( ( ~( in @ Xx @ A ) ) => ( ~( in @ Xx @ ( setminus @ A @ B ) ) ) ))).
% 4.78/1.42 thf('27', plain,
% 4.78/1.42 (( setminusILneg ) =
% 4.78/1.42 ( ![X4:$i,X6:$i,X8:$i]:
% 4.78/1.42 ( ( ~( in @ X8 @ X4 ) ) => ( ~( in @ X8 @ ( setminus @ X4 @ X6 ) ) ) ) )),
% 4.78/1.42 define([status(thm)])).
% 4.78/1.42 thf(setminusELneg, axiom, setminusELneg =
% 4.78/1.42 (![A:$i,B:$i,Xx:$i]:
% 4.78/1.42 ( ( ~( in @ Xx @ ( setminus @ A @ B ) ) ) =>
% 4.78/1.42 ( ( ~( in @ Xx @ B ) ) => ( ~( in @ Xx @ A ) ) ) ))).
% 4.78/1.42 thf('28', plain,
% 4.78/1.42 (( setminusELneg ) =
% 4.78/1.42 ( ![X4:$i,X6:$i,X8:$i]:
% 4.78/1.42 ( ( ~( in @ X8 @ ( setminus @ X4 @ X6 ) ) ) =>
% 4.78/1.42 ( ( ~( in @ X8 @ X6 ) ) => ( ~( in @ X8 @ X4 ) ) ) ) )),
% 4.78/1.42 define([status(thm)])).
% 4.78/1.42 thf(setminusERneg, axiom, setminusERneg =
% 4.78/1.42 (![A:$i,B:$i,Xx:$i]:
% 4.78/1.42 ( ( ~( in @ Xx @ ( setminus @ A @ B ) ) ) =>
% 4.78/1.42 ( ( in @ Xx @ A ) => ( in @ Xx @ B ) ) ))).
% 4.78/1.42 thf('29', plain,
% 4.78/1.42 (( setminusERneg ) =
% 4.78/1.42 ( ![X4:$i,X6:$i,X8:$i]:
% 4.78/1.42 ( ( ~( in @ X8 @ ( setminus @ X4 @ X6 ) ) ) =>
% 4.78/1.42 ( ( in @ X8 @ X4 ) => ( in @ X8 @ X6 ) ) ) )),
% 4.78/1.42 define([status(thm)])).
% 4.78/1.42 thf(setminusSubset2, axiom, setminusSubset2 =
% 4.78/1.42 (![A:$i,B:$i]:
% 4.78/1.42 ( ( subset @ A @ B ) => ( ( setminus @ A @ B ) = ( emptyset ) ) ))).
% 4.78/1.42 thf('30', plain,
% 4.78/1.42 (( setminusSubset2 ) =
% 4.78/1.42 ( ![X4:$i,X6:$i]:
% 4.78/1.42 ( ( subset @ X4 @ X6 ) => ( ( setminus @ X4 @ X6 ) = ( emptyset ) ) ) )),
% 4.78/1.42 define([status(thm)])).
% 4.78/1.42 thf(setminusER, axiom, setminusER =
% 4.78/1.42 (![A:$i,B:$i,Xx:$i]:
% 4.78/1.42 ( ( in @ Xx @ ( setminus @ A @ B ) ) => ( ~( in @ Xx @ B ) ) ))).
% 4.78/1.42 thf('31', plain,
% 4.78/1.42 (( setminusER ) =
% 4.78/1.42 ( ![X4:$i,X6:$i,X8:$i]:
% 4.78/1.42 ( ( in @ X8 @ ( setminus @ X4 @ X6 ) ) => ( ~( in @ X8 @ X6 ) ) ) )),
% 4.78/1.42 define([status(thm)])).
% 4.78/1.42 thf(setminusEL, axiom, setminusEL =
% 4.78/1.42 (![A:$i,B:$i,Xx:$i]:
% 4.78/1.42 ( ( in @ Xx @ ( setminus @ A @ B ) ) => ( in @ Xx @ A ) ))).
% 4.78/1.42 thf('32', plain,
% 4.78/1.42 (( setminusEL ) =
% 4.78/1.42 ( ![X4:$i,X6:$i,X8:$i]:
% 4.78/1.42 ( ( in @ X8 @ ( setminus @ X4 @ X6 ) ) => ( in @ X8 @ X4 ) ) )),
% 4.78/1.42 define([status(thm)])).
% 4.78/1.42 thf(setminusI, axiom, setminusI =
% 4.78/1.42 (![A:$i,B:$i,Xx:$i]:
% 4.78/1.42 ( ( in @ Xx @ A ) =>
% 4.78/1.42 ( ( ~( in @ Xx @ B ) ) => ( in @ Xx @ ( setminus @ A @ B ) ) ) ))).
% 4.78/1.42 thf('33', plain,
% 4.78/1.42 (( setminusI ) =
% 4.78/1.42 ( ![X4:$i,X6:$i,X8:$i]:
% 4.78/1.42 ( ( in @ X8 @ X4 ) =>
% 4.78/1.42 ( ( ~( in @ X8 @ X6 ) ) => ( in @ X8 @ ( setminus @ X4 @ X6 ) ) ) ) )),
% 4.78/1.42 define([status(thm)])).
% 4.78/1.42 thf(binintersectSubset1, axiom, binintersectSubset1 =
% 4.78/1.42 (![A:$i,B:$i]:
% 4.78/1.42 ( ( ( binintersect @ A @ B ) = ( A ) ) => ( subset @ A @ B ) ))).
% 4.78/1.42 thf('34', plain,
% 4.78/1.42 (( binintersectSubset1 ) =
% 4.78/1.42 ( ![X4:$i,X6:$i]:
% 4.78/1.42 ( ( ( binintersect @ X4 @ X6 ) = ( X4 ) ) => ( subset @ X4 @ X6 ) ) )),
% 4.78/1.42 define([status(thm)])).
% 4.78/1.42 thf(binintersectSubset4, axiom, binintersectSubset4 =
% 4.78/1.42 (![A:$i,B:$i]:
% 4.78/1.42 ( ( subset @ B @ A ) => ( ( binintersect @ A @ B ) = ( B ) ) ))).
% 4.78/1.42 thf('35', plain,
% 4.78/1.42 (( binintersectSubset4 ) =
% 4.78/1.42 ( ![X4:$i,X6:$i]:
% 4.78/1.42 ( ( subset @ X6 @ X4 ) => ( ( binintersect @ X4 @ X6 ) = ( X6 ) ) ) )),
% 4.78/1.42 define([status(thm)])).
% 4.78/1.42 thf(binintersectRsub, axiom, binintersectRsub =
% 4.78/1.42 (![A:$i,B:$i]: ( subset @ ( binintersect @ A @ B ) @ B ))).
% 4.78/1.42 thf('36', plain,
% 4.78/1.42 (( binintersectRsub ) =
% 4.78/1.42 ( ![X4:$i,X6:$i]: ( subset @ ( binintersect @ X4 @ X6 ) @ X6 ) )),
% 4.78/1.42 define([status(thm)])).
% 4.78/1.42 thf(disjointsetsI1, axiom, disjointsetsI1 =
% 4.78/1.42 (![A:$i,B:$i]:
% 4.78/1.42 ( ( ~( ?[Xx:$i]: ( ( in @ Xx @ B ) & ( in @ Xx @ A ) ) ) ) =>
% 4.78/1.42 ( ( binintersect @ A @ B ) = ( emptyset ) ) ))).
% 4.78/1.42 thf('37', plain,
% 4.78/1.42 (( disjointsetsI1 ) =
% 4.78/1.42 ( ![X4:$i,X6:$i]:
% 4.78/1.42 ( ( ~( ?[X8:$i]: ( ( in @ X8 @ X6 ) & ( in @ X8 @ X4 ) ) ) ) =>
% 4.78/1.42 ( ( binintersect @ X4 @ X6 ) = ( emptyset ) ) ) )),
% 4.78/1.42 define([status(thm)])).
% 4.78/1.42 thf(binintersectER, axiom, binintersectER =
% 4.78/1.42 (![A:$i,B:$i,Xx:$i]:
% 4.78/1.42 ( ( in @ Xx @ ( binintersect @ A @ B ) ) => ( in @ Xx @ B ) ))).
% 4.78/1.42 thf('38', plain,
% 4.78/1.42 (( binintersectER ) =
% 4.78/1.42 ( ![X4:$i,X6:$i,X8:$i]:
% 4.78/1.42 ( ( in @ X8 @ ( binintersect @ X4 @ X6 ) ) => ( in @ X8 @ X6 ) ) )),
% 4.78/1.42 define([status(thm)])).
% 4.78/1.42 thf(binintersectSubset3, axiom, binintersectSubset3 =
% 4.78/1.42 (![A:$i,B:$i]:
% 4.78/1.42 ( ( ( binintersect @ A @ B ) = ( B ) ) => ( subset @ B @ A ) ))).
% 4.78/1.42 thf('39', plain,
% 4.78/1.42 (( binintersectSubset3 ) =
% 4.78/1.42 ( ![X4:$i,X6:$i]:
% 4.78/1.42 ( ( ( binintersect @ X4 @ X6 ) = ( X6 ) ) => ( subset @ X6 @ X4 ) ) )),
% 4.78/1.42 define([status(thm)])).
% 4.78/1.42 thf(binintersectSubset2, axiom, binintersectSubset2 =
% 4.78/1.42 (![A:$i,B:$i]:
% 4.78/1.42 ( ( subset @ A @ B ) => ( ( binintersect @ A @ B ) = ( A ) ) ))).
% 4.78/1.42 thf('40', plain,
% 4.78/1.42 (( binintersectSubset2 ) =
% 4.78/1.42 ( ![X4:$i,X6:$i]:
% 4.78/1.42 ( ( subset @ X4 @ X6 ) => ( ( binintersect @ X4 @ X6 ) = ( X4 ) ) ) )),
% 4.78/1.42 define([status(thm)])).
% 4.78/1.42 thf(binintersectLsub, axiom, binintersectLsub =
% 4.78/1.42 (![A:$i,B:$i]: ( subset @ ( binintersect @ A @ B ) @ A ))).
% 4.78/1.42 thf('41', plain,
% 4.78/1.42 (( binintersectLsub ) =
% 4.78/1.42 ( ![X4:$i,X6:$i]: ( subset @ ( binintersect @ X4 @ X6 ) @ X4 ) )),
% 4.78/1.42 define([status(thm)])).
% 4.78/1.42 thf(binintersectEL, axiom, binintersectEL =
% 4.78/1.42 (![A:$i,B:$i,Xx:$i]:
% 4.78/1.42 ( ( in @ Xx @ ( binintersect @ A @ B ) ) => ( in @ Xx @ A ) ))).
% 4.78/1.42 thf('42', plain,
% 4.78/1.42 (( binintersectEL ) =
% 4.78/1.42 ( ![X4:$i,X6:$i,X8:$i]:
% 4.78/1.42 ( ( in @ X8 @ ( binintersect @ X4 @ X6 ) ) => ( in @ X8 @ X4 ) ) )),
% 4.78/1.42 define([status(thm)])).
% 4.78/1.42 thf(binintersectSubset5, axiom, binintersectSubset5 =
% 4.78/1.42 (![A:$i,B:$i,C:$i]:
% 4.78/1.42 ( ( subset @ C @ A ) =>
% 4.78/1.42 ( ( subset @ C @ B ) => ( subset @ C @ ( binintersect @ A @ B ) ) ) ))).
% 4.78/1.42 thf('43', plain,
% 4.78/1.42 (( binintersectSubset5 ) =
% 4.78/1.42 ( ![X4:$i,X6:$i,X8:$i]:
% 4.78/1.42 ( ( subset @ X8 @ X4 ) =>
% 4.78/1.42 ( ( subset @ X8 @ X6 ) =>
% 4.78/1.42 ( subset @ X8 @ ( binintersect @ X4 @ X6 ) ) ) ) )),
% 4.78/1.42 define([status(thm)])).
% 4.78/1.42 thf(binintersectI, axiom, binintersectI =
% 4.78/1.42 (![A:$i,B:$i,Xx:$i]:
% 4.78/1.42 ( ( in @ Xx @ A ) =>
% 4.78/1.42 ( ( in @ Xx @ B ) => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ))).
% 4.78/1.42 thf('44', plain,
% 4.78/1.42 (( binintersectI ) =
% 4.78/1.42 ( ![X4:$i,X6:$i,X8:$i]:
% 4.78/1.42 ( ( in @ X8 @ X4 ) =>
% 4.78/1.42 ( ( in @ X8 @ X6 ) => ( in @ X8 @ ( binintersect @ X4 @ X6 ) ) ) ) )),
% 4.78/1.42 define([status(thm)])).
% 4.78/1.42 thf(powersetsubset, axiom, powersetsubset =
% 4.78/1.42 (![A:$i,B:$i]:
% 4.78/1.42 ( ( subset @ A @ B ) => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ))).
% 4.78/1.42 thf('45', plain,
% 4.78/1.42 (( powersetsubset ) =
% 4.78/1.42 ( ![X4:$i,X6:$i]:
% 4.78/1.42 ( ( subset @ X4 @ X6 ) =>
% 4.78/1.42 ( subset @ ( powerset @ X4 ) @ ( powerset @ X6 ) ) ) )),
% 4.78/1.42 define([status(thm)])).
% 4.78/1.42 thf(inPowerset, axiom, inPowerset = (![A:$i]: ( in @ A @ ( powerset @ A ) ))).
% 4.78/1.42 thf('46', plain,
% 4.78/1.42 (( inPowerset ) = ( ![X4:$i]: ( in @ X4 @ ( powerset @ X4 ) ) )),
% 4.78/1.42 define([status(thm)])).
% 4.78/1.42 thf(powersetE1, axiom, powersetE1 =
% 4.78/1.42 (![A:$i,B:$i]: ( ( in @ B @ ( powerset @ A ) ) => ( subset @ B @ A ) ))).
% 4.78/1.42 thf('47', plain,
% 4.78/1.42 (( powersetE1 ) =
% 4.78/1.42 ( ![X4:$i,X6:$i]:
% 4.78/1.42 ( ( in @ X6 @ ( powerset @ X4 ) ) => ( subset @ X6 @ X4 ) ) )),
% 4.78/1.42 define([status(thm)])).
% 4.78/1.42 thf(powersetI1, axiom, powersetI1 =
% 4.78/1.42 (![A:$i,B:$i]: ( ( subset @ B @ A ) => ( in @ B @ ( powerset @ A ) ) ))).
% 4.78/1.42 thf('48', plain,
% 4.78/1.42 (( powersetI1 ) =
% 4.78/1.42 ( ![X4:$i,X6:$i]:
% 4.78/1.42 ( ( subset @ X6 @ X4 ) => ( in @ X6 @ ( powerset @ X4 ) ) ) )),
% 4.78/1.42 define([status(thm)])).
% 4.78/1.42 thf(subsetemptysetimpeq, axiom, subsetemptysetimpeq =
% 4.78/1.42 (![A:$i]: ( ( subset @ A @ emptyset ) => ( ( A ) = ( emptyset ) ) ))).
% 4.78/1.42 thf('49', plain,
% 4.78/1.42 (( subsetemptysetimpeq ) =
% 4.78/1.42 ( ![X4:$i]: ( ( subset @ X4 @ emptyset ) => ( ( X4 ) = ( emptyset ) ) ) )),
% 4.78/1.42 define([status(thm)])).
% 4.78/1.42 thf(setextsub, axiom, setextsub =
% 4.78/1.42 (![A:$i,B:$i]:
% 4.78/1.42 ( ( subset @ A @ B ) => ( ( subset @ B @ A ) => ( ( A ) = ( B ) ) ) ))).
% 4.78/1.42 thf('50', plain,
% 4.78/1.42 (( setextsub ) =
% 4.78/1.42 ( ![X4:$i,X6:$i]:
% 4.78/1.42 ( ( subset @ X4 @ X6 ) =>
% 4.78/1.42 ( ( subset @ X6 @ X4 ) => ( ( X4 ) = ( X6 ) ) ) ) )),
% 4.78/1.42 define([status(thm)])).
% 4.78/1.42 thf(subset2powerset, axiom, subset2powerset =
% 4.78/1.42 (![A:$i,B:$i]: ( ( subset @ A @ B ) => ( in @ A @ ( powerset @ B ) ) ))).
% 4.78/1.42 thf('51', plain,
% 4.78/1.42 (( subset2powerset ) =
% 4.78/1.42 ( ![X4:$i,X6:$i]:
% 4.78/1.42 ( ( subset @ X4 @ X6 ) => ( in @ X4 @ ( powerset @ X6 ) ) ) )),
% 4.78/1.42 define([status(thm)])).
% 4.78/1.42 thf(subsetTrans, axiom, subsetTrans =
% 4.78/1.42 (![A:$i,B:$i,C:$i]:
% 4.78/1.42 ( ( subset @ A @ B ) => ( ( subset @ B @ C ) => ( subset @ A @ C ) ) ))).
% 4.78/1.42 thf('52', plain,
% 4.78/1.42 (( subsetTrans ) =
% 4.78/1.42 ( ![X4:$i,X6:$i,X8:$i]:
% 4.78/1.42 ( ( subset @ X4 @ X6 ) =>
% 4.78/1.42 ( ( subset @ X6 @ X8 ) => ( subset @ X4 @ X8 ) ) ) )),
% 4.78/1.42 define([status(thm)])).
% 4.78/1.42 thf(subsetRefl, axiom, subsetRefl = (![A:$i]: ( subset @ A @ A ))).
% 4.78/1.42 thf('53', plain, (( subsetRefl ) = ( ![X4:$i]: ( subset @ X4 @ X4 ) )),
% 4.78/1.42 define([status(thm)])).
% 4.78/1.42 thf(notequalI1, axiom, notequalI1 =
% 4.78/1.42 (![A:$i,B:$i]: ( ( ~( subset @ A @ B ) ) => ( ( A ) != ( B ) ) ))).
% 4.78/1.42 thf('54', plain,
% 4.78/1.42 (( notequalI1 ) =
% 4.78/1.42 ( ![X4:$i,X6:$i]: ( ( ~( subset @ X4 @ X6 ) ) => ( ( X4 ) != ( X6 ) ) ) )),
% 4.78/1.42 define([status(thm)])).
% 4.78/1.42 thf(notsubsetI, axiom, notsubsetI =
% 4.78/1.42 (![A:$i,B:$i,Xx:$i]:
% 4.78/1.42 ( ( in @ Xx @ A ) => ( ( ~( in @ Xx @ B ) ) => ( ~( subset @ A @ B ) ) ) ))).
% 4.78/1.42 thf('55', plain,
% 4.78/1.42 (( notsubsetI ) =
% 4.78/1.42 ( ![X4:$i,X6:$i,X8:$i]:
% 4.78/1.42 ( ( in @ X8 @ X4 ) =>
% 4.78/1.42 ( ( ~( in @ X8 @ X6 ) ) => ( ~( subset @ X4 @ X6 ) ) ) ) )),
% 4.78/1.42 define([status(thm)])).
% 4.78/1.42 thf(subsetE2, axiom, subsetE2 =
% 4.78/1.42 (![A:$i,B:$i,Xx:$i]:
% 4.78/1.42 ( ( subset @ A @ B ) => ( ( ~( in @ Xx @ B ) ) => ( ~( in @ Xx @ A ) ) ) ))).
% 4.78/1.42 thf('56', plain,
% 4.78/1.42 (( subsetE2 ) =
% 4.78/1.42 ( ![X4:$i,X6:$i,X8:$i]:
% 4.78/1.42 ( ( subset @ X4 @ X6 ) =>
% 4.78/1.42 ( ( ~( in @ X8 @ X6 ) ) => ( ~( in @ X8 @ X4 ) ) ) ) )),
% 4.78/1.42 define([status(thm)])).
% 4.78/1.42 thf(subsetE, axiom, subsetE =
% 4.78/1.42 (![A:$i,B:$i,Xx:$i]:
% 4.78/1.42 ( ( subset @ A @ B ) => ( ( in @ Xx @ A ) => ( in @ Xx @ B ) ) ))).
% 4.78/1.42 thf('57', plain,
% 4.78/1.42 (( subsetE ) =
% 4.78/1.42 ( ![X4:$i,X6:$i,X8:$i]:
% 4.78/1.42 ( ( subset @ X4 @ X6 ) => ( ( in @ X8 @ X4 ) => ( in @ X8 @ X6 ) ) ) )),
% 4.78/1.42 define([status(thm)])).
% 4.78/1.42 thf(emptysetsubset, axiom, emptysetsubset =
% 4.78/1.42 (![A:$i]: ( subset @ emptyset @ A ))).
% 4.78/1.42 thf('58', plain,
% 4.78/1.42 (( emptysetsubset ) = ( ![X4:$i]: ( subset @ emptyset @ X4 ) )),
% 4.78/1.42 define([status(thm)])).
% 4.78/1.42 thf(subsetI2, axiom, subsetI2 =
% 4.78/1.42 (![A:$i,B:$i]:
% 4.78/1.42 ( ( ![Xx:$i]: ( ( in @ Xx @ A ) => ( in @ Xx @ B ) ) ) =>
% 4.78/1.42 ( subset @ A @ B ) ))).
% 4.78/1.42 thf('59', plain,
% 4.78/1.42 (( subsetI2 ) =
% 4.78/1.42 ( ![X4:$i,X6:$i]:
% 4.78/1.42 ( ( ![X8:$i]: ( ( in @ X8 @ X4 ) => ( in @ X8 @ X6 ) ) ) =>
% 4.78/1.42 ( subset @ X4 @ X6 ) ) )),
% 4.78/1.42 define([status(thm)])).
% 4.78/1.42 thf(eqimpsubset1, axiom, eqimpsubset1 =
% 4.78/1.42 (![A:$i,B:$i]: ( ( ( A ) = ( B ) ) => ( subset @ A @ B ) ))).
% 4.78/1.42 thf('60', plain,
% 4.78/1.42 (( eqimpsubset1 ) =
% 4.78/1.42 ( ![X4:$i,X6:$i]: ( ( ( X4 ) = ( X6 ) ) => ( subset @ X4 @ X6 ) ) )),
% 4.78/1.42 define([status(thm)])).
% 4.78/1.42 thf(eqimpsubset2, axiom, eqimpsubset2 =
% 4.78/1.42 (![A:$i,B:$i]: ( ( ( A ) = ( B ) ) => ( subset @ B @ A ) ))).
% 4.78/1.42 thf('61', plain,
% 4.78/1.42 (( eqimpsubset2 ) =
% 4.78/1.42 ( ![X4:$i,X6:$i]: ( ( ( X4 ) = ( X6 ) ) => ( subset @ X6 @ X4 ) ) )),
% 4.78/1.42 define([status(thm)])).
% 4.78/1.42 thf(subsetI1, axiom, subsetI1 =
% 4.78/1.42 (![A:$i,B:$i]:
% 4.78/1.42 ( ( ![Xx:$i]: ( ( in @ Xx @ A ) => ( in @ Xx @ B ) ) ) =>
% 4.78/1.42 ( subset @ A @ B ) ))).
% 4.78/1.42 thf('62', plain,
% 4.78/1.42 (( subsetI1 ) =
% 4.78/1.42 ( ![X4:$i,X6:$i]:
% 4.78/1.42 ( ( ![X8:$i]: ( ( in @ X8 @ X4 ) => ( in @ X8 @ X6 ) ) ) =>
% 4.78/1.42 ( subset @ X4 @ X6 ) ) )),
% 4.78/1.42 define([status(thm)])).
% 4.78/1.42 thf(powerset__Cong, axiom, powerset__Cong =
% 4.78/1.42 (![A:$i,B:$i]:
% 4.78/1.42 ( ( ( A ) = ( B ) ) => ( ( powerset @ A ) = ( powerset @ B ) ) ))).
% 4.78/1.42 thf('63', plain,
% 4.78/1.42 (( powerset__Cong ) =
% 4.78/1.42 ( ![X4:$i,X6:$i]:
% 4.78/1.42 ( ( ( X4 ) = ( X6 ) ) => ( ( powerset @ X4 ) = ( powerset @ X6 ) ) ) )),
% 4.78/1.42 define([status(thm)])).
% 4.78/1.42 thf(powersetE, axiom, powersetE =
% 4.78/1.42 (![A:$i,B:$i,Xx:$i]:
% 4.78/1.42 ( ( in @ B @ ( powerset @ A ) ) => ( ( in @ Xx @ B ) => ( in @ Xx @ A ) ) ))).
% 4.78/1.42 thf('64', plain,
% 4.78/1.42 (( powersetE ) =
% 4.78/1.42 ( ![X4:$i,X6:$i,X8:$i]:
% 4.78/1.42 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 4.78/1.42 ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ) )),
% 4.78/1.42 define([status(thm)])).
% 4.78/1.42 thf(emptyInPowerset, axiom, emptyInPowerset =
% 4.78/1.42 (![A:$i]: ( in @ emptyset @ ( powerset @ A ) ))).
% 4.78/1.42 thf('65', plain,
% 4.78/1.42 (( emptyInPowerset ) =
% 4.78/1.42 ( ![X4:$i]: ( in @ emptyset @ ( powerset @ X4 ) ) )),
% 4.78/1.42 define([status(thm)])).
% 4.78/1.42 thf(emptyinPowerset, axiom, emptyinPowerset =
% 4.78/1.42 (![A:$i]: ( in @ emptyset @ ( powerset @ A ) ))).
% 4.78/1.42 thf('66', plain,
% 4.78/1.42 (( emptyinPowerset ) =
% 4.78/1.42 ( ![X4:$i]: ( in @ emptyset @ ( powerset @ X4 ) ) )),
% 4.78/1.42 define([status(thm)])).
% 4.78/1.42 thf(powersetI, axiom, powersetI =
% 4.78/1.42 (![A:$i,B:$i]:
% 4.78/1.42 ( ( ![Xx:$i]: ( ( in @ Xx @ B ) => ( in @ Xx @ A ) ) ) =>
% 4.78/1.42 ( in @ B @ ( powerset @ A ) ) ))).
% 4.78/1.42 thf('67', plain,
% 4.78/1.42 (( powersetI ) =
% 4.78/1.42 ( ![X4:$i,X6:$i]:
% 4.78/1.42 ( ( ![X8:$i]: ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ) =>
% 4.78/1.42 ( in @ X6 @ ( powerset @ X4 ) ) ) )),
% 4.78/1.42 define([status(thm)])).
% 4.78/1.42 thf(powersetAx, axiom, powersetAx =
% 4.78/1.42 (![A:$i,B:$i]:
% 4.78/1.42 ( ( in @ B @ ( powerset @ A ) ) <=>
% 4.78/1.42 ( ![Xx:$i]: ( ( in @ Xx @ B ) => ( in @ Xx @ A ) ) ) ))).
% 4.78/1.42 thf('68', plain,
% 4.78/1.42 (( powersetAx ) =
% 4.78/1.42 ( ![X4:$i,X6:$i]:
% 4.78/1.42 ( ( in @ X6 @ ( powerset @ X4 ) ) <=>
% 4.78/1.42 ( ![X8:$i]: ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ) ) )),
% 4.78/1.42 define([status(thm)])).
% 4.78/1.42 thf(complementSubsetComplementIntersect, conjecture,
% 4.78/1.42 (( setextAx ) =>
% 4.78/1.42 ( ( emptysetAx ) =>
% 4.78/1.42 ( ( setadjoinAx ) =>
% 4.78/1.42 ( ( powersetAx ) =>
% 4.78/1.42 ( ( setunionAx ) =>
% 4.78/1.42 ( ( omega0Ax ) =>
% 4.78/1.42 ( ( omegaSAx ) =>
% 4.78/1.42 ( ( omegaIndAx ) =>
% 4.78/1.42 ( ( replAx ) =>
% 4.78/1.42 ( ( foundationAx ) =>
% 4.78/1.42 ( ( wellorderingAx ) =>
% 4.78/1.42 ( ( descrp ) =>
% 4.78/1.42 ( ( dsetconstrI ) =>
% 4.78/1.42 ( ( dsetconstrEL ) =>
% 4.78/1.42 ( ( dsetconstrER ) =>
% 4.78/1.42 ( ( exuE1 ) =>
% 4.78/1.42 ( ( prop2setE ) =>
% 4.78/1.42 ( ( emptysetE ) =>
% 4.78/1.42 ( ( emptysetimpfalse ) =>
% 4.78/1.42 ( ( notinemptyset ) =>
% 4.78/1.42 ( ( exuE3e ) =>
% 4.78/1.42 ( ( setext ) =>
% 4.78/1.42 ( ( emptyI ) =>
% 4.78/1.42 ( ( noeltsimpempty ) =>
% 4.78/1.42 ( ( setbeta ) =>
% 4.78/1.42 ( ( nonemptyE1 ) =>
% 4.78/1.42 ( ( nonemptyI ) =>
% 4.78/1.42 ( ( nonemptyI1 ) =>
% 4.78/1.42 ( ( setadjoinIL ) =>
% 4.78/1.42 ( ( emptyinunitempty ) =>
% 4.78/1.42 ( ( setadjoinIR ) =>
% 4.78/1.42 ( ( setadjoinE ) =>
% 4.78/1.42 ( (
% 4.78/1.42 setadjoinOr ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 setoftrueEq ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 powersetI ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 emptyinPowerset ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 emptyInPowerset ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 powersetE ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 setunionI ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 setunionE ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 subPowSU ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 exuE2 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 nonemptyImpWitness ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 uniqinunit ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 notinsingleton ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 eqinunit ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 singletonsswitch ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 upairsetE ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 upairsetIL ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 upairsetIR ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 emptyE1 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 vacuousDall ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 quantDeMorgan1 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 quantDeMorgan2 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 quantDeMorgan3 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 quantDeMorgan4 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 prop2setI ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 prop2set2propI ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 notdexE ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 notdallE ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 exuI1 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 exuI3 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 exuI2 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 inCongP ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 in__Cong ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 exuE3u ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 exu__Cong ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 emptyset__Cong ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 setadjoin__Cong ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 powerset__Cong ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 setunion__Cong ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 omega__Cong ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 exuEu ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 descr__Cong ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 dsetconstr__Cong ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 subsetI1 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 eqimpsubset2 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 eqimpsubset1 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 subsetI2 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 emptysetsubset ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 subsetE ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 subsetE2 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 notsubsetI ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 notequalI1 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 notequalI2 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 subsetRefl ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 subsetTrans ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 setadjoinSub ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 setadjoinSub2 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 subset2powerset ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 setextsub ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 subsetemptysetimpeq ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 powersetI1 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 powersetE1 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 inPowerset ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 powersetsubset ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 sepInPowerset ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 sepSubset ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 binunionIL ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 upairset2IR ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 binunionIR ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 binunionEcases ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 binunionE ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 binunionLsub ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 binunionRsub ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 binintersectI ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 binintersectSubset5 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 binintersectEL ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 binintersectLsub ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 binintersectSubset2 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 binintersectSubset3 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 binintersectER ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 disjointsetsI1 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 binintersectRsub ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 binintersectSubset4 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 binintersectSubset1 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 bs114d ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 setminusI ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 setminusEL ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 setminusER ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 setminusSubset2 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 setminusERneg ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 setminusELneg ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 setminusILneg ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 setminusIRneg ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 setminusLsub ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 setminusSubset1 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 symdiffE ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 symdiffI1 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 symdiffI2 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 symdiffIneg1 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 symdiffIneg2 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 secondinupair ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 setukpairIL ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 setukpairIR ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 kpairiskpair ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 kpairp ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 singletonsubset ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 singletoninpowerset ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 singletoninpowunion ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 upairset2E ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 upairsubunion ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 upairinpowunion ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 ubforcartprodlem1 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 ubforcartprodlem2 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 ubforcartprodlem3 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 cartprodpairin ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 cartprodmempair1 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 cartprodmempair ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 setunionE2 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 setunionsingleton1 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 setunionsingleton2 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 setunionsingleton ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 singletonprop ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 ex1E1 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 ex1I ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 ex1I2 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 singletonsuniq ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 setukpairinjL1 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 kfstsingleton ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 theprop ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 kfstpairEq ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 cartprodfstin ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 setukpairinjL2 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 setukpairinjL ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 setukpairinjR11 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 setukpairinjR12 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 setukpairinjR1 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 upairequniteq ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 setukpairinjR2 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 setukpairinjR ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 ksndsingleton ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 ksndpairEq ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 kpairsurjEq ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 cartprodsndin ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 cartprodpairmemEL ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 cartprodpairmemER ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 cartprodmempaircEq ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 cartprodfstpairEq ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 cartprodsndpairEq ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 cartprodpairsurjEq ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 dpsetconstrI ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 dpsetconstrSub ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 setOfPairsIsBReln ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 dpsetconstrERa ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 dpsetconstrEL1 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 dpsetconstrEL2 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 dpsetconstrER ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 funcImageSingleton ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 apProp ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 app ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 infuncsetfunc ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 ap2p ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 funcinfuncset ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 lamProp ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 lamp ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 lam2p ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 brelnall1 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 brelnall2 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 ex1E2 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 funcGraphProp1 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 funcGraphProp3 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 funcGraphProp2 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 funcextLem ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 funcGraphProp4 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 subbreln ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 eqbreln ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 funcext ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 funcext2 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 ap2apEq1 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 ap2apEq2 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 beta1 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 eta1 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 lam2lamEq ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 beta2 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 eta2 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 iffalseProp1 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 iffalseProp2 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 iftrueProp1 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 iftrueProp2 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 ifSingleton ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 ifp ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 theeq ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 iftrue ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 iffalse ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 iftrueorfalse ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 binintersectT_lem ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 binunionT_lem ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 powersetT_lem ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 setminusT_lem ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 complementT_lem ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 setextT ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 subsetTI ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 powersetTI1 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 powersetTE1 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 complementTI1 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 complementTE1 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 binintersectTELcontra ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 binintersectTERcontra ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 contrasubsetT ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 contrasubsetT1 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 contrasubsetT2 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 contrasubsetT3 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 doubleComplementI1 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 doubleComplementE1 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 doubleComplementSub1 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 doubleComplementSub2 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 doubleComplementEq ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 complementTnotintersectT ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 complementImpComplementIntersect ) =>
% 4.78/1.42 (
% 4.78/1.42 ![
% 4.78/1.42 A:$i,X:$i]:
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 in @
% 4.78/1.42 X @
% 4.78/1.42 (
% 4.78/1.42 powerset @
% 4.78/1.42 A ) ) =>
% 4.78/1.42 (
% 4.78/1.42 ![
% 4.78/1.42 Y:$i]:
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 in @
% 4.78/1.42 Y @
% 4.78/1.42 (
% 4.78/1.42 powerset @
% 4.78/1.42 A ) ) =>
% 4.78/1.42 (
% 4.78/1.42 subset @
% 4.78/1.42 (
% 4.78/1.42 setminus @
% 4.78/1.42 A @ X ) @
% 4.78/1.42 (
% 4.78/1.42 setminus @
% 4.78/1.42 A @
% 4.78/1.42 (
% 4.78/1.42 binintersect
% 4.78/1.42 @
% 4.78/1.42 X @ Y ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 4.78/1.42 thf(zf_stmt_0, conjecture,
% 4.78/1.42 (( setextAx ) =>
% 4.78/1.42 ( ( emptysetAx ) =>
% 4.78/1.42 ( ( setadjoinAx ) =>
% 4.78/1.42 ( ( ![X4:$i,X6:$i]:
% 4.78/1.42 ( ( in @ X6 @ ( powerset @ X4 ) ) <=>
% 4.78/1.42 ( ![X8:$i]: ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ) ) ) =>
% 4.78/1.42 ( ( setunionAx ) =>
% 4.78/1.42 ( ( omega0Ax ) =>
% 4.78/1.42 ( ( omegaSAx ) =>
% 4.78/1.42 ( ( omegaIndAx ) =>
% 4.78/1.42 ( ( replAx ) =>
% 4.78/1.42 ( ( foundationAx ) =>
% 4.78/1.42 ( ( wellorderingAx ) =>
% 4.78/1.42 ( ( descrp ) =>
% 4.78/1.42 ( ( dsetconstrI ) =>
% 4.78/1.42 ( ( dsetconstrEL ) =>
% 4.78/1.42 ( ( dsetconstrER ) =>
% 4.78/1.42 ( ( exuE1 ) =>
% 4.78/1.42 ( ( prop2setE ) =>
% 4.78/1.42 ( ( emptysetE ) =>
% 4.78/1.42 ( ( emptysetimpfalse ) =>
% 4.78/1.42 ( ( notinemptyset ) =>
% 4.78/1.42 ( ( exuE3e ) =>
% 4.78/1.42 ( ( setext ) =>
% 4.78/1.42 ( ( emptyI ) =>
% 4.78/1.42 ( ( noeltsimpempty ) =>
% 4.78/1.42 ( ( setbeta ) =>
% 4.78/1.42 ( ( nonemptyE1 ) =>
% 4.78/1.42 ( ( nonemptyI ) =>
% 4.78/1.42 ( ( nonemptyI1 ) =>
% 4.78/1.42 ( ( setadjoinIL ) =>
% 4.78/1.42 ( ( emptyinunitempty ) =>
% 4.78/1.42 ( ( setadjoinIR ) =>
% 4.78/1.42 ( ( setadjoinE ) =>
% 4.78/1.42 ( (
% 4.78/1.42 setadjoinOr ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 setoftrueEq ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 ![
% 4.78/1.42 X10:$i,
% 4.78/1.42 X12:$i]:
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 ![
% 4.78/1.42 X14:$i]:
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 in @
% 4.78/1.42 X14 @ X12 ) =>
% 4.78/1.42 (
% 4.78/1.42 in @
% 4.78/1.42 X14 @ X10 ) ) ) =>
% 4.78/1.42 (
% 4.78/1.42 in @
% 4.78/1.42 X12 @
% 4.78/1.42 (
% 4.78/1.42 powerset @
% 4.78/1.42 X10 ) ) ) ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 ![
% 4.78/1.42 X16:$i]:
% 4.78/1.42 (
% 4.78/1.42 in @
% 4.78/1.42 emptyset @
% 4.78/1.42 (
% 4.78/1.42 powerset @
% 4.78/1.42 X16 ) ) ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 ![
% 4.78/1.42 X18:$i]:
% 4.78/1.42 (
% 4.78/1.42 in @
% 4.78/1.42 emptyset @
% 4.78/1.42 (
% 4.78/1.42 powerset @
% 4.78/1.42 X18 ) ) ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 ![
% 4.78/1.42 X20:$i,
% 4.78/1.42 X22:$i,
% 4.78/1.42 X24:$i]:
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 in @
% 4.78/1.42 X22 @
% 4.78/1.42 (
% 4.78/1.42 powerset @
% 4.78/1.42 X20 ) ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 in @
% 4.78/1.42 X24 @ X22 ) =>
% 4.78/1.42 (
% 4.78/1.42 in @
% 4.78/1.42 X24 @ X20 ) ) ) ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 setunionI ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 setunionE ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 subPowSU ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 exuE2 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 nonemptyImpWitness ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 uniqinunit ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 notinsingleton ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 eqinunit ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 singletonsswitch ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 upairsetE ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 upairsetIL ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 upairsetIR ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 emptyE1 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 vacuousDall ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 quantDeMorgan1 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 quantDeMorgan2 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 quantDeMorgan3 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 quantDeMorgan4 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 prop2setI ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 prop2set2propI ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 notdexE ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 notdallE ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 exuI1 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 exuI3 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 exuI2 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 inCongP ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 in__Cong ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 exuE3u ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 exu__Cong ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 emptyset__Cong ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 setadjoin__Cong ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 ![
% 4.78/1.42 X26:$i,
% 4.78/1.42 X28:$i]:
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 X26 ) =
% 4.78/1.42 (
% 4.78/1.42 X28 ) ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 powerset @
% 4.78/1.42 X26 ) =
% 4.78/1.42 (
% 4.78/1.42 powerset @
% 4.78/1.42 X28 ) ) ) ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 setunion__Cong ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 omega__Cong ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 exuEu ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 descr__Cong ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 dsetconstr__Cong ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 ![
% 4.78/1.42 X30:$i,
% 4.78/1.42 X32:$i]:
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 ![
% 4.78/1.42 X34:$i]:
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 in @
% 4.78/1.42 X34 @ X30 ) =>
% 4.78/1.42 (
% 4.78/1.42 in @
% 4.78/1.42 X34 @ X32 ) ) ) =>
% 4.78/1.42 (
% 4.78/1.42 subset @
% 4.78/1.42 X30 @ X32 ) ) ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 ![
% 4.78/1.42 X36:$i,
% 4.78/1.42 X38:$i]:
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 X36 ) =
% 4.78/1.42 (
% 4.78/1.42 X38 ) ) =>
% 4.78/1.42 (
% 4.78/1.42 subset @
% 4.78/1.42 X38 @ X36 ) ) ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 ![
% 4.78/1.42 X40:$i,
% 4.78/1.42 X42:$i]:
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 X40 ) =
% 4.78/1.42 (
% 4.78/1.42 X42 ) ) =>
% 4.78/1.42 (
% 4.78/1.42 subset @
% 4.78/1.42 X40 @ X42 ) ) ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 ![
% 4.78/1.42 X44:$i,
% 4.78/1.42 X46:$i]:
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 ![
% 4.78/1.42 X48:$i]:
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 in @
% 4.78/1.42 X48 @ X44 ) =>
% 4.78/1.42 (
% 4.78/1.42 in @
% 4.78/1.42 X48 @ X46 ) ) ) =>
% 4.78/1.42 (
% 4.78/1.42 subset @
% 4.78/1.42 X44 @ X46 ) ) ) =>
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% 4.78/1.42 (
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% 4.78/1.42 (
% 4.78/1.42 upairset2IR ) =>
% 4.78/1.42 (
% 4.78/1.42 (
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% 4.78/1.42 (
% 4.78/1.42 (
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% 4.78/1.42 (
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% 4.78/1.42 X162:$i,
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% 4.78/1.42 ![
% 4.78/1.42 X210:$i,
% 4.78/1.42 X212:$i]:
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 setminus @
% 4.78/1.42 X210 @
% 4.78/1.42 X212 ) =
% 4.78/1.42 (
% 4.78/1.42 emptyset ) ) =>
% 4.78/1.42 (
% 4.78/1.42 subset @
% 4.78/1.42 X210 @
% 4.78/1.42 X212 ) ) ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 symdiffE ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 symdiffI1 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 symdiffI2 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 symdiffIneg1 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 symdiffIneg2 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 secondinupair ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 setukpairIL ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 setukpairIR ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 kpairiskpair ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 kpairp ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 singletonsubset ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 ![
% 4.78/1.42 X214:$i,
% 4.78/1.42 X216:$i]:
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 in @
% 4.78/1.42 X216 @
% 4.78/1.42 X214 ) =>
% 4.78/1.42 (
% 4.78/1.42 in @
% 4.78/1.42 (
% 4.78/1.42 setadjoin
% 4.78/1.42 @
% 4.78/1.42 X216 @
% 4.78/1.42 emptyset ) @
% 4.78/1.42 (
% 4.78/1.42 powerset @
% 4.78/1.42 X214 ) ) ) ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 singletoninpowunion ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 upairset2E ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 upairsubunion ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 upairinpowunion ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 ubforcartprodlem1 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 ubforcartprodlem2 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 ubforcartprodlem3 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 cartprodpairin ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 cartprodmempair1 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 cartprodmempair ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 setunionE2 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 setunionsingleton1 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 setunionsingleton2 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 setunionsingleton ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 singletonprop ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 ex1E1 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 ex1I ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 ex1I2 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 singletonsuniq ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 setukpairinjL1 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 kfstsingleton ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 theprop ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 kfstpairEq ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 cartprodfstin ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 setukpairinjL2 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 setukpairinjL ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 setukpairinjR11 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 setukpairinjR12 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 setukpairinjR1 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 upairequniteq ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 setukpairinjR2 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 setukpairinjR ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 ksndsingleton ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 ksndpairEq ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 kpairsurjEq ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 cartprodsndin ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 cartprodpairmemEL ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 cartprodpairmemER ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 cartprodmempaircEq ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 cartprodfstpairEq ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 cartprodsndpairEq ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 cartprodpairsurjEq ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 dpsetconstrI ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 dpsetconstrSub ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 setOfPairsIsBReln ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 dpsetconstrERa ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 dpsetconstrEL1 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 dpsetconstrEL2 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 dpsetconstrER ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 funcImageSingleton ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 apProp ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 app ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 infuncsetfunc ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 ap2p ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 funcinfuncset ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 lamProp ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 lamp ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 lam2p ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 brelnall1 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 brelnall2 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 ex1E2 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 funcGraphProp1 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 funcGraphProp3 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 funcGraphProp2 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 funcextLem ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 funcGraphProp4 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 subbreln ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 eqbreln ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 funcext ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 funcext2 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 ap2apEq1 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 ap2apEq2 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 beta1 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 eta1 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 lam2lamEq ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 beta2 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 eta2 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 iffalseProp1 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 iffalseProp2 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 iftrueProp1 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 iftrueProp2 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 ifSingleton ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 ifp ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 theeq ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 iftrue ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 iffalse ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 iftrueorfalse ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 ![
% 4.78/1.42 X218:$i,
% 4.78/1.42 X220:$i]:
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 in @
% 4.78/1.42 X220 @
% 4.78/1.42 (
% 4.78/1.42 powerset @
% 4.78/1.42 X218 ) ) =>
% 4.78/1.42 (
% 4.78/1.42 ![
% 4.78/1.42 X222:$i]:
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 in @
% 4.78/1.42 X222 @
% 4.78/1.42 (
% 4.78/1.42 powerset @
% 4.78/1.42 X218 ) ) =>
% 4.78/1.42 (
% 4.78/1.42 in @
% 4.78/1.42 (
% 4.78/1.42 binintersect
% 4.78/1.42 @
% 4.78/1.42 X220 @
% 4.78/1.42 X222 ) @
% 4.78/1.42 (
% 4.78/1.42 powerset @
% 4.78/1.42 X218 ) ) ) ) ) ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 binunionT_lem ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 ![
% 4.78/1.42 X224:$i,
% 4.78/1.42 X226:$i]:
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 in @
% 4.78/1.42 X226 @
% 4.78/1.42 (
% 4.78/1.42 powerset @
% 4.78/1.42 X224 ) ) =>
% 4.78/1.42 (
% 4.78/1.42 in @
% 4.78/1.42 (
% 4.78/1.42 powerset @
% 4.78/1.42 X226 ) @
% 4.78/1.42 (
% 4.78/1.42 powerset @
% 4.78/1.42 (
% 4.78/1.42 powerset @
% 4.78/1.42 X224 ) ) ) ) ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 ![
% 4.78/1.42 X228:$i,
% 4.78/1.42 X230:$i]:
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 in @
% 4.78/1.42 X230 @
% 4.78/1.42 (
% 4.78/1.42 powerset @
% 4.78/1.42 X228 ) ) =>
% 4.78/1.42 (
% 4.78/1.42 ![
% 4.78/1.42 X232:$i]:
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 in @
% 4.78/1.42 X232 @
% 4.78/1.42 (
% 4.78/1.42 powerset @
% 4.78/1.42 X228 ) ) =>
% 4.78/1.42 (
% 4.78/1.42 in @
% 4.78/1.42 (
% 4.78/1.42 setminus @
% 4.78/1.42 X230 @
% 4.78/1.42 X232 ) @
% 4.78/1.42 (
% 4.78/1.42 powerset @
% 4.78/1.42 X228 ) ) ) ) ) ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 ![
% 4.78/1.42 X234:$i,
% 4.78/1.42 X236:$i]:
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 in @
% 4.78/1.42 X236 @
% 4.78/1.42 (
% 4.78/1.42 powerset @
% 4.78/1.42 X234 ) ) =>
% 4.78/1.42 (
% 4.78/1.42 in @
% 4.78/1.42 (
% 4.78/1.42 setminus @
% 4.78/1.42 X234 @
% 4.78/1.42 X236 ) @
% 4.78/1.42 (
% 4.78/1.42 powerset @
% 4.78/1.42 X234 ) ) ) ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 ![
% 4.78/1.42 X238:$i,
% 4.78/1.42 X240:$i]:
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 in @
% 4.78/1.42 X240 @
% 4.78/1.42 (
% 4.78/1.42 powerset @
% 4.78/1.42 X238 ) ) =>
% 4.78/1.42 (
% 4.78/1.42 ![
% 4.78/1.42 X242:$i]:
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 in @
% 4.78/1.42 X242 @
% 4.78/1.42 (
% 4.78/1.42 powerset @
% 4.78/1.42 X238 ) ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 ![
% 4.78/1.42 X244:$i]:
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 in @
% 4.78/1.42 X244 @
% 4.78/1.42 X238 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 in @
% 4.78/1.42 X244 @
% 4.78/1.42 X240 ) =>
% 4.78/1.42 (
% 4.78/1.42 in @
% 4.78/1.42 X244 @
% 4.78/1.42 X242 ) ) ) ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 ![
% 4.78/1.42 X246:$i]:
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 in @
% 4.78/1.42 X246 @
% 4.78/1.42 X238 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 in @
% 4.78/1.42 X246 @
% 4.78/1.42 X242 ) =>
% 4.78/1.42 (
% 4.78/1.42 in @
% 4.78/1.42 X246 @
% 4.78/1.42 X240 ) ) ) ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 X240 ) =
% 4.78/1.42 (
% 4.78/1.42 X242 ) ) ) ) ) ) ) ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 ![
% 4.78/1.42 X248:$i,
% 4.78/1.42 X250:$i]:
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 in @
% 4.78/1.42 X250 @
% 4.78/1.42 (
% 4.78/1.42 powerset @
% 4.78/1.42 X248 ) ) =>
% 4.78/1.42 (
% 4.78/1.42 ![
% 4.78/1.42 X252:$i]:
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 in @
% 4.78/1.42 X252 @
% 4.78/1.42 (
% 4.78/1.42 powerset @
% 4.78/1.42 X248 ) ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 ![
% 4.78/1.42 X254:$i]:
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 in @
% 4.78/1.42 X254 @
% 4.78/1.42 X248 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 in @
% 4.78/1.42 X254 @
% 4.78/1.42 X250 ) =>
% 4.78/1.42 (
% 4.78/1.42 in @
% 4.78/1.42 X254 @
% 4.78/1.42 X252 ) ) ) ) =>
% 4.78/1.42 (
% 4.78/1.42 subset @
% 4.78/1.42 X250 @
% 4.78/1.42 X252 ) ) ) ) ) ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 ![
% 4.78/1.42 X256:$i,
% 4.78/1.42 X258:$i]:
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 in @
% 4.78/1.42 X258 @
% 4.78/1.42 (
% 4.78/1.42 powerset @
% 4.78/1.42 X256 ) ) =>
% 4.78/1.42 (
% 4.78/1.42 ![
% 4.78/1.42 X260:$i]:
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 in @
% 4.78/1.42 X260 @
% 4.78/1.42 (
% 4.78/1.42 powerset @
% 4.78/1.42 X256 ) ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 ![
% 4.78/1.42 X262:$i]:
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 in @
% 4.78/1.42 X262 @
% 4.78/1.42 X256 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 in @
% 4.78/1.42 X262 @
% 4.78/1.42 X258 ) =>
% 4.78/1.42 (
% 4.78/1.42 in @
% 4.78/1.42 X262 @
% 4.78/1.42 X260 ) ) ) ) =>
% 4.78/1.42 (
% 4.78/1.42 in @
% 4.78/1.42 X258 @
% 4.78/1.42 (
% 4.78/1.42 powerset @
% 4.78/1.42 X260 ) ) ) ) ) ) ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 ![
% 4.78/1.42 X264:$i,
% 4.78/1.42 X266:$i]:
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 in @
% 4.78/1.42 X266 @
% 4.78/1.42 (
% 4.78/1.42 powerset @
% 4.78/1.42 X264 ) ) =>
% 4.78/1.42 (
% 4.78/1.42 ![
% 4.78/1.42 X268:$i]:
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 in @
% 4.78/1.42 X268 @
% 4.78/1.42 (
% 4.78/1.42 powerset @
% 4.78/1.42 X264 ) ) =>
% 4.78/1.42 (
% 4.78/1.42 ![
% 4.78/1.42 X270:$i]:
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 in @
% 4.78/1.42 X270 @
% 4.78/1.42 X264 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 in @
% 4.78/1.42 X266 @
% 4.78/1.42 (
% 4.78/1.42 powerset @
% 4.78/1.42 X268 ) ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 in @
% 4.78/1.42 X270 @
% 4.78/1.42 X266 ) =>
% 4.78/1.42 (
% 4.78/1.42 in @
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% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 ![
% 4.78/1.42 X272:$i,
% 4.78/1.42 X274:$i]:
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 in @
% 4.78/1.42 X274 @
% 4.78/1.42 (
% 4.78/1.42 powerset @
% 4.78/1.42 X272 ) ) =>
% 4.78/1.42 (
% 4.78/1.42 ![
% 4.78/1.42 X276:$i]:
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 in @
% 4.78/1.42 X276 @
% 4.78/1.42 X272 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 in @
% 4.78/1.42 X276 @
% 4.78/1.42 X274 ) =>
% 4.78/1.42 (
% 4.78/1.42 ~(
% 4.78/1.42 in @
% 4.78/1.42 X276 @
% 4.78/1.42 (
% 4.78/1.42 setminus
% 4.78/1.42 @
% 4.78/1.42 X272 @
% 4.78/1.42 X274 ) ) ) ) ) ) ) ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 ![
% 4.78/1.42 X278:$i,
% 4.78/1.42 X280:$i]:
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 in @
% 4.78/1.42 X280 @
% 4.78/1.42 (
% 4.78/1.42 powerset @
% 4.78/1.42 X278 ) ) =>
% 4.78/1.42 (
% 4.78/1.42 ![
% 4.78/1.42 X282:$i]:
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 in @
% 4.78/1.42 X282 @
% 4.78/1.42 X278 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 ~(
% 4.78/1.42 in @
% 4.78/1.42 X282 @
% 4.78/1.42 (
% 4.78/1.42 setminus
% 4.78/1.42 @
% 4.78/1.42 X278 @
% 4.78/1.42 X280 ) ) ) =>
% 4.78/1.42 (
% 4.78/1.42 in @
% 4.78/1.42 X282 @
% 4.78/1.42 X280 ) ) ) ) ) ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 ![
% 4.78/1.42 X284:$i,
% 4.78/1.42 X286:$i]:
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 in @
% 4.78/1.42 X286 @
% 4.78/1.42 (
% 4.78/1.42 powerset @
% 4.78/1.42 X284 ) ) =>
% 4.78/1.42 (
% 4.78/1.42 ![
% 4.78/1.42 X288:$i]:
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 in @
% 4.78/1.42 X288 @
% 4.78/1.42 (
% 4.78/1.42 powerset @
% 4.78/1.42 X284 ) ) =>
% 4.78/1.42 (
% 4.78/1.42 ![
% 4.78/1.42 X290:$i]:
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 in @
% 4.78/1.42 X290 @
% 4.78/1.42 X284 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 ~(
% 4.78/1.42 in @
% 4.78/1.42 X290 @
% 4.78/1.42 X286 ) ) =>
% 4.78/1.42 (
% 4.78/1.42 ~(
% 4.78/1.42 in @
% 4.78/1.42 X290 @
% 4.78/1.42 (
% 4.78/1.42 binintersect
% 4.78/1.42 @
% 4.78/1.42 X286 @
% 4.78/1.42 X288 ) ) ) ) ) ) ) ) ) ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 ![
% 4.78/1.42 X292:$i,
% 4.78/1.42 X294:$i]:
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 in @
% 4.78/1.42 X294 @
% 4.78/1.42 (
% 4.78/1.42 powerset @
% 4.78/1.42 X292 ) ) =>
% 4.78/1.42 (
% 4.78/1.42 ![
% 4.78/1.42 X296:$i]:
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 in @
% 4.78/1.42 X296 @
% 4.78/1.42 (
% 4.78/1.42 powerset @
% 4.78/1.42 X292 ) ) =>
% 4.78/1.42 (
% 4.78/1.42 ![
% 4.78/1.42 X298:$i]:
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 in @
% 4.78/1.42 X298 @
% 4.78/1.42 X292 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 ~(
% 4.78/1.42 in @
% 4.78/1.42 X298 @
% 4.78/1.42 X296 ) ) =>
% 4.78/1.42 (
% 4.78/1.42 ~(
% 4.78/1.42 in @
% 4.78/1.42 X298 @
% 4.78/1.42 (
% 4.78/1.42 binintersect
% 4.78/1.42 @
% 4.78/1.42 X294 @
% 4.78/1.42 X296 ) ) ) ) ) ) ) ) ) ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 ![
% 4.78/1.42 X300:$i,
% 4.78/1.42 X302:$i]:
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 in @
% 4.78/1.42 X302 @
% 4.78/1.42 (
% 4.78/1.42 powerset @
% 4.78/1.42 X300 ) ) =>
% 4.78/1.42 (
% 4.78/1.42 ![
% 4.78/1.42 X304:$i]:
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 in @
% 4.78/1.42 X304 @
% 4.78/1.42 (
% 4.78/1.42 powerset @
% 4.78/1.42 X300 ) ) =>
% 4.78/1.42 (
% 4.78/1.42 ![
% 4.78/1.42 X306:$i]:
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 in @
% 4.78/1.42 X306 @
% 4.78/1.42 X300 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 subset @
% 4.78/1.42 X302 @
% 4.78/1.42 (
% 4.78/1.42 setminus @
% 4.78/1.42 X300 @
% 4.78/1.42 X304 ) ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 in @
% 4.78/1.42 X306 @
% 4.78/1.42 X304 ) =>
% 4.78/1.42 (
% 4.78/1.42 ~(
% 4.78/1.42 in @
% 4.78/1.42 X306 @
% 4.78/1.42 X302 ) ) ) ) ) ) ) ) ) ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 ![
% 4.78/1.42 X308:$i,
% 4.78/1.42 X310:$i]:
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 in @
% 4.78/1.42 X310 @
% 4.78/1.42 (
% 4.78/1.42 powerset @
% 4.78/1.42 X308 ) ) =>
% 4.78/1.42 (
% 4.78/1.42 ![
% 4.78/1.42 X312:$i]:
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 in @
% 4.78/1.42 X312 @
% 4.78/1.42 (
% 4.78/1.42 powerset @
% 4.78/1.42 X308 ) ) =>
% 4.78/1.42 (
% 4.78/1.42 ![
% 4.78/1.42 X314:$i]:
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 in @
% 4.78/1.42 X314 @
% 4.78/1.42 X308 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 subset @
% 4.78/1.42 X310 @
% 4.78/1.42 X312 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 ~(
% 4.78/1.42 in @
% 4.78/1.42 X314 @
% 4.78/1.42 X312 ) ) =>
% 4.78/1.42 (
% 4.78/1.42 ~(
% 4.78/1.42 in @
% 4.78/1.42 X314 @
% 4.78/1.42 X310 ) ) ) ) ) ) ) ) ) ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 ![
% 4.78/1.42 X316:$i,
% 4.78/1.42 X318:$i]:
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 in @
% 4.78/1.42 X318 @
% 4.78/1.42 (
% 4.78/1.42 powerset @
% 4.78/1.42 X316 ) ) =>
% 4.78/1.42 (
% 4.78/1.42 ![
% 4.78/1.42 X320:$i]:
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 in @
% 4.78/1.42 X320 @
% 4.78/1.42 (
% 4.78/1.42 powerset @
% 4.78/1.42 X316 ) ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 subset @
% 4.78/1.42 X318 @
% 4.78/1.42 X320 ) =>
% 4.78/1.42 (
% 4.78/1.42 subset @
% 4.78/1.42 (
% 4.78/1.42 setminus @
% 4.78/1.42 X316 @
% 4.78/1.42 X320 ) @
% 4.78/1.42 (
% 4.78/1.42 setminus @
% 4.78/1.42 X316 @
% 4.78/1.42 X318 ) ) ) ) ) ) ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 ![
% 4.78/1.42 X322:$i,
% 4.78/1.42 X324:$i]:
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 in @
% 4.78/1.42 X324 @
% 4.78/1.42 (
% 4.78/1.42 powerset @
% 4.78/1.42 X322 ) ) =>
% 4.78/1.42 (
% 4.78/1.42 ![
% 4.78/1.42 X326:$i]:
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 in @
% 4.78/1.42 X326 @
% 4.78/1.42 (
% 4.78/1.42 powerset @
% 4.78/1.42 X322 ) ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 subset @
% 4.78/1.42 (
% 4.78/1.42 setminus @
% 4.78/1.42 X322 @
% 4.78/1.42 X326 ) @
% 4.78/1.42 (
% 4.78/1.42 setminus @
% 4.78/1.42 X322 @
% 4.78/1.42 X324 ) ) =>
% 4.78/1.42 (
% 4.78/1.42 subset @
% 4.78/1.42 X324 @
% 4.78/1.42 X326 ) ) ) ) ) ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 ![
% 4.78/1.42 X328:$i,
% 4.78/1.42 X330:$i]:
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 in @
% 4.78/1.42 X330 @
% 4.78/1.42 (
% 4.78/1.42 powerset @
% 4.78/1.42 X328 ) ) =>
% 4.78/1.42 (
% 4.78/1.42 ![
% 4.78/1.42 X332:$i]:
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 in @
% 4.78/1.42 X332 @
% 4.78/1.42 X328 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 in @
% 4.78/1.42 X332 @
% 4.78/1.42 X330 ) =>
% 4.78/1.42 (
% 4.78/1.42 in @
% 4.78/1.42 X332 @
% 4.78/1.42 (
% 4.78/1.42 setminus @
% 4.78/1.42 X328 @
% 4.78/1.42 (
% 4.78/1.42 setminus @
% 4.78/1.42 X328 @
% 4.78/1.42 X330 ) ) ) ) ) ) ) ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 ![
% 4.78/1.42 X334:$i,
% 4.78/1.42 X336:$i]:
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 in @
% 4.78/1.42 X336 @
% 4.78/1.42 (
% 4.78/1.42 powerset @
% 4.78/1.42 X334 ) ) =>
% 4.78/1.42 (
% 4.78/1.42 ![
% 4.78/1.42 X338:$i]:
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 in @
% 4.78/1.42 X338 @
% 4.78/1.42 X334 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 in @
% 4.78/1.42 X338 @
% 4.78/1.42 (
% 4.78/1.42 setminus @
% 4.78/1.42 X334 @
% 4.78/1.42 (
% 4.78/1.42 setminus @
% 4.78/1.42 X334 @
% 4.78/1.42 X336 ) ) ) =>
% 4.78/1.42 (
% 4.78/1.42 in @
% 4.78/1.42 X338 @
% 4.78/1.42 X336 ) ) ) ) ) ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 ![
% 4.78/1.42 X340:$i,
% 4.78/1.42 X342:$i]:
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 in @
% 4.78/1.42 X342 @
% 4.78/1.42 (
% 4.78/1.42 powerset @
% 4.78/1.42 X340 ) ) =>
% 4.78/1.42 (
% 4.78/1.42 subset @
% 4.78/1.42 X342 @
% 4.78/1.42 (
% 4.78/1.42 setminus @
% 4.78/1.42 X340 @
% 4.78/1.42 (
% 4.78/1.42 setminus @
% 4.78/1.42 X340 @
% 4.78/1.42 X342 ) ) ) ) ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 ![
% 4.78/1.42 X344:$i,
% 4.78/1.42 X346:$i]:
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 in @
% 4.78/1.42 X346 @
% 4.78/1.42 (
% 4.78/1.42 powerset @
% 4.78/1.42 X344 ) ) =>
% 4.78/1.42 (
% 4.78/1.42 subset @
% 4.78/1.42 (
% 4.78/1.42 setminus @
% 4.78/1.42 X344 @
% 4.78/1.42 (
% 4.78/1.42 setminus @
% 4.78/1.42 X344 @
% 4.78/1.42 X346 ) ) @
% 4.78/1.42 X346 ) ) ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 ![
% 4.78/1.42 X348:$i,
% 4.78/1.42 X350:$i]:
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 in @
% 4.78/1.42 X350 @
% 4.78/1.42 (
% 4.78/1.42 powerset @
% 4.78/1.42 X348 ) ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 X350 ) =
% 4.78/1.42 (
% 4.78/1.42 setminus @
% 4.78/1.42 X348 @
% 4.78/1.42 (
% 4.78/1.42 setminus @
% 4.78/1.42 X348 @
% 4.78/1.42 X350 ) ) ) ) ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 ![
% 4.78/1.42 X352:$i,
% 4.78/1.42 X354:$i]:
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 in @
% 4.78/1.42 X354 @
% 4.78/1.42 (
% 4.78/1.42 powerset @
% 4.78/1.42 X352 ) ) =>
% 4.78/1.42 (
% 4.78/1.42 ![
% 4.78/1.42 X356:$i]:
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 in @
% 4.78/1.42 X356 @
% 4.78/1.42 (
% 4.78/1.42 powerset @
% 4.78/1.42 X352 ) ) =>
% 4.78/1.42 (
% 4.78/1.42 ![
% 4.78/1.42 X358:$i]:
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 in @
% 4.78/1.42 X358 @
% 4.78/1.42 X352 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 in @
% 4.78/1.42 X358 @
% 4.78/1.42 (
% 4.78/1.42 setminus @
% 4.78/1.42 X352 @
% 4.78/1.42 X354 ) ) =>
% 4.78/1.42 (
% 4.78/1.42 ~(
% 4.78/1.42 in @
% 4.78/1.42 X358 @
% 4.78/1.42 (
% 4.78/1.42 binintersect
% 4.78/1.42 @
% 4.78/1.42 X354 @
% 4.78/1.42 X356 ) ) ) ) ) ) ) ) ) ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 ![
% 4.78/1.42 X360:$i,
% 4.78/1.42 X362:$i]:
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 in @
% 4.78/1.42 X362 @
% 4.78/1.42 (
% 4.78/1.42 powerset @
% 4.78/1.42 X360 ) ) =>
% 4.78/1.42 (
% 4.78/1.42 ![
% 4.78/1.42 X364:$i]:
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 in @
% 4.78/1.42 X364 @
% 4.78/1.42 (
% 4.78/1.42 powerset @
% 4.78/1.42 X360 ) ) =>
% 4.78/1.42 (
% 4.78/1.42 ![
% 4.78/1.42 X366:$i]:
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 in @
% 4.78/1.42 X366 @
% 4.78/1.42 X360 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 in @
% 4.78/1.42 X366 @
% 4.78/1.42 (
% 4.78/1.42 setminus @
% 4.78/1.42 X360 @
% 4.78/1.42 X362 ) ) =>
% 4.78/1.42 (
% 4.78/1.42 in @
% 4.78/1.42 X366 @
% 4.78/1.42 (
% 4.78/1.42 setminus @
% 4.78/1.42 X360 @
% 4.78/1.42 (
% 4.78/1.42 binintersect
% 4.78/1.42 @
% 4.78/1.42 X362 @
% 4.78/1.42 X364 ) ) ) ) ) ) ) ) ) ) =>
% 4.78/1.42 (
% 4.78/1.42 ![
% 4.78/1.42 X368:$i,
% 4.78/1.42 X370:$i]:
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 in @
% 4.78/1.42 X370 @
% 4.78/1.42 (
% 4.78/1.42 powerset @
% 4.78/1.42 X368 ) ) =>
% 4.78/1.42 (
% 4.78/1.42 ![
% 4.78/1.42 X372:$i]:
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 in @
% 4.78/1.42 X372 @
% 4.78/1.42 (
% 4.78/1.42 powerset @
% 4.78/1.42 X368 ) ) =>
% 4.78/1.42 (
% 4.78/1.42 subset @
% 4.78/1.42 (
% 4.78/1.42 setminus @
% 4.78/1.42 X368 @
% 4.78/1.42 X370 ) @
% 4.78/1.42 (
% 4.78/1.42 setminus @
% 4.78/1.42 X368 @
% 4.78/1.42 (
% 4.78/1.42 binintersect
% 4.78/1.42 @
% 4.78/1.42 X370 @
% 4.78/1.42 X372 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 4.78/1.42 thf(zf_stmt_1, type, zip_tseitin_0 : $i > $i > $i > $o).
% 4.78/1.42 thf(zf_stmt_2, axiom,
% 4.78/1.42 (![X8:$i,X6:$i,X4:$i]:
% 4.78/1.42 ( ( zip_tseitin_0 @ X8 @ X6 @ X4 ) <=>
% 4.78/1.42 ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ))).
% 4.78/1.42 thf(zf_stmt_3, conjecture,
% 4.78/1.42 (( setextAx ) =>
% 4.78/1.42 ( ( emptysetAx ) =>
% 4.78/1.42 ( ( setadjoinAx ) =>
% 4.78/1.42 ( ( ![X4:$i,X6:$i]:
% 4.78/1.42 ( ( in @ X6 @ ( powerset @ X4 ) ) <=>
% 4.78/1.42 ( ![X8:$i]: ( zip_tseitin_0 @ X8 @ X6 @ X4 ) ) ) ) =>
% 4.78/1.42 ( ( setunionAx ) =>
% 4.78/1.42 ( ( omega0Ax ) =>
% 4.78/1.42 ( ( omegaSAx ) =>
% 4.78/1.42 ( ( omegaIndAx ) =>
% 4.78/1.42 ( ( replAx ) =>
% 4.78/1.42 ( ( foundationAx ) =>
% 4.78/1.42 ( ( wellorderingAx ) =>
% 4.78/1.42 ( ( descrp ) =>
% 4.78/1.42 ( ( dsetconstrI ) =>
% 4.78/1.42 ( ( dsetconstrEL ) =>
% 4.78/1.42 ( ( dsetconstrER ) =>
% 4.78/1.42 ( ( exuE1 ) =>
% 4.78/1.42 ( ( prop2setE ) =>
% 4.78/1.42 ( ( emptysetE ) =>
% 4.78/1.42 ( ( emptysetimpfalse ) =>
% 4.78/1.42 ( ( notinemptyset ) =>
% 4.78/1.42 ( ( exuE3e ) =>
% 4.78/1.42 ( ( setext ) =>
% 4.78/1.42 ( ( emptyI ) =>
% 4.78/1.42 ( ( noeltsimpempty ) =>
% 4.78/1.42 ( ( setbeta ) =>
% 4.78/1.42 ( ( nonemptyE1 ) =>
% 4.78/1.42 ( ( nonemptyI ) =>
% 4.78/1.42 ( ( nonemptyI1 ) =>
% 4.78/1.42 ( ( setadjoinIL ) =>
% 4.78/1.42 ( ( emptyinunitempty ) =>
% 4.78/1.42 ( ( setadjoinIR ) =>
% 4.78/1.42 ( ( setadjoinE ) =>
% 4.78/1.42 ( (
% 4.78/1.42 setadjoinOr ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 setoftrueEq ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 ![
% 4.78/1.42 X10:$i,
% 4.78/1.42 X12:$i]:
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 ![
% 4.78/1.42 X14:$i]:
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 in @
% 4.78/1.42 X14 @ X12 ) =>
% 4.78/1.42 (
% 4.78/1.42 in @
% 4.78/1.42 X14 @ X10 ) ) ) =>
% 4.78/1.42 (
% 4.78/1.42 in @
% 4.78/1.42 X12 @
% 4.78/1.42 (
% 4.78/1.42 powerset @
% 4.78/1.42 X10 ) ) ) ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 ![
% 4.78/1.42 X16:$i]:
% 4.78/1.42 (
% 4.78/1.42 in @
% 4.78/1.42 emptyset @
% 4.78/1.42 (
% 4.78/1.42 powerset @
% 4.78/1.42 X16 ) ) ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 ![
% 4.78/1.42 X18:$i]:
% 4.78/1.42 (
% 4.78/1.42 in @
% 4.78/1.42 emptyset @
% 4.78/1.42 (
% 4.78/1.42 powerset @
% 4.78/1.42 X18 ) ) ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 ![
% 4.78/1.42 X20:$i,
% 4.78/1.42 X22:$i,
% 4.78/1.42 X24:$i]:
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 in @
% 4.78/1.42 X22 @
% 4.78/1.42 (
% 4.78/1.42 powerset @
% 4.78/1.42 X20 ) ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 in @
% 4.78/1.42 X24 @ X22 ) =>
% 4.78/1.42 (
% 4.78/1.42 in @
% 4.78/1.42 X24 @ X20 ) ) ) ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 setunionI ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 setunionE ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 subPowSU ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 exuE2 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 nonemptyImpWitness ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 uniqinunit ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 notinsingleton ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 eqinunit ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 singletonsswitch ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 upairsetE ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 upairsetIL ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 upairsetIR ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 emptyE1 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 vacuousDall ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 quantDeMorgan1 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 quantDeMorgan2 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 quantDeMorgan3 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 quantDeMorgan4 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 prop2setI ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 prop2set2propI ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 notdexE ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 notdallE ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 exuI1 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 exuI3 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 exuI2 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 inCongP ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 in__Cong ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 exuE3u ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 exu__Cong ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 emptyset__Cong ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 setadjoin__Cong ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 ![
% 4.78/1.42 X26:$i,
% 4.78/1.42 X28:$i]:
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 X26 ) =
% 4.78/1.42 (
% 4.78/1.42 X28 ) ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 powerset @
% 4.78/1.42 X26 ) =
% 4.78/1.42 (
% 4.78/1.42 powerset @
% 4.78/1.42 X28 ) ) ) ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 setunion__Cong ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 omega__Cong ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 exuEu ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 descr__Cong ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 dsetconstr__Cong ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 ![
% 4.78/1.42 X30:$i,
% 4.78/1.42 X32:$i]:
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 ![
% 4.78/1.42 X34:$i]:
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 in @
% 4.78/1.42 X34 @ X30 ) =>
% 4.78/1.42 (
% 4.78/1.42 in @
% 4.78/1.42 X34 @ X32 ) ) ) =>
% 4.78/1.42 (
% 4.78/1.42 subset @
% 4.78/1.42 X30 @ X32 ) ) ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 ![
% 4.78/1.42 X36:$i,
% 4.78/1.42 X38:$i]:
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 X36 ) =
% 4.78/1.42 (
% 4.78/1.42 X38 ) ) =>
% 4.78/1.42 (
% 4.78/1.42 subset @
% 4.78/1.42 X38 @ X36 ) ) ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 ![
% 4.78/1.42 X40:$i,
% 4.78/1.42 X42:$i]:
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 X40 ) =
% 4.78/1.42 (
% 4.78/1.42 X42 ) ) =>
% 4.78/1.42 (
% 4.78/1.42 subset @
% 4.78/1.42 X40 @ X42 ) ) ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 ![
% 4.78/1.42 X44:$i,
% 4.78/1.42 X46:$i]:
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 ![
% 4.78/1.42 X48:$i]:
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 in @
% 4.78/1.42 X48 @ X44 ) =>
% 4.78/1.42 (
% 4.78/1.42 in @
% 4.78/1.42 X48 @ X46 ) ) ) =>
% 4.78/1.42 (
% 4.78/1.42 subset @
% 4.78/1.42 X44 @ X46 ) ) ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 ![
% 4.78/1.42 X50:$i]:
% 4.78/1.42 (
% 4.78/1.42 subset @
% 4.78/1.42 emptyset @
% 4.78/1.42 X50 ) ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 ![
% 4.78/1.42 X52:$i,
% 4.78/1.42 X54:$i,
% 4.78/1.42 X56:$i]:
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 subset @
% 4.78/1.42 X52 @ X54 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 in @
% 4.78/1.42 X56 @ X52 ) =>
% 4.78/1.42 (
% 4.78/1.42 in @
% 4.78/1.42 X56 @ X54 ) ) ) ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 ![
% 4.78/1.42 X58:$i,
% 4.78/1.42 X60:$i,
% 4.78/1.42 X62:$i]:
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 subset @
% 4.78/1.42 X58 @ X60 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 ~(
% 4.78/1.42 in @
% 4.78/1.42 X62 @ X60 ) ) =>
% 4.78/1.42 (
% 4.78/1.42 ~(
% 4.78/1.42 in @
% 4.78/1.42 X62 @ X58 ) ) ) ) ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 ![
% 4.78/1.42 X64:$i,
% 4.78/1.42 X66:$i,
% 4.78/1.42 X68:$i]:
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 in @
% 4.78/1.42 X68 @ X64 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 ~(
% 4.78/1.42 in @
% 4.78/1.42 X68 @ X66 ) ) =>
% 4.78/1.42 (
% 4.78/1.42 ~(
% 4.78/1.42 subset @
% 4.78/1.42 X64 @ X66 ) ) ) ) ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 ![
% 4.78/1.42 X70:$i,
% 4.78/1.42 X72:$i]:
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 ~(
% 4.78/1.42 subset @
% 4.78/1.42 X70 @ X72 ) ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 X70 ) !=
% 4.78/1.42 (
% 4.78/1.42 X72 ) ) ) ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 notequalI2 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 ![
% 4.78/1.42 X74:$i]:
% 4.78/1.42 (
% 4.78/1.42 subset @
% 4.78/1.42 X74 @ X74 ) ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 ![
% 4.78/1.42 X76:$i,
% 4.78/1.42 X78:$i,
% 4.78/1.42 X80:$i]:
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 subset @
% 4.78/1.42 X76 @ X78 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 subset @
% 4.78/1.42 X78 @ X80 ) =>
% 4.78/1.42 (
% 4.78/1.42 subset @
% 4.78/1.42 X76 @ X80 ) ) ) ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 setadjoinSub ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 setadjoinSub2 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 ![
% 4.78/1.42 X82:$i,
% 4.78/1.42 X84:$i]:
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 subset @
% 4.78/1.42 X82 @ X84 ) =>
% 4.78/1.42 (
% 4.78/1.42 in @
% 4.78/1.42 X82 @
% 4.78/1.42 (
% 4.78/1.42 powerset @
% 4.78/1.42 X84 ) ) ) ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 ![
% 4.78/1.42 X86:$i,
% 4.78/1.42 X88:$i]:
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 subset @
% 4.78/1.42 X86 @ X88 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 subset @
% 4.78/1.42 X88 @ X86 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 X86 ) =
% 4.78/1.42 (
% 4.78/1.42 X88 ) ) ) ) ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 ![
% 4.78/1.42 X90:$i]:
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 subset @
% 4.78/1.42 X90 @
% 4.78/1.42 emptyset ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 X90 ) =
% 4.78/1.42 (
% 4.78/1.42 emptyset ) ) ) ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 ![
% 4.78/1.42 X92:$i,
% 4.78/1.42 X94:$i]:
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 subset @
% 4.78/1.42 X94 @ X92 ) =>
% 4.78/1.42 (
% 4.78/1.42 in @
% 4.78/1.42 X94 @
% 4.78/1.42 (
% 4.78/1.42 powerset @
% 4.78/1.42 X92 ) ) ) ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 ![
% 4.78/1.42 X96:$i,
% 4.78/1.42 X98:$i]:
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 in @
% 4.78/1.42 X98 @
% 4.78/1.42 (
% 4.78/1.42 powerset @
% 4.78/1.42 X96 ) ) =>
% 4.78/1.42 (
% 4.78/1.42 subset @
% 4.78/1.42 X98 @ X96 ) ) ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 ![
% 4.78/1.42 X100:$i]:
% 4.78/1.42 (
% 4.78/1.42 in @
% 4.78/1.42 X100 @
% 4.78/1.42 (
% 4.78/1.42 powerset @
% 4.78/1.42 X100 ) ) ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 ![
% 4.78/1.42 X102:$i,
% 4.78/1.42 X104:$i]:
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 subset @
% 4.78/1.42 X102 @
% 4.78/1.42 X104 ) =>
% 4.78/1.42 (
% 4.78/1.42 subset @
% 4.78/1.42 (
% 4.78/1.42 powerset @
% 4.78/1.42 X102 ) @
% 4.78/1.42 (
% 4.78/1.42 powerset @
% 4.78/1.42 X104 ) ) ) ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 sepInPowerset ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 sepSubset ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 binunionIL ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 upairset2IR ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 binunionIR ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 binunionEcases ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 binunionE ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 binunionLsub ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 binunionRsub ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 ![
% 4.78/1.42 X106:$i,
% 4.78/1.42 X108:$i,
% 4.78/1.42 X110:$i]:
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 in @
% 4.78/1.42 X110 @
% 4.78/1.42 X106 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 in @
% 4.78/1.42 X110 @
% 4.78/1.42 X108 ) =>
% 4.78/1.42 (
% 4.78/1.42 in @
% 4.78/1.42 X110 @
% 4.78/1.42 (
% 4.78/1.42 binintersect
% 4.78/1.42 @
% 4.78/1.42 X106 @
% 4.78/1.42 X108 ) ) ) ) ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 ![
% 4.78/1.42 X112:$i,
% 4.78/1.42 X114:$i,
% 4.78/1.42 X116:$i]:
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 subset @
% 4.78/1.42 X116 @
% 4.78/1.42 X112 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 subset @
% 4.78/1.42 X116 @
% 4.78/1.42 X114 ) =>
% 4.78/1.42 (
% 4.78/1.42 subset @
% 4.78/1.42 X116 @
% 4.78/1.42 (
% 4.78/1.42 binintersect
% 4.78/1.42 @
% 4.78/1.42 X112 @
% 4.78/1.42 X114 ) ) ) ) ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 ![
% 4.78/1.42 X118:$i,
% 4.78/1.42 X120:$i,
% 4.78/1.42 X122:$i]:
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 in @
% 4.78/1.42 X122 @
% 4.78/1.42 (
% 4.78/1.42 binintersect
% 4.78/1.42 @
% 4.78/1.42 X118 @
% 4.78/1.42 X120 ) ) =>
% 4.78/1.42 (
% 4.78/1.42 in @
% 4.78/1.42 X122 @
% 4.78/1.42 X118 ) ) ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 ![
% 4.78/1.42 X124:$i,
% 4.78/1.42 X126:$i]:
% 4.78/1.42 (
% 4.78/1.42 subset @
% 4.78/1.42 (
% 4.78/1.42 binintersect
% 4.78/1.42 @
% 4.78/1.42 X124 @
% 4.78/1.42 X126 ) @
% 4.78/1.42 X124 ) ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 ![
% 4.78/1.42 X128:$i,
% 4.78/1.42 X130:$i]:
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 subset @
% 4.78/1.42 X128 @
% 4.78/1.42 X130 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 binintersect
% 4.78/1.42 @
% 4.78/1.42 X128 @
% 4.78/1.42 X130 ) =
% 4.78/1.42 (
% 4.78/1.42 X128 ) ) ) ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 ![
% 4.78/1.42 X132:$i,
% 4.78/1.42 X134:$i]:
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 binintersect
% 4.78/1.42 @
% 4.78/1.42 X132 @
% 4.78/1.42 X134 ) =
% 4.78/1.42 (
% 4.78/1.42 X134 ) ) =>
% 4.78/1.42 (
% 4.78/1.42 subset @
% 4.78/1.42 X134 @
% 4.78/1.42 X132 ) ) ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 ![
% 4.78/1.42 X136:$i,
% 4.78/1.42 X138:$i,
% 4.78/1.42 X140:$i]:
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 in @
% 4.78/1.42 X140 @
% 4.78/1.42 (
% 4.78/1.42 binintersect
% 4.78/1.42 @
% 4.78/1.42 X136 @
% 4.78/1.42 X138 ) ) =>
% 4.78/1.42 (
% 4.78/1.42 in @
% 4.78/1.42 X140 @
% 4.78/1.42 X138 ) ) ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 ![
% 4.78/1.42 X142:$i,
% 4.78/1.42 X144:$i]:
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 ~(
% 4.78/1.42 ?[
% 4.78/1.42 X146:$i]:
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 in @
% 4.78/1.42 X146 @
% 4.78/1.42 X144 ) &
% 4.78/1.42 (
% 4.78/1.42 in @
% 4.78/1.42 X146 @
% 4.78/1.42 X142 ) ) ) ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 binintersect
% 4.78/1.42 @
% 4.78/1.42 X142 @
% 4.78/1.42 X144 ) =
% 4.78/1.42 (
% 4.78/1.42 emptyset ) ) ) ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 ![
% 4.78/1.42 X148:$i,
% 4.78/1.42 X150:$i]:
% 4.78/1.42 (
% 4.78/1.42 subset @
% 4.78/1.42 (
% 4.78/1.42 binintersect
% 4.78/1.42 @
% 4.78/1.42 X148 @
% 4.78/1.42 X150 ) @
% 4.78/1.42 X150 ) ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 ![
% 4.78/1.42 X152:$i,
% 4.78/1.42 X154:$i]:
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 subset @
% 4.78/1.42 X154 @
% 4.78/1.42 X152 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 binintersect
% 4.78/1.42 @
% 4.78/1.42 X152 @
% 4.78/1.42 X154 ) =
% 4.78/1.42 (
% 4.78/1.42 X154 ) ) ) ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 ![
% 4.78/1.42 X156:$i,
% 4.78/1.42 X158:$i]:
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 binintersect
% 4.78/1.42 @
% 4.78/1.42 X156 @
% 4.78/1.42 X158 ) =
% 4.78/1.42 (
% 4.78/1.42 X156 ) ) =>
% 4.78/1.42 (
% 4.78/1.42 subset @
% 4.78/1.42 X156 @
% 4.78/1.42 X158 ) ) ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 bs114d ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 ![
% 4.78/1.42 X160:$i,
% 4.78/1.42 X162:$i,
% 4.78/1.42 X164:$i]:
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 in @
% 4.78/1.42 X164 @
% 4.78/1.42 X160 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 ~(
% 4.78/1.42 in @
% 4.78/1.42 X164 @
% 4.78/1.42 X162 ) ) =>
% 4.78/1.42 (
% 4.78/1.42 in @
% 4.78/1.42 X164 @
% 4.78/1.42 (
% 4.78/1.42 setminus @
% 4.78/1.42 X160 @
% 4.78/1.42 X162 ) ) ) ) ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 ![
% 4.78/1.42 X166:$i,
% 4.78/1.42 X168:$i,
% 4.78/1.42 X170:$i]:
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 in @
% 4.78/1.42 X170 @
% 4.78/1.42 (
% 4.78/1.42 setminus @
% 4.78/1.42 X166 @
% 4.78/1.42 X168 ) ) =>
% 4.78/1.42 (
% 4.78/1.42 in @
% 4.78/1.42 X170 @
% 4.78/1.42 X166 ) ) ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 ![
% 4.78/1.42 X172:$i,
% 4.78/1.42 X174:$i,
% 4.78/1.42 X176:$i]:
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 in @
% 4.78/1.42 X176 @
% 4.78/1.42 (
% 4.78/1.42 setminus @
% 4.78/1.42 X172 @
% 4.78/1.42 X174 ) ) =>
% 4.78/1.42 (
% 4.78/1.42 ~(
% 4.78/1.42 in @
% 4.78/1.42 X176 @
% 4.78/1.42 X174 ) ) ) ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 ![
% 4.78/1.42 X178:$i,
% 4.78/1.42 X180:$i]:
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 subset @
% 4.78/1.42 X178 @
% 4.78/1.42 X180 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 setminus @
% 4.78/1.42 X178 @
% 4.78/1.42 X180 ) =
% 4.78/1.42 (
% 4.78/1.42 emptyset ) ) ) ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 ![
% 4.78/1.42 X182:$i,
% 4.78/1.42 X184:$i,
% 4.78/1.42 X186:$i]:
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 ~(
% 4.78/1.42 in @
% 4.78/1.42 X186 @
% 4.78/1.42 (
% 4.78/1.42 setminus
% 4.78/1.42 @
% 4.78/1.42 X182 @
% 4.78/1.42 X184 ) ) ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 in @
% 4.78/1.42 X186 @
% 4.78/1.42 X182 ) =>
% 4.78/1.42 (
% 4.78/1.42 in @
% 4.78/1.42 X186 @
% 4.78/1.42 X184 ) ) ) ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 ![
% 4.78/1.42 X188:$i,
% 4.78/1.42 X190:$i,
% 4.78/1.42 X192:$i]:
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 ~(
% 4.78/1.42 in @
% 4.78/1.42 X192 @
% 4.78/1.42 (
% 4.78/1.42 setminus
% 4.78/1.42 @
% 4.78/1.42 X188 @
% 4.78/1.42 X190 ) ) ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 ~(
% 4.78/1.42 in @
% 4.78/1.42 X192 @
% 4.78/1.42 X190 ) ) =>
% 4.78/1.42 (
% 4.78/1.42 ~(
% 4.78/1.42 in @
% 4.78/1.42 X192 @
% 4.78/1.42 X188 ) ) ) ) ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 ![
% 4.78/1.42 X194:$i,
% 4.78/1.42 X196:$i,
% 4.78/1.42 X198:$i]:
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 ~(
% 4.78/1.42 in @
% 4.78/1.42 X198 @
% 4.78/1.42 X194 ) ) =>
% 4.78/1.42 (
% 4.78/1.42 ~(
% 4.78/1.42 in @
% 4.78/1.42 X198 @
% 4.78/1.42 (
% 4.78/1.42 setminus
% 4.78/1.42 @
% 4.78/1.42 X194 @
% 4.78/1.42 X196 ) ) ) ) ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 ![
% 4.78/1.42 X200:$i,
% 4.78/1.42 X202:$i,
% 4.78/1.42 X204:$i]:
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 in @
% 4.78/1.42 X204 @
% 4.78/1.42 X202 ) =>
% 4.78/1.42 (
% 4.78/1.42 ~(
% 4.78/1.42 in @
% 4.78/1.42 X204 @
% 4.78/1.42 (
% 4.78/1.42 setminus
% 4.78/1.42 @
% 4.78/1.42 X200 @
% 4.78/1.42 X202 ) ) ) ) ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 ![
% 4.78/1.42 X206:$i,
% 4.78/1.42 X208:$i]:
% 4.78/1.42 (
% 4.78/1.42 subset @
% 4.78/1.42 (
% 4.78/1.42 setminus @
% 4.78/1.42 X206 @
% 4.78/1.42 X208 ) @
% 4.78/1.42 X206 ) ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 ![
% 4.78/1.42 X210:$i,
% 4.78/1.42 X212:$i]:
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 setminus @
% 4.78/1.42 X210 @
% 4.78/1.42 X212 ) =
% 4.78/1.42 (
% 4.78/1.42 emptyset ) ) =>
% 4.78/1.42 (
% 4.78/1.42 subset @
% 4.78/1.42 X210 @
% 4.78/1.42 X212 ) ) ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 symdiffE ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 symdiffI1 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 symdiffI2 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 symdiffIneg1 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 symdiffIneg2 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 secondinupair ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 setukpairIL ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 setukpairIR ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 kpairiskpair ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 kpairp ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 singletonsubset ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 ![
% 4.78/1.42 X214:$i,
% 4.78/1.42 X216:$i]:
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 in @
% 4.78/1.42 X216 @
% 4.78/1.42 X214 ) =>
% 4.78/1.42 (
% 4.78/1.42 in @
% 4.78/1.42 (
% 4.78/1.42 setadjoin
% 4.78/1.42 @
% 4.78/1.42 X216 @
% 4.78/1.42 emptyset ) @
% 4.78/1.42 (
% 4.78/1.42 powerset @
% 4.78/1.42 X214 ) ) ) ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 singletoninpowunion ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 upairset2E ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 upairsubunion ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 upairinpowunion ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 ubforcartprodlem1 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 ubforcartprodlem2 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 ubforcartprodlem3 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 cartprodpairin ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 cartprodmempair1 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 cartprodmempair ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 setunionE2 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 setunionsingleton1 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 setunionsingleton2 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 setunionsingleton ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 singletonprop ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 ex1E1 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 ex1I ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 ex1I2 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 singletonsuniq ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 setukpairinjL1 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 kfstsingleton ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 theprop ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 kfstpairEq ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 cartprodfstin ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 setukpairinjL2 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 setukpairinjL ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 setukpairinjR11 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 setukpairinjR12 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 setukpairinjR1 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 upairequniteq ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 setukpairinjR2 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 setukpairinjR ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 ksndsingleton ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 ksndpairEq ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 kpairsurjEq ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 cartprodsndin ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 cartprodpairmemEL ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 cartprodpairmemER ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 cartprodmempaircEq ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 cartprodfstpairEq ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 cartprodsndpairEq ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 cartprodpairsurjEq ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 dpsetconstrI ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 dpsetconstrSub ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 setOfPairsIsBReln ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 dpsetconstrERa ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 dpsetconstrEL1 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 dpsetconstrEL2 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 dpsetconstrER ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 funcImageSingleton ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 apProp ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 app ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 infuncsetfunc ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 ap2p ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 funcinfuncset ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 lamProp ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 lamp ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 lam2p ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 brelnall1 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 brelnall2 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 ex1E2 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 funcGraphProp1 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 funcGraphProp3 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 funcGraphProp2 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 funcextLem ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 funcGraphProp4 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 subbreln ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 eqbreln ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 funcext ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 funcext2 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 ap2apEq1 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 ap2apEq2 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 beta1 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 eta1 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 lam2lamEq ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 beta2 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 eta2 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 iffalseProp1 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 iffalseProp2 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 iftrueProp1 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 iftrueProp2 ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 ifSingleton ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 ifp ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 theeq ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 iftrue ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 iffalse ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 iftrueorfalse ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 ![
% 4.78/1.42 X218:$i,
% 4.78/1.42 X220:$i]:
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 in @
% 4.78/1.42 X220 @
% 4.78/1.42 (
% 4.78/1.42 powerset @
% 4.78/1.42 X218 ) ) =>
% 4.78/1.42 (
% 4.78/1.42 ![
% 4.78/1.42 X222:$i]:
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 in @
% 4.78/1.42 X222 @
% 4.78/1.42 (
% 4.78/1.42 powerset @
% 4.78/1.42 X218 ) ) =>
% 4.78/1.42 (
% 4.78/1.42 in @
% 4.78/1.42 (
% 4.78/1.42 binintersect
% 4.78/1.42 @
% 4.78/1.42 X220 @
% 4.78/1.42 X222 ) @
% 4.78/1.42 (
% 4.78/1.42 powerset @
% 4.78/1.42 X218 ) ) ) ) ) ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 binunionT_lem ) =>
% 4.78/1.42 (
% 4.78/1.42 (
% 4.78/1.42 ![
% 4.78/1.42 X224:$i,
% 4.78/1.42 X226:$i]:
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% 4.78/1.43 (
% 4.78/1.43 in @
% 4.78/1.43 X338 @
% 4.78/1.43 (
% 4.78/1.43 setminus @
% 4.78/1.43 X334 @
% 4.78/1.43 (
% 4.78/1.43 setminus @
% 4.78/1.43 X334 @
% 4.78/1.43 X336 ) ) ) =>
% 4.78/1.43 (
% 4.78/1.43 in @
% 4.78/1.43 X338 @
% 4.78/1.43 X336 ) ) ) ) ) ) =>
% 4.78/1.43 (
% 4.78/1.43 (
% 4.78/1.43 ![
% 4.78/1.43 X340:$i,
% 4.78/1.43 X342:$i]:
% 4.78/1.43 (
% 4.78/1.43 (
% 4.78/1.43 in @
% 4.78/1.43 X342 @
% 4.78/1.43 (
% 4.78/1.43 powerset @
% 4.78/1.43 X340 ) ) =>
% 4.78/1.43 (
% 4.78/1.43 subset @
% 4.78/1.43 X342 @
% 4.78/1.43 (
% 4.78/1.43 setminus @
% 4.78/1.43 X340 @
% 4.78/1.43 (
% 4.78/1.43 setminus @
% 4.78/1.43 X340 @
% 4.78/1.43 X342 ) ) ) ) ) =>
% 4.78/1.43 (
% 4.78/1.43 (
% 4.78/1.43 ![
% 4.78/1.43 X344:$i,
% 4.78/1.43 X346:$i]:
% 4.78/1.43 (
% 4.78/1.43 (
% 4.78/1.43 in @
% 4.78/1.43 X346 @
% 4.78/1.43 (
% 4.78/1.43 powerset @
% 4.78/1.43 X344 ) ) =>
% 4.78/1.43 (
% 4.78/1.43 subset @
% 4.78/1.43 (
% 4.78/1.43 setminus @
% 4.78/1.43 X344 @
% 4.78/1.43 (
% 4.78/1.43 setminus @
% 4.78/1.43 X344 @
% 4.78/1.43 X346 ) ) @
% 4.78/1.43 X346 ) ) ) =>
% 4.78/1.43 (
% 4.78/1.43 (
% 4.78/1.43 ![
% 4.78/1.43 X348:$i,
% 4.78/1.43 X350:$i]:
% 4.78/1.43 (
% 4.78/1.43 (
% 4.78/1.43 in @
% 4.78/1.43 X350 @
% 4.78/1.43 (
% 4.78/1.43 powerset @
% 4.78/1.43 X348 ) ) =>
% 4.78/1.43 (
% 4.78/1.43 (
% 4.78/1.43 X350 ) =
% 4.78/1.43 (
% 4.78/1.43 setminus @
% 4.78/1.43 X348 @
% 4.78/1.43 (
% 4.78/1.43 setminus @
% 4.78/1.43 X348 @
% 4.78/1.43 X350 ) ) ) ) ) =>
% 4.78/1.43 (
% 4.78/1.43 (
% 4.78/1.43 ![
% 4.78/1.43 X352:$i,
% 4.78/1.43 X354:$i]:
% 4.78/1.43 (
% 4.78/1.43 (
% 4.78/1.43 in @
% 4.78/1.43 X354 @
% 4.78/1.43 (
% 4.78/1.43 powerset @
% 4.78/1.43 X352 ) ) =>
% 4.78/1.43 (
% 4.78/1.43 ![
% 4.78/1.43 X356:$i]:
% 4.78/1.43 (
% 4.78/1.43 (
% 4.78/1.43 in @
% 4.78/1.43 X356 @
% 4.78/1.43 (
% 4.78/1.43 powerset @
% 4.78/1.43 X352 ) ) =>
% 4.78/1.43 (
% 4.78/1.43 ![
% 4.78/1.43 X358:$i]:
% 4.78/1.43 (
% 4.78/1.43 (
% 4.78/1.43 in @
% 4.78/1.43 X358 @
% 4.78/1.43 X352 ) =>
% 4.78/1.43 (
% 4.78/1.43 (
% 4.78/1.43 in @
% 4.78/1.43 X358 @
% 4.78/1.43 (
% 4.78/1.43 setminus @
% 4.78/1.43 X352 @
% 4.78/1.43 X354 ) ) =>
% 4.78/1.43 (
% 4.78/1.43 ~(
% 4.78/1.43 in @
% 4.78/1.43 X358 @
% 4.78/1.43 (
% 4.78/1.43 binintersect
% 4.78/1.43 @
% 4.78/1.43 X354 @
% 4.78/1.43 X356 ) ) ) ) ) ) ) ) ) ) =>
% 4.78/1.43 (
% 4.78/1.43 (
% 4.78/1.43 ![
% 4.78/1.43 X360:$i,
% 4.78/1.43 X362:$i]:
% 4.78/1.43 (
% 4.78/1.43 (
% 4.78/1.43 in @
% 4.78/1.43 X362 @
% 4.78/1.43 (
% 4.78/1.43 powerset @
% 4.78/1.43 X360 ) ) =>
% 4.78/1.43 (
% 4.78/1.43 ![
% 4.78/1.43 X364:$i]:
% 4.78/1.43 (
% 4.78/1.43 (
% 4.78/1.43 in @
% 4.78/1.43 X364 @
% 4.78/1.43 (
% 4.78/1.43 powerset @
% 4.78/1.43 X360 ) ) =>
% 4.78/1.43 (
% 4.78/1.43 ![
% 4.78/1.43 X366:$i]:
% 4.78/1.43 (
% 4.78/1.43 (
% 4.78/1.43 in @
% 4.78/1.43 X366 @
% 4.78/1.43 X360 ) =>
% 4.78/1.43 (
% 4.78/1.43 (
% 4.78/1.43 in @
% 4.78/1.43 X366 @
% 4.78/1.43 (
% 4.78/1.43 setminus @
% 4.78/1.43 X360 @
% 4.78/1.43 X362 ) ) =>
% 4.78/1.43 (
% 4.78/1.43 in @
% 4.78/1.43 X366 @
% 4.78/1.43 (
% 4.78/1.43 setminus @
% 4.78/1.43 X360 @
% 4.78/1.43 (
% 4.78/1.43 binintersect
% 4.78/1.43 @
% 4.78/1.43 X362 @
% 4.78/1.43 X364 ) ) ) ) ) ) ) ) ) ) =>
% 4.78/1.43 (
% 4.78/1.43 ![
% 4.78/1.43 X368:$i,
% 4.78/1.43 X370:$i]:
% 4.78/1.43 (
% 4.78/1.43 (
% 4.78/1.43 in @
% 4.78/1.43 X370 @
% 4.78/1.43 (
% 4.78/1.43 powerset @
% 4.78/1.43 X368 ) ) =>
% 4.78/1.43 (
% 4.78/1.43 ![
% 4.78/1.43 X372:$i]:
% 4.78/1.43 (
% 4.78/1.43 (
% 4.78/1.43 in @
% 4.78/1.43 X372 @
% 4.78/1.43 (
% 4.78/1.43 powerset @
% 4.78/1.43 X368 ) ) =>
% 4.78/1.43 (
% 4.78/1.43 subset @
% 4.78/1.43 (
% 4.78/1.43 setminus @
% 4.78/1.43 X368 @
% 4.78/1.43 X370 ) @
% 4.78/1.43 (
% 4.78/1.43 setminus @
% 4.78/1.43 X368 @
% 4.78/1.43 (
% 4.78/1.43 binintersect
% 4.78/1.43 @
% 4.78/1.43 X370 @
% 4.78/1.43 X372 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 4.78/1.43 thf(zf_stmt_4, negated_conjecture,
% 4.78/1.43 (~( ( setextAx ) =>
% 4.78/1.43 ( ( emptysetAx ) =>
% 4.78/1.43 ( ( setadjoinAx ) =>
% 4.78/1.43 ( ( ![X4:$i,X6:$i]:
% 4.78/1.43 ( ( in @ X6 @ ( powerset @ X4 ) ) <=>
% 4.78/1.43 ( ![X8:$i]: ( zip_tseitin_0 @ X8 @ X6 @ X4 ) ) ) ) =>
% 4.78/1.43 ( ( setunionAx ) =>
% 4.78/1.43 ( ( omega0Ax ) =>
% 4.78/1.43 ( ( omegaSAx ) =>
% 4.78/1.43 ( ( omegaIndAx ) =>
% 4.78/1.43 ( ( replAx ) =>
% 4.78/1.43 ( ( foundationAx ) =>
% 4.78/1.43 ( ( wellorderingAx ) =>
% 4.78/1.43 ( ( descrp ) =>
% 4.78/1.43 ( ( dsetconstrI ) =>
% 4.78/1.43 ( ( dsetconstrEL ) =>
% 4.78/1.43 ( ( dsetconstrER ) =>
% 4.78/1.43 ( ( exuE1 ) =>
% 4.78/1.43 ( ( prop2setE ) =>
% 4.78/1.43 ( ( emptysetE ) =>
% 4.78/1.43 ( ( emptysetimpfalse ) =>
% 4.78/1.43 ( ( notinemptyset ) =>
% 4.78/1.43 ( ( exuE3e ) =>
% 4.78/1.43 ( ( setext ) =>
% 4.78/1.43 ( ( emptyI ) =>
% 4.78/1.43 ( ( noeltsimpempty ) =>
% 4.78/1.43 ( ( setbeta ) =>
% 4.78/1.43 ( ( nonemptyE1 ) =>
% 4.78/1.43 ( ( nonemptyI ) =>
% 4.78/1.43 ( ( nonemptyI1 ) =>
% 4.78/1.43 ( ( setadjoinIL ) =>
% 4.78/1.43 ( ( emptyinunitempty ) =>
% 4.78/1.43 ( ( setadjoinIR ) =>
% 4.78/1.43 ( (
% 4.78/1.43 setadjoinE ) =>
% 4.78/1.43 (
% 4.78/1.43 (
% 4.78/1.43 setadjoinOr ) =>
% 4.78/1.43 (
% 4.78/1.43 (
% 4.78/1.43 setoftrueEq ) =>
% 4.78/1.43 (
% 4.78/1.43 (
% 4.78/1.43 ![
% 4.78/1.43 X10:$i,
% 4.78/1.43 X12:$i]:
% 4.78/1.43 (
% 4.78/1.43 (
% 4.78/1.43 ![
% 4.78/1.43 X14:$i]:
% 4.78/1.43 (
% 4.78/1.43 (
% 4.78/1.43 in @
% 4.78/1.43 X14 @ X12 ) =>
% 4.78/1.43 (
% 4.78/1.43 in @
% 4.78/1.43 X14 @ X10 ) ) ) =>
% 4.78/1.43 (
% 4.78/1.43 in @
% 4.78/1.43 X12 @
% 4.78/1.43 (
% 4.78/1.43 powerset
% 4.78/1.43 @
% 4.78/1.43 X10 ) ) ) ) =>
% 4.78/1.43 (
% 4.78/1.43 (
% 4.78/1.43 ![
% 4.78/1.43 X16:$i]:
% 4.78/1.43 (
% 4.78/1.43 in @
% 4.78/1.43 emptyset @
% 4.78/1.43 (
% 4.78/1.43 powerset
% 4.78/1.43 @
% 4.78/1.43 X16 ) ) ) =>
% 4.78/1.43 (
% 4.78/1.43 (
% 4.78/1.43 ![
% 4.78/1.43 X18:$i]:
% 4.78/1.43 (
% 4.78/1.43 in @
% 4.78/1.43 emptyset @
% 4.78/1.43 (
% 4.78/1.43 powerset
% 4.78/1.43 @
% 4.78/1.43 X18 ) ) ) =>
% 4.78/1.43 (
% 4.78/1.43 (
% 4.78/1.43 ![
% 4.78/1.43 X20:$i,
% 4.78/1.43 X22:$i,
% 4.78/1.43 X24:$i]:
% 4.78/1.43 (
% 4.78/1.43 (
% 4.78/1.43 in @
% 4.78/1.43 X22 @
% 4.78/1.43 (
% 4.78/1.43 powerset
% 4.78/1.43 @
% 4.78/1.43 X20 ) ) =>
% 4.78/1.43 (
% 4.78/1.43 (
% 4.78/1.43 in @
% 4.78/1.43 X24 @ X22 ) =>
% 4.78/1.43 (
% 4.78/1.43 in @
% 4.78/1.43 X24 @ X20 ) ) ) ) =>
% 4.78/1.43 (
% 4.78/1.43 (
% 4.78/1.43 setunionI ) =>
% 4.78/1.43 (
% 4.78/1.43 (
% 4.78/1.43 setunionE ) =>
% 4.78/1.43 (
% 4.78/1.43 (
% 4.78/1.43 subPowSU ) =>
% 4.78/1.43 (
% 4.78/1.43 (
% 4.78/1.43 exuE2 ) =>
% 4.78/1.43 (
% 4.78/1.43 (
% 4.78/1.43 nonemptyImpWitness ) =>
% 4.78/1.43 (
% 4.78/1.43 (
% 4.78/1.43 uniqinunit ) =>
% 4.78/1.43 (
% 4.78/1.43 (
% 4.78/1.43 notinsingleton ) =>
% 4.78/1.43 (
% 4.78/1.43 (
% 4.78/1.43 eqinunit ) =>
% 4.78/1.43 (
% 4.78/1.43 (
% 4.78/1.43 singletonsswitch ) =>
% 4.78/1.43 (
% 4.78/1.43 (
% 4.78/1.43 upairsetE ) =>
% 4.78/1.43 (
% 4.78/1.43 (
% 4.78/1.43 upairsetIL ) =>
% 4.78/1.43 (
% 4.78/1.43 (
% 4.78/1.43 upairsetIR ) =>
% 4.78/1.43 (
% 4.78/1.43 (
% 4.78/1.43 emptyE1 ) =>
% 4.78/1.43 (
% 4.78/1.43 (
% 4.78/1.43 vacuousDall ) =>
% 4.78/1.43 (
% 4.78/1.43 (
% 4.78/1.43 quantDeMorgan1 ) =>
% 4.78/1.43 (
% 4.78/1.43 (
% 4.78/1.43 quantDeMorgan2 ) =>
% 4.78/1.43 (
% 4.78/1.43 (
% 4.78/1.43 quantDeMorgan3 ) =>
% 4.78/1.43 (
% 4.78/1.43 (
% 4.78/1.43 quantDeMorgan4 ) =>
% 4.78/1.43 (
% 4.78/1.43 (
% 4.78/1.43 prop2setI ) =>
% 4.78/1.43 (
% 4.78/1.43 (
% 4.78/1.43 prop2set2propI ) =>
% 4.78/1.43 (
% 4.78/1.43 (
% 4.78/1.43 notdexE ) =>
% 4.78/1.43 (
% 4.78/1.43 (
% 4.78/1.43 notdallE ) =>
% 4.78/1.43 (
% 4.78/1.43 (
% 4.78/1.43 exuI1 ) =>
% 4.78/1.43 (
% 4.78/1.43 (
% 4.78/1.43 exuI3 ) =>
% 4.78/1.43 (
% 4.78/1.43 (
% 4.78/1.43 exuI2 ) =>
% 4.78/1.43 (
% 4.78/1.43 (
% 4.78/1.43 inCongP ) =>
% 4.78/1.43 (
% 4.78/1.43 (
% 4.78/1.43 in__Cong ) =>
% 4.78/1.43 (
% 4.78/1.43 (
% 4.78/1.43 exuE3u ) =>
% 4.78/1.43 (
% 4.78/1.43 (
% 4.78/1.43 exu__Cong ) =>
% 4.78/1.43 (
% 4.78/1.43 (
% 4.78/1.43 emptyset__Cong ) =>
% 4.78/1.43 (
% 4.78/1.43 (
% 4.78/1.43 setadjoin__Cong ) =>
% 4.78/1.43 (
% 4.78/1.43 (
% 4.78/1.43 ![
% 4.78/1.43 X26:$i,
% 4.78/1.43 X28:$i]:
% 4.78/1.43 (
% 4.78/1.43 (
% 4.78/1.43 (
% 4.78/1.43 X26 ) =
% 4.78/1.43 (
% 4.78/1.43 X28 ) ) =>
% 4.78/1.43 (
% 4.78/1.43 (
% 4.78/1.43 powerset
% 4.78/1.43 @
% 4.78/1.43 X26 ) =
% 4.78/1.43 (
% 4.78/1.43 powerset
% 4.78/1.43 @
% 4.78/1.43 X28 ) ) ) ) =>
% 4.78/1.43 (
% 4.78/1.43 (
% 4.78/1.43 setunion__Cong ) =>
% 4.78/1.43 (
% 4.78/1.43 (
% 4.78/1.43 omega__Cong ) =>
% 4.78/1.43 (
% 4.78/1.43 (
% 4.78/1.43 exuEu ) =>
% 4.78/1.43 (
% 4.78/1.43 (
% 4.78/1.43 descr__Cong ) =>
% 4.78/1.43 (
% 4.78/1.43 (
% 4.78/1.43 dsetconstr__Cong ) =>
% 4.78/1.43 (
% 4.78/1.43 (
% 4.78/1.43 ![
% 4.78/1.43 X30:$i,
% 4.78/1.43 X32:$i]:
% 4.78/1.43 (
% 4.78/1.43 (
% 4.78/1.43 ![
% 4.78/1.43 X34:$i]:
% 4.78/1.43 (
% 4.78/1.43 (
% 4.78/1.43 in @
% 4.78/1.43 X34 @ X30 ) =>
% 4.78/1.43 (
% 4.78/1.43 in @
% 4.78/1.43 X34 @ X32 ) ) ) =>
% 4.78/1.43 (
% 4.78/1.43 subset @
% 4.78/1.43 X30 @ X32 ) ) ) =>
% 4.78/1.43 (
% 4.78/1.43 (
% 4.78/1.43 ![
% 4.78/1.43 X36:$i,
% 4.78/1.43 X38:$i]:
% 4.78/1.43 (
% 4.78/1.43 (
% 4.78/1.43 (
% 4.78/1.43 X36 ) =
% 4.78/1.43 (
% 4.78/1.43 X38 ) ) =>
% 4.78/1.43 (
% 4.78/1.43 subset @
% 4.78/1.43 X38 @ X36 ) ) ) =>
% 4.78/1.43 (
% 4.78/1.43 (
% 4.78/1.43 ![
% 4.78/1.43 X40:$i,
% 4.78/1.43 X42:$i]:
% 4.78/1.43 (
% 4.78/1.43 (
% 4.78/1.43 (
% 4.78/1.43 X40 ) =
% 4.78/1.43 (
% 4.78/1.43 X42 ) ) =>
% 4.78/1.43 (
% 4.78/1.43 subset @
% 4.78/1.43 X40 @ X42 ) ) ) =>
% 4.78/1.43 (
% 4.78/1.43 (
% 4.78/1.43 ![
% 4.78/1.43 X44:$i,
% 4.78/1.43 X46:$i]:
% 4.78/1.43 (
% 4.78/1.43 (
% 4.78/1.43 ![
% 4.78/1.43 X48:$i]:
% 4.78/1.43 (
% 4.78/1.43 (
% 4.78/1.43 in @
% 4.78/1.43 X48 @ X44 ) =>
% 4.78/1.43 (
% 4.78/1.43 in @
% 4.78/1.43 X48 @ X46 ) ) ) =>
% 4.78/1.43 (
% 4.78/1.43 subset @
% 4.78/1.43 X44 @ X46 ) ) ) =>
% 4.78/1.43 (
% 4.78/1.43 (
% 4.78/1.43 ![
% 4.78/1.43 X50:$i]:
% 4.78/1.43 (
% 4.78/1.43 subset @
% 4.78/1.43 emptyset @
% 4.78/1.43 X50 ) ) =>
% 4.78/1.43 (
% 4.78/1.43 (
% 4.78/1.43 ![
% 4.78/1.43 X52:$i,
% 4.78/1.43 X54:$i,
% 4.78/1.43 X56:$i]:
% 4.78/1.43 (
% 4.78/1.43 (
% 4.78/1.43 subset @
% 4.78/1.43 X52 @ X54 ) =>
% 4.78/1.43 (
% 4.78/1.43 (
% 4.78/1.43 in @
% 4.78/1.43 X56 @ X52 ) =>
% 4.78/1.43 (
% 4.78/1.43 in @
% 4.78/1.43 X56 @ X54 ) ) ) ) =>
% 4.78/1.43 (
% 4.78/1.43 (
% 4.78/1.43 ![
% 4.78/1.43 X58:$i,
% 4.78/1.43 X60:$i,
% 4.78/1.43 X62:$i]:
% 4.78/1.43 (
% 4.78/1.43 (
% 4.78/1.43 subset @
% 4.78/1.43 X58 @ X60 ) =>
% 4.78/1.43 (
% 4.78/1.43 (
% 4.78/1.43 ~
% 4.78/1.43 (
% 4.78/1.43 in @
% 4.78/1.43 X62 @ X60 ) ) =>
% 4.78/1.43 (
% 4.78/1.43 ~
% 4.78/1.43 (
% 4.78/1.43 in @
% 4.78/1.43 X62 @ X58 ) ) ) ) ) =>
% 4.78/1.43 (
% 4.78/1.43 (
% 4.78/1.43 ![
% 4.78/1.43 X64:$i,
% 4.78/1.43 X66:$i,
% 4.78/1.43 X68:$i]:
% 4.78/1.43 (
% 4.78/1.43 (
% 4.78/1.43 in @
% 4.78/1.43 X68 @ X64 ) =>
% 4.78/1.43 (
% 4.78/1.43 (
% 4.78/1.43 ~
% 4.78/1.43 (
% 4.78/1.43 in @
% 4.78/1.43 X68 @ X66 ) ) =>
% 4.78/1.43 (
% 4.78/1.43 ~
% 4.78/1.43 (
% 4.78/1.43 subset @
% 4.78/1.43 X64 @ X66 ) ) ) ) ) =>
% 4.78/1.43 (
% 4.78/1.43 (
% 4.78/1.43 ![
% 4.78/1.43 X70:$i,
% 4.78/1.43 X72:$i]:
% 4.78/1.43 (
% 4.78/1.43 (
% 4.78/1.43 ~
% 4.78/1.43 (
% 4.78/1.43 subset @
% 4.78/1.43 X70 @ X72 ) ) =>
% 4.78/1.43 (
% 4.78/1.43 (
% 4.78/1.43 X70 ) !=
% 4.78/1.43 (
% 4.78/1.43 X72 ) ) ) ) =>
% 4.78/1.43 (
% 4.78/1.43 (
% 4.78/1.43 notequalI2 ) =>
% 4.78/1.43 (
% 4.78/1.43 (
% 4.78/1.43 ![
% 4.78/1.43 X74:$i]:
% 4.78/1.43 (
% 4.78/1.43 subset @
% 4.78/1.43 X74 @ X74 ) ) =>
% 4.78/1.43 (
% 4.78/1.43 (
% 4.78/1.43 ![
% 4.78/1.43 X76:$i,
% 4.78/1.43 X78:$i,
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% 4.78/1.43 (
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% 4.78/1.43 (
% 4.78/1.43 (
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% 4.78/1.43 (
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% 4.78/1.43 (
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% 4.78/1.43 (
% 4.78/1.43 (
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% 4.78/1.43 X368:$i,
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% 4.78/1.43 subset @
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% 4.78/1.43 X372 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )),
% 4.78/1.43 inference('cnf.neg', [status(esa)], [zf_stmt_3])).
% 4.78/1.43 thf(zip_derived_cl119, plain,
% 4.78/1.43 (![X47 : $i, X48 : $i, X49 : $i]:
% 4.78/1.43 (~ (in @ X47 @ (powerset @ X48))
% 4.78/1.43 | (in @ (binintersect @ X49 @ X47) @ (powerset @ X48))
% 4.78/1.43 | ~ (in @ X49 @ (powerset @ X48)))),
% 4.78/1.43 inference('cnf', [status(esa)], [zf_stmt_4])).
% 4.78/1.43 thf(zip_derived_cl140, plain,
% 4.78/1.43 (![X95 : $i, X96 : $i, X97 : $i]:
% 4.78/1.43 (~ (in @ X95 @ (powerset @ X96))
% 4.78/1.43 | (subset @ (setminus @ X96 @ X95) @ (setminus @ X96 @ X97))
% 4.78/1.43 | ~ (subset @ X97 @ X95)
% 4.78/1.43 | ~ (in @ X97 @ (powerset @ X96)))),
% 4.78/1.43 inference('cnf', [status(esa)], [zf_stmt_4])).
% 4.78/1.43 thf(zip_derived_cl134, plain,
% 4.78/1.43 (~ (subset @ (setminus @ sk__188 @ sk__189) @
% 4.78/1.43 (setminus @ sk__188 @ (binintersect @ sk__189 @ sk__190)))),
% 4.78/1.43 inference('cnf', [status(esa)], [zf_stmt_4])).
% 4.78/1.43 thf(zip_derived_cl1957, plain,
% 4.78/1.43 ((~ (in @ (binintersect @ sk__189 @ sk__190) @ (powerset @ sk__188))
% 4.78/1.43 | ~ (subset @ (binintersect @ sk__189 @ sk__190) @ sk__189)
% 4.78/1.43 | ~ (in @ sk__189 @ (powerset @ sk__188)))),
% 4.78/1.43 inference('sup-', [status(thm)], [zip_derived_cl140, zip_derived_cl134])).
% 4.78/1.43 thf(zip_derived_cl59, plain,
% 4.78/1.43 (![X24 : $i, X25 : $i]: (subset @ (binintersect @ X24 @ X25) @ X24)),
% 4.78/1.43 inference('cnf', [status(esa)], [zf_stmt_4])).
% 4.78/1.43 thf(zip_derived_cl135, plain, ( (in @ sk__189 @ (powerset @ sk__188))),
% 4.78/1.43 inference('cnf', [status(esa)], [zf_stmt_4])).
% 4.78/1.43 thf(zip_derived_cl2009, plain,
% 4.78/1.43 (~ (in @ (binintersect @ sk__189 @ sk__190) @ (powerset @ sk__188))),
% 4.78/1.43 inference('demod', [status(thm)],
% 4.78/1.43 [zip_derived_cl1957, zip_derived_cl59, zip_derived_cl135])).
% 4.78/1.43 thf(zip_derived_cl2072, plain,
% 4.78/1.43 ((~ (in @ sk__189 @ (powerset @ sk__188))
% 4.78/1.43 | ~ (in @ sk__190 @ (powerset @ sk__188)))),
% 4.78/1.43 inference('sup-', [status(thm)], [zip_derived_cl119, zip_derived_cl2009])).
% 4.78/1.43 thf(zip_derived_cl135, plain, ( (in @ sk__189 @ (powerset @ sk__188))),
% 4.78/1.43 inference('cnf', [status(esa)], [zf_stmt_4])).
% 4.78/1.43 thf(zip_derived_cl133, plain, ( (in @ sk__190 @ (powerset @ sk__188))),
% 4.78/1.43 inference('cnf', [status(esa)], [zf_stmt_4])).
% 4.78/1.43 thf(zip_derived_cl2076, plain, ($false),
% 4.78/1.43 inference('demod', [status(thm)],
% 4.78/1.43 [zip_derived_cl2072, zip_derived_cl135, zip_derived_cl133])).
% 4.78/1.43
% 4.78/1.43 % SZS output end Refutation
% 4.78/1.43
% 4.78/1.43
% 4.78/1.43 % Terminating...
% 5.42/1.61 % Runner terminated.
% 5.42/1.63 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------