%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SEU733^1 : TPTP v9.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.HG9NV6Stc1 true
% Computer : n026.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 16.36s 4.35s
% Output : Refutation 16.36s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.10 % Problem : SEU733^1 : TPTP v9.2.0. Released v3.7.0.
% 0.02/0.11 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.HG9NV6Stc1 true
% 0.14/0.31 % Computer : n026.cluster.edu
% 0.14/0.31 % Model : x86_64 x86_64
% 0.14/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.31 % Memory : 8042.1875MB
% 0.14/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.31 % CPULimit : 300
% 0.14/0.31 % WCLimit : 300
% 0.14/0.31 % DateTime : Wed Oct 1 16:01:38 EDT 2025
% 0.14/0.31 % CPUTime :
% 0.14/0.31 % Running portfolio for 300 s
% 0.14/0.31 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.31 % Number of cores: 8
% 0.14/0.32 % Python version: Python 3.6.8
% 0.14/0.32 % Running in HO mode
% 0.46/0.66 % Total configuration time : 828
% 0.46/0.66 % Estimated wc time : 1656
% 0.46/0.66 % Estimated cpu time (8 cpus) : 207.0
% 0.46/0.80 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s
% 0.46/0.81 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.47/0.88 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s
% 0.47/0.92 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s
% 0.47/0.97 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s
% 0.47/0.97 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.47/0.99 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s
% 0.47/0.99 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s
% 16.36/4.35 % Solved by lams/40_c_ic.sh.
% 16.36/4.35 % done 1639 iterations in 3.255s
% 16.36/4.35 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 16.36/4.35 % SZS output start Refutation
% 16.36/4.35 thf(setadjoinAx_type, type, setadjoinAx: $o).
% 16.36/4.35 thf(notdexE_type, type, notdexE: $o).
% 16.36/4.35 thf(setukpairinjL2_type, type, setukpairinjL2: $o).
% 16.36/4.35 thf(doubleComplementI1_type, type, doubleComplementI1: $o).
% 16.36/4.35 thf(setunionAx_type, type, setunionAx: $o).
% 16.36/4.35 thf(setminusELneg_type, type, setminusELneg: $o).
% 16.36/4.35 thf(cartprodsndin_type, type, cartprodsndin: $o).
% 16.36/4.35 thf(ex1E1_type, type, ex1E1: $o).
% 16.36/4.35 thf(powersetE_type, type, powersetE: $o).
% 16.36/4.35 thf(omegaSAx_type, type, omegaSAx: $o).
% 16.36/4.35 thf(exuI1_type, type, exuI1: $o).
% 16.36/4.35 thf(exuI2_type, type, exuI2: $o).
% 16.36/4.35 thf(notequalI2_type, type, notequalI2: $o).
% 16.36/4.35 thf(setukpairinjL_type, type, setukpairinjL: $o).
% 16.36/4.35 thf(kpairiskpair_type, type, kpairiskpair: $o).
% 16.36/4.35 thf(upairsubunion_type, type, upairsubunion: $o).
% 16.36/4.35 thf(funcGraphProp3_type, type, funcGraphProp3: $o).
% 16.36/4.35 thf(cartprodmempaircEq_type, type, cartprodmempaircEq: $o).
% 16.36/4.35 thf(binintersectTERcontra_type, type, binintersectTERcontra: $o).
% 16.36/4.35 thf(powerset__Cong_type, type, powerset__Cong: $o).
% 16.36/4.35 thf(setminusILneg_type, type, setminusILneg: $o).
% 16.36/4.35 thf(wellorderingAx_type, type, wellorderingAx: $o).
% 16.36/4.35 thf(ksndpairEq_type, type, ksndpairEq: $o).
% 16.36/4.35 thf(funcGraphProp2_type, type, funcGraphProp2: $o).
% 16.36/4.35 thf(setadjoinSub2_type, type, setadjoinSub2: $o).
% 16.36/4.35 thf(binintersectSubset5_type, type, binintersectSubset5: $o).
% 16.36/4.35 thf(iftrue_type, type, iftrue: $o).
% 16.36/4.35 thf(upairinpowunion_type, type, upairinpowunion: $o).
% 16.36/4.35 thf(ifSingleton_type, type, ifSingleton: $o).
% 16.36/4.35 thf(doubleComplementSub2_type, type, doubleComplementSub2: $o).
% 16.36/4.35 thf(setoftrueEq_type, type, setoftrueEq: $o).
% 16.36/4.35 thf(funcImageSingleton_type, type, funcImageSingleton: $o).
% 16.36/4.35 thf(dpsetconstrERa_type, type, dpsetconstrERa: $o).
% 16.36/4.35 thf(lamProp_type, type, lamProp: $o).
% 16.36/4.35 thf(cartprodpairmemEL_type, type, cartprodpairmemEL: $o).
% 16.36/4.35 thf(emptyset__Cong_type, type, emptyset__Cong: $o).
% 16.36/4.35 thf(dpsetconstrER_type, type, dpsetconstrER: $o).
% 16.36/4.35 thf(sepInPowerset_type, type, sepInPowerset: $o).
% 16.36/4.35 thf(setukpairIR_type, type, setukpairIR: $o).
% 16.36/4.35 thf(setukpairinjR1_type, type, setukpairinjR1: $o).
% 16.36/4.35 thf(lam2p_type, type, lam2p: $o).
% 16.36/4.35 thf(binunionE_type, type, binunionE: $o).
% 16.36/4.35 thf(setext_type, type, setext: $o).
% 16.36/4.35 thf(emptyinPowerset_type, type, emptyinPowerset: $o).
% 16.36/4.35 thf(ubforcartprodlem1_type, type, ubforcartprodlem1: $o).
% 16.36/4.35 thf(descr__Cong_type, type, descr__Cong: $o).
% 16.36/4.35 thf(kfstsingleton_type, type, kfstsingleton: $o).
% 16.36/4.35 thf(binintersectTELcontra_type, type, binintersectTELcontra: $o).
% 16.36/4.35 thf(doubleComplementEq_type, type, doubleComplementEq: $o).
% 16.36/4.35 thf(sk__156_type, type, sk__156: $i).
% 16.36/4.35 thf(eqbreln_type, type, eqbreln: $o).
% 16.36/4.35 thf(binintersectSubset1_type, type, binintersectSubset1: $o).
% 16.36/4.35 thf(in_type, type, in: $i > $i > $o).
% 16.36/4.35 thf(binunionT_lem_type, type, binunionT_lem: $o).
% 16.36/4.35 thf(quantDeMorgan1_type, type, quantDeMorgan1: $o).
% 16.36/4.35 thf(complementT_lem_type, type, complementT_lem: $o).
% 16.36/4.35 thf(kpairsurjEq_type, type, kpairsurjEq: $o).
% 16.36/4.35 thf(setadjoinIR_type, type, setadjoinIR: $o).
% 16.36/4.35 thf(doubleComplementE1_type, type, doubleComplementE1: $o).
% 16.36/4.35 thf(beta1_type, type, beta1: $o).
% 16.36/4.35 thf(setadjoin__Cong_type, type, setadjoin__Cong: $o).
% 16.36/4.35 thf(powersetTE1_type, type, powersetTE1: $o).
% 16.36/4.35 thf(symdiffI2_type, type, symdiffI2: $o).
% 16.36/4.35 thf(iftrueProp2_type, type, iftrueProp2: $o).
% 16.36/4.35 thf(upairset2IR_type, type, upairset2IR: $o).
% 16.36/4.35 thf(iffalseProp2_type, type, iffalseProp2: $o).
% 16.36/4.35 thf(subsetE_type, type, subsetE: $o).
% 16.36/4.35 thf(prop2set2propI_type, type, prop2set2propI: $o).
% 16.36/4.35 thf(dsetconstrEL_type, type, dsetconstrEL: $o).
% 16.36/4.35 thf(setbeta_type, type, setbeta: $o).
% 16.36/4.35 thf(eqinunit_type, type, eqinunit: $o).
% 16.36/4.35 thf(upairsetIL_type, type, upairsetIL: $o).
% 16.36/4.35 thf(powersetI1_type, type, powersetI1: $o).
% 16.36/4.35 thf(kfstpairEq_type, type, kfstpairEq: $o).
% 16.36/4.35 thf(binintersectSubset3_type, type, binintersectSubset3: $o).
% 16.36/4.35 thf(setminusIRneg_type, type, setminusIRneg: $o).
% 16.36/4.35 thf(ap2apEq1_type, type, ap2apEq1: $o).
% 16.36/4.35 thf(powersetAx_type, type, powersetAx: $o).
% 16.36/4.35 thf(binintersectSubset4_type, type, binintersectSubset4: $o).
% 16.36/4.35 thf(singletoninpowunion_type, type, singletoninpowunion: $o).
% 16.36/4.35 thf(powersetI_type, type, powersetI: $o).
% 16.36/4.35 thf(cartprodmempair_type, type, cartprodmempair: $o).
% 16.36/4.35 thf(upairsetIR_type, type, upairsetIR: $o).
% 16.36/4.35 thf(lamp_type, type, lamp: $o).
% 16.36/4.35 thf(dpsetconstrEL1_type, type, dpsetconstrEL1: $o).
% 16.36/4.35 thf(inCongP_type, type, inCongP: $o).
% 16.36/4.35 thf(sk__155_type, type, sk__155: $i).
% 16.36/4.35 thf(setadjoinSub_type, type, setadjoinSub: $o).
% 16.36/4.35 thf(exuE3e_type, type, exuE3e: $o).
% 16.36/4.35 thf(emptysetE_type, type, emptysetE: $o).
% 16.36/4.35 thf(binintersectSubset2_type, type, binintersectSubset2: $o).
% 16.36/4.35 thf(setunionI_type, type, setunionI: $o).
% 16.36/4.35 thf(setunion__Cong_type, type, setunion__Cong: $o).
% 16.36/4.35 thf(prop2setI_type, type, prop2setI: $o).
% 16.36/4.35 thf(singletonsuniq_type, type, singletonsuniq: $o).
% 16.36/4.35 thf(nonemptyImpWitness_type, type, nonemptyImpWitness: $o).
% 16.36/4.35 thf(zip_tseitin_0_type, type, zip_tseitin_0: $i > $i > $i > $o).
% 16.36/4.35 thf(setminusER_type, type, setminusER: $o).
% 16.36/4.35 thf(exuE2_type, type, exuE2: $o).
% 16.36/4.35 thf(emptyset_type, type, emptyset: $i).
% 16.36/4.35 thf(setukpairinjR11_type, type, setukpairinjR11: $o).
% 16.36/4.35 thf(ex1I_type, type, ex1I: $o).
% 16.36/4.35 thf(ex1E2_type, type, ex1E2: $o).
% 16.36/4.35 thf(setminus_type, type, setminus: $i > $i > $i).
% 16.36/4.35 thf(setukpairinjL1_type, type, setukpairinjL1: $o).
% 16.36/4.35 thf(powersetsubset_type, type, powersetsubset: $o).
% 16.36/4.35 thf(subPowSU_type, type, subPowSU: $o).
% 16.36/4.35 thf(notequalI1_type, type, notequalI1: $o).
% 16.36/4.35 thf(contrasubsetT_type, type, contrasubsetT: $o).
% 16.36/4.35 thf(notinemptyset_type, type, notinemptyset: $o).
% 16.36/4.35 thf(lam2lamEq_type, type, lam2lamEq: $o).
% 16.36/4.35 thf(nonemptyI1_type, type, nonemptyI1: $o).
% 16.36/4.35 thf(subsetTrans_type, type, subsetTrans: $o).
% 16.36/4.35 thf(kpairp_type, type, kpairp: $o).
% 16.36/4.35 thf(setukpairinjR12_type, type, setukpairinjR12: $o).
% 16.36/4.35 thf(setminusI_type, type, setminusI: $o).
% 16.36/4.35 thf(binunionIL_type, type, binunionIL: $o).
% 16.36/4.35 thf(dpsetconstrSub_type, type, dpsetconstrSub: $o).
% 16.36/4.35 thf(setunionsingleton_type, type, setunionsingleton: $o).
% 16.36/4.35 thf(subsetE2_type, type, subsetE2: $o).
% 16.36/4.35 thf(singletonsswitch_type, type, singletonsswitch: $o).
% 16.36/4.35 thf(ubforcartprodlem3_type, type, ubforcartprodlem3: $o).
% 16.36/4.35 thf(beta2_type, type, beta2: $o).
% 16.36/4.35 thf(dpsetconstrI_type, type, dpsetconstrI: $o).
% 16.36/4.35 thf(setextsub_type, type, setextsub: $o).
% 16.36/4.35 thf(binunionLsub_type, type, binunionLsub: $o).
% 16.36/4.35 thf(setunionsingleton1_type, type, setunionsingleton1: $o).
% 16.36/4.35 thf(binintersect_type, type, binintersect: $i > $i > $i).
% 16.36/4.35 thf(iftrueorfalse_type, type, iftrueorfalse: $o).
% 16.36/4.35 thf(emptysetsubset_type, type, emptysetsubset: $o).
% 16.36/4.35 thf(quantDeMorgan3_type, type, quantDeMorgan3: $o).
% 16.36/4.35 thf(cartprodpairsurjEq_type, type, cartprodpairsurjEq: $o).
% 16.36/4.35 thf(setOfPairsIsBReln_type, type, setOfPairsIsBReln: $o).
% 16.36/4.35 thf(setunionE_type, type, setunionE: $o).
% 16.36/4.35 thf(ksndsingleton_type, type, ksndsingleton: $o).
% 16.36/4.35 thf(setminusSubset1_type, type, setminusSubset1: $o).
% 16.36/4.35 thf(sk__157_type, type, sk__157: $i).
% 16.36/4.35 thf(powersetT_lem_type, type, powersetT_lem: $o).
% 16.36/4.35 thf(emptyinunitempty_type, type, emptyinunitempty: $o).
% 16.36/4.35 thf(binunionIR_type, type, binunionIR: $o).
% 16.36/4.35 thf(theeq_type, type, theeq: $o).
% 16.36/4.35 thf(setadjoinE_type, type, setadjoinE: $o).
% 16.36/4.35 thf(doubleComplementSub1_type, type, doubleComplementSub1: $o).
% 16.36/4.35 thf(infuncsetfunc_type, type, infuncsetfunc: $o).
% 16.36/4.35 thf(ap2apEq2_type, type, ap2apEq2: $o).
% 16.36/4.35 thf(ap2p_type, type, ap2p: $o).
% 16.36/4.35 thf(setadjoinIL_type, type, setadjoinIL: $o).
% 16.36/4.35 thf(cartprodsndpairEq_type, type, cartprodsndpairEq: $o).
% 16.36/4.35 thf(exuE1_type, type, exuE1: $o).
% 16.36/4.35 thf(ubforcartprodlem2_type, type, ubforcartprodlem2: $o).
% 16.36/4.35 thf(binintersectRsub_type, type, binintersectRsub: $o).
% 16.36/4.35 thf(setminusLsub_type, type, setminusLsub: $o).
% 16.36/4.35 thf(funcextLem_type, type, funcextLem: $o).
% 16.36/4.35 thf(setukpairinjR_type, type, setukpairinjR: $o).
% 16.36/4.35 thf(notinsingleton_type, type, notinsingleton: $o).
% 16.36/4.35 thf(eqimpsubset2_type, type, eqimpsubset2: $o).
% 16.36/4.35 thf(exuEu_type, type, exuEu: $o).
% 16.36/4.35 thf(emptysetimpfalse_type, type, emptysetimpfalse: $o).
% 16.36/4.35 thf(upairsetE_type, type, upairsetE: $o).
% 16.36/4.35 thf(omega0Ax_type, type, omega0Ax: $o).
% 16.36/4.35 thf(subsetTI_type, type, subsetTI: $o).
% 16.36/4.35 thf(notsubsetI_type, type, notsubsetI: $o).
% 16.36/4.35 thf(iffalseProp1_type, type, iffalseProp1: $o).
% 16.36/4.35 thf(quantDeMorgan4_type, type, quantDeMorgan4: $o).
% 16.36/4.35 thf(setextAx_type, type, setextAx: $o).
% 16.36/4.35 thf(cartprodpairmemER_type, type, cartprodpairmemER: $o).
% 16.36/4.35 thf(powersetE1_type, type, powersetE1: $o).
% 16.36/4.35 thf(bs114d_type, type, bs114d: $o).
% 16.36/4.35 thf(contrasubsetT3_type, type, contrasubsetT3: $o).
% 16.36/4.35 thf(noeltsimpempty_type, type, noeltsimpempty: $o).
% 16.36/4.35 thf(sk__154_type, type, sk__154: $i).
% 16.36/4.35 thf(ifp_type, type, ifp: $o).
% 16.36/4.35 thf(powersetTI1_type, type, powersetTI1: $o).
% 16.36/4.35 thf(binintersectLsub_type, type, binintersectLsub: $o).
% 16.36/4.35 thf(subsetI1_type, type, subsetI1: $o).
% 16.36/4.35 thf(symdiffE_type, type, symdiffE: $o).
% 16.36/4.35 thf(descrp_type, type, descrp: $o).
% 16.36/4.35 thf(dsetconstr__Cong_type, type, dsetconstr__Cong: $o).
% 16.36/4.35 thf(foundationAx_type, type, foundationAx: $o).
% 16.36/4.35 thf(emptysetAx_type, type, emptysetAx: $o).
% 16.36/4.35 thf(emptyI_type, type, emptyI: $o).
% 16.36/4.35 thf(setadjoinOr_type, type, setadjoinOr: $o).
% 16.36/4.35 thf(eta2_type, type, eta2: $o).
% 16.36/4.35 thf(binintersectEL_type, type, binintersectEL: $o).
% 16.36/4.35 thf(emptyE1_type, type, emptyE1: $o).
% 16.36/4.35 thf(emptyInPowerset_type, type, emptyInPowerset: $o).
% 16.36/4.35 thf(complementTI1_type, type, complementTI1: $o).
% 16.36/4.35 thf(vacuousDall_type, type, vacuousDall: $o).
% 16.36/4.35 thf(dsetconstrER_type, type, dsetconstrER: $o).
% 16.36/4.35 thf(binintersectI_type, type, binintersectI: $o).
% 16.36/4.35 thf(funcext_type, type, funcext: $o).
% 16.36/4.35 thf(funcGraphProp4_type, type, funcGraphProp4: $o).
% 16.36/4.35 thf(cartprodpairin_type, type, cartprodpairin: $o).
% 16.36/4.35 thf(cartprodmempair1_type, type, cartprodmempair1: $o).
% 16.36/4.35 thf(brelnall2_type, type, brelnall2: $o).
% 16.36/4.35 thf(setextT_type, type, setextT: $o).
% 16.36/4.35 thf(ex1I2_type, type, ex1I2: $o).
% 16.36/4.35 thf(symdiffI1_type, type, symdiffI1: $o).
% 16.36/4.35 thf(setukpairinjR2_type, type, setukpairinjR2: $o).
% 16.36/4.35 thf(dpsetconstrEL2_type, type, dpsetconstrEL2: $o).
% 16.36/4.35 thf(theprop_type, type, theprop: $o).
% 16.36/4.35 thf(subsetI2_type, type, subsetI2: $o).
% 16.36/4.35 thf(setminusT_lem_type, type, setminusT_lem: $o).
% 16.36/4.35 thf(symdiffIneg1_type, type, symdiffIneg1: $o).
% 16.36/4.35 thf(setminusERneg_type, type, setminusERneg: $o).
% 16.36/4.35 thf(symdiffIneg2_type, type, symdiffIneg2: $o).
% 16.36/4.35 thf(omega__Cong_type, type, omega__Cong: $o).
% 16.36/4.35 thf(subsetRefl_type, type, subsetRefl: $o).
% 16.36/4.35 thf(uniqinunit_type, type, uniqinunit: $o).
% 16.36/4.35 thf(setminusSubset2_type, type, setminusSubset2: $o).
% 16.36/4.35 thf(prop2setE_type, type, prop2setE: $o).
% 16.36/4.35 thf(binunionEcases_type, type, binunionEcases: $o).
% 16.36/4.35 thf(funcinfuncset_type, type, funcinfuncset: $o).
% 16.36/4.35 thf(complementTE1_type, type, complementTE1: $o).
% 16.36/4.35 thf(nonemptyI_type, type, nonemptyI: $o).
% 16.36/4.35 thf(app_type, type, app: $o).
% 16.36/4.35 thf(disjointsetsI1_type, type, disjointsetsI1: $o).
% 16.36/4.35 thf(exuE3u_type, type, exuE3u: $o).
% 16.36/4.35 thf(eta1_type, type, eta1: $o).
% 16.36/4.35 thf(setminusEL_type, type, setminusEL: $o).
% 16.36/4.35 thf(cartprodfstin_type, type, cartprodfstin: $o).
% 16.36/4.35 thf(setunionsingleton2_type, type, setunionsingleton2: $o).
% 16.36/4.35 thf(sepSubset_type, type, sepSubset: $o).
% 16.36/4.35 thf(complementTnotintersectT_type, type, complementTnotintersectT: $o).
% 16.36/4.35 thf(upairset2E_type, type, upairset2E: $o).
% 16.36/4.35 thf(eqimpsubset1_type, type, eqimpsubset1: $o).
% 16.36/4.35 thf(exuI3_type, type, exuI3: $o).
% 16.36/4.35 thf(cartprodfstpairEq_type, type, cartprodfstpairEq: $o).
% 16.36/4.35 thf(apProp_type, type, apProp: $o).
% 16.36/4.35 thf(notdallE_type, type, notdallE: $o).
% 16.36/4.35 thf(iftrueProp1_type, type, iftrueProp1: $o).
% 16.36/4.35 thf(binintersectER_type, type, binintersectER: $o).
% 16.36/4.35 thf(brelnall1_type, type, brelnall1: $o).
% 16.36/4.35 thf(powerset_type, type, powerset: $i > $i).
% 16.36/4.35 thf(dsetconstrI_type, type, dsetconstrI: $o).
% 16.36/4.35 thf(funcGraphProp1_type, type, funcGraphProp1: $o).
% 16.36/4.35 thf(binintersectT_lem_type, type, binintersectT_lem: $o).
% 16.36/4.35 thf(setadjoin_type, type, setadjoin: $i > $i > $i).
% 16.36/4.35 thf(exu__Cong_type, type, exu__Cong: $o).
% 16.36/4.35 thf(quantDeMorgan2_type, type, quantDeMorgan2: $o).
% 16.36/4.35 thf(contrasubsetT2_type, type, contrasubsetT2: $o).
% 16.36/4.35 thf(secondinupair_type, type, secondinupair: $o).
% 16.36/4.35 thf(singletonprop_type, type, singletonprop: $o).
% 16.36/4.35 thf(singletonsubset_type, type, singletonsubset: $o).
% 16.36/4.35 thf(contrasubsetT1_type, type, contrasubsetT1: $o).
% 16.36/4.35 thf(singletoninpowerset_type, type, singletoninpowerset: $o).
% 16.36/4.35 thf(subsetemptysetimpeq_type, type, subsetemptysetimpeq: $o).
% 16.36/4.35 thf(replAx_type, type, replAx: $o).
% 16.36/4.35 thf(upairequniteq_type, type, upairequniteq: $o).
% 16.36/4.35 thf(nonemptyE1_type, type, nonemptyE1: $o).
% 16.36/4.35 thf(omegaIndAx_type, type, omegaIndAx: $o).
% 16.36/4.35 thf(setukpairIL_type, type, setukpairIL: $o).
% 16.36/4.35 thf(setunionE2_type, type, setunionE2: $o).
% 16.36/4.35 thf(inPowerset_type, type, inPowerset: $o).
% 16.36/4.35 thf(iffalse_type, type, iffalse: $o).
% 16.36/4.35 thf(funcext2_type, type, funcext2: $o).
% 16.36/4.35 thf(subset_type, type, subset: $i > $i > $o).
% 16.36/4.35 thf(subbreln_type, type, subbreln: $o).
% 16.36/4.35 thf(in__Cong_type, type, in__Cong: $o).
% 16.36/4.35 thf(binunionRsub_type, type, binunionRsub: $o).
% 16.36/4.35 thf(subset2powerset_type, type, subset2powerset: $o).
% 16.36/4.35 thf(complementTnotintersectT, axiom, complementTnotintersectT =
% 16.36/4.35 (![A:$i,X:$i]:
% 16.36/4.35 ( ( in @ X @ ( powerset @ A ) ) =>
% 16.36/4.35 ( ![Y:$i]:
% 16.36/4.35 ( ( in @ Y @ ( powerset @ A ) ) =>
% 16.36/4.35 ( ![Xx:$i]:
% 16.36/4.35 ( ( in @ Xx @ A ) =>
% 16.36/4.35 ( ( in @ Xx @ ( setminus @ A @ X ) ) =>
% 16.36/4.35 ( ~( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ))).
% 16.36/4.35 thf('0', plain,
% 16.36/4.35 (( complementTnotintersectT ) =
% 16.36/4.35 ( ![X4:$i,X6:$i]:
% 16.36/4.35 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 16.36/4.35 ( ![X8:$i]:
% 16.36/4.35 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 16.36/4.35 ( ![X10:$i]:
% 16.36/4.35 ( ( in @ X10 @ X4 ) =>
% 16.36/4.35 ( ( in @ X10 @ ( setminus @ X4 @ X6 ) ) =>
% 16.36/4.35 ( ~( in @ X10 @ ( binintersect @ X6 @ X8 ) ) ) ) ) ) ) ) ) )),
% 16.36/4.35 define([status(thm)])).
% 16.36/4.35 thf(doubleComplementEq, axiom, doubleComplementEq =
% 16.36/4.35 (![A:$i,X:$i]:
% 16.36/4.35 ( ( in @ X @ ( powerset @ A ) ) =>
% 16.36/4.35 ( ( X ) = ( setminus @ A @ ( setminus @ A @ X ) ) ) ))).
% 16.36/4.35 thf('1', plain,
% 16.36/4.35 (( doubleComplementEq ) =
% 16.36/4.35 ( ![X4:$i,X6:$i]:
% 16.36/4.35 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 16.36/4.35 ( ( X6 ) = ( setminus @ X4 @ ( setminus @ X4 @ X6 ) ) ) ) )),
% 16.36/4.35 define([status(thm)])).
% 16.36/4.35 thf(doubleComplementSub2, axiom, doubleComplementSub2 =
% 16.36/4.35 (![A:$i,X:$i]:
% 16.36/4.35 ( ( in @ X @ ( powerset @ A ) ) =>
% 16.36/4.35 ( subset @ ( setminus @ A @ ( setminus @ A @ X ) ) @ X ) ))).
% 16.36/4.35 thf('2', plain,
% 16.36/4.35 (( doubleComplementSub2 ) =
% 16.36/4.35 ( ![X4:$i,X6:$i]:
% 16.36/4.35 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 16.36/4.35 ( subset @ ( setminus @ X4 @ ( setminus @ X4 @ X6 ) ) @ X6 ) ) )),
% 16.36/4.35 define([status(thm)])).
% 16.36/4.35 thf(doubleComplementSub1, axiom, doubleComplementSub1 =
% 16.36/4.35 (![A:$i,X:$i]:
% 16.36/4.35 ( ( in @ X @ ( powerset @ A ) ) =>
% 16.36/4.35 ( subset @ X @ ( setminus @ A @ ( setminus @ A @ X ) ) ) ))).
% 16.36/4.35 thf('3', plain,
% 16.36/4.35 (( doubleComplementSub1 ) =
% 16.36/4.35 ( ![X4:$i,X6:$i]:
% 16.36/4.35 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 16.36/4.35 ( subset @ X6 @ ( setminus @ X4 @ ( setminus @ X4 @ X6 ) ) ) ) )),
% 16.36/4.35 define([status(thm)])).
% 16.36/4.35 thf(doubleComplementE1, axiom, doubleComplementE1 =
% 16.36/4.35 (![A:$i,X:$i]:
% 16.36/4.35 ( ( in @ X @ ( powerset @ A ) ) =>
% 16.36/4.35 ( ![Xx:$i]:
% 16.36/4.35 ( ( in @ Xx @ A ) =>
% 16.36/4.35 ( ( in @ Xx @ ( setminus @ A @ ( setminus @ A @ X ) ) ) =>
% 16.36/4.35 ( in @ Xx @ X ) ) ) ) ))).
% 16.36/4.35 thf('4', plain,
% 16.36/4.35 (( doubleComplementE1 ) =
% 16.36/4.35 ( ![X4:$i,X6:$i]:
% 16.36/4.35 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 16.36/4.35 ( ![X8:$i]:
% 16.36/4.35 ( ( in @ X8 @ X4 ) =>
% 16.36/4.35 ( ( in @ X8 @ ( setminus @ X4 @ ( setminus @ X4 @ X6 ) ) ) =>
% 16.36/4.35 ( in @ X8 @ X6 ) ) ) ) ) )),
% 16.36/4.35 define([status(thm)])).
% 16.36/4.35 thf(doubleComplementI1, axiom, doubleComplementI1 =
% 16.36/4.35 (![A:$i,X:$i]:
% 16.36/4.35 ( ( in @ X @ ( powerset @ A ) ) =>
% 16.36/4.35 ( ![Xx:$i]:
% 16.36/4.35 ( ( in @ Xx @ A ) =>
% 16.36/4.35 ( ( in @ Xx @ X ) =>
% 16.36/4.35 ( in @ Xx @ ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) ))).
% 16.36/4.35 thf('5', plain,
% 16.36/4.35 (( doubleComplementI1 ) =
% 16.36/4.35 ( ![X4:$i,X6:$i]:
% 16.36/4.35 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 16.36/4.35 ( ![X8:$i]:
% 16.36/4.35 ( ( in @ X8 @ X4 ) =>
% 16.36/4.35 ( ( in @ X8 @ X6 ) =>
% 16.36/4.35 ( in @ X8 @ ( setminus @ X4 @ ( setminus @ X4 @ X6 ) ) ) ) ) ) ) )),
% 16.36/4.35 define([status(thm)])).
% 16.36/4.35 thf(contrasubsetT3, axiom, contrasubsetT3 =
% 16.36/4.35 (![A:$i,X:$i]:
% 16.36/4.35 ( ( in @ X @ ( powerset @ A ) ) =>
% 16.36/4.35 ( ![Y:$i]:
% 16.36/4.35 ( ( in @ Y @ ( powerset @ A ) ) =>
% 16.36/4.35 ( ( subset @ ( setminus @ A @ Y ) @ ( setminus @ A @ X ) ) =>
% 16.36/4.35 ( subset @ X @ Y ) ) ) ) ))).
% 16.36/4.35 thf('6', plain,
% 16.36/4.35 (( contrasubsetT3 ) =
% 16.36/4.35 ( ![X4:$i,X6:$i]:
% 16.36/4.35 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 16.36/4.35 ( ![X8:$i]:
% 16.36/4.35 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 16.36/4.35 ( ( subset @ ( setminus @ X4 @ X8 ) @ ( setminus @ X4 @ X6 ) ) =>
% 16.36/4.35 ( subset @ X6 @ X8 ) ) ) ) ) )),
% 16.36/4.35 define([status(thm)])).
% 16.36/4.35 thf(contrasubsetT2, axiom, contrasubsetT2 =
% 16.36/4.35 (![A:$i,X:$i]:
% 16.36/4.35 ( ( in @ X @ ( powerset @ A ) ) =>
% 16.36/4.35 ( ![Y:$i]:
% 16.36/4.35 ( ( in @ Y @ ( powerset @ A ) ) =>
% 16.36/4.35 ( ( subset @ X @ Y ) =>
% 16.36/4.35 ( subset @ ( setminus @ A @ Y ) @ ( setminus @ A @ X ) ) ) ) ) ))).
% 16.36/4.35 thf('7', plain,
% 16.36/4.35 (( contrasubsetT2 ) =
% 16.36/4.35 ( ![X4:$i,X6:$i]:
% 16.36/4.35 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 16.36/4.35 ( ![X8:$i]:
% 16.36/4.35 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 16.36/4.35 ( ( subset @ X6 @ X8 ) =>
% 16.36/4.35 ( subset @ ( setminus @ X4 @ X8 ) @ ( setminus @ X4 @ X6 ) ) ) ) ) ) )),
% 16.36/4.35 define([status(thm)])).
% 16.36/4.35 thf(contrasubsetT1, axiom, contrasubsetT1 =
% 16.36/4.35 (![A:$i,X:$i]:
% 16.36/4.35 ( ( in @ X @ ( powerset @ A ) ) =>
% 16.36/4.35 ( ![Y:$i]:
% 16.36/4.35 ( ( in @ Y @ ( powerset @ A ) ) =>
% 16.36/4.35 ( ![Xx:$i]:
% 16.36/4.35 ( ( in @ Xx @ A ) =>
% 16.36/4.35 ( ( subset @ X @ Y ) =>
% 16.36/4.35 ( ( ~( in @ Xx @ Y ) ) => ( ~( in @ Xx @ X ) ) ) ) ) ) ) ) ))).
% 16.36/4.35 thf('8', plain,
% 16.36/4.35 (( contrasubsetT1 ) =
% 16.36/4.35 ( ![X4:$i,X6:$i]:
% 16.36/4.35 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 16.36/4.35 ( ![X8:$i]:
% 16.36/4.35 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 16.36/4.35 ( ![X10:$i]:
% 16.36/4.35 ( ( in @ X10 @ X4 ) =>
% 16.36/4.35 ( ( subset @ X6 @ X8 ) =>
% 16.36/4.35 ( ( ~( in @ X10 @ X8 ) ) => ( ~( in @ X10 @ X6 ) ) ) ) ) ) ) ) ) )),
% 16.36/4.35 define([status(thm)])).
% 16.36/4.35 thf(contrasubsetT, axiom, contrasubsetT =
% 16.36/4.35 (![A:$i,X:$i]:
% 16.36/4.35 ( ( in @ X @ ( powerset @ A ) ) =>
% 16.36/4.35 ( ![Y:$i]:
% 16.36/4.35 ( ( in @ Y @ ( powerset @ A ) ) =>
% 16.36/4.35 ( ![Xx:$i]:
% 16.36/4.35 ( ( in @ Xx @ A ) =>
% 16.36/4.35 ( ( subset @ X @ ( setminus @ A @ Y ) ) =>
% 16.36/4.35 ( ( in @ Xx @ Y ) => ( ~( in @ Xx @ X ) ) ) ) ) ) ) ) ))).
% 16.36/4.35 thf('9', plain,
% 16.36/4.35 (( contrasubsetT ) =
% 16.36/4.35 ( ![X4:$i,X6:$i]:
% 16.36/4.35 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 16.36/4.35 ( ![X8:$i]:
% 16.36/4.35 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 16.36/4.35 ( ![X10:$i]:
% 16.36/4.35 ( ( in @ X10 @ X4 ) =>
% 16.36/4.35 ( ( subset @ X6 @ ( setminus @ X4 @ X8 ) ) =>
% 16.36/4.35 ( ( in @ X10 @ X8 ) => ( ~( in @ X10 @ X6 ) ) ) ) ) ) ) ) ) )),
% 16.36/4.35 define([status(thm)])).
% 16.36/4.35 thf(binintersectTERcontra, axiom, binintersectTERcontra =
% 16.36/4.35 (![A:$i,X:$i]:
% 16.36/4.35 ( ( in @ X @ ( powerset @ A ) ) =>
% 16.36/4.35 ( ![Y:$i]:
% 16.36/4.35 ( ( in @ Y @ ( powerset @ A ) ) =>
% 16.36/4.35 ( ![Xx:$i]:
% 16.36/4.35 ( ( in @ Xx @ A ) =>
% 16.36/4.35 ( ( ~( in @ Xx @ Y ) ) =>
% 16.36/4.35 ( ~( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ))).
% 16.36/4.35 thf('10', plain,
% 16.36/4.35 (( binintersectTERcontra ) =
% 16.36/4.35 ( ![X4:$i,X6:$i]:
% 16.36/4.35 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 16.36/4.35 ( ![X8:$i]:
% 16.36/4.35 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 16.36/4.35 ( ![X10:$i]:
% 16.36/4.35 ( ( in @ X10 @ X4 ) =>
% 16.36/4.35 ( ( ~( in @ X10 @ X8 ) ) =>
% 16.36/4.35 ( ~( in @ X10 @ ( binintersect @ X6 @ X8 ) ) ) ) ) ) ) ) ) )),
% 16.36/4.35 define([status(thm)])).
% 16.36/4.35 thf(binintersectTELcontra, axiom, binintersectTELcontra =
% 16.36/4.35 (![A:$i,X:$i]:
% 16.36/4.35 ( ( in @ X @ ( powerset @ A ) ) =>
% 16.36/4.35 ( ![Y:$i]:
% 16.36/4.35 ( ( in @ Y @ ( powerset @ A ) ) =>
% 16.36/4.35 ( ![Xx:$i]:
% 16.36/4.35 ( ( in @ Xx @ A ) =>
% 16.36/4.35 ( ( ~( in @ Xx @ X ) ) =>
% 16.36/4.35 ( ~( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ))).
% 16.36/4.35 thf('11', plain,
% 16.36/4.35 (( binintersectTELcontra ) =
% 16.36/4.35 ( ![X4:$i,X6:$i]:
% 16.36/4.35 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 16.36/4.35 ( ![X8:$i]:
% 16.36/4.35 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 16.36/4.35 ( ![X10:$i]:
% 16.36/4.35 ( ( in @ X10 @ X4 ) =>
% 16.36/4.35 ( ( ~( in @ X10 @ X6 ) ) =>
% 16.36/4.35 ( ~( in @ X10 @ ( binintersect @ X6 @ X8 ) ) ) ) ) ) ) ) ) )),
% 16.36/4.35 define([status(thm)])).
% 16.36/4.35 thf(complementTE1, axiom, complementTE1 =
% 16.36/4.35 (![A:$i,X:$i]:
% 16.36/4.35 ( ( in @ X @ ( powerset @ A ) ) =>
% 16.36/4.35 ( ![Xx:$i]:
% 16.36/4.35 ( ( in @ Xx @ A ) =>
% 16.36/4.35 ( ( ~( in @ Xx @ ( setminus @ A @ X ) ) ) => ( in @ Xx @ X ) ) ) ) ))).
% 16.36/4.35 thf('12', plain,
% 16.36/4.35 (( complementTE1 ) =
% 16.36/4.35 ( ![X4:$i,X6:$i]:
% 16.36/4.35 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 16.36/4.35 ( ![X8:$i]:
% 16.36/4.35 ( ( in @ X8 @ X4 ) =>
% 16.36/4.35 ( ( ~( in @ X8 @ ( setminus @ X4 @ X6 ) ) ) => ( in @ X8 @ X6 ) ) ) ) ) )),
% 16.36/4.35 define([status(thm)])).
% 16.36/4.35 thf(complementTI1, axiom, complementTI1 =
% 16.36/4.35 (![A:$i,X:$i]:
% 16.36/4.35 ( ( in @ X @ ( powerset @ A ) ) =>
% 16.36/4.35 ( ![Xx:$i]:
% 16.36/4.35 ( ( in @ Xx @ A ) =>
% 16.36/4.35 ( ( in @ Xx @ X ) => ( ~( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ))).
% 16.36/4.35 thf('13', plain,
% 16.36/4.35 (( complementTI1 ) =
% 16.36/4.35 ( ![X4:$i,X6:$i]:
% 16.36/4.35 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 16.36/4.35 ( ![X8:$i]:
% 16.36/4.35 ( ( in @ X8 @ X4 ) =>
% 16.36/4.35 ( ( in @ X8 @ X6 ) => ( ~( in @ X8 @ ( setminus @ X4 @ X6 ) ) ) ) ) ) ) )),
% 16.36/4.35 define([status(thm)])).
% 16.36/4.35 thf(powersetTE1, axiom, powersetTE1 =
% 16.36/4.35 (![A:$i,X:$i]:
% 16.36/4.35 ( ( in @ X @ ( powerset @ A ) ) =>
% 16.36/4.35 ( ![Y:$i]:
% 16.36/4.35 ( ( in @ Y @ ( powerset @ A ) ) =>
% 16.36/4.35 ( ![Xx:$i]:
% 16.36/4.35 ( ( in @ Xx @ A ) =>
% 16.36/4.35 ( ( in @ X @ ( powerset @ Y ) ) =>
% 16.36/4.35 ( ( in @ Xx @ X ) => ( in @ Xx @ Y ) ) ) ) ) ) ) ))).
% 16.36/4.35 thf('14', plain,
% 16.36/4.35 (( powersetTE1 ) =
% 16.36/4.35 ( ![X4:$i,X6:$i]:
% 16.36/4.35 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 16.36/4.35 ( ![X8:$i]:
% 16.36/4.35 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 16.36/4.35 ( ![X10:$i]:
% 16.36/4.35 ( ( in @ X10 @ X4 ) =>
% 16.36/4.35 ( ( in @ X6 @ ( powerset @ X8 ) ) =>
% 16.36/4.35 ( ( in @ X10 @ X6 ) => ( in @ X10 @ X8 ) ) ) ) ) ) ) ) )),
% 16.36/4.35 define([status(thm)])).
% 16.36/4.35 thf(powersetTI1, axiom, powersetTI1 =
% 16.36/4.35 (![A:$i,X:$i]:
% 16.36/4.35 ( ( in @ X @ ( powerset @ A ) ) =>
% 16.36/4.35 ( ![Y:$i]:
% 16.36/4.35 ( ( in @ Y @ ( powerset @ A ) ) =>
% 16.36/4.35 ( ( ![Xx:$i]:
% 16.36/4.35 ( ( in @ Xx @ A ) => ( ( in @ Xx @ X ) => ( in @ Xx @ Y ) ) ) ) =>
% 16.36/4.35 ( in @ X @ ( powerset @ Y ) ) ) ) ) ))).
% 16.36/4.35 thf('15', plain,
% 16.36/4.35 (( powersetTI1 ) =
% 16.36/4.35 ( ![X4:$i,X6:$i]:
% 16.36/4.35 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 16.36/4.35 ( ![X8:$i]:
% 16.36/4.35 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 16.36/4.35 ( ( ![X10:$i]:
% 16.36/4.35 ( ( in @ X10 @ X4 ) =>
% 16.36/4.35 ( ( in @ X10 @ X6 ) => ( in @ X10 @ X8 ) ) ) ) =>
% 16.36/4.35 ( in @ X6 @ ( powerset @ X8 ) ) ) ) ) ) )),
% 16.36/4.35 define([status(thm)])).
% 16.36/4.35 thf(subsetTI, axiom, subsetTI =
% 16.36/4.35 (![A:$i,X:$i]:
% 16.36/4.35 ( ( in @ X @ ( powerset @ A ) ) =>
% 16.36/4.35 ( ![Y:$i]:
% 16.36/4.35 ( ( in @ Y @ ( powerset @ A ) ) =>
% 16.36/4.35 ( ( ![Xx:$i]:
% 16.36/4.35 ( ( in @ Xx @ A ) => ( ( in @ Xx @ X ) => ( in @ Xx @ Y ) ) ) ) =>
% 16.36/4.35 ( subset @ X @ Y ) ) ) ) ))).
% 16.36/4.35 thf('16', plain,
% 16.36/4.35 (( subsetTI ) =
% 16.36/4.35 ( ![X4:$i,X6:$i]:
% 16.36/4.35 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 16.36/4.35 ( ![X8:$i]:
% 16.36/4.35 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 16.36/4.35 ( ( ![X10:$i]:
% 16.36/4.35 ( ( in @ X10 @ X4 ) =>
% 16.36/4.35 ( ( in @ X10 @ X6 ) => ( in @ X10 @ X8 ) ) ) ) =>
% 16.36/4.35 ( subset @ X6 @ X8 ) ) ) ) ) )),
% 16.36/4.35 define([status(thm)])).
% 16.36/4.35 thf(setextT, axiom, setextT =
% 16.36/4.35 (![A:$i,X:$i]:
% 16.36/4.35 ( ( in @ X @ ( powerset @ A ) ) =>
% 16.36/4.35 ( ![Y:$i]:
% 16.36/4.35 ( ( in @ Y @ ( powerset @ A ) ) =>
% 16.36/4.35 ( ( ![Xx:$i]:
% 16.36/4.35 ( ( in @ Xx @ A ) => ( ( in @ Xx @ X ) => ( in @ Xx @ Y ) ) ) ) =>
% 16.36/4.35 ( ( ![Xx:$i]:
% 16.36/4.35 ( ( in @ Xx @ A ) => ( ( in @ Xx @ Y ) => ( in @ Xx @ X ) ) ) ) =>
% 16.36/4.35 ( ( X ) = ( Y ) ) ) ) ) ) ))).
% 16.36/4.35 thf('17', plain,
% 16.36/4.35 (( setextT ) =
% 16.36/4.35 ( ![X4:$i,X6:$i]:
% 16.36/4.35 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 16.36/4.35 ( ![X8:$i]:
% 16.36/4.35 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 16.36/4.35 ( ( ![X10:$i]:
% 16.36/4.35 ( ( in @ X10 @ X4 ) =>
% 16.36/4.35 ( ( in @ X10 @ X6 ) => ( in @ X10 @ X8 ) ) ) ) =>
% 16.36/4.35 ( ( ![X12:$i]:
% 16.36/4.35 ( ( in @ X12 @ X4 ) =>
% 16.36/4.35 ( ( in @ X12 @ X8 ) => ( in @ X12 @ X6 ) ) ) ) =>
% 16.36/4.35 ( ( X6 ) = ( X8 ) ) ) ) ) ) ) )),
% 16.36/4.35 define([status(thm)])).
% 16.36/4.35 thf(complementT_lem, axiom, complementT_lem =
% 16.36/4.35 (![A:$i,X:$i]:
% 16.36/4.35 ( ( in @ X @ ( powerset @ A ) ) =>
% 16.36/4.35 ( in @ ( setminus @ A @ X ) @ ( powerset @ A ) ) ))).
% 16.36/4.35 thf('18', plain,
% 16.36/4.35 (( complementT_lem ) =
% 16.36/4.35 ( ![X4:$i,X6:$i]:
% 16.36/4.35 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 16.36/4.35 ( in @ ( setminus @ X4 @ X6 ) @ ( powerset @ X4 ) ) ) )),
% 16.36/4.35 define([status(thm)])).
% 16.36/4.35 thf(setminusT_lem, axiom, setminusT_lem =
% 16.36/4.35 (![A:$i,X:$i]:
% 16.36/4.35 ( ( in @ X @ ( powerset @ A ) ) =>
% 16.36/4.35 ( ![Y:$i]:
% 16.36/4.35 ( ( in @ Y @ ( powerset @ A ) ) =>
% 16.36/4.35 ( in @ ( setminus @ X @ Y ) @ ( powerset @ A ) ) ) ) ))).
% 16.36/4.35 thf('19', plain,
% 16.36/4.35 (( setminusT_lem ) =
% 16.36/4.35 ( ![X4:$i,X6:$i]:
% 16.36/4.35 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 16.36/4.35 ( ![X8:$i]:
% 16.36/4.35 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 16.36/4.35 ( in @ ( setminus @ X6 @ X8 ) @ ( powerset @ X4 ) ) ) ) ) )),
% 16.36/4.35 define([status(thm)])).
% 16.36/4.35 thf(powersetT_lem, axiom, powersetT_lem =
% 16.36/4.35 (![A:$i,X:$i]:
% 16.36/4.35 ( ( in @ X @ ( powerset @ A ) ) =>
% 16.36/4.35 ( in @ ( powerset @ X ) @ ( powerset @ ( powerset @ A ) ) ) ))).
% 16.36/4.35 thf('20', plain,
% 16.36/4.35 (( powersetT_lem ) =
% 16.36/4.35 ( ![X4:$i,X6:$i]:
% 16.36/4.35 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 16.36/4.35 ( in @ ( powerset @ X6 ) @ ( powerset @ ( powerset @ X4 ) ) ) ) )),
% 16.36/4.35 define([status(thm)])).
% 16.36/4.35 thf(binintersectT_lem, axiom, binintersectT_lem =
% 16.36/4.35 (![A:$i,X:$i]:
% 16.36/4.35 ( ( in @ X @ ( powerset @ A ) ) =>
% 16.36/4.35 ( ![Y:$i]:
% 16.36/4.35 ( ( in @ Y @ ( powerset @ A ) ) =>
% 16.36/4.35 ( in @ ( binintersect @ X @ Y ) @ ( powerset @ A ) ) ) ) ))).
% 16.36/4.35 thf('21', plain,
% 16.36/4.35 (( binintersectT_lem ) =
% 16.36/4.35 ( ![X4:$i,X6:$i]:
% 16.36/4.35 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 16.36/4.35 ( ![X8:$i]:
% 16.36/4.35 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 16.36/4.35 ( in @ ( binintersect @ X6 @ X8 ) @ ( powerset @ X4 ) ) ) ) ) )),
% 16.36/4.35 define([status(thm)])).
% 16.36/4.35 thf(singletoninpowerset, axiom, singletoninpowerset =
% 16.36/4.35 (![A:$i,Xx:$i]:
% 16.36/4.35 ( ( in @ Xx @ A ) =>
% 16.36/4.35 ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) ))).
% 16.36/4.35 thf('22', plain,
% 16.36/4.35 (( singletoninpowerset ) =
% 16.36/4.35 ( ![X4:$i,X6:$i]:
% 16.36/4.35 ( ( in @ X6 @ X4 ) =>
% 16.36/4.35 ( in @ ( setadjoin @ X6 @ emptyset ) @ ( powerset @ X4 ) ) ) )),
% 16.36/4.35 define([status(thm)])).
% 16.36/4.35 thf(setminusSubset1, axiom, setminusSubset1 =
% 16.36/4.35 (![A:$i,B:$i]:
% 16.36/4.35 ( ( ( setminus @ A @ B ) = ( emptyset ) ) => ( subset @ A @ B ) ))).
% 16.36/4.35 thf('23', plain,
% 16.36/4.35 (( setminusSubset1 ) =
% 16.36/4.35 ( ![X4:$i,X6:$i]:
% 16.36/4.35 ( ( ( setminus @ X4 @ X6 ) = ( emptyset ) ) => ( subset @ X4 @ X6 ) ) )),
% 16.36/4.35 define([status(thm)])).
% 16.36/4.35 thf(setminusLsub, axiom, setminusLsub =
% 16.36/4.35 (![A:$i,B:$i]: ( subset @ ( setminus @ A @ B ) @ A ))).
% 16.36/4.35 thf('24', plain,
% 16.36/4.35 (( setminusLsub ) =
% 16.36/4.35 ( ![X4:$i,X6:$i]: ( subset @ ( setminus @ X4 @ X6 ) @ X4 ) )),
% 16.36/4.35 define([status(thm)])).
% 16.36/4.35 thf(setminusIRneg, axiom, setminusIRneg =
% 16.36/4.35 (![A:$i,B:$i,Xx:$i]:
% 16.36/4.35 ( ( in @ Xx @ B ) => ( ~( in @ Xx @ ( setminus @ A @ B ) ) ) ))).
% 16.36/4.35 thf('25', plain,
% 16.36/4.35 (( setminusIRneg ) =
% 16.36/4.35 ( ![X4:$i,X6:$i,X8:$i]:
% 16.36/4.35 ( ( in @ X8 @ X6 ) => ( ~( in @ X8 @ ( setminus @ X4 @ X6 ) ) ) ) )),
% 16.36/4.35 define([status(thm)])).
% 16.36/4.35 thf(setminusILneg, axiom, setminusILneg =
% 16.36/4.35 (![A:$i,B:$i,Xx:$i]:
% 16.36/4.35 ( ( ~( in @ Xx @ A ) ) => ( ~( in @ Xx @ ( setminus @ A @ B ) ) ) ))).
% 16.36/4.35 thf('26', plain,
% 16.36/4.35 (( setminusILneg ) =
% 16.36/4.35 ( ![X4:$i,X6:$i,X8:$i]:
% 16.36/4.35 ( ( ~( in @ X8 @ X4 ) ) => ( ~( in @ X8 @ ( setminus @ X4 @ X6 ) ) ) ) )),
% 16.36/4.35 define([status(thm)])).
% 16.36/4.35 thf(setminusELneg, axiom, setminusELneg =
% 16.36/4.35 (![A:$i,B:$i,Xx:$i]:
% 16.36/4.35 ( ( ~( in @ Xx @ ( setminus @ A @ B ) ) ) =>
% 16.36/4.35 ( ( ~( in @ Xx @ B ) ) => ( ~( in @ Xx @ A ) ) ) ))).
% 16.36/4.35 thf('27', plain,
% 16.36/4.35 (( setminusELneg ) =
% 16.36/4.35 ( ![X4:$i,X6:$i,X8:$i]:
% 16.36/4.35 ( ( ~( in @ X8 @ ( setminus @ X4 @ X6 ) ) ) =>
% 16.36/4.35 ( ( ~( in @ X8 @ X6 ) ) => ( ~( in @ X8 @ X4 ) ) ) ) )),
% 16.36/4.35 define([status(thm)])).
% 16.36/4.35 thf(setminusERneg, axiom, setminusERneg =
% 16.36/4.35 (![A:$i,B:$i,Xx:$i]:
% 16.36/4.35 ( ( ~( in @ Xx @ ( setminus @ A @ B ) ) ) =>
% 16.36/4.35 ( ( in @ Xx @ A ) => ( in @ Xx @ B ) ) ))).
% 16.36/4.35 thf('28', plain,
% 16.36/4.35 (( setminusERneg ) =
% 16.36/4.35 ( ![X4:$i,X6:$i,X8:$i]:
% 16.36/4.35 ( ( ~( in @ X8 @ ( setminus @ X4 @ X6 ) ) ) =>
% 16.36/4.35 ( ( in @ X8 @ X4 ) => ( in @ X8 @ X6 ) ) ) )),
% 16.36/4.35 define([status(thm)])).
% 16.36/4.35 thf(setminusSubset2, axiom, setminusSubset2 =
% 16.36/4.35 (![A:$i,B:$i]:
% 16.36/4.35 ( ( subset @ A @ B ) => ( ( setminus @ A @ B ) = ( emptyset ) ) ))).
% 16.36/4.35 thf('29', plain,
% 16.36/4.35 (( setminusSubset2 ) =
% 16.36/4.35 ( ![X4:$i,X6:$i]:
% 16.36/4.35 ( ( subset @ X4 @ X6 ) => ( ( setminus @ X4 @ X6 ) = ( emptyset ) ) ) )),
% 16.36/4.35 define([status(thm)])).
% 16.36/4.35 thf(setminusER, axiom, setminusER =
% 16.36/4.35 (![A:$i,B:$i,Xx:$i]:
% 16.36/4.35 ( ( in @ Xx @ ( setminus @ A @ B ) ) => ( ~( in @ Xx @ B ) ) ))).
% 16.36/4.35 thf('30', plain,
% 16.36/4.35 (( setminusER ) =
% 16.36/4.35 ( ![X4:$i,X6:$i,X8:$i]:
% 16.36/4.35 ( ( in @ X8 @ ( setminus @ X4 @ X6 ) ) => ( ~( in @ X8 @ X6 ) ) ) )),
% 16.36/4.35 define([status(thm)])).
% 16.36/4.35 thf(setminusEL, axiom, setminusEL =
% 16.36/4.35 (![A:$i,B:$i,Xx:$i]:
% 16.36/4.35 ( ( in @ Xx @ ( setminus @ A @ B ) ) => ( in @ Xx @ A ) ))).
% 16.36/4.35 thf('31', plain,
% 16.36/4.35 (( setminusEL ) =
% 16.36/4.35 ( ![X4:$i,X6:$i,X8:$i]:
% 16.36/4.35 ( ( in @ X8 @ ( setminus @ X4 @ X6 ) ) => ( in @ X8 @ X4 ) ) )),
% 16.36/4.35 define([status(thm)])).
% 16.36/4.35 thf(setminusI, axiom, setminusI =
% 16.36/4.35 (![A:$i,B:$i,Xx:$i]:
% 16.36/4.35 ( ( in @ Xx @ A ) =>
% 16.36/4.35 ( ( ~( in @ Xx @ B ) ) => ( in @ Xx @ ( setminus @ A @ B ) ) ) ))).
% 16.36/4.35 thf('32', plain,
% 16.36/4.35 (( setminusI ) =
% 16.36/4.35 ( ![X4:$i,X6:$i,X8:$i]:
% 16.36/4.35 ( ( in @ X8 @ X4 ) =>
% 16.36/4.35 ( ( ~( in @ X8 @ X6 ) ) => ( in @ X8 @ ( setminus @ X4 @ X6 ) ) ) ) )),
% 16.36/4.35 define([status(thm)])).
% 16.36/4.35 thf(binintersectSubset1, axiom, binintersectSubset1 =
% 16.36/4.35 (![A:$i,B:$i]:
% 16.36/4.35 ( ( ( binintersect @ A @ B ) = ( A ) ) => ( subset @ A @ B ) ))).
% 16.36/4.35 thf('33', plain,
% 16.36/4.35 (( binintersectSubset1 ) =
% 16.36/4.35 ( ![X4:$i,X6:$i]:
% 16.36/4.35 ( ( ( binintersect @ X4 @ X6 ) = ( X4 ) ) => ( subset @ X4 @ X6 ) ) )),
% 16.36/4.35 define([status(thm)])).
% 16.36/4.35 thf(binintersectSubset4, axiom, binintersectSubset4 =
% 16.36/4.35 (![A:$i,B:$i]:
% 16.36/4.35 ( ( subset @ B @ A ) => ( ( binintersect @ A @ B ) = ( B ) ) ))).
% 16.36/4.35 thf('34', plain,
% 16.36/4.35 (( binintersectSubset4 ) =
% 16.36/4.35 ( ![X4:$i,X6:$i]:
% 16.36/4.35 ( ( subset @ X6 @ X4 ) => ( ( binintersect @ X4 @ X6 ) = ( X6 ) ) ) )),
% 16.36/4.35 define([status(thm)])).
% 16.36/4.35 thf(binintersectRsub, axiom, binintersectRsub =
% 16.36/4.35 (![A:$i,B:$i]: ( subset @ ( binintersect @ A @ B ) @ B ))).
% 16.36/4.35 thf('35', plain,
% 16.36/4.35 (( binintersectRsub ) =
% 16.36/4.35 ( ![X4:$i,X6:$i]: ( subset @ ( binintersect @ X4 @ X6 ) @ X6 ) )),
% 16.36/4.35 define([status(thm)])).
% 16.36/4.35 thf(disjointsetsI1, axiom, disjointsetsI1 =
% 16.36/4.35 (![A:$i,B:$i]:
% 16.36/4.35 ( ( ~( ?[Xx:$i]: ( ( in @ Xx @ B ) & ( in @ Xx @ A ) ) ) ) =>
% 16.36/4.35 ( ( binintersect @ A @ B ) = ( emptyset ) ) ))).
% 16.36/4.35 thf('36', plain,
% 16.36/4.35 (( disjointsetsI1 ) =
% 16.36/4.35 ( ![X4:$i,X6:$i]:
% 16.36/4.35 ( ( ~( ?[X8:$i]: ( ( in @ X8 @ X6 ) & ( in @ X8 @ X4 ) ) ) ) =>
% 16.36/4.35 ( ( binintersect @ X4 @ X6 ) = ( emptyset ) ) ) )),
% 16.36/4.35 define([status(thm)])).
% 16.36/4.35 thf(binintersectER, axiom, binintersectER =
% 16.36/4.35 (![A:$i,B:$i,Xx:$i]:
% 16.36/4.35 ( ( in @ Xx @ ( binintersect @ A @ B ) ) => ( in @ Xx @ B ) ))).
% 16.36/4.35 thf('37', plain,
% 16.36/4.35 (( binintersectER ) =
% 16.36/4.35 ( ![X4:$i,X6:$i,X8:$i]:
% 16.36/4.35 ( ( in @ X8 @ ( binintersect @ X4 @ X6 ) ) => ( in @ X8 @ X6 ) ) )),
% 16.36/4.35 define([status(thm)])).
% 16.36/4.35 thf(binintersectSubset3, axiom, binintersectSubset3 =
% 16.36/4.35 (![A:$i,B:$i]:
% 16.36/4.35 ( ( ( binintersect @ A @ B ) = ( B ) ) => ( subset @ B @ A ) ))).
% 16.36/4.35 thf('38', plain,
% 16.36/4.35 (( binintersectSubset3 ) =
% 16.36/4.35 ( ![X4:$i,X6:$i]:
% 16.36/4.35 ( ( ( binintersect @ X4 @ X6 ) = ( X6 ) ) => ( subset @ X6 @ X4 ) ) )),
% 16.36/4.35 define([status(thm)])).
% 16.36/4.35 thf(binintersectSubset2, axiom, binintersectSubset2 =
% 16.36/4.35 (![A:$i,B:$i]:
% 16.36/4.35 ( ( subset @ A @ B ) => ( ( binintersect @ A @ B ) = ( A ) ) ))).
% 16.36/4.35 thf('39', plain,
% 16.36/4.35 (( binintersectSubset2 ) =
% 16.36/4.35 ( ![X4:$i,X6:$i]:
% 16.36/4.35 ( ( subset @ X4 @ X6 ) => ( ( binintersect @ X4 @ X6 ) = ( X4 ) ) ) )),
% 16.36/4.35 define([status(thm)])).
% 16.36/4.35 thf(binintersectLsub, axiom, binintersectLsub =
% 16.36/4.35 (![A:$i,B:$i]: ( subset @ ( binintersect @ A @ B ) @ A ))).
% 16.36/4.35 thf('40', plain,
% 16.36/4.35 (( binintersectLsub ) =
% 16.36/4.35 ( ![X4:$i,X6:$i]: ( subset @ ( binintersect @ X4 @ X6 ) @ X4 ) )),
% 16.36/4.35 define([status(thm)])).
% 16.36/4.35 thf(binintersectEL, axiom, binintersectEL =
% 16.36/4.35 (![A:$i,B:$i,Xx:$i]:
% 16.36/4.35 ( ( in @ Xx @ ( binintersect @ A @ B ) ) => ( in @ Xx @ A ) ))).
% 16.36/4.35 thf('41', plain,
% 16.36/4.35 (( binintersectEL ) =
% 16.36/4.35 ( ![X4:$i,X6:$i,X8:$i]:
% 16.36/4.35 ( ( in @ X8 @ ( binintersect @ X4 @ X6 ) ) => ( in @ X8 @ X4 ) ) )),
% 16.36/4.35 define([status(thm)])).
% 16.36/4.35 thf(binintersectSubset5, axiom, binintersectSubset5 =
% 16.36/4.35 (![A:$i,B:$i,C:$i]:
% 16.36/4.35 ( ( subset @ C @ A ) =>
% 16.36/4.35 ( ( subset @ C @ B ) => ( subset @ C @ ( binintersect @ A @ B ) ) ) ))).
% 16.36/4.35 thf('42', plain,
% 16.36/4.35 (( binintersectSubset5 ) =
% 16.36/4.35 ( ![X4:$i,X6:$i,X8:$i]:
% 16.36/4.35 ( ( subset @ X8 @ X4 ) =>
% 16.36/4.35 ( ( subset @ X8 @ X6 ) =>
% 16.36/4.35 ( subset @ X8 @ ( binintersect @ X4 @ X6 ) ) ) ) )),
% 16.36/4.35 define([status(thm)])).
% 16.36/4.35 thf(binintersectI, axiom, binintersectI =
% 16.36/4.35 (![A:$i,B:$i,Xx:$i]:
% 16.36/4.35 ( ( in @ Xx @ A ) =>
% 16.36/4.35 ( ( in @ Xx @ B ) => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ))).
% 16.36/4.35 thf('43', plain,
% 16.36/4.35 (( binintersectI ) =
% 16.36/4.35 ( ![X4:$i,X6:$i,X8:$i]:
% 16.36/4.35 ( ( in @ X8 @ X4 ) =>
% 16.36/4.35 ( ( in @ X8 @ X6 ) => ( in @ X8 @ ( binintersect @ X4 @ X6 ) ) ) ) )),
% 16.36/4.35 define([status(thm)])).
% 16.36/4.35 thf(powersetsubset, axiom, powersetsubset =
% 16.36/4.35 (![A:$i,B:$i]:
% 16.36/4.35 ( ( subset @ A @ B ) => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ))).
% 16.36/4.35 thf('44', plain,
% 16.36/4.35 (( powersetsubset ) =
% 16.36/4.35 ( ![X4:$i,X6:$i]:
% 16.36/4.35 ( ( subset @ X4 @ X6 ) =>
% 16.36/4.35 ( subset @ ( powerset @ X4 ) @ ( powerset @ X6 ) ) ) )),
% 16.36/4.35 define([status(thm)])).
% 16.36/4.35 thf(inPowerset, axiom, inPowerset = (![A:$i]: ( in @ A @ ( powerset @ A ) ))).
% 16.36/4.35 thf('45', plain,
% 16.36/4.35 (( inPowerset ) = ( ![X4:$i]: ( in @ X4 @ ( powerset @ X4 ) ) )),
% 16.36/4.35 define([status(thm)])).
% 16.36/4.35 thf(powersetE1, axiom, powersetE1 =
% 16.36/4.35 (![A:$i,B:$i]: ( ( in @ B @ ( powerset @ A ) ) => ( subset @ B @ A ) ))).
% 16.36/4.35 thf('46', plain,
% 16.36/4.35 (( powersetE1 ) =
% 16.36/4.35 ( ![X4:$i,X6:$i]:
% 16.36/4.35 ( ( in @ X6 @ ( powerset @ X4 ) ) => ( subset @ X6 @ X4 ) ) )),
% 16.36/4.35 define([status(thm)])).
% 16.36/4.35 thf(powersetI1, axiom, powersetI1 =
% 16.36/4.35 (![A:$i,B:$i]: ( ( subset @ B @ A ) => ( in @ B @ ( powerset @ A ) ) ))).
% 16.36/4.35 thf('47', plain,
% 16.36/4.35 (( powersetI1 ) =
% 16.36/4.35 ( ![X4:$i,X6:$i]:
% 16.36/4.35 ( ( subset @ X6 @ X4 ) => ( in @ X6 @ ( powerset @ X4 ) ) ) )),
% 16.36/4.35 define([status(thm)])).
% 16.36/4.35 thf(subset2powerset, axiom, subset2powerset =
% 16.36/4.35 (![A:$i,B:$i]: ( ( subset @ A @ B ) => ( in @ A @ ( powerset @ B ) ) ))).
% 16.36/4.35 thf('48', plain,
% 16.36/4.35 (( subset2powerset ) =
% 16.36/4.35 ( ![X4:$i,X6:$i]:
% 16.36/4.35 ( ( subset @ X4 @ X6 ) => ( in @ X4 @ ( powerset @ X6 ) ) ) )),
% 16.36/4.35 define([status(thm)])).
% 16.36/4.35 thf(powerset__Cong, axiom, powerset__Cong =
% 16.36/4.35 (![A:$i,B:$i]:
% 16.36/4.35 ( ( ( A ) = ( B ) ) => ( ( powerset @ A ) = ( powerset @ B ) ) ))).
% 16.36/4.35 thf('49', plain,
% 16.36/4.35 (( powerset__Cong ) =
% 16.36/4.35 ( ![X4:$i,X6:$i]:
% 16.36/4.35 ( ( ( X4 ) = ( X6 ) ) => ( ( powerset @ X4 ) = ( powerset @ X6 ) ) ) )),
% 16.36/4.35 define([status(thm)])).
% 16.36/4.35 thf(powersetE, axiom, powersetE =
% 16.36/4.35 (![A:$i,B:$i,Xx:$i]:
% 16.36/4.35 ( ( in @ B @ ( powerset @ A ) ) => ( ( in @ Xx @ B ) => ( in @ Xx @ A ) ) ))).
% 16.36/4.35 thf('50', plain,
% 16.36/4.35 (( powersetE ) =
% 16.36/4.35 ( ![X4:$i,X6:$i,X8:$i]:
% 16.36/4.35 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 16.36/4.35 ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ) )),
% 16.36/4.35 define([status(thm)])).
% 16.36/4.35 thf(emptyInPowerset, axiom, emptyInPowerset =
% 16.36/4.35 (![A:$i]: ( in @ emptyset @ ( powerset @ A ) ))).
% 16.36/4.35 thf('51', plain,
% 16.36/4.35 (( emptyInPowerset ) =
% 16.36/4.35 ( ![X4:$i]: ( in @ emptyset @ ( powerset @ X4 ) ) )),
% 16.36/4.35 define([status(thm)])).
% 16.36/4.35 thf(emptyinPowerset, axiom, emptyinPowerset =
% 16.36/4.35 (![A:$i]: ( in @ emptyset @ ( powerset @ A ) ))).
% 16.36/4.35 thf('52', plain,
% 16.36/4.35 (( emptyinPowerset ) =
% 16.36/4.35 ( ![X4:$i]: ( in @ emptyset @ ( powerset @ X4 ) ) )),
% 16.36/4.35 define([status(thm)])).
% 16.36/4.35 thf(powersetI, axiom, powersetI =
% 16.36/4.35 (![A:$i,B:$i]:
% 16.36/4.35 ( ( ![Xx:$i]: ( ( in @ Xx @ B ) => ( in @ Xx @ A ) ) ) =>
% 16.36/4.35 ( in @ B @ ( powerset @ A ) ) ))).
% 16.36/4.35 thf('53', plain,
% 16.36/4.35 (( powersetI ) =
% 16.36/4.35 ( ![X4:$i,X6:$i]:
% 16.36/4.35 ( ( ![X8:$i]: ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ) =>
% 16.36/4.35 ( in @ X6 @ ( powerset @ X4 ) ) ) )),
% 16.36/4.35 define([status(thm)])).
% 16.36/4.35 thf(powersetAx, axiom, powersetAx =
% 16.36/4.35 (![A:$i,B:$i]:
% 16.36/4.35 ( ( in @ B @ ( powerset @ A ) ) <=>
% 16.36/4.35 ( ![Xx:$i]: ( ( in @ Xx @ B ) => ( in @ Xx @ A ) ) ) ))).
% 16.36/4.35 thf('54', plain,
% 16.36/4.35 (( powersetAx ) =
% 16.36/4.35 ( ![X4:$i,X6:$i]:
% 16.36/4.35 ( ( in @ X6 @ ( powerset @ X4 ) ) <=>
% 16.36/4.35 ( ![X8:$i]: ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ) ) )),
% 16.36/4.35 define([status(thm)])).
% 16.36/4.35 thf(complementImpComplementIntersect, conjecture,
% 16.36/4.35 (( setextAx ) =>
% 16.36/4.35 ( ( emptysetAx ) =>
% 16.36/4.35 ( ( setadjoinAx ) =>
% 16.36/4.35 ( ( powersetAx ) =>
% 16.36/4.35 ( ( setunionAx ) =>
% 16.36/4.35 ( ( omega0Ax ) =>
% 16.36/4.35 ( ( omegaSAx ) =>
% 16.36/4.35 ( ( omegaIndAx ) =>
% 16.36/4.35 ( ( replAx ) =>
% 16.36/4.35 ( ( foundationAx ) =>
% 16.36/4.35 ( ( wellorderingAx ) =>
% 16.36/4.35 ( ( descrp ) =>
% 16.36/4.35 ( ( dsetconstrI ) =>
% 16.36/4.35 ( ( dsetconstrEL ) =>
% 16.36/4.35 ( ( dsetconstrER ) =>
% 16.36/4.35 ( ( exuE1 ) =>
% 16.36/4.35 ( ( prop2setE ) =>
% 16.36/4.35 ( ( emptysetE ) =>
% 16.36/4.35 ( ( emptysetimpfalse ) =>
% 16.36/4.35 ( ( notinemptyset ) =>
% 16.36/4.35 ( ( exuE3e ) =>
% 16.36/4.35 ( ( setext ) =>
% 16.36/4.35 ( ( emptyI ) =>
% 16.36/4.35 ( ( noeltsimpempty ) =>
% 16.36/4.35 ( ( setbeta ) =>
% 16.36/4.35 ( ( nonemptyE1 ) =>
% 16.36/4.35 ( ( nonemptyI ) =>
% 16.36/4.35 ( ( nonemptyI1 ) =>
% 16.36/4.35 ( ( setadjoinIL ) =>
% 16.36/4.35 ( ( emptyinunitempty ) =>
% 16.36/4.35 ( ( setadjoinIR ) =>
% 16.36/4.35 ( ( setadjoinE ) =>
% 16.36/4.35 ( (
% 16.36/4.35 setadjoinOr ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 setoftrueEq ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 powersetI ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 emptyinPowerset ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 emptyInPowerset ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 powersetE ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 setunionI ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 setunionE ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 subPowSU ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 exuE2 ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 nonemptyImpWitness ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 uniqinunit ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 notinsingleton ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 eqinunit ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 singletonsswitch ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 upairsetE ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 upairsetIL ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 upairsetIR ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 emptyE1 ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 vacuousDall ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 quantDeMorgan1 ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 quantDeMorgan2 ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 quantDeMorgan3 ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 quantDeMorgan4 ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 prop2setI ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 prop2set2propI ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 notdexE ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 notdallE ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 exuI1 ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 exuI3 ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 exuI2 ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 inCongP ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 in__Cong ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 exuE3u ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 exu__Cong ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 emptyset__Cong ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 setadjoin__Cong ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 powerset__Cong ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 setunion__Cong ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 omega__Cong ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 exuEu ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 descr__Cong ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 dsetconstr__Cong ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 subsetI1 ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 eqimpsubset2 ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 eqimpsubset1 ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 subsetI2 ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 emptysetsubset ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 subsetE ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 subsetE2 ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 notsubsetI ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 notequalI1 ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 notequalI2 ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 subsetRefl ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 subsetTrans ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 setadjoinSub ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 setadjoinSub2 ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 subset2powerset ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 setextsub ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 subsetemptysetimpeq ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 powersetI1 ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 powersetE1 ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 inPowerset ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 powersetsubset ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 sepInPowerset ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 sepSubset ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 binunionIL ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 upairset2IR ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 binunionIR ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 binunionEcases ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 binunionE ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 binunionLsub ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 binunionRsub ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 binintersectI ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 binintersectSubset5 ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 binintersectEL ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 binintersectLsub ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 binintersectSubset2 ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 binintersectSubset3 ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 binintersectER ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 disjointsetsI1 ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 binintersectRsub ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 binintersectSubset4 ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 binintersectSubset1 ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 bs114d ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 setminusI ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 setminusEL ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 setminusER ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 setminusSubset2 ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 setminusERneg ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 setminusELneg ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 setminusILneg ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 setminusIRneg ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 setminusLsub ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 setminusSubset1 ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 symdiffE ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 symdiffI1 ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 symdiffI2 ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 symdiffIneg1 ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 symdiffIneg2 ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 secondinupair ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 setukpairIL ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 setukpairIR ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 kpairiskpair ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 kpairp ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 singletonsubset ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 singletoninpowerset ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 singletoninpowunion ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 upairset2E ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 upairsubunion ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 upairinpowunion ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 ubforcartprodlem1 ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 ubforcartprodlem2 ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 ubforcartprodlem3 ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 cartprodpairin ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 cartprodmempair1 ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 cartprodmempair ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 setunionE2 ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 setunionsingleton1 ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 setunionsingleton2 ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 setunionsingleton ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 singletonprop ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 ex1E1 ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 ex1I ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 ex1I2 ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 singletonsuniq ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 setukpairinjL1 ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 kfstsingleton ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 theprop ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 kfstpairEq ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 cartprodfstin ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 setukpairinjL2 ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 setukpairinjL ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 setukpairinjR11 ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 setukpairinjR12 ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 setukpairinjR1 ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 upairequniteq ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 setukpairinjR2 ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 setukpairinjR ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 ksndsingleton ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 ksndpairEq ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 kpairsurjEq ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 cartprodsndin ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 cartprodpairmemEL ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 cartprodpairmemER ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 cartprodmempaircEq ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 cartprodfstpairEq ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 cartprodsndpairEq ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 cartprodpairsurjEq ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 dpsetconstrI ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 dpsetconstrSub ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 setOfPairsIsBReln ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 dpsetconstrERa ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 dpsetconstrEL1 ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 dpsetconstrEL2 ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 dpsetconstrER ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 funcImageSingleton ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 apProp ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 app ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 infuncsetfunc ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 ap2p ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 funcinfuncset ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 lamProp ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 lamp ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 lam2p ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 brelnall1 ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 brelnall2 ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 ex1E2 ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 funcGraphProp1 ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 funcGraphProp3 ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 funcGraphProp2 ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 funcextLem ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 funcGraphProp4 ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 subbreln ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 eqbreln ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 funcext ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 funcext2 ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 ap2apEq1 ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 ap2apEq2 ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 beta1 ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 eta1 ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 lam2lamEq ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 beta2 ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 eta2 ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 iffalseProp1 ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 iffalseProp2 ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 iftrueProp1 ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 iftrueProp2 ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 ifSingleton ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 ifp ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 theeq ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 iftrue ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 iffalse ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 iftrueorfalse ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 binintersectT_lem ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 binunionT_lem ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 powersetT_lem ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 setminusT_lem ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 complementT_lem ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 setextT ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 subsetTI ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 powersetTI1 ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 powersetTE1 ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 complementTI1 ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 complementTE1 ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 binintersectTELcontra ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 binintersectTERcontra ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 contrasubsetT ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 contrasubsetT1 ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 contrasubsetT2 ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 contrasubsetT3 ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 doubleComplementI1 ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 doubleComplementE1 ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 doubleComplementSub1 ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 doubleComplementSub2 ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 doubleComplementEq ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 complementTnotintersectT ) =>
% 16.36/4.35 (
% 16.36/4.35 ![
% 16.36/4.35 A:$i,X:$i]:
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 in @
% 16.36/4.35 X @
% 16.36/4.35 (
% 16.36/4.35 powerset @
% 16.36/4.35 A ) ) =>
% 16.36/4.35 (
% 16.36/4.35 ![
% 16.36/4.35 Y:$i]:
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 in @
% 16.36/4.35 Y @
% 16.36/4.35 (
% 16.36/4.35 powerset @
% 16.36/4.35 A ) ) =>
% 16.36/4.35 (
% 16.36/4.35 ![
% 16.36/4.35 Xx:$i]:
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 in @
% 16.36/4.35 Xx @ A ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 in @
% 16.36/4.35 Xx @
% 16.36/4.35 (
% 16.36/4.35 setminus @
% 16.36/4.35 A @ X ) ) =>
% 16.36/4.35 (
% 16.36/4.35 in @
% 16.36/4.35 Xx @
% 16.36/4.35 (
% 16.36/4.35 setminus @
% 16.36/4.35 A @
% 16.36/4.35 (
% 16.36/4.35 binintersect
% 16.36/4.35 @
% 16.36/4.35 X @ Y ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 16.36/4.35 thf(zf_stmt_0, conjecture,
% 16.36/4.35 (( setextAx ) =>
% 16.36/4.35 ( ( emptysetAx ) =>
% 16.36/4.35 ( ( setadjoinAx ) =>
% 16.36/4.35 ( ( ![X4:$i,X6:$i]:
% 16.36/4.35 ( ( in @ X6 @ ( powerset @ X4 ) ) <=>
% 16.36/4.35 ( ![X8:$i]: ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ) ) ) =>
% 16.36/4.35 ( ( setunionAx ) =>
% 16.36/4.35 ( ( omega0Ax ) =>
% 16.36/4.35 ( ( omegaSAx ) =>
% 16.36/4.35 ( ( omegaIndAx ) =>
% 16.36/4.35 ( ( replAx ) =>
% 16.36/4.35 ( ( foundationAx ) =>
% 16.36/4.35 ( ( wellorderingAx ) =>
% 16.36/4.35 ( ( descrp ) =>
% 16.36/4.35 ( ( dsetconstrI ) =>
% 16.36/4.35 ( ( dsetconstrEL ) =>
% 16.36/4.35 ( ( dsetconstrER ) =>
% 16.36/4.35 ( ( exuE1 ) =>
% 16.36/4.35 ( ( prop2setE ) =>
% 16.36/4.35 ( ( emptysetE ) =>
% 16.36/4.35 ( ( emptysetimpfalse ) =>
% 16.36/4.35 ( ( notinemptyset ) =>
% 16.36/4.35 ( ( exuE3e ) =>
% 16.36/4.35 ( ( setext ) =>
% 16.36/4.35 ( ( emptyI ) =>
% 16.36/4.35 ( ( noeltsimpempty ) =>
% 16.36/4.35 ( ( setbeta ) =>
% 16.36/4.35 ( ( nonemptyE1 ) =>
% 16.36/4.35 ( ( nonemptyI ) =>
% 16.36/4.35 ( ( nonemptyI1 ) =>
% 16.36/4.35 ( ( setadjoinIL ) =>
% 16.36/4.35 ( ( emptyinunitempty ) =>
% 16.36/4.35 ( ( setadjoinIR ) =>
% 16.36/4.35 ( ( setadjoinE ) =>
% 16.36/4.35 ( (
% 16.36/4.35 setadjoinOr ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 setoftrueEq ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 ![
% 16.36/4.35 X10:$i,
% 16.36/4.35 X12:$i]:
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 ![
% 16.36/4.35 X14:$i]:
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 in @
% 16.36/4.35 X14 @ X12 ) =>
% 16.36/4.35 (
% 16.36/4.35 in @
% 16.36/4.35 X14 @ X10 ) ) ) =>
% 16.36/4.35 (
% 16.36/4.35 in @
% 16.36/4.35 X12 @
% 16.36/4.35 (
% 16.36/4.35 powerset @
% 16.36/4.35 X10 ) ) ) ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 ![
% 16.36/4.35 X16:$i]:
% 16.36/4.35 (
% 16.36/4.35 in @
% 16.36/4.35 emptyset @
% 16.36/4.35 (
% 16.36/4.35 powerset @
% 16.36/4.35 X16 ) ) ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 ![
% 16.36/4.35 X18:$i]:
% 16.36/4.35 (
% 16.36/4.35 in @
% 16.36/4.35 emptyset @
% 16.36/4.35 (
% 16.36/4.35 powerset @
% 16.36/4.35 X18 ) ) ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 ![
% 16.36/4.35 X20:$i,
% 16.36/4.35 X22:$i,
% 16.36/4.35 X24:$i]:
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 in @
% 16.36/4.35 X22 @
% 16.36/4.35 (
% 16.36/4.35 powerset @
% 16.36/4.35 X20 ) ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 in @
% 16.36/4.35 X24 @ X22 ) =>
% 16.36/4.35 (
% 16.36/4.35 in @
% 16.36/4.35 X24 @ X20 ) ) ) ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 setunionI ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 setunionE ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 subPowSU ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 exuE2 ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 nonemptyImpWitness ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 uniqinunit ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 notinsingleton ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 eqinunit ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 singletonsswitch ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 upairsetE ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 upairsetIL ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 upairsetIR ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 emptyE1 ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 vacuousDall ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 quantDeMorgan1 ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 quantDeMorgan2 ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 quantDeMorgan3 ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 quantDeMorgan4 ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 prop2setI ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 prop2set2propI ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 notdexE ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 notdallE ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 exuI1 ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 exuI3 ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 exuI2 ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 inCongP ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 in__Cong ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 exuE3u ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 exu__Cong ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 emptyset__Cong ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 setadjoin__Cong ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 ![
% 16.36/4.35 X26:$i,
% 16.36/4.35 X28:$i]:
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 X26 ) =
% 16.36/4.35 (
% 16.36/4.35 X28 ) ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 powerset @
% 16.36/4.35 X26 ) =
% 16.36/4.35 (
% 16.36/4.35 powerset @
% 16.36/4.35 X28 ) ) ) ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 setunion__Cong ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 omega__Cong ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 exuEu ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 descr__Cong ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 dsetconstr__Cong ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 subsetI1 ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 eqimpsubset2 ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 eqimpsubset1 ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 subsetI2 ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 emptysetsubset ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 subsetE ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 subsetE2 ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 notsubsetI ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 notequalI1 ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 notequalI2 ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 subsetRefl ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 subsetTrans ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 setadjoinSub ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 setadjoinSub2 ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 ![
% 16.36/4.35 X30:$i,
% 16.36/4.35 X32:$i]:
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 subset @
% 16.36/4.35 X30 @ X32 ) =>
% 16.36/4.35 (
% 16.36/4.35 in @
% 16.36/4.35 X30 @
% 16.36/4.35 (
% 16.36/4.35 powerset @
% 16.36/4.35 X32 ) ) ) ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 setextsub ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 subsetemptysetimpeq ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 ![
% 16.36/4.35 X34:$i,
% 16.36/4.35 X36:$i]:
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 subset @
% 16.36/4.35 X36 @ X34 ) =>
% 16.36/4.35 (
% 16.36/4.35 in @
% 16.36/4.35 X36 @
% 16.36/4.35 (
% 16.36/4.35 powerset @
% 16.36/4.35 X34 ) ) ) ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 ![
% 16.36/4.35 X38:$i,
% 16.36/4.35 X40:$i]:
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 in @
% 16.36/4.35 X40 @
% 16.36/4.35 (
% 16.36/4.35 powerset @
% 16.36/4.35 X38 ) ) =>
% 16.36/4.35 (
% 16.36/4.35 subset @
% 16.36/4.35 X40 @ X38 ) ) ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 ![
% 16.36/4.35 X42:$i]:
% 16.36/4.35 (
% 16.36/4.35 in @
% 16.36/4.35 X42 @
% 16.36/4.35 (
% 16.36/4.35 powerset @
% 16.36/4.35 X42 ) ) ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 ![
% 16.36/4.35 X44:$i,
% 16.36/4.35 X46:$i]:
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 subset @
% 16.36/4.35 X44 @ X46 ) =>
% 16.36/4.35 (
% 16.36/4.35 subset @
% 16.36/4.35 (
% 16.36/4.35 powerset @
% 16.36/4.35 X44 ) @
% 16.36/4.35 (
% 16.36/4.35 powerset @
% 16.36/4.35 X46 ) ) ) ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 sepInPowerset ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 sepSubset ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 binunionIL ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 upairset2IR ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 binunionIR ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 binunionEcases ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 binunionE ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 binunionLsub ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 binunionRsub ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 ![
% 16.36/4.35 X48:$i,
% 16.36/4.35 X50:$i,
% 16.36/4.35 X52:$i]:
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 in @
% 16.36/4.35 X52 @ X48 ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 in @
% 16.36/4.35 X52 @ X50 ) =>
% 16.36/4.35 (
% 16.36/4.35 in @
% 16.36/4.35 X52 @
% 16.36/4.35 (
% 16.36/4.35 binintersect
% 16.36/4.35 @
% 16.36/4.35 X48 @ X50 ) ) ) ) ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 ![
% 16.36/4.35 X54:$i,
% 16.36/4.35 X56:$i,
% 16.36/4.35 X58:$i]:
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 subset @
% 16.36/4.35 X58 @ X54 ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 subset @
% 16.36/4.35 X58 @ X56 ) =>
% 16.36/4.35 (
% 16.36/4.35 subset @
% 16.36/4.35 X58 @
% 16.36/4.35 (
% 16.36/4.35 binintersect
% 16.36/4.35 @
% 16.36/4.35 X54 @ X56 ) ) ) ) ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 ![
% 16.36/4.35 X60:$i,
% 16.36/4.35 X62:$i,
% 16.36/4.35 X64:$i]:
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 in @
% 16.36/4.35 X64 @
% 16.36/4.35 (
% 16.36/4.35 binintersect
% 16.36/4.35 @
% 16.36/4.35 X60 @ X62 ) ) =>
% 16.36/4.35 (
% 16.36/4.35 in @
% 16.36/4.35 X64 @ X60 ) ) ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 ![
% 16.36/4.35 X66:$i,
% 16.36/4.35 X68:$i]:
% 16.36/4.35 (
% 16.36/4.35 subset @
% 16.36/4.35 (
% 16.36/4.35 binintersect
% 16.36/4.35 @
% 16.36/4.35 X66 @ X68 ) @
% 16.36/4.35 X66 ) ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 ![
% 16.36/4.35 X70:$i,
% 16.36/4.35 X72:$i]:
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 subset @
% 16.36/4.35 X70 @ X72 ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 binintersect
% 16.36/4.35 @
% 16.36/4.35 X70 @ X72 ) =
% 16.36/4.35 (
% 16.36/4.35 X70 ) ) ) ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 ![
% 16.36/4.35 X74:$i,
% 16.36/4.35 X76:$i]:
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 binintersect
% 16.36/4.35 @
% 16.36/4.35 X74 @ X76 ) =
% 16.36/4.35 (
% 16.36/4.35 X76 ) ) =>
% 16.36/4.35 (
% 16.36/4.35 subset @
% 16.36/4.35 X76 @ X74 ) ) ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 ![
% 16.36/4.35 X78:$i,
% 16.36/4.35 X80:$i,
% 16.36/4.35 X82:$i]:
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 in @
% 16.36/4.35 X82 @
% 16.36/4.35 (
% 16.36/4.35 binintersect
% 16.36/4.35 @
% 16.36/4.35 X78 @ X80 ) ) =>
% 16.36/4.35 (
% 16.36/4.35 in @
% 16.36/4.35 X82 @ X80 ) ) ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 ![
% 16.36/4.35 X84:$i,
% 16.36/4.35 X86:$i]:
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 ~(
% 16.36/4.35 ?[
% 16.36/4.35 X88:$i]:
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 in @
% 16.36/4.35 X88 @ X84 ) &
% 16.36/4.35 (
% 16.36/4.35 in @
% 16.36/4.35 X88 @ X86 ) ) ) ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 binintersect
% 16.36/4.35 @
% 16.36/4.35 X84 @ X86 ) =
% 16.36/4.35 (
% 16.36/4.35 emptyset ) ) ) ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 ![
% 16.36/4.35 X90:$i,
% 16.36/4.35 X92:$i]:
% 16.36/4.35 (
% 16.36/4.35 subset @
% 16.36/4.35 (
% 16.36/4.35 binintersect
% 16.36/4.35 @
% 16.36/4.35 X90 @ X92 ) @
% 16.36/4.35 X92 ) ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 ![
% 16.36/4.35 X94:$i,
% 16.36/4.35 X96:$i]:
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 subset @
% 16.36/4.35 X96 @ X94 ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 binintersect
% 16.36/4.35 @
% 16.36/4.35 X94 @ X96 ) =
% 16.36/4.35 (
% 16.36/4.35 X96 ) ) ) ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 ![
% 16.36/4.35 X98:$i,
% 16.36/4.35 X100:$i]:
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 binintersect
% 16.36/4.35 @
% 16.36/4.35 X98 @ X100 ) =
% 16.36/4.35 (
% 16.36/4.35 X98 ) ) =>
% 16.36/4.35 (
% 16.36/4.35 subset @
% 16.36/4.35 X98 @ X100 ) ) ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 bs114d ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 ![
% 16.36/4.35 X102:$i,
% 16.36/4.35 X104:$i,
% 16.36/4.35 X106:$i]:
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 in @
% 16.36/4.35 X106 @
% 16.36/4.35 X102 ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 ~(
% 16.36/4.35 in @
% 16.36/4.35 X106 @
% 16.36/4.35 X104 ) ) =>
% 16.36/4.35 (
% 16.36/4.35 in @
% 16.36/4.35 X106 @
% 16.36/4.35 (
% 16.36/4.35 setminus @
% 16.36/4.35 X102 @
% 16.36/4.35 X104 ) ) ) ) ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 ![
% 16.36/4.35 X108:$i,
% 16.36/4.35 X110:$i,
% 16.36/4.35 X112:$i]:
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 in @
% 16.36/4.35 X112 @
% 16.36/4.35 (
% 16.36/4.35 setminus @
% 16.36/4.35 X108 @
% 16.36/4.35 X110 ) ) =>
% 16.36/4.35 (
% 16.36/4.35 in @
% 16.36/4.35 X112 @
% 16.36/4.35 X108 ) ) ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 ![
% 16.36/4.35 X114:$i,
% 16.36/4.35 X116:$i,
% 16.36/4.35 X118:$i]:
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 in @
% 16.36/4.35 X118 @
% 16.36/4.35 (
% 16.36/4.35 setminus @
% 16.36/4.35 X114 @
% 16.36/4.35 X116 ) ) =>
% 16.36/4.35 (
% 16.36/4.35 ~(
% 16.36/4.35 in @
% 16.36/4.35 X118 @
% 16.36/4.35 X116 ) ) ) ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 ![
% 16.36/4.35 X120:$i,
% 16.36/4.35 X122:$i]:
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 subset @
% 16.36/4.35 X120 @
% 16.36/4.35 X122 ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 setminus @
% 16.36/4.35 X120 @
% 16.36/4.35 X122 ) =
% 16.36/4.35 (
% 16.36/4.35 emptyset ) ) ) ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 ![
% 16.36/4.35 X124:$i,
% 16.36/4.35 X126:$i,
% 16.36/4.35 X128:$i]:
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 ~(
% 16.36/4.35 in @
% 16.36/4.35 X128 @
% 16.36/4.35 (
% 16.36/4.35 setminus
% 16.36/4.35 @
% 16.36/4.35 X124 @
% 16.36/4.35 X126 ) ) ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 in @
% 16.36/4.35 X128 @
% 16.36/4.35 X124 ) =>
% 16.36/4.35 (
% 16.36/4.35 in @
% 16.36/4.35 X128 @
% 16.36/4.35 X126 ) ) ) ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 ![
% 16.36/4.35 X130:$i,
% 16.36/4.35 X132:$i,
% 16.36/4.35 X134:$i]:
% 16.36/4.35 (
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% 16.36/4.35 ~(
% 16.36/4.35 in @
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% 16.36/4.35 X132 ) ) ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 ~(
% 16.36/4.35 in @
% 16.36/4.35 X134 @
% 16.36/4.35 X132 ) ) =>
% 16.36/4.35 (
% 16.36/4.35 ~(
% 16.36/4.35 in @
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% 16.36/4.35 X130 ) ) ) ) ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 ![
% 16.36/4.35 X136:$i,
% 16.36/4.35 X138:$i,
% 16.36/4.35 X140:$i]:
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% 16.36/4.35 (
% 16.36/4.35 ~(
% 16.36/4.35 in @
% 16.36/4.35 X140 @
% 16.36/4.35 X136 ) ) =>
% 16.36/4.35 (
% 16.36/4.35 ~(
% 16.36/4.35 in @
% 16.36/4.35 X140 @
% 16.36/4.35 (
% 16.36/4.35 setminus
% 16.36/4.35 @
% 16.36/4.35 X136 @
% 16.36/4.35 X138 ) ) ) ) ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 ![
% 16.36/4.35 X142:$i,
% 16.36/4.35 X144:$i,
% 16.36/4.35 X146:$i]:
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 in @
% 16.36/4.35 X146 @
% 16.36/4.35 X144 ) =>
% 16.36/4.35 (
% 16.36/4.35 ~(
% 16.36/4.35 in @
% 16.36/4.35 X146 @
% 16.36/4.35 (
% 16.36/4.35 setminus
% 16.36/4.35 @
% 16.36/4.35 X142 @
% 16.36/4.35 X144 ) ) ) ) ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 ![
% 16.36/4.35 X148:$i,
% 16.36/4.35 X150:$i]:
% 16.36/4.35 (
% 16.36/4.35 subset @
% 16.36/4.35 (
% 16.36/4.35 setminus @
% 16.36/4.35 X148 @
% 16.36/4.35 X150 ) @
% 16.36/4.35 X148 ) ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 ![
% 16.36/4.35 X152:$i,
% 16.36/4.35 X154:$i]:
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 setminus @
% 16.36/4.35 X152 @
% 16.36/4.35 X154 ) =
% 16.36/4.35 (
% 16.36/4.35 emptyset ) ) =>
% 16.36/4.35 (
% 16.36/4.35 subset @
% 16.36/4.35 X152 @
% 16.36/4.35 X154 ) ) ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 symdiffE ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 symdiffI1 ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 symdiffI2 ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 symdiffIneg1 ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 symdiffIneg2 ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 secondinupair ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 setukpairIL ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 setukpairIR ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 kpairiskpair ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 kpairp ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 singletonsubset ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 ![
% 16.36/4.35 X156:$i,
% 16.36/4.35 X158:$i]:
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 in @
% 16.36/4.35 X158 @
% 16.36/4.35 X156 ) =>
% 16.36/4.35 (
% 16.36/4.35 in @
% 16.36/4.35 (
% 16.36/4.35 setadjoin
% 16.36/4.35 @
% 16.36/4.35 X158 @
% 16.36/4.35 emptyset ) @
% 16.36/4.35 (
% 16.36/4.35 powerset @
% 16.36/4.35 X156 ) ) ) ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 singletoninpowunion ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 upairset2E ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 upairsubunion ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 upairinpowunion ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 ubforcartprodlem1 ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 ubforcartprodlem2 ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 ubforcartprodlem3 ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 cartprodpairin ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 cartprodmempair1 ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 cartprodmempair ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 setunionE2 ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 setunionsingleton1 ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 setunionsingleton2 ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 setunionsingleton ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 singletonprop ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 ex1E1 ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 ex1I ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 ex1I2 ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 singletonsuniq ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 setukpairinjL1 ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 kfstsingleton ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 theprop ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 kfstpairEq ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 cartprodfstin ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 setukpairinjL2 ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 setukpairinjL ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 setukpairinjR11 ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 setukpairinjR12 ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 setukpairinjR1 ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 upairequniteq ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 setukpairinjR2 ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 setukpairinjR ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 ksndsingleton ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 ksndpairEq ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 kpairsurjEq ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 cartprodsndin ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 cartprodpairmemEL ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 cartprodpairmemER ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 cartprodmempaircEq ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 cartprodfstpairEq ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 cartprodsndpairEq ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 cartprodpairsurjEq ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 dpsetconstrI ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 dpsetconstrSub ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 setOfPairsIsBReln ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 dpsetconstrERa ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 dpsetconstrEL1 ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 dpsetconstrEL2 ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 dpsetconstrER ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 funcImageSingleton ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 apProp ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 app ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 infuncsetfunc ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 ap2p ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 funcinfuncset ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 lamProp ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 lamp ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 lam2p ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 brelnall1 ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 brelnall2 ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 ex1E2 ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 funcGraphProp1 ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 funcGraphProp3 ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 funcGraphProp2 ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 funcextLem ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 funcGraphProp4 ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 subbreln ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 eqbreln ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 funcext ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 funcext2 ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 ap2apEq1 ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 ap2apEq2 ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 beta1 ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 eta1 ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 lam2lamEq ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 beta2 ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 eta2 ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 iffalseProp1 ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 iffalseProp2 ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 iftrueProp1 ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 iftrueProp2 ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 ifSingleton ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 ifp ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 theeq ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 iftrue ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 iffalse ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 iftrueorfalse ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 ![
% 16.36/4.35 X160:$i,
% 16.36/4.35 X162:$i]:
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 in @
% 16.36/4.35 X162 @
% 16.36/4.35 (
% 16.36/4.35 powerset @
% 16.36/4.35 X160 ) ) =>
% 16.36/4.35 (
% 16.36/4.35 ![
% 16.36/4.35 X164:$i]:
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 in @
% 16.36/4.35 X164 @
% 16.36/4.35 (
% 16.36/4.35 powerset @
% 16.36/4.35 X160 ) ) =>
% 16.36/4.35 (
% 16.36/4.35 in @
% 16.36/4.35 (
% 16.36/4.35 binintersect
% 16.36/4.35 @
% 16.36/4.35 X162 @
% 16.36/4.35 X164 ) @
% 16.36/4.35 (
% 16.36/4.35 powerset @
% 16.36/4.35 X160 ) ) ) ) ) ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 binunionT_lem ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 ![
% 16.36/4.35 X166:$i,
% 16.36/4.35 X168:$i]:
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 in @
% 16.36/4.35 X168 @
% 16.36/4.35 (
% 16.36/4.35 powerset @
% 16.36/4.35 X166 ) ) =>
% 16.36/4.35 (
% 16.36/4.35 in @
% 16.36/4.35 (
% 16.36/4.35 powerset @
% 16.36/4.35 X168 ) @
% 16.36/4.35 (
% 16.36/4.35 powerset @
% 16.36/4.35 (
% 16.36/4.35 powerset @
% 16.36/4.35 X166 ) ) ) ) ) =>
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 ![
% 16.36/4.35 X170:$i,
% 16.36/4.35 X172:$i]:
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 in @
% 16.36/4.35 X172 @
% 16.36/4.35 (
% 16.36/4.35 powerset @
% 16.36/4.35 X170 ) ) =>
% 16.36/4.35 (
% 16.36/4.35 ![
% 16.36/4.35 X174:$i]:
% 16.36/4.35 (
% 16.36/4.35 (
% 16.36/4.35 in @
% 16.36/4.35 X174 @
% 16.36/4.35 (
% 16.36/4.35 powerset @
% 16.36/4.35 X170 ) ) =>
% 16.36/4.35 (
% 16.36/4.35 in @
% 16.36/4.35 (
% 16.36/4.35 setminus @
% 16.36/4.35 X172 @
% 16.36/4.35 X174 ) @
% 16.36/4.35 (
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% 16.36/4.36 (
% 16.36/4.36 subset @
% 16.36/4.36 (
% 16.36/4.36 setminus @
% 16.36/4.36 X286 @
% 16.36/4.36 (
% 16.36/4.36 setminus @
% 16.36/4.36 X286 @
% 16.36/4.36 X288 ) ) @
% 16.36/4.36 X288 ) ) ) =>
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 ![
% 16.36/4.36 X290:$i,
% 16.36/4.36 X292:$i]:
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 in @
% 16.36/4.36 X292 @
% 16.36/4.36 (
% 16.36/4.36 powerset @
% 16.36/4.36 X290 ) ) =>
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 X292 ) =
% 16.36/4.36 (
% 16.36/4.36 setminus @
% 16.36/4.36 X290 @
% 16.36/4.36 (
% 16.36/4.36 setminus @
% 16.36/4.36 X290 @
% 16.36/4.36 X292 ) ) ) ) ) =>
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 ![
% 16.36/4.36 X294:$i,
% 16.36/4.36 X296:$i]:
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 in @
% 16.36/4.36 X296 @
% 16.36/4.36 (
% 16.36/4.36 powerset @
% 16.36/4.36 X294 ) ) =>
% 16.36/4.36 (
% 16.36/4.36 ![
% 16.36/4.36 X298:$i]:
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 in @
% 16.36/4.36 X298 @
% 16.36/4.36 (
% 16.36/4.36 powerset @
% 16.36/4.36 X294 ) ) =>
% 16.36/4.36 (
% 16.36/4.36 ![
% 16.36/4.36 X300:$i]:
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 in @
% 16.36/4.36 X300 @
% 16.36/4.36 X294 ) =>
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 in @
% 16.36/4.36 X300 @
% 16.36/4.36 (
% 16.36/4.36 setminus @
% 16.36/4.36 X294 @
% 16.36/4.36 X296 ) ) =>
% 16.36/4.36 (
% 16.36/4.36 ~(
% 16.36/4.36 in @
% 16.36/4.36 X300 @
% 16.36/4.36 (
% 16.36/4.36 binintersect
% 16.36/4.36 @
% 16.36/4.36 X296 @
% 16.36/4.36 X298 ) ) ) ) ) ) ) ) ) ) =>
% 16.36/4.36 (
% 16.36/4.36 ![
% 16.36/4.36 X302:$i,
% 16.36/4.36 X304:$i]:
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 in @
% 16.36/4.36 X304 @
% 16.36/4.36 (
% 16.36/4.36 powerset @
% 16.36/4.36 X302 ) ) =>
% 16.36/4.36 (
% 16.36/4.36 ![
% 16.36/4.36 X306:$i]:
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 in @
% 16.36/4.36 X306 @
% 16.36/4.36 (
% 16.36/4.36 powerset @
% 16.36/4.36 X302 ) ) =>
% 16.36/4.36 (
% 16.36/4.36 ![
% 16.36/4.36 X308:$i]:
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 in @
% 16.36/4.36 X308 @
% 16.36/4.36 X302 ) =>
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 in @
% 16.36/4.36 X308 @
% 16.36/4.36 (
% 16.36/4.36 setminus @
% 16.36/4.36 X302 @
% 16.36/4.36 X304 ) ) =>
% 16.36/4.36 (
% 16.36/4.36 in @
% 16.36/4.36 X308 @
% 16.36/4.36 (
% 16.36/4.36 setminus @
% 16.36/4.36 X302 @
% 16.36/4.36 (
% 16.36/4.36 binintersect
% 16.36/4.36 @
% 16.36/4.36 X304 @
% 16.36/4.36 X306 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 16.36/4.36 thf(zf_stmt_1, type, zip_tseitin_0 : $i > $i > $i > $o).
% 16.36/4.36 thf(zf_stmt_2, axiom,
% 16.36/4.36 (![X8:$i,X6:$i,X4:$i]:
% 16.36/4.36 ( ( zip_tseitin_0 @ X8 @ X6 @ X4 ) <=>
% 16.36/4.36 ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ))).
% 16.36/4.36 thf(zf_stmt_3, conjecture,
% 16.36/4.36 (( setextAx ) =>
% 16.36/4.36 ( ( emptysetAx ) =>
% 16.36/4.36 ( ( setadjoinAx ) =>
% 16.36/4.36 ( ( ![X4:$i,X6:$i]:
% 16.36/4.36 ( ( in @ X6 @ ( powerset @ X4 ) ) <=>
% 16.36/4.36 ( ![X8:$i]: ( zip_tseitin_0 @ X8 @ X6 @ X4 ) ) ) ) =>
% 16.36/4.36 ( ( setunionAx ) =>
% 16.36/4.36 ( ( omega0Ax ) =>
% 16.36/4.36 ( ( omegaSAx ) =>
% 16.36/4.36 ( ( omegaIndAx ) =>
% 16.36/4.36 ( ( replAx ) =>
% 16.36/4.36 ( ( foundationAx ) =>
% 16.36/4.36 ( ( wellorderingAx ) =>
% 16.36/4.36 ( ( descrp ) =>
% 16.36/4.36 ( ( dsetconstrI ) =>
% 16.36/4.36 ( ( dsetconstrEL ) =>
% 16.36/4.36 ( ( dsetconstrER ) =>
% 16.36/4.36 ( ( exuE1 ) =>
% 16.36/4.36 ( ( prop2setE ) =>
% 16.36/4.36 ( ( emptysetE ) =>
% 16.36/4.36 ( ( emptysetimpfalse ) =>
% 16.36/4.36 ( ( notinemptyset ) =>
% 16.36/4.36 ( ( exuE3e ) =>
% 16.36/4.36 ( ( setext ) =>
% 16.36/4.36 ( ( emptyI ) =>
% 16.36/4.36 ( ( noeltsimpempty ) =>
% 16.36/4.36 ( ( setbeta ) =>
% 16.36/4.36 ( ( nonemptyE1 ) =>
% 16.36/4.36 ( ( nonemptyI ) =>
% 16.36/4.36 ( ( nonemptyI1 ) =>
% 16.36/4.36 ( ( setadjoinIL ) =>
% 16.36/4.36 ( ( emptyinunitempty ) =>
% 16.36/4.36 ( ( setadjoinIR ) =>
% 16.36/4.36 ( ( setadjoinE ) =>
% 16.36/4.36 ( (
% 16.36/4.36 setadjoinOr ) =>
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 setoftrueEq ) =>
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 ![
% 16.36/4.36 X10:$i,
% 16.36/4.36 X12:$i]:
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 ![
% 16.36/4.36 X14:$i]:
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 in @
% 16.36/4.36 X14 @ X12 ) =>
% 16.36/4.36 (
% 16.36/4.36 in @
% 16.36/4.36 X14 @ X10 ) ) ) =>
% 16.36/4.36 (
% 16.36/4.36 in @
% 16.36/4.36 X12 @
% 16.36/4.36 (
% 16.36/4.36 powerset @
% 16.36/4.36 X10 ) ) ) ) =>
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 ![
% 16.36/4.36 X16:$i]:
% 16.36/4.36 (
% 16.36/4.36 in @
% 16.36/4.36 emptyset @
% 16.36/4.36 (
% 16.36/4.36 powerset @
% 16.36/4.36 X16 ) ) ) =>
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 ![
% 16.36/4.36 X18:$i]:
% 16.36/4.36 (
% 16.36/4.36 in @
% 16.36/4.36 emptyset @
% 16.36/4.36 (
% 16.36/4.36 powerset @
% 16.36/4.36 X18 ) ) ) =>
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 ![
% 16.36/4.36 X20:$i,
% 16.36/4.36 X22:$i,
% 16.36/4.36 X24:$i]:
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 in @
% 16.36/4.36 X22 @
% 16.36/4.36 (
% 16.36/4.36 powerset @
% 16.36/4.36 X20 ) ) =>
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 in @
% 16.36/4.36 X24 @ X22 ) =>
% 16.36/4.36 (
% 16.36/4.36 in @
% 16.36/4.36 X24 @ X20 ) ) ) ) =>
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 setunionI ) =>
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 setunionE ) =>
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 subPowSU ) =>
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 exuE2 ) =>
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 nonemptyImpWitness ) =>
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 uniqinunit ) =>
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 notinsingleton ) =>
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 eqinunit ) =>
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 singletonsswitch ) =>
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 upairsetE ) =>
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 upairsetIL ) =>
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 upairsetIR ) =>
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 emptyE1 ) =>
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 vacuousDall ) =>
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 quantDeMorgan1 ) =>
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 quantDeMorgan2 ) =>
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 quantDeMorgan3 ) =>
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 quantDeMorgan4 ) =>
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 prop2setI ) =>
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 prop2set2propI ) =>
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 notdexE ) =>
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 notdallE ) =>
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 exuI1 ) =>
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 exuI3 ) =>
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 exuI2 ) =>
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 inCongP ) =>
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 in__Cong ) =>
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 exuE3u ) =>
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 exu__Cong ) =>
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 emptyset__Cong ) =>
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 setadjoin__Cong ) =>
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 ![
% 16.36/4.36 X26:$i,
% 16.36/4.36 X28:$i]:
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 X26 ) =
% 16.36/4.36 (
% 16.36/4.36 X28 ) ) =>
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 powerset @
% 16.36/4.36 X26 ) =
% 16.36/4.36 (
% 16.36/4.36 powerset @
% 16.36/4.36 X28 ) ) ) ) =>
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 setunion__Cong ) =>
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 omega__Cong ) =>
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 exuEu ) =>
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 descr__Cong ) =>
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 dsetconstr__Cong ) =>
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 subsetI1 ) =>
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 eqimpsubset2 ) =>
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 eqimpsubset1 ) =>
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 subsetI2 ) =>
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 emptysetsubset ) =>
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 subsetE ) =>
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 subsetE2 ) =>
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 notsubsetI ) =>
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 notequalI1 ) =>
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 notequalI2 ) =>
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 subsetRefl ) =>
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 subsetTrans ) =>
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 setadjoinSub ) =>
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 setadjoinSub2 ) =>
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 ![
% 16.36/4.36 X30:$i,
% 16.36/4.36 X32:$i]:
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 subset @
% 16.36/4.36 X30 @ X32 ) =>
% 16.36/4.36 (
% 16.36/4.36 in @
% 16.36/4.36 X30 @
% 16.36/4.36 (
% 16.36/4.36 powerset @
% 16.36/4.36 X32 ) ) ) ) =>
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 setextsub ) =>
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 subsetemptysetimpeq ) =>
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 ![
% 16.36/4.36 X34:$i,
% 16.36/4.36 X36:$i]:
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 subset @
% 16.36/4.36 X36 @ X34 ) =>
% 16.36/4.36 (
% 16.36/4.36 in @
% 16.36/4.36 X36 @
% 16.36/4.36 (
% 16.36/4.36 powerset @
% 16.36/4.36 X34 ) ) ) ) =>
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 ![
% 16.36/4.36 X38:$i,
% 16.36/4.36 X40:$i]:
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 in @
% 16.36/4.36 X40 @
% 16.36/4.36 (
% 16.36/4.36 powerset @
% 16.36/4.36 X38 ) ) =>
% 16.36/4.36 (
% 16.36/4.36 subset @
% 16.36/4.36 X40 @ X38 ) ) ) =>
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 ![
% 16.36/4.36 X42:$i]:
% 16.36/4.36 (
% 16.36/4.36 in @
% 16.36/4.36 X42 @
% 16.36/4.36 (
% 16.36/4.36 powerset @
% 16.36/4.36 X42 ) ) ) =>
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 ![
% 16.36/4.36 X44:$i,
% 16.36/4.36 X46:$i]:
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 subset @
% 16.36/4.36 X44 @ X46 ) =>
% 16.36/4.36 (
% 16.36/4.36 subset @
% 16.36/4.36 (
% 16.36/4.36 powerset @
% 16.36/4.36 X44 ) @
% 16.36/4.36 (
% 16.36/4.36 powerset @
% 16.36/4.36 X46 ) ) ) ) =>
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 sepInPowerset ) =>
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 sepSubset ) =>
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 binunionIL ) =>
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 upairset2IR ) =>
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 binunionIR ) =>
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 binunionEcases ) =>
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 binunionE ) =>
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 binunionLsub ) =>
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 binunionRsub ) =>
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 ![
% 16.36/4.36 X48:$i,
% 16.36/4.36 X50:$i,
% 16.36/4.36 X52:$i]:
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 in @
% 16.36/4.36 X52 @ X48 ) =>
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 in @
% 16.36/4.36 X52 @ X50 ) =>
% 16.36/4.36 (
% 16.36/4.36 in @
% 16.36/4.36 X52 @
% 16.36/4.36 (
% 16.36/4.36 binintersect
% 16.36/4.36 @
% 16.36/4.36 X48 @ X50 ) ) ) ) ) =>
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 ![
% 16.36/4.36 X54:$i,
% 16.36/4.36 X56:$i,
% 16.36/4.36 X58:$i]:
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 subset @
% 16.36/4.36 X58 @ X54 ) =>
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 subset @
% 16.36/4.36 X58 @ X56 ) =>
% 16.36/4.36 (
% 16.36/4.36 subset @
% 16.36/4.36 X58 @
% 16.36/4.36 (
% 16.36/4.36 binintersect
% 16.36/4.36 @
% 16.36/4.36 X54 @ X56 ) ) ) ) ) =>
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 ![
% 16.36/4.36 X60:$i,
% 16.36/4.36 X62:$i,
% 16.36/4.36 X64:$i]:
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 in @
% 16.36/4.36 X64 @
% 16.36/4.36 (
% 16.36/4.36 binintersect
% 16.36/4.36 @
% 16.36/4.36 X60 @ X62 ) ) =>
% 16.36/4.36 (
% 16.36/4.36 in @
% 16.36/4.36 X64 @ X60 ) ) ) =>
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 ![
% 16.36/4.36 X66:$i,
% 16.36/4.36 X68:$i]:
% 16.36/4.36 (
% 16.36/4.36 subset @
% 16.36/4.36 (
% 16.36/4.36 binintersect
% 16.36/4.36 @
% 16.36/4.36 X66 @ X68 ) @
% 16.36/4.36 X66 ) ) =>
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 ![
% 16.36/4.36 X70:$i,
% 16.36/4.36 X72:$i]:
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 subset @
% 16.36/4.36 X70 @ X72 ) =>
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 binintersect
% 16.36/4.36 @
% 16.36/4.36 X70 @ X72 ) =
% 16.36/4.36 (
% 16.36/4.36 X70 ) ) ) ) =>
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 ![
% 16.36/4.36 X74:$i,
% 16.36/4.36 X76:$i]:
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 binintersect
% 16.36/4.36 @
% 16.36/4.36 X74 @ X76 ) =
% 16.36/4.36 (
% 16.36/4.36 X76 ) ) =>
% 16.36/4.36 (
% 16.36/4.36 subset @
% 16.36/4.36 X76 @ X74 ) ) ) =>
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 ![
% 16.36/4.36 X78:$i,
% 16.36/4.36 X80:$i,
% 16.36/4.36 X82:$i]:
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 in @
% 16.36/4.36 X82 @
% 16.36/4.36 (
% 16.36/4.36 binintersect
% 16.36/4.36 @
% 16.36/4.36 X78 @ X80 ) ) =>
% 16.36/4.36 (
% 16.36/4.36 in @
% 16.36/4.36 X82 @ X80 ) ) ) =>
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 ![
% 16.36/4.36 X84:$i,
% 16.36/4.36 X86:$i]:
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 ~(
% 16.36/4.36 ?[
% 16.36/4.36 X88:$i]:
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 in @
% 16.36/4.36 X88 @ X86 ) &
% 16.36/4.36 (
% 16.36/4.36 in @
% 16.36/4.36 X88 @ X84 ) ) ) ) =>
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 binintersect
% 16.36/4.36 @
% 16.36/4.36 X84 @ X86 ) =
% 16.36/4.36 (
% 16.36/4.36 emptyset ) ) ) ) =>
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 ![
% 16.36/4.36 X90:$i,
% 16.36/4.36 X92:$i]:
% 16.36/4.36 (
% 16.36/4.36 subset @
% 16.36/4.36 (
% 16.36/4.36 binintersect
% 16.36/4.36 @
% 16.36/4.36 X90 @ X92 ) @
% 16.36/4.36 X92 ) ) =>
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 ![
% 16.36/4.36 X94:$i,
% 16.36/4.36 X96:$i]:
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 subset @
% 16.36/4.36 X96 @ X94 ) =>
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 binintersect
% 16.36/4.36 @
% 16.36/4.36 X94 @ X96 ) =
% 16.36/4.36 (
% 16.36/4.36 X96 ) ) ) ) =>
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 ![
% 16.36/4.36 X98:$i,
% 16.36/4.36 X100:$i]:
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 binintersect
% 16.36/4.36 @
% 16.36/4.36 X98 @ X100 ) =
% 16.36/4.36 (
% 16.36/4.36 X98 ) ) =>
% 16.36/4.36 (
% 16.36/4.36 subset @
% 16.36/4.36 X98 @ X100 ) ) ) =>
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 bs114d ) =>
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 ![
% 16.36/4.36 X102:$i,
% 16.36/4.36 X104:$i,
% 16.36/4.36 X106:$i]:
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 in @
% 16.36/4.36 X106 @
% 16.36/4.36 X102 ) =>
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 ~(
% 16.36/4.36 in @
% 16.36/4.36 X106 @
% 16.36/4.36 X104 ) ) =>
% 16.36/4.36 (
% 16.36/4.36 in @
% 16.36/4.36 X106 @
% 16.36/4.36 (
% 16.36/4.36 setminus @
% 16.36/4.36 X102 @
% 16.36/4.36 X104 ) ) ) ) ) =>
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 ![
% 16.36/4.36 X108:$i,
% 16.36/4.36 X110:$i,
% 16.36/4.36 X112:$i]:
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 in @
% 16.36/4.36 X112 @
% 16.36/4.36 (
% 16.36/4.36 setminus @
% 16.36/4.36 X108 @
% 16.36/4.36 X110 ) ) =>
% 16.36/4.36 (
% 16.36/4.36 in @
% 16.36/4.36 X112 @
% 16.36/4.36 X108 ) ) ) =>
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 ![
% 16.36/4.36 X114:$i,
% 16.36/4.36 X116:$i,
% 16.36/4.36 X118:$i]:
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 in @
% 16.36/4.36 X118 @
% 16.36/4.36 (
% 16.36/4.36 setminus @
% 16.36/4.36 X114 @
% 16.36/4.36 X116 ) ) =>
% 16.36/4.36 (
% 16.36/4.36 ~(
% 16.36/4.36 in @
% 16.36/4.36 X118 @
% 16.36/4.36 X116 ) ) ) ) =>
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 ![
% 16.36/4.36 X120:$i,
% 16.36/4.36 X122:$i]:
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 subset @
% 16.36/4.36 X120 @
% 16.36/4.36 X122 ) =>
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 setminus @
% 16.36/4.36 X120 @
% 16.36/4.36 X122 ) =
% 16.36/4.36 (
% 16.36/4.36 emptyset ) ) ) ) =>
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 ![
% 16.36/4.36 X124:$i,
% 16.36/4.36 X126:$i,
% 16.36/4.36 X128:$i]:
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 ~(
% 16.36/4.36 in @
% 16.36/4.36 X128 @
% 16.36/4.36 (
% 16.36/4.36 setminus
% 16.36/4.36 @
% 16.36/4.36 X124 @
% 16.36/4.36 X126 ) ) ) =>
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 in @
% 16.36/4.36 X128 @
% 16.36/4.36 X124 ) =>
% 16.36/4.36 (
% 16.36/4.36 in @
% 16.36/4.36 X128 @
% 16.36/4.36 X126 ) ) ) ) =>
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 ![
% 16.36/4.36 X130:$i,
% 16.36/4.36 X132:$i,
% 16.36/4.36 X134:$i]:
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 ~(
% 16.36/4.36 in @
% 16.36/4.36 X134 @
% 16.36/4.36 (
% 16.36/4.36 setminus
% 16.36/4.36 @
% 16.36/4.36 X130 @
% 16.36/4.36 X132 ) ) ) =>
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 ~(
% 16.36/4.36 in @
% 16.36/4.36 X134 @
% 16.36/4.36 X132 ) ) =>
% 16.36/4.36 (
% 16.36/4.36 ~(
% 16.36/4.36 in @
% 16.36/4.36 X134 @
% 16.36/4.36 X130 ) ) ) ) ) =>
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 ![
% 16.36/4.36 X136:$i,
% 16.36/4.36 X138:$i,
% 16.36/4.36 X140:$i]:
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 ~(
% 16.36/4.36 in @
% 16.36/4.36 X140 @
% 16.36/4.36 X136 ) ) =>
% 16.36/4.36 (
% 16.36/4.36 ~(
% 16.36/4.36 in @
% 16.36/4.36 X140 @
% 16.36/4.36 (
% 16.36/4.36 setminus
% 16.36/4.36 @
% 16.36/4.36 X136 @
% 16.36/4.36 X138 ) ) ) ) ) =>
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 ![
% 16.36/4.36 X142:$i,
% 16.36/4.36 X144:$i,
% 16.36/4.36 X146:$i]:
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 in @
% 16.36/4.36 X146 @
% 16.36/4.36 X144 ) =>
% 16.36/4.36 (
% 16.36/4.36 ~(
% 16.36/4.36 in @
% 16.36/4.36 X146 @
% 16.36/4.36 (
% 16.36/4.36 setminus
% 16.36/4.36 @
% 16.36/4.36 X142 @
% 16.36/4.36 X144 ) ) ) ) ) =>
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 ![
% 16.36/4.36 X148:$i,
% 16.36/4.36 X150:$i]:
% 16.36/4.36 (
% 16.36/4.36 subset @
% 16.36/4.36 (
% 16.36/4.36 setminus @
% 16.36/4.36 X148 @
% 16.36/4.36 X150 ) @
% 16.36/4.36 X148 ) ) =>
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 ![
% 16.36/4.36 X152:$i,
% 16.36/4.36 X154:$i]:
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 setminus @
% 16.36/4.36 X152 @
% 16.36/4.36 X154 ) =
% 16.36/4.36 (
% 16.36/4.36 emptyset ) ) =>
% 16.36/4.36 (
% 16.36/4.36 subset @
% 16.36/4.36 X152 @
% 16.36/4.36 X154 ) ) ) =>
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 symdiffE ) =>
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 symdiffI1 ) =>
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 symdiffI2 ) =>
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 symdiffIneg1 ) =>
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 symdiffIneg2 ) =>
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 secondinupair ) =>
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 setukpairIL ) =>
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 setukpairIR ) =>
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 kpairiskpair ) =>
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 kpairp ) =>
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 singletonsubset ) =>
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 ![
% 16.36/4.36 X156:$i,
% 16.36/4.36 X158:$i]:
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 in @
% 16.36/4.36 X158 @
% 16.36/4.36 X156 ) =>
% 16.36/4.36 (
% 16.36/4.36 in @
% 16.36/4.36 (
% 16.36/4.36 setadjoin
% 16.36/4.36 @
% 16.36/4.36 X158 @
% 16.36/4.36 emptyset ) @
% 16.36/4.36 (
% 16.36/4.36 powerset @
% 16.36/4.36 X156 ) ) ) ) =>
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 singletoninpowunion ) =>
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 upairset2E ) =>
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 upairsubunion ) =>
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 upairinpowunion ) =>
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 ubforcartprodlem1 ) =>
% 16.36/4.36 (
% 16.36/4.36 (
% 16.36/4.36 ubforcartprodlem2 ) =>
% 16.36/4.37 (
% 16.36/4.37 (
% 16.36/4.37 ubforcartprodlem3 ) =>
% 16.36/4.37 (
% 16.36/4.37 (
% 16.36/4.37 cartprodpairin ) =>
% 16.36/4.37 (
% 16.36/4.37 (
% 16.36/4.37 cartprodmempair1 ) =>
% 16.36/4.37 (
% 16.36/4.37 (
% 16.36/4.37 cartprodmempair ) =>
% 16.36/4.37 (
% 16.36/4.37 (
% 16.36/4.37 setunionE2 ) =>
% 16.36/4.37 (
% 16.36/4.37 (
% 16.36/4.37 setunionsingleton1 ) =>
% 16.36/4.37 (
% 16.36/4.37 (
% 16.36/4.37 setunionsingleton2 ) =>
% 16.36/4.37 (
% 16.36/4.37 (
% 16.36/4.37 setunionsingleton ) =>
% 16.36/4.37 (
% 16.36/4.37 (
% 16.36/4.37 singletonprop ) =>
% 16.36/4.37 (
% 16.36/4.37 (
% 16.36/4.37 ex1E1 ) =>
% 16.36/4.37 (
% 16.36/4.37 (
% 16.36/4.37 ex1I ) =>
% 16.36/4.37 (
% 16.36/4.37 (
% 16.36/4.37 ex1I2 ) =>
% 16.36/4.37 (
% 16.36/4.37 (
% 16.36/4.37 singletonsuniq ) =>
% 16.36/4.37 (
% 16.36/4.37 (
% 16.36/4.37 setukpairinjL1 ) =>
% 16.36/4.37 (
% 16.36/4.37 (
% 16.36/4.37 kfstsingleton ) =>
% 16.36/4.37 (
% 16.36/4.37 (
% 16.36/4.37 theprop ) =>
% 16.36/4.37 (
% 16.36/4.37 (
% 16.36/4.37 kfstpairEq ) =>
% 16.36/4.37 (
% 16.36/4.37 (
% 16.36/4.37 cartprodfstin ) =>
% 16.36/4.37 (
% 16.36/4.37 (
% 16.36/4.37 setukpairinjL2 ) =>
% 16.36/4.37 (
% 16.36/4.37 (
% 16.36/4.37 setukpairinjL ) =>
% 16.36/4.37 (
% 16.36/4.37 (
% 16.36/4.37 setukpairinjR11 ) =>
% 16.36/4.37 (
% 16.36/4.37 (
% 16.36/4.37 setukpairinjR12 ) =>
% 16.36/4.37 (
% 16.36/4.37 (
% 16.36/4.37 setukpairinjR1 ) =>
% 16.36/4.37 (
% 16.36/4.37 (
% 16.36/4.37 upairequniteq ) =>
% 16.36/4.37 (
% 16.36/4.37 (
% 16.36/4.37 setukpairinjR2 ) =>
% 16.36/4.37 (
% 16.36/4.37 (
% 16.36/4.37 setukpairinjR ) =>
% 16.36/4.37 (
% 16.36/4.37 (
% 16.36/4.37 ksndsingleton ) =>
% 16.36/4.37 (
% 16.36/4.37 (
% 16.36/4.37 ksndpairEq ) =>
% 16.36/4.37 (
% 16.36/4.37 (
% 16.36/4.37 kpairsurjEq ) =>
% 16.36/4.37 (
% 16.36/4.37 (
% 16.36/4.37 cartprodsndin ) =>
% 16.36/4.37 (
% 16.36/4.37 (
% 16.36/4.37 cartprodpairmemEL ) =>
% 16.36/4.37 (
% 16.36/4.37 (
% 16.36/4.37 cartprodpairmemER ) =>
% 16.36/4.37 (
% 16.36/4.37 (
% 16.36/4.37 cartprodmempaircEq ) =>
% 16.36/4.37 (
% 16.36/4.37 (
% 16.36/4.37 cartprodfstpairEq ) =>
% 16.36/4.37 (
% 16.36/4.37 (
% 16.36/4.37 cartprodsndpairEq ) =>
% 16.36/4.37 (
% 16.36/4.37 (
% 16.36/4.37 cartprodpairsurjEq ) =>
% 16.36/4.37 (
% 16.36/4.37 (
% 16.36/4.37 dpsetconstrI ) =>
% 16.36/4.37 (
% 16.36/4.37 (
% 16.36/4.37 dpsetconstrSub ) =>
% 16.36/4.37 (
% 16.36/4.37 (
% 16.36/4.37 setOfPairsIsBReln ) =>
% 16.36/4.37 (
% 16.36/4.37 (
% 16.36/4.37 dpsetconstrERa ) =>
% 16.36/4.37 (
% 16.36/4.37 (
% 16.36/4.37 dpsetconstrEL1 ) =>
% 16.36/4.37 (
% 16.36/4.37 (
% 16.36/4.37 dpsetconstrEL2 ) =>
% 16.36/4.37 (
% 16.36/4.37 (
% 16.36/4.37 dpsetconstrER ) =>
% 16.36/4.37 (
% 16.36/4.37 (
% 16.36/4.37 funcImageSingleton ) =>
% 16.36/4.37 (
% 16.36/4.37 (
% 16.36/4.37 apProp ) =>
% 16.36/4.37 (
% 16.36/4.37 (
% 16.36/4.37 app ) =>
% 16.36/4.37 (
% 16.36/4.37 (
% 16.36/4.37 infuncsetfunc ) =>
% 16.36/4.37 (
% 16.36/4.37 (
% 16.36/4.37 ap2p ) =>
% 16.36/4.37 (
% 16.36/4.37 (
% 16.36/4.37 funcinfuncset ) =>
% 16.36/4.37 (
% 16.36/4.37 (
% 16.36/4.37 lamProp ) =>
% 16.36/4.37 (
% 16.36/4.37 (
% 16.36/4.37 lamp ) =>
% 16.36/4.37 (
% 16.36/4.37 (
% 16.36/4.37 lam2p ) =>
% 16.36/4.37 (
% 16.36/4.37 (
% 16.36/4.37 brelnall1 ) =>
% 16.36/4.37 (
% 16.36/4.37 (
% 16.36/4.37 brelnall2 ) =>
% 16.36/4.37 (
% 16.36/4.37 (
% 16.36/4.37 ex1E2 ) =>
% 16.36/4.37 (
% 16.36/4.37 (
% 16.36/4.37 funcGraphProp1 ) =>
% 16.36/4.37 (
% 16.36/4.37 (
% 16.36/4.37 funcGraphProp3 ) =>
% 16.36/4.37 (
% 16.36/4.37 (
% 16.36/4.37 funcGraphProp2 ) =>
% 16.36/4.37 (
% 16.36/4.37 (
% 16.36/4.37 funcextLem ) =>
% 16.36/4.37 (
% 16.36/4.37 (
% 16.36/4.37 funcGraphProp4 ) =>
% 16.36/4.37 (
% 16.36/4.37 (
% 16.36/4.37 subbreln ) =>
% 16.36/4.37 (
% 16.36/4.37 (
% 16.36/4.37 eqbreln ) =>
% 16.36/4.37 (
% 16.36/4.37 (
% 16.36/4.37 funcext ) =>
% 16.36/4.37 (
% 16.36/4.37 (
% 16.36/4.37 funcext2 ) =>
% 16.36/4.37 (
% 16.36/4.37 (
% 16.36/4.37 ap2apEq1 ) =>
% 16.36/4.37 (
% 16.36/4.37 (
% 16.36/4.37 ap2apEq2 ) =>
% 16.36/4.37 (
% 16.36/4.37 (
% 16.36/4.37 beta1 ) =>
% 16.36/4.37 (
% 16.36/4.37 (
% 16.36/4.37 eta1 ) =>
% 16.36/4.37 (
% 16.36/4.37 (
% 16.36/4.37 lam2lamEq ) =>
% 16.36/4.37 (
% 16.36/4.37 (
% 16.36/4.37 beta2 ) =>
% 16.36/4.37 (
% 16.36/4.37 (
% 16.36/4.37 eta2 ) =>
% 16.36/4.37 (
% 16.36/4.37 (
% 16.36/4.37 iffalseProp1 ) =>
% 16.36/4.37 (
% 16.36/4.37 (
% 16.36/4.37 iffalseProp2 ) =>
% 16.36/4.37 (
% 16.36/4.37 (
% 16.36/4.37 iftrueProp1 ) =>
% 16.36/4.37 (
% 16.36/4.37 (
% 16.36/4.37 iftrueProp2 ) =>
% 16.36/4.37 (
% 16.36/4.37 (
% 16.36/4.37 ifSingleton ) =>
% 16.36/4.37 (
% 16.36/4.37 (
% 16.36/4.37 ifp ) =>
% 16.36/4.37 (
% 16.36/4.37 (
% 16.36/4.37 theeq ) =>
% 16.36/4.37 (
% 16.36/4.37 (
% 16.36/4.37 iftrue ) =>
% 16.36/4.37 (
% 16.36/4.37 (
% 16.36/4.37 iffalse ) =>
% 16.36/4.37 (
% 16.36/4.37 (
% 16.36/4.37 iftrueorfalse ) =>
% 16.36/4.37 (
% 16.36/4.37 (
% 16.36/4.37 ![
% 16.36/4.37 X160:$i,
% 16.36/4.37 X162:$i]:
% 16.36/4.37 (
% 16.36/4.37 (
% 16.36/4.37 in @
% 16.36/4.37 X162 @
% 16.36/4.37 (
% 16.36/4.37 powerset @
% 16.36/4.37 X160 ) ) =>
% 16.36/4.37 (
% 16.36/4.37 ![
% 16.36/4.37 X164:$i]:
% 16.36/4.37 (
% 16.36/4.37 (
% 16.36/4.37 in @
% 16.36/4.37 X164 @
% 16.36/4.37 (
% 16.36/4.37 powerset @
% 16.36/4.37 X160 ) ) =>
% 16.36/4.37 (
% 16.36/4.37 in @
% 16.36/4.37 (
% 16.36/4.37 binintersect
% 16.36/4.37 @
% 16.36/4.37 X162 @
% 16.36/4.37 X164 ) @
% 16.36/4.37 (
% 16.36/4.37 powerset @
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% 16.36/4.37 ![
% 16.36/4.37 X280:$i]:
% 16.36/4.37 (
% 16.36/4.37 (
% 16.36/4.37 in @
% 16.36/4.37 X280 @
% 16.36/4.37 X276 ) =>
% 16.36/4.37 (
% 16.36/4.37 (
% 16.36/4.37 in @
% 16.36/4.37 X280 @
% 16.36/4.37 (
% 16.36/4.37 setminus @
% 16.36/4.37 X276 @
% 16.36/4.37 (
% 16.36/4.37 setminus @
% 16.36/4.37 X276 @
% 16.36/4.37 X278 ) ) ) =>
% 16.36/4.37 (
% 16.36/4.37 in @
% 16.36/4.37 X280 @
% 16.36/4.37 X278 ) ) ) ) ) ) =>
% 16.36/4.37 (
% 16.36/4.37 (
% 16.36/4.37 ![
% 16.36/4.37 X282:$i,
% 16.36/4.37 X284:$i]:
% 16.36/4.37 (
% 16.36/4.37 (
% 16.36/4.37 in @
% 16.36/4.37 X284 @
% 16.36/4.37 (
% 16.36/4.37 powerset @
% 16.36/4.37 X282 ) ) =>
% 16.36/4.37 (
% 16.36/4.37 subset @
% 16.36/4.37 X284 @
% 16.36/4.37 (
% 16.36/4.37 setminus @
% 16.36/4.37 X282 @
% 16.36/4.37 (
% 16.36/4.37 setminus @
% 16.36/4.37 X282 @
% 16.36/4.37 X284 ) ) ) ) ) =>
% 16.36/4.37 (
% 16.36/4.37 (
% 16.36/4.37 ![
% 16.36/4.37 X286:$i,
% 16.36/4.37 X288:$i]:
% 16.36/4.37 (
% 16.36/4.37 (
% 16.36/4.37 in @
% 16.36/4.37 X288 @
% 16.36/4.37 (
% 16.36/4.37 powerset @
% 16.36/4.37 X286 ) ) =>
% 16.36/4.37 (
% 16.36/4.37 subset @
% 16.36/4.37 (
% 16.36/4.37 setminus @
% 16.36/4.37 X286 @
% 16.36/4.37 (
% 16.36/4.37 setminus @
% 16.36/4.37 X286 @
% 16.36/4.37 X288 ) ) @
% 16.36/4.37 X288 ) ) ) =>
% 16.36/4.37 (
% 16.36/4.37 (
% 16.36/4.37 ![
% 16.36/4.37 X290:$i,
% 16.36/4.37 X292:$i]:
% 16.36/4.37 (
% 16.36/4.37 (
% 16.36/4.37 in @
% 16.36/4.37 X292 @
% 16.36/4.37 (
% 16.36/4.37 powerset @
% 16.36/4.37 X290 ) ) =>
% 16.36/4.37 (
% 16.36/4.37 (
% 16.36/4.37 X292 ) =
% 16.36/4.37 (
% 16.36/4.37 setminus @
% 16.36/4.37 X290 @
% 16.36/4.37 (
% 16.36/4.37 setminus @
% 16.36/4.37 X290 @
% 16.36/4.37 X292 ) ) ) ) ) =>
% 16.36/4.37 (
% 16.36/4.37 (
% 16.36/4.37 ![
% 16.36/4.37 X294:$i,
% 16.36/4.37 X296:$i]:
% 16.36/4.37 (
% 16.36/4.37 (
% 16.36/4.37 in @
% 16.36/4.37 X296 @
% 16.36/4.37 (
% 16.36/4.37 powerset @
% 16.36/4.37 X294 ) ) =>
% 16.36/4.37 (
% 16.36/4.37 ![
% 16.36/4.37 X298:$i]:
% 16.36/4.37 (
% 16.36/4.37 (
% 16.36/4.37 in @
% 16.36/4.37 X298 @
% 16.36/4.37 (
% 16.36/4.37 powerset @
% 16.36/4.37 X294 ) ) =>
% 16.36/4.37 (
% 16.36/4.37 ![
% 16.36/4.37 X300:$i]:
% 16.36/4.37 (
% 16.36/4.37 (
% 16.36/4.37 in @
% 16.36/4.37 X300 @
% 16.36/4.37 X294 ) =>
% 16.36/4.37 (
% 16.36/4.37 (
% 16.36/4.37 in @
% 16.36/4.37 X300 @
% 16.36/4.37 (
% 16.36/4.37 setminus @
% 16.36/4.37 X294 @
% 16.36/4.37 X296 ) ) =>
% 16.36/4.37 (
% 16.36/4.37 ~(
% 16.36/4.37 in @
% 16.36/4.37 X300 @
% 16.36/4.37 (
% 16.36/4.37 binintersect
% 16.36/4.37 @
% 16.36/4.37 X296 @
% 16.36/4.37 X298 ) ) ) ) ) ) ) ) ) ) =>
% 16.36/4.37 (
% 16.36/4.37 ![
% 16.36/4.37 X302:$i,
% 16.36/4.37 X304:$i]:
% 16.36/4.37 (
% 16.36/4.37 (
% 16.36/4.37 in @
% 16.36/4.37 X304 @
% 16.36/4.37 (
% 16.36/4.37 powerset @
% 16.36/4.37 X302 ) ) =>
% 16.36/4.37 (
% 16.36/4.37 ![
% 16.36/4.37 X306:$i]:
% 16.36/4.37 (
% 16.36/4.37 (
% 16.36/4.37 in @
% 16.36/4.37 X306 @
% 16.36/4.37 (
% 16.36/4.37 powerset @
% 16.36/4.37 X302 ) ) =>
% 16.36/4.37 (
% 16.36/4.37 ![
% 16.36/4.37 X308:$i]:
% 16.36/4.37 (
% 16.36/4.37 (
% 16.36/4.37 in @
% 16.36/4.37 X308 @
% 16.36/4.37 X302 ) =>
% 16.36/4.37 (
% 16.36/4.37 (
% 16.36/4.37 in @
% 16.36/4.37 X308 @
% 16.36/4.37 (
% 16.36/4.37 setminus @
% 16.36/4.37 X302 @
% 16.36/4.37 X304 ) ) =>
% 16.36/4.37 (
% 16.36/4.37 in @
% 16.36/4.37 X308 @
% 16.36/4.37 (
% 16.36/4.37 setminus @
% 16.36/4.37 X302 @
% 16.36/4.37 (
% 16.36/4.37 binintersect
% 16.36/4.37 @
% 16.36/4.37 X304 @
% 16.36/4.37 X306 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 16.36/4.37 thf(zf_stmt_4, negated_conjecture,
% 16.36/4.37 (~( ( setextAx ) =>
% 16.36/4.37 ( ( emptysetAx ) =>
% 16.36/4.37 ( ( setadjoinAx ) =>
% 16.36/4.37 ( ( ![X4:$i,X6:$i]:
% 16.36/4.37 ( ( in @ X6 @ ( powerset @ X4 ) ) <=>
% 16.36/4.37 ( ![X8:$i]: ( zip_tseitin_0 @ X8 @ X6 @ X4 ) ) ) ) =>
% 16.36/4.37 ( ( setunionAx ) =>
% 16.36/4.37 ( ( omega0Ax ) =>
% 16.36/4.37 ( ( omegaSAx ) =>
% 16.36/4.37 ( ( omegaIndAx ) =>
% 16.36/4.37 ( ( replAx ) =>
% 16.36/4.37 ( ( foundationAx ) =>
% 16.36/4.37 ( ( wellorderingAx ) =>
% 16.36/4.37 ( ( descrp ) =>
% 16.36/4.37 ( ( dsetconstrI ) =>
% 16.36/4.37 ( ( dsetconstrEL ) =>
% 16.36/4.37 ( ( dsetconstrER ) =>
% 16.36/4.37 ( ( exuE1 ) =>
% 16.36/4.37 ( ( prop2setE ) =>
% 16.36/4.37 ( ( emptysetE ) =>
% 16.36/4.37 ( ( emptysetimpfalse ) =>
% 16.36/4.37 ( ( notinemptyset ) =>
% 16.36/4.37 ( ( exuE3e ) =>
% 16.36/4.37 ( ( setext ) =>
% 16.36/4.37 ( ( emptyI ) =>
% 16.36/4.37 ( ( noeltsimpempty ) =>
% 16.36/4.37 ( ( setbeta ) =>
% 16.36/4.37 ( ( nonemptyE1 ) =>
% 16.36/4.37 ( ( nonemptyI ) =>
% 16.36/4.37 ( ( nonemptyI1 ) =>
% 16.36/4.37 ( ( setadjoinIL ) =>
% 16.36/4.37 ( ( emptyinunitempty ) =>
% 16.36/4.37 ( ( setadjoinIR ) =>
% 16.36/4.37 ( (
% 16.36/4.37 setadjoinE ) =>
% 16.36/4.37 (
% 16.36/4.37 (
% 16.36/4.37 setadjoinOr ) =>
% 16.36/4.37 (
% 16.36/4.37 (
% 16.36/4.37 setoftrueEq ) =>
% 16.36/4.37 (
% 16.36/4.37 (
% 16.36/4.37 ![
% 16.36/4.37 X10:$i,
% 16.36/4.37 X12:$i]:
% 16.36/4.37 (
% 16.36/4.37 (
% 16.36/4.37 ![
% 16.36/4.37 X14:$i]:
% 16.36/4.37 (
% 16.36/4.37 (
% 16.36/4.37 in @
% 16.36/4.37 X14 @ X12 ) =>
% 16.36/4.37 (
% 16.36/4.37 in @
% 16.36/4.37 X14 @ X10 ) ) ) =>
% 16.36/4.37 (
% 16.36/4.37 in @
% 16.36/4.37 X12 @
% 16.36/4.37 (
% 16.36/4.37 powerset
% 16.36/4.37 @
% 16.36/4.37 X10 ) ) ) ) =>
% 16.36/4.37 (
% 16.36/4.37 (
% 16.36/4.37 ![
% 16.36/4.37 X16:$i]:
% 16.36/4.37 (
% 16.36/4.37 in @
% 16.36/4.37 emptyset @
% 16.36/4.37 (
% 16.36/4.37 powerset
% 16.36/4.37 @
% 16.36/4.37 X16 ) ) ) =>
% 16.36/4.37 (
% 16.36/4.37 (
% 16.36/4.37 ![
% 16.36/4.37 X18:$i]:
% 16.36/4.37 (
% 16.36/4.37 in @
% 16.36/4.37 emptyset @
% 16.36/4.37 (
% 16.36/4.37 powerset
% 16.36/4.37 @
% 16.36/4.37 X18 ) ) ) =>
% 16.36/4.37 (
% 16.36/4.37 (
% 16.36/4.37 ![
% 16.36/4.37 X20:$i,
% 16.36/4.37 X22:$i,
% 16.36/4.37 X24:$i]:
% 16.36/4.37 (
% 16.36/4.37 (
% 16.36/4.37 in @
% 16.36/4.37 X22 @
% 16.36/4.37 (
% 16.36/4.37 powerset
% 16.36/4.37 @
% 16.36/4.37 X20 ) ) =>
% 16.36/4.37 (
% 16.36/4.37 (
% 16.36/4.37 in @
% 16.36/4.37 X24 @ X22 ) =>
% 16.36/4.37 (
% 16.36/4.37 in @
% 16.36/4.37 X24 @ X20 ) ) ) ) =>
% 16.36/4.37 (
% 16.36/4.37 (
% 16.36/4.37 setunionI ) =>
% 16.36/4.37 (
% 16.36/4.37 (
% 16.36/4.37 setunionE ) =>
% 16.36/4.37 (
% 16.36/4.37 (
% 16.36/4.37 subPowSU ) =>
% 16.36/4.37 (
% 16.36/4.37 (
% 16.36/4.37 exuE2 ) =>
% 16.36/4.37 (
% 16.36/4.37 (
% 16.36/4.37 nonemptyImpWitness ) =>
% 16.36/4.37 (
% 16.36/4.37 (
% 16.36/4.37 uniqinunit ) =>
% 16.36/4.37 (
% 16.36/4.37 (
% 16.36/4.38 notinsingleton ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 eqinunit ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 singletonsswitch ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 upairsetE ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 upairsetIL ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 upairsetIR ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 emptyE1 ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 vacuousDall ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 quantDeMorgan1 ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 quantDeMorgan2 ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 quantDeMorgan3 ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 quantDeMorgan4 ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 prop2setI ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 prop2set2propI ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 notdexE ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 notdallE ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 exuI1 ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 exuI3 ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 exuI2 ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 inCongP ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 in__Cong ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 exuE3u ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 exu__Cong ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 emptyset__Cong ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 setadjoin__Cong ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 ![
% 16.36/4.38 X26:$i,
% 16.36/4.38 X28:$i]:
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 X26 ) =
% 16.36/4.38 (
% 16.36/4.38 X28 ) ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 powerset
% 16.36/4.38 @
% 16.36/4.38 X26 ) =
% 16.36/4.38 (
% 16.36/4.38 powerset
% 16.36/4.38 @
% 16.36/4.38 X28 ) ) ) ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 setunion__Cong ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 omega__Cong ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 exuEu ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 descr__Cong ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 dsetconstr__Cong ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 subsetI1 ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 eqimpsubset2 ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 eqimpsubset1 ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 subsetI2 ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 emptysetsubset ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 subsetE ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 subsetE2 ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 notsubsetI ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 notequalI1 ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 notequalI2 ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 subsetRefl ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 subsetTrans ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 setadjoinSub ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 setadjoinSub2 ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 ![
% 16.36/4.38 X30:$i,
% 16.36/4.38 X32:$i]:
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 subset @
% 16.36/4.38 X30 @ X32 ) =>
% 16.36/4.38 (
% 16.36/4.38 in @
% 16.36/4.38 X30 @
% 16.36/4.38 (
% 16.36/4.38 powerset
% 16.36/4.38 @
% 16.36/4.38 X32 ) ) ) ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 setextsub ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 subsetemptysetimpeq ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 ![
% 16.36/4.38 X34:$i,
% 16.36/4.38 X36:$i]:
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 subset @
% 16.36/4.38 X36 @ X34 ) =>
% 16.36/4.38 (
% 16.36/4.38 in @
% 16.36/4.38 X36 @
% 16.36/4.38 (
% 16.36/4.38 powerset
% 16.36/4.38 @
% 16.36/4.38 X34 ) ) ) ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 ![
% 16.36/4.38 X38:$i,
% 16.36/4.38 X40:$i]:
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 in @
% 16.36/4.38 X40 @
% 16.36/4.38 (
% 16.36/4.38 powerset
% 16.36/4.38 @
% 16.36/4.38 X38 ) ) =>
% 16.36/4.38 (
% 16.36/4.38 subset @
% 16.36/4.38 X40 @ X38 ) ) ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 ![
% 16.36/4.38 X42:$i]:
% 16.36/4.38 (
% 16.36/4.38 in @
% 16.36/4.38 X42 @
% 16.36/4.38 (
% 16.36/4.38 powerset
% 16.36/4.38 @
% 16.36/4.38 X42 ) ) ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 ![
% 16.36/4.38 X44:$i,
% 16.36/4.38 X46:$i]:
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 subset @
% 16.36/4.38 X44 @ X46 ) =>
% 16.36/4.38 (
% 16.36/4.38 subset @
% 16.36/4.38 (
% 16.36/4.38 powerset
% 16.36/4.38 @
% 16.36/4.38 X44 ) @
% 16.36/4.38 (
% 16.36/4.38 powerset
% 16.36/4.38 @
% 16.36/4.38 X46 ) ) ) ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 sepInPowerset ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 sepSubset ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 binunionIL ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 upairset2IR ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 binunionIR ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 binunionEcases ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 binunionE ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 binunionLsub ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 binunionRsub ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 ![
% 16.36/4.38 X48:$i,
% 16.36/4.38 X50:$i,
% 16.36/4.38 X52:$i]:
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 in @
% 16.36/4.38 X52 @ X48 ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 in @
% 16.36/4.38 X52 @ X50 ) =>
% 16.36/4.38 (
% 16.36/4.38 in @
% 16.36/4.38 X52 @
% 16.36/4.38 (
% 16.36/4.38 binintersect
% 16.36/4.38 @
% 16.36/4.38 X48 @ X50 ) ) ) ) ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 ![
% 16.36/4.38 X54:$i,
% 16.36/4.38 X56:$i,
% 16.36/4.38 X58:$i]:
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 subset @
% 16.36/4.38 X58 @ X54 ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 subset @
% 16.36/4.38 X58 @ X56 ) =>
% 16.36/4.38 (
% 16.36/4.38 subset @
% 16.36/4.38 X58 @
% 16.36/4.38 (
% 16.36/4.38 binintersect
% 16.36/4.38 @
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% 16.36/4.38 (
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% 16.36/4.38 in @
% 16.36/4.38 X64 @
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% 16.36/4.38 X66 ) ) =>
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% 16.36/4.38 X72:$i]:
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% 16.36/4.38 (
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% 16.36/4.38 X76:$i]:
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% 16.36/4.38 in @
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% 16.36/4.38 X78 @ X80 ) ) =>
% 16.36/4.38 (
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% 16.36/4.38 (
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% 16.36/4.38 X88:$i]:
% 16.36/4.38 (
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% 16.36/4.38 X88 @ X86 ) &
% 16.36/4.38 (
% 16.36/4.38 in @
% 16.36/4.38 X88 @ X84 ) ) ) ) =>
% 16.36/4.38 (
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% 16.36/4.38 (
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% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 ![
% 16.36/4.38 X90:$i,
% 16.36/4.38 X92:$i]:
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% 16.36/4.38 X90 @ X92 ) @
% 16.36/4.38 X92 ) ) =>
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% 16.36/4.38 X96:$i]:
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% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 ![
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% 16.36/4.38 X100:$i]:
% 16.36/4.38 (
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% 16.36/4.38 X98 @
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% 16.36/4.38 (
% 16.36/4.38 X98 ) ) =>
% 16.36/4.38 (
% 16.36/4.38 subset @
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% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 bs114d ) =>
% 16.36/4.38 (
% 16.36/4.38 (
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% 16.36/4.38 X102:$i,
% 16.36/4.38 X104:$i,
% 16.36/4.38 X106:$i]:
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 in @
% 16.36/4.38 X106 @
% 16.36/4.38 X102 ) =>
% 16.36/4.38 (
% 16.36/4.38 (
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% 16.36/4.38 X104 ) ) =>
% 16.36/4.38 (
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% 16.36/4.38 (
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% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 ![
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% 16.36/4.38 X110:$i,
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% 16.36/4.38 (
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% 16.36/4.38 in @
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% 16.36/4.38 (
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% 16.36/4.38 (
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% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 ![
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% 16.36/4.38 X116:$i,
% 16.36/4.38 X118:$i]:
% 16.36/4.38 (
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% 16.36/4.38 in @
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% 16.36/4.38 (
% 16.36/4.38 setminus
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% 16.36/4.38 X116 ) ) =>
% 16.36/4.38 (
% 16.36/4.38 ~
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% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 ![
% 16.36/4.38 X120:$i,
% 16.36/4.38 X122:$i]:
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 subset @
% 16.36/4.38 X120 @
% 16.36/4.38 X122 ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 setminus
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% 16.36/4.38 X122 ) =
% 16.36/4.38 (
% 16.36/4.38 emptyset ) ) ) ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 ![
% 16.36/4.38 X124:$i,
% 16.36/4.38 X126:$i,
% 16.36/4.38 X128:$i]:
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% 16.36/4.38 ~
% 16.36/4.38 (
% 16.36/4.38 in @
% 16.36/4.38 X128 @
% 16.36/4.38 (
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% 16.36/4.38 X124 @
% 16.36/4.38 X126 ) ) ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 in @
% 16.36/4.38 X128 @
% 16.36/4.38 X124 ) =>
% 16.36/4.38 (
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% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 ![
% 16.36/4.38 X130:$i,
% 16.36/4.38 X132:$i,
% 16.36/4.38 X134:$i]:
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 ~
% 16.36/4.38 (
% 16.36/4.38 in @
% 16.36/4.38 X134 @
% 16.36/4.38 (
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% 16.36/4.38 X132 ) ) ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 ~
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% 16.36/4.38 X134 @
% 16.36/4.38 X132 ) ) =>
% 16.36/4.38 (
% 16.36/4.38 ~
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% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 ![
% 16.36/4.38 X136:$i,
% 16.36/4.38 X138:$i,
% 16.36/4.38 X140:$i]:
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 ~
% 16.36/4.38 (
% 16.36/4.38 in @
% 16.36/4.38 X140 @
% 16.36/4.38 X136 ) ) =>
% 16.36/4.38 (
% 16.36/4.38 ~
% 16.36/4.38 (
% 16.36/4.38 in @
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% 16.36/4.38 (
% 16.36/4.38 setminus
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% 16.36/4.38 X136 @
% 16.36/4.38 X138 ) ) ) ) ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 ![
% 16.36/4.38 X142:$i,
% 16.36/4.38 X144:$i,
% 16.36/4.38 X146:$i]:
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 in @
% 16.36/4.38 X146 @
% 16.36/4.38 X144 ) =>
% 16.36/4.38 (
% 16.36/4.38 ~
% 16.36/4.38 (
% 16.36/4.38 in @
% 16.36/4.38 X146 @
% 16.36/4.38 (
% 16.36/4.38 setminus
% 16.36/4.38 @
% 16.36/4.38 X142 @
% 16.36/4.38 X144 ) ) ) ) ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 ![
% 16.36/4.38 X148:$i,
% 16.36/4.38 X150:$i]:
% 16.36/4.38 (
% 16.36/4.38 subset @
% 16.36/4.38 (
% 16.36/4.38 setminus
% 16.36/4.38 @
% 16.36/4.38 X148 @
% 16.36/4.38 X150 ) @
% 16.36/4.38 X148 ) ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 ![
% 16.36/4.38 X152:$i,
% 16.36/4.38 X154:$i]:
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 setminus
% 16.36/4.38 @
% 16.36/4.38 X152 @
% 16.36/4.38 X154 ) =
% 16.36/4.38 (
% 16.36/4.38 emptyset ) ) =>
% 16.36/4.38 (
% 16.36/4.38 subset @
% 16.36/4.38 X152 @
% 16.36/4.38 X154 ) ) ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 symdiffE ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 symdiffI1 ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 symdiffI2 ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 symdiffIneg1 ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 symdiffIneg2 ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 secondinupair ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 setukpairIL ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 setukpairIR ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 kpairiskpair ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 kpairp ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 singletonsubset ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 ![
% 16.36/4.38 X156:$i,
% 16.36/4.38 X158:$i]:
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 in @
% 16.36/4.38 X158 @
% 16.36/4.38 X156 ) =>
% 16.36/4.38 (
% 16.36/4.38 in @
% 16.36/4.38 (
% 16.36/4.38 setadjoin
% 16.36/4.38 @
% 16.36/4.38 X158 @
% 16.36/4.38 emptyset ) @
% 16.36/4.38 (
% 16.36/4.38 powerset
% 16.36/4.38 @
% 16.36/4.38 X156 ) ) ) ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 singletoninpowunion ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 upairset2E ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 upairsubunion ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 upairinpowunion ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 ubforcartprodlem1 ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 ubforcartprodlem2 ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 ubforcartprodlem3 ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 cartprodpairin ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 cartprodmempair1 ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 cartprodmempair ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 setunionE2 ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 setunionsingleton1 ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 setunionsingleton2 ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 setunionsingleton ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 singletonprop ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 ex1E1 ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 ex1I ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 ex1I2 ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 singletonsuniq ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 setukpairinjL1 ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 kfstsingleton ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 theprop ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 kfstpairEq ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 cartprodfstin ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 setukpairinjL2 ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 setukpairinjL ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 setukpairinjR11 ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 setukpairinjR12 ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 setukpairinjR1 ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 upairequniteq ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 setukpairinjR2 ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 setukpairinjR ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 ksndsingleton ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 ksndpairEq ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 kpairsurjEq ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 cartprodsndin ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 cartprodpairmemEL ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 cartprodpairmemER ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 cartprodmempaircEq ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 cartprodfstpairEq ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 cartprodsndpairEq ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 cartprodpairsurjEq ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 dpsetconstrI ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 dpsetconstrSub ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 setOfPairsIsBReln ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 dpsetconstrERa ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 dpsetconstrEL1 ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 dpsetconstrEL2 ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 dpsetconstrER ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 funcImageSingleton ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 apProp ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 app ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 infuncsetfunc ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 ap2p ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 funcinfuncset ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 lamProp ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 lamp ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 lam2p ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 brelnall1 ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 brelnall2 ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 ex1E2 ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 funcGraphProp1 ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 funcGraphProp3 ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 funcGraphProp2 ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 funcextLem ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 funcGraphProp4 ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 subbreln ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 eqbreln ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 funcext ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 funcext2 ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 ap2apEq1 ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 ap2apEq2 ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 beta1 ) =>
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% 16.36/4.38 (
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% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 in @
% 16.36/4.38 X262 @
% 16.36/4.38 (
% 16.36/4.38 powerset
% 16.36/4.38 @
% 16.36/4.38 X258 ) ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 subset @
% 16.36/4.38 X260 @
% 16.36/4.38 X262 ) =>
% 16.36/4.38 (
% 16.36/4.38 subset @
% 16.36/4.38 (
% 16.36/4.38 setminus
% 16.36/4.38 @
% 16.36/4.38 X258 @
% 16.36/4.38 X262 ) @
% 16.36/4.38 (
% 16.36/4.38 setminus
% 16.36/4.38 @
% 16.36/4.38 X258 @
% 16.36/4.38 X260 ) ) ) ) ) ) ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 ![
% 16.36/4.38 X264:$i,
% 16.36/4.38 X266:$i]:
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 in @
% 16.36/4.38 X266 @
% 16.36/4.38 (
% 16.36/4.38 powerset
% 16.36/4.38 @
% 16.36/4.38 X264 ) ) =>
% 16.36/4.38 (
% 16.36/4.38 ![
% 16.36/4.38 X268:$i]:
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 in @
% 16.36/4.38 X268 @
% 16.36/4.38 (
% 16.36/4.38 powerset
% 16.36/4.38 @
% 16.36/4.38 X264 ) ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 subset @
% 16.36/4.38 (
% 16.36/4.38 setminus
% 16.36/4.38 @
% 16.36/4.38 X264 @
% 16.36/4.38 X268 ) @
% 16.36/4.38 (
% 16.36/4.38 setminus
% 16.36/4.38 @
% 16.36/4.38 X264 @
% 16.36/4.38 X266 ) ) =>
% 16.36/4.38 (
% 16.36/4.38 subset @
% 16.36/4.38 X266 @
% 16.36/4.38 X268 ) ) ) ) ) ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 ![
% 16.36/4.38 X270:$i,
% 16.36/4.38 X272:$i]:
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 in @
% 16.36/4.38 X272 @
% 16.36/4.38 (
% 16.36/4.38 powerset
% 16.36/4.38 @
% 16.36/4.38 X270 ) ) =>
% 16.36/4.38 (
% 16.36/4.38 ![
% 16.36/4.38 X274:$i]:
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 in @
% 16.36/4.38 X274 @
% 16.36/4.38 X270 ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 in @
% 16.36/4.38 X274 @
% 16.36/4.38 X272 ) =>
% 16.36/4.38 (
% 16.36/4.38 in @
% 16.36/4.38 X274 @
% 16.36/4.38 (
% 16.36/4.38 setminus
% 16.36/4.38 @
% 16.36/4.38 X270 @
% 16.36/4.38 (
% 16.36/4.38 setminus
% 16.36/4.38 @
% 16.36/4.38 X270 @
% 16.36/4.38 X272 ) ) ) ) ) ) ) ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 ![
% 16.36/4.38 X276:$i,
% 16.36/4.38 X278:$i]:
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 in @
% 16.36/4.38 X278 @
% 16.36/4.38 (
% 16.36/4.38 powerset
% 16.36/4.38 @
% 16.36/4.38 X276 ) ) =>
% 16.36/4.38 (
% 16.36/4.38 ![
% 16.36/4.38 X280:$i]:
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 in @
% 16.36/4.38 X280 @
% 16.36/4.38 X276 ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 in @
% 16.36/4.38 X280 @
% 16.36/4.38 (
% 16.36/4.38 setminus
% 16.36/4.38 @
% 16.36/4.38 X276 @
% 16.36/4.38 (
% 16.36/4.38 setminus
% 16.36/4.38 @
% 16.36/4.38 X276 @
% 16.36/4.38 X278 ) ) ) =>
% 16.36/4.38 (
% 16.36/4.38 in @
% 16.36/4.38 X280 @
% 16.36/4.38 X278 ) ) ) ) ) ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 ![
% 16.36/4.38 X282:$i,
% 16.36/4.38 X284:$i]:
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 in @
% 16.36/4.38 X284 @
% 16.36/4.38 (
% 16.36/4.38 powerset
% 16.36/4.38 @
% 16.36/4.38 X282 ) ) =>
% 16.36/4.38 (
% 16.36/4.38 subset @
% 16.36/4.38 X284 @
% 16.36/4.38 (
% 16.36/4.38 setminus
% 16.36/4.38 @
% 16.36/4.38 X282 @
% 16.36/4.38 (
% 16.36/4.38 setminus
% 16.36/4.38 @
% 16.36/4.38 X282 @
% 16.36/4.38 X284 ) ) ) ) ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 ![
% 16.36/4.38 X286:$i,
% 16.36/4.38 X288:$i]:
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 in @
% 16.36/4.38 X288 @
% 16.36/4.38 (
% 16.36/4.38 powerset
% 16.36/4.38 @
% 16.36/4.38 X286 ) ) =>
% 16.36/4.38 (
% 16.36/4.38 subset @
% 16.36/4.38 (
% 16.36/4.38 setminus
% 16.36/4.38 @
% 16.36/4.38 X286 @
% 16.36/4.38 (
% 16.36/4.38 setminus
% 16.36/4.38 @
% 16.36/4.38 X286 @
% 16.36/4.38 X288 ) ) @
% 16.36/4.38 X288 ) ) ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 ![
% 16.36/4.38 X290:$i,
% 16.36/4.38 X292:$i]:
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 in @
% 16.36/4.38 X292 @
% 16.36/4.38 (
% 16.36/4.38 powerset
% 16.36/4.38 @
% 16.36/4.38 X290 ) ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 X292 ) =
% 16.36/4.38 (
% 16.36/4.38 setminus
% 16.36/4.38 @
% 16.36/4.38 X290 @
% 16.36/4.38 (
% 16.36/4.38 setminus
% 16.36/4.38 @
% 16.36/4.38 X290 @
% 16.36/4.38 X292 ) ) ) ) ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 ![
% 16.36/4.38 X294:$i,
% 16.36/4.38 X296:$i]:
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 in @
% 16.36/4.38 X296 @
% 16.36/4.38 (
% 16.36/4.38 powerset
% 16.36/4.38 @
% 16.36/4.38 X294 ) ) =>
% 16.36/4.38 (
% 16.36/4.38 ![
% 16.36/4.38 X298:$i]:
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 in @
% 16.36/4.38 X298 @
% 16.36/4.38 (
% 16.36/4.38 powerset
% 16.36/4.38 @
% 16.36/4.38 X294 ) ) =>
% 16.36/4.38 (
% 16.36/4.38 ![
% 16.36/4.38 X300:$i]:
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 in @
% 16.36/4.38 X300 @
% 16.36/4.38 X294 ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 in @
% 16.36/4.38 X300 @
% 16.36/4.38 (
% 16.36/4.38 setminus
% 16.36/4.38 @
% 16.36/4.38 X294 @
% 16.36/4.38 X296 ) ) =>
% 16.36/4.38 (
% 16.36/4.38 ~
% 16.36/4.38 (
% 16.36/4.38 in @
% 16.36/4.38 X300 @
% 16.36/4.38 (
% 16.36/4.38 binintersect
% 16.36/4.38 @
% 16.36/4.38 X296 @
% 16.36/4.38 X298 ) ) ) ) ) ) ) ) ) ) =>
% 16.36/4.38 (
% 16.36/4.38 ![
% 16.36/4.38 X302:$i,
% 16.36/4.38 X304:$i]:
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 in @
% 16.36/4.38 X304 @
% 16.36/4.38 (
% 16.36/4.38 powerset
% 16.36/4.38 @
% 16.36/4.38 X302 ) ) =>
% 16.36/4.38 (
% 16.36/4.38 ![
% 16.36/4.38 X306:$i]:
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 in @
% 16.36/4.38 X306 @
% 16.36/4.38 (
% 16.36/4.38 powerset
% 16.36/4.38 @
% 16.36/4.38 X302 ) ) =>
% 16.36/4.38 (
% 16.36/4.38 ![
% 16.36/4.38 X308:$i]:
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 in @
% 16.36/4.38 X308 @
% 16.36/4.38 X302 ) =>
% 16.36/4.38 (
% 16.36/4.38 (
% 16.36/4.38 in @
% 16.36/4.38 X308 @
% 16.36/4.38 (
% 16.36/4.38 setminus
% 16.36/4.38 @
% 16.36/4.38 X302 @
% 16.36/4.38 X304 ) ) =>
% 16.36/4.38 (
% 16.36/4.38 in @
% 16.36/4.38 X308 @
% 16.36/4.38 (
% 16.36/4.38 setminus
% 16.36/4.38 @
% 16.36/4.38 X302 @
% 16.36/4.38 (
% 16.36/4.38 binintersect
% 16.36/4.38 @
% 16.36/4.38 X304 @
% 16.36/4.38 X306 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )),
% 16.36/4.38 inference('cnf.neg', [status(esa)], [zf_stmt_3])).
% 16.36/4.38 thf(zip_derived_cl133, plain,
% 16.36/4.38 ( (in @ sk__157 @ (setminus @ sk__154 @ sk__155))),
% 16.36/4.38 inference('cnf', [status(esa)], [zf_stmt_4])).
% 16.36/4.38 thf(zip_derived_cl67, plain,
% 16.36/4.38 (![X25 : $i, X26 : $i, X27 : $i]:
% 16.36/4.38 (~ (in @ X25 @ (setminus @ X26 @ X27)) | ~ (in @ X25 @ X27))),
% 16.36/4.38 inference('cnf', [status(esa)], [zf_stmt_4])).
% 16.36/4.38 thf(zip_derived_cl296, plain, (~ (in @ sk__157 @ sk__155)),
% 16.36/4.38 inference('sup-', [status(thm)], [zip_derived_cl133, zip_derived_cl67])).
% 16.36/4.38 thf(zip_derived_cl135, plain, ( (in @ sk__157 @ sk__154)),
% 16.36/4.38 inference('cnf', [status(esa)], [zf_stmt_4])).
% 16.36/4.38 thf(zip_derived_cl66, plain,
% 16.36/4.38 (![X22 : $i, X23 : $i, X24 : $i]:
% 16.36/4.38 ( (in @ X22 @ X23)
% 16.36/4.38 | ~ (in @ X22 @ X24)
% 16.36/4.38 | (in @ X22 @ (setminus @ X24 @ X23)))),
% 16.36/4.38 inference('cnf', [status(esa)], [zf_stmt_4])).
% 16.36/4.38 thf(zip_derived_cl439, plain,
% 16.36/4.38 (![X0 : $i]:
% 16.36/4.38 ( (in @ sk__157 @ (setminus @ sk__154 @ X0)) | (in @ sk__157 @ X0))),
% 16.36/4.38 inference('sup-', [status(thm)], [zip_derived_cl135, zip_derived_cl66])).
% 16.36/4.38 thf(zip_derived_cl134, plain,
% 16.36/4.38 (~ (in @ sk__157 @
% 16.36/4.38 (setminus @ sk__154 @ (binintersect @ sk__155 @ sk__156)))),
% 16.36/4.38 inference('cnf', [status(esa)], [zf_stmt_4])).
% 16.36/4.38 thf(zip_derived_cl4854, plain,
% 16.36/4.38 ( (in @ sk__157 @ (binintersect @ sk__155 @ sk__156))),
% 16.36/4.38 inference('sup-', [status(thm)], [zip_derived_cl439, zip_derived_cl134])).
% 16.36/4.38 thf(zip_derived_cl217, plain,
% 16.36/4.38 (![X122 : $i, X123 : $i, X124 : $i]:
% 16.36/4.38 ( (in @ X122 @ X123) | ~ (in @ X122 @ (binintersect @ X123 @ X124)))),
% 16.36/4.38 inference('cnf', [status(esa)], [zf_stmt_4])).
% 16.36/4.38 thf(zip_derived_cl4888, plain, ( (in @ sk__157 @ sk__155)),
% 16.36/4.38 inference('sup-', [status(thm)], [zip_derived_cl4854, zip_derived_cl217])).
% 16.36/4.38 thf(zip_derived_cl4904, plain, ($false),
% 16.36/4.38 inference('demod', [status(thm)], [zip_derived_cl296, zip_derived_cl4888])).
% 16.36/4.38
% 16.36/4.38 % SZS output end Refutation
% 16.36/4.38
% 16.36/4.38
% 16.36/4.38 % Terminating...
% 17.07/4.57 % Runner terminated.
% 17.07/4.58 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------