%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SEU728^1 : 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.GwZUVAiXdV 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 04:55:59 PM UTC 2025
% Result : Theorem 5.35s 1.25s
% Output : Refutation 5.35s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SEU728^1 : TPTP v9.2.0. Released v3.7.0.
% 0.03/0.14 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.GwZUVAiXdV true
% 0.13/0.35 % Computer : n026.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Wed Oct 1 16:08:08 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.13/0.35 % Running portfolio for 300 s
% 0.13/0.35 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.35 % Number of cores: 8
% 0.13/0.36 % Python version: Python 3.6.8
% 0.13/0.36 % Running in HO mode
% 0.49/0.64 % Total configuration time : 828
% 0.49/0.64 % Estimated wc time : 1656
% 0.49/0.64 % Estimated cpu time (8 cpus) : 207.0
% 0.49/0.70 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s
% 0.49/0.71 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.49/0.73 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s
% 0.49/0.73 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s
% 0.49/0.73 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s
% 0.49/0.73 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.49/0.73 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s
% 0.49/0.74 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s
% 5.35/1.25 % Solved by lams/40_c_ic.sh.
% 5.35/1.25 % done 421 iterations in 0.392s
% 5.35/1.25 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 5.35/1.25 % SZS output start Refutation
% 5.35/1.25 thf(setadjoinAx_type, type, setadjoinAx: $o).
% 5.35/1.25 thf(notdexE_type, type, notdexE: $o).
% 5.35/1.25 thf(sk__104_type, type, sk__104: $i).
% 5.35/1.25 thf(setukpairinjL2_type, type, setukpairinjL2: $o).
% 5.35/1.25 thf(doubleComplementI1_type, type, doubleComplementI1: $o).
% 5.35/1.25 thf(setunionAx_type, type, setunionAx: $o).
% 5.35/1.25 thf(setminusELneg_type, type, setminusELneg: $o).
% 5.35/1.25 thf(cartprodsndin_type, type, cartprodsndin: $o).
% 5.35/1.25 thf(ex1E1_type, type, ex1E1: $o).
% 5.35/1.25 thf(powersetE_type, type, powersetE: $o).
% 5.35/1.25 thf(omegaSAx_type, type, omegaSAx: $o).
% 5.35/1.25 thf(exuI1_type, type, exuI1: $o).
% 5.35/1.25 thf(exuI2_type, type, exuI2: $o).
% 5.35/1.25 thf(notequalI2_type, type, notequalI2: $o).
% 5.35/1.25 thf(setukpairinjL_type, type, setukpairinjL: $o).
% 5.35/1.25 thf(kpairiskpair_type, type, kpairiskpair: $o).
% 5.35/1.25 thf(upairsubunion_type, type, upairsubunion: $o).
% 5.35/1.25 thf(funcGraphProp3_type, type, funcGraphProp3: $o).
% 5.35/1.25 thf(cartprodmempaircEq_type, type, cartprodmempaircEq: $o).
% 5.35/1.25 thf(binintersectTERcontra_type, type, binintersectTERcontra: $o).
% 5.35/1.25 thf(powerset__Cong_type, type, powerset__Cong: $o).
% 5.35/1.25 thf(setminusILneg_type, type, setminusILneg: $o).
% 5.35/1.25 thf(wellorderingAx_type, type, wellorderingAx: $o).
% 5.35/1.25 thf(ksndpairEq_type, type, ksndpairEq: $o).
% 5.35/1.25 thf(funcGraphProp2_type, type, funcGraphProp2: $o).
% 5.35/1.25 thf(setadjoinSub2_type, type, setadjoinSub2: $o).
% 5.35/1.25 thf(binintersectSubset5_type, type, binintersectSubset5: $o).
% 5.35/1.25 thf(iftrue_type, type, iftrue: $o).
% 5.35/1.25 thf(upairinpowunion_type, type, upairinpowunion: $o).
% 5.35/1.25 thf(ifSingleton_type, type, ifSingleton: $o).
% 5.35/1.25 thf(setoftrueEq_type, type, setoftrueEq: $o).
% 5.35/1.25 thf(funcImageSingleton_type, type, funcImageSingleton: $o).
% 5.35/1.25 thf(dpsetconstrERa_type, type, dpsetconstrERa: $o).
% 5.35/1.25 thf(lamProp_type, type, lamProp: $o).
% 5.35/1.25 thf(cartprodpairmemEL_type, type, cartprodpairmemEL: $o).
% 5.35/1.25 thf(emptyset__Cong_type, type, emptyset__Cong: $o).
% 5.35/1.25 thf(dpsetconstrER_type, type, dpsetconstrER: $o).
% 5.35/1.25 thf(sepInPowerset_type, type, sepInPowerset: $o).
% 5.35/1.25 thf(setukpairIR_type, type, setukpairIR: $o).
% 5.35/1.25 thf(setukpairinjR1_type, type, setukpairinjR1: $o).
% 5.35/1.25 thf(lam2p_type, type, lam2p: $o).
% 5.35/1.25 thf(binunionE_type, type, binunionE: $o).
% 5.35/1.25 thf(setext_type, type, setext: $o).
% 5.35/1.25 thf(zip_tseitin_0_type, type, zip_tseitin_0: $i > $i > $i > $o).
% 5.35/1.25 thf(emptyinPowerset_type, type, emptyinPowerset: $o).
% 5.35/1.25 thf(ubforcartprodlem1_type, type, ubforcartprodlem1: $o).
% 5.35/1.25 thf(descr__Cong_type, type, descr__Cong: $o).
% 5.35/1.25 thf(kfstsingleton_type, type, kfstsingleton: $o).
% 5.35/1.25 thf(binintersectTELcontra_type, type, binintersectTELcontra: $o).
% 5.35/1.25 thf(eqbreln_type, type, eqbreln: $o).
% 5.35/1.25 thf(binintersectSubset1_type, type, binintersectSubset1: $o).
% 5.35/1.25 thf(in_type, type, in: $i > $i > $o).
% 5.35/1.25 thf(binunionT_lem_type, type, binunionT_lem: $o).
% 5.35/1.25 thf(quantDeMorgan1_type, type, quantDeMorgan1: $o).
% 5.35/1.25 thf(complementT_lem_type, type, complementT_lem: $o).
% 5.35/1.25 thf(kpairsurjEq_type, type, kpairsurjEq: $o).
% 5.35/1.25 thf(setadjoinIR_type, type, setadjoinIR: $o).
% 5.35/1.25 thf(beta1_type, type, beta1: $o).
% 5.35/1.25 thf(setadjoin__Cong_type, type, setadjoin__Cong: $o).
% 5.35/1.25 thf(powersetTE1_type, type, powersetTE1: $o).
% 5.35/1.25 thf(symdiffI2_type, type, symdiffI2: $o).
% 5.35/1.25 thf(iftrueProp2_type, type, iftrueProp2: $o).
% 5.35/1.25 thf(upairset2IR_type, type, upairset2IR: $o).
% 5.35/1.25 thf(iffalseProp2_type, type, iffalseProp2: $o).
% 5.35/1.25 thf(subsetE_type, type, subsetE: $o).
% 5.35/1.25 thf(prop2set2propI_type, type, prop2set2propI: $o).
% 5.35/1.25 thf(dsetconstrEL_type, type, dsetconstrEL: $o).
% 5.35/1.25 thf(setbeta_type, type, setbeta: $o).
% 5.35/1.25 thf(eqinunit_type, type, eqinunit: $o).
% 5.35/1.25 thf(upairsetIL_type, type, upairsetIL: $o).
% 5.35/1.25 thf(powersetI1_type, type, powersetI1: $o).
% 5.35/1.25 thf(kfstpairEq_type, type, kfstpairEq: $o).
% 5.35/1.25 thf(binintersectSubset3_type, type, binintersectSubset3: $o).
% 5.35/1.25 thf(setminusIRneg_type, type, setminusIRneg: $o).
% 5.35/1.25 thf(ap2apEq1_type, type, ap2apEq1: $o).
% 5.35/1.25 thf(powersetAx_type, type, powersetAx: $o).
% 5.35/1.25 thf(binintersectSubset4_type, type, binintersectSubset4: $o).
% 5.35/1.25 thf(singletoninpowunion_type, type, singletoninpowunion: $o).
% 5.35/1.25 thf(powersetI_type, type, powersetI: $o).
% 5.35/1.25 thf(cartprodmempair_type, type, cartprodmempair: $o).
% 5.35/1.25 thf(upairsetIR_type, type, upairsetIR: $o).
% 5.35/1.25 thf(lamp_type, type, lamp: $o).
% 5.35/1.25 thf(dpsetconstrEL1_type, type, dpsetconstrEL1: $o).
% 5.35/1.25 thf(inCongP_type, type, inCongP: $o).
% 5.35/1.25 thf(setadjoinSub_type, type, setadjoinSub: $o).
% 5.35/1.25 thf(exuE3e_type, type, exuE3e: $o).
% 5.35/1.25 thf(emptysetE_type, type, emptysetE: $o).
% 5.35/1.25 thf(binintersectSubset2_type, type, binintersectSubset2: $o).
% 5.35/1.25 thf(setunionI_type, type, setunionI: $o).
% 5.35/1.25 thf(setunion__Cong_type, type, setunion__Cong: $o).
% 5.35/1.25 thf(prop2setI_type, type, prop2setI: $o).
% 5.35/1.25 thf(singletonsuniq_type, type, singletonsuniq: $o).
% 5.35/1.25 thf(nonemptyImpWitness_type, type, nonemptyImpWitness: $o).
% 5.35/1.25 thf(setminusER_type, type, setminusER: $o).
% 5.35/1.25 thf(exuE2_type, type, exuE2: $o).
% 5.35/1.25 thf(emptyset_type, type, emptyset: $i).
% 5.35/1.25 thf(setukpairinjR11_type, type, setukpairinjR11: $o).
% 5.35/1.25 thf(ex1I_type, type, ex1I: $o).
% 5.35/1.25 thf(ex1E2_type, type, ex1E2: $o).
% 5.35/1.25 thf(setminus_type, type, setminus: $i > $i > $i).
% 5.35/1.25 thf(setukpairinjL1_type, type, setukpairinjL1: $o).
% 5.35/1.25 thf(powersetsubset_type, type, powersetsubset: $o).
% 5.35/1.25 thf(subPowSU_type, type, subPowSU: $o).
% 5.35/1.25 thf(notequalI1_type, type, notequalI1: $o).
% 5.35/1.25 thf(contrasubsetT_type, type, contrasubsetT: $o).
% 5.35/1.25 thf(notinemptyset_type, type, notinemptyset: $o).
% 5.35/1.25 thf(lam2lamEq_type, type, lam2lamEq: $o).
% 5.35/1.25 thf(nonemptyI1_type, type, nonemptyI1: $o).
% 5.35/1.25 thf(subsetTrans_type, type, subsetTrans: $o).
% 5.35/1.25 thf(kpairp_type, type, kpairp: $o).
% 5.35/1.25 thf(setukpairinjR12_type, type, setukpairinjR12: $o).
% 5.35/1.25 thf(setminusI_type, type, setminusI: $o).
% 5.35/1.25 thf(binunionIL_type, type, binunionIL: $o).
% 5.35/1.25 thf(dpsetconstrSub_type, type, dpsetconstrSub: $o).
% 5.35/1.25 thf(setunionsingleton_type, type, setunionsingleton: $o).
% 5.35/1.25 thf(subsetE2_type, type, subsetE2: $o).
% 5.35/1.25 thf(singletonsswitch_type, type, singletonsswitch: $o).
% 5.35/1.25 thf(ubforcartprodlem3_type, type, ubforcartprodlem3: $o).
% 5.35/1.25 thf(beta2_type, type, beta2: $o).
% 5.35/1.25 thf(dpsetconstrI_type, type, dpsetconstrI: $o).
% 5.35/1.25 thf(setextsub_type, type, setextsub: $o).
% 5.35/1.25 thf(binunionLsub_type, type, binunionLsub: $o).
% 5.35/1.25 thf(setunionsingleton1_type, type, setunionsingleton1: $o).
% 5.35/1.25 thf(iftrueorfalse_type, type, iftrueorfalse: $o).
% 5.35/1.25 thf(emptysetsubset_type, type, emptysetsubset: $o).
% 5.35/1.25 thf(quantDeMorgan3_type, type, quantDeMorgan3: $o).
% 5.35/1.25 thf(cartprodpairsurjEq_type, type, cartprodpairsurjEq: $o).
% 5.35/1.25 thf(setOfPairsIsBReln_type, type, setOfPairsIsBReln: $o).
% 5.35/1.25 thf(setunionE_type, type, setunionE: $o).
% 5.35/1.25 thf(ksndsingleton_type, type, ksndsingleton: $o).
% 5.35/1.25 thf(setminusSubset1_type, type, setminusSubset1: $o).
% 5.35/1.25 thf(powersetT_lem_type, type, powersetT_lem: $o).
% 5.35/1.25 thf(emptyinunitempty_type, type, emptyinunitempty: $o).
% 5.35/1.25 thf(binunionIR_type, type, binunionIR: $o).
% 5.35/1.25 thf(theeq_type, type, theeq: $o).
% 5.35/1.25 thf(setadjoinE_type, type, setadjoinE: $o).
% 5.35/1.25 thf(infuncsetfunc_type, type, infuncsetfunc: $o).
% 5.35/1.25 thf(ap2apEq2_type, type, ap2apEq2: $o).
% 5.35/1.25 thf(ap2p_type, type, ap2p: $o).
% 5.35/1.25 thf(setadjoinIL_type, type, setadjoinIL: $o).
% 5.35/1.25 thf(cartprodsndpairEq_type, type, cartprodsndpairEq: $o).
% 5.35/1.25 thf(exuE1_type, type, exuE1: $o).
% 5.35/1.25 thf(ubforcartprodlem2_type, type, ubforcartprodlem2: $o).
% 5.35/1.25 thf(binintersectRsub_type, type, binintersectRsub: $o).
% 5.35/1.25 thf(setminusLsub_type, type, setminusLsub: $o).
% 5.35/1.25 thf(funcextLem_type, type, funcextLem: $o).
% 5.35/1.25 thf(setukpairinjR_type, type, setukpairinjR: $o).
% 5.35/1.25 thf(notinsingleton_type, type, notinsingleton: $o).
% 5.35/1.25 thf(eqimpsubset2_type, type, eqimpsubset2: $o).
% 5.35/1.25 thf(exuEu_type, type, exuEu: $o).
% 5.35/1.25 thf(emptysetimpfalse_type, type, emptysetimpfalse: $o).
% 5.35/1.25 thf(upairsetE_type, type, upairsetE: $o).
% 5.35/1.25 thf(omega0Ax_type, type, omega0Ax: $o).
% 5.35/1.25 thf(subsetTI_type, type, subsetTI: $o).
% 5.35/1.25 thf(notsubsetI_type, type, notsubsetI: $o).
% 5.35/1.25 thf(iffalseProp1_type, type, iffalseProp1: $o).
% 5.35/1.25 thf(quantDeMorgan4_type, type, quantDeMorgan4: $o).
% 5.35/1.25 thf(setextAx_type, type, setextAx: $o).
% 5.35/1.25 thf(cartprodpairmemER_type, type, cartprodpairmemER: $o).
% 5.35/1.25 thf(powersetE1_type, type, powersetE1: $o).
% 5.35/1.25 thf(bs114d_type, type, bs114d: $o).
% 5.35/1.25 thf(contrasubsetT3_type, type, contrasubsetT3: $o).
% 5.35/1.25 thf(noeltsimpempty_type, type, noeltsimpempty: $o).
% 5.35/1.25 thf(ifp_type, type, ifp: $o).
% 5.35/1.25 thf(powersetTI1_type, type, powersetTI1: $o).
% 5.35/1.25 thf(binintersectLsub_type, type, binintersectLsub: $o).
% 5.35/1.25 thf(subsetI1_type, type, subsetI1: $o).
% 5.35/1.25 thf(symdiffE_type, type, symdiffE: $o).
% 5.35/1.25 thf(descrp_type, type, descrp: $o).
% 5.35/1.25 thf(dsetconstr__Cong_type, type, dsetconstr__Cong: $o).
% 5.35/1.25 thf(foundationAx_type, type, foundationAx: $o).
% 5.35/1.25 thf(emptysetAx_type, type, emptysetAx: $o).
% 5.35/1.25 thf(emptyI_type, type, emptyI: $o).
% 5.35/1.25 thf(setadjoinOr_type, type, setadjoinOr: $o).
% 5.35/1.25 thf(eta2_type, type, eta2: $o).
% 5.35/1.25 thf(binintersectEL_type, type, binintersectEL: $o).
% 5.35/1.25 thf(emptyE1_type, type, emptyE1: $o).
% 5.35/1.25 thf(emptyInPowerset_type, type, emptyInPowerset: $o).
% 5.35/1.25 thf(complementTI1_type, type, complementTI1: $o).
% 5.35/1.25 thf(vacuousDall_type, type, vacuousDall: $o).
% 5.35/1.25 thf(dsetconstrER_type, type, dsetconstrER: $o).
% 5.35/1.25 thf(binintersectI_type, type, binintersectI: $o).
% 5.35/1.25 thf(funcext_type, type, funcext: $o).
% 5.35/1.25 thf(funcGraphProp4_type, type, funcGraphProp4: $o).
% 5.35/1.25 thf(cartprodpairin_type, type, cartprodpairin: $o).
% 5.35/1.25 thf(sk__103_type, type, sk__103: $i).
% 5.35/1.25 thf(cartprodmempair1_type, type, cartprodmempair1: $o).
% 5.35/1.25 thf(brelnall2_type, type, brelnall2: $o).
% 5.35/1.25 thf(setextT_type, type, setextT: $o).
% 5.35/1.25 thf(ex1I2_type, type, ex1I2: $o).
% 5.35/1.25 thf(symdiffI1_type, type, symdiffI1: $o).
% 5.35/1.25 thf(setukpairinjR2_type, type, setukpairinjR2: $o).
% 5.35/1.25 thf(dpsetconstrEL2_type, type, dpsetconstrEL2: $o).
% 5.35/1.26 thf(theprop_type, type, theprop: $o).
% 5.35/1.26 thf(subsetI2_type, type, subsetI2: $o).
% 5.35/1.26 thf(setminusT_lem_type, type, setminusT_lem: $o).
% 5.35/1.26 thf(symdiffIneg1_type, type, symdiffIneg1: $o).
% 5.35/1.26 thf(setminusERneg_type, type, setminusERneg: $o).
% 5.35/1.26 thf(symdiffIneg2_type, type, symdiffIneg2: $o).
% 5.35/1.26 thf(omega__Cong_type, type, omega__Cong: $o).
% 5.35/1.26 thf(subsetRefl_type, type, subsetRefl: $o).
% 5.35/1.26 thf(uniqinunit_type, type, uniqinunit: $o).
% 5.35/1.26 thf(setminusSubset2_type, type, setminusSubset2: $o).
% 5.35/1.26 thf(prop2setE_type, type, prop2setE: $o).
% 5.35/1.26 thf(binunionEcases_type, type, binunionEcases: $o).
% 5.35/1.26 thf(funcinfuncset_type, type, funcinfuncset: $o).
% 5.35/1.26 thf(complementTE1_type, type, complementTE1: $o).
% 5.35/1.26 thf(nonemptyI_type, type, nonemptyI: $o).
% 5.35/1.26 thf(app_type, type, app: $o).
% 5.35/1.26 thf(disjointsetsI1_type, type, disjointsetsI1: $o).
% 5.35/1.26 thf(sk__105_type, type, sk__105: $i).
% 5.35/1.26 thf(exuE3u_type, type, exuE3u: $o).
% 5.35/1.26 thf(eta1_type, type, eta1: $o).
% 5.35/1.26 thf(setminusEL_type, type, setminusEL: $o).
% 5.35/1.26 thf(cartprodfstin_type, type, cartprodfstin: $o).
% 5.35/1.26 thf(setunionsingleton2_type, type, setunionsingleton2: $o).
% 5.35/1.26 thf(sepSubset_type, type, sepSubset: $o).
% 5.35/1.26 thf(upairset2E_type, type, upairset2E: $o).
% 5.35/1.26 thf(eqimpsubset1_type, type, eqimpsubset1: $o).
% 5.35/1.26 thf(exuI3_type, type, exuI3: $o).
% 5.35/1.26 thf(cartprodfstpairEq_type, type, cartprodfstpairEq: $o).
% 5.35/1.26 thf(apProp_type, type, apProp: $o).
% 5.35/1.26 thf(notdallE_type, type, notdallE: $o).
% 5.35/1.26 thf(iftrueProp1_type, type, iftrueProp1: $o).
% 5.35/1.26 thf(binintersectER_type, type, binintersectER: $o).
% 5.35/1.26 thf(brelnall1_type, type, brelnall1: $o).
% 5.35/1.26 thf(powerset_type, type, powerset: $i > $i).
% 5.35/1.26 thf(dsetconstrI_type, type, dsetconstrI: $o).
% 5.35/1.26 thf(funcGraphProp1_type, type, funcGraphProp1: $o).
% 5.35/1.26 thf(binintersectT_lem_type, type, binintersectT_lem: $o).
% 5.35/1.26 thf(setadjoin_type, type, setadjoin: $i > $i > $i).
% 5.35/1.26 thf(exu__Cong_type, type, exu__Cong: $o).
% 5.35/1.26 thf(quantDeMorgan2_type, type, quantDeMorgan2: $o).
% 5.35/1.26 thf(contrasubsetT2_type, type, contrasubsetT2: $o).
% 5.35/1.26 thf(secondinupair_type, type, secondinupair: $o).
% 5.35/1.26 thf(singletonprop_type, type, singletonprop: $o).
% 5.35/1.26 thf(singletonsubset_type, type, singletonsubset: $o).
% 5.35/1.26 thf(contrasubsetT1_type, type, contrasubsetT1: $o).
% 5.35/1.26 thf(singletoninpowerset_type, type, singletoninpowerset: $o).
% 5.35/1.26 thf(subsetemptysetimpeq_type, type, subsetemptysetimpeq: $o).
% 5.35/1.26 thf(replAx_type, type, replAx: $o).
% 5.35/1.26 thf(upairequniteq_type, type, upairequniteq: $o).
% 5.35/1.26 thf(nonemptyE1_type, type, nonemptyE1: $o).
% 5.35/1.26 thf(omegaIndAx_type, type, omegaIndAx: $o).
% 5.35/1.26 thf(setukpairIL_type, type, setukpairIL: $o).
% 5.35/1.26 thf(setunionE2_type, type, setunionE2: $o).
% 5.35/1.26 thf(inPowerset_type, type, inPowerset: $o).
% 5.35/1.26 thf(iffalse_type, type, iffalse: $o).
% 5.35/1.26 thf(funcext2_type, type, funcext2: $o).
% 5.35/1.26 thf(subset_type, type, subset: $i > $i > $o).
% 5.35/1.26 thf(subbreln_type, type, subbreln: $o).
% 5.35/1.26 thf(in__Cong_type, type, in__Cong: $o).
% 5.35/1.26 thf(binunionRsub_type, type, binunionRsub: $o).
% 5.35/1.26 thf(subset2powerset_type, type, subset2powerset: $o).
% 5.35/1.26 thf(doubleComplementI1, axiom, doubleComplementI1 =
% 5.35/1.26 (![A:$i,X:$i]:
% 5.35/1.26 ( ( in @ X @ ( powerset @ A ) ) =>
% 5.35/1.26 ( ![Xx:$i]:
% 5.35/1.26 ( ( in @ Xx @ A ) =>
% 5.35/1.26 ( ( in @ Xx @ X ) =>
% 5.35/1.26 ( in @ Xx @ ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) ))).
% 5.35/1.26 thf('0', plain,
% 5.35/1.26 (( doubleComplementI1 ) =
% 5.35/1.26 ( ![X4:$i,X6:$i]:
% 5.35/1.26 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 5.35/1.26 ( ![X8:$i]:
% 5.35/1.26 ( ( in @ X8 @ X4 ) =>
% 5.35/1.26 ( ( in @ X8 @ X6 ) =>
% 5.35/1.26 ( in @ X8 @ ( setminus @ X4 @ ( setminus @ X4 @ X6 ) ) ) ) ) ) ) )),
% 5.35/1.26 define([status(thm)])).
% 5.35/1.26 thf(contrasubsetT3, axiom, contrasubsetT3 =
% 5.35/1.26 (![A:$i,X:$i]:
% 5.35/1.26 ( ( in @ X @ ( powerset @ A ) ) =>
% 5.35/1.26 ( ![Y:$i]:
% 5.35/1.26 ( ( in @ Y @ ( powerset @ A ) ) =>
% 5.35/1.26 ( ( subset @ ( setminus @ A @ Y ) @ ( setminus @ A @ X ) ) =>
% 5.35/1.26 ( subset @ X @ Y ) ) ) ) ))).
% 5.35/1.26 thf('1', plain,
% 5.35/1.26 (( contrasubsetT3 ) =
% 5.35/1.26 ( ![X4:$i,X6:$i]:
% 5.35/1.26 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 5.35/1.26 ( ![X8:$i]:
% 5.35/1.26 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 5.35/1.26 ( ( subset @ ( setminus @ X4 @ X8 ) @ ( setminus @ X4 @ X6 ) ) =>
% 5.35/1.26 ( subset @ X6 @ X8 ) ) ) ) ) )),
% 5.35/1.26 define([status(thm)])).
% 5.35/1.26 thf(contrasubsetT2, axiom, contrasubsetT2 =
% 5.35/1.26 (![A:$i,X:$i]:
% 5.35/1.26 ( ( in @ X @ ( powerset @ A ) ) =>
% 5.35/1.26 ( ![Y:$i]:
% 5.35/1.26 ( ( in @ Y @ ( powerset @ A ) ) =>
% 5.35/1.26 ( ( subset @ X @ Y ) =>
% 5.35/1.26 ( subset @ ( setminus @ A @ Y ) @ ( setminus @ A @ X ) ) ) ) ) ))).
% 5.35/1.26 thf('2', plain,
% 5.35/1.26 (( contrasubsetT2 ) =
% 5.35/1.26 ( ![X4:$i,X6:$i]:
% 5.35/1.26 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 5.35/1.26 ( ![X8:$i]:
% 5.35/1.26 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 5.35/1.26 ( ( subset @ X6 @ X8 ) =>
% 5.35/1.26 ( subset @ ( setminus @ X4 @ X8 ) @ ( setminus @ X4 @ X6 ) ) ) ) ) ) )),
% 5.35/1.26 define([status(thm)])).
% 5.35/1.26 thf(contrasubsetT1, axiom, contrasubsetT1 =
% 5.35/1.26 (![A:$i,X:$i]:
% 5.35/1.26 ( ( in @ X @ ( powerset @ A ) ) =>
% 5.35/1.26 ( ![Y:$i]:
% 5.35/1.26 ( ( in @ Y @ ( powerset @ A ) ) =>
% 5.35/1.26 ( ![Xx:$i]:
% 5.35/1.26 ( ( in @ Xx @ A ) =>
% 5.35/1.26 ( ( subset @ X @ Y ) =>
% 5.35/1.26 ( ( ~( in @ Xx @ Y ) ) => ( ~( in @ Xx @ X ) ) ) ) ) ) ) ) ))).
% 5.35/1.26 thf('3', plain,
% 5.35/1.26 (( contrasubsetT1 ) =
% 5.35/1.26 ( ![X4:$i,X6:$i]:
% 5.35/1.26 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 5.35/1.26 ( ![X8:$i]:
% 5.35/1.26 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 5.35/1.26 ( ![X10:$i]:
% 5.35/1.26 ( ( in @ X10 @ X4 ) =>
% 5.35/1.26 ( ( subset @ X6 @ X8 ) =>
% 5.35/1.26 ( ( ~( in @ X10 @ X8 ) ) => ( ~( in @ X10 @ X6 ) ) ) ) ) ) ) ) ) )),
% 5.35/1.26 define([status(thm)])).
% 5.35/1.26 thf(contrasubsetT, axiom, contrasubsetT =
% 5.35/1.26 (![A:$i,X:$i]:
% 5.35/1.26 ( ( in @ X @ ( powerset @ A ) ) =>
% 5.35/1.26 ( ![Y:$i]:
% 5.35/1.26 ( ( in @ Y @ ( powerset @ A ) ) =>
% 5.35/1.26 ( ![Xx:$i]:
% 5.35/1.26 ( ( in @ Xx @ A ) =>
% 5.35/1.26 ( ( subset @ X @ ( setminus @ A @ Y ) ) =>
% 5.35/1.26 ( ( in @ Xx @ Y ) => ( ~( in @ Xx @ X ) ) ) ) ) ) ) ) ))).
% 5.35/1.26 thf('4', plain,
% 5.35/1.26 (( contrasubsetT ) =
% 5.35/1.26 ( ![X4:$i,X6:$i]:
% 5.35/1.26 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 5.35/1.26 ( ![X8:$i]:
% 5.35/1.26 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 5.35/1.26 ( ![X10:$i]:
% 5.35/1.26 ( ( in @ X10 @ X4 ) =>
% 5.35/1.26 ( ( subset @ X6 @ ( setminus @ X4 @ X8 ) ) =>
% 5.35/1.26 ( ( in @ X10 @ X8 ) => ( ~( in @ X10 @ X6 ) ) ) ) ) ) ) ) ) )),
% 5.35/1.26 define([status(thm)])).
% 5.35/1.26 thf(complementTE1, axiom, complementTE1 =
% 5.35/1.26 (![A:$i,X:$i]:
% 5.35/1.26 ( ( in @ X @ ( powerset @ A ) ) =>
% 5.35/1.26 ( ![Xx:$i]:
% 5.35/1.26 ( ( in @ Xx @ A ) =>
% 5.35/1.26 ( ( ~( in @ Xx @ ( setminus @ A @ X ) ) ) => ( in @ Xx @ X ) ) ) ) ))).
% 5.35/1.26 thf('5', plain,
% 5.35/1.26 (( complementTE1 ) =
% 5.35/1.26 ( ![X4:$i,X6:$i]:
% 5.35/1.26 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 5.35/1.26 ( ![X8:$i]:
% 5.35/1.26 ( ( in @ X8 @ X4 ) =>
% 5.35/1.26 ( ( ~( in @ X8 @ ( setminus @ X4 @ X6 ) ) ) => ( in @ X8 @ X6 ) ) ) ) ) )),
% 5.35/1.26 define([status(thm)])).
% 5.35/1.26 thf(complementTI1, axiom, complementTI1 =
% 5.35/1.26 (![A:$i,X:$i]:
% 5.35/1.26 ( ( in @ X @ ( powerset @ A ) ) =>
% 5.35/1.26 ( ![Xx:$i]:
% 5.35/1.26 ( ( in @ Xx @ A ) =>
% 5.35/1.26 ( ( in @ Xx @ X ) => ( ~( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ))).
% 5.35/1.26 thf('6', plain,
% 5.35/1.26 (( complementTI1 ) =
% 5.35/1.26 ( ![X4:$i,X6:$i]:
% 5.35/1.26 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 5.35/1.26 ( ![X8:$i]:
% 5.35/1.26 ( ( in @ X8 @ X4 ) =>
% 5.35/1.26 ( ( in @ X8 @ X6 ) => ( ~( in @ X8 @ ( setminus @ X4 @ X6 ) ) ) ) ) ) ) )),
% 5.35/1.26 define([status(thm)])).
% 5.35/1.26 thf(powersetTE1, axiom, powersetTE1 =
% 5.35/1.26 (![A:$i,X:$i]:
% 5.35/1.26 ( ( in @ X @ ( powerset @ A ) ) =>
% 5.35/1.26 ( ![Y:$i]:
% 5.35/1.26 ( ( in @ Y @ ( powerset @ A ) ) =>
% 5.35/1.26 ( ![Xx:$i]:
% 5.35/1.26 ( ( in @ Xx @ A ) =>
% 5.35/1.26 ( ( in @ X @ ( powerset @ Y ) ) =>
% 5.35/1.26 ( ( in @ Xx @ X ) => ( in @ Xx @ Y ) ) ) ) ) ) ) ))).
% 5.35/1.26 thf('7', plain,
% 5.35/1.26 (( powersetTE1 ) =
% 5.35/1.26 ( ![X4:$i,X6:$i]:
% 5.35/1.26 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 5.35/1.26 ( ![X8:$i]:
% 5.35/1.26 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 5.35/1.26 ( ![X10:$i]:
% 5.35/1.26 ( ( in @ X10 @ X4 ) =>
% 5.35/1.26 ( ( in @ X6 @ ( powerset @ X8 ) ) =>
% 5.35/1.26 ( ( in @ X10 @ X6 ) => ( in @ X10 @ X8 ) ) ) ) ) ) ) ) )),
% 5.35/1.26 define([status(thm)])).
% 5.35/1.26 thf(powersetTI1, axiom, powersetTI1 =
% 5.35/1.26 (![A:$i,X:$i]:
% 5.35/1.26 ( ( in @ X @ ( powerset @ A ) ) =>
% 5.35/1.26 ( ![Y:$i]:
% 5.35/1.26 ( ( in @ Y @ ( powerset @ A ) ) =>
% 5.35/1.26 ( ( ![Xx:$i]:
% 5.35/1.26 ( ( in @ Xx @ A ) => ( ( in @ Xx @ X ) => ( in @ Xx @ Y ) ) ) ) =>
% 5.35/1.26 ( in @ X @ ( powerset @ Y ) ) ) ) ) ))).
% 5.35/1.26 thf('8', plain,
% 5.35/1.26 (( powersetTI1 ) =
% 5.35/1.26 ( ![X4:$i,X6:$i]:
% 5.35/1.26 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 5.35/1.26 ( ![X8:$i]:
% 5.35/1.26 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 5.35/1.26 ( ( ![X10:$i]:
% 5.35/1.26 ( ( in @ X10 @ X4 ) =>
% 5.35/1.26 ( ( in @ X10 @ X6 ) => ( in @ X10 @ X8 ) ) ) ) =>
% 5.35/1.26 ( in @ X6 @ ( powerset @ X8 ) ) ) ) ) ) )),
% 5.35/1.26 define([status(thm)])).
% 5.35/1.26 thf(subsetTI, axiom, subsetTI =
% 5.35/1.26 (![A:$i,X:$i]:
% 5.35/1.26 ( ( in @ X @ ( powerset @ A ) ) =>
% 5.35/1.26 ( ![Y:$i]:
% 5.35/1.26 ( ( in @ Y @ ( powerset @ A ) ) =>
% 5.35/1.26 ( ( ![Xx:$i]:
% 5.35/1.26 ( ( in @ Xx @ A ) => ( ( in @ Xx @ X ) => ( in @ Xx @ Y ) ) ) ) =>
% 5.35/1.26 ( subset @ X @ Y ) ) ) ) ))).
% 5.35/1.26 thf('9', plain,
% 5.35/1.26 (( subsetTI ) =
% 5.35/1.26 ( ![X4:$i,X6:$i]:
% 5.35/1.26 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 5.35/1.26 ( ![X8:$i]:
% 5.35/1.26 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 5.35/1.26 ( ( ![X10:$i]:
% 5.35/1.26 ( ( in @ X10 @ X4 ) =>
% 5.35/1.26 ( ( in @ X10 @ X6 ) => ( in @ X10 @ X8 ) ) ) ) =>
% 5.35/1.26 ( subset @ X6 @ X8 ) ) ) ) ) )),
% 5.35/1.26 define([status(thm)])).
% 5.35/1.26 thf(setextT, axiom, setextT =
% 5.35/1.26 (![A:$i,X:$i]:
% 5.35/1.26 ( ( in @ X @ ( powerset @ A ) ) =>
% 5.35/1.26 ( ![Y:$i]:
% 5.35/1.26 ( ( in @ Y @ ( powerset @ A ) ) =>
% 5.35/1.26 ( ( ![Xx:$i]:
% 5.35/1.26 ( ( in @ Xx @ A ) => ( ( in @ Xx @ X ) => ( in @ Xx @ Y ) ) ) ) =>
% 5.35/1.26 ( ( ![Xx:$i]:
% 5.35/1.26 ( ( in @ Xx @ A ) => ( ( in @ Xx @ Y ) => ( in @ Xx @ X ) ) ) ) =>
% 5.35/1.26 ( ( X ) = ( Y ) ) ) ) ) ) ))).
% 5.35/1.26 thf('10', plain,
% 5.35/1.26 (( setextT ) =
% 5.35/1.26 ( ![X4:$i,X6:$i]:
% 5.35/1.26 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 5.35/1.26 ( ![X8:$i]:
% 5.35/1.26 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 5.35/1.26 ( ( ![X10:$i]:
% 5.35/1.26 ( ( in @ X10 @ X4 ) =>
% 5.35/1.26 ( ( in @ X10 @ X6 ) => ( in @ X10 @ X8 ) ) ) ) =>
% 5.35/1.26 ( ( ![X12:$i]:
% 5.35/1.26 ( ( in @ X12 @ X4 ) =>
% 5.35/1.26 ( ( in @ X12 @ X8 ) => ( in @ X12 @ X6 ) ) ) ) =>
% 5.35/1.26 ( ( X6 ) = ( X8 ) ) ) ) ) ) ) )),
% 5.35/1.26 define([status(thm)])).
% 5.35/1.26 thf(complementT_lem, axiom, complementT_lem =
% 5.35/1.26 (![A:$i,X:$i]:
% 5.35/1.26 ( ( in @ X @ ( powerset @ A ) ) =>
% 5.35/1.26 ( in @ ( setminus @ A @ X ) @ ( powerset @ A ) ) ))).
% 5.35/1.26 thf('11', plain,
% 5.35/1.26 (( complementT_lem ) =
% 5.35/1.26 ( ![X4:$i,X6:$i]:
% 5.35/1.26 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 5.35/1.26 ( in @ ( setminus @ X4 @ X6 ) @ ( powerset @ X4 ) ) ) )),
% 5.35/1.26 define([status(thm)])).
% 5.35/1.26 thf(setminusT_lem, axiom, setminusT_lem =
% 5.35/1.26 (![A:$i,X:$i]:
% 5.35/1.26 ( ( in @ X @ ( powerset @ A ) ) =>
% 5.35/1.26 ( ![Y:$i]:
% 5.35/1.26 ( ( in @ Y @ ( powerset @ A ) ) =>
% 5.35/1.26 ( in @ ( setminus @ X @ Y ) @ ( powerset @ A ) ) ) ) ))).
% 5.35/1.26 thf('12', plain,
% 5.35/1.26 (( setminusT_lem ) =
% 5.35/1.26 ( ![X4:$i,X6:$i]:
% 5.35/1.26 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 5.35/1.26 ( ![X8:$i]:
% 5.35/1.26 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 5.35/1.26 ( in @ ( setminus @ X6 @ X8 ) @ ( powerset @ X4 ) ) ) ) ) )),
% 5.35/1.26 define([status(thm)])).
% 5.35/1.26 thf(powersetT_lem, axiom, powersetT_lem =
% 5.35/1.26 (![A:$i,X:$i]:
% 5.35/1.26 ( ( in @ X @ ( powerset @ A ) ) =>
% 5.35/1.26 ( in @ ( powerset @ X ) @ ( powerset @ ( powerset @ A ) ) ) ))).
% 5.35/1.26 thf('13', plain,
% 5.35/1.26 (( powersetT_lem ) =
% 5.35/1.26 ( ![X4:$i,X6:$i]:
% 5.35/1.26 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 5.35/1.26 ( in @ ( powerset @ X6 ) @ ( powerset @ ( powerset @ X4 ) ) ) ) )),
% 5.35/1.26 define([status(thm)])).
% 5.35/1.26 thf(singletoninpowerset, axiom, singletoninpowerset =
% 5.35/1.26 (![A:$i,Xx:$i]:
% 5.35/1.26 ( ( in @ Xx @ A ) =>
% 5.35/1.26 ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) ))).
% 5.35/1.26 thf('14', plain,
% 5.35/1.26 (( singletoninpowerset ) =
% 5.35/1.26 ( ![X4:$i,X6:$i]:
% 5.35/1.26 ( ( in @ X6 @ X4 ) =>
% 5.35/1.26 ( in @ ( setadjoin @ X6 @ emptyset ) @ ( powerset @ X4 ) ) ) )),
% 5.35/1.26 define([status(thm)])).
% 5.35/1.26 thf(setminusSubset1, axiom, setminusSubset1 =
% 5.35/1.26 (![A:$i,B:$i]:
% 5.35/1.26 ( ( ( setminus @ A @ B ) = ( emptyset ) ) => ( subset @ A @ B ) ))).
% 5.35/1.26 thf('15', plain,
% 5.35/1.26 (( setminusSubset1 ) =
% 5.35/1.26 ( ![X4:$i,X6:$i]:
% 5.35/1.26 ( ( ( setminus @ X4 @ X6 ) = ( emptyset ) ) => ( subset @ X4 @ X6 ) ) )),
% 5.35/1.26 define([status(thm)])).
% 5.35/1.26 thf(setminusLsub, axiom, setminusLsub =
% 5.35/1.26 (![A:$i,B:$i]: ( subset @ ( setminus @ A @ B ) @ A ))).
% 5.35/1.26 thf('16', plain,
% 5.35/1.26 (( setminusLsub ) =
% 5.35/1.26 ( ![X4:$i,X6:$i]: ( subset @ ( setminus @ X4 @ X6 ) @ X4 ) )),
% 5.35/1.26 define([status(thm)])).
% 5.35/1.26 thf(setminusIRneg, axiom, setminusIRneg =
% 5.35/1.26 (![A:$i,B:$i,Xx:$i]:
% 5.35/1.26 ( ( in @ Xx @ B ) => ( ~( in @ Xx @ ( setminus @ A @ B ) ) ) ))).
% 5.35/1.26 thf('17', plain,
% 5.35/1.26 (( setminusIRneg ) =
% 5.35/1.26 ( ![X4:$i,X6:$i,X8:$i]:
% 5.35/1.26 ( ( in @ X8 @ X6 ) => ( ~( in @ X8 @ ( setminus @ X4 @ X6 ) ) ) ) )),
% 5.35/1.26 define([status(thm)])).
% 5.35/1.26 thf(setminusILneg, axiom, setminusILneg =
% 5.35/1.26 (![A:$i,B:$i,Xx:$i]:
% 5.35/1.26 ( ( ~( in @ Xx @ A ) ) => ( ~( in @ Xx @ ( setminus @ A @ B ) ) ) ))).
% 5.35/1.26 thf('18', plain,
% 5.35/1.26 (( setminusILneg ) =
% 5.35/1.26 ( ![X4:$i,X6:$i,X8:$i]:
% 5.35/1.26 ( ( ~( in @ X8 @ X4 ) ) => ( ~( in @ X8 @ ( setminus @ X4 @ X6 ) ) ) ) )),
% 5.35/1.26 define([status(thm)])).
% 5.35/1.26 thf(setminusELneg, axiom, setminusELneg =
% 5.35/1.26 (![A:$i,B:$i,Xx:$i]:
% 5.35/1.26 ( ( ~( in @ Xx @ ( setminus @ A @ B ) ) ) =>
% 5.35/1.26 ( ( ~( in @ Xx @ B ) ) => ( ~( in @ Xx @ A ) ) ) ))).
% 5.35/1.26 thf('19', plain,
% 5.35/1.26 (( setminusELneg ) =
% 5.35/1.26 ( ![X4:$i,X6:$i,X8:$i]:
% 5.35/1.26 ( ( ~( in @ X8 @ ( setminus @ X4 @ X6 ) ) ) =>
% 5.35/1.26 ( ( ~( in @ X8 @ X6 ) ) => ( ~( in @ X8 @ X4 ) ) ) ) )),
% 5.35/1.26 define([status(thm)])).
% 5.35/1.26 thf(setminusERneg, axiom, setminusERneg =
% 5.35/1.26 (![A:$i,B:$i,Xx:$i]:
% 5.35/1.26 ( ( ~( in @ Xx @ ( setminus @ A @ B ) ) ) =>
% 5.35/1.26 ( ( in @ Xx @ A ) => ( in @ Xx @ B ) ) ))).
% 5.35/1.26 thf('20', plain,
% 5.35/1.26 (( setminusERneg ) =
% 5.35/1.26 ( ![X4:$i,X6:$i,X8:$i]:
% 5.35/1.26 ( ( ~( in @ X8 @ ( setminus @ X4 @ X6 ) ) ) =>
% 5.35/1.26 ( ( in @ X8 @ X4 ) => ( in @ X8 @ X6 ) ) ) )),
% 5.35/1.26 define([status(thm)])).
% 5.35/1.26 thf(setminusSubset2, axiom, setminusSubset2 =
% 5.35/1.26 (![A:$i,B:$i]:
% 5.35/1.26 ( ( subset @ A @ B ) => ( ( setminus @ A @ B ) = ( emptyset ) ) ))).
% 5.35/1.26 thf('21', plain,
% 5.35/1.26 (( setminusSubset2 ) =
% 5.35/1.26 ( ![X4:$i,X6:$i]:
% 5.35/1.26 ( ( subset @ X4 @ X6 ) => ( ( setminus @ X4 @ X6 ) = ( emptyset ) ) ) )),
% 5.35/1.26 define([status(thm)])).
% 5.35/1.26 thf(setminusER, axiom, setminusER =
% 5.35/1.26 (![A:$i,B:$i,Xx:$i]:
% 5.35/1.26 ( ( in @ Xx @ ( setminus @ A @ B ) ) => ( ~( in @ Xx @ B ) ) ))).
% 5.35/1.26 thf('22', plain,
% 5.35/1.26 (( setminusER ) =
% 5.35/1.26 ( ![X4:$i,X6:$i,X8:$i]:
% 5.35/1.26 ( ( in @ X8 @ ( setminus @ X4 @ X6 ) ) => ( ~( in @ X8 @ X6 ) ) ) )),
% 5.35/1.26 define([status(thm)])).
% 5.35/1.26 thf(setminusEL, axiom, setminusEL =
% 5.35/1.26 (![A:$i,B:$i,Xx:$i]:
% 5.35/1.26 ( ( in @ Xx @ ( setminus @ A @ B ) ) => ( in @ Xx @ A ) ))).
% 5.35/1.26 thf('23', plain,
% 5.35/1.26 (( setminusEL ) =
% 5.35/1.26 ( ![X4:$i,X6:$i,X8:$i]:
% 5.35/1.26 ( ( in @ X8 @ ( setminus @ X4 @ X6 ) ) => ( in @ X8 @ X4 ) ) )),
% 5.35/1.26 define([status(thm)])).
% 5.35/1.26 thf(setminusI, axiom, setminusI =
% 5.35/1.26 (![A:$i,B:$i,Xx:$i]:
% 5.35/1.26 ( ( in @ Xx @ A ) =>
% 5.35/1.26 ( ( ~( in @ Xx @ B ) ) => ( in @ Xx @ ( setminus @ A @ B ) ) ) ))).
% 5.35/1.26 thf('24', plain,
% 5.35/1.26 (( setminusI ) =
% 5.35/1.26 ( ![X4:$i,X6:$i,X8:$i]:
% 5.35/1.26 ( ( in @ X8 @ X4 ) =>
% 5.35/1.26 ( ( ~( in @ X8 @ X6 ) ) => ( in @ X8 @ ( setminus @ X4 @ X6 ) ) ) ) )),
% 5.35/1.26 define([status(thm)])).
% 5.35/1.26 thf(powersetsubset, axiom, powersetsubset =
% 5.35/1.26 (![A:$i,B:$i]:
% 5.35/1.26 ( ( subset @ A @ B ) => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ))).
% 5.35/1.26 thf('25', plain,
% 5.35/1.26 (( powersetsubset ) =
% 5.35/1.26 ( ![X4:$i,X6:$i]:
% 5.35/1.26 ( ( subset @ X4 @ X6 ) =>
% 5.35/1.26 ( subset @ ( powerset @ X4 ) @ ( powerset @ X6 ) ) ) )),
% 5.35/1.26 define([status(thm)])).
% 5.35/1.26 thf(inPowerset, axiom, inPowerset = (![A:$i]: ( in @ A @ ( powerset @ A ) ))).
% 5.35/1.26 thf('26', plain,
% 5.35/1.26 (( inPowerset ) = ( ![X4:$i]: ( in @ X4 @ ( powerset @ X4 ) ) )),
% 5.35/1.26 define([status(thm)])).
% 5.35/1.26 thf(powersetE1, axiom, powersetE1 =
% 5.35/1.26 (![A:$i,B:$i]: ( ( in @ B @ ( powerset @ A ) ) => ( subset @ B @ A ) ))).
% 5.35/1.26 thf('27', plain,
% 5.35/1.26 (( powersetE1 ) =
% 5.35/1.26 ( ![X4:$i,X6:$i]:
% 5.35/1.26 ( ( in @ X6 @ ( powerset @ X4 ) ) => ( subset @ X6 @ X4 ) ) )),
% 5.35/1.26 define([status(thm)])).
% 5.35/1.26 thf(powersetI1, axiom, powersetI1 =
% 5.35/1.26 (![A:$i,B:$i]: ( ( subset @ B @ A ) => ( in @ B @ ( powerset @ A ) ) ))).
% 5.35/1.26 thf('28', plain,
% 5.35/1.26 (( powersetI1 ) =
% 5.35/1.26 ( ![X4:$i,X6:$i]:
% 5.35/1.26 ( ( subset @ X6 @ X4 ) => ( in @ X6 @ ( powerset @ X4 ) ) ) )),
% 5.35/1.26 define([status(thm)])).
% 5.35/1.26 thf(subset2powerset, axiom, subset2powerset =
% 5.35/1.26 (![A:$i,B:$i]: ( ( subset @ A @ B ) => ( in @ A @ ( powerset @ B ) ) ))).
% 5.35/1.26 thf('29', plain,
% 5.35/1.26 (( subset2powerset ) =
% 5.35/1.26 ( ![X4:$i,X6:$i]:
% 5.35/1.26 ( ( subset @ X4 @ X6 ) => ( in @ X4 @ ( powerset @ X6 ) ) ) )),
% 5.35/1.26 define([status(thm)])).
% 5.35/1.26 thf(powerset__Cong, axiom, powerset__Cong =
% 5.35/1.26 (![A:$i,B:$i]:
% 5.35/1.26 ( ( ( A ) = ( B ) ) => ( ( powerset @ A ) = ( powerset @ B ) ) ))).
% 5.35/1.26 thf('30', plain,
% 5.35/1.26 (( powerset__Cong ) =
% 5.35/1.26 ( ![X4:$i,X6:$i]:
% 5.35/1.26 ( ( ( X4 ) = ( X6 ) ) => ( ( powerset @ X4 ) = ( powerset @ X6 ) ) ) )),
% 5.35/1.26 define([status(thm)])).
% 5.35/1.26 thf(powersetE, axiom, powersetE =
% 5.35/1.26 (![A:$i,B:$i,Xx:$i]:
% 5.35/1.26 ( ( in @ B @ ( powerset @ A ) ) => ( ( in @ Xx @ B ) => ( in @ Xx @ A ) ) ))).
% 5.35/1.26 thf('31', plain,
% 5.35/1.26 (( powersetE ) =
% 5.35/1.26 ( ![X4:$i,X6:$i,X8:$i]:
% 5.35/1.26 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 5.35/1.26 ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ) )),
% 5.35/1.26 define([status(thm)])).
% 5.35/1.26 thf(emptyInPowerset, axiom, emptyInPowerset =
% 5.35/1.26 (![A:$i]: ( in @ emptyset @ ( powerset @ A ) ))).
% 5.35/1.26 thf('32', plain,
% 5.35/1.26 (( emptyInPowerset ) =
% 5.35/1.26 ( ![X4:$i]: ( in @ emptyset @ ( powerset @ X4 ) ) )),
% 5.35/1.26 define([status(thm)])).
% 5.35/1.26 thf(emptyinPowerset, axiom, emptyinPowerset =
% 5.35/1.26 (![A:$i]: ( in @ emptyset @ ( powerset @ A ) ))).
% 5.35/1.26 thf('33', plain,
% 5.35/1.26 (( emptyinPowerset ) =
% 5.35/1.26 ( ![X4:$i]: ( in @ emptyset @ ( powerset @ X4 ) ) )),
% 5.35/1.26 define([status(thm)])).
% 5.35/1.26 thf(powersetI, axiom, powersetI =
% 5.35/1.26 (![A:$i,B:$i]:
% 5.35/1.26 ( ( ![Xx:$i]: ( ( in @ Xx @ B ) => ( in @ Xx @ A ) ) ) =>
% 5.35/1.26 ( in @ B @ ( powerset @ A ) ) ))).
% 5.35/1.26 thf('34', plain,
% 5.35/1.26 (( powersetI ) =
% 5.35/1.26 ( ![X4:$i,X6:$i]:
% 5.35/1.26 ( ( ![X8:$i]: ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ) =>
% 5.35/1.26 ( in @ X6 @ ( powerset @ X4 ) ) ) )),
% 5.35/1.26 define([status(thm)])).
% 5.35/1.26 thf(powersetAx, axiom, powersetAx =
% 5.35/1.26 (![A:$i,B:$i]:
% 5.35/1.26 ( ( in @ B @ ( powerset @ A ) ) <=>
% 5.35/1.26 ( ![Xx:$i]: ( ( in @ Xx @ B ) => ( in @ Xx @ A ) ) ) ))).
% 5.35/1.26 thf('35', plain,
% 5.35/1.26 (( powersetAx ) =
% 5.35/1.26 ( ![X4:$i,X6:$i]:
% 5.35/1.26 ( ( in @ X6 @ ( powerset @ X4 ) ) <=>
% 5.35/1.26 ( ![X8:$i]: ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ) ) )),
% 5.35/1.26 define([status(thm)])).
% 5.35/1.26 thf(doubleComplementE1, conjecture,
% 5.35/1.26 (( setextAx ) =>
% 5.35/1.26 ( ( emptysetAx ) =>
% 5.35/1.26 ( ( setadjoinAx ) =>
% 5.35/1.26 ( ( powersetAx ) =>
% 5.35/1.26 ( ( setunionAx ) =>
% 5.35/1.26 ( ( omega0Ax ) =>
% 5.35/1.26 ( ( omegaSAx ) =>
% 5.35/1.26 ( ( omegaIndAx ) =>
% 5.35/1.26 ( ( replAx ) =>
% 5.35/1.26 ( ( foundationAx ) =>
% 5.35/1.26 ( ( wellorderingAx ) =>
% 5.35/1.26 ( ( descrp ) =>
% 5.35/1.26 ( ( dsetconstrI ) =>
% 5.35/1.26 ( ( dsetconstrEL ) =>
% 5.35/1.26 ( ( dsetconstrER ) =>
% 5.35/1.26 ( ( exuE1 ) =>
% 5.35/1.26 ( ( prop2setE ) =>
% 5.35/1.26 ( ( emptysetE ) =>
% 5.35/1.26 ( ( emptysetimpfalse ) =>
% 5.35/1.26 ( ( notinemptyset ) =>
% 5.35/1.26 ( ( exuE3e ) =>
% 5.35/1.26 ( ( setext ) =>
% 5.35/1.26 ( ( emptyI ) =>
% 5.35/1.26 ( ( noeltsimpempty ) =>
% 5.35/1.26 ( ( setbeta ) =>
% 5.35/1.26 ( ( nonemptyE1 ) =>
% 5.35/1.26 ( ( nonemptyI ) =>
% 5.35/1.26 ( ( nonemptyI1 ) =>
% 5.35/1.26 ( ( setadjoinIL ) =>
% 5.35/1.26 ( ( emptyinunitempty ) =>
% 5.35/1.26 ( ( setadjoinIR ) =>
% 5.35/1.26 ( ( setadjoinE ) =>
% 5.35/1.26 ( (
% 5.35/1.26 setadjoinOr ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 setoftrueEq ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 powersetI ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 emptyinPowerset ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 emptyInPowerset ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 powersetE ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 setunionI ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 setunionE ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 subPowSU ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 exuE2 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 nonemptyImpWitness ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 uniqinunit ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 notinsingleton ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 eqinunit ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 singletonsswitch ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 upairsetE ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 upairsetIL ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 upairsetIR ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 emptyE1 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 vacuousDall ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 quantDeMorgan1 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 quantDeMorgan2 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 quantDeMorgan3 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 quantDeMorgan4 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 prop2setI ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 prop2set2propI ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 notdexE ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 notdallE ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 exuI1 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 exuI3 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 exuI2 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 inCongP ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 in__Cong ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 exuE3u ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 exu__Cong ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 emptyset__Cong ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 setadjoin__Cong ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 powerset__Cong ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 setunion__Cong ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 omega__Cong ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 exuEu ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 descr__Cong ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 dsetconstr__Cong ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 subsetI1 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 eqimpsubset2 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 eqimpsubset1 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 subsetI2 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 emptysetsubset ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 subsetE ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 subsetE2 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 notsubsetI ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 notequalI1 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 notequalI2 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 subsetRefl ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 subsetTrans ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 setadjoinSub ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 setadjoinSub2 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 subset2powerset ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 setextsub ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 subsetemptysetimpeq ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 powersetI1 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 powersetE1 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 inPowerset ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 powersetsubset ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 sepInPowerset ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 sepSubset ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 binunionIL ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 upairset2IR ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 binunionIR ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 binunionEcases ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 binunionE ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 binunionLsub ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 binunionRsub ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 binintersectI ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 binintersectSubset5 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 binintersectEL ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 binintersectLsub ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 binintersectSubset2 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 binintersectSubset3 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 binintersectER ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 disjointsetsI1 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 binintersectRsub ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 binintersectSubset4 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 binintersectSubset1 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 bs114d ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 setminusI ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 setminusEL ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 setminusER ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 setminusSubset2 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 setminusERneg ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 setminusELneg ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 setminusILneg ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 setminusIRneg ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 setminusLsub ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 setminusSubset1 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 symdiffE ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 symdiffI1 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 symdiffI2 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 symdiffIneg1 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 symdiffIneg2 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 secondinupair ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 setukpairIL ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 setukpairIR ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 kpairiskpair ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 kpairp ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 singletonsubset ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 singletoninpowerset ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 singletoninpowunion ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 upairset2E ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 upairsubunion ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 upairinpowunion ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 ubforcartprodlem1 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 ubforcartprodlem2 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 ubforcartprodlem3 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 cartprodpairin ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 cartprodmempair1 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 cartprodmempair ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 setunionE2 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 setunionsingleton1 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 setunionsingleton2 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 setunionsingleton ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 singletonprop ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 ex1E1 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 ex1I ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 ex1I2 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 singletonsuniq ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 setukpairinjL1 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 kfstsingleton ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 theprop ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 kfstpairEq ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 cartprodfstin ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 setukpairinjL2 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 setukpairinjL ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 setukpairinjR11 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 setukpairinjR12 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 setukpairinjR1 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 upairequniteq ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 setukpairinjR2 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 setukpairinjR ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 ksndsingleton ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 ksndpairEq ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 kpairsurjEq ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 cartprodsndin ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 cartprodpairmemEL ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 cartprodpairmemER ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 cartprodmempaircEq ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 cartprodfstpairEq ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 cartprodsndpairEq ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 cartprodpairsurjEq ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 dpsetconstrI ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 dpsetconstrSub ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 setOfPairsIsBReln ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 dpsetconstrERa ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 dpsetconstrEL1 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 dpsetconstrEL2 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 dpsetconstrER ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 funcImageSingleton ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 apProp ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 app ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 infuncsetfunc ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 ap2p ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 funcinfuncset ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 lamProp ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 lamp ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 lam2p ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 brelnall1 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 brelnall2 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 ex1E2 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 funcGraphProp1 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 funcGraphProp3 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 funcGraphProp2 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 funcextLem ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 funcGraphProp4 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 subbreln ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 eqbreln ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 funcext ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 funcext2 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 ap2apEq1 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 ap2apEq2 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 beta1 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 eta1 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 lam2lamEq ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 beta2 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 eta2 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 iffalseProp1 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 iffalseProp2 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 iftrueProp1 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 iftrueProp2 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 ifSingleton ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 ifp ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 theeq ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 iftrue ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 iffalse ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 iftrueorfalse ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 binintersectT_lem ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 binunionT_lem ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 powersetT_lem ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 setminusT_lem ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 complementT_lem ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 setextT ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 subsetTI ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 powersetTI1 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 powersetTE1 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 complementTI1 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 complementTE1 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 binintersectTELcontra ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 binintersectTERcontra ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 contrasubsetT ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 contrasubsetT1 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 contrasubsetT2 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 contrasubsetT3 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 doubleComplementI1 ) =>
% 5.35/1.26 (
% 5.35/1.26 ![
% 5.35/1.26 A:$i,X:$i]:
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 in @
% 5.35/1.26 X @
% 5.35/1.26 (
% 5.35/1.26 powerset @
% 5.35/1.26 A ) ) =>
% 5.35/1.26 (
% 5.35/1.26 ![
% 5.35/1.26 Xx:$i]:
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 in @
% 5.35/1.26 Xx @ A ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 in @
% 5.35/1.26 Xx @
% 5.35/1.26 (
% 5.35/1.26 setminus @
% 5.35/1.26 A @
% 5.35/1.26 (
% 5.35/1.26 setminus @
% 5.35/1.26 A @ X ) ) ) =>
% 5.35/1.26 (
% 5.35/1.26 in @
% 5.35/1.26 Xx @ X ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 5.35/1.26 thf(zf_stmt_0, conjecture,
% 5.35/1.26 (( setextAx ) =>
% 5.35/1.26 ( ( emptysetAx ) =>
% 5.35/1.26 ( ( setadjoinAx ) =>
% 5.35/1.26 ( ( ![X4:$i,X6:$i]:
% 5.35/1.26 ( ( in @ X6 @ ( powerset @ X4 ) ) <=>
% 5.35/1.26 ( ![X8:$i]: ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ) ) ) =>
% 5.35/1.26 ( ( setunionAx ) =>
% 5.35/1.26 ( ( omega0Ax ) =>
% 5.35/1.26 ( ( omegaSAx ) =>
% 5.35/1.26 ( ( omegaIndAx ) =>
% 5.35/1.26 ( ( replAx ) =>
% 5.35/1.26 ( ( foundationAx ) =>
% 5.35/1.26 ( ( wellorderingAx ) =>
% 5.35/1.26 ( ( descrp ) =>
% 5.35/1.26 ( ( dsetconstrI ) =>
% 5.35/1.26 ( ( dsetconstrEL ) =>
% 5.35/1.26 ( ( dsetconstrER ) =>
% 5.35/1.26 ( ( exuE1 ) =>
% 5.35/1.26 ( ( prop2setE ) =>
% 5.35/1.26 ( ( emptysetE ) =>
% 5.35/1.26 ( ( emptysetimpfalse ) =>
% 5.35/1.26 ( ( notinemptyset ) =>
% 5.35/1.26 ( ( exuE3e ) =>
% 5.35/1.26 ( ( setext ) =>
% 5.35/1.26 ( ( emptyI ) =>
% 5.35/1.26 ( ( noeltsimpempty ) =>
% 5.35/1.26 ( ( setbeta ) =>
% 5.35/1.26 ( ( nonemptyE1 ) =>
% 5.35/1.26 ( ( nonemptyI ) =>
% 5.35/1.26 ( ( nonemptyI1 ) =>
% 5.35/1.26 ( ( setadjoinIL ) =>
% 5.35/1.26 ( ( emptyinunitempty ) =>
% 5.35/1.26 ( ( setadjoinIR ) =>
% 5.35/1.26 ( ( setadjoinE ) =>
% 5.35/1.26 ( (
% 5.35/1.26 setadjoinOr ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 setoftrueEq ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 ![
% 5.35/1.26 X10:$i,
% 5.35/1.26 X12:$i]:
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 ![
% 5.35/1.26 X14:$i]:
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 in @
% 5.35/1.26 X14 @ X12 ) =>
% 5.35/1.26 (
% 5.35/1.26 in @
% 5.35/1.26 X14 @ X10 ) ) ) =>
% 5.35/1.26 (
% 5.35/1.26 in @
% 5.35/1.26 X12 @
% 5.35/1.26 (
% 5.35/1.26 powerset @
% 5.35/1.26 X10 ) ) ) ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 ![
% 5.35/1.26 X16:$i]:
% 5.35/1.26 (
% 5.35/1.26 in @
% 5.35/1.26 emptyset @
% 5.35/1.26 (
% 5.35/1.26 powerset @
% 5.35/1.26 X16 ) ) ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 ![
% 5.35/1.26 X18:$i]:
% 5.35/1.26 (
% 5.35/1.26 in @
% 5.35/1.26 emptyset @
% 5.35/1.26 (
% 5.35/1.26 powerset @
% 5.35/1.26 X18 ) ) ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 ![
% 5.35/1.26 X20:$i,
% 5.35/1.26 X22:$i,
% 5.35/1.26 X24:$i]:
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 in @
% 5.35/1.26 X22 @
% 5.35/1.26 (
% 5.35/1.26 powerset @
% 5.35/1.26 X20 ) ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 in @
% 5.35/1.26 X24 @ X22 ) =>
% 5.35/1.26 (
% 5.35/1.26 in @
% 5.35/1.26 X24 @ X20 ) ) ) ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 setunionI ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 setunionE ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 subPowSU ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 exuE2 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 nonemptyImpWitness ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 uniqinunit ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 notinsingleton ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 eqinunit ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 singletonsswitch ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 upairsetE ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 upairsetIL ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 upairsetIR ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 emptyE1 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 vacuousDall ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 quantDeMorgan1 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 quantDeMorgan2 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 quantDeMorgan3 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 quantDeMorgan4 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 prop2setI ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 prop2set2propI ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 notdexE ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 notdallE ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 exuI1 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 exuI3 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 exuI2 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 inCongP ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 in__Cong ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 exuE3u ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 exu__Cong ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 emptyset__Cong ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 setadjoin__Cong ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 ![
% 5.35/1.26 X26:$i,
% 5.35/1.26 X28:$i]:
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 X26 ) =
% 5.35/1.26 (
% 5.35/1.26 X28 ) ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 powerset @
% 5.35/1.26 X26 ) =
% 5.35/1.26 (
% 5.35/1.26 powerset @
% 5.35/1.26 X28 ) ) ) ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 setunion__Cong ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 omega__Cong ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 exuEu ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 descr__Cong ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 dsetconstr__Cong ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 subsetI1 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 eqimpsubset2 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 eqimpsubset1 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 subsetI2 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 emptysetsubset ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 subsetE ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 subsetE2 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 notsubsetI ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 notequalI1 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 notequalI2 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 subsetRefl ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 subsetTrans ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 setadjoinSub ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 setadjoinSub2 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 ![
% 5.35/1.26 X30:$i,
% 5.35/1.26 X32:$i]:
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 subset @
% 5.35/1.26 X30 @ X32 ) =>
% 5.35/1.26 (
% 5.35/1.26 in @
% 5.35/1.26 X30 @
% 5.35/1.26 (
% 5.35/1.26 powerset @
% 5.35/1.26 X32 ) ) ) ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 setextsub ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 subsetemptysetimpeq ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 ![
% 5.35/1.26 X34:$i,
% 5.35/1.26 X36:$i]:
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 subset @
% 5.35/1.26 X36 @ X34 ) =>
% 5.35/1.26 (
% 5.35/1.26 in @
% 5.35/1.26 X36 @
% 5.35/1.26 (
% 5.35/1.26 powerset @
% 5.35/1.26 X34 ) ) ) ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 ![
% 5.35/1.26 X38:$i,
% 5.35/1.26 X40:$i]:
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 in @
% 5.35/1.26 X40 @
% 5.35/1.26 (
% 5.35/1.26 powerset @
% 5.35/1.26 X38 ) ) =>
% 5.35/1.26 (
% 5.35/1.26 subset @
% 5.35/1.26 X40 @ X38 ) ) ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 ![
% 5.35/1.26 X42:$i]:
% 5.35/1.26 (
% 5.35/1.26 in @
% 5.35/1.26 X42 @
% 5.35/1.26 (
% 5.35/1.26 powerset @
% 5.35/1.26 X42 ) ) ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 ![
% 5.35/1.26 X44:$i,
% 5.35/1.26 X46:$i]:
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 subset @
% 5.35/1.26 X44 @ X46 ) =>
% 5.35/1.26 (
% 5.35/1.26 subset @
% 5.35/1.26 (
% 5.35/1.26 powerset @
% 5.35/1.26 X44 ) @
% 5.35/1.26 (
% 5.35/1.26 powerset @
% 5.35/1.26 X46 ) ) ) ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 sepInPowerset ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 sepSubset ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 binunionIL ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 upairset2IR ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 binunionIR ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 binunionEcases ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 binunionE ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 binunionLsub ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 binunionRsub ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 binintersectI ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 binintersectSubset5 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 binintersectEL ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 binintersectLsub ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 binintersectSubset2 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 binintersectSubset3 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 binintersectER ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 disjointsetsI1 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 binintersectRsub ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 binintersectSubset4 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 binintersectSubset1 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 bs114d ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 ![
% 5.35/1.26 X48:$i,
% 5.35/1.26 X50:$i,
% 5.35/1.26 X52:$i]:
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 in @
% 5.35/1.26 X52 @ X48 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 ~(
% 5.35/1.26 in @
% 5.35/1.26 X52 @ X50 ) ) =>
% 5.35/1.26 (
% 5.35/1.26 in @
% 5.35/1.26 X52 @
% 5.35/1.26 (
% 5.35/1.26 setminus @
% 5.35/1.26 X48 @ X50 ) ) ) ) ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 ![
% 5.35/1.26 X54:$i,
% 5.35/1.26 X56:$i,
% 5.35/1.26 X58:$i]:
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 in @
% 5.35/1.26 X58 @
% 5.35/1.26 (
% 5.35/1.26 setminus @
% 5.35/1.26 X54 @ X56 ) ) =>
% 5.35/1.26 (
% 5.35/1.26 in @
% 5.35/1.26 X58 @ X54 ) ) ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 ![
% 5.35/1.26 X60:$i,
% 5.35/1.26 X62:$i,
% 5.35/1.26 X64:$i]:
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 in @
% 5.35/1.26 X64 @
% 5.35/1.26 (
% 5.35/1.26 setminus @
% 5.35/1.26 X60 @ X62 ) ) =>
% 5.35/1.26 (
% 5.35/1.26 ~(
% 5.35/1.26 in @
% 5.35/1.26 X64 @ X62 ) ) ) ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 ![
% 5.35/1.26 X66:$i,
% 5.35/1.26 X68:$i]:
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 subset @
% 5.35/1.26 X66 @ X68 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 setminus @
% 5.35/1.26 X66 @ X68 ) =
% 5.35/1.26 (
% 5.35/1.26 emptyset ) ) ) ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 ![
% 5.35/1.26 X70:$i,
% 5.35/1.26 X72:$i,
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% 5.35/1.26 (
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% 5.35/1.26 ~(
% 5.35/1.26 in @
% 5.35/1.26 X74 @
% 5.35/1.26 (
% 5.35/1.26 setminus
% 5.35/1.26 @
% 5.35/1.26 X70 @ X72 ) ) ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 in @
% 5.35/1.26 X74 @ X70 ) =>
% 5.35/1.26 (
% 5.35/1.26 in @
% 5.35/1.26 X74 @ X72 ) ) ) ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 ![
% 5.35/1.26 X76:$i,
% 5.35/1.26 X78:$i,
% 5.35/1.26 X80:$i]:
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 ~(
% 5.35/1.26 in @
% 5.35/1.26 X80 @
% 5.35/1.26 (
% 5.35/1.26 setminus
% 5.35/1.26 @
% 5.35/1.26 X76 @ X78 ) ) ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 ~(
% 5.35/1.26 in @
% 5.35/1.26 X80 @ X78 ) ) =>
% 5.35/1.26 (
% 5.35/1.26 ~(
% 5.35/1.26 in @
% 5.35/1.26 X80 @ X76 ) ) ) ) ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 ![
% 5.35/1.26 X82:$i,
% 5.35/1.26 X84:$i,
% 5.35/1.26 X86:$i]:
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 ~(
% 5.35/1.26 in @
% 5.35/1.26 X86 @ X82 ) ) =>
% 5.35/1.26 (
% 5.35/1.26 ~(
% 5.35/1.26 in @
% 5.35/1.26 X86 @
% 5.35/1.26 (
% 5.35/1.26 setminus
% 5.35/1.26 @
% 5.35/1.26 X82 @ X84 ) ) ) ) ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 ![
% 5.35/1.26 X88:$i,
% 5.35/1.26 X90:$i,
% 5.35/1.26 X92:$i]:
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 in @
% 5.35/1.26 X92 @ X90 ) =>
% 5.35/1.26 (
% 5.35/1.26 ~(
% 5.35/1.26 in @
% 5.35/1.26 X92 @
% 5.35/1.26 (
% 5.35/1.26 setminus
% 5.35/1.26 @
% 5.35/1.26 X88 @ X90 ) ) ) ) ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 ![
% 5.35/1.26 X94:$i,
% 5.35/1.26 X96:$i]:
% 5.35/1.26 (
% 5.35/1.26 subset @
% 5.35/1.26 (
% 5.35/1.26 setminus @
% 5.35/1.26 X94 @ X96 ) @
% 5.35/1.26 X94 ) ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 ![
% 5.35/1.26 X98:$i,
% 5.35/1.26 X100:$i]:
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 setminus @
% 5.35/1.26 X98 @ X100 ) =
% 5.35/1.26 (
% 5.35/1.26 emptyset ) ) =>
% 5.35/1.26 (
% 5.35/1.26 subset @
% 5.35/1.26 X98 @ X100 ) ) ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 symdiffE ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 symdiffI1 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 symdiffI2 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 symdiffIneg1 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 symdiffIneg2 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 secondinupair ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 setukpairIL ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 setukpairIR ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 kpairiskpair ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 kpairp ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 singletonsubset ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 ![
% 5.35/1.26 X102:$i,
% 5.35/1.26 X104:$i]:
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 in @
% 5.35/1.26 X104 @
% 5.35/1.26 X102 ) =>
% 5.35/1.26 (
% 5.35/1.26 in @
% 5.35/1.26 (
% 5.35/1.26 setadjoin
% 5.35/1.26 @
% 5.35/1.26 X104 @
% 5.35/1.26 emptyset ) @
% 5.35/1.26 (
% 5.35/1.26 powerset @
% 5.35/1.26 X102 ) ) ) ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 singletoninpowunion ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 upairset2E ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 upairsubunion ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 upairinpowunion ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 ubforcartprodlem1 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 ubforcartprodlem2 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 ubforcartprodlem3 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 cartprodpairin ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 cartprodmempair1 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 cartprodmempair ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 setunionE2 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 setunionsingleton1 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 setunionsingleton2 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 setunionsingleton ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 singletonprop ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 ex1E1 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 ex1I ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 ex1I2 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 singletonsuniq ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 setukpairinjL1 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 kfstsingleton ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 theprop ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 kfstpairEq ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 cartprodfstin ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 setukpairinjL2 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 setukpairinjL ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 setukpairinjR11 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 setukpairinjR12 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 setukpairinjR1 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 upairequniteq ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 setukpairinjR2 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 setukpairinjR ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 ksndsingleton ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 ksndpairEq ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 kpairsurjEq ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 cartprodsndin ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 cartprodpairmemEL ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 cartprodpairmemER ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 cartprodmempaircEq ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 cartprodfstpairEq ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 cartprodsndpairEq ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 cartprodpairsurjEq ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 dpsetconstrI ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 dpsetconstrSub ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 setOfPairsIsBReln ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 dpsetconstrERa ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 dpsetconstrEL1 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 dpsetconstrEL2 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 dpsetconstrER ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 funcImageSingleton ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 apProp ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 app ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 infuncsetfunc ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 ap2p ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 funcinfuncset ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 lamProp ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 lamp ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 lam2p ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 brelnall1 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 brelnall2 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 ex1E2 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 funcGraphProp1 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 funcGraphProp3 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 funcGraphProp2 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 funcextLem ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 funcGraphProp4 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 subbreln ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 eqbreln ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 funcext ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 funcext2 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 ap2apEq1 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 ap2apEq2 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 beta1 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 eta1 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 lam2lamEq ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 beta2 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 eta2 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 iffalseProp1 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 iffalseProp2 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 iftrueProp1 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 iftrueProp2 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 ifSingleton ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 ifp ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 theeq ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 iftrue ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 iffalse ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 iftrueorfalse ) =>
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% 5.35/1.26 (
% 5.35/1.26 binintersectT_lem ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 binunionT_lem ) =>
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% 5.35/1.26 (
% 5.35/1.26 ![
% 5.35/1.26 X106:$i,
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% 5.35/1.26 (
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% 5.35/1.26 X108 @
% 5.35/1.26 (
% 5.35/1.26 powerset @
% 5.35/1.26 X106 ) ) =>
% 5.35/1.26 (
% 5.35/1.26 in @
% 5.35/1.26 (
% 5.35/1.26 powerset @
% 5.35/1.26 X108 ) @
% 5.35/1.26 (
% 5.35/1.26 powerset @
% 5.35/1.26 (
% 5.35/1.26 powerset @
% 5.35/1.26 X106 ) ) ) ) ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 ![
% 5.35/1.26 X110:$i,
% 5.35/1.26 X112:$i]:
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 in @
% 5.35/1.26 X112 @
% 5.35/1.26 (
% 5.35/1.26 powerset @
% 5.35/1.26 X110 ) ) =>
% 5.35/1.26 (
% 5.35/1.26 ![
% 5.35/1.26 X114:$i]:
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 in @
% 5.35/1.26 X114 @
% 5.35/1.26 (
% 5.35/1.26 powerset @
% 5.35/1.26 X110 ) ) =>
% 5.35/1.26 (
% 5.35/1.26 in @
% 5.35/1.26 (
% 5.35/1.26 setminus @
% 5.35/1.26 X112 @
% 5.35/1.26 X114 ) @
% 5.35/1.26 (
% 5.35/1.26 powerset @
% 5.35/1.26 X110 ) ) ) ) ) ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 ![
% 5.35/1.26 X116:$i,
% 5.35/1.26 X118:$i]:
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 in @
% 5.35/1.26 X118 @
% 5.35/1.26 (
% 5.35/1.26 powerset @
% 5.35/1.26 X116 ) ) =>
% 5.35/1.26 (
% 5.35/1.26 in @
% 5.35/1.26 (
% 5.35/1.26 setminus @
% 5.35/1.26 X116 @
% 5.35/1.26 X118 ) @
% 5.35/1.26 (
% 5.35/1.26 powerset @
% 5.35/1.26 X116 ) ) ) ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 ![
% 5.35/1.26 X120:$i,
% 5.35/1.26 X122:$i]:
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% 5.35/1.26 (
% 5.35/1.26 in @
% 5.35/1.26 X122 @
% 5.35/1.26 (
% 5.35/1.26 powerset @
% 5.35/1.26 X120 ) ) =>
% 5.35/1.26 (
% 5.35/1.26 ![
% 5.35/1.26 X124:$i]:
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 in @
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% 5.35/1.26 (
% 5.35/1.26 powerset @
% 5.35/1.26 X120 ) ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 ![
% 5.35/1.26 X126:$i]:
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 in @
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% 5.35/1.26 (
% 5.35/1.26 (
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% 5.35/1.26 (
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% 5.35/1.26 ![
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% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 in @
% 5.35/1.26 X128 @
% 5.35/1.26 X124 ) =>
% 5.35/1.26 (
% 5.35/1.26 in @
% 5.35/1.26 X128 @
% 5.35/1.26 X122 ) ) ) ) =>
% 5.35/1.26 (
% 5.35/1.26 (
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% 5.35/1.26 (
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% 5.35/1.26 ![
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% 5.35/1.26 in @
% 5.35/1.26 X132 @
% 5.35/1.26 (
% 5.35/1.26 powerset @
% 5.35/1.26 X130 ) ) =>
% 5.35/1.26 (
% 5.35/1.26 ![
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% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 in @
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% 5.35/1.26 X130 ) ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 ![
% 5.35/1.26 X136:$i]:
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 in @
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% 5.35/1.26 X130 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 in @
% 5.35/1.26 X136 @
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% 5.35/1.26 X136 @
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% 5.35/1.26 in @
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% 5.35/1.26 (
% 5.35/1.26 ![
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% 5.35/1.26 X138 ) ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 ![
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% 5.35/1.26 (
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% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 ![
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% 5.35/1.26 (
% 5.35/1.26 in @
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% 5.35/1.26 (
% 5.35/1.26 powerset @
% 5.35/1.26 X146 ) ) =>
% 5.35/1.26 (
% 5.35/1.26 ![
% 5.35/1.26 X150:$i]:
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 in @
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% 5.35/1.26 powerset @
% 5.35/1.26 X146 ) ) =>
% 5.35/1.26 (
% 5.35/1.26 ![
% 5.35/1.26 X152:$i]:
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 in @
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% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 in @
% 5.35/1.26 X148 @
% 5.35/1.26 (
% 5.35/1.26 powerset @
% 5.35/1.26 X150 ) ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 in @
% 5.35/1.26 X152 @
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% 5.35/1.26 (
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% 5.35/1.26 (
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% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 in @
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% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 in @
% 5.35/1.26 X158 @
% 5.35/1.26 X156 ) =>
% 5.35/1.26 (
% 5.35/1.26 ~(
% 5.35/1.26 in @
% 5.35/1.26 X158 @
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% 5.35/1.26 (
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% 5.35/1.26 ![
% 5.35/1.26 X160:$i,
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% 5.35/1.26 in @
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% 5.35/1.26 (
% 5.35/1.26 ![
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% 5.35/1.26 (
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% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 ~(
% 5.35/1.26 in @
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% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 binintersectTELcontra ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 binintersectTERcontra ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 ![
% 5.35/1.26 X166:$i,
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% 5.35/1.26 ![
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% 5.35/1.26 X172:$i]:
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% 5.35/1.26 (
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% 5.35/1.26 subset @
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% 5.35/1.26 (
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% 5.35/1.26 in @
% 5.35/1.26 X172 @
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% 5.35/1.26 (
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% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 ![
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% 5.35/1.26 (
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% 5.35/1.26 X178:$i]:
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% 5.35/1.26 (
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% 5.35/1.26 X180:$i]:
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% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 ~(
% 5.35/1.26 in @
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% 5.35/1.26 (
% 5.35/1.26 ~(
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% 5.35/1.26 X176 ) ) ) ) ) ) ) ) ) ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 ![
% 5.35/1.26 X182:$i,
% 5.35/1.26 X184:$i]:
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 in @
% 5.35/1.26 X184 @
% 5.35/1.26 (
% 5.35/1.26 powerset @
% 5.35/1.26 X182 ) ) =>
% 5.35/1.26 (
% 5.35/1.26 ![
% 5.35/1.26 X186:$i]:
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 in @
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% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 subset @
% 5.35/1.26 X184 @
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% 5.35/1.26 (
% 5.35/1.26 subset @
% 5.35/1.26 (
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% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 ![
% 5.35/1.26 X188:$i,
% 5.35/1.26 X190:$i]:
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 in @
% 5.35/1.26 X190 @
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% 5.35/1.26 (
% 5.35/1.26 ![
% 5.35/1.26 X192:$i]:
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 in @
% 5.35/1.26 X192 @
% 5.35/1.26 (
% 5.35/1.26 powerset @
% 5.35/1.26 X188 ) ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 subset @
% 5.35/1.26 (
% 5.35/1.26 setminus @
% 5.35/1.26 X188 @
% 5.35/1.26 X192 ) @
% 5.35/1.26 (
% 5.35/1.26 setminus @
% 5.35/1.26 X188 @
% 5.35/1.26 X190 ) ) =>
% 5.35/1.26 (
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% 5.35/1.26 X190 @
% 5.35/1.26 X192 ) ) ) ) ) ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 ![
% 5.35/1.26 X194:$i,
% 5.35/1.26 X196:$i]:
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 in @
% 5.35/1.26 X196 @
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% 5.35/1.26 powerset @
% 5.35/1.26 X194 ) ) =>
% 5.35/1.26 (
% 5.35/1.26 ![
% 5.35/1.26 X198:$i]:
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 in @
% 5.35/1.26 X198 @
% 5.35/1.26 X194 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 in @
% 5.35/1.26 X198 @
% 5.35/1.26 X196 ) =>
% 5.35/1.26 (
% 5.35/1.26 in @
% 5.35/1.26 X198 @
% 5.35/1.26 (
% 5.35/1.26 setminus @
% 5.35/1.26 X194 @
% 5.35/1.26 (
% 5.35/1.26 setminus @
% 5.35/1.26 X194 @
% 5.35/1.26 X196 ) ) ) ) ) ) ) ) =>
% 5.35/1.26 (
% 5.35/1.26 ![
% 5.35/1.26 X200:$i,
% 5.35/1.26 X202:$i]:
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 in @
% 5.35/1.26 X202 @
% 5.35/1.26 (
% 5.35/1.26 powerset @
% 5.35/1.26 X200 ) ) =>
% 5.35/1.26 (
% 5.35/1.26 ![
% 5.35/1.26 X204:$i]:
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 in @
% 5.35/1.26 X204 @
% 5.35/1.26 X200 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 in @
% 5.35/1.26 X204 @
% 5.35/1.26 (
% 5.35/1.26 setminus @
% 5.35/1.26 X200 @
% 5.35/1.26 (
% 5.35/1.26 setminus @
% 5.35/1.26 X200 @
% 5.35/1.26 X202 ) ) ) =>
% 5.35/1.26 (
% 5.35/1.26 in @
% 5.35/1.26 X204 @
% 5.35/1.26 X202 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 5.35/1.26 thf(zf_stmt_1, type, zip_tseitin_0 : $i > $i > $i > $o).
% 5.35/1.26 thf(zf_stmt_2, axiom,
% 5.35/1.26 (![X8:$i,X6:$i,X4:$i]:
% 5.35/1.26 ( ( zip_tseitin_0 @ X8 @ X6 @ X4 ) <=>
% 5.35/1.26 ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ))).
% 5.35/1.26 thf(zf_stmt_3, conjecture,
% 5.35/1.26 (( setextAx ) =>
% 5.35/1.26 ( ( emptysetAx ) =>
% 5.35/1.26 ( ( setadjoinAx ) =>
% 5.35/1.26 ( ( ![X4:$i,X6:$i]:
% 5.35/1.26 ( ( in @ X6 @ ( powerset @ X4 ) ) <=>
% 5.35/1.26 ( ![X8:$i]: ( zip_tseitin_0 @ X8 @ X6 @ X4 ) ) ) ) =>
% 5.35/1.26 ( ( setunionAx ) =>
% 5.35/1.26 ( ( omega0Ax ) =>
% 5.35/1.26 ( ( omegaSAx ) =>
% 5.35/1.26 ( ( omegaIndAx ) =>
% 5.35/1.26 ( ( replAx ) =>
% 5.35/1.26 ( ( foundationAx ) =>
% 5.35/1.26 ( ( wellorderingAx ) =>
% 5.35/1.26 ( ( descrp ) =>
% 5.35/1.26 ( ( dsetconstrI ) =>
% 5.35/1.26 ( ( dsetconstrEL ) =>
% 5.35/1.26 ( ( dsetconstrER ) =>
% 5.35/1.26 ( ( exuE1 ) =>
% 5.35/1.26 ( ( prop2setE ) =>
% 5.35/1.26 ( ( emptysetE ) =>
% 5.35/1.26 ( ( emptysetimpfalse ) =>
% 5.35/1.26 ( ( notinemptyset ) =>
% 5.35/1.26 ( ( exuE3e ) =>
% 5.35/1.26 ( ( setext ) =>
% 5.35/1.26 ( ( emptyI ) =>
% 5.35/1.26 ( ( noeltsimpempty ) =>
% 5.35/1.26 ( ( setbeta ) =>
% 5.35/1.26 ( ( nonemptyE1 ) =>
% 5.35/1.26 ( ( nonemptyI ) =>
% 5.35/1.26 ( ( nonemptyI1 ) =>
% 5.35/1.26 ( ( setadjoinIL ) =>
% 5.35/1.26 ( ( emptyinunitempty ) =>
% 5.35/1.26 ( ( setadjoinIR ) =>
% 5.35/1.26 ( ( setadjoinE ) =>
% 5.35/1.26 ( (
% 5.35/1.26 setadjoinOr ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 setoftrueEq ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 ![
% 5.35/1.26 X10:$i,
% 5.35/1.26 X12:$i]:
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 ![
% 5.35/1.26 X14:$i]:
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 in @
% 5.35/1.26 X14 @ X12 ) =>
% 5.35/1.26 (
% 5.35/1.26 in @
% 5.35/1.26 X14 @ X10 ) ) ) =>
% 5.35/1.26 (
% 5.35/1.26 in @
% 5.35/1.26 X12 @
% 5.35/1.26 (
% 5.35/1.26 powerset @
% 5.35/1.26 X10 ) ) ) ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 ![
% 5.35/1.26 X16:$i]:
% 5.35/1.26 (
% 5.35/1.26 in @
% 5.35/1.26 emptyset @
% 5.35/1.26 (
% 5.35/1.26 powerset @
% 5.35/1.26 X16 ) ) ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 ![
% 5.35/1.26 X18:$i]:
% 5.35/1.26 (
% 5.35/1.26 in @
% 5.35/1.26 emptyset @
% 5.35/1.26 (
% 5.35/1.26 powerset @
% 5.35/1.26 X18 ) ) ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 ![
% 5.35/1.26 X20:$i,
% 5.35/1.26 X22:$i,
% 5.35/1.26 X24:$i]:
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 in @
% 5.35/1.26 X22 @
% 5.35/1.26 (
% 5.35/1.26 powerset @
% 5.35/1.26 X20 ) ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 in @
% 5.35/1.26 X24 @ X22 ) =>
% 5.35/1.26 (
% 5.35/1.26 in @
% 5.35/1.26 X24 @ X20 ) ) ) ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 setunionI ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 setunionE ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 subPowSU ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 exuE2 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 nonemptyImpWitness ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 uniqinunit ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 notinsingleton ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 eqinunit ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 singletonsswitch ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 upairsetE ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 upairsetIL ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 upairsetIR ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 emptyE1 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 vacuousDall ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 quantDeMorgan1 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 quantDeMorgan2 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 quantDeMorgan3 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 quantDeMorgan4 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 prop2setI ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 prop2set2propI ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 notdexE ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 notdallE ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 exuI1 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 exuI3 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 exuI2 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 inCongP ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 in__Cong ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 exuE3u ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 exu__Cong ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 emptyset__Cong ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 setadjoin__Cong ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 ![
% 5.35/1.26 X26:$i,
% 5.35/1.26 X28:$i]:
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 X26 ) =
% 5.35/1.26 (
% 5.35/1.26 X28 ) ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 powerset @
% 5.35/1.26 X26 ) =
% 5.35/1.26 (
% 5.35/1.26 powerset @
% 5.35/1.26 X28 ) ) ) ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 setunion__Cong ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 omega__Cong ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 exuEu ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 descr__Cong ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 dsetconstr__Cong ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 subsetI1 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 eqimpsubset2 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 eqimpsubset1 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 subsetI2 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 emptysetsubset ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 subsetE ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 subsetE2 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 notsubsetI ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 notequalI1 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 notequalI2 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 subsetRefl ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 subsetTrans ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 setadjoinSub ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 setadjoinSub2 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 ![
% 5.35/1.26 X30:$i,
% 5.35/1.26 X32:$i]:
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 subset @
% 5.35/1.26 X30 @ X32 ) =>
% 5.35/1.26 (
% 5.35/1.26 in @
% 5.35/1.26 X30 @
% 5.35/1.26 (
% 5.35/1.26 powerset @
% 5.35/1.26 X32 ) ) ) ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 setextsub ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 subsetemptysetimpeq ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 ![
% 5.35/1.26 X34:$i,
% 5.35/1.26 X36:$i]:
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 subset @
% 5.35/1.26 X36 @ X34 ) =>
% 5.35/1.26 (
% 5.35/1.26 in @
% 5.35/1.26 X36 @
% 5.35/1.26 (
% 5.35/1.26 powerset @
% 5.35/1.26 X34 ) ) ) ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 ![
% 5.35/1.26 X38:$i,
% 5.35/1.26 X40:$i]:
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 in @
% 5.35/1.26 X40 @
% 5.35/1.26 (
% 5.35/1.26 powerset @
% 5.35/1.26 X38 ) ) =>
% 5.35/1.26 (
% 5.35/1.26 subset @
% 5.35/1.26 X40 @ X38 ) ) ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 ![
% 5.35/1.26 X42:$i]:
% 5.35/1.26 (
% 5.35/1.26 in @
% 5.35/1.26 X42 @
% 5.35/1.26 (
% 5.35/1.26 powerset @
% 5.35/1.26 X42 ) ) ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 ![
% 5.35/1.26 X44:$i,
% 5.35/1.26 X46:$i]:
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 subset @
% 5.35/1.26 X44 @ X46 ) =>
% 5.35/1.26 (
% 5.35/1.26 subset @
% 5.35/1.26 (
% 5.35/1.26 powerset @
% 5.35/1.26 X44 ) @
% 5.35/1.26 (
% 5.35/1.26 powerset @
% 5.35/1.26 X46 ) ) ) ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 sepInPowerset ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 sepSubset ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 binunionIL ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 upairset2IR ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 binunionIR ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 binunionEcases ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 binunionE ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 binunionLsub ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 binunionRsub ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 binintersectI ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 binintersectSubset5 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 binintersectEL ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 binintersectLsub ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 binintersectSubset2 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 binintersectSubset3 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 binintersectER ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 disjointsetsI1 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 binintersectRsub ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 binintersectSubset4 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 binintersectSubset1 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 bs114d ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 ![
% 5.35/1.26 X48:$i,
% 5.35/1.26 X50:$i,
% 5.35/1.26 X52:$i]:
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 in @
% 5.35/1.26 X52 @ X48 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 ~(
% 5.35/1.26 in @
% 5.35/1.26 X52 @ X50 ) ) =>
% 5.35/1.26 (
% 5.35/1.26 in @
% 5.35/1.26 X52 @
% 5.35/1.26 (
% 5.35/1.26 setminus @
% 5.35/1.26 X48 @ X50 ) ) ) ) ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 ![
% 5.35/1.26 X54:$i,
% 5.35/1.26 X56:$i,
% 5.35/1.26 X58:$i]:
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 in @
% 5.35/1.26 X58 @
% 5.35/1.26 (
% 5.35/1.26 setminus @
% 5.35/1.26 X54 @ X56 ) ) =>
% 5.35/1.26 (
% 5.35/1.26 in @
% 5.35/1.26 X58 @ X54 ) ) ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 ![
% 5.35/1.26 X60:$i,
% 5.35/1.26 X62:$i,
% 5.35/1.26 X64:$i]:
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 in @
% 5.35/1.26 X64 @
% 5.35/1.26 (
% 5.35/1.26 setminus @
% 5.35/1.26 X60 @ X62 ) ) =>
% 5.35/1.26 (
% 5.35/1.26 ~(
% 5.35/1.26 in @
% 5.35/1.26 X64 @ X62 ) ) ) ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 ![
% 5.35/1.26 X66:$i,
% 5.35/1.26 X68:$i]:
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 subset @
% 5.35/1.26 X66 @ X68 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 setminus @
% 5.35/1.26 X66 @ X68 ) =
% 5.35/1.26 (
% 5.35/1.26 emptyset ) ) ) ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 ![
% 5.35/1.26 X70:$i,
% 5.35/1.26 X72:$i,
% 5.35/1.26 X74:$i]:
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 ~(
% 5.35/1.26 in @
% 5.35/1.26 X74 @
% 5.35/1.26 (
% 5.35/1.26 setminus
% 5.35/1.26 @
% 5.35/1.26 X70 @ X72 ) ) ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 in @
% 5.35/1.26 X74 @ X70 ) =>
% 5.35/1.26 (
% 5.35/1.26 in @
% 5.35/1.26 X74 @ X72 ) ) ) ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 ![
% 5.35/1.26 X76:$i,
% 5.35/1.26 X78:$i,
% 5.35/1.26 X80:$i]:
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 ~(
% 5.35/1.26 in @
% 5.35/1.26 X80 @
% 5.35/1.26 (
% 5.35/1.26 setminus
% 5.35/1.26 @
% 5.35/1.26 X76 @ X78 ) ) ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 ~(
% 5.35/1.26 in @
% 5.35/1.26 X80 @ X78 ) ) =>
% 5.35/1.26 (
% 5.35/1.26 ~(
% 5.35/1.26 in @
% 5.35/1.26 X80 @ X76 ) ) ) ) ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 ![
% 5.35/1.26 X82:$i,
% 5.35/1.26 X84:$i,
% 5.35/1.26 X86:$i]:
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 ~(
% 5.35/1.26 in @
% 5.35/1.26 X86 @ X82 ) ) =>
% 5.35/1.26 (
% 5.35/1.26 ~(
% 5.35/1.26 in @
% 5.35/1.26 X86 @
% 5.35/1.26 (
% 5.35/1.26 setminus
% 5.35/1.26 @
% 5.35/1.26 X82 @ X84 ) ) ) ) ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 ![
% 5.35/1.26 X88:$i,
% 5.35/1.26 X90:$i,
% 5.35/1.26 X92:$i]:
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 in @
% 5.35/1.26 X92 @ X90 ) =>
% 5.35/1.26 (
% 5.35/1.26 ~(
% 5.35/1.26 in @
% 5.35/1.26 X92 @
% 5.35/1.26 (
% 5.35/1.26 setminus
% 5.35/1.26 @
% 5.35/1.26 X88 @ X90 ) ) ) ) ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 ![
% 5.35/1.26 X94:$i,
% 5.35/1.26 X96:$i]:
% 5.35/1.26 (
% 5.35/1.26 subset @
% 5.35/1.26 (
% 5.35/1.26 setminus @
% 5.35/1.26 X94 @ X96 ) @
% 5.35/1.26 X94 ) ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 ![
% 5.35/1.26 X98:$i,
% 5.35/1.26 X100:$i]:
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 setminus @
% 5.35/1.26 X98 @ X100 ) =
% 5.35/1.26 (
% 5.35/1.26 emptyset ) ) =>
% 5.35/1.26 (
% 5.35/1.26 subset @
% 5.35/1.26 X98 @ X100 ) ) ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 symdiffE ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 symdiffI1 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 symdiffI2 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 symdiffIneg1 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 symdiffIneg2 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 secondinupair ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 setukpairIL ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 setukpairIR ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 kpairiskpair ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 kpairp ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 singletonsubset ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 ![
% 5.35/1.26 X102:$i,
% 5.35/1.26 X104:$i]:
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 in @
% 5.35/1.26 X104 @
% 5.35/1.26 X102 ) =>
% 5.35/1.26 (
% 5.35/1.26 in @
% 5.35/1.26 (
% 5.35/1.26 setadjoin
% 5.35/1.26 @
% 5.35/1.26 X104 @
% 5.35/1.26 emptyset ) @
% 5.35/1.26 (
% 5.35/1.26 powerset @
% 5.35/1.26 X102 ) ) ) ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 singletoninpowunion ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 upairset2E ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 upairsubunion ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 upairinpowunion ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 ubforcartprodlem1 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 ubforcartprodlem2 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 ubforcartprodlem3 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 cartprodpairin ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 cartprodmempair1 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 cartprodmempair ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 setunionE2 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 setunionsingleton1 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 setunionsingleton2 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 setunionsingleton ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 singletonprop ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 ex1E1 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 ex1I ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 ex1I2 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 singletonsuniq ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 setukpairinjL1 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 kfstsingleton ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 theprop ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 kfstpairEq ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 cartprodfstin ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 setukpairinjL2 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 setukpairinjL ) =>
% 5.35/1.26 (
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% 5.35/1.26 (
% 5.35/1.26 ksndsingleton ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 ksndpairEq ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 kpairsurjEq ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 cartprodsndin ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 cartprodpairmemEL ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 cartprodpairmemER ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 cartprodmempaircEq ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 cartprodfstpairEq ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 cartprodsndpairEq ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 cartprodpairsurjEq ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 dpsetconstrI ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 dpsetconstrSub ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 setOfPairsIsBReln ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 dpsetconstrERa ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 dpsetconstrEL1 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 dpsetconstrEL2 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 dpsetconstrER ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 funcImageSingleton ) =>
% 5.35/1.26 (
% 5.35/1.26 (
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% 5.35/1.26 (
% 5.35/1.26 (
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% 5.35/1.26 (
% 5.35/1.26 infuncsetfunc ) =>
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% 5.35/1.26 (
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% 5.35/1.26 (
% 5.35/1.26 lamProp ) =>
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% 5.35/1.26 (
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% 5.35/1.26 brelnall1 ) =>
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% 5.35/1.26 (
% 5.35/1.26 funcGraphProp4 ) =>
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% 5.35/1.26 subbreln ) =>
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% 5.35/1.26 (
% 5.35/1.26 eqbreln ) =>
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% 5.35/1.26 (
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% 5.35/1.26 (
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% 5.35/1.26 (
% 5.35/1.26 ap2apEq1 ) =>
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% 5.35/1.26 (
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% 5.35/1.26 (
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% 5.35/1.26 (
% 5.35/1.26 eta1 ) =>
% 5.35/1.26 (
% 5.35/1.26 (
% 5.35/1.26 lam2lamEq ) =>
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% 5.35/1.26 (
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% 5.35/1.26 iffalseProp1 ) =>
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% 5.35/1.27 in @
% 5.35/1.27 X186 @
% 5.35/1.27 (
% 5.35/1.27 powerset @
% 5.35/1.27 X182 ) ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 subset @
% 5.35/1.27 X184 @
% 5.35/1.27 X186 ) =>
% 5.35/1.27 (
% 5.35/1.27 subset @
% 5.35/1.27 (
% 5.35/1.27 setminus @
% 5.35/1.27 X182 @
% 5.35/1.27 X186 ) @
% 5.35/1.27 (
% 5.35/1.27 setminus @
% 5.35/1.27 X182 @
% 5.35/1.27 X184 ) ) ) ) ) ) ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 ![
% 5.35/1.27 X188:$i,
% 5.35/1.27 X190:$i]:
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 in @
% 5.35/1.27 X190 @
% 5.35/1.27 (
% 5.35/1.27 powerset @
% 5.35/1.27 X188 ) ) =>
% 5.35/1.27 (
% 5.35/1.27 ![
% 5.35/1.27 X192:$i]:
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 in @
% 5.35/1.27 X192 @
% 5.35/1.27 (
% 5.35/1.27 powerset @
% 5.35/1.27 X188 ) ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 subset @
% 5.35/1.27 (
% 5.35/1.27 setminus @
% 5.35/1.27 X188 @
% 5.35/1.27 X192 ) @
% 5.35/1.27 (
% 5.35/1.27 setminus @
% 5.35/1.27 X188 @
% 5.35/1.27 X190 ) ) =>
% 5.35/1.27 (
% 5.35/1.27 subset @
% 5.35/1.27 X190 @
% 5.35/1.27 X192 ) ) ) ) ) ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 ![
% 5.35/1.27 X194:$i,
% 5.35/1.27 X196:$i]:
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 in @
% 5.35/1.27 X196 @
% 5.35/1.27 (
% 5.35/1.27 powerset @
% 5.35/1.27 X194 ) ) =>
% 5.35/1.27 (
% 5.35/1.27 ![
% 5.35/1.27 X198:$i]:
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 in @
% 5.35/1.27 X198 @
% 5.35/1.27 X194 ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 in @
% 5.35/1.27 X198 @
% 5.35/1.27 X196 ) =>
% 5.35/1.27 (
% 5.35/1.27 in @
% 5.35/1.27 X198 @
% 5.35/1.27 (
% 5.35/1.27 setminus @
% 5.35/1.27 X194 @
% 5.35/1.27 (
% 5.35/1.27 setminus @
% 5.35/1.27 X194 @
% 5.35/1.27 X196 ) ) ) ) ) ) ) ) =>
% 5.35/1.27 (
% 5.35/1.27 ![
% 5.35/1.27 X200:$i,
% 5.35/1.27 X202:$i]:
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 in @
% 5.35/1.27 X202 @
% 5.35/1.27 (
% 5.35/1.27 powerset @
% 5.35/1.27 X200 ) ) =>
% 5.35/1.27 (
% 5.35/1.27 ![
% 5.35/1.27 X204:$i]:
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 in @
% 5.35/1.27 X204 @
% 5.35/1.27 X200 ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 in @
% 5.35/1.27 X204 @
% 5.35/1.27 (
% 5.35/1.27 setminus @
% 5.35/1.27 X200 @
% 5.35/1.27 (
% 5.35/1.27 setminus @
% 5.35/1.27 X200 @
% 5.35/1.27 X202 ) ) ) =>
% 5.35/1.27 (
% 5.35/1.27 in @
% 5.35/1.27 X204 @
% 5.35/1.27 X202 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 5.35/1.27 thf(zf_stmt_4, negated_conjecture,
% 5.35/1.27 (~( ( setextAx ) =>
% 5.35/1.27 ( ( emptysetAx ) =>
% 5.35/1.27 ( ( setadjoinAx ) =>
% 5.35/1.27 ( ( ![X4:$i,X6:$i]:
% 5.35/1.27 ( ( in @ X6 @ ( powerset @ X4 ) ) <=>
% 5.35/1.27 ( ![X8:$i]: ( zip_tseitin_0 @ X8 @ X6 @ X4 ) ) ) ) =>
% 5.35/1.27 ( ( setunionAx ) =>
% 5.35/1.27 ( ( omega0Ax ) =>
% 5.35/1.27 ( ( omegaSAx ) =>
% 5.35/1.27 ( ( omegaIndAx ) =>
% 5.35/1.27 ( ( replAx ) =>
% 5.35/1.27 ( ( foundationAx ) =>
% 5.35/1.27 ( ( wellorderingAx ) =>
% 5.35/1.27 ( ( descrp ) =>
% 5.35/1.27 ( ( dsetconstrI ) =>
% 5.35/1.27 ( ( dsetconstrEL ) =>
% 5.35/1.27 ( ( dsetconstrER ) =>
% 5.35/1.27 ( ( exuE1 ) =>
% 5.35/1.27 ( ( prop2setE ) =>
% 5.35/1.27 ( ( emptysetE ) =>
% 5.35/1.27 ( ( emptysetimpfalse ) =>
% 5.35/1.27 ( ( notinemptyset ) =>
% 5.35/1.27 ( ( exuE3e ) =>
% 5.35/1.27 ( ( setext ) =>
% 5.35/1.27 ( ( emptyI ) =>
% 5.35/1.27 ( ( noeltsimpempty ) =>
% 5.35/1.27 ( ( setbeta ) =>
% 5.35/1.27 ( ( nonemptyE1 ) =>
% 5.35/1.27 ( ( nonemptyI ) =>
% 5.35/1.27 ( ( nonemptyI1 ) =>
% 5.35/1.27 ( ( setadjoinIL ) =>
% 5.35/1.27 ( ( emptyinunitempty ) =>
% 5.35/1.27 ( ( setadjoinIR ) =>
% 5.35/1.27 ( (
% 5.35/1.27 setadjoinE ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 setadjoinOr ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 setoftrueEq ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 ![
% 5.35/1.27 X10:$i,
% 5.35/1.27 X12:$i]:
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 ![
% 5.35/1.27 X14:$i]:
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 in @
% 5.35/1.27 X14 @ X12 ) =>
% 5.35/1.27 (
% 5.35/1.27 in @
% 5.35/1.27 X14 @ X10 ) ) ) =>
% 5.35/1.27 (
% 5.35/1.27 in @
% 5.35/1.27 X12 @
% 5.35/1.27 (
% 5.35/1.27 powerset
% 5.35/1.27 @
% 5.35/1.27 X10 ) ) ) ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 ![
% 5.35/1.27 X16:$i]:
% 5.35/1.27 (
% 5.35/1.27 in @
% 5.35/1.27 emptyset @
% 5.35/1.27 (
% 5.35/1.27 powerset
% 5.35/1.27 @
% 5.35/1.27 X16 ) ) ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 ![
% 5.35/1.27 X18:$i]:
% 5.35/1.27 (
% 5.35/1.27 in @
% 5.35/1.27 emptyset @
% 5.35/1.27 (
% 5.35/1.27 powerset
% 5.35/1.27 @
% 5.35/1.27 X18 ) ) ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 ![
% 5.35/1.27 X20:$i,
% 5.35/1.27 X22:$i,
% 5.35/1.27 X24:$i]:
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 in @
% 5.35/1.27 X22 @
% 5.35/1.27 (
% 5.35/1.27 powerset
% 5.35/1.27 @
% 5.35/1.27 X20 ) ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 in @
% 5.35/1.27 X24 @ X22 ) =>
% 5.35/1.27 (
% 5.35/1.27 in @
% 5.35/1.27 X24 @ X20 ) ) ) ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 setunionI ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 setunionE ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 subPowSU ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 exuE2 ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 nonemptyImpWitness ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 uniqinunit ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 notinsingleton ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 eqinunit ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 singletonsswitch ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 upairsetE ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 upairsetIL ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 upairsetIR ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 emptyE1 ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 vacuousDall ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 quantDeMorgan1 ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 quantDeMorgan2 ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 quantDeMorgan3 ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 quantDeMorgan4 ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 prop2setI ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 prop2set2propI ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 notdexE ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 notdallE ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 exuI1 ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 exuI3 ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 exuI2 ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 inCongP ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 in__Cong ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 exuE3u ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 exu__Cong ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 emptyset__Cong ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 setadjoin__Cong ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 ![
% 5.35/1.27 X26:$i,
% 5.35/1.27 X28:$i]:
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 X26 ) =
% 5.35/1.27 (
% 5.35/1.27 X28 ) ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 powerset
% 5.35/1.27 @
% 5.35/1.27 X26 ) =
% 5.35/1.27 (
% 5.35/1.27 powerset
% 5.35/1.27 @
% 5.35/1.27 X28 ) ) ) ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 setunion__Cong ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 omega__Cong ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 exuEu ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 descr__Cong ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 dsetconstr__Cong ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 subsetI1 ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 eqimpsubset2 ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 eqimpsubset1 ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 subsetI2 ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 emptysetsubset ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 subsetE ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 subsetE2 ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 notsubsetI ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 notequalI1 ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 notequalI2 ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 subsetRefl ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 subsetTrans ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 setadjoinSub ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 setadjoinSub2 ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 ![
% 5.35/1.27 X30:$i,
% 5.35/1.27 X32:$i]:
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 subset @
% 5.35/1.27 X30 @ X32 ) =>
% 5.35/1.27 (
% 5.35/1.27 in @
% 5.35/1.27 X30 @
% 5.35/1.27 (
% 5.35/1.27 powerset
% 5.35/1.27 @
% 5.35/1.27 X32 ) ) ) ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 setextsub ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 subsetemptysetimpeq ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 ![
% 5.35/1.27 X34:$i,
% 5.35/1.27 X36:$i]:
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 subset @
% 5.35/1.27 X36 @ X34 ) =>
% 5.35/1.27 (
% 5.35/1.27 in @
% 5.35/1.27 X36 @
% 5.35/1.27 (
% 5.35/1.27 powerset
% 5.35/1.27 @
% 5.35/1.27 X34 ) ) ) ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 ![
% 5.35/1.27 X38:$i,
% 5.35/1.27 X40:$i]:
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 in @
% 5.35/1.27 X40 @
% 5.35/1.27 (
% 5.35/1.27 powerset
% 5.35/1.27 @
% 5.35/1.27 X38 ) ) =>
% 5.35/1.27 (
% 5.35/1.27 subset @
% 5.35/1.27 X40 @ X38 ) ) ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 ![
% 5.35/1.27 X42:$i]:
% 5.35/1.27 (
% 5.35/1.27 in @
% 5.35/1.27 X42 @
% 5.35/1.27 (
% 5.35/1.27 powerset
% 5.35/1.27 @
% 5.35/1.27 X42 ) ) ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 ![
% 5.35/1.27 X44:$i,
% 5.35/1.27 X46:$i]:
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 subset @
% 5.35/1.27 X44 @ X46 ) =>
% 5.35/1.27 (
% 5.35/1.27 subset @
% 5.35/1.27 (
% 5.35/1.27 powerset
% 5.35/1.27 @
% 5.35/1.27 X44 ) @
% 5.35/1.27 (
% 5.35/1.27 powerset
% 5.35/1.27 @
% 5.35/1.27 X46 ) ) ) ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 sepInPowerset ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 sepSubset ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 binunionIL ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 upairset2IR ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 binunionIR ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 binunionEcases ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 binunionE ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 binunionLsub ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 binunionRsub ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 binintersectI ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 binintersectSubset5 ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 binintersectEL ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 binintersectLsub ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 binintersectSubset2 ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 binintersectSubset3 ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 binintersectER ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 disjointsetsI1 ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 binintersectRsub ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 binintersectSubset4 ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 binintersectSubset1 ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 bs114d ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 ![
% 5.35/1.27 X48:$i,
% 5.35/1.27 X50:$i,
% 5.35/1.27 X52:$i]:
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 in @
% 5.35/1.27 X52 @ X48 ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 ~
% 5.35/1.27 (
% 5.35/1.27 in @
% 5.35/1.27 X52 @ X50 ) ) =>
% 5.35/1.27 (
% 5.35/1.27 in @
% 5.35/1.27 X52 @
% 5.35/1.27 (
% 5.35/1.27 setminus
% 5.35/1.27 @
% 5.35/1.27 X48 @ X50 ) ) ) ) ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 ![
% 5.35/1.27 X54:$i,
% 5.35/1.27 X56:$i,
% 5.35/1.27 X58:$i]:
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 in @
% 5.35/1.27 X58 @
% 5.35/1.27 (
% 5.35/1.27 setminus
% 5.35/1.27 @
% 5.35/1.27 X54 @ X56 ) ) =>
% 5.35/1.27 (
% 5.35/1.27 in @
% 5.35/1.27 X58 @ X54 ) ) ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 ![
% 5.35/1.27 X60:$i,
% 5.35/1.27 X62:$i,
% 5.35/1.27 X64:$i]:
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 in @
% 5.35/1.27 X64 @
% 5.35/1.27 (
% 5.35/1.27 setminus
% 5.35/1.27 @
% 5.35/1.27 X60 @ X62 ) ) =>
% 5.35/1.27 (
% 5.35/1.27 ~
% 5.35/1.27 (
% 5.35/1.27 in @
% 5.35/1.27 X64 @ X62 ) ) ) ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 ![
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% 5.35/1.27 X68:$i]:
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% 5.35/1.27 (
% 5.35/1.27 subset @
% 5.35/1.27 X66 @ X68 ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 setminus
% 5.35/1.27 @
% 5.35/1.27 X66 @ X68 ) =
% 5.35/1.27 (
% 5.35/1.27 emptyset ) ) ) ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 ![
% 5.35/1.27 X70:$i,
% 5.35/1.27 X72:$i,
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% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 ~
% 5.35/1.27 (
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% 5.35/1.27 X74 @
% 5.35/1.27 (
% 5.35/1.27 setminus
% 5.35/1.27 @
% 5.35/1.27 X70 @ X72 ) ) ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 in @
% 5.35/1.27 X74 @ X70 ) =>
% 5.35/1.27 (
% 5.35/1.27 in @
% 5.35/1.27 X74 @ X72 ) ) ) ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 ![
% 5.35/1.27 X76:$i,
% 5.35/1.27 X78:$i,
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% 5.35/1.27 ~
% 5.35/1.27 (
% 5.35/1.27 in @
% 5.35/1.27 X80 @
% 5.35/1.27 (
% 5.35/1.27 setminus
% 5.35/1.27 @
% 5.35/1.27 X76 @ X78 ) ) ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 ~
% 5.35/1.27 (
% 5.35/1.27 in @
% 5.35/1.27 X80 @ X78 ) ) =>
% 5.35/1.27 (
% 5.35/1.27 ~
% 5.35/1.27 (
% 5.35/1.27 in @
% 5.35/1.27 X80 @ X76 ) ) ) ) ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 ![
% 5.35/1.27 X82:$i,
% 5.35/1.27 X84:$i,
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% 5.35/1.27 ~
% 5.35/1.27 (
% 5.35/1.27 in @
% 5.35/1.27 X86 @ X82 ) ) =>
% 5.35/1.27 (
% 5.35/1.27 ~
% 5.35/1.27 (
% 5.35/1.27 in @
% 5.35/1.27 X86 @
% 5.35/1.27 (
% 5.35/1.27 setminus
% 5.35/1.27 @
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% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 ![
% 5.35/1.27 X88:$i,
% 5.35/1.27 X90:$i,
% 5.35/1.27 X92:$i]:
% 5.35/1.27 (
% 5.35/1.27 (
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% 5.35/1.27 X92 @ X90 ) =>
% 5.35/1.27 (
% 5.35/1.27 ~
% 5.35/1.27 (
% 5.35/1.27 in @
% 5.35/1.27 X92 @
% 5.35/1.27 (
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% 5.35/1.27 @
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% 5.35/1.27 (
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% 5.35/1.27 (
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% 5.35/1.27 @
% 5.35/1.27 X94 @ X96 ) @
% 5.35/1.27 X94 ) ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 ![
% 5.35/1.27 X98:$i,
% 5.35/1.27 X100:$i]:
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 setminus
% 5.35/1.27 @
% 5.35/1.27 X98 @
% 5.35/1.27 X100 ) =
% 5.35/1.27 (
% 5.35/1.27 emptyset ) ) =>
% 5.35/1.27 (
% 5.35/1.27 subset @
% 5.35/1.27 X98 @
% 5.35/1.27 X100 ) ) ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 symdiffE ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 symdiffI1 ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 symdiffI2 ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 symdiffIneg1 ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 symdiffIneg2 ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 secondinupair ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 setukpairIL ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 setukpairIR ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 kpairiskpair ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 kpairp ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 singletonsubset ) =>
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% 5.35/1.27 (
% 5.35/1.27 ![
% 5.35/1.27 X102:$i,
% 5.35/1.27 X104:$i]:
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 in @
% 5.35/1.27 X104 @
% 5.35/1.27 X102 ) =>
% 5.35/1.27 (
% 5.35/1.27 in @
% 5.35/1.27 (
% 5.35/1.27 setadjoin
% 5.35/1.27 @
% 5.35/1.27 X104 @
% 5.35/1.27 emptyset ) @
% 5.35/1.27 (
% 5.35/1.27 powerset
% 5.35/1.27 @
% 5.35/1.27 X102 ) ) ) ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 singletoninpowunion ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 upairset2E ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 upairsubunion ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 upairinpowunion ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 ubforcartprodlem1 ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 ubforcartprodlem2 ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 ubforcartprodlem3 ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 cartprodpairin ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 cartprodmempair1 ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 cartprodmempair ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 setunionE2 ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 setunionsingleton1 ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 setunionsingleton2 ) =>
% 5.35/1.27 (
% 5.35/1.27 (
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% 5.35/1.27 (
% 5.35/1.27 singletonprop ) =>
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% 5.35/1.27 ex1E1 ) =>
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% 5.35/1.27 ex1I ) =>
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% 5.35/1.27 (
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% 5.35/1.27 (
% 5.35/1.27 singletonsuniq ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 setukpairinjL1 ) =>
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% 5.35/1.27 (
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% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 theprop ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 kfstpairEq ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 cartprodfstin ) =>
% 5.35/1.27 (
% 5.35/1.27 (
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% 5.35/1.27 (
% 5.35/1.27 setukpairinjL ) =>
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% 5.35/1.27 (
% 5.35/1.27 setukpairinjR11 ) =>
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% 5.35/1.27 (
% 5.35/1.27 setukpairinjR12 ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 setukpairinjR1 ) =>
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% 5.35/1.27 (
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% 5.35/1.27 (
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% 5.35/1.27 (
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% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 ksndpairEq ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 kpairsurjEq ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 cartprodsndin ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 cartprodpairmemEL ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 cartprodpairmemER ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 cartprodmempaircEq ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 cartprodfstpairEq ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 cartprodsndpairEq ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 cartprodpairsurjEq ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 dpsetconstrI ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 dpsetconstrSub ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 setOfPairsIsBReln ) =>
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% 5.35/1.27 (
% 5.35/1.27 dpsetconstrERa ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 dpsetconstrEL1 ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 dpsetconstrEL2 ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 dpsetconstrER ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 funcImageSingleton ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 apProp ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 app ) =>
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% 5.35/1.27 (
% 5.35/1.27 infuncsetfunc ) =>
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% 5.35/1.27 (
% 5.35/1.27 ap2p ) =>
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% 5.35/1.27 (
% 5.35/1.27 funcinfuncset ) =>
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% 5.35/1.27 (
% 5.35/1.27 lamProp ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 lamp ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 lam2p ) =>
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% 5.35/1.27 brelnall1 ) =>
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% 5.35/1.27 (
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% 5.35/1.27 (
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% 5.35/1.27 (
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% 5.35/1.27 (
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% 5.35/1.27 (
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% 5.35/1.27 @
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% 5.35/1.27 @
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% 5.35/1.27 (
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% 5.35/1.27 X110:$i,
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% 5.35/1.27 (
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% 5.35/1.27 X116:$i,
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% 5.35/1.27 @
% 5.35/1.27 X116 @
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% 5.35/1.27 X130:$i,
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% 5.35/1.27 (
% 5.35/1.27 subset @
% 5.35/1.27 X132 @
% 5.35/1.27 X134 ) ) ) ) ) ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 ![
% 5.35/1.27 X138:$i,
% 5.35/1.27 X140:$i]:
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 in @
% 5.35/1.27 X140 @
% 5.35/1.27 (
% 5.35/1.27 powerset
% 5.35/1.27 @
% 5.35/1.27 X138 ) ) =>
% 5.35/1.27 (
% 5.35/1.27 ![
% 5.35/1.27 X142:$i]:
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 in @
% 5.35/1.27 X142 @
% 5.35/1.27 (
% 5.35/1.27 powerset
% 5.35/1.27 @
% 5.35/1.27 X138 ) ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 ![
% 5.35/1.27 X144:$i]:
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 in @
% 5.35/1.27 X144 @
% 5.35/1.27 X138 ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 in @
% 5.35/1.27 X144 @
% 5.35/1.27 X140 ) =>
% 5.35/1.27 (
% 5.35/1.27 in @
% 5.35/1.27 X144 @
% 5.35/1.27 X142 ) ) ) ) =>
% 5.35/1.27 (
% 5.35/1.27 in @
% 5.35/1.27 X140 @
% 5.35/1.27 (
% 5.35/1.27 powerset
% 5.35/1.27 @
% 5.35/1.27 X142 ) ) ) ) ) ) ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 ![
% 5.35/1.27 X146:$i,
% 5.35/1.27 X148:$i]:
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 in @
% 5.35/1.27 X148 @
% 5.35/1.27 (
% 5.35/1.27 powerset
% 5.35/1.27 @
% 5.35/1.27 X146 ) ) =>
% 5.35/1.27 (
% 5.35/1.27 ![
% 5.35/1.27 X150:$i]:
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 in @
% 5.35/1.27 X150 @
% 5.35/1.27 (
% 5.35/1.27 powerset
% 5.35/1.27 @
% 5.35/1.27 X146 ) ) =>
% 5.35/1.27 (
% 5.35/1.27 ![
% 5.35/1.27 X152:$i]:
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 in @
% 5.35/1.27 X152 @
% 5.35/1.27 X146 ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 in @
% 5.35/1.27 X148 @
% 5.35/1.27 (
% 5.35/1.27 powerset
% 5.35/1.27 @
% 5.35/1.27 X150 ) ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 in @
% 5.35/1.27 X152 @
% 5.35/1.27 X148 ) =>
% 5.35/1.27 (
% 5.35/1.27 in @
% 5.35/1.27 X152 @
% 5.35/1.27 X150 ) ) ) ) ) ) ) ) ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 ![
% 5.35/1.27 X154:$i,
% 5.35/1.27 X156:$i]:
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 in @
% 5.35/1.27 X156 @
% 5.35/1.27 (
% 5.35/1.27 powerset
% 5.35/1.27 @
% 5.35/1.27 X154 ) ) =>
% 5.35/1.27 (
% 5.35/1.27 ![
% 5.35/1.27 X158:$i]:
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 in @
% 5.35/1.27 X158 @
% 5.35/1.27 X154 ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 in @
% 5.35/1.27 X158 @
% 5.35/1.27 X156 ) =>
% 5.35/1.27 (
% 5.35/1.27 ~
% 5.35/1.27 (
% 5.35/1.27 in @
% 5.35/1.27 X158 @
% 5.35/1.27 (
% 5.35/1.27 setminus
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% 5.35/1.27 X154 @
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% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 ![
% 5.35/1.27 X160:$i,
% 5.35/1.27 X162:$i]:
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 in @
% 5.35/1.27 X162 @
% 5.35/1.27 (
% 5.35/1.27 powerset
% 5.35/1.27 @
% 5.35/1.27 X160 ) ) =>
% 5.35/1.27 (
% 5.35/1.27 ![
% 5.35/1.27 X164:$i]:
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 in @
% 5.35/1.27 X164 @
% 5.35/1.27 X160 ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 ~
% 5.35/1.27 (
% 5.35/1.27 in @
% 5.35/1.27 X164 @
% 5.35/1.27 (
% 5.35/1.27 setminus
% 5.35/1.27 @
% 5.35/1.27 X160 @
% 5.35/1.27 X162 ) ) ) =>
% 5.35/1.27 (
% 5.35/1.27 in @
% 5.35/1.27 X164 @
% 5.35/1.27 X162 ) ) ) ) ) ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 binintersectTELcontra ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 binintersectTERcontra ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 ![
% 5.35/1.27 X166:$i,
% 5.35/1.27 X168:$i]:
% 5.35/1.27 (
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% 5.35/1.27 (
% 5.35/1.27 ![
% 5.35/1.27 X170:$i]:
% 5.35/1.27 (
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% 5.35/1.27 X166 ) ) =>
% 5.35/1.27 (
% 5.35/1.27 ![
% 5.35/1.27 X172:$i]:
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 in @
% 5.35/1.27 X172 @
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% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 subset @
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% 5.35/1.27 (
% 5.35/1.27 setminus
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% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 in @
% 5.35/1.27 X172 @
% 5.35/1.27 X170 ) =>
% 5.35/1.27 (
% 5.35/1.27 ~
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% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 ![
% 5.35/1.27 X174:$i,
% 5.35/1.27 X176:$i]:
% 5.35/1.27 (
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% 5.35/1.27 (
% 5.35/1.27 ![
% 5.35/1.27 X178:$i]:
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 in @
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% 5.35/1.27 powerset
% 5.35/1.27 @
% 5.35/1.27 X174 ) ) =>
% 5.35/1.27 (
% 5.35/1.27 ![
% 5.35/1.27 X180:$i]:
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 in @
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% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 subset @
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% 5.35/1.27 X178 ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 ~
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% 5.35/1.27 in @
% 5.35/1.27 X180 @
% 5.35/1.27 X178 ) ) =>
% 5.35/1.27 (
% 5.35/1.27 ~
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% 5.35/1.27 in @
% 5.35/1.27 X180 @
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% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 ![
% 5.35/1.27 X182:$i,
% 5.35/1.27 X184:$i]:
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 in @
% 5.35/1.27 X184 @
% 5.35/1.27 (
% 5.35/1.27 powerset
% 5.35/1.27 @
% 5.35/1.27 X182 ) ) =>
% 5.35/1.27 (
% 5.35/1.27 ![
% 5.35/1.27 X186:$i]:
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 in @
% 5.35/1.27 X186 @
% 5.35/1.27 (
% 5.35/1.27 powerset
% 5.35/1.27 @
% 5.35/1.27 X182 ) ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 subset @
% 5.35/1.27 X184 @
% 5.35/1.27 X186 ) =>
% 5.35/1.27 (
% 5.35/1.27 subset @
% 5.35/1.27 (
% 5.35/1.27 setminus
% 5.35/1.27 @
% 5.35/1.27 X182 @
% 5.35/1.27 X186 ) @
% 5.35/1.27 (
% 5.35/1.27 setminus
% 5.35/1.27 @
% 5.35/1.27 X182 @
% 5.35/1.27 X184 ) ) ) ) ) ) ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 ![
% 5.35/1.27 X188:$i,
% 5.35/1.27 X190:$i]:
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 in @
% 5.35/1.27 X190 @
% 5.35/1.27 (
% 5.35/1.27 powerset
% 5.35/1.27 @
% 5.35/1.27 X188 ) ) =>
% 5.35/1.27 (
% 5.35/1.27 ![
% 5.35/1.27 X192:$i]:
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 in @
% 5.35/1.27 X192 @
% 5.35/1.27 (
% 5.35/1.27 powerset
% 5.35/1.27 @
% 5.35/1.27 X188 ) ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 subset @
% 5.35/1.27 (
% 5.35/1.27 setminus
% 5.35/1.27 @
% 5.35/1.27 X188 @
% 5.35/1.27 X192 ) @
% 5.35/1.27 (
% 5.35/1.27 setminus
% 5.35/1.27 @
% 5.35/1.27 X188 @
% 5.35/1.27 X190 ) ) =>
% 5.35/1.27 (
% 5.35/1.27 subset @
% 5.35/1.27 X190 @
% 5.35/1.27 X192 ) ) ) ) ) ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 ![
% 5.35/1.27 X194:$i,
% 5.35/1.27 X196:$i]:
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 in @
% 5.35/1.27 X196 @
% 5.35/1.27 (
% 5.35/1.27 powerset
% 5.35/1.27 @
% 5.35/1.27 X194 ) ) =>
% 5.35/1.27 (
% 5.35/1.27 ![
% 5.35/1.27 X198:$i]:
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 in @
% 5.35/1.27 X198 @
% 5.35/1.27 X194 ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 in @
% 5.35/1.27 X198 @
% 5.35/1.27 X196 ) =>
% 5.35/1.27 (
% 5.35/1.27 in @
% 5.35/1.27 X198 @
% 5.35/1.27 (
% 5.35/1.27 setminus
% 5.35/1.27 @
% 5.35/1.27 X194 @
% 5.35/1.27 (
% 5.35/1.27 setminus
% 5.35/1.27 @
% 5.35/1.27 X194 @
% 5.35/1.27 X196 ) ) ) ) ) ) ) ) =>
% 5.35/1.27 (
% 5.35/1.27 ![
% 5.35/1.27 X200:$i,
% 5.35/1.27 X202:$i]:
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 in @
% 5.35/1.27 X202 @
% 5.35/1.27 (
% 5.35/1.27 powerset
% 5.35/1.27 @
% 5.35/1.27 X200 ) ) =>
% 5.35/1.27 (
% 5.35/1.27 ![
% 5.35/1.27 X204:$i]:
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 in @
% 5.35/1.27 X204 @
% 5.35/1.27 X200 ) =>
% 5.35/1.27 (
% 5.35/1.27 (
% 5.35/1.27 in @
% 5.35/1.27 X204 @
% 5.35/1.27 (
% 5.35/1.27 setminus
% 5.35/1.27 @
% 5.35/1.27 X200 @
% 5.35/1.27 (
% 5.35/1.27 setminus
% 5.35/1.27 @
% 5.35/1.27 X200 @
% 5.35/1.27 X202 ) ) ) =>
% 5.35/1.27 (
% 5.35/1.27 in @
% 5.35/1.27 X204 @
% 5.35/1.27 X202 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )),
% 5.35/1.27 inference('cnf.neg', [status(esa)], [zf_stmt_3])).
% 5.35/1.27 thf(zip_derived_cl129, plain, (~ (in @ sk__105 @ sk__104)),
% 5.35/1.27 inference('cnf', [status(esa)], [zf_stmt_4])).
% 5.35/1.27 thf(zip_derived_cl128, plain, ( (in @ sk__105 @ sk__103)),
% 5.35/1.27 inference('cnf', [status(esa)], [zf_stmt_4])).
% 5.35/1.27 thf(zip_derived_cl65, plain,
% 5.35/1.27 (![X11 : $i, X12 : $i, X13 : $i]:
% 5.35/1.27 ( (in @ X11 @ X12)
% 5.35/1.27 | ~ (in @ X11 @ X13)
% 5.35/1.27 | (in @ X11 @ (setminus @ X13 @ X12)))),
% 5.35/1.27 inference('cnf', [status(esa)], [zf_stmt_4])).
% 5.35/1.27 thf(zip_derived_cl287, plain,
% 5.35/1.27 (![X0 : $i]:
% 5.35/1.27 ( (in @ sk__105 @ (setminus @ sk__103 @ X0)) | (in @ sk__105 @ X0))),
% 5.35/1.27 inference('sup-', [status(thm)], [zip_derived_cl128, zip_derived_cl65])).
% 5.35/1.27 thf(zip_derived_cl130, plain,
% 5.35/1.27 ( (in @ sk__105 @ (setminus @ sk__103 @ (setminus @ sk__103 @ sk__104)))),
% 5.35/1.27 inference('cnf', [status(esa)], [zf_stmt_4])).
% 5.35/1.27 thf(zip_derived_cl66, plain,
% 5.35/1.27 (![X14 : $i, X15 : $i, X16 : $i]:
% 5.35/1.27 (~ (in @ X14 @ (setminus @ X15 @ X16)) | ~ (in @ X14 @ X16))),
% 5.35/1.27 inference('cnf', [status(esa)], [zf_stmt_4])).
% 5.35/1.27 thf(zip_derived_cl769, plain,
% 5.35/1.27 (~ (in @ sk__105 @ (setminus @ sk__103 @ sk__104))),
% 5.35/1.27 inference('sup-', [status(thm)], [zip_derived_cl130, zip_derived_cl66])).
% 5.35/1.27 thf(zip_derived_cl792, plain, ( (in @ sk__105 @ sk__104)),
% 5.35/1.27 inference('sup-', [status(thm)], [zip_derived_cl287, zip_derived_cl769])).
% 5.35/1.27 thf(zip_derived_cl797, plain, ($false),
% 5.35/1.27 inference('demod', [status(thm)], [zip_derived_cl129, zip_derived_cl792])).
% 5.35/1.27
% 5.35/1.27 % SZS output end Refutation
% 5.35/1.27
% 5.35/1.27
% 5.35/1.27 % Terminating...
% 5.86/1.35 % Runner terminated.
% 5.86/1.37 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------