%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SEU716^1 : TPTP v9.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.fTg19LQ1PQ true
% Computer : n025.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Oct 2 04:55:56 PM UTC 2025
% Result : Theorem 21.01s 3.28s
% Output : Refutation 21.01s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.11 % Problem : SEU716^1 : TPTP v9.2.0. Released v3.7.0.
% 0.02/0.12 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.fTg19LQ1PQ true
% 0.13/0.33 % Computer : n025.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Wed Oct 1 16:01:38 EDT 2025
% 0.13/0.33 % CPUTime :
% 0.13/0.33 % Running portfolio for 300 s
% 0.13/0.33 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.34 % Number of cores: 8
% 0.13/0.34 % Python version: Python 3.6.8
% 0.13/0.34 % Running in HO mode
% 0.56/0.65 % Total configuration time : 828
% 0.56/0.65 % Estimated wc time : 1656
% 0.56/0.65 % Estimated cpu time (8 cpus) : 207.0
% 0.56/0.74 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
% 0.56/0.74 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.56/0.75 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
% 0.56/0.75 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
% 0.56/0.75 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s
% 0.56/0.75 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s
% 0.56/0.76 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.58/0.78 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s
% 21.01/3.28 % Solved by lams/40_c_ic.sh.
% 21.01/3.28 % done 1399 iterations in 2.457s
% 21.01/3.28 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 21.01/3.28 % SZS output start Refutation
% 21.01/3.28 thf(setadjoinAx_type, type, setadjoinAx: $o).
% 21.01/3.28 thf(notdexE_type, type, notdexE: $o).
% 21.01/3.28 thf(setukpairinjL2_type, type, setukpairinjL2: $o).
% 21.01/3.28 thf(setunionAx_type, type, setunionAx: $o).
% 21.01/3.28 thf(setminusELneg_type, type, setminusELneg: $o).
% 21.01/3.28 thf(cartprodsndin_type, type, cartprodsndin: $o).
% 21.01/3.28 thf(ex1E1_type, type, ex1E1: $o).
% 21.01/3.28 thf(powersetE_type, type, powersetE: $o).
% 21.01/3.28 thf(omegaSAx_type, type, omegaSAx: $o).
% 21.01/3.28 thf(exuI1_type, type, exuI1: $o).
% 21.01/3.28 thf(exuI2_type, type, exuI2: $o).
% 21.01/3.28 thf(notequalI2_type, type, notequalI2: $o).
% 21.01/3.28 thf(setukpairinjL_type, type, setukpairinjL: $o).
% 21.01/3.28 thf(kpairiskpair_type, type, kpairiskpair: $o).
% 21.01/3.28 thf(upairsubunion_type, type, upairsubunion: $o).
% 21.01/3.28 thf(funcGraphProp3_type, type, funcGraphProp3: $o).
% 21.01/3.28 thf(cartprodmempaircEq_type, type, cartprodmempaircEq: $o).
% 21.01/3.28 thf(powerset__Cong_type, type, powerset__Cong: $o).
% 21.01/3.28 thf(setminusILneg_type, type, setminusILneg: $o).
% 21.01/3.28 thf(wellorderingAx_type, type, wellorderingAx: $o).
% 21.01/3.28 thf(ksndpairEq_type, type, ksndpairEq: $o).
% 21.01/3.28 thf(funcGraphProp2_type, type, funcGraphProp2: $o).
% 21.01/3.28 thf(setadjoinSub2_type, type, setadjoinSub2: $o).
% 21.01/3.28 thf(binintersectSubset5_type, type, binintersectSubset5: $o).
% 21.01/3.28 thf(iftrue_type, type, iftrue: $o).
% 21.01/3.28 thf(upairinpowunion_type, type, upairinpowunion: $o).
% 21.01/3.28 thf(ifSingleton_type, type, ifSingleton: $o).
% 21.01/3.28 thf(setoftrueEq_type, type, setoftrueEq: $o).
% 21.01/3.28 thf(funcImageSingleton_type, type, funcImageSingleton: $o).
% 21.01/3.28 thf(dpsetconstrERa_type, type, dpsetconstrERa: $o).
% 21.01/3.28 thf(lamProp_type, type, lamProp: $o).
% 21.01/3.28 thf(cartprodpairmemEL_type, type, cartprodpairmemEL: $o).
% 21.01/3.28 thf(emptyset__Cong_type, type, emptyset__Cong: $o).
% 21.01/3.28 thf(dpsetconstrER_type, type, dpsetconstrER: $o).
% 21.01/3.28 thf(sepInPowerset_type, type, sepInPowerset: $o).
% 21.01/3.28 thf(setukpairIR_type, type, setukpairIR: $o).
% 21.01/3.28 thf(setukpairinjR1_type, type, setukpairinjR1: $o).
% 21.01/3.28 thf(lam2p_type, type, lam2p: $o).
% 21.01/3.28 thf(binunionE_type, type, binunionE: $o).
% 21.01/3.28 thf(setext_type, type, setext: $o).
% 21.01/3.28 thf(emptyinPowerset_type, type, emptyinPowerset: $o).
% 21.01/3.28 thf(ubforcartprodlem1_type, type, ubforcartprodlem1: $o).
% 21.01/3.28 thf(descr__Cong_type, type, descr__Cong: $o).
% 21.01/3.28 thf(kfstsingleton_type, type, kfstsingleton: $o).
% 21.01/3.28 thf(eqbreln_type, type, eqbreln: $o).
% 21.01/3.28 thf(binintersectSubset1_type, type, binintersectSubset1: $o).
% 21.01/3.28 thf(in_type, type, in: $i > $i > $o).
% 21.01/3.28 thf(binunionT_lem_type, type, binunionT_lem: $o).
% 21.01/3.28 thf(quantDeMorgan1_type, type, quantDeMorgan1: $o).
% 21.01/3.28 thf(complementT_lem_type, type, complementT_lem: $o).
% 21.01/3.28 thf(sk__76_type, type, sk__76: $i > $i > $i).
% 21.01/3.28 thf(kpairsurjEq_type, type, kpairsurjEq: $o).
% 21.01/3.28 thf(setadjoinIR_type, type, setadjoinIR: $o).
% 21.01/3.28 thf(beta1_type, type, beta1: $o).
% 21.01/3.28 thf(setadjoin__Cong_type, type, setadjoin__Cong: $o).
% 21.01/3.28 thf(symdiffI2_type, type, symdiffI2: $o).
% 21.01/3.28 thf(iftrueProp2_type, type, iftrueProp2: $o).
% 21.01/3.28 thf(upairset2IR_type, type, upairset2IR: $o).
% 21.01/3.28 thf(iffalseProp2_type, type, iffalseProp2: $o).
% 21.01/3.28 thf(subsetE_type, type, subsetE: $o).
% 21.01/3.28 thf(prop2set2propI_type, type, prop2set2propI: $o).
% 21.01/3.28 thf(dsetconstrEL_type, type, dsetconstrEL: $o).
% 21.01/3.28 thf(setbeta_type, type, setbeta: $o).
% 21.01/3.28 thf(eqinunit_type, type, eqinunit: $o).
% 21.01/3.28 thf(upairsetIL_type, type, upairsetIL: $o).
% 21.01/3.28 thf(powersetI1_type, type, powersetI1: $o).
% 21.01/3.28 thf(kfstpairEq_type, type, kfstpairEq: $o).
% 21.01/3.28 thf(binintersectSubset3_type, type, binintersectSubset3: $o).
% 21.01/3.28 thf(setminusIRneg_type, type, setminusIRneg: $o).
% 21.01/3.28 thf(ap2apEq1_type, type, ap2apEq1: $o).
% 21.01/3.28 thf(powersetAx_type, type, powersetAx: $o).
% 21.01/3.28 thf(binintersectSubset4_type, type, binintersectSubset4: $o).
% 21.01/3.28 thf(singletoninpowunion_type, type, singletoninpowunion: $o).
% 21.01/3.28 thf(powersetI_type, type, powersetI: $o).
% 21.01/3.28 thf(cartprodmempair_type, type, cartprodmempair: $o).
% 21.01/3.28 thf(upairsetIR_type, type, upairsetIR: $o).
% 21.01/3.28 thf(lamp_type, type, lamp: $o).
% 21.01/3.28 thf(dpsetconstrEL1_type, type, dpsetconstrEL1: $o).
% 21.01/3.28 thf(inCongP_type, type, inCongP: $o).
% 21.01/3.28 thf(setadjoinSub_type, type, setadjoinSub: $o).
% 21.01/3.28 thf(exuE3e_type, type, exuE3e: $o).
% 21.01/3.28 thf(emptysetE_type, type, emptysetE: $o).
% 21.01/3.28 thf(binintersectSubset2_type, type, binintersectSubset2: $o).
% 21.01/3.28 thf(setunionI_type, type, setunionI: $o).
% 21.01/3.28 thf(setunion__Cong_type, type, setunion__Cong: $o).
% 21.01/3.28 thf(prop2setI_type, type, prop2setI: $o).
% 21.01/3.28 thf(singletonsuniq_type, type, singletonsuniq: $o).
% 21.01/3.28 thf(nonemptyImpWitness_type, type, nonemptyImpWitness: $o).
% 21.01/3.28 thf(setminusER_type, type, setminusER: $o).
% 21.01/3.28 thf(exuE2_type, type, exuE2: $o).
% 21.01/3.28 thf(emptyset_type, type, emptyset: $i).
% 21.01/3.28 thf(setukpairinjR11_type, type, setukpairinjR11: $o).
% 21.01/3.28 thf(ex1I_type, type, ex1I: $o).
% 21.01/3.28 thf(ex1E2_type, type, ex1E2: $o).
% 21.01/3.28 thf(setukpairinjL1_type, type, setukpairinjL1: $o).
% 21.01/3.28 thf(powersetsubset_type, type, powersetsubset: $o).
% 21.01/3.28 thf(subPowSU_type, type, subPowSU: $o).
% 21.01/3.28 thf(notequalI1_type, type, notequalI1: $o).
% 21.01/3.28 thf(notinemptyset_type, type, notinemptyset: $o).
% 21.01/3.28 thf(lam2lamEq_type, type, lam2lamEq: $o).
% 21.01/3.28 thf(nonemptyI1_type, type, nonemptyI1: $o).
% 21.01/3.28 thf(subsetTrans_type, type, subsetTrans: $o).
% 21.01/3.28 thf(kpairp_type, type, kpairp: $o).
% 21.01/3.28 thf(setukpairinjR12_type, type, setukpairinjR12: $o).
% 21.01/3.28 thf(setminusI_type, type, setminusI: $o).
% 21.01/3.28 thf(binunionIL_type, type, binunionIL: $o).
% 21.01/3.28 thf(dpsetconstrSub_type, type, dpsetconstrSub: $o).
% 21.01/3.28 thf(setunionsingleton_type, type, setunionsingleton: $o).
% 21.01/3.28 thf(subsetE2_type, type, subsetE2: $o).
% 21.01/3.28 thf(singletonsswitch_type, type, singletonsswitch: $o).
% 21.01/3.28 thf(ubforcartprodlem3_type, type, ubforcartprodlem3: $o).
% 21.01/3.28 thf(beta2_type, type, beta2: $o).
% 21.01/3.28 thf(dpsetconstrI_type, type, dpsetconstrI: $o).
% 21.01/3.28 thf(setextsub_type, type, setextsub: $o).
% 21.01/3.28 thf(binunionLsub_type, type, binunionLsub: $o).
% 21.01/3.28 thf(setunionsingleton1_type, type, setunionsingleton1: $o).
% 21.01/3.28 thf(iftrueorfalse_type, type, iftrueorfalse: $o).
% 21.01/3.28 thf(emptysetsubset_type, type, emptysetsubset: $o).
% 21.01/3.28 thf(quantDeMorgan3_type, type, quantDeMorgan3: $o).
% 21.01/3.28 thf(cartprodpairsurjEq_type, type, cartprodpairsurjEq: $o).
% 21.01/3.28 thf(setOfPairsIsBReln_type, type, setOfPairsIsBReln: $o).
% 21.01/3.28 thf(setunionE_type, type, setunionE: $o).
% 21.01/3.28 thf(ksndsingleton_type, type, ksndsingleton: $o).
% 21.01/3.28 thf(setminusSubset1_type, type, setminusSubset1: $o).
% 21.01/3.28 thf(powersetT_lem_type, type, powersetT_lem: $o).
% 21.01/3.28 thf(emptyinunitempty_type, type, emptyinunitempty: $o).
% 21.01/3.28 thf(binunionIR_type, type, binunionIR: $o).
% 21.01/3.28 thf(theeq_type, type, theeq: $o).
% 21.01/3.28 thf(setadjoinE_type, type, setadjoinE: $o).
% 21.01/3.28 thf(zip_tseitin_0_type, type, zip_tseitin_0: $i > $i > $i > $o).
% 21.01/3.28 thf(infuncsetfunc_type, type, infuncsetfunc: $o).
% 21.01/3.28 thf(ap2apEq2_type, type, ap2apEq2: $o).
% 21.01/3.28 thf(ap2p_type, type, ap2p: $o).
% 21.01/3.28 thf(setadjoinIL_type, type, setadjoinIL: $o).
% 21.01/3.28 thf(cartprodsndpairEq_type, type, cartprodsndpairEq: $o).
% 21.01/3.28 thf(exuE1_type, type, exuE1: $o).
% 21.01/3.28 thf(ubforcartprodlem2_type, type, ubforcartprodlem2: $o).
% 21.01/3.28 thf(binintersectRsub_type, type, binintersectRsub: $o).
% 21.01/3.28 thf(setminusLsub_type, type, setminusLsub: $o).
% 21.01/3.28 thf(funcextLem_type, type, funcextLem: $o).
% 21.01/3.28 thf(setukpairinjR_type, type, setukpairinjR: $o).
% 21.01/3.28 thf(notinsingleton_type, type, notinsingleton: $o).
% 21.01/3.28 thf(eqimpsubset2_type, type, eqimpsubset2: $o).
% 21.01/3.28 thf(exuEu_type, type, exuEu: $o).
% 21.01/3.28 thf(emptysetimpfalse_type, type, emptysetimpfalse: $o).
% 21.01/3.28 thf(sk__72_type, type, sk__72: $i).
% 21.01/3.28 thf(upairsetE_type, type, upairsetE: $o).
% 21.01/3.28 thf(omega0Ax_type, type, omega0Ax: $o).
% 21.01/3.28 thf(notsubsetI_type, type, notsubsetI: $o).
% 21.01/3.28 thf(iffalseProp1_type, type, iffalseProp1: $o).
% 21.01/3.28 thf(quantDeMorgan4_type, type, quantDeMorgan4: $o).
% 21.01/3.28 thf(setextAx_type, type, setextAx: $o).
% 21.01/3.28 thf(cartprodpairmemER_type, type, cartprodpairmemER: $o).
% 21.01/3.28 thf(sk__73_type, type, sk__73: $i).
% 21.01/3.28 thf(powersetE1_type, type, powersetE1: $o).
% 21.01/3.28 thf(bs114d_type, type, bs114d: $o).
% 21.01/3.28 thf(noeltsimpempty_type, type, noeltsimpempty: $o).
% 21.01/3.28 thf(ifp_type, type, ifp: $o).
% 21.01/3.28 thf(binintersectLsub_type, type, binintersectLsub: $o).
% 21.01/3.28 thf(subsetI1_type, type, subsetI1: $o).
% 21.01/3.28 thf(symdiffE_type, type, symdiffE: $o).
% 21.01/3.28 thf(descrp_type, type, descrp: $o).
% 21.01/3.28 thf(dsetconstr__Cong_type, type, dsetconstr__Cong: $o).
% 21.01/3.28 thf(foundationAx_type, type, foundationAx: $o).
% 21.01/3.28 thf(emptysetAx_type, type, emptysetAx: $o).
% 21.01/3.28 thf(emptyI_type, type, emptyI: $o).
% 21.01/3.28 thf(setadjoinOr_type, type, setadjoinOr: $o).
% 21.01/3.28 thf(eta2_type, type, eta2: $o).
% 21.01/3.28 thf(binintersectEL_type, type, binintersectEL: $o).
% 21.01/3.28 thf(emptyE1_type, type, emptyE1: $o).
% 21.01/3.28 thf(emptyInPowerset_type, type, emptyInPowerset: $o).
% 21.01/3.28 thf(vacuousDall_type, type, vacuousDall: $o).
% 21.01/3.28 thf(dsetconstrER_type, type, dsetconstrER: $o).
% 21.01/3.28 thf(binintersectI_type, type, binintersectI: $o).
% 21.01/3.28 thf(funcext_type, type, funcext: $o).
% 21.01/3.28 thf(funcGraphProp4_type, type, funcGraphProp4: $o).
% 21.01/3.28 thf(sk__74_type, type, sk__74: $i).
% 21.01/3.28 thf(cartprodpairin_type, type, cartprodpairin: $o).
% 21.01/3.28 thf(cartprodmempair1_type, type, cartprodmempair1: $o).
% 21.01/3.28 thf(brelnall2_type, type, brelnall2: $o).
% 21.01/3.28 thf(setextT_type, type, setextT: $o).
% 21.01/3.28 thf(ex1I2_type, type, ex1I2: $o).
% 21.01/3.28 thf(symdiffI1_type, type, symdiffI1: $o).
% 21.01/3.28 thf(setukpairinjR2_type, type, setukpairinjR2: $o).
% 21.01/3.28 thf(dpsetconstrEL2_type, type, dpsetconstrEL2: $o).
% 21.01/3.28 thf(theprop_type, type, theprop: $o).
% 21.01/3.28 thf(subsetI2_type, type, subsetI2: $o).
% 21.01/3.28 thf(setminusT_lem_type, type, setminusT_lem: $o).
% 21.01/3.28 thf(symdiffIneg1_type, type, symdiffIneg1: $o).
% 21.01/3.28 thf(setminusERneg_type, type, setminusERneg: $o).
% 21.01/3.28 thf(symdiffIneg2_type, type, symdiffIneg2: $o).
% 21.01/3.28 thf(omega__Cong_type, type, omega__Cong: $o).
% 21.01/3.28 thf(subsetRefl_type, type, subsetRefl: $o).
% 21.01/3.28 thf(uniqinunit_type, type, uniqinunit: $o).
% 21.01/3.28 thf(setminusSubset2_type, type, setminusSubset2: $o).
% 21.01/3.28 thf(prop2setE_type, type, prop2setE: $o).
% 21.01/3.28 thf(binunionEcases_type, type, binunionEcases: $o).
% 21.01/3.28 thf(funcinfuncset_type, type, funcinfuncset: $o).
% 21.01/3.28 thf(nonemptyI_type, type, nonemptyI: $o).
% 21.01/3.28 thf(app_type, type, app: $o).
% 21.01/3.28 thf(disjointsetsI1_type, type, disjointsetsI1: $o).
% 21.01/3.28 thf(exuE3u_type, type, exuE3u: $o).
% 21.01/3.28 thf(eta1_type, type, eta1: $o).
% 21.01/3.28 thf(setminusEL_type, type, setminusEL: $o).
% 21.01/3.28 thf(cartprodfstin_type, type, cartprodfstin: $o).
% 21.01/3.28 thf(setunionsingleton2_type, type, setunionsingleton2: $o).
% 21.01/3.28 thf(sepSubset_type, type, sepSubset: $o).
% 21.01/3.28 thf(upairset2E_type, type, upairset2E: $o).
% 21.01/3.28 thf(eqimpsubset1_type, type, eqimpsubset1: $o).
% 21.01/3.28 thf(exuI3_type, type, exuI3: $o).
% 21.01/3.28 thf(cartprodfstpairEq_type, type, cartprodfstpairEq: $o).
% 21.01/3.28 thf(apProp_type, type, apProp: $o).
% 21.01/3.28 thf(notdallE_type, type, notdallE: $o).
% 21.01/3.28 thf(iftrueProp1_type, type, iftrueProp1: $o).
% 21.01/3.28 thf(binintersectER_type, type, binintersectER: $o).
% 21.01/3.28 thf(brelnall1_type, type, brelnall1: $o).
% 21.01/3.28 thf(powerset_type, type, powerset: $i > $i).
% 21.01/3.28 thf(dsetconstrI_type, type, dsetconstrI: $o).
% 21.01/3.28 thf(funcGraphProp1_type, type, funcGraphProp1: $o).
% 21.01/3.28 thf(binintersectT_lem_type, type, binintersectT_lem: $o).
% 21.01/3.28 thf(setadjoin_type, type, setadjoin: $i > $i > $i).
% 21.01/3.28 thf(exu__Cong_type, type, exu__Cong: $o).
% 21.01/3.28 thf(quantDeMorgan2_type, type, quantDeMorgan2: $o).
% 21.01/3.28 thf(secondinupair_type, type, secondinupair: $o).
% 21.01/3.28 thf(singletonprop_type, type, singletonprop: $o).
% 21.01/3.28 thf(singletonsubset_type, type, singletonsubset: $o).
% 21.01/3.28 thf(singletoninpowerset_type, type, singletoninpowerset: $o).
% 21.01/3.28 thf(subsetemptysetimpeq_type, type, subsetemptysetimpeq: $o).
% 21.01/3.28 thf(replAx_type, type, replAx: $o).
% 21.01/3.28 thf(upairequniteq_type, type, upairequniteq: $o).
% 21.01/3.28 thf(nonemptyE1_type, type, nonemptyE1: $o).
% 21.01/3.28 thf(omegaIndAx_type, type, omegaIndAx: $o).
% 21.01/3.28 thf(setukpairIL_type, type, setukpairIL: $o).
% 21.01/3.28 thf(setunionE2_type, type, setunionE2: $o).
% 21.01/3.28 thf(inPowerset_type, type, inPowerset: $o).
% 21.01/3.28 thf(iffalse_type, type, iffalse: $o).
% 21.01/3.28 thf(funcext2_type, type, funcext2: $o).
% 21.01/3.28 thf(subset_type, type, subset: $i > $i > $o).
% 21.01/3.28 thf(subbreln_type, type, subbreln: $o).
% 21.01/3.28 thf(in__Cong_type, type, in__Cong: $o).
% 21.01/3.28 thf(binunionRsub_type, type, binunionRsub: $o).
% 21.01/3.28 thf(subset2powerset_type, type, subset2powerset: $o).
% 21.01/3.28 thf(setextT, axiom, setextT =
% 21.01/3.28 (![A:$i,X:$i]:
% 21.01/3.28 ( ( in @ X @ ( powerset @ A ) ) =>
% 21.01/3.28 ( ![Y:$i]:
% 21.01/3.28 ( ( in @ Y @ ( powerset @ A ) ) =>
% 21.01/3.28 ( ( ![Xx:$i]:
% 21.01/3.28 ( ( in @ Xx @ A ) => ( ( in @ Xx @ X ) => ( in @ Xx @ Y ) ) ) ) =>
% 21.01/3.28 ( ( ![Xx:$i]:
% 21.01/3.28 ( ( in @ Xx @ A ) => ( ( in @ Xx @ Y ) => ( in @ Xx @ X ) ) ) ) =>
% 21.01/3.28 ( ( X ) = ( Y ) ) ) ) ) ) ))).
% 21.01/3.28 thf('0', plain,
% 21.01/3.28 (( setextT ) =
% 21.01/3.28 ( ![X4:$i,X6:$i]:
% 21.01/3.28 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 21.01/3.28 ( ![X8:$i]:
% 21.01/3.28 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 21.01/3.28 ( ( ![X10:$i]:
% 21.01/3.28 ( ( in @ X10 @ X4 ) =>
% 21.01/3.28 ( ( in @ X10 @ X6 ) => ( in @ X10 @ X8 ) ) ) ) =>
% 21.01/3.28 ( ( ![X12:$i]:
% 21.01/3.28 ( ( in @ X12 @ X4 ) =>
% 21.01/3.28 ( ( in @ X12 @ X8 ) => ( in @ X12 @ X6 ) ) ) ) =>
% 21.01/3.28 ( ( X6 ) = ( X8 ) ) ) ) ) ) ) )),
% 21.01/3.28 define([status(thm)])).
% 21.01/3.28 thf(powersetT_lem, axiom, powersetT_lem =
% 21.01/3.28 (![A:$i,X:$i]:
% 21.01/3.28 ( ( in @ X @ ( powerset @ A ) ) =>
% 21.01/3.28 ( in @ ( powerset @ X ) @ ( powerset @ ( powerset @ A ) ) ) ))).
% 21.01/3.28 thf('1', plain,
% 21.01/3.28 (( powersetT_lem ) =
% 21.01/3.28 ( ![X4:$i,X6:$i]:
% 21.01/3.28 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 21.01/3.28 ( in @ ( powerset @ X6 ) @ ( powerset @ ( powerset @ X4 ) ) ) ) )),
% 21.01/3.28 define([status(thm)])).
% 21.01/3.28 thf(singletoninpowerset, axiom, singletoninpowerset =
% 21.01/3.28 (![A:$i,Xx:$i]:
% 21.01/3.28 ( ( in @ Xx @ A ) =>
% 21.01/3.28 ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) ))).
% 21.01/3.28 thf('2', plain,
% 21.01/3.28 (( singletoninpowerset ) =
% 21.01/3.28 ( ![X4:$i,X6:$i]:
% 21.01/3.28 ( ( in @ X6 @ X4 ) =>
% 21.01/3.28 ( in @ ( setadjoin @ X6 @ emptyset ) @ ( powerset @ X4 ) ) ) )),
% 21.01/3.28 define([status(thm)])).
% 21.01/3.28 thf(singletonsubset, axiom, singletonsubset =
% 21.01/3.28 (![A:$i,Xx:$i]:
% 21.01/3.28 ( ( in @ Xx @ A ) => ( subset @ ( setadjoin @ Xx @ emptyset ) @ A ) ))).
% 21.01/3.28 thf('3', plain,
% 21.01/3.28 (( singletonsubset ) =
% 21.01/3.28 ( ![X4:$i,X6:$i]:
% 21.01/3.28 ( ( in @ X6 @ X4 ) => ( subset @ ( setadjoin @ X6 @ emptyset ) @ X4 ) ) )),
% 21.01/3.28 define([status(thm)])).
% 21.01/3.28 thf(powersetsubset, axiom, powersetsubset =
% 21.01/3.28 (![A:$i,B:$i]:
% 21.01/3.28 ( ( subset @ A @ B ) => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ))).
% 21.01/3.28 thf('4', plain,
% 21.01/3.28 (( powersetsubset ) =
% 21.01/3.28 ( ![X4:$i,X6:$i]:
% 21.01/3.28 ( ( subset @ X4 @ X6 ) =>
% 21.01/3.28 ( subset @ ( powerset @ X4 ) @ ( powerset @ X6 ) ) ) )),
% 21.01/3.28 define([status(thm)])).
% 21.01/3.28 thf(inPowerset, axiom, inPowerset = (![A:$i]: ( in @ A @ ( powerset @ A ) ))).
% 21.01/3.28 thf('5', plain,
% 21.01/3.28 (( inPowerset ) = ( ![X4:$i]: ( in @ X4 @ ( powerset @ X4 ) ) )),
% 21.01/3.28 define([status(thm)])).
% 21.01/3.28 thf(powersetE1, axiom, powersetE1 =
% 21.01/3.28 (![A:$i,B:$i]: ( ( in @ B @ ( powerset @ A ) ) => ( subset @ B @ A ) ))).
% 21.01/3.28 thf('6', plain,
% 21.01/3.28 (( powersetE1 ) =
% 21.01/3.28 ( ![X4:$i,X6:$i]:
% 21.01/3.28 ( ( in @ X6 @ ( powerset @ X4 ) ) => ( subset @ X6 @ X4 ) ) )),
% 21.01/3.28 define([status(thm)])).
% 21.01/3.28 thf(powersetI1, axiom, powersetI1 =
% 21.01/3.28 (![A:$i,B:$i]: ( ( subset @ B @ A ) => ( in @ B @ ( powerset @ A ) ) ))).
% 21.01/3.28 thf('7', plain,
% 21.01/3.28 (( powersetI1 ) =
% 21.01/3.28 ( ![X4:$i,X6:$i]:
% 21.01/3.28 ( ( subset @ X6 @ X4 ) => ( in @ X6 @ ( powerset @ X4 ) ) ) )),
% 21.01/3.28 define([status(thm)])).
% 21.01/3.28 thf(subsetemptysetimpeq, axiom, subsetemptysetimpeq =
% 21.01/3.28 (![A:$i]: ( ( subset @ A @ emptyset ) => ( ( A ) = ( emptyset ) ) ))).
% 21.01/3.28 thf('8', plain,
% 21.01/3.28 (( subsetemptysetimpeq ) =
% 21.01/3.28 ( ![X4:$i]: ( ( subset @ X4 @ emptyset ) => ( ( X4 ) = ( emptyset ) ) ) )),
% 21.01/3.28 define([status(thm)])).
% 21.01/3.28 thf(setextsub, axiom, setextsub =
% 21.01/3.28 (![A:$i,B:$i]:
% 21.01/3.28 ( ( subset @ A @ B ) => ( ( subset @ B @ A ) => ( ( A ) = ( B ) ) ) ))).
% 21.01/3.28 thf('9', plain,
% 21.01/3.28 (( setextsub ) =
% 21.01/3.28 ( ![X4:$i,X6:$i]:
% 21.01/3.28 ( ( subset @ X4 @ X6 ) =>
% 21.01/3.28 ( ( subset @ X6 @ X4 ) => ( ( X4 ) = ( X6 ) ) ) ) )),
% 21.01/3.28 define([status(thm)])).
% 21.01/3.28 thf(subset2powerset, axiom, subset2powerset =
% 21.01/3.28 (![A:$i,B:$i]: ( ( subset @ A @ B ) => ( in @ A @ ( powerset @ B ) ) ))).
% 21.01/3.28 thf('10', plain,
% 21.01/3.28 (( subset2powerset ) =
% 21.01/3.28 ( ![X4:$i,X6:$i]:
% 21.01/3.28 ( ( subset @ X4 @ X6 ) => ( in @ X4 @ ( powerset @ X6 ) ) ) )),
% 21.01/3.28 define([status(thm)])).
% 21.01/3.28 thf(setadjoinSub2, axiom, setadjoinSub2 =
% 21.01/3.28 (![A:$i,Xx:$i,B:$i]:
% 21.01/3.28 ( ( subset @ A @ B ) => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ))).
% 21.01/3.28 thf('11', plain,
% 21.01/3.28 (( setadjoinSub2 ) =
% 21.01/3.28 ( ![X4:$i,X6:$i,X8:$i]:
% 21.01/3.28 ( ( subset @ X4 @ X8 ) => ( subset @ X4 @ ( setadjoin @ X6 @ X8 ) ) ) )),
% 21.01/3.28 define([status(thm)])).
% 21.01/3.28 thf(setadjoinSub, axiom, setadjoinSub =
% 21.01/3.28 (![Xx:$i,A:$i]: ( subset @ A @ ( setadjoin @ Xx @ A ) ))).
% 21.01/3.28 thf('12', plain,
% 21.01/3.28 (( setadjoinSub ) =
% 21.01/3.28 ( ![X4:$i,X6:$i]: ( subset @ X6 @ ( setadjoin @ X4 @ X6 ) ) )),
% 21.01/3.28 define([status(thm)])).
% 21.01/3.28 thf(subsetTrans, axiom, subsetTrans =
% 21.01/3.28 (![A:$i,B:$i,C:$i]:
% 21.01/3.28 ( ( subset @ A @ B ) => ( ( subset @ B @ C ) => ( subset @ A @ C ) ) ))).
% 21.01/3.28 thf('13', plain,
% 21.01/3.28 (( subsetTrans ) =
% 21.01/3.28 ( ![X4:$i,X6:$i,X8:$i]:
% 21.01/3.28 ( ( subset @ X4 @ X6 ) =>
% 21.01/3.28 ( ( subset @ X6 @ X8 ) => ( subset @ X4 @ X8 ) ) ) )),
% 21.01/3.28 define([status(thm)])).
% 21.01/3.28 thf(subsetRefl, axiom, subsetRefl = (![A:$i]: ( subset @ A @ A ))).
% 21.01/3.28 thf('14', plain, (( subsetRefl ) = ( ![X4:$i]: ( subset @ X4 @ X4 ) )),
% 21.01/3.28 define([status(thm)])).
% 21.01/3.28 thf(notequalI1, axiom, notequalI1 =
% 21.01/3.28 (![A:$i,B:$i]: ( ( ~( subset @ A @ B ) ) => ( ( A ) != ( B ) ) ))).
% 21.01/3.28 thf('15', plain,
% 21.01/3.28 (( notequalI1 ) =
% 21.01/3.28 ( ![X4:$i,X6:$i]: ( ( ~( subset @ X4 @ X6 ) ) => ( ( X4 ) != ( X6 ) ) ) )),
% 21.01/3.28 define([status(thm)])).
% 21.01/3.28 thf(notsubsetI, axiom, notsubsetI =
% 21.01/3.28 (![A:$i,B:$i,Xx:$i]:
% 21.01/3.28 ( ( in @ Xx @ A ) => ( ( ~( in @ Xx @ B ) ) => ( ~( subset @ A @ B ) ) ) ))).
% 21.01/3.28 thf('16', plain,
% 21.01/3.28 (( notsubsetI ) =
% 21.01/3.28 ( ![X4:$i,X6:$i,X8:$i]:
% 21.01/3.28 ( ( in @ X8 @ X4 ) =>
% 21.01/3.28 ( ( ~( in @ X8 @ X6 ) ) => ( ~( subset @ X4 @ X6 ) ) ) ) )),
% 21.01/3.28 define([status(thm)])).
% 21.01/3.28 thf(subsetE2, axiom, subsetE2 =
% 21.01/3.28 (![A:$i,B:$i,Xx:$i]:
% 21.01/3.28 ( ( subset @ A @ B ) => ( ( ~( in @ Xx @ B ) ) => ( ~( in @ Xx @ A ) ) ) ))).
% 21.01/3.28 thf('17', plain,
% 21.01/3.28 (( subsetE2 ) =
% 21.01/3.28 ( ![X4:$i,X6:$i,X8:$i]:
% 21.01/3.28 ( ( subset @ X4 @ X6 ) =>
% 21.01/3.28 ( ( ~( in @ X8 @ X6 ) ) => ( ~( in @ X8 @ X4 ) ) ) ) )),
% 21.01/3.28 define([status(thm)])).
% 21.01/3.28 thf(subsetE, axiom, subsetE =
% 21.01/3.28 (![A:$i,B:$i,Xx:$i]:
% 21.01/3.28 ( ( subset @ A @ B ) => ( ( in @ Xx @ A ) => ( in @ Xx @ B ) ) ))).
% 21.01/3.28 thf('18', plain,
% 21.01/3.28 (( subsetE ) =
% 21.01/3.28 ( ![X4:$i,X6:$i,X8:$i]:
% 21.01/3.28 ( ( subset @ X4 @ X6 ) => ( ( in @ X8 @ X4 ) => ( in @ X8 @ X6 ) ) ) )),
% 21.01/3.28 define([status(thm)])).
% 21.01/3.28 thf(emptysetsubset, axiom, emptysetsubset =
% 21.01/3.28 (![A:$i]: ( subset @ emptyset @ A ))).
% 21.01/3.28 thf('19', plain,
% 21.01/3.28 (( emptysetsubset ) = ( ![X4:$i]: ( subset @ emptyset @ X4 ) )),
% 21.01/3.28 define([status(thm)])).
% 21.01/3.28 thf(subsetI2, axiom, subsetI2 =
% 21.01/3.28 (![A:$i,B:$i]:
% 21.01/3.28 ( ( ![Xx:$i]: ( ( in @ Xx @ A ) => ( in @ Xx @ B ) ) ) =>
% 21.01/3.28 ( subset @ A @ B ) ))).
% 21.01/3.28 thf('20', plain,
% 21.01/3.28 (( subsetI2 ) =
% 21.01/3.28 ( ![X4:$i,X6:$i]:
% 21.01/3.28 ( ( ![X8:$i]: ( ( in @ X8 @ X4 ) => ( in @ X8 @ X6 ) ) ) =>
% 21.01/3.28 ( subset @ X4 @ X6 ) ) )),
% 21.01/3.28 define([status(thm)])).
% 21.01/3.28 thf(eqimpsubset1, axiom, eqimpsubset1 =
% 21.01/3.28 (![A:$i,B:$i]: ( ( ( A ) = ( B ) ) => ( subset @ A @ B ) ))).
% 21.01/3.28 thf('21', plain,
% 21.01/3.28 (( eqimpsubset1 ) =
% 21.01/3.28 ( ![X4:$i,X6:$i]: ( ( ( X4 ) = ( X6 ) ) => ( subset @ X4 @ X6 ) ) )),
% 21.01/3.28 define([status(thm)])).
% 21.01/3.28 thf(eqimpsubset2, axiom, eqimpsubset2 =
% 21.01/3.28 (![A:$i,B:$i]: ( ( ( A ) = ( B ) ) => ( subset @ B @ A ) ))).
% 21.01/3.28 thf('22', plain,
% 21.01/3.28 (( eqimpsubset2 ) =
% 21.01/3.28 ( ![X4:$i,X6:$i]: ( ( ( X4 ) = ( X6 ) ) => ( subset @ X6 @ X4 ) ) )),
% 21.01/3.28 define([status(thm)])).
% 21.01/3.28 thf(subsetI1, axiom, subsetI1 =
% 21.01/3.28 (![A:$i,B:$i]:
% 21.01/3.28 ( ( ![Xx:$i]: ( ( in @ Xx @ A ) => ( in @ Xx @ B ) ) ) =>
% 21.01/3.28 ( subset @ A @ B ) ))).
% 21.01/3.28 thf('23', plain,
% 21.01/3.28 (( subsetI1 ) =
% 21.01/3.28 ( ![X4:$i,X6:$i]:
% 21.01/3.28 ( ( ![X8:$i]: ( ( in @ X8 @ X4 ) => ( in @ X8 @ X6 ) ) ) =>
% 21.01/3.28 ( subset @ X4 @ X6 ) ) )),
% 21.01/3.28 define([status(thm)])).
% 21.01/3.28 thf(powerset__Cong, axiom, powerset__Cong =
% 21.01/3.28 (![A:$i,B:$i]:
% 21.01/3.28 ( ( ( A ) = ( B ) ) => ( ( powerset @ A ) = ( powerset @ B ) ) ))).
% 21.01/3.28 thf('24', plain,
% 21.01/3.28 (( powerset__Cong ) =
% 21.01/3.28 ( ![X4:$i,X6:$i]:
% 21.01/3.28 ( ( ( X4 ) = ( X6 ) ) => ( ( powerset @ X4 ) = ( powerset @ X6 ) ) ) )),
% 21.01/3.28 define([status(thm)])).
% 21.01/3.28 thf(powersetE, axiom, powersetE =
% 21.01/3.28 (![A:$i,B:$i,Xx:$i]:
% 21.01/3.28 ( ( in @ B @ ( powerset @ A ) ) => ( ( in @ Xx @ B ) => ( in @ Xx @ A ) ) ))).
% 21.01/3.28 thf('25', plain,
% 21.01/3.28 (( powersetE ) =
% 21.01/3.28 ( ![X4:$i,X6:$i,X8:$i]:
% 21.01/3.28 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 21.01/3.28 ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ) )),
% 21.01/3.28 define([status(thm)])).
% 21.01/3.28 thf(emptyInPowerset, axiom, emptyInPowerset =
% 21.01/3.28 (![A:$i]: ( in @ emptyset @ ( powerset @ A ) ))).
% 21.01/3.28 thf('26', plain,
% 21.01/3.28 (( emptyInPowerset ) =
% 21.01/3.28 ( ![X4:$i]: ( in @ emptyset @ ( powerset @ X4 ) ) )),
% 21.01/3.28 define([status(thm)])).
% 21.01/3.28 thf(emptyinPowerset, axiom, emptyinPowerset =
% 21.01/3.28 (![A:$i]: ( in @ emptyset @ ( powerset @ A ) ))).
% 21.01/3.28 thf('27', plain,
% 21.01/3.28 (( emptyinPowerset ) =
% 21.01/3.28 ( ![X4:$i]: ( in @ emptyset @ ( powerset @ X4 ) ) )),
% 21.01/3.28 define([status(thm)])).
% 21.01/3.28 thf(powersetI, axiom, powersetI =
% 21.01/3.28 (![A:$i,B:$i]:
% 21.01/3.28 ( ( ![Xx:$i]: ( ( in @ Xx @ B ) => ( in @ Xx @ A ) ) ) =>
% 21.01/3.28 ( in @ B @ ( powerset @ A ) ) ))).
% 21.01/3.28 thf('28', plain,
% 21.01/3.28 (( powersetI ) =
% 21.01/3.28 ( ![X4:$i,X6:$i]:
% 21.01/3.28 ( ( ![X8:$i]: ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ) =>
% 21.01/3.28 ( in @ X6 @ ( powerset @ X4 ) ) ) )),
% 21.01/3.28 define([status(thm)])).
% 21.01/3.28 thf(powersetAx, axiom, powersetAx =
% 21.01/3.28 (![A:$i,B:$i]:
% 21.01/3.28 ( ( in @ B @ ( powerset @ A ) ) <=>
% 21.01/3.28 ( ![Xx:$i]: ( ( in @ Xx @ B ) => ( in @ Xx @ A ) ) ) ))).
% 21.01/3.28 thf('29', plain,
% 21.01/3.28 (( powersetAx ) =
% 21.01/3.28 ( ![X4:$i,X6:$i]:
% 21.01/3.28 ( ( in @ X6 @ ( powerset @ X4 ) ) <=>
% 21.01/3.28 ( ![X8:$i]: ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ) ) )),
% 21.01/3.28 define([status(thm)])).
% 21.01/3.28 thf(subsetTI, conjecture,
% 21.01/3.28 (( setextAx ) =>
% 21.01/3.28 ( ( emptysetAx ) =>
% 21.01/3.28 ( ( setadjoinAx ) =>
% 21.01/3.28 ( ( powersetAx ) =>
% 21.01/3.28 ( ( setunionAx ) =>
% 21.01/3.28 ( ( omega0Ax ) =>
% 21.01/3.28 ( ( omegaSAx ) =>
% 21.01/3.28 ( ( omegaIndAx ) =>
% 21.01/3.28 ( ( replAx ) =>
% 21.01/3.28 ( ( foundationAx ) =>
% 21.01/3.28 ( ( wellorderingAx ) =>
% 21.01/3.28 ( ( descrp ) =>
% 21.01/3.28 ( ( dsetconstrI ) =>
% 21.01/3.28 ( ( dsetconstrEL ) =>
% 21.01/3.28 ( ( dsetconstrER ) =>
% 21.01/3.28 ( ( exuE1 ) =>
% 21.01/3.28 ( ( prop2setE ) =>
% 21.01/3.28 ( ( emptysetE ) =>
% 21.01/3.28 ( ( emptysetimpfalse ) =>
% 21.01/3.28 ( ( notinemptyset ) =>
% 21.01/3.28 ( ( exuE3e ) =>
% 21.01/3.28 ( ( setext ) =>
% 21.01/3.28 ( ( emptyI ) =>
% 21.01/3.28 ( ( noeltsimpempty ) =>
% 21.01/3.28 ( ( setbeta ) =>
% 21.01/3.28 ( ( nonemptyE1 ) =>
% 21.01/3.28 ( ( nonemptyI ) =>
% 21.01/3.28 ( ( nonemptyI1 ) =>
% 21.01/3.28 ( ( setadjoinIL ) =>
% 21.01/3.28 ( ( emptyinunitempty ) =>
% 21.01/3.28 ( ( setadjoinIR ) =>
% 21.01/3.28 ( ( setadjoinE ) =>
% 21.01/3.28 ( (
% 21.01/3.28 setadjoinOr ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 setoftrueEq ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 powersetI ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 emptyinPowerset ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 emptyInPowerset ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 powersetE ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 setunionI ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 setunionE ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 subPowSU ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 exuE2 ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 nonemptyImpWitness ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 uniqinunit ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 notinsingleton ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 eqinunit ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 singletonsswitch ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 upairsetE ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 upairsetIL ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 upairsetIR ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 emptyE1 ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 vacuousDall ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 quantDeMorgan1 ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 quantDeMorgan2 ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 quantDeMorgan3 ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 quantDeMorgan4 ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 prop2setI ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 prop2set2propI ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 notdexE ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 notdallE ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 exuI1 ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 exuI3 ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 exuI2 ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 inCongP ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 in__Cong ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 exuE3u ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 exu__Cong ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 emptyset__Cong ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 setadjoin__Cong ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 powerset__Cong ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 setunion__Cong ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 omega__Cong ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 exuEu ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 descr__Cong ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 dsetconstr__Cong ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 subsetI1 ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 eqimpsubset2 ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 eqimpsubset1 ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 subsetI2 ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 emptysetsubset ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 subsetE ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 subsetE2 ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 notsubsetI ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 notequalI1 ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 notequalI2 ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 subsetRefl ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 subsetTrans ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 setadjoinSub ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 setadjoinSub2 ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 subset2powerset ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 setextsub ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 subsetemptysetimpeq ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 powersetI1 ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 powersetE1 ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 inPowerset ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 powersetsubset ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 sepInPowerset ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 sepSubset ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 binunionIL ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 upairset2IR ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 binunionIR ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 binunionEcases ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 binunionE ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 binunionLsub ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 binunionRsub ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 binintersectI ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 binintersectSubset5 ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 binintersectEL ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 binintersectLsub ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 binintersectSubset2 ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 binintersectSubset3 ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 binintersectER ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 disjointsetsI1 ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 binintersectRsub ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 binintersectSubset4 ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 binintersectSubset1 ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 bs114d ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 setminusI ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 setminusEL ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 setminusER ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 setminusSubset2 ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 setminusERneg ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 setminusELneg ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 setminusILneg ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 setminusIRneg ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 setminusLsub ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 setminusSubset1 ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 symdiffE ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 symdiffI1 ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 symdiffI2 ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 symdiffIneg1 ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 symdiffIneg2 ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 secondinupair ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 setukpairIL ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 setukpairIR ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 kpairiskpair ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 kpairp ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 singletonsubset ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 singletoninpowerset ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 singletoninpowunion ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 upairset2E ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 upairsubunion ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 upairinpowunion ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 ubforcartprodlem1 ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 ubforcartprodlem2 ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 ubforcartprodlem3 ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 cartprodpairin ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 cartprodmempair1 ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 cartprodmempair ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 setunionE2 ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 setunionsingleton1 ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 setunionsingleton2 ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 setunionsingleton ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 singletonprop ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 ex1E1 ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 ex1I ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 ex1I2 ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 singletonsuniq ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 setukpairinjL1 ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 kfstsingleton ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 theprop ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 kfstpairEq ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 cartprodfstin ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 setukpairinjL2 ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 setukpairinjL ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 setukpairinjR11 ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 setukpairinjR12 ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 setukpairinjR1 ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 upairequniteq ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 setukpairinjR2 ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 setukpairinjR ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 ksndsingleton ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 ksndpairEq ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 kpairsurjEq ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 cartprodsndin ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 cartprodpairmemEL ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 cartprodpairmemER ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 cartprodmempaircEq ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 cartprodfstpairEq ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 cartprodsndpairEq ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 cartprodpairsurjEq ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 dpsetconstrI ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 dpsetconstrSub ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 setOfPairsIsBReln ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 dpsetconstrERa ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 dpsetconstrEL1 ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 dpsetconstrEL2 ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 dpsetconstrER ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 funcImageSingleton ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 apProp ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 app ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 infuncsetfunc ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 ap2p ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 funcinfuncset ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 lamProp ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 lamp ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 lam2p ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 brelnall1 ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 brelnall2 ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 ex1E2 ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 funcGraphProp1 ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 funcGraphProp3 ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 funcGraphProp2 ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 funcextLem ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 funcGraphProp4 ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 subbreln ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 eqbreln ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 funcext ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 funcext2 ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 ap2apEq1 ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 ap2apEq2 ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 beta1 ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 eta1 ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 lam2lamEq ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 beta2 ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 eta2 ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 iffalseProp1 ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 iffalseProp2 ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 iftrueProp1 ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 iftrueProp2 ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 ifSingleton ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 ifp ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 theeq ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 iftrue ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 iffalse ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 iftrueorfalse ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 binintersectT_lem ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.28 binunionT_lem ) =>
% 21.01/3.28 (
% 21.01/3.28 (
% 21.01/3.29 powersetT_lem ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 setminusT_lem ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 complementT_lem ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 setextT ) =>
% 21.01/3.29 (
% 21.01/3.29 ![
% 21.01/3.29 A:$i,X:$i]:
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 in @
% 21.01/3.29 X @
% 21.01/3.29 (
% 21.01/3.29 powerset @
% 21.01/3.29 A ) ) =>
% 21.01/3.29 (
% 21.01/3.29 ![
% 21.01/3.29 Y:$i]:
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 in @
% 21.01/3.29 Y @
% 21.01/3.29 (
% 21.01/3.29 powerset @
% 21.01/3.29 A ) ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 ![
% 21.01/3.29 Xx:$i]:
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 in @
% 21.01/3.29 Xx @ A ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 in @
% 21.01/3.29 Xx @ X ) =>
% 21.01/3.29 (
% 21.01/3.29 in @
% 21.01/3.29 Xx @ Y ) ) ) ) =>
% 21.01/3.29 (
% 21.01/3.29 subset @
% 21.01/3.29 X @ Y ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 21.01/3.29 thf(zf_stmt_0, conjecture,
% 21.01/3.29 (( setextAx ) =>
% 21.01/3.29 ( ( emptysetAx ) =>
% 21.01/3.29 ( ( setadjoinAx ) =>
% 21.01/3.29 ( ( ![X4:$i,X6:$i]:
% 21.01/3.29 ( ( in @ X6 @ ( powerset @ X4 ) ) <=>
% 21.01/3.29 ( ![X8:$i]: ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ) ) ) =>
% 21.01/3.29 ( ( setunionAx ) =>
% 21.01/3.29 ( ( omega0Ax ) =>
% 21.01/3.29 ( ( omegaSAx ) =>
% 21.01/3.29 ( ( omegaIndAx ) =>
% 21.01/3.29 ( ( replAx ) =>
% 21.01/3.29 ( ( foundationAx ) =>
% 21.01/3.29 ( ( wellorderingAx ) =>
% 21.01/3.29 ( ( descrp ) =>
% 21.01/3.29 ( ( dsetconstrI ) =>
% 21.01/3.29 ( ( dsetconstrEL ) =>
% 21.01/3.29 ( ( dsetconstrER ) =>
% 21.01/3.29 ( ( exuE1 ) =>
% 21.01/3.29 ( ( prop2setE ) =>
% 21.01/3.29 ( ( emptysetE ) =>
% 21.01/3.29 ( ( emptysetimpfalse ) =>
% 21.01/3.29 ( ( notinemptyset ) =>
% 21.01/3.29 ( ( exuE3e ) =>
% 21.01/3.29 ( ( setext ) =>
% 21.01/3.29 ( ( emptyI ) =>
% 21.01/3.29 ( ( noeltsimpempty ) =>
% 21.01/3.29 ( ( setbeta ) =>
% 21.01/3.29 ( ( nonemptyE1 ) =>
% 21.01/3.29 ( ( nonemptyI ) =>
% 21.01/3.29 ( ( nonemptyI1 ) =>
% 21.01/3.29 ( ( setadjoinIL ) =>
% 21.01/3.29 ( ( emptyinunitempty ) =>
% 21.01/3.29 ( ( setadjoinIR ) =>
% 21.01/3.29 ( ( setadjoinE ) =>
% 21.01/3.29 ( (
% 21.01/3.29 setadjoinOr ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 setoftrueEq ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 ![
% 21.01/3.29 X10:$i,
% 21.01/3.29 X12:$i]:
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 ![
% 21.01/3.29 X14:$i]:
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 in @
% 21.01/3.29 X14 @ X12 ) =>
% 21.01/3.29 (
% 21.01/3.29 in @
% 21.01/3.29 X14 @ X10 ) ) ) =>
% 21.01/3.29 (
% 21.01/3.29 in @
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% 21.01/3.29 (
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% 21.01/3.29 (
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% 21.01/3.29 (
% 21.01/3.29 powerset @
% 21.01/3.29 X20 ) ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 in @
% 21.01/3.29 X24 @ X22 ) =>
% 21.01/3.29 (
% 21.01/3.29 in @
% 21.01/3.29 X24 @ X20 ) ) ) ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 setunionI ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 setunionE ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 subPowSU ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 exuE2 ) =>
% 21.01/3.29 (
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% 21.01/3.29 nonemptyImpWitness ) =>
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% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 X26 ) =
% 21.01/3.29 (
% 21.01/3.29 X28 ) ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 powerset @
% 21.01/3.29 X26 ) =
% 21.01/3.29 (
% 21.01/3.29 powerset @
% 21.01/3.29 X28 ) ) ) ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 setunion__Cong ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 omega__Cong ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 exuEu ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 descr__Cong ) =>
% 21.01/3.29 (
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% 21.01/3.29 (
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% 21.01/3.29 X36 ) =
% 21.01/3.29 (
% 21.01/3.29 X38 ) ) =>
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% 21.01/3.29 subset @
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% 21.01/3.29 X42:$i]:
% 21.01/3.29 (
% 21.01/3.29 (
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% 21.01/3.29 X40 ) =
% 21.01/3.29 (
% 21.01/3.29 X42 ) ) =>
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% 21.01/3.29 X56 @ X52 ) =>
% 21.01/3.29 (
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% 21.01/3.29 X56 @ X54 ) ) ) ) =>
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% 21.01/3.29 (
% 21.01/3.29 ~(
% 21.01/3.29 in @
% 21.01/3.29 X62 @ X60 ) ) =>
% 21.01/3.29 (
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% 21.01/3.29 in @
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% 21.01/3.29 ~(
% 21.01/3.29 in @
% 21.01/3.29 X68 @ X66 ) ) =>
% 21.01/3.29 (
% 21.01/3.29 ~(
% 21.01/3.29 subset @
% 21.01/3.29 X64 @ X66 ) ) ) ) ) =>
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% 21.01/3.29 (
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% 21.01/3.29 subset @
% 21.01/3.29 X70 @ X72 ) ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 X70 ) !=
% 21.01/3.29 (
% 21.01/3.29 X72 ) ) ) ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 notequalI2 ) =>
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% 21.01/3.29 (
% 21.01/3.29 powerset @
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% 21.01/3.29 (
% 21.01/3.29 powerset @
% 21.01/3.29 X112 ) @
% 21.01/3.29 (
% 21.01/3.29 powerset @
% 21.01/3.29 X114 ) ) ) ) =>
% 21.01/3.29 (
% 21.01/3.29 (
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% 21.01/3.29 (
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% 21.01/3.29 in @
% 21.01/3.29 (
% 21.01/3.29 setadjoin
% 21.01/3.29 @
% 21.01/3.29 X122 @
% 21.01/3.29 emptyset ) @
% 21.01/3.29 (
% 21.01/3.29 powerset @
% 21.01/3.29 X120 ) ) ) ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 singletoninpowunion ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 upairset2E ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 upairsubunion ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 upairinpowunion ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 ubforcartprodlem1 ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 ubforcartprodlem2 ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 ubforcartprodlem3 ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 cartprodpairin ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 cartprodmempair1 ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 cartprodmempair ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 setunionE2 ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 setunionsingleton1 ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 setunionsingleton2 ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 setunionsingleton ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 singletonprop ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 ex1E1 ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 ex1I ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 ex1I2 ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 singletonsuniq ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 setukpairinjL1 ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 kfstsingleton ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 theprop ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 kfstpairEq ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 cartprodfstin ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 setukpairinjL2 ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 setukpairinjL ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 setukpairinjR11 ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 setukpairinjR12 ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 setukpairinjR1 ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 upairequniteq ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 setukpairinjR2 ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 setukpairinjR ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 ksndsingleton ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 ksndpairEq ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 kpairsurjEq ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 cartprodsndin ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 cartprodpairmemEL ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 cartprodpairmemER ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 cartprodmempaircEq ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 cartprodfstpairEq ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 cartprodsndpairEq ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 cartprodpairsurjEq ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 dpsetconstrI ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 dpsetconstrSub ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 setOfPairsIsBReln ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 dpsetconstrERa ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 dpsetconstrEL1 ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 dpsetconstrEL2 ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 dpsetconstrER ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 funcImageSingleton ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 apProp ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 app ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 infuncsetfunc ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 ap2p ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 funcinfuncset ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 lamProp ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 lamp ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 lam2p ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 brelnall1 ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 brelnall2 ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 ex1E2 ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 funcGraphProp1 ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 funcGraphProp3 ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 funcGraphProp2 ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 funcextLem ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 funcGraphProp4 ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 subbreln ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 eqbreln ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 funcext ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 funcext2 ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 ap2apEq1 ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 ap2apEq2 ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 beta1 ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 eta1 ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 lam2lamEq ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 beta2 ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 eta2 ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 iffalseProp1 ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 iffalseProp2 ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 iftrueProp1 ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 iftrueProp2 ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 ifSingleton ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 ifp ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 theeq ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 iftrue ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 iffalse ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 iftrueorfalse ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 binintersectT_lem ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 binunionT_lem ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 ![
% 21.01/3.29 X124:$i,
% 21.01/3.29 X126:$i]:
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 in @
% 21.01/3.29 X126 @
% 21.01/3.29 (
% 21.01/3.29 powerset @
% 21.01/3.29 X124 ) ) =>
% 21.01/3.29 (
% 21.01/3.29 in @
% 21.01/3.29 (
% 21.01/3.29 powerset @
% 21.01/3.29 X126 ) @
% 21.01/3.29 (
% 21.01/3.29 powerset @
% 21.01/3.29 (
% 21.01/3.29 powerset @
% 21.01/3.29 X124 ) ) ) ) ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 setminusT_lem ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 complementT_lem ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 ![
% 21.01/3.29 X128:$i,
% 21.01/3.29 X130:$i]:
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 in @
% 21.01/3.29 X130 @
% 21.01/3.29 (
% 21.01/3.29 powerset @
% 21.01/3.29 X128 ) ) =>
% 21.01/3.29 (
% 21.01/3.29 ![
% 21.01/3.29 X132:$i]:
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 in @
% 21.01/3.29 X132 @
% 21.01/3.29 (
% 21.01/3.29 powerset @
% 21.01/3.29 X128 ) ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 ![
% 21.01/3.29 X134:$i]:
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 in @
% 21.01/3.29 X134 @
% 21.01/3.29 X128 ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 in @
% 21.01/3.29 X134 @
% 21.01/3.29 X130 ) =>
% 21.01/3.29 (
% 21.01/3.29 in @
% 21.01/3.29 X134 @
% 21.01/3.29 X132 ) ) ) ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 ![
% 21.01/3.29 X136:$i]:
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 in @
% 21.01/3.29 X136 @
% 21.01/3.29 X128 ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 in @
% 21.01/3.29 X136 @
% 21.01/3.29 X132 ) =>
% 21.01/3.29 (
% 21.01/3.29 in @
% 21.01/3.29 X136 @
% 21.01/3.29 X130 ) ) ) ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 X130 ) =
% 21.01/3.29 (
% 21.01/3.29 X132 ) ) ) ) ) ) ) ) =>
% 21.01/3.29 (
% 21.01/3.29 ![
% 21.01/3.29 X138:$i,
% 21.01/3.29 X140:$i]:
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 in @
% 21.01/3.29 X140 @
% 21.01/3.29 (
% 21.01/3.29 powerset @
% 21.01/3.29 X138 ) ) =>
% 21.01/3.29 (
% 21.01/3.29 ![
% 21.01/3.29 X142:$i]:
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 in @
% 21.01/3.29 X142 @
% 21.01/3.29 (
% 21.01/3.29 powerset @
% 21.01/3.29 X138 ) ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 ![
% 21.01/3.29 X144:$i]:
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 in @
% 21.01/3.29 X144 @
% 21.01/3.29 X138 ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 in @
% 21.01/3.29 X144 @
% 21.01/3.29 X140 ) =>
% 21.01/3.29 (
% 21.01/3.29 in @
% 21.01/3.29 X144 @
% 21.01/3.29 X142 ) ) ) ) =>
% 21.01/3.29 (
% 21.01/3.29 subset @
% 21.01/3.29 X140 @
% 21.01/3.29 X142 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 21.01/3.29 thf(zf_stmt_1, type, zip_tseitin_0 : $i > $i > $i > $o).
% 21.01/3.29 thf(zf_stmt_2, axiom,
% 21.01/3.29 (![X8:$i,X6:$i,X4:$i]:
% 21.01/3.29 ( ( zip_tseitin_0 @ X8 @ X6 @ X4 ) <=>
% 21.01/3.29 ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ))).
% 21.01/3.29 thf(zf_stmt_3, conjecture,
% 21.01/3.29 (( setextAx ) =>
% 21.01/3.29 ( ( emptysetAx ) =>
% 21.01/3.29 ( ( setadjoinAx ) =>
% 21.01/3.29 ( ( ![X4:$i,X6:$i]:
% 21.01/3.29 ( ( in @ X6 @ ( powerset @ X4 ) ) <=>
% 21.01/3.29 ( ![X8:$i]: ( zip_tseitin_0 @ X8 @ X6 @ X4 ) ) ) ) =>
% 21.01/3.29 ( ( setunionAx ) =>
% 21.01/3.29 ( ( omega0Ax ) =>
% 21.01/3.29 ( ( omegaSAx ) =>
% 21.01/3.29 ( ( omegaIndAx ) =>
% 21.01/3.29 ( ( replAx ) =>
% 21.01/3.29 ( ( foundationAx ) =>
% 21.01/3.29 ( ( wellorderingAx ) =>
% 21.01/3.29 ( ( descrp ) =>
% 21.01/3.29 ( ( dsetconstrI ) =>
% 21.01/3.29 ( ( dsetconstrEL ) =>
% 21.01/3.29 ( ( dsetconstrER ) =>
% 21.01/3.29 ( ( exuE1 ) =>
% 21.01/3.29 ( ( prop2setE ) =>
% 21.01/3.29 ( ( emptysetE ) =>
% 21.01/3.29 ( ( emptysetimpfalse ) =>
% 21.01/3.29 ( ( notinemptyset ) =>
% 21.01/3.29 ( ( exuE3e ) =>
% 21.01/3.29 ( ( setext ) =>
% 21.01/3.29 ( ( emptyI ) =>
% 21.01/3.29 ( ( noeltsimpempty ) =>
% 21.01/3.29 ( ( setbeta ) =>
% 21.01/3.29 ( ( nonemptyE1 ) =>
% 21.01/3.29 ( ( nonemptyI ) =>
% 21.01/3.29 ( ( nonemptyI1 ) =>
% 21.01/3.29 ( ( setadjoinIL ) =>
% 21.01/3.29 ( ( emptyinunitempty ) =>
% 21.01/3.29 ( ( setadjoinIR ) =>
% 21.01/3.29 ( ( setadjoinE ) =>
% 21.01/3.29 ( (
% 21.01/3.29 setadjoinOr ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 setoftrueEq ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 ![
% 21.01/3.29 X10:$i,
% 21.01/3.29 X12:$i]:
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 ![
% 21.01/3.29 X14:$i]:
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 in @
% 21.01/3.29 X14 @ X12 ) =>
% 21.01/3.29 (
% 21.01/3.29 in @
% 21.01/3.29 X14 @ X10 ) ) ) =>
% 21.01/3.29 (
% 21.01/3.29 in @
% 21.01/3.29 X12 @
% 21.01/3.29 (
% 21.01/3.29 powerset @
% 21.01/3.29 X10 ) ) ) ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 ![
% 21.01/3.29 X16:$i]:
% 21.01/3.29 (
% 21.01/3.29 in @
% 21.01/3.29 emptyset @
% 21.01/3.29 (
% 21.01/3.29 powerset @
% 21.01/3.29 X16 ) ) ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 ![
% 21.01/3.29 X18:$i]:
% 21.01/3.29 (
% 21.01/3.29 in @
% 21.01/3.29 emptyset @
% 21.01/3.29 (
% 21.01/3.29 powerset @
% 21.01/3.29 X18 ) ) ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 ![
% 21.01/3.29 X20:$i,
% 21.01/3.29 X22:$i,
% 21.01/3.29 X24:$i]:
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 in @
% 21.01/3.29 X22 @
% 21.01/3.29 (
% 21.01/3.29 powerset @
% 21.01/3.29 X20 ) ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 in @
% 21.01/3.29 X24 @ X22 ) =>
% 21.01/3.29 (
% 21.01/3.29 in @
% 21.01/3.29 X24 @ X20 ) ) ) ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 setunionI ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 setunionE ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 subPowSU ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 exuE2 ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 nonemptyImpWitness ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 uniqinunit ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 notinsingleton ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 eqinunit ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 singletonsswitch ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 upairsetE ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 upairsetIL ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 upairsetIR ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 emptyE1 ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 vacuousDall ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 quantDeMorgan1 ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 quantDeMorgan2 ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 quantDeMorgan3 ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 quantDeMorgan4 ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 prop2setI ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 prop2set2propI ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 notdexE ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 notdallE ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 exuI1 ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 exuI3 ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 exuI2 ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 inCongP ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 in__Cong ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 exuE3u ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 exu__Cong ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 emptyset__Cong ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 setadjoin__Cong ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 ![
% 21.01/3.29 X26:$i,
% 21.01/3.29 X28:$i]:
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 X26 ) =
% 21.01/3.29 (
% 21.01/3.29 X28 ) ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 powerset @
% 21.01/3.29 X26 ) =
% 21.01/3.29 (
% 21.01/3.29 powerset @
% 21.01/3.29 X28 ) ) ) ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 setunion__Cong ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 omega__Cong ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 exuEu ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 descr__Cong ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 dsetconstr__Cong ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 ![
% 21.01/3.29 X30:$i,
% 21.01/3.29 X32:$i]:
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 ![
% 21.01/3.29 X34:$i]:
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 in @
% 21.01/3.29 X34 @ X30 ) =>
% 21.01/3.29 (
% 21.01/3.29 in @
% 21.01/3.29 X34 @ X32 ) ) ) =>
% 21.01/3.29 (
% 21.01/3.29 subset @
% 21.01/3.29 X30 @ X32 ) ) ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 ![
% 21.01/3.29 X36:$i,
% 21.01/3.29 X38:$i]:
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 X36 ) =
% 21.01/3.29 (
% 21.01/3.29 X38 ) ) =>
% 21.01/3.29 (
% 21.01/3.29 subset @
% 21.01/3.29 X38 @ X36 ) ) ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 ![
% 21.01/3.29 X40:$i,
% 21.01/3.29 X42:$i]:
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 X40 ) =
% 21.01/3.29 (
% 21.01/3.29 X42 ) ) =>
% 21.01/3.29 (
% 21.01/3.29 subset @
% 21.01/3.29 X40 @ X42 ) ) ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 ![
% 21.01/3.29 X44:$i,
% 21.01/3.29 X46:$i]:
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 ![
% 21.01/3.29 X48:$i]:
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 in @
% 21.01/3.29 X48 @ X44 ) =>
% 21.01/3.29 (
% 21.01/3.29 in @
% 21.01/3.29 X48 @ X46 ) ) ) =>
% 21.01/3.29 (
% 21.01/3.29 subset @
% 21.01/3.29 X44 @ X46 ) ) ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 ![
% 21.01/3.29 X50:$i]:
% 21.01/3.29 (
% 21.01/3.29 subset @
% 21.01/3.29 emptyset @
% 21.01/3.29 X50 ) ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 ![
% 21.01/3.29 X52:$i,
% 21.01/3.29 X54:$i,
% 21.01/3.29 X56:$i]:
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 subset @
% 21.01/3.29 X52 @ X54 ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 in @
% 21.01/3.29 X56 @ X52 ) =>
% 21.01/3.29 (
% 21.01/3.29 in @
% 21.01/3.29 X56 @ X54 ) ) ) ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 ![
% 21.01/3.29 X58:$i,
% 21.01/3.29 X60:$i,
% 21.01/3.29 X62:$i]:
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 subset @
% 21.01/3.29 X58 @ X60 ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 ~(
% 21.01/3.29 in @
% 21.01/3.29 X62 @ X60 ) ) =>
% 21.01/3.29 (
% 21.01/3.29 ~(
% 21.01/3.29 in @
% 21.01/3.29 X62 @ X58 ) ) ) ) ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 ![
% 21.01/3.29 X64:$i,
% 21.01/3.29 X66:$i,
% 21.01/3.29 X68:$i]:
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 in @
% 21.01/3.29 X68 @ X64 ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 ~(
% 21.01/3.29 in @
% 21.01/3.29 X68 @ X66 ) ) =>
% 21.01/3.29 (
% 21.01/3.29 ~(
% 21.01/3.29 subset @
% 21.01/3.29 X64 @ X66 ) ) ) ) ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 ![
% 21.01/3.29 X70:$i,
% 21.01/3.29 X72:$i]:
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 ~(
% 21.01/3.29 subset @
% 21.01/3.29 X70 @ X72 ) ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 X70 ) !=
% 21.01/3.29 (
% 21.01/3.29 X72 ) ) ) ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 notequalI2 ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 ![
% 21.01/3.29 X74:$i]:
% 21.01/3.29 (
% 21.01/3.29 subset @
% 21.01/3.29 X74 @ X74 ) ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 ![
% 21.01/3.29 X76:$i,
% 21.01/3.29 X78:$i,
% 21.01/3.29 X80:$i]:
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 subset @
% 21.01/3.29 X76 @ X78 ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 subset @
% 21.01/3.29 X78 @ X80 ) =>
% 21.01/3.29 (
% 21.01/3.29 subset @
% 21.01/3.29 X76 @ X80 ) ) ) ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 ![
% 21.01/3.29 X82:$i,
% 21.01/3.29 X84:$i]:
% 21.01/3.29 (
% 21.01/3.29 subset @
% 21.01/3.29 X84 @
% 21.01/3.29 (
% 21.01/3.29 setadjoin
% 21.01/3.29 @
% 21.01/3.29 X82 @ X84 ) ) ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 ![
% 21.01/3.29 X86:$i,
% 21.01/3.29 X88:$i,
% 21.01/3.29 X90:$i]:
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 subset @
% 21.01/3.29 X86 @ X90 ) =>
% 21.01/3.29 (
% 21.01/3.29 subset @
% 21.01/3.29 X86 @
% 21.01/3.29 (
% 21.01/3.29 setadjoin
% 21.01/3.29 @
% 21.01/3.29 X88 @ X90 ) ) ) ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 ![
% 21.01/3.29 X92:$i,
% 21.01/3.29 X94:$i]:
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 subset @
% 21.01/3.29 X92 @ X94 ) =>
% 21.01/3.29 (
% 21.01/3.29 in @
% 21.01/3.29 X92 @
% 21.01/3.29 (
% 21.01/3.29 powerset @
% 21.01/3.29 X94 ) ) ) ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 ![
% 21.01/3.29 X96:$i,
% 21.01/3.29 X98:$i]:
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 subset @
% 21.01/3.29 X96 @ X98 ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 subset @
% 21.01/3.29 X98 @ X96 ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 X96 ) =
% 21.01/3.29 (
% 21.01/3.29 X98 ) ) ) ) ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 ![
% 21.01/3.29 X100:$i]:
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 subset @
% 21.01/3.29 X100 @
% 21.01/3.29 emptyset ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 X100 ) =
% 21.01/3.29 (
% 21.01/3.29 emptyset ) ) ) ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 ![
% 21.01/3.29 X102:$i,
% 21.01/3.29 X104:$i]:
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 subset @
% 21.01/3.29 X104 @
% 21.01/3.29 X102 ) =>
% 21.01/3.29 (
% 21.01/3.29 in @
% 21.01/3.29 X104 @
% 21.01/3.29 (
% 21.01/3.29 powerset @
% 21.01/3.29 X102 ) ) ) ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 ![
% 21.01/3.29 X106:$i,
% 21.01/3.29 X108:$i]:
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 in @
% 21.01/3.29 X108 @
% 21.01/3.29 (
% 21.01/3.29 powerset @
% 21.01/3.29 X106 ) ) =>
% 21.01/3.29 (
% 21.01/3.29 subset @
% 21.01/3.29 X108 @
% 21.01/3.29 X106 ) ) ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 ![
% 21.01/3.29 X110:$i]:
% 21.01/3.29 (
% 21.01/3.29 in @
% 21.01/3.29 X110 @
% 21.01/3.29 (
% 21.01/3.29 powerset @
% 21.01/3.29 X110 ) ) ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 ![
% 21.01/3.29 X112:$i,
% 21.01/3.29 X114:$i]:
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 subset @
% 21.01/3.29 X112 @
% 21.01/3.29 X114 ) =>
% 21.01/3.29 (
% 21.01/3.29 subset @
% 21.01/3.29 (
% 21.01/3.29 powerset @
% 21.01/3.29 X112 ) @
% 21.01/3.29 (
% 21.01/3.29 powerset @
% 21.01/3.29 X114 ) ) ) ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 sepInPowerset ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 sepSubset ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 binunionIL ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 upairset2IR ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 binunionIR ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 binunionEcases ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 binunionE ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 binunionLsub ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 binunionRsub ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 binintersectI ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 binintersectSubset5 ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 binintersectEL ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 binintersectLsub ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 binintersectSubset2 ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 binintersectSubset3 ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 binintersectER ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 disjointsetsI1 ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 binintersectRsub ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 binintersectSubset4 ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 binintersectSubset1 ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 bs114d ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 setminusI ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 setminusEL ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 setminusER ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 setminusSubset2 ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 setminusERneg ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 setminusELneg ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 setminusILneg ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 setminusIRneg ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 setminusLsub ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 setminusSubset1 ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 symdiffE ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 symdiffI1 ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 symdiffI2 ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 symdiffIneg1 ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 symdiffIneg2 ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 secondinupair ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 setukpairIL ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 setukpairIR ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 kpairiskpair ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 kpairp ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 ![
% 21.01/3.29 X116:$i,
% 21.01/3.29 X118:$i]:
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 in @
% 21.01/3.29 X118 @
% 21.01/3.29 X116 ) =>
% 21.01/3.29 (
% 21.01/3.29 subset @
% 21.01/3.29 (
% 21.01/3.29 setadjoin
% 21.01/3.29 @
% 21.01/3.29 X118 @
% 21.01/3.29 emptyset ) @
% 21.01/3.29 X116 ) ) ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 ![
% 21.01/3.29 X120:$i,
% 21.01/3.29 X122:$i]:
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 in @
% 21.01/3.29 X122 @
% 21.01/3.29 X120 ) =>
% 21.01/3.29 (
% 21.01/3.29 in @
% 21.01/3.29 (
% 21.01/3.29 setadjoin
% 21.01/3.29 @
% 21.01/3.29 X122 @
% 21.01/3.29 emptyset ) @
% 21.01/3.29 (
% 21.01/3.29 powerset @
% 21.01/3.29 X120 ) ) ) ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 singletoninpowunion ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 upairset2E ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 upairsubunion ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 upairinpowunion ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 ubforcartprodlem1 ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 ubforcartprodlem2 ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 ubforcartprodlem3 ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 cartprodpairin ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 cartprodmempair1 ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 cartprodmempair ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 setunionE2 ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 setunionsingleton1 ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 setunionsingleton2 ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 setunionsingleton ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 singletonprop ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 ex1E1 ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 ex1I ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 ex1I2 ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 singletonsuniq ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 setukpairinjL1 ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 kfstsingleton ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 theprop ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 kfstpairEq ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 cartprodfstin ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 setukpairinjL2 ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 setukpairinjL ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 setukpairinjR11 ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 setukpairinjR12 ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 setukpairinjR1 ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 upairequniteq ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 setukpairinjR2 ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 setukpairinjR ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 ksndsingleton ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 ksndpairEq ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 kpairsurjEq ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 cartprodsndin ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 cartprodpairmemEL ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 cartprodpairmemER ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 cartprodmempaircEq ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 cartprodfstpairEq ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 cartprodsndpairEq ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 cartprodpairsurjEq ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 dpsetconstrI ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 dpsetconstrSub ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 setOfPairsIsBReln ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 dpsetconstrERa ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 dpsetconstrEL1 ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 dpsetconstrEL2 ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 dpsetconstrER ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 funcImageSingleton ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 apProp ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 app ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 infuncsetfunc ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 ap2p ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 funcinfuncset ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 lamProp ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 lamp ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 lam2p ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 brelnall1 ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 brelnall2 ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 ex1E2 ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 funcGraphProp1 ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 funcGraphProp3 ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 funcGraphProp2 ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 funcextLem ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 funcGraphProp4 ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 subbreln ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 eqbreln ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 funcext ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 funcext2 ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 ap2apEq1 ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 ap2apEq2 ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 beta1 ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 eta1 ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 lam2lamEq ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 beta2 ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 eta2 ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 iffalseProp1 ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 iffalseProp2 ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 iftrueProp1 ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 iftrueProp2 ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 ifSingleton ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 ifp ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 theeq ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 iftrue ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 iffalse ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 iftrueorfalse ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 binintersectT_lem ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 binunionT_lem ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 ![
% 21.01/3.29 X124:$i,
% 21.01/3.29 X126:$i]:
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 in @
% 21.01/3.29 X126 @
% 21.01/3.29 (
% 21.01/3.29 powerset @
% 21.01/3.29 X124 ) ) =>
% 21.01/3.29 (
% 21.01/3.29 in @
% 21.01/3.29 (
% 21.01/3.29 powerset @
% 21.01/3.29 X126 ) @
% 21.01/3.29 (
% 21.01/3.29 powerset @
% 21.01/3.29 (
% 21.01/3.29 powerset @
% 21.01/3.29 X124 ) ) ) ) ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 setminusT_lem ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 complementT_lem ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 ![
% 21.01/3.29 X128:$i,
% 21.01/3.29 X130:$i]:
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 in @
% 21.01/3.29 X130 @
% 21.01/3.29 (
% 21.01/3.29 powerset @
% 21.01/3.29 X128 ) ) =>
% 21.01/3.29 (
% 21.01/3.29 ![
% 21.01/3.29 X132:$i]:
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 in @
% 21.01/3.29 X132 @
% 21.01/3.29 (
% 21.01/3.29 powerset @
% 21.01/3.29 X128 ) ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 ![
% 21.01/3.29 X134:$i]:
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 in @
% 21.01/3.29 X134 @
% 21.01/3.29 X128 ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 in @
% 21.01/3.29 X134 @
% 21.01/3.29 X130 ) =>
% 21.01/3.29 (
% 21.01/3.29 in @
% 21.01/3.29 X134 @
% 21.01/3.29 X132 ) ) ) ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 ![
% 21.01/3.29 X136:$i]:
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 in @
% 21.01/3.29 X136 @
% 21.01/3.29 X128 ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 in @
% 21.01/3.29 X136 @
% 21.01/3.29 X132 ) =>
% 21.01/3.29 (
% 21.01/3.29 in @
% 21.01/3.29 X136 @
% 21.01/3.29 X130 ) ) ) ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 X130 ) =
% 21.01/3.29 (
% 21.01/3.29 X132 ) ) ) ) ) ) ) ) =>
% 21.01/3.29 (
% 21.01/3.29 ![
% 21.01/3.29 X138:$i,
% 21.01/3.29 X140:$i]:
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 in @
% 21.01/3.29 X140 @
% 21.01/3.29 (
% 21.01/3.29 powerset @
% 21.01/3.29 X138 ) ) =>
% 21.01/3.29 (
% 21.01/3.29 ![
% 21.01/3.29 X142:$i]:
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 in @
% 21.01/3.29 X142 @
% 21.01/3.29 (
% 21.01/3.29 powerset @
% 21.01/3.29 X138 ) ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 ![
% 21.01/3.29 X144:$i]:
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 in @
% 21.01/3.29 X144 @
% 21.01/3.29 X138 ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 in @
% 21.01/3.29 X144 @
% 21.01/3.29 X140 ) =>
% 21.01/3.29 (
% 21.01/3.29 in @
% 21.01/3.29 X144 @
% 21.01/3.29 X142 ) ) ) ) =>
% 21.01/3.29 (
% 21.01/3.29 subset @
% 21.01/3.29 X140 @
% 21.01/3.29 X142 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 21.01/3.29 thf(zf_stmt_4, negated_conjecture,
% 21.01/3.29 (~( ( setextAx ) =>
% 21.01/3.29 ( ( emptysetAx ) =>
% 21.01/3.29 ( ( setadjoinAx ) =>
% 21.01/3.29 ( ( ![X4:$i,X6:$i]:
% 21.01/3.29 ( ( in @ X6 @ ( powerset @ X4 ) ) <=>
% 21.01/3.29 ( ![X8:$i]: ( zip_tseitin_0 @ X8 @ X6 @ X4 ) ) ) ) =>
% 21.01/3.29 ( ( setunionAx ) =>
% 21.01/3.29 ( ( omega0Ax ) =>
% 21.01/3.29 ( ( omegaSAx ) =>
% 21.01/3.29 ( ( omegaIndAx ) =>
% 21.01/3.29 ( ( replAx ) =>
% 21.01/3.29 ( ( foundationAx ) =>
% 21.01/3.29 ( ( wellorderingAx ) =>
% 21.01/3.29 ( ( descrp ) =>
% 21.01/3.29 ( ( dsetconstrI ) =>
% 21.01/3.29 ( ( dsetconstrEL ) =>
% 21.01/3.29 ( ( dsetconstrER ) =>
% 21.01/3.29 ( ( exuE1 ) =>
% 21.01/3.29 ( ( prop2setE ) =>
% 21.01/3.29 ( ( emptysetE ) =>
% 21.01/3.29 ( ( emptysetimpfalse ) =>
% 21.01/3.29 ( ( notinemptyset ) =>
% 21.01/3.29 ( ( exuE3e ) =>
% 21.01/3.29 ( ( setext ) =>
% 21.01/3.29 ( ( emptyI ) =>
% 21.01/3.29 ( ( noeltsimpempty ) =>
% 21.01/3.29 ( ( setbeta ) =>
% 21.01/3.29 ( ( nonemptyE1 ) =>
% 21.01/3.29 ( ( nonemptyI ) =>
% 21.01/3.29 ( ( nonemptyI1 ) =>
% 21.01/3.29 ( ( setadjoinIL ) =>
% 21.01/3.29 ( ( emptyinunitempty ) =>
% 21.01/3.29 ( ( setadjoinIR ) =>
% 21.01/3.29 ( (
% 21.01/3.29 setadjoinE ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 setadjoinOr ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 setoftrueEq ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 ![
% 21.01/3.29 X10:$i,
% 21.01/3.29 X12:$i]:
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 ![
% 21.01/3.29 X14:$i]:
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 in @
% 21.01/3.29 X14 @ X12 ) =>
% 21.01/3.29 (
% 21.01/3.29 in @
% 21.01/3.29 X14 @ X10 ) ) ) =>
% 21.01/3.29 (
% 21.01/3.29 in @
% 21.01/3.29 X12 @
% 21.01/3.29 (
% 21.01/3.29 powerset
% 21.01/3.29 @
% 21.01/3.29 X10 ) ) ) ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 ![
% 21.01/3.29 X16:$i]:
% 21.01/3.29 (
% 21.01/3.29 in @
% 21.01/3.29 emptyset @
% 21.01/3.29 (
% 21.01/3.29 powerset
% 21.01/3.29 @
% 21.01/3.29 X16 ) ) ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 ![
% 21.01/3.29 X18:$i]:
% 21.01/3.29 (
% 21.01/3.29 in @
% 21.01/3.29 emptyset @
% 21.01/3.29 (
% 21.01/3.29 powerset
% 21.01/3.29 @
% 21.01/3.29 X18 ) ) ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 ![
% 21.01/3.29 X20:$i,
% 21.01/3.29 X22:$i,
% 21.01/3.29 X24:$i]:
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 in @
% 21.01/3.29 X22 @
% 21.01/3.29 (
% 21.01/3.29 powerset
% 21.01/3.29 @
% 21.01/3.29 X20 ) ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 in @
% 21.01/3.29 X24 @ X22 ) =>
% 21.01/3.29 (
% 21.01/3.29 in @
% 21.01/3.29 X24 @ X20 ) ) ) ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 setunionI ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 setunionE ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 subPowSU ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 exuE2 ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 nonemptyImpWitness ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 uniqinunit ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 notinsingleton ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 eqinunit ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 singletonsswitch ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 upairsetE ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 upairsetIL ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 upairsetIR ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 emptyE1 ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 vacuousDall ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 quantDeMorgan1 ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 quantDeMorgan2 ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 quantDeMorgan3 ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 quantDeMorgan4 ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 prop2setI ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 prop2set2propI ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 notdexE ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 notdallE ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 exuI1 ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 exuI3 ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 exuI2 ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 inCongP ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 in__Cong ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 exuE3u ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 exu__Cong ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 emptyset__Cong ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 setadjoin__Cong ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 ![
% 21.01/3.29 X26:$i,
% 21.01/3.29 X28:$i]:
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 X26 ) =
% 21.01/3.29 (
% 21.01/3.29 X28 ) ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 powerset
% 21.01/3.29 @
% 21.01/3.29 X26 ) =
% 21.01/3.29 (
% 21.01/3.29 powerset
% 21.01/3.29 @
% 21.01/3.29 X28 ) ) ) ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 setunion__Cong ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 omega__Cong ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 exuEu ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 descr__Cong ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 dsetconstr__Cong ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 ![
% 21.01/3.29 X30:$i,
% 21.01/3.29 X32:$i]:
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 ![
% 21.01/3.29 X34:$i]:
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 in @
% 21.01/3.29 X34 @ X30 ) =>
% 21.01/3.29 (
% 21.01/3.29 in @
% 21.01/3.29 X34 @ X32 ) ) ) =>
% 21.01/3.29 (
% 21.01/3.29 subset @
% 21.01/3.29 X30 @ X32 ) ) ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 ![
% 21.01/3.29 X36:$i,
% 21.01/3.29 X38:$i]:
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 X36 ) =
% 21.01/3.29 (
% 21.01/3.29 X38 ) ) =>
% 21.01/3.29 (
% 21.01/3.29 subset @
% 21.01/3.29 X38 @ X36 ) ) ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 ![
% 21.01/3.29 X40:$i,
% 21.01/3.29 X42:$i]:
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 X40 ) =
% 21.01/3.29 (
% 21.01/3.29 X42 ) ) =>
% 21.01/3.29 (
% 21.01/3.29 subset @
% 21.01/3.29 X40 @ X42 ) ) ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 ![
% 21.01/3.29 X44:$i,
% 21.01/3.29 X46:$i]:
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 ![
% 21.01/3.29 X48:$i]:
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 in @
% 21.01/3.29 X48 @ X44 ) =>
% 21.01/3.29 (
% 21.01/3.29 in @
% 21.01/3.29 X48 @ X46 ) ) ) =>
% 21.01/3.29 (
% 21.01/3.29 subset @
% 21.01/3.29 X44 @ X46 ) ) ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 ![
% 21.01/3.29 X50:$i]:
% 21.01/3.29 (
% 21.01/3.29 subset @
% 21.01/3.29 emptyset @
% 21.01/3.29 X50 ) ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 ![
% 21.01/3.29 X52:$i,
% 21.01/3.29 X54:$i,
% 21.01/3.29 X56:$i]:
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 subset @
% 21.01/3.29 X52 @ X54 ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 in @
% 21.01/3.29 X56 @ X52 ) =>
% 21.01/3.29 (
% 21.01/3.29 in @
% 21.01/3.29 X56 @ X54 ) ) ) ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 ![
% 21.01/3.29 X58:$i,
% 21.01/3.29 X60:$i,
% 21.01/3.29 X62:$i]:
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 subset @
% 21.01/3.29 X58 @ X60 ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 ~
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% 21.01/3.29 @
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% 21.01/3.29 (
% 21.01/3.29 setadjoin
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% 21.01/3.29 X116 ) ) ) =>
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% 21.01/3.29 X120:$i,
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% 21.01/3.29 (
% 21.01/3.29 in @
% 21.01/3.29 (
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% 21.01/3.29 @
% 21.01/3.29 X122 @
% 21.01/3.29 emptyset ) @
% 21.01/3.29 (
% 21.01/3.29 powerset
% 21.01/3.29 @
% 21.01/3.29 X120 ) ) ) ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 singletoninpowunion ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 upairset2E ) =>
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% 21.01/3.29 (
% 21.01/3.29 ubforcartprodlem1 ) =>
% 21.01/3.29 (
% 21.01/3.29 (
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% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 ubforcartprodlem3 ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 cartprodpairin ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 cartprodmempair1 ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 cartprodmempair ) =>
% 21.01/3.29 (
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% 21.01/3.29 setunionE2 ) =>
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% 21.01/3.29 (
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% 21.01/3.29 setukpairinjL1 ) =>
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% 21.01/3.29 (
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% 21.01/3.29 kfstpairEq ) =>
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% 21.01/3.29 (
% 21.01/3.29 cartprodfstin ) =>
% 21.01/3.29 (
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% 21.01/3.29 (
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% 21.01/3.29 (
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% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 ksndpairEq ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 kpairsurjEq ) =>
% 21.01/3.29 (
% 21.01/3.29 (
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% 21.01/3.29 (
% 21.01/3.29 (
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% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 cartprodpairmemER ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 cartprodmempaircEq ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 cartprodfstpairEq ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 cartprodsndpairEq ) =>
% 21.01/3.29 (
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% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 dpsetconstrI ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 dpsetconstrSub ) =>
% 21.01/3.29 (
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% 21.01/3.29 setOfPairsIsBReln ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 dpsetconstrERa ) =>
% 21.01/3.29 (
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% 21.01/3.29 (
% 21.01/3.29 (
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% 21.01/3.29 (
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% 21.01/3.29 (
% 21.01/3.29 (
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% 21.01/3.29 (
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% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 app ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 infuncsetfunc ) =>
% 21.01/3.29 (
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% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 lamp ) =>
% 21.01/3.29 (
% 21.01/3.29 (
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% 21.01/3.29 brelnall2 ) =>
% 21.01/3.29 (
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% 21.01/3.29 (
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% 21.01/3.29 subbreln ) =>
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% 21.01/3.29 (
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% 21.01/3.29 ap2apEq1 ) =>
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% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 beta1 ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 eta1 ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 lam2lamEq ) =>
% 21.01/3.29 (
% 21.01/3.29 (
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% 21.01/3.29 (
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% 21.01/3.29 (
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% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 ifp ) =>
% 21.01/3.29 (
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% 21.01/3.29 theeq ) =>
% 21.01/3.29 (
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% 21.01/3.29 iftrue ) =>
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% 21.01/3.29 (
% 21.01/3.29 iffalse ) =>
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% 21.01/3.29 (
% 21.01/3.29 iftrueorfalse ) =>
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% 21.01/3.29 (
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% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 binunionT_lem ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 ![
% 21.01/3.29 X124:$i,
% 21.01/3.29 X126:$i]:
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 in @
% 21.01/3.29 X126 @
% 21.01/3.29 (
% 21.01/3.29 powerset
% 21.01/3.29 @
% 21.01/3.29 X124 ) ) =>
% 21.01/3.29 (
% 21.01/3.29 in @
% 21.01/3.29 (
% 21.01/3.29 powerset
% 21.01/3.29 @
% 21.01/3.29 X126 ) @
% 21.01/3.29 (
% 21.01/3.29 powerset
% 21.01/3.29 @
% 21.01/3.29 (
% 21.01/3.29 powerset
% 21.01/3.29 @
% 21.01/3.29 X124 ) ) ) ) ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 setminusT_lem ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 complementT_lem ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 ![
% 21.01/3.29 X128:$i,
% 21.01/3.29 X130:$i]:
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 in @
% 21.01/3.29 X130 @
% 21.01/3.29 (
% 21.01/3.29 powerset
% 21.01/3.29 @
% 21.01/3.29 X128 ) ) =>
% 21.01/3.29 (
% 21.01/3.29 ![
% 21.01/3.29 X132:$i]:
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 in @
% 21.01/3.29 X132 @
% 21.01/3.29 (
% 21.01/3.29 powerset
% 21.01/3.29 @
% 21.01/3.29 X128 ) ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 ![
% 21.01/3.29 X134:$i]:
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 in @
% 21.01/3.29 X134 @
% 21.01/3.29 X128 ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 in @
% 21.01/3.29 X134 @
% 21.01/3.29 X130 ) =>
% 21.01/3.29 (
% 21.01/3.29 in @
% 21.01/3.29 X134 @
% 21.01/3.29 X132 ) ) ) ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 ![
% 21.01/3.29 X136:$i]:
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 in @
% 21.01/3.29 X136 @
% 21.01/3.29 X128 ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 in @
% 21.01/3.29 X136 @
% 21.01/3.29 X132 ) =>
% 21.01/3.29 (
% 21.01/3.29 in @
% 21.01/3.29 X136 @
% 21.01/3.29 X130 ) ) ) ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 X130 ) =
% 21.01/3.29 (
% 21.01/3.29 X132 ) ) ) ) ) ) ) ) =>
% 21.01/3.29 (
% 21.01/3.29 ![
% 21.01/3.29 X138:$i,
% 21.01/3.29 X140:$i]:
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 in @
% 21.01/3.29 X140 @
% 21.01/3.29 (
% 21.01/3.29 powerset
% 21.01/3.29 @
% 21.01/3.29 X138 ) ) =>
% 21.01/3.29 (
% 21.01/3.29 ![
% 21.01/3.29 X142:$i]:
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 in @
% 21.01/3.29 X142 @
% 21.01/3.29 (
% 21.01/3.29 powerset
% 21.01/3.29 @
% 21.01/3.29 X138 ) ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 ![
% 21.01/3.29 X144:$i]:
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 in @
% 21.01/3.29 X144 @
% 21.01/3.29 X138 ) =>
% 21.01/3.29 (
% 21.01/3.29 (
% 21.01/3.29 in @
% 21.01/3.29 X144 @
% 21.01/3.29 X140 ) =>
% 21.01/3.29 (
% 21.01/3.29 in @
% 21.01/3.29 X144 @
% 21.01/3.29 X142 ) ) ) ) =>
% 21.01/3.29 (
% 21.01/3.29 subset @
% 21.01/3.29 X140 @
% 21.01/3.29 X142 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )),
% 21.01/3.29 inference('cnf.neg', [status(esa)], [zf_stmt_3])).
% 21.01/3.29 thf(zip_derived_cl202, plain,
% 21.01/3.29 (![X36 : $i, X37 : $i]:
% 21.01/3.29 ( (subset @ X36 @ X37) | ~ (in @ X36 @ (powerset @ X37)))),
% 21.01/3.29 inference('cnf', [status(esa)], [zf_stmt_4])).
% 21.01/3.29 thf(zip_derived_cl122, plain, (~ (subset @ sk__73 @ sk__74)),
% 21.01/3.29 inference('cnf', [status(esa)], [zf_stmt_4])).
% 21.01/3.29 thf(zip_derived_cl314, plain, (~ (in @ sk__73 @ (powerset @ sk__74))),
% 21.01/3.29 inference('sup-', [status(thm)], [zip_derived_cl202, zip_derived_cl122])).
% 21.01/3.29 thf(zip_derived_cl21, plain,
% 21.01/3.29 (![X0 : $i, X1 : $i]:
% 21.01/3.29 ( (in @ X0 @ (powerset @ X1)) | (in @ (sk__76 @ X0 @ X1) @ X0))),
% 21.01/3.29 inference('cnf', [status(esa)], [zf_stmt_4])).
% 21.01/3.29 thf(zip_derived_cl123, plain,
% 21.01/3.29 (![X28 : $i]:
% 21.01/3.29 (~ (in @ X28 @ sk__73) | (in @ X28 @ sk__74) | ~ (in @ X28 @ sk__72))),
% 21.01/3.29 inference('cnf', [status(esa)], [zf_stmt_4])).
% 21.01/3.29 thf(zip_derived_cl20, plain,
% 21.01/3.29 (![X0 : $i, X1 : $i]:
% 21.01/3.29 ( (in @ X0 @ (powerset @ X1)) | ~ (in @ (sk__76 @ X0 @ X1) @ X1))),
% 21.01/3.29 inference('cnf', [status(esa)], [zf_stmt_4])).
% 21.01/3.29 thf(zip_derived_cl538, plain,
% 21.01/3.29 (![X0 : $i]:
% 21.01/3.29 (~ (in @ (sk__76 @ X0 @ sk__74) @ sk__72)
% 21.01/3.29 | ~ (in @ (sk__76 @ X0 @ sk__74) @ sk__73)
% 21.01/3.29 | (in @ X0 @ (powerset @ sk__74)))),
% 21.01/3.29 inference('sup-', [status(thm)], [zip_derived_cl123, zip_derived_cl20])).
% 21.01/3.29 thf(zip_derived_cl124, plain, ( (in @ sk__73 @ (powerset @ sk__72))),
% 21.01/3.29 inference('cnf', [status(esa)], [zf_stmt_4])).
% 21.01/3.29 thf(zip_derived_cl231, plain,
% 21.01/3.29 (![X56 : $i, X57 : $i, X58 : $i]:
% 21.01/3.29 (~ (in @ X56 @ (powerset @ X57))
% 21.01/3.29 | (in @ X58 @ X57)
% 21.01/3.29 | ~ (in @ X58 @ X56))),
% 21.01/3.29 inference('cnf', [status(esa)], [zf_stmt_4])).
% 21.01/3.29 thf(zip_derived_cl586, plain,
% 21.01/3.29 (![X0 : $i]: (~ (in @ X0 @ sk__73) | (in @ X0 @ sk__72))),
% 21.01/3.29 inference('sup-', [status(thm)], [zip_derived_cl124, zip_derived_cl231])).
% 21.01/3.29 thf(zip_derived_cl4798, plain,
% 21.01/3.29 (![X0 : $i]:
% 21.01/3.29 ( (in @ X0 @ (powerset @ sk__74))
% 21.01/3.29 | ~ (in @ (sk__76 @ X0 @ sk__74) @ sk__73))),
% 21.01/3.29 inference('clc', [status(thm)], [zip_derived_cl538, zip_derived_cl586])).
% 21.01/3.29 thf(zip_derived_cl4803, plain,
% 21.01/3.29 (( (in @ sk__73 @ (powerset @ sk__74))
% 21.01/3.29 | (in @ sk__73 @ (powerset @ sk__74)))),
% 21.01/3.29 inference('sup-', [status(thm)], [zip_derived_cl21, zip_derived_cl4798])).
% 21.01/3.29 thf(zip_derived_cl4814, plain, ( (in @ sk__73 @ (powerset @ sk__74))),
% 21.01/3.29 inference('simplify', [status(thm)], [zip_derived_cl4803])).
% 21.01/3.29 thf(zip_derived_cl4819, plain, ($false),
% 21.01/3.29 inference('demod', [status(thm)], [zip_derived_cl314, zip_derived_cl4814])).
% 21.01/3.29
% 21.01/3.29 % SZS output end Refutation
% 21.01/3.29
% 21.01/3.29
% 21.01/3.29 % Terminating...
% 21.56/3.38 % Runner terminated.
% 21.56/3.41 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------