%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SEU720^1 : 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.2K4jFc9HGr true
% Computer : n007.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 04:55:57 PM UTC 2025
% Result : Theorem 3.23s 1.44s
% Output : Refutation 3.56s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.16 % Problem : SEU720^1 : TPTP v9.2.0. Released v3.7.0.
% 0.05/0.19 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.2K4jFc9HGr true
% 0.09/0.38 % Computer : n007.cluster.edu
% 0.09/0.38 % Model : x86_64 x86_64
% 0.09/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.38 % Memory : 8042.1875MB
% 0.09/0.38 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.38 % CPULimit : 300
% 0.09/0.38 % WCLimit : 300
% 0.09/0.38 % DateTime : Wed Oct 1 16:11:38 EDT 2025
% 0.09/0.39 % CPUTime :
% 0.09/0.39 % Running portfolio for 300 s
% 0.09/0.39 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.40 % Number of cores: 8
% 0.09/0.41 % Python version: Python 3.6.8
% 0.14/0.42 % Running in HO mode
% 0.44/0.72 % Total configuration time : 828
% 0.44/0.72 % Estimated wc time : 1656
% 0.44/0.72 % Estimated cpu time (8 cpus) : 207.0
% 0.44/0.94 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
% 0.44/0.95 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.44/0.95 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
% 0.44/0.96 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
% 0.44/0.97 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s
% 0.44/0.98 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s
% 0.44/0.98 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.44/0.99 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s
% 3.23/1.44 % Solved by lams/40_c_ic.sh.
% 3.23/1.44 % done 381 iterations in 0.411s
% 3.23/1.44 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 3.23/1.44 % SZS output start Refutation
% 3.23/1.44 thf(setadjoinAx_type, type, setadjoinAx: $o).
% 3.23/1.44 thf(notdexE_type, type, notdexE: $o).
% 3.23/1.44 thf(setukpairinjL2_type, type, setukpairinjL2: $o).
% 3.23/1.44 thf(setunionAx_type, type, setunionAx: $o).
% 3.23/1.44 thf(setminusELneg_type, type, setminusELneg: $o).
% 3.23/1.44 thf(cartprodsndin_type, type, cartprodsndin: $o).
% 3.23/1.44 thf(ex1E1_type, type, ex1E1: $o).
% 3.23/1.44 thf(powersetE_type, type, powersetE: $o).
% 3.23/1.44 thf(omegaSAx_type, type, omegaSAx: $o).
% 3.23/1.44 thf(exuI1_type, type, exuI1: $o).
% 3.23/1.44 thf(exuI2_type, type, exuI2: $o).
% 3.23/1.44 thf(notequalI2_type, type, notequalI2: $o).
% 3.23/1.44 thf(setukpairinjL_type, type, setukpairinjL: $o).
% 3.23/1.44 thf(kpairiskpair_type, type, kpairiskpair: $o).
% 3.23/1.44 thf(upairsubunion_type, type, upairsubunion: $o).
% 3.23/1.44 thf(funcGraphProp3_type, type, funcGraphProp3: $o).
% 3.23/1.44 thf(cartprodmempaircEq_type, type, cartprodmempaircEq: $o).
% 3.23/1.44 thf(powerset__Cong_type, type, powerset__Cong: $o).
% 3.23/1.44 thf(setminusILneg_type, type, setminusILneg: $o).
% 3.23/1.44 thf(wellorderingAx_type, type, wellorderingAx: $o).
% 3.23/1.44 thf(ksndpairEq_type, type, ksndpairEq: $o).
% 3.23/1.44 thf(funcGraphProp2_type, type, funcGraphProp2: $o).
% 3.23/1.44 thf(setadjoinSub2_type, type, setadjoinSub2: $o).
% 3.23/1.44 thf(binintersectSubset5_type, type, binintersectSubset5: $o).
% 3.23/1.44 thf(iftrue_type, type, iftrue: $o).
% 3.23/1.44 thf(upairinpowunion_type, type, upairinpowunion: $o).
% 3.23/1.44 thf(ifSingleton_type, type, ifSingleton: $o).
% 3.23/1.44 thf(setoftrueEq_type, type, setoftrueEq: $o).
% 3.23/1.44 thf(funcImageSingleton_type, type, funcImageSingleton: $o).
% 3.23/1.44 thf(dpsetconstrERa_type, type, dpsetconstrERa: $o).
% 3.23/1.44 thf(lamProp_type, type, lamProp: $o).
% 3.23/1.44 thf(cartprodpairmemEL_type, type, cartprodpairmemEL: $o).
% 3.23/1.44 thf(emptyset__Cong_type, type, emptyset__Cong: $o).
% 3.23/1.44 thf(dpsetconstrER_type, type, dpsetconstrER: $o).
% 3.23/1.44 thf(sepInPowerset_type, type, sepInPowerset: $o).
% 3.23/1.44 thf(setukpairIR_type, type, setukpairIR: $o).
% 3.23/1.44 thf(setukpairinjR1_type, type, setukpairinjR1: $o).
% 3.23/1.44 thf(lam2p_type, type, lam2p: $o).
% 3.23/1.44 thf(binunionE_type, type, binunionE: $o).
% 3.23/1.44 thf(setext_type, type, setext: $o).
% 3.23/1.44 thf(emptyinPowerset_type, type, emptyinPowerset: $o).
% 3.23/1.44 thf(ubforcartprodlem1_type, type, ubforcartprodlem1: $o).
% 3.23/1.44 thf(descr__Cong_type, type, descr__Cong: $o).
% 3.23/1.44 thf(kfstsingleton_type, type, kfstsingleton: $o).
% 3.23/1.44 thf(eqbreln_type, type, eqbreln: $o).
% 3.23/1.44 thf(binintersectSubset1_type, type, binintersectSubset1: $o).
% 3.23/1.44 thf(in_type, type, in: $i > $i > $o).
% 3.23/1.44 thf(binunionT_lem_type, type, binunionT_lem: $o).
% 3.23/1.44 thf(quantDeMorgan1_type, type, quantDeMorgan1: $o).
% 3.23/1.44 thf(complementT_lem_type, type, complementT_lem: $o).
% 3.23/1.44 thf(kpairsurjEq_type, type, kpairsurjEq: $o).
% 3.23/1.44 thf(setadjoinIR_type, type, setadjoinIR: $o).
% 3.23/1.44 thf(beta1_type, type, beta1: $o).
% 3.23/1.44 thf(setadjoin__Cong_type, type, setadjoin__Cong: $o).
% 3.23/1.44 thf(powersetTE1_type, type, powersetTE1: $o).
% 3.23/1.44 thf(symdiffI2_type, type, symdiffI2: $o).
% 3.23/1.44 thf(iftrueProp2_type, type, iftrueProp2: $o).
% 3.23/1.44 thf(upairset2IR_type, type, upairset2IR: $o).
% 3.23/1.44 thf(iffalseProp2_type, type, iffalseProp2: $o).
% 3.23/1.44 thf(subsetE_type, type, subsetE: $o).
% 3.23/1.44 thf(prop2set2propI_type, type, prop2set2propI: $o).
% 3.23/1.44 thf(dsetconstrEL_type, type, dsetconstrEL: $o).
% 3.23/1.44 thf(setbeta_type, type, setbeta: $o).
% 3.23/1.44 thf(eqinunit_type, type, eqinunit: $o).
% 3.23/1.44 thf(upairsetIL_type, type, upairsetIL: $o).
% 3.23/1.44 thf(powersetI1_type, type, powersetI1: $o).
% 3.23/1.44 thf(kfstpairEq_type, type, kfstpairEq: $o).
% 3.23/1.44 thf(binintersectSubset3_type, type, binintersectSubset3: $o).
% 3.23/1.44 thf(setminusIRneg_type, type, setminusIRneg: $o).
% 3.23/1.44 thf(ap2apEq1_type, type, ap2apEq1: $o).
% 3.23/1.44 thf(powersetAx_type, type, powersetAx: $o).
% 3.23/1.44 thf(binintersectSubset4_type, type, binintersectSubset4: $o).
% 3.23/1.44 thf(singletoninpowunion_type, type, singletoninpowunion: $o).
% 3.23/1.44 thf(powersetI_type, type, powersetI: $o).
% 3.23/1.44 thf(cartprodmempair_type, type, cartprodmempair: $o).
% 3.23/1.44 thf(upairsetIR_type, type, upairsetIR: $o).
% 3.23/1.44 thf(lamp_type, type, lamp: $o).
% 3.23/1.44 thf(dpsetconstrEL1_type, type, dpsetconstrEL1: $o).
% 3.23/1.44 thf(inCongP_type, type, inCongP: $o).
% 3.23/1.44 thf(setadjoinSub_type, type, setadjoinSub: $o).
% 3.23/1.44 thf(exuE3e_type, type, exuE3e: $o).
% 3.23/1.44 thf(emptysetE_type, type, emptysetE: $o).
% 3.23/1.44 thf(binintersectSubset2_type, type, binintersectSubset2: $o).
% 3.23/1.44 thf(setunionI_type, type, setunionI: $o).
% 3.23/1.44 thf(setunion__Cong_type, type, setunion__Cong: $o).
% 3.23/1.44 thf(prop2setI_type, type, prop2setI: $o).
% 3.23/1.44 thf(singletonsuniq_type, type, singletonsuniq: $o).
% 3.23/1.44 thf(nonemptyImpWitness_type, type, nonemptyImpWitness: $o).
% 3.23/1.44 thf(setminusER_type, type, setminusER: $o).
% 3.23/1.44 thf(exuE2_type, type, exuE2: $o).
% 3.23/1.44 thf(emptyset_type, type, emptyset: $i).
% 3.23/1.44 thf(setukpairinjR11_type, type, setukpairinjR11: $o).
% 3.23/1.44 thf(ex1I_type, type, ex1I: $o).
% 3.23/1.44 thf(ex1E2_type, type, ex1E2: $o).
% 3.23/1.44 thf(setminus_type, type, setminus: $i > $i > $i).
% 3.23/1.44 thf(setukpairinjL1_type, type, setukpairinjL1: $o).
% 3.23/1.44 thf(powersetsubset_type, type, powersetsubset: $o).
% 3.23/1.44 thf(subPowSU_type, type, subPowSU: $o).
% 3.23/1.44 thf(notequalI1_type, type, notequalI1: $o).
% 3.23/1.44 thf(notinemptyset_type, type, notinemptyset: $o).
% 3.23/1.44 thf(lam2lamEq_type, type, lam2lamEq: $o).
% 3.23/1.44 thf(nonemptyI1_type, type, nonemptyI1: $o).
% 3.23/1.44 thf(subsetTrans_type, type, subsetTrans: $o).
% 3.23/1.44 thf(kpairp_type, type, kpairp: $o).
% 3.23/1.44 thf(setukpairinjR12_type, type, setukpairinjR12: $o).
% 3.23/1.44 thf(setminusI_type, type, setminusI: $o).
% 3.23/1.44 thf(binunionIL_type, type, binunionIL: $o).
% 3.23/1.44 thf(dpsetconstrSub_type, type, dpsetconstrSub: $o).
% 3.23/1.44 thf(setunionsingleton_type, type, setunionsingleton: $o).
% 3.23/1.44 thf(subsetE2_type, type, subsetE2: $o).
% 3.23/1.44 thf(singletonsswitch_type, type, singletonsswitch: $o).
% 3.23/1.44 thf(ubforcartprodlem3_type, type, ubforcartprodlem3: $o).
% 3.23/1.44 thf(beta2_type, type, beta2: $o).
% 3.23/1.44 thf(dpsetconstrI_type, type, dpsetconstrI: $o).
% 3.23/1.44 thf(setextsub_type, type, setextsub: $o).
% 3.23/1.44 thf(binunionLsub_type, type, binunionLsub: $o).
% 3.23/1.44 thf(setunionsingleton1_type, type, setunionsingleton1: $o).
% 3.23/1.44 thf(iftrueorfalse_type, type, iftrueorfalse: $o).
% 3.23/1.44 thf(emptysetsubset_type, type, emptysetsubset: $o).
% 3.23/1.44 thf(quantDeMorgan3_type, type, quantDeMorgan3: $o).
% 3.23/1.44 thf(cartprodpairsurjEq_type, type, cartprodpairsurjEq: $o).
% 3.23/1.44 thf(setOfPairsIsBReln_type, type, setOfPairsIsBReln: $o).
% 3.23/1.44 thf(setunionE_type, type, setunionE: $o).
% 3.23/1.44 thf(ksndsingleton_type, type, ksndsingleton: $o).
% 3.23/1.44 thf(setminusSubset1_type, type, setminusSubset1: $o).
% 3.23/1.44 thf(powersetT_lem_type, type, powersetT_lem: $o).
% 3.23/1.44 thf(emptyinunitempty_type, type, emptyinunitempty: $o).
% 3.23/1.44 thf(binunionIR_type, type, binunionIR: $o).
% 3.23/1.44 thf(theeq_type, type, theeq: $o).
% 3.23/1.44 thf(setadjoinE_type, type, setadjoinE: $o).
% 3.23/1.44 thf(infuncsetfunc_type, type, infuncsetfunc: $o).
% 3.23/1.44 thf(ap2apEq2_type, type, ap2apEq2: $o).
% 3.23/1.44 thf(ap2p_type, type, ap2p: $o).
% 3.23/1.44 thf(setadjoinIL_type, type, setadjoinIL: $o).
% 3.23/1.44 thf(cartprodsndpairEq_type, type, cartprodsndpairEq: $o).
% 3.23/1.44 thf(exuE1_type, type, exuE1: $o).
% 3.23/1.44 thf(ubforcartprodlem2_type, type, ubforcartprodlem2: $o).
% 3.23/1.44 thf(binintersectRsub_type, type, binintersectRsub: $o).
% 3.23/1.44 thf(setminusLsub_type, type, setminusLsub: $o).
% 3.23/1.44 thf(funcextLem_type, type, funcextLem: $o).
% 3.23/1.44 thf(setukpairinjR_type, type, setukpairinjR: $o).
% 3.23/1.44 thf(notinsingleton_type, type, notinsingleton: $o).
% 3.23/1.44 thf(eqimpsubset2_type, type, eqimpsubset2: $o).
% 3.23/1.44 thf(exuEu_type, type, exuEu: $o).
% 3.23/1.44 thf(emptysetimpfalse_type, type, emptysetimpfalse: $o).
% 3.23/1.44 thf(upairsetE_type, type, upairsetE: $o).
% 3.23/1.44 thf(omega0Ax_type, type, omega0Ax: $o).
% 3.23/1.44 thf(subsetTI_type, type, subsetTI: $o).
% 3.23/1.44 thf(notsubsetI_type, type, notsubsetI: $o).
% 3.23/1.44 thf(iffalseProp1_type, type, iffalseProp1: $o).
% 3.23/1.44 thf(zip_tseitin_0_type, type, zip_tseitin_0: $i > $i > $i > $o).
% 3.23/1.44 thf(quantDeMorgan4_type, type, quantDeMorgan4: $o).
% 3.23/1.44 thf(setextAx_type, type, setextAx: $o).
% 3.23/1.44 thf(cartprodpairmemER_type, type, cartprodpairmemER: $o).
% 3.23/1.44 thf(powersetE1_type, type, powersetE1: $o).
% 3.23/1.44 thf(bs114d_type, type, bs114d: $o).
% 3.23/1.44 thf(noeltsimpempty_type, type, noeltsimpempty: $o).
% 3.23/1.44 thf(ifp_type, type, ifp: $o).
% 3.23/1.44 thf(powersetTI1_type, type, powersetTI1: $o).
% 3.23/1.44 thf(binintersectLsub_type, type, binintersectLsub: $o).
% 3.23/1.44 thf(subsetI1_type, type, subsetI1: $o).
% 3.23/1.44 thf(symdiffE_type, type, symdiffE: $o).
% 3.23/1.44 thf(descrp_type, type, descrp: $o).
% 3.23/1.44 thf(dsetconstr__Cong_type, type, dsetconstr__Cong: $o).
% 3.23/1.44 thf(foundationAx_type, type, foundationAx: $o).
% 3.23/1.44 thf(emptysetAx_type, type, emptysetAx: $o).
% 3.23/1.44 thf(emptyI_type, type, emptyI: $o).
% 3.23/1.44 thf(setadjoinOr_type, type, setadjoinOr: $o).
% 3.23/1.44 thf(eta2_type, type, eta2: $o).
% 3.23/1.44 thf(binintersectEL_type, type, binintersectEL: $o).
% 3.23/1.44 thf(emptyE1_type, type, emptyE1: $o).
% 3.23/1.44 thf(emptyInPowerset_type, type, emptyInPowerset: $o).
% 3.23/1.44 thf(complementTI1_type, type, complementTI1: $o).
% 3.23/1.44 thf(vacuousDall_type, type, vacuousDall: $o).
% 3.23/1.44 thf(dsetconstrER_type, type, dsetconstrER: $o).
% 3.23/1.44 thf(binintersectI_type, type, binintersectI: $o).
% 3.23/1.44 thf(funcext_type, type, funcext: $o).
% 3.23/1.44 thf(funcGraphProp4_type, type, funcGraphProp4: $o).
% 3.23/1.44 thf(cartprodpairin_type, type, cartprodpairin: $o).
% 3.23/1.44 thf(cartprodmempair1_type, type, cartprodmempair1: $o).
% 3.23/1.44 thf(sk__84_type, type, sk__84: $i).
% 3.23/1.44 thf(brelnall2_type, type, brelnall2: $o).
% 3.23/1.44 thf(setextT_type, type, setextT: $o).
% 3.23/1.44 thf(ex1I2_type, type, ex1I2: $o).
% 3.23/1.44 thf(symdiffI1_type, type, symdiffI1: $o).
% 3.23/1.44 thf(setukpairinjR2_type, type, setukpairinjR2: $o).
% 3.23/1.44 thf(dpsetconstrEL2_type, type, dpsetconstrEL2: $o).
% 3.23/1.44 thf(theprop_type, type, theprop: $o).
% 3.23/1.44 thf(subsetI2_type, type, subsetI2: $o).
% 3.23/1.44 thf(setminusT_lem_type, type, setminusT_lem: $o).
% 3.23/1.44 thf(symdiffIneg1_type, type, symdiffIneg1: $o).
% 3.23/1.44 thf(sk__85_type, type, sk__85: $i).
% 3.23/1.44 thf(setminusERneg_type, type, setminusERneg: $o).
% 3.23/1.44 thf(symdiffIneg2_type, type, symdiffIneg2: $o).
% 3.23/1.44 thf(omega__Cong_type, type, omega__Cong: $o).
% 3.23/1.44 thf(subsetRefl_type, type, subsetRefl: $o).
% 3.23/1.44 thf(uniqinunit_type, type, uniqinunit: $o).
% 3.23/1.44 thf(sk__83_type, type, sk__83: $i).
% 3.23/1.44 thf(setminusSubset2_type, type, setminusSubset2: $o).
% 3.23/1.44 thf(prop2setE_type, type, prop2setE: $o).
% 3.23/1.44 thf(binunionEcases_type, type, binunionEcases: $o).
% 3.23/1.44 thf(funcinfuncset_type, type, funcinfuncset: $o).
% 3.23/1.44 thf(nonemptyI_type, type, nonemptyI: $o).
% 3.23/1.44 thf(app_type, type, app: $o).
% 3.23/1.44 thf(disjointsetsI1_type, type, disjointsetsI1: $o).
% 3.23/1.44 thf(exuE3u_type, type, exuE3u: $o).
% 3.23/1.44 thf(eta1_type, type, eta1: $o).
% 3.23/1.44 thf(setminusEL_type, type, setminusEL: $o).
% 3.23/1.44 thf(cartprodfstin_type, type, cartprodfstin: $o).
% 3.23/1.44 thf(setunionsingleton2_type, type, setunionsingleton2: $o).
% 3.23/1.44 thf(sepSubset_type, type, sepSubset: $o).
% 3.23/1.44 thf(upairset2E_type, type, upairset2E: $o).
% 3.23/1.44 thf(eqimpsubset1_type, type, eqimpsubset1: $o).
% 3.23/1.44 thf(exuI3_type, type, exuI3: $o).
% 3.23/1.44 thf(cartprodfstpairEq_type, type, cartprodfstpairEq: $o).
% 3.23/1.44 thf(apProp_type, type, apProp: $o).
% 3.23/1.44 thf(notdallE_type, type, notdallE: $o).
% 3.23/1.44 thf(iftrueProp1_type, type, iftrueProp1: $o).
% 3.23/1.44 thf(binintersectER_type, type, binintersectER: $o).
% 3.23/1.44 thf(brelnall1_type, type, brelnall1: $o).
% 3.23/1.44 thf(powerset_type, type, powerset: $i > $i).
% 3.23/1.44 thf(dsetconstrI_type, type, dsetconstrI: $o).
% 3.23/1.44 thf(funcGraphProp1_type, type, funcGraphProp1: $o).
% 3.23/1.44 thf(binintersectT_lem_type, type, binintersectT_lem: $o).
% 3.23/1.44 thf(setadjoin_type, type, setadjoin: $i > $i > $i).
% 3.23/1.44 thf(exu__Cong_type, type, exu__Cong: $o).
% 3.23/1.44 thf(quantDeMorgan2_type, type, quantDeMorgan2: $o).
% 3.23/1.44 thf(secondinupair_type, type, secondinupair: $o).
% 3.23/1.44 thf(singletonprop_type, type, singletonprop: $o).
% 3.23/1.44 thf(singletonsubset_type, type, singletonsubset: $o).
% 3.23/1.44 thf(singletoninpowerset_type, type, singletoninpowerset: $o).
% 3.23/1.44 thf(subsetemptysetimpeq_type, type, subsetemptysetimpeq: $o).
% 3.23/1.44 thf(replAx_type, type, replAx: $o).
% 3.23/1.44 thf(upairequniteq_type, type, upairequniteq: $o).
% 3.23/1.44 thf(nonemptyE1_type, type, nonemptyE1: $o).
% 3.23/1.44 thf(omegaIndAx_type, type, omegaIndAx: $o).
% 3.23/1.44 thf(setukpairIL_type, type, setukpairIL: $o).
% 3.23/1.44 thf(setunionE2_type, type, setunionE2: $o).
% 3.23/1.44 thf(inPowerset_type, type, inPowerset: $o).
% 3.23/1.44 thf(iffalse_type, type, iffalse: $o).
% 3.23/1.44 thf(funcext2_type, type, funcext2: $o).
% 3.23/1.44 thf(subset_type, type, subset: $i > $i > $o).
% 3.23/1.44 thf(subbreln_type, type, subbreln: $o).
% 3.23/1.44 thf(in__Cong_type, type, in__Cong: $o).
% 3.23/1.44 thf(binunionRsub_type, type, binunionRsub: $o).
% 3.23/1.44 thf(subset2powerset_type, type, subset2powerset: $o).
% 3.23/1.44 thf(complementTI1, axiom, complementTI1 =
% 3.23/1.44 (![A:$i,X:$i]:
% 3.23/1.44 ( ( in @ X @ ( powerset @ A ) ) =>
% 3.23/1.44 ( ![Xx:$i]:
% 3.23/1.44 ( ( in @ Xx @ A ) =>
% 3.23/1.44 ( ( in @ Xx @ X ) => ( ~( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ))).
% 3.23/1.44 thf('0', plain,
% 3.23/1.44 (( complementTI1 ) =
% 3.23/1.44 ( ![X4:$i,X6:$i]:
% 3.23/1.44 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 3.23/1.44 ( ![X8:$i]:
% 3.23/1.44 ( ( in @ X8 @ X4 ) =>
% 3.23/1.44 ( ( in @ X8 @ X6 ) => ( ~( in @ X8 @ ( setminus @ X4 @ X6 ) ) ) ) ) ) ) )),
% 3.23/1.44 define([status(thm)])).
% 3.23/1.44 thf(powersetTE1, axiom, powersetTE1 =
% 3.23/1.44 (![A:$i,X:$i]:
% 3.23/1.44 ( ( in @ X @ ( powerset @ A ) ) =>
% 3.23/1.44 ( ![Y:$i]:
% 3.23/1.44 ( ( in @ Y @ ( powerset @ A ) ) =>
% 3.23/1.44 ( ![Xx:$i]:
% 3.23/1.44 ( ( in @ Xx @ A ) =>
% 3.23/1.44 ( ( in @ X @ ( powerset @ Y ) ) =>
% 3.23/1.44 ( ( in @ Xx @ X ) => ( in @ Xx @ Y ) ) ) ) ) ) ) ))).
% 3.23/1.44 thf('1', plain,
% 3.23/1.44 (( powersetTE1 ) =
% 3.23/1.44 ( ![X4:$i,X6:$i]:
% 3.23/1.44 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 3.23/1.44 ( ![X8:$i]:
% 3.23/1.44 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 3.23/1.44 ( ![X10:$i]:
% 3.23/1.44 ( ( in @ X10 @ X4 ) =>
% 3.23/1.44 ( ( in @ X6 @ ( powerset @ X8 ) ) =>
% 3.23/1.44 ( ( in @ X10 @ X6 ) => ( in @ X10 @ X8 ) ) ) ) ) ) ) ) )),
% 3.23/1.44 define([status(thm)])).
% 3.23/1.44 thf(powersetTI1, axiom, powersetTI1 =
% 3.23/1.44 (![A:$i,X:$i]:
% 3.23/1.44 ( ( in @ X @ ( powerset @ A ) ) =>
% 3.23/1.44 ( ![Y:$i]:
% 3.23/1.44 ( ( in @ Y @ ( powerset @ A ) ) =>
% 3.23/1.44 ( ( ![Xx:$i]:
% 3.23/1.44 ( ( in @ Xx @ A ) => ( ( in @ Xx @ X ) => ( in @ Xx @ Y ) ) ) ) =>
% 3.23/1.44 ( in @ X @ ( powerset @ Y ) ) ) ) ) ))).
% 3.23/1.44 thf('2', plain,
% 3.23/1.44 (( powersetTI1 ) =
% 3.23/1.44 ( ![X4:$i,X6:$i]:
% 3.23/1.44 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 3.23/1.44 ( ![X8:$i]:
% 3.23/1.44 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 3.23/1.44 ( ( ![X10:$i]:
% 3.23/1.44 ( ( in @ X10 @ X4 ) =>
% 3.23/1.44 ( ( in @ X10 @ X6 ) => ( in @ X10 @ X8 ) ) ) ) =>
% 3.23/1.44 ( in @ X6 @ ( powerset @ X8 ) ) ) ) ) ) )),
% 3.23/1.44 define([status(thm)])).
% 3.23/1.44 thf(subsetTI, axiom, subsetTI =
% 3.23/1.44 (![A:$i,X:$i]:
% 3.23/1.44 ( ( in @ X @ ( powerset @ A ) ) =>
% 3.23/1.44 ( ![Y:$i]:
% 3.23/1.44 ( ( in @ Y @ ( powerset @ A ) ) =>
% 3.23/1.44 ( ( ![Xx:$i]:
% 3.23/1.44 ( ( in @ Xx @ A ) => ( ( in @ Xx @ X ) => ( in @ Xx @ Y ) ) ) ) =>
% 3.23/1.44 ( subset @ X @ Y ) ) ) ) ))).
% 3.23/1.44 thf('3', plain,
% 3.23/1.44 (( subsetTI ) =
% 3.23/1.44 ( ![X4:$i,X6:$i]:
% 3.23/1.44 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 3.23/1.44 ( ![X8:$i]:
% 3.23/1.44 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 3.23/1.44 ( ( ![X10:$i]:
% 3.23/1.44 ( ( in @ X10 @ X4 ) =>
% 3.23/1.44 ( ( in @ X10 @ X6 ) => ( in @ X10 @ X8 ) ) ) ) =>
% 3.23/1.44 ( subset @ X6 @ X8 ) ) ) ) ) )),
% 3.23/1.44 define([status(thm)])).
% 3.23/1.44 thf(setextT, axiom, setextT =
% 3.23/1.44 (![A:$i,X:$i]:
% 3.23/1.44 ( ( in @ X @ ( powerset @ A ) ) =>
% 3.23/1.44 ( ![Y:$i]:
% 3.23/1.44 ( ( in @ Y @ ( powerset @ A ) ) =>
% 3.23/1.44 ( ( ![Xx:$i]:
% 3.23/1.44 ( ( in @ Xx @ A ) => ( ( in @ Xx @ X ) => ( in @ Xx @ Y ) ) ) ) =>
% 3.23/1.44 ( ( ![Xx:$i]:
% 3.23/1.44 ( ( in @ Xx @ A ) => ( ( in @ Xx @ Y ) => ( in @ Xx @ X ) ) ) ) =>
% 3.23/1.44 ( ( X ) = ( Y ) ) ) ) ) ) ))).
% 3.23/1.44 thf('4', plain,
% 3.23/1.44 (( setextT ) =
% 3.23/1.44 ( ![X4:$i,X6:$i]:
% 3.23/1.44 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 3.23/1.44 ( ![X8:$i]:
% 3.23/1.44 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 3.23/1.44 ( ( ![X10:$i]:
% 3.23/1.44 ( ( in @ X10 @ X4 ) =>
% 3.23/1.44 ( ( in @ X10 @ X6 ) => ( in @ X10 @ X8 ) ) ) ) =>
% 3.23/1.44 ( ( ![X12:$i]:
% 3.23/1.44 ( ( in @ X12 @ X4 ) =>
% 3.23/1.44 ( ( in @ X12 @ X8 ) => ( in @ X12 @ X6 ) ) ) ) =>
% 3.23/1.44 ( ( X6 ) = ( X8 ) ) ) ) ) ) ) )),
% 3.23/1.44 define([status(thm)])).
% 3.23/1.44 thf(complementT_lem, axiom, complementT_lem =
% 3.23/1.44 (![A:$i,X:$i]:
% 3.23/1.44 ( ( in @ X @ ( powerset @ A ) ) =>
% 3.23/1.44 ( in @ ( setminus @ A @ X ) @ ( powerset @ A ) ) ))).
% 3.23/1.44 thf('5', plain,
% 3.23/1.44 (( complementT_lem ) =
% 3.23/1.44 ( ![X4:$i,X6:$i]:
% 3.23/1.44 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 3.23/1.44 ( in @ ( setminus @ X4 @ X6 ) @ ( powerset @ X4 ) ) ) )),
% 3.23/1.44 define([status(thm)])).
% 3.23/1.44 thf(setminusT_lem, axiom, setminusT_lem =
% 3.23/1.44 (![A:$i,X:$i]:
% 3.23/1.44 ( ( in @ X @ ( powerset @ A ) ) =>
% 3.23/1.44 ( ![Y:$i]:
% 3.23/1.44 ( ( in @ Y @ ( powerset @ A ) ) =>
% 3.23/1.44 ( in @ ( setminus @ X @ Y ) @ ( powerset @ A ) ) ) ) ))).
% 3.23/1.44 thf('6', plain,
% 3.23/1.44 (( setminusT_lem ) =
% 3.23/1.44 ( ![X4:$i,X6:$i]:
% 3.23/1.44 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 3.23/1.44 ( ![X8:$i]:
% 3.23/1.44 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 3.23/1.44 ( in @ ( setminus @ X6 @ X8 ) @ ( powerset @ X4 ) ) ) ) ) )),
% 3.23/1.44 define([status(thm)])).
% 3.23/1.44 thf(powersetT_lem, axiom, powersetT_lem =
% 3.23/1.44 (![A:$i,X:$i]:
% 3.23/1.44 ( ( in @ X @ ( powerset @ A ) ) =>
% 3.23/1.44 ( in @ ( powerset @ X ) @ ( powerset @ ( powerset @ A ) ) ) ))).
% 3.23/1.44 thf('7', plain,
% 3.23/1.44 (( powersetT_lem ) =
% 3.23/1.44 ( ![X4:$i,X6:$i]:
% 3.23/1.44 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 3.23/1.44 ( in @ ( powerset @ X6 ) @ ( powerset @ ( powerset @ X4 ) ) ) ) )),
% 3.23/1.44 define([status(thm)])).
% 3.23/1.44 thf(singletoninpowerset, axiom, singletoninpowerset =
% 3.23/1.44 (![A:$i,Xx:$i]:
% 3.23/1.44 ( ( in @ Xx @ A ) =>
% 3.23/1.44 ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) ))).
% 3.23/1.44 thf('8', plain,
% 3.23/1.44 (( singletoninpowerset ) =
% 3.23/1.44 ( ![X4:$i,X6:$i]:
% 3.23/1.44 ( ( in @ X6 @ X4 ) =>
% 3.23/1.44 ( in @ ( setadjoin @ X6 @ emptyset ) @ ( powerset @ X4 ) ) ) )),
% 3.23/1.44 define([status(thm)])).
% 3.23/1.44 thf(setminusSubset1, axiom, setminusSubset1 =
% 3.23/1.44 (![A:$i,B:$i]:
% 3.23/1.44 ( ( ( setminus @ A @ B ) = ( emptyset ) ) => ( subset @ A @ B ) ))).
% 3.23/1.44 thf('9', plain,
% 3.23/1.44 (( setminusSubset1 ) =
% 3.23/1.44 ( ![X4:$i,X6:$i]:
% 3.23/1.44 ( ( ( setminus @ X4 @ X6 ) = ( emptyset ) ) => ( subset @ X4 @ X6 ) ) )),
% 3.23/1.44 define([status(thm)])).
% 3.23/1.44 thf(setminusLsub, axiom, setminusLsub =
% 3.23/1.44 (![A:$i,B:$i]: ( subset @ ( setminus @ A @ B ) @ A ))).
% 3.23/1.44 thf('10', plain,
% 3.23/1.44 (( setminusLsub ) =
% 3.23/1.44 ( ![X4:$i,X6:$i]: ( subset @ ( setminus @ X4 @ X6 ) @ X4 ) )),
% 3.23/1.44 define([status(thm)])).
% 3.23/1.44 thf(setminusIRneg, axiom, setminusIRneg =
% 3.23/1.44 (![A:$i,B:$i,Xx:$i]:
% 3.23/1.44 ( ( in @ Xx @ B ) => ( ~( in @ Xx @ ( setminus @ A @ B ) ) ) ))).
% 3.23/1.44 thf('11', plain,
% 3.23/1.44 (( setminusIRneg ) =
% 3.23/1.44 ( ![X4:$i,X6:$i,X8:$i]:
% 3.23/1.44 ( ( in @ X8 @ X6 ) => ( ~( in @ X8 @ ( setminus @ X4 @ X6 ) ) ) ) )),
% 3.23/1.44 define([status(thm)])).
% 3.23/1.44 thf(setminusILneg, axiom, setminusILneg =
% 3.23/1.44 (![A:$i,B:$i,Xx:$i]:
% 3.23/1.44 ( ( ~( in @ Xx @ A ) ) => ( ~( in @ Xx @ ( setminus @ A @ B ) ) ) ))).
% 3.23/1.44 thf('12', plain,
% 3.23/1.44 (( setminusILneg ) =
% 3.23/1.44 ( ![X4:$i,X6:$i,X8:$i]:
% 3.23/1.44 ( ( ~( in @ X8 @ X4 ) ) => ( ~( in @ X8 @ ( setminus @ X4 @ X6 ) ) ) ) )),
% 3.23/1.44 define([status(thm)])).
% 3.23/1.44 thf(setminusELneg, axiom, setminusELneg =
% 3.23/1.44 (![A:$i,B:$i,Xx:$i]:
% 3.23/1.44 ( ( ~( in @ Xx @ ( setminus @ A @ B ) ) ) =>
% 3.23/1.44 ( ( ~( in @ Xx @ B ) ) => ( ~( in @ Xx @ A ) ) ) ))).
% 3.23/1.44 thf('13', plain,
% 3.23/1.44 (( setminusELneg ) =
% 3.23/1.44 ( ![X4:$i,X6:$i,X8:$i]:
% 3.23/1.44 ( ( ~( in @ X8 @ ( setminus @ X4 @ X6 ) ) ) =>
% 3.23/1.44 ( ( ~( in @ X8 @ X6 ) ) => ( ~( in @ X8 @ X4 ) ) ) ) )),
% 3.23/1.44 define([status(thm)])).
% 3.23/1.44 thf(setminusERneg, axiom, setminusERneg =
% 3.23/1.44 (![A:$i,B:$i,Xx:$i]:
% 3.23/1.44 ( ( ~( in @ Xx @ ( setminus @ A @ B ) ) ) =>
% 3.23/1.44 ( ( in @ Xx @ A ) => ( in @ Xx @ B ) ) ))).
% 3.23/1.44 thf('14', plain,
% 3.23/1.44 (( setminusERneg ) =
% 3.23/1.44 ( ![X4:$i,X6:$i,X8:$i]:
% 3.23/1.44 ( ( ~( in @ X8 @ ( setminus @ X4 @ X6 ) ) ) =>
% 3.23/1.44 ( ( in @ X8 @ X4 ) => ( in @ X8 @ X6 ) ) ) )),
% 3.23/1.44 define([status(thm)])).
% 3.23/1.44 thf(setminusSubset2, axiom, setminusSubset2 =
% 3.23/1.44 (![A:$i,B:$i]:
% 3.23/1.44 ( ( subset @ A @ B ) => ( ( setminus @ A @ B ) = ( emptyset ) ) ))).
% 3.23/1.44 thf('15', plain,
% 3.23/1.44 (( setminusSubset2 ) =
% 3.23/1.44 ( ![X4:$i,X6:$i]:
% 3.23/1.44 ( ( subset @ X4 @ X6 ) => ( ( setminus @ X4 @ X6 ) = ( emptyset ) ) ) )),
% 3.23/1.44 define([status(thm)])).
% 3.23/1.44 thf(setminusER, axiom, setminusER =
% 3.23/1.44 (![A:$i,B:$i,Xx:$i]:
% 3.23/1.44 ( ( in @ Xx @ ( setminus @ A @ B ) ) => ( ~( in @ Xx @ B ) ) ))).
% 3.23/1.44 thf('16', plain,
% 3.23/1.44 (( setminusER ) =
% 3.23/1.44 ( ![X4:$i,X6:$i,X8:$i]:
% 3.23/1.44 ( ( in @ X8 @ ( setminus @ X4 @ X6 ) ) => ( ~( in @ X8 @ X6 ) ) ) )),
% 3.23/1.44 define([status(thm)])).
% 3.23/1.44 thf(setminusEL, axiom, setminusEL =
% 3.23/1.44 (![A:$i,B:$i,Xx:$i]:
% 3.23/1.44 ( ( in @ Xx @ ( setminus @ A @ B ) ) => ( in @ Xx @ A ) ))).
% 3.23/1.44 thf('17', plain,
% 3.23/1.44 (( setminusEL ) =
% 3.23/1.44 ( ![X4:$i,X6:$i,X8:$i]:
% 3.23/1.44 ( ( in @ X8 @ ( setminus @ X4 @ X6 ) ) => ( in @ X8 @ X4 ) ) )),
% 3.23/1.44 define([status(thm)])).
% 3.23/1.44 thf(setminusI, axiom, setminusI =
% 3.23/1.44 (![A:$i,B:$i,Xx:$i]:
% 3.23/1.44 ( ( in @ Xx @ A ) =>
% 3.23/1.44 ( ( ~( in @ Xx @ B ) ) => ( in @ Xx @ ( setminus @ A @ B ) ) ) ))).
% 3.23/1.44 thf('18', plain,
% 3.23/1.44 (( setminusI ) =
% 3.23/1.44 ( ![X4:$i,X6:$i,X8:$i]:
% 3.23/1.44 ( ( in @ X8 @ X4 ) =>
% 3.23/1.44 ( ( ~( in @ X8 @ X6 ) ) => ( in @ X8 @ ( setminus @ X4 @ X6 ) ) ) ) )),
% 3.23/1.44 define([status(thm)])).
% 3.23/1.44 thf(powersetsubset, axiom, powersetsubset =
% 3.23/1.44 (![A:$i,B:$i]:
% 3.23/1.44 ( ( subset @ A @ B ) => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ))).
% 3.23/1.44 thf('19', plain,
% 3.23/1.44 (( powersetsubset ) =
% 3.23/1.44 ( ![X4:$i,X6:$i]:
% 3.23/1.44 ( ( subset @ X4 @ X6 ) =>
% 3.23/1.44 ( subset @ ( powerset @ X4 ) @ ( powerset @ X6 ) ) ) )),
% 3.23/1.44 define([status(thm)])).
% 3.23/1.44 thf(inPowerset, axiom, inPowerset = (![A:$i]: ( in @ A @ ( powerset @ A ) ))).
% 3.23/1.44 thf('20', plain,
% 3.23/1.44 (( inPowerset ) = ( ![X4:$i]: ( in @ X4 @ ( powerset @ X4 ) ) )),
% 3.23/1.44 define([status(thm)])).
% 3.23/1.44 thf(powersetE1, axiom, powersetE1 =
% 3.23/1.44 (![A:$i,B:$i]: ( ( in @ B @ ( powerset @ A ) ) => ( subset @ B @ A ) ))).
% 3.23/1.44 thf('21', plain,
% 3.23/1.44 (( powersetE1 ) =
% 3.23/1.44 ( ![X4:$i,X6:$i]:
% 3.23/1.44 ( ( in @ X6 @ ( powerset @ X4 ) ) => ( subset @ X6 @ X4 ) ) )),
% 3.23/1.44 define([status(thm)])).
% 3.23/1.44 thf(powersetI1, axiom, powersetI1 =
% 3.23/1.44 (![A:$i,B:$i]: ( ( subset @ B @ A ) => ( in @ B @ ( powerset @ A ) ) ))).
% 3.23/1.44 thf('22', plain,
% 3.23/1.44 (( powersetI1 ) =
% 3.23/1.44 ( ![X4:$i,X6:$i]:
% 3.23/1.44 ( ( subset @ X6 @ X4 ) => ( in @ X6 @ ( powerset @ X4 ) ) ) )),
% 3.23/1.44 define([status(thm)])).
% 3.23/1.44 thf(subset2powerset, axiom, subset2powerset =
% 3.23/1.44 (![A:$i,B:$i]: ( ( subset @ A @ B ) => ( in @ A @ ( powerset @ B ) ) ))).
% 3.23/1.44 thf('23', plain,
% 3.23/1.44 (( subset2powerset ) =
% 3.23/1.44 ( ![X4:$i,X6:$i]:
% 3.23/1.44 ( ( subset @ X4 @ X6 ) => ( in @ X4 @ ( powerset @ X6 ) ) ) )),
% 3.23/1.44 define([status(thm)])).
% 3.23/1.44 thf(powerset__Cong, axiom, powerset__Cong =
% 3.23/1.44 (![A:$i,B:$i]:
% 3.23/1.44 ( ( ( A ) = ( B ) ) => ( ( powerset @ A ) = ( powerset @ B ) ) ))).
% 3.23/1.44 thf('24', plain,
% 3.23/1.44 (( powerset__Cong ) =
% 3.23/1.44 ( ![X4:$i,X6:$i]:
% 3.23/1.44 ( ( ( X4 ) = ( X6 ) ) => ( ( powerset @ X4 ) = ( powerset @ X6 ) ) ) )),
% 3.23/1.44 define([status(thm)])).
% 3.23/1.44 thf(powersetE, axiom, powersetE =
% 3.23/1.44 (![A:$i,B:$i,Xx:$i]:
% 3.23/1.44 ( ( in @ B @ ( powerset @ A ) ) => ( ( in @ Xx @ B ) => ( in @ Xx @ A ) ) ))).
% 3.23/1.44 thf('25', plain,
% 3.23/1.44 (( powersetE ) =
% 3.23/1.44 ( ![X4:$i,X6:$i,X8:$i]:
% 3.23/1.44 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 3.23/1.44 ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ) )),
% 3.23/1.44 define([status(thm)])).
% 3.23/1.44 thf(emptyInPowerset, axiom, emptyInPowerset =
% 3.23/1.44 (![A:$i]: ( in @ emptyset @ ( powerset @ A ) ))).
% 3.23/1.44 thf('26', plain,
% 3.23/1.44 (( emptyInPowerset ) =
% 3.23/1.44 ( ![X4:$i]: ( in @ emptyset @ ( powerset @ X4 ) ) )),
% 3.23/1.44 define([status(thm)])).
% 3.23/1.44 thf(emptyinPowerset, axiom, emptyinPowerset =
% 3.23/1.44 (![A:$i]: ( in @ emptyset @ ( powerset @ A ) ))).
% 3.23/1.44 thf('27', plain,
% 3.23/1.44 (( emptyinPowerset ) =
% 3.23/1.44 ( ![X4:$i]: ( in @ emptyset @ ( powerset @ X4 ) ) )),
% 3.23/1.44 define([status(thm)])).
% 3.23/1.44 thf(powersetI, axiom, powersetI =
% 3.23/1.44 (![A:$i,B:$i]:
% 3.23/1.44 ( ( ![Xx:$i]: ( ( in @ Xx @ B ) => ( in @ Xx @ A ) ) ) =>
% 3.23/1.44 ( in @ B @ ( powerset @ A ) ) ))).
% 3.23/1.44 thf('28', plain,
% 3.23/1.44 (( powersetI ) =
% 3.23/1.44 ( ![X4:$i,X6:$i]:
% 3.23/1.44 ( ( ![X8:$i]: ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ) =>
% 3.23/1.44 ( in @ X6 @ ( powerset @ X4 ) ) ) )),
% 3.23/1.44 define([status(thm)])).
% 3.23/1.44 thf(powersetAx, axiom, powersetAx =
% 3.23/1.44 (![A:$i,B:$i]:
% 3.23/1.44 ( ( in @ B @ ( powerset @ A ) ) <=>
% 3.23/1.44 ( ![Xx:$i]: ( ( in @ Xx @ B ) => ( in @ Xx @ A ) ) ) ))).
% 3.23/1.44 thf('29', plain,
% 3.23/1.44 (( powersetAx ) =
% 3.23/1.44 ( ![X4:$i,X6:$i]:
% 3.23/1.44 ( ( in @ X6 @ ( powerset @ X4 ) ) <=>
% 3.23/1.44 ( ![X8:$i]: ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ) ) )),
% 3.23/1.44 define([status(thm)])).
% 3.23/1.44 thf(complementTE1, conjecture,
% 3.23/1.44 (( setextAx ) =>
% 3.23/1.44 ( ( emptysetAx ) =>
% 3.23/1.44 ( ( setadjoinAx ) =>
% 3.23/1.44 ( ( powersetAx ) =>
% 3.23/1.44 ( ( setunionAx ) =>
% 3.23/1.44 ( ( omega0Ax ) =>
% 3.23/1.44 ( ( omegaSAx ) =>
% 3.23/1.44 ( ( omegaIndAx ) =>
% 3.23/1.44 ( ( replAx ) =>
% 3.23/1.44 ( ( foundationAx ) =>
% 3.23/1.44 ( ( wellorderingAx ) =>
% 3.23/1.44 ( ( descrp ) =>
% 3.23/1.44 ( ( dsetconstrI ) =>
% 3.23/1.44 ( ( dsetconstrEL ) =>
% 3.23/1.44 ( ( dsetconstrER ) =>
% 3.23/1.44 ( ( exuE1 ) =>
% 3.23/1.44 ( ( prop2setE ) =>
% 3.23/1.44 ( ( emptysetE ) =>
% 3.23/1.44 ( ( emptysetimpfalse ) =>
% 3.23/1.44 ( ( notinemptyset ) =>
% 3.23/1.44 ( ( exuE3e ) =>
% 3.23/1.44 ( ( setext ) =>
% 3.23/1.44 ( ( emptyI ) =>
% 3.23/1.44 ( ( noeltsimpempty ) =>
% 3.23/1.44 ( ( setbeta ) =>
% 3.23/1.44 ( ( nonemptyE1 ) =>
% 3.23/1.44 ( ( nonemptyI ) =>
% 3.23/1.44 ( ( nonemptyI1 ) =>
% 3.23/1.44 ( ( setadjoinIL ) =>
% 3.23/1.44 ( ( emptyinunitempty ) =>
% 3.23/1.44 ( ( setadjoinIR ) =>
% 3.23/1.44 ( ( setadjoinE ) =>
% 3.23/1.44 ( (
% 3.23/1.44 setadjoinOr ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 setoftrueEq ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 powersetI ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 emptyinPowerset ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 emptyInPowerset ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 powersetE ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 setunionI ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 setunionE ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 subPowSU ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 exuE2 ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 nonemptyImpWitness ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 uniqinunit ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 notinsingleton ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 eqinunit ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 singletonsswitch ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 upairsetE ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 upairsetIL ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 upairsetIR ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 emptyE1 ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 vacuousDall ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 quantDeMorgan1 ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 quantDeMorgan2 ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 quantDeMorgan3 ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 quantDeMorgan4 ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 prop2setI ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 prop2set2propI ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 notdexE ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 notdallE ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 exuI1 ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 exuI3 ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 exuI2 ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 inCongP ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 in__Cong ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 exuE3u ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 exu__Cong ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 emptyset__Cong ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 setadjoin__Cong ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 powerset__Cong ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 setunion__Cong ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 omega__Cong ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 exuEu ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 descr__Cong ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 dsetconstr__Cong ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 subsetI1 ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 eqimpsubset2 ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 eqimpsubset1 ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 subsetI2 ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 emptysetsubset ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 subsetE ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 subsetE2 ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 notsubsetI ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 notequalI1 ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 notequalI2 ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 subsetRefl ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 subsetTrans ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 setadjoinSub ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 setadjoinSub2 ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 subset2powerset ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 setextsub ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 subsetemptysetimpeq ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 powersetI1 ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 powersetE1 ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 inPowerset ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 powersetsubset ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 sepInPowerset ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 sepSubset ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 binunionIL ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 upairset2IR ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 binunionIR ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 binunionEcases ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 binunionE ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 binunionLsub ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 binunionRsub ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 binintersectI ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 binintersectSubset5 ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 binintersectEL ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 binintersectLsub ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 binintersectSubset2 ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 binintersectSubset3 ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 binintersectER ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 disjointsetsI1 ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 binintersectRsub ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 binintersectSubset4 ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 binintersectSubset1 ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 bs114d ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 setminusI ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 setminusEL ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 setminusER ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 setminusSubset2 ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 setminusERneg ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 setminusELneg ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 setminusILneg ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 setminusIRneg ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 setminusLsub ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 setminusSubset1 ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 symdiffE ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 symdiffI1 ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 symdiffI2 ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 symdiffIneg1 ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 symdiffIneg2 ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 secondinupair ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 setukpairIL ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 setukpairIR ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 kpairiskpair ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 kpairp ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 singletonsubset ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 singletoninpowerset ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 singletoninpowunion ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 upairset2E ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 upairsubunion ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 upairinpowunion ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 ubforcartprodlem1 ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 ubforcartprodlem2 ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 ubforcartprodlem3 ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 cartprodpairin ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 cartprodmempair1 ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 cartprodmempair ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 setunionE2 ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 setunionsingleton1 ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 setunionsingleton2 ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 setunionsingleton ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 singletonprop ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 ex1E1 ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 ex1I ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 ex1I2 ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 singletonsuniq ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 setukpairinjL1 ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 kfstsingleton ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 theprop ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 kfstpairEq ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 cartprodfstin ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 setukpairinjL2 ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 setukpairinjL ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 setukpairinjR11 ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 setukpairinjR12 ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 setukpairinjR1 ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 upairequniteq ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 setukpairinjR2 ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 setukpairinjR ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 ksndsingleton ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 ksndpairEq ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 kpairsurjEq ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 cartprodsndin ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 cartprodpairmemEL ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 cartprodpairmemER ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 cartprodmempaircEq ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 cartprodfstpairEq ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 cartprodsndpairEq ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 cartprodpairsurjEq ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 dpsetconstrI ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 dpsetconstrSub ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 setOfPairsIsBReln ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 dpsetconstrERa ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 dpsetconstrEL1 ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 dpsetconstrEL2 ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 dpsetconstrER ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 funcImageSingleton ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 apProp ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 app ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 infuncsetfunc ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 ap2p ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 funcinfuncset ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 lamProp ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 lamp ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 lam2p ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 brelnall1 ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 brelnall2 ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 ex1E2 ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 funcGraphProp1 ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 funcGraphProp3 ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 funcGraphProp2 ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 funcextLem ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 funcGraphProp4 ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 subbreln ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 eqbreln ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 funcext ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 funcext2 ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 ap2apEq1 ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 ap2apEq2 ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 beta1 ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 eta1 ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 lam2lamEq ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 beta2 ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 eta2 ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 iffalseProp1 ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 iffalseProp2 ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 iftrueProp1 ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 iftrueProp2 ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 ifSingleton ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 ifp ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 theeq ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 iftrue ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 iffalse ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 iftrueorfalse ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 binintersectT_lem ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 binunionT_lem ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 powersetT_lem ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 setminusT_lem ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 complementT_lem ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 setextT ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 subsetTI ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 powersetTI1 ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 powersetTE1 ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 complementTI1 ) =>
% 3.23/1.44 (
% 3.23/1.44 ![
% 3.23/1.44 A:$i,X:$i]:
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 in @
% 3.23/1.44 X @
% 3.23/1.44 (
% 3.23/1.44 powerset @
% 3.23/1.44 A ) ) =>
% 3.23/1.44 (
% 3.23/1.44 ![
% 3.23/1.44 Xx:$i]:
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 in @
% 3.23/1.44 Xx @ A ) =>
% 3.23/1.44 (
% 3.23/1.44 (
% 3.23/1.44 ~(
% 3.23/1.44 in @
% 3.23/1.44 Xx @
% 3.23/1.44 (
% 3.23/1.44 setminus
% 3.23/1.44 @
% 3.23/1.44 A @ X ) ) ) =>
% 3.23/1.44 (
% 3.23/1.44 in @
% 3.23/1.44 Xx @ X ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 3.23/1.44 thf(zf_stmt_0, conjecture,
% 3.23/1.44 (( setextAx ) =>
% 3.23/1.44 ( ( emptysetAx ) =>
% 3.23/1.44 ( ( setadjoinAx ) =>
% 3.23/1.44 ( ( ![X4:$i,X6:$i]:
% 3.23/1.44 ( ( in @ X6 @ ( powerset @ X4 ) ) <=>
% 3.23/1.44 ( ![X8:$i]: ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ) ) ) =>
% 3.23/1.44 ( ( setunionAx ) =>
% 3.23/1.44 ( ( omega0Ax ) =>
% 3.23/1.44 ( ( omegaSAx ) =>
% 3.23/1.44 ( ( omegaIndAx ) =>
% 3.23/1.44 ( ( replAx ) =>
% 3.23/1.44 ( ( foundationAx ) =>
% 3.23/1.44 ( ( wellorderingAx ) =>
% 3.23/1.44 ( ( descrp ) =>
% 3.23/1.44 ( ( dsetconstrI ) =>
% 3.23/1.44 ( ( dsetconstrEL ) =>
% 3.23/1.45 ( ( dsetconstrER ) =>
% 3.23/1.45 ( ( exuE1 ) =>
% 3.23/1.45 ( ( prop2setE ) =>
% 3.23/1.45 ( ( emptysetE ) =>
% 3.23/1.45 ( ( emptysetimpfalse ) =>
% 3.23/1.45 ( ( notinemptyset ) =>
% 3.23/1.45 ( ( exuE3e ) =>
% 3.23/1.45 ( ( setext ) =>
% 3.23/1.45 ( ( emptyI ) =>
% 3.23/1.45 ( ( noeltsimpempty ) =>
% 3.23/1.45 ( ( setbeta ) =>
% 3.23/1.45 ( ( nonemptyE1 ) =>
% 3.23/1.45 ( ( nonemptyI ) =>
% 3.23/1.45 ( ( nonemptyI1 ) =>
% 3.23/1.45 ( ( setadjoinIL ) =>
% 3.23/1.45 ( ( emptyinunitempty ) =>
% 3.23/1.45 ( ( setadjoinIR ) =>
% 3.23/1.45 ( ( setadjoinE ) =>
% 3.23/1.45 ( (
% 3.23/1.45 setadjoinOr ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 setoftrueEq ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 ![
% 3.23/1.45 X10:$i,
% 3.23/1.45 X12:$i]:
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 ![
% 3.23/1.45 X14:$i]:
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 in @
% 3.23/1.45 X14 @ X12 ) =>
% 3.23/1.45 (
% 3.23/1.45 in @
% 3.23/1.45 X14 @ X10 ) ) ) =>
% 3.23/1.45 (
% 3.23/1.45 in @
% 3.23/1.45 X12 @
% 3.23/1.45 (
% 3.23/1.45 powerset @
% 3.23/1.45 X10 ) ) ) ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 ![
% 3.23/1.45 X16:$i]:
% 3.23/1.45 (
% 3.23/1.45 in @
% 3.23/1.45 emptyset @
% 3.23/1.45 (
% 3.23/1.45 powerset @
% 3.23/1.45 X16 ) ) ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 ![
% 3.23/1.45 X18:$i]:
% 3.23/1.45 (
% 3.23/1.45 in @
% 3.23/1.45 emptyset @
% 3.23/1.45 (
% 3.23/1.45 powerset @
% 3.23/1.45 X18 ) ) ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 ![
% 3.23/1.45 X20:$i,
% 3.23/1.45 X22:$i,
% 3.23/1.45 X24:$i]:
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 in @
% 3.23/1.45 X22 @
% 3.23/1.45 (
% 3.23/1.45 powerset @
% 3.23/1.45 X20 ) ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 in @
% 3.23/1.45 X24 @ X22 ) =>
% 3.23/1.45 (
% 3.23/1.45 in @
% 3.23/1.45 X24 @ X20 ) ) ) ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 setunionI ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 setunionE ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 subPowSU ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 exuE2 ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 nonemptyImpWitness ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 uniqinunit ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 notinsingleton ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 eqinunit ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 singletonsswitch ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 upairsetE ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 upairsetIL ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 upairsetIR ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 emptyE1 ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 vacuousDall ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 quantDeMorgan1 ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 quantDeMorgan2 ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 quantDeMorgan3 ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 quantDeMorgan4 ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 prop2setI ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 prop2set2propI ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 notdexE ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 notdallE ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 exuI1 ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 exuI3 ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 exuI2 ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 inCongP ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 in__Cong ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 exuE3u ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 exu__Cong ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 emptyset__Cong ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 setadjoin__Cong ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 ![
% 3.23/1.45 X26:$i,
% 3.23/1.45 X28:$i]:
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 X26 ) =
% 3.23/1.45 (
% 3.23/1.45 X28 ) ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 powerset @
% 3.23/1.45 X26 ) =
% 3.23/1.45 (
% 3.23/1.45 powerset @
% 3.23/1.45 X28 ) ) ) ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 setunion__Cong ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 omega__Cong ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 exuEu ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 descr__Cong ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 dsetconstr__Cong ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 subsetI1 ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 eqimpsubset2 ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 eqimpsubset1 ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 subsetI2 ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 emptysetsubset ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 subsetE ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 subsetE2 ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 notsubsetI ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 notequalI1 ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 notequalI2 ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 subsetRefl ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 subsetTrans ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 setadjoinSub ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 setadjoinSub2 ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 ![
% 3.23/1.45 X30:$i,
% 3.23/1.45 X32:$i]:
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 subset @
% 3.23/1.45 X30 @ X32 ) =>
% 3.23/1.45 (
% 3.23/1.45 in @
% 3.23/1.45 X30 @
% 3.23/1.45 (
% 3.23/1.45 powerset @
% 3.23/1.45 X32 ) ) ) ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 setextsub ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 subsetemptysetimpeq ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 ![
% 3.23/1.45 X34:$i,
% 3.23/1.45 X36:$i]:
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 subset @
% 3.23/1.45 X36 @ X34 ) =>
% 3.23/1.45 (
% 3.23/1.45 in @
% 3.23/1.45 X36 @
% 3.23/1.45 (
% 3.23/1.45 powerset @
% 3.23/1.45 X34 ) ) ) ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 ![
% 3.23/1.45 X38:$i,
% 3.23/1.45 X40:$i]:
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 in @
% 3.23/1.45 X40 @
% 3.23/1.45 (
% 3.23/1.45 powerset @
% 3.23/1.45 X38 ) ) =>
% 3.23/1.45 (
% 3.23/1.45 subset @
% 3.23/1.45 X40 @ X38 ) ) ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 ![
% 3.23/1.45 X42:$i]:
% 3.23/1.45 (
% 3.23/1.45 in @
% 3.23/1.45 X42 @
% 3.23/1.45 (
% 3.23/1.45 powerset @
% 3.23/1.45 X42 ) ) ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 ![
% 3.23/1.45 X44:$i,
% 3.23/1.45 X46:$i]:
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 subset @
% 3.23/1.45 X44 @ X46 ) =>
% 3.23/1.45 (
% 3.23/1.45 subset @
% 3.23/1.45 (
% 3.23/1.45 powerset @
% 3.23/1.45 X44 ) @
% 3.23/1.45 (
% 3.23/1.45 powerset @
% 3.23/1.45 X46 ) ) ) ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 sepInPowerset ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 sepSubset ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 binunionIL ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 upairset2IR ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 binunionIR ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 binunionEcases ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 binunionE ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 binunionLsub ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 binunionRsub ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 binintersectI ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 binintersectSubset5 ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 binintersectEL ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 binintersectLsub ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 binintersectSubset2 ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 binintersectSubset3 ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 binintersectER ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 disjointsetsI1 ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 binintersectRsub ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 binintersectSubset4 ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 binintersectSubset1 ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 bs114d ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 ![
% 3.23/1.45 X48:$i,
% 3.23/1.45 X50:$i,
% 3.23/1.45 X52:$i]:
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 in @
% 3.23/1.45 X52 @ X48 ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 ~(
% 3.23/1.45 in @
% 3.23/1.45 X52 @ X50 ) ) =>
% 3.23/1.45 (
% 3.23/1.45 in @
% 3.23/1.45 X52 @
% 3.23/1.45 (
% 3.23/1.45 setminus @
% 3.23/1.45 X48 @ X50 ) ) ) ) ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 ![
% 3.23/1.45 X54:$i,
% 3.23/1.45 X56:$i,
% 3.23/1.45 X58:$i]:
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 in @
% 3.23/1.45 X58 @
% 3.23/1.45 (
% 3.23/1.45 setminus @
% 3.23/1.45 X54 @ X56 ) ) =>
% 3.23/1.45 (
% 3.23/1.45 in @
% 3.23/1.45 X58 @ X54 ) ) ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 ![
% 3.23/1.45 X60:$i,
% 3.23/1.45 X62:$i,
% 3.23/1.45 X64:$i]:
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 in @
% 3.23/1.45 X64 @
% 3.23/1.45 (
% 3.23/1.45 setminus @
% 3.23/1.45 X60 @ X62 ) ) =>
% 3.23/1.45 (
% 3.23/1.45 ~(
% 3.23/1.45 in @
% 3.23/1.45 X64 @ X62 ) ) ) ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 ![
% 3.23/1.45 X66:$i,
% 3.23/1.45 X68:$i]:
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 subset @
% 3.23/1.45 X66 @ X68 ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 setminus @
% 3.23/1.45 X66 @ X68 ) =
% 3.23/1.45 (
% 3.23/1.45 emptyset ) ) ) ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 ![
% 3.23/1.45 X70:$i,
% 3.23/1.45 X72:$i,
% 3.23/1.45 X74:$i]:
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 ~(
% 3.23/1.45 in @
% 3.23/1.45 X74 @
% 3.23/1.45 (
% 3.23/1.45 setminus
% 3.23/1.45 @
% 3.23/1.45 X70 @ X72 ) ) ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 in @
% 3.23/1.45 X74 @ X70 ) =>
% 3.23/1.45 (
% 3.23/1.45 in @
% 3.23/1.45 X74 @ X72 ) ) ) ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 ![
% 3.23/1.45 X76:$i,
% 3.23/1.45 X78:$i,
% 3.23/1.45 X80:$i]:
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 ~(
% 3.23/1.45 in @
% 3.23/1.45 X80 @
% 3.23/1.45 (
% 3.23/1.45 setminus
% 3.23/1.45 @
% 3.23/1.45 X76 @ X78 ) ) ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 ~(
% 3.23/1.45 in @
% 3.23/1.45 X80 @ X78 ) ) =>
% 3.23/1.45 (
% 3.23/1.45 ~(
% 3.23/1.45 in @
% 3.23/1.45 X80 @ X76 ) ) ) ) ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 ![
% 3.23/1.45 X82:$i,
% 3.23/1.45 X84:$i,
% 3.23/1.45 X86:$i]:
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 ~(
% 3.23/1.45 in @
% 3.23/1.45 X86 @ X82 ) ) =>
% 3.23/1.45 (
% 3.23/1.45 ~(
% 3.23/1.45 in @
% 3.23/1.45 X86 @
% 3.23/1.45 (
% 3.23/1.45 setminus
% 3.23/1.45 @
% 3.23/1.45 X82 @ X84 ) ) ) ) ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 ![
% 3.23/1.45 X88:$i,
% 3.23/1.45 X90:$i,
% 3.23/1.45 X92:$i]:
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 in @
% 3.23/1.45 X92 @ X90 ) =>
% 3.23/1.45 (
% 3.23/1.45 ~(
% 3.23/1.45 in @
% 3.23/1.45 X92 @
% 3.23/1.45 (
% 3.23/1.45 setminus
% 3.23/1.45 @
% 3.23/1.45 X88 @ X90 ) ) ) ) ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 ![
% 3.23/1.45 X94:$i,
% 3.23/1.45 X96:$i]:
% 3.23/1.45 (
% 3.23/1.45 subset @
% 3.23/1.45 (
% 3.23/1.45 setminus @
% 3.23/1.45 X94 @ X96 ) @
% 3.23/1.45 X94 ) ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 ![
% 3.23/1.45 X98:$i,
% 3.23/1.45 X100:$i]:
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 setminus @
% 3.23/1.45 X98 @ X100 ) =
% 3.23/1.45 (
% 3.23/1.45 emptyset ) ) =>
% 3.23/1.45 (
% 3.23/1.45 subset @
% 3.23/1.45 X98 @ X100 ) ) ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 symdiffE ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 symdiffI1 ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 symdiffI2 ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 symdiffIneg1 ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 symdiffIneg2 ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 secondinupair ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 setukpairIL ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 setukpairIR ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 kpairiskpair ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 kpairp ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 singletonsubset ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 ![
% 3.23/1.45 X102:$i,
% 3.23/1.45 X104:$i]:
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 in @
% 3.23/1.45 X104 @
% 3.23/1.45 X102 ) =>
% 3.23/1.45 (
% 3.23/1.45 in @
% 3.23/1.45 (
% 3.23/1.45 setadjoin
% 3.23/1.45 @
% 3.23/1.45 X104 @
% 3.23/1.45 emptyset ) @
% 3.23/1.45 (
% 3.23/1.45 powerset @
% 3.23/1.45 X102 ) ) ) ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 singletoninpowunion ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 upairset2E ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 upairsubunion ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 upairinpowunion ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 ubforcartprodlem1 ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 ubforcartprodlem2 ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 ubforcartprodlem3 ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 cartprodpairin ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 cartprodmempair1 ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 cartprodmempair ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 setunionE2 ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 setunionsingleton1 ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 setunionsingleton2 ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 setunionsingleton ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 singletonprop ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 ex1E1 ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 ex1I ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 ex1I2 ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 singletonsuniq ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 setukpairinjL1 ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 kfstsingleton ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 theprop ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 kfstpairEq ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 cartprodfstin ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 setukpairinjL2 ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 setukpairinjL ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 setukpairinjR11 ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 setukpairinjR12 ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 setukpairinjR1 ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 upairequniteq ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 setukpairinjR2 ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 setukpairinjR ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 ksndsingleton ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 ksndpairEq ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 kpairsurjEq ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 cartprodsndin ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 cartprodpairmemEL ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 cartprodpairmemER ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 cartprodmempaircEq ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 cartprodfstpairEq ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 cartprodsndpairEq ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 cartprodpairsurjEq ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 dpsetconstrI ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 dpsetconstrSub ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 setOfPairsIsBReln ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 dpsetconstrERa ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 dpsetconstrEL1 ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 dpsetconstrEL2 ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 dpsetconstrER ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 funcImageSingleton ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 apProp ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 app ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 infuncsetfunc ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 ap2p ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 funcinfuncset ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 lamProp ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 lamp ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 lam2p ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 brelnall1 ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 brelnall2 ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 ex1E2 ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 funcGraphProp1 ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 funcGraphProp3 ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 funcGraphProp2 ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 funcextLem ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 funcGraphProp4 ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 subbreln ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 eqbreln ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 funcext ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 funcext2 ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 ap2apEq1 ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 ap2apEq2 ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 beta1 ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 eta1 ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 lam2lamEq ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 beta2 ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 eta2 ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 iffalseProp1 ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 iffalseProp2 ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 iftrueProp1 ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 iftrueProp2 ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 ifSingleton ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 ifp ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 theeq ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 iftrue ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 iffalse ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 iftrueorfalse ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 binintersectT_lem ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 binunionT_lem ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 ![
% 3.23/1.45 X106:$i,
% 3.23/1.45 X108:$i]:
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 in @
% 3.23/1.45 X108 @
% 3.23/1.45 (
% 3.23/1.45 powerset @
% 3.23/1.45 X106 ) ) =>
% 3.23/1.45 (
% 3.23/1.45 in @
% 3.23/1.45 (
% 3.23/1.45 powerset @
% 3.23/1.45 X108 ) @
% 3.23/1.45 (
% 3.23/1.45 powerset @
% 3.23/1.45 (
% 3.23/1.45 powerset @
% 3.23/1.45 X106 ) ) ) ) ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 ![
% 3.23/1.45 X110:$i,
% 3.23/1.45 X112:$i]:
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 in @
% 3.23/1.45 X112 @
% 3.23/1.45 (
% 3.23/1.45 powerset @
% 3.23/1.45 X110 ) ) =>
% 3.23/1.45 (
% 3.23/1.45 ![
% 3.23/1.45 X114:$i]:
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 in @
% 3.23/1.45 X114 @
% 3.23/1.45 (
% 3.23/1.45 powerset @
% 3.23/1.45 X110 ) ) =>
% 3.23/1.45 (
% 3.23/1.45 in @
% 3.23/1.45 (
% 3.23/1.45 setminus @
% 3.23/1.45 X112 @
% 3.23/1.45 X114 ) @
% 3.23/1.45 (
% 3.23/1.45 powerset @
% 3.23/1.45 X110 ) ) ) ) ) ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 ![
% 3.23/1.45 X116:$i,
% 3.23/1.45 X118:$i]:
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 in @
% 3.23/1.45 X118 @
% 3.23/1.45 (
% 3.23/1.45 powerset @
% 3.23/1.45 X116 ) ) =>
% 3.23/1.45 (
% 3.23/1.45 in @
% 3.23/1.45 (
% 3.23/1.45 setminus @
% 3.23/1.45 X116 @
% 3.23/1.45 X118 ) @
% 3.23/1.45 (
% 3.23/1.45 powerset @
% 3.23/1.45 X116 ) ) ) ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 ![
% 3.23/1.45 X120:$i,
% 3.23/1.45 X122:$i]:
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 in @
% 3.23/1.45 X122 @
% 3.23/1.45 (
% 3.23/1.45 powerset @
% 3.23/1.45 X120 ) ) =>
% 3.23/1.45 (
% 3.23/1.45 ![
% 3.23/1.45 X124:$i]:
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 in @
% 3.23/1.45 X124 @
% 3.23/1.45 (
% 3.23/1.45 powerset @
% 3.23/1.45 X120 ) ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 ![
% 3.23/1.45 X126:$i]:
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 in @
% 3.23/1.45 X126 @
% 3.23/1.45 X120 ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 in @
% 3.23/1.45 X126 @
% 3.23/1.45 X122 ) =>
% 3.23/1.45 (
% 3.23/1.45 in @
% 3.23/1.45 X126 @
% 3.23/1.45 X124 ) ) ) ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 ![
% 3.23/1.45 X128:$i]:
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 in @
% 3.23/1.45 X128 @
% 3.23/1.45 X120 ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 in @
% 3.23/1.45 X128 @
% 3.23/1.45 X124 ) =>
% 3.23/1.45 (
% 3.23/1.45 in @
% 3.23/1.45 X128 @
% 3.23/1.45 X122 ) ) ) ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 X122 ) =
% 3.23/1.45 (
% 3.23/1.45 X124 ) ) ) ) ) ) ) ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 ![
% 3.23/1.45 X130:$i,
% 3.23/1.45 X132:$i]:
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 in @
% 3.23/1.45 X132 @
% 3.23/1.45 (
% 3.23/1.45 powerset @
% 3.23/1.45 X130 ) ) =>
% 3.23/1.45 (
% 3.23/1.45 ![
% 3.23/1.45 X134:$i]:
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 in @
% 3.23/1.45 X134 @
% 3.23/1.45 (
% 3.23/1.45 powerset @
% 3.23/1.45 X130 ) ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 ![
% 3.23/1.45 X136:$i]:
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 in @
% 3.23/1.45 X136 @
% 3.23/1.45 X130 ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 in @
% 3.23/1.45 X136 @
% 3.23/1.45 X132 ) =>
% 3.23/1.45 (
% 3.23/1.45 in @
% 3.23/1.45 X136 @
% 3.23/1.45 X134 ) ) ) ) =>
% 3.23/1.45 (
% 3.23/1.45 subset @
% 3.23/1.45 X132 @
% 3.23/1.45 X134 ) ) ) ) ) ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 ![
% 3.23/1.45 X138:$i,
% 3.23/1.45 X140:$i]:
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 in @
% 3.23/1.45 X140 @
% 3.23/1.45 (
% 3.23/1.45 powerset @
% 3.23/1.45 X138 ) ) =>
% 3.23/1.45 (
% 3.23/1.45 ![
% 3.23/1.45 X142:$i]:
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 in @
% 3.23/1.45 X142 @
% 3.23/1.45 (
% 3.23/1.45 powerset @
% 3.23/1.45 X138 ) ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 ![
% 3.23/1.45 X144:$i]:
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 in @
% 3.23/1.45 X144 @
% 3.23/1.45 X138 ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 in @
% 3.23/1.45 X144 @
% 3.23/1.45 X140 ) =>
% 3.23/1.45 (
% 3.23/1.45 in @
% 3.23/1.45 X144 @
% 3.23/1.45 X142 ) ) ) ) =>
% 3.23/1.45 (
% 3.23/1.45 in @
% 3.23/1.45 X140 @
% 3.23/1.45 (
% 3.23/1.45 powerset @
% 3.23/1.45 X142 ) ) ) ) ) ) ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 ![
% 3.23/1.45 X146:$i,
% 3.23/1.45 X148:$i]:
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 in @
% 3.23/1.45 X148 @
% 3.23/1.45 (
% 3.23/1.45 powerset @
% 3.23/1.45 X146 ) ) =>
% 3.23/1.45 (
% 3.23/1.45 ![
% 3.23/1.45 X150:$i]:
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 in @
% 3.23/1.45 X150 @
% 3.23/1.45 (
% 3.23/1.45 powerset @
% 3.23/1.45 X146 ) ) =>
% 3.23/1.45 (
% 3.23/1.45 ![
% 3.23/1.45 X152:$i]:
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 in @
% 3.23/1.45 X152 @
% 3.23/1.45 X146 ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 in @
% 3.23/1.45 X148 @
% 3.23/1.45 (
% 3.23/1.45 powerset @
% 3.23/1.45 X150 ) ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 in @
% 3.23/1.45 X152 @
% 3.23/1.45 X148 ) =>
% 3.23/1.45 (
% 3.23/1.45 in @
% 3.23/1.45 X152 @
% 3.23/1.45 X150 ) ) ) ) ) ) ) ) ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 ![
% 3.23/1.45 X154:$i,
% 3.23/1.45 X156:$i]:
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 in @
% 3.23/1.45 X156 @
% 3.23/1.45 (
% 3.23/1.45 powerset @
% 3.23/1.45 X154 ) ) =>
% 3.23/1.45 (
% 3.23/1.45 ![
% 3.23/1.45 X158:$i]:
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 in @
% 3.23/1.45 X158 @
% 3.23/1.45 X154 ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 in @
% 3.23/1.45 X158 @
% 3.23/1.45 X156 ) =>
% 3.23/1.45 (
% 3.23/1.45 ~(
% 3.23/1.45 in @
% 3.23/1.45 X158 @
% 3.23/1.45 (
% 3.23/1.45 setminus
% 3.23/1.45 @
% 3.23/1.45 X154 @
% 3.23/1.45 X156 ) ) ) ) ) ) ) ) =>
% 3.23/1.45 (
% 3.23/1.45 ![
% 3.23/1.45 X160:$i,
% 3.23/1.45 X162:$i]:
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 in @
% 3.23/1.45 X162 @
% 3.23/1.45 (
% 3.23/1.45 powerset @
% 3.23/1.45 X160 ) ) =>
% 3.23/1.45 (
% 3.23/1.45 ![
% 3.23/1.45 X164:$i]:
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 in @
% 3.23/1.45 X164 @
% 3.23/1.45 X160 ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 ~(
% 3.23/1.45 in @
% 3.23/1.45 X164 @
% 3.23/1.45 (
% 3.23/1.45 setminus
% 3.23/1.45 @
% 3.23/1.45 X160 @
% 3.23/1.45 X162 ) ) ) =>
% 3.23/1.45 (
% 3.23/1.45 in @
% 3.23/1.45 X164 @
% 3.23/1.45 X162 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 3.23/1.45 thf(zf_stmt_1, type, zip_tseitin_0 : $i > $i > $i > $o).
% 3.23/1.45 thf(zf_stmt_2, axiom,
% 3.23/1.45 (![X8:$i,X6:$i,X4:$i]:
% 3.23/1.45 ( ( zip_tseitin_0 @ X8 @ X6 @ X4 ) <=>
% 3.23/1.45 ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ))).
% 3.23/1.45 thf(zf_stmt_3, conjecture,
% 3.23/1.45 (( setextAx ) =>
% 3.23/1.45 ( ( emptysetAx ) =>
% 3.23/1.45 ( ( setadjoinAx ) =>
% 3.23/1.45 ( ( ![X4:$i,X6:$i]:
% 3.23/1.45 ( ( in @ X6 @ ( powerset @ X4 ) ) <=>
% 3.23/1.45 ( ![X8:$i]: ( zip_tseitin_0 @ X8 @ X6 @ X4 ) ) ) ) =>
% 3.23/1.45 ( ( setunionAx ) =>
% 3.23/1.45 ( ( omega0Ax ) =>
% 3.23/1.45 ( ( omegaSAx ) =>
% 3.23/1.45 ( ( omegaIndAx ) =>
% 3.23/1.45 ( ( replAx ) =>
% 3.23/1.45 ( ( foundationAx ) =>
% 3.23/1.45 ( ( wellorderingAx ) =>
% 3.23/1.45 ( ( descrp ) =>
% 3.23/1.45 ( ( dsetconstrI ) =>
% 3.23/1.45 ( ( dsetconstrEL ) =>
% 3.23/1.45 ( ( dsetconstrER ) =>
% 3.23/1.45 ( ( exuE1 ) =>
% 3.23/1.45 ( ( prop2setE ) =>
% 3.23/1.45 ( ( emptysetE ) =>
% 3.23/1.45 ( ( emptysetimpfalse ) =>
% 3.23/1.45 ( ( notinemptyset ) =>
% 3.23/1.45 ( ( exuE3e ) =>
% 3.23/1.45 ( ( setext ) =>
% 3.23/1.45 ( ( emptyI ) =>
% 3.23/1.45 ( ( noeltsimpempty ) =>
% 3.23/1.45 ( ( setbeta ) =>
% 3.23/1.45 ( ( nonemptyE1 ) =>
% 3.23/1.45 ( ( nonemptyI ) =>
% 3.23/1.45 ( ( nonemptyI1 ) =>
% 3.23/1.45 ( ( setadjoinIL ) =>
% 3.23/1.45 ( ( emptyinunitempty ) =>
% 3.23/1.45 ( ( setadjoinIR ) =>
% 3.23/1.45 ( ( setadjoinE ) =>
% 3.23/1.45 ( (
% 3.23/1.45 setadjoinOr ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 setoftrueEq ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 ![
% 3.23/1.45 X10:$i,
% 3.23/1.45 X12:$i]:
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 ![
% 3.23/1.45 X14:$i]:
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 in @
% 3.23/1.45 X14 @ X12 ) =>
% 3.23/1.45 (
% 3.23/1.45 in @
% 3.23/1.45 X14 @ X10 ) ) ) =>
% 3.23/1.45 (
% 3.23/1.45 in @
% 3.23/1.45 X12 @
% 3.23/1.45 (
% 3.23/1.45 powerset @
% 3.23/1.45 X10 ) ) ) ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 ![
% 3.23/1.45 X16:$i]:
% 3.23/1.45 (
% 3.23/1.45 in @
% 3.23/1.45 emptyset @
% 3.23/1.45 (
% 3.23/1.45 powerset @
% 3.23/1.45 X16 ) ) ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 ![
% 3.23/1.45 X18:$i]:
% 3.23/1.45 (
% 3.23/1.45 in @
% 3.23/1.45 emptyset @
% 3.23/1.45 (
% 3.23/1.45 powerset @
% 3.23/1.45 X18 ) ) ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 ![
% 3.23/1.45 X20:$i,
% 3.23/1.45 X22:$i,
% 3.23/1.45 X24:$i]:
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 in @
% 3.23/1.45 X22 @
% 3.23/1.45 (
% 3.23/1.45 powerset @
% 3.23/1.45 X20 ) ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 in @
% 3.23/1.45 X24 @ X22 ) =>
% 3.23/1.45 (
% 3.23/1.45 in @
% 3.23/1.45 X24 @ X20 ) ) ) ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 setunionI ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 setunionE ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 subPowSU ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 exuE2 ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 nonemptyImpWitness ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 uniqinunit ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 notinsingleton ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 eqinunit ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 singletonsswitch ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 upairsetE ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 upairsetIL ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 upairsetIR ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 emptyE1 ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 vacuousDall ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 quantDeMorgan1 ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 quantDeMorgan2 ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 quantDeMorgan3 ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 quantDeMorgan4 ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 prop2setI ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 prop2set2propI ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 notdexE ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 notdallE ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 exuI1 ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 exuI3 ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 exuI2 ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 inCongP ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 in__Cong ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 exuE3u ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 exu__Cong ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 emptyset__Cong ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 setadjoin__Cong ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 ![
% 3.23/1.45 X26:$i,
% 3.23/1.45 X28:$i]:
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 X26 ) =
% 3.23/1.45 (
% 3.23/1.45 X28 ) ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 powerset @
% 3.23/1.45 X26 ) =
% 3.23/1.45 (
% 3.23/1.45 powerset @
% 3.23/1.45 X28 ) ) ) ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 setunion__Cong ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 omega__Cong ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 exuEu ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 descr__Cong ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 dsetconstr__Cong ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 subsetI1 ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 eqimpsubset2 ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 eqimpsubset1 ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 subsetI2 ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 emptysetsubset ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 subsetE ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 subsetE2 ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 notsubsetI ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 notequalI1 ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 notequalI2 ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 subsetRefl ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 subsetTrans ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 setadjoinSub ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 setadjoinSub2 ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 ![
% 3.23/1.45 X30:$i,
% 3.23/1.45 X32:$i]:
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 subset @
% 3.23/1.45 X30 @ X32 ) =>
% 3.23/1.45 (
% 3.23/1.45 in @
% 3.23/1.45 X30 @
% 3.23/1.45 (
% 3.23/1.45 powerset @
% 3.23/1.45 X32 ) ) ) ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 setextsub ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 subsetemptysetimpeq ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 ![
% 3.23/1.45 X34:$i,
% 3.23/1.45 X36:$i]:
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 subset @
% 3.23/1.45 X36 @ X34 ) =>
% 3.23/1.45 (
% 3.23/1.45 in @
% 3.23/1.45 X36 @
% 3.23/1.45 (
% 3.23/1.45 powerset @
% 3.23/1.45 X34 ) ) ) ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 ![
% 3.23/1.45 X38:$i,
% 3.23/1.45 X40:$i]:
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 in @
% 3.23/1.45 X40 @
% 3.23/1.45 (
% 3.23/1.45 powerset @
% 3.23/1.45 X38 ) ) =>
% 3.23/1.45 (
% 3.23/1.45 subset @
% 3.23/1.45 X40 @ X38 ) ) ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 ![
% 3.23/1.45 X42:$i]:
% 3.23/1.45 (
% 3.23/1.45 in @
% 3.23/1.45 X42 @
% 3.23/1.45 (
% 3.23/1.45 powerset @
% 3.23/1.45 X42 ) ) ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 ![
% 3.23/1.45 X44:$i,
% 3.23/1.45 X46:$i]:
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 subset @
% 3.23/1.45 X44 @ X46 ) =>
% 3.23/1.45 (
% 3.23/1.45 subset @
% 3.23/1.45 (
% 3.23/1.45 powerset @
% 3.23/1.45 X44 ) @
% 3.23/1.45 (
% 3.23/1.45 powerset @
% 3.23/1.45 X46 ) ) ) ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 sepInPowerset ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 sepSubset ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 binunionIL ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 upairset2IR ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 binunionIR ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 binunionEcases ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 binunionE ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 binunionLsub ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 binunionRsub ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 binintersectI ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 binintersectSubset5 ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 binintersectEL ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 binintersectLsub ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 binintersectSubset2 ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 binintersectSubset3 ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 binintersectER ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 disjointsetsI1 ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 binintersectRsub ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 binintersectSubset4 ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 binintersectSubset1 ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 bs114d ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 ![
% 3.23/1.45 X48:$i,
% 3.23/1.45 X50:$i,
% 3.23/1.45 X52:$i]:
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 in @
% 3.23/1.45 X52 @ X48 ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 ~(
% 3.23/1.45 in @
% 3.23/1.45 X52 @ X50 ) ) =>
% 3.23/1.45 (
% 3.23/1.45 in @
% 3.23/1.45 X52 @
% 3.23/1.45 (
% 3.23/1.45 setminus @
% 3.23/1.45 X48 @ X50 ) ) ) ) ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 ![
% 3.23/1.45 X54:$i,
% 3.23/1.45 X56:$i,
% 3.23/1.45 X58:$i]:
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 in @
% 3.23/1.45 X58 @
% 3.23/1.45 (
% 3.23/1.45 setminus @
% 3.23/1.45 X54 @ X56 ) ) =>
% 3.23/1.45 (
% 3.23/1.45 in @
% 3.23/1.45 X58 @ X54 ) ) ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 ![
% 3.23/1.45 X60:$i,
% 3.23/1.45 X62:$i,
% 3.23/1.45 X64:$i]:
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 in @
% 3.23/1.45 X64 @
% 3.23/1.45 (
% 3.23/1.45 setminus @
% 3.23/1.45 X60 @ X62 ) ) =>
% 3.23/1.45 (
% 3.23/1.45 ~(
% 3.23/1.45 in @
% 3.23/1.45 X64 @ X62 ) ) ) ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 ![
% 3.23/1.45 X66:$i,
% 3.23/1.45 X68:$i]:
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 subset @
% 3.23/1.45 X66 @ X68 ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 setminus @
% 3.23/1.45 X66 @ X68 ) =
% 3.23/1.45 (
% 3.23/1.45 emptyset ) ) ) ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 ![
% 3.23/1.45 X70:$i,
% 3.23/1.45 X72:$i,
% 3.23/1.45 X74:$i]:
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 ~(
% 3.23/1.45 in @
% 3.23/1.45 X74 @
% 3.23/1.45 (
% 3.23/1.45 setminus
% 3.23/1.45 @
% 3.23/1.45 X70 @ X72 ) ) ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 in @
% 3.23/1.45 X74 @ X70 ) =>
% 3.23/1.45 (
% 3.23/1.45 in @
% 3.23/1.45 X74 @ X72 ) ) ) ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 ![
% 3.23/1.45 X76:$i,
% 3.23/1.45 X78:$i,
% 3.23/1.45 X80:$i]:
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 ~(
% 3.23/1.45 in @
% 3.23/1.45 X80 @
% 3.23/1.45 (
% 3.23/1.45 setminus
% 3.23/1.45 @
% 3.23/1.45 X76 @ X78 ) ) ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 ~(
% 3.23/1.45 in @
% 3.23/1.45 X80 @ X78 ) ) =>
% 3.23/1.45 (
% 3.23/1.45 ~(
% 3.23/1.45 in @
% 3.23/1.45 X80 @ X76 ) ) ) ) ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 ![
% 3.23/1.45 X82:$i,
% 3.23/1.45 X84:$i,
% 3.23/1.45 X86:$i]:
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 ~(
% 3.23/1.45 in @
% 3.23/1.45 X86 @ X82 ) ) =>
% 3.23/1.45 (
% 3.23/1.45 ~(
% 3.23/1.45 in @
% 3.23/1.45 X86 @
% 3.23/1.45 (
% 3.23/1.45 setminus
% 3.23/1.45 @
% 3.23/1.45 X82 @ X84 ) ) ) ) ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 ![
% 3.23/1.45 X88:$i,
% 3.23/1.45 X90:$i,
% 3.23/1.45 X92:$i]:
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 in @
% 3.23/1.45 X92 @ X90 ) =>
% 3.23/1.45 (
% 3.23/1.45 ~(
% 3.23/1.45 in @
% 3.23/1.45 X92 @
% 3.23/1.45 (
% 3.23/1.45 setminus
% 3.23/1.45 @
% 3.23/1.45 X88 @ X90 ) ) ) ) ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 ![
% 3.23/1.45 X94:$i,
% 3.23/1.45 X96:$i]:
% 3.23/1.45 (
% 3.23/1.45 subset @
% 3.23/1.45 (
% 3.23/1.45 setminus @
% 3.23/1.45 X94 @ X96 ) @
% 3.23/1.45 X94 ) ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 ![
% 3.23/1.45 X98:$i,
% 3.23/1.45 X100:$i]:
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 setminus @
% 3.23/1.45 X98 @ X100 ) =
% 3.23/1.45 (
% 3.23/1.45 emptyset ) ) =>
% 3.23/1.45 (
% 3.23/1.45 subset @
% 3.23/1.45 X98 @ X100 ) ) ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 symdiffE ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 symdiffI1 ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 symdiffI2 ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 symdiffIneg1 ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 symdiffIneg2 ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 secondinupair ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 setukpairIL ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 setukpairIR ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 kpairiskpair ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 kpairp ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 singletonsubset ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 ![
% 3.23/1.45 X102:$i,
% 3.23/1.45 X104:$i]:
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 in @
% 3.23/1.45 X104 @
% 3.23/1.45 X102 ) =>
% 3.23/1.45 (
% 3.23/1.45 in @
% 3.23/1.45 (
% 3.23/1.45 setadjoin
% 3.23/1.45 @
% 3.23/1.45 X104 @
% 3.23/1.45 emptyset ) @
% 3.23/1.45 (
% 3.23/1.45 powerset @
% 3.23/1.45 X102 ) ) ) ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 singletoninpowunion ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 upairset2E ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 upairsubunion ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 upairinpowunion ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 ubforcartprodlem1 ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 ubforcartprodlem2 ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 ubforcartprodlem3 ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 cartprodpairin ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 cartprodmempair1 ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 cartprodmempair ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 setunionE2 ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 setunionsingleton1 ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 setunionsingleton2 ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 setunionsingleton ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 singletonprop ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 ex1E1 ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 ex1I ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 ex1I2 ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 singletonsuniq ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 setukpairinjL1 ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 kfstsingleton ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 theprop ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 kfstpairEq ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 cartprodfstin ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 setukpairinjL2 ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 setukpairinjL ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 setukpairinjR11 ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 setukpairinjR12 ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 setukpairinjR1 ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 upairequniteq ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 setukpairinjR2 ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 setukpairinjR ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 ksndsingleton ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 ksndpairEq ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 kpairsurjEq ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 cartprodsndin ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 cartprodpairmemEL ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 cartprodpairmemER ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 cartprodmempaircEq ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 cartprodfstpairEq ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 cartprodsndpairEq ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 cartprodpairsurjEq ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 dpsetconstrI ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 dpsetconstrSub ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 setOfPairsIsBReln ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 dpsetconstrERa ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 dpsetconstrEL1 ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 dpsetconstrEL2 ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 dpsetconstrER ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 funcImageSingleton ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 apProp ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 app ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 infuncsetfunc ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 ap2p ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 funcinfuncset ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 lamProp ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 lamp ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 lam2p ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 brelnall1 ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 brelnall2 ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 ex1E2 ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 funcGraphProp1 ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 funcGraphProp3 ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 funcGraphProp2 ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 funcextLem ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 funcGraphProp4 ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 subbreln ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 eqbreln ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 funcext ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 funcext2 ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 ap2apEq1 ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 ap2apEq2 ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 beta1 ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 eta1 ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 lam2lamEq ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 beta2 ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 eta2 ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 iffalseProp1 ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 iffalseProp2 ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 iftrueProp1 ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 iftrueProp2 ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 ifSingleton ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 ifp ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 theeq ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 iftrue ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 iffalse ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 iftrueorfalse ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 binintersectT_lem ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 binunionT_lem ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 ![
% 3.23/1.45 X106:$i,
% 3.23/1.45 X108:$i]:
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 in @
% 3.23/1.45 X108 @
% 3.23/1.45 (
% 3.23/1.45 powerset @
% 3.23/1.45 X106 ) ) =>
% 3.23/1.45 (
% 3.23/1.45 in @
% 3.23/1.45 (
% 3.23/1.45 powerset @
% 3.23/1.45 X108 ) @
% 3.23/1.45 (
% 3.23/1.45 powerset @
% 3.23/1.45 (
% 3.23/1.45 powerset @
% 3.23/1.45 X106 ) ) ) ) ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 ![
% 3.23/1.45 X110:$i,
% 3.23/1.45 X112:$i]:
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 in @
% 3.23/1.45 X112 @
% 3.23/1.45 (
% 3.23/1.45 powerset @
% 3.23/1.45 X110 ) ) =>
% 3.23/1.45 (
% 3.23/1.45 ![
% 3.23/1.45 X114:$i]:
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 in @
% 3.23/1.45 X114 @
% 3.23/1.45 (
% 3.23/1.45 powerset @
% 3.23/1.45 X110 ) ) =>
% 3.23/1.45 (
% 3.23/1.45 in @
% 3.23/1.45 (
% 3.23/1.45 setminus @
% 3.23/1.45 X112 @
% 3.23/1.45 X114 ) @
% 3.23/1.45 (
% 3.23/1.45 powerset @
% 3.23/1.45 X110 ) ) ) ) ) ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 ![
% 3.23/1.45 X116:$i,
% 3.23/1.45 X118:$i]:
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 in @
% 3.23/1.45 X118 @
% 3.23/1.45 (
% 3.23/1.45 powerset @
% 3.23/1.45 X116 ) ) =>
% 3.23/1.45 (
% 3.23/1.45 in @
% 3.23/1.45 (
% 3.23/1.45 setminus @
% 3.23/1.45 X116 @
% 3.23/1.45 X118 ) @
% 3.23/1.45 (
% 3.23/1.45 powerset @
% 3.23/1.45 X116 ) ) ) ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 ![
% 3.23/1.45 X120:$i,
% 3.23/1.45 X122:$i]:
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 in @
% 3.23/1.45 X122 @
% 3.23/1.45 (
% 3.23/1.45 powerset @
% 3.23/1.45 X120 ) ) =>
% 3.23/1.45 (
% 3.23/1.45 ![
% 3.23/1.45 X124:$i]:
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 in @
% 3.23/1.45 X124 @
% 3.23/1.45 (
% 3.23/1.45 powerset @
% 3.23/1.45 X120 ) ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 ![
% 3.23/1.45 X126:$i]:
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 in @
% 3.23/1.45 X126 @
% 3.23/1.45 X120 ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 in @
% 3.23/1.45 X126 @
% 3.23/1.45 X122 ) =>
% 3.23/1.45 (
% 3.23/1.45 in @
% 3.23/1.45 X126 @
% 3.23/1.45 X124 ) ) ) ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 ![
% 3.23/1.45 X128:$i]:
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 in @
% 3.23/1.45 X128 @
% 3.23/1.45 X120 ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 in @
% 3.23/1.45 X128 @
% 3.23/1.45 X124 ) =>
% 3.23/1.45 (
% 3.23/1.45 in @
% 3.23/1.45 X128 @
% 3.23/1.45 X122 ) ) ) ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 X122 ) =
% 3.23/1.45 (
% 3.23/1.45 X124 ) ) ) ) ) ) ) ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 ![
% 3.23/1.45 X130:$i,
% 3.23/1.45 X132:$i]:
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 in @
% 3.23/1.45 X132 @
% 3.23/1.45 (
% 3.23/1.45 powerset @
% 3.23/1.45 X130 ) ) =>
% 3.23/1.45 (
% 3.23/1.45 ![
% 3.23/1.45 X134:$i]:
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 in @
% 3.23/1.45 X134 @
% 3.23/1.45 (
% 3.23/1.45 powerset @
% 3.23/1.45 X130 ) ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 ![
% 3.23/1.45 X136:$i]:
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 in @
% 3.23/1.45 X136 @
% 3.23/1.45 X130 ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 in @
% 3.23/1.45 X136 @
% 3.23/1.45 X132 ) =>
% 3.23/1.45 (
% 3.23/1.45 in @
% 3.23/1.45 X136 @
% 3.23/1.45 X134 ) ) ) ) =>
% 3.23/1.45 (
% 3.23/1.45 subset @
% 3.23/1.45 X132 @
% 3.23/1.45 X134 ) ) ) ) ) ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 ![
% 3.23/1.45 X138:$i,
% 3.23/1.45 X140:$i]:
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 in @
% 3.23/1.45 X140 @
% 3.23/1.45 (
% 3.23/1.45 powerset @
% 3.23/1.45 X138 ) ) =>
% 3.23/1.45 (
% 3.23/1.45 ![
% 3.23/1.45 X142:$i]:
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 in @
% 3.23/1.45 X142 @
% 3.23/1.45 (
% 3.23/1.45 powerset @
% 3.23/1.45 X138 ) ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 ![
% 3.23/1.45 X144:$i]:
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 in @
% 3.23/1.45 X144 @
% 3.23/1.45 X138 ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 in @
% 3.23/1.45 X144 @
% 3.23/1.45 X140 ) =>
% 3.23/1.45 (
% 3.23/1.45 in @
% 3.23/1.45 X144 @
% 3.23/1.45 X142 ) ) ) ) =>
% 3.23/1.45 (
% 3.23/1.45 in @
% 3.23/1.45 X140 @
% 3.23/1.45 (
% 3.23/1.45 powerset @
% 3.23/1.45 X142 ) ) ) ) ) ) ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 ![
% 3.23/1.45 X146:$i,
% 3.23/1.45 X148:$i]:
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 in @
% 3.23/1.45 X148 @
% 3.23/1.45 (
% 3.23/1.45 powerset @
% 3.23/1.45 X146 ) ) =>
% 3.23/1.45 (
% 3.23/1.45 ![
% 3.23/1.45 X150:$i]:
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 in @
% 3.23/1.45 X150 @
% 3.23/1.45 (
% 3.23/1.45 powerset @
% 3.23/1.45 X146 ) ) =>
% 3.23/1.45 (
% 3.23/1.45 ![
% 3.23/1.45 X152:$i]:
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 in @
% 3.23/1.45 X152 @
% 3.23/1.45 X146 ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 in @
% 3.23/1.45 X148 @
% 3.23/1.45 (
% 3.23/1.45 powerset @
% 3.23/1.45 X150 ) ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 in @
% 3.23/1.45 X152 @
% 3.23/1.45 X148 ) =>
% 3.23/1.45 (
% 3.23/1.45 in @
% 3.23/1.45 X152 @
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% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 ![
% 3.23/1.45 X154:$i,
% 3.23/1.45 X156:$i]:
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 in @
% 3.23/1.45 X156 @
% 3.23/1.45 (
% 3.23/1.45 powerset @
% 3.23/1.45 X154 ) ) =>
% 3.23/1.45 (
% 3.23/1.45 ![
% 3.23/1.45 X158:$i]:
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 in @
% 3.23/1.45 X158 @
% 3.23/1.45 X154 ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 in @
% 3.23/1.45 X158 @
% 3.23/1.45 X156 ) =>
% 3.23/1.45 (
% 3.23/1.45 ~(
% 3.23/1.45 in @
% 3.23/1.45 X158 @
% 3.23/1.45 (
% 3.23/1.45 setminus
% 3.23/1.45 @
% 3.23/1.45 X154 @
% 3.23/1.45 X156 ) ) ) ) ) ) ) ) =>
% 3.23/1.45 (
% 3.23/1.45 ![
% 3.23/1.45 X160:$i,
% 3.23/1.45 X162:$i]:
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 in @
% 3.23/1.45 X162 @
% 3.23/1.45 (
% 3.23/1.45 powerset @
% 3.23/1.45 X160 ) ) =>
% 3.23/1.45 (
% 3.23/1.45 ![
% 3.23/1.45 X164:$i]:
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 in @
% 3.23/1.45 X164 @
% 3.23/1.45 X160 ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 ~(
% 3.23/1.45 in @
% 3.23/1.45 X164 @
% 3.23/1.45 (
% 3.23/1.45 setminus
% 3.23/1.45 @
% 3.23/1.45 X160 @
% 3.23/1.45 X162 ) ) ) =>
% 3.23/1.45 (
% 3.23/1.45 in @
% 3.23/1.45 X164 @
% 3.23/1.45 X162 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 3.23/1.45 thf(zf_stmt_4, negated_conjecture,
% 3.23/1.45 (~( ( setextAx ) =>
% 3.23/1.45 ( ( emptysetAx ) =>
% 3.23/1.45 ( ( setadjoinAx ) =>
% 3.23/1.45 ( ( ![X4:$i,X6:$i]:
% 3.23/1.45 ( ( in @ X6 @ ( powerset @ X4 ) ) <=>
% 3.23/1.45 ( ![X8:$i]: ( zip_tseitin_0 @ X8 @ X6 @ X4 ) ) ) ) =>
% 3.23/1.45 ( ( setunionAx ) =>
% 3.23/1.45 ( ( omega0Ax ) =>
% 3.23/1.45 ( ( omegaSAx ) =>
% 3.23/1.45 ( ( omegaIndAx ) =>
% 3.23/1.45 ( ( replAx ) =>
% 3.23/1.45 ( ( foundationAx ) =>
% 3.23/1.45 ( ( wellorderingAx ) =>
% 3.23/1.45 ( ( descrp ) =>
% 3.23/1.45 ( ( dsetconstrI ) =>
% 3.23/1.45 ( ( dsetconstrEL ) =>
% 3.23/1.45 ( ( dsetconstrER ) =>
% 3.23/1.45 ( ( exuE1 ) =>
% 3.23/1.45 ( ( prop2setE ) =>
% 3.23/1.45 ( ( emptysetE ) =>
% 3.23/1.45 ( ( emptysetimpfalse ) =>
% 3.23/1.45 ( ( notinemptyset ) =>
% 3.23/1.45 ( ( exuE3e ) =>
% 3.23/1.45 ( ( setext ) =>
% 3.23/1.45 ( ( emptyI ) =>
% 3.23/1.45 ( ( noeltsimpempty ) =>
% 3.23/1.45 ( ( setbeta ) =>
% 3.23/1.45 ( ( nonemptyE1 ) =>
% 3.23/1.45 ( ( nonemptyI ) =>
% 3.23/1.45 ( ( nonemptyI1 ) =>
% 3.23/1.45 ( ( setadjoinIL ) =>
% 3.23/1.45 ( ( emptyinunitempty ) =>
% 3.23/1.45 ( ( setadjoinIR ) =>
% 3.23/1.45 ( (
% 3.23/1.45 setadjoinE ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 setadjoinOr ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 setoftrueEq ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 ![
% 3.23/1.45 X10:$i,
% 3.23/1.45 X12:$i]:
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 ![
% 3.23/1.45 X14:$i]:
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 in @
% 3.23/1.45 X14 @ X12 ) =>
% 3.23/1.45 (
% 3.23/1.45 in @
% 3.23/1.45 X14 @ X10 ) ) ) =>
% 3.23/1.45 (
% 3.23/1.45 in @
% 3.23/1.45 X12 @
% 3.23/1.45 (
% 3.23/1.45 powerset
% 3.23/1.45 @
% 3.23/1.45 X10 ) ) ) ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 ![
% 3.23/1.45 X16:$i]:
% 3.23/1.45 (
% 3.23/1.45 in @
% 3.23/1.45 emptyset @
% 3.23/1.45 (
% 3.23/1.45 powerset
% 3.23/1.45 @
% 3.23/1.45 X16 ) ) ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 ![
% 3.23/1.45 X18:$i]:
% 3.23/1.45 (
% 3.23/1.45 in @
% 3.23/1.45 emptyset @
% 3.23/1.45 (
% 3.23/1.45 powerset
% 3.23/1.45 @
% 3.23/1.45 X18 ) ) ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 ![
% 3.23/1.45 X20:$i,
% 3.23/1.45 X22:$i,
% 3.23/1.45 X24:$i]:
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 in @
% 3.23/1.45 X22 @
% 3.23/1.45 (
% 3.23/1.45 powerset
% 3.23/1.45 @
% 3.23/1.45 X20 ) ) =>
% 3.23/1.45 (
% 3.23/1.45 (
% 3.23/1.45 in @
% 3.23/1.45 X24 @ X22 ) =>
% 3.23/1.45 (
% 3.23/1.45 in @
% 3.23/1.45 X24 @ X20 ) ) ) ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 setunionI ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 setunionE ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 subPowSU ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 exuE2 ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 nonemptyImpWitness ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 uniqinunit ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 notinsingleton ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 eqinunit ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 singletonsswitch ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 upairsetE ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 upairsetIL ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 upairsetIR ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 emptyE1 ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 vacuousDall ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 quantDeMorgan1 ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 quantDeMorgan2 ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 quantDeMorgan3 ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 quantDeMorgan4 ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 prop2setI ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 prop2set2propI ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 notdexE ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 notdallE ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 exuI1 ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 exuI3 ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 exuI2 ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 inCongP ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 in__Cong ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 exuE3u ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 exu__Cong ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 emptyset__Cong ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 setadjoin__Cong ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 ![
% 3.54/1.45 X26:$i,
% 3.54/1.45 X28:$i]:
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 X26 ) =
% 3.54/1.45 (
% 3.54/1.45 X28 ) ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 powerset
% 3.54/1.45 @
% 3.54/1.45 X26 ) =
% 3.54/1.45 (
% 3.54/1.45 powerset
% 3.54/1.45 @
% 3.54/1.45 X28 ) ) ) ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 setunion__Cong ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 omega__Cong ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 exuEu ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 descr__Cong ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 dsetconstr__Cong ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 subsetI1 ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 eqimpsubset2 ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 eqimpsubset1 ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 subsetI2 ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 emptysetsubset ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 subsetE ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 subsetE2 ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 notsubsetI ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 notequalI1 ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 notequalI2 ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 subsetRefl ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 subsetTrans ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 setadjoinSub ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 setadjoinSub2 ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 ![
% 3.54/1.45 X30:$i,
% 3.54/1.45 X32:$i]:
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 subset @
% 3.54/1.45 X30 @ X32 ) =>
% 3.54/1.45 (
% 3.54/1.45 in @
% 3.54/1.45 X30 @
% 3.54/1.45 (
% 3.54/1.45 powerset
% 3.54/1.45 @
% 3.54/1.45 X32 ) ) ) ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 setextsub ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 subsetemptysetimpeq ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 ![
% 3.54/1.45 X34:$i,
% 3.54/1.45 X36:$i]:
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 subset @
% 3.54/1.45 X36 @ X34 ) =>
% 3.54/1.45 (
% 3.54/1.45 in @
% 3.54/1.45 X36 @
% 3.54/1.45 (
% 3.54/1.45 powerset
% 3.54/1.45 @
% 3.54/1.45 X34 ) ) ) ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 ![
% 3.54/1.45 X38:$i,
% 3.54/1.45 X40:$i]:
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 in @
% 3.54/1.45 X40 @
% 3.54/1.45 (
% 3.54/1.45 powerset
% 3.54/1.45 @
% 3.54/1.45 X38 ) ) =>
% 3.54/1.45 (
% 3.54/1.45 subset @
% 3.54/1.45 X40 @ X38 ) ) ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 ![
% 3.54/1.45 X42:$i]:
% 3.54/1.45 (
% 3.54/1.45 in @
% 3.54/1.45 X42 @
% 3.54/1.45 (
% 3.54/1.45 powerset
% 3.54/1.45 @
% 3.54/1.45 X42 ) ) ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 ![
% 3.54/1.45 X44:$i,
% 3.54/1.45 X46:$i]:
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 subset @
% 3.54/1.45 X44 @ X46 ) =>
% 3.54/1.45 (
% 3.54/1.45 subset @
% 3.54/1.45 (
% 3.54/1.45 powerset
% 3.54/1.45 @
% 3.54/1.45 X44 ) @
% 3.54/1.45 (
% 3.54/1.45 powerset
% 3.54/1.45 @
% 3.54/1.45 X46 ) ) ) ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 sepInPowerset ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 sepSubset ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 binunionIL ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 upairset2IR ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 binunionIR ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 binunionEcases ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 binunionE ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 binunionLsub ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 binunionRsub ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 binintersectI ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 binintersectSubset5 ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 binintersectEL ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 binintersectLsub ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 binintersectSubset2 ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 binintersectSubset3 ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 binintersectER ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 disjointsetsI1 ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 binintersectRsub ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 binintersectSubset4 ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 binintersectSubset1 ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 bs114d ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 ![
% 3.54/1.45 X48:$i,
% 3.54/1.45 X50:$i,
% 3.54/1.45 X52:$i]:
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 in @
% 3.54/1.45 X52 @ X48 ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 ~
% 3.54/1.45 (
% 3.54/1.45 in @
% 3.54/1.45 X52 @ X50 ) ) =>
% 3.54/1.45 (
% 3.54/1.45 in @
% 3.54/1.45 X52 @
% 3.54/1.45 (
% 3.54/1.45 setminus
% 3.54/1.45 @
% 3.54/1.45 X48 @ X50 ) ) ) ) ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 ![
% 3.54/1.45 X54:$i,
% 3.54/1.45 X56:$i,
% 3.54/1.45 X58:$i]:
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 in @
% 3.54/1.45 X58 @
% 3.54/1.45 (
% 3.54/1.45 setminus
% 3.54/1.45 @
% 3.54/1.45 X54 @ X56 ) ) =>
% 3.54/1.45 (
% 3.54/1.45 in @
% 3.54/1.45 X58 @ X54 ) ) ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 ![
% 3.54/1.45 X60:$i,
% 3.54/1.45 X62:$i,
% 3.54/1.45 X64:$i]:
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 in @
% 3.54/1.45 X64 @
% 3.54/1.45 (
% 3.54/1.45 setminus
% 3.54/1.45 @
% 3.54/1.45 X60 @ X62 ) ) =>
% 3.54/1.45 (
% 3.54/1.45 ~
% 3.54/1.45 (
% 3.54/1.45 in @
% 3.54/1.45 X64 @ X62 ) ) ) ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 ![
% 3.54/1.45 X66:$i,
% 3.54/1.45 X68:$i]:
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 subset @
% 3.54/1.45 X66 @ X68 ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 setminus
% 3.54/1.45 @
% 3.54/1.45 X66 @ X68 ) =
% 3.54/1.45 (
% 3.54/1.45 emptyset ) ) ) ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 ![
% 3.54/1.45 X70:$i,
% 3.54/1.45 X72:$i,
% 3.54/1.45 X74:$i]:
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 ~
% 3.54/1.45 (
% 3.54/1.45 in @
% 3.54/1.45 X74 @
% 3.54/1.45 (
% 3.54/1.45 setminus
% 3.54/1.45 @
% 3.54/1.45 X70 @ X72 ) ) ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 in @
% 3.54/1.45 X74 @ X70 ) =>
% 3.54/1.45 (
% 3.54/1.45 in @
% 3.54/1.45 X74 @ X72 ) ) ) ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 ![
% 3.54/1.45 X76:$i,
% 3.54/1.45 X78:$i,
% 3.54/1.45 X80:$i]:
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 ~
% 3.54/1.45 (
% 3.54/1.45 in @
% 3.54/1.45 X80 @
% 3.54/1.45 (
% 3.54/1.45 setminus
% 3.54/1.45 @
% 3.54/1.45 X76 @ X78 ) ) ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 ~
% 3.54/1.45 (
% 3.54/1.45 in @
% 3.54/1.45 X80 @ X78 ) ) =>
% 3.54/1.45 (
% 3.54/1.45 ~
% 3.54/1.45 (
% 3.54/1.45 in @
% 3.54/1.45 X80 @ X76 ) ) ) ) ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 ![
% 3.54/1.45 X82:$i,
% 3.54/1.45 X84:$i,
% 3.54/1.45 X86:$i]:
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 ~
% 3.54/1.45 (
% 3.54/1.45 in @
% 3.54/1.45 X86 @ X82 ) ) =>
% 3.54/1.45 (
% 3.54/1.45 ~
% 3.54/1.45 (
% 3.54/1.45 in @
% 3.54/1.45 X86 @
% 3.54/1.45 (
% 3.54/1.45 setminus
% 3.54/1.45 @
% 3.54/1.45 X82 @ X84 ) ) ) ) ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 ![
% 3.54/1.45 X88:$i,
% 3.54/1.45 X90:$i,
% 3.54/1.45 X92:$i]:
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 in @
% 3.54/1.45 X92 @ X90 ) =>
% 3.54/1.45 (
% 3.54/1.45 ~
% 3.54/1.45 (
% 3.54/1.45 in @
% 3.54/1.45 X92 @
% 3.54/1.45 (
% 3.54/1.45 setminus
% 3.54/1.45 @
% 3.54/1.45 X88 @ X90 ) ) ) ) ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 ![
% 3.54/1.45 X94:$i,
% 3.54/1.45 X96:$i]:
% 3.54/1.45 (
% 3.54/1.45 subset @
% 3.54/1.45 (
% 3.54/1.45 setminus
% 3.54/1.45 @
% 3.54/1.45 X94 @ X96 ) @
% 3.54/1.45 X94 ) ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 ![
% 3.54/1.45 X98:$i,
% 3.54/1.45 X100:$i]:
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 setminus
% 3.54/1.45 @
% 3.54/1.45 X98 @
% 3.54/1.45 X100 ) =
% 3.54/1.45 (
% 3.54/1.45 emptyset ) ) =>
% 3.54/1.45 (
% 3.54/1.45 subset @
% 3.54/1.45 X98 @
% 3.54/1.45 X100 ) ) ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 symdiffE ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 symdiffI1 ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 symdiffI2 ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 symdiffIneg1 ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 symdiffIneg2 ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 secondinupair ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 setukpairIL ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 setukpairIR ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 kpairiskpair ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 kpairp ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 singletonsubset ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 ![
% 3.54/1.45 X102:$i,
% 3.54/1.45 X104:$i]:
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 in @
% 3.54/1.45 X104 @
% 3.54/1.45 X102 ) =>
% 3.54/1.45 (
% 3.54/1.45 in @
% 3.54/1.45 (
% 3.54/1.45 setadjoin
% 3.54/1.45 @
% 3.54/1.45 X104 @
% 3.54/1.45 emptyset ) @
% 3.54/1.45 (
% 3.54/1.45 powerset
% 3.54/1.45 @
% 3.54/1.45 X102 ) ) ) ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 singletoninpowunion ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 upairset2E ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 upairsubunion ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 upairinpowunion ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 ubforcartprodlem1 ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 ubforcartprodlem2 ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 ubforcartprodlem3 ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 cartprodpairin ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 cartprodmempair1 ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 cartprodmempair ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 setunionE2 ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 setunionsingleton1 ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 setunionsingleton2 ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 setunionsingleton ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 singletonprop ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 ex1E1 ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 ex1I ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 ex1I2 ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 singletonsuniq ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 setukpairinjL1 ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 kfstsingleton ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 theprop ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 kfstpairEq ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 cartprodfstin ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 setukpairinjL2 ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 setukpairinjL ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 setukpairinjR11 ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 setukpairinjR12 ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 setukpairinjR1 ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 upairequniteq ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 setukpairinjR2 ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 setukpairinjR ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 ksndsingleton ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 ksndpairEq ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 kpairsurjEq ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 cartprodsndin ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 cartprodpairmemEL ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 cartprodpairmemER ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 cartprodmempaircEq ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 cartprodfstpairEq ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 cartprodsndpairEq ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 cartprodpairsurjEq ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 dpsetconstrI ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 dpsetconstrSub ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 setOfPairsIsBReln ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 dpsetconstrERa ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 dpsetconstrEL1 ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 dpsetconstrEL2 ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 dpsetconstrER ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 funcImageSingleton ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 apProp ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 app ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 infuncsetfunc ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 ap2p ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 funcinfuncset ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 lamProp ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 lamp ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 lam2p ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 brelnall1 ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 brelnall2 ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 ex1E2 ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 funcGraphProp1 ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 funcGraphProp3 ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 funcGraphProp2 ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 funcextLem ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 funcGraphProp4 ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 subbreln ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 eqbreln ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 funcext ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 funcext2 ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 ap2apEq1 ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 ap2apEq2 ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 beta1 ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 eta1 ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 lam2lamEq ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 beta2 ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 eta2 ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 iffalseProp1 ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 iffalseProp2 ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 iftrueProp1 ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 iftrueProp2 ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 ifSingleton ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 ifp ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 theeq ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 iftrue ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 iffalse ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 iftrueorfalse ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 binintersectT_lem ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 binunionT_lem ) =>
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 ![
% 3.54/1.45 X106:$i,
% 3.54/1.45 X108:$i]:
% 3.54/1.45 (
% 3.54/1.45 (
% 3.54/1.45 in @
% 3.54/1.45 X108 @
% 3.54/1.45 (
% 3.54/1.45 powerset
% 3.54/1.45 @
% 3.54/1.45 X106 ) ) =>
% 3.54/1.45 (
% 3.54/1.45 in @
% 3.54/1.45 (
% 3.54/1.45 powerset
% 3.54/1.45 @
% 3.54/1.45 X108 ) @
% 3.54/1.45 (
% 3.54/1.45 powerset
% 3.54/1.45 @
% 3.54/1.45 (
% 3.54/1.45 powerset
% 3.54/1.45 @
% 3.54/1.46 X106 ) ) ) ) ) =>
% 3.54/1.46 (
% 3.54/1.46 (
% 3.54/1.46 ![
% 3.54/1.46 X110:$i,
% 3.54/1.46 X112:$i]:
% 3.54/1.46 (
% 3.54/1.46 (
% 3.54/1.46 in @
% 3.54/1.46 X112 @
% 3.54/1.46 (
% 3.54/1.46 powerset
% 3.54/1.46 @
% 3.54/1.46 X110 ) ) =>
% 3.54/1.46 (
% 3.54/1.46 ![
% 3.54/1.46 X114:$i]:
% 3.54/1.46 (
% 3.54/1.46 (
% 3.54/1.46 in @
% 3.54/1.46 X114 @
% 3.54/1.46 (
% 3.54/1.46 powerset
% 3.54/1.46 @
% 3.54/1.46 X110 ) ) =>
% 3.54/1.46 (
% 3.54/1.46 in @
% 3.54/1.46 (
% 3.54/1.46 setminus
% 3.54/1.46 @
% 3.54/1.46 X112 @
% 3.54/1.46 X114 ) @
% 3.54/1.46 (
% 3.54/1.46 powerset
% 3.54/1.46 @
% 3.54/1.46 X110 ) ) ) ) ) ) =>
% 3.54/1.46 (
% 3.54/1.46 (
% 3.54/1.46 ![
% 3.54/1.46 X116:$i,
% 3.54/1.46 X118:$i]:
% 3.54/1.46 (
% 3.54/1.46 (
% 3.54/1.46 in @
% 3.54/1.46 X118 @
% 3.54/1.46 (
% 3.54/1.46 powerset
% 3.54/1.46 @
% 3.54/1.46 X116 ) ) =>
% 3.54/1.46 (
% 3.54/1.46 in @
% 3.54/1.46 (
% 3.54/1.46 setminus
% 3.54/1.46 @
% 3.54/1.46 X116 @
% 3.54/1.46 X118 ) @
% 3.54/1.46 (
% 3.54/1.46 powerset
% 3.54/1.46 @
% 3.54/1.46 X116 ) ) ) ) =>
% 3.54/1.46 (
% 3.54/1.46 (
% 3.54/1.46 ![
% 3.54/1.46 X120:$i,
% 3.54/1.46 X122:$i]:
% 3.54/1.46 (
% 3.54/1.46 (
% 3.54/1.46 in @
% 3.54/1.46 X122 @
% 3.54/1.46 (
% 3.54/1.46 powerset
% 3.54/1.46 @
% 3.54/1.46 X120 ) ) =>
% 3.54/1.46 (
% 3.54/1.46 ![
% 3.54/1.46 X124:$i]:
% 3.54/1.46 (
% 3.54/1.46 (
% 3.54/1.46 in @
% 3.54/1.46 X124 @
% 3.54/1.46 (
% 3.54/1.46 powerset
% 3.54/1.46 @
% 3.54/1.46 X120 ) ) =>
% 3.54/1.46 (
% 3.54/1.46 (
% 3.54/1.46 ![
% 3.54/1.46 X126:$i]:
% 3.54/1.46 (
% 3.54/1.46 (
% 3.54/1.46 in @
% 3.54/1.46 X126 @
% 3.54/1.46 X120 ) =>
% 3.54/1.46 (
% 3.54/1.46 (
% 3.54/1.46 in @
% 3.54/1.46 X126 @
% 3.54/1.46 X122 ) =>
% 3.54/1.46 (
% 3.54/1.46 in @
% 3.54/1.46 X126 @
% 3.54/1.46 X124 ) ) ) ) =>
% 3.54/1.46 (
% 3.54/1.46 (
% 3.54/1.46 ![
% 3.54/1.46 X128:$i]:
% 3.54/1.46 (
% 3.54/1.46 (
% 3.54/1.46 in @
% 3.54/1.46 X128 @
% 3.54/1.46 X120 ) =>
% 3.54/1.46 (
% 3.54/1.46 (
% 3.54/1.46 in @
% 3.54/1.46 X128 @
% 3.54/1.46 X124 ) =>
% 3.54/1.46 (
% 3.54/1.46 in @
% 3.54/1.46 X128 @
% 3.54/1.46 X122 ) ) ) ) =>
% 3.54/1.46 (
% 3.54/1.46 (
% 3.54/1.46 X122 ) =
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% 3.54/1.46 X124 ) ) ) ) ) ) ) ) =>
% 3.54/1.46 (
% 3.54/1.46 (
% 3.54/1.46 ![
% 3.54/1.46 X130:$i,
% 3.54/1.46 X132:$i]:
% 3.54/1.46 (
% 3.54/1.46 (
% 3.54/1.46 in @
% 3.54/1.46 X132 @
% 3.54/1.46 (
% 3.54/1.46 powerset
% 3.54/1.46 @
% 3.54/1.46 X130 ) ) =>
% 3.54/1.46 (
% 3.54/1.46 ![
% 3.54/1.46 X134:$i]:
% 3.54/1.46 (
% 3.54/1.46 (
% 3.54/1.46 in @
% 3.54/1.46 X134 @
% 3.54/1.46 (
% 3.54/1.46 powerset
% 3.54/1.46 @
% 3.54/1.46 X130 ) ) =>
% 3.54/1.46 (
% 3.54/1.46 (
% 3.54/1.46 ![
% 3.54/1.46 X136:$i]:
% 3.54/1.46 (
% 3.54/1.46 (
% 3.54/1.46 in @
% 3.54/1.46 X136 @
% 3.54/1.46 X130 ) =>
% 3.54/1.46 (
% 3.54/1.46 (
% 3.54/1.46 in @
% 3.54/1.46 X136 @
% 3.54/1.46 X132 ) =>
% 3.54/1.46 (
% 3.54/1.46 in @
% 3.54/1.46 X136 @
% 3.54/1.46 X134 ) ) ) ) =>
% 3.54/1.46 (
% 3.54/1.46 subset @
% 3.54/1.46 X132 @
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% 3.54/1.46 (
% 3.54/1.46 (
% 3.54/1.46 ![
% 3.54/1.46 X138:$i,
% 3.54/1.46 X140:$i]:
% 3.54/1.46 (
% 3.54/1.46 (
% 3.54/1.46 in @
% 3.54/1.46 X140 @
% 3.54/1.46 (
% 3.54/1.46 powerset
% 3.54/1.46 @
% 3.54/1.46 X138 ) ) =>
% 3.54/1.46 (
% 3.54/1.46 ![
% 3.54/1.46 X142:$i]:
% 3.54/1.46 (
% 3.54/1.46 (
% 3.54/1.46 in @
% 3.54/1.46 X142 @
% 3.54/1.46 (
% 3.54/1.46 powerset
% 3.54/1.46 @
% 3.54/1.46 X138 ) ) =>
% 3.54/1.46 (
% 3.54/1.46 (
% 3.54/1.46 ![
% 3.54/1.46 X144:$i]:
% 3.54/1.46 (
% 3.54/1.46 (
% 3.54/1.46 in @
% 3.54/1.46 X144 @
% 3.54/1.46 X138 ) =>
% 3.54/1.46 (
% 3.54/1.46 (
% 3.54/1.46 in @
% 3.54/1.46 X144 @
% 3.54/1.46 X140 ) =>
% 3.54/1.46 (
% 3.54/1.46 in @
% 3.54/1.46 X144 @
% 3.54/1.46 X142 ) ) ) ) =>
% 3.54/1.46 (
% 3.54/1.46 in @
% 3.54/1.46 X140 @
% 3.54/1.46 (
% 3.54/1.46 powerset
% 3.54/1.46 @
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% 3.54/1.46 (
% 3.54/1.46 (
% 3.54/1.46 ![
% 3.54/1.46 X146:$i,
% 3.54/1.46 X148:$i]:
% 3.54/1.46 (
% 3.54/1.46 (
% 3.54/1.46 in @
% 3.54/1.46 X148 @
% 3.54/1.46 (
% 3.54/1.46 powerset
% 3.54/1.46 @
% 3.54/1.46 X146 ) ) =>
% 3.54/1.46 (
% 3.54/1.46 ![
% 3.54/1.46 X150:$i]:
% 3.54/1.46 (
% 3.54/1.46 (
% 3.54/1.46 in @
% 3.54/1.46 X150 @
% 3.54/1.46 (
% 3.54/1.46 powerset
% 3.54/1.46 @
% 3.54/1.46 X146 ) ) =>
% 3.54/1.46 (
% 3.54/1.46 ![
% 3.54/1.46 X152:$i]:
% 3.54/1.46 (
% 3.54/1.46 (
% 3.54/1.46 in @
% 3.54/1.46 X152 @
% 3.54/1.46 X146 ) =>
% 3.54/1.46 (
% 3.54/1.46 (
% 3.54/1.46 in @
% 3.54/1.46 X148 @
% 3.54/1.46 (
% 3.54/1.46 powerset
% 3.54/1.46 @
% 3.54/1.46 X150 ) ) =>
% 3.54/1.46 (
% 3.54/1.46 (
% 3.54/1.46 in @
% 3.54/1.46 X152 @
% 3.54/1.46 X148 ) =>
% 3.54/1.46 (
% 3.54/1.46 in @
% 3.54/1.46 X152 @
% 3.54/1.46 X150 ) ) ) ) ) ) ) ) ) =>
% 3.54/1.46 (
% 3.54/1.46 (
% 3.54/1.46 ![
% 3.54/1.46 X154:$i,
% 3.54/1.46 X156:$i]:
% 3.54/1.46 (
% 3.54/1.46 (
% 3.54/1.46 in @
% 3.54/1.46 X156 @
% 3.54/1.46 (
% 3.54/1.46 powerset
% 3.54/1.46 @
% 3.54/1.46 X154 ) ) =>
% 3.54/1.46 (
% 3.54/1.46 ![
% 3.54/1.46 X158:$i]:
% 3.54/1.46 (
% 3.54/1.46 (
% 3.54/1.46 in @
% 3.54/1.46 X158 @
% 3.54/1.46 X154 ) =>
% 3.54/1.46 (
% 3.54/1.46 (
% 3.54/1.46 in @
% 3.54/1.46 X158 @
% 3.54/1.46 X156 ) =>
% 3.54/1.46 (
% 3.54/1.46 ~
% 3.54/1.46 (
% 3.54/1.46 in @
% 3.54/1.46 X158 @
% 3.54/1.46 (
% 3.54/1.46 setminus
% 3.54/1.46 @
% 3.54/1.46 X154 @
% 3.54/1.46 X156 ) ) ) ) ) ) ) ) =>
% 3.54/1.46 (
% 3.54/1.46 ![
% 3.54/1.46 X160:$i,
% 3.54/1.46 X162:$i]:
% 3.54/1.46 (
% 3.54/1.46 (
% 3.54/1.46 in @
% 3.54/1.46 X162 @
% 3.54/1.46 (
% 3.54/1.46 powerset
% 3.54/1.46 @
% 3.54/1.46 X160 ) ) =>
% 3.54/1.46 (
% 3.54/1.46 ![
% 3.54/1.46 X164:$i]:
% 3.54/1.46 (
% 3.54/1.46 (
% 3.54/1.46 in @
% 3.54/1.46 X164 @
% 3.54/1.46 X160 ) =>
% 3.54/1.46 (
% 3.54/1.46 (
% 3.54/1.46 ~
% 3.54/1.46 (
% 3.54/1.46 in @
% 3.54/1.46 X164 @
% 3.54/1.46 (
% 3.56/1.46 setminus
% 3.56/1.46 @
% 3.56/1.46 X160 @
% 3.56/1.46 X162 ) ) ) =>
% 3.56/1.46 (
% 3.56/1.46 in @
% 3.56/1.46 X164 @
% 3.56/1.46 X162 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )),
% 3.56/1.46 inference('cnf.neg', [status(esa)], [zf_stmt_3])).
% 3.56/1.46 thf(zip_derived_cl125, plain, (~ (in @ sk__85 @ sk__84)),
% 3.56/1.46 inference('cnf', [status(esa)], [zf_stmt_4])).
% 3.56/1.46 thf(zip_derived_cl124, plain, ( (in @ sk__85 @ sk__83)),
% 3.56/1.46 inference('cnf', [status(esa)], [zf_stmt_4])).
% 3.56/1.46 thf(zip_derived_cl65, plain,
% 3.56/1.46 (![X11 : $i, X12 : $i, X13 : $i]:
% 3.56/1.46 ( (in @ X11 @ X12)
% 3.56/1.46 | ~ (in @ X11 @ X13)
% 3.56/1.46 | (in @ X11 @ (setminus @ X13 @ X12)))),
% 3.56/1.46 inference('cnf', [status(esa)], [zf_stmt_4])).
% 3.56/1.46 thf(zip_derived_cl279, plain,
% 3.56/1.46 (![X0 : $i]:
% 3.56/1.46 ( (in @ sk__85 @ (setminus @ sk__83 @ X0)) | (in @ sk__85 @ X0))),
% 3.56/1.46 inference('sup-', [status(thm)], [zip_derived_cl124, zip_derived_cl65])).
% 3.56/1.46 thf(zip_derived_cl126, plain,
% 3.56/1.46 (~ (in @ sk__85 @ (setminus @ sk__83 @ sk__84))),
% 3.56/1.46 inference('cnf', [status(esa)], [zf_stmt_4])).
% 3.56/1.46 thf(zip_derived_cl634, plain, ( (in @ sk__85 @ sk__84)),
% 3.56/1.46 inference('sup-', [status(thm)], [zip_derived_cl279, zip_derived_cl126])).
% 3.56/1.46 thf(zip_derived_cl644, plain, ($false),
% 3.56/1.46 inference('demod', [status(thm)], [zip_derived_cl125, zip_derived_cl634])).
% 3.56/1.46
% 3.56/1.46 % SZS output end Refutation
% 3.56/1.46
% 3.56/1.46
% 3.56/1.46 % Terminating...
% 3.77/1.60 % Runner terminated.
% 3.77/1.62 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------