%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SEU714^1 : 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.0BVWQiKDmI true
% Computer : n009.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 04:55:54 PM UTC 2025
% Result : Theorem 0.47s 1.09s
% Output : Refutation 0.47s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SEU714^1 : TPTP v9.2.0. Released v3.7.0.
% 0.00/0.09 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.0BVWQiKDmI true
% 0.08/0.30 % Computer : n009.cluster.edu
% 0.08/0.30 % Model : x86_64 x86_64
% 0.08/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.30 % Memory : 8042.1875MB
% 0.08/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.30 % CPULimit : 300
% 0.08/0.30 % WCLimit : 300
% 0.08/0.30 % DateTime : Wed Oct 1 16:13:53 EDT 2025
% 0.08/0.30 % CPUTime :
% 0.08/0.30 % Running portfolio for 300 s
% 0.08/0.30 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.30 % Number of cores: 8
% 0.08/0.30 % Python version: Python 3.6.8
% 0.08/0.30 % Running in HO mode
% 0.45/0.64 % Total configuration time : 828
% 0.45/0.64 % Estimated wc time : 1656
% 0.45/0.64 % Estimated cpu time (8 cpus) : 207.0
% 0.45/0.75 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
% 0.45/0.76 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.45/0.77 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
% 0.45/0.77 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
% 0.45/0.78 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s
% 0.45/0.78 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.46/0.79 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s
% 0.46/0.80 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s
% 0.47/1.09 % Solved by lams/40_c_ic.sh.
% 0.47/1.09 % done 282 iterations in 0.205s
% 0.47/1.09 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 0.47/1.09 % SZS output start Refutation
% 0.47/1.09 thf(setadjoinAx_type, type, setadjoinAx: $o).
% 0.47/1.09 thf(notdexE_type, type, notdexE: $o).
% 0.47/1.09 thf(setukpairinjL2_type, type, setukpairinjL2: $o).
% 0.47/1.09 thf(zip_tseitin_0_type, type, zip_tseitin_0: $i > $i > $i > $o).
% 0.47/1.09 thf(setunionAx_type, type, setunionAx: $o).
% 0.47/1.09 thf(setminusELneg_type, type, setminusELneg: $o).
% 0.47/1.09 thf(cartprodsndin_type, type, cartprodsndin: $o).
% 0.47/1.09 thf(ex1E1_type, type, ex1E1: $o).
% 0.47/1.09 thf(powersetE_type, type, powersetE: $o).
% 0.47/1.09 thf(omegaSAx_type, type, omegaSAx: $o).
% 0.47/1.09 thf(exuI1_type, type, exuI1: $o).
% 0.47/1.09 thf(exuI2_type, type, exuI2: $o).
% 0.47/1.09 thf(notequalI2_type, type, notequalI2: $o).
% 0.47/1.09 thf(setukpairinjL_type, type, setukpairinjL: $o).
% 0.47/1.09 thf(kpairiskpair_type, type, kpairiskpair: $o).
% 0.47/1.09 thf(upairsubunion_type, type, upairsubunion: $o).
% 0.47/1.09 thf(funcGraphProp3_type, type, funcGraphProp3: $o).
% 0.47/1.09 thf(cartprodmempaircEq_type, type, cartprodmempaircEq: $o).
% 0.47/1.09 thf(powerset__Cong_type, type, powerset__Cong: $o).
% 0.47/1.09 thf(setminusILneg_type, type, setminusILneg: $o).
% 0.47/1.09 thf(wellorderingAx_type, type, wellorderingAx: $o).
% 0.47/1.09 thf(ksndpairEq_type, type, ksndpairEq: $o).
% 0.47/1.09 thf(funcGraphProp2_type, type, funcGraphProp2: $o).
% 0.47/1.09 thf(setadjoinSub2_type, type, setadjoinSub2: $o).
% 0.47/1.09 thf(binintersectSubset5_type, type, binintersectSubset5: $o).
% 0.47/1.09 thf(iftrue_type, type, iftrue: $o).
% 0.47/1.09 thf(upairinpowunion_type, type, upairinpowunion: $o).
% 0.47/1.09 thf(ifSingleton_type, type, ifSingleton: $o).
% 0.47/1.09 thf(setoftrueEq_type, type, setoftrueEq: $o).
% 0.47/1.09 thf(funcImageSingleton_type, type, funcImageSingleton: $o).
% 0.47/1.09 thf(dpsetconstrERa_type, type, dpsetconstrERa: $o).
% 0.47/1.09 thf(lamProp_type, type, lamProp: $o).
% 0.47/1.09 thf(cartprodpairmemEL_type, type, cartprodpairmemEL: $o).
% 0.47/1.09 thf(emptyset__Cong_type, type, emptyset__Cong: $o).
% 0.47/1.09 thf(dpsetconstrER_type, type, dpsetconstrER: $o).
% 0.47/1.09 thf(sepInPowerset_type, type, sepInPowerset: $o).
% 0.47/1.09 thf(setukpairIR_type, type, setukpairIR: $o).
% 0.47/1.09 thf(setukpairinjR1_type, type, setukpairinjR1: $o).
% 0.47/1.09 thf(lam2p_type, type, lam2p: $o).
% 0.47/1.09 thf(binunionE_type, type, binunionE: $o).
% 0.47/1.09 thf(setext_type, type, setext: $o).
% 0.47/1.09 thf(emptyinPowerset_type, type, emptyinPowerset: $o).
% 0.47/1.09 thf(ubforcartprodlem1_type, type, ubforcartprodlem1: $o).
% 0.47/1.09 thf(descr__Cong_type, type, descr__Cong: $o).
% 0.47/1.09 thf(kfstsingleton_type, type, kfstsingleton: $o).
% 0.47/1.09 thf(eqbreln_type, type, eqbreln: $o).
% 0.47/1.09 thf(binintersectSubset1_type, type, binintersectSubset1: $o).
% 0.47/1.09 thf(in_type, type, in: $i > $i > $o).
% 0.47/1.09 thf(binunionT_lem_type, type, binunionT_lem: $o).
% 0.47/1.09 thf(quantDeMorgan1_type, type, quantDeMorgan1: $o).
% 0.47/1.09 thf(kpairsurjEq_type, type, kpairsurjEq: $o).
% 0.47/1.09 thf(setadjoinIR_type, type, setadjoinIR: $o).
% 0.47/1.09 thf(beta1_type, type, beta1: $o).
% 0.47/1.09 thf(setadjoin__Cong_type, type, setadjoin__Cong: $o).
% 0.47/1.09 thf(symdiffI2_type, type, symdiffI2: $o).
% 0.47/1.09 thf(iftrueProp2_type, type, iftrueProp2: $o).
% 0.47/1.09 thf(upairset2IR_type, type, upairset2IR: $o).
% 0.47/1.09 thf(iffalseProp2_type, type, iffalseProp2: $o).
% 0.47/1.09 thf(subsetE_type, type, subsetE: $o).
% 0.47/1.09 thf(prop2set2propI_type, type, prop2set2propI: $o).
% 0.47/1.09 thf(dsetconstrEL_type, type, dsetconstrEL: $o).
% 0.47/1.09 thf(setbeta_type, type, setbeta: $o).
% 0.47/1.09 thf(eqinunit_type, type, eqinunit: $o).
% 0.47/1.09 thf(upairsetIL_type, type, upairsetIL: $o).
% 0.47/1.09 thf(powersetI1_type, type, powersetI1: $o).
% 0.47/1.09 thf(kfstpairEq_type, type, kfstpairEq: $o).
% 0.47/1.09 thf(binintersectSubset3_type, type, binintersectSubset3: $o).
% 0.47/1.09 thf(setminusIRneg_type, type, setminusIRneg: $o).
% 0.47/1.09 thf(ap2apEq1_type, type, ap2apEq1: $o).
% 0.47/1.09 thf(powersetAx_type, type, powersetAx: $o).
% 0.47/1.09 thf(binintersectSubset4_type, type, binintersectSubset4: $o).
% 0.47/1.09 thf(singletoninpowunion_type, type, singletoninpowunion: $o).
% 0.47/1.09 thf(powersetI_type, type, powersetI: $o).
% 0.47/1.09 thf(cartprodmempair_type, type, cartprodmempair: $o).
% 0.47/1.09 thf(upairsetIR_type, type, upairsetIR: $o).
% 0.47/1.09 thf(lamp_type, type, lamp: $o).
% 0.47/1.09 thf(dpsetconstrEL1_type, type, dpsetconstrEL1: $o).
% 0.47/1.09 thf(inCongP_type, type, inCongP: $o).
% 0.47/1.09 thf(setadjoinSub_type, type, setadjoinSub: $o).
% 0.47/1.09 thf(exuE3e_type, type, exuE3e: $o).
% 0.47/1.09 thf(emptysetE_type, type, emptysetE: $o).
% 0.47/1.09 thf(binintersectSubset2_type, type, binintersectSubset2: $o).
% 0.47/1.09 thf(setunionI_type, type, setunionI: $o).
% 0.47/1.09 thf(setunion__Cong_type, type, setunion__Cong: $o).
% 0.47/1.09 thf(prop2setI_type, type, prop2setI: $o).
% 0.47/1.09 thf(singletonsuniq_type, type, singletonsuniq: $o).
% 0.47/1.09 thf(nonemptyImpWitness_type, type, nonemptyImpWitness: $o).
% 0.47/1.09 thf(setminusER_type, type, setminusER: $o).
% 0.47/1.09 thf(exuE2_type, type, exuE2: $o).
% 0.47/1.09 thf(emptyset_type, type, emptyset: $i).
% 0.47/1.09 thf(setukpairinjR11_type, type, setukpairinjR11: $o).
% 0.47/1.09 thf(ex1I_type, type, ex1I: $o).
% 0.47/1.09 thf(ex1E2_type, type, ex1E2: $o).
% 0.47/1.09 thf(setminus_type, type, setminus: $i > $i > $i).
% 0.47/1.09 thf(setukpairinjL1_type, type, setukpairinjL1: $o).
% 0.47/1.09 thf(powersetsubset_type, type, powersetsubset: $o).
% 0.47/1.09 thf(subPowSU_type, type, subPowSU: $o).
% 0.47/1.09 thf(notequalI1_type, type, notequalI1: $o).
% 0.47/1.09 thf(notinemptyset_type, type, notinemptyset: $o).
% 0.47/1.09 thf(lam2lamEq_type, type, lam2lamEq: $o).
% 0.47/1.09 thf(nonemptyI1_type, type, nonemptyI1: $o).
% 0.47/1.09 thf(subsetTrans_type, type, subsetTrans: $o).
% 0.47/1.09 thf(kpairp_type, type, kpairp: $o).
% 0.47/1.09 thf(setukpairinjR12_type, type, setukpairinjR12: $o).
% 0.47/1.09 thf(setminusI_type, type, setminusI: $o).
% 0.47/1.09 thf(binunionIL_type, type, binunionIL: $o).
% 0.47/1.09 thf(dpsetconstrSub_type, type, dpsetconstrSub: $o).
% 0.47/1.09 thf(setunionsingleton_type, type, setunionsingleton: $o).
% 0.47/1.09 thf(subsetE2_type, type, subsetE2: $o).
% 0.47/1.09 thf(singletonsswitch_type, type, singletonsswitch: $o).
% 0.47/1.09 thf(ubforcartprodlem3_type, type, ubforcartprodlem3: $o).
% 0.47/1.09 thf(beta2_type, type, beta2: $o).
% 0.47/1.09 thf(dpsetconstrI_type, type, dpsetconstrI: $o).
% 0.47/1.09 thf(setextsub_type, type, setextsub: $o).
% 0.47/1.09 thf(binunionLsub_type, type, binunionLsub: $o).
% 0.47/1.09 thf(setunionsingleton1_type, type, setunionsingleton1: $o).
% 0.47/1.09 thf(iftrueorfalse_type, type, iftrueorfalse: $o).
% 0.47/1.09 thf(emptysetsubset_type, type, emptysetsubset: $o).
% 0.47/1.09 thf(quantDeMorgan3_type, type, quantDeMorgan3: $o).
% 0.47/1.09 thf(cartprodpairsurjEq_type, type, cartprodpairsurjEq: $o).
% 0.47/1.09 thf(setOfPairsIsBReln_type, type, setOfPairsIsBReln: $o).
% 0.47/1.09 thf(setunionE_type, type, setunionE: $o).
% 0.47/1.09 thf(ksndsingleton_type, type, ksndsingleton: $o).
% 0.47/1.09 thf(setminusSubset1_type, type, setminusSubset1: $o).
% 0.47/1.09 thf(powersetT_lem_type, type, powersetT_lem: $o).
% 0.47/1.09 thf(emptyinunitempty_type, type, emptyinunitempty: $o).
% 0.47/1.09 thf(binunionIR_type, type, binunionIR: $o).
% 0.47/1.09 thf(theeq_type, type, theeq: $o).
% 0.47/1.09 thf(setadjoinE_type, type, setadjoinE: $o).
% 0.47/1.09 thf(infuncsetfunc_type, type, infuncsetfunc: $o).
% 0.47/1.09 thf(ap2apEq2_type, type, ap2apEq2: $o).
% 0.47/1.09 thf(ap2p_type, type, ap2p: $o).
% 0.47/1.09 thf(setadjoinIL_type, type, setadjoinIL: $o).
% 0.47/1.09 thf(cartprodsndpairEq_type, type, cartprodsndpairEq: $o).
% 0.47/1.09 thf(exuE1_type, type, exuE1: $o).
% 0.47/1.09 thf(ubforcartprodlem2_type, type, ubforcartprodlem2: $o).
% 0.47/1.09 thf(binintersectRsub_type, type, binintersectRsub: $o).
% 0.47/1.09 thf(setminusLsub_type, type, setminusLsub: $o).
% 0.47/1.09 thf(funcextLem_type, type, funcextLem: $o).
% 0.47/1.09 thf(setukpairinjR_type, type, setukpairinjR: $o).
% 0.47/1.09 thf(notinsingleton_type, type, notinsingleton: $o).
% 0.47/1.09 thf(eqimpsubset2_type, type, eqimpsubset2: $o).
% 0.47/1.09 thf(exuEu_type, type, exuEu: $o).
% 0.47/1.09 thf(emptysetimpfalse_type, type, emptysetimpfalse: $o).
% 0.47/1.09 thf(upairsetE_type, type, upairsetE: $o).
% 0.47/1.09 thf(omega0Ax_type, type, omega0Ax: $o).
% 0.47/1.09 thf(notsubsetI_type, type, notsubsetI: $o).
% 0.47/1.09 thf(iffalseProp1_type, type, iffalseProp1: $o).
% 0.47/1.09 thf(quantDeMorgan4_type, type, quantDeMorgan4: $o).
% 0.47/1.09 thf(setextAx_type, type, setextAx: $o).
% 0.47/1.09 thf(cartprodpairmemER_type, type, cartprodpairmemER: $o).
% 0.47/1.09 thf(powersetE1_type, type, powersetE1: $o).
% 0.47/1.09 thf(bs114d_type, type, bs114d: $o).
% 0.47/1.09 thf(noeltsimpempty_type, type, noeltsimpempty: $o).
% 0.47/1.09 thf(ifp_type, type, ifp: $o).
% 0.47/1.09 thf(binintersectLsub_type, type, binintersectLsub: $o).
% 0.47/1.09 thf(subsetI1_type, type, subsetI1: $o).
% 0.47/1.09 thf(symdiffE_type, type, symdiffE: $o).
% 0.47/1.09 thf(descrp_type, type, descrp: $o).
% 0.47/1.09 thf(dsetconstr__Cong_type, type, dsetconstr__Cong: $o).
% 0.47/1.09 thf(foundationAx_type, type, foundationAx: $o).
% 0.47/1.09 thf(emptysetAx_type, type, emptysetAx: $o).
% 0.47/1.09 thf(emptyI_type, type, emptyI: $o).
% 0.47/1.09 thf(setadjoinOr_type, type, setadjoinOr: $o).
% 0.47/1.09 thf(eta2_type, type, eta2: $o).
% 0.47/1.09 thf(binintersectEL_type, type, binintersectEL: $o).
% 0.47/1.09 thf(emptyE1_type, type, emptyE1: $o).
% 0.47/1.09 thf(emptyInPowerset_type, type, emptyInPowerset: $o).
% 0.47/1.09 thf(vacuousDall_type, type, vacuousDall: $o).
% 0.47/1.09 thf(dsetconstrER_type, type, dsetconstrER: $o).
% 0.47/1.09 thf(binintersectI_type, type, binintersectI: $o).
% 0.47/1.09 thf(funcext_type, type, funcext: $o).
% 0.47/1.09 thf(funcGraphProp4_type, type, funcGraphProp4: $o).
% 0.47/1.09 thf(cartprodpairin_type, type, cartprodpairin: $o).
% 0.47/1.09 thf(cartprodmempair1_type, type, cartprodmempair1: $o).
% 0.47/1.09 thf(sk__59_type, type, sk__59: $i).
% 0.47/1.09 thf(brelnall2_type, type, brelnall2: $o).
% 0.47/1.09 thf(ex1I2_type, type, ex1I2: $o).
% 0.47/1.09 thf(symdiffI1_type, type, symdiffI1: $o).
% 0.47/1.09 thf(setukpairinjR2_type, type, setukpairinjR2: $o).
% 0.47/1.09 thf(dpsetconstrEL2_type, type, dpsetconstrEL2: $o).
% 0.47/1.09 thf(theprop_type, type, theprop: $o).
% 0.47/1.09 thf(subsetI2_type, type, subsetI2: $o).
% 0.47/1.09 thf(setminusT_lem_type, type, setminusT_lem: $o).
% 0.47/1.09 thf(symdiffIneg1_type, type, symdiffIneg1: $o).
% 0.47/1.09 thf(setminusERneg_type, type, setminusERneg: $o).
% 0.47/1.09 thf(symdiffIneg2_type, type, symdiffIneg2: $o).
% 0.47/1.09 thf(omega__Cong_type, type, omega__Cong: $o).
% 0.47/1.09 thf(subsetRefl_type, type, subsetRefl: $o).
% 0.47/1.09 thf(uniqinunit_type, type, uniqinunit: $o).
% 0.47/1.09 thf(setminusSubset2_type, type, setminusSubset2: $o).
% 0.47/1.09 thf(prop2setE_type, type, prop2setE: $o).
% 0.47/1.09 thf(binunionEcases_type, type, binunionEcases: $o).
% 0.47/1.09 thf(funcinfuncset_type, type, funcinfuncset: $o).
% 0.47/1.09 thf(nonemptyI_type, type, nonemptyI: $o).
% 0.47/1.09 thf(app_type, type, app: $o).
% 0.47/1.09 thf(disjointsetsI1_type, type, disjointsetsI1: $o).
% 0.47/1.09 thf(exuE3u_type, type, exuE3u: $o).
% 0.47/1.09 thf(eta1_type, type, eta1: $o).
% 0.47/1.09 thf(setminusEL_type, type, setminusEL: $o).
% 0.47/1.09 thf(cartprodfstin_type, type, cartprodfstin: $o).
% 0.47/1.09 thf(setunionsingleton2_type, type, setunionsingleton2: $o).
% 0.47/1.09 thf(sepSubset_type, type, sepSubset: $o).
% 0.47/1.09 thf(upairset2E_type, type, upairset2E: $o).
% 0.47/1.09 thf(eqimpsubset1_type, type, eqimpsubset1: $o).
% 0.47/1.09 thf(exuI3_type, type, exuI3: $o).
% 0.47/1.09 thf(cartprodfstpairEq_type, type, cartprodfstpairEq: $o).
% 0.47/1.09 thf(apProp_type, type, apProp: $o).
% 0.47/1.09 thf(notdallE_type, type, notdallE: $o).
% 0.47/1.09 thf(iftrueProp1_type, type, iftrueProp1: $o).
% 0.47/1.09 thf(binintersectER_type, type, binintersectER: $o).
% 0.47/1.09 thf(brelnall1_type, type, brelnall1: $o).
% 0.47/1.09 thf(powerset_type, type, powerset: $i > $i).
% 0.47/1.09 thf(dsetconstrI_type, type, dsetconstrI: $o).
% 0.47/1.09 thf(funcGraphProp1_type, type, funcGraphProp1: $o).
% 0.47/1.09 thf(binintersectT_lem_type, type, binintersectT_lem: $o).
% 0.47/1.09 thf(setadjoin_type, type, setadjoin: $i > $i > $i).
% 0.47/1.09 thf(exu__Cong_type, type, exu__Cong: $o).
% 0.47/1.09 thf(quantDeMorgan2_type, type, quantDeMorgan2: $o).
% 0.47/1.09 thf(secondinupair_type, type, secondinupair: $o).
% 0.47/1.09 thf(singletonprop_type, type, singletonprop: $o).
% 0.47/1.09 thf(singletonsubset_type, type, singletonsubset: $o).
% 0.47/1.09 thf(singletoninpowerset_type, type, singletoninpowerset: $o).
% 0.47/1.09 thf(subsetemptysetimpeq_type, type, subsetemptysetimpeq: $o).
% 0.47/1.09 thf(replAx_type, type, replAx: $o).
% 0.47/1.09 thf(upairequniteq_type, type, upairequniteq: $o).
% 0.47/1.09 thf(nonemptyE1_type, type, nonemptyE1: $o).
% 0.47/1.09 thf(omegaIndAx_type, type, omegaIndAx: $o).
% 0.47/1.09 thf(setukpairIL_type, type, setukpairIL: $o).
% 0.47/1.09 thf(setunionE2_type, type, setunionE2: $o).
% 0.47/1.09 thf(inPowerset_type, type, inPowerset: $o).
% 0.47/1.09 thf(iffalse_type, type, iffalse: $o).
% 0.47/1.09 thf(funcext2_type, type, funcext2: $o).
% 0.47/1.09 thf(subset_type, type, subset: $i > $i > $o).
% 0.47/1.09 thf(sk__58_type, type, sk__58: $i).
% 0.47/1.09 thf(subbreln_type, type, subbreln: $o).
% 0.47/1.09 thf(in__Cong_type, type, in__Cong: $o).
% 0.47/1.09 thf(binunionRsub_type, type, binunionRsub: $o).
% 0.47/1.09 thf(subset2powerset_type, type, subset2powerset: $o).
% 0.47/1.09 thf(setminusT_lem, axiom, setminusT_lem =
% 0.47/1.09 (![A:$i,X:$i]:
% 0.47/1.09 ( ( in @ X @ ( powerset @ A ) ) =>
% 0.47/1.09 ( ![Y:$i]:
% 0.47/1.09 ( ( in @ Y @ ( powerset @ A ) ) =>
% 0.47/1.09 ( in @ ( setminus @ X @ Y ) @ ( powerset @ A ) ) ) ) ))).
% 0.47/1.09 thf('0', plain,
% 0.47/1.09 (( setminusT_lem ) =
% 0.47/1.09 ( ![X4:$i,X6:$i]:
% 0.47/1.09 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 0.47/1.09 ( ![X8:$i]:
% 0.47/1.09 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 0.47/1.09 ( in @ ( setminus @ X6 @ X8 ) @ ( powerset @ X4 ) ) ) ) ) )),
% 0.47/1.09 define([status(thm)])).
% 0.47/1.09 thf(powersetT_lem, axiom, powersetT_lem =
% 0.47/1.09 (![A:$i,X:$i]:
% 0.47/1.09 ( ( in @ X @ ( powerset @ A ) ) =>
% 0.47/1.09 ( in @ ( powerset @ X ) @ ( powerset @ ( powerset @ A ) ) ) ))).
% 0.47/1.09 thf('1', plain,
% 0.47/1.09 (( powersetT_lem ) =
% 0.47/1.09 ( ![X4:$i,X6:$i]:
% 0.47/1.09 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 0.47/1.09 ( in @ ( powerset @ X6 ) @ ( powerset @ ( powerset @ X4 ) ) ) ) )),
% 0.47/1.09 define([status(thm)])).
% 0.47/1.09 thf(singletoninpowerset, axiom, singletoninpowerset =
% 0.47/1.09 (![A:$i,Xx:$i]:
% 0.47/1.09 ( ( in @ Xx @ A ) =>
% 0.47/1.09 ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) ))).
% 0.47/1.09 thf('2', plain,
% 0.47/1.09 (( singletoninpowerset ) =
% 0.47/1.09 ( ![X4:$i,X6:$i]:
% 0.47/1.09 ( ( in @ X6 @ X4 ) =>
% 0.47/1.09 ( in @ ( setadjoin @ X6 @ emptyset ) @ ( powerset @ X4 ) ) ) )),
% 0.47/1.09 define([status(thm)])).
% 0.47/1.09 thf(setminusSubset1, axiom, setminusSubset1 =
% 0.47/1.09 (![A:$i,B:$i]:
% 0.47/1.09 ( ( ( setminus @ A @ B ) = ( emptyset ) ) => ( subset @ A @ B ) ))).
% 0.47/1.09 thf('3', plain,
% 0.47/1.09 (( setminusSubset1 ) =
% 0.47/1.09 ( ![X4:$i,X6:$i]:
% 0.47/1.09 ( ( ( setminus @ X4 @ X6 ) = ( emptyset ) ) => ( subset @ X4 @ X6 ) ) )),
% 0.47/1.09 define([status(thm)])).
% 0.47/1.09 thf(setminusLsub, axiom, setminusLsub =
% 0.47/1.09 (![A:$i,B:$i]: ( subset @ ( setminus @ A @ B ) @ A ))).
% 0.47/1.09 thf('4', plain,
% 0.47/1.09 (( setminusLsub ) =
% 0.47/1.09 ( ![X4:$i,X6:$i]: ( subset @ ( setminus @ X4 @ X6 ) @ X4 ) )),
% 0.47/1.09 define([status(thm)])).
% 0.47/1.09 thf(setminusIRneg, axiom, setminusIRneg =
% 0.47/1.09 (![A:$i,B:$i,Xx:$i]:
% 0.47/1.09 ( ( in @ Xx @ B ) => ( ~( in @ Xx @ ( setminus @ A @ B ) ) ) ))).
% 0.47/1.09 thf('5', plain,
% 0.47/1.09 (( setminusIRneg ) =
% 0.47/1.09 ( ![X4:$i,X6:$i,X8:$i]:
% 0.47/1.09 ( ( in @ X8 @ X6 ) => ( ~( in @ X8 @ ( setminus @ X4 @ X6 ) ) ) ) )),
% 0.47/1.09 define([status(thm)])).
% 0.47/1.09 thf(setminusILneg, axiom, setminusILneg =
% 0.47/1.09 (![A:$i,B:$i,Xx:$i]:
% 0.47/1.09 ( ( ~( in @ Xx @ A ) ) => ( ~( in @ Xx @ ( setminus @ A @ B ) ) ) ))).
% 0.47/1.09 thf('6', plain,
% 0.47/1.09 (( setminusILneg ) =
% 0.47/1.09 ( ![X4:$i,X6:$i,X8:$i]:
% 0.47/1.09 ( ( ~( in @ X8 @ X4 ) ) => ( ~( in @ X8 @ ( setminus @ X4 @ X6 ) ) ) ) )),
% 0.47/1.09 define([status(thm)])).
% 0.47/1.09 thf(setminusELneg, axiom, setminusELneg =
% 0.47/1.09 (![A:$i,B:$i,Xx:$i]:
% 0.47/1.09 ( ( ~( in @ Xx @ ( setminus @ A @ B ) ) ) =>
% 0.47/1.09 ( ( ~( in @ Xx @ B ) ) => ( ~( in @ Xx @ A ) ) ) ))).
% 0.47/1.09 thf('7', plain,
% 0.47/1.09 (( setminusELneg ) =
% 0.47/1.09 ( ![X4:$i,X6:$i,X8:$i]:
% 0.47/1.09 ( ( ~( in @ X8 @ ( setminus @ X4 @ X6 ) ) ) =>
% 0.47/1.09 ( ( ~( in @ X8 @ X6 ) ) => ( ~( in @ X8 @ X4 ) ) ) ) )),
% 0.47/1.09 define([status(thm)])).
% 0.47/1.09 thf(setminusERneg, axiom, setminusERneg =
% 0.47/1.09 (![A:$i,B:$i,Xx:$i]:
% 0.47/1.09 ( ( ~( in @ Xx @ ( setminus @ A @ B ) ) ) =>
% 0.47/1.09 ( ( in @ Xx @ A ) => ( in @ Xx @ B ) ) ))).
% 0.47/1.09 thf('8', plain,
% 0.47/1.09 (( setminusERneg ) =
% 0.47/1.09 ( ![X4:$i,X6:$i,X8:$i]:
% 0.47/1.09 ( ( ~( in @ X8 @ ( setminus @ X4 @ X6 ) ) ) =>
% 0.47/1.09 ( ( in @ X8 @ X4 ) => ( in @ X8 @ X6 ) ) ) )),
% 0.47/1.09 define([status(thm)])).
% 0.47/1.09 thf(setminusSubset2, axiom, setminusSubset2 =
% 0.47/1.09 (![A:$i,B:$i]:
% 0.47/1.09 ( ( subset @ A @ B ) => ( ( setminus @ A @ B ) = ( emptyset ) ) ))).
% 0.47/1.09 thf('9', plain,
% 0.47/1.09 (( setminusSubset2 ) =
% 0.47/1.09 ( ![X4:$i,X6:$i]:
% 0.47/1.09 ( ( subset @ X4 @ X6 ) => ( ( setminus @ X4 @ X6 ) = ( emptyset ) ) ) )),
% 0.47/1.09 define([status(thm)])).
% 0.47/1.09 thf(setminusER, axiom, setminusER =
% 0.47/1.09 (![A:$i,B:$i,Xx:$i]:
% 0.47/1.09 ( ( in @ Xx @ ( setminus @ A @ B ) ) => ( ~( in @ Xx @ B ) ) ))).
% 0.47/1.09 thf('10', plain,
% 0.47/1.09 (( setminusER ) =
% 0.47/1.09 ( ![X4:$i,X6:$i,X8:$i]:
% 0.47/1.09 ( ( in @ X8 @ ( setminus @ X4 @ X6 ) ) => ( ~( in @ X8 @ X6 ) ) ) )),
% 0.47/1.09 define([status(thm)])).
% 0.47/1.09 thf(setminusEL, axiom, setminusEL =
% 0.47/1.09 (![A:$i,B:$i,Xx:$i]:
% 0.47/1.09 ( ( in @ Xx @ ( setminus @ A @ B ) ) => ( in @ Xx @ A ) ))).
% 0.47/1.09 thf('11', plain,
% 0.47/1.09 (( setminusEL ) =
% 0.47/1.09 ( ![X4:$i,X6:$i,X8:$i]:
% 0.47/1.09 ( ( in @ X8 @ ( setminus @ X4 @ X6 ) ) => ( in @ X8 @ X4 ) ) )),
% 0.47/1.09 define([status(thm)])).
% 0.47/1.09 thf(setminusI, axiom, setminusI =
% 0.47/1.09 (![A:$i,B:$i,Xx:$i]:
% 0.47/1.09 ( ( in @ Xx @ A ) =>
% 0.47/1.09 ( ( ~( in @ Xx @ B ) ) => ( in @ Xx @ ( setminus @ A @ B ) ) ) ))).
% 0.47/1.09 thf('12', plain,
% 0.47/1.09 (( setminusI ) =
% 0.47/1.09 ( ![X4:$i,X6:$i,X8:$i]:
% 0.47/1.09 ( ( in @ X8 @ X4 ) =>
% 0.47/1.09 ( ( ~( in @ X8 @ X6 ) ) => ( in @ X8 @ ( setminus @ X4 @ X6 ) ) ) ) )),
% 0.47/1.09 define([status(thm)])).
% 0.47/1.09 thf(powersetsubset, axiom, powersetsubset =
% 0.47/1.09 (![A:$i,B:$i]:
% 0.47/1.09 ( ( subset @ A @ B ) => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ))).
% 0.47/1.09 thf('13', plain,
% 0.47/1.09 (( powersetsubset ) =
% 0.47/1.09 ( ![X4:$i,X6:$i]:
% 0.47/1.09 ( ( subset @ X4 @ X6 ) =>
% 0.47/1.09 ( subset @ ( powerset @ X4 ) @ ( powerset @ X6 ) ) ) )),
% 0.47/1.09 define([status(thm)])).
% 0.47/1.09 thf(inPowerset, axiom, inPowerset = (![A:$i]: ( in @ A @ ( powerset @ A ) ))).
% 0.47/1.09 thf('14', plain,
% 0.47/1.09 (( inPowerset ) = ( ![X4:$i]: ( in @ X4 @ ( powerset @ X4 ) ) )),
% 0.47/1.09 define([status(thm)])).
% 0.47/1.09 thf(powersetE1, axiom, powersetE1 =
% 0.47/1.09 (![A:$i,B:$i]: ( ( in @ B @ ( powerset @ A ) ) => ( subset @ B @ A ) ))).
% 0.47/1.09 thf('15', plain,
% 0.47/1.09 (( powersetE1 ) =
% 0.47/1.09 ( ![X4:$i,X6:$i]:
% 0.47/1.09 ( ( in @ X6 @ ( powerset @ X4 ) ) => ( subset @ X6 @ X4 ) ) )),
% 0.47/1.09 define([status(thm)])).
% 0.47/1.09 thf(powersetI1, axiom, powersetI1 =
% 0.47/1.09 (![A:$i,B:$i]: ( ( subset @ B @ A ) => ( in @ B @ ( powerset @ A ) ) ))).
% 0.47/1.09 thf('16', plain,
% 0.47/1.09 (( powersetI1 ) =
% 0.47/1.09 ( ![X4:$i,X6:$i]:
% 0.47/1.09 ( ( subset @ X6 @ X4 ) => ( in @ X6 @ ( powerset @ X4 ) ) ) )),
% 0.47/1.09 define([status(thm)])).
% 0.47/1.09 thf(subset2powerset, axiom, subset2powerset =
% 0.47/1.09 (![A:$i,B:$i]: ( ( subset @ A @ B ) => ( in @ A @ ( powerset @ B ) ) ))).
% 0.47/1.09 thf('17', plain,
% 0.47/1.09 (( subset2powerset ) =
% 0.47/1.09 ( ![X4:$i,X6:$i]:
% 0.47/1.09 ( ( subset @ X4 @ X6 ) => ( in @ X4 @ ( powerset @ X6 ) ) ) )),
% 0.47/1.09 define([status(thm)])).
% 0.47/1.09 thf(powerset__Cong, axiom, powerset__Cong =
% 0.47/1.09 (![A:$i,B:$i]:
% 0.47/1.09 ( ( ( A ) = ( B ) ) => ( ( powerset @ A ) = ( powerset @ B ) ) ))).
% 0.47/1.09 thf('18', plain,
% 0.47/1.09 (( powerset__Cong ) =
% 0.47/1.09 ( ![X4:$i,X6:$i]:
% 0.47/1.09 ( ( ( X4 ) = ( X6 ) ) => ( ( powerset @ X4 ) = ( powerset @ X6 ) ) ) )),
% 0.47/1.09 define([status(thm)])).
% 0.47/1.09 thf(powersetE, axiom, powersetE =
% 0.47/1.09 (![A:$i,B:$i,Xx:$i]:
% 0.47/1.09 ( ( in @ B @ ( powerset @ A ) ) => ( ( in @ Xx @ B ) => ( in @ Xx @ A ) ) ))).
% 0.47/1.09 thf('19', plain,
% 0.47/1.09 (( powersetE ) =
% 0.47/1.09 ( ![X4:$i,X6:$i,X8:$i]:
% 0.47/1.09 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 0.47/1.09 ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ) )),
% 0.47/1.09 define([status(thm)])).
% 0.47/1.09 thf(emptyInPowerset, axiom, emptyInPowerset =
% 0.47/1.09 (![A:$i]: ( in @ emptyset @ ( powerset @ A ) ))).
% 0.47/1.09 thf('20', plain,
% 0.47/1.09 (( emptyInPowerset ) =
% 0.47/1.09 ( ![X4:$i]: ( in @ emptyset @ ( powerset @ X4 ) ) )),
% 0.47/1.09 define([status(thm)])).
% 0.47/1.09 thf(emptyinPowerset, axiom, emptyinPowerset =
% 0.47/1.09 (![A:$i]: ( in @ emptyset @ ( powerset @ A ) ))).
% 0.47/1.09 thf('21', plain,
% 0.47/1.09 (( emptyinPowerset ) =
% 0.47/1.09 ( ![X4:$i]: ( in @ emptyset @ ( powerset @ X4 ) ) )),
% 0.47/1.09 define([status(thm)])).
% 0.47/1.09 thf(powersetI, axiom, powersetI =
% 0.47/1.09 (![A:$i,B:$i]:
% 0.47/1.09 ( ( ![Xx:$i]: ( ( in @ Xx @ B ) => ( in @ Xx @ A ) ) ) =>
% 0.47/1.09 ( in @ B @ ( powerset @ A ) ) ))).
% 0.47/1.09 thf('22', plain,
% 0.47/1.09 (( powersetI ) =
% 0.47/1.09 ( ![X4:$i,X6:$i]:
% 0.47/1.09 ( ( ![X8:$i]: ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ) =>
% 0.47/1.09 ( in @ X6 @ ( powerset @ X4 ) ) ) )),
% 0.47/1.09 define([status(thm)])).
% 0.47/1.09 thf(powersetAx, axiom, powersetAx =
% 0.47/1.09 (![A:$i,B:$i]:
% 0.47/1.09 ( ( in @ B @ ( powerset @ A ) ) <=>
% 0.47/1.09 ( ![Xx:$i]: ( ( in @ Xx @ B ) => ( in @ Xx @ A ) ) ) ))).
% 0.47/1.09 thf('23', plain,
% 0.47/1.09 (( powersetAx ) =
% 0.47/1.09 ( ![X4:$i,X6:$i]:
% 0.47/1.09 ( ( in @ X6 @ ( powerset @ X4 ) ) <=>
% 0.47/1.09 ( ![X8:$i]: ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ) ) )),
% 0.47/1.09 define([status(thm)])).
% 0.47/1.09 thf(complementT_lem, conjecture,
% 0.47/1.09 (( setextAx ) =>
% 0.47/1.09 ( ( emptysetAx ) =>
% 0.47/1.09 ( ( setadjoinAx ) =>
% 0.47/1.09 ( ( powersetAx ) =>
% 0.47/1.09 ( ( setunionAx ) =>
% 0.47/1.09 ( ( omega0Ax ) =>
% 0.47/1.09 ( ( omegaSAx ) =>
% 0.47/1.09 ( ( omegaIndAx ) =>
% 0.47/1.09 ( ( replAx ) =>
% 0.47/1.09 ( ( foundationAx ) =>
% 0.47/1.09 ( ( wellorderingAx ) =>
% 0.47/1.09 ( ( descrp ) =>
% 0.47/1.09 ( ( dsetconstrI ) =>
% 0.47/1.09 ( ( dsetconstrEL ) =>
% 0.47/1.09 ( ( dsetconstrER ) =>
% 0.47/1.09 ( ( exuE1 ) =>
% 0.47/1.09 ( ( prop2setE ) =>
% 0.47/1.09 ( ( emptysetE ) =>
% 0.47/1.09 ( ( emptysetimpfalse ) =>
% 0.47/1.09 ( ( notinemptyset ) =>
% 0.47/1.09 ( ( exuE3e ) =>
% 0.47/1.09 ( ( setext ) =>
% 0.47/1.09 ( ( emptyI ) =>
% 0.47/1.09 ( ( noeltsimpempty ) =>
% 0.47/1.09 ( ( setbeta ) =>
% 0.47/1.09 ( ( nonemptyE1 ) =>
% 0.47/1.09 ( ( nonemptyI ) =>
% 0.47/1.09 ( ( nonemptyI1 ) =>
% 0.47/1.09 ( ( setadjoinIL ) =>
% 0.47/1.09 ( ( emptyinunitempty ) =>
% 0.47/1.09 ( ( setadjoinIR ) =>
% 0.47/1.09 ( ( setadjoinE ) =>
% 0.47/1.09 ( (
% 0.47/1.09 setadjoinOr ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 setoftrueEq ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 powersetI ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 emptyinPowerset ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 emptyInPowerset ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 powersetE ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 setunionI ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 setunionE ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 subPowSU ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 exuE2 ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 nonemptyImpWitness ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 uniqinunit ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 notinsingleton ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 eqinunit ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 singletonsswitch ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 upairsetE ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 upairsetIL ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 upairsetIR ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 emptyE1 ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 vacuousDall ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 quantDeMorgan1 ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 quantDeMorgan2 ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 quantDeMorgan3 ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 quantDeMorgan4 ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 prop2setI ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 prop2set2propI ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 notdexE ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 notdallE ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 exuI1 ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 exuI3 ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 exuI2 ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 inCongP ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 in__Cong ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 exuE3u ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 exu__Cong ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 emptyset__Cong ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 setadjoin__Cong ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 powerset__Cong ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 setunion__Cong ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 omega__Cong ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 exuEu ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 descr__Cong ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 dsetconstr__Cong ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 subsetI1 ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 eqimpsubset2 ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 eqimpsubset1 ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 subsetI2 ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 emptysetsubset ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 subsetE ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 subsetE2 ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 notsubsetI ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 notequalI1 ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 notequalI2 ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 subsetRefl ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 subsetTrans ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 setadjoinSub ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 setadjoinSub2 ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 subset2powerset ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 setextsub ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 subsetemptysetimpeq ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 powersetI1 ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 powersetE1 ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 inPowerset ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 powersetsubset ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 sepInPowerset ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 sepSubset ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 binunionIL ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 upairset2IR ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 binunionIR ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 binunionEcases ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 binunionE ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 binunionLsub ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 binunionRsub ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 binintersectI ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 binintersectSubset5 ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 binintersectEL ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 binintersectLsub ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 binintersectSubset2 ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 binintersectSubset3 ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 binintersectER ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 disjointsetsI1 ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 binintersectRsub ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 binintersectSubset4 ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 binintersectSubset1 ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 bs114d ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 setminusI ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 setminusEL ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 setminusER ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 setminusSubset2 ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 setminusERneg ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 setminusELneg ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 setminusILneg ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 setminusIRneg ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 setminusLsub ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 setminusSubset1 ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 symdiffE ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 symdiffI1 ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 symdiffI2 ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 symdiffIneg1 ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 symdiffIneg2 ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 secondinupair ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 setukpairIL ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 setukpairIR ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 kpairiskpair ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 kpairp ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 singletonsubset ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 singletoninpowerset ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 singletoninpowunion ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 upairset2E ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 upairsubunion ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 upairinpowunion ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 ubforcartprodlem1 ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 ubforcartprodlem2 ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 ubforcartprodlem3 ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 cartprodpairin ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 cartprodmempair1 ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 cartprodmempair ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 setunionE2 ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 setunionsingleton1 ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 setunionsingleton2 ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 setunionsingleton ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 singletonprop ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 ex1E1 ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 ex1I ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 ex1I2 ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 singletonsuniq ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 setukpairinjL1 ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 kfstsingleton ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 theprop ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 kfstpairEq ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 cartprodfstin ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 setukpairinjL2 ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 setukpairinjL ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 setukpairinjR11 ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 setukpairinjR12 ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 setukpairinjR1 ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 upairequniteq ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 setukpairinjR2 ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 setukpairinjR ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 ksndsingleton ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 ksndpairEq ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 kpairsurjEq ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 cartprodsndin ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 cartprodpairmemEL ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 cartprodpairmemER ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 cartprodmempaircEq ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 cartprodfstpairEq ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 cartprodsndpairEq ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 cartprodpairsurjEq ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 dpsetconstrI ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 dpsetconstrSub ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 setOfPairsIsBReln ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 dpsetconstrERa ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 dpsetconstrEL1 ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 dpsetconstrEL2 ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 dpsetconstrER ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 funcImageSingleton ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 apProp ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 app ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 infuncsetfunc ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 ap2p ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 funcinfuncset ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 lamProp ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 lamp ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 lam2p ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 brelnall1 ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 brelnall2 ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 ex1E2 ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 funcGraphProp1 ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 funcGraphProp3 ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 funcGraphProp2 ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 funcextLem ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 funcGraphProp4 ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 subbreln ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 eqbreln ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 funcext ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 funcext2 ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 ap2apEq1 ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 ap2apEq2 ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 beta1 ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 eta1 ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 lam2lamEq ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 beta2 ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 eta2 ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 iffalseProp1 ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 iffalseProp2 ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 iftrueProp1 ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 iftrueProp2 ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 ifSingleton ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 ifp ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 theeq ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 iftrue ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 iffalse ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 iftrueorfalse ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 binintersectT_lem ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 binunionT_lem ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 powersetT_lem ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 setminusT_lem ) =>
% 0.47/1.09 (
% 0.47/1.09 ![
% 0.47/1.09 A:$i,X:$i]:
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 in @
% 0.47/1.09 X @
% 0.47/1.09 (
% 0.47/1.09 powerset @
% 0.47/1.09 A ) ) =>
% 0.47/1.09 (
% 0.47/1.09 in @
% 0.47/1.09 (
% 0.47/1.09 setminus @
% 0.47/1.09 A @ X ) @
% 0.47/1.09 (
% 0.47/1.09 powerset @
% 0.47/1.09 A ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 0.47/1.09 thf(zf_stmt_0, conjecture,
% 0.47/1.09 (( setextAx ) =>
% 0.47/1.09 ( ( emptysetAx ) =>
% 0.47/1.09 ( ( setadjoinAx ) =>
% 0.47/1.09 ( ( ![X4:$i,X6:$i]:
% 0.47/1.09 ( ( in @ X6 @ ( powerset @ X4 ) ) <=>
% 0.47/1.09 ( ![X8:$i]: ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ) ) ) =>
% 0.47/1.09 ( ( setunionAx ) =>
% 0.47/1.09 ( ( omega0Ax ) =>
% 0.47/1.09 ( ( omegaSAx ) =>
% 0.47/1.09 ( ( omegaIndAx ) =>
% 0.47/1.09 ( ( replAx ) =>
% 0.47/1.09 ( ( foundationAx ) =>
% 0.47/1.09 ( ( wellorderingAx ) =>
% 0.47/1.09 ( ( descrp ) =>
% 0.47/1.09 ( ( dsetconstrI ) =>
% 0.47/1.09 ( ( dsetconstrEL ) =>
% 0.47/1.09 ( ( dsetconstrER ) =>
% 0.47/1.09 ( ( exuE1 ) =>
% 0.47/1.09 ( ( prop2setE ) =>
% 0.47/1.09 ( ( emptysetE ) =>
% 0.47/1.09 ( ( emptysetimpfalse ) =>
% 0.47/1.09 ( ( notinemptyset ) =>
% 0.47/1.09 ( ( exuE3e ) =>
% 0.47/1.09 ( ( setext ) =>
% 0.47/1.09 ( ( emptyI ) =>
% 0.47/1.09 ( ( noeltsimpempty ) =>
% 0.47/1.09 ( ( setbeta ) =>
% 0.47/1.09 ( ( nonemptyE1 ) =>
% 0.47/1.09 ( ( nonemptyI ) =>
% 0.47/1.09 ( ( nonemptyI1 ) =>
% 0.47/1.09 ( ( setadjoinIL ) =>
% 0.47/1.09 ( ( emptyinunitempty ) =>
% 0.47/1.09 ( ( setadjoinIR ) =>
% 0.47/1.09 ( ( setadjoinE ) =>
% 0.47/1.09 ( (
% 0.47/1.09 setadjoinOr ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 setoftrueEq ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 ![
% 0.47/1.09 X10:$i,
% 0.47/1.09 X12:$i]:
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 ![
% 0.47/1.09 X14:$i]:
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 in @
% 0.47/1.09 X14 @ X12 ) =>
% 0.47/1.09 (
% 0.47/1.09 in @
% 0.47/1.09 X14 @ X10 ) ) ) =>
% 0.47/1.09 (
% 0.47/1.09 in @
% 0.47/1.09 X12 @
% 0.47/1.09 (
% 0.47/1.09 powerset @
% 0.47/1.09 X10 ) ) ) ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 ![
% 0.47/1.09 X16:$i]:
% 0.47/1.09 (
% 0.47/1.09 in @
% 0.47/1.09 emptyset @
% 0.47/1.09 (
% 0.47/1.09 powerset @
% 0.47/1.09 X16 ) ) ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 ![
% 0.47/1.09 X18:$i]:
% 0.47/1.09 (
% 0.47/1.09 in @
% 0.47/1.09 emptyset @
% 0.47/1.09 (
% 0.47/1.09 powerset @
% 0.47/1.09 X18 ) ) ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 ![
% 0.47/1.09 X20:$i,
% 0.47/1.09 X22:$i,
% 0.47/1.09 X24:$i]:
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 in @
% 0.47/1.09 X22 @
% 0.47/1.09 (
% 0.47/1.09 powerset @
% 0.47/1.09 X20 ) ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 in @
% 0.47/1.09 X24 @ X22 ) =>
% 0.47/1.09 (
% 0.47/1.09 in @
% 0.47/1.09 X24 @ X20 ) ) ) ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 setunionI ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 setunionE ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 subPowSU ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 exuE2 ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 nonemptyImpWitness ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 uniqinunit ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 notinsingleton ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 eqinunit ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 singletonsswitch ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 upairsetE ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 upairsetIL ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 upairsetIR ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 emptyE1 ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 vacuousDall ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 quantDeMorgan1 ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 quantDeMorgan2 ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 quantDeMorgan3 ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 quantDeMorgan4 ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 prop2setI ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 prop2set2propI ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 notdexE ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 notdallE ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 exuI1 ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 exuI3 ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 exuI2 ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 inCongP ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 in__Cong ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 exuE3u ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 exu__Cong ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 emptyset__Cong ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 setadjoin__Cong ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 ![
% 0.47/1.09 X26:$i,
% 0.47/1.09 X28:$i]:
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 X26 ) =
% 0.47/1.09 (
% 0.47/1.09 X28 ) ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 powerset @
% 0.47/1.09 X26 ) =
% 0.47/1.09 (
% 0.47/1.09 powerset @
% 0.47/1.09 X28 ) ) ) ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 setunion__Cong ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 omega__Cong ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 exuEu ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 descr__Cong ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 dsetconstr__Cong ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 subsetI1 ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 eqimpsubset2 ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 eqimpsubset1 ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 subsetI2 ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 emptysetsubset ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 subsetE ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 subsetE2 ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 notsubsetI ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 notequalI1 ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 notequalI2 ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 subsetRefl ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 subsetTrans ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 setadjoinSub ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 setadjoinSub2 ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 ![
% 0.47/1.09 X30:$i,
% 0.47/1.09 X32:$i]:
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 subset @
% 0.47/1.09 X30 @ X32 ) =>
% 0.47/1.09 (
% 0.47/1.09 in @
% 0.47/1.09 X30 @
% 0.47/1.09 (
% 0.47/1.09 powerset @
% 0.47/1.09 X32 ) ) ) ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 setextsub ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 subsetemptysetimpeq ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 ![
% 0.47/1.09 X34:$i,
% 0.47/1.09 X36:$i]:
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 subset @
% 0.47/1.09 X36 @ X34 ) =>
% 0.47/1.09 (
% 0.47/1.09 in @
% 0.47/1.09 X36 @
% 0.47/1.09 (
% 0.47/1.09 powerset @
% 0.47/1.09 X34 ) ) ) ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 ![
% 0.47/1.09 X38:$i,
% 0.47/1.09 X40:$i]:
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 in @
% 0.47/1.09 X40 @
% 0.47/1.09 (
% 0.47/1.09 powerset @
% 0.47/1.09 X38 ) ) =>
% 0.47/1.09 (
% 0.47/1.09 subset @
% 0.47/1.09 X40 @ X38 ) ) ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 ![
% 0.47/1.09 X42:$i]:
% 0.47/1.09 (
% 0.47/1.09 in @
% 0.47/1.09 X42 @
% 0.47/1.09 (
% 0.47/1.09 powerset @
% 0.47/1.09 X42 ) ) ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 ![
% 0.47/1.09 X44:$i,
% 0.47/1.09 X46:$i]:
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 subset @
% 0.47/1.09 X44 @ X46 ) =>
% 0.47/1.09 (
% 0.47/1.09 subset @
% 0.47/1.09 (
% 0.47/1.09 powerset @
% 0.47/1.09 X44 ) @
% 0.47/1.09 (
% 0.47/1.09 powerset @
% 0.47/1.09 X46 ) ) ) ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 sepInPowerset ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 sepSubset ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 binunionIL ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 upairset2IR ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 binunionIR ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 binunionEcases ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 binunionE ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 binunionLsub ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 binunionRsub ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 binintersectI ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 binintersectSubset5 ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 binintersectEL ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 binintersectLsub ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 binintersectSubset2 ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 binintersectSubset3 ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 binintersectER ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 disjointsetsI1 ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 binintersectRsub ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 binintersectSubset4 ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 binintersectSubset1 ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 bs114d ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 ![
% 0.47/1.09 X48:$i,
% 0.47/1.09 X50:$i,
% 0.47/1.09 X52:$i]:
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 in @
% 0.47/1.09 X52 @ X48 ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 ~(
% 0.47/1.09 in @
% 0.47/1.09 X52 @ X50 ) ) =>
% 0.47/1.09 (
% 0.47/1.09 in @
% 0.47/1.09 X52 @
% 0.47/1.09 (
% 0.47/1.09 setminus @
% 0.47/1.09 X48 @ X50 ) ) ) ) ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 ![
% 0.47/1.09 X54:$i,
% 0.47/1.09 X56:$i,
% 0.47/1.09 X58:$i]:
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 in @
% 0.47/1.09 X58 @
% 0.47/1.09 (
% 0.47/1.09 setminus @
% 0.47/1.09 X54 @ X56 ) ) =>
% 0.47/1.09 (
% 0.47/1.09 in @
% 0.47/1.09 X58 @ X54 ) ) ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 ![
% 0.47/1.09 X60:$i,
% 0.47/1.09 X62:$i,
% 0.47/1.09 X64:$i]:
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 in @
% 0.47/1.09 X64 @
% 0.47/1.09 (
% 0.47/1.09 setminus @
% 0.47/1.09 X60 @ X62 ) ) =>
% 0.47/1.09 (
% 0.47/1.09 ~(
% 0.47/1.09 in @
% 0.47/1.09 X64 @ X62 ) ) ) ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 ![
% 0.47/1.09 X66:$i,
% 0.47/1.09 X68:$i]:
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 subset @
% 0.47/1.09 X66 @ X68 ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 setminus @
% 0.47/1.09 X66 @ X68 ) =
% 0.47/1.09 (
% 0.47/1.09 emptyset ) ) ) ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 ![
% 0.47/1.09 X70:$i,
% 0.47/1.09 X72:$i,
% 0.47/1.09 X74:$i]:
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 ~(
% 0.47/1.09 in @
% 0.47/1.09 X74 @
% 0.47/1.09 (
% 0.47/1.09 setminus
% 0.47/1.09 @
% 0.47/1.09 X70 @ X72 ) ) ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 in @
% 0.47/1.09 X74 @ X70 ) =>
% 0.47/1.09 (
% 0.47/1.09 in @
% 0.47/1.09 X74 @ X72 ) ) ) ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 ![
% 0.47/1.09 X76:$i,
% 0.47/1.09 X78:$i,
% 0.47/1.09 X80:$i]:
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 ~(
% 0.47/1.09 in @
% 0.47/1.09 X80 @
% 0.47/1.09 (
% 0.47/1.09 setminus
% 0.47/1.09 @
% 0.47/1.09 X76 @ X78 ) ) ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 ~(
% 0.47/1.09 in @
% 0.47/1.09 X80 @ X78 ) ) =>
% 0.47/1.09 (
% 0.47/1.09 ~(
% 0.47/1.09 in @
% 0.47/1.09 X80 @ X76 ) ) ) ) ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 ![
% 0.47/1.09 X82:$i,
% 0.47/1.09 X84:$i,
% 0.47/1.09 X86:$i]:
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 ~(
% 0.47/1.09 in @
% 0.47/1.09 X86 @ X82 ) ) =>
% 0.47/1.09 (
% 0.47/1.09 ~(
% 0.47/1.09 in @
% 0.47/1.09 X86 @
% 0.47/1.09 (
% 0.47/1.09 setminus
% 0.47/1.09 @
% 0.47/1.09 X82 @ X84 ) ) ) ) ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 ![
% 0.47/1.09 X88:$i,
% 0.47/1.09 X90:$i,
% 0.47/1.09 X92:$i]:
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 in @
% 0.47/1.09 X92 @ X90 ) =>
% 0.47/1.09 (
% 0.47/1.09 ~(
% 0.47/1.09 in @
% 0.47/1.09 X92 @
% 0.47/1.09 (
% 0.47/1.09 setminus
% 0.47/1.09 @
% 0.47/1.09 X88 @ X90 ) ) ) ) ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 ![
% 0.47/1.09 X94:$i,
% 0.47/1.09 X96:$i]:
% 0.47/1.09 (
% 0.47/1.09 subset @
% 0.47/1.09 (
% 0.47/1.09 setminus @
% 0.47/1.09 X94 @ X96 ) @
% 0.47/1.09 X94 ) ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 ![
% 0.47/1.09 X98:$i,
% 0.47/1.09 X100:$i]:
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 setminus @
% 0.47/1.09 X98 @ X100 ) =
% 0.47/1.09 (
% 0.47/1.09 emptyset ) ) =>
% 0.47/1.09 (
% 0.47/1.09 subset @
% 0.47/1.09 X98 @ X100 ) ) ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 symdiffE ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 symdiffI1 ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 symdiffI2 ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 symdiffIneg1 ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 symdiffIneg2 ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 secondinupair ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 setukpairIL ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 setukpairIR ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 kpairiskpair ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 kpairp ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 singletonsubset ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 ![
% 0.47/1.09 X102:$i,
% 0.47/1.09 X104:$i]:
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 in @
% 0.47/1.09 X104 @
% 0.47/1.09 X102 ) =>
% 0.47/1.09 (
% 0.47/1.09 in @
% 0.47/1.09 (
% 0.47/1.09 setadjoin
% 0.47/1.09 @
% 0.47/1.09 X104 @
% 0.47/1.09 emptyset ) @
% 0.47/1.09 (
% 0.47/1.09 powerset @
% 0.47/1.09 X102 ) ) ) ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 singletoninpowunion ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 upairset2E ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 upairsubunion ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 upairinpowunion ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 ubforcartprodlem1 ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 ubforcartprodlem2 ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 ubforcartprodlem3 ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 cartprodpairin ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 cartprodmempair1 ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 cartprodmempair ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 setunionE2 ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 setunionsingleton1 ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 setunionsingleton2 ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 setunionsingleton ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 singletonprop ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 ex1E1 ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 ex1I ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 ex1I2 ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 singletonsuniq ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 setukpairinjL1 ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 kfstsingleton ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 theprop ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 kfstpairEq ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 cartprodfstin ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 setukpairinjL2 ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 setukpairinjL ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 setukpairinjR11 ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 setukpairinjR12 ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 setukpairinjR1 ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 upairequniteq ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 setukpairinjR2 ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 setukpairinjR ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 ksndsingleton ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 ksndpairEq ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 kpairsurjEq ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 cartprodsndin ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 cartprodpairmemEL ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 cartprodpairmemER ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 cartprodmempaircEq ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 cartprodfstpairEq ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 cartprodsndpairEq ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 cartprodpairsurjEq ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 dpsetconstrI ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 dpsetconstrSub ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 setOfPairsIsBReln ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 dpsetconstrERa ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 dpsetconstrEL1 ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 dpsetconstrEL2 ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 dpsetconstrER ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 funcImageSingleton ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 apProp ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 app ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 infuncsetfunc ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 ap2p ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 funcinfuncset ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 lamProp ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 lamp ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 lam2p ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 brelnall1 ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 brelnall2 ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 ex1E2 ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 funcGraphProp1 ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 funcGraphProp3 ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 funcGraphProp2 ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 funcextLem ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 funcGraphProp4 ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 subbreln ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 eqbreln ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 funcext ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 funcext2 ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 ap2apEq1 ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 ap2apEq2 ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 beta1 ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 eta1 ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 lam2lamEq ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 beta2 ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 eta2 ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 iffalseProp1 ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 iffalseProp2 ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 iftrueProp1 ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 iftrueProp2 ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 ifSingleton ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 ifp ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 theeq ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 iftrue ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 iffalse ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 iftrueorfalse ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 binintersectT_lem ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 binunionT_lem ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 ![
% 0.47/1.09 X106:$i,
% 0.47/1.09 X108:$i]:
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 in @
% 0.47/1.09 X108 @
% 0.47/1.09 (
% 0.47/1.09 powerset @
% 0.47/1.09 X106 ) ) =>
% 0.47/1.09 (
% 0.47/1.09 in @
% 0.47/1.09 (
% 0.47/1.09 powerset @
% 0.47/1.09 X108 ) @
% 0.47/1.09 (
% 0.47/1.09 powerset @
% 0.47/1.09 (
% 0.47/1.09 powerset @
% 0.47/1.09 X106 ) ) ) ) ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 ![
% 0.47/1.09 X110:$i,
% 0.47/1.09 X112:$i]:
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 in @
% 0.47/1.09 X112 @
% 0.47/1.09 (
% 0.47/1.09 powerset @
% 0.47/1.09 X110 ) ) =>
% 0.47/1.09 (
% 0.47/1.09 ![
% 0.47/1.09 X114:$i]:
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 in @
% 0.47/1.09 X114 @
% 0.47/1.09 (
% 0.47/1.09 powerset @
% 0.47/1.09 X110 ) ) =>
% 0.47/1.09 (
% 0.47/1.09 in @
% 0.47/1.09 (
% 0.47/1.09 setminus @
% 0.47/1.09 X112 @
% 0.47/1.09 X114 ) @
% 0.47/1.09 (
% 0.47/1.09 powerset @
% 0.47/1.09 X110 ) ) ) ) ) ) =>
% 0.47/1.09 (
% 0.47/1.09 ![
% 0.47/1.09 X116:$i,
% 0.47/1.09 X118:$i]:
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 in @
% 0.47/1.09 X118 @
% 0.47/1.09 (
% 0.47/1.09 powerset @
% 0.47/1.09 X116 ) ) =>
% 0.47/1.09 (
% 0.47/1.09 in @
% 0.47/1.09 (
% 0.47/1.09 setminus @
% 0.47/1.09 X116 @
% 0.47/1.09 X118 ) @
% 0.47/1.09 (
% 0.47/1.09 powerset @
% 0.47/1.09 X116 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 0.47/1.09 thf(zf_stmt_1, type, zip_tseitin_0 : $i > $i > $i > $o).
% 0.47/1.09 thf(zf_stmt_2, axiom,
% 0.47/1.09 (![X8:$i,X6:$i,X4:$i]:
% 0.47/1.09 ( ( zip_tseitin_0 @ X8 @ X6 @ X4 ) <=>
% 0.47/1.09 ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ))).
% 0.47/1.09 thf(zf_stmt_3, conjecture,
% 0.47/1.09 (( setextAx ) =>
% 0.47/1.09 ( ( emptysetAx ) =>
% 0.47/1.09 ( ( setadjoinAx ) =>
% 0.47/1.09 ( ( ![X4:$i,X6:$i]:
% 0.47/1.09 ( ( in @ X6 @ ( powerset @ X4 ) ) <=>
% 0.47/1.09 ( ![X8:$i]: ( zip_tseitin_0 @ X8 @ X6 @ X4 ) ) ) ) =>
% 0.47/1.09 ( ( setunionAx ) =>
% 0.47/1.09 ( ( omega0Ax ) =>
% 0.47/1.09 ( ( omegaSAx ) =>
% 0.47/1.09 ( ( omegaIndAx ) =>
% 0.47/1.09 ( ( replAx ) =>
% 0.47/1.09 ( ( foundationAx ) =>
% 0.47/1.09 ( ( wellorderingAx ) =>
% 0.47/1.09 ( ( descrp ) =>
% 0.47/1.09 ( ( dsetconstrI ) =>
% 0.47/1.09 ( ( dsetconstrEL ) =>
% 0.47/1.09 ( ( dsetconstrER ) =>
% 0.47/1.09 ( ( exuE1 ) =>
% 0.47/1.09 ( ( prop2setE ) =>
% 0.47/1.09 ( ( emptysetE ) =>
% 0.47/1.09 ( ( emptysetimpfalse ) =>
% 0.47/1.09 ( ( notinemptyset ) =>
% 0.47/1.09 ( ( exuE3e ) =>
% 0.47/1.09 ( ( setext ) =>
% 0.47/1.09 ( ( emptyI ) =>
% 0.47/1.09 ( ( noeltsimpempty ) =>
% 0.47/1.09 ( ( setbeta ) =>
% 0.47/1.09 ( ( nonemptyE1 ) =>
% 0.47/1.09 ( ( nonemptyI ) =>
% 0.47/1.09 ( ( nonemptyI1 ) =>
% 0.47/1.09 ( ( setadjoinIL ) =>
% 0.47/1.09 ( ( emptyinunitempty ) =>
% 0.47/1.09 ( ( setadjoinIR ) =>
% 0.47/1.09 ( ( setadjoinE ) =>
% 0.47/1.09 ( (
% 0.47/1.09 setadjoinOr ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 setoftrueEq ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 ![
% 0.47/1.09 X10:$i,
% 0.47/1.09 X12:$i]:
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 ![
% 0.47/1.09 X14:$i]:
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 in @
% 0.47/1.09 X14 @ X12 ) =>
% 0.47/1.09 (
% 0.47/1.09 in @
% 0.47/1.09 X14 @ X10 ) ) ) =>
% 0.47/1.09 (
% 0.47/1.09 in @
% 0.47/1.09 X12 @
% 0.47/1.09 (
% 0.47/1.09 powerset @
% 0.47/1.09 X10 ) ) ) ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 ![
% 0.47/1.09 X16:$i]:
% 0.47/1.09 (
% 0.47/1.09 in @
% 0.47/1.09 emptyset @
% 0.47/1.09 (
% 0.47/1.09 powerset @
% 0.47/1.09 X16 ) ) ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 ![
% 0.47/1.09 X18:$i]:
% 0.47/1.09 (
% 0.47/1.09 in @
% 0.47/1.09 emptyset @
% 0.47/1.09 (
% 0.47/1.09 powerset @
% 0.47/1.09 X18 ) ) ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 ![
% 0.47/1.09 X20:$i,
% 0.47/1.09 X22:$i,
% 0.47/1.09 X24:$i]:
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 in @
% 0.47/1.09 X22 @
% 0.47/1.09 (
% 0.47/1.09 powerset @
% 0.47/1.09 X20 ) ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 in @
% 0.47/1.09 X24 @ X22 ) =>
% 0.47/1.09 (
% 0.47/1.09 in @
% 0.47/1.09 X24 @ X20 ) ) ) ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 setunionI ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 setunionE ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 subPowSU ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 exuE2 ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 nonemptyImpWitness ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 uniqinunit ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 notinsingleton ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 eqinunit ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 singletonsswitch ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 upairsetE ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 upairsetIL ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 upairsetIR ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 emptyE1 ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 vacuousDall ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 quantDeMorgan1 ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 quantDeMorgan2 ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 quantDeMorgan3 ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 quantDeMorgan4 ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 prop2setI ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 prop2set2propI ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 notdexE ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 notdallE ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 exuI1 ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 exuI3 ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 exuI2 ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 inCongP ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 in__Cong ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 exuE3u ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 exu__Cong ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 emptyset__Cong ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 setadjoin__Cong ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 ![
% 0.47/1.09 X26:$i,
% 0.47/1.09 X28:$i]:
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 X26 ) =
% 0.47/1.09 (
% 0.47/1.09 X28 ) ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 powerset @
% 0.47/1.09 X26 ) =
% 0.47/1.09 (
% 0.47/1.09 powerset @
% 0.47/1.09 X28 ) ) ) ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 setunion__Cong ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 omega__Cong ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 exuEu ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 descr__Cong ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 dsetconstr__Cong ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 subsetI1 ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 eqimpsubset2 ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 eqimpsubset1 ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 subsetI2 ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 emptysetsubset ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 subsetE ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 subsetE2 ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 notsubsetI ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 notequalI1 ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 notequalI2 ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 subsetRefl ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 subsetTrans ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 setadjoinSub ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 setadjoinSub2 ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 ![
% 0.47/1.09 X30:$i,
% 0.47/1.09 X32:$i]:
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 subset @
% 0.47/1.09 X30 @ X32 ) =>
% 0.47/1.09 (
% 0.47/1.09 in @
% 0.47/1.09 X30 @
% 0.47/1.09 (
% 0.47/1.09 powerset @
% 0.47/1.09 X32 ) ) ) ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 setextsub ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 subsetemptysetimpeq ) =>
% 0.47/1.09 (
% 0.47/1.09 (
% 0.47/1.09 ![
% 0.47/1.09 X34:$i,
% 0.47/1.09 X36:$i]:
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 subset @
% 0.47/1.10 X36 @ X34 ) =>
% 0.47/1.10 (
% 0.47/1.10 in @
% 0.47/1.10 X36 @
% 0.47/1.10 (
% 0.47/1.10 powerset @
% 0.47/1.10 X34 ) ) ) ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 ![
% 0.47/1.10 X38:$i,
% 0.47/1.10 X40:$i]:
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 in @
% 0.47/1.10 X40 @
% 0.47/1.10 (
% 0.47/1.10 powerset @
% 0.47/1.10 X38 ) ) =>
% 0.47/1.10 (
% 0.47/1.10 subset @
% 0.47/1.10 X40 @ X38 ) ) ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 ![
% 0.47/1.10 X42:$i]:
% 0.47/1.10 (
% 0.47/1.10 in @
% 0.47/1.10 X42 @
% 0.47/1.10 (
% 0.47/1.10 powerset @
% 0.47/1.10 X42 ) ) ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 ![
% 0.47/1.10 X44:$i,
% 0.47/1.10 X46:$i]:
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 subset @
% 0.47/1.10 X44 @ X46 ) =>
% 0.47/1.10 (
% 0.47/1.10 subset @
% 0.47/1.10 (
% 0.47/1.10 powerset @
% 0.47/1.10 X44 ) @
% 0.47/1.10 (
% 0.47/1.10 powerset @
% 0.47/1.10 X46 ) ) ) ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 sepInPowerset ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 sepSubset ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 binunionIL ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 upairset2IR ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 binunionIR ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 binunionEcases ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 binunionE ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 binunionLsub ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 binunionRsub ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 binintersectI ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 binintersectSubset5 ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 binintersectEL ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 binintersectLsub ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 binintersectSubset2 ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 binintersectSubset3 ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 binintersectER ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 disjointsetsI1 ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 binintersectRsub ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 binintersectSubset4 ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 binintersectSubset1 ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 bs114d ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 ![
% 0.47/1.10 X48:$i,
% 0.47/1.10 X50:$i,
% 0.47/1.10 X52:$i]:
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 in @
% 0.47/1.10 X52 @ X48 ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 ~(
% 0.47/1.10 in @
% 0.47/1.10 X52 @ X50 ) ) =>
% 0.47/1.10 (
% 0.47/1.10 in @
% 0.47/1.10 X52 @
% 0.47/1.10 (
% 0.47/1.10 setminus @
% 0.47/1.10 X48 @ X50 ) ) ) ) ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 ![
% 0.47/1.10 X54:$i,
% 0.47/1.10 X56:$i,
% 0.47/1.10 X58:$i]:
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 in @
% 0.47/1.10 X58 @
% 0.47/1.10 (
% 0.47/1.10 setminus @
% 0.47/1.10 X54 @ X56 ) ) =>
% 0.47/1.10 (
% 0.47/1.10 in @
% 0.47/1.10 X58 @ X54 ) ) ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 ![
% 0.47/1.10 X60:$i,
% 0.47/1.10 X62:$i,
% 0.47/1.10 X64:$i]:
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 in @
% 0.47/1.10 X64 @
% 0.47/1.10 (
% 0.47/1.10 setminus @
% 0.47/1.10 X60 @ X62 ) ) =>
% 0.47/1.10 (
% 0.47/1.10 ~(
% 0.47/1.10 in @
% 0.47/1.10 X64 @ X62 ) ) ) ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 ![
% 0.47/1.10 X66:$i,
% 0.47/1.10 X68:$i]:
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 subset @
% 0.47/1.10 X66 @ X68 ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 setminus @
% 0.47/1.10 X66 @ X68 ) =
% 0.47/1.10 (
% 0.47/1.10 emptyset ) ) ) ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 ![
% 0.47/1.10 X70:$i,
% 0.47/1.10 X72:$i,
% 0.47/1.10 X74:$i]:
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 ~(
% 0.47/1.10 in @
% 0.47/1.10 X74 @
% 0.47/1.10 (
% 0.47/1.10 setminus
% 0.47/1.10 @
% 0.47/1.10 X70 @ X72 ) ) ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 in @
% 0.47/1.10 X74 @ X70 ) =>
% 0.47/1.10 (
% 0.47/1.10 in @
% 0.47/1.10 X74 @ X72 ) ) ) ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 ![
% 0.47/1.10 X76:$i,
% 0.47/1.10 X78:$i,
% 0.47/1.10 X80:$i]:
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 ~(
% 0.47/1.10 in @
% 0.47/1.10 X80 @
% 0.47/1.10 (
% 0.47/1.10 setminus
% 0.47/1.10 @
% 0.47/1.10 X76 @ X78 ) ) ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 ~(
% 0.47/1.10 in @
% 0.47/1.10 X80 @ X78 ) ) =>
% 0.47/1.10 (
% 0.47/1.10 ~(
% 0.47/1.10 in @
% 0.47/1.10 X80 @ X76 ) ) ) ) ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 ![
% 0.47/1.10 X82:$i,
% 0.47/1.10 X84:$i,
% 0.47/1.10 X86:$i]:
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 ~(
% 0.47/1.10 in @
% 0.47/1.10 X86 @ X82 ) ) =>
% 0.47/1.10 (
% 0.47/1.10 ~(
% 0.47/1.10 in @
% 0.47/1.10 X86 @
% 0.47/1.10 (
% 0.47/1.10 setminus
% 0.47/1.10 @
% 0.47/1.10 X82 @ X84 ) ) ) ) ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 ![
% 0.47/1.10 X88:$i,
% 0.47/1.10 X90:$i,
% 0.47/1.10 X92:$i]:
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 in @
% 0.47/1.10 X92 @ X90 ) =>
% 0.47/1.10 (
% 0.47/1.10 ~(
% 0.47/1.10 in @
% 0.47/1.10 X92 @
% 0.47/1.10 (
% 0.47/1.10 setminus
% 0.47/1.10 @
% 0.47/1.10 X88 @ X90 ) ) ) ) ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 ![
% 0.47/1.10 X94:$i,
% 0.47/1.10 X96:$i]:
% 0.47/1.10 (
% 0.47/1.10 subset @
% 0.47/1.10 (
% 0.47/1.10 setminus @
% 0.47/1.10 X94 @ X96 ) @
% 0.47/1.10 X94 ) ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 ![
% 0.47/1.10 X98:$i,
% 0.47/1.10 X100:$i]:
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 setminus @
% 0.47/1.10 X98 @ X100 ) =
% 0.47/1.10 (
% 0.47/1.10 emptyset ) ) =>
% 0.47/1.10 (
% 0.47/1.10 subset @
% 0.47/1.10 X98 @ X100 ) ) ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 symdiffE ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 symdiffI1 ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 symdiffI2 ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 symdiffIneg1 ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 symdiffIneg2 ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 secondinupair ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 setukpairIL ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 setukpairIR ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 kpairiskpair ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 kpairp ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 singletonsubset ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 ![
% 0.47/1.10 X102:$i,
% 0.47/1.10 X104:$i]:
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 in @
% 0.47/1.10 X104 @
% 0.47/1.10 X102 ) =>
% 0.47/1.10 (
% 0.47/1.10 in @
% 0.47/1.10 (
% 0.47/1.10 setadjoin
% 0.47/1.10 @
% 0.47/1.10 X104 @
% 0.47/1.10 emptyset ) @
% 0.47/1.10 (
% 0.47/1.10 powerset @
% 0.47/1.10 X102 ) ) ) ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 singletoninpowunion ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 upairset2E ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 upairsubunion ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 upairinpowunion ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 ubforcartprodlem1 ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 ubforcartprodlem2 ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 ubforcartprodlem3 ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 cartprodpairin ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 cartprodmempair1 ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 cartprodmempair ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 setunionE2 ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 setunionsingleton1 ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 setunionsingleton2 ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 setunionsingleton ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 singletonprop ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 ex1E1 ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 ex1I ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 ex1I2 ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 singletonsuniq ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 setukpairinjL1 ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 kfstsingleton ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 theprop ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 kfstpairEq ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 cartprodfstin ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 setukpairinjL2 ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 setukpairinjL ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 setukpairinjR11 ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 setukpairinjR12 ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 setukpairinjR1 ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 upairequniteq ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 setukpairinjR2 ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 setukpairinjR ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 ksndsingleton ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 ksndpairEq ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 kpairsurjEq ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 cartprodsndin ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 cartprodpairmemEL ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 cartprodpairmemER ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 cartprodmempaircEq ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 cartprodfstpairEq ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 cartprodsndpairEq ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 cartprodpairsurjEq ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 dpsetconstrI ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 dpsetconstrSub ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 setOfPairsIsBReln ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 dpsetconstrERa ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 dpsetconstrEL1 ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 dpsetconstrEL2 ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 dpsetconstrER ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 funcImageSingleton ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 apProp ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 app ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 infuncsetfunc ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 ap2p ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 funcinfuncset ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 lamProp ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 lamp ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 lam2p ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 brelnall1 ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 brelnall2 ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 ex1E2 ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 funcGraphProp1 ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 funcGraphProp3 ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 funcGraphProp2 ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 funcextLem ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 funcGraphProp4 ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 subbreln ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 eqbreln ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 funcext ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 funcext2 ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 ap2apEq1 ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 ap2apEq2 ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 beta1 ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 eta1 ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 lam2lamEq ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 beta2 ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 eta2 ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 iffalseProp1 ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 iffalseProp2 ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 iftrueProp1 ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 iftrueProp2 ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 ifSingleton ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 ifp ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 theeq ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 iftrue ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 iffalse ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 iftrueorfalse ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 binintersectT_lem ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 binunionT_lem ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 ![
% 0.47/1.10 X106:$i,
% 0.47/1.10 X108:$i]:
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 in @
% 0.47/1.10 X108 @
% 0.47/1.10 (
% 0.47/1.10 powerset @
% 0.47/1.10 X106 ) ) =>
% 0.47/1.10 (
% 0.47/1.10 in @
% 0.47/1.10 (
% 0.47/1.10 powerset @
% 0.47/1.10 X108 ) @
% 0.47/1.10 (
% 0.47/1.10 powerset @
% 0.47/1.10 (
% 0.47/1.10 powerset @
% 0.47/1.10 X106 ) ) ) ) ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 ![
% 0.47/1.10 X110:$i,
% 0.47/1.10 X112:$i]:
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 in @
% 0.47/1.10 X112 @
% 0.47/1.10 (
% 0.47/1.10 powerset @
% 0.47/1.10 X110 ) ) =>
% 0.47/1.10 (
% 0.47/1.10 ![
% 0.47/1.10 X114:$i]:
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 in @
% 0.47/1.10 X114 @
% 0.47/1.10 (
% 0.47/1.10 powerset @
% 0.47/1.10 X110 ) ) =>
% 0.47/1.10 (
% 0.47/1.10 in @
% 0.47/1.10 (
% 0.47/1.10 setminus @
% 0.47/1.10 X112 @
% 0.47/1.10 X114 ) @
% 0.47/1.10 (
% 0.47/1.10 powerset @
% 0.47/1.10 X110 ) ) ) ) ) ) =>
% 0.47/1.10 (
% 0.47/1.10 ![
% 0.47/1.10 X116:$i,
% 0.47/1.10 X118:$i]:
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 in @
% 0.47/1.10 X118 @
% 0.47/1.10 (
% 0.47/1.10 powerset @
% 0.47/1.10 X116 ) ) =>
% 0.47/1.10 (
% 0.47/1.10 in @
% 0.47/1.10 (
% 0.47/1.10 setminus @
% 0.47/1.10 X116 @
% 0.47/1.10 X118 ) @
% 0.47/1.10 (
% 0.47/1.10 powerset @
% 0.47/1.10 X116 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 0.47/1.10 thf(zf_stmt_4, negated_conjecture,
% 0.47/1.10 (~( ( setextAx ) =>
% 0.47/1.10 ( ( emptysetAx ) =>
% 0.47/1.10 ( ( setadjoinAx ) =>
% 0.47/1.10 ( ( ![X4:$i,X6:$i]:
% 0.47/1.10 ( ( in @ X6 @ ( powerset @ X4 ) ) <=>
% 0.47/1.10 ( ![X8:$i]: ( zip_tseitin_0 @ X8 @ X6 @ X4 ) ) ) ) =>
% 0.47/1.10 ( ( setunionAx ) =>
% 0.47/1.10 ( ( omega0Ax ) =>
% 0.47/1.10 ( ( omegaSAx ) =>
% 0.47/1.10 ( ( omegaIndAx ) =>
% 0.47/1.10 ( ( replAx ) =>
% 0.47/1.10 ( ( foundationAx ) =>
% 0.47/1.10 ( ( wellorderingAx ) =>
% 0.47/1.10 ( ( descrp ) =>
% 0.47/1.10 ( ( dsetconstrI ) =>
% 0.47/1.10 ( ( dsetconstrEL ) =>
% 0.47/1.10 ( ( dsetconstrER ) =>
% 0.47/1.10 ( ( exuE1 ) =>
% 0.47/1.10 ( ( prop2setE ) =>
% 0.47/1.10 ( ( emptysetE ) =>
% 0.47/1.10 ( ( emptysetimpfalse ) =>
% 0.47/1.10 ( ( notinemptyset ) =>
% 0.47/1.10 ( ( exuE3e ) =>
% 0.47/1.10 ( ( setext ) =>
% 0.47/1.10 ( ( emptyI ) =>
% 0.47/1.10 ( ( noeltsimpempty ) =>
% 0.47/1.10 ( ( setbeta ) =>
% 0.47/1.10 ( ( nonemptyE1 ) =>
% 0.47/1.10 ( ( nonemptyI ) =>
% 0.47/1.10 ( ( nonemptyI1 ) =>
% 0.47/1.10 ( ( setadjoinIL ) =>
% 0.47/1.10 ( ( emptyinunitempty ) =>
% 0.47/1.10 ( ( setadjoinIR ) =>
% 0.47/1.10 ( (
% 0.47/1.10 setadjoinE ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 setadjoinOr ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 setoftrueEq ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 ![
% 0.47/1.10 X10:$i,
% 0.47/1.10 X12:$i]:
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 ![
% 0.47/1.10 X14:$i]:
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 in @
% 0.47/1.10 X14 @ X12 ) =>
% 0.47/1.10 (
% 0.47/1.10 in @
% 0.47/1.10 X14 @ X10 ) ) ) =>
% 0.47/1.10 (
% 0.47/1.10 in @
% 0.47/1.10 X12 @
% 0.47/1.10 (
% 0.47/1.10 powerset
% 0.47/1.10 @
% 0.47/1.10 X10 ) ) ) ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 ![
% 0.47/1.10 X16:$i]:
% 0.47/1.10 (
% 0.47/1.10 in @
% 0.47/1.10 emptyset @
% 0.47/1.10 (
% 0.47/1.10 powerset
% 0.47/1.10 @
% 0.47/1.10 X16 ) ) ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 ![
% 0.47/1.10 X18:$i]:
% 0.47/1.10 (
% 0.47/1.10 in @
% 0.47/1.10 emptyset @
% 0.47/1.10 (
% 0.47/1.10 powerset
% 0.47/1.10 @
% 0.47/1.10 X18 ) ) ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 ![
% 0.47/1.10 X20:$i,
% 0.47/1.10 X22:$i,
% 0.47/1.10 X24:$i]:
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 in @
% 0.47/1.10 X22 @
% 0.47/1.10 (
% 0.47/1.10 powerset
% 0.47/1.10 @
% 0.47/1.10 X20 ) ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 in @
% 0.47/1.10 X24 @ X22 ) =>
% 0.47/1.10 (
% 0.47/1.10 in @
% 0.47/1.10 X24 @ X20 ) ) ) ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 setunionI ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 setunionE ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 subPowSU ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 exuE2 ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 nonemptyImpWitness ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 uniqinunit ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 notinsingleton ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 eqinunit ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 singletonsswitch ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 upairsetE ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 upairsetIL ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 upairsetIR ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 emptyE1 ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 vacuousDall ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 quantDeMorgan1 ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 quantDeMorgan2 ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 quantDeMorgan3 ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 quantDeMorgan4 ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 prop2setI ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 prop2set2propI ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 notdexE ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 notdallE ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 exuI1 ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 exuI3 ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 exuI2 ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 inCongP ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 in__Cong ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 exuE3u ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 exu__Cong ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 emptyset__Cong ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 setadjoin__Cong ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 ![
% 0.47/1.10 X26:$i,
% 0.47/1.10 X28:$i]:
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 X26 ) =
% 0.47/1.10 (
% 0.47/1.10 X28 ) ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 powerset
% 0.47/1.10 @
% 0.47/1.10 X26 ) =
% 0.47/1.10 (
% 0.47/1.10 powerset
% 0.47/1.10 @
% 0.47/1.10 X28 ) ) ) ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 setunion__Cong ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 omega__Cong ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 exuEu ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 descr__Cong ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 dsetconstr__Cong ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 subsetI1 ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 eqimpsubset2 ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 eqimpsubset1 ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 subsetI2 ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 emptysetsubset ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 subsetE ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 subsetE2 ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 notsubsetI ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 notequalI1 ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 notequalI2 ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 subsetRefl ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 subsetTrans ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 setadjoinSub ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 setadjoinSub2 ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 ![
% 0.47/1.10 X30:$i,
% 0.47/1.10 X32:$i]:
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 subset @
% 0.47/1.10 X30 @ X32 ) =>
% 0.47/1.10 (
% 0.47/1.10 in @
% 0.47/1.10 X30 @
% 0.47/1.10 (
% 0.47/1.10 powerset
% 0.47/1.10 @
% 0.47/1.10 X32 ) ) ) ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 setextsub ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 subsetemptysetimpeq ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 ![
% 0.47/1.10 X34:$i,
% 0.47/1.10 X36:$i]:
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 subset @
% 0.47/1.10 X36 @ X34 ) =>
% 0.47/1.10 (
% 0.47/1.10 in @
% 0.47/1.10 X36 @
% 0.47/1.10 (
% 0.47/1.10 powerset
% 0.47/1.10 @
% 0.47/1.10 X34 ) ) ) ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 ![
% 0.47/1.10 X38:$i,
% 0.47/1.10 X40:$i]:
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 in @
% 0.47/1.10 X40 @
% 0.47/1.10 (
% 0.47/1.10 powerset
% 0.47/1.10 @
% 0.47/1.10 X38 ) ) =>
% 0.47/1.10 (
% 0.47/1.10 subset @
% 0.47/1.10 X40 @ X38 ) ) ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 ![
% 0.47/1.10 X42:$i]:
% 0.47/1.10 (
% 0.47/1.10 in @
% 0.47/1.10 X42 @
% 0.47/1.10 (
% 0.47/1.10 powerset
% 0.47/1.10 @
% 0.47/1.10 X42 ) ) ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 ![
% 0.47/1.10 X44:$i,
% 0.47/1.10 X46:$i]:
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 subset @
% 0.47/1.10 X44 @ X46 ) =>
% 0.47/1.10 (
% 0.47/1.10 subset @
% 0.47/1.10 (
% 0.47/1.10 powerset
% 0.47/1.10 @
% 0.47/1.10 X44 ) @
% 0.47/1.10 (
% 0.47/1.10 powerset
% 0.47/1.10 @
% 0.47/1.10 X46 ) ) ) ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 sepInPowerset ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 sepSubset ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 binunionIL ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 upairset2IR ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 binunionIR ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 binunionEcases ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 binunionE ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 binunionLsub ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 binunionRsub ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 binintersectI ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 binintersectSubset5 ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 binintersectEL ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 binintersectLsub ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 binintersectSubset2 ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 binintersectSubset3 ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 binintersectER ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 disjointsetsI1 ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 binintersectRsub ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 binintersectSubset4 ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 binintersectSubset1 ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 bs114d ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 ![
% 0.47/1.10 X48:$i,
% 0.47/1.10 X50:$i,
% 0.47/1.10 X52:$i]:
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 in @
% 0.47/1.10 X52 @ X48 ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 ~
% 0.47/1.10 (
% 0.47/1.10 in @
% 0.47/1.10 X52 @ X50 ) ) =>
% 0.47/1.10 (
% 0.47/1.10 in @
% 0.47/1.10 X52 @
% 0.47/1.10 (
% 0.47/1.10 setminus
% 0.47/1.10 @
% 0.47/1.10 X48 @ X50 ) ) ) ) ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 ![
% 0.47/1.10 X54:$i,
% 0.47/1.10 X56:$i,
% 0.47/1.10 X58:$i]:
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 in @
% 0.47/1.10 X58 @
% 0.47/1.10 (
% 0.47/1.10 setminus
% 0.47/1.10 @
% 0.47/1.10 X54 @ X56 ) ) =>
% 0.47/1.10 (
% 0.47/1.10 in @
% 0.47/1.10 X58 @ X54 ) ) ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 ![
% 0.47/1.10 X60:$i,
% 0.47/1.10 X62:$i,
% 0.47/1.10 X64:$i]:
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 in @
% 0.47/1.10 X64 @
% 0.47/1.10 (
% 0.47/1.10 setminus
% 0.47/1.10 @
% 0.47/1.10 X60 @ X62 ) ) =>
% 0.47/1.10 (
% 0.47/1.10 ~
% 0.47/1.10 (
% 0.47/1.10 in @
% 0.47/1.10 X64 @ X62 ) ) ) ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 ![
% 0.47/1.10 X66:$i,
% 0.47/1.10 X68:$i]:
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 subset @
% 0.47/1.10 X66 @ X68 ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 setminus
% 0.47/1.10 @
% 0.47/1.10 X66 @ X68 ) =
% 0.47/1.10 (
% 0.47/1.10 emptyset ) ) ) ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 ![
% 0.47/1.10 X70:$i,
% 0.47/1.10 X72:$i,
% 0.47/1.10 X74:$i]:
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 ~
% 0.47/1.10 (
% 0.47/1.10 in @
% 0.47/1.10 X74 @
% 0.47/1.10 (
% 0.47/1.10 setminus
% 0.47/1.10 @
% 0.47/1.10 X70 @ X72 ) ) ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 in @
% 0.47/1.10 X74 @ X70 ) =>
% 0.47/1.10 (
% 0.47/1.10 in @
% 0.47/1.10 X74 @ X72 ) ) ) ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 ![
% 0.47/1.10 X76:$i,
% 0.47/1.10 X78:$i,
% 0.47/1.10 X80:$i]:
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 ~
% 0.47/1.10 (
% 0.47/1.10 in @
% 0.47/1.10 X80 @
% 0.47/1.10 (
% 0.47/1.10 setminus
% 0.47/1.10 @
% 0.47/1.10 X76 @ X78 ) ) ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 ~
% 0.47/1.10 (
% 0.47/1.10 in @
% 0.47/1.10 X80 @ X78 ) ) =>
% 0.47/1.10 (
% 0.47/1.10 ~
% 0.47/1.10 (
% 0.47/1.10 in @
% 0.47/1.10 X80 @ X76 ) ) ) ) ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 ![
% 0.47/1.10 X82:$i,
% 0.47/1.10 X84:$i,
% 0.47/1.10 X86:$i]:
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 ~
% 0.47/1.10 (
% 0.47/1.10 in @
% 0.47/1.10 X86 @ X82 ) ) =>
% 0.47/1.10 (
% 0.47/1.10 ~
% 0.47/1.10 (
% 0.47/1.10 in @
% 0.47/1.10 X86 @
% 0.47/1.10 (
% 0.47/1.10 setminus
% 0.47/1.10 @
% 0.47/1.10 X82 @ X84 ) ) ) ) ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 ![
% 0.47/1.10 X88:$i,
% 0.47/1.10 X90:$i,
% 0.47/1.10 X92:$i]:
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 in @
% 0.47/1.10 X92 @ X90 ) =>
% 0.47/1.10 (
% 0.47/1.10 ~
% 0.47/1.10 (
% 0.47/1.10 in @
% 0.47/1.10 X92 @
% 0.47/1.10 (
% 0.47/1.10 setminus
% 0.47/1.10 @
% 0.47/1.10 X88 @ X90 ) ) ) ) ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 ![
% 0.47/1.10 X94:$i,
% 0.47/1.10 X96:$i]:
% 0.47/1.10 (
% 0.47/1.10 subset @
% 0.47/1.10 (
% 0.47/1.10 setminus
% 0.47/1.10 @
% 0.47/1.10 X94 @ X96 ) @
% 0.47/1.10 X94 ) ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 ![
% 0.47/1.10 X98:$i,
% 0.47/1.10 X100:$i]:
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 setminus
% 0.47/1.10 @
% 0.47/1.10 X98 @
% 0.47/1.10 X100 ) =
% 0.47/1.10 (
% 0.47/1.10 emptyset ) ) =>
% 0.47/1.10 (
% 0.47/1.10 subset @
% 0.47/1.10 X98 @
% 0.47/1.10 X100 ) ) ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 symdiffE ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 symdiffI1 ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 symdiffI2 ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 symdiffIneg1 ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 symdiffIneg2 ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 secondinupair ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 setukpairIL ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 setukpairIR ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 kpairiskpair ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 kpairp ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 singletonsubset ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 ![
% 0.47/1.10 X102:$i,
% 0.47/1.10 X104:$i]:
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 in @
% 0.47/1.10 X104 @
% 0.47/1.10 X102 ) =>
% 0.47/1.10 (
% 0.47/1.10 in @
% 0.47/1.10 (
% 0.47/1.10 setadjoin
% 0.47/1.10 @
% 0.47/1.10 X104 @
% 0.47/1.10 emptyset ) @
% 0.47/1.10 (
% 0.47/1.10 powerset
% 0.47/1.10 @
% 0.47/1.10 X102 ) ) ) ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 singletoninpowunion ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 upairset2E ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 upairsubunion ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 upairinpowunion ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 ubforcartprodlem1 ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 ubforcartprodlem2 ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 ubforcartprodlem3 ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 cartprodpairin ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 cartprodmempair1 ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 cartprodmempair ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 setunionE2 ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 setunionsingleton1 ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 setunionsingleton2 ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 setunionsingleton ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 singletonprop ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 ex1E1 ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 ex1I ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 ex1I2 ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 singletonsuniq ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 setukpairinjL1 ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 kfstsingleton ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 theprop ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 kfstpairEq ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 cartprodfstin ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 setukpairinjL2 ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 setukpairinjL ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 setukpairinjR11 ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 setukpairinjR12 ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 setukpairinjR1 ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 upairequniteq ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 setukpairinjR2 ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 setukpairinjR ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 ksndsingleton ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 ksndpairEq ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 kpairsurjEq ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 cartprodsndin ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 cartprodpairmemEL ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 cartprodpairmemER ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 cartprodmempaircEq ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 cartprodfstpairEq ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 cartprodsndpairEq ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 cartprodpairsurjEq ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 dpsetconstrI ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 dpsetconstrSub ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 setOfPairsIsBReln ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 dpsetconstrERa ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 dpsetconstrEL1 ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 dpsetconstrEL2 ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 dpsetconstrER ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 funcImageSingleton ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 apProp ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 app ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 infuncsetfunc ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 ap2p ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 funcinfuncset ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 lamProp ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 lamp ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 lam2p ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 brelnall1 ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 brelnall2 ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 ex1E2 ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 funcGraphProp1 ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 funcGraphProp3 ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 funcGraphProp2 ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 funcextLem ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 funcGraphProp4 ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 subbreln ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 eqbreln ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 funcext ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 funcext2 ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 ap2apEq1 ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 ap2apEq2 ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 beta1 ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 eta1 ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 lam2lamEq ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 beta2 ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 eta2 ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 iffalseProp1 ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 iffalseProp2 ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 iftrueProp1 ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 iftrueProp2 ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 ifSingleton ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 ifp ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 theeq ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 iftrue ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 iffalse ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 iftrueorfalse ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 binintersectT_lem ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 binunionT_lem ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 ![
% 0.47/1.10 X106:$i,
% 0.47/1.10 X108:$i]:
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 in @
% 0.47/1.10 X108 @
% 0.47/1.10 (
% 0.47/1.10 powerset
% 0.47/1.10 @
% 0.47/1.10 X106 ) ) =>
% 0.47/1.10 (
% 0.47/1.10 in @
% 0.47/1.10 (
% 0.47/1.10 powerset
% 0.47/1.10 @
% 0.47/1.10 X108 ) @
% 0.47/1.10 (
% 0.47/1.10 powerset
% 0.47/1.10 @
% 0.47/1.10 (
% 0.47/1.10 powerset
% 0.47/1.10 @
% 0.47/1.10 X106 ) ) ) ) ) =>
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 ![
% 0.47/1.10 X110:$i,
% 0.47/1.10 X112:$i]:
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 in @
% 0.47/1.10 X112 @
% 0.47/1.10 (
% 0.47/1.10 powerset
% 0.47/1.10 @
% 0.47/1.10 X110 ) ) =>
% 0.47/1.10 (
% 0.47/1.10 ![
% 0.47/1.10 X114:$i]:
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 in @
% 0.47/1.10 X114 @
% 0.47/1.10 (
% 0.47/1.10 powerset
% 0.47/1.10 @
% 0.47/1.10 X110 ) ) =>
% 0.47/1.10 (
% 0.47/1.10 in @
% 0.47/1.10 (
% 0.47/1.10 setminus
% 0.47/1.10 @
% 0.47/1.10 X112 @
% 0.47/1.10 X114 ) @
% 0.47/1.10 (
% 0.47/1.10 powerset
% 0.47/1.10 @
% 0.47/1.10 X110 ) ) ) ) ) ) =>
% 0.47/1.10 (
% 0.47/1.10 ![
% 0.47/1.10 X116:$i,
% 0.47/1.10 X118:$i]:
% 0.47/1.10 (
% 0.47/1.10 (
% 0.47/1.10 in @
% 0.47/1.10 X118 @
% 0.47/1.10 (
% 0.47/1.10 powerset
% 0.47/1.10 @
% 0.47/1.10 X116 ) ) =>
% 0.47/1.10 (
% 0.47/1.10 in @
% 0.47/1.10 (
% 0.47/1.10 setminus
% 0.47/1.10 @
% 0.47/1.10 X116 @
% 0.47/1.10 X118 ) @
% 0.47/1.10 (
% 0.47/1.10 powerset
% 0.47/1.10 @
% 0.47/1.10 X116 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )),
% 0.47/1.10 inference('cnf.neg', [status(esa)], [zf_stmt_3])).
% 0.47/1.10 thf(zip_derived_cl121, plain,
% 0.47/1.10 (![X23 : $i, X24 : $i, X25 : $i]:
% 0.47/1.10 (~ (in @ X23 @ (powerset @ X24))
% 0.47/1.10 | (in @ (setminus @ X25 @ X23) @ (powerset @ X24))
% 0.47/1.10 | ~ (in @ X25 @ (powerset @ X24)))),
% 0.47/1.10 inference('cnf', [status(esa)], [zf_stmt_4])).
% 0.47/1.10 thf(zip_derived_cl119, plain,
% 0.47/1.10 (~ (in @ (setminus @ sk__58 @ sk__59) @ (powerset @ sk__58))),
% 0.47/1.10 inference('cnf', [status(esa)], [zf_stmt_4])).
% 0.47/1.10 thf(zip_derived_cl394, plain,
% 0.47/1.10 ((~ (in @ sk__58 @ (powerset @ sk__58))
% 0.47/1.10 | ~ (in @ sk__59 @ (powerset @ sk__58)))),
% 0.47/1.10 inference('sup-', [status(thm)], [zip_derived_cl121, zip_derived_cl119])).
% 0.47/1.10 thf(zip_derived_cl51, plain, (![X5 : $i]: (in @ X5 @ (powerset @ X5))),
% 0.47/1.10 inference('cnf', [status(esa)], [zf_stmt_4])).
% 0.47/1.10 thf(zip_derived_cl120, plain, ( (in @ sk__59 @ (powerset @ sk__58))),
% 0.47/1.10 inference('cnf', [status(esa)], [zf_stmt_4])).
% 0.47/1.10 thf(zip_derived_cl409, plain, ($false),
% 0.47/1.10 inference('demod', [status(thm)],
% 0.47/1.10 [zip_derived_cl394, zip_derived_cl51, zip_derived_cl120])).
% 0.47/1.10
% 0.47/1.10 % SZS output end Refutation
% 0.47/1.10
% 0.47/1.10
% 0.47/1.10 % Terminating...
% 1.66/1.26 % Runner terminated.
% 1.66/1.30 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------