%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SEU713^1 : 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.rR2bwntVqA true
% Computer : n001.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 3.81s 1.18s
% Output : Refutation 4.06s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.11 % Problem : SEU713^1 : TPTP v9.2.0. Released v3.7.0.
% 0.05/0.12 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.rR2bwntVqA true
% 0.11/0.32 % Computer : n001.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Wed Oct 1 16:05:23 EDT 2025
% 0.11/0.32 % CPUTime :
% 0.11/0.32 % Running portfolio for 300 s
% 0.11/0.32 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.33 % Number of cores: 8
% 0.11/0.33 % Python version: Python 3.6.8
% 0.11/0.33 % Running in HO mode
% 0.51/0.64 % Total configuration time : 828
% 0.51/0.64 % Estimated wc time : 1656
% 0.51/0.64 % Estimated cpu time (8 cpus) : 207.0
% 0.52/0.71 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
% 0.52/0.73 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.52/0.75 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
% 0.52/0.78 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
% 0.52/0.78 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s
% 0.52/0.79 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s
% 0.52/0.79 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.52/0.80 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s
% 3.81/1.18 % Solved by lams/40_c_ic.sh.
% 3.81/1.18 % done 348 iterations in 0.338s
% 3.81/1.18 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 3.81/1.18 % SZS output start Refutation
% 3.81/1.18 thf(setadjoinAx_type, type, setadjoinAx: $o).
% 3.81/1.18 thf(notdexE_type, type, notdexE: $o).
% 3.81/1.18 thf(setukpairinjL2_type, type, setukpairinjL2: $o).
% 3.81/1.18 thf(setunionAx_type, type, setunionAx: $o).
% 3.81/1.18 thf(setminusELneg_type, type, setminusELneg: $o).
% 3.81/1.18 thf(cartprodsndin_type, type, cartprodsndin: $o).
% 3.81/1.18 thf(ex1E1_type, type, ex1E1: $o).
% 3.81/1.18 thf(powersetE_type, type, powersetE: $o).
% 3.81/1.18 thf(omegaSAx_type, type, omegaSAx: $o).
% 3.81/1.18 thf(exuI1_type, type, exuI1: $o).
% 3.81/1.18 thf(exuI2_type, type, exuI2: $o).
% 3.81/1.18 thf(notequalI2_type, type, notequalI2: $o).
% 3.81/1.18 thf(setukpairinjL_type, type, setukpairinjL: $o).
% 3.81/1.18 thf(kpairiskpair_type, type, kpairiskpair: $o).
% 3.81/1.18 thf(upairsubunion_type, type, upairsubunion: $o).
% 3.81/1.18 thf(funcGraphProp3_type, type, funcGraphProp3: $o).
% 3.81/1.18 thf(cartprodmempaircEq_type, type, cartprodmempaircEq: $o).
% 3.81/1.18 thf(powerset__Cong_type, type, powerset__Cong: $o).
% 3.81/1.18 thf(sk__55_type, type, sk__55: $i).
% 3.81/1.18 thf(setminusILneg_type, type, setminusILneg: $o).
% 3.81/1.18 thf(wellorderingAx_type, type, wellorderingAx: $o).
% 3.81/1.18 thf(ksndpairEq_type, type, ksndpairEq: $o).
% 3.81/1.18 thf(funcGraphProp2_type, type, funcGraphProp2: $o).
% 3.81/1.18 thf(setadjoinSub2_type, type, setadjoinSub2: $o).
% 3.81/1.18 thf(binintersectSubset5_type, type, binintersectSubset5: $o).
% 3.81/1.18 thf(iftrue_type, type, iftrue: $o).
% 3.81/1.18 thf(upairinpowunion_type, type, upairinpowunion: $o).
% 3.81/1.18 thf(ifSingleton_type, type, ifSingleton: $o).
% 3.81/1.18 thf(setoftrueEq_type, type, setoftrueEq: $o).
% 3.81/1.18 thf(funcImageSingleton_type, type, funcImageSingleton: $o).
% 3.81/1.18 thf(dpsetconstrERa_type, type, dpsetconstrERa: $o).
% 3.81/1.18 thf(lamProp_type, type, lamProp: $o).
% 3.81/1.18 thf(cartprodpairmemEL_type, type, cartprodpairmemEL: $o).
% 3.81/1.18 thf(emptyset__Cong_type, type, emptyset__Cong: $o).
% 3.81/1.18 thf(sk__56_type, type, sk__56: $i).
% 3.81/1.18 thf(dpsetconstrER_type, type, dpsetconstrER: $o).
% 3.81/1.18 thf(sepInPowerset_type, type, sepInPowerset: $o).
% 3.81/1.18 thf(setukpairIR_type, type, setukpairIR: $o).
% 3.81/1.18 thf(setukpairinjR1_type, type, setukpairinjR1: $o).
% 3.81/1.18 thf(lam2p_type, type, lam2p: $o).
% 3.81/1.18 thf(binunionE_type, type, binunionE: $o).
% 3.81/1.18 thf(setext_type, type, setext: $o).
% 3.81/1.18 thf(emptyinPowerset_type, type, emptyinPowerset: $o).
% 3.81/1.18 thf(ubforcartprodlem1_type, type, ubforcartprodlem1: $o).
% 3.81/1.18 thf(descr__Cong_type, type, descr__Cong: $o).
% 3.81/1.18 thf(kfstsingleton_type, type, kfstsingleton: $o).
% 3.81/1.18 thf(eqbreln_type, type, eqbreln: $o).
% 3.81/1.18 thf(binintersectSubset1_type, type, binintersectSubset1: $o).
% 3.81/1.18 thf(in_type, type, in: $i > $i > $o).
% 3.81/1.18 thf(binunionT_lem_type, type, binunionT_lem: $o).
% 3.81/1.18 thf(quantDeMorgan1_type, type, quantDeMorgan1: $o).
% 3.81/1.18 thf(kpairsurjEq_type, type, kpairsurjEq: $o).
% 3.81/1.18 thf(setadjoinIR_type, type, setadjoinIR: $o).
% 3.81/1.18 thf(beta1_type, type, beta1: $o).
% 3.81/1.18 thf(setadjoin__Cong_type, type, setadjoin__Cong: $o).
% 3.81/1.18 thf(symdiffI2_type, type, symdiffI2: $o).
% 3.81/1.18 thf(iftrueProp2_type, type, iftrueProp2: $o).
% 3.81/1.18 thf(upairset2IR_type, type, upairset2IR: $o).
% 3.81/1.18 thf(iffalseProp2_type, type, iffalseProp2: $o).
% 3.81/1.18 thf(subsetE_type, type, subsetE: $o).
% 3.81/1.18 thf(prop2set2propI_type, type, prop2set2propI: $o).
% 3.81/1.18 thf(dsetconstrEL_type, type, dsetconstrEL: $o).
% 3.81/1.18 thf(setbeta_type, type, setbeta: $o).
% 3.81/1.18 thf(eqinunit_type, type, eqinunit: $o).
% 3.81/1.18 thf(upairsetIL_type, type, upairsetIL: $o).
% 3.81/1.18 thf(powersetI1_type, type, powersetI1: $o).
% 3.81/1.18 thf(kfstpairEq_type, type, kfstpairEq: $o).
% 3.81/1.18 thf(binintersectSubset3_type, type, binintersectSubset3: $o).
% 3.81/1.18 thf(setminusIRneg_type, type, setminusIRneg: $o).
% 3.81/1.18 thf(ap2apEq1_type, type, ap2apEq1: $o).
% 3.81/1.18 thf(powersetAx_type, type, powersetAx: $o).
% 3.81/1.18 thf(binintersectSubset4_type, type, binintersectSubset4: $o).
% 3.81/1.18 thf(singletoninpowunion_type, type, singletoninpowunion: $o).
% 3.81/1.18 thf(powersetI_type, type, powersetI: $o).
% 3.81/1.18 thf(cartprodmempair_type, type, cartprodmempair: $o).
% 3.81/1.18 thf(upairsetIR_type, type, upairsetIR: $o).
% 3.81/1.18 thf(lamp_type, type, lamp: $o).
% 3.81/1.18 thf(dpsetconstrEL1_type, type, dpsetconstrEL1: $o).
% 3.81/1.18 thf(inCongP_type, type, inCongP: $o).
% 3.81/1.18 thf(setadjoinSub_type, type, setadjoinSub: $o).
% 3.81/1.18 thf(exuE3e_type, type, exuE3e: $o).
% 3.81/1.18 thf(emptysetE_type, type, emptysetE: $o).
% 3.81/1.18 thf(binintersectSubset2_type, type, binintersectSubset2: $o).
% 3.81/1.18 thf(setunionI_type, type, setunionI: $o).
% 3.81/1.18 thf(setunion__Cong_type, type, setunion__Cong: $o).
% 3.81/1.18 thf(prop2setI_type, type, prop2setI: $o).
% 3.81/1.18 thf(singletonsuniq_type, type, singletonsuniq: $o).
% 3.81/1.18 thf(nonemptyImpWitness_type, type, nonemptyImpWitness: $o).
% 3.81/1.18 thf(setminusER_type, type, setminusER: $o).
% 3.81/1.18 thf(exuE2_type, type, exuE2: $o).
% 3.81/1.18 thf(emptyset_type, type, emptyset: $i).
% 3.81/1.18 thf(setukpairinjR11_type, type, setukpairinjR11: $o).
% 3.81/1.18 thf(ex1I_type, type, ex1I: $o).
% 3.81/1.18 thf(ex1E2_type, type, ex1E2: $o).
% 3.81/1.18 thf(setminus_type, type, setminus: $i > $i > $i).
% 3.81/1.18 thf(setukpairinjL1_type, type, setukpairinjL1: $o).
% 3.81/1.18 thf(powersetsubset_type, type, powersetsubset: $o).
% 3.81/1.18 thf(zip_tseitin_0_type, type, zip_tseitin_0: $i > $i > $i > $o).
% 3.81/1.18 thf(subPowSU_type, type, subPowSU: $o).
% 3.81/1.18 thf(notequalI1_type, type, notequalI1: $o).
% 3.81/1.18 thf(notinemptyset_type, type, notinemptyset: $o).
% 3.81/1.18 thf(lam2lamEq_type, type, lam2lamEq: $o).
% 3.81/1.18 thf(nonemptyI1_type, type, nonemptyI1: $o).
% 3.81/1.18 thf(subsetTrans_type, type, subsetTrans: $o).
% 3.81/1.18 thf(kpairp_type, type, kpairp: $o).
% 3.81/1.18 thf(setukpairinjR12_type, type, setukpairinjR12: $o).
% 3.81/1.18 thf(setminusI_type, type, setminusI: $o).
% 3.81/1.18 thf(binunionIL_type, type, binunionIL: $o).
% 3.81/1.18 thf(dpsetconstrSub_type, type, dpsetconstrSub: $o).
% 3.81/1.18 thf(setunionsingleton_type, type, setunionsingleton: $o).
% 3.81/1.18 thf(subsetE2_type, type, subsetE2: $o).
% 3.81/1.18 thf(singletonsswitch_type, type, singletonsswitch: $o).
% 3.81/1.18 thf(ubforcartprodlem3_type, type, ubforcartprodlem3: $o).
% 3.81/1.18 thf(beta2_type, type, beta2: $o).
% 3.81/1.18 thf(dpsetconstrI_type, type, dpsetconstrI: $o).
% 3.81/1.18 thf(setextsub_type, type, setextsub: $o).
% 3.81/1.18 thf(binunionLsub_type, type, binunionLsub: $o).
% 3.81/1.18 thf(setunionsingleton1_type, type, setunionsingleton1: $o).
% 3.81/1.18 thf(iftrueorfalse_type, type, iftrueorfalse: $o).
% 3.81/1.18 thf(emptysetsubset_type, type, emptysetsubset: $o).
% 3.81/1.18 thf(quantDeMorgan3_type, type, quantDeMorgan3: $o).
% 3.81/1.18 thf(cartprodpairsurjEq_type, type, cartprodpairsurjEq: $o).
% 3.81/1.18 thf(setOfPairsIsBReln_type, type, setOfPairsIsBReln: $o).
% 3.81/1.18 thf(setunionE_type, type, setunionE: $o).
% 3.81/1.18 thf(ksndsingleton_type, type, ksndsingleton: $o).
% 3.81/1.18 thf(setminusSubset1_type, type, setminusSubset1: $o).
% 3.81/1.18 thf(powersetT_lem_type, type, powersetT_lem: $o).
% 3.81/1.18 thf(emptyinunitempty_type, type, emptyinunitempty: $o).
% 3.81/1.18 thf(binunionIR_type, type, binunionIR: $o).
% 3.81/1.18 thf(theeq_type, type, theeq: $o).
% 3.81/1.18 thf(setadjoinE_type, type, setadjoinE: $o).
% 3.81/1.18 thf(infuncsetfunc_type, type, infuncsetfunc: $o).
% 3.81/1.18 thf(ap2apEq2_type, type, ap2apEq2: $o).
% 3.81/1.18 thf(ap2p_type, type, ap2p: $o).
% 3.81/1.18 thf(setadjoinIL_type, type, setadjoinIL: $o).
% 3.81/1.18 thf(cartprodsndpairEq_type, type, cartprodsndpairEq: $o).
% 3.81/1.18 thf(exuE1_type, type, exuE1: $o).
% 3.81/1.18 thf(ubforcartprodlem2_type, type, ubforcartprodlem2: $o).
% 3.81/1.18 thf(binintersectRsub_type, type, binintersectRsub: $o).
% 3.81/1.18 thf(setminusLsub_type, type, setminusLsub: $o).
% 3.81/1.18 thf(funcextLem_type, type, funcextLem: $o).
% 3.81/1.18 thf(setukpairinjR_type, type, setukpairinjR: $o).
% 3.81/1.18 thf(notinsingleton_type, type, notinsingleton: $o).
% 3.81/1.18 thf(eqimpsubset2_type, type, eqimpsubset2: $o).
% 3.81/1.18 thf(exuEu_type, type, exuEu: $o).
% 3.81/1.18 thf(emptysetimpfalse_type, type, emptysetimpfalse: $o).
% 3.81/1.18 thf(upairsetE_type, type, upairsetE: $o).
% 3.81/1.18 thf(omega0Ax_type, type, omega0Ax: $o).
% 3.81/1.18 thf(notsubsetI_type, type, notsubsetI: $o).
% 3.81/1.18 thf(iffalseProp1_type, type, iffalseProp1: $o).
% 3.81/1.18 thf(quantDeMorgan4_type, type, quantDeMorgan4: $o).
% 3.81/1.18 thf(setextAx_type, type, setextAx: $o).
% 3.81/1.18 thf(cartprodpairmemER_type, type, cartprodpairmemER: $o).
% 3.81/1.18 thf(powersetE1_type, type, powersetE1: $o).
% 3.81/1.18 thf(bs114d_type, type, bs114d: $o).
% 3.81/1.18 thf(sk__57_type, type, sk__57: $i).
% 3.81/1.18 thf(noeltsimpempty_type, type, noeltsimpempty: $o).
% 3.81/1.18 thf(ifp_type, type, ifp: $o).
% 3.81/1.18 thf(binintersectLsub_type, type, binintersectLsub: $o).
% 3.81/1.18 thf(subsetI1_type, type, subsetI1: $o).
% 3.81/1.18 thf(symdiffE_type, type, symdiffE: $o).
% 3.81/1.18 thf(descrp_type, type, descrp: $o).
% 3.81/1.18 thf(dsetconstr__Cong_type, type, dsetconstr__Cong: $o).
% 3.81/1.18 thf(foundationAx_type, type, foundationAx: $o).
% 3.81/1.18 thf(emptysetAx_type, type, emptysetAx: $o).
% 3.81/1.18 thf(emptyI_type, type, emptyI: $o).
% 3.81/1.18 thf(setadjoinOr_type, type, setadjoinOr: $o).
% 3.81/1.18 thf(eta2_type, type, eta2: $o).
% 3.81/1.18 thf(binintersectEL_type, type, binintersectEL: $o).
% 3.81/1.18 thf(emptyE1_type, type, emptyE1: $o).
% 3.81/1.18 thf(emptyInPowerset_type, type, emptyInPowerset: $o).
% 3.81/1.18 thf(vacuousDall_type, type, vacuousDall: $o).
% 3.81/1.18 thf(dsetconstrER_type, type, dsetconstrER: $o).
% 3.81/1.18 thf(binintersectI_type, type, binintersectI: $o).
% 3.81/1.18 thf(funcext_type, type, funcext: $o).
% 3.81/1.18 thf(funcGraphProp4_type, type, funcGraphProp4: $o).
% 3.81/1.18 thf(cartprodpairin_type, type, cartprodpairin: $o).
% 3.81/1.18 thf(cartprodmempair1_type, type, cartprodmempair1: $o).
% 3.81/1.18 thf(brelnall2_type, type, brelnall2: $o).
% 3.81/1.18 thf(ex1I2_type, type, ex1I2: $o).
% 3.81/1.18 thf(symdiffI1_type, type, symdiffI1: $o).
% 3.81/1.18 thf(setukpairinjR2_type, type, setukpairinjR2: $o).
% 3.81/1.18 thf(dpsetconstrEL2_type, type, dpsetconstrEL2: $o).
% 3.81/1.18 thf(theprop_type, type, theprop: $o).
% 3.81/1.18 thf(subsetI2_type, type, subsetI2: $o).
% 3.81/1.18 thf(symdiffIneg1_type, type, symdiffIneg1: $o).
% 3.81/1.18 thf(setminusERneg_type, type, setminusERneg: $o).
% 3.81/1.18 thf(symdiffIneg2_type, type, symdiffIneg2: $o).
% 3.81/1.18 thf(omega__Cong_type, type, omega__Cong: $o).
% 3.81/1.18 thf(subsetRefl_type, type, subsetRefl: $o).
% 3.81/1.18 thf(uniqinunit_type, type, uniqinunit: $o).
% 3.81/1.18 thf(setminusSubset2_type, type, setminusSubset2: $o).
% 3.81/1.18 thf(prop2setE_type, type, prop2setE: $o).
% 3.81/1.18 thf(binunionEcases_type, type, binunionEcases: $o).
% 3.81/1.18 thf(funcinfuncset_type, type, funcinfuncset: $o).
% 3.81/1.18 thf(nonemptyI_type, type, nonemptyI: $o).
% 3.81/1.18 thf(app_type, type, app: $o).
% 3.81/1.18 thf(disjointsetsI1_type, type, disjointsetsI1: $o).
% 3.81/1.18 thf(exuE3u_type, type, exuE3u: $o).
% 3.81/1.18 thf(eta1_type, type, eta1: $o).
% 3.81/1.18 thf(setminusEL_type, type, setminusEL: $o).
% 3.81/1.18 thf(cartprodfstin_type, type, cartprodfstin: $o).
% 3.81/1.18 thf(setunionsingleton2_type, type, setunionsingleton2: $o).
% 3.81/1.18 thf(sepSubset_type, type, sepSubset: $o).
% 3.81/1.18 thf(upairset2E_type, type, upairset2E: $o).
% 3.81/1.18 thf(eqimpsubset1_type, type, eqimpsubset1: $o).
% 3.81/1.18 thf(exuI3_type, type, exuI3: $o).
% 3.81/1.18 thf(cartprodfstpairEq_type, type, cartprodfstpairEq: $o).
% 3.81/1.18 thf(apProp_type, type, apProp: $o).
% 3.81/1.18 thf(notdallE_type, type, notdallE: $o).
% 3.81/1.18 thf(iftrueProp1_type, type, iftrueProp1: $o).
% 3.81/1.18 thf(binintersectER_type, type, binintersectER: $o).
% 3.81/1.18 thf(brelnall1_type, type, brelnall1: $o).
% 3.81/1.18 thf(powerset_type, type, powerset: $i > $i).
% 3.81/1.18 thf(dsetconstrI_type, type, dsetconstrI: $o).
% 3.81/1.18 thf(funcGraphProp1_type, type, funcGraphProp1: $o).
% 3.81/1.18 thf(binintersectT_lem_type, type, binintersectT_lem: $o).
% 3.81/1.18 thf(setadjoin_type, type, setadjoin: $i > $i > $i).
% 3.81/1.18 thf(exu__Cong_type, type, exu__Cong: $o).
% 3.81/1.18 thf(quantDeMorgan2_type, type, quantDeMorgan2: $o).
% 3.81/1.18 thf(secondinupair_type, type, secondinupair: $o).
% 3.81/1.18 thf(singletonprop_type, type, singletonprop: $o).
% 3.81/1.18 thf(singletonsubset_type, type, singletonsubset: $o).
% 3.81/1.18 thf(singletoninpowerset_type, type, singletoninpowerset: $o).
% 3.81/1.18 thf(subsetemptysetimpeq_type, type, subsetemptysetimpeq: $o).
% 3.81/1.18 thf(replAx_type, type, replAx: $o).
% 3.81/1.18 thf(upairequniteq_type, type, upairequniteq: $o).
% 3.81/1.18 thf(nonemptyE1_type, type, nonemptyE1: $o).
% 3.81/1.18 thf(omegaIndAx_type, type, omegaIndAx: $o).
% 3.81/1.18 thf(setukpairIL_type, type, setukpairIL: $o).
% 3.81/1.18 thf(setunionE2_type, type, setunionE2: $o).
% 3.81/1.18 thf(inPowerset_type, type, inPowerset: $o).
% 3.81/1.18 thf(iffalse_type, type, iffalse: $o).
% 3.81/1.18 thf(funcext2_type, type, funcext2: $o).
% 3.81/1.18 thf(subset_type, type, subset: $i > $i > $o).
% 3.81/1.18 thf(subbreln_type, type, subbreln: $o).
% 3.81/1.18 thf(in__Cong_type, type, in__Cong: $o).
% 3.81/1.18 thf(binunionRsub_type, type, binunionRsub: $o).
% 3.81/1.18 thf(subset2powerset_type, type, subset2powerset: $o).
% 3.81/1.18 thf(powersetT_lem, axiom, powersetT_lem =
% 3.81/1.18 (![A:$i,X:$i]:
% 3.81/1.18 ( ( in @ X @ ( powerset @ A ) ) =>
% 3.81/1.18 ( in @ ( powerset @ X ) @ ( powerset @ ( powerset @ A ) ) ) ))).
% 3.81/1.18 thf('0', plain,
% 3.81/1.18 (( powersetT_lem ) =
% 3.81/1.18 ( ![X4:$i,X6:$i]:
% 3.81/1.18 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 3.81/1.18 ( in @ ( powerset @ X6 ) @ ( powerset @ ( powerset @ X4 ) ) ) ) )),
% 3.81/1.18 define([status(thm)])).
% 3.81/1.18 thf(singletoninpowerset, axiom, singletoninpowerset =
% 3.81/1.18 (![A:$i,Xx:$i]:
% 3.81/1.18 ( ( in @ Xx @ A ) =>
% 3.81/1.18 ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) ))).
% 3.81/1.18 thf('1', plain,
% 3.81/1.18 (( singletoninpowerset ) =
% 3.81/1.18 ( ![X4:$i,X6:$i]:
% 3.81/1.18 ( ( in @ X6 @ X4 ) =>
% 3.81/1.18 ( in @ ( setadjoin @ X6 @ emptyset ) @ ( powerset @ X4 ) ) ) )),
% 3.81/1.18 define([status(thm)])).
% 3.81/1.18 thf(setminusSubset1, axiom, setminusSubset1 =
% 3.81/1.18 (![A:$i,B:$i]:
% 3.81/1.18 ( ( ( setminus @ A @ B ) = ( emptyset ) ) => ( subset @ A @ B ) ))).
% 3.81/1.18 thf('2', plain,
% 3.81/1.18 (( setminusSubset1 ) =
% 3.81/1.18 ( ![X4:$i,X6:$i]:
% 3.81/1.18 ( ( ( setminus @ X4 @ X6 ) = ( emptyset ) ) => ( subset @ X4 @ X6 ) ) )),
% 3.81/1.18 define([status(thm)])).
% 3.81/1.18 thf(setminusLsub, axiom, setminusLsub =
% 3.81/1.18 (![A:$i,B:$i]: ( subset @ ( setminus @ A @ B ) @ A ))).
% 3.81/1.18 thf('3', plain,
% 3.81/1.18 (( setminusLsub ) =
% 3.81/1.18 ( ![X4:$i,X6:$i]: ( subset @ ( setminus @ X4 @ X6 ) @ X4 ) )),
% 3.81/1.18 define([status(thm)])).
% 3.81/1.18 thf(setminusIRneg, axiom, setminusIRneg =
% 3.81/1.18 (![A:$i,B:$i,Xx:$i]:
% 3.81/1.18 ( ( in @ Xx @ B ) => ( ~( in @ Xx @ ( setminus @ A @ B ) ) ) ))).
% 3.81/1.18 thf('4', plain,
% 3.81/1.18 (( setminusIRneg ) =
% 3.81/1.18 ( ![X4:$i,X6:$i,X8:$i]:
% 3.81/1.18 ( ( in @ X8 @ X6 ) => ( ~( in @ X8 @ ( setminus @ X4 @ X6 ) ) ) ) )),
% 3.81/1.18 define([status(thm)])).
% 3.81/1.18 thf(setminusILneg, axiom, setminusILneg =
% 3.81/1.18 (![A:$i,B:$i,Xx:$i]:
% 3.81/1.18 ( ( ~( in @ Xx @ A ) ) => ( ~( in @ Xx @ ( setminus @ A @ B ) ) ) ))).
% 3.81/1.18 thf('5', plain,
% 3.81/1.18 (( setminusILneg ) =
% 3.81/1.18 ( ![X4:$i,X6:$i,X8:$i]:
% 3.81/1.18 ( ( ~( in @ X8 @ X4 ) ) => ( ~( in @ X8 @ ( setminus @ X4 @ X6 ) ) ) ) )),
% 3.81/1.18 define([status(thm)])).
% 3.81/1.18 thf(setminusELneg, axiom, setminusELneg =
% 3.81/1.18 (![A:$i,B:$i,Xx:$i]:
% 3.81/1.18 ( ( ~( in @ Xx @ ( setminus @ A @ B ) ) ) =>
% 3.81/1.18 ( ( ~( in @ Xx @ B ) ) => ( ~( in @ Xx @ A ) ) ) ))).
% 3.81/1.18 thf('6', plain,
% 3.81/1.18 (( setminusELneg ) =
% 3.81/1.18 ( ![X4:$i,X6:$i,X8:$i]:
% 3.81/1.18 ( ( ~( in @ X8 @ ( setminus @ X4 @ X6 ) ) ) =>
% 3.81/1.18 ( ( ~( in @ X8 @ X6 ) ) => ( ~( in @ X8 @ X4 ) ) ) ) )),
% 3.81/1.18 define([status(thm)])).
% 3.81/1.18 thf(setminusERneg, axiom, setminusERneg =
% 3.81/1.18 (![A:$i,B:$i,Xx:$i]:
% 3.81/1.18 ( ( ~( in @ Xx @ ( setminus @ A @ B ) ) ) =>
% 3.81/1.18 ( ( in @ Xx @ A ) => ( in @ Xx @ B ) ) ))).
% 3.81/1.18 thf('7', plain,
% 3.81/1.18 (( setminusERneg ) =
% 3.81/1.18 ( ![X4:$i,X6:$i,X8:$i]:
% 3.81/1.18 ( ( ~( in @ X8 @ ( setminus @ X4 @ X6 ) ) ) =>
% 3.81/1.18 ( ( in @ X8 @ X4 ) => ( in @ X8 @ X6 ) ) ) )),
% 3.81/1.18 define([status(thm)])).
% 3.81/1.18 thf(setminusSubset2, axiom, setminusSubset2 =
% 3.81/1.18 (![A:$i,B:$i]:
% 3.81/1.18 ( ( subset @ A @ B ) => ( ( setminus @ A @ B ) = ( emptyset ) ) ))).
% 3.81/1.18 thf('8', plain,
% 3.81/1.18 (( setminusSubset2 ) =
% 3.81/1.18 ( ![X4:$i,X6:$i]:
% 3.81/1.18 ( ( subset @ X4 @ X6 ) => ( ( setminus @ X4 @ X6 ) = ( emptyset ) ) ) )),
% 3.81/1.18 define([status(thm)])).
% 3.81/1.18 thf(setminusER, axiom, setminusER =
% 3.81/1.18 (![A:$i,B:$i,Xx:$i]:
% 3.81/1.18 ( ( in @ Xx @ ( setminus @ A @ B ) ) => ( ~( in @ Xx @ B ) ) ))).
% 3.81/1.18 thf('9', plain,
% 3.81/1.18 (( setminusER ) =
% 3.81/1.18 ( ![X4:$i,X6:$i,X8:$i]:
% 3.81/1.18 ( ( in @ X8 @ ( setminus @ X4 @ X6 ) ) => ( ~( in @ X8 @ X6 ) ) ) )),
% 3.81/1.18 define([status(thm)])).
% 3.81/1.18 thf(setminusEL, axiom, setminusEL =
% 3.81/1.18 (![A:$i,B:$i,Xx:$i]:
% 3.81/1.18 ( ( in @ Xx @ ( setminus @ A @ B ) ) => ( in @ Xx @ A ) ))).
% 3.81/1.18 thf('10', plain,
% 3.81/1.18 (( setminusEL ) =
% 3.81/1.18 ( ![X4:$i,X6:$i,X8:$i]:
% 3.81/1.18 ( ( in @ X8 @ ( setminus @ X4 @ X6 ) ) => ( in @ X8 @ X4 ) ) )),
% 3.81/1.18 define([status(thm)])).
% 3.81/1.18 thf(setminusI, axiom, setminusI =
% 3.81/1.18 (![A:$i,B:$i,Xx:$i]:
% 3.81/1.18 ( ( in @ Xx @ A ) =>
% 3.81/1.18 ( ( ~( in @ Xx @ B ) ) => ( in @ Xx @ ( setminus @ A @ B ) ) ) ))).
% 3.81/1.18 thf('11', plain,
% 3.81/1.18 (( setminusI ) =
% 3.81/1.18 ( ![X4:$i,X6:$i,X8:$i]:
% 3.81/1.18 ( ( in @ X8 @ X4 ) =>
% 3.81/1.18 ( ( ~( in @ X8 @ X6 ) ) => ( in @ X8 @ ( setminus @ X4 @ X6 ) ) ) ) )),
% 3.81/1.18 define([status(thm)])).
% 3.81/1.18 thf(powersetsubset, axiom, powersetsubset =
% 3.81/1.18 (![A:$i,B:$i]:
% 3.81/1.18 ( ( subset @ A @ B ) => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ))).
% 3.81/1.18 thf('12', plain,
% 3.81/1.18 (( powersetsubset ) =
% 3.81/1.18 ( ![X4:$i,X6:$i]:
% 3.81/1.18 ( ( subset @ X4 @ X6 ) =>
% 3.81/1.18 ( subset @ ( powerset @ X4 ) @ ( powerset @ X6 ) ) ) )),
% 3.81/1.18 define([status(thm)])).
% 3.81/1.18 thf(inPowerset, axiom, inPowerset = (![A:$i]: ( in @ A @ ( powerset @ A ) ))).
% 3.81/1.18 thf('13', plain,
% 3.81/1.18 (( inPowerset ) = ( ![X4:$i]: ( in @ X4 @ ( powerset @ X4 ) ) )),
% 3.81/1.18 define([status(thm)])).
% 3.81/1.18 thf(powersetE1, axiom, powersetE1 =
% 3.81/1.18 (![A:$i,B:$i]: ( ( in @ B @ ( powerset @ A ) ) => ( subset @ B @ A ) ))).
% 3.81/1.18 thf('14', plain,
% 3.81/1.18 (( powersetE1 ) =
% 3.81/1.18 ( ![X4:$i,X6:$i]:
% 3.81/1.18 ( ( in @ X6 @ ( powerset @ X4 ) ) => ( subset @ X6 @ X4 ) ) )),
% 3.81/1.18 define([status(thm)])).
% 3.81/1.18 thf(powersetI1, axiom, powersetI1 =
% 3.81/1.18 (![A:$i,B:$i]: ( ( subset @ B @ A ) => ( in @ B @ ( powerset @ A ) ) ))).
% 3.81/1.18 thf('15', plain,
% 3.81/1.18 (( powersetI1 ) =
% 3.81/1.18 ( ![X4:$i,X6:$i]:
% 3.81/1.18 ( ( subset @ X6 @ X4 ) => ( in @ X6 @ ( powerset @ X4 ) ) ) )),
% 3.81/1.18 define([status(thm)])).
% 3.81/1.18 thf(subset2powerset, axiom, subset2powerset =
% 3.81/1.18 (![A:$i,B:$i]: ( ( subset @ A @ B ) => ( in @ A @ ( powerset @ B ) ) ))).
% 3.81/1.18 thf('16', plain,
% 3.81/1.18 (( subset2powerset ) =
% 3.81/1.18 ( ![X4:$i,X6:$i]:
% 3.81/1.18 ( ( subset @ X4 @ X6 ) => ( in @ X4 @ ( powerset @ X6 ) ) ) )),
% 3.81/1.18 define([status(thm)])).
% 3.81/1.18 thf(powerset__Cong, axiom, powerset__Cong =
% 3.81/1.18 (![A:$i,B:$i]:
% 3.81/1.18 ( ( ( A ) = ( B ) ) => ( ( powerset @ A ) = ( powerset @ B ) ) ))).
% 3.81/1.18 thf('17', plain,
% 3.81/1.18 (( powerset__Cong ) =
% 3.81/1.18 ( ![X4:$i,X6:$i]:
% 3.81/1.18 ( ( ( X4 ) = ( X6 ) ) => ( ( powerset @ X4 ) = ( powerset @ X6 ) ) ) )),
% 3.81/1.18 define([status(thm)])).
% 3.81/1.18 thf(powersetE, axiom, powersetE =
% 3.81/1.18 (![A:$i,B:$i,Xx:$i]:
% 3.81/1.18 ( ( in @ B @ ( powerset @ A ) ) => ( ( in @ Xx @ B ) => ( in @ Xx @ A ) ) ))).
% 3.81/1.18 thf('18', plain,
% 3.81/1.18 (( powersetE ) =
% 3.81/1.18 ( ![X4:$i,X6:$i,X8:$i]:
% 3.81/1.18 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 3.81/1.18 ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ) )),
% 3.81/1.18 define([status(thm)])).
% 3.81/1.18 thf(emptyInPowerset, axiom, emptyInPowerset =
% 3.81/1.18 (![A:$i]: ( in @ emptyset @ ( powerset @ A ) ))).
% 3.81/1.18 thf('19', plain,
% 3.81/1.18 (( emptyInPowerset ) =
% 3.81/1.18 ( ![X4:$i]: ( in @ emptyset @ ( powerset @ X4 ) ) )),
% 3.81/1.18 define([status(thm)])).
% 3.81/1.18 thf(emptyinPowerset, axiom, emptyinPowerset =
% 3.81/1.18 (![A:$i]: ( in @ emptyset @ ( powerset @ A ) ))).
% 3.81/1.18 thf('20', plain,
% 3.81/1.18 (( emptyinPowerset ) =
% 3.81/1.18 ( ![X4:$i]: ( in @ emptyset @ ( powerset @ X4 ) ) )),
% 3.81/1.18 define([status(thm)])).
% 3.81/1.18 thf(powersetI, axiom, powersetI =
% 3.81/1.18 (![A:$i,B:$i]:
% 3.81/1.18 ( ( ![Xx:$i]: ( ( in @ Xx @ B ) => ( in @ Xx @ A ) ) ) =>
% 3.81/1.18 ( in @ B @ ( powerset @ A ) ) ))).
% 3.81/1.18 thf('21', plain,
% 3.81/1.18 (( powersetI ) =
% 3.81/1.18 ( ![X4:$i,X6:$i]:
% 3.81/1.18 ( ( ![X8:$i]: ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ) =>
% 3.81/1.18 ( in @ X6 @ ( powerset @ X4 ) ) ) )),
% 3.81/1.18 define([status(thm)])).
% 3.81/1.18 thf(powersetAx, axiom, powersetAx =
% 3.81/1.18 (![A:$i,B:$i]:
% 3.81/1.18 ( ( in @ B @ ( powerset @ A ) ) <=>
% 3.81/1.18 ( ![Xx:$i]: ( ( in @ Xx @ B ) => ( in @ Xx @ A ) ) ) ))).
% 3.81/1.18 thf('22', plain,
% 3.81/1.18 (( powersetAx ) =
% 3.81/1.18 ( ![X4:$i,X6:$i]:
% 3.81/1.18 ( ( in @ X6 @ ( powerset @ X4 ) ) <=>
% 3.81/1.18 ( ![X8:$i]: ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ) ) )),
% 3.81/1.18 define([status(thm)])).
% 3.81/1.18 thf(setminusT_lem, conjecture,
% 3.81/1.18 (( setextAx ) =>
% 3.81/1.18 ( ( emptysetAx ) =>
% 3.81/1.18 ( ( setadjoinAx ) =>
% 3.81/1.18 ( ( powersetAx ) =>
% 3.81/1.18 ( ( setunionAx ) =>
% 3.81/1.18 ( ( omega0Ax ) =>
% 3.81/1.18 ( ( omegaSAx ) =>
% 3.81/1.18 ( ( omegaIndAx ) =>
% 3.81/1.18 ( ( replAx ) =>
% 3.81/1.18 ( ( foundationAx ) =>
% 3.81/1.18 ( ( wellorderingAx ) =>
% 3.81/1.18 ( ( descrp ) =>
% 3.81/1.18 ( ( dsetconstrI ) =>
% 3.81/1.18 ( ( dsetconstrEL ) =>
% 3.81/1.18 ( ( dsetconstrER ) =>
% 3.81/1.18 ( ( exuE1 ) =>
% 3.81/1.18 ( ( prop2setE ) =>
% 3.81/1.18 ( ( emptysetE ) =>
% 3.81/1.18 ( ( emptysetimpfalse ) =>
% 3.81/1.18 ( ( notinemptyset ) =>
% 3.81/1.18 ( ( exuE3e ) =>
% 3.81/1.18 ( ( setext ) =>
% 3.81/1.18 ( ( emptyI ) =>
% 3.81/1.18 ( ( noeltsimpempty ) =>
% 3.81/1.18 ( ( setbeta ) =>
% 3.81/1.18 ( ( nonemptyE1 ) =>
% 3.81/1.18 ( ( nonemptyI ) =>
% 3.81/1.18 ( ( nonemptyI1 ) =>
% 3.81/1.18 ( ( setadjoinIL ) =>
% 3.81/1.18 ( ( emptyinunitempty ) =>
% 3.81/1.18 ( ( setadjoinIR ) =>
% 3.81/1.18 ( ( setadjoinE ) =>
% 3.81/1.18 ( (
% 3.81/1.18 setadjoinOr ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 setoftrueEq ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 powersetI ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 emptyinPowerset ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 emptyInPowerset ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 powersetE ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 setunionI ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 setunionE ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 subPowSU ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 exuE2 ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 nonemptyImpWitness ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 uniqinunit ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 notinsingleton ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 eqinunit ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 singletonsswitch ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 upairsetE ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 upairsetIL ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 upairsetIR ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 emptyE1 ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 vacuousDall ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 quantDeMorgan1 ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 quantDeMorgan2 ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 quantDeMorgan3 ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 quantDeMorgan4 ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 prop2setI ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 prop2set2propI ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 notdexE ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 notdallE ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 exuI1 ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 exuI3 ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 exuI2 ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 inCongP ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 in__Cong ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 exuE3u ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 exu__Cong ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 emptyset__Cong ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 setadjoin__Cong ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 powerset__Cong ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 setunion__Cong ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 omega__Cong ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 exuEu ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 descr__Cong ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 dsetconstr__Cong ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 subsetI1 ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 eqimpsubset2 ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 eqimpsubset1 ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 subsetI2 ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 emptysetsubset ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 subsetE ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 subsetE2 ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 notsubsetI ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 notequalI1 ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 notequalI2 ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 subsetRefl ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 subsetTrans ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 setadjoinSub ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 setadjoinSub2 ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 subset2powerset ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 setextsub ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 subsetemptysetimpeq ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 powersetI1 ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 powersetE1 ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 inPowerset ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 powersetsubset ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 sepInPowerset ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 sepSubset ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 binunionIL ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 upairset2IR ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 binunionIR ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 binunionEcases ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 binunionE ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 binunionLsub ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 binunionRsub ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 binintersectI ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 binintersectSubset5 ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 binintersectEL ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 binintersectLsub ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 binintersectSubset2 ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 binintersectSubset3 ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 binintersectER ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 disjointsetsI1 ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 binintersectRsub ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 binintersectSubset4 ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 binintersectSubset1 ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 bs114d ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 setminusI ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 setminusEL ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 setminusER ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 setminusSubset2 ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 setminusERneg ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 setminusELneg ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 setminusILneg ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 setminusIRneg ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 setminusLsub ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 setminusSubset1 ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 symdiffE ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 symdiffI1 ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 symdiffI2 ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 symdiffIneg1 ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 symdiffIneg2 ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 secondinupair ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 setukpairIL ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 setukpairIR ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 kpairiskpair ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 kpairp ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 singletonsubset ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 singletoninpowerset ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 singletoninpowunion ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 upairset2E ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 upairsubunion ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 upairinpowunion ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 ubforcartprodlem1 ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 ubforcartprodlem2 ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 ubforcartprodlem3 ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 cartprodpairin ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 cartprodmempair1 ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 cartprodmempair ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 setunionE2 ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 setunionsingleton1 ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 setunionsingleton2 ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 setunionsingleton ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 singletonprop ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 ex1E1 ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 ex1I ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 ex1I2 ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 singletonsuniq ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 setukpairinjL1 ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 kfstsingleton ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 theprop ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 kfstpairEq ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 cartprodfstin ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 setukpairinjL2 ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 setukpairinjL ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 setukpairinjR11 ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 setukpairinjR12 ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 setukpairinjR1 ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 upairequniteq ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 setukpairinjR2 ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 setukpairinjR ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 ksndsingleton ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 ksndpairEq ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 kpairsurjEq ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 cartprodsndin ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 cartprodpairmemEL ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 cartprodpairmemER ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 cartprodmempaircEq ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 cartprodfstpairEq ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 cartprodsndpairEq ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 cartprodpairsurjEq ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 dpsetconstrI ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 dpsetconstrSub ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 setOfPairsIsBReln ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 dpsetconstrERa ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 dpsetconstrEL1 ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 dpsetconstrEL2 ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 dpsetconstrER ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 funcImageSingleton ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 apProp ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 app ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 infuncsetfunc ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 ap2p ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 funcinfuncset ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 lamProp ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 lamp ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 lam2p ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 brelnall1 ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 brelnall2 ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 ex1E2 ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 funcGraphProp1 ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 funcGraphProp3 ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 funcGraphProp2 ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 funcextLem ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 funcGraphProp4 ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 subbreln ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 eqbreln ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 funcext ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 funcext2 ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 ap2apEq1 ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 ap2apEq2 ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 beta1 ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 eta1 ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 lam2lamEq ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 beta2 ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 eta2 ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 iffalseProp1 ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 iffalseProp2 ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 iftrueProp1 ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 iftrueProp2 ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 ifSingleton ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 ifp ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 theeq ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 iftrue ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 iffalse ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 iftrueorfalse ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 binintersectT_lem ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 binunionT_lem ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 powersetT_lem ) =>
% 3.81/1.18 (
% 3.81/1.18 ![
% 3.81/1.18 A:$i,X:$i]:
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 in @
% 3.81/1.18 X @
% 3.81/1.18 (
% 3.81/1.18 powerset @
% 3.81/1.18 A ) ) =>
% 3.81/1.18 (
% 3.81/1.18 ![
% 3.81/1.18 Y:$i]:
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 in @
% 3.81/1.18 Y @
% 3.81/1.18 (
% 3.81/1.18 powerset @
% 3.81/1.18 A ) ) =>
% 3.81/1.18 (
% 3.81/1.18 in @
% 3.81/1.18 (
% 3.81/1.18 setminus @
% 3.81/1.18 X @ Y ) @
% 3.81/1.18 (
% 3.81/1.18 powerset @
% 3.81/1.18 A ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 3.81/1.18 thf(zf_stmt_0, conjecture,
% 3.81/1.18 (( setextAx ) =>
% 3.81/1.18 ( ( emptysetAx ) =>
% 3.81/1.18 ( ( setadjoinAx ) =>
% 3.81/1.18 ( ( ![X4:$i,X6:$i]:
% 3.81/1.18 ( ( in @ X6 @ ( powerset @ X4 ) ) <=>
% 3.81/1.18 ( ![X8:$i]: ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ) ) ) =>
% 3.81/1.18 ( ( setunionAx ) =>
% 3.81/1.18 ( ( omega0Ax ) =>
% 3.81/1.18 ( ( omegaSAx ) =>
% 3.81/1.18 ( ( omegaIndAx ) =>
% 3.81/1.18 ( ( replAx ) =>
% 3.81/1.18 ( ( foundationAx ) =>
% 3.81/1.18 ( ( wellorderingAx ) =>
% 3.81/1.18 ( ( descrp ) =>
% 3.81/1.18 ( ( dsetconstrI ) =>
% 3.81/1.18 ( ( dsetconstrEL ) =>
% 3.81/1.18 ( ( dsetconstrER ) =>
% 3.81/1.18 ( ( exuE1 ) =>
% 3.81/1.18 ( ( prop2setE ) =>
% 3.81/1.18 ( ( emptysetE ) =>
% 3.81/1.18 ( ( emptysetimpfalse ) =>
% 3.81/1.18 ( ( notinemptyset ) =>
% 3.81/1.18 ( ( exuE3e ) =>
% 3.81/1.18 ( ( setext ) =>
% 3.81/1.18 ( ( emptyI ) =>
% 3.81/1.18 ( ( noeltsimpempty ) =>
% 3.81/1.18 ( ( setbeta ) =>
% 3.81/1.18 ( ( nonemptyE1 ) =>
% 3.81/1.18 ( ( nonemptyI ) =>
% 3.81/1.18 ( ( nonemptyI1 ) =>
% 3.81/1.18 ( ( setadjoinIL ) =>
% 3.81/1.18 ( ( emptyinunitempty ) =>
% 3.81/1.18 ( ( setadjoinIR ) =>
% 3.81/1.18 ( ( setadjoinE ) =>
% 3.81/1.18 ( (
% 3.81/1.18 setadjoinOr ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 setoftrueEq ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 ![
% 3.81/1.18 X10:$i,
% 3.81/1.18 X12:$i]:
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 ![
% 3.81/1.18 X14:$i]:
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 in @
% 3.81/1.18 X14 @ X12 ) =>
% 3.81/1.18 (
% 3.81/1.18 in @
% 3.81/1.18 X14 @ X10 ) ) ) =>
% 3.81/1.18 (
% 3.81/1.18 in @
% 3.81/1.18 X12 @
% 3.81/1.18 (
% 3.81/1.18 powerset @
% 3.81/1.18 X10 ) ) ) ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 ![
% 3.81/1.18 X16:$i]:
% 3.81/1.18 (
% 3.81/1.18 in @
% 3.81/1.18 emptyset @
% 3.81/1.18 (
% 3.81/1.18 powerset @
% 3.81/1.18 X16 ) ) ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 ![
% 3.81/1.18 X18:$i]:
% 3.81/1.18 (
% 3.81/1.18 in @
% 3.81/1.18 emptyset @
% 3.81/1.18 (
% 3.81/1.18 powerset @
% 3.81/1.18 X18 ) ) ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 ![
% 3.81/1.18 X20:$i,
% 3.81/1.18 X22:$i,
% 3.81/1.18 X24:$i]:
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 in @
% 3.81/1.18 X22 @
% 3.81/1.18 (
% 3.81/1.18 powerset @
% 3.81/1.18 X20 ) ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 in @
% 3.81/1.18 X24 @ X22 ) =>
% 3.81/1.18 (
% 3.81/1.18 in @
% 3.81/1.18 X24 @ X20 ) ) ) ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 setunionI ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 setunionE ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 subPowSU ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 exuE2 ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 nonemptyImpWitness ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 uniqinunit ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 notinsingleton ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 eqinunit ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 singletonsswitch ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 upairsetE ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 upairsetIL ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 upairsetIR ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 emptyE1 ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 vacuousDall ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 quantDeMorgan1 ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 quantDeMorgan2 ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 quantDeMorgan3 ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 quantDeMorgan4 ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 prop2setI ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 prop2set2propI ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 notdexE ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 notdallE ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 exuI1 ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 exuI3 ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 exuI2 ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 inCongP ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 in__Cong ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 exuE3u ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 exu__Cong ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 emptyset__Cong ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 setadjoin__Cong ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 ![
% 3.81/1.18 X26:$i,
% 3.81/1.18 X28:$i]:
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 X26 ) =
% 3.81/1.18 (
% 3.81/1.18 X28 ) ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 powerset @
% 3.81/1.18 X26 ) =
% 3.81/1.18 (
% 3.81/1.18 powerset @
% 3.81/1.18 X28 ) ) ) ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 setunion__Cong ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 omega__Cong ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 exuEu ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 descr__Cong ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 dsetconstr__Cong ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 subsetI1 ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 eqimpsubset2 ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 eqimpsubset1 ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 subsetI2 ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 emptysetsubset ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 subsetE ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 subsetE2 ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 notsubsetI ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 notequalI1 ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 notequalI2 ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 subsetRefl ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 subsetTrans ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 setadjoinSub ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 setadjoinSub2 ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 ![
% 3.81/1.18 X30:$i,
% 3.81/1.18 X32:$i]:
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 subset @
% 3.81/1.18 X30 @ X32 ) =>
% 3.81/1.18 (
% 3.81/1.18 in @
% 3.81/1.18 X30 @
% 3.81/1.18 (
% 3.81/1.18 powerset @
% 3.81/1.18 X32 ) ) ) ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 setextsub ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 subsetemptysetimpeq ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 ![
% 3.81/1.18 X34:$i,
% 3.81/1.18 X36:$i]:
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 subset @
% 3.81/1.18 X36 @ X34 ) =>
% 3.81/1.18 (
% 3.81/1.18 in @
% 3.81/1.18 X36 @
% 3.81/1.18 (
% 3.81/1.18 powerset @
% 3.81/1.18 X34 ) ) ) ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 ![
% 3.81/1.18 X38:$i,
% 3.81/1.18 X40:$i]:
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 in @
% 3.81/1.18 X40 @
% 3.81/1.18 (
% 3.81/1.18 powerset @
% 3.81/1.18 X38 ) ) =>
% 3.81/1.18 (
% 3.81/1.18 subset @
% 3.81/1.18 X40 @ X38 ) ) ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 ![
% 3.81/1.18 X42:$i]:
% 3.81/1.18 (
% 3.81/1.18 in @
% 3.81/1.18 X42 @
% 3.81/1.18 (
% 3.81/1.18 powerset @
% 3.81/1.18 X42 ) ) ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 ![
% 3.81/1.18 X44:$i,
% 3.81/1.18 X46:$i]:
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 subset @
% 3.81/1.18 X44 @ X46 ) =>
% 3.81/1.18 (
% 3.81/1.18 subset @
% 3.81/1.18 (
% 3.81/1.18 powerset @
% 3.81/1.18 X44 ) @
% 3.81/1.18 (
% 3.81/1.18 powerset @
% 3.81/1.18 X46 ) ) ) ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 sepInPowerset ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 sepSubset ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 binunionIL ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 upairset2IR ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 binunionIR ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 binunionEcases ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 binunionE ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 binunionLsub ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 binunionRsub ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 binintersectI ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 binintersectSubset5 ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 binintersectEL ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 binintersectLsub ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 binintersectSubset2 ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 binintersectSubset3 ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 binintersectER ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 disjointsetsI1 ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 binintersectRsub ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 binintersectSubset4 ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 binintersectSubset1 ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 bs114d ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 ![
% 3.81/1.18 X48:$i,
% 3.81/1.18 X50:$i,
% 3.81/1.18 X52:$i]:
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 in @
% 3.81/1.18 X52 @ X48 ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 ~(
% 3.81/1.18 in @
% 3.81/1.18 X52 @ X50 ) ) =>
% 3.81/1.18 (
% 3.81/1.18 in @
% 3.81/1.18 X52 @
% 3.81/1.18 (
% 3.81/1.18 setminus @
% 3.81/1.18 X48 @ X50 ) ) ) ) ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 ![
% 3.81/1.18 X54:$i,
% 3.81/1.18 X56:$i,
% 3.81/1.18 X58:$i]:
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 in @
% 3.81/1.18 X58 @
% 3.81/1.18 (
% 3.81/1.18 setminus @
% 3.81/1.18 X54 @ X56 ) ) =>
% 3.81/1.18 (
% 3.81/1.18 in @
% 3.81/1.18 X58 @ X54 ) ) ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 ![
% 3.81/1.18 X60:$i,
% 3.81/1.18 X62:$i,
% 3.81/1.18 X64:$i]:
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 in @
% 3.81/1.18 X64 @
% 3.81/1.18 (
% 3.81/1.18 setminus @
% 3.81/1.18 X60 @ X62 ) ) =>
% 3.81/1.18 (
% 3.81/1.18 ~(
% 3.81/1.18 in @
% 3.81/1.18 X64 @ X62 ) ) ) ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 ![
% 3.81/1.18 X66:$i,
% 3.81/1.18 X68:$i]:
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 subset @
% 3.81/1.18 X66 @ X68 ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 setminus @
% 3.81/1.18 X66 @ X68 ) =
% 3.81/1.18 (
% 3.81/1.18 emptyset ) ) ) ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 ![
% 3.81/1.18 X70:$i,
% 3.81/1.18 X72:$i,
% 3.81/1.18 X74:$i]:
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 ~(
% 3.81/1.18 in @
% 3.81/1.18 X74 @
% 3.81/1.18 (
% 3.81/1.18 setminus
% 3.81/1.18 @
% 3.81/1.18 X70 @ X72 ) ) ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 in @
% 3.81/1.18 X74 @ X70 ) =>
% 3.81/1.18 (
% 3.81/1.18 in @
% 3.81/1.18 X74 @ X72 ) ) ) ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 ![
% 3.81/1.18 X76:$i,
% 3.81/1.18 X78:$i,
% 3.81/1.18 X80:$i]:
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 ~(
% 3.81/1.18 in @
% 3.81/1.18 X80 @
% 3.81/1.18 (
% 3.81/1.18 setminus
% 3.81/1.18 @
% 3.81/1.18 X76 @ X78 ) ) ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 ~(
% 3.81/1.18 in @
% 3.81/1.18 X80 @ X78 ) ) =>
% 3.81/1.18 (
% 3.81/1.18 ~(
% 3.81/1.18 in @
% 3.81/1.18 X80 @ X76 ) ) ) ) ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 ![
% 3.81/1.18 X82:$i,
% 3.81/1.18 X84:$i,
% 3.81/1.18 X86:$i]:
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 ~(
% 3.81/1.18 in @
% 3.81/1.18 X86 @ X82 ) ) =>
% 3.81/1.18 (
% 3.81/1.18 ~(
% 3.81/1.18 in @
% 3.81/1.18 X86 @
% 3.81/1.18 (
% 3.81/1.18 setminus
% 3.81/1.18 @
% 3.81/1.18 X82 @ X84 ) ) ) ) ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 ![
% 3.81/1.18 X88:$i,
% 3.81/1.18 X90:$i,
% 3.81/1.18 X92:$i]:
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 in @
% 3.81/1.18 X92 @ X90 ) =>
% 3.81/1.18 (
% 3.81/1.18 ~(
% 3.81/1.18 in @
% 3.81/1.18 X92 @
% 3.81/1.18 (
% 3.81/1.18 setminus
% 3.81/1.18 @
% 3.81/1.18 X88 @ X90 ) ) ) ) ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 ![
% 3.81/1.18 X94:$i,
% 3.81/1.18 X96:$i]:
% 3.81/1.18 (
% 3.81/1.18 subset @
% 3.81/1.18 (
% 3.81/1.18 setminus @
% 3.81/1.18 X94 @ X96 ) @
% 3.81/1.18 X94 ) ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 ![
% 3.81/1.18 X98:$i,
% 3.81/1.18 X100:$i]:
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 setminus @
% 3.81/1.18 X98 @ X100 ) =
% 3.81/1.18 (
% 3.81/1.18 emptyset ) ) =>
% 3.81/1.18 (
% 3.81/1.18 subset @
% 3.81/1.18 X98 @ X100 ) ) ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 symdiffE ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 symdiffI1 ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 symdiffI2 ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 symdiffIneg1 ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 symdiffIneg2 ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 secondinupair ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 setukpairIL ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 setukpairIR ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 kpairiskpair ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 kpairp ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 singletonsubset ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 ![
% 3.81/1.18 X102:$i,
% 3.81/1.18 X104:$i]:
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 in @
% 3.81/1.18 X104 @
% 3.81/1.18 X102 ) =>
% 3.81/1.18 (
% 3.81/1.18 in @
% 3.81/1.18 (
% 3.81/1.18 setadjoin
% 3.81/1.18 @
% 3.81/1.18 X104 @
% 3.81/1.18 emptyset ) @
% 3.81/1.18 (
% 3.81/1.18 powerset @
% 3.81/1.18 X102 ) ) ) ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 singletoninpowunion ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 upairset2E ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 upairsubunion ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 upairinpowunion ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 ubforcartprodlem1 ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 ubforcartprodlem2 ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 ubforcartprodlem3 ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 cartprodpairin ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 cartprodmempair1 ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 cartprodmempair ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 setunionE2 ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 setunionsingleton1 ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 setunionsingleton2 ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 setunionsingleton ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 singletonprop ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 ex1E1 ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 ex1I ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 ex1I2 ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 singletonsuniq ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 setukpairinjL1 ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 kfstsingleton ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 theprop ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 kfstpairEq ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 cartprodfstin ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 setukpairinjL2 ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 setukpairinjL ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 setukpairinjR11 ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 setukpairinjR12 ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 setukpairinjR1 ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 upairequniteq ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 setukpairinjR2 ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 setukpairinjR ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 ksndsingleton ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 ksndpairEq ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 kpairsurjEq ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 cartprodsndin ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 cartprodpairmemEL ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 cartprodpairmemER ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 cartprodmempaircEq ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 cartprodfstpairEq ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 cartprodsndpairEq ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 cartprodpairsurjEq ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 dpsetconstrI ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 dpsetconstrSub ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 setOfPairsIsBReln ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 dpsetconstrERa ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 dpsetconstrEL1 ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 dpsetconstrEL2 ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 dpsetconstrER ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 funcImageSingleton ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 apProp ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 app ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 infuncsetfunc ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 ap2p ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 funcinfuncset ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 lamProp ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 lamp ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 lam2p ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 brelnall1 ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 brelnall2 ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 ex1E2 ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 funcGraphProp1 ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 funcGraphProp3 ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 funcGraphProp2 ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 funcextLem ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 funcGraphProp4 ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 subbreln ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 eqbreln ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 funcext ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 funcext2 ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 ap2apEq1 ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 ap2apEq2 ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 beta1 ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 eta1 ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 lam2lamEq ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 beta2 ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 eta2 ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 iffalseProp1 ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 iffalseProp2 ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 iftrueProp1 ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 iftrueProp2 ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 ifSingleton ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 ifp ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 theeq ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 iftrue ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 iffalse ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 iftrueorfalse ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 binintersectT_lem ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 binunionT_lem ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 ![
% 3.81/1.18 X106:$i,
% 3.81/1.18 X108:$i]:
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 in @
% 3.81/1.18 X108 @
% 3.81/1.18 (
% 3.81/1.18 powerset @
% 3.81/1.18 X106 ) ) =>
% 3.81/1.18 (
% 3.81/1.18 in @
% 3.81/1.18 (
% 3.81/1.18 powerset @
% 3.81/1.18 X108 ) @
% 3.81/1.18 (
% 3.81/1.18 powerset @
% 3.81/1.18 (
% 3.81/1.18 powerset @
% 3.81/1.18 X106 ) ) ) ) ) =>
% 3.81/1.18 (
% 3.81/1.18 ![
% 3.81/1.18 X110:$i,
% 3.81/1.18 X112:$i]:
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 in @
% 3.81/1.18 X112 @
% 3.81/1.18 (
% 3.81/1.18 powerset @
% 3.81/1.18 X110 ) ) =>
% 3.81/1.18 (
% 3.81/1.18 ![
% 3.81/1.18 X114:$i]:
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 in @
% 3.81/1.18 X114 @
% 3.81/1.18 (
% 3.81/1.18 powerset @
% 3.81/1.18 X110 ) ) =>
% 3.81/1.18 (
% 3.81/1.18 in @
% 3.81/1.18 (
% 3.81/1.18 setminus @
% 3.81/1.18 X112 @
% 3.81/1.18 X114 ) @
% 3.81/1.18 (
% 3.81/1.18 powerset @
% 3.81/1.18 X110 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 3.81/1.18 thf(zf_stmt_1, type, zip_tseitin_0 : $i > $i > $i > $o).
% 3.81/1.18 thf(zf_stmt_2, axiom,
% 3.81/1.18 (![X8:$i,X6:$i,X4:$i]:
% 3.81/1.18 ( ( zip_tseitin_0 @ X8 @ X6 @ X4 ) <=>
% 3.81/1.18 ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ))).
% 3.81/1.18 thf(zf_stmt_3, conjecture,
% 3.81/1.18 (( setextAx ) =>
% 3.81/1.18 ( ( emptysetAx ) =>
% 3.81/1.18 ( ( setadjoinAx ) =>
% 3.81/1.18 ( ( ![X4:$i,X6:$i]:
% 3.81/1.18 ( ( in @ X6 @ ( powerset @ X4 ) ) <=>
% 3.81/1.18 ( ![X8:$i]: ( zip_tseitin_0 @ X8 @ X6 @ X4 ) ) ) ) =>
% 3.81/1.18 ( ( setunionAx ) =>
% 3.81/1.18 ( ( omega0Ax ) =>
% 3.81/1.18 ( ( omegaSAx ) =>
% 3.81/1.18 ( ( omegaIndAx ) =>
% 3.81/1.18 ( ( replAx ) =>
% 3.81/1.18 ( ( foundationAx ) =>
% 3.81/1.18 ( ( wellorderingAx ) =>
% 3.81/1.18 ( ( descrp ) =>
% 3.81/1.18 ( ( dsetconstrI ) =>
% 3.81/1.18 ( ( dsetconstrEL ) =>
% 3.81/1.18 ( ( dsetconstrER ) =>
% 3.81/1.18 ( ( exuE1 ) =>
% 3.81/1.18 ( ( prop2setE ) =>
% 3.81/1.18 ( ( emptysetE ) =>
% 3.81/1.18 ( ( emptysetimpfalse ) =>
% 3.81/1.18 ( ( notinemptyset ) =>
% 3.81/1.18 ( ( exuE3e ) =>
% 3.81/1.18 ( ( setext ) =>
% 3.81/1.18 ( ( emptyI ) =>
% 3.81/1.18 ( ( noeltsimpempty ) =>
% 3.81/1.18 ( ( setbeta ) =>
% 3.81/1.18 ( ( nonemptyE1 ) =>
% 3.81/1.18 ( ( nonemptyI ) =>
% 3.81/1.18 ( ( nonemptyI1 ) =>
% 3.81/1.18 ( ( setadjoinIL ) =>
% 3.81/1.18 ( ( emptyinunitempty ) =>
% 3.81/1.18 ( ( setadjoinIR ) =>
% 3.81/1.18 ( ( setadjoinE ) =>
% 3.81/1.18 ( (
% 3.81/1.18 setadjoinOr ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 setoftrueEq ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 ![
% 3.81/1.18 X10:$i,
% 3.81/1.18 X12:$i]:
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 ![
% 3.81/1.18 X14:$i]:
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 in @
% 3.81/1.18 X14 @ X12 ) =>
% 3.81/1.18 (
% 3.81/1.18 in @
% 3.81/1.18 X14 @ X10 ) ) ) =>
% 3.81/1.18 (
% 3.81/1.18 in @
% 3.81/1.18 X12 @
% 3.81/1.18 (
% 3.81/1.18 powerset @
% 3.81/1.18 X10 ) ) ) ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 ![
% 3.81/1.18 X16:$i]:
% 3.81/1.18 (
% 3.81/1.18 in @
% 3.81/1.18 emptyset @
% 3.81/1.18 (
% 3.81/1.18 powerset @
% 3.81/1.18 X16 ) ) ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 ![
% 3.81/1.18 X18:$i]:
% 3.81/1.18 (
% 3.81/1.18 in @
% 3.81/1.18 emptyset @
% 3.81/1.18 (
% 3.81/1.18 powerset @
% 3.81/1.18 X18 ) ) ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 ![
% 3.81/1.18 X20:$i,
% 3.81/1.18 X22:$i,
% 3.81/1.18 X24:$i]:
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 in @
% 3.81/1.18 X22 @
% 3.81/1.18 (
% 3.81/1.18 powerset @
% 3.81/1.18 X20 ) ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 in @
% 3.81/1.18 X24 @ X22 ) =>
% 3.81/1.18 (
% 3.81/1.18 in @
% 3.81/1.18 X24 @ X20 ) ) ) ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 setunionI ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 setunionE ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 subPowSU ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 exuE2 ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 nonemptyImpWitness ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 uniqinunit ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 notinsingleton ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 eqinunit ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 singletonsswitch ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 upairsetE ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 upairsetIL ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 upairsetIR ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 emptyE1 ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 vacuousDall ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 quantDeMorgan1 ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 quantDeMorgan2 ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 quantDeMorgan3 ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 quantDeMorgan4 ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 prop2setI ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 prop2set2propI ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 notdexE ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 notdallE ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 exuI1 ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 exuI3 ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 exuI2 ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 inCongP ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 in__Cong ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 exuE3u ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 exu__Cong ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 emptyset__Cong ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 setadjoin__Cong ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 ![
% 3.81/1.18 X26:$i,
% 3.81/1.18 X28:$i]:
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 X26 ) =
% 3.81/1.18 (
% 3.81/1.18 X28 ) ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 powerset @
% 3.81/1.18 X26 ) =
% 3.81/1.18 (
% 3.81/1.18 powerset @
% 3.81/1.18 X28 ) ) ) ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 setunion__Cong ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 omega__Cong ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 exuEu ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 descr__Cong ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 dsetconstr__Cong ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 subsetI1 ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 eqimpsubset2 ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 eqimpsubset1 ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 subsetI2 ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 emptysetsubset ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 subsetE ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 subsetE2 ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 notsubsetI ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 notequalI1 ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 notequalI2 ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 subsetRefl ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 subsetTrans ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 setadjoinSub ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 setadjoinSub2 ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 ![
% 3.81/1.18 X30:$i,
% 3.81/1.18 X32:$i]:
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 subset @
% 3.81/1.18 X30 @ X32 ) =>
% 3.81/1.18 (
% 3.81/1.18 in @
% 3.81/1.18 X30 @
% 3.81/1.18 (
% 3.81/1.18 powerset @
% 3.81/1.18 X32 ) ) ) ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 setextsub ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 subsetemptysetimpeq ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 ![
% 3.81/1.18 X34:$i,
% 3.81/1.18 X36:$i]:
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 subset @
% 3.81/1.18 X36 @ X34 ) =>
% 3.81/1.18 (
% 3.81/1.18 in @
% 3.81/1.18 X36 @
% 3.81/1.18 (
% 3.81/1.18 powerset @
% 3.81/1.18 X34 ) ) ) ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 ![
% 3.81/1.18 X38:$i,
% 3.81/1.18 X40:$i]:
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 in @
% 3.81/1.18 X40 @
% 3.81/1.18 (
% 3.81/1.18 powerset @
% 3.81/1.18 X38 ) ) =>
% 3.81/1.18 (
% 3.81/1.18 subset @
% 3.81/1.18 X40 @ X38 ) ) ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 ![
% 3.81/1.18 X42:$i]:
% 3.81/1.18 (
% 3.81/1.18 in @
% 3.81/1.18 X42 @
% 3.81/1.18 (
% 3.81/1.18 powerset @
% 3.81/1.18 X42 ) ) ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 ![
% 3.81/1.18 X44:$i,
% 3.81/1.18 X46:$i]:
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 subset @
% 3.81/1.18 X44 @ X46 ) =>
% 3.81/1.18 (
% 3.81/1.18 subset @
% 3.81/1.18 (
% 3.81/1.18 powerset @
% 3.81/1.18 X44 ) @
% 3.81/1.18 (
% 3.81/1.18 powerset @
% 3.81/1.18 X46 ) ) ) ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 sepInPowerset ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 sepSubset ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 3.81/1.18 binunionIL ) =>
% 3.81/1.18 (
% 3.81/1.18 (
% 4.06/1.18 upairset2IR ) =>
% 4.06/1.18 (
% 4.06/1.18 (
% 4.06/1.18 binunionIR ) =>
% 4.06/1.18 (
% 4.06/1.18 (
% 4.06/1.18 binunionEcases ) =>
% 4.06/1.18 (
% 4.06/1.18 (
% 4.06/1.18 binunionE ) =>
% 4.06/1.18 (
% 4.06/1.18 (
% 4.06/1.18 binunionLsub ) =>
% 4.06/1.18 (
% 4.06/1.18 (
% 4.06/1.18 binunionRsub ) =>
% 4.06/1.18 (
% 4.06/1.18 (
% 4.06/1.18 binintersectI ) =>
% 4.06/1.18 (
% 4.06/1.18 (
% 4.06/1.18 binintersectSubset5 ) =>
% 4.06/1.18 (
% 4.06/1.18 (
% 4.06/1.18 binintersectEL ) =>
% 4.06/1.18 (
% 4.06/1.18 (
% 4.06/1.18 binintersectLsub ) =>
% 4.06/1.18 (
% 4.06/1.18 (
% 4.06/1.18 binintersectSubset2 ) =>
% 4.06/1.18 (
% 4.06/1.18 (
% 4.06/1.18 binintersectSubset3 ) =>
% 4.06/1.18 (
% 4.06/1.18 (
% 4.06/1.18 binintersectER ) =>
% 4.06/1.18 (
% 4.06/1.18 (
% 4.06/1.18 disjointsetsI1 ) =>
% 4.06/1.18 (
% 4.06/1.18 (
% 4.06/1.18 binintersectRsub ) =>
% 4.06/1.18 (
% 4.06/1.18 (
% 4.06/1.18 binintersectSubset4 ) =>
% 4.06/1.18 (
% 4.06/1.18 (
% 4.06/1.18 binintersectSubset1 ) =>
% 4.06/1.18 (
% 4.06/1.18 (
% 4.06/1.18 bs114d ) =>
% 4.06/1.18 (
% 4.06/1.18 (
% 4.06/1.18 ![
% 4.06/1.18 X48:$i,
% 4.06/1.18 X50:$i,
% 4.06/1.18 X52:$i]:
% 4.06/1.18 (
% 4.06/1.18 (
% 4.06/1.18 in @
% 4.06/1.18 X52 @ X48 ) =>
% 4.06/1.18 (
% 4.06/1.18 (
% 4.06/1.18 ~(
% 4.06/1.18 in @
% 4.06/1.18 X52 @ X50 ) ) =>
% 4.06/1.18 (
% 4.06/1.18 in @
% 4.06/1.18 X52 @
% 4.06/1.18 (
% 4.06/1.18 setminus @
% 4.06/1.18 X48 @ X50 ) ) ) ) ) =>
% 4.06/1.18 (
% 4.06/1.18 (
% 4.06/1.18 ![
% 4.06/1.18 X54:$i,
% 4.06/1.18 X56:$i,
% 4.06/1.18 X58:$i]:
% 4.06/1.18 (
% 4.06/1.18 (
% 4.06/1.18 in @
% 4.06/1.18 X58 @
% 4.06/1.18 (
% 4.06/1.18 setminus @
% 4.06/1.18 X54 @ X56 ) ) =>
% 4.06/1.18 (
% 4.06/1.18 in @
% 4.06/1.18 X58 @ X54 ) ) ) =>
% 4.06/1.18 (
% 4.06/1.18 (
% 4.06/1.18 ![
% 4.06/1.18 X60:$i,
% 4.06/1.18 X62:$i,
% 4.06/1.18 X64:$i]:
% 4.06/1.18 (
% 4.06/1.18 (
% 4.06/1.18 in @
% 4.06/1.18 X64 @
% 4.06/1.18 (
% 4.06/1.18 setminus @
% 4.06/1.18 X60 @ X62 ) ) =>
% 4.06/1.18 (
% 4.06/1.18 ~(
% 4.06/1.18 in @
% 4.06/1.18 X64 @ X62 ) ) ) ) =>
% 4.06/1.18 (
% 4.06/1.18 (
% 4.06/1.18 ![
% 4.06/1.18 X66:$i,
% 4.06/1.18 X68:$i]:
% 4.06/1.18 (
% 4.06/1.18 (
% 4.06/1.18 subset @
% 4.06/1.18 X66 @ X68 ) =>
% 4.06/1.18 (
% 4.06/1.18 (
% 4.06/1.18 setminus @
% 4.06/1.18 X66 @ X68 ) =
% 4.06/1.18 (
% 4.06/1.18 emptyset ) ) ) ) =>
% 4.06/1.18 (
% 4.06/1.18 (
% 4.06/1.18 ![
% 4.06/1.18 X70:$i,
% 4.06/1.18 X72:$i,
% 4.06/1.18 X74:$i]:
% 4.06/1.18 (
% 4.06/1.18 (
% 4.06/1.18 ~(
% 4.06/1.18 in @
% 4.06/1.18 X74 @
% 4.06/1.18 (
% 4.06/1.18 setminus
% 4.06/1.18 @
% 4.06/1.18 X70 @ X72 ) ) ) =>
% 4.06/1.18 (
% 4.06/1.18 (
% 4.06/1.18 in @
% 4.06/1.18 X74 @ X70 ) =>
% 4.06/1.18 (
% 4.06/1.18 in @
% 4.06/1.18 X74 @ X72 ) ) ) ) =>
% 4.06/1.18 (
% 4.06/1.18 (
% 4.06/1.18 ![
% 4.06/1.18 X76:$i,
% 4.06/1.18 X78:$i,
% 4.06/1.18 X80:$i]:
% 4.06/1.18 (
% 4.06/1.18 (
% 4.06/1.18 ~(
% 4.06/1.18 in @
% 4.06/1.18 X80 @
% 4.06/1.18 (
% 4.06/1.18 setminus
% 4.06/1.18 @
% 4.06/1.18 X76 @ X78 ) ) ) =>
% 4.06/1.18 (
% 4.06/1.18 (
% 4.06/1.18 ~(
% 4.06/1.18 in @
% 4.06/1.18 X80 @ X78 ) ) =>
% 4.06/1.18 (
% 4.06/1.18 ~(
% 4.06/1.18 in @
% 4.06/1.18 X80 @ X76 ) ) ) ) ) =>
% 4.06/1.18 (
% 4.06/1.18 (
% 4.06/1.18 ![
% 4.06/1.18 X82:$i,
% 4.06/1.18 X84:$i,
% 4.06/1.18 X86:$i]:
% 4.06/1.18 (
% 4.06/1.18 (
% 4.06/1.18 ~(
% 4.06/1.18 in @
% 4.06/1.18 X86 @ X82 ) ) =>
% 4.06/1.18 (
% 4.06/1.19 ~(
% 4.06/1.19 in @
% 4.06/1.19 X86 @
% 4.06/1.19 (
% 4.06/1.19 setminus
% 4.06/1.19 @
% 4.06/1.19 X82 @ X84 ) ) ) ) ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 ![
% 4.06/1.19 X88:$i,
% 4.06/1.19 X90:$i,
% 4.06/1.19 X92:$i]:
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 in @
% 4.06/1.19 X92 @ X90 ) =>
% 4.06/1.19 (
% 4.06/1.19 ~(
% 4.06/1.19 in @
% 4.06/1.19 X92 @
% 4.06/1.19 (
% 4.06/1.19 setminus
% 4.06/1.19 @
% 4.06/1.19 X88 @ X90 ) ) ) ) ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 ![
% 4.06/1.19 X94:$i,
% 4.06/1.19 X96:$i]:
% 4.06/1.19 (
% 4.06/1.19 subset @
% 4.06/1.19 (
% 4.06/1.19 setminus @
% 4.06/1.19 X94 @ X96 ) @
% 4.06/1.19 X94 ) ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 ![
% 4.06/1.19 X98:$i,
% 4.06/1.19 X100:$i]:
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 setminus @
% 4.06/1.19 X98 @ X100 ) =
% 4.06/1.19 (
% 4.06/1.19 emptyset ) ) =>
% 4.06/1.19 (
% 4.06/1.19 subset @
% 4.06/1.19 X98 @ X100 ) ) ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 symdiffE ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 symdiffI1 ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 symdiffI2 ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 symdiffIneg1 ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 symdiffIneg2 ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 secondinupair ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 setukpairIL ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 setukpairIR ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 kpairiskpair ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 kpairp ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 singletonsubset ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 ![
% 4.06/1.19 X102:$i,
% 4.06/1.19 X104:$i]:
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 in @
% 4.06/1.19 X104 @
% 4.06/1.19 X102 ) =>
% 4.06/1.19 (
% 4.06/1.19 in @
% 4.06/1.19 (
% 4.06/1.19 setadjoin
% 4.06/1.19 @
% 4.06/1.19 X104 @
% 4.06/1.19 emptyset ) @
% 4.06/1.19 (
% 4.06/1.19 powerset @
% 4.06/1.19 X102 ) ) ) ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 singletoninpowunion ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 upairset2E ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 upairsubunion ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 upairinpowunion ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 ubforcartprodlem1 ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 ubforcartprodlem2 ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 ubforcartprodlem3 ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 cartprodpairin ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 cartprodmempair1 ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 cartprodmempair ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 setunionE2 ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 setunionsingleton1 ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 setunionsingleton2 ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 setunionsingleton ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 singletonprop ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 ex1E1 ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 ex1I ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 ex1I2 ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 singletonsuniq ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 setukpairinjL1 ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 kfstsingleton ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 theprop ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 kfstpairEq ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 cartprodfstin ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 setukpairinjL2 ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 setukpairinjL ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 setukpairinjR11 ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 setukpairinjR12 ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 setukpairinjR1 ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 upairequniteq ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 setukpairinjR2 ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 setukpairinjR ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 ksndsingleton ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 ksndpairEq ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 kpairsurjEq ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 cartprodsndin ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 cartprodpairmemEL ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 cartprodpairmemER ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 cartprodmempaircEq ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 cartprodfstpairEq ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 cartprodsndpairEq ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 cartprodpairsurjEq ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 dpsetconstrI ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 dpsetconstrSub ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 setOfPairsIsBReln ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 dpsetconstrERa ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 dpsetconstrEL1 ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 dpsetconstrEL2 ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 dpsetconstrER ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 funcImageSingleton ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 apProp ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 app ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 infuncsetfunc ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 ap2p ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 funcinfuncset ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 lamProp ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 lamp ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 lam2p ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 brelnall1 ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 brelnall2 ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 ex1E2 ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 funcGraphProp1 ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 funcGraphProp3 ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 funcGraphProp2 ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 funcextLem ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 funcGraphProp4 ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 subbreln ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 eqbreln ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 funcext ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 funcext2 ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 ap2apEq1 ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 ap2apEq2 ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 beta1 ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 eta1 ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 lam2lamEq ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 beta2 ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 eta2 ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 iffalseProp1 ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 iffalseProp2 ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 iftrueProp1 ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 iftrueProp2 ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 ifSingleton ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 ifp ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 theeq ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 iftrue ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 iffalse ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 iftrueorfalse ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 binintersectT_lem ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 binunionT_lem ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 ![
% 4.06/1.19 X106:$i,
% 4.06/1.19 X108:$i]:
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 in @
% 4.06/1.19 X108 @
% 4.06/1.19 (
% 4.06/1.19 powerset @
% 4.06/1.19 X106 ) ) =>
% 4.06/1.19 (
% 4.06/1.19 in @
% 4.06/1.19 (
% 4.06/1.19 powerset @
% 4.06/1.19 X108 ) @
% 4.06/1.19 (
% 4.06/1.19 powerset @
% 4.06/1.19 (
% 4.06/1.19 powerset @
% 4.06/1.19 X106 ) ) ) ) ) =>
% 4.06/1.19 (
% 4.06/1.19 ![
% 4.06/1.19 X110:$i,
% 4.06/1.19 X112:$i]:
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 in @
% 4.06/1.19 X112 @
% 4.06/1.19 (
% 4.06/1.19 powerset @
% 4.06/1.19 X110 ) ) =>
% 4.06/1.19 (
% 4.06/1.19 ![
% 4.06/1.19 X114:$i]:
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 in @
% 4.06/1.19 X114 @
% 4.06/1.19 (
% 4.06/1.19 powerset @
% 4.06/1.19 X110 ) ) =>
% 4.06/1.19 (
% 4.06/1.19 in @
% 4.06/1.19 (
% 4.06/1.19 setminus @
% 4.06/1.19 X112 @
% 4.06/1.19 X114 ) @
% 4.06/1.19 (
% 4.06/1.19 powerset @
% 4.06/1.19 X110 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 4.06/1.19 thf(zf_stmt_4, negated_conjecture,
% 4.06/1.19 (~( ( setextAx ) =>
% 4.06/1.19 ( ( emptysetAx ) =>
% 4.06/1.19 ( ( setadjoinAx ) =>
% 4.06/1.19 ( ( ![X4:$i,X6:$i]:
% 4.06/1.19 ( ( in @ X6 @ ( powerset @ X4 ) ) <=>
% 4.06/1.19 ( ![X8:$i]: ( zip_tseitin_0 @ X8 @ X6 @ X4 ) ) ) ) =>
% 4.06/1.19 ( ( setunionAx ) =>
% 4.06/1.19 ( ( omega0Ax ) =>
% 4.06/1.19 ( ( omegaSAx ) =>
% 4.06/1.19 ( ( omegaIndAx ) =>
% 4.06/1.19 ( ( replAx ) =>
% 4.06/1.19 ( ( foundationAx ) =>
% 4.06/1.19 ( ( wellorderingAx ) =>
% 4.06/1.19 ( ( descrp ) =>
% 4.06/1.19 ( ( dsetconstrI ) =>
% 4.06/1.19 ( ( dsetconstrEL ) =>
% 4.06/1.19 ( ( dsetconstrER ) =>
% 4.06/1.19 ( ( exuE1 ) =>
% 4.06/1.19 ( ( prop2setE ) =>
% 4.06/1.19 ( ( emptysetE ) =>
% 4.06/1.19 ( ( emptysetimpfalse ) =>
% 4.06/1.19 ( ( notinemptyset ) =>
% 4.06/1.19 ( ( exuE3e ) =>
% 4.06/1.19 ( ( setext ) =>
% 4.06/1.19 ( ( emptyI ) =>
% 4.06/1.19 ( ( noeltsimpempty ) =>
% 4.06/1.19 ( ( setbeta ) =>
% 4.06/1.19 ( ( nonemptyE1 ) =>
% 4.06/1.19 ( ( nonemptyI ) =>
% 4.06/1.19 ( ( nonemptyI1 ) =>
% 4.06/1.19 ( ( setadjoinIL ) =>
% 4.06/1.19 ( ( emptyinunitempty ) =>
% 4.06/1.19 ( ( setadjoinIR ) =>
% 4.06/1.19 ( (
% 4.06/1.19 setadjoinE ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 setadjoinOr ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 setoftrueEq ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 ![
% 4.06/1.19 X10:$i,
% 4.06/1.19 X12:$i]:
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 ![
% 4.06/1.19 X14:$i]:
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 in @
% 4.06/1.19 X14 @ X12 ) =>
% 4.06/1.19 (
% 4.06/1.19 in @
% 4.06/1.19 X14 @ X10 ) ) ) =>
% 4.06/1.19 (
% 4.06/1.19 in @
% 4.06/1.19 X12 @
% 4.06/1.19 (
% 4.06/1.19 powerset
% 4.06/1.19 @
% 4.06/1.19 X10 ) ) ) ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 ![
% 4.06/1.19 X16:$i]:
% 4.06/1.19 (
% 4.06/1.19 in @
% 4.06/1.19 emptyset @
% 4.06/1.19 (
% 4.06/1.19 powerset
% 4.06/1.19 @
% 4.06/1.19 X16 ) ) ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 ![
% 4.06/1.19 X18:$i]:
% 4.06/1.19 (
% 4.06/1.19 in @
% 4.06/1.19 emptyset @
% 4.06/1.19 (
% 4.06/1.19 powerset
% 4.06/1.19 @
% 4.06/1.19 X18 ) ) ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 ![
% 4.06/1.19 X20:$i,
% 4.06/1.19 X22:$i,
% 4.06/1.19 X24:$i]:
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 in @
% 4.06/1.19 X22 @
% 4.06/1.19 (
% 4.06/1.19 powerset
% 4.06/1.19 @
% 4.06/1.19 X20 ) ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 in @
% 4.06/1.19 X24 @ X22 ) =>
% 4.06/1.19 (
% 4.06/1.19 in @
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% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 setunionI ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 setunionE ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 subPowSU ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 exuE2 ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 nonemptyImpWitness ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 uniqinunit ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 notinsingleton ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 eqinunit ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 singletonsswitch ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 upairsetE ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 upairsetIL ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 upairsetIR ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 emptyE1 ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 vacuousDall ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 quantDeMorgan1 ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 quantDeMorgan2 ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 quantDeMorgan3 ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 quantDeMorgan4 ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 prop2setI ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 prop2set2propI ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 notdexE ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 notdallE ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 exuI1 ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 exuI3 ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 exuI2 ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 inCongP ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 in__Cong ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 exuE3u ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 exu__Cong ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 emptyset__Cong ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 setadjoin__Cong ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 ![
% 4.06/1.19 X26:$i,
% 4.06/1.19 X28:$i]:
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 X26 ) =
% 4.06/1.19 (
% 4.06/1.19 X28 ) ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 powerset
% 4.06/1.19 @
% 4.06/1.19 X26 ) =
% 4.06/1.19 (
% 4.06/1.19 powerset
% 4.06/1.19 @
% 4.06/1.19 X28 ) ) ) ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 setunion__Cong ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 omega__Cong ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 exuEu ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 descr__Cong ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 dsetconstr__Cong ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 subsetI1 ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 eqimpsubset2 ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 eqimpsubset1 ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 subsetI2 ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 emptysetsubset ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 subsetE ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 subsetE2 ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 notsubsetI ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 notequalI1 ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 notequalI2 ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 subsetRefl ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 subsetTrans ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 setadjoinSub ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 setadjoinSub2 ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 ![
% 4.06/1.19 X30:$i,
% 4.06/1.19 X32:$i]:
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 subset @
% 4.06/1.19 X30 @ X32 ) =>
% 4.06/1.19 (
% 4.06/1.19 in @
% 4.06/1.19 X30 @
% 4.06/1.19 (
% 4.06/1.19 powerset
% 4.06/1.19 @
% 4.06/1.19 X32 ) ) ) ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 setextsub ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 subsetemptysetimpeq ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 ![
% 4.06/1.19 X34:$i,
% 4.06/1.19 X36:$i]:
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 subset @
% 4.06/1.19 X36 @ X34 ) =>
% 4.06/1.19 (
% 4.06/1.19 in @
% 4.06/1.19 X36 @
% 4.06/1.19 (
% 4.06/1.19 powerset
% 4.06/1.19 @
% 4.06/1.19 X34 ) ) ) ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 ![
% 4.06/1.19 X38:$i,
% 4.06/1.19 X40:$i]:
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 in @
% 4.06/1.19 X40 @
% 4.06/1.19 (
% 4.06/1.19 powerset
% 4.06/1.19 @
% 4.06/1.19 X38 ) ) =>
% 4.06/1.19 (
% 4.06/1.19 subset @
% 4.06/1.19 X40 @ X38 ) ) ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 ![
% 4.06/1.19 X42:$i]:
% 4.06/1.19 (
% 4.06/1.19 in @
% 4.06/1.19 X42 @
% 4.06/1.19 (
% 4.06/1.19 powerset
% 4.06/1.19 @
% 4.06/1.19 X42 ) ) ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 ![
% 4.06/1.19 X44:$i,
% 4.06/1.19 X46:$i]:
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 subset @
% 4.06/1.19 X44 @ X46 ) =>
% 4.06/1.19 (
% 4.06/1.19 subset @
% 4.06/1.19 (
% 4.06/1.19 powerset
% 4.06/1.19 @
% 4.06/1.19 X44 ) @
% 4.06/1.19 (
% 4.06/1.19 powerset
% 4.06/1.19 @
% 4.06/1.19 X46 ) ) ) ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 sepInPowerset ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 sepSubset ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 binunionIL ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 upairset2IR ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 binunionIR ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 binunionEcases ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 binunionE ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 binunionLsub ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 binunionRsub ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 binintersectI ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 binintersectSubset5 ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 binintersectEL ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 binintersectLsub ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 binintersectSubset2 ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 binintersectSubset3 ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 binintersectER ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 disjointsetsI1 ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 binintersectRsub ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 binintersectSubset4 ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 binintersectSubset1 ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 bs114d ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 ![
% 4.06/1.19 X48:$i,
% 4.06/1.19 X50:$i,
% 4.06/1.19 X52:$i]:
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 in @
% 4.06/1.19 X52 @ X48 ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 ~
% 4.06/1.19 (
% 4.06/1.19 in @
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% 4.06/1.19 (
% 4.06/1.19 in @
% 4.06/1.19 X52 @
% 4.06/1.19 (
% 4.06/1.19 setminus
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% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 ![
% 4.06/1.19 X54:$i,
% 4.06/1.19 X56:$i,
% 4.06/1.19 X58:$i]:
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 in @
% 4.06/1.19 X58 @
% 4.06/1.19 (
% 4.06/1.19 setminus
% 4.06/1.19 @
% 4.06/1.19 X54 @ X56 ) ) =>
% 4.06/1.19 (
% 4.06/1.19 in @
% 4.06/1.19 X58 @ X54 ) ) ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 ![
% 4.06/1.19 X60:$i,
% 4.06/1.19 X62:$i,
% 4.06/1.19 X64:$i]:
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 in @
% 4.06/1.19 X64 @
% 4.06/1.19 (
% 4.06/1.19 setminus
% 4.06/1.19 @
% 4.06/1.19 X60 @ X62 ) ) =>
% 4.06/1.19 (
% 4.06/1.19 ~
% 4.06/1.19 (
% 4.06/1.19 in @
% 4.06/1.19 X64 @ X62 ) ) ) ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 ![
% 4.06/1.19 X66:$i,
% 4.06/1.19 X68:$i]:
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 subset @
% 4.06/1.19 X66 @ X68 ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 setminus
% 4.06/1.19 @
% 4.06/1.19 X66 @ X68 ) =
% 4.06/1.19 (
% 4.06/1.19 emptyset ) ) ) ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 ![
% 4.06/1.19 X70:$i,
% 4.06/1.19 X72:$i,
% 4.06/1.19 X74:$i]:
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 ~
% 4.06/1.19 (
% 4.06/1.19 in @
% 4.06/1.19 X74 @
% 4.06/1.19 (
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% 4.06/1.19 @
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% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 in @
% 4.06/1.19 X74 @ X70 ) =>
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% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 ![
% 4.06/1.19 X76:$i,
% 4.06/1.19 X78:$i,
% 4.06/1.19 X80:$i]:
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 ~
% 4.06/1.19 (
% 4.06/1.19 in @
% 4.06/1.19 X80 @
% 4.06/1.19 (
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% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 ~
% 4.06/1.19 (
% 4.06/1.19 in @
% 4.06/1.19 X80 @ X78 ) ) =>
% 4.06/1.19 (
% 4.06/1.19 ~
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% 4.06/1.19 in @
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% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 ![
% 4.06/1.19 X82:$i,
% 4.06/1.19 X84:$i,
% 4.06/1.19 X86:$i]:
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 ~
% 4.06/1.19 (
% 4.06/1.19 in @
% 4.06/1.19 X86 @ X82 ) ) =>
% 4.06/1.19 (
% 4.06/1.19 ~
% 4.06/1.19 (
% 4.06/1.19 in @
% 4.06/1.19 X86 @
% 4.06/1.19 (
% 4.06/1.19 setminus
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% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 ![
% 4.06/1.19 X88:$i,
% 4.06/1.19 X90:$i,
% 4.06/1.19 X92:$i]:
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 in @
% 4.06/1.19 X92 @ X90 ) =>
% 4.06/1.19 (
% 4.06/1.19 ~
% 4.06/1.19 (
% 4.06/1.19 in @
% 4.06/1.19 X92 @
% 4.06/1.19 (
% 4.06/1.19 setminus
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% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 ![
% 4.06/1.19 X94:$i,
% 4.06/1.19 X96:$i]:
% 4.06/1.19 (
% 4.06/1.19 subset @
% 4.06/1.19 (
% 4.06/1.19 setminus
% 4.06/1.19 @
% 4.06/1.19 X94 @ X96 ) @
% 4.06/1.19 X94 ) ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 ![
% 4.06/1.19 X98:$i,
% 4.06/1.19 X100:$i]:
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 setminus
% 4.06/1.19 @
% 4.06/1.19 X98 @
% 4.06/1.19 X100 ) =
% 4.06/1.19 (
% 4.06/1.19 emptyset ) ) =>
% 4.06/1.19 (
% 4.06/1.19 subset @
% 4.06/1.19 X98 @
% 4.06/1.19 X100 ) ) ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 symdiffE ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 symdiffI1 ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 symdiffI2 ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 symdiffIneg1 ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 symdiffIneg2 ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 secondinupair ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 setukpairIL ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 setukpairIR ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 kpairiskpair ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 kpairp ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 singletonsubset ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 ![
% 4.06/1.19 X102:$i,
% 4.06/1.19 X104:$i]:
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 in @
% 4.06/1.19 X104 @
% 4.06/1.19 X102 ) =>
% 4.06/1.19 (
% 4.06/1.19 in @
% 4.06/1.19 (
% 4.06/1.19 setadjoin
% 4.06/1.19 @
% 4.06/1.19 X104 @
% 4.06/1.19 emptyset ) @
% 4.06/1.19 (
% 4.06/1.19 powerset
% 4.06/1.19 @
% 4.06/1.19 X102 ) ) ) ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 singletoninpowunion ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 upairset2E ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 upairsubunion ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 upairinpowunion ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 ubforcartprodlem1 ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 ubforcartprodlem2 ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 ubforcartprodlem3 ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 cartprodpairin ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 cartprodmempair1 ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 cartprodmempair ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 setunionE2 ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 setunionsingleton1 ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 setunionsingleton2 ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 setunionsingleton ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 singletonprop ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 ex1E1 ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 ex1I ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 ex1I2 ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 singletonsuniq ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 setukpairinjL1 ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 kfstsingleton ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 theprop ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 kfstpairEq ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 cartprodfstin ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 setukpairinjL2 ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 setukpairinjL ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 setukpairinjR11 ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 setukpairinjR12 ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 setukpairinjR1 ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 upairequniteq ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 setukpairinjR2 ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 setukpairinjR ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 ksndsingleton ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 ksndpairEq ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 kpairsurjEq ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 cartprodsndin ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 cartprodpairmemEL ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 cartprodpairmemER ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 cartprodmempaircEq ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 cartprodfstpairEq ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 cartprodsndpairEq ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 cartprodpairsurjEq ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 dpsetconstrI ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 dpsetconstrSub ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 setOfPairsIsBReln ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 dpsetconstrERa ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 dpsetconstrEL1 ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 dpsetconstrEL2 ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 dpsetconstrER ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 funcImageSingleton ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 apProp ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 app ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 infuncsetfunc ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 ap2p ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 funcinfuncset ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 lamProp ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 lamp ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 lam2p ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 brelnall1 ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 brelnall2 ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 ex1E2 ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 funcGraphProp1 ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 funcGraphProp3 ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 funcGraphProp2 ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 funcextLem ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 funcGraphProp4 ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 subbreln ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 eqbreln ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 funcext ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 funcext2 ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 ap2apEq1 ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 ap2apEq2 ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 beta1 ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 eta1 ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 lam2lamEq ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 beta2 ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 eta2 ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 iffalseProp1 ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 iffalseProp2 ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 iftrueProp1 ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 iftrueProp2 ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 ifSingleton ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 ifp ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 theeq ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 iftrue ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 iffalse ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 iftrueorfalse ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 binintersectT_lem ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 binunionT_lem ) =>
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 ![
% 4.06/1.19 X106:$i,
% 4.06/1.19 X108:$i]:
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 in @
% 4.06/1.19 X108 @
% 4.06/1.19 (
% 4.06/1.19 powerset
% 4.06/1.19 @
% 4.06/1.19 X106 ) ) =>
% 4.06/1.19 (
% 4.06/1.19 in @
% 4.06/1.19 (
% 4.06/1.19 powerset
% 4.06/1.19 @
% 4.06/1.19 X108 ) @
% 4.06/1.19 (
% 4.06/1.19 powerset
% 4.06/1.19 @
% 4.06/1.19 (
% 4.06/1.19 powerset
% 4.06/1.19 @
% 4.06/1.19 X106 ) ) ) ) ) =>
% 4.06/1.19 (
% 4.06/1.19 ![
% 4.06/1.19 X110:$i,
% 4.06/1.19 X112:$i]:
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 in @
% 4.06/1.19 X112 @
% 4.06/1.19 (
% 4.06/1.19 powerset
% 4.06/1.19 @
% 4.06/1.19 X110 ) ) =>
% 4.06/1.19 (
% 4.06/1.19 ![
% 4.06/1.19 X114:$i]:
% 4.06/1.19 (
% 4.06/1.19 (
% 4.06/1.19 in @
% 4.06/1.19 X114 @
% 4.06/1.19 (
% 4.06/1.19 powerset
% 4.06/1.19 @
% 4.06/1.19 X110 ) ) =>
% 4.06/1.19 (
% 4.06/1.19 in @
% 4.06/1.19 (
% 4.06/1.19 setminus
% 4.06/1.19 @
% 4.06/1.19 X112 @
% 4.06/1.19 X114 ) @
% 4.06/1.19 (
% 4.06/1.19 powerset
% 4.06/1.19 @
% 4.06/1.19 X110 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )),
% 4.06/1.19 inference('cnf.neg', [status(esa)], [zf_stmt_3])).
% 4.06/1.19 thf(zip_derived_cl120, plain,
% 4.06/1.19 (~ (in @ (setminus @ sk__56 @ sk__57) @ (powerset @ sk__55))),
% 4.06/1.19 inference('cnf', [status(esa)], [zf_stmt_4])).
% 4.06/1.19 thf(zip_derived_cl121, plain, ( (in @ sk__56 @ (powerset @ sk__55))),
% 4.06/1.19 inference('cnf', [status(esa)], [zf_stmt_4])).
% 4.06/1.19 thf(zip_derived_cl118, plain,
% 4.06/1.19 (![X21 : $i, X22 : $i]:
% 4.06/1.19 ( (in @ (powerset @ X21) @ (powerset @ (powerset @ X22)))
% 4.06/1.19 | ~ (in @ X21 @ (powerset @ X22)))),
% 4.06/1.19 inference('cnf', [status(esa)], [zf_stmt_4])).
% 4.06/1.19 thf(zip_derived_cl217, plain,
% 4.06/1.19 (![X45 : $i, X46 : $i, X47 : $i]:
% 4.06/1.19 (~ (in @ X45 @ (powerset @ X46))
% 4.06/1.19 | (in @ X47 @ X46)
% 4.06/1.19 | ~ (in @ X47 @ X45))),
% 4.06/1.19 inference('cnf', [status(esa)], [zf_stmt_4])).
% 4.06/1.19 thf(zip_derived_cl354, plain,
% 4.06/1.19 (![X0 : $i, X1 : $i, X2 : $i]:
% 4.06/1.19 (~ (in @ X1 @ (powerset @ X0))
% 4.06/1.19 | ~ (in @ X2 @ (powerset @ X1))
% 4.06/1.19 | (in @ X2 @ (powerset @ X0)))),
% 4.06/1.19 inference('sup-', [status(thm)], [zip_derived_cl118, zip_derived_cl217])).
% 4.06/1.19 thf(zip_derived_cl414, plain,
% 4.06/1.19 (![X0 : $i]:
% 4.06/1.19 ( (in @ X0 @ (powerset @ sk__55)) | ~ (in @ X0 @ (powerset @ sk__56)))),
% 4.06/1.19 inference('sup-', [status(thm)], [zip_derived_cl121, zip_derived_cl354])).
% 4.06/1.19 thf(zip_derived_cl173, plain,
% 4.06/1.19 (![X23 : $i, X24 : $i]: (subset @ (setminus @ X23 @ X24) @ X23)),
% 4.06/1.19 inference('cnf', [status(esa)], [zf_stmt_4])).
% 4.06/1.19 thf(zip_derived_cl50, plain,
% 4.06/1.19 (![X3 : $i, X4 : $i]:
% 4.06/1.19 ( (in @ X3 @ (powerset @ X4)) | ~ (subset @ X3 @ X4))),
% 4.06/1.19 inference('cnf', [status(esa)], [zf_stmt_4])).
% 4.06/1.19 thf(zip_derived_cl297, plain,
% 4.06/1.19 (![X0 : $i, X1 : $i]: (in @ (setminus @ X0 @ X1) @ (powerset @ X0))),
% 4.06/1.19 inference('sup-', [status(thm)], [zip_derived_cl173, zip_derived_cl50])).
% 4.06/1.19 thf(zip_derived_cl455, plain,
% 4.06/1.19 (![X0 : $i]: (in @ (setminus @ sk__56 @ X0) @ (powerset @ sk__55))),
% 4.06/1.19 inference('sup+', [status(thm)], [zip_derived_cl414, zip_derived_cl297])).
% 4.06/1.19 thf(zip_derived_cl514, plain, ($false),
% 4.06/1.19 inference('demod', [status(thm)], [zip_derived_cl120, zip_derived_cl455])).
% 4.06/1.19
% 4.06/1.19 % SZS output end Refutation
% 4.06/1.19
% 4.06/1.19
% 4.06/1.19 % Terminating...
% 4.47/1.33 % Runner terminated.
% 4.50/1.36 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------