%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SEU723^1 : TPTP v9.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.8eQIy3UnaK true
% Computer : n012.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 04:55:58 PM UTC 2025
% Result : Theorem 5.67s 1.36s
% Output : Refutation 6.17s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU723^1 : TPTP v9.2.0. Released v3.7.0.
% 0.12/0.13 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.8eQIy3UnaK true
% 0.15/0.34 % Computer : n012.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Wed Oct 1 16:05:38 EDT 2025
% 0.15/0.34 % CPUTime :
% 0.15/0.34 % Running portfolio for 300 s
% 0.15/0.34 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.35 % Number of cores: 8
% 0.21/0.35 % Python version: Python 3.6.8
% 0.21/0.35 % Running in HO mode
% 0.56/0.67 % Total configuration time : 828
% 0.56/0.67 % Estimated wc time : 1656
% 0.56/0.67 % Estimated cpu time (8 cpus) : 207.0
% 0.56/0.70 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s
% 0.56/0.71 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.56/0.75 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s
% 0.56/0.75 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s
% 0.56/0.75 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s
% 0.56/0.75 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s
% 0.56/0.75 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.57/0.77 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s
% 5.67/1.36 % Solved by lams/40_c_ic.sh.
% 5.67/1.36 % done 744 iterations in 0.563s
% 5.67/1.36 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 5.67/1.36 % SZS output start Refutation
% 5.67/1.36 thf(setadjoinAx_type, type, setadjoinAx: $o).
% 5.67/1.36 thf(notdexE_type, type, notdexE: $o).
% 5.67/1.36 thf(setukpairinjL2_type, type, setukpairinjL2: $o).
% 5.67/1.36 thf(setunionAx_type, type, setunionAx: $o).
% 5.67/1.36 thf(setminusELneg_type, type, setminusELneg: $o).
% 5.67/1.36 thf(cartprodsndin_type, type, cartprodsndin: $o).
% 5.67/1.36 thf(sk__124_type, type, sk__124: $i).
% 5.67/1.36 thf(ex1E1_type, type, ex1E1: $o).
% 5.67/1.36 thf(powersetE_type, type, powersetE: $o).
% 5.67/1.36 thf(omegaSAx_type, type, omegaSAx: $o).
% 5.67/1.36 thf(exuI1_type, type, exuI1: $o).
% 5.67/1.36 thf(exuI2_type, type, exuI2: $o).
% 5.67/1.36 thf(notequalI2_type, type, notequalI2: $o).
% 5.67/1.36 thf(setukpairinjL_type, type, setukpairinjL: $o).
% 5.67/1.36 thf(kpairiskpair_type, type, kpairiskpair: $o).
% 5.67/1.36 thf(upairsubunion_type, type, upairsubunion: $o).
% 5.67/1.36 thf(funcGraphProp3_type, type, funcGraphProp3: $o).
% 5.67/1.36 thf(cartprodmempaircEq_type, type, cartprodmempaircEq: $o).
% 5.67/1.36 thf(binintersectTERcontra_type, type, binintersectTERcontra: $o).
% 5.67/1.36 thf(powerset__Cong_type, type, powerset__Cong: $o).
% 5.67/1.36 thf(sk__123_type, type, sk__123: $i).
% 5.67/1.36 thf(setminusILneg_type, type, setminusILneg: $o).
% 5.67/1.36 thf(wellorderingAx_type, type, wellorderingAx: $o).
% 5.67/1.36 thf(ksndpairEq_type, type, ksndpairEq: $o).
% 5.67/1.36 thf(funcGraphProp2_type, type, funcGraphProp2: $o).
% 5.67/1.36 thf(setadjoinSub2_type, type, setadjoinSub2: $o).
% 5.67/1.36 thf(binintersectSubset5_type, type, binintersectSubset5: $o).
% 5.67/1.36 thf(iftrue_type, type, iftrue: $o).
% 5.67/1.36 thf(upairinpowunion_type, type, upairinpowunion: $o).
% 5.67/1.36 thf(ifSingleton_type, type, ifSingleton: $o).
% 5.67/1.36 thf(setoftrueEq_type, type, setoftrueEq: $o).
% 5.67/1.36 thf(funcImageSingleton_type, type, funcImageSingleton: $o).
% 5.67/1.36 thf(dpsetconstrERa_type, type, dpsetconstrERa: $o).
% 5.67/1.36 thf(lamProp_type, type, lamProp: $o).
% 5.67/1.36 thf(cartprodpairmemEL_type, type, cartprodpairmemEL: $o).
% 5.67/1.36 thf(emptyset__Cong_type, type, emptyset__Cong: $o).
% 5.67/1.36 thf(dpsetconstrER_type, type, dpsetconstrER: $o).
% 5.67/1.36 thf(sepInPowerset_type, type, sepInPowerset: $o).
% 5.67/1.36 thf(setukpairIR_type, type, setukpairIR: $o).
% 5.67/1.36 thf(setukpairinjR1_type, type, setukpairinjR1: $o).
% 5.67/1.36 thf(lam2p_type, type, lam2p: $o).
% 5.67/1.36 thf(binunionE_type, type, binunionE: $o).
% 5.67/1.36 thf(setext_type, type, setext: $o).
% 5.67/1.36 thf(emptyinPowerset_type, type, emptyinPowerset: $o).
% 5.67/1.36 thf(ubforcartprodlem1_type, type, ubforcartprodlem1: $o).
% 5.67/1.36 thf(descr__Cong_type, type, descr__Cong: $o).
% 5.67/1.36 thf(kfstsingleton_type, type, kfstsingleton: $o).
% 5.67/1.36 thf(binintersectTELcontra_type, type, binintersectTELcontra: $o).
% 5.67/1.36 thf(eqbreln_type, type, eqbreln: $o).
% 5.67/1.36 thf(binintersectSubset1_type, type, binintersectSubset1: $o).
% 5.67/1.36 thf(in_type, type, in: $i > $i > $o).
% 5.67/1.36 thf(binunionT_lem_type, type, binunionT_lem: $o).
% 5.67/1.36 thf(quantDeMorgan1_type, type, quantDeMorgan1: $o).
% 5.67/1.36 thf(complementT_lem_type, type, complementT_lem: $o).
% 5.67/1.36 thf(kpairsurjEq_type, type, kpairsurjEq: $o).
% 5.67/1.36 thf(setadjoinIR_type, type, setadjoinIR: $o).
% 5.67/1.36 thf(beta1_type, type, beta1: $o).
% 5.67/1.36 thf(setadjoin__Cong_type, type, setadjoin__Cong: $o).
% 5.67/1.36 thf(powersetTE1_type, type, powersetTE1: $o).
% 5.67/1.36 thf(symdiffI2_type, type, symdiffI2: $o).
% 5.67/1.36 thf(iftrueProp2_type, type, iftrueProp2: $o).
% 5.67/1.36 thf(upairset2IR_type, type, upairset2IR: $o).
% 5.67/1.36 thf(iffalseProp2_type, type, iffalseProp2: $o).
% 5.67/1.36 thf(subsetE_type, type, subsetE: $o).
% 5.67/1.36 thf(prop2set2propI_type, type, prop2set2propI: $o).
% 5.67/1.36 thf(dsetconstrEL_type, type, dsetconstrEL: $o).
% 5.67/1.36 thf(setbeta_type, type, setbeta: $o).
% 5.67/1.36 thf(eqinunit_type, type, eqinunit: $o).
% 5.67/1.36 thf(upairsetIL_type, type, upairsetIL: $o).
% 5.67/1.36 thf(powersetI1_type, type, powersetI1: $o).
% 5.67/1.36 thf(kfstpairEq_type, type, kfstpairEq: $o).
% 5.67/1.36 thf(binintersectSubset3_type, type, binintersectSubset3: $o).
% 5.67/1.36 thf(setminusIRneg_type, type, setminusIRneg: $o).
% 5.67/1.36 thf(ap2apEq1_type, type, ap2apEq1: $o).
% 5.67/1.36 thf(powersetAx_type, type, powersetAx: $o).
% 5.67/1.36 thf(binintersectSubset4_type, type, binintersectSubset4: $o).
% 5.67/1.36 thf(singletoninpowunion_type, type, singletoninpowunion: $o).
% 5.67/1.36 thf(powersetI_type, type, powersetI: $o).
% 5.67/1.36 thf(cartprodmempair_type, type, cartprodmempair: $o).
% 5.67/1.36 thf(upairsetIR_type, type, upairsetIR: $o).
% 5.67/1.36 thf(lamp_type, type, lamp: $o).
% 5.67/1.36 thf(dpsetconstrEL1_type, type, dpsetconstrEL1: $o).
% 5.67/1.36 thf(inCongP_type, type, inCongP: $o).
% 5.67/1.36 thf(setadjoinSub_type, type, setadjoinSub: $o).
% 5.67/1.36 thf(exuE3e_type, type, exuE3e: $o).
% 5.67/1.36 thf(emptysetE_type, type, emptysetE: $o).
% 5.67/1.36 thf(binintersectSubset2_type, type, binintersectSubset2: $o).
% 5.67/1.36 thf(setunionI_type, type, setunionI: $o).
% 5.67/1.36 thf(setunion__Cong_type, type, setunion__Cong: $o).
% 5.67/1.36 thf(prop2setI_type, type, prop2setI: $o).
% 5.67/1.36 thf(singletonsuniq_type, type, singletonsuniq: $o).
% 5.67/1.36 thf(nonemptyImpWitness_type, type, nonemptyImpWitness: $o).
% 5.67/1.36 thf(setminusER_type, type, setminusER: $o).
% 5.67/1.36 thf(exuE2_type, type, exuE2: $o).
% 5.67/1.36 thf(emptyset_type, type, emptyset: $i).
% 5.67/1.36 thf(setukpairinjR11_type, type, setukpairinjR11: $o).
% 5.67/1.36 thf(ex1I_type, type, ex1I: $o).
% 5.67/1.36 thf(ex1E2_type, type, ex1E2: $o).
% 5.67/1.36 thf(setminus_type, type, setminus: $i > $i > $i).
% 5.67/1.36 thf(setukpairinjL1_type, type, setukpairinjL1: $o).
% 5.67/1.36 thf(powersetsubset_type, type, powersetsubset: $o).
% 5.67/1.36 thf(subPowSU_type, type, subPowSU: $o).
% 5.67/1.36 thf(notequalI1_type, type, notequalI1: $o).
% 5.67/1.36 thf(notinemptyset_type, type, notinemptyset: $o).
% 5.67/1.36 thf(lam2lamEq_type, type, lam2lamEq: $o).
% 5.67/1.36 thf(nonemptyI1_type, type, nonemptyI1: $o).
% 5.67/1.36 thf(subsetTrans_type, type, subsetTrans: $o).
% 5.67/1.36 thf(kpairp_type, type, kpairp: $o).
% 5.67/1.36 thf(setukpairinjR12_type, type, setukpairinjR12: $o).
% 5.67/1.36 thf(setminusI_type, type, setminusI: $o).
% 5.67/1.36 thf(binunionIL_type, type, binunionIL: $o).
% 5.67/1.36 thf(dpsetconstrSub_type, type, dpsetconstrSub: $o).
% 5.67/1.36 thf(setunionsingleton_type, type, setunionsingleton: $o).
% 5.67/1.36 thf(subsetE2_type, type, subsetE2: $o).
% 5.67/1.36 thf(singletonsswitch_type, type, singletonsswitch: $o).
% 5.67/1.36 thf(ubforcartprodlem3_type, type, ubforcartprodlem3: $o).
% 5.67/1.36 thf(beta2_type, type, beta2: $o).
% 5.67/1.36 thf(dpsetconstrI_type, type, dpsetconstrI: $o).
% 5.67/1.36 thf(setextsub_type, type, setextsub: $o).
% 5.67/1.36 thf(binunionLsub_type, type, binunionLsub: $o).
% 5.67/1.36 thf(setunionsingleton1_type, type, setunionsingleton1: $o).
% 5.67/1.36 thf(zip_tseitin_0_type, type, zip_tseitin_0: $i > $i > $i > $o).
% 5.67/1.36 thf(iftrueorfalse_type, type, iftrueorfalse: $o).
% 5.67/1.36 thf(emptysetsubset_type, type, emptysetsubset: $o).
% 5.67/1.36 thf(quantDeMorgan3_type, type, quantDeMorgan3: $o).
% 5.67/1.36 thf(cartprodpairsurjEq_type, type, cartprodpairsurjEq: $o).
% 5.67/1.36 thf(setOfPairsIsBReln_type, type, setOfPairsIsBReln: $o).
% 5.67/1.36 thf(setunionE_type, type, setunionE: $o).
% 5.67/1.36 thf(ksndsingleton_type, type, ksndsingleton: $o).
% 5.67/1.36 thf(setminusSubset1_type, type, setminusSubset1: $o).
% 5.67/1.36 thf(powersetT_lem_type, type, powersetT_lem: $o).
% 5.67/1.36 thf(emptyinunitempty_type, type, emptyinunitempty: $o).
% 5.67/1.36 thf(binunionIR_type, type, binunionIR: $o).
% 5.67/1.36 thf(theeq_type, type, theeq: $o).
% 5.67/1.36 thf(setadjoinE_type, type, setadjoinE: $o).
% 5.67/1.36 thf(infuncsetfunc_type, type, infuncsetfunc: $o).
% 5.67/1.36 thf(ap2apEq2_type, type, ap2apEq2: $o).
% 5.67/1.36 thf(ap2p_type, type, ap2p: $o).
% 5.67/1.36 thf(setadjoinIL_type, type, setadjoinIL: $o).
% 5.67/1.36 thf(cartprodsndpairEq_type, type, cartprodsndpairEq: $o).
% 5.67/1.36 thf(exuE1_type, type, exuE1: $o).
% 5.67/1.36 thf(ubforcartprodlem2_type, type, ubforcartprodlem2: $o).
% 5.67/1.36 thf(binintersectRsub_type, type, binintersectRsub: $o).
% 5.67/1.36 thf(setminusLsub_type, type, setminusLsub: $o).
% 5.67/1.36 thf(funcextLem_type, type, funcextLem: $o).
% 5.67/1.36 thf(setukpairinjR_type, type, setukpairinjR: $o).
% 5.67/1.36 thf(notinsingleton_type, type, notinsingleton: $o).
% 5.67/1.36 thf(eqimpsubset2_type, type, eqimpsubset2: $o).
% 5.67/1.36 thf(exuEu_type, type, exuEu: $o).
% 5.67/1.36 thf(emptysetimpfalse_type, type, emptysetimpfalse: $o).
% 5.67/1.36 thf(upairsetE_type, type, upairsetE: $o).
% 5.67/1.36 thf(omega0Ax_type, type, omega0Ax: $o).
% 5.67/1.36 thf(subsetTI_type, type, subsetTI: $o).
% 5.67/1.36 thf(notsubsetI_type, type, notsubsetI: $o).
% 5.67/1.36 thf(iffalseProp1_type, type, iffalseProp1: $o).
% 5.67/1.36 thf(quantDeMorgan4_type, type, quantDeMorgan4: $o).
% 5.67/1.36 thf(setextAx_type, type, setextAx: $o).
% 5.67/1.36 thf(cartprodpairmemER_type, type, cartprodpairmemER: $o).
% 5.67/1.36 thf(powersetE1_type, type, powersetE1: $o).
% 5.67/1.36 thf(bs114d_type, type, bs114d: $o).
% 5.67/1.36 thf(noeltsimpempty_type, type, noeltsimpempty: $o).
% 5.67/1.36 thf(ifp_type, type, ifp: $o).
% 5.67/1.36 thf(powersetTI1_type, type, powersetTI1: $o).
% 5.67/1.36 thf(binintersectLsub_type, type, binintersectLsub: $o).
% 5.67/1.36 thf(subsetI1_type, type, subsetI1: $o).
% 5.67/1.36 thf(symdiffE_type, type, symdiffE: $o).
% 5.67/1.36 thf(descrp_type, type, descrp: $o).
% 5.67/1.36 thf(dsetconstr__Cong_type, type, dsetconstr__Cong: $o).
% 5.67/1.36 thf(foundationAx_type, type, foundationAx: $o).
% 5.67/1.36 thf(emptysetAx_type, type, emptysetAx: $o).
% 5.67/1.36 thf(emptyI_type, type, emptyI: $o).
% 5.67/1.36 thf(setadjoinOr_type, type, setadjoinOr: $o).
% 5.67/1.36 thf(eta2_type, type, eta2: $o).
% 5.67/1.36 thf(binintersectEL_type, type, binintersectEL: $o).
% 5.67/1.36 thf(emptyE1_type, type, emptyE1: $o).
% 5.67/1.36 thf(emptyInPowerset_type, type, emptyInPowerset: $o).
% 5.67/1.36 thf(complementTI1_type, type, complementTI1: $o).
% 5.67/1.36 thf(sk__125_type, type, sk__125: $i).
% 5.67/1.36 thf(vacuousDall_type, type, vacuousDall: $o).
% 5.67/1.36 thf(dsetconstrER_type, type, dsetconstrER: $o).
% 5.67/1.36 thf(binintersectI_type, type, binintersectI: $o).
% 5.67/1.36 thf(funcext_type, type, funcext: $o).
% 5.67/1.36 thf(funcGraphProp4_type, type, funcGraphProp4: $o).
% 5.67/1.36 thf(cartprodpairin_type, type, cartprodpairin: $o).
% 5.67/1.36 thf(cartprodmempair1_type, type, cartprodmempair1: $o).
% 5.67/1.36 thf(brelnall2_type, type, brelnall2: $o).
% 5.67/1.36 thf(setextT_type, type, setextT: $o).
% 5.67/1.36 thf(ex1I2_type, type, ex1I2: $o).
% 5.67/1.36 thf(symdiffI1_type, type, symdiffI1: $o).
% 5.67/1.36 thf(setukpairinjR2_type, type, setukpairinjR2: $o).
% 5.67/1.36 thf(dpsetconstrEL2_type, type, dpsetconstrEL2: $o).
% 5.67/1.36 thf(theprop_type, type, theprop: $o).
% 5.67/1.36 thf(subsetI2_type, type, subsetI2: $o).
% 5.67/1.36 thf(setminusT_lem_type, type, setminusT_lem: $o).
% 5.67/1.36 thf(symdiffIneg1_type, type, symdiffIneg1: $o).
% 5.67/1.36 thf(setminusERneg_type, type, setminusERneg: $o).
% 5.67/1.36 thf(symdiffIneg2_type, type, symdiffIneg2: $o).
% 5.67/1.36 thf(omega__Cong_type, type, omega__Cong: $o).
% 5.67/1.36 thf(subsetRefl_type, type, subsetRefl: $o).
% 5.67/1.36 thf(uniqinunit_type, type, uniqinunit: $o).
% 5.67/1.36 thf(setminusSubset2_type, type, setminusSubset2: $o).
% 5.67/1.36 thf(prop2setE_type, type, prop2setE: $o).
% 5.67/1.36 thf(sk__126_type, type, sk__126: $i).
% 5.67/1.36 thf(binunionEcases_type, type, binunionEcases: $o).
% 5.67/1.36 thf(funcinfuncset_type, type, funcinfuncset: $o).
% 5.67/1.36 thf(complementTE1_type, type, complementTE1: $o).
% 5.67/1.36 thf(nonemptyI_type, type, nonemptyI: $o).
% 5.67/1.36 thf(app_type, type, app: $o).
% 5.67/1.36 thf(disjointsetsI1_type, type, disjointsetsI1: $o).
% 5.67/1.36 thf(exuE3u_type, type, exuE3u: $o).
% 5.67/1.36 thf(eta1_type, type, eta1: $o).
% 5.67/1.36 thf(setminusEL_type, type, setminusEL: $o).
% 5.67/1.36 thf(cartprodfstin_type, type, cartprodfstin: $o).
% 5.67/1.36 thf(setunionsingleton2_type, type, setunionsingleton2: $o).
% 5.67/1.36 thf(sepSubset_type, type, sepSubset: $o).
% 5.67/1.36 thf(upairset2E_type, type, upairset2E: $o).
% 5.67/1.36 thf(eqimpsubset1_type, type, eqimpsubset1: $o).
% 5.67/1.36 thf(exuI3_type, type, exuI3: $o).
% 5.67/1.36 thf(cartprodfstpairEq_type, type, cartprodfstpairEq: $o).
% 5.67/1.36 thf(apProp_type, type, apProp: $o).
% 5.67/1.36 thf(notdallE_type, type, notdallE: $o).
% 5.67/1.36 thf(iftrueProp1_type, type, iftrueProp1: $o).
% 5.67/1.36 thf(binintersectER_type, type, binintersectER: $o).
% 5.67/1.36 thf(brelnall1_type, type, brelnall1: $o).
% 5.67/1.36 thf(powerset_type, type, powerset: $i > $i).
% 5.67/1.36 thf(dsetconstrI_type, type, dsetconstrI: $o).
% 5.67/1.36 thf(funcGraphProp1_type, type, funcGraphProp1: $o).
% 5.67/1.36 thf(binintersectT_lem_type, type, binintersectT_lem: $o).
% 5.67/1.36 thf(setadjoin_type, type, setadjoin: $i > $i > $i).
% 5.67/1.36 thf(exu__Cong_type, type, exu__Cong: $o).
% 5.67/1.36 thf(quantDeMorgan2_type, type, quantDeMorgan2: $o).
% 5.67/1.36 thf(secondinupair_type, type, secondinupair: $o).
% 5.67/1.36 thf(singletonprop_type, type, singletonprop: $o).
% 5.67/1.36 thf(singletonsubset_type, type, singletonsubset: $o).
% 5.67/1.36 thf(singletoninpowerset_type, type, singletoninpowerset: $o).
% 5.67/1.36 thf(subsetemptysetimpeq_type, type, subsetemptysetimpeq: $o).
% 5.67/1.36 thf(replAx_type, type, replAx: $o).
% 5.67/1.36 thf(upairequniteq_type, type, upairequniteq: $o).
% 5.67/1.36 thf(nonemptyE1_type, type, nonemptyE1: $o).
% 5.67/1.36 thf(omegaIndAx_type, type, omegaIndAx: $o).
% 5.67/1.36 thf(setukpairIL_type, type, setukpairIL: $o).
% 5.67/1.36 thf(setunionE2_type, type, setunionE2: $o).
% 5.67/1.36 thf(inPowerset_type, type, inPowerset: $o).
% 5.67/1.36 thf(iffalse_type, type, iffalse: $o).
% 5.67/1.36 thf(funcext2_type, type, funcext2: $o).
% 5.67/1.36 thf(subset_type, type, subset: $i > $i > $o).
% 5.67/1.36 thf(subbreln_type, type, subbreln: $o).
% 5.67/1.36 thf(in__Cong_type, type, in__Cong: $o).
% 5.67/1.36 thf(binunionRsub_type, type, binunionRsub: $o).
% 5.67/1.36 thf(subset2powerset_type, type, subset2powerset: $o).
% 5.67/1.36 thf(complementTE1, axiom, complementTE1 =
% 5.67/1.36 (![A:$i,X:$i]:
% 5.67/1.36 ( ( in @ X @ ( powerset @ A ) ) =>
% 5.67/1.36 ( ![Xx:$i]:
% 5.67/1.36 ( ( in @ Xx @ A ) =>
% 5.67/1.36 ( ( ~( in @ Xx @ ( setminus @ A @ X ) ) ) => ( in @ Xx @ X ) ) ) ) ))).
% 5.67/1.36 thf('0', plain,
% 5.67/1.36 (( complementTE1 ) =
% 5.67/1.36 ( ![X4:$i,X6:$i]:
% 5.67/1.36 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 5.67/1.36 ( ![X8:$i]:
% 5.67/1.36 ( ( in @ X8 @ X4 ) =>
% 5.67/1.36 ( ( ~( in @ X8 @ ( setminus @ X4 @ X6 ) ) ) => ( in @ X8 @ X6 ) ) ) ) ) )),
% 5.67/1.36 define([status(thm)])).
% 5.67/1.36 thf(complementTI1, axiom, complementTI1 =
% 5.67/1.36 (![A:$i,X:$i]:
% 5.67/1.36 ( ( in @ X @ ( powerset @ A ) ) =>
% 5.67/1.36 ( ![Xx:$i]:
% 5.67/1.36 ( ( in @ Xx @ A ) =>
% 5.67/1.36 ( ( in @ Xx @ X ) => ( ~( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ))).
% 5.67/1.36 thf('1', plain,
% 5.67/1.36 (( complementTI1 ) =
% 5.67/1.36 ( ![X4:$i,X6:$i]:
% 5.67/1.36 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 5.67/1.36 ( ![X8:$i]:
% 5.67/1.36 ( ( in @ X8 @ X4 ) =>
% 5.67/1.36 ( ( in @ X8 @ X6 ) => ( ~( in @ X8 @ ( setminus @ X4 @ X6 ) ) ) ) ) ) ) )),
% 5.67/1.36 define([status(thm)])).
% 5.67/1.36 thf(powersetTE1, axiom, powersetTE1 =
% 5.67/1.36 (![A:$i,X:$i]:
% 5.67/1.36 ( ( in @ X @ ( powerset @ A ) ) =>
% 5.67/1.36 ( ![Y:$i]:
% 5.67/1.36 ( ( in @ Y @ ( powerset @ A ) ) =>
% 5.67/1.36 ( ![Xx:$i]:
% 5.67/1.36 ( ( in @ Xx @ A ) =>
% 5.67/1.36 ( ( in @ X @ ( powerset @ Y ) ) =>
% 5.67/1.36 ( ( in @ Xx @ X ) => ( in @ Xx @ Y ) ) ) ) ) ) ) ))).
% 5.67/1.36 thf('2', plain,
% 5.67/1.36 (( powersetTE1 ) =
% 5.67/1.36 ( ![X4:$i,X6:$i]:
% 5.67/1.36 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 5.67/1.36 ( ![X8:$i]:
% 5.67/1.36 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 5.67/1.36 ( ![X10:$i]:
% 5.67/1.36 ( ( in @ X10 @ X4 ) =>
% 5.67/1.36 ( ( in @ X6 @ ( powerset @ X8 ) ) =>
% 5.67/1.36 ( ( in @ X10 @ X6 ) => ( in @ X10 @ X8 ) ) ) ) ) ) ) ) )),
% 5.67/1.36 define([status(thm)])).
% 5.67/1.36 thf(powersetTI1, axiom, powersetTI1 =
% 5.67/1.36 (![A:$i,X:$i]:
% 5.67/1.36 ( ( in @ X @ ( powerset @ A ) ) =>
% 5.67/1.36 ( ![Y:$i]:
% 5.67/1.36 ( ( in @ Y @ ( powerset @ A ) ) =>
% 5.67/1.36 ( ( ![Xx:$i]:
% 5.67/1.36 ( ( in @ Xx @ A ) => ( ( in @ Xx @ X ) => ( in @ Xx @ Y ) ) ) ) =>
% 5.67/1.36 ( in @ X @ ( powerset @ Y ) ) ) ) ) ))).
% 5.67/1.36 thf('3', plain,
% 5.67/1.36 (( powersetTI1 ) =
% 5.67/1.36 ( ![X4:$i,X6:$i]:
% 5.67/1.36 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 5.67/1.36 ( ![X8:$i]:
% 5.67/1.36 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 5.67/1.36 ( ( ![X10:$i]:
% 5.67/1.36 ( ( in @ X10 @ X4 ) =>
% 5.67/1.36 ( ( in @ X10 @ X6 ) => ( in @ X10 @ X8 ) ) ) ) =>
% 5.67/1.36 ( in @ X6 @ ( powerset @ X8 ) ) ) ) ) ) )),
% 5.67/1.36 define([status(thm)])).
% 5.67/1.36 thf(subsetTI, axiom, subsetTI =
% 5.67/1.36 (![A:$i,X:$i]:
% 5.67/1.36 ( ( in @ X @ ( powerset @ A ) ) =>
% 5.67/1.36 ( ![Y:$i]:
% 5.67/1.36 ( ( in @ Y @ ( powerset @ A ) ) =>
% 5.67/1.36 ( ( ![Xx:$i]:
% 5.67/1.36 ( ( in @ Xx @ A ) => ( ( in @ Xx @ X ) => ( in @ Xx @ Y ) ) ) ) =>
% 5.67/1.36 ( subset @ X @ Y ) ) ) ) ))).
% 5.67/1.36 thf('4', plain,
% 5.67/1.36 (( subsetTI ) =
% 5.67/1.36 ( ![X4:$i,X6:$i]:
% 5.67/1.36 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 5.67/1.36 ( ![X8:$i]:
% 5.67/1.36 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 5.67/1.36 ( ( ![X10:$i]:
% 5.67/1.36 ( ( in @ X10 @ X4 ) =>
% 5.67/1.36 ( ( in @ X10 @ X6 ) => ( in @ X10 @ X8 ) ) ) ) =>
% 5.67/1.36 ( subset @ X6 @ X8 ) ) ) ) ) )),
% 5.67/1.36 define([status(thm)])).
% 5.67/1.36 thf(setextT, axiom, setextT =
% 5.67/1.36 (![A:$i,X:$i]:
% 5.67/1.36 ( ( in @ X @ ( powerset @ A ) ) =>
% 5.67/1.36 ( ![Y:$i]:
% 5.67/1.36 ( ( in @ Y @ ( powerset @ A ) ) =>
% 5.67/1.36 ( ( ![Xx:$i]:
% 5.67/1.36 ( ( in @ Xx @ A ) => ( ( in @ Xx @ X ) => ( in @ Xx @ Y ) ) ) ) =>
% 5.67/1.36 ( ( ![Xx:$i]:
% 5.67/1.36 ( ( in @ Xx @ A ) => ( ( in @ Xx @ Y ) => ( in @ Xx @ X ) ) ) ) =>
% 5.67/1.36 ( ( X ) = ( Y ) ) ) ) ) ) ))).
% 5.67/1.36 thf('5', plain,
% 5.67/1.36 (( setextT ) =
% 5.67/1.36 ( ![X4:$i,X6:$i]:
% 5.67/1.36 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 5.67/1.36 ( ![X8:$i]:
% 5.67/1.36 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 5.67/1.36 ( ( ![X10:$i]:
% 5.67/1.36 ( ( in @ X10 @ X4 ) =>
% 5.67/1.36 ( ( in @ X10 @ X6 ) => ( in @ X10 @ X8 ) ) ) ) =>
% 5.67/1.36 ( ( ![X12:$i]:
% 5.67/1.36 ( ( in @ X12 @ X4 ) =>
% 5.67/1.36 ( ( in @ X12 @ X8 ) => ( in @ X12 @ X6 ) ) ) ) =>
% 5.67/1.36 ( ( X6 ) = ( X8 ) ) ) ) ) ) ) )),
% 5.67/1.36 define([status(thm)])).
% 5.67/1.36 thf(complementT_lem, axiom, complementT_lem =
% 5.67/1.36 (![A:$i,X:$i]:
% 5.67/1.36 ( ( in @ X @ ( powerset @ A ) ) =>
% 5.67/1.36 ( in @ ( setminus @ A @ X ) @ ( powerset @ A ) ) ))).
% 5.67/1.36 thf('6', plain,
% 5.67/1.36 (( complementT_lem ) =
% 5.67/1.36 ( ![X4:$i,X6:$i]:
% 5.67/1.36 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 5.67/1.36 ( in @ ( setminus @ X4 @ X6 ) @ ( powerset @ X4 ) ) ) )),
% 5.67/1.36 define([status(thm)])).
% 5.67/1.36 thf(setminusT_lem, axiom, setminusT_lem =
% 5.67/1.36 (![A:$i,X:$i]:
% 5.67/1.36 ( ( in @ X @ ( powerset @ A ) ) =>
% 5.67/1.36 ( ![Y:$i]:
% 5.67/1.36 ( ( in @ Y @ ( powerset @ A ) ) =>
% 5.67/1.36 ( in @ ( setminus @ X @ Y ) @ ( powerset @ A ) ) ) ) ))).
% 5.67/1.36 thf('7', plain,
% 5.67/1.36 (( setminusT_lem ) =
% 5.67/1.36 ( ![X4:$i,X6:$i]:
% 5.67/1.36 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 5.67/1.36 ( ![X8:$i]:
% 5.67/1.36 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 5.67/1.36 ( in @ ( setminus @ X6 @ X8 ) @ ( powerset @ X4 ) ) ) ) ) )),
% 5.67/1.36 define([status(thm)])).
% 5.67/1.36 thf(powersetT_lem, axiom, powersetT_lem =
% 5.67/1.36 (![A:$i,X:$i]:
% 5.67/1.36 ( ( in @ X @ ( powerset @ A ) ) =>
% 5.67/1.36 ( in @ ( powerset @ X ) @ ( powerset @ ( powerset @ A ) ) ) ))).
% 5.67/1.36 thf('8', plain,
% 5.67/1.36 (( powersetT_lem ) =
% 5.67/1.36 ( ![X4:$i,X6:$i]:
% 5.67/1.36 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 5.67/1.36 ( in @ ( powerset @ X6 ) @ ( powerset @ ( powerset @ X4 ) ) ) ) )),
% 5.67/1.36 define([status(thm)])).
% 5.67/1.36 thf(singletoninpowerset, axiom, singletoninpowerset =
% 5.67/1.36 (![A:$i,Xx:$i]:
% 5.67/1.36 ( ( in @ Xx @ A ) =>
% 5.67/1.36 ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) ))).
% 5.67/1.36 thf('9', plain,
% 5.67/1.36 (( singletoninpowerset ) =
% 5.67/1.36 ( ![X4:$i,X6:$i]:
% 5.67/1.36 ( ( in @ X6 @ X4 ) =>
% 5.67/1.36 ( in @ ( setadjoin @ X6 @ emptyset ) @ ( powerset @ X4 ) ) ) )),
% 5.67/1.36 define([status(thm)])).
% 5.67/1.36 thf(singletonsubset, axiom, singletonsubset =
% 5.67/1.36 (![A:$i,Xx:$i]:
% 5.67/1.36 ( ( in @ Xx @ A ) => ( subset @ ( setadjoin @ Xx @ emptyset ) @ A ) ))).
% 5.67/1.36 thf('10', plain,
% 5.67/1.36 (( singletonsubset ) =
% 5.67/1.36 ( ![X4:$i,X6:$i]:
% 5.67/1.36 ( ( in @ X6 @ X4 ) => ( subset @ ( setadjoin @ X6 @ emptyset ) @ X4 ) ) )),
% 5.67/1.36 define([status(thm)])).
% 5.67/1.36 thf(setminusSubset1, axiom, setminusSubset1 =
% 5.67/1.36 (![A:$i,B:$i]:
% 5.67/1.36 ( ( ( setminus @ A @ B ) = ( emptyset ) ) => ( subset @ A @ B ) ))).
% 5.67/1.36 thf('11', plain,
% 5.67/1.36 (( setminusSubset1 ) =
% 5.67/1.36 ( ![X4:$i,X6:$i]:
% 5.67/1.36 ( ( ( setminus @ X4 @ X6 ) = ( emptyset ) ) => ( subset @ X4 @ X6 ) ) )),
% 5.67/1.36 define([status(thm)])).
% 5.67/1.36 thf(setminusLsub, axiom, setminusLsub =
% 5.67/1.36 (![A:$i,B:$i]: ( subset @ ( setminus @ A @ B ) @ A ))).
% 5.67/1.36 thf('12', plain,
% 5.67/1.36 (( setminusLsub ) =
% 5.67/1.36 ( ![X4:$i,X6:$i]: ( subset @ ( setminus @ X4 @ X6 ) @ X4 ) )),
% 5.67/1.36 define([status(thm)])).
% 5.67/1.36 thf(setminusIRneg, axiom, setminusIRneg =
% 5.67/1.36 (![A:$i,B:$i,Xx:$i]:
% 5.67/1.36 ( ( in @ Xx @ B ) => ( ~( in @ Xx @ ( setminus @ A @ B ) ) ) ))).
% 5.67/1.36 thf('13', plain,
% 5.67/1.36 (( setminusIRneg ) =
% 5.67/1.36 ( ![X4:$i,X6:$i,X8:$i]:
% 5.67/1.36 ( ( in @ X8 @ X6 ) => ( ~( in @ X8 @ ( setminus @ X4 @ X6 ) ) ) ) )),
% 5.67/1.36 define([status(thm)])).
% 5.67/1.36 thf(setminusILneg, axiom, setminusILneg =
% 5.67/1.36 (![A:$i,B:$i,Xx:$i]:
% 5.67/1.36 ( ( ~( in @ Xx @ A ) ) => ( ~( in @ Xx @ ( setminus @ A @ B ) ) ) ))).
% 5.67/1.36 thf('14', plain,
% 5.67/1.36 (( setminusILneg ) =
% 5.67/1.36 ( ![X4:$i,X6:$i,X8:$i]:
% 5.67/1.36 ( ( ~( in @ X8 @ X4 ) ) => ( ~( in @ X8 @ ( setminus @ X4 @ X6 ) ) ) ) )),
% 5.67/1.36 define([status(thm)])).
% 5.67/1.36 thf(setminusELneg, axiom, setminusELneg =
% 5.67/1.36 (![A:$i,B:$i,Xx:$i]:
% 5.67/1.36 ( ( ~( in @ Xx @ ( setminus @ A @ B ) ) ) =>
% 5.67/1.36 ( ( ~( in @ Xx @ B ) ) => ( ~( in @ Xx @ A ) ) ) ))).
% 5.67/1.36 thf('15', plain,
% 5.67/1.36 (( setminusELneg ) =
% 5.67/1.36 ( ![X4:$i,X6:$i,X8:$i]:
% 5.67/1.36 ( ( ~( in @ X8 @ ( setminus @ X4 @ X6 ) ) ) =>
% 5.67/1.36 ( ( ~( in @ X8 @ X6 ) ) => ( ~( in @ X8 @ X4 ) ) ) ) )),
% 5.67/1.36 define([status(thm)])).
% 5.67/1.36 thf(setminusERneg, axiom, setminusERneg =
% 5.67/1.36 (![A:$i,B:$i,Xx:$i]:
% 5.67/1.36 ( ( ~( in @ Xx @ ( setminus @ A @ B ) ) ) =>
% 5.67/1.36 ( ( in @ Xx @ A ) => ( in @ Xx @ B ) ) ))).
% 5.67/1.36 thf('16', plain,
% 5.67/1.36 (( setminusERneg ) =
% 5.67/1.36 ( ![X4:$i,X6:$i,X8:$i]:
% 5.67/1.36 ( ( ~( in @ X8 @ ( setminus @ X4 @ X6 ) ) ) =>
% 5.67/1.36 ( ( in @ X8 @ X4 ) => ( in @ X8 @ X6 ) ) ) )),
% 5.67/1.36 define([status(thm)])).
% 5.67/1.36 thf(setminusSubset2, axiom, setminusSubset2 =
% 5.67/1.36 (![A:$i,B:$i]:
% 5.67/1.36 ( ( subset @ A @ B ) => ( ( setminus @ A @ B ) = ( emptyset ) ) ))).
% 5.67/1.36 thf('17', plain,
% 5.67/1.36 (( setminusSubset2 ) =
% 5.67/1.36 ( ![X4:$i,X6:$i]:
% 5.67/1.36 ( ( subset @ X4 @ X6 ) => ( ( setminus @ X4 @ X6 ) = ( emptyset ) ) ) )),
% 5.67/1.36 define([status(thm)])).
% 5.67/1.36 thf(setminusER, axiom, setminusER =
% 5.67/1.36 (![A:$i,B:$i,Xx:$i]:
% 5.67/1.36 ( ( in @ Xx @ ( setminus @ A @ B ) ) => ( ~( in @ Xx @ B ) ) ))).
% 5.67/1.36 thf('18', plain,
% 5.67/1.36 (( setminusER ) =
% 5.67/1.36 ( ![X4:$i,X6:$i,X8:$i]:
% 5.67/1.36 ( ( in @ X8 @ ( setminus @ X4 @ X6 ) ) => ( ~( in @ X8 @ X6 ) ) ) )),
% 5.67/1.36 define([status(thm)])).
% 5.67/1.36 thf(setminusEL, axiom, setminusEL =
% 5.67/1.36 (![A:$i,B:$i,Xx:$i]:
% 5.67/1.36 ( ( in @ Xx @ ( setminus @ A @ B ) ) => ( in @ Xx @ A ) ))).
% 5.67/1.36 thf('19', plain,
% 5.67/1.36 (( setminusEL ) =
% 5.67/1.36 ( ![X4:$i,X6:$i,X8:$i]:
% 5.67/1.36 ( ( in @ X8 @ ( setminus @ X4 @ X6 ) ) => ( in @ X8 @ X4 ) ) )),
% 5.67/1.36 define([status(thm)])).
% 5.67/1.36 thf(setminusI, axiom, setminusI =
% 5.67/1.36 (![A:$i,B:$i,Xx:$i]:
% 5.67/1.36 ( ( in @ Xx @ A ) =>
% 5.67/1.36 ( ( ~( in @ Xx @ B ) ) => ( in @ Xx @ ( setminus @ A @ B ) ) ) ))).
% 5.67/1.36 thf('20', plain,
% 5.67/1.36 (( setminusI ) =
% 5.67/1.36 ( ![X4:$i,X6:$i,X8:$i]:
% 5.67/1.36 ( ( in @ X8 @ X4 ) =>
% 5.67/1.36 ( ( ~( in @ X8 @ X6 ) ) => ( in @ X8 @ ( setminus @ X4 @ X6 ) ) ) ) )),
% 5.67/1.36 define([status(thm)])).
% 5.67/1.36 thf(powersetsubset, axiom, powersetsubset =
% 5.67/1.36 (![A:$i,B:$i]:
% 5.67/1.36 ( ( subset @ A @ B ) => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ))).
% 5.67/1.36 thf('21', plain,
% 5.67/1.36 (( powersetsubset ) =
% 5.67/1.36 ( ![X4:$i,X6:$i]:
% 5.67/1.36 ( ( subset @ X4 @ X6 ) =>
% 5.67/1.36 ( subset @ ( powerset @ X4 ) @ ( powerset @ X6 ) ) ) )),
% 5.67/1.36 define([status(thm)])).
% 5.67/1.36 thf(inPowerset, axiom, inPowerset = (![A:$i]: ( in @ A @ ( powerset @ A ) ))).
% 5.67/1.36 thf('22', plain,
% 5.67/1.36 (( inPowerset ) = ( ![X4:$i]: ( in @ X4 @ ( powerset @ X4 ) ) )),
% 5.67/1.36 define([status(thm)])).
% 5.67/1.36 thf(powersetE1, axiom, powersetE1 =
% 5.67/1.36 (![A:$i,B:$i]: ( ( in @ B @ ( powerset @ A ) ) => ( subset @ B @ A ) ))).
% 5.67/1.36 thf('23', plain,
% 5.67/1.36 (( powersetE1 ) =
% 5.67/1.36 ( ![X4:$i,X6:$i]:
% 5.67/1.36 ( ( in @ X6 @ ( powerset @ X4 ) ) => ( subset @ X6 @ X4 ) ) )),
% 5.67/1.36 define([status(thm)])).
% 5.67/1.36 thf(powersetI1, axiom, powersetI1 =
% 5.67/1.36 (![A:$i,B:$i]: ( ( subset @ B @ A ) => ( in @ B @ ( powerset @ A ) ) ))).
% 5.67/1.36 thf('24', plain,
% 5.67/1.36 (( powersetI1 ) =
% 5.67/1.36 ( ![X4:$i,X6:$i]:
% 5.67/1.36 ( ( subset @ X6 @ X4 ) => ( in @ X6 @ ( powerset @ X4 ) ) ) )),
% 5.67/1.36 define([status(thm)])).
% 5.67/1.36 thf(subsetemptysetimpeq, axiom, subsetemptysetimpeq =
% 5.67/1.36 (![A:$i]: ( ( subset @ A @ emptyset ) => ( ( A ) = ( emptyset ) ) ))).
% 5.67/1.36 thf('25', plain,
% 5.67/1.36 (( subsetemptysetimpeq ) =
% 5.67/1.36 ( ![X4:$i]: ( ( subset @ X4 @ emptyset ) => ( ( X4 ) = ( emptyset ) ) ) )),
% 5.67/1.36 define([status(thm)])).
% 5.67/1.36 thf(setextsub, axiom, setextsub =
% 5.67/1.36 (![A:$i,B:$i]:
% 5.67/1.36 ( ( subset @ A @ B ) => ( ( subset @ B @ A ) => ( ( A ) = ( B ) ) ) ))).
% 5.67/1.36 thf('26', plain,
% 5.67/1.36 (( setextsub ) =
% 5.67/1.36 ( ![X4:$i,X6:$i]:
% 5.67/1.36 ( ( subset @ X4 @ X6 ) =>
% 5.67/1.36 ( ( subset @ X6 @ X4 ) => ( ( X4 ) = ( X6 ) ) ) ) )),
% 5.67/1.36 define([status(thm)])).
% 5.67/1.36 thf(subset2powerset, axiom, subset2powerset =
% 5.67/1.36 (![A:$i,B:$i]: ( ( subset @ A @ B ) => ( in @ A @ ( powerset @ B ) ) ))).
% 5.67/1.36 thf('27', plain,
% 5.67/1.36 (( subset2powerset ) =
% 5.67/1.36 ( ![X4:$i,X6:$i]:
% 5.67/1.36 ( ( subset @ X4 @ X6 ) => ( in @ X4 @ ( powerset @ X6 ) ) ) )),
% 5.67/1.36 define([status(thm)])).
% 5.67/1.36 thf(setadjoinSub2, axiom, setadjoinSub2 =
% 5.67/1.36 (![A:$i,Xx:$i,B:$i]:
% 5.67/1.36 ( ( subset @ A @ B ) => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ))).
% 5.67/1.36 thf('28', plain,
% 5.67/1.36 (( setadjoinSub2 ) =
% 5.67/1.36 ( ![X4:$i,X6:$i,X8:$i]:
% 5.67/1.36 ( ( subset @ X4 @ X8 ) => ( subset @ X4 @ ( setadjoin @ X6 @ X8 ) ) ) )),
% 5.67/1.36 define([status(thm)])).
% 5.67/1.36 thf(setadjoinSub, axiom, setadjoinSub =
% 5.67/1.36 (![Xx:$i,A:$i]: ( subset @ A @ ( setadjoin @ Xx @ A ) ))).
% 5.67/1.36 thf('29', plain,
% 5.67/1.36 (( setadjoinSub ) =
% 5.67/1.36 ( ![X4:$i,X6:$i]: ( subset @ X6 @ ( setadjoin @ X4 @ X6 ) ) )),
% 5.67/1.36 define([status(thm)])).
% 5.67/1.36 thf(subsetTrans, axiom, subsetTrans =
% 5.67/1.36 (![A:$i,B:$i,C:$i]:
% 5.67/1.36 ( ( subset @ A @ B ) => ( ( subset @ B @ C ) => ( subset @ A @ C ) ) ))).
% 5.67/1.36 thf('30', plain,
% 5.67/1.36 (( subsetTrans ) =
% 5.67/1.36 ( ![X4:$i,X6:$i,X8:$i]:
% 5.67/1.36 ( ( subset @ X4 @ X6 ) =>
% 5.67/1.36 ( ( subset @ X6 @ X8 ) => ( subset @ X4 @ X8 ) ) ) )),
% 5.67/1.36 define([status(thm)])).
% 5.67/1.36 thf(subsetRefl, axiom, subsetRefl = (![A:$i]: ( subset @ A @ A ))).
% 5.67/1.36 thf('31', plain, (( subsetRefl ) = ( ![X4:$i]: ( subset @ X4 @ X4 ) )),
% 5.67/1.36 define([status(thm)])).
% 5.67/1.36 thf(notequalI1, axiom, notequalI1 =
% 5.67/1.36 (![A:$i,B:$i]: ( ( ~( subset @ A @ B ) ) => ( ( A ) != ( B ) ) ))).
% 5.67/1.36 thf('32', plain,
% 5.67/1.36 (( notequalI1 ) =
% 5.67/1.36 ( ![X4:$i,X6:$i]: ( ( ~( subset @ X4 @ X6 ) ) => ( ( X4 ) != ( X6 ) ) ) )),
% 5.67/1.36 define([status(thm)])).
% 5.67/1.36 thf(notsubsetI, axiom, notsubsetI =
% 5.67/1.36 (![A:$i,B:$i,Xx:$i]:
% 5.67/1.36 ( ( in @ Xx @ A ) => ( ( ~( in @ Xx @ B ) ) => ( ~( subset @ A @ B ) ) ) ))).
% 5.67/1.36 thf('33', plain,
% 5.67/1.36 (( notsubsetI ) =
% 5.67/1.36 ( ![X4:$i,X6:$i,X8:$i]:
% 5.67/1.36 ( ( in @ X8 @ X4 ) =>
% 5.67/1.36 ( ( ~( in @ X8 @ X6 ) ) => ( ~( subset @ X4 @ X6 ) ) ) ) )),
% 5.67/1.36 define([status(thm)])).
% 5.67/1.36 thf(subsetE2, axiom, subsetE2 =
% 5.67/1.36 (![A:$i,B:$i,Xx:$i]:
% 5.67/1.36 ( ( subset @ A @ B ) => ( ( ~( in @ Xx @ B ) ) => ( ~( in @ Xx @ A ) ) ) ))).
% 5.67/1.36 thf('34', plain,
% 5.67/1.36 (( subsetE2 ) =
% 5.67/1.36 ( ![X4:$i,X6:$i,X8:$i]:
% 5.67/1.36 ( ( subset @ X4 @ X6 ) =>
% 5.67/1.36 ( ( ~( in @ X8 @ X6 ) ) => ( ~( in @ X8 @ X4 ) ) ) ) )),
% 5.67/1.36 define([status(thm)])).
% 5.67/1.36 thf(subsetE, axiom, subsetE =
% 5.67/1.36 (![A:$i,B:$i,Xx:$i]:
% 5.67/1.36 ( ( subset @ A @ B ) => ( ( in @ Xx @ A ) => ( in @ Xx @ B ) ) ))).
% 5.67/1.36 thf('35', plain,
% 5.67/1.36 (( subsetE ) =
% 5.67/1.36 ( ![X4:$i,X6:$i,X8:$i]:
% 5.67/1.36 ( ( subset @ X4 @ X6 ) => ( ( in @ X8 @ X4 ) => ( in @ X8 @ X6 ) ) ) )),
% 5.67/1.36 define([status(thm)])).
% 5.67/1.36 thf(emptysetsubset, axiom, emptysetsubset =
% 5.67/1.36 (![A:$i]: ( subset @ emptyset @ A ))).
% 5.67/1.36 thf('36', plain,
% 5.67/1.36 (( emptysetsubset ) = ( ![X4:$i]: ( subset @ emptyset @ X4 ) )),
% 5.67/1.36 define([status(thm)])).
% 5.67/1.36 thf(subsetI2, axiom, subsetI2 =
% 5.67/1.36 (![A:$i,B:$i]:
% 5.67/1.36 ( ( ![Xx:$i]: ( ( in @ Xx @ A ) => ( in @ Xx @ B ) ) ) =>
% 5.67/1.36 ( subset @ A @ B ) ))).
% 5.67/1.36 thf('37', plain,
% 5.67/1.36 (( subsetI2 ) =
% 5.67/1.36 ( ![X4:$i,X6:$i]:
% 5.67/1.36 ( ( ![X8:$i]: ( ( in @ X8 @ X4 ) => ( in @ X8 @ X6 ) ) ) =>
% 5.67/1.36 ( subset @ X4 @ X6 ) ) )),
% 5.67/1.36 define([status(thm)])).
% 5.67/1.36 thf(eqimpsubset1, axiom, eqimpsubset1 =
% 5.67/1.36 (![A:$i,B:$i]: ( ( ( A ) = ( B ) ) => ( subset @ A @ B ) ))).
% 5.67/1.36 thf('38', plain,
% 5.67/1.36 (( eqimpsubset1 ) =
% 5.67/1.36 ( ![X4:$i,X6:$i]: ( ( ( X4 ) = ( X6 ) ) => ( subset @ X4 @ X6 ) ) )),
% 5.67/1.36 define([status(thm)])).
% 5.67/1.36 thf(eqimpsubset2, axiom, eqimpsubset2 =
% 5.67/1.36 (![A:$i,B:$i]: ( ( ( A ) = ( B ) ) => ( subset @ B @ A ) ))).
% 5.67/1.36 thf('39', plain,
% 5.67/1.36 (( eqimpsubset2 ) =
% 5.67/1.36 ( ![X4:$i,X6:$i]: ( ( ( X4 ) = ( X6 ) ) => ( subset @ X6 @ X4 ) ) )),
% 5.67/1.36 define([status(thm)])).
% 5.67/1.36 thf(subsetI1, axiom, subsetI1 =
% 5.67/1.36 (![A:$i,B:$i]:
% 5.67/1.36 ( ( ![Xx:$i]: ( ( in @ Xx @ A ) => ( in @ Xx @ B ) ) ) =>
% 5.67/1.36 ( subset @ A @ B ) ))).
% 5.67/1.36 thf('40', plain,
% 5.67/1.36 (( subsetI1 ) =
% 5.67/1.36 ( ![X4:$i,X6:$i]:
% 5.67/1.36 ( ( ![X8:$i]: ( ( in @ X8 @ X4 ) => ( in @ X8 @ X6 ) ) ) =>
% 5.67/1.36 ( subset @ X4 @ X6 ) ) )),
% 5.67/1.36 define([status(thm)])).
% 5.67/1.36 thf(powerset__Cong, axiom, powerset__Cong =
% 5.67/1.36 (![A:$i,B:$i]:
% 5.67/1.36 ( ( ( A ) = ( B ) ) => ( ( powerset @ A ) = ( powerset @ B ) ) ))).
% 5.67/1.36 thf('41', plain,
% 5.67/1.36 (( powerset__Cong ) =
% 5.67/1.36 ( ![X4:$i,X6:$i]:
% 5.67/1.36 ( ( ( X4 ) = ( X6 ) ) => ( ( powerset @ X4 ) = ( powerset @ X6 ) ) ) )),
% 5.67/1.36 define([status(thm)])).
% 5.67/1.36 thf(powersetE, axiom, powersetE =
% 5.67/1.36 (![A:$i,B:$i,Xx:$i]:
% 5.67/1.36 ( ( in @ B @ ( powerset @ A ) ) => ( ( in @ Xx @ B ) => ( in @ Xx @ A ) ) ))).
% 5.67/1.36 thf('42', plain,
% 5.67/1.36 (( powersetE ) =
% 5.67/1.36 ( ![X4:$i,X6:$i,X8:$i]:
% 5.67/1.36 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 5.67/1.36 ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ) )),
% 5.67/1.36 define([status(thm)])).
% 5.67/1.36 thf(emptyInPowerset, axiom, emptyInPowerset =
% 5.67/1.36 (![A:$i]: ( in @ emptyset @ ( powerset @ A ) ))).
% 5.67/1.36 thf('43', plain,
% 5.67/1.36 (( emptyInPowerset ) =
% 5.67/1.36 ( ![X4:$i]: ( in @ emptyset @ ( powerset @ X4 ) ) )),
% 5.67/1.36 define([status(thm)])).
% 5.67/1.36 thf(emptyinPowerset, axiom, emptyinPowerset =
% 5.67/1.36 (![A:$i]: ( in @ emptyset @ ( powerset @ A ) ))).
% 5.67/1.36 thf('44', plain,
% 5.67/1.36 (( emptyinPowerset ) =
% 5.67/1.36 ( ![X4:$i]: ( in @ emptyset @ ( powerset @ X4 ) ) )),
% 5.67/1.36 define([status(thm)])).
% 5.67/1.36 thf(powersetI, axiom, powersetI =
% 5.67/1.36 (![A:$i,B:$i]:
% 5.67/1.36 ( ( ![Xx:$i]: ( ( in @ Xx @ B ) => ( in @ Xx @ A ) ) ) =>
% 5.67/1.36 ( in @ B @ ( powerset @ A ) ) ))).
% 5.67/1.36 thf('45', plain,
% 5.67/1.36 (( powersetI ) =
% 5.67/1.36 ( ![X4:$i,X6:$i]:
% 5.67/1.36 ( ( ![X8:$i]: ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ) =>
% 5.67/1.36 ( in @ X6 @ ( powerset @ X4 ) ) ) )),
% 5.67/1.36 define([status(thm)])).
% 5.67/1.36 thf(powersetAx, axiom, powersetAx =
% 5.67/1.36 (![A:$i,B:$i]:
% 5.67/1.36 ( ( in @ B @ ( powerset @ A ) ) <=>
% 5.67/1.36 ( ![Xx:$i]: ( ( in @ Xx @ B ) => ( in @ Xx @ A ) ) ) ))).
% 5.67/1.36 thf('46', plain,
% 5.67/1.36 (( powersetAx ) =
% 5.67/1.36 ( ![X4:$i,X6:$i]:
% 5.67/1.36 ( ( in @ X6 @ ( powerset @ X4 ) ) <=>
% 5.67/1.36 ( ![X8:$i]: ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ) ) )),
% 5.67/1.36 define([status(thm)])).
% 5.67/1.36 thf(contrasubsetT, conjecture,
% 5.67/1.36 (( setextAx ) =>
% 5.67/1.36 ( ( emptysetAx ) =>
% 5.67/1.36 ( ( setadjoinAx ) =>
% 5.67/1.36 ( ( powersetAx ) =>
% 5.67/1.36 ( ( setunionAx ) =>
% 5.67/1.36 ( ( omega0Ax ) =>
% 5.67/1.36 ( ( omegaSAx ) =>
% 5.67/1.36 ( ( omegaIndAx ) =>
% 5.67/1.36 ( ( replAx ) =>
% 6.17/1.36 ( ( foundationAx ) =>
% 6.17/1.36 ( ( wellorderingAx ) =>
% 6.17/1.36 ( ( descrp ) =>
% 6.17/1.36 ( ( dsetconstrI ) =>
% 6.17/1.36 ( ( dsetconstrEL ) =>
% 6.17/1.36 ( ( dsetconstrER ) =>
% 6.17/1.36 ( ( exuE1 ) =>
% 6.17/1.36 ( ( prop2setE ) =>
% 6.17/1.36 ( ( emptysetE ) =>
% 6.17/1.36 ( ( emptysetimpfalse ) =>
% 6.17/1.36 ( ( notinemptyset ) =>
% 6.17/1.36 ( ( exuE3e ) =>
% 6.17/1.36 ( ( setext ) =>
% 6.17/1.36 ( ( emptyI ) =>
% 6.17/1.36 ( ( noeltsimpempty ) =>
% 6.17/1.36 ( ( setbeta ) =>
% 6.17/1.36 ( ( nonemptyE1 ) =>
% 6.17/1.36 ( ( nonemptyI ) =>
% 6.17/1.36 ( ( nonemptyI1 ) =>
% 6.17/1.36 ( ( setadjoinIL ) =>
% 6.17/1.36 ( ( emptyinunitempty ) =>
% 6.17/1.36 ( ( setadjoinIR ) =>
% 6.17/1.36 ( ( setadjoinE ) =>
% 6.17/1.36 ( (
% 6.17/1.36 setadjoinOr ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 setoftrueEq ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 powersetI ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 emptyinPowerset ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 emptyInPowerset ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 powersetE ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 setunionI ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 setunionE ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 subPowSU ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 exuE2 ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 nonemptyImpWitness ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 uniqinunit ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 notinsingleton ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 eqinunit ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 singletonsswitch ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 upairsetE ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 upairsetIL ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 upairsetIR ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 emptyE1 ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 vacuousDall ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 quantDeMorgan1 ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 quantDeMorgan2 ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 quantDeMorgan3 ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 quantDeMorgan4 ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 prop2setI ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 prop2set2propI ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 notdexE ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 notdallE ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 exuI1 ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 exuI3 ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 exuI2 ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 inCongP ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 in__Cong ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 exuE3u ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 exu__Cong ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 emptyset__Cong ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 setadjoin__Cong ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 powerset__Cong ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 setunion__Cong ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 omega__Cong ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 exuEu ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 descr__Cong ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 dsetconstr__Cong ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 subsetI1 ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 eqimpsubset2 ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 eqimpsubset1 ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 subsetI2 ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 emptysetsubset ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 subsetE ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 subsetE2 ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 notsubsetI ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 notequalI1 ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 notequalI2 ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 subsetRefl ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 subsetTrans ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 setadjoinSub ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 setadjoinSub2 ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 subset2powerset ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 setextsub ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 subsetemptysetimpeq ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 powersetI1 ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 powersetE1 ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 inPowerset ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 powersetsubset ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 sepInPowerset ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 sepSubset ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 binunionIL ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 upairset2IR ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 binunionIR ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 binunionEcases ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 binunionE ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 binunionLsub ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 binunionRsub ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 binintersectI ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 binintersectSubset5 ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 binintersectEL ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 binintersectLsub ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 binintersectSubset2 ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 binintersectSubset3 ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 binintersectER ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 disjointsetsI1 ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 binintersectRsub ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 binintersectSubset4 ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 binintersectSubset1 ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 bs114d ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 setminusI ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 setminusEL ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 setminusER ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 setminusSubset2 ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 setminusERneg ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 setminusELneg ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 setminusILneg ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 setminusIRneg ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 setminusLsub ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 setminusSubset1 ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 symdiffE ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 symdiffI1 ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 symdiffI2 ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 symdiffIneg1 ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 symdiffIneg2 ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 secondinupair ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 setukpairIL ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 setukpairIR ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 kpairiskpair ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 kpairp ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 singletonsubset ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 singletoninpowerset ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 singletoninpowunion ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 upairset2E ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 upairsubunion ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 upairinpowunion ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 ubforcartprodlem1 ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 ubforcartprodlem2 ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 ubforcartprodlem3 ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 cartprodpairin ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 cartprodmempair1 ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 cartprodmempair ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 setunionE2 ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 setunionsingleton1 ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 setunionsingleton2 ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 setunionsingleton ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 singletonprop ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 ex1E1 ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 ex1I ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 ex1I2 ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 singletonsuniq ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 setukpairinjL1 ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 kfstsingleton ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 theprop ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 kfstpairEq ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 cartprodfstin ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 setukpairinjL2 ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 setukpairinjL ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 setukpairinjR11 ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 setukpairinjR12 ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 setukpairinjR1 ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 upairequniteq ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 setukpairinjR2 ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 setukpairinjR ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 ksndsingleton ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 ksndpairEq ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 kpairsurjEq ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 cartprodsndin ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 cartprodpairmemEL ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 cartprodpairmemER ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 cartprodmempaircEq ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 cartprodfstpairEq ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 cartprodsndpairEq ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 cartprodpairsurjEq ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 dpsetconstrI ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 dpsetconstrSub ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 setOfPairsIsBReln ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 dpsetconstrERa ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 dpsetconstrEL1 ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 dpsetconstrEL2 ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 dpsetconstrER ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 funcImageSingleton ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 apProp ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 app ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 infuncsetfunc ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 ap2p ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 funcinfuncset ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 lamProp ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 lamp ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 lam2p ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 brelnall1 ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 brelnall2 ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 ex1E2 ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 funcGraphProp1 ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 funcGraphProp3 ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 funcGraphProp2 ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 funcextLem ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 funcGraphProp4 ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 subbreln ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 eqbreln ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 funcext ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 funcext2 ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 ap2apEq1 ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 ap2apEq2 ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 beta1 ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 eta1 ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 lam2lamEq ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 beta2 ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 eta2 ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 iffalseProp1 ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 iffalseProp2 ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 iftrueProp1 ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 iftrueProp2 ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 ifSingleton ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 ifp ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 theeq ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 iftrue ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 iffalse ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 iftrueorfalse ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 binintersectT_lem ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 binunionT_lem ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 powersetT_lem ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 setminusT_lem ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 complementT_lem ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 setextT ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 subsetTI ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 powersetTI1 ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 powersetTE1 ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 complementTI1 ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 complementTE1 ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 binintersectTELcontra ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 binintersectTERcontra ) =>
% 6.17/1.36 (
% 6.17/1.36 ![
% 6.17/1.36 A:$i,X:$i]:
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 in @
% 6.17/1.36 X @
% 6.17/1.36 (
% 6.17/1.36 powerset @
% 6.17/1.36 A ) ) =>
% 6.17/1.36 (
% 6.17/1.36 ![
% 6.17/1.36 Y:$i]:
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 in @
% 6.17/1.36 Y @
% 6.17/1.36 (
% 6.17/1.36 powerset @
% 6.17/1.36 A ) ) =>
% 6.17/1.36 (
% 6.17/1.36 ![
% 6.17/1.36 Xx:$i]:
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 in @
% 6.17/1.36 Xx @ A ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 subset @
% 6.17/1.36 X @
% 6.17/1.36 (
% 6.17/1.36 setminus @
% 6.17/1.36 A @ Y ) ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 in @
% 6.17/1.36 Xx @ Y ) =>
% 6.17/1.36 (
% 6.17/1.36 ~(
% 6.17/1.36 in @
% 6.17/1.36 Xx @ X ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 6.17/1.36 thf(zf_stmt_0, conjecture,
% 6.17/1.36 (( setextAx ) =>
% 6.17/1.36 ( ( emptysetAx ) =>
% 6.17/1.36 ( ( setadjoinAx ) =>
% 6.17/1.36 ( ( ![X4:$i,X6:$i]:
% 6.17/1.36 ( ( in @ X6 @ ( powerset @ X4 ) ) <=>
% 6.17/1.36 ( ![X8:$i]: ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ) ) ) =>
% 6.17/1.36 ( ( setunionAx ) =>
% 6.17/1.36 ( ( omega0Ax ) =>
% 6.17/1.36 ( ( omegaSAx ) =>
% 6.17/1.36 ( ( omegaIndAx ) =>
% 6.17/1.36 ( ( replAx ) =>
% 6.17/1.36 ( ( foundationAx ) =>
% 6.17/1.36 ( ( wellorderingAx ) =>
% 6.17/1.36 ( ( descrp ) =>
% 6.17/1.36 ( ( dsetconstrI ) =>
% 6.17/1.36 ( ( dsetconstrEL ) =>
% 6.17/1.36 ( ( dsetconstrER ) =>
% 6.17/1.36 ( ( exuE1 ) =>
% 6.17/1.36 ( ( prop2setE ) =>
% 6.17/1.36 ( ( emptysetE ) =>
% 6.17/1.36 ( ( emptysetimpfalse ) =>
% 6.17/1.36 ( ( notinemptyset ) =>
% 6.17/1.36 ( ( exuE3e ) =>
% 6.17/1.36 ( ( setext ) =>
% 6.17/1.36 ( ( emptyI ) =>
% 6.17/1.36 ( ( noeltsimpempty ) =>
% 6.17/1.36 ( ( setbeta ) =>
% 6.17/1.36 ( ( nonemptyE1 ) =>
% 6.17/1.36 ( ( nonemptyI ) =>
% 6.17/1.36 ( ( nonemptyI1 ) =>
% 6.17/1.36 ( ( setadjoinIL ) =>
% 6.17/1.36 ( ( emptyinunitempty ) =>
% 6.17/1.36 ( ( setadjoinIR ) =>
% 6.17/1.36 ( ( setadjoinE ) =>
% 6.17/1.36 ( (
% 6.17/1.36 setadjoinOr ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 setoftrueEq ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 ![
% 6.17/1.36 X10:$i,
% 6.17/1.36 X12:$i]:
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 ![
% 6.17/1.36 X14:$i]:
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 in @
% 6.17/1.36 X14 @ X12 ) =>
% 6.17/1.36 (
% 6.17/1.36 in @
% 6.17/1.36 X14 @ X10 ) ) ) =>
% 6.17/1.36 (
% 6.17/1.36 in @
% 6.17/1.36 X12 @
% 6.17/1.36 (
% 6.17/1.36 powerset @
% 6.17/1.36 X10 ) ) ) ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 ![
% 6.17/1.36 X16:$i]:
% 6.17/1.36 (
% 6.17/1.36 in @
% 6.17/1.36 emptyset @
% 6.17/1.36 (
% 6.17/1.36 powerset @
% 6.17/1.36 X16 ) ) ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 ![
% 6.17/1.36 X18:$i]:
% 6.17/1.36 (
% 6.17/1.36 in @
% 6.17/1.36 emptyset @
% 6.17/1.36 (
% 6.17/1.36 powerset @
% 6.17/1.36 X18 ) ) ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 ![
% 6.17/1.36 X20:$i,
% 6.17/1.36 X22:$i,
% 6.17/1.36 X24:$i]:
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 in @
% 6.17/1.36 X22 @
% 6.17/1.36 (
% 6.17/1.36 powerset @
% 6.17/1.36 X20 ) ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 in @
% 6.17/1.36 X24 @ X22 ) =>
% 6.17/1.36 (
% 6.17/1.36 in @
% 6.17/1.36 X24 @ X20 ) ) ) ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 setunionI ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 setunionE ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 subPowSU ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 exuE2 ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 nonemptyImpWitness ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 uniqinunit ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 notinsingleton ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 eqinunit ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 singletonsswitch ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 upairsetE ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 upairsetIL ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 upairsetIR ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 emptyE1 ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 vacuousDall ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 quantDeMorgan1 ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 quantDeMorgan2 ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 quantDeMorgan3 ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 quantDeMorgan4 ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 prop2setI ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 prop2set2propI ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 notdexE ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 notdallE ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 exuI1 ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 exuI3 ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 exuI2 ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 inCongP ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 in__Cong ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 exuE3u ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 exu__Cong ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 emptyset__Cong ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 setadjoin__Cong ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 ![
% 6.17/1.36 X26:$i,
% 6.17/1.36 X28:$i]:
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 X26 ) =
% 6.17/1.36 (
% 6.17/1.36 X28 ) ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 powerset @
% 6.17/1.36 X26 ) =
% 6.17/1.36 (
% 6.17/1.36 powerset @
% 6.17/1.36 X28 ) ) ) ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 setunion__Cong ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 omega__Cong ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 exuEu ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 descr__Cong ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 dsetconstr__Cong ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 ![
% 6.17/1.36 X30:$i,
% 6.17/1.36 X32:$i]:
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 ![
% 6.17/1.36 X34:$i]:
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 in @
% 6.17/1.36 X34 @ X30 ) =>
% 6.17/1.36 (
% 6.17/1.36 in @
% 6.17/1.36 X34 @ X32 ) ) ) =>
% 6.17/1.36 (
% 6.17/1.36 subset @
% 6.17/1.36 X30 @ X32 ) ) ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 ![
% 6.17/1.36 X36:$i,
% 6.17/1.36 X38:$i]:
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 X36 ) =
% 6.17/1.36 (
% 6.17/1.36 X38 ) ) =>
% 6.17/1.36 (
% 6.17/1.36 subset @
% 6.17/1.36 X38 @ X36 ) ) ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 ![
% 6.17/1.36 X40:$i,
% 6.17/1.36 X42:$i]:
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 X40 ) =
% 6.17/1.36 (
% 6.17/1.36 X42 ) ) =>
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% 6.17/1.36 singletonprop ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 ex1E1 ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 ex1I ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 ex1I2 ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 singletonsuniq ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 setukpairinjL1 ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 kfstsingleton ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 theprop ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 kfstpairEq ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 cartprodfstin ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 setukpairinjL2 ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 setukpairinjL ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 setukpairinjR11 ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 setukpairinjR12 ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 setukpairinjR1 ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 upairequniteq ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 setukpairinjR2 ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 setukpairinjR ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 ksndsingleton ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 ksndpairEq ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 kpairsurjEq ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 cartprodsndin ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 cartprodpairmemEL ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 cartprodpairmemER ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 cartprodmempaircEq ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 cartprodfstpairEq ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 cartprodsndpairEq ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 cartprodpairsurjEq ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 dpsetconstrI ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 dpsetconstrSub ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 setOfPairsIsBReln ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 dpsetconstrERa ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 dpsetconstrEL1 ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 dpsetconstrEL2 ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 dpsetconstrER ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 funcImageSingleton ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 apProp ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 app ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 infuncsetfunc ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 ap2p ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 funcinfuncset ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 lamProp ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 lamp ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 lam2p ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 brelnall1 ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 brelnall2 ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 ex1E2 ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 funcGraphProp1 ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 funcGraphProp3 ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 funcGraphProp2 ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 funcextLem ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 funcGraphProp4 ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 subbreln ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 eqbreln ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 funcext ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 funcext2 ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 ap2apEq1 ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 ap2apEq2 ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 beta1 ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 eta1 ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 lam2lamEq ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 beta2 ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 eta2 ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 iffalseProp1 ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 iffalseProp2 ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 iftrueProp1 ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 iftrueProp2 ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 ifSingleton ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 ifp ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 theeq ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 iftrue ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 iffalse ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 iftrueorfalse ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 binintersectT_lem ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 binunionT_lem ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 ![
% 6.17/1.36 X178:$i,
% 6.17/1.36 X180:$i]:
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 in @
% 6.17/1.36 X180 @
% 6.17/1.36 (
% 6.17/1.36 powerset @
% 6.17/1.36 X178 ) ) =>
% 6.17/1.36 (
% 6.17/1.36 in @
% 6.17/1.36 (
% 6.17/1.36 powerset @
% 6.17/1.36 X180 ) @
% 6.17/1.36 (
% 6.17/1.36 powerset @
% 6.17/1.36 (
% 6.17/1.36 powerset @
% 6.17/1.36 X178 ) ) ) ) ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 ![
% 6.17/1.36 X182:$i,
% 6.17/1.36 X184:$i]:
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 in @
% 6.17/1.36 X184 @
% 6.17/1.36 (
% 6.17/1.36 powerset @
% 6.17/1.36 X182 ) ) =>
% 6.17/1.36 (
% 6.17/1.36 ![
% 6.17/1.36 X186:$i]:
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 in @
% 6.17/1.36 X186 @
% 6.17/1.36 (
% 6.17/1.36 powerset @
% 6.17/1.36 X182 ) ) =>
% 6.17/1.36 (
% 6.17/1.36 in @
% 6.17/1.36 (
% 6.17/1.36 setminus @
% 6.17/1.36 X184 @
% 6.17/1.36 X186 ) @
% 6.17/1.36 (
% 6.17/1.36 powerset @
% 6.17/1.36 X182 ) ) ) ) ) ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 ![
% 6.17/1.36 X188:$i,
% 6.17/1.36 X190:$i]:
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 in @
% 6.17/1.36 X190 @
% 6.17/1.36 (
% 6.17/1.36 powerset @
% 6.17/1.36 X188 ) ) =>
% 6.17/1.36 (
% 6.17/1.36 in @
% 6.17/1.36 (
% 6.17/1.36 setminus @
% 6.17/1.36 X188 @
% 6.17/1.36 X190 ) @
% 6.17/1.36 (
% 6.17/1.36 powerset @
% 6.17/1.36 X188 ) ) ) ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 ![
% 6.17/1.36 X192:$i,
% 6.17/1.36 X194:$i]:
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 in @
% 6.17/1.36 X194 @
% 6.17/1.36 (
% 6.17/1.36 powerset @
% 6.17/1.36 X192 ) ) =>
% 6.17/1.36 (
% 6.17/1.36 ![
% 6.17/1.36 X196:$i]:
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 in @
% 6.17/1.36 X196 @
% 6.17/1.36 (
% 6.17/1.36 powerset @
% 6.17/1.36 X192 ) ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 ![
% 6.17/1.36 X198:$i]:
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 in @
% 6.17/1.36 X198 @
% 6.17/1.36 X192 ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 in @
% 6.17/1.36 X198 @
% 6.17/1.36 X194 ) =>
% 6.17/1.36 (
% 6.17/1.36 in @
% 6.17/1.36 X198 @
% 6.17/1.36 X196 ) ) ) ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 ![
% 6.17/1.36 X200:$i]:
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 in @
% 6.17/1.36 X200 @
% 6.17/1.36 X192 ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 in @
% 6.17/1.36 X200 @
% 6.17/1.36 X196 ) =>
% 6.17/1.36 (
% 6.17/1.36 in @
% 6.17/1.36 X200 @
% 6.17/1.36 X194 ) ) ) ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 X194 ) =
% 6.17/1.36 (
% 6.17/1.36 X196 ) ) ) ) ) ) ) ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 ![
% 6.17/1.36 X202:$i,
% 6.17/1.36 X204:$i]:
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 in @
% 6.17/1.36 X204 @
% 6.17/1.36 (
% 6.17/1.36 powerset @
% 6.17/1.36 X202 ) ) =>
% 6.17/1.36 (
% 6.17/1.36 ![
% 6.17/1.36 X206:$i]:
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 in @
% 6.17/1.36 X206 @
% 6.17/1.36 (
% 6.17/1.36 powerset @
% 6.17/1.36 X202 ) ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 ![
% 6.17/1.36 X208:$i]:
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 in @
% 6.17/1.36 X208 @
% 6.17/1.36 X202 ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 in @
% 6.17/1.36 X208 @
% 6.17/1.36 X204 ) =>
% 6.17/1.36 (
% 6.17/1.36 in @
% 6.17/1.36 X208 @
% 6.17/1.36 X206 ) ) ) ) =>
% 6.17/1.36 (
% 6.17/1.36 subset @
% 6.17/1.36 X204 @
% 6.17/1.36 X206 ) ) ) ) ) ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 ![
% 6.17/1.36 X210:$i,
% 6.17/1.36 X212:$i]:
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 in @
% 6.17/1.36 X212 @
% 6.17/1.36 (
% 6.17/1.36 powerset @
% 6.17/1.36 X210 ) ) =>
% 6.17/1.36 (
% 6.17/1.36 ![
% 6.17/1.36 X214:$i]:
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 in @
% 6.17/1.36 X214 @
% 6.17/1.36 (
% 6.17/1.36 powerset @
% 6.17/1.36 X210 ) ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 ![
% 6.17/1.36 X216:$i]:
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 in @
% 6.17/1.36 X216 @
% 6.17/1.36 X210 ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 in @
% 6.17/1.36 X216 @
% 6.17/1.36 X212 ) =>
% 6.17/1.36 (
% 6.17/1.36 in @
% 6.17/1.36 X216 @
% 6.17/1.36 X214 ) ) ) ) =>
% 6.17/1.36 (
% 6.17/1.36 in @
% 6.17/1.36 X212 @
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% 6.17/1.36 powerset @
% 6.17/1.36 X214 ) ) ) ) ) ) ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 ![
% 6.17/1.36 X218:$i,
% 6.17/1.36 X220:$i]:
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 in @
% 6.17/1.36 X220 @
% 6.17/1.36 (
% 6.17/1.36 powerset @
% 6.17/1.36 X218 ) ) =>
% 6.17/1.36 (
% 6.17/1.36 ![
% 6.17/1.36 X222:$i]:
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 in @
% 6.17/1.36 X222 @
% 6.17/1.36 (
% 6.17/1.36 powerset @
% 6.17/1.36 X218 ) ) =>
% 6.17/1.36 (
% 6.17/1.36 ![
% 6.17/1.36 X224:$i]:
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 in @
% 6.17/1.36 X224 @
% 6.17/1.36 X218 ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 in @
% 6.17/1.36 X220 @
% 6.17/1.36 (
% 6.17/1.36 powerset @
% 6.17/1.36 X222 ) ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 in @
% 6.17/1.36 X224 @
% 6.17/1.36 X220 ) =>
% 6.17/1.36 (
% 6.17/1.36 in @
% 6.17/1.36 X224 @
% 6.17/1.36 X222 ) ) ) ) ) ) ) ) ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 ![
% 6.17/1.36 X226:$i,
% 6.17/1.36 X228:$i]:
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 in @
% 6.17/1.36 X228 @
% 6.17/1.36 (
% 6.17/1.36 powerset @
% 6.17/1.36 X226 ) ) =>
% 6.17/1.36 (
% 6.17/1.36 ![
% 6.17/1.36 X230:$i]:
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 in @
% 6.17/1.36 X230 @
% 6.17/1.36 X226 ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 in @
% 6.17/1.36 X230 @
% 6.17/1.36 X228 ) =>
% 6.17/1.36 (
% 6.17/1.36 ~(
% 6.17/1.36 in @
% 6.17/1.36 X230 @
% 6.17/1.36 (
% 6.17/1.36 setminus
% 6.17/1.36 @
% 6.17/1.36 X226 @
% 6.17/1.36 X228 ) ) ) ) ) ) ) ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 ![
% 6.17/1.36 X232:$i,
% 6.17/1.36 X234:$i]:
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 in @
% 6.17/1.36 X234 @
% 6.17/1.36 (
% 6.17/1.36 powerset @
% 6.17/1.36 X232 ) ) =>
% 6.17/1.36 (
% 6.17/1.36 ![
% 6.17/1.36 X236:$i]:
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 in @
% 6.17/1.36 X236 @
% 6.17/1.36 X232 ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 ~(
% 6.17/1.36 in @
% 6.17/1.36 X236 @
% 6.17/1.36 (
% 6.17/1.36 setminus
% 6.17/1.36 @
% 6.17/1.36 X232 @
% 6.17/1.36 X234 ) ) ) =>
% 6.17/1.36 (
% 6.17/1.36 in @
% 6.17/1.36 X236 @
% 6.17/1.36 X234 ) ) ) ) ) ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 binintersectTELcontra ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 binintersectTERcontra ) =>
% 6.17/1.36 (
% 6.17/1.36 ![
% 6.17/1.36 X238:$i,
% 6.17/1.36 X240:$i]:
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 in @
% 6.17/1.36 X240 @
% 6.17/1.36 (
% 6.17/1.36 powerset @
% 6.17/1.36 X238 ) ) =>
% 6.17/1.36 (
% 6.17/1.36 ![
% 6.17/1.36 X242:$i]:
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 in @
% 6.17/1.36 X242 @
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% 6.17/1.36 powerset @
% 6.17/1.36 X238 ) ) =>
% 6.17/1.36 (
% 6.17/1.36 ![
% 6.17/1.36 X244:$i]:
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 in @
% 6.17/1.36 X244 @
% 6.17/1.36 X238 ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 subset @
% 6.17/1.36 X240 @
% 6.17/1.36 (
% 6.17/1.36 setminus @
% 6.17/1.36 X238 @
% 6.17/1.36 X242 ) ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 in @
% 6.17/1.36 X244 @
% 6.17/1.36 X242 ) =>
% 6.17/1.36 (
% 6.17/1.36 ~(
% 6.17/1.36 in @
% 6.17/1.36 X244 @
% 6.17/1.36 X240 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 6.17/1.36 thf(zf_stmt_1, type, zip_tseitin_0 : $i > $i > $i > $o).
% 6.17/1.36 thf(zf_stmt_2, axiom,
% 6.17/1.36 (![X8:$i,X6:$i,X4:$i]:
% 6.17/1.36 ( ( zip_tseitin_0 @ X8 @ X6 @ X4 ) <=>
% 6.17/1.36 ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ))).
% 6.17/1.36 thf(zf_stmt_3, conjecture,
% 6.17/1.36 (( setextAx ) =>
% 6.17/1.36 ( ( emptysetAx ) =>
% 6.17/1.36 ( ( setadjoinAx ) =>
% 6.17/1.36 ( ( ![X4:$i,X6:$i]:
% 6.17/1.36 ( ( in @ X6 @ ( powerset @ X4 ) ) <=>
% 6.17/1.36 ( ![X8:$i]: ( zip_tseitin_0 @ X8 @ X6 @ X4 ) ) ) ) =>
% 6.17/1.36 ( ( setunionAx ) =>
% 6.17/1.36 ( ( omega0Ax ) =>
% 6.17/1.36 ( ( omegaSAx ) =>
% 6.17/1.36 ( ( omegaIndAx ) =>
% 6.17/1.36 ( ( replAx ) =>
% 6.17/1.36 ( ( foundationAx ) =>
% 6.17/1.36 ( ( wellorderingAx ) =>
% 6.17/1.36 ( ( descrp ) =>
% 6.17/1.36 ( ( dsetconstrI ) =>
% 6.17/1.36 ( ( dsetconstrEL ) =>
% 6.17/1.36 ( ( dsetconstrER ) =>
% 6.17/1.36 ( ( exuE1 ) =>
% 6.17/1.36 ( ( prop2setE ) =>
% 6.17/1.36 ( ( emptysetE ) =>
% 6.17/1.36 ( ( emptysetimpfalse ) =>
% 6.17/1.36 ( ( notinemptyset ) =>
% 6.17/1.36 ( ( exuE3e ) =>
% 6.17/1.36 ( ( setext ) =>
% 6.17/1.36 ( ( emptyI ) =>
% 6.17/1.36 ( ( noeltsimpempty ) =>
% 6.17/1.36 ( ( setbeta ) =>
% 6.17/1.36 ( ( nonemptyE1 ) =>
% 6.17/1.36 ( ( nonemptyI ) =>
% 6.17/1.36 ( ( nonemptyI1 ) =>
% 6.17/1.36 ( ( setadjoinIL ) =>
% 6.17/1.36 ( ( emptyinunitempty ) =>
% 6.17/1.36 ( ( setadjoinIR ) =>
% 6.17/1.36 ( ( setadjoinE ) =>
% 6.17/1.36 ( (
% 6.17/1.36 setadjoinOr ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 setoftrueEq ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 ![
% 6.17/1.36 X10:$i,
% 6.17/1.36 X12:$i]:
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 ![
% 6.17/1.36 X14:$i]:
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 in @
% 6.17/1.36 X14 @ X12 ) =>
% 6.17/1.36 (
% 6.17/1.36 in @
% 6.17/1.36 X14 @ X10 ) ) ) =>
% 6.17/1.36 (
% 6.17/1.36 in @
% 6.17/1.36 X12 @
% 6.17/1.36 (
% 6.17/1.36 powerset @
% 6.17/1.36 X10 ) ) ) ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 ![
% 6.17/1.36 X16:$i]:
% 6.17/1.36 (
% 6.17/1.36 in @
% 6.17/1.36 emptyset @
% 6.17/1.36 (
% 6.17/1.36 powerset @
% 6.17/1.36 X16 ) ) ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 ![
% 6.17/1.36 X18:$i]:
% 6.17/1.36 (
% 6.17/1.36 in @
% 6.17/1.36 emptyset @
% 6.17/1.36 (
% 6.17/1.36 powerset @
% 6.17/1.36 X18 ) ) ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 ![
% 6.17/1.36 X20:$i,
% 6.17/1.36 X22:$i,
% 6.17/1.36 X24:$i]:
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 in @
% 6.17/1.36 X22 @
% 6.17/1.36 (
% 6.17/1.36 powerset @
% 6.17/1.36 X20 ) ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 in @
% 6.17/1.36 X24 @ X22 ) =>
% 6.17/1.36 (
% 6.17/1.36 in @
% 6.17/1.36 X24 @ X20 ) ) ) ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 setunionI ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 setunionE ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 subPowSU ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 exuE2 ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 nonemptyImpWitness ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 uniqinunit ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 notinsingleton ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 eqinunit ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 singletonsswitch ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 upairsetE ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 upairsetIL ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 upairsetIR ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 emptyE1 ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 vacuousDall ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 quantDeMorgan1 ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 quantDeMorgan2 ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 quantDeMorgan3 ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 quantDeMorgan4 ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 prop2setI ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 prop2set2propI ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 notdexE ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 notdallE ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 exuI1 ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 exuI3 ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 exuI2 ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 inCongP ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 in__Cong ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 exuE3u ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 exu__Cong ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 emptyset__Cong ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 setadjoin__Cong ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 ![
% 6.17/1.36 X26:$i,
% 6.17/1.36 X28:$i]:
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 X26 ) =
% 6.17/1.36 (
% 6.17/1.36 X28 ) ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 powerset @
% 6.17/1.36 X26 ) =
% 6.17/1.36 (
% 6.17/1.36 powerset @
% 6.17/1.36 X28 ) ) ) ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 setunion__Cong ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 omega__Cong ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 exuEu ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 descr__Cong ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 dsetconstr__Cong ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 ![
% 6.17/1.36 X30:$i,
% 6.17/1.36 X32:$i]:
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 ![
% 6.17/1.36 X34:$i]:
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 in @
% 6.17/1.36 X34 @ X30 ) =>
% 6.17/1.36 (
% 6.17/1.36 in @
% 6.17/1.36 X34 @ X32 ) ) ) =>
% 6.17/1.36 (
% 6.17/1.36 subset @
% 6.17/1.36 X30 @ X32 ) ) ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 ![
% 6.17/1.36 X36:$i,
% 6.17/1.36 X38:$i]:
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 X36 ) =
% 6.17/1.36 (
% 6.17/1.36 X38 ) ) =>
% 6.17/1.36 (
% 6.17/1.36 subset @
% 6.17/1.36 X38 @ X36 ) ) ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 ![
% 6.17/1.36 X40:$i,
% 6.17/1.36 X42:$i]:
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 X40 ) =
% 6.17/1.36 (
% 6.17/1.36 X42 ) ) =>
% 6.17/1.36 (
% 6.17/1.36 subset @
% 6.17/1.36 X40 @ X42 ) ) ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 ![
% 6.17/1.36 X44:$i,
% 6.17/1.36 X46:$i]:
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 ![
% 6.17/1.36 X48:$i]:
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 in @
% 6.17/1.36 X48 @ X44 ) =>
% 6.17/1.36 (
% 6.17/1.36 in @
% 6.17/1.36 X48 @ X46 ) ) ) =>
% 6.17/1.36 (
% 6.17/1.36 subset @
% 6.17/1.36 X44 @ X46 ) ) ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 ![
% 6.17/1.36 X50:$i]:
% 6.17/1.36 (
% 6.17/1.36 subset @
% 6.17/1.36 emptyset @
% 6.17/1.36 X50 ) ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 ![
% 6.17/1.36 X52:$i,
% 6.17/1.36 X54:$i,
% 6.17/1.36 X56:$i]:
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 subset @
% 6.17/1.36 X52 @ X54 ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 in @
% 6.17/1.36 X56 @ X52 ) =>
% 6.17/1.36 (
% 6.17/1.36 in @
% 6.17/1.36 X56 @ X54 ) ) ) ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 ![
% 6.17/1.36 X58:$i,
% 6.17/1.36 X60:$i,
% 6.17/1.36 X62:$i]:
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 subset @
% 6.17/1.36 X58 @ X60 ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 ~(
% 6.17/1.36 in @
% 6.17/1.36 X62 @ X60 ) ) =>
% 6.17/1.36 (
% 6.17/1.36 ~(
% 6.17/1.36 in @
% 6.17/1.36 X62 @ X58 ) ) ) ) ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 ![
% 6.17/1.36 X64:$i,
% 6.17/1.36 X66:$i,
% 6.17/1.36 X68:$i]:
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 in @
% 6.17/1.36 X68 @ X64 ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 ~(
% 6.17/1.36 in @
% 6.17/1.36 X68 @ X66 ) ) =>
% 6.17/1.36 (
% 6.17/1.36 ~(
% 6.17/1.36 subset @
% 6.17/1.36 X64 @ X66 ) ) ) ) ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 ![
% 6.17/1.36 X70:$i,
% 6.17/1.36 X72:$i]:
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 ~(
% 6.17/1.36 subset @
% 6.17/1.36 X70 @ X72 ) ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 X70 ) !=
% 6.17/1.36 (
% 6.17/1.36 X72 ) ) ) ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 notequalI2 ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 ![
% 6.17/1.36 X74:$i]:
% 6.17/1.36 (
% 6.17/1.36 subset @
% 6.17/1.36 X74 @ X74 ) ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 ![
% 6.17/1.36 X76:$i,
% 6.17/1.36 X78:$i,
% 6.17/1.36 X80:$i]:
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 subset @
% 6.17/1.36 X76 @ X78 ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 subset @
% 6.17/1.36 X78 @ X80 ) =>
% 6.17/1.36 (
% 6.17/1.36 subset @
% 6.17/1.36 X76 @ X80 ) ) ) ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 ![
% 6.17/1.36 X82:$i,
% 6.17/1.36 X84:$i]:
% 6.17/1.36 (
% 6.17/1.36 subset @
% 6.17/1.36 X84 @
% 6.17/1.36 (
% 6.17/1.36 setadjoin
% 6.17/1.36 @
% 6.17/1.36 X82 @ X84 ) ) ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 ![
% 6.17/1.36 X86:$i,
% 6.17/1.36 X88:$i,
% 6.17/1.36 X90:$i]:
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 subset @
% 6.17/1.36 X86 @ X90 ) =>
% 6.17/1.36 (
% 6.17/1.36 subset @
% 6.17/1.36 X86 @
% 6.17/1.36 (
% 6.17/1.36 setadjoin
% 6.17/1.36 @
% 6.17/1.36 X88 @ X90 ) ) ) ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 ![
% 6.17/1.36 X92:$i,
% 6.17/1.36 X94:$i]:
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 subset @
% 6.17/1.36 X92 @ X94 ) =>
% 6.17/1.36 (
% 6.17/1.36 in @
% 6.17/1.36 X92 @
% 6.17/1.36 (
% 6.17/1.36 powerset @
% 6.17/1.36 X94 ) ) ) ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 ![
% 6.17/1.36 X96:$i,
% 6.17/1.36 X98:$i]:
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 subset @
% 6.17/1.36 X96 @ X98 ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 subset @
% 6.17/1.36 X98 @ X96 ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 X96 ) =
% 6.17/1.36 (
% 6.17/1.36 X98 ) ) ) ) ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 ![
% 6.17/1.36 X100:$i]:
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 subset @
% 6.17/1.36 X100 @
% 6.17/1.36 emptyset ) =>
% 6.17/1.36 (
% 6.17/1.36 (
% 6.17/1.36 X100 ) =
% 6.17/1.36 (
% 6.17/1.36 emptyset ) ) ) ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 ![
% 6.17/1.37 X102:$i,
% 6.17/1.37 X104:$i]:
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 subset @
% 6.17/1.37 X104 @
% 6.17/1.37 X102 ) =>
% 6.17/1.37 (
% 6.17/1.37 in @
% 6.17/1.37 X104 @
% 6.17/1.37 (
% 6.17/1.37 powerset @
% 6.17/1.37 X102 ) ) ) ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 ![
% 6.17/1.37 X106:$i,
% 6.17/1.37 X108:$i]:
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 in @
% 6.17/1.37 X108 @
% 6.17/1.37 (
% 6.17/1.37 powerset @
% 6.17/1.37 X106 ) ) =>
% 6.17/1.37 (
% 6.17/1.37 subset @
% 6.17/1.37 X108 @
% 6.17/1.37 X106 ) ) ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 ![
% 6.17/1.37 X110:$i]:
% 6.17/1.37 (
% 6.17/1.37 in @
% 6.17/1.37 X110 @
% 6.17/1.37 (
% 6.17/1.37 powerset @
% 6.17/1.37 X110 ) ) ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 ![
% 6.17/1.37 X112:$i,
% 6.17/1.37 X114:$i]:
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 subset @
% 6.17/1.37 X112 @
% 6.17/1.37 X114 ) =>
% 6.17/1.37 (
% 6.17/1.37 subset @
% 6.17/1.37 (
% 6.17/1.37 powerset @
% 6.17/1.37 X112 ) @
% 6.17/1.37 (
% 6.17/1.37 powerset @
% 6.17/1.37 X114 ) ) ) ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 sepInPowerset ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 sepSubset ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 binunionIL ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 upairset2IR ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 binunionIR ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 binunionEcases ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 binunionE ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 binunionLsub ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 binunionRsub ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 binintersectI ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 binintersectSubset5 ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 binintersectEL ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 binintersectLsub ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 binintersectSubset2 ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 binintersectSubset3 ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 binintersectER ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 disjointsetsI1 ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 binintersectRsub ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 binintersectSubset4 ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 binintersectSubset1 ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 bs114d ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 ![
% 6.17/1.37 X116:$i,
% 6.17/1.37 X118:$i,
% 6.17/1.37 X120:$i]:
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 in @
% 6.17/1.37 X120 @
% 6.17/1.37 X116 ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 ~(
% 6.17/1.37 in @
% 6.17/1.37 X120 @
% 6.17/1.37 X118 ) ) =>
% 6.17/1.37 (
% 6.17/1.37 in @
% 6.17/1.37 X120 @
% 6.17/1.37 (
% 6.17/1.37 setminus @
% 6.17/1.37 X116 @
% 6.17/1.37 X118 ) ) ) ) ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 ![
% 6.17/1.37 X122:$i,
% 6.17/1.37 X124:$i,
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% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 in @
% 6.17/1.37 X126 @
% 6.17/1.37 (
% 6.17/1.37 setminus @
% 6.17/1.37 X122 @
% 6.17/1.37 X124 ) ) =>
% 6.17/1.37 (
% 6.17/1.37 in @
% 6.17/1.37 X126 @
% 6.17/1.37 X122 ) ) ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 ![
% 6.17/1.37 X128:$i,
% 6.17/1.37 X130:$i,
% 6.17/1.37 X132:$i]:
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 in @
% 6.17/1.37 X132 @
% 6.17/1.37 (
% 6.17/1.37 setminus @
% 6.17/1.37 X128 @
% 6.17/1.37 X130 ) ) =>
% 6.17/1.37 (
% 6.17/1.37 ~(
% 6.17/1.37 in @
% 6.17/1.37 X132 @
% 6.17/1.37 X130 ) ) ) ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 ![
% 6.17/1.37 X134:$i,
% 6.17/1.37 X136:$i]:
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 subset @
% 6.17/1.37 X134 @
% 6.17/1.37 X136 ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 setminus @
% 6.17/1.37 X134 @
% 6.17/1.37 X136 ) =
% 6.17/1.37 (
% 6.17/1.37 emptyset ) ) ) ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 ![
% 6.17/1.37 X138:$i,
% 6.17/1.37 X140:$i,
% 6.17/1.37 X142:$i]:
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 ~(
% 6.17/1.37 in @
% 6.17/1.37 X142 @
% 6.17/1.37 (
% 6.17/1.37 setminus
% 6.17/1.37 @
% 6.17/1.37 X138 @
% 6.17/1.37 X140 ) ) ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 in @
% 6.17/1.37 X142 @
% 6.17/1.37 X138 ) =>
% 6.17/1.37 (
% 6.17/1.37 in @
% 6.17/1.37 X142 @
% 6.17/1.37 X140 ) ) ) ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 ![
% 6.17/1.37 X144:$i,
% 6.17/1.37 X146:$i,
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% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 ~(
% 6.17/1.37 in @
% 6.17/1.37 X148 @
% 6.17/1.37 (
% 6.17/1.37 setminus
% 6.17/1.37 @
% 6.17/1.37 X144 @
% 6.17/1.37 X146 ) ) ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 ~(
% 6.17/1.37 in @
% 6.17/1.37 X148 @
% 6.17/1.37 X146 ) ) =>
% 6.17/1.37 (
% 6.17/1.37 ~(
% 6.17/1.37 in @
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% 6.17/1.37 X144 ) ) ) ) ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 ![
% 6.17/1.37 X150:$i,
% 6.17/1.37 X152:$i,
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% 6.17/1.37 (
% 6.17/1.37 ~(
% 6.17/1.37 in @
% 6.17/1.37 X154 @
% 6.17/1.37 X150 ) ) =>
% 6.17/1.37 (
% 6.17/1.37 ~(
% 6.17/1.37 in @
% 6.17/1.37 X154 @
% 6.17/1.37 (
% 6.17/1.37 setminus
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% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 ![
% 6.17/1.37 X156:$i,
% 6.17/1.37 X158:$i,
% 6.17/1.37 X160:$i]:
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 in @
% 6.17/1.37 X160 @
% 6.17/1.37 X158 ) =>
% 6.17/1.37 (
% 6.17/1.37 ~(
% 6.17/1.37 in @
% 6.17/1.37 X160 @
% 6.17/1.37 (
% 6.17/1.37 setminus
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% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 ![
% 6.17/1.37 X162:$i,
% 6.17/1.37 X164:$i]:
% 6.17/1.37 (
% 6.17/1.37 subset @
% 6.17/1.37 (
% 6.17/1.37 setminus @
% 6.17/1.37 X162 @
% 6.17/1.37 X164 ) @
% 6.17/1.37 X162 ) ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 ![
% 6.17/1.37 X166:$i,
% 6.17/1.37 X168:$i]:
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 setminus @
% 6.17/1.37 X166 @
% 6.17/1.37 X168 ) =
% 6.17/1.37 (
% 6.17/1.37 emptyset ) ) =>
% 6.17/1.37 (
% 6.17/1.37 subset @
% 6.17/1.37 X166 @
% 6.17/1.37 X168 ) ) ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 symdiffE ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 symdiffI1 ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 symdiffI2 ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 symdiffIneg1 ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 symdiffIneg2 ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 secondinupair ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 setukpairIL ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 setukpairIR ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 kpairiskpair ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 kpairp ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 ![
% 6.17/1.37 X170:$i,
% 6.17/1.37 X172:$i]:
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 in @
% 6.17/1.37 X172 @
% 6.17/1.37 X170 ) =>
% 6.17/1.37 (
% 6.17/1.37 subset @
% 6.17/1.37 (
% 6.17/1.37 setadjoin
% 6.17/1.37 @
% 6.17/1.37 X172 @
% 6.17/1.37 emptyset ) @
% 6.17/1.37 X170 ) ) ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 ![
% 6.17/1.37 X174:$i,
% 6.17/1.37 X176:$i]:
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 in @
% 6.17/1.37 X176 @
% 6.17/1.37 X174 ) =>
% 6.17/1.37 (
% 6.17/1.37 in @
% 6.17/1.37 (
% 6.17/1.37 setadjoin
% 6.17/1.37 @
% 6.17/1.37 X176 @
% 6.17/1.37 emptyset ) @
% 6.17/1.37 (
% 6.17/1.37 powerset @
% 6.17/1.37 X174 ) ) ) ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 singletoninpowunion ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 upairset2E ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 upairsubunion ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 upairinpowunion ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 ubforcartprodlem1 ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 ubforcartprodlem2 ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 ubforcartprodlem3 ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 cartprodpairin ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 cartprodmempair1 ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 cartprodmempair ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 setunionE2 ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 setunionsingleton1 ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 setunionsingleton2 ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 setunionsingleton ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 singletonprop ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 ex1E1 ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 ex1I ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 ex1I2 ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 singletonsuniq ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 setukpairinjL1 ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 kfstsingleton ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 theprop ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 kfstpairEq ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 cartprodfstin ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 setukpairinjL2 ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 setukpairinjL ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 setukpairinjR11 ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 setukpairinjR12 ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 setukpairinjR1 ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 upairequniteq ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 setukpairinjR2 ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 setukpairinjR ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 ksndsingleton ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 ksndpairEq ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 kpairsurjEq ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 cartprodsndin ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 cartprodpairmemEL ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 cartprodpairmemER ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 cartprodmempaircEq ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 cartprodfstpairEq ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 cartprodsndpairEq ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 cartprodpairsurjEq ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 dpsetconstrI ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 dpsetconstrSub ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 setOfPairsIsBReln ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 dpsetconstrERa ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 dpsetconstrEL1 ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 dpsetconstrEL2 ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 dpsetconstrER ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 funcImageSingleton ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 apProp ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 app ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 infuncsetfunc ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 ap2p ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 funcinfuncset ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 lamProp ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 lamp ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 lam2p ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 brelnall1 ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 brelnall2 ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 ex1E2 ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 funcGraphProp1 ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 funcGraphProp3 ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 funcGraphProp2 ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 funcextLem ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 funcGraphProp4 ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 subbreln ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 eqbreln ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 funcext ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 funcext2 ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 ap2apEq1 ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 ap2apEq2 ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 beta1 ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 eta1 ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 lam2lamEq ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 beta2 ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 eta2 ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 iffalseProp1 ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 iffalseProp2 ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 iftrueProp1 ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 iftrueProp2 ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 ifSingleton ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 ifp ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 theeq ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 iftrue ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 iffalse ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 iftrueorfalse ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 binintersectT_lem ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 binunionT_lem ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 ![
% 6.17/1.37 X178:$i,
% 6.17/1.37 X180:$i]:
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 in @
% 6.17/1.37 X180 @
% 6.17/1.37 (
% 6.17/1.37 powerset @
% 6.17/1.37 X178 ) ) =>
% 6.17/1.37 (
% 6.17/1.37 in @
% 6.17/1.37 (
% 6.17/1.37 powerset @
% 6.17/1.37 X180 ) @
% 6.17/1.37 (
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% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 ![
% 6.17/1.37 X182:$i,
% 6.17/1.37 X184:$i]:
% 6.17/1.37 (
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% 6.17/1.37 in @
% 6.17/1.37 X184 @
% 6.17/1.37 (
% 6.17/1.37 powerset @
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% 6.17/1.37 (
% 6.17/1.37 ![
% 6.17/1.37 X186:$i]:
% 6.17/1.37 (
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% 6.17/1.37 (
% 6.17/1.37 in @
% 6.17/1.37 (
% 6.17/1.37 setminus @
% 6.17/1.37 X184 @
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% 6.17/1.37 (
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% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 ![
% 6.17/1.37 X188:$i,
% 6.17/1.37 X190:$i]:
% 6.17/1.37 (
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% 6.17/1.37 in @
% 6.17/1.37 X190 @
% 6.17/1.37 (
% 6.17/1.37 powerset @
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% 6.17/1.37 (
% 6.17/1.37 in @
% 6.17/1.37 (
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% 6.17/1.37 X190 ) @
% 6.17/1.37 (
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% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 ![
% 6.17/1.37 X192:$i,
% 6.17/1.37 X194:$i]:
% 6.17/1.37 (
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% 6.17/1.37 in @
% 6.17/1.37 X194 @
% 6.17/1.37 (
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% 6.17/1.37 (
% 6.17/1.37 ![
% 6.17/1.37 X196:$i]:
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 in @
% 6.17/1.37 X196 @
% 6.17/1.37 (
% 6.17/1.37 powerset @
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% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 ![
% 6.17/1.37 X198:$i]:
% 6.17/1.37 (
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% 6.17/1.37 in @
% 6.17/1.37 X198 @
% 6.17/1.37 X192 ) =>
% 6.17/1.37 (
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% 6.17/1.37 in @
% 6.17/1.37 X198 @
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% 6.17/1.37 (
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% 6.17/1.37 (
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% 6.17/1.37 ![
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% 6.17/1.37 (
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% 6.17/1.37 (
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% 6.17/1.37 X200 @
% 6.17/1.37 X194 ) ) ) ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 X194 ) =
% 6.17/1.37 (
% 6.17/1.37 X196 ) ) ) ) ) ) ) ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 ![
% 6.17/1.37 X202:$i,
% 6.17/1.37 X204:$i]:
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 in @
% 6.17/1.37 X204 @
% 6.17/1.37 (
% 6.17/1.37 powerset @
% 6.17/1.37 X202 ) ) =>
% 6.17/1.37 (
% 6.17/1.37 ![
% 6.17/1.37 X206:$i]:
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 in @
% 6.17/1.37 X206 @
% 6.17/1.37 (
% 6.17/1.37 powerset @
% 6.17/1.37 X202 ) ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 ![
% 6.17/1.37 X208:$i]:
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 in @
% 6.17/1.37 X208 @
% 6.17/1.37 X202 ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 in @
% 6.17/1.37 X208 @
% 6.17/1.37 X204 ) =>
% 6.17/1.37 (
% 6.17/1.37 in @
% 6.17/1.37 X208 @
% 6.17/1.37 X206 ) ) ) ) =>
% 6.17/1.37 (
% 6.17/1.37 subset @
% 6.17/1.37 X204 @
% 6.17/1.37 X206 ) ) ) ) ) ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 ![
% 6.17/1.37 X210:$i,
% 6.17/1.37 X212:$i]:
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 in @
% 6.17/1.37 X212 @
% 6.17/1.37 (
% 6.17/1.37 powerset @
% 6.17/1.37 X210 ) ) =>
% 6.17/1.37 (
% 6.17/1.37 ![
% 6.17/1.37 X214:$i]:
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 in @
% 6.17/1.37 X214 @
% 6.17/1.37 (
% 6.17/1.37 powerset @
% 6.17/1.37 X210 ) ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 ![
% 6.17/1.37 X216:$i]:
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 in @
% 6.17/1.37 X216 @
% 6.17/1.37 X210 ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 in @
% 6.17/1.37 X216 @
% 6.17/1.37 X212 ) =>
% 6.17/1.37 (
% 6.17/1.37 in @
% 6.17/1.37 X216 @
% 6.17/1.37 X214 ) ) ) ) =>
% 6.17/1.37 (
% 6.17/1.37 in @
% 6.17/1.37 X212 @
% 6.17/1.37 (
% 6.17/1.37 powerset @
% 6.17/1.37 X214 ) ) ) ) ) ) ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 ![
% 6.17/1.37 X218:$i,
% 6.17/1.37 X220:$i]:
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 in @
% 6.17/1.37 X220 @
% 6.17/1.37 (
% 6.17/1.37 powerset @
% 6.17/1.37 X218 ) ) =>
% 6.17/1.37 (
% 6.17/1.37 ![
% 6.17/1.37 X222:$i]:
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 in @
% 6.17/1.37 X222 @
% 6.17/1.37 (
% 6.17/1.37 powerset @
% 6.17/1.37 X218 ) ) =>
% 6.17/1.37 (
% 6.17/1.37 ![
% 6.17/1.37 X224:$i]:
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 in @
% 6.17/1.37 X224 @
% 6.17/1.37 X218 ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 in @
% 6.17/1.37 X220 @
% 6.17/1.37 (
% 6.17/1.37 powerset @
% 6.17/1.37 X222 ) ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 in @
% 6.17/1.37 X224 @
% 6.17/1.37 X220 ) =>
% 6.17/1.37 (
% 6.17/1.37 in @
% 6.17/1.37 X224 @
% 6.17/1.37 X222 ) ) ) ) ) ) ) ) ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 ![
% 6.17/1.37 X226:$i,
% 6.17/1.37 X228:$i]:
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 in @
% 6.17/1.37 X228 @
% 6.17/1.37 (
% 6.17/1.37 powerset @
% 6.17/1.37 X226 ) ) =>
% 6.17/1.37 (
% 6.17/1.37 ![
% 6.17/1.37 X230:$i]:
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 in @
% 6.17/1.37 X230 @
% 6.17/1.37 X226 ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 in @
% 6.17/1.37 X230 @
% 6.17/1.37 X228 ) =>
% 6.17/1.37 (
% 6.17/1.37 ~(
% 6.17/1.37 in @
% 6.17/1.37 X230 @
% 6.17/1.37 (
% 6.17/1.37 setminus
% 6.17/1.37 @
% 6.17/1.37 X226 @
% 6.17/1.37 X228 ) ) ) ) ) ) ) ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 ![
% 6.17/1.37 X232:$i,
% 6.17/1.37 X234:$i]:
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 in @
% 6.17/1.37 X234 @
% 6.17/1.37 (
% 6.17/1.37 powerset @
% 6.17/1.37 X232 ) ) =>
% 6.17/1.37 (
% 6.17/1.37 ![
% 6.17/1.37 X236:$i]:
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 in @
% 6.17/1.37 X236 @
% 6.17/1.37 X232 ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 ~(
% 6.17/1.37 in @
% 6.17/1.37 X236 @
% 6.17/1.37 (
% 6.17/1.37 setminus
% 6.17/1.37 @
% 6.17/1.37 X232 @
% 6.17/1.37 X234 ) ) ) =>
% 6.17/1.37 (
% 6.17/1.37 in @
% 6.17/1.37 X236 @
% 6.17/1.37 X234 ) ) ) ) ) ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 binintersectTELcontra ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 binintersectTERcontra ) =>
% 6.17/1.37 (
% 6.17/1.37 ![
% 6.17/1.37 X238:$i,
% 6.17/1.37 X240:$i]:
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 in @
% 6.17/1.37 X240 @
% 6.17/1.37 (
% 6.17/1.37 powerset @
% 6.17/1.37 X238 ) ) =>
% 6.17/1.37 (
% 6.17/1.37 ![
% 6.17/1.37 X242:$i]:
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 in @
% 6.17/1.37 X242 @
% 6.17/1.37 (
% 6.17/1.37 powerset @
% 6.17/1.37 X238 ) ) =>
% 6.17/1.37 (
% 6.17/1.37 ![
% 6.17/1.37 X244:$i]:
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 in @
% 6.17/1.37 X244 @
% 6.17/1.37 X238 ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 subset @
% 6.17/1.37 X240 @
% 6.17/1.37 (
% 6.17/1.37 setminus @
% 6.17/1.37 X238 @
% 6.17/1.37 X242 ) ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 in @
% 6.17/1.37 X244 @
% 6.17/1.37 X242 ) =>
% 6.17/1.37 (
% 6.17/1.37 ~(
% 6.17/1.37 in @
% 6.17/1.37 X244 @
% 6.17/1.37 X240 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 6.17/1.37 thf(zf_stmt_4, negated_conjecture,
% 6.17/1.37 (~( ( setextAx ) =>
% 6.17/1.37 ( ( emptysetAx ) =>
% 6.17/1.37 ( ( setadjoinAx ) =>
% 6.17/1.37 ( ( ![X4:$i,X6:$i]:
% 6.17/1.37 ( ( in @ X6 @ ( powerset @ X4 ) ) <=>
% 6.17/1.37 ( ![X8:$i]: ( zip_tseitin_0 @ X8 @ X6 @ X4 ) ) ) ) =>
% 6.17/1.37 ( ( setunionAx ) =>
% 6.17/1.37 ( ( omega0Ax ) =>
% 6.17/1.37 ( ( omegaSAx ) =>
% 6.17/1.37 ( ( omegaIndAx ) =>
% 6.17/1.37 ( ( replAx ) =>
% 6.17/1.37 ( ( foundationAx ) =>
% 6.17/1.37 ( ( wellorderingAx ) =>
% 6.17/1.37 ( ( descrp ) =>
% 6.17/1.37 ( ( dsetconstrI ) =>
% 6.17/1.37 ( ( dsetconstrEL ) =>
% 6.17/1.37 ( ( dsetconstrER ) =>
% 6.17/1.37 ( ( exuE1 ) =>
% 6.17/1.37 ( ( prop2setE ) =>
% 6.17/1.37 ( ( emptysetE ) =>
% 6.17/1.37 ( ( emptysetimpfalse ) =>
% 6.17/1.37 ( ( notinemptyset ) =>
% 6.17/1.37 ( ( exuE3e ) =>
% 6.17/1.37 ( ( setext ) =>
% 6.17/1.37 ( ( emptyI ) =>
% 6.17/1.37 ( ( noeltsimpempty ) =>
% 6.17/1.37 ( ( setbeta ) =>
% 6.17/1.37 ( ( nonemptyE1 ) =>
% 6.17/1.37 ( ( nonemptyI ) =>
% 6.17/1.37 ( ( nonemptyI1 ) =>
% 6.17/1.37 ( ( setadjoinIL ) =>
% 6.17/1.37 ( ( emptyinunitempty ) =>
% 6.17/1.37 ( ( setadjoinIR ) =>
% 6.17/1.37 ( (
% 6.17/1.37 setadjoinE ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 setadjoinOr ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 setoftrueEq ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 ![
% 6.17/1.37 X10:$i,
% 6.17/1.37 X12:$i]:
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 ![
% 6.17/1.37 X14:$i]:
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 in @
% 6.17/1.37 X14 @ X12 ) =>
% 6.17/1.37 (
% 6.17/1.37 in @
% 6.17/1.37 X14 @ X10 ) ) ) =>
% 6.17/1.37 (
% 6.17/1.37 in @
% 6.17/1.37 X12 @
% 6.17/1.37 (
% 6.17/1.37 powerset
% 6.17/1.37 @
% 6.17/1.37 X10 ) ) ) ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 ![
% 6.17/1.37 X16:$i]:
% 6.17/1.37 (
% 6.17/1.37 in @
% 6.17/1.37 emptyset @
% 6.17/1.37 (
% 6.17/1.37 powerset
% 6.17/1.37 @
% 6.17/1.37 X16 ) ) ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 ![
% 6.17/1.37 X18:$i]:
% 6.17/1.37 (
% 6.17/1.37 in @
% 6.17/1.37 emptyset @
% 6.17/1.37 (
% 6.17/1.37 powerset
% 6.17/1.37 @
% 6.17/1.37 X18 ) ) ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 ![
% 6.17/1.37 X20:$i,
% 6.17/1.37 X22:$i,
% 6.17/1.37 X24:$i]:
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 in @
% 6.17/1.37 X22 @
% 6.17/1.37 (
% 6.17/1.37 powerset
% 6.17/1.37 @
% 6.17/1.37 X20 ) ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 in @
% 6.17/1.37 X24 @ X22 ) =>
% 6.17/1.37 (
% 6.17/1.37 in @
% 6.17/1.37 X24 @ X20 ) ) ) ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 setunionI ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 setunionE ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 subPowSU ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 exuE2 ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 nonemptyImpWitness ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 uniqinunit ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 notinsingleton ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 eqinunit ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 singletonsswitch ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 upairsetE ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 upairsetIL ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 upairsetIR ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 emptyE1 ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 vacuousDall ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 quantDeMorgan1 ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 quantDeMorgan2 ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 quantDeMorgan3 ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 quantDeMorgan4 ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 prop2setI ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 prop2set2propI ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 notdexE ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 notdallE ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 exuI1 ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 exuI3 ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 exuI2 ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 inCongP ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 in__Cong ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 exuE3u ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 exu__Cong ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 emptyset__Cong ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 setadjoin__Cong ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 ![
% 6.17/1.37 X26:$i,
% 6.17/1.37 X28:$i]:
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 X26 ) =
% 6.17/1.37 (
% 6.17/1.37 X28 ) ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 powerset
% 6.17/1.37 @
% 6.17/1.37 X26 ) =
% 6.17/1.37 (
% 6.17/1.37 powerset
% 6.17/1.37 @
% 6.17/1.37 X28 ) ) ) ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 setunion__Cong ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 omega__Cong ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 exuEu ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 descr__Cong ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 dsetconstr__Cong ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 ![
% 6.17/1.37 X30:$i,
% 6.17/1.37 X32:$i]:
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 ![
% 6.17/1.37 X34:$i]:
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 in @
% 6.17/1.37 X34 @ X30 ) =>
% 6.17/1.37 (
% 6.17/1.37 in @
% 6.17/1.37 X34 @ X32 ) ) ) =>
% 6.17/1.37 (
% 6.17/1.37 subset @
% 6.17/1.37 X30 @ X32 ) ) ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 ![
% 6.17/1.37 X36:$i,
% 6.17/1.37 X38:$i]:
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 X36 ) =
% 6.17/1.37 (
% 6.17/1.37 X38 ) ) =>
% 6.17/1.37 (
% 6.17/1.37 subset @
% 6.17/1.37 X38 @ X36 ) ) ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 ![
% 6.17/1.37 X40:$i,
% 6.17/1.37 X42:$i]:
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 X40 ) =
% 6.17/1.37 (
% 6.17/1.37 X42 ) ) =>
% 6.17/1.37 (
% 6.17/1.37 subset @
% 6.17/1.37 X40 @ X42 ) ) ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 ![
% 6.17/1.37 X44:$i,
% 6.17/1.37 X46:$i]:
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 ![
% 6.17/1.37 X48:$i]:
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 in @
% 6.17/1.37 X48 @ X44 ) =>
% 6.17/1.37 (
% 6.17/1.37 in @
% 6.17/1.37 X48 @ X46 ) ) ) =>
% 6.17/1.37 (
% 6.17/1.37 subset @
% 6.17/1.37 X44 @ X46 ) ) ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 ![
% 6.17/1.37 X50:$i]:
% 6.17/1.37 (
% 6.17/1.37 subset @
% 6.17/1.37 emptyset @
% 6.17/1.37 X50 ) ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 ![
% 6.17/1.37 X52:$i,
% 6.17/1.37 X54:$i,
% 6.17/1.37 X56:$i]:
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 subset @
% 6.17/1.37 X52 @ X54 ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 in @
% 6.17/1.37 X56 @ X52 ) =>
% 6.17/1.37 (
% 6.17/1.37 in @
% 6.17/1.37 X56 @ X54 ) ) ) ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 ![
% 6.17/1.37 X58:$i,
% 6.17/1.37 X60:$i,
% 6.17/1.37 X62:$i]:
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 subset @
% 6.17/1.37 X58 @ X60 ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 ~
% 6.17/1.37 (
% 6.17/1.37 in @
% 6.17/1.37 X62 @ X60 ) ) =>
% 6.17/1.37 (
% 6.17/1.37 ~
% 6.17/1.37 (
% 6.17/1.37 in @
% 6.17/1.37 X62 @ X58 ) ) ) ) ) =>
% 6.17/1.37 (
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% 6.17/1.37 setukpairinjR2 ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 setukpairinjR ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 ksndsingleton ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 ksndpairEq ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 kpairsurjEq ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 cartprodsndin ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 cartprodpairmemEL ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 cartprodpairmemER ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 cartprodmempaircEq ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 cartprodfstpairEq ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 cartprodsndpairEq ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 cartprodpairsurjEq ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 dpsetconstrI ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 dpsetconstrSub ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 setOfPairsIsBReln ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 dpsetconstrERa ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 dpsetconstrEL1 ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 dpsetconstrEL2 ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 dpsetconstrER ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 funcImageSingleton ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 apProp ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 app ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 infuncsetfunc ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 ap2p ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 funcinfuncset ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 lamProp ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 lamp ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 lam2p ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 brelnall1 ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 brelnall2 ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 ex1E2 ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 funcGraphProp1 ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 funcGraphProp3 ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 funcGraphProp2 ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 funcextLem ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 funcGraphProp4 ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 subbreln ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 eqbreln ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 funcext ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 funcext2 ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 ap2apEq1 ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 ap2apEq2 ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 beta1 ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 eta1 ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 lam2lamEq ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 beta2 ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 eta2 ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 iffalseProp1 ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 iffalseProp2 ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 iftrueProp1 ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 iftrueProp2 ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 ifSingleton ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 ifp ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 theeq ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 iftrue ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 iffalse ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 iftrueorfalse ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 binintersectT_lem ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 binunionT_lem ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 ![
% 6.17/1.37 X178:$i,
% 6.17/1.37 X180:$i]:
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 in @
% 6.17/1.37 X180 @
% 6.17/1.37 (
% 6.17/1.37 powerset
% 6.17/1.37 @
% 6.17/1.37 X178 ) ) =>
% 6.17/1.37 (
% 6.17/1.37 in @
% 6.17/1.37 (
% 6.17/1.37 powerset
% 6.17/1.37 @
% 6.17/1.37 X180 ) @
% 6.17/1.37 (
% 6.17/1.37 powerset
% 6.17/1.37 @
% 6.17/1.37 (
% 6.17/1.37 powerset
% 6.17/1.37 @
% 6.17/1.37 X178 ) ) ) ) ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 ![
% 6.17/1.37 X182:$i,
% 6.17/1.37 X184:$i]:
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 in @
% 6.17/1.37 X184 @
% 6.17/1.37 (
% 6.17/1.37 powerset
% 6.17/1.37 @
% 6.17/1.37 X182 ) ) =>
% 6.17/1.37 (
% 6.17/1.37 ![
% 6.17/1.37 X186:$i]:
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 in @
% 6.17/1.37 X186 @
% 6.17/1.37 (
% 6.17/1.37 powerset
% 6.17/1.37 @
% 6.17/1.37 X182 ) ) =>
% 6.17/1.37 (
% 6.17/1.37 in @
% 6.17/1.37 (
% 6.17/1.37 setminus
% 6.17/1.37 @
% 6.17/1.37 X184 @
% 6.17/1.37 X186 ) @
% 6.17/1.37 (
% 6.17/1.37 powerset
% 6.17/1.37 @
% 6.17/1.37 X182 ) ) ) ) ) ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 ![
% 6.17/1.37 X188:$i,
% 6.17/1.37 X190:$i]:
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 in @
% 6.17/1.37 X190 @
% 6.17/1.37 (
% 6.17/1.37 powerset
% 6.17/1.37 @
% 6.17/1.37 X188 ) ) =>
% 6.17/1.37 (
% 6.17/1.37 in @
% 6.17/1.37 (
% 6.17/1.37 setminus
% 6.17/1.37 @
% 6.17/1.37 X188 @
% 6.17/1.37 X190 ) @
% 6.17/1.37 (
% 6.17/1.37 powerset
% 6.17/1.37 @
% 6.17/1.37 X188 ) ) ) ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 ![
% 6.17/1.37 X192:$i,
% 6.17/1.37 X194:$i]:
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 in @
% 6.17/1.37 X194 @
% 6.17/1.37 (
% 6.17/1.37 powerset
% 6.17/1.37 @
% 6.17/1.37 X192 ) ) =>
% 6.17/1.37 (
% 6.17/1.37 ![
% 6.17/1.37 X196:$i]:
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 in @
% 6.17/1.37 X196 @
% 6.17/1.37 (
% 6.17/1.37 powerset
% 6.17/1.37 @
% 6.17/1.37 X192 ) ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 ![
% 6.17/1.37 X198:$i]:
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 in @
% 6.17/1.37 X198 @
% 6.17/1.37 X192 ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 in @
% 6.17/1.37 X198 @
% 6.17/1.37 X194 ) =>
% 6.17/1.37 (
% 6.17/1.37 in @
% 6.17/1.37 X198 @
% 6.17/1.37 X196 ) ) ) ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 ![
% 6.17/1.37 X200:$i]:
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 in @
% 6.17/1.37 X200 @
% 6.17/1.37 X192 ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 in @
% 6.17/1.37 X200 @
% 6.17/1.37 X196 ) =>
% 6.17/1.37 (
% 6.17/1.37 in @
% 6.17/1.37 X200 @
% 6.17/1.37 X194 ) ) ) ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 X194 ) =
% 6.17/1.37 (
% 6.17/1.37 X196 ) ) ) ) ) ) ) ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 ![
% 6.17/1.37 X202:$i,
% 6.17/1.37 X204:$i]:
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 in @
% 6.17/1.37 X204 @
% 6.17/1.37 (
% 6.17/1.37 powerset
% 6.17/1.37 @
% 6.17/1.37 X202 ) ) =>
% 6.17/1.37 (
% 6.17/1.37 ![
% 6.17/1.37 X206:$i]:
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 in @
% 6.17/1.37 X206 @
% 6.17/1.37 (
% 6.17/1.37 powerset
% 6.17/1.37 @
% 6.17/1.37 X202 ) ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 ![
% 6.17/1.37 X208:$i]:
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 in @
% 6.17/1.37 X208 @
% 6.17/1.37 X202 ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 in @
% 6.17/1.37 X208 @
% 6.17/1.37 X204 ) =>
% 6.17/1.37 (
% 6.17/1.37 in @
% 6.17/1.37 X208 @
% 6.17/1.37 X206 ) ) ) ) =>
% 6.17/1.37 (
% 6.17/1.37 subset @
% 6.17/1.37 X204 @
% 6.17/1.37 X206 ) ) ) ) ) ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 ![
% 6.17/1.37 X210:$i,
% 6.17/1.37 X212:$i]:
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 in @
% 6.17/1.37 X212 @
% 6.17/1.37 (
% 6.17/1.37 powerset
% 6.17/1.37 @
% 6.17/1.37 X210 ) ) =>
% 6.17/1.37 (
% 6.17/1.37 ![
% 6.17/1.37 X214:$i]:
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 in @
% 6.17/1.37 X214 @
% 6.17/1.37 (
% 6.17/1.37 powerset
% 6.17/1.37 @
% 6.17/1.37 X210 ) ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 ![
% 6.17/1.37 X216:$i]:
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 in @
% 6.17/1.37 X216 @
% 6.17/1.37 X210 ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 in @
% 6.17/1.37 X216 @
% 6.17/1.37 X212 ) =>
% 6.17/1.37 (
% 6.17/1.37 in @
% 6.17/1.37 X216 @
% 6.17/1.37 X214 ) ) ) ) =>
% 6.17/1.37 (
% 6.17/1.37 in @
% 6.17/1.37 X212 @
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% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 ![
% 6.17/1.37 X218:$i,
% 6.17/1.37 X220:$i]:
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 in @
% 6.17/1.37 X220 @
% 6.17/1.37 (
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% 6.17/1.37 @
% 6.17/1.37 X218 ) ) =>
% 6.17/1.37 (
% 6.17/1.37 ![
% 6.17/1.37 X222:$i]:
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 in @
% 6.17/1.37 X222 @
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% 6.17/1.37 @
% 6.17/1.37 X218 ) ) =>
% 6.17/1.37 (
% 6.17/1.37 ![
% 6.17/1.37 X224:$i]:
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 in @
% 6.17/1.37 X224 @
% 6.17/1.37 X218 ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 in @
% 6.17/1.37 X220 @
% 6.17/1.37 (
% 6.17/1.37 powerset
% 6.17/1.37 @
% 6.17/1.37 X222 ) ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 in @
% 6.17/1.37 X224 @
% 6.17/1.37 X220 ) =>
% 6.17/1.37 (
% 6.17/1.37 in @
% 6.17/1.37 X224 @
% 6.17/1.37 X222 ) ) ) ) ) ) ) ) ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 ![
% 6.17/1.37 X226:$i,
% 6.17/1.37 X228:$i]:
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 in @
% 6.17/1.37 X228 @
% 6.17/1.37 (
% 6.17/1.37 powerset
% 6.17/1.37 @
% 6.17/1.37 X226 ) ) =>
% 6.17/1.37 (
% 6.17/1.37 ![
% 6.17/1.37 X230:$i]:
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 in @
% 6.17/1.37 X230 @
% 6.17/1.37 X226 ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 in @
% 6.17/1.37 X230 @
% 6.17/1.37 X228 ) =>
% 6.17/1.37 (
% 6.17/1.37 ~
% 6.17/1.37 (
% 6.17/1.37 in @
% 6.17/1.37 X230 @
% 6.17/1.37 (
% 6.17/1.37 setminus
% 6.17/1.37 @
% 6.17/1.37 X226 @
% 6.17/1.37 X228 ) ) ) ) ) ) ) ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 ![
% 6.17/1.37 X232:$i,
% 6.17/1.37 X234:$i]:
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 in @
% 6.17/1.37 X234 @
% 6.17/1.37 (
% 6.17/1.37 powerset
% 6.17/1.37 @
% 6.17/1.37 X232 ) ) =>
% 6.17/1.37 (
% 6.17/1.37 ![
% 6.17/1.37 X236:$i]:
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 in @
% 6.17/1.37 X236 @
% 6.17/1.37 X232 ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 ~
% 6.17/1.37 (
% 6.17/1.37 in @
% 6.17/1.37 X236 @
% 6.17/1.37 (
% 6.17/1.37 setminus
% 6.17/1.37 @
% 6.17/1.37 X232 @
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% 6.17/1.37 (
% 6.17/1.37 in @
% 6.17/1.37 X236 @
% 6.17/1.37 X234 ) ) ) ) ) ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 binintersectTELcontra ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 binintersectTERcontra ) =>
% 6.17/1.37 (
% 6.17/1.37 ![
% 6.17/1.37 X238:$i,
% 6.17/1.37 X240:$i]:
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 in @
% 6.17/1.37 X240 @
% 6.17/1.37 (
% 6.17/1.37 powerset
% 6.17/1.37 @
% 6.17/1.37 X238 ) ) =>
% 6.17/1.37 (
% 6.17/1.37 ![
% 6.17/1.37 X242:$i]:
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 in @
% 6.17/1.37 X242 @
% 6.17/1.37 (
% 6.17/1.37 powerset
% 6.17/1.37 @
% 6.17/1.37 X238 ) ) =>
% 6.17/1.37 (
% 6.17/1.37 ![
% 6.17/1.37 X244:$i]:
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 in @
% 6.17/1.37 X244 @
% 6.17/1.37 X238 ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 subset @
% 6.17/1.37 X240 @
% 6.17/1.37 (
% 6.17/1.37 setminus
% 6.17/1.37 @
% 6.17/1.37 X238 @
% 6.17/1.37 X242 ) ) =>
% 6.17/1.37 (
% 6.17/1.37 (
% 6.17/1.37 in @
% 6.17/1.37 X244 @
% 6.17/1.37 X242 ) =>
% 6.17/1.37 (
% 6.17/1.37 ~
% 6.17/1.37 (
% 6.17/1.37 in @
% 6.17/1.37 X244 @
% 6.17/1.37 X240 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )),
% 6.17/1.37 inference('cnf.neg', [status(esa)], [zf_stmt_3])).
% 6.17/1.37 thf(zip_derived_cl129, plain, ( (in @ sk__126 @ sk__124)),
% 6.17/1.37 inference('cnf', [status(esa)], [zf_stmt_4])).
% 6.17/1.37 thf(zip_derived_cl128, plain,
% 6.17/1.37 ( (subset @ sk__124 @ (setminus @ sk__123 @ sk__125))),
% 6.17/1.37 inference('cnf', [status(esa)], [zf_stmt_4])).
% 6.17/1.37 thf(zip_derived_cl45, plain,
% 6.17/1.37 (![X7 : $i, X8 : $i, X9 : $i]:
% 6.17/1.37 (~ (subset @ X7 @ X8) | (in @ X9 @ X8) | ~ (in @ X9 @ X7))),
% 6.17/1.37 inference('cnf', [status(esa)], [zf_stmt_4])).
% 6.17/1.37 thf(zip_derived_cl333, plain,
% 6.17/1.37 (![X0 : $i]:
% 6.17/1.37 (~ (in @ X0 @ sk__124) | (in @ X0 @ (setminus @ sk__123 @ sk__125)))),
% 6.17/1.37 inference('sup-', [status(thm)], [zip_derived_cl128, zip_derived_cl45])).
% 6.17/1.37 thf(zip_derived_cl67, plain,
% 6.17/1.37 (![X32 : $i, X33 : $i, X34 : $i]:
% 6.17/1.37 (~ (in @ X32 @ (setminus @ X33 @ X34)) | ~ (in @ X32 @ X34))),
% 6.17/1.37 inference('cnf', [status(esa)], [zf_stmt_4])).
% 6.17/1.37 thf(zip_derived_cl1835, plain,
% 6.17/1.37 (![X0 : $i]: (~ (in @ X0 @ sk__124) | ~ (in @ X0 @ sk__125))),
% 6.17/1.37 inference('sup-', [status(thm)], [zip_derived_cl333, zip_derived_cl67])).
% 6.17/1.37 thf(zip_derived_cl1863, plain, (~ (in @ sk__126 @ sk__125)),
% 6.17/1.37 inference('sup-', [status(thm)], [zip_derived_cl129, zip_derived_cl1835])).
% 6.17/1.37 thf(zip_derived_cl130, plain, ( (in @ sk__126 @ sk__125)),
% 6.17/1.37 inference('cnf', [status(esa)], [zf_stmt_4])).
% 6.17/1.37 thf(zip_derived_cl1869, plain, ($false),
% 6.17/1.37 inference('demod', [status(thm)], [zip_derived_cl1863, zip_derived_cl130])).
% 6.17/1.37
% 6.17/1.37 % SZS output end Refutation
% 6.17/1.37
% 6.17/1.37
% 6.17/1.37 % Terminating...
% 6.90/1.51 % Runner terminated.
% 6.90/1.52 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------